LMFDB - Embedded newform 462.2.u.a.139.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.7
Character	$\chi$	$=$	462.139
Dual form			462.2.u.a.349.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.08816 + 1.49773i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.23342 + 1.41839i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.08816 + 1.49773i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.23342 + 1.41839i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +1.85129 q^{10} +(3.19071 + 0.905177i) q^{11} -1.00000i q^{12} +(3.89530 + 2.83010i) q^{13} +(-0.165270 + 2.64058i) q^{14} +(0.572081 + 1.76068i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.59769 - 3.34042i) q^{17} +(0.951057 - 0.309017i) q^{18} +(1.53993 - 4.73941i) q^{19} +(1.08816 - 1.49773i) q^{20} +(-2.56242 + 0.658804i) q^{21} +(2.60776 - 2.04929i) q^{22} -4.28567 q^{23} +(-0.809017 - 0.587785i) q^{24} +(0.485995 - 1.49574i) q^{25} +(4.57920 - 1.48787i) q^{26} +(0.587785 + 0.809017i) q^{27} +(2.03913 + 1.68580i) q^{28} +(-7.07198 + 2.29783i) q^{29} +(1.76068 + 0.572081i) q^{30} +(-5.47895 + 7.54113i) q^{31} +1.00000i q^{32} +(2.75483 + 1.84686i) q^{33} -5.68305i q^{34} +(-4.55469 - 1.80162i) q^{35} +(0.309017 - 0.951057i) q^{36} +(1.14721 + 3.53075i) q^{37} +(-2.92911 - 4.03158i) q^{38} +(2.83010 + 3.89530i) q^{39} +(-0.572081 - 1.76068i) q^{40} +(-0.770735 + 2.37208i) q^{41} +(-0.973167 + 2.46027i) q^{42} -11.6765i q^{43} +(-0.125111 - 3.31426i) q^{44} +1.85129i q^{45} +(-2.51906 + 3.46718i) q^{46} +(-1.28314 - 0.416917i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(2.97634 - 6.33572i) q^{49} +(-0.924418 - 1.27235i) q^{50} +(5.40491 - 1.75616i) q^{51} +(1.48787 - 4.57920i) q^{52} +(-8.64436 - 6.28050i) q^{53} +1.00000 q^{54} +(2.11631 + 5.76380i) q^{55} +(2.56242 - 0.658804i) q^{56} +(2.92911 - 4.03158i) q^{57} +(-2.29783 + 7.07198i) q^{58} +(-6.16590 + 2.00342i) q^{59} +(1.49773 - 1.08816i) q^{60} +(9.01388 - 6.54896i) q^{61} +(2.88046 + 8.86513i) q^{62} +(-2.64058 - 0.165270i) q^{63} +(0.809017 + 0.587785i) q^{64} +8.91371i q^{65} +(3.11339 - 1.14315i) q^{66} -0.825302 q^{67} +(-4.59769 - 3.34042i) q^{68} +(-4.07592 - 1.32435i) q^{69} +(-4.13472 + 2.62586i) q^{70} +(-4.25924 + 3.09452i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(1.97557 + 6.08018i) q^{73} +(3.53075 + 1.14721i) q^{74} +(0.924418 - 1.27235i) q^{75} -4.98331 q^{76} +(-8.41010 + 2.50404i) q^{77} +4.81485 q^{78} +(7.82401 - 10.7688i) q^{79} +(-1.76068 - 0.572081i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.46603 + 2.01781i) q^{82} +(-8.22320 + 5.97450i) q^{83} +(1.41839 + 2.23342i) q^{84} +(10.0061 + 3.25117i) q^{85} +(-9.44649 - 6.86328i) q^{86} -7.43592 q^{87} +(-2.75483 - 1.84686i) q^{88} -9.76208i q^{89} +(1.49773 + 1.08816i) q^{90} +(-12.7140 - 0.795752i) q^{91} +(1.32435 + 4.07592i) q^{92} +(-7.54113 + 5.47895i) q^{93} +(-1.09150 + 0.793023i) q^{94} +(8.77403 - 2.85086i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-10.0905 + 13.8883i) q^{97} +(-3.37626 - 6.13195i) q^{98} +(2.04929 + 2.60776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.08816	+	1.49773i	0.486641	+	0.669804i	0.979764	−	0.200156i	$-0.0641447\pi$
$5$	1.08816	+	1.49773i	0.486641	+	0.669804i	−0.493123	+	0.869960i	$0.664145\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−2.23342	+	1.41839i	−0.844154	+	0.536101i
$7$	−2.23342	+	1.41839i	−0.844154	+	0.536101i
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	1.85129			0.585430
$11$	3.19071	+	0.905177i	0.962036	+	0.272921i
$11$	3.19071	+	0.905177i	0.962036	+	0.272921i
$12$		−	1.00000i		−	0.288675i
$13$	3.89530	+	2.83010i	1.08036	+	0.784929i	0.977746	−	0.209792i	$-0.0672788\pi$
$13$	3.89530	+	2.83010i	1.08036	+	0.784929i	0.102616	+	0.994721i	$0.467279\pi$
$14$	−0.165270	+	2.64058i	−0.0441703	+	0.705726i
$15$	0.572081	+	1.76068i	0.147711	+	0.454607i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.59769	−	3.34042i	1.11510	−	0.810170i	0.131643	−	0.991297i	$-0.457975\pi$
$17$	4.59769	−	3.34042i	1.11510	−	0.810170i	0.983460	+	0.181127i	$0.0579746\pi$
$18$	0.951057	−	0.309017i	0.224166	−	0.0728360i
$19$	1.53993	−	4.73941i	0.353283	−	1.08729i	−0.603715	−	0.797200i	$-0.706313\pi$
$19$	1.53993	−	4.73941i	0.353283	−	1.08729i	0.956998	−	0.290094i	$-0.0936866\pi$
$20$	1.08816	−	1.49773i	0.243321	−	0.334902i
$21$	−2.56242	+	0.658804i	−0.559165	+	0.143763i
$22$	2.60776	−	2.04929i	0.555976	−	0.436911i
$23$	−4.28567			−0.893625			−0.446812	−	0.894628i	$-0.647441\pi$
$23$	−4.28567			−0.893625			−0.446812	+	0.894628i	$0.647441\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	0.485995	−	1.49574i	0.0971991	−	0.299148i
$26$	4.57920	−	1.48787i	0.898055	−	0.291796i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	2.03913	+	1.68580i	0.385360	+	0.318587i
$29$	−7.07198	+	2.29783i	−1.31323	+	0.426696i	−0.880166	−	0.474666i	$-0.842569\pi$
$29$	−7.07198	+	2.29783i	−1.31323	+	0.426696i	−0.433068	+	0.901361i	$0.642569\pi$
$30$	1.76068	+	0.572081i	0.321456	+	0.104447i
$31$	−5.47895	+	7.54113i	−0.984049	+	1.35443i	−0.0494299	+	0.998778i	$0.515740\pi$
$31$	−5.47895	+	7.54113i	−0.984049	+	1.35443i	−0.934619	+	0.355650i	$0.884260\pi$
$32$			1.00000i			0.176777i
$33$	2.75483	+	1.84686i	0.479555	+	0.321497i
$34$		−	5.68305i		−	0.974636i
$35$	−4.55469	−	1.80162i	−0.769883	−	0.304529i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	1.14721	+	3.53075i	0.188600	+	0.580452i	0.999992	−	0.00405123i	$-0.00128955\pi$
$37$	1.14721	+	3.53075i	0.188600	+	0.580452i	−0.811392	+	0.584503i	$0.801290\pi$
$38$	−2.92911	−	4.03158i	−0.475165	−	0.654009i
$39$	2.83010	+	3.89530i	0.453179	+	0.623747i
$40$	−0.572081	−	1.76068i	−0.0904539	−	0.278389i
$41$	−0.770735	+	2.37208i	−0.120369	+	0.370457i	−0.993029	−	0.117871i	$-0.962393\pi$
$41$	−0.770735	+	2.37208i	−0.120369	+	0.370457i	0.872660	+	0.488328i	$0.162393\pi$
$42$	−0.973167	+	2.46027i	−0.150163	+	0.379628i
$43$		−	11.6765i		−	1.78065i	−0.455325	−	0.890326i	$-0.650477\pi$
$43$		−	11.6765i		−	1.78065i	0.455325	−	0.890326i	$-0.349523\pi$
$44$	−0.125111	−	3.31426i	−0.0188612	−	0.499644i
$45$			1.85129i			0.275974i
$46$	−2.51906	+	3.46718i	−0.371414	+	0.511208i
$47$	−1.28314	−	0.416917i	−0.187165	−	0.0608136i	0.213935	−	0.976848i	$-0.431372\pi$
$47$	−1.28314	−	0.416917i	−0.187165	−	0.0608136i	−0.401100	+	0.916034i	$0.631372\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	2.97634	−	6.33572i	0.425191	−	0.905104i
$50$	−0.924418	−	1.27235i	−0.130732	−	0.179938i
$51$	5.40491	−	1.75616i	0.756838	−	0.245912i
$52$	1.48787	−	4.57920i	0.206331	−	0.635021i
$53$	−8.64436	−	6.28050i	−1.18739	−	0.862693i	−0.194408	−	0.980921i	$-0.562279\pi$
$53$	−8.64436	−	6.28050i	−1.18739	−	0.862693i	−0.992986	+	0.118228i	$0.962279\pi$
$54$	1.00000			0.136083
$55$	2.11631	+	5.76380i	0.285363	+	0.777191i
$56$	2.56242	−	0.658804i	0.342417	−	0.0880364i
$57$	2.92911	−	4.03158i	0.387971	−	0.533996i
$58$	−2.29783	+	7.07198i	−0.301719	+	0.928597i
$59$	−6.16590	+	2.00342i	−0.802732	+	0.260823i	−0.681516	−	0.731803i	$-0.738679\pi$
$59$	−6.16590	+	2.00342i	−0.802732	+	0.260823i	−0.121215	+	0.992626i	$0.538679\pi$
$60$	1.49773	−	1.08816i	0.193356	−	0.140481i
$61$	9.01388	−	6.54896i	1.15411	−	0.838509i	0.165087	−	0.986279i	$-0.447210\pi$
$61$	9.01388	−	6.54896i	1.15411	−	0.838509i	0.989022	+	0.147770i	$0.0472096\pi$
$62$	2.88046	+	8.86513i	0.365818	+	1.12587i
$63$	−2.64058	−	0.165270i	−0.332682	−	0.0208221i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$			8.91371i			1.10561i
$66$	3.11339	−	1.14315i	0.383232	−	0.140712i
$67$	−0.825302			−0.100827			−0.0504134	−	0.998728i	$-0.516054\pi$
$67$	−0.825302			−0.100827			−0.0504134	+	0.998728i	$0.516054\pi$
$68$	−4.59769	−	3.34042i	−0.557552	−	0.405085i
$69$	−4.07592	−	1.32435i	−0.490683	−	0.159432i
$70$	−4.13472	+	2.62586i	−0.494193	+	0.313850i
$71$	−4.25924	+	3.09452i	−0.505479	+	0.367252i	−0.811106	−	0.584900i	$-0.801134\pi$
$71$	−4.25924	+	3.09452i	−0.505479	+	0.367252i	0.305627	+	0.952151i	$0.401134\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	1.97557	+	6.08018i	0.231223	+	0.711631i	0.997600	+	0.0692403i	$0.0220575\pi$
$73$	1.97557	+	6.08018i	0.231223	+	0.711631i	−0.766377	+	0.642391i	$0.777942\pi$
$74$	3.53075	+	1.14721i	0.410441	+	0.133360i
$75$	0.924418	−	1.27235i	0.106743	−	0.146919i
$76$	−4.98331			−0.571624
$77$	−8.41010	+	2.50404i	−0.958420	+	0.285361i
$78$	4.81485			0.545175
$79$	7.82401	−	10.7688i	0.880270	−	1.21159i	−0.0960756	−	0.995374i	$-0.530629\pi$
$79$	7.82401	−	10.7688i	0.880270	−	1.21159i	0.976346	−	0.216214i	$-0.0693709\pi$
$80$	−1.76068	−	0.572081i	−0.196850	−	0.0639606i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.46603	+	2.01781i	0.161895	+	0.222830i
$83$	−8.22320	+	5.97450i	−0.902613	+	0.655787i	−0.939136	−	0.343546i	$-0.888372\pi$
$83$	−8.22320	+	5.97450i	−0.902613	+	0.655787i	0.0365226	+	0.999333i	$0.488372\pi$
$84$	1.41839	+	2.23342i	0.154759	+	0.243686i
$85$	10.0061	+	3.25117i	1.08531	+	0.352639i
$86$	−9.44649	−	6.86328i	−1.01864	−	0.740087i
$87$	−7.43592			−0.797214
$88$	−2.75483	−	1.84686i	−0.293666	−	0.196876i
$89$		−	9.76208i		−	1.03478i	−0.855750	−	0.517389i	$-0.826904\pi$
$89$		−	9.76208i		−	1.03478i	0.855750	−	0.517389i	$-0.173096\pi$
$90$	1.49773	+	1.08816i	0.157874	+	0.114702i
$91$	−12.7140	−	0.795752i	−1.33279	−	0.0834175i
$92$	1.32435	+	4.07592i	0.138073	+	0.424944i
$93$	−7.54113	+	5.47895i	−0.781979	+	0.568141i
$94$	−1.09150	+	0.793023i	−0.112580	+	0.0817941i
$95$	8.77403	−	2.85086i	0.900196	−	0.292492i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	−10.0905	+	13.8883i	−1.02453	+	1.41015i	−0.115553	+	0.993301i	$0.536864\pi$
$97$	−10.0905	+	13.8883i	−1.02453	+	1.41015i	−0.908978	+	0.416844i	$0.863136\pi$
$98$	−3.37626	−	6.13195i	−0.341054	−	0.619421i
$99$	2.04929	+	2.60776i	0.205962	+	0.262090i
$100$	−1.57271			−0.157271
$101$	0.520155	+	0.377915i	0.0517574	+	0.0376039i	0.613363	−	0.789801i	$-0.289816\pi$
$101$	0.520155	+	0.377915i	0.0517574	+	0.0376039i	−0.561606	+	0.827405i	$0.689816\pi$
$102$	1.75616	−	5.40491i	0.173886	−	0.535165i
$103$	8.07770	−	2.62460i	0.795920	−	0.258610i	0.117297	−	0.993097i	$-0.462577\pi$
$103$	8.07770	−	2.62460i	0.795920	−	0.258610i	0.678623	+	0.734487i	$0.262577\pi$
$104$	−2.83010	−	3.89530i	−0.277514	−	0.381965i
$105$	−3.77504	−	3.12092i	−0.368406	−	0.304570i
$106$	−10.1621	+	3.30185i	−0.987026	+	0.320704i
$107$	−6.26117	−	2.03438i	−0.605291	−	0.196671i	−0.00969198	−	0.999953i	$-0.503085\pi$
$107$	−6.26117	−	2.03438i	−0.605291	−	0.196671i	−0.595599	+	0.803282i	$0.703085\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$		−	12.6209i		−	1.20886i	−0.796657	−	0.604431i	$-0.793401\pi$
$109$		−	12.6209i		−	1.20886i	0.796657	−	0.604431i	$-0.206599\pi$
$110$	5.90695	+	1.67575i	0.563205	+	0.159776i
$111$			3.71245i			0.352370i
$112$	0.973167	−	2.46027i	0.0919556	−	0.232474i
$113$	−2.04174	+	6.28384i	−0.192071	+	0.591133i	0.807927	+	0.589282i	$0.200589\pi$
$113$	−2.04174	+	6.28384i	−0.192071	+	0.591133i	−0.999998	+	0.00185141i	$0.999411\pi$
$114$	−1.53993	−	4.73941i	−0.144227	−	0.443886i
$115$	−4.66351	−	6.41877i	−0.434875	−	0.598553i
$116$	4.37073	+	6.01579i	0.405812	+	0.558552i
$117$	1.48787	+	4.57920i	0.137554	+	0.423347i
$118$	−2.00342	+	6.16590i	−0.184430	+	0.567617i
$119$	−5.53056	+	13.9819i	−0.506986	+	1.28172i
$120$		−	1.85129i		−	0.168999i
$121$	9.36131	+	5.77632i	0.851028	+	0.525120i
$122$		−	11.1418i		−	1.00873i
$123$	−1.46603	+	2.01781i	−0.132187	+	0.181940i
$124$	8.86513	+	2.88046i	0.796113	+	0.258673i
$125$	11.5725	−	3.76012i	1.03507	−	0.336316i
$126$	−1.68580	+	2.03913i	−0.150183	+	0.181661i
$127$	4.45816	+	6.13613i	0.395598	+	0.544494i	0.959632	−	0.281257i	$-0.0907515\pi$
$127$	4.45816	+	6.13613i	0.395598	+	0.544494i	−0.564034	+	0.825751i	$0.690751\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	3.60824	−	11.1050i	0.317688	−	0.977743i
$130$	7.21134	+	5.23935i	0.632476	+	0.459521i
$131$	8.39371			0.733362			0.366681	−	0.930347i	$-0.380494\pi$
$131$	8.39371			0.733362			0.366681	+	0.930347i	$0.380494\pi$
$132$	0.905177	−	3.19071i	0.0787855	−	0.277716i
$133$	3.28302	+	12.7693i	0.284674	+	1.10724i
$134$	−0.485100	+	0.667683i	−0.0419063	+	0.0576791i
$135$	−0.572081	+	1.76068i	−0.0492369	+	0.151536i
$136$	−5.40491	+	1.75616i	−0.463467	+	0.150590i
$137$	−0.578005	+	0.419945i	−0.0493823	+	0.0358783i	−0.612203	−	0.790701i	$-0.709716\pi$
$137$	−0.578005	+	0.419945i	−0.0493823	+	0.0358783i	0.562820	+	0.826579i	$0.309716\pi$
$138$	−3.46718	+	2.51906i	−0.295146	+	0.214436i
$139$	−1.86114	−	5.72799i	−0.157860	−	0.485842i	0.840580	−	0.541688i	$-0.182214\pi$
$139$	−1.86114	−	5.72799i	−0.157860	−	0.485842i	−0.998439	+	0.0558460i	$0.982214\pi$
$140$	−0.305964	+	4.88850i	−0.0258586	+	0.413153i
$141$	−1.09150	−	0.793023i	−0.0919211	−	0.0667846i
$142$			5.26471i			0.441805i
$143$	9.86704	+	12.5560i	0.825124	+	1.04998i
$144$	−1.00000			−0.0833333
$145$	−11.1370	−	8.09149i	−0.924876	−	0.671962i
$146$	6.08018	+	1.97557i	0.503199	+	0.163499i
$147$	4.78851	−	5.10589i	0.394950	−	0.421127i
$148$	3.00344	−	2.18212i	0.246881	−	0.179369i
$149$	−7.02738	−	9.67235i	−0.575705	−	0.792390i	0.417511	−	0.908672i	$-0.362902\pi$
$149$	−7.02738	−	9.67235i	−0.575705	−	0.792390i	−0.993216	+	0.116282i	$0.962902\pi$
$150$	−0.485995	−	1.49574i	−0.0396814	−	0.122127i
$151$	−21.5136	−	6.99018i	−1.75075	−	0.568853i	−0.754573	−	0.656216i	$-0.772156\pi$
$151$	−21.5136	−	6.99018i	−1.75075	−	0.568853i	−0.996177	+	0.0873628i	$0.972156\pi$
$152$	−2.92911	+	4.03158i	−0.237583	+	0.327004i
$153$	5.68305			0.459448
$154$	−2.91752	+	8.27575i	−0.235101	+	0.666879i
$155$	−17.2566			−1.38608
$156$	2.83010	−	3.89530i	0.226589	−	0.311874i
$157$	4.45321	+	1.44694i	0.355405	+	0.115478i	0.481277	−	0.876568i	$-0.340173\pi$
$157$	4.45321	+	1.44694i	0.355405	+	0.115478i	−0.125872	+	0.992046i	$0.540173\pi$
$158$	−4.11333	−	12.6595i	−0.327239	−	1.00714i
$159$	−6.28050	−	8.64436i	−0.498076	−	0.685543i
$160$	−1.49773	+	1.08816i	−0.118406	+	0.0860268i
$161$	9.57171	−	6.07876i	0.754357	−	0.479073i
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	5.24338	+	3.80954i	0.410693	+	0.298386i	0.773882	−	0.633329i	$-0.218312\pi$
$163$	5.24338	+	3.80954i	0.410693	+	0.298386i	−0.363189	+	0.931715i	$0.618312\pi$
$164$	2.49415			0.194761
$165$	0.231617	+	6.13567i	0.0180313	+	0.477662i
$166$			10.1644i			0.788913i
$167$	−19.3438	−	14.0541i	−1.49687	−	1.08754i	−0.971609	−	0.236592i	$-0.923969\pi$
$167$	−19.3438	−	14.0541i	−1.49687	−	1.08754i	−0.525256	−	0.850944i	$-0.676031\pi$
$168$	2.64058	+	0.165270i	0.203726	+	0.0127509i
$169$	3.14666	+	9.68444i	0.242051	+	0.744957i
$170$	8.51167	−	6.18409i	0.652815	−	0.474298i
$171$	4.03158	−	2.92911i	0.308303	−	0.223995i
$172$	−11.1050	+	3.60824i	−0.846750	+	0.275126i
$173$	4.13140	−	12.7151i	0.314104	−	0.966714i	−0.662017	−	0.749489i	$-0.730299\pi$
$173$	4.13140	−	12.7151i	0.314104	−	0.966714i	0.976121	−	0.217225i	$-0.0697006\pi$
$174$	−4.37073	+	6.01579i	−0.331344	+	0.456056i
$175$	1.03611	+	4.02995i	0.0783226	+	0.304635i
$176$	−3.11339	+	1.14315i	−0.234681	+	0.0861683i
$177$	−6.48321			−0.487308
$178$	−7.89769	−	5.73801i	−0.591957	−	0.430082i
$179$	1.23096	−	3.78852i	0.0920065	−	0.283167i	−0.894455	−	0.447157i	$-0.852437\pi$
$179$	1.23096	−	3.78852i	0.0920065	−	0.283167i	0.986462	+	0.163990i	$0.0524365\pi$
$180$	1.76068	−	0.572081i	0.131234	−	0.0426404i
$181$	7.13647	+	9.82251i	0.530450	+	0.730101i	0.987199	−	0.159494i	$-0.0509863\pi$
$181$	7.13647	+	9.82251i	0.530450	+	0.730101i	−0.456749	+	0.889596i	$0.650986\pi$
$182$	−8.11690	+	9.81813i	−0.601664	+	0.727769i
$183$	10.5964	−	3.44299i	0.783312	−	0.254513i
$184$	4.07592	+	1.32435i	0.300481	+	0.0976321i
$185$	−4.03975	+	5.56024i	−0.297008	+	0.408797i
$186$			9.32135i			0.683475i
$187$	17.6936	−	6.49659i	1.29388	−	0.475078i
$188$			1.34917i			0.0983985i
$189$	−2.46027	−	0.973167i	−0.178959	−	0.0707875i
$190$	2.85086	−	8.77403i	0.206823	−	0.636535i
$191$	−0.457789	−	1.40893i	−0.0331245	−	0.101947i	0.933127	−	0.359546i	$-0.117068\pi$
$191$	−0.457789	−	1.40893i	−0.0331245	−	0.101947i	−0.966252	+	0.257600i	$0.917068\pi$
$192$	0.587785	+	0.809017i	0.0424197	+	0.0583858i
$193$	7.63207	+	10.5046i	0.549369	+	0.756141i	0.989926	−	0.141583i	$-0.0452192\pi$
$193$	7.63207	+	10.5046i	0.549369	+	0.756141i	−0.440558	+	0.897724i	$0.645219\pi$
$194$	5.30487	+	16.3267i	0.380867	+	1.17219i
$195$	−2.75449	+	8.47744i	−0.197253	+	0.607082i
$196$	−6.94537	−	0.872820i	−0.496098	−	0.0623443i
$197$			12.3214i			0.877863i	0.898521	+	0.438932i	$0.144643\pi$
$197$			12.3214i			0.877863i	−0.898521	+	0.438932i	$0.855357\pi$
$198$	3.31426	−	0.125111i	0.235535	−	0.00889124i
$199$		−	5.37272i		−	0.380862i	−0.981701	−	0.190431i	$-0.939011\pi$
$199$		−	5.37272i		−	0.380862i	0.981701	−	0.190431i	$-0.0609885\pi$
$200$	−0.924418	+	1.27235i	−0.0653662	+	0.0899689i
$201$	−0.784909	−	0.255032i	−0.0553632	−	0.0179886i
$202$	0.611479	−	0.198682i	0.0430235	−	0.0139792i
$203$	12.5355	−	15.1628i	0.879820	−	1.06422i
$204$	−3.34042	−	4.59769i	−0.233876	−	0.321903i
$205$	−4.39141	+	1.42686i	−0.306710	+	0.0996560i
$206$	2.62460	−	8.07770i	0.182865	−	0.562800i
$207$	−3.46718	−	2.51906i	−0.240986	−	0.175086i
$208$	−4.81485			−0.333850
$209$	9.20346	−	13.7282i	0.636617	−	0.949598i
$210$	−4.74378	+	1.21964i	−0.327352	+	0.0841631i
$211$	−1.03116	+	1.41928i	−0.0709883	+	0.0977070i	−0.843035	−	0.537859i	$-0.819233\pi$
$211$	−1.03116	+	1.41928i	−0.0709883	+	0.0977070i	0.772046	+	0.635566i	$0.219233\pi$
$212$	−3.30185	+	10.1621i	−0.226772	+	0.697933i
$213$	−5.00704	+	1.62688i	−0.343076	+	0.111472i
$214$	−5.32607	+	3.86962i	−0.364083	+	0.264522i
$215$	17.4882	−	12.7059i	1.19269	−	0.866538i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	1.54054	−	24.6138i	0.104579	−	1.67089i
$218$	−10.2105	−	7.41837i	−0.691543	−	0.502436i
$219$			6.39308i			0.432004i
$220$	4.82772	−	3.79384i	0.325485	−	0.255781i
$221$	27.3631			1.84064
$222$	3.00344	+	2.18212i	0.201577	+	0.146455i
$223$	−16.7455	−	5.44094i	−1.12136	−	0.364352i	−0.311074	−	0.950386i	$-0.600689\pi$
$223$	−16.7455	−	5.44094i	−1.12136	−	0.364352i	−0.810287	+	0.586034i	$0.800689\pi$
$224$	−1.41839	−	2.23342i	−0.0947702	−	0.149227i
$225$	1.27235	−	0.924418i	0.0848235	−	0.0616279i
$226$	3.88362	+	5.34535i	0.258335	+	0.355567i
$227$	−2.89812	−	8.91948i	−0.192355	−	0.592007i	−0.999997	−	0.00233450i	$-0.999257\pi$
$227$	−2.89812	−	8.91948i	−0.192355	−	0.592007i	0.807643	−	0.589672i	$-0.200743\pi$
$228$	−4.73941	−	1.53993i	−0.313875	−	0.101984i
$229$	−1.39524	+	1.92038i	−0.0921999	+	0.126902i	−0.852625	−	0.522524i	$-0.824991\pi$
$229$	−1.39524	+	1.92038i	−0.0921999	+	0.126902i	0.760425	+	0.649426i	$0.224991\pi$
$230$	−7.93404			−0.523155
$231$	−8.77227	−	0.217383i	−0.577173	−	0.0143028i
$232$	7.43592			0.488192
$233$	−3.79886	+	5.22868i	−0.248871	+	0.342542i	−0.915116	−	0.403192i	$-0.867901\pi$
$233$	−3.79886	+	5.22868i	−0.248871	+	0.342542i	0.666244	+	0.745734i	$0.267901\pi$
$234$	4.57920	+	1.48787i	0.299352	+	0.0972652i
$235$	−0.771836	−	2.37547i	−0.0503490	−	0.154958i
$236$	3.81073	+	5.24503i	0.248058	+	0.341422i
$237$	10.7688	−	7.82401i	0.699511	−	0.508224i
$238$	8.06079	+	12.6927i	0.522503	+	0.822742i
$239$	21.1510	+	6.87238i	1.36815	+	0.444537i	0.898754	−	0.438453i	$-0.144473\pi$
$239$	21.1510	+	6.87238i	1.36815	+	0.444537i	0.469391	+	0.882990i	$0.344473\pi$
$240$	−1.49773	−	1.08816i	−0.0966779	−	0.0702406i
$241$	26.4087			1.70113			0.850566	−	0.525869i	$-0.176260\pi$
$241$	26.4087			1.70113			0.850566	+	0.525869i	$0.176260\pi$
$242$	10.1756	−	4.17822i	0.654111	−	0.268586i
$243$			1.00000i			0.0641500i
$244$	−9.01388	−	6.54896i	−0.577054	−	0.419254i
$245$	12.7279	−	2.43656i	0.813158	−	0.155666i
$246$	0.770735	+	2.37208i	0.0491403	+	0.151238i
$247$	19.4115	−	14.1033i	1.23512	−	0.897369i
$248$	7.54113	−	5.47895i	0.478862	−	0.347914i
$249$	−9.66695	+	3.14098i	−0.612618	+	0.199052i
$250$	3.76012	−	11.5725i	0.237811	−	0.731908i
$251$	−13.9848	+	19.2485i	−0.882715	+	1.21495i	0.0929467	+	0.995671i	$0.470371\pi$
$251$	−13.9848	+	19.2485i	−0.882715	+	1.21495i	−0.975662	+	0.219282i	$0.929629\pi$
$252$	0.658804	+	2.56242i	0.0415008	+	0.161417i
$253$	−13.6744	−	3.87929i	−0.859699	−	0.243889i
$254$	7.58468			0.475905
$255$	8.51167	+	6.18409i	0.533021	+	0.387263i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	21.3366	−	6.93269i	1.33094	−	0.432450i	0.444704	−	0.895678i	$-0.353309\pi$
$257$	21.3366	−	6.93269i	1.33094	−	0.432450i	0.886239	+	0.463228i	$0.153309\pi$
$258$	−6.86328	−	9.44649i	−0.427289	−	0.588113i
$259$	−7.57018	−	6.25846i	−0.470388	−	0.388882i
$260$	8.47744	−	2.75449i	0.525748	−	0.170826i
$261$	−7.07198	−	2.29783i	−0.437745	−	0.142232i
$262$	4.93370	−	6.79065i	0.304805	−	0.419528i
$263$			26.4309i			1.62980i	0.579600	+	0.814901i	$0.303209\pi$
$263$			26.4309i			1.62980i	−0.579600	+	0.814901i	$0.696791\pi$
$264$	−2.04929	−	2.60776i	−0.126125	−	0.160496i
$265$		−	19.7811i		−	1.21514i
$266$	12.2603	+	4.84959i	0.751727	+	0.297347i
$267$	3.01665	−	9.28429i	0.184616	−	0.568189i
$268$	0.255032	+	0.784909i	0.0155786	+	0.0479459i
$269$	0.737911	+	1.01565i	0.0449913	+	0.0619251i	0.830920	−	0.556392i	$-0.187815\pi$
$269$	0.737911	+	1.01565i	0.0449913	+	0.0619251i	−0.785929	+	0.618317i	$0.787815\pi$
$270$	1.08816	+	1.49773i	0.0662235	+	0.0911488i
$271$	−2.32063	−	7.14215i	−0.140968	−	0.433855i	0.855502	−	0.517799i	$-0.173248\pi$
$271$	−2.32063	−	7.14215i	−0.140968	−	0.433855i	−0.996470	+	0.0839438i	$0.973248\pi$
$272$	−1.75616	+	5.40491i	−0.106483	+	0.327721i
$273$	−11.8459	−	4.68566i	−0.716944	−	0.283589i
$274$			0.714453i			0.0431617i
$275$	2.90458	−	4.33257i	0.175153	−	0.261264i
$276$			4.28567i			0.257967i
$277$	3.01043	−	4.14350i	0.180879	−	0.248959i	−0.708944	−	0.705265i	$-0.750828\pi$
$277$	3.01043	−	4.14350i	0.180879	−	0.248959i	0.889823	+	0.456306i	$0.150828\pi$
$278$	−5.72799	−	1.86114i	−0.343542	−	0.111624i
$279$	−8.86513	+	2.88046i	−0.530742	+	0.172448i
$280$	3.77504	+	3.12092i	0.225601	+	0.186510i
$281$	−5.38217	−	7.40792i	−0.321073	−	0.441919i	0.617721	−	0.786397i	$-0.288056\pi$
$281$	−5.38217	−	7.40792i	−0.321073	−	0.441919i	−0.938794	+	0.344478i	$0.888056\pi$
$282$	−1.28314	+	0.416917i	−0.0764098	+	0.0248270i
$283$	−5.57773	+	17.1665i	−0.331562	+	1.02044i	0.636829	+	0.771005i	$0.280246\pi$
$283$	−5.57773	+	17.1665i	−0.331562	+	1.02044i	−0.968391	+	0.249437i	$0.919754\pi$
$284$	4.25924	+	3.09452i	0.252739	+	0.183626i
$285$	9.22556			0.546475
$286$	15.9577	−	0.602390i	0.943599	−	0.0356201i
$287$	−1.64316	−	6.39106i	−0.0969925	−	0.377252i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	4.72707	−	14.5484i	0.278063	−	0.855789i
$290$	−13.0923	+	4.25395i	−0.768807	+	0.249801i
$291$	−13.8883	+	10.0905i	−0.814148	+	0.591513i
$292$	5.17211	−	3.75776i	0.302675	−	0.219906i
$293$	9.65178	+	29.7051i	0.563863	+	1.73539i	0.671306	+	0.741180i	$0.265734\pi$
$293$	9.65178	+	29.7051i	0.563863	+	1.73539i	−0.107443	+	0.994211i	$0.534266\pi$
$294$	−1.31614	−	6.87516i	−0.0767587	−	0.400967i
$295$	−9.71008	−	7.05479i	−0.565343	−	0.410746i
$296$		−	3.71245i		−	0.215782i
$297$	1.14315	+	3.11339i	0.0663324	+	0.180657i
$298$	−11.9557			−0.692574
$299$	−16.6940	−	12.1289i	−0.965438	−	0.701432i
$300$	−1.49574	−	0.485995i	−0.0863566	−	0.0280590i
$301$	16.5618	+	26.0786i	0.954609	+	1.50314i
$302$	−18.3005	+	13.2961i	−1.05308	+	0.765106i
$303$	0.377915	+	0.520155i	0.0217106	+	0.0298821i
$304$	1.53993	+	4.73941i	0.0883208	+	0.271824i
$305$	19.6171	+	6.37399i	1.12327	+	0.364974i
$306$	3.34042	−	4.59769i	0.190959	−	0.262832i
$307$	13.8073			0.788023			0.394011	−	0.919106i	$-0.371087\pi$
$307$	13.8073			0.788023			0.394011	+	0.919106i	$0.371087\pi$
$308$	4.98034	+	7.22469i	0.283781	+	0.411665i
$309$	8.49340			0.483173
$310$	−10.1431	+	13.9608i	−0.576092	+	0.792923i
$311$	0.776007	+	0.252140i	0.0440033	+	0.0142976i	0.330936	−	0.943653i	$-0.392636\pi$
$311$	0.776007	+	0.252140i	0.0440033	+	0.0142976i	−0.286933	+	0.957951i	$0.592636\pi$
$312$	−1.48787	−	4.57920i	−0.0842342	−	0.259246i
$313$	0.464157	+	0.638857i	0.0262357	+	0.0361104i	0.821933	−	0.569584i	$-0.192896\pi$
$313$	0.464157	+	0.638857i	0.0262357	+	0.0361104i	−0.795698	+	0.605694i	$0.792896\pi$
$314$	3.78813	−	2.75224i	0.213777	−	0.155318i
$315$	−2.62586	−	4.13472i	−0.147950	−	0.232965i
$316$	−12.6595	−	4.11333i	−0.712154	−	0.231393i
$317$	12.7666	+	9.27546i	0.717042	+	0.520962i	0.885438	−	0.464758i	$-0.153859\pi$
$317$	12.7666	+	9.27546i	0.717042	+	0.520962i	−0.168396	+	0.985720i	$0.553859\pi$
$318$	−10.6850			−0.599186
$319$	−24.6446	+	0.930314i	−1.37983	+	0.0520876i
$320$			1.85129i			0.103490i
$321$	−5.32607	−	3.86962i	−0.297272	−	0.215981i
$322$	0.708294	−	11.3167i	0.0394717	−	0.630654i
$323$	−8.75149	−	26.9343i	−0.486946	−	1.49866i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	6.12619	−	4.45094i	0.339820	−	0.246894i
$326$	6.16396	−	2.00279i	0.341390	−	0.110924i
$327$	3.90007	−	12.0032i	0.215674	−	0.663777i
$328$	1.46603	−	2.01781i	0.0809477	−	0.111415i
$329$	3.45714	−	0.888840i	0.190598	−	0.0490033i
$330$	5.10001	+	3.41908i	0.280746	+	0.188214i
$331$	−18.2041			−1.00059			−0.500294	−	0.865856i	$-0.666775\pi$
$331$	−18.2041			−1.00059			−0.500294	+	0.865856i	$0.666775\pi$
$332$	8.22320	+	5.97450i	0.451307	+	0.327893i
$333$	−1.14721	+	3.53075i	−0.0628667	+	0.193484i
$334$	−22.7400	+	7.38866i	−1.24428	+	0.404289i
$335$	−0.898063	−	1.23608i	−0.0490664	−	0.0675341i
$336$	1.68580	−	2.03913i	0.0919681	−	0.111244i
$337$	9.27664	−	3.01416i	0.505331	−	0.164192i	−0.0452470	−	0.998976i	$-0.514407\pi$
$337$	9.27664	−	3.01416i	0.505331	−	0.164192i	0.550578	+	0.834784i	$0.314407\pi$
$338$	9.68444	+	3.14666i	0.526764	+	0.171156i
$339$	−3.88362	+	5.34535i	−0.210929	+	0.290320i
$340$		−	10.5210i		−	0.570581i
$341$	−24.3078	+	19.1022i	−1.31634	+	1.03444i
$342$		−	4.98331i		−	0.269466i
$343$	2.33911	+	18.3720i	0.126300	+	0.991992i
$344$	−3.60824	+	11.1050i	−0.194543	+	0.598743i
$345$	−2.45175	−	7.54572i	−0.131998	−	0.406248i
$346$	−7.85839	−	10.8161i	−0.422470	−	0.581479i
$347$	7.14716	+	9.83723i	0.383680	+	0.528090i	0.956555	−	0.291553i	$-0.0941719\pi$
$347$	7.14716	+	9.83723i	0.383680	+	0.528090i	−0.572875	+	0.819643i	$0.694172\pi$
$348$	2.29783	+	7.07198i	0.123176	+	0.379098i
$349$	−2.32262	+	7.14829i	−0.124327	+	0.382639i	−0.993778	−	0.111380i	$-0.964473\pi$
$349$	−2.32262	+	7.14829i	−0.124327	+	0.382639i	0.869451	+	0.494019i	$0.164473\pi$
$350$	3.86931	+	1.53051i	0.206823	+	0.0818094i
$351$			4.81485i			0.256998i
$352$	−0.905177	+	3.19071i	−0.0482461	+	0.170066i
$353$			27.2930i			1.45266i	0.687347	+	0.726329i	$0.258775\pi$
$353$			27.2930i			1.45266i	−0.687347	+	0.726329i	$0.741225\pi$
$354$	−3.81073	+	5.24503i	−0.202538	+	0.278770i
$355$	−9.26949	−	3.01184i	−0.491974	−	0.159852i
$356$	−9.28429	+	3.01665i	−0.492066	+	0.159882i
$357$	−9.58051	+	11.5885i	−0.507054	+	0.613329i
$358$	−2.34143	−	3.22270i	−0.123748	−	0.170325i
$359$	−4.46025	+	1.44922i	−0.235403	+	0.0764871i	−0.424343	−	0.905502i	$-0.639495\pi$
$359$	−4.46025	+	1.44922i	−0.235403	+	0.0764871i	0.188940	+	0.981989i	$0.439495\pi$
$360$	0.572081	−	1.76068i	0.0301513	−	0.0927962i
$361$	−4.71928	−	3.42875i	−0.248383	−	0.180461i
$362$	12.1413			0.638132
$363$	7.11815	+	8.38641i	0.373606	+	0.440172i
$364$	3.17205	+	12.3377i	0.166260	+	0.646669i
$365$	−6.95671	+	9.57509i	−0.364131	+	0.501183i
$366$	3.44299	−	10.5964i	0.179968	−	0.553885i
$367$	1.64422	−	0.534240i	0.0858277	−	0.0278871i	−0.265788	−	0.964031i	$-0.585632\pi$
$367$	1.64422	−	0.534240i	0.0858277	−	0.0278871i	0.351616	+	0.936144i	$0.385632\pi$
$368$	3.46718	−	2.51906i	0.180739	−	0.131315i
$369$	−2.01781	+	1.46603i	−0.105043	+	0.0763182i
$370$	2.12382	+	6.53645i	0.110412	+	0.339814i
$371$	28.2147	+	1.76591i	1.46483	+	0.0916817i
$372$	7.54113	+	5.47895i	0.390990	+	0.284071i
$373$		−	28.4790i		−	1.47459i	−0.675573	−	0.737293i	$-0.736104\pi$
$373$		−	28.4790i		−	1.47459i	0.675573	−	0.737293i	$-0.263896\pi$
$374$	5.14417	−	18.1330i	0.265999	−	0.937635i
$375$	12.1680			0.628354
$376$	1.09150	+	0.793023i	0.0562900	+	0.0408971i
$377$	−34.0506	−	11.0637i	−1.75369	−	0.569809i
$378$	−2.23342	+	1.41839i	−0.114875	+	0.0729541i
$379$	−7.44071	+	5.40599i	−0.382203	+	0.277687i	−0.762253	−	0.647279i	$-0.775907\pi$
$379$	−7.44071	+	5.40599i	−0.382203	+	0.277687i	0.380050	+	0.924966i	$0.375907\pi$
$380$	−5.42265	−	7.46364i	−0.278176	−	0.382876i
$381$	2.34379	+	7.21346i	0.120076	+	0.369557i
$382$	−1.40893	−	0.457789i	−0.0720872	−	0.0234225i
$383$	−0.615474	+	0.847128i	−0.0314493	+	0.0432862i	−0.824452	−	0.565932i	$-0.808517\pi$
$383$	−0.615474	+	0.847128i	−0.0314493	+	0.0432862i	0.793003	+	0.609218i	$0.208517\pi$
$384$	1.00000			0.0510310
$385$	−12.9019	−	9.87124i	−0.657543	−	0.503085i
$386$	12.9845			0.660892
$387$	6.86328	−	9.44649i	0.348880	−	0.480192i
$388$	16.3267	+	5.30487i	0.828863	+	0.269314i
$389$	0.137465	+	0.423073i	0.00696973	+	0.0214506i	0.954481	−	0.298272i	$-0.0964103\pi$
$389$	0.137465	+	0.423073i	0.00696973	+	0.0214506i	−0.947511	+	0.319723i	$0.896410\pi$
$390$	5.23935	+	7.21134i	0.265305	+	0.365160i
$391$	−19.7042	+	14.3159i	−0.996483	+	0.723988i
$392$	−4.78851	+	5.10589i	−0.241856	+	0.257887i
$393$	7.98289	+	2.59380i	0.402684	+	0.130840i
$394$	9.96822	+	7.24233i	0.502192	+	0.364864i
$395$	24.6426			1.23990
$396$	1.84686	−	2.75483i	0.0928082	−	0.138436i
$397$			22.4125i			1.12485i	0.826849	+	0.562425i	$0.190131\pi$
$397$			22.4125i			1.12485i	−0.826849	+	0.562425i	$0.809869\pi$
$398$	−4.34662	−	3.15801i	−0.217876	−	0.158296i
$399$	−0.823592	+	13.1588i	−0.0412312	+	0.658766i
$400$	0.485995	+	1.49574i	0.0242998	+	0.0747870i
$401$	7.54111	−	5.47894i	0.376585	−	0.273605i	−0.383351	−	0.923603i	$-0.625230\pi$
$401$	7.54111	−	5.47894i	0.376585	−	0.273605i	0.759936	+	0.649997i	$0.225230\pi$
$402$	−0.667683	+	0.485100i	−0.0333010	+	0.0241946i
$403$	−42.6843	+	13.8690i	−2.12626	+	0.690863i
$404$	0.198682	−	0.611479i	0.00988478	−	0.0304222i
$405$	−1.08816	+	1.49773i	−0.0540712	+	0.0744227i
$406$	−4.89882	−	19.0539i	−0.243124	−	0.945631i
$407$	0.464467	+	12.3040i	0.0230228	+	0.609889i
$408$	−5.68305			−0.281353
$409$	−7.08842	−	5.15004i	−0.350500	−	0.254653i	0.398579	−	0.917134i	$-0.369504\pi$
$409$	−7.08842	−	5.15004i	−0.350500	−	0.254653i	−0.749079	+	0.662481i	$0.769504\pi$
$410$	−1.42686	+	4.39141i	−0.0704674	+	0.216876i
$411$	−0.679486	+	0.220778i	−0.0335165	+	0.0108902i
$412$	−4.99229	−	6.87130i	−0.245953	−	0.338525i
$413$	10.9294	−	13.2201i	0.537801	−	0.650520i
$414$	−4.07592	+	1.32435i	−0.200320	+	0.0650880i
$415$	−17.8964	−	5.81488i	−0.878498	−	0.285441i
$416$	−2.83010	+	3.89530i	−0.138757	+	0.190983i
$417$		−	6.02276i		−	0.294936i
$418$	−5.69667	−	15.5150i	−0.278633	−	0.758863i
$419$			1.41646i			0.0691987i	0.999401	+	0.0345994i	$0.0110155\pi$
$419$			1.41646i			0.0691987i	−0.999401	+	0.0345994i	$0.988984\pi$
$420$	−1.80162	+	4.55469i	−0.0879099	+	0.222246i
$421$	3.74312	−	11.5202i	0.182429	−	0.561458i	−0.817466	−	0.575977i	$-0.804622\pi$
$421$	3.74312	−	11.5202i	0.182429	−	0.561458i	0.999895	+	0.0145191i	$0.00462175\pi$
$422$	0.542115	+	1.66846i	0.0263898	+	0.0812193i
$423$	−0.793023	−	1.09150i	−0.0385581	−	0.0530707i
$424$	6.28050	+	8.64436i	0.305008	+	0.419807i
$425$	−2.76194	−	8.50037i	−0.133974	−	0.412329i
$426$	−1.62688	+	5.00704i	−0.0788228	+	0.242592i
$427$	−10.8428	+	27.4118i	−0.524720	+	1.32655i
$428$			6.58339i			0.318220i
$429$	5.50411	+	14.9905i	0.265741	+	0.723749i
$430$		−	21.6166i		−	1.04245i
$431$	10.4711	−	14.4122i	0.504375	−	0.694212i	−0.478583	−	0.878042i	$-0.658850\pi$
$431$	10.4711	−	14.4122i	0.504375	−	0.694212i	0.982958	+	0.183830i	$0.0588495\pi$
$432$	−0.951057	−	0.309017i	−0.0457577	−	0.0148676i
$433$	2.32424	−	0.755191i	0.111696	−	0.0362922i	−0.252636	−	0.967561i	$-0.581297\pi$
$433$	2.32424	−	0.755191i	0.111696	−	0.0362922i	0.364332	+	0.931269i	$0.381297\pi$
$434$	−19.0075	−	15.7140i	−0.912389	−	0.754294i
$435$	−8.09149	−	11.1370i	−0.387957	−	0.533978i
$436$	−12.0032	+	3.90007i	−0.574848	+	0.186779i
$437$	−6.59962	+	20.3115i	−0.315703	+	0.971633i
$438$	5.17211	+	3.75776i	0.247133	+	0.179553i
$439$	−7.42959			−0.354595			−0.177297	−	0.984157i	$-0.556735\pi$
$439$	−7.42959			−0.354595			−0.177297	+	0.984157i	$0.556735\pi$
$440$	−0.231617	−	6.13567i	−0.0110419	−	0.292507i
$441$	6.13195	−	3.37626i	0.291998	−	0.160774i
$442$	16.0836	−	22.1372i	0.765019	−	1.05296i
$443$	0.0799729	−	0.246131i	0.00379963	−	0.0116941i	−0.949139	−	0.314858i	$-0.898043\pi$
$443$	0.0799729	−	0.246131i	0.00379963	−	0.0116941i	0.952938	+	0.303164i	$0.0980430\pi$
$444$	3.53075	−	1.14721i	0.167562	−	0.0544442i
$445$	14.6209	−	10.6227i	0.693099	−	0.503566i
$446$	−14.2446	+	10.3493i	−0.674499	+	0.490052i
$447$	−3.69451	−	11.3705i	−0.174744	−	0.537808i
$448$	−2.64058	−	0.165270i	−0.124756	−	0.00780828i
$449$	−22.9080	−	16.6436i	−1.08110	−	0.785462i	−0.103222	−	0.994658i	$-0.532915\pi$
$449$	−22.9080	−	16.6436i	−1.08110	−	0.785462i	−0.977874	+	0.209197i	$0.932915\pi$
$450$		−	1.57271i		−	0.0741385i
$451$	−4.60635	+	6.87098i	−0.216904	+	0.323542i
$452$	6.60722			0.310777
$453$	−18.3005	−	13.2961i	−0.859834	−	0.624706i
$454$	−8.91948	−	2.89812i	−0.418612	−	0.136015i
$455$	−12.6431	−	19.9081i	−0.592718	−	0.933304i
$456$	−4.03158	+	2.92911i	−0.188796	+	0.137168i
$457$	8.28436	+	11.4024i	0.387526	+	0.533384i	0.957559	−	0.288238i	$-0.0930694\pi$
$457$	8.28436	+	11.4024i	0.387526	+	0.533384i	−0.570033	+	0.821622i	$0.693069\pi$
$458$	0.733520	+	2.25754i	0.0342751	+	0.105488i
$459$	5.40491	+	1.75616i	0.252279	+	0.0819705i
$460$	−4.66351	+	6.41877i	−0.217437	+	0.299277i
$461$	−4.14157			−0.192892			−0.0964461	−	0.995338i	$-0.530748\pi$
$461$	−4.14157			−0.192892			−0.0964461	+	0.995338i	$0.530748\pi$
$462$	−5.33208	+	6.96914i	−0.248071	+	0.324234i
$463$	31.6743			1.47203			0.736014	−	0.676966i	$-0.236706\pi$
$463$	31.6743			1.47203			0.736014	+	0.676966i	$0.236706\pi$
$464$	4.37073	−	6.01579i	0.202906	−	0.279276i
$465$	−16.4120	−	5.33257i	−0.761086	−	0.247292i
$466$	1.99718	+	6.14668i	0.0925175	+	0.284739i
$467$	4.34131	+	5.97530i	0.200892	+	0.276504i	0.897562	−	0.440887i	$-0.145336\pi$
$467$	4.34131	+	5.97530i	0.200892	+	0.276504i	−0.696671	+	0.717391i	$0.745336\pi$
$468$	3.89530	−	2.83010i	0.180060	−	0.130821i
$469$	1.84325	−	1.17060i	0.0851132	−	0.0540533i
$470$	−2.37547	−	0.771836i	−0.109572	−	0.0356021i
$471$	3.78813	+	2.75224i	0.174548	+	0.126816i
$472$	6.48321			0.298414
$473$	10.5693	−	37.2564i	0.485977	−	1.71305i
$474$		−	13.3110i		−	0.611395i
$475$	−6.34052	−	4.60666i	−0.290923	−	0.211368i
$476$	15.0066	+	0.939239i	0.687826	+	0.0430500i
$477$	−3.30185	−	10.1621i	−0.151181	−	0.465289i
$478$	17.9921	−	13.0720i	0.822941	−	0.597902i
$479$	4.94813	−	3.59503i	0.226086	−	0.164261i	−0.468976	−	0.883211i	$-0.655377\pi$
$479$	4.94813	−	3.59503i	0.226086	−	0.164261i	0.695062	+	0.718950i	$0.255377\pi$
$480$	−1.76068	+	0.572081i	−0.0803639	+	0.0261118i
$481$	−5.52365	+	17.0000i	−0.251857	+	0.775135i
$482$	15.5226	−	21.3651i	0.707036	−	0.973152i
$483$	10.9817	−	2.82342i	0.499684	−	0.128470i
$484$	2.60080	−	10.6881i	0.118218	−	0.485823i
$485$	−31.7810			−1.44310
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	5.71883	−	17.6007i	0.259145	−	0.797565i	−0.733840	−	0.679322i	$-0.762274\pi$
$487$	5.71883	−	17.6007i	0.259145	−	0.797565i	0.992985	−	0.118243i	$-0.0377262\pi$
$488$	−10.5964	+	3.44299i	−0.479679	+	0.155857i
$489$	3.80954	+	5.24338i	0.172273	+	0.237114i
$490$	5.51007	−	11.7293i	0.248920	−	0.529875i
$491$	−7.94795	+	2.58245i	−0.358686	+	0.116544i	−0.482816	−	0.875722i	$-0.660386\pi$
$491$	−7.94795	+	2.58245i	−0.358686	+	0.116544i	0.124130	+	0.992266i	$0.460386\pi$
$492$	2.37208	+	0.770735i	0.106942	+	0.0347474i
$493$	−24.8391	+	34.1880i	−1.11870	+	1.53975i
$494$		−	23.9939i		−	1.07954i
$495$	−1.67575	+	5.90695i	−0.0753192	+	0.265497i
$496$		−	9.32135i		−	0.418541i
$497$	5.12344	−	12.9526i	0.229818	−	0.581005i
$498$	−3.14098	+	9.66695i	−0.140751	+	0.433186i
$499$	9.17079	+	28.2248i	0.410541	+	1.26352i	0.916179	+	0.400769i	$0.131257\pi$
$499$	9.17079	+	28.2248i	0.410541	+	1.26352i	−0.505638	+	0.862746i	$0.668743\pi$
$500$	−7.15218	−	9.84413i	−0.319855	−	0.440243i
$501$	−14.0541	−	19.3438i	−0.627889	−	0.864216i
$502$	7.35226	+	22.6279i	0.328148	+	1.00993i
$503$	−7.41827	+	22.8311i	−0.330764	+	1.01799i	0.638007	+	0.770031i	$0.279759\pi$
$503$	−7.41827	+	22.8311i	−0.330764	+	1.01799i	−0.968771	+	0.247957i	$0.920241\pi$
$504$	2.46027	+	0.973167i	0.109589	+	0.0433483i
$505$			1.19028i			0.0529669i
$506$	−11.1760	+	8.78260i	−0.496834	+	0.390434i
$507$			10.1828i			0.452235i
$508$	4.45816	−	6.13613i	0.197799	−	0.272247i
$509$	−37.1477	−	12.0700i	−1.64654	−	0.534994i	−0.668557	−	0.743661i	$-0.733088\pi$
$509$	−37.1477	−	12.0700i	−1.64654	−	0.534994i	−0.977987	+	0.208667i	$0.933088\pi$
$510$	10.0061	−	3.25117i	0.443076	−	0.143964i
$511$	−13.0364	−	10.7775i	−0.576694	−	0.476767i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	4.73941	−	1.53993i	0.209250	−	0.0679894i
$514$	6.93269	−	21.3366i	0.305788	−	0.941119i
$515$	12.7208	+	9.24220i	0.560545	+	0.407260i
$516$	−11.6765			−0.514030
$517$	−3.71674	−	2.49173i	−0.163462	−	0.109586i
$518$	−9.51284	+	2.44578i	−0.417970	+	0.107461i
$519$	7.85839	−	10.8161i	0.344945	−	0.474776i
$520$	2.75449	−	8.47744i	0.120792	−	0.371760i
$521$	−33.2900	+	10.8166i	−1.45846	+	0.473883i	−0.927600	−	0.373574i	$-0.878132\pi$
$521$	−33.2900	+	10.8166i	−1.45846	+	0.473883i	−0.530863	+	0.847458i	$0.678132\pi$
$522$	−6.01579	+	4.37073i	−0.263304	+	0.191301i
$523$	−2.83146	+	2.05718i	−0.123811	+	0.0899541i	−0.647968	−	0.761668i	$-0.724381\pi$
$523$	−2.83146	+	2.05718i	−0.123811	+	0.0899541i	0.524156	+	0.851622i	$0.324381\pi$
$524$	−2.59380	−	7.98289i	−0.113311	−	0.348734i
$525$	−0.259923	+	4.15288i	−0.0113440	+	0.181247i
$526$	21.3831	+	15.5357i	0.932347	+	0.677390i
$527$			52.9738i			2.30757i
$528$	−3.31426	+	0.125111i	−0.144235	+	0.00544475i
$529$	−4.63301			−0.201435
$530$	−16.0032	−	11.6270i	−0.695137	−	0.505046i
$531$	−6.16590	−	2.00342i	−0.267577	−	0.0869411i
$532$	11.1298	−	7.06827i	0.482539	−	0.306449i
$533$	−9.71547	+	7.05870i	−0.420824	+	0.305746i
$534$	−5.73801	−	7.89769i	−0.248308	−	0.341766i
$535$	−3.76623	−	11.5913i	−0.162828	−	0.501134i
$536$	0.784909	+	0.255032i	0.0339029	+	0.0110157i
$537$	2.34143	−	3.22270i	0.101040	−	0.139070i
$538$	1.25541			0.0541246
$539$	15.2316	−	17.5214i	0.656071	−	0.754699i
$540$	1.85129			0.0796670
$541$	−18.1934	+	25.0411i	−0.782196	+	1.07660i	0.212840	+	0.977087i	$0.431729\pi$
$541$	−18.1934	+	25.0411i	−0.782196	+	1.07660i	−0.995036	+	0.0995137i	$0.968271\pi$
$542$	−7.14215	−	2.32063i	−0.306782	−	0.0996794i
$543$	3.75187	+	11.5471i	0.161008	+	0.495532i
$544$	3.34042	+	4.59769i	0.143219	+	0.197124i
$545$	18.9027	−	13.7336i	0.809701	−	0.588282i
$546$	−10.7536	+	6.82934i	−0.460211	+	0.292269i
$547$	−5.28096	−	1.71589i	−0.225797	−	0.0733660i	0.193933	−	0.981015i	$-0.437875\pi$
$547$	−5.28096	−	1.71589i	−0.225797	−	0.0733660i	−0.419731	+	0.907649i	$0.637875\pi$
$548$	0.578005	+	0.419945i	0.0246911	+	0.0179392i
$549$	11.1418			0.475519
$550$	−1.79785	−	4.89647i	−0.0766606	−	0.208786i
$551$			37.0555i			1.57862i
$552$	3.46718	+	2.51906i	0.147573	+	0.107218i
$553$	−2.19991	+	35.1488i	−0.0935498	+	1.49468i
$554$	−1.58268	−	4.87098i	−0.0672415	−	0.206948i
$555$	−5.56024	+	4.03975i	−0.236019	+	0.171478i
$556$	−4.87252	+	3.54009i	−0.206641	+	0.150133i
$557$	−17.4159	+	5.65878i	−0.737937	+	0.239770i	−0.653782	−	0.756683i	$-0.726819\pi$
$557$	−17.4159	+	5.65878i	−0.737937	+	0.239770i	−0.0841543	+	0.996453i	$0.526819\pi$
$558$	−2.88046	+	8.86513i	−0.121939	+	0.375291i
$559$	33.0457	−	45.4835i	1.39768	−	1.92375i
$560$	4.74378	−	1.21964i	0.200461	−	0.0515392i
$561$	18.8351	−	0.711011i	0.795220	−	0.0300189i
$562$	−9.15669			−0.386252
$563$	28.0132	+	20.3528i	1.18062	+	0.857769i	0.992241	−	0.124328i	$-0.0396776\pi$
$563$	28.0132	+	20.3528i	1.18062	+	0.857769i	0.188376	+	0.982097i	$0.439678\pi$
$564$	−0.416917	+	1.28314i	−0.0175554	+	0.0540299i
$565$	−11.6332	+	3.77986i	−0.489413	+	0.159020i
$566$	10.6095	+	14.6027i	0.445950	+	0.613797i
$567$	−2.03913	−	1.68580i	−0.0856356	−	0.0707971i
$568$	5.00704	−	1.62688i	0.210091	−	0.0682626i
$569$	−5.90464	−	1.91854i	−0.247536	−	0.0804292i	0.182621	−	0.983183i	$-0.441542\pi$
$569$	−5.90464	−	1.91854i	−0.247536	−	0.0804292i	−0.430157	+	0.902754i	$0.641542\pi$
$570$	5.42265	−	7.46364i	0.227130	−	0.312617i
$571$			13.9350i			0.583164i	0.956546	+	0.291582i	$0.0941815\pi$
$571$			13.9350i			0.583164i	−0.956546	+	0.291582i	$0.905818\pi$
$572$	8.89236	−	13.2641i	0.371808	−	0.554601i
$573$		−	1.48144i		−	0.0618879i
$574$	−6.13630	−	2.42723i	−0.256124	−	0.101310i
$575$	−2.08282	+	6.41025i	−0.0868595	+	0.267326i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−8.42782	−	11.5999i	−0.350855	−	0.482910i	0.596718	−	0.802451i	$-0.296471\pi$
$577$	−8.42782	−	11.5999i	−0.350855	−	0.482910i	−0.947572	+	0.319541i	$0.896471\pi$
$578$	−8.99141	−	12.3756i	−0.373993	−	0.514758i
$579$	4.01242	+	12.3490i	0.166750	+	0.513205i
$580$	−4.25395	+	13.0923i	−0.176636	+	0.543629i
$581$	9.89169	−	25.0073i	0.410376	−	1.03748i
$582$			17.1669i			0.711591i
$583$	−21.8967	−	27.8639i	−0.906870	−	1.15401i
$584$		−	6.39308i		−	0.264548i
$585$	−5.23935	+	7.21134i	−0.216620	+	0.298152i
$586$	29.7051	+	9.65178i	1.22711	+	0.398711i
$587$	39.5599	−	12.8538i	1.63281	−	0.530532i	0.657895	−	0.753110i	$-0.271447\pi$
$587$	39.5599	−	12.8538i	1.63281	−	0.530532i	0.974915	+	0.222577i	$0.0714470\pi$
$588$	−6.33572	−	2.97634i	−0.261281	−	0.122742i
$589$	27.3033	+	37.5798i	1.12501	+	1.54845i
$590$	−11.4149	+	3.70892i	−0.469943	+	0.152694i
$591$	−3.80752	+	11.7183i	−0.156620	+	0.482028i
$592$	−3.00344	−	2.18212i	−0.123440	−	0.0896847i
$593$	−30.2528			−1.24233			−0.621166	−	0.783679i	$-0.713341\pi$
$593$	−30.2528			−1.24233			−0.621166	+	0.783679i	$0.713341\pi$
$594$	3.19071	+	0.905177i	0.130917	+	0.0371398i
$595$	−26.9592	+	6.93128i	−1.10522	+	0.284155i
$596$	−7.02738	+	9.67235i	−0.287853	+	0.396195i
$597$	1.66026	−	5.10976i	0.0679500	−	0.209129i
$598$	−19.6249	+	6.37653i	−0.802524	+	0.260756i
$599$	22.4145	−	16.2851i	0.915831	−	0.665390i	−0.0266519	−	0.999645i	$-0.508485\pi$
$599$	22.4145	−	16.2851i	0.915831	−	0.665390i	0.942483	+	0.334255i	$0.108485\pi$
$600$	−1.27235	+	0.924418i	−0.0519436	+	0.0377392i
$601$	−6.89307	−	21.2147i	−0.281174	−	0.865365i	−0.987519	−	0.157498i	$-0.949657\pi$
$601$	−6.89307	−	21.2147i	−0.281174	−	0.865365i	0.706345	−	0.707868i	$-0.250343\pi$
$602$	30.8328	+	1.92978i	1.25665	+	0.0786519i
$603$	−0.667683	−	0.485100i	−0.0271902	−	0.0197548i
$604$			22.6207i			0.920424i
$605$	1.53528	+	20.3063i	0.0624179	+	0.825567i
$606$	0.642947			0.0261179
$607$	−3.13578	−	2.27828i	−0.127277	−	0.0924725i	0.522325	−	0.852746i	$-0.325065\pi$
$607$	−3.13578	−	2.27828i	−0.127277	−	0.0924725i	−0.649603	+	0.760274i	$0.725065\pi$
$608$	4.73941	+	1.53993i	0.192208	+	0.0624523i
$609$	16.6075	−	10.5470i	0.672972	−	0.427388i
$610$	16.6873	−	12.1241i	0.675650	−	0.490888i
$611$	−3.81829	−	5.25543i	−0.154472	−	0.212612i
$612$	−1.75616	−	5.40491i	−0.0709886	−	0.218480i
$613$	24.9551	+	8.10841i	1.00793	+	0.327496i	0.766029	−	0.642806i	$-0.222230\pi$
$613$	24.9551	+	8.10841i	1.00793	+	0.327496i	0.241899	+	0.970301i	$0.422230\pi$
$614$	8.11571	−	11.1703i	0.327523	−	0.450797i
$615$	−4.61741			−0.186192
$616$	8.77227	+	0.217383i	0.353445	+	0.00875863i
$617$	−38.1546			−1.53605			−0.768023	−	0.640422i	$-0.778759\pi$
$617$	−38.1546			−1.53605			−0.768023	+	0.640422i	$0.778759\pi$
$618$	4.99229	−	6.87130i	0.200820	−	0.276404i
$619$	24.7061	+	8.02750i	0.993022	+	0.322652i	0.760074	−	0.649837i	$-0.225163\pi$
$619$	24.7061	+	8.02750i	0.993022	+	0.322652i	0.232948	+	0.972489i	$0.425163\pi$
$620$	5.33257	+	16.4120i	0.214161	+	0.659120i
$621$	−2.51906	−	3.46718i	−0.101086	−	0.139133i
$622$	0.660111	−	0.479599i	0.0264681	−	0.0192302i
$623$	13.8464	+	21.8028i	0.554746	+	0.873512i
$624$	−4.57920	−	1.48787i	−0.183315	−	0.0595625i
$625$	11.8626	+	8.61869i	0.474505	+	0.344748i
$626$	0.789671			0.0315616
$627$	12.9953	−	10.2123i	0.518981	−	0.407838i
$628$		−	4.68239i		−	0.186848i
$629$	17.0687	+	12.4011i	0.680573	+	0.494465i
$630$	−4.88850	−	0.305964i	−0.194762	−	0.0121899i
$631$	−1.83177	−	5.63761i	−0.0729216	−	0.224430i	0.907952	−	0.419073i	$-0.137645\pi$
$631$	−1.83177	−	5.63761i	−0.0729216	−	0.224430i	−0.980874	+	0.194644i	$0.937645\pi$
$632$	−10.7688	+	7.82401i	−0.428361	+	0.311223i
$633$	−1.41928	+	1.03116i	−0.0564112	+	0.0409851i
$634$	15.0080	−	4.87640i	0.596044	−	0.193667i
$635$	−4.33905	+	13.3542i	−0.172190	+	0.529946i
$636$	−6.28050	+	8.64436i	−0.249038	+	0.342771i
$637$	29.5245	−	16.2562i	1.16980	−	0.644094i
$638$	−13.7331	+	20.4847i	−0.543699	+	0.810998i
$639$	−5.26471			−0.208269
$640$	1.49773	+	1.08816i	0.0592029	+	0.0430134i
$641$	2.17477	−	6.69325i	0.0858982	−	0.264367i	−0.898877	−	0.438202i	$-0.855616\pi$
$641$	2.17477	−	6.69325i	0.0858982	−	0.264367i	0.984775	+	0.173834i	$0.0556156\pi$
$642$	−6.26117	+	2.03438i	−0.247109	+	0.0802905i
$643$	13.3815	+	18.4181i	0.527715	+	0.726338i	0.986780	−	0.162065i	$-0.0518155\pi$
$643$	13.3815	+	18.4181i	0.527715	+	0.726338i	−0.459065	+	0.888403i	$0.651815\pi$
$644$	−8.73906	−	7.22480i	−0.344367	−	0.284697i
$645$	20.5586	−	6.67991i	0.809496	−	0.263021i
$646$	−26.9343	−	8.75149i	−1.05972	−	0.344323i
$647$	4.28361	−	5.89589i	0.168406	−	0.231791i	−0.716470	−	0.697618i	$-0.754243\pi$
$647$	4.28361	−	5.89589i	0.168406	−	0.231791i	0.884876	+	0.465827i	$0.154243\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−21.4871	+	0.811119i	−0.843441	+	0.0318392i
$650$		−	7.57239i		−	0.297014i
$651$	9.07123	−	22.9331i	0.355530	−	0.898818i
$652$	2.00279	−	6.16396i	0.0784354	−	0.241399i
$653$	−1.24974	−	3.84630i	−0.0489060	−	0.150517i	0.923621	−	0.383307i	$-0.125215\pi$
$653$	−1.24974	−	3.84630i	−0.0489060	−	0.150517i	−0.972527	+	0.232789i	$0.925215\pi$
$654$	−7.41837	−	10.2105i	−0.290081	−	0.399263i
$655$	9.13372	+	12.5715i	0.356884	+	0.491209i
$656$	−0.770735	−	2.37208i	−0.0300922	−	0.0926141i
$657$	−1.97557	+	6.08018i	−0.0770744	+	0.237210i
$658$	1.31297	−	3.31933i	0.0511849	−	0.129401i
$659$		−	28.0755i		−	1.09367i	−0.837241	−	0.546834i	$-0.815833\pi$
$659$		−	28.0755i		−	1.09367i	0.837241	−	0.546834i	$-0.184167\pi$
$660$	5.76380	−	2.11631i	0.224356	−	0.0823772i
$661$		−	7.40313i		−	0.287948i	−0.989581	−	0.143974i	$-0.954012\pi$
$661$		−	7.40313i		−	0.287948i	0.989581	−	0.143974i	$-0.0459882\pi$
$662$	−10.7001	+	14.7274i	−0.415871	+	0.572398i
$663$	26.0238	+	8.45566i	1.01068	+	0.328390i
$664$	9.66695	−	3.14098i	0.375150	−	0.121894i
$665$	−15.5525	+	18.8122i	−0.603099	+	0.729504i
$666$	2.18212	+	3.00344i	0.0845556	+	0.116381i
$667$	30.3082	−	9.84773i	1.17354	−	0.381306i
$668$	−7.38866	+	22.7400i	−0.285876	+	0.879835i
$669$	−14.2446	−	10.3493i	−0.550726	−	0.400126i
$670$	−1.52788			−0.0590270
$671$	34.6887	−	12.7367i	1.33914	−	0.491696i
$672$	−0.658804	−	2.56242i	−0.0254139	−	0.0988474i
$673$	−15.9992	+	22.0211i	−0.616726	+	0.848850i	−0.997109	−	0.0759787i	$-0.975792\pi$
$673$	−15.9992	+	22.0211i	−0.616726	+	0.848850i	0.380384	+	0.924829i	$0.375792\pi$
$674$	3.01416	−	9.27664i	0.116101	−	0.357323i
$675$	1.49574	−	0.485995i	0.0575711	−	0.0187060i
$676$	8.23808	−	5.98531i	0.316849	−	0.230204i
$677$	−1.40412	+	1.02015i	−0.0539647	+	0.0392077i	−0.614441	−	0.788963i	$-0.710618\pi$
$677$	−1.40412	+	1.02015i	−0.0539647	+	0.0392077i	0.560476	+	0.828171i	$0.310618\pi$
$678$	2.04174	+	6.28384i	0.0784126	+	0.241329i
$679$	2.83718	−	45.3307i	0.108881	−	1.73963i
$680$	−8.51167	−	6.18409i	−0.326408	−	0.237149i
$681$		−	9.37850i		−	0.359385i
$682$	1.16620	+	30.8934i	0.0446562	+	1.18297i
$683$	−22.2244			−0.850393			−0.425197	−	0.905101i	$-0.639795\pi$
$683$	−22.2244			−0.850393			−0.425197	+	0.905101i	$0.639795\pi$
$684$	−4.03158	−	2.92911i	−0.154151	−	0.111997i
$685$	−1.25793	−	0.408725i	−0.0480629	−	0.0156166i
$686$	16.2381	+	8.90638i	0.619974	+	0.340047i
$687$	−1.92038	+	1.39524i	−0.0732671	+	0.0532316i
$688$	6.86328	+	9.44649i	0.261660	+	0.360144i
$689$	−15.8979	−	48.9288i	−0.605663	−	1.86404i
$690$	−7.54572	−	2.45175i	−0.287261	−	0.0933366i
$691$	23.5522	−	32.4169i	0.895969	−	1.23320i	−0.0757670	−	0.997126i	$-0.524141\pi$
$691$	23.5522	−	32.4169i	0.895969	−	1.23320i	0.971736	−	0.236070i	$-0.0758595\pi$
$692$	−13.3695			−0.508232
$693$	−8.27575	−	2.91752i	−0.314370	−	0.110828i
$694$	12.1595			0.461568
$695$	6.55375	−	9.02046i	0.248598	−	0.342165i
$696$	7.07198	+	2.29783i	0.268063	+	0.0870989i
$697$	4.38013	+	13.4807i	0.165909	+	0.510616i
$698$	4.41789	+	6.08070i	0.167219	+	0.230158i
$699$	−5.22868	+	3.79886i	−0.197767	+	0.143686i
$700$	3.51253	−	2.23072i	0.132761	−	0.0843134i
$701$	−27.9300	−	9.07502i	−1.05490	−	0.342759i	−0.270312	−	0.962773i	$-0.587127\pi$
$701$	−27.9300	−	9.07502i	−1.05490	−	0.342759i	−0.784591	+	0.620014i	$0.787127\pi$
$702$	3.89530	+	2.83010i	0.147019	+	0.106815i
$703$	18.5003			0.697751
$704$	2.04929	+	2.60776i	0.0772356	+	0.0982836i
$705$		−	2.49771i		−	0.0940693i
$706$	22.0805	+	16.0424i	0.831010	+	0.603764i
$707$	−1.69776	−	0.106260i	−0.0638507	−	0.00399632i
$708$	2.00342	+	6.16590i	0.0752932	+	0.231729i
$709$	12.6627	−	9.20001i	0.475559	−	0.345514i	−0.324045	−	0.946042i	$-0.605043\pi$
$709$	12.6627	−	9.20001i	0.475559	−	0.345514i	0.799604	+	0.600528i	$0.205043\pi$
$710$	−7.88510	+	5.72886i	−0.295923	+	0.215000i
$711$	12.6595	−	4.11333i	0.474769	−	0.154262i
$712$	−3.01665	+	9.28429i	−0.113054	+	0.347943i
$713$	23.4810	−	32.3188i	0.879371	−	1.21035i
$714$	3.74402	+	14.5624i	0.140116	+	0.544982i
$715$	−8.06848	+	28.4411i	−0.301744	+	1.06364i
$716$	−3.98348			−0.148870
$717$	17.9921	+	13.0720i	0.671928	+	0.488185i
$718$	−1.44922	+	4.46025i	−0.0540845	+	0.166455i
$719$	37.4324	−	12.1625i	1.39599	−	0.453585i	0.488099	−	0.872788i	$-0.337690\pi$
$719$	37.4324	−	12.1625i	1.39599	−	0.453585i	0.907893	+	0.419203i	$0.137690\pi$
$720$	−1.08816	−	1.49773i	−0.0405534	−	0.0558170i
$721$	−14.3182	+	17.3192i	−0.533237	+	0.645000i
$722$	−5.54784	+	1.80260i	−0.206469	+	0.0670859i
$723$	25.1161	+	8.16072i	0.934079	+	0.303501i
$724$	7.13647	−	9.82251i	0.265225	−	0.365051i
$725$			11.6946i			0.434326i
$726$	10.9687	−	0.829300i	0.407086	−	0.0307782i
$727$			36.2708i			1.34521i	0.740001	+	0.672606i	$0.234825\pi$
$727$			36.2708i			1.34521i	−0.740001	+	0.672606i	$0.765175\pi$
$728$	11.8459	+	4.68566i	0.439037	+	0.173662i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	3.65736	+	11.2562i	0.135365	+	0.416611i
$731$	−39.0044	−	53.6849i	−1.44263	−	1.98561i
$732$	−6.54896	−	9.01388i	−0.242057	−	0.333162i
$733$	11.5204	+	35.4561i	0.425515	+	1.30960i	0.902500	+	0.430690i	$0.141730\pi$
$733$	11.5204	+	35.4561i	0.425515	+	1.30960i	−0.476985	+	0.878912i	$0.658270\pi$
$734$	0.534240	−	1.64422i	0.0197192	−	0.0606893i
$735$	12.8579	+	1.61584i	0.474271	+	0.0596013i
$736$		−	4.28567i		−	0.157972i
$737$	−2.63330	−	0.747044i	−0.0969990	−	0.0275177i
$738$			2.49415i			0.0918110i
$739$	7.94829	−	10.9399i	0.292383	−	0.402430i	−0.637404	−	0.770530i	$-0.719992\pi$
$739$	7.94829	−	10.9399i	0.292383	−	0.402430i	0.929786	+	0.368100i	$0.119992\pi$
$740$	6.53645	+	2.12382i	0.240285	+	0.0780733i
$741$	22.8196	−	7.41452i	0.838297	−	0.272379i
$742$	18.0128	−	21.7882i	0.661272	−	0.799870i
$743$	−7.54289	−	10.3819i	−0.276722	−	0.380875i	0.647923	−	0.761706i	$-0.275638\pi$
$743$	−7.54289	−	10.3819i	−0.276722	−	0.380875i	−0.924645	+	0.380831i	$0.875638\pi$
$744$	8.86513	−	2.88046i	0.325012	−	0.105603i
$745$	6.83962	−	21.0502i	0.250584	−	0.771219i
$746$	−23.0400	−	16.7395i	−0.843553	−	0.612877i
$747$	−10.1644			−0.371897
$748$	−11.6462	−	14.8200i	−0.425829	−	0.541874i
$749$	16.8694	−	4.33716i	0.616394	−	0.158477i
$750$	7.15218	−	9.84413i	0.261161	−	0.359457i
$751$	7.52591	−	23.1624i	0.274624	−	0.845207i	−0.714694	−	0.699437i	$-0.753434\pi$
$751$	7.52591	−	23.1624i	0.274624	−	0.845207i	0.989319	−	0.145770i	$-0.0465659\pi$
$752$	1.28314	−	0.416917i	0.0467913	−	0.0152034i
$753$	−19.2485	+	13.9848i	−0.701453	+	0.509636i
$754$	−28.9651	+	21.0444i	−1.05485	+	0.766392i
$755$	−12.9409	−	39.8279i	−0.470967	−	1.44949i
$756$	−0.165270	+	2.64058i	−0.00601082	+	0.0960371i
$757$	−2.03549	−	1.47887i	−0.0739812	−	0.0537505i	0.550180	−	0.835046i	$-0.314559\pi$
$757$	−2.03549	−	1.47887i	−0.0739812	−	0.0537505i	−0.624161	+	0.781296i	$0.714559\pi$
$758$			9.19722i			0.334058i
$759$	−11.8063	−	7.91503i	−0.428542	−	0.287298i
$760$	−9.22556			−0.334646
$761$	14.8357	+	10.7787i	0.537792	+	0.390729i	0.823264	−	0.567658i	$-0.192150\pi$
$761$	14.8357	+	10.7787i	0.537792	+	0.390729i	−0.285472	+	0.958387i	$0.592150\pi$
$762$	7.21346	+	2.34379i	0.261316	+	0.0849067i
$763$	17.9013	+	28.1878i	0.648072	+	1.02047i
$764$	−1.19851	+	0.870767i	−0.0433605	+	0.0315032i
$765$	6.18409	+	8.51167i	0.223586	+	0.307740i
$766$	0.323574	+	0.995858i	0.0116912	+	0.0359818i
$767$	−29.6879	−	9.64618i	−1.07197	−	0.348304i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	31.1988			1.12506			0.562528	−	0.826778i	$-0.309829\pi$
$769$	31.1988			1.12506			0.562528	+	0.826778i	$0.309829\pi$
$770$	−15.5696	+	4.63571i	−0.561088	+	0.167059i
$771$	22.4347			0.807965
$772$	7.63207	−	10.5046i	0.274684	−	0.378071i
$773$	3.06511	+	0.995913i	0.110244	+	0.0358205i	0.363620	−	0.931548i	$-0.381541\pi$
$773$	3.06511	+	0.995913i	0.110244	+	0.0358205i	−0.253375	+	0.967368i	$0.581541\pi$
$774$	−3.60824	−	11.1050i	−0.129696	−	0.399162i
$775$	8.61683	+	11.8600i	0.309526	+	0.426025i
$776$	13.8883	−	10.0905i	0.498562	−	0.362226i
$777$	−5.26570	−	8.29146i	−0.188906	−	0.297455i
$778$	0.423073	+	0.137465i	0.0151679	+	0.00492834i
$779$	10.0554	+	7.30566i	0.360271	+	0.261752i
$780$	8.91371			0.319162
$781$	−16.3911	+	6.01836i	−0.586520	+	0.215354i
$782$			24.3557i			0.870959i
$783$	−6.01579	−	4.37073i	−0.214987	−	0.156197i
$784$	1.31614	+	6.87516i	0.0470049	+	0.245541i
$785$	2.67870	+	8.24420i	0.0956071	+	0.294248i
$786$	6.79065	−	4.93370i	0.242215	−	0.175979i
$787$	1.77556	−	1.29002i	0.0632919	−	0.0459843i	−0.555689	−	0.831390i	$-0.687546\pi$
$787$	1.77556	−	1.29002i	0.0632919	−	0.0459843i	0.618981	+	0.785406i	$0.287546\pi$
$788$	11.7183	−	3.80752i	0.417449	−	0.135637i
$789$	−8.16761	+	25.1373i	−0.290775	+	0.894912i
$790$	14.4845	−	19.9363i	0.515337	−	0.709300i
$791$	−4.35286	−	16.9304i	−0.154770	−	0.601977i
$792$	−1.14315	−	3.11339i	−0.0406201	−	0.110630i
$793$	53.6460			1.90502
$794$	18.1321	+	13.1737i	0.643483	+	0.467518i
$795$	6.11270	−	18.8129i	0.216795	−	0.667226i
$796$	−5.10976	+	1.66026i	−0.181111	+	0.0588464i
$797$	22.5371	+	31.0197i	0.798306	+	1.09877i	0.993024	+	0.117915i	$0.0376210\pi$
$797$	22.5371	+	31.0197i	0.798306	+	1.09877i	−0.194717	+	0.980859i	$0.562379\pi$
$798$	10.1616	+	8.40087i	0.359718	+	0.297388i
$799$	−7.29215	+	2.36936i	−0.257978	+	0.0838220i
$800$	1.49574	+	0.485995i	0.0528824	+	0.0171825i
$801$	5.73801	−	7.89769i	0.202742	−	0.279051i
$802$		−	9.32133i		−	0.329148i
$803$	0.799843	+	21.1884i	0.0282259	+	0.747721i
$804$			0.825302i			0.0291062i
$805$	19.5199	+	7.72114i	0.687986	+	0.272134i
$806$	−13.8690	+	42.6843i	−0.488514	+	1.50349i
$807$	0.387943	+	1.19397i	0.0136562	+	0.0420296i
$808$	−0.377915	−	0.520155i	−0.0132950	−	0.0182990i
$809$	5.76836	+	7.93947i	0.202805	+	0.279137i	0.898290	−	0.439404i	$-0.144810\pi$
$809$	5.76836	+	7.93947i	0.202805	+	0.279137i	−0.695485	+	0.718541i	$0.744810\pi$
$810$	0.572081	+	1.76068i	0.0201009	+	0.0618641i
$811$	−14.6472	+	45.0794i	−0.514332	+	1.58295i	0.270163	+	0.962815i	$0.412922\pi$
$811$	−14.6472	+	45.0794i	−0.514332	+	1.58295i	−0.784495	+	0.620136i	$0.787078\pi$
$812$	−18.2944	−	7.23639i	−0.642008	−	0.253948i
$813$		−	7.50970i		−	0.263377i
$814$	10.2272	+	6.85637i	0.358463	+	0.240316i
$815$			11.9986i			0.420291i
$816$	−3.34042	+	4.59769i	−0.116938	+	0.160951i
$817$	−55.3397	−	17.9810i	−1.93609	−	0.629074i
$818$	−8.33294	+	2.70754i	−0.291354	+	0.0946668i
$819$	−9.81813	−	8.11690i	−0.343073	−	0.283627i
$820$	2.71404	+	3.73556i	0.0947785	+	0.130451i
$821$	−7.20633	+	2.34148i	−0.251502	+	0.0817181i	−0.432055	−	0.901847i	$-0.642211\pi$
$821$	−7.20633	+	2.34148i	−0.251502	+	0.0817181i	0.180553	+	0.983565i	$0.442211\pi$
$822$	−0.220778	+	0.679486i	−0.00770052	+	0.0236998i
$823$	32.4363	+	23.5664i	1.13066	+	0.821472i	0.985791	−	0.167979i	$-0.0537240\pi$
$823$	32.4363	+	23.5664i	1.13066	+	0.821472i	0.144869	+	0.989451i	$0.453724\pi$
$824$	−8.49340			−0.295882
$825$	4.10126	−	3.22295i	0.142787	−	0.112209i
$826$	−4.27117	−	16.6127i	−0.148613	−	0.578029i
$827$	−29.0579	+	39.9947i	−1.01044	+	1.39075i	−0.0917478	+	0.995782i	$0.529245\pi$
$827$	−29.0579	+	39.9947i	−1.01044	+	1.39075i	−0.918694	+	0.394971i	$0.870755\pi$
$828$	−1.32435	+	4.07592i	−0.0460242	+	0.141648i
$829$	−46.6602	+	15.1608i	−1.62058	+	0.526557i	−0.972078	−	0.234658i	$-0.924603\pi$
$829$	−46.6602	+	15.1608i	−1.62058	+	0.526557i	−0.648499	+	0.761216i	$0.724603\pi$
$830$	−15.2236	+	11.0606i	−0.528417	+	0.383918i
$831$	4.14350	−	3.01043i	0.143736	−	0.104431i
$832$	1.48787	+	4.57920i	0.0515827	+	0.158755i
$833$	−7.47968	−	39.0719i	−0.259155	−	1.35376i
$834$	−4.87252	−	3.54009i	−0.168721	−	0.122583i
$835$		−	44.2648i		−	1.53185i
$836$	−15.9003	−	4.51077i	−0.549924	−	0.156008i
$837$	−9.32135			−0.322193
$838$	1.14594	+	0.832576i	0.0395859	+	0.0287609i
$839$	9.91654	+	3.22208i	0.342357	+	0.111239i	0.475149	−	0.879905i	$-0.342394\pi$
$839$	9.91654	+	3.22208i	0.342357	+	0.111239i	−0.132792	+	0.991144i	$0.542394\pi$
$840$	2.62586	+	4.13472i	0.0906006	+	0.142661i
$841$	21.2714	−	15.4546i	0.733498	−	0.532917i
$842$	−7.11985	−	9.79963i	−0.245366	−	0.337717i
$843$	−2.82957	−	8.70853i	−0.0974557	−	0.299938i
$844$	1.66846	+	0.542115i	0.0574307	+	0.0186604i
$845$	−11.0806	+	15.2511i	−0.381183	+	0.524654i
$846$	−1.34917			−0.0463855
$847$	−29.1008	+	0.377039i	−0.999916	+	0.0129552i
$848$	10.6850			0.366925
$849$	−10.6095	+	14.6027i	−0.364116	+	0.501163i
$850$	−8.50037	−	2.76194i	−0.291560	−	0.0947337i
$851$	−4.91657	−	15.1316i	−0.168538	−	0.518706i
$852$	3.09452	+	4.25924i	0.106016	+	0.145919i
$853$	40.4898	−	29.4176i	1.38635	−	1.00724i	0.390090	−	0.920777i	$-0.372444\pi$
$853$	40.4898	−	29.4176i	1.38635	−	1.00724i	0.996255	−	0.0864622i	$-0.0275562\pi$
$854$	15.8034	+	24.8842i	0.540780	+	0.851521i
$855$	8.77403	+	2.85086i	0.300065	+	0.0974972i
$856$	5.32607	+	3.86962i	0.182041	+	0.132261i
$857$	−27.7628			−0.948359			−0.474179	−	0.880428i	$-0.657255\pi$
$857$	−27.7628			−0.948359			−0.474179	+	0.880428i	$0.657255\pi$
$858$	15.3628	+	4.35829i	0.524478	+	0.148790i
$859$		−	0.919865i		−	0.0313854i	−0.999877	−	0.0156927i	$-0.995005\pi$
$859$		−	0.919865i		−	0.0313854i	0.999877	−	0.0156927i	$-0.00499534\pi$
$860$	−17.4882	−	12.7059i	−0.596344	−	0.433269i
$861$	0.412209	−	6.58602i	0.0140480	−	0.224451i
$862$	−5.50498	−	16.9426i	−0.187500	−	0.577067i
$863$	−34.0077	+	24.7081i	−1.15764	+	0.841072i	−0.989477	−	0.144688i	$-0.953782\pi$
$863$	−34.0077	+	24.7081i	−1.15764	+	0.841072i	−0.168159	+	0.985760i	$0.553782\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	23.5394	−	7.64843i	0.800365	−	0.260054i
$866$	0.755191	−	2.32424i	0.0256624	−	0.0789808i
$867$	8.99141	−	12.3756i	0.305364	−	0.420298i
$868$	−23.8852	+	6.14095i	−0.810716	+	0.208437i
$869$	34.7119	−	27.2781i	1.17752	−	0.925348i
$870$	−13.7661			−0.466713
$871$	−3.21480	−	2.33569i	−0.108929	−	0.0791418i
$872$	−3.90007	+	12.0032i	−0.132073	+	0.406479i
$873$	−16.3267	+	5.30487i	−0.552575	+	0.179543i
$874$	12.5532	+	17.2780i	0.424619	+	0.584438i
$875$	−20.5129	+	24.8122i	−0.693462	+	0.838806i
$876$	6.08018	−	1.97557i	0.205430	−	0.0667484i
$877$	−27.3894	−	8.89935i	−0.924874	−	0.300510i	−0.192409	−	0.981315i	$-0.561630\pi$
$877$	−27.3894	−	8.89935i	−0.924874	−	0.300510i	−0.732465	+	0.680805i	$0.761630\pi$
$878$	−4.36700	+	6.01066i	−0.147379	+	0.202850i
$879$			31.2338i			1.05349i
$880$	−5.10001	−	3.41908i	−0.171921	−	0.115257i
$881$		−	42.2224i		−	1.42251i	−0.702935	−	0.711254i	$-0.748128\pi$
$881$		−	42.2224i		−	1.42251i	0.702935	−	0.711254i	$-0.251872\pi$
$882$	0.872820	−	6.94537i	0.0293894	−	0.233863i
$883$	−9.23856	+	28.4334i	−0.310902	+	0.956859i	0.666506	+	0.745499i	$0.267789\pi$
$883$	−9.23856	+	28.4334i	−0.310902	+	0.956859i	−0.977408	+	0.211359i	$0.932211\pi$
$884$	−8.45566	−	26.0238i	−0.284394	−	0.875276i
$885$	−7.05479	−	9.71008i	−0.237144	−	0.326401i
$886$	−0.152118	−	0.209372i	−0.00511049	−	0.00703399i
$887$	−6.43303	−	19.7988i	−0.216000	−	0.664780i	−0.999081	−	0.0428600i	$-0.986353\pi$
$887$	−6.43303	−	19.7988i	−0.216000	−	0.664780i	0.783081	−	0.621920i	$-0.213647\pi$
$888$	1.14721	−	3.53075i	0.0384979	−	0.118484i
$889$	−18.6604	−	7.38116i	−0.625849	−	0.247556i
$890$		−	18.0725i		−	0.605790i
$891$	0.125111	+	3.31426i	0.00419137	+	0.111032i
$892$			17.6072i			0.589534i
$893$	−3.95188	+	5.43929i	−0.132245	+	0.182019i
$894$	−11.3705	−	3.69451i	−0.380287	−	0.123563i
$895$	7.01365	−	2.27887i	0.234441	−	0.0761744i
$896$	−1.68580	+	2.03913i	−0.0563187	+	0.0681227i
$897$	−12.1289	−	16.6940i	−0.404972	−	0.557396i
$898$	−26.9300	+	8.75008i	−0.898665	+	0.291994i
$899$	21.4188	−	65.9204i	0.714359	−	2.19857i
$900$	−1.27235	−	0.924418i	−0.0424117	−	0.0308139i
$901$	−60.7235			−2.02299
$902$	2.85119	+	7.76527i	0.0949343	+	0.258555i
$903$	7.69253	+	29.9201i	0.255991	+	0.995678i
$904$	3.88362	−	5.34535i	0.129167	−	0.177784i
$905$	−6.94580	+	21.3770i	−0.230886	+	0.710595i
$906$	−21.5136	+	6.99018i	−0.714741	+	0.232233i
$907$	−2.23576	+	1.62437i	−0.0742370	+	0.0539364i	−0.624285	−	0.781197i	$-0.714610\pi$
$907$	−2.23576	+	1.62437i	−0.0742370	+	0.0539364i	0.550048	+	0.835133i	$0.314610\pi$
$908$	−7.58736	+	5.51254i	−0.251796	+	0.182940i
$909$	0.198682	+	0.611479i	0.00658985	+	0.0202815i
$910$	−23.5374	−	1.47317i	−0.780257	−	0.0488351i
$911$	6.03876	+	4.38741i	0.200073	+	0.145361i	0.683311	−	0.730128i	$-0.260539\pi$
$911$	6.03876	+	4.38741i	0.200073	+	0.145361i	−0.483238	+	0.875489i	$0.660539\pi$
$912$			4.98331i			0.165014i
$913$	−31.6459	+	11.6195i	−1.04732	+	0.384549i
$914$	14.0942			0.466195
$915$	16.6873	+	12.1241i	0.551666	+	0.400809i
$916$	2.25754	+	0.733520i	0.0745913	+	0.0242362i
$917$	−18.7467	+	11.9056i	−0.619070	+	0.393156i
$918$	4.59769	−	3.34042i	0.151746	−	0.110250i
$919$	−1.07953	−	1.48585i	−0.0356105	−	0.0490137i	0.790840	−	0.612022i	$-0.209644\pi$
$919$	−1.07953	−	1.48585i	−0.0356105	−	0.0490137i	−0.826451	+	0.563009i	$0.809644\pi$
$920$	2.45175	+	7.54572i	0.0808319	+	0.248775i
$921$	13.1315	+	4.26668i	0.432698	+	0.140592i
$922$	−2.43436	+	3.35060i	−0.0801712	+	0.110346i
$923$	−25.3488			−0.834366
$924$	2.50404	+	8.41010i	0.0823768	+	0.276672i
$925$	5.83862			0.191973
$926$	18.6177	−	25.6250i	0.611815	−	0.842091i
$927$	8.07770	+	2.62460i	0.265307	+	0.0862033i
$928$	−2.29783	−	7.07198i	−0.0754298	−	0.232149i
$929$	9.12758	+	12.5630i	0.299466	+	0.412180i	0.932060	−	0.362304i	$-0.118010\pi$
$929$	9.12758	+	12.5630i	0.299466	+	0.412180i	−0.632594	+	0.774484i	$0.718010\pi$
$930$	−13.9608	+	10.1431i	−0.457794	+	0.332607i
$931$	−25.4442	−	23.8626i	−0.833901	−	0.782066i
$932$	6.14668	+	1.99718i	0.201341	+	0.0654197i
$933$	0.660111	+	0.479599i	0.0216111	+	0.0157014i
$934$	7.38587			0.241673
$935$	28.9836	+	19.4308i	0.947865	+	0.635455i
$936$		−	4.81485i		−	0.157378i
$937$	−14.1813	−	10.3033i	−0.463283	−	0.336595i	0.331535	−	0.943443i	$-0.392434\pi$
$937$	−14.1813	−	10.3033i	−0.463283	−	0.336595i	−0.794818	+	0.606848i	$0.792434\pi$
$938$	0.136398	−	2.17928i	0.00445355	−	0.0711560i
$939$	0.244022	+	0.751022i	0.00796335	+	0.0245087i
$940$	−2.02069	+	1.46812i	−0.0659077	+	0.0478847i
$941$	3.83831	−	2.78869i	0.125125	−	0.0909088i	−0.523462	−	0.852049i	$-0.675360\pi$
$941$	3.83831	−	2.78869i	0.125125	−	0.0909088i	0.648588	+	0.761140i	$0.275360\pi$
$942$	4.45321	−	1.44694i	0.145094	−	0.0471438i
$943$	3.30312	−	10.1660i	0.107564	−	0.331049i
$944$	3.81073	−	5.24503i	0.124029	−	0.170711i
$945$	−1.21964	−	4.74378i	−0.0396749	−	0.154315i
$946$	−23.9286	−	30.4495i	−0.777985	−	0.989999i
$947$	23.4052			0.760565			0.380283	−	0.924870i	$-0.375827\pi$
$947$	23.4052			0.760565			0.380283	+	0.924870i	$0.375827\pi$
$948$	−10.7688	−	7.82401i	−0.349755	−	0.254112i
$949$	−9.51209	+	29.2752i	−0.308775	+	0.950313i
$950$	−7.45373	+	2.42186i	−0.241831	+	0.0785756i
$951$	9.27546	+	12.7666i	0.300777	+	0.413985i
$952$	9.58051	−	11.5885i	0.310506	−	0.375586i
$953$	46.3958	−	15.0749i	1.50291	−	0.488325i	0.562044	−	0.827107i	$-0.310015\pi$
$953$	46.3958	−	15.0749i	1.50291	−	0.488325i	0.940865	+	0.338783i	$0.110015\pi$
$954$	−10.1621	−	3.30185i	−0.329009	−	0.106901i
$955$	1.61204	−	2.21879i	0.0521645	−	0.0717983i
$956$		−	22.2395i		−	0.719277i
$957$	−23.7259	−	6.73082i	−0.766949	−	0.217577i
$958$		−	6.11623i		−	0.197606i
$959$	0.695282	−	1.75775i	0.0224518	−	0.0567607i
$960$	−0.572081	+	1.76068i	−0.0184638	+	0.0568258i
$961$	−17.2702	−	53.1523i	−0.557104	−	1.71459i
$962$	10.5066	+	14.4611i	0.338747	+	0.466245i
$963$	−3.86962	−	5.32607i	−0.124697	−	0.171630i
$964$	−8.16072	−	25.1161i	−0.262839	−	0.808936i
$965$	−7.42816	+	22.8615i	−0.239121	+	0.735939i
$966$	4.17067	−	10.5439i	0.134189	−	0.339245i
$967$		−	40.4487i		−	1.30074i	−0.759617	−	0.650371i	$-0.774614\pi$
$967$		−	40.4487i		−	1.30074i	0.759617	−	0.650371i	$-0.225386\pi$
$968$	−7.11815	−	8.38641i	−0.228786	−	0.269549i
$969$		−	28.3204i		−	0.909782i
$970$	−18.6804	+	25.7114i	−0.599791	+	0.825542i
$971$	10.2147	+	3.31895i	0.327805	+	0.106510i	0.468296	−	0.883572i	$-0.344868\pi$
$971$	10.2147	+	3.31895i	0.327805	+	0.106510i	−0.140491	+	0.990082i	$0.544868\pi$
$972$	0.951057	−	0.309017i	0.0305052	−	0.00991172i
$973$	12.2812	+	10.1532i	0.393718	+	0.325496i
$974$	−10.8779	−	14.9721i	−0.348549	−	0.479736i
$975$	7.20177	−	2.34000i	0.230641	−	0.0749399i
$976$	−3.44299	+	10.5964i	−0.110208	+	0.339184i
$977$	−27.3081	−	19.8405i	−0.873662	−	0.634753i	0.0579049	−	0.998322i	$-0.481558\pi$
$977$	−27.3081	−	19.8405i	−0.873662	−	0.634753i	−0.931567	+	0.363569i	$0.881558\pi$
$978$	6.48117			0.207245
$979$	8.83640	−	31.1480i	0.282413	−	0.995494i
$980$	−6.25045	−	11.3520i	−0.199663	−	0.362628i
$981$	7.41837	−	10.2105i	0.236850	−	0.325997i
$982$	−2.58245	+	7.94795i	−0.0824091	+	0.253629i
$983$	1.61438	−	0.524545i	0.0514908	−	0.0167304i	−0.283158	−	0.959073i	$-0.591382\pi$
$983$	1.61438	−	0.524545i	0.0514908	−	0.0167304i	0.334649	+	0.942343i	$0.391382\pi$
$984$	2.01781	−	1.46603i	0.0643255	−	0.0467352i
$985$	−18.4541	+	13.4077i	−0.587996	+	0.427204i
$986$	13.0587	+	40.1905i	0.415873	+	1.27992i
$987$	3.56260	+	0.222978i	0.113399	+	0.00709746i
$988$	−19.4115	−	14.1033i	−0.617561	−	0.448684i
$989$			50.0417i			1.59123i
$990$	3.79384	+	4.82772i	0.120576	+	0.153435i
$991$	−21.5021			−0.683038			−0.341519	−	0.939875i	$-0.610941\pi$
$991$	−21.5021			−0.683038			−0.341519	+	0.939875i	$0.610941\pi$
$992$	−7.54113	−	5.47895i	−0.239431	−	0.173957i
$993$	−17.3131	−	5.62538i	−0.549415	−	0.178516i
$994$	−7.46741	−	11.7583i	−0.236852	−	0.372951i
$995$	8.04687	−	5.84639i	0.255103	−	0.185343i
$996$	5.97450	+	8.22320i	0.189309	+	0.260562i
$997$	−10.3653	−	31.9011i	−0.328272	−	1.01032i	−0.969942	−	0.243336i	$-0.921758\pi$
$997$	−10.3653	−	31.9011i	−0.328272	−	1.01032i	0.641670	−	0.766981i	$-0.278242\pi$
$998$	28.2248	+	9.17079i	0.893440	+	0.290296i
$999$	−2.18212	+	3.00344i	−0.0690393	+	0.0950245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.a.139.7	✓	32
7.6	odd	2		462.2.u.b.139.6	yes	32
11.8	odd	10		462.2.u.b.349.6	yes	32
77.41	even	10	inner	462.2.u.a.349.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.7	✓	32	1.1	even	1	trivial
462.2.u.a.349.7	yes	32	77.41	even	10	inner
462.2.u.b.139.6	yes	32	7.6	odd	2
462.2.u.b.349.6	yes	32	11.8	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.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.08816 + 1.49773i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.23342 + 1.41839i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.08816 + 1.49773i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.23342 + 1.41839i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +1.85129 q^{10} +(3.19071 + 0.905177i) q^{11} -1.00000i q^{12} +(3.89530 + 2.83010i) q^{13} +(-0.165270 + 2.64058i) q^{14} +(0.572081 + 1.76068i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.59769 - 3.34042i) q^{17} +(0.951057 - 0.309017i) q^{18} +(1.53993 - 4.73941i) q^{19} +(1.08816 - 1.49773i) q^{20} +(-2.56242 + 0.658804i) q^{21} +(2.60776 - 2.04929i) q^{22} -4.28567 q^{23} +(-0.809017 - 0.587785i) q^{24} +(0.485995 - 1.49574i) q^{25} +(4.57920 - 1.48787i) q^{26} +(0.587785 + 0.809017i) q^{27} +(2.03913 + 1.68580i) q^{28} +(-7.07198 + 2.29783i) q^{29} +(1.76068 + 0.572081i) q^{30} +(-5.47895 + 7.54113i) q^{31} +1.00000i q^{32} +(2.75483 + 1.84686i) q^{33} -5.68305i q^{34} +(-4.55469 - 1.80162i) q^{35} +(0.309017 - 0.951057i) q^{36} +(1.14721 + 3.53075i) q^{37} +(-2.92911 - 4.03158i) q^{38} +(2.83010 + 3.89530i) q^{39} +(-0.572081 - 1.76068i) q^{40} +(-0.770735 + 2.37208i) q^{41} +(-0.973167 + 2.46027i) q^{42} -11.6765i q^{43} +(-0.125111 - 3.31426i) q^{44} +1.85129i q^{45} +(-2.51906 + 3.46718i) q^{46} +(-1.28314 - 0.416917i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(2.97634 - 6.33572i) q^{49} +(-0.924418 - 1.27235i) q^{50} +(5.40491 - 1.75616i) q^{51} +(1.48787 - 4.57920i) q^{52} +(-8.64436 - 6.28050i) q^{53} +1.00000 q^{54} +(2.11631 + 5.76380i) q^{55} +(2.56242 - 0.658804i) q^{56} +(2.92911 - 4.03158i) q^{57} +(-2.29783 + 7.07198i) q^{58} +(-6.16590 + 2.00342i) q^{59} +(1.49773 - 1.08816i) q^{60} +(9.01388 - 6.54896i) q^{61} +(2.88046 + 8.86513i) q^{62} +(-2.64058 - 0.165270i) q^{63} +(0.809017 + 0.587785i) q^{64} +8.91371i q^{65} +(3.11339 - 1.14315i) q^{66} -0.825302 q^{67} +(-4.59769 - 3.34042i) q^{68} +(-4.07592 - 1.32435i) q^{69} +(-4.13472 + 2.62586i) q^{70} +(-4.25924 + 3.09452i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(1.97557 + 6.08018i) q^{73} +(3.53075 + 1.14721i) q^{74} +(0.924418 - 1.27235i) q^{75} -4.98331 q^{76} +(-8.41010 + 2.50404i) q^{77} +4.81485 q^{78} +(7.82401 - 10.7688i) q^{79} +(-1.76068 - 0.572081i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.46603 + 2.01781i) q^{82} +(-8.22320 + 5.97450i) q^{83} +(1.41839 + 2.23342i) q^{84} +(10.0061 + 3.25117i) q^{85} +(-9.44649 - 6.86328i) q^{86} -7.43592 q^{87} +(-2.75483 - 1.84686i) q^{88} -9.76208i q^{89} +(1.49773 + 1.08816i) q^{90} +(-12.7140 - 0.795752i) q^{91} +(1.32435 + 4.07592i) q^{92} +(-7.54113 + 5.47895i) q^{93} +(-1.09150 + 0.793023i) q^{94} +(8.77403 - 2.85086i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-10.0905 + 13.8883i) q^{97} +(-3.37626 - 6.13195i) q^{98} +(2.04929 + 2.60776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

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