LMFDB - Embedded newform 770.2.w.b.139.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.6
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.497687 + 1.53172i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.22362 - 0.235570i) q^{5} +(-1.30296 + 0.946658i) q^{6} +(-1.37179 + 2.26234i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.328565 + 0.238717i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.497687 + 1.53172i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.22362 - 0.235570i) q^{5} +(-1.30296 + 0.946658i) q^{6} +(-1.37179 + 2.26234i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.328565 + 0.238717i) q^{9} +(1.93741 + 1.11643i) q^{10} +(-0.104345 + 3.31498i) q^{11} -1.61055 q^{12} +(2.29058 - 3.15272i) q^{13} +(-2.43957 + 1.02395i) q^{14} +(-0.745842 + 3.52322i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.79279 - 3.84395i) q^{17} +(0.125501 + 0.386251i) q^{18} +(-1.00111 + 3.08110i) q^{19} +(0.911178 + 2.04200i) q^{20} +(-2.78256 - 3.22714i) q^{21} +(-2.03291 + 2.62055i) q^{22} -0.417354i q^{23} +(-1.30296 - 0.946658i) q^{24} +(4.88901 - 1.04764i) q^{25} +(3.70624 - 1.20423i) q^{26} +(-4.43806 + 3.22444i) q^{27} +(-2.57552 - 0.605550i) q^{28} +(4.40885 - 1.43252i) q^{29} +(-2.67430 + 2.41195i) q^{30} +(-1.16996 + 1.61032i) q^{31} -1.00000 q^{32} +(-5.02571 - 1.80965i) q^{33} -4.75138i q^{34} +(-2.51741 + 5.35375i) q^{35} +(-0.125501 + 0.386251i) q^{36} +(7.41451 - 2.40912i) q^{37} +(-2.62094 + 1.90422i) q^{38} +(3.68910 + 5.07761i) q^{39} +(-0.463098 + 2.18759i) q^{40} +(-2.84940 + 8.76954i) q^{41} +(-0.354269 - 4.24636i) q^{42} -12.1733 q^{43} +(-3.18498 + 0.925148i) q^{44} +(0.786840 + 0.453416i) q^{45} +(0.245314 - 0.337646i) q^{46} +(3.70007 - 11.3876i) q^{47} +(-0.497687 - 1.53172i) q^{48} +(-3.23638 - 6.20692i) q^{49} +(4.57108 + 2.02613i) q^{50} +(7.27780 - 2.36470i) q^{51} +(3.70624 + 1.20423i) q^{52} +(-7.96576 + 10.9639i) q^{53} -5.48574 q^{54} +(0.548886 + 7.39586i) q^{55} +(-1.72771 - 2.00375i) q^{56} +(-4.22115 - 3.06685i) q^{57} +(4.40885 + 1.43252i) q^{58} +(9.09311 - 2.95453i) q^{59} +(-3.58126 + 0.379397i) q^{60} +(1.64874 - 1.19788i) q^{61} +(-1.89304 + 0.615086i) q^{62} +(-0.990781 + 0.415857i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.35071 - 7.55005i) q^{65} +(-3.00220 - 4.41808i) q^{66} -1.41951i q^{67} +(2.79279 - 3.84395i) q^{68} +(0.639271 + 0.207712i) q^{69} +(-5.18348 + 2.85158i) q^{70} +(5.32006 - 3.86525i) q^{71} +(-0.328565 + 0.238717i) q^{72} +(-0.451901 + 0.146832i) q^{73} +(7.41451 + 2.40912i) q^{74} +(-0.828510 + 8.01002i) q^{75} -3.23966 q^{76} +(-7.35648 - 4.78353i) q^{77} +6.27627i q^{78} +(7.13084 - 9.81476i) q^{79} +(-1.66049 + 1.49759i) q^{80} +(-2.35368 - 7.24389i) q^{81} +(-7.45982 + 5.41987i) q^{82} +(-1.17790 - 1.62123i) q^{83} +(2.20934 - 3.64361i) q^{84} +(-7.11564 - 7.88960i) q^{85} +(-9.84844 - 7.15531i) q^{86} +7.46609i q^{87} +(-3.12049 - 1.12362i) q^{88} +3.09087i q^{89} +(0.370056 + 0.829314i) q^{90} +(3.99032 + 9.50695i) q^{91} +(0.396927 - 0.128969i) q^{92} +(-1.88428 - 2.59350i) q^{93} +(9.68690 - 7.03794i) q^{94} +(-1.50028 + 7.08704i) q^{95} +(0.497687 - 1.53172i) q^{96} +(9.99328 + 7.26054i) q^{97} +(1.03005 - 6.92380i) q^{98} +(-0.825625 + 1.06428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.497687	+	1.53172i	−0.287340	+	0.884341i	0.698348	+	0.715759i	$0.253919\pi$
$3$	−0.497687	+	1.53172i	−0.287340	+	0.884341i	−0.985688	+	0.168583i	$0.946081\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	2.22362	−	0.235570i	0.994435	−	0.105350i
$5$	2.22362	−	0.235570i	0.994435	−	0.105350i
$6$	−1.30296	+	0.946658i	−0.531932	+	0.386471i
$7$	−1.37179	+	2.26234i	−0.518489	+	0.855085i
$7$	−1.37179	+	2.26234i	−0.518489	+	0.855085i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.328565	+	0.238717i	0.109522	+	0.0795722i
$10$	1.93741	+	1.11643i	0.612664	+	0.353047i
$11$	−0.104345	+	3.31498i	−0.0314611	+	0.999505i
$11$	−0.104345	+	3.31498i	−0.0314611	+	0.999505i
$12$	−1.61055			−0.464926
$13$	2.29058	−	3.15272i	0.635293	−	0.874406i	−0.363060	−	0.931766i	$-0.618268\pi$
$13$	2.29058	−	3.15272i	0.635293	−	0.874406i	0.998354	+	0.0573595i	$0.0182681\pi$
$14$	−2.43957	+	1.02395i	−0.652003	+	0.273663i
$15$	−0.745842	+	3.52322i	−0.192576	+	0.909691i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.79279	−	3.84395i	−0.677351	−	0.932294i	0.322547	−	0.946553i	$-0.395461\pi$
$17$	−2.79279	−	3.84395i	−0.677351	−	0.932294i	−0.999898	+	0.0142594i	$0.995461\pi$
$18$	0.125501	+	0.386251i	0.0295808	+	0.0910403i
$19$	−1.00111	+	3.08110i	−0.229670	+	0.706853i	0.768113	+	0.640314i	$0.221196\pi$
$19$	−1.00111	+	3.08110i	−0.229670	+	0.706853i	−0.997784	+	0.0665390i	$0.978804\pi$
$20$	0.911178	+	2.04200i	0.203746	+	0.456605i
$21$	−2.78256	−	3.22714i	−0.607204	−	0.704221i
$22$	−2.03291	+	2.62055i	−0.433419	+	0.558702i
$23$		−	0.417354i		−	0.0870243i	−0.999053	−	0.0435121i	$-0.986145\pi$
$23$		−	0.417354i		−	0.0870243i	0.999053	−	0.0435121i	$-0.0138547\pi$
$24$	−1.30296	−	0.946658i	−0.265966	−	0.193236i
$25$	4.88901	−	1.04764i	0.977803	−	0.209527i
$26$	3.70624	−	1.20423i	0.726853	−	0.236169i
$27$	−4.43806	+	3.22444i	−0.854105	+	0.620543i
$28$	−2.57552	−	0.605550i	−0.486728	−	0.114438i
$29$	4.40885	−	1.43252i	0.818703	−	0.266013i	0.130424	−	0.991458i	$-0.458366\pi$
$29$	4.40885	−	1.43252i	0.818703	−	0.266013i	0.688280	+	0.725446i	$0.258366\pi$
$30$	−2.67430	+	2.41195i	−0.488257	+	0.440360i
$31$	−1.16996	+	1.61032i	−0.210132	+	0.289221i	−0.901053	−	0.433708i	$-0.857205\pi$
$31$	−1.16996	+	1.61032i	−0.210132	+	0.289221i	0.690922	+	0.722930i	$0.257205\pi$
$32$	−1.00000			−0.176777
$33$	−5.02571	−	1.80965i	−0.874863	−	0.315020i
$34$		−	4.75138i		−	0.814855i
$35$	−2.51741	+	5.35375i	−0.425520	+	0.904949i
$36$	−0.125501	+	0.386251i	−0.0209168	+	0.0643752i
$37$	7.41451	−	2.40912i	1.21894	−	0.396057i	0.372243	−	0.928136i	$-0.378589\pi$
$37$	7.41451	−	2.40912i	1.21894	−	0.396057i	0.846695	+	0.532079i	$0.178589\pi$
$38$	−2.62094	+	1.90422i	−0.425173	+	0.308906i
$39$	3.68910	+	5.07761i	0.590728	+	0.813068i
$40$	−0.463098	+	2.18759i	−0.0732222	+	0.345888i
$41$	−2.84940	+	8.76954i	−0.445001	+	1.36957i	0.437482	+	0.899227i	$0.355870\pi$
$41$	−2.84940	+	8.76954i	−0.445001	+	1.36957i	−0.882483	+	0.470345i	$0.844130\pi$
$42$	−0.354269	−	4.24636i	−0.0546650	−	0.655228i
$43$	−12.1733			−1.85642			−0.928209	−	0.372060i	$-0.878651\pi$
$43$	−12.1733			−1.85642			−0.928209	+	0.372060i	$0.878651\pi$
$44$	−3.18498	+	0.925148i	−0.480154	+	0.139471i
$45$	0.786840	+	0.453416i	0.117295	+	0.0675913i
$46$	0.245314	−	0.337646i	0.0361696	−	0.0497832i
$47$	3.70007	−	11.3876i	0.539710	−	1.66106i	−0.193536	−	0.981093i	$-0.561996\pi$
$47$	3.70007	−	11.3876i	0.539710	−	1.66106i	0.733246	−	0.679964i	$-0.238004\pi$
$48$	−0.497687	−	1.53172i	−0.0718350	−	0.221085i
$49$	−3.23638	−	6.20692i	−0.462339	−	0.886703i
$50$	4.57108	+	2.02613i	0.646448	+	0.286539i
$51$	7.27780	−	2.36470i	1.01910	−	0.331124i
$52$	3.70624	+	1.20423i	0.513963	+	0.166997i
$53$	−7.96576	+	10.9639i	−1.09418	+	1.50601i	−0.251301	+	0.967909i	$0.580858\pi$
$53$	−7.96576	+	10.9639i	−1.09418	+	1.50601i	−0.842880	+	0.538102i	$0.819142\pi$
$54$	−5.48574			−0.746515
$55$	0.548886	+	7.39586i	0.0740117	+	0.997257i
$56$	−1.72771	−	2.00375i	−0.230875	−	0.267763i
$57$	−4.22115	−	3.06685i	−0.559106	−	0.406214i
$58$	4.40885	+	1.43252i	0.578911	+	0.188099i
$59$	9.09311	−	2.95453i	1.18382	−	0.384647i	0.350037	−	0.936736i	$-0.386169\pi$
$59$	9.09311	−	2.95453i	1.18382	−	0.384647i	0.833785	+	0.552089i	$0.186169\pi$
$60$	−3.58126	+	0.379397i	−0.462339	+	0.0489799i
$61$	1.64874	−	1.19788i	0.211100	−	0.153373i	−0.477212	−	0.878788i	$-0.658352\pi$
$61$	1.64874	−	1.19788i	0.211100	−	0.153373i	0.688311	+	0.725416i	$0.258352\pi$
$62$	−1.89304	+	0.615086i	−0.240416	+	0.0781160i
$63$	−0.990781	+	0.415857i	−0.124827	+	0.0523931i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.35071	−	7.55005i	0.539639	−	0.936468i
$66$	−3.00220	−	4.41808i	−0.369545	−	0.543828i
$67$		−	1.41951i		−	0.173421i	−0.996234	−	0.0867104i	$-0.972365\pi$
$67$		−	1.41951i		−	0.173421i	0.996234	−	0.0867104i	$-0.0276355\pi$
$68$	2.79279	−	3.84395i	0.338676	−	0.466147i
$69$	0.639271	+	0.207712i	0.0769592	+	0.0250056i
$70$	−5.18348	+	2.85158i	−0.619545	+	0.340829i
$71$	5.32006	−	3.86525i	0.631374	−	0.458720i	−0.225502	−	0.974243i	$-0.572402\pi$
$71$	5.32006	−	3.86525i	0.631374	−	0.458720i	0.856876	+	0.515522i	$0.172402\pi$
$72$	−0.328565	+	0.238717i	−0.0387218	+	0.0281330i
$73$	−0.451901	+	0.146832i	−0.0528910	+	0.0171853i	−0.335343	−	0.942096i	$-0.608852\pi$
$73$	−0.451901	+	0.146832i	−0.0528910	+	0.0171853i	0.282452	+	0.959281i	$0.408852\pi$
$74$	7.41451	+	2.40912i	0.861919	+	0.280054i
$75$	−0.828510	+	8.01002i	−0.0956681	+	0.924917i
$76$	−3.23966			−0.371614
$77$	−7.35648	−	4.78353i	−0.838349	−	0.545134i
$78$			6.27627i			0.710647i
$79$	7.13084	−	9.81476i	0.802282	−	1.10425i	−0.190186	−	0.981748i	$-0.560909\pi$
$79$	7.13084	−	9.81476i	0.802282	−	1.10425i	0.992469	−	0.122499i	$-0.0390907\pi$
$80$	−1.66049	+	1.49759i	−0.185648	+	0.167436i
$81$	−2.35368	−	7.24389i	−0.261520	−	0.804876i
$82$	−7.45982	+	5.41987i	−0.823799	+	0.598525i
$83$	−1.17790	−	1.62123i	−0.129291	−	0.177954i	0.739464	−	0.673196i	$-0.235079\pi$
$83$	−1.17790	−	1.62123i	−0.129291	−	0.177954i	−0.868755	+	0.495243i	$0.835079\pi$
$84$	2.20934	−	3.64361i	0.241059	−	0.397551i
$85$	−7.11564	−	7.88960i	−0.771799	−	0.855747i
$86$	−9.84844	−	7.15531i	−1.06198	−	0.771577i
$87$			7.46609i			0.800449i
$88$	−3.12049	−	1.12362i	−0.332646	−	0.119779i
$89$			3.09087i			0.327631i	0.986491	+	0.163816i	$0.0523802\pi$
$89$			3.09087i			0.327631i	−0.986491	+	0.163816i	$0.947620\pi$
$90$	0.370056	+	0.829314i	0.0390073	+	0.0874174i
$91$	3.99032	+	9.50695i	0.418299	+	0.996599i
$92$	0.396927	−	0.128969i	0.0413825	−	0.0134460i
$93$	−1.88428	−	2.59350i	−0.195391	−	0.268933i
$94$	9.68690	−	7.03794i	0.999127	−	0.725908i
$95$	−1.50028	+	7.08704i	−0.153925	+	0.727115i
$96$	0.497687	−	1.53172i	0.0507950	−	0.156331i
$97$	9.99328	+	7.26054i	1.01466	+	0.737196i	0.965182	−	0.261579i	$-0.0842431\pi$
$97$	9.99328	+	7.26054i	1.01466	+	0.737196i	0.0494816	+	0.998775i	$0.484243\pi$
$98$	1.03005	−	6.92380i	0.104051	−	0.699409i
$99$	−0.825625	+	1.06428i	−0.0829785	+	0.106964i
$100$	2.50715	+	4.32599i	0.250715	+	0.432599i
$101$	0.305648	+	0.222066i	0.0304131	+	0.0220964i	0.602888	−	0.797826i	$-0.294017\pi$
$101$	0.305648	+	0.222066i	0.0304131	+	0.0220964i	−0.572475	+	0.819922i	$0.694017\pi$
$102$	7.27780	+	2.36470i	0.720610	+	0.234140i
$103$	1.97988	+	6.09343i	0.195083	+	0.600404i	0.999976	+	0.00698328i	$0.00222286\pi$
$103$	1.97988	+	6.09343i	0.195083	+	0.600404i	−0.804893	+	0.593421i	$0.797777\pi$
$104$	2.29058	+	3.15272i	0.224610	+	0.309149i
$105$	−6.94758	−	6.52047i	−0.678015	−	0.636333i
$106$	−12.8889	+	4.18785i	−1.25188	+	0.406760i
$107$	2.80265	−	8.62568i	0.270943	−	0.833876i	−0.719322	−	0.694677i	$-0.755547\pi$
$107$	2.80265	−	8.62568i	0.270943	−	0.833876i	0.990264	−	0.139199i	$-0.0444528\pi$
$108$	−4.43806	−	3.22444i	−0.427052	−	0.310272i
$109$		−	3.17952i		−	0.304542i	−0.988339	−	0.152271i	$-0.951341\pi$
$109$		−	3.17952i		−	0.304542i	0.988339	−	0.152271i	$-0.0486587\pi$
$110$	−3.90312	+	6.30600i	−0.372148	+	0.601254i
$111$			12.5560i			1.19176i
$112$	−0.219968	−	2.63659i	−0.0207850	−	0.249134i
$113$	8.02326	+	2.60691i	0.754765	+	0.245238i	0.661030	−	0.750359i	$-0.270120\pi$
$113$	8.02326	+	2.60691i	0.754765	+	0.245238i	0.0937345	+	0.995597i	$0.470120\pi$
$114$	−1.61234	−	4.96227i	−0.151009	−	0.464759i
$115$	−0.0983159	−	0.928038i	−0.00916800	−	0.0865400i
$116$	2.72482	+	3.75039i	0.252993	+	0.348215i
$117$	1.50521	−	0.489073i	0.139157	−	0.0452148i
$118$	9.09311	+	2.95453i	0.837089	+	0.271987i
$119$	12.5274	−	1.04515i	1.14839	−	0.0958089i
$120$	−3.12030	−	1.79807i	−0.284843	−	0.164141i
$121$	−10.9782	−	0.691802i	−0.998020	−	0.0628911i
$122$	2.03795			0.184508
$123$	−12.0144	−	8.72898i	−1.08330	−	0.787065i
$124$	−1.89304	−	0.615086i	−0.170000	−	0.0552364i
$125$	10.6245	−	3.48125i	0.950288	−	0.311373i
$126$	−1.04599	−	0.245931i	−0.0931845	−	0.0219093i
$127$	12.4315	−	9.03204i	1.10312	−	0.801464i	0.121554	−	0.992585i	$-0.461212\pi$
$127$	12.4315	−	9.03204i	1.10312	−	0.801464i	0.981567	+	0.191120i	$0.0612121\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	6.05852	−	18.6462i	0.533423	−	1.64171i
$130$	7.95761	−	3.55083i	0.697928	−	0.311429i
$131$	3.70831			0.323997			0.161998	−	0.986791i	$-0.448206\pi$
$131$	3.70831			0.323997			0.161998	+	0.986791i	$0.448206\pi$
$132$	0.168052	−	5.33895i	0.0146271	−	0.464696i
$133$	−5.59718	−	6.49148i	−0.485337	−	0.562883i
$134$	0.834367	−	1.14841i	0.0720784	−	0.0992074i
$135$	−9.10899	+	8.21541i	−0.783977	+	0.707070i
$136$	4.51883	−	1.46826i	0.387486	−	0.125902i
$137$	3.15954	+	4.34874i	0.269938	+	0.371538i	0.922369	−	0.386311i	$-0.126251\pi$
$137$	3.15954	+	4.34874i	0.269938	+	0.371538i	−0.652431	+	0.757848i	$0.726251\pi$
$138$	0.395091	+	0.543796i	0.0336324	+	0.0462910i
$139$	4.35142	+	13.3923i	0.369083	+	1.13592i	0.947385	+	0.320097i	$0.103715\pi$
$139$	4.35142	+	13.3923i	0.369083	+	1.13592i	−0.578302	+	0.815822i	$0.696285\pi$
$140$	−5.86964	−	0.739800i	−0.496075	−	0.0625245i
$141$	15.6012	+	11.3350i	1.31386	+	0.954576i
$142$	6.57595			0.551841
$143$	10.2122	+	7.92221i	0.853986	+	0.662489i
$144$	−0.406129			−0.0338441
$145$	9.46617	−	4.22398i	0.786123	−	0.350783i
$146$	−0.451901	−	0.146832i	−0.0373996	−	0.0121519i
$147$	11.1180	−	1.86813i	0.916997	−	0.154081i
$148$	4.58242	+	6.30716i	0.376672	+	0.518445i
$149$	6.68531	+	9.20154i	0.547682	+	0.753820i	0.989695	−	0.143189i	$-0.0457357\pi$
$149$	6.68531	+	9.20154i	0.547682	+	0.753820i	−0.442013	+	0.897008i	$0.645736\pi$
$150$	−5.37845	+	5.99325i	−0.439148	+	0.489347i
$151$	−5.26447	−	1.71053i	−0.428417	−	0.139201i	0.0868685	−	0.996220i	$-0.472314\pi$
$151$	−5.26447	−	1.71053i	−0.428417	−	0.139201i	−0.515285	+	0.857019i	$0.672314\pi$
$152$	−2.62094	−	1.90422i	−0.212586	−	0.154453i
$153$		−	1.92967i		−	0.156005i
$154$	−3.13983	−	8.19399i	−0.253015	−	0.660290i
$155$	−2.22222	+	3.85635i	−0.178493	+	0.309749i
$156$	−3.68910	+	5.07761i	−0.295364	+	0.406534i
$157$	0.405138	−	1.24689i	0.0323335	−	0.0995124i	−0.933587	−	0.358350i	$-0.883339\pi$
$157$	0.405138	−	1.24689i	0.0323335	−	0.0995124i	0.965921	+	0.258838i	$0.0833395\pi$
$158$	11.5379	−	3.74890i	0.917909	−	0.298247i
$159$	−12.8292	−	17.6579i	−1.01743	−	1.40037i
$160$	−2.22362	+	0.235570i	−0.175793	+	0.0186234i
$161$	0.944197	+	0.572523i	0.0744131	+	0.0451211i
$162$	2.35368	−	7.24389i	0.184923	−	0.569133i
$163$	13.0284	−	17.9321i	1.02046	−	1.40455i	0.108586	−	0.994087i	$-0.465368\pi$
$163$	13.0284	−	17.9321i	1.02046	−	1.40455i	0.911878	−	0.410461i	$-0.134632\pi$
$164$	−9.22084			−0.720027
$165$	−11.6016	−	2.84008i	−0.903182	−	0.221100i
$166$		−	2.00396i		−	0.155537i
$167$	6.92908	−	9.53706i	0.536188	−	0.738000i	−0.451870	−	0.892084i	$-0.649243\pi$
$167$	6.92908	−	9.53706i	0.536188	−	0.738000i	0.988058	+	0.154084i	$0.0492427\pi$
$168$	3.92906	−	1.64913i	0.303133	−	0.127233i
$169$	−0.675630	−	2.07938i	−0.0519716	−	0.159952i
$170$	−1.11928	−	10.5653i	−0.0858449	−	0.810320i
$171$	−1.06444	+	0.773360i	−0.0813997	+	0.0591403i
$172$	−3.76177	−	11.5775i	−0.286832	−	0.882779i
$173$	10.1842	+	3.30905i	0.774290	+	0.251582i	0.669400	−	0.742902i	$-0.266551\pi$
$173$	10.1842	+	3.30905i	0.774290	+	0.251582i	0.104890	+	0.994484i	$0.466551\pi$
$174$	−4.38846	+	6.04019i	−0.332688	+	0.457906i
$175$	−4.33660	+	12.4978i	−0.327816	+	0.944742i
$176$	−1.86408	−	2.74321i	−0.140510	−	0.206777i
$177$			15.3986i			1.15743i
$178$	−1.81677	+	2.50056i	−0.136172	+	0.187425i
$179$	5.91945	−	18.2182i	0.442440	−	1.36169i	−0.442827	−	0.896607i	$-0.646024\pi$
$179$	5.91945	−	18.2182i	0.442440	−	1.36169i	0.885267	−	0.465084i	$-0.153976\pi$
$180$	−0.188077	+	0.888442i	−0.0140185	+	0.0662206i
$181$	1.69693	+	2.33562i	0.126132	+	0.173605i	0.867413	−	0.497589i	$-0.165781\pi$
$181$	1.69693	+	2.33562i	0.126132	+	0.173605i	−0.741281	+	0.671195i	$0.765781\pi$
$182$	−2.35981	+	10.0367i	−0.174921	+	0.743972i
$183$	1.01426	+	3.12158i	0.0749766	+	0.230754i
$184$	0.396927	+	0.128969i	0.0292619	+	0.00950775i
$185$	15.9196	−	7.10361i	1.17043	−	0.522268i
$186$		−	3.20574i		−	0.235056i
$187$	13.0340	−	8.85696i	0.953143	−	0.647685i
$188$	11.9737			0.873269
$189$	−1.20669	−	14.4637i	−0.0877736	−	1.05208i
$190$	−5.37941	+	4.85169i	−0.390263	+	0.351979i
$191$	2.31702	+	7.13105i	0.167654	+	0.515985i	0.999222	−	0.0394376i	$-0.0125566\pi$
$191$	2.31702	+	7.13105i	0.167654	+	0.515985i	−0.831568	+	0.555422i	$0.812557\pi$
$192$	1.30296	−	0.946658i	0.0940332	−	0.0683191i
$193$	13.0560	−	9.48577i	0.939795	−	0.682801i	−0.00857636	−	0.999963i	$-0.502730\pi$
$193$	13.0560	−	9.48577i	0.939795	−	0.682801i	0.948371	+	0.317162i	$0.102730\pi$
$194$	3.81709	+	11.7478i	0.274051	+	0.843443i
$195$	9.39930	+	10.4217i	0.673098	+	0.746310i
$196$	4.90304	−	4.99602i	0.350217	−	0.356859i
$197$	−17.1046			−1.21866			−0.609328	−	0.792919i	$-0.708561\pi$
$197$	−17.1046			−1.21866			−0.609328	+	0.792919i	$0.708561\pi$
$198$	−1.29351	+	0.375729i	−0.0919259	+	0.0267019i
$199$		−	22.9014i		−	1.62344i	−0.584047	−	0.811720i	$-0.698532\pi$
$199$		−	22.9014i		−	1.62344i	0.584047	−	0.811720i	$-0.301468\pi$
$200$	−0.514427	+	4.97347i	−0.0363755	+	0.351677i
$201$	2.17430	+	0.706472i	0.153363	+	0.0498307i
$202$	0.116747	+	0.359311i	0.00821430	+	0.0252810i
$203$	−2.80717	+	11.9394i	−0.197025	+	0.837985i
$204$	4.49793	+	6.19087i	0.314918	+	0.433447i
$205$	−4.27015	+	20.1714i	−0.298240	+	1.40883i
$206$	−1.97988	+	6.09343i	−0.137945	+	0.424550i
$207$	0.0996293	−	0.137128i	0.00692471	−	0.00953105i
$208$			3.89697i			0.270206i
$209$	−10.1093	−	3.64016i	−0.699277	−	0.251795i
$210$	−1.78808	−	9.35886i	−0.123389	−	0.645823i
$211$	−6.16147	+	8.48054i	−0.424173	+	0.583824i	−0.966604	−	0.256276i	$-0.917504\pi$
$211$	−6.16147	+	8.48054i	−0.424173	+	0.583824i	0.542430	+	0.840101i	$0.317504\pi$
$212$	−12.8889	−	4.18785i	−0.885211	−	0.287622i
$213$	3.27277	+	10.0725i	0.224246	+	0.690159i
$214$	7.33744	−	5.33096i	0.501577	−	0.364417i
$215$	−27.0689	+	2.86767i	−1.84609	+	0.195573i
$216$	−1.69519	−	5.21725i	−0.115343	−	0.354989i
$217$	−2.03814	−	4.85588i	−0.138358	−	0.329638i
$218$	1.86887	−	2.57228i	0.126576	−	0.174217i
$219$		−	0.765264i		−	0.0517118i
$220$	−6.86426	+	2.80747i	−0.462789	+	0.189279i
$221$	−18.5160			−1.24552
$222$	−7.38021	+	10.1580i	−0.495327	+	0.681760i
$223$	−9.01091	+	27.7327i	−0.603415	+	1.85712i	−0.0960750	+	0.995374i	$0.530629\pi$
$223$	−9.01091	+	27.7327i	−0.603415	+	1.85712i	−0.507340	+	0.861746i	$0.669371\pi$
$224$	1.37179	−	2.26234i	0.0916567	−	0.151159i
$225$	1.85645	+	0.822872i	0.123763	+	0.0548581i
$226$	4.95865	+	6.82499i	0.329844	+	0.453992i
$227$	−22.9294	+	7.45021i	−1.52188	+	0.494488i	−0.946308	−	0.323266i	$-0.895219\pi$
$227$	−22.9294	+	7.45021i	−1.52188	+	0.494488i	−0.575569	+	0.817754i	$0.695219\pi$
$228$	1.61234	−	4.96227i	0.106780	−	0.328634i
$229$	4.39329	−	6.04685i	0.290317	−	0.399587i	−0.638800	−	0.769373i	$-0.720569\pi$
$229$	4.39329	−	6.04685i	0.290317	−	0.399587i	0.929117	+	0.369786i	$0.120569\pi$
$230$	0.465948	−	0.808587i	0.0307237	−	0.0533167i
$231$	10.9883	−	8.88740i	0.722975	−	0.584748i
$232$			4.63574i			0.304351i
$233$	−20.6153	−	14.9779i	−1.35055	−	0.981234i	−0.998984	−	0.0450714i	$-0.985648\pi$
$233$	−20.6153	−	14.9779i	−1.35055	−	0.981234i	−0.351568	−	0.936162i	$-0.614352\pi$
$234$	1.50521	+	0.489073i	0.0983987	+	0.0319717i
$235$	5.54498	−	26.1934i	0.361714	−	1.70867i
$236$	5.61985	+	7.73506i	0.365821	+	0.503510i
$237$	11.4846	+	15.8072i	0.746003	+	1.02679i
$238$	10.7492	+	6.51790i	0.696770	+	0.422493i
$239$	−23.8886	−	7.76186i	−1.54522	−	0.502073i	−0.592411	−	0.805636i	$-0.701824\pi$
$239$	−23.8886	−	7.76186i	−1.54522	−	0.502073i	−0.952811	+	0.303563i	$0.901824\pi$
$240$	−1.46750	−	3.28874i	−0.0947265	−	0.212287i
$241$	0.921939			0.0593873			0.0296937	−	0.999559i	$-0.490547\pi$
$241$	0.921939			0.0593873			0.0296937	+	0.999559i	$0.490547\pi$
$242$	−8.47494	−	7.01252i	−0.544790	−	0.450782i
$243$	−4.19019			−0.268801
$244$	1.64874	+	1.19788i	0.105550	+	0.0766864i
$245$	−8.65865	−	13.0395i	−0.553181	−	0.833061i
$246$	−4.58909	−	14.1238i	−0.292590	−	0.900499i
$247$	7.42071	+	10.2137i	0.472168	+	0.649884i
$248$	−1.16996	−	1.61032i	−0.0742928	−	0.102255i
$249$	3.06951	−	0.997343i	0.194522	−	0.0632041i
$250$	10.6417	+	3.42855i	0.673038	+	0.216841i
$251$	−13.4530	+	18.5165i	−0.849145	+	1.16875i	0.134905	+	0.990858i	$0.456927\pi$
$251$	−13.4530	+	18.5165i	−0.849145	+	1.16875i	−0.984050	+	0.177890i	$0.943073\pi$
$252$	−0.701672	−	0.813782i	−0.0442012	−	0.0512634i
$253$	1.38352	+	0.0435487i	0.0869812	+	0.00273788i
$254$	15.3662			0.964163
$255$	15.6260	−	6.97264i	0.978541	−	0.436643i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.59421	−	4.90648i	−0.0994442	−	0.306058i	0.888942	−	0.458019i	$-0.151441\pi$
$257$	−1.59421	−	4.90648i	−0.0994442	−	0.306058i	−0.988386	+	0.151962i	$0.951441\pi$
$258$	15.8614	−	11.5240i	0.987488	−	0.717452i
$259$	−4.72091	+	20.0790i	−0.293343	+	1.24765i
$260$	8.52497	+	1.80468i	0.528696	+	0.111921i
$261$	1.79056	+	0.581789i	0.110833	+	0.0360118i
$262$	3.00009	+	2.17969i	0.185346	+	0.134662i
$263$	0.533719			0.0329105			0.0164553	−	0.999865i	$-0.494762\pi$
$263$	0.533719			0.0329105			0.0164553	+	0.999865i	$0.494762\pi$
$264$	3.27411	−	4.22052i	0.201508	−	0.259755i
$265$	−15.1301	+	26.2561i	−0.929434	+	1.61290i
$266$	−0.712622	−	8.54166i	−0.0436936	−	0.523723i
$267$	−4.73436	−	1.53829i	−0.289738	−	0.0941415i
$268$	1.35003	−	0.438653i	0.0824665	−	0.0267950i
$269$	−10.6247	−	14.6236i	−0.647797	−	0.891616i	0.351204	−	0.936299i	$-0.385772\pi$
$269$	−10.6247	−	14.6236i	−0.647797	−	0.891616i	−0.999001	+	0.0446827i	$0.985772\pi$
$270$	−12.1982	+	1.29227i	−0.742361	+	0.0786453i
$271$	−1.40333	−	4.31900i	−0.0852461	−	0.262361i	0.899343	−	0.437244i	$-0.144045\pi$
$271$	−1.40333	−	4.31900i	−0.0852461	−	0.262361i	−0.984589	+	0.174883i	$0.944045\pi$
$272$	4.51883	+	1.46826i	0.273994	+	0.0890262i
$273$	−16.5480	+	1.38058i	−1.00153	+	0.0835564i
$274$			5.37533i			0.324736i
$275$	2.96275	+	16.3163i	0.178661	+	0.983911i
$276$			0.672169i			0.0404598i
$277$	6.14677	+	4.46589i	0.369324	+	0.268329i	0.756930	−	0.653495i	$-0.226698\pi$
$277$	6.14677	+	4.46589i	0.369324	+	0.268329i	−0.387607	+	0.921825i	$0.626698\pi$
$278$	−4.35142	+	13.3923i	−0.260981	+	0.803216i
$279$	−0.768819	+	0.249804i	−0.0460280	+	0.0149554i
$280$	−4.31380	−	4.04860i	−0.257799	−	0.241950i
$281$	−13.8040	−	18.9996i	−0.823480	−	1.13342i	−0.989102	−	0.147234i	$-0.952963\pi$
$281$	−13.8040	−	18.9996i	−0.823480	−	1.13342i	0.165621	−	0.986189i	$-0.447037\pi$
$282$	5.95914	+	18.3403i	0.354862	+	1.09215i
$283$	4.62628	+	1.50317i	0.275004	+	0.0893541i	0.443272	−	0.896387i	$-0.353818\pi$
$283$	4.62628	+	1.50317i	0.275004	+	0.0893541i	−0.168268	+	0.985741i	$0.553818\pi$
$284$	5.32006	+	3.86525i	0.315687	+	0.229360i
$285$	−10.1087	−	5.82514i	−0.598789	−	0.345052i
$286$	3.60528	+	12.4118i	0.213184	+	0.733924i
$287$	−15.9309	−	18.4763i	−0.940372	−	1.09062i
$288$	−0.328565	−	0.238717i	−0.0193609	−	0.0140665i
$289$	−1.72296	+	5.30272i	−0.101350	+	0.311924i
$290$	10.1411	+	2.14680i	0.595505	+	0.126065i
$291$	−16.0947	+	11.6935i	−0.943487	+	0.685483i
$292$	−0.279290	−	0.384410i	−0.0163442	−	0.0224959i
$293$	0.227218	−	0.0738277i	0.0132742	−	0.00431306i	−0.302372	−	0.953190i	$-0.597779\pi$
$293$	0.227218	−	0.0738277i	0.0132742	−	0.00431306i	0.315647	+	0.948877i	$0.397779\pi$
$294$	10.0927	+	5.02365i	0.588618	+	0.292985i
$295$	19.5237	−	8.71183i	1.13671	−	0.507222i
$296$			7.79607i			0.453138i
$297$	−10.2259	−	15.0485i	−0.593365	−	0.873205i
$298$			11.3737i			0.658862i
$299$	−1.31580	−	0.955983i	−0.0760946	−	0.0552859i
$300$	−7.87400	+	1.68727i	−0.454606	+	0.0974147i
$301$	16.6993	−	27.5402i	0.962531	−	1.58739i
$302$	−3.25362	−	4.47823i	−0.187225	−	0.257693i
$303$	−0.492262	+	0.357649i	−0.0282797	+	0.0205464i
$304$	−1.00111	−	3.08110i	−0.0574176	−	0.176713i
$305$	3.38399	−	3.05203i	0.193767	−	0.174759i
$306$	1.13423	−	1.56114i	0.0648398	−	0.0892443i
$307$		−	4.99724i		−	0.285208i	−0.989780	−	0.142604i	$-0.954453\pi$
$307$		−	4.99724i		−	0.285208i	0.989780	−	0.142604i	$-0.0455475\pi$
$308$	2.27613	−	8.47462i	0.129694	−	0.482886i
$309$	−10.3188			−0.587017
$310$	−4.06452	+	1.81366i	−0.230849	+	0.103009i
$311$	−19.1909	−	6.23549i	−1.08821	−	0.353582i	−0.290658	−	0.956827i	$-0.593874\pi$
$311$	−19.1909	−	6.23549i	−1.08821	−	0.353582i	−0.797556	+	0.603245i	$0.793874\pi$
$312$	−5.96908	+	1.93947i	−0.337933	+	0.109801i
$313$	−12.9133	+	9.38208i	−0.729904	+	0.530306i	−0.889533	−	0.456871i	$-0.848970\pi$
$313$	−12.9133	+	9.38208i	−0.729904	+	0.530306i	0.159629	+	0.987177i	$0.448970\pi$
$314$	1.06067	−	0.770618i	0.0598568	−	0.0434885i
$315$	−2.10516	+	1.15811i	−0.118612	+	0.0652520i
$316$	11.5379	+	3.74890i	0.649060	+	0.210892i
$317$	0.137880	−	0.189775i	0.00774409	−	0.0106588i	−0.805127	−	0.593102i	$-0.797903\pi$
$317$	0.137880	−	0.189775i	0.00774409	−	0.0106588i	0.812871	+	0.582443i	$0.197903\pi$
$318$		−	21.8264i		−	1.22397i
$319$	4.28875	+	14.7647i	0.240124	+	0.826667i
$320$	−1.93741	−	1.11643i	−0.108305	−	0.0624106i
$321$	11.8173	+	8.58578i	0.659578	+	0.479212i
$322$	0.427351	+	1.01817i	0.0238153	+	0.0567401i
$323$	14.6395	−	4.75665i	0.814562	−	0.264667i
$324$	6.16202	−	4.47697i	0.342334	−	0.248720i
$325$	7.89579	−	17.8134i	0.437980	−	0.988108i
$326$	21.0804	−	6.84944i	1.16754	−	0.379355i
$327$	4.87014	+	1.58241i	0.269319	+	0.0875072i
$328$	−7.45982	−	5.41987i	−0.411899	−	0.299262i
$329$	20.6870	+	23.9923i	1.14051	+	1.32274i
$330$	−7.71652	−	9.11692i	−0.424781	−	0.501870i
$331$	18.5581			1.02005			0.510023	−	0.860161i	$-0.329637\pi$
$331$	18.5581			1.02005			0.510023	+	0.860161i	$0.329637\pi$
$332$	1.17790	−	1.62123i	0.0646454	−	0.0889768i
$333$	3.01124	+	0.978413i	0.165015	+	0.0536167i
$334$	11.2115	−	3.64283i	0.613465	−	0.199327i
$335$	−0.334394	−	3.15646i	−0.0182699	−	0.172456i
$336$	4.14801	+	0.975268i	0.226292	+	0.0532052i
$337$	5.26313	+	16.1983i	0.286701	+	0.882375i	0.985884	+	0.167432i	$0.0535475\pi$
$337$	5.26313	+	16.1983i	0.286701	+	0.882375i	−0.699183	+	0.714943i	$0.746453\pi$
$338$	0.675630	−	2.07938i	0.0367494	−	0.113103i
$339$	−7.98615	+	10.9920i	−0.433748	+	0.597003i
$340$	5.30460	−	9.20539i	0.287682	−	0.499232i
$341$	−5.21609	−	4.04644i	−0.282467	−	0.219127i
$342$	−1.31572			−0.0711460
$343$	18.4818	+	1.19282i	0.997924	+	0.0644061i
$344$	3.76177	−	11.5775i	0.202821	−	0.624219i
$345$	1.47043	+	0.311280i	0.0791652	+	0.0167588i
$346$	6.29418	+	8.66319i	0.338377	+	0.465736i
$347$	−22.9934	+	16.7057i	−1.23435	+	0.896808i	−0.997208	−	0.0746676i	$-0.976210\pi$
$347$	−22.9934	+	16.7057i	−1.23435	+	0.896808i	−0.237141	+	0.971475i	$0.576210\pi$
$348$	−7.10067	+	2.30715i	−0.380636	+	0.123676i
$349$	3.47336	−	10.6899i	0.185925	−	0.572218i	−0.814038	−	0.580811i	$-0.802735\pi$
$349$	3.47336	−	10.6899i	0.185925	−	0.572218i	0.999963	+	0.00859338i	$0.00273539\pi$
$350$	−10.8544	+	7.56191i	−0.580191	+	0.404201i
$351$			21.3778i			1.14106i
$352$	0.104345	−	3.31498i	0.00556160	−	0.176689i
$353$	−35.5730			−1.89336			−0.946679	−	0.322179i	$-0.895585\pi$
$353$	−35.5730			−1.89336			−0.946679	+	0.322179i	$0.895585\pi$
$354$	−9.05105	+	12.4577i	−0.481058	+	0.662120i
$355$	10.9193	−	9.84810i	0.579535	−	0.522683i
$356$	−2.93959	+	0.955130i	−0.155798	+	0.0506218i
$357$	−4.63387	+	19.7087i	−0.245250	+	1.04310i
$358$	15.4973	−	11.2595i	0.819058	−	0.595081i
$359$	2.41958	−	0.786170i	0.127701	−	0.0414925i	−0.244469	−	0.969657i	$-0.578614\pi$
$359$	2.41958	−	0.786170i	0.127701	−	0.0414925i	0.372170	+	0.928165i	$0.378614\pi$
$360$	−0.674371	+	0.608216i	−0.0355425	+	0.0320558i
$361$	6.88037	+	4.99888i	0.362125	+	0.263099i
$362$			2.88699i			0.151737i
$363$	6.52337	−	16.4713i	0.342388	−	0.864520i
$364$	−7.80857	+	6.73283i	−0.409280	+	0.352896i
$365$	−0.970270	+	0.432953i	−0.0507862	+	0.0226618i
$366$	−1.01426	+	3.12158i	−0.0530164	+	0.163168i
$367$	−0.332798	−	1.02425i	−0.0173719	−	0.0534652i	0.941995	−	0.335628i	$-0.108948\pi$
$367$	−0.332798	−	1.02425i	−0.0173719	−	0.0534652i	−0.959367	+	0.282162i	$0.908948\pi$
$368$	0.245314	+	0.337646i	0.0127879	+	0.0176010i
$369$	−3.02965	+	2.20117i	−0.157717	+	0.114588i
$370$	17.0546	+	3.61034i	0.886626	+	0.187693i
$371$	−13.8768	−	33.0615i	−0.720446	−	1.71647i
$372$	1.88428	−	2.59350i	0.0976956	−	0.134466i
$373$	−24.2204			−1.25408			−0.627042	−	0.778985i	$-0.715735\pi$
$373$	−24.2204			−1.25408			−0.627042	+	0.778985i	$0.715735\pi$
$374$	15.7507	+	0.495782i	0.814451	+	0.0256363i
$375$	0.0446210	+	18.0064i	0.00230422	+	0.929849i
$376$	9.68690	+	7.03794i	0.499564	+	0.362954i
$377$	5.58250	−	17.1812i	0.287513	−	0.884875i
$378$	7.52529	−	12.4106i	0.387059	−	0.638333i
$379$	22.7032	−	16.4948i	1.16618	−	0.847282i	0.175636	−	0.984455i	$-0.443802\pi$
$379$	22.7032	−	16.4948i	1.16618	−	0.847282i	0.990547	+	0.137174i	$0.0438018\pi$
$380$	−7.20379	+	0.763165i	−0.369547	+	0.0391496i
$381$	7.64758	+	23.5368i	0.391797	+	1.20583i
$382$	−2.31702	+	7.13105i	−0.118549	+	0.364856i
$383$	10.7161	+	7.78569i	0.547566	+	0.397830i	0.826887	−	0.562368i	$-0.190109\pi$
$383$	10.7161	+	7.78569i	0.547566	+	0.397830i	−0.279321	+	0.960198i	$0.590109\pi$
$384$	1.61055			0.0821880
$385$	−17.4849	−	8.90381i	−0.891114	−	0.453780i
$386$	16.1382			0.821411
$387$	−3.99974	−	2.90598i	−0.203318	−	0.147719i
$388$	−3.81709	+	11.7478i	−0.193784	+	0.596404i
$389$	5.77898	+	17.7859i	0.293006	+	0.901780i	0.983884	+	0.178808i	$0.0572242\pi$
$389$	5.77898	+	17.7859i	0.293006	+	0.901780i	−0.690878	+	0.722971i	$0.742776\pi$
$390$	1.47850	+	13.9561i	0.0748666	+	0.706693i
$391$	−1.60429	+	1.16558i	−0.0811322	+	0.0589460i
$392$	6.90323	−	1.15993i	0.348666	−	0.0585854i
$393$	−1.84558	+	5.68011i	−0.0930971	+	0.286524i
$394$	−13.8379	−	10.0539i	−0.697146	−	0.506506i
$395$	13.5443	−	23.5042i	0.681485	−	1.18262i
$396$	−1.26732	−	0.456336i	−0.0636853	−	0.0229317i
$397$	12.4988			0.627297			0.313649	−	0.949539i	$-0.398449\pi$
$397$	12.4988			0.627297			0.313649	+	0.949539i	$0.398449\pi$
$398$	13.4611	−	18.5277i	0.674745	−	0.928707i
$399$	12.7288	−	5.34262i	0.637237	−	0.267465i
$400$	−3.33951	+	3.72125i	−0.166975	+	0.186062i
$401$	−15.8475	+	11.5139i	−0.791386	+	0.574975i	−0.908374	−	0.418158i	$-0.862676\pi$
$401$	−15.8475	+	11.5139i	−0.791386	+	0.574975i	0.116989	+	0.993133i	$0.462676\pi$
$402$	1.34379	+	1.84957i	0.0670222	+	0.0922481i
$403$	2.39697	+	7.37713i	0.119402	+	0.367481i
$404$	−0.116747	+	0.359311i	−0.00580839	+	0.0178764i
$405$	−6.94014	−	15.5532i	−0.344858	−	0.772846i
$406$	−9.28888	+	8.00920i	−0.460999	+	0.397490i
$407$	7.21252	+	24.8303i	0.357512	+	1.23079i
$408$			7.65233i			0.378847i
$409$	−2.19165	−	1.59233i	−0.108370	−	0.0787356i	0.532280	−	0.846568i	$-0.321335\pi$
$409$	−2.19165	−	1.59233i	−0.108370	−	0.0787356i	−0.640651	+	0.767833i	$0.721335\pi$
$410$	−15.3111	+	13.8091i	−0.756160	+	0.681981i
$411$	−8.23353	+	2.67524i	−0.406130	+	0.131960i
$412$	−5.18338	+	3.76595i	−0.255367	+	0.185535i
$413$	−5.78970	+	24.6247i	−0.284892	+	1.21170i
$414$	0.161204	−	0.0523782i	0.00792272	−	0.00257425i
$415$	−3.00111	−	3.32754i	−0.147319	−	0.163343i
$416$	−2.29058	+	3.15272i	−0.112305	+	0.154575i
$417$	−22.6789			−1.11059
$418$	−6.03899	−	8.88707i	−0.295377	−	0.434681i
$419$			4.29519i			0.209834i	0.994481	+	0.104917i	$0.0334577\pi$
$419$			4.29519i			0.209834i	−0.994481	+	0.104917i	$0.966542\pi$
$420$	4.05442	−	8.62248i	0.197835	−	0.420734i
$421$	6.61780	−	20.3675i	0.322532	−	0.992651i	−0.650011	−	0.759925i	$-0.725236\pi$
$421$	6.61780	−	20.3675i	0.322532	−	0.992651i	0.972542	−	0.232726i	$-0.0747644\pi$
$422$	−9.96947	+	3.23928i	−0.485306	+	0.157686i
$423$	3.93413	−	2.85831i	0.191284	−	0.138976i
$424$	−7.96576	−	10.9639i	−0.386851	−	0.532455i
$425$	−17.6811	−	15.8673i	−0.857657	−	0.769676i
$426$	−3.27277	+	10.0725i	−0.158566	+	0.488016i
$427$	0.448285	+	5.37325i	0.0216940	+	0.260030i
$428$	9.06958			0.438395
$429$	−17.2171	+	11.6995i	−0.831250	+	0.564856i
$430$	−23.5848	−	13.5907i	−1.13736	−	0.655403i
$431$	3.20582	−	4.41243i	0.154419	−	0.212539i	−0.724798	−	0.688962i	$-0.758067\pi$
$431$	3.20582	−	4.41243i	0.154419	−	0.212539i	0.879216	+	0.476423i	$0.158067\pi$
$432$	1.69519	−	5.21725i	0.0815597	−	0.251015i
$433$	9.83744	+	30.2765i	0.472757	+	1.45500i	0.848959	+	0.528459i	$0.177230\pi$
$433$	9.83744	+	30.2765i	0.472757	+	1.45500i	−0.376202	+	0.926538i	$0.622770\pi$
$434$	1.20532	−	5.12647i	0.0578573	−	0.246079i
$435$	1.75878	+	16.6018i	0.0843272	+	0.795995i
$436$	3.02390	−	0.982525i	0.144819	−	0.0470544i
$437$	1.28591	+	0.417817i	0.0615134	+	0.0199869i
$438$	0.449811	−	0.619112i	0.0214928	−	0.0295823i
$439$	−7.47858			−0.356933			−0.178467	−	0.983946i	$-0.557114\pi$
$439$	−7.47858			−0.356933			−0.178467	+	0.983946i	$0.557114\pi$
$440$	−7.20349	−	1.76342i	−0.343413	−	0.0840680i
$441$	0.418335	−	2.81195i	0.0199207	−	0.133903i
$442$	−14.9797	−	10.8834i	−0.712514	−	0.517672i
$443$	−17.4106	−	5.65703i	−0.827200	−	0.268774i	−0.135335	−	0.990800i	$-0.543211\pi$
$443$	−17.4106	−	5.65703i	−0.827200	−	0.268774i	−0.691866	+	0.722026i	$0.743211\pi$
$444$	−11.9414	+	3.88001i	−0.566715	+	0.184137i
$445$	0.728114	+	6.87293i	0.0345159	+	0.325808i
$446$	−23.5909	+	17.1398i	−1.11706	+	0.811591i
$447$	−17.4214	+	5.66056i	−0.824005	+	0.267735i
$448$	2.43957	−	1.02395i	0.115259	−	0.0483773i
$449$	−29.7371	−	21.6053i	−1.40338	−	1.01962i	−0.994244	−	0.107144i	$-0.965830\pi$
$449$	−29.7371	−	21.6053i	−1.40338	−	1.01962i	−0.409138	−	0.912473i	$-0.634170\pi$
$450$	1.01823	+	1.75691i	0.0479996	+	0.0828215i
$451$	−28.7736	−	10.3608i	−1.35489	−	0.487869i
$452$			8.43615i			0.396803i
$453$	5.24012	−	7.21241i	0.246202	−	0.338869i
$454$	−22.9294	−	7.45021i	−1.07613	−	0.349656i
$455$	11.1125	+	20.1999i	0.520963	+	0.946985i
$456$	4.22115	−	3.06685i	0.197674	−	0.143618i
$457$	−21.6493	+	15.7291i	−1.01271	+	0.735776i	−0.964776	−	0.263074i	$-0.915264\pi$
$457$	−21.6493	+	15.7291i	−1.01271	+	0.735776i	−0.0479337	+	0.998851i	$0.515264\pi$
$458$	7.10850	−	2.30969i	0.332158	−	0.107925i
$459$	24.7891	+	8.05448i	1.15706	+	0.375951i
$460$	0.852236	−	0.380284i	0.0397357	−	0.0177308i
$461$	7.89843			0.367866			0.183933	−	0.982939i	$-0.441117\pi$
$461$	7.89843			0.367866			0.183933	+	0.982939i	$0.441117\pi$
$462$	14.1136	−	0.731312i	0.656623	−	0.0340237i
$463$			35.2290i			1.63723i	0.574344	+	0.818614i	$0.305257\pi$
$463$			35.2290i			1.63723i	−0.574344	+	0.818614i	$0.694743\pi$
$464$	−2.72482	+	3.75039i	−0.126497	+	0.174108i
$465$	−4.80089	−	5.32308i	−0.222636	−	0.246852i
$466$	−7.87434	−	24.2347i	−0.364772	−	1.12265i
$467$	13.0443	−	9.47727i	0.603620	−	0.438556i	−0.243542	−	0.969890i	$-0.578309\pi$
$467$	13.0443	−	9.47727i	0.603620	−	0.438556i	0.847162	+	0.531335i	$0.178309\pi$
$468$	0.930272	+	1.28041i	0.0430018	+	0.0591869i
$469$	3.21142	+	1.94727i	0.148289	+	0.0899167i
$470$	19.8821	−	17.9317i	0.917093	−	0.827127i
$471$	1.70825	+	1.24112i	0.0787122	+	0.0571878i
$472$			9.56106i			0.440084i
$473$	1.27022	−	40.3544i	0.0584050	−	1.85550i
$474$			19.5387i			0.897443i
$475$	−1.66657	+	16.1123i	−0.0764674	+	0.739285i
$476$	4.86519	+	11.5913i	0.222996	+	0.531288i
$477$	−5.23454	+	1.70081i	−0.239673	+	0.0778745i
$478$	−14.7639	−	20.3208i	−0.675287	−	0.929453i
$479$	0.412531	−	0.299721i	0.0188490	−	0.0136946i	−0.578321	−	0.815809i	$-0.696292\pi$
$479$	0.412531	−	0.299721i	0.0188490	−	0.0136946i	0.597170	+	0.802115i	$0.296292\pi$
$480$	0.745842	−	3.52322i	0.0340429	−	0.160812i
$481$	9.38827	−	28.8941i	0.428068	−	1.31746i
$482$	0.745864	+	0.541902i	0.0339732	+	0.0246830i
$483$	−1.34686	+	1.16131i	−0.0612843	+	0.0528415i
$484$	−2.73451	−	10.6547i	−0.124296	−	0.484304i
$485$	23.9317	+	13.7906i	1.08668	+	0.626199i
$486$	−3.38993	−	2.46293i	−0.153771	−	0.111721i
$487$	−22.4223	−	7.28546i	−1.01605	−	0.330136i	−0.246791	−	0.969069i	$-0.579376\pi$
$487$	−22.4223	−	7.28546i	−1.01605	−	0.330136i	−0.769262	+	0.638933i	$0.779376\pi$
$488$	0.629763	+	1.93821i	0.0285080	+	0.0877386i
$489$	20.9829	+	28.8805i	0.948880	+	1.30602i
$490$	0.659418	−	15.6386i	0.0297895	−	0.706479i
$491$	12.9381	−	4.20386i	0.583890	−	0.189717i	−0.00215226	−	0.999998i	$-0.500685\pi$
$491$	12.9381	−	4.20386i	0.583890	−	0.189717i	0.586043	+	0.810280i	$0.300685\pi$
$492$	4.58909	−	14.1238i	0.206892	−	0.636749i
$493$	−17.8195	−	12.9467i	−0.802552	−	0.583088i
$494$			12.6249i			0.568019i
$495$	−1.58517	+	2.56105i	−0.0712481	+	0.115111i
$496$		−	1.99046i		−	0.0893743i
$497$	1.44650	+	17.3381i	0.0648843	+	0.777720i
$498$	3.06951	+	0.997343i	0.137548	+	0.0446920i
$499$	−1.55790	−	4.79473i	−0.0697412	−	0.214641i	0.910111	−	0.414364i	$-0.135996\pi$
$499$	−1.55790	−	4.79473i	−0.0697412	−	0.214641i	−0.979852	+	0.199723i	$0.935996\pi$
$500$	6.59403	+	9.02877i	0.294894	+	0.403779i
$501$	11.1596	+	15.3599i	0.498575	+	0.686230i
$502$	−21.7674	+	7.07265i	−0.971526	+	0.315668i
$503$	−38.0192	−	12.3532i	−1.69519	−	0.550802i	−0.707433	−	0.706780i	$-0.750147\pi$
$503$	−38.0192	−	12.3532i	−1.69519	−	0.550802i	−0.987760	+	0.155978i	$0.950147\pi$
$504$	−0.0893354	−	1.07080i	−0.00397931	−	0.0476970i
$505$	0.731959	+	0.421791i	0.0325717	+	0.0187694i
$506$	1.09369	+	0.848445i	0.0486207	+	0.0377180i
$507$	3.52128			0.156386
$508$	12.4315	+	9.03204i	0.551561	+	0.400732i
$509$	−17.2029	−	5.58956i	−0.762505	−	0.247753i	−0.0981514	−	0.995171i	$-0.531293\pi$
$509$	−17.2029	−	5.58956i	−0.762505	−	0.247753i	−0.664353	+	0.747419i	$0.731293\pi$
$510$	16.7402	+	3.54378i	0.741266	+	0.156921i
$511$	0.287731	−	1.22378i	0.0127285	−	0.0541367i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−5.49183	−	16.9021i	−0.242470	−	0.746247i
$514$	1.59421	−	4.90648i	0.0703177	−	0.216416i
$515$	5.83793	+	13.0831i	0.257250	+	0.576511i
$516$	19.6058			0.863096
$517$	37.3637	+	13.4539i	1.64325	+	0.591702i
$518$	−15.6214	+	13.4693i	−0.686365	+	0.591809i
$519$	−10.1371	+	13.9525i	−0.444969	+	0.612447i
$520$	5.83608	+	6.47087i	0.255929	+	0.283766i
$521$	−34.6699	+	11.2649i	−1.51892	+	0.493526i	−0.945468	−	0.325714i	$-0.894395\pi$
$521$	−34.6699	+	11.2649i	−1.51892	+	0.493526i	−0.573450	+	0.819241i	$0.694395\pi$
$522$	1.10663	+	1.52314i	0.0484358	+	0.0666661i
$523$	8.55494	+	11.7749i	0.374081	+	0.514879i	0.954004	−	0.299793i	$-0.0969175\pi$
$523$	8.55494	+	11.7749i	0.374081	+	0.514879i	−0.579923	+	0.814671i	$0.696917\pi$
$524$	1.14593	+	3.52681i	0.0500602	+	0.154070i
$525$	−16.9848	−	12.8624i	−0.741279	−	0.561363i
$526$	0.431788	+	0.313712i	0.0188268	+	0.0136785i
$527$	9.45744			0.411972
$528$	5.12957	−	1.49000i	0.223236	−	0.0648438i
$529$	22.8258			0.992427
$530$	−27.6735	+	12.3484i	−1.20206	+	0.536381i
$531$	3.69297	+	1.19992i	0.160261	+	0.0520721i
$532$	4.44414	−	7.32922i	0.192678	−	0.317762i
$533$	21.1211	+	29.0707i	0.914856	+	1.25919i
$534$	−2.92599	−	4.02728i	−0.126620	−	0.174278i
$535$	4.20010	−	19.8405i	0.181586	−	0.857780i
$536$	1.35003	+	0.438653i	0.0583126	+	0.0189469i
$537$	24.9592	+	18.1339i	1.07707	+	0.782536i
$538$		−	18.0758i		−	0.779301i
$539$	20.9135	−	10.0809i	0.900810	−	0.434214i
$540$	−10.6282	−	6.12447i	−0.457363	−	0.263555i
$541$	10.2345	−	14.0866i	0.440018	−	0.605632i	−0.530199	−	0.847874i	$-0.677883\pi$
$541$	10.2345	−	14.0866i	0.440018	−	0.605632i	0.970216	+	0.242241i	$0.0778826\pi$
$542$	1.40333	−	4.31900i	0.0602781	−	0.185517i
$543$	−4.42207	+	1.43682i	−0.189769	+	0.0616597i
$544$	2.79279	+	3.84395i	0.119740	+	0.164808i
$545$	−0.748997	−	7.07005i	−0.0320835	−	0.302848i
$546$	−14.1991	−	8.60973i	−0.607664	−	0.368462i
$547$	11.2236	−	34.5426i	0.479886	−	1.47694i	−0.359367	−	0.933196i	$-0.617008\pi$
$547$	11.2236	−	34.5426i	0.479886	−	1.47694i	0.839253	−	0.543741i	$-0.182992\pi$
$548$	−3.15954	+	4.34874i	−0.134969	+	0.185769i
$549$	0.827672			0.0353242
$550$	−7.19357	+	14.9416i	−0.306735	+	0.637114i
$551$			15.0182i			0.639798i
$552$	−0.395091	+	0.543796i	−0.0168162	+	0.0231455i
$553$	12.4223	+	29.5962i	0.528250	+	1.25856i
$554$	2.34786	+	7.22597i	0.0997510	+	0.307002i
$555$	2.95780	+	27.9198i	0.125552	+	1.18513i
$556$	−11.3922	+	8.27689i	−0.483135	+	0.351018i
$557$	6.89040	+	21.2065i	0.291956	+	0.898547i	0.984227	+	0.176910i	$0.0566102\pi$
$557$	6.89040	+	21.2065i	0.291956	+	0.898547i	−0.692271	+	0.721637i	$0.743390\pi$
$558$	−0.768819	−	0.249804i	−0.0325467	−	0.0105751i
$559$	−27.8840	+	38.3791i	−1.17937	+	1.62326i
$560$	−1.11023	−	5.81097i	−0.0469157	−	0.245558i
$561$	7.07954	+	24.3725i	0.298899	+	1.02901i
$562$		−	23.4848i		−	0.990648i
$563$	5.05245	−	6.95410i	0.212935	−	0.293080i	−0.689167	−	0.724603i	$-0.742023\pi$
$563$	5.05245	−	6.95410i	0.212935	−	0.293080i	0.902102	+	0.431522i	$0.142023\pi$
$564$	−5.95914	+	18.3403i	−0.250925	+	0.772268i
$565$	18.4548	+	3.90676i	0.776400	+	0.164359i
$566$	2.85920	+	3.93535i	0.120181	+	0.165415i
$567$	19.6169	+	4.61227i	0.823832	+	0.193697i
$568$	2.03208	+	6.25410i	0.0852642	+	0.262416i
$569$	−5.29076	−	1.71907i	−0.221800	−	0.0720672i	0.196009	−	0.980602i	$-0.437202\pi$
$569$	−5.29076	−	1.71907i	−0.221800	−	0.0720672i	−0.417809	+	0.908535i	$0.637202\pi$
$570$	−4.75419	−	10.6544i	−0.199131	−	0.446264i
$571$		−	4.56403i		−	0.190999i	−0.995430	−	0.0954993i	$-0.969555\pi$
$571$		−	4.56403i		−	0.190999i	0.995430	−	0.0954993i	$-0.0304448\pi$
$572$	−4.37873	+	12.1605i	−0.183084	+	0.508455i
$573$	−12.0760			−0.504480
$574$	−2.02829	−	24.3116i	−0.0846592	−	1.01475i
$575$	−0.437235	−	2.04045i	−0.0182340	−	0.0850926i
$576$	−0.125501	−	0.386251i	−0.00522920	−	0.0160938i
$577$	5.33333	−	3.87489i	0.222030	−	0.161314i	−0.471210	−	0.882021i	$-0.656183\pi$
$577$	5.33333	−	3.87489i	0.222030	−	0.161314i	0.693240	+	0.720707i	$0.256183\pi$
$578$	−4.51076	+	3.27726i	−0.187623	+	0.136316i
$579$	8.03176	+	24.7192i	0.333789	+	1.02730i
$580$	6.94246	+	7.69758i	0.288270	+	0.319625i
$581$	5.28361	−	0.440806i	0.219201	−	0.0182877i
$582$	−19.8941			−0.824638
$583$	−35.5140	−	27.5504i	−1.47084	−	1.14102i
$584$		−	0.475157i		−	0.0196621i
$585$	3.23181	−	1.44210i	0.133619	−	0.0596233i
$586$	0.227218	+	0.0738277i	0.00938630	+	0.00304979i
$587$	2.58449	+	7.95425i	0.106673	+	0.328307i	0.990120	−	0.140226i	$-0.0447828\pi$
$587$	2.58449	+	7.95425i	0.106673	+	0.328307i	−0.883446	+	0.468533i	$0.844783\pi$
$588$	5.21234	+	9.99656i	0.214953	+	0.412251i
$589$	−3.79028	−	5.21688i	−0.156176	−	0.214958i
$590$	20.9157	+	4.42771i	0.861084	+	0.182286i
$591$	8.51276	−	26.1996i	0.350168	−	1.07771i
$592$	−4.58242	+	6.30716i	−0.188336	+	0.259223i
$593$		−	24.1867i		−	0.993227i	−0.867972	−	0.496614i	$-0.834577\pi$
$593$		−	24.1867i		−	0.993227i	0.867972	−	0.496614i	$-0.165423\pi$
$594$	0.572408	−	18.1851i	0.0234862	−	0.746145i
$595$	27.6101	−	5.27511i	1.13191	−	0.216258i
$596$	−6.68531	+	9.20154i	−0.273841	+	0.376910i
$597$	35.0787	+	11.3978i	1.43567	+	0.466479i
$598$	−0.502590	−	1.54681i	−0.0205524	−	0.0632539i
$599$	−8.89267	+	6.46091i	−0.363345	+	0.263985i	−0.754446	−	0.656362i	$-0.772094\pi$
$599$	−8.89267	+	6.46091i	−0.363345	+	0.263985i	0.391101	+	0.920348i	$0.372094\pi$
$600$	−7.36195	−	3.26319i	−0.300551	−	0.133219i
$601$	−11.4674	−	35.2931i	−0.467765	−	1.43963i	−0.855471	−	0.517850i	$-0.826732\pi$
$601$	−11.4674	−	35.2931i	−0.467765	−	1.43963i	0.387706	−	0.921783i	$-0.373268\pi$
$602$	29.6978	−	12.4649i	1.21039	−	0.508033i
$603$	0.338861	−	0.466402i	0.0137995	−	0.0189933i
$604$		−	5.53539i		−	0.225232i
$605$	−24.5744	+	1.04783i	−0.999092	+	0.0426002i
$606$	−0.608469			−0.0247174
$607$	−11.9627	+	16.4652i	−0.485550	+	0.668302i	−0.979560	−	0.201154i	$-0.935531\pi$
$607$	−11.9627	+	16.4652i	−0.485550	+	0.668302i	0.494010	+	0.869456i	$0.335531\pi$
$608$	1.00111	−	3.08110i	0.0406004	−	0.124955i
$609$	−16.8908	−	10.2419i	−0.684452	−	0.415024i
$610$	4.53165	−	0.480080i	0.183481	−	0.0194379i
$611$	−27.4267	−	37.7496i	−1.10956	−	1.52718i
$612$	1.83523	−	0.596301i	0.0741847	−	0.0241041i
$613$	−0.759512	+	2.33754i	−0.0306764	+	0.0944122i	−0.965222	−	0.261430i	$-0.915806\pi$
$613$	−0.759512	+	2.33754i	−0.0306764	+	0.0944122i	0.934546	+	0.355842i	$0.115806\pi$
$614$	2.93731	−	4.04285i	0.118540	−	0.163156i
$615$	−28.7718	−	16.5797i	−1.16019	−	0.668560i
$616$	6.82269	−	5.51824i	0.274894	−	0.222336i
$617$		−	18.0222i		−	0.725545i	−0.931878	−	0.362772i	$-0.881830\pi$
$617$		−	18.0222i		−	0.725545i	0.931878	−	0.362772i	$-0.118170\pi$
$618$	−8.34810	−	6.06525i	−0.335810	−	0.243980i
$619$	27.2541	+	8.85541i	1.09544	+	0.355929i	0.800345	−	0.599540i	$-0.204650\pi$
$619$	27.2541	+	8.85541i	1.09544	+	0.355929i	0.295092	+	0.955469i	$0.404650\pi$
$620$	−4.35431	−	0.921778i	−0.174873	−	0.0370195i
$621$	1.34573	+	1.85224i	0.0540023	+	0.0743278i
$622$	−11.8606	−	16.3247i	−0.475567	−	0.654562i
$623$	−6.99260	−	4.24003i	−0.280152	−	0.169873i
$624$	−5.96908	−	1.93947i	−0.238955	−	0.0776411i
$625$	22.8049	−	10.2438i	0.912197	−	0.409753i
$626$	−15.9617			−0.637960
$627$	10.6070	−	13.6730i	0.423603	−	0.546049i
$628$	1.31105			0.0523168
$629$	−29.9677	−	21.7728i	−1.19489	−	0.868138i
$630$	−2.38383	−	0.300454i	−0.0949741	−	0.0119704i
$631$	5.83775	+	17.9667i	0.232397	+	0.715244i	0.997456	+	0.0712842i	$0.0227097\pi$
$631$	5.83775	+	17.9667i	0.232397	+	0.715244i	−0.765059	+	0.643960i	$0.777290\pi$
$632$	7.13084	+	9.81476i	0.283650	+	0.390410i
$633$	−9.92336	−	13.6583i	−0.394418	−	0.542870i
$634$	0.223094	−	0.0724876i	0.00886019	−	0.00287885i
$635$	25.5154	−	23.0124i	1.01255	−	0.913218i
$636$	12.8292	−	17.6579i	0.508713	−	0.700183i
$637$	−26.9818	−	4.01409i	−1.06906	−	0.159044i
$638$	−5.20883	+	14.4658i	−0.206219	+	0.572706i
$639$	2.67068			0.105651
$640$	−0.911178	−	2.04200i	−0.0360175	−	0.0807170i
$641$	−6.53372	+	20.1087i	−0.258066	+	0.794247i	0.735144	+	0.677912i	$0.237115\pi$
$641$	−6.53372	+	20.1087i	−0.258066	+	0.794247i	−0.993210	+	0.116335i	$0.962885\pi$
$642$	4.51381	+	13.8921i	0.178146	+	0.548277i
$643$	2.12750	−	1.54572i	0.0839006	−	0.0609573i	−0.545044	−	0.838407i	$-0.683487\pi$
$643$	2.12750	−	1.54572i	0.0839006	−	0.0609573i	0.628945	+	0.777450i	$0.283487\pi$
$644$	−0.252728	+	1.07490i	−0.00995889	+	0.0423571i
$645$	9.07939	−	42.8894i	0.357501	−	1.68877i
$646$	14.6395	+	4.75665i	0.575982	+	0.187148i
$647$	10.2436	+	7.44239i	0.402717	+	0.292591i	0.770647	−	0.637263i	$-0.219933\pi$
$647$	10.2436	+	7.44239i	0.402717	+	0.292591i	−0.367930	+	0.929853i	$0.619933\pi$
$648$	7.61667			0.299211
$649$	8.84540	+	30.4518i	0.347212	+	1.19534i
$650$	16.8583	−	9.77029i	0.661235	−	0.383222i
$651$	8.45222	−	0.705160i	0.331269	−	0.0276374i
$652$	21.0804	+	6.84944i	0.825573	+	0.268245i
$653$	10.3228	−	3.35408i	0.403962	−	0.131255i	−0.0999868	−	0.994989i	$-0.531880\pi$
$653$	10.3228	−	3.35408i	0.403962	−	0.131255i	0.503949	+	0.863734i	$0.331880\pi$
$654$	3.00991	+	4.14279i	0.117697	+	0.161996i
$655$	8.24589	−	0.873565i	0.322194	−	0.0341330i
$656$	−2.84940	−	8.76954i	−0.111250	−	0.342393i
$657$	−0.183530	−	0.0596325i	−0.00716019	−	0.00232649i
$658$	2.63382	+	31.5697i	0.102677	+	1.23071i
$659$			12.3335i			0.480444i	0.970718	+	0.240222i	$0.0772203\pi$
$659$			12.3335i			0.480444i	−0.970718	+	0.240222i	$0.922780\pi$
$660$	−0.884008	−	11.9114i	−0.0344099	−	0.463651i
$661$		−	5.89992i		−	0.229480i	−0.993396	−	0.114740i	$-0.963396\pi$
$661$		−	5.89992i		−	0.229480i	0.993396	−	0.114740i	$-0.0366035\pi$
$662$	15.0138	+	10.9082i	0.583529	+	0.423959i
$663$	9.21517	−	28.3614i	0.357888	−	1.10146i
$664$	1.90587	−	0.619256i	0.0739623	−	0.0240318i
$665$	−13.9752	−	13.1161i	−0.541936	−	0.508620i
$666$	1.86105	+	2.56152i	0.0721143	+	0.0992568i
$667$	−0.597869	−	1.84005i	−0.0231496	−	0.0712471i
$668$	11.2115	+	3.64283i	0.433785	+	0.140945i
$669$	−37.9943	−	27.6044i	−1.46894	−	1.06725i
$670$	1.58479	−	2.75018i	0.0612258	−	0.106249i
$671$	3.79891	+	5.59054i	0.146655	+	0.215820i
$672$	2.78256	+	3.22714i	0.107340	+	0.124490i
$673$	−40.8502	−	29.6794i	−1.57466	−	1.14406i	−0.922515	−	0.385961i	$-0.873870\pi$
$673$	−40.8502	−	29.6794i	−1.57466	−	1.14406i	−0.652143	−	0.758096i	$-0.726130\pi$
$674$	−5.26313	+	16.1983i	−0.202728	+	0.623934i
$675$	−18.3197	+	20.4138i	−0.705125	+	0.785727i
$676$	1.76882	−	1.28513i	0.0680317	−	0.0494279i
$677$	0.666767	+	0.917726i	0.0256259	+	0.0352711i	0.821638	−	0.570010i	$-0.193061\pi$
$677$	0.666767	+	0.917726i	0.0256259	+	0.0352711i	−0.796012	+	0.605281i	$0.793061\pi$
$678$	−12.9219	+	4.19857i	−0.496261	+	0.161245i
$679$	−30.1345	+	12.6483i	−1.15646	+	0.485396i
$680$	9.70231	−	4.32935i	0.372066	−	0.166023i
$681$		−	38.8294i		−	1.48794i
$682$	−1.84147	−	6.33958i	−0.0705136	−	0.242755i
$683$		−	3.86934i		−	0.148056i	−0.997256	−	0.0740281i	$-0.976415\pi$
$683$		−	3.86934i		−	0.148056i	0.997256	−	0.0740281i	$-0.0235855\pi$
$684$	−1.06444	−	0.773360i	−0.0406999	−	0.0295702i
$685$	8.05006	+	8.92566i	0.307577	+	0.341032i
$686$	14.2510	+	11.8283i	0.544105	+	0.451608i
$687$	7.07562	+	9.73875i	0.269952	+	0.371557i
$688$	9.84844	−	7.15531i	0.375468	−	0.272794i
$689$	16.3199	+	50.2275i	0.621739	+	1.91352i
$690$	1.00664	+	1.11613i	0.0383220	+	0.0424902i
$691$	24.6263	−	33.8951i	0.936827	−	1.28943i	−0.0203096	−	0.999794i	$-0.506465\pi$
$691$	24.6263	−	33.8951i	0.936827	−	1.28943i	0.957136	−	0.289638i	$-0.0935348\pi$
$692$			10.7083i			0.407068i
$693$	−1.27518	−	3.32782i	−0.0484399	−	0.126413i
$694$	−28.4214			−1.07886
$695$	12.8307	+	28.7544i	0.486698	+	1.09072i
$696$	−7.10067	−	2.30715i	−0.269150	−	0.0874523i
$697$	41.6674	−	13.5386i	1.57827	−	0.512810i
$698$	9.09338	−	6.60673i	0.344190	−	0.250068i
$699$	33.2019	−	24.1226i	1.25581	−	0.912402i
$700$	−13.2262	−	0.262329i	−0.499902	−	0.00991512i
$701$	−23.9326	−	7.77616i	−0.903921	−	0.293702i	−0.180066	−	0.983654i	$-0.557631\pi$
$701$	−23.9326	−	7.77616i	−0.903921	−	0.293702i	−0.723854	+	0.689953i	$0.757631\pi$
$702$	−12.5655	+	17.2950i	−0.474256	+	0.652757i
$703$			25.2566i			0.952572i
$704$	2.03291	−	2.62055i	0.0766184	−	0.0987655i
$705$	37.3615	+	21.5295i	1.40711	+	0.810849i
$706$	−28.7791	−	20.9093i	−1.08312	−	0.786930i
$707$	−0.921675	+	0.386852i	−0.0346632	+	0.0145490i
$708$	−14.6449	+	4.75842i	−0.550389	+	0.178832i
$709$	−24.6784	+	17.9299i	−0.926816	+	0.673372i	−0.945211	−	0.326459i	$-0.894144\pi$
$709$	−24.6784	+	17.9299i	−0.926816	+	0.673372i	0.0183949	+	0.999831i	$0.494144\pi$
$710$	14.6224	−	1.54909i	0.548771	−	0.0581365i
$711$	4.68589	−	1.52254i	0.175735	−	0.0570996i
$712$	−2.93959	−	0.955130i	−0.110166	−	0.0357950i
$713$	0.672072	+	0.488289i	0.0251693	+	0.0182866i
$714$	−15.3334	+	13.2210i	−0.573838	+	0.494783i
$715$	24.5743	+	15.2103i	0.919027	+	0.568835i
$716$	19.1557			0.715883
$717$	23.7781	−	32.7277i	0.888008	−	1.22224i
$718$	2.41958	+	0.786170i	0.0902981	+	0.0293396i
$719$	24.5228	−	7.96795i	0.914548	−	0.297155i	0.186319	−	0.982489i	$-0.440344\pi$
$719$	24.5228	−	7.96795i	0.914548	−	0.297155i	0.728228	+	0.685335i	$0.240344\pi$
$720$	−0.903078	+	0.0956716i	−0.0336557	+	0.00356547i
$721$	−16.5014	−	3.87976i	−0.614544	−	0.144490i
$722$	2.62807	+	8.08836i	0.0978065	+	0.301018i
$723$	−0.458837	+	1.41216i	−0.0170643	+	0.0525187i
$724$	−1.69693	+	2.33562i	−0.0630659	+	0.0868027i
$725$	20.0542	−	11.6225i	0.744793	−	0.431649i
$726$	14.9591	−	9.49123i	0.555185	−	0.352252i
$727$	−22.4196			−0.831496			−0.415748	−	0.909480i	$-0.636480\pi$
$727$	−22.4196			−0.831496			−0.415748	+	0.909480i	$0.636480\pi$
$728$	−10.2747	+	0.857209i	−0.380807	+	0.0317703i
$729$	9.14645	−	28.1499i	0.338757	−	1.04259i
$730$	−1.03945	−	0.220044i	−0.0384717	−	0.00814420i
$731$	33.9976	+	46.7937i	1.25745	+	1.73073i
$732$	−2.65538	+	1.92925i	−0.0981456	+	0.0713070i
$733$	6.93678	−	2.25390i	0.256216	−	0.0832496i	−0.178093	−	0.984014i	$-0.556993\pi$
$733$	6.93678	−	2.25390i	0.256216	−	0.0832496i	0.434309	+	0.900764i	$0.356993\pi$
$734$	0.332798	−	1.02425i	0.0122838	−	0.0378056i
$735$	24.2822	−	6.77308i	0.895661	−	0.249829i
$736$			0.417354i			0.0153839i
$737$	4.70565	+	0.148119i	0.173335	+	0.00545602i
$738$	−3.74485			−0.137850
$739$	18.8457	−	25.9389i	0.693251	−	0.954178i	−0.306746	−	0.951791i	$-0.599240\pi$
$739$	18.8457	−	25.9389i	0.693251	−	0.954178i	0.999997	−	0.00238655i	$-0.000759662\pi$
$740$	11.6754	+	12.9453i	0.429194	+	0.475878i
$741$	−19.3378	+	6.28323i	−0.710392	+	0.230820i
$742$	8.20650	−	34.9039i	0.301270	−	1.28136i
$743$	3.22316	−	2.34176i	0.118246	−	0.0859110i	−0.527090	−	0.849809i	$-0.676717\pi$
$743$	3.22316	−	2.34176i	0.118246	−	0.0859110i	0.645337	+	0.763898i	$0.276717\pi$
$744$	3.04884	−	0.990627i	0.111776	−	0.0363182i
$745$	17.0332	+	18.8859i	0.624049	+	0.691926i
$746$	−19.5947	−	14.2364i	−0.717413	−	0.521231i
$747$		−	0.813864i		−	0.0297777i
$748$	12.4512	+	9.65915i	0.455261	+	0.353173i
$749$	15.6696	+	18.1732i	0.572554	+	0.664034i
$750$	−10.5478	+	14.5937i	−0.385152	+	0.532888i
$751$	−4.65210	+	14.3177i	−0.169758	+	0.522460i	−0.999355	−	0.0359012i	$-0.988570\pi$
$751$	−4.65210	+	14.3177i	−0.169758	+	0.522460i	0.829598	+	0.558362i	$0.188570\pi$
$752$	3.70007	+	11.3876i	0.134928	+	0.415264i
$753$	−21.6667	−	29.8217i	−0.789579	−	1.08676i
$754$	14.6152	−	10.6185i	0.532253	−	0.386705i
$755$	−12.1092	−	2.56343i	−0.440697	−	0.0932927i
$756$	13.3829	−	5.61714i	0.486730	−	0.204294i
$757$	−3.02676	+	4.16598i	−0.110009	+	0.151415i	−0.860472	−	0.509498i	$-0.829831\pi$
$757$	−3.02676	+	4.16598i	−0.110009	+	0.151415i	0.750462	+	0.660913i	$0.229831\pi$
$758$	28.0626			1.01928
$759$	−0.755265	+	2.09750i	−0.0274144	+	0.0761344i
$760$	−6.27656	−	3.61687i	−0.227675	−	0.131198i
$761$	−7.09069	−	5.15169i	−0.257037	−	0.186749i	0.451803	−	0.892118i	$-0.350781\pi$
$761$	−7.09069	−	5.15169i	−0.257037	−	0.186749i	−0.708840	+	0.705369i	$0.750781\pi$
$762$	−7.64758	+	23.5368i	−0.277043	+	0.852649i
$763$	7.19315	+	4.36163i	0.260410	+	0.157902i
$764$	−6.06603	+	4.40723i	−0.219461	+	0.159448i
$765$	−0.454572	−	4.29087i	−0.0164351	−	0.155137i
$766$	4.09318	+	12.5975i	0.147893	+	0.455166i
$767$	11.5137	−	35.4356i	0.415736	−	1.27951i
$768$	1.30296	+	0.946658i	0.0470166	+	0.0341596i
$769$	41.4983			1.49647			0.748233	−	0.663436i	$-0.230903\pi$
$769$	41.4983			1.49647			0.748233	+	0.663436i	$0.230903\pi$
$770$	−8.91206	−	17.4807i	−0.321168	−	0.629961i
$771$	8.30879			0.299234
$772$	13.0560	+	9.48577i	0.469897	+	0.341400i
$773$	13.4811	−	41.4906i	0.484882	−	1.49231i	−0.347270	−	0.937765i	$-0.612891\pi$
$773$	13.4811	−	41.4906i	0.484882	−	1.49231i	0.832152	−	0.554547i	$-0.187109\pi$
$774$	−1.52776	−	4.70197i	−0.0549143	−	0.169009i
$775$	−4.03294	+	9.09856i	−0.144868	+	0.326830i
$776$	−9.99328	+	7.26054i	−0.358738	+	0.260638i
$777$	−28.4059	−	17.2242i	−1.01906	−	0.617914i
$778$	−5.77898	+	17.7859i	−0.207187	+	0.637655i
$779$	−24.1673	−	17.5585i	−0.865882	−	0.629100i
$780$	−7.00704	+	12.1597i	−0.250892	+	0.435388i
$781$	12.2581	+	18.0392i	0.438630	+	0.645494i
$782$	−1.98301			−0.0709122
$783$	−14.9477	+	20.5737i	−0.534186	+	0.735243i
$784$	6.26662	+	3.11921i	0.223808	+	0.111400i
$785$	0.607146	−	2.86805i	0.0216700	−	0.102365i
$786$	−4.83179	+	3.51050i	−0.172344	+	0.125215i
$787$	−22.2126	−	30.5731i	−0.791794	−	1.08981i	−0.993882	−	0.110444i	$-0.964773\pi$
$787$	−22.2126	−	30.5731i	−0.791794	−	1.08981i	0.202088	−	0.979367i	$-0.435227\pi$
$788$	−5.28562	−	16.2675i	−0.188293	−	0.579505i
$789$	−0.265625	+	0.817510i	−0.00945651	+	0.0291041i
$790$	24.7729	−	11.0541i	0.881381	−	0.393289i
$791$	−16.9040	+	14.5752i	−0.601036	+	0.518235i
$792$	−0.757057	−	1.11410i	−0.0269009	−	0.0395877i
$793$		−	7.94185i		−	0.282023i
$794$	10.1117	+	7.34661i	0.358852	+	0.260722i
$795$	−32.6871	−	36.2425i	−1.15929	−	1.28539i
$796$	21.7806	−	7.07693i	0.771991	−	0.250835i
$797$	2.34592	−	1.70441i	0.0830968	−	0.0603733i	−0.545461	−	0.838136i	$-0.683645\pi$
$797$	2.34592	−	1.70441i	0.0830968	−	0.0603733i	0.628558	+	0.777763i	$0.283645\pi$
$798$	13.4381	+	3.15954i	0.475705	+	0.111846i
$799$	−54.1070	+	17.5804i	−1.91417	+	0.621950i
$800$	−4.88901	+	1.04764i	−0.172853	+	0.0370396i
$801$	−0.737841	+	1.01555i	−0.0260703	+	0.0358827i
$802$	−19.5886			−0.691696
$803$	−0.439591	−	1.51337i	−0.0155128	−	0.0534055i
$804$			2.28619i			0.0806278i
$805$	2.23441	+	1.05065i	0.0787525	+	0.0370306i
$806$	−2.39697	+	7.37713i	−0.0844298	+	0.259848i
$807$	27.6871	−	8.99607i	0.974631	−	0.316677i
$808$	−0.305648	+	0.222066i	−0.0107527	+	0.00781227i
$809$	19.2517	+	26.4977i	0.676853	+	0.931609i	0.999891	−	0.0147774i	$-0.00470397\pi$
$809$	19.2517	+	26.4977i	0.676853	+	0.931609i	−0.323037	+	0.946386i	$0.604704\pi$
$810$	3.52726	−	16.6621i	0.123935	−	0.585448i
$811$	−0.0259942	+	0.0800019i	−0.000912779	+	0.00280925i	−0.951512	−	0.307612i	$-0.900470\pi$
$811$	−0.0259942	+	0.0800019i	−0.000912779	+	0.00280925i	0.950599	+	0.310421i	$0.100470\pi$
$812$	−12.2226	+	1.01971i	−0.428928	+	0.0357850i
$813$	7.31393			0.256511
$814$	−8.75985	+	24.3276i	−0.307033	+	0.852681i
$815$	24.7460	−	42.9433i	0.866816	−	1.50424i
$816$	−4.49793	+	6.19087i	−0.157459	+	0.216724i
$817$	12.1869	−	37.5073i	0.426364	−	1.31221i
$818$	−0.837137	−	2.57644i	−0.0292698	−	0.0900832i
$819$	−0.958387	+	4.07621i	−0.0334887	+	0.142434i
$820$	−20.5037	+	2.17215i	−0.716020	+	0.0758547i
$821$	23.6129	−	7.67230i	0.824097	−	0.267765i	0.133540	−	0.991043i	$-0.457366\pi$
$821$	23.6129	−	7.67230i	0.824097	−	0.267765i	0.690557	+	0.723278i	$0.257366\pi$
$822$	−8.23353	−	2.67524i	−0.287177	−	0.0933095i
$823$	1.45089	−	1.99698i	0.0505749	−	0.0696103i	−0.782981	−	0.622046i	$-0.786302\pi$
$823$	1.45089	−	1.99698i	0.0505749	−	0.0696103i	0.833555	+	0.552436i	$0.186302\pi$
$824$	−6.40701			−0.223199
$825$	−26.4666	−	3.58230i	−0.921449	−	0.124720i
$826$	−19.1580	+	16.5187i	−0.666593	+	0.574760i
$827$	−39.9914	−	29.0554i	−1.39064	−	1.01036i	−0.995795	−	0.0916072i	$-0.970800\pi$
$827$	−39.9914	−	29.0554i	−1.39064	−	1.01036i	−0.394841	−	0.918749i	$-0.629200\pi$
$828$	0.161204	+	0.0523782i	0.00560221	+	0.00182027i
$829$	−23.6258	+	7.67648i	−0.820557	+	0.266615i	−0.689063	−	0.724702i	$-0.741977\pi$
$829$	−23.6258	+	7.67648i	−0.820557	+	0.266615i	−0.131494	+	0.991317i	$0.541977\pi$
$830$	−0.472071	−	4.45604i	−0.0163858	−	0.154672i
$831$	−9.89969	+	7.19254i	−0.343416	+	0.249507i
$832$	−3.70624	+	1.20423i	−0.128491	+	0.0417492i
$833$	−14.8206	+	29.7751i	−0.513502	+	1.03165i
$834$	−18.3476	−	13.3303i	−0.635327	−	0.461592i
$835$	13.1610	−	22.8391i	0.455456	−	0.790380i
$836$	0.338042	−	10.7394i	0.0116914	−	0.371431i
$837$		−	10.9192i		−	0.377421i
$838$	−2.52465	+	3.47488i	−0.0872126	+	0.120038i
$839$	15.1763	+	4.93108i	0.523944	+	0.170240i	0.559034	−	0.829144i	$-0.311172\pi$
$839$	15.1763	+	4.93108i	0.523944	+	0.170240i	−0.0350906	+	0.999384i	$0.511172\pi$
$840$	8.34826	−	4.59261i	0.288042	−	0.158460i
$841$	−6.07565	+	4.41422i	−0.209505	+	0.152214i
$842$	17.3256	−	12.5878i	0.597080	−	0.433804i
$843$	35.9723	−	11.6881i	1.23895	−	0.402560i
$844$	−9.96947	−	3.23928i	−0.343163	−	0.111501i
$845$	−1.99219	−	4.46460i	−0.0685333	−	0.153587i
$846$	4.86285			0.167188
$847$	16.6249	−	23.8875i	0.571239	−	0.820784i
$848$		−	13.5522i		−	0.465383i
$849$	−4.60488	+	6.33807i	−0.158039	+	0.217522i
$850$	−4.97772	−	23.2296i	−0.170734	−	0.796767i
$851$	−1.00546	−	3.09447i	−0.0344666	−	0.106077i
$852$	−8.56821	+	6.22517i	−0.293542	+	0.213271i
$853$	22.4543	+	30.9057i	0.768821	+	1.05819i	0.996429	+	0.0844383i	$0.0269096\pi$
$853$	22.4543	+	30.9057i	0.768821	+	1.05819i	−0.227608	+	0.973753i	$0.573090\pi$
$854$	−2.79565	+	4.61055i	−0.0956651	+	0.157770i
$855$	−2.18473	+	1.97041i	−0.0747163	+	0.0673867i
$856$	7.33744	+	5.33096i	0.250789	+	0.182209i
$857$			23.2459i			0.794065i	0.917805	+	0.397032i	$0.129960\pi$
$857$			23.2459i			0.794065i	−0.917805	+	0.397032i	$0.870040\pi$
$858$	−20.8057	−	0.654896i	−0.710296	−	0.0223578i
$859$		−	6.09210i		−	0.207860i	−0.994585	−	0.103930i	$-0.966858\pi$
$859$		−	6.09210i		−	0.207860i	0.994585	−	0.103930i	$-0.0331418\pi$
$860$	−11.0921	−	24.8579i	−0.378237	−	0.847649i
$861$	36.2292	−	15.2063i	1.23469	−	0.518231i
$862$	5.18712	−	1.68540i	0.176674	−	0.0574049i
$863$	−11.7473	−	16.1687i	−0.399881	−	0.550389i	0.560833	−	0.827929i	$-0.310481\pi$
$863$	−11.7473	−	16.1687i	−0.399881	−	0.550389i	−0.960714	+	0.277540i	$0.910481\pi$
$864$	4.43806	−	3.22444i	0.150986	−	0.109698i
$865$	23.4253	+	4.95899i	0.796485	+	0.168611i
$866$	−9.83744	+	30.2765i	−0.334290	+	1.02884i
$867$	−7.26480	−	5.27819i	−0.246726	−	0.179257i
$868$	3.98839	−	3.43893i	0.135375	−	0.116725i
$869$	31.7917	+	24.6627i	1.07846	+	0.836626i
$870$	−8.33540	+	14.4649i	−0.282596	+	0.490407i
$871$	−4.47531	−	3.25151i	−0.151640	−	0.110173i
$872$	3.02390	+	0.982525i	0.102402	+	0.0332725i
$873$	1.55023	+	4.77112i	0.0524674	+	0.161478i
$874$	0.794735	+	1.09386i	0.0268823	+	0.0370003i
$875$	−6.69887	+	28.8119i	−0.226463	+	0.974020i
$876$	0.727809	−	0.236480i	0.0245904	−	0.00798991i
$877$	−11.9364	+	36.7365i	−0.403064	+	1.24050i	0.519437	+	0.854509i	$0.326142\pi$
$877$	−11.9364	+	36.7365i	−0.403064	+	1.24050i	−0.922501	+	0.385994i	$0.873858\pi$
$878$	−6.05030	−	4.39580i	−0.204188	−	0.148351i
$879$			0.384779i			0.0129783i
$880$	−4.79123	−	5.66075i	−0.161512	−	0.190824i
$881$		−	51.3821i		−	1.73111i	−0.500815	−	0.865554i	$-0.666966\pi$
$881$		−	51.3821i		−	1.73111i	0.500815	−	0.865554i	$-0.333034\pi$
$882$	1.99127	−	2.02903i	0.0670494	−	0.0683209i
$883$	34.1826	+	11.1066i	1.15033	+	0.373766i	0.821269	−	0.570541i	$-0.193266\pi$
$883$	34.1826	+	11.1066i	1.15033	+	0.373766i	0.329065	+	0.944307i	$0.393266\pi$
$884$	−5.72176	−	17.6098i	−0.192443	−	0.592280i
$885$	3.62743	+	34.2406i	0.121935	+	1.15099i
$886$	−10.7603	−	14.8103i	−0.361500	−	0.497562i
$887$	−39.3477	+	12.7848i	−1.32117	+	0.429273i	−0.882895	−	0.469570i	$-0.844409\pi$
$887$	−39.3477	+	12.7848i	−1.32117	+	0.429273i	−0.438271	+	0.898843i	$0.644409\pi$
$888$	−11.9414	−	3.88001i	−0.400728	−	0.130205i
$889$	3.38008	+	40.5145i	0.113364	+	1.35881i
$890$	−3.45075	+	5.98829i	−0.115669	+	0.200728i
$891$	24.2590	−	7.04655i	0.812706	−	0.236068i
$892$	−29.1599			−0.976346
$893$	31.3823	+	22.8005i	1.05017	+	0.762991i
$894$	−17.4214	−	5.66056i	−0.582659	−	0.189317i
$895$	8.87098	−	41.9048i	0.296524	−	1.40072i
$896$	2.57552	+	0.605550i	0.0860421	+	0.0202300i
$897$	2.11916	−	1.53966i	0.0707566	−	0.0514077i
$898$	−11.3586	−	34.9581i	−0.379040	−	1.16657i
$899$	−2.85138	+	8.77565i	−0.0950989	+	0.292684i
$900$	−0.208924	+	2.01987i	−0.00696412	+	0.0673289i
$901$	64.3914			2.14519
$902$	−17.1884	−	25.2947i	−0.572311	−	0.842221i
$903$	33.8730	+	39.2851i	1.12722	+	1.30733i
$904$	−4.95865	+	6.82499i	−0.164922	+	0.226996i
$905$	4.32354	+	4.79380i	0.143719	+	0.159351i
$906$	8.47870	−	2.75490i	0.281686	−	0.0915253i
$907$	4.27534	+	5.88449i	0.141960	+	0.195391i	0.874077	−	0.485788i	$-0.161467\pi$
$907$	4.27534	+	5.88449i	0.141960	+	0.195391i	−0.732116	+	0.681180i	$0.761467\pi$
$908$	−14.1711	−	19.5049i	−0.470286	−	0.647293i
$909$	0.0474144	+	0.145927i	0.00157264	+	0.00484008i
$910$	−2.88298	+	22.8738i	−0.0955699	+	0.758260i
$911$	−17.4987	−	12.7136i	−0.579759	−	0.421220i	0.258878	−	0.965910i	$-0.416647\pi$
$911$	−17.4987	−	12.7136i	−0.579759	−	0.421220i	−0.838637	+	0.544690i	$0.816647\pi$
$912$	5.21763			0.172773
$913$	5.49727	−	3.73554i	0.181933	−	0.123628i
$914$	−26.7599			−0.885140
$915$	2.99069	+	6.70230i	0.0988693	+	0.221571i
$916$	7.10850	+	2.30969i	0.234871	+	0.0763143i
$917$	−5.08703	+	8.38946i	−0.167988	+	0.277044i
$918$	15.3205	+	21.0869i	0.505653	+	0.695971i
$919$	−8.93106	−	12.2926i	−0.294609	−	0.405494i	0.635896	−	0.771775i	$-0.280631\pi$
$919$	−8.93106	−	12.2926i	−0.294609	−	0.405494i	−0.930504	+	0.366281i	$0.880631\pi$
$920$	0.912998	+	0.193276i	0.0301007	+	0.00637211i
$921$	7.65440	+	2.48706i	0.252221	+	0.0819516i
$922$	6.38996	+	4.64258i	0.210442	+	0.152895i
$923$		−	25.6263i		−	0.843500i
$924$	11.8480	+	7.70411i	0.389770	+	0.253447i
$925$	33.7257	−	19.5459i	1.10890	−	0.642666i
$926$	−20.7071	+	28.5008i	−0.680476	+	0.936595i
$927$	−0.804085	+	2.47472i	−0.0264096	+	0.0812804i
$928$	−4.40885	+	1.43252i	−0.144728	+	0.0470249i
$929$	−22.4026	−	30.8345i	−0.735004	−	1.01165i	−0.998891	−	0.0470930i	$-0.985004\pi$
$929$	−22.4026	−	30.8345i	−0.735004	−	1.01165i	0.263886	−	0.964554i	$-0.414996\pi$
$930$	−0.755174	−	7.12836i	−0.0247631	−	0.233748i
$931$	22.3641	−	3.75778i	0.732954	−	0.123156i
$932$	7.87434	−	24.2347i	0.257933	−	0.793835i
$933$	19.1021	−	26.2918i	0.625374	−	0.860754i
$934$	16.1237			0.527583
$935$	26.8964	−	22.7650i	0.879605	−	0.744494i
$936$			1.58267i			0.0517313i
$937$	6.93643	−	9.54718i	0.226603	−	0.311893i	−0.680543	−	0.732708i	$-0.738256\pi$
$937$	6.93643	−	9.54718i	0.226603	−	0.311893i	0.907146	+	0.420815i	$0.138256\pi$
$938$	1.45351	+	3.46300i	0.0474589	+	0.113071i
$939$	−7.94396	−	24.4490i	−0.259241	−	0.797863i
$940$	26.6249	−	2.82063i	0.868410	−	0.0919988i
$941$	13.4775	−	9.79199i	0.439355	−	0.319210i	−0.346024	−	0.938226i	$-0.612468\pi$
$941$	13.4775	−	9.79199i	0.439355	−	0.319210i	0.785378	+	0.619016i	$0.212468\pi$
$942$	0.652495	+	2.00817i	0.0212594	+	0.0654298i
$943$	3.66000	+	1.18921i	0.119186	+	0.0387259i
$944$	−5.61985	+	7.73506i	−0.182911	+	0.251755i
$945$	−6.09042	−	31.8775i	−0.198121	−	1.03697i
$946$	24.7474	−	31.9008i	0.804606	−	1.03718i
$947$			0.375227i			0.0121932i	0.999981	+	0.00609662i	$0.00194063\pi$
$947$			0.375227i			0.0121932i	−0.999981	+	0.00609662i	$0.998059\pi$
$948$	−11.4846	+	15.8072i	−0.373002	+	0.513393i
$949$	−0.572199	+	1.76105i	−0.0185744	+	0.0571660i
$950$	−10.8189	+	12.0556i	−0.351011	+	0.391134i
$951$	0.222062	+	0.305642i	0.00720086	+	0.00991113i
$952$	−2.87720	+	12.2373i	−0.0932504	+	0.396612i
$953$	15.9832	+	49.1911i	0.517745	+	1.59346i	0.778231	+	0.627979i	$0.216117\pi$
$953$	15.9832	+	49.1911i	0.517745	+	1.59346i	−0.260485	+	0.965478i	$0.583883\pi$
$954$	−5.23454	−	1.70081i	−0.169474	−	0.0550656i
$955$	6.83204	+	15.3110i	0.221080	+	0.495451i
$956$		−	25.1179i		−	0.812372i
$957$	−24.7500	−	0.779048i	−0.800053	−	0.0251830i
$958$	0.509916			0.0164746
$959$	−14.1726	+	1.18240i	−0.457656	+	0.0381817i
$960$	2.67430	−	2.41195i	0.0863125	−	0.0778453i
$961$	8.35522	+	25.7147i	0.269523	+	0.829507i
$962$	24.5788	−	17.8575i	0.792453	−	0.575750i
$963$	2.97995	−	2.16506i	0.0960275	−	0.0697680i
$964$	0.284895	+	0.876816i	0.00917585	+	0.0282403i
$965$	26.7972	−	24.1684i	0.862632	−	0.778009i
$966$	−1.77224	+	0.147856i	−0.0570207	+	0.00475718i
$967$	19.7718			0.635819			0.317910	−	0.948121i	$-0.397019\pi$
$967$	19.7718			0.635819			0.317910	+	0.948121i	$0.397019\pi$
$968$	4.05040	−	10.2271i	0.130185	−	0.328713i
$969$			24.7910i			0.796400i
$970$	11.2552	+	25.2235i	0.361383	+	0.809878i
$971$	−14.4014	−	4.67928i	−0.462161	−	0.150165i	0.0686761	−	0.997639i	$-0.478123\pi$
$971$	−14.4014	−	4.67928i	−0.462161	−	0.150165i	−0.530837	+	0.847474i	$0.678123\pi$
$972$	−1.29484	−	3.98511i	−0.0415320	−	0.127822i
$973$	−36.2672	−	8.52704i	−1.16267	−	0.273364i
$974$	−13.8578	−	19.0736i	−0.444032	−	0.611157i
$975$	23.3555	+	20.9597i	0.747976	+	0.671246i
$976$	−0.629763	+	1.93821i	−0.0201582	+	0.0620406i
$977$	−19.1794	+	26.3981i	−0.613602	+	0.844551i	−0.996868	−	0.0790871i	$-0.974799\pi$
$977$	−19.1794	+	26.3981i	−0.613602	+	0.844551i	0.383265	+	0.923638i	$0.374799\pi$
$978$			35.6983i			1.14150i
$979$	−10.2462	−	0.322516i	−0.327469	−	0.0103077i
$980$	9.72561	−	12.2643i	0.310673	−	0.391768i
$981$	0.759003	−	1.04468i	0.0242331	−	0.0333540i
$982$	12.9381	+	4.20386i	0.412873	+	0.134151i
$983$	12.5116	+	38.5068i	0.399058	+	1.22818i	0.925756	+	0.378123i	$0.123430\pi$
$983$	12.5116	+	38.5068i	0.399058	+	1.22818i	−0.526697	+	0.850053i	$0.676570\pi$
$984$	12.0144	−	8.72898i	0.383005	−	0.278270i
$985$	−38.0343	+	4.02933i	−1.21187	+	0.128385i
$986$	−6.80646	−	20.9481i	−0.216762	−	0.667124i
$987$	−47.0452	+	19.7461i	−1.49746	+	0.628526i
$988$	−7.42071	+	10.2137i	−0.236084	+	0.324942i
$989$			5.08059i			0.161553i
$990$	−2.78778	+	1.14019i	−0.0886013	+	0.0362377i
$991$	10.0501			0.319251			0.159626	−	0.987178i	$-0.448971\pi$
$991$	10.0501			0.319251			0.159626	+	0.987178i	$0.448971\pi$
$992$	1.16996	−	1.61032i	0.0371464	−	0.0511276i
$993$	−9.23613	+	28.4259i	−0.293100	+	0.902069i
$994$	−9.02083	+	14.8770i	−0.286123	+	0.471871i
$995$	−5.39488	−	50.9242i	−0.171029	−	1.61441i
$996$	1.89706	+	2.61108i	0.0601106	+	0.0827352i
$997$	23.0606	−	7.49285i	0.730337	−	0.237301i	0.0798378	−	0.996808i	$-0.474560\pi$
$997$	23.0606	−	7.49285i	0.730337	−	0.237301i	0.650499	+	0.759507i	$0.274560\pi$
$998$	1.55790	−	4.79473i	0.0493145	−	0.151774i
$999$	−25.1380	+	34.5994i	−0.795330	+	1.09468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.6	yes	96
5.4	even	2		770.2.w.a.139.19	yes	96
7.6	odd	2	inner	770.2.w.b.139.19	yes	96
11.8	odd	10		770.2.w.a.349.6	yes	96
35.34	odd	2		770.2.w.a.139.6	✓	96
55.19	odd	10	inner	770.2.w.b.349.19	yes	96
77.41	even	10		770.2.w.a.349.19	yes	96
385.349	even	10	inner	770.2.w.b.349.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.6	✓	96	35.34	odd	2
770.2.w.a.139.19	yes	96	5.4	even	2
770.2.w.a.349.6	yes	96	11.8	odd	10
770.2.w.a.349.19	yes	96	77.41	even	10
770.2.w.b.139.6	yes	96	1.1	even	1	trivial
770.2.w.b.139.19	yes	96	7.6	odd	2	inner
770.2.w.b.349.6	yes	96	385.349	even	10	inner
770.2.w.b.349.19	yes	96	55.19	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.497687 + 1.53172i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.22362 - 0.235570i) q^{5} +(-1.30296 + 0.946658i) q^{6} +(-1.37179 + 2.26234i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.328565 + 0.238717i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.497687 + 1.53172i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.22362 - 0.235570i) q^{5} +(-1.30296 + 0.946658i) q^{6} +(-1.37179 + 2.26234i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.328565 + 0.238717i) q^{9} +(1.93741 + 1.11643i) q^{10} +(-0.104345 + 3.31498i) q^{11} -1.61055 q^{12} +(2.29058 - 3.15272i) q^{13} +(-2.43957 + 1.02395i) q^{14} +(-0.745842 + 3.52322i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.79279 - 3.84395i) q^{17} +(0.125501 + 0.386251i) q^{18} +(-1.00111 + 3.08110i) q^{19} +(0.911178 + 2.04200i) q^{20} +(-2.78256 - 3.22714i) q^{21} +(-2.03291 + 2.62055i) q^{22} -0.417354i q^{23} +(-1.30296 - 0.946658i) q^{24} +(4.88901 - 1.04764i) q^{25} +(3.70624 - 1.20423i) q^{26} +(-4.43806 + 3.22444i) q^{27} +(-2.57552 - 0.605550i) q^{28} +(4.40885 - 1.43252i) q^{29} +(-2.67430 + 2.41195i) q^{30} +(-1.16996 + 1.61032i) q^{31} -1.00000 q^{32} +(-5.02571 - 1.80965i) q^{33} -4.75138i q^{34} +(-2.51741 + 5.35375i) q^{35} +(-0.125501 + 0.386251i) q^{36} +(7.41451 - 2.40912i) q^{37} +(-2.62094 + 1.90422i) q^{38} +(3.68910 + 5.07761i) q^{39} +(-0.463098 + 2.18759i) q^{40} +(-2.84940 + 8.76954i) q^{41} +(-0.354269 - 4.24636i) q^{42} -12.1733 q^{43} +(-3.18498 + 0.925148i) q^{44} +(0.786840 + 0.453416i) q^{45} +(0.245314 - 0.337646i) q^{46} +(3.70007 - 11.3876i) q^{47} +(-0.497687 - 1.53172i) q^{48} +(-3.23638 - 6.20692i) q^{49} +(4.57108 + 2.02613i) q^{50} +(7.27780 - 2.36470i) q^{51} +(3.70624 + 1.20423i) q^{52} +(-7.96576 + 10.9639i) q^{53} -5.48574 q^{54} +(0.548886 + 7.39586i) q^{55} +(-1.72771 - 2.00375i) q^{56} +(-4.22115 - 3.06685i) q^{57} +(4.40885 + 1.43252i) q^{58} +(9.09311 - 2.95453i) q^{59} +(-3.58126 + 0.379397i) q^{60} +(1.64874 - 1.19788i) q^{61} +(-1.89304 + 0.615086i) q^{62} +(-0.990781 + 0.415857i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.35071 - 7.55005i) q^{65} +(-3.00220 - 4.41808i) q^{66} -1.41951i q^{67} +(2.79279 - 3.84395i) q^{68} +(0.639271 + 0.207712i) q^{69} +(-5.18348 + 2.85158i) q^{70} +(5.32006 - 3.86525i) q^{71} +(-0.328565 + 0.238717i) q^{72} +(-0.451901 + 0.146832i) q^{73} +(7.41451 + 2.40912i) q^{74} +(-0.828510 + 8.01002i) q^{75} -3.23966 q^{76} +(-7.35648 - 4.78353i) q^{77} +6.27627i q^{78} +(7.13084 - 9.81476i) q^{79} +(-1.66049 + 1.49759i) q^{80} +(-2.35368 - 7.24389i) q^{81} +(-7.45982 + 5.41987i) q^{82} +(-1.17790 - 1.62123i) q^{83} +(2.20934 - 3.64361i) q^{84} +(-7.11564 - 7.88960i) q^{85} +(-9.84844 - 7.15531i) q^{86} +7.46609i q^{87} +(-3.12049 - 1.12362i) q^{88} +3.09087i q^{89} +(0.370056 + 0.829314i) q^{90} +(3.99032 + 9.50695i) q^{91} +(0.396927 - 0.128969i) q^{92} +(-1.88428 - 2.59350i) q^{93} +(9.68690 - 7.03794i) q^{94} +(-1.50028 + 7.08704i) q^{95} +(0.497687 - 1.53172i) q^{96} +(9.99328 + 7.26054i) q^{97} +(1.03005 - 6.92380i) q^{98} +(-0.825625 + 1.06428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

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