LMFDB - Embedded newform 588.2.n.h.263.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(263,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("588.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.2
Character	$\chi$	$=$	588.263
Dual form			588.2.n.h.275.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38541 + 0.283947i) q^{2} +(0.299892 + 1.70589i) q^{3} +(1.83875 - 0.786769i) q^{4} +(-0.695526 + 0.401562i) q^{5} +(-0.899858 - 2.27821i) q^{6} +(-2.32403 + 1.61211i) q^{8} +(-2.82013 + 1.02317i) q^{9} +(0.849569 - 0.753822i) q^{10} +(1.17273 - 2.03122i) q^{11} +(1.89357 + 2.90076i) q^{12} -5.26858 q^{13} +(-0.893604 - 1.06607i) q^{15} +(2.76199 - 2.89334i) q^{16} +(1.02661 + 0.592715i) q^{17} +(3.61652 - 2.21828i) q^{18} +(-6.16982 + 3.56215i) q^{19} +(-0.962960 + 1.28559i) q^{20} +(-1.04795 + 3.14708i) q^{22} +(-3.94356 - 6.83044i) q^{23} +(-3.44704 - 3.48108i) q^{24} +(-2.17750 + 3.77153i) q^{25} +(7.29917 - 1.49600i) q^{26} +(-2.59115 - 4.50399i) q^{27} +4.23132i q^{29} +(1.54072 + 1.22321i) q^{30} +(4.24264 + 2.44949i) q^{31} +(-3.00494 + 4.79274i) q^{32} +(3.81673 + 1.39140i) q^{33} +(-1.59058 - 0.529652i) q^{34} +(-4.38051 + 4.10014i) q^{36} +(-0.523976 - 0.907554i) q^{37} +(7.53630 - 6.68696i) q^{38} +(-1.58001 - 8.98762i) q^{39} +(0.969059 - 2.05450i) q^{40} +7.16942i q^{41} -7.94315i q^{43} +(0.558245 - 4.65757i) q^{44} +(1.55061 - 1.84410i) q^{45} +(7.40294 + 8.34323i) q^{46} +(-3.04954 - 5.28195i) q^{47} +(5.76402 + 3.84396i) q^{48} +(1.94582 - 5.84343i) q^{50} +(-0.703234 + 1.92904i) q^{51} +(-9.68759 + 4.14516i) q^{52} +(-7.55175 - 4.36001i) q^{53} +(4.86871 + 5.50415i) q^{54} +1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-1.20147 - 5.86214i) q^{58} +(-0.331087 + 0.573459i) q^{59} +(-2.48186 - 1.25717i) q^{60} +(0.479062 + 0.829760i) q^{61} +(-6.57334 - 2.18887i) q^{62} +(2.80221 - 7.49317i) q^{64} +(3.66443 - 2.11566i) q^{65} +(-5.68284 - 0.843910i) q^{66} +(-7.29738 - 4.21314i) q^{67} +(2.35401 + 0.282146i) q^{68} +(10.4693 - 8.77567i) q^{69} +9.67432 q^{71} +(4.90460 - 6.92422i) q^{72} +(-0.707107 + 1.22474i) q^{73} +(0.983622 + 1.10856i) q^{74} +(-7.08684 - 2.58352i) q^{75} +(-8.54216 + 11.4041i) q^{76} +(4.74097 + 12.0029i) q^{78} +(-6.00000 + 3.46410i) q^{79} +(-0.759178 + 3.12150i) q^{80} +(6.90626 - 5.77092i) q^{81} +(-2.03574 - 9.93263i) q^{82} +5.18229 q^{83} -0.952047 q^{85} +(2.25543 + 11.0046i) q^{86} +(-7.21818 + 1.26894i) q^{87} +(0.549103 + 6.61118i) q^{88} +(-14.1733 + 8.18296i) q^{89} +(-1.62461 + 2.99513i) q^{90} +(-12.6252 - 9.45679i) q^{92} +(-2.90623 + 7.97207i) q^{93} +(5.72467 + 6.45179i) q^{94} +(2.86085 - 4.95513i) q^{95} +(-9.07704 - 3.68880i) q^{96} +4.37827 q^{97} +(-1.22896 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) $ 24 * q + 12 * q^4 + 60 * q^16 + 24 * q^18 + 12 * q^25 + 36 * q^30 + 12 * q^36 - 96 * q^39 + 24 * q^46 + 12 * q^51 - 24 * q^57 + 48 * q^58 + 12 * q^60 - 48 * q^64 - 48 * q^67 - 36 * q^72 - 24 * q^78 - 144 * q^79 + 12 * q^81 - 48 * q^85 + 192 * q^88 - 24 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.38541	+	0.283947i	−0.979636	+	0.200781i
$2$	−1.38541	+	0.283947i	−0.979636	+	0.200781i
$3$	0.299892	+	1.70589i	0.173143	+	0.984897i
$3$	0.299892	+	1.70589i	0.173143	+	0.984897i
$4$	1.83875	−	0.786769i	0.919374	−	0.393385i
$5$	−0.695526	+	0.401562i	−0.311049	+	0.179584i	−0.647396	−	0.762154i	$-0.724142\pi$
$5$	−0.695526	+	0.401562i	−0.311049	+	0.179584i	0.336347	+	0.941738i	$0.390808\pi$
$6$	−0.899858	−	2.27821i	−0.367365	−	0.930077i
$7$		0			0
$7$		0			0
$8$	−2.32403	+	1.61211i	−0.821668	+	0.569967i
$9$	−2.82013	+	1.02317i	−0.940043	+	0.341056i
$10$	0.849569	−	0.753822i	0.268657	−	0.238380i
$11$	1.17273	−	2.03122i	0.353590	−	0.612436i	−0.633285	−	0.773918i	$-0.718294\pi$
$11$	1.17273	−	2.03122i	0.353590	−	0.612436i	0.986876	+	0.161482i	$0.0516274\pi$
$12$	1.89357	+	2.90076i	0.546626	+	0.837377i
$13$	−5.26858			−1.46124			−0.730621	−	0.682784i	$-0.760769\pi$
$13$	−5.26858			−1.46124			−0.730621	+	0.682784i	$0.760769\pi$
$14$		0			0
$15$	−0.893604	−	1.06607i	−0.230727	−	0.275257i
$16$	2.76199	−	2.89334i	0.690497	−	0.723335i
$17$	1.02661	+	0.592715i	0.248990	+	0.143754i	0.619302	−	0.785153i	$-0.287416\pi$
$17$	1.02661	+	0.592715i	0.248990	+	0.143754i	−0.370312	+	0.928908i	$0.620749\pi$
$18$	3.61652	−	2.21828i	0.852423	−	0.522853i
$19$	−6.16982	+	3.56215i	−1.41545	+	0.817213i	−0.995895	−	0.0905147i	$-0.971149\pi$
$19$	−6.16982	+	3.56215i	−1.41545	+	0.817213i	−0.419560	+	0.907728i	$0.637815\pi$
$20$	−0.962960	+	1.28559i	−0.215324	+	0.287467i
$21$		0			0
$22$	−1.04795	+	3.14708i	−0.223424	+	0.670959i
$23$	−3.94356	−	6.83044i	−0.822288	−	1.42425i	−0.903974	−	0.427587i	$-0.859364\pi$
$23$	−3.94356	−	6.83044i	−0.822288	−	1.42425i	0.0816860	−	0.996658i	$-0.473970\pi$
$24$	−3.44704	−	3.48108i	−0.703624	−	0.710572i
$25$	−2.17750	+	3.77153i	−0.435499	+	0.754307i
$26$	7.29917	−	1.49600i	1.43148	−	0.293389i
$27$	−2.59115	−	4.50399i	−0.498666	−	0.866794i
$28$		0			0
$29$			4.23132i			0.785737i	0.919595	+	0.392868i	$0.128517\pi$
$29$			4.23132i			0.785737i	−0.919595	+	0.392868i	$0.871483\pi$
$30$	1.54072	+	1.22321i	0.281295	+	0.223326i
$31$	4.24264	+	2.44949i	0.762001	+	0.439941i	0.830014	−	0.557743i	$-0.188333\pi$
$31$	4.24264	+	2.44949i	0.762001	+	0.439941i	−0.0680129	+	0.997684i	$0.521666\pi$
$32$	−3.00494	+	4.79274i	−0.531204	+	0.847244i
$33$	3.81673	+	1.39140i	0.664408	+	0.242211i
$34$	−1.59058	−	0.529652i	−0.272783	−	0.0908346i
$35$		0			0
$36$	−4.38051	+	4.10014i	−0.730085	+	0.683356i
$37$	−0.523976	−	0.907554i	−0.0861412	−	0.149201i	0.819736	−	0.572742i	$-0.194120\pi$
$37$	−0.523976	−	0.907554i	−0.0861412	−	0.149201i	−0.905877	+	0.423541i	$0.860787\pi$
$38$	7.53630	−	6.68696i	1.22255	−	1.08477i
$39$	−1.58001	−	8.98762i	−0.253003	−	1.43917i
$40$	0.969059	−	2.05450i	0.153222	−	0.324846i
$41$			7.16942i			1.11968i	0.828602	+	0.559838i	$0.189137\pi$
$41$			7.16942i			1.11968i	−0.828602	+	0.559838i	$0.810863\pi$
$42$		0			0
$43$		−	7.94315i		−	1.21132i	−0.795724	−	0.605659i	$-0.792909\pi$
$43$		−	7.94315i		−	1.21132i	0.795724	−	0.605659i	$-0.207091\pi$
$44$	0.558245	−	4.65757i	0.0841587	−	0.702155i
$45$	1.55061	−	1.84410i	0.231151	−	0.274902i
$46$	7.40294	+	8.34323i	1.09150	+	1.23014i
$47$	−3.04954	−	5.28195i	−0.444821	−	0.770452i	0.553219	−	0.833036i	$-0.313399\pi$
$47$	−3.04954	−	5.28195i	−0.444821	−	0.770452i	−0.998040	+	0.0625838i	$0.980066\pi$
$48$	5.76402	+	3.84396i	0.831965	+	0.554828i
$49$		0			0
$50$	1.94582	−	5.84343i	0.275180	−	0.826386i
$51$	−0.703234	+	1.92904i	−0.0984725	+	0.270120i
$52$	−9.68759	+	4.14516i	−1.34343	+	0.574830i
$53$	−7.55175	−	4.36001i	−1.03731	−	0.598893i	−0.118242	−	0.992985i	$-0.537726\pi$
$53$	−7.55175	−	4.36001i	−1.03731	−	0.598893i	−0.919071	+	0.394092i	$0.871059\pi$
$54$	4.86871	+	5.50415i	0.662547	+	0.749020i
$55$			1.88369i			0.253997i
$56$		0			0
$57$	−7.92692	−	9.45679i	−1.04995	−	1.25258i
$58$	−1.20147	−	5.86214i	−0.157761	−	0.769736i
$59$	−0.331087	+	0.573459i	−0.0431038	+	0.0746580i	−0.886772	−	0.462206i	$-0.847058\pi$
$59$	−0.331087	+	0.573459i	−0.0431038	+	0.0746580i	0.843669	+	0.536864i	$0.180391\pi$
$60$	−2.48186	−	1.25717i	−0.320407	−	0.162300i
$61$	0.479062	+	0.829760i	0.0613376	+	0.106240i	0.895064	−	0.445939i	$-0.147130\pi$
$61$	0.479062	+	0.829760i	0.0613376	+	0.106240i	−0.833726	+	0.552178i	$0.813797\pi$
$62$	−6.57334	−	2.18887i	−0.834815	−	0.277987i
$63$		0			0
$64$	2.80221	−	7.49317i	0.350276	−	0.936647i
$65$	3.66443	−	2.11566i	0.454517	−	0.262416i
$66$	−5.68284	−	0.843910i	−0.699510	−	0.103878i
$67$	−7.29738	−	4.21314i	−0.891517	−	0.514717i	−0.0170783	−	0.999854i	$-0.505436\pi$
$67$	−7.29738	−	4.21314i	−0.891517	−	0.514717i	−0.874438	+	0.485137i	$0.838770\pi$
$68$	2.35401	+	0.282146i	0.285466	+	0.0342153i
$69$	10.4693	−	8.77567i	1.26036	−	1.05647i
$70$		0			0
$71$	9.67432			1.14813			0.574065	−	0.818810i	$-0.305366\pi$
$71$	9.67432			1.14813			0.574065	+	0.818810i	$0.305366\pi$
$72$	4.90460	−	6.92422i	0.578013	−	0.816028i
$73$	−0.707107	+	1.22474i	−0.0827606	+	0.143346i	−0.904435	−	0.426612i	$-0.859707\pi$
$73$	−0.707107	+	1.22474i	−0.0827606	+	0.143346i	0.821674	+	0.569958i	$0.193040\pi$
$74$	0.983622	+	1.10856i	0.114344	+	0.128867i
$75$	−7.08684	−	2.58352i	−0.818318	−	0.298319i
$76$	−8.54216	+	11.4041i	−0.979853	+	1.30814i
$77$		0			0
$78$	4.74097	+	12.0029i	0.536810	+	1.35907i
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	−0.797988	−	0.602673i	$-0.794102\pi$
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	0.122936	+	0.992415i	$0.460769\pi$
$80$	−0.759178	+	3.12150i	−0.0848787	+	0.348995i
$81$	6.90626	−	5.77092i	0.767362	−	0.641214i
$82$	−2.03574	−	9.93263i	−0.224810	−	1.09688i
$83$	5.18229			0.568830			0.284415	−	0.958701i	$-0.408201\pi$
$83$	5.18229			0.568830			0.284415	+	0.958701i	$0.408201\pi$
$84$		0			0
$85$	−0.952047			−0.103264
$86$	2.25543	+	11.0046i	0.243210	+	1.18665i
$87$	−7.21818	+	1.26894i	−0.773870	+	0.136045i
$88$	0.549103	+	6.61118i	0.0585345	+	0.704754i
$89$	−14.1733	+	8.18296i	−1.50237	+	0.867392i	−0.502370	+	0.864653i	$0.667539\pi$
$89$	−14.1733	+	8.18296i	−1.50237	+	0.867392i	−0.999996	+	0.00273917i	$0.999128\pi$
$90$	−1.62461	+	2.99513i	−0.171249	+	0.315714i
$91$		0			0
$92$	−12.6252	−	9.45679i	−1.31627	−	0.985938i
$93$	−2.90623	+	7.97207i	−0.301362	+	0.826665i
$94$	5.72467	+	6.45179i	0.590455	+	0.665451i
$95$	2.86085	−	4.95513i	0.293517	−	0.508386i
$96$	−9.07704	−	3.68880i	−0.926422	−	0.376487i
$97$	4.37827			0.444546			0.222273	−	0.974984i	$-0.428652\pi$
$97$	4.37827			0.444546			0.222273	+	0.974984i	$0.428652\pi$
$98$		0			0
$99$	−1.22896	+	6.92820i	−0.123515	+	0.696311i
$100$	−1.03654	+	8.64809i	−0.103654	+	0.864809i
$101$	−7.26887	−	4.19668i	−0.723279	−	0.417586i	0.0926791	−	0.995696i	$-0.470457\pi$
$101$	−7.26887	−	4.19668i	−0.723279	−	0.417586i	−0.815959	+	0.578110i	$0.803790\pi$
$102$	0.426526	−	2.87220i	0.0422323	−	0.284390i
$103$	2.22304	−	1.28347i	0.219043	−	0.126465i	−0.386464	−	0.922304i	$-0.626304\pi$
$103$	2.22304	−	1.28347i	0.219043	−	0.126465i	0.605507	+	0.795840i	$0.292970\pi$
$104$	12.2443	−	8.49353i	1.20065	−	0.832859i
$105$		0			0
$106$	11.7003	+	3.89612i	1.13644	+	0.378424i
$107$	3.04995	+	5.28267i	0.294850	+	0.510695i	0.974950	−	0.222424i	$-0.0713970\pi$
$107$	3.04995	+	5.28267i	0.294850	+	0.510695i	−0.680100	+	0.733119i	$0.738064\pi$
$108$	−8.30807	−	6.24308i	−0.799444	−	0.600740i
$109$	−2.72545	+	4.72062i	−0.261051	+	0.452153i	−0.966521	−	0.256586i	$-0.917402\pi$
$109$	−2.72545	+	4.72062i	−0.261051	+	0.452153i	0.705471	+	0.708739i	$0.250736\pi$
$110$	−0.534868	−	2.60969i	−0.0509977	−	0.248824i
$111$	1.39105	−	1.16601i	0.132033	−	0.110673i
$112$		0			0
$113$			7.09803i			0.667726i	0.942622	+	0.333863i	$0.108352\pi$
$113$			7.09803i			0.667726i	−0.942622	+	0.333863i	$0.891648\pi$
$114$	13.6673	+	10.8507i	1.28006	+	1.01627i
$115$	5.48569	+	3.16716i	0.511543	+	0.295340i
$116$	3.32907	+	7.78034i	0.309097	+	0.722386i
$117$	14.8581	−	5.39064i	1.37363	−	0.498364i
$118$	0.295860	−	0.888490i	0.0272361	−	0.0817921i
$119$		0			0
$120$	3.79537	+	1.03698i	0.346469	+	0.0946629i
$121$	2.74943	+	4.76214i	0.249948	+	0.432922i
$122$	−0.899307	−	1.01353i	−0.0814195	−	0.0917610i
$123$	−12.2303	+	2.15005i	−1.10277	+	0.193864i
$124$	9.72833	+	1.16601i	0.873630	+	0.104711i
$125$		−	7.51322i		−	0.672003i
$126$		0			0
$127$			4.16202i			0.369320i	0.982802	+	0.184660i	$0.0591184\pi$
$127$			4.16202i			0.369320i	−0.982802	+	0.184660i	$0.940882\pi$
$128$	−1.75456	+	11.1768i	−0.155082	+	0.987902i
$129$	13.5501	−	2.38209i	1.19302	−	0.209731i
$130$	−4.47602	+	3.97157i	−0.392573	+	0.348330i
$131$	5.24594	+	9.08624i	0.458340	+	0.793869i	0.998873	−	0.0474541i	$-0.0151108\pi$
$131$	5.24594	+	9.08624i	0.458340	+	0.793869i	−0.540533	+	0.841323i	$0.681777\pi$
$132$	8.11272	−	0.444463i	0.706122	−	0.0386855i
$133$		0			0
$134$	11.3062	+	3.76488i	0.976707	+	0.325236i
$135$	3.61084	+	2.09214i	0.310772	+	0.180063i
$136$	−3.34140	+	0.277525i	−0.286522	+	0.0237976i
$137$	11.6844	+	6.74600i	0.998267	+	0.576350i	0.907735	−	0.419544i	$-0.137810\pi$
$137$	11.6844	+	6.74600i	0.998267	+	0.576350i	0.0905318	+	0.995894i	$0.471143\pi$
$138$	−12.0126	+	15.1307i	−1.02258	+	1.28801i
$139$			7.57264i			0.642303i	0.947028	+	0.321151i	$0.104070\pi$
$139$			7.57264i			0.642303i	−0.947028	+	0.321151i	$0.895930\pi$
$140$		0			0
$141$	8.09591	−	6.78619i	0.681798	−	0.571501i
$142$	−13.4029	+	2.74700i	−1.12475	+	0.230523i
$143$	−6.17860	+	10.7017i	−0.516681	+	0.894917i
$144$	−4.82879	+	10.9856i	−0.402400	+	0.915464i
$145$	−1.69914	−	2.94299i	−0.141106	−	0.244402i
$146$	0.631873	−	1.89756i	0.0522942	−	0.157043i
$147$		0			0
$148$	−1.67750	−	1.25651i	−0.137889	−	0.103285i
$149$	13.9442	−	8.05067i	1.14235	−	0.659536i	0.195339	−	0.980736i	$-0.437419\pi$
$149$	13.9442	−	8.05067i	1.14235	−	0.659536i	0.947012	+	0.321199i	$0.104086\pi$
$150$	10.5518	+	1.56696i	0.861550	+	0.127941i
$151$	15.0553	+	8.69219i	1.22518	+	0.707360i	0.966019	−	0.258473i	$-0.0832192\pi$
$151$	15.0553	+	8.69219i	1.22518	+	0.707360i	0.259166	+	0.965833i	$0.416552\pi$
$152$	8.59627	−	18.2250i	0.697249	−	1.47824i
$153$	−3.50163	−	0.621137i	−0.283090	−	0.0502160i
$154$		0			0
$155$	−3.93449			−0.316026
$156$	−9.97642	−	15.2829i	−0.798753	−	1.22361i
$157$	−1.96109	+	3.39671i	−0.156512	+	0.271087i	−0.933609	−	0.358295i	$-0.883358\pi$
$157$	−1.96109	+	3.39671i	−0.156512	+	0.271087i	0.777096	+	0.629381i	$0.216692\pi$
$158$	7.32887	−	6.50290i	0.583053	−	0.517343i
$159$	5.17299	−	14.1900i	0.410244	−	1.12534i
$160$	0.165435	−	4.54014i	0.0130788	−	0.358930i
$161$		0			0
$162$	−7.92940	+	9.95614i	−0.622992	+	0.782228i
$163$	−6.32987	+	3.65455i	−0.495793	+	0.286246i	−0.726975	−	0.686664i	$-0.759074\pi$
$163$	−6.32987	+	3.65455i	−0.495793	+	0.286246i	0.231181	+	0.972911i	$0.425741\pi$
$164$	5.64068	+	13.1828i	0.440463	+	1.02940i
$165$	−3.21337	+	0.564904i	−0.250160	+	0.0439777i
$166$	−7.17962	+	1.47150i	−0.557247	+	0.114210i
$167$	8.37196			0.647842			0.323921	−	0.946084i	$-0.394999\pi$
$167$	8.37196			0.647842			0.323921	+	0.946084i	$0.394999\pi$
$168$		0			0
$169$	14.7579			1.13523
$170$	1.31898	−	0.270331i	0.101161	−	0.0207335i
$171$	13.7550	−	16.3585i	1.05187	−	1.25096i
$172$	−6.24943	−	14.6054i	−0.476514	−	1.11365i
$173$	−11.0601	+	6.38556i	−0.840884	+	0.485485i	−0.857565	−	0.514376i	$-0.828024\pi$
$173$	−11.0601	+	6.38556i	−0.840884	+	0.485485i	0.0166803	+	0.999861i	$0.494690\pi$
$174$	9.63986	−	3.80759i	0.730796	−	0.288653i
$175$		0			0
$176$	−2.63796	−	9.00331i	−0.198844	−	0.678650i
$177$	−1.07755	−	0.392822i	−0.0809935	−	0.0295263i
$178$	17.3124	−	15.3613i	1.29762	−	1.15137i
$179$	−10.5589	+	18.2885i	−0.789206	+	1.36694i	0.137248	+	0.990537i	$0.456174\pi$
$179$	−10.5589	+	18.2885i	−0.789206	+	1.36694i	−0.926454	+	0.376408i	$0.877159\pi$
$180$	1.40030	−	4.61080i	0.104372	−	0.343669i
$181$	−12.4075			−0.922239			−0.461120	−	0.887338i	$-0.652552\pi$
$181$	−12.4075			−0.922239			−0.461120	+	0.887338i	$0.652552\pi$
$182$		0			0
$183$	−1.27181	+	1.06607i	−0.0940151	+	0.0788059i
$184$	20.1763	+	9.51669i	1.48742	+	0.701579i
$185$	0.728878	+	0.420818i	0.0535882	+	0.0309392i
$186$	1.76269	−	11.8698i	0.129246	−	0.870338i
$187$	2.40787	−	1.39019i	0.176081	−	0.101660i
$188$	−9.76301	−	7.31290i	−0.712041	−	0.533348i
$189$		0			0
$190$	−2.55646	+	7.67724i	−0.185465	+	0.556966i
$191$	3.04995	+	5.28267i	0.220687	+	0.382241i	0.955017	−	0.296552i	$-0.0958368\pi$
$191$	3.04995	+	5.28267i	0.220687	+	0.382241i	−0.734330	+	0.678793i	$0.762503\pi$
$192$	13.6229	+	2.53312i	0.983148	+	0.182812i
$193$	−0.322504	+	0.558593i	−0.0232144	+	0.0402084i	−0.877399	−	0.479761i	$-0.840723\pi$
$193$	−0.322504	+	0.558593i	−0.0232144	+	0.0402084i	0.854185	+	0.519969i	$0.174057\pi$
$194$	−6.06572	+	1.24320i	−0.435493	+	0.0892564i
$195$	4.70802	+	5.61665i	0.337149	+	0.402217i
$196$		0			0
$197$			14.9111i			1.06237i	0.847256	+	0.531185i	$0.178253\pi$
$197$			14.9111i			1.06237i	−0.847256	+	0.531185i	$0.821747\pi$
$198$	−0.264622	−	9.94740i	−0.0188059	−	0.706931i
$199$	−16.1940	−	9.34962i	−1.14796	−	0.662777i	−0.199573	−	0.979883i	$-0.563956\pi$
$199$	−16.1940	−	9.34962i	−1.14796	−	0.662777i	−0.948390	+	0.317106i	$0.897289\pi$
$200$	−1.01956	−	12.2755i	−0.0720940	−	0.868010i
$201$	4.99874	−	13.7120i	0.352584	−	0.967171i
$202$	11.2620	+	3.75017i	0.792394	+	0.263861i
$203$		0			0
$204$	0.224639	+	4.10030i	0.0157278	+	0.287078i
$205$	−2.87897	−	4.98652i	−0.201076	−	0.348274i
$206$	−2.71540	+	2.40937i	−0.189191	+	0.167869i
$207$	18.1100	+	15.2278i	1.25873	+	1.05841i
$208$	−14.5518	+	15.2438i	−1.00898	+	1.05697i
$209$			16.7097i			1.15583i
$210$		0			0
$211$			11.7243i			0.807132i	0.914950	+	0.403566i	$0.132229\pi$
$211$			11.7243i			0.807132i	−0.914950	+	0.403566i	$0.867771\pi$
$212$	−17.3161	−	2.07547i	−1.18927	−	0.142544i
$213$	2.90125	+	16.5033i	0.198791	+	1.13079i
$214$	−5.72545	−	6.45267i	−0.391384	−	0.441095i
$215$	3.18967	+	5.52466i	0.217533	+	0.376779i
$216$	13.2828	+	6.29020i	0.903782	+	0.427994i
$217$		0			0
$218$	2.43547	−	7.31389i	0.164951	−	0.495359i
$219$	−2.30134	−	0.838956i	−0.155510	−	0.0566914i
$220$	1.48203	+	3.46363i	0.0999184	+	0.233518i
$221$	−5.40879	−	3.12277i	−0.363835	−	0.210060i
$222$	−1.59610	+	2.01040i	−0.107123	+	0.134929i
$223$			0.683260i			0.0457545i	0.999738	+	0.0228772i	$0.00728269\pi$
$223$			0.683260i			0.0457545i	−0.999738	+	0.0228772i	$0.992717\pi$
$224$		0			0
$225$	2.28191	−	12.8642i	0.152128	−	0.857610i
$226$	−2.01546	−	9.83371i	−0.134067	−	0.654129i
$227$	4.37694	−	7.58108i	0.290507	−	0.503174i	−0.683422	−	0.730023i	$-0.739509\pi$
$227$	4.37694	−	7.58108i	0.290507	−	0.503174i	0.973930	+	0.226850i	$0.0728426\pi$
$228$	−22.0159	−	11.1520i	−1.45804	−	0.738559i
$229$	−9.24927	−	16.0202i	−0.611209	−	1.05864i	−0.991037	−	0.133588i	$-0.957350\pi$
$229$	−9.24927	−	16.0202i	−0.611209	−	1.05864i	0.379828	−	0.925057i	$-0.375983\pi$
$230$	−8.49926	−	2.83019i	−0.560425	−	0.186617i
$231$		0			0
$232$	−6.82135	−	9.83371i	−0.447844	−	0.645615i
$233$	−8.78072	+	5.06955i	−0.575244	+	0.332117i	−0.759241	−	0.650810i	$-0.774430\pi$
$233$	−8.78072	+	5.06955i	−0.575244	+	0.332117i	0.183997	+	0.982927i	$0.441096\pi$
$234$	−19.0539	+	11.6872i	−1.24560	+	0.764015i
$235$	4.24206	+	2.44916i	0.276722	+	0.159765i
$236$	−0.157605	+	1.31494i	−0.0102592	+	0.0855950i
$237$	−7.70873	−	9.19649i	−0.500736	−	0.597376i
$238$		0			0
$239$	−1.49470			−0.0966841			−0.0483421	−	0.998831i	$-0.515394\pi$
$239$	−1.49470			−0.0966841			−0.0483421	+	0.998831i	$0.515394\pi$
$240$	−5.55262	−	0.358961i	−0.358420	−	0.0231709i
$241$	−5.16686	+	8.94926i	−0.332827	+	0.576472i	−0.983065	−	0.183258i	$-0.941336\pi$
$241$	−5.16686	+	8.94926i	−0.332827	+	0.576472i	0.650238	+	0.759730i	$0.274669\pi$
$242$	−5.16129	−	5.81685i	−0.331780	−	0.373921i
$243$	11.9157	+	10.0507i	0.764393	+	0.644751i
$244$	1.53370	+	1.14881i	0.0981853	+	0.0735449i
$245$		0			0
$246$	16.3335	−	6.45146i	1.04138	−	0.411330i
$247$	32.5062	−	18.7675i	2.06832	−	1.19415i
$248$	−13.8089	+	1.14692i	−0.876863	+	0.0728294i
$249$	1.55413	+	8.84042i	0.0984889	+	0.560239i
$250$	2.13336	+	10.4089i	0.134925	+	0.658318i
$251$	−26.9555			−1.70142			−0.850709	−	0.525636i	$-0.823827\pi$
$251$	−26.9555			−1.70142			−0.850709	+	0.525636i	$0.823827\pi$
$252$		0			0
$253$	−18.4989			−1.16301
$254$	−1.18179	−	5.76613i	−0.0741524	−	0.361799i
$255$	−0.285511	−	1.62409i	−0.0178794	−	0.101704i
$256$	−0.742842	−	15.9827i	−0.0464276	−	0.998922i
$257$	2.41766	−	1.39584i	0.150810	−	0.0870700i	−0.422696	−	0.906271i	$-0.638916\pi$
$257$	2.41766	−	1.39584i	0.150810	−	0.0870700i	0.573506	+	0.819201i	$0.305583\pi$
$258$	−18.0962	+	7.14771i	−1.12662	+	0.444997i
$259$		0			0
$260$	5.07343	−	6.77323i	0.314641	−	0.420058i
$261$	−4.32935	−	11.9329i	−0.267980	−	0.738627i
$262$	−9.84782	−	11.0986i	−0.608400	−	0.685676i
$263$	7.65516	−	13.2591i	0.472037	−	0.817592i	−0.527451	−	0.849586i	$-0.676852\pi$
$263$	7.65516	−	13.2591i	0.472037	−	0.817592i	0.999488	+	0.0319931i	$0.0101855\pi$
$264$	−11.1133	+	2.91935i	−0.683975	+	0.179674i
$265$	7.00325			0.430206
$266$		0			0
$267$	−18.2097	−	21.7241i	−1.11442	−	1.32949i
$268$	−16.7328	−	2.00556i	−1.02212	−	0.122509i
$269$	−26.5752	−	15.3432i	−1.62032	−	0.935492i	−0.986834	−	0.161739i	$-0.948290\pi$
$269$	−26.5752	−	15.3432i	−1.62032	−	0.935492i	−0.633487	−	0.773754i	$-0.718377\pi$
$270$	−5.59657	−	1.87319i	−0.340596	−	0.113999i
$271$	17.0488	−	9.84312i	1.03564	−	0.597927i	0.117045	−	0.993127i	$-0.462658\pi$
$271$	17.0488	−	9.84312i	1.03564	−	0.597927i	0.918595	+	0.395199i	$0.129325\pi$
$272$	4.55042	−	1.33327i	0.275910	−	0.0808412i
$273$		0			0
$274$	−18.1033	−	6.02825i	−1.09366	−	0.364180i
$275$	5.10721	+	8.84595i	0.307977	+	0.533431i
$276$	12.3461	−	24.3732i	0.743145	−	1.46709i
$277$	6.55646	−	11.3561i	0.393940	−	0.682324i	−0.599025	−	0.800730i	$-0.704445\pi$
$277$	6.55646	−	11.3561i	0.393940	−	0.682324i	0.992965	+	0.118406i	$0.0377785\pi$
$278$	−2.15023	−	10.4912i	−0.128962	−	0.629223i
$279$	−14.4710	−	2.56695i	−0.866358	−	0.153679i
$280$		0			0
$281$			2.86670i			0.171013i	0.996338	+	0.0855066i	$0.0272509\pi$
$281$			2.86670i			0.171013i	−0.996338	+	0.0855066i	$0.972749\pi$
$282$	−9.28927	+	11.7005i	−0.553168	+	0.696755i
$283$	−1.72374	−	0.995200i	−0.102466	−	0.0591585i	0.447892	−	0.894088i	$-0.352175\pi$
$283$	−1.72374	−	0.995200i	−0.102466	−	0.0591585i	−0.550357	+	0.834929i	$0.685508\pi$
$284$	17.7886	−	7.61146i	1.05556	−	0.451657i
$285$	9.31086	+	3.39429i	0.551528	+	0.201060i
$286$	5.52122	−	16.5806i	0.326477	−	0.980433i
$287$		0			0
$288$	3.57056	−	16.5907i	0.210397	−	0.977616i
$289$	−7.79738	−	13.5055i	−0.458669	−	0.794439i
$290$	3.18967	+	3.59480i	0.187304	+	0.211094i
$291$	1.31301	+	7.46886i	0.0769700	+	0.437832i
$292$	−0.336600	+	2.80833i	−0.0196980	+	0.164345i
$293$			16.7482i			0.978441i	0.872160	+	0.489221i	$0.162719\pi$
$293$			16.7482i			0.978441i	−0.872160	+	0.489221i	$0.837281\pi$
$294$		0			0
$295$		−	0.531807i		−	0.0309630i
$296$	2.68081	+	1.26447i	0.155819	+	0.0734960i
$297$	−12.1873	−	0.0187619i	−0.707180	−	0.00108867i
$298$	−17.0325	+	15.1129i	−0.986666	+	0.875468i
$299$	20.7769	+	35.9867i	1.20156	+	2.08117i
$300$	−15.0635	+	0.825270i	−0.869694	+	0.0476470i
$301$		0			0
$302$	−23.3260	−	7.76737i	−1.34226	−	0.446962i
$303$	4.97921	−	13.6585i	0.286048	−	0.784657i
$304$	−6.73447	+	27.6900i	−0.386248	+	1.58813i
$305$	−0.666400	−	0.384746i	−0.0381579	−	0.0220305i
$306$	5.02757	−	0.133744i	0.287407	−	0.00764565i
$307$		−	15.4869i		−	0.883885i	−0.897043	−	0.441942i	$-0.854290\pi$
$307$		−	15.4869i		−	0.883885i	0.897043	−	0.441942i	$-0.145710\pi$
$308$		0			0
$309$	2.85614	+	3.40737i	0.162480	+	0.193838i
$310$	5.45090	−	1.11719i	0.309590	−	0.0634519i
$311$	5.44973	−	9.43920i	0.309026	−	0.535248i	−0.669124	−	0.743151i	$-0.733330\pi$
$311$	5.44973	−	9.43920i	0.309026	−	0.535248i	0.978149	+	0.207903i	$0.0666638\pi$
$312$	18.1610	+	18.3403i	1.02816	+	1.03832i
$313$	16.9011	+	29.2736i	0.955308	+	1.65464i	0.733662	+	0.679514i	$0.237810\pi$
$313$	16.9011	+	29.2736i	0.955308	+	1.65464i	0.221646	+	0.975127i	$0.428857\pi$
$314$	1.75244	−	5.26270i	0.0988958	−	0.296991i
$315$		0			0
$316$	−8.30704	+	11.0902i	−0.467307	+	0.623874i
$317$	−8.04243	+	4.64330i	−0.451708	+	0.260794i	−0.708551	−	0.705659i	$-0.750651\pi$
$317$	−8.04243	+	4.64330i	−0.451708	+	0.260794i	0.256843	+	0.966453i	$0.417318\pi$
$318$	−3.13752	+	21.1279i	−0.175943	+	1.18479i
$319$	8.59476	+	4.96218i	0.481214	+	0.277829i
$320$	1.05996	+	6.33695i	0.0592538	+	0.354247i
$321$	−8.09701	+	6.78712i	−0.451931	+	0.378820i
$322$		0			0
$323$	−8.44536			−0.469912
$324$	8.15849	−	16.0449i	0.453249	−	0.891384i
$325$	11.4723	−	19.8706i	0.636369	−	1.10222i
$326$	7.73179	−	6.86041i	0.428224	−	0.379963i
$327$	−8.87020	−	3.23364i	−0.490523	−	0.178821i
$328$	−11.5579	−	16.6619i	−0.638178	−	0.920002i
$329$		0			0
$330$	4.29145	−	1.69505i	0.236236	−	0.0933096i
$331$	0.878968	−	0.507473i	0.0483125	−	0.0278932i	−0.475649	−	0.879635i	$-0.657787\pi$
$331$	0.878968	−	0.507473i	0.0483125	−	0.0278932i	0.523962	+	0.851742i	$0.324453\pi$
$332$	9.52893	−	4.07727i	0.522968	−	0.223769i
$333$	2.40626	+	2.02330i	0.131862	+	0.110876i
$334$	−11.5986	+	2.37719i	−0.634649	+	0.130074i
$335$	6.76735			0.369740
$336$		0			0
$337$	−12.6597			−0.689620			−0.344810	−	0.938673i	$-0.612057\pi$
$337$	−12.6597			−0.689620			−0.344810	+	0.938673i	$0.612057\pi$
$338$	−20.4459	+	4.19047i	−1.11211	+	0.227932i
$339$	−12.1085	+	2.12864i	−0.657641	+	0.115612i
$340$	−1.75057	+	0.749041i	−0.0949383	+	0.0406225i
$341$	9.95091	−	5.74516i	0.538872	−	0.311118i
$342$	−14.4115	+	26.5690i	−0.779283	+	1.43669i
$343$		0			0
$344$	12.8052	+	18.4601i	0.690411	+	0.995302i
$345$	−3.75772	+	10.3078i	−0.202309	+	0.554953i
$346$	13.5097	−	11.9871i	0.726285	−	0.644432i
$347$	−12.8143	+	22.1950i	−0.687907	+	1.19149i	0.284607	+	0.958644i	$0.408137\pi$
$347$	−12.8143	+	22.1950i	−0.687907	+	1.19149i	−0.972514	+	0.232846i	$0.925196\pi$
$348$	−12.2740	+	8.01230i	−0.657958	+	0.429504i
$349$	28.1235			1.50542			0.752709	−	0.658354i	$-0.228747\pi$
$349$	28.1235			1.50542			0.752709	+	0.658354i	$0.228747\pi$
$350$		0			0
$351$	13.6517	+	23.7297i	0.728672	+	1.26660i
$352$	6.21113	+	11.7243i	0.331055	+	0.624906i
$353$	8.92430	+	5.15245i	0.474993	+	0.274237i	0.718327	−	0.695705i	$-0.244908\pi$
$353$	8.92430	+	5.15245i	0.474993	+	0.274237i	−0.243335	+	0.969942i	$0.578241\pi$
$354$	1.60439	+	0.238254i	0.0852725	+	0.0126631i
$355$	−6.72874	+	3.88484i	−0.357124	+	0.206186i
$356$	−19.6230	+	26.1975i	−1.04002	+	1.38847i
$357$		0			0
$358$	9.43543	−	28.3353i	0.498678	−	1.49757i
$359$	−13.4197	−	23.2436i	−0.708265	−	1.22675i	−0.965500	−	0.260402i	$-0.916145\pi$
$359$	−13.4197	−	23.2436i	−0.708265	−	1.22675i	0.257235	−	0.966349i	$-0.417188\pi$
$360$	−0.630772	+	6.78548i	−0.0332446	+	0.357626i
$361$	15.8778	−	27.5012i	0.835675	−	1.44743i
$362$	17.1895	−	3.52306i	0.903459	−	0.185168i
$363$	−7.29917	+	6.11835i	−0.383107	+	0.321130i
$364$		0			0
$365$		−	1.13579i		−	0.0594499i
$366$	1.45928	−	1.83807i	0.0762779	−	0.0960775i
$367$	−11.5631	−	6.67596i	−0.603589	−	0.348482i	0.166863	−	0.985980i	$-0.446636\pi$
$367$	−11.5631	−	6.67596i	−0.603589	−	0.348482i	−0.770452	+	0.637498i	$0.779969\pi$
$368$	−30.6548	−	7.45554i	−1.59799	−	0.388647i
$369$	−7.33552	−	20.2187i	−0.381872	−	1.05254i
$370$	−1.12929	−	0.376045i	−0.0587089	−	0.0195496i
$371$		0			0
$372$	0.928355	+	16.9452i	0.0481330	+	0.878565i
$373$	11.4029	+	19.7505i	0.590422	+	1.02264i	0.994176	+	0.107773i	$0.0343720\pi$
$373$	11.4029	+	19.7505i	0.590422	+	1.02264i	−0.403753	+	0.914868i	$0.632295\pi$
$374$	−2.94116	+	2.60969i	−0.152084	+	0.134944i
$375$	12.8167	−	2.25315i	0.661853	−	0.116352i
$376$	15.6023	+	7.35922i	0.804627	+	0.379523i
$377$		−	22.2931i		−	1.14815i
$378$		0			0
$379$		−	1.98122i		−	0.101768i	−0.998705	−	0.0508842i	$-0.983796\pi$
$379$		−	1.98122i		−	0.101768i	0.998705	−	0.0508842i	$-0.0162040\pi$
$380$	1.36183	−	11.3621i	0.0698605	−	0.582862i
$381$	−7.09996	+	1.24816i	−0.363742	+	0.0639451i
$382$	−5.72545	−	6.45267i	−0.292939	−	0.330147i
$383$	−14.4104	−	24.9596i	−0.736339	−	1.27538i	−0.954134	−	0.299381i	$-0.903220\pi$
$383$	−14.4104	−	24.9596i	−0.736339	−	1.27538i	0.217795	−	0.975995i	$-0.430114\pi$
$384$	−19.5926	+	0.358762i	−0.999832	+	0.0183080i
$385$		0			0
$386$	0.288191	−	0.865458i	0.0146685	−	0.0440506i
$387$	8.12716	+	22.4007i	0.413127	+	1.13869i
$388$	8.05054	−	3.44469i	0.408704	−	0.174878i
$389$	1.69719	+	0.979873i	0.0860509	+	0.0496815i	0.542408	−	0.840115i	$-0.317513\pi$
$389$	1.69719	+	0.979873i	0.0860509	+	0.0496815i	−0.456357	+	0.889797i	$0.650846\pi$
$390$	−8.11740	−	6.44457i	−0.411040	−	0.326333i
$391$		−	9.34962i		−	0.472831i
$392$		0			0
$393$	−13.9269	+	11.6739i	−0.702520	+	0.588870i
$394$	−4.23396	−	20.6580i	−0.213304	−	1.04074i
$395$	2.78210	−	4.81874i	0.139983	−	0.242457i
$396$	3.19115	+	13.7061i	0.160361	+	0.688759i
$397$	−2.28155	−	3.95176i	−0.114508	−	0.198333i	0.803075	−	0.595878i	$-0.203196\pi$
$397$	−2.28155	−	3.95176i	−0.114508	−	0.198333i	−0.917583	+	0.397545i	$0.869862\pi$
$398$	25.0902	+	8.35485i	1.25766	+	0.418791i
$399$		0			0
$400$	4.89811	+	16.7172i	0.244906	+	0.835858i
$401$	23.1931	−	13.3905i	1.15821	−	0.668692i	0.207335	−	0.978270i	$-0.433521\pi$
$401$	23.1931	−	13.3905i	1.15821	−	0.668692i	0.950874	+	0.309578i	$0.100188\pi$
$402$	−3.03183	+	20.4162i	−0.151214	+	1.01827i
$403$	−22.3527	−	12.9053i	−1.11347	−	0.642860i
$404$	−16.6674	−	1.99772i	−0.829236	−	0.0993903i
$405$	−2.48610	+	6.78712i	−0.123535	+	0.337255i
$406$		0			0
$407$	−2.45792			−0.121835
$408$	−1.47549	−	5.61683i	−0.0730475	−	0.278075i
$409$	9.02122	−	15.6252i	0.446071	−	0.772617i	−0.552055	−	0.833807i	$-0.686156\pi$
$409$	9.02122	−	15.6252i	0.446071	−	0.772617i	0.998126	+	0.0611902i	$0.0194896\pi$
$410$	5.40447	+	6.09092i	0.266908	+	0.300809i
$411$	−8.00388	+	21.9554i	−0.394802	+	1.08298i
$412$	3.07782	−	4.10901i	0.151633	−	0.202436i
$413$		0			0
$414$	−29.4138	−	15.9545i	−1.44561	−	0.784123i
$415$	−3.60442	+	2.08101i	−0.176934	+	0.102153i
$416$	15.8318	−	25.2509i	0.776217	−	1.23803i
$417$	−12.9181	+	2.27097i	−0.632602	+	0.111210i
$418$	−4.74468	−	23.1499i	−0.232070	−	1.13230i
$419$	17.5395			0.856861			0.428430	−	0.903575i	$-0.359067\pi$
$419$	17.5395			0.856861			0.428430	+	0.903575i	$0.359067\pi$
$420$		0			0
$421$	15.4006			0.750582			0.375291	−	0.926907i	$-0.377543\pi$
$421$	15.4006			0.750582			0.375291	+	0.926907i	$0.377543\pi$
$422$	−3.32907	−	16.2430i	−0.162057	−	0.790696i
$423$	14.0044	+	11.7756i	0.680918	+	0.572550i
$424$	24.5793	−	2.04147i	1.19368	−	0.0991428i
$425$	−4.47089	+	2.58127i	−0.216870	+	0.125210i
$426$	−8.70551	−	22.0402i	−0.421784	−	1.06785i
$427$		0			0
$428$	9.76434	+	7.31389i	0.471977	+	0.353530i
$429$	−20.1088	−	7.33068i	−0.970861	−	0.353929i
$430$	−5.98772	−	6.74825i	−0.288754	−	0.325430i
$431$	4.50180	−	7.79735i	0.216844	−	0.375585i	−0.736997	−	0.675896i	$-0.763757\pi$
$431$	4.50180	−	7.79735i	0.216844	−	0.375585i	0.953841	+	0.300311i	$0.0970903\pi$
$432$	−20.1883	−	4.94291i	−0.971310	−	0.237816i
$433$	6.15889			0.295977			0.147989	−	0.988989i	$-0.452720\pi$
$433$	6.15889			0.295977			0.147989	+	0.988989i	$0.452720\pi$
$434$		0			0
$435$	4.51087	−	3.78113i	0.216280	−	0.181291i
$436$	−1.29738	+	10.8243i	−0.0621331	+	0.518391i
$437$	48.6621	+	28.0951i	2.32782	+	1.34397i
$438$	3.42653	+	0.508844i	0.163726	+	0.0243135i
$439$	25.3306	−	14.6246i	1.20896	−	0.697996i	0.246432	−	0.969160i	$-0.420742\pi$
$439$	25.3306	−	14.6246i	1.20896	−	0.697996i	0.962533	+	0.271164i	$0.0874086\pi$
$440$	−3.03671	−	4.37775i	−0.144770	−	0.208701i
$441$		0			0
$442$	8.38012	+	2.79052i	0.398602	+	0.132731i
$443$	−3.60820	−	6.24958i	−0.171431	−	0.296927i	0.767490	−	0.641061i	$-0.221506\pi$
$443$	−3.60820	−	6.24958i	−0.171431	−	0.296927i	−0.938920	+	0.344135i	$0.888172\pi$
$444$	1.64041	−	3.23844i	0.0778503	−	0.153690i
$445$	6.57193	−	11.3829i	0.311539	−	0.539602i
$446$	−0.194010	−	0.946599i	−0.00918663	−	0.0448227i
$447$	17.9153	+	21.3729i	0.847365	+	1.01090i
$448$		0			0
$449$			4.43423i			0.209264i	0.994511	+	0.104632i	$0.0333665\pi$
$449$			4.43423i			0.209264i	−0.994511	+	0.104632i	$0.966634\pi$
$450$	0.491345	+	18.4701i	0.0231622	+	0.870690i
$451$	14.5627	+	8.40777i	0.685730	+	0.395907i
$452$	5.58451	+	13.0515i	0.262673	+	0.613890i
$453$	−10.3130	+	28.2894i	−0.484545	+	1.32915i
$454$	−3.91125	+	11.7458i	−0.183564	+	0.551256i
$455$		0			0
$456$	33.6678	+	9.19877i	1.57664	+	0.430772i
$457$	−6.83102	−	11.8317i	−0.319541	−	0.553462i	0.660851	−	0.750517i	$-0.270196\pi$
$457$	−6.83102	−	11.8317i	−0.319541	−	0.553462i	−0.980392	+	0.197055i	$0.936862\pi$
$458$	17.3630	+	19.5683i	0.811318	+	0.914368i
$459$	0.00948255	−	6.15967i	0.000442608	−	0.287509i
$460$	12.5786	+	1.50764i	0.586482	+	0.0702943i
$461$		−	5.25789i		−	0.244885i	−0.992476	−	0.122442i	$-0.960927\pi$
$461$		−	5.25789i		−	0.244885i	0.992476	−	0.122442i	$-0.0390726\pi$
$462$		0			0
$463$			15.8863i			0.738299i	0.929370	+	0.369149i	$0.120351\pi$
$463$			15.8863i			0.738299i	−0.929370	+	0.369149i	$0.879649\pi$
$464$	12.2427	+	11.6869i	0.568351	+	0.542549i
$465$	−1.17992	−	6.71181i	−0.0547176	−	0.311253i
$466$	10.7254	−	9.51669i	0.496847	−	0.440852i
$467$	−13.5384	−	23.4491i	−0.626481	−	1.08510i	−0.988252	−	0.152830i	$-0.951161\pi$
$467$	−13.5384	−	23.4491i	−0.626481	−	1.08510i	0.361771	−	0.932267i	$-0.382172\pi$
$468$	23.0791	−	21.6019i	1.06683	−	0.998548i
$469$		0			0
$470$	−6.57245	−	2.18858i	−0.303164	−	0.100951i
$471$	−6.38253	−	2.32676i	−0.294092	−	0.107212i
$472$	−0.155024	−	1.86648i	−0.00713555	−	0.0859118i
$473$	−16.1343	−	9.31514i	−0.741856	−	0.428311i
$474$	13.2911	+	10.5521i	0.610481	+	0.484673i
$475$		−	31.0263i		−	1.42358i
$476$		0			0
$477$	25.7579	+	4.56908i	1.17937	+	0.209204i
$478$	2.07078	−	0.424416i	0.0947152	−	0.0194123i
$479$	−7.63026	+	13.2160i	−0.348635	+	0.603854i	−0.986007	−	0.166702i	$-0.946688\pi$
$479$	−7.63026	+	13.2160i	−0.348635	+	0.603854i	0.637372	+	0.770556i	$0.280021\pi$
$480$	7.79460	−	1.07934i	0.355773	−	0.0492649i
$481$	2.76061	+	4.78152i	0.125873	+	0.218019i
$482$	4.61712	−	13.8655i	0.210304	−	0.631558i
$483$		0			0
$484$	8.80221	+	6.59322i	0.400100	+	0.299692i
$485$	−3.04520	+	1.75815i	−0.138275	+	0.0798334i
$486$	−19.3621	−	10.5409i	−0.878280	−	0.478146i
$487$	−5.25172	−	3.03208i	−0.237978	−	0.137397i	0.376269	−	0.926511i	$-0.377207\pi$
$487$	−5.25172	−	3.03208i	−0.237978	−	0.137397i	−0.614247	+	0.789114i	$0.710540\pi$
$488$	−2.45102	−	1.15608i	−0.110952	−	0.0523335i
$489$	−8.13254	−	9.70209i	−0.367766	−	0.438744i
$490$		0			0
$491$	4.03833			0.182247			0.0911235	−	0.995840i	$-0.470954\pi$
$491$	4.03833			0.182247			0.0911235	+	0.995840i	$0.470954\pi$
$492$	−20.7968	+	13.5758i	−0.937591	+	0.612044i
$493$	−2.50797	+	4.34393i	−0.112953	+	0.195641i
$494$	−39.7056	+	35.2308i	−1.78644	+	1.58511i
$495$	−1.92733	−	5.31225i	−0.0866270	−	0.238768i
$496$	18.8053	−	5.50994i	0.844384	−	0.247404i
$497$		0			0
$498$	−4.66333	−	11.8064i	−0.208969	−	0.529056i
$499$	−33.3430	+	19.2506i	−1.49264	+	0.861776i	−0.999964	−	0.00843800i	$-0.997314\pi$
$499$	−33.3430	+	19.2506i	−1.49264	+	0.861776i	−0.492675	+	0.870214i	$0.663981\pi$
$500$	−5.91117	−	13.8149i	−0.264356	−	0.617822i
$501$	2.51068	+	14.2816i	0.112169	+	0.638057i
$502$	37.3446	−	7.65395i	1.66677	−	0.341613i
$503$	−14.3498			−0.639827			−0.319914	−	0.947447i	$-0.603654\pi$
$503$	−14.3498			−0.639827			−0.319914	+	0.947447i	$0.603654\pi$
$504$		0			0
$505$	6.74091			0.299967
$506$	25.6286	−	5.25270i	1.13933	−	0.233511i
$507$	4.42579	+	25.1754i	0.196556	+	1.11808i
$508$	3.27455	+	7.65291i	0.145285	+	0.339543i
$509$	10.4646	−	6.04176i	0.463837	−	0.267796i	−0.249819	−	0.968292i	$-0.580371\pi$
$509$	10.4646	−	6.04176i	0.463837	−	0.267796i	0.713656	+	0.700496i	$0.247038\pi$
$510$	0.856707	+	2.16897i	0.0379356	+	0.0960435i
$511$		0			0
$512$	5.56740	+	21.9318i	0.246047	+	0.969258i
$513$	32.0308	+	18.5588i	1.41419	+	0.819391i
$514$	−2.95312	+	2.62030i	−0.130257	+	0.115577i
$515$	−1.03079	+	1.78538i	−0.0454220	+	0.0786732i
$516$	23.0412	−	15.0409i	1.01433	−	0.662139i
$517$	−14.3051			−0.629137
$518$		0			0
$519$	−14.2099	−	16.9524i	−0.623746	−	0.744126i
$520$	−5.10557	+	10.8243i	−0.223894	+	0.474678i
$521$	−27.6002	−	15.9350i	−1.20919	−	0.698125i	−0.246606	−	0.969116i	$-0.579316\pi$
$521$	−27.6002	−	15.9350i	−1.20919	−	0.698125i	−0.962582	+	0.270990i	$0.912649\pi$
$522$	9.38625	+	15.3027i	0.410825	+	0.669780i
$523$	−31.7039	+	18.3043i	−1.38631	+	0.800389i	−0.992898	−	0.118971i	$-0.962040\pi$
$523$	−31.7039	+	18.3043i	−1.38631	+	0.800389i	−0.393417	+	0.919360i	$0.628707\pi$
$524$	16.7947	+	12.5800i	0.733682	+	0.549558i
$525$		0			0
$526$	−6.84068	+	20.5430i	−0.298268	+	0.895719i
$527$	2.90370	+	5.02935i	0.126487	+	0.219082i
$528$	14.5676	−	7.20009i	0.633972	−	0.313344i
$529$	−19.6033	+	33.9539i	−0.852316	+	1.47625i
$530$	−9.70241	+	1.98855i	−0.421446	+	0.0863773i
$531$	0.346963	−	1.95599i	0.0150569	−	0.0848825i
$532$		0			0
$533$		−	37.7727i		−	1.63612i
$534$	31.3965	+	24.9263i	1.35866	+	1.07867i
$535$	−4.24264	−	2.44949i	−0.183425	−	0.105901i
$536$	23.7514	−	1.97271i	1.02590	−	0.0852080i
$537$	−34.3647	−	12.5277i	−1.48294	−	0.540610i
$538$	41.1744	+	13.7108i	1.77515	+	0.591113i
$539$		0			0
$540$	8.28546	+	1.00602i	0.356549	+	0.0432921i
$541$	18.1033	+	31.3558i	0.778320	+	1.34809i	0.932909	+	0.360111i	$0.117261\pi$
$541$	18.1033	+	31.3558i	0.778320	+	1.34809i	−0.154589	+	0.987979i	$0.549405\pi$
$542$	−20.8247	+	18.4778i	−0.894498	+	0.793688i
$543$	−3.72090	−	21.1658i	−0.159679	−	0.908311i
$544$	−5.92564	+	3.13921i	−0.254060	+	0.134592i
$545$		−	4.37775i		−	0.187522i
$546$		0			0
$547$		−	31.3917i		−	1.34221i	−0.741361	−	0.671106i	$-0.765820\pi$
$547$		−	31.3917i		−	1.34221i	0.741361	−	0.671106i	$-0.234180\pi$
$548$	26.7922	+	3.21126i	1.14451	+	0.137178i
$549$	−2.20000	−	1.84987i	−0.0938937	−	0.0789505i
$550$	−9.58739	−	10.8051i	−0.408808	−	0.460733i
$551$	−15.0726	−	26.1065i	−0.642115	−	1.11218i
$552$	−10.1837	+	37.2726i	−0.433447	+	1.58643i
$553$		0			0
$554$	−5.85888	+	17.5946i	−0.248920	+	0.747525i
$555$	−0.499285	+	1.36959i	−0.0211935	+	0.0581357i
$556$	5.95792	+	13.9242i	0.252672	+	0.590517i
$557$	30.5691	+	17.6491i	1.29526	+	0.747816i	0.979581	−	0.201051i	$-0.0644356\pi$
$557$	30.5691	+	17.6491i	1.29526	+	0.747816i	0.315675	+	0.948867i	$0.397769\pi$
$558$	20.7773	−	0.552719i	0.879572	−	0.0233985i
$559$			41.8491i			1.77003i
$560$		0			0
$561$	3.09361	+	3.69066i	0.130612	+	0.155820i
$562$	−0.813993	−	3.97157i	−0.0343362	−	0.167531i
$563$	13.2232	−	22.9032i	0.557290	−	0.965254i	−0.440432	−	0.897786i	$-0.645175\pi$
$563$	13.2232	−	22.9032i	0.557290	−	0.965254i	0.997721	−	0.0674681i	$-0.0214921\pi$
$564$	9.54716	−	18.8477i	0.402008	−	0.793632i
$565$	−2.85030	−	4.93686i	−0.119913	−	0.207695i
$566$	2.67067	+	0.889314i	0.112257	+	0.0373807i
$567$		0			0
$568$	−22.4834	+	15.5961i	−0.943382	+	0.654396i
$569$	−23.7332	+	13.7024i	−0.994948	+	0.574434i	−0.906750	−	0.421669i	$-0.861444\pi$
$569$	−23.7332	+	13.7024i	−0.994948	+	0.574434i	−0.0881985	+	0.996103i	$0.528111\pi$
$570$	−13.8632	−	2.05870i	−0.580666	−	0.0862296i
$571$	−24.3299	−	14.0469i	−1.01817	−	0.587843i	−0.104599	−	0.994514i	$-0.533356\pi$
$571$	−24.3299	−	14.0469i	−1.01817	−	0.587843i	−0.913574	+	0.406672i	$0.866689\pi$
$572$	−2.94116	+	24.5388i	−0.122976	+	1.02602i
$573$	−8.09701	+	6.78712i	−0.338257	+	0.283536i
$574$		0			0
$575$	34.3483			1.43242
$576$	−0.235827	+	23.9988i	−0.00982612	+	0.999952i
$577$	−11.4154	+	19.7721i	−0.475231	+	0.823124i	−0.999598	−	0.0283688i	$-0.990969\pi$
$577$	−11.4154	+	19.7721i	−0.475231	+	0.823124i	0.524367	+	0.851492i	$0.324302\pi$
$578$	14.6374	+	16.4966i	0.608837	+	0.686169i
$579$	−1.04962	−	0.382639i	−0.0436206	−	0.0159019i
$580$	−5.43974	−	4.07459i	−0.225873	−	0.169188i
$581$		0			0
$582$	−3.93982	−	9.97464i	−0.163311	−	0.413462i
$583$	−17.7123	+	10.2262i	−0.733568	+	0.423526i
$584$	−0.331087	−	3.98627i	−0.0137005	−	0.164953i
$585$	−8.16950	+	9.71577i	−0.337767	+	0.401697i
$586$	−4.75561	−	23.2032i	−0.196452	−	0.958517i
$587$	28.4011			1.17224			0.586119	−	0.810225i	$-0.300655\pi$
$587$	28.4011			1.17224			0.586119	+	0.810225i	$0.300655\pi$
$588$		0			0
$589$	−34.9018			−1.43810
$590$	0.151005	+	0.736774i	0.00621679	+	0.0303325i
$591$	−25.4367	+	4.47172i	−1.04633	+	0.183942i
$592$	−4.07308	−	0.990610i	−0.167403	−	0.0407138i
$593$	20.6799	−	11.9396i	0.849223	−	0.490299i	−0.0111655	−	0.999938i	$-0.503554\pi$
$593$	20.6799	−	11.9396i	0.849223	−	0.490299i	0.860389	+	0.509638i	$0.170221\pi$
$594$	16.8898	−	3.43456i	0.692998	−	0.140922i
$595$		0			0
$596$	19.3058	−	25.7740i	0.790796	−	1.05574i
$597$	11.0930	−	30.4291i	0.454005	−	1.24538i
$598$	−39.0030	−	43.9570i	−1.59495	−	1.79753i
$599$	19.5625	−	33.8832i	0.799300	−	1.38443i	−0.120772	−	0.992680i	$-0.538537\pi$
$599$	19.5625	−	33.8832i	0.799300	−	1.38443i	0.920072	−	0.391749i	$-0.128130\pi$
$600$	20.6349	−	5.42059i	0.842417	−	0.221295i
$601$	4.88356			0.199204			0.0996022	−	0.995027i	$-0.468243\pi$
$601$	4.88356			0.199204			0.0996022	+	0.995027i	$0.468243\pi$
$602$		0			0
$603$	24.8903	+	4.41518i	1.01361	+	0.179800i
$604$	34.5217	+	4.13769i	1.40467	+	0.168360i
$605$	−3.82459	−	2.20813i	−0.155492	−	0.0897732i
$606$	−3.01999	+	20.3365i	−0.122679	+	0.826112i
$607$	−27.4754	+	15.8630i	−1.11519	+	0.643857i	−0.940170	−	0.340707i	$-0.889334\pi$
$607$	−27.4754	+	15.8630i	−1.11519	+	0.643857i	−0.175024	+	0.984564i	$0.556000\pi$
$608$	1.46753	−	40.2744i	0.0595161	−	1.63334i
$609$		0			0
$610$	1.03249	+	0.343811i	0.0418042	+	0.0139205i
$611$	16.0667	+	27.8284i	0.649990	+	1.12582i
$612$	−6.92730	+	1.61286i	−0.280019	+	0.0651959i
$613$	−16.4834	+	28.5501i	−0.665758	+	1.15313i	0.313322	+	0.949647i	$0.398558\pi$
$613$	−16.4834	+	28.5501i	−0.665758	+	1.15313i	−0.979079	+	0.203479i	$0.934775\pi$
$614$	4.39746	+	21.4558i	0.177467	+	0.865885i
$615$	7.64308	−	6.40662i	0.308199	−	0.258340i
$616$		0			0
$617$		−	14.3990i		−	0.579680i	−0.957075	−	0.289840i	$-0.906398\pi$
$617$		−	14.3990i		−	0.579680i	0.957075	−	0.289840i	$-0.0936021\pi$
$618$	−4.92445	−	3.90962i	−0.198091	−	0.157268i
$619$	21.3838	+	12.3460i	0.859489	+	0.496226i	0.863841	−	0.503764i	$-0.168052\pi$
$619$	21.3838	+	12.3460i	0.859489	+	0.496226i	−0.00435197	+	0.999991i	$0.501385\pi$
$620$	−7.23453	+	3.09553i	−0.290546	+	0.124320i
$621$	−20.5459	+	35.4604i	−0.824480	+	1.42298i
$622$	−4.86990	+	14.6246i	−0.195265	+	0.586395i
$623$		0			0
$624$	−30.3682	−	20.2522i	−1.21570	−	0.810738i
$625$	−7.87046	−	13.6320i	−0.314818	−	0.545281i
$626$	−31.7272	−	35.7571i	−1.26807	−	1.42914i
$627$	−28.5049	+	5.01111i	−1.13838	+	0.200124i
$628$	−0.933526	+	7.78862i	−0.0372517	+	0.310800i
$629$		−	1.24227i		−	0.0495327i
$630$		0			0
$631$			15.8863i			0.632423i	0.948689	+	0.316212i	$0.102411\pi$
$631$			15.8863i			0.632423i	−0.948689	+	0.316212i	$0.897589\pi$
$632$	8.35966	−	17.7233i	0.332529	−	0.704996i
$633$	−20.0003	+	3.51602i	−0.794942	+	0.139749i
$634$	9.82365	−	8.71652i	0.390147	−	0.346177i
$635$	−1.67131	−	2.89479i	−0.0663239	−	0.114876i
$636$	−1.65244	−	30.1618i	−0.0655235	−	1.19599i
$637$		0			0
$638$	−13.3163	−	4.43423i	−0.527197	−	0.175553i
$639$	−27.2828	+	9.89844i	−1.07929	+	0.391576i
$640$	−3.26785	−	8.47834i	−0.129173	−	0.335136i
$641$	−16.8007	−	9.69989i	−0.663588	−	0.383122i	0.130055	−	0.991507i	$-0.458485\pi$
$641$	−16.8007	−	9.69989i	−0.663588	−	0.383122i	−0.793643	+	0.608384i	$0.791818\pi$
$642$	9.29053	−	11.7021i	0.366668	−	0.461845i
$643$			37.0568i			1.46138i	0.682710	+	0.730690i	$0.260801\pi$
$643$			37.0568i			1.46138i	−0.682710	+	0.730690i	$0.739199\pi$
$644$		0			0
$645$	−8.46792	+	7.09803i	−0.333424	+	0.279485i
$646$	11.7003	−	2.39804i	0.460343	−	0.0943494i
$647$	−22.7029	+	39.3225i	−0.892542	+	1.54593i	−0.0557235	+	0.998446i	$0.517747\pi$
$647$	−22.7029	+	39.3225i	−0.892542	+	1.54593i	−0.836818	+	0.547481i	$0.815587\pi$
$648$	−6.74698	+	24.5454i	−0.265046	+	0.964236i
$649$	0.776548	+	1.34502i	0.0304822	+	0.0527967i
$650$	−10.2517	+	30.7866i	−0.402105	+	1.20755i
$651$		0			0
$652$	−8.76374	+	11.6999i	−0.343215	+	0.458205i
$653$	0.855070	−	0.493675i	0.0334615	−	0.0193190i	−0.483176	−	0.875523i	$-0.660517\pi$
$653$	0.855070	−	0.493675i	0.0334615	−	0.0193190i	0.516637	+	0.856204i	$0.327184\pi$
$654$	13.2071	+	1.96127i	0.516438	+	0.0766917i
$655$	−7.29738	−	4.21314i	−0.285132	−	0.164621i
$656$	20.7436	+	19.8019i	0.809901	+	0.773133i
$657$	0.741015	−	4.17743i	0.0289097	−	0.162977i
$658$		0			0
$659$	−6.67629			−0.260071			−0.130036	−	0.991509i	$-0.541509\pi$
$659$	−6.67629			−0.260071			−0.130036	+	0.991509i	$0.541509\pi$
$660$	−5.46413	+	3.56690i	−0.212691	+	0.138841i
$661$	1.35571	−	2.34815i	0.0527309	−	0.0913326i	−0.838455	−	0.544971i	$-0.816541\pi$
$661$	1.35571	−	2.34815i	0.0527309	−	0.0913326i	0.891186	+	0.453638i	$0.149874\pi$
$662$	−1.07364	+	0.952641i	−0.0417282	+	0.0370254i
$663$	3.70505	−	10.1633i	0.143892	−	0.394710i
$664$	−12.0438	+	8.35442i	−0.467390	+	0.324214i
$665$		0			0
$666$	−3.90818	−	2.11986i	−0.151439	−	0.0821431i
$667$	28.9018	−	16.6865i	1.11908	−	0.646102i
$668$	15.3939	−	6.58680i	0.595609	−	0.254851i
$669$	−1.16557	+	0.204904i	−0.0450634	+	0.00792206i
$670$	−9.37559	+	1.92157i	−0.362211	+	0.0742368i
$671$	2.24723			0.0867535
$672$		0			0
$673$	37.2088			1.43430			0.717148	−	0.696921i	$-0.245447\pi$
$673$	37.2088			1.43430			0.717148	+	0.696921i	$0.245447\pi$
$674$	17.5390	−	3.59470i	0.675576	−	0.138462i
$675$	22.6292	+	0.0348367i	0.870997	+	0.00134086i
$676$	27.1361	−	11.6111i	1.04370	−	0.446580i
$677$	−9.63730	+	5.56410i	−0.370392	+	0.213846i	−0.673630	−	0.739069i	$-0.735266\pi$
$677$	−9.63730	+	5.56410i	−0.370392	+	0.213846i	0.303238	+	0.952915i	$0.401932\pi$
$678$	16.1708	−	6.38722i	0.621037	−	0.245300i
$679$		0			0
$680$	2.21258	−	1.53480i	0.0848487	−	0.0588570i
$681$	14.2451	+	5.19307i	0.545873	+	0.198999i
$682$	−12.1548	+	10.7850i	−0.465432	+	0.412978i
$683$	4.83716	−	8.37821i	0.185089	−	0.320583i	−0.758518	−	0.651652i	$-0.774076\pi$
$683$	4.83716	−	8.37821i	0.185089	−	0.320583i	0.943606	+	0.331069i	$0.107409\pi$
$684$	12.4217	−	40.9012i	0.474955	−	1.56389i
$685$	−10.8357			−0.414013
$686$		0			0
$687$	24.5549	−	20.5826i	0.936829	−	0.785274i
$688$	−22.9822	−	21.9389i	−0.876190	−	0.836412i
$689$	39.7870	+	22.9710i	1.51576	+	0.875127i
$690$	2.27913	−	15.3476i	0.0867652	−	0.584272i
$691$	7.20943	−	4.16236i	0.274260	−	0.158344i	−0.356562	−	0.934272i	$-0.616051\pi$
$691$	7.20943	−	4.16236i	0.274260	−	0.158344i	0.630822	+	0.775928i	$0.282718\pi$
$692$	−15.3128	+	20.4432i	−0.582105	+	0.777133i
$693$		0			0
$694$	11.4509	−	34.3879i	0.434670	−	1.30535i
$695$	−3.04088	−	5.26697i	−0.115347	−	0.199787i
$696$	14.7296	−	14.5855i	0.558323	−	0.552863i
$697$	−4.24943	+	7.36022i	−0.160958	+	0.278788i
$698$	−38.9627	+	7.98559i	−1.47476	+	0.302259i
$699$	−11.2814	−	13.4586i	−0.426700	−	0.509052i
$700$		0			0
$701$		−	34.0535i		−	1.28618i	−0.765790	−	0.643091i	$-0.777652\pi$
$701$		−	34.0535i		−	1.28618i	0.765790	−	0.643091i	$-0.222348\pi$
$702$	−25.6512	−	28.9991i	−0.968141	−	1.09450i
$703$	6.46568	+	3.73296i	0.243858	+	0.140791i
$704$	−11.9341	−	14.4793i	−0.449782	−	0.545711i
$705$	−2.90583	+	7.97098i	−0.109440	+	0.300205i
$706$	−13.8269	−	4.60425i	−0.520382	−	0.173283i
$707$		0			0
$708$	−2.29040	+	0.125482i	−0.0860785	+	0.00471589i
$709$	−4.82135	−	8.35083i	−0.181070	−	0.313622i	0.761175	−	0.648546i	$-0.224623\pi$
$709$	−4.82135	−	8.35083i	−0.181070	−	0.313622i	−0.942245	+	0.334924i	$0.891289\pi$
$710$	8.21900	−	7.29272i	0.308454	−	0.273691i
$711$	13.3764	−	15.9082i	0.501655	−	0.596605i
$712$	19.7473	−	41.8663i	0.740062	−	1.56901i
$713$		−	38.6388i		−	1.44703i
$714$		0			0
$715$		−	9.92437i		−	0.371150i
$716$	−5.02626	+	41.9353i	−0.187840	+	1.56719i
$717$	−0.448249	−	2.54980i	−0.0167402	−	0.0952239i
$718$	25.1918	+	28.3915i	0.940150	+	1.05956i
$719$	−4.04585	−	7.00762i	−0.150885	−	0.261340i	0.780668	−	0.624946i	$-0.214879\pi$
$719$	−4.04585	−	7.00762i	−0.150885	−	0.261340i	−0.931553	+	0.363606i	$0.881546\pi$
$720$	−1.05284	−	9.57981i	−0.0392369	−	0.357018i
$721$		0			0
$722$	−14.1885	+	42.6090i	−0.528040	+	1.58574i
$723$	−16.8160	−	6.13028i	−0.625392	−	0.227988i
$724$	−22.8142	+	9.76181i	−0.847883	+	0.362795i
$725$	−15.9586	−	9.21369i	−0.592687	−	0.342188i
$726$	8.37509	−	10.5490i	0.310829	−	0.391511i
$727$		−	36.9501i		−	1.37040i	−0.728353	−	0.685202i	$-0.759714\pi$
$727$		−	36.9501i		−	1.37040i	0.728353	−	0.685202i	$-0.240286\pi$
$728$		0			0
$729$	−13.5719	+	23.3410i	−0.502664	+	0.864482i
$730$	0.322504	+	1.57354i	0.0119364	+	0.0582393i
$731$	4.70802	−	8.15453i	0.174133	−	0.301606i
$732$	−1.49980	+	2.96085i	−0.0554340	+	0.109436i
$733$	−18.9776	−	32.8702i	−0.700954	−	1.21409i	−0.968132	−	0.250440i	$-0.919425\pi$
$733$	−18.9776	−	32.8702i	−0.700954	−	1.21409i	0.267178	−	0.963647i	$-0.413909\pi$
$734$	17.9153	+	5.96566i	0.661266	+	0.220197i
$735$		0			0
$736$	44.5867	+	1.62466i	1.64349	+	0.0598857i
$737$	−17.1157	+	9.88173i	−0.630463	+	0.363998i
$738$	15.9038	+	25.9284i	0.585426	+	0.954437i
$739$	−19.1667	−	11.0659i	−0.705058	−	0.407065i	0.104171	−	0.994559i	$-0.466781\pi$
$739$	−19.1667	−	11.0659i	−0.705058	−	0.407065i	−0.809228	+	0.587494i	$0.800115\pi$
$740$	1.67131	+	0.200319i	0.0614386	+	0.00736388i
$741$	41.7636	+	49.8238i	1.53422	+	1.83032i
$742$		0			0
$743$	−21.7884			−0.799340			−0.399670	−	0.916659i	$-0.630875\pi$
$743$	−21.7884			−0.799340			−0.399670	+	0.916659i	$0.630875\pi$
$744$	−6.09769	−	23.2125i	−0.223552	−	0.851010i
$745$	−6.46568	+	11.1989i	−0.236884	+	0.410296i
$746$	−21.4059	−	24.1248i	−0.783726	−	0.883271i
$747$	−14.6147	+	5.30235i	−0.534725	+	0.194003i
$748$	3.33371	−	4.45064i	0.121893	−	0.162731i
$749$		0			0
$750$	−17.1167	+	6.76083i	−0.625014	+	0.246871i
$751$	−4.44124	+	2.56415i	−0.162063	+	0.0935671i	−0.578838	−	0.815443i	$-0.696494\pi$
$751$	−4.44124	+	2.56415i	−0.162063	+	0.0935671i	0.416775	+	0.909010i	$0.363160\pi$
$752$	−23.7053	−	5.76534i	−0.864443	−	0.210240i
$753$	−8.08376	−	45.9832i	−0.294588	−	1.67572i
$754$	6.33005	+	30.8851i	0.230527	+	1.12477i
$755$	−13.9618			−0.508122
$756$		0			0
$757$	−30.4486			−1.10667			−0.553337	−	0.832958i	$-0.686646\pi$
$757$	−30.4486			−1.10667			−0.553337	+	0.832958i	$0.686646\pi$
$758$	0.562562	+	2.74481i	0.0204332	+	0.0996961i
$759$	−5.54766	−	31.5570i	−0.201367	−	1.14545i
$760$	1.33953	+	16.1279i	0.0485897	+	0.585019i
$761$	37.0224	−	21.3749i	1.34206	−	0.774839i	0.354951	−	0.934885i	$-0.384498\pi$
$761$	37.0224	−	21.3749i	1.34206	−	0.774839i	0.987110	+	0.160046i	$0.0511642\pi$
$762$	9.48197	−	3.74523i	0.343496	−	0.135675i
$763$		0			0
$764$	9.76434	+	7.31389i	0.353261	+	0.264607i
$765$	2.68490	−	0.974103i	0.0970726	−	0.0352188i
$766$	27.0516	+	30.4876i	0.977415	+	1.10156i
$767$	1.74436	−	3.02131i	0.0629851	−	0.109093i
$768$	27.0421	−	6.06031i	0.975796	−	0.218683i
$769$	−7.77655			−0.280430			−0.140215	−	0.990121i	$-0.544779\pi$
$769$	−7.77655			−0.280430			−0.140215	+	0.990121i	$0.544779\pi$
$770$		0			0
$771$	3.10619	+	3.70567i	0.111867	+	0.133456i
$772$	−0.153520	+	1.28085i	−0.00552529	+	0.0460988i
$773$	−1.04249	−	0.601881i	−0.0374957	−	0.0216482i	0.481135	−	0.876647i	$-0.340225\pi$
$773$	−1.04249	−	0.601881i	−0.0374957	−	0.0216482i	−0.518631	+	0.854998i	$0.673558\pi$
$774$	−17.6201	−	28.7266i	−0.633342	−	1.03256i
$775$	−18.4767	+	10.6675i	−0.663701	+	0.383188i
$776$	−10.1752	+	7.05825i	−0.365269	+	0.253376i
$777$		0			0
$778$	−2.62954	−	0.875618i	−0.0942737	−	0.0313924i
$779$	−25.5386	−	44.2341i	−0.915014	−	1.58485i
$780$	13.0759	+	6.62348i	0.468192	+	0.237159i
$781$	11.3453	−	19.6507i	0.405968	−	0.703157i
$782$	2.65480	+	12.9531i	0.0949354	+	0.463202i
$783$	19.0579	−	10.9640i	0.681072	−	0.391820i
$784$		0			0
$785$		−	3.15000i		−	0.112428i
$786$	15.9798	−	20.1277i	0.569980	−	0.717931i
$787$	−19.4895	−	11.2522i	−0.694724	−	0.401099i	0.110655	−	0.993859i	$-0.464705\pi$
$787$	−19.4895	−	11.2522i	−0.694724	−	0.401099i	−0.805380	+	0.592760i	$0.798038\pi$
$788$	11.7316	+	27.4177i	0.417920	+	0.976716i
$789$	24.9143	+	9.08256i	0.886974	+	0.323348i
$790$	−2.48610	+	7.46593i	−0.0884514	+	0.265626i
$791$		0			0
$792$	−8.31288	−	18.0826i	−0.295385	−	0.642536i
$793$	−2.52398	−	4.37166i	−0.0896290	−	0.155242i
$794$	4.28298	+	4.82699i	0.151997	+	0.171303i
$795$	2.10022	+	11.9468i	0.0744871	+	0.423709i
$796$	−37.1327	−	4.45064i	−1.31613	−	0.157749i
$797$			18.3911i			0.651447i	0.945465	+	0.325724i	$0.105608\pi$
$797$			18.3911i			0.651447i	−0.945465	+	0.325724i	$0.894392\pi$
$798$		0			0
$799$		−	7.23003i		−	0.255780i
$800$	−11.5327	−	21.7694i	−0.407743	−	0.769665i
$801$	31.5980	−	37.5786i	1.11646	−	1.32778i
$802$	−28.3299	+	25.1371i	−1.00036	+	0.887621i
$803$	1.65849	+	2.87258i	0.0585267	+	0.101371i
$804$	−1.59678	−	29.1458i	−0.0563140	−	1.02789i
$805$		0			0
$806$	34.6322	+	11.5323i	1.21987	+	0.406206i
$807$	18.2042	−	49.9358i	0.640817	−	1.75782i
$808$	23.6586	−	1.96500i	0.832305	−	0.0691285i
$809$	11.5087	+	6.64455i	0.404624	+	0.233610i	0.688477	−	0.725258i	$-0.258279\pi$
$809$	11.5087	+	6.64455i	0.404624	+	0.233610i	−0.283853	+	0.958868i	$0.591613\pi$
$810$	1.51709	−	10.1089i	0.0533052	−	0.355190i
$811$		−	6.46254i		−	0.226930i	−0.993542	−	0.113465i	$-0.963805\pi$
$811$		−	6.46254i		−	0.226930i	0.993542	−	0.113465i	$-0.0361950\pi$
$812$		0			0
$813$	21.9041	+	26.1315i	0.768210	+	0.916472i
$814$	3.40524	−	0.697921i	0.119354	−	0.0244621i
$815$	2.93506	−	5.08367i	0.102811	−	0.178073i
$816$	3.63904	+	7.36268i	0.127392	+	0.257745i
$817$	28.2947	+	49.0078i	0.989906	+	1.71457i
$818$	−8.06140	+	24.2090i	−0.281860	+	0.846446i
$819$		0			0
$820$	−9.21694	−	6.90387i	−0.321869	−	0.241094i
$821$	−24.1767	+	13.9584i	−0.843774	+	0.487153i	−0.858545	−	0.512738i	$-0.828631\pi$
$821$	−24.1767	+	13.9584i	−0.843774	+	0.487153i	0.0147715	+	0.999891i	$0.495298\pi$
$822$	4.85451	−	32.6900i	0.169321	−	1.14020i
$823$	38.9668	+	22.4975i	1.35830	+	0.784213i	0.989394	−	0.145256i	$-0.0464004\pi$
$823$	38.9668	+	22.4975i	1.35830	+	0.784213i	0.368902	+	0.929468i	$0.379734\pi$
$824$	−3.09731	+	6.56662i	−0.107900	+	0.228759i
$825$	−13.5586	+	11.3652i	−0.472051	+	0.395685i
$826$		0			0
$827$	−34.2989			−1.19269			−0.596344	−	0.802729i	$-0.703381\pi$
$827$	−34.2989			−1.19269			−0.596344	+	0.802729i	$0.703381\pi$
$828$	45.2805	+	13.7517i	1.57361	+	0.477904i
$829$	11.5078	−	19.9322i	0.399684	−	0.692273i	−0.594003	−	0.804463i	$-0.702453\pi$
$829$	11.5078	−	19.9322i	0.399684	−	0.692273i	0.993687	+	0.112190i	$0.0357865\pi$
$830$	4.40272	−	3.90653i	0.152820	−	0.135598i
$831$	21.3386	+	7.77900i	0.740226	+	0.269851i
$832$	−14.7637	+	39.4784i	−0.511838	+	1.36867i
$833$		0			0
$834$	17.2521	−	6.81430i	0.597391	−	0.235960i
$835$	−5.82291	+	3.36186i	−0.201510	+	0.116342i
$836$	13.1467	+	30.7249i	0.454688	+	1.06264i
$837$	0.0391882	−	25.4558i	0.00135454	−	0.879882i
$838$	−24.2995	+	4.98029i	−0.839412	+	0.172041i
$839$	−46.9847			−1.62209			−0.811046	−	0.584983i	$-0.801101\pi$
$839$	−46.9847			−1.62209			−0.811046	+	0.584983i	$0.801101\pi$
$840$		0			0
$841$	11.0959			0.382617
$842$	−21.3363	+	4.37297i	−0.735297	+	0.150703i
$843$	−4.89029	+	0.859702i	−0.168430	+	0.0296097i
$844$	9.22430	+	21.5580i	0.317513	+	0.742056i
$845$	−10.2645	+	5.92623i	−0.353110	+	0.203868i
$846$	−22.7456	−	12.3376i	−0.782009	−	0.424175i
$847$		0			0
$848$	−33.4728	+	9.80751i	−1.14946	+	0.336791i
$849$	1.18077	−	3.23896i	0.0405238	−	0.111161i
$850$	5.46109	−	4.84562i	0.187314	−	0.166204i
$851$	−4.13266	+	7.15798i	−0.141666	+	0.245372i
$852$	18.3190	+	28.0629i	0.627598	+	0.961418i
$853$	−12.7498			−0.436545			−0.218272	−	0.975888i	$-0.570042\pi$
$853$	−12.7498			−0.436545			−0.218272	+	0.975888i	$0.570042\pi$
$854$		0			0
$855$	−2.99803	+	16.9012i	−0.102531	+	0.578010i
$856$	−15.6044	−	7.36022i	−0.533348	−	0.251567i
$857$	−26.1774	−	15.1136i	−0.894204	−	0.516269i	−0.0188889	−	0.999822i	$-0.506013\pi$
$857$	−26.1774	−	15.1136i	−0.894204	−	0.516269i	−0.875315	+	0.483553i	$0.839346\pi$
$858$	29.9405	+	4.44621i	1.02215	+	0.151791i
$859$	−15.8982	+	9.17880i	−0.542438	+	0.313177i	−0.746066	−	0.665872i	$-0.768060\pi$
$859$	−15.8982	+	9.17880i	−0.542438	+	0.313177i	0.203628	+	0.979048i	$0.434727\pi$
$860$	10.2116	+	7.64893i	0.348214	+	0.260826i
$861$		0			0
$862$	−4.02283	+	12.0808i	−0.137018	+	0.411475i
$863$	13.1968	+	22.8576i	0.449225	+	0.778080i	0.998336	−	0.0576693i	$-0.0183669\pi$
$863$	13.1968	+	22.8576i	0.449225	+	0.778080i	−0.549111	+	0.835749i	$0.685034\pi$
$864$	29.3727	+	1.11557i	0.999280	+	0.0379525i
$865$	5.12839	−	8.88264i	0.174371	−	0.302019i
$866$	−8.53261	+	1.74880i	−0.289950	+	0.0594266i
$867$	20.7005	−	17.3517i	0.703025	−	0.589293i
$868$		0			0
$869$			16.2498i			0.551236i
$870$	−5.17578	+	6.51928i	−0.175476	+	0.221024i
$871$	38.4468	+	22.1973i	1.30272	+	0.752126i
$872$	−1.27613	−	15.3646i	−0.0432152	−	0.520310i
$873$	−12.3473	+	4.47970i	−0.417893	+	0.151615i
$874$	−75.3947	−	25.1059i	−2.55026	−	0.849218i
$875$		0			0
$876$	−4.89164	+	0.267993i	−0.165273	+	0.00905464i
$877$	0.468662	+	0.811746i	0.0158256	+	0.0274107i	0.873830	−	0.486232i	$-0.161629\pi$
$877$	0.468662	+	0.811746i	0.0158256	+	0.0274107i	−0.858004	+	0.513643i	$0.828296\pi$
$878$	−30.9408	+	27.4538i	−1.04420	+	0.926519i
$879$	−28.5706	+	5.02266i	−0.963664	+	0.169410i
$880$	5.45016	+	5.20273i	0.183725	+	0.175384i
$881$		−	37.1298i		−	1.25093i	−0.780251	−	0.625467i	$-0.784909\pi$
$881$		−	37.1298i		−	1.25093i	0.780251	−	0.625467i	$-0.215091\pi$
$882$		0			0
$883$			5.76235i			0.193918i	0.995288	+	0.0969592i	$0.0309116\pi$
$883$			5.76235i			0.193918i	−0.995288	+	0.0969592i	$0.969088\pi$
$884$	−12.4023	−	1.48651i	−0.417134	−	0.0499968i
$885$	0.907205	−	0.159485i	0.0304954	−	0.00536102i
$886$	6.77340	+	7.63372i	0.227557	+	0.256460i
$887$	13.0672	+	22.6330i	0.438752	+	0.759941i	0.997594	−	0.0693335i	$-0.0220873\pi$
$887$	13.0672	+	22.6330i	0.438752	+	0.759941i	−0.558841	+	0.829275i	$0.688754\pi$
$888$	−1.35310	+	4.95238i	−0.0454070	+	0.166191i
$889$		0			0
$890$	−5.87270	+	17.6361i	−0.196853	+	0.591165i
$891$	−3.62287	−	20.7959i	−0.121371	−	0.696688i
$892$	0.537568	+	1.25634i	0.0179991	+	0.0420655i
$893$	37.6302	+	21.7258i	1.25925	+	0.727027i
$894$	−30.8889	−	24.5233i	−1.03308	−	0.820183i
$895$		−	16.9601i		−	0.566915i
$896$		0			0
$897$	−55.1586	+	46.2353i	−1.84169	+	1.54375i
$898$	−1.25909	−	6.14324i	−0.0420163	−	0.205003i
$899$	−10.3646	+	17.9520i	−0.345678	+	0.598732i
$900$	−5.92526	−	25.4493i	−0.197509	−	0.848309i
$901$	−5.16848	−	8.95207i	−0.172187	−	0.298237i
$902$	−22.5627	−	7.51322i	−0.751257	−	0.250163i
$903$		0			0
$904$	−11.4428	−	16.4960i	−0.380582	−	0.548649i
$905$	8.62971	−	4.98237i	0.286861	−	0.165619i
$906$	6.25502	−	42.1210i	0.207809	−	1.39937i
$907$	35.3624	+	20.4165i	1.17419	+	0.677918i	0.954663	−	0.297689i	$-0.0962160\pi$
$907$	35.3624	+	20.4165i	1.17419	+	0.677918i	0.219525	+	0.975607i	$0.429549\pi$
$908$	2.08352	−	17.3833i	0.0691442	−	0.576886i
$909$	24.7931	+	4.39793i	0.822334	+	0.145870i
$910$		0			0
$911$	−4.31270			−0.142886			−0.0714430	−	0.997445i	$-0.522760\pi$
$911$	−4.31270			−0.142886			−0.0714430	+	0.997445i	$0.522760\pi$
$912$	−49.2558	−	3.18425i	−1.63102	−	0.105441i
$913$	6.07741	−	10.5264i	0.201133	−	0.348372i
$914$	12.8234	+	14.4521i	0.424159	+	0.478034i
$915$	0.456487	−	1.25219i	0.0150910	−	0.0413961i
$916$	−29.6113	−	22.1801i	−0.978384	−	0.732850i
$917$		0			0
$918$	1.73588	+	8.53639i	0.0572927	+	0.281743i
$919$	14.9668	−	8.64107i	0.493708	−	0.285043i	−0.232403	−	0.972620i	$-0.574659\pi$
$919$	14.9668	−	8.64107i	0.493708	−	0.285043i	0.726112	+	0.687577i	$0.241326\pi$
$920$	−17.8547	+	1.48295i	−0.588652	+	0.0488915i
$921$	26.4190	−	4.64440i	0.870535	−	0.153038i
$922$	1.49296	+	7.28436i	0.0491682	+	0.239898i
$923$	−50.9699			−1.67770
$924$		0			0
$925$	4.56383			0.150058
$926$	−4.51087	−	22.0091i	−0.148236	−	0.723264i
$927$	−4.95606	+	5.89411i	−0.162778	+	0.193588i
$928$	−20.2796	−	12.7149i	−0.665711	−	0.417387i
$929$	20.0527	−	11.5774i	0.657908	−	0.379843i	−0.133571	−	0.991039i	$-0.542645\pi$
$929$	20.0527	−	11.5774i	0.657908	−	0.379843i	0.791479	+	0.611196i	$0.209311\pi$
$930$	3.54048	+	8.96360i	0.116097	+	0.293928i
$931$		0			0
$932$	−12.1570	+	16.2300i	−0.398214	+	0.531632i
$933$	17.7366	+	6.46590i	0.580670	+	0.211684i
$934$	25.4146	+	28.6426i	0.831590	+	0.937215i
$935$	−1.11649	+	1.93382i	−0.0365132	+	0.0632426i
$936$	−25.8403	+	36.4808i	−0.844616	+	1.19241i
$937$	3.10294			0.101369			0.0506843	−	0.998715i	$-0.483860\pi$
$937$	3.10294			0.101369			0.0506843	+	0.998715i	$0.483860\pi$
$938$		0			0
$939$	−44.8691	+	37.6104i	−1.46425	+	1.22737i
$940$	9.72701	+	1.16586i	0.317260	+	0.0380260i
$941$	20.4823	+	11.8254i	0.667703	+	0.385498i	0.795206	−	0.606340i	$-0.207363\pi$
$941$	20.4823	+	11.8254i	0.667703	+	0.385498i	−0.127503	+	0.991838i	$0.540696\pi$
$942$	9.50313	+	1.41123i	0.309629	+	0.0459803i
$943$	48.9703	−	28.2730i	1.59469	−	0.920696i
$944$	0.744755	+	2.54183i	0.0242397	+	0.0827296i
$945$		0			0
$946$	24.9977	+	8.32404i	0.812745	+	0.270638i
$947$	28.7686	+	49.8286i	0.934852	+	1.61921i	0.774897	+	0.632087i	$0.217802\pi$
$947$	28.7686	+	49.8286i	0.934852	+	1.61921i	0.159955	+	0.987124i	$0.448865\pi$
$948$	−21.4099	−	10.8450i	−0.695362	−	0.352230i
$949$	3.72545	−	6.45267i	0.120933	−	0.209462i
$950$	8.80982	+	42.9842i	0.285828	+	1.39459i
$951$	−10.3328	−	12.3270i	−0.335065	−	0.399731i
$952$		0			0
$953$		−	14.1961i		−	0.459855i	−0.973208	−	0.229928i	$-0.926151\pi$
$953$		−	14.1961i		−	0.459855i	0.973208	−	0.229928i	$-0.0738490\pi$
$954$	−36.9828	+	0.983821i	−1.19736	+	0.0318524i
$955$	−4.24264	−	2.44949i	−0.137289	−	0.0792636i
$956$	−2.74838	+	1.17598i	−0.0888889	+	0.0380340i
$957$	−5.88745	+	16.1498i	−0.190314	+	0.522050i
$958$	6.81842	−	20.4762i	0.220293	−	0.661557i
$959$		0			0
$960$	−10.4923	+	3.70859i	−0.338637	+	0.119694i
$961$	−3.50000	−	6.06218i	−0.112903	−	0.195554i
$962$	−5.18229	−	5.84052i	−0.167084	−	0.188306i
$963$	−14.0063	−	11.7772i	−0.451347	−	0.379515i
$964$	−2.45955	+	20.5206i	−0.0792166	+	0.660923i
$965$		−	0.518021i		−	0.0166757i
$966$		0			0
$967$		−	31.5730i		−	1.01532i	−0.861558	−	0.507660i	$-0.830511\pi$
$967$		−	31.5730i		−	1.01532i	0.861558	−	0.507660i	$-0.169489\pi$
$968$	−14.0668	−	6.63498i	−0.452125	−	0.213256i
$969$	−2.53270	−	14.4069i	−0.0813619	−	0.462815i
$970$	3.71964	−	3.30044i	0.119431	−	0.105971i
$971$	14.6620	+	25.3953i	0.470526	+	0.814974i	0.999432	−	0.0337060i	$-0.0107310\pi$
$971$	14.6620	+	25.3953i	0.470526	+	0.814974i	−0.528906	+	0.848680i	$0.677398\pi$
$972$	29.8175	+	9.10575i	0.956398	+	0.292067i
$973$		0			0
$974$	8.13677	+	2.70948i	0.260719	+	0.0868174i
$975$	37.3376	+	13.6115i	1.19576	+	0.435916i
$976$	3.72394	+	0.905697i	0.119200	+	0.0289907i
$977$	−10.3022	−	5.94797i	−0.329596	−	0.190292i	0.326066	−	0.945347i	$-0.394277\pi$
$977$	−10.3022	−	5.94797i	−0.329596	−	0.190292i	−0.655662	+	0.755055i	$0.727610\pi$
$978$	14.0218	+	11.1322i	0.448368	+	0.355969i
$979$			38.3855i			1.22681i
$980$		0			0
$981$	2.85614	−	16.1013i	0.0911896	−	0.514076i
$982$	−5.59476	+	1.14667i	−0.178536	+	0.0365918i
$983$	7.49013	−	12.9733i	0.238898	−	0.413783i	−0.721500	−	0.692414i	$-0.756547\pi$
$983$	7.49013	−	12.9733i	0.238898	−	0.413783i	0.960398	+	0.278631i	$0.0898805\pi$
$984$	24.9573	−	24.7133i	0.795611	−	0.787831i
$985$	−5.98772	−	10.3710i	−0.190785	−	0.330449i
$986$	2.24113	−	6.73027i	0.0713721	−	0.214336i
$987$		0			0
$988$	45.0051	−	60.0835i	1.43180	−	1.91151i
$989$	−54.2552	+	31.3243i	−1.72521	+	0.996053i
$990$	4.17855	+	6.81241i	0.132803	+	0.216513i
$991$	18.0000	+	10.3923i	0.571789	+	0.330122i	0.757863	−	0.652413i	$-0.226243\pi$
$991$	18.0000	+	10.3923i	0.571789	+	0.330122i	−0.186075	+	0.982536i	$0.559577\pi$
$992$	−24.4887	+	12.9733i	−0.777515	+	0.411902i
$993$	1.12929	+	1.34724i	0.0358369	+	0.0427533i
$994$		0			0
$995$	15.0178			0.476096
$996$	9.81302	+	15.0326i	0.310938	+	0.476325i
$997$	−9.81912	+	17.0072i	−0.310975	+	0.538624i	−0.978574	−	0.205897i	$-0.933989\pi$
$997$	−9.81912	+	17.0072i	−0.310975	+	0.538624i	0.667599	+	0.744521i	$0.267322\pi$
$998$	40.7278	−	36.1377i	1.28922	−	1.14392i
$999$	−2.72992	+	4.71159i	−0.0863708	+	0.149068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.h.263.2		24
3.2	odd	2	inner	588.2.n.h.263.12		24
4.3	odd	2		588.2.n.d.263.3		24
7.2	even	3		588.2.n.d.275.9		24
7.3	odd	6		588.2.e.f.491.13	yes	24
7.4	even	3		588.2.e.f.491.14	yes	24
7.5	odd	6		588.2.n.d.275.10		24
7.6	odd	2	inner	588.2.n.h.263.1		24
12.11	even	2		588.2.n.d.263.9		24
21.2	odd	6		588.2.n.d.275.3		24
21.5	even	6		588.2.n.d.275.4		24
21.11	odd	6		588.2.e.f.491.11	yes	24
21.17	even	6		588.2.e.f.491.12	yes	24
21.20	even	2	inner	588.2.n.h.263.11		24
28.3	even	6		588.2.e.f.491.10	yes	24
28.11	odd	6		588.2.e.f.491.9	✓	24
28.19	even	6	inner	588.2.n.h.275.11		24
28.23	odd	6	inner	588.2.n.h.275.12		24
28.27	even	2		588.2.n.d.263.4		24
84.11	even	6		588.2.e.f.491.16	yes	24
84.23	even	6	inner	588.2.n.h.275.2		24
84.47	odd	6	inner	588.2.n.h.275.1		24
84.59	odd	6		588.2.e.f.491.15	yes	24
84.83	odd	2		588.2.n.d.263.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.9	✓	24	28.11	odd	6
588.2.e.f.491.10	yes	24	28.3	even	6
588.2.e.f.491.11	yes	24	21.11	odd	6
588.2.e.f.491.12	yes	24	21.17	even	6
588.2.e.f.491.13	yes	24	7.3	odd	6
588.2.e.f.491.14	yes	24	7.4	even	3
588.2.e.f.491.15	yes	24	84.59	odd	6
588.2.e.f.491.16	yes	24	84.11	even	6
588.2.n.d.263.3		24	4.3	odd	2
588.2.n.d.263.4		24	28.27	even	2
588.2.n.d.263.9		24	12.11	even	2
588.2.n.d.263.10		24	84.83	odd	2
588.2.n.d.275.3		24	21.2	odd	6
588.2.n.d.275.4		24	21.5	even	6
588.2.n.d.275.9		24	7.2	even	3
588.2.n.d.275.10		24	7.5	odd	6
588.2.n.h.263.1		24	7.6	odd	2	inner
588.2.n.h.263.2		24	1.1	even	1	trivial
588.2.n.h.263.11		24	21.20	even	2	inner
588.2.n.h.263.12		24	3.2	odd	2	inner
588.2.n.h.275.1		24	84.47	odd	6	inner
588.2.n.h.275.2		24	84.23	even	6	inner
588.2.n.h.275.11		24	28.19	even	6	inner
588.2.n.h.275.12		24	28.23	odd	6	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38541 + 0.283947i) q^{2} +(0.299892 + 1.70589i) q^{3} +(1.83875 - 0.786769i) q^{4} +(-0.695526 + 0.401562i) q^{5} +(-0.899858 - 2.27821i) q^{6} +(-2.32403 + 1.61211i) q^{8} +(-2.82013 + 1.02317i) q^{9} +(0.849569 - 0.753822i) q^{10} +(1.17273 - 2.03122i) q^{11} +(1.89357 + 2.90076i) q^{12} -5.26858 q^{13} +(-0.893604 - 1.06607i) q^{15} +(2.76199 - 2.89334i) q^{16} +(1.02661 + 0.592715i) q^{17} +(3.61652 - 2.21828i) q^{18} +(-6.16982 + 3.56215i) q^{19} +(-0.962960 + 1.28559i) q^{20} +(-1.04795 + 3.14708i) q^{22} +(-3.94356 - 6.83044i) q^{23} +(-3.44704 - 3.48108i) q^{24} +(-2.17750 + 3.77153i) q^{25} +(7.29917 - 1.49600i) q^{26} +(-2.59115 - 4.50399i) q^{27} +4.23132i q^{29} +(1.54072 + 1.22321i) q^{30} +(4.24264 + 2.44949i) q^{31} +(-3.00494 + 4.79274i) q^{32} +(3.81673 + 1.39140i) q^{33} +(-1.59058 - 0.529652i) q^{34} +(-4.38051 + 4.10014i) q^{36} +(-0.523976 - 0.907554i) q^{37} +(7.53630 - 6.68696i) q^{38} +(-1.58001 - 8.98762i) q^{39} +(0.969059 - 2.05450i) q^{40} +7.16942i q^{41} -7.94315i q^{43} +(0.558245 - 4.65757i) q^{44} +(1.55061 - 1.84410i) q^{45} +(7.40294 + 8.34323i) q^{46} +(-3.04954 - 5.28195i) q^{47} +(5.76402 + 3.84396i) q^{48} +(1.94582 - 5.84343i) q^{50} +(-0.703234 + 1.92904i) q^{51} +(-9.68759 + 4.14516i) q^{52} +(-7.55175 - 4.36001i) q^{53} +(4.86871 + 5.50415i) q^{54} +1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-1.20147 - 5.86214i) q^{58} +(-0.331087 + 0.573459i) q^{59} +(-2.48186 - 1.25717i) q^{60} +(0.479062 + 0.829760i) q^{61} +(-6.57334 - 2.18887i) q^{62} +(2.80221 - 7.49317i) q^{64} +(3.66443 - 2.11566i) q^{65} +(-5.68284 - 0.843910i) q^{66} +(-7.29738 - 4.21314i) q^{67} +(2.35401 + 0.282146i) q^{68} +(10.4693 - 8.77567i) q^{69} +9.67432 q^{71} +(4.90460 - 6.92422i) q^{72} +(-0.707107 + 1.22474i) q^{73} +(0.983622 + 1.10856i) q^{74} +(-7.08684 - 2.58352i) q^{75} +(-8.54216 + 11.4041i) q^{76} +(4.74097 + 12.0029i) q^{78} +(-6.00000 + 3.46410i) q^{79} +(-0.759178 + 3.12150i) q^{80} +(6.90626 - 5.77092i) q^{81} +(-2.03574 - 9.93263i) q^{82} +5.18229 q^{83} -0.952047 q^{85} +(2.25543 + 11.0046i) q^{86} +(-7.21818 + 1.26894i) q^{87} +(0.549103 + 6.61118i) q^{88} +(-14.1733 + 8.18296i) q^{89} +(-1.62461 + 2.99513i) q^{90} +(-12.6252 - 9.45679i) q^{92} +(-2.90623 + 7.97207i) q^{93} +(5.72467 + 6.45179i) q^{94} +(2.86085 - 4.95513i) q^{95} +(-9.07704 - 3.68880i) q^{96} +4.37827 q^{97} +(-1.22896 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) 24 * q + 12 * q^4 + 60 * q^16 + 24 * q^18 + 12 * q^25 + 36 * q^30 + 12 * q^36 - 96 * q^39 + 24 * q^46 + 12 * q^51 - 24 * q^57 + 48 * q^58 + 12 * q^60 - 48 * q^64 - 48 * q^67 - 36 * q^72 - 24 * q^78 - 144 * q^79 + 12 * q^81 - 48 * q^85 + 192 * q^88 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

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Database

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