LMFDB - Embedded newform 770.2.n.d.421.1

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			421.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.d.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.30902 + 0.951057i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.30902 + 0.951057i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +1.00000 q^{10} +(-0.309017 - 3.30220i) q^{11} +1.61803 q^{12} +(4.23607 - 3.07768i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.11803 - 1.53884i) q^{17} +(0.118034 - 0.363271i) q^{18} +(2.42705 + 7.46969i) q^{19} +(0.809017 - 0.587785i) q^{20} +1.61803 q^{21} +(-2.19098 - 2.48990i) q^{22} -0.472136 q^{23} +(1.30902 - 0.951057i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.61803 - 4.97980i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(1.38197 - 4.25325i) q^{29} +(0.500000 + 1.53884i) q^{30} +(-2.00000 + 1.45309i) q^{31} -1.00000 q^{32} +(4.92705 - 2.12663i) q^{33} -2.61803 q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(-3.47214 + 10.6861i) q^{37} +(6.35410 + 4.61653i) q^{38} +(6.85410 + 4.97980i) q^{39} +(0.309017 - 0.951057i) q^{40} +(0.881966 + 2.71441i) q^{41} +(1.30902 - 0.951057i) q^{42} -2.09017 q^{43} +(-3.23607 - 0.726543i) q^{44} +0.381966 q^{45} +(-0.381966 + 0.277515i) q^{46} +(1.47214 + 4.53077i) q^{47} +(0.500000 - 1.53884i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(1.30902 - 4.02874i) q^{51} +(-1.61803 - 4.97980i) q^{52} +(2.23607 - 1.62460i) q^{53} +5.47214 q^{54} +(1.69098 - 2.85317i) q^{55} -1.00000 q^{56} +(-10.2812 + 7.46969i) q^{57} +(-1.38197 - 4.25325i) q^{58} +(1.28115 - 3.94298i) q^{59} +(1.30902 + 0.951057i) q^{60} +(-11.0902 - 8.05748i) q^{61} +(-0.763932 + 2.35114i) q^{62} +(-0.118034 - 0.363271i) q^{63} +(-0.809017 + 0.587785i) q^{64} +5.23607 q^{65} +(2.73607 - 4.61653i) q^{66} -3.38197 q^{67} +(-2.11803 + 1.53884i) q^{68} +(-0.236068 - 0.726543i) q^{69} +(0.309017 - 0.951057i) q^{70} +(-8.85410 - 6.43288i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(0.881966 - 2.71441i) q^{73} +(3.47214 + 10.6861i) q^{74} +(-1.30902 + 0.951057i) q^{75} +7.85410 q^{76} +(-3.23607 - 0.726543i) q^{77} +8.47214 q^{78} +(-3.23607 + 2.35114i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(2.30902 + 1.67760i) q^{82} +(7.16312 + 5.20431i) q^{83} +(0.500000 - 1.53884i) q^{84} +(-0.809017 - 2.48990i) q^{85} +(-1.69098 + 1.22857i) q^{86} +7.23607 q^{87} +(-3.04508 + 1.31433i) q^{88} -14.8541 q^{89} +(0.309017 - 0.224514i) q^{90} +(-1.61803 - 4.97980i) q^{91} +(-0.145898 + 0.449028i) q^{92} +(-3.23607 - 2.35114i) q^{93} +(3.85410 + 2.80017i) q^{94} +(-2.42705 + 7.46969i) q^{95} +(-0.500000 - 1.53884i) q^{96} +(6.78115 - 4.92680i) q^{97} -1.00000 q^{98} +(-0.836881 - 0.951057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 2 q^{3} - q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 + 2 * q^3 - q^4 + q^5 + 3 * q^6 - q^7 + q^8 - q^9	\( 4 q + q^{2} + 2 q^{3} - q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + q^{11} + 2 q^{12} + 8 q^{13} + q^{14} - 2 q^{15} - q^{16} - 4 q^{17} - 4 q^{18} + 3 q^{19} + q^{20} + 2 q^{21} - 11 q^{22} + 16 q^{23} + 3 q^{24} - q^{25} + 2 q^{26} + 11 q^{27} - q^{28} + 10 q^{29} + 2 q^{30} - 8 q^{31} - 4 q^{32} + 13 q^{33} - 6 q^{34} + q^{35} + 4 q^{36} + 4 q^{37} + 12 q^{38} + 14 q^{39} - q^{40} + 8 q^{41} + 3 q^{42} + 14 q^{43} - 4 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 2 q^{48} - q^{49} + q^{50} + 3 q^{51} - 2 q^{52} + 4 q^{54} + 9 q^{55} - 4 q^{56} - 21 q^{57} - 10 q^{58} - 15 q^{59} + 3 q^{60} - 22 q^{61} - 12 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} + 2 q^{66} - 18 q^{67} - 4 q^{68} + 8 q^{69} - q^{70} - 22 q^{71} + q^{72} + 8 q^{73} - 4 q^{74} - 3 q^{75} + 18 q^{76} - 4 q^{77} + 16 q^{78} - 4 q^{79} + q^{80} - 14 q^{81} + 7 q^{82} + 13 q^{83} + 2 q^{84} - q^{85} - 9 q^{86} + 20 q^{87} - q^{88} - 46 q^{89} - q^{90} - 2 q^{91} - 14 q^{92} - 4 q^{93} + 2 q^{94} - 3 q^{95} - 2 q^{96} + 7 q^{97} - 4 q^{98} - 19 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - q^4 + q^5 + 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + q^11 + 2 * q^12 + 8 * q^13 + q^14 - 2 * q^15 - q^16 - 4 * q^17 - 4 * q^18 + 3 * q^19 + q^20 + 2 * q^21 - 11 * q^22 + 16 * q^23 + 3 * q^24 - q^25 + 2 * q^26 + 11 * q^27 - q^28 + 10 * q^29 + 2 * q^30 - 8 * q^31 - 4 * q^32 + 13 * q^33 - 6 * q^34 + q^35 + 4 * q^36 + 4 * q^37 + 12 * q^38 + 14 * q^39 - q^40 + 8 * q^41 + 3 * q^42 + 14 * q^43 - 4 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 2 * q^48 - q^49 + q^50 + 3 * q^51 - 2 * q^52 + 4 * q^54 + 9 * q^55 - 4 * q^56 - 21 * q^57 - 10 * q^58 - 15 * q^59 + 3 * q^60 - 22 * q^61 - 12 * q^62 + 4 * q^63 - q^64 + 12 * q^65 + 2 * q^66 - 18 * q^67 - 4 * q^68 + 8 * q^69 - q^70 - 22 * q^71 + q^72 + 8 * q^73 - 4 * q^74 - 3 * q^75 + 18 * q^76 - 4 * q^77 + 16 * q^78 - 4 * q^79 + q^80 - 14 * q^81 + 7 * q^82 + 13 * q^83 + 2 * q^84 - q^85 - 9 * q^86 + 20 * q^87 - q^88 - 46 * q^89 - q^90 - 2 * q^91 - 14 * q^92 - 4 * q^93 + 2 * q^94 - 3 * q^95 - 2 * q^96 + 7 * q^97 - 4 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	0.985273	+	0.170989i	$0.0546962\pi$
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	−0.696598	+	0.717462i	$0.745304\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	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
$9$	0.309017	−	0.224514i	0.103006	−	0.0748380i
$10$	1.00000			0.316228
$11$	−0.309017	−	3.30220i	−0.0931721	−	0.995650i
$11$	−0.309017	−	3.30220i	−0.0931721	−	0.995650i
$12$	1.61803			0.467086
$13$	4.23607	−	3.07768i	1.17487	−	0.853596i	0.183290	−	0.983059i	$-0.441325\pi$
$13$	4.23607	−	3.07768i	1.17487	−	0.853596i	0.991584	+	0.129463i	$0.0413254\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−0.500000	+	1.53884i	−0.129099	+	0.397327i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.11803	−	1.53884i	−0.513699	−	0.373224i	0.300526	−	0.953774i	$-0.402838\pi$
$17$	−2.11803	−	1.53884i	−0.513699	−	0.373224i	−0.814225	+	0.580550i	$0.802838\pi$
$18$	0.118034	−	0.363271i	0.0278209	−	0.0856239i
$19$	2.42705	+	7.46969i	0.556804	+	1.71367i	0.691132	+	0.722729i	$0.257112\pi$
$19$	2.42705	+	7.46969i	0.556804	+	1.71367i	−0.134328	+	0.990937i	$0.542888\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	1.61803			0.353084
$22$	−2.19098	−	2.48990i	−0.467119	−	0.530848i
$23$	−0.472136			−0.0984472			−0.0492236	−	0.998788i	$-0.515675\pi$
$23$	−0.472136			−0.0984472			−0.0492236	+	0.998788i	$0.515675\pi$
$24$	1.30902	−	0.951057i	0.267202	−	0.194134i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.61803	−	4.97980i	0.317323	−	0.976618i
$27$	4.42705	+	3.21644i	0.851986	+	0.619004i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	−0.736881	−	0.676023i	$-0.763702\pi$
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	0.993505	−	0.113787i	$-0.0362980\pi$
$30$	0.500000	+	1.53884i	0.0912871	+	0.280953i
$31$	−2.00000	+	1.45309i	−0.359211	+	0.260982i	−0.752723	−	0.658338i	$-0.771260\pi$
$31$	−2.00000	+	1.45309i	−0.359211	+	0.260982i	0.393512	+	0.919319i	$0.371260\pi$
$32$	−1.00000			−0.176777
$33$	4.92705	−	2.12663i	0.857689	−	0.370198i
$34$	−2.61803			−0.448989
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	−3.47214	+	10.6861i	−0.570816	+	1.75679i	0.0791890	+	0.996860i	$0.474767\pi$
$37$	−3.47214	+	10.6861i	−0.570816	+	1.75679i	−0.650005	+	0.759930i	$0.725233\pi$
$38$	6.35410	+	4.61653i	1.03077	+	0.748899i
$39$	6.85410	+	4.97980i	1.09753	+	0.797406i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	0.881966	+	2.71441i	0.137740	+	0.423920i	0.996006	−	0.0892848i	$-0.0284581\pi$
$41$	0.881966	+	2.71441i	0.137740	+	0.423920i	−0.858266	+	0.513205i	$0.828458\pi$
$42$	1.30902	−	0.951057i	0.201986	−	0.146751i
$43$	−2.09017			−0.318748			−0.159374	−	0.987218i	$-0.550948\pi$
$43$	−2.09017			−0.318748			−0.159374	+	0.987218i	$0.550948\pi$
$44$	−3.23607	−	0.726543i	−0.487856	−	0.109530i
$45$	0.381966			0.0569401
$46$	−0.381966	+	0.277515i	−0.0563178	+	0.0409173i
$47$	1.47214	+	4.53077i	0.214733	+	0.660881i	0.999172	+	0.0406750i	$0.0129508\pi$
$47$	1.47214	+	4.53077i	0.214733	+	0.660881i	−0.784439	+	0.620206i	$0.787049\pi$
$48$	0.500000	−	1.53884i	0.0721688	−	0.222113i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	1.30902	−	4.02874i	0.183299	−	0.564136i
$52$	−1.61803	−	4.97980i	−0.224381	−	0.690574i
$53$	2.23607	−	1.62460i	0.307148	−	0.223156i	−0.423524	−	0.905885i	$-0.639207\pi$
$53$	2.23607	−	1.62460i	0.307148	−	0.223156i	0.730672	+	0.682729i	$0.239207\pi$
$54$	5.47214			0.744663
$55$	1.69098	−	2.85317i	0.228012	−	0.384721i
$56$	−1.00000			−0.133631
$57$	−10.2812	+	7.46969i	−1.36177	+	0.989385i
$58$	−1.38197	−	4.25325i	−0.181461	−	0.558480i
$59$	1.28115	−	3.94298i	0.166792	−	0.513333i	−0.832372	−	0.554217i	$-0.813018\pi$
$59$	1.28115	−	3.94298i	0.166792	−	0.513333i	0.999164	+	0.0408847i	$0.0130176\pi$
$60$	1.30902	+	0.951057i	0.168993	+	0.122781i
$61$	−11.0902	−	8.05748i	−1.41995	−	1.03165i	−0.991780	−	0.127957i	$-0.959158\pi$
$61$	−11.0902	−	8.05748i	−1.41995	−	1.03165i	−0.428171	−	0.903698i	$-0.640842\pi$
$62$	−0.763932	+	2.35114i	−0.0970195	+	0.298595i
$63$	−0.118034	−	0.363271i	−0.0148709	−	0.0457679i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	5.23607			0.649454
$66$	2.73607	−	4.61653i	0.336787	−	0.568255i
$67$	−3.38197			−0.413173			−0.206586	−	0.978428i	$-0.566235\pi$
$67$	−3.38197			−0.413173			−0.206586	+	0.978428i	$0.566235\pi$
$68$	−2.11803	+	1.53884i	−0.256849	+	0.186612i
$69$	−0.236068	−	0.726543i	−0.0284192	−	0.0874654i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	−8.85410	−	6.43288i	−1.05079	−	0.763443i	−0.0784263	−	0.996920i	$-0.524990\pi$
$71$	−8.85410	−	6.43288i	−1.05079	−	0.763443i	−0.972362	+	0.233477i	$0.924990\pi$
$72$	−0.309017	−	0.224514i	−0.0364180	−	0.0264592i
$73$	0.881966	−	2.71441i	0.103226	−	0.317698i	−0.886084	−	0.463525i	$-0.846584\pi$
$73$	0.881966	−	2.71441i	0.103226	−	0.317698i	0.989310	+	0.145827i	$0.0465844\pi$
$74$	3.47214	+	10.6861i	0.403628	+	1.24224i
$75$	−1.30902	+	0.951057i	−0.151152	+	0.109819i
$76$	7.85410			0.900927
$77$	−3.23607	−	0.726543i	−0.368784	−	0.0827972i
$78$	8.47214			0.959280
$79$	−3.23607	+	2.35114i	−0.364086	+	0.264524i	−0.754754	−	0.656007i	$-0.772244\pi$
$79$	−3.23607	+	2.35114i	−0.364086	+	0.264524i	0.390668	+	0.920532i	$0.372244\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	2.30902	+	1.67760i	0.254988	+	0.185260i
$83$	7.16312	+	5.20431i	0.786254	+	0.571247i	0.906850	−	0.421454i	$-0.138480\pi$
$83$	7.16312	+	5.20431i	0.786254	+	0.571247i	−0.120595	+	0.992702i	$0.538480\pi$
$84$	0.500000	−	1.53884i	0.0545545	−	0.167901i
$85$	−0.809017	−	2.48990i	−0.0877502	−	0.270067i
$86$	−1.69098	+	1.22857i	−0.182343	+	0.132480i
$87$	7.23607			0.775788
$88$	−3.04508	+	1.31433i	−0.324607	+	0.140108i
$89$	−14.8541			−1.57453			−0.787266	−	0.616614i	$-0.788504\pi$
$89$	−14.8541			−1.57453			−0.787266	+	0.616614i	$0.788504\pi$
$90$	0.309017	−	0.224514i	0.0325733	−	0.0236659i
$91$	−1.61803	−	4.97980i	−0.169616	−	0.522025i
$92$	−0.145898	+	0.449028i	−0.0152109	+	0.0468144i
$93$	−3.23607	−	2.35114i	−0.335565	−	0.243802i
$94$	3.85410	+	2.80017i	0.397520	+	0.288815i
$95$	−2.42705	+	7.46969i	−0.249010	+	0.766375i
$96$	−0.500000	−	1.53884i	−0.0510310	−	0.157057i
$97$	6.78115	−	4.92680i	0.688522	−	0.500240i	−0.187652	−	0.982236i	$-0.560088\pi$
$97$	6.78115	−	4.92680i	0.688522	−	0.500240i	0.876174	+	0.481995i	$0.160088\pi$
$98$	−1.00000			−0.101015
$99$	−0.836881	−	0.951057i	−0.0841097	−	0.0955848i
$100$	1.00000			0.100000
$101$	12.0902	−	8.78402i	1.20302	−	0.874043i	0.208439	−	0.978035i	$-0.433162\pi$
$101$	12.0902	−	8.78402i	1.20302	−	0.874043i	0.994578	+	0.103992i	$0.0331618\pi$
$102$	−1.30902	−	4.02874i	−0.129612	−	0.398905i
$103$	−1.85410	+	5.70634i	−0.182690	+	0.562262i	−0.999901	−	0.0140765i	$-0.995519\pi$
$103$	−1.85410	+	5.70634i	−0.182690	+	0.562262i	0.817211	+	0.576339i	$0.195519\pi$
$104$	−4.23607	−	3.07768i	−0.415381	−	0.301792i
$105$	1.30902	+	0.951057i	0.127747	+	0.0928136i
$106$	0.854102	−	2.62866i	0.0829577	−	0.255318i
$107$	0.881966	+	2.71441i	0.0852629	+	0.262412i	0.984594	−	0.174856i	$-0.0559460\pi$
$107$	0.881966	+	2.71441i	0.0852629	+	0.262412i	−0.899331	+	0.437268i	$0.855946\pi$
$108$	4.42705	−	3.21644i	0.425993	−	0.309502i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	−0.309017	−	3.30220i	−0.0294636	−	0.314852i
$111$	−18.1803			−1.72560
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	1.33688	+	4.11450i	0.125763	+	0.387059i	0.994039	−	0.109022i	$-0.0347718\pi$
$113$	1.33688	+	4.11450i	0.125763	+	0.387059i	−0.868276	+	0.496081i	$0.834772\pi$
$114$	−3.92705	+	12.0862i	−0.367802	+	1.13198i
$115$	−0.381966	−	0.277515i	−0.0356185	−	0.0258784i
$116$	−3.61803	−	2.62866i	−0.335926	−	0.244065i
$117$	0.618034	−	1.90211i	0.0571373	−	0.175850i
$118$	−1.28115	−	3.94298i	−0.117940	−	0.362981i
$119$	−2.11803	+	1.53884i	−0.194160	+	0.141065i
$120$	1.61803			0.147706
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$	−13.7082			−1.24108
$123$	−3.73607	+	2.71441i	−0.336870	+	0.244750i
$124$	0.763932	+	2.35114i	0.0686031	+	0.211139i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−0.309017	−	0.224514i	−0.0275294	−	0.0200013i
$127$	−10.0902	−	7.33094i	−0.895358	−	0.650516i	0.0419116	−	0.999121i	$-0.486655\pi$
$127$	−10.0902	−	7.33094i	−0.895358	−	0.650516i	−0.937269	+	0.348606i	$0.886655\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−1.04508	−	3.21644i	−0.0920146	−	0.283192i
$130$	4.23607	−	3.07768i	0.371528	−	0.269931i
$131$	5.09017			0.444730			0.222365	−	0.974963i	$-0.428622\pi$
$131$	5.09017			0.444730			0.222365	+	0.974963i	$0.428622\pi$
$132$	−0.500000	−	5.34307i	−0.0435194	−	0.465054i
$133$	7.85410			0.681037
$134$	−2.73607	+	1.98787i	−0.236360	+	0.171726i
$135$	1.69098	+	5.20431i	0.145537	+	0.447916i
$136$	−0.809017	+	2.48990i	−0.0693726	+	0.213507i
$137$	−3.92705	−	2.85317i	−0.335511	−	0.243763i	0.407255	−	0.913315i	$-0.366486\pi$
$137$	−3.92705	−	2.85317i	−0.335511	−	0.243763i	−0.742765	+	0.669552i	$0.766486\pi$
$138$	−0.618034	−	0.449028i	−0.0526105	−	0.0382238i
$139$	−1.52786	+	4.70228i	−0.129592	+	0.398842i	−0.994710	−	0.102726i	$-0.967243\pi$
$139$	−1.52786	+	4.70228i	−0.129592	+	0.398842i	0.865118	+	0.501568i	$0.167243\pi$
$140$	−0.309017	−	0.951057i	−0.0261167	−	0.0803789i
$141$	−6.23607	+	4.53077i	−0.525172	+	0.381560i
$142$	−10.9443			−0.918423
$143$	−11.4721	−	13.0373i	−0.959348	−	1.09023i
$144$	−0.381966			−0.0318305
$145$	3.61803	−	2.62866i	0.300461	−	0.218298i
$146$	−0.881966	−	2.71441i	−0.0729920	−	0.224646i
$147$	0.500000	−	1.53884i	0.0412393	−	0.126922i
$148$	9.09017	+	6.60440i	0.747207	+	0.542878i
$149$	−9.47214	−	6.88191i	−0.775988	−	0.563788i	0.127785	−	0.991802i	$-0.459213\pi$
$149$	−9.47214	−	6.88191i	−0.775988	−	0.563788i	−0.903772	+	0.428014i	$0.859213\pi$
$150$	−0.500000	+	1.53884i	−0.0408248	+	0.125646i
$151$	5.70820	+	17.5680i	0.464527	+	1.42967i	0.859576	+	0.511007i	$0.170728\pi$
$151$	5.70820	+	17.5680i	0.464527	+	1.42967i	−0.395049	+	0.918660i	$0.629272\pi$
$152$	6.35410	−	4.61653i	0.515386	−	0.374450i
$153$	−1.00000			−0.0808452
$154$	−3.04508	+	1.31433i	−0.245380	+	0.105912i
$155$	−2.47214			−0.198567
$156$	6.85410	−	4.97980i	0.548767	−	0.398703i
$157$	−4.61803	−	14.2128i	−0.368559	−	1.13431i	−0.947722	−	0.319097i	$-0.896620\pi$
$157$	−4.61803	−	14.2128i	−0.368559	−	1.13431i	0.579163	−	0.815212i	$-0.303380\pi$
$158$	−1.23607	+	3.80423i	−0.0983363	+	0.302648i
$159$	3.61803	+	2.62866i	0.286929	+	0.208466i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	−0.145898	+	0.449028i	−0.0114984	+	0.0353884i
$162$	2.38197	+	7.33094i	0.187145	+	0.575973i
$163$	−18.4443	+	13.4005i	−1.44467	+	1.04961i	−0.457626	+	0.889145i	$0.651300\pi$
$163$	−18.4443	+	13.4005i	−1.44467	+	1.04961i	−0.987041	+	0.160467i	$0.948700\pi$
$164$	2.85410			0.222868
$165$	5.23607	+	1.17557i	0.407627	+	0.0915180i
$166$	8.85410			0.687212
$167$	−6.70820	+	4.87380i	−0.519096	+	0.377146i	−0.816263	−	0.577680i	$-0.803958\pi$
$167$	−6.70820	+	4.87380i	−0.519096	+	0.377146i	0.297167	+	0.954826i	$0.403958\pi$
$168$	−0.500000	−	1.53884i	−0.0385758	−	0.118724i
$169$	4.45492	−	13.7108i	0.342686	−	1.05468i
$170$	−2.11803	−	1.53884i	−0.162446	−	0.118024i
$171$	2.42705	+	1.76336i	0.185601	+	0.134847i
$172$	−0.645898	+	1.98787i	−0.0492493	+	0.151574i
$173$	6.14590	+	18.9151i	0.467264	+	1.43809i	0.856113	+	0.516789i	$0.172873\pi$
$173$	6.14590	+	18.9151i	0.467264	+	1.43809i	−0.388849	+	0.921302i	$0.627127\pi$
$174$	5.85410	−	4.25325i	0.443798	−	0.322438i
$175$	1.00000			0.0755929
$176$	−1.69098	+	2.85317i	−0.127463	+	0.215066i
$177$	6.70820			0.504219
$178$	−12.0172	+	8.73102i	−0.900729	+	0.654418i
$179$	0.663119	+	2.04087i	0.0495638	+	0.152542i	0.972775	−	0.231751i	$-0.0744454\pi$
$179$	0.663119	+	2.04087i	0.0495638	+	0.152542i	−0.923211	+	0.384293i	$0.874445\pi$
$180$	0.118034	−	0.363271i	0.00879773	−	0.0270766i
$181$	−16.9443	−	12.3107i	−1.25946	−	0.915050i	−0.260727	−	0.965413i	$-0.583962\pi$
$181$	−16.9443	−	12.3107i	−1.25946	−	0.915050i	−0.998731	+	0.0503630i	$0.983962\pi$
$182$	−4.23607	−	3.07768i	−0.313998	−	0.228133i
$183$	6.85410	−	21.0948i	0.506670	−	1.55937i
$184$	0.145898	+	0.449028i	0.0107557	+	0.0331028i
$185$	−9.09017	+	6.60440i	−0.668323	+	0.485565i
$186$	−4.00000			−0.293294
$187$	−4.42705	+	7.46969i	−0.323738	+	0.546238i
$188$	4.76393			0.347445
$189$	4.42705	−	3.21644i	0.322021	−	0.233962i
$190$	2.42705	+	7.46969i	0.176077	+	0.541909i
$191$	−0.381966	+	1.17557i	−0.0276381	+	0.0850613i	−0.963924	−	0.266177i	$-0.914239\pi$
$191$	−0.381966	+	1.17557i	−0.0276381	+	0.0850613i	0.936286	+	0.351238i	$0.114239\pi$
$192$	−1.30902	−	0.951057i	−0.0944702	−	0.0686366i
$193$	17.3262	+	12.5882i	1.24717	+	0.906122i	0.998054	−	0.0623518i	$-0.0198601\pi$
$193$	17.3262	+	12.5882i	1.24717	+	0.906122i	0.249116	+	0.968474i	$0.419860\pi$
$194$	2.59017	−	7.97172i	0.185963	−	0.572336i
$195$	2.61803	+	8.05748i	0.187481	+	0.577008i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	11.5279			0.821326			0.410663	−	0.911787i	$-0.365297\pi$
$197$	11.5279			0.821326			0.410663	+	0.911787i	$0.365297\pi$
$198$	−1.23607	−	0.277515i	−0.0878435	−	0.0197221i
$199$	5.05573			0.358391			0.179196	−	0.983813i	$-0.442651\pi$
$199$	5.05573			0.358391			0.179196	+	0.983813i	$0.442651\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	−1.69098	−	5.20431i	−0.119273	−	0.367084i
$202$	4.61803	−	14.2128i	0.324924	−	1.00001i
$203$	−3.61803	−	2.62866i	−0.253936	−	0.184495i
$204$	−3.42705	−	2.48990i	−0.239942	−	0.174328i
$205$	−0.881966	+	2.71441i	−0.0615992	+	0.189583i
$206$	1.85410	+	5.70634i	0.129181	+	0.397579i
$207$	−0.145898	+	0.106001i	−0.0101406	+	0.00736759i
$208$	−5.23607			−0.363056
$209$	23.9164	−	10.3229i	1.65433	−	0.714047i
$210$	1.61803			0.111655
$211$	−8.63525	+	6.27388i	−0.594475	+	0.431912i	−0.843914	−	0.536479i	$-0.819754\pi$
$211$	−8.63525	+	6.27388i	−0.594475	+	0.431912i	0.249438	+	0.968391i	$0.419754\pi$
$212$	−0.854102	−	2.62866i	−0.0586600	−	0.180537i
$213$	5.47214	−	16.8415i	0.374945	−	1.15396i
$214$	2.30902	+	1.67760i	0.157841	+	0.114678i
$215$	−1.69098	−	1.22857i	−0.115324	−	0.0837879i
$216$	1.69098	−	5.20431i	0.115057	−	0.354108i
$217$	0.763932	+	2.35114i	0.0518591	+	0.159606i
$218$	3.23607	−	2.35114i	0.219174	−	0.159239i
$219$	4.61803			0.312058
$220$	−2.19098	−	2.48990i	−0.147716	−	0.167869i
$221$	−13.7082			−0.922114
$222$	−14.7082	+	10.6861i	−0.987150	+	0.717206i
$223$	4.05573	+	12.4822i	0.271592	+	0.835873i	0.990101	+	0.140356i	$0.0448247\pi$
$223$	4.05573	+	12.4822i	0.271592	+	0.835873i	−0.718509	+	0.695517i	$0.755175\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	0.309017	+	0.224514i	0.0206011	+	0.0149676i
$226$	3.50000	+	2.54290i	0.232817	+	0.169151i
$227$	4.22542	−	13.0045i	0.280451	−	0.863140i	−0.707274	−	0.706940i	$-0.750075\pi$
$227$	4.22542	−	13.0045i	0.280451	−	0.863140i	0.987725	−	0.156201i	$-0.0499247\pi$
$228$	3.92705	+	12.0862i	0.260075	+	0.800429i
$229$	−18.0902	+	13.1433i	−1.19543	+	0.868532i	−0.993828	−	0.110935i	$-0.964616\pi$
$229$	−18.0902	+	13.1433i	−1.19543	+	0.868532i	−0.201604	+	0.979467i	$0.564616\pi$
$230$	−0.472136			−0.0311317
$231$	−0.500000	−	5.34307i	−0.0328976	−	0.351548i
$232$	−4.47214			−0.293610
$233$	−0.545085	+	0.396027i	−0.0357097	+	0.0259446i	−0.605497	−	0.795848i	$-0.707026\pi$
$233$	−0.545085	+	0.396027i	−0.0357097	+	0.0259446i	0.569787	+	0.821792i	$0.307026\pi$
$234$	−0.618034	−	1.90211i	−0.0404021	−	0.124345i
$235$	−1.47214	+	4.53077i	−0.0960316	+	0.295555i
$236$	−3.35410	−	2.43690i	−0.218333	−	0.158629i
$237$	−5.23607	−	3.80423i	−0.340119	−	0.247111i
$238$	−0.809017	+	2.48990i	−0.0524408	+	0.161396i
$239$	1.94427	+	5.98385i	0.125764	+	0.387063i	0.994040	−	0.109020i	$-0.0347712\pi$
$239$	1.94427	+	5.98385i	0.125764	+	0.387063i	−0.868275	+	0.496083i	$0.834771\pi$
$240$	1.30902	−	0.951057i	0.0844967	−	0.0613904i
$241$	−30.9787			−1.99551			−0.997757	−	0.0669372i	$-0.978677\pi$
$241$	−30.9787			−1.99551			−0.997757	+	0.0669372i	$0.978677\pi$
$242$	−7.54508	+	8.00448i	−0.485016	+	0.514547i
$243$	3.94427			0.253025
$244$	−11.0902	+	8.05748i	−0.709975	+	0.515827i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	−1.42705	+	4.39201i	−0.0909854	+	0.280024i
$247$	33.2705	+	24.1724i	2.11695	+	1.53806i
$248$	2.00000	+	1.45309i	0.127000	+	0.0922710i
$249$	−4.42705	+	13.6251i	−0.280553	+	0.863453i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−16.1803	+	11.7557i	−1.02129	+	0.742014i	−0.966548	−	0.256487i	$-0.917435\pi$
$251$	−16.1803	+	11.7557i	−1.02129	+	0.742014i	−0.0547463	+	0.998500i	$0.517435\pi$
$252$	−0.381966			−0.0240616
$253$	0.145898	+	1.55909i	0.00917253	+	0.0980189i
$254$	−12.4721			−0.782571
$255$	3.42705	−	2.48990i	0.214610	−	0.155923i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	4.59017	−	14.1271i	0.286327	−	0.881224i	−0.699671	−	0.714465i	$-0.746670\pi$
$257$	4.59017	−	14.1271i	0.286327	−	0.881224i	0.985998	−	0.166758i	$-0.0533300\pi$
$258$	−2.73607	−	1.98787i	−0.170340	−	0.123759i
$259$	9.09017	+	6.60440i	0.564836	+	0.410377i
$260$	1.61803	−	4.97980i	0.100346	−	0.308834i
$261$	−0.527864	−	1.62460i	−0.0326740	−	0.100560i
$262$	4.11803	−	2.99193i	0.254413	−	0.184842i
$263$	26.3607			1.62547			0.812735	−	0.582634i	$-0.197978\pi$
$263$	26.3607			1.62547			0.812735	+	0.582634i	$0.197978\pi$
$264$	−3.54508	−	4.02874i	−0.218185	−	0.247952i
$265$	2.76393			0.169787
$266$	6.35410	−	4.61653i	0.389595	−	0.283057i
$267$	−7.42705	−	22.8581i	−0.454528	−	1.39889i
$268$	−1.04508	+	3.21644i	−0.0638387	+	0.196475i
$269$	15.0902	+	10.9637i	0.920064	+	0.668466i	0.943540	−	0.331259i	$-0.107473\pi$
$269$	15.0902	+	10.9637i	0.920064	+	0.668466i	−0.0234760	+	0.999724i	$0.507473\pi$
$270$	4.42705	+	3.21644i	0.269422	+	0.195746i
$271$	−1.90983	+	5.87785i	−0.116014	+	0.357054i	−0.992157	−	0.124997i	$-0.960108\pi$
$271$	−1.90983	+	5.87785i	−0.116014	+	0.357054i	0.876143	+	0.482051i	$0.160108\pi$
$272$	0.809017	+	2.48990i	0.0490539	+	0.150972i
$273$	6.85410	−	4.97980i	0.414829	−	0.301391i
$274$	−4.85410			−0.293247
$275$	3.04508	−	1.31433i	0.183626	−	0.0792569i
$276$	−0.763932			−0.0459833
$277$	9.70820	−	7.05342i	0.583309	−	0.423799i	−0.256606	−	0.966516i	$-0.582604\pi$
$277$	9.70820	−	7.05342i	0.583309	−	0.423799i	0.839916	+	0.542717i	$0.182604\pi$
$278$	1.52786	+	4.70228i	0.0916352	+	0.282024i
$279$	−0.291796	+	0.898056i	−0.0174694	+	0.0537652i
$280$	−0.809017	−	0.587785i	−0.0483480	−	0.0351269i
$281$	−9.16312	−	6.65740i	−0.546626	−	0.397147i	0.279914	−	0.960025i	$-0.409694\pi$
$281$	−9.16312	−	6.65740i	−0.546626	−	0.397147i	−0.826540	+	0.562878i	$0.809694\pi$
$282$	−2.38197	+	7.33094i	−0.141844	+	0.436551i
$283$	5.05573	+	15.5599i	0.300532	+	0.924942i	0.981307	+	0.192449i	$0.0616431\pi$
$283$	5.05573	+	15.5599i	0.300532	+	0.924942i	−0.680775	+	0.732493i	$0.738357\pi$
$284$	−8.85410	+	6.43288i	−0.525394	+	0.381721i
$285$	−12.7082			−0.752769
$286$	−16.9443	−	3.80423i	−1.00194	−	0.224949i
$287$	2.85410			0.168472
$288$	−0.309017	+	0.224514i	−0.0182090	+	0.0132296i
$289$	−3.13525	−	9.64932i	−0.184427	−	0.567607i
$290$	1.38197	−	4.25325i	0.0811518	−	0.249760i
$291$	10.9721	+	7.97172i	0.643198	+	0.467311i
$292$	−2.30902	−	1.67760i	−0.135125	−	0.0981741i
$293$	5.70820	−	17.5680i	0.333477	−	1.02634i	−0.633991	−	0.773341i	$-0.718584\pi$
$293$	5.70820	−	17.5680i	0.333477	−	1.02634i	0.967467	−	0.252995i	$-0.0814158\pi$
$294$	−0.500000	−	1.53884i	−0.0291606	−	0.0897471i
$295$	3.35410	−	2.43690i	0.195283	−	0.141882i
$296$	11.2361			0.653083
$297$	9.25329	−	15.6129i	0.536930	−	0.905954i
$298$	−11.7082			−0.678238
$299$	−2.00000	+	1.45309i	−0.115663	+	0.0840341i
$300$	0.500000	+	1.53884i	0.0288675	+	0.0888451i
$301$	−0.645898	+	1.98787i	−0.0372289	+	0.114579i
$302$	14.9443	+	10.8576i	0.859946	+	0.624787i
$303$	19.5623	+	14.2128i	1.12383	+	0.816507i
$304$	2.42705	−	7.46969i	0.139201	−	0.428416i
$305$	−4.23607	−	13.0373i	−0.242557	−	0.746512i
$306$	−0.809017	+	0.587785i	−0.0462484	+	0.0336014i
$307$	18.5623			1.05941			0.529703	−	0.848183i	$-0.322303\pi$
$307$	18.5623			1.05941			0.529703	+	0.848183i	$0.322303\pi$
$308$	−1.69098	+	2.85317i	−0.0963527	+	0.162574i
$309$	−9.70820			−0.552280
$310$	−2.00000	+	1.45309i	−0.113592	+	0.0825297i
$311$	−0.673762	−	2.07363i	−0.0382055	−	0.117585i	0.930135	−	0.367218i	$-0.119690\pi$
$311$	−0.673762	−	2.07363i	−0.0382055	−	0.117585i	−0.968340	+	0.249634i	$0.919690\pi$
$312$	2.61803	−	8.05748i	0.148217	−	0.456165i
$313$	25.2984	+	18.3803i	1.42995	+	1.03892i	0.990026	+	0.140883i	$0.0449940\pi$
$313$	25.2984	+	18.3803i	1.42995	+	1.03892i	0.439922	+	0.898036i	$0.355006\pi$
$314$	−12.0902	−	8.78402i	−0.682288	−	0.495711i
$315$	0.118034	−	0.363271i	0.00665046	−	0.0204680i
$316$	1.23607	+	3.80423i	0.0695343	+	0.214004i
$317$	−24.5623	+	17.8456i	−1.37956	+	1.00231i	−0.382635	+	0.923900i	$0.624983\pi$
$317$	−24.5623	+	17.8456i	−1.37956	+	1.00231i	−0.996921	+	0.0784069i	$0.975017\pi$
$318$	4.47214			0.250785
$319$	−14.4721	−	3.24920i	−0.810284	−	0.181920i
$320$	−1.00000			−0.0559017
$321$	−3.73607	+	2.71441i	−0.208527	+	0.151504i
$322$	0.145898	+	0.449028i	0.00813058	+	0.0250234i
$323$	6.35410	−	19.5559i	0.353552	−	1.08812i
$324$	6.23607	+	4.53077i	0.346448	+	0.251709i
$325$	4.23607	+	3.07768i	0.234975	+	0.170719i
$326$	−7.04508	+	21.6825i	−0.390191	+	1.20088i
$327$	2.00000	+	6.15537i	0.110600	+	0.340393i
$328$	2.30902	−	1.67760i	0.127494	−	0.0926299i
$329$	4.76393			0.262644
$330$	4.92705	−	2.12663i	0.271225	−	0.117067i
$331$	−0.965558			−0.0530719			−0.0265359	−	0.999648i	$-0.508448\pi$
$331$	−0.965558			−0.0530719			−0.0265359	+	0.999648i	$0.508448\pi$
$332$	7.16312	−	5.20431i	0.393127	−	0.285624i
$333$	1.32624	+	4.08174i	0.0726774	+	0.223678i
$334$	−2.56231	+	7.88597i	−0.140203	+	0.431501i
$335$	−2.73607	−	1.98787i	−0.149487	−	0.108609i
$336$	−1.30902	−	0.951057i	−0.0714127	−	0.0518844i
$337$	−0.371323	+	1.14281i	−0.0202272	+	0.0622531i	−0.960661	−	0.277725i	$-0.910420\pi$
$337$	−0.371323	+	1.14281i	−0.0202272	+	0.0622531i	0.940433	+	0.339978i	$0.110420\pi$
$338$	−4.45492	−	13.7108i	−0.242315	−	0.745770i
$339$	−5.66312	+	4.11450i	−0.307578	+	0.223469i
$340$	−2.61803			−0.141983
$341$	5.41641	+	6.15537i	0.293315	+	0.333332i
$342$	3.00000			0.162221
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.645898	+	1.98787i	0.0348245	+	0.107179i
$345$	0.236068	−	0.726543i	0.0127095	−	0.0391157i
$346$	16.0902	+	11.6902i	0.865013	+	0.628469i
$347$	−12.2082	−	8.86978i	−0.655371	−	0.476155i	0.209726	−	0.977760i	$-0.432743\pi$
$347$	−12.2082	−	8.86978i	−0.655371	−	0.476155i	−0.865096	+	0.501606i	$0.832743\pi$
$348$	2.23607	−	6.88191i	0.119866	−	0.368909i
$349$	−6.00000	−	18.4661i	−0.321173	−	0.988468i	−0.973139	−	0.230220i	$-0.926056\pi$
$349$	−6.00000	−	18.4661i	−0.321173	−	0.988468i	0.651966	−	0.758248i	$-0.273944\pi$
$350$	0.809017	−	0.587785i	0.0432438	−	0.0314184i
$351$	28.6525			1.52936
$352$	0.309017	+	3.30220i	0.0164707	+	0.176008i
$353$	−11.5623			−0.615399			−0.307700	−	0.951484i	$-0.599559\pi$
$353$	−11.5623			−0.615399			−0.307700	+	0.951484i	$0.599559\pi$
$354$	5.42705	−	3.94298i	0.288445	−	0.209567i
$355$	−3.38197	−	10.4086i	−0.179496	−	0.552432i
$356$	−4.59017	+	14.1271i	−0.243279	+	0.748734i
$357$	−3.42705	−	2.48990i	−0.181379	−	0.131779i
$358$	1.73607	+	1.26133i	0.0917540	+	0.0666632i
$359$	9.14590	−	28.1482i	0.482702	−	1.48560i	−0.352580	−	0.935782i	$-0.614695\pi$
$359$	9.14590	−	28.1482i	0.482702	−	1.48560i	0.835282	−	0.549822i	$-0.185305\pi$
$360$	−0.118034	−	0.363271i	−0.00622094	−	0.0191461i
$361$	−34.5344	+	25.0907i	−1.81760	+	1.32057i
$362$	−20.9443			−1.10081
$363$	−8.54508	−	15.6129i	−0.448501	−	0.819466i
$364$	−5.23607			−0.274445
$365$	2.30902	−	1.67760i	0.120859	−	0.0878095i
$366$	−6.85410	−	21.0948i	−0.358270	−	1.10264i
$367$	4.90983	−	15.1109i	0.256291	−	0.788783i	−0.737282	−	0.675586i	$-0.763891\pi$
$367$	4.90983	−	15.1109i	0.256291	−	0.788783i	0.993573	−	0.113197i	$-0.0361091\pi$
$368$	0.381966	+	0.277515i	0.0199114	+	0.0144664i
$369$	0.881966	+	0.640786i	0.0459133	+	0.0333580i
$370$	−3.47214	+	10.6861i	−0.180508	+	0.555546i
$371$	−0.854102	−	2.62866i	−0.0443428	−	0.136473i
$372$	−3.23607	+	2.35114i	−0.167782	+	0.121901i
$373$	14.6525			0.758676			0.379338	−	0.925258i	$-0.376152\pi$
$373$	14.6525			0.758676			0.379338	+	0.925258i	$0.376152\pi$
$374$	0.809017	+	8.64527i	0.0418333	+	0.447036i
$375$	−1.61803			−0.0835549
$376$	3.85410	−	2.80017i	0.198760	−	0.144408i
$377$	−7.23607	−	22.2703i	−0.372676	−	1.14698i
$378$	1.69098	−	5.20431i	0.0869748	−	0.267681i
$379$	−12.6353	−	9.18005i	−0.649029	−	0.471547i	0.213911	−	0.976853i	$-0.431380\pi$
$379$	−12.6353	−	9.18005i	−0.649029	−	0.471547i	−0.862940	+	0.505306i	$0.831380\pi$
$380$	6.35410	+	4.61653i	0.325959	+	0.236823i
$381$	6.23607	−	19.1926i	0.319483	−	0.983269i
$382$	0.381966	+	1.17557i	0.0195431	+	0.0601474i
$383$	16.3262	−	11.8617i	0.834232	−	0.606105i	−0.0865216	−	0.996250i	$-0.527575\pi$
$383$	16.3262	−	11.8617i	0.834232	−	0.606105i	0.920753	+	0.390145i	$0.127575\pi$
$384$	−1.61803			−0.0825700
$385$	−2.19098	−	2.48990i	−0.111663	−	0.126897i
$386$	21.4164			1.09007
$387$	−0.645898	+	0.469272i	−0.0328328	+	0.0238545i
$388$	−2.59017	−	7.97172i	−0.131496	−	0.404703i
$389$	7.94427	−	24.4500i	0.402791	−	1.23966i	−0.519935	−	0.854206i	$-0.674044\pi$
$389$	7.94427	−	24.4500i	0.402791	−	1.23966i	0.922726	−	0.385456i	$-0.125956\pi$
$390$	6.85410	+	4.97980i	0.347071	+	0.252162i
$391$	1.00000	+	0.726543i	0.0505722	+	0.0367428i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	2.54508	+	7.83297i	0.128383	+	0.395121i
$394$	9.32624	−	6.77591i	0.469849	−	0.341365i
$395$	−4.00000			−0.201262
$396$	−1.16312	+	0.502029i	−0.0584489	+	0.0252279i
$397$	0.111456			0.00559383			0.00279691	−	0.999996i	$-0.499110\pi$
$397$	0.111456			0.00559383			0.00279691	+	0.999996i	$0.499110\pi$
$398$	4.09017	−	2.97168i	0.205022	−	0.148957i
$399$	3.92705	+	12.0862i	0.196598	+	0.605068i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−2.07295	−	1.50609i	−0.103518	−	0.0752103i	0.534822	−	0.844965i	$-0.320379\pi$
$401$	−2.07295	−	1.50609i	−0.103518	−	0.0752103i	−0.638340	+	0.769754i	$0.720379\pi$
$402$	−4.42705	−	3.21644i	−0.220801	−	0.160421i
$403$	−4.00000	+	12.3107i	−0.199254	+	0.613241i
$404$	−4.61803	−	14.2128i	−0.229756	−	0.707116i
$405$	−6.23607	+	4.53077i	−0.309873	+	0.225136i
$406$	−4.47214			−0.221948
$407$	36.3607	+	8.16348i	1.80233	+	0.404649i
$408$	−4.23607			−0.209717
$409$	18.5623	−	13.4863i	0.917847	−	0.666855i	−0.0251402	−	0.999684i	$-0.508003\pi$
$409$	18.5623	−	13.4863i	0.917847	−	0.666855i	0.942987	+	0.332829i	$0.108003\pi$
$410$	0.881966	+	2.71441i	0.0435572	+	0.134055i
$411$	2.42705	−	7.46969i	0.119718	−	0.368453i
$412$	4.85410	+	3.52671i	0.239144	+	0.173749i
$413$	−3.35410	−	2.43690i	−0.165045	−	0.119912i
$414$	−0.0557281	+	0.171513i	−0.00273889	+	0.00842942i
$415$	2.73607	+	8.42075i	0.134308	+	0.413358i
$416$	−4.23607	+	3.07768i	−0.207690	+	0.150896i
$417$	−8.00000			−0.391762
$418$	13.2812	−	22.4091i	0.649602	−	1.09606i
$419$	22.5623			1.10224			0.551120	−	0.834426i	$-0.314200\pi$
$419$	22.5623			1.10224			0.551120	+	0.834426i	$0.314200\pi$
$420$	1.30902	−	0.951057i	0.0638735	−	0.0464068i
$421$	−11.3820	−	35.0301i	−0.554723	−	1.70726i	−0.696674	−	0.717388i	$-0.745337\pi$
$421$	−11.3820	−	35.0301i	−0.554723	−	1.70726i	0.141950	−	0.989874i	$-0.454663\pi$
$422$	−3.29837	+	10.1514i	−0.160562	+	0.494160i
$423$	1.47214	+	1.06957i	0.0715777	+	0.0520042i
$424$	−2.23607	−	1.62460i	−0.108593	−	0.0788975i
$425$	0.809017	−	2.48990i	0.0392431	−	0.120778i
$426$	−5.47214	−	16.8415i	−0.265126	−	0.815973i
$427$	−11.0902	+	8.05748i	−0.536691	+	0.389929i
$428$	2.85410			0.137958
$429$	14.3262	−	24.1724i	0.691677	−	1.16706i
$430$	−2.09017			−0.100797
$431$	0.527864	−	0.383516i	0.0254263	−	0.0184733i	−0.575000	−	0.818154i	$-0.694998\pi$
$431$	0.527864	−	0.383516i	0.0254263	−	0.0184733i	0.600426	+	0.799680i	$0.294998\pi$
$432$	−1.69098	−	5.20431i	−0.0813575	−	0.250393i
$433$	−2.71885	+	8.36775i	−0.130659	+	0.402128i	−0.994890	−	0.100968i	$-0.967806\pi$
$433$	−2.71885	+	8.36775i	−0.130659	+	0.402128i	0.864230	+	0.503097i	$0.167806\pi$
$434$	2.00000	+	1.45309i	0.0960031	+	0.0697503i
$435$	5.85410	+	4.25325i	0.280683	+	0.203928i
$436$	1.23607	−	3.80423i	0.0591969	−	0.182189i
$437$	−1.14590	−	3.52671i	−0.0548157	−	0.168705i
$438$	3.73607	−	2.71441i	0.178516	−	0.129700i
$439$	30.5410			1.45764			0.728822	−	0.684704i	$-0.240068\pi$
$439$	30.5410			1.45764			0.728822	+	0.684704i	$0.240068\pi$
$440$	−3.23607	−	0.726543i	−0.154273	−	0.0346366i
$441$	−0.381966			−0.0181889
$442$	−11.0902	+	8.05748i	−0.527506	+	0.383255i
$443$	−8.82624	−	27.1644i	−0.419347	−	1.29062i	−0.908304	−	0.418310i	$-0.862623\pi$
$443$	−8.82624	−	27.1644i	−0.419347	−	1.29062i	0.488957	−	0.872308i	$-0.337377\pi$
$444$	−5.61803	+	17.2905i	−0.266620	+	0.820572i
$445$	−12.0172	−	8.73102i	−0.569671	−	0.413890i
$446$	10.6180	+	7.71445i	0.502778	+	0.365290i
$447$	5.85410	−	18.0171i	0.276890	−	0.852178i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	16.2082	−	11.7759i	0.764912	−	0.555741i	−0.135501	−	0.990777i	$-0.543264\pi$
$449$	16.2082	−	11.7759i	0.764912	−	0.555741i	0.900413	+	0.435036i	$0.143264\pi$
$450$	0.381966			0.0180061
$451$	8.69098	−	3.75123i	0.409242	−	0.176638i
$452$	4.32624			0.203489
$453$	−24.1803	+	17.5680i	−1.13609	+	0.825419i
$454$	−4.22542	−	13.0045i	−0.198309	−	0.610332i
$455$	1.61803	−	4.97980i	0.0758546	−	0.233456i
$456$	10.2812	+	7.46969i	0.481459	+	0.349801i
$457$	21.0172	+	15.2699i	0.983144	+	0.714296i	0.958409	−	0.285398i	$-0.0921258\pi$
$457$	21.0172	+	15.2699i	0.983144	+	0.714296i	0.0247350	+	0.999694i	$0.492126\pi$
$458$	−6.90983	+	21.2663i	−0.322875	+	0.993708i
$459$	−4.42705	−	13.6251i	−0.206637	−	0.635963i
$460$	−0.381966	+	0.277515i	−0.0178093	+	0.0129392i
$461$	23.0557			1.07381			0.536906	−	0.843642i	$-0.319593\pi$
$461$	23.0557			1.07381			0.536906	+	0.843642i	$0.319593\pi$
$462$	−3.54508	−	4.02874i	−0.164932	−	0.187434i
$463$	−10.9443			−0.508623			−0.254312	−	0.967122i	$-0.581849\pi$
$463$	−10.9443			−0.508623			−0.254312	+	0.967122i	$0.581849\pi$
$464$	−3.61803	+	2.62866i	−0.167963	+	0.122032i
$465$	−1.23607	−	3.80423i	−0.0573213	−	0.176417i
$466$	−0.208204	+	0.640786i	−0.00964486	+	0.0296838i
$467$	−10.4721	−	7.60845i	−0.484593	−	0.352077i	0.318508	−	0.947920i	$-0.396818\pi$
$467$	−10.4721	−	7.60845i	−0.484593	−	0.352077i	−0.803101	+	0.595843i	$0.796818\pi$
$468$	−1.61803	−	1.17557i	−0.0747936	−	0.0543408i
$469$	−1.04508	+	3.21644i	−0.0482575	+	0.148521i
$470$	1.47214	+	4.53077i	0.0679046	+	0.208989i
$471$	19.5623	−	14.2128i	0.901383	−	0.654893i
$472$	−4.14590			−0.190830
$473$	0.645898	+	6.90215i	0.0296984	+	0.317361i
$474$	−6.47214			−0.297275
$475$	−6.35410	+	4.61653i	−0.291546	+	0.211821i
$476$	0.809017	+	2.48990i	0.0370812	+	0.114124i
$477$	0.326238	−	1.00406i	0.0149374	−	0.0459726i
$478$	5.09017	+	3.69822i	0.232819	+	0.169153i
$479$	−18.0344	−	13.1028i	−0.824015	−	0.598682i	0.0938450	−	0.995587i	$-0.470084\pi$
$479$	−18.0344	−	13.1028i	−0.824015	−	0.598682i	−0.917860	+	0.396905i	$0.870084\pi$
$480$	0.500000	−	1.53884i	0.0228218	−	0.0702382i
$481$	18.1803	+	55.9533i	0.828952	+	2.55125i
$482$	−25.0623	+	18.2088i	−1.14156	+	0.829390i
$483$	−0.763932			−0.0347601
$484$	−1.39919	+	10.9106i	−0.0635994	+	0.495939i
$485$	8.38197			0.380605
$486$	3.19098	−	2.31838i	0.144746	−	0.105164i
$487$	11.7984	+	36.3117i	0.534635	+	1.64544i	0.744436	+	0.667694i	$0.232719\pi$
$487$	11.7984	+	36.3117i	0.534635	+	1.64544i	−0.209800	+	0.977744i	$0.567281\pi$
$488$	−4.23607	+	13.0373i	−0.191758	+	0.590170i
$489$	−29.8435	−	21.6825i	−1.34957	−	0.980518i
$490$	−0.809017	−	0.587785i	−0.0365477	−	0.0265534i
$491$	−5.93769	+	18.2743i	−0.267964	+	0.824710i	0.723031	+	0.690815i	$0.242748\pi$
$491$	−5.93769	+	18.2743i	−0.267964	+	0.824710i	−0.990996	+	0.133894i	$0.957252\pi$
$492$	1.42705	+	4.39201i	0.0643364	+	0.198007i
$493$	−9.47214	+	6.88191i	−0.426604	+	0.309946i
$494$	41.1246			1.85028
$495$	−0.118034	−	1.26133i	−0.00530523	−	0.0566924i
$496$	2.47214			0.111002
$497$	−8.85410	+	6.43288i	−0.397161	+	0.288554i
$498$	4.42705	+	13.6251i	0.198381	+	0.610554i
$499$	−6.17376	+	19.0009i	−0.276376	+	0.850596i	0.712477	+	0.701696i	$0.247573\pi$
$499$	−6.17376	+	19.0009i	−0.276376	+	0.850596i	−0.988852	+	0.148901i	$0.952427\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−10.8541	−	7.88597i	−0.484926	−	0.352319i
$502$	−6.18034	+	19.0211i	−0.275842	+	0.848955i
$503$	−6.38197	−	19.6417i	−0.284558	−	0.875779i	−0.986531	−	0.163575i	$-0.947697\pi$
$503$	−6.38197	−	19.6417i	−0.284558	−	0.875779i	0.701973	−	0.712204i	$-0.252303\pi$
$504$	−0.309017	+	0.224514i	−0.0137647	+	0.0100006i
$505$	14.9443			0.665011
$506$	1.03444	+	1.17557i	0.0459865	+	0.0522605i
$507$	23.3262			1.03595
$508$	−10.0902	+	7.33094i	−0.447679	+	0.325258i
$509$	4.05573	+	12.4822i	0.179767	+	0.553266i	0.999819	−	0.0190230i	$-0.00605559\pi$
$509$	4.05573	+	12.4822i	0.179767	+	0.553266i	−0.820052	+	0.572289i	$0.806056\pi$
$510$	1.30902	−	4.02874i	0.0579642	−	0.178396i
$511$	−2.30902	−	1.67760i	−0.102145	−	0.0742126i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−13.2812	+	40.8752i	−0.586377	+	1.80468i
$514$	−4.59017	−	14.1271i	−0.202464	−	0.623119i
$515$	−4.85410	+	3.52671i	−0.213897	+	0.155405i
$516$	−3.38197			−0.148883
$517$	14.5066	−	6.26137i	0.637999	−	0.275375i
$518$	11.2361			0.493684
$519$	−26.0344	+	18.9151i	−1.14279	+	0.830282i
$520$	−1.61803	−	4.97980i	−0.0709555	−	0.218379i
$521$	−2.98936	+	9.20029i	−0.130966	+	0.403072i	−0.994941	−	0.100463i	$-0.967968\pi$
$521$	−2.98936	+	9.20029i	−0.130966	+	0.403072i	0.863975	+	0.503535i	$0.167968\pi$
$522$	−1.38197	−	1.00406i	−0.0604870	−	0.0439464i
$523$	16.8262	+	12.2250i	0.735760	+	0.534561i	0.891380	−	0.453256i	$-0.149738\pi$
$523$	16.8262	+	12.2250i	0.735760	+	0.534561i	−0.155620	+	0.987817i	$0.549738\pi$
$524$	1.57295	−	4.84104i	0.0687146	−	0.211482i
$525$	0.500000	+	1.53884i	0.0218218	+	0.0671606i
$526$	21.3262	−	15.4944i	0.929868	−	0.675589i
$527$	6.47214			0.281931
$528$	−5.23607	−	1.17557i	−0.227871	−	0.0511601i
$529$	−22.7771			−0.990308
$530$	2.23607	−	1.62460i	0.0971286	−	0.0705680i
$531$	−0.489357	−	1.50609i	−0.0212363	−	0.0653585i
$532$	2.42705	−	7.46969i	0.105226	−	0.323852i
$533$	12.0902	+	8.78402i	0.523683	+	0.380478i
$534$	−19.4443	−	14.1271i	−0.841436	−	0.611339i
$535$	−0.881966	+	2.71441i	−0.0381307	+	0.117354i
$536$	1.04508	+	3.21644i	0.0451408	+	0.138929i
$537$	−2.80902	+	2.04087i	−0.121218	+	0.0880701i
$538$	18.6525			0.804165
$539$	−1.69098	+	2.85317i	−0.0728358	+	0.122895i
$540$	5.47214			0.235483
$541$	34.7984	−	25.2825i	1.49610	−	1.08698i	0.524196	−	0.851598i	$-0.324366\pi$
$541$	34.7984	−	25.2825i	1.49610	−	1.08698i	0.971903	−	0.235382i	$-0.0756341\pi$
$542$	1.90983	+	5.87785i	0.0820342	+	0.252475i
$543$	10.4721	−	32.2299i	0.449402	−	1.38312i
$544$	2.11803	+	1.53884i	0.0908100	+	0.0659773i
$545$	3.23607	+	2.35114i	0.138618	+	0.100712i
$546$	2.61803	−	8.05748i	0.112042	−	0.344828i
$547$	−6.84346	−	21.0620i	−0.292605	−	0.900546i	−0.984015	−	0.178084i	$-0.943010\pi$
$547$	−6.84346	−	21.0620i	−0.292605	−	0.900546i	0.691410	−	0.722462i	$-0.256990\pi$
$548$	−3.92705	+	2.85317i	−0.167755	+	0.121881i
$549$	−5.23607			−0.223470
$550$	1.69098	−	2.85317i	0.0721038	−	0.121660i
$551$	35.1246			1.49636
$552$	−0.618034	+	0.449028i	−0.0263053	+	0.0191119i
$553$	1.23607	+	3.80423i	0.0525630	+	0.161772i
$554$	3.70820	−	11.4127i	0.157546	−	0.484878i
$555$	−14.7082	−	10.6861i	−0.624328	−	0.453601i
$556$	4.00000	+	2.90617i	0.169638	+	0.123249i
$557$	5.79837	−	17.8456i	0.245685	−	0.756141i	−0.749838	−	0.661621i	$-0.769869\pi$
$557$	5.79837	−	17.8456i	0.245685	−	0.756141i	0.995523	−	0.0945192i	$-0.0301314\pi$
$558$	0.291796	+	0.898056i	0.0123527	+	0.0380177i
$559$	−8.85410	+	6.43288i	−0.374489	+	0.272082i
$560$	−1.00000			−0.0422577
$561$	−13.7082	−	3.07768i	−0.578761	−	0.129940i
$562$	−11.3262			−0.477769
$563$	−23.9615	+	17.4090i	−1.00986	+	0.733704i	−0.964179	−	0.265253i	$-0.914545\pi$
$563$	−23.9615	+	17.4090i	−1.00986	+	0.733704i	−0.0456775	+	0.998956i	$0.514545\pi$
$564$	2.38197	+	7.33094i	0.100299	+	0.308688i
$565$	−1.33688	+	4.11450i	−0.0562430	+	0.173098i
$566$	13.2361	+	9.61657i	0.556353	+	0.404214i
$567$	6.23607	+	4.53077i	0.261890	+	0.190274i
$568$	−3.38197	+	10.4086i	−0.141904	+	0.436736i
$569$	13.6976	+	42.1568i	0.574232	+	1.76730i	0.638781	+	0.769389i	$0.279439\pi$
$569$	13.6976	+	42.1568i	0.574232	+	1.76730i	−0.0645493	+	0.997915i	$0.520561\pi$
$570$	−10.2812	+	7.46969i	−0.430630	+	0.312871i
$571$	−34.8328			−1.45771			−0.728854	−	0.684669i	$-0.759947\pi$
$571$	−34.8328			−1.45771			−0.728854	+	0.684669i	$0.759947\pi$
$572$	−15.9443	+	6.88191i	−0.666663	+	0.287747i
$573$	−2.00000			−0.0835512
$574$	2.30902	−	1.67760i	0.0963765	−	0.0700216i
$575$	−0.145898	−	0.449028i	−0.00608437	−	0.0187258i
$576$	−0.118034	+	0.363271i	−0.00491808	+	0.0151363i
$577$	21.3541	+	15.5147i	0.888983	+	0.645884i	0.935613	−	0.353028i	$-0.114848\pi$
$577$	21.3541	+	15.5147i	0.888983	+	0.645884i	−0.0466297	+	0.998912i	$0.514848\pi$
$578$	−8.20820	−	5.96361i	−0.341416	−	0.248053i
$579$	−10.7082	+	32.9565i	−0.445018	+	1.36962i
$580$	−1.38197	−	4.25325i	−0.0573830	−	0.176607i
$581$	7.16312	−	5.20431i	0.297176	−	0.215911i
$582$	13.5623			0.562176
$583$	−6.05573	−	6.88191i	−0.250803	−	0.285020i
$584$	−2.85410			−0.118104
$585$	1.61803	−	1.17557i	0.0668975	−	0.0486039i
$586$	−5.70820	−	17.5680i	−0.235804	−	0.725729i
$587$	−2.53851	+	7.81272i	−0.104775	+	0.322466i	−0.989678	−	0.143311i	$-0.954225\pi$
$587$	−2.53851	+	7.81272i	−0.104775	+	0.322466i	0.884902	+	0.465777i	$0.154225\pi$
$588$	−1.30902	−	0.951057i	−0.0539830	−	0.0392209i
$589$	−15.7082	−	11.4127i	−0.647245	−	0.470251i
$590$	1.28115	−	3.94298i	0.0527442	−	0.162330i
$591$	5.76393	+	17.7396i	0.237096	+	0.729708i
$592$	9.09017	−	6.60440i	0.373604	−	0.271439i
$593$	−34.0344			−1.39763			−0.698814	−	0.715304i	$-0.746288\pi$
$593$	−34.0344			−1.39763			−0.698814	+	0.715304i	$0.746288\pi$
$594$	−1.69098	−	18.0701i	−0.0693819	−	0.741424i
$595$	−2.61803			−0.107329
$596$	−9.47214	+	6.88191i	−0.387994	+	0.281894i
$597$	2.52786	+	7.77997i	0.103459	+	0.318413i
$598$	−0.763932	+	2.35114i	−0.0312395	+	0.0961453i
$599$	29.1803	+	21.2008i	1.19228	+	0.866239i	0.993503	−	0.113806i	$-0.0363042\pi$
$599$	29.1803	+	21.2008i	1.19228	+	0.866239i	0.198773	+	0.980045i	$0.436304\pi$
$600$	1.30902	+	0.951057i	0.0534404	+	0.0388267i
$601$	−10.2984	+	31.6951i	−0.420079	+	1.29287i	0.487548	+	0.873096i	$0.337891\pi$
$601$	−10.2984	+	31.6951i	−0.420079	+	1.29287i	−0.907628	+	0.419776i	$0.862109\pi$
$602$	0.645898	+	1.98787i	0.0263248	+	0.0810195i
$603$	−1.04508	+	0.759299i	−0.0425592	+	0.0309210i
$604$	18.4721			0.751621
$605$	−9.94427	−	4.70228i	−0.404292	−	0.191175i
$606$	24.1803			0.982259
$607$	5.52786	−	4.01623i	0.224369	−	0.163014i	−0.469922	−	0.882708i	$-0.655718\pi$
$607$	5.52786	−	4.01623i	0.224369	−	0.163014i	0.694291	+	0.719694i	$0.255718\pi$
$608$	−2.42705	−	7.46969i	−0.0984299	−	0.302936i
$609$	2.23607	−	6.88191i	0.0906100	−	0.278869i
$610$	−11.0902	−	8.05748i	−0.449028	−	0.326238i
$611$	20.1803	+	14.6619i	0.816409	+	0.593156i
$612$	−0.309017	+	0.951057i	−0.0124913	+	0.0384442i
$613$	−3.23607	−	9.95959i	−0.130704	−	0.402264i	0.864193	−	0.503160i	$-0.167829\pi$
$613$	−3.23607	−	9.95959i	−0.130704	−	0.402264i	−0.994897	+	0.100895i	$0.967829\pi$
$614$	15.0172	−	10.9106i	0.606046	−	0.440318i
$615$	−4.61803			−0.186217
$616$	0.309017	+	3.30220i	0.0124506	+	0.133049i
$617$	−5.56231			−0.223930			−0.111965	−	0.993712i	$-0.535714\pi$
$617$	−5.56231			−0.223930			−0.111965	+	0.993712i	$0.535714\pi$
$618$	−7.85410	+	5.70634i	−0.315938	+	0.229543i
$619$	13.3713	+	41.1527i	0.537439	+	1.65407i	0.738320	+	0.674451i	$0.235620\pi$
$619$	13.3713	+	41.1527i	0.537439	+	1.65407i	−0.200881	+	0.979616i	$0.564380\pi$
$620$	−0.763932	+	2.35114i	−0.0306802	+	0.0944241i
$621$	−2.09017	−	1.51860i	−0.0838756	−	0.0609392i
$622$	−1.76393	−	1.28157i	−0.0707272	−	0.0513863i
$623$	−4.59017	+	14.1271i	−0.183901	+	0.565990i
$624$	−2.61803	−	8.05748i	−0.104805	−	0.322557i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	31.2705			1.24982
$627$	27.8435	+	31.6421i	1.11196	+	1.26367i
$628$	−14.9443			−0.596341
$629$	23.7984	−	17.2905i	0.948903	−	0.689419i
$630$	−0.118034	−	0.363271i	−0.00470259	−	0.0144731i
$631$	7.76393	−	23.8949i	0.309077	−	0.951242i	−0.669047	−	0.743220i	$-0.733297\pi$
$631$	7.76393	−	23.8949i	0.309077	−	0.951242i	0.978124	−	0.208022i	$-0.0667025\pi$
$632$	3.23607	+	2.35114i	0.128724	+	0.0935234i
$633$	−13.9721	−	10.1514i	−0.555343	−	0.403480i
$634$	−9.38197	+	28.8747i	−0.372605	+	1.14676i
$635$	−3.85410	−	11.8617i	−0.152945	−	0.470717i
$636$	3.61803	−	2.62866i	0.143464	−	0.104233i
$637$	−5.23607			−0.207461
$638$	−13.6180	+	5.87785i	−0.539143	+	0.232706i
$639$	−4.18034			−0.165372
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−12.6246	−	38.8546i	−0.498642	−	1.53466i	−0.811203	−	0.584765i	$-0.801187\pi$
$641$	−12.6246	−	38.8546i	−0.498642	−	1.53466i	0.312561	−	0.949898i	$-0.398813\pi$
$642$	−1.42705	+	4.39201i	−0.0563212	+	0.173339i
$643$	11.4894	+	8.34751i	0.453096	+	0.329194i	0.790817	−	0.612053i	$-0.209656\pi$
$643$	11.4894	+	8.34751i	0.453096	+	0.329194i	−0.337721	+	0.941246i	$0.609656\pi$
$644$	0.381966	+	0.277515i	0.0150516	+	0.0109356i
$645$	1.04508	−	3.21644i	0.0411502	−	0.126647i
$646$	−6.35410	−	19.5559i	−0.249999	−	0.769417i
$647$	−30.5066	+	22.1643i	−1.19934	+	0.871370i	−0.994219	−	0.107368i	$-0.965758\pi$
$647$	−30.5066	+	22.1643i	−1.19934	+	0.871370i	−0.205118	+	0.978737i	$0.565758\pi$
$648$	7.70820			0.302807
$649$	−13.4164	−	3.01217i	−0.526640	−	0.118238i
$650$	5.23607			0.205375
$651$	−3.23607	+	2.35114i	−0.126832	+	0.0921485i
$652$	7.04508	+	21.6825i	0.275907	+	0.849154i
$653$	13.7984	−	42.4670i	0.539972	−	1.66186i	−0.192681	−	0.981261i	$-0.561718\pi$
$653$	13.7984	−	42.4670i	0.539972	−	1.66186i	0.732653	−	0.680602i	$-0.238282\pi$
$654$	5.23607	+	3.80423i	0.204746	+	0.148757i
$655$	4.11803	+	2.99193i	0.160905	+	0.116904i
$656$	0.881966	−	2.71441i	0.0344350	−	0.105980i
$657$	−0.336881	−	1.03681i	−0.0131430	−	0.0404499i
$658$	3.85410	−	2.80017i	0.150249	−	0.109162i
$659$	−20.9787			−0.817215			−0.408607	−	0.912710i	$-0.633985\pi$
$659$	−20.9787			−0.817215			−0.408607	+	0.912710i	$0.633985\pi$
$660$	2.73607	−	4.61653i	0.106501	−	0.179698i
$661$	1.81966			0.0707766			0.0353883	−	0.999374i	$-0.488733\pi$
$661$	1.81966			0.0707766			0.0353883	+	0.999374i	$0.488733\pi$
$662$	−0.781153	+	0.567541i	−0.0303604	+	0.0220581i
$663$	−6.85410	−	21.0948i	−0.266191	−	0.819252i
$664$	2.73607	−	8.42075i	0.106180	−	0.326789i
$665$	6.35410	+	4.61653i	0.246402	+	0.179021i
$666$	3.47214	+	2.52265i	0.134543	+	0.0977509i
$667$	−0.652476	+	2.00811i	−0.0252640	+	0.0777545i
$668$	2.56231	+	7.88597i	0.0991386	+	0.305117i
$669$	−17.1803	+	12.4822i	−0.664230	+	0.482592i
$670$	−3.38197			−0.130657
$671$	−23.1803	+	39.1118i	−0.894867	+	1.50990i
$672$	−1.61803			−0.0624170
$673$	−12.5000	+	9.08178i	−0.481840	+	0.350077i	−0.802037	−	0.597274i	$-0.796251\pi$
$673$	−12.5000	+	9.08178i	−0.481840	+	0.350077i	0.320198	+	0.947351i	$0.396251\pi$
$674$	0.371323	+	1.14281i	0.0143028	+	0.0440196i
$675$	−1.69098	+	5.20431i	−0.0650860	+	0.200314i
$676$	−11.6631	−	8.47375i	−0.448581	−	0.325914i
$677$	−9.23607	−	6.71040i	−0.354971	−	0.257901i	0.395980	−	0.918259i	$-0.370405\pi$
$677$	−9.23607	−	6.71040i	−0.354971	−	0.257901i	−0.750951	+	0.660357i	$0.770405\pi$
$678$	−2.16312	+	6.65740i	−0.0830741	+	0.255676i
$679$	−2.59017	−	7.97172i	−0.0994016	−	0.305927i
$680$	−2.11803	+	1.53884i	−0.0812229	+	0.0590119i
$681$	22.1246			0.847817
$682$	8.00000	+	1.79611i	0.306336	+	0.0687767i
$683$	21.5279			0.823741			0.411870	−	0.911242i	$-0.364876\pi$
$683$	21.5279			0.823741			0.411870	+	0.911242i	$0.364876\pi$
$684$	2.42705	−	1.76336i	0.0928006	−	0.0674236i
$685$	−1.50000	−	4.61653i	−0.0573121	−	0.176388i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	−29.2705	−	21.2663i	−1.11674	−	0.811359i
$688$	1.69098	+	1.22857i	0.0644681	+	0.0468388i
$689$	4.47214	−	13.7638i	0.170375	−	0.524360i
$690$	−0.236068	−	0.726543i	−0.00898695	−	0.0276590i
$691$	6.11803	−	4.44501i	0.232741	−	0.169096i	−0.465302	−	0.885152i	$-0.654054\pi$
$691$	6.11803	−	4.44501i	0.232741	−	0.169096i	0.698043	+	0.716056i	$0.254054\pi$
$692$	19.8885			0.756049
$693$	−1.16312	+	0.502029i	−0.0441832	+	0.0190705i
$694$	−15.0902			−0.572815
$695$	−4.00000	+	2.90617i	−0.151729	+	0.110237i
$696$	−2.23607	−	6.88191i	−0.0847579	−	0.260858i
$697$	2.30902	−	7.10642i	0.0874603	−	0.269175i
$698$	−15.7082	−	11.4127i	−0.594564	−	0.431976i
$699$	−0.881966	−	0.640786i	−0.0333590	−	0.0242367i
$700$	0.309017	−	0.951057i	0.0116797	−	0.0359466i
$701$	−10.7639	−	33.1280i	−0.406548	−	1.25123i	−0.919596	−	0.392866i	$-0.871484\pi$
$701$	−10.7639	−	33.1280i	−0.406548	−	1.25123i	0.513048	−	0.858360i	$-0.328516\pi$
$702$	23.1803	−	16.8415i	0.874886	−	0.635642i
$703$	−88.2492			−3.32838
$704$	2.19098	+	2.48990i	0.0825758	+	0.0938416i
$705$	−7.70820			−0.290308
$706$	−9.35410	+	6.79615i	−0.352046	+	0.255777i
$707$	−4.61803	−	14.2128i	−0.173679	−	0.534529i
$708$	2.07295	−	6.37988i	0.0779062	−	0.239771i
$709$	−27.3262	−	19.8537i	−1.02626	−	0.745620i	−0.0587020	−	0.998276i	$-0.518696\pi$
$709$	−27.3262	−	19.8537i	−1.02626	−	0.745620i	−0.967556	+	0.252655i	$0.918696\pi$
$710$	−8.85410	−	6.43288i	−0.332289	−	0.241422i
$711$	−0.472136	+	1.45309i	−0.0177065	+	0.0544949i
$712$	4.59017	+	14.1271i	0.172024	+	0.529435i
$713$	0.944272	−	0.686054i	0.0353633	−	0.0256929i
$714$	−4.23607			−0.158531
$715$	−1.61803	−	17.2905i	−0.0605110	−	0.646629i
$716$	2.14590			0.0801960
$717$	−8.23607	+	5.98385i	−0.307582	+	0.223471i
$718$	−9.14590	−	28.1482i	−0.341322	−	1.05048i
$719$	7.43769	−	22.8909i	0.277379	−	0.853685i	−0.711201	−	0.702989i	$-0.751848\pi$
$719$	7.43769	−	22.8909i	0.277379	−	0.853685i	0.988580	−	0.150697i	$-0.0481516\pi$
$720$	−0.309017	−	0.224514i	−0.0115164	−	0.00836714i
$721$	4.85410	+	3.52671i	0.180776	+	0.131342i
$722$	−13.1910	+	40.5977i	−0.490918	+	1.51089i
$723$	−15.4894	−	47.6713i	−0.576055	−	1.77292i
$724$	−16.9443	+	12.3107i	−0.629729	+	0.457525i
$725$	4.47214			0.166091
$726$	−16.0902	−	7.60845i	−0.597162	−	0.282376i
$727$	50.2492			1.86364			0.931820	−	0.362920i	$-0.118220\pi$
$727$	50.2492			1.86364			0.931820	+	0.362920i	$0.118220\pi$
$728$	−4.23607	+	3.07768i	−0.156999	+	0.114067i
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$	0.881966	−	2.71441i	0.0326430	−	0.100465i
$731$	4.42705	+	3.21644i	0.163740	+	0.118964i
$732$	−17.9443	−	13.0373i	−0.663239	−	0.481872i
$733$	−11.0000	+	33.8545i	−0.406294	+	1.25045i	0.513515	+	0.858080i	$0.328343\pi$
$733$	−11.0000	+	33.8545i	−0.406294	+	1.25045i	−0.919810	+	0.392365i	$0.871657\pi$
$734$	−4.90983	−	15.1109i	−0.181225	−	0.557754i
$735$	1.30902	−	0.951057i	0.0482838	−	0.0350802i
$736$	0.472136			0.0174032
$737$	1.04508	+	11.1679i	0.0384962	+	0.411376i
$738$	1.09017			0.0401297
$739$	−8.20820	+	5.96361i	−0.301944	+	0.219375i	−0.728432	−	0.685118i	$-0.759751\pi$
$739$	−8.20820	+	5.96361i	−0.301944	+	0.219375i	0.426488	+	0.904493i	$0.359751\pi$
$740$	3.47214	+	10.6861i	0.127638	+	0.392830i
$741$	−20.5623	+	63.2843i	−0.755375	+	2.32481i
$742$	−2.23607	−	1.62460i	−0.0820886	−	0.0596409i
$743$	32.5623	+	23.6579i	1.19460	+	0.867924i	0.993742	−	0.111697i	$-0.0356287\pi$
$743$	32.5623	+	23.6579i	1.19460	+	0.867924i	0.200853	+	0.979621i	$0.435629\pi$
$744$	−1.23607	+	3.80423i	−0.0453165	+	0.139470i
$745$	−3.61803	−	11.1352i	−0.132555	−	0.407961i
$746$	11.8541	−	8.61251i	0.434010	−	0.315326i
$747$	3.38197			0.123740
$748$	5.73607	+	6.51864i	0.209731	+	0.238345i
$749$	2.85410			0.104287
$750$	−1.30902	+	0.951057i	−0.0477985	+	0.0347277i
$751$	−14.0000	−	43.0876i	−0.510867	−	1.57229i	−0.790678	−	0.612233i	$-0.790272\pi$
$751$	−14.0000	−	43.0876i	−0.510867	−	1.57229i	0.279811	−	0.960055i	$-0.409728\pi$
$752$	1.47214	−	4.53077i	0.0536833	−	0.165220i
$753$	−26.1803	−	19.0211i	−0.954065	−	0.693169i
$754$	−18.9443	−	13.7638i	−0.689910	−	0.501249i
$755$	−5.70820	+	17.5680i	−0.207743	+	0.639367i
$756$	−1.69098	−	5.20431i	−0.0615005	−	0.189279i
$757$	−36.1246	+	26.2461i	−1.31297	+	0.953930i	−0.312980	+	0.949760i	$0.601327\pi$
$757$	−36.1246	+	26.2461i	−1.31297	+	0.953930i	−0.999991	+	0.00416982i	$0.998673\pi$
$758$	−15.6180			−0.567273
$759$	−2.32624	+	1.00406i	−0.0844371	+	0.0364450i
$760$	7.85410			0.284898
$761$	40.2984	−	29.2785i	1.46081	−	1.06134i	0.477665	−	0.878542i	$-0.341483\pi$
$761$	40.2984	−	29.2785i	1.46081	−	1.06134i	0.983150	−	0.182802i	$-0.0585168\pi$
$762$	−6.23607	−	19.1926i	−0.225909	−	0.695276i
$763$	1.23607	−	3.80423i	0.0447487	−	0.137722i
$764$	1.00000	+	0.726543i	0.0361787	+	0.0262854i
$765$	−0.809017	−	0.587785i	−0.0292501	−	0.0212514i
$766$	6.23607	−	19.1926i	0.225318	−	0.693458i
$767$	−6.70820	−	20.6457i	−0.242219	−	0.745474i
$768$	−1.30902	+	0.951057i	−0.0472351	+	0.0343183i
$769$	31.3050			1.12889			0.564443	−	0.825472i	$-0.309091\pi$
$769$	31.3050			1.12889			0.564443	+	0.825472i	$0.309091\pi$
$770$	−3.23607	−	0.726543i	−0.116620	−	0.0261828i
$771$	24.0344			0.865579
$772$	17.3262	−	12.5882i	0.623585	−	0.453061i
$773$	10.7426	+	33.0625i	0.386386	+	1.18917i	0.935470	+	0.353407i	$0.114977\pi$
$773$	10.7426	+	33.0625i	0.386386	+	1.18917i	−0.549084	+	0.835767i	$0.685023\pi$
$774$	−0.246711	+	0.759299i	−0.00886785	+	0.0272924i
$775$	−2.00000	−	1.45309i	−0.0718421	−	0.0521964i
$776$	−6.78115	−	4.92680i	−0.243429	−	0.176862i
$777$	−5.61803	+	17.2905i	−0.201546	+	0.620294i
$778$	−7.94427	−	24.4500i	−0.284816	−	0.876573i
$779$	−18.1353	+	13.1760i	−0.649763	+	0.472080i
$780$	8.47214			0.303351
$781$	−18.5066	+	31.2259i	−0.662217	+	1.11735i
$782$	1.23607			0.0442017
$783$	19.7984	−	14.3844i	0.707536	−	0.514055i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	4.61803	−	14.2128i	0.164825	−	0.507278i
$786$	6.66312	+	4.84104i	0.237666	+	0.172674i
$787$	−35.0066	−	25.4338i	−1.24785	−	0.906616i	−0.249755	−	0.968309i	$-0.580350\pi$
$787$	−35.0066	−	25.4338i	−1.24785	−	0.906616i	−0.998095	+	0.0616933i	$0.980350\pi$
$788$	3.56231	−	10.9637i	0.126902	−	0.390564i
$789$	13.1803	+	40.5649i	0.469233	+	1.44415i
$790$	−3.23607	+	2.35114i	−0.115134	+	0.0836498i
$791$	4.32624			0.153823
$792$	−0.645898	+	1.08981i	−0.0229510	+	0.0387248i
$793$	−71.7771			−2.54888
$794$	0.0901699	−	0.0655123i	0.00320001	−	0.00232494i
$795$	1.38197	+	4.25325i	0.0490133	+	0.150847i
$796$	1.56231	−	4.80828i	0.0553745	−	0.170425i
$797$	6.61803	+	4.80828i	0.234423	+	0.170318i	0.698795	−	0.715322i	$-0.253720\pi$
$797$	6.61803	+	4.80828i	0.234423	+	0.170318i	−0.464372	+	0.885640i	$0.653720\pi$
$798$	10.2812	+	7.46969i	0.363949	+	0.264424i
$799$	3.85410	−	11.8617i	0.136348	−	0.419637i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$	−4.59017	+	3.33495i	−0.162186	+	0.117835i
$802$	−2.56231			−0.0904782
$803$	−9.23607	−	2.07363i	−0.325934	−	0.0731767i
$804$	−5.47214			−0.192987
$805$	−0.381966	+	0.277515i	−0.0134625	+	0.00978110i
$806$	4.00000	+	12.3107i	0.140894	+	0.433627i
$807$	−9.32624	+	28.7032i	−0.328299	+	1.01040i
$808$	−12.0902	−	8.78402i	−0.425331	−	0.309021i
$809$	−21.9721	−	15.9637i	−0.772499	−	0.561253i	0.130219	−	0.991485i	$-0.458432\pi$
$809$	−21.9721	−	15.9637i	−0.772499	−	0.561253i	−0.902718	+	0.430232i	$0.858432\pi$
$810$	−2.38197	+	7.33094i	−0.0836938	+	0.257583i
$811$	11.0279	+	33.9403i	0.387241	+	1.19180i	0.934842	+	0.355065i	$0.115541\pi$
$811$	11.0279	+	33.9403i	0.387241	+	1.19180i	−0.547601	+	0.836740i	$0.684459\pi$
$812$	−3.61803	+	2.62866i	−0.126968	+	0.0922477i
$813$	−10.0000			−0.350715
$814$	34.2148	−	14.7679i	1.19923	−	0.517614i
$815$	−22.7984			−0.798592
$816$	−3.42705	+	2.48990i	−0.119971	+	0.0871639i
$817$	−5.07295	−	15.6129i	−0.177480	−	0.546227i
$818$	7.09017	−	21.8213i	0.247902	−	0.762964i
$819$	−1.61803	−	1.17557i	−0.0565387	−	0.0410778i
$820$	2.30902	+	1.67760i	0.0806344	+	0.0585843i
$821$	−0.0344419	+	0.106001i	−0.00120203	+	0.00369946i	−0.951656	−	0.307167i	$-0.900619\pi$
$821$	−0.0344419	+	0.106001i	−0.00120203	+	0.00369946i	0.950454	+	0.310866i	$0.100619\pi$
$822$	−2.42705	−	7.46969i	−0.0846531	−	0.260536i
$823$	3.09017	−	2.24514i	0.107717	−	0.0782607i	−0.532623	−	0.846353i	$-0.678794\pi$
$823$	3.09017	−	2.24514i	0.107717	−	0.0782607i	0.640340	+	0.768092i	$0.278794\pi$
$824$	6.00000			0.209020
$825$	3.54508	+	4.02874i	0.123424	+	0.140263i
$826$	−4.14590			−0.144254
$827$	−42.3328	+	30.7566i	−1.47206	+	1.06951i	−0.492045	+	0.870570i	$0.663750\pi$
$827$	−42.3328	+	30.7566i	−1.47206	+	1.06951i	−0.980011	+	0.198942i	$0.936250\pi$
$828$	0.0557281	+	0.171513i	0.00193669	+	0.00596050i
$829$	10.3607	−	31.8869i	0.359841	−	1.10748i	−0.593308	−	0.804976i	$-0.702178\pi$
$829$	10.3607	−	31.8869i	0.359841	−	1.10748i	0.953149	−	0.302502i	$-0.0978218\pi$
$830$	7.16312	+	5.20431i	0.248635	+	0.180644i
$831$	15.7082	+	11.4127i	0.544912	+	0.395901i
$832$	−1.61803	+	4.97980i	−0.0560952	+	0.172643i
$833$	0.809017	+	2.48990i	0.0280308	+	0.0862699i
$834$	−6.47214	+	4.70228i	−0.224112	+	0.162827i
$835$	−8.29180			−0.286949
$836$	−2.42705	−	25.9358i	−0.0839413	−	0.897008i
$837$	−13.5279			−0.467591
$838$	18.2533	−	13.2618i	0.630549	−	0.458121i
$839$	11.2148	+	34.5155i	0.387177	+	1.19161i	0.934888	+	0.354942i	$0.115499\pi$
$839$	11.2148	+	34.5155i	0.387177	+	1.19161i	−0.547711	+	0.836667i	$0.684501\pi$
$840$	0.500000	−	1.53884i	0.0172516	−	0.0530951i
$841$	7.28115	+	5.29007i	0.251074	+	0.182416i
$842$	−29.7984	−	21.6498i	−1.02692	−	0.746101i
$843$	5.66312	−	17.4293i	0.195048	−	0.600297i
$844$	3.29837	+	10.1514i	0.113535	+	0.349424i
$845$	11.6631	−	8.47375i	0.401223	−	0.291506i
$846$	1.81966			0.0625612
$847$	−1.39919	+	10.9106i	−0.0480766	+	0.374894i
$848$	−2.76393			−0.0949138
$849$	−21.4164	+	15.5599i	−0.735009	+	0.534015i
$850$	−0.809017	−	2.48990i	−0.0277491	−	0.0854028i
$851$	1.63932	−	5.04531i	0.0561952	−	0.172951i
$852$	−14.3262	−	10.4086i	−0.490809	−	0.356593i
$853$	10.8541	+	7.88597i	0.371637	+	0.270010i	0.757890	−	0.652383i	$-0.226231\pi$
$853$	10.8541	+	7.88597i	0.371637	+	0.270010i	−0.386252	+	0.922393i	$0.626231\pi$
$854$	−4.23607	+	13.0373i	−0.144955	+	0.446126i
$855$	0.927051	+	2.85317i	0.0317045	+	0.0975763i
$856$	2.30902	−	1.67760i	0.0789206	−	0.0573392i
$857$	24.5623			0.839032			0.419516	−	0.907748i	$-0.362200\pi$
$857$	24.5623			0.839032			0.419516	+	0.907748i	$0.362200\pi$
$858$	−2.61803	−	27.9767i	−0.0893782	−	0.955108i
$859$	14.3262			0.488805			0.244402	−	0.969674i	$-0.421408\pi$
$859$	14.3262			0.488805			0.244402	+	0.969674i	$0.421408\pi$
$860$	−1.69098	+	1.22857i	−0.0576620	+	0.0418939i
$861$	1.42705	+	4.39201i	0.0486338	+	0.149679i
$862$	0.201626	−	0.620541i	0.00686741	−	0.0211357i
$863$	11.4164	+	8.29451i	0.388619	+	0.282348i	0.764889	−	0.644162i	$-0.222794\pi$
$863$	11.4164	+	8.29451i	0.388619	+	0.282348i	−0.376270	+	0.926510i	$0.622794\pi$
$864$	−4.42705	−	3.21644i	−0.150611	−	0.109426i
$865$	−6.14590	+	18.9151i	−0.208967	+	0.643134i
$866$	2.71885	+	8.36775i	0.0923902	+	0.284348i
$867$	13.2812	−	9.64932i	0.451052	−	0.327708i
$868$	2.47214			0.0839098
$869$	8.76393	+	9.95959i	0.297296	+	0.337856i
$870$	7.23607			0.245326
$871$	−14.3262	+	10.4086i	−0.485426	+	0.352683i
$872$	−1.23607	−	3.80423i	−0.0418585	−	0.128827i
$873$	0.989357	−	3.04493i	0.0334847	−	0.103055i
$874$	−3.00000	−	2.17963i	−0.101477	−	0.0737270i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	1.42705	−	4.39201i	0.0482156	−	0.148392i
$877$	−0.854102	−	2.62866i	−0.0288410	−	0.0887634i	0.935600	−	0.353062i	$-0.114860\pi$
$877$	−0.854102	−	2.62866i	−0.0288410	−	0.0887634i	−0.964441	+	0.264299i	$0.914860\pi$
$878$	24.7082	−	17.9516i	0.833861	−	0.605836i
$879$	29.8885			1.00812
$880$	−3.04508	+	1.31433i	−0.102650	+	0.0443060i
$881$	14.6738			0.494372			0.247186	−	0.968968i	$-0.420494\pi$
$881$	14.6738			0.494372			0.247186	+	0.968968i	$0.420494\pi$
$882$	−0.309017	+	0.224514i	−0.0104051	+	0.00755978i
$883$	−13.3541	−	41.0997i	−0.449401	−	1.38312i	−0.877584	−	0.479423i	$-0.840846\pi$
$883$	−13.3541	−	41.0997i	−0.449401	−	1.38312i	0.428183	−	0.903692i	$-0.359154\pi$
$884$	−4.23607	+	13.0373i	−0.142474	+	0.438491i
$885$	5.42705	+	3.94298i	0.182428	+	0.132542i
$886$	−23.1074	−	16.7885i	−0.776308	−	0.564021i
$887$	8.20163	−	25.2420i	0.275384	−	0.847544i	−0.713734	−	0.700417i	$-0.752997\pi$
$887$	8.20163	−	25.2420i	0.275384	−	0.847544i	0.989118	−	0.147127i	$-0.0470026\pi$
$888$	5.61803	+	17.2905i	0.188529	+	0.580232i
$889$	−10.0902	+	7.33094i	−0.338413	+	0.245872i
$890$	−14.8541			−0.497911
$891$	24.9443	+	5.60034i	0.835665	+	0.187618i
$892$	13.1246			0.439445
$893$	−30.2705	+	21.9928i	−1.01296	+	0.735961i
$894$	−5.85410	−	18.0171i	−0.195790	−	0.602581i
$895$	−0.663119	+	2.04087i	−0.0221656	+	0.0682188i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	−3.23607	−	2.35114i	−0.108049	−	0.0785023i
$898$	6.19098	−	19.0539i	0.206596	−	0.635836i
$899$	3.41641	+	10.5146i	0.113944	+	0.350682i
$900$	0.309017	−	0.224514i	0.0103006	−	0.00748380i
$901$	−7.23607			−0.241068
$902$	4.82624	−	8.14324i	0.160696	−	0.271140i
$903$	−3.38197			−0.112545
$904$	3.50000	−	2.54290i	0.116408	−	0.0845756i
$905$	−6.47214	−	19.9192i	−0.215141	−	0.662136i
$906$	−9.23607	+	28.4257i	−0.306848	+	0.944380i
$907$	−20.9164	−	15.1967i	−0.694518	−	0.504597i	0.183624	−	0.982997i	$-0.441217\pi$
$907$	−20.9164	−	15.1967i	−0.694518	−	0.504597i	−0.878142	+	0.478400i	$0.841217\pi$
$908$	−11.0623	−	8.03724i	−0.367116	−	0.266725i
$909$	1.76393	−	5.42882i	0.0585059	−	0.180063i
$910$	−1.61803	−	4.97980i	−0.0536373	−	0.165079i
$911$	−7.70820	+	5.60034i	−0.255384	+	0.185547i	−0.708110	−	0.706102i	$-0.750452\pi$
$911$	−7.70820	+	5.60034i	−0.255384	+	0.185547i	0.452725	+	0.891650i	$0.350452\pi$
$912$	12.7082			0.420811
$913$	14.9721	−	25.2623i	0.495505	−	0.836059i
$914$	25.9787			0.859299
$915$	17.9443	−	13.0373i	0.593219	−	0.430999i
$916$	6.90983	+	21.2663i	0.228307	+	0.702657i
$917$	1.57295	−	4.84104i	0.0519434	−	0.159865i
$918$	−11.5902	−	8.42075i	−0.382533	−	0.277926i
$919$	−5.70820	−	4.14725i	−0.188296	−	0.136805i	0.489643	−	0.871923i	$-0.337127\pi$
$919$	−5.70820	−	4.14725i	−0.188296	−	0.136805i	−0.677940	+	0.735118i	$0.737127\pi$
$920$	−0.145898	+	0.449028i	−0.00481012	+	0.0148040i
$921$	9.28115	+	28.5645i	0.305824	+	0.941231i
$922$	18.6525	−	13.5518i	0.614287	−	0.446305i
$923$	−57.3050			−1.88622
$924$	−5.23607	−	1.17557i	−0.172254	−	0.0386734i
$925$	−11.2361			−0.369440
$926$	−8.85410	+	6.43288i	−0.290964	+	0.211398i
$927$	0.708204	+	2.17963i	0.0232605	+	0.0715884i
$928$	−1.38197	+	4.25325i	−0.0453653	+	0.139620i
$929$	−8.82624	−	6.41264i	−0.289579	−	0.210392i	0.433505	−	0.901151i	$-0.357276\pi$
$929$	−8.82624	−	6.41264i	−0.289579	−	0.210392i	−0.723085	+	0.690759i	$0.757276\pi$
$930$	−3.23607	−	2.35114i	−0.106115	−	0.0770970i
$931$	2.42705	−	7.46969i	0.0795434	−	0.244809i
$932$	0.208204	+	0.640786i	0.00681995	+	0.0209896i
$933$	2.85410	−	2.07363i	0.0934391	−	0.0678875i
$934$	−12.9443			−0.423550
$935$	−7.97214	+	3.44095i	−0.260717	+	0.112531i
$936$	−2.00000			−0.0653720
$937$	23.0623	−	16.7557i	0.753413	−	0.547386i	−0.143470	−	0.989655i	$-0.545826\pi$
$937$	23.0623	−	16.7557i	0.753413	−	0.547386i	0.896883	+	0.442268i	$0.145826\pi$
$938$	1.04508	+	3.21644i	0.0341232	+	0.105021i
$939$	−15.6353	+	48.1204i	−0.510237	+	1.57035i
$940$	3.85410	+	2.80017i	0.125707	+	0.0913314i
$941$	19.7082	+	14.3188i	0.642469	+	0.466781i	0.860698	−	0.509117i	$-0.170028\pi$
$941$	19.7082	+	14.3188i	0.642469	+	0.466781i	−0.218228	+	0.975898i	$0.570028\pi$
$942$	7.47214	−	22.9969i	0.243455	−	0.749279i
$943$	−0.416408	−	1.28157i	−0.0135601	−	0.0417337i
$944$	−3.35410	+	2.43690i	−0.109167	+	0.0793143i
$945$	5.47214			0.178009
$946$	4.57953	+	5.20431i	0.148893	+	0.169207i
$947$	−53.6312			−1.74278			−0.871390	−	0.490591i	$-0.836781\pi$
$947$	−53.6312			−1.74278			−0.871390	+	0.490591i	$0.836781\pi$
$948$	−5.23607	+	3.80423i	−0.170060	+	0.123556i
$949$	−4.61803	−	14.2128i	−0.149908	−	0.461369i
$950$	−2.42705	+	7.46969i	−0.0787439	+	0.242349i
$951$	−39.7426	−	28.8747i	−1.28874	−	0.936327i
$952$	2.11803	+	1.53884i	0.0686459	+	0.0498741i
$953$	0.263932	−	0.812299i	0.00854960	−	0.0263130i	−0.946691	−	0.322144i	$-0.895597\pi$
$953$	0.263932	−	0.812299i	0.00854960	−	0.0263130i	0.955240	+	0.295831i	$0.0955965\pi$
$954$	−0.326238	−	1.00406i	−0.0105623	−	0.0325075i
$955$	−1.00000	+	0.726543i	−0.0323592	+	0.0235104i
$956$	6.29180			0.203491
$957$	−2.23607	−	23.8949i	−0.0722818	−	0.772413i
$958$	−22.2918			−0.720215
$959$	−3.92705	+	2.85317i	−0.126811	+	0.0921337i
$960$	−0.500000	−	1.53884i	−0.0161374	−	0.0496659i
$961$	−7.69098	+	23.6704i	−0.248096	+	0.763562i
$962$	47.5967	+	34.5811i	1.53458	+	1.11494i
$963$	0.881966	+	0.640786i	0.0284210	+	0.0206490i
$964$	−9.57295	+	29.4625i	−0.308324	+	0.948923i
$965$	6.61803	+	20.3682i	0.213042	+	0.655676i
$966$	−0.618034	+	0.449028i	−0.0198849	+	0.0144472i
$967$	17.3475			0.557859			0.278929	−	0.960312i	$-0.410020\pi$
$967$	17.3475			0.557859			0.278929	+	0.960312i	$0.410020\pi$
$968$	5.28115	+	9.64932i	0.169743	+	0.310141i
$969$	33.2705			1.06880
$970$	6.78115	−	4.92680i	0.217730	−	0.158190i
$971$	−10.7639	−	33.1280i	−0.345431	−	1.06313i	−0.961353	−	0.275320i	$-0.911216\pi$
$971$	−10.7639	−	33.1280i	−0.345431	−	1.06313i	0.615922	−	0.787807i	$-0.288784\pi$
$972$	1.21885	−	3.75123i	0.0390945	−	0.120321i
$973$	4.00000	+	2.90617i	0.128234	+	0.0931675i
$974$	30.8885	+	22.4418i	0.989733	+	0.719083i
$975$	−2.61803	+	8.05748i	−0.0838442	+	0.258046i
$976$	4.23607	+	13.0373i	0.135593	+	0.417313i
$977$	30.0902	−	21.8618i	0.962670	−	0.699421i	0.00890056	−	0.999960i	$-0.497167\pi$
$977$	30.0902	−	21.8618i	0.962670	−	0.699421i	0.953769	+	0.300540i	$0.0971668\pi$
$978$	−36.8885			−1.17957
$979$	4.59017	+	49.0512i	0.146702	+	1.56768i
$980$	−1.00000			−0.0319438
$981$	1.23607	−	0.898056i	0.0394646	−	0.0286727i
$982$	5.93769	+	18.2743i	0.189479	+	0.583158i
$983$	−2.76393	+	8.50651i	−0.0881557	+	0.271315i	−0.985410	−	0.170199i	$-0.945559\pi$
$983$	−2.76393	+	8.50651i	−0.0881557	+	0.271315i	0.897254	+	0.441515i	$0.145559\pi$
$984$	3.73607	+	2.71441i	0.119101	+	0.0865323i
$985$	9.32624	+	6.77591i	0.297159	+	0.215898i
$986$	−3.61803	+	11.1352i	−0.115222	+	0.354616i
$987$	2.38197	+	7.33094i	0.0758188	+	0.233346i
$988$	33.2705	−	24.1724i	1.05848	−	0.769028i
$989$	0.986844			0.0313798
$990$	−0.836881	−	0.951057i	−0.0265978	−	0.0302266i
$991$	34.3607			1.09150			0.545751	−	0.837947i	$-0.316244\pi$
$991$	34.3607			1.09150			0.545751	+	0.837947i	$0.316244\pi$
$992$	2.00000	−	1.45309i	0.0635001	−	0.0461355i
$993$	−0.482779	−	1.48584i	−0.0153205	−	0.0471517i
$994$	−3.38197	+	10.4086i	−0.107269	+	0.330141i
$995$	4.09017	+	2.97168i	0.129667	+	0.0942087i
$996$	11.5902	+	8.42075i	0.367249	+	0.266822i
$997$	−15.0902	+	46.4428i	−0.477910	+	1.47086i	0.364081	+	0.931367i	$0.381383\pi$
$997$	−15.0902	+	46.4428i	−0.477910	+	1.47086i	−0.841992	+	0.539490i	$0.818617\pi$
$998$	6.17376	+	19.0009i	0.195427	+	0.601463i
$999$	−49.7426	+	36.1401i	−1.57379	+	1.14342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.d.421.1	✓	4
11.2	odd	10		8470.2.a.cb.1.2		2
11.4	even	5	inner	770.2.n.d.631.1	yes	4
11.9	even	5		8470.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.d.421.1	✓	4	1.1	even	1	trivial
770.2.n.d.631.1	yes	4	11.4	even	5	inner
8470.2.a.bp.1.2		2	11.9	even	5
8470.2.a.cb.1.2		2	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.30902 + 0.951057i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.30902 + 0.951057i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +1.00000 q^{10} +(-0.309017 - 3.30220i) q^{11} +1.61803 q^{12} +(4.23607 - 3.07768i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.11803 - 1.53884i) q^{17} +(0.118034 - 0.363271i) q^{18} +(2.42705 + 7.46969i) q^{19} +(0.809017 - 0.587785i) q^{20} +1.61803 q^{21} +(-2.19098 - 2.48990i) q^{22} -0.472136 q^{23} +(1.30902 - 0.951057i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.61803 - 4.97980i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(1.38197 - 4.25325i) q^{29} +(0.500000 + 1.53884i) q^{30} +(-2.00000 + 1.45309i) q^{31} -1.00000 q^{32} +(4.92705 - 2.12663i) q^{33} -2.61803 q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(-3.47214 + 10.6861i) q^{37} +(6.35410 + 4.61653i) q^{38} +(6.85410 + 4.97980i) q^{39} +(0.309017 - 0.951057i) q^{40} +(0.881966 + 2.71441i) q^{41} +(1.30902 - 0.951057i) q^{42} -2.09017 q^{43} +(-3.23607 - 0.726543i) q^{44} +0.381966 q^{45} +(-0.381966 + 0.277515i) q^{46} +(1.47214 + 4.53077i) q^{47} +(0.500000 - 1.53884i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(1.30902 - 4.02874i) q^{51} +(-1.61803 - 4.97980i) q^{52} +(2.23607 - 1.62460i) q^{53} +5.47214 q^{54} +(1.69098 - 2.85317i) q^{55} -1.00000 q^{56} +(-10.2812 + 7.46969i) q^{57} +(-1.38197 - 4.25325i) q^{58} +(1.28115 - 3.94298i) q^{59} +(1.30902 + 0.951057i) q^{60} +(-11.0902 - 8.05748i) q^{61} +(-0.763932 + 2.35114i) q^{62} +(-0.118034 - 0.363271i) q^{63} +(-0.809017 + 0.587785i) q^{64} +5.23607 q^{65} +(2.73607 - 4.61653i) q^{66} -3.38197 q^{67} +(-2.11803 + 1.53884i) q^{68} +(-0.236068 - 0.726543i) q^{69} +(0.309017 - 0.951057i) q^{70} +(-8.85410 - 6.43288i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(0.881966 - 2.71441i) q^{73} +(3.47214 + 10.6861i) q^{74} +(-1.30902 + 0.951057i) q^{75} +7.85410 q^{76} +(-3.23607 - 0.726543i) q^{77} +8.47214 q^{78} +(-3.23607 + 2.35114i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(2.30902 + 1.67760i) q^{82} +(7.16312 + 5.20431i) q^{83} +(0.500000 - 1.53884i) q^{84} +(-0.809017 - 2.48990i) q^{85} +(-1.69098 + 1.22857i) q^{86} +7.23607 q^{87} +(-3.04508 + 1.31433i) q^{88} -14.8541 q^{89} +(0.309017 - 0.224514i) q^{90} +(-1.61803 - 4.97980i) q^{91} +(-0.145898 + 0.449028i) q^{92} +(-3.23607 - 2.35114i) q^{93} +(3.85410 + 2.80017i) q^{94} +(-2.42705 + 7.46969i) q^{95} +(-0.500000 - 1.53884i) q^{96} +(6.78115 - 4.92680i) q^{97} -1.00000 q^{98} +(-0.836881 - 0.951057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 2 q^{3} - q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 + 2 * q^3 - q^4 + q^5 + 3 * q^6 - q^7 + q^8 - q^9	\( 4 q + q^{2} + 2 q^{3} - q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + q^{11} + 2 q^{12} + 8 q^{13} + q^{14} - 2 q^{15} - q^{16} - 4 q^{17} - 4 q^{18} + 3 q^{19} + q^{20} + 2 q^{21} - 11 q^{22} + 16 q^{23} + 3 q^{24} - q^{25} + 2 q^{26} + 11 q^{27} - q^{28} + 10 q^{29} + 2 q^{30} - 8 q^{31} - 4 q^{32} + 13 q^{33} - 6 q^{34} + q^{35} + 4 q^{36} + 4 q^{37} + 12 q^{38} + 14 q^{39} - q^{40} + 8 q^{41} + 3 q^{42} + 14 q^{43} - 4 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 2 q^{48} - q^{49} + q^{50} + 3 q^{51} - 2 q^{52} + 4 q^{54} + 9 q^{55} - 4 q^{56} - 21 q^{57} - 10 q^{58} - 15 q^{59} + 3 q^{60} - 22 q^{61} - 12 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} + 2 q^{66} - 18 q^{67} - 4 q^{68} + 8 q^{69} - q^{70} - 22 q^{71} + q^{72} + 8 q^{73} - 4 q^{74} - 3 q^{75} + 18 q^{76} - 4 q^{77} + 16 q^{78} - 4 q^{79} + q^{80} - 14 q^{81} + 7 q^{82} + 13 q^{83} + 2 q^{84} - q^{85} - 9 q^{86} + 20 q^{87} - q^{88} - 46 q^{89} - q^{90} - 2 q^{91} - 14 q^{92} - 4 q^{93} + 2 q^{94} - 3 q^{95} - 2 q^{96} + 7 q^{97} - 4 q^{98} - 19 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - q^4 + q^5 + 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + q^11 + 2 * q^12 + 8 * q^13 + q^14 - 2 * q^15 - q^16 - 4 * q^17 - 4 * q^18 + 3 * q^19 + q^20 + 2 * q^21 - 11 * q^22 + 16 * q^23 + 3 * q^24 - q^25 + 2 * q^26 + 11 * q^27 - q^28 + 10 * q^29 + 2 * q^30 - 8 * q^31 - 4 * q^32 + 13 * q^33 - 6 * q^34 + q^35 + 4 * q^36 + 4 * q^37 + 12 * q^38 + 14 * q^39 - q^40 + 8 * q^41 + 3 * q^42 + 14 * q^43 - 4 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 2 * q^48 - q^49 + q^50 + 3 * q^51 - 2 * q^52 + 4 * q^54 + 9 * q^55 - 4 * q^56 - 21 * q^57 - 10 * q^58 - 15 * q^59 + 3 * q^60 - 22 * q^61 - 12 * q^62 + 4 * q^63 - q^64 + 12 * q^65 + 2 * q^66 - 18 * q^67 - 4 * q^68 + 8 * q^69 - q^70 - 22 * q^71 + q^72 + 8 * q^73 - 4 * q^74 - 3 * q^75 + 18 * q^76 - 4 * q^77 + 16 * q^78 - 4 * q^79 + q^80 - 14 * q^81 + 7 * q^82 + 13 * q^83 + 2 * q^84 - q^85 - 9 * q^86 + 20 * q^87 - q^88 - 46 * q^89 - q^90 - 2 * q^91 - 14 * q^92 - 4 * q^93 + 2 * q^94 - 3 * q^95 - 2 * q^96 + 7 * q^97 - 4 * q^98 - 19 * q^99

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