LMFDB - Embedded newform 462.2.j.c.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	462.169
Dual form			462.2.j.c.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.92705 - 2.12663i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.92705 - 2.12663i) 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} +3.61803 q^{10} +(0.809017 - 3.21644i) q^{11} +1.00000 q^{12} +(-2.61803 - 1.90211i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.11803 - 3.44095i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.35410 + 3.16344i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-2.19098 + 6.74315i) q^{19} +(2.92705 + 2.12663i) q^{20} -1.00000 q^{21} +(2.54508 - 2.12663i) q^{22} +6.32624 q^{23} +(0.809017 + 0.587785i) q^{24} +(2.50000 - 7.69421i) q^{25} +(-1.00000 - 3.07768i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.809017 - 0.587785i) q^{28} +(1.00000 + 3.07768i) q^{29} +(1.11803 - 3.44095i) q^{30} +(8.16312 + 5.93085i) q^{31} -1.00000 q^{32} +(-2.80902 - 1.76336i) q^{33} -5.38197 q^{34} +(-2.92705 - 2.12663i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-1.97214 - 6.06961i) q^{37} +(-5.73607 + 4.16750i) q^{38} +(-2.61803 + 1.90211i) q^{39} +(1.11803 + 3.44095i) q^{40} +(1.59017 - 4.89404i) q^{41} +(-0.809017 - 0.587785i) q^{42} +0.763932 q^{43} +(3.30902 - 0.224514i) q^{44} -3.61803 q^{45} +(5.11803 + 3.71847i) q^{46} +(-3.76393 + 11.5842i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(6.54508 - 4.75528i) q^{50} +(1.66312 + 5.11855i) q^{51} +(1.00000 - 3.07768i) q^{52} +(7.23607 + 5.25731i) q^{53} -1.00000 q^{54} +(-4.47214 - 11.1352i) q^{55} +1.00000 q^{56} +(5.73607 + 4.16750i) q^{57} +(-1.00000 + 3.07768i) q^{58} +(2.76393 + 8.50651i) q^{59} +(2.92705 - 2.12663i) q^{60} +(3.85410 - 2.80017i) q^{61} +(3.11803 + 9.59632i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} -11.7082 q^{65} +(-1.23607 - 3.07768i) q^{66} +3.23607 q^{67} +(-4.35410 - 3.16344i) q^{68} +(1.95492 - 6.01661i) q^{69} +(-1.11803 - 3.44095i) q^{70} +(-8.47214 + 6.15537i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-2.47214 - 7.60845i) q^{73} +(1.97214 - 6.06961i) q^{74} +(-6.54508 - 4.75528i) q^{75} -7.09017 q^{76} +(-3.30902 + 0.224514i) q^{77} -3.23607 q^{78} +(-4.61803 - 3.35520i) q^{79} +(-1.11803 + 3.44095i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.16312 - 3.02468i) q^{82} +(-8.70820 + 6.32688i) q^{83} +(-0.309017 - 0.951057i) q^{84} +(-6.01722 + 18.5191i) q^{85} +(0.618034 + 0.449028i) q^{86} +3.23607 q^{87} +(2.80902 + 1.76336i) q^{88} -11.8541 q^{89} +(-2.92705 - 2.12663i) q^{90} +(-1.00000 + 3.07768i) q^{91} +(1.95492 + 6.01661i) q^{92} +(8.16312 - 5.93085i) q^{93} +(-9.85410 + 7.15942i) q^{94} +(7.92705 + 24.3970i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-5.47214 - 3.97574i) q^{97} -1.00000 q^{98} +(-2.54508 + 2.12663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9	$ 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9} + 10 q^{10} + q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - q^{16} - 4 q^{17} + q^{18} - 11 q^{19} + 5 q^{20} - 4 q^{21} - q^{22} - 6 q^{23} + q^{24} + 10 q^{25} - 4 q^{26} - q^{27} + q^{28} + 4 q^{29} + 17 q^{31} - 4 q^{32} - 9 q^{33} - 26 q^{34} - 5 q^{35} - q^{36} + 10 q^{37} - 14 q^{38} - 6 q^{39} - 16 q^{41} - q^{42} + 12 q^{43} + 11 q^{44} - 10 q^{45} + 16 q^{46} - 24 q^{47} - q^{48} - q^{49} + 15 q^{50} - 9 q^{51} + 4 q^{52} + 20 q^{53} - 4 q^{54} + 4 q^{56} + 14 q^{57} - 4 q^{58} + 20 q^{59} + 5 q^{60} + 2 q^{61} + 8 q^{62} + q^{63} - q^{64} - 20 q^{65} + 4 q^{66} + 4 q^{67} - 4 q^{68} + 19 q^{69} - 16 q^{71} + q^{72} + 8 q^{73} - 10 q^{74} - 15 q^{75} - 6 q^{76} - 11 q^{77} - 4 q^{78} - 14 q^{79} - q^{81} + q^{82} - 8 q^{83} + q^{84} + 5 q^{85} - 2 q^{86} + 4 q^{87} + 9 q^{88} - 34 q^{89} - 5 q^{90} - 4 q^{91} + 19 q^{92} + 17 q^{93} - 26 q^{94} + 25 q^{95} + q^{96} - 4 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9 + 10 * q^10 + q^11 + 4 * q^12 - 6 * q^13 - q^14 - q^16 - 4 * q^17 + q^18 - 11 * q^19 + 5 * q^20 - 4 * q^21 - q^22 - 6 * q^23 + q^24 + 10 * q^25 - 4 * q^26 - q^27 + q^28 + 4 * q^29 + 17 * q^31 - 4 * q^32 - 9 * q^33 - 26 * q^34 - 5 * q^35 - q^36 + 10 * q^37 - 14 * q^38 - 6 * q^39 - 16 * q^41 - q^42 + 12 * q^43 + 11 * q^44 - 10 * q^45 + 16 * q^46 - 24 * q^47 - q^48 - q^49 + 15 * q^50 - 9 * q^51 + 4 * q^52 + 20 * q^53 - 4 * q^54 + 4 * q^56 + 14 * q^57 - 4 * q^58 + 20 * q^59 + 5 * q^60 + 2 * q^61 + 8 * q^62 + q^63 - q^64 - 20 * q^65 + 4 * q^66 + 4 * q^67 - 4 * q^68 + 19 * q^69 - 16 * q^71 + q^72 + 8 * q^73 - 10 * q^74 - 15 * q^75 - 6 * q^76 - 11 * q^77 - 4 * q^78 - 14 * q^79 - q^81 + q^82 - 8 * q^83 + q^84 + 5 * q^85 - 2 * q^86 + 4 * q^87 + 9 * q^88 - 34 * q^89 - 5 * q^90 - 4 * q^91 + 19 * q^92 + 17 * q^93 - 26 * q^94 + 25 * q^95 + q^96 - 4 * q^97 - 4 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.92705	−	2.12663i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$5$	2.92705	−	2.12663i	1.30902	−	0.951057i	1.00000			$0$
$6$	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
$10$	3.61803			1.14412
$11$	0.809017	−	3.21644i	0.243928	−	0.969793i
$11$	0.809017	−	3.21644i	0.243928	−	0.969793i
$12$	1.00000			0.288675
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	0.162219	−	0.986755i	$-0.448135\pi$
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	−0.888331	+	0.459204i	$0.848135\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	−1.11803	−	3.44095i	−0.288675	−	0.888451i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.35410	+	3.16344i	−1.05602	+	0.767247i	−0.973349	−	0.229330i	$-0.926347\pi$
$17$	−4.35410	+	3.16344i	−1.05602	+	0.767247i	−0.0826760	+	0.996576i	$0.526347\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	−2.19098	+	6.74315i	−0.502646	+	1.54699i	0.302046	+	0.953293i	$0.402330\pi$
$19$	−2.19098	+	6.74315i	−0.502646	+	1.54699i	−0.804692	+	0.593692i	$0.797670\pi$
$20$	2.92705	+	2.12663i	0.654508	+	0.475528i
$21$	−1.00000			−0.218218
$22$	2.54508	−	2.12663i	0.542614	−	0.453398i
$23$	6.32624			1.31911			0.659556	−	0.751656i	$-0.270744\pi$
$23$	6.32624			1.31911			0.659556	+	0.751656i	$0.270744\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	2.50000	−	7.69421i	0.500000	−	1.53884i
$26$	−1.00000	−	3.07768i	−0.196116	−	0.603583i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	1.00000	+	3.07768i	0.185695	+	0.571511i	0.999960	−	0.00898281i	$-0.00285936\pi$
$29$	1.00000	+	3.07768i	0.185695	+	0.571511i	−0.814264	+	0.580494i	$0.802859\pi$
$30$	1.11803	−	3.44095i	0.204124	−	0.628230i
$31$	8.16312	+	5.93085i	1.46614	+	1.06521i	0.981710	+	0.190382i	$0.0609728\pi$
$31$	8.16312	+	5.93085i	1.46614	+	1.06521i	0.484429	+	0.874830i	$0.339027\pi$
$32$	−1.00000			−0.176777
$33$	−2.80902	−	1.76336i	−0.488987	−	0.306961i
$34$	−5.38197			−0.923000
$35$	−2.92705	−	2.12663i	−0.494762	−	0.359466i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−1.97214	−	6.06961i	−0.324217	−	0.997838i	−0.971793	−	0.235837i	$-0.924217\pi$
$37$	−1.97214	−	6.06961i	−0.324217	−	0.997838i	0.647576	−	0.762001i	$-0.275783\pi$
$38$	−5.73607	+	4.16750i	−0.930513	+	0.676057i
$39$	−2.61803	+	1.90211i	−0.419221	+	0.304582i
$40$	1.11803	+	3.44095i	0.176777	+	0.544063i
$41$	1.59017	−	4.89404i	0.248343	−	0.764321i	−0.746726	−	0.665132i	$-0.768375\pi$
$41$	1.59017	−	4.89404i	0.248343	−	0.764321i	0.995069	−	0.0991886i	$-0.0316247\pi$
$42$	−0.809017	−	0.587785i	−0.124834	−	0.0906972i
$43$	0.763932			0.116499			0.0582493	−	0.998302i	$-0.481448\pi$
$43$	0.763932			0.116499			0.0582493	+	0.998302i	$0.481448\pi$
$44$	3.30902	−	0.224514i	0.498853	−	0.0338468i
$45$	−3.61803			−0.539345
$46$	5.11803	+	3.71847i	0.754613	+	0.548258i
$47$	−3.76393	+	11.5842i	−0.549026	+	1.68973i	0.162194	+	0.986759i	$0.448143\pi$
$47$	−3.76393	+	11.5842i	−0.549026	+	1.68973i	−0.711220	+	0.702969i	$0.751857\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	6.54508	−	4.75528i	0.925615	−	0.672499i
$51$	1.66312	+	5.11855i	0.232883	+	0.716741i
$52$	1.00000	−	3.07768i	0.138675	−	0.426798i
$53$	7.23607	+	5.25731i	0.993950	+	0.722147i	0.960783	−	0.277303i	$-0.0894404\pi$
$53$	7.23607	+	5.25731i	0.993950	+	0.722147i	0.0331677	+	0.999450i	$0.489440\pi$
$54$	−1.00000			−0.136083
$55$	−4.47214	−	11.1352i	−0.603023	−	1.50147i
$56$	1.00000			0.133631
$57$	5.73607	+	4.16750i	0.759761	+	0.551999i
$58$	−1.00000	+	3.07768i	−0.131306	+	0.404120i
$59$	2.76393	+	8.50651i	0.359833	+	1.10745i	0.953154	+	0.302487i	$0.0978167\pi$
$59$	2.76393	+	8.50651i	0.359833	+	1.10745i	−0.593320	+	0.804966i	$0.702183\pi$
$60$	2.92705	−	2.12663i	0.377881	−	0.274546i
$61$	3.85410	−	2.80017i	0.493467	−	0.358525i	−0.313049	−	0.949737i	$-0.601350\pi$
$61$	3.85410	−	2.80017i	0.493467	−	0.358525i	0.806516	+	0.591212i	$0.201350\pi$
$62$	3.11803	+	9.59632i	0.395991	+	1.21873i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−11.7082			−1.45222
$66$	−1.23607	−	3.07768i	−0.152149	−	0.378837i
$67$	3.23607			0.395349			0.197674	−	0.980268i	$-0.436661\pi$
$67$	3.23607			0.395349			0.197674	+	0.980268i	$0.436661\pi$
$68$	−4.35410	−	3.16344i	−0.528012	−	0.383623i
$69$	1.95492	−	6.01661i	0.235344	−	0.724315i
$70$	−1.11803	−	3.44095i	−0.133631	−	0.411273i
$71$	−8.47214	+	6.15537i	−1.00546	+	0.730508i	−0.963251	−	0.268601i	$-0.913439\pi$
$71$	−8.47214	+	6.15537i	−1.00546	+	0.730508i	−0.0422061	+	0.999109i	$0.513439\pi$
$72$	0.809017	−	0.587785i	0.0953436	−	0.0692712i
$73$	−2.47214	−	7.60845i	−0.289342	−	0.890502i	−0.985064	−	0.172191i	$-0.944915\pi$
$73$	−2.47214	−	7.60845i	−0.289342	−	0.890502i	0.695722	−	0.718311i	$-0.255085\pi$
$74$	1.97214	−	6.06961i	0.229256	−	0.705578i
$75$	−6.54508	−	4.75528i	−0.755761	−	0.549093i
$76$	−7.09017			−0.813298
$77$	−3.30902	+	0.224514i	−0.377097	+	0.0255857i
$78$	−3.23607			−0.366413
$79$	−4.61803	−	3.35520i	−0.519569	−	0.377489i	0.296872	−	0.954917i	$-0.404056\pi$
$79$	−4.61803	−	3.35520i	−0.519569	−	0.377489i	−0.816442	+	0.577428i	$0.804056\pi$
$80$	−1.11803	+	3.44095i	−0.125000	+	0.384710i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.16312	−	3.02468i	0.459740	−	0.334020i
$83$	−8.70820	+	6.32688i	−0.955850	+	0.694465i	−0.952183	−	0.305528i	$-0.901167\pi$
$83$	−8.70820	+	6.32688i	−0.955850	+	0.694465i	−0.00366644	+	0.999993i	$0.501167\pi$
$84$	−0.309017	−	0.951057i	−0.0337165	−	0.103769i
$85$	−6.01722	+	18.5191i	−0.652659	+	2.00868i
$86$	0.618034	+	0.449028i	0.0666443	+	0.0484199i
$87$	3.23607			0.346943
$88$	2.80902	+	1.76336i	0.299442	+	0.187974i
$89$	−11.8541			−1.25653			−0.628266	−	0.777998i	$-0.716235\pi$
$89$	−11.8541			−1.25653			−0.628266	+	0.777998i	$0.716235\pi$
$90$	−2.92705	−	2.12663i	−0.308538	−	0.224166i
$91$	−1.00000	+	3.07768i	−0.104828	+	0.322629i
$92$	1.95492	+	6.01661i	0.203814	+	0.627275i
$93$	8.16312	−	5.93085i	0.846476	−	0.615001i
$94$	−9.85410	+	7.15942i	−1.01637	+	0.738438i
$95$	7.92705	+	24.3970i	0.813298	+	2.50307i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	−5.47214	−	3.97574i	−0.555611	−	0.403675i	0.274239	−	0.961662i	$-0.411574\pi$
$97$	−5.47214	−	3.97574i	−0.555611	−	0.403675i	−0.829850	+	0.557986i	$0.811574\pi$
$98$	−1.00000			−0.101015
$99$	−2.54508	+	2.12663i	−0.255791	+	0.213734i
$100$	8.09017			0.809017
$101$	−4.16312	−	3.02468i	−0.414246	−	0.300967i	0.361073	−	0.932538i	$-0.382411\pi$
$101$	−4.16312	−	3.02468i	−0.414246	−	0.300967i	−0.775318	+	0.631570i	$0.782411\pi$
$102$	−1.66312	+	5.11855i	−0.164673	+	0.506812i
$103$	−5.80902	−	17.8783i	−0.572379	−	1.76160i	−0.644934	−	0.764238i	$-0.723115\pi$
$103$	−5.80902	−	17.8783i	−0.572379	−	1.76160i	0.0725544	−	0.997364i	$-0.476885\pi$
$104$	2.61803	−	1.90211i	0.256719	−	0.186518i
$105$	−2.92705	+	2.12663i	−0.285651	+	0.207538i
$106$	2.76393	+	8.50651i	0.268457	+	0.826225i
$107$	3.10081	−	9.54332i	0.299767	−	0.922588i	−0.681811	−	0.731528i	$-0.738808\pi$
$107$	3.10081	−	9.54332i	0.299767	−	0.922588i	0.981578	−	0.191060i	$-0.0611924\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	2.38197			0.228151			0.114075	−	0.993472i	$-0.463609\pi$
$109$	2.38197			0.228151			0.114075	+	0.993472i	$0.463609\pi$
$110$	2.92705	−	11.6372i	0.279083	−	1.10956i
$111$	−6.38197			−0.605749
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	0.763932	−	2.35114i	0.0718647	−	0.221177i	−0.908673	−	0.417509i	$-0.862903\pi$
$113$	0.763932	−	2.35114i	0.0718647	−	0.221177i	0.980537	+	0.196332i	$0.0629032\pi$
$114$	2.19098	+	6.74315i	0.205204	+	0.631554i
$115$	18.5172	−	13.4535i	1.72674	−	1.25455i
$116$	−2.61803	+	1.90211i	−0.243078	+	0.176607i
$117$	1.00000	+	3.07768i	0.0924500	+	0.284532i
$118$	−2.76393	+	8.50651i	−0.254441	+	0.783088i
$119$	4.35410	+	3.16344i	0.399140	+	0.289992i
$120$	3.61803			0.330280
$121$	−9.69098	−	5.20431i	−0.880998	−	0.473119i
$122$	4.76393			0.431306
$123$	−4.16312	−	3.02468i	−0.375376	−	0.272726i
$124$	−3.11803	+	9.59632i	−0.280008	+	0.861775i
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$	−0.809017	+	0.587785i	−0.0720730	+	0.0523641i
$127$	−5.47214	+	3.97574i	−0.485574	+	0.352790i	−0.803480	−	0.595332i	$-0.797020\pi$
$127$	−5.47214	+	3.97574i	−0.485574	+	0.352790i	0.317906	+	0.948122i	$0.397020\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.236068	−	0.726543i	0.0207846	−	0.0639685i
$130$	−9.47214	−	6.88191i	−0.830761	−	0.603583i
$131$	10.7639			0.940449			0.470225	−	0.882547i	$-0.344173\pi$
$131$	10.7639			0.940449			0.470225	+	0.882547i	$0.344173\pi$
$132$	0.809017	−	3.21644i	0.0704159	−	0.279955i
$133$	7.09017			0.614796
$134$	2.61803	+	1.90211i	0.226164	+	0.164318i
$135$	−1.11803	+	3.44095i	−0.0962250	+	0.296150i
$136$	−1.66312	−	5.11855i	−0.142611	−	0.438912i
$137$	2.00000	−	1.45309i	0.170872	−	0.124145i	−0.499063	−	0.866566i	$-0.666322\pi$
$137$	2.00000	−	1.45309i	0.170872	−	0.124145i	0.669934	+	0.742420i	$0.266322\pi$
$138$	5.11803	−	3.71847i	0.435676	−	0.316537i
$139$	3.13525	+	9.64932i	0.265929	+	0.818445i	0.991478	+	0.130274i	$0.0415858\pi$
$139$	3.13525	+	9.64932i	0.265929	+	0.818445i	−0.725549	+	0.688170i	$0.758414\pi$
$140$	1.11803	−	3.44095i	0.0944911	−	0.290814i
$141$	9.85410	+	7.15942i	0.829865	+	0.602932i
$142$	−10.4721			−0.878802
$143$	−8.23607	+	6.88191i	−0.688735	+	0.575494i
$144$	1.00000			0.0833333
$145$	9.47214	+	6.88191i	0.786618	+	0.571511i
$146$	2.47214	−	7.60845i	0.204595	−	0.629680i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	5.16312	−	3.75123i	0.424406	−	0.308349i
$149$	−6.00000	+	4.35926i	−0.491539	+	0.357124i	−0.805776	−	0.592221i	$-0.798251\pi$
$149$	−6.00000	+	4.35926i	−0.491539	+	0.357124i	0.314237	+	0.949345i	$0.398251\pi$
$150$	−2.50000	−	7.69421i	−0.204124	−	0.628230i
$151$	2.76393	−	8.50651i	0.224926	−	0.692250i	−0.773374	−	0.633951i	$-0.781432\pi$
$151$	2.76393	−	8.50651i	0.224926	−	0.692250i	0.998299	−	0.0582992i	$-0.0185677\pi$
$152$	−5.73607	−	4.16750i	−0.465257	−	0.338029i
$153$	5.38197			0.435106
$154$	−2.80902	−	1.76336i	−0.226357	−	0.142095i
$155$	36.5066			2.93228
$156$	−2.61803	−	1.90211i	−0.209610	−	0.152291i
$157$	−3.00000	+	9.23305i	−0.239426	+	0.736878i	0.757077	+	0.653325i	$0.226627\pi$
$157$	−3.00000	+	9.23305i	−0.239426	+	0.736878i	−0.996503	+	0.0835524i	$0.973373\pi$
$158$	−1.76393	−	5.42882i	−0.140331	−	0.431894i
$159$	7.23607	−	5.25731i	0.573858	−	0.416932i
$160$	−2.92705	+	2.12663i	−0.231404	+	0.168125i
$161$	−1.95492	−	6.01661i	−0.154069	−	0.474175i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	−9.32624	−	6.77591i	−0.730487	−	0.530730i	0.159230	−	0.987241i	$-0.449099\pi$
$163$	−9.32624	−	6.77591i	−0.730487	−	0.530730i	−0.889718	+	0.456511i	$0.849099\pi$
$164$	5.14590			0.401827
$165$	−11.9721	+	0.812299i	−0.932030	+	0.0632374i
$166$	−10.7639			−0.835443
$167$	−13.3262	−	9.68208i	−1.03122	−	0.749222i	−0.0626637	−	0.998035i	$-0.519960\pi$
$167$	−13.3262	−	9.68208i	−1.03122	−	0.749222i	−0.968552	+	0.248813i	$0.919960\pi$
$168$	0.309017	−	0.951057i	0.0238412	−	0.0733756i
$169$	−0.781153	−	2.40414i	−0.0600887	−	0.184934i
$170$	−15.7533	+	11.4454i	−1.20822	+	0.877825i
$171$	5.73607	−	4.16750i	0.438648	−	0.318696i
$172$	0.236068	+	0.726543i	0.0180000	+	0.0553983i
$173$	0.0450850	−	0.138757i	0.00342775	−	0.0105495i	−0.949328	−	0.314287i	$-0.898235\pi$
$173$	0.0450850	−	0.138757i	0.00342775	−	0.0105495i	0.952756	+	0.303737i	$0.0982346\pi$
$174$	2.61803	+	1.90211i	0.198473	+	0.144199i
$175$	−8.09017			−0.611559
$176$	1.23607	+	3.07768i	0.0931721	+	0.231989i
$177$	8.94427			0.672293
$178$	−9.59017	−	6.96767i	−0.718814	−	0.522249i
$179$	0.444272	−	1.36733i	0.0332064	−	0.102199i	−0.933080	−	0.359670i	$-0.882889\pi$
$179$	0.444272	−	1.36733i	0.0332064	−	0.102199i	0.966286	+	0.257471i	$0.0828892\pi$
$180$	−1.11803	−	3.44095i	−0.0833333	−	0.256474i
$181$	−6.47214	+	4.70228i	−0.481070	+	0.349518i	−0.801740	−	0.597673i	$-0.796092\pi$
$181$	−6.47214	+	4.70228i	−0.481070	+	0.349518i	0.320670	+	0.947191i	$0.396092\pi$
$182$	−2.61803	+	1.90211i	−0.194062	+	0.140994i
$183$	−1.47214	−	4.53077i	−0.108823	−	0.334924i
$184$	−1.95492	+	6.01661i	−0.144118	+	0.443550i
$185$	−18.6803	−	13.5721i	−1.37341	−	0.997838i
$186$	10.0902			0.739847
$187$	6.65248	+	16.5640i	0.486477	+	1.21128i
$188$	−12.1803			−0.888343
$189$	0.809017	+	0.587785i	0.0588473	+	0.0427551i
$190$	−7.92705	+	24.3970i	−0.575089	+	1.76994i
$191$	−0.0278640	−	0.0857567i	−0.00201617	−	0.00620514i	0.950043	−	0.312118i	$-0.101038\pi$
$191$	−0.0278640	−	0.0857567i	−0.00201617	−	0.00620514i	−0.952060	+	0.305913i	$0.901038\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	−3.92705	+	2.85317i	−0.282675	+	0.205376i	−0.720083	−	0.693887i	$-0.755897\pi$
$193$	−3.92705	+	2.85317i	−0.282675	+	0.205376i	0.437408	+	0.899263i	$0.355897\pi$
$194$	−2.09017	−	6.43288i	−0.150065	−	0.461854i
$195$	−3.61803	+	11.1352i	−0.259093	+	0.797406i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	23.2361			1.65550			0.827751	−	0.561096i	$-0.189620\pi$
$197$	23.2361			1.65550			0.827751	+	0.561096i	$0.189620\pi$
$198$	−3.30902	+	0.224514i	−0.235162	+	0.0159555i
$199$	25.2705			1.79138			0.895689	−	0.444680i	$-0.146683\pi$
$199$	25.2705			1.79138			0.895689	+	0.444680i	$0.146683\pi$
$200$	6.54508	+	4.75528i	0.462807	+	0.336249i
$201$	1.00000	−	3.07768i	0.0705346	−	0.217083i
$202$	−1.59017	−	4.89404i	−0.111884	−	0.344343i
$203$	2.61803	−	1.90211i	0.183750	−	0.133502i
$204$	−4.35410	+	3.16344i	−0.304848	+	0.221485i
$205$	−5.75329	−	17.7068i	−0.401827	−	1.23670i
$206$	5.80902	−	17.8783i	0.404733	−	1.24564i
$207$	−5.11803	−	3.71847i	−0.355728	−	0.258451i
$208$	3.23607			0.224381
$209$	19.9164	+	12.5025i	1.37765	+	0.864815i
$210$	−3.61803			−0.249668
$211$	−4.23607	−	3.07768i	−0.291623	−	0.211876i	0.432348	−	0.901707i	$-0.357685\pi$
$211$	−4.23607	−	3.07768i	−0.291623	−	0.211876i	−0.723971	+	0.689830i	$0.757685\pi$
$212$	−2.76393	+	8.50651i	−0.189828	+	0.584229i
$213$	3.23607	+	9.95959i	0.221732	+	0.682420i
$214$	8.11803	−	5.89810i	0.554937	−	0.403186i
$215$	2.23607	−	1.62460i	0.152499	−	0.110797i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	3.11803	−	9.59632i	0.211666	−	0.651441i
$218$	1.92705	+	1.40008i	0.130516	+	0.0948257i
$219$	−8.00000			−0.540590
$220$	9.20820	−	7.69421i	0.620817	−	0.518743i
$221$	17.4164			1.17155
$222$	−5.16312	−	3.75123i	−0.346526	−	0.251766i
$223$	3.04508	−	9.37181i	0.203914	−	0.627583i	−0.795842	−	0.605504i	$-0.792972\pi$
$223$	3.04508	−	9.37181i	0.203914	−	0.627583i	0.999756	−	0.0220787i	$-0.00702843\pi$
$224$	0.309017	+	0.951057i	0.0206471	+	0.0635451i
$225$	−6.54508	+	4.75528i	−0.436339	+	0.317019i
$226$	2.00000	−	1.45309i	0.133038	−	0.0966578i
$227$	6.94427	+	21.3723i	0.460908	+	1.41853i	0.864057	+	0.503393i	$0.167915\pi$
$227$	6.94427	+	21.3723i	0.460908	+	1.41853i	−0.403150	+	0.915134i	$0.632085\pi$
$228$	−2.19098	+	6.74315i	−0.145101	+	0.446576i
$229$	−20.0902	−	14.5964i	−1.32760	−	0.964555i	−0.999804	−	0.0198049i	$-0.993696\pi$
$229$	−20.0902	−	14.5964i	−1.32760	−	0.964555i	−0.327792	−	0.944750i	$-0.606304\pi$
$230$	22.8885			1.50923
$231$	−0.809017	+	3.21644i	−0.0532294	+	0.211626i
$232$	−3.23607			−0.212458
$233$	12.8541	+	9.33905i	0.842100	+	0.611822i	0.922957	−	0.384904i	$-0.125765\pi$
$233$	12.8541	+	9.33905i	0.842100	+	0.611822i	−0.0808563	+	0.996726i	$0.525765\pi$
$234$	−1.00000	+	3.07768i	−0.0653720	+	0.201194i
$235$	13.6180	+	41.9120i	0.888343	+	2.73404i
$236$	−7.23607	+	5.25731i	−0.471028	+	0.342222i
$237$	−4.61803	+	3.35520i	−0.299974	+	0.217944i
$238$	1.66312	+	5.11855i	0.107804	+	0.331787i
$239$	2.89919	−	8.92278i	0.187533	−	0.577167i	−0.812450	−	0.583031i	$-0.801867\pi$
$239$	2.89919	−	8.92278i	0.187533	−	0.577167i	0.999983	+	0.00586423i	$0.00186665\pi$
$240$	2.92705	+	2.12663i	0.188940	+	0.137273i
$241$	16.1803			1.04227			0.521134	−	0.853475i	$-0.325509\pi$
$241$	16.1803			1.04227			0.521134	+	0.853475i	$0.325509\pi$
$242$	−4.78115	−	9.90659i	−0.307344	−	0.636820i
$243$	1.00000			0.0641500
$244$	3.85410	+	2.80017i	0.246734	+	0.179262i
$245$	−1.11803	+	3.44095i	−0.0714286	+	0.219835i
$246$	−1.59017	−	4.89404i	−0.101386	−	0.312033i
$247$	18.5623	−	13.4863i	1.18109	−	0.858113i
$248$	−8.16312	+	5.93085i	−0.518359	+	0.376610i
$249$	3.32624	+	10.2371i	0.210792	+	0.648750i
$250$	3.45492	−	10.6331i	0.218508	−	0.672499i
$251$	−7.23607	−	5.25731i	−0.456737	−	0.331839i	0.335513	−	0.942036i	$-0.391090\pi$
$251$	−7.23607	−	5.25731i	−0.456737	−	0.331839i	−0.792250	+	0.610197i	$0.791090\pi$
$252$	−1.00000			−0.0629941
$253$	5.11803	−	20.3480i	0.321768	−	1.27927i
$254$	−6.76393			−0.424407
$255$	15.7533	+	11.4454i	0.986509	+	0.716741i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.89919	−	15.0781i	−0.305603	−	0.940549i	−0.979452	−	0.201680i	$-0.935360\pi$
$257$	−4.89919	−	15.0781i	−0.305603	−	0.940549i	0.673849	−	0.738869i	$-0.264640\pi$
$258$	0.618034	−	0.449028i	0.0384771	−	0.0279553i
$259$	−5.16312	+	3.75123i	−0.320821	+	0.233090i
$260$	−3.61803	−	11.1352i	−0.224381	−	0.690574i
$261$	1.00000	−	3.07768i	0.0618984	−	0.190504i
$262$	8.70820	+	6.32688i	0.537995	+	0.390876i
$263$	−22.0344			−1.35870			−0.679351	−	0.733814i	$-0.737739\pi$
$263$	−22.0344			−1.35870			−0.679351	+	0.733814i	$0.737739\pi$
$264$	2.54508	−	2.12663i	0.156639	−	0.130885i
$265$	32.3607			1.98790
$266$	5.73607	+	4.16750i	0.351701	+	0.255526i
$267$	−3.66312	+	11.2739i	−0.224179	+	0.689953i
$268$	1.00000	+	3.07768i	0.0610847	+	0.187999i
$269$	−4.85410	+	3.52671i	−0.295960	+	0.215027i	−0.725849	−	0.687854i	$-0.758553\pi$
$269$	−4.85410	+	3.52671i	−0.295960	+	0.215027i	0.429889	+	0.902882i	$0.358553\pi$
$270$	−2.92705	+	2.12663i	−0.178135	+	0.129422i
$271$	−1.88197	−	5.79210i	−0.114321	−	0.351845i	0.877484	−	0.479607i	$-0.159221\pi$
$271$	−1.88197	−	5.79210i	−0.114321	−	0.351845i	−0.991805	+	0.127762i	$0.959221\pi$
$272$	1.66312	−	5.11855i	0.100841	−	0.310358i
$273$	2.61803	+	1.90211i	0.158451	+	0.115121i
$274$	2.47214			0.149347
$275$	−22.7254	−	14.2658i	−1.37039	−	0.860263i
$276$	6.32624			0.380795
$277$	−7.97214	−	5.79210i	−0.478999	−	0.348013i	0.321939	−	0.946760i	$-0.395665\pi$
$277$	−7.97214	−	5.79210i	−0.478999	−	0.348013i	−0.800938	+	0.598747i	$0.795665\pi$
$278$	−3.13525	+	9.64932i	−0.188040	+	0.578728i
$279$	−3.11803	−	9.59632i	−0.186672	−	0.574517i
$280$	2.92705	−	2.12663i	0.174925	−	0.127090i
$281$	13.4721	−	9.78808i	0.803680	−	0.583908i	−0.108311	−	0.994117i	$-0.534544\pi$
$281$	13.4721	−	9.78808i	0.803680	−	0.583908i	0.911991	+	0.410209i	$0.134544\pi$
$282$	3.76393	+	11.5842i	0.224139	+	0.689829i
$283$	−3.11803	+	9.59632i	−0.185348	+	0.570442i	−0.999954	−	0.00957216i	$-0.996953\pi$
$283$	−3.11803	+	9.59632i	−0.185348	+	0.570442i	0.814606	+	0.580014i	$0.196953\pi$
$284$	−8.47214	−	6.15537i	−0.502729	−	0.365254i
$285$	25.6525			1.51952
$286$	−10.7082	+	0.726543i	−0.633189	+	0.0429614i
$287$	−5.14590			−0.303753
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	3.69756	−	11.3799i	0.217504	−	0.669407i
$290$	3.61803	+	11.1352i	0.212458	+	0.653879i
$291$	−5.47214	+	3.97574i	−0.320782	+	0.233062i
$292$	6.47214	−	4.70228i	0.378753	−	0.275180i
$293$	−4.88197	−	15.0251i	−0.285207	−	0.877778i	−0.986336	−	0.164744i	$-0.947320\pi$
$293$	−4.88197	−	15.0251i	−0.285207	−	0.877778i	0.701129	−	0.713035i	$-0.252680\pi$
$294$	−0.309017	+	0.951057i	−0.0180222	+	0.0554667i
$295$	26.1803	+	19.0211i	1.52428	+	1.10745i
$296$	6.38197			0.370944
$297$	1.23607	+	3.07768i	0.0717239	+	0.178585i
$298$	−7.41641			−0.429621
$299$	−16.5623	−	12.0332i	−0.957823	−	0.695899i
$300$	2.50000	−	7.69421i	0.144338	−	0.444225i
$301$	−0.236068	−	0.726543i	−0.0136067	−	0.0418772i
$302$	7.23607	−	5.25731i	0.416389	−	0.302524i
$303$	−4.16312	+	3.02468i	−0.239165	+	0.173763i
$304$	−2.19098	−	6.74315i	−0.125661	−	0.386746i
$305$	5.32624	−	16.3925i	0.304979	−	0.938630i
$306$	4.35410	+	3.16344i	0.248907	+	0.180842i
$307$	9.14590			0.521984			0.260992	−	0.965341i	$-0.415950\pi$
$307$	9.14590			0.521984			0.260992	+	0.965341i	$0.415950\pi$
$308$	−1.23607	−	3.07768i	−0.0704315	−	0.175367i
$309$	−18.7984			−1.06940
$310$	29.5344	+	21.4580i	1.67744	+	1.21873i
$311$	−6.94427	+	21.3723i	−0.393774	+	1.21191i	0.536139	+	0.844130i	$0.319882\pi$
$311$	−6.94427	+	21.3723i	−0.393774	+	1.21191i	−0.929913	+	0.367781i	$0.880118\pi$
$312$	−1.00000	−	3.07768i	−0.0566139	−	0.174240i
$313$	−22.4164	+	16.2865i	−1.26705	+	0.920566i	−0.999081	−	0.0428615i	$-0.986353\pi$
$313$	−22.4164	+	16.2865i	−1.26705	+	0.920566i	−0.267969	+	0.963427i	$0.586353\pi$
$314$	−7.85410	+	5.70634i	−0.443233	+	0.322027i
$315$	1.11803	+	3.44095i	0.0629941	+	0.193876i
$316$	1.76393	−	5.42882i	0.0992289	−	0.305395i
$317$	−9.70820	−	7.05342i	−0.545267	−	0.396160i	0.280770	−	0.959775i	$-0.409410\pi$
$317$	−9.70820	−	7.05342i	−0.545267	−	0.396160i	−0.826037	+	0.563615i	$0.809410\pi$
$318$	8.94427			0.501570
$319$	10.7082	−	0.726543i	0.599544	−	0.0406786i
$320$	−3.61803			−0.202254
$321$	−8.11803	−	5.89810i	−0.453104	−	0.329200i
$322$	1.95492	−	6.01661i	0.108943	−	0.335293i
$323$	−11.7918	−	36.2914i	−0.656113	−	2.01931i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−21.1803	+	15.3884i	−1.17487	+	0.853596i
$326$	−3.56231	−	10.9637i	−0.197298	−	0.607220i
$327$	0.736068	−	2.26538i	0.0407047	−	0.125276i
$328$	4.16312	+	3.02468i	0.229870	+	0.167010i
$329$	12.1803			0.671524
$330$	−10.1631	−	6.37988i	−0.559461	−	0.351201i
$331$	22.1803			1.21914			0.609571	−	0.792732i	$-0.291342\pi$
$331$	22.1803			1.21914			0.609571	+	0.792732i	$0.291342\pi$
$332$	−8.70820	−	6.32688i	−0.477925	−	0.347233i
$333$	−1.97214	+	6.06961i	−0.108072	+	0.332613i
$334$	−5.09017	−	15.6659i	−0.278522	−	0.857202i
$335$	9.47214	−	6.88191i	0.517518	−	0.375999i
$336$	0.809017	−	0.587785i	0.0441355	−	0.0320663i
$337$	2.26393	+	6.96767i	0.123324	+	0.379553i	0.993592	−	0.113026i	$-0.0360543\pi$
$337$	2.26393	+	6.96767i	0.123324	+	0.379553i	−0.870268	+	0.492579i	$0.836054\pi$
$338$	0.781153	−	2.40414i	0.0424891	−	0.130768i
$339$	−2.00000	−	1.45309i	−0.108625	−	0.0789207i
$340$	−19.4721			−1.05602
$341$	25.6803	−	21.4580i	1.39067	−	1.16202i
$342$	7.09017			0.383392
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−0.236068	+	0.726543i	−0.0127279	+	0.0391725i
$345$	−7.07295	−	21.7683i	−0.380795	−	1.17197i
$346$	0.118034	−	0.0857567i	0.00634555	−	0.00461031i
$347$	11.1631	−	8.11048i	0.599268	−	0.435393i	−0.246351	−	0.969181i	$-0.579232\pi$
$347$	11.1631	−	8.11048i	0.599268	−	0.435393i	0.845619	+	0.533787i	$0.179232\pi$
$348$	1.00000	+	3.07768i	0.0536056	+	0.164981i
$349$	−5.70820	+	17.5680i	−0.305553	+	0.940396i	0.673917	+	0.738807i	$0.264610\pi$
$349$	−5.70820	+	17.5680i	−0.305553	+	0.940396i	−0.979470	+	0.201589i	$0.935390\pi$
$350$	−6.54508	−	4.75528i	−0.349850	−	0.254181i
$351$	3.23607			0.172729
$352$	−0.809017	+	3.21644i	−0.0431208	+	0.171437i
$353$	5.05573			0.269089			0.134545	−	0.990908i	$-0.457043\pi$
$353$	5.05573			0.269089			0.134545	+	0.990908i	$0.457043\pi$
$354$	7.23607	+	5.25731i	0.384593	+	0.279423i
$355$	−11.7082	+	36.0341i	−0.621407	+	1.91249i
$356$	−3.66312	−	11.2739i	−0.194145	−	0.597517i
$357$	4.35410	−	3.16344i	0.230444	−	0.167427i
$358$	1.16312	−	0.845055i	0.0614727	−	0.0446626i
$359$	6.55573	+	20.1765i	0.345998	+	1.06487i	0.961047	+	0.276384i	$0.0891361\pi$
$359$	6.55573	+	20.1765i	0.345998	+	1.06487i	−0.615049	+	0.788489i	$0.710864\pi$
$360$	1.11803	−	3.44095i	0.0589256	−	0.181354i
$361$	−25.2984	−	18.3803i	−1.33149	−	0.967387i
$362$	−8.00000			−0.420471
$363$	−7.94427	+	7.60845i	−0.416966	+	0.399340i
$364$	−3.23607			−0.169616
$365$	−23.4164	−	17.0130i	−1.22567	−	0.890502i
$366$	1.47214	−	4.53077i	0.0769498	−	0.236827i
$367$	0.173762	+	0.534785i	0.00907031	+	0.0279155i	0.955489	−	0.295026i	$-0.0953283\pi$
$367$	0.173762	+	0.534785i	0.00907031	+	0.0279155i	−0.946419	+	0.322941i	$0.895328\pi$
$368$	−5.11803	+	3.71847i	−0.266796	+	0.193839i
$369$	−4.16312	+	3.02468i	−0.216723	+	0.157459i
$370$	−7.13525	−	21.9601i	−0.370944	−	1.14165i
$371$	2.76393	−	8.50651i	0.143496	−	0.441636i
$372$	8.16312	+	5.93085i	0.423238	+	0.307500i
$373$	−11.5066			−0.595788			−0.297894	−	0.954599i	$-0.596284\pi$
$373$	−11.5066			−0.595788			−0.297894	+	0.954599i	$0.596284\pi$
$374$	−4.35410	+	17.3108i	−0.225145	+	0.895119i
$375$	−11.1803			−0.577350
$376$	−9.85410	−	7.15942i	−0.508187	−	0.369219i
$377$	3.23607	−	9.95959i	0.166666	−	0.512945i
$378$	0.309017	+	0.951057i	0.0158941	+	0.0489171i
$379$	−6.70820	+	4.87380i	−0.344577	+	0.250350i	−0.746591	−	0.665284i	$-0.768311\pi$
$379$	−6.70820	+	4.87380i	−0.344577	+	0.250350i	0.402013	+	0.915634i	$0.368311\pi$
$380$	−20.7533	+	15.0781i	−1.06462	+	0.773493i
$381$	2.09017	+	6.43288i	0.107083	+	0.329567i
$382$	0.0278640	−	0.0857567i	0.00142565	−	0.00438770i
$383$	−4.85410	−	3.52671i	−0.248033	−	0.180207i	0.456822	−	0.889558i	$-0.348988\pi$
$383$	−4.85410	−	3.52671i	−0.248033	−	0.180207i	−0.704855	+	0.709352i	$0.748988\pi$
$384$	−1.00000			−0.0510310
$385$	−9.20820	+	7.69421i	−0.469294	+	0.392133i
$386$	−4.85410			−0.247067
$387$	−0.618034	−	0.449028i	−0.0314164	−	0.0228254i
$388$	2.09017	−	6.43288i	0.106112	−	0.326580i
$389$	1.18034	+	3.63271i	0.0598456	+	0.184186i	0.976510	−	0.215472i	$-0.0691290\pi$
$389$	1.18034	+	3.63271i	0.0598456	+	0.184186i	−0.916664	+	0.399658i	$0.869129\pi$
$390$	−9.47214	+	6.88191i	−0.479640	+	0.348479i
$391$	−27.5451	+	20.0127i	−1.39301	+	1.01208i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	3.32624	−	10.2371i	0.167787	−	0.516394i
$394$	18.7984	+	13.6578i	0.947048	+	0.688071i
$395$	−20.6525			−1.03914
$396$	−2.80902	−	1.76336i	−0.141158	−	0.0886120i
$397$	16.0000			0.803017			0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000			0.803017			0.401508	+	0.915855i	$0.368486\pi$
$398$	20.4443	+	14.8536i	1.02478	+	0.744545i
$399$	2.19098	−	6.74315i	0.109686	−	0.337580i
$400$	2.50000	+	7.69421i	0.125000	+	0.384710i
$401$	−1.38197	+	1.00406i	−0.0690121	+	0.0501402i	−0.621756	−	0.783211i	$-0.713581\pi$
$401$	−1.38197	+	1.00406i	−0.0690121	+	0.0501402i	0.552744	+	0.833351i	$0.313581\pi$
$402$	2.61803	−	1.90211i	0.130576	−	0.0948688i
$403$	−10.0902	−	31.0543i	−0.502627	−	1.54693i
$404$	1.59017	−	4.89404i	0.0791139	−	0.243488i
$405$	2.92705	+	2.12663i	0.145446	+	0.105673i
$406$	3.23607			0.160603
$407$	−21.1180	+	1.43284i	−1.04678	+	0.0710233i
$408$	−5.38197			−0.266447
$409$	18.0344	+	13.1028i	0.891746	+	0.647891i	0.936333	−	0.351114i	$-0.114197\pi$
$409$	18.0344	+	13.1028i	0.891746	+	0.647891i	−0.0445868	+	0.999006i	$0.514197\pi$
$410$	5.75329	−	17.7068i	0.284135	−	0.874477i
$411$	−0.763932	−	2.35114i	−0.0376820	−	0.115973i
$412$	15.2082	−	11.0494i	0.749254	−	0.544365i
$413$	7.23607	−	5.25731i	0.356064	−	0.258695i
$414$	−1.95492	−	6.01661i	−0.0960788	−	0.295700i
$415$	−12.0344	+	37.0382i	−0.590748	+	1.81813i
$416$	2.61803	+	1.90211i	0.128360	+	0.0932588i
$417$	10.1459			0.496847
$418$	8.76393	+	21.8213i	0.428658	+	1.06731i
$419$	−14.9443			−0.730075			−0.365038	−	0.930993i	$-0.618944\pi$
$419$	−14.9443			−0.730075			−0.365038	+	0.930993i	$0.618944\pi$
$420$	−2.92705	−	2.12663i	−0.142825	−	0.103769i
$421$	0.100813	−	0.310271i	0.00491333	−	0.0151217i	−0.948570	−	0.316568i	$-0.897469\pi$
$421$	0.100813	−	0.310271i	0.00491333	−	0.0151217i	0.953483	+	0.301446i	$0.0974694\pi$
$422$	−1.61803	−	4.97980i	−0.0787647	−	0.242413i
$423$	9.85410	−	7.15942i	0.479123	−	0.348103i
$424$	−7.23607	+	5.25731i	−0.351415	+	0.255318i
$425$	13.4549	+	41.4100i	0.652659	+	2.00868i
$426$	−3.23607	+	9.95959i	−0.156788	+	0.482544i
$427$	−3.85410	−	2.80017i	−0.186513	−	0.135510i
$428$	10.0344			0.485033
$429$	4.00000	+	9.95959i	0.193122	+	0.480854i
$430$	2.76393			0.133289
$431$	19.6353	+	14.2658i	0.945797	+	0.687162i	0.949809	−	0.312830i	$-0.101277\pi$
$431$	19.6353	+	14.2658i	0.945797	+	0.687162i	−0.00401210	+	0.999992i	$0.501277\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−10.7082	−	32.9565i	−0.514603	−	1.58379i	−0.784002	−	0.620758i	$-0.786825\pi$
$433$	−10.7082	−	32.9565i	−0.514603	−	1.58379i	0.269399	−	0.963029i	$-0.413175\pi$
$434$	8.16312	−	5.93085i	0.391842	−	0.284690i
$435$	9.47214	−	6.88191i	0.454154	−	0.329962i
$436$	0.736068	+	2.26538i	0.0352513	+	0.108492i
$437$	−13.8607	+	42.6588i	−0.663046	+	2.04065i
$438$	−6.47214	−	4.70228i	−0.309251	−	0.224684i
$439$	−7.03444			−0.335736			−0.167868	−	0.985810i	$-0.553688\pi$
$439$	−7.03444			−0.335736			−0.167868	+	0.985810i	$0.553688\pi$
$440$	11.9721	−	0.812299i	0.570749	−	0.0387248i
$441$	1.00000			0.0476190
$442$	14.0902	+	10.2371i	0.670201	+	0.486930i
$443$	8.33688	−	25.6583i	0.396097	−	1.21906i	−0.532007	−	0.846740i	$-0.678562\pi$
$443$	8.33688	−	25.6583i	0.396097	−	1.21906i	0.928104	−	0.372322i	$-0.121438\pi$
$444$	−1.97214	−	6.06961i	−0.0935934	−	0.288051i
$445$	−34.6976	+	25.2093i	−1.64482	+	1.19503i
$446$	7.97214	−	5.79210i	0.377492	−	0.274264i
$447$	2.29180	+	7.05342i	0.108398	+	0.333615i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	8.23607	+	5.98385i	0.388684	+	0.282396i	0.764916	−	0.644130i	$-0.222780\pi$
$449$	8.23607	+	5.98385i	0.388684	+	0.282396i	−0.376232	+	0.926526i	$0.622780\pi$
$450$	−8.09017			−0.381374
$451$	−14.4549	−	9.07405i	−0.680655	−	0.427280i
$452$	2.47214			0.116279
$453$	−7.23607	−	5.25731i	−0.339980	−	0.247010i
$454$	−6.94427	+	21.3723i	−0.325911	+	1.00305i
$455$	3.61803	+	11.1352i	0.169616	+	0.522025i
$456$	−5.73607	+	4.16750i	−0.268616	+	0.195161i
$457$	27.0344	−	19.6417i	1.26462	−	0.918799i	0.265643	−	0.964071i	$-0.414416\pi$
$457$	27.0344	−	19.6417i	1.26462	−	0.918799i	0.998975	+	0.0452728i	$0.0144157\pi$
$458$	−7.67376	−	23.6174i	−0.358571	−	1.10357i
$459$	1.66312	−	5.11855i	0.0776277	−	0.238914i
$460$	18.5172	+	13.4535i	0.863370	+	0.627275i
$461$	−15.8885			−0.740003			−0.370002	−	0.929031i	$-0.620643\pi$
$461$	−15.8885			−0.740003			−0.370002	+	0.929031i	$0.620643\pi$
$462$	−2.54508	+	2.12663i	−0.118408	+	0.0989396i
$463$	−10.5836			−0.491861			−0.245931	−	0.969287i	$-0.579094\pi$
$463$	−10.5836			−0.491861			−0.245931	+	0.969287i	$0.579094\pi$
$464$	−2.61803	−	1.90211i	−0.121539	−	0.0883034i
$465$	11.2812	−	34.7198i	0.523151	−	1.61009i
$466$	4.90983	+	15.1109i	0.227443	+	0.699999i
$467$	−6.47214	+	4.70228i	−0.299495	+	0.217596i	−0.727376	−	0.686239i	$-0.759260\pi$
$467$	−6.47214	+	4.70228i	−0.299495	+	0.217596i	0.427881	+	0.903835i	$0.359260\pi$
$468$	−2.61803	+	1.90211i	−0.121019	+	0.0879252i
$469$	−1.00000	−	3.07768i	−0.0461757	−	0.142114i
$470$	−13.6180	+	41.9120i	−0.628153	+	1.93326i
$471$	7.85410	+	5.70634i	0.361898	+	0.262934i
$472$	−8.94427			−0.411693
$473$	0.618034	−	2.45714i	0.0284172	−	0.112980i
$474$	−5.70820			−0.262186
$475$	46.4058	+	33.7158i	2.12924	+	1.54699i
$476$	−1.66312	+	5.11855i	−0.0762289	+	0.234609i
$477$	−2.76393	−	8.50651i	−0.126552	−	0.389486i
$478$	7.59017	−	5.51458i	0.347166	−	0.252231i
$479$	10.4721	−	7.60845i	0.478484	−	0.347639i	−0.322254	−	0.946653i	$-0.604441\pi$
$479$	10.4721	−	7.60845i	0.478484	−	0.347639i	0.800739	+	0.599014i	$0.204441\pi$
$480$	1.11803	+	3.44095i	0.0510310	+	0.157057i
$481$	−6.38197	+	19.6417i	−0.290993	+	0.895583i
$482$	13.0902	+	9.51057i	0.596241	+	0.433194i
$483$	−6.32624			−0.287854
$484$	1.95492	−	10.8249i	0.0888598	−	0.492041i
$485$	−24.4721			−1.11122
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−3.81966	+	11.7557i	−0.173085	+	0.532702i	−0.999541	−	0.0303002i	$-0.990354\pi$
$487$	−3.81966	+	11.7557i	−0.173085	+	0.532702i	0.826456	+	0.563002i	$0.190354\pi$
$488$	1.47214	+	4.53077i	0.0666405	+	0.205098i
$489$	−9.32624	+	6.77591i	−0.421747	+	0.306417i
$490$	−2.92705	+	2.12663i	−0.132231	+	0.0960712i
$491$	12.4271	+	38.2465i	0.560825	+	1.72604i	0.680042	+	0.733173i	$0.261962\pi$
$491$	12.4271	+	38.2465i	0.560825	+	1.72604i	−0.119217	+	0.992868i	$0.538038\pi$
$492$	1.59017	−	4.89404i	0.0716904	−	0.220640i
$493$	−14.0902	−	10.2371i	−0.634589	−	0.461056i
$494$	22.9443			1.03231
$495$	−2.92705	+	11.6372i	−0.131561	+	0.523053i
$496$	−10.0902			−0.453062
$497$	8.47214	+	6.15537i	0.380027	+	0.276106i
$498$	−3.32624	+	10.2371i	−0.149052	+	0.458736i
$499$	2.70820	+	8.33499i	0.121236	+	0.373126i	0.993197	−	0.116450i	$-0.0371516\pi$
$499$	2.70820	+	8.33499i	0.121236	+	0.373126i	−0.871961	+	0.489576i	$0.837152\pi$
$500$	9.04508	−	6.57164i	0.404508	−	0.293893i
$501$	−13.3262	+	9.68208i	−0.595372	+	0.432563i
$502$	−2.76393	−	8.50651i	−0.123360	−	0.379664i
$503$	11.4721	−	35.3076i	0.511517	−	1.57429i	−0.278013	−	0.960577i	$-0.589676\pi$
$503$	11.4721	−	35.3076i	0.511517	−	1.57429i	0.789531	−	0.613711i	$-0.210324\pi$
$504$	−0.809017	−	0.587785i	−0.0360365	−	0.0261820i
$505$	−18.6180			−0.828492
$506$	16.1008	−	13.4535i	0.715768	−	0.598083i
$507$	−2.52786			−0.112266
$508$	−5.47214	−	3.97574i	−0.242787	−	0.176395i
$509$	−6.06231	+	18.6579i	−0.268707	+	0.826995i	0.722109	+	0.691779i	$0.243173\pi$
$509$	−6.06231	+	18.6579i	−0.268707	+	0.826995i	−0.990816	+	0.135216i	$0.956827\pi$
$510$	6.01722	+	18.5191i	0.266447	+	0.820040i
$511$	−6.47214	+	4.70228i	−0.286310	+	0.208017i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.19098	−	6.74315i	−0.0967343	−	0.297717i
$514$	4.89919	−	15.0781i	0.216094	−	0.665069i
$515$	−55.0238	−	39.9771i	−2.42464	−	1.76160i
$516$	0.763932			0.0336302
$517$	34.2148	+	21.4783i	1.50476	+	0.944613i
$518$	−6.38197			−0.280407
$519$	−0.118034	−	0.0857567i	−0.00518112	−	0.00376430i
$520$	3.61803	−	11.1352i	0.158661	−	0.488309i
$521$	−2.93769	−	9.04129i	−0.128703	−	0.396106i	0.865855	−	0.500295i	$-0.166775\pi$
$521$	−2.93769	−	9.04129i	−0.128703	−	0.396106i	−0.994557	+	0.104189i	$0.966775\pi$
$522$	2.61803	−	1.90211i	0.114588	−	0.0832532i
$523$	−5.73607	+	4.16750i	−0.250821	+	0.182232i	−0.706090	−	0.708122i	$-0.749543\pi$
$523$	−5.73607	+	4.16750i	−0.250821	+	0.182232i	0.455270	+	0.890354i	$0.349543\pi$
$524$	3.32624	+	10.2371i	0.145307	+	0.447210i
$525$	−2.50000	+	7.69421i	−0.109109	+	0.335803i
$526$	−17.8262	−	12.9515i	−0.777261	−	0.564713i
$527$	−54.3050			−2.36556
$528$	3.30902	−	0.224514i	0.144006	−	0.00977072i
$529$	17.0213			0.740056
$530$	26.1803	+	19.0211i	1.13720	+	0.826225i
$531$	2.76393	−	8.50651i	0.119944	−	0.369151i
$532$	2.19098	+	6.74315i	0.0949912	+	0.292353i
$533$	−13.4721	+	9.78808i	−0.583543	+	0.423969i
$534$	−9.59017	+	6.96767i	−0.415007	+	0.301520i
$535$	−11.2188	−	34.5281i	−0.485033	−	1.49278i
$536$	−1.00000	+	3.07768i	−0.0431934	+	0.132936i
$537$	−1.16312	−	0.845055i	−0.0501923	−	0.0364668i
$538$	−6.00000			−0.258678
$539$	1.23607	+	3.07768i	0.0532412	+	0.132565i
$540$	−3.61803			−0.155695
$541$	−13.7812	−	10.0126i	−0.592498	−	0.430475i	0.250710	−	0.968062i	$-0.419336\pi$
$541$	−13.7812	−	10.0126i	−0.592498	−	0.430475i	−0.843208	+	0.537587i	$0.819336\pi$
$542$	1.88197	−	5.79210i	0.0808374	−	0.248792i
$543$	2.47214	+	7.60845i	0.106090	+	0.326510i
$544$	4.35410	−	3.16344i	0.186681	−	0.135631i
$545$	6.97214	−	5.06555i	0.298653	−	0.216984i
$546$	1.00000	+	3.07768i	0.0427960	+	0.131713i
$547$	8.18034	−	25.1765i	0.349766	−	1.07647i	−0.609216	−	0.793004i	$-0.708516\pi$
$547$	8.18034	−	25.1765i	0.349766	−	1.07647i	0.958982	−	0.283465i	$-0.0914841\pi$
$548$	2.00000	+	1.45309i	0.0854358	+	0.0620727i
$549$	−4.76393			−0.203320
$550$	−10.0000	−	24.8990i	−0.426401	−	1.06170i
$551$	−22.9443			−0.977459
$552$	5.11803	+	3.71847i	0.217838	+	0.158269i
$553$	−1.76393	+	5.42882i	−0.0750100	+	0.230857i
$554$	−3.04508	−	9.37181i	−0.129373	−	0.398170i
$555$	−18.6803	+	13.5721i	−0.792936	+	0.576102i
$556$	−8.20820	+	5.96361i	−0.348105	+	0.252913i
$557$	7.67376	+	23.6174i	0.325148	+	1.00070i	0.971374	+	0.237556i	$0.0763463\pi$
$557$	7.67376	+	23.6174i	0.325148	+	1.00070i	−0.646226	+	0.763146i	$0.723654\pi$
$558$	3.11803	−	9.59632i	0.131997	−	0.406245i
$559$	−2.00000	−	1.45309i	−0.0845910	−	0.0614589i
$560$	3.61803			0.152890
$561$	17.8090	−	1.20833i	0.751897	−	0.0510156i
$562$	16.6525			0.702442
$563$	−2.85410	−	2.07363i	−0.120286	−	0.0873929i	0.526016	−	0.850475i	$-0.323685\pi$
$563$	−2.85410	−	2.07363i	−0.120286	−	0.0873929i	−0.646302	+	0.763082i	$0.723685\pi$
$564$	−3.76393	+	11.5842i	−0.158490	+	0.487782i
$565$	−2.76393	−	8.50651i	−0.116279	−	0.357871i
$566$	−8.16312	+	5.93085i	−0.343121	+	0.249292i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	−3.23607	−	9.95959i	−0.135782	−	0.417895i
$569$	−5.29180	+	16.2865i	−0.221844	+	0.682764i	0.776753	+	0.629805i	$0.216865\pi$
$569$	−5.29180	+	16.2865i	−0.221844	+	0.682764i	−0.998597	+	0.0529592i	$0.983135\pi$
$570$	20.7533	+	15.0781i	0.869260	+	0.631554i
$571$	−6.29180			−0.263303			−0.131652	−	0.991296i	$-0.542028\pi$
$571$	−6.29180			−0.263303			−0.131652	+	0.991296i	$0.542028\pi$
$572$	−9.09017	−	5.70634i	−0.380079	−	0.238594i
$573$	−0.0901699			−0.00376690
$574$	−4.16312	−	3.02468i	−0.173765	−	0.126248i
$575$	15.8156	−	48.6754i	0.659556	−	2.02990i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−8.47214	+	6.15537i	−0.352700	+	0.256251i	−0.750001	−	0.661437i	$-0.769947\pi$
$577$	−8.47214	+	6.15537i	−0.352700	+	0.256251i	0.397301	+	0.917688i	$0.369947\pi$
$578$	9.68034	−	7.03318i	0.402649	−	0.292542i
$579$	1.50000	+	4.61653i	0.0623379	+	0.191856i
$580$	−3.61803	+	11.1352i	−0.150231	+	0.462363i
$581$	8.70820	+	6.32688i	0.361277	+	0.262483i
$582$	−6.76393			−0.280374
$583$	22.7639	−	19.0211i	0.942786	−	0.787775i
$584$	8.00000			0.331042
$585$	9.47214	+	6.88191i	0.391625	+	0.284532i
$586$	4.88197	−	15.0251i	0.201672	−	0.620683i
$587$	3.67376	+	11.3067i	0.151632	+	0.466677i	0.997804	−	0.0662338i	$-0.0210983\pi$
$587$	3.67376	+	11.3067i	0.151632	+	0.466677i	−0.846172	+	0.532910i	$0.821098\pi$
$588$	−0.809017	+	0.587785i	−0.0333633	+	0.0242399i
$589$	−57.8779	+	42.0508i	−2.38482	+	1.73267i
$590$	10.0000	+	30.7768i	0.411693	+	1.26706i
$591$	7.18034	−	22.0988i	0.295360	−	0.909024i
$592$	5.16312	+	3.75123i	0.212203	+	0.154174i
$593$	28.7426			1.18032			0.590159	−	0.807287i	$-0.299065\pi$
$593$	28.7426			1.18032			0.590159	+	0.807287i	$0.299065\pi$
$594$	−0.809017	+	3.21644i	−0.0331944	+	0.131972i
$595$	19.4721			0.798280
$596$	−6.00000	−	4.35926i	−0.245770	−	0.178562i
$597$	7.80902	−	24.0337i	0.319602	−	0.983633i
$598$	−6.32624	−	19.4702i	−0.258699	−	0.796194i
$599$	−12.8262	+	9.31881i	−0.524066	+	0.380756i	−0.818133	−	0.575029i	$-0.804991\pi$
$599$	−12.8262	+	9.31881i	−0.524066	+	0.380756i	0.294067	+	0.955785i	$0.404991\pi$
$600$	6.54508	−	4.75528i	0.267202	−	0.194134i
$601$	−5.09017	−	15.6659i	−0.207632	−	0.639027i	−0.999595	−	0.0284572i	$-0.990941\pi$
$601$	−5.09017	−	15.6659i	−0.207632	−	0.639027i	0.791963	−	0.610570i	$-0.209059\pi$
$602$	0.236068	−	0.726543i	0.00962141	−	0.0296117i
$603$	−2.61803	−	1.90211i	−0.106615	−	0.0774600i
$604$	8.94427			0.363937
$605$	−39.4336	+	5.37582i	−1.60320	+	0.218558i
$606$	−5.14590			−0.209038
$607$	−26.3885	−	19.1724i	−1.07108	−	0.778184i	−0.0949722	−	0.995480i	$-0.530276\pi$
$607$	−26.3885	−	19.1724i	−1.07108	−	0.778184i	−0.976106	+	0.217296i	$0.930276\pi$
$608$	2.19098	−	6.74315i	0.0888561	−	0.273471i
$609$	−1.00000	−	3.07768i	−0.0405220	−	0.124714i
$610$	13.9443	−	10.1311i	0.564587	−	0.410197i
$611$	31.8885	−	23.1684i	1.29007	−	0.937292i
$612$	1.66312	+	5.11855i	0.0672276	+	0.206905i
$613$	7.51722	−	23.1356i	0.303618	−	0.934439i	−0.676572	−	0.736377i	$-0.736535\pi$
$613$	7.51722	−	23.1356i	0.303618	−	0.934439i	0.980189	−	0.198062i	$-0.0634649\pi$
$614$	7.39919	+	5.37582i	0.298607	+	0.216951i
$615$	−18.6180			−0.750752
$616$	0.809017	−	3.21644i	0.0325962	−	0.129594i
$617$	−6.58359			−0.265045			−0.132523	−	0.991180i	$-0.542308\pi$
$617$	−6.58359			−0.265045			−0.132523	+	0.991180i	$0.542308\pi$
$618$	−15.2082	−	11.0494i	−0.611764	−	0.444472i
$619$	10.1180	−	31.1401i	0.406678	−	1.25163i	−0.512808	−	0.858503i	$-0.671395\pi$
$619$	10.1180	−	31.1401i	0.406678	−	1.25163i	0.919486	−	0.393123i	$-0.128605\pi$
$620$	11.2812	+	34.7198i	0.453062	+	1.39438i
$621$	−5.11803	+	3.71847i	−0.205380	+	0.149217i
$622$	−18.1803	+	13.2088i	−0.728965	+	0.529624i
$623$	3.66312	+	11.2739i	0.146760	+	0.451680i
$624$	1.00000	−	3.07768i	0.0400320	−	0.123206i
$625$		0			0
$626$	−27.7082			−1.10744
$627$	18.0451	−	15.0781i	0.720651	−	0.602163i
$628$	−9.70820			−0.387400
$629$	27.7877	+	20.1890i	1.10797	+	0.804987i
$630$	−1.11803	+	3.44095i	−0.0445435	+	0.137091i
$631$	−9.94427	−	30.6053i	−0.395875	−	1.21838i	−0.928278	−	0.371887i	$-0.878711\pi$
$631$	−9.94427	−	30.6053i	−0.395875	−	1.21838i	0.532403	−	0.846491i	$-0.321289\pi$
$632$	4.61803	−	3.35520i	0.183696	−	0.133463i
$633$	−4.23607	+	3.07768i	−0.168369	+	0.122327i
$634$	−3.70820	−	11.4127i	−0.147272	−	0.453255i
$635$	−7.56231	+	23.2744i	−0.300101	+	0.923616i
$636$	7.23607	+	5.25731i	0.286929	+	0.208466i
$637$	3.23607			0.128218
$638$	9.09017	+	5.70634i	0.359883	+	0.225916i
$639$	10.4721			0.414271
$640$	−2.92705	−	2.12663i	−0.115702	−	0.0840623i
$641$	3.88854	−	11.9677i	0.153588	−	0.472696i	−0.844427	−	0.535671i	$-0.820059\pi$
$641$	3.88854	−	11.9677i	0.153588	−	0.472696i	0.998015	+	0.0629748i	$0.0200588\pi$
$642$	−3.10081	−	9.54332i	−0.122379	−	0.376645i
$643$	29.1525	−	21.1805i	1.14966	−	0.835278i	0.161226	−	0.986918i	$-0.448455\pi$
$643$	29.1525	−	21.1805i	1.14966	−	0.835278i	0.988436	+	0.151640i	$0.0484553\pi$
$644$	5.11803	−	3.71847i	0.201679	−	0.146528i
$645$	−0.854102	−	2.62866i	−0.0336302	−	0.103503i
$646$	11.7918	−	36.2914i	0.463942	−	1.42787i
$647$	−2.61803	−	1.90211i	−0.102926	−	0.0747798i	0.535132	−	0.844768i	$-0.320262\pi$
$647$	−2.61803	−	1.90211i	−0.102926	−	0.0747798i	−0.638058	+	0.769989i	$0.720262\pi$
$648$	−1.00000			−0.0392837
$649$	29.5967	−	2.00811i	1.16177	−	0.0788254i
$650$	−26.1803			−1.02688
$651$	−8.16312	−	5.93085i	−0.319938	−	0.232448i
$652$	3.56231	−	10.9637i	0.139511	−	0.429370i
$653$	10.9098	+	33.5770i	0.426935	+	1.31397i	0.901130	+	0.433550i	$0.142739\pi$
$653$	10.9098	+	33.5770i	0.426935	+	1.31397i	−0.474195	+	0.880420i	$0.657261\pi$
$654$	1.92705	−	1.40008i	0.0753537	−	0.0547476i
$655$	31.5066	−	22.8909i	1.23106	−	0.894420i
$656$	1.59017	+	4.89404i	0.0620857	+	0.191080i
$657$	−2.47214	+	7.60845i	−0.0964472	+	0.296834i
$658$	9.85410	+	7.15942i	0.384153	+	0.279103i
$659$	38.1591			1.48647			0.743233	−	0.669033i	$-0.233291\pi$
$659$	38.1591			1.48647			0.743233	+	0.669033i	$0.233291\pi$
$660$	−4.47214	−	11.1352i	−0.174078	−	0.433436i
$661$	−19.8885			−0.773575			−0.386787	−	0.922169i	$-0.626415\pi$
$661$	−19.8885			−0.773575			−0.386787	+	0.922169i	$0.626415\pi$
$662$	17.9443	+	13.0373i	0.697424	+	0.506708i
$663$	5.38197	−	16.5640i	0.209018	−	0.643292i
$664$	−3.32624	−	10.2371i	−0.129083	−	0.397277i
$665$	20.7533	−	15.0781i	0.804778	−	0.584705i
$666$	−5.16312	+	3.75123i	−0.200067	+	0.145357i
$667$	6.32624	+	19.4702i	0.244953	+	0.753888i
$668$	5.09017	−	15.6659i	0.196945	−	0.606133i
$669$	−7.97214	−	5.79210i	−0.308221	−	0.223935i
$670$	11.7082			0.452327
$671$	−5.88854	−	14.6619i	−0.227325	−	0.566015i
$672$	1.00000			0.0385758
$673$	−28.5623	−	20.7517i	−1.10100	−	0.799920i	−0.119774	−	0.992801i	$-0.538217\pi$
$673$	−28.5623	−	20.7517i	−1.10100	−	0.799920i	−0.981222	+	0.192881i	$0.938217\pi$
$674$	−2.26393	+	6.96767i	−0.0872034	+	0.268384i
$675$	2.50000	+	7.69421i	0.0962250	+	0.296150i
$676$	2.04508	−	1.48584i	0.0786571	−	0.0571477i
$677$	10.8541	−	7.88597i	0.417157	−	0.303082i	−0.359336	−	0.933208i	$-0.616997\pi$
$677$	10.8541	−	7.88597i	0.417157	−	0.303082i	0.776493	+	0.630126i	$0.216997\pi$
$678$	−0.763932	−	2.35114i	−0.0293386	−	0.0902950i
$679$	−2.09017	+	6.43288i	−0.0802134	+	0.246871i
$680$	−15.7533	−	11.4454i	−0.604111	−	0.438912i
$681$	22.4721			0.861134
$682$	33.3885	−	2.26538i	1.27851	−	0.0867460i
$683$	38.5623			1.47555			0.737773	−	0.675049i	$-0.235878\pi$
$683$	38.5623			1.47555			0.737773	+	0.675049i	$0.235878\pi$
$684$	5.73607	+	4.16750i	0.219324	+	0.159348i
$685$	2.76393	−	8.50651i	0.105604	−	0.325017i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	−20.0902	+	14.5964i	−0.766488	+	0.556886i
$688$	−0.618034	+	0.449028i	−0.0235623	+	0.0171190i
$689$	−8.94427	−	27.5276i	−0.340750	−	1.04872i
$690$	7.07295	−	21.7683i	0.269263	−	0.828705i
$691$	−7.50000	−	5.44907i	−0.285313	−	0.207292i	0.435918	−	0.899986i	$-0.356424\pi$
$691$	−7.50000	−	5.44907i	−0.285313	−	0.207292i	−0.721232	+	0.692694i	$0.756424\pi$
$692$	0.145898			0.00554621
$693$	2.80902	+	1.76336i	0.106706	+	0.0669843i
$694$	13.7984			0.523779
$695$	29.6976	+	21.5765i	1.12649	+	0.818445i
$696$	−1.00000	+	3.07768i	−0.0379049	+	0.116659i
$697$	8.55824	+	26.3396i	0.324166	+	0.997682i
$698$	−14.9443	+	10.8576i	−0.565649	+	0.410968i
$699$	12.8541	−	9.33905i	0.486187	−	0.353235i
$700$	−2.50000	−	7.69421i	−0.0944911	−	0.290814i
$701$	−12.9098	+	39.7324i	−0.487598	+	1.50067i	0.340586	+	0.940213i	$0.389375\pi$
$701$	−12.9098	+	39.7324i	−0.487598	+	1.50067i	−0.828183	+	0.560457i	$0.810625\pi$
$702$	2.61803	+	1.90211i	0.0988113	+	0.0717906i
$703$	45.2492			1.70661
$704$	−2.54508	+	2.12663i	−0.0959215	+	0.0801503i
$705$	44.0689			1.65973
$706$	4.09017	+	2.97168i	0.153936	+	0.111841i
$707$	−1.59017	+	4.89404i	−0.0598045	+	0.184059i
$708$	2.76393	+	8.50651i	0.103875	+	0.319694i
$709$	−16.3992	+	11.9147i	−0.615884	+	0.447466i	−0.851482	−	0.524385i	$-0.824295\pi$
$709$	−16.3992	+	11.9147i	−0.615884	+	0.447466i	0.235597	+	0.971851i	$0.424295\pi$
$710$	−30.6525	+	22.2703i	−1.15037	+	0.835790i
$711$	1.76393	+	5.42882i	0.0661526	+	0.203597i
$712$	3.66312	−	11.2739i	0.137281	−	0.422508i
$713$	51.6418	+	37.5200i	1.93400	+	1.40513i
$714$	5.38197			0.201415
$715$	−9.47214	+	37.6587i	−0.354238	+	1.40836i
$716$	1.43769			0.0537292
$717$	−7.59017	−	5.51458i	−0.283460	−	0.205946i
$718$	−6.55573	+	20.1765i	−0.244658	+	0.752979i
$719$	13.0902	+	40.2874i	0.488181	+	1.50247i	0.827320	+	0.561730i	$0.189864\pi$
$719$	13.0902	+	40.2874i	0.488181	+	1.50247i	−0.339139	+	0.940736i	$0.610136\pi$
$720$	2.92705	−	2.12663i	0.109085	−	0.0792547i
$721$	−15.2082	+	11.0494i	−0.566383	+	0.411501i
$722$	−9.66312	−	29.7400i	−0.359624	−	1.10681i
$723$	5.00000	−	15.3884i	0.185952	−	0.572301i
$724$	−6.47214	−	4.70228i	−0.240535	−	0.174759i
$725$	26.1803			0.972313
$726$	−10.8992	+	1.48584i	−0.404507	+	0.0551447i
$727$	−14.5066			−0.538019			−0.269010	−	0.963137i	$-0.586696\pi$
$727$	−14.5066			−0.538019			−0.269010	+	0.963137i	$0.586696\pi$
$728$	−2.61803	−	1.90211i	−0.0970308	−	0.0704970i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−8.94427	−	27.5276i	−0.331042	−	1.01884i
$731$	−3.32624	+	2.41665i	−0.123025	+	0.0893832i
$732$	3.85410	−	2.80017i	0.142452	−	0.103497i
$733$	10.4721	+	32.2299i	0.386797	+	1.19044i	0.935168	+	0.354204i	$0.115248\pi$
$733$	10.4721	+	32.2299i	0.386797	+	1.19044i	−0.548371	+	0.836235i	$0.684752\pi$
$734$	−0.173762	+	0.534785i	−0.00641368	+	0.0197393i
$735$	2.92705	+	2.12663i	0.107966	+	0.0784418i
$736$	−6.32624			−0.233188
$737$	2.61803	−	10.4086i	0.0964365	−	0.383406i
$738$	−5.14590			−0.189423
$739$	−4.23607	−	3.07768i	−0.155826	−	0.113214i	0.507140	−	0.861864i	$-0.330703\pi$
$739$	−4.23607	−	3.07768i	−0.155826	−	0.113214i	−0.662966	+	0.748649i	$0.730703\pi$
$740$	7.13525	−	21.9601i	0.262297	−	0.807268i
$741$	−7.09017	−	21.8213i	−0.260464	−	0.801625i
$742$	7.23607	−	5.25731i	0.265644	−	0.193002i
$743$	32.8713	−	23.8824i	1.20593	−	0.876161i	0.211077	−	0.977469i	$-0.432303\pi$
$743$	32.8713	−	23.8824i	1.20593	−	0.876161i	0.994855	+	0.101309i	$0.0323030\pi$
$744$	3.11803	+	9.59632i	0.114313	+	0.351818i
$745$	−8.29180	+	25.5195i	−0.303788	+	0.934963i
$746$	−9.30902	−	6.76340i	−0.340827	−	0.247626i
$747$	10.7639			0.393832
$748$	−13.6976	+	11.4454i	−0.500832	+	0.418487i
$749$	−10.0344			−0.366651
$750$	−9.04508	−	6.57164i	−0.330280	−	0.239962i
$751$	−2.32624	+	7.15942i	−0.0848856	+	0.261251i	−0.984486	−	0.175463i	$-0.943858\pi$
$751$	−2.32624	+	7.15942i	−0.0848856	+	0.261251i	0.899600	+	0.436714i	$0.143858\pi$
$752$	−3.76393	−	11.5842i	−0.137256	−	0.422432i
$753$	−7.23607	+	5.25731i	−0.263697	+	0.191587i
$754$	8.47214	−	6.15537i	0.308537	−	0.224165i
$755$	−10.0000	−	30.7768i	−0.363937	−	1.12008i
$756$	−0.309017	+	0.951057i	−0.0112388	+	0.0345896i
$757$	−10.9721	−	7.97172i	−0.398789	−	0.289737i	0.370259	−	0.928929i	$-0.379269\pi$
$757$	−10.9721	−	7.97172i	−0.398789	−	0.289737i	−0.769048	+	0.639192i	$0.779269\pi$
$758$	−8.29180			−0.301172
$759$	−17.7705	−	11.1554i	−0.645029	−	0.404916i
$760$	−25.6525			−0.930513
$761$	23.3262	+	16.9475i	0.845575	+	0.614347i	0.923923	−	0.382580i	$-0.124964\pi$
$761$	23.3262	+	16.9475i	0.845575	+	0.614347i	−0.0783471	+	0.996926i	$0.524964\pi$
$762$	−2.09017	+	6.43288i	−0.0757189	+	0.233039i
$763$	−0.736068	−	2.26538i	−0.0266474	−	0.0820124i
$764$	0.0729490	−	0.0530006i	0.00263920	−	0.00191749i
$765$	15.7533	−	11.4454i	0.569561	−	0.413811i
$766$	−1.85410	−	5.70634i	−0.0669914	−	0.206178i
$767$	8.94427	−	27.5276i	0.322959	−	0.993965i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	1.52786			0.0550962			0.0275481	−	0.999620i	$-0.491230\pi$
$769$	1.52786			0.0550962			0.0275481	+	0.999620i	$0.491230\pi$
$770$	−11.9721	+	0.812299i	−0.431446	+	0.0292732i
$771$	−15.8541			−0.570972
$772$	−3.92705	−	2.85317i	−0.141338	−	0.102688i
$773$	12.4377	−	38.2793i	0.447353	−	1.37681i	−0.432530	−	0.901620i	$-0.642379\pi$
$773$	12.4377	−	38.2793i	0.447353	−	1.37681i	0.879883	−	0.475191i	$-0.157621\pi$
$774$	−0.236068	−	0.726543i	−0.00848529	−	0.0261150i
$775$	66.0410	−	47.9816i	2.37226	−	1.72355i
$776$	5.47214	−	3.97574i	0.196438	−	0.142721i
$777$	1.97214	+	6.06961i	0.0707500	+	0.217746i
$778$	−1.18034	+	3.63271i	−0.0423172	+	0.130239i
$779$	29.5172	+	21.4455i	1.05756	+	0.768365i
$780$	−11.7082			−0.419221
$781$	12.9443	+	32.2299i	0.463182	+	1.15328i
$782$	−34.0476			−1.21754
$783$	−2.61803	−	1.90211i	−0.0935609	−	0.0679760i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	10.8541	+	33.4055i	0.387400	+	1.19229i
$786$	8.70820	−	6.32688i	0.310611	−	0.225672i
$787$	21.1074	−	15.3354i	0.752397	−	0.546649i	−0.144172	−	0.989553i	$-0.546052\pi$
$787$	21.1074	−	15.3354i	0.752397	−	0.546649i	0.896569	+	0.442904i	$0.146052\pi$
$788$	7.18034	+	22.0988i	0.255789	+	0.787238i
$789$	−6.80902	+	20.9560i	−0.242407	+	0.746053i
$790$	−16.7082	−	12.1392i	−0.594451	−	0.431894i
$791$	−2.47214			−0.0878990
$792$	−1.23607	−	3.07768i	−0.0439218	−	0.109361i
$793$	−15.4164			−0.547453
$794$	12.9443	+	9.40456i	0.459375	+	0.333755i
$795$	10.0000	−	30.7768i	0.354663	−	1.09154i
$796$	7.80902	+	24.0337i	0.276783	+	0.851851i
$797$	−33.5795	+	24.3970i	−1.18945	+	0.864184i	−0.993206	−	0.116371i	$-0.962874\pi$
$797$	−33.5795	+	24.3970i	−1.18945	+	0.864184i	−0.196242	+	0.980555i	$0.562874\pi$
$798$	5.73607	−	4.16750i	0.203055	−	0.147528i
$799$	−20.2574	−	62.3457i	−0.716654	−	2.20563i
$800$	−2.50000	+	7.69421i	−0.0883883	+	0.272031i
$801$	9.59017	+	6.96767i	0.338852	+	0.246190i
$802$	−1.70820			−0.0603188
$803$	−26.4721	+	1.79611i	−0.934181	+	0.0633834i
$804$	3.23607			0.114127
$805$	−18.5172	−	13.4535i	−0.652646	−	0.474175i
$806$	10.0902	−	31.0543i	0.355411	−	1.09384i
$807$	1.85410	+	5.70634i	0.0652675	+	0.200873i
$808$	4.16312	−	3.02468i	0.146458	−	0.106408i
$809$	13.8541	−	10.0656i	0.487084	−	0.353887i	−0.316978	−	0.948433i	$-0.602668\pi$
$809$	13.8541	−	10.0656i	0.487084	−	0.353887i	0.804062	+	0.594546i	$0.202668\pi$
$810$	1.11803	+	3.44095i	0.0392837	+	0.120903i
$811$	−15.4164	+	47.4468i	−0.541343	+	1.66608i	0.188186	+	0.982133i	$0.439739\pi$
$811$	−15.4164	+	47.4468i	−0.541343	+	1.66608i	−0.729529	+	0.683950i	$0.760261\pi$
$812$	2.61803	+	1.90211i	0.0918750	+	0.0667511i
$813$	−6.09017			−0.213592
$814$	−17.9271	−	11.2537i	−0.628343	−	0.394441i
$815$	−41.7082			−1.46097
$816$	−4.35410	−	3.16344i	−0.152424	−	0.110743i
$817$	−1.67376	+	5.15131i	−0.0585575	+	0.180222i
$818$	6.88854	+	21.2008i	0.240852	+	0.741267i
$819$	2.61803	−	1.90211i	0.0914815	−	0.0664652i
$820$	15.0623	−	10.9434i	0.525999	−	0.382160i
$821$	−1.94427	−	5.98385i	−0.0678556	−	0.208838i	0.911379	−	0.411568i	$-0.135019\pi$
$821$	−1.94427	−	5.98385i	−0.0678556	−	0.208838i	−0.979235	+	0.202730i	$0.935019\pi$
$822$	0.763932	−	2.35114i	0.0266452	−	0.0820055i
$823$	41.4164	+	30.0908i	1.44369	+	1.04890i	0.987256	+	0.159139i	$0.0508718\pi$
$823$	41.4164	+	30.0908i	1.44369	+	1.04890i	0.456429	+	0.889760i	$0.349128\pi$
$824$	18.7984			0.654872
$825$	−20.5902	+	17.2048i	−0.716858	+	0.598993i
$826$	8.94427			0.311211
$827$	−39.2984	−	28.5519i	−1.36654	−	0.992848i	−0.997999	−	0.0632362i	$-0.979858\pi$
$827$	−39.2984	−	28.5519i	−1.36654	−	0.992848i	−0.368540	−	0.929612i	$-0.620142\pi$
$828$	1.95492	−	6.01661i	0.0679380	−	0.209092i
$829$	0.381966	+	1.17557i	0.0132662	+	0.0408293i	0.957471	−	0.288531i	$-0.0931669\pi$
$829$	0.381966	+	1.17557i	0.0132662	+	0.0408293i	−0.944204	+	0.329360i	$0.893167\pi$
$830$	−31.5066	+	22.8909i	−1.09361	+	0.794554i
$831$	−7.97214	+	5.79210i	−0.276550	+	0.200926i
$832$	1.00000	+	3.07768i	0.0346688	+	0.106699i
$833$	1.66312	−	5.11855i	0.0576237	−	0.177347i
$834$	8.20820	+	5.96361i	0.284227	+	0.206503i
$835$	−59.5967			−2.06243
$836$	−5.73607	+	22.8051i	−0.198386	+	0.788731i
$837$	−10.0902			−0.348767
$838$	−12.0902	−	8.78402i	−0.417648	−	0.303439i
$839$	−9.88854	+	30.4338i	−0.341390	+	1.05069i	0.622097	+	0.782940i	$0.286281\pi$
$839$	−9.88854	+	30.4338i	−0.341390	+	1.05069i	−0.963488	+	0.267752i	$0.913719\pi$
$840$	−1.11803	−	3.44095i	−0.0385758	−	0.118724i
$841$	14.9894	−	10.8904i	0.516874	−	0.375531i
$842$	0.263932	−	0.191758i	0.00909570	−	0.00660841i
$843$	−5.14590	−	15.8374i	−0.177234	−	0.545471i
$844$	1.61803	−	4.97980i	0.0556950	−	0.171412i
$845$	−7.39919	−	5.37582i	−0.254540	−	0.184934i
$846$	12.1803			0.418769
$847$	−1.95492	+	10.8249i	−0.0671717	+	0.371948i
$848$	−8.94427			−0.307148
$849$	8.16312	+	5.93085i	0.280158	+	0.203546i
$850$	−13.4549	+	41.4100i	−0.461500	+	1.42035i
$851$	−12.4762	−	38.3978i	−0.427679	−	1.31626i
$852$	−8.47214	+	6.15537i	−0.290251	+	0.210879i
$853$	29.1803	−	21.2008i	0.999116	−	0.725900i	0.0372174	−	0.999307i	$-0.488151\pi$
$853$	29.1803	−	21.2008i	0.999116	−	0.725900i	0.961898	+	0.273407i	$0.0881506\pi$
$854$	−1.47214	−	4.53077i	−0.0503755	−	0.155040i
$855$	7.92705	−	24.3970i	0.271099	−	0.834358i
$856$	8.11803	+	5.89810i	0.277469	+	0.201593i
$857$	55.3050			1.88918			0.944591	−	0.328251i	$-0.106459\pi$
$857$	55.3050			1.88918			0.944591	+	0.328251i	$0.106459\pi$
$858$	−2.61803	+	10.4086i	−0.0893782	+	0.355344i
$859$	34.4721			1.17617			0.588087	−	0.808798i	$-0.299881\pi$
$859$	34.4721			1.17617			0.588087	+	0.808798i	$0.299881\pi$
$860$	2.23607	+	1.62460i	0.0762493	+	0.0553983i
$861$	−1.59017	+	4.89404i	−0.0541928	+	0.166788i
$862$	7.50000	+	23.0826i	0.255451	+	0.786197i
$863$	−0.0729490	+	0.0530006i	−0.00248321	+	0.00180416i	−0.589026	−	0.808114i	$-0.700489\pi$
$863$	−0.0729490	+	0.0530006i	−0.00248321	+	0.00180416i	0.586543	+	0.809918i	$0.300489\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	−0.163119	−	0.502029i	−0.00554621	−	0.0170695i
$866$	10.7082	−	32.9565i	0.363880	−	1.11991i
$867$	−9.68034	−	7.03318i	−0.328762	−	0.238859i
$868$	10.0902			0.342483
$869$	−14.5279	+	12.1392i	−0.492824	+	0.411795i
$870$	11.7082			0.396945
$871$	−8.47214	−	6.15537i	−0.287067	−	0.208567i
$872$	−0.736068	+	2.26538i	−0.0249264	+	0.0767156i
$873$	2.09017	+	6.43288i	0.0707415	+	0.217720i
$874$	−36.2877	+	26.3646i	−1.22745	+	0.891795i
$875$	−9.04508	+	6.57164i	−0.305780	+	0.222162i
$876$	−2.47214	−	7.60845i	−0.0835257	−	0.257066i
$877$	−7.20163	+	22.1643i	−0.243182	+	0.748436i	0.752749	+	0.658308i	$0.228728\pi$
$877$	−7.20163	+	22.1643i	−0.243182	+	0.748436i	−0.995930	+	0.0901280i	$0.971272\pi$
$878$	−5.69098	−	4.13474i	−0.192061	−	0.139541i
$879$	−15.7984			−0.532866
$880$	10.1631	+	6.37988i	0.342599	+	0.215066i
$881$	28.2148			0.950580			0.475290	−	0.879829i	$-0.342343\pi$
$881$	28.2148			0.950580			0.475290	+	0.879829i	$0.342343\pi$
$882$	0.809017	+	0.587785i	0.0272410	+	0.0197918i
$883$	0.618034	−	1.90211i	0.0207985	−	0.0640112i	−0.940119	−	0.340848i	$-0.889286\pi$
$883$	0.618034	−	1.90211i	0.0207985	−	0.0640112i	0.960917	+	0.276836i	$0.0892860\pi$
$884$	5.38197	+	16.5640i	0.181015	+	0.557107i
$885$	26.1803	−	19.0211i	0.880042	−	0.639388i
$886$	21.8262	−	15.8577i	0.733267	−	0.532750i
$887$	−6.00000	−	18.4661i	−0.201460	−	0.620031i	−0.999840	−	0.0178769i	$-0.994309\pi$
$887$	−6.00000	−	18.4661i	−0.201460	−	0.620031i	0.798380	−	0.602154i	$-0.205691\pi$
$888$	1.97214	−	6.06961i	0.0661805	−	0.203683i
$889$	5.47214	+	3.97574i	0.183530	+	0.133342i
$890$	−42.8885			−1.43763
$891$	3.30902	−	0.224514i	0.110856	−	0.00752150i
$892$	9.85410			0.329940
$893$	−69.8673	−	50.7615i	−2.33802	−	1.69867i
$894$	−2.29180	+	7.05342i	−0.0766491	+	0.235902i
$895$	−1.60739	−	4.94704i	−0.0537292	−	0.165361i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	−16.5623	+	12.0332i	−0.552999	+	0.401778i
$898$	3.14590	+	9.68208i	0.104980	+	0.323095i
$899$	−10.0902	+	31.0543i	−0.336526	+	1.03572i
$900$	−6.54508	−	4.75528i	−0.218169	−	0.158509i
$901$	−48.1378			−1.60370
$902$	−6.36068	−	15.8374i	−0.211787	−	0.527329i
$903$	−0.763932			−0.0254221
$904$	2.00000	+	1.45309i	0.0665190	+	0.0483289i
$905$	−8.94427	+	27.5276i	−0.297318	+	0.915050i
$906$	−2.76393	−	8.50651i	−0.0918255	−	0.282610i
$907$	−11.3820	+	8.26948i	−0.377932	+	0.274584i	−0.760492	−	0.649347i	$-0.775042\pi$
$907$	−11.3820	+	8.26948i	−0.377932	+	0.274584i	0.382560	+	0.923930i	$0.375042\pi$
$908$	−18.1803	+	13.2088i	−0.603336	+	0.438349i
$909$	1.59017	+	4.89404i	0.0527426	+	0.162325i
$910$	−3.61803	+	11.1352i	−0.119937	+	0.369127i
$911$	−31.5967	−	22.9564i	−1.04685	−	0.760579i	−0.0752366	−	0.997166i	$-0.523971\pi$
$911$	−31.5967	−	22.9564i	−1.04685	−	0.760579i	−0.971610	+	0.236587i	$0.923971\pi$
$912$	−7.09017			−0.234779
$913$	13.3050	+	33.1280i	0.440330	+	1.09638i
$914$	33.4164			1.10532
$915$	−13.9443	−	10.1311i	−0.460983	−	0.334924i
$916$	7.67376	−	23.6174i	0.253548	−	0.780341i
$917$	−3.32624	−	10.2371i	−0.109842	−	0.338059i
$918$	4.35410	−	3.16344i	0.143707	−	0.104409i
$919$	−28.3262	+	20.5802i	−0.934396	+	0.678879i	−0.947065	−	0.321041i	$-0.895967\pi$
$919$	−28.3262	+	20.5802i	−0.934396	+	0.678879i	0.0126689	+	0.999920i	$0.495967\pi$
$920$	7.07295	+	21.7683i	0.233188	+	0.717680i
$921$	2.82624	−	8.69827i	0.0931277	−	0.286618i
$922$	−12.8541	−	9.33905i	−0.423327	−	0.307565i
$923$	33.8885			1.11546
$924$	−3.30902	+	0.224514i	−0.108859	+	0.00738597i
$925$	−51.6312			−1.69762
$926$	−8.56231	−	6.22088i	−0.281375	−	0.204431i
$927$	−5.80902	+	17.8783i	−0.190793	+	0.587201i
$928$	−1.00000	−	3.07768i	−0.0328266	−	0.101030i
$929$	45.1869	−	32.8302i	1.48253	−	1.07712i	0.505806	−	0.862647i	$-0.331195\pi$
$929$	45.1869	−	32.8302i	1.48253	−	1.07712i	0.976729	−	0.214477i	$-0.0688047\pi$
$930$	29.5344	−	21.4580i	0.968473	−	0.703636i
$931$	−2.19098	−	6.74315i	−0.0718066	−	0.220998i
$932$	−4.90983	+	15.1109i	−0.160827	+	0.494974i
$933$	18.1803	+	13.2088i	0.595198	+	0.432436i
$934$	−8.00000			−0.261768
$935$	54.6976	+	34.3363i	1.78880	+	1.12292i
$936$	−3.23607			−0.105774
$937$	−28.1803	−	20.4742i	−0.920612	−	0.668863i	0.0230646	−	0.999734i	$-0.492658\pi$
$937$	−28.1803	−	20.4742i	−0.920612	−	0.668863i	−0.943676	+	0.330871i	$0.892658\pi$
$938$	1.00000	−	3.07768i	0.0326512	−	0.100490i
$939$	8.56231	+	26.3521i	0.279420	+	0.859967i
$940$	−35.6525	+	25.9030i	−1.16286	+	0.844864i
$941$	−6.35410	+	4.61653i	−0.207138	+	0.150494i	−0.686518	−	0.727113i	$-0.740862\pi$
$941$	−6.35410	+	4.61653i	−0.207138	+	0.150494i	0.479380	+	0.877607i	$0.340862\pi$
$942$	3.00000	+	9.23305i	0.0977453	+	0.300829i
$943$	10.0598	−	30.9609i	0.327592	−	1.00822i
$944$	−7.23607	−	5.25731i	−0.235514	−	0.171111i
$945$	3.61803			0.117695
$946$	1.94427	−	1.62460i	0.0632137	−	0.0528203i
$947$	5.61803			0.182562			0.0912808	−	0.995825i	$-0.470904\pi$
$947$	5.61803			0.182562			0.0912808	+	0.995825i	$0.470904\pi$
$948$	−4.61803	−	3.35520i	−0.149987	−	0.108972i
$949$	−8.00000	+	24.6215i	−0.259691	+	0.799247i
$950$	17.7254	+	54.5532i	0.575089	+	1.76994i
$951$	−9.70820	+	7.05342i	−0.314810	+	0.228723i
$952$	−4.35410	+	3.16344i	−0.141117	+	0.102528i
$953$	7.47214	+	22.9969i	0.242046	+	0.744942i	0.996108	+	0.0881385i	$0.0280918\pi$
$953$	7.47214	+	22.9969i	0.242046	+	0.744942i	−0.754062	+	0.656803i	$0.771908\pi$
$954$	2.76393	−	8.50651i	0.0894856	−	0.275408i
$955$	−0.263932	−	0.191758i	−0.00854064	−	0.00620514i
$956$	9.38197			0.303434
$957$	2.61803	−	10.4086i	0.0846290	−	0.336463i
$958$	12.9443			0.418210
$959$	−2.00000	−	1.45309i	−0.0645834	−	0.0469226i
$960$	−1.11803	+	3.44095i	−0.0360844	+	0.111056i
$961$	21.8820	+	67.3458i	0.705870	+	2.17244i
$962$	−16.7082	+	12.1392i	−0.538694	+	0.391384i
$963$	−8.11803	+	5.89810i	−0.261600	+	0.190064i
$964$	5.00000	+	15.3884i	0.161039	+	0.495628i
$965$	−5.42705	+	16.7027i	−0.174703	+	0.537680i
$966$	−5.11803	−	3.71847i	−0.164670	−	0.119640i
$967$	−2.18034			−0.0701150			−0.0350575	−	0.999385i	$-0.511161\pi$
$967$	−2.18034			−0.0701150			−0.0350575	+	0.999385i	$0.511161\pi$
$968$	7.94427	−	7.60845i	0.255339	−	0.244545i
$969$	−38.1591			−1.22585
$970$	−19.7984	−	14.3844i	−0.635687	−	0.461854i
$971$	−12.4377	+	38.2793i	−0.399145	+	1.22844i	0.526542	+	0.850149i	$0.323488\pi$
$971$	−12.4377	+	38.2793i	−0.399145	+	1.22844i	−0.925686	+	0.378292i	$0.876512\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	8.20820	−	5.96361i	0.263143	−	0.191185i
$974$	−10.0000	+	7.26543i	−0.320421	+	0.232799i
$975$	8.09017	+	24.8990i	0.259093	+	0.797406i
$976$	−1.47214	+	4.53077i	−0.0471219	+	0.145026i
$977$	−21.8541	−	15.8779i	−0.699175	−	0.507980i	0.180489	−	0.983577i	$-0.442232\pi$
$977$	−21.8541	−	15.8779i	−0.699175	−	0.507980i	−0.879663	+	0.475597i	$0.842232\pi$
$978$	−11.5279			−0.368620
$979$	−9.59017	+	38.1280i	−0.306503	+	1.21858i
$980$	−3.61803			−0.115574
$981$	−1.92705	−	1.40008i	−0.0615260	−	0.0447013i
$982$	−12.4271	+	38.2465i	−0.396563	+	1.22050i
$983$	7.56231	+	23.2744i	0.241200	+	0.742338i	0.996238	+	0.0866567i	$0.0276183\pi$
$983$	7.56231	+	23.2744i	0.241200	+	0.742338i	−0.755038	+	0.655681i	$0.772382\pi$
$984$	4.16312	−	3.02468i	0.132715	−	0.0964234i
$985$	68.0132	−	49.4145i	2.16708	−	1.57448i
$986$	−5.38197	−	16.5640i	−0.171397	−	0.527505i
$987$	3.76393	−	11.5842i	0.119807	−	0.368729i
$988$	18.5623	+	13.4863i	0.590546	+	0.429057i
$989$	4.83282			0.153675
$990$	−9.20820	+	7.69421i	−0.292656	+	0.244538i
$991$	17.7082			0.562520			0.281260	−	0.959632i	$-0.409248\pi$
$991$	17.7082			0.562520			0.281260	+	0.959632i	$0.409248\pi$
$992$	−8.16312	−	5.93085i	−0.259179	−	0.188305i
$993$	6.85410	−	21.0948i	0.217508	−	0.669422i
$994$	3.23607	+	9.95959i	0.102642	+	0.315899i
$995$	73.9681	−	53.7409i	2.34495	−	1.70370i
$996$	−8.70820	+	6.32688i	−0.275930	+	0.200475i
$997$	−5.67376	−	17.4620i	−0.179690	−	0.553028i	0.820127	−	0.572182i	$-0.193903\pi$
$997$	−5.67376	−	17.4620i	−0.179690	−	0.553028i	−0.999817	+	0.0191535i	$0.993903\pi$
$998$	−2.70820	+	8.33499i	−0.0857267	+	0.263840i
$999$	5.16312	+	3.75123i	0.163354	+	0.118684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.c.169.1	✓	4
11.3	even	5	inner	462.2.j.c.421.1	yes	4
11.5	even	5		5082.2.a.bh.1.1		2
11.6	odd	10		5082.2.a.br.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.c.169.1	✓	4	1.1	even	1	trivial
462.2.j.c.421.1	yes	4	11.3	even	5	inner
5082.2.a.bh.1.1		2	11.5	even	5
5082.2.a.br.1.1		2	11.6	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.92705 - 2.12663i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.92705 - 2.12663i) 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} +3.61803 q^{10} +(0.809017 - 3.21644i) q^{11} +1.00000 q^{12} +(-2.61803 - 1.90211i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.11803 - 3.44095i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.35410 + 3.16344i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-2.19098 + 6.74315i) q^{19} +(2.92705 + 2.12663i) q^{20} -1.00000 q^{21} +(2.54508 - 2.12663i) q^{22} +6.32624 q^{23} +(0.809017 + 0.587785i) q^{24} +(2.50000 - 7.69421i) q^{25} +(-1.00000 - 3.07768i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.809017 - 0.587785i) q^{28} +(1.00000 + 3.07768i) q^{29} +(1.11803 - 3.44095i) q^{30} +(8.16312 + 5.93085i) q^{31} -1.00000 q^{32} +(-2.80902 - 1.76336i) q^{33} -5.38197 q^{34} +(-2.92705 - 2.12663i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-1.97214 - 6.06961i) q^{37} +(-5.73607 + 4.16750i) q^{38} +(-2.61803 + 1.90211i) q^{39} +(1.11803 + 3.44095i) q^{40} +(1.59017 - 4.89404i) q^{41} +(-0.809017 - 0.587785i) q^{42} +0.763932 q^{43} +(3.30902 - 0.224514i) q^{44} -3.61803 q^{45} +(5.11803 + 3.71847i) q^{46} +(-3.76393 + 11.5842i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(6.54508 - 4.75528i) q^{50} +(1.66312 + 5.11855i) q^{51} +(1.00000 - 3.07768i) q^{52} +(7.23607 + 5.25731i) q^{53} -1.00000 q^{54} +(-4.47214 - 11.1352i) q^{55} +1.00000 q^{56} +(5.73607 + 4.16750i) q^{57} +(-1.00000 + 3.07768i) q^{58} +(2.76393 + 8.50651i) q^{59} +(2.92705 - 2.12663i) q^{60} +(3.85410 - 2.80017i) q^{61} +(3.11803 + 9.59632i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} -11.7082 q^{65} +(-1.23607 - 3.07768i) q^{66} +3.23607 q^{67} +(-4.35410 - 3.16344i) q^{68} +(1.95492 - 6.01661i) q^{69} +(-1.11803 - 3.44095i) q^{70} +(-8.47214 + 6.15537i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-2.47214 - 7.60845i) q^{73} +(1.97214 - 6.06961i) q^{74} +(-6.54508 - 4.75528i) q^{75} -7.09017 q^{76} +(-3.30902 + 0.224514i) q^{77} -3.23607 q^{78} +(-4.61803 - 3.35520i) q^{79} +(-1.11803 + 3.44095i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.16312 - 3.02468i) q^{82} +(-8.70820 + 6.32688i) q^{83} +(-0.309017 - 0.951057i) q^{84} +(-6.01722 + 18.5191i) q^{85} +(0.618034 + 0.449028i) q^{86} +3.23607 q^{87} +(2.80902 + 1.76336i) q^{88} -11.8541 q^{89} +(-2.92705 - 2.12663i) q^{90} +(-1.00000 + 3.07768i) q^{91} +(1.95492 + 6.01661i) q^{92} +(8.16312 - 5.93085i) q^{93} +(-9.85410 + 7.15942i) q^{94} +(7.92705 + 24.3970i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-5.47214 - 3.97574i) q^{97} -1.00000 q^{98} +(-2.54508 + 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9} + 10 q^{10} + q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - q^{16} - 4 q^{17} + q^{18} - 11 q^{19} + 5 q^{20} - 4 q^{21} - q^{22} - 6 q^{23} + q^{24} + 10 q^{25} - 4 q^{26} - q^{27} + q^{28} + 4 q^{29} + 17 q^{31} - 4 q^{32} - 9 q^{33} - 26 q^{34} - 5 q^{35} - q^{36} + 10 q^{37} - 14 q^{38} - 6 q^{39} - 16 q^{41} - q^{42} + 12 q^{43} + 11 q^{44} - 10 q^{45} + 16 q^{46} - 24 q^{47} - q^{48} - q^{49} + 15 q^{50} - 9 q^{51} + 4 q^{52} + 20 q^{53} - 4 q^{54} + 4 q^{56} + 14 q^{57} - 4 q^{58} + 20 q^{59} + 5 q^{60} + 2 q^{61} + 8 q^{62} + q^{63} - q^{64} - 20 q^{65} + 4 q^{66} + 4 q^{67} - 4 q^{68} + 19 q^{69} - 16 q^{71} + q^{72} + 8 q^{73} - 10 q^{74} - 15 q^{75} - 6 q^{76} - 11 q^{77} - 4 q^{78} - 14 q^{79} - q^{81} + q^{82} - 8 q^{83} + q^{84} + 5 q^{85} - 2 q^{86} + 4 q^{87} + 9 q^{88} - 34 q^{89} - 5 q^{90} - 4 q^{91} + 19 q^{92} + 17 q^{93} - 26 q^{94} + 25 q^{95} + q^{96} - 4 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9 + 10 * q^10 + q^11 + 4 * q^12 - 6 * q^13 - q^14 - q^16 - 4 * q^17 + q^18 - 11 * q^19 + 5 * q^20 - 4 * q^21 - q^22 - 6 * q^23 + q^24 + 10 * q^25 - 4 * q^26 - q^27 + q^28 + 4 * q^29 + 17 * q^31 - 4 * q^32 - 9 * q^33 - 26 * q^34 - 5 * q^35 - q^36 + 10 * q^37 - 14 * q^38 - 6 * q^39 - 16 * q^41 - q^42 + 12 * q^43 + 11 * q^44 - 10 * q^45 + 16 * q^46 - 24 * q^47 - q^48 - q^49 + 15 * q^50 - 9 * q^51 + 4 * q^52 + 20 * q^53 - 4 * q^54 + 4 * q^56 + 14 * q^57 - 4 * q^58 + 20 * q^59 + 5 * q^60 + 2 * q^61 + 8 * q^62 + q^63 - q^64 - 20 * q^65 + 4 * q^66 + 4 * q^67 - 4 * q^68 + 19 * q^69 - 16 * q^71 + q^72 + 8 * q^73 - 10 * q^74 - 15 * q^75 - 6 * q^76 - 11 * q^77 - 4 * q^78 - 14 * q^79 - q^81 + q^82 - 8 * q^83 + q^84 + 5 * q^85 - 2 * q^86 + 4 * q^87 + 9 * q^88 - 34 * q^89 - 5 * q^90 - 4 * q^91 + 19 * q^92 + 17 * q^93 - 26 * q^94 + 25 * q^95 + q^96 - 4 * q^97 - 4 * q^98 + q^99

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