LMFDB - Embedded newform 287.2.n.a.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(64,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("287.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.n (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.4
Character	$\chi$	$=$	287.64
Dual form			287.2.n.a.148.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.668701 - 2.05805i) q^{2} -2.12658i q^{3} +(-2.17038 + 1.57687i) q^{4} +(2.21996 - 1.61290i) q^{5} +(-4.37661 + 1.42205i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(1.19526 + 0.868404i) q^{8} -1.52235 q^{9} +O(q^{10})$	\(q+(-0.668701 - 2.05805i) q^{2} -2.12658i q^{3} +(-2.17038 + 1.57687i) q^{4} +(2.21996 - 1.61290i) q^{5} +(-4.37661 + 1.42205i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(1.19526 + 0.868404i) q^{8} -1.52235 q^{9} +(-4.80391 - 3.49025i) q^{10} +(0.260473 - 0.358510i) q^{11} +(3.35335 + 4.61549i) q^{12} +(-1.67780 + 0.545151i) q^{13} +2.16396i q^{14} +(-3.42995 - 4.72093i) q^{15} +(-0.670072 + 2.06227i) q^{16} +(1.92413 - 2.64834i) q^{17} +(1.01800 + 3.13307i) q^{18} +(2.74074 + 0.890521i) q^{19} +(-2.27483 + 7.00119i) q^{20} +(-0.657150 + 2.02250i) q^{21} +(-0.912010 - 0.296330i) q^{22} +(1.09947 + 3.38382i) q^{23} +(1.84673 - 2.54181i) q^{24} +(0.781708 - 2.40585i) q^{25} +(2.24390 + 3.08846i) q^{26} -3.14235i q^{27} +(2.55143 - 0.829011i) q^{28} +(4.77827 + 6.57672i) q^{29} +(-7.42230 + 10.2159i) q^{30} +(-0.537975 - 0.390862i) q^{31} +7.64717 q^{32} +(-0.762401 - 0.553916i) q^{33} +(-6.73709 - 2.18901i) q^{34} +(-2.60972 + 0.847950i) q^{35} +(3.30408 - 2.40055i) q^{36} +(-1.99396 + 1.44870i) q^{37} -6.23608i q^{38} +(1.15931 + 3.56798i) q^{39} +4.05407 q^{40} +(4.73692 + 4.30832i) q^{41} +4.60184 q^{42} +(-2.73095 - 8.40501i) q^{43} +1.18884i q^{44} +(-3.37956 + 2.45539i) q^{45} +(6.22886 - 4.52553i) q^{46} +(-0.671110 + 0.218057i) q^{47} +(4.38558 + 1.42496i) q^{48} +(0.809017 + 0.587785i) q^{49} -5.47409 q^{50} +(-5.63191 - 4.09182i) q^{51} +(2.78183 - 3.82886i) q^{52} +(-6.04706 - 8.32307i) q^{53} +(-6.46711 + 2.10129i) q^{54} -1.21599i q^{55} +(-0.868404 - 1.19526i) q^{56} +(1.89377 - 5.82841i) q^{57} +(10.3400 - 14.2318i) q^{58} +(-2.02156 - 6.22171i) q^{59} +(14.8886 + 4.83760i) q^{60} +(-1.36264 + 4.19377i) q^{61} +(-0.444669 + 1.36855i) q^{62} +(1.44784 + 0.470432i) q^{63} +(-3.77353 - 11.6137i) q^{64} +(-2.84538 + 3.91633i) q^{65} +(-0.630170 + 1.93946i) q^{66} +(-2.97928 - 4.10063i) q^{67} +8.78201i q^{68} +(7.19597 - 2.33811i) q^{69} +(3.49025 + 4.80391i) q^{70} +(-4.33452 + 5.96595i) q^{71} +(-1.81960 - 1.32201i) q^{72} +13.9101 q^{73} +(4.31485 + 3.13492i) q^{74} +(-5.11624 - 1.66237i) q^{75} +(-7.35269 + 2.38903i) q^{76} +(-0.358510 + 0.260473i) q^{77} +(6.56786 - 4.77183i) q^{78} -15.3204i q^{79} +(1.83869 + 5.65891i) q^{80} -11.2495 q^{81} +(5.69916 - 12.6298i) q^{82} -8.46668 q^{83} +(-1.76296 - 5.42583i) q^{84} -8.98263i q^{85} +(-15.4718 + 11.2409i) q^{86} +(13.9859 - 10.1614i) q^{87} +(0.622663 - 0.202315i) q^{88} +(-9.25909 - 3.00846i) q^{89} +(7.31323 + 5.31338i) q^{90} +1.76414 q^{91} +(-7.72212 - 5.61045i) q^{92} +(-0.831200 + 1.14405i) q^{93} +(0.897545 + 1.23536i) q^{94} +(7.52066 - 2.44361i) q^{95} -16.2623i q^{96} +(8.69396 + 11.9662i) q^{97} +(0.668701 - 2.05805i) q^{98} +(-0.396530 + 0.545777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.668701	−	2.05805i	−0.472843	−	1.45526i	−0.848844	−	0.528643i	$-0.822701\pi$
$2$	−0.668701	−	2.05805i	−0.472843	−	1.45526i	0.376001	−	0.926619i	$-0.377299\pi$
$3$		−	2.12658i		−	1.22778i	−0.789391	−	0.613891i	$-0.789603\pi$
$3$		−	2.12658i		−	1.22778i	0.789391	−	0.613891i	$-0.210397\pi$
$4$	−2.17038	+	1.57687i	−1.08519	+	0.788437i
$5$	2.21996	−	1.61290i	0.992797	−	0.721309i	0.0322650	−	0.999479i	$-0.489728\pi$
$5$	2.21996	−	1.61290i	0.992797	−	0.721309i	0.960532	+	0.278170i	$0.0897280\pi$
$6$	−4.37661	+	1.42205i	−1.78675	+	0.580549i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$8$	1.19526	+	0.868404i	0.422587	+	0.307027i
$9$	−1.52235			−0.507450
$10$	−4.80391	−	3.49025i	−1.51913	−	1.10371i
$11$	0.260473	−	0.358510i	0.0785355	−	0.108095i	−0.767942	−	0.640520i	$-0.778719\pi$
$11$	0.260473	−	0.358510i	0.0785355	−	0.108095i	0.846477	+	0.532425i	$0.178719\pi$
$12$	3.35335	+	4.61549i	0.968029	+	1.33238i
$13$	−1.67780	+	0.545151i	−0.465338	+	0.151198i	−0.532296	−	0.846558i	$-0.678671\pi$
$13$	−1.67780	+	0.545151i	−0.465338	+	0.151198i	0.0669579	+	0.997756i	$0.478671\pi$
$14$			2.16396i			0.578343i
$15$	−3.42995	−	4.72093i	−0.885611	−	1.21894i
$16$	−0.670072	+	2.06227i	−0.167518	+	0.515567i
$17$	1.92413	−	2.64834i	0.466670	−	0.642316i	−0.509205	−	0.860645i	$-0.670061\pi$
$17$	1.92413	−	2.64834i	0.466670	−	0.642316i	0.975875	+	0.218329i	$0.0700605\pi$
$18$	1.01800	+	3.13307i	0.239944	+	0.738472i
$19$	2.74074	+	0.890521i	0.628769	+	0.204300i	0.606030	−	0.795442i	$-0.292761\pi$
$19$	2.74074	+	0.890521i	0.628769	+	0.204300i	0.0227394	+	0.999741i	$0.492761\pi$
$20$	−2.27483	+	7.00119i	−0.508666	+	1.56551i
$21$	−0.657150	+	2.02250i	−0.143402	+	0.441346i
$22$	−0.912010	−	0.296330i	−0.194441	−	0.0631778i
$23$	1.09947	+	3.38382i	0.229255	+	0.705575i	0.997832	+	0.0658173i	$0.0209655\pi$
$23$	1.09947	+	3.38382i	0.229255	+	0.705575i	−0.768576	+	0.639758i	$0.779035\pi$
$24$	1.84673	−	2.54181i	0.376963	−	0.518844i
$25$	0.781708	−	2.40585i	0.156342	−	0.481170i
$26$	2.24390	+	3.08846i	0.440064	+	0.605696i
$27$		−	3.14235i		−	0.604745i
$28$	2.55143	−	0.829011i	0.482176	−	0.156668i
$29$	4.77827	+	6.57672i	0.887302	+	1.22127i	0.974344	+	0.225062i	$0.0722585\pi$
$29$	4.77827	+	6.57672i	0.887302	+	1.22127i	−0.0870423	+	0.996205i	$0.527742\pi$
$30$	−7.42230	+	10.2159i	−1.35512	+	1.86516i
$31$	−0.537975	−	0.390862i	−0.0966232	−	0.0702009i	0.538425	−	0.842674i	$-0.319020\pi$
$31$	−0.537975	−	0.390862i	−0.0966232	−	0.0702009i	−0.635048	+	0.772473i	$0.719020\pi$
$32$	7.64717			1.35184
$33$	−0.762401	−	0.553916i	−0.132717	−	0.0964245i
$34$	−6.73709	−	2.18901i	−1.15540	−	0.375412i
$35$	−2.60972	+	0.847950i	−0.441123	+	0.143330i
$36$	3.30408	−	2.40055i	0.550679	−	0.400092i
$37$	−1.99396	+	1.44870i	−0.327805	+	0.238164i	−0.739499	−	0.673158i	$-0.764937\pi$
$37$	−1.99396	+	1.44870i	−0.327805	+	0.238164i	0.411694	+	0.911322i	$0.364937\pi$
$38$		−	6.23608i		−	1.01163i
$39$	1.15931	+	3.56798i	0.185638	+	0.571334i
$40$	4.05407			0.641004
$41$	4.73692	+	4.30832i	0.739782	+	0.672846i
$41$	4.73692	+	4.30832i	0.739782	+	0.672846i
$42$	4.60184			0.710080
$43$	−2.73095	−	8.40501i	−0.416467	−	1.28175i	−0.910933	−	0.412555i	$-0.864636\pi$
$43$	−2.73095	−	8.40501i	−0.416467	−	1.28175i	0.494466	−	0.869197i	$-0.335364\pi$
$44$			1.18884i			0.179224i
$45$	−3.37956	+	2.45539i	−0.503794	+	0.366028i
$46$	6.22886	−	4.52553i	0.918395	−	0.667253i
$47$	−0.671110	+	0.218057i	−0.0978915	+	0.0318069i	−0.357553	−	0.933893i	$-0.616389\pi$
$47$	−0.671110	+	0.218057i	−0.0978915	+	0.0318069i	0.259662	+	0.965700i	$0.416389\pi$
$48$	4.38558	+	1.42496i	0.633004	+	0.205676i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−5.47409			−0.774154
$51$	−5.63191	−	4.09182i	−0.788625	−	0.572969i
$52$	2.78183	−	3.82886i	0.385771	−	0.530968i
$53$	−6.04706	−	8.32307i	−0.830628	−	1.14326i	−0.987806	−	0.155691i	$-0.950240\pi$
$53$	−6.04706	−	8.32307i	−0.830628	−	1.14326i	0.157178	−	0.987570i	$-0.449760\pi$
$54$	−6.46711	+	2.10129i	−0.880062	+	0.285949i
$55$		−	1.21599i		−	0.163965i
$56$	−0.868404	−	1.19526i	−0.116045	−	0.159723i
$57$	1.89377	−	5.82841i	0.250835	−	0.771992i
$58$	10.3400	−	14.2318i	1.35771	−	1.86872i
$59$	−2.02156	−	6.22171i	−0.263184	−	0.809998i	−0.992106	−	0.125401i	$-0.959978\pi$
$59$	−2.02156	−	6.22171i	−0.263184	−	0.809998i	0.728922	−	0.684597i	$-0.240022\pi$
$60$	14.8886	+	4.83760i	1.92211	+	0.624532i
$61$	−1.36264	+	4.19377i	−0.174468	+	0.536957i	−0.999609	−	0.0279703i	$-0.991096\pi$
$61$	−1.36264	+	4.19377i	−0.174468	+	0.536957i	0.825141	+	0.564927i	$0.191096\pi$
$62$	−0.444669	+	1.36855i	−0.0564730	+	0.173806i
$63$	1.44784	+	0.470432i	0.182411	+	0.0592688i
$64$	−3.77353	−	11.6137i	−0.471691	−	1.45172i
$65$	−2.84538	+	3.91633i	−0.352926	+	0.485761i
$66$	−0.630170	+	1.93946i	−0.0775686	+	0.238732i
$67$	−2.97928	−	4.10063i	−0.363977	−	0.500972i	0.587274	−	0.809388i	$-0.300201\pi$
$67$	−2.97928	−	4.10063i	−0.363977	−	0.500972i	−0.951251	+	0.308416i	$0.900201\pi$
$68$			8.78201i			1.06498i
$69$	7.19597	−	2.33811i	0.866293	−	0.281476i
$70$	3.49025	+	4.80391i	0.417164	+	0.574178i
$71$	−4.33452	+	5.96595i	−0.514413	+	0.708028i	−0.984656	−	0.174509i	$-0.944166\pi$
$71$	−4.33452	+	5.96595i	−0.514413	+	0.708028i	0.470243	+	0.882537i	$0.344166\pi$
$72$	−1.81960	−	1.32201i	−0.214441	−	0.155801i
$73$	13.9101			1.62806			0.814028	−	0.580825i	$-0.197270\pi$
$73$	13.9101			1.62806			0.814028	+	0.580825i	$0.197270\pi$
$74$	4.31485	+	3.13492i	0.501591	+	0.364427i
$75$	−5.11624	−	1.66237i	−0.590772	−	0.191953i
$76$	−7.35269	+	2.38903i	−0.843411	+	0.274041i
$77$	−0.358510	+	0.260473i	−0.0408560	+	0.0296836i
$78$	6.56786	−	4.77183i	0.743663	−	0.540303i
$79$		−	15.3204i		−	1.72368i	−0.507181	−	0.861840i	$-0.669312\pi$
$79$		−	15.3204i		−	1.72368i	0.507181	−	0.861840i	$-0.330688\pi$
$80$	1.83869	+	5.65891i	0.205572	+	0.632685i
$81$	−11.2495			−1.24994
$82$	5.69916	−	12.6298i	0.629367	−	1.39473i
$83$	−8.46668			−0.929339			−0.464669	−	0.885484i	$-0.653827\pi$
$83$	−8.46668			−0.929339			−0.464669	+	0.885484i	$0.653827\pi$
$84$	−1.76296	−	5.42583i	−0.192355	−	0.592007i
$85$		−	8.98263i		−	0.974303i
$86$	−15.4718	+	11.2409i	−1.66836	+	1.21214i
$87$	13.9859	−	10.1614i	1.49945	−	1.08941i
$88$	0.622663	−	0.202315i	0.0663761	−	0.0215669i
$89$	−9.25909	−	3.00846i	−0.981462	−	0.318896i	−0.226028	−	0.974121i	$-0.572574\pi$
$89$	−9.25909	−	3.00846i	−0.981462	−	0.318896i	−0.755434	+	0.655225i	$0.772574\pi$
$90$	7.31323	+	5.31338i	0.770882	+	0.560079i
$91$	1.76414			0.184933
$92$	−7.72212	−	5.61045i	−0.805087	−	0.584930i
$93$	−0.831200	+	1.14405i	−0.0861914	+	0.118632i
$94$	0.897545	+	1.23536i	0.0925747	+	0.127418i
$95$	7.52066	−	2.44361i	0.771603	−	0.250709i
$96$		−	16.2623i		−	1.65977i
$97$	8.69396	+	11.9662i	0.882738	+	1.21499i	0.975655	+	0.219311i	$0.0703810\pi$
$97$	8.69396	+	11.9662i	0.882738	+	1.21499i	−0.0929166	+	0.995674i	$0.529619\pi$
$98$	0.668701	−	2.05805i	0.0675490	−	0.207895i
$99$	−0.396530	+	0.545777i	−0.0398528	+	0.0548527i
$100$	2.09712	+	6.45426i	0.209712	+	0.645426i
$101$	17.4960	+	5.68479i	1.74092	+	0.565658i	0.994954	−	0.100332i	$-0.0319905\pi$
$101$	17.4960	+	5.68479i	1.74092	+	0.565658i	0.745961	+	0.665990i	$0.231990\pi$
$102$	−4.65511	+	14.3270i	−0.460925	+	1.41858i
$103$	−1.30349	+	4.01174i	−0.128437	+	0.395288i	−0.994512	−	0.104626i	$-0.966635\pi$
$103$	−1.30349	+	4.01174i	−0.128437	+	0.395288i	0.866075	+	0.499915i	$0.166635\pi$
$104$	−2.47881	−	0.805415i	−0.243068	−	0.0789774i
$105$	1.80323	+	5.54978i	0.175978	+	0.541603i
$106$	−13.0856	+	18.0108i	−1.27099	+	1.74936i
$107$	−3.09175	+	9.51543i	−0.298891	+	0.919891i	0.682996	+	0.730422i	$0.260677\pi$
$107$	−3.09175	+	9.51543i	−0.298891	+	0.919891i	−0.981887	+	0.189469i	$0.939323\pi$
$108$	4.95508	+	6.82008i	0.476803	+	0.656263i
$109$		−	8.13241i		−	0.778944i	−0.921038	−	0.389472i	$-0.872658\pi$
$109$		−	8.13241i		−	0.778944i	0.921038	−	0.389472i	$-0.127342\pi$
$110$	−2.50258	+	0.813137i	−0.238611	+	0.0775295i
$111$	3.08077	+	4.24032i	0.292414	+	0.402473i
$112$	1.27455	−	1.75427i	0.120434	−	0.165763i
$113$	13.1959	+	9.58741i	1.24137	+	0.901908i	0.997689	−	0.0679476i	$-0.0216451\pi$
$113$	13.1959	+	9.58741i	1.24137	+	0.901908i	0.243681	+	0.969855i	$0.421645\pi$
$114$	−13.2615			−1.24206
$115$	7.89853	+	5.73862i	0.736542	+	0.535129i
$116$	−20.7413	−	6.73926i	−1.92578	−	0.625725i
$117$	2.55420	−	0.829909i	0.236136	−	0.0767252i
$118$	−11.4528	+	8.32094i	−1.05431	+	0.766004i
$119$	−2.64834	+	1.92413i	−0.242773	+	0.176385i
$120$		−	8.62130i		−	0.787014i
$121$	3.33850	+	10.2749i	0.303500	+	0.934078i
$122$	9.54218			0.863908
$123$	9.16199	−	10.0734i	0.826109	−	0.908292i
$124$	1.78395			0.160203
$125$	2.09472	+	6.44690i	0.187358	+	0.576628i
$126$		−	3.29431i		−	0.293480i
$127$	−3.03087	+	2.20206i	−0.268946	+	0.195401i	−0.714082	−	0.700062i	$-0.753156\pi$
$127$	−3.03087	+	2.20206i	−0.268946	+	0.195401i	0.445135	+	0.895463i	$0.353156\pi$
$128$	−9.00490	+	6.54244i	−0.795928	+	0.578276i
$129$	−17.8739	+	5.80760i	−1.57371	+	0.511330i
$130$	9.96272	+	3.23708i	0.873788	+	0.283911i
$131$	12.5280	+	9.10215i	1.09458	+	0.795258i	0.980167	−	0.198175i	$-0.0635014\pi$
$131$	12.5280	+	9.10215i	1.09458	+	0.795258i	0.114413	+	0.993433i	$0.463501\pi$
$132$	2.52815			0.220048
$133$	−2.33141	−	1.69387i	−0.202159	−	0.146877i
$134$	−6.44706	+	8.87361i	−0.556941	+	0.766563i
$135$	−5.06828	−	6.97588i	−0.436208	−	0.600388i
$136$	4.59966	−	1.49452i	0.394417	−	0.128154i
$137$		−	15.5168i		−	1.32569i	−0.748757	−	0.662844i	$-0.769349\pi$
$137$		−	15.5168i		−	1.32569i	0.748757	−	0.662844i	$-0.230651\pi$
$138$	−9.62391	−	13.2462i	−0.819242	−	1.12759i
$139$	1.68040	−	5.17175i	0.142530	−	0.438662i	−0.854155	−	0.520018i	$-0.825925\pi$
$139$	1.68040	−	5.17175i	0.142530	−	0.438662i	0.996685	+	0.0813563i	$0.0259252\pi$
$140$	4.32698	−	5.95557i	0.365696	−	0.503338i
$141$	0.463716	+	1.42717i	0.0390519	+	0.120189i
$142$	15.1767	+	4.93122i	1.27360	+	0.413819i
$143$	−0.241579	+	0.743505i	−0.0202019	+	0.0621750i
$144$	1.02008	−	3.13949i	0.0850069	−	0.261624i
$145$	21.2151	+	6.89322i	1.76182	+	0.572450i
$146$	−9.30172	−	28.6277i	−0.769816	−	2.36925i
$147$	1.24997	−	1.72044i	0.103096	−	0.141900i
$148$	2.04324	−	6.28844i	0.167953	−	0.516906i
$149$	−4.16715	−	5.73559i	−0.341386	−	0.469878i	0.603460	−	0.797394i	$-0.293788\pi$
$149$	−4.16715	−	5.73559i	−0.341386	−	0.469878i	−0.944846	+	0.327516i	$0.893788\pi$
$150$			11.6411i			0.950492i
$151$	−14.2723	+	4.63734i	−1.16146	+	0.377382i	−0.825449	−	0.564476i	$-0.809078\pi$
$151$	−14.2723	+	4.63734i	−1.16146	+	0.377382i	−0.336012	+	0.941858i	$0.609078\pi$
$152$	2.50255	+	3.44447i	0.202984	+	0.279384i
$153$	−2.92920	+	4.03170i	−0.236812	+	0.325943i
$154$	0.775802	+	0.563653i	0.0625159	+	0.0454205i
$155$	−1.82470			−0.146564
$156$	−8.14239	−	5.91579i	−0.651913	−	0.473642i
$157$	−5.56650	−	1.80866i	−0.444255	−	0.144347i	0.0783430	−	0.996926i	$-0.475037\pi$
$157$	−5.56650	−	1.80866i	−0.444255	−	0.144347i	−0.522598	+	0.852579i	$0.675037\pi$
$158$	−31.5302	+	10.2448i	−2.50840	+	0.815030i
$159$	−17.6997	+	12.8596i	−1.40368	+	1.01983i
$160$	16.9764	−	12.3341i	1.34210	−	0.975095i
$161$		−	3.55796i		−	0.280407i
$162$	7.52256	+	23.1520i	0.591028	+	1.81900i
$163$	−7.45086			−0.583597			−0.291798	−	0.956480i	$-0.594254\pi$
$163$	−7.45086			−0.583597			−0.291798	+	0.956480i	$0.594254\pi$
$164$	−17.0746	−	1.88117i	−1.33330	−	0.146895i
$165$	−2.58591			−0.201313
$166$	5.66168	+	17.4249i	0.439432	+	1.35243i
$167$			5.19271i			0.401824i	0.979609	+	0.200912i	$0.0643905\pi$
$167$			5.19271i			0.401824i	−0.979609	+	0.200912i	$0.935610\pi$
$168$	−2.54181	+	1.84673i	−0.196105	+	0.142478i
$169$	−7.99939	+	5.81190i	−0.615338	+	0.447069i
$170$	−18.4867	+	6.00670i	−1.41787	+	0.460693i
$171$	−4.17237	−	1.35568i	−0.319069	−	0.103672i
$172$	19.1808	+	13.9357i	1.46253	+	1.06259i
$173$	18.8212			1.43095			0.715475	−	0.698638i	$-0.246210\pi$
$173$	18.8212			1.43095			0.715475	+	0.698638i	$0.246210\pi$
$174$	−30.2650	−	21.9888i	−2.29439	−	1.66697i
$175$	−1.48690	+	2.04654i	−0.112399	+	0.154704i
$176$	0.564808	+	0.777392i	0.0425740	+	0.0585981i
$177$	−13.2310	+	4.29901i	−0.994502	+	0.323133i
$178$			21.0674i			1.57907i
$179$	−6.89553	−	9.49088i	−0.515396	−	0.709382i	0.469422	−	0.882974i	$-0.344462\pi$
$179$	−6.89553	−	9.49088i	−0.515396	−	0.709382i	−0.984818	+	0.173592i	$0.944462\pi$
$180$	3.46308	−	10.6583i	0.258123	−	0.794420i
$181$	−1.03669	+	1.42688i	−0.0770564	+	0.106059i	−0.845805	−	0.533492i	$-0.820880\pi$
$181$	−1.03669	+	1.42688i	−0.0770564	+	0.106059i	0.768749	+	0.639551i	$0.220880\pi$
$182$	−1.17969	−	3.63070i	−0.0874441	−	0.269125i
$183$	8.91838	+	2.89776i	0.659266	+	0.214208i
$184$	−1.62438	+	4.99932i	−0.119751	+	0.368554i
$185$	−2.08991	+	6.43210i	−0.153654	+	0.472897i
$186$	2.91033	+	0.945625i	0.213396	+	0.0693366i
$187$	−0.448272	−	1.37964i	−0.0327809	−	0.100889i
$188$	1.11272	−	1.53152i	0.0811531	−	0.111698i
$189$	−0.971038	+	2.98855i	−0.0706326	+	0.217385i
$190$	−10.0581	−	13.8439i	−0.729695	−	1.00434i
$191$			10.9041i			0.788991i	0.918898	+	0.394496i	$0.129081\pi$
$191$			10.9041i			0.788991i	−0.918898	+	0.394496i	$0.870919\pi$
$192$	−24.6975	+	8.02471i	−1.78239	+	0.579134i
$193$	−6.78040	−	9.33242i	−0.488064	−	0.671762i	0.491966	−	0.870615i	$-0.336279\pi$
$193$	−6.78040	−	9.33242i	−0.488064	−	0.671762i	−0.980029	+	0.198853i	$0.936279\pi$
$194$	18.8134	−	25.8945i	1.35072	−	1.85911i
$195$	8.32840	+	6.05094i	0.596409	+	0.433316i
$196$	−2.68274			−0.191624
$197$	14.3407	+	10.4191i	1.02173	+	0.742330i	0.966637	−	0.256152i	$-0.0824546\pi$
$197$	14.3407	+	10.4191i	1.02173	+	0.742330i	0.0550926	+	0.998481i	$0.482455\pi$
$198$	1.38840	+	0.451118i	0.0986691	+	0.0320595i
$199$	−9.57754	+	3.11193i	−0.678934	+	0.220599i	−0.628128	−	0.778110i	$-0.716179\pi$
$199$	−9.57754	+	3.11193i	−0.678934	+	0.220599i	−0.0508053	+	0.998709i	$0.516179\pi$
$200$	3.02359	−	2.19677i	0.213800	−	0.155335i
$201$	−8.72032	+	6.33569i	−0.615084	+	0.446885i
$202$		−	39.8091i		−	2.80096i
$203$	−2.51208	−	7.73140i	−0.176314	−	0.542638i
$204$	18.6757			1.30756
$205$	17.4646	+	1.92415i	1.21978	+	0.134388i
$206$	9.12801			0.635978
$207$	−1.67378	−	5.15136i	−0.116336	−	0.358044i
$208$		−	3.82537i		−	0.265241i
$209$	1.03315	−	0.750627i	0.0714644	−	0.0519219i
$210$	10.2159	−	7.42230i	0.704965	−	0.512187i
$211$	15.9511	−	5.18283i	1.09812	−	0.356801i	0.296741	−	0.954958i	$-0.404100\pi$
$211$	15.9511	−	5.18283i	1.09812	−	0.356801i	0.801379	+	0.598157i	$0.204100\pi$
$212$	26.2488	+	8.52877i	1.80278	+	0.585758i
$213$	12.6871	+	9.21771i	0.869305	+	0.631587i
$214$	21.6507			1.48001
$215$	−19.6190	−	14.2541i	−1.33801	−	0.972118i
$216$	2.72883	−	3.75591i	0.185673	−	0.255557i
$217$	0.390862	+	0.537975i	0.0265334	+	0.0365201i
$218$	−16.7369	+	5.43816i	−1.13357	+	0.368318i
$219$		−	29.5810i		−	1.99890i
$220$	1.91747	+	2.63917i	0.129276	+	0.177933i
$221$	−1.78456	+	5.49233i	−0.120043	+	0.369454i
$222$	6.66667	−	9.17589i	0.447438	−	0.615845i
$223$	7.30866	+	22.4937i	0.489424	+	1.50629i	0.825470	+	0.564447i	$0.190910\pi$
$223$	7.30866	+	22.4937i	0.489424	+	1.50629i	−0.336045	+	0.941846i	$0.609090\pi$
$224$	−7.27289	−	2.36310i	−0.485940	−	0.157892i
$225$	−1.19003	+	3.66254i	−0.0793355	+	0.244170i
$226$	10.9072	−	33.5690i	0.725539	−	2.23298i
$227$	17.1132	+	5.56040i	1.13584	+	0.369057i	0.815792	−	0.578345i	$-0.196301\pi$
$227$	17.1132	+	5.56040i	1.13584	+	0.369057i	0.320047	+	0.947402i	$0.396301\pi$
$228$	5.08047	+	15.6361i	0.336463	+	1.03553i
$229$	8.47682	−	11.6673i	0.560164	−	0.771000i	−0.431183	−	0.902264i	$-0.641904\pi$
$229$	8.47682	−	11.6673i	0.560164	−	0.771000i	0.991347	+	0.131265i	$0.0419038\pi$
$230$	6.52861	−	20.0930i	0.430484	−	1.32489i
$231$	0.553916	+	0.762401i	0.0364450	+	0.0501623i
$232$			12.0103i			0.788517i
$233$	18.0409	−	5.86186i	1.18190	−	0.384023i	0.348829	−	0.937186i	$-0.386579\pi$
$233$	18.0409	−	5.86186i	1.18190	−	0.384023i	0.833073	+	0.553163i	$0.186579\pi$
$234$	−3.41599	−	4.70171i	−0.223310	−	0.307360i
$235$	−1.13814	+	1.56651i	−0.0742438	+	0.102188i
$236$	14.1984	+	10.3157i	0.924237	+	0.671498i
$237$	−32.5801			−2.11630
$238$	5.73091	+	4.16375i	0.371480	+	0.269896i
$239$	18.6548	+	6.06130i	1.20668	+	0.392073i	0.842213	−	0.539145i	$-0.181253\pi$
$239$	18.6548	+	6.06130i	1.20668	+	0.392073i	0.364463	+	0.931218i	$0.381253\pi$
$240$	12.0341	−	3.91013i	0.776800	−	0.252398i
$241$	−18.6796	+	13.5715i	−1.20326	+	0.874220i	−0.994601	−	0.103769i	$-0.966910\pi$
$241$	−18.6796	+	13.5715i	−1.20326	+	0.874220i	−0.208659	+	0.977988i	$0.566910\pi$
$242$	18.9137	−	13.7416i	1.21582	−	0.883345i
$243$			14.4959i			0.929915i
$244$	−3.65560	−	11.2508i	−0.234026	−	0.720257i
$245$	2.74402			0.175309
$246$	−26.8583	−	12.1197i	−1.71242	−	0.772726i
$247$	−5.08389			−0.323480
$248$	−0.303592	−	0.934360i	−0.0192781	−	0.0593319i
$249$			18.0051i			1.14103i
$250$	11.8673	−	8.62210i	0.750554	−	0.545309i
$251$	0.998923	−	0.725760i	0.0630515	−	0.0458096i	−0.555813	−	0.831307i	$-0.687593\pi$
$251$	0.998923	−	0.725760i	0.0630515	−	0.0458096i	0.618865	+	0.785498i	$0.287593\pi$
$252$	−3.88417	+	1.26204i	−0.244680	+	0.0795013i
$253$	1.49952	+	0.487222i	0.0942737	+	0.0306314i
$254$	6.55869	+	4.76517i	0.411529	+	0.298993i
$255$	−19.1023			−1.19623
$256$	−0.272172	−	0.197744i	−0.0170107	−	0.0123590i
$257$	7.47036	−	10.2821i	0.465988	−	0.641378i	−0.509749	−	0.860323i	$-0.670262\pi$
$257$	7.47036	−	10.2821i	0.465988	−	0.641378i	0.975737	+	0.218946i	$0.0702617\pi$
$258$	23.9047	+	32.9019i	1.48824	+	2.04839i
$259$	2.34404	−	0.761624i	0.145651	−	0.0473250i
$260$		−	12.9867i		−	0.805403i
$261$	−7.27419	−	10.0121i	−0.450261	−	0.619731i
$262$	10.3552	−	31.8700i	0.639745	−	1.96893i
$263$	−9.97806	+	13.7336i	−0.615273	+	0.846851i	−0.996998	−	0.0774249i	$-0.975330\pi$
$263$	−9.97806	+	13.7336i	−0.615273	+	0.846851i	0.381725	+	0.924276i	$0.375330\pi$
$264$	−0.430240	−	1.32414i	−0.0264795	−	0.0814954i
$265$	−26.8485	−	8.72360i	−1.64929	−	0.535887i
$266$	−1.92705	+	5.93086i	−0.118155	+	0.363645i
$267$	−6.39774	+	19.6902i	−0.391535	+	1.20502i
$268$	12.9323	+	4.20197i	0.789969	+	0.256676i
$269$	−7.02934	−	21.6341i	−0.428586	−	1.31905i	−0.899518	−	0.436883i	$-0.856082\pi$
$269$	−7.02934	−	21.6341i	−0.428586	−	1.31905i	0.470932	−	0.882169i	$-0.343918\pi$
$270$	−10.9676	+	15.0956i	−0.667465	+	0.918686i
$271$	−0.341475	+	1.05095i	−0.0207431	+	0.0638408i	−0.960892	−	0.276923i	$-0.910685\pi$
$271$	−0.341475	+	1.05095i	−0.0207431	+	0.0638408i	0.940149	+	0.340763i	$0.110685\pi$
$272$	4.17228	+	5.74265i	0.252982	+	0.348199i
$273$		−	3.75160i		−	0.227057i
$274$	−31.9343	+	10.3761i	−1.92922	+	0.626843i
$275$	−0.658907	−	0.906908i	−0.0397336	−	0.0546886i
$276$	−11.9311	+	16.4217i	−0.718167	+	0.988472i
$277$	4.58080	+	3.32815i	0.275234	+	0.199969i	0.716836	−	0.697242i	$-0.245590\pi$
$277$	4.58080	+	3.32815i	0.275234	+	0.199969i	−0.441602	+	0.897211i	$0.645590\pi$
$278$	−11.7674			−0.705762
$279$	0.818986	+	0.595028i	0.0490314	+	0.0356234i
$280$	−3.85565	−	1.25278i	−0.230419	−	0.0748676i
$281$	7.59781	−	2.46868i	0.453247	−	0.147269i	−0.0734920	−	0.997296i	$-0.523414\pi$
$281$	7.59781	−	2.46868i	0.453247	−	0.147269i	0.526739	+	0.850027i	$0.323414\pi$
$282$	2.62710	−	1.90870i	0.156442	−	0.113662i
$283$	−2.20387	+	1.60120i	−0.131006	+	0.0951816i	−0.651359	−	0.758770i	$-0.725801\pi$
$283$	−2.20387	+	1.60120i	−0.131006	+	0.0951816i	0.520352	+	0.853952i	$0.325801\pi$
$284$		−	19.7834i		−	1.17393i
$285$	−5.19654	−	15.9933i	−0.307816	−	0.947361i
$286$	1.69172			0.100033
$287$	−3.17373	−	5.56124i	−0.187339	−	0.328270i
$288$	−11.6417			−0.685991
$289$	1.94187	+	5.97646i	0.114228	+	0.351557i
$290$		−	48.2713i		−	2.83459i
$291$	25.4471	−	18.4884i	1.49174	−	1.08381i
$292$	−30.1902	+	21.9345i	−1.76675	+	1.28362i
$293$	−29.6666	+	9.63925i	−1.73314	+	0.563131i	−0.993897	−	0.110309i	$-0.964816\pi$
$293$	−29.6666	+	9.63925i	−1.73314	+	0.563131i	−0.739242	+	0.673440i	$0.764816\pi$
$294$	−4.37661	−	1.42205i	−0.255249	−	0.0829355i
$295$	−14.5228	−	10.5514i	−0.845548	−	0.614326i
$296$	−3.64134			−0.211649
$297$	−1.12656	−	0.818495i	−0.0653698	−	0.0474939i
$298$	−9.01756	+	12.4116i	−0.522373	+	0.718985i
$299$	−3.68938	−	5.07800i	−0.213363	−	0.293668i
$300$	13.7255	−	4.45969i	0.792443	−	0.257480i
$301$			8.83755i			0.509388i
$302$	19.0878	+	26.2721i	1.09838	+	1.51179i
$303$	12.0892	−	37.2066i	0.694504	−	2.13746i
$304$	−3.67299	+	5.05543i	−0.210660	+	0.289949i
$305$	3.73911	+	11.5078i	0.214101	+	0.658934i
$306$	10.2562	+	3.33244i	0.586308	+	0.190503i
$307$	7.25268	−	22.3214i	0.413932	−	1.27395i	−0.499271	−	0.866446i	$-0.666399\pi$
$307$	7.25268	−	22.3214i	0.413932	−	1.27395i	0.913203	−	0.407506i	$-0.133601\pi$
$308$	0.367370	−	1.13065i	0.0209329	−	0.0644247i
$309$	8.53129	+	2.77198i	0.485328	+	0.157693i
$310$	1.22018	+	3.75533i	0.0693017	+	0.213289i
$311$	4.51977	−	6.22094i	0.256293	−	0.352757i	−0.661410	−	0.750025i	$-0.730042\pi$
$311$	4.51977	−	6.22094i	0.256293	−	0.352757i	0.917703	+	0.397268i	$0.130042\pi$
$312$	−1.71278	+	5.27140i	−0.0969671	+	0.298434i
$313$	−5.61491	−	7.72826i	−0.317373	−	0.436827i	0.620290	−	0.784373i	$-0.287015\pi$
$313$	−5.61491	−	7.72826i	−0.317373	−	0.436827i	−0.937663	+	0.347546i	$0.887015\pi$
$314$			12.6656i			0.714761i
$315$	3.97291	−	1.29088i	0.223848	−	0.0727326i
$316$	24.1583	+	33.2511i	1.35901	+	1.87052i
$317$	−16.1551	+	22.2356i	−0.907363	+	1.24888i	0.0606957	+	0.998156i	$0.480668\pi$
$317$	−16.1551	+	22.2356i	−0.907363	+	1.24888i	−0.968059	+	0.250722i	$0.919332\pi$
$318$	38.3015	+	27.8276i	2.14784	+	1.56050i
$319$	3.60243			0.201697
$320$	−27.1088	−	19.6957i	−1.51543	−	1.10102i
$321$	20.2353	+	6.57486i	1.12943	+	0.366973i
$322$	−7.32246	+	2.37921i	−0.408065	+	0.132588i
$323$	7.63195	−	5.54493i	0.424653	−	0.308528i
$324$	24.4157	−	17.7390i	1.35643	−	0.985502i
$325$			4.46269i			0.247545i
$326$	4.98240	+	15.3343i	0.275950	+	0.849286i
$327$	−17.2942			−0.956374
$328$	1.92046	+	9.26310i	0.106040	+	0.511469i
$329$	0.705647			0.0389036
$330$	1.72920	+	5.32193i	0.0951894	+	0.292963i
$331$			30.1269i			1.65592i	0.560786	+	0.827961i	$0.310499\pi$
$331$			30.1269i			1.65592i	−0.560786	+	0.827961i	$0.689501\pi$
$332$	18.3759	−	13.3509i	1.00851	−	0.732725i
$333$	3.03550	−	2.20542i	0.166344	−	0.120856i
$334$	10.6869	−	3.47237i	0.584759	−	0.190000i
$335$	−13.2278	−	4.29797i	−0.722711	−	0.234823i
$336$	−3.73060	−	2.71044i	−0.203521	−	0.147867i
$337$	−27.6713			−1.50735			−0.753677	−	0.657246i	$-0.771721\pi$
$337$	−27.6713			−1.50735			−0.753677	+	0.657246i	$0.771721\pi$
$338$	17.3104	+	12.5767i	0.941561	+	0.684084i
$339$	20.3884	−	28.0622i	1.10735	−	1.52413i
$340$	14.1645	+	19.4957i	0.768176	+	1.05730i
$341$	−0.280256	+	0.0910606i	−0.0151767	+	0.00493121i
$342$			9.49349i			0.513349i
$343$	−0.587785	−	0.809017i	−0.0317374	−	0.0436828i
$344$	4.03476	−	12.4177i	0.217540	−	0.669518i
$345$	12.2036	−	16.7969i	0.657022	−	0.904313i
$346$	−12.5858	−	38.7350i	−0.676615	−	2.08241i
$347$	0.768738	+	0.249778i	0.0412680	+	0.0134088i	0.329578	−	0.944128i	$-0.393093\pi$
$347$	0.768738	+	0.249778i	0.0412680	+	0.0134088i	−0.288310	+	0.957537i	$0.593093\pi$
$348$	−14.3316	+	44.1081i	−0.768254	+	2.36444i
$349$	−0.934309	+	2.87551i	−0.0500124	+	0.153922i	−0.972944	−	0.231042i	$-0.925786\pi$
$349$	−0.934309	+	2.87551i	−0.0500124	+	0.153922i	0.922931	+	0.384965i	$0.125786\pi$
$350$	5.20617	+	1.69159i	0.278282	+	0.0904192i
$351$	1.71305	+	5.27223i	0.0914359	+	0.281411i
$352$	1.99188	−	2.74158i	0.106167	−	0.146127i
$353$	−8.18512	+	25.1912i	−0.435650	+	1.34079i	0.456770	+	0.889585i	$0.349006\pi$
$353$	−8.18512	+	25.1912i	−0.435650	+	1.34079i	−0.892419	+	0.451207i	$0.850994\pi$
$354$	17.6952	+	24.3553i	0.940487	+	1.29447i
$355$			20.2353i			1.07398i
$356$	24.8397	−	8.07091i	1.31650	−	0.427757i
$357$	4.09182	+	5.63191i	0.216562	+	0.298072i
$358$	−14.9217	+	20.5379i	−0.788635	+	1.08546i
$359$	10.8451	+	7.87944i	0.572384	+	0.415861i	0.835970	−	0.548775i	$-0.184905\pi$
$359$	10.8451	+	7.87944i	0.572384	+	0.415861i	−0.263587	+	0.964636i	$0.584905\pi$
$360$	−6.17170			−0.325277
$361$	−8.65269	−	6.28654i	−0.455405	−	0.330871i
$362$	3.62982	+	1.17940i	0.190779	+	0.0619879i
$363$	21.8503	−	7.09960i	1.14684	−	0.372632i
$364$	−3.82886	+	2.78183i	−0.200687	+	0.145808i
$365$	30.8799	−	22.4356i	1.61633	−	1.17433i
$366$		−	20.2922i		−	1.06069i
$367$	6.53302	+	20.1066i	0.341021	+	1.04955i	0.963680	+	0.267061i	$0.0860524\pi$
$367$	6.53302	+	20.1066i	0.341021	+	1.04955i	−0.622659	+	0.782493i	$0.713948\pi$
$368$	−7.71507			−0.402176
$369$	−7.21124	−	6.55877i	−0.375402	−	0.341436i
$370$	14.6351			0.760843
$371$	3.17913	+	9.78435i	0.165052	+	0.507978i
$372$		−	3.79372i		−	0.196695i
$373$	−17.3659	+	12.6170i	−0.899171	+	0.653286i	−0.938253	−	0.345950i	$-0.887557\pi$
$373$	−17.3659	+	12.6170i	−0.899171	+	0.653286i	0.0390819	+	0.999236i	$0.487557\pi$
$374$	−2.53961	+	1.84513i	−0.131320	+	0.0954096i
$375$	13.7099	−	4.45460i	0.707974	−	0.230035i
$376$	−0.991510	−	0.322161i	−0.0511332	−	0.0166142i
$377$	−11.6023	−	8.42955i	−0.597548	−	0.434144i
$378$	6.79992			0.349750
$379$	−20.4540	−	14.8607i	−1.05065	−	0.763344i	−0.0783166	−	0.996929i	$-0.524955\pi$
$379$	−20.4540	−	14.8607i	−1.05065	−	0.763344i	−0.972337	+	0.233584i	$0.924955\pi$
$380$	−12.4694	+	17.1627i	−0.639668	+	0.880427i
$381$	4.68285	+	6.44539i	0.239910	+	0.330207i
$382$	22.4411	−	7.29157i	1.14819	−	0.373069i
$383$		−	25.3381i		−	1.29472i	−0.762185	−	0.647359i	$-0.775873\pi$
$383$		−	25.3381i		−	1.29472i	0.762185	−	0.647359i	$-0.224127\pi$
$384$	13.9130	+	19.1497i	0.709997	+	0.977227i
$385$	−0.375763	+	1.15648i	−0.0191506	+	0.0589396i
$386$	−14.6725	+	20.1950i	−0.746812	+	1.02790i
$387$	4.15746	+	12.7954i	0.211336	+	0.650425i
$388$	−37.7384	−	12.2620i	−1.91588	−	0.622506i
$389$	−3.19167	+	9.82294i	−0.161824	+	0.498043i	−0.998788	−	0.0492147i	$-0.984328\pi$
$389$	−3.19167	+	9.82294i	−0.161824	+	0.498043i	0.836964	+	0.547257i	$0.184328\pi$
$390$	6.88392	−	21.1865i	0.348581	−	1.07282i
$391$	11.0770	+	3.59914i	0.560189	+	0.182017i
$392$	0.456547	+	1.40511i	0.0230591	+	0.0709686i
$393$	19.3565	−	26.6419i	0.976404	−	1.34391i
$394$	11.8534	−	36.4811i	0.597166	−	1.83789i
$395$	−24.7102	−	34.0107i	−1.24331	−	1.71126i
$396$		−	1.80982i		−	0.0909470i
$397$	−19.3775	+	6.29613i	−0.972528	+	0.315993i	−0.751836	−	0.659350i	$-0.770832\pi$
$397$	−19.3775	+	6.29613i	−0.972528	+	0.315993i	−0.220692	+	0.975344i	$0.570832\pi$
$398$	12.8090	+	17.6301i	0.642059	+	0.883718i
$399$	−3.60216	+	4.95794i	−0.180333	+	0.248208i
$400$	4.43771	+	3.22418i	0.221885	+	0.161209i
$401$	8.60159			0.429543			0.214771	−	0.976664i	$-0.431099\pi$
$401$	8.60159			0.429543			0.214771	+	0.976664i	$0.431099\pi$
$402$	18.8705	+	13.7102i	0.941173	+	0.683802i
$403$	1.11569	+	0.362511i	0.0555767	+	0.0180580i
$404$	−46.9371	+	15.2508i	−2.33521	+	0.758755i
$405$	−24.9735	+	18.1443i	−1.24094	+	0.901596i
$406$	−14.2318	+	10.3400i	−0.706312	+	0.513165i
$407$			1.09220i			0.0541383i
$408$	−3.17822	−	9.78154i	−0.157345	−	0.484259i
$409$	−29.1681			−1.44227			−0.721135	−	0.692795i	$-0.756379\pi$
$409$	−29.1681			−1.44227			−0.721135	+	0.692795i	$0.756379\pi$
$410$	−7.71864	−	37.2298i	−0.381196	−	1.83865i
$411$	−32.9977			−1.62766
$412$	−3.49693	−	10.7624i	−0.172281	−	0.530227i
$413$			6.54190i			0.321906i
$414$	−9.48250	+	6.88944i	−0.466039	+	0.338597i
$415$	−18.7957	+	13.6559i	−0.922644	+	0.670340i
$416$	−12.8304	+	4.16886i	−0.629063	+	0.204395i
$417$	−10.9981	−	3.57351i	−0.538581	−	0.174996i
$418$	−2.23570	−	1.62433i	−0.109351	−	0.0794485i
$419$	18.1594			0.887144			0.443572	−	0.896239i	$-0.353711\pi$
$419$	18.1594			0.887144			0.443572	+	0.896239i	$0.353711\pi$
$420$	−12.6650	−	9.20167i	−0.617989	−	0.448995i
$421$	−2.20767	+	3.03860i	−0.107595	+	0.148092i	−0.859419	−	0.511272i	$-0.829174\pi$
$421$	−2.20767	+	3.03860i	−0.107595	+	0.148092i	0.751824	+	0.659364i	$0.229174\pi$
$422$	−21.3331	−	29.3625i	−1.03848	−	1.42934i
$423$	1.02166	−	0.331959i	0.0496750	−	0.0161404i
$424$		−	15.1995i		−	0.738152i
$425$	−4.86740	−	6.69940i	−0.236103	−	0.324968i
$426$	10.4866	−	32.2746i	0.508079	−	1.56371i
$427$	2.59189	−	3.56743i	0.125430	−	0.172640i
$428$	−8.29435	−	25.5274i	−0.400923	−	1.23391i
$429$	1.58112	+	0.513738i	0.0763374	+	0.0248035i
$430$	−16.2163	+	49.9087i	−0.782020	+	2.40681i
$431$	−0.494580	+	1.52216i	−0.0238231	+	0.0733200i	−0.962261	−	0.272127i	$-0.912273\pi$
$431$	−0.494580	+	1.52216i	−0.0238231	+	0.0733200i	0.938438	+	0.345447i	$0.112273\pi$
$432$	6.48036	+	2.10560i	0.311786	+	0.101306i
$433$	7.33449	+	22.5732i	0.352473	+	1.08480i	0.957460	+	0.288565i	$0.0931781\pi$
$433$	7.33449	+	22.5732i	0.352473	+	1.08480i	−0.604987	+	0.796235i	$0.706822\pi$
$434$	0.845811	−	1.16416i	0.0406002	−	0.0558814i
$435$	14.6590	−	45.1157i	0.702845	−	2.16313i
$436$	12.8238	+	17.6504i	0.614148	+	0.845302i
$437$			10.2533i			0.490481i
$438$	−60.8792	+	19.7809i	−2.90892	+	0.945166i
$439$	12.4854	+	17.1847i	0.595895	+	0.820179i	0.995325	−	0.0965846i	$-0.0307918\pi$
$439$	12.4854	+	17.1847i	0.595895	+	0.820179i	−0.399430	+	0.916764i	$0.630792\pi$
$440$	1.05597	−	1.45342i	0.0503416	−	0.0692892i
$441$	−1.23161	−	0.894814i	−0.0586479	−	0.0426102i
$442$	12.4968			0.594414
$443$	−24.6198	−	17.8873i	−1.16972	−	0.849854i	−0.178747	−	0.983895i	$-0.557204\pi$
$443$	−24.6198	−	17.8873i	−1.16972	−	0.849854i	−0.990976	+	0.134041i	$0.957204\pi$
$444$	−13.3729	−	4.34511i	−0.634649	−	0.206210i
$445$	−25.4072	+	8.25529i	−1.20441	+	0.391338i
$446$	41.4060	−	30.0832i	1.96063	−	1.42448i
$447$	−12.1972	+	8.86178i	−0.576908	+	0.419148i
$448$			12.2114i			0.576934i
$449$	−1.09227	−	3.36166i	−0.0515474	−	0.158647i	0.921969	−	0.387264i	$-0.126580\pi$
$449$	−1.09227	−	3.36166i	−0.0515474	−	0.158647i	−0.973516	+	0.228617i	$0.926580\pi$
$450$	8.33348			0.392844
$451$	2.77841	−	0.576032i	0.130830	−	0.0271243i
$452$	−43.7583			−2.05822
$453$	9.86169	+	30.3512i	0.463343	+	1.42602i
$454$		−	38.9380i		−	1.82745i
$455$	3.91633	−	2.84538i	0.183600	−	0.133394i
$456$	7.32495	−	5.32189i	0.343022	−	0.249220i
$457$	−17.1102	+	5.55944i	−0.800381	+	0.260060i	−0.680518	−	0.732731i	$-0.738245\pi$
$457$	−17.1102	+	5.55944i	−0.800381	+	0.260060i	−0.119863	+	0.992790i	$0.538245\pi$
$458$	−29.6804	−	9.64376i	−1.38688	−	0.450623i
$459$	−8.32199	−	6.04628i	−0.388437	−	0.282216i
$460$	−26.1919			−1.22120
$461$	18.7901	+	13.6518i	0.875141	+	0.635827i	0.931962	−	0.362557i	$-0.118096\pi$
$461$	18.7901	+	13.6518i	0.875141	+	0.635827i	−0.0568203	+	0.998384i	$0.518096\pi$
$462$	1.19865	−	1.64981i	0.0557665	−	0.0767560i
$463$	−17.3475	−	23.8768i	−0.806206	−	1.10965i	−0.991898	−	0.127040i	$-0.959452\pi$
$463$	−17.3475	−	23.8768i	−0.806206	−	1.10965i	0.185691	−	0.982608i	$-0.440548\pi$
$464$	−16.7647	+	5.44720i	−0.778284	+	0.252880i
$465$			3.88038i			0.179948i
$466$	−24.1280	−	33.2094i	−1.11771	−	1.53839i
$467$	−1.05794	+	3.25601i	−0.0489558	+	0.150670i	−0.972546	−	0.232711i	$-0.925240\pi$
$467$	−1.05794	+	3.25601i	−0.0489558	+	0.150670i	0.923590	+	0.383381i	$0.125240\pi$
$468$	−4.23492	+	5.82887i	−0.195759	+	0.269439i
$469$	1.56630	+	4.82058i	0.0723251	+	0.222594i
$470$	3.98503	+	1.29481i	0.183816	+	0.0597253i
$471$	−3.84627	+	11.8376i	−0.177227	+	0.545448i
$472$	2.98668	−	9.19207i	0.137473	−	0.423099i
$473$	−3.72462	−	1.21020i	−0.171258	−	0.0556451i
$474$	21.7863	+	67.0515i	1.00068	+	3.07978i
$475$	4.28492	−	5.89769i	0.196606	−	0.270604i
$476$	2.71379	−	8.35219i	0.124386	−	0.382822i
$477$	9.20574	+	12.6706i	0.421502	+	0.580148i
$478$		−	42.4456i		−	1.94142i
$479$	2.95721	−	0.960856i	0.135118	−	0.0439026i	−0.240677	−	0.970605i	$-0.577370\pi$
$479$	2.95721	−	0.960856i	0.135118	−	0.0439026i	0.375796	+	0.926703i	$0.377370\pi$
$480$	−26.2294	−	36.1017i	−1.19720	−	1.64781i
$481$	2.55571	−	3.51763i	0.116530	−	0.160390i
$482$	40.4220	+	29.3683i	1.84117	+	1.33769i
$483$	−7.56629			−0.344278
$484$	−23.4480	−	17.0359i	−1.06582	−	0.774361i
$485$	38.6005	+	12.5421i	1.75276	+	0.569506i
$486$	29.8334	−	9.69346i	1.35327	−	0.439704i
$487$	15.5700	−	11.3122i	0.705542	−	0.512606i	−0.176190	−	0.984356i	$-0.556377\pi$
$487$	15.5700	−	11.3122i	0.705542	−	0.512606i	0.881732	+	0.471750i	$0.156377\pi$
$488$	−5.27058	+	3.82930i	−0.238588	+	0.173344i
$489$			15.8449i			0.716530i
$490$	−1.83493	−	5.64734i	−0.0828938	−	0.255121i
$491$	1.86781			0.0842933			0.0421467	−	0.999111i	$-0.486580\pi$
$491$	1.86781			0.0842933			0.0421467	+	0.999111i	$0.486580\pi$
$492$	−4.00047	+	36.3105i	−0.180355	+	1.63700i
$493$	26.6114			1.19852
$494$	3.39960	+	10.4629i	0.152955	+	0.470748i
$495$			1.85117i			0.0832037i
$496$	1.16654	−	0.847544i	0.0523794	−	0.0380558i
$497$	5.96595	−	4.33452i	0.267610	−	0.194430i
$498$	37.0554	−	12.0400i	1.66049	−	0.539526i
$499$	18.8792	+	6.13421i	0.845148	+	0.274605i	0.699412	−	0.714719i	$-0.253445\pi$
$499$	18.8792	+	6.13421i	0.845148	+	0.274605i	0.145735	+	0.989324i	$0.453445\pi$
$500$	−14.7123	−	10.6891i	−0.657953	−	0.478031i
$501$	11.0427			0.493352
$502$	−2.16163	−	1.57052i	−0.0964784	−	0.0700957i
$503$	4.08821	−	5.62694i	0.182284	−	0.250893i	−0.708090	−	0.706122i	$-0.750443\pi$
$503$	4.08821	−	5.62694i	0.182284	−	0.250893i	0.890374	+	0.455230i	$0.150443\pi$
$504$	1.32201	+	1.81960i	0.0588872	+	0.0810513i
$505$	48.0094	−	15.5992i	2.13639	−	0.694155i
$506$		−	3.41189i		−	0.151677i
$507$	12.3595	+	17.0114i	0.548904	+	0.755501i
$508$	3.10578	−	9.55859i	0.137797	−	0.424094i
$509$	18.9266	−	26.0502i	0.838905	−	1.15465i	−0.147295	−	0.989093i	$-0.547057\pi$
$509$	18.9266	−	26.0502i	0.838905	−	1.15465i	0.986200	−	0.165561i	$-0.0529434\pi$
$510$	12.7737	+	39.3135i	0.565630	+	1.74083i
$511$	−13.2293	−	4.29846i	−0.585230	−	0.190153i
$512$	−7.10410	+	21.8642i	−0.313960	+	0.966269i
$513$	2.79832	−	8.61236i	0.123549	−	0.380245i
$514$	−26.1565	−	8.49875i	−1.15371	−	0.374864i
$515$	3.57681	+	11.0083i	0.157613	+	0.485084i
$516$	29.6354	−	40.7896i	1.30463	−	1.79566i
$517$	−0.0966303	+	0.297398i	−0.00424980	+	0.0130795i
$518$	−3.13492	−	4.31485i	−0.137741	−	0.189584i
$519$		−	40.0249i		−	1.75690i
$520$	−6.80192	+	2.21008i	−0.298284	+	0.0969183i
$521$	−13.8416	−	19.0514i	−0.606413	−	0.834655i	0.389864	−	0.920873i	$-0.372522\pi$
$521$	−13.8416	−	19.0514i	−0.606413	−	0.834655i	−0.996276	+	0.0862173i	$0.972522\pi$
$522$	−15.7411	+	21.6657i	−0.688968	+	0.948284i
$523$	−3.44179	−	2.50061i	−0.150499	−	0.109344i	0.509988	−	0.860182i	$-0.329650\pi$
$523$	−3.44179	−	2.50061i	−0.150499	−	0.109344i	−0.660487	+	0.750838i	$0.729650\pi$
$524$	−41.5435			−1.81484
$525$	4.35213	+	3.16201i	0.189943	+	0.138001i
$526$	34.9368	+	11.3517i	1.52332	+	0.494956i
$527$	−2.07027	+	0.672671i	−0.0901823	+	0.0293020i
$528$	1.65319	−	1.20111i	0.0719457	−	0.0522716i
$529$	8.36598	−	6.07824i	0.363738	−	0.264271i
$530$			61.0891i			2.65354i
$531$	3.07752	+	9.47162i	0.133553	+	0.411033i
$532$	7.73107			0.335185
$533$	−10.2963	−	4.64617i	−0.445982	−	0.201248i
$534$	44.8016			1.93876
$535$	8.48383	+	26.1106i	0.366788	+	1.12886i
$536$		−	7.48852i		−	0.323455i
$537$	−20.1831	+	14.6639i	−0.870967	+	0.632794i
$538$	−39.8235	+	28.9335i	−1.71691	+	1.24741i
$539$	0.421454	−	0.136939i	0.0181533	−	0.00589836i
$540$	22.0002	+	7.14829i	0.946736	+	0.307613i
$541$	0.362536	+	0.263398i	0.0155866	+	0.0113244i	0.595551	−	0.803317i	$-0.296934\pi$
$541$	0.362536	+	0.263398i	0.0155866	+	0.0113244i	−0.579965	+	0.814642i	$0.696934\pi$
$542$	2.39126			0.102713
$543$	3.03437	+	2.20460i	0.130217	+	0.0946085i
$544$	14.7141	−	20.2523i	0.630864	−	0.868309i
$545$	−13.1167	−	18.0536i	−0.561859	−	0.773333i
$546$	−7.72098	+	2.50870i	−0.330427	+	0.107362i
$547$			12.2594i			0.524174i	0.965044	+	0.262087i	$0.0844107\pi$
$547$			12.2594i			0.524174i	−0.965044	+	0.262087i	$0.915589\pi$
$548$	24.4680	+	33.6773i	1.04522	+	1.43862i
$549$	2.07441	−	6.38437i	0.0885336	−	0.272478i
$550$	−1.42585	+	1.96252i	−0.0607985	+	0.0836820i
$551$	7.23929	+	22.2802i	0.308404	+	0.949170i
$552$	10.6315	+	3.45437i	0.452505	+	0.147028i
$553$	−4.73426	+	14.5706i	−0.201321	+	0.619603i
$554$	3.78631	−	11.6531i	0.160865	−	0.495091i
$555$	13.6784	+	4.44437i	0.580615	+	0.188653i
$556$	4.50808	+	13.8744i	0.191185	+	0.588407i
$557$	−2.36343	+	3.25298i	−0.100142	+	0.137833i	−0.856147	−	0.516732i	$-0.827148\pi$
$557$	−2.36343	+	3.25298i	−0.100142	+	0.137833i	0.756005	+	0.654565i	$0.227148\pi$
$558$	0.676942	−	2.08341i	0.0286572	−	0.0881979i
$559$	9.16399	+	12.6132i	0.387596	+	0.533480i
$560$		−	5.95013i		−	0.251439i
$561$	−2.93392	+	0.953287i	−0.123870	+	0.0402478i
$562$	−10.1613	−	13.9859i	−0.428630	−	0.589959i
$563$	14.9191	−	20.5344i	0.628766	−	0.865422i	−0.369188	−	0.929355i	$-0.620364\pi$
$563$	14.9191	−	20.5344i	0.628766	−	0.865422i	0.997954	+	0.0639328i	$0.0203643\pi$
$564$	−3.25691	−	2.36628i	−0.137140	−	0.0996384i
$565$	44.7580			1.88298
$566$	4.76909	+	3.46494i	0.200460	+	0.145642i
$567$	10.6989	+	3.47629i	0.449312	+	0.145990i
$568$	−10.3617	+	3.36673i	−0.434768	+	0.141265i
$569$	−4.97799	+	3.61672i	−0.208688	+	0.151621i	−0.687220	−	0.726449i	$-0.741169\pi$
$569$	−4.97799	+	3.61672i	−0.208688	+	0.151621i	0.478532	+	0.878070i	$0.341169\pi$
$570$	−29.4401	+	21.3895i	−1.23311	+	0.895906i
$571$			8.90651i			0.372726i	0.982481	+	0.186363i	$0.0596700\pi$
$571$			8.90651i			0.372726i	−0.982481	+	0.186363i	$0.940330\pi$
$572$	−0.648094	−	1.99463i	−0.0270982	−	0.0833996i
$573$	23.1884			0.968710
$574$	−9.32304	+	10.2505i	−0.389136	+	0.427848i
$575$	9.00043			0.375344
$576$	5.74463	+	17.6801i	0.239359	+	0.736672i
$577$		−	21.9860i		−	0.915290i	−0.889135	−	0.457645i	$-0.848693\pi$
$577$		−	21.9860i		−	0.915290i	0.889135	−	0.457645i	$-0.151307\pi$
$578$	11.0013	−	7.99294i	0.457595	−	0.332462i
$579$	−19.8461	+	14.4191i	−0.824777	+	0.599236i
$580$	−56.9146	+	18.4927i	−2.36325	+	0.767867i
$581$	8.05229	+	2.61635i	0.334065	+	0.108544i
$582$	−55.0667	−	40.0083i	−2.28259	−	1.65840i
$583$	−4.55900			−0.188814
$584$	16.6262	+	12.0796i	0.687995	+	0.499858i
$585$	4.33166	−	5.96202i	0.179092	−	0.246499i
$586$	39.6761	+	54.6095i	1.63901	+	2.25590i
$587$	25.8893	−	8.41194i	1.06857	−	0.347198i	0.278637	−	0.960397i	$-0.410118\pi$
$587$	25.8893	−	8.41194i	1.06857	−	0.347198i	0.789929	+	0.613199i	$0.210118\pi$
$588$			5.70506i			0.235273i
$589$	−1.12638	−	1.55033i	−0.0464117	−	0.0638802i
$590$	−12.0039	+	36.9443i	−0.494194	+	1.52097i
$591$	22.1571	−	30.4966i	0.911419	−	1.25446i
$592$	−1.65150	−	5.08281i	−0.0678764	−	0.208902i
$593$	−43.3610	−	14.0888i	−1.78062	−	0.578560i	−0.781644	−	0.623725i	$-0.785618\pi$
$593$	−43.3610	−	14.0888i	−1.78062	−	0.578560i	−0.998980	+	0.0451658i	$0.985618\pi$
$594$	−0.931172	+	2.86585i	−0.0382064	+	0.117587i
$595$	−2.77579	+	8.54299i	−0.113796	+	0.350228i
$596$	18.0886	+	5.87734i	0.740937	+	0.240745i
$597$	6.61778	+	20.3674i	0.270848	+	0.833583i
$598$	−7.98369	+	10.9886i	−0.326477	+	0.449358i
$599$	−14.7179	+	45.2971i	−0.601358	+	1.85079i	−0.0812408	+	0.996695i	$0.525888\pi$
$599$	−14.7179	+	45.2971i	−0.601358	+	1.85079i	−0.520117	+	0.854095i	$0.674112\pi$
$600$	−4.67160	−	6.42991i	−0.190717	−	0.262500i
$601$		−	29.3717i		−	1.19810i	−0.800713	−	0.599048i	$-0.795546\pi$
$601$		−	29.3717i		−	1.19810i	0.800713	−	0.599048i	$-0.204454\pi$
$602$	18.1881	−	5.90968i	0.741293	−	0.240861i
$603$	4.53551	+	6.24259i	0.184700	+	0.254218i
$604$	23.6638	−	32.5704i	0.962864	−	1.32527i
$605$	23.9836	+	17.4251i	0.975073	+	0.708432i
$606$	−84.6572			−3.43896
$607$	−12.6778	−	9.21098i	−0.514577	−	0.373862i	0.299980	−	0.953946i	$-0.403020\pi$
$607$	−12.6778	−	9.21098i	−0.514577	−	0.373862i	−0.814557	+	0.580083i	$0.803020\pi$
$608$	20.9589	+	6.80996i	0.849996	+	0.276180i
$609$	−16.4415	+	5.34215i	−0.666241	+	0.216475i
$610$	21.1833	−	15.3905i	0.857686	−	0.623145i
$611$	1.00712	−	0.731712i	0.0407435	−	0.0296019i
$612$		−	13.3693i		−	0.540421i
$613$	−1.68595	−	5.18882i	−0.0680949	−	0.209574i	0.911219	−	0.411923i	$-0.135143\pi$
$613$	−1.68595	−	5.18882i	−0.0680949	−	0.209574i	−0.979314	+	0.202348i	$0.935143\pi$
$614$	−50.7885			−2.04966
$615$	4.09185	−	37.1400i	0.164999	−	1.49763i
$616$	−0.654707			−0.0263789
$617$	−11.8591	−	36.4986i	−0.477430	−	1.46938i	−0.842653	−	0.538457i	$-0.819007\pi$
$617$	−11.8591	−	36.4986i	−0.477430	−	1.46938i	0.365223	−	0.930920i	$-0.380993\pi$
$618$		−	19.4115i		−	0.780843i
$619$	−4.49027	+	3.26237i	−0.180479	+	0.131126i	−0.674357	−	0.738406i	$-0.735579\pi$
$619$	−4.49027	+	3.26237i	−0.180479	+	0.131126i	0.493878	+	0.869531i	$0.335579\pi$
$620$	3.96030	−	2.87733i	0.159049	−	0.115556i
$621$	10.6331	−	3.45491i	0.426693	−	0.138641i
$622$	−15.8254	−	5.14198i	−0.634540	−	0.206175i
$623$	7.87625	+	5.72243i	0.315555	+	0.229264i
$624$	−8.13495			−0.325659
$625$	25.2811	+	18.3678i	1.01124	+	0.734711i
$626$	−12.1505	+	16.7237i	−0.485630	+	0.668412i
$627$	−1.59627	−	2.19708i	−0.0637488	−	0.0877427i
$628$	14.9334	−	4.85217i	0.595909	−	0.193623i
$629$			8.06816i			0.321698i
$630$	−5.31338	−	7.31323i	−0.211690	−	0.291366i
$631$	−1.89552	+	5.83382i	−0.0754596	+	0.232241i	−0.981671	−	0.190585i	$-0.938962\pi$
$631$	−1.89552	+	5.83382i	−0.0754596	+	0.232241i	0.906211	+	0.422825i	$0.138962\pi$
$632$	13.3043	−	18.3118i	0.529216	−	0.728404i
$633$	−11.0217	−	33.9214i	−0.438074	−	1.34825i
$634$	56.5651	+	18.3791i	2.24649	+	0.729928i
$635$	−3.17673	+	9.77696i	−0.126065	+	0.387987i
$636$	18.1371	−	55.8203i	0.719184	−	2.21342i
$637$	−1.67780	−	0.545151i	−0.0664769	−	0.0215997i
$638$	−2.40895	−	7.41398i	−0.0953712	−	0.293522i
$639$	6.59865	−	9.08226i	0.261039	−	0.359289i
$640$	−9.43825	+	29.0479i	−0.373079	+	1.14822i
$641$	−13.5404	−	18.6367i	−0.534812	−	0.736106i	0.453042	−	0.891489i	$-0.350339\pi$
$641$	−13.5404	−	18.6367i	−0.534812	−	0.736106i	−0.987854	+	0.155383i	$0.950339\pi$
$642$		−	46.0420i		−	1.81713i
$643$	22.6704	−	7.36607i	0.894035	−	0.290490i	0.174262	−	0.984699i	$-0.444246\pi$
$643$	22.6704	−	7.36607i	0.894035	−	0.290490i	0.719773	+	0.694210i	$0.244246\pi$
$644$	5.61045	+	7.72212i	0.221083	+	0.304294i
$645$	−30.3124	+	41.7214i	−1.19355	+	1.64278i
$646$	−16.5152	−	11.9990i	−0.649784	−	0.472096i
$647$	37.6325			1.47949			0.739743	−	0.672890i	$-0.234947\pi$
$647$	37.6325			1.47949			0.739743	+	0.672890i	$0.234947\pi$
$648$	−13.4460	−	9.76911i	−0.528210	−	0.383767i
$649$	−2.75711	−	0.895838i	−0.108226	−	0.0351647i
$650$	9.18444	−	2.98420i	0.360243	−	0.117050i
$651$	1.14405	−	0.831200i	0.0448388	−	0.0325773i
$652$	16.1712	−	11.7491i	0.633313	−	0.460129i
$653$		−	11.3439i		−	0.443920i	−0.975056	−	0.221960i	$-0.928755\pi$
$653$		−	11.3439i		−	0.443920i	0.975056	−	0.221960i	$-0.0712454\pi$
$654$	11.5647	+	35.5924i	0.452215	+	1.39177i
$655$	42.4926			1.66032
$656$	−12.0590	+	6.88191i	−0.470824	+	0.268693i
$657$	−21.1761			−0.826157
$658$	−0.471867	−	1.45226i	−0.0183953	−	0.0566149i
$659$			47.7914i			1.86169i	0.365418	+	0.930843i	$0.380926\pi$
$659$			47.7914i			1.86169i	−0.365418	+	0.930843i	$0.619074\pi$
$660$	5.61240	−	4.07765i	0.218463	−	0.158722i
$661$	−13.1913	+	9.58402i	−0.513081	+	0.372775i	−0.813991	−	0.580877i	$-0.802710\pi$
$661$	−13.1913	+	9.58402i	−0.513081	+	0.372775i	0.300910	+	0.953653i	$0.402710\pi$
$662$	62.0026	−	20.1459i	2.40980	−	0.782992i
$663$	11.6799	+	3.79502i	0.453609	+	0.147386i
$664$	−10.1198	−	7.35250i	−0.392726	−	0.285332i
$665$	−7.90769			−0.306647
$666$	−6.56871	−	4.77245i	−0.254532	−	0.184929i
$667$	−17.0009	+	23.3997i	−0.658277	+	0.906040i
$668$	−8.18824	−	11.2701i	−0.316813	−	0.436055i
$669$	47.8348	−	15.5425i	1.84940	−	0.600906i
$670$			30.0975i			1.16277i
$671$	1.14858	+	1.58088i	0.0443403	+	0.0610292i
$672$	−5.02533	+	15.4664i	−0.193856	+	0.596629i
$673$	12.7884	−	17.6018i	0.492958	−	0.678498i	−0.487972	−	0.872859i	$-0.662263\pi$
$673$	12.7884	−	17.6018i	0.492958	−	0.678498i	0.980930	+	0.194361i	$0.0622633\pi$
$674$	18.5039	+	56.9490i	0.712742	+	2.19359i
$675$	−7.56001	−	2.45640i	−0.290985	−	0.0945467i
$676$	8.19709	−	25.2281i	0.315273	−	0.970310i
$677$	−3.69956	+	11.3861i	−0.142186	+	0.437603i	−0.996638	−	0.0819265i	$-0.973893\pi$
$677$	−3.69956	+	11.3861i	−0.142186	+	0.437603i	0.854453	+	0.519529i	$0.173893\pi$
$678$	−71.3873	−	23.1951i	−2.74161	−	0.890804i
$679$	−4.57069	−	14.0671i	−0.175407	−	0.539847i
$680$	7.80055	−	10.7365i	0.299138	−	0.411727i
$681$	11.8246	−	36.3925i	0.453121	−	1.39456i
$682$	0.374815	+	0.515888i	0.0143524	+	0.0197544i
$683$		−	20.1534i		−	0.771148i	−0.922677	−	0.385574i	$-0.874003\pi$
$683$		−	20.1534i		−	0.771148i	0.922677	−	0.385574i	$-0.125997\pi$
$684$	11.1934	−	3.63694i	0.427989	−	0.139062i
$685$	−25.0270	−	34.4466i	−0.956231	−	1.31614i
$686$	−1.27195	+	1.75068i	−0.0485631	+	0.0668414i
$687$	−24.8115	−	18.0266i	−0.946620	−	0.687759i
$688$	19.1633			0.730595
$689$	14.6831	+	10.6679i	0.559381	+	0.406414i
$690$	−42.7294	−	13.8836i	−1.62668	−	0.528541i
$691$	−36.5747	+	11.8838i	−1.39137	+	0.452083i	−0.906389	−	0.422444i	$-0.861172\pi$
$691$	−36.5747	+	11.8838i	−1.39137	+	0.452083i	−0.484978	+	0.874526i	$0.661172\pi$
$692$	−40.8492	+	29.6787i	−1.55285	+	1.12821i
$693$	0.545777	−	0.396530i	0.0207324	−	0.0150629i
$694$		−	1.74913i		−	0.0663960i
$695$	−4.61106	−	14.1914i	−0.174908	−	0.538310i
$696$	25.5409			0.968127
$697$	20.5243	−	4.25519i	0.777415	−	0.161177i
$698$	6.54272			0.247645
$699$	−12.4657	−	38.3655i	−0.471497	−	1.45112i
$700$		−	6.78641i		−	0.256502i
$701$	5.44115	−	3.95323i	0.205509	−	0.149311i	−0.480270	−	0.877121i	$-0.659461\pi$
$701$	5.44115	−	3.95323i	0.205509	−	0.149311i	0.685780	+	0.727809i	$0.259461\pi$
$702$	9.70500	−	7.05110i	0.366292	−	0.266126i
$703$	−6.75502	+	2.19484i	−0.254770	+	0.0827799i
$704$	−5.14654	−	1.67221i	−0.193967	−	0.0630238i
$705$	3.33131	+	2.42034i	0.125464	+	0.0911552i
$706$	57.3182			2.15720
$707$	−14.8830	−	10.8131i	−0.559732	−	0.406669i
$708$	21.9373	−	30.1941i	0.824453	−	1.13476i
$709$	−13.0182	−	17.9180i	−0.488908	−	0.672924i	0.491278	−	0.871003i	$-0.336530\pi$
$709$	−13.0182	−	17.9180i	−0.488908	−	0.672924i	−0.980186	+	0.198079i	$0.936530\pi$
$710$	41.6453	−	13.5314i	1.56292	−	0.507824i
$711$			23.3230i			0.874680i
$712$	−8.45442	−	11.6365i	−0.316843	−	0.436097i
$713$	0.731119	−	2.25015i	0.0273806	−	0.0842689i
$714$	8.85455	−	12.1872i	0.331373	−	0.456096i
$715$	0.662900	+	2.04019i	0.0247910	+	0.0762990i
$716$	29.9318	+	9.72544i	1.11861	+	0.363457i
$717$	12.8898	−	39.6709i	0.481380	−	1.48154i
$718$	8.96415	−	27.5888i	0.334539	−	1.02961i
$719$	20.8200	+	6.76484i	0.776456	+	0.252286i	0.670326	−	0.742067i	$-0.266154\pi$
$719$	20.8200	+	6.76484i	0.776456	+	0.252286i	0.106130	+	0.994352i	$0.466154\pi$
$720$	−2.79913	−	8.61484i	−0.104317	−	0.321056i
$721$	2.47939	−	3.41259i	0.0923373	−	0.127091i
$722$	−7.15197	+	22.0115i	−0.266169	+	0.819183i
$723$	28.8610	+	39.7237i	1.07335	+	1.47734i
$724$		−	4.73159i		−	0.175848i
$725$	19.5578	−	6.35472i	0.726359	−	0.236008i
$726$	−29.2227	−	40.2216i	−1.08456	−	1.49276i
$727$	−15.8977	+	21.8814i	−0.589614	+	0.811535i	−0.994708	−	0.102741i	$-0.967239\pi$
$727$	−15.8977	+	21.8814i	−0.589614	+	0.811535i	0.405094	+	0.914275i	$0.367239\pi$
$728$	2.10860	+	1.53199i	0.0781500	+	0.0567793i
$729$	−2.92169			−0.108211
$730$	−66.8230	−	48.5498i	−2.47323	−	1.79691i
$731$	−27.5140	−	8.93985i	−1.01764	−	0.330652i
$732$	−23.9257	+	7.77392i	−0.884318	+	0.287332i
$733$	0.868937	−	0.631320i	0.0320949	−	0.0233183i	−0.571622	−	0.820517i	$-0.693686\pi$
$733$	0.868937	−	0.631320i	0.0320949	−	0.0233183i	0.603717	+	0.797199i	$0.293686\pi$
$734$	37.0117	−	26.8906i	1.36613	−	0.992549i
$735$		−	5.83539i		−	0.215242i
$736$	8.40783	+	25.8766i	0.309917	+	0.953826i
$737$	−2.24614			−0.0827376
$738$	−8.67611	+	19.2270i	−0.319372	+	0.707754i
$739$	29.4993			1.08515			0.542575	−	0.840007i	$-0.317449\pi$
$739$	29.4993			1.08515			0.542575	+	0.840007i	$0.317449\pi$
$740$	−5.60669	−	17.2556i	−0.206106	−	0.634329i
$741$			10.8113i			0.397163i
$742$	18.0108	−	13.0856i	0.661198	−	0.480388i
$743$	−7.55697	+	5.49046i	−0.277238	+	0.201425i	−0.717712	−	0.696340i	$-0.754811\pi$
$743$	−7.55697	+	5.49046i	−0.277238	+	0.201425i	0.440474	+	0.897766i	$0.354811\pi$
$744$	−1.98699	+	0.645613i	−0.0728467	+	0.0236693i
$745$	−18.5018	−	6.01160i	−0.677854	−	0.220248i
$746$	37.5791	+	27.3028i	1.37587	+	0.999628i
$747$	12.8892			0.471593
$748$	3.14844	+	2.28747i	0.115118	+	0.0836383i
$749$	5.88086	−	8.09431i	0.214882	−	0.295760i
$750$	−18.3356	−	25.2368i	−0.669521	−	0.921517i
$751$	−35.1882	+	11.4333i	−1.28404	+	0.417209i	−0.870000	−	0.493051i	$-0.835881\pi$
$751$	−35.1882	+	11.4333i	−1.28404	+	0.417209i	−0.414037	+	0.910260i	$0.635881\pi$
$752$		−	1.53012i		−	0.0557978i
$753$	−1.54339	−	2.12429i	−0.0562442	−	0.0774135i
$754$	−9.58999	+	29.5150i	−0.349247	+	1.07487i
$755$	−24.2043	+	33.3144i	−0.880886	+	1.21244i
$756$	−2.60504	−	8.01749i	−0.0947444	−	0.291593i
$757$	−30.1774	−	9.80523i	−1.09682	−	0.356377i	−0.295939	−	0.955207i	$-0.595633\pi$
$757$	−30.1774	−	9.80523i	−1.09682	−	0.356377i	−0.800876	+	0.598830i	$0.795633\pi$
$758$	−16.9065	+	52.0328i	−0.614072	+	1.88992i
$759$	1.03612	−	3.18884i	0.0376087	−	0.115748i
$760$	11.1111	+	3.61023i	0.403044	+	0.130957i
$761$	−2.19136	−	6.74431i	−0.0794368	−	0.244481i	0.903450	−	0.428694i	$-0.141026\pi$
$761$	−2.19136	−	6.74431i	−0.0794368	−	0.244481i	−0.982886	+	0.184213i	$0.941026\pi$
$762$	10.1335	−	13.9476i	0.367099	−	0.505268i
$763$	−2.51305	+	7.73439i	−0.0909787	+	0.280004i
$764$	−17.1943	−	23.6660i	−0.622070	−	0.856205i
$765$			13.6747i			0.494410i
$766$	−52.1472	+	16.9436i	−1.88415	+	0.612199i
$767$	6.78354	+	9.33674i	0.244940	+	0.337130i
$768$	−0.420519	+	0.578795i	−0.0151742	+	0.0208855i
$769$	−36.8385	−	26.7648i	−1.32843	−	0.965162i	−0.999786	−	0.0207092i	$-0.993408\pi$
$769$	−36.8385	−	26.7648i	−1.32843	−	0.965162i	−0.328646	−	0.944453i	$-0.606592\pi$
$770$	2.63136			0.0948278
$771$	−21.8657	−	15.8863i	−0.787472	−	0.572132i
$772$	29.4321	+	9.56306i	1.05928	+	0.344182i
$773$	15.5727	−	5.05987i	0.560111	−	0.181991i	−0.0152604	−	0.999884i	$-0.504858\pi$
$773$	15.5727	−	5.05987i	0.560111	−	0.181991i	0.575371	+	0.817893i	$0.304858\pi$
$774$	23.5534	−	17.1126i	0.846610	−	0.615098i
$775$	−1.36089	+	0.988748i	−0.0488848	+	0.0355169i
$776$			21.8526i			0.784461i
$777$	−1.61966	−	4.98479i	−0.0581048	−	0.178828i
$778$	22.3504			0.801300
$779$	9.14602	+	16.0263i	0.327690	+	0.574202i
$780$	−27.6173			−0.988860
$781$	1.00983	+	3.10794i	0.0361345	+	0.111211i
$782$		−	25.2038i		−	0.901288i
$783$	20.6663	−	15.0150i	0.738554	−	0.536591i
$784$	−1.75427	+	1.27455i	−0.0626525	+	0.0455197i
$785$	−15.2746	+	4.96302i	−0.545174	+	0.177138i
$786$	−67.7741	−	22.0211i	−2.41742	−	0.785468i
$787$	−28.6665	−	20.8275i	−1.02185	−	0.742419i	−0.0551899	−	0.998476i	$-0.517576\pi$
$787$	−28.6665	−	20.8275i	−1.02185	−	0.742419i	−0.966662	+	0.256057i	$0.917576\pi$
$788$	−47.5543			−1.69405
$789$	29.2057	+	21.2192i	1.03975	+	0.755422i
$790$	−53.4720	+	73.5979i	−1.90245	+	2.61849i
$791$	−9.58741	−	13.1959i	−0.340889	−	0.469194i
$792$	−0.947910	+	0.307995i	−0.0336825	+	0.0109441i
$793$		−	7.77915i		−	0.276246i
$794$	25.9155	+	35.6696i	0.919707	+	1.26587i
$795$	−18.5515	+	57.0955i	−0.657952	+	2.02497i
$796$	15.8798	−	21.8566i	0.562844	−	0.774688i
$797$	2.59866	+	7.99786i	0.0920493	+	0.283299i	0.986473	−	0.163921i	$-0.0524142\pi$
$797$	2.59866	+	7.99786i	0.0920493	+	0.283299i	−0.894424	+	0.447220i	$0.852414\pi$
$798$	12.6125	+	4.09804i	0.446476	+	0.145069i
$799$	−0.713815	+	2.19690i	−0.0252530	+	0.0777206i
$800$	5.97785	−	18.3979i	0.211349	−	0.650465i
$801$	14.0956	+	4.57993i	0.498042	+	0.161824i
$802$	−5.75189	−	17.7025i	−0.203106	−	0.625097i
$803$	3.62321	−	4.98692i	0.127860	−	0.175984i
$804$	8.93584	−	27.5017i	0.315143	−	0.969910i
$805$	−5.73862	−	7.89853i	−0.202260	−	0.278387i
$806$		−	2.53857i		−	0.0894172i
$807$	−46.0066	+	14.9485i	−1.61951	+	0.526211i
$808$	15.9755	+	21.9884i	0.562015	+	0.773548i
$809$	24.5824	−	33.8348i	0.864271	−	1.18957i	−0.116263	−	0.993218i	$-0.537091\pi$
$809$	24.5824	−	33.8348i	0.864271	−	1.18957i	0.980534	−	0.196349i	$-0.0629085\pi$
$810$	54.0416	+	39.2635i	1.89883	+	1.37958i
$811$	−28.1451			−0.988308			−0.494154	−	0.869374i	$-0.664522\pi$
$811$	−28.1451			−0.988308			−0.494154	+	0.869374i	$0.664522\pi$
$812$	17.6436	+	12.8188i	0.619169	+	0.449853i
$813$	2.23493	+	0.726174i	0.0783826	+	0.0254680i
$814$	2.24780	−	0.730355i	0.0787854	−	0.0255989i
$815$	−16.5406	+	12.0175i	−0.579393	+	0.420954i
$816$	12.2122	−	8.87269i	0.427513	−	0.310606i
$817$		−	25.4679i		−	0.891010i
$818$	19.5047	+	60.0294i	0.681967	+	2.09888i
$819$	−2.68564			−0.0938440
$820$	−40.9390	+	23.3634i	−1.42965	+	0.815885i
$821$	22.0289			0.768812			0.384406	−	0.923164i	$-0.374406\pi$
$821$	22.0289			0.768812			0.384406	+	0.923164i	$0.374406\pi$
$822$	22.0656	+	67.9110i	0.769626	+	2.36867i
$823$			42.0902i			1.46717i	0.679597	+	0.733585i	$0.262155\pi$
$823$			42.0902i			1.46717i	−0.679597	+	0.733585i	$0.737845\pi$
$824$	−5.04182	+	3.66309i	−0.175640	+	0.127610i
$825$	−1.92861	+	1.40122i	−0.0671457	+	0.0487842i
$826$	13.4636	−	4.37458i	0.468457	−	0.152211i
$827$	−46.8581	−	15.2251i	−1.62942	−	0.529429i	−0.655279	−	0.755387i	$-0.727449\pi$
$827$	−46.8581	−	15.2251i	−1.62942	−	0.529429i	−0.974137	+	0.225958i	$0.927449\pi$
$828$	11.7558	+	8.54106i	0.408541	+	0.296823i
$829$	20.7035			0.719061			0.359531	−	0.933133i	$-0.382937\pi$
$829$	20.7035			0.719061			0.359531	+	0.933133i	$0.382937\pi$
$830$	40.6732	+	29.5508i	1.41179	+	1.02572i
$831$	7.07758	−	9.74145i	0.245518	−	0.337927i
$832$	12.6625	+	17.4284i	0.438992	+	0.604220i
$833$	3.11331	−	1.01158i	0.107870	−	0.0350490i
$834$			25.0244i			0.866522i
$835$	8.37530	+	11.5276i	0.289839	+	0.398929i
$836$	−1.05868	+	3.25829i	−0.0366153	+	0.112690i
$837$	−1.22822	+	1.69050i	−0.0424536	+	0.0584324i
$838$	−12.1432	−	37.3729i	−0.419480	−	1.29103i
$839$	−42.2844	−	13.7390i	−1.45982	−	0.474324i	−0.531805	−	0.846867i	$-0.678486\pi$
$839$	−42.2844	−	13.7390i	−1.45982	−	0.474324i	−0.928015	+	0.372542i	$0.878486\pi$
$840$	−2.66413	+	8.19935i	−0.0919212	+	0.282904i
$841$	−11.4599	+	35.2700i	−0.395170	+	1.21621i
$842$	7.72987	+	2.51159i	0.266389	+	0.0865550i
$843$	−5.24985	−	16.1574i	−0.180814	−	0.556489i
$844$	−26.4473	+	36.4016i	−0.910354	+	1.25300i
$845$	−8.38435	+	25.8044i	−0.288430	+	0.887698i
$846$	−1.36638	−	1.88066i	−0.0469770	−	0.0646583i
$847$		−	10.8036i		−	0.371217i
$848$	21.2164	−	6.89361i	0.728573	−	0.236728i
$849$	3.40509	+	4.68670i	0.116862	+	0.160847i
$850$	−10.5329	+	14.4972i	−0.361274	+	0.497251i
$851$	−7.09442	−	5.15440i	−0.243194	−	0.176691i
$852$	−42.0709			−1.44133
$853$	37.2155	+	27.0386i	1.27423	+	0.925786i	0.999363	−	0.0356953i	$-0.0113646\pi$
$853$	37.2155	+	27.0386i	1.27423	+	0.925786i	0.274872	+	0.961481i	$0.411365\pi$
$854$	−9.07515	−	2.94870i	−0.310545	−	0.100902i
$855$	−11.4491	+	3.72003i	−0.391550	+	0.127222i
$856$	−11.9587	+	8.68848i	−0.408739	+	0.296966i
$857$	−43.6049	+	31.6808i	−1.48951	+	1.08220i	−0.515182	+	0.857081i	$0.672276\pi$
$857$	−43.6049	+	31.6808i	−1.48951	+	1.08220i	−0.974332	+	0.225115i	$0.927724\pi$
$858$		−	3.59757i		−	0.122819i
$859$	0.771086	+	2.37316i	0.0263091	+	0.0809711i	0.963349	−	0.268251i	$-0.0864458\pi$
$859$	0.771086	+	2.37316i	0.0263091	+	0.0809711i	−0.937040	+	0.349222i	$0.886446\pi$
$860$	65.0576			2.21844
$861$	−11.8264	+	6.74920i	−0.403044	+	0.230012i
$862$	3.46341			0.117964
$863$	−13.6261	−	41.9367i	−0.463836	−	1.42754i	−0.860440	−	0.509551i	$-0.829811\pi$
$863$	−13.6261	−	41.9367i	−0.463836	−	1.42754i	0.396604	−	0.917990i	$-0.370189\pi$
$864$		−	24.0300i		−	0.817518i
$865$	41.7824	−	30.3567i	1.42064	−	1.03216i
$866$	41.5523	−	30.1895i	1.41200	−	1.02588i
$867$	12.7094	−	4.12955i	0.431635	−	0.140247i
$868$	−1.69664	−	0.551271i	−0.0575876	−	0.0187114i
$869$	−5.49251	−	3.99054i	−0.186321	−	0.135370i
$870$	−102.653			−3.48026
$871$	7.23410	+	5.25588i	0.245118	+	0.178089i
$872$	7.06222	−	9.72031i	0.239157	−	0.329171i
$873$	−13.2352	−	18.2168i	−0.447945	−	0.616544i
$874$	21.1018	−	6.85638i	0.713778	−	0.231921i
$875$		−	6.77867i		−	0.229161i
$876$	46.6455	+	64.2020i	1.57601	+	2.16919i
$877$	15.6274	−	48.0960i	0.527698	−	1.62409i	−0.231220	−	0.972902i	$-0.574272\pi$
$877$	15.6274	−	48.0960i	0.527698	−	1.62409i	0.758918	−	0.651186i	$-0.225728\pi$
$878$	27.0179	−	37.1870i	0.911811	−	1.25500i
$879$	20.4987	+	63.0884i	0.691402	+	2.12792i
$880$	2.50770	+	0.814803i	0.0845347	+	0.0274670i
$881$	12.9641	−	39.8994i	0.436772	−	1.34425i	−0.454488	−	0.890753i	$-0.650178\pi$
$881$	12.9641	−	39.8994i	0.436772	−	1.34425i	0.891260	−	0.453492i	$-0.149822\pi$
$882$	−1.01800	+	3.13307i	−0.0342777	+	0.105496i
$883$	26.8893	+	8.73687i	0.904898	+	0.294019i	0.724257	−	0.689530i	$-0.242183\pi$
$883$	26.8893	+	8.73687i	0.904898	+	0.294019i	0.180641	+	0.983549i	$0.442183\pi$
$884$	−4.78752	−	14.7345i	−0.161022	−	0.495574i
$885$	−22.4384	+	30.8838i	−0.754259	+	1.03815i
$886$	−20.3498	+	62.6302i	−0.683664	+	2.10410i
$887$	−11.1199	−	15.3052i	−0.373370	−	0.513899i	0.580443	−	0.814301i	$-0.302879\pi$
$887$	−11.1199	−	15.3052i	−0.373370	−	0.513899i	−0.953813	+	0.300402i	$0.902879\pi$
$888$			7.74361i			0.259859i
$889$	3.56300	−	1.15769i	0.119499	−	0.0388277i
$890$	33.9796	+	46.7689i	1.13900	+	1.56770i
$891$	−2.93019	+	4.03306i	−0.0981650	+	0.135113i
$892$	−51.3323	−	37.2951i	−1.71873	−	1.24873i
$893$	−2.03352			−0.0680493
$894$	26.3943	+	19.1766i	0.882757	+	0.641360i
$895$	−30.6156	−	9.94762i	−1.02337	−	0.332512i
$896$	10.5859	−	3.43957i	0.353650	−	0.114908i
$897$	−10.7988	+	7.84578i	−0.360561	+	0.261963i
$898$	−6.18807	+	4.49590i	−0.206499	+	0.150030i
$899$		−	5.40576i		−	0.180292i
$900$	−3.19254	−	9.82564i	−0.106418	−	0.327521i
$901$	−33.6776			−1.12196
$902$	−3.04343	−	5.33292i	−0.101335	−	0.177567i
$903$	18.7938			0.625418
$904$	7.44678	+	22.9188i	0.247676	+	0.762269i
$905$			4.83968i			0.160876i
$906$	55.8697	−	40.5917i	1.85615	−	1.34857i
$907$	−17.2008	+	12.4971i	−0.571144	+	0.414961i	−0.835521	−	0.549459i	$-0.814834\pi$
$907$	−17.2008	+	12.4971i	−0.571144	+	0.414961i	0.264376	+	0.964420i	$0.414834\pi$
$908$	−45.9101	+	14.9171i	−1.52358	+	0.495041i
$909$	−26.6350	−	8.65423i	−0.883427	−	0.287043i
$910$	−8.47480	−	6.15730i	−0.280937	−	0.204113i
$911$	8.05890			0.267003			0.133502	−	0.991049i	$-0.457378\pi$
$911$	8.05890			0.267003			0.133502	+	0.991049i	$0.457378\pi$
$912$	10.7508	+	7.81090i	0.355994	+	0.258645i
$913$	−2.20534	+	3.03539i	−0.0729861	+	0.100457i
$914$	22.8832	+	31.4960i	0.756910	+	1.04180i
$915$	24.4722	−	7.95151i	0.809028	−	0.262869i
$916$			38.6894i			1.27833i
$917$	−9.10215	−	12.5280i	−0.300579	−	0.413712i
$918$	−6.87863	+	21.1702i	−0.227029	+	0.698722i
$919$	21.3154	−	29.3381i	0.703130	−	0.967775i	−0.296788	−	0.954943i	$-0.595915\pi$
$919$	21.3154	−	29.3381i	0.703130	−	0.967775i	0.999918	−	0.0128319i	$-0.00408464\pi$
$920$	4.45732	+	13.7182i	0.146954	+	0.452277i
$921$	−47.4684	−	15.4234i	−1.56414	−	0.508218i
$922$	15.5311	−	47.7999i	0.511491	−	1.57421i
$923$	4.02012	−	12.3726i	0.132324	−	0.407251i
$924$	−2.40442	−	0.781243i	−0.0790995	−	0.0257010i
$925$	1.92665	+	5.92962i	0.0633479	+	0.194965i
$926$	−37.5393	+	51.6685i	−1.23362	+	1.69793i
$927$	1.98437	−	6.10726i	0.0651753	−	0.200589i
$928$	36.5402	+	50.2933i	1.19949	+	1.65096i
$929$		−	3.90446i		−	0.128101i	−0.997947	−	0.0640506i	$-0.979598\pi$
$929$		−	3.90446i		−	0.128101i	0.997947	−	0.0640506i	$-0.0204019\pi$
$930$	7.98602	−	2.59482i	0.261872	−	0.0850874i
$931$	1.69387	+	2.33141i	0.0555144	+	0.0764090i
$932$	−29.9123	+	41.1707i	−0.979810	+	1.34859i
$933$	−13.2293	−	9.61167i	−0.433109	−	0.314672i
$934$	7.40849			0.242413
$935$	−3.22036	−	2.33973i	−0.105317	−	0.0765174i
$936$	3.77362	+	1.22612i	0.123345	+	0.0400771i
$937$	−17.1287	+	5.56545i	−0.559570	+	0.181815i	−0.575128	−	0.818064i	$-0.695048\pi$
$937$	−17.1287	+	5.56545i	−0.559570	+	0.181815i	0.0155578	+	0.999879i	$0.495048\pi$
$938$	8.87361	−	6.44706i	0.289734	−	0.210504i
$939$	−16.4348	+	11.9406i	−0.536328	+	0.389665i
$940$		−	5.19461i		−	0.169430i
$941$	1.76659	+	5.43700i	0.0575891	+	0.177241i	0.975713	−	0.219052i	$-0.0702964\pi$
$941$	1.76659	+	5.43700i	0.0575891	+	0.177241i	−0.918124	+	0.396293i	$0.870296\pi$
$942$	26.9344			0.877571
$943$	−9.37048	+	20.7657i	−0.305145	+	0.676226i
$944$	14.1854			0.461696
$945$	2.66455	+	8.20064i	0.0866778	+	0.266767i
$946$			8.47472i			0.275537i
$947$	−39.7631	+	28.8896i	−1.29213	+	0.938785i	−0.999846	−	0.0175477i	$-0.994414\pi$
$947$	−39.7631	+	28.8896i	−1.29213	+	0.938785i	−0.292281	+	0.956333i	$0.594414\pi$
$948$	70.7111	−	51.3746i	2.29659	−	1.66857i
$949$	−23.3384	+	7.58311i	−0.757597	+	0.246158i
$950$	−15.0031	−	4.87479i	−0.486764	−	0.158159i
$951$	47.2859	+	34.3552i	1.53335	+	1.11404i
$952$	−4.83636			−0.156747
$953$	33.7780	+	24.5411i	1.09418	+	0.794966i	0.980100	−	0.198506i	$-0.0636090\pi$
$953$	33.7780	+	24.5411i	1.09418	+	0.794966i	0.114077	+	0.993472i	$0.463609\pi$
$954$	19.9209	−	27.4187i	0.644962	−	0.887715i
$955$	17.5871	+	24.2066i	0.569107	+	0.783308i
$956$	−50.0458	+	16.2609i	−1.61860	+	0.525914i
$957$		−	7.66086i		−	0.247640i
$958$	−3.95498	−	5.44356i	−0.127780	−	0.175874i
$959$	−4.79495	+	14.7573i	−0.154837	+	0.476539i
$960$	−41.8845	+	57.6491i	−1.35182	+	1.86062i
$961$	−9.44288	−	29.0622i	−0.304609	−	0.937490i
$962$	−8.94847	−	2.90753i	−0.288510	−	0.0937427i
$963$	4.70672	−	14.4858i	0.151672	−	0.466799i
$964$	19.1413	−	58.9108i	0.616499	−	1.89739i
$965$	−30.1044	−	9.78152i	−0.969096	−	0.314878i
$966$	5.05959	+	15.5718i	0.162790	+	0.501015i
$967$	−19.6274	+	27.0147i	−0.631173	+	0.868735i	−0.998106	−	0.0615119i	$-0.980408\pi$
$967$	−19.6274	+	27.0147i	−0.631173	+	0.868735i	0.366933	+	0.930247i	$0.380408\pi$
$968$	−4.93236	+	15.1803i	−0.158532	+	0.487912i
$969$	−11.7918	−	16.2300i	−0.378806	−	0.521381i
$970$		−	87.8288i		−	2.82001i
$971$	16.6647	−	5.41469i	0.534796	−	0.173766i	−0.0291538	−	0.999575i	$-0.509281\pi$
$971$	16.6647	−	5.41469i	0.534796	−	0.173766i	0.563950	+	0.825809i	$0.309281\pi$
$972$	−22.8583	−	31.4617i	−0.733179	−	1.00913i
$973$	−3.19632	+	4.39935i	−0.102469	+	0.141037i
$974$	−33.6928	−	24.4793i	−1.07959	−	0.784366i
$975$	9.49027			0.303932
$976$	−7.73560	−	5.62025i	−0.247611	−	0.179900i
$977$	−32.7674	−	10.6468i	−1.04832	−	0.340620i	−0.266311	−	0.963887i	$-0.585805\pi$
$977$	−32.7674	−	10.6468i	−1.04832	−	0.340620i	−0.782009	+	0.623267i	$0.785805\pi$
$978$	32.6096	−	10.5955i	1.04274	−	0.338806i
$979$	−3.49030	+	2.53585i	−0.111551	+	0.0810462i
$980$	−5.95557	+	4.32698i	−0.190244	+	0.138220i
$981$			12.3804i			0.395275i
$982$	−1.24901	−	3.84406i	−0.0398575	−	0.122669i
$983$	21.5729			0.688068			0.344034	−	0.938957i	$-0.388206\pi$
$983$	21.5729			0.688068			0.344034	+	0.938957i	$0.388206\pi$
$984$	19.6987	−	4.08402i	0.627973	−	0.130194i
$985$	48.6406			1.54982
$986$	−17.7951	−	54.7676i	−0.566711	−	1.74416i
$987$		−	1.50062i		−	0.0477651i
$988$	11.0340	−	8.01664i	0.351037	−	0.255043i
$989$	25.4385	−	18.4821i	0.808896	−	0.587697i
$990$	3.80980	−	1.23788i	0.121083	−	0.0393423i
$991$	−13.4544	−	4.37159i	−0.427392	−	0.138868i	0.0874194	−	0.996172i	$-0.472138\pi$
$991$	−13.4544	−	4.37159i	−0.427392	−	0.138868i	−0.514811	+	0.857304i	$0.672138\pi$
$992$	−4.11399	−	2.98899i	−0.130619	−	0.0949004i
$993$	64.0672			2.03311
$994$	−12.9101	−	9.37974i	−0.409484	−	0.297507i
$995$	−16.2425	+	22.3559i	−0.514923	+	0.708731i
$996$	−28.3917	−	39.0779i	−0.899626	−	1.23823i
$997$	38.9363	−	12.6512i	1.23313	−	0.400667i	0.381281	−	0.924459i	$-0.375483\pi$
$997$	38.9363	−	12.6512i	1.23313	−	0.400667i	0.851846	+	0.523792i	$0.175483\pi$
$998$		−	42.9563i		−	1.35976i
$999$	4.55230	+	6.26571i	0.144028	+	0.198238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.n.a.64.4	✓	88
41.25	even	10	inner	287.2.n.a.148.4	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.n.a.64.4	✓	88	1.1	even	1	trivial
287.2.n.a.148.4	yes	88	41.25	even	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.668701 - 2.05805i) q^{2} -2.12658i q^{3} +(-2.17038 + 1.57687i) q^{4} +(2.21996 - 1.61290i) q^{5} +(-4.37661 + 1.42205i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(1.19526 + 0.868404i) q^{8} -1.52235 q^{9} +O(q^{10})\)	\(q+(-0.668701 - 2.05805i) q^{2} -2.12658i q^{3} +(-2.17038 + 1.57687i) q^{4} +(2.21996 - 1.61290i) q^{5} +(-4.37661 + 1.42205i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(1.19526 + 0.868404i) q^{8} -1.52235 q^{9} +(-4.80391 - 3.49025i) q^{10} +(0.260473 - 0.358510i) q^{11} +(3.35335 + 4.61549i) q^{12} +(-1.67780 + 0.545151i) q^{13} +2.16396i q^{14} +(-3.42995 - 4.72093i) q^{15} +(-0.670072 + 2.06227i) q^{16} +(1.92413 - 2.64834i) q^{17} +(1.01800 + 3.13307i) q^{18} +(2.74074 + 0.890521i) q^{19} +(-2.27483 + 7.00119i) q^{20} +(-0.657150 + 2.02250i) q^{21} +(-0.912010 - 0.296330i) q^{22} +(1.09947 + 3.38382i) q^{23} +(1.84673 - 2.54181i) q^{24} +(0.781708 - 2.40585i) q^{25} +(2.24390 + 3.08846i) q^{26} -3.14235i q^{27} +(2.55143 - 0.829011i) q^{28} +(4.77827 + 6.57672i) q^{29} +(-7.42230 + 10.2159i) q^{30} +(-0.537975 - 0.390862i) q^{31} +7.64717 q^{32} +(-0.762401 - 0.553916i) q^{33} +(-6.73709 - 2.18901i) q^{34} +(-2.60972 + 0.847950i) q^{35} +(3.30408 - 2.40055i) q^{36} +(-1.99396 + 1.44870i) q^{37} -6.23608i q^{38} +(1.15931 + 3.56798i) q^{39} +4.05407 q^{40} +(4.73692 + 4.30832i) q^{41} +4.60184 q^{42} +(-2.73095 - 8.40501i) q^{43} +1.18884i q^{44} +(-3.37956 + 2.45539i) q^{45} +(6.22886 - 4.52553i) q^{46} +(-0.671110 + 0.218057i) q^{47} +(4.38558 + 1.42496i) q^{48} +(0.809017 + 0.587785i) q^{49} -5.47409 q^{50} +(-5.63191 - 4.09182i) q^{51} +(2.78183 - 3.82886i) q^{52} +(-6.04706 - 8.32307i) q^{53} +(-6.46711 + 2.10129i) q^{54} -1.21599i q^{55} +(-0.868404 - 1.19526i) q^{56} +(1.89377 - 5.82841i) q^{57} +(10.3400 - 14.2318i) q^{58} +(-2.02156 - 6.22171i) q^{59} +(14.8886 + 4.83760i) q^{60} +(-1.36264 + 4.19377i) q^{61} +(-0.444669 + 1.36855i) q^{62} +(1.44784 + 0.470432i) q^{63} +(-3.77353 - 11.6137i) q^{64} +(-2.84538 + 3.91633i) q^{65} +(-0.630170 + 1.93946i) q^{66} +(-2.97928 - 4.10063i) q^{67} +8.78201i q^{68} +(7.19597 - 2.33811i) q^{69} +(3.49025 + 4.80391i) q^{70} +(-4.33452 + 5.96595i) q^{71} +(-1.81960 - 1.32201i) q^{72} +13.9101 q^{73} +(4.31485 + 3.13492i) q^{74} +(-5.11624 - 1.66237i) q^{75} +(-7.35269 + 2.38903i) q^{76} +(-0.358510 + 0.260473i) q^{77} +(6.56786 - 4.77183i) q^{78} -15.3204i q^{79} +(1.83869 + 5.65891i) q^{80} -11.2495 q^{81} +(5.69916 - 12.6298i) q^{82} -8.46668 q^{83} +(-1.76296 - 5.42583i) q^{84} -8.98263i q^{85} +(-15.4718 + 11.2409i) q^{86} +(13.9859 - 10.1614i) q^{87} +(0.622663 - 0.202315i) q^{88} +(-9.25909 - 3.00846i) q^{89} +(7.31323 + 5.31338i) q^{90} +1.76414 q^{91} +(-7.72212 - 5.61045i) q^{92} +(-0.831200 + 1.14405i) q^{93} +(0.897545 + 1.23536i) q^{94} +(7.52066 - 2.44361i) q^{95} -16.2623i q^{96} +(8.69396 + 11.9662i) q^{97} +(0.668701 - 2.05805i) q^{98} +(-0.396530 + 0.545777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

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