LMFDB - Embedded newform 770.2.n.e.421.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$0.581882 + 1.79085i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.e.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.941506 + 2.89766i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.46489 + 1.79085i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.08293 + 3.69296i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.941506 + 2.89766i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.46489 + 1.79085i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.08293 + 3.69296i) q^{9} +1.00000 q^{10} +(3.28837 - 0.432036i) q^{11} +3.04678 q^{12} +(0.285629 - 0.207522i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.941506 + 2.89766i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.655877 + 0.476522i) q^{17} +(-1.94151 + 5.97534i) q^{18} +(0.801129 + 2.46562i) q^{19} +(0.809017 - 0.587785i) q^{20} -3.04678 q^{21} +(2.40640 - 2.28238i) q^{22} -2.00000 q^{23} +(2.46489 - 1.79085i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.109101 - 0.335777i) q^{26} +(-8.09186 - 5.87908i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-2.95044 + 9.08052i) q^{29} +(0.941506 + 2.89766i) q^{30} +(4.61803 - 3.35520i) q^{31} -1.00000 q^{32} +(4.34790 + 9.12179i) q^{33} +0.810708 q^{34} +(-0.809017 + 0.587785i) q^{35} +(1.94151 + 5.97534i) q^{36} +(1.10121 - 3.38918i) q^{37} +(2.09738 + 1.52384i) q^{38} +(0.870248 + 0.632272i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-2.55165 - 7.85318i) q^{41} +(-2.46489 + 1.79085i) q^{42} -9.49338 q^{43} +(0.605270 - 3.26093i) q^{44} -6.28284 q^{45} +(-1.61803 + 1.17557i) q^{46} +(-2.65993 - 8.18644i) q^{47} +(0.941506 - 2.89766i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-0.763286 + 2.34915i) q^{51} +(-0.109101 - 0.335777i) q^{52} +(2.26498 - 1.64560i) q^{53} -10.0021 q^{54} +(2.91429 + 1.58333i) q^{55} +1.00000 q^{56} +(-6.39025 + 4.64279i) q^{57} +(2.95044 + 9.08052i) q^{58} +(4.08188 - 12.5627i) q^{59} +(2.46489 + 1.79085i) q^{60} +(5.42536 + 3.94175i) q^{61} +(1.76393 - 5.42882i) q^{62} +(-1.94151 - 5.97534i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.353057 q^{65} +(8.87918 + 4.82405i) q^{66} -1.40749 q^{67} +(0.655877 - 0.476522i) q^{68} +(-1.88301 - 5.79531i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(10.4515 + 7.59345i) q^{71} +(5.08293 + 3.69296i) q^{72} +(-1.59146 + 4.89802i) q^{73} +(-1.10121 - 3.38918i) q^{74} +(-2.46489 + 1.79085i) q^{75} +2.59251 q^{76} +(-0.605270 + 3.26093i) q^{77} +1.07569 q^{78} +(2.95044 - 2.14362i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(3.59251 - 11.0566i) q^{81} +(-6.68031 - 4.85353i) q^{82} +(2.15861 + 1.56832i) q^{83} +(-0.941506 + 2.89766i) q^{84} +(0.250523 + 0.771029i) q^{85} +(-7.68031 + 5.58007i) q^{86} -29.0901 q^{87} +(-1.42705 - 2.99391i) q^{88} +9.63799 q^{89} +(-5.08293 + 3.69296i) q^{90} +(0.109101 + 0.335777i) q^{91} +(-0.618034 + 1.90211i) q^{92} +(14.0701 + 10.2225i) q^{93} +(-6.96380 - 5.05950i) q^{94} +(-0.801129 + 2.46562i) q^{95} +(-0.941506 - 2.89766i) q^{96} +(7.92705 - 5.75934i) q^{97} -1.00000 q^{98} +(-15.1190 + 14.3398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9} + 8 q^{10} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} - 9 q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} - 4 q^{21} - 8 q^{22} - 16 q^{23} + q^{24} - 2 q^{25} + 7 q^{26} - 22 q^{27} + 2 q^{28} - q^{30} + 28 q^{31} - 8 q^{32} - q^{33} + 4 q^{34} - 2 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 13 q^{39} - 2 q^{40} + 8 q^{41} - q^{42} - 14 q^{43} - 7 q^{44} - 12 q^{45} - 4 q^{46} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} - 7 q^{52} + 10 q^{53} - 28 q^{54} + 7 q^{55} + 8 q^{56} - 17 q^{57} + 31 q^{59} + q^{60} + 28 q^{61} + 32 q^{62} - 7 q^{63} - 2 q^{64} + 2 q^{65} + 36 q^{66} - 26 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} + 34 q^{71} + 13 q^{72} - 24 q^{73} - 4 q^{74} - q^{75} + 6 q^{76} + 7 q^{77} - 2 q^{78} + 2 q^{80} + 14 q^{81} - 3 q^{82} - 21 q^{83} + q^{84} - 11 q^{85} - 11 q^{86} - 52 q^{87} + 2 q^{88} - 14 q^{89} - 13 q^{90} + 7 q^{91} + 4 q^{92} + 14 q^{93} + 5 q^{94} + 9 q^{95} + q^{96} + 50 q^{97} - 8 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9 + 8 * q^10 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 2 * q^14 + q^15 - 2 * q^16 - 9 * q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 - 4 * q^21 - 8 * q^22 - 16 * q^23 + q^24 - 2 * q^25 + 7 * q^26 - 22 * q^27 + 2 * q^28 - q^30 + 28 * q^31 - 8 * q^32 - q^33 + 4 * q^34 - 2 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 13 * q^39 - 2 * q^40 + 8 * q^41 - q^42 - 14 * q^43 - 7 * q^44 - 12 * q^45 - 4 * q^46 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 - 7 * q^52 + 10 * q^53 - 28 * q^54 + 7 * q^55 + 8 * q^56 - 17 * q^57 + 31 * q^59 + q^60 + 28 * q^61 + 32 * q^62 - 7 * q^63 - 2 * q^64 + 2 * q^65 + 36 * q^66 - 26 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 + 34 * q^71 + 13 * q^72 - 24 * q^73 - 4 * q^74 - q^75 + 6 * q^76 + 7 * q^77 - 2 * q^78 + 2 * q^80 + 14 * q^81 - 3 * q^82 - 21 * q^83 + q^84 - 11 * q^85 - 11 * q^86 - 52 * q^87 + 2 * q^88 - 14 * q^89 - 13 * q^90 + 7 * q^91 + 4 * q^92 + 14 * q^93 + 5 * q^94 + 9 * q^95 + q^96 + 50 * q^97 - 8 * q^98 - 18 * 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
$3$	0.941506	+	2.89766i	0.543578	+	1.67296i	0.724346	+	0.689437i	$0.242142\pi$
$3$	0.941506	+	2.89766i	0.543578	+	1.67296i	−0.180767	+	0.983526i	$0.557858\pi$
$4$	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
$6$	2.46489	+	1.79085i	1.00629	+	0.731111i
$7$	−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
$9$	−5.08293	+	3.69296i	−1.69431	+	1.23099i
$10$	1.00000			0.316228
$11$	3.28837	−	0.432036i	0.991479	−	0.130264i
$11$	3.28837	−	0.432036i	0.991479	−	0.130264i
$12$	3.04678			0.879528
$13$	0.285629	−	0.207522i	0.0792192	−	0.0575561i	−0.547471	−	0.836825i	$-0.684409\pi$
$13$	0.285629	−	0.207522i	0.0792192	−	0.0575561i	0.626690	+	0.779269i	$0.284409\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	−0.941506	+	2.89766i	−0.243096	+	0.748172i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.655877	+	0.476522i	0.159073	+	0.115574i	0.664474	−	0.747311i	$-0.268655\pi$
$17$	0.655877	+	0.476522i	0.159073	+	0.115574i	−0.505401	+	0.862885i	$0.668655\pi$
$18$	−1.94151	+	5.97534i	−0.457617	+	1.40840i
$19$	0.801129	+	2.46562i	0.183792	+	0.565652i	0.999925	−	0.0122107i	$-0.00388687\pi$
$19$	0.801129	+	2.46562i	0.183792	+	0.565652i	−0.816134	+	0.577863i	$0.803887\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	−3.04678			−0.664861
$22$	2.40640	−	2.28238i	0.513046	−	0.486604i
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$	2.46489	−	1.79085i	0.503144	−	0.365556i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.109101	−	0.335777i	0.0213964	−	0.0658513i
$27$	−8.09186	−	5.87908i	−1.55728	−	1.13143i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	−2.95044	+	9.08052i	−0.547883	+	1.68621i	0.166153	+	0.986100i	$0.446866\pi$
$29$	−2.95044	+	9.08052i	−0.547883	+	1.68621i	−0.714035	+	0.700110i	$0.753134\pi$
$30$	0.941506	+	2.89766i	0.171895	+	0.529037i
$31$	4.61803	−	3.35520i	0.829423	−	0.602611i	−0.0899727	−	0.995944i	$-0.528678\pi$
$31$	4.61803	−	3.35520i	0.829423	−	0.602611i	0.919396	+	0.393333i	$0.128678\pi$
$32$	−1.00000			−0.176777
$33$	4.34790	+	9.12179i	0.756873	+	1.58790i
$34$	0.810708			0.139035
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	1.94151	+	5.97534i	0.323584	+	0.995890i
$37$	1.10121	−	3.38918i	0.181038	−	0.557178i	−0.818819	−	0.574051i	$-0.805371\pi$
$37$	1.10121	−	3.38918i	0.181038	−	0.557178i	0.999858	+	0.0168729i	$0.00537106\pi$
$38$	2.09738	+	1.52384i	0.340240	+	0.247199i
$39$	0.870248	+	0.632272i	0.139351	+	0.101245i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−2.55165	−	7.85318i	−0.398501	−	1.22646i	−0.926201	−	0.377029i	$-0.876946\pi$
$41$	−2.55165	−	7.85318i	−0.398501	−	1.22646i	0.527700	−	0.849431i	$-0.323054\pi$
$42$	−2.46489	+	1.79085i	−0.380341	+	0.276334i
$43$	−9.49338			−1.44773			−0.723864	−	0.689943i	$-0.757636\pi$
$43$	−9.49338			−1.44773			−0.723864	+	0.689943i	$0.757636\pi$
$44$	0.605270	−	3.26093i	0.0912480	−	0.491603i
$45$	−6.28284			−0.936591
$46$	−1.61803	+	1.17557i	−0.238566	+	0.173328i
$47$	−2.65993	−	8.18644i	−0.387991	−	1.19411i	−0.934287	−	0.356522i	$-0.883962\pi$
$47$	−2.65993	−	8.18644i	−0.387991	−	1.19411i	0.546296	−	0.837593i	$-0.316038\pi$
$48$	0.941506	−	2.89766i	0.135895	−	0.418241i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	−0.763286	+	2.34915i	−0.106881	+	0.328947i
$52$	−0.109101	−	0.335777i	−0.0151295	−	0.0465639i
$53$	2.26498	−	1.64560i	0.311119	−	0.226041i	−0.421258	−	0.906941i	$-0.638411\pi$
$53$	2.26498	−	1.64560i	0.311119	−	0.226041i	0.732376	+	0.680900i	$0.238411\pi$
$54$	−10.0021			−1.36111
$55$	2.91429	+	1.58333i	0.392962	+	0.213496i
$56$	1.00000			0.133631
$57$	−6.39025	+	4.64279i	−0.846410	+	0.614953i
$58$	2.95044	+	9.08052i	0.387412	+	1.19233i
$59$	4.08188	−	12.5627i	0.531416	−	1.63553i	−0.219853	−	0.975533i	$-0.570558\pi$
$59$	4.08188	−	12.5627i	0.531416	−	1.63553i	0.751269	−	0.659997i	$-0.229442\pi$
$60$	2.46489	+	1.79085i	0.318216	+	0.231198i
$61$	5.42536	+	3.94175i	0.694646	+	0.504690i	0.878184	−	0.478323i	$-0.158755\pi$
$61$	5.42536	+	3.94175i	0.694646	+	0.504690i	−0.183538	+	0.983013i	$0.558755\pi$
$62$	1.76393	−	5.42882i	0.224020	−	0.689461i
$63$	−1.94151	−	5.97534i	−0.244607	−	0.752822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.353057			0.0437913
$66$	8.87918	+	4.82405i	1.09295	+	0.593799i
$67$	−1.40749			−0.171953			−0.0859763	−	0.996297i	$-0.527401\pi$
$67$	−1.40749			−0.171953			−0.0859763	+	0.996297i	$0.527401\pi$
$68$	0.655877	−	0.476522i	0.0795367	−	0.0577868i
$69$	−1.88301	−	5.79531i	−0.226688	−	0.697674i
$70$	−0.309017	+	0.951057i	−0.0369346	+	0.113673i
$71$	10.4515	+	7.59345i	1.24036	+	0.901176i	0.997623	−	0.0689148i	$-0.0219537\pi$
$71$	10.4515	+	7.59345i	1.24036	+	0.901176i	0.242740	+	0.970091i	$0.421954\pi$
$72$	5.08293	+	3.69296i	0.599029	+	0.435220i
$73$	−1.59146	+	4.89802i	−0.186267	+	0.573269i	−0.999968	−	0.00801375i	$-0.997449\pi$
$73$	−1.59146	+	4.89802i	−0.186267	+	0.573269i	0.813701	+	0.581283i	$0.197449\pi$
$74$	−1.10121	−	3.38918i	−0.128013	−	0.393985i
$75$	−2.46489	+	1.79085i	−0.284621	+	0.206790i
$76$	2.59251			0.297381
$77$	−0.605270	+	3.26093i	−0.0689770	+	0.371617i
$78$	1.07569			0.121797
$79$	2.95044	−	2.14362i	0.331950	−	0.241176i	−0.409307	−	0.912397i	$-0.634230\pi$
$79$	2.95044	−	2.14362i	0.331950	−	0.241176i	0.741258	+	0.671221i	$0.234230\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	3.59251	−	11.0566i	0.399167	−	1.22851i
$82$	−6.68031	−	4.85353i	−0.737717	−	0.535983i
$83$	2.15861	+	1.56832i	0.236939	+	0.172146i	0.699918	−	0.714223i	$-0.253220\pi$
$83$	2.15861	+	1.56832i	0.236939	+	0.172146i	−0.462980	+	0.886369i	$0.653220\pi$
$84$	−0.941506	+	2.89766i	−0.102727	+	0.316160i
$85$	0.250523	+	0.771029i	0.0271730	+	0.0836299i
$86$	−7.68031	+	5.58007i	−0.828189	+	0.601715i
$87$	−29.0901			−3.11878
$88$	−1.42705	−	2.99391i	−0.152124	−	0.319152i
$89$	9.63799			1.02163			0.510813	−	0.859692i	$-0.329345\pi$
$89$	9.63799			1.02163			0.510813	+	0.859692i	$0.329345\pi$
$90$	−5.08293	+	3.69296i	−0.535788	+	0.389272i
$91$	0.109101	+	0.335777i	0.0114368	+	0.0351990i
$92$	−0.618034	+	1.90211i	−0.0644345	+	0.198309i
$93$	14.0701	+	10.2225i	1.45900	+	1.06003i
$94$	−6.96380	−	5.05950i	−0.718261	−	0.521847i
$95$	−0.801129	+	2.46562i	−0.0821941	+	0.252967i
$96$	−0.941506	−	2.89766i	−0.0960920	−	0.295741i
$97$	7.92705	−	5.75934i	0.804870	−	0.584772i	−0.107469	−	0.994208i	$-0.534275\pi$
$97$	7.92705	−	5.75934i	0.804870	−	0.584772i	0.912339	+	0.409436i	$0.134275\pi$
$98$	−1.00000			−0.101015
$99$	−15.1190	+	14.3398i	−1.51952	+	1.44121i
$100$	1.00000			0.100000
$101$	0.731641	−	0.531568i	0.0728010	−	0.0528930i	−0.550789	−	0.834644i	$-0.685673\pi$
$101$	0.731641	−	0.531568i	0.0728010	−	0.0528930i	0.623590	+	0.781751i	$0.285673\pi$
$102$	0.763286	+	2.34915i	0.0755766	+	0.232601i
$103$	3.46726	−	10.6711i	0.341639	−	1.05146i	−0.621719	−	0.783240i	$-0.713565\pi$
$103$	3.46726	−	10.6711i	0.341639	−	1.05146i	0.963358	−	0.268217i	$-0.0864346\pi$
$104$	−0.285629	−	0.207522i	−0.0280082	−	0.0203492i
$105$	−2.46489	−	1.79085i	−0.240549	−	0.174769i
$106$	0.865144	−	2.66264i	0.0840302	−	0.258618i
$107$	2.74906	+	8.46074i	0.265762	+	0.817930i	0.991517	+	0.129977i	$0.0414904\pi$
$107$	2.74906	+	8.46074i	0.265762	+	0.817930i	−0.725755	+	0.687953i	$0.758510\pi$
$108$	−8.09186	+	5.87908i	−0.778640	+	0.565715i
$109$	18.4763			1.76971			0.884855	−	0.465866i	$-0.154257\pi$
$109$	18.4763			1.76971			0.884855	+	0.465866i	$0.154257\pi$
$110$	3.28837	−	0.432036i	0.313533	−	0.0411930i
$111$	10.8575			1.03055
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	−3.92150	−	12.0691i	−0.368904	−	1.13537i	−0.947500	−	0.319755i	$-0.896399\pi$
$113$	−3.92150	−	12.0691i	−0.368904	−	1.13537i	0.578597	−	0.815614i	$-0.303601\pi$
$114$	−2.44086	+	7.51219i	−0.228607	+	0.703581i
$115$	−1.61803	−	1.17557i	−0.150882	−	0.109623i
$116$	7.72435	+	5.61207i	0.717188	+	0.521067i
$117$	−0.685462	+	2.10963i	−0.0633710	+	0.195036i
$118$	−4.08188	−	12.5627i	−0.375768	−	1.15649i
$119$	−0.655877	+	0.476522i	−0.0601241	+	0.0436827i
$120$	3.04678			0.278131
$121$	10.6267	−	2.84138i	0.966063	−	0.258307i
$122$	6.70611			0.607143
$123$	20.3534	−	14.7876i	1.83520	−	1.33335i
$124$	−1.76393	−	5.42882i	−0.158406	−	0.487523i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−5.08293	−	3.69296i	−0.452823	−	0.328995i
$127$	−13.1369	−	9.54455i	−1.16572	−	0.846942i	−0.175226	−	0.984528i	$-0.556066\pi$
$127$	−13.1369	−	9.54455i	−1.16572	−	0.846942i	−0.990490	+	0.137586i	$0.956066\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−8.93807	−	27.5086i	−0.786954	−	2.42199i
$130$	0.285629	−	0.207522i	0.0250513	−	0.0182008i
$131$	−8.08882			−0.706723			−0.353362	−	0.935487i	$-0.614961\pi$
$131$	−8.08882			−0.706723			−0.353362	+	0.935487i	$0.614961\pi$
$132$	10.0189	−	1.31632i	0.872034	−	0.114571i
$133$	−2.59251			−0.224799
$134$	−1.13869	+	0.827304i	−0.0983675	+	0.0714682i
$135$	−3.09082	−	9.51255i	−0.266015	−	0.818710i
$136$	0.250523	−	0.771029i	0.0214821	−	0.0661152i
$137$	−8.41533	−	6.11410i	−0.718970	−	0.522363i	0.167085	−	0.985943i	$-0.446565\pi$
$137$	−8.41533	−	6.11410i	−0.718970	−	0.522363i	−0.886055	+	0.463580i	$0.846565\pi$
$138$	−4.92979	−	3.58170i	−0.419651	−	0.304895i
$139$	0.233978	−	0.720109i	0.0198457	−	0.0610789i	−0.940643	−	0.339397i	$-0.889777\pi$
$139$	0.233978	−	0.720109i	0.0198457	−	0.0610789i	0.960489	+	0.278318i	$0.0897770\pi$
$140$	0.309017	+	0.951057i	0.0261167	+	0.0803789i
$141$	21.2171	−	15.4152i	1.78681	−	1.29819i
$142$	12.9187			1.08412
$143$	0.849596	−	0.805809i	0.0710468	−	0.0673851i
$144$	6.28284			0.523570
$145$	−7.72435	+	5.61207i	−0.641472	+	0.466057i
$146$	1.59146	+	4.89802i	0.131710	+	0.405363i
$147$	0.941506	−	2.89766i	0.0776541	−	0.238995i
$148$	−2.88301	−	2.09463i	−0.236982	−	0.172178i
$149$	7.25672	+	5.27232i	0.594494	+	0.431925i	0.843920	−	0.536469i	$-0.180242\pi$
$149$	7.25672	+	5.27232i	0.594494	+	0.431925i	−0.249426	+	0.968394i	$0.580242\pi$
$150$	−0.941506	+	2.89766i	−0.0768736	+	0.236593i
$151$	−6.79006	−	20.8976i	−0.552567	−	1.70063i	−0.702284	−	0.711897i	$-0.747836\pi$
$151$	−6.79006	−	20.8976i	−0.552567	−	1.70063i	0.149717	−	0.988729i	$-0.452164\pi$
$152$	2.09738	−	1.52384i	0.170120	−	0.123600i
$153$	−5.09355			−0.411789
$154$	1.42705	+	2.99391i	0.114995	+	0.241257i
$155$	5.70820			0.458494
$156$	0.870248	−	0.632272i	0.0696756	−	0.0506223i
$157$	0.0206519	+	0.0635599i	0.00164820	+	0.00507263i	0.951877	−	0.306480i	$-0.0991511\pi$
$157$	0.0206519	+	0.0635599i	0.00164820	+	0.00507263i	−0.950229	+	0.311552i	$0.899151\pi$
$158$	1.12697	−	3.46845i	0.0896567	−	0.275935i
$159$	6.90088	+	5.01378i	0.547275	+	0.397619i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	0.618034	−	1.90211i	0.0487079	−	0.149908i
$162$	−3.59251	−	11.0566i	−0.282254	−	0.868688i
$163$	−18.0161	+	13.0895i	−1.41113	+	1.02525i	−0.417975	+	0.908458i	$0.637260\pi$
$163$	−18.0161	+	13.0895i	−1.41113	+	1.02525i	−0.993157	+	0.116789i	$0.962740\pi$
$164$	−8.25732			−0.644788
$165$	−1.84412	+	9.93532i	−0.143565	+	0.773463i
$166$	2.66819			0.207092
$167$	9.70820	−	7.05342i	0.751243	−	0.545810i	−0.144969	−	0.989436i	$-0.546308\pi$
$167$	9.70820	−	7.05342i	0.751243	−	0.545810i	0.896212	+	0.443626i	$0.146308\pi$
$168$	0.941506	+	2.89766i	0.0726387	+	0.223559i
$169$	−3.97870	+	12.2452i	−0.306054	+	0.941937i
$170$	0.655877	+	0.476522i	0.0503034	+	0.0365476i
$171$	−13.1775	−	9.57403i	−1.00771	−	0.732145i
$172$	−2.93362	+	9.02875i	−0.223686	+	0.688435i
$173$	6.14010	+	18.8973i	0.466823	+	1.43673i	0.856675	+	0.515856i	$0.172526\pi$
$173$	6.14010	+	18.8973i	0.466823	+	1.43673i	−0.389852	+	0.920878i	$0.627474\pi$
$174$	−23.5344	+	17.0987i	−1.78414	+	1.29625i
$175$	−1.00000			−0.0755929
$176$	−2.91429	−	1.58333i	−0.219673	−	0.119348i
$177$	40.2456			3.02505
$178$	7.79730	−	5.66507i	0.584432	−	0.424615i
$179$	−2.66140	−	8.19094i	−0.198922	−	0.612220i	−0.999908	−	0.0135367i	$-0.995691\pi$
$179$	−2.66140	−	8.19094i	−0.198922	−	0.612220i	0.800986	−	0.598683i	$-0.204309\pi$
$180$	−1.94151	+	5.97534i	−0.144711	+	0.445376i
$181$	−9.49338	−	6.89735i	−0.705638	−	0.512676i	0.176126	−	0.984368i	$-0.443643\pi$
$181$	−9.49338	−	6.89735i	−0.705638	−	0.512676i	−0.881763	+	0.471692i	$0.843643\pi$
$182$	0.285629	+	0.207522i	0.0211722	+	0.0153825i
$183$	−6.31384	+	19.4320i	−0.466733	+	1.43646i
$184$	0.618034	+	1.90211i	0.0455621	+	0.140226i
$185$	2.88301	−	2.09463i	0.211963	−	0.154000i
$186$	17.3916			1.27522
$187$	2.36264	+	1.28362i	0.172773	+	0.0938674i
$188$	−8.60773			−0.627783
$189$	8.09186	−	5.87908i	0.588596	−	0.427640i
$190$	0.801129	+	2.46562i	0.0581200	+	0.178875i
$191$	−2.51868	+	7.75171i	−0.182246	+	0.560894i	−0.999890	−	0.0148293i	$-0.995280\pi$
$191$	−2.51868	+	7.75171i	−0.182246	+	0.560894i	0.817644	+	0.575723i	$0.195280\pi$
$192$	−2.46489	−	1.79085i	−0.177888	−	0.129243i
$193$	−7.07230	−	5.13833i	−0.509076	−	0.369865i	0.303397	−	0.952864i	$-0.401879\pi$
$193$	−7.07230	−	5.13833i	−0.509076	−	0.369865i	−0.812473	+	0.582999i	$0.801879\pi$
$194$	3.02786	−	9.31881i	0.217388	−	0.669051i
$195$	0.332405	+	1.02304i	0.0238040	+	0.0732612i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	14.4568			1.03001			0.515003	−	0.857189i	$-0.327791\pi$
$197$	14.4568			1.03001			0.515003	+	0.857189i	$0.327791\pi$
$198$	−3.80282	+	20.4879i	−0.270255	+	1.45601i
$199$	−11.0446			−0.782930			−0.391465	−	0.920193i	$-0.628032\pi$
$199$	−11.0446			−0.782930			−0.391465	+	0.920193i	$0.628032\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	−1.32516	−	4.07843i	−0.0934698	−	0.287670i
$202$	0.279462	−	0.860095i	0.0196629	−	0.0605161i
$203$	−7.72435	−	5.61207i	−0.542143	−	0.393890i
$204$	1.99831	+	1.45186i	0.139910	+	0.101650i
$205$	2.55165	−	7.85318i	0.178215	−	0.548490i
$206$	−3.46726	−	10.6711i	−0.241576	−	0.743493i
$207$	10.1659	−	7.38593i	0.706576	−	0.513357i
$208$	−0.353057			−0.0244801
$209$	3.69964	+	7.76174i	0.255909	+	0.536891i
$210$	−3.04678			−0.210248
$211$	−19.1820	+	13.9365i	−1.32054	+	0.959428i	−0.320615	+	0.947210i	$0.603889\pi$
$211$	−19.1820	+	13.9365i	−1.32054	+	0.959428i	−0.999925	+	0.0122188i	$0.996111\pi$
$212$	−0.865144	−	2.66264i	−0.0594184	−	0.182871i
$213$	−12.1631	+	37.4341i	−0.833400	+	2.56494i
$214$	7.19713	+	5.22902i	0.491986	+	0.357449i
$215$	−7.68031	−	5.58007i	−0.523793	−	0.380558i
$216$	−3.09082	+	9.51255i	−0.210303	+	0.647247i
$217$	1.76393	+	5.42882i	0.119744	+	0.368533i
$218$	14.9477	−	10.8601i	1.01238	−	0.735539i
$219$	−15.6911			−1.06031
$220$	2.40640	−	2.28238i	0.162239	−	0.153878i
$221$	0.286226			0.0192536
$222$	8.78389	−	6.38187i	0.589536	−	0.428323i
$223$	−1.72736	−	5.31628i	−0.115673	−	0.356004i	0.876414	−	0.481558i	$-0.159929\pi$
$223$	−1.72736	−	5.31628i	−0.115673	−	0.356004i	−0.992087	+	0.125554i	$0.959929\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−5.08293	−	3.69296i	−0.338862	−	0.246198i
$226$	−10.2666	−	7.45914i	−0.682925	−	0.496174i
$227$	−1.95362	+	6.01263i	−0.129667	+	0.399073i	−0.994722	−	0.102603i	$-0.967283\pi$
$227$	−1.95362	+	6.01263i	−0.129667	+	0.399073i	0.865056	+	0.501676i	$0.167283\pi$
$228$	2.44086	+	7.51219i	0.161650	+	0.497507i
$229$	3.14799	−	2.28715i	0.208025	−	0.151139i	−0.478895	−	0.877872i	$-0.658962\pi$
$229$	3.14799	−	2.28715i	0.208025	−	0.151139i	0.686920	+	0.726733i	$0.258962\pi$
$230$	−2.00000			−0.131876
$231$	−10.0189	+	1.31632i	−0.659196	+	0.0866072i
$232$	9.54782			0.626845
$233$	−12.2694	+	8.91427i	−0.803797	+	0.583993i	−0.912026	−	0.410133i	$-0.865482\pi$
$233$	−12.2694	+	8.91427i	−0.803797	+	0.583993i	0.108228	+	0.994126i	$0.465482\pi$
$234$	0.685462	+	2.10963i	0.0448100	+	0.137911i
$235$	2.65993	−	8.18644i	0.173515	−	0.534024i
$236$	−10.6865	−	7.76420i	−0.695632	−	0.505406i
$237$	8.98933	+	6.53113i	0.583920	+	0.424242i
$238$	−0.250523	+	0.771029i	−0.0162390	+	0.0499784i
$239$	−6.51868	−	20.0624i	−0.421659	−	1.29773i	−0.906158	−	0.422940i	$-0.860998\pi$
$239$	−6.51868	−	20.0624i	−0.421659	−	1.29773i	0.484499	−	0.874792i	$-0.339002\pi$
$240$	2.46489	−	1.79085i	0.159108	−	0.115599i
$241$	−11.9416			−0.769228			−0.384614	−	0.923078i	$-0.625665\pi$
$241$	−11.9416			−0.769228			−0.384614	+	0.923078i	$0.625665\pi$
$242$	6.92705	−	8.54494i	0.445288	−	0.549289i
$243$	5.41432			0.347329
$244$	5.42536	−	3.94175i	0.347323	−	0.252345i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	7.77431	−	23.9269i	0.495672	−	1.52552i
$247$	0.740495	+	0.538001i	0.0471166	+	0.0342322i
$248$	−4.61803	−	3.35520i	−0.293245	−	0.213055i
$249$	−2.51212	+	7.73150i	−0.159199	+	0.489964i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−1.71377	+	1.24513i	−0.108172	+	0.0785919i	−0.640556	−	0.767911i	$-0.721296\pi$
$251$	−1.71377	+	1.24513i	−0.108172	+	0.0785919i	0.532384	+	0.846503i	$0.321296\pi$
$252$	−6.28284			−0.395782
$253$	−6.57673	+	0.864071i	−0.413475	+	0.0543237i
$254$	−16.2382			−1.01887
$255$	−1.99831	+	1.45186i	−0.125139	+	0.0909188i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.40088	+	19.6999i	−0.399276	+	1.22884i	0.526305	+	0.850296i	$0.323577\pi$
$257$	−6.40088	+	19.6999i	−0.399276	+	1.22884i	−0.925581	+	0.378549i	$0.876423\pi$
$258$	−23.4002	−	17.0012i	−1.45683	−	1.05845i
$259$	2.88301	+	2.09463i	0.179142	+	0.130154i
$260$	0.109101	−	0.335777i	0.00676613	−	0.0208240i
$261$	−18.5371	−	57.0515i	−1.14742	−	3.53140i
$262$	−6.54399	+	4.75449i	−0.404289	+	0.293733i
$263$	3.89531			0.240195			0.120097	−	0.992762i	$-0.461679\pi$
$263$	3.89531			0.240195			0.120097	+	0.992762i	$0.461679\pi$
$264$	7.33176	−	6.95389i	0.451239	−	0.427982i
$265$	2.79967			0.171982
$266$	−2.09738	+	1.52384i	−0.128599	+	0.0934325i
$267$	9.07422	+	27.9276i	0.555333	+	1.70914i
$268$	−0.434939	+	1.33861i	−0.0265681	+	0.0817683i
$269$	18.5009	+	13.4417i	1.12802	+	0.819556i	0.985406	−	0.170222i	$-0.0544483\pi$
$269$	18.5009	+	13.4417i	1.12802	+	0.819556i	0.142617	+	0.989778i	$0.454448\pi$
$270$	−8.09186	−	5.87908i	−0.492455	−	0.357789i
$271$	6.36828	−	19.5995i	0.386845	−	1.19059i	−0.548287	−	0.836290i	$-0.684720\pi$
$271$	6.36828	−	19.5995i	0.386845	−	1.19059i	0.935133	−	0.354298i	$-0.115280\pi$
$272$	−0.250523	−	0.771029i	−0.0151902	−	0.0467505i
$273$	−0.870248	+	0.632272i	−0.0526698	+	0.0382668i
$274$	−10.4019			−0.628403
$275$	1.42705	+	2.99391i	0.0860544	+	0.180540i
$276$	−6.09355			−0.366789
$277$	−13.9187	+	10.1126i	−0.836296	+	0.607605i	−0.921334	−	0.388773i	$-0.872899\pi$
$277$	−13.9187	+	10.1126i	−0.836296	+	0.607605i	0.0850373	+	0.996378i	$0.472899\pi$
$278$	−0.233978	−	0.720109i	−0.0140331	−	0.0431893i
$279$	−11.0825	+	34.1085i	−0.663492	+	2.04202i
$280$	0.809017	+	0.587785i	0.0483480	+	0.0351269i
$281$	−24.6301	−	17.8948i	−1.46931	−	1.06751i	−0.980814	−	0.194945i	$-0.937547\pi$
$281$	−24.6301	−	17.8948i	−1.46931	−	1.06751i	−0.488492	−	0.872569i	$-0.662453\pi$
$282$	8.10423	−	24.9422i	0.482600	−	1.48529i
$283$	3.08868	+	9.50597i	0.183603	+	0.565071i	0.999921	−	0.0125305i	$-0.00398868\pi$
$283$	3.08868	+	9.50597i	0.183603	+	0.565071i	−0.816319	+	0.577602i	$0.803989\pi$
$284$	10.4515	−	7.59345i	0.620181	−	0.450588i
$285$	−7.89879			−0.467884
$286$	0.213695	−	1.15129i	0.0126360	−	0.0680774i
$287$	8.25732			0.487414
$288$	5.08293	−	3.69296i	0.299514	−	0.217610i
$289$	−5.05019	−	15.5429i	−0.297070	−	0.914287i
$290$	−2.95044	+	9.08052i	−0.173256	+	0.533226i
$291$	24.1519	+	17.5474i	1.41581	+	1.02865i
$292$	4.16650	+	3.02714i	0.243826	+	0.177150i
$293$	−1.99871	+	6.15139i	−0.116766	+	0.359368i	−0.992311	−	0.123768i	$-0.960502\pi$
$293$	−1.99871	+	6.15139i	−0.116766	+	0.359368i	0.875545	+	0.483136i	$0.160502\pi$
$294$	−0.941506	−	2.89766i	−0.0549097	−	0.168995i
$295$	10.6865	−	7.76420i	0.622192	−	0.452049i
$296$	−3.56360			−0.207130
$297$	−29.1490	−	15.8366i	−1.69139	−	0.918932i
$298$	8.96980			0.519607
$299$	−0.571258	+	0.415043i	−0.0330367	+	0.0240026i
$300$	0.941506	+	2.89766i	0.0543578	+	0.167296i
$301$	2.93362	−	9.02875i	0.169091	−	0.520408i
$302$	−17.7766	−	12.9155i	−1.02293	−	0.743201i
$303$	2.22915	+	1.61957i	0.128061	+	0.0930418i
$304$	0.801129	−	2.46562i	0.0459479	−	0.141413i
$305$	2.07230	+	6.37789i	0.118660	+	0.365197i
$306$	−4.12077	+	2.99391i	−0.235569	+	0.171151i
$307$	−20.6473			−1.17840			−0.589202	−	0.807986i	$-0.700558\pi$
$307$	−20.6473			−1.17840			−0.589202	+	0.807986i	$0.700558\pi$
$308$	2.91429	+	1.58333i	0.166057	+	0.0902185i
$309$	34.1857			1.94476
$310$	4.61803	−	3.35520i	0.262287	−	0.190562i
$311$	7.24289	+	22.2913i	0.410707	+	1.26403i	0.916035	+	0.401098i	$0.131371\pi$
$311$	7.24289	+	22.2913i	0.410707	+	1.26403i	−0.505328	+	0.862927i	$0.668629\pi$
$312$	0.332405	−	1.02304i	0.0188187	−	0.0579181i
$313$	−9.63207	−	6.99811i	−0.544437	−	0.395557i	0.281293	−	0.959622i	$-0.409237\pi$
$313$	−9.63207	−	6.99811i	−0.544437	−	0.395557i	−0.825730	+	0.564065i	$0.809237\pi$
$314$	0.0540673	+	0.0392822i	0.00305119	+	0.00221682i
$315$	1.94151	−	5.97534i	0.109391	−	0.336672i
$316$	−1.12697	−	3.46845i	−0.0633969	−	0.195116i
$317$	27.8451	−	20.2307i	1.56394	−	1.13627i	0.631255	−	0.775575i	$-0.282540\pi$
$317$	27.8451	−	20.2307i	1.56394	−	1.13627i	0.932685	−	0.360693i	$-0.117460\pi$
$318$	8.52995			0.478336
$319$	−5.77901	+	31.1348i	−0.323563	+	1.74321i
$320$	−1.00000			−0.0559017
$321$	−21.9280	+	15.9317i	−1.22390	+	0.889218i
$322$	−0.618034	−	1.90211i	−0.0344417	−	0.106001i
$323$	−0.649481	+	1.99890i	−0.0361381	+	0.111222i
$324$	−9.40531	−	6.83335i	−0.522517	−	0.379631i
$325$	0.285629	+	0.207522i	0.0158438	+	0.0115112i
$326$	−6.88155	+	21.1792i	−0.381134	+	1.17301i
$327$	17.3956	+	53.5380i	0.961976	+	2.96066i
$328$	−6.68031	+	4.85353i	−0.368858	+	0.267991i
$329$	8.60773			0.474559
$330$	4.34790	+	9.12179i	0.239344	+	0.502138i
$331$	−11.6770			−0.641829			−0.320914	−	0.947108i	$-0.603990\pi$
$331$	−11.6770			−0.641829			−0.320914	+	0.947108i	$0.603990\pi$
$332$	2.15861	−	1.56832i	0.118469	−	0.0860730i
$333$	6.91874	+	21.2937i	0.379145	+	1.16689i
$334$	3.70820	−	11.4127i	0.202904	−	0.624474i
$335$	−1.13869	−	0.827304i	−0.0622131	−	0.0452004i
$336$	2.46489	+	1.79085i	0.134471	+	0.0976989i
$337$	−3.19330	+	9.82797i	−0.173950	+	0.535364i	−0.999584	−	0.0288428i	$-0.990818\pi$
$337$	−3.19330	+	9.82797i	−0.173950	+	0.535364i	0.825634	+	0.564206i	$0.190818\pi$
$338$	3.97870	+	12.2452i	0.216413	+	0.666050i
$339$	31.2801	−	22.7263i	1.69890	−	1.23432i
$340$	0.810708			0.0439668
$341$	13.7362	−	13.0283i	0.743858	−	0.705520i
$342$	−16.2883			−0.880771
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	2.93362	+	9.02875i	0.158170	+	0.486797i
$345$	1.88301	−	5.79531i	0.101378	−	0.312009i
$346$	16.0750	+	11.6792i	0.864197	+	0.627876i
$347$	14.8214	+	10.7684i	0.795652	+	0.578075i	0.909635	−	0.415407i	$-0.136361\pi$
$347$	14.8214	+	10.7684i	0.795652	+	0.578075i	−0.113983	+	0.993483i	$0.536361\pi$
$348$	−8.98933	+	27.6663i	−0.481878	+	1.48307i
$349$	−9.24627	−	28.4571i	−0.494942	−	1.52327i	−0.817048	−	0.576570i	$-0.804391\pi$
$349$	−9.24627	−	28.4571i	−0.494942	−	1.52327i	0.322106	−	0.946704i	$-0.395609\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	−3.53131			−0.188487
$352$	−3.28837	+	0.432036i	−0.175270	+	0.0230276i
$353$	−8.93024			−0.475309			−0.237654	−	0.971350i	$-0.576379\pi$
$353$	−8.93024			−0.475309			−0.237654	+	0.971350i	$0.576379\pi$
$354$	32.5594	−	23.6558i	1.73051	−	1.25729i
$355$	3.99211	+	12.2865i	0.211879	+	0.652097i
$356$	2.97830	−	9.16627i	0.157850	−	0.485812i
$357$	−1.99831	−	1.45186i	−0.105762	−	0.0768404i
$358$	−6.96763	−	5.06228i	−0.368251	−	0.267550i
$359$	−9.20610	+	28.3334i	−0.485879	+	1.49538i	0.344824	+	0.938667i	$0.387938\pi$
$359$	−9.20610	+	28.3334i	−0.485879	+	1.49538i	−0.830704	+	0.556715i	$0.812062\pi$
$360$	1.94151	+	5.97534i	0.102326	+	0.314928i
$361$	9.93385	−	7.21736i	0.522834	−	0.379861i
$362$	−11.7345			−0.616750
$363$	18.2384	+	28.1173i	0.957270	+	1.47578i
$364$	0.353057			0.0185052
$365$	−4.16650	+	3.02714i	−0.218085	+	0.158448i
$366$	6.31384	+	19.4320i	0.330030	+	1.01573i
$367$	−7.64926	+	23.5420i	−0.399288	+	1.22888i	0.526283	+	0.850309i	$0.323585\pi$
$367$	−7.64926	+	23.5420i	−0.399288	+	1.22888i	−0.925571	+	0.378573i	$0.876415\pi$
$368$	1.61803	+	1.17557i	0.0843459	+	0.0612808i
$369$	41.9713	+	30.4940i	2.18494	+	1.58745i
$370$	1.10121	−	3.38918i	0.0572493	−	0.176195i
$371$	0.865144	+	2.66264i	0.0449161	+	0.138237i
$372$	14.0701	−	10.2225i	0.729501	−	0.530014i
$373$	−9.75070			−0.504872			−0.252436	−	0.967614i	$-0.581232\pi$
$373$	−9.75070			−0.504872			−0.252436	+	0.967614i	$0.581232\pi$
$374$	2.66590	−	0.350255i	0.137851	−	0.0181112i
$375$	−3.04678			−0.157335
$376$	−6.96380	+	5.05950i	−0.359131	+	0.260924i
$377$	1.04167	+	3.20594i	0.0536489	+	0.165114i
$378$	3.09082	−	9.51255i	0.158974	−	0.489273i
$379$	−17.0261	−	12.3702i	−0.874571	−	0.635413i	0.0572388	−	0.998361i	$-0.481770\pi$
$379$	−17.0261	−	12.3702i	−0.874571	−	0.635413i	−0.931810	+	0.362948i	$0.881770\pi$
$380$	2.09738	+	1.52384i	0.107593	+	0.0781712i
$381$	15.2883	−	47.0526i	0.783244	−	2.41058i
$382$	2.51868	+	7.75171i	0.128867	+	0.396612i
$383$	28.2208	−	20.5036i	1.44202	−	1.04769i	0.454398	−	0.890799i	$-0.349854\pi$
$383$	28.2208	−	20.5036i	1.44202	−	1.04769i	0.987617	−	0.156887i	$-0.0501457\pi$
$384$	−3.04678			−0.155480
$385$	−2.40640	+	2.28238i	−0.122641	+	0.116321i
$386$	−8.74185			−0.444948
$387$	48.2542	−	35.0587i	2.45290	−	1.78213i
$388$	−3.02786	−	9.31881i	−0.153717	−	0.473091i
$389$	−3.92663	+	12.0849i	−0.199088	+	0.612730i	0.800816	+	0.598910i	$0.204399\pi$
$389$	−3.92663	+	12.0849i	−0.199088	+	0.612730i	−0.999904	+	0.0138204i	$0.995601\pi$
$390$	0.870248	+	0.632272i	0.0440667	+	0.0320163i
$391$	−1.31175	−	0.953044i	−0.0663382	−	0.0481975i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	−7.61567	−	23.4386i	−0.384160	−	1.18232i
$394$	11.6958	−	8.49750i	0.589226	−	0.428098i
$395$	3.64694			0.183498
$396$	8.96594	+	18.8103i	0.450555	+	0.945253i
$397$	3.33036			0.167146			0.0835729	−	0.996502i	$-0.473367\pi$
$397$	3.33036			0.167146			0.0835729	+	0.996502i	$0.473367\pi$
$398$	−8.93526	+	6.49185i	−0.447884	+	0.325407i
$399$	−2.44086	−	7.51219i	−0.122196	−	0.376080i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	7.50159	+	5.45023i	0.374612	+	0.272171i	0.759121	−	0.650950i	$-0.225629\pi$
$401$	7.50159	+	5.45023i	0.374612	+	0.272171i	−0.384509	+	0.923121i	$0.625629\pi$
$402$	−3.46932	−	2.52061i	−0.173034	−	0.125717i
$403$	0.622768	−	1.91668i	0.0310223	−	0.0954768i
$404$	−0.279462	−	0.860095i	−0.0139038	−	0.0427913i
$405$	9.40531	−	6.83335i	0.467353	−	0.339552i
$406$	−9.54782			−0.473850
$407$	2.15694	−	11.6206i	0.106916	−	0.576013i
$408$	2.47005			0.122285
$409$	0.282844	−	0.205498i	0.0139857	−	0.0101612i	−0.580770	−	0.814067i	$-0.697249\pi$
$409$	0.282844	−	0.205498i	0.0139857	−	0.0101612i	0.594756	+	0.803906i	$0.297249\pi$
$410$	−2.55165	−	7.85318i	−0.126017	−	0.387841i
$411$	9.79347	−	30.1412i	0.483076	−	1.48676i
$412$	−9.07741	−	6.59512i	−0.447212	−	0.324918i
$413$	10.6865	+	7.76420i	0.525849	+	0.382051i
$414$	3.88301	−	11.9507i	0.190840	−	0.587344i
$415$	0.824517	+	2.53760i	0.0404739	+	0.124566i
$416$	−0.285629	+	0.207522i	−0.0140041	+	0.0101746i
$417$	2.30692			0.112970
$418$	7.55531	+	4.10479i	0.369542	+	0.200772i
$419$	27.9340			1.36466			0.682332	−	0.731043i	$-0.260966\pi$
$419$	27.9340			1.36466			0.682332	+	0.731043i	$0.260966\pi$
$420$	−2.46489	+	1.79085i	−0.120274	+	0.0873845i
$421$	2.49445	+	7.67712i	0.121572	+	0.374160i	0.993261	−	0.115899i	$-0.0369750\pi$
$421$	2.49445	+	7.67712i	0.121572	+	0.374160i	−0.871689	+	0.490060i	$0.836975\pi$
$422$	−7.32685	+	22.5497i	−0.356666	+	1.09770i
$423$	43.7525	+	31.7880i	2.12732	+	1.54559i
$424$	−2.26498	−	1.64560i	−0.109997	−	0.0799175i
$425$	−0.250523	+	0.771029i	−0.0121521	+	0.0374004i
$426$	12.1631	+	37.4341i	0.589303	+	1.81369i
$427$	−5.42536	+	3.94175i	−0.262552	+	0.190755i
$428$	8.89614			0.430011
$429$	3.13486	+	1.70316i	0.151352	+	0.0822295i
$430$	−9.49338			−0.457812
$431$	−16.1875	+	11.7609i	−0.779723	+	0.566502i	−0.904896	−	0.425633i	$-0.860051\pi$
$431$	−16.1875	+	11.7609i	−0.779723	+	0.566502i	0.125173	+	0.992135i	$0.460051\pi$
$432$	3.09082	+	9.51255i	0.148707	+	0.457673i
$433$	−11.9728	+	36.8484i	−0.575375	+	1.77082i	0.0595231	+	0.998227i	$0.481042\pi$
$433$	−11.9728	+	36.8484i	−0.575375	+	1.77082i	−0.634898	+	0.772596i	$0.718958\pi$
$434$	4.61803	+	3.35520i	0.221673	+	0.161055i
$435$	−23.5344	−	17.0987i	−1.12839	−	0.819821i
$436$	5.70950	−	17.5720i	0.273435	−	0.841547i
$437$	−1.60226	−	4.93124i	−0.0766464	−	0.235893i
$438$	−12.6944	+	9.22302i	−0.606562	+	0.440693i
$439$	5.62560			0.268495			0.134248	−	0.990948i	$-0.457138\pi$
$439$	5.62560			0.268495			0.134248	+	0.990948i	$0.457138\pi$
$440$	0.605270	−	3.26093i	0.0288551	−	0.155459i
$441$	6.28284			0.299183
$442$	0.231562	−	0.168239i	0.0110143	−	0.00800233i
$443$	−4.84425	−	14.9091i	−0.230157	−	0.708351i	−0.997727	−	0.0673854i	$-0.978534\pi$
$443$	−4.84425	−	14.9091i	−0.230157	−	0.708351i	0.767570	−	0.640965i	$-0.221466\pi$
$444$	3.35515	−	10.3261i	0.159228	−	0.490054i
$445$	7.79730	+	5.66507i	0.369627	+	0.268550i
$446$	−4.52229	−	3.28564i	−0.214137	−	0.155580i
$447$	−8.44512	+	25.9914i	−0.399440	+	1.22935i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	21.1179	−	15.3431i	0.996617	−	0.724085i	0.0352568	−	0.999378i	$-0.488775\pi$
$449$	21.1179	−	15.3431i	0.996617	−	0.724085i	0.961360	+	0.275294i	$0.0887751\pi$
$450$	−6.28284			−0.296176
$451$	−11.7836	−	24.7217i	−0.554869	−	1.16410i
$452$	−12.6902			−0.596899
$453$	54.1613	−	39.3505i	2.54472	−	1.84885i
$454$	1.95362	+	6.01263i	0.0916881	+	0.282187i
$455$	−0.109101	+	0.335777i	−0.00511471	+	0.0157415i
$456$	6.39025	+	4.64279i	0.299251	+	0.217419i
$457$	28.7938	+	20.9199i	1.34692	+	0.978593i	0.999159	+	0.0410094i	$0.0130573\pi$
$457$	28.7938	+	20.9199i	1.34692	+	0.978593i	0.347759	+	0.937584i	$0.386943\pi$
$458$	1.20242	−	3.70068i	0.0561856	−	0.172922i
$459$	−2.50575	−	7.71190i	−0.116958	−	0.359961i
$460$	−1.61803	+	1.17557i	−0.0754412	+	0.0548113i
$461$	−9.66571			−0.450177			−0.225088	−	0.974338i	$-0.572267\pi$
$461$	−9.66571			−0.450177			−0.225088	+	0.974338i	$0.572267\pi$
$462$	−7.33176	+	6.95389i	−0.341104	+	0.323524i
$463$	−29.9726			−1.39295			−0.696473	−	0.717583i	$-0.745248\pi$
$463$	−29.9726			−1.39295			−0.696473	+	0.717583i	$0.745248\pi$
$464$	7.72435	−	5.61207i	0.358594	−	0.260534i
$465$	5.37431	+	16.5404i	0.249227	+	0.767043i
$466$	−4.68651	+	14.4236i	−0.217098	+	0.668160i
$467$	−24.6820	−	17.9325i	−1.14215	−	0.829818i	−0.154729	−	0.987957i	$-0.549450\pi$
$467$	−24.6820	−	17.9325i	−1.14215	−	0.829818i	−0.987417	+	0.158139i	$0.949450\pi$
$468$	1.79456	+	1.30383i	0.0829537	+	0.0602694i
$469$	0.434939	−	1.33861i	0.0200836	−	0.0618111i
$470$	−2.65993	−	8.18644i	−0.122694	−	0.377612i
$471$	−0.164731	+	0.119684i	−0.00759040	+	0.00551475i
$472$	−13.2092			−0.608005
$473$	−31.2177	+	4.10148i	−1.43539	+	0.188586i
$474$	11.1114			0.510364
$475$	−2.09738	+	1.52384i	−0.0962345	+	0.0699185i
$476$	0.250523	+	0.771029i	0.0114827	+	0.0353401i
$477$	−5.43557	+	16.7290i	−0.248877	+	0.765966i
$478$	−17.0661	−	12.3993i	−0.780587	−	0.567130i
$479$	31.3192	+	22.7547i	1.43101	+	1.03969i	0.989827	+	0.142274i	$0.0454415\pi$
$479$	31.3192	+	22.7547i	1.43101	+	1.03969i	0.441184	+	0.897417i	$0.354559\pi$
$480$	0.941506	−	2.89766i	0.0429737	−	0.132259i
$481$	−0.388791	−	1.19657i	−0.0177273	−	0.0545591i
$482$	−9.66098	+	7.01911i	−0.440046	+	0.319712i
$483$	6.09355			0.277266
$484$	0.581513	−	10.9846i	0.0264324	−	0.499301i
$485$	9.79837			0.444921
$486$	4.38027	−	3.18246i	0.198693	−	0.144359i
$487$	10.4564	+	32.1814i	0.473823	+	1.45828i	0.847539	+	0.530734i	$0.178084\pi$
$487$	10.4564	+	32.1814i	0.473823	+	1.45828i	−0.373716	+	0.927543i	$0.621916\pi$
$488$	2.07230	−	6.37789i	0.0938088	−	0.288714i
$489$	−54.8911	−	39.8807i	−2.48226	−	1.80347i
$490$	−0.809017	−	0.587785i	−0.0365477	−	0.0265534i
$491$	−5.74014	+	17.6663i	−0.259049	+	0.797271i	0.733956	+	0.679197i	$0.237672\pi$
$491$	−5.74014	+	17.6663i	−0.259049	+	0.797271i	−0.993005	+	0.118074i	$0.962328\pi$
$492$	−7.77431	−	23.9269i	−0.350493	−	1.07871i
$493$	−6.26219	+	4.54975i	−0.282035	+	0.204910i
$494$	0.915302			0.0411814
$495$	−20.6603	+	2.71441i	−0.928611	+	0.122004i
$496$	−5.70820			−0.256306
$497$	−10.4515	+	7.59345i	−0.468813	+	0.340613i
$498$	2.51212	+	7.73150i	0.112571	+	0.346457i
$499$	−4.54469	+	13.9871i	−0.203448	+	0.626149i	0.796325	+	0.604868i	$0.206774\pi$
$499$	−4.54469	+	13.9871i	−0.203448	+	0.626149i	−0.999774	+	0.0212804i	$0.993226\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	29.5787	+	21.4902i	1.32148	+	0.960111i
$502$	−0.654603	+	2.01466i	−0.0292164	+	0.0899188i
$503$	1.70032	+	5.23303i	0.0758133	+	0.233329i	0.981781	−	0.190018i	$-0.0608548\pi$
$503$	1.70032	+	5.23303i	0.0758133	+	0.233329i	−0.905967	+	0.423348i	$0.860855\pi$
$504$	−5.08293	+	3.69296i	−0.226412	+	0.164498i
$505$	0.904358			0.0402434
$506$	−4.81280	+	4.56475i	−0.213955	+	0.202928i
$507$	−39.2283			−1.74219
$508$	−13.1369	+	9.54455i	−0.582858	+	0.423471i
$509$	7.44870	+	22.9247i	0.330158	+	1.01612i	0.969058	+	0.246832i	$0.0793895\pi$
$509$	7.44870	+	22.9247i	0.330158	+	1.01612i	−0.638901	+	0.769289i	$0.720610\pi$
$510$	−0.763286	+	2.34915i	−0.0337989	+	0.104022i
$511$	−4.16650	−	3.02714i	−0.184315	−	0.133913i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	8.01296	−	24.6614i	0.353781	−	1.08883i
$514$	6.40088	+	19.6999i	0.282331	+	0.868924i
$515$	9.07741	−	6.59512i	0.399998	−	0.290616i
$516$	−28.9242			−1.27332
$517$	−12.2837	−	25.7708i	−0.540235	−	1.13340i
$518$	3.56360			0.156575
$519$	−48.9769	+	35.5838i	−2.14985	+	1.56196i
$520$	−0.109101	−	0.335777i	−0.00478438	−	0.0147248i
$521$	2.69862	−	8.30551i	0.118229	−	0.363871i	−0.874378	−	0.485246i	$-0.838730\pi$
$521$	2.69862	−	8.30551i	0.118229	−	0.363871i	0.992607	+	0.121374i	$0.0387302\pi$
$522$	−48.5309	−	35.2598i	−2.12414	−	1.54328i
$523$	−35.7970	−	26.0080i	−1.56529	−	1.13725i	−0.931495	−	0.363754i	$-0.881495\pi$
$523$	−35.7970	−	26.0080i	−1.56529	−	1.13725i	−0.633799	−	0.773498i	$-0.718505\pi$
$524$	−2.49958	+	7.69292i	−0.109195	+	0.336067i
$525$	−0.941506	−	2.89766i	−0.0410907	−	0.126464i
$526$	3.15137	−	2.28960i	0.137406	−	0.0998315i
$527$	4.62769			0.201585
$528$	1.84412	−	9.93532i	0.0802552	−	0.432379i
$529$	−19.0000			−0.826087
$530$	2.26498	−	1.64560i	0.0983843	−	0.0714804i
$531$	25.6458	+	78.9298i	1.11293	+	3.42526i
$532$	−0.801129	+	2.46562i	−0.0347333	+	0.106898i
$533$	−2.35853	−	1.71357i	−0.102159	−	0.0742230i
$534$	23.7566	+	17.2602i	1.02805	+	0.746922i
$535$	−2.74906	+	8.46074i	−0.118852	+	0.365789i
$536$	0.434939	+	1.33861i	0.0187865	+	0.0578190i
$537$	21.2288	−	15.4236i	0.916091	−	0.665579i
$538$	22.8684			0.985928
$539$	−2.91429	−	1.58333i	−0.125527	−	0.0681988i
$540$	−10.0021			−0.430421
$541$	−11.3591	+	8.25289i	−0.488367	+	0.354819i	−0.804556	−	0.593877i	$-0.797597\pi$
$541$	−11.3591	+	8.25289i	−0.488367	+	0.354819i	0.316189	+	0.948696i	$0.397597\pi$
$542$	−6.36828	−	19.5995i	−0.273541	−	0.841873i
$543$	11.0481	−	34.0025i	0.474118	−	1.45919i
$544$	−0.655877	−	0.476522i	−0.0281205	−	0.0204307i
$545$	14.9477	+	10.8601i	0.640287	+	0.465196i
$546$	−0.332405	+	1.02304i	−0.0142256	+	0.0437820i
$547$	2.00272	+	6.16373i	0.0856300	+	0.263542i	0.984699	−	0.174266i	$-0.0557551\pi$
$547$	2.00272	+	6.16373i	0.0856300	+	0.263542i	−0.899069	+	0.437808i	$0.855755\pi$
$548$	−8.41533	+	6.11410i	−0.359485	+	0.261181i
$549$	−42.1335			−1.79821
$550$	2.91429	+	1.58333i	0.124266	+	0.0675133i
$551$	−24.7528			−1.05450
$552$	−4.92979	+	3.58170i	−0.209826	+	0.152447i
$553$	1.12697	+	3.46845i	0.0479235	+	0.147493i
$554$	−5.31649	+	16.3625i	−0.225876	+	0.695175i
$555$	8.78389	+	6.38187i	0.372855	+	0.270895i
$556$	−0.612562	−	0.445052i	−0.0259784	−	0.0188744i
$557$	3.09355	−	9.52097i	0.131078	−	0.403417i	−0.863881	−	0.503695i	$-0.831973\pi$
$557$	3.09355	−	9.52097i	0.131078	−	0.403417i	0.994959	+	0.100279i	$0.0319734\pi$
$558$	11.0825	+	34.1085i	0.469160	+	1.44393i
$559$	−2.71159	+	1.97008i	−0.114688	+	0.0833256i
$560$	1.00000			0.0422577
$561$	−1.49505	+	8.05464i	−0.0631209	+	0.340067i
$562$	−30.4444			−1.28422
$563$	−2.68760	+	1.95266i	−0.113269	+	0.0822947i	−0.642978	−	0.765885i	$-0.722301\pi$
$563$	−2.68760	+	1.95266i	−0.113269	+	0.0822947i	0.529709	+	0.848180i	$0.322301\pi$
$564$	−8.10423	−	24.9422i	−0.341249	−	1.05026i
$565$	3.92150	−	12.0691i	0.164979	−	0.507752i
$566$	8.08626	+	5.87501i	0.339891	+	0.246945i
$567$	9.40531	+	6.83335i	0.394986	+	0.286974i
$568$	3.99211	−	12.2865i	0.167505	−	0.515528i
$569$	9.42871	+	29.0186i	0.395272	+	1.21652i	0.928749	+	0.370708i	$0.120885\pi$
$569$	9.42871	+	29.0186i	0.395272	+	1.21652i	−0.533477	+	0.845814i	$0.679115\pi$
$570$	−6.39025	+	4.64279i	−0.267658	+	0.194465i
$571$	2.37904			0.0995597			0.0497799	−	0.998760i	$-0.484148\pi$
$571$	2.37904			0.0995597			0.0497799	+	0.998760i	$0.484148\pi$
$572$	−0.503830	−	1.05702i	−0.0210662	−	0.0441963i
$573$	−24.8332			−1.03742
$574$	6.68031	−	4.85353i	0.278831	−	0.202582i
$575$	−0.618034	−	1.90211i	−0.0257738	−	0.0793236i
$576$	1.94151	−	5.97534i	0.0808961	−	0.248972i
$577$	10.1438	+	7.36989i	0.422291	+	0.306813i	0.778559	−	0.627571i	$-0.215951\pi$
$577$	10.1438	+	7.36989i	0.422291	+	0.306813i	−0.356268	+	0.934384i	$0.615951\pi$
$578$	−13.2216	−	9.60603i	−0.549945	−	0.399558i
$579$	8.23050	−	25.3309i	0.342048	−	1.05271i
$580$	2.95044	+	9.08052i	0.122510	+	0.377048i
$581$	−2.15861	+	1.56832i	−0.0895543	+	0.0650650i
$582$	29.8535			1.23747
$583$	6.73711	−	6.38989i	0.279023	−	0.264642i
$584$	5.15008			0.213112
$585$	−1.79456	+	1.30383i	−0.0741960	+	0.0539066i
$586$	1.99871	+	6.15139i	0.0825659	+	0.254112i
$587$	13.4670	−	41.4471i	0.555841	−	1.71070i	−0.137870	−	0.990450i	$-0.544026\pi$
$587$	13.4670	−	41.4471i	0.555841	−	1.71070i	0.693712	−	0.720253i	$-0.255974\pi$
$588$	−2.46489	−	1.79085i	−0.101650	−	0.0738534i
$589$	11.9723	+	8.69837i	0.493309	+	0.358410i
$590$	4.08188	−	12.5627i	0.168048	−	0.517200i
$591$	13.6112	+	41.8909i	0.559889	+	1.72316i
$592$	−2.88301	+	2.09463i	−0.118491	+	0.0860888i
$593$	0.0535401			0.00219863			0.00109931	−	0.999999i	$-0.499650\pi$
$593$	0.0535401			0.00219863			0.00109931	+	0.999999i	$0.499650\pi$
$594$	−32.8905	+	4.32126i	−1.34951	+	0.177303i
$595$	−0.810708			−0.0332358
$596$	7.25672	−	5.27232i	0.297247	−	0.215962i
$597$	−10.3985	−	32.0034i	−0.425584	−	1.30981i
$598$	−0.218201	+	0.671554i	−0.00892291	+	0.0274619i
$599$	−23.4214	−	17.0166i	−0.956971	−	0.695280i	−0.00452535	−	0.999990i	$-0.501440\pi$
$599$	−23.4214	−	17.0166i	−0.956971	−	0.695280i	−0.952445	+	0.304710i	$0.901440\pi$
$600$	2.46489	+	1.79085i	0.100629	+	0.0731111i
$601$	9.59206	−	29.5213i	0.391268	−	1.20420i	−0.540562	−	0.841304i	$-0.681788\pi$
$601$	9.59206	−	29.5213i	0.391268	−	1.20420i	0.931830	−	0.362895i	$-0.118212\pi$
$602$	−2.93362	−	9.02875i	−0.119565	−	0.367984i
$603$	7.15419	−	5.19782i	0.291341	−	0.211672i
$604$	−21.9731			−0.894072
$605$	10.2673	+	3.94749i	0.417425	+	0.160488i
$606$	2.75538			0.111929
$607$	−6.63627	+	4.82153i	−0.269358	+	0.195700i	−0.714262	−	0.699878i	$-0.753238\pi$
$607$	−6.63627	+	4.82153i	−0.269358	+	0.195700i	0.444904	+	0.895578i	$0.353238\pi$
$608$	−0.801129	−	2.46562i	−0.0324901	−	0.0999941i
$609$	8.98933	−	27.6663i	0.364266	−	1.12110i
$610$	5.42536	+	3.94175i	0.219666	+	0.159597i
$611$	−2.45862	−	1.78629i	−0.0994650	−	0.0722656i
$612$	−1.57399	+	4.84426i	−0.0636249	+	0.195817i
$613$	−6.67585	−	20.5462i	−0.269635	−	0.829852i	−0.990589	−	0.136869i	$-0.956296\pi$
$613$	−6.67585	−	20.5462i	−0.269635	−	0.829852i	0.720954	−	0.692983i	$-0.243704\pi$
$614$	−16.7040	+	12.1362i	−0.674119	+	0.489776i
$615$	25.1582			1.01448
$616$	3.28837	−	0.432036i	0.132492	−	0.0174072i
$617$	16.5772			0.667372			0.333686	−	0.942684i	$-0.391707\pi$
$617$	16.5772			0.667372			0.333686	+	0.942684i	$0.391707\pi$
$618$	27.6568	−	20.0939i	1.11252	−	0.808294i
$619$	−5.50460	−	16.9414i	−0.221248	−	0.680933i	−0.998651	−	0.0519291i	$-0.983463\pi$
$619$	−5.50460	−	16.9414i	−0.221248	−	0.680933i	0.777402	−	0.629004i	$-0.216537\pi$
$620$	1.76393	−	5.42882i	0.0708412	−	0.218027i
$621$	16.1837	+	11.7582i	0.649430	+	0.471839i
$622$	18.9621	+	13.7768i	0.760312	+	0.552399i
$623$	−2.97830	+	9.16627i	−0.119323	+	0.367239i
$624$	−0.332405	−	1.02304i	−0.0133068	−	0.0409543i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−11.9059			−0.475855
$627$	−19.0076	+	18.0280i	−0.759092	+	0.719969i
$628$	0.0668308			0.00266684
$629$	2.33728	−	1.69813i	0.0931935	−	0.0677090i
$630$	−1.94151	−	5.97534i	−0.0773514	−	0.238063i
$631$	4.17546	−	12.8508i	0.166223	−	0.511581i	−0.832902	−	0.553421i	$-0.813322\pi$
$631$	4.17546	−	12.8508i	0.166223	−	0.511581i	0.999124	+	0.0418403i	$0.0133221\pi$
$632$	−2.95044	−	2.14362i	−0.117362	−	0.0852686i
$633$	−58.4431	−	42.4614i	−2.32291	−	1.68769i
$634$	10.6359	−	32.7339i	0.422406	−	1.30003i
$635$	−5.01787	−	15.4434i	−0.199128	−	0.612853i
$636$	6.90088	−	5.01378i	0.273638	−	0.198809i
$637$	−0.353057			−0.0139886
$638$	13.6252	+	28.5854i	0.539428	+	1.13171i
$639$	−81.1665			−3.21090
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	13.6930	+	42.1429i	0.540843	+	1.66454i	0.730674	+	0.682726i	$0.239206\pi$
$641$	13.6930	+	42.1429i	0.540843	+	1.66454i	−0.189832	+	0.981817i	$0.560794\pi$
$642$	−8.37577	+	25.7780i	−0.330565	+	1.01738i
$643$	−27.7373	−	20.1524i	−1.09385	−	0.794731i	−0.113808	−	0.993503i	$-0.536305\pi$
$643$	−27.7373	−	20.1524i	−1.09385	−	0.794731i	−0.980046	+	0.198772i	$0.936305\pi$
$644$	−1.61803	−	1.17557i	−0.0637595	−	0.0463240i
$645$	8.93807	−	27.5086i	0.351936	−	1.08315i
$646$	0.649481	+	1.99890i	0.0255535	+	0.0786456i
$647$	−22.5507	+	16.3841i	−0.886561	+	0.644124i	−0.934979	−	0.354703i	$-0.884582\pi$
$647$	−22.5507	+	16.3841i	−0.886561	+	0.644124i	0.0484181	+	0.998827i	$0.484582\pi$
$648$	−11.6256			−0.456697
$649$	7.99517	−	43.0744i	0.313838	−	1.69082i
$650$	0.353057			0.0138480
$651$	−14.0701	+	10.2225i	−0.551451	+	0.400653i
$652$	6.88155	+	21.1792i	0.269502	+	0.829443i
$653$	−8.52365	+	26.2331i	−0.333556	+	1.02658i	0.633873	+	0.773437i	$0.281464\pi$
$653$	−8.52365	+	26.2331i	−0.333556	+	1.02658i	−0.967429	+	0.253143i	$0.918536\pi$
$654$	45.5422	+	33.0883i	1.78084	+	1.29386i
$655$	−6.54399	−	4.75449i	−0.255695	−	0.185773i
$656$	−2.55165	+	7.85318i	−0.0996252	+	0.306615i
$657$	−9.99891	−	30.7735i	−0.390094	−	1.20059i
$658$	6.96380	−	5.05950i	0.271477	−	0.197240i
$659$	2.49969			0.0973742			0.0486871	−	0.998814i	$-0.484496\pi$
$659$	2.49969			0.0973742			0.0486871	+	0.998814i	$0.484496\pi$
$660$	8.87918	+	4.82405i	0.345622	+	0.187776i
$661$	10.1499			0.394785			0.197393	−	0.980325i	$-0.436753\pi$
$661$	10.1499			0.394785			0.197393	+	0.980325i	$0.436753\pi$
$662$	−9.44693	+	6.86360i	−0.367165	+	0.266761i
$663$	0.269483	+	0.829385i	0.0104659	+	0.0322106i
$664$	0.824517	−	2.53760i	0.0319975	−	0.0984780i
$665$	−2.09738	−	1.52384i	−0.0813330	−	0.0590919i
$666$	18.1135	+	13.1602i	0.701884	+	0.509949i
$667$	5.90088	−	18.1610i	0.228483	−	0.703198i
$668$	−3.70820	−	11.4127i	−0.143475	−	0.441570i
$669$	13.7784	−	10.0106i	0.532704	−	0.387032i
$670$	−1.40749			−0.0543762
$671$	19.5435	+	10.6180i	0.754470	+	0.409903i
$672$	3.04678			0.117532
$673$	−29.8922	+	21.7180i	−1.15226	+	0.837166i	−0.988780	−	0.149381i	$-0.952272\pi$
$673$	−29.8922	+	21.7180i	−1.15226	+	0.837166i	−0.163480	+	0.986547i	$0.552272\pi$
$674$	3.19330	+	9.82797i	0.123001	+	0.378559i
$675$	3.09082	−	9.51255i	0.118966	−	0.366138i
$676$	10.4164	+	7.56794i	0.400630	+	0.291075i
$677$	−7.14971	−	5.19457i	−0.274786	−	0.199643i	0.441854	−	0.897087i	$-0.354321\pi$
$677$	−7.14971	−	5.19457i	−0.274786	−	0.199643i	−0.716640	+	0.697443i	$0.754321\pi$
$678$	11.9479	−	36.7720i	0.458858	−	1.41222i
$679$	3.02786	+	9.31881i	0.116199	+	0.357623i
$680$	0.655877	−	0.476522i	0.0251517	−	0.0182738i
$681$	−19.2619			−0.738117
$682$	3.45501	−	18.6140i	0.132299	−	0.712768i
$683$	33.0803			1.26578			0.632892	−	0.774240i	$-0.281868\pi$
$683$	33.0803			1.26578			0.632892	+	0.774240i	$0.281868\pi$
$684$	−13.1775	+	9.57403i	−0.503855	+	0.366072i
$685$	−3.21437	−	9.89282i	−0.122815	−	0.377985i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	9.59122	+	6.96843i	0.365928	+	0.265862i
$688$	7.68031	+	5.58007i	0.292809	+	0.212738i
$689$	0.305445	−	0.940063i	0.0116365	−	0.0358136i
$690$	−1.88301	−	5.79531i	−0.0716850	−	0.220624i
$691$	7.46019	−	5.42014i	0.283799	−	0.206192i	−0.436774	−	0.899571i	$-0.643879\pi$
$691$	7.46019	−	5.42014i	0.283799	−	0.206192i	0.720573	+	0.693379i	$0.243879\pi$
$692$	19.8698			0.755336
$693$	−8.96594	−	18.8103i	−0.340588	−	0.714544i
$694$	18.3202			0.695426
$695$	0.612562	−	0.445052i	0.0232358	−	0.0168818i
$696$	8.98933	+	27.6663i	0.340740	+	1.04869i
$697$	2.06864	−	6.36663i	0.0783555	−	0.241153i
$698$	−24.2071	−	17.5875i	−0.916251	−	0.665695i
$699$	−37.3822	−	27.1598i	−1.41393	−	1.02728i
$700$	−0.309017	+	0.951057i	−0.0116797	+	0.0359466i
$701$	8.12619	+	25.0098i	0.306922	+	0.944608i	0.978953	+	0.204085i	$0.0654220\pi$
$701$	8.12619	+	25.0098i	0.306922	+	0.944608i	−0.672031	+	0.740523i	$0.734578\pi$
$702$	−2.85689	+	2.07565i	−0.107826	+	0.0783404i
$703$	9.23865			0.348442
$704$	−2.40640	+	2.28238i	−0.0906946	+	0.0860203i
$705$	26.2258			0.987722
$706$	−7.22472	+	5.24907i	−0.271906	+	0.197551i
$707$	0.279462	+	0.860095i	0.0105102	+	0.0323472i
$708$	12.4366	−	38.2759i	0.467395	−	1.43849i
$709$	28.0104	+	20.3508i	1.05195	+	0.764289i	0.972583	−	0.232557i	$-0.0747091\pi$
$709$	28.0104	+	20.3508i	1.05195	+	0.764289i	0.0793701	+	0.996845i	$0.474709\pi$
$710$	10.4515	+	7.59345i	0.392237	+	0.284977i
$711$	−7.08056	+	21.7917i	−0.265542	+	0.817254i
$712$	−2.97830	−	9.16627i	−0.111617	−	0.343521i
$713$	−9.23607	+	6.71040i	−0.345893	+	0.251306i
$714$	−2.47005			−0.0924391
$715$	1.16098	−	0.152533i	0.0434182	−	0.00570442i
$716$	−8.61246			−0.321863
$717$	51.9967	−	37.7778i	1.94185	−	1.41084i
$718$	9.20610	+	28.3334i	0.343568	+	1.05739i
$719$	−11.4905	+	35.3640i	−0.428522	+	1.31885i	0.471060	+	0.882101i	$0.343872\pi$
$719$	−11.4905	+	35.3640i	−0.428522	+	1.31885i	−0.899581	+	0.436753i	$0.856128\pi$
$720$	5.08293	+	3.69296i	0.189430	+	0.137629i
$721$	9.07741	+	6.59512i	0.338060	+	0.245615i
$722$	3.79439	−	11.6779i	0.141213	−	0.434608i
$723$	−11.2431	−	34.6027i	−0.418136	−	1.28689i
$724$	−9.49338	+	6.89735i	−0.352819	+	0.256338i
$725$	−9.54782			−0.354597
$726$	31.2821	+	12.0271i	1.16099	+	0.446368i
$727$	16.8666			0.625547			0.312773	−	0.949828i	$-0.398742\pi$
$727$	16.8666			0.625547			0.312773	+	0.949828i	$0.398742\pi$
$728$	0.285629	−	0.207522i	0.0105861	−	0.00769126i
$729$	−5.67991	−	17.4810i	−0.210367	−	0.647443i
$730$	−1.59146	+	4.89802i	−0.0589026	+	0.181284i
$731$	−6.22649	−	4.52381i	−0.230295	−	0.167319i
$732$	16.5299	+	12.0096i	0.610961	+	0.443889i
$733$	10.8449	−	33.3771i	0.400564	−	1.23281i	−0.523979	−	0.851731i	$-0.675553\pi$
$733$	10.8449	−	33.3771i	0.400564	−	1.23281i	0.924543	−	0.381078i	$-0.124447\pi$
$734$	7.64926	+	23.5420i	0.282339	+	0.868951i
$735$	2.46489	−	1.79085i	0.0909190	−	0.0660565i
$736$	2.00000			0.0737210
$737$	−4.62835	+	0.608087i	−0.170488	+	0.0223992i
$738$	51.8794			1.90971
$739$	7.27016	−	5.28208i	0.267437	−	0.194304i	−0.445982	−	0.895042i	$-0.647146\pi$
$739$	7.27016	−	5.28208i	0.267437	−	0.194304i	0.713419	+	0.700737i	$0.247146\pi$
$740$	−1.10121	−	3.38918i	−0.0404814	−	0.124589i
$741$	−0.861762	+	2.65223i	−0.0316576	+	0.0974322i
$742$	2.26498	+	1.64560i	0.0831499	+	0.0604120i
$743$	7.76383	+	5.64076i	0.284827	+	0.206939i	0.721020	−	0.692914i	$-0.243673\pi$
$743$	7.76383	+	5.64076i	0.284827	+	0.206939i	−0.436193	+	0.899853i	$0.643673\pi$
$744$	5.37431	−	16.5404i	0.197032	−	0.606401i
$745$	2.77182	+	8.53079i	0.101552	+	0.312544i
$746$	−7.88848	+	5.73132i	−0.288818	+	0.209838i
$747$	−16.7638			−0.613357
$748$	1.95089	−	1.85034i	0.0713315	−	0.0676552i
$749$	−8.89614			−0.325058
$750$	−2.46489	+	1.79085i	−0.0900052	+	0.0653926i
$751$	−4.37232	−	13.4566i	−0.159548	−	0.491039i	0.839045	−	0.544062i	$-0.183114\pi$
$751$	−4.37232	−	13.4566i	−0.159548	−	0.491039i	−0.998593	+	0.0530230i	$0.983114\pi$
$752$	−2.65993	+	8.18644i	−0.0969978	+	0.298529i
$753$	−5.22149	−	3.79363i	−0.190282	−	0.138248i
$754$	2.72713	+	1.98138i	0.0993164	+	0.0721576i
$755$	6.79006	−	20.8976i	0.247115	−	0.760543i
$756$	−3.09082	−	9.51255i	−0.112412	−	0.345968i
$757$	−36.9530	+	26.8479i	−1.34308	+	0.975805i	−0.343756	+	0.939059i	$0.611699\pi$
$757$	−36.9530	+	26.8479i	−1.34308	+	0.975805i	−0.999325	+	0.0367462i	$0.988301\pi$
$758$	−21.0454			−0.764403
$759$	−8.69581	−	18.2436i	−0.315638	−	0.662200i
$760$	2.59251			0.0940401
$761$	13.3680	−	9.71241i	0.484589	−	0.352075i	−0.318510	−	0.947919i	$-0.603183\pi$
$761$	13.3680	−	9.71241i	0.484589	−	0.352075i	0.803100	+	0.595845i	$0.203183\pi$
$762$	−15.2883	−	47.0526i	−0.553837	−	1.70454i
$763$	−5.70950	+	17.5720i	−0.206698	+	0.636150i
$764$	6.59400	+	4.79082i	0.238563	+	0.173326i
$765$	−4.12077	−	2.99391i	−0.148987	−	0.108245i
$766$	10.7794	−	33.1755i	0.389475	−	1.19868i
$767$	−1.44114	−	4.43536i	−0.0520364	−	0.160152i
$768$	−2.46489	+	1.79085i	−0.0889442	+	0.0646217i
$769$	26.5929			0.958963			0.479482	−	0.877552i	$-0.340825\pi$
$769$	26.5929			0.958963			0.479482	+	0.877552i	$0.340825\pi$
$770$	−0.605270	+	3.26093i	−0.0218124	+	0.117516i
$771$	−63.1099			−2.27285
$772$	−7.07230	+	5.13833i	−0.254538	+	0.184933i
$773$	10.9632	+	33.7413i	0.394319	+	1.21359i	0.929491	+	0.368846i	$0.120247\pi$
$773$	10.9632	+	33.7413i	0.394319	+	1.21359i	−0.535172	+	0.844743i	$0.679753\pi$
$774$	18.4315	−	56.7262i	0.662505	−	2.03898i
$775$	4.61803	+	3.35520i	0.165885	+	0.120522i
$776$	−7.92705	−	5.75934i	−0.284565	−	0.206748i
$777$	−3.35515	+	10.3261i	−0.120365	+	0.370446i
$778$	3.92663	+	12.0849i	0.140777	+	0.433266i
$779$	17.3187	−	12.5828i	0.620509	−	0.450826i
$780$	1.07569			0.0385157
$781$	37.6489	+	20.4546i	1.34718	+	0.731924i
$782$	−1.62142			−0.0579817
$783$	77.2596	−	56.1324i	2.76103	−	2.00601i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−0.0206519	+	0.0635599i	−0.000737097	+	0.00226855i
$786$	−19.9381	−	14.4859i	−0.711168	−	0.516693i
$787$	13.0244	+	9.46277i	0.464269	+	0.337311i	0.795204	−	0.606342i	$-0.207364\pi$
$787$	13.0244	+	9.46277i	0.464269	+	0.337311i	−0.330934	+	0.943654i	$0.607364\pi$
$788$	4.46740	−	13.7492i	0.159145	−	0.489797i
$789$	3.66745	+	11.2873i	0.130565	+	0.401837i
$790$	2.95044	−	2.14362i	0.104972	−	0.0762666i
$791$	12.6902			0.451213
$792$	18.3100	+	9.94781i	0.650618	+	0.353480i
$793$	2.36764			0.0840773
$794$	2.69432	−	1.95754i	0.0956177	−	0.0694703i
$795$	2.63590	+	8.11247i	0.0934858	+	0.287720i
$796$	−3.41297	+	10.5040i	−0.120969	+	0.372305i
$797$	−30.7797	−	22.3627i	−1.09027	−	0.792128i	−0.110826	−	0.993840i	$-0.535350\pi$
$797$	−30.7797	−	22.3627i	−1.09027	−	0.792128i	−0.979445	+	0.201711i	$0.935350\pi$
$798$	−6.39025	−	4.64279i	−0.226213	−	0.164353i
$799$	2.15643	−	6.63681i	0.0762890	−	0.234793i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$	−48.9892	+	35.5927i	−1.73095	+	1.25761i
$802$	9.27248			0.327423
$803$	−3.11719	+	16.7940i	−0.110003	+	0.592649i
$804$	−4.28832			−0.151237
$805$	1.61803	−	1.17557i	0.0570282	−	0.0414334i
$806$	−0.622768	−	1.91668i	−0.0219361	−	0.0675123i
$807$	−21.5308	+	66.2648i	−0.757918	+	2.33263i
$808$	−0.731641	−	0.531568i	−0.0257390	−	0.0187005i
$809$	−11.9721	−	8.69827i	−0.420918	−	0.305815i	0.357089	−	0.934070i	$-0.383769\pi$
$809$	−11.9721	−	8.69827i	−0.420918	−	0.305815i	−0.778007	+	0.628256i	$0.783769\pi$
$810$	3.59251	−	11.0566i	0.126228	−	0.388489i
$811$	−0.217015	−	0.667904i	−0.00762043	−	0.0234533i	0.947174	−	0.320720i	$-0.103925\pi$
$811$	−0.217015	−	0.667904i	−0.00762043	−	0.0234533i	−0.954794	+	0.297267i	$0.903925\pi$
$812$	−7.72435	+	5.61207i	−0.271072	+	0.196945i
$813$	62.7885			2.20209
$814$	−5.08544	−	10.6691i	−0.178244	−	0.373952i
$815$	−22.2692			−0.780055
$816$	1.99831	−	1.45186i	0.0699548	−	0.0508251i
$817$	−7.60542	−	23.4071i	−0.266080	−	0.818910i
$818$	0.108037	−	0.332503i	0.00377742	−	0.0116257i
$819$	−1.79456	−	1.30383i	−0.0627071	−	0.0455594i
$820$	−6.68031	−	4.85353i	−0.233287	−	0.169493i
$821$	−0.465627	+	1.43305i	−0.0162505	+	0.0500138i	−0.958853	−	0.283903i	$-0.908371\pi$
$821$	−0.465627	+	1.43305i	−0.0162505	+	0.0500138i	0.942602	+	0.333917i	$0.108371\pi$
$822$	−9.79347	−	30.1412i	−0.341586	−	1.05129i
$823$	24.9977	−	18.1619i	0.871366	−	0.633084i	−0.0595875	−	0.998223i	$-0.518979\pi$
$823$	24.9977	−	18.1619i	0.871366	−	0.633084i	0.930953	+	0.365139i	$0.118979\pi$
$824$	−11.2203			−0.390877
$825$	−7.33176	+	6.95389i	−0.255259	+	0.242103i
$826$	13.2092			0.459609
$827$	42.6884	−	31.0149i	1.48442	−	1.07850i	0.508323	−	0.861167i	$-0.330266\pi$
$827$	42.6884	−	31.0149i	1.48442	−	1.07850i	0.976099	−	0.217328i	$-0.0697343\pi$
$828$	−3.88301	−	11.9507i	−0.134944	−	0.415315i
$829$	−8.57753	+	26.3989i	−0.297910	+	0.916872i	0.684319	+	0.729183i	$0.260100\pi$
$829$	−8.57753	+	26.3989i	−0.297910	+	0.916872i	−0.982228	+	0.187689i	$0.939900\pi$
$830$	2.15861	+	1.56832i	0.0749265	+	0.0544373i
$831$	−42.4073	−	30.8107i	−1.47109	−	1.06881i
$832$	−0.109101	+	0.335777i	−0.00378238	+	0.0116410i
$833$	−0.250523	−	0.771029i	−0.00868009	−	0.0267146i
$834$	1.86634	−	1.35597i	0.0646260	−	0.0469535i
$835$	12.0000			0.415277
$836$	8.52511	−	1.12006i	0.294847	−	0.0387379i
$837$	−57.0940			−1.97346
$838$	22.5991	−	16.4192i	0.780671	−	0.567191i
$839$	−14.8401	−	45.6732i	−0.512338	−	1.57682i	−0.788073	−	0.615581i	$-0.788921\pi$
$839$	−14.8401	−	45.6732i	−0.512338	−	1.57682i	0.275735	−	0.961234i	$-0.411079\pi$
$840$	−0.941506	+	2.89766i	−0.0324850	+	0.0999786i
$841$	−50.2892	−	36.5373i	−1.73411	−	1.25991i
$842$	6.53055	+	4.74472i	0.225058	+	0.163514i
$843$	28.6636	−	88.2175i	0.987227	−	3.03837i
$844$	7.32685	+	22.5497i	0.252201	+	0.776194i
$845$	−10.4164	+	7.56794i	−0.358334	+	0.260345i
$846$	54.0810			1.85934
$847$	−0.581513	+	10.9846i	−0.0199810	+	0.377436i
$848$	−2.79967			−0.0961409
$849$	−24.6370	+	17.8998i	−0.845541	+	0.614321i
$850$	0.250523	+	0.771029i	0.00859285	+	0.0264461i
$851$	−2.20242	+	6.77837i	−0.0754981	+	0.232359i
$852$	31.8433	+	23.1355i	1.09093	+	0.792610i
$853$	−29.1396	−	21.1712i	−0.997722	−	0.724887i	−0.0361235	−	0.999347i	$-0.511501\pi$
$853$	−29.1396	−	21.1712i	−0.997722	−	0.724887i	−0.961599	+	0.274460i	$0.911501\pi$
$854$	−2.07230	+	6.37789i	−0.0709128	+	0.218247i
$855$	−5.03337	−	15.4911i	−0.172138	−	0.529785i
$856$	7.19713	−	5.22902i	0.245993	−	0.178724i
$857$	−5.73142			−0.195782			−0.0978908	−	0.995197i	$-0.531210\pi$
$857$	−5.73142			−0.195782			−0.0978908	+	0.995197i	$0.531210\pi$
$858$	3.53725	−	0.464734i	0.120760	−	0.0158658i
$859$	33.4569			1.14153			0.570767	−	0.821112i	$-0.306646\pi$
$859$	33.4569			1.14153			0.570767	+	0.821112i	$0.306646\pi$
$860$	−7.68031	+	5.58007i	−0.261896	+	0.190279i
$861$	7.77431	+	23.9269i	0.264948	+	0.815425i
$862$	−6.18306	+	19.0295i	−0.210596	+	0.648148i
$863$	−8.77961	−	6.37876i	−0.298861	−	0.217136i	0.428241	−	0.903665i	$-0.359133\pi$
$863$	−8.77961	−	6.37876i	−0.298861	−	0.217136i	−0.727102	+	0.686529i	$0.759133\pi$
$864$	8.09186	+	5.87908i	0.275291	+	0.200010i
$865$	−6.14010	+	18.8973i	−0.208770	+	0.642527i
$866$	11.9728	+	36.8484i	0.406852	+	1.25216i
$867$	40.2831	−	29.2674i	1.36809	−	0.993974i
$868$	5.70820			0.193749
$869$	8.77600	−	8.32370i	0.297705	−	0.282362i
$870$	−29.0901			−0.986246
$871$	−0.402021	+	0.292085i	−0.0136220	+	0.00989693i
$872$	−5.70950	−	17.5720i	−0.193348	−	0.595064i
$873$	−19.0236	+	58.5486i	−0.643851	+	1.98157i
$874$	−4.19476	−	3.04767i	−0.141890	−	0.103089i
$875$	−0.809017	−	0.587785i	−0.0273498	−	0.0198708i
$876$	−4.84883	+	14.9232i	−0.163827	+	0.504207i
$877$	6.52912	+	20.0946i	0.220473	+	0.678545i	0.998720	+	0.0505868i	$0.0161092\pi$
$877$	6.52912	+	20.0946i	0.220473	+	0.678545i	−0.778247	+	0.627958i	$0.783891\pi$
$878$	4.55120	−	3.30664i	0.153596	−	0.111594i
$879$	−19.7064			−0.664681
$880$	−1.42705	−	2.99391i	−0.0481059	−	0.100925i
$881$	24.5805			0.828137			0.414069	−	0.910246i	$-0.364107\pi$
$881$	24.5805			0.828137			0.414069	+	0.910246i	$0.364107\pi$
$882$	5.08293	−	3.69296i	0.171151	−	0.124349i
$883$	−4.78135	−	14.7155i	−0.160905	−	0.495215i	0.837806	−	0.545968i	$-0.183838\pi$
$883$	−4.78135	−	14.7155i	−0.160905	−	0.495215i	−0.998711	+	0.0507526i	$0.983838\pi$
$884$	0.0884487	−	0.272217i	0.00297485	−	0.00915565i
$885$	32.5594	+	23.6558i	1.09447	+	0.795180i
$886$	−12.6824	−	9.21430i	−0.426074	−	0.309561i
$887$	6.31499	−	19.4356i	0.212037	−	0.652582i	−0.787314	−	0.616552i	$-0.788529\pi$
$887$	6.31499	−	19.4356i	0.212037	−	0.652582i	0.999351	−	0.0360297i	$-0.0114711\pi$
$888$	−3.35515	−	10.3261i	−0.112591	−	0.346521i
$889$	13.1369	−	9.54455i	0.440599	−	0.320114i
$890$	9.63799			0.323066
$891$	7.03663	−	37.9102i	0.235736	−	1.27004i
$892$	−5.58986			−0.187162
$893$	18.0537	−	13.1168i	0.604144	−	0.438936i
$894$	8.44512	+	25.9914i	0.282447	+	0.869282i
$895$	2.66140	−	8.19094i	0.0889607	−	0.273793i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	−1.74050	−	1.26454i	−0.0581134	−	0.0422219i
$898$	8.06633	−	24.8256i	0.269177	−	0.828442i
$899$	16.8417	+	51.8334i	0.561702	+	1.72874i
$900$	−5.08293	+	3.69296i	−0.169431	+	0.123099i
$901$	2.26971			0.0756151
$902$	−24.0642	−	13.0740i	−0.801250	−	0.435318i
$903$	28.9242			0.962538
$904$	−10.2666	+	7.45914i	−0.341463	+	0.248087i
$905$	−3.62615	−	11.1601i	−0.120537	−	0.370976i
$906$	20.6878	−	63.6704i	0.687305	−	2.11531i
$907$	−25.0615	−	18.2082i	−0.832152	−	0.604594i	0.0880154	−	0.996119i	$-0.471948\pi$
$907$	−25.0615	−	18.2082i	−0.832152	−	0.604594i	−0.920167	+	0.391525i	$0.871948\pi$
$908$	5.11465	+	3.71601i	0.169736	+	0.123320i
$909$	−1.75582	+	5.40384i	−0.0582367	+	0.179234i
$910$	0.109101	+	0.335777i	0.00361665	+	0.0111309i
$911$	23.5171	−	17.0862i	0.779156	−	0.566090i	−0.125570	−	0.992085i	$-0.540076\pi$
$911$	23.5171	−	17.0862i	0.779156	−	0.566090i	0.904726	+	0.425995i	$0.140076\pi$
$912$	7.89879			0.261555
$913$	7.77588	+	4.22462i	0.257344	+	0.139815i
$914$	35.5911			1.17725
$915$	−16.5299	+	12.0096i	−0.546460	+	0.397027i
$916$	−1.20242	−	3.70068i	−0.0397292	−	0.122274i
$917$	2.49958	−	7.69292i	0.0825435	−	0.254043i
$918$	−6.56014	−	4.76622i	−0.216517	−	0.157309i
$919$	−30.9348	−	22.4754i	−1.02044	−	0.741396i	−0.0540707	−	0.998537i	$-0.517220\pi$
$919$	−30.9348	−	22.4754i	−1.02044	−	0.741396i	−0.966374	+	0.257141i	$0.917220\pi$
$920$	−0.618034	+	1.90211i	−0.0203760	+	0.0627108i
$921$	−19.4395	−	59.8288i	−0.640555	−	1.97143i
$922$	−7.81972	+	5.68136i	−0.257529	+	0.187106i
$923$	4.56105			0.150129
$924$	−1.84412	+	9.93532i	−0.0606672	+	0.326848i
$925$	3.56360			0.117170
$926$	−24.2484	+	17.6175i	−0.796851	+	0.578946i
$927$	21.7843	+	67.0451i	0.715489	+	2.20205i
$928$	2.95044	−	9.08052i	0.0968529	−	0.298083i
$929$	−31.3555	−	22.7811i	−1.02874	−	0.747424i	−0.0606843	−	0.998157i	$-0.519328\pi$
$929$	−31.3555	−	22.7811i	−1.02874	−	0.747424i	−0.968056	+	0.250733i	$0.919328\pi$
$930$	14.0701	+	10.2225i	0.461377	+	0.335210i
$931$	0.801129	−	2.46562i	0.0262559	−	0.0808075i
$932$	4.68651	+	14.4236i	0.153512	+	0.472460i
$933$	−57.7734	+	41.9748i	−1.89142	+	1.37419i
$934$	−30.5086			−0.998272
$935$	1.15692	+	2.42719i	0.0378354	+	0.0793776i
$936$	2.21820			0.0725042
$937$	−8.49443	+	6.17156i	−0.277501	+	0.201616i	−0.717827	−	0.696222i	$-0.754863\pi$
$937$	−8.49443	+	6.17156i	−0.277501	+	0.201616i	0.440326	+	0.897838i	$0.354863\pi$
$938$	−0.434939	−	1.33861i	−0.0142013	−	0.0437070i
$939$	11.2095	−	34.4992i	0.365807	−	1.12584i
$940$	−6.96380	−	5.05950i	−0.227134	−	0.165023i
$941$	8.24846	+	5.99286i	0.268892	+	0.195362i	0.714058	−	0.700087i	$-0.246855\pi$
$941$	8.24846	+	5.99286i	0.268892	+	0.195362i	−0.445166	+	0.895448i	$0.646855\pi$
$942$	−0.0629216	+	0.193653i	−0.00205010	+	0.00630955i
$943$	5.10330	+	15.7064i	0.166186	+	0.511469i
$944$	−10.6865	+	7.76420i	−0.347816	+	0.252703i
$945$	10.0021			0.325368
$946$	−22.8449	+	21.6675i	−0.742751	+	0.704471i
$947$	−47.2023			−1.53387			−0.766934	−	0.641726i	$-0.778219\pi$
$947$	−47.2023			−1.53387			−0.766934	+	0.641726i	$0.778219\pi$
$948$	8.98933	−	6.53113i	0.291960	−	0.212121i
$949$	0.561876	+	1.72928i	0.0182393	+	0.0561347i
$950$	−0.801129	+	2.46562i	−0.0259920	+	0.0799953i
$951$	84.8379	+	61.6384i	2.75106	+	1.99876i
$952$	0.655877	+	0.476522i	0.0212571	+	0.0154442i
$953$	1.60316	−	4.93402i	0.0519315	−	0.159829i	−0.921727	−	0.387839i	$-0.873222\pi$
$953$	1.60316	−	4.93402i	0.0519315	−	0.159829i	0.973659	+	0.228010i	$0.0732218\pi$
$954$	5.43557	+	16.7290i	0.175983	+	0.541620i
$955$	−6.59400	+	4.79082i	−0.213377	+	0.155027i
$956$	−21.0949			−0.682258
$957$	−95.6588	+	12.5679i	−3.09221	+	0.406264i
$958$	38.7127			1.25075
$959$	8.41533	−	6.11410i	0.271745	−	0.197434i
$960$	−0.941506	−	2.89766i	−0.0303870	−	0.0935215i
$961$	0.489357	−	1.50609i	0.0157857	−	0.0485834i
$962$	−1.01787	−	0.739524i	−0.0328173	−	0.0238432i
$963$	−45.2185	−	32.8531i	−1.45714	−	1.05868i
$964$	−3.69017	+	11.3572i	−0.118852	+	0.365790i
$965$	−2.70138	−	8.31399i	−0.0869605	−	0.267637i
$966$	4.92979	−	3.58170i	0.158613	−	0.115239i
$967$	18.9841			0.610486			0.305243	−	0.952274i	$-0.401262\pi$
$967$	18.9841			0.610486			0.305243	+	0.952274i	$0.401262\pi$
$968$	−5.98614	−	9.22855i	−0.192402	−	0.296617i
$969$	−6.40361			−0.205714
$970$	7.92705	−	5.75934i	0.254522	−	0.184921i
$971$	−12.9503	−	39.8569i	−0.415595	−	1.27907i	−0.911718	−	0.410817i	$-0.865243\pi$
$971$	−12.9503	−	39.8569i	−0.415595	−	1.27907i	0.496123	−	0.868252i	$-0.334757\pi$
$972$	1.67312	−	5.14932i	0.0536652	−	0.165165i
$973$	0.612562	+	0.445052i	0.0196378	+	0.0142677i
$974$	27.3751	+	19.8892i	0.877155	+	0.637290i
$975$	−0.332405	+	1.02304i	−0.0106455	+	0.0327634i
$976$	−2.07230	−	6.37789i	−0.0663328	−	0.204151i
$977$	−6.56981	+	4.77324i	−0.210187	+	0.152710i	−0.687898	−	0.725807i	$-0.741466\pi$
$977$	−6.56981	+	4.77324i	−0.210187	+	0.152710i	0.477711	+	0.878517i	$0.341466\pi$
$978$	−67.8491			−2.16958
$979$	31.6932	−	4.16396i	1.01292	−	0.133081i
$980$	−1.00000			−0.0319438
$981$	−93.9138	+	68.2324i	−2.99844	+	2.17849i
$982$	5.74014	+	17.6663i	0.183175	+	0.563756i
$983$	−11.9943	+	36.9146i	−0.382558	+	1.17739i	0.555678	+	0.831398i	$0.312459\pi$
$983$	−11.9943	+	36.9146i	−0.382558	+	1.17739i	−0.938236	+	0.345996i	$0.887541\pi$
$984$	−20.3534	−	14.7876i	−0.648843	−	0.471412i
$985$	11.6958	+	8.49750i	0.372659	+	0.270753i
$986$	−2.39194	+	7.36165i	−0.0761750	+	0.234443i
$987$	8.10423	+	24.9422i	0.257960	+	0.793920i
$988$	0.740495	−	0.538001i	0.0235583	−	0.0171161i
$989$	18.9868			0.603744
$990$	−15.1190	+	14.3398i	−0.480514	+	0.455749i
$991$	1.30139			0.0413400			0.0206700	−	0.999786i	$-0.493420\pi$
$991$	1.30139			0.0413400			0.0206700	+	0.999786i	$0.493420\pi$
$992$	−4.61803	+	3.35520i	−0.146623	+	0.106528i
$993$	−10.9940	−	33.8361i	−0.348884	−	1.07376i
$994$	−3.99211	+	12.2865i	−0.126622	+	0.389703i
$995$	−8.93526	−	6.49185i	−0.283267	−	0.205805i
$996$	6.57681	+	4.77833i	0.208394	+	0.151407i
$997$	4.57401	−	14.0773i	0.144860	−	0.445834i	−0.852133	−	0.523326i	$-0.824691\pi$
$997$	4.57401	−	14.0773i	0.144860	−	0.445834i	0.996993	+	0.0774917i	$0.0246911\pi$
$998$	4.54469	+	13.9871i	0.143860	+	0.442754i
$999$	−28.8361	+	20.9507i	−0.912335	+	0.662850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.e.421.2	✓	8
11.2	odd	10		8470.2.a.ct.1.4		4
11.4	even	5	inner	770.2.n.e.631.2	yes	8
11.9	even	5		8470.2.a.cq.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.e.421.2	✓	8	1.1	even	1	trivial
770.2.n.e.631.2	yes	8	11.4	even	5	inner
8470.2.a.cq.1.4		4	11.9	even	5
8470.2.a.ct.1.4		4	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.941506 + 2.89766i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.46489 + 1.79085i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.08293 + 3.69296i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.941506 + 2.89766i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.46489 + 1.79085i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.08293 + 3.69296i) q^{9} +1.00000 q^{10} +(3.28837 - 0.432036i) q^{11} +3.04678 q^{12} +(0.285629 - 0.207522i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.941506 + 2.89766i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.655877 + 0.476522i) q^{17} +(-1.94151 + 5.97534i) q^{18} +(0.801129 + 2.46562i) q^{19} +(0.809017 - 0.587785i) q^{20} -3.04678 q^{21} +(2.40640 - 2.28238i) q^{22} -2.00000 q^{23} +(2.46489 - 1.79085i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.109101 - 0.335777i) q^{26} +(-8.09186 - 5.87908i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-2.95044 + 9.08052i) q^{29} +(0.941506 + 2.89766i) q^{30} +(4.61803 - 3.35520i) q^{31} -1.00000 q^{32} +(4.34790 + 9.12179i) q^{33} +0.810708 q^{34} +(-0.809017 + 0.587785i) q^{35} +(1.94151 + 5.97534i) q^{36} +(1.10121 - 3.38918i) q^{37} +(2.09738 + 1.52384i) q^{38} +(0.870248 + 0.632272i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-2.55165 - 7.85318i) q^{41} +(-2.46489 + 1.79085i) q^{42} -9.49338 q^{43} +(0.605270 - 3.26093i) q^{44} -6.28284 q^{45} +(-1.61803 + 1.17557i) q^{46} +(-2.65993 - 8.18644i) q^{47} +(0.941506 - 2.89766i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-0.763286 + 2.34915i) q^{51} +(-0.109101 - 0.335777i) q^{52} +(2.26498 - 1.64560i) q^{53} -10.0021 q^{54} +(2.91429 + 1.58333i) q^{55} +1.00000 q^{56} +(-6.39025 + 4.64279i) q^{57} +(2.95044 + 9.08052i) q^{58} +(4.08188 - 12.5627i) q^{59} +(2.46489 + 1.79085i) q^{60} +(5.42536 + 3.94175i) q^{61} +(1.76393 - 5.42882i) q^{62} +(-1.94151 - 5.97534i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.353057 q^{65} +(8.87918 + 4.82405i) q^{66} -1.40749 q^{67} +(0.655877 - 0.476522i) q^{68} +(-1.88301 - 5.79531i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(10.4515 + 7.59345i) q^{71} +(5.08293 + 3.69296i) q^{72} +(-1.59146 + 4.89802i) q^{73} +(-1.10121 - 3.38918i) q^{74} +(-2.46489 + 1.79085i) q^{75} +2.59251 q^{76} +(-0.605270 + 3.26093i) q^{77} +1.07569 q^{78} +(2.95044 - 2.14362i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(3.59251 - 11.0566i) q^{81} +(-6.68031 - 4.85353i) q^{82} +(2.15861 + 1.56832i) q^{83} +(-0.941506 + 2.89766i) q^{84} +(0.250523 + 0.771029i) q^{85} +(-7.68031 + 5.58007i) q^{86} -29.0901 q^{87} +(-1.42705 - 2.99391i) q^{88} +9.63799 q^{89} +(-5.08293 + 3.69296i) q^{90} +(0.109101 + 0.335777i) q^{91} +(-0.618034 + 1.90211i) q^{92} +(14.0701 + 10.2225i) q^{93} +(-6.96380 - 5.05950i) q^{94} +(-0.801129 + 2.46562i) q^{95} +(-0.941506 - 2.89766i) q^{96} +(7.92705 - 5.75934i) q^{97} -1.00000 q^{98} +(-15.1190 + 14.3398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9} + 8 q^{10} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} - 9 q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} - 4 q^{21} - 8 q^{22} - 16 q^{23} + q^{24} - 2 q^{25} + 7 q^{26} - 22 q^{27} + 2 q^{28} - q^{30} + 28 q^{31} - 8 q^{32} - q^{33} + 4 q^{34} - 2 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 13 q^{39} - 2 q^{40} + 8 q^{41} - q^{42} - 14 q^{43} - 7 q^{44} - 12 q^{45} - 4 q^{46} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} - 7 q^{52} + 10 q^{53} - 28 q^{54} + 7 q^{55} + 8 q^{56} - 17 q^{57} + 31 q^{59} + q^{60} + 28 q^{61} + 32 q^{62} - 7 q^{63} - 2 q^{64} + 2 q^{65} + 36 q^{66} - 26 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} + 34 q^{71} + 13 q^{72} - 24 q^{73} - 4 q^{74} - q^{75} + 6 q^{76} + 7 q^{77} - 2 q^{78} + 2 q^{80} + 14 q^{81} - 3 q^{82} - 21 q^{83} + q^{84} - 11 q^{85} - 11 q^{86} - 52 q^{87} + 2 q^{88} - 14 q^{89} - 13 q^{90} + 7 q^{91} + 4 q^{92} + 14 q^{93} + 5 q^{94} + 9 q^{95} + q^{96} + 50 q^{97} - 8 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9 + 8 * q^10 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 2 * q^14 + q^15 - 2 * q^16 - 9 * q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 - 4 * q^21 - 8 * q^22 - 16 * q^23 + q^24 - 2 * q^25 + 7 * q^26 - 22 * q^27 + 2 * q^28 - q^30 + 28 * q^31 - 8 * q^32 - q^33 + 4 * q^34 - 2 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 13 * q^39 - 2 * q^40 + 8 * q^41 - q^42 - 14 * q^43 - 7 * q^44 - 12 * q^45 - 4 * q^46 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 - 7 * q^52 + 10 * q^53 - 28 * q^54 + 7 * q^55 + 8 * q^56 - 17 * q^57 + 31 * q^59 + q^60 + 28 * q^61 + 32 * q^62 - 7 * q^63 - 2 * q^64 + 2 * q^65 + 36 * q^66 - 26 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 + 34 * q^71 + 13 * q^72 - 24 * q^73 - 4 * q^74 - q^75 + 6 * q^76 + 7 * q^77 - 2 * q^78 + 2 * q^80 + 14 * q^81 - 3 * q^82 - 21 * q^83 + q^84 - 11 * q^85 - 11 * q^86 - 52 * q^87 + 2 * q^88 - 14 * q^89 - 13 * q^90 + 7 * q^91 + 4 * q^92 + 14 * q^93 + 5 * q^94 + 9 * q^95 + q^96 + 50 * q^97 - 8 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more