LMFDB - Embedded newform 896.2.bn.a.141.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			141.19
Character	$\chi$	$=$	896.141
Dual form			896.2.bn.a.197.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374168 + 1.36382i) q^{2} +(0.270613 + 0.892093i) q^{3} +(-1.72000 - 1.02059i) q^{4} +(0.415950 + 4.22321i) q^{5} +(-1.31791 + 0.0352744i) q^{6} +(0.555570 - 0.831470i) q^{7} +(2.03547 - 1.96389i) q^{8} +(1.77181 - 1.18389i) q^{9} +O(q^{10})$	\(q+(-0.374168 + 1.36382i) q^{2} +(0.270613 + 0.892093i) q^{3} +(-1.72000 - 1.02059i) q^{4} +(0.415950 + 4.22321i) q^{5} +(-1.31791 + 0.0352744i) q^{6} +(0.555570 - 0.831470i) q^{7} +(2.03547 - 1.96389i) q^{8} +(1.77181 - 1.18389i) q^{9} +(-5.91533 - 1.01291i) q^{10} +(-2.93844 + 1.57063i) q^{11} +(0.445011 - 1.81058i) q^{12} +(-6.37383 - 0.627767i) q^{13} +(0.926096 + 1.06881i) q^{14} +(-3.65494 + 1.51392i) q^{15} +(1.91677 + 3.51084i) q^{16} +(-1.20397 - 0.498700i) q^{17} +(0.951649 + 2.85940i) q^{18} +(-0.384518 + 0.315566i) q^{19} +(3.59476 - 7.68843i) q^{20} +(0.892093 + 0.270613i) q^{21} +(-1.04258 - 4.59518i) q^{22} +(0.211215 - 1.06185i) q^{23} +(2.30280 + 1.28438i) q^{24} +(-12.7586 + 2.53784i) q^{25} +(3.24104 - 8.45785i) q^{26} +(3.69749 + 3.03445i) q^{27} +(-1.80417 + 0.863113i) q^{28} +(-3.72386 + 6.96685i) q^{29} +(-0.697155 - 5.55113i) q^{30} +(-1.26509 + 1.26509i) q^{31} +(-5.50534 + 1.30049i) q^{32} +(-2.19633 - 2.19633i) q^{33} +(1.13062 - 1.45540i) q^{34} +(3.74256 + 2.00044i) q^{35} +(-4.25578 + 0.227979i) q^{36} +(-0.337646 + 0.411423i) q^{37} +(-0.286500 - 0.642488i) q^{38} +(-1.16482 - 5.85593i) q^{39} +(9.14057 + 7.77936i) q^{40} +(4.19557 + 0.834552i) q^{41} +(-0.702860 + 1.11540i) q^{42} +(1.77901 - 5.86460i) q^{43} +(6.65709 + 0.297480i) q^{44} +(5.73679 + 6.99030i) q^{45} +(1.36914 + 0.685370i) q^{46} +(0.267711 - 0.646311i) q^{47} +(-2.61329 + 2.66002i) q^{48} +(-0.382683 - 0.923880i) q^{49} +(1.31271 - 18.3500i) q^{50} +(0.119077 - 1.20901i) q^{51} +(10.3223 + 7.58485i) q^{52} +(-1.48939 - 2.78645i) q^{53} +(-5.52193 + 3.90731i) q^{54} +(-7.85536 - 11.7564i) q^{55} +(-0.502064 - 2.78351i) q^{56} +(-0.385570 - 0.257630i) q^{57} +(-8.10816 - 7.68544i) q^{58} +(12.5967 - 1.24067i) q^{59} +(7.83158 + 1.12626i) q^{60} +(-8.43075 + 2.55744i) q^{61} +(-1.25200 - 2.19871i) q^{62} -2.13094i q^{63} +(0.286297 - 7.99488i) q^{64} -27.1792i q^{65} +(3.81719 - 2.17360i) q^{66} +(-7.19029 + 2.18115i) q^{67} +(1.56185 + 2.08653i) q^{68} +(1.00443 - 0.0989275i) q^{69} +(-4.12859 + 4.35567i) q^{70} +(-7.29949 - 4.87736i) q^{71} +(1.28145 - 5.88940i) q^{72} +(3.87109 + 5.79349i) q^{73} +(-0.434769 - 0.614429i) q^{74} +(-5.71664 - 10.6951i) q^{75} +(0.983435 - 0.150335i) q^{76} +(-0.326580 + 3.31582i) q^{77} +(8.42225 + 0.602505i) q^{78} +(4.68886 + 11.3199i) q^{79} +(-14.0297 + 9.55528i) q^{80} +(0.740002 - 1.78652i) q^{81} +(-2.70803 + 5.40974i) q^{82} +(5.70042 + 6.94598i) q^{83} +(-1.25821 - 1.37592i) q^{84} +(1.60533 - 5.29206i) q^{85} +(7.33260 + 4.62059i) q^{86} +(-7.22280 - 1.43670i) q^{87} +(-2.89658 + 8.96775i) q^{88} +(-2.07470 - 10.4302i) q^{89} +(-11.6800 + 5.20839i) q^{90} +(-4.06308 + 4.95087i) q^{91} +(-1.44701 + 1.61082i) q^{92} +(-1.47093 - 0.786228i) q^{93} +(0.781281 + 0.606938i) q^{94} +(-1.49264 - 1.49264i) q^{95} +(-2.64997 - 4.55934i) q^{96} +(-8.16327 + 8.16327i) q^{97} +(1.40319 - 0.176224i) q^{98} +(-3.34692 + 6.26164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q+O(q^{10}) $ 752 * q	$ 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) $ 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{32}\right)$

Coefficient data

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

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

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

$2$	−0.374168	+	1.36382i	−0.264577	+	0.964365i
$2$	−0.374168	+	1.36382i	−0.264577	+	0.964365i
$3$	0.270613	+	0.892093i	0.156239	+	0.515050i	0.999757	−	0.0220507i	$-0.00701952\pi$
$3$	0.270613	+	0.892093i	0.156239	+	0.515050i	−0.843518	+	0.537101i	$0.819520\pi$
$4$	−1.72000	−	1.02059i	−0.859998	−	0.510297i
$5$	0.415950	+	4.22321i	0.186019	+	1.88868i	0.407040	+	0.913410i	$0.366561\pi$
$5$	0.415950	+	4.22321i	0.186019	+	1.88868i	−0.221022	+	0.975269i	$0.570939\pi$
$6$	−1.31791	+	0.0352744i	−0.538033	+	0.0144007i
$7$	0.555570	−	0.831470i	0.209986	−	0.314266i
$7$	0.555570	−	0.831470i	0.209986	−	0.314266i
$8$	2.03547	−	1.96389i	0.719648	−	0.694339i
$9$	1.77181	−	1.18389i	0.590604	−	0.394629i
$10$	−5.91533	−	1.01291i	−1.87059	−	0.320311i
$11$	−2.93844	+	1.57063i	−0.885974	+	0.473563i	−0.850601	−	0.525811i	$-0.823762\pi$
$11$	−2.93844	+	1.57063i	−0.885974	+	0.473563i	−0.0353728	+	0.999374i	$0.511262\pi$
$12$	0.445011	−	1.81058i	0.128464	−	0.522670i
$13$	−6.37383	−	0.627767i	−1.76778	−	0.174111i	−0.838850	−	0.544363i	$-0.816772\pi$
$13$	−6.37383	−	0.627767i	−1.76778	−	0.174111i	−0.928932	+	0.370252i	$0.879272\pi$
$14$	0.926096	+	1.06881i	0.247510	+	0.285650i
$15$	−3.65494	+	1.51392i	−0.943701	+	0.390894i
$16$	1.91677	+	3.51084i	0.479193	+	0.877709i
$17$	−1.20397	−	0.498700i	−0.292005	−	0.120953i	0.231872	−	0.972746i	$-0.425515\pi$
$17$	−1.20397	−	0.498700i	−0.292005	−	0.120953i	−0.523877	+	0.851794i	$0.675515\pi$
$18$	0.951649	+	2.85940i	0.224306	+	0.673967i
$19$	−0.384518	+	0.315566i	−0.0882146	+	0.0723958i	−0.677467	−	0.735553i	$-0.736922\pi$
$19$	−0.384518	+	0.315566i	−0.0882146	+	0.0723958i	0.589252	+	0.807949i	$0.299422\pi$
$20$	3.59476	−	7.68843i	0.803812	−	1.71919i
$21$	0.892093	+	0.270613i	0.194671	+	0.0590527i
$22$	−1.04258	−	4.59518i	−0.222279	−	0.979696i
$23$	0.211215	−	1.06185i	0.0440414	−	0.221411i	−0.952497	−	0.304549i	$-0.901494\pi$
$23$	0.211215	−	1.06185i	0.0440414	−	0.221411i	0.996538	+	0.0831379i	$0.0264942\pi$
$24$	2.30280	+	1.28438i	0.470056	+	0.262172i
$25$	−12.7586	+	2.53784i	−2.55172	+	0.507569i
$26$	3.24104	−	8.45785i	0.635621	−	1.65872i
$27$	3.69749	+	3.03445i	0.711583	+	0.583981i
$28$	−1.80417	+	0.863113i	−0.340956	+	0.163113i
$29$	−3.72386	+	6.96685i	−0.691503	+	1.29371i	0.253717	+	0.967278i	$0.418347\pi$
$29$	−3.72386	+	6.96685i	−0.691503	+	1.29371i	−0.945220	+	0.326433i	$0.894153\pi$
$30$	−0.697155	−	5.55113i	−0.127283	−	1.01349i
$31$	−1.26509	+	1.26509i	−0.227217	+	0.227217i	−0.811529	−	0.584312i	$-0.801364\pi$
$31$	−1.26509	+	1.26509i	−0.227217	+	0.227217i	0.584312	+	0.811529i	$0.301364\pi$
$32$	−5.50534	+	1.30049i	−0.973215	+	0.229896i
$33$	−2.19633	−	2.19633i	−0.382332	−	0.382332i
$34$	1.13062	−	1.45540i	0.193900	−	0.249598i
$35$	3.74256	+	2.00044i	0.632609	+	0.338136i
$36$	−4.25578	+	0.227979i	−0.709296	+	0.0379966i
$37$	−0.337646	+	0.411423i	−0.0555087	+	0.0676375i	−0.800025	−	0.599967i	$-0.795180\pi$
$37$	−0.337646	+	0.411423i	−0.0555087	+	0.0676375i	0.744516	+	0.667605i	$0.232680\pi$
$38$	−0.286500	−	0.642488i	−0.0464764	−	0.104225i
$39$	−1.16482	−	5.85593i	−0.186520	−	0.937699i
$40$	9.14057	+	7.77936i	1.44525	+	1.23002i
$41$	4.19557	+	0.834552i	0.655239	+	0.130335i	0.511504	−	0.859281i	$-0.329089\pi$
$41$	4.19557	+	0.834552i	0.655239	+	0.130335i	0.143735	+	0.989616i	$0.454089\pi$
$42$	−0.702860	+	1.11540i	−0.108454	+	0.172109i
$43$	1.77901	−	5.86460i	0.271296	−	0.894344i	−0.710385	−	0.703813i	$-0.751479\pi$
$43$	1.77901	−	5.86460i	0.271296	−	0.894344i	0.981681	−	0.190531i	$-0.0610208\pi$
$44$	6.65709	+	0.297480i	1.00359	+	0.0448468i
$45$	5.73679	+	6.99030i	0.855190	+	1.04205i
$46$	1.36914	+	0.685370i	0.201869	+	0.101052i
$47$	0.267711	−	0.646311i	0.0390496	−	0.0942742i	−0.903151	−	0.429322i	$-0.858753\pi$
$47$	0.267711	−	0.646311i	0.0390496	−	0.0942742i	0.942201	+	0.335048i	$0.108753\pi$
$48$	−2.61329	+	2.66002i	−0.377196	+	0.383941i
$49$	−0.382683	−	0.923880i	−0.0546691	−	0.131983i
$50$	1.31271	−	18.3500i	0.185645	−	2.59508i
$51$	0.119077	−	1.20901i	0.0166741	−	0.169295i
$52$	10.3223	+	7.58485i	1.43144	+	1.05183i
$53$	−1.48939	−	2.78645i	−0.204583	−	0.382748i	0.758615	−	0.651539i	$-0.225876\pi$
$53$	−1.48939	−	2.78645i	−0.204583	−	0.382748i	−0.963199	+	0.268790i	$0.913376\pi$
$54$	−5.52193	+	3.90731i	−0.751439	+	0.531717i
$55$	−7.85536	−	11.7564i	−1.05922	−	1.58523i
$56$	−0.502064	−	2.78351i	−0.0670911	−	0.371962i
$57$	−0.385570	−	0.257630i	−0.0510700	−	0.0341239i
$58$	−8.10816	−	7.68544i	−1.06465	−	1.00915i
$59$	12.5967	−	1.24067i	1.63995	−	0.161521i	0.764433	−	0.644703i	$-0.223019\pi$
$59$	12.5967	−	1.24067i	1.63995	−	0.161521i	0.875520	+	0.483182i	$0.160519\pi$
$60$	7.83158	+	1.12626i	1.01105	+	0.145400i
$61$	−8.43075	+	2.55744i	−1.07945	+	0.327447i	−0.779431	−	0.626488i	$-0.784492\pi$
$61$	−8.43075	+	2.55744i	−1.07945	+	0.327447i	−0.300016	+	0.953934i	$0.596992\pi$
$62$	−1.25200	−	2.19871i	−0.159004	−	0.279236i
$63$		−	2.13094i		−	0.268473i
$64$	0.286297	−	7.99488i	0.0357872	−	0.999359i
$65$		−	27.1792i		−	3.37116i
$66$	3.81719	−	2.17360i	0.469864	−	0.267551i
$67$	−7.19029	+	2.18115i	−0.878433	+	0.266470i	−0.697119	−	0.716955i	$-0.745535\pi$
$67$	−7.19029	+	2.18115i	−0.878433	+	0.266470i	−0.181314	+	0.983425i	$0.558035\pi$
$68$	1.56185	+	2.08653i	0.189402	+	0.253029i
$69$	1.00443	−	0.0989275i	0.120919	−	0.0119095i
$70$	−4.12859	+	4.35567i	−0.493461	+	0.520602i
$71$	−7.29949	−	4.87736i	−0.866290	−	0.578836i	0.0410865	−	0.999156i	$-0.486918\pi$
$71$	−7.29949	−	4.87736i	−0.866290	−	0.578836i	−0.907376	+	0.420319i	$0.861918\pi$
$72$	1.28145	−	5.88940i	0.151021	−	0.694073i
$73$	3.87109	+	5.79349i	0.453076	+	0.678077i	0.985745	−	0.168247i	$-0.0538107\pi$
$73$	3.87109	+	5.79349i	0.453076	+	0.678077i	−0.532668	+	0.846324i	$0.678811\pi$
$74$	−0.434769	−	0.614429i	−0.0505409	−	0.0714259i
$75$	−5.71664	−	10.6951i	−0.660101	−	1.23496i
$76$	0.983435	−	0.150335i	0.112808	−	0.0172446i
$77$	−0.326580	+	3.31582i	−0.0372172	+	0.377873i
$78$	8.42225	+	0.602505i	0.953632	+	0.0682203i
$79$	4.68886	+	11.3199i	0.527538	+	1.27359i	0.933131	+	0.359536i	$0.117065\pi$
$79$	4.68886	+	11.3199i	0.527538	+	1.27359i	−0.405593	+	0.914054i	$0.632935\pi$
$80$	−14.0297	+	9.55528i	−1.56857	+	1.06831i
$81$	0.740002	−	1.78652i	0.0822224	−	0.198503i
$82$	−2.70803	+	5.40974i	−0.299052	+	0.597405i
$83$	5.70042	+	6.94598i	0.625702	+	0.762420i	0.985327	−	0.170677i	$-0.0545954\pi$
$83$	5.70042	+	6.94598i	0.625702	+	0.762420i	−0.359625	+	0.933097i	$0.617095\pi$
$84$	−1.25821	−	1.37592i	−0.137282	−	0.150125i
$85$	1.60533	−	5.29206i	0.174122	−	0.574004i
$86$	7.33260	+	4.62059i	0.790695	+	0.498251i
$87$	−7.22280	−	1.43670i	−0.774366	−	0.154031i
$88$	−2.89658	+	8.96775i	−0.308776	+	0.955965i
$89$	−2.07470	−	10.4302i	−0.219918	−	1.10560i	−0.920114	−	0.391650i	$-0.871904\pi$
$89$	−2.07470	−	10.4302i	−0.219918	−	1.10560i	0.700197	−	0.713950i	$-0.253096\pi$
$90$	−11.6800	+	5.20839i	−1.23118	+	0.549012i
$91$	−4.06308	+	4.95087i	−0.425926	+	0.518993i
$92$	−1.44701	+	1.61082i	−0.150861	+	0.167939i
$93$	−1.47093	−	0.786228i	−0.152528	−	0.0815280i
$94$	0.781281	+	0.606938i	0.0805830	+	0.0626008i
$95$	−1.49264	−	1.49264i	−0.153142	−	0.153142i
$96$	−2.64997	−	4.55934i	−0.270462	−	0.465336i
$97$	−8.16327	+	8.16327i	−0.828855	+	0.828855i	−0.987358	−	0.158503i	$-0.949333\pi$
$97$	−8.16327	+	8.16327i	−0.828855	+	0.828855i	0.158503	+	0.987358i	$0.449333\pi$
$98$	1.40319	−	0.176224i	0.141744	−	0.0178013i
$99$	−3.34692	+	6.26164i	−0.336378	+	0.629319i
$100$	24.5349	+	8.65628i	2.45349	+	0.865628i
$101$	5.77299	+	4.73777i	0.574434	+	0.471425i	0.876194	−	0.481958i	$-0.160074\pi$
$101$	5.77299	+	4.73777i	0.574434	+	0.471425i	−0.301761	+	0.953384i	$0.597574\pi$
$102$	1.60431	+	0.614771i	0.158850	+	0.0608714i
$103$	18.2854	−	3.63719i	1.80171	−	0.358383i	0.823715	−	0.567004i	$-0.191897\pi$
$103$	18.2854	−	3.63719i	1.80171	−	0.358383i	0.977997	+	0.208621i	$0.0668975\pi$
$104$	−14.2066	+	11.2397i	−1.39307	+	1.10214i
$105$	−0.771792	+	3.88006i	−0.0753192	+	0.378655i
$106$	4.35749	−	0.988653i	0.423237	−	0.0960264i
$107$	−0.916043	−	0.277879i	−0.0885573	−	0.0268636i	0.245695	−	0.969347i	$-0.420984\pi$
$107$	−0.916043	−	0.277879i	−0.0885573	−	0.0268636i	−0.334252	+	0.942484i	$0.608484\pi$
$108$	−3.26273	−	8.99289i	−0.313956	−	0.865341i
$109$	−10.9340	+	8.97326i	−1.04728	+	0.859483i	−0.990307	−	0.138893i	$-0.955646\pi$
$109$	−10.9340	+	8.97326i	−1.04728	+	0.859483i	−0.0569753	+	0.998376i	$0.518146\pi$
$110$	18.9728	−	6.31441i	1.80898	−	0.602056i
$111$	−0.458399	−	0.189875i	−0.0435093	−	0.0180221i
$112$	3.98406	+	0.356777i	0.376458	+	0.0337123i
$113$	−0.487039	+	0.201738i	−0.0458167	+	0.0189779i	−0.405474	−	0.914107i	$-0.632894\pi$
$113$	−0.487039	+	0.201738i	−0.0458167	+	0.0189779i	0.359657	+	0.933084i	$0.382894\pi$
$114$	0.495628	−	0.429450i	0.0464198	−	0.0402217i
$115$	4.57228	+	0.450330i	0.426367	+	0.0419935i
$116$	13.5153	−	8.18240i	1.25487	−	0.759717i
$117$	−12.0364	+	6.43360i	−1.11277	+	0.594787i
$118$	−3.02125	+	17.6438i	−0.278128	+	1.62425i
$119$	−1.08354	+	0.724001i	−0.0993283	+	0.0663690i
$120$	−4.46635	+	10.2594i	−0.407720	+	0.936554i
$121$	0.0562969	−	0.0842543i	0.00511790	−	0.00765948i
$122$	−0.333362	−	12.4549i	−0.0301812	−	1.12762i
$123$	0.390881	+	3.96868i	0.0352446	+	0.357844i
$124$	3.46710	−	0.884807i	0.311354	−	0.0794580i
$125$	−9.86547	−	32.5221i	−0.882395	−	2.90887i
$126$	2.90621	+	0.797330i	0.258906	+	0.0710318i
$127$	8.05129			0.714436			0.357218	−	0.934021i	$-0.383725\pi$
$127$	8.05129			0.714436			0.357218	+	0.934021i	$0.383725\pi$
$128$	10.7964	+	3.38189i	0.954278	+	0.298919i
$129$	5.71319			0.503019
$130$	37.0674	+	10.1696i	3.25103	+	0.891931i
$131$	4.10431	+	13.5301i	0.358595	+	1.18213i	0.931878	+	0.362772i	$0.118170\pi$
$131$	4.10431	+	13.5301i	0.358595	+	1.18213i	−0.573283	+	0.819357i	$0.694330\pi$
$132$	1.53612	+	6.01924i	0.133702	+	0.523908i
$133$	0.0487566	+	0.495035i	0.00422774	+	0.0429249i
$134$	−0.284313	−	10.6224i	−0.0245609	−	0.917632i
$135$	−11.2772	+	16.8775i	−0.970585	+	1.45258i
$136$	−3.43004	+	1.34937i	−0.294123	+	0.115707i
$137$	5.64438	−	3.77145i	0.482232	−	0.322217i	−0.290582	−	0.956850i	$-0.593849\pi$
$137$	5.64438	−	3.77145i	0.482232	−	0.322217i	0.772814	+	0.634633i	$0.218849\pi$
$138$	−0.240906	+	1.40687i	−0.0205073	+	0.119761i
$139$	2.50061	−	1.33660i	0.212099	−	0.113369i	−0.361927	−	0.932207i	$-0.617881\pi$
$139$	2.50061	−	1.33660i	0.212099	−	0.113369i	0.574026	+	0.818837i	$0.305381\pi$
$140$	−4.39556	−	7.26039i	−0.371492	−	0.613615i
$141$	0.649015	+	0.0639224i	0.0546570	+	0.00538324i
$142$	9.38307	−	8.13022i	0.787410	−	0.682272i
$143$	19.7151	−	8.16627i	1.64866	−	0.682898i
$144$	7.55259	+	3.95130i	0.629383	+	0.329275i
$145$	−30.9714	−	12.8288i	−2.57204	−	1.06537i
$146$	−9.34970	+	3.11172i	−0.773787	+	0.257527i
$147$	0.720627	−	0.591403i	0.0594363	−	0.0487781i
$148$	1.00065	−	0.363046i	0.0822526	−	0.0298422i
$149$	−15.6376	−	4.74362i	−1.28108	−	0.388613i	−0.424880	−	0.905250i	$-0.639684\pi$
$149$	−15.6376	−	4.74362i	−1.28108	−	0.388613i	−0.856205	+	0.516637i	$0.827184\pi$
$150$	16.7251	−	3.79469i	1.36560	−	0.309835i
$151$	−0.860813	+	4.32760i	−0.0700520	+	0.352175i	−0.999875	−	0.0158328i	$-0.994960\pi$
$151$	−0.860813	+	4.32760i	−0.0700520	+	0.352175i	0.929823	+	0.368008i	$0.119960\pi$
$152$	−0.162941	+	1.39748i	−0.0132162	+	0.113350i
$153$	−2.72361	+	0.541760i	−0.220191	+	0.0437987i
$154$	−4.39998	−	1.68607i	−0.354561	−	0.135867i
$155$	−5.86896	−	4.81653i	−0.471407	−	0.386873i
$156$	−3.97305	+	11.2610i	−0.318098	+	0.901600i
$157$	−4.26590	+	7.98094i	−0.340456	+	0.636949i	−0.992639	−	0.121113i	$-0.961354\pi$
$157$	−4.26590	+	7.98094i	−0.340456	+	0.636949i	0.652183	+	0.758062i	$0.273854\pi$
$158$	−17.1927	+	2.15920i	−1.36778	+	0.171777i
$159$	2.08272	−	2.08272i	0.165171	−	0.165171i
$160$	−7.78218	−	22.7093i	−0.615235	−	1.79533i
$161$	−0.765552	−	0.765552i	−0.0603340	−	0.0603340i
$162$	2.15961	+	1.67769i	0.169675	+	0.131812i
$163$	−4.40562	−	2.35485i	−0.345075	−	0.184446i	0.289750	−	0.957102i	$-0.406428\pi$
$163$	−4.40562	−	2.35485i	−0.345075	−	0.184446i	−0.634825	+	0.772656i	$0.718928\pi$
$164$	−6.36463	−	5.71741i	−0.496994	−	0.446454i
$165$	8.36201	−	10.1891i	0.650982	−	0.793223i
$166$	−11.6060	+	5.17536i	−0.900797	+	0.401686i
$167$	2.34744	+	11.8014i	0.181651	+	0.913220i	0.958839	+	0.283951i	$0.0916454\pi$
$167$	2.34744	+	11.8014i	0.181651	+	0.913220i	−0.777188	+	0.629268i	$0.783355\pi$
$168$	2.34728	−	1.20114i	0.181097	−	0.0926702i
$169$	27.4814	+	5.46638i	2.11395	+	0.420491i
$170$	6.61673	+	4.16949i	0.507480	+	0.319786i
$171$	−0.307700	+	1.01435i	−0.0235304	+	0.0775693i
$172$	−9.04527	+	8.27145i	−0.689695	+	0.630692i
$173$	10.8297	+	13.1960i	0.823365	+	1.00327i	0.999820	+	0.0189640i	$0.00603680\pi$
$173$	10.8297	+	13.1960i	0.823365	+	1.00327i	−0.176456	+	0.984309i	$0.556463\pi$
$174$	4.66195	−	9.31301i	0.353421	−	0.706018i
$175$	−4.97816	+	12.0183i	−0.376314	+	0.908501i
$176$	−11.1466	−	7.30585i	−0.840204	−	0.550699i
$177$	4.51563	+	10.9017i	0.339416	+	0.819422i
$178$	15.0012	+	1.07314i	1.12439	+	0.0804356i
$179$	−1.47943	+	15.0209i	−0.110578	+	1.12271i	0.766460	+	0.642293i	$0.222017\pi$
$179$	−1.47943	+	15.0209i	−0.110578	+	1.12271i	−0.877037	+	0.480422i	$0.840483\pi$
$180$	−2.73300	−	17.8782i	−0.203706	−	1.33256i
$181$	1.69245	+	3.16635i	0.125799	+	0.235353i	0.936935	−	0.349505i	$-0.113650\pi$
$181$	1.69245	+	3.16635i	0.125799	+	0.235353i	−0.811136	+	0.584858i	$0.801150\pi$
$182$	−5.23181	−	7.39376i	−0.387808	−	0.548062i
$183$	−4.56295	−	6.82893i	−0.337303	−	0.504809i
$184$	−1.65543	−	2.57617i	−0.122040	−	0.189918i
$185$	−1.87797	−	1.25482i	−0.138071	−	0.0922562i
$186$	1.62265	−	1.71190i	0.118978	−	0.125522i
$187$	4.32107	−	0.425588i	0.315988	−	0.0311221i
$188$	−1.12008	+	0.838428i	−0.0816904	+	0.0611487i
$189$	4.57727	−	1.38850i	0.332948	−	0.100999i
$190$	2.59419	−	1.47719i	0.188203	−	0.107167i
$191$			23.8505i			1.72576i	0.505410	+	0.862879i	$0.331341\pi$
$191$			23.8505i			1.72576i	−0.505410	+	0.862879i	$0.668659\pi$
$192$	7.20965	−	1.90812i	0.520311	−	0.137706i
$193$		−	18.4180i		−	1.32576i	−0.748727	−	0.662878i	$-0.769335\pi$
$193$		−	18.4180i		−	1.32576i	0.748727	−	0.662878i	$-0.230665\pi$
$194$	−8.07878	−	14.1877i	−0.580022	−	1.01861i
$195$	24.2463	−	7.35504i	1.73632	−	0.526706i
$196$	−0.284692	+	1.97963i	−0.0203352	+	0.141402i
$197$	12.3457	−	1.21594i	0.879594	−	0.0866324i	0.351870	−	0.936049i	$-0.385546\pi$
$197$	12.3457	−	1.21594i	0.879594	−	0.0866324i	0.527723	+	0.849416i	$0.323046\pi$
$198$	−7.28743	−	6.90749i	−0.517895	−	0.490894i
$199$	6.39665	+	4.27410i	0.453446	+	0.302983i	0.761240	−	0.648470i	$-0.224591\pi$
$199$	6.39665	+	4.27410i	0.453446	+	0.302983i	−0.307794	+	0.951453i	$0.599591\pi$
$200$	−20.9857	+	30.2222i	−1.48392	+	2.13703i
$201$	−3.89158	−	5.82415i	−0.274491	−	0.410804i
$202$	−8.62152	+	6.10058i	−0.606608	+	0.429235i
$203$	3.72386	+	6.96685i	0.261364	+	0.488977i
$204$	−1.43872	+	1.95796i	−0.100730	+	0.137085i
$205$	−1.77934	+	18.0659i	−0.124275	+	1.26178i
$206$	−1.88135	+	26.2988i	−0.131080	+	1.83233i
$207$	−0.882878	−	2.13145i	−0.0613642	−	0.148146i
$208$	−10.0132	−	23.5808i	−0.694290	−	1.63503i
$209$	0.634248	−	1.53121i	0.0438718	−	0.105916i
$210$	−5.00291	−	2.50438i	−0.345234	−	0.172819i
$211$	−16.4144	−	20.0011i	−1.13002	−	1.37693i	−0.916522	−	0.399985i	$-0.869015\pi$
$211$	−16.4144	−	20.0011i	−1.13002	−	1.37693i	−0.213495	−	0.976944i	$-0.568485\pi$
$212$	−0.282093	+	6.31274i	−0.0193742	+	0.433561i
$213$	2.37572	−	7.83170i	0.162782	−	0.536619i
$214$	0.721730	−	1.14534i	0.0493365	−	0.0782940i
$215$	25.5075	+	5.07375i	1.73959	+	0.346027i
$216$	13.4855	−	1.08491i	0.917570	−	0.0738187i
$217$	0.349038	+	1.75473i	0.0236942	+	0.119119i
$218$	−8.14675	−	18.2694i	−0.551768	−	1.23736i
$219$	−4.12076	+	5.02116i	−0.278455	+	0.339299i
$220$	1.51270	+	28.2381i	0.101986	+	1.90381i
$221$	7.36082	+	3.93444i	0.495143	+	0.264659i
$222$	0.430473	−	0.554127i	0.0288915	−	0.0371906i
$223$	13.2547	+	13.2547i	0.887599	+	0.887599i	0.994292	−	0.106693i	$-0.0340262\pi$
$223$	13.2547	+	13.2547i	0.887599	+	0.887599i	−0.106693	+	0.994292i	$0.534026\pi$
$224$	−1.97729	+	5.30003i	−0.132113	+	0.354123i
$225$	−19.6013	+	19.6013i	−1.30675	+	1.30675i
$226$	−0.0928994	−	0.739716i	−0.00617958	−	0.0492052i
$227$	9.48488	−	17.7450i	0.629534	−	1.17777i	−0.341737	−	0.939796i	$-0.611015\pi$
$227$	9.48488	−	17.7450i	0.629534	−	1.17777i	0.971270	−	0.237979i	$-0.0764848\pi$
$228$	0.400244	+	0.836633i	0.0265068	+	0.0554074i
$229$	5.49011	+	4.50562i	0.362797	+	0.297740i	0.798077	−	0.602555i	$-0.205851\pi$
$229$	5.49011	+	4.50562i	0.362797	+	0.297740i	−0.435280	+	0.900295i	$0.643351\pi$
$230$	−2.32497	+	6.06726i	−0.153304	+	0.400063i
$231$	−3.04640	+	0.605966i	−0.200438	+	0.0398696i
$232$	6.10229	+	21.4941i	0.400635	+	1.41115i
$233$	−5.24021	+	26.3443i	−0.343297	+	1.72587i	0.294485	+	0.955656i	$0.404852\pi$
$233$	−5.24021	+	26.3443i	−0.343297	+	1.72587i	−0.637782	+	0.770217i	$0.720148\pi$
$234$	−4.27061	−	18.8227i	−0.279179	−	1.23048i
$235$	2.84086	+	0.861767i	0.185318	+	0.0562155i
$236$	−22.9325	−	10.7222i	−1.49278	−	0.697956i
$237$	−8.82955	+	7.24622i	−0.573541	+	0.470693i
$238$	−0.581977	−	1.74865i	−0.0377240	−	0.113348i
$239$	−25.0171	−	10.3624i	−1.61822	−	0.670289i	−0.624381	−	0.781120i	$-0.714649\pi$
$239$	−25.0171	−	10.3624i	−1.61822	−	0.670289i	−0.993839	+	0.110831i	$0.964649\pi$
$240$	−12.3208	−	9.93004i	−0.795306	−	0.640981i
$241$	−13.7412	+	5.69180i	−0.885149	+	0.366641i	−0.778492	−	0.627655i	$-0.784015\pi$
$241$	−13.7412	+	5.69180i	−0.885149	+	0.366641i	−0.106658	+	0.994296i	$0.534015\pi$
$242$	0.0938429	+	0.108304i	0.00603245	+	0.00696204i
$243$	16.0746	+	1.58321i	1.03119	+	0.101563i
$244$	17.1110	+	4.20559i	1.09542	+	0.269235i
$245$	3.74256	−	2.00044i	0.239104	−	0.127804i
$246$	−5.55881	−	0.951865i	−0.354417	−	0.0606887i
$247$	2.64896	−	1.76998i	0.168549	−	0.112621i
$248$	−0.0905626	+	5.05955i	−0.00575073	+	0.321282i
$249$	−4.65385	+	6.96497i	−0.294926	+	0.441387i
$250$	48.0456	−	1.28596i	3.03867	−	0.0813315i
$251$	−0.853253	−	8.66322i	−0.0538569	−	0.546818i	−0.983819	−	0.179163i	$-0.942661\pi$
$251$	−0.853253	−	8.66322i	−0.0538569	−	0.546818i	0.929962	−	0.367654i	$-0.119839\pi$
$252$	−2.17482	+	3.66521i	−0.137001	+	0.230886i
$253$	1.04713	+	3.45193i	0.0658326	+	0.217021i
$254$	−3.01254	+	10.9805i	−0.189023	+	0.688977i
$255$	5.15543			0.322845
$256$	−8.65196	+	13.4590i	−0.540747	+	0.841185i
$257$	−14.2361			−0.888025			−0.444013	−	0.896021i	$-0.646445\pi$
$257$	−14.2361			−0.888025			−0.444013	+	0.896021i	$0.646445\pi$
$258$	−2.13770	+	7.79175i	−0.133087	+	0.485093i
$259$	0.154500	+	0.509317i	0.00960013	+	0.0316474i
$260$	−27.7389	+	46.7481i	−1.72029	+	2.89919i
$261$	1.64998	+	16.7526i	0.102131	+	1.03696i
$262$	−19.9883	+	0.534996i	−1.23488	+	0.0330522i
$263$	−8.91965	+	13.3492i	−0.550009	+	0.823147i	−0.997465	−	0.0711589i	$-0.977330\pi$
$263$	−8.91965	+	13.3492i	−0.550009	+	0.823147i	0.447456	+	0.894306i	$0.352330\pi$
$264$	−8.78391	−	0.157226i	−0.540613	−	0.00967660i
$265$	11.1483	−	7.44903i	0.684832	−	0.457590i
$266$	−0.693380	−	0.118731i	−0.0425139	−	0.00727987i
$267$	8.74327	−	4.67338i	0.535080	−	0.286006i
$268$	14.5933	+	3.58680i	0.891430	+	0.219099i
$269$	3.87435	+	0.381590i	0.236223	+	0.0232659i	0.215436	−	0.976518i	$-0.430883\pi$
$269$	3.87435	+	0.381590i	0.236223	+	0.0232659i	0.0207872	+	0.999784i	$0.493383\pi$
$270$	−18.7983	−	21.6950i	−1.14403	−	1.32032i
$271$	−28.2978	+	11.7213i	−1.71897	+	0.712019i	−0.719114	+	0.694892i	$0.755452\pi$
$271$	−28.2978	+	11.7213i	−1.71897	+	0.712019i	−0.999853	+	0.0171270i	$0.994548\pi$
$272$	−0.556881	−	5.18284i	−0.0337659	−	0.314256i
$273$	−5.51616	−	2.28487i	−0.333853	−	0.138287i
$274$	3.03163	+	9.10906i	0.183147	+	0.550299i
$275$	33.5044	−	27.4964i	2.02039	−	1.65809i
$276$	−1.82858	−	0.854958i	−0.110067	−	0.0514624i
$277$	−0.560704	−	0.170088i	−0.0336895	−	0.0102196i	0.273395	−	0.961902i	$-0.411853\pi$
$277$	−0.560704	−	0.170088i	−0.0336895	−	0.0102196i	−0.307084	+	0.951682i	$0.599353\pi$
$278$	0.887235	+	3.91049i	0.0532128	+	0.234536i
$279$	−0.743778	+	3.73923i	−0.0445288	+	0.223862i
$280$	11.5465	−	3.27813i	0.690037	−	0.195906i
$281$	−10.8202	+	2.15228i	−0.645482	+	0.128394i	−0.506966	−	0.861966i	$-0.669233\pi$
$281$	−10.8202	+	2.15228i	−0.645482	+	0.128394i	−0.138516	+	0.990360i	$0.544233\pi$
$282$	−0.330020	+	0.861221i	−0.0196524	+	0.0512850i
$283$	3.19069	+	2.61853i	0.189667	+	0.155656i	0.724435	−	0.689344i	$-0.242101\pi$
$283$	3.19069	+	2.61853i	0.189667	+	0.155656i	−0.534768	+	0.844999i	$0.679601\pi$
$284$	7.57728	+	15.8389i	0.449629	+	0.939863i
$285$	0.927648	−	1.73551i	0.0549491	−	0.102803i
$286$	3.76053	+	29.9434i	0.222365	+	1.77059i
$287$	3.02484	−	3.02484i	0.178551	−	0.178551i
$288$	−8.21479	+	8.82191i	−0.484061	+	0.519836i
$289$	−10.8200	−	10.8200i	−0.636469	−	0.636469i
$290$	29.0847	−	37.4393i	1.70791	−	2.19851i
$291$	−9.49149	−	5.07331i	−0.556401	−	0.297403i
$292$	−0.745450	−	13.9156i	−0.0436242	−	0.814348i
$293$	−18.4251	+	22.4510i	−1.07641	+	1.31160i	−0.128973	+	0.991648i	$0.541168\pi$
$293$	−18.4251	+	22.4510i	−1.07641	+	1.31160i	−0.947433	+	0.319956i	$0.896332\pi$
$294$	0.536930	+	1.20409i	0.0313144	+	0.0702238i
$295$	10.4792	+	52.6826i	0.610124	+	3.06730i
$296$	0.120719	+	1.50054i	0.00701663	+	0.0872170i
$297$	−15.6309	−	3.10918i	−0.906996	−	0.180413i
$298$	12.3205	−	19.5520i	0.713710	−	1.13261i
$299$	−2.01285	+	6.63546i	−0.116406	+	0.383739i
$300$	−1.08274	+	24.2299i	−0.0625121	+	1.39891i
$301$	−3.88788	−	4.73739i	−0.224093	−	0.273059i
$302$	−5.57997	−	2.79324i	−0.321091	−	0.160733i
$303$	−2.66428	+	6.43214i	−0.153059	+	0.369517i
$304$	−1.84494	−	0.745113i	−0.105814	−	0.0427351i
$305$	−14.3074	−	34.5411i	−0.819239	−	1.97782i
$306$	0.280227	−	3.91722i	0.0160195	−	0.223932i
$307$	3.20101	−	32.5004i	0.182691	−	1.85489i	−0.269534	−	0.962991i	$-0.586870\pi$
$307$	3.20101	−	32.5004i	0.182691	−	1.85489i	0.452225	−	0.891904i	$-0.350630\pi$
$308$	3.94583	−	5.36990i	0.224834	−	0.305978i
$309$	8.19298	+	15.3280i	0.466082	+	0.871978i
$310$	8.76485	−	6.20200i	0.497810	−	0.352250i
$311$	−12.8912	−	19.2931i	−0.730995	−	1.09401i	−0.991698	−	0.128592i	$-0.958954\pi$
$311$	−12.8912	−	19.2931i	−0.730995	−	1.09401i	0.260702	−	0.965419i	$-0.416046\pi$
$312$	−13.8713	−	9.63201i	−0.785309	−	0.545305i
$313$	10.3098	+	6.88881i	0.582747	+	0.389379i	0.811714	−	0.584055i	$-0.198535\pi$
$313$	10.3098	+	6.88881i	0.582747	+	0.389379i	−0.228967	+	0.973434i	$0.573535\pi$
$314$	−9.28838	−	8.80413i	−0.524174	−	0.496846i
$315$	8.99941	−	0.886365i	0.507060	−	0.0499410i
$316$	3.48822	−	24.2556i	0.196228	−	1.36449i
$317$	−12.3468	+	3.74535i	−0.693463	+	0.210360i	−0.617291	−	0.786735i	$-0.711770\pi$
$317$	−12.3468	+	3.74535i	−0.693463	+	0.210360i	−0.0761721	+	0.997095i	$0.524270\pi$
$318$	2.06117	+	3.61974i	0.115584	+	0.202985i
$319$		−	26.3205i		−	1.47366i
$320$	33.8832	−	2.11638i	1.89413	−	0.118309i
$321$		−	0.892393i		−	0.0498085i
$322$	1.33052	−	0.757628i	0.0741469	−	0.0422210i
$323$	0.620321	−	0.188172i	0.0345156	−	0.0104702i
$324$	−3.09612	+	2.31757i	−0.172006	+	0.128754i
$325$	82.9143	−	8.16635i	4.59926	−	0.452987i
$326$	4.86003	−	5.12735i	0.269172	−	0.283978i
$327$	−10.9639	−	7.32581i	−0.606303	−	0.405118i
$328$	10.1789	−	6.54093i	0.562038	−	0.361162i
$329$	−0.388656	−	0.581665i	−0.0214273	−	0.0320682i
$330$	10.7673	+	15.2167i	0.592722	+	0.837652i
$331$	7.75119	+	14.5014i	0.426044	+	0.797072i	0.999758	−	0.0219836i	$-0.00699815\pi$
$331$	7.75119	+	14.5014i	0.426044	+	0.797072i	−0.573715	+	0.819055i	$0.694498\pi$
$332$	−2.71567	−	17.7649i	−0.149042	−	0.974974i
$333$	−0.111167	+	1.12870i	−0.00609192	+	0.0618523i
$334$	−16.9733	−	1.21422i	−0.928737	−	0.0664394i
$335$	−12.2023	−	29.4589i	−0.666681	−	1.60951i
$336$	0.759860	+	3.65070i	0.0414538	+	0.199162i
$337$	3.99895	−	9.65433i	0.217837	−	0.525905i	−0.776750	−	0.629809i	$-0.783133\pi$
$337$	3.99895	−	9.65433i	0.217837	−	0.525905i	0.994587	+	0.103904i	$0.0331333\pi$
$338$	−17.7378	+	35.4342i	−0.964809	+	1.92737i
$339$	−0.311768	−	0.379891i	−0.0169329	−	0.0206328i
$340$	−8.16220	+	7.46393i	−0.442657	+	0.404788i
$341$	1.73041	−	5.70439i	0.0937068	−	0.308910i
$342$	−1.26826	−	0.799184i	−0.0685794	−	0.0432149i
$343$	−0.980785	−	0.195090i	−0.0529574	−	0.0105339i
$344$	−7.89630	−	15.4310i	−0.425740	−	0.831984i
$345$	0.835584	+	4.20076i	0.0449863	+	0.226162i
$346$	−22.0490	+	9.83217i	−1.18536	+	0.528581i
$347$	18.9034	−	23.0339i	1.01479	−	1.23652i	0.0433925	−	0.999058i	$-0.486183\pi$
$347$	18.9034	−	23.0339i	1.01479	−	1.23652i	0.971396	−	0.237465i	$-0.0763166\pi$
$348$	10.9569	+	9.84268i	0.587351	+	0.527623i
$349$	0.132279	+	0.0707047i	0.00708075	+	0.00378474i	0.474933	−	0.880022i	$-0.342472\pi$
$349$	0.132279	+	0.0707047i	0.00708075	+	0.00378474i	−0.467853	+	0.883807i	$0.654972\pi$
$350$	−14.5282	−	11.2862i	−0.776563	−	0.603272i
$351$	−21.6622	−	21.6622i	−1.15625	−	1.15625i
$352$	14.1345	−	12.4683i	0.753373	−	0.664560i
$353$	8.47198	−	8.47198i	0.450918	−	0.450918i	−0.444741	−	0.895659i	$-0.646704\pi$
$353$	8.47198	−	8.47198i	0.450918	−	0.450918i	0.895659	+	0.444741i	$0.146704\pi$
$354$	−16.5575	+	2.07943i	−0.880023	+	0.110520i
$355$	17.5619	−	32.8560i	0.932090	−	1.74382i
$356$	−7.07654	+	20.0573i	−0.375056	+	1.06304i
$357$	−0.939097	−	0.770697i	−0.0497023	−	0.0407896i
$358$	−19.9322	−	7.63802i	−1.05345	−	0.403682i
$359$	18.9844	−	3.77624i	1.00196	−	0.199302i	0.333260	−	0.942835i	$-0.391851\pi$
$359$	18.9844	−	3.77624i	1.00196	−	0.199302i	0.668700	+	0.743533i	$0.266851\pi$
$360$	25.4052	+	2.96216i	1.33897	+	0.156119i
$361$	−3.65844	+	18.3922i	−0.192550	+	0.968013i
$362$	−4.95159	+	1.12345i	−0.260250	+	0.0590470i
$363$	0.0903973	+	0.0274217i	0.00474463	+	0.00143927i
$364$	12.0413	−	4.36873i	0.631136	−	0.228984i
$365$	−22.8570	+	18.7582i	−1.19639	+	0.981851i
$366$	11.0207	−	3.66786i	0.576063	−	0.191722i
$367$	6.40820	+	2.65436i	0.334505	+	0.138557i	0.543613	−	0.839336i	$-0.317056\pi$
$367$	6.40820	+	2.65436i	0.334505	+	0.138557i	−0.209108	+	0.977893i	$0.567056\pi$
$368$	4.13284	−	1.29379i	0.215439	−	0.0674433i
$369$	8.42178	−	3.48842i	0.438420	−	0.181600i
$370$	2.41402	−	2.09170i	0.125499	−	0.108742i
$371$	−3.14431	−	0.309687i	−0.163244	−	0.0160782i
$372$	1.72757	+	2.85353i	0.0895704	+	0.147949i
$373$	12.7522	−	6.81622i	0.660286	−	0.352930i	−0.106978	−	0.994261i	$-0.534117\pi$
$373$	12.7522	−	6.81622i	0.660286	−	0.352930i	0.767264	+	0.641331i	$0.221617\pi$
$374$	−1.03638	+	6.05239i	−0.0535901	+	0.312962i
$375$	26.3430	−	17.6018i	1.36035	−	0.908955i
$376$	−0.724364	−	1.84130i	−0.0373562	−	0.0949579i
$377$	28.1088	−	42.0678i	1.44768	−	2.16660i
$378$	0.180991	+	6.76210i	0.00930917	+	0.347805i
$379$	−0.640101	−	6.49905i	−0.0328798	−	0.333834i	−0.997527	−	0.0702883i	$-0.977608\pi$
$379$	−0.640101	−	6.49905i	−0.0328798	−	0.333834i	0.964647	−	0.263546i	$-0.0848919\pi$
$380$	1.04396	+	4.09073i	0.0535539	+	0.209850i
$381$	2.17879	+	7.18249i	0.111623	+	0.367970i
$382$	−32.5277	−	8.92408i	−1.66426	−	0.456596i
$383$	35.4486			1.81134			0.905670	−	0.423984i	$-0.139369\pi$
$383$	35.4486			1.81134			0.905670	+	0.423984i	$0.139369\pi$
$384$	−0.0952985	+	10.5466i	−0.00486318	+	0.538204i
$385$	−14.1393			−0.720604
$386$	25.1188	+	6.89143i	1.27851	+	0.350764i
$387$	−3.79096	−	12.4971i	−0.192705	−	0.635264i
$388$	22.3722	−	5.70941i	1.13578	−	0.289851i
$389$	−0.885945	−	8.99515i	−0.0449192	−	0.456072i	−0.991166	−	0.132627i	$-0.957659\pi$
$389$	−0.885945	−	8.99515i	−0.0449192	−	0.456072i	0.946247	−	0.323445i	$-0.104841\pi$
$390$	0.958730	+	35.8196i	0.0485472	+	1.81380i
$391$	−0.783843	+	1.17310i	−0.0396406	+	0.0593264i
$392$	−2.59334	−	1.12898i	−0.130983	−	0.0570223i
$393$	−10.9594	+	7.32284i	−0.552829	+	0.369389i
$394$	−2.96104	+	17.2922i	−0.149175	+	0.871170i
$395$	−45.8561	+	24.5106i	−2.30727	+	1.23326i
$396$	12.1473	−	7.35416i	0.610424	−	0.369560i
$397$	15.9063	+	1.56664i	0.798317	+	0.0786273i	0.488946	−	0.872314i	$-0.337382\pi$
$397$	15.9063	+	1.56664i	0.798317	+	0.0786273i	0.309371	+	0.950942i	$0.399882\pi$
$398$	−8.22252	+	7.12462i	−0.412158	+	0.357125i
$399$	−0.428423	+	0.177458i	−0.0214480	+	0.00888403i
$400$	−33.3653	−	39.9289i	−1.66827	−	1.99645i
$401$	14.0473	+	5.81857i	0.701487	+	0.290566i	0.704777	−	0.709429i	$-0.251047\pi$
$401$	14.0473	+	5.81857i	0.701487	+	0.290566i	−0.00328959	+	0.999995i	$0.501047\pi$
$402$	9.39919	−	3.12819i	0.468789	−	0.156020i
$403$	8.85765	−	7.26929i	0.441231	−	0.362109i
$404$	−5.09417	−	14.0408i	−0.253445	−	0.698557i
$405$	7.85267	+	2.38208i	0.390202	+	0.118367i
$406$	−10.8949	+	2.47189i	−0.540703	+	0.122678i
$407$	0.345960	−	1.73926i	0.0171486	−	0.0862119i
$408$	−2.13198	−	2.69475i	−0.105549	−	0.133410i
$409$	−13.6447	+	2.71409i	−0.674685	+	0.134203i	−0.520530	−	0.853844i	$-0.674265\pi$
$409$	−13.6447	+	2.71409i	−0.674685	+	0.134203i	−0.154155	+	0.988047i	$0.549265\pi$
$410$	−23.9729	−	9.18640i	−1.18394	−	0.453684i
$411$	4.89193	+	4.01471i	0.241301	+	0.198031i
$412$	−35.1629	−	12.4060i	−1.73235	−	0.611200i
$413$	5.96678	−	11.1631i	0.293606	−	0.549299i
$414$	3.23726	−	0.406561i	0.159103	−	0.0199814i
$415$	−26.9633	+	26.9633i	−1.32357	+	1.32357i
$416$	35.9065	−	4.83300i	1.76046	−	0.236957i
$417$	1.86907	+	1.86907i	0.0915289	+	0.0915289i
$418$	1.85098	+	1.43793i	0.0905342	+	0.0703314i
$419$	−19.3248	−	10.3293i	−0.944076	−	0.504619i	−0.0738486	−	0.997269i	$-0.523528\pi$
$419$	−19.3248	−	10.3293i	−0.944076	−	0.504619i	−0.870227	+	0.492650i	$0.836028\pi$
$420$	5.28745	−	5.88600i	0.258001	−	0.287208i
$421$	10.4188	−	12.6953i	0.507779	−	0.618731i	−0.454516	−	0.890739i	$-0.650188\pi$
$421$	10.4188	−	12.6953i	0.507779	−	0.618731i	0.962295	+	0.272008i	$0.0876877\pi$
$422$	33.4195	−	14.9025i	1.62684	−	0.725444i
$423$	−0.290826	−	1.46208i	−0.0141404	−	0.0710888i
$424$	−8.50388	−	2.74675i	−0.412985	−	0.133394i
$425$	16.6266	+	3.30723i	0.806508	+	0.160424i
$426$	9.79209	+	6.17042i	0.474428	+	0.298958i
$427$	−2.55744	+	8.43075i	−0.123763	+	0.407993i
$428$	1.29199	+	1.41286i	0.0624507	+	0.0682931i
$429$	12.6202	+	15.3778i	0.609311	+	0.742448i
$430$	−16.4638	+	32.8891i	−0.793953	+	1.58605i
$431$	−10.6020	+	25.5954i	−0.510679	+	1.23289i	0.432810	+	0.901485i	$0.357522\pi$
$431$	−10.6020	+	25.5954i	−0.510679	+	1.23289i	−0.943489	+	0.331403i	$0.892478\pi$
$432$	−3.56622	+	18.7977i	−0.171580	+	0.904403i
$433$	4.86601	+	11.7476i	0.233845	+	0.564553i	0.996623	−	0.0821075i	$-0.0261651\pi$
$433$	4.86601	+	11.7476i	0.233845	+	0.564553i	−0.762778	+	0.646660i	$0.776165\pi$
$434$	−2.52373	−	0.180541i	−0.121143	−	0.00866624i
$435$	3.06318	−	31.1010i	0.146868	−	1.49118i
$436$	27.9644	−	4.27485i	1.33925	−	0.204728i
$437$	0.253868	+	0.474954i	0.0121442	+	0.0227201i
$438$	−5.30609	−	7.49873i	−0.253535	−	0.358303i
$439$	−1.09583	−	1.64002i	−0.0523011	−	0.0782741i	0.804397	−	0.594091i	$-0.202488\pi$
$439$	−1.09583	−	1.64002i	−0.0523011	−	0.0782741i	−0.856699	+	0.515817i	$0.827488\pi$
$440$	−39.0776	−	8.50274i	−1.86295	−	0.405352i
$441$	−1.77181	−	1.18389i	−0.0843720	−	0.0563755i
$442$	−8.12005	+	8.56668i	−0.386231	+	0.407475i
$443$	23.9182	−	2.35573i	1.13639	−	0.111924i	0.487722	−	0.872999i	$-0.337828\pi$
$443$	23.9182	−	2.35573i	1.13639	−	0.111924i	0.648664	+	0.761075i	$0.275328\pi$
$444$	0.594659	+	0.794424i	0.0282213	+	0.0377017i
$445$	43.1860	−	13.1003i	2.04722	−	0.621016i
$446$	−23.0364	+	13.1175i	−1.09081	+	0.621131i
$447$		−	15.2339i		−	0.720539i
$448$	−6.48844	−	4.67976i	−0.306550	−	0.221098i
$449$			35.7838i			1.68874i	0.535757	+	0.844372i	$0.320026\pi$
$449$			35.7838i			1.68874i	−0.535757	+	0.844372i	$0.679974\pi$
$450$	−19.3984	−	34.0668i	−0.914451	−	1.60592i
$451$	−13.6392	+	4.13742i	−0.642246	+	0.194823i
$452$	1.04360	+	0.150080i	0.0490867	+	0.00705918i
$453$	−4.09357	+	0.403181i	−0.192333	+	0.0189431i
$454$	20.6519	+	19.5752i	0.969244	+	0.918712i
$455$	−22.5986	−	15.0999i	−1.05944	−	0.707896i
$456$	−1.29077	+	0.232818i	−0.0604460	+	0.0109027i
$457$	−10.5713	−	15.8211i	−0.494506	−	0.740080i	0.497336	−	0.867558i	$-0.334312\pi$
$457$	−10.5713	−	15.8211i	−0.494506	−	0.740080i	−0.991841	+	0.127478i	$0.959312\pi$
$458$	−8.19907	+	5.80165i	−0.383117	+	0.271093i
$459$	−2.93838	−	5.49733i	−0.137152	−	0.256593i
$460$	−7.40470	−	5.44101i	−0.345246	−	0.253689i
$461$	2.99878	−	30.4471i	0.139667	−	1.41806i	−0.628497	−	0.777812i	$-0.716330\pi$
$461$	2.99878	−	30.4471i	0.139667	−	1.41806i	0.768165	−	0.640252i	$-0.221170\pi$
$462$	0.313438	−	4.38146i	0.0145825	−	0.203844i
$463$	0.0806578	+	0.194725i	0.00374848	+	0.00904964i	0.925743	−	0.378154i	$-0.123441\pi$
$463$	0.0806578	+	0.194725i	0.00374848	+	0.00904964i	−0.921994	+	0.387204i	$0.873441\pi$
$464$	−31.5973	+	0.280013i	−1.46687	+	0.0129993i
$465$	2.70858	−	6.53908i	0.125607	−	0.303243i
$466$	−33.9681	−	17.0039i	−1.57354	−	0.787690i
$467$	12.1682	+	14.8269i	0.563075	+	0.686109i	0.974256	−	0.225445i	$-0.0723836\pi$
$467$	12.1682	+	14.8269i	0.563075	+	0.686109i	−0.411181	+	0.911554i	$0.634884\pi$
$468$	27.2687	+	1.21854i	1.26050	+	0.0563268i
$469$	−2.18115	+	7.19029i	−0.100716	+	0.332017i
$470$	−2.23825	+	3.55198i	−0.103243	+	0.163840i
$471$	−8.27415	−	1.64583i	−0.381253	−	0.0758359i
$472$	23.2037	−	27.2639i	1.06804	−	1.25492i
$473$	3.98361	+	20.0270i	0.183167	+	0.920841i
$474$	−6.57879	−	14.7532i	−0.302174	−	0.677637i
$475$	4.10506	−	5.00203i	0.188353	−	0.229509i
$476$	2.60260	−	0.139420i	0.119290	−	0.00639030i
$477$	−5.93775	−	3.17380i	−0.271871	−	0.145318i
$478$	23.4930	−	30.2414i	1.07455	−	1.38321i
$479$	−9.70358	−	9.70358i	−0.443368	−	0.443368i	0.449774	−	0.893142i	$-0.351504\pi$
$479$	−9.70358	−	9.70358i	−0.443368	−	0.443368i	−0.893142	+	0.449774i	$0.851504\pi$
$480$	18.1528	−	13.0879i	0.828559	−	0.597376i
$481$	2.41038	−	2.41038i	0.109904	−	0.109904i
$482$	−2.62105	−	20.8702i	−0.119385	−	0.950611i
$483$	0.475775	−	0.890112i	0.0216485	−	0.0405015i
$484$	−0.182820	+	0.0874607i	−0.00831000	+	0.00397549i
$485$	−37.8708	−	31.0797i	−1.71962	−	1.41126i
$486$	−8.17382	+	21.3305i	−0.370772	+	0.967569i
$487$	23.4018	−	4.65490i	1.06044	−	0.210934i	0.366093	−	0.930578i	$-0.380695\pi$
$487$	23.4018	−	4.65490i	1.06044	−	0.210934i	0.694343	+	0.719645i	$0.255695\pi$
$488$	−12.1380	+	21.7626i	−0.549463	+	0.985148i
$489$	0.908527	−	4.56747i	0.0410850	−	0.206548i
$490$	1.32789	+	5.85268i	0.0599879	+	0.264397i
$491$	14.7527	+	4.47520i	0.665782	+	0.201963i	0.605045	−	0.796191i	$-0.293155\pi$
$491$	14.7527	+	4.47520i	0.665782	+	0.201963i	0.0607367	+	0.998154i	$0.480655\pi$
$492$	3.37810	−	7.22505i	0.152297	−	0.325730i
$493$	7.95778	−	6.53078i	0.358400	−	0.294132i
$494$	1.42277	+	4.27496i	0.0640134	+	0.192340i
$495$	−27.8364	−	11.5302i	−1.25115	−	0.518245i
$496$	−6.86642	−	2.01663i	−0.308311	−	0.0905496i
$497$	−8.11076	+	3.35959i	−0.363817	+	0.150698i
$498$	−7.75763	−	8.95307i	−0.347628	−	0.401197i
$499$	−13.5486	−	1.33442i	−0.606520	−	0.0597370i	−0.209905	−	0.977722i	$-0.567315\pi$
$499$	−13.5486	−	1.33442i	−0.606520	−	0.0597370i	−0.396615	+	0.917985i	$0.629815\pi$
$500$	−16.2233	+	66.0066i	−0.725528	+	2.95190i
$501$	−9.89269	+	5.28775i	−0.441973	+	0.236239i
$502$	12.1343	+	2.07782i	0.541581	+	0.0927377i
$503$	26.3015	−	17.5741i	1.17273	−	0.783591i	0.192467	−	0.981303i	$-0.438351\pi$
$503$	26.3015	−	17.5741i	1.17273	−	0.783591i	0.980260	+	0.197712i	$0.0633511\pi$
$504$	−4.18492	−	4.33747i	−0.186411	−	0.193206i
$505$	−17.6073	+	26.3512i	−0.783516	+	1.17261i
$506$	−5.09961	+	0.136494i	−0.226705	+	0.00606788i
$507$	2.56030	+	25.9952i	0.113707	+	1.15449i
$508$	−13.8482	−	8.21710i	−0.614414	−	0.364575i
$509$	10.9957	+	36.2478i	0.487374	+	1.60666i	0.763686	+	0.645588i	$0.223388\pi$
$509$	10.9957	+	36.2478i	0.487374	+	1.60666i	−0.276312	+	0.961068i	$0.589112\pi$
$510$	−1.92900	+	7.03106i	−0.0854174	+	0.311341i
$511$	6.96777			0.308236
$512$	−15.1183	−	16.8356i	−0.668140	−	0.744036i
$513$	−2.37933			−0.105050
$514$	5.32671	−	19.4155i	0.234951	−	0.856380i
$515$	22.9664	+	75.7102i	1.01202	+	3.33619i
$516$	−9.82667	−	5.83085i	−0.432595	−	0.256689i
$517$	0.228463	+	2.31962i	0.0100478	+	0.102017i
$518$	−0.752424	+	0.0201390i	−0.0330596	+	0.000884857i
$519$	−8.84139	+	13.2321i	−0.388094	+	0.580824i
$520$	−53.3768	−	55.3224i	−2.34073	−	2.42605i
$521$	32.7718	−	21.8974i	1.43576	−	0.959343i	0.437569	−	0.899185i	$-0.355840\pi$
$521$	32.7718	−	21.8974i	1.43576	−	0.959343i	0.998189	−	0.0601578i	$-0.0191604\pi$
$522$	−23.4648	−	4.01800i	−1.02703	−	0.175863i
$523$	−20.0437	+	10.7136i	−0.876448	+	0.468471i	−0.847307	−	0.531104i	$-0.821777\pi$
$523$	−20.0437	+	10.7136i	−0.876448	+	0.468471i	−0.0291417	+	0.999575i	$0.509277\pi$
$524$	6.74934	−	27.4605i	0.294846	−	1.19962i
$525$	−12.0686	−	1.18866i	−0.526718	−	0.0518772i
$526$	−14.8684	−	17.1596i	−0.648294	−	0.748195i
$527$	2.15403	−	0.892229i	0.0938311	−	0.0388661i
$528$	3.50109	−	11.9208i	0.152365	−	0.518787i
$529$	20.1663	+	8.35316i	0.876796	+	0.363181i
$530$	5.98779	+	17.9914i	0.260093	+	0.781496i
$531$	20.8502	−	17.1113i	0.904821	−	0.742568i
$532$	0.421368	−	0.901218i	0.0182686	−	0.0390728i
$533$	−26.2180	−	7.95313i	−1.13563	−	0.344488i
$534$	3.10218	+	13.6729i	0.134244	+	0.591682i
$535$	0.792513	−	3.98423i	0.0342633	−	0.172253i
$536$	−10.3521	+	18.5606i	−0.447143	+	0.801695i
$537$	−13.8004	+	2.74507i	−0.595531	+	0.118458i
$538$	−1.97008	+	5.14112i	−0.0849360	+	0.221650i
$539$	2.57557	+	2.11371i	0.110938	+	0.0910441i
$540$	36.6218	−	17.5198i	1.57595	−	0.753932i
$541$	16.1577	−	30.2288i	0.694672	−	1.29964i	−0.248919	−	0.968524i	$-0.580075\pi$
$541$	16.1577	−	30.2288i	0.694672	−	1.29964i	0.943590	−	0.331115i	$-0.107425\pi$
$542$	−5.39761	−	42.9787i	−0.231847	−	1.84609i
$543$	−2.36668	+	2.36668i	−0.101564	+	0.101564i
$544$	7.27681	+	1.17977i	0.311991	+	0.0505822i
$545$	−42.4440	−	42.4440i	−1.81810	−	1.81810i
$546$	5.18012	−	6.66811i	0.221689	−	0.285369i
$547$	−19.6637	−	10.5105i	−0.840758	−	0.449395i	−0.00598090	−	0.999982i	$-0.501904\pi$
$547$	−19.6637	−	10.5105i	−0.840758	−	0.449395i	−0.834778	+	0.550587i	$0.814404\pi$
$548$	−13.5574	+	0.726264i	−0.579145	+	0.0310245i
$549$	−11.9100	+	14.5124i	−0.508305	+	0.619372i
$550$	24.9637	+	55.9822i	1.06446	+	2.38709i
$551$	−0.766609	−	3.85401i	−0.0326587	−	0.164186i
$552$	1.85020	−	2.17395i	0.0787498	−	0.0925293i
$553$	12.0172	+	2.39036i	0.511022	+	0.101649i
$554$	0.441767	−	0.701057i	0.0187689	−	0.0297851i
$555$	0.611212	−	2.01490i	0.0259445	−	0.0855276i
$556$	−5.66517	−	0.253155i	−0.240257	−	0.0107362i
$557$	−22.6649	−	27.6173i	−0.960343	−	1.17018i	−0.985359	−	0.170494i	$-0.945464\pi$
$557$	−22.6649	−	27.6173i	−0.960343	−	1.17018i	0.0250163	−	0.999687i	$-0.492036\pi$
$558$	−4.82132	−	2.41348i	−0.204103	−	0.102171i
$559$	−15.0207	+	36.2632i	−0.635308	+	1.53377i
$560$	0.150422	+	16.9739i	0.00635649	+	0.717279i
$561$	1.54900	+	3.73963i	0.0653990	+	0.157887i
$562$	1.11327	−	15.5622i	0.0469607	−	0.656450i
$563$	−1.28271	+	13.0236i	−0.0540597	+	0.548878i	0.929566	+	0.368655i	$0.120182\pi$
$563$	−1.28271	+	13.0236i	−0.0540597	+	0.548878i	−0.983626	+	0.180222i	$0.942318\pi$
$564$	−1.05107	−	0.772328i	−0.0442578	−	0.0325209i
$565$	−1.05457	−	1.97296i	−0.0443660	−	0.0830029i
$566$	−4.76505	+	3.37175i	−0.200290	+	0.141725i
$567$	−1.07432	−	1.60783i	−0.0451170	−	0.0675224i
$568$	−24.4365	+	4.40763i	−1.02533	+	0.184940i
$569$	4.44343	+	2.96901i	0.186278	+	0.124467i	0.645213	−	0.764003i	$-0.276769\pi$
$569$	4.44343	+	2.96901i	0.186278	+	0.124467i	−0.458934	+	0.888470i	$0.651769\pi$
$570$	2.01982	+	1.91451i	0.0846009	+	0.0801901i
$571$	−13.1115	+	1.29137i	−0.548698	+	0.0540421i	−0.368568	−	0.929601i	$-0.620152\pi$
$571$	−13.1115	+	1.29137i	−0.548698	+	0.0540421i	−0.180130	+	0.983643i	$0.557652\pi$
$572$	−42.2444	−	6.07519i	−1.76633	−	0.254016i
$573$	−21.2768	+	6.45425i	−0.888852	+	0.269630i
$574$	2.99353	+	5.25713i	0.124948	+	0.219428i
$575$			14.0838i			0.587334i
$576$	−8.95776	−	14.5044i	−0.373240	−	0.604348i
$577$		−	27.0858i		−	1.12759i	−0.825913	−	0.563797i	$-0.809340\pi$
$577$		−	27.0858i		−	1.12759i	0.825913	−	0.563797i	$-0.190660\pi$
$578$	18.8050	−	10.7080i	0.782183	−	0.445393i
$579$	16.4306	−	4.98415i	0.682831	−	0.207134i
$580$	40.1778	+	53.6747i	1.66829	+	2.22872i
$581$	8.94235	−	0.880745i	0.370991	−	0.0365394i
$582$	10.4705	−	11.0464i	0.434015	−	0.457888i
$583$	8.75297	+	5.84855i	0.362511	+	0.242222i
$584$	19.2573	+	4.19012i	0.796871	+	0.173388i
$585$	−32.1770	−	48.1563i	−1.33036	−	1.99102i
$586$	−23.7250	−	33.5289i	−0.980072	−	1.38507i
$587$	−13.1309	−	24.5661i	−0.541969	−	1.01395i	−0.992622	−	0.121253i	$-0.961309\pi$
$587$	−13.1309	−	24.5661i	−0.541969	−	1.01395i	0.450653	−	0.892699i	$-0.351191\pi$
$588$	−1.84306	+	0.281743i	−0.0760065	+	0.0116189i
$589$	0.0872309	−	0.885670i	0.00359429	−	0.0364934i
$590$	−75.7704	−	5.42041i	−3.11942	−	0.223155i
$591$	4.42564	+	10.6844i	0.182047	+	0.439499i
$592$	−2.09163	−	0.396816i	−0.0859655	−	0.0163090i
$593$	3.73591	−	9.01929i	0.153416	−	0.370378i	−0.828421	−	0.560106i	$-0.810761\pi$
$593$	3.73591	−	9.01929i	0.153416	−	0.370378i	0.981837	+	0.189728i	$0.0607605\pi$
$594$	10.0889	−	20.1543i	0.413954	−	0.826942i
$595$	−3.50831	−	4.27489i	−0.143827	−	0.175253i
$596$	22.0553	+	24.1187i	0.903422	+	0.987940i
$597$	−2.08188	+	6.86303i	−0.0852056	+	0.280885i
$598$	−8.29642	−	5.22793i	−0.339266	−	0.213786i
$599$	10.1734	+	2.02361i	0.415673	+	0.0826824i	0.398496	−	0.917170i	$-0.369532\pi$
$599$	10.1734	+	2.02361i	0.415673	+	0.0826824i	0.0171766	+	0.999852i	$0.494532\pi$
$600$	−32.6400	−	10.5427i	−1.33252	−	0.430404i
$601$	3.97774	+	19.9975i	0.162256	+	0.815714i	0.973088	+	0.230435i	$0.0740149\pi$
$601$	3.97774	+	19.9975i	0.162256	+	0.815714i	−0.810832	+	0.585279i	$0.800985\pi$
$602$	7.91566	−	3.52977i	0.322618	−	0.143863i
$603$	−10.1576	+	12.3771i	−0.413649	+	0.504033i
$604$	5.89732	−	6.56491i	0.239959	−	0.267123i
$605$	0.379241	+	0.202708i	0.0154183	+	0.00824127i
$606$	−7.77538	−	6.04029i	−0.315853	−	0.245370i
$607$	0.488805	+	0.488805i	0.0198400	+	0.0198400i	0.716957	−	0.697117i	$-0.245534\pi$
$607$	0.488805	+	0.488805i	0.0198400	+	0.0198400i	−0.697117	+	0.716957i	$0.745534\pi$
$608$	1.70651	−	2.23736i	0.0692083	−	0.0907369i
$609$	−5.20735	+	5.20735i	−0.211012	+	0.211012i
$610$	52.4611	−	6.58849i	2.12409	−	0.266760i
$611$	−2.11207	+	3.95141i	−0.0854454	+	0.159857i
$612$	5.23752	+	1.84788i	0.211714	+	0.0746960i
$613$	26.1551	+	21.4649i	1.05639	+	0.866960i	0.991392	−	0.130925i	$-0.0417947\pi$
$613$	26.1551	+	21.4649i	1.05639	+	0.866960i	0.0650018	+	0.997885i	$0.479295\pi$
$614$	43.1269	+	16.5262i	1.74046	+	0.666943i
$615$	−16.5980	+	3.30155i	−0.669296	+	0.133131i
$616$	5.84715	+	7.39063i	0.235589	+	0.297777i
$617$	0.203424	−	1.02268i	0.00818956	−	0.0411717i	−0.976474	−	0.215633i	$-0.930818\pi$
$617$	0.203424	−	1.02268i	0.00818956	−	0.0411717i	0.984664	+	0.174461i	$0.0558185\pi$
$618$	−23.9701	+	5.43848i	−0.964220	+	0.218768i
$619$	17.5874	+	5.33508i	0.706897	+	0.214435i	0.623207	−	0.782057i	$-0.285829\pi$
$619$	17.5874	+	5.33508i	0.706897	+	0.214435i	0.0836902	+	0.996492i	$0.473329\pi$
$620$	5.17887	+	14.2743i	0.207988	+	0.573268i
$621$	4.00311	−	3.28526i	0.160639	−	0.131833i
$622$	31.1358	−	10.3624i	1.24843	−	0.415496i
$623$	−9.82504	−	4.06967i	−0.393632	−	0.163048i
$624$	18.3265	−	15.3140i	0.733648	−	0.613049i
$625$	73.1526	−	30.3008i	2.92610	−	1.21203i
$626$	−13.2527	+	11.4832i	−0.529684	+	0.458960i
$627$	1.53762	+	0.151442i	0.0614065	+	0.00604801i
$628$	15.4826	−	9.37343i	0.617825	−	0.374041i
$629$	0.611692	−	0.326956i	0.0243898	−	0.0130366i
$630$	−2.15846	+	12.6052i	−0.0859949	+	0.502203i
$631$	8.03127	−	5.36633i	0.319720	−	0.213630i	−0.385345	−	0.922772i	$-0.625918\pi$
$631$	8.03127	−	5.36633i	0.319720	−	0.213630i	0.705065	+	0.709142i	$0.250918\pi$
$632$	31.7751	+	13.8330i	1.26395	+	0.550247i
$633$	13.4008	−	20.0558i	0.532635	−	0.797145i
$634$	−0.488206	−	18.2401i	−0.0193891	−	0.724407i
$635$	3.34894	+	34.0023i	0.132898	+	1.34934i
$636$	−5.70789	+	1.45666i	−0.226333	+	0.0577603i
$637$	1.85918	+	6.12888i	0.0736633	+	0.242835i
$638$	35.8964	+	9.84830i	1.42115	+	0.389898i
$639$	−18.7076			−0.740059
$640$	−9.79165	+	47.0023i	−0.387049	+	1.85793i
$641$	33.7851			1.33443			0.667216	−	0.744865i	$-0.267486\pi$
$641$	33.7851			1.33443			0.667216	+	0.744865i	$0.267486\pi$
$642$	1.21706	+	0.333905i	0.0480336	+	0.0131782i
$643$	−2.83195	−	9.33570i	−0.111681	−	0.368164i	0.883227	−	0.468945i	$-0.155366\pi$
$643$	−2.83195	−	9.33570i	−0.111681	−	0.368164i	−0.994909	+	0.100781i	$0.967866\pi$
$644$	0.535429	+	2.09807i	0.0210988	+	0.0826754i
$645$	2.37641	+	24.1280i	0.0935709	+	0.950041i
$646$	0.0245283	+	0.916413i	0.000965052	+	0.0360558i
$647$	−10.9054	+	16.3211i	−0.428736	+	0.641649i	−0.981449	−	0.191723i	$-0.938593\pi$
$647$	−10.9054	+	16.3211i	−0.428736	+	0.641649i	0.552713	+	0.833372i	$0.313593\pi$
$648$	−2.00227	−	5.08970i	−0.0786568	−	0.199942i
$649$	−35.0661	+	23.4304i	−1.37647	+	0.919725i
$650$	−19.8865	+	116.136i	−0.780013	+	4.55521i
$651$	−1.47093	+	0.786228i	−0.0576502	+	0.0308147i
$652$	5.17430	+	8.54669i	0.202641	+	0.334714i
$653$	−17.4332	−	1.71702i	−0.682215	−	0.0671923i	−0.249028	−	0.968496i	$-0.580111\pi$
$653$	−17.4332	−	1.71702i	−0.682215	−	0.0671923i	−0.433187	+	0.901304i	$0.642611\pi$
$654$	14.0934	−	12.2116i	0.551096	−	0.477512i
$655$	−55.4333	+	22.9612i	−2.16596	+	0.897169i
$656$	5.11199	+	16.3296i	0.199590	+	0.637565i
$657$	13.7177	+	5.68204i	0.535177	+	0.221678i
$658$	0.938707	−	0.312415i	0.0365946	−	0.0121792i
$659$	36.1323	−	29.6530i	1.40752	−	1.15512i	0.441308	−	0.897356i	$-0.354515\pi$
$659$	36.1323	−	29.6530i	1.40752	−	1.15512i	0.966208	−	0.257763i	$-0.0829854\pi$
$660$	−24.7816	+	8.99106i	−0.964623	+	0.349977i
$661$	−18.4348	−	5.59214i	−0.717031	−	0.217509i	−0.0893729	−	0.995998i	$-0.528486\pi$
$661$	−18.4348	−	5.59214i	−0.717031	−	0.217509i	−0.627658	+	0.778489i	$0.715986\pi$
$662$	−22.6776	+	5.14522i	−0.881389	+	0.199975i
$663$	−1.51795	+	7.63125i	−0.0589523	+	0.296373i
$664$	25.2442	+	2.94337i	0.979663	+	0.114225i
$665$	−2.07036	+	0.411820i	−0.0802850	+	0.0159697i
$666$	−1.49774	−	0.573935i	−0.0580364	−	0.0222395i
$667$	6.61122	+	5.42569i	0.255988	+	0.210084i
$668$	8.00685	−	22.6942i	0.309794	−	0.878063i
$669$	−8.23751	+	15.4113i	−0.318480	+	0.595835i
$670$	44.7422	−	5.61909i	1.72854	−	0.217084i
$671$	20.7565	−	20.7565i	0.801295	−	0.801295i
$672$	−5.26320	−	0.329664i	−0.203032	−	0.0127171i
$673$	31.1044	+	31.1044i	1.19899	+	1.19899i	0.974471	+	0.224515i	$0.0720799\pi$
$673$	31.1044	+	31.1044i	1.19899	+	1.19899i	0.224515	+	0.974471i	$0.427920\pi$
$674$	11.6705	+	9.06619i	0.449529	+	0.349217i
$675$	−54.8758	−	29.3317i	−2.11217	−	1.12898i
$676$	−41.6889	−	37.4495i	−1.60342	−	1.44036i
$677$	−11.6620	+	14.2102i	−0.448208	+	0.546143i	−0.947276	−	0.320420i	$-0.896176\pi$
$677$	−11.6620	+	14.2102i	−0.448208	+	0.546143i	0.499067	+	0.866563i	$0.333676\pi$
$678$	0.634755	−	0.283052i	0.0243776	−	0.0108705i
$679$	2.25224	+	11.3228i	0.0864331	+	0.434529i
$680$	−7.12540	−	13.9245i	−0.273247	−	0.533981i
$681$	18.3969	+	3.65937i	0.704970	+	0.140227i
$682$	7.13228	+	4.49436i	0.273109	+	0.172098i
$683$	9.48292	−	31.2610i	0.362854	−	1.19617i	−0.565587	−	0.824688i	$-0.691350\pi$
$683$	9.48292	−	31.2610i	0.362854	−	1.19617i	0.928441	−	0.371480i	$-0.121150\pi$
$684$	1.56448	−	1.43064i	0.0598195	−	0.0547019i
$685$	18.2754	+	22.2687i	0.698269	+	0.850843i
$686$	0.633046	−	1.26462i	0.0241698	−	0.0482832i
$687$	−2.53373	+	6.11697i	−0.0966679	+	0.233377i
$688$	23.9996	−	4.99531i	0.914977	−	0.190444i
$689$	7.74386	+	18.6953i	0.295018	+	0.712236i
$690$	−6.04173	−	0.432209i	−0.230005	−	0.0164539i
$691$	−4.07490	+	41.3732i	−0.155017	+	1.57391i	0.531667	+	0.846953i	$0.321566\pi$
$691$	−4.07490	+	41.3732i	−0.155017	+	1.57391i	−0.686684	+	0.726956i	$0.740934\pi$
$692$	−5.15924	−	33.7498i	−0.196125	−	1.28297i
$693$	3.34692	+	6.26164i	0.127139	+	0.237860i
$694$	24.3409	+	34.3994i	0.923970	+	1.30578i
$695$	6.68490	+	10.0047i	0.253573	+	0.379498i
$696$	−17.5233	+	11.2604i	−0.664220	+	0.426824i
$697$	−4.63515	−	3.09711i	−0.175569	−	0.117311i
$698$	−0.145923	+	0.153949i	−0.00552327	+	0.00582707i
$699$	−24.9196	+	2.45437i	−0.942547	+	0.0928328i
$700$	20.8283	−	15.5908i	0.787235	−	0.589278i
$701$	0.0312054	−	0.00946606i	0.00117861	−	0.000357528i	−0.289695	−	0.957119i	$-0.593554\pi$
$701$	0.0312054	−	0.00946606i	0.00117861	−	0.000357528i	0.290874	+	0.956761i	$0.406054\pi$
$702$	37.6487	−	21.4380i	1.42096	−	0.809126i
$703$		−	0.264749i		−	0.00998521i
$704$	11.7157	+	23.9422i	0.441553	+	0.902354i
$705$			2.76752i			0.104231i
$706$	8.38429	+	14.7242i	0.315547	+	0.554152i
$707$	7.14661	−	2.16790i	0.268776	−	0.0815323i
$708$	3.35934	−	23.3595i	0.126252	−	0.877904i
$709$	−6.00277	+	0.591222i	−0.225439	+	0.0222038i	−0.210106	−	0.977679i	$-0.567381\pi$
$709$	−6.00277	+	0.591222i	−0.225439	+	0.0222038i	−0.0153331	+	0.999882i	$0.504881\pi$
$710$	38.2385	+	36.2449i	1.43507	+	1.36025i
$711$	21.7093	+	14.5057i	0.814161	+	0.544005i
$712$	−24.7067	−	17.1559i	−0.925924	−	0.642946i
$713$	1.07613	+	1.61054i	0.0403014	+	0.0603154i
$714$	1.40247	−	0.992387i	0.0524861	−	0.0371391i
$715$	42.6884	+	79.8644i	1.59646	+	2.98676i
$716$	17.8749	−	24.3260i	0.668015	−	0.909105i
$717$	2.47428	−	25.1218i	0.0924036	−	0.938189i
$718$	−1.95327	+	27.3042i	−0.0728955	+	1.01899i
$719$	−12.8622	−	31.0521i	−0.479679	−	1.15805i	−0.959759	−	0.280824i	$-0.909392\pi$
$719$	−12.8622	−	31.0521i	−0.479679	−	1.15805i	0.480080	−	0.877225i	$-0.340608\pi$
$720$	−13.5457	+	33.5398i	−0.504818	+	1.24995i
$721$	7.13460	−	17.2244i	0.265706	−	0.641472i
$722$	−23.7148	−	11.8712i	−0.882573	−	0.441802i
$723$	−8.79616	−	10.7182i	−0.327133	−	0.398613i
$724$	0.320553	−	7.17342i	0.0119133	−	0.266598i
$725$	29.8305	−	98.3378i	1.10788	−	3.65218i
$726$	−0.0712220	+	0.113025i	−0.00264330	+	0.00419475i
$727$	−21.2373	−	4.22437i	−0.787649	−	0.156673i	−0.215153	−	0.976580i	$-0.569025\pi$
$727$	−21.2373	−	4.22437i	−0.787649	−	0.156673i	−0.572497	+	0.819907i	$0.694025\pi$
$728$	1.45267	+	18.0568i	0.0538397	+	0.669229i
$729$	1.80589	+	9.07880i	0.0668846	+	0.336252i
$730$	−17.0305	−	38.1915i	−0.630325	−	1.41353i
$731$	−5.06655	+	6.17361i	−0.187393	+	0.228339i
$732$	0.878680	+	16.4027i	0.0324770	+	0.606260i
$733$	−6.29704	−	3.36584i	−0.232587	−	0.124320i	0.350987	−	0.936380i	$-0.385846\pi$
$733$	−6.29704	−	3.36584i	−0.232587	−	0.124320i	−0.583574	+	0.812060i	$0.698346\pi$
$734$	−6.01781	+	7.74643i	−0.222121	+	0.285926i
$735$	2.79737	+	2.79737i	0.103182	+	0.103182i
$736$	0.218111	+	6.12053i	0.00803967	+	0.225606i
$737$	17.7025	−	17.7025i	0.652079	−	0.652079i
$738$	1.60640	+	12.7910i	0.0591324	+	0.470844i
$739$	3.04110	−	5.68950i	0.111869	−	0.209292i	−0.819756	−	0.572712i	$-0.805891\pi$
$739$	3.04110	−	5.68950i	0.111869	−	0.209292i	0.931625	+	0.363421i	$0.118391\pi$
$740$	1.94944	+	4.07493i	0.0716629	+	0.149798i
$741$	2.29583	+	1.88414i	0.0843393	+	0.0692154i
$742$	1.59886	−	4.17239i	0.0586959	−	0.153173i
$743$	14.7209	−	2.92816i	0.540056	−	0.107424i	0.0824773	−	0.996593i	$-0.473717\pi$
$743$	14.7209	−	2.92816i	0.540056	−	0.107424i	0.457579	+	0.889169i	$0.348717\pi$
$744$	−4.53810	+	1.28839i	−0.166375	+	0.0472348i
$745$	13.5289	−	68.0142i	0.495659	−	2.49185i
$746$	4.52459	+	19.9421i	0.165657	+	0.730134i
$747$	18.3233	+	5.55832i	0.670415	+	0.203368i
$748$	−7.86658	−	3.67805i	−0.287631	−	0.134483i
$749$	−0.739974	+	0.607281i	−0.0270381	+	0.0221896i
$750$	14.1490	+	42.5131i	0.516647	+	1.55236i
$751$	−16.1659	−	6.69612i	−0.589901	−	0.244345i	0.0677071	−	0.997705i	$-0.478432\pi$
$751$	−16.1659	−	6.69612i	−0.589901	−	0.244345i	−0.657608	+	0.753360i	$0.728432\pi$
$752$	2.78223	−	0.298943i	0.101458	−	0.0109013i
$753$	7.49750	−	3.10556i	0.273224	−	0.113173i
$754$	46.8553	+	54.0757i	1.70637	+	1.96932i
$755$	−18.6344	−	1.83533i	−0.678177	−	0.0667946i
$756$	−9.28999	−	2.28332i	−0.337874	−	0.0830437i
$757$	11.8425	−	6.32993i	0.430422	−	0.230065i	−0.241935	−	0.970292i	$-0.577782\pi$
$757$	11.8425	−	6.32993i	0.430422	−	0.230065i	0.672357	+	0.740227i	$0.265282\pi$
$758$	9.10303	+	1.55876i	0.330637	+	0.0566167i
$759$	−2.79608	+	1.86828i	−0.101491	+	0.0678142i
$760$	−5.96962	−	0.106852i	−0.216541	−	0.00387594i
$761$	−18.5396	+	27.7465i	−0.672061	+	1.00581i	0.326109	+	0.945332i	$0.394262\pi$
$761$	−18.5396	+	27.7465i	−0.672061	+	1.00581i	−0.998170	+	0.0604777i	$0.980738\pi$
$762$	−10.6108	+	0.284005i	−0.384390	+	0.0102884i
$763$	1.38642	+	14.0765i	0.0501917	+	0.509604i
$764$	24.3416	−	41.0227i	0.880650	−	1.48415i
$765$	−3.42085	−	11.2770i	−0.123681	−	0.407723i
$766$	−13.2637	+	48.3454i	−0.479239	+	1.74679i
$767$	−81.0682			−2.92720
$768$	−14.3480	−	4.07617i	−0.517738	−	0.147086i
$769$	25.0654			0.903881			0.451940	−	0.892048i	$-0.350732\pi$
$769$	25.0654			0.903881			0.451940	+	0.892048i	$0.350732\pi$
$770$	5.29047	−	19.2834i	0.190655	−	0.694925i
$771$	−3.85249	−	12.6999i	−0.138744	−	0.457377i
$772$	−18.7973	+	31.6789i	−0.676530	+	1.14015i
$773$	1.08612	+	11.0276i	0.0390651	+	0.396634i	0.994757	+	0.102266i	$0.0326093\pi$
$773$	1.08612	+	11.0276i	0.0390651	+	0.396634i	−0.955692	+	0.294368i	$0.904891\pi$
$774$	18.4622	−	0.494151i	0.663611	−	0.0177619i
$775$	12.9302	−	19.3514i	0.464466	−	0.695123i
$776$	−0.584375	+	32.6479i	−0.0209778	+	1.17199i
$777$	−0.412548	+	0.275656i	−0.0148001	+	0.00988910i
$778$	12.5992	+	2.15743i	0.451704	+	0.0773477i
$779$	−1.87663	+	1.00308i	−0.0672373	+	0.0359391i
$780$	−49.2101	−	12.0950i	−1.76200	−	0.433071i
$781$	29.1097	+	2.86705i	1.04163	+	0.102591i
$782$	−1.30661	−	1.50796i	−0.0467243	−	0.0539244i
$783$	−34.9095	+	14.4600i	−1.24756	+	0.516758i
$784$	2.51007	−	3.11441i	0.0896455	−	0.111229i
$785$	−35.4796	−	14.6961i	−1.26632	−	0.524528i
$786$	−5.88636	−	17.6866i	−0.209959	−	0.630861i
$787$	−17.7531	+	14.5696i	−0.632831	+	0.519351i	−0.895227	−	0.445609i	$-0.852987\pi$
$787$	−17.7531	+	14.5696i	−0.632831	+	0.519351i	0.262397	+	0.964960i	$0.415487\pi$
$788$	−22.4755	−	10.5085i	−0.800657	−	0.374351i
$789$	−14.3225	−	4.34468i	−0.509895	−	0.154675i
$790$	−16.2701	−	71.7105i	−0.578864	−	2.55134i
$791$	−0.102845	+	0.517037i	−0.00365675	+	0.0183837i
$792$	5.48460	+	19.3184i	0.194887	+	0.686449i
$793$	55.3416	−	11.0081i	1.96524	−	0.390910i
$794$	−8.08826	+	21.1072i	−0.287042	+	0.749065i
$795$	9.66210	+	7.92948i	0.342679	+	0.281230i
$796$	−6.64008	−	13.8798i	−0.235351	−	0.491957i
$797$	7.53559	−	14.0981i	0.266924	−	0.499380i	−0.712375	−	0.701799i	$-0.752380\pi$
$797$	7.53559	−	14.0981i	0.266924	−	0.499380i	0.979299	+	0.202419i	$0.0648803\pi$
$798$	−0.0817188	−	0.650689i	−0.00289281	−	0.0230342i
$799$	−0.644631	+	0.644631i	−0.0228054	+	0.0228054i
$800$	66.9400	−	30.5641i	2.36669	−	1.08060i
$801$	−16.0242	−	16.0242i	−0.566186	−	0.566186i
$802$	−13.1915	+	16.9808i	−0.465808	+	0.599613i
$803$	−20.4744	−	10.9438i	−0.722526	−	0.386198i
$804$	0.749395	+	13.9892i	0.0264291	+	0.493363i
$805$	2.91466	−	3.55152i	0.102728	−	0.125175i
$806$	6.59973	+	14.8002i	0.232465	+	0.521313i
$807$	0.708036	+	3.55954i	0.0249241	+	0.125302i
$808$	21.0552	−	1.69390i	0.740719	−	0.0595910i
$809$	35.7920	+	7.11948i	1.25838	+	0.250307i	0.778846	−	0.627215i	$-0.215805\pi$
$809$	35.7920	+	7.11948i	1.25838	+	0.250307i	0.479535	+	0.877523i	$0.340805\pi$
$810$	−6.18695	+	9.81831i	−0.217387	+	0.344980i
$811$	1.60349	−	5.28600i	0.0563061	−	0.185616i	−0.924276	−	0.381724i	$-0.875330\pi$
$811$	1.60349	−	5.28600i	0.0563061	−	0.185616i	0.980582	+	0.196108i	$0.0628303\pi$
$812$	0.705305	−	15.7835i	0.0247514	−	0.553892i
$813$	−18.1143	−	22.0723i	−0.635295	−	0.774109i
$814$	2.24259	+	1.12260i	0.0786026	+	0.0393472i
$815$	8.11253	−	19.5854i	0.284169	−	0.686046i
$816$	4.47287	−	1.89933i	0.156582	−	0.0664900i
$817$	1.16661	+	2.81644i	0.0408145	+	0.0985349i
$818$	1.40387	−	19.6243i	0.0490852	−	0.686149i
$819$	−1.33773	+	13.5822i	−0.0467442	+	0.474602i
$820$	21.4985	−	29.2574i	0.750759	−	1.02171i
$821$	14.8342	+	27.7529i	0.517718	+	0.968582i	0.995912	+	0.0903278i	$0.0287915\pi$
$821$	14.8342	+	27.7529i	0.517718	+	0.968582i	−0.478194	+	0.878254i	$0.658709\pi$
$822$	−7.30573	+	5.16953i	−0.254817	+	0.180308i
$823$	1.44432	+	2.16157i	0.0503457	+	0.0753477i	0.855789	−	0.517326i	$-0.173072\pi$
$823$	1.44432	+	2.16157i	0.0503457	+	0.0753477i	−0.805443	+	0.592674i	$0.798072\pi$
$824$	30.0764	−	43.3138i	1.04776	−	1.50891i
$825$	33.5961	+	22.4482i	1.16966	+	0.781545i
$826$	12.9918	+	12.3145i	0.452043	+	0.428475i
$827$	−33.4911	+	3.29858i	−1.16460	+	0.114703i	−0.661786	−	0.749693i	$-0.730201\pi$
$827$	−33.4911	+	3.29858i	−1.16460	+	0.114703i	−0.502813	+	0.864395i	$0.667701\pi$
$828$	−0.656805	+	4.56715i	−0.0228256	+	0.158720i
$829$	−22.9621	+	6.96548i	−0.797508	+	0.241921i	−0.662636	−	0.748942i	$-0.730562\pi$
$829$	−22.9621	+	6.96548i	−0.797508	+	0.241921i	−0.134872	+	0.990863i	$0.543062\pi$
$830$	−26.6842	−	46.8618i	−0.926221	−	1.62660i
$831$		−	0.546228i		−	0.0189485i
$832$	−6.84373	+	50.7782i	−0.237264	+	1.76042i
$833$			1.30317i			0.0451521i
$834$	−3.24842	+	1.84973i	−0.112484	+	0.0640508i
$835$	−48.8634	+	14.8226i	−1.69099	+	0.512956i
$836$	−2.65365	+	1.98637i	−0.0917783	+	0.0686999i
$837$	−8.51652	+	0.838804i	−0.294374	+	0.0289933i
$838$	21.3180	−	22.4905i	0.736418	−	0.776923i
$839$	3.39809	+	2.27053i	0.117315	+	0.0783873i	0.612843	−	0.790204i	$-0.290026\pi$
$839$	3.39809	+	2.27053i	0.117315	+	0.0783873i	−0.495529	+	0.868592i	$0.665026\pi$
$840$	6.04904	+	9.41347i	0.208712	+	0.324796i
$841$	−18.5583	−	27.7745i	−0.639942	−	0.957741i
$842$	13.4157	+	18.9595i	0.462335	+	0.653386i
$843$	−4.84814	−	9.07022i	−0.166979	−	0.312395i
$844$	7.81981	+	51.1542i	0.269169	+	1.76080i
$845$	−11.6548	+	118.333i	−0.400938	+	4.07079i
$846$	2.10283	+	0.150431i	0.0722967	+	0.00517191i
$847$	−0.0387780	−	0.0936183i	−0.00133243	−	0.00321676i
$848$	6.92795	−	10.5700i	0.237907	−	0.362975i
$849$	−1.47253	+	3.55500i	−0.0505371	+	0.122007i
$850$	−10.7316	+	21.4382i	−0.368091	+	0.735323i
$851$	0.365554	+	0.445429i	0.0125310	+	0.0152691i
$852$	−12.0792	+	11.0458i	−0.413827	+	0.378424i
$853$	0.508349	−	1.67580i	0.0174055	−	0.0573783i	−0.947807	−	0.318843i	$-0.896706\pi$
$853$	0.508349	−	1.67580i	0.0174055	−	0.0573783i	0.965213	+	0.261465i	$0.0842056\pi$
$854$	−10.5411	−	6.64240i	−0.360709	−	0.227298i
$855$	−4.41180	−	0.877562i	−0.150881	−	0.0300120i
$856$	−2.41030	+	1.23339i	−0.0823825	+	0.0421564i
$857$	5.55213	+	27.9124i	0.189657	+	0.953470i	0.951954	+	0.306242i	$0.0990718\pi$
$857$	5.55213	+	27.9124i	0.189657	+	0.953470i	−0.762297	+	0.647228i	$0.775928\pi$
$858$	−25.6946	+	11.4578i	−0.877200	+	0.391164i
$859$	−7.13330	+	8.69195i	−0.243385	+	0.296566i	−0.880348	−	0.474329i	$-0.842691\pi$
$859$	−7.13330	+	8.69195i	−0.243385	+	0.296566i	0.636962	+	0.770895i	$0.280191\pi$
$860$	−38.6945	−	34.7596i	−1.31947	−	1.18529i
$861$	3.51700	+	1.87988i	0.119859	+	0.0640660i
$862$	−30.9406	−	24.0361i	−1.05384	−	0.818674i
$863$	−19.6336	−	19.6336i	−0.668335	−	0.668335i	0.288995	−	0.957330i	$-0.406679\pi$
$863$	−19.6336	−	19.6336i	−0.668335	−	0.668335i	−0.957330	+	0.288995i	$0.906679\pi$
$864$	−24.3022	−	11.8972i	−0.826778	−	0.404749i
$865$	−51.2249	+	51.2249i	−1.74170	+	1.74170i
$866$	−17.8423	+	2.24077i	−0.606305	+	0.0761446i
$867$	6.72439	−	12.5805i	0.228372	−	0.427255i
$868$	1.19053	−	3.37436i	0.0404091	−	0.114533i
$869$	−31.5574	−	25.8985i	−1.07051	−	0.878545i
$870$	41.2700	+	15.8146i	1.39918	+	0.536167i
$871$	47.1989	−	9.38845i	1.59927	−	0.318115i
$872$	−4.63329	+	39.7379i	−0.156903	+	1.34569i
$873$	−4.79939	+	24.1282i	−0.162435	+	0.816615i
$874$	−0.742740	+	0.168517i	−0.0251235	+	0.00570018i
$875$	−32.5221	−	9.86547i	−1.09945	−	0.333514i
$876$	12.2123	−	4.43076i	0.412614	−	0.149701i
$877$	−38.8754	+	31.9042i	−1.31273	+	1.07733i	−0.321261	+	0.946991i	$0.604107\pi$
$877$	−38.8754	+	31.9042i	−1.31273	+	1.07733i	−0.991470	+	0.130339i	$0.958393\pi$
$878$	2.64672	−	0.880866i	0.0893224	−	0.0297278i
$879$	−25.0145	−	10.3613i	−0.843718	−	0.349479i
$880$	26.2178	−	50.1132i	0.883801	−	1.68932i
$881$	−13.3974	+	5.54939i	−0.451371	+	0.186964i	−0.596775	−	0.802408i	$-0.703552\pi$
$881$	−13.3974	+	5.54939i	−0.451371	+	0.186964i	0.145405	+	0.989372i	$0.453552\pi$
$882$	2.27756	−	1.97345i	0.0766894	−	0.0664497i
$883$	6.15622	+	0.606334i	0.207173	+	0.0204048i	0.201071	−	0.979577i	$-0.435558\pi$
$883$	6.15622	+	0.606334i	0.207173	+	0.0204048i	0.00610186	+	0.999981i	$0.498058\pi$
$884$	−8.64512	−	14.2796i	−0.290767	−	0.480276i
$885$	−44.1619	+	23.6050i	−1.48449	+	0.793475i
$886$	−5.73663	+	33.5014i	−0.192726	+	1.12550i
$887$	−4.96821	+	3.31965i	−0.166816	+	0.111463i	−0.636176	−	0.771544i	$-0.719485\pi$
$887$	−4.96821	+	3.31965i	−0.166816	+	0.111463i	0.469360	+	0.883007i	$0.344485\pi$
$888$	−1.30595	+	0.513758i	−0.0438249	+	0.0172406i
$889$	4.47306	−	6.69440i	0.150021	−	0.224523i
$890$	1.70763	+	63.7996i	0.0572399	+	2.13857i
$891$	0.631514	+	6.41187i	0.0211565	+	0.214806i
$892$	−9.27034	−	36.3256i	−0.310394	−	1.21627i
$893$	0.101014	+	0.332999i	0.00338031	+	0.0111434i
$894$	20.7763	+	5.70004i	0.694862	+	0.190638i
$895$	−64.0519			−2.14102
$896$	8.81011	−	7.09803i	0.294325	−	0.237128i
$897$	−6.46415			−0.215832
$898$	−48.8026	−	13.3892i	−1.62856	−	0.446803i
$899$	−4.10268	−	13.5247i	−0.136832	−	0.451074i
$900$	53.7192	−	13.7092i	1.79064	−	0.456973i
$901$	0.403574	+	4.09756i	0.0134450	+	0.136509i
$902$	−0.539312	−	20.1495i	−0.0179571	−	0.670905i
$903$	3.17408	−	4.75035i	0.105627	−	0.158082i
$904$	−0.595163	+	1.36712i	−0.0197948	+	0.0454698i
$905$	−12.6682	+	8.46463i	−0.421106	+	0.281374i
$906$	0.981818	−	5.73374i	0.0326187	−	0.190491i
$907$	7.47221	−	3.99398i	0.248111	−	0.132618i	−0.342654	−	0.939462i	$-0.611326\pi$
$907$	7.47221	−	3.99398i	0.248111	−	0.132618i	0.590765	+	0.806844i	$0.298826\pi$
$908$	−34.4244	+	20.8410i	−1.14241	+	0.691634i
$909$	15.8376	+	1.55987i	0.525301	+	0.0517376i
$910$	29.0492	−	25.1705i	0.962973	−	0.834394i
$911$	35.9415	−	14.8875i	1.19079	−	0.493243i	0.302781	−	0.953060i	$-0.402085\pi$
$911$	35.9415	−	14.8875i	1.19079	−	0.493243i	0.888014	+	0.459817i	$0.152085\pi$
$912$	0.165445	−	1.84749i	0.00547844	−	0.0611766i
$913$	−27.6599	−	11.4571i	−0.915410	−	0.379175i
$914$	25.5326	−	8.49760i	0.844542	−	0.281076i
$915$	26.9421	−	22.1108i	0.890678	−	0.730961i
$916$	−4.84456	−	13.3528i	−0.160069	−	0.441190i
$917$	13.5301	+	4.10431i	0.446803	+	0.135536i
$918$	8.59681	−	1.95049i	0.283737	−	0.0643759i
$919$	−5.56731	+	27.9887i	−0.183649	+	0.923264i	0.773529	+	0.633761i	$0.218490\pi$
$919$	−5.56731	+	27.9887i	−0.183649	+	0.923264i	−0.957177	+	0.289502i	$0.906510\pi$
$920$	10.1912	−	8.06281i	0.335992	−	0.265823i
$921$	29.8596	−	5.93944i	0.983907	−	0.195711i
$922$	40.4023	+	15.4821i	1.33058	+	0.509877i
$923$	43.4638	+	35.6698i	1.43063	+	1.17409i
$924$	5.85824	+	2.06688i	0.192722	+	0.0679953i
$925$	3.26376	−	6.10607i	0.107312	−	0.200766i
$926$	−0.295749	+	0.0371425i	−0.00971892	+	0.00122058i
$927$	28.0922	−	28.0922i	0.922669	−	0.922669i
$928$	11.4408	−	43.1977i	0.375563	−	1.41803i
$929$	14.3211	+	14.3211i	0.469860	+	0.469860i	0.901869	−	0.432009i	$-0.142195\pi$
$929$	14.3211	+	14.3211i	0.469860	+	0.469860i	−0.432009	+	0.901869i	$0.642195\pi$
$930$	7.90465	+	6.14072i	0.259204	+	0.201362i
$931$	0.438694	+	0.234487i	0.0143776	+	0.00768499i
$932$	35.9000	−	39.9640i	1.17594	−	1.30906i
$933$	13.7227	−	16.7212i	0.449261	−	0.547426i
$934$	−24.7742	+	11.0474i	−0.810636	+	0.361481i
$935$	3.59470	+	18.0718i	0.117559	+	0.591010i
$936$	−11.8649	+	36.7336i	−0.387818	+	1.20067i
$937$	−47.1584	−	9.38038i	−1.54060	−	0.306444i	−0.649537	−	0.760330i	$-0.725037\pi$
$937$	−47.1584	−	9.38038i	−1.54060	−	0.306444i	−0.891060	+	0.453886i	$0.850037\pi$
$938$	−8.99012	−	5.66507i	−0.293538	−	0.184971i
$939$	−3.35548	+	11.0615i	−0.109502	+	0.360980i
$940$	−4.00676	−	4.38161i	−0.130686	−	0.142912i
$941$	26.4912	+	32.2796i	0.863587	+	1.05228i	0.998115	+	0.0613744i	$0.0195484\pi$
$941$	26.4912	+	32.2796i	0.863587	+	1.05228i	−0.134527	+	0.990910i	$0.542952\pi$
$942$	5.34054	−	10.6686i	0.174004	−	0.347602i
$943$	1.77234	−	4.27881i	0.0577153	−	0.139337i
$944$	28.5008	+	41.8469i	0.927624	+	1.36200i
$945$	7.76786	+	18.7533i	0.252688	+	0.610044i
$946$	−28.8037	−	2.06054i	−0.936488	−	0.0669939i
$947$	1.54097	−	15.6458i	0.0500750	−	0.508420i	−0.937132	−	0.348975i	$-0.886530\pi$
$947$	1.54097	−	15.6458i	0.0500750	−	0.508420i	0.987207	−	0.159444i	$-0.0509703\pi$
$948$	22.5822	−	3.45209i	0.733437	−	0.112119i
$949$	−21.0367	−	39.3568i	−0.682879	−	1.27758i
$950$	5.28587	+	7.47015i	0.171496	+	0.242364i
$951$	−6.68239	−	10.0009i	−0.216692	−	0.324302i
$952$	−0.783668	+	3.60164i	−0.0253988	+	0.116730i
$953$	−12.6969	−	8.48377i	−0.411292	−	0.274816i	0.332664	−	0.943045i	$-0.392053\pi$
$953$	−12.6969	−	8.48377i	−0.411292	−	0.274816i	−0.743956	+	0.668229i	$0.767053\pi$
$954$	6.55020	−	6.91048i	0.212070	−	0.223735i
$955$	−100.726	+	9.92060i	−3.25940	+	0.321023i
$956$	32.4535	+	43.3556i	1.04962	+	1.40222i
$957$	23.4803	−	7.12268i	0.759011	−	0.230243i
$958$	16.8647	−	9.60314i	0.544873	−	0.310263i
$959$		−	6.78844i		−	0.219210i
$960$	11.0572	+	29.6542i	0.356871	+	0.957085i
$961$			27.7991i			0.896745i
$962$	2.38543	+	4.18920i	0.0769092	+	0.135065i
$963$	−1.95203	+	0.592143i	−0.0629034	+	0.0190815i
$964$	29.4438	+	4.23434i	0.948322	+	0.136379i
$965$	77.7831	−	7.66097i	2.50393	−	0.246615i
$966$	1.03593	+	0.981922i	0.0333305	+	0.0315928i
$967$	2.76854	+	1.84988i	0.0890301	+	0.0594880i	0.599288	−	0.800533i	$-0.295450\pi$
$967$	2.76854	+	1.84988i	0.0890301	+	0.0594880i	−0.510258	+	0.860021i	$0.670450\pi$
$968$	−0.0508750	−	0.282058i	−0.00163519	−	0.00906569i
$969$	0.335734	+	0.502462i	0.0107853	+	0.0161414i
$970$	56.5571	−	40.0198i	1.81594	−	1.28496i
$971$	−0.188533	−	0.352721i	−0.00605031	−	0.0113193i	0.878878	−	0.477047i	$-0.158293\pi$
$971$	−0.188533	−	0.352721i	−0.00605031	−	0.0113193i	−0.884928	+	0.465727i	$0.845793\pi$
$972$	−26.0325	−	19.1288i	−0.834991	−	0.613556i
$973$	0.277919	−	2.82176i	0.00890967	−	0.0904614i
$974$	−2.40776	+	33.6575i	−0.0771498	+	1.07845i
$975$	29.7229	+	71.7573i	0.951893	+	2.29807i
$976$	−25.1386	−	24.6970i	−0.804667	−	0.790530i
$977$	14.0643	−	33.9541i	0.449955	−	1.08629i	−0.522383	−	0.852711i	$-0.674957\pi$
$977$	14.0643	−	33.9541i	0.449955	−	1.08629i	0.972338	−	0.233577i	$-0.0750431\pi$
$978$	5.88926	+	2.94807i	0.188318	+	0.0942689i
$979$	22.4784	+	27.3900i	0.718413	+	0.875388i
$980$	−8.47884	−	0.378887i	−0.270847	−	0.0121031i
$981$	−8.74957	+	28.8435i	−0.279352	+	0.920902i
$982$	−11.6234	+	18.4456i	−0.370916	+	0.588622i
$983$	55.4779	+	11.0352i	1.76947	+	0.351970i	0.968935	−	0.247316i	$-0.0795486\pi$
$983$	55.4779	+	11.0352i	1.76947	+	0.351970i	0.800535	+	0.599286i	$0.204549\pi$
$984$	8.58967	+	7.31050i	0.273829	+	0.233050i
$985$	10.2704	+	51.6327i	0.327242	+	1.64516i
$986$	5.92925	+	13.2966i	0.188826	+	0.423449i
$987$	0.413723	−	0.504123i	0.0131690	−	0.0160464i
$988$	−6.36262	+	0.340842i	−0.202422	+	0.0108436i
$989$	−5.85158	−	3.12774i	−0.186070	−	0.0994563i
$990$	26.1406	−	33.6496i	0.830804	−	1.06945i
$991$	−24.3886	−	24.3886i	−0.774730	−	0.774730i	0.204200	−	0.978929i	$-0.434541\pi$
$991$	−24.3886	−	24.3886i	−0.774730	−	0.774730i	−0.978929	+	0.204200i	$0.934541\pi$
$992$	5.31952	−	8.60998i	0.168895	−	0.273367i
$993$	−10.8391	+	10.8391i	−0.343967	+	0.343967i
$994$	−1.54707	−	12.3186i	−0.0490702	−	0.390724i
$995$	−15.3898	+	28.7922i	−0.487888	+	0.912775i
$996$	15.1130	−	7.23004i	0.478874	−	0.229093i
$997$	20.1785	+	16.5601i	0.639060	+	0.524463i	0.897189	−	0.441648i	$-0.145606\pi$
$997$	20.1785	+	16.5601i	0.639060	+	0.524463i	−0.258129	+	0.966111i	$0.583106\pi$
$998$	6.88938	−	17.9786i	0.218079	−	0.569101i
$999$	−2.49689	+	0.496662i	−0.0789980	+	0.0157137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.a.141.19	✓	752
128.69	even	32	inner	896.2.bn.a.197.19	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.a.141.19	✓	752	1.1	even	1	trivial
896.2.bn.a.197.19	yes	752	128.69	even	32	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374168 + 1.36382i) q^{2} +(0.270613 + 0.892093i) q^{3} +(-1.72000 - 1.02059i) q^{4} +(0.415950 + 4.22321i) q^{5} +(-1.31791 + 0.0352744i) q^{6} +(0.555570 - 0.831470i) q^{7} +(2.03547 - 1.96389i) q^{8} +(1.77181 - 1.18389i) q^{9} +O(q^{10})\)	\(q+(-0.374168 + 1.36382i) q^{2} +(0.270613 + 0.892093i) q^{3} +(-1.72000 - 1.02059i) q^{4} +(0.415950 + 4.22321i) q^{5} +(-1.31791 + 0.0352744i) q^{6} +(0.555570 - 0.831470i) q^{7} +(2.03547 - 1.96389i) q^{8} +(1.77181 - 1.18389i) q^{9} +(-5.91533 - 1.01291i) q^{10} +(-2.93844 + 1.57063i) q^{11} +(0.445011 - 1.81058i) q^{12} +(-6.37383 - 0.627767i) q^{13} +(0.926096 + 1.06881i) q^{14} +(-3.65494 + 1.51392i) q^{15} +(1.91677 + 3.51084i) q^{16} +(-1.20397 - 0.498700i) q^{17} +(0.951649 + 2.85940i) q^{18} +(-0.384518 + 0.315566i) q^{19} +(3.59476 - 7.68843i) q^{20} +(0.892093 + 0.270613i) q^{21} +(-1.04258 - 4.59518i) q^{22} +(0.211215 - 1.06185i) q^{23} +(2.30280 + 1.28438i) q^{24} +(-12.7586 + 2.53784i) q^{25} +(3.24104 - 8.45785i) q^{26} +(3.69749 + 3.03445i) q^{27} +(-1.80417 + 0.863113i) q^{28} +(-3.72386 + 6.96685i) q^{29} +(-0.697155 - 5.55113i) q^{30} +(-1.26509 + 1.26509i) q^{31} +(-5.50534 + 1.30049i) q^{32} +(-2.19633 - 2.19633i) q^{33} +(1.13062 - 1.45540i) q^{34} +(3.74256 + 2.00044i) q^{35} +(-4.25578 + 0.227979i) q^{36} +(-0.337646 + 0.411423i) q^{37} +(-0.286500 - 0.642488i) q^{38} +(-1.16482 - 5.85593i) q^{39} +(9.14057 + 7.77936i) q^{40} +(4.19557 + 0.834552i) q^{41} +(-0.702860 + 1.11540i) q^{42} +(1.77901 - 5.86460i) q^{43} +(6.65709 + 0.297480i) q^{44} +(5.73679 + 6.99030i) q^{45} +(1.36914 + 0.685370i) q^{46} +(0.267711 - 0.646311i) q^{47} +(-2.61329 + 2.66002i) q^{48} +(-0.382683 - 0.923880i) q^{49} +(1.31271 - 18.3500i) q^{50} +(0.119077 - 1.20901i) q^{51} +(10.3223 + 7.58485i) q^{52} +(-1.48939 - 2.78645i) q^{53} +(-5.52193 + 3.90731i) q^{54} +(-7.85536 - 11.7564i) q^{55} +(-0.502064 - 2.78351i) q^{56} +(-0.385570 - 0.257630i) q^{57} +(-8.10816 - 7.68544i) q^{58} +(12.5967 - 1.24067i) q^{59} +(7.83158 + 1.12626i) q^{60} +(-8.43075 + 2.55744i) q^{61} +(-1.25200 - 2.19871i) q^{62} -2.13094i q^{63} +(0.286297 - 7.99488i) q^{64} -27.1792i q^{65} +(3.81719 - 2.17360i) q^{66} +(-7.19029 + 2.18115i) q^{67} +(1.56185 + 2.08653i) q^{68} +(1.00443 - 0.0989275i) q^{69} +(-4.12859 + 4.35567i) q^{70} +(-7.29949 - 4.87736i) q^{71} +(1.28145 - 5.88940i) q^{72} +(3.87109 + 5.79349i) q^{73} +(-0.434769 - 0.614429i) q^{74} +(-5.71664 - 10.6951i) q^{75} +(0.983435 - 0.150335i) q^{76} +(-0.326580 + 3.31582i) q^{77} +(8.42225 + 0.602505i) q^{78} +(4.68886 + 11.3199i) q^{79} +(-14.0297 + 9.55528i) q^{80} +(0.740002 - 1.78652i) q^{81} +(-2.70803 + 5.40974i) q^{82} +(5.70042 + 6.94598i) q^{83} +(-1.25821 - 1.37592i) q^{84} +(1.60533 - 5.29206i) q^{85} +(7.33260 + 4.62059i) q^{86} +(-7.22280 - 1.43670i) q^{87} +(-2.89658 + 8.96775i) q^{88} +(-2.07470 - 10.4302i) q^{89} +(-11.6800 + 5.20839i) q^{90} +(-4.06308 + 4.95087i) q^{91} +(-1.44701 + 1.61082i) q^{92} +(-1.47093 - 0.786228i) q^{93} +(0.781281 + 0.606938i) q^{94} +(-1.49264 - 1.49264i) q^{95} +(-2.64997 - 4.55934i) q^{96} +(-8.16327 + 8.16327i) q^{97} +(1.40319 - 0.176224i) q^{98} +(-3.34692 + 6.26164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q+O(q^{10}) \) 752 * q	\( 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) \) 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more