LMFDB - Embedded newform 605.2.g.g.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.1
Root			$-0.762262 + 2.34600i$ of defining polynomial
Character	$\chi$	$=$	605.511
Dual form			605.2.g.g.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780121 - 2.40097i) q^{2} +(1.99563 + 1.44991i) q^{3} +(-3.53801 + 2.57052i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.92435 - 5.92254i) q^{6} +(1.69369 - 1.23053i) q^{7} +(4.84703 + 3.52157i) q^{8} +(0.953245 + 2.93379i) q^{9} +O(q^{10})$	\(q+(-0.780121 - 2.40097i) q^{2} +(1.99563 + 1.44991i) q^{3} +(-3.53801 + 2.57052i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.92435 - 5.92254i) q^{6} +(1.69369 - 1.23053i) q^{7} +(4.84703 + 3.52157i) q^{8} +(0.953245 + 2.93379i) q^{9} -2.52452 q^{10} -10.7876 q^{12} +(-0.398155 - 1.22539i) q^{13} +(-4.27575 - 3.10651i) q^{14} +(1.99563 - 1.44991i) q^{15} +(1.97110 - 6.06643i) q^{16} +(0.924349 - 2.84485i) q^{17} +(6.30027 - 4.57742i) q^{18} +(1.74044 + 1.26450i) q^{19} +(1.35140 + 4.15918i) q^{20} +5.16413 q^{21} +8.77882 q^{23} +(4.56691 + 14.0555i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-2.63152 + 1.91191i) q^{26} +(-0.0646137 + 0.198861i) q^{27} +(-2.82917 + 8.70729i) q^{28} +(-0.495628 + 0.360095i) q^{29} +(-5.03801 - 3.66033i) q^{30} +(-1.12637 - 3.46661i) q^{31} -4.12048 q^{32} -7.55150 q^{34} +(-0.646930 - 1.99105i) q^{35} +(-10.9139 - 7.92944i) q^{36} +(1.51349 - 1.09961i) q^{37} +(1.67828 - 5.16520i) q^{38} +(0.982141 - 3.02272i) q^{39} +(4.84703 - 3.52157i) q^{40} +(-4.13152 - 3.00173i) q^{41} +(-4.02864 - 12.3989i) q^{42} -5.17287 q^{43} +3.08477 q^{45} +(-6.84854 - 21.0776i) q^{46} +(5.91123 + 4.29476i) q^{47} +(12.7294 - 9.24842i) q^{48} +(-0.808764 + 2.48912i) q^{49} +(-0.780121 + 2.40097i) q^{50} +(5.96943 - 4.33705i) q^{51} +(4.55857 + 3.31200i) q^{52} +(-0.909192 - 2.79821i) q^{53} +0.527864 q^{54} +12.5428 q^{56} +(1.63986 + 5.04696i) q^{57} +(1.25122 + 0.909068i) q^{58} +(5.25393 - 3.81720i) q^{59} +(-3.33354 + 10.2596i) q^{60} +(0.155265 - 0.477858i) q^{61} +(-7.44450 + 5.40875i) q^{62} +(5.22462 + 3.79591i) q^{63} +(-0.727733 - 2.23973i) q^{64} -1.28846 q^{65} -7.80964 q^{67} +(4.04238 + 12.4412i) q^{68} +(17.5193 + 12.7285i) q^{69} +(-4.27575 + 3.10651i) q^{70} +(-3.49318 + 10.7509i) q^{71} +(-5.71114 + 17.5771i) q^{72} +(-8.99396 + 6.53449i) q^{73} +(-3.82083 - 2.77600i) q^{74} +(-0.762262 - 2.34600i) q^{75} -9.40812 q^{76} -8.02363 q^{78} +(-1.65604 - 5.09678i) q^{79} +(-5.16042 - 3.74926i) q^{80} +(7.06961 - 5.13637i) q^{81} +(-3.98395 + 12.2613i) q^{82} +(-3.35140 + 10.3145i) q^{83} +(-18.2707 + 13.2745i) q^{84} +(-2.41998 - 1.75822i) q^{85} +(4.03546 + 12.4199i) q^{86} -1.51119 q^{87} -4.32336 q^{89} +(-2.40649 - 7.40641i) q^{90} +(-2.18224 - 1.58549i) q^{91} +(-31.0596 + 22.5661i) q^{92} +(2.77845 - 8.55119i) q^{93} +(5.70010 - 17.5431i) q^{94} +(1.74044 - 1.26450i) q^{95} +(-8.22295 - 5.97432i) q^{96} +(-0.108667 - 0.334441i) q^{97} +6.60723 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9	$ 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9} - 6 q^{10} - 28 q^{12} + 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} + 4 q^{17} + 16 q^{18} + 11 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} + 10 q^{24} - 2 q^{25} + q^{26} - 5 q^{27} + 11 q^{28} + 11 q^{29} - 13 q^{30} - 9 q^{31} - 12 q^{32} - 20 q^{34} + 3 q^{35} - 29 q^{36} - q^{37} - 6 q^{38} + 6 q^{39} + 7 q^{40} - 11 q^{41} - 31 q^{42} - 42 q^{43} - 29 q^{46} - q^{47} + 21 q^{48} - q^{50} + 22 q^{51} + q^{52} + 8 q^{53} + 40 q^{54} + 30 q^{56} + 4 q^{58} + 26 q^{59} - 8 q^{60} + 2 q^{61} - 27 q^{62} + 4 q^{63} + 21 q^{64} - 14 q^{65} - 2 q^{67} + 20 q^{68} + 49 q^{69} - 14 q^{70} - 25 q^{71} - 21 q^{72} - 32 q^{73} + 12 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} + 23 q^{79} - 20 q^{80} + 20 q^{81} + 42 q^{82} - 10 q^{83} - 51 q^{84} - q^{85} + 34 q^{86} - 30 q^{87} - 14 q^{90} + 8 q^{91} - 99 q^{92} - 8 q^{93} + 22 q^{94} + 11 q^{95} - 3 q^{96} - 18 q^{97} + 84 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9 - 6 * q^10 - 28 * q^12 + 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 + 4 * q^17 + 16 * q^18 + 11 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 + 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 + 11 * q^28 + 11 * q^29 - 13 * q^30 - 9 * q^31 - 12 * q^32 - 20 * q^34 + 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 + 6 * q^39 + 7 * q^40 - 11 * q^41 - 31 * q^42 - 42 * q^43 - 29 * q^46 - q^47 + 21 * q^48 - q^50 + 22 * q^51 + q^52 + 8 * q^53 + 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 + 2 * q^61 - 27 * q^62 + 4 * q^63 + 21 * q^64 - 14 * q^65 - 2 * q^67 + 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 - 21 * q^72 - 32 * q^73 + 12 * q^74 + q^75 - 16 * q^76 + 12 * q^78 + 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 - 10 * q^83 - 51 * q^84 - q^85 + 34 * q^86 - 30 * q^87 - 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 + 22 * q^94 + 11 * q^95 - 3 * q^96 - 18 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.780121	−	2.40097i	−0.551629	−	1.69774i	−0.704684	−	0.709521i	$-0.748911\pi$
$2$	−0.780121	−	2.40097i	−0.551629	−	1.69774i	0.153055	−	0.988218i	$-0.451089\pi$
$3$	1.99563	+	1.44991i	1.15218	+	0.837105i	0.988769	−	0.149454i	$-0.0477514\pi$
$3$	1.99563	+	1.44991i	1.15218	+	0.837105i	0.163408	+	0.986559i	$0.447751\pi$
$4$	−3.53801	+	2.57052i	−1.76901	+	1.28526i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	1.92435	−	5.92254i	0.785612	−	2.41787i
$7$	1.69369	−	1.23053i	0.640153	−	0.465098i	−0.219750	−	0.975556i	$-0.570524\pi$
$7$	1.69369	−	1.23053i	0.640153	−	0.465098i	0.859903	+	0.510458i	$0.170524\pi$
$8$	4.84703	+	3.52157i	1.71368	+	1.24506i
$9$	0.953245	+	2.93379i	0.317748	+	0.977929i
$10$	−2.52452			−0.798325
$11$		0			0
$11$		0			0
$12$	−10.7876			−3.11410
$13$	−0.398155	−	1.22539i	−0.110428	−	0.339863i	0.880538	−	0.473976i	$-0.157182\pi$
$13$	−0.398155	−	1.22539i	−0.110428	−	0.339863i	−0.990966	+	0.134113i	$0.957182\pi$
$14$	−4.27575	−	3.10651i	−1.14274	−	0.830251i
$15$	1.99563	−	1.44991i	0.515269	−	0.374365i
$16$	1.97110	−	6.06643i	0.492776	−	1.51661i
$17$	0.924349	−	2.84485i	0.224188	−	0.689978i	−0.774186	−	0.632959i	$-0.781840\pi$
$17$	0.924349	−	2.84485i	0.224188	−	0.689978i	0.998373	−	0.0570196i	$-0.0181597\pi$
$18$	6.30027	−	4.57742i	1.48499	−	1.07891i
$19$	1.74044	+	1.26450i	0.399284	+	0.290097i	0.769249	−	0.638949i	$-0.220630\pi$
$19$	1.74044	+	1.26450i	0.399284	+	0.290097i	−0.369965	+	0.929046i	$0.620630\pi$
$20$	1.35140	+	4.15918i	0.302182	+	0.930021i
$21$	5.16413			1.12690
$22$		0			0
$23$	8.77882			1.83051			0.915255	−	0.402874i	$-0.131989\pi$
$23$	8.77882			1.83051			0.915255	+	0.402874i	$0.131989\pi$
$24$	4.56691	+	14.0555i	0.932216	+	2.86907i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−2.63152	+	1.91191i	−0.516084	+	0.374957i
$27$	−0.0646137	+	0.198861i	−0.0124349	+	0.0382708i
$28$	−2.82917	+	8.70729i	−0.534663	+	1.64552i
$29$	−0.495628	+	0.360095i	−0.0920358	+	0.0668679i	−0.632851	−	0.774273i	$-0.718116\pi$
$29$	−0.495628	+	0.360095i	−0.0920358	+	0.0668679i	0.540816	+	0.841141i	$0.318116\pi$
$30$	−5.03801	−	3.66033i	−0.919811	−	0.668282i
$31$	−1.12637	−	3.46661i	−0.202302	−	0.622621i	−0.999813	−	0.0193175i	$-0.993851\pi$
$31$	−1.12637	−	3.46661i	−0.202302	−	0.622621i	0.797512	−	0.603304i	$-0.206149\pi$
$32$	−4.12048			−0.728405
$33$		0			0
$34$	−7.55150			−1.29507
$35$	−0.646930	−	1.99105i	−0.109351	−	0.336548i
$36$	−10.9139	−	7.92944i	−1.81899	−	1.32157i
$37$	1.51349	−	1.09961i	0.248816	−	0.180775i	−0.456386	−	0.889782i	$-0.650856\pi$
$37$	1.51349	−	1.09961i	0.248816	−	0.180775i	0.705202	+	0.709007i	$0.250856\pi$
$38$	1.67828	−	5.16520i	0.272252	−	0.837906i
$39$	0.982141	−	3.02272i	0.157268	−	0.484023i
$40$	4.84703	−	3.52157i	0.766382	−	0.556809i
$41$	−4.13152	−	3.00173i	−0.645235	−	0.468791i	0.216410	−	0.976303i	$-0.430565\pi$
$41$	−4.13152	−	3.00173i	−0.645235	−	0.468791i	−0.861645	+	0.507512i	$0.830565\pi$
$42$	−4.02864	−	12.3989i	−0.621633	−	1.91319i
$43$	−5.17287			−0.788856			−0.394428	−	0.918927i	$-0.629057\pi$
$43$	−5.17287			−0.788856			−0.394428	+	0.918927i	$0.629057\pi$
$44$		0			0
$45$	3.08477			0.459850
$46$	−6.84854	−	21.0776i	−1.00976	−	3.10773i
$47$	5.91123	+	4.29476i	0.862242	+	0.626455i	0.928494	−	0.371347i	$-0.121104\pi$
$47$	5.91123	+	4.29476i	0.862242	+	0.626455i	−0.0662520	+	0.997803i	$0.521104\pi$
$48$	12.7294	−	9.24842i	1.83733	−	1.33490i
$49$	−0.808764	+	2.48912i	−0.115538	+	0.355589i
$50$	−0.780121	+	2.40097i	−0.110326	+	0.339548i
$51$	5.96943	−	4.33705i	0.835888	−	0.607308i
$52$	4.55857	+	3.31200i	0.632160	+	0.459291i
$53$	−0.909192	−	2.79821i	−0.124887	−	0.384363i	0.868993	−	0.494824i	$-0.164767\pi$
$53$	−0.909192	−	2.79821i	−0.124887	−	0.384363i	−0.993880	+	0.110461i	$0.964767\pi$
$54$	0.527864			0.0718332
$55$		0			0
$56$	12.5428			1.67610
$57$	1.63986	+	5.04696i	0.217204	+	0.668486i
$58$	1.25122	+	0.909068i	0.164294	+	0.119366i
$59$	5.25393	−	3.81720i	0.684003	−	0.496957i	−0.190680	−	0.981652i	$-0.561069\pi$
$59$	5.25393	−	3.81720i	0.684003	−	0.496957i	0.874683	+	0.484695i	$0.161069\pi$
$60$	−3.33354	+	10.2596i	−0.430358	+	1.32451i
$61$	0.155265	−	0.477858i	0.0198797	−	0.0611834i	−0.940625	−	0.339449i	$-0.889759\pi$
$61$	0.155265	−	0.477858i	0.0198797	−	0.0611834i	0.960504	+	0.278265i	$0.0897595\pi$
$62$	−7.44450	+	5.40875i	−0.945453	+	0.686911i
$63$	5.22462	+	3.79591i	0.658240	+	0.478240i
$64$	−0.727733	−	2.23973i	−0.0909666	−	0.279966i
$65$	−1.28846			−0.159813
$66$		0			0
$67$	−7.80964			−0.954099			−0.477050	−	0.878876i	$-0.658294\pi$
$67$	−7.80964			−0.954099			−0.477050	+	0.878876i	$0.658294\pi$
$68$	4.04238	+	12.4412i	0.490211	+	1.50871i
$69$	17.5193	+	12.7285i	2.10907	+	1.53233i
$70$	−4.27575	+	3.10651i	−0.511050	+	0.371299i
$71$	−3.49318	+	10.7509i	−0.414564	+	1.27590i	0.498076	+	0.867133i	$0.334040\pi$
$71$	−3.49318	+	10.7509i	−0.414564	+	1.27590i	−0.912640	+	0.408764i	$0.865960\pi$
$72$	−5.71114	+	17.5771i	−0.673064	+	2.07148i
$73$	−8.99396	+	6.53449i	−1.05266	+	0.764805i	−0.972717	−	0.231995i	$-0.925475\pi$
$73$	−8.99396	+	6.53449i	−1.05266	+	0.764805i	−0.0799461	+	0.996799i	$0.525475\pi$
$74$	−3.82083	−	2.77600i	−0.444163	−	0.322703i
$75$	−0.762262	−	2.34600i	−0.0880184	−	0.270893i
$76$	−9.40812			−1.07919
$77$		0			0
$78$	−8.02363			−0.908498
$79$	−1.65604	−	5.09678i	−0.186320	−	0.573433i	0.813649	−	0.581356i	$-0.197478\pi$
$79$	−1.65604	−	5.09678i	−0.186320	−	0.573433i	−0.999969	+	0.00792366i	$0.997478\pi$
$80$	−5.16042	−	3.74926i	−0.576952	−	0.419180i
$81$	7.06961	−	5.13637i	0.785512	−	0.570708i
$82$	−3.98395	+	12.2613i	−0.439954	+	1.35404i
$83$	−3.35140	+	10.3145i	−0.367864	+	1.13217i	0.580304	+	0.814400i	$0.302934\pi$
$83$	−3.35140	+	10.3145i	−0.367864	+	1.13217i	−0.948168	+	0.317769i	$0.897066\pi$
$84$	−18.2707	+	13.2745i	−1.99350	+	1.44836i
$85$	−2.41998	−	1.75822i	−0.262483	−	0.190705i
$86$	4.03546	+	12.4199i	0.435155	+	1.33927i
$87$	−1.51119			−0.162017
$88$		0			0
$89$	−4.32336			−0.458275			−0.229137	−	0.973394i	$-0.573591\pi$
$89$	−4.32336			−0.458275			−0.229137	+	0.973394i	$0.573591\pi$
$90$	−2.40649	−	7.40641i	−0.253666	−	0.780705i
$91$	−2.18224	−	1.58549i	−0.228761	−	0.166204i
$92$	−31.0596	+	22.5661i	−3.23818	+	2.35268i
$93$	2.77845	−	8.55119i	0.288112	−	0.886717i
$94$	5.70010	−	17.5431i	0.587920	−	1.80943i
$95$	1.74044	−	1.26450i	0.178565	−	0.129735i
$96$	−8.22295	−	5.97432i	−0.839252	−	0.609752i
$97$	−0.108667	−	0.334441i	−0.0110334	−	0.0339574i	0.945388	−	0.325946i	$-0.105683\pi$
$97$	−0.108667	−	0.334441i	−0.0110334	−	0.0339574i	−0.956422	+	0.291989i	$0.905683\pi$
$98$	6.60723			0.667431
$99$		0			0
$100$	4.37322			0.437322
$101$	4.85140	+	14.9311i	0.482732	+	1.48570i	0.835238	+	0.549888i	$0.185330\pi$
$101$	4.85140	+	14.9311i	0.482732	+	1.48570i	−0.352506	+	0.935809i	$0.614670\pi$
$102$	−15.0700	−	10.9490i	−1.49215	−	1.08411i
$103$	−5.40416	+	3.92635i	−0.532488	+	0.386875i	−0.821287	−	0.570515i	$-0.806744\pi$
$103$	−5.40416	+	3.92635i	−0.532488	+	0.386875i	0.288800	+	0.957389i	$0.406744\pi$
$104$	2.38545	−	7.34165i	0.233912	−	0.719908i
$105$	1.59580	−	4.91138i	0.155734	−	0.479301i
$106$	−6.00911	+	4.36588i	−0.583657	+	0.424051i
$107$	12.6271	+	9.17413i	1.22071	+	0.886897i	0.996159	−	0.0875657i	$-0.0279088\pi$
$107$	12.6271	+	9.17413i	1.22071	+	0.886897i	0.224550	+	0.974463i	$0.427909\pi$
$108$	−0.282570	−	0.869662i	−0.0271903	−	0.0836832i
$109$	−11.5070			−1.10217			−0.551087	−	0.834448i	$-0.685787\pi$
$109$	−11.5070			−1.10217			−0.551087	+	0.834448i	$0.685787\pi$
$110$		0			0
$111$	4.61469			0.438007
$112$	−4.12653	−	12.7001i	−0.389920	−	1.20005i
$113$	−7.32017	−	5.31842i	−0.688624	−	0.500315i	0.187584	−	0.982249i	$-0.439934\pi$
$113$	−7.32017	−	5.31842i	−0.688624	−	0.500315i	−0.876207	+	0.481934i	$0.839934\pi$
$114$	10.8383	−	7.87447i	1.01510	−	0.737512i
$115$	2.71281	−	8.34916i	0.252970	−	0.778563i
$116$	0.827908	−	2.54804i	0.0768693	−	0.236579i
$117$	3.21551	−	2.33620i	0.297274	−	0.215982i
$118$	−13.2637	−	9.63662i	−1.22102	−	0.887122i
$119$	−1.93513	−	5.95573i	−0.177393	−	0.545961i
$120$	14.7788			1.34912
$121$		0			0
$122$	−1.26845			−0.114840
$123$	−3.89275	−	11.9807i	−0.350998	−	1.08026i
$124$	12.8961	+	9.36955i	1.15810	+	0.841410i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	5.03801	−	15.5054i	0.448822	−	1.38133i
$127$	−5.82005	+	17.9123i	−0.516446	+	1.58946i	0.264189	+	0.964471i	$0.414896\pi$
$127$	−5.82005	+	17.9123i	−0.516446	+	1.58946i	−0.780635	+	0.624987i	$0.785104\pi$
$128$	−11.4769	+	8.33844i	−1.01442	+	0.737021i
$129$	−10.3231	−	7.50019i	−0.908901	−	0.660355i
$130$	1.00515	+	3.09354i	0.0881576	+	0.271321i
$131$	20.0997			1.75612			0.878058	−	0.478555i	$-0.158839\pi$
$131$	20.0997			1.75612			0.878058	+	0.478555i	$0.158839\pi$
$132$		0			0
$133$	4.50377			0.390527
$134$	6.09246	+	18.7507i	0.526309	+	1.61981i
$135$	0.169161	+	0.122903i	0.0145591	+	0.0105778i
$136$	14.4987	−	10.5339i	1.24325	−	0.903276i
$137$	−5.55342	+	17.0917i	−0.474461	+	1.46024i	0.372223	+	0.928143i	$0.378596\pi$
$137$	−5.55342	+	17.0917i	−0.474461	+	1.46024i	−0.846684	+	0.532097i	$0.821404\pi$
$138$	16.8935	−	51.9929i	1.43807	−	4.42593i
$139$	13.6425	−	9.91187i	1.15714	−	0.840714i	0.167729	−	0.985833i	$-0.446357\pi$
$139$	13.6425	−	9.91187i	1.15714	−	0.840714i	0.989414	+	0.145119i	$0.0463566\pi$
$140$	7.40686	+	5.38140i	0.625994	+	0.454811i
$141$	5.56961	+	17.1415i	0.469046	+	1.44357i
$142$	28.5376			2.39482
$143$		0			0
$144$	19.6766			1.63971
$145$	0.189313	+	0.582646i	0.0157216	+	0.0483861i
$146$	22.7055	+	16.4965i	1.87912	+	1.36526i
$147$	−5.22299	+	3.79472i	−0.430785	+	0.312984i
$148$	−2.52816	+	7.78088i	−0.207814	+	0.639585i
$149$	−0.721140	+	2.21944i	−0.0590781	+	0.181824i	−0.976240	−	0.216690i	$-0.930474\pi$
$149$	−0.721140	+	2.21944i	−0.0590781	+	0.181824i	0.917162	+	0.398514i	$0.130474\pi$
$150$	−5.03801	+	3.66033i	−0.411352	+	0.298865i
$151$	−3.18661	−	2.31521i	−0.259323	−	0.188409i	0.450526	−	0.892763i	$-0.351237\pi$
$151$	−3.18661	−	2.31521i	−0.259323	−	0.188409i	−0.709848	+	0.704354i	$0.751237\pi$
$152$	3.98292	+	12.2582i	0.323058	+	0.994269i
$153$	9.22732			0.745985
$154$		0			0
$155$	−3.64501			−0.292774
$156$	4.29512	+	13.2190i	0.343885	+	1.05837i
$157$	3.94887	+	2.86902i	0.315154	+	0.228973i	0.734105	−	0.679036i	$-0.237602\pi$
$157$	3.94887	+	2.86902i	0.315154	+	0.228973i	−0.418951	+	0.908009i	$0.637602\pi$
$158$	−10.9453	+	7.95221i	−0.870760	+	0.632644i
$159$	2.24273	−	6.90242i	0.177860	−	0.547398i
$160$	−1.27330	+	3.91881i	−0.100663	+	0.309809i
$161$	14.8686	−	10.8026i	1.17181	−	0.851367i
$162$	−17.8474	−	12.9669i	−1.40222	−	1.01878i
$163$	−2.17416	−	6.69137i	−0.170293	−	0.524108i	0.829094	−	0.559109i	$-0.188857\pi$
$163$	−2.17416	−	6.69137i	−0.170293	−	0.524108i	−0.999387	+	0.0350007i	$0.988857\pi$
$164$	22.3333			1.74394
$165$		0			0
$166$	27.3794			2.12505
$167$	−3.31250	−	10.1948i	−0.256329	−	0.788899i	−0.993565	−	0.113264i	$-0.963869\pi$
$167$	−3.31250	−	10.1948i	−0.256329	−	0.788899i	0.737236	−	0.675635i	$-0.236131\pi$
$168$	25.0307	+	18.1858i	1.93116	+	1.40307i
$169$	9.17416	−	6.66541i	0.705704	−	0.512724i
$170$	−2.33354	+	7.18190i	−0.178974	+	0.550827i
$171$	−2.05072	+	6.31146i	−0.156822	+	0.482650i
$172$	18.3017	−	13.2969i	1.39549	−	1.01388i
$173$	6.80531	+	4.94434i	0.517398	+	0.375912i	0.815623	−	0.578584i	$-0.196395\pi$
$173$	6.80531	+	4.94434i	0.517398	+	0.375912i	−0.298225	+	0.954496i	$0.596395\pi$
$174$	1.17891	+	3.62832i	0.0893732	+	0.275062i
$175$	−2.09351			−0.158254
$176$		0			0
$177$	16.0195			1.20410
$178$	3.37274	+	10.3802i	0.252798	+	0.778031i
$179$	−17.0189	−	12.3649i	−1.27205	−	0.924198i	−0.272767	−	0.962080i	$-0.587939\pi$
$179$	−17.0189	−	12.3649i	−1.27205	−	0.924198i	−0.999282	+	0.0378827i	$0.987939\pi$
$180$	−10.9139	+	7.92944i	−0.813477	+	0.591025i
$181$	−0.538649	+	1.65779i	−0.0400374	+	0.123223i	−0.969077	−	0.246757i	$-0.920635\pi$
$181$	−0.538649	+	1.65779i	−0.0400374	+	0.123223i	0.929040	+	0.369979i	$0.120635\pi$
$182$	−2.10429	+	6.47635i	−0.155981	+	0.480059i
$183$	1.00270	−	0.728506i	0.0741219	−	0.0538527i
$184$	42.5512	+	30.9153i	3.13692	+	2.27910i
$185$	−0.578100	−	1.77921i	−0.0425028	−	0.130810i
$186$	−22.6986			−1.66435
$187$		0			0
$188$	−31.9538			−2.33047
$189$	0.135270	+	0.416317i	0.00983941	+	0.0302826i
$190$	−4.39378	−	3.19227i	−0.318759	−	0.231592i
$191$	−0.0201903	+	0.0146691i	−0.00146092	+	0.00106142i	−0.588515	−	0.808486i	$-0.700287\pi$
$191$	−0.0201903	+	0.0146691i	−0.00146092	+	0.00106142i	0.587055	+	0.809547i	$0.300287\pi$
$192$	1.79512	−	5.52482i	0.129552	−	0.398719i
$193$	−0.450314	+	1.38592i	−0.0324143	+	0.0997610i	−0.965955	−	0.258711i	$-0.916702\pi$
$193$	−0.450314	+	1.38592i	−0.0324143	+	0.0997610i	0.933540	+	0.358472i	$0.116702\pi$
$194$	−0.718209	+	0.521810i	−0.0515644	+	0.0374637i
$195$	−2.57128	−	1.86814i	−0.184133	−	0.133781i
$196$	−3.53691	−	10.8855i	−0.252636	−	0.777534i
$197$	−22.7027			−1.61750			−0.808751	−	0.588151i	$-0.799856\pi$
$197$	−22.7027			−1.61750			−0.808751	+	0.588151i	$0.799856\pi$
$198$		0			0
$199$	−6.62834			−0.469870			−0.234935	−	0.972011i	$-0.575488\pi$
$199$	−6.62834			−0.469870			−0.234935	+	0.972011i	$0.575488\pi$
$200$	−1.85140	−	5.69802i	−0.130914	−	0.402911i
$201$	−15.5851	−	11.3233i	−1.09929	−	0.798681i
$202$	32.0643	−	23.2961i	2.25604	−	1.63911i
$203$	−0.396329	+	1.21977i	−0.0278168	+	0.0856114i
$204$	−9.97147	+	30.6890i	−0.698143	+	2.14866i
$205$	−4.13152	+	3.00173i	−0.288558	+	0.209650i
$206$	13.6429	+	9.91217i	0.950548	+	0.690613i
$207$	8.36837	+	25.7552i	0.581642	+	1.79011i
$208$	−8.21858			−0.569856
$209$		0			0
$210$	−13.0370			−0.899636
$211$	−1.74829	−	5.38069i	−0.120357	−	0.370422i	0.872669	−	0.488312i	$-0.162387\pi$
$211$	−1.74829	−	5.38069i	−0.120357	−	0.370422i	−0.993027	+	0.117890i	$0.962387\pi$
$212$	10.4096	+	7.56299i	0.714932	+	0.519428i
$213$	−22.5589	+	16.3900i	−1.54571	+	1.12302i
$214$	12.1761	−	37.4742i	0.832341	−	2.56168i
$215$	−1.59851	+	4.91969i	−0.109017	+	0.335520i
$216$	−1.01349	+	0.736341i	−0.0689590	+	0.0501017i
$217$	−6.17349	−	4.48531i	−0.419084	−	0.304482i
$218$	8.97688	+	27.6280i	0.607991	+	1.87120i
$219$	−27.4230			−1.85308
$220$		0			0
$221$	−3.85410			−0.259255
$222$	−3.60002	−	11.0797i	−0.241617	−	0.743622i
$223$	−6.37863	−	4.63434i	−0.427144	−	0.310339i	0.353362	−	0.935487i	$-0.385039\pi$
$223$	−6.37863	−	4.63434i	−0.427144	−	0.310339i	−0.780506	+	0.625148i	$0.785039\pi$
$224$	−6.97880	+	5.07040i	−0.466291	+	0.338780i
$225$	0.953245	−	2.93379i	0.0635497	−	0.195586i
$226$	−7.05871	+	21.7245i	−0.469539	+	1.44509i
$227$	−9.07021	+	6.58989i	−0.602011	+	0.437387i	−0.846592	−	0.532242i	$-0.821350\pi$
$227$	−9.07021	+	6.58989i	−0.602011	+	0.437387i	0.244581	+	0.969629i	$0.421350\pi$
$228$	−18.7751	−	13.6409i	−1.24341	−	0.903392i
$229$	8.34059	+	25.6697i	0.551162	+	1.69630i	0.705870	+	0.708341i	$0.250556\pi$
$229$	8.34059	+	25.6697i	0.551162	+	1.69630i	−0.154708	+	0.987960i	$0.549444\pi$
$230$	−22.1623			−1.46134
$231$		0			0
$232$	−3.67042			−0.240975
$233$	3.35307	+	10.3197i	0.219667	+	0.676065i	0.998789	+	0.0491934i	$0.0156651\pi$
$233$	3.35307	+	10.3197i	0.219667	+	0.676065i	−0.779122	+	0.626872i	$0.784335\pi$
$234$	−8.11763	−	5.89780i	−0.530666	−	0.385551i
$235$	5.91123	−	4.29476i	0.385606	−	0.280159i
$236$	−8.77628	+	27.0106i	−0.571287	+	1.75824i
$237$	4.08502	−	12.5724i	0.265350	−	0.816665i
$238$	−12.7899	+	9.29238i	−0.829043	+	0.602335i
$239$	−9.27641	−	6.73971i	−0.600041	−	0.435955i	0.245852	−	0.969307i	$-0.420932\pi$
$239$	−9.27641	−	6.73971i	−0.600041	−	0.435955i	−0.845893	+	0.533352i	$0.820932\pi$
$240$	−4.86218	−	14.9643i	−0.313853	−	0.965939i
$241$	−12.7542			−0.821572			−0.410786	−	0.911732i	$-0.634746\pi$
$241$	−12.7542			−0.821572			−0.410786	+	0.911732i	$0.634746\pi$
$242$		0			0
$243$	22.1829			1.42303
$244$	0.679010	+	2.08978i	0.0434692	+	0.133784i
$245$	2.11737	+	1.53836i	0.135274	+	0.0982823i
$246$	−25.7283	+	18.6927i	−1.64038	+	1.19180i
$247$	0.856551	−	2.63619i	0.0545011	−	0.167737i
$248$	6.74837	−	20.7693i	0.428522	−	1.31885i
$249$	−21.6433	+	15.7248i	−1.37159	+	0.996517i
$250$	2.04238	+	1.48388i	0.129172	+	0.0938487i
$251$	−3.77050	−	11.6044i	−0.237992	−	0.732464i	−0.996710	−	0.0810452i	$-0.974174\pi$
$251$	−3.77050	−	11.6044i	−0.237992	−	0.732464i	0.758719	−	0.651419i	$-0.225826\pi$
$252$	−28.2422			−1.77909
$253$		0			0
$254$	47.5471			2.98337
$255$	−2.28012	−	7.01749i	−0.142787	−	0.439452i
$256$	25.1632	+	18.2821i	1.57270	+	1.14263i
$257$	4.77000	−	3.46561i	0.297544	−	0.216179i	−0.428989	−	0.903310i	$-0.641130\pi$
$257$	4.77000	−	3.46561i	0.297544	−	0.216179i	0.726534	+	0.687131i	$0.241130\pi$
$258$	−9.95441	+	30.6365i	−0.619734	+	1.90735i
$259$	1.21026	−	3.72479i	0.0752018	−	0.231447i
$260$	4.55857	−	3.31200i	0.282711	−	0.205401i
$261$	−1.52890	−	1.11081i	−0.0946363	−	0.0687573i
$262$	−15.6802	−	48.2586i	−0.968724	−	2.98142i
$263$	21.7305			1.33996			0.669980	−	0.742379i	$-0.266302\pi$
$263$	21.7305			1.33996			0.669980	+	0.742379i	$0.266302\pi$
$264$		0			0
$265$	−2.94221			−0.180738
$266$	−3.51349	−	10.8134i	−0.215426	−	0.663012i
$267$	−8.62781	−	6.26847i	−0.528013	−	0.383624i
$268$	27.6306	−	20.0748i	1.68781	−	1.22626i
$269$	−1.39815	+	4.30308i	−0.0852470	+	0.262363i	−0.984589	−	0.174882i	$-0.944046\pi$
$269$	−1.39815	+	4.30308i	−0.0852470	+	0.262363i	0.899342	+	0.437245i	$0.144046\pi$
$270$	0.163119	−	0.502029i	0.00992710	−	0.0305525i
$271$	−17.6049	+	12.7907i	−1.06942	+	0.776979i	−0.975808	−	0.218629i	$-0.929841\pi$
$271$	−17.6049	+	12.7907i	−1.06942	+	0.776979i	−0.0936123	+	0.995609i	$0.529841\pi$
$272$	−15.4361	−	11.2150i	−0.935953	−	0.680009i
$273$	−2.05612	−	6.32809i	−0.124442	−	0.382994i
$274$	45.3688			2.74083
$275$		0			0
$276$	−94.7021			−5.70040
$277$	4.02791	+	12.3966i	0.242014	+	0.744841i	0.996113	+	0.0880813i	$0.0280735\pi$
$277$	4.02791	+	12.3966i	0.242014	+	0.744841i	−0.754100	+	0.656760i	$0.771926\pi$
$278$	−34.4409	−	25.0228i	−2.06563	−	1.50077i
$279$	9.09658	−	6.60905i	0.544598	−	0.395674i
$280$	3.87592	−	11.9289i	0.231631	−	0.712886i
$281$	−2.90031	+	8.92623i	−0.173018	+	0.532494i	−0.999537	−	0.0304140i	$-0.990317\pi$
$281$	−2.90031	+	8.92623i	−0.173018	+	0.532494i	0.826520	+	0.562908i	$0.190317\pi$
$282$	36.8112	−	26.7449i	2.19207	−	1.59263i
$283$	11.2774	+	8.19354i	0.670374	+	0.487055i	0.870150	−	0.492786i	$-0.164021\pi$
$283$	11.2774	+	8.19354i	0.670374	+	0.487055i	−0.199776	+	0.979842i	$0.564021\pi$
$284$	−15.2764	−	47.0161i	−0.906490	−	2.78989i
$285$	5.30669			0.314341
$286$		0			0
$287$	−10.6912			−0.631083
$288$	−3.92783	−	12.0886i	−0.231450	−	0.712329i
$289$	6.51452	+	4.73307i	0.383207	+	0.278416i
$290$	1.25122	−	0.909068i	0.0734744	−	0.0533823i
$291$	0.268051	−	0.824977i	0.0157135	−	0.0483610i
$292$	15.0237	−	46.2382i	0.879196	−	2.70589i
$293$	24.6508	−	17.9098i	1.44011	−	1.04630i	0.452095	−	0.891970i	$-0.350677\pi$
$293$	24.6508	−	17.9098i	1.44011	−	1.04630i	0.988019	−	0.154335i	$-0.0493234\pi$
$294$	13.1856	+	9.57987i	0.768998	+	0.558710i
$295$	−2.00682	−	6.17636i	−0.116842	−	0.359602i
$296$	11.2083			0.651468
$297$		0			0
$298$	5.89138			0.341278
$299$	−3.49533	−	10.7575i	−0.202140	−	0.622123i
$300$	8.72732	+	6.34077i	0.503872	+	0.366085i
$301$	−8.76122	+	6.36540i	−0.504988	+	0.366895i
$302$	−3.07279	+	9.45708i	−0.176819	+	0.544194i
$303$	−11.9671	+	36.8310i	−0.687492	+	2.11588i
$304$	11.1016	−	8.06580i	0.636721	−	0.462605i
$305$	−0.406490	−	0.295332i	−0.0232756	−	0.0169107i
$306$	−7.19843	−	22.1545i	−0.411507	−	1.26649i
$307$	−5.08609			−0.290278			−0.145139	−	0.989411i	$-0.546363\pi$
$307$	−5.08609			−0.290278			−0.145139	+	0.989411i	$0.546363\pi$
$308$		0			0
$309$	−16.4775			−0.937375
$310$	2.84355	+	8.75154i	0.161503	+	0.497054i
$311$	−11.1332	−	8.08871i	−0.631303	−	0.458669i	0.225548	−	0.974232i	$-0.427583\pi$
$311$	−11.1332	−	8.08871i	−0.631303	−	0.458669i	−0.856851	+	0.515563i	$0.827583\pi$
$312$	15.4052	−	11.1925i	0.872147	−	0.633652i
$313$	4.92966	−	15.1719i	0.278641	−	0.857568i	−0.709592	−	0.704612i	$-0.751121\pi$
$313$	4.92966	−	15.1719i	0.278641	−	0.857568i	0.988233	−	0.152955i	$-0.0488791\pi$
$314$	3.80783	−	11.7193i	0.214888	−	0.661358i
$315$	5.22462	−	3.79591i	0.294374	−	0.213875i
$316$	18.9605	+	13.7756i	1.06661	+	0.774937i
$317$	3.30876	+	10.1833i	0.185839	+	0.571953i	0.999962	−	0.00873957i	$-0.00278193\pi$
$317$	3.30876	+	10.1833i	0.185839	+	0.571953i	−0.814123	+	0.580692i	$0.802782\pi$
$318$	−18.3221			−1.02745
$319$		0			0
$320$	−2.35499			−0.131648
$321$	11.8974	+	36.6163i	0.664046	+	2.04372i
$322$	−37.5360	−	27.2715i	−2.09180	−	1.51978i
$323$	5.20610	−	3.78245i	0.289675	−	0.210461i
$324$	−11.8092	+	36.3451i	−0.656068	+	2.01917i
$325$	−0.398155	+	1.22539i	−0.0220857	+	0.0679727i
$326$	−14.3696	+	10.4401i	−0.795860	+	0.578226i
$327$	−22.9638	−	16.6842i	−1.26990	−	0.922636i
$328$	−9.45480	−	29.0989i	−0.522054	−	1.60672i
$329$	15.2966			0.843330
$330$		0			0
$331$	−8.84618			−0.486230			−0.243115	−	0.969997i	$-0.578169\pi$
$331$	−8.84618			−0.486230			−0.243115	+	0.969997i	$0.578169\pi$
$332$	−14.6564	−	45.1078i	−0.804375	−	2.47561i
$333$	4.66875	+	3.39205i	0.255846	+	0.185883i
$334$	−21.8933	+	15.9064i	−1.19795	+	0.870359i
$335$	−2.41331	+	7.42741i	−0.131853	+	0.405803i
$336$	10.1790	−	31.3278i	0.555312	−	1.70907i
$337$	−9.37629	+	6.81228i	−0.510759	+	0.371088i	−0.813112	−	0.582108i	$-0.802228\pi$
$337$	−9.37629	+	6.81228i	−0.510759	+	0.371088i	0.302352	+	0.953196i	$0.402228\pi$
$338$	−23.1604	−	16.8270i	−1.25976	−	0.915268i
$339$	−6.89712	−	21.2272i	−0.374600	−	1.15290i
$340$	13.0814			0.709440
$341$		0			0
$342$	16.7534			0.905920
$343$	6.22167	+	19.1483i	0.335938	+	1.03391i
$344$	−25.0731	−	18.2166i	−1.35185	−	0.982175i
$345$	17.5193	−	12.7285i	0.943205	−	0.685279i
$346$	6.56224	−	20.1965i	0.352788	−	1.08577i
$347$	1.51078	−	4.64972i	0.0811032	−	0.249610i	−0.902280	−	0.431150i	$-0.858108\pi$
$347$	1.51078	−	4.64972i	0.0811032	−	0.249610i	0.983384	+	0.181540i	$0.0581081\pi$
$348$	5.34662	−	3.88455i	0.286609	−	0.208234i
$349$	0.771415	+	0.560466i	0.0412929	+	0.0300010i	0.608240	−	0.793753i	$-0.291876\pi$
$349$	0.771415	+	0.560466i	0.0412929	+	0.0300010i	−0.566947	+	0.823754i	$0.691876\pi$
$350$	1.63319	+	5.02644i	0.0872977	+	0.268675i
$351$	0.269409			0.0143800
$352$		0			0
$353$	−15.5166			−0.825865			−0.412933	−	0.910762i	$-0.635495\pi$
$353$	−15.5166			−0.825865			−0.412933	+	0.910762i	$0.635495\pi$
$354$	−12.4971	−	38.4622i	−0.664215	−	2.04424i
$355$	9.14526	+	6.64442i	0.485380	+	0.352649i
$356$	15.2961	−	11.1133i	0.810691	−	0.589001i
$357$	4.77346	−	14.6912i	0.252638	−	0.777540i
$358$	−16.4110	+	50.5078i	−0.867347	+	2.66942i
$359$	16.3867	−	11.9056i	0.864855	−	0.628354i	−0.0643461	−	0.997928i	$-0.520496\pi$
$359$	16.3867	−	11.9056i	0.864855	−	0.628354i	0.929202	+	0.369573i	$0.120496\pi$
$360$	14.9519	+	10.8632i	0.788037	+	0.572542i
$361$	−4.44116	−	13.6685i	−0.233745	−	0.719394i
$362$	4.40051			0.231286
$363$		0			0
$364$	11.7963			0.618295
$365$	3.43539	+	10.5730i	0.179816	+	0.553418i
$366$	−2.53135	−	1.83913i	−0.132316	−	0.0961329i
$367$	−28.8455	+	20.9575i	−1.50572	+	1.09397i	−0.537692	+	0.843142i	$0.680704\pi$
$367$	−28.8455	+	20.9575i	−1.50572	+	1.09397i	−0.968031	+	0.250830i	$0.919296\pi$
$368$	17.3040	−	53.2561i	0.902032	−	2.77617i
$369$	4.86807	−	14.9824i	0.253422	−	0.779952i
$370$	−3.82083	+	2.77600i	−0.198636	+	0.144317i
$371$	−4.98317	−	3.62049i	−0.258713	−	0.187966i
$372$	12.1508	+	37.3963i	0.629989	+	1.93891i
$373$	−12.1358			−0.628370			−0.314185	−	0.949362i	$-0.601731\pi$
$373$	−12.1358			−0.628370			−0.314185	+	0.949362i	$0.601731\pi$
$374$		0			0
$375$	−2.46673			−0.127381
$376$	13.5276	+	41.6337i	0.697633	+	2.14709i
$377$	0.638595	+	0.463966i	0.0328893	+	0.0238955i
$378$	0.894035	−	0.649555i	0.0459842	−	0.0334095i
$379$	2.20765	−	6.79446i	0.113400	−	0.349008i	−0.878210	−	0.478275i	$-0.841262\pi$
$379$	2.20765	−	6.79446i	0.113400	−	0.349008i	0.991610	+	0.129267i	$0.0412623\pi$
$380$	−2.90727	+	8.94766i	−0.149140	+	0.459005i
$381$	−37.5858	+	27.3077i	−1.92558	+	1.39902i
$382$	0.0509708	+	0.0370325i	0.00260789	+	0.00189475i
$383$	4.93283	+	15.1817i	0.252056	+	0.775747i	0.994396	+	0.105724i	$0.0337160\pi$
$383$	4.93283	+	15.1817i	0.252056	+	0.775747i	−0.742340	+	0.670023i	$0.766284\pi$
$384$	−34.9936			−1.78576
$385$		0			0
$386$	3.67885			0.187249
$387$	−4.93101	−	15.1761i	−0.250658	−	0.771445i
$388$	1.24415	+	0.903928i	0.0631622	+	0.0458900i
$389$	20.2986	−	14.7478i	1.02918	−	0.747742i	0.0610341	−	0.998136i	$-0.480560\pi$
$389$	20.2986	−	14.7478i	1.02918	−	0.747742i	0.968144	+	0.250394i	$0.0805602\pi$
$390$	−2.47944	+	7.63093i	−0.125551	+	0.386407i
$391$	8.11469	−	24.9745i	0.410378	−	1.26301i
$392$	−12.6857	+	9.21672i	−0.640726	+	0.465514i
$393$	40.1114	+	29.1427i	2.02335	+	1.47005i
$394$	17.7109	+	54.5084i	0.892261	+	2.74610i
$395$	−5.35907			−0.269644
$396$		0			0
$397$	3.57490			0.179419			0.0897094	−	0.995968i	$-0.471406\pi$
$397$	3.57490			0.179419			0.0897094	+	0.995968i	$0.471406\pi$
$398$	5.17090	+	15.9144i	0.259194	+	0.797717i
$399$	8.98785	+	6.53006i	0.449956	+	0.326912i
$400$	−5.16042	+	3.74926i	−0.258021	+	0.187463i
$401$	8.92560	−	27.4702i	0.445723	−	1.37179i	−0.435966	−	0.899963i	$-0.643593\pi$
$401$	8.92560	−	27.4702i	0.445723	−	1.37179i	0.881689	−	0.471831i	$-0.156407\pi$
$402$	−15.0285	+	46.2529i	−0.749552	+	2.30688i
$403$	−3.79949	+	2.76049i	−0.189266	+	0.137510i
$404$	−55.5449	−	40.3557i	−2.76346	−	2.00777i
$405$	−2.70035	−	8.31082i	−0.134181	−	0.412968i
$406$	3.23782			0.160690
$407$		0			0
$408$	44.2072			2.18858
$409$	−2.97245	−	9.14826i	−0.146978	−	0.452352i	0.850282	−	0.526327i	$-0.176431\pi$
$409$	−2.97245	−	9.14826i	−0.146978	−	0.452352i	−0.997260	+	0.0739753i	$0.976431\pi$
$410$	10.4301	+	7.57793i	0.515107	+	0.374247i
$411$	−35.8639	+	26.0567i	−1.76904	+	1.28528i
$412$	9.02723	−	27.7829i	0.444740	−	1.36877i
$413$	4.20130	−	12.9303i	0.206732	−	0.636257i
$414$	55.3090	−	40.1843i	2.71829	−	1.97495i
$415$	8.77408	+	6.37474i	0.430703	+	0.312924i
$416$	1.64059	+	5.04922i	0.0804366	+	0.247558i
$417$	41.5967			2.03700
$418$		0			0
$419$	−30.6537			−1.49753			−0.748765	−	0.662836i	$-0.769353\pi$
$419$	−30.6537			−1.49753			−0.748765	+	0.662836i	$0.769353\pi$
$420$	6.97880	+	21.4785i	0.340531	+	1.04805i
$421$	5.62237	+	4.08489i	0.274017	+	0.199085i	0.716304	−	0.697789i	$-0.245832\pi$
$421$	5.62237	+	4.08489i	0.274017	+	0.199085i	−0.442286	+	0.896874i	$0.645832\pi$
$422$	−11.5550	+	8.39518i	−0.562488	+	0.408671i
$423$	−6.96506	+	21.4363i	−0.338653	+	1.04227i
$424$	5.44720	−	16.7648i	0.264540	−	0.814169i
$425$	−2.41998	+	1.75822i	−0.117386	+	0.0852860i
$426$	56.9505	+	41.3770i	2.75926	+	2.00472i
$427$	−0.325050	−	1.00040i	−0.0157303	−	0.0484127i
$428$	−68.2571			−3.29933
$429$		0			0
$430$	13.0590			0.629763
$431$	0.999362	+	3.07572i	0.0481376	+	0.148152i	0.972236	−	0.234002i	$-0.0751823\pi$
$431$	0.999362	+	3.07572i	0.0481376	+	0.148152i	−0.924099	+	0.382154i	$0.875182\pi$
$432$	1.07901	+	0.783950i	0.0519141	+	0.0377178i
$433$	24.5875	−	17.8639i	1.18160	−	0.858484i	0.189251	−	0.981929i	$-0.439394\pi$
$433$	24.5875	−	17.8639i	1.18160	−	0.858484i	0.992351	+	0.123445i	$0.0393941\pi$
$434$	−5.95299	+	18.3214i	−0.285753	+	0.879457i
$435$	−0.466984	+	1.43723i	−0.0223902	+	0.0689099i
$436$	40.7120	−	29.5790i	1.94975	−	1.41658i
$437$	15.2790	+	11.1009i	0.730894	+	0.531026i
$438$	21.3933	+	65.8417i	1.02221	+	3.14604i
$439$	−36.5311			−1.74353			−0.871767	−	0.489921i	$-0.837026\pi$
$439$	−36.5311			−1.74353			−0.871767	+	0.489921i	$0.837026\pi$
$440$		0			0
$441$	−8.07350			−0.384452
$442$	3.00667	+	9.25356i	0.143012	+	0.440147i
$443$	1.74871	+	1.27051i	0.0830839	+	0.0603640i	0.628552	−	0.777768i	$-0.283648\pi$
$443$	1.74871	+	1.27051i	0.0830839	+	0.0603640i	−0.545468	+	0.838132i	$0.683648\pi$
$444$	−16.3268	+	11.8621i	−0.774837	+	0.562952i
$445$	−1.33599	+	4.11176i	−0.0633320	+	0.194916i
$446$	−6.15080	+	18.9302i	−0.291249	+	0.896371i
$447$	−4.65712	+	3.38359i	−0.220274	+	0.160038i
$448$	−3.98862	−	2.89790i	−0.188444	−	0.136913i
$449$	−3.56040	−	10.9578i	−0.168026	−	0.517130i	0.831221	−	0.555942i	$-0.187642\pi$
$449$	−3.56040	−	10.9578i	−0.168026	−	0.517130i	−0.999247	+	0.0388127i	$0.987642\pi$
$450$	−7.78757			−0.367109
$451$		0			0
$452$	39.5699			1.86121
$453$	−3.00245	−	9.24059i	−0.141067	−	0.434161i
$454$	22.8980	+	16.6363i	1.07465	+	0.780782i
$455$	−2.18224	+	1.58549i	−0.102305	+	0.0743289i
$456$	−9.82480	+	30.2376i	−0.460088	+	1.41601i
$457$	4.92309	−	15.1517i	0.230292	−	0.708767i	−0.767419	−	0.641146i	$-0.778459\pi$
$457$	4.92309	−	15.1517i	0.230292	−	0.708767i	0.997711	−	0.0676207i	$-0.0215408\pi$
$458$	55.1254	−	40.0509i	2.57584	−	1.87146i
$459$	0.506004	+	0.367633i	0.0236182	+	0.0171597i
$460$	11.8637	+	36.5127i	0.553148	+	1.70241i
$461$	−1.52527			−0.0710387			−0.0355193	−	0.999369i	$-0.511309\pi$
$461$	−1.52527			−0.0710387			−0.0355193	+	0.999369i	$0.511309\pi$
$462$		0			0
$463$	14.2073			0.660268			0.330134	−	0.943934i	$-0.392906\pi$
$463$	14.2073			0.660268			0.330134	+	0.943934i	$0.392906\pi$
$464$	1.20756	+	3.71648i	0.0560594	+	0.172533i
$465$	−7.27408	−	5.28493i	−0.337327	−	0.245083i
$466$	22.1614	−	16.1012i	1.02661	−	0.745874i
$467$	−1.87171	+	5.76053i	−0.0866123	+	0.266565i	−0.984977	−	0.172685i	$-0.944756\pi$
$467$	−1.87171	+	5.76053i	−0.0866123	+	0.266565i	0.898365	+	0.439250i	$0.144756\pi$
$468$	−5.37125	+	16.5310i	−0.248286	+	0.764147i
$469$	−13.2271	+	9.61003i	−0.610769	+	0.443750i
$470$	−14.9230	−	10.8422i	−0.688349	−	0.500115i
$471$	3.72066	+	11.4510i	0.171439	+	0.527635i
$472$	38.9085			1.79091
$473$		0			0
$474$	−33.3727			−1.53286
$475$	−0.664789	−	2.04601i	−0.0305026	−	0.0938774i
$476$	22.1558	+	16.0971i	1.01551	+	0.737811i
$477$	7.34266	−	5.33475i	0.336197	−	0.244262i
$478$	−8.94508	+	27.5301i	−0.409138	+	1.25920i
$479$	5.44130	−	16.7466i	0.248619	−	0.765172i	−0.746401	−	0.665497i	$-0.768220\pi$
$479$	5.44130	−	16.7466i	0.248619	−	0.765172i	0.995020	−	0.0996751i	$-0.0317803\pi$
$480$	−8.22295	+	5.97432i	−0.375325	+	0.272689i
$481$	−1.95006	−	1.41680i	−0.0889151	−	0.0646006i
$482$	9.94984	+	30.6224i	0.453203	+	1.39481i
$483$	45.3350			2.06281
$484$		0			0
$485$	−0.351653			−0.0159677
$486$	−17.3053	−	53.2603i	−0.784985	−	2.41594i
$487$	−5.48789	−	3.98719i	−0.248680	−	0.180677i	0.456462	−	0.889743i	$-0.349117\pi$
$487$	−5.48789	−	3.98719i	−0.248680	−	0.180677i	−0.705142	+	0.709066i	$0.749117\pi$
$488$	2.43539	−	1.76941i	0.110245	−	0.0800975i
$489$	5.36306	−	16.5058i	0.242526	−	0.746418i
$490$	2.04175	−	6.28385i	0.0922366	−	0.283875i
$491$	0.419568	−	0.304834i	0.0189348	−	0.0137570i	−0.578278	−	0.815840i	$-0.696275\pi$
$491$	0.419568	−	0.304834i	0.0189348	−	0.0137570i	0.597212	+	0.802083i	$0.296275\pi$
$492$	44.5691	+	32.3813i	2.00933	+	1.45986i
$493$	0.566284	+	1.74284i	0.0255041	+	0.0784937i
$494$	−6.99762			−0.314838
$495$		0			0
$496$	−23.2501			−1.04396
$497$	7.31300	+	22.5071i	0.328033	+	1.00958i
$498$	54.6390	+	39.6976i	2.44843	+	1.77889i
$499$	−17.6857	+	12.8494i	−0.791722	+	0.575219i	−0.908474	−	0.417942i	$-0.862752\pi$
$499$	−17.6857	+	12.8494i	−0.791722	+	0.575219i	0.116752	+	0.993161i	$0.462752\pi$
$500$	1.35140	−	4.15918i	0.0604364	−	0.186004i
$501$	8.17105	−	25.1479i	0.365055	−	1.12352i
$502$	−24.9203	+	18.1057i	−1.11225	+	0.808096i
$503$	2.44054	+	1.77315i	0.108818	+	0.0790610i	0.640864	−	0.767655i	$-0.278576\pi$
$503$	2.44054	+	1.77315i	0.108818	+	0.0790610i	−0.532045	+	0.846716i	$0.678576\pi$
$504$	11.9563	+	36.7978i	0.532577	+	1.63910i
$505$	15.6995			0.698617
$506$		0			0
$507$	27.9724			1.24230
$508$	−25.4524	−	78.3344i	−1.12927	−	3.47553i
$509$	20.7981	+	15.1107i	0.921861	+	0.669771i	0.943986	−	0.329984i	$-0.107043\pi$
$509$	20.7981	+	15.1107i	0.921861	+	0.669771i	−0.0221259	+	0.999755i	$0.507043\pi$
$510$	−15.0700	+	10.9490i	−0.667310	+	0.484829i
$511$	−7.19202	+	22.1347i	−0.318156	+	0.979184i
$512$	15.4969	−	47.6945i	0.684872	−	2.10782i
$513$	−0.363916	+	0.264401i	−0.0160673	+	0.0116736i
$514$	−12.0420	−	8.74901i	−0.531149	−	0.385902i
$515$	2.06420	+	6.35297i	0.0909597	+	0.279945i
$516$	55.8027			2.45658
$517$		0			0
$518$	−9.88725			−0.434421
$519$	6.41201	+	19.7341i	0.281456	+	0.866233i
$520$	−6.24518	−	4.53739i	−0.273869	−	0.198978i
$521$	−9.00647	+	6.54359i	−0.394581	+	0.286680i	−0.767330	−	0.641252i	$-0.778415\pi$
$521$	−9.00647	+	6.54359i	−0.394581	+	0.286680i	0.372749	+	0.927932i	$0.378415\pi$
$522$	−1.47429	+	4.53739i	−0.0645278	+	0.198596i
$523$	2.02048	−	6.21839i	0.0883493	−	0.271911i	−0.897114	−	0.441799i	$-0.854340\pi$
$523$	2.02048	−	6.21839i	0.0883493	−	0.271911i	0.985463	+	0.169888i	$0.0543405\pi$
$524$	−71.1128	+	51.6665i	−3.10658	+	2.25706i
$525$	−4.17787	−	3.03540i	−0.182337	−	0.132476i
$526$	−16.9524	−	52.1742i	−0.739161	−	2.27490i
$527$	−10.9032			−0.474949
$528$		0			0
$529$	54.0677			2.35077
$530$	2.29528	+	7.06414i	0.0997005	+	0.306847i
$531$	16.2071	+	11.7752i	0.703330	+	0.510999i
$532$	−15.9344	+	11.5770i	−0.690844	+	0.501927i
$533$	−2.03331	+	6.25789i	−0.0880726	+	0.271060i
$534$	−8.31965	+	25.6052i	−0.360026	+	1.10805i
$535$	12.6271	−	9.17413i	0.545918	−	0.396632i
$536$	−37.8535	−	27.5022i	−1.63502	−	1.18791i
$537$	−16.0353	−	49.3516i	−0.691974	−	2.12968i
$538$	11.4223			0.492449
$539$		0			0
$540$	−0.914417			−0.0393502
$541$	−12.8984	−	39.6971i	−0.554544	−	1.70671i	−0.697144	−	0.716931i	$-0.745546\pi$
$541$	−12.8984	−	39.6971i	−0.554544	−	1.70671i	0.142600	−	0.989780i	$-0.454454\pi$
$542$	44.4439	+	32.2904i	1.90903	+	1.38699i
$543$	−3.47859	+	2.52734i	−0.149280	+	0.108459i
$544$	−3.80876	+	11.7222i	−0.163299	+	0.502584i
$545$	−3.55587	+	10.9438i	−0.152317	+	0.468783i
$546$	−13.5895	+	9.87336i	−0.581577	+	0.422541i
$547$	−3.60511	−	2.61926i	−0.154143	−	0.111992i	0.508040	−	0.861333i	$-0.330370\pi$
$547$	−3.60511	−	2.61926i	−0.154143	−	0.111992i	−0.662184	+	0.749342i	$0.730370\pi$
$548$	−24.2863	−	74.7457i	−1.03746	−	3.19298i
$549$	1.54994			0.0661498
$550$		0			0
$551$	−1.31795			−0.0561466
$552$	40.0921	+	123.391i	1.70643	+	5.25186i
$553$	−9.07658	−	6.59452i	−0.385976	−	0.280428i
$554$	26.6216	−	19.3417i	1.13104	−	0.821752i
$555$	1.42602	−	4.38883i	0.0605311	−	0.186296i
$556$	−22.7888	+	70.1366i	−0.966459	+	2.97445i
$557$	15.6718	−	11.3862i	0.664034	−	0.482449i	−0.203989	−	0.978973i	$-0.565391\pi$
$557$	15.6718	−	11.3862i	0.664034	−	0.482449i	0.868023	+	0.496524i	$0.165391\pi$
$558$	−22.9645	−	16.6847i	−0.972167	−	0.706320i
$559$	2.05960	+	6.33881i	0.0871120	+	0.268103i
$560$	−13.3537			−0.564298
$561$		0			0
$562$	23.6941			0.999477
$563$	−6.40999	−	19.7279i	−0.270149	−	0.831432i	−0.990462	−	0.137784i	$-0.956002\pi$
$563$	−6.40999	−	19.7279i	−0.270149	−	0.831432i	0.720314	−	0.693649i	$-0.243998\pi$
$564$	−63.7678	−	46.3300i	−2.68511	−	1.95085i
$565$	−7.32017	+	5.31842i	−0.307962	+	0.223747i
$566$	10.8746	−	33.4687i	0.457095	−	1.40679i
$567$	5.65321	−	17.3988i	0.237413	−	0.730681i
$568$	−54.7916	+	39.8084i	−2.29900	+	1.67032i
$569$	−34.2819	−	24.9072i	−1.43717	−	1.04417i	−0.988624	−	0.150405i	$-0.951942\pi$
$569$	−34.2819	−	24.9072i	−1.43717	−	1.04417i	−0.448546	−	0.893760i	$-0.648058\pi$
$570$	−4.13986	−	12.7412i	−0.173399	−	0.533669i
$571$	5.03980			0.210909			0.105455	−	0.994424i	$-0.466370\pi$
$571$	5.03980			0.210909			0.105455	+	0.994424i	$0.466370\pi$
$572$		0			0
$573$	−0.0615611			−0.00257175
$574$	8.34044	+	25.6692i	0.348123	+	1.07141i
$575$	−7.10222	−	5.16006i	−0.296183	−	0.215189i
$576$	5.87719	−	4.27002i	0.244883	−	0.177918i
$577$	10.7668	−	33.1367i	0.448226	−	1.37950i	−0.430681	−	0.902504i	$-0.641727\pi$
$577$	10.7668	−	33.1367i	0.448226	−	1.37950i	0.878907	−	0.476993i	$-0.158273\pi$
$578$	6.28184	−	19.3335i	0.261290	−	0.804168i
$579$	−2.90812	+	2.11287i	−0.120857	+	0.0878081i
$580$	−2.16749	−	1.57477i	−0.0900002	−	0.0653889i
$581$	7.01619	+	21.5936i	0.291081	+	0.895854i
$582$	−2.18985			−0.0907724
$583$		0			0
$584$	−66.6057			−2.75616
$585$	−1.22821	−	3.78006i	−0.0507804	−	0.156286i
$586$	−62.2315	−	45.2138i	−2.57076	−	1.86777i
$587$	11.1469	−	8.09867i	0.460080	−	0.334268i	−0.333483	−	0.942756i	$-0.608224\pi$
$587$	11.1469	−	8.09867i	0.460080	−	0.334268i	0.793563	+	0.608489i	$0.208224\pi$
$588$	8.72460	−	26.8516i	0.359796	−	1.10734i
$589$	2.42316	−	7.45772i	0.0998446	−	0.307290i
$590$	−13.2637	+	9.63662i	−0.546056	+	0.396733i
$591$	−45.3062	−	32.9169i	−1.86365	−	1.35402i
$592$	−3.68749	−	11.3489i	−0.151555	−	0.466438i
$593$	25.1595			1.03318			0.516588	−	0.856234i	$-0.327202\pi$
$593$	25.1595			1.03318			0.516588	+	0.856234i	$0.327202\pi$
$594$		0			0
$595$	−6.26222			−0.256726
$596$	−3.15371	−	9.70611i	−0.129181	−	0.397578i
$597$	−13.2277	−	9.61048i	−0.541373	−	0.393331i
$598$	−23.1017	+	16.7843i	−0.944697	+	0.686362i
$599$	−5.10073	+	15.6984i	−0.208410	+	0.641420i	0.791146	+	0.611627i	$0.209485\pi$
$599$	−5.10073	+	15.6984i	−0.208410	+	0.641420i	−0.999556	+	0.0297928i	$0.990515\pi$
$600$	4.56691	−	14.0555i	0.186443	−	0.573813i
$601$	32.0734	−	23.3027i	1.30830	−	0.950535i	0.308300	−	0.951289i	$-0.400240\pi$
$601$	32.0734	−	23.3027i	1.30830	−	0.950535i	1.00000		0.000753830i	$0.000239952\pi$
$602$	22.1179	+	16.0696i	0.901458	+	0.654948i
$603$	−7.44450	−	22.9118i	−0.303164	−	0.933041i
$604$	17.2255			0.700897
$605$		0			0
$606$	97.7656			3.97146
$607$	−4.38479	−	13.4950i	−0.177973	−	0.547744i	0.821784	−	0.569799i	$-0.192979\pi$
$607$	−4.38479	−	13.4950i	−0.177973	−	0.547744i	−0.999757	+	0.0220550i	$0.992979\pi$
$608$	−7.17145	−	5.21037i	−0.290841	−	0.211308i
$609$	−2.55949	+	1.85958i	−0.103716	+	0.0753538i
$610$	−0.391971	+	1.20636i	−0.0158705	+	0.0488442i
$611$	2.90919	−	8.95357i	0.117693	−	0.362223i
$612$	−32.6464	+	23.7190i	−1.31965	+	0.958783i
$613$	24.3954	+	17.7243i	0.985320	+	0.715877i	0.958891	−	0.283774i	$-0.0915865\pi$
$613$	24.3954	+	17.7243i	0.985320	+	0.715877i	0.0264287	+	0.999651i	$0.491586\pi$
$614$	3.96776	+	12.2115i	0.160126	+	0.492817i
$615$	−12.5972			−0.507968
$616$		0			0
$617$	−31.3844			−1.26349			−0.631744	−	0.775177i	$-0.717661\pi$
$617$	−31.3844			−1.26349			−0.631744	+	0.775177i	$0.717661\pi$
$618$	12.8545	+	39.5620i	0.517083	+	1.59142i
$619$	−28.5042	−	20.7095i	−1.14568	−	0.832386i	−0.157781	−	0.987474i	$-0.550434\pi$
$619$	−28.5042	−	20.7095i	−1.14568	−	0.832386i	−0.987901	+	0.155088i	$0.950434\pi$
$620$	12.8961	−	9.36955i	0.517919	−	0.376290i
$621$	−0.567233	+	1.74576i	−0.0227623	+	0.0700550i
$622$	−10.7355	+	33.0405i	−0.430454	+	1.32480i
$623$	−7.32240	+	5.32004i	−0.293366	+	0.213143i
$624$	−16.4012	−	11.9162i	−0.656575	−	0.477029i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−40.2730			−1.60963
$627$		0			0
$628$	−21.3460			−0.851799
$629$	−1.72925	−	5.32207i	−0.0689496	−	0.212205i
$630$	−13.1897	−	9.58287i	−0.525490	−	0.381791i
$631$	−4.63949	+	3.37078i	−0.184695	+	0.134189i	−0.676291	−	0.736635i	$-0.736414\pi$
$631$	−4.63949	+	3.37078i	−0.184695	+	0.134189i	0.491596	+	0.870823i	$0.336414\pi$
$632$	9.92179	−	30.5361i	0.394668	−	1.21466i
$633$	4.31257	−	13.2727i	0.171409	−	0.527544i
$634$	21.8686	−	15.8885i	0.868512	−	0.631011i
$635$	15.2371	+	11.0704i	0.604666	+	0.439315i
$636$	9.80797	+	30.1858i	0.388911	+	1.19695i
$637$	3.37217			0.133610
$638$		0			0
$639$	−34.8707			−1.37946
$640$	4.38378	+	13.4919i	0.173284	+	0.533313i
$641$	5.76405	+	4.18783i	0.227666	+	0.165409i	0.695771	−	0.718264i	$-0.255063\pi$
$641$	5.76405	+	4.18783i	0.227666	+	0.165409i	−0.468105	+	0.883673i	$0.655063\pi$
$642$	78.6331	−	57.1303i	3.10340	−	2.25475i
$643$	−6.54793	+	20.1525i	−0.258225	+	0.794735i	0.734952	+	0.678119i	$0.237205\pi$
$643$	−6.54793	+	20.1525i	−0.258225	+	0.794735i	−0.993177	+	0.116616i	$0.962795\pi$
$644$	−24.8368	+	76.4397i	−0.978706	+	3.01215i
$645$	−10.3231	+	7.50019i	−0.406473	+	0.295320i
$646$	−13.1429	−	9.54890i	−0.517102	−	0.375696i
$647$	−1.74587	−	5.37322i	−0.0686371	−	0.211243i	0.910855	−	0.412727i	$-0.135424\pi$
$647$	−1.74587	−	5.37322i	−0.0686371	−	0.211243i	−0.979492	+	0.201484i	$0.935424\pi$
$648$	52.3547			2.05669
$649$		0			0
$650$	3.25274			0.127583
$651$	−5.81671	−	17.9020i	−0.227975	−	0.701635i
$652$	24.8924	+	18.0854i	0.974863	+	0.708280i
$653$	12.7122	−	9.23596i	0.497467	−	0.361431i	−0.310582	−	0.950547i	$-0.600524\pi$
$653$	12.7122	−	9.23596i	0.497467	−	0.361431i	0.808049	+	0.589116i	$0.200524\pi$
$654$	−22.1436	+	68.1508i	−0.865881	+	2.66491i
$655$	6.21114	−	19.1159i	0.242689	−	0.746920i
$656$	−26.3534	+	19.1469i	−1.02893	+	0.747560i
$657$	−27.7443	−	20.1574i	−1.08241	−	0.786414i
$658$	−11.9332	−	36.7266i	−0.465205	−	1.43175i
$659$	41.7884			1.62784			0.813922	−	0.580975i	$-0.197329\pi$
$659$	41.7884			1.62784			0.813922	+	0.580975i	$0.197329\pi$
$660$		0			0
$661$	15.8742			0.617435			0.308717	−	0.951154i	$-0.400100\pi$
$661$	15.8742			0.617435			0.308717	+	0.951154i	$0.400100\pi$
$662$	6.90109	+	21.2394i	0.268218	+	0.825491i
$663$	−7.69135	−	5.58810i	−0.298707	−	0.217024i
$664$	−52.5678	+	38.1927i	−2.04002	+	1.48216i
$665$	1.39174	−	4.28334i	0.0539694	−	0.166101i
$666$	4.50200	−	13.8557i	0.174449	−	0.536898i
$667$	−4.35103	+	3.16121i	−0.168473	+	0.122402i
$668$	37.9256	+	27.5546i	1.46739	+	1.06612i
$669$	−6.00999	−	18.4968i	−0.232360	−	0.715130i
$670$	19.7156			0.761681
$671$		0			0
$672$	−21.2787			−0.820844
$673$	−9.96413	−	30.6664i	−0.384089	−	1.18210i	−0.937139	−	0.348956i	$-0.886536\pi$
$673$	−9.96413	−	30.6664i	−0.384089	−	1.18210i	0.553050	−	0.833148i	$-0.313464\pi$
$674$	23.6707	+	17.1978i	0.911761	+	0.662433i
$675$	0.169161	−	0.122903i	0.00651101	−	0.00473053i
$676$	−15.3247	+	47.1646i	−0.589412	+	1.81402i
$677$	−5.42712	+	16.7030i	−0.208581	+	0.641947i	0.790966	+	0.611860i	$0.209578\pi$
$677$	−5.42712	+	16.7030i	−0.208581	+	0.641947i	−0.999547	+	0.0300871i	$0.990422\pi$
$678$	−45.5851	+	33.1195i	−1.75068	+	1.27195i
$679$	−0.595589	−	0.432721i	−0.0228566	−	0.0166063i
$680$	−5.53801	−	17.0442i	−0.212373	−	0.653617i
$681$	−27.6555			−1.05976
$682$		0			0
$683$	−5.93856			−0.227233			−0.113616	−	0.993525i	$-0.536243\pi$
$683$	−5.93856			−0.227233			−0.113616	+	0.993525i	$0.536243\pi$
$684$	−8.96825	−	27.6014i	−0.342909	−	1.05537i
$685$	14.5390	+	10.5632i	0.555508	+	0.403600i
$686$	41.1208	−	29.8760i	1.57000	−	1.14067i
$687$	−20.5740	+	63.3203i	−0.784947	+	2.41582i
$688$	−10.1963	+	31.3809i	−0.388729	+	1.19638i
$689$	−3.06691	+	2.22824i	−0.116840	+	0.0848891i
$690$	−44.2278	−	32.1334i	−1.68372	−	1.22330i
$691$	6.77847	+	20.8620i	0.257865	+	0.793628i	0.993252	+	0.115980i	$0.0370007\pi$
$691$	6.77847	+	20.8620i	0.257865	+	0.793628i	−0.735386	+	0.677648i	$0.762999\pi$
$692$	−36.7868			−1.39842
$693$		0			0
$694$	−12.3424			−0.468511
$695$	−5.21098	−	16.0377i	−0.197664	−	0.608346i
$696$	−7.32480	−	5.32178i	−0.277646	−	0.201721i
$697$	−12.3584	+	8.97893i	−0.468109	+	0.340101i
$698$	0.743862	−	2.28937i	0.0281556	−	0.0866540i
$699$	−8.27112	+	25.4559i	−0.312843	+	0.962831i
$700$	7.40686	−	5.38140i	0.279953	−	0.203398i
$701$	26.2290	+	19.0565i	0.990657	+	0.719754i	0.960065	−	0.279778i	$-0.0902607\pi$
$701$	26.2290	+	19.0565i	0.990657	+	0.719754i	0.0305921	+	0.999532i	$0.490261\pi$
$702$	−0.210172	−	0.646842i	−0.00793242	−	0.0244135i
$703$	4.02460			0.151791
$704$		0			0
$705$	18.0236			0.678809
$706$	12.1048	+	37.2548i	0.455571	+	1.40210i
$707$	26.5899	+	19.3187i	1.00002	+	0.726555i
$708$	−56.6771	+	41.1783i	−2.13006	+	1.54758i
$709$	−4.97532	+	15.3125i	−0.186852	+	0.575071i	−0.999975	−	0.00701999i	$-0.997765\pi$
$709$	−4.97532	+	15.3125i	−0.186852	+	0.575071i	0.813123	+	0.582091i	$0.197765\pi$
$710$	8.81861	−	27.1409i	0.330957	−	1.01858i
$711$	13.3743	−	9.71696i	0.501574	−	0.364415i
$712$	−20.9554	−	15.2250i	−0.785338	−	0.570581i
$713$	−9.88819	−	30.4327i	−0.370316	−	1.13971i
$714$	−38.9969			−1.45942
$715$		0			0
$716$	91.9971			3.43809
$717$	−8.74031	−	26.8999i	−0.326413	−	1.00459i
$718$	−41.3685	−	30.0560i	−1.54386	−	1.12168i
$719$	6.32017	−	4.59187i	0.235703	−	0.171248i	−0.463664	−	0.886011i	$-0.653466\pi$
$719$	6.32017	−	4.59187i	0.235703	−	0.171248i	0.699367	+	0.714763i	$0.253466\pi$
$720$	6.08039	−	18.7135i	0.226603	−	0.697412i
$721$	−4.32143	+	13.3000i	−0.160939	+	0.495318i
$722$	−29.3529	+	21.3261i	−1.09240	+	0.793677i
$723$	−25.4527	−	18.4925i	−0.946596	−	0.687742i
$724$	−2.35563	−	7.24988i	−0.0875463	−	0.269440i
$725$	0.612630			0.0227525
$726$		0			0
$727$	−49.1218			−1.82183			−0.910914	−	0.412597i	$-0.864622\pi$
$727$	−49.1218			−1.82183			−0.910914	+	0.412597i	$0.864622\pi$
$728$	−4.99396	−	15.3698i	−0.185088	−	0.569644i
$729$	23.0599	+	16.7540i	0.854071	+	0.620519i
$730$	22.7055	−	16.4965i	0.840367	−	0.610562i
$731$	−4.78154	+	14.7161i	−0.176852	+	0.544293i
$732$	−1.67494	+	5.15492i	−0.0619074	+	0.190531i
$733$	−0.540381	+	0.392609i	−0.0199594	+	0.0145014i	−0.597720	−	0.801705i	$-0.703927\pi$
$733$	−0.540381	+	0.392609i	−0.0199594	+	0.0145014i	0.577761	+	0.816206i	$0.303927\pi$
$734$	72.8212	+	52.9077i	2.68788	+	1.95286i
$735$	1.99500	+	6.13999i	0.0735869	+	0.226477i
$736$	−36.1730			−1.33335
$737$		0			0
$738$	−39.7699			−1.46395
$739$	−11.7717	−	36.2295i	−0.433028	−	1.33272i	−0.895094	−	0.445878i	$-0.852892\pi$
$739$	−11.7717	−	36.2295i	−0.433028	−	1.33272i	0.462066	−	0.886846i	$-0.347108\pi$
$740$	6.61881	+	4.80885i	0.243312	+	0.176777i
$741$	5.53160	−	4.01894i	0.203208	−	0.147639i
$742$	−4.80519	+	14.7888i	−0.176404	+	0.542915i
$743$	9.68325	−	29.8020i	0.355244	−	1.09333i	−0.600624	−	0.799532i	$-0.705081\pi$
$743$	9.68325	−	29.8020i	0.355244	−	1.09333i	0.955868	−	0.293797i	$-0.0949189\pi$
$744$	43.5809	−	31.6634i	1.59775	−	1.16083i
$745$	1.88797	+	1.37169i	0.0691699	+	0.0502548i
$746$	9.46741	+	29.1377i	0.346627	+	1.06681i
$747$	−33.4554			−1.22407
$748$		0			0
$749$	32.6754			1.19393
$750$	1.92435	+	5.92254i	0.0702673	+	0.216260i
$751$	30.0852	+	21.8582i	1.09783	+	0.797617i	0.980704	−	0.195500i	$-0.0626330\pi$
$751$	30.0852	+	21.8582i	1.09783	+	0.797617i	0.117122	+	0.993117i	$0.462633\pi$
$752$	37.7055	−	27.3947i	1.37498	−	0.998981i
$753$	9.30081	−	28.6250i	0.338941	−	1.04315i
$754$	0.615786	−	1.89519i	0.0224256	−	0.0690189i
$755$	−3.18661	+	2.31521i	−0.115973	+	0.0842591i
$756$	−1.54873	−	1.12522i	−0.0563269	−	0.0409239i
$757$	2.06444	+	6.35370i	0.0750335	+	0.230929i	0.981538	−	0.191267i	$-0.0612595\pi$
$757$	2.06444	+	6.35370i	0.0750335	+	0.230929i	−0.906505	+	0.422196i	$0.861259\pi$
$758$	−18.0355			−0.655079
$759$		0			0
$760$	12.8890			0.467533
$761$	7.07452	+	21.7731i	0.256451	+	0.789276i	0.993540	+	0.113480i	$0.0361998\pi$
$761$	7.07452	+	21.7731i	0.256451	+	0.789276i	−0.737089	+	0.675796i	$0.763800\pi$
$762$	94.8864	+	68.9390i	3.43737	+	2.49740i
$763$	−19.4893	+	14.1598i	−0.705560	+	0.512619i
$764$	0.0337263	−	0.103799i	0.00122017	−	0.00375531i
$765$	2.85140	−	8.77571i	0.103093	−	0.317286i
$766$	32.6025	−	23.6871i	1.17798	−	0.855849i
$767$	−6.76945	−	4.91830i	−0.244431	−	0.177589i
$768$	23.7090	+	72.9687i	0.855523	+	2.63303i
$769$	13.1946			0.475808			0.237904	−	0.971289i	$-0.423540\pi$
$769$	13.1946			0.475808			0.237904	+	0.971289i	$0.423540\pi$
$770$		0			0
$771$	14.5440			0.523788
$772$	−1.96932	−	6.06095i	−0.0708775	−	0.218138i
$773$	10.0487	+	7.30082i	0.361427	+	0.262592i	0.753647	−	0.657279i	$-0.228293\pi$
$773$	10.0487	+	7.30082i	0.361427	+	0.262592i	−0.392220	+	0.919871i	$0.628293\pi$
$774$	−32.5905	+	23.6784i	−1.17144	+	0.851102i
$775$	−1.12637	+	3.46661i	−0.0404604	+	0.124524i
$776$	0.651050	−	2.00372i	0.0233713	−	0.0719295i
$777$	7.81584	−	5.67854i	0.280392	−	0.203716i
$778$	−51.2442	−	37.2311i	−1.83719	−	1.33480i
$779$	−3.39497	−	10.4486i	−0.121637	−	0.374362i
$780$	13.8993			0.497675
$781$		0			0
$782$	−66.2932			−2.37064
$783$	−0.0395843	−	0.121828i	−0.00141463	−	0.00435378i
$784$	13.5059	+	9.81263i	0.482355	+	0.350451i
$785$	3.94887	−	2.86902i	0.140941	−	0.102400i
$786$	38.6787	−	119.041i	1.37963	−	4.24605i
$787$	−6.63926	+	20.4336i	−0.236664	+	0.728377i	0.760232	+	0.649652i	$0.225085\pi$
$787$	−6.63926	+	20.4336i	−0.236664	+	0.728377i	−0.996896	+	0.0787259i	$0.974915\pi$
$788$	80.3225	−	58.3577i	2.86137	−	2.07891i
$789$	43.3660	+	31.5073i	1.54387	+	1.12169i
$790$	4.18073	+	12.8669i	0.148744	+	0.457785i
$791$	−18.9426			−0.673520
$792$		0			0
$793$	−0.647384			−0.0229893
$794$	−2.78885	−	8.58320i	−0.0989726	−	0.304606i
$795$	−5.87155	−	4.26593i	−0.208242	−	0.151297i
$796$	23.4511	−	17.0382i	0.831203	−	0.603904i
$797$	0.657991	−	2.02509i	0.0233072	−	0.0717323i	−0.938726	−	0.344663i	$-0.887993\pi$
$797$	0.657991	−	2.02509i	0.0233072	−	0.0717323i	0.962034	+	0.272931i	$0.0879931\pi$
$798$	8.66683	−	26.6738i	0.306802	−	0.944241i
$799$	17.6820	−	12.8467i	0.625545	−	0.454485i
$800$	3.33354	+	2.42196i	0.117858	+	0.0856292i
$801$	−4.12122	−	12.6838i	−0.145616	−	0.448160i
$802$	−72.9179			−2.57482
$803$		0			0
$804$	84.2470			2.97116
$805$	−5.67928	−	17.4790i	−0.200168	−	0.616055i
$806$	9.59191	+	6.96893i	0.337861	+	0.245470i
$807$	−9.02927	+	6.56015i	−0.317845	+	0.230928i
$808$	−29.0660	+	89.4559i	−1.02254	+	3.14705i
$809$	1.65705	−	5.09986i	0.0582587	−	0.179302i	−0.917692	−	0.397292i	$-0.869950\pi$
$809$	1.65705	−	5.09986i	0.0582587	−	0.179302i	0.975951	+	0.217990i	$0.0699501\pi$
$810$	−17.8474	+	12.9669i	−0.627094	+	0.455610i
$811$	15.8403	+	11.5087i	0.556230	+	0.404125i	0.830077	−	0.557649i	$-0.188296\pi$
$811$	15.8403	+	11.5087i	0.556230	+	0.404125i	−0.273847	+	0.961773i	$0.588296\pi$
$812$	−1.73323	−	5.33434i	−0.0608246	−	0.187199i
$813$	−53.6781			−1.88257
$814$		0			0
$815$	−7.03572			−0.246450
$816$	−14.5440	−	44.7619i	−0.509143	−	1.56698i
$817$	−9.00307	−	6.54112i	−0.314978	−	0.228845i
$818$	−19.6458	+	14.2735i	−0.686898	+	0.499061i
$819$	2.57128	−	7.91358i	0.0898478	−	0.276523i
$820$	6.90138	−	21.2403i	0.241007	−	0.741743i
$821$	−13.4592	+	9.77866i	−0.469728	+	0.341278i	−0.797335	−	0.603536i	$-0.793758\pi$
$821$	−13.4592	+	9.77866i	−0.469728	+	0.341278i	0.327607	+	0.944814i	$0.393758\pi$
$822$	90.5393	+	65.7807i	3.15792	+	2.29436i
$823$	−5.65282	−	17.3976i	−0.197045	−	0.606441i	−0.999947	−	0.0103302i	$-0.996712\pi$
$823$	−5.65282	−	17.3976i	−0.197045	−	0.606441i	0.802902	−	0.596111i	$-0.203288\pi$
$824$	−40.0210			−1.39420
$825$		0			0
$826$	−34.3227			−1.19424
$827$	11.7483	+	36.1576i	0.408529	+	1.25732i	0.917912	+	0.396784i	$0.129874\pi$
$827$	11.7483	+	36.1576i	0.408529	+	1.25732i	−0.509383	+	0.860540i	$0.670126\pi$
$828$	−95.8115	−	69.6111i	−3.32968	−	2.41915i
$829$	−41.8263	+	30.3886i	−1.45269	+	1.05544i	−0.467494	+	0.883996i	$0.654843\pi$
$829$	−41.8263	+	30.3886i	−1.45269	+	1.05544i	−0.985194	+	0.171443i	$0.945157\pi$
$830$	8.46069	−	26.0393i	0.293675	−	0.903838i
$831$	−9.93577	+	30.5792i	−0.344668	+	1.06078i
$832$	−2.45480	+	1.78352i	−0.0851050	+	0.0618324i
$833$	6.33360	+	4.60163i	0.219446	+	0.159437i
$834$	−32.4505	−	99.8722i	−1.12367	−	3.45829i
$835$	−10.7195			−0.370963
$836$		0			0
$837$	0.762151			0.0263438
$838$	23.9136	+	73.5984i	0.826081	+	2.54241i
$839$	−31.2301	−	22.6900i	−1.07818	−	0.783346i	−0.100818	−	0.994905i	$-0.532146\pi$
$839$	−31.2301	−	22.6900i	−1.07818	−	0.783346i	−0.977365	+	0.211559i	$0.932146\pi$
$840$	25.0307	−	18.1858i	0.863640	−	0.627471i
$841$	−8.84551	+	27.2237i	−0.305018	+	0.938748i
$842$	5.42155	−	16.6858i	0.186839	−	0.575031i
$843$	−18.7301	+	13.6082i	−0.645100	+	0.468693i
$844$	20.0166	+	14.5429i	0.689001	+	0.500589i
$845$	−3.50422	−	10.7849i	−0.120549	−	0.371011i
$846$	56.9013			1.95631
$847$		0			0
$848$	−18.7672			−0.644470
$849$	10.6257	+	32.7025i	0.364673	+	1.12235i
$850$	6.10929	+	4.43866i	0.209547	+	0.152245i
$851$	13.2866	−	9.65330i	0.455460	−	0.330911i
$852$	37.6829	−	115.976i	1.29099	−	3.97327i
$853$	−10.4775	+	32.2463i	−0.358741	+	1.10409i	0.595067	+	0.803676i	$0.297126\pi$
$853$	−10.4775	+	32.2463i	−0.358741	+	1.10409i	−0.953808	+	0.300416i	$0.902874\pi$
$854$	−2.14835	+	1.56087i	−0.0735149	+	0.0534117i
$855$	5.36885	+	3.90070i	0.183611	+	0.133401i
$856$	28.8966	+	88.9346i	0.987665	+	3.03972i
$857$	56.7117			1.93723			0.968617	−	0.248558i	$-0.0799568\pi$
$857$	56.7117			1.93723			0.968617	+	0.248558i	$0.0799568\pi$
$858$		0			0
$859$	−25.7505			−0.878597			−0.439298	−	0.898341i	$-0.644773\pi$
$859$	−25.7505			−0.878597			−0.439298	+	0.898341i	$0.644773\pi$
$860$	−6.99062	−	21.5149i	−0.238378	−	0.733652i
$861$	−21.3357	−	15.5013i	−0.727119	−	0.528283i
$862$	6.60507	−	4.79887i	0.224970	−	0.163450i
$863$	11.0520	−	34.0146i	0.376215	−	1.15787i	−0.566441	−	0.824102i	$-0.691680\pi$
$863$	11.0520	−	34.0146i	0.376215	−	1.15787i	0.942656	−	0.333767i	$-0.108320\pi$
$864$	0.266240	−	0.819402i	0.00905766	−	0.0278766i
$865$	6.80531	−	4.94434i	0.231387	−	0.168113i
$866$	−62.0719	−	45.0978i	−2.10929	−	1.53249i
$867$	6.13803	+	18.8909i	0.208458	+	0.641569i
$868$	33.3714			1.13270
$869$		0			0
$870$	3.81504			0.129342
$871$	3.10945	+	9.56989i	0.105360	+	0.324263i
$872$	−55.7749	−	40.5229i	−1.88878	−	1.37228i
$873$	0.877594	−	0.637609i	0.0297021	−	0.0215798i
$874$	14.7333	−	45.3444i	0.498361	−	1.53380i
$875$	−0.646930	+	1.99105i	−0.0218702	+	0.0673096i
$876$	97.0229	−	70.4913i	3.27810	−	2.38168i
$877$	14.0042	+	10.1746i	0.472888	+	0.343573i	0.798566	−	0.601907i	$-0.205592\pi$
$877$	14.0042	+	10.1746i	0.472888	+	0.343573i	−0.325678	+	0.945481i	$0.605592\pi$
$878$	28.4987	+	87.7099i	0.961784	+	2.96007i
$879$	75.1614			2.53513
$880$		0			0
$881$	−4.15822			−0.140094			−0.0700470	−	0.997544i	$-0.522315\pi$
$881$	−4.15822			−0.140094			−0.0700470	+	0.997544i	$0.522315\pi$
$882$	6.29831	+	19.3842i	0.212075	+	0.652700i
$883$	33.3885	+	24.2582i	1.12361	+	0.816352i	0.984753	−	0.173960i	$-0.0556564\pi$
$883$	33.3885	+	24.2582i	1.12361	+	0.816352i	0.138859	+	0.990312i	$0.455656\pi$
$884$	13.6359	−	9.90703i	0.458623	−	0.333209i
$885$	4.95029	−	15.2354i	0.166402	−	0.512133i
$886$	1.68625	−	5.18975i	0.0566508	−	0.174353i
$887$	24.6580	−	17.9151i	0.827936	−	0.601531i	−0.0910385	−	0.995847i	$-0.529019\pi$
$887$	24.6580	−	17.9151i	0.827936	−	0.601531i	0.918975	+	0.394317i	$0.129019\pi$
$888$	22.3676	+	16.2510i	0.750606	+	0.545347i
$889$	12.1843	+	37.4995i	0.408650	+	1.25769i
$890$	10.9144			0.365852
$891$		0			0
$892$	34.4803			1.15449
$893$	4.85740	+	14.9496i	0.162547	+	0.500268i
$894$	11.7570	+	8.54196i	0.393213	+	0.285686i
$895$	−17.0189	+	12.3649i	−0.568878	+	0.413314i
$896$	−9.17748	+	28.2454i	−0.306598	+	0.943612i
$897$	8.62204	−	26.5359i	0.287882	−	0.886008i
$898$	−23.5317	+	17.0968i	−0.785263	+	0.570527i
$899$	1.80657	+	1.31255i	0.0602524	+	0.0437759i
$900$	4.16875	+	12.8301i	0.138958	+	0.427670i
$901$	−8.80090			−0.293200
$902$		0			0
$903$	−26.7134			−0.888965
$904$	−16.7519	−	51.5570i	−0.557160	−	1.71476i
$905$	1.41020	+	1.02457i	0.0468767	+	0.0340579i
$906$	−19.8441	+	14.4176i	−0.659275	+	0.478991i
$907$	3.48864	−	10.7369i	0.115838	−	0.356514i	−0.876283	−	0.481797i	$-0.839984\pi$
$907$	3.48864	−	10.7369i	0.115838	−	0.356514i	0.992121	+	0.125284i	$0.0399841\pi$
$908$	15.1511	−	46.6302i	0.502806	−	1.54748i
$909$	−39.1800	+	28.4659i	−1.29952	+	0.944156i
$910$	5.50911	+	4.00261i	0.182625	+	0.132685i
$911$	15.6383	+	48.1298i	0.518121	+	1.59461i	0.777531	+	0.628845i	$0.216472\pi$
$911$	15.6383	+	48.1298i	0.518121	+	1.59461i	−0.259410	+	0.965767i	$0.583528\pi$
$912$	33.8494			1.12086
$913$		0			0
$914$	−40.2193			−1.33034
$915$	−0.382998	−	1.17875i	−0.0126615	−	0.0389682i
$916$	−95.4935	−	69.3801i	−3.15519	−	2.29238i
$917$	34.0425	−	24.7333i	1.12418	−	0.816766i
$918$	0.487931	−	1.50170i	0.0161041	−	0.0495633i
$919$	8.41081	−	25.8858i	0.277447	−	0.853894i	−0.711115	−	0.703076i	$-0.751809\pi$
$919$	8.41081	−	25.8858i	0.277447	−	0.853894i	0.988562	−	0.150818i	$-0.0481907\pi$
$920$	42.5512	−	30.9153i	1.40287	−	1.01925i
$921$	−10.1499	−	7.37436i	−0.334452	−	0.242994i
$922$	1.18989	+	3.66211i	0.0391870	+	0.120605i
$923$	14.5649			0.479410
$924$		0			0
$925$	−1.87077			−0.0615106
$926$	−11.0834	−	34.1112i	−0.364223	−	1.12096i
$927$	−16.6706	−	12.1119i	−0.547533	−	0.397806i
$928$	2.04223	−	1.48376i	0.0670394	−	0.0487070i
$929$	−7.17240	+	22.0744i	−0.235319	+	0.724237i	0.761760	+	0.647859i	$0.224336\pi$
$929$	−7.17240	+	22.0744i	−0.235319	+	0.724237i	−0.997079	+	0.0763779i	$0.975664\pi$
$930$	−7.01427	+	21.5877i	−0.230007	+	0.707888i
$931$	−4.55511	+	3.30948i	−0.149288	+	0.108464i
$932$	−38.3901	−	27.8921i	−1.25751	−	0.913634i
$933$	−10.4897	−	32.2841i	−0.343419	−	1.05693i
$934$	15.2910			0.500336
$935$		0			0
$936$	23.8128			0.778344
$937$	13.0441	+	40.1457i	0.426133	+	1.31150i	0.901905	+	0.431935i	$0.142169\pi$
$937$	13.0441	+	40.1457i	0.426133	+	1.31150i	−0.475772	+	0.879569i	$0.657831\pi$
$938$	33.3921	+	24.2608i	1.09029	+	0.792142i
$939$	31.8357	−	23.1300i	1.03892	−	0.754818i
$940$	−9.87425	+	30.3898i	−0.322063	+	0.991207i
$941$	9.02725	−	27.7830i	0.294280	−	0.905700i	−0.689183	−	0.724588i	$-0.742030\pi$
$941$	9.02725	−	27.7830i	0.294280	−	0.905700i	0.983462	−	0.181113i	$-0.0579698\pi$
$942$	24.5909	−	17.8663i	0.801215	−	0.582117i
$943$	−36.2699	−	26.3516i	−1.18111	−	0.858127i
$944$	−12.8008	−	39.3967i	−0.416629	−	1.28225i
$945$	0.437741			0.0142397
$946$		0			0
$947$	9.63809			0.313196			0.156598	−	0.987662i	$-0.449947\pi$
$947$	9.63809			0.313196			0.156598	+	0.987662i	$0.449947\pi$
$948$	17.8647	+	54.9819i	0.580218	+	1.78573i
$949$	11.5883	+	8.41941i	0.376173	+	0.273306i
$950$	−4.39378	+	3.19227i	−0.142553	+	0.103571i
$951$	−8.16183	+	25.1195i	−0.264666	+	0.814557i
$952$	11.5939	−	35.6823i	0.375760	−	1.15647i
$953$	4.22427	−	3.06912i	0.136838	−	0.0994184i	−0.517261	−	0.855828i	$-0.673048\pi$
$953$	4.22427	−	3.06912i	0.136838	−	0.0994184i	0.654098	+	0.756410i	$0.273048\pi$
$954$	−18.5367	−	13.4677i	−0.600148	−	0.436033i
$955$	0.00771200	+	0.0237351i	0.000249554	+	0.000768050i
$956$	50.1446			1.62179
$957$		0			0
$958$	−44.4529			−1.43621
$959$	11.6261	+	35.7816i	0.375428	+	1.15545i
$960$	−4.69969	−	3.41452i	−0.151682	−	0.110203i
$961$	14.3309	−	10.4120i	0.462286	−	0.335870i
$962$	−1.88041	+	5.78731i	−0.0606268	+	0.186590i
$963$	−14.8782	+	45.7904i	−0.479444	+	1.47558i
$964$	45.1246	−	32.7849i	1.45337	−	1.05593i
$965$	1.17894	+	0.856548i	0.0379513	+	0.0275733i
$966$	−35.3667	−	108.848i	−1.13791	−	3.50212i
$967$	−38.4583			−1.23674			−0.618368	−	0.785889i	$-0.712206\pi$
$967$	−38.4583			−1.23674			−0.618368	+	0.785889i	$0.712206\pi$
$968$		0			0
$969$	15.8737			0.509935
$970$	0.274331	+	0.844306i	0.00880825	+	0.0271090i
$971$	−35.3247	−	25.6649i	−1.13362	−	0.823626i	−0.147406	−	0.989076i	$-0.547092\pi$
$971$	−35.3247	−	25.6649i	−1.13362	−	0.823626i	−0.986218	+	0.165450i	$0.947092\pi$
$972$	−78.4832	+	57.0214i	−2.51735	+	1.82896i
$973$	10.9092	−	33.5752i	0.349734	−	1.07637i
$974$	−5.29188	+	16.2867i	−0.169563	+	0.521860i
$975$	−2.57128	+	1.86814i	−0.0823468	+	0.0598285i
$976$	−2.59285	−	1.88381i	−0.0829951	−	0.0602994i
$977$	−3.62994	−	11.1718i	−0.116132	−	0.357418i	0.876049	−	0.482221i	$-0.160170\pi$
$977$	−3.62994	−	11.1718i	−0.116132	−	0.357418i	−0.992181	+	0.124804i	$0.960170\pi$
$978$	−43.8137			−1.40101
$979$		0			0
$980$	−11.4457			−0.365618
$981$	−10.9690	−	33.7592i	−0.350214	−	1.07785i
$982$	−1.05921	−	0.769561i	−0.0338007	−	0.0245577i
$983$	−7.56584	+	5.49690i	−0.241313	+	0.175324i	−0.701868	−	0.712307i	$-0.747650\pi$
$983$	−7.56584	+	5.49690i	−0.241313	+	0.175324i	0.460555	+	0.887631i	$0.347650\pi$
$984$	23.3225	−	71.7792i	0.743493	−	2.28824i
$985$	−7.01553	+	21.5916i	−0.223533	+	0.687965i
$986$	3.74273	−	2.71925i	0.119193	−	0.0865987i
$987$	30.5264	+	22.1787i	0.971665	+	0.705956i
$988$	3.74589	+	11.5287i	0.119173	+	0.366776i
$989$	−45.4117			−1.44401
$990$		0			0
$991$	−32.3450			−1.02747			−0.513737	−	0.857948i	$-0.671739\pi$
$991$	−32.3450			−1.02747			−0.513737	+	0.857948i	$0.671739\pi$
$992$	4.64119	+	14.2841i	0.147358	+	0.453521i
$993$	−17.6537	−	12.8261i	−0.560222	−	0.407025i
$994$	48.3338	−	35.1165i	1.53305	−	1.11383i
$995$	−2.04827	+	6.30392i	−0.0649345	+	0.199848i
$996$	36.1534	−	111.269i	1.14557	−	3.52569i
$997$	−23.5565	+	17.1148i	−0.746040	+	0.542030i	−0.894597	−	0.446874i	$-0.852537\pi$
$997$	−23.5565	+	17.1148i	−0.746040	+	0.542030i	0.148557	+	0.988904i	$0.452537\pi$
$998$	44.6480	+	32.4387i	1.41331	+	1.02683i
$999$	0.120878	+	0.372023i	0.00382440	+	0.0117703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.g.511.1		8
11.2	odd	10		605.2.g.j.251.2		8
11.3	even	5		605.2.a.i.1.1		4
11.4	even	5		605.2.g.n.366.2		8
11.5	even	5		605.2.g.n.81.2		8
11.6	odd	10		55.2.g.a.26.1	✓	8
11.7	odd	10		55.2.g.a.36.1	yes	8
11.8	odd	10		605.2.a.l.1.4		4
11.9	even	5	inner	605.2.g.g.251.1		8
11.10	odd	2		605.2.g.j.511.2		8
33.8	even	10		5445.2.a.bg.1.1		4
33.14	odd	10		5445.2.a.bu.1.4		4
33.17	even	10		495.2.n.f.136.2		8
33.29	even	10		495.2.n.f.91.2		8
44.3	odd	10		9680.2.a.cv.1.4		4
44.7	even	10		880.2.bo.e.641.2		8
44.19	even	10		9680.2.a.cs.1.4		4
44.39	even	10		880.2.bo.e.81.2		8
55.7	even	20		275.2.z.b.124.1		16
55.14	even	10		3025.2.a.be.1.4		4
55.17	even	20		275.2.z.b.224.4		16
55.18	even	20		275.2.z.b.124.4		16
55.19	odd	10		3025.2.a.v.1.1		4
55.28	even	20		275.2.z.b.224.1		16
55.29	odd	10		275.2.h.b.201.2		8
55.39	odd	10		275.2.h.b.26.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	11.6	odd	10
55.2.g.a.36.1	yes	8	11.7	odd	10
275.2.h.b.26.2		8	55.39	odd	10
275.2.h.b.201.2		8	55.29	odd	10
275.2.z.b.124.1		16	55.7	even	20
275.2.z.b.124.4		16	55.18	even	20
275.2.z.b.224.1		16	55.28	even	20
275.2.z.b.224.4		16	55.17	even	20
495.2.n.f.91.2		8	33.29	even	10
495.2.n.f.136.2		8	33.17	even	10
605.2.a.i.1.1		4	11.3	even	5
605.2.a.l.1.4		4	11.8	odd	10
605.2.g.g.251.1		8	11.9	even	5	inner
605.2.g.g.511.1		8	1.1	even	1	trivial
605.2.g.j.251.2		8	11.2	odd	10
605.2.g.j.511.2		8	11.10	odd	2
605.2.g.n.81.2		8	11.5	even	5
605.2.g.n.366.2		8	11.4	even	5
880.2.bo.e.81.2		8	44.39	even	10
880.2.bo.e.641.2		8	44.7	even	10
3025.2.a.v.1.1		4	55.19	odd	10
3025.2.a.be.1.4		4	55.14	even	10
5445.2.a.bg.1.1		4	33.8	even	10
5445.2.a.bu.1.4		4	33.14	odd	10
9680.2.a.cs.1.4		4	44.19	even	10
9680.2.a.cv.1.4		4	44.3	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780121 - 2.40097i) q^{2} +(1.99563 + 1.44991i) q^{3} +(-3.53801 + 2.57052i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.92435 - 5.92254i) q^{6} +(1.69369 - 1.23053i) q^{7} +(4.84703 + 3.52157i) q^{8} +(0.953245 + 2.93379i) q^{9} +O(q^{10})\)	\(q+(-0.780121 - 2.40097i) q^{2} +(1.99563 + 1.44991i) q^{3} +(-3.53801 + 2.57052i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.92435 - 5.92254i) q^{6} +(1.69369 - 1.23053i) q^{7} +(4.84703 + 3.52157i) q^{8} +(0.953245 + 2.93379i) q^{9} -2.52452 q^{10} -10.7876 q^{12} +(-0.398155 - 1.22539i) q^{13} +(-4.27575 - 3.10651i) q^{14} +(1.99563 - 1.44991i) q^{15} +(1.97110 - 6.06643i) q^{16} +(0.924349 - 2.84485i) q^{17} +(6.30027 - 4.57742i) q^{18} +(1.74044 + 1.26450i) q^{19} +(1.35140 + 4.15918i) q^{20} +5.16413 q^{21} +8.77882 q^{23} +(4.56691 + 14.0555i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-2.63152 + 1.91191i) q^{26} +(-0.0646137 + 0.198861i) q^{27} +(-2.82917 + 8.70729i) q^{28} +(-0.495628 + 0.360095i) q^{29} +(-5.03801 - 3.66033i) q^{30} +(-1.12637 - 3.46661i) q^{31} -4.12048 q^{32} -7.55150 q^{34} +(-0.646930 - 1.99105i) q^{35} +(-10.9139 - 7.92944i) q^{36} +(1.51349 - 1.09961i) q^{37} +(1.67828 - 5.16520i) q^{38} +(0.982141 - 3.02272i) q^{39} +(4.84703 - 3.52157i) q^{40} +(-4.13152 - 3.00173i) q^{41} +(-4.02864 - 12.3989i) q^{42} -5.17287 q^{43} +3.08477 q^{45} +(-6.84854 - 21.0776i) q^{46} +(5.91123 + 4.29476i) q^{47} +(12.7294 - 9.24842i) q^{48} +(-0.808764 + 2.48912i) q^{49} +(-0.780121 + 2.40097i) q^{50} +(5.96943 - 4.33705i) q^{51} +(4.55857 + 3.31200i) q^{52} +(-0.909192 - 2.79821i) q^{53} +0.527864 q^{54} +12.5428 q^{56} +(1.63986 + 5.04696i) q^{57} +(1.25122 + 0.909068i) q^{58} +(5.25393 - 3.81720i) q^{59} +(-3.33354 + 10.2596i) q^{60} +(0.155265 - 0.477858i) q^{61} +(-7.44450 + 5.40875i) q^{62} +(5.22462 + 3.79591i) q^{63} +(-0.727733 - 2.23973i) q^{64} -1.28846 q^{65} -7.80964 q^{67} +(4.04238 + 12.4412i) q^{68} +(17.5193 + 12.7285i) q^{69} +(-4.27575 + 3.10651i) q^{70} +(-3.49318 + 10.7509i) q^{71} +(-5.71114 + 17.5771i) q^{72} +(-8.99396 + 6.53449i) q^{73} +(-3.82083 - 2.77600i) q^{74} +(-0.762262 - 2.34600i) q^{75} -9.40812 q^{76} -8.02363 q^{78} +(-1.65604 - 5.09678i) q^{79} +(-5.16042 - 3.74926i) q^{80} +(7.06961 - 5.13637i) q^{81} +(-3.98395 + 12.2613i) q^{82} +(-3.35140 + 10.3145i) q^{83} +(-18.2707 + 13.2745i) q^{84} +(-2.41998 - 1.75822i) q^{85} +(4.03546 + 12.4199i) q^{86} -1.51119 q^{87} -4.32336 q^{89} +(-2.40649 - 7.40641i) q^{90} +(-2.18224 - 1.58549i) q^{91} +(-31.0596 + 22.5661i) q^{92} +(2.77845 - 8.55119i) q^{93} +(5.70010 - 17.5431i) q^{94} +(1.74044 - 1.26450i) q^{95} +(-8.22295 - 5.97432i) q^{96} +(-0.108667 - 0.334441i) q^{97} +6.60723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9	\( 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9} - 6 q^{10} - 28 q^{12} + 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} + 4 q^{17} + 16 q^{18} + 11 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} + 10 q^{24} - 2 q^{25} + q^{26} - 5 q^{27} + 11 q^{28} + 11 q^{29} - 13 q^{30} - 9 q^{31} - 12 q^{32} - 20 q^{34} + 3 q^{35} - 29 q^{36} - q^{37} - 6 q^{38} + 6 q^{39} + 7 q^{40} - 11 q^{41} - 31 q^{42} - 42 q^{43} - 29 q^{46} - q^{47} + 21 q^{48} - q^{50} + 22 q^{51} + q^{52} + 8 q^{53} + 40 q^{54} + 30 q^{56} + 4 q^{58} + 26 q^{59} - 8 q^{60} + 2 q^{61} - 27 q^{62} + 4 q^{63} + 21 q^{64} - 14 q^{65} - 2 q^{67} + 20 q^{68} + 49 q^{69} - 14 q^{70} - 25 q^{71} - 21 q^{72} - 32 q^{73} + 12 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} + 23 q^{79} - 20 q^{80} + 20 q^{81} + 42 q^{82} - 10 q^{83} - 51 q^{84} - q^{85} + 34 q^{86} - 30 q^{87} - 14 q^{90} + 8 q^{91} - 99 q^{92} - 8 q^{93} + 22 q^{94} + 11 q^{95} - 3 q^{96} - 18 q^{97} + 84 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9 - 6 * q^10 - 28 * q^12 + 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 + 4 * q^17 + 16 * q^18 + 11 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 + 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 + 11 * q^28 + 11 * q^29 - 13 * q^30 - 9 * q^31 - 12 * q^32 - 20 * q^34 + 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 + 6 * q^39 + 7 * q^40 - 11 * q^41 - 31 * q^42 - 42 * q^43 - 29 * q^46 - q^47 + 21 * q^48 - q^50 + 22 * q^51 + q^52 + 8 * q^53 + 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 + 2 * q^61 - 27 * q^62 + 4 * q^63 + 21 * q^64 - 14 * q^65 - 2 * q^67 + 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 - 21 * q^72 - 32 * q^73 + 12 * q^74 + q^75 - 16 * q^76 + 12 * q^78 + 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 - 10 * q^83 - 51 * q^84 - q^85 + 34 * q^86 - 30 * q^87 - 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 + 22 * q^94 + 11 * q^95 - 3 * q^96 - 18 * q^97 + 84 * q^98

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