LMFDB - Embedded newform 160.2.z.a.29.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(29,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("160.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.z (of order $8$, 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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.18
Character	$\chi$	$=$	160.29
Dual form			160.2.z.a.149.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08863 - 0.902710i) q^{2} +(0.624514 - 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(0.221383 + 2.22508i) q^{5} +(-0.681161 - 2.20509i) q^{6} +(-0.611546 - 0.611546i) q^{7} +(-1.37117 - 2.47384i) q^{8} +(0.238149 + 0.238149i) q^{9} +O(q^{10})$	\(q+(1.08863 - 0.902710i) q^{2} +(0.624514 - 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(0.221383 + 2.22508i) q^{5} +(-0.681161 - 2.20509i) q^{6} +(-0.611546 - 0.611546i) q^{7} +(-1.37117 - 2.47384i) q^{8} +(0.238149 + 0.238149i) q^{9} +(2.24961 + 2.22245i) q^{10} +(-4.25876 + 1.76403i) q^{11} +(-2.73209 - 1.78564i) q^{12} +(4.13489 + 1.71273i) q^{13} +(-1.21779 - 0.113698i) q^{14} +(3.49303 + 1.05581i) q^{15} +(-3.72586 - 1.45532i) q^{16} -4.50676 q^{17} +(0.474235 + 0.0442765i) q^{18} +(0.256449 - 0.619122i) q^{19} +(4.45521 + 0.388676i) q^{20} +(-1.30395 + 0.540115i) q^{21} +(-3.04380 + 5.76480i) q^{22} +(0.846443 - 0.846443i) q^{23} +(-4.58615 + 0.522387i) q^{24} +(-4.90198 + 0.985190i) q^{25} +(6.04746 - 1.86808i) q^{26} +(5.03092 - 2.08387i) q^{27} +(-1.42836 + 0.975541i) q^{28} +(7.97948 + 3.30521i) q^{29} +(4.75571 - 2.00381i) q^{30} +5.35031 q^{31} +(-5.36982 + 1.77907i) q^{32} +7.52263i q^{33} +(-4.90620 + 4.06830i) q^{34} +(1.22535 - 1.49612i) q^{35} +(0.556235 - 0.379896i) q^{36} +(-6.33734 + 2.62501i) q^{37} +(-0.279710 - 0.905493i) q^{38} +(5.16459 - 5.16459i) q^{39} +(5.20094 - 3.59864i) q^{40} +(-5.53167 - 5.53167i) q^{41} +(-0.931954 + 1.76508i) q^{42} +(0.793372 + 1.91537i) q^{43} +(1.89038 + 9.02340i) q^{44} +(-0.477178 + 0.582622i) q^{45} +(0.157370 - 1.68556i) q^{46} -10.7288 q^{47} +(-4.52105 + 4.70865i) q^{48} -6.25202i q^{49} +(-4.44710 + 5.49757i) q^{50} +(-2.81454 + 6.79489i) q^{51} +(4.89710 - 7.49275i) q^{52} +(-0.169544 - 0.409316i) q^{53} +(3.59567 - 6.81003i) q^{54} +(-4.86794 - 9.08556i) q^{55} +(-0.674329 + 2.35140i) q^{56} +(-0.773300 - 0.773300i) q^{57} +(11.6703 - 3.60501i) q^{58} +(0.711433 + 1.71755i) q^{59} +(3.36835 - 6.47444i) q^{60} +(0.0780876 + 0.0323449i) q^{61} +(5.82451 - 4.82978i) q^{62} -0.291277i q^{63} +(-4.23976 + 6.78413i) q^{64} +(-2.89556 + 9.57963i) q^{65} +(6.79076 + 8.18936i) q^{66} +(0.479290 - 1.15711i) q^{67} +(-1.66853 + 8.85774i) q^{68} +(-0.747575 - 1.80481i) q^{69} +(-0.0166110 - 2.73486i) q^{70} +(2.14664 - 2.14664i) q^{71} +(0.262598 - 0.915684i) q^{72} +(3.71274 - 3.71274i) q^{73} +(-4.52939 + 8.57845i) q^{74} +(-1.57597 + 8.00603i) q^{75} +(-1.12190 - 0.733250i) q^{76} +(3.68321 + 1.52564i) q^{77} +(0.960198 - 10.2845i) q^{78} -9.02383i q^{79} +(2.41337 - 8.61253i) q^{80} -7.87619i q^{81} +(-11.0154 - 1.02845i) q^{82} +(-12.3092 - 5.09863i) q^{83} +(0.578799 + 2.76280i) q^{84} +(-0.997720 - 10.0279i) q^{85} +(2.59271 + 1.36894i) q^{86} +(9.96659 - 9.96659i) q^{87} +(10.2034 + 8.11668i) q^{88} +(-3.03609 + 3.03609i) q^{89} +(0.00646867 + 1.06501i) q^{90} +(-1.48126 - 3.57608i) q^{91} +(-1.35025 - 1.97701i) q^{92} +(3.34134 - 8.06672i) q^{93} +(-11.6797 + 9.68500i) q^{94} +(1.43437 + 0.433556i) q^{95} +(-0.671207 + 9.20718i) q^{96} -9.11036i q^{97} +(-5.64377 - 6.80614i) q^{98} +(-1.43432 - 0.594114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	1.08863	−	0.902710i	0.769777	−	0.638312i
$2$	1.08863	−	0.902710i	0.769777	−	0.638312i
$3$	0.624514	−	1.50771i	0.360563	−	0.870477i	−0.634655	−	0.772796i	$-0.718858\pi$
$3$	0.624514	−	1.50771i	0.360563	−	0.870477i	0.995218	−	0.0976808i	$-0.0311424\pi$
$4$	0.370229	−	1.96543i	0.185114	−	0.982717i
$5$	0.221383	+	2.22508i	0.0990054	+	0.995087i
$5$	0.221383	+	2.22508i	0.0990054	+	0.995087i
$6$	−0.681161	−	2.20509i	−0.278083	−	0.900225i
$7$	−0.611546	−	0.611546i	−0.231142	−	0.231142i	0.582027	−	0.813169i	$-0.302260\pi$
$7$	−0.611546	−	0.611546i	−0.231142	−	0.231142i	−0.813169	+	0.582027i	$0.802260\pi$
$8$	−1.37117	−	2.47384i	−0.484784	−	0.874634i
$9$	0.238149	+	0.238149i	0.0793828	+	0.0793828i
$10$	2.24961	+	2.22245i	0.711388	+	0.702799i
$11$	−4.25876	+	1.76403i	−1.28406	+	0.531877i	−0.917211	−	0.398403i	$-0.869565\pi$
$11$	−4.25876	+	1.76403i	−1.28406	+	0.531877i	−0.366853	+	0.930279i	$0.619565\pi$
$12$	−2.73209	−	1.78564i	−0.788687	−	0.515469i
$13$	4.13489	+	1.71273i	1.14681	+	0.475025i	0.873463	−	0.486890i	$-0.161869\pi$
$13$	4.13489	+	1.71273i	1.14681	+	0.475025i	0.273348	+	0.961915i	$0.411869\pi$
$14$	−1.21779	−	0.113698i	−0.325469	−	0.0303871i
$15$	3.49303	+	1.05581i	0.901898	+	0.272610i
$16$	−3.72586	−	1.45532i	−0.931465	−	0.363830i
$17$	−4.50676			−1.09305			−0.546525	−	0.837443i	$-0.684050\pi$
$17$	−4.50676			−1.09305			−0.546525	+	0.837443i	$0.684050\pi$
$18$	0.474235	+	0.0442765i	0.111778	+	0.0104361i
$19$	0.256449	−	0.619122i	0.0588334	−	0.142036i	−0.891729	−	0.452569i	$-0.850508\pi$
$19$	0.256449	−	0.619122i	0.0588334	−	0.142036i	0.950563	+	0.310533i	$0.100508\pi$
$20$	4.45521	+	0.388676i	0.996216	+	0.0869107i
$21$	−1.30395	+	0.540115i	−0.284546	+	0.117863i
$22$	−3.04380	+	5.76480i	−0.648940	+	1.22906i
$23$	0.846443	−	0.846443i	0.176496	−	0.176496i	−0.613331	−	0.789826i	$-0.710171\pi$
$23$	0.846443	−	0.846443i	0.176496	−	0.176496i	0.789826	+	0.613331i	$0.210171\pi$
$24$	−4.58615	+	0.522387i	−0.936144	+	0.106632i
$25$	−4.90198	+	0.985190i	−0.980396	+	0.197038i
$26$	6.04746	−	1.86808i	1.18600	−	0.366361i
$27$	5.03092	−	2.08387i	0.968200	−	0.401042i
$28$	−1.42836	+	0.975541i	−0.269935	+	0.184360i
$29$	7.97948	+	3.30521i	1.48175	+	0.613762i	0.969504	−	0.245075i	$-0.0788127\pi$
$29$	7.97948	+	3.30521i	1.48175	+	0.613762i	0.512248	+	0.858837i	$0.328813\pi$
$30$	4.75571	−	2.00381i	0.868271	−	0.365844i
$31$	5.35031			0.960945			0.480472	−	0.877010i	$-0.340465\pi$
$31$	5.35031			0.960945			0.480472	+	0.877010i	$0.340465\pi$
$32$	−5.36982	+	1.77907i	−0.949258	+	0.314498i
$33$			7.52263i			1.30952i
$34$	−4.90620	+	4.06830i	−0.841406	+	0.697708i
$35$	1.22535	−	1.49612i	0.207123	−	0.252891i
$36$	0.556235	−	0.379896i	0.0927058	−	0.0633160i
$37$	−6.33734	+	2.62501i	−1.04185	+	0.431550i	−0.836977	−	0.547238i	$-0.815679\pi$
$37$	−6.33734	+	2.62501i	−1.04185	+	0.431550i	−0.204876	+	0.978788i	$0.565679\pi$
$38$	−0.279710	−	0.905493i	−0.0453749	−	0.146890i
$39$	5.16459	−	5.16459i	0.826996	−	0.826996i
$40$	5.20094	−	3.59864i	0.822341	−	0.568995i
$41$	−5.53167	−	5.53167i	−0.863902	−	0.863902i	0.127887	−	0.991789i	$-0.459181\pi$
$41$	−5.53167	−	5.53167i	−0.863902	−	0.863902i	−0.991789	+	0.127887i	$0.959181\pi$
$42$	−0.931954	+	1.76508i	−0.143804	+	0.272357i
$43$	0.793372	+	1.91537i	0.120988	+	0.292091i	0.972757	−	0.231826i	$-0.0744701\pi$
$43$	0.793372	+	1.91537i	0.120988	+	0.292091i	−0.851769	+	0.523917i	$0.824470\pi$
$44$	1.89038	+	9.02340i	0.284985	+	1.36033i
$45$	−0.477178	+	0.582622i	−0.0711335	+	0.0868522i
$46$	0.157370	−	1.68556i	0.0232030	−	0.248522i
$47$	−10.7288			−1.56496			−0.782479	−	0.622678i	$-0.786045\pi$
$47$	−10.7288			−1.56496			−0.782479	+	0.622678i	$0.786045\pi$
$48$	−4.52105	+	4.70865i	−0.652558	+	0.679635i
$49$		−	6.25202i		−	0.893146i
$50$	−4.44710	+	5.49757i	−0.628915	+	0.777474i
$51$	−2.81454	+	6.79489i	−0.394114	+	0.951475i
$52$	4.89710	−	7.49275i	0.679106	−	1.03906i
$53$	−0.169544	−	0.409316i	−0.0232887	−	0.0562239i	0.911807	−	0.410618i	$-0.134687\pi$
$53$	−0.169544	−	0.409316i	−0.0232887	−	0.0562239i	−0.935096	+	0.354394i	$0.884687\pi$
$54$	3.59567	−	6.81003i	0.489309	−	0.926727i
$55$	−4.86794	−	9.08556i	−0.656393	−	1.22510i
$56$	−0.674329	+	2.35140i	−0.0901110	+	0.314219i
$57$	−0.773300	−	0.773300i	−0.102426	−	0.102426i
$58$	11.6703	−	3.60501i	1.53239	−	0.473361i
$59$	0.711433	+	1.71755i	0.0926207	+	0.223606i	0.963400	−	0.268068i	$-0.0863851\pi$
$59$	0.711433	+	1.71755i	0.0926207	+	0.223606i	−0.870779	+	0.491674i	$0.836385\pi$
$60$	3.36835	−	6.47444i	0.434853	−	0.835846i
$61$	0.0780876	+	0.0323449i	0.00999809	+	0.00414134i	0.387677	−	0.921795i	$-0.373278\pi$
$61$	0.0780876	+	0.0323449i	0.00999809	+	0.00414134i	−0.377679	+	0.925937i	$0.623278\pi$
$62$	5.82451	−	4.82978i	0.739713	−	0.613383i
$63$		−	0.291277i		−	0.0366975i
$64$	−4.23976	+	6.78413i	−0.529970	+	0.848017i
$65$	−2.89556	+	9.57963i	−0.359150	+	1.18821i
$66$	6.79076	+	8.18936i	0.835885	+	1.00804i
$67$	0.479290	−	1.15711i	0.0585546	−	0.141363i	−0.891894	−	0.452244i	$-0.850624\pi$
$67$	0.479290	−	1.15711i	0.0585546	−	0.141363i	0.950449	+	0.310880i	$0.100624\pi$
$68$	−1.66853	+	8.85774i	−0.202339	+	1.07416i
$69$	−0.747575	−	1.80481i	−0.0899975	−	0.217273i
$70$	−0.0166110	−	2.73486i	−0.00198539	−	0.326879i
$71$	2.14664	−	2.14664i	0.254759	−	0.254759i	−0.568159	−	0.822919i	$-0.692344\pi$
$71$	2.14664	−	2.14664i	0.254759	−	0.254759i	0.822919	+	0.568159i	$0.192344\pi$
$72$	0.262598	−	0.915684i	0.0309474	−	0.107914i
$73$	3.71274	−	3.71274i	0.434543	−	0.434543i	−0.455628	−	0.890170i	$-0.650585\pi$
$73$	3.71274	−	3.71274i	0.434543	−	0.434543i	0.890170	+	0.455628i	$0.150585\pi$
$74$	−4.52939	+	8.57845i	−0.526531	+	0.997225i
$75$	−1.57597	+	8.00603i	−0.181978	+	0.924456i
$76$	−1.12190	−	0.733250i	−0.128691	−	0.0841095i
$77$	3.68321	+	1.52564i	0.419741	+	0.173862i
$78$	0.960198	−	10.2845i	0.108721	−	1.16448i
$79$		−	9.02383i		−	1.01526i	−0.861575	−	0.507630i	$-0.830522\pi$
$79$		−	9.02383i		−	1.01526i	0.861575	−	0.507630i	$-0.169478\pi$
$80$	2.41337	−	8.61253i	0.269823	−	0.962910i
$81$		−	7.87619i		−	0.875132i
$82$	−11.0154	−	1.02845i	−1.21645	−	0.113573i
$83$	−12.3092	−	5.09863i	−1.35111	−	0.559648i	−0.414508	−	0.910045i	$-0.636046\pi$
$83$	−12.3092	−	5.09863i	−1.35111	−	0.559648i	−0.936601	+	0.350398i	$0.886046\pi$
$84$	0.578799	+	2.76280i	0.0631521	+	0.301446i
$85$	−0.997720	−	10.0279i	−0.108218	−	1.08768i
$86$	2.59271	+	1.36894i	0.279579	+	0.147617i
$87$	9.96659	−	9.96659i	1.06853	−	1.06853i
$88$	10.2034	+	8.11668i	1.08769	+	0.865241i
$89$	−3.03609	+	3.03609i	−0.321825	+	0.321825i	−0.849467	−	0.527642i	$-0.823076\pi$
$89$	−3.03609	+	3.03609i	−0.321825	+	0.321825i	0.527642	+	0.849467i	$0.323076\pi$
$90$	0.00646867	+	1.06501i	0.000681858	+	0.112262i
$91$	−1.48126	−	3.57608i	−0.155278	−	0.374875i
$92$	−1.35025	−	1.97701i	−0.140773	−	0.206117i
$93$	3.34134	−	8.06672i	0.346481	−	0.836480i
$94$	−11.6797	+	9.68500i	−1.20467	+	0.998932i
$95$	1.43437	+	0.433556i	0.147163	+	0.0444819i
$96$	−0.671207	+	9.20718i	−0.0685048	+	0.939704i
$97$		−	9.11036i		−	0.925017i	−0.886615	−	0.462509i	$-0.846949\pi$
$97$		−	9.11036i		−	0.925017i	0.886615	−	0.462509i	$-0.153051\pi$
$98$	−5.64377	−	6.80614i	−0.570106	−	0.687524i
$99$	−1.43432	−	0.594114i	−0.144154	−	0.0597107i
$100$	0.121471	+	9.99926i	0.0121471	+	0.999926i
$101$	5.13422	+	12.3951i	0.510874	+	1.23336i	0.943376	+	0.331726i	$0.107631\pi$
$101$	5.13422	+	12.3951i	0.510874	+	1.23336i	−0.432502	+	0.901633i	$0.642369\pi$
$102$	3.06983	+	9.93783i	0.303958	+	0.983992i
$103$	−4.92485	−	4.92485i	−0.485259	−	0.485259i	0.421547	−	0.906807i	$-0.361487\pi$
$103$	−4.92485	−	4.92485i	−0.485259	−	0.485259i	−0.906807	+	0.421547i	$0.861487\pi$
$104$	−1.43264	−	12.5775i	−0.140482	−	1.23332i
$105$	−1.49047	−	2.78183i	−0.145455	−	0.271479i
$106$	−0.554065	−	0.292544i	−0.0538155	−	0.0284144i
$107$	7.64337	+	18.4527i	0.738913	+	1.78389i	0.610256	+	0.792204i	$0.291067\pi$
$107$	7.64337	+	18.4527i	0.738913	+	1.78389i	0.128657	+	0.991689i	$0.458933\pi$
$108$	−2.23313	−	10.6594i	−0.214883	−	1.02571i
$109$	3.93470	−	9.49920i	0.376876	−	0.909858i	−0.615672	−	0.788002i	$-0.711115\pi$
$109$	3.93470	−	9.49920i	0.376876	−	0.909858i	0.992548	−	0.121856i	$-0.0388846\pi$
$110$	−13.5010	−	5.49647i	−1.28727	−	0.524068i
$111$			11.1942i			1.06251i
$112$	1.38854	+	3.16853i	0.131205	+	0.299398i
$113$	10.8052			1.01647			0.508233	−	0.861220i	$-0.330299\pi$
$113$	10.8052			1.01647			0.508233	+	0.861220i	$0.330299\pi$
$114$	−1.53990	−	0.143772i	−0.144225	−	0.0134654i
$115$	2.07079	+	1.69602i	0.193102	+	0.158154i
$116$	9.45040	−	14.4595i	0.877448	−	1.34253i
$117$	0.576834	+	1.39260i	0.0533283	+	0.128746i
$118$	2.32494	+	1.22756i	0.214028	+	0.113006i
$119$	2.75609	+	2.75609i	0.252650	+	0.252650i
$120$	−2.17765	−	10.0889i	−0.198791	−	0.920987i
$121$	7.24702	−	7.24702i	0.658820	−	0.658820i
$122$	0.114207	−	0.0352788i	0.0103398	−	0.00319399i
$123$	−11.7948	+	4.88555i	−1.06350	+	0.440515i
$124$	1.98084	−	10.5157i	0.177885	−	0.944336i
$125$	−3.27734	−	10.6892i	−0.293134	−	0.956071i
$126$	−0.262939	−	0.317093i	−0.0234245	−	0.0282489i
$127$			18.1202i			1.60791i	0.594689	+	0.803956i	$0.297275\pi$
$127$			18.1202i			1.60791i	−0.594689	+	0.803956i	$0.702725\pi$
$128$	1.50858	+	11.2127i	0.133341	+	0.991070i
$129$	3.38329			0.297882
$130$	5.49543	+	13.0425i	0.481981	+	1.14391i
$131$	−12.7551	−	5.28333i	−1.11442	−	0.461607i	−0.251961	−	0.967737i	$-0.581075\pi$
$131$	−12.7551	−	5.28333i	−1.11442	−	0.461607i	−0.862457	+	0.506130i	$0.831075\pi$
$132$	14.7852	+	2.78510i	1.28689	+	0.242412i
$133$	−0.535451	+	0.221791i	−0.0464295	+	0.0192317i
$134$	−0.522764	−	1.69232i	−0.0451600	−	0.146194i
$135$	5.75055	+	10.7329i	0.494928	+	0.923738i
$136$	6.17956	+	11.1490i	0.529893	+	0.956019i
$137$	6.77568	−	6.77568i	0.578885	−	0.578885i	−0.355711	−	0.934596i	$-0.615761\pi$
$137$	6.77568	−	6.77568i	0.578885	−	0.578885i	0.934596	+	0.355711i	$0.115761\pi$
$138$	−2.44305	−	1.28992i	−0.207966	−	0.109805i
$139$	20.0431	−	8.30211i	1.70003	−	0.704176i	0.700079	−	0.714065i	$-0.253148\pi$
$139$	20.0431	−	8.30211i	1.70003	−	0.704176i	0.999951	+	0.00988962i	$0.00314801\pi$
$140$	−2.48687	−	2.96226i	−0.210179	−	0.250357i
$141$	−6.70029	+	16.1759i	−0.564266	+	1.36226i
$142$	0.399102	−	4.27469i	0.0334919	−	0.358724i
$143$	−20.6308			−1.72523
$144$	−0.540726	−	1.23389i	−0.0450605	−	0.102824i
$145$	−5.58784	+	18.4867i	−0.464045	+	1.53524i
$146$	0.690270	−	7.39332i	0.0571271	−	0.611875i
$147$	−9.42624	−	3.90448i	−0.777463	−	0.322036i
$148$	2.81302	+	13.4275i	0.231229	+	1.10373i
$149$	−3.33390	+	1.38095i	−0.273124	+	0.113131i	−0.515042	−	0.857165i	$-0.672223\pi$
$149$	−3.33390	+	1.38095i	−0.273124	+	0.113131i	0.241918	+	0.970297i	$0.422223\pi$
$150$	5.51147	+	10.1382i	0.450010	+	0.827784i
$151$	6.13023	+	6.13023i	0.498871	+	0.498871i	0.911087	−	0.412215i	$-0.135245\pi$
$151$	6.13023	+	6.13023i	0.498871	+	0.498871i	−0.412215	+	0.911087i	$0.635245\pi$
$152$	−1.88324	+	0.214512i	−0.152751	+	0.0173992i
$153$	−1.07328	−	1.07328i	−0.0867695	−	0.0867695i
$154$	5.38686	−	1.66402i	0.434086	−	0.134091i
$155$	1.18447	+	11.9049i	0.0951387	+	0.956223i
$156$	−8.23858	−	12.0627i	−0.659614	−	0.965792i
$157$	−3.66780	+	8.85486i	−0.292722	+	0.706695i	−1.00000		0.000241450i	$-0.999923\pi$
$157$	−3.66780	+	8.85486i	−0.292722	+	0.706695i	0.707277	+	0.706936i	$0.249923\pi$
$158$	−8.14590	−	9.82361i	−0.648053	−	0.781524i
$159$	−0.723013			−0.0573386
$160$	−5.14736	−	11.5544i	−0.406934	−	0.913457i
$161$	−1.03528			−0.0815912
$162$	−7.10992	−	8.57426i	−0.558608	−	0.673657i
$163$	−0.429458	+	1.03680i	−0.0336378	+	0.0812087i	−0.939806	−	0.341709i	$-0.888994\pi$
$163$	−0.429458	+	1.03680i	−0.0336378	+	0.0812087i	0.906168	+	0.422918i	$0.138994\pi$
$164$	−12.9201	+	8.82415i	−1.00889	+	0.689050i
$165$	−16.7385	+	1.66538i	−1.30309	+	0.129650i
$166$	−18.0027	+	5.56111i	−1.39728	+	0.431626i
$167$	1.04298	+	1.04298i	0.0807084	+	0.0807084i	0.746309	−	0.665600i	$-0.231824\pi$
$167$	1.04298	+	1.04298i	0.0807084	+	0.0807084i	−0.665600	+	0.746309i	$0.731824\pi$
$168$	3.12410	+	2.48518i	0.241030	+	0.191735i
$169$	4.97147	+	4.97147i	0.382421	+	0.382421i
$170$	−10.1384	−	10.0160i	−0.777584	−	0.768195i
$171$	0.208516	−	0.0863701i	0.0159456	−	0.00660489i
$172$	4.05826	−	0.850195i	0.309440	−	0.0648268i
$173$	19.4640	+	8.06226i	1.47982	+	0.612962i	0.969075	−	0.246768i	$-0.0793686\pi$
$173$	19.4640	+	8.06226i	1.47982	+	0.612962i	0.510748	+	0.859731i	$0.329369\pi$
$174$	1.85298	−	19.8469i	0.140474	−	1.50459i
$175$	3.60027	+	2.39530i	0.272155	+	0.181067i
$176$	18.4348	−	0.374691i	1.38957	−	0.0282434i
$177$	3.03387			0.228040
$178$	−0.564468	+	6.04589i	−0.0423087	+	0.453158i
$179$	−9.14150	+	22.0695i	−0.683267	+	1.64955i	0.0746555	+	0.997209i	$0.476214\pi$
$179$	−9.14150	+	22.0695i	−0.683267	+	1.64955i	−0.757923	+	0.652344i	$0.773786\pi$
$180$	0.968440	+	1.15357i	0.0721832	+	0.0859817i
$181$	−0.399581	+	0.165512i	−0.0297006	+	0.0123024i	−0.397484	−	0.917609i	$-0.630117\pi$
$181$	−0.399581	+	0.165512i	−0.0297006	+	0.0123024i	0.367784	+	0.929911i	$0.380117\pi$
$182$	−4.84071	−	2.55588i	−0.358817	−	0.189454i
$183$	0.0975335	−	0.0975335i	0.00720989	−	0.00720989i
$184$	−3.25458	−	0.933342i	−0.239931	−	0.0688069i
$185$	−7.24385	−	13.5200i	−0.532578	−	0.994008i
$186$	−3.64442	−	11.7979i	−0.267222	−	0.865067i
$187$	19.1932	−	7.95009i	1.40355	−	0.581368i
$188$	−3.97211	+	21.0868i	−0.289696	+	1.53791i
$189$	−4.35102	−	1.80225i	−0.316490	−	0.131094i
$190$	1.95287	−	0.822838i	0.141676	−	0.0596950i
$191$	5.99552			0.433820			0.216910	−	0.976192i	$-0.430402\pi$
$191$	5.99552			0.433820			0.216910	+	0.976192i	$0.430402\pi$
$192$	7.58072	+	10.6291i	0.547091	+	0.767090i
$193$			14.3427i			1.03241i	0.856466	+	0.516204i	$0.172655\pi$
$193$			14.3427i			1.03241i	−0.856466	+	0.516204i	$0.827345\pi$
$194$	−8.22402	−	9.91781i	−0.590450	−	0.712057i
$195$	12.6350	+	10.3483i	0.904810	+	0.741056i
$196$	−12.2879	−	2.31468i	−0.877710	−	0.165334i
$197$	19.9166	−	8.24973i	1.41900	−	0.587769i	0.464391	−	0.885630i	$-0.346273\pi$
$197$	19.9166	−	8.24973i	1.41900	−	0.587769i	0.954609	+	0.297861i	$0.0962733\pi$
$198$	−2.09775	+	0.648004i	−0.149081	+	0.0460516i
$199$	−15.5462	+	15.5462i	−1.10204	+	1.10204i	−0.107874	+	0.994165i	$0.534404\pi$
$199$	−15.5462	+	15.5462i	−1.10204	+	1.10204i	−0.994165	+	0.107874i	$0.965596\pi$
$200$	9.15867	+	10.7758i	0.647616	+	0.761967i
$201$	−1.44526	−	1.44526i	−0.101941	−	0.101941i
$202$	16.7784	+	8.85896i	1.18053	+	0.623314i
$203$	−2.85853	−	6.90110i	−0.200629	−	0.484362i
$204$	12.3129	+	8.04745i	0.862075	+	0.563434i
$205$	11.0838	−	13.5330i	0.774126	−	0.945188i
$206$	−9.80704	−	0.915625i	−0.683289	−	0.0637946i
$207$	0.403158			0.0280214
$208$	−12.9134	−	12.3990i	−0.895387	−	0.859714i
$209$			3.08907i			0.213676i
$210$	−4.13376	−	1.68292i	−0.285256	−	0.116132i
$211$	8.13089	−	19.6297i	0.559754	−	1.35136i	−0.350208	−	0.936672i	$-0.613889\pi$
$211$	8.13089	−	19.6297i	0.559754	−	1.35136i	0.909962	−	0.414693i	$-0.136111\pi$
$212$	−0.867254	+	0.181687i	−0.0595632	+	0.0124783i
$213$	−1.89590	−	4.57711i	−0.129905	−	0.313619i
$214$	24.9783	+	13.1884i	1.70748	+	0.901544i
$215$	−4.08622	+	2.18935i	−0.278678	+	0.149312i
$216$	−12.0534	−	9.58832i	−0.820132	−	0.652403i
$217$	−3.27196	−	3.27196i	−0.222115	−	0.222115i
$218$	−4.29160	−	13.8930i	−0.290664	−	0.940953i
$219$	−3.27907	−	7.91638i	−0.221579	−	0.534940i
$220$	−19.6593	+	6.20387i	−1.32543	+	0.418265i
$221$	−18.6350	−	7.71885i	−1.25352	−	0.519226i
$222$	10.1051	+	12.1864i	0.678213	+	0.817896i
$223$			0.0197422i			0.00132204i	1.00000		0.000661019i	$0.000210409\pi$
$223$			0.0197422i			0.00132204i	−1.00000		0.000661019i	$0.999790\pi$
$224$	4.37187	+	2.19591i	0.292108	+	0.146720i
$225$	−1.40202	−	0.932778i	−0.0934680	−	0.0621852i
$226$	11.7628	−	9.75395i	0.782453	−	0.648823i
$227$	5.26664	−	12.7148i	0.349559	−	0.843910i	−0.647113	−	0.762394i	$-0.724024\pi$
$227$	5.26664	−	12.7148i	0.349559	−	0.843910i	0.996672	−	0.0815159i	$-0.0259761\pi$
$228$	−1.80617	+	1.23357i	−0.119616	+	0.0816954i
$229$	−1.80969	−	4.36899i	−0.119588	−	0.288711i	0.852738	−	0.522339i	$-0.174940\pi$
$229$	−1.80969	−	4.36899i	−0.119588	−	0.288711i	−0.972326	+	0.233628i	$0.924940\pi$
$230$	3.78534	−	0.0229914i	0.249598	−	0.00151601i
$231$	4.60043	−	4.60043i	0.302686	−	0.302686i
$232$	−2.76471	−	24.2720i	−0.181512	−	1.59353i
$233$	12.3958	−	12.3958i	0.812073	−	0.812073i	−0.172871	−	0.984944i	$-0.555304\pi$
$233$	12.3958	−	12.3958i	0.812073	−	0.812073i	0.984944	+	0.172871i	$0.0553045\pi$
$234$	1.88507	+	0.995312i	0.123231	+	0.0650656i
$235$	−2.37517	−	23.8725i	−0.154939	−	1.55727i
$236$	3.63913	−	0.762388i	0.236887	−	0.0496272i
$237$	−13.6053	−	5.63551i	−0.883760	−	0.366066i
$238$	5.48831	+	0.512411i	0.355755	+	0.0332147i
$239$			1.44231i			0.0932956i	0.998911	+	0.0466478i	$0.0148538\pi$
$239$			1.44231i			0.0932956i	−0.998911	+	0.0466478i	$0.985146\pi$
$240$	−11.4780	−	9.01730i	−0.740903	−	0.582064i
$241$			13.6482i			0.879159i	0.898204	+	0.439579i	$0.144872\pi$
$241$			13.6482i			0.879159i	−0.898204	+	0.439579i	$0.855128\pi$
$242$	1.34736	−	14.4313i	0.0866117	−	0.927677i
$243$	3.21773	+	1.33283i	0.206418	+	0.0855010i
$244$	0.0924821	−	0.141501i	0.00592056	−	0.00905867i
$245$	13.9113	−	1.38409i	0.888758	−	0.0884263i
$246$	−8.42989	+	15.9658i	−0.537470	+	1.01794i
$247$	2.12077	−	2.12077i	0.134942	−	0.134942i
$248$	−7.33621	−	13.2358i	−0.465850	−	0.840475i
$249$	−15.3745	+	15.3745i	−0.974321	+	0.974321i
$250$	−13.2171	−	8.67809i	−0.835920	−	0.548851i
$251$	−4.45278	−	10.7500i	−0.281057	−	0.678532i	0.718804	−	0.695213i	$-0.244690\pi$
$251$	−4.45278	−	10.7500i	−0.281057	−	0.678532i	−0.999861	+	0.0166810i	$0.994690\pi$
$252$	−0.572486	−	0.107839i	−0.0360632	−	0.00679324i
$253$	−2.11164	+	5.09795i	−0.132758	+	0.320505i
$254$	16.3573	+	19.7262i	1.02635	+	1.23773i
$255$	−15.7423	−	4.75830i	−0.985820	−	0.297976i
$256$	11.7641	+	10.8446i	0.735255	+	0.677790i
$257$			5.86206i			0.365665i	0.983144	+	0.182833i	$0.0585266\pi$
$257$			5.86206i			0.365665i	−0.983144	+	0.182833i	$0.941473\pi$
$258$	3.68315	−	3.05413i	0.229303	−	0.190142i
$259$	5.48089	+	2.27026i	0.340566	+	0.141067i
$260$	17.7561	+	9.23769i	1.10119	+	0.572897i
$261$	1.11317	+	2.68743i	0.0689035	+	0.166348i
$262$	−18.6549	+	5.76256i	−1.15250	+	0.356012i
$263$	6.13543	+	6.13543i	0.378327	+	0.378327i	0.870498	−	0.492171i	$-0.163797\pi$
$263$	6.13543	+	6.13543i	0.378327	+	0.378327i	−0.492171	+	0.870498i	$0.663797\pi$
$264$	18.6098	−	10.3148i	1.14535	−	0.634835i
$265$	0.873228	−	0.467865i	0.0536419	−	0.0287407i
$266$	−0.382695	+	0.724806i	−0.0234645	+	0.0444407i
$267$	2.68146	+	6.47362i	0.164103	+	0.396179i
$268$	−2.09677	−	1.37041i	−0.128081	−	0.0837110i
$269$	5.51096	−	13.3046i	0.336009	−	0.811198i	−0.662082	−	0.749432i	$-0.730327\pi$
$269$	5.51096	−	13.3046i	0.336009	−	0.811198i	0.998091	−	0.0617658i	$-0.0196732\pi$
$270$	15.9489	+	6.49304i	0.970618	+	0.395154i
$271$		−	11.3045i		−	0.686697i	−0.939208	−	0.343348i	$-0.888439\pi$
$271$		−	11.3045i		−	0.686697i	0.939208	−	0.343348i	$-0.111561\pi$
$272$	16.7916	+	6.55879i	1.01814	+	0.397685i
$273$	−6.31676			−0.382308
$274$	1.25973	−	13.4927i	0.0761031	−	0.815123i
$275$	19.1384	−	12.8429i	1.15409	−	0.774459i
$276$	−3.82400	+	0.801118i	−0.230178	+	0.0482216i
$277$	−2.93560	−	7.08716i	−0.176383	−	0.425826i	0.810820	−	0.585296i	$-0.199022\pi$
$277$	−2.93560	−	7.08716i	−0.176383	−	0.425826i	−0.987203	+	0.159470i	$0.949022\pi$
$278$	14.3251	−	27.1310i	0.859161	−	1.62721i
$279$	1.27417	+	1.27417i	0.0762825	+	0.0762825i
$280$	−5.38135	−	0.979878i	−0.321597	−	0.0585589i
$281$	12.6041	−	12.6041i	0.751897	−	0.751897i	−0.222936	−	0.974833i	$-0.571564\pi$
$281$	12.6041	−	12.6041i	0.751897	−	0.751897i	0.974833	+	0.222936i	$0.0715641\pi$
$282$	7.30804	+	23.6580i	0.435187	+	1.40881i
$283$	7.29150	−	3.02024i	0.433434	−	0.179534i	−0.155289	−	0.987869i	$-0.549631\pi$
$283$	7.29150	−	3.02024i	0.433434	−	0.179534i	0.588723	+	0.808335i	$0.299631\pi$
$284$	−3.42433	−	5.01382i	−0.203196	−	0.297516i
$285$	1.54946	−	1.89185i	0.0917822	−	0.112064i
$286$	−22.4593	+	18.6236i	−1.32805	+	1.10124i
$287$			6.76574i			0.399369i
$288$	−1.70250	−	0.855131i	−0.100321	−	0.0503891i
$289$	3.31091			0.194760
$290$	10.6051	+	25.1694i	0.622750	+	1.47800i
$291$	−13.7358	−	5.68955i	−0.805206	−	0.333527i
$292$	−5.92257	−	8.67170i	−0.346592	−	0.507473i
$293$	−17.9886	+	7.45113i	−1.05091	+	0.435300i	−0.840215	−	0.542253i	$-0.817572\pi$
$293$	−17.9886	+	7.45113i	−1.05091	+	0.435300i	−0.210691	+	0.977553i	$0.567572\pi$
$294$	−13.7863	+	4.25863i	−0.804033	+	0.248369i
$295$	−3.66420	+	1.96323i	−0.213338	+	0.114304i
$296$	15.1835	+	12.0782i	0.882521	+	0.702032i
$297$	−17.7494	+	17.7494i	−1.02993	+	1.02993i
$298$	−2.38279	+	4.51288i	−0.138031	+	0.261424i
$299$	4.94967	−	2.05022i	0.286247	−	0.118567i
$300$	15.1518	+	6.06153i	0.874792	+	0.349963i
$301$	0.686153	−	1.65652i	0.0395492	−	0.0954802i
$302$	12.2074	+	1.13973i	0.702456	+	0.0655841i
$303$	21.8946			1.25781
$304$	−1.85651	+	1.93355i	−0.106478	+	0.110897i
$305$	−0.0546829	+	0.180912i	−0.00313113	+	0.0103590i
$306$	−2.13726	−	0.199543i	−0.122179	−	0.0114071i
$307$	−14.1319	−	5.85364i	−0.806552	−	0.334085i	−0.0589748	−	0.998259i	$-0.518783\pi$
$307$	−14.1319	−	5.85364i	−0.806552	−	0.334085i	−0.747578	+	0.664175i	$0.768783\pi$
$308$	4.36217	−	6.67427i	0.248558	−	0.380302i
$309$	−10.5009	+	4.34960i	−0.597374	+	0.247440i
$310$	12.0361	+	11.8908i	0.683605	+	0.675351i
$311$	0.257698	+	0.257698i	0.0146127	+	0.0146127i	0.714375	−	0.699763i	$-0.246711\pi$
$311$	0.257698	+	0.257698i	0.0146127	+	0.0146127i	−0.699763	+	0.714375i	$0.746711\pi$
$312$	−19.8579	−	5.69481i	−1.12423	−	0.322405i
$313$	3.05500	+	3.05500i	0.172679	+	0.172679i	0.788155	−	0.615477i	$-0.211036\pi$
$313$	3.05500	+	3.05500i	0.172679	+	0.172679i	−0.615477	+	0.788155i	$0.711036\pi$
$314$	4.00049	+	12.9506i	0.225761	+	0.730846i
$315$	0.648116	−	0.0644838i	0.0365172	−	0.00363325i
$316$	−17.7357	−	3.34088i	−0.997713	−	0.187939i
$317$	−7.09958	+	17.1399i	−0.398752	+	0.962673i	0.589210	+	0.807980i	$0.299439\pi$
$317$	−7.09958	+	17.1399i	−0.398752	+	0.962673i	−0.987963	+	0.154693i	$0.950561\pi$
$318$	−0.787093	+	0.652671i	−0.0441380	+	0.0366000i
$319$	−39.8132			−2.22911
$320$	−16.0339	−	7.93192i	−0.896320	−	0.443408i
$321$	32.5948			1.81926
$322$	−1.12703	+	0.934555i	−0.0628071	+	0.0520807i
$323$	−1.15575	+	2.79024i	−0.0643078	+	0.155253i
$324$	−15.4801	−	2.91599i	−0.860008	−	0.162000i
$325$	−21.9565	−	4.32210i	−1.21793	−	0.239747i
$326$	0.468412	+	1.51637i	0.0259430	+	0.0839840i
$327$	−11.8648	−	11.8648i	−0.656123	−	0.656123i
$328$	−6.09957	+	21.2694i	−0.336793	+	1.17440i
$329$	6.56115	+	6.56115i	0.361728	+	0.361728i
$330$	−16.7186	+	16.9230i	−0.920331	+	0.931579i
$331$	−15.3792	+	6.37028i	−0.845319	+	0.350143i	−0.762949	−	0.646459i	$-0.776249\pi$
$331$	−15.3792	+	6.37028i	−0.845319	+	0.350143i	−0.0823703	+	0.996602i	$0.526249\pi$
$332$	−14.5782	+	22.3052i	−0.800085	+	1.22416i
$333$	−2.13437	−	0.884086i	−0.116963	−	0.0484476i
$334$	2.07693	+	0.193911i	0.113645	+	0.0106103i
$335$	2.68077	+	0.810296i	0.146466	+	0.0442712i
$336$	5.64438	−	0.114723i	0.307926	−	0.00625868i
$337$	−11.6900			−0.636797			−0.318399	−	0.947957i	$-0.603145\pi$
$337$	−11.6900			−0.636797			−0.318399	+	0.947957i	$0.603145\pi$
$338$	9.89989	+	0.924293i	0.538483	+	0.0502749i
$339$	6.74799	−	16.2911i	0.366500	−	0.884810i
$340$	−20.0786	−	1.75167i	−1.08891	−	0.0949977i
$341$	−22.7857	+	9.43814i	−1.23391	+	0.511104i
$342$	0.149029	−	0.282254i	0.00805858	−	0.0152626i
$343$	−8.10422	+	8.10422i	−0.437587	+	0.437587i
$344$	3.65046	−	4.58898i	0.196820	−	0.247421i
$345$	3.85034	−	2.06297i	0.207295	−	0.111067i
$346$	28.4670	−	8.79355i	1.53040	−	0.472744i
$347$	−20.3616	+	8.43404i	−1.09307	+	0.452763i	−0.855075	−	0.518504i	$-0.826489\pi$
$347$	−20.3616	+	8.43404i	−1.09307	+	0.452763i	−0.237992	+	0.971267i	$0.576489\pi$
$348$	−15.8988	−	23.2786i	−0.852263	−	1.24786i
$349$	−4.40476	−	1.82451i	−0.235781	−	0.0976638i	0.261664	−	0.965159i	$-0.415729\pi$
$349$	−4.40476	−	1.82451i	−0.235781	−	0.0976638i	−0.497446	+	0.867495i	$0.665729\pi$
$350$	6.08162	−	0.642413i	0.325076	−	0.0343384i
$351$	24.3714			1.30085
$352$	19.7304	−	17.0492i	1.05163	−	0.908723i
$353$		−	16.1954i		−	0.861992i	−0.902354	−	0.430996i	$-0.858162\pi$
$353$		−	16.1954i		−	0.861992i	0.902354	−	0.430996i	$-0.141838\pi$
$354$	3.30276	−	2.73871i	0.175540	−	0.145561i
$355$	5.25167	+	4.30122i	0.278730	+	0.228285i
$356$	4.84319	+	7.09128i	0.256688	+	0.375837i
$357$	5.87660	−	2.43417i	0.311023	−	0.128830i
$358$	9.97068	+	32.2777i	0.526967	+	1.70593i
$359$	−6.53093	+	6.53093i	−0.344689	+	0.344689i	−0.858127	−	0.513438i	$-0.828372\pi$
$359$	−6.53093	+	6.53093i	−0.344689	+	0.344689i	0.513438	+	0.858127i	$0.328372\pi$
$360$	2.09561	+	0.381585i	0.110448	+	0.0201113i
$361$	13.1175	+	13.1175i	0.690394	+	0.690394i
$362$	−0.285586	+	0.540887i	−0.0150101	+	0.0284284i
$363$	−6.40054	−	15.4523i	−0.335941	−	0.811033i
$364$	−7.57696	+	1.58735i	−0.397141	+	0.0831999i
$365$	9.08308	+	7.43920i	0.475430	+	0.389386i
$366$	0.0181334	−	0.194222i	0.000947847	−	0.0101522i
$367$	16.6503			0.869139			0.434569	−	0.900638i	$-0.356901\pi$
$367$	16.6503			0.869139			0.434569	+	0.900638i	$0.356901\pi$
$368$	−4.38557	+	1.92188i	−0.228614	+	0.100185i
$369$		−	2.63472i		−	0.137158i
$370$	−20.0905	−	8.17915i	−1.04445	−	0.425214i
$371$	−0.146631	+	0.353999i	−0.00761272	+	0.0183787i
$372$	−14.6175	−	9.55373i	−0.757884	−	0.495338i
$373$	11.4407	+	27.6204i	0.592378	+	1.43013i	0.881200	+	0.472744i	$0.156737\pi$
$373$	11.4407	+	27.6204i	0.592378	+	1.43013i	−0.288821	+	0.957383i	$0.593263\pi$
$374$	13.7177	−	25.9806i	0.709324	−	1.34342i
$375$	−18.1630	−	1.73427i	−0.937931	−	0.0895575i
$376$	14.7111	+	26.5413i	0.758665	+	1.36876i
$377$	27.3333	+	27.3333i	1.40774	+	1.40774i
$378$	−6.36356	+	1.96572i	−0.327306	+	0.101106i
$379$	2.64740	+	6.39139i	0.135988	+	0.328303i	0.977173	−	0.212443i	$-0.0681419\pi$
$379$	2.64740	+	6.39139i	0.135988	+	0.328303i	−0.841186	+	0.540746i	$0.818142\pi$
$380$	1.38317	−	2.65864i	0.0709552	−	0.136386i
$381$	27.3201	+	11.3163i	1.39965	+	0.579754i
$382$	6.52690	−	5.41221i	0.333945	−	0.276913i
$383$		−	21.7935i		−	1.11359i	−0.830649	−	0.556797i	$-0.812030\pi$
$383$		−	21.7935i		−	1.11359i	0.830649	−	0.556797i	$-0.187970\pi$
$384$	17.8476	+	4.72798i	0.910781	+	0.241274i
$385$	−2.57927	+	8.53320i	−0.131452	+	0.434892i
$386$	12.9473	+	15.6139i	0.658999	+	0.794724i
$387$	−0.267202	+	0.645083i	−0.0135826	+	0.0327914i
$388$	−17.9058	−	3.37292i	−0.909030	−	0.171234i
$389$	−6.66882	−	16.1000i	−0.338122	−	0.816300i	−0.997896	−	0.0648353i	$-0.979348\pi$
$389$	−6.66882	−	16.1000i	−0.338122	−	0.816300i	0.659773	−	0.751465i	$-0.270652\pi$
$390$	23.0963	−	0.140282i	1.16953	−	0.00710347i
$391$	−3.81472	+	3.81472i	−0.192919	+	0.192919i
$392$	−15.4665	+	8.57262i	−0.781176	+	0.432983i
$393$	−15.9315	+	15.9315i	−0.803637	+	0.803637i
$394$	14.2347	−	26.9598i	0.717134	−	1.35822i
$395$	20.0788	−	1.99772i	1.01027	−	0.100516i
$396$	−1.69872	+	2.59910i	−0.0853638	+	0.130610i
$397$	−36.7175	−	15.2089i	−1.84280	−	0.763313i	−0.949416	−	0.314021i	$-0.898324\pi$
$397$	−36.7175	−	15.2089i	−1.84280	−	0.763313i	−0.893385	−	0.449292i	$-0.851676\pi$
$398$	−2.89034	+	30.9577i	−0.144879	+	1.55177i
$399$			0.945817i			0.0473501i
$400$	19.6979	+	3.46327i	0.984893	+	0.173164i
$401$		−	28.3311i		−	1.41479i	−0.706819	−	0.707394i	$-0.749871\pi$
$401$		−	28.3311i		−	1.41479i	0.706819	−	0.707394i	$-0.250129\pi$
$402$	−2.87801	−	0.268702i	−0.143542	−	0.0134017i
$403$	22.1229	+	9.16362i	1.10202	+	0.456472i
$404$	26.2626	−	5.50194i	1.30661	−	0.273732i
$405$	17.5252	−	1.74365i	0.870833	−	0.0866429i
$406$	−9.34157	−	4.93232i	−0.463615	−	0.244787i
$407$	22.3586	−	22.3586i	1.10827	−	1.10827i
$408$	20.6687	−	2.35428i	1.02325	−	0.116554i
$409$	−6.22929	+	6.22929i	−0.308019	+	0.308019i	−0.844141	−	0.536122i	$-0.819889\pi$
$409$	−6.22929	+	6.22929i	−0.308019	+	0.308019i	0.536122	+	0.844141i	$0.319889\pi$
$410$	−0.150253	−	24.7379i	−0.00742047	−	1.22172i
$411$	−5.98425	−	14.4473i	−0.295181	−	0.712631i
$412$	−11.5028	+	7.85614i	−0.566701	+	0.387044i
$413$	0.615287	−	1.48544i	0.0302763	−	0.0730935i
$414$	0.438890	−	0.363935i	0.0215703	−	0.0178864i
$415$	8.61984	−	28.5177i	0.423131	−	1.39988i
$416$	−25.2506	−	1.84078i	−1.23801	−	0.0902518i
$417$		−	35.4039i		−	1.73374i
$418$	2.78854	+	3.36286i	0.136392	+	0.164483i
$419$	−8.92511	−	3.69690i	−0.436020	−	0.180606i	0.153866	−	0.988092i	$-0.450828\pi$
$419$	−8.92511	−	3.69690i	−0.436020	−	0.180606i	−0.589887	+	0.807486i	$0.700828\pi$
$420$	−6.01932	+	1.89951i	−0.293713	+	0.0926866i
$421$	−2.66698	−	6.43866i	−0.129981	−	0.313801i	0.845469	−	0.534025i	$-0.179321\pi$
$421$	−2.66698	−	6.43866i	−0.129981	−	0.313801i	−0.975449	+	0.220224i	$0.929321\pi$
$422$	−8.86841	−	28.7093i	−0.431707	−	1.39755i
$423$	−2.55505	−	2.55505i	−0.124231	−	0.124231i
$424$	−0.780107	+	0.980669i	−0.0378854	+	0.0476255i
$425$	22.0921	−	4.44002i	1.07162	−	0.215372i
$426$	−6.19574	−	3.27133i	−0.300185	−	0.158496i
$427$	−0.0279737	−	0.0675345i	−0.00135374	−	0.00326822i
$428$	39.0974	−	8.19081i	1.88985	−	0.395918i
$429$	−12.8842	+	31.1052i	−0.622056	+	1.50178i
$430$	−2.47203	+	6.07206i	−0.119212	+	0.292821i
$431$			37.5421i			1.80834i	0.427175	+	0.904169i	$0.359509\pi$
$431$			37.5421i			1.80834i	−0.427175	+	0.904169i	$0.640491\pi$
$432$	−21.7772	+	0.442627i	−1.04776	+	0.0212959i
$433$	15.2945			0.735006			0.367503	−	0.930022i	$-0.380213\pi$
$433$	15.2945			0.735006			0.367503	+	0.930022i	$0.380213\pi$
$434$	−6.51558	−	0.608321i	−0.312758	−	0.0292003i
$435$	24.3829	+	19.9701i	1.16907	+	0.957491i
$436$	−17.2133	−	11.2503i	−0.824368	−	0.538790i
$437$	−0.306982	−	0.741120i	−0.0146849	−	0.0354526i
$438$	−10.7159	−	5.65796i	−0.512025	−	0.270348i
$439$	−4.05364	−	4.05364i	−0.193470	−	0.193470i	0.603724	−	0.797194i	$-0.293683\pi$
$439$	−4.05364	−	4.05364i	−0.193470	−	0.193470i	−0.797194	+	0.603724i	$0.793683\pi$
$440$	−15.8014	+	24.5004i	−0.753303	+	1.16801i
$441$	1.48891	−	1.48891i	0.0709005	−	0.0709005i
$442$	−27.2544	+	8.41899i	−1.29636	+	0.400451i
$443$	−4.19920	+	1.73937i	−0.199510	+	0.0826398i	−0.480201	−	0.877158i	$-0.659436\pi$
$443$	−4.19920	+	1.73937i	−0.199510	+	0.0826398i	0.280691	+	0.959798i	$0.409436\pi$
$444$	22.0015	+	4.14443i	1.04415	+	0.196686i
$445$	−7.42769	−	6.08341i	−0.352106	−	0.288381i
$446$	0.0178215	+	0.0214920i	0.000843874	+	0.00101768i
$447$			5.88897i			0.278539i
$448$	6.74161	−	1.55600i	0.318511	−	0.0735141i
$449$	−21.6426			−1.02138			−0.510688	−	0.859766i	$-0.670609\pi$
$449$	−21.6426			−1.02138			−0.510688	+	0.859766i	$0.670609\pi$
$450$	−2.36831	+	0.250169i	−0.111643	+	0.0117931i
$451$	33.3161	+	13.8000i	1.56879	+	0.649816i
$452$	4.00039	−	21.2369i	0.188163	−	0.998898i
$453$	13.0710	−	5.41420i	0.614131	−	0.254381i
$454$	−5.74435	−	18.5959i	−0.269596	−	0.872751i
$455$	7.62915	−	4.08761i	0.357660	−	0.191630i
$456$	−0.852691	+	2.97335i	−0.0399309	+	0.139240i
$457$	−12.4735	+	12.4735i	−0.583485	+	0.583485i	−0.935859	−	0.352374i	$-0.885374\pi$
$457$	−12.4735	+	12.4735i	−0.583485	+	0.583485i	0.352374	+	0.935859i	$0.385374\pi$
$458$	−5.91402	−	3.12258i	−0.276344	−	0.145909i
$459$	−22.6731	+	9.39152i	−1.05829	+	0.438359i
$460$	4.10008	−	3.44209i	0.191167	−	0.160488i
$461$	−5.56763	+	13.4414i	−0.259310	+	0.626030i	−0.998893	−	0.0470351i	$-0.985023\pi$
$461$	−5.56763	+	13.4414i	−0.259310	+	0.626030i	0.739583	+	0.673065i	$0.235023\pi$
$462$	0.855310	−	9.16103i	0.0397926	−	0.426210i
$463$	14.3416			0.666509			0.333254	−	0.942837i	$-0.391853\pi$
$463$	14.3416			0.666509			0.333254	+	0.942837i	$0.391853\pi$
$464$	−24.9203	−	23.9275i	−1.15690	−	1.11080i
$465$	18.6888	+	5.64893i	0.866674	+	0.261963i
$466$	2.30461	−	24.6842i	0.106759	−	1.14347i
$467$	−35.3127	−	14.6270i	−1.63408	−	0.676857i	−0.638398	−	0.769707i	$-0.720402\pi$
$467$	−35.3127	−	14.6270i	−1.63408	−	0.676857i	−0.995680	+	0.0928497i	$0.970402\pi$
$468$	2.95062	−	0.618148i	0.136393	−	0.0285739i
$469$	−1.00073	+	0.414517i	−0.0462095	+	0.0191406i
$470$	−24.1356	−	23.8442i	−1.11329	−	1.09985i
$471$	11.0600	+	11.0600i	0.509616	+	0.509616i
$472$	3.27345	−	4.11504i	0.150673	−	0.189410i
$473$	−6.75756	−	6.75756i	−0.310713	−	0.310713i
$474$	−19.8984	+	6.14668i	−0.913963	+	0.282326i
$475$	−0.647153	+	3.28757i	−0.0296934	+	0.150844i
$476$	6.43730	−	4.39653i	0.295053	−	0.201515i
$477$	0.0571013	−	0.137855i	0.00261449	−	0.00631193i
$478$	1.30199	+	1.57015i	0.0595517	+	0.0718168i
$479$	18.2305			0.832973			0.416487	−	0.909142i	$-0.363261\pi$
$479$	18.2305			0.832973			0.416487	+	0.909142i	$0.363261\pi$
$480$	−20.6353	+	0.544820i	−0.941869	+	0.0248675i
$481$	−30.7001			−1.39981
$482$	12.3204	+	14.8578i	0.561178	+	0.676756i
$483$	−0.646545	+	1.56090i	−0.0294188	+	0.0710233i
$484$	−11.5605	−	16.9266i	−0.525476	−	0.769390i
$485$	20.2713	−	2.01688i	0.920473	−	0.0915817i
$486$	4.70608	−	1.45372i	0.213472	−	0.0659423i
$487$	12.6563	+	12.6563i	0.573513	+	0.573513i	0.933108	−	0.359595i	$-0.117085\pi$
$487$	12.6563	+	12.6563i	0.573513	+	0.573513i	−0.359595	+	0.933108i	$0.617085\pi$
$488$	−0.0270556	−	0.237527i	−0.00122475	−	0.0107523i
$489$	1.29500	+	1.29500i	0.0585618	+	0.0585618i
$490$	13.8948	−	14.0646i	0.627702	−	0.635374i
$491$	−9.20404	+	3.81244i	−0.415372	+	0.172053i	−0.580575	−	0.814207i	$-0.697172\pi$
$491$	−9.20404	+	3.81244i	−0.415372	+	0.172053i	0.165203	+	0.986260i	$0.447172\pi$
$492$	5.23546	+	24.9906i	0.236033	+	1.12666i
$493$	−35.9616	−	14.8958i	−1.61963	−	0.670873i
$494$	0.394293	−	4.22318i	0.0177401	−	0.190010i
$495$	1.00442	−	3.32300i	0.0451453	−	0.149358i
$496$	−19.9345	−	7.78642i	−0.895086	−	0.349621i
$497$	−2.62553			−0.117771
$498$	−2.85842	+	30.6159i	−0.128089	+	1.37193i
$499$	−2.15797	+	5.20979i	−0.0966039	+	0.233222i	−0.964793	−	0.263012i	$-0.915284\pi$
$499$	−2.15797	+	5.20979i	−0.0966039	+	0.233222i	0.868189	+	0.496234i	$0.165284\pi$
$500$	−22.2223	+	2.48395i	−0.993811	+	0.111086i
$501$	2.22387	−	0.921158i	0.0993553	−	0.0411543i
$502$	−14.5515	−	7.68316i	−0.649467	−	0.342916i
$503$	−15.0438	+	15.0438i	−0.670771	+	0.670771i	−0.957894	−	0.287123i	$-0.907301\pi$
$503$	−15.0438	+	15.0438i	−0.670771	+	0.670771i	0.287123	+	0.957894i	$0.407301\pi$
$504$	−0.720573	+	0.399392i	−0.0320969	+	0.0177903i
$505$	−26.4435	+	14.1681i	−1.17672	+	0.630473i
$506$	2.30318	+	7.45598i	0.102389	+	0.331459i
$507$	10.6003	−	4.39078i	0.470775	−	0.195002i
$508$	35.6141	+	6.70864i	1.58012	+	0.297648i
$509$	20.7512	+	8.59543i	0.919781	+	0.380986i	0.791793	−	0.610790i	$-0.209148\pi$
$509$	20.7512	+	8.59543i	0.919781	+	0.380986i	0.127988	+	0.991776i	$0.459148\pi$
$510$	−21.4329	+	9.03069i	−0.949064	+	0.399886i
$511$	−4.54101			−0.200883
$512$	22.5963	+	1.18625i	0.998625	+	0.0524252i
$513$		−	3.64916i		−	0.161114i
$514$	5.29174	+	6.38161i	0.233409	+	0.281481i
$515$	9.86791	−	12.0485i	0.434832	−	0.530919i
$516$	1.25259	−	6.64964i	0.0551423	−	0.292734i
$517$	45.6914	−	18.9260i	2.00950	−	0.832364i
$518$	8.01604	−	2.47618i	0.352205	−	0.108797i
$519$	24.3111	−	24.3111i	1.06714	−	1.06714i
$520$	27.6688	−	5.97219i	1.21336	−	0.261898i
$521$	−18.1800	−	18.1800i	−0.796481	−	0.796481i	0.186058	−	0.982539i	$-0.440429\pi$
$521$	−18.1800	−	18.1800i	−0.796481	−	0.796481i	−0.982539	+	0.186058i	$0.940429\pi$
$522$	3.63780	+	1.92075i	0.159222	+	0.0840688i
$523$	−0.208289	−	0.502855i	−0.00910786	−	0.0219883i	0.919260	−	0.393650i	$-0.128788\pi$
$523$	−0.208289	−	0.502855i	−0.00910786	−	0.0219883i	−0.928368	+	0.371662i	$0.878788\pi$
$524$	−15.1064	+	23.1133i	−0.659924	+	1.00971i
$525$	5.85983	−	3.93227i	0.255744	−	0.171618i
$526$	12.2177	+	1.14070i	0.532718	+	0.0497367i
$527$	−24.1126			−1.05036
$528$	10.9478	−	28.0283i	0.476444	−	1.21977i
$529$			21.5671i			0.937699i
$530$	0.528275	−	1.29760i	0.0229468	−	0.0563643i
$531$	−0.239606	+	0.578459i	−0.0103980	+	0.0251030i
$532$	0.237676	+	1.13451i	0.0103046	+	0.0491871i
$533$	−13.3986	−	32.3471i	−0.580358	−	1.40111i
$534$	8.76292	+	4.62679i	0.379209	+	0.200221i
$535$	−39.3667	+	21.0923i	−1.70197	+	0.911898i
$536$	−3.51969	+	0.400912i	−0.152028	+	0.0173168i
$537$	27.5654	+	27.5654i	1.18954	+	1.18954i
$538$	−6.01083	−	19.4586i	−0.259145	−	0.838920i
$539$	11.0288	+	26.6258i	0.475044	+	1.14686i
$540$	23.2238	−	7.32871i	0.999391	−	0.315377i
$541$	−2.60877	−	1.08059i	−0.112160	−	0.0464581i	0.325898	−	0.945405i	$-0.394333\pi$
$541$	−2.60877	−	1.08059i	−0.112160	−	0.0464581i	−0.438058	+	0.898947i	$0.644333\pi$
$542$	−10.2046	−	12.3064i	−0.438327	−	0.528604i
$543$			0.705817i			0.0302895i
$544$	24.2005	−	8.01783i	1.03759	−	0.343762i
$545$	22.0076	+	6.65206i	0.942701	+	0.284943i
$546$	−6.87662	+	5.70221i	−0.294292	+	0.244032i
$547$	−17.3653	+	41.9235i	−0.742486	+	1.79252i	−0.147029	+	0.989132i	$0.546971\pi$
$547$	−17.3653	+	41.9235i	−0.742486	+	1.79252i	−0.595457	+	0.803387i	$0.703029\pi$
$548$	−10.8086	−	15.8257i	−0.461720	−	0.676041i
$549$	0.0108935	+	0.0262993i	0.000464925	+	0.00112243i
$550$	9.24120	−	31.2577i	0.394046	−	1.33283i
$551$	4.09265	−	4.09265i	0.174353	−	0.174353i
$552$	−3.43974	+	4.32408i	−0.146405	+	0.184045i
$553$	−5.51848	+	5.51848i	−0.234670	+	0.234670i
$554$	−9.59343	−	5.06530i	−0.407586	−	0.215204i
$555$	−24.9081	+	2.47821i	−1.05729	+	0.105194i
$556$	−8.89672	−	42.4670i	−0.377305	−	1.80100i
$557$	−6.40538	−	2.65320i	−0.271405	−	0.112420i	0.242830	−	0.970069i	$-0.421924\pi$
$557$	−6.40538	−	2.65320i	−0.271405	−	0.112420i	−0.514235	+	0.857649i	$0.671924\pi$
$558$	2.53730	+	0.236893i	0.107413	+	0.0100285i
$559$			9.27867i			0.392446i
$560$	−6.74284	+	3.79107i	−0.284937	+	0.160202i
$561$		−	33.9027i		−	1.43137i
$562$	2.34335	−	25.0990i	0.0988481	−	1.05874i
$563$	33.2595	+	13.7766i	1.40172	+	0.580612i	0.950198	−	0.311647i	$-0.100880\pi$
$563$	33.2595	+	13.7766i	1.40172	+	0.580612i	0.451524	+	0.892259i	$0.350880\pi$
$564$	29.3121	+	19.1578i	1.23426	+	0.806688i
$565$	2.39208	+	24.0424i	0.100636	+	1.01147i
$566$	5.21134	−	9.87003i	0.219049	−	0.414868i
$567$	−4.81665	+	4.81665i	−0.202280	+	0.202280i
$568$	−8.25385	−	2.36702i	−0.346324	−	0.0993180i
$569$	17.6527	−	17.6527i	0.740039	−	0.740039i	−0.232546	−	0.972585i	$-0.574706\pi$
$569$	17.6527	−	17.6527i	0.740039	−	0.740039i	0.972585	+	0.232546i	$0.0747058\pi$
$570$	−0.0210046	−	3.45824i	−0.000879788	−	0.144850i
$571$	10.4627	+	25.2591i	0.437848	+	1.05706i	0.976690	+	0.214653i	$0.0688620\pi$
$571$	10.4627	+	25.2591i	0.437848	+	1.05706i	−0.538842	+	0.842407i	$0.681138\pi$
$572$	−7.63811	+	40.5484i	−0.319366	+	1.69542i
$573$	3.74428	−	9.03950i	0.156420	−	0.377631i
$574$	6.10750	+	7.36538i	0.254922	+	0.307425i
$575$	−3.31534	+	4.98315i	−0.138259	+	0.207812i
$576$	−2.62532	+	0.605939i	−0.109388	+	0.0252475i
$577$		−	41.1102i		−	1.71144i	−0.517438	−	0.855721i	$-0.673114\pi$
$577$		−	41.1102i		−	1.71144i	0.517438	−	0.855721i	$-0.326886\pi$
$578$	3.60436	−	2.98879i	0.149921	−	0.124317i
$579$	21.6246	+	8.95720i	0.898687	+	0.372248i
$580$	34.2656	+	17.8268i	1.42280	+	0.740220i
$581$	4.40958	+	10.6457i	0.182940	+	0.441657i
$582$	−20.0892	+	6.20562i	−0.832724	+	0.257231i
$583$	1.44410	+	1.44410i	0.0598083	+	0.0598083i
$584$	−14.2755	−	4.09390i	−0.590725	−	0.169407i
$585$	−2.97095	+	1.59180i	−0.122834	+	0.0658129i
$586$	−12.8567	+	24.3500i	−0.531107	+	1.00589i
$587$	−5.01910	−	12.1172i	−0.207160	−	0.500129i	0.785813	−	0.618464i	$-0.212245\pi$
$587$	−5.01910	−	12.1172i	−0.207160	−	0.500129i	−0.992974	+	0.118334i	$0.962245\pi$
$588$	−11.1639	+	17.0811i	−0.460390	+	0.704413i
$589$	1.37208	−	3.31250i	0.0565356	−	0.136489i
$590$	−2.21672	+	5.44494i	−0.0912609	+	0.224165i
$591$		−	35.1805i		−	1.44713i
$592$	27.4323	−	0.557568i	1.12746	−	0.0229159i
$593$	−31.1472			−1.27906			−0.639531	−	0.768766i	$-0.720871\pi$
$593$	−31.1472			−1.27906			−0.639531	+	0.768766i	$0.720871\pi$
$594$	−3.29996	+	35.3451i	−0.135399	+	1.45023i
$595$	−5.52238	+	6.74268i	−0.226395	+	0.276423i
$596$	1.47985	+	7.06382i	0.0606171	+	0.289345i
$597$	13.7303	+	33.1479i	0.561945	+	1.35665i
$598$	3.53760	−	6.70005i	0.144663	−	0.273985i
$599$	−3.11717	−	3.11717i	−0.127364	−	0.127364i	0.640551	−	0.767915i	$-0.278706\pi$
$599$	−3.11717	−	3.11717i	−0.127364	−	0.127364i	−0.767915	+	0.640551i	$0.778706\pi$
$600$	21.9666	−	7.07896i	0.896781	−	0.288997i
$601$	−0.580658	+	0.580658i	−0.0236856	+	0.0236856i	−0.718850	−	0.695165i	$-0.755331\pi$
$601$	−0.580658	+	0.580658i	−0.0236856	+	0.0236856i	0.695165	+	0.718850i	$0.255331\pi$
$602$	−0.748390	−	2.42273i	−0.0305021	−	0.0987432i
$603$	0.389706	−	0.161422i	0.0158701	−	0.00657359i
$604$	14.3182	−	9.77898i	0.582598	−	0.397901i
$605$	17.7296	+	14.5208i	0.720809	+	0.590356i
$606$	23.8351	−	19.7645i	0.968236	−	0.802877i
$607$			11.0053i			0.446693i	0.974739	+	0.223346i	$0.0716981\pi$
$607$			11.0053i			0.446693i	−0.974739	+	0.223346i	$0.928302\pi$
$608$	−0.275623	+	3.78081i	−0.0111780	+	0.153332i
$609$	−12.1901			−0.493966
$610$	0.103782	+	0.246309i	0.00420199	+	0.00997275i
$611$	−44.3624	−	18.3755i	−1.79471	−	0.743393i
$612$	−2.50682	+	1.71210i	−0.101332	+	0.0692075i
$613$	9.78571	−	4.05337i	0.395241	−	0.163714i	−0.176206	−	0.984353i	$-0.556382\pi$
$613$	9.78571	−	4.05337i	0.395241	−	0.163714i	0.571447	+	0.820639i	$0.306382\pi$
$614$	−20.6686	+	6.38460i	−0.834116	+	0.257661i
$615$	−13.4819	−	25.1627i	−0.543643	−	1.01466i
$616$	−1.27615	−	11.2036i	−0.0514175	−	0.451405i
$617$	−17.2460	+	17.2460i	−0.694297	+	0.694297i	−0.963175	−	0.268877i	$-0.913347\pi$
$617$	−17.2460	+	17.2460i	−0.694297	+	0.694297i	0.268877	+	0.963175i	$0.413347\pi$
$618$	−7.50513	+	14.2144i	−0.301901	+	0.571785i
$619$	−11.4309	+	4.73483i	−0.459446	+	0.190309i	−0.600388	−	0.799709i	$-0.704987\pi$
$619$	−11.4309	+	4.73483i	−0.459446	+	0.190309i	0.140942	+	0.990018i	$0.454987\pi$
$620$	23.8368	+	2.07954i	0.957308	+	0.0835163i
$621$	2.49450	−	6.02226i	0.100101	−	0.241665i
$622$	0.513164	+	0.0479111i	0.0205760	+	0.00192106i
$623$	3.71341			0.148775
$624$	−26.7587	+	11.7264i	−1.07120	+	0.469432i
$625$	23.0588	−	9.65876i	0.922352	−	0.386350i
$626$	6.08354	+	0.567983i	0.243147	+	0.0227012i
$627$	4.65743	+	1.92917i	0.186000	+	0.0770436i
$628$	16.0457	+	10.4871i	0.640294	+	0.418483i
$629$	28.5609	−	11.8303i	1.13880	−	0.471705i
$630$	0.647348	−	0.655260i	0.0257910	−	0.0261062i
$631$	6.09072	+	6.09072i	0.242468	+	0.242468i	0.817870	−	0.575403i	$-0.195155\pi$
$631$	6.09072	+	6.09072i	0.242468	+	0.242468i	−0.575403	+	0.817870i	$0.695155\pi$
$632$	−22.3235	+	12.3733i	−0.887981	+	0.492181i
$633$	−24.5180	−	24.5180i	−0.974505	−	0.974505i
$634$	7.74355	+	25.0679i	0.307536	+	0.995573i
$635$	−40.3190	+	4.01151i	−1.60001	+	0.159192i
$636$	−0.267680	+	1.42103i	−0.0106142	+	0.0563476i
$637$	10.7080	−	25.8514i	0.424267	−	1.02427i
$638$	−43.3418	+	35.9398i	−1.71592	+	1.42287i
$639$	1.02244			0.0404470
$640$	−24.6152	+	5.83900i	−0.973000	+	0.230807i
$641$	−6.99186			−0.276162			−0.138081	−	0.990421i	$-0.544093\pi$
$641$	−6.99186			−0.276162			−0.138081	+	0.990421i	$0.544093\pi$
$642$	35.4836	−	29.4236i	1.40043	−	1.16126i
$643$	3.50596	−	8.46413i	0.138261	−	0.333793i	−0.839549	−	0.543284i	$-0.817181\pi$
$643$	3.50596	−	8.46413i	0.138261	−	0.333793i	0.977811	+	0.209491i	$0.0671808\pi$
$644$	−0.383289	+	2.03477i	−0.0151037	+	0.0801811i
$645$	0.749003	+	7.52811i	0.0294920	+	0.296419i
$646$	1.26059	+	4.08084i	0.0495971	+	0.160559i
$647$	−6.68343	−	6.68343i	−0.262753	−	0.262753i	0.563419	−	0.826171i	$-0.309486\pi$
$647$	−6.68343	−	6.68343i	−0.262753	−	0.262753i	−0.826171	+	0.563419i	$0.809486\pi$
$648$	−19.4844	+	10.7996i	−0.765421	+	0.424250i
$649$	−6.05964	−	6.05964i	−0.237862	−	0.237862i
$650$	−27.8041	+	15.1152i	−1.09057	+	0.592866i
$651$	−6.97655	+	2.88978i	−0.273433	+	0.113259i
$652$	1.87877	+	1.22793i	0.0735784	+	0.0480893i
$653$	16.4481	+	6.81301i	0.643662	+	0.266614i	0.680545	−	0.732706i	$-0.261743\pi$
$653$	16.4481	+	6.81301i	0.643662	+	0.266614i	−0.0368832	+	0.999320i	$0.511743\pi$
$654$	−23.6268	−	2.20589i	−0.923880	−	0.0862572i
$655$	8.93209	−	29.5508i	0.349006	−	1.15464i
$656$	12.5599	+	28.6606i	0.490381	+	1.11901i
$657$	1.76836			0.0689905
$658$	13.0655	+	1.21985i	0.509346	+	0.0475546i
$659$	8.03556	−	19.3996i	0.313021	−	0.755699i	−0.686569	−	0.727065i	$-0.740884\pi$
$659$	8.03556	−	19.3996i	0.313021	−	0.755699i	0.999590	−	0.0286348i	$-0.00911597\pi$
$660$	−2.92387	+	33.5149i	−0.113811	+	1.30457i
$661$	29.2553	−	12.1180i	1.13790	−	0.471334i	0.267442	−	0.963574i	$-0.413822\pi$
$661$	29.2553	−	12.1180i	1.13790	−	0.471334i	0.870460	+	0.492240i	$0.163822\pi$
$662$	−10.9918	+	20.8179i	−0.427207	+	0.809109i
$663$	−23.2756	+	23.2756i	−0.903949	+	0.903949i
$664$	4.26486	+	37.4421i	0.165509	+	1.45303i
$665$	−0.612043	−	1.14232i	−0.0237340	−	0.0442974i
$666$	−3.12161	+	0.964277i	−0.120960	+	0.0373650i
$667$	9.55185	−	3.95650i	0.369849	−	0.153196i
$668$	2.43606	−	1.66377i	0.0942538	−	0.0643733i
$669$	0.0297656	+	0.0123293i	0.00115080	+	0.000476679i
$670$	3.64983	−	1.53785i	0.141005	−	0.0594121i
$671$	−0.389614			−0.0150409
$672$	6.04108	−	5.22013i	0.233040	−	0.201371i
$673$		−	15.9426i		−	0.614541i	−0.951622	−	0.307270i	$-0.900584\pi$
$673$		−	15.9426i		−	0.614541i	0.951622	−	0.307270i	$-0.0994156\pi$
$674$	−12.7261	+	10.5527i	−0.490192	+	0.406476i
$675$	−22.6084	+	15.1715i	−0.870199	+	0.583952i
$676$	11.6117	−	7.93052i	0.446603	−	0.305020i
$677$	16.8509	−	6.97989i	0.647634	−	0.268259i	−0.0345903	−	0.999402i	$-0.511013\pi$
$677$	16.8509	−	6.97989i	0.647634	−	0.268259i	0.682225	+	0.731143i	$0.261013\pi$
$678$	−7.36007	−	23.8264i	−0.282662	−	0.915049i
$679$	−5.57140	+	5.57140i	−0.213811	+	0.213811i
$680$	−23.4394	+	16.2182i	−0.898860	+	0.621941i
$681$	−15.8811	−	15.8811i	−0.608566	−	0.608566i
$682$	−16.2853	+	30.8435i	−0.623595	+	1.18106i
$683$	7.09008	+	17.1170i	0.271295	+	0.654963i	0.999539	−	0.0303543i	$-0.00966356\pi$
$683$	7.09008	+	17.1170i	0.271295	+	0.654963i	−0.728245	+	0.685317i	$0.759664\pi$
$684$	−0.0925561	−	0.441801i	−0.00353897	−	0.0168927i
$685$	16.5765	+	13.5764i	0.633354	+	0.518728i
$686$	−1.50673	+	16.1382i	−0.0575273	+	0.616161i
$687$	−7.71735			−0.294435
$688$	−0.168517	−	8.29101i	−0.00642464	−	0.316092i
$689$		−	1.98286i		−	0.0755409i
$690$	2.32933	−	5.72155i	0.0886762	−	0.217816i
$691$	−9.96168	+	24.0496i	−0.378960	+	0.914890i	0.613201	+	0.789927i	$0.289881\pi$
$691$	−9.96168	+	24.0496i	−0.378960	+	0.914890i	−0.992161	+	0.124964i	$0.960119\pi$
$692$	23.0520	−	35.2704i	0.876305	−	1.34078i
$693$	0.513823	+	1.24048i	0.0195185	+	0.0471219i
$694$	−14.5527	+	27.5622i	−0.552414	+	1.04625i
$695$	22.9101	+	42.7595i	0.869028	+	1.62196i
$696$	−38.3217	−	10.9898i	−1.45258	−	0.416567i
$697$	24.9299	+	24.9299i	0.944288	+	0.944288i
$698$	−6.44215	+	1.99000i	−0.243839	+	0.0753227i
$699$	−10.9479	−	26.4305i	−0.414087	−	0.999695i
$700$	6.04072	−	6.18929i	0.228318	−	0.233933i
$701$	−10.4942	−	4.34682i	−0.396359	−	0.164177i	0.175596	−	0.984462i	$-0.443815\pi$
$701$	−10.4942	−	4.34682i	−0.396359	−	0.164177i	−0.571955	+	0.820285i	$0.693815\pi$
$702$	26.5314	−	22.0003i	1.00136	−	0.830347i
$703$			4.59677i			0.173370i
$704$	6.08865	−	36.3710i	0.229475	−	1.37079i
$705$	−37.4761	−	11.3276i	−1.41143	−	0.426623i
$706$	−14.6197	−	17.6307i	−0.550220	−	0.663542i
$707$	4.44036	−	10.7200i	0.166997	−	0.403166i
$708$	1.12323	−	5.96287i	0.0422134	−	0.224098i
$709$	6.25960	+	15.1120i	0.235084	+	0.567543i	0.996762	−	0.0804130i	$-0.0256239\pi$
$709$	6.25960	+	15.1120i	0.235084	+	0.567543i	−0.761678	+	0.647956i	$0.775624\pi$
$710$	9.59988	−	0.0583077i	0.360277	−	0.00218825i
$711$	2.14901	−	2.14901i	0.0805942	−	0.0805942i
$712$	11.6738	+	3.34779i	0.437494	+	0.125464i
$713$	4.52873	−	4.52873i	0.169602	−	0.169602i
$714$	4.20010	−	7.95478i	0.157185	−	0.297700i
$715$	−4.56730	−	45.9052i	−0.170807	−	1.71676i
$716$	39.9917	+	26.1378i	1.49456	+	0.976815i
$717$	2.17459	+	0.900745i	0.0812116	+	0.0336390i
$718$	−1.21423	+	13.0053i	−0.0453145	+	0.485353i
$719$		−	46.1588i		−	1.72143i	−0.509086	−	0.860716i	$-0.670016\pi$
$719$		−	46.1588i		−	1.72143i	0.509086	−	0.860716i	$-0.329984\pi$
$720$	2.62580	−	1.47632i	0.0978578	−	0.0550193i
$721$			6.02354i			0.224328i
$722$	26.1214	+	2.43880i	0.972137	+	0.0907626i
$723$	20.5775	+	8.52350i	0.765287	+	0.316992i
$724$	0.177366	+	0.846627i	0.00659176	+	0.0314647i
$725$	−42.3715	−	8.34076i	−1.57364	−	0.309768i
$726$	−20.9167	−	11.0440i	−0.776292	−	0.409880i
$727$	−4.16643	+	4.16643i	−0.154524	+	0.154524i	−0.780135	−	0.625611i	$-0.784850\pi$
$727$	−4.16643	+	4.16643i	−0.154524	+	0.154524i	0.625611	+	0.780135i	$0.284850\pi$
$728$	−6.81558	+	8.56784i	−0.252602	+	0.317545i
$729$	20.7270	−	20.7270i	0.767665	−	0.767665i
$730$	16.6036	−	0.100847i	0.614525	−	0.00373250i
$731$	−3.57554	−	8.63212i	−0.132246	−	0.319270i
$732$	−0.155586	−	0.227805i	−0.00575062	−	0.00841993i
$733$	−5.03088	+	12.1456i	−0.185820	+	0.448608i	−0.989147	−	0.146929i	$-0.953061\pi$
$733$	−5.03088	+	12.1456i	−0.185820	+	0.448608i	0.803327	+	0.595538i	$0.203061\pi$
$734$	18.1260	−	15.0304i	0.669043	−	0.554782i
$735$	6.60097	−	21.8385i	0.243481	−	0.805527i
$736$	−3.03936	+	6.05112i	−0.112032	+	0.223047i
$737$			5.77333i			0.212663i
$738$	−2.37839	−	2.86823i	−0.0875496	−	0.105581i
$739$	−20.4359	−	8.46483i	−0.751747	−	0.311384i	−0.0262930	−	0.999654i	$-0.508370\pi$
$739$	−20.4359	−	8.46483i	−0.751747	−	0.311384i	−0.725454	+	0.688270i	$0.758370\pi$
$740$	−29.2545	+	9.23182i	−1.07542	+	0.339368i
$741$	−1.87306	−	4.52196i	−0.0688085	−	0.166118i
$742$	0.159932	+	0.517740i	0.00587127	+	0.0190068i
$743$	20.6141	+	20.6141i	0.756260	+	0.756260i	0.975640	−	0.219380i	$-0.0704034\pi$
$743$	20.6141	+	20.6141i	0.756260	+	0.756260i	−0.219380	+	0.975640i	$0.570403\pi$
$744$	−24.5373	+	2.79494i	−0.899582	+	0.102467i
$745$	−3.81078	−	7.11248i	−0.139616	−	0.260581i
$746$	37.3879	+	19.7407i	1.36887	+	0.722757i
$747$	−1.71718	−	4.14565i	−0.0628285	−	0.151681i
$748$	−8.51949	−	40.6663i	−0.311503	−	1.48691i
$749$	6.61042	−	15.9590i	0.241539	−	0.583128i
$750$	−21.3383	+	14.5079i	−0.779164	+	0.529754i
$751$			13.5949i			0.496086i	0.968749	+	0.248043i	$0.0797874\pi$
$751$			13.5949i			0.496086i	−0.968749	+	0.248043i	$0.920213\pi$
$752$	39.9740	+	15.6139i	1.45770	+	0.569379i
$753$	−18.9887			−0.691985
$754$	54.4300	+	5.08180i	1.98222	+	0.185068i
$755$	−12.2831	+	14.9974i	−0.447029	+	0.545811i
$756$	−5.15308	+	7.88439i	−0.187416	+	0.286753i
$757$	−10.7516	−	25.9568i	−0.390775	−	0.943414i	−0.989771	−	0.142662i	$-0.954434\pi$
$757$	−10.7516	−	25.9568i	−0.390775	−	0.943414i	0.598996	−	0.800752i	$-0.295566\pi$
$758$	8.65160	+	4.56802i	0.314240	+	0.165918i
$759$	6.36748	+	6.36748i	0.231125	+	0.231125i
$760$	−0.894224	−	4.14288i	−0.0324369	−	0.150278i
$761$	−2.81953	+	2.81953i	−0.102208	+	0.102208i	−0.756362	−	0.654154i	$-0.773025\pi$
$761$	−2.81953	+	2.81953i	−0.102208	+	0.102208i	0.654154	+	0.756362i	$0.273025\pi$
$762$	39.9568	−	12.3428i	1.44748	−	0.447132i
$763$	−8.21544	+	3.40295i	−0.297419	+	0.123195i
$764$	2.21971	−	11.7838i	0.0803064	−	0.426323i
$765$	2.15053	−	2.62574i	0.0777525	−	0.0949338i
$766$	−19.6732	−	23.7250i	−0.710821	−	0.857219i
$767$			8.32037i			0.300431i
$768$	23.6974	−	10.9642i	0.855107	−	0.395636i
$769$	11.3808			0.410403			0.205202	−	0.978720i	$-0.434215\pi$
$769$	11.3808			0.410403			0.205202	+	0.978720i	$0.434215\pi$
$770$	4.89514	+	11.6178i	0.176409	+	0.418677i
$771$	8.83829	+	3.66094i	0.318303	+	0.131845i
$772$	28.1896	+	5.31007i	1.01456	+	0.191114i
$773$	−37.9415	+	15.7159i	−1.36466	+	0.565261i	−0.940336	−	0.340248i	$-0.889489\pi$
$773$	−37.9415	+	15.7159i	−1.36466	+	0.565261i	−0.424326	+	0.905509i	$0.639489\pi$
$774$	0.291439	+	0.943462i	0.0104755	+	0.0339120i
$775$	−26.2271	+	5.27107i	−0.942106	+	0.189343i
$776$	−22.5376	+	12.4919i	−0.809052	+	0.448433i
$777$	6.84578	−	6.84578i	0.245591	−	0.245591i
$778$	−21.7935	−	11.5069i	−0.781333	−	0.412541i
$779$	−4.84337	+	2.00619i	−0.173532	+	0.0718792i
$780$	25.0167	−	21.0020i	0.895742	−	0.751992i
$781$	−5.35527	+	12.9288i	−0.191626	+	0.462627i
$782$	−0.709230	+	7.59640i	−0.0253620	+	0.271647i
$783$	47.0317			1.68078
$784$	−9.09870	+	23.2942i	−0.324954	+	0.831935i
$785$	−20.5148	−	6.20085i	−0.732204	−	0.221318i
$786$	−2.96197	+	31.7250i	−0.105650	+	1.13159i
$787$	20.0758	+	8.31566i	0.715624	+	0.296421i	0.710630	−	0.703566i	$-0.248410\pi$
$787$	20.0758	+	8.31566i	0.715624	+	0.296421i	0.00499439	+	0.999988i	$0.498410\pi$
$788$	−8.84060	−	42.1991i	−0.314933	−	1.50328i
$789$	13.0821	−	5.41879i	0.465736	−	0.192914i
$790$	20.0550	−	20.3001i	0.713524	−	0.722244i
$791$	−6.60786	−	6.60786i	−0.234949	−	0.234949i
$792$	0.496959	+	4.36291i	0.0176587	+	0.155029i
$793$	0.267485	+	0.267485i	0.00949868	+	0.00949868i
$794$	−53.7010	+	16.5884i	−1.90578	+	0.588702i
$795$	−0.160063	−	1.60876i	−0.00567684	−	0.0570569i
$796$	24.7993	+	36.3106i	0.878989	+	1.28700i
$797$	−9.61080	+	23.2025i	−0.340432	+	0.821875i	0.657240	+	0.753681i	$0.271724\pi$
$797$	−9.61080	+	23.2025i	−0.340432	+	0.821875i	−0.997672	+	0.0681942i	$0.978276\pi$
$798$	0.853799	+	1.02964i	0.0302241	+	0.0364490i
$799$	48.3522			1.71058
$800$	24.5700	−	14.0112i	0.868681	−	0.495372i
$801$	−1.44608			−0.0510947
$802$	−25.5748	−	30.8421i	−0.903077	−	1.08907i
$803$	−9.26224	+	22.3610i	−0.326857	+	0.789104i
$804$	−3.37564	+	2.30549i	−0.119050	+	0.0813083i
$805$	−0.229193	−	2.30358i	−0.00807797	−	0.0811904i
$806$	32.3558	−	9.99481i	1.13968	−	0.352052i
$807$	−16.6179	−	16.6179i	−0.584976	−	0.584976i
$808$	23.6236	−	29.6971i	0.831074	−	1.04474i
$809$	−31.5660	−	31.5660i	−1.10980	−	1.10980i	−0.993176	−	0.116624i	$-0.962793\pi$
$809$	−31.5660	−	31.5660i	−1.10980	−	1.10980i	−0.116624	−	0.993176i	$-0.537207\pi$
$810$	17.5044	−	17.7183i	0.615042	−	0.622559i
$811$	25.4378	−	10.5367i	0.893242	−	0.369993i	0.111624	−	0.993751i	$-0.464395\pi$
$811$	25.4378	−	10.5367i	0.893242	−	0.369993i	0.781618	+	0.623758i	$0.214395\pi$
$812$	−14.6220	+	3.06326i	−0.513131	+	0.107500i
$813$	−17.0438	−	7.05979i	−0.597754	−	0.247598i
$814$	4.15690	−	44.5235i	0.145699	−	1.56055i
$815$	−2.40205	−	0.726049i	−0.0841401	−	0.0254324i
$816$	20.3753	−	21.2208i	0.713279	−	0.742876i
$817$	1.38931			0.0486057
$818$	−1.15815	+	12.4046i	−0.0404936	+	0.433718i
$819$	0.498878	−	1.20440i	0.0174322	−	0.0420851i
$820$	−22.4947	−	26.7948i	−0.785551	−	0.935715i
$821$	−19.9548	+	8.26554i	−0.696426	+	0.288469i	−0.702675	−	0.711511i	$-0.748011\pi$
$821$	−19.9548	+	8.26554i	−0.696426	+	0.288469i	0.00624834	+	0.999980i	$0.498011\pi$
$822$	−19.5563	−	10.3257i	−0.682105	−	0.360149i
$823$	19.3907	−	19.3907i	0.675919	−	0.675919i	−0.283155	−	0.959074i	$-0.591381\pi$
$823$	19.3907	−	19.3907i	0.675919	−	0.675919i	0.959074	+	0.283155i	$0.0913812\pi$
$824$	−5.43045	+	18.9361i	−0.189179	+	0.659670i
$825$	−7.41122	−	36.8758i	−0.258026	−	1.28385i
$826$	−0.671097	−	2.17252i	−0.0233505	−	0.0755915i
$827$	21.2398	−	8.79781i	0.738580	−	0.305930i	0.0185075	−	0.999829i	$-0.494109\pi$
$827$	21.2398	−	8.79781i	0.738580	−	0.305930i	0.720072	+	0.693899i	$0.244109\pi$
$828$	0.149261	−	0.792381i	0.00518717	−	0.0275371i
$829$	−38.2016	−	15.8236i	−1.32680	−	0.549577i	−0.397056	−	0.917794i	$-0.629968\pi$
$829$	−38.2016	−	15.8236i	−1.32680	−	0.549577i	−0.929740	+	0.368218i	$0.879968\pi$
$830$	−16.3594	−	38.8264i	−0.567844	−	1.34769i
$831$	−12.5187			−0.434269
$832$	−29.1503	+	20.7901i	−1.01060	+	0.720766i
$833$			28.1764i			0.976254i
$834$	−31.9595	−	38.5417i	−1.10667	−	1.33459i
$835$	−2.08982	+	2.55162i	−0.0723213	+	0.0883025i
$836$	6.07137	+	1.14366i	0.209983	+	0.0395545i
$837$	26.9170	−	11.1494i	0.930387	−	0.385379i
$838$	−13.0534	+	4.03223i	−0.450921	+	0.139291i
$839$	18.0352	−	18.0352i	0.622645	−	0.622645i	−0.323562	−	0.946207i	$-0.604881\pi$
$839$	18.0352	−	18.0352i	0.622645	−	0.622645i	0.946207	+	0.323562i	$0.104881\pi$
$840$	−4.83810	+	7.50156i	−0.166930	+	0.258828i
$841$	32.2416	+	32.2416i	1.11178	+	1.11178i
$842$	−8.71559	−	4.60180i	−0.300359	−	0.158589i
$843$	−11.1319	−	26.8747i	−0.383403	−	0.925616i
$844$	−35.5706	−	23.2482i	−1.22439	−	0.800236i
$845$	−9.96133	+	12.1625i	−0.342680	+	0.418404i
$846$	−5.08797	−	0.475033i	−0.174928	−	0.0163320i
$847$	−8.86376			−0.304562
$848$	0.0360122	+	1.77180i	0.00123666	+	0.0608437i
$849$		−	12.8796i		−	0.442028i
$850$	20.0420	−	24.7763i	0.687436	−	0.849819i
$851$	−3.14227	+	7.58612i	−0.107716	+	0.260049i
$852$	−9.69793	+	2.03169i	−0.332246	+	0.0696046i
$853$	7.62598	+	18.4107i	0.261109	+	0.630372i	0.999008	−	0.0445392i	$-0.0141820\pi$
$853$	7.62598	+	18.4107i	0.261109	+	0.630372i	−0.737899	+	0.674911i	$0.764182\pi$
$854$	−0.0914171	−	0.0482679i	−0.00312823	−	0.00165169i
$855$	0.238342	+	0.444844i	0.00815114	+	0.0152133i
$856$	35.1687	−	44.2104i	1.20204	−	1.51108i
$857$	−8.09740	−	8.09740i	−0.276602	−	0.276602i	0.555149	−	0.831751i	$-0.312661\pi$
$857$	−8.09740	−	8.09740i	−0.276602	−	0.276602i	−0.831751	+	0.555149i	$0.812661\pi$
$858$	14.0529	+	45.4928i	0.479757	+	1.55310i
$859$	3.09681	+	7.47637i	0.105662	+	0.255090i	0.967864	−	0.251474i	$-0.0809153\pi$
$859$	3.09681	+	7.47637i	0.105662	+	0.255090i	−0.862202	+	0.506564i	$0.830915\pi$
$860$	2.79018	+	8.84175i	0.0951445	+	0.301501i
$861$	10.2008	+	4.22530i	0.347641	+	0.143998i
$862$	33.8896	+	40.8694i	1.15428	+	1.39202i
$863$		−	43.7401i		−	1.48893i	−0.667661	−	0.744466i	$-0.732704\pi$
$863$		−	43.7401i		−	1.48893i	0.667661	−	0.744466i	$-0.267296\pi$
$864$	−23.3077	+	20.1404i	−0.792945	+	0.685189i
$865$	−13.6302	+	45.0939i	−0.463440	+	1.53324i
$866$	16.6500	−	13.8065i	0.565791	−	0.469163i
$867$	2.06771	−	4.99190i	0.0702231	−	0.169534i
$868$	−7.64220	+	5.21945i	−0.259393	+	0.177160i
$869$	15.9184	+	38.4303i	0.539993	+	1.30366i
$870$	44.5711	−	0.270716i	1.51110	−	0.00917813i
$871$	3.96362	−	3.96362i	0.134302	−	0.134302i
$872$	−28.8946	+	3.29126i	−0.978496	+	0.111456i
$873$	2.16962	−	2.16962i	0.0734305	−	0.0734305i
$874$	−1.00321	−	0.529690i	−0.0339340	−	0.0179170i
$875$	−4.53269	+	8.54118i	−0.153233	+	0.288745i
$876$	−16.7731	+	3.51393i	−0.566712	+	0.118725i
$877$	−5.41238	−	2.24188i	−0.182763	−	0.0757030i	0.289425	−	0.957201i	$-0.406536\pi$
$877$	−5.41238	−	2.24188i	−0.182763	−	0.0757030i	−0.472188	+	0.881498i	$0.656536\pi$
$878$	−8.07217	−	0.753651i	−0.272423	−	0.0254345i
$879$			31.7750i			1.07174i
$880$	4.91486	+	40.9359i	0.165680	+	1.37995i
$881$			54.1204i			1.82336i	0.410899	+	0.911681i	$0.365215\pi$
$881$			54.1204i			1.82336i	−0.410899	+	0.911681i	$0.634785\pi$
$882$	0.276817	−	2.96493i	0.00932093	−	0.0998343i
$883$	2.40776	+	0.997327i	0.0810276	+	0.0335627i	0.422829	−	0.906209i	$-0.361037\pi$
$883$	2.40776	+	0.997327i	0.0810276	+	0.0335627i	−0.341801	+	0.939772i	$0.611037\pi$
$884$	−22.0701	+	33.7680i	−0.742297	+	1.13574i
$885$	0.671647	+	6.75061i	0.0225772	+	0.226919i
$886$	−3.00123	+	5.68419i	−0.100828	+	0.190964i
$887$	34.7876	−	34.7876i	1.16805	−	1.16805i	0.185386	−	0.982666i	$-0.440646\pi$
$887$	34.7876	−	34.7876i	1.16805	−	1.16805i	0.982666	−	0.185386i	$-0.0593535\pi$
$888$	27.6927	−	15.3493i	0.929307	−	0.515087i
$889$	11.0814	−	11.0814i	0.371657	−	0.371657i
$890$	−13.5776	+	0.0824673i	−0.455121	+	0.00276431i
$891$	13.8939	+	33.5428i	0.465462	+	1.12373i
$892$	0.0388021	+	0.00730915i	0.00129919	+	0.000244728i
$893$	−2.75139	+	6.64244i	−0.0920717	+	0.222281i
$894$	5.31603	+	6.41091i	0.177795	+	0.214413i
$895$	−51.1303	−	15.4548i	−1.70910	−	0.516596i
$896$	5.93450	−	7.77963i	0.198258	−	0.259899i
$897$		−	8.74306i		−	0.291922i
$898$	−23.5607	+	19.5370i	−0.786232	+	0.651957i
$899$	42.6927	+	17.6839i	1.42388	+	0.589791i
$900$	−2.35238	+	2.41024i	−0.0784127	+	0.0803413i
$901$	0.764096	+	1.84469i	0.0254557	+	0.0614555i
$902$	48.7263	−	15.0517i	1.62241	−	0.501167i
$903$	−2.06904	−	2.06904i	−0.0688533	−	0.0688533i
$904$	−14.8158	−	26.7303i	−0.492766	−	0.889036i
$905$	−0.456738	−	0.852459i	−0.0151825	−	0.0283367i
$906$	9.34206	−	17.6934i	0.310369	−	0.587824i
$907$	13.1461	+	31.7376i	0.436510	+	1.05383i	0.977146	+	0.212571i	$0.0681838\pi$
$907$	13.1461	+	31.7376i	0.436510	+	1.05383i	−0.540635	+	0.841257i	$0.681816\pi$
$908$	−23.0402	−	15.0586i	−0.764616	−	0.499737i
$909$	−1.72917	+	4.17458i	−0.0573529	+	0.138462i
$910$	4.61539	−	11.3368i	0.152999	−	0.375811i
$911$		−	55.6853i		−	1.84494i	−0.386072	−	0.922469i	$-0.626168\pi$
$911$		−	55.6853i		−	1.84494i	0.386072	−	0.922469i	$-0.373832\pi$
$912$	1.75581	+	4.00661i	0.0581407	+	0.132672i
$913$	61.4160			2.03257
$914$	−2.31906	+	24.8389i	−0.0767078	+	0.821599i
$915$	0.238612	+	0.195428i	0.00788828	+	0.00646065i
$916$	−9.25696	+	1.93931i	−0.305859	+	0.0640766i
$917$	4.56932	+	11.0313i	0.150892	+	0.364286i
$918$	−16.2048	+	30.6912i	−0.534839	+	1.01296i
$919$	−6.79277	−	6.79277i	−0.224073	−	0.224073i	0.586138	−	0.810211i	$-0.300648\pi$
$919$	−6.79277	−	6.79277i	−0.224073	−	0.224073i	−0.810211	+	0.586138i	$0.800648\pi$
$920$	1.35625	−	7.44834i	0.0447144	−	0.245565i
$921$	−17.6512	+	17.6512i	−0.581626	+	0.581626i
$922$	6.07264	+	19.6587i	0.199992	+	0.647425i
$923$	12.5527	−	5.19950i	0.413177	−	0.171144i
$924$	−7.33864	−	10.7451i	−0.241423	−	0.353487i
$925$	28.4794	−	19.1112i	0.936396	−	0.628374i
$926$	15.6127	−	12.9463i	0.513064	−	0.425441i
$927$		−	2.34569i		−	0.0770425i
$928$	−48.7285	−	3.55233i	−1.59959	−	0.116611i
$929$	32.5126			1.06670			0.533351	−	0.845894i	$-0.320932\pi$
$929$	32.5126			1.06670			0.533351	+	0.845894i	$0.320932\pi$
$930$	25.4446	−	10.7210i	0.834360	−	0.351555i
$931$	−3.87076	−	1.60332i	−0.126859	−	0.0525468i
$932$	−19.7738	−	28.9523i	−0.647712	−	0.948364i
$933$	0.549470	−	0.227598i	0.0179888	−	0.00745122i
$934$	−51.6464	+	15.9538i	−1.68992	+	0.522023i
$935$	21.9386	+	40.9464i	0.717470	+	1.33909i
$936$	2.65413	−	3.33649i	0.0867529	−	0.109057i
$937$	−7.91685	+	7.91685i	−0.258632	+	0.258632i	−0.824498	−	0.565865i	$-0.808542\pi$
$937$	−7.91685	+	7.91685i	−0.258632	+	0.258632i	0.565865	+	0.824498i	$0.308542\pi$
$938$	−0.715239	+	1.35463i	−0.0233534	+	0.0442301i
$939$	6.51394	−	2.69816i	0.212574	−	0.0880511i
$940$	−47.7991	−	4.17003i	−1.55904	−	0.136011i
$941$	4.75082	−	11.4695i	0.154872	−	0.373895i	−0.827331	−	0.561714i	$-0.810142\pi$
$941$	4.75082	−	11.4695i	0.154872	−	0.373895i	0.982204	+	0.187820i	$0.0601420\pi$
$942$	22.0241	+	2.05626i	0.717585	+	0.0669967i
$943$	−9.36449			−0.304950
$944$	−0.151113	−	7.43472i	−0.00491830	−	0.241980i
$945$	3.04691	−	10.0804i	0.0991161	−	0.327914i
$946$	−13.4566	−	1.25636i	−0.437512	−	0.0408478i
$947$	−30.1996	−	12.5091i	−0.981356	−	0.406491i	−0.166428	−	0.986054i	$-0.553223\pi$
$947$	−30.1996	−	12.5091i	−0.981356	−	0.406491i	−0.814928	+	0.579563i	$0.803223\pi$
$948$	−16.1133	+	24.6539i	−0.523336	+	0.800722i
$949$	21.7106	−	8.99284i	0.704757	−	0.291920i
$950$	2.26322	+	4.16314i	0.0734284	+	0.135070i
$951$	21.4082	+	21.4082i	0.694209	+	0.694209i
$952$	3.03904	−	10.5972i	0.0984959	−	0.343457i
$953$	2.22439	+	2.22439i	0.0720550	+	0.0720550i	0.742216	−	0.670161i	$-0.233775\pi$
$953$	2.22439	+	2.22439i	0.0720550	+	0.0720550i	−0.670161	+	0.742216i	$0.733775\pi$
$954$	−0.0622807	−	0.201619i	−0.00201641	−	0.00652764i
$955$	1.32730	+	13.3405i	0.0429506	+	0.431689i
$956$	2.83477	+	0.533986i	0.0916831	+	0.0172704i
$957$	−24.8639	+	60.0267i	−0.803735	+	1.94039i
$958$	19.8463	−	16.4569i	0.641204	−	0.531697i
$959$	−8.28727			−0.267610
$960$	−21.9724	+	19.2208i	−0.709156	+	0.620349i
$961$	−2.37415			−0.0765856
$962$	−33.4211	+	27.7133i	−1.07754	+	0.893513i
$963$	−2.57423	+	6.21475i	−0.0829535	+	0.200268i
$964$	26.8247	+	5.05296i	0.863964	+	0.162745i
$965$	−31.9136	+	3.17522i	−1.02734	+	0.102214i
$966$	0.705190	+	2.28288i	0.0226891	+	0.0734505i
$967$	−4.97762	−	4.97762i	−0.160069	−	0.160069i	0.622528	−	0.782597i	$-0.286106\pi$
$967$	−4.97762	−	4.97762i	−0.160069	−	0.160069i	−0.782597	+	0.622528i	$0.786106\pi$
$968$	−27.8649	−	7.99102i	−0.895611	−	0.256841i
$969$	3.48508	+	3.48508i	0.111957	+	0.111957i
$970$	20.2473	−	20.4947i	0.650101	−	0.658047i
$971$	−2.80613	+	1.16234i	−0.0900529	+	0.0373011i	−0.427255	−	0.904131i	$-0.640519\pi$
$971$	−2.80613	+	1.16234i	−0.0900529	+	0.0373011i	0.337202	+	0.941432i	$0.390519\pi$
$972$	3.81089	−	5.83079i	0.122234	−	0.187023i
$973$	−17.3344	−	7.18013i	−0.555714	−	0.230184i
$974$	25.2031	+	2.35306i	0.807558	+	0.0753969i
$975$	−20.2286	+	30.4048i	−0.647834	+	0.973733i
$976$	−0.243871	−	0.234155i	−0.00780613	−	0.00749512i
$977$	−6.32798			−0.202450			−0.101225	−	0.994864i	$-0.532276\pi$
$977$	−6.32798			−0.202450			−0.101225	+	0.994864i	$0.532276\pi$
$978$	2.57878	+	0.240765i	0.0824602	+	0.00769882i
$979$	7.57420	−	18.2857i	0.242072	−	0.584415i
$980$	2.43001	−	27.8541i	0.0776239	−	0.889767i
$981$	3.19926	−	1.32518i	0.102145	−	0.0423097i
$982$	−6.57826	+	12.4589i	−0.209921	+	0.397580i
$983$	24.9181	−	24.9181i	0.794765	−	0.794765i	−0.187500	−	0.982265i	$-0.560038\pi$
$983$	24.9181	−	24.9181i	0.794765	−	0.794765i	0.982265	+	0.187500i	$0.0600384\pi$
$984$	28.2587	+	22.4794i	0.900856	+	0.716617i
$985$	22.7655	+	42.4897i	0.725370	+	1.35384i
$986$	−52.5955	+	16.2469i	−1.67498	+	0.517407i
$987$	13.9898	−	5.79478i	0.445302	−	0.184450i
$988$	−3.38307	−	4.95341i	−0.107630	−	0.157589i
$989$	2.29280	+	0.949707i	0.0729066	+	0.0301989i
$990$	−1.90627	−	4.52422i	−0.0605852	−	0.143789i
$991$	−49.3454			−1.56751			−0.783755	−	0.621071i	$-0.786698\pi$
$991$	−49.3454			−1.56751			−0.783755	+	0.621071i	$0.786698\pi$
$992$	−28.7302	+	9.51857i	−0.912185	+	0.302215i
$993$			27.1657i			0.862079i
$994$	−2.85823	+	2.37010i	−0.0906577	+	0.0751749i
$995$	−38.0332	−	31.1499i	−1.20573	−	0.987517i
$996$	24.5255	+	35.9097i	0.777121	+	1.13784i
$997$	−22.4611	+	9.30368i	−0.711349	+	0.294650i	−0.708863	−	0.705346i	$-0.750791\pi$
$997$	−22.4611	+	9.30368i	−0.711349	+	0.294650i	−0.00248643	+	0.999997i	$0.500791\pi$
$998$	2.35371	+	7.61956i	0.0745053	+	0.241193i
$999$	−26.4124	+	26.4124i	−0.835653	+	0.835653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.z.a.29.18	yes	88
4.3	odd	2		640.2.z.a.209.7		88
5.2	odd	4		800.2.y.f.701.16		88
5.3	odd	4		800.2.y.f.701.7		88
5.4	even	2	inner	160.2.z.a.29.5	✓	88
20.19	odd	2		640.2.z.a.209.16		88
32.11	odd	8		640.2.z.a.49.16		88
32.21	even	8	inner	160.2.z.a.149.5	yes	88
160.53	odd	8		800.2.y.f.501.7		88
160.117	odd	8		800.2.y.f.501.16		88
160.139	odd	8		640.2.z.a.49.7		88
160.149	even	8	inner	160.2.z.a.149.18	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.z.a.29.5	✓	88	5.4	even	2	inner
160.2.z.a.29.18	yes	88	1.1	even	1	trivial
160.2.z.a.149.5	yes	88	32.21	even	8	inner
160.2.z.a.149.18	yes	88	160.149	even	8	inner
640.2.z.a.49.7		88	160.139	odd	8
640.2.z.a.49.16		88	32.11	odd	8
640.2.z.a.209.7		88	4.3	odd	2
640.2.z.a.209.16		88	20.19	odd	2
800.2.y.f.501.7		88	160.53	odd	8
800.2.y.f.501.16		88	160.117	odd	8
800.2.y.f.701.7		88	5.3	odd	4
800.2.y.f.701.16		88	5.2	odd	4

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08863 - 0.902710i) q^{2} +(0.624514 - 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(0.221383 + 2.22508i) q^{5} +(-0.681161 - 2.20509i) q^{6} +(-0.611546 - 0.611546i) q^{7} +(-1.37117 - 2.47384i) q^{8} +(0.238149 + 0.238149i) q^{9} +O(q^{10})\)	\(q+(1.08863 - 0.902710i) q^{2} +(0.624514 - 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(0.221383 + 2.22508i) q^{5} +(-0.681161 - 2.20509i) q^{6} +(-0.611546 - 0.611546i) q^{7} +(-1.37117 - 2.47384i) q^{8} +(0.238149 + 0.238149i) q^{9} +(2.24961 + 2.22245i) q^{10} +(-4.25876 + 1.76403i) q^{11} +(-2.73209 - 1.78564i) q^{12} +(4.13489 + 1.71273i) q^{13} +(-1.21779 - 0.113698i) q^{14} +(3.49303 + 1.05581i) q^{15} +(-3.72586 - 1.45532i) q^{16} -4.50676 q^{17} +(0.474235 + 0.0442765i) q^{18} +(0.256449 - 0.619122i) q^{19} +(4.45521 + 0.388676i) q^{20} +(-1.30395 + 0.540115i) q^{21} +(-3.04380 + 5.76480i) q^{22} +(0.846443 - 0.846443i) q^{23} +(-4.58615 + 0.522387i) q^{24} +(-4.90198 + 0.985190i) q^{25} +(6.04746 - 1.86808i) q^{26} +(5.03092 - 2.08387i) q^{27} +(-1.42836 + 0.975541i) q^{28} +(7.97948 + 3.30521i) q^{29} +(4.75571 - 2.00381i) q^{30} +5.35031 q^{31} +(-5.36982 + 1.77907i) q^{32} +7.52263i q^{33} +(-4.90620 + 4.06830i) q^{34} +(1.22535 - 1.49612i) q^{35} +(0.556235 - 0.379896i) q^{36} +(-6.33734 + 2.62501i) q^{37} +(-0.279710 - 0.905493i) q^{38} +(5.16459 - 5.16459i) q^{39} +(5.20094 - 3.59864i) q^{40} +(-5.53167 - 5.53167i) q^{41} +(-0.931954 + 1.76508i) q^{42} +(0.793372 + 1.91537i) q^{43} +(1.89038 + 9.02340i) q^{44} +(-0.477178 + 0.582622i) q^{45} +(0.157370 - 1.68556i) q^{46} -10.7288 q^{47} +(-4.52105 + 4.70865i) q^{48} -6.25202i q^{49} +(-4.44710 + 5.49757i) q^{50} +(-2.81454 + 6.79489i) q^{51} +(4.89710 - 7.49275i) q^{52} +(-0.169544 - 0.409316i) q^{53} +(3.59567 - 6.81003i) q^{54} +(-4.86794 - 9.08556i) q^{55} +(-0.674329 + 2.35140i) q^{56} +(-0.773300 - 0.773300i) q^{57} +(11.6703 - 3.60501i) q^{58} +(0.711433 + 1.71755i) q^{59} +(3.36835 - 6.47444i) q^{60} +(0.0780876 + 0.0323449i) q^{61} +(5.82451 - 4.82978i) q^{62} -0.291277i q^{63} +(-4.23976 + 6.78413i) q^{64} +(-2.89556 + 9.57963i) q^{65} +(6.79076 + 8.18936i) q^{66} +(0.479290 - 1.15711i) q^{67} +(-1.66853 + 8.85774i) q^{68} +(-0.747575 - 1.80481i) q^{69} +(-0.0166110 - 2.73486i) q^{70} +(2.14664 - 2.14664i) q^{71} +(0.262598 - 0.915684i) q^{72} +(3.71274 - 3.71274i) q^{73} +(-4.52939 + 8.57845i) q^{74} +(-1.57597 + 8.00603i) q^{75} +(-1.12190 - 0.733250i) q^{76} +(3.68321 + 1.52564i) q^{77} +(0.960198 - 10.2845i) q^{78} -9.02383i q^{79} +(2.41337 - 8.61253i) q^{80} -7.87619i q^{81} +(-11.0154 - 1.02845i) q^{82} +(-12.3092 - 5.09863i) q^{83} +(0.578799 + 2.76280i) q^{84} +(-0.997720 - 10.0279i) q^{85} +(2.59271 + 1.36894i) q^{86} +(9.96659 - 9.96659i) q^{87} +(10.2034 + 8.11668i) q^{88} +(-3.03609 + 3.03609i) q^{89} +(0.00646867 + 1.06501i) q^{90} +(-1.48126 - 3.57608i) q^{91} +(-1.35025 - 1.97701i) q^{92} +(3.34134 - 8.06672i) q^{93} +(-11.6797 + 9.68500i) q^{94} +(1.43437 + 0.433556i) q^{95} +(-0.671207 + 9.20718i) q^{96} -9.11036i q^{97} +(-5.64377 - 6.80614i) q^{98} +(-1.43432 - 0.594114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

Introduction

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