LMFDB - Embedded newform 770.2.n.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (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:	$6.14848095564$
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			71.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.a.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-1.30902 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.118034 - 0.363271i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-1.30902 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.118034 - 0.363271i) q^{9} +1.00000 q^{10} +(-2.54508 + 2.12663i) q^{11} +1.61803 q^{12} +(1.73607 + 5.34307i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-1.30902 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.42705 - 4.39201i) q^{17} +(0.309017 - 0.224514i) q^{18} +(4.23607 + 3.07768i) q^{19} +(0.309017 + 0.951057i) q^{20} +1.61803 q^{21} +(-2.80902 - 1.76336i) q^{22} +8.47214 q^{23} +(0.500000 + 1.53884i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.54508 + 3.30220i) q^{26} +(-1.69098 + 5.20431i) q^{27} +(0.309017 - 0.951057i) q^{28} +(4.73607 - 3.44095i) q^{29} +(-1.30902 - 0.951057i) q^{30} +(1.61803 + 4.97980i) q^{31} +1.00000 q^{32} +(5.35410 - 0.363271i) q^{33} +4.61803 q^{34} +(0.309017 + 0.951057i) q^{35} +(0.309017 + 0.224514i) q^{36} +(3.00000 - 2.17963i) q^{37} +(-1.61803 + 4.97980i) q^{38} +(2.80902 - 8.64527i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-7.23607 - 5.25731i) q^{41} +(0.500000 + 1.53884i) q^{42} +3.23607 q^{43} +(0.809017 - 3.21644i) q^{44} -0.381966 q^{45} +(2.61803 + 8.05748i) q^{46} +(10.5902 + 7.69421i) q^{47} +(-1.30902 + 0.951057i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-6.04508 + 4.39201i) q^{51} +(-4.54508 - 3.30220i) q^{52} +(2.00000 + 6.15537i) q^{53} -5.47214 q^{54} +(1.23607 + 3.07768i) q^{55} +1.00000 q^{56} +(-2.61803 - 8.05748i) q^{57} +(4.73607 + 3.44095i) q^{58} +(-3.85410 + 2.80017i) q^{59} +(0.500000 - 1.53884i) q^{60} +(-3.61803 + 11.1352i) q^{61} +(-4.23607 + 3.07768i) q^{62} +(0.309017 + 0.224514i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.61803 q^{65} +(2.00000 + 4.97980i) q^{66} -1.23607 q^{67} +(1.42705 + 4.39201i) q^{68} +(-11.0902 - 8.05748i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-2.26393 + 6.96767i) q^{71} +(-0.118034 + 0.363271i) q^{72} +(-3.50000 + 2.54290i) q^{73} +(3.00000 + 2.17963i) q^{74} +(0.500000 + 1.53884i) q^{75} -5.23607 q^{76} +(0.809017 - 3.21644i) q^{77} +9.09017 q^{78} +(-0.263932 - 0.812299i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(6.23607 - 4.53077i) q^{81} +(2.76393 - 8.50651i) q^{82} +(4.20820 - 12.9515i) q^{83} +(-1.30902 + 0.951057i) q^{84} +(-3.73607 - 2.71441i) q^{85} +(1.00000 + 3.07768i) q^{86} -9.47214 q^{87} +(3.30902 - 0.224514i) q^{88} +0.291796 q^{89} +(-0.118034 - 0.363271i) q^{90} +(-4.54508 - 3.30220i) q^{91} +(-6.85410 + 4.97980i) q^{92} +(2.61803 - 8.05748i) q^{93} +(-4.04508 + 12.4495i) q^{94} +(4.23607 - 3.07768i) q^{95} +(-1.30902 - 0.951057i) q^{96} +(-1.04508 - 3.21644i) q^{97} +1.00000 q^{98} +(1.07295 + 0.673542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9	\( 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9} + 4 q^{10} + q^{11} + 2 q^{12} - 2 q^{13} - q^{14} - 3 q^{15} - q^{16} - q^{17} - q^{18} + 8 q^{19} - q^{20} + 2 q^{21} - 9 q^{22} + 16 q^{23} + 2 q^{24} - q^{25} - 7 q^{26} - 9 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 14 q^{34} - q^{35} - q^{36} + 12 q^{37} - 2 q^{38} + 9 q^{39} - q^{40} - 20 q^{41} + 2 q^{42} + 4 q^{43} + q^{44} - 6 q^{45} + 6 q^{46} + 20 q^{47} - 3 q^{48} - q^{49} - q^{50} - 13 q^{51} - 7 q^{52} + 8 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 6 q^{57} + 10 q^{58} - 2 q^{59} + 2 q^{60} - 10 q^{61} - 8 q^{62} - q^{63} - q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} - q^{68} - 22 q^{69} - q^{70} - 18 q^{71} + 4 q^{72} - 14 q^{73} + 12 q^{74} + 2 q^{75} - 12 q^{76} + q^{77} + 14 q^{78} - 10 q^{79} - q^{80} + 16 q^{81} + 20 q^{82} - 10 q^{83} - 3 q^{84} - 6 q^{85} + 4 q^{86} - 20 q^{87} + 11 q^{88} + 28 q^{89} + 4 q^{90} - 7 q^{91} - 14 q^{92} + 6 q^{93} - 5 q^{94} + 8 q^{95} - 3 q^{96} + 7 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9 + 4 * q^10 + q^11 + 2 * q^12 - 2 * q^13 - q^14 - 3 * q^15 - q^16 - q^17 - q^18 + 8 * q^19 - q^20 + 2 * q^21 - 9 * q^22 + 16 * q^23 + 2 * q^24 - q^25 - 7 * q^26 - 9 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 14 * q^34 - q^35 - q^36 + 12 * q^37 - 2 * q^38 + 9 * q^39 - q^40 - 20 * q^41 + 2 * q^42 + 4 * q^43 + q^44 - 6 * q^45 + 6 * q^46 + 20 * q^47 - 3 * q^48 - q^49 - q^50 - 13 * q^51 - 7 * q^52 + 8 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 6 * q^57 + 10 * q^58 - 2 * q^59 + 2 * q^60 - 10 * q^61 - 8 * q^62 - q^63 - q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 - q^68 - 22 * q^69 - q^70 - 18 * q^71 + 4 * q^72 - 14 * q^73 + 12 * q^74 + 2 * q^75 - 12 * q^76 + q^77 + 14 * q^78 - 10 * q^79 - q^80 + 16 * q^81 + 20 * q^82 - 10 * q^83 - 3 * q^84 - 6 * q^85 + 4 * q^86 - 20 * q^87 + 11 * q^88 + 28 * q^89 + 4 * q^90 - 7 * q^91 - 14 * q^92 + 6 * q^93 - 5 * q^94 + 8 * q^95 - 3 * q^96 + 7 * q^97 + 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−1.30902	−	0.951057i	−0.755761	−	0.549093i	0.141846	−	0.989889i	$-0.454696\pi$
$3$	−1.30902	−	0.951057i	−0.755761	−	0.549093i	−0.897607	+	0.440796i	$0.854696\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	0.500000	−	1.53884i	0.204124	−	0.628230i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.118034	−	0.363271i	−0.0393447	−	0.121090i
$10$	1.00000			0.316228
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$	1.61803			0.467086
$13$	1.73607	+	5.34307i	0.481499	+	1.48190i	0.836989	+	0.547220i	$0.184314\pi$
$13$	1.73607	+	5.34307i	0.481499	+	1.48190i	−0.355490	+	0.934680i	$0.615686\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	−1.30902	+	0.951057i	−0.337987	+	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.42705	−	4.39201i	0.346111	−	1.06522i	−0.614876	−	0.788624i	$-0.710794\pi$
$17$	1.42705	−	4.39201i	0.346111	−	1.06522i	0.960987	−	0.276595i	$-0.0892061\pi$
$18$	0.309017	−	0.224514i	0.0728360	−	0.0529185i
$19$	4.23607	+	3.07768i	0.971821	+	0.706069i	0.955866	−	0.293804i	$-0.0949212\pi$
$19$	4.23607	+	3.07768i	0.971821	+	0.706069i	0.0159549	+	0.999873i	$0.494921\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	1.61803			0.353084
$22$	−2.80902	−	1.76336i	−0.598884	−	0.375949i
$23$	8.47214			1.76656			0.883281	−	0.468844i	$-0.155329\pi$
$23$	8.47214			1.76656			0.883281	+	0.468844i	$0.155329\pi$
$24$	0.500000	+	1.53884i	0.102062	+	0.314115i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−4.54508	+	3.30220i	−0.891364	+	0.647614i
$27$	−1.69098	+	5.20431i	−0.325430	+	1.00157i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	4.73607	−	3.44095i	0.879466	−	0.638969i	−0.0536443	−	0.998560i	$-0.517084\pi$
$29$	4.73607	−	3.44095i	0.879466	−	0.638969i	0.933110	+	0.359591i	$0.117084\pi$
$30$	−1.30902	−	0.951057i	−0.238993	−	0.173638i
$31$	1.61803	+	4.97980i	0.290607	+	0.894398i	0.984662	+	0.174475i	$0.0558228\pi$
$31$	1.61803	+	4.97980i	0.290607	+	0.894398i	−0.694054	+	0.719923i	$0.744177\pi$
$32$	1.00000			0.176777
$33$	5.35410	−	0.363271i	0.932030	−	0.0632374i
$34$	4.61803			0.791986
$35$	0.309017	+	0.951057i	0.0522334	+	0.160758i
$36$	0.309017	+	0.224514i	0.0515028	+	0.0374190i
$37$	3.00000	−	2.17963i	0.493197	−	0.358329i	−0.313215	−	0.949682i	$-0.601406\pi$
$37$	3.00000	−	2.17963i	0.493197	−	0.358329i	0.806412	+	0.591354i	$0.201406\pi$
$38$	−1.61803	+	4.97980i	−0.262480	+	0.807830i
$39$	2.80902	−	8.64527i	0.449803	−	1.38435i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−7.23607	−	5.25731i	−1.13008	−	0.821054i	−0.144377	−	0.989523i	$-0.546118\pi$
$41$	−7.23607	−	5.25731i	−1.13008	−	0.821054i	−0.985707	+	0.168469i	$0.946118\pi$
$42$	0.500000	+	1.53884i	0.0771517	+	0.237448i
$43$	3.23607			0.493496			0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607			0.493496			0.246748	+	0.969080i	$0.420638\pi$
$44$	0.809017	−	3.21644i	0.121964	−	0.484897i
$45$	−0.381966			−0.0569401
$46$	2.61803	+	8.05748i	0.386008	+	1.18801i
$47$	10.5902	+	7.69421i	1.54474	+	1.12232i	0.947277	+	0.320415i	$0.103823\pi$
$47$	10.5902	+	7.69421i	1.54474	+	1.12232i	0.597458	+	0.801900i	$0.296177\pi$
$48$	−1.30902	+	0.951057i	−0.188940	+	0.137273i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	−6.04508	+	4.39201i	−0.846481	+	0.615005i
$52$	−4.54508	−	3.30220i	−0.630290	−	0.457932i
$53$	2.00000	+	6.15537i	0.274721	+	0.845505i	0.989293	+	0.145943i	$0.0466215\pi$
$53$	2.00000	+	6.15537i	0.274721	+	0.845505i	−0.714572	+	0.699562i	$0.753378\pi$
$54$	−5.47214			−0.744663
$55$	1.23607	+	3.07768i	0.166671	+	0.414995i
$56$	1.00000			0.133631
$57$	−2.61803	−	8.05748i	−0.346767	−	1.06724i
$58$	4.73607	+	3.44095i	0.621876	+	0.451820i
$59$	−3.85410	+	2.80017i	−0.501761	+	0.364551i	−0.809689	−	0.586859i	$-0.800364\pi$
$59$	−3.85410	+	2.80017i	−0.501761	+	0.364551i	0.307928	+	0.951410i	$0.400364\pi$
$60$	0.500000	−	1.53884i	0.0645497	−	0.198664i
$61$	−3.61803	+	11.1352i	−0.463242	+	1.42571i	0.397939	+	0.917412i	$0.369726\pi$
$61$	−3.61803	+	11.1352i	−0.463242	+	1.42571i	−0.861180	+	0.508300i	$0.830274\pi$
$62$	−4.23607	+	3.07768i	−0.537981	+	0.390866i
$63$	0.309017	+	0.224514i	0.0389325	+	0.0282861i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.61803			0.696831
$66$	2.00000	+	4.97980i	0.246183	+	0.612971i
$67$	−1.23607			−0.151010			−0.0755049	−	0.997145i	$-0.524057\pi$
$67$	−1.23607			−0.151010			−0.0755049	+	0.997145i	$0.524057\pi$
$68$	1.42705	+	4.39201i	0.173055	+	0.532610i
$69$	−11.0902	−	8.05748i	−1.33510	−	0.970007i
$70$	−0.809017	+	0.587785i	−0.0966960	+	0.0702538i
$71$	−2.26393	+	6.96767i	−0.268679	+	0.826910i	0.722144	+	0.691743i	$0.243157\pi$
$71$	−2.26393	+	6.96767i	−0.268679	+	0.826910i	−0.990823	+	0.135167i	$0.956843\pi$
$72$	−0.118034	+	0.363271i	−0.0139104	+	0.0428119i
$73$	−3.50000	+	2.54290i	−0.409644	+	0.297624i	−0.773458	−	0.633848i	$-0.781474\pi$
$73$	−3.50000	+	2.54290i	−0.409644	+	0.297624i	0.363814	+	0.931472i	$0.381474\pi$
$74$	3.00000	+	2.17963i	0.348743	+	0.253377i
$75$	0.500000	+	1.53884i	0.0577350	+	0.177690i
$76$	−5.23607			−0.600618
$77$	0.809017	−	3.21644i	0.0921960	−	0.366547i
$78$	9.09017			1.02926
$79$	−0.263932	−	0.812299i	−0.0296947	−	0.0913908i	0.935111	−	0.354356i	$-0.115300\pi$
$79$	−0.263932	−	0.812299i	−0.0296947	−	0.0913908i	−0.964805	+	0.262965i	$0.915300\pi$
$80$	−0.809017	−	0.587785i	−0.0904508	−	0.0657164i
$81$	6.23607	−	4.53077i	0.692896	−	0.503419i
$82$	2.76393	−	8.50651i	0.305225	−	0.939387i
$83$	4.20820	−	12.9515i	0.461910	−	1.42161i	−0.400917	−	0.916115i	$-0.631308\pi$
$83$	4.20820	−	12.9515i	0.461910	−	1.42161i	0.862827	−	0.505499i	$-0.168692\pi$
$84$	−1.30902	+	0.951057i	−0.142825	+	0.103769i
$85$	−3.73607	−	2.71441i	−0.405233	−	0.294419i
$86$	1.00000	+	3.07768i	0.107833	+	0.331875i
$87$	−9.47214			−1.01552
$88$	3.30902	−	0.224514i	0.352742	−	0.0239333i
$89$	0.291796			0.0309303			0.0154652	−	0.999880i	$-0.495077\pi$
$89$	0.291796			0.0309303			0.0154652	+	0.999880i	$0.495077\pi$
$90$	−0.118034	−	0.363271i	−0.0124419	−	0.0382922i
$91$	−4.54508	−	3.30220i	−0.476454	−	0.346164i
$92$	−6.85410	+	4.97980i	−0.714590	+	0.519180i
$93$	2.61803	−	8.05748i	0.271477	−	0.835522i
$94$	−4.04508	+	12.4495i	−0.417219	+	1.28407i
$95$	4.23607	−	3.07768i	0.434611	−	0.315764i
$96$	−1.30902	−	0.951057i	−0.133601	−	0.0970668i
$97$	−1.04508	−	3.21644i	−0.106112	−	0.326580i	0.883878	−	0.467718i	$-0.154924\pi$
$97$	−1.04508	−	3.21644i	−0.106112	−	0.326580i	−0.989990	+	0.141138i	$0.954924\pi$
$98$	1.00000			0.101015
$99$	1.07295	+	0.673542i	0.107835	+	0.0676935i
$100$	1.00000			0.100000
$101$	−1.61803	−	4.97980i	−0.161000	−	0.495508i	0.837719	−	0.546102i	$-0.183889\pi$
$101$	−1.61803	−	4.97980i	−0.161000	−	0.495508i	−0.998719	+	0.0505933i	$0.983889\pi$
$102$	−6.04508	−	4.39201i	−0.598553	−	0.434874i
$103$	−2.88197	+	2.09387i	−0.283969	+	0.206315i	−0.720647	−	0.693303i	$-0.756155\pi$
$103$	−2.88197	+	2.09387i	−0.283969	+	0.206315i	0.436678	+	0.899618i	$0.356155\pi$
$104$	1.73607	−	5.34307i	0.170235	−	0.523931i
$105$	0.500000	−	1.53884i	0.0487950	−	0.150176i
$106$	−5.23607	+	3.80423i	−0.508572	+	0.369499i
$107$	8.70820	+	6.32688i	0.841854	+	0.611643i	0.922888	−	0.385069i	$-0.125822\pi$
$107$	8.70820	+	6.32688i	0.841854	+	0.611643i	−0.0810341	+	0.996711i	$0.525822\pi$
$108$	−1.69098	−	5.20431i	−0.162715	−	0.500785i
$109$	3.52786			0.337908			0.168954	−	0.985624i	$-0.445961\pi$
$109$	3.52786			0.337908			0.168954	+	0.985624i	$0.445961\pi$
$110$	−2.54508	+	2.12663i	−0.242664	+	0.202766i
$111$	−6.00000			−0.569495
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	1.23607	+	0.898056i	0.116279	+	0.0844820i	0.644405	−	0.764684i	$-0.277105\pi$
$113$	1.23607	+	0.898056i	0.116279	+	0.0844820i	−0.528126	+	0.849166i	$0.677105\pi$
$114$	6.85410	−	4.97980i	0.641945	−	0.466401i
$115$	2.61803	−	8.05748i	0.244133	−	0.751364i
$116$	−1.80902	+	5.56758i	−0.167963	+	0.516937i
$117$	1.73607	−	1.26133i	0.160500	−	0.116610i
$118$	−3.85410	−	2.80017i	−0.354799	−	0.257776i
$119$	1.42705	+	4.39201i	0.130818	+	0.402615i
$120$	1.61803			0.147706
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	−11.7082			−1.06001
$123$	4.47214	+	13.7638i	0.403239	+	1.24104i
$124$	−4.23607	−	3.07768i	−0.380410	−	0.276384i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	−0.118034	+	0.363271i	−0.0105153	+	0.0323628i
$127$	6.23607	−	19.1926i	0.553362	−	1.70307i	−0.146870	−	0.989156i	$-0.546920\pi$
$127$	6.23607	−	19.1926i	0.553362	−	1.70307i	0.700231	−	0.713916i	$-0.253080\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−4.23607	−	3.07768i	−0.372965	−	0.270975i
$130$	1.73607	+	5.34307i	0.152263	+	0.468618i
$131$	−11.4164			−0.997456			−0.498728	−	0.866758i	$-0.666199\pi$
$131$	−11.4164			−0.997456			−0.498728	+	0.866758i	$0.666199\pi$
$132$	−4.11803	+	3.44095i	−0.358429	+	0.299497i
$133$	−5.23607			−0.454025
$134$	−0.381966	−	1.17557i	−0.0329968	−	0.101554i
$135$	4.42705	+	3.21644i	0.381020	+	0.276827i
$136$	−3.73607	+	2.71441i	−0.320365	+	0.232759i
$137$	−4.94427	+	15.2169i	−0.422418	+	1.30007i	0.483028	+	0.875605i	$0.339537\pi$
$137$	−4.94427	+	15.2169i	−0.422418	+	1.30007i	−0.905445	+	0.424463i	$0.860463\pi$
$138$	4.23607	−	13.0373i	0.360598	−	1.10981i
$139$	−7.23607	+	5.25731i	−0.613755	+	0.445919i	−0.850735	−	0.525595i	$-0.823843\pi$
$139$	−7.23607	+	5.25731i	−0.613755	+	0.445919i	0.236979	+	0.971515i	$0.423843\pi$
$140$	−0.809017	−	0.587785i	−0.0683744	−	0.0496769i
$141$	−6.54508	−	20.1437i	−0.551196	−	1.69641i
$142$	−7.32624			−0.614804
$143$	−15.7812	−	9.90659i	−1.31969	−	0.828431i
$144$	−0.381966			−0.0318305
$145$	−1.80902	−	5.56758i	−0.150231	−	0.462363i
$146$	−3.50000	−	2.54290i	−0.289662	−	0.210452i
$147$	−1.30902	+	0.951057i	−0.107966	+	0.0784418i
$148$	−1.14590	+	3.52671i	−0.0941922	+	0.289894i
$149$	6.44427	−	19.8334i	0.527935	−	1.62482i	−0.230502	−	0.973072i	$-0.574037\pi$
$149$	6.44427	−	19.8334i	0.527935	−	1.62482i	0.758437	−	0.651746i	$-0.225963\pi$
$150$	−1.30902	+	0.951057i	−0.106881	+	0.0776534i
$151$	−17.2984	−	12.5680i	−1.40772	−	1.02277i	−0.993649	−	0.112526i	$-0.964106\pi$
$151$	−17.2984	−	12.5680i	−1.40772	−	1.02277i	−0.414073	−	0.910244i	$-0.635894\pi$
$152$	−1.61803	−	4.97980i	−0.131240	−	0.403915i
$153$	−1.76393			−0.142605
$154$	3.30902	−	0.224514i	0.266648	−	0.0180919i
$155$	5.23607			0.420571
$156$	2.80902	+	8.64527i	0.224901	+	0.692175i
$157$	8.97214	+	6.51864i	0.716054	+	0.520244i	0.885121	−	0.465361i	$-0.154075\pi$
$157$	8.97214	+	6.51864i	0.716054	+	0.520244i	−0.169067	+	0.985605i	$0.554075\pi$
$158$	0.690983	−	0.502029i	0.0549717	−	0.0399392i
$159$	3.23607	−	9.95959i	0.256637	−	0.789847i
$160$	0.309017	−	0.951057i	0.0244299	−	0.0751876i
$161$	−6.85410	+	4.97980i	−0.540179	+	0.392463i
$162$	6.23607	+	4.53077i	0.489952	+	0.355971i
$163$	−4.52786	−	13.9353i	−0.354650	−	1.09150i	−0.956212	−	0.292674i	$-0.905455\pi$
$163$	−4.52786	−	13.9353i	−0.354650	−	1.09150i	0.601563	−	0.798826i	$-0.294545\pi$
$164$	8.94427			0.698430
$165$	1.30902	−	5.20431i	0.101907	−	0.405155i
$166$	13.6180			1.05696
$167$	6.18034	+	19.0211i	0.478249	+	1.47190i	0.841525	+	0.540218i	$0.181658\pi$
$167$	6.18034	+	19.0211i	0.478249	+	1.47190i	−0.363276	+	0.931681i	$0.618342\pi$
$168$	−1.30902	−	0.951057i	−0.100993	−	0.0733756i
$169$	−15.0172	+	10.9106i	−1.15517	+	0.839281i
$170$	1.42705	−	4.39201i	0.109450	−	0.336852i
$171$	0.618034	−	1.90211i	0.0472622	−	0.145458i
$172$	−2.61803	+	1.90211i	−0.199623	+	0.145035i
$173$	12.5451	+	9.11454i	0.953785	+	0.692965i	0.951699	−	0.307032i	$-0.0993360\pi$
$173$	12.5451	+	9.11454i	0.953785	+	0.692965i	0.00208607	+	0.999998i	$0.499336\pi$
$174$	−2.92705	−	9.00854i	−0.221899	−	0.682935i
$175$	1.00000			0.0755929
$176$	1.23607	+	3.07768i	0.0931721	+	0.231989i
$177$	7.70820			0.579384
$178$	0.0901699	+	0.277515i	0.00675852	+	0.0208006i
$179$	15.8262	+	11.4984i	1.18291	+	0.859433i	0.992497	−	0.122271i	$-0.0390177\pi$
$179$	15.8262	+	11.4984i	1.18291	+	0.859433i	0.190412	+	0.981704i	$0.439018\pi$
$180$	0.309017	−	0.224514i	0.0230328	−	0.0167343i
$181$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$181$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$182$	1.73607	−	5.34307i	0.128686	−	0.396055i
$183$	15.3262	−	11.1352i	1.13295	−	0.823135i
$184$	−6.85410	−	4.97980i	−0.505291	−	0.367115i
$185$	−1.14590	−	3.52671i	−0.0842481	−	0.259289i
$186$	8.47214			0.621207
$187$	5.70820	+	14.2128i	0.417425	+	1.03935i
$188$	−13.0902			−0.954699
$189$	−1.69098	−	5.20431i	−0.123001	−	0.378558i
$190$	4.23607	+	3.07768i	0.307317	+	0.223279i
$191$	−0.690983	+	0.502029i	−0.0499978	+	0.0363255i	−0.612503	−	0.790468i	$-0.709837\pi$
$191$	−0.690983	+	0.502029i	−0.0499978	+	0.0363255i	0.562506	+	0.826793i	$0.309837\pi$
$192$	0.500000	−	1.53884i	0.0360844	−	0.111056i
$193$	4.00000	−	12.3107i	0.287926	−	0.886146i	−0.697580	−	0.716507i	$-0.745740\pi$
$193$	4.00000	−	12.3107i	0.287926	−	0.886146i	0.985506	−	0.169639i	$-0.0542602\pi$
$194$	2.73607	−	1.98787i	0.196438	−	0.142721i
$195$	−7.35410	−	5.34307i	−0.526638	−	0.382625i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	−15.4164			−1.09837			−0.549187	−	0.835700i	$-0.685062\pi$
$197$	−15.4164			−1.09837			−0.549187	+	0.835700i	$0.685062\pi$
$198$	−0.309017	+	1.22857i	−0.0219609	+	0.0873107i
$199$	−10.9443			−0.775819			−0.387909	−	0.921697i	$-0.626803\pi$
$199$	−10.9443			−0.775819			−0.387909	+	0.921697i	$0.626803\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	1.61803	+	1.17557i	0.114127	+	0.0829184i
$202$	4.23607	−	3.07768i	0.298049	−	0.216545i
$203$	−1.80902	+	5.56758i	−0.126968	+	0.390768i
$204$	2.30902	−	7.10642i	0.161664	−	0.497549i
$205$	−7.23607	+	5.25731i	−0.505389	+	0.367187i
$206$	−2.88197	−	2.09387i	−0.200796	−	0.145887i
$207$	−1.00000	−	3.07768i	−0.0695048	−	0.213914i
$208$	5.61803			0.389541
$209$	−17.3262	+	1.17557i	−1.19848	+	0.0813159i
$210$	1.61803			0.111655
$211$	4.73607	+	14.5761i	0.326044	+	1.00346i	0.970967	+	0.239214i	$0.0768896\pi$
$211$	4.73607	+	14.5761i	0.326044	+	1.00346i	−0.644923	+	0.764248i	$0.723110\pi$
$212$	−5.23607	−	3.80423i	−0.359615	−	0.261275i
$213$	9.59017	−	6.96767i	0.657108	−	0.477417i
$214$	−3.32624	+	10.2371i	−0.227377	+	0.699794i
$215$	1.00000	−	3.07768i	0.0681994	−	0.209896i
$216$	4.42705	−	3.21644i	0.301223	−	0.218851i
$217$	−4.23607	−	3.07768i	−0.287563	−	0.208927i
$218$	1.09017	+	3.35520i	0.0738356	+	0.227243i
$219$	7.00000			0.473016
$220$	−2.80902	−	1.76336i	−0.189384	−	0.118885i
$221$	25.9443			1.74520
$222$	−1.85410	−	5.70634i	−0.124439	−	0.382984i
$223$	14.9443	+	10.8576i	1.00074	+	0.727082i	0.962247	−	0.272177i	$-0.0877436\pi$
$223$	14.9443	+	10.8576i	1.00074	+	0.727082i	0.0384952	+	0.999259i	$0.487744\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	−0.118034	+	0.363271i	−0.00786893	+	0.0242181i
$226$	−0.472136	+	1.45309i	−0.0314060	+	0.0966578i
$227$	−5.78115	+	4.20025i	−0.383709	+	0.278781i	−0.762873	−	0.646549i	$-0.776212\pi$
$227$	−5.78115	+	4.20025i	−0.383709	+	0.278781i	0.379164	+	0.925330i	$0.376212\pi$
$228$	6.85410	+	4.97980i	0.453924	+	0.329795i
$229$	2.38197	+	7.33094i	0.157405	+	0.484442i	0.998397	−	0.0566058i	$-0.0180278\pi$
$229$	2.38197	+	7.33094i	0.157405	+	0.484442i	−0.840992	+	0.541048i	$0.818028\pi$
$230$	8.47214			0.558636
$231$	−4.11803	+	3.44095i	−0.270947	+	0.226398i
$232$	−5.85410			−0.384341
$233$	−5.14590	−	15.8374i	−0.337119	−	1.03755i	−0.965669	−	0.259776i	$-0.916351\pi$
$233$	−5.14590	−	15.8374i	−0.337119	−	1.03755i	0.628550	−	0.777769i	$-0.283649\pi$
$234$	1.73607	+	1.26133i	0.113490	+	0.0824555i
$235$	10.5902	−	7.69421i	0.690827	−	0.501915i
$236$	1.47214	−	4.53077i	0.0958279	−	0.294928i
$237$	−0.427051	+	1.31433i	−0.0277399	+	0.0853748i
$238$	−3.73607	+	2.71441i	−0.242173	+	0.175949i
$239$	−7.16312	−	5.20431i	−0.463344	−	0.336639i	0.331498	−	0.943456i	$-0.392446\pi$
$239$	−7.16312	−	5.20431i	−0.463344	−	0.336639i	−0.794841	+	0.606817i	$0.792446\pi$
$240$	0.500000	+	1.53884i	0.0322749	+	0.0993318i
$241$	−3.70820			−0.238866			−0.119433	−	0.992842i	$-0.538108\pi$
$241$	−3.70820			−0.238866			−0.119433	+	0.992842i	$0.538108\pi$
$242$	10.8992	−	1.48584i	0.700626	−	0.0955135i
$243$	3.94427			0.253025
$244$	−3.61803	−	11.1352i	−0.231621	−	0.712856i
$245$	−0.809017	−	0.587785i	−0.0516862	−	0.0375522i
$246$	−11.7082	+	8.50651i	−0.746488	+	0.542355i
$247$	−9.09017	+	27.9767i	−0.578394	+	1.78011i
$248$	1.61803	−	4.97980i	0.102745	−	0.316217i
$249$	−17.8262	+	12.9515i	−1.12969	+	0.820769i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	0.236068	+	0.726543i	0.0149005	+	0.0458590i	0.958230	−	0.285998i	$-0.0923250\pi$
$251$	0.236068	+	0.726543i	0.0149005	+	0.0458590i	−0.943330	+	0.331857i	$0.892325\pi$
$252$	−0.381966			−0.0240616
$253$	−21.5623	+	18.0171i	−1.35561	+	1.13272i
$254$	20.1803			1.26623
$255$	2.30902	+	7.10642i	0.144596	+	0.445022i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	10.7361	−	7.80021i	0.669698	−	0.486564i	−0.200226	−	0.979750i	$-0.564168\pi$
$257$	10.7361	−	7.80021i	0.669698	−	0.486564i	0.869924	+	0.493186i	$0.164168\pi$
$258$	1.61803	−	4.97980i	0.100734	−	0.310029i
$259$	−1.14590	+	3.52671i	−0.0712026	+	0.219139i
$260$	−4.54508	+	3.30220i	−0.281874	+	0.204794i
$261$	−1.80902	−	1.31433i	−0.111975	−	0.0813548i
$262$	−3.52786	−	10.8576i	−0.217952	−	0.670788i
$263$	14.2918			0.881270			0.440635	−	0.897686i	$-0.354753\pi$
$263$	14.2918			0.881270			0.440635	+	0.897686i	$0.354753\pi$
$264$	−4.54508	−	2.85317i	−0.279731	−	0.175600i
$265$	6.47214			0.397580
$266$	−1.61803	−	4.97980i	−0.0992080	−	0.305331i
$267$	−0.381966	−	0.277515i	−0.0233759	−	0.0169836i
$268$	1.00000	−	0.726543i	0.0610847	−	0.0443806i
$269$	6.09017	−	18.7436i	0.371324	−	1.14282i	−0.574601	−	0.818434i	$-0.694843\pi$
$269$	6.09017	−	18.7436i	0.371324	−	1.14282i	0.945925	−	0.324385i	$-0.105157\pi$
$270$	−1.69098	+	5.20431i	−0.102910	+	0.316724i
$271$	−12.2361	+	8.89002i	−0.743288	+	0.540030i	−0.893739	−	0.448587i	$-0.851927\pi$
$271$	−12.2361	+	8.89002i	−0.743288	+	0.540030i	0.150451	+	0.988617i	$0.451927\pi$
$272$	−3.73607	−	2.71441i	−0.226532	−	0.164585i
$273$	2.80902	+	8.64527i	0.170009	+	0.523235i
$274$	−16.0000			−0.966595
$275$	3.30902	−	0.224514i	0.199541	−	0.0135387i
$276$	13.7082			0.825137
$277$	4.14590	+	12.7598i	0.249103	+	0.766660i	0.994935	+	0.100525i	$0.0320523\pi$
$277$	4.14590	+	12.7598i	0.249103	+	0.766660i	−0.745832	+	0.666135i	$0.767948\pi$
$278$	−7.23607	−	5.25731i	−0.433991	−	0.315313i
$279$	1.61803	−	1.17557i	0.0968692	−	0.0703796i
$280$	0.309017	−	0.951057i	0.0184673	−	0.0568365i
$281$	5.67376	−	17.4620i	0.338468	−	1.04170i	−0.626520	−	0.779405i	$-0.715521\pi$
$281$	5.67376	−	17.4620i	0.338468	−	1.04170i	0.964988	−	0.262293i	$-0.0844787\pi$
$282$	17.1353	−	12.4495i	1.02039	−	0.741356i
$283$	11.5902	+	8.42075i	0.688964	+	0.500562i	0.876319	−	0.481730i	$-0.159992\pi$
$283$	11.5902	+	8.42075i	0.688964	+	0.500562i	−0.187355	+	0.982292i	$0.559992\pi$
$284$	−2.26393	−	6.96767i	−0.134340	−	0.413455i
$285$	−8.47214			−0.501846
$286$	4.54508	−	18.0701i	0.268757	−	1.06851i
$287$	8.94427			0.527964
$288$	−0.118034	−	0.363271i	−0.00695522	−	0.0214060i
$289$	−3.50000	−	2.54290i	−0.205882	−	0.149582i
$290$	4.73607	−	3.44095i	0.278111	−	0.202060i
$291$	−1.69098	+	5.20431i	−0.0991272	+	0.305082i
$292$	1.33688	−	4.11450i	0.0782350	−	0.240783i
$293$	20.5623	−	14.9394i	1.20126	−	0.872768i	0.206854	−	0.978372i	$-0.433677\pi$
$293$	20.5623	−	14.9394i	1.20126	−	0.872768i	0.994408	+	0.105603i	$0.0336774\pi$
$294$	−1.30902	−	0.951057i	−0.0763434	−	0.0554667i
$295$	1.47214	+	4.53077i	0.0857111	+	0.263792i
$296$	−3.70820			−0.215535
$297$	−6.76393	−	16.8415i	−0.392483	−	0.977243i
$298$	20.8541			1.20805
$299$	14.7082	+	45.2672i	0.850597	+	2.61787i
$300$	−1.30902	−	0.951057i	−0.0755761	−	0.0549093i
$301$	−2.61803	+	1.90211i	−0.150901	+	0.109636i
$302$	6.60739	−	20.3355i	0.380213	−	1.17017i
$303$	−2.61803	+	8.05748i	−0.150402	+	0.462890i
$304$	4.23607	−	3.07768i	0.242955	−	0.176517i
$305$	9.47214	+	6.88191i	0.542373	+	0.394057i
$306$	−0.545085	−	1.67760i	−0.0311604	−	0.0959020i
$307$	−33.4508			−1.90914			−0.954570	−	0.297985i	$-0.903685\pi$
$307$	−33.4508			−1.90914			−0.954570	+	0.297985i	$0.903685\pi$
$308$	1.23607	+	3.07768i	0.0704315	+	0.175367i
$309$	5.76393			0.327899
$310$	1.61803	+	4.97980i	0.0918982	+	0.282833i
$311$	−8.23607	−	5.98385i	−0.467025	−	0.339313i	0.329256	−	0.944241i	$-0.393202\pi$
$311$	−8.23607	−	5.98385i	−0.467025	−	0.339313i	−0.796281	+	0.604927i	$0.793202\pi$
$312$	−7.35410	+	5.34307i	−0.416344	+	0.302492i
$313$	3.67376	−	11.3067i	0.207653	−	0.639091i	−0.791941	−	0.610598i	$-0.790929\pi$
$313$	3.67376	−	11.3067i	0.207653	−	0.639091i	0.999594	−	0.0284931i	$-0.00907087\pi$
$314$	−3.42705	+	10.5474i	−0.193400	+	0.595223i
$315$	0.309017	−	0.224514i	0.0174111	−	0.0126499i
$316$	0.690983	+	0.502029i	0.0388708	+	0.0282413i
$317$	5.52786	+	17.0130i	0.310476	+	0.955546i	0.977577	+	0.210579i	$0.0675349\pi$
$317$	5.52786	+	17.0130i	0.310476	+	0.955546i	−0.667101	+	0.744967i	$0.732465\pi$
$318$	10.4721			0.587248
$319$	−4.73607	+	18.8294i	−0.265169	+	1.05424i
$320$	1.00000			0.0559017
$321$	−5.38197	−	16.5640i	−0.300392	−	0.924512i
$322$	−6.85410	−	4.97980i	−0.381964	−	0.277513i
$323$	19.5623	−	14.2128i	1.08848	−	0.790824i
$324$	−2.38197	+	7.33094i	−0.132331	+	0.407274i
$325$	1.73607	−	5.34307i	0.0962997	−	0.296380i
$326$	11.8541	−	8.61251i	0.656538	−	0.477003i
$327$	−4.61803	−	3.35520i	−0.255378	−	0.185543i
$328$	2.76393	+	8.50651i	0.152613	+	0.469693i
$329$	−13.0902			−0.721684
$330$	5.35410	−	0.363271i	0.294734	−	0.0199974i
$331$	−6.38197			−0.350785			−0.175392	−	0.984499i	$-0.556119\pi$
$331$	−6.38197			−0.350785			−0.175392	+	0.984499i	$0.556119\pi$
$332$	4.20820	+	12.9515i	0.230955	+	0.710807i
$333$	−1.14590	−	0.832544i	−0.0627948	−	0.0456231i
$334$	−16.1803	+	11.7557i	−0.885349	+	0.643244i
$335$	−0.381966	+	1.17557i	−0.0208690	+	0.0642283i
$336$	0.500000	−	1.53884i	0.0272772	−	0.0839507i
$337$	−6.47214	+	4.70228i	−0.352560	+	0.256150i	−0.749942	−	0.661503i	$-0.769919\pi$
$337$	−6.47214	+	4.70228i	−0.352560	+	0.256150i	0.397382	+	0.917653i	$0.369919\pi$
$338$	−15.0172	−	10.9106i	−0.816829	−	0.593461i
$339$	−0.763932	−	2.35114i	−0.0414911	−	0.127696i
$340$	4.61803			0.250448
$341$	−14.7082	−	9.23305i	−0.796494	−	0.499998i
$342$	2.00000			0.108148
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−2.61803	−	1.90211i	−0.141155	−	0.102555i
$345$	−11.0902	+	8.05748i	−0.597075	+	0.433800i
$346$	−4.79180	+	14.7476i	−0.257609	+	0.792838i
$347$	8.00000	−	24.6215i	0.429463	−	1.32175i	−0.469193	−	0.883095i	$-0.655455\pi$
$347$	8.00000	−	24.6215i	0.429463	−	1.32175i	0.898656	−	0.438654i	$-0.144545\pi$
$348$	7.66312	−	5.56758i	0.410786	−	0.298454i
$349$	21.7984	+	15.8374i	1.16684	+	0.847759i	0.990627	−	0.136593i	$-0.0436153\pi$
$349$	21.7984	+	15.8374i	1.16684	+	0.847759i	0.176213	+	0.984352i	$0.443615\pi$
$350$	0.309017	+	0.951057i	0.0165177	+	0.0508361i
$351$	−30.7426			−1.64092
$352$	−2.54508	+	2.12663i	−0.135653	+	0.113350i
$353$	−24.4508			−1.30139			−0.650694	−	0.759340i	$-0.725522\pi$
$353$	−24.4508			−1.30139			−0.650694	+	0.759340i	$0.725522\pi$
$354$	2.38197	+	7.33094i	0.126600	+	0.389635i
$355$	5.92705	+	4.30625i	0.314575	+	0.228552i
$356$	−0.236068	+	0.171513i	−0.0125116	+	0.00909019i
$357$	2.30902	−	7.10642i	0.122206	−	0.376112i
$358$	−6.04508	+	18.6049i	−0.319493	+	0.983297i
$359$	−14.5451	+	10.5676i	−0.767660	+	0.557738i	−0.901250	−	0.433299i	$-0.857349\pi$
$359$	−14.5451	+	10.5676i	−0.767660	+	0.557738i	0.133590	+	0.991037i	$0.457349\pi$
$360$	0.309017	+	0.224514i	0.0162866	+	0.0118329i
$361$	2.60081	+	8.00448i	0.136885	+	0.421288i
$362$		0			0
$363$	−12.8541	+	12.3107i	−0.674665	+	0.646146i
$364$	5.61803			0.294465
$365$	1.33688	+	4.11450i	0.0699756	+	0.215363i
$366$	15.3262	+	11.1352i	0.801115	+	0.582044i
$367$	−28.5795	+	20.7642i	−1.49184	+	1.08388i	−0.518345	+	0.855171i	$0.673452\pi$
$367$	−28.5795	+	20.7642i	−1.49184	+	1.08388i	−0.973494	+	0.228713i	$0.926548\pi$
$368$	2.61803	−	8.05748i	0.136474	−	0.420025i
$369$	−1.05573	+	3.24920i	−0.0549590	+	0.169146i
$370$	3.00000	−	2.17963i	0.155963	−	0.113313i
$371$	−5.23607	−	3.80423i	−0.271843	−	0.197506i
$372$	2.61803	+	8.05748i	0.135739	+	0.417761i
$373$	−2.65248			−0.137340			−0.0686700	−	0.997639i	$-0.521876\pi$
$373$	−2.65248			−0.137340			−0.0686700	+	0.997639i	$0.521876\pi$
$374$	−11.7533	+	9.82084i	−0.607748	+	0.507823i
$375$	1.61803			0.0835549
$376$	−4.04508	−	12.4495i	−0.208609	−	0.642033i
$377$	26.6074	+	19.3314i	1.37035	+	0.995618i
$378$	4.42705	−	3.21644i	0.227703	−	0.165436i
$379$	4.98936	−	15.3557i	0.256286	−	0.788767i	−0.737288	−	0.675579i	$-0.763894\pi$
$379$	4.98936	−	15.3557i	0.256286	−	0.788767i	0.993574	−	0.113188i	$-0.0361063\pi$
$380$	−1.61803	+	4.97980i	−0.0830034	+	0.255458i
$381$	−26.4164	+	19.1926i	−1.35335	+	0.983269i
$382$	−0.690983	−	0.502029i	−0.0353538	−	0.0256860i
$383$	2.73607	+	8.42075i	0.139807	+	0.430280i	0.996307	−	0.0858666i	$-0.0273659\pi$
$383$	2.73607	+	8.42075i	0.139807	+	0.430280i	−0.856500	+	0.516147i	$0.827366\pi$
$384$	1.61803			0.0825700
$385$	−2.80902	−	1.76336i	−0.143161	−	0.0898689i
$386$	12.9443			0.658846
$387$	−0.381966	−	1.17557i	−0.0194164	−	0.0597576i
$388$	2.73607	+	1.98787i	0.138903	+	0.100919i
$389$	16.3992	−	11.9147i	0.831472	−	0.604100i	−0.0885036	−	0.996076i	$-0.528208\pi$
$389$	16.3992	−	11.9147i	0.831472	−	0.604100i	0.919975	+	0.391976i	$0.128208\pi$
$390$	2.80902	−	8.64527i	0.142240	−	0.437770i
$391$	12.0902	−	37.2097i	0.611426	−	1.88178i
$392$	−0.809017	+	0.587785i	−0.0408615	+	0.0296876i
$393$	14.9443	+	10.8576i	0.753839	+	0.547696i
$394$	−4.76393	−	14.6619i	−0.240003	−	0.738655i
$395$	−0.854102			−0.0429745
$396$	−1.26393	+	0.0857567i	−0.0635150	+	0.00430944i
$397$	−30.5623			−1.53388			−0.766939	−	0.641720i	$-0.778221\pi$
$397$	−30.5623			−1.53388			−0.766939	+	0.641720i	$0.778221\pi$
$398$	−3.38197	−	10.4086i	−0.169523	−	0.521737i
$399$	6.85410	+	4.97980i	0.343134	+	0.249302i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−11.3156	+	34.8258i	−0.565074	+	1.73912i	0.102658	+	0.994717i	$0.467265\pi$
$401$	−11.3156	+	34.8258i	−0.565074	+	1.73912i	−0.667732	+	0.744402i	$0.732735\pi$
$402$	−0.618034	+	1.90211i	−0.0308247	+	0.0948688i
$403$	−23.7984	+	17.2905i	−1.18548	+	0.861303i
$404$	4.23607	+	3.07768i	0.210752	+	0.153120i
$405$	−2.38197	−	7.33094i	−0.118361	−	0.364277i
$406$	−5.85410			−0.290534
$407$	−3.00000	+	11.9272i	−0.148704	+	0.591210i
$408$	7.47214			0.369926
$409$	1.61803	+	4.97980i	0.0800066	+	0.246235i	0.983057	−	0.183299i	$-0.0586777\pi$
$409$	1.61803	+	4.97980i	0.0800066	+	0.246235i	−0.903051	+	0.429534i	$0.858678\pi$
$410$	−7.23607	−	5.25731i	−0.357364	−	0.259640i
$411$	20.9443	−	15.2169i	1.03310	−	0.750595i
$412$	1.10081	−	3.38795i	0.0542332	−	0.166913i
$413$	1.47214	−	4.53077i	0.0724391	−	0.222945i
$414$	2.61803	−	1.90211i	0.128669	−	0.0934838i
$415$	−11.0172	−	8.00448i	−0.540814	−	0.392924i
$416$	1.73607	+	5.34307i	0.0851177	+	0.261965i
$417$	14.4721			0.708704
$418$	−6.47214	−	16.1150i	−0.316563	−	0.788208i
$419$	6.94427			0.339250			0.169625	−	0.985509i	$-0.445744\pi$
$419$	6.94427			0.339250			0.169625	+	0.985509i	$0.445744\pi$
$420$	0.500000	+	1.53884i	0.0243975	+	0.0750878i
$421$	9.16312	+	6.65740i	0.446583	+	0.324462i	0.788245	−	0.615361i	$-0.210990\pi$
$421$	9.16312	+	6.65740i	0.446583	+	0.324462i	−0.341662	+	0.939823i	$0.610990\pi$
$422$	−12.3992	+	9.00854i	−0.603583	+	0.438529i
$423$	1.54508	−	4.75528i	0.0751246	−	0.231210i
$424$	2.00000	−	6.15537i	0.0971286	−	0.298931i
$425$	−3.73607	+	2.71441i	−0.181226	+	0.131668i
$426$	9.59017	+	6.96767i	0.464645	+	0.337585i
$427$	−3.61803	−	11.1352i	−0.175089	−	0.538868i
$428$	−10.7639			−0.520294
$429$	11.2361	+	27.9767i	0.542482	+	1.35073i
$430$	3.23607			0.156057
$431$	−4.80902	−	14.8006i	−0.231642	−	0.712921i	−0.997549	−	0.0699699i	$-0.977710\pi$
$431$	−4.80902	−	14.8006i	−0.231642	−	0.712921i	0.765907	−	0.642951i	$-0.222290\pi$
$432$	4.42705	+	3.21644i	0.212997	+	0.154751i
$433$	−3.30902	+	2.40414i	−0.159021	+	0.115536i	−0.664450	−	0.747333i	$-0.731334\pi$
$433$	−3.30902	+	2.40414i	−0.159021	+	0.115536i	0.505429	+	0.862868i	$0.331334\pi$
$434$	1.61803	−	4.97980i	0.0776681	−	0.239038i
$435$	−2.92705	+	9.00854i	−0.140341	+	0.431926i
$436$	−2.85410	+	2.07363i	−0.136687	+	0.0993087i
$437$	35.8885	+	26.0746i	1.71678	+	1.24732i
$438$	2.16312	+	6.65740i	0.103358	+	0.318103i
$439$	−10.6525			−0.508415			−0.254207	−	0.967150i	$-0.581815\pi$
$439$	−10.6525			−0.508415			−0.254207	+	0.967150i	$0.581815\pi$
$440$	0.809017	−	3.21644i	0.0385684	−	0.153338i
$441$	−0.381966			−0.0181889
$442$	8.01722	+	24.6745i	0.381340	+	1.17364i
$443$	12.3262	+	8.95554i	0.585637	+	0.425490i	0.840752	−	0.541420i	$-0.182113\pi$
$443$	12.3262	+	8.95554i	0.585637	+	0.425490i	−0.255115	+	0.966911i	$0.582113\pi$
$444$	4.85410	−	3.52671i	0.230365	−	0.167370i
$445$	0.0901699	−	0.277515i	0.00427447	−	0.0131555i
$446$	−5.70820	+	17.5680i	−0.270291	+	0.831871i
$447$	−27.2984	+	19.8334i	−1.29117	+	0.938089i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	−6.02786	−	18.5519i	−0.284472	−	0.875516i	−0.986556	−	0.163422i	$-0.947747\pi$
$449$	−6.02786	−	18.5519i	−0.284472	−	0.875516i	0.702084	−	0.712094i	$-0.252253\pi$
$450$	−0.381966			−0.0180061
$451$	29.5967	−	2.00811i	1.39366	−	0.0945584i
$452$	−1.52786			−0.0718647
$453$	10.6910	+	32.9035i	0.502306	+	1.54594i
$454$	−5.78115	−	4.20025i	−0.271323	−	0.197128i
$455$	−4.54508	+	3.30220i	−0.213077	+	0.154809i
$456$	−2.61803	+	8.05748i	−0.122601	+	0.377326i
$457$	−4.32624	+	13.3148i	−0.202373	+	0.622840i	0.797438	+	0.603401i	$0.206188\pi$
$457$	−4.32624	+	13.3148i	−0.202373	+	0.622840i	−0.999811	+	0.0194390i	$0.993812\pi$
$458$	−6.23607	+	4.53077i	−0.291392	+	0.211709i
$459$	20.4443	+	14.8536i	0.954257	+	0.693308i
$460$	2.61803	+	8.05748i	0.122066	+	0.375682i
$461$	25.1246			1.17017			0.585085	−	0.810972i	$-0.301061\pi$
$461$	25.1246			1.17017			0.585085	+	0.810972i	$0.301061\pi$
$462$	−4.54508	−	2.85317i	−0.211456	−	0.132741i
$463$	−14.1803			−0.659016			−0.329508	−	0.944153i	$-0.606883\pi$
$463$	−14.1803			−0.659016			−0.329508	+	0.944153i	$0.606883\pi$
$464$	−1.80902	−	5.56758i	−0.0839815	−	0.258468i
$465$	−6.85410	−	4.97980i	−0.317851	−	0.230933i
$466$	13.4721	−	9.78808i	0.624085	−	0.453424i
$467$	6.68034	−	20.5600i	0.309129	−	0.951402i	−0.668975	−	0.743285i	$-0.733267\pi$
$467$	6.68034	−	20.5600i	0.309129	−	0.951402i	0.978104	−	0.208117i	$-0.0667334\pi$
$468$	−0.663119	+	2.04087i	−0.0306527	+	0.0943393i
$469$	1.00000	−	0.726543i	0.0461757	−	0.0335486i
$470$	10.5902	+	7.69421i	0.488488	+	0.354907i
$471$	−5.54508	−	17.0660i	−0.255504	−	0.786361i
$472$	4.76393			0.219278
$473$	−8.23607	+	6.88191i	−0.378695	+	0.316431i
$474$	−1.38197			−0.0634758
$475$	−1.61803	−	4.97980i	−0.0742405	−	0.228489i
$476$	−3.73607	−	2.71441i	−0.171242	−	0.124415i
$477$	2.00000	−	1.45309i	0.0915737	−	0.0665322i
$478$	2.73607	−	8.42075i	0.125145	−	0.385156i
$479$	−10.8541	+	33.4055i	−0.495937	+	1.52634i	0.319555	+	0.947568i	$0.396466\pi$
$479$	−10.8541	+	33.4055i	−0.495937	+	1.52634i	−0.815492	+	0.578768i	$0.803534\pi$
$480$	−1.30902	+	0.951057i	−0.0597482	+	0.0434096i
$481$	16.8541	+	12.2452i	0.768481	+	0.558334i
$482$	−1.14590	−	3.52671i	−0.0521942	−	0.160637i
$483$	13.7082			0.623745
$484$	4.78115	+	9.90659i	0.217325	+	0.450300i
$485$	−3.38197			−0.153567
$486$	1.21885	+	3.75123i	0.0552880	+	0.170159i
$487$	−9.56231	−	6.94742i	−0.433309	−	0.314818i	0.349661	−	0.936876i	$-0.386297\pi$
$487$	−9.56231	−	6.94742i	−0.433309	−	0.314818i	−0.782971	+	0.622058i	$0.786297\pi$
$488$	9.47214	−	6.88191i	0.428783	−	0.311529i
$489$	−7.32624	+	22.5478i	−0.331304	+	1.01965i
$490$	0.309017	−	0.951057i	0.0139600	−	0.0429644i
$491$	−0.763932	+	0.555029i	−0.0344758	+	0.0250481i	−0.604890	−	0.796309i	$-0.706783\pi$
$491$	−0.763932	+	0.555029i	−0.0344758	+	0.0250481i	0.570414	+	0.821357i	$0.306783\pi$
$492$	−11.7082	−	8.50651i	−0.527847	−	0.383503i
$493$	−8.35410	−	25.7113i	−0.376250	−	1.15798i
$494$	−29.4164			−1.32351
$495$	0.972136	−	0.812299i	0.0436943	−	0.0365101i
$496$	5.23607			0.235106
$497$	−2.26393	−	6.96767i	−0.101551	−	0.312543i
$498$	−17.8262	−	12.9515i	−0.798813	−	0.580371i
$499$	20.0623	−	14.5761i	0.898112	−	0.652517i	−0.0398683	−	0.999205i	$-0.512694\pi$
$499$	20.0623	−	14.5761i	0.898112	−	0.652517i	0.937980	+	0.346688i	$0.112694\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	10.0000	−	30.7768i	0.446767	−	1.37501i
$502$	−0.618034	+	0.449028i	−0.0275842	+	0.0200411i
$503$	−21.0172	−	15.2699i	−0.937112	−	0.680851i	0.0106121	−	0.999944i	$-0.496622\pi$
$503$	−21.0172	−	15.2699i	−0.937112	−	0.680851i	−0.947724	+	0.319092i	$0.896622\pi$
$504$	−0.118034	−	0.363271i	−0.00525765	−	0.0161814i
$505$	−5.23607			−0.233002
$506$	−23.7984	−	14.9394i	−1.05797	−	0.664137i
$507$	30.0344			1.33388
$508$	6.23607	+	19.1926i	0.276681	+	0.851536i
$509$	16.0902	+	11.6902i	0.713184	+	0.518159i	0.884199	−	0.467110i	$-0.154705\pi$
$509$	16.0902	+	11.6902i	0.713184	+	0.518159i	−0.171015	+	0.985268i	$0.554705\pi$
$510$	−6.04508	+	4.39201i	−0.267681	+	0.194482i
$511$	1.33688	−	4.11450i	0.0591401	−	0.182015i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−23.1803	+	16.8415i	−1.02344	+	0.743571i
$514$	10.7361	+	7.80021i	0.473548	+	0.344053i
$515$	1.10081	+	3.38795i	0.0485076	+	0.149291i
$516$	5.23607			0.230505
$517$	−43.3156	+	2.93893i	−1.90502	+	0.129254i
$518$	−3.70820			−0.162929
$519$	−7.75329	−	23.8622i	−0.340332	−	1.04743i
$520$	−4.54508	−	3.30220i	−0.199315	−	0.144811i
$521$	26.3262	−	19.1271i	1.15337	−	0.837975i	0.164448	−	0.986386i	$-0.447416\pi$
$521$	26.3262	−	19.1271i	1.15337	−	0.837975i	0.988926	+	0.148411i	$0.0474158\pi$
$522$	0.690983	−	2.12663i	0.0302435	−	0.0930799i
$523$	−3.01064	+	9.26581i	−0.131646	+	0.405165i	−0.995053	−	0.0993425i	$-0.968326\pi$
$523$	−3.01064	+	9.26581i	−0.131646	+	0.405165i	0.863407	+	0.504508i	$0.168326\pi$
$524$	9.23607	−	6.71040i	0.403480	−	0.293145i
$525$	−1.30902	−	0.951057i	−0.0571302	−	0.0415075i
$526$	4.41641	+	13.5923i	0.192565	+	0.592653i
$527$	24.1803			1.05331
$528$	1.30902	−	5.20431i	0.0569677	−	0.226489i
$529$	48.7771			2.12074
$530$	2.00000	+	6.15537i	0.0868744	+	0.267372i
$531$	1.47214	+	1.06957i	0.0638853	+	0.0464154i
$532$	4.23607	−	3.07768i	0.183657	−	0.133435i
$533$	15.5279	−	47.7899i	0.672586	−	2.07001i
$534$	0.145898	−	0.449028i	0.00631363	−	0.0194313i
$535$	8.70820	−	6.32688i	0.376488	−	0.273535i
$536$	1.00000	+	0.726543i	0.0431934	+	0.0313819i
$537$	−9.78115	−	30.1033i	−0.422088	−	1.29905i
$538$	19.7082			0.849681
$539$	1.23607	+	3.07768i	0.0532412	+	0.132565i
$540$	−5.47214			−0.235483
$541$	−2.50000	−	7.69421i	−0.107483	−	0.330800i	0.882822	−	0.469708i	$-0.155641\pi$
$541$	−2.50000	−	7.69421i	−0.107483	−	0.330800i	−0.990305	+	0.138908i	$0.955641\pi$
$542$	−12.2361	−	8.89002i	−0.525584	−	0.381859i
$543$		0			0
$544$	1.42705	−	4.39201i	0.0611843	−	0.188306i
$545$	1.09017	−	3.35520i	0.0466977	−	0.143721i
$546$	−7.35410	+	5.34307i	−0.314727	+	0.228662i
$547$	17.9443	+	13.0373i	0.767242	+	0.557434i	0.901123	−	0.433564i	$-0.142744\pi$
$547$	17.9443	+	13.0373i	0.767242	+	0.557434i	−0.133881	+	0.990997i	$0.542744\pi$
$548$	−4.94427	−	15.2169i	−0.211209	−	0.650034i
$549$	4.47214			0.190866
$550$	1.23607	+	3.07768i	0.0527061	+	0.131233i
$551$	30.6525			1.30584
$552$	4.23607	+	13.0373i	0.180299	+	0.554903i
$553$	0.690983	+	0.502029i	0.0293836	+	0.0213484i
$554$	−10.8541	+	7.88597i	−0.461147	+	0.335043i
$555$	−1.85410	+	5.70634i	−0.0787022	+	0.242221i
$556$	2.76393	−	8.50651i	0.117217	−	0.360756i
$557$	36.8885	−	26.8011i	1.56302	−	1.13560i	0.629538	−	0.776970i	$-0.283244\pi$
$557$	36.8885	−	26.8011i	1.56302	−	1.13560i	0.933480	−	0.358629i	$-0.116756\pi$
$558$	1.61803	+	1.17557i	0.0684968	+	0.0497659i
$559$	5.61803	+	17.2905i	0.237618	+	0.731312i
$560$	1.00000			0.0422577
$561$	6.04508	−	24.0337i	0.255224	−	1.01470i
$562$	18.3607			0.774499
$563$	−7.28115	−	22.4091i	−0.306864	−	0.944430i	−0.978975	−	0.203980i	$-0.934612\pi$
$563$	−7.28115	−	22.4091i	−0.306864	−	0.944430i	0.672111	−	0.740450i	$-0.265388\pi$
$564$	17.1353	+	12.4495i	0.721524	+	0.524218i
$565$	1.23607	−	0.898056i	0.0520018	−	0.0377815i
$566$	−4.42705	+	13.6251i	−0.186083	+	0.572704i
$567$	−2.38197	+	7.33094i	−0.100033	+	0.307870i
$568$	5.92705	−	4.30625i	0.248694	−	0.180686i
$569$	−15.2082	−	11.0494i	−0.637561	−	0.463215i	0.221450	−	0.975172i	$-0.428921\pi$
$569$	−15.2082	−	11.0494i	−0.637561	−	0.463215i	−0.859011	+	0.511956i	$0.828921\pi$
$570$	−2.61803	−	8.05748i	−0.109657	−	0.337491i
$571$	−43.8541			−1.83524			−0.917619	−	0.397462i	$-0.869891\pi$
$571$	−43.8541			−1.83524			−0.917619	+	0.397462i	$0.869891\pi$
$572$	18.5902	−	1.26133i	0.777294	−	0.0527387i
$573$	1.38197			0.0577325
$574$	2.76393	+	8.50651i	0.115364	+	0.355055i
$575$	−6.85410	−	4.97980i	−0.285836	−	0.207672i
$576$	0.309017	−	0.224514i	0.0128757	−	0.00935475i
$577$	13.0451	−	40.1486i	0.543074	−	1.67141i	−0.182452	−	0.983215i	$-0.558403\pi$
$577$	13.0451	−	40.1486i	0.543074	−	1.67141i	0.725526	−	0.688195i	$-0.241597\pi$
$578$	1.33688	−	4.11450i	0.0556069	−	0.171141i
$579$	−16.9443	+	12.3107i	−0.704180	+	0.511617i
$580$	4.73607	+	3.44095i	0.196655	+	0.142878i
$581$	4.20820	+	12.9515i	0.174586	+	0.537320i
$582$	−5.47214			−0.226827
$583$	−18.1803	−	11.4127i	−0.752953	−	0.472665i
$584$	4.32624			0.179021
$585$	−0.663119	−	2.04087i	−0.0274166	−	0.0843796i
$586$	20.5623	+	14.9394i	0.849421	+	0.617141i
$587$	−15.7812	+	11.4657i	−0.651358	+	0.473239i	−0.863733	−	0.503949i	$-0.831880\pi$
$587$	−15.7812	+	11.4657i	−0.651358	+	0.473239i	0.212376	+	0.977188i	$0.431880\pi$
$588$	0.500000	−	1.53884i	0.0206197	−	0.0634608i
$589$	−8.47214	+	26.0746i	−0.349088	+	1.07438i
$590$	−3.85410	+	2.80017i	−0.158671	+	0.115281i
$591$	20.1803	+	14.6619i	0.830108	+	0.603109i
$592$	−1.14590	−	3.52671i	−0.0470961	−	0.144947i
$593$	14.7984			0.607696			0.303848	−	0.952720i	$-0.401728\pi$
$593$	14.7984			0.607696			0.303848	+	0.952720i	$0.401728\pi$
$594$	13.9271	−	11.6372i	0.571434	−	0.477480i
$595$	4.61803			0.189321
$596$	6.44427	+	19.8334i	0.263968	+	0.812409i
$597$	14.3262	+	10.4086i	0.586334	+	0.425997i
$598$	−38.5066	+	27.9767i	−1.57465	+	1.14405i
$599$	11.8647	−	36.5159i	0.484780	−	1.49200i	−0.347518	−	0.937673i	$-0.612976\pi$
$599$	11.8647	−	36.5159i	0.484780	−	1.49200i	0.832299	−	0.554327i	$-0.187024\pi$
$600$	0.500000	−	1.53884i	0.0204124	−	0.0628230i
$601$	6.47214	−	4.70228i	0.264004	−	0.191810i	−0.447906	−	0.894080i	$-0.647830\pi$
$601$	6.47214	−	4.70228i	0.264004	−	0.191810i	0.711910	+	0.702270i	$0.247830\pi$
$602$	−2.61803	−	1.90211i	−0.106703	−	0.0775243i
$603$	0.145898	+	0.449028i	0.00594143	+	0.0182858i
$604$	21.3820			0.870020
$605$	−9.69098	−	5.20431i	−0.393994	−	0.211585i
$606$	−8.47214			−0.344157
$607$	−11.9549	−	36.7934i	−0.485235	−	1.49340i	−0.831640	−	0.555315i	$-0.812598\pi$
$607$	−11.9549	−	36.7934i	−0.485235	−	1.49340i	0.346405	−	0.938085i	$-0.387402\pi$
$608$	4.23607	+	3.07768i	0.171795	+	0.124817i
$609$	7.66312	−	5.56758i	0.310525	−	0.225610i
$610$	−3.61803	+	11.1352i	−0.146490	+	0.450850i
$611$	−22.7254	+	69.9417i	−0.919372	+	2.82954i
$612$	1.42705	−	1.03681i	0.0576851	−	0.0419107i
$613$	18.5623	+	13.4863i	0.749724	+	0.544707i	0.895741	−	0.444575i	$-0.146645\pi$
$613$	18.5623	+	13.4863i	0.749724	+	0.544707i	−0.146017	+	0.989282i	$0.546645\pi$
$614$	−10.3369	−	31.8136i	−0.417163	−	1.28389i
$615$	14.4721			0.583573
$616$	−2.54508	+	2.12663i	−0.102544	+	0.0856842i
$617$	−3.81966			−0.153774			−0.0768869	−	0.997040i	$-0.524498\pi$
$617$	−3.81966			−0.153774			−0.0768869	+	0.997040i	$0.524498\pi$
$618$	1.78115	+	5.48183i	0.0716485	+	0.220511i
$619$	−0.472136	−	0.343027i	−0.0189767	−	0.0137874i	0.578256	−	0.815855i	$-0.303733\pi$
$619$	−0.472136	−	0.343027i	−0.0189767	−	0.0137874i	−0.597233	+	0.802068i	$0.703733\pi$
$620$	−4.23607	+	3.07768i	−0.170125	+	0.123603i
$621$	−14.3262	+	44.0916i	−0.574892	+	1.76934i
$622$	3.14590	−	9.68208i	0.126139	−	0.388216i
$623$	−0.236068	+	0.171513i	−0.00945786	+	0.00687154i
$624$	−7.35410	−	5.34307i	−0.294400	−	0.213894i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	11.8885			0.475162
$627$	23.7984	+	14.9394i	0.950416	+	0.596622i
$628$	−11.0902			−0.442546
$629$	−5.29180	−	16.2865i	−0.210998	−	0.649384i
$630$	0.309017	+	0.224514i	0.0123115	+	0.00894485i
$631$	−7.64590	+	5.55507i	−0.304378	+	0.221144i	−0.729481	−	0.684002i	$-0.760238\pi$
$631$	−7.64590	+	5.55507i	−0.304378	+	0.221144i	0.425102	+	0.905145i	$0.360238\pi$
$632$	−0.263932	+	0.812299i	−0.0104987	+	0.0323115i
$633$	7.66312	−	23.5847i	0.304582	−	0.937406i
$634$	−14.4721	+	10.5146i	−0.574762	+	0.417589i
$635$	−16.3262	−	11.8617i	−0.647887	−	0.470717i
$636$	3.23607	+	9.95959i	0.128318	+	0.394924i
$637$	5.61803			0.222595
$638$	−19.3713	+	1.31433i	−0.766918	+	0.0520347i
$639$	2.79837			0.110702
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−7.92705	−	5.75934i	−0.313100	−	0.227480i	0.420126	−	0.907466i	$-0.361986\pi$
$641$	−7.92705	−	5.75934i	−0.313100	−	0.227480i	−0.733225	+	0.679986i	$0.761986\pi$
$642$	14.0902	−	10.2371i	0.556095	−	0.404026i
$643$	−4.68034	+	14.4046i	−0.184575	+	0.568062i	−0.999941	−	0.0108834i	$-0.996536\pi$
$643$	−4.68034	+	14.4046i	−0.184575	+	0.568062i	0.815366	+	0.578946i	$0.196536\pi$
$644$	2.61803	−	8.05748i	0.103165	−	0.317509i
$645$	−4.23607	+	3.07768i	−0.166795	+	0.121184i
$646$	19.5623	+	14.2128i	0.769669	+	0.559197i
$647$	−12.8992	−	39.6996i	−0.507119	−	1.56075i	−0.797178	−	0.603744i	$-0.793675\pi$
$647$	−12.8992	−	39.6996i	−0.507119	−	1.56075i	0.290059	−	0.957009i	$-0.406325\pi$
$648$	−7.70820			−0.302807
$649$	3.85410	−	15.3229i	0.151287	−	0.601477i
$650$	5.61803			0.220357
$651$	2.61803	+	8.05748i	0.102609	+	0.315798i
$652$	11.8541	+	8.61251i	0.464242	+	0.337292i
$653$	11.5623	−	8.40051i	0.452468	−	0.328737i	−0.338101	−	0.941110i	$-0.609785\pi$
$653$	11.5623	−	8.40051i	0.452468	−	0.328737i	0.790569	+	0.612372i	$0.209785\pi$
$654$	1.76393	−	5.42882i	0.0689752	−	0.212284i
$655$	−3.52786	+	10.8576i	−0.137845	+	0.424243i
$656$	−7.23607	+	5.25731i	−0.282521	+	0.205264i
$657$	1.33688	+	0.971301i	0.0521567	+	0.0378941i
$658$	−4.04508	−	12.4495i	−0.157694	−	0.485332i
$659$	5.25735			0.204797			0.102399	−	0.994743i	$-0.467348\pi$
$659$	5.25735			0.204797			0.102399	+	0.994743i	$0.467348\pi$
$660$	2.00000	+	4.97980i	0.0778499	+	0.193838i
$661$	−18.9443			−0.736847			−0.368423	−	0.929658i	$-0.620102\pi$
$661$	−18.9443			−0.736847			−0.368423	+	0.929658i	$0.620102\pi$
$662$	−1.97214	−	6.06961i	−0.0766492	−	0.235902i
$663$	−33.9615	−	24.6745i	−1.31896	−	0.958277i
$664$	−11.0172	+	8.00448i	−0.427551	+	0.310634i
$665$	−1.61803	+	4.97980i	−0.0627447	+	0.193108i
$666$	0.437694	−	1.34708i	0.0169603	−	0.0521984i
$667$	40.1246	−	29.1522i	1.55363	−	1.12878i
$668$	−16.1803	−	11.7557i	−0.626036	−	0.454842i
$669$	−9.23607	−	28.4257i	−0.357087	−	1.09900i
$670$	−1.23607			−0.0477535
$671$	−14.4721	−	36.0341i	−0.558691	−	1.39108i
$672$	1.61803			0.0624170
$673$	−1.41641	−	4.35926i	−0.0545985	−	0.168037i	0.920039	−	0.391827i	$-0.128157\pi$
$673$	−1.41641	−	4.35926i	−0.0545985	−	0.168037i	−0.974637	+	0.223790i	$0.928157\pi$
$674$	−6.47214	−	4.70228i	−0.249297	−	0.181125i
$675$	4.42705	−	3.21644i	0.170397	−	0.123801i
$676$	5.73607	−	17.6538i	0.220618	−	0.678992i
$677$	−4.30244	+	13.2415i	−0.165356	+	0.508914i	−0.999062	−	0.0432943i	$-0.986215\pi$
$677$	−4.30244	+	13.2415i	−0.165356	+	0.508914i	0.833706	+	0.552208i	$0.186215\pi$
$678$	2.00000	−	1.45309i	0.0768095	−	0.0558054i
$679$	2.73607	+	1.98787i	0.105001	+	0.0762874i
$680$	1.42705	+	4.39201i	0.0547249	+	0.168426i
$681$	11.5623			0.443069
$682$	4.23607	−	16.8415i	0.162207	−	0.644894i
$683$	−43.5967			−1.66818			−0.834092	−	0.551626i	$-0.814008\pi$
$683$	−43.5967			−1.66818			−0.834092	+	0.551626i	$0.814008\pi$
$684$	0.618034	+	1.90211i	0.0236311	+	0.0727291i
$685$	12.9443	+	9.40456i	0.494575	+	0.359330i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	3.85410	−	11.8617i	0.147043	−	0.452552i
$688$	1.00000	−	3.07768i	0.0381246	−	0.117336i
$689$	−29.4164	+	21.3723i	−1.12068	+	0.814219i
$690$	−11.0902	−	8.05748i	−0.422196	−	0.306743i
$691$	0.763932	+	2.35114i	0.0290613	+	0.0894416i	0.964535	−	0.263954i	$-0.0850268\pi$
$691$	0.763932	+	2.35114i	0.0290613	+	0.0894416i	−0.935474	+	0.353396i	$0.885027\pi$
$692$	−15.5066			−0.589472
$693$	−1.26393	+	0.0857567i	−0.0480128	+	0.00325763i
$694$	25.8885			0.982716
$695$	2.76393	+	8.50651i	0.104842	+	0.322670i
$696$	7.66312	+	5.56758i	0.290470	+	0.211039i
$697$	−33.4164	+	24.2784i	−1.26574	+	0.919612i
$698$	−8.32624	+	25.6255i	−0.315153	+	0.969940i
$699$	−8.32624	+	25.6255i	−0.314927	+	0.969246i
$700$	−0.809017	+	0.587785i	−0.0305780	+	0.0222162i
$701$	−31.9787	−	23.2339i	−1.20782	−	0.877532i	−0.212788	−	0.977098i	$-0.568255\pi$
$701$	−31.9787	−	23.2339i	−1.20782	−	0.877532i	−0.995031	+	0.0995662i	$0.968255\pi$
$702$	−9.50000	−	29.2380i	−0.358554	−	1.10352i
$703$	19.4164			0.732304
$704$	−2.80902	−	1.76336i	−0.105869	−	0.0664590i
$705$	−21.1803			−0.797698
$706$	−7.55573	−	23.2541i	−0.284364	−	0.875181i
$707$	4.23607	+	3.07768i	0.159314	+	0.115748i
$708$	−6.23607	+	4.53077i	−0.234366	+	0.170277i
$709$	2.15248	−	6.62464i	0.0808379	−	0.248794i	−0.902467	−	0.430759i	$-0.858246\pi$
$709$	2.15248	−	6.62464i	0.0808379	−	0.248794i	0.983305	+	0.181965i	$0.0582459\pi$
$710$	−2.26393	+	6.96767i	−0.0849639	+	0.261492i
$711$	−0.263932	+	0.191758i	−0.00989822	+	0.00719148i
$712$	−0.236068	−	0.171513i	−0.00884702	−	0.00642774i
$713$	13.7082	+	42.1895i	0.513376	+	1.58001i
$714$	7.47214			0.279638
$715$	−14.2984	+	11.9475i	−0.534729	+	0.446810i
$716$	−19.5623			−0.731078
$717$	4.42705	+	13.6251i	0.165331	+	0.508837i
$718$	−14.5451	−	10.5676i	−0.542818	−	0.394380i
$719$	26.1803	−	19.0211i	0.976362	−	0.709368i	0.0194693	−	0.999810i	$-0.493802\pi$
$719$	26.1803	−	19.0211i	0.976362	−	0.709368i	0.956893	+	0.290442i	$0.0938023\pi$
$720$	−0.118034	+	0.363271i	−0.00439887	+	0.0135383i
$721$	1.10081	−	3.38795i	0.0409964	−	0.126174i
$722$	−6.80902	+	4.94704i	−0.253405	+	0.184110i
$723$	4.85410	+	3.52671i	0.180526	+	0.131160i
$724$		0			0
$725$	−5.85410			−0.217416
$726$	−15.6803	−	8.42075i	−0.581952	−	0.312523i
$727$	39.3262			1.45853			0.729265	−	0.684232i	$-0.239862\pi$
$727$	39.3262			1.45853			0.729265	+	0.684232i	$0.239862\pi$
$728$	1.73607	+	5.34307i	0.0643430	+	0.198027i
$729$	−23.8713	−	17.3435i	−0.884123	−	0.642353i
$730$	−3.50000	+	2.54290i	−0.129541	+	0.0941169i
$731$	4.61803	−	14.2128i	0.170804	−	0.525681i
$732$	−5.85410	+	18.0171i	−0.216374	+	0.665930i
$733$	−4.25329	+	3.09020i	−0.157099	+	0.114139i	−0.663558	−	0.748125i	$-0.730954\pi$
$733$	−4.25329	+	3.09020i	−0.157099	+	0.114139i	0.506459	+	0.862264i	$0.330954\pi$
$734$	−28.5795	−	20.7642i	−1.05489	−	0.766422i
$735$	0.500000	+	1.53884i	0.0184428	+	0.0567610i
$736$	8.47214			0.312287
$737$	3.14590	−	2.62866i	0.115881	−	0.0968278i
$738$	−3.41641			−0.125760
$739$	−6.18034	−	19.0211i	−0.227347	−	0.699704i	−0.998045	−	0.0625022i	$-0.980092\pi$
$739$	−6.18034	−	19.0211i	−0.227347	−	0.699704i	0.770697	−	0.637201i	$-0.219908\pi$
$740$	3.00000	+	2.17963i	0.110282	+	0.0801247i
$741$	38.5066	−	27.9767i	1.41457	−	1.02775i
$742$	2.00000	−	6.15537i	0.0734223	−	0.225971i
$743$	−5.90983	+	18.1886i	−0.216811	+	0.667275i	0.782209	+	0.623016i	$0.214093\pi$
$743$	−5.90983	+	18.1886i	−0.216811	+	0.667275i	−0.999020	+	0.0442590i	$0.985907\pi$
$744$	−6.85410	+	4.97980i	−0.251284	+	0.182568i
$745$	−16.8713	−	12.2577i	−0.618117	−	0.449089i
$746$	−0.819660	−	2.52265i	−0.0300099	−	0.0923609i
$747$	−5.20163			−0.190318
$748$	−12.9721	−	8.14324i	−0.474308	−	0.297746i
$749$	−10.7639			−0.393306
$750$	0.500000	+	1.53884i	0.0182574	+	0.0561906i
$751$	12.3541	+	8.97578i	0.450808	+	0.327531i	0.789915	−	0.613217i	$-0.210125\pi$
$751$	12.3541	+	8.97578i	0.450808	+	0.327531i	−0.339107	+	0.940748i	$0.610125\pi$
$752$	10.5902	−	7.69421i	0.386184	−	0.280579i
$753$	0.381966	−	1.17557i	0.0139196	−	0.0428402i
$754$	−10.1631	+	31.2789i	−0.370119	+	1.13911i
$755$	−17.2984	+	12.5680i	−0.629552	+	0.457397i
$756$	4.42705	+	3.21644i	0.161010	+	0.116981i
$757$	−3.90983	−	12.0332i	−0.142105	−	0.437355i	0.854522	−	0.519415i	$-0.173850\pi$
$757$	−3.90983	−	12.0332i	−0.142105	−	0.437355i	−0.996627	+	0.0820601i	$0.973850\pi$
$758$	16.1459			0.586445
$759$	45.3607	−	3.07768i	1.64649	−	0.111713i
$760$	−5.23607			−0.189932
$761$	5.74265	+	17.6740i	0.208171	+	0.640684i	0.999568	+	0.0293818i	$0.00935387\pi$
$761$	5.74265	+	17.6740i	0.208171	+	0.640684i	−0.791398	+	0.611302i	$0.790646\pi$
$762$	−26.4164	−	19.1926i	−0.956965	−	0.695276i
$763$	−2.85410	+	2.07363i	−0.103325	+	0.0750703i
$764$	0.263932	−	0.812299i	0.00954873	−	0.0293880i
$765$	−0.545085	+	1.67760i	−0.0197076	+	0.0606537i
$766$	−7.16312	+	5.20431i	−0.258814	+	0.188039i
$767$	−21.6525	−	15.7314i	−0.781826	−	0.568030i
$768$	0.500000	+	1.53884i	0.0180422	+	0.0555282i
$769$	−21.7082			−0.782818			−0.391409	−	0.920217i	$-0.628012\pi$
$769$	−21.7082			−0.782818			−0.391409	+	0.920217i	$0.628012\pi$
$770$	0.809017	−	3.21644i	0.0291549	−	0.115912i
$771$	−21.4721			−0.773300
$772$	4.00000	+	12.3107i	0.143963	+	0.443073i
$773$	−31.9615	−	23.2214i	−1.14957	−	0.835215i	−0.161151	−	0.986930i	$-0.551521\pi$
$773$	−31.9615	−	23.2214i	−1.14957	−	0.835215i	−0.988424	+	0.151715i	$0.951521\pi$
$774$	1.00000	−	0.726543i	0.0359443	−	0.0261150i
$775$	1.61803	−	4.97980i	0.0581215	−	0.178880i
$776$	−1.04508	+	3.21644i	−0.0375164	+	0.115463i
$777$	4.85410	−	3.52671i	0.174140	−	0.126520i
$778$	16.3992	+	11.9147i	0.587939	+	0.427163i
$779$	−14.4721	−	44.5407i	−0.518518	−	1.59583i
$780$	9.09017			0.325480
$781$	−9.05573	−	22.5478i	−0.324039	−	0.806825i
$782$	39.1246			1.39909
$783$	9.89919	+	30.4666i	0.353768	+	1.08879i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	8.97214	−	6.51864i	0.320229	−	0.232660i
$786$	−5.70820	+	17.5680i	−0.203605	+	0.626631i
$787$	−4.91641	+	15.1311i	−0.175251	+	0.539367i	−0.999645	−	0.0266495i	$-0.991516\pi$
$787$	−4.91641	+	15.1311i	−0.175251	+	0.539367i	0.824394	+	0.566017i	$0.191516\pi$
$788$	12.4721	−	9.06154i	0.444301	−	0.322804i
$789$	−18.7082	−	13.5923i	−0.666030	−	0.483899i
$790$	−0.263932	−	0.812299i	−0.00939028	−	0.0289003i
$791$	−1.52786			−0.0543246
$792$	−0.472136	−	1.17557i	−0.0167766	−	0.0417721i
$793$	−65.7771			−2.33581
$794$	−9.44427	−	29.0665i	−0.335165	−	1.03153i
$795$	−8.47214	−	6.15537i	−0.300476	−	0.218308i
$796$	8.85410	−	6.43288i	0.313825	−	0.228007i
$797$	−10.0967	+	31.0746i	−0.357645	+	1.10072i	0.596815	+	0.802379i	$0.296433\pi$
$797$	−10.0967	+	31.0746i	−0.357645	+	1.10072i	−0.954460	+	0.298339i	$0.903567\pi$
$798$	−2.61803	+	8.05748i	−0.0926774	+	0.285232i
$799$	48.9058	−	35.5321i	1.73016	−	1.25704i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$	−0.0344419	−	0.106001i	−0.00121694	−	0.00374537i
$802$	−36.6180			−1.29303
$803$	3.50000	−	13.9151i	0.123512	−	0.491053i
$804$	−2.00000			−0.0705346
$805$	2.61803	+	8.05748i	0.0922736	+	0.283989i
$806$	−23.7984	−	17.2905i	−0.838262	−	0.609033i
$807$	−25.7984	+	18.7436i	−0.908146	+	0.659807i
$808$	−1.61803	+	4.97980i	−0.0569222	+	0.175189i
$809$	−8.55573	+	26.3318i	−0.300803	+	0.925778i	0.680407	+	0.732835i	$0.261803\pi$
$809$	−8.55573	+	26.3318i	−0.300803	+	0.925778i	−0.981210	+	0.192943i	$0.938197\pi$
$810$	6.23607	−	4.53077i	0.219113	−	0.159195i
$811$	14.6525	+	10.6456i	0.514518	+	0.373819i	0.814535	−	0.580115i	$-0.196992\pi$
$811$	14.6525	+	10.6456i	0.514518	+	0.373819i	−0.300017	+	0.953934i	$0.596992\pi$
$812$	−1.80902	−	5.56758i	−0.0634841	−	0.195384i
$813$	24.4721			0.858275
$814$	−12.2705	+	0.832544i	−0.430081	+	0.0291806i
$815$	−14.6525			−0.513254
$816$	2.30902	+	7.10642i	0.0808318	+	0.248775i
$817$	13.7082	+	9.95959i	0.479589	+	0.348442i
$818$	−4.23607	+	3.07768i	−0.148111	+	0.107609i
$819$	−0.663119	+	2.04087i	−0.0231713	+	0.0713138i
$820$	2.76393	−	8.50651i	0.0965207	−	0.297060i
$821$	−11.5000	+	8.35524i	−0.401353	+	0.291600i	−0.770092	−	0.637933i	$-0.779790\pi$
$821$	−11.5000	+	8.35524i	−0.401353	+	0.291600i	0.368739	+	0.929533i	$0.379790\pi$
$822$	20.9443	+	15.2169i	0.730515	+	0.530750i
$823$	−12.4721	−	38.3853i	−0.434751	−	1.33803i	−0.893341	−	0.449379i	$-0.851645\pi$
$823$	−12.4721	−	38.3853i	−0.434751	−	1.33803i	0.458590	−	0.888648i	$-0.348355\pi$
$824$	3.56231			0.124099
$825$	−4.54508	−	2.85317i	−0.158240	−	0.0993346i
$826$	4.76393			0.165758
$827$	−10.1803	−	31.3319i	−0.354005	−	1.08952i	−0.956584	−	0.291456i	$-0.905860\pi$
$827$	−10.1803	−	31.3319i	−0.354005	−	1.08952i	0.602579	−	0.798059i	$-0.294140\pi$
$828$	2.61803	+	1.90211i	0.0909830	+	0.0661030i
$829$	−24.1803	+	17.5680i	−0.839818	+	0.610163i	−0.922320	−	0.386427i	$-0.873709\pi$
$829$	−24.1803	+	17.5680i	−0.839818	+	0.610163i	0.0825019	+	0.996591i	$0.473709\pi$
$830$	4.20820	−	12.9515i	0.146069	−	0.449554i
$831$	6.70820	−	20.6457i	0.232705	−	0.716192i
$832$	−4.54508	+	3.30220i	−0.157572	+	0.114483i
$833$	−3.73607	−	2.71441i	−0.129447	−	0.0940488i
$834$	4.47214	+	13.7638i	0.154857	+	0.476602i
$835$	20.0000			0.692129
$836$	13.3262	−	11.1352i	0.460898	−	0.385118i
$837$	−28.6525			−0.990374
$838$	2.14590	+	6.60440i	0.0741288	+	0.228145i
$839$	0.291796	+	0.212002i	0.0100739	+	0.00731913i	0.592811	−	0.805342i	$-0.298018\pi$
$839$	0.291796	+	0.212002i	0.0100739	+	0.00731913i	−0.582737	+	0.812661i	$0.698018\pi$
$840$	−1.30902	+	0.951057i	−0.0451654	+	0.0328146i
$841$	1.62868	−	5.01255i	0.0561613	−	0.172847i
$842$	−3.50000	+	10.7719i	−0.120618	+	0.371224i
$843$	−24.0344	+	17.4620i	−0.827790	+	0.601425i
$844$	−12.3992	−	9.00854i	−0.426798	−	0.310087i
$845$	5.73607	+	17.6538i	0.197327	+	0.607309i
$846$	5.00000			0.171904
$847$	4.78115	+	9.90659i	0.164282	+	0.340395i
$848$	6.47214			0.222254
$849$	−7.16312	−	22.0458i	−0.245838	−	0.756610i
$850$	−3.73607	−	2.71441i	−0.128146	−	0.0931036i
$851$	25.4164	−	18.4661i	0.871263	−	0.633010i
$852$	−3.66312	+	11.2739i	−0.125496	+	0.386238i
$853$	2.55573	−	7.86572i	0.0875065	−	0.269317i	−0.897722	−	0.440562i	$-0.854779\pi$
$853$	2.55573	−	7.86572i	0.0875065	−	0.269317i	0.985228	+	0.171245i	$0.0547790\pi$
$854$	9.47214	−	6.88191i	0.324130	−	0.235494i
$855$	−1.61803	−	1.17557i	−0.0553356	−	0.0402037i
$856$	−3.32624	−	10.2371i	−0.113688	−	0.349897i
$857$	33.4164			1.14148			0.570741	−	0.821130i	$-0.306656\pi$
$857$	33.4164			1.14148			0.570741	+	0.821130i	$0.306656\pi$
$858$	−23.1353	+	19.3314i	−0.789825	+	0.659963i
$859$	55.4164			1.89078			0.945392	−	0.325936i	$-0.105680\pi$
$859$	55.4164			1.89078			0.945392	+	0.325936i	$0.105680\pi$
$860$	1.00000	+	3.07768i	0.0340997	+	0.104948i
$861$	−11.7082	−	8.50651i	−0.399015	−	0.289901i
$862$	12.5902	−	9.14729i	0.428823	−	0.311558i
$863$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$863$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$864$	−1.69098	+	5.20431i	−0.0575284	+	0.177054i
$865$	12.5451	−	9.11454i	0.426546	−	0.309904i
$866$	−3.30902	−	2.40414i	−0.112445	−	0.0816961i
$867$	2.16312	+	6.65740i	0.0734634	+	0.226097i
$868$	5.23607			0.177724
$869$	2.39919	+	1.50609i	0.0813868	+	0.0510905i
$870$	−9.47214			−0.321135
$871$	−2.14590	−	6.60440i	−0.0727110	−	0.223781i
$872$	−2.85410	−	2.07363i	−0.0966521	−	0.0702219i
$873$	−1.04508	+	0.759299i	−0.0353708	+	0.0256984i
$874$	−13.7082	+	42.1895i	−0.463687	+	1.42708i
$875$	0.309017	−	0.951057i	0.0104467	−	0.0321516i
$876$	−5.66312	+	4.11450i	−0.191339	+	0.139016i
$877$	−21.4721	−	15.6004i	−0.725063	−	0.526789i	0.162935	−	0.986637i	$-0.447904\pi$
$877$	−21.4721	−	15.6004i	−0.725063	−	0.526789i	−0.887998	+	0.459848i	$0.847904\pi$
$878$	−3.29180	−	10.1311i	−0.111093	−	0.341908i
$879$	−41.1246			−1.38710
$880$	3.30902	−	0.224514i	0.111547	−	0.00756837i
$881$	37.4853			1.26291			0.631456	−	0.775412i	$-0.282458\pi$
$881$	37.4853			1.26291			0.631456	+	0.775412i	$0.282458\pi$
$882$	−0.118034	−	0.363271i	−0.00397441	−	0.0122320i
$883$	34.9787	+	25.4135i	1.17713	+	0.855233i	0.991845	−	0.127452i	$-0.0406799\pi$
$883$	34.9787	+	25.4135i	1.17713	+	0.855233i	0.185283	+	0.982685i	$0.440680\pi$
$884$	−20.9894	+	15.2497i	−0.705948	+	0.512902i
$885$	2.38197	−	7.33094i	0.0800689	−	0.246427i
$886$	−4.70820	+	14.4904i	−0.158175	+	0.486813i
$887$	−29.0066	+	21.0745i	−0.973946	+	0.707613i	−0.956347	−	0.292232i	$-0.905602\pi$
$887$	−29.0066	+	21.0745i	−0.973946	+	0.707613i	−0.0175982	+	0.999845i	$0.505602\pi$
$888$	4.85410	+	3.52671i	0.162893	+	0.118349i
$889$	6.23607	+	19.1926i	0.209151	+	0.643701i
$890$	0.291796			0.00978103
$891$	−6.23607	+	24.7930i	−0.208916	+	0.830596i
$892$	−18.4721			−0.618493
$893$	21.1803	+	65.1864i	0.708773	+	2.18138i
$894$	−27.2984	−	19.8334i	−0.912994	−	0.663329i
$895$	15.8262	−	11.4984i	0.529013	−	0.384350i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	23.7984	−	73.2439i	0.794605	−	2.44554i
$898$	15.7812	−	11.4657i	0.526624	−	0.382615i
$899$	24.7984	+	18.0171i	0.827072	+	0.600903i
$900$	−0.118034	−	0.363271i	−0.00393447	−	0.0121090i
$901$	29.8885			0.995732
$902$	11.0557	+	27.5276i	0.368115	+	0.916570i
$903$	5.23607			0.174245
$904$	−0.472136	−	1.45309i	−0.0157030	−	0.0483289i
$905$		0			0
$906$	−27.9894	+	20.3355i	−0.929884	+	0.675600i
$907$	−9.38197	+	28.8747i	−0.311523	+	0.958769i	0.665639	+	0.746274i	$0.268159\pi$
$907$	−9.38197	+	28.8747i	−0.311523	+	0.958769i	−0.977162	+	0.212496i	$0.931841\pi$
$908$	2.20820	−	6.79615i	0.0732818	−	0.225538i
$909$	−1.61803	+	1.17557i	−0.0536668	+	0.0389912i
$910$	−4.54508	−	3.30220i	−0.150668	−	0.109467i
$911$	5.39261	+	16.5967i	0.178665	+	0.549875i	0.999782	−	0.0208856i	$-0.00664857\pi$
$911$	5.39261	+	16.5967i	0.178665	+	0.549875i	−0.821117	+	0.570760i	$0.806649\pi$
$912$	−8.47214			−0.280540
$913$	16.8328	+	41.9120i	0.557085	+	1.38708i
$914$	−14.0000			−0.463079
$915$	−5.85410	−	18.0171i	−0.193531	−	0.595626i
$916$	−6.23607	−	4.53077i	−0.206045	−	0.149701i
$917$	9.23607	−	6.71040i	0.305002	−	0.221597i
$918$	−7.80902	+	24.0337i	−0.257736	+	0.793230i
$919$	16.2254	−	49.9367i	0.535227	−	1.64726i	−0.207930	−	0.978144i	$-0.566673\pi$
$919$	16.2254	−	49.9367i	0.535227	−	1.64726i	0.743157	−	0.669117i	$-0.233327\pi$
$920$	−6.85410	+	4.97980i	−0.225973	+	0.164179i
$921$	43.7877	+	31.8136i	1.44285	+	1.04830i
$922$	7.76393	+	23.8949i	0.255691	+	0.786937i
$923$	−41.1591			−1.35477
$924$	1.30902	−	5.20431i	0.0430635	−	0.171209i
$925$	−3.70820			−0.121925
$926$	−4.38197	−	13.4863i	−0.144000	−	0.443187i
$927$	1.10081	+	0.799788i	0.0361554	+	0.0262685i
$928$	4.73607	−	3.44095i	0.155469	−	0.112955i
$929$	8.58359	−	26.4176i	0.281619	−	0.866733i	−0.705773	−	0.708438i	$-0.749400\pi$
$929$	8.58359	−	26.4176i	0.281619	−	0.866733i	0.987392	−	0.158295i	$-0.0505997\pi$
$930$	2.61803	−	8.05748i	0.0858487	−	0.264215i
$931$	4.23607	−	3.07768i	0.138832	−	0.100867i
$932$	13.4721	+	9.78808i	0.441294	+	0.320619i
$933$	5.09017	+	15.6659i	0.166645	+	0.512880i
$934$	21.6180			0.707364
$935$	15.2812	−	1.03681i	0.499747	−	0.0339074i
$936$	−2.14590			−0.0701409
$937$	−11.5557	−	35.5649i	−0.377509	−	1.16185i	−0.941770	−	0.336257i	$-0.890839\pi$
$937$	−11.5557	−	35.5649i	−0.377509	−	1.16185i	0.564261	−	0.825596i	$-0.309161\pi$
$938$	1.00000	+	0.726543i	0.0326512	+	0.0237225i
$939$	−15.5623	+	11.3067i	−0.507857	+	0.368979i
$940$	−4.04508	+	12.4495i	−0.131936	+	0.406058i
$941$	13.1803	−	40.5649i	0.429667	−	1.32238i	−0.468787	−	0.883311i	$-0.655309\pi$
$941$	13.1803	−	40.5649i	0.429667	−	1.32238i	0.898454	−	0.439067i	$-0.144691\pi$
$942$	14.5172	−	10.5474i	0.472997	−	0.343652i
$943$	−61.3050	−	44.5407i	−1.99636	−	1.45044i
$944$	1.47214	+	4.53077i	0.0479139	+	0.147464i
$945$	−5.47214			−0.178009
$946$	−9.09017	−	5.70634i	−0.295547	−	0.185529i
$947$	32.6525			1.06106			0.530531	−	0.847665i	$-0.321992\pi$
$947$	32.6525			1.06106			0.530531	+	0.847665i	$0.321992\pi$
$948$	−0.427051	−	1.31433i	−0.0138700	−	0.0426874i
$949$	−19.6631	−	14.2861i	−0.638292	−	0.463746i
$950$	4.23607	−	3.07768i	0.137436	−	0.0998532i
$951$	8.94427	−	27.5276i	0.290038	−	0.892645i
$952$	1.42705	−	4.39201i	0.0462510	−	0.142346i
$953$	−2.09017	+	1.51860i	−0.0677072	+	0.0491922i	−0.621124	−	0.783712i	$-0.713324\pi$
$953$	−2.09017	+	1.51860i	−0.0677072	+	0.0491922i	0.553417	+	0.832904i	$0.313324\pi$
$954$	2.00000	+	1.45309i	0.0647524	+	0.0470454i
$955$	0.263932	+	0.812299i	0.00854064	+	0.0262854i
$956$	8.85410			0.286362
$957$	24.1074	−	20.1437i	0.779281	−	0.651153i
$958$	−35.1246			−1.13482
$959$	−4.94427	−	15.2169i	−0.159659	−	0.491379i
$960$	−1.30902	−	0.951057i	−0.0422483	−	0.0306952i
$961$	2.89919	−	2.10638i	0.0935222	−	0.0679478i
$962$	−6.43769	+	19.8132i	−0.207560	+	0.638803i
$963$	1.27051	−	3.91023i	0.0409416	−	0.126005i
$964$	3.00000	−	2.17963i	0.0966235	−	0.0702011i
$965$	−10.4721	−	7.60845i	−0.337110	−	0.244925i
$966$	4.23607	+	13.0373i	0.136293	+	0.419468i
$967$	−4.29180			−0.138015			−0.0690074	−	0.997616i	$-0.521983\pi$
$967$	−4.29180			−0.138015			−0.0690074	+	0.997616i	$0.521983\pi$
$968$	−7.94427	+	7.60845i	−0.255339	+	0.244545i
$969$	−39.1246			−1.25686
$970$	−1.04508	−	3.21644i	−0.0335557	−	0.103274i
$971$	−34.2705	−	24.8990i	−1.09979	−	0.799046i	−0.118767	−	0.992922i	$-0.537894\pi$
$971$	−34.2705	−	24.8990i	−1.09979	−	0.799046i	−0.981026	+	0.193876i	$0.937894\pi$
$972$	−3.19098	+	2.31838i	−0.102351	+	0.0743622i
$973$	2.76393	−	8.50651i	0.0886076	−	0.272706i
$974$	3.65248	−	11.2412i	0.117033	−	0.360190i
$975$	−7.35410	+	5.34307i	−0.235520	+	0.171115i
$976$	9.47214	+	6.88191i	0.303196	+	0.220285i
$977$	16.3475	+	50.3125i	0.523004	+	1.60964i	0.768230	+	0.640174i	$0.221138\pi$
$977$	16.3475	+	50.3125i	0.523004	+	1.60964i	−0.245226	+	0.969466i	$0.578862\pi$
$978$	−23.7082			−0.758105
$979$	−0.742646	+	0.620541i	−0.0237351	+	0.0198326i
$980$	1.00000			0.0319438
$981$	−0.416408	−	1.28157i	−0.0132949	−	0.0409174i
$982$	−0.763932	−	0.555029i	−0.0243781	−	0.0177117i
$983$	24.2984	−	17.6538i	0.774998	−	0.563069i	−0.128476	−	0.991713i	$-0.541008\pi$
$983$	24.2984	−	17.6538i	0.774998	−	0.563069i	0.903474	+	0.428644i	$0.141008\pi$
$984$	4.47214	−	13.7638i	0.142566	−	0.438775i
$985$	−4.76393	+	14.6619i	−0.151791	+	0.467166i
$986$	21.8713	−	15.8904i	0.696525	−	0.506055i
$987$	17.1353	+	12.4495i	0.545421	+	0.396272i
$988$	−9.09017	−	27.9767i	−0.289197	−	0.890056i
$989$	27.4164			0.871791
$990$	1.07295	+	0.673542i	0.0341006	+	0.0214066i
$991$	10.9230			0.346980			0.173490	−	0.984836i	$-0.444496\pi$
$991$	10.9230			0.346980			0.173490	+	0.984836i	$0.444496\pi$
$992$	1.61803	+	4.97980i	0.0513726	+	0.158109i
$993$	8.35410	+	6.06961i	0.265109	+	0.192613i
$994$	5.92705	−	4.30625i	0.187995	−	0.136586i
$995$	−3.38197	+	10.4086i	−0.107216	+	0.329975i
$996$	6.80902	−	20.9560i	0.215752	−	0.664016i
$997$	−14.2082	+	10.3229i	−0.449978	+	0.326928i	−0.789587	−	0.613638i	$-0.789705\pi$
$997$	−14.2082	+	10.3229i	−0.449978	+	0.326928i	0.339609	+	0.940567i	$0.389705\pi$
$998$	20.0623	+	14.5761i	0.635061	+	0.461399i
$999$	6.27051	+	19.2986i	0.198390	+	0.610582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.a.71.1	✓	4
11.3	even	5		8470.2.a.cc.1.2		2
11.8	odd	10		8470.2.a.bq.1.2		2
11.9	even	5	inner	770.2.n.a.141.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.a.71.1	✓	4	1.1	even	1	trivial
770.2.n.a.141.1	yes	4	11.9	even	5	inner
8470.2.a.bq.1.2		2	11.8	odd	10
8470.2.a.cc.1.2		2	11.3	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.30902 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.118034 - 0.363271i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.30902 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.118034 - 0.363271i) q^{9} +1.00000 q^{10} +(-2.54508 + 2.12663i) q^{11} +1.61803 q^{12} +(1.73607 + 5.34307i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-1.30902 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.42705 - 4.39201i) q^{17} +(0.309017 - 0.224514i) q^{18} +(4.23607 + 3.07768i) q^{19} +(0.309017 + 0.951057i) q^{20} +1.61803 q^{21} +(-2.80902 - 1.76336i) q^{22} +8.47214 q^{23} +(0.500000 + 1.53884i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.54508 + 3.30220i) q^{26} +(-1.69098 + 5.20431i) q^{27} +(0.309017 - 0.951057i) q^{28} +(4.73607 - 3.44095i) q^{29} +(-1.30902 - 0.951057i) q^{30} +(1.61803 + 4.97980i) q^{31} +1.00000 q^{32} +(5.35410 - 0.363271i) q^{33} +4.61803 q^{34} +(0.309017 + 0.951057i) q^{35} +(0.309017 + 0.224514i) q^{36} +(3.00000 - 2.17963i) q^{37} +(-1.61803 + 4.97980i) q^{38} +(2.80902 - 8.64527i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-7.23607 - 5.25731i) q^{41} +(0.500000 + 1.53884i) q^{42} +3.23607 q^{43} +(0.809017 - 3.21644i) q^{44} -0.381966 q^{45} +(2.61803 + 8.05748i) q^{46} +(10.5902 + 7.69421i) q^{47} +(-1.30902 + 0.951057i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-6.04508 + 4.39201i) q^{51} +(-4.54508 - 3.30220i) q^{52} +(2.00000 + 6.15537i) q^{53} -5.47214 q^{54} +(1.23607 + 3.07768i) q^{55} +1.00000 q^{56} +(-2.61803 - 8.05748i) q^{57} +(4.73607 + 3.44095i) q^{58} +(-3.85410 + 2.80017i) q^{59} +(0.500000 - 1.53884i) q^{60} +(-3.61803 + 11.1352i) q^{61} +(-4.23607 + 3.07768i) q^{62} +(0.309017 + 0.224514i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.61803 q^{65} +(2.00000 + 4.97980i) q^{66} -1.23607 q^{67} +(1.42705 + 4.39201i) q^{68} +(-11.0902 - 8.05748i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-2.26393 + 6.96767i) q^{71} +(-0.118034 + 0.363271i) q^{72} +(-3.50000 + 2.54290i) q^{73} +(3.00000 + 2.17963i) q^{74} +(0.500000 + 1.53884i) q^{75} -5.23607 q^{76} +(0.809017 - 3.21644i) q^{77} +9.09017 q^{78} +(-0.263932 - 0.812299i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(6.23607 - 4.53077i) q^{81} +(2.76393 - 8.50651i) q^{82} +(4.20820 - 12.9515i) q^{83} +(-1.30902 + 0.951057i) q^{84} +(-3.73607 - 2.71441i) q^{85} +(1.00000 + 3.07768i) q^{86} -9.47214 q^{87} +(3.30902 - 0.224514i) q^{88} +0.291796 q^{89} +(-0.118034 - 0.363271i) q^{90} +(-4.54508 - 3.30220i) q^{91} +(-6.85410 + 4.97980i) q^{92} +(2.61803 - 8.05748i) q^{93} +(-4.04508 + 12.4495i) q^{94} +(4.23607 - 3.07768i) q^{95} +(-1.30902 - 0.951057i) q^{96} +(-1.04508 - 3.21644i) q^{97} +1.00000 q^{98} +(1.07295 + 0.673542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9	\( 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9} + 4 q^{10} + q^{11} + 2 q^{12} - 2 q^{13} - q^{14} - 3 q^{15} - q^{16} - q^{17} - q^{18} + 8 q^{19} - q^{20} + 2 q^{21} - 9 q^{22} + 16 q^{23} + 2 q^{24} - q^{25} - 7 q^{26} - 9 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 14 q^{34} - q^{35} - q^{36} + 12 q^{37} - 2 q^{38} + 9 q^{39} - q^{40} - 20 q^{41} + 2 q^{42} + 4 q^{43} + q^{44} - 6 q^{45} + 6 q^{46} + 20 q^{47} - 3 q^{48} - q^{49} - q^{50} - 13 q^{51} - 7 q^{52} + 8 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 6 q^{57} + 10 q^{58} - 2 q^{59} + 2 q^{60} - 10 q^{61} - 8 q^{62} - q^{63} - q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} - q^{68} - 22 q^{69} - q^{70} - 18 q^{71} + 4 q^{72} - 14 q^{73} + 12 q^{74} + 2 q^{75} - 12 q^{76} + q^{77} + 14 q^{78} - 10 q^{79} - q^{80} + 16 q^{81} + 20 q^{82} - 10 q^{83} - 3 q^{84} - 6 q^{85} + 4 q^{86} - 20 q^{87} + 11 q^{88} + 28 q^{89} + 4 q^{90} - 7 q^{91} - 14 q^{92} + 6 q^{93} - 5 q^{94} + 8 q^{95} - 3 q^{96} + 7 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9 + 4 * q^10 + q^11 + 2 * q^12 - 2 * q^13 - q^14 - 3 * q^15 - q^16 - q^17 - q^18 + 8 * q^19 - q^20 + 2 * q^21 - 9 * q^22 + 16 * q^23 + 2 * q^24 - q^25 - 7 * q^26 - 9 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 14 * q^34 - q^35 - q^36 + 12 * q^37 - 2 * q^38 + 9 * q^39 - q^40 - 20 * q^41 + 2 * q^42 + 4 * q^43 + q^44 - 6 * q^45 + 6 * q^46 + 20 * q^47 - 3 * q^48 - q^49 - q^50 - 13 * q^51 - 7 * q^52 + 8 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 6 * q^57 + 10 * q^58 - 2 * q^59 + 2 * q^60 - 10 * q^61 - 8 * q^62 - q^63 - q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 - q^68 - 22 * q^69 - q^70 - 18 * q^71 + 4 * q^72 - 14 * q^73 + 12 * q^74 + 2 * q^75 - 12 * q^76 + q^77 + 14 * q^78 - 10 * q^79 - q^80 + 16 * q^81 + 20 * q^82 - 10 * q^83 - 3 * q^84 - 6 * q^85 + 4 * q^86 - 20 * q^87 + 11 * q^88 + 28 * q^89 + 4 * q^90 - 7 * q^91 - 14 * q^92 + 6 * q^93 - 5 * q^94 + 8 * q^95 - 3 * q^96 + 7 * q^97 + 4 * q^98 + 11 * q^99

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