LMFDB - Embedded newform 588.2.n.d.275.3

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			275.3
Character	$\chi$	$=$	588.275
Dual form			588.2.n.d.263.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.938613 - 1.05783i) q^{2} +(-0.299892 + 1.70589i) q^{3} +(-0.238012 + 1.98579i) q^{4} +(-0.695526 - 0.401562i) q^{5} +(2.08603 - 1.28394i) q^{6} +(2.32403 - 1.61211i) q^{8} +(-2.82013 - 1.02317i) q^{9} +(0.228045 + 1.11266i) q^{10} +(-1.17273 - 2.03122i) q^{11} +(-3.31616 - 1.00154i) q^{12} -5.26858 q^{13} +(0.893604 - 1.06607i) q^{15} +(-3.88670 - 0.945282i) q^{16} +(1.02661 - 0.592715i) q^{17} +(1.56467 + 3.94358i) 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} +(2.05313 + 4.44800i) q^{24} +(-2.17750 - 3.77153i) q^{25} +(4.94516 + 5.57327i) q^{26} +(2.59115 - 4.50399i) q^{27} -4.23132i q^{29} +(-1.96647 + 0.0553417i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(2.64816 + 4.99872i) q^{32} +(3.81673 - 1.39140i) q^{33} +(-1.59058 - 0.529652i) q^{34} +(2.70302 - 5.35665i) q^{36} +(-0.523976 + 0.907554i) q^{37} +(-2.02292 - 9.87011i) q^{38} +(1.58001 - 8.98762i) q^{39} +(-2.26378 + 0.188022i) q^{40} -7.16942i q^{41} -7.94315i q^{43} +(4.31270 - 1.84533i) q^{44} +(1.55061 + 1.84410i) q^{45} +(-10.9269 + 2.23952i) q^{46} +(3.04954 - 5.28195i) q^{47} +(2.77814 - 6.34681i) q^{48} +(-1.94582 + 5.84343i) q^{50} +(0.703234 + 1.92904i) q^{51} +(1.25398 - 10.4623i) q^{52} +(-7.55175 + 4.36001i) q^{53} +(-7.19655 + 1.48651i) q^{54} +1.88369i q^{55} +(-7.92692 + 9.45679i) q^{57} +(-4.47602 + 3.97157i) q^{58} +(0.331087 + 0.573459i) q^{59} +(1.90429 + 2.02824i) 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} +(-5.05430 - 2.73148i) q^{66} +(7.29738 - 4.21314i) q^{67} +(0.932660 + 2.17971i) q^{68} +(10.4693 + 8.77567i) q^{69} -9.67432 q^{71} +(-8.20351 + 2.16849i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(1.45185 - 0.297563i) q^{74} +(7.08684 - 2.58352i) q^{75} +(-8.54216 + 11.4041i) q^{76} +(-10.9904 + 6.76452i) q^{78} +(6.00000 + 3.46410i) q^{79} +(2.32371 + 2.21822i) q^{80} +(6.90626 + 5.77092i) q^{81} +(-7.58404 + 6.72931i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(-8.40251 + 7.45554i) q^{86} +(7.21818 + 1.26894i) q^{87} +(-6.00000 - 2.83005i) q^{88} +(-14.1733 - 8.18296i) q^{89} +(0.495321 - 3.37117i) q^{90} +(12.6252 + 9.45679i) q^{92} +(-2.90623 - 7.97207i) q^{93} +(-8.44975 + 1.73182i) q^{94} +(-2.86085 - 4.95513i) q^{95} +(-9.32144 + 3.01839i) q^{96} +4.37827 q^{97} +(1.22896 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) $ 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Character values

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

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

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 $

$2$	−0.938613	−	1.05783i	−0.663700	−	0.747999i
$2$	−0.938613	−	1.05783i	−0.663700	−	0.747999i
$3$	−0.299892	+	1.70589i	−0.173143	+	0.984897i
$3$	−0.299892	+	1.70589i	−0.173143	+	0.984897i
$4$	−0.238012	+	1.98579i	−0.119006	+	0.992894i
$5$	−0.695526	−	0.401562i	−0.311049	−	0.179584i	0.336347	−	0.941738i	$-0.390808\pi$
$5$	−0.695526	−	0.401562i	−0.311049	−	0.179584i	−0.647396	+	0.762154i	$0.724142\pi$
$6$	2.08603	−	1.28394i	0.851617	−	0.524165i
$7$		0			0
$7$		0			0
$8$	2.32403	−	1.61211i	0.821668	−	0.569967i
$9$	−2.82013	−	1.02317i	−0.940043	−	0.341056i
$10$	0.228045	+	1.11266i	0.0721141	+	0.351854i
$11$	−1.17273	−	2.03122i	−0.353590	−	0.612436i	0.633285	−	0.773918i	$-0.281706\pi$
$11$	−1.17273	−	2.03122i	−0.353590	−	0.612436i	−0.986876	+	0.161482i	$0.948373\pi$
$12$	−3.31616	−	1.00154i	−0.957293	−	0.289121i
$13$	−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
$16$	−3.88670	−	0.945282i	−0.971675	−	0.236320i
$17$	1.02661	−	0.592715i	0.248990	−	0.143754i	−0.370312	−	0.928908i	$-0.620749\pi$
$17$	1.02661	−	0.592715i	0.248990	−	0.143754i	0.619302	+	0.785153i	$0.287416\pi$
$18$	1.56467	+	3.94358i	0.368797	+	0.929510i
$19$	6.16982	+	3.56215i	1.41545	+	0.817213i	0.995895	−	0.0905147i	$-0.0288512\pi$
$19$	6.16982	+	3.56215i	1.41545	+	0.817213i	0.419560	+	0.907728i	$0.362185\pi$
$20$	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	−0.0816860	−	0.996658i	$-0.526030\pi$
$23$	3.94356	−	6.83044i	0.822288	−	1.42425i	0.903974	−	0.427587i	$-0.140636\pi$
$24$	2.05313	+	4.44800i	0.419092	+	0.907944i
$25$	−2.17750	−	3.77153i	−0.435499	−	0.754307i
$26$	4.94516	+	5.57327i	0.969825	+	1.09301i
$27$	2.59115	−	4.50399i	0.498666	−	0.866794i
$28$		0			0
$29$		−	4.23132i		−	0.785737i	−0.919595	−	0.392868i	$-0.871483\pi$
$29$		−	4.23132i		−	0.785737i	0.919595	−	0.392868i	$-0.128517\pi$
$30$	−1.96647	+	0.0553417i	−0.359026	+	0.0101040i
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	2.64816	+	4.99872i	0.468133	+	0.883658i
$33$	3.81673	−	1.39140i	0.664408	−	0.242211i
$34$	−1.59058	−	0.529652i	−0.272783	−	0.0908346i
$35$		0			0
$36$	2.70302	−	5.35665i	0.450503	−	0.892775i
$37$	−0.523976	+	0.907554i	−0.0861412	+	0.149201i	−0.905877	−	0.423541i	$-0.860787\pi$
$37$	−0.523976	+	0.907554i	−0.0861412	+	0.149201i	0.819736	+	0.572742i	$0.194120\pi$
$38$	−2.02292	−	9.87011i	−0.328162	−	1.60114i
$39$	1.58001	−	8.98762i	0.253003	−	1.43917i
$40$	−2.26378	+	0.188022i	−0.357935	+	0.0297289i
$41$		−	7.16942i		−	1.11968i	−0.828602	−	0.559838i	$-0.810863\pi$
$41$		−	7.16942i		−	1.11968i	0.828602	−	0.559838i	$-0.189137\pi$
$42$		0			0
$43$		−	7.94315i		−	1.21132i	−0.795724	−	0.605659i	$-0.792909\pi$
$43$		−	7.94315i		−	1.21132i	0.795724	−	0.605659i	$-0.207091\pi$
$44$	4.31270	−	1.84533i	0.650164	−	0.278194i
$45$	1.55061	+	1.84410i	0.231151	+	0.274902i
$46$	−10.9269	+	2.23952i	−1.61109	+	0.330200i
$47$	3.04954	−	5.28195i	0.444821	−	0.770452i	−0.553219	−	0.833036i	$-0.686601\pi$
$47$	3.04954	−	5.28195i	0.444821	−	0.770452i	0.998040	+	0.0625838i	$0.0199341\pi$
$48$	2.77814	−	6.34681i	0.400990	−	0.916083i
$49$		0			0
$50$	−1.94582	+	5.84343i	−0.275180	+	0.826386i
$51$	0.703234	+	1.92904i	0.0984725	+	0.270120i
$52$	1.25398	−	10.4623i	0.173896	−	1.45086i
$53$	−7.55175	+	4.36001i	−1.03731	+	0.598893i	−0.919071	−	0.394092i	$-0.871059\pi$
$53$	−7.55175	+	4.36001i	−1.03731	+	0.598893i	−0.118242	+	0.992985i	$0.537726\pi$
$54$	−7.19655	+	1.48651i	−0.979326	+	0.202289i
$55$			1.88369i			0.253997i
$56$		0			0
$57$	−7.92692	+	9.45679i	−1.04995	+	1.25258i
$58$	−4.47602	+	3.97157i	−0.587731	+	0.521493i
$59$	0.331087	+	0.573459i	0.0431038	+	0.0746580i	0.886772	−	0.462206i	$-0.152942\pi$
$59$	0.331087	+	0.573459i	0.0431038	+	0.0746580i	−0.843669	+	0.536864i	$0.819609\pi$
$60$	1.90429	+	2.02824i	0.245843	+	0.261845i
$61$	0.479062	−	0.829760i	0.0613376	−	0.106240i	−0.833726	−	0.552178i	$-0.813797\pi$
$61$	0.479062	−	0.829760i	0.0613376	−	0.106240i	0.895064	+	0.445939i	$0.147130\pi$
$62$	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
$66$	−5.05430	−	2.73148i	−0.622141	−	0.336222i
$67$	7.29738	−	4.21314i	0.891517	−	0.514717i	0.0170783	−	0.999854i	$-0.494564\pi$
$67$	7.29738	−	4.21314i	0.891517	−	0.514717i	0.874438	+	0.485137i	$0.161230\pi$
$68$	0.932660	+	2.17971i	0.113102	+	0.264328i
$69$	10.4693	+	8.77567i	1.26036	+	1.05647i
$70$		0			0
$71$	−9.67432			−1.14813			−0.574065	−	0.818810i	$-0.694634\pi$
$71$	−9.67432			−1.14813			−0.574065	+	0.818810i	$0.694634\pi$
$72$	−8.20351	+	2.16849i	−0.966794	+	0.255559i
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	0.821674	−	0.569958i	$-0.193040\pi$
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	−0.904435	+	0.426612i	$0.859707\pi$
$74$	1.45185	−	0.297563i	0.168774	−	0.0345910i
$75$	7.08684	−	2.58352i	0.818318	−	0.298319i
$76$	−8.54216	+	11.4041i	−0.979853	+	1.30814i
$77$		0			0
$78$	−10.9904	+	6.76452i	−1.24442	+	0.765931i
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	0.797988	−	0.602673i	$-0.205898\pi$
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	−0.122936	+	0.992415i	$0.539231\pi$
$80$	2.32371	+	2.21822i	0.259799	+	0.248004i
$81$	6.90626	+	5.77092i	0.767362	+	0.641214i
$82$	−7.58404	+	6.72931i	−0.837517	+	0.743128i
$83$	−5.18229			−0.568830			−0.284415	−	0.958701i	$-0.591799\pi$
$83$	−5.18229			−0.568830			−0.284415	+	0.958701i	$0.591799\pi$
$84$		0			0
$85$	−0.952047			−0.103264
$86$	−8.40251	+	7.45554i	−0.906066	+	0.803952i
$87$	7.21818	+	1.26894i	0.773870	+	0.136045i
$88$	−6.00000	−	2.83005i	−0.639602	−	0.301685i
$89$	−14.1733	−	8.18296i	−1.50237	−	0.867392i	−0.999996	−	0.00273917i	$-0.999128\pi$
$89$	−14.1733	−	8.18296i	−1.50237	−	0.867392i	−0.502370	−	0.864653i	$-0.667539\pi$
$90$	0.495321	−	3.37117i	0.0522114	−	0.355353i
$91$		0			0
$92$	12.6252	+	9.45679i	1.31627	+	0.985938i
$93$	−2.90623	−	7.97207i	−0.301362	−	0.826665i
$94$	−8.44975	+	1.73182i	−0.871525	+	0.178623i
$95$	−2.86085	−	4.95513i	−0.293517	−	0.508386i
$96$	−9.32144	+	3.01839i	−0.951366	+	0.308064i
$97$	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
$100$	8.00773	−	3.42637i	0.800773	−	0.342637i
$101$	−7.26887	+	4.19668i	−0.723279	+	0.417586i	−0.815959	−	0.578110i	$-0.803790\pi$
$101$	−7.26887	+	4.19668i	−0.723279	+	0.417586i	0.0926791	+	0.995696i	$0.470457\pi$
$102$	1.38053	−	2.55452i	0.136693	−	0.252936i
$103$	−2.22304	−	1.28347i	−0.219043	−	0.126465i	0.386464	−	0.922304i	$-0.373696\pi$
$103$	−2.22304	−	1.28347i	−0.219043	−	0.126465i	−0.605507	+	0.795840i	$0.707030\pi$
$104$	−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	$-0.928603\pi$
$107$	−3.04995	+	5.28267i	−0.294850	+	0.510695i	0.680100	+	0.733119i	$0.261936\pi$
$108$	8.32725	+	6.21747i	0.801290	+	0.598276i
$109$	−2.72545	−	4.72062i	−0.261051	−	0.452153i	0.705471	−	0.708739i	$-0.250736\pi$
$109$	−2.72545	−	4.72062i	−0.261051	−	0.452153i	−0.966521	+	0.256586i	$0.917402\pi$
$110$	1.99262	−	1.76806i	0.189989	−	0.168577i
$111$	−1.39105	−	1.16601i	−0.132033	−	0.110673i
$112$		0			0
$113$		−	7.09803i		−	0.667726i	−0.942622	−	0.333863i	$-0.891648\pi$
$113$		−	7.09803i		−	0.667726i	0.942622	−	0.333863i	$-0.108352\pi$
$114$	17.4440	−	0.490922i	1.63378	−	0.0459790i
$115$	−5.48569	+	3.16716i	−0.511543	+	0.295340i
$116$	8.40251	+	1.00710i	0.780153	+	0.0935073i
$117$	14.8581	+	5.39064i	1.37363	+	0.498364i
$118$	0.295860	−	0.888490i	0.0272361	−	0.0817921i
$119$		0			0
$120$	0.358145	−	3.91815i	0.0326940	−	0.357677i
$121$	2.74943	−	4.76214i	0.249948	−	0.432922i
$122$	−1.32740	+	0.272057i	−0.120177	+	0.0246308i
$123$	12.2303	+	2.15005i	1.10277	+	0.193864i
$124$	−3.85437	−	9.00799i	−0.346132	−	0.808941i
$125$			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	$0.940882\pi$
$128$	−10.5567	+	4.06893i	−0.933089	+	0.359646i
$129$	13.5501	+	2.38209i	1.19302	+	0.209731i
$130$	−1.20147	−	5.86214i	−0.105376	−	0.514143i
$131$	−5.24594	+	9.08624i	−0.458340	+	0.793869i	−0.998873	−	0.0474541i	$-0.984889\pi$
$131$	−5.24594	+	9.08624i	−0.458340	+	0.793869i	0.540533	+	0.841323i	$0.318223\pi$
$132$	1.85459	+	7.91039i	0.161421	+	0.688511i
$133$		0			0
$134$	−11.3062	−	3.76488i	−0.976707	−	0.325236i
$135$	−3.61084	+	2.09214i	−0.310772	+	0.180063i
$136$	1.43035	−	3.03250i	0.122652	−	0.260034i
$137$	11.6844	−	6.74600i	0.998267	−	0.576350i	0.0905318	−	0.995894i	$-0.471143\pi$
$137$	11.6844	−	6.74600i	0.998267	−	0.576350i	0.907735	+	0.419544i	$0.137810\pi$
$138$	−0.543486	−	19.3118i	−0.0462646	−	1.64393i
$139$			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
$142$	9.08044	+	10.2338i	0.762014	+	0.858801i
$143$	6.17860	+	10.7017i	0.516681	+	0.894917i
$144$	9.99382	+	6.64256i	0.832818	+	0.553547i
$145$	−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	0.947012	−	0.321199i	$-0.104086\pi$
$149$	13.9442	+	8.05067i	1.14235	+	0.659536i	0.195339	+	0.980736i	$0.437419\pi$
$150$	−9.38472	−	5.07175i	−0.766259	−	0.414107i
$151$	−15.0553	+	8.69219i	−1.22518	+	0.707360i	−0.966019	−	0.258473i	$-0.916781\pi$
$151$	−15.0553	+	8.69219i	−1.22518	+	0.707360i	−0.259166	+	0.965833i	$0.583448\pi$
$152$	20.0814	−	1.66790i	1.62882	−	0.135284i
$153$	−3.50163	+	0.621137i	−0.283090	+	0.0502160i
$154$		0			0
$155$	3.93449			0.316026
$156$	17.4714	+	5.27672i	1.39884	+	0.422475i
$157$	−1.96109	−	3.39671i	−0.156512	−	0.271087i	0.777096	−	0.629381i	$-0.216692\pi$
$157$	−1.96109	−	3.39671i	−0.156512	−	0.271087i	−0.933609	+	0.358295i	$0.883358\pi$
$158$	−1.96724	−	9.59843i	−0.156506	−	0.763610i
$159$	−5.17299	−	14.1900i	−0.410244	−	1.12534i
$160$	0.165435	−	4.54014i	0.0130788	−	0.358930i
$161$		0			0
$162$	−0.377643	−	12.7223i	−0.0296704	−	0.999560i
$163$	6.32987	+	3.65455i	0.495793	+	0.286246i	0.726975	−	0.686664i	$-0.240926\pi$
$163$	6.32987	+	3.65455i	0.495793	+	0.286246i	−0.231181	+	0.972911i	$0.574259\pi$
$164$	14.2370	+	1.70641i	1.11172	+	0.133248i
$165$	−3.21337	−	0.564904i	−0.250160	−	0.0439777i
$166$	4.86417	+	5.48199i	0.377532	+	0.425485i
$167$	−8.37196			−0.647842			−0.323921	−	0.946084i	$-0.605001\pi$
$167$	−8.37196			−0.647842			−0.323921	+	0.946084i	$0.605001\pi$
$168$		0			0
$169$	14.7579			1.13523
$170$	0.893604	+	1.00710i	0.0685363	+	0.0772414i
$171$	−13.7550	−	16.3585i	−1.05187	−	1.25096i
$172$	15.7734	+	1.89056i	1.20271	+	0.144154i
$173$	−11.0601	−	6.38556i	−0.840884	−	0.485485i	0.0166803	−	0.999861i	$-0.494690\pi$
$173$	−11.0601	−	6.38556i	−0.840884	−	0.485485i	−0.857565	+	0.514376i	$0.828024\pi$
$174$	−5.43275	−	8.82665i	−0.411856	−	0.669147i
$175$		0			0
$176$	2.63796	+	9.00331i	0.198844	+	0.678650i
$177$	−1.07755	+	0.392822i	−0.0809935	+	0.0295263i
$178$	4.64706	+	22.6736i	0.348312	+	1.69946i
$179$	10.5589	+	18.2885i	0.789206	+	1.36694i	0.926454	+	0.376408i	$0.122841\pi$
$179$	10.5589	+	18.2885i	0.789206	+	1.36694i	−0.137248	+	0.990537i	$0.543826\pi$
$180$	−4.03104	+	2.64026i	−0.300456	+	0.196793i
$181$	−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
$184$	−1.84648	−	22.2316i	−0.136124	−	1.63893i
$185$	0.728878	−	0.420818i	0.0535882	−	0.0309392i
$186$	−5.70527	+	10.5570i	−0.418331	+	0.774075i
$187$	−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	$-0.904163\pi$
$191$	−3.04995	+	5.28267i	−0.220687	+	0.382241i	0.734330	+	0.678793i	$0.237497\pi$
$192$	11.9422	+	7.02741i	0.861852	+	0.507159i
$193$	−0.322504	−	0.558593i	−0.0232144	−	0.0402084i	0.854185	−	0.519969i	$-0.174057\pi$
$193$	−0.322504	−	0.558593i	−0.0232144	−	0.0402084i	−0.877399	+	0.479761i	$0.840723\pi$
$194$	−4.10950	−	4.63147i	−0.295045	−	0.332520i
$195$	−4.70802	+	5.61665i	−0.337149	+	0.402217i
$196$		0			0
$197$		−	14.9111i		−	1.06237i	−0.847256	−	0.531185i	$-0.821747\pi$
$197$		−	14.9111i		−	1.06237i	0.847256	−	0.531185i	$-0.178253\pi$
$198$	6.17535	−	7.80293i	0.438863	−	0.554530i
$199$	16.1940	−	9.34962i	1.14796	−	0.662777i	0.199573	−	0.979883i	$-0.436044\pi$
$199$	16.1940	−	9.34962i	1.14796	−	0.662777i	0.948390	+	0.317106i	$0.102711\pi$
$200$	−11.1407	−	5.25479i	−0.787765	−	0.371570i
$201$	4.99874	+	13.7120i	0.352584	+	0.967171i
$202$	11.2620	+	3.75017i	0.792394	+	0.263861i
$203$		0			0
$204$	−3.99804	+	0.937339i	−0.279919	+	0.0656269i
$205$	−2.87897	+	4.98652i	−0.201076	+	0.348274i
$206$	0.728878	+	3.55629i	0.0507833	+	0.247778i
$207$	−18.1100	+	15.2278i	−1.25873	+	1.05841i
$208$	20.4774	+	4.98029i	1.41985	+	0.345321i
$209$		−	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	$0.867771\pi$
$212$	−6.86064	−	16.0339i	−0.471191	−	1.10121i
$213$	2.90125	−	16.5033i	0.198791	−	1.13079i
$214$	8.45090	−	1.73205i	0.577691	−	0.118401i
$215$	−3.18967	+	5.52466i	−0.217533	+	0.376779i
$216$	−1.23904	−	14.6446i	−0.0843057	−	0.996440i
$217$		0			0
$218$	−2.43547	+	7.31389i	−0.164951	+	0.495359i
$219$	2.30134	−	0.838956i	0.155510	−	0.0566914i
$220$	−3.74061	−	0.448340i	−0.252192	−	0.0302271i
$221$	−5.40879	+	3.12277i	−0.363835	+	0.210060i
$222$	0.0722124	+	2.56593i	0.00484658	+	0.172214i
$223$			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
$226$	−7.50851	+	6.66230i	−0.499459	+	0.443170i
$227$	−4.37694	−	7.58108i	−0.290507	−	0.503174i	0.683422	−	0.730023i	$-0.260491\pi$
$227$	−4.37694	−	7.58108i	−0.290507	−	0.503174i	−0.973930	+	0.226850i	$0.927157\pi$
$228$	−16.8925	−	17.9920i	−1.11873	−	1.19155i
$229$	−9.24927	+	16.0202i	−0.611209	+	1.05864i	0.379828	+	0.925057i	$0.375983\pi$
$229$	−9.24927	+	16.0202i	−0.611209	+	1.05864i	−0.991037	+	0.133588i	$0.957350\pi$
$230$	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	0.183997	−	0.982927i	$-0.441096\pi$
$233$	−8.78072	−	5.06955i	−0.575244	−	0.332117i	−0.759241	+	0.650810i	$0.774430\pi$
$234$	−8.24360	−	20.7771i	−0.538901	−	1.35824i
$235$	−4.24206	+	2.44916i	−0.276722	+	0.159765i
$236$	−1.21757	+	0.520978i	−0.0792571	+	0.0339128i
$237$	−7.70873	+	9.19649i	−0.500736	+	0.597376i
$238$		0			0
$239$	1.49470			0.0966841			0.0483421	−	0.998831i	$-0.484606\pi$
$239$	1.49470			0.0966841			0.0483421	+	0.998831i	$0.484606\pi$
$240$	−4.48090	+	3.29877i	−0.289241	+	0.212935i
$241$	−5.16686	−	8.94926i	−0.332827	−	0.576472i	0.650238	−	0.759730i	$-0.274669\pi$
$241$	−5.16686	−	8.94926i	−0.332827	−	0.576472i	−0.983065	+	0.183258i	$0.941336\pi$
$242$	−7.61819	+	1.56138i	−0.489716	+	0.100370i
$243$	−11.9157	+	10.0507i	−0.764393	+	0.644751i
$244$	1.53370	+	1.14881i	0.0981853	+	0.0735449i
$245$		0			0
$246$	−9.20508	−	14.9556i	−0.586895	−	0.953535i
$247$	−32.5062	−	18.7675i	−2.06832	−	1.19415i
$248$	−5.91117	+	12.5323i	−0.375360	+	0.795801i
$249$	1.55413	−	8.84042i	0.0984889	−	0.560239i
$250$	7.94771	−	7.05200i	0.502658	−	0.446008i
$251$	26.9555			1.70142			0.850709	−	0.525636i	$-0.176173\pi$
$251$	26.9555			1.70142			0.850709	+	0.525636i	$0.176173\pi$
$252$		0			0
$253$	−18.4989			−1.16301
$254$	4.40272	−	3.90653i	0.276251	−	0.245117i
$255$	0.285511	−	1.62409i	0.0178794	−	0.101704i
$256$	14.2129	+	7.34805i	0.888305	+	0.459253i
$257$	2.41766	+	1.39584i	0.150810	+	0.0870700i	0.573506	−	0.819201i	$-0.305583\pi$
$257$	2.41766	+	1.39584i	0.150810	+	0.0870700i	−0.422696	+	0.906271i	$0.638916\pi$
$258$	−10.1985	−	16.5696i	−0.634931	−	1.03158i
$259$		0			0
$260$	−5.07343	+	6.77323i	−0.314641	+	0.420058i
$261$	−4.32935	+	11.9329i	−0.267980	+	0.738627i
$262$	14.5356	−	2.97914i	0.898013	−	0.184052i
$263$	−7.65516	−	13.2591i	−0.472037	−	0.817592i	0.527451	−	0.849586i	$-0.323148\pi$
$263$	−7.65516	−	13.2591i	−0.472037	−	0.817592i	−0.999488	+	0.0319931i	$0.989815\pi$
$264$	6.62711	−	9.38664i	0.407871	−	0.577708i
$265$	7.00325			0.430206
$266$		0			0
$267$	18.2097	−	21.7241i	1.11442	−	1.32949i
$268$	6.62954	+	15.4938i	0.404964	+	0.946435i
$269$	−26.5752	+	15.3432i	−1.62032	+	0.935492i	−0.633487	+	0.773754i	$0.718377\pi$
$269$	−26.5752	+	15.3432i	−1.62032	+	0.935492i	−0.986834	+	0.161739i	$0.948290\pi$
$270$	5.60231	+	1.85595i	0.340946	+	0.112950i
$271$	−17.0488	−	9.84312i	−1.03564	−	0.597927i	−0.117045	−	0.993127i	$-0.537342\pi$
$271$	−17.0488	−	9.84312i	−1.03564	−	0.597927i	−0.918595	+	0.395199i	$0.870675\pi$
$272$	−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
$276$	−19.9184	+	18.7012i	−1.19895	+	1.12568i
$277$	6.55646	+	11.3561i	0.393940	+	0.682324i	0.992965	−	0.118406i	$-0.0377785\pi$
$277$	6.55646	+	11.3561i	0.393940	+	0.682324i	−0.599025	+	0.800730i	$0.704445\pi$
$278$	8.01057	−	7.10778i	0.480442	−	0.426296i
$279$	14.4710	−	2.56695i	0.866358	−	0.153679i
$280$		0			0
$281$		−	2.86670i		−	0.171013i	−0.996338	−	0.0855066i	$-0.972749\pi$
$281$		−	2.86670i		−	0.171013i	0.996338	−	0.0855066i	$-0.0272509\pi$
$282$	−0.420275	−	14.9337i	−0.0250270	−	0.889289i
$283$	1.72374	−	0.995200i	0.102466	−	0.0591585i	−0.447892	−	0.894088i	$-0.647825\pi$
$283$	1.72374	−	0.995200i	0.102466	−	0.0591585i	0.550357	+	0.834929i	$0.314492\pi$
$284$	2.30260	−	19.2111i	0.136634	−	1.13997i
$285$	9.31086	−	3.39429i	0.551528	−	0.201060i
$286$	5.52122	−	16.5806i	0.326477	−	0.980433i
$287$		0			0
$288$	−2.35362	−	16.8066i	−0.138689	−	0.990336i
$289$	−7.79738	+	13.5055i	−0.458669	+	0.794439i
$290$	4.70802	−	0.964931i	0.276465	−	0.0566627i
$291$	−1.31301	+	7.46886i	−0.0769700	+	0.437832i
$292$	2.60038	−	1.11266i	0.152176	−	0.0651135i
$293$		−	16.7482i		−	0.978441i	−0.872160	−	0.489221i	$-0.837281\pi$
$293$		−	16.7482i		−	0.978441i	0.872160	−	0.489221i	$-0.162719\pi$
$294$		0			0
$295$		−	0.531807i		−	0.0309630i
$296$	0.245340	+	2.95389i	0.0142601	+	0.171691i
$297$	−12.1873	+	0.0187619i	−0.707180	+	0.00108867i
$298$	−4.57193	−	22.3070i	−0.264845	−	1.29221i
$299$	−20.7769	+	35.9867i	−1.20156	+	2.08117i
$300$	3.44356	+	14.6879i	0.198814	+	0.848004i
$301$		0			0
$302$	23.3260	+	7.76737i	1.34226	+	0.446962i
$303$	−4.97921	−	13.6585i	−0.286048	−	0.784657i
$304$	−20.6130	−	19.6772i	−1.18224	−	1.12857i
$305$	−0.666400	+	0.384746i	−0.0381579	+	0.0220305i
$306$	3.94373	+	3.12112i	0.225448	+	0.178423i
$307$		−	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
$310$	−3.69296	−	4.16202i	−0.209746	−	0.236387i
$311$	−5.44973	−	9.43920i	−0.309026	−	0.535248i	0.669124	−	0.743151i	$-0.266670\pi$
$311$	−5.44973	−	9.43920i	−0.309026	−	0.535248i	−0.978149	+	0.207903i	$0.933336\pi$
$312$	−10.8171	−	23.4346i	−0.612395	−	1.32672i
$313$	16.9011	−	29.2736i	0.955308	−	1.65464i	0.221646	−	0.975127i	$-0.428857\pi$
$313$	16.9011	−	29.2736i	0.955308	−	1.65464i	0.733662	−	0.679514i	$-0.237810\pi$
$314$	−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	0.256843	−	0.966453i	$-0.417318\pi$
$317$	−8.04243	−	4.64330i	−0.451708	−	0.260794i	−0.708551	+	0.705659i	$0.750651\pi$
$318$	−10.1552	+	18.7911i	−0.569475	+	1.05375i
$319$	−8.59476	+	4.96218i	−0.481214	+	0.277829i
$320$	−4.95798	+	4.08643i	−0.277160	+	0.228439i
$321$	−8.09701	−	6.78712i	−0.451931	−	0.378820i
$322$		0			0
$323$	8.44536			0.469912
$324$	−13.1036	+	12.3408i	−0.727978	+	0.685601i
$325$	11.4723	+	19.8706i	0.636369	+	1.10222i
$326$	−2.07540	−	10.1261i	−0.114946	−	0.560835i
$327$	8.87020	−	3.23364i	0.490523	−	0.178821i
$328$	−11.5579	−	16.6619i	−0.638178	−	0.920002i
$329$		0			0
$330$	2.41854	+	3.92943i	0.133136	+	0.216308i
$331$	−0.878968	−	0.507473i	−0.0483125	−	0.0278932i	0.475649	−	0.879635i	$-0.342213\pi$
$331$	−0.878968	−	0.507473i	−0.0483125	−	0.0278932i	−0.523962	+	0.851742i	$0.675547\pi$
$332$	1.23345	−	10.2909i	0.0676942	−	0.564788i
$333$	2.40626	−	2.02330i	0.131862	−	0.110876i
$334$	7.85803	+	8.85611i	0.429972	+	0.484585i
$335$	−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	$0.612057\pi$
$338$	−13.8520	−	15.6114i	−0.753449	−	0.849148i
$339$	12.1085	+	2.12864i	0.657641	+	0.115612i
$340$	0.226598	−	1.89056i	0.0122890	−	0.102530i
$341$	9.95091	+	5.74516i	0.538872	+	0.311118i
$342$	−4.39386	+	29.9048i	−0.237593	+	1.61706i
$343$		0			0
$344$	−12.8052	−	18.4601i	−0.690411	−	0.995302i
$345$	−3.75772	−	10.3078i	−0.202309	−	0.554953i
$346$	3.62632	+	17.6933i	0.194952	+	0.951197i
$347$	12.8143	+	22.1950i	0.687907	+	1.19149i	0.972514	+	0.232846i	$0.0748037\pi$
$347$	12.8143	+	22.1950i	0.687907	+	1.19149i	−0.284607	+	0.958644i	$0.591863\pi$
$348$	−4.23786	+	14.0317i	−0.227173	+	0.752180i
$349$	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
$352$	7.04795	−	11.2411i	0.375657	−	0.599155i
$353$	8.92430	−	5.15245i	0.474993	−	0.274237i	−0.243335	−	0.969942i	$-0.578241\pi$
$353$	8.92430	−	5.15245i	0.474993	−	0.274237i	0.718327	+	0.695705i	$0.244908\pi$
$354$	1.42694	+	0.771157i	0.0758410	+	0.0409865i
$355$	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	−0.257235	−	0.966349i	$-0.582812\pi$
$359$	13.4197	−	23.2436i	0.708265	−	1.22675i	0.965500	−	0.260402i	$-0.0838551\pi$
$360$	6.57654	+	1.78598i	0.346614	+	0.0941294i
$361$	15.8778	+	27.5012i	0.835675	+	1.44743i
$362$	11.6458	+	13.1250i	0.612090	+	0.689834i
$363$	7.29917	+	6.11835i	0.383107	+	0.321130i
$364$		0			0
$365$			1.13579i			0.0594499i
$366$	−0.0660225	−	2.34599i	−0.00345105	−	0.122627i
$367$	11.5631	−	6.67596i	0.603589	−	0.348482i	−0.166863	−	0.985980i	$-0.553364\pi$
$367$	11.5631	−	6.67596i	0.603589	−	0.348482i	0.770452	+	0.637498i	$0.220031\pi$
$368$	−21.7841	+	22.8201i	−1.13558	+	1.18958i
$369$	−7.33552	+	20.2187i	−0.381872	+	1.05254i
$370$	−1.12929	−	0.376045i	−0.0587089	−	0.0195496i
$371$		0			0
$372$	16.5225	−	3.87371i	0.856654	−	0.200842i
$373$	11.4029	−	19.7505i	0.590422	−	1.02264i	−0.403753	−	0.914868i	$-0.632295\pi$
$373$	11.4029	−	19.7505i	0.590422	−	1.02264i	0.994176	−	0.107773i	$-0.0343720\pi$
$374$	0.789478	+	3.85197i	0.0408230	+	0.199180i
$375$	−12.8167	−	2.25315i	−0.661853	−	0.116352i
$376$	−1.42788	−	17.1916i	−0.0736371	−	0.886589i
$377$			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	$-0.0162040\pi$
$380$	10.5208	−	4.50165i	0.539703	−	0.230930i
$381$	−7.09996	−	1.24816i	−0.363742	−	0.0639451i
$382$	8.45090	−	1.73205i	0.432386	−	0.0886194i
$383$	14.4104	−	24.9596i	0.736339	−	1.27538i	−0.217795	−	0.975995i	$-0.569886\pi$
$383$	14.4104	−	24.9596i	0.736339	−	1.27538i	0.954134	−	0.299381i	$-0.0967803\pi$
$384$	−3.77527	−	19.2288i	−0.192656	−	0.981266i
$385$		0			0
$386$	−0.288191	+	0.865458i	−0.0146685	+	0.0440506i
$387$	−8.12716	+	22.4007i	−0.413127	+	1.13869i
$388$	−1.04208	+	8.69432i	−0.0529036	+	0.441387i
$389$	1.69719	−	0.979873i	0.0860509	−	0.0496815i	−0.456357	−	0.889797i	$-0.650846\pi$
$389$	1.69719	−	0.979873i	0.0860509	−	0.0496815i	0.542408	+	0.840115i	$0.317513\pi$
$390$	10.3605	−	0.291572i	0.524623	−	0.0147643i
$391$		−	9.34962i		−	0.472831i
$392$		0			0
$393$	−13.9269	−	11.6739i	−0.702520	−	0.588870i
$394$	−15.7734	+	13.9957i	−0.794652	+	0.705095i
$395$	−2.78210	−	4.81874i	−0.139983	−	0.242457i
$396$	−14.0504	+	0.791463i	−0.706061	+	0.0397725i
$397$	−2.28155	+	3.95176i	−0.114508	+	0.198333i	−0.917583	−	0.397545i	$-0.869862\pi$
$397$	−2.28155	+	3.95176i	−0.114508	+	0.198333i	0.803075	+	0.595878i	$0.203196\pi$
$398$	−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	0.950874	−	0.309578i	$-0.100188\pi$
$401$	23.1931	+	13.3905i	1.15821	+	0.668692i	0.207335	+	0.978270i	$0.433521\pi$
$402$	9.81312	−	18.1581i	0.489434	−	0.905644i
$403$	22.3527	−	12.9053i	1.11347	−	0.642860i
$404$	−6.60364	−	15.4333i	−0.328544	−	0.767835i
$405$	−2.48610	−	6.78712i	−0.123535	−	0.337255i
$406$		0			0
$407$	2.45792			0.121835
$408$	4.74416	+	3.34945i	0.234871	+	0.165823i
$409$	9.02122	+	15.6252i	0.446071	+	0.772617i	0.998126	−	0.0611902i	$-0.0194896\pi$
$409$	9.02122	+	15.6252i	0.446071	+	0.772617i	−0.552055	+	0.833807i	$0.686156\pi$
$410$	7.97713	−	1.63495i	0.393962	−	0.0807444i
$411$	8.00388	+	21.9554i	0.394802	+	1.08298i
$412$	3.07782	−	4.10901i	0.151633	−	0.202436i
$413$		0			0
$414$	33.1067	+	4.86432i	1.62711	+	0.239068i
$415$	3.60442	+	2.08101i	0.176934	+	0.102153i
$416$	−13.9520	−	26.3362i	−0.684055	−	1.29124i
$417$	−12.9181	−	2.27097i	−0.632602	−	0.111210i
$418$	−17.6760	+	15.6839i	−0.864564	+	0.767127i
$419$	−17.5395			−0.856861			−0.428430	−	0.903575i	$-0.640933\pi$
$419$	−17.5395			−0.856861			−0.428430	+	0.903575i	$0.640933\pi$
$420$		0			0
$421$	15.4006			0.750582			0.375291	−	0.926907i	$-0.377543\pi$
$421$	15.4006			0.750582			0.375291	+	0.926907i	$0.377543\pi$
$422$	12.4023	−	11.0046i	0.603734	−	0.535693i
$423$	−14.0044	+	11.7756i	−0.680918	+	0.572550i
$424$	−10.5217	+	22.3070i	−0.510978	+	1.08333i
$425$	−4.47089	−	2.58127i	−0.216870	−	0.125210i
$426$	−20.1809	+	12.4212i	−0.977767	+	0.601810i
$427$		0			0
$428$	−9.76434	−	7.31389i	−0.471977	−	0.353530i
$429$	−20.1088	+	7.33068i	−0.970861	+	0.353929i
$430$	8.83802	−	1.81139i	0.426207	−	0.0873532i
$431$	−4.50180	−	7.79735i	−0.216844	−	0.375585i	0.736997	−	0.675896i	$-0.236243\pi$
$431$	−4.50180	−	7.79735i	−0.216844	−	0.375585i	−0.953841	+	0.300311i	$0.902910\pi$
$432$	−14.3286	+	15.0563i	−0.689383	+	0.724397i
$433$	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
$436$	10.0228	−	4.28860i	0.480006	−	0.205387i
$437$	48.6621	−	28.0951i	2.32782	−	1.34397i
$438$	−3.04754	−	1.64697i	−0.145617	−	0.0786953i
$439$	−25.3306	−	14.6246i	−1.20896	−	0.697996i	−0.246432	−	0.969160i	$-0.579258\pi$
$439$	−25.3306	−	14.6246i	−1.20896	−	0.697996i	−0.962533	+	0.271164i	$0.912591\pi$
$440$	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	$-0.778494\pi$
$443$	3.60820	−	6.24958i	0.171431	−	0.296927i	0.938920	+	0.344135i	$0.111828\pi$
$444$	2.64654	−	2.48481i	0.125599	−	0.117924i
$445$	6.57193	+	11.3829i	0.311539	+	0.539602i
$446$	0.722774	−	0.641317i	0.0342243	−	0.0303672i
$447$	−17.9153	+	21.3729i	−0.847365	+	1.01090i
$448$		0			0
$449$		−	4.43423i		−	0.209264i	−0.994511	−	0.104632i	$-0.966634\pi$
$449$		−	4.43423i		−	0.209264i	0.994511	−	0.104632i	$-0.0333665\pi$
$450$	11.4663	−	14.4883i	0.540525	−	0.682987i
$451$	−14.5627	+	8.40777i	−0.685730	+	0.395907i
$452$	14.0952	+	1.68941i	0.662981	+	0.0794634i
$453$	−10.3130	−	28.2894i	−0.484545	−	1.32915i
$454$	−3.91125	+	11.7458i	−0.183564	+	0.551256i
$455$		0			0
$456$	−3.17701	+	34.7569i	−0.148777	+	1.62764i
$457$	−6.83102	+	11.8317i	−0.319541	+	0.553462i	−0.980392	−	0.197055i	$-0.936862\pi$
$457$	−6.83102	+	11.8317i	−0.319541	+	0.553462i	0.660851	+	0.750517i	$0.270196\pi$
$458$	25.6281	−	5.25261i	1.19752	−	0.245438i
$459$	−0.00948255	−	6.15967i	−0.000442608	−	0.287509i
$460$	−4.98366	−	11.6472i	−0.232364	−	0.543055i
$461$			5.25789i			0.244885i	0.992476	+	0.122442i	$0.0390726\pi$
$461$			5.25789i			0.244885i	−0.992476	+	0.122442i	$0.960927\pi$
$462$		0			0
$463$			15.8863i			0.738299i	0.929370	+	0.369149i	$0.120351\pi$
$463$			15.8863i			0.738299i	−0.929370	+	0.369149i	$0.879649\pi$
$464$	−3.99979	+	16.4459i	−0.185686	+	0.763481i
$465$	−1.17992	+	6.71181i	−0.0547176	+	0.311253i
$466$	2.87897	+	14.0469i	0.133366	+	0.650708i
$467$	13.5384	−	23.4491i	0.626481	−	1.08510i	−0.361771	−	0.932267i	$-0.617828\pi$
$467$	13.5384	−	23.4491i	0.626481	−	1.08510i	0.988252	−	0.152830i	$-0.0488388\pi$
$468$	−14.2411	+	28.2219i	−0.658293	+	1.30456i
$469$		0			0
$470$	6.57245	+	2.18858i	0.303164	+	0.100951i
$471$	6.38253	−	2.32676i	0.294092	−	0.107212i
$472$	1.69393	+	0.798987i	0.0779696	+	0.0367763i
$473$	−16.1343	+	9.31514i	−0.741856	+	0.428311i
$474$	16.9638	−	0.477409i	0.779175	−	0.0219281i
$475$		−	31.0263i		−	1.42358i
$476$		0			0
$477$	25.7579	−	4.56908i	1.17937	−	0.209204i
$478$	−1.40294	−	1.58114i	−0.0641692	−	0.0723196i
$479$	7.63026	+	13.2160i	0.348635	+	0.603854i	0.986007	−	0.166702i	$-0.0533119\pi$
$479$	7.63026	+	13.2160i	0.348635	+	0.603854i	−0.637372	+	0.770556i	$0.719979\pi$
$480$	7.69538	+	1.64377i	0.351244	+	0.0750273i
$481$	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
$486$	21.8161	+	3.17111i	0.989600	+	0.143844i
$487$	5.25172	−	3.03208i	0.237978	−	0.137397i	−0.376269	−	0.926511i	$-0.622793\pi$
$487$	5.25172	−	3.03208i	0.237978	−	0.137397i	0.614247	+	0.789114i	$0.289460\pi$
$488$	−0.224310	−	2.70068i	−0.0101540	−	0.122254i
$489$	−8.13254	+	9.70209i	−0.367766	+	0.438744i
$490$		0			0
$491$	−4.03833			−0.182247			−0.0911235	−	0.995840i	$-0.529046\pi$
$491$	−4.03833			−0.182247			−0.0911235	+	0.995840i	$0.529046\pi$
$492$	−7.18049	+	23.7749i	−0.323722	+	1.07186i
$493$	−2.50797	−	4.34393i	−0.112953	−	0.195641i
$494$	10.6579	+	52.0015i	0.479523	+	2.33966i
$495$	1.92733	−	5.31225i	0.0866270	−	0.238768i
$496$	18.8053	−	5.50994i	0.844384	−	0.247404i
$497$		0			0
$498$	−10.8104	+	6.65373i	−0.484426	+	0.298161i
$499$	33.3430	+	19.2506i	1.49264	+	0.861776i	0.999964	−	0.00843800i	$-0.00268593\pi$
$499$	33.3430	+	19.2506i	1.49264	+	0.861776i	0.492675	+	0.870214i	$0.336019\pi$
$500$	−14.9197	−	1.78823i	−0.667227	−	0.0799723i
$501$	2.51068	−	14.2816i	0.112169	−	0.638057i
$502$	−25.3008	−	28.5144i	−1.12923	−	1.27266i
$503$	14.3498			0.639827			0.319914	−	0.947447i	$-0.396346\pi$
$503$	14.3498			0.639827			0.319914	+	0.947447i	$0.396346\pi$
$504$		0			0
$505$	6.74091			0.299967
$506$	17.3633	+	19.5687i	0.771891	+	0.869933i
$507$	−4.42579	+	25.1754i	−0.196556	+	1.11808i
$508$	−8.26489	−	0.990610i	−0.366695	−	0.0439512i
$509$	10.4646	+	6.04176i	0.463837	+	0.267796i	0.713656	−	0.700496i	$-0.247038\pi$
$509$	10.4646	+	6.04176i	0.463837	+	0.267796i	−0.249819	+	0.968292i	$0.580371\pi$
$510$	−1.98600	+	1.22237i	−0.0879414	+	0.0541274i
$511$		0			0
$512$	−5.56740	−	21.9318i	−0.246047	−	0.969258i
$513$	32.0308	−	18.5588i	1.41419	−	0.819391i
$514$	−0.792689	−	3.86763i	−0.0349640	−	0.170594i
$515$	1.03079	+	1.78538i	0.0454220	+	0.0786732i
$516$	−7.95541	+	26.3407i	−0.350218	+	1.15959i
$517$	−14.3051			−0.629137
$518$		0			0
$519$	14.2099	−	16.9524i	0.623746	−	0.744126i
$520$	11.9269	−	0.990610i	0.523030	−	0.0434411i
$521$	−27.6002	+	15.9350i	−1.20919	+	0.698125i	−0.962582	−	0.270990i	$-0.912649\pi$
$521$	−27.6002	+	15.9350i	−1.20919	+	0.698125i	−0.246606	+	0.969116i	$0.579316\pi$
$522$	16.6865	−	6.62064i	0.730350	−	0.289777i
$523$	31.7039	+	18.3043i	1.38631	+	0.800389i	0.992898	−	0.118971i	$-0.0379596\pi$
$523$	31.7039	+	18.3043i	1.38631	+	0.800389i	0.393417	+	0.919360i	$0.371293\pi$
$524$	−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
$528$	−16.1498	+	1.80005i	−0.702828	+	0.0783372i
$529$	−19.6033	−	33.9539i	−0.852316	−	1.47625i
$530$	−6.57334	−	7.40826i	−0.285528	−	0.321794i
$531$	−0.346963	−	1.95599i	−0.0150569	−	0.0848825i
$532$		0			0
$533$			37.7727i			1.63612i
$534$	−40.0723	+	1.12774i	−1.73410	+	0.0488022i
$535$	4.24264	−	2.44949i	0.183425	−	0.105901i
$536$	10.1673	−	21.5556i	0.439159	−	0.931061i
$537$	−34.3647	+	12.5277i	−1.48294	+	0.540610i
$538$	41.1744	+	13.7108i	1.77515	+	0.591113i
$539$		0			0
$540$	−3.29512	−	7.66832i	−0.141799	−	0.329992i
$541$	18.1033	−	31.3558i	0.778320	−	1.34809i	−0.154589	−	0.987979i	$-0.549405\pi$
$541$	18.1033	−	31.3558i	0.778320	−	1.34809i	0.932909	−	0.360111i	$-0.117261\pi$
$542$	5.58985	+	27.2736i	0.240105	+	1.17150i
$543$	3.72090	−	21.1658i	0.159679	−	0.908311i
$544$	5.68145	+	3.56215i	0.243590	+	0.152726i
$545$			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	$-0.234180\pi$
$548$	10.6151	+	24.8084i	0.453454	+	1.05976i
$549$	−2.20000	+	1.84987i	−0.0938937	+	0.0789505i
$550$	14.1512	−	2.90036i	0.603410	−	0.123672i
$551$	15.0726	−	26.1065i	0.642115	−	1.11218i
$552$	38.4784	+	3.51718i	1.63775	+	0.149701i
$553$		0			0
$554$	5.85888	−	17.5946i	0.248920	−	0.747525i
$555$	0.499285	+	1.36959i	0.0211935	+	0.0581357i
$556$	−15.0376	−	1.80238i	−0.637738	−	0.0764378i
$557$	30.5691	−	17.6491i	1.29526	−	0.747816i	0.315675	−	0.948867i	$-0.397769\pi$
$557$	30.5691	−	17.6491i	1.29526	−	0.747816i	0.979581	+	0.201051i	$0.0644356\pi$
$558$	−16.2981	−	12.8985i	−0.689953	−	0.546038i
$559$			41.8491i			1.77003i
$560$		0			0
$561$	3.09361	−	3.69066i	0.130612	−	0.155820i
$562$	−3.03249	+	2.69073i	−0.127918	+	0.113501i
$563$	−13.2232	−	22.9032i	−0.557290	−	0.965254i	−0.997721	−	0.0674681i	$-0.978508\pi$
$563$	−13.2232	−	22.9032i	−0.557290	−	0.965254i	0.440432	−	0.897786i	$-0.354825\pi$
$564$	−15.4029	+	14.4616i	−0.648577	+	0.608941i
$565$	−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	−0.0881985	−	0.996103i	$-0.528111\pi$
$569$	−23.7332	−	13.7024i	−0.994948	−	0.574434i	−0.906750	+	0.421669i	$0.861444\pi$
$570$	−12.3299	−	6.66339i	−0.516442	−	0.279099i
$571$	24.3299	−	14.0469i	1.01817	−	0.587843i	0.104599	−	0.994514i	$-0.466644\pi$
$571$	24.3299	−	14.0469i	1.01817	−	0.587843i	0.913574	+	0.406672i	$0.133311\pi$
$572$	−22.7218	+	9.72227i	−0.950046	+	0.406509i
$573$	−8.09701	−	6.78712i	−0.338257	−	0.283536i
$574$		0			0
$575$	−34.3483			−1.43242
$576$	−15.5694	+	18.2646i	−0.648723	+	0.761025i
$577$	−11.4154	−	19.7721i	−0.475231	−	0.823124i	0.524367	−	0.851492i	$-0.324302\pi$
$577$	−11.4154	−	19.7721i	−0.475231	−	0.823124i	−0.999598	+	0.0283688i	$0.990969\pi$
$578$	21.6052	−	4.42809i	0.898658	−	0.184184i
$579$	1.04962	−	0.382639i	0.0436206	−	0.0159019i
$580$	−5.43974	−	4.07459i	−0.225873	−	0.169188i
$581$		0			0
$582$	9.13319	−	5.62142i	0.378583	−	0.233015i
$583$	17.7123	+	10.2262i	0.733568	+	0.423526i
$584$	−3.61776	−	1.70641i	−0.149704	−	0.0706116i
$585$	−8.16950	−	9.71577i	−0.337767	−	0.401697i
$586$	−17.7168	+	15.7201i	−0.731874	+	0.649391i
$587$	−28.4011			−1.17224			−0.586119	−	0.810225i	$-0.699345\pi$
$587$	−28.4011			−1.17224			−0.586119	+	0.810225i	$0.699345\pi$
$588$		0			0
$589$	−34.9018			−1.43810
$590$	−0.562562	+	0.499161i	−0.0231603	+	0.0205501i
$591$	25.4367	+	4.47172i	1.04633	+	0.183942i
$592$	2.89443	−	3.03208i	0.118960	−	0.124618i
$593$	20.6799	+	11.9396i	0.849223	+	0.490299i	0.860389	−	0.509638i	$-0.170221\pi$
$593$	20.6799	+	11.9396i	0.849223	+	0.490299i	−0.0111655	+	0.999938i	$0.503554\pi$
$594$	11.4590	+	12.8745i	0.470169	+	0.528247i
$595$		0			0
$596$	−19.3058	+	25.7740i	−0.790796	+	1.05574i
$597$	11.0930	+	30.4291i	0.454005	+	1.24538i
$598$	57.5694	−	11.7991i	2.35419	−	0.482501i
$599$	−19.5625	−	33.8832i	−0.799300	−	1.38443i	−0.920072	−	0.391749i	$-0.871870\pi$
$599$	−19.5625	−	33.8832i	−0.799300	−	1.38443i	0.120772	−	0.992680i	$-0.461463\pi$
$600$	12.3051	−	17.4289i	0.502354	−	0.711533i
$601$	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
$604$	−13.6775	−	31.9655i	−0.556529	−	1.30066i
$605$	−3.82459	+	2.20813i	−0.155492	+	0.0897732i
$606$	−9.77478	+	18.0872i	−0.397073	+	0.734741i
$607$	27.4754	+	15.8630i	1.11519	+	0.643857i	0.940170	−	0.340707i	$-0.110666\pi$
$607$	27.4754	+	15.8630i	1.11519	+	0.643857i	0.175024	+	0.984564i	$0.444000\pi$
$608$	−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
$612$	−0.400018	−	7.10132i	−0.0161698	−	0.287054i
$613$	−16.4834	−	28.5501i	−0.665758	−	1.15313i	−0.979079	−	0.203479i	$-0.934775\pi$
$613$	−16.4834	−	28.5501i	−0.665758	−	1.15313i	0.313322	−	0.949647i	$-0.398558\pi$
$614$	−16.3825	+	14.5362i	−0.661145	+	0.586634i
$615$	−7.64308	−	6.40662i	−0.308199	−	0.258340i
$616$		0			0
$617$			14.3990i			0.579680i	0.957075	+	0.289840i	$0.0936021\pi$
$617$			14.3990i			0.579680i	−0.957075	+	0.289840i	$0.906398\pi$
$618$	−6.28523	+	0.176884i	−0.252829	+	0.00711530i
$619$	−21.3838	+	12.3460i	−0.859489	+	0.496226i	−0.863841	−	0.503764i	$-0.831948\pi$
$619$	−21.3838	+	12.3460i	−0.859489	+	0.496226i	0.00435197	+	0.999991i	$0.498615\pi$
$620$	−0.936455	+	7.81306i	−0.0376089	+	0.313780i
$621$	−20.5459	−	35.4604i	−0.824480	−	1.42298i
$622$	−4.86990	+	14.6246i	−0.195265	+	0.586395i
$623$		0			0
$624$	−14.6368	+	33.4387i	−0.585943	+	1.33862i
$625$	−7.87046	+	13.6320i	−0.314818	+	0.545281i
$626$	−46.8301	+	9.59805i	−1.87171	+	0.383615i
$627$	28.5049	+	5.01111i	1.13838	+	0.200124i
$628$	7.21190	−	3.08585i	0.287786	−	0.123139i
$629$			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	$0.897589\pi$
$632$	19.5287	−	1.62199i	0.776809	−	0.0645192i
$633$	−20.0003	−	3.51602i	−0.794942	−	0.139749i
$634$	2.63690	+	12.8658i	0.104725	+	0.510966i
$635$	1.67131	−	2.89479i	0.0663239	−	0.114876i
$636$	29.4096	−	6.89506i	1.16616	−	0.273407i
$637$		0			0
$638$	13.3163	+	4.43423i	0.527197	+	0.175553i
$639$	27.2828	+	9.89844i	1.07929	+	0.391576i
$640$	8.97638	+	1.40913i	0.354823	+	0.0557006i
$641$	−16.8007	+	9.69989i	−0.663588	+	0.383122i	−0.793643	−	0.608384i	$-0.791818\pi$
$641$	−16.8007	+	9.69989i	−0.663588	+	0.383122i	0.130055	+	0.991507i	$0.458485\pi$
$642$	0.420333	+	14.9357i	0.0165892	+	0.589467i
$643$			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
$646$	−7.92692	−	8.93376i	−0.311881	−	0.351494i
$647$	22.7029	+	39.3225i	0.892542	+	1.54593i	0.836818	+	0.547481i	$0.184413\pi$
$647$	22.7029	+	39.3225i	0.892542	+	1.54593i	0.0557235	+	0.998446i	$0.482253\pi$
$648$	25.3537	+	2.27814i	0.995987	+	0.0894939i
$649$	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	0.516637	−	0.856204i	$-0.327184\pi$
$653$	0.855070	+	0.493675i	0.0334615	+	0.0193190i	−0.483176	+	0.875523i	$0.660517\pi$
$654$	−11.7463	−	6.34803i	−0.459318	−	0.248228i
$655$	7.29738	−	4.21314i	0.285132	−	0.164621i
$656$	−6.77712	+	27.8654i	−0.264602	+	1.08796i
$657$	0.741015	+	4.17743i	0.0289097	+	0.162977i
$658$		0			0
$659$	6.67629			0.260071			0.130036	−	0.991509i	$-0.458491\pi$
$659$	6.67629			0.260071			0.130036	+	0.991509i	$0.458491\pi$
$660$	1.88660	−	6.24661i	0.0734357	−	0.243149i
$661$	1.35571	+	2.34815i	0.0527309	+	0.0913326i	0.891186	−	0.453638i	$-0.149874\pi$
$661$	1.35571	+	2.34815i	0.0527309	+	0.0913326i	−0.838455	+	0.544971i	$0.816541\pi$
$662$	0.288191	+	1.40612i	0.0112009	+	0.0546504i
$663$	−3.70505	−	10.1633i	−0.143892	−	0.394710i
$664$	−12.0438	+	8.35442i	−0.467390	+	0.324214i
$665$		0			0
$666$	−4.39886	−	0.646317i	−0.170452	−	0.0250443i
$667$	−28.9018	−	16.6865i	−1.11908	−	0.646102i
$668$	1.99262	−	16.6249i	0.0770970	−	0.643238i
$669$	−1.16557	−	0.204904i	−0.0450634	−	0.00792206i
$670$	6.35192	+	7.15871i	0.245396	+	0.276565i
$671$	−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	$0.245447\pi$
$674$	11.8826	+	13.3919i	0.457700	+	0.515835i
$675$	−22.6292	+	0.0348367i	−0.870997	+	0.00134086i
$676$	−3.51256	+	29.3061i	−0.135099	+	1.12716i
$677$	−9.63730	−	5.56410i	−0.370392	−	0.213846i	0.303238	−	0.952915i	$-0.401932\pi$
$677$	−9.63730	−	5.56410i	−0.370392	−	0.213846i	−0.673630	+	0.739069i	$0.735266\pi$
$678$	−9.11341	−	14.8067i	−0.349999	−	0.568647i
$679$		0			0
$680$	−2.21258	+	1.53480i	−0.0848487	+	0.0588570i
$681$	14.2451	−	5.19307i	0.545873	−	0.198999i
$682$	−3.26265	−	15.9189i	−0.124933	−	0.609565i
$683$	−4.83716	−	8.37821i	−0.185089	−	0.320583i	0.758518	−	0.651652i	$-0.225924\pi$
$683$	−4.83716	−	8.37821i	−0.185089	−	0.320583i	−0.943606	+	0.331069i	$0.892591\pi$
$684$	35.7583	−	23.4210i	1.36725	−	0.895526i
$685$	−10.8357			−0.414013
$686$		0			0
$687$	−24.5549	−	20.5826i	−0.936829	−	0.785274i
$688$	−7.50851	+	30.8726i	−0.286259	+	1.17701i
$689$	39.7870	−	22.9710i	1.51576	−	0.875127i
$690$	−7.37686	+	13.6501i	−0.280832	+	0.519649i
$691$	−7.20943	−	4.16236i	−0.274260	−	0.158344i	0.356562	−	0.934272i	$-0.383949\pi$
$691$	−7.20943	−	4.16236i	−0.274260	−	0.158344i	−0.630822	+	0.775928i	$0.717282\pi$
$692$	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
$696$	18.8209	−	8.68744i	0.713405	−	0.329296i
$697$	−4.24943	−	7.36022i	−0.160958	−	0.278788i
$698$	−26.3971	−	29.7499i	−0.999145	−	1.12605i
$699$	11.2814	−	13.4586i	0.426700	−	0.509052i
$700$		0			0
$701$			34.0535i			1.28618i	0.765790	+	0.643091i	$0.222348\pi$
$701$			34.0535i			1.28618i	−0.765790	+	0.643091i	$0.777652\pi$
$702$	37.9156	−	7.83182i	1.43103	−	0.295593i
$703$	−6.46568	+	3.73296i	−0.243858	+	0.140791i
$704$	−18.5065	+	3.09553i	−0.697491	+	0.116667i
$705$	−2.90583	−	7.97098i	−0.109440	−	0.300205i
$706$	−13.8269	−	4.60425i	−0.520382	−	0.173283i
$707$		0			0
$708$	−0.523592	−	2.23328i	−0.0196778	−	0.0839318i
$709$	−4.82135	+	8.35083i	−0.181070	+	0.313622i	−0.942245	−	0.334924i	$-0.891289\pi$
$709$	−4.82135	+	8.35083i	−0.181070	+	0.313622i	0.761175	+	0.648546i	$0.224623\pi$
$710$	−2.20618	−	10.7642i	−0.0827964	−	0.403974i
$711$	−13.3764	−	15.9082i	−0.501655	−	0.596605i
$712$	−46.1310	+	3.83148i	−1.72883	+	0.143591i
$713$			38.6388i			1.44703i
$714$		0			0
$715$		−	9.92437i		−	0.371150i
$716$	−38.8301	+	16.6148i	−1.45115	+	0.620923i
$717$	−0.448249	+	2.54980i	−0.0167402	+	0.0952239i
$718$	−37.1837	+	7.62097i	−1.38768	+	0.284412i
$719$	4.04585	−	7.00762i	0.150885	−	0.261340i	−0.780668	−	0.624946i	$-0.785121\pi$
$719$	4.04585	−	7.00762i	0.150885	−	0.261340i	0.931553	+	0.363606i	$0.118454\pi$
$720$	−4.28356	−	8.63321i	−0.159639	−	0.321741i
$721$		0			0
$722$	14.1885	−	42.6090i	0.528040	−	1.58574i
$723$	16.8160	−	6.13028i	0.625392	−	0.227988i
$724$	2.95312	−	24.6386i	0.109752	−	0.915686i
$725$	−15.9586	+	9.21369i	−0.592687	+	0.342188i
$726$	−0.378915	−	13.4640i	−0.0140629	−	0.499698i
$727$		−	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
$730$	1.20147	−	1.06607i	0.0444685	−	0.0394569i
$731$	−4.70802	−	8.15453i	−0.174133	−	0.301606i
$732$	−2.41969	+	2.27181i	−0.0894342	+	0.0839686i
$733$	−18.9776	+	32.8702i	−0.700954	+	1.21409i	0.267178	+	0.963647i	$0.413909\pi$
$733$	−18.9776	+	32.8702i	−0.700954	+	1.21409i	−0.968132	+	0.250440i	$0.919425\pi$
$734$	−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
$738$	28.2732	−	11.2178i	1.04075	−	0.412933i
$739$	19.1667	−	11.0659i	0.705058	−	0.407065i	−0.104171	−	0.994559i	$-0.533219\pi$
$739$	19.1667	−	11.0659i	0.705058	−	0.407065i	0.809228	+	0.587494i	$0.199885\pi$
$740$	0.662173	+	1.54756i	0.0243420	+	0.0568893i
$741$	41.7636	−	49.8238i	1.53422	−	1.83032i
$742$		0			0
$743$	21.7884			0.799340			0.399670	−	0.916659i	$-0.369125\pi$
$743$	21.7884			0.799340			0.399670	+	0.916659i	$0.369125\pi$
$744$	−19.6060	−	13.8421i	−0.718791	−	0.507478i
$745$	−6.46568	−	11.1989i	−0.236884	−	0.410296i
$746$	−31.5956	+	6.47567i	−1.15680	+	0.237091i
$747$	14.6147	+	5.30235i	0.534725	+	0.194003i
$748$	3.33371	−	4.45064i	0.121893	−	0.162731i
$749$		0			0
$750$	9.64649	+	15.6728i	0.352240	+	0.572289i
$751$	4.44124	+	2.56415i	0.162063	+	0.0935671i	0.578838	−	0.815443i	$-0.303506\pi$
$751$	4.44124	+	2.56415i	0.162063	+	0.0935671i	−0.416775	+	0.909010i	$0.636840\pi$
$752$	−16.8456	+	17.6467i	−0.614295	+	0.643509i
$753$	−8.08376	+	45.9832i	−0.294588	+	1.67572i
$754$	23.5823	−	20.9246i	0.858816	−	0.762027i
$755$	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	$0.686646\pi$
$758$	−2.09580	+	1.85960i	−0.0761228	+	0.0675437i
$759$	5.54766	−	31.5570i	0.201367	−	1.14545i
$760$	−14.6369	−	6.90387i	−0.530936	−	0.250430i
$761$	37.0224	+	21.3749i	1.34206	+	0.774839i	0.987110	−	0.160046i	$-0.0511642\pi$
$761$	37.0224	+	21.3749i	1.34206	+	0.774839i	0.354951	+	0.934885i	$0.384498\pi$
$762$	5.34377	+	8.68209i	0.193584	+	0.314519i
$763$		0			0
$764$	−9.76434	−	7.31389i	−0.353261	−	0.264607i
$765$	2.68490	+	0.974103i	0.0970726	+	0.0352188i
$766$	−39.9288	+	8.18360i	−1.44269	+	0.295686i
$767$	−1.74436	−	3.02131i	−0.0629851	−	0.109093i
$768$	−16.7973	+	22.0420i	−0.606121	+	0.795373i
$769$	−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
$772$	1.18601	−	0.507473i	0.0426853	−	0.0182643i
$773$	−1.04249	+	0.601881i	−0.0374957	+	0.0216482i	−0.518631	−	0.854998i	$-0.673558\pi$
$773$	−1.04249	+	0.601881i	−0.0374957	+	0.0216482i	0.481135	+	0.876647i	$0.340225\pi$
$774$	31.3244	−	12.4284i	1.12593	−	0.446731i
$775$	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
$780$	−10.0329	−	10.6860i	−0.359236	−	0.382619i
$781$	11.3453	+	19.6507i	0.405968	+	0.703157i
$782$	−9.89031	+	8.77567i	−0.353677	+	0.313817i
$783$	−19.0579	−	10.9640i	−0.681072	−	0.391820i
$784$		0			0
$785$			3.15000i			0.112428i
$786$	0.722976	+	25.6896i	0.0257877	+	0.916318i
$787$	19.4895	−	11.2522i	0.694724	−	0.401099i	−0.110655	−	0.993859i	$-0.535295\pi$
$787$	19.4895	−	11.2522i	0.694724	−	0.401099i	0.805380	+	0.592760i	$0.201962\pi$
$788$	29.6102	+	3.54901i	1.05482	+	0.126428i
$789$	24.9143	−	9.08256i	0.886974	−	0.323348i
$790$	−2.48610	+	7.46593i	−0.0884514	+	0.265626i
$791$		0			0
$792$	14.0252	+	14.1201i	0.498362	+	0.501736i
$793$	−2.52398	+	4.37166i	−0.0896290	+	0.155242i
$794$	6.32179	−	1.29568i	0.224352	−	0.0459819i
$795$	−2.10022	+	11.9468i	−0.0744871	+	0.423709i
$796$	14.7120	+	34.3832i	0.521452	+	1.21868i
$797$		−	18.3911i		−	0.651447i	−0.945465	−	0.325724i	$-0.894392\pi$
$797$		−	18.3911i		−	0.651447i	0.945465	−	0.325724i	$-0.105608\pi$
$798$		0			0
$799$		−	7.23003i		−	0.255780i
$800$	13.0865	−	20.8723i	0.462678	−	0.737948i
$801$	31.5980	+	37.5786i	1.11646	+	1.32778i
$802$	−7.60442	−	37.1029i	−0.268521	−	1.31015i
$803$	−1.65849	+	2.87258i	−0.0585267	+	0.101371i
$804$	−28.4189	+	6.66281i	−1.00226	+	0.234979i
$805$		0			0
$806$	−34.6322	−	11.5323i	−1.21987	−	0.406206i
$807$	−18.2042	−	49.9358i	−0.640817	−	1.75782i
$808$	−10.1275	+	21.4714i	−0.356286	+	0.755362i
$809$	11.5087	−	6.64455i	0.404624	−	0.233610i	−0.283853	−	0.958868i	$-0.591613\pi$
$809$	11.5087	−	6.64455i	0.404624	−	0.233610i	0.688477	+	0.725258i	$0.258279\pi$
$810$	−4.84614	+	9.00035i	−0.170276	+	0.316240i
$811$		−	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
$814$	−2.30704	−	2.60007i	−0.0808617	−	0.0911323i
$815$	−2.93506	−	5.08367i	−0.102811	−	0.178073i
$816$	−0.909776	−	8.16235i	−0.0318485	−	0.285740i
$817$	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	0.0147715	−	0.999891i	$-0.495298\pi$
$821$	−24.1767	−	13.9584i	−0.843774	−	0.487153i	−0.858545	+	0.512738i	$0.828631\pi$
$822$	15.7126	−	29.0744i	0.548039	−	1.01409i
$823$	−38.9668	+	22.4975i	−1.35830	+	0.784213i	−0.989394	−	0.145256i	$-0.953600\pi$
$823$	−38.9668	+	22.4975i	−1.35830	+	0.784213i	−0.368902	+	0.929468i	$0.620266\pi$
$824$	−7.23552	+	0.600958i	−0.252061	+	0.0209354i
$825$	−13.5586	−	11.3652i	−0.472051	−	0.395685i
$826$		0			0
$827$	34.2989			1.19269			0.596344	−	0.802729i	$-0.296619\pi$
$827$	34.2989			1.19269			0.596344	+	0.802729i	$0.296619\pi$
$828$	−25.9288	−	39.5870i	−0.901088	−	1.37574i
$829$	11.5078	+	19.9322i	0.399684	+	0.692273i	0.993687	−	0.112190i	$-0.0357865\pi$
$829$	11.5078	+	19.9322i	0.399684	+	0.692273i	−0.594003	+	0.804463i	$0.702453\pi$
$830$	−1.18179	−	5.76613i	−0.0410207	−	0.200145i
$831$	−21.3386	+	7.77900i	−0.740226	+	0.269851i
$832$	−14.7637	+	39.4784i	−0.511838	+	1.36867i
$833$		0			0
$834$	9.72279	+	15.7967i	0.336673	+	0.546996i
$835$	5.82291	+	3.36186i	0.201510	+	0.116342i
$836$	33.1819	+	3.97711i	1.14762	+	0.137551i
$837$	0.0391882	+	25.4558i	0.00135454	+	0.879882i
$838$	16.4628	+	18.5538i	0.568698	+	0.640931i
$839$	46.9847			1.62209			0.811046	−	0.584983i	$-0.198899\pi$
$839$	46.9847			1.62209			0.811046	+	0.584983i	$0.198899\pi$
$840$		0			0
$841$	11.0959			0.382617
$842$	−14.4552	−	16.2913i	−0.498161	−	0.561434i
$843$	4.89029	+	0.859702i	0.168430	+	0.0296097i
$844$	−23.2819	−	2.79052i	−0.801396	−	0.0960535i
$845$	−10.2645	−	5.92623i	−0.353110	−	0.203868i
$846$	25.6013	+	3.76156i	0.880191	+	0.129325i
$847$		0			0
$848$	33.4728	−	9.80751i	1.14946	−	0.336791i
$849$	1.18077	+	3.23896i	0.0405238	+	0.111161i
$850$	1.46589	+	7.15226i	0.0502795	+	0.245320i
$851$	4.13266	+	7.15798i	0.141666	+	0.245372i
$852$	32.0816	+	9.68926i	1.09910	+	0.331949i
$853$	−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
$856$	1.42807	+	17.1939i	0.0488105	+	0.587676i
$857$	−26.1774	+	15.1136i	−0.894204	+	0.516269i	−0.875315	−	0.483553i	$-0.839346\pi$
$857$	−26.1774	+	15.1136i	−0.894204	+	0.516269i	−0.0188889	+	0.999822i	$0.506013\pi$
$858$	26.6290	+	14.3910i	0.909098	+	0.491301i
$859$	15.8982	+	9.17880i	0.542438	+	0.313177i	0.746066	−	0.665872i	$-0.231940\pi$
$859$	15.8982	+	9.17880i	0.542438	+	0.313177i	−0.203628	+	0.979048i	$0.565273\pi$
$860$	−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	$-0.981633\pi$
$863$	−13.1968	+	22.8576i	−0.449225	+	0.778080i	0.549111	+	0.835749i	$0.314966\pi$
$864$	29.3760	+	1.02513i	0.999392	+	0.0348756i
$865$	5.12839	+	8.88264i	0.174371	+	0.302019i
$866$	−5.78081	−	6.51506i	−0.196440	−	0.221391i
$867$	−20.7005	−	17.3517i	−0.703025	−	0.589293i
$868$		0			0
$869$		−	16.2498i		−	0.551236i
$870$	0.234169	+	8.32075i	0.00793906	+	0.282100i
$871$	−38.4468	+	22.1973i	−1.30272	+	0.752126i
$872$	−13.9442	−	6.57712i	−0.472209	−	0.222729i
$873$	−12.3473	−	4.47970i	−0.417893	−	0.151615i
$874$	−75.3947	−	25.1059i	−2.55026	−	0.849218i
$875$		0			0
$876$	1.11824	+	4.76965i	0.0377819	+	0.161151i
$877$	0.468662	−	0.811746i	0.0158256	−	0.0274107i	−0.858004	−	0.513643i	$-0.828296\pi$
$877$	0.468662	−	0.811746i	0.0158256	−	0.0274107i	0.873830	+	0.486232i	$0.161629\pi$
$878$	8.30525	+	40.5224i	0.280289	+	1.36756i
$879$	28.5706	+	5.02266i	0.963664	+	0.169410i
$880$	1.78062	−	7.32134i	0.0600246	−	0.246802i
$881$			37.1298i			1.25093i	0.780251	+	0.625467i	$0.215091\pi$
$881$			37.1298i			1.25093i	−0.780251	+	0.625467i	$0.784909\pi$
$882$		0			0
$883$			5.76235i			0.193918i	0.995288	+	0.0969592i	$0.0309116\pi$
$883$			5.76235i			0.193918i	−0.995288	+	0.0969592i	$0.969088\pi$
$884$	−4.91379	−	11.4840i	−0.165269	−	0.386247i
$885$	0.907205	+	0.159485i	0.0304954	+	0.00536102i
$886$	−9.99770	+	2.04908i	−0.335879	+	0.0688400i
$887$	−13.0672	+	22.6330i	−0.438752	+	0.759941i	−0.997594	−	0.0693335i	$-0.977913\pi$
$887$	−13.0672	+	22.6330i	−0.438752	+	0.759941i	0.558841	+	0.829275i	$0.311246\pi$
$888$	−5.11259	−	0.467324i	−0.171567	−	0.0156824i
$889$		0			0
$890$	5.87270	−	17.6361i	0.196853	−	0.591165i
$891$	3.62287	−	20.7959i	0.121371	−	0.696688i
$892$	−1.35681	−	0.162624i	−0.0454293	−	0.00544505i
$893$	37.6302	−	21.7258i	1.25925	−	0.727027i
$894$	39.4244	−	1.10951i	1.31855	−	0.0371076i
$895$		−	16.9601i		−	0.566915i
$896$		0			0
$897$	−55.1586	−	46.2353i	−1.84169	−	1.54375i
$898$	−4.69066	+	4.16202i	−0.156529	+	0.138888i
$899$	10.3646	+	17.9520i	0.345678	+	0.598732i
$900$	−26.0886	+	1.46957i	−0.869620	+	0.0489858i
$901$	−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
$906$	−20.2456	+	37.4622i	−0.672614	+	1.24460i
$907$	−35.3624	+	20.4165i	−1.17419	+	0.677918i	−0.954663	−	0.297689i	$-0.903784\pi$
$907$	−35.3624	+	20.4165i	−1.17419	+	0.677918i	−0.219525	+	0.975607i	$0.570451\pi$
$908$	16.0962	−	6.88728i	0.534170	−	0.228562i
$909$	24.7931	−	4.39793i	0.822334	−	0.145870i
$910$		0			0
$911$	4.31270			0.142886			0.0714430	−	0.997445i	$-0.477240\pi$
$911$	4.31270			0.142886			0.0714430	+	0.997445i	$0.477240\pi$
$912$	39.7489	−	29.2625i	1.31622	−	0.968979i
$913$	6.07741	+	10.5264i	0.201133	+	0.348372i
$914$	18.9276	−	3.87930i	0.626069	−	0.128316i
$915$	−0.456487	−	1.25219i	−0.0150910	−	0.0413961i
$916$	−29.6113	−	22.1801i	−0.978384	−	0.732850i
$917$		0			0
$918$	−6.50699	+	5.79157i	−0.214763	+	0.191150i
$919$	−14.9668	−	8.64107i	−0.493708	−	0.285043i	0.232403	−	0.972620i	$-0.425341\pi$
$919$	−14.9668	−	8.64107i	−0.493708	−	0.285043i	−0.726112	+	0.687577i	$0.758674\pi$
$920$	−7.64308	+	16.2041i	−0.251985	+	0.534234i
$921$	26.4190	+	4.64440i	0.870535	+	0.153038i
$922$	5.56196	−	4.93513i	0.183173	−	0.162530i
$923$	50.9699			1.67770
$924$		0			0
$925$	4.56383			0.150058
$926$	16.8050	−	14.9111i	0.552247	−	0.490009i
$927$	4.95606	+	5.89411i	0.162778	+	0.193588i
$928$	21.1512	−	11.2052i	0.694323	−	0.367829i
$929$	20.0527	+	11.5774i	0.657908	+	0.379843i	0.791479	−	0.611196i	$-0.209311\pi$
$929$	20.0527	+	11.5774i	0.657908	+	0.379843i	−0.133571	+	0.991039i	$0.542645\pi$
$930$	8.20745	−	5.05163i	0.269133	−	0.165650i
$931$		0			0
$932$	12.1570	−	16.2300i	0.398214	−	0.531632i
$933$	17.7366	−	6.46590i	0.580670	−	0.211684i
$934$	−37.5125	+	7.68837i	−1.22745	+	0.251571i
$935$	1.11649	+	1.93382i	0.0365132	+	0.0632426i
$936$	43.2209	−	11.4249i	1.41272	−	0.373433i
$937$	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
$940$	−3.85384	−	9.00676i	−0.125698	−	0.293768i
$941$	20.4823	−	11.8254i	0.667703	−	0.385498i	−0.127503	−	0.991838i	$-0.540696\pi$
$941$	20.4823	−	11.8254i	0.667703	−	0.385498i	0.795206	+	0.606340i	$0.207363\pi$
$942$	−8.45205	−	4.56771i	−0.275383	−	0.148824i
$943$	−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	−0.159955	+	0.987124i	$0.551135\pi$
$947$	−28.7686	+	49.8286i	−0.934852	+	1.61921i	−0.774897	+	0.632087i	$0.782198\pi$
$948$	−16.4275	−	17.4968i	−0.533540	−	0.568269i
$949$	3.72545	+	6.45267i	0.120933	+	0.209462i
$950$	−32.8205	+	29.1217i	−1.06484	+	0.944831i
$951$	10.3328	−	12.3270i	0.335065	−	0.399731i
$952$		0			0
$953$			14.1961i			0.459855i	0.973208	+	0.229928i	$0.0738490\pi$
$953$			14.1961i			0.459855i	−0.973208	+	0.229928i	$0.926151\pi$
$954$	−29.0100	−	22.9589i	−0.939235	−	0.743323i
$955$	4.24264	−	2.44949i	0.137289	−	0.0792636i
$956$	−0.355756	+	2.96816i	−0.0115060	+	0.0959970i
$957$	−5.88745	−	16.1498i	−0.190314	−	0.522050i
$958$	6.81842	−	20.4762i	0.220293	−	0.661557i
$959$		0			0
$960$	−5.48415	−	9.68327i	−0.177000	−	0.312526i
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$	−7.64918	+	1.56774i	−0.246620	+	0.0505458i
$963$	14.0063	−	11.7772i	0.451347	−	0.379515i
$964$	19.0011	−	8.13025i	0.611984	−	0.261858i
$965$			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	$-0.169489\pi$
$968$	−1.28736	−	15.4997i	−0.0413772	−	0.498180i
$969$	−2.53270	+	14.4069i	−0.0813619	+	0.462815i
$970$	0.998442	+	4.87153i	0.0320580	+	0.156415i
$971$	−14.6620	+	25.3953i	−0.470526	+	0.814974i	−0.999432	−	0.0337060i	$-0.989269\pi$
$971$	−14.6620	+	25.3953i	−0.470526	+	0.814974i	0.528906	+	0.848680i	$0.322602\pi$
$972$	−17.1224	−	26.0542i	−0.549202	−	0.835690i
$973$		0			0
$974$	−8.13677	−	2.70948i	−0.260719	−	0.0868174i
$975$	−37.3376	+	13.6115i	−1.19576	+	0.435916i
$976$	−2.64633	+	2.77218i	−0.0847069	+	0.0887353i
$977$	−10.3022	+	5.94797i	−0.329596	+	0.190292i	−0.655662	−	0.755055i	$-0.727610\pi$
$977$	−10.3022	+	5.94797i	−0.329596	+	0.190292i	0.326066	+	0.945347i	$0.394277\pi$
$978$	17.8965	−	0.503656i	0.572266	−	0.0161051i
$979$			38.3855i			1.22681i
$980$		0			0
$981$	2.85614	+	16.1013i	0.0911896	+	0.514076i
$982$	3.79042	+	4.27187i	0.120957	+	0.136321i
$983$	−7.49013	−	12.9733i	−0.238898	−	0.413783i	0.721500	−	0.692414i	$-0.243453\pi$
$983$	−7.49013	−	12.9733i	−0.238898	−	0.413783i	−0.960398	+	0.278631i	$0.910119\pi$
$984$	31.8896	−	14.7197i	1.01660	−	0.469248i
$985$	−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
$990$	−7.42847	+	2.94736i	−0.236092	+	0.0936732i
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	−0.757863	−	0.652413i	$-0.773757\pi$
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	0.186075	+	0.982536i	$0.440423\pi$
$992$	−23.4795	−	14.7212i	−0.745475	−	0.467397i
$993$	1.12929	−	1.34724i	0.0358369	−	0.0427533i
$994$		0			0
$995$	−15.0178			−0.476096
$996$	17.1853	+	5.19029i	0.544537	+	0.164461i
$997$	−9.81912	−	17.0072i	−0.310975	−	0.538624i	0.667599	−	0.744521i	$-0.267322\pi$
$997$	−9.81912	−	17.0072i	−0.310975	−	0.538624i	−0.978574	+	0.205897i	$0.933989\pi$
$998$	−10.9323	−	53.3402i	−0.346056	−	1.68845i
$999$	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.d.275.3		24
3.2	odd	2	inner	588.2.n.d.275.9		24
4.3	odd	2		588.2.n.h.275.2		24
7.2	even	3		588.2.e.f.491.11	yes	24
7.3	odd	6		588.2.n.h.263.11		24
7.4	even	3		588.2.n.h.263.12		24
7.5	odd	6		588.2.e.f.491.12	yes	24
7.6	odd	2	inner	588.2.n.d.275.4		24
12.11	even	2		588.2.n.h.275.12		24
21.2	odd	6		588.2.e.f.491.14	yes	24
21.5	even	6		588.2.e.f.491.13	yes	24
21.11	odd	6		588.2.n.h.263.2		24
21.17	even	6		588.2.n.h.263.1		24
21.20	even	2	inner	588.2.n.d.275.10		24
28.3	even	6	inner	588.2.n.d.263.10		24
28.11	odd	6	inner	588.2.n.d.263.9		24
28.19	even	6		588.2.e.f.491.15	yes	24
28.23	odd	6		588.2.e.f.491.16	yes	24
28.27	even	2		588.2.n.h.275.1		24
84.11	even	6	inner	588.2.n.d.263.3		24
84.23	even	6		588.2.e.f.491.9	✓	24
84.47	odd	6		588.2.e.f.491.10	yes	24
84.59	odd	6	inner	588.2.n.d.263.4		24
84.83	odd	2		588.2.n.h.275.11		24

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

\(f(q)\)	\(=\)	\(q+(-0.938613 - 1.05783i) q^{2} +(-0.299892 + 1.70589i) q^{3} +(-0.238012 + 1.98579i) q^{4} +(-0.695526 - 0.401562i) q^{5} +(2.08603 - 1.28394i) q^{6} +(2.32403 - 1.61211i) q^{8} +(-2.82013 - 1.02317i) q^{9} +(0.228045 + 1.11266i) q^{10} +(-1.17273 - 2.03122i) q^{11} +(-3.31616 - 1.00154i) q^{12} -5.26858 q^{13} +(0.893604 - 1.06607i) q^{15} +(-3.88670 - 0.945282i) q^{16} +(1.02661 - 0.592715i) q^{17} +(1.56467 + 3.94358i) 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} +(2.05313 + 4.44800i) q^{24} +(-2.17750 - 3.77153i) q^{25} +(4.94516 + 5.57327i) q^{26} +(2.59115 - 4.50399i) q^{27} -4.23132i q^{29} +(-1.96647 + 0.0553417i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(2.64816 + 4.99872i) q^{32} +(3.81673 - 1.39140i) q^{33} +(-1.59058 - 0.529652i) q^{34} +(2.70302 - 5.35665i) q^{36} +(-0.523976 + 0.907554i) q^{37} +(-2.02292 - 9.87011i) q^{38} +(1.58001 - 8.98762i) q^{39} +(-2.26378 + 0.188022i) q^{40} -7.16942i q^{41} -7.94315i q^{43} +(4.31270 - 1.84533i) q^{44} +(1.55061 + 1.84410i) q^{45} +(-10.9269 + 2.23952i) q^{46} +(3.04954 - 5.28195i) q^{47} +(2.77814 - 6.34681i) q^{48} +(-1.94582 + 5.84343i) q^{50} +(0.703234 + 1.92904i) q^{51} +(1.25398 - 10.4623i) q^{52} +(-7.55175 + 4.36001i) q^{53} +(-7.19655 + 1.48651i) q^{54} +1.88369i q^{55} +(-7.92692 + 9.45679i) q^{57} +(-4.47602 + 3.97157i) q^{58} +(0.331087 + 0.573459i) q^{59} +(1.90429 + 2.02824i) 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} +(-5.05430 - 2.73148i) q^{66} +(7.29738 - 4.21314i) q^{67} +(0.932660 + 2.17971i) q^{68} +(10.4693 + 8.77567i) q^{69} -9.67432 q^{71} +(-8.20351 + 2.16849i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(1.45185 - 0.297563i) q^{74} +(7.08684 - 2.58352i) q^{75} +(-8.54216 + 11.4041i) q^{76} +(-10.9904 + 6.76452i) q^{78} +(6.00000 + 3.46410i) q^{79} +(2.32371 + 2.21822i) q^{80} +(6.90626 + 5.77092i) q^{81} +(-7.58404 + 6.72931i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(-8.40251 + 7.45554i) q^{86} +(7.21818 + 1.26894i) q^{87} +(-6.00000 - 2.83005i) q^{88} +(-14.1733 - 8.18296i) q^{89} +(0.495321 - 3.37117i) q^{90} +(12.6252 + 9.45679i) q^{92} +(-2.90623 - 7.97207i) q^{93} +(-8.44975 + 1.73182i) q^{94} +(-2.86085 - 4.95513i) q^{95} +(-9.32144 + 3.01839i) q^{96} +4.37827 q^{97} +(1.22896 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more