LMFDB - Embedded newform 280.2.w.a.267.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))

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

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

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (of order $4$, degree $2$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.27
Character	$\chi$	$=$	280.267
Dual form			280.2.w.a.43.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.914975 + 1.07834i) q^{2} +(1.73985 - 1.73985i) q^{3} +(-0.325640 + 1.97331i) q^{4} +(0.452388 - 2.18983i) q^{5} +(3.46808 + 0.284233i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.42586 + 1.45438i) q^{8} -3.05418i q^{9} +O(q^{10})$	\(q+(0.914975 + 1.07834i) q^{2} +(1.73985 - 1.73985i) q^{3} +(-0.325640 + 1.97331i) q^{4} +(0.452388 - 2.18983i) q^{5} +(3.46808 + 0.284233i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.42586 + 1.45438i) q^{8} -3.05418i q^{9} +(2.77531 - 1.51581i) q^{10} +1.30862 q^{11} +(2.86671 + 3.99984i) q^{12} +(2.88709 + 2.88709i) q^{13} +(-1.40949 - 0.115517i) q^{14} +(-3.02289 - 4.59707i) q^{15} +(-3.78792 - 1.28518i) q^{16} +(-2.71513 - 2.71513i) q^{17} +(3.29345 - 2.79450i) q^{18} +0.00415458i q^{19} +(4.17390 + 1.60580i) q^{20} +2.46052i q^{21} +(1.19736 + 1.41114i) q^{22} +(-0.0393783 - 0.0393783i) q^{23} +(-1.69022 + 6.75104i) q^{24} +(-4.59069 - 1.98130i) q^{25} +(-0.471651 + 5.75488i) q^{26} +(-0.0942655 - 0.0942655i) q^{27} +(-1.16508 - 1.62560i) q^{28} -9.77322 q^{29} +(2.19134 - 7.46591i) q^{30} +8.07040i q^{31} +(-2.07999 - 5.26057i) q^{32} +(2.27681 - 2.27681i) q^{33} +(0.443560 - 5.41212i) q^{34} +(1.22856 + 1.86833i) q^{35} +(6.02685 + 0.994562i) q^{36} +(4.15579 - 4.15579i) q^{37} +(-0.00448005 + 0.00380134i) q^{38} +10.0462 q^{39} +(2.08742 + 5.97015i) q^{40} -2.28881 q^{41} +(-2.65328 + 2.25132i) q^{42} +(-8.33507 + 8.33507i) q^{43} +(-0.426140 + 2.58232i) q^{44} +(-6.68813 - 1.38167i) q^{45} +(0.00643307 - 0.0784935i) q^{46} +(-1.03359 + 1.03359i) q^{47} +(-8.82644 + 4.35440i) q^{48} -1.00000i q^{49} +(-2.06385 - 6.76317i) q^{50} -9.44787 q^{51} +(-6.63727 + 4.75697i) q^{52} +(6.55677 + 6.55677i) q^{53} +(0.0153998 - 0.187901i) q^{54} +(0.592005 - 2.86566i) q^{55} +(0.686936 - 2.74374i) q^{56} +(0.00722836 + 0.00722836i) q^{57} +(-8.94226 - 10.5389i) q^{58} +5.64348i q^{59} +(10.0558 - 4.46812i) q^{60} -8.63760i q^{61} +(-8.70265 + 7.38422i) q^{62} +(2.15963 + 2.15963i) q^{63} +(3.76955 - 7.05624i) q^{64} +(7.62830 - 5.01614i) q^{65} +(4.53841 + 0.371953i) q^{66} +(0.465518 + 0.465518i) q^{67} +(6.24196 - 4.47365i) q^{68} -0.137025 q^{69} +(-0.890597 + 3.03428i) q^{70} -14.0140i q^{71} +(4.44194 + 7.40900i) q^{72} +(6.82937 - 6.82937i) q^{73} +(8.28382 + 0.678915i) q^{74} +(-11.4343 + 4.53995i) q^{75} +(-0.00819828 - 0.00135290i) q^{76} +(-0.925336 + 0.925336i) q^{77} +(9.19204 + 10.8332i) q^{78} +1.48280 q^{79} +(-4.52792 + 7.71349i) q^{80} +8.83452 q^{81} +(-2.09421 - 2.46812i) q^{82} +(5.58822 - 5.58822i) q^{83} +(-4.85538 - 0.801245i) q^{84} +(-7.17396 + 4.71738i) q^{85} +(-16.6144 - 1.36167i) q^{86} +(-17.0040 + 17.0040i) q^{87} +(-3.17453 + 1.90324i) q^{88} -12.7029i q^{89} +(-4.62956 - 8.47628i) q^{90} -4.08296 q^{91} +(0.0905289 - 0.0648826i) q^{92} +(14.0413 + 14.0413i) q^{93} +(-2.06026 - 0.168852i) q^{94} +(0.00909781 + 0.00187948i) q^{95} +(-12.7715 - 5.53375i) q^{96} +(0.598142 + 0.598142i) q^{97} +(1.07834 - 0.914975i) q^{98} -3.99677i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.914975	+	1.07834i	0.646985	+	0.762502i
$2$	0.914975	+	1.07834i	0.646985	+	0.762502i
$3$	1.73985	−	1.73985i	1.00450	−	1.00450i	0.00451506	−	0.999990i	$-0.498563\pi$
$3$	1.73985	−	1.73985i	1.00450	−	1.00450i	0.999990	−	0.00451506i	$-0.00143719\pi$
$4$	−0.325640	+	1.97331i	−0.162820	+	0.986656i
$5$	0.452388	−	2.18983i	0.202314	−	0.979321i
$5$	0.452388	−	2.18983i	0.202314	−	0.979321i
$6$	3.46808	+	0.284233i	1.41584	+	0.116037i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−2.42586	+	1.45438i	−0.857670	+	0.514201i
$9$		−	3.05418i		−	1.01806i
$10$	2.77531	−	1.51581i	0.877629	−	0.479341i
$11$	1.30862			0.394565			0.197282	−	0.980347i	$-0.436788\pi$
$11$	1.30862			0.394565			0.197282	+	0.980347i	$0.436788\pi$
$12$	2.86671	+	3.99984i	0.827547	+	1.15465i
$13$	2.88709	+	2.88709i	0.800733	+	0.800733i	0.983210	−	0.182477i	$-0.0584114\pi$
$13$	2.88709	+	2.88709i	0.800733	+	0.800733i	−0.182477	+	0.983210i	$0.558411\pi$
$14$	−1.40949	−	0.115517i	−0.376701	−	0.0308732i
$15$	−3.02289	−	4.59707i	−0.780507	−	1.18696i
$16$	−3.78792	−	1.28518i	−0.946979	−	0.321294i
$17$	−2.71513	−	2.71513i	−0.658516	−	0.658516i	0.296513	−	0.955029i	$-0.404176\pi$
$17$	−2.71513	−	2.71513i	−0.658516	−	0.658516i	−0.955029	+	0.296513i	$0.904176\pi$
$18$	3.29345	−	2.79450i	0.776273	−	0.658670i
$19$			0.00415458i			0.000953126i	1.00000		0.000476563i	$0.000151695\pi$
$19$			0.00415458i			0.000953126i	−1.00000		0.000476563i	$0.999848\pi$
$20$	4.17390	+	1.60580i	0.933312	+	0.359067i
$21$			2.46052i			0.536930i
$22$	1.19736	+	1.41114i	0.255278	+	0.300857i
$23$	−0.0393783	−	0.0393783i	−0.00821095	−	0.00821095i	0.702989	−	0.711200i	$-0.251848\pi$
$23$	−0.0393783	−	0.0393783i	−0.00821095	−	0.00821095i	−0.711200	+	0.702989i	$0.751848\pi$
$24$	−1.69022	+	6.75104i	−0.345015	+	1.37805i
$25$	−4.59069	−	1.98130i	−0.918138	−	0.396260i
$26$	−0.471651	+	5.75488i	−0.0924984	+	1.12862i
$27$	−0.0942655	−	0.0942655i	−0.0181414	−	0.0181414i
$28$	−1.16508	−	1.62560i	−0.220179	−	0.307210i
$29$	−9.77322			−1.81484			−0.907421	−	0.420223i	$-0.861952\pi$
$29$	−9.77322			−1.81484			−0.907421	+	0.420223i	$0.861952\pi$
$30$	2.19134	−	7.46591i	0.400081	−	1.36308i
$31$			8.07040i			1.44949i	0.689019	+	0.724743i	$0.258042\pi$
$31$			8.07040i			1.44949i	−0.689019	+	0.724743i	$0.741958\pi$
$32$	−2.07999	−	5.26057i	−0.367694	−	0.929947i
$33$	2.27681	−	2.27681i	0.396342	−	0.396342i
$34$	0.443560	−	5.41212i	0.0760699	−	0.928171i
$35$	1.22856	+	1.86833i	0.207664	+	0.315805i
$36$	6.02685	+	0.994562i	1.00447	+	0.165760i
$37$	4.15579	−	4.15579i	0.683208	−	0.683208i	−0.277513	−	0.960722i	$-0.589510\pi$
$37$	4.15579	−	4.15579i	0.683208	−	0.683208i	0.960722	+	0.277513i	$0.0895103\pi$
$38$	−0.00448005	+	0.00380134i	−0.000726761	+	0.000616658i
$39$	10.0462			1.60868
$40$	2.08742	+	5.97015i	0.330050	+	0.943964i
$41$	−2.28881			−0.357452			−0.178726	−	0.983899i	$-0.557198\pi$
$41$	−2.28881			−0.357452			−0.178726	+	0.983899i	$0.557198\pi$
$42$	−2.65328	+	2.25132i	−0.409411	+	0.347386i
$43$	−8.33507	+	8.33507i	−1.27109	+	1.27109i	−0.325568	+	0.945518i	$0.605556\pi$
$43$	−8.33507	+	8.33507i	−1.27109	+	1.27109i	−0.945518	+	0.325568i	$0.894444\pi$
$44$	−0.426140	+	2.58232i	−0.0642430	+	0.389300i
$45$	−6.68813	−	1.38167i	−0.997007	−	0.205968i
$46$	0.00643307	−	0.0784935i	0.000948505	−	0.0115732i
$47$	−1.03359	+	1.03359i	−0.150764	+	0.150764i	−0.778459	−	0.627695i	$-0.783998\pi$
$47$	−1.03359	+	1.03359i	−0.150764	+	0.150764i	0.627695	+	0.778459i	$0.283998\pi$
$48$	−8.82644	+	4.35440i	−1.27399	+	0.628504i
$49$		−	1.00000i		−	0.142857i
$50$	−2.06385	−	6.76317i	−0.291872	−	0.956457i
$51$	−9.44787			−1.32297
$52$	−6.63727	+	4.75697i	−0.920424	+	0.659673i
$53$	6.55677	+	6.55677i	0.900642	+	0.900642i	0.995492	−	0.0948499i	$-0.0302371\pi$
$53$	6.55677	+	6.55677i	0.900642	+	0.900642i	−0.0948499	+	0.995492i	$0.530237\pi$
$54$	0.0153998	−	0.187901i	0.00209564	−	0.0255701i
$55$	0.592005	−	2.86566i	0.0798259	−	0.386405i
$56$	0.686936	−	2.74374i	0.0917957	−	0.366648i
$57$	0.00722836	+	0.00722836i	0.000957419	+	0.000957419i
$58$	−8.94226	−	10.5389i	−1.17418	−	1.38382i
$59$			5.64348i			0.734718i	0.930079	+	0.367359i	$0.119738\pi$
$59$			5.64348i			0.734718i	−0.930079	+	0.367359i	$0.880262\pi$
$60$	10.0558	−	4.46812i	1.29820	−	0.576832i
$61$		−	8.63760i		−	1.10593i	−0.833204	−	0.552966i	$-0.813496\pi$
$61$		−	8.63760i		−	1.10593i	0.833204	−	0.552966i	$-0.186504\pi$
$62$	−8.70265	+	7.38422i	−1.10524	+	0.937797i
$63$	2.15963	+	2.15963i	0.272088	+	0.272088i
$64$	3.76955	−	7.05624i	0.471194	−	0.882030i
$65$	7.62830	−	5.01614i	0.946174	−	0.622175i
$66$	4.53841	+	0.371953i	0.558639	+	0.0457843i
$67$	0.465518	+	0.465518i	0.0568721	+	0.0568721i	0.734971	−	0.678099i	$-0.237196\pi$
$67$	0.465518	+	0.465518i	0.0568721	+	0.0568721i	−0.678099	+	0.734971i	$0.737196\pi$
$68$	6.24196	−	4.47365i	0.756949	−	0.542509i
$69$	−0.137025			−0.0164959
$70$	−0.890597	+	3.03428i	−0.106447	+	0.362665i
$71$		−	14.0140i		−	1.66316i	−0.555408	−	0.831578i	$-0.687438\pi$
$71$		−	14.0140i		−	1.66316i	0.555408	−	0.831578i	$-0.312562\pi$
$72$	4.44194	+	7.40900i	0.523488	+	0.873159i
$73$	6.82937	−	6.82937i	0.799317	−	0.799317i	−0.183671	−	0.982988i	$-0.558798\pi$
$73$	6.82937	−	6.82937i	0.799317	−	0.799317i	0.982988	+	0.183671i	$0.0587980\pi$
$74$	8.28382	+	0.678915i	0.962974	+	0.0789222i
$75$	−11.4343	+	4.53995i	−1.32032	+	0.524229i
$76$	−0.00819828	−	0.00135290i	−0.000940407	−	0.000155188i
$77$	−0.925336	+	0.925336i	−0.105452	+	0.105452i
$78$	9.19204	+	10.8332i	1.04079	+	1.22662i
$79$	1.48280			0.166828			0.0834138	−	0.996515i	$-0.473418\pi$
$79$	1.48280			0.166828			0.0834138	+	0.996515i	$0.473418\pi$
$80$	−4.52792	+	7.71349i	−0.506237	+	0.862394i
$81$	8.83452			0.981614
$82$	−2.09421	−	2.46812i	−0.231266	−	0.272558i
$83$	5.58822	−	5.58822i	0.613386	−	0.613386i	−0.330441	−	0.943827i	$-0.607197\pi$
$83$	5.58822	−	5.58822i	0.613386	−	0.613386i	0.943827	+	0.330441i	$0.107197\pi$
$84$	−4.85538	−	0.801245i	−0.529766	−	0.0874229i
$85$	−7.17396	+	4.71738i	−0.778126	+	0.511672i
$86$	−16.6144	−	1.36167i	−1.79158	−	0.146832i
$87$	−17.0040	+	17.0040i	−1.82302	+	1.82302i
$88$	−3.17453	+	1.90324i	−0.338406	+	0.202886i
$89$		−	12.7029i		−	1.34651i	−0.739411	−	0.673254i	$-0.764896\pi$
$89$		−	12.7029i		−	1.34651i	0.739411	−	0.673254i	$-0.235104\pi$
$90$	−4.62956	−	8.47628i	−0.487998	−	0.893479i
$91$	−4.08296			−0.428010
$92$	0.0905289	−	0.0648826i	0.00943829	−	0.00676447i
$93$	14.0413	+	14.0413i	1.45602	+	1.45602i
$94$	−2.06026	−	0.168852i	−0.212500	−	0.0174158i
$95$	0.00909781	+	0.00187948i	0.000933416	+	0.000192831i
$96$	−12.7715	−	5.53375i	−1.30349	−	0.564786i
$97$	0.598142	+	0.598142i	0.0607322	+	0.0607322i	0.736821	−	0.676088i	$-0.236326\pi$
$97$	0.598142	+	0.598142i	0.0607322	+	0.0607322i	−0.676088	+	0.736821i	$0.736326\pi$
$98$	1.07834	−	0.914975i	0.108929	−	0.0924265i
$99$		−	3.99677i		−	0.401691i
$100$	5.40464	−	8.41367i	0.540464	−	0.841367i
$101$		−	17.3572i		−	1.72711i	−0.504259	−	0.863553i	$-0.668234\pi$
$101$		−	17.3572i		−	1.72711i	0.504259	−	0.863553i	$-0.331766\pi$
$102$	−8.64456	−	10.1880i	−0.855939	−	1.00876i
$103$	3.33049	+	3.33049i	0.328163	+	0.328163i	0.851887	−	0.523725i	$-0.175458\pi$
$103$	3.33049	+	3.33049i	0.328163	+	0.328163i	−0.523725	+	0.851887i	$0.675458\pi$
$104$	−11.2026	−	2.80473i	−1.09850	−	0.275026i
$105$	5.38812	+	1.11311i	0.525827	+	0.108628i
$106$	−1.07115	+	13.0697i	−0.104039	+	1.26944i
$107$	11.1111	+	11.1111i	1.07415	+	1.07415i	0.997021	+	0.0771313i	$0.0245761\pi$
$107$	11.1111	+	11.1111i	1.07415	+	1.07415i	0.0771313	+	0.997021i	$0.475424\pi$
$108$	0.216712	−	0.155319i	0.0208531	−	0.0149455i
$109$	−8.49566			−0.813737			−0.406868	−	0.913487i	$-0.633379\pi$
$109$	−8.49566			−0.813737			−0.406868	+	0.913487i	$0.633379\pi$
$110$	3.63183	−	1.98362i	0.346281	−	0.189131i
$111$		−	14.4609i		−	1.37257i
$112$	3.58722	−	1.76970i	0.338960	−	0.167221i
$113$	5.83008	−	5.83008i	0.548448	−	0.548448i	−0.377544	−	0.925992i	$-0.623231\pi$
$113$	5.83008	−	5.83008i	0.548448	−	0.548448i	0.925992	+	0.377544i	$0.123231\pi$
$114$	−0.00118087	+	0.0144084i	−0.000110598	+	0.00134947i
$115$	−0.104046	+	0.0684175i	−0.00970234	+	0.00637996i
$116$	3.18255	−	19.2856i	0.295492	−	1.79062i
$117$	8.81768	−	8.81768i	0.815195	−	0.815195i
$118$	−6.08560	+	5.16364i	−0.560224	+	0.475352i
$119$	3.83978			0.351992
$120$	14.0190	+	6.75539i	1.27975	+	0.616680i
$121$	−9.28751			−0.844319
$122$	9.31428	−	7.90319i	0.843275	−	0.715521i
$123$	−3.98219	+	3.98219i	−0.359062	+	0.359062i
$124$	−15.9254	−	2.62804i	−1.43014	−	0.236005i
$125$	−6.41548	+	9.15651i	−0.573818	+	0.818983i
$126$	−0.352810	+	4.30483i	−0.0314308	+	0.383505i
$127$	−8.28915	+	8.28915i	−0.735543	+	0.735543i	−0.971712	−	0.236169i	$-0.924108\pi$
$127$	−8.28915	+	8.28915i	−0.735543	+	0.735543i	0.236169	+	0.971712i	$0.424108\pi$
$128$	11.0581	−	2.39142i	0.977405	−	0.211374i
$129$			29.0036i			2.55363i
$130$	12.3888	+	3.63627i	1.08657	+	0.318922i
$131$	15.9462			1.39323			0.696614	−	0.717446i	$-0.254689\pi$
$131$	15.9462			1.39323			0.696614	+	0.717446i	$0.254689\pi$
$132$	3.75144	+	5.23428i	0.326521	+	0.455586i
$133$	−0.00293773	−	0.00293773i	−0.000254734	−	0.000254734i
$134$	−0.0760497	+	0.927925i	−0.00656969	+	0.0801605i
$135$	−0.249070	+	0.163781i	−0.0214365	+	0.0140960i
$136$	10.5354	+	2.63768i	0.903399	+	0.226179i
$137$	2.37062	+	2.37062i	0.202536	+	0.202536i	0.801086	−	0.598550i	$-0.204256\pi$
$137$	2.37062	+	2.37062i	0.202536	+	0.202536i	−0.598550	+	0.801086i	$0.704256\pi$
$138$	−0.125375	−	0.147760i	−0.0106726	−	0.0125781i
$139$			18.6915i			1.58539i	0.609616	+	0.792697i	$0.291323\pi$
$139$			18.6915i			1.58539i	−0.609616	+	0.792697i	$0.708677\pi$
$140$	−4.08686	+	1.81592i	−0.345403	+	0.153473i
$141$			3.59657i			0.302886i
$142$	15.1119	−	12.8225i	1.26816	−	1.07604i
$143$	3.77811	+	3.77811i	0.315941	+	0.315941i
$144$	−3.92516	+	11.5690i	−0.327097	+	0.964082i
$145$	−4.42128	+	21.4017i	−0.367168	+	1.77731i
$146$	13.6131	+	1.11569i	1.12663	+	0.0923348i
$147$	−1.73985	−	1.73985i	−0.143501	−	0.143501i
$148$	6.84739	+	9.55397i	0.562852	+	0.785331i
$149$	7.09531			0.581270			0.290635	−	0.956834i	$-0.406133\pi$
$149$	7.09531			0.581270			0.290635	+	0.956834i	$0.406133\pi$
$150$	−15.3577	−	8.17614i	−1.25395	−	0.667579i
$151$		−	11.9219i		−	0.970188i	−0.874462	−	0.485094i	$-0.838785\pi$
$151$		−	11.9219i		−	0.970188i	0.874462	−	0.485094i	$-0.161215\pi$
$152$	−0.00604234	−	0.0100784i	−0.000490098	−	0.000817467i
$153$	−8.29250	+	8.29250i	−0.670409	+	0.670409i
$154$	−1.84449	−	0.151168i	−0.148633	−	0.0121815i
$155$	17.6728	+	3.65095i	1.41951	+	0.293251i
$156$	−3.27145	+	19.8243i	−0.261925	+	1.58721i
$157$	11.7561	−	11.7561i	0.938238	−	0.938238i	−0.0599622	−	0.998201i	$-0.519098\pi$
$157$	11.7561	−	11.7561i	0.938238	−	0.938238i	0.998201	+	0.0599622i	$0.0190980\pi$
$158$	1.35672	+	1.59896i	0.107935	+	0.127206i
$159$	22.8156			1.80940
$160$	−12.4607	+	2.17501i	−0.985106	+	0.171949i
$161$	0.0556894			0.00438894
$162$	8.08337	+	9.52663i	0.635090	+	0.748483i
$163$	0.503911	−	0.503911i	0.0394694	−	0.0394694i	−0.687097	−	0.726566i	$-0.741115\pi$
$163$	0.503911	−	0.503911i	0.0394694	−	0.0394694i	0.726566	+	0.687097i	$0.241115\pi$
$164$	0.745328	−	4.51654i	0.0582003	−	0.352682i
$165$	−3.95582	−	6.01583i	−0.307961	−	0.468332i
$166$	11.1391	+	0.912923i	0.864560	+	0.0708566i
$167$	−6.38768	+	6.38768i	−0.494294	+	0.494294i	−0.909656	−	0.415362i	$-0.863655\pi$
$167$	−6.38768	+	6.38768i	−0.494294	+	0.494294i	0.415362	+	0.909656i	$0.363655\pi$
$168$	−3.57854	−	5.96888i	−0.276090	−	0.460509i
$169$			3.67053i			0.282348i
$170$	−11.6509	−	3.41970i	−0.893587	−	0.262279i
$171$	0.0126888			0.000970339
$172$	−13.7335	−	19.1619i	−1.04717	−	1.46108i
$173$	6.93068	+	6.93068i	0.526930	+	0.526930i	0.919656	−	0.392726i	$-0.128468\pi$
$173$	6.93068	+	6.93068i	0.526930	+	0.526930i	−0.392726	+	0.919656i	$0.628468\pi$
$174$	−33.8943	−	2.77787i	−2.56952	−	0.210590i
$175$	4.64710	−	1.84512i	0.351288	−	0.139478i
$176$	−4.95696	−	1.68181i	−0.373645	−	0.126771i
$177$	9.81883	+	9.81883i	0.738028	+	0.738028i
$178$	13.6981	−	11.6229i	1.02672	−	0.871171i
$179$		−	18.9475i		−	1.41620i	−0.706110	−	0.708102i	$-0.749552\pi$
$179$		−	18.9475i		−	1.41620i	0.706110	−	0.708102i	$-0.250448\pi$
$180$	4.90439	−	12.7478i	0.365552	−	0.950167i
$181$			19.1043i			1.42001i	0.704196	+	0.710005i	$0.251307\pi$
$181$			19.1043i			1.42001i	−0.704196	+	0.710005i	$0.748693\pi$
$182$	−3.73580	−	4.40282i	−0.276916	−	0.326359i
$183$	−15.0282	−	15.0282i	−1.11091	−	1.11091i
$184$	0.152797	+	0.0382551i	0.0112644	+	0.00282020i
$185$	−7.22044	−	10.9805i	−0.530858	−	0.807303i
$186$	−2.29387	+	27.9888i	−0.168195	+	2.05224i
$187$	−3.55308	−	3.55308i	−0.259827	−	0.259827i
$188$	−1.70301	−	2.37616i	−0.124205	−	0.173299i
$189$	0.133312			0.00969699
$190$	0.00629755	+	0.0115302i	0.000456872	+	0.000836490i
$191$		−	10.9982i		−	0.795802i	−0.917428	−	0.397901i	$-0.869739\pi$
$191$		−	10.9982i		−	0.795802i	0.917428	−	0.397901i	$-0.130261\pi$
$192$	−5.71835	−	18.8353i	−0.412686	−	1.35932i
$193$	−13.4833	+	13.4833i	−0.970550	+	0.970550i	−0.999579	−	0.0290287i	$-0.990759\pi$
$193$	−13.4833	+	13.4833i	−0.970550	+	0.970550i	0.0290287	+	0.999579i	$0.490759\pi$
$194$	−0.0977160	+	1.19229i	−0.00701560	+	0.0856012i
$195$	4.54478	−	21.9995i	0.325459	−	1.57541i
$196$	1.97331	+	0.325640i	0.140951	+	0.0232600i
$197$	−7.77593	+	7.77593i	−0.554012	+	0.554012i	−0.927596	−	0.373584i	$-0.878129\pi$
$197$	−7.77593	+	7.77593i	−0.554012	+	0.554012i	0.373584	+	0.927596i	$0.378129\pi$
$198$	4.30988	−	3.65695i	0.306290	−	0.259888i
$199$	0.858420			0.0608517			0.0304259	−	0.999537i	$-0.490314\pi$
$199$	0.858420			0.0608517			0.0304259	+	0.999537i	$0.490314\pi$
$200$	14.0179	−	1.87026i	0.991217	−	0.132247i
$201$	1.61987			0.114257
$202$	18.7170	−	15.8814i	1.31692	−	1.11741i
$203$	6.91071	−	6.91071i	0.485037	−	0.485037i
$204$	3.07660	−	18.6436i	0.215405	−	1.30531i
$205$	−1.03543	+	5.01210i	−0.0723175	+	0.350060i
$206$	−0.544087	+	6.63871i	−0.0379084	+	0.462541i
$207$	−0.120269	+	0.120269i	−0.00835924	+	0.00835924i
$208$	−7.22562	−	14.6465i	−0.501007	−	1.01555i
$209$			0.00543678i			0.000376070i
$210$	3.72969	+	6.82871i	0.257373	+	0.471225i
$211$	0.628748			0.0432848			0.0216424	−	0.999766i	$-0.493110\pi$
$211$	0.628748			0.0432848			0.0216424	+	0.999766i	$0.493110\pi$
$212$	−15.0737	+	10.8034i	−1.03527	+	0.741981i
$213$	−24.3823	−	24.3823i	−1.67065	−	1.67065i
$214$	−1.81518	+	22.1480i	−0.124083	+	1.51400i
$215$	14.4817	+	22.0231i	0.987643	+	1.50196i
$216$	0.365773	+	0.0915766i	0.0248877	+	0.00623100i
$217$	−5.70663	−	5.70663i	−0.387392	−	0.387392i
$218$	−7.77332	−	9.16122i	−0.526476	−	0.620476i
$219$		−	23.7642i		−	1.60584i
$220$	5.46206	+	2.10138i	0.368252	+	0.141675i
$221$		−	15.6776i		−	1.05459i
$222$	15.5938	−	13.2314i	1.04659	−	0.888034i
$223$	1.17864	+	1.17864i	0.0789273	+	0.0789273i	0.745468	−	0.666541i	$-0.232226\pi$
$223$	1.17864	+	1.17864i	0.0789273	+	0.0789273i	−0.666541	+	0.745468i	$0.732226\pi$
$224$	5.19056	+	2.24901i	0.346809	+	0.150268i
$225$	−6.05125	+	14.0208i	−0.403417	+	0.934720i
$226$	11.6212	+	0.952435i	0.773030	+	0.0633550i
$227$	2.26573	+	2.26573i	0.150382	+	0.150382i	0.778289	−	0.627907i	$-0.216088\pi$
$227$	2.26573	+	2.26573i	0.150382	+	0.150382i	−0.627907	+	0.778289i	$0.716088\pi$
$228$	−0.0166176	+	0.0119100i	−0.00110053	+	0.000788756i
$229$	−2.29139			−0.151419			−0.0757096	−	0.997130i	$-0.524122\pi$
$229$	−2.29139			−0.151419			−0.0757096	+	0.997130i	$0.524122\pi$
$230$	−0.168977	−	0.0495968i	−0.0111420	−	0.00327032i
$231$			3.21990i			0.211854i
$232$	23.7084	−	14.2140i	1.55653	−	0.933194i
$233$	−6.39463	+	6.39463i	−0.418926	+	0.418926i	−0.884834	−	0.465907i	$-0.845728\pi$
$233$	−6.39463	+	6.39463i	−0.418926	+	0.418926i	0.465907	+	0.884834i	$0.345728\pi$
$234$	17.5764	+	1.44051i	1.14901	+	0.0941689i
$235$	1.79579	+	2.73095i	0.117145	+	0.178148i
$236$	−11.1363	−	1.83774i	−0.724914	−	0.119627i
$237$	2.57985	−	2.57985i	0.167579	−	0.167579i
$238$	3.51330	+	4.14059i	0.227734	+	0.268395i
$239$	−20.3556			−1.31670			−0.658349	−	0.752713i	$-0.728745\pi$
$239$	−20.3556			−1.31670			−0.658349	+	0.752713i	$0.728745\pi$
$240$	5.54241	+	21.2983i	0.357761	+	1.37480i
$241$	−17.1419			−1.10421			−0.552103	−	0.833776i	$-0.686175\pi$
$241$	−17.1419			−1.10421			−0.552103	+	0.833776i	$0.686175\pi$
$242$	−8.49784	−	10.0151i	−0.546262	−	0.643795i
$243$	15.6536	−	15.6536i	1.00418	−	1.00418i
$244$	17.0447	+	2.81275i	1.09117	+	0.180068i
$245$	−2.18983	−	0.452388i	−0.139903	−	0.0289020i
$246$	−7.93778	−	0.650554i	−0.506094	−	0.0414778i
$247$	−0.0119946	+	0.0119946i	−0.000763199	+	0.000763199i
$248$	−11.7374	−	19.5776i	−0.745328	−	1.24318i
$249$		−	19.4454i		−	1.23230i
$250$	−15.7438	+	1.45990i	−0.995728	+	0.0923321i
$251$	−1.64403			−0.103770			−0.0518850	−	0.998653i	$-0.516523\pi$
$251$	−1.64403			−0.103770			−0.0518850	+	0.998653i	$0.516523\pi$
$252$	−4.96489	+	3.55836i	−0.312759	+	0.224156i
$253$	−0.0515314	−	0.0515314i	−0.00323975	−	0.00323975i
$254$	−16.5229	−	1.35416i	−1.03674	−	0.0849678i
$255$	−4.27410	+	20.6892i	−0.267654	+	1.29561i
$256$	12.6966	+	9.73629i	0.793540	+	0.608518i
$257$	−8.79733	−	8.79733i	−0.548763	−	0.548763i	0.377320	−	0.926083i	$-0.376846\pi$
$257$	−8.79733	−	8.79733i	−0.548763	−	0.548763i	−0.926083	+	0.377320i	$0.876846\pi$
$258$	−31.2758	+	26.5376i	−1.94715	+	1.65216i
$259$			5.87718i			0.365190i
$260$	7.41433	+	16.6865i	0.459817	+	1.03485i
$261$			29.8492i			1.84762i
$262$	14.5904	+	17.1955i	0.901398	+	1.06234i
$263$	−7.81481	−	7.81481i	−0.481882	−	0.481882i	0.423850	−	0.905732i	$-0.360678\pi$
$263$	−7.81481	−	7.81481i	−0.481882	−	0.481882i	−0.905732	+	0.423850i	$0.860678\pi$
$264$	−2.21187	+	8.83457i	−0.136131	+	0.543730i
$265$	17.3244	−	11.3920i	1.06423	−	0.699805i
$266$	0.000479925	−	0.00585583i	2.94261e−5	−	0.000359044i
$267$	−22.1012	−	22.1012i	−1.35257	−	1.35257i
$268$	−1.07020	+	0.767021i	−0.0653730	+	0.0468532i
$269$	−0.703190			−0.0428743			−0.0214371	−	0.999770i	$-0.506824\pi$
$269$	−0.703190			−0.0428743			−0.0214371	+	0.999770i	$0.506824\pi$
$270$	−0.404504	−	0.118727i	−0.0246173	−	0.00722549i
$271$			9.22447i			0.560347i	0.959949	+	0.280173i	$0.0903919\pi$
$271$			9.22447i			0.560347i	−0.959949	+	0.280173i	$0.909608\pi$
$272$	6.79527	+	13.7741i	0.412024	+	0.835179i
$273$	−7.10374	+	7.10374i	−0.429938	+	0.429938i
$274$	−0.387278	+	4.72540i	−0.0233963	+	0.285472i
$275$	−6.00748	−	2.59278i	−0.362265	−	0.156350i
$276$	0.0446208	−	0.270393i	0.00268586	−	0.0162758i
$277$	0.316910	−	0.316910i	0.0190413	−	0.0190413i	−0.697522	−	0.716563i	$-0.745714\pi$
$277$	0.316910	−	0.316910i	0.0190413	−	0.0190413i	0.716563	+	0.697522i	$0.245714\pi$
$278$	−20.1558	+	17.1023i	−1.20887	+	1.02573i
$279$	24.6485			1.47566
$280$	−5.69756	−	2.74551i	−0.340494	−	0.164075i
$281$	−23.4150			−1.39682			−0.698410	−	0.715698i	$-0.746109\pi$
$281$	−23.4150			−1.39682			−0.698410	+	0.715698i	$0.746109\pi$
$282$	−3.87833	+	3.29078i	−0.230951	+	0.195963i
$283$	−0.717892	+	0.717892i	−0.0426743	+	0.0426743i	−0.728122	−	0.685448i	$-0.759607\pi$
$283$	−0.717892	+	0.717892i	−0.0426743	+	0.0426743i	0.685448	+	0.728122i	$0.259607\pi$
$284$	27.6540	+	4.56352i	1.64096	+	0.270795i
$285$	0.0190989	−	0.0125588i	0.00113132	−	0.000743921i
$286$	−0.617213	+	7.53096i	−0.0364966	+	0.445315i
$287$	1.61843	−	1.61843i	0.0955331	−	0.0955331i
$288$	−16.0667	+	6.35267i	−0.946742	+	0.374335i
$289$		−	2.25611i		−	0.132712i
$290$	−27.1237	+	14.8143i	−1.59276	+	0.869929i
$291$	2.08136			0.122012
$292$	11.2526	+	15.7004i	0.658506	+	0.918796i
$293$	23.4122	+	23.4122i	1.36776	+	1.36776i	0.863630	+	0.504126i	$0.168185\pi$
$293$	23.4122	+	23.4122i	1.36776	+	1.36776i	0.504126	+	0.863630i	$0.331815\pi$
$294$	0.284233	−	3.46808i	0.0165768	−	0.202262i
$295$	12.3582	+	2.55304i	0.719525	+	0.148644i
$296$	−4.03725	+	16.1255i	−0.234660	+	0.937274i
$297$	−0.123358	−	0.123358i	−0.00715796	−	0.00715796i
$298$	6.49204	+	7.65117i	0.376074	+	0.443220i
$299$		−	0.227377i		−	0.0131496i
$300$	−5.23528	−	24.0418i	−0.302259	−	1.38806i
$301$		−	11.7876i		−	0.679425i
$302$	12.8558	−	10.9082i	0.739771	−	0.627697i
$303$	−30.1990	−	30.1990i	−1.73489	−	1.73489i
$304$	0.00533937	−	0.0157372i	0.000306234	−	0.000902590i
$305$	−18.9149	−	3.90754i	−1.08306	−	0.223745i
$306$	−16.5296	−	1.35471i	−0.944934	−	0.0774437i
$307$	−18.0726	−	18.0726i	−1.03146	−	1.03146i	−0.999489	−	0.0319699i	$-0.989822\pi$
$307$	−18.0726	−	18.0726i	−1.03146	−	1.03146i	−0.0319699	−	0.999489i	$-0.510178\pi$
$308$	−1.52465	−	2.12730i	−0.0868750	−	0.121214i
$309$	11.5891			0.659282
$310$	12.2332	+	22.3978i	0.694799	+	1.27211i
$311$		−	17.1402i		−	0.971932i	−0.873978	−	0.485966i	$-0.838468\pi$
$311$		−	17.1402i		−	0.971932i	0.873978	−	0.485966i	$-0.161532\pi$
$312$	−24.3707	+	14.6110i	−1.37972	+	0.827186i
$313$	3.24238	−	3.24238i	0.183270	−	0.183270i	−0.609509	−	0.792779i	$-0.708633\pi$
$313$	3.24238	−	3.24238i	0.183270	−	0.183270i	0.792779	+	0.609509i	$0.208633\pi$
$314$	23.4336	+	1.92054i	1.32244	+	0.108383i
$315$	5.70621	−	3.75223i	0.321509	−	0.211414i
$316$	−0.482857	+	2.92602i	−0.0271628	+	0.164601i
$317$	−4.46728	+	4.46728i	−0.250908	+	0.250908i	−0.821343	−	0.570435i	$-0.806775\pi$
$317$	−4.46728	+	4.46728i	−0.250908	+	0.250908i	0.570435	+	0.821343i	$0.306775\pi$
$318$	20.8757	+	24.6030i	1.17065	+	1.37967i
$319$	−12.7895			−0.716072
$320$	−13.7466	−	11.4468i	−0.768461	−	0.639897i
$321$	38.6634			2.15798
$322$	0.0509544	+	0.0600521i	0.00283958	+	0.00334657i
$323$	0.0112802	−	0.0112802i	0.000627649	−	0.000627649i
$324$	−2.87687	+	17.4333i	−0.159826	+	0.968515i
$325$	−7.53353	−	18.9739i	−0.417885	−	1.05248i
$326$	1.00445	+	0.0823218i	0.0556316	+	0.00455938i
$327$	−14.7812	+	14.7812i	−0.817403	+	0.817403i
$328$	5.55232	−	3.32880i	0.306576	−	0.183802i
$329$		−	1.46171i		−	0.0805867i
$330$	2.86763	−	9.77006i	0.157858	−	0.537824i
$331$	−14.3494			−0.788717			−0.394358	−	0.918957i	$-0.629033\pi$
$331$	−14.3494			−0.788717			−0.394358	+	0.918957i	$0.629033\pi$
$332$	9.20754	+	12.8470i	0.505330	+	0.705073i
$333$	−12.6925	−	12.6925i	−0.695547	−	0.695547i
$334$	−12.7327	−	1.04353i	−0.696701	−	0.0570993i
$335$	1.23000	−	0.808809i	0.0672020	−	0.0441900i
$336$	3.16221	−	9.32026i	0.172513	−	0.508462i
$337$	11.8774	+	11.8774i	0.647002	+	0.647002i	0.952267	−	0.305265i	$-0.0987451\pi$
$337$	11.8774	+	11.8774i	0.647002	+	0.647002i	−0.305265	+	0.952267i	$0.598745\pi$
$338$	−3.95808	+	3.35844i	−0.215291	+	0.182675i
$339$		−	20.2870i		−	1.10184i
$340$	−6.97273	−	15.6926i	−0.378150	−	0.851053i
$341$			10.5611i			0.571916i
$342$	0.0116100	+	0.0136829i	0.000627795	+	0.000739886i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	8.09731	−	32.3421i	0.436578	−	1.74377i
$345$	−0.0619884	+	0.300061i	−0.00333735	+	0.0161548i
$346$	−1.13224	+	13.8150i	−0.0608694	+	0.742701i
$347$	9.16983	+	9.16983i	0.492262	+	0.492262i	0.909018	−	0.416756i	$-0.136833\pi$
$347$	9.16983	+	9.16983i	0.492262	+	0.492262i	−0.416756	+	0.909018i	$0.636833\pi$
$348$	−28.0170	−	39.0913i	−1.50187	−	2.09551i
$349$	29.4132			1.57445			0.787226	−	0.616664i	$-0.211516\pi$
$349$	29.4132			1.57445			0.787226	+	0.616664i	$0.211516\pi$
$350$	6.24165	+	3.32292i	0.333630	+	0.177618i
$351$		−	0.544305i		−	0.0290529i
$352$	−2.72193	−	6.88411i	−0.145079	−	0.366924i
$353$	11.5202	−	11.5202i	0.613160	−	0.613160i	−0.330608	−	0.943768i	$-0.607254\pi$
$353$	11.5202	−	11.5202i	0.613160	−	0.613160i	0.943768	+	0.330608i	$0.107254\pi$
$354$	−1.60406	+	19.5720i	−0.0852548	+	1.04024i
$355$	−30.6882	−	6.33976i	−1.62876	−	0.336480i
$356$	25.0669	+	4.13658i	1.32854	+	0.219238i
$357$	6.68065	−	6.68065i	0.353577	−	0.353577i
$358$	20.4319	−	17.3365i	1.07986	−	0.916263i
$359$	−4.21843			−0.222640			−0.111320	−	0.993785i	$-0.535508\pi$
$359$	−4.21843			−0.222640			−0.111320	+	0.993785i	$0.535508\pi$
$360$	18.2339	−	6.37535i	0.961012	−	0.336010i
$361$	19.0000			0.999999
$362$	−20.6009	+	17.4800i	−1.08276	+	0.918726i
$363$	−16.1589	+	16.1589i	−0.848122	+	0.848122i
$364$	1.32957	−	8.05694i	0.0696885	−	0.422299i
$365$	−11.8656	−	18.0447i	−0.621075	−	0.944501i
$366$	2.45509	−	29.9559i	0.128329	−	1.56582i
$367$	20.2745	−	20.2745i	1.05832	−	1.05832i	0.0601290	−	0.998191i	$-0.480849\pi$
$367$	20.2745	−	20.2745i	1.05832	−	1.05832i	0.998191	−	0.0601290i	$-0.0191512\pi$
$368$	0.0985537	+	0.199770i	0.00513747	+	0.0104137i
$369$			6.99044i			0.363908i
$370$	5.23420	−	17.8330i	0.272113	−	0.927093i
$371$	−9.27267			−0.481413
$372$	−32.2803	+	23.1355i	−1.67366	+	1.19952i
$373$	1.06359	+	1.06359i	0.0550708	+	0.0550708i	0.734106	−	0.679035i	$-0.237602\pi$
$373$	1.06359	+	1.06359i	0.0550708	+	0.0550708i	−0.679035	+	0.734106i	$0.737602\pi$
$374$	0.580452	−	7.08242i	0.0300145	−	0.366223i
$375$	4.76898	+	27.0930i	0.246269	+	1.39908i
$376$	1.00410	−	4.01056i	0.0517826	−	0.206829i
$377$	−28.2161	−	28.2161i	−1.45320	−	1.45320i
$378$	0.121977	+	0.143755i	0.00627381	+	0.00739398i
$379$		−	10.0709i		−	0.517308i	−0.965970	−	0.258654i	$-0.916721\pi$
$379$		−	10.0709i		−	0.517308i	0.965970	−	0.258654i	$-0.0832789\pi$
$380$	−0.00667141	+	0.0173408i	−0.000342236	+	0.000889563i
$381$			28.8438i			1.47771i
$382$	11.8598	−	10.0631i	0.606801	−	0.514872i
$383$	11.9937	+	11.9937i	0.612851	+	0.612851i	0.943688	−	0.330837i	$-0.107331\pi$
$383$	11.9937	+	11.9937i	0.612851	+	0.612851i	−0.330837	+	0.943688i	$0.607331\pi$
$384$	15.0787	−	23.4002i	0.769483	−	1.19413i
$385$	1.60772	+	2.44494i	0.0819368	+	0.124606i
$386$	−26.8765	−	2.20271i	−1.36798	−	0.112115i
$387$	25.4568	+	25.4568i	1.29404	+	1.29404i
$388$	−1.37510	+	0.985542i	−0.0698101	+	0.0500333i
$389$	−10.8885			−0.552067			−0.276034	−	0.961148i	$-0.589020\pi$
$389$	−10.8885			−0.552067			−0.276034	+	0.961148i	$0.589020\pi$
$390$	27.8813	−	15.2282i	1.41182	−	0.771107i
$391$			0.213835i			0.0108141i
$392$	1.45438	+	2.42586i	0.0734573	+	0.122524i
$393$	27.7441	−	27.7441i	1.39950	−	1.39950i
$394$	−15.4999	−	1.27032i	−0.780873	−	0.0639979i
$395$	0.670798	−	3.24707i	0.0337515	−	0.163378i
$396$	7.88687	+	1.30151i	0.396330	+	0.0654032i
$397$	−5.39736	+	5.39736i	−0.270886	+	0.270886i	−0.829457	−	0.558571i	$-0.811350\pi$
$397$	−5.39736	+	5.39736i	−0.270886	+	0.270886i	0.558571	+	0.829457i	$0.311350\pi$
$398$	0.785433	+	0.925669i	0.0393702	+	0.0463996i
$399$	−0.0102224			−0.000511762
$400$	14.8428	+	13.4049i	0.742142	+	0.670243i
$401$	−6.89076			−0.344108			−0.172054	−	0.985088i	$-0.555040\pi$
$401$	−6.89076			−0.344108			−0.172054	+	0.985088i	$0.555040\pi$
$402$	1.48214	+	1.74677i	0.0739223	+	0.0871209i
$403$	−23.2999	+	23.2999i	−1.16065	+	1.16065i
$404$	34.2512	+	5.65219i	1.70406	+	0.281207i
$405$	3.99663	−	19.3461i	0.198594	−	0.961315i
$406$	13.7752	+	1.12897i	0.683653	+	0.0560300i
$407$	5.43837	−	5.43837i	0.269570	−	0.269570i
$408$	22.9192	−	13.7408i	1.13467	−	0.680271i
$409$			9.40345i			0.464971i	0.972600	+	0.232485i	$0.0746858\pi$
$409$			9.40345i			0.464971i	−0.972600	+	0.232485i	$0.925314\pi$
$410$	−6.35215	+	3.46940i	−0.313710	+	0.171342i
$411$	8.24907			0.406897
$412$	−7.65663	+	5.48755i	−0.377215	+	0.270352i
$413$	−3.99054	−	3.99054i	−0.196362	−	0.196362i
$414$	−0.239733	−	0.0196478i	−0.0117822	−	0.000965635i
$415$	−9.70919	−	14.7653i	−0.476605	−	0.724798i
$416$	9.18261	−	21.1928i	0.450215	−	1.03906i
$417$	32.5205	+	32.5205i	1.59254	+	1.59254i
$418$	−0.00586270	+	0.00497452i	−0.000286754	+	0.000243312i
$419$			33.7007i			1.64639i	0.567760	+	0.823194i	$0.307810\pi$
$419$			33.7007i			1.64639i	−0.567760	+	0.823194i	$0.692190\pi$
$420$	−3.95110	+	10.2700i	−0.192794	+	0.501123i
$421$			28.0664i			1.36787i	0.729541	+	0.683937i	$0.239734\pi$
$421$			28.0664i			1.36787i	−0.729541	+	0.683937i	$0.760266\pi$
$422$	0.575289	+	0.678005i	0.0280046	+	0.0330048i
$423$	3.15676	+	3.15676i	0.153487	+	0.153487i
$424$	−25.4418	−	6.36974i	−1.23556	−	0.309342i
$425$	7.08484	+	17.8438i	0.343665	+	0.865553i
$426$	3.98323	−	48.6017i	0.192988	−	2.35476i
$427$	6.10770	+	6.10770i	0.295572	+	0.295572i
$428$	−25.5439	+	18.3075i	−1.23471	+	0.884925i
$429$	13.1467			0.634729
$430$	−10.4980	+	35.7668i	−0.506258	+	1.72483i
$431$			30.0844i			1.44912i	0.689214	+	0.724558i	$0.257956\pi$
$431$			30.0844i			1.44912i	−0.689214	+	0.724558i	$0.742044\pi$
$432$	0.235922	+	0.478218i	0.0113508	+	0.0230083i
$433$	−14.8121	+	14.8121i	−0.711823	+	0.711823i	−0.966916	−	0.255094i	$-0.917894\pi$
$433$	−14.8121	+	14.8121i	−0.711823	+	0.711823i	0.255094	+	0.966916i	$0.417894\pi$
$434$	0.932269	−	11.3751i	0.0447503	−	0.546024i
$435$	29.5434	+	44.9282i	1.41650	+	2.15414i
$436$	2.76653	−	16.7646i	0.132493	−	0.802878i
$437$	0.000163600	0	0.000163600i	7.82606e−6	0	7.82606e-6i
$438$	25.6259	−	21.7437i	1.22445	−	1.03895i
$439$	−20.4630			−0.976646			−0.488323	−	0.872663i	$-0.662391\pi$
$439$	−20.4630			−0.976646			−0.488323	+	0.872663i	$0.662391\pi$
$440$	2.73164	+	7.81268i	0.130226	+	0.372455i
$441$	−3.05418			−0.145437
$442$	16.9058	−	14.3447i	0.804129	−	0.682306i
$443$	18.8504	−	18.8504i	0.895608	−	0.895608i	−0.0994359	−	0.995044i	$-0.531704\pi$
$443$	18.8504	−	18.8504i	0.895608	−	0.895608i	0.995044	+	0.0994359i	$0.0317038\pi$
$444$	28.5360	+	4.70906i	1.35426	+	0.223482i
$445$	−27.8172	−	5.74665i	−1.31866	−	0.272417i
$446$	−0.192549	+	2.34940i	−0.00911745	+	0.111247i
$447$	12.3448	−	12.3448i	0.583889	−	0.583889i
$448$	2.32404	+	7.65499i	0.109800	+	0.361664i
$449$			20.0989i			0.948527i	0.880383	+	0.474264i	$0.157286\pi$
$449$			20.0989i			0.948527i	−0.880383	+	0.474264i	$0.842714\pi$
$450$	−20.6560	+	6.30337i	−0.973731	+	0.297144i
$451$	−2.99519			−0.141038
$452$	9.60606	+	13.4031i	0.451831	+	0.630427i
$453$	−20.7423	−	20.7423i	−0.974559	−	0.974559i
$454$	−0.370143	+	4.51632i	−0.0173717	+	0.211961i
$455$	−1.84708	+	8.94097i	−0.0865924	+	0.419159i
$456$	−0.0280477	−	0.00702217i	−0.00131346	−	0.000328843i
$457$	−7.09629	−	7.09629i	−0.331950	−	0.331950i	0.521376	−	0.853327i	$-0.325419\pi$
$457$	−7.09629	−	7.09629i	−0.331950	−	0.331950i	−0.853327	+	0.521376i	$0.825419\pi$
$458$	−2.09657	−	2.47090i	−0.0979661	−	0.115458i
$459$			0.511887i			0.0238928i
$460$	−0.101127	−	0.227595i	−0.00471509	−	0.0106117i
$461$		−	16.8451i		−	0.784557i	−0.919847	−	0.392278i	$-0.871687\pi$
$461$		−	16.8451i		−	0.784557i	0.919847	−	0.392278i	$-0.128313\pi$
$462$	−3.47215	+	2.94613i	−0.161539	+	0.137066i
$463$	9.74924	+	9.74924i	0.453086	+	0.453086i	0.896377	−	0.443292i	$-0.146189\pi$
$463$	9.74924	+	9.74924i	0.453086	+	0.453086i	−0.443292	+	0.896377i	$0.646189\pi$
$464$	37.0202	+	12.5603i	1.71862	+	0.583098i
$465$	37.1002	−	24.3959i	1.72048	−	1.13133i
$466$	−12.7465	−	1.04466i	−0.590472	−	0.0483931i
$467$	13.2412	+	13.2412i	0.612730	+	0.612730i	0.943656	−	0.330927i	$-0.107361\pi$
$467$	13.2412	+	13.2412i	0.612730	+	0.612730i	−0.330927	+	0.943656i	$0.607361\pi$
$468$	14.5286	+	20.2714i	0.671587	+	0.937047i
$469$	−0.658342			−0.0303994
$470$	−1.30180	+	4.43523i	−0.0600473	+	0.204582i
$471$		−	40.9078i		−	1.88493i
$472$	−8.20777	−	13.6903i	−0.377793	−	0.630146i
$473$	−10.9075	+	10.9075i	−0.501526	+	0.501526i
$474$	5.14245	+	0.421459i	0.236201	+	0.0193582i
$475$	0.00823147	−	0.0190724i	0.000377686	−	0.000875101i
$476$	−1.25038	+	7.57708i	−0.0573113	+	0.347295i
$477$	20.0256	−	20.0256i	0.916907	−	0.916907i
$478$	−18.6249	−	21.9503i	−0.851884	−	1.00398i
$479$	16.4802			0.753000			0.376500	−	0.926417i	$-0.377127\pi$
$479$	16.4802			0.753000			0.376500	+	0.926417i	$0.377127\pi$
$480$	−17.8956	+	25.4640i	−0.816820	+	1.16227i
$481$	23.9963			1.09414
$482$	−15.6844	−	18.4848i	−0.714405	−	0.841960i
$483$	0.0968913	−	0.0968913i	0.00440871	−	0.00440871i
$484$	3.02438	−	18.3271i	0.137472	−	0.833052i
$485$	1.58042	−	1.03924i	0.0717632	−	0.0471893i
$486$	31.2025	+	2.55726i	1.41538	+	0.116000i
$487$	−14.9145	+	14.9145i	−0.675839	+	0.675839i	−0.959056	−	0.283217i	$-0.908598\pi$
$487$	−14.9145	+	14.9145i	−0.675839	+	0.675839i	0.283217	+	0.959056i	$0.408598\pi$
$488$	12.5624	+	20.9536i	0.568671	+	0.948523i
$489$		−	1.75346i		−	0.0792943i
$490$	−1.51581	−	2.77531i	−0.0684773	−	0.125376i
$491$	10.6844			0.482182			0.241091	−	0.970503i	$-0.422495\pi$
$491$	10.6844			0.482182			0.241091	+	0.970503i	$0.422495\pi$
$492$	−6.56135	−	9.15487i	−0.295809	−	0.412733i
$493$	26.5356	+	26.5356i	1.19510	+	1.19510i
$494$	−0.0239091	−	0.00195951i	−0.00107572	−	8.81626e-5i
$495$	−8.75224	−	1.80809i	−0.393384	−	0.0812676i
$496$	10.3719	−	30.5700i	0.465712	−	1.37263i
$497$	9.90939	+	9.90939i	0.444497	+	0.444497i
$498$	20.9687	−	17.7920i	0.939631	−	0.797279i
$499$			11.1875i			0.500823i	0.968140	+	0.250411i	$0.0805658\pi$
$499$			11.1875i			0.500823i	−0.968140	+	0.250411i	$0.919434\pi$
$500$	−15.9795	−	15.6415i	−0.714625	−	0.699508i
$501$			22.2273i			0.993041i
$502$	−1.50424	−	1.77282i	−0.0671377	−	0.0791249i
$503$	−20.3232	−	20.3232i	−0.906166	−	0.906166i	0.0897941	−	0.995960i	$-0.471379\pi$
$503$	−20.3232	−	20.3232i	−0.906166	−	0.906166i	−0.995960	+	0.0897941i	$0.971379\pi$
$504$	−8.37988	−	2.09803i	−0.373270	−	0.0934536i
$505$	−38.0093	−	7.85218i	−1.69139	−	0.349417i
$506$	0.00841847	−	0.102718i	0.000374246	−	0.00456639i
$507$	6.38618	+	6.38618i	0.283620	+	0.283620i
$508$	−13.6578	−	19.0564i	−0.605967	−	0.845489i
$509$	−3.60037			−0.159584			−0.0797918	−	0.996812i	$-0.525426\pi$
$509$	−3.60037			−0.159584			−0.0797918	+	0.996812i	$0.525426\pi$
$510$	−26.2207	+	14.3212i	−1.16107	+	0.634152i
$511$			9.65819i			0.427253i
$512$	1.11807	+	22.5998i	0.0494120	+	0.998778i
$513$	0.000391633	0	0.000391633i	1.72910e−5	0	1.72910e-5i
$514$	1.43718	−	17.5359i	0.0633914	−	0.773474i
$515$	8.79986	−	5.78652i	0.387768	−	0.254985i
$516$	−57.2332	−	9.44473i	−2.51955	−	0.415781i
$517$	−1.35257	+	1.35257i	−0.0594861	+	0.0594861i
$518$	−6.33761	+	5.37748i	−0.278458	+	0.236273i
$519$	24.1167			1.05861
$520$	−11.2098	+	23.2629i	−0.491582	+	1.02014i
$521$	−20.7217			−0.907832			−0.453916	−	0.891044i	$-0.649973\pi$
$521$	−20.7217			−0.907832			−0.453916	+	0.891044i	$0.649973\pi$
$522$	−32.1876	+	27.3113i	−1.40881	+	1.19538i
$523$	16.1365	−	16.1365i	0.705602	−	0.705602i	−0.260005	−	0.965607i	$-0.583724\pi$
$523$	16.1365	−	16.1365i	0.705602	−	0.705602i	0.965607	+	0.260005i	$0.0837243\pi$
$524$	−5.19273	+	31.4669i	−0.226845	+	1.37464i
$525$	4.87504	−	11.2955i	0.212764	−	0.492976i
$526$	1.27667	−	15.5774i	0.0556656	−	0.679207i
$527$	21.9122	−	21.9122i	0.954511	−	0.954511i
$528$	−11.5505	+	5.69827i	−0.502670	+	0.247985i
$529$		−	22.9969i		−	0.999865i
$530$	28.1359	+	8.25822i	1.22214	+	0.358714i
$531$	17.2362			0.747987
$532$	0.00675370	−	0.00484042i	0.000292810	−	0.000209859i
$533$	−6.60799	−	6.60799i	−0.286224	−	0.286224i
$534$	3.61059	−	44.0548i	0.156245	−	1.90644i
$535$	29.3580	−	19.3049i	1.26926	−	0.834624i
$536$	−1.80632	−	0.452239i	−0.0780211	−	0.0195337i
$537$	−32.9659	−	32.9659i	−1.42258	−	1.42258i
$538$	−0.643402	−	0.758279i	−0.0277390	−	0.0326917i
$539$		−	1.30862i		−	0.0563664i
$540$	−0.242083	−	0.544826i	−0.0104176	−	0.0234456i
$541$			43.3077i			1.86194i	0.365090	+	0.930972i	$0.381038\pi$
$541$			43.3077i			1.86194i	−0.365090	+	0.930972i	$0.618962\pi$
$542$	−9.94713	+	8.44016i	−0.427266	+	0.362536i
$543$	33.2387	+	33.2387i	1.42641	+	1.42641i
$544$	−8.63570	+	19.9306i	−0.370253	+	0.854518i
$545$	−3.84333	+	18.6040i	−0.164630	+	0.796909i
$546$	−14.1600	−	1.16051i	−0.605993	−	0.0496652i
$547$	−25.0351	−	25.0351i	−1.07042	−	1.07042i	−0.997325	−	0.0730991i	$-0.976711\pi$
$547$	−25.0351	−	25.0351i	−1.07042	−	1.07042i	−0.0730991	−	0.997325i	$-0.523289\pi$
$548$	−5.44994	+	3.90601i	−0.232810	+	0.166856i
$549$	−26.3808			−1.12590
$550$	−2.70080	−	8.85045i	−0.115163	−	0.377384i
$551$		−	0.0406036i		−	0.00172977i
$552$	0.332403	−	0.199287i	0.0141480	−	0.00848220i
$553$	−1.04849	+	1.04849i	−0.0445865	+	0.0445865i
$554$	0.631702	+	0.0517722i	0.0268384	+	0.00219959i
$555$	−31.6670	−	6.54195i	−1.34419	−	0.277690i
$556$	−36.8842	−	6.08670i	−1.56424	−	0.258134i
$557$	23.5478	−	23.5478i	0.997753	−	0.997753i	−0.00224488	−	0.999997i	$-0.500715\pi$
$557$	23.5478	−	23.5478i	0.997753	−	0.997753i	0.999997	+	0.00224488i	$0.000714568\pi$
$558$	22.5527	+	26.5794i	0.954733	+	1.12520i
$559$	−48.1281			−2.03560
$560$	−2.25253	−	8.65599i	−0.0951869	−	0.365782i
$561$	−12.3637			−0.521996
$562$	−21.4241	−	25.2493i	−0.903722	−	1.06508i
$563$	−31.1689	+	31.1689i	−1.31361	+	1.31361i	−0.394882	+	0.918732i	$0.629214\pi$
$563$	−31.1689	+	31.1689i	−1.31361	+	1.31361i	−0.918732	+	0.394882i	$0.870786\pi$
$564$	−7.09716	−	1.17119i	−0.298844	−	0.0493159i
$565$	−10.1294	−	15.4043i	−0.426148	−	0.648065i
$566$	−1.43099	−	0.117279i	−0.0601488	−	0.00492960i
$567$	−6.24695	+	6.24695i	−0.262347	+	0.262347i
$568$	20.3817	+	33.9959i	0.855197	+	1.42644i
$569$		−	18.2902i		−	0.766766i	−0.923589	−	0.383383i	$-0.874759\pi$
$569$		−	18.2902i		−	0.766766i	0.923589	−	0.383383i	$-0.125241\pi$
$570$	0.0310177	+	0.00910408i	0.00129919	+	0.000381328i
$571$	13.0433			0.545846			0.272923	−	0.962036i	$-0.412010\pi$
$571$	13.0433			0.545846			0.272923	+	0.962036i	$0.412010\pi$
$572$	−8.68568	+	6.22508i	−0.363167	+	0.260284i
$573$	−19.1353	−	19.1353i	−0.799387	−	0.799387i
$574$	3.22605	+	0.264397i	0.134653	+	0.0110357i
$575$	0.102753	+	0.258794i	0.00428511	+	0.0107925i
$576$	−21.5510	−	11.5129i	−0.897959	−	0.479704i
$577$	3.41311	+	3.41311i	0.142090	+	0.142090i	0.774574	−	0.632484i	$-0.217965\pi$
$577$	3.41311	+	3.41311i	0.142090	+	0.142090i	−0.632484	+	0.774574i	$0.717965\pi$
$578$	2.43286	−	2.06429i	0.101194	−	0.0858630i
$579$			46.9180i			1.94984i
$580$	−40.7924	−	15.6938i	−1.69381	−	0.651650i
$581$			7.90293i			0.327869i
$582$	1.90439	+	2.24442i	0.0789397	+	0.0930341i
$583$	8.58034	+	8.58034i	0.355361	+	0.355361i
$584$	−6.63456	+	26.4996i	−0.274540	+	1.09656i
$585$	−15.3202	−	23.2982i	−0.633412	−	0.963262i
$586$	−3.82476	+	46.6680i	−0.157999	+	1.92784i
$587$	−1.41656	−	1.41656i	−0.0584675	−	0.0584675i	0.677268	−	0.735736i	$-0.263164\pi$
$587$	−1.41656	−	1.41656i	−0.0584675	−	0.0584675i	−0.735736	+	0.677268i	$0.763164\pi$
$588$	3.99984	−	2.86671i	0.164951	−	0.118221i
$589$	−0.0335291			−0.00138154
$590$	8.55444	+	15.6624i	0.352181	+	0.644810i
$591$			27.0580i			1.11302i
$592$	−21.0827	+	10.4009i	−0.866495	+	0.427473i
$593$	−4.79747	+	4.79747i	−0.197008	+	0.197008i	−0.798716	−	0.601708i	$-0.794487\pi$
$593$	−4.79747	+	4.79747i	−0.197008	+	0.197008i	0.601708	+	0.798716i	$0.294487\pi$
$594$	0.0201525	−	0.245892i	0.000826866	−	0.0100891i
$595$	1.73707	−	8.40845i	0.0712128	−	0.344713i
$596$	−2.31052	+	14.0013i	−0.0946424	+	0.573514i
$597$	1.49352	−	1.49352i	0.0611259	−	0.0611259i
$598$	0.245190	−	0.208045i	0.0100266	−	0.00850757i
$599$	−40.0226			−1.63528			−0.817640	−	0.575729i	$-0.804718\pi$
$599$	−40.0226			−1.63528			−0.817640	+	0.575729i	$0.804718\pi$
$600$	21.1352	−	27.6431i	0.862839	−	1.12853i
$601$	19.6533			0.801675			0.400838	−	0.916149i	$-0.368719\pi$
$601$	19.6533			0.801675			0.400838	+	0.916149i	$0.368719\pi$
$602$	12.7110	−	10.7853i	0.518063	−	0.439578i
$603$	1.42178	−	1.42178i	0.0578992	−	0.0578992i
$604$	23.5256	+	3.88223i	0.957242	+	0.157966i
$605$	−4.20155	+	20.3380i	−0.170817	+	0.826859i
$606$	4.93348	−	60.1961i	0.200409	−	2.44530i
$607$	20.7274	−	20.7274i	0.841300	−	0.841300i	−0.147728	−	0.989028i	$-0.547196\pi$
$607$	20.7274	−	20.7274i	0.841300	−	0.841300i	0.989028	+	0.147728i	$0.0471961\pi$
$608$	0.0218555	−	0.00864149i	0.000886356	−	0.000350459i
$609$		−	24.0472i		−	0.974444i
$610$	−13.0930	−	23.9720i	−0.530118	−	0.970597i
$611$	−5.96810			−0.241443
$612$	−13.6633	−	19.0641i	−0.552307	−	0.770619i
$613$	−3.26867	−	3.26867i	−0.132020	−	0.132020i	0.638009	−	0.770029i	$-0.279758\pi$
$613$	−3.26867	−	3.26867i	−0.132020	−	0.132020i	−0.770029	+	0.638009i	$0.779758\pi$
$614$	2.95245	−	36.0245i	0.119151	−	1.45383i
$615$	6.91882	+	10.5218i	0.278994	+	0.424281i
$616$	0.898941	−	3.59052i	0.0362194	−	0.144666i
$617$	13.1261	+	13.1261i	0.528437	+	0.528437i	0.920106	−	0.391669i	$-0.128102\pi$
$617$	13.1261	+	13.1261i	0.528437	+	0.528437i	−0.391669	+	0.920106i	$0.628102\pi$
$618$	10.6038	+	12.4970i	0.426546	+	0.502704i
$619$		−	20.9612i		−	0.842501i	−0.906944	−	0.421251i	$-0.861591\pi$
$619$		−	20.9612i		−	0.842501i	0.906944	−	0.421251i	$-0.138409\pi$
$620$	−12.9594	+	33.6850i	−0.520463	+	1.35282i
$621$			0.00742404i			0.000297916i
$622$	18.4830	−	15.6829i	0.741100	−	0.628826i
$623$	8.98233	+	8.98233i	0.359870	+	0.359870i
$624$	−38.0542	−	12.9112i	−1.52339	−	0.516860i
$625$	17.1489	+	18.1911i	0.685955	+	0.727644i
$626$	6.46309	+	0.529694i	0.258317	+	0.0211708i
$627$	0.00945919	+	0.00945919i	0.000377764	+	0.000377764i
$628$	19.3702	+	27.0267i	0.772955	+	1.07848i
$629$	−22.5671			−0.899808
$630$	9.26723	+	2.72004i	0.369215	+	0.108369i
$631$			24.0006i			0.955450i	0.878510	+	0.477725i	$0.158538\pi$
$631$			24.0006i			0.955450i	−0.878510	+	0.477725i	$0.841462\pi$
$632$	−3.59705	+	2.15655i	−0.143083	+	0.0857829i
$633$	1.09393	−	1.09393i	0.0434798	−	0.0434798i
$634$	−8.90471	−	0.729801i	−0.353651	−	0.0289841i
$635$	14.4019	+	21.9017i	0.571522	+	0.869143i
$636$	−7.42968	+	45.0224i	−0.294606	+	1.78525i
$637$	2.88709	−	2.88709i	0.114390	−	0.114390i
$638$	−11.7020	−	13.7914i	−0.463288	−	0.546007i
$639$	−42.8013			−1.69319
$640$	−0.234260	−	25.2971i	−0.00925993	−	0.999957i
$641$	2.21612			0.0875315			0.0437658	−	0.999042i	$-0.486064\pi$
$641$	2.21612			0.0875315			0.0437658	+	0.999042i	$0.486064\pi$
$642$	35.3761	+	41.6924i	1.39618	+	1.64547i
$643$	26.7141	−	26.7141i	1.05350	−	1.05350i	0.0550173	−	0.998485i	$-0.482479\pi$
$643$	26.7141	−	26.7141i	1.05350	−	1.05350i	0.998485	−	0.0550173i	$-0.0175214\pi$
$644$	−0.0181347	+	0.109892i	−0.000714606	+	0.00433037i
$645$	63.5129	+	13.1209i	2.50082	+	0.516634i
$646$	0.0224851	+	0.00184280i	0.000884663	+	7.25041e-5i
$647$	7.74545	−	7.74545i	0.304505	−	0.304505i	−0.538268	−	0.842773i	$-0.680921\pi$
$647$	7.74545	−	7.74545i	0.304505	−	0.304505i	0.842773	+	0.538268i	$0.180921\pi$
$648$	−21.4313	+	12.8488i	−0.841900	+	0.504747i
$649$			7.38519i			0.289894i
$650$	13.5674	−	25.4844i	0.532155	−	0.999579i
$651$	−19.8574			−0.778273
$652$	0.830280	+	1.15847i	0.0325163	+	0.0453691i
$653$	22.9683	+	22.9683i	0.898819	+	0.898819i	0.995332	−	0.0965128i	$-0.0307689\pi$
$653$	22.9683	+	22.9683i	0.898819	+	0.898819i	−0.0965128	+	0.995332i	$0.530769\pi$
$654$	−29.4636	−	2.41474i	−1.15212	−	0.0944240i
$655$	7.21388	−	34.9195i	0.281869	−	1.36442i
$656$	8.66982	+	2.94153i	0.338500	+	0.114847i
$657$	−20.8581	−	20.8581i	−0.813753	−	0.813753i
$658$	1.57622	−	1.33743i	0.0614475	−	0.0521384i
$659$			29.9305i			1.16593i	0.812499	+	0.582963i	$0.198107\pi$
$659$			29.9305i			1.16593i	−0.812499	+	0.582963i	$0.801893\pi$
$660$	13.1593	−	5.84708i	0.512224	−	0.227597i
$661$		−	6.89458i		−	0.268168i	−0.990970	−	0.134084i	$-0.957191\pi$
$661$		−	6.89458i		−	0.268168i	0.990970	−	0.134084i	$-0.0428092\pi$
$662$	−13.1294	−	15.4736i	−0.510288	−	0.601398i
$663$	−27.2768	−	27.2768i	−1.05934	−	1.05934i
$664$	−5.42881	+	21.6836i	−0.210679	+	0.841487i
$665$	−0.00776212	+	0.00510413i	−0.000301002	+	0.000197930i
$666$	2.07353	−	25.3003i	0.0803476	−	0.980365i
$667$	0.384853	+	0.384853i	0.0149016	+	0.0149016i
$668$	−10.5248	−	14.6850i	−0.407217	−	0.568179i
$669$	4.10131			0.158566
$670$	1.99759	+	0.586317i	0.0771737	+	0.0226514i
$671$		−	11.3034i		−	0.436361i
$672$	12.9438	−	5.11787i	0.499317	−	0.197426i
$673$	23.0235	−	23.0235i	0.887489	−	0.887489i	−0.106792	−	0.994281i	$-0.534058\pi$
$673$	23.0235	−	23.0235i	0.887489	−	0.887489i	0.994281	+	0.106792i	$0.0340580\pi$
$674$	−1.94036	+	23.6754i	−0.0747398	+	0.911942i
$675$	0.245975	+	0.619512i	0.00946760	+	0.0238450i
$676$	−7.24309	−	1.19527i	−0.278580	−	0.0459719i
$677$	−1.87869	+	1.87869i	−0.0722040	+	0.0722040i	−0.742287	−	0.670083i	$-0.766259\pi$
$677$	−1.87869	+	1.87869i	−0.0722040	+	0.0722040i	0.670083	+	0.742287i	$0.266259\pi$
$678$	21.8763	−	18.5621i	0.840153	−	0.712872i
$679$	−0.845901			−0.0324627
$680$	10.5421	−	21.8774i	0.404272	−	0.838958i
$681$	7.88408			0.302119
$682$	−11.3885	+	9.66316i	−0.436088	+	0.370021i
$683$	−14.3638	+	14.3638i	−0.549615	+	0.549615i	−0.926329	−	0.376714i	$-0.877054\pi$
$683$	−14.3638	+	14.3638i	−0.549615	+	0.549615i	0.376714	+	0.926329i	$0.377054\pi$
$684$	−0.00413199	+	0.0250390i	−0.000157990	+	0.000957391i
$685$	6.26369	−	4.11881i	0.239323	−	0.157372i
$686$	−0.115517	+	1.40949i	−0.00441046	+	0.0538145i
$687$	−3.98668	+	3.98668i	−0.152101	+	0.152101i
$688$	42.2846	−	20.8605i	1.61209	−	0.795300i
$689$			37.8599i			1.44235i
$690$	−0.380286	+	0.207704i	−0.0144773	+	0.00790716i
$691$	−37.0758			−1.41043			−0.705216	−	0.708993i	$-0.749150\pi$
$691$	−37.0758			−1.41043			−0.705216	+	0.708993i	$0.749150\pi$
$692$	−15.9333	+	11.4195i	−0.605693	+	0.434104i
$693$	2.82614	+	2.82614i	0.107356	+	0.107356i
$694$	−1.49804	+	18.2784i	−0.0568647	+	0.693838i
$695$	40.9312	+	8.45581i	1.55261	+	0.320747i
$696$	16.5189	−	65.9794i	0.626148	−	2.50094i
$697$	6.21442	+	6.21442i	0.235388	+	0.235388i
$698$	26.9124	+	31.7175i	1.01865	+	1.20052i
$699$			22.2515i			0.841627i
$700$	2.12771	+	9.77102i	0.0804198	+	0.369310i
$701$		−	49.8531i		−	1.88293i	−0.337117	−	0.941463i	$-0.609452\pi$
$701$		−	49.8531i		−	1.88293i	0.337117	−	0.941463i	$-0.390548\pi$
$702$	0.586947	−	0.498026i	0.0221529	−	0.0187968i
$703$	0.0172656	+	0.0172656i	0.000651183	+	0.000651183i
$704$	4.93292	−	9.23395i	0.185917	−	0.348018i
$705$	7.87588	+	1.62705i	0.296623	+	0.0612781i
$706$	22.9635	+	1.88201i	0.864242	+	0.0708305i
$707$	12.2734	+	12.2734i	0.461588	+	0.461588i
$708$	−22.5730	+	16.1782i	−0.848345	+	0.608014i
$709$	−34.9839			−1.31385			−0.656924	−	0.753957i	$-0.728143\pi$
$709$	−34.9839			−1.31385			−0.656924	+	0.753957i	$0.728143\pi$
$710$	−21.2426	−	38.8931i	−0.797219	−	1.45963i
$711$		−	4.52872i		−	0.169840i
$712$	18.4749	+	30.8155i	0.692377	+	1.15486i
$713$	0.317799	−	0.317799i	0.0119017	−	0.0119017i
$714$	13.3167	+	1.09139i	0.498363	+	0.0408442i
$715$	9.98257	−	6.56423i	0.373327	−	0.245488i
$716$	37.3894	+	6.17006i	1.39731	+	0.230586i
$717$	−35.4158	+	35.4158i	−1.32263	+	1.32263i
$718$	−3.85976	−	4.54891i	−0.144045	−	0.169764i
$719$	−14.5278			−0.541794			−0.270897	−	0.962608i	$-0.587320\pi$
$719$	−14.5278			−0.541794			−0.270897	+	0.962608i	$0.587320\pi$
$720$	23.5584	+	13.8291i	0.877969	+	0.515380i
$721$	−4.71002			−0.175410
$722$	17.3845	+	20.4885i	0.646985	+	0.762502i
$723$	−29.8244	+	29.8244i	−1.10918	+	1.10918i
$724$	−37.6987	−	6.22112i	−1.40106	−	0.231206i
$725$	44.8658	+	19.3637i	1.66628	+	0.719150i
$726$	−32.2098	−	2.63981i	−1.19542	−	0.0979726i
$727$	−16.0156	+	16.0156i	−0.593986	+	0.593986i	−0.938706	−	0.344720i	$-0.887974\pi$
$727$	−16.0156	+	16.0156i	−0.593986	+	0.593986i	0.344720	+	0.938706i	$0.387974\pi$
$728$	9.90466	−	5.93817i	0.367091	−	0.220083i
$729$		−	27.9663i		−	1.03579i
$730$	8.60156	−	29.3056i	0.318358	−	1.08465i
$731$	45.2617			1.67406
$732$	34.5490	−	24.7615i	1.27697	−	0.915210i
$733$	−24.3683	−	24.3683i	−0.900065	−	0.900065i	0.0953761	−	0.995441i	$-0.469595\pi$
$733$	−24.3683	−	24.3683i	−0.900065	−	0.900065i	−0.995441	+	0.0953761i	$0.969595\pi$
$734$	40.4135	+	3.31216i	1.49169	+	0.122254i
$735$	−4.59707	+	3.02289i	−0.169565	+	0.111501i
$736$	−0.125246	+	0.289059i	−0.00461663	+	0.0106549i
$737$	0.609187	+	0.609187i	0.0224397	+	0.0224397i
$738$	−7.53808	+	6.39608i	−0.277481	+	0.235443i
$739$		−	2.62146i		−	0.0964320i	−0.998837	−	0.0482160i	$-0.984646\pi$
$739$		−	2.62146i		−	0.0964320i	0.998837	−	0.0482160i	$-0.0153536\pi$
$740$	24.0192	−	10.6725i	0.882964	−	0.392329i
$741$			0.0417378i			0.00153328i
$742$	−8.48427	−	9.99911i	−0.311467	−	0.367079i
$743$	−2.88327	−	2.88327i	−0.105777	−	0.105777i	0.652238	−	0.758014i	$-0.273830\pi$
$743$	−2.88327	−	2.88327i	−0.105777	−	0.105777i	−0.758014	+	0.652238i	$0.773830\pi$
$744$	−54.4836	−	13.6408i	−1.99747	−	0.500095i
$745$	3.20983	−	15.5375i	0.117599	−	0.569250i
$746$	−0.173755	+	2.12008i	−0.00636161	+	0.0776216i
$747$	−17.0674	−	17.0674i	−0.624464	−	0.624464i
$748$	8.16837	−	5.85432i	0.298665	−	0.214055i
$749$	−15.7135			−0.574159
$750$	−24.8520	+	29.9320i	−0.907466	+	1.09296i
$751$			26.7563i			0.976350i	0.872746	+	0.488175i	$0.162337\pi$
$751$			26.7563i			0.976350i	−0.872746	+	0.488175i	$0.837663\pi$
$752$	5.24348	−	2.58680i	0.191210	−	0.0943307i
$753$	−2.86036	+	2.86036i	−0.104237	+	0.104237i
$754$	4.60955	−	56.2437i	0.167870	−	2.04827i
$755$	−26.1068	−	5.39331i	−0.950125	−	0.196283i
$756$	−0.0434116	+	0.263065i	−0.00157886	+	0.00956759i
$757$	12.4382	−	12.4382i	0.452073	−	0.452073i	−0.443969	−	0.896042i	$-0.646430\pi$
$757$	12.4382	−	12.4382i	0.452073	−	0.452073i	0.896042	+	0.443969i	$0.146430\pi$
$758$	10.8599	−	9.21463i	0.394448	−	0.334691i
$759$	−0.179314			−0.00650869
$760$	−0.0248035	+	0.00867233i	−0.000899716	+	0.000314579i
$761$	0.572688			0.0207599			0.0103800	−	0.999946i	$-0.496696\pi$
$761$	0.572688			0.0207599			0.0103800	+	0.999946i	$0.496696\pi$
$762$	−31.1035	+	26.3914i	−1.12676	+	0.956059i
$763$	6.00734	−	6.00734i	0.217480	−	0.217480i
$764$	21.7029	+	3.58145i	0.785183	+	0.129572i
$765$	14.4077	+	21.9106i	0.520913	+	0.792179i
$766$	−1.95937	+	23.9073i	−0.0707948	+	0.863806i
$767$	−16.2932	+	16.2932i	−0.588314	+	0.588314i
$768$	39.0300	−	5.15057i	1.40837	−	0.185855i
$769$			7.01357i			0.252916i	0.991972	+	0.126458i	$0.0403609\pi$
$769$			7.01357i			0.252916i	−0.991972	+	0.126458i	$0.959639\pi$
$770$	−1.16546	+	3.97072i	−0.0420001	+	0.143095i
$771$	−30.6121			−1.10247
$772$	−22.2161	−	30.9975i	−0.799574	−	1.11562i
$773$	−1.28265	−	1.28265i	−0.0461339	−	0.0461339i	0.683663	−	0.729797i	$-0.260386\pi$
$773$	−1.28265	−	1.28265i	−0.0461339	−	0.0461339i	−0.729797	+	0.683663i	$0.760386\pi$
$774$	−4.15877	+	50.7435i	−0.149484	+	1.82394i
$775$	15.9899	−	37.0487i	0.574374	−	1.33083i
$776$	−2.32093	−	0.581080i	−0.0833167	−	0.0208596i
$777$	10.2254	+	10.2254i	0.366835	+	0.366835i
$778$	−9.96268	−	11.7415i	−0.357179	−	0.420953i
$779$		−	0.00950904i		−	0.000340697i
$780$	41.9319	+	16.1322i	1.50140	+	0.577624i
$781$		−	18.3390i		−	0.656223i
$782$	−0.230587	+	0.195654i	−0.00824577	+	0.00699656i
$783$	0.921278	+	0.921278i	0.0329238	+	0.0329238i
$784$	−1.28518	+	3.78792i	−0.0458992	+	0.135283i
$785$	−20.4255	−	31.0621i	−0.729018	−	1.10866i
$786$	55.3028	+	4.53244i	1.97258	+	0.161667i
$787$	21.3487	+	21.3487i	0.760997	+	0.760997i	0.976503	−	0.215505i	$-0.0691399\pi$
$787$	21.3487	+	21.3487i	0.760997	+	0.760997i	−0.215505	+	0.976503i	$0.569140\pi$
$788$	−12.8122	−	17.8765i	−0.456415	−	0.636824i
$789$	−27.1933			−0.968106
$790$	4.11521	−	2.24764i	0.146413	−	0.0799673i
$791$			8.24497i			0.293158i
$792$	5.81283	+	9.69559i	0.206550	+	0.344518i
$793$	24.9375	−	24.9375i	0.885556	−	0.885556i
$794$	−10.7586	−	0.881744i	−0.381810	−	0.0312919i
$795$	10.3215	−	49.9623i	0.366066	−	1.77198i
$796$	−0.279536	+	1.69393i	−0.00990787	+	0.0600397i
$797$	−14.4703	+	14.4703i	−0.512566	+	0.512566i	−0.915312	−	0.402746i	$-0.868056\pi$
$797$	−14.4703	+	14.4703i	−0.512566	+	0.512566i	0.402746	+	0.915312i	$0.368056\pi$
$798$	−0.00935328	−	0.0110233i	−0.000331103	−	0.000390220i
$799$	5.61264			0.198561
$800$	−0.874186	+	28.2708i	−0.0309071	+	0.999522i
$801$	−38.7971			−1.37083
$802$	−6.30487	−	7.43059i	−0.222633	−	0.262383i
$803$	8.93707	−	8.93707i	0.315382	−	0.315382i
$804$	−0.527493	+	3.19650i	−0.0186032	+	0.112732i
$805$	0.0251932	−	0.121950i	0.000887943	−	0.00429818i
$806$	−46.4442	−	3.80641i	−1.63593	−	0.134075i
$807$	−1.22345	+	1.22345i	−0.0430674	+	0.0430674i
$808$	25.2440	+	42.1060i	0.888080	+	1.48129i
$809$		−	4.32577i		−	0.152086i	−0.997105	−	0.0760429i	$-0.975771\pi$
$809$		−	4.32577i		−	0.152086i	0.997105	−	0.0760429i	$-0.0242286\pi$
$810$	24.5185	−	13.3915i	0.861492	−	0.470528i
$811$	−8.47333			−0.297539			−0.148769	−	0.988872i	$-0.547531\pi$
$811$	−8.47333			−0.297539			−0.148769	+	0.988872i	$0.547531\pi$
$812$	11.3866	+	15.8874i	0.399591	+	0.557538i
$813$	16.0492	+	16.0492i	0.562871	+	0.562871i
$814$	10.8404	+	0.888443i	0.379956	+	0.0311399i
$815$	−0.875515	−	1.33144i	−0.0306680	−	0.0466384i
$816$	35.7877	+	12.1422i	1.25282	+	0.425061i
$817$	−0.0346287	−	0.0346287i	−0.00121151	−	0.00121151i
$818$	−10.1401	+	8.60393i	−0.354541	+	0.300829i
$819$			12.4701i			0.435740i
$820$	−9.55326	−	3.67536i	−0.333614	−	0.128349i
$821$		−	32.9538i		−	1.15010i	−0.818119	−	0.575049i	$-0.804983\pi$
$821$		−	32.9538i		−	1.15010i	0.818119	−	0.575049i	$-0.195017\pi$
$822$	7.54769	+	8.89531i	0.263256	+	0.310260i
$823$	12.5766	+	12.5766i	0.438394	+	0.438394i	0.891471	−	0.453077i	$-0.149674\pi$
$823$	12.5766	+	12.5766i	0.438394	+	0.438394i	−0.453077	+	0.891471i	$0.649674\pi$
$824$	−12.9231	−	3.23548i	−0.450197	−	0.112713i
$825$	−14.9632	+	5.94109i	−0.520952	+	0.206842i
$826$	0.651918	−	7.95441i	0.0226831	−	0.276769i
$827$	−21.2471	−	21.2471i	−0.738834	−	0.738834i	0.233519	−	0.972352i	$-0.424976\pi$
$827$	−21.2471	−	21.2471i	−0.738834	−	0.738834i	−0.972352	+	0.233519i	$0.924976\pi$
$828$	−0.198163	−	0.276491i	−0.00688664	−	0.00960874i
$829$	46.9092			1.62922			0.814612	−	0.580006i	$-0.196950\pi$
$829$	46.9092			1.62922			0.814612	+	0.580006i	$0.196950\pi$
$830$	7.03833	−	23.9797i	0.244304	−	0.832347i
$831$		−	1.10275i		−	0.0382541i
$832$	31.2550	−	9.48894i	1.08357	−	0.328970i
$833$	−2.71513	+	2.71513i	−0.0940738	+	0.0940738i
$834$	−5.31273	+	64.8236i	−0.183965	+	2.24466i
$835$	11.0982	+	16.8776i	0.384070	+	0.584075i
$836$	−0.0107285	−	0.00177043i	−0.000371051	−	6.12316e-5i
$837$	0.760761	−	0.760761i	0.0262957	−	0.0262957i
$838$	−36.3409	+	30.8353i	−1.25538	+	1.06519i
$839$	27.1748			0.938179			0.469090	−	0.883151i	$-0.344582\pi$
$839$	27.1748			0.938179			0.469090	+	0.883151i	$0.344582\pi$
$840$	−14.6897	+	5.13614i	−0.506843	+	0.177214i
$841$	66.5158			2.29365
$842$	−30.2652	+	25.6801i	−1.04301	+	0.884995i
$843$	−40.7386	+	40.7386i	−1.40311	+	1.40311i
$844$	−0.204745	+	1.24072i	−0.00704763	+	0.0427072i
$845$	8.03782	+	1.66050i	0.276509	+	0.0571230i
$846$	−0.515706	+	6.29241i	−0.0177303	+	0.216338i
$847$	6.56726	−	6.56726i	0.225654	−	0.225654i
$848$	−16.4099	−	33.2631i	−0.563518	−	1.14226i
$849$			2.49805i			0.0857330i
$850$	−12.7593	+	23.9665i	−0.437640	+	0.822045i
$851$	−0.327296			−0.0112196
$852$	56.0537	−	40.1740i	1.92037	−	1.37634i
$853$	−5.74165	−	5.74165i	−0.196591	−	0.196591i	0.601946	−	0.798537i	$-0.294392\pi$
$853$	−5.74165	−	5.74165i	−0.196591	−	0.196591i	−0.798537	+	0.601946i	$0.794392\pi$
$854$	−0.997790	+	12.1746i	−0.0341437	+	0.416606i
$855$	0.00574027	−	0.0277863i	0.000196313	−	0.000950273i
$856$	−43.1138	−	10.7942i	−1.47360	−	0.368937i
$857$	3.03471	+	3.03471i	0.103664	+	0.103664i	0.757036	−	0.653373i	$-0.226646\pi$
$857$	3.03471	+	3.03471i	0.103664	+	0.103664i	−0.653373	+	0.757036i	$0.726646\pi$
$858$	12.0289	+	14.1766i	0.410660	+	0.483982i
$859$		−	45.3066i		−	1.54584i	−0.634502	−	0.772921i	$-0.718795\pi$
$859$		−	45.3066i		−	1.54584i	0.634502	−	0.772921i	$-0.281205\pi$
$860$	−48.1742	+	21.4053i	−1.64273	+	0.729915i
$861$		−	5.63167i		−	0.191927i
$862$	−32.4413	+	27.5265i	−1.10495	+	0.937557i
$863$	−11.2915	−	11.2915i	−0.384366	−	0.384366i	0.488306	−	0.872672i	$-0.337615\pi$
$863$	−11.2915	−	11.2915i	−0.384366	−	0.384366i	−0.872672	+	0.488306i	$0.837615\pi$
$864$	−0.299819	+	0.691962i	−0.0102001	+	0.0235410i
$865$	18.3123	−	12.0416i	0.622638	−	0.409428i
$866$	−29.5252	−	2.41979i	−1.00331	−	0.0822277i
$867$	−3.92530	−	3.92530i	−0.133310	−	0.133310i
$868$	13.1193	−	9.40266i	0.445297	−	0.319147i
$869$	1.94042			0.0658243
$870$	−21.4164	+	72.9660i	−0.726084	+	2.47378i
$871$			2.68798i			0.0910787i
$872$	20.6093	−	12.3559i	0.697917	−	0.418425i
$873$	1.82683	−	1.82683i	0.0618290	−	0.0618290i
$874$	0.000326107	0	2.67267e-5i	1.10307e−5	0	9.04044e-7i
$875$	−1.93820	−	11.0111i	−0.0655230	−	0.372242i
$876$	46.8942	+	7.73857i	1.58441	+	0.261462i
$877$	−34.5820	+	34.5820i	−1.16775	+	1.16775i	−0.185016	+	0.982736i	$0.559234\pi$
$877$	−34.5820	+	34.5820i	−1.16775	+	1.16775i	−0.982736	+	0.185016i	$0.940766\pi$
$878$	−18.7231	−	22.0661i	−0.631875	−	0.744695i
$879$	81.4677			2.74784
$880$	−5.92535	+	10.0940i	−0.199743	+	0.340270i
$881$	0.426856			0.0143812			0.00719058	−	0.999974i	$-0.497711\pi$
$881$	0.426856			0.0143812			0.00719058	+	0.999974i	$0.497711\pi$
$882$	−2.79450	−	3.29345i	−0.0940957	−	0.110896i
$883$	3.50567	−	3.50567i	0.117975	−	0.117975i	−0.645654	−	0.763630i	$-0.723415\pi$
$883$	3.50567	−	3.50567i	0.117975	−	0.117975i	0.763630	+	0.645654i	$0.223415\pi$
$884$	30.9369	+	5.10526i	1.04052	+	0.171709i
$885$	25.9435	−	17.0596i	0.872080	−	0.573453i
$886$	37.5748	+	3.07951i	1.26235	+	0.103458i
$887$	−13.0653	+	13.0653i	−0.438688	+	0.438688i	−0.891570	−	0.452882i	$-0.850396\pi$
$887$	−13.0653	+	13.0653i	−0.438688	+	0.438688i	0.452882	+	0.891570i	$0.350396\pi$
$888$	21.0317	+	35.0802i	0.705779	+	1.17721i
$889$		−	11.7226i		−	0.393164i
$890$	−19.2552	−	35.2545i	−0.645437	−	1.18173i
$891$	11.5611			0.387310
$892$	−2.70963	+	1.94201i	−0.0907250	+	0.0650232i
$893$	−0.00429411	−	0.00429411i	−0.000143697	−	0.000143697i
$894$	24.6071	+	2.01672i	0.822984	+	0.0674491i
$895$	−41.4918	−	8.57162i	−1.38692	−	0.286518i
$896$	−6.12825	+	9.51023i	−0.204731	+	0.317715i
$897$	−0.395603	−	0.395603i	−0.0132088	−	0.0132088i
$898$	−21.6735	+	18.3900i	−0.723254	+	0.613683i
$899$		−	78.8738i		−	2.63059i
$900$	−25.6969	−	16.5067i	−0.856562	−	0.550225i
$901$		−	35.6050i		−	1.18617i
$902$	−2.74053	−	3.22984i	−0.0912495	−	0.107542i
$903$	−20.5087	−	20.5087i	−0.682485	−	0.682485i
$904$	−5.66377	+	22.6221i	−0.188374	+	0.752399i
$905$	41.8351	+	8.64254i	1.39065	+	0.287288i
$906$	3.38858	−	41.3460i	0.112578	−	1.37363i
$907$	3.89206	+	3.89206i	0.129234	+	0.129234i	0.768765	−	0.639531i	$-0.220872\pi$
$907$	3.89206	+	3.89206i	0.129234	+	0.129234i	−0.639531	+	0.768765i	$0.720872\pi$
$908$	−5.20881	+	3.73318i	−0.172860	+	0.123890i
$909$	−53.0120			−1.75830
$910$	−11.3314	+	6.18899i	−0.375634	+	0.205163i
$911$			8.00373i			0.265176i	0.991171	+	0.132588i	$0.0423286\pi$
$911$			8.00373i			0.265176i	−0.991171	+	0.132588i	$0.957671\pi$
$912$	−0.0180907	−	0.0366701i	−0.000599043	−	0.00121427i
$913$	7.31287	−	7.31287i	0.242021	−	0.242021i
$914$	1.15929	−	14.1452i	0.0383459	−	0.467880i
$915$	−39.7076	+	26.1105i	−1.31269	+	0.863187i
$916$	0.746168	−	4.52163i	0.0246541	−	0.149399i
$917$	−11.2757	+	11.2757i	−0.372356	+	0.372356i
$918$	−0.551989	+	0.468364i	−0.0182183	+	0.0154583i
$919$	24.9926			0.824431			0.412216	−	0.911086i	$-0.364755\pi$
$919$	24.9926			0.824431			0.412216	+	0.911086i	$0.364755\pi$
$920$	0.152896	−	0.317293i	0.00504082	−	0.0104609i
$921$	−62.8874			−2.07221
$922$	18.1648	−	15.4129i	0.598226	−	0.507597i
$923$	40.4596	−	40.4596i	1.33174	−	1.33174i
$924$	−6.35386	−	1.04853i	−0.209027	−	0.0344940i
$925$	−27.3119	+	10.8441i	−0.898008	+	0.356551i
$926$	−1.59269	+	19.4333i	−0.0523391	+	0.638619i
$927$	10.1719	−	10.1719i	0.334089	−	0.334089i
$928$	20.3282	+	51.4127i	0.667306	+	1.68771i
$929$		−	13.3018i		−	0.436417i	−0.975902	−	0.218208i	$-0.929979\pi$
$929$		−	13.3018i		−	0.436417i	0.975902	−	0.218208i	$-0.0700213\pi$
$930$	60.2529	+	17.6850i	1.97577	+	0.579913i
$931$	0.00415458			0.000136161
$932$	−10.5363	−	14.7010i	−0.345127	−	0.481546i
$933$	−29.8214	−	29.8214i	−0.976310	−	0.976310i
$934$	−2.16316	+	26.3939i	−0.0707807	+	0.863635i
$935$	−9.38802	+	6.17327i	−0.307021	+	0.201888i
$936$	−8.56615	+	34.2147i	−0.279993	+	1.11834i
$937$	20.8147	+	20.8147i	0.679988	+	0.679988i	0.959997	−	0.280009i	$-0.0903375\pi$
$937$	20.8147	+	20.8147i	0.679988	+	0.679988i	−0.280009	+	0.959997i	$0.590338\pi$
$938$	−0.602366	−	0.709917i	−0.0196680	−	0.0231796i
$939$		−	11.2825i		−	0.368192i
$940$	−5.97381	+	2.65435i	−0.194844	+	0.0865754i
$941$		−	3.17487i		−	0.103498i	−0.998660	−	0.0517488i	$-0.983520\pi$
$941$		−	3.17487i		−	0.103498i	0.998660	−	0.0517488i	$-0.0164795\pi$
$942$	44.1125	−	37.4296i	1.43726	−	1.21952i
$943$	0.0901295	+	0.0901295i	0.00293502	+	0.00293502i
$944$	7.25287	−	21.3770i	0.236061	−	0.695763i
$945$	0.0603085	−	0.291929i	0.00196184	−	0.00949647i
$946$	−21.7420	−	1.78191i	−0.706895	−	0.0579348i
$947$	−11.6779	−	11.6779i	−0.379481	−	0.379481i	0.491434	−	0.870915i	$-0.336473\pi$
$947$	−11.6779	−	11.6779i	−0.379481	−	0.379481i	−0.870915	+	0.491434i	$0.836473\pi$
$948$	4.25074	+	5.93094i	0.138058	+	0.192628i
$949$	39.4339			1.28008
$950$	0.0280981	−	0.00857442i	0.000911624	−	0.000278191i
$951$			15.5448i			0.504076i
$952$	−9.31475	+	5.58450i	−0.301893	+	0.180995i
$953$	−6.38788	+	6.38788i	−0.206924	+	0.206924i	−0.802959	−	0.596035i	$-0.796742\pi$
$953$	−6.38788	+	6.38788i	−0.206924	+	0.206924i	0.596035	+	0.802959i	$0.296742\pi$
$954$	39.9173	+	3.27149i	1.29237	+	0.105918i
$955$	−24.0842	−	4.97545i	−0.779346	−	0.161002i
$956$	6.62861	−	40.1680i	0.214384	−	1.29913i
$957$	−22.2518	+	22.2518i	−0.719298	+	0.719298i
$958$	15.0790	+	17.7713i	0.487180	+	0.574165i
$959$	−3.35257			−0.108260
$960$	−43.8329	+	4.00135i	−1.41470	+	0.129143i
$961$	−34.1314			−1.10101
$962$	21.9560	+	25.8762i	0.707890	+	0.834281i
$963$	33.9354	−	33.9354i	1.09355	−	1.09355i
$964$	5.58208	−	33.8263i	0.179787	−	1.08947i
$965$	23.4264	+	35.6258i	0.754124	+	1.14684i
$966$	0.193135	+	0.0158287i	0.00621402	+	0.000509281i
$967$	−23.1452	+	23.1452i	−0.744300	+	0.744300i	−0.973402	−	0.229102i	$-0.926421\pi$
$967$	−23.1452	+	23.1452i	−0.744300	+	0.744300i	0.229102	+	0.973402i	$0.426421\pi$
$968$	22.5301	−	13.5076i	0.724146	−	0.434150i
$969$		−	0.0392519i		−	0.00126095i
$970$	2.56670	+	0.753357i	0.0824117	+	0.0241888i
$971$	−2.02280			−0.0649147			−0.0324574	−	0.999473i	$-0.510333\pi$
$971$	−2.02280			−0.0649147			−0.0324574	+	0.999473i	$0.510333\pi$
$972$	25.7920	+	35.9868i	0.827277	+	1.15428i
$973$	−13.2169	−	13.2169i	−0.423714	−	0.423714i
$974$	−29.7293	−	2.43651i	−0.952587	−	0.0780709i
$975$	−46.1191	−	19.9046i	−1.47699	−	0.637457i
$976$	−11.1008	+	32.7185i	−0.355329	+	1.04729i
$977$	1.06508	+	1.06508i	0.0340749	+	0.0340749i	0.723939	−	0.689864i	$-0.242330\pi$
$977$	1.06508	+	1.06508i	0.0340749	+	0.0340749i	−0.689864	+	0.723939i	$0.742330\pi$
$978$	1.89083	−	1.60438i	0.0604621	−	0.0513023i
$979$		−	16.6234i		−	0.531285i
$980$	1.60580	−	4.17390i	0.0512953	−	0.133330i
$981$			25.9473i			0.828433i
$982$	9.77600	+	11.5215i	0.311965	+	0.367665i
$983$	−1.14286	−	1.14286i	−0.0364515	−	0.0364515i	0.688646	−	0.725098i	$-0.258205\pi$
$983$	−1.14286	−	1.14286i	−0.0364515	−	0.0364515i	−0.725098	+	0.688646i	$0.758205\pi$
$984$	3.86860	−	15.4519i	0.123327	−	0.492587i
$985$	13.5102	+	20.5457i	0.430471	+	0.654640i
$986$	−4.33501	+	52.8938i	−0.138055	+	1.68448i
$987$	−2.54316	−	2.54316i	−0.0809497	−	0.0809497i
$988$	−0.0197632	−	0.0275751i	−0.000628751	−	0.000877279i
$989$	0.656443			0.0208737
$990$	−6.05835	−	11.0923i	−0.192547	−	0.352535i
$991$			8.36841i			0.265831i	0.991127	+	0.132916i	$0.0424339\pi$
$991$			8.36841i			0.265831i	−0.991127	+	0.132916i	$0.957566\pi$
$992$	42.4549	−	16.7864i	1.34795	−	0.532968i
$993$	−24.9659	+	24.9659i	−0.792270	+	0.792270i
$994$	−1.61886	+	19.7526i	−0.0513470	+	0.626513i
$995$	0.388338	−	1.87979i	0.0123112	−	0.0595934i
$996$	38.3717	+	6.33218i	1.21586	+	0.200643i
$997$	32.8486	−	32.8486i	1.04033	−	1.04033i	0.0411742	−	0.999152i	$-0.486890\pi$
$997$	32.8486	−	32.8486i	1.04033	−	1.04033i	0.999152	−	0.0411742i	$-0.0131099\pi$
$998$	−12.0640	+	10.2363i	−0.381878	+	0.324025i
$999$	−0.783496			−0.0247887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.267.27	yes	72
4.3	odd	2		1120.2.bi.a.687.8		72
5.3	odd	4	inner	280.2.w.a.43.29	yes	72
8.3	odd	2	inner	280.2.w.a.267.29	yes	72
8.5	even	2		1120.2.bi.a.687.7		72
20.3	even	4		1120.2.bi.a.463.7		72
40.3	even	4	inner	280.2.w.a.43.27	✓	72
40.13	odd	4		1120.2.bi.a.463.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.27	✓	72	40.3	even	4	inner
280.2.w.a.43.29	yes	72	5.3	odd	4	inner
280.2.w.a.267.27	yes	72	1.1	even	1	trivial
280.2.w.a.267.29	yes	72	8.3	odd	2	inner
1120.2.bi.a.463.7		72	20.3	even	4
1120.2.bi.a.463.8		72	40.13	odd	4
1120.2.bi.a.687.7		72	8.5	even	2
1120.2.bi.a.687.8		72	4.3	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.914975 + 1.07834i) q^{2} +(1.73985 - 1.73985i) q^{3} +(-0.325640 + 1.97331i) q^{4} +(0.452388 - 2.18983i) q^{5} +(3.46808 + 0.284233i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.42586 + 1.45438i) q^{8} -3.05418i q^{9} +O(q^{10})\)	\(q+(0.914975 + 1.07834i) q^{2} +(1.73985 - 1.73985i) q^{3} +(-0.325640 + 1.97331i) q^{4} +(0.452388 - 2.18983i) q^{5} +(3.46808 + 0.284233i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.42586 + 1.45438i) q^{8} -3.05418i q^{9} +(2.77531 - 1.51581i) q^{10} +1.30862 q^{11} +(2.86671 + 3.99984i) q^{12} +(2.88709 + 2.88709i) q^{13} +(-1.40949 - 0.115517i) q^{14} +(-3.02289 - 4.59707i) q^{15} +(-3.78792 - 1.28518i) q^{16} +(-2.71513 - 2.71513i) q^{17} +(3.29345 - 2.79450i) q^{18} +0.00415458i q^{19} +(4.17390 + 1.60580i) q^{20} +2.46052i q^{21} +(1.19736 + 1.41114i) q^{22} +(-0.0393783 - 0.0393783i) q^{23} +(-1.69022 + 6.75104i) q^{24} +(-4.59069 - 1.98130i) q^{25} +(-0.471651 + 5.75488i) q^{26} +(-0.0942655 - 0.0942655i) q^{27} +(-1.16508 - 1.62560i) q^{28} -9.77322 q^{29} +(2.19134 - 7.46591i) q^{30} +8.07040i q^{31} +(-2.07999 - 5.26057i) q^{32} +(2.27681 - 2.27681i) q^{33} +(0.443560 - 5.41212i) q^{34} +(1.22856 + 1.86833i) q^{35} +(6.02685 + 0.994562i) q^{36} +(4.15579 - 4.15579i) q^{37} +(-0.00448005 + 0.00380134i) q^{38} +10.0462 q^{39} +(2.08742 + 5.97015i) q^{40} -2.28881 q^{41} +(-2.65328 + 2.25132i) q^{42} +(-8.33507 + 8.33507i) q^{43} +(-0.426140 + 2.58232i) q^{44} +(-6.68813 - 1.38167i) q^{45} +(0.00643307 - 0.0784935i) q^{46} +(-1.03359 + 1.03359i) q^{47} +(-8.82644 + 4.35440i) q^{48} -1.00000i q^{49} +(-2.06385 - 6.76317i) q^{50} -9.44787 q^{51} +(-6.63727 + 4.75697i) q^{52} +(6.55677 + 6.55677i) q^{53} +(0.0153998 - 0.187901i) q^{54} +(0.592005 - 2.86566i) q^{55} +(0.686936 - 2.74374i) q^{56} +(0.00722836 + 0.00722836i) q^{57} +(-8.94226 - 10.5389i) q^{58} +5.64348i q^{59} +(10.0558 - 4.46812i) q^{60} -8.63760i q^{61} +(-8.70265 + 7.38422i) q^{62} +(2.15963 + 2.15963i) q^{63} +(3.76955 - 7.05624i) q^{64} +(7.62830 - 5.01614i) q^{65} +(4.53841 + 0.371953i) q^{66} +(0.465518 + 0.465518i) q^{67} +(6.24196 - 4.47365i) q^{68} -0.137025 q^{69} +(-0.890597 + 3.03428i) q^{70} -14.0140i q^{71} +(4.44194 + 7.40900i) q^{72} +(6.82937 - 6.82937i) q^{73} +(8.28382 + 0.678915i) q^{74} +(-11.4343 + 4.53995i) q^{75} +(-0.00819828 - 0.00135290i) q^{76} +(-0.925336 + 0.925336i) q^{77} +(9.19204 + 10.8332i) q^{78} +1.48280 q^{79} +(-4.52792 + 7.71349i) q^{80} +8.83452 q^{81} +(-2.09421 - 2.46812i) q^{82} +(5.58822 - 5.58822i) q^{83} +(-4.85538 - 0.801245i) q^{84} +(-7.17396 + 4.71738i) q^{85} +(-16.6144 - 1.36167i) q^{86} +(-17.0040 + 17.0040i) q^{87} +(-3.17453 + 1.90324i) q^{88} -12.7029i q^{89} +(-4.62956 - 8.47628i) q^{90} -4.08296 q^{91} +(0.0905289 - 0.0648826i) q^{92} +(14.0413 + 14.0413i) q^{93} +(-2.06026 - 0.168852i) q^{94} +(0.00909781 + 0.00187948i) q^{95} +(-12.7715 - 5.53375i) q^{96} +(0.598142 + 0.598142i) q^{97} +(1.07834 - 0.914975i) q^{98} -3.99677i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

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