LMFDB - Embedded newform 160.2.z.a.29.5

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			29.5
Character	$\chi$	$=$	160.29
Dual form			160.2.z.a.149.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08863 + 0.902710i) q^{2} +(-0.624514 + 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(1.41683 + 1.72991i) q^{5} +(-0.681161 - 2.20509i) q^{6} +(0.611546 + 0.611546i) q^{7} +(1.37117 + 2.47384i) q^{8} +(0.238149 + 0.238149i) q^{9} +O(q^{10})$	\(q+(-1.08863 + 0.902710i) q^{2} +(-0.624514 + 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(1.41683 + 1.72991i) 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} +(-3.10401 - 0.604247i) 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} +(3.92458 - 2.14422i) 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} +(-0.985190 + 4.90198i) 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} +(2.84953 - 4.30259i) q^{30} +5.35031 q^{31} +(5.36982 - 1.77907i) q^{32} -7.52263i q^{33} +(-4.90620 + 4.06830i) q^{34} +(-0.191464 + 1.92438i) 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} +(-2.33680 + 5.87702i) 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} +(-0.0745602 + 0.749392i) q^{45} +(0.157370 - 1.68556i) q^{46} +10.7288 q^{47} +(4.52105 - 4.70865i) q^{48} -6.25202i q^{49} +(-3.35256 - 6.22578i) 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} +(-9.08556 - 4.86794i) 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} +(0.781909 + 7.25622i) 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} +(-1.52872 - 2.26777i) 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} +(-6.77550 - 4.54674i) q^{75} +(-1.12190 - 0.733250i) q^{76} +(-3.68321 - 1.52564i) q^{77} +(-0.960198 + 10.2845i) q^{78} -9.02383i q^{79} +(-2.76133 - 8.50735i) q^{80} -7.87619i q^{81} +(11.0154 + 1.02845i) q^{82} +(12.3092 + 5.09863i) q^{83} +(0.578799 + 2.76280i) q^{84} +(6.38531 + 7.79630i) 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} +(-0.595315 - 0.883116i) 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	$0.281142\pi$
$3$	−0.624514	+	1.50771i	−0.360563	+	0.870477i	−0.995218	+	0.0976808i	$0.968858\pi$
$4$	0.370229	−	1.96543i	0.185114	−	0.982717i
$5$	1.41683	+	1.72991i	0.633625	+	0.773640i
$5$	1.41683	+	1.72991i	0.633625	+	0.773640i
$6$	−0.681161	−	2.20509i	−0.278083	−	0.900225i
$7$	0.611546	+	0.611546i	0.231142	+	0.231142i	0.813169	−	0.582027i	$-0.197740\pi$
$7$	0.611546	+	0.611546i	0.231142	+	0.231142i	−0.582027	+	0.813169i	$0.697740\pi$
$8$	1.37117	+	2.47384i	0.484784	+	0.874634i
$9$	0.238149	+	0.238149i	0.0793828	+	0.0793828i
$10$	−3.10401	−	0.604247i	−0.981575	−	0.191080i
$11$	−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	−0.273348	−	0.961915i	$-0.588131\pi$
$13$	−4.13489	−	1.71273i	−1.14681	−	0.475025i	−0.873463	+	0.486890i	$0.838131\pi$
$14$	−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	$-0.315950\pi$
$17$	4.50676			1.09305			0.546525	+	0.837443i	$0.315950\pi$
$18$	−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	$0.100508\pi$
$20$	3.92458	−	2.14422i	0.877562	−	0.479462i
$21$	−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	−0.789826	−	0.613331i	$-0.789829\pi$
$23$	−0.846443	+	0.846443i	−0.176496	+	0.176496i	0.613331	+	0.789826i	$0.289829\pi$
$24$	−4.58615	+	0.522387i	−0.936144	+	0.106632i
$25$	−0.985190	+	4.90198i	−0.197038	+	0.980396i
$26$	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	$0.328813\pi$
$30$	2.84953	−	4.30259i	0.520250	−	0.785541i
$31$	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
$35$	−0.191464	+	1.92438i	−0.0323634	+	0.325279i
$36$	0.556235	−	0.379896i	0.0927058	−	0.0633160i
$37$	6.33734	−	2.62501i	1.04185	−	0.431550i	0.204876	−	0.978788i	$-0.434321\pi$
$37$	6.33734	−	2.62501i	1.04185	−	0.431550i	0.836977	+	0.547238i	$0.184321\pi$
$38$	0.279710	+	0.905493i	0.0453749	+	0.146890i
$39$	5.16459	−	5.16459i	0.826996	−	0.826996i
$40$	−2.33680	+	5.87702i	−0.369481	+	0.929238i
$41$	−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	0.851769	−	0.523917i	$-0.175530\pi$
$43$	−0.793372	−	1.91537i	−0.120988	−	0.292091i	−0.972757	+	0.231826i	$0.925530\pi$
$44$	1.89038	+	9.02340i	0.284985	+	1.36033i
$45$	−0.0745602	+	0.749392i	−0.0111148	+	0.111713i
$46$	0.157370	−	1.68556i	0.0232030	−	0.248522i
$47$	10.7288			1.56496			0.782479	−	0.622678i	$-0.213955\pi$
$47$	10.7288			1.56496			0.782479	+	0.622678i	$0.213955\pi$
$48$	4.52105	−	4.70865i	0.652558	−	0.679635i
$49$		−	6.25202i		−	0.893146i
$50$	−3.35256	−	6.22578i	−0.474123	−	0.880458i
$51$	−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	0.935096	−	0.354394i	$-0.115313\pi$
$53$	0.169544	+	0.409316i	0.0232887	+	0.0562239i	−0.911807	+	0.410618i	$0.865313\pi$
$54$	3.59567	−	6.81003i	0.489309	−	0.926727i
$55$	−9.08556	−	4.86794i	−1.22510	−	0.656393i
$56$	−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	$0.836385\pi$
$60$	0.781909	+	7.25622i	0.100944	+	0.936774i
$61$	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	−0.950449	−	0.310880i	$-0.899376\pi$
$67$	−0.479290	+	1.15711i	−0.0585546	+	0.141363i	0.891894	+	0.452244i	$0.149376\pi$
$68$	1.66853	−	8.85774i	0.202339	−	1.07416i
$69$	−0.747575	−	1.80481i	−0.0899975	−	0.217273i
$70$	−1.52872	−	2.26777i	−0.182717	−	0.271050i
$71$	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	−0.890170	−	0.455628i	$-0.849415\pi$
$73$	−3.71274	+	3.71274i	−0.434543	+	0.434543i	0.455628	+	0.890170i	$0.349415\pi$
$74$	−4.52939	+	8.57845i	−0.526531	+	0.997225i
$75$	−6.77550	−	4.54674i	−0.782367	−	0.525012i
$76$	−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	$-0.169478\pi$
$80$	−2.76133	−	8.50735i	−0.308726	−	0.951151i
$81$		−	7.87619i		−	0.875132i
$82$	11.0154	+	1.02845i	1.21645	+	0.113573i
$83$	12.3092	+	5.09863i	1.35111	+	0.559648i	0.936601	−	0.350398i	$-0.113954\pi$
$83$	12.3092	+	5.09863i	1.35111	+	0.559648i	0.414508	+	0.910045i	$0.363954\pi$
$84$	0.578799	+	2.76280i	0.0631521	+	0.301446i
$85$	6.38531	+	7.79630i	0.692584	+	0.845628i
$86$	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	$0.323076\pi$
$90$	−0.595315	−	0.883116i	−0.0627517	−	0.0930886i
$91$	−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	$0.153051\pi$
$97$			9.11036i			0.925017i	−0.886615	+	0.462509i	$0.846949\pi$
$98$	5.64377	+	6.80614i	0.570106	+	0.687524i
$99$	−1.43432	−	0.594114i	−0.144154	−	0.0597107i
$100$	9.26977	+	3.75118i	0.926977	+	0.375118i
$101$	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	0.906807	−	0.421547i	$-0.138513\pi$
$103$	4.92485	+	4.92485i	0.485259	+	0.485259i	−0.421547	+	0.906807i	$0.638513\pi$
$104$	−1.43264	−	12.5775i	−0.140482	−	1.23332i
$105$	−2.78183	−	1.49047i	−0.271479	−	0.145455i
$106$	−0.554065	−	0.292544i	−0.0538155	−	0.0284144i
$107$	−7.64337	−	18.4527i	−0.738913	−	1.78389i	−0.610256	−	0.792204i	$-0.708933\pi$
$107$	−7.64337	−	18.4527i	−0.738913	−	1.78389i	−0.128657	−	0.991689i	$-0.541067\pi$
$108$	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	$-0.0388846\pi$
$110$	14.2851	−	2.90224i	1.36203	−	0.276718i
$111$			11.1942i			1.06251i
$112$	−1.38854	−	3.16853i	−0.131205	−	0.299398i
$113$	−10.8052			−1.01647			−0.508233	−	0.861220i	$-0.669701\pi$
$113$	−10.8052			−1.01647			−0.508233	+	0.861220i	$0.669701\pi$
$114$	−1.53990	−	0.143772i	−0.144225	−	0.0134654i
$115$	−2.66354	−	0.265007i	−0.248376	−	0.0247120i
$116$	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
$120$	−7.40147	−	7.19350i	−0.675659	−	0.656674i
$121$	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
$125$	−9.87584	+	5.24098i	−0.883322	+	0.468767i
$126$	−0.262939	−	0.317093i	−0.0234245	−	0.0282489i
$127$		−	18.1202i		−	1.60791i	−0.594689	−	0.803956i	$-0.702725\pi$
$127$		−	18.1202i		−	1.60791i	0.594689	−	0.803956i	$-0.297275\pi$
$128$	−1.50858	−	11.2127i	−0.133341	−	0.991070i
$129$	3.38329			0.297882
$130$	11.7998	+	7.81482i	1.03491	+	0.685405i
$131$	−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
$135$	−10.7329	−	5.75055i	−0.923738	−	0.494928i
$136$	6.17956	+	11.1490i	0.529893	+	0.956019i
$137$	−6.77568	+	6.77568i	−0.578885	+	0.578885i	−0.934596	−	0.355711i	$-0.884239\pi$
$137$	−6.77568	+	6.77568i	−0.578885	+	0.578885i	0.355711	+	0.934596i	$0.384239\pi$
$138$	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	$0.00314801\pi$
$140$	3.71135	+	1.08877i	0.313666	+	0.0920178i
$141$	−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	$0.422223\pi$
$150$	11.4804	−	1.16660i	0.937370	−	0.0952525i
$151$	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
$155$	7.58048	+	9.25557i	0.608879	+	0.743425i
$156$	−8.23858	−	12.0627i	−0.659614	−	0.965792i
$157$	3.66780	−	8.85486i	0.292722	−	0.706695i	−0.707277	−	0.706936i	$-0.750077\pi$
$157$	3.66780	−	8.85486i	0.292722	−	0.706695i	1.00000		0.000241450i	$7.68561e-5\pi$
$158$	8.14590	+	9.82361i	0.648053	+	0.781524i
$159$	−0.723013			−0.0573386
$160$	10.6857	+	6.76867i	0.844782	+	0.535111i
$161$	−1.03528			−0.0815912
$162$	7.10992	+	8.57426i	0.558608	+	0.673657i
$163$	0.429458	−	1.03680i	0.0336378	−	0.0812087i	−0.906168	−	0.422918i	$-0.861006\pi$
$163$	0.429458	−	1.03680i	0.0336378	−	0.0812087i	0.939806	+	0.341709i	$0.111006\pi$
$164$	−12.9201	+	8.82415i	−1.00889	+	0.689050i
$165$	13.0135	−	10.6583i	1.01310	−	0.829747i
$166$	−18.0027	+	5.56111i	−1.39728	+	0.431626i
$167$	−1.04298	−	1.04298i	−0.0807084	−	0.0807084i	0.665600	−	0.746309i	$-0.268176\pi$
$167$	−1.04298	−	1.04298i	−0.0807084	−	0.0807084i	−0.746309	+	0.665600i	$0.768176\pi$
$168$	−3.12410	−	2.48518i	−0.241030	−	0.191735i
$169$	4.97147	+	4.97147i	0.382421	+	0.382421i
$170$	−13.9890	−	2.72320i	−1.07291	−	0.208860i
$171$	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	−0.510748	−	0.859731i	$-0.670631\pi$
$173$	−19.4640	−	8.06226i	−1.47982	−	0.612962i	−0.969075	+	0.246768i	$0.920631\pi$
$174$	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	$0.773786\pi$
$180$	1.44528	+	0.423990i	0.107724	+	0.0316023i
$181$	−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
$185$	13.5200	+	7.24385i	0.994008	+	0.532578i
$186$	−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
$190$	−1.17012	+	1.76680i	−0.0848896	+	0.128177i
$191$	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	$-0.827345\pi$
$193$		−	14.3427i		−	1.03241i	0.856466	−	0.516204i	$-0.172655\pi$
$194$	−8.22402	−	9.91781i	−0.590450	−	0.712057i
$195$	16.2516	+	1.61694i	1.16380	+	0.115792i
$196$	−12.2879	−	2.31468i	−0.877710	−	0.165334i
$197$	−19.9166	+	8.24973i	−1.41900	+	0.587769i	−0.954609	−	0.297861i	$-0.903727\pi$
$197$	−19.9166	+	8.24973i	−1.41900	+	0.587769i	−0.464391	+	0.885630i	$0.653727\pi$
$198$	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	$0.965596\pi$
$200$	−13.4776	+	4.28427i	−0.953008	+	0.302944i
$201$	−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
$205$	1.73187	−	17.4067i	0.120959	−	1.21574i
$206$	−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
$210$	4.37384	−	0.888612i	0.301824	−	0.0613201i
$211$	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
$215$	2.18935	−	4.08622i	0.149312	−	0.278678i
$216$	−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
$220$	−12.9313	+	16.0548i	−0.871831	+	1.08241i
$221$	−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	$-0.999790\pi$
$223$		−	0.0197422i		−	0.00132204i	1.00000		0.000661019i	$-0.000210409\pi$
$224$	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	$0.275976\pi$
$227$	−5.26664	+	12.7148i	−0.349559	+	0.843910i	−0.996672	+	0.0815159i	$0.974024\pi$
$228$	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	$0.924940\pi$
$230$	3.13883	−	2.11591i	0.206968	−	0.139519i
$231$	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	−0.984944	−	0.172871i	$-0.944696\pi$
$233$	−12.3958	+	12.3958i	−0.812073	+	0.812073i	0.172871	+	0.984944i	$0.444696\pi$
$234$	1.88507	+	0.995312i	0.123231	+	0.0650656i
$235$	15.2009	+	18.5599i	0.991596	+	1.21071i
$236$	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	$0.985146\pi$
$240$	14.5511	+	1.14967i	0.939270	+	0.0742110i
$241$			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
$245$	10.8155	−	8.85805i	0.690974	−	0.565920i
$246$	−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
$250$	6.02005	−	14.6205i	0.380741	−	0.924682i
$251$	−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	$-0.941473\pi$
$257$		−	5.86206i		−	0.365665i	0.983144	−	0.182833i	$-0.0585266\pi$
$258$	−3.68315	+	3.05413i	−0.229303	+	0.190142i
$259$	5.48089	+	2.27026i	0.340566	+	0.141067i
$260$	−19.9002	+	2.14438i	−1.23416	+	0.132989i
$261$	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	0.492171	−	0.870498i	$-0.336203\pi$
$263$	−6.13543	−	6.13543i	−0.378327	−	0.378327i	−0.870498	+	0.492171i	$0.836203\pi$
$264$	18.6098	−	10.3148i	1.14535	−	0.634835i
$265$	−0.467865	+	0.873228i	−0.0287407	+	0.0536419i
$266$	−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	$-0.0196732\pi$
$270$	16.8752	−	3.42845i	1.02699	−	0.208649i
$271$		−	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
$275$	−4.45158	−	22.6142i	−0.268440	−	1.36369i
$276$	−3.82400	+	0.801118i	−0.230178	+	0.0482216i
$277$	2.93560	+	7.08716i	0.176383	+	0.425826i	0.987203	−	0.159470i	$-0.0509784\pi$
$277$	2.93560	+	7.08716i	0.176383	+	0.425826i	−0.810820	+	0.585296i	$0.800978\pi$
$278$	−14.3251	+	27.1310i	−0.859161	+	1.62721i
$279$	1.27417	+	1.27417i	0.0762825	+	0.0762825i
$280$	−5.02313	+	2.16500i	−0.300189	+	0.129384i
$281$	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	−0.588723	−	0.808335i	$-0.700369\pi$
$283$	−7.29150	+	3.02024i	−0.433434	+	0.179534i	0.155289	+	0.987869i	$0.450369\pi$
$284$	−3.42433	−	5.01382i	−0.203196	−	0.297516i
$285$	−0.242107	+	2.43338i	−0.0143412	+	0.144141i
$286$	−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
$290$	−22.7712	−	15.0810i	−1.33717	−	0.885586i
$291$	−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	0.210691	−	0.977553i	$-0.432428\pi$
$293$	17.9886	−	7.45113i	1.05091	−	0.435300i	0.840215	+	0.542253i	$0.182428\pi$
$294$	−13.7863	+	4.25863i	−0.804033	+	0.248369i
$295$	−1.96323	+	3.66420i	−0.114304	+	0.213338i
$296$	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
$300$	−11.4448	+	11.6335i	−0.660765	+	0.671658i
$301$	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	0.747578	−	0.664175i	$-0.231217\pi$
$307$	14.1319	+	5.85364i	0.806552	+	0.334085i	0.0589748	+	0.998259i	$0.481217\pi$
$308$	−4.36217	+	6.67427i	−0.248558	+	0.380302i
$309$	−10.5009	+	4.34960i	−0.597374	+	0.247440i
$310$	−16.6074	−	3.23291i	−0.943239	−	0.183617i
$311$	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	0.615477	−	0.788155i	$-0.288964\pi$
$313$	−3.05500	−	3.05500i	−0.172679	−	0.172679i	−0.788155	+	0.615477i	$0.788964\pi$
$314$	4.00049	+	12.9506i	0.225761	+	0.730846i
$315$	−0.503884	+	0.412690i	−0.0283907	+	0.0232525i
$316$	−17.7357	−	3.34088i	−0.997713	−	0.187939i
$317$	7.09958	−	17.1399i	0.398752	−	0.962673i	−0.589210	−	0.807980i	$-0.700561\pi$
$317$	7.09958	−	17.1399i	0.398752	−	0.962673i	0.987963	−	0.154693i	$-0.0494390\pi$
$318$	0.787093	−	0.652671i	0.0441380	−	0.0366000i
$319$	−39.8132			−2.22911
$320$	−17.7430	+	2.27755i	−0.991862	+	0.127319i
$321$	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
$325$	12.4694	−	18.5818i	0.691678	−	1.03073i
$326$	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
$330$	−4.54553	+	23.3503i	−0.250223	+	1.28539i
$331$	−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	$-0.396855\pi$
$337$	11.6900			0.636797			0.318399	+	0.947957i	$0.396855\pi$
$338$	−9.89989	−	0.924293i	−0.538483	−	0.0502749i
$339$	6.74799	−	16.2911i	0.366500	−	0.884810i
$340$	17.6871	−	9.66350i	0.959220	−	0.524077i
$341$	−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
$345$	2.06297	−	3.85034i	0.111067	−	0.207295i
$346$	28.4670	−	8.79355i	1.53040	−	0.472744i
$347$	20.3616	−	8.43404i	1.09307	−	0.452763i	0.237992	−	0.971267i	$-0.423511\pi$
$347$	20.3616	−	8.43404i	1.09307	−	0.452763i	0.855075	+	0.518504i	$0.173511\pi$
$348$	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	$0.665729\pi$
$350$	1.75711	−	5.85759i	0.0939213	−	0.313101i
$351$	24.3714			1.30085
$352$	−19.7304	+	17.0492i	−1.05163	+	0.908723i
$353$			16.1954i			0.861992i	0.902354	+	0.430996i	$0.141838\pi$
$353$			16.1954i			0.861992i	−0.902354	+	0.430996i	$0.858162\pi$
$354$	3.30276	−	2.73871i	0.175540	−	0.145561i
$355$	6.75491	+	0.672075i	0.358514	+	0.0356700i
$356$	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	$0.328372\pi$
$360$	−1.95611	+	0.843097i	−0.103096	+	0.0444351i
$361$	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
$365$	−11.6830	−	1.16239i	−0.611517	−	0.0608424i
$366$	0.0181334	−	0.194222i	0.000947847	−	0.0101522i
$367$	−16.6503			−0.869139			−0.434569	−	0.900638i	$-0.643099\pi$
$367$	−16.6503			−0.869139			−0.434569	+	0.900638i	$0.643099\pi$
$368$	4.38557	−	1.92188i	0.228614	−	0.100185i
$369$		−	2.63472i		−	0.137158i
$370$	−21.2573	+	4.31875i	−1.10512	+	0.224521i
$371$	−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	$-0.843263\pi$
$373$	−11.4407	−	27.6204i	−0.592378	−	1.43013i	0.288821	−	0.957383i	$-0.406737\pi$
$374$	13.7177	−	25.9806i	0.709324	−	1.34342i
$375$	−1.73427	−	18.1630i	−0.0895575	−	0.937931i
$376$	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	$0.818142\pi$
$380$	−0.321081	−	2.97968i	−0.0164711	−	0.152854i
$381$	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	$0.187970\pi$
$383$			21.7935i			1.11359i	−0.830649	+	0.556797i	$0.812030\pi$
$384$	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	$-0.270652\pi$
$390$	−19.1516	+	12.9103i	−0.969781	+	0.653736i
$391$	−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
$395$	15.6104	−	12.7852i	0.785446	−	0.643295i
$396$	−1.69872	+	2.59910i	−0.0853638	+	0.130610i
$397$	36.7175	+	15.2089i	1.84280	+	0.763313i	0.949416	+	0.314021i	$0.101676\pi$
$397$	36.7175	+	15.2089i	1.84280	+	0.763313i	0.893385	+	0.449292i	$0.148324\pi$
$398$	2.89034	−	30.9577i	0.144879	−	1.55177i
$399$			0.945817i			0.0473501i
$400$	10.8046	−	16.8303i	0.540232	−	0.841516i
$401$		−	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
$405$	13.6251	−	11.1592i	0.677038	−	0.554506i
$406$	−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	$0.319889\pi$
$410$	13.8279	+	20.5129i	0.682910	+	1.01306i
$411$	−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	$0.700828\pi$
$420$	−3.95934	+	4.91568i	−0.193196	+	0.239861i
$421$	−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
$425$	−4.44002	+	22.0921i	−0.215372	+	1.07162i
$426$	−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
$430$	1.30528	+	6.42472i	0.0629461	+	0.309828i
$431$			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	$-0.619787\pi$
$433$	−15.2945			−0.735006			−0.367503	+	0.930022i	$0.619787\pi$
$434$	−6.51558	−	0.608321i	−0.312758	−	0.0292003i
$435$	−31.3623	−	3.12037i	−1.50371	−	0.149610i
$436$	−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	$0.793683\pi$
$440$	−0.415393	−	29.1510i	−0.0198031	−	1.38972i
$441$	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	−0.280691	−	0.959798i	$-0.590564\pi$
$443$	4.19920	−	1.73937i	0.199510	−	0.0826398i	0.480201	+	0.877158i	$0.340564\pi$
$444$	22.0015	+	4.14443i	1.04415	+	0.196686i
$445$	−9.55379	−	0.950547i	−0.452893	−	0.0450602i
$446$	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	$0.670609\pi$
$450$	0.684253	−	2.28107i	0.0322560	−	0.107531i
$451$	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
$455$	4.08761	−	7.62915i	0.191630	−	0.357660i
$456$	−0.852691	+	2.97335i	−0.0399309	+	0.139240i
$457$	12.4735	−	12.4735i	0.583485	−	0.583485i	−0.352374	−	0.935859i	$-0.614626\pi$
$457$	12.4735	−	12.4735i	0.583485	−	0.583485i	0.935859	+	0.352374i	$0.114626\pi$
$458$	5.91402	+	3.12258i	0.276344	+	0.145909i
$459$	−22.6731	+	9.39152i	−1.05829	+	0.438359i
$460$	−1.50697	+	5.13689i	−0.0702629	+	0.239509i
$461$	−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	$-0.608147\pi$
$463$	−14.3416			−0.666509			−0.333254	+	0.942837i	$0.608147\pi$
$464$	−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	0.995680	−	0.0928497i	$-0.0295976\pi$
$467$	35.3127	+	14.6270i	1.63408	+	0.676857i	0.638398	+	0.769707i	$0.279598\pi$
$468$	−2.95062	+	0.618148i	−0.136393	+	0.0285739i
$469$	−1.00073	+	0.414517i	−0.0462095	+	0.0191406i
$470$	−33.3023	−	6.48285i	−1.53612	−	0.299032i
$471$	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
$475$	2.78227	+	1.86706i	0.127659	+	0.0856665i
$476$	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	$0.363261\pi$
$480$	−16.8786	+	11.8839i	−0.770399	+	0.542422i
$481$	−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
$485$	−15.7601	+	12.9078i	−0.715630	+	0.586114i
$486$	4.70608	−	1.45372i	0.213472	−	0.0659423i
$487$	−12.6563	−	12.6563i	−0.573513	−	0.573513i	0.359595	−	0.933108i	$-0.382915\pi$
$487$	−12.6563	−	12.6563i	−0.573513	−	0.573513i	−0.933108	+	0.359595i	$0.882915\pi$
$488$	0.0270556	+	0.237527i	0.00122475	+	0.0107523i
$489$	1.29500	+	1.29500i	0.0585618	+	0.0585618i
$490$	−3.77777	+	19.4064i	−0.170662	+	0.876690i
$491$	−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	$0.165284\pi$
$500$	6.64447	+	21.3507i	0.297150	+	0.954831i
$501$	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	−0.287123	−	0.957894i	$-0.592699\pi$
$503$	15.0438	−	15.0438i	0.670771	−	0.670771i	0.957894	+	0.287123i	$0.0926989\pi$
$504$	−0.720573	+	0.399392i	−0.0320969	+	0.0177903i
$505$	−14.1681	+	26.4435i	−0.630473	+	1.17672i
$506$	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	$0.459148\pi$
$510$	12.8421	−	19.3907i	0.568660	−	0.858637i
$511$	−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
$515$	−1.54188	+	15.4972i	−0.0679435	+	0.682889i
$516$	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
$520$	19.7281	−	20.2985i	0.865136	−	0.890148i
$521$	−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	0.928368	−	0.371662i	$-0.121212\pi$
$523$	0.208289	+	0.502855i	0.00910786	+	0.0219883i	−0.919260	+	0.393650i	$0.871212\pi$
$524$	−15.1064	+	23.1133i	−0.659924	+	1.00971i
$525$	−1.36299	−	6.92406i	−0.0594858	−	0.302191i
$526$	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
$530$	−0.278939	−	1.37297i	−0.0121163	−	0.0596379i
$531$	−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
$535$	21.0923	−	39.3667i	0.911898	−	1.70197i
$536$	−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
$540$	−15.2759	+	18.9657i	−0.657372	+	0.816155i
$541$	−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	$-0.453029\pi$
$547$	17.3653	−	41.9235i	0.742486	−	1.79252i	0.595457	−	0.803387i	$-0.296971\pi$
$548$	10.8086	+	15.8257i	0.461720	+	0.676041i
$549$	0.0108935	+	0.0262993i	0.000464925	+	0.00112243i
$550$	25.2602	+	20.6001i	1.07710	+	0.878389i
$551$	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
$555$	−19.3650	+	15.8603i	−0.822000	+	0.673233i
$556$	−8.89672	−	42.4670i	−0.377305	−	1.80100i
$557$	6.40538	+	2.65320i	0.271405	+	0.112420i	0.514235	−	0.857649i	$-0.328076\pi$
$557$	6.40538	+	2.65320i	0.271405	+	0.112420i	−0.242830	+	0.970069i	$0.578076\pi$
$558$	−2.53730	−	0.236893i	−0.107413	−	0.0100285i
$559$			9.27867i			0.392446i
$560$	3.51395	−	6.89131i	0.148492	−	0.291211i
$561$		−	33.9027i		−	1.43137i
$562$	−2.34335	+	25.0990i	−0.0988481	+	1.05874i
$563$	−33.2595	−	13.7766i	−1.40172	−	0.580612i	−0.451524	−	0.892259i	$-0.649120\pi$
$563$	−33.2595	−	13.7766i	−1.40172	−	0.580612i	−0.950198	+	0.311647i	$0.899120\pi$
$564$	29.3121	+	19.1578i	1.23426	+	0.806688i
$565$	−15.3091	−	18.6920i	−0.644059	−	0.786379i
$566$	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	$0.0747058\pi$
$570$	−1.93307	−	2.86760i	−0.0809673	−	0.120110i
$571$	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	$0.326886\pi$
$577$			41.1102i			1.71144i	−0.517438	+	0.855721i	$0.673114\pi$
$578$	−3.60436	+	2.98879i	−0.149921	+	0.124317i
$579$	21.6246	+	8.95720i	0.898687	+	0.372248i
$580$	38.4032	−	4.13822i	1.59461	−	0.171830i
$581$	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
$585$	1.59180	−	2.97095i	0.0658129	−	0.122834i
$586$	−12.8567	+	24.3500i	−0.531107	+	1.00589i
$587$	5.01910	+	12.1172i	0.207160	+	0.500129i	0.992974	−	0.118334i	$-0.0377554\pi$
$587$	5.01910	+	12.1172i	0.207160	+	0.500129i	−0.785813	+	0.618464i	$0.787755\pi$
$588$	11.1639	−	17.0811i	0.460390	−	0.704413i
$589$	1.37208	−	3.31250i	0.0565356	−	0.136489i
$590$	−1.17047	−	5.76118i	−0.0481875	−	0.237184i
$591$		−	35.1805i		−	1.44713i
$592$	−27.4323	+	0.557568i	−1.12746	+	0.0229159i
$593$	31.1472			1.27906			0.639531	−	0.768766i	$-0.279129\pi$
$593$	31.1472			1.27906			0.639531	+	0.768766i	$0.279129\pi$
$594$	−3.29996	+	35.3451i	−0.135399	+	1.45023i
$595$	−0.862884	+	8.67270i	−0.0353748	+	0.355546i
$596$	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	$0.778706\pi$
$600$	1.95750	−	22.9959i	0.0799145	−	0.938802i
$601$	−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
$605$	22.8045	+	2.26891i	0.927134	+	0.0922445i
$606$	23.8351	−	19.7645i	0.968236	−	0.802877i
$607$		−	11.0053i		−	0.446693i	−0.974739	−	0.223346i	$-0.928302\pi$
$607$		−	11.0053i		−	0.446693i	0.974739	−	0.223346i	$-0.0716981\pi$
$608$	0.275623	−	3.78081i	0.0111780	−	0.153332i
$609$	−12.1901			−0.493966
$610$	−0.222840	−	0.147583i	−0.00902254	−	0.00597547i
$611$	−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	−0.571447	−	0.820639i	$-0.693618\pi$
$613$	−9.78571	+	4.05337i	−0.395241	+	0.163714i	0.176206	+	0.984353i	$0.443618\pi$
$614$	−20.6686	+	6.38460i	−0.834116	+	0.257661i
$615$	25.1627	+	13.4819i	1.01466	+	0.543643i
$616$	−1.27615	−	11.2036i	−0.0514175	−	0.451405i
$617$	17.2460	−	17.2460i	0.694297	−	0.694297i	−0.268877	−	0.963175i	$-0.586653\pi$
$617$	17.2460	−	17.2460i	0.694297	−	0.694297i	0.963175	+	0.268877i	$0.0866525\pi$
$618$	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	$0.454987\pi$
$620$	20.9977	−	11.4723i	0.843289	−	0.460737i
$621$	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
$630$	0.176004	−	0.904128i	0.00701215	−	0.0360213i
$631$	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
$635$	31.3464	−	25.6733i	1.24394	−	1.01881i
$636$	−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
$640$	17.2596	−	18.4962i	0.682244	−	0.731125i
$641$	−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	−0.977811	−	0.209491i	$-0.932819\pi$
$643$	−3.50596	+	8.46413i	−0.138261	+	0.333793i	0.839549	+	0.543284i	$0.182819\pi$
$644$	−0.383289	+	2.03477i	−0.0151037	+	0.0801811i
$645$	4.79355	+	5.85280i	0.188746	+	0.230454i
$646$	1.26059	+	4.08084i	0.0495971	+	0.160559i
$647$	6.68343	+	6.68343i	0.262753	+	0.262753i	0.826171	−	0.563419i	$-0.190514\pi$
$647$	6.68343	+	6.68343i	0.262753	+	0.262753i	−0.563419	+	0.826171i	$0.690514\pi$
$648$	19.4844	−	10.7996i	0.765421	−	0.424250i
$649$	−6.05964	−	6.05964i	−0.237862	−	0.237862i
$650$	3.19940	+	31.4849i	0.125491	+	1.23494i
$651$	−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	0.0368832	−	0.999320i	$-0.488257\pi$
$653$	−16.4481	−	6.81301i	−0.643662	−	0.266614i	−0.680545	+	0.732706i	$0.738257\pi$
$654$	−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	$-0.00911597\pi$
$660$	−16.1302	−	29.5232i	−0.627867	−	1.14919i
$661$	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
$665$	1.14232	+	0.612043i	0.0442974	+	0.0237340i
$666$	−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
$670$	2.18690	−	3.30207i	0.0844874	−	0.127570i
$671$	−0.389614			−0.0150409
$672$	−6.04108	+	5.22013i	−0.233040	+	0.201371i
$673$			15.9426i			0.614541i	0.951622	+	0.307270i	$0.0994156\pi$
$673$			15.9426i			0.614541i	−0.951622	+	0.307270i	$0.900584\pi$
$674$	−12.7261	+	10.5527i	−0.490192	+	0.406476i
$675$	−5.25870	−	26.7145i	−0.202407	−	1.02824i
$676$	11.6117	−	7.93052i	0.446603	−	0.305020i
$677$	−16.8509	+	6.97989i	−0.647634	+	0.268259i	−0.682225	−	0.731143i	$-0.738987\pi$
$677$	−16.8509	+	6.97989i	−0.647634	+	0.268259i	0.0345903	+	0.999402i	$0.488987\pi$
$678$	7.36007	+	23.8264i	0.282662	+	0.915049i
$679$	−5.57140	+	5.57140i	−0.213811	+	0.213811i
$680$	−10.5314	+	26.4863i	−0.403861	+	1.01570i
$681$	−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	0.728245	−	0.685317i	$-0.240336\pi$
$683$	−7.09008	−	17.1170i	−0.271295	−	0.654963i	−0.999539	+	0.0303543i	$0.990336\pi$
$684$	−0.0925561	−	0.441801i	−0.00353897	−	0.0168927i
$685$	−21.3213	−	2.12135i	−0.814645	−	0.0810525i
$686$	−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
$690$	1.22993	+	6.05386i	0.0468227	+	0.230466i
$691$	−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
$695$	42.7595	+	22.9101i	1.62196	+	0.869028i
$696$	−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
$700$	3.37487	+	7.96290i	0.127558	+	0.300970i
$701$	−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	$0.775624\pi$
$710$	−7.96029	+	5.36609i	−0.298744	+	0.201386i
$711$	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
$715$	29.2303	+	35.6894i	1.09315	+	1.33471i
$716$	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	$-0.329984\pi$
$720$	1.36841	−	2.68362i	0.0509975	−	0.100013i
$721$			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
$725$	−24.0634	+	35.8590i	−0.893691	+	1.33177i
$726$	−20.9167	−	11.0440i	−0.776292	−	0.409880i
$727$	4.16643	−	4.16643i	0.154524	−	0.154524i	−0.625611	−	0.780135i	$-0.715150\pi$
$727$	4.16643	−	4.16643i	0.154524	−	0.154524i	0.780135	+	0.625611i	$0.215150\pi$
$728$	6.81558	−	8.56784i	0.252602	−	0.317545i
$729$	20.7270	−	20.7270i	0.767665	−	0.767665i
$730$	13.7678	−	9.28096i	0.509568	−	0.343504i
$731$	−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	−0.803327	−	0.595538i	$-0.796939\pi$
$733$	5.03088	−	12.1456i	0.185820	−	0.448608i	0.989147	+	0.146929i	$0.0469390\pi$
$734$	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	$0.758370\pi$
$740$	19.2428	−	23.8907i	0.707379	−	0.878241i
$741$	−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	0.219380	−	0.975640i	$-0.429597\pi$
$743$	−20.6141	−	20.6141i	−0.756260	−	0.756260i	−0.975640	+	0.219380i	$0.929597\pi$
$744$	−24.5373	+	2.79494i	−0.899582	+	0.102467i
$745$	−7.11248	−	3.81078i	−0.260581	−	0.139616i
$746$	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
$750$	18.2839	+	18.2072i	0.667633	+	0.664833i
$751$			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
$755$	−1.91927	+	19.2903i	−0.0698494	+	0.702044i
$756$	−5.15308	+	7.88439i	−0.187416	+	0.286753i
$757$	10.7516	+	25.9568i	0.390775	+	0.943414i	0.989771	+	0.142662i	$0.0455663\pi$
$757$	10.7516	+	25.9568i	0.390775	+	0.943414i	−0.598996	+	0.800752i	$0.704434\pi$
$758$	−8.65160	−	4.56802i	−0.314240	−	0.165918i
$759$	6.36748	+	6.36748i	0.231125	+	0.231125i
$760$	3.03932	+	2.95392i	0.110248	+	0.107150i
$761$	−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
$765$	−0.336025	+	3.37733i	−0.0121490	+	0.122108i
$766$	−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	$0.434215\pi$
$770$	10.5109	+	6.96116i	0.378785	+	0.250863i
$771$	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	0.424326	−	0.905509i	$-0.360511\pi$
$773$	37.9415	−	15.7159i	1.36466	−	0.565261i	0.940336	+	0.340248i	$0.110511\pi$
$774$	0.291439	+	0.943462i	0.0104755	+	0.0339120i
$775$	−5.27107	+	26.2271i	−0.189343	+	0.942106i
$776$	−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
$780$	9.19482	−	31.3429i	0.329227	−	1.12225i
$781$	−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	−0.00499439	−	0.999988i	$-0.501590\pi$
$787$	−20.0758	−	8.31566i	−0.715624	−	0.296421i	−0.710630	+	0.703566i	$0.751590\pi$
$788$	8.84060	+	42.1991i	0.314933	+	1.50328i
$789$	13.0821	−	5.41879i	0.465736	−	0.192914i
$790$	−5.45262	+	28.0101i	−0.193996	+	0.996554i
$791$	−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
$795$	−1.02439	−	1.25075i	−0.0363312	−	0.0443595i
$796$	24.7993	+	36.3106i	0.878989	+	1.28700i
$797$	9.61080	−	23.2025i	0.340432	−	0.821875i	−0.657240	−	0.753681i	$-0.728276\pi$
$797$	9.61080	−	23.2025i	0.340432	−	0.821875i	0.997672	−	0.0681942i	$-0.0217237\pi$
$798$	−0.853799	−	1.02964i	−0.0302241	−	0.0364490i
$799$	48.3522			1.71058
$800$	3.43066	+	28.0754i	0.121292	+	0.992617i
$801$	−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
$805$	−1.46681	−	1.79094i	−0.0516983	−	0.0631223i
$806$	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	$-0.537207\pi$
$810$	−4.75917	+	24.4478i	−0.167220	+	0.859008i
$811$	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
$820$	−33.5706	−	9.84835i	−1.17234	−	0.343919i
$821$	−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	−0.959074	−	0.283155i	$-0.908619\pi$
$823$	−19.3907	+	19.3907i	−0.675919	+	0.675919i	0.283155	+	0.959074i	$0.408619\pi$
$824$	−5.43045	+	18.9361i	−0.189179	+	0.659670i
$825$	36.8758	+	7.41122i	1.28385	+	0.258026i
$826$	−0.671097	−	2.17252i	−0.0233505	−	0.0755915i
$827$	−21.2398	+	8.79781i	−0.738580	+	0.305930i	−0.720072	−	0.693899i	$-0.755891\pi$
$827$	−21.2398	+	8.79781i	−0.738580	+	0.305930i	−0.0185075	+	0.999829i	$0.505891\pi$
$828$	−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	$0.879968\pi$
$830$	−35.1270	−	23.2640i	−1.21928	−	0.807506i
$831$	−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
$835$	0.326540	−	3.28200i	0.0113004	−	0.113578i
$836$	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	$0.104881\pi$
$840$	−0.127186	−	8.92549i	−0.00438832	−	0.307959i
$841$	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
$845$	−1.55648	+	15.6439i	−0.0535446	+	0.538168i
$846$	−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
$850$	−15.1092	−	28.0581i	−0.518241	−	0.962386i
$851$	−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	0.737899	−	0.674911i	$-0.235818\pi$
$853$	−7.62598	−	18.4107i	−0.261109	−	0.630372i	−0.999008	+	0.0445392i	$0.985818\pi$
$854$	−0.0914171	−	0.0482679i	−0.00312823	−	0.00165169i
$855$	0.444844	+	0.238342i	0.0152133	+	0.00815114i
$856$	35.1687	−	44.2104i	1.20204	−	1.51108i
$857$	8.09740	+	8.09740i	0.276602	+	0.276602i	0.831751	−	0.555149i	$-0.187339\pi$
$857$	8.09740	+	8.09740i	0.276602	+	0.276602i	−0.555149	+	0.831751i	$0.687339\pi$
$858$	−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	$0.830915\pi$
$860$	−7.22063	−	5.81585i	−0.246221	−	0.198319i
$861$	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	$0.267296\pi$
$863$			43.7401i			1.48893i	−0.667661	+	0.744466i	$0.732704\pi$
$864$	−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
$870$	36.9587	−	24.9141i	1.25302	−	0.844668i
$871$	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
$875$	−9.24462	−	2.83443i	−0.312525	−	0.0958212i
$876$	−16.7731	+	3.51393i	−0.566712	+	0.118725i
$877$	5.41238	+	2.24188i	0.182763	+	0.0757030i	0.472188	−	0.881498i	$-0.343464\pi$
$877$	5.41238	+	2.24188i	0.182763	+	0.0757030i	−0.289425	+	0.957201i	$0.593464\pi$
$878$	8.07217	+	0.753651i	0.272423	+	0.0254345i
$879$			31.7750i			1.07174i
$880$	26.7671	+	31.3597i	0.902319	+	1.05713i
$881$			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	0.341801	−	0.939772i	$-0.388963\pi$
$883$	−2.40776	−	0.997327i	−0.0810276	−	0.0335627i	−0.422829	+	0.906209i	$0.638963\pi$
$884$	−22.0701	+	33.7680i	−0.742297	+	1.13574i
$885$	−4.29848	−	5.24833i	−0.144492	−	0.176421i
$886$	−3.00123	+	5.68419i	−0.100828	+	0.190964i
$887$	−34.7876	+	34.7876i	−1.16805	+	1.16805i	−0.185386	+	0.982666i	$0.559354\pi$
$887$	−34.7876	+	34.7876i	−1.16805	+	1.16805i	−0.982666	+	0.185386i	$0.940646\pi$
$888$	−27.6927	+	15.3493i	−0.929307	+	0.515087i
$889$	11.0814	−	11.0814i	0.371657	−	0.371657i
$890$	11.2586	−	7.58951i	0.377389	−	0.254401i
$891$	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
$900$	1.31424	+	3.10092i	0.0438081	+	0.103364i
$901$	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
$905$	−0.852459	−	0.456738i	−0.0283367	−	0.0151825i
$906$	9.34206	−	17.6934i	0.310369	−	0.587824i
$907$	−13.1461	−	31.7376i	−0.436510	−	1.05383i	−0.977146	−	0.212571i	$-0.931816\pi$
$907$	−13.1461	−	31.7376i	−0.436510	−	1.05383i	0.540635	−	0.841257i	$-0.318184\pi$
$908$	23.0402	+	15.0586i	0.764616	+	0.499737i
$909$	−1.72917	+	4.17458i	−0.0573529	+	0.138462i
$910$	2.43702	+	11.9952i	0.0807863	+	0.397639i
$911$		−	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
$915$	−0.306913	−	0.0305361i	−0.0101462	−	0.00100949i
$916$	−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	$0.800648\pi$
$920$	−2.99659	−	6.95253i	−0.0987947	−	0.229218i
$921$	−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
$925$	6.62427	+	33.6517i	0.217805	+	1.10646i
$926$	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	$0.320932\pi$
$930$	15.2459	−	23.0202i	0.499932	−	0.754862i
$931$	−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
$935$	−40.9464	−	21.9386i	−1.33909	−	0.717470i
$936$	2.65413	−	3.33649i	0.0867529	−	0.109057i
$937$	7.91685	−	7.91685i	0.258632	−	0.258632i	−0.565865	−	0.824498i	$-0.691458\pi$
$937$	7.91685	−	7.91685i	0.258632	−	0.258632i	0.824498	+	0.565865i	$0.191458\pi$
$938$	0.715239	−	1.35463i	0.0233534	−	0.0442301i
$939$	6.51394	−	2.69816i	0.212574	−	0.0880511i
$940$	42.1060	−	23.0049i	1.37335	−	0.750338i
$941$	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	0.814928	−	0.579563i	$-0.196777\pi$
$947$	30.1996	+	12.5091i	0.981356	+	0.406491i	0.166428	+	0.986054i	$0.446777\pi$
$948$	16.1133	−	24.6539i	0.523336	−	0.800722i
$949$	21.7106	−	8.99284i	0.704757	−	0.291920i
$950$	−4.71428	+	0.479050i	−0.152951	+	0.0155424i
$951$	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	0.670161	−	0.742216i	$-0.266225\pi$
$953$	−2.22439	−	2.22439i	−0.0720550	−	0.0720550i	−0.742216	+	0.670161i	$0.766225\pi$
$954$	−0.0622807	−	0.201619i	−0.00201641	−	0.00652764i
$955$	8.49462	+	10.3717i	0.274880	+	0.335621i
$956$	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
$960$	7.64685	−	28.1736i	0.246801	−	0.909299i
$961$	−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
$965$	24.8115	−	20.3211i	0.798712	−	0.654160i
$966$	0.705190	+	2.28288i	0.0226891	+	0.0734505i
$967$	4.97762	+	4.97762i	0.160069	+	0.160069i	0.782597	−	0.622528i	$-0.213894\pi$
$967$	4.97762	+	4.97762i	0.160069	+	0.160069i	−0.622528	+	0.782597i	$0.713894\pi$
$968$	27.8649	+	7.99102i	0.895611	+	0.256841i
$969$	3.48508	+	3.48508i	0.111957	+	0.111957i
$970$	5.50491	−	28.2787i	0.176752	−	0.907973i
$971$	−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	$-0.467724\pi$
$977$	6.32798			0.202450			0.101225	+	0.994864i	$0.467724\pi$
$978$	−2.57878	−	0.240765i	−0.0824602	−	0.00769882i
$979$	7.57420	−	18.2857i	0.242072	−	0.584415i
$980$	−13.4057	−	24.5366i	−0.428230	−	0.783792i
$981$	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	−0.982265	−	0.187500i	$-0.939962\pi$
$983$	−24.9181	+	24.9181i	−0.794765	+	0.794765i	0.187500	+	0.982265i	$0.439962\pi$
$984$	28.2587	+	22.4794i	0.900856	+	0.716617i
$985$	−42.4897	−	22.7655i	−1.35384	−	0.725370i
$986$	−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
$990$	4.09315	+	2.71082i	0.130089	+	0.0861555i
$991$	−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
$995$	−48.9198	−	4.86724i	−1.55086	−	0.154302i
$996$	24.5255	+	35.9097i	0.777121	+	1.13784i
$997$	22.4611	−	9.30368i	0.711349	−	0.294650i	0.00248643	−	0.999997i	$-0.499209\pi$
$997$	22.4611	−	9.30368i	0.711349	−	0.294650i	0.708863	+	0.705346i	$0.249209\pi$
$998$	−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.29.5	✓	88
4.3	odd	2		640.2.z.a.209.16		88
5.2	odd	4		800.2.y.f.701.7		88
5.3	odd	4		800.2.y.f.701.16		88
5.4	even	2	inner	160.2.z.a.29.18	yes	88
20.19	odd	2		640.2.z.a.209.7		88
32.11	odd	8		640.2.z.a.49.7		88
32.21	even	8	inner	160.2.z.a.149.18	yes	88
160.53	odd	8		800.2.y.f.501.16		88
160.117	odd	8		800.2.y.f.501.7		88
160.139	odd	8		640.2.z.a.49.16		88
160.149	even	8	inner	160.2.z.a.149.5	yes	88

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

\(f(q)\)	\(=\)	\(q+(-1.08863 + 0.902710i) q^{2} +(-0.624514 + 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(1.41683 + 1.72991i) q^{5} +(-0.681161 - 2.20509i) q^{6} +(0.611546 + 0.611546i) q^{7} +(1.37117 + 2.47384i) q^{8} +(0.238149 + 0.238149i) q^{9} +O(q^{10})\)	\(q+(-1.08863 + 0.902710i) q^{2} +(-0.624514 + 1.50771i) q^{3} +(0.370229 - 1.96543i) q^{4} +(1.41683 + 1.72991i) 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} +(-3.10401 - 0.604247i) 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} +(3.92458 - 2.14422i) 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} +(-0.985190 + 4.90198i) 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} +(2.84953 - 4.30259i) q^{30} +5.35031 q^{31} +(5.36982 - 1.77907i) q^{32} -7.52263i q^{33} +(-4.90620 + 4.06830i) q^{34} +(-0.191464 + 1.92438i) 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} +(-2.33680 + 5.87702i) 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} +(-0.0745602 + 0.749392i) q^{45} +(0.157370 - 1.68556i) q^{46} +10.7288 q^{47} +(4.52105 - 4.70865i) q^{48} -6.25202i q^{49} +(-3.35256 - 6.22578i) 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} +(-9.08556 - 4.86794i) 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} +(0.781909 + 7.25622i) 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} +(-1.52872 - 2.26777i) 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} +(-6.77550 - 4.54674i) q^{75} +(-1.12190 - 0.733250i) q^{76} +(-3.68321 - 1.52564i) q^{77} +(-0.960198 + 10.2845i) q^{78} -9.02383i q^{79} +(-2.76133 - 8.50735i) q^{80} -7.87619i q^{81} +(11.0154 + 1.02845i) q^{82} +(12.3092 + 5.09863i) q^{83} +(0.578799 + 2.76280i) q^{84} +(6.38531 + 7.79630i) 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} +(-0.595315 - 0.883116i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more