LMFDB - Embedded newform 441.2.i.d.68.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.15
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.664297i q^{2} +(-1.15747 - 1.28852i) q^{3} +1.55871 q^{4} +(-0.0141520 - 0.0245119i) q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(-0.320544 + 2.98283i) q^{9} +O(q^{10})$	\(q+0.664297i q^{2} +(-1.15747 - 1.28852i) q^{3} +1.55871 q^{4} +(-0.0141520 - 0.0245119i) q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(-0.320544 + 2.98283i) q^{9} +(0.0162832 - 0.00940110i) q^{10} +(0.885324 + 0.511142i) q^{11} +(-1.80415 - 2.00842i) q^{12} +(4.87844 + 2.81657i) q^{13} +(-0.0152036 + 0.0466067i) q^{15} +1.54700 q^{16} +(-2.83940 - 4.91798i) q^{17} +(-1.98148 - 0.212936i) q^{18} +(1.81237 + 1.04637i) q^{19} +(-0.0220588 - 0.0382070i) q^{20} +(-0.339550 + 0.588118i) q^{22} +(6.28849 - 3.63066i) q^{23} +(3.04610 - 2.73630i) q^{24} +(2.49960 - 4.32943i) q^{25} +(-1.87104 + 3.24073i) q^{26} +(4.21444 - 3.03949i) q^{27} +(-3.52577 + 2.03560i) q^{29} +(-0.0309607 - 0.0100997i) q^{30} +3.31820i q^{31} +5.75574i q^{32} +(-0.366118 - 1.73238i) q^{33} +(3.26700 - 1.88620i) q^{34} +(-0.499635 + 4.64936i) q^{36} +(1.23632 - 2.14137i) q^{37} +(-0.695101 + 1.20395i) q^{38} +(-2.01744 - 9.54604i) q^{39} +(0.0579471 - 0.0334558i) q^{40} +(-3.52867 + 6.11183i) q^{41} +(-1.15994 - 2.00908i) q^{43} +(1.37996 + 0.796722i) q^{44} +(0.0776511 - 0.0343557i) q^{45} +(2.41184 + 4.17742i) q^{46} +10.8799 q^{47} +(-1.79060 - 1.99333i) q^{48} +(2.87603 + 1.66048i) q^{50} +(-3.05039 + 9.35101i) q^{51} +(7.60408 + 4.39022i) q^{52} +(-10.0454 + 5.79973i) q^{53} +(2.01913 + 2.79964i) q^{54} -0.0289346i q^{55} +(-0.749489 - 3.54640i) q^{57} +(-1.35224 - 2.34215i) q^{58} -6.02222 q^{59} +(-0.0236979 + 0.0726464i) q^{60} -2.36968i q^{61} -2.20427 q^{62} -0.729528 q^{64} -0.159440i q^{65} +(1.15082 - 0.243211i) q^{66} +12.7799 q^{67} +(-4.42580 - 7.66571i) q^{68} +(-11.9569 - 3.90045i) q^{69} -7.93415i q^{71} +(-7.05152 - 0.757778i) q^{72} +(-9.43889 + 5.44955i) q^{73} +(1.42251 + 0.821285i) q^{74} +(-8.47174 + 1.79040i) q^{75} +(2.82496 + 1.63099i) q^{76} +(6.34140 - 1.34018i) q^{78} -15.6004 q^{79} +(-0.0218930 - 0.0379198i) q^{80} +(-8.79450 - 1.91225i) q^{81} +(-4.06007 - 2.34408i) q^{82} +(-3.07406 - 5.32442i) q^{83} +(-0.0803661 + 0.139198i) q^{85} +(1.33463 - 0.770546i) q^{86} +(6.70386 + 2.18686i) q^{87} +(-1.20836 + 2.09294i) q^{88} +(-6.02582 + 10.4370i) q^{89} +(0.0228224 + 0.0515834i) q^{90} +(9.80194 - 5.65915i) q^{92} +(4.27555 - 3.84070i) q^{93} +7.22751i q^{94} -0.0592328i q^{95} +(7.41636 - 6.66208i) q^{96} +(-6.77565 + 3.91192i) q^{97} +(-1.80843 + 2.47692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^9	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			0.664297i			0.469729i	0.972028	+	0.234864i	$0.0754646\pi$
$2$			0.664297i			0.469729i	−0.972028	+	0.234864i	$0.924535\pi$
$3$	−1.15747	−	1.28852i	−0.668263	−	0.743925i
$3$	−1.15747	−	1.28852i	−0.668263	−	0.743925i
$4$	1.55871			0.779355
$5$	−0.0141520	−	0.0245119i	−0.00632895	−	0.0109621i	0.862844	−	0.505471i	$-0.168681\pi$
$5$	−0.0141520	−	0.0245119i	−0.00632895	−	0.0109621i	−0.869173	+	0.494509i	$0.835348\pi$
$6$	0.855956	−	0.768901i	0.349443	−	0.313903i
$7$		0			0
$7$		0			0
$8$			2.36404i			0.835814i
$9$	−0.320544	+	2.98283i	−0.106848	+	0.994275i
$10$	0.0162832	−	0.00940110i	0.00514919	−	0.00297289i
$11$	0.885324	+	0.511142i	0.266935	+	0.154115i	0.627494	−	0.778621i	$-0.284081\pi$
$11$	0.885324	+	0.511142i	0.266935	+	0.154115i	−0.360559	+	0.932736i	$0.617414\pi$
$12$	−1.80415	−	2.00842i	−0.520814	−	0.579781i
$13$	4.87844	+	2.81657i	1.35304	+	0.781176i	0.988674	−	0.150081i	$-0.0479534\pi$
$13$	4.87844	+	2.81657i	1.35304	+	0.781176i	0.364363	+	0.931257i	$0.381287\pi$
$14$		0			0
$15$	−0.0152036	+	0.0466067i	−0.00392554	+	0.0120338i
$16$	1.54700			0.386749
$17$	−2.83940	−	4.91798i	−0.688656	−	1.19279i	−0.972273	−	0.233849i	$-0.924868\pi$
$17$	−2.83940	−	4.91798i	−0.688656	−	1.19279i	0.283617	−	0.958938i	$-0.408465\pi$
$18$	−1.98148	−	0.212936i	−0.467040	−	0.0501895i
$19$	1.81237	+	1.04637i	0.415786	+	0.240054i	0.693273	−	0.720675i	$-0.256168\pi$
$19$	1.81237	+	1.04637i	0.415786	+	0.240054i	−0.277487	+	0.960729i	$0.589502\pi$
$20$	−0.0220588	−	0.0382070i	−0.00493250	−	0.00854334i
$21$		0			0
$22$	−0.339550	+	0.588118i	−0.0723923	+	0.125387i
$23$	6.28849	−	3.63066i	1.31124	−	0.757046i	0.328940	−	0.944351i	$-0.393309\pi$
$23$	6.28849	−	3.63066i	1.31124	−	0.757046i	0.982302	+	0.187305i	$0.0599754\pi$
$24$	3.04610	−	2.73630i	0.621783	−	0.558544i
$25$	2.49960	−	4.32943i	0.499920	−	0.865887i
$26$	−1.87104	+	3.24073i	−0.366941	+	0.635560i
$27$	4.21444	−	3.03949i	0.811069	−	0.584951i
$28$		0			0
$29$	−3.52577	+	2.03560i	−0.654718	+	0.378002i	−0.790262	−	0.612770i	$-0.790055\pi$
$29$	−3.52577	+	2.03560i	−0.654718	+	0.378002i	0.135543	+	0.990771i	$0.456722\pi$
$30$	−0.0309607	−	0.0100997i	−0.00565262	−	0.00184394i
$31$			3.31820i			0.595966i	0.954571	+	0.297983i	$0.0963139\pi$
$31$			3.31820i			0.595966i	−0.954571	+	0.297983i	$0.903686\pi$
$32$			5.75574i			1.01748i
$33$	−0.366118	−	1.73238i	−0.0637330	−	0.301569i
$34$	3.26700	−	1.88620i	0.560286	−	0.323481i
$35$		0			0
$36$	−0.499635	+	4.64936i	−0.0832725	+	0.774893i
$37$	1.23632	−	2.14137i	0.203250	−	0.352040i	−0.746324	−	0.665583i	$-0.768183\pi$
$37$	1.23632	−	2.14137i	0.203250	−	0.352040i	0.949574	+	0.313543i	$0.101516\pi$
$38$	−0.695101	+	1.20395i	−0.112760	+	0.195306i
$39$	−2.01744	−	9.54604i	−0.323049	−	1.52859i
$40$	0.0579471	−	0.0334558i	0.00916224	−	0.00528982i
$41$	−3.52867	+	6.11183i	−0.551085	+	0.954508i	0.447111	+	0.894478i	$0.352453\pi$
$41$	−3.52867	+	6.11183i	−0.551085	+	0.954508i	−0.998197	+	0.0600295i	$0.980881\pi$
$42$		0			0
$43$	−1.15994	−	2.00908i	−0.176890	−	0.306382i	0.763924	−	0.645306i	$-0.223270\pi$
$43$	−1.15994	−	2.00908i	−0.176890	−	0.306382i	−0.940814	+	0.338924i	$0.889937\pi$
$44$	1.37996	+	0.796722i	0.208037	+	0.120110i
$45$	0.0776511	−	0.0343557i	0.0115755	−	0.00512144i
$46$	2.41184	+	4.17742i	0.355606	+	0.615928i
$47$	10.8799			1.58700			0.793502	−	0.608568i	$-0.208256\pi$
$47$	10.8799			1.58700			0.793502	+	0.608568i	$0.208256\pi$
$48$	−1.79060	−	1.99333i	−0.258450	−	0.287712i
$49$		0			0
$50$	2.87603	+	1.66048i	0.406732	+	0.234827i
$51$	−3.05039	+	9.35101i	−0.427140	+	1.30940i
$52$	7.60408	+	4.39022i	1.05450	+	0.608814i
$53$	−10.0454	+	5.79973i	−1.37985	+	0.796655i	−0.992141	−	0.125128i	$-0.960066\pi$
$53$	−10.0454	+	5.79973i	−1.37985	+	0.796655i	−0.387706	+	0.921783i	$0.626732\pi$
$54$	2.01913	+	2.79964i	0.274768	+	0.380982i
$55$		−	0.0289346i		−	0.00390155i
$56$		0			0
$57$	−0.749489	−	3.54640i	−0.0992723	−	0.469733i
$58$	−1.35224	−	2.34215i	−0.177558	−	0.307540i
$59$	−6.02222			−0.784027			−0.392013	−	0.919960i	$-0.628221\pi$
$59$	−6.02222			−0.784027			−0.392013	+	0.919960i	$0.628221\pi$
$60$	−0.0236979	+	0.0726464i	−0.00305939	+	0.00937861i
$61$		−	2.36968i		−	0.303406i	−0.988426	−	0.151703i	$-0.951524\pi$
$61$		−	2.36968i		−	0.303406i	0.988426	−	0.151703i	$-0.0484757\pi$
$62$	−2.20427			−0.279942
$63$		0			0
$64$	−0.729528			−0.0911909
$65$		−	0.159440i		−	0.0197761i
$66$	1.15082	−	0.243211i	0.141656	−	0.0299372i
$67$	12.7799			1.56131			0.780656	−	0.624960i	$-0.214885\pi$
$67$	12.7799			1.56131			0.780656	+	0.624960i	$0.214885\pi$
$68$	−4.42580	−	7.66571i	−0.536707	−	0.929604i
$69$	−11.9569	−	3.90045i	−1.43944	−	0.469559i
$70$		0			0
$71$		−	7.93415i		−	0.941610i	−0.882237	−	0.470805i	$-0.843964\pi$
$71$		−	7.93415i		−	0.941610i	0.882237	−	0.470805i	$-0.156036\pi$
$72$	−7.05152	−	0.757778i	−0.831029	−	0.0893050i
$73$	−9.43889	+	5.44955i	−1.10474	+	0.637821i	−0.937462	−	0.348089i	$-0.886831\pi$
$73$	−9.43889	+	5.44955i	−1.10474	+	0.637821i	−0.167277	+	0.985910i	$0.553497\pi$
$74$	1.42251	+	0.821285i	0.165363	+	0.0954725i
$75$	−8.47174	+	1.79040i	−0.978233	+	0.206738i
$76$	2.82496	+	1.63099i	0.324045	+	0.187087i
$77$		0			0
$78$	6.34140	−	1.34018i	0.718022	−	0.151745i
$79$	−15.6004			−1.75518			−0.877588	−	0.479415i	$-0.840849\pi$
$79$	−15.6004			−1.75518			−0.877588	+	0.479415i	$0.840849\pi$
$80$	−0.0218930	−	0.0379198i	−0.00244772	−	0.00423957i
$81$	−8.79450	−	1.91225i	−0.977167	−	0.212473i
$82$	−4.06007	−	2.34408i	−0.448360	−	0.258861i
$83$	−3.07406	−	5.32442i	−0.337421	−	0.584431i	0.646526	−	0.762892i	$-0.276221\pi$
$83$	−3.07406	−	5.32442i	−0.337421	−	0.584431i	−0.983947	+	0.178461i	$0.942888\pi$
$84$		0			0
$85$	−0.0803661	+	0.139198i	−0.00871693	+	0.0150982i
$86$	1.33463	−	0.770546i	0.143916	−	0.0830902i
$87$	6.70386	+	2.18686i	0.718729	+	0.234456i
$88$	−1.20836	+	2.09294i	−0.128812	+	0.223108i
$89$	−6.02582	+	10.4370i	−0.638736	+	1.10632i	0.346975	+	0.937874i	$0.387209\pi$
$89$	−6.02582	+	10.4370i	−0.638736	+	1.10632i	−0.985711	+	0.168448i	$0.946124\pi$
$90$	0.0228224	+	0.0515834i	0.00240569	+	0.00543736i
$91$		0			0
$92$	9.80194	−	5.65915i	1.02192	−	0.590007i
$93$	4.27555	−	3.84070i	0.443354	−	0.398262i
$94$			7.22751i			0.745461i
$95$		−	0.0592328i		−	0.00607716i
$96$	7.41636	−	6.66208i	0.756929	−	0.679946i
$97$	−6.77565	+	3.91192i	−0.687963	+	0.397196i	−0.802848	−	0.596183i	$-0.796683\pi$
$97$	−6.77565	+	3.91192i	−0.687963	+	0.397196i	0.114885	+	0.993379i	$0.463350\pi$
$98$		0			0
$99$	−1.80843	+	2.47692i	−0.181754	+	0.248940i
$100$	3.89615	−	6.74833i	0.389615	−	0.674833i
$101$	0.226924	−	0.393043i	0.0225797	−	0.0391093i	−0.854515	−	0.519427i	$-0.826145\pi$
$101$	0.226924	−	0.393043i	0.0225797	−	0.0391093i	0.877094	+	0.480318i	$0.159479\pi$
$102$	−6.21185	−	2.02636i	−0.615064	−	0.200640i
$103$	4.58316	−	2.64609i	0.451592	−	0.260727i	−0.256910	−	0.966435i	$-0.582704\pi$
$103$	4.58316	−	2.64609i	0.451592	−	0.260727i	0.708502	+	0.705708i	$0.249371\pi$
$104$	−6.65848	+	11.5328i	−0.652918	+	1.13089i
$105$		0			0
$106$	−3.85274	−	6.67315i	−0.374212	−	0.648153i
$107$	−7.85273	−	4.53377i	−0.759152	−	0.438296i	0.0698394	−	0.997558i	$-0.477751\pi$
$107$	−7.85273	−	4.53377i	−0.759152	−	0.438296i	−0.828991	+	0.559262i	$0.811085\pi$
$108$	6.56908	−	4.73769i	0.632110	−	0.455885i
$109$	−2.36514	−	4.09654i	−0.226539	−	0.392377i	0.730241	−	0.683190i	$-0.239408\pi$
$109$	−2.36514	−	4.09654i	−0.226539	−	0.392377i	−0.956780	+	0.290812i	$0.906074\pi$
$110$	0.0192212			0.00183267
$111$	−4.19020	+	0.885547i	−0.397716	+	0.0840524i
$112$		0			0
$113$	−8.21108	−	4.74067i	−0.772433	−	0.445965i	0.0613086	−	0.998119i	$-0.480473\pi$
$113$	−8.21108	−	4.74067i	−0.772433	−	0.445965i	−0.833742	+	0.552154i	$0.813806\pi$
$114$	2.35586	−	0.497883i	0.220647	−	0.0466310i
$115$	−0.177989	−	0.102762i	−0.0165976	−	0.00958261i
$116$	−5.49565	+	3.17291i	−0.510258	+	0.294598i
$117$	−9.96510	+	13.6487i	−0.921273	+	1.26182i
$118$		−	4.00054i		−	0.368280i
$119$		0			0
$120$	−0.110180	−	0.0359418i	−0.0100580	−	0.00328102i
$121$	−4.97747	−	8.62123i	−0.452497	−	0.783748i
$122$	1.57417			0.142519
$123$	11.9595	−	2.52750i	1.07835	−	0.227897i
$124$			5.17211i			0.464469i
$125$	−0.283017			−0.0253138
$126$		0			0
$127$	4.37297			0.388039			0.194019	−	0.980998i	$-0.437848\pi$
$127$	4.37297			0.388039			0.194019	+	0.980998i	$0.437848\pi$
$128$			11.0269i			0.974646i
$129$	−1.24614	+	3.82005i	−0.109716	+	0.336336i
$130$	0.105915			0.00928940
$131$	−1.27231	−	2.20371i	−0.111162	−	0.192539i	0.805077	−	0.593171i	$-0.202124\pi$
$131$	−1.27231	−	2.20371i	−0.111162	−	0.192539i	−0.916239	+	0.400632i	$0.868791\pi$
$132$	−0.570672	−	2.70028i	−0.0496706	−	0.235029i
$133$		0			0
$134$			8.48964i			0.733393i
$135$	−0.134146	−	0.0602891i	−0.0115455	−	0.00518886i
$136$	11.6263	−	6.71245i	0.996948	−	0.575588i
$137$	9.82536	+	5.67267i	0.839437	+	0.484649i	0.857073	−	0.515195i	$-0.172281\pi$
$137$	9.82536	+	5.67267i	0.839437	+	0.484649i	−0.0176357	+	0.999844i	$0.505614\pi$
$138$	2.59106	−	7.94292i	0.220565	−	0.676146i
$139$	−3.04891	−	1.76029i	−0.258605	−	0.149306i	0.365093	−	0.930971i	$-0.381037\pi$
$139$	−3.04891	−	1.76029i	−0.258605	−	0.149306i	−0.623698	+	0.781665i	$0.714371\pi$
$140$		0			0
$141$	−12.5932	−	14.0190i	−1.06054	−	1.18061i
$142$	5.27063			0.442301
$143$	2.87933	+	4.98715i	0.240782	+	0.417047i
$144$	−0.495880	+	4.61442i	−0.0413233	+	0.384535i
$145$	0.0997930	+	0.0576155i	0.00828736	+	0.00478471i
$146$	−3.62012	−	6.27022i	−0.299603	−	0.518927i
$147$		0			0
$148$	1.92707	−	3.33778i	0.158404	−	0.274364i
$149$	13.7806	−	7.95623i	1.12895	−	0.651800i	0.185279	−	0.982686i	$-0.440681\pi$
$149$	13.7806	−	7.95623i	1.12895	−	0.651800i	0.943671	+	0.330886i	$0.107348\pi$
$150$	−1.18936	−	5.62775i	−0.0971106	−	0.459504i
$151$	−1.73008	+	2.99659i	−0.140792	+	0.243859i	−0.927795	−	0.373090i	$-0.878298\pi$
$151$	−1.73008	+	2.99659i	−0.140792	+	0.243859i	0.787003	+	0.616949i	$0.211632\pi$
$152$	−2.47366	+	4.28451i	−0.200640	+	0.347520i
$153$	15.5796	−	6.89301i	1.25954	−	0.557267i
$154$		0			0
$155$	0.0813354	−	0.0469590i	0.00653302	−	0.00377184i
$156$	−3.14460	−	14.8795i	−0.251770	−	1.19131i
$157$		−	16.3488i		−	1.30478i	−0.757883	−	0.652390i	$-0.773766\pi$
$157$		−	16.3488i		−	1.30478i	0.757883	−	0.652390i	$-0.226234\pi$
$158$		−	10.3633i		−	0.824457i
$159$	19.1003	+	6.23070i	1.51475	+	0.494127i
$160$	0.141084	−	0.0814550i	0.0111537	−	0.00643959i
$161$		0			0
$162$	1.27030	−	5.84216i	0.0998044	−	0.459003i
$163$	−5.17782	+	8.96824i	−0.405558	+	0.702447i	−0.994386	−	0.105811i	$-0.966256\pi$
$163$	−5.17782	+	8.96824i	−0.405558	+	0.702447i	0.588828	+	0.808258i	$0.299589\pi$
$164$	−5.50017	+	9.52657i	−0.429491	+	0.743900i
$165$	−0.0372827	+	0.0334909i	−0.00290246	+	0.00260726i
$166$	3.53699	−	2.04208i	0.274524	−	0.158497i
$167$	2.94297	−	5.09738i	0.227734	−	0.394447i	−0.729402	−	0.684085i	$-0.760202\pi$
$167$	2.94297	−	5.09738i	0.227734	−	0.394447i	0.957136	+	0.289638i	$0.0935349\pi$
$168$		0			0
$169$	9.36614	+	16.2226i	0.720473	+	1.24790i
$170$	−0.0924689	−	0.0533870i	−0.00709204	−	0.00409459i
$171$	−3.70209	+	5.07057i	−0.283106	+	0.387756i
$172$	−1.80802	−	3.13157i	−0.137860	−	0.238780i
$173$	4.86551			0.369918			0.184959	−	0.982746i	$-0.440785\pi$
$173$	4.86551			0.369918			0.184959	+	0.982746i	$0.440785\pi$
$174$	−1.45273	+	4.45335i	−0.110131	+	0.337608i
$175$		0			0
$176$	1.36959	+	0.790735i	0.103237	+	0.0596039i
$177$	6.97052	+	7.75973i	0.523936	+	0.583257i
$178$	−6.93328	−	4.00293i	−0.519671	−	0.300032i
$179$	−0.175495	+	0.101322i	−0.0131171	+	0.00757319i	−0.506544	−	0.862214i	$-0.669077\pi$
$179$	−0.175495	+	0.101322i	−0.0131171	+	0.00757319i	0.493427	+	0.869787i	$0.335744\pi$
$180$	0.121036	−	0.0535506i	0.00902146	−	0.00399142i
$181$			6.26273i			0.465505i	0.972536	+	0.232753i	$0.0747732\pi$
$181$			6.26273i			0.465505i	−0.972536	+	0.232753i	$0.925227\pi$
$182$		0			0
$183$	−3.05337	+	2.74282i	−0.225711	+	0.202755i
$184$	8.58303	+	14.8662i	0.632749	+	1.09595i
$185$	−0.0699856			−0.00514544
$186$	2.55137	+	2.84023i	0.187075	+	0.208256i
$187$		−	5.80534i		−	0.424529i
$188$	16.9587			1.23684
$189$		0			0
$190$	0.0393482			0.00285462
$191$			13.8034i			0.998776i	0.866379	+	0.499388i	$0.166442\pi$
$191$			13.8034i			0.998776i	−0.866379	+	0.499388i	$0.833558\pi$
$192$	0.844404	+	0.940007i	0.0609396	+	0.0678392i
$193$	−21.0774			−1.51719			−0.758593	−	0.651565i	$-0.774113\pi$
$193$	−21.0774			−1.51719			−0.758593	+	0.651565i	$0.774113\pi$
$194$	−2.59868	−	4.50104i	−0.186574	−	0.323156i
$195$	−0.205441	+	0.184546i	−0.0147119	+	0.0132156i
$196$		0			0
$197$			15.1679i			1.08067i	0.841451	+	0.540334i	$0.181702\pi$
$197$			15.1679i			1.08067i	−0.841451	+	0.540334i	$0.818298\pi$
$198$	−1.64541	−	1.20134i	−0.116934	−	0.0853752i
$199$	−8.38940	+	4.84362i	−0.594709	+	0.343355i	−0.766957	−	0.641698i	$-0.778230\pi$
$199$	−8.38940	+	4.84362i	−0.594709	+	0.343355i	0.172249	+	0.985054i	$0.444897\pi$
$200$	10.2349	+	5.90915i	0.723720	+	0.417840i
$201$	−14.7923	−	16.4671i	−1.04337	−	1.16150i
$202$	0.261097	+	0.150745i	0.0183707	+	0.0106064i
$203$		0			0
$204$	−4.75467	+	14.5755i	−0.332894	+	1.02049i
$205$	0.199750			0.0139512
$206$	1.75779	+	3.04458i	0.122471	+	0.212126i
$207$	8.81390	+	19.9213i	0.612608	+	1.38462i
$208$	7.54694	+	4.35723i	0.523286	+	0.302119i
$209$	1.06969	+	1.85275i	0.0739919	+	0.128158i
$210$		0			0
$211$	−7.05942	+	12.2273i	−0.485991	+	0.841761i	−0.999870	−	0.0161017i	$-0.994874\pi$
$211$	−7.05942	+	12.2273i	−0.485991	+	0.841761i	0.513880	+	0.857862i	$0.328208\pi$
$212$	−15.6579	+	9.04010i	−1.07539	+	0.620877i
$213$	−10.2233	+	9.18351i	−0.700487	+	0.629243i
$214$	3.01177	−	5.21654i	0.205880	−	0.356595i
$215$	−0.0328309	+	0.0568649i	−0.00223905	+	0.00387815i
$216$	7.18549	+	9.96309i	0.488910	+	0.677903i
$217$		0			0
$218$	2.72132	−	1.57115i	0.184311	−	0.106412i
$219$	17.9470	+	5.85449i	1.21275	+	0.395610i
$220$		−	0.0451007i		−	0.00304069i
$221$		−	31.9895i		−	2.15185i
$222$	−0.588266	−	2.78353i	−0.0394818	−	0.186819i
$223$	2.58777	−	1.49405i	0.173290	−	0.100049i	−0.410846	−	0.911705i	$-0.634767\pi$
$223$	2.58777	−	1.49405i	0.173290	−	0.100049i	0.584136	+	0.811656i	$0.301433\pi$
$224$		0			0
$225$	12.1127	+	8.84364i	0.807514	+	0.589576i
$226$	3.14921	−	5.45459i	0.209482	−	0.362834i
$227$	14.3867	−	24.9184i	0.954876	−	1.65389i	0.220224	−	0.975449i	$-0.429321\pi$
$227$	14.3867	−	24.9184i	0.954876	−	1.65389i	0.734652	−	0.678444i	$-0.237346\pi$
$228$	−1.16824	−	5.52781i	−0.0773684	−	0.366088i
$229$	−7.67401	+	4.43059i	−0.507113	+	0.292782i	−0.731646	−	0.681685i	$-0.761248\pi$
$229$	−7.67401	+	4.43059i	−0.507113	+	0.292782i	0.224533	+	0.974466i	$0.427914\pi$
$230$	0.0682645	−	0.118238i	0.00450122	−	0.00779635i
$231$		0			0
$232$	−4.81224	−	8.33505i	−0.315939	−	0.547223i
$233$	−11.1789	−	6.45412i	−0.732351	−	0.422823i	0.0869305	−	0.996214i	$-0.472294\pi$
$233$	−11.1789	−	6.45412i	−0.732351	−	0.422823i	−0.819282	+	0.573391i	$0.805628\pi$
$234$	−9.06680	−	6.61978i	−0.592715	−	0.432749i
$235$	−0.153973	−	0.266688i	−0.0100441	−	0.0173968i
$236$	−9.38690			−0.611035
$237$	18.0569	+	20.1013i	1.17292	+	1.30572i
$238$		0			0
$239$	−4.85712	−	2.80426i	−0.314181	−	0.181392i	0.334615	−	0.942355i	$-0.391394\pi$
$239$	−4.85712	−	2.80426i	−0.314181	−	0.181392i	−0.648796	+	0.760963i	$0.724727\pi$
$240$	−0.0235199	+	0.0721005i	−0.00151820	+	0.00465406i
$241$	−9.51481	−	5.49338i	−0.612903	−	0.353860i	0.161198	−	0.986922i	$-0.448464\pi$
$241$	−9.51481	−	5.49338i	−0.612903	−	0.353860i	−0.774101	+	0.633063i	$0.781798\pi$
$242$	5.72705	−	3.30652i	0.368149	−	0.212551i
$243$	7.71537	+	13.5452i	0.494941	+	0.868926i
$244$		−	3.69364i		−	0.236461i
$245$		0			0
$246$	1.67901	+	7.94466i	0.107050	+	0.506533i
$247$	5.89436	+	10.2093i	0.375049	+	0.649604i
$248$	−7.84435			−0.498117
$249$	−3.30248	+	10.1238i	−0.209286	+	0.641570i
$250$		−	0.188007i		−	0.0118906i
$251$	24.2241			1.52901			0.764505	−	0.644618i	$-0.222984\pi$
$251$	24.2241			1.52901			0.764505	+	0.644618i	$0.222984\pi$
$252$		0			0
$253$	7.42314			0.466689
$254$			2.90495i			0.182273i
$255$	0.272380	−	0.0575643i	0.0170571	−	0.00360481i
$256$	−8.78416			−0.549010
$257$	−8.86142	−	15.3484i	−0.552760	−	0.957409i	−0.998074	−	0.0620341i	$-0.980241\pi$
$257$	−8.86142	−	15.3484i	−0.552760	−	0.957409i	0.445314	−	0.895375i	$-0.353092\pi$
$258$	−2.53765	−	0.827804i	−0.157987	−	0.0515368i
$259$		0			0
$260$		−	0.248521i		−	0.0154126i
$261$	−4.94168	−	11.1692i	−0.305883	−	0.691359i
$262$	1.46392	−	0.845193i	0.0904411	−	0.0522162i
$263$	−2.51031	−	1.44933i	−0.154793	−	0.0893695i	0.420603	−	0.907245i	$-0.361819\pi$
$263$	−2.51031	−	1.44933i	−0.154793	−	0.0893695i	−0.575396	+	0.817875i	$0.695152\pi$
$264$	4.09542	−	0.865518i	0.252056	−	0.0532689i
$265$	0.284325	+	0.164155i	0.0174660	+	0.0100840i
$266$		0			0
$267$	20.4230	−	4.31614i	1.24986	−	0.264144i
$268$	19.9202			1.21682
$269$	10.9469	+	18.9606i	0.667444	+	1.15605i	0.978616	+	0.205694i	$0.0659451\pi$
$269$	10.9469	+	18.9606i	0.667444	+	1.15605i	−0.311172	+	0.950354i	$0.600722\pi$
$270$	0.0400498	−	0.0891130i	0.00243736	−	0.00542324i
$271$	−7.77992	−	4.49174i	−0.472596	−	0.272854i	0.244730	−	0.969591i	$-0.421301\pi$
$271$	−7.77992	−	4.49174i	−0.472596	−	0.272854i	−0.717326	+	0.696738i	$0.754634\pi$
$272$	−4.39254	−	7.60811i	−0.266337	−	0.461309i
$273$		0			0
$274$	−3.76834	+	6.52695i	−0.227654	+	0.394308i
$275$	4.42591	−	2.55530i	0.266892	−	0.154090i
$276$	−18.6373	−	6.07967i	−1.12183	−	0.365953i
$277$	−7.95091	+	13.7714i	−0.477724	+	0.827442i	−0.999674	−	0.0255339i	$-0.991871\pi$
$277$	−7.95091	+	13.7714i	−0.477724	+	0.827442i	0.521950	+	0.852976i	$0.325205\pi$
$278$	1.16936	−	2.02538i	0.0701333	−	0.121474i
$279$	−9.89761	−	1.06363i	−0.592554	−	0.0636777i
$280$		0			0
$281$	−4.50324	+	2.59995i	−0.268641	+	0.155100i	−0.628270	−	0.777996i	$-0.716237\pi$
$281$	−4.50324	+	2.59995i	−0.268641	+	0.155100i	0.359629	+	0.933095i	$0.382903\pi$
$282$	9.31276	−	8.36560i	0.554567	−	0.498164i
$283$		−	18.7739i		−	1.11599i	−0.829844	−	0.557995i	$-0.811571\pi$
$283$		−	18.7739i		−	1.11599i	0.829844	−	0.557995i	$-0.188429\pi$
$284$		−	12.3670i		−	0.733848i
$285$	−0.0763224	+	0.0685600i	−0.00452095	+	0.00406114i
$286$	−3.31295	+	1.91273i	−0.195899	+	0.113102i
$287$		0			0
$288$	−17.1684	−	1.84497i	−1.01166	−	0.108716i
$289$	−7.62438	+	13.2058i	−0.448493	+	0.776813i
$290$	−0.0382738	+	0.0662922i	−0.00224751	+	0.00389281i
$291$	12.8832	+	4.20261i	0.755224	+	0.246361i
$292$	−14.7125	+	8.49426i	−0.860983	+	0.497089i
$293$	11.4201	−	19.7802i	0.667169	−	1.15557i	−0.311523	−	0.950238i	$-0.600839\pi$
$293$	11.4201	−	19.7802i	0.667169	−	1.15557i	0.978692	−	0.205332i	$-0.0658274\pi$
$294$		0			0
$295$	0.0852263	+	0.147616i	0.00496206	+	0.00859455i
$296$	5.06229	+	2.92272i	0.294240	+	0.169879i
$297$	5.28475	−	0.536762i	0.306652	−	0.0311461i
$298$	5.28530	+	9.15440i	0.306169	+	0.530300i
$299$	40.9041			2.36554
$300$	−13.2050	+	2.79072i	−0.762390	+	0.161122i
$301$		0			0
$302$	−1.99062	−	1.14929i	−0.114548	−	0.0661341i
$303$	−0.769099	+	0.162540i	−0.0441836	+	0.00933766i
$304$	2.80373	+	1.61873i	0.160805	+	0.0928407i
$305$	−0.0580853	+	0.0335356i	−0.00332596	+	0.00192024i
$306$	4.57900	+	10.3495i	0.261764	+	0.591642i
$307$		−	18.6325i		−	1.06341i	−0.846928	−	0.531707i	$-0.821551\pi$
$307$		−	18.6325i		−	1.06341i	0.846928	−	0.531707i	$-0.178449\pi$
$308$		0			0
$309$	−8.71438	−	2.84271i	−0.495744	−	0.161716i
$310$	0.0311947	+	0.0540308i	0.00177174	+	0.00306875i
$311$	20.5495			1.16526			0.582628	−	0.812739i	$-0.302025\pi$
$311$	20.5495			1.16526			0.582628	+	0.812739i	$0.302025\pi$
$312$	22.5672	−	4.76931i	1.27762	−	0.270009i
$313$		−	0.721071i		−	0.0407574i	−0.999792	−	0.0203787i	$-0.993513\pi$
$313$		−	0.721071i		−	0.0407574i	0.999792	−	0.0203787i	$-0.00648718\pi$
$314$	10.8605			0.612893
$315$		0			0
$316$	−24.3164			−1.36791
$317$		−	21.9295i		−	1.23168i	−0.787871	−	0.615841i	$-0.788816\pi$
$317$		−	21.9295i		−	1.23168i	0.787871	−	0.615841i	$-0.211184\pi$
$318$	−4.13903	+	12.6883i	−0.232105	+	0.711523i
$319$	−4.16193			−0.233023
$320$	0.0103242	+	0.0178821i	0.000577143	+	0.000999641i
$321$	3.24743	+	15.3660i	0.181254	+	0.857649i
$322$		0			0
$323$		−	11.8843i		−	0.661258i
$324$	−13.7081	−	2.98065i	−0.761560	−	0.165592i
$325$	24.3883	−	14.0806i	1.35282	−	0.781051i
$326$	−5.95757	−	3.43961i	−0.329959	−	0.190502i
$327$	−2.54089	+	7.78912i	−0.140511	+	0.430739i
$328$	−14.4486	−	8.34191i	−0.797791	−	0.460605i
$329$		0			0
$330$	−0.0222479	−	0.0247668i	−0.00122470	−	0.00136337i
$331$	21.6676			1.19096			0.595480	−	0.803370i	$-0.296962\pi$
$331$	21.6676			1.19096			0.595480	+	0.803370i	$0.296962\pi$
$332$	−4.79156	−	8.29923i	−0.262971	−	0.455479i
$333$	5.99105	+	4.37414i	0.328308	+	0.239701i
$334$	3.38617	+	1.95501i	0.185283	+	0.106973i
$335$	−0.180861	−	0.313260i	−0.00988147	−	0.0171152i
$336$		0			0
$337$	12.6455	−	21.9026i	0.688844	−	1.19311i	−0.283369	−	0.959011i	$-0.591452\pi$
$337$	12.6455	−	21.9026i	0.688844	−	1.19311i	0.972212	−	0.234101i	$-0.0752147\pi$
$338$	−10.7766	+	6.22190i	−0.586172	+	0.338427i
$339$	3.39562	+	16.0673i	0.184425	+	0.872654i
$340$	−0.125268	+	0.216970i	−0.00679358	+	0.0117668i
$341$	−1.69607	+	2.93768i	−0.0918474	+	0.159084i
$342$	−3.36836	−	2.45928i	−0.182140	−	0.132983i
$343$		0			0
$344$	4.74955	−	2.74215i	0.256078	−	0.147847i
$345$	0.0736058	+	0.348285i	0.00396281	+	0.0187510i
$346$			3.23215i			0.173761i
$347$			5.68598i			0.305239i	0.988285	+	0.152620i	$0.0487709\pi$
$347$			5.68598i			0.305239i	−0.988285	+	0.152620i	$0.951229\pi$
$348$	10.4494	+	3.40869i	0.560145	+	0.182725i
$349$	−9.68412	+	5.59113i	−0.518379	+	0.299286i	−0.736271	−	0.676687i	$-0.763415\pi$
$349$	−9.68412	+	5.59113i	−0.518379	+	0.299286i	0.217892	+	0.975973i	$0.430082\pi$
$350$		0			0
$351$	29.1208	−	2.95775i	1.55436	−	0.157873i
$352$	−2.94200	+	5.09570i	−0.156809	+	0.271601i
$353$	7.02111	−	12.1609i	0.373696	−	0.647260i	−0.616435	−	0.787406i	$-0.711424\pi$
$353$	7.02111	−	12.1609i	0.373696	−	0.647260i	0.990131	+	0.140146i	$0.0447571\pi$
$354$	−5.15476	+	4.63049i	−0.273972	+	0.246108i
$355$	−0.194481	+	0.112284i	−0.0103220	+	0.00595940i
$356$	−9.39250	+	16.2683i	−0.497802	+	0.862218i
$357$		0			0
$358$	−0.0673081	−	0.116581i	−0.00355734	−	0.00616150i
$359$	−23.5052	−	13.5707i	−1.24056	−	0.716235i	−0.271348	−	0.962481i	$-0.587469\pi$
$359$	−23.5052	−	13.5707i	−1.24056	−	0.716235i	−0.969207	+	0.246246i	$0.920803\pi$
$360$	0.0812182	+	0.183570i	0.00428058	+	0.00967500i
$361$	−7.31022	−	12.6617i	−0.384748	−	0.666403i
$362$	−4.16031			−0.218661
$363$	−5.34733	+	16.3923i	−0.280662	+	0.860374i
$364$		0			0
$365$	0.267158	+	0.154244i	0.0139837	+	0.00807347i
$366$	−1.82205	−	2.02834i	−0.0952399	−	0.106023i
$367$	−5.95891	−	3.44038i	−0.311053	−	0.179586i	0.336345	−	0.941739i	$-0.390809\pi$
$367$	−5.95891	−	3.44038i	−0.311053	−	0.179586i	−0.647397	+	0.762153i	$0.724143\pi$
$368$	9.72828	−	5.61662i	0.507122	−	0.292787i
$369$	−17.0994	−	12.4845i	−0.890161	−	0.649918i
$370$		−	0.0464912i		−	0.00241696i
$371$		0			0
$372$	6.66434	−	5.98654i	0.345530	−	0.310388i
$373$	0.123926	+	0.214645i	0.00641662	+	0.0111139i	0.869216	−	0.494433i	$-0.164624\pi$
$373$	0.123926	+	0.214645i	0.00641662	+	0.0111139i	−0.862799	+	0.505547i	$0.831291\pi$
$374$	3.85647			0.199413
$375$	0.327582	+	0.364671i	0.0169163	+	0.0188315i
$376$			25.7206i			1.32644i
$377$	−22.9337			−1.18114
$378$		0			0
$379$	−8.91863			−0.458119			−0.229060	−	0.973412i	$-0.573565\pi$
$379$	−8.91863			−0.458119			−0.229060	+	0.973412i	$0.573565\pi$
$380$		−	0.0923268i		−	0.00473626i
$381$	−5.06157	−	5.63465i	−0.259312	−	0.288672i
$382$	−9.16952			−0.469154
$383$	0.163545	+	0.283268i	0.00835675	+	0.0144743i	0.870174	−	0.492745i	$-0.164007\pi$
$383$	0.163545	+	0.283268i	0.00835675	+	0.0144743i	−0.861817	+	0.507220i	$0.830673\pi$
$384$	14.2083	−	12.7632i	0.725063	−	0.651320i
$385$		0			0
$386$		−	14.0017i		−	0.712665i
$387$	6.36455	−	2.81591i	0.323528	−	0.143141i
$388$	−10.5613	+	6.09755i	−0.536167	+	0.309556i
$389$	5.72348	+	3.30445i	0.290192	+	0.167542i	0.638028	−	0.770013i	$-0.279750\pi$
$389$	5.72348	+	3.30445i	0.290192	+	0.167542i	−0.347837	+	0.937555i	$0.613084\pi$
$390$	−0.122594	−	0.136474i	−0.00620777	−	0.00691061i
$391$	−35.7111	−	20.6178i	−1.80599	−	1.04269i
$392$		0			0
$393$	−1.36686	+	4.19011i	−0.0689487	+	0.211363i
$394$	−10.0760			−0.507621
$395$	0.220776	+	0.382394i	0.0111084	+	0.0192404i
$396$	−2.81882	+	3.86080i	−0.141651	+	0.194013i
$397$	−6.50435	−	3.75529i	−0.326444	−	0.188472i	0.327817	−	0.944741i	$-0.393687\pi$
$397$	−6.50435	−	3.75529i	−0.326444	−	0.188472i	−0.654261	+	0.756269i	$0.727020\pi$
$398$	−3.21760	−	5.57305i	−0.161284	−	0.279352i
$399$		0			0
$400$	3.86687	−	6.69762i	0.193344	−	0.334881i
$401$	5.48595	−	3.16732i	0.273956	−	0.158168i	−0.356728	−	0.934208i	$-0.616108\pi$
$401$	5.48595	−	3.16732i	0.273956	−	0.158168i	0.630684	+	0.776040i	$0.282774\pi$
$402$	10.9390	−	9.82647i	0.545589	−	0.490100i
$403$	−9.34594	+	16.1876i	−0.465555	+	0.806364i
$404$	0.353708	−	0.612640i	0.0175976	−	0.0304800i
$405$	0.0775865	+	0.242632i	0.00385530	+	0.0120565i
$406$		0			0
$407$	2.18909	−	1.26387i	0.108509	−	0.0626479i
$408$	−22.1062	−	7.21124i	−1.09442	−	0.357010i
$409$			33.4915i			1.65605i	0.560693	+	0.828024i	$0.310535\pi$
$409$			33.4915i			1.65605i	−0.560693	+	0.828024i	$0.689465\pi$
$410$			0.132693i			0.00655326i
$411$	−4.06319	−	19.2261i	−0.200423	−	0.948351i
$412$	7.14382	−	4.12448i	0.351951	−	0.203199i
$413$		0			0
$414$	−13.2336	+	5.85504i	−0.650398	+	0.287760i
$415$	−0.0870078	+	0.150702i	−0.00427105	+	0.00739767i
$416$	−16.2115	+	28.0791i	−0.794832	+	1.37669i
$417$	1.26085	+	5.96605i	0.0617442	+	0.292159i
$418$	−1.23078	+	0.710590i	−0.0601993	+	0.0347561i
$419$	0.896459	−	1.55271i	0.0437949	−	0.0758550i	−0.843297	−	0.537448i	$-0.819389\pi$
$419$	0.896459	−	1.55271i	0.0437949	−	0.0758550i	0.887092	+	0.461593i	$0.152722\pi$
$420$		0			0
$421$	1.90262	+	3.29543i	0.0927278	+	0.160609i	0.908658	−	0.417541i	$-0.137108\pi$
$421$	1.90262	+	3.29543i	0.0927278	+	0.160609i	−0.815930	+	0.578150i	$0.803775\pi$
$422$	−8.12254	−	4.68955i	−0.395399	−	0.228284i
$423$	−3.48750	+	32.4530i	−0.169568	+	1.57792i
$424$	−13.7108	−	23.7478i	−0.665855	−	1.15330i
$425$	−28.3894			−1.37709
$426$	−6.10057	−	6.79128i	−0.295574	−	0.329039i
$427$		0			0
$428$	−12.2401	−	7.06684i	−0.591649	−	0.341589i
$429$	3.09329	−	9.48253i	0.149346	−	0.457821i
$430$	−0.0377751	−	0.0218095i	−0.00182168	−	0.00105175i
$431$	−1.15145	+	0.664787i	−0.0554632	+	0.0320217i	−0.527475	−	0.849570i	$-0.676861\pi$
$431$	−1.15145	+	0.664787i	−0.0554632	+	0.0320217i	0.472012	+	0.881592i	$0.343528\pi$
$432$	6.51972	−	4.70209i	0.313680	−	0.226229i
$433$			37.4292i			1.79873i	0.437194	+	0.899367i	$0.355972\pi$
$433$			37.4292i			1.79873i	−0.437194	+	0.899367i	$0.644028\pi$
$434$		0			0
$435$	−0.0412686	−	0.195273i	−0.00197868	−	0.00936262i
$436$	−3.68656	−	6.38531i	−0.176554	−	0.305801i
$437$	15.1961			0.726927
$438$	−3.88912	+	11.9221i	−0.185829	+	0.569662i
$439$		−	23.7388i		−	1.13299i	−0.824064	−	0.566496i	$-0.808298\pi$
$439$		−	23.7388i		−	1.13299i	0.824064	−	0.566496i	$-0.191702\pi$
$440$	0.0684026			0.00326097
$441$		0			0
$442$	21.2505			1.01078
$443$			11.2504i			0.534525i	0.963624	+	0.267262i	$0.0861191\pi$
$443$			11.2504i			0.534525i	−0.963624	+	0.267262i	$0.913881\pi$
$444$	−6.53130	+	1.38031i	−0.309962	+	0.0655067i
$445$	0.341109			0.0161701
$446$	0.992491	+	1.71904i	0.0469958	+	0.0813991i
$447$	−26.2023	−	8.54744i	−1.23933	−	0.404280i
$448$		0			0
$449$			14.3953i			0.679357i	0.940542	+	0.339679i	$0.110318\pi$
$449$			14.3953i			0.679357i	−0.940542	+	0.339679i	$0.889682\pi$
$450$	−5.87480	+	8.04644i	−0.276941	+	0.379313i
$451$	−6.24803	+	3.60730i	−0.294208	+	0.169861i
$452$	−12.7987	−	7.38933i	−0.602000	−	0.347565i
$453$	5.86366	−	1.23921i	0.275499	−	0.0582234i
$454$	16.5532	+	9.55701i	0.776881	+	0.448533i
$455$		0			0
$456$	8.38384	−	1.77182i	0.392609	−	0.0829732i
$457$	−20.6269			−0.964888			−0.482444	−	0.875927i	$-0.660251\pi$
$457$	−20.6269			−0.964888			−0.482444	+	0.875927i	$0.660251\pi$
$458$	−2.94323	−	5.09782i	−0.137528	−	0.238206i
$459$	−26.9147	−	12.0962i	−1.25627	−	0.564602i
$460$	−0.277433	−	0.160176i	−0.0129354	−	0.00746825i
$461$	−0.832511	−	1.44195i	−0.0387739	−	0.0671584i	0.845987	−	0.533203i	$-0.179012\pi$
$461$	−0.832511	−	1.44195i	−0.0387739	−	0.0671584i	−0.884761	+	0.466045i	$0.845679\pi$
$462$		0			0
$463$	0.604175	−	1.04646i	0.0280784	−	0.0486332i	−0.851645	−	0.524119i	$-0.824395\pi$
$463$	0.604175	−	1.04646i	0.0280784	−	0.0486332i	0.879723	+	0.475486i	$0.157728\pi$
$464$	−5.45435	+	3.14907i	−0.253212	+	0.146192i
$465$	−0.154650	−	0.0504484i	−0.00717174	−	0.00233949i
$466$	4.28745	−	7.42608i	0.198612	−	0.344006i
$467$	4.61994	−	8.00197i	0.213785	−	0.370287i	−0.739111	−	0.673584i	$-0.764754\pi$
$467$	4.61994	−	8.00197i	0.213785	−	0.370287i	0.952896	+	0.303297i	$0.0980874\pi$
$468$	−15.5327	+	21.2744i	−0.717999	+	0.983409i
$469$		0			0
$470$	0.177160	−	0.102283i	0.00817179	−	0.00471798i
$471$	−21.0657	+	18.9232i	−0.970658	+	0.871937i
$472$		−	14.2368i		−	0.655300i
$473$		−	2.37158i		−	0.109045i
$474$	−13.3532	+	11.9951i	−0.613334	+	0.550954i
$475$	9.06039	−	5.23102i	0.415719	−	0.240016i
$476$		0			0
$477$	−14.0796	−	31.8229i	−0.644660	−	1.45707i
$478$	1.86286	−	3.22657i	0.0852052	−	0.147580i
$479$	−8.77241	+	15.1943i	−0.400822	+	0.694243i	−0.993825	−	0.110956i	$-0.964609\pi$
$479$	−8.77241	+	15.1943i	−0.400822	+	0.694243i	0.593004	+	0.805200i	$0.297942\pi$
$480$	−0.268256	−	0.0875078i	−0.0122442	−	0.00399417i
$481$	12.0627	−	6.96438i	0.550010	−	0.317549i
$482$	3.64923	−	6.32066i	0.166218	−	0.287898i
$483$		0			0
$484$	−7.75843	−	13.4380i	−0.352656	−	0.610818i
$485$	0.191777	+	0.110723i	0.00870817	+	0.00502766i
$486$	−8.99804	+	5.12530i	−0.408160	+	0.232488i
$487$	21.5949	+	37.4034i	0.978558	+	1.69491i	0.667657	+	0.744469i	$0.267297\pi$
$487$	21.5949	+	37.4034i	0.978558	+	1.69491i	0.310900	+	0.950442i	$0.399369\pi$
$488$	5.60201			0.253591
$489$	17.5489	−	3.70874i	0.793587	−	0.167715i
$490$		0			0
$491$	23.0046	+	13.2817i	1.03818	+	0.599396i	0.919319	−	0.393514i	$-0.128741\pi$
$491$	23.0046	+	13.2817i	1.03818	+	0.599396i	0.118866	+	0.992910i	$0.462074\pi$
$492$	18.6414	−	3.93963i	0.840419	−	0.177612i
$493$	20.0221	+	11.5598i	0.901751	+	0.520626i
$494$	−6.78202	+	3.91560i	−0.305138	+	0.176171i
$495$	0.0863070	+	0.00927482i	0.00387921	+	0.000416872i
$496$			5.13324i			0.230489i
$497$		0			0
$498$	−6.72521	−	2.19383i	−0.301364	−	0.0983078i
$499$	−2.65759	−	4.60308i	−0.118970	−	0.206062i	0.800390	−	0.599480i	$-0.204626\pi$
$499$	−2.65759	−	4.60308i	−0.118970	−	0.206062i	−0.919360	+	0.393418i	$0.871293\pi$
$500$	−0.441141			−0.0197284
$501$	−9.97445	+	2.10798i	−0.445625	+	0.0941776i
$502$			16.0920i			0.718220i
$503$	−35.5334			−1.58436			−0.792178	−	0.610290i	$-0.791053\pi$
$503$	−35.5334			−1.58436			−0.792178	+	0.610290i	$0.791053\pi$
$504$		0			0
$505$	−0.0128457			−0.000571624
$506$			4.93116i			0.219217i
$507$	10.0621	−	30.8456i	0.446874	−	1.36990i
$508$	6.81620			0.302420
$509$	6.81654	+	11.8066i	0.302138	+	0.523318i	0.976620	−	0.214973i	$-0.0689663\pi$
$509$	6.81654	+	11.8066i	0.302138	+	0.523318i	−0.674482	+	0.738291i	$0.735633\pi$
$510$	0.0382397	+	0.180941i	0.00169328	+	0.00801221i
$511$		0			0
$512$			16.2184i			0.716760i
$513$	10.8185	−	1.09882i	0.477651	−	0.0485141i
$514$	10.1959	−	5.88661i	0.449722	−	0.259647i
$515$	−0.129721	−	0.0748947i	−0.00571621	−	0.00330025i
$516$	−1.94236	+	5.95435i	−0.0855078	+	0.262125i
$517$	9.63227	+	5.56120i	0.423627	+	0.244581i
$518$		0			0
$519$	−5.63167	−	6.26929i	−0.247203	−	0.275191i
$520$	0.376922			0.0165291
$521$	5.11259	+	8.85526i	0.223987	+	0.387956i	0.956015	−	0.293318i	$-0.0947595\pi$
$521$	5.11259	+	8.85526i	0.223987	+	0.387956i	−0.732028	+	0.681274i	$0.761426\pi$
$522$	7.41969	−	3.28274i	0.324751	−	0.143682i
$523$	4.48150	+	2.58740i	0.195962	+	0.113139i	0.594771	−	0.803895i	$-0.297243\pi$
$523$	4.48150	+	2.58740i	0.195962	+	0.113139i	−0.398808	+	0.917034i	$0.630576\pi$
$524$	−1.98317	−	3.43495i	−0.0866350	−	0.150056i
$525$		0			0
$526$	0.962785	−	1.66759i	0.0419794	−	0.0727105i
$527$	16.3189	−	9.42169i	0.710860	−	0.410415i
$528$	−0.566383	−	2.67999i	−0.0246487	−	0.116632i
$529$	14.8634	−	25.7442i	0.646236	−	1.11931i
$530$	−0.109048	+	0.188876i	−0.00473673	+	0.00820426i
$531$	1.93039	−	17.9632i	0.0837716	−	0.779538i
$532$		0			0
$533$	−34.4288	+	19.8775i	−1.49128	+	0.860990i
$534$	2.86720	+	13.5669i	0.124076	+	0.587097i
$535$			0.256647i			0.0110958i
$536$			30.2122i			1.30497i
$537$	0.333685	+	0.108851i	0.0143996	+	0.00469728i
$538$	−12.5955	+	7.27199i	−0.543029	+	0.313518i
$539$		0			0
$540$	−0.209095	−	0.0939732i	−0.00899803	−	0.00404396i
$541$	12.7197	−	22.0312i	0.546864	−	0.947196i	−0.451623	−	0.892209i	$-0.649155\pi$
$541$	12.7197	−	22.0312i	0.546864	−	0.947196i	0.998487	−	0.0549871i	$-0.0175118\pi$
$542$	2.98385	−	5.16817i	0.128167	−	0.221992i
$543$	8.06963	−	7.24890i	0.346301	−	0.311080i
$544$	28.3067	−	16.3429i	1.21364	−	0.700694i
$545$	−0.0669427	+	0.115948i	−0.00286751	+	0.00496667i
$546$		0			0
$547$	14.7771	+	25.5947i	0.631824	+	1.09435i	0.987179	+	0.159620i	$0.0510267\pi$
$547$	14.7771	+	25.5947i	0.631824	+	1.09435i	−0.355355	+	0.934732i	$0.615640\pi$
$548$	15.3149	+	8.84205i	0.654219	+	0.377714i
$549$	7.06833	+	0.759585i	0.301669	+	0.0324183i
$550$	1.69748	+	2.94012i	0.0723807	+	0.125367i
$551$	−8.51998			−0.362963
$552$	9.22082	−	28.2665i	0.392464	−	1.20310i
$553$		0			0
$554$	−9.14828	−	5.28176i	−0.388673	−	0.224401i
$555$	0.0810060	+	0.0901775i	0.00343851	+	0.00382782i
$556$	−4.75237	−	2.74378i	−0.201545	−	0.116362i
$557$	16.9788	−	9.80269i	0.719413	−	0.415353i	−0.0951237	−	0.995465i	$-0.530325\pi$
$557$	16.9788	−	9.80269i	0.719413	−	0.415353i	0.814537	+	0.580112i	$0.196991\pi$
$558$	0.706565	−	6.57495i	0.0299113	−	0.278340i
$559$		−	13.0683i		−	0.552728i
$560$		0			0
$561$	−7.48028	+	6.71949i	−0.315817	+	0.283697i
$562$	−1.72714	−	2.99149i	−0.0728548	−	0.126188i
$563$	−14.4759			−0.610087			−0.305044	−	0.952338i	$-0.598671\pi$
$563$	−14.4759			−0.610087			−0.305044	+	0.952338i	$0.598671\pi$
$564$	−19.6291	−	21.8515i	−0.826534	−	0.920115i
$565$			0.268359i			0.0112899i
$566$	12.4714			0.524213
$567$		0			0
$568$	18.7566			0.787011
$569$			7.74769i			0.324800i	0.986725	+	0.162400i	$0.0519235\pi$
$569$			7.74769i			0.324800i	−0.986725	+	0.162400i	$0.948076\pi$
$570$	−0.0455442	−	0.0507007i	−0.00190764	−	0.00212362i
$571$	16.1371			0.675318			0.337659	−	0.941269i	$-0.390365\pi$
$571$	16.1371			0.675318			0.337659	+	0.941269i	$0.390365\pi$
$572$	4.48805	+	7.77353i	0.187655	+	0.325027i
$573$	17.7858	−	15.9769i	0.743014	−	0.667445i
$574$		0			0
$575$		−	36.3008i		−	1.51385i
$576$	0.233846	−	2.17605i	0.00974356	−	0.0906689i
$577$	−10.5403	+	6.08542i	−0.438797	+	0.253339i	−0.703087	−	0.711104i	$-0.748196\pi$
$577$	−10.5403	+	6.08542i	−0.438797	+	0.253339i	0.264290	+	0.964443i	$0.414862\pi$
$578$	−8.77258	−	5.06485i	−0.364891	−	0.210670i
$579$	24.3964	+	27.1586i	1.01388	+	1.12867i
$580$	0.155548	+	0.0898059i	0.00645879	+	0.00372899i
$581$		0			0
$582$	−2.79178	+	8.55824i	−0.115723	+	0.354750i
$583$	−11.8579			−0.491106
$584$	−12.8829	−	22.3139i	−0.533100	−	0.923356i
$585$	0.475582	+	0.0511075i	0.0196629	+	0.00211304i
$586$	13.1399	+	7.58633i	0.542805	+	0.313388i
$587$	16.8761	+	29.2302i	0.696550	+	1.20646i	0.969655	+	0.244476i	$0.0786158\pi$
$587$	16.8761	+	29.2302i	0.696550	+	1.20646i	−0.273106	+	0.961984i	$0.588051\pi$
$588$		0			0
$589$	−3.47207	+	6.01380i	−0.143064	+	0.247794i
$590$	−0.0980610	+	0.0566155i	−0.00403711	+	0.00233082i
$591$	19.5441	−	17.5563i	0.803936	−	0.722171i
$592$	1.91259	−	3.31270i	0.0786069	−	0.136151i
$593$	−9.15123	+	15.8504i	−0.375796	+	0.650897i	−0.990446	−	0.137903i	$-0.955964\pi$
$593$	−9.15123	+	15.8504i	−0.375796	+	0.650897i	0.614650	+	0.788800i	$0.289297\pi$
$594$	0.356569	+	3.51064i	0.0146302	+	0.144043i
$595$		0			0
$596$	21.4799	−	12.4015i	0.879853	−	0.507983i
$597$	15.9515	+	5.20354i	0.652852	+	0.212967i
$598$			27.1724i			1.11116i
$599$			39.4798i			1.61310i	0.591165	+	0.806551i	$0.298668\pi$
$599$			39.4798i			1.61310i	−0.591165	+	0.806551i	$0.701332\pi$
$600$	−4.23258	−	20.0275i	−0.172794	−	0.817621i
$601$	34.4865	−	19.9108i	1.40673	−	0.812177i	0.411661	−	0.911337i	$-0.364949\pi$
$601$	34.4865	−	19.9108i	1.40673	−	0.812177i	0.995072	+	0.0991600i	$0.0316155\pi$
$602$		0			0
$603$	−4.09652	+	38.1202i	−0.166823	+	1.55237i
$604$	−2.69670	+	4.67082i	−0.109727	+	0.190053i
$605$	−0.140882	+	0.244015i	−0.00572766	+	0.00992060i
$606$	−0.107975	−	0.510910i	−0.00438617	−	0.0207543i
$607$	−21.6104	+	12.4768i	−0.877140	+	0.506417i	−0.869714	−	0.493555i	$-0.835697\pi$
$607$	−21.6104	+	12.4768i	−0.877140	+	0.506417i	−0.00742570	+	0.999972i	$0.502364\pi$
$608$	−6.02264	+	10.4315i	−0.244250	+	0.423054i
$609$		0			0
$610$	−0.0222776	−	0.0385859i	−0.000901992	−	0.00156230i
$611$	53.0772	+	30.6441i	2.14727	+	1.23973i
$612$	24.2841	−	10.7442i	0.981628	−	0.434308i
$613$	−14.0285	−	24.2980i	−0.566605	−	0.981388i	−0.996898	−	0.0786994i	$-0.974923\pi$
$613$	−14.0285	−	24.2980i	−0.566605	−	0.981388i	0.430294	−	0.902689i	$-0.358410\pi$
$614$	12.3775			0.499516
$615$	−0.231204	−	0.257381i	−0.00932305	−	0.0103786i
$616$		0			0
$617$	29.8093	+	17.2104i	1.20008	+	0.692865i	0.960573	−	0.278030i	$-0.0896813\pi$
$617$	29.8093	+	17.2104i	1.20008	+	0.692865i	0.239506	+	0.970895i	$0.423015\pi$
$618$	1.88841	−	5.78893i	0.0759628	−	0.232865i
$619$	−17.2889	−	9.98173i	−0.694898	−	0.401200i	0.110546	−	0.993871i	$-0.464740\pi$
$619$	−17.2889	−	9.98173i	−0.694898	−	0.401200i	−0.805444	+	0.592671i	$0.798073\pi$
$620$	0.126778	−	0.0731955i	0.00509154	−	0.00293960i
$621$	15.4671	−	34.4150i	0.620672	−	1.38103i
$622$			13.6510i			0.547354i
$623$		0			0
$624$	−3.12097	−	14.7677i	−0.124939	−	0.591181i
$625$	−12.4940	−	21.6402i	−0.499760	−	0.865609i
$626$	0.479005			0.0191449
$627$	1.14917	−	3.52281i	0.0458936	−	0.140687i
$628$		−	25.4831i		−	1.01689i
$629$	−14.0417			−0.559878
$630$		0			0
$631$	−46.8447			−1.86486			−0.932429	−	0.361354i	$-0.882314\pi$
$631$	−46.8447			−1.86486			−0.932429	+	0.361354i	$0.882314\pi$
$632$		−	36.8798i		−	1.46700i
$633$	23.9261	−	5.05649i	0.950976	−	0.200977i
$634$	14.5677			0.578556
$635$	−0.0618862	−	0.107190i	−0.00245588	−	0.00425370i
$636$	29.7718	+	9.71185i	1.18053	+	0.385100i
$637$		0			0
$638$		−	2.76475i		−	0.109458i
$639$	23.6662	+	2.54324i	0.936220	+	0.100609i
$640$	0.270290	−	0.156052i	0.0106841	−	0.00616849i
$641$	3.34281	+	1.92997i	0.132033	+	0.0762293i	0.564562	−	0.825391i	$-0.309045\pi$
$641$	3.34281	+	1.92997i	0.132033	+	0.0762293i	−0.432529	+	0.901620i	$0.642379\pi$
$642$	−10.2076	+	2.15726i	−0.402862	+	0.0851401i
$643$	31.0233	+	17.9113i	1.22344	+	0.706352i	0.965649	−	0.259849i	$-0.0836727\pi$
$643$	31.0233	+	17.9113i	1.22344	+	0.706352i	0.257789	+	0.966201i	$0.417006\pi$
$644$		0			0
$645$	0.111272	−	0.0235160i	0.00438133	−	0.000925941i
$646$	7.89468			0.310612
$647$	−21.8246	−	37.8013i	−0.858013	−	1.48612i	−0.873821	−	0.486248i	$-0.838365\pi$
$647$	−21.8246	−	37.8013i	−0.858013	−	1.48612i	0.0158075	−	0.999875i	$-0.494968\pi$
$648$	4.52064	−	20.7906i	0.177588	−	0.816730i
$649$	−5.33162	−	3.07821i	−0.209284	−	0.120830i
$650$	9.35369	+	16.2011i	0.366882	+	0.635458i
$651$		0			0
$652$	−8.07072	+	13.9789i	−0.316074	+	0.547456i
$653$	−6.45191	+	3.72501i	−0.252483	+	0.145771i	−0.620901	−	0.783889i	$-0.713233\pi$
$653$	−6.45191	+	3.72501i	−0.252483	+	0.145771i	0.368418	+	0.929660i	$0.379900\pi$
$654$	−5.17429	−	1.68790i	−0.202331	−	0.0660022i
$655$	−0.0360114	+	0.0623736i	−0.00140708	+	0.00243714i
$656$	−5.45884	+	9.45498i	−0.213132	+	0.369155i
$657$	−13.2295	−	29.9014i	−0.516131	−	1.16656i
$658$		0			0
$659$	−7.52607	+	4.34518i	−0.293174	+	0.169264i	−0.639372	−	0.768897i	$-0.720806\pi$
$659$	−7.52607	+	4.34518i	−0.293174	+	0.169264i	0.346198	+	0.938161i	$0.387472\pi$
$660$	−0.0581130	+	0.0522025i	−0.00226204	+	0.00203198i
$661$		−	28.8505i		−	1.12215i	−0.827763	−	0.561077i	$-0.810387\pi$
$661$		−	28.8505i		−	1.12215i	0.827763	−	0.561077i	$-0.189613\pi$
$662$			14.3937i			0.559428i
$663$	−41.2189	+	37.0267i	−1.60081	+	1.43800i
$664$	12.5871	−	7.26719i	0.488476	−	0.282022i
$665$		0			0
$666$	−2.90573	+	3.97984i	−0.112595	+	0.154216i
$667$	−14.7812	+	25.6017i	−0.572329	+	0.991303i
$668$	4.58724	−	7.94534i	0.177486	−	0.307414i
$669$	−4.92036	−	1.60507i	−0.190232	−	0.0620555i
$670$	0.208097	−	0.120145i	0.00803950	−	0.00464161i
$671$	1.21124	−	2.09793i	0.0467594	−	0.0809897i
$672$		0			0
$673$	−3.60695	−	6.24742i	−0.139038	−	0.240820i	0.788095	−	0.615554i	$-0.211068\pi$
$673$	−3.60695	−	6.24742i	−0.139038	−	0.240820i	−0.927133	+	0.374733i	$0.877734\pi$
$674$	14.5498	+	8.40036i	0.560439	+	0.323570i
$675$	−2.62489	−	25.8436i	−0.101032	−	0.994722i
$676$	14.5991	+	25.2864i	0.561504	+	0.972553i
$677$	−36.3821			−1.39828			−0.699140	−	0.714985i	$-0.746433\pi$
$677$	−36.3821			−1.39828			−0.699140	+	0.714985i	$0.746433\pi$
$678$	−10.6734	+	2.25570i	−0.409911	+	0.0866297i
$679$		0			0
$680$	−0.329070	−	0.189989i	−0.0126193	−	0.00728573i
$681$	−48.7598	+	10.3048i	−1.86848	+	0.394881i
$682$	−1.95149	−	1.12669i	−0.0747265	−	0.0431433i
$683$	−20.5530	+	11.8663i	−0.786438	+	0.454050i	−0.838707	−	0.544583i	$-0.816688\pi$
$683$	−20.5530	+	11.8663i	−0.786438	+	0.454050i	0.0522688	+	0.998633i	$0.483355\pi$
$684$	−5.77048	+	7.90355i	−0.220640	+	0.302200i
$685$		−	0.321118i		−	0.0122693i
$686$		0			0
$687$	14.5913	+	4.75982i	0.556693	+	0.181599i
$688$	−1.79443	−	3.10804i	−0.0684119	−	0.118493i
$689$	−65.3415			−2.48931
$690$	−0.231365	+	0.0488961i	−0.00880790	+	0.00186144i
$691$		−	3.30391i		−	0.125687i	−0.998023	−	0.0628433i	$-0.979983\pi$
$691$		−	3.30391i		−	0.125687i	0.998023	−	0.0628433i	$-0.0200168\pi$
$692$	7.58393			0.288298
$693$		0			0
$694$	−3.77718			−0.143380
$695$			0.0996463i			0.00377980i
$696$	−5.16983	+	15.8482i	−0.195962	+	0.600724i
$697$	40.0772			1.51803
$698$	−3.71417	−	6.43313i	−0.140583	−	0.243498i
$699$	4.62292	+	21.8746i	0.174855	+	0.827371i
$700$		0			0
$701$			0.873603i			0.0329955i	0.999864	+	0.0164978i	$0.00525164\pi$
$701$			0.873603i			0.0329955i	−0.999864	+	0.0164978i	$0.994748\pi$
$702$	1.96482	+	19.3449i	0.0741574	+	0.730125i
$703$	4.48135	−	2.58731i	0.169017	−	0.0975821i
$704$	−0.645868	−	0.372892i	−0.0243421	−	0.0140539i
$705$	−0.165414	+	0.507079i	−0.00622985	+	0.0190977i
$706$	8.07845	+	4.66410i	0.304037	+	0.175536i
$707$		0			0
$708$	10.8650	+	12.0952i	0.408332	+	0.454564i
$709$	16.1553			0.606727			0.303363	−	0.952875i	$-0.401890\pi$
$709$	16.1553			0.606727			0.303363	+	0.952875i	$0.401890\pi$
$710$	−0.0745897	−	0.129193i	−0.00279930	−	0.00484853i
$711$	5.00060	−	46.5331i	0.187537	−	1.74513i
$712$	−24.6735	−	14.2453i	−0.924680	−	0.533864i
$713$	12.0473	+	20.8665i	0.451174	+	0.781456i
$714$		0			0
$715$	0.0814965	−	0.141156i	0.00304779	−	0.00527894i
$716$	−0.273546	+	0.157932i	−0.0102229	+	0.00590220i
$717$	2.00862	+	9.50430i	0.0750133	+	0.354945i
$718$	9.01498	−	15.6144i	0.336436	−	0.582724i
$719$	22.5953	−	39.1361i	0.842661	−	1.45953i	−0.0449767	−	0.998988i	$-0.514321\pi$
$719$	22.5953	−	39.1361i	0.842661	−	1.45953i	0.887637	−	0.460543i	$-0.152345\pi$
$720$	0.120126	−	0.0531481i	0.00447683	−	0.00198071i
$721$		0			0
$722$	8.41110	−	4.85615i	0.313029	−	0.180727i
$723$	3.93477	+	18.6184i	0.146336	+	0.692425i
$724$			9.76178i			0.362794i
$725$			20.3528i			0.755883i
$726$	−10.8894	−	3.55222i	−0.404142	−	0.131835i
$727$	−7.15775	+	4.13253i	−0.265466	+	0.153267i	−0.626826	−	0.779160i	$-0.715646\pi$
$727$	−7.15775	+	4.13253i	−0.265466	+	0.153267i	0.361359	+	0.932427i	$0.382313\pi$
$728$		0			0
$729$	8.52294	−	25.6195i	0.315664	−	0.948871i
$730$	−0.102463	+	0.177472i	−0.00379234	+	0.00656853i
$731$	−6.58709	+	11.4092i	−0.243632	+	0.421983i
$732$	−4.75931	+	4.27526i	−0.175909	+	0.158018i
$733$	10.5799	−	6.10830i	0.390777	−	0.225615i	−0.291720	−	0.956504i	$-0.594227\pi$
$733$	10.5799	−	6.10830i	0.390777	−	0.225615i	0.682497	+	0.730889i	$0.260894\pi$
$734$	2.28543	−	3.95849i	0.0843569	−	0.146110i
$735$		0			0
$736$	20.8972	+	36.1949i	0.770280	+	1.33416i
$737$	11.3143	+	6.53234i	0.416769	+	0.240622i
$738$	8.29342	−	11.3591i	0.305285	−	0.418134i
$739$	10.3536	+	17.9330i	0.380863	+	0.659674i	0.991186	−	0.132478i	$-0.0422935\pi$
$739$	10.3536	+	17.9330i	0.380863	+	0.659674i	−0.610323	+	0.792153i	$0.708960\pi$
$740$	−0.109087			−0.00401013
$741$	6.33235	−	19.4119i	0.232625	−	0.713115i
$742$		0			0
$743$	10.2862	+	5.93873i	0.377363	+	0.217871i	0.676670	−	0.736286i	$-0.263422\pi$
$743$	10.2862	+	5.93873i	0.377363	+	0.217871i	−0.299307	+	0.954157i	$0.596756\pi$
$744$	9.07957	+	10.1076i	0.332873	+	0.370561i
$745$	−0.390045	−	0.225192i	−0.0142901	−	0.00825041i
$746$	−0.142588	+	0.0823233i	−0.00522053	+	0.00301407i
$747$	16.8672	−	7.46266i	0.617138	−	0.273045i
$748$		−	9.04885i		−	0.330859i
$749$		0			0
$750$	−0.242250	+	0.217612i	−0.00884571	+	0.00794606i
$751$	−11.8554	−	20.5342i	−0.432610	−	0.749303i	0.564487	−	0.825442i	$-0.309074\pi$
$751$	−11.8554	−	20.5342i	−0.432610	−	0.749303i	−0.997097	+	0.0761390i	$0.975741\pi$
$752$	16.8312			0.613772
$753$	−28.0385	−	31.2131i	−1.02178	−	1.13747i
$754$		−	15.2348i		−	0.554817i
$755$	0.0979362			0.00356426
$756$		0			0
$757$	44.2494			1.60827			0.804136	−	0.594446i	$-0.202628\pi$
$757$	44.2494			1.60827			0.804136	+	0.594446i	$0.202628\pi$
$758$		−	5.92462i		−	0.215192i
$759$	−8.59203	−	9.56482i	−0.311871	−	0.347181i
$760$	0.140029			0.00507937
$761$	24.3767	+	42.2217i	0.883656	+	1.53054i	0.847246	+	0.531200i	$0.178259\pi$
$761$	24.3767	+	42.2217i	0.883656	+	1.53054i	0.0364098	+	0.999337i	$0.488408\pi$
$762$	3.74308	−	3.36238i	0.135597	−	0.121806i
$763$		0			0
$764$			21.5154i			0.778401i
$765$	−0.389443	−	0.284337i	−0.0140804	−	0.0102802i
$766$	−0.188174	+	0.108642i	−0.00679900	+	0.00392540i
$767$	−29.3791	−	16.9620i	−1.06082	−	0.612463i
$768$	10.1674	+	11.3185i	0.366883	+	0.408422i
$769$	23.3870	+	13.5025i	0.843357	+	0.486912i	0.858404	−	0.512975i	$-0.171457\pi$
$769$	23.3870	+	13.5025i	0.843357	+	0.486912i	−0.0150472	+	0.999887i	$0.504790\pi$
$770$		0			0
$771$	−9.51989	+	29.1834i	−0.342851	+	1.05101i
$772$	−32.8536			−1.18243
$773$	13.3567	+	23.1345i	0.480408	+	0.832092i	0.999747	−	0.0224765i	$-0.00715509\pi$
$773$	13.3567	+	23.1345i	0.480408	+	0.832092i	−0.519339	+	0.854568i	$0.673822\pi$
$774$	1.87060	+	4.22795i	0.0672373	+	0.151971i
$775$	14.3659	+	8.29417i	0.516039	+	0.297935i
$776$	−9.24794	−	16.0179i	−0.331982	−	0.575009i
$777$		0			0
$778$	−2.19514	+	3.80209i	−0.0786994	+	0.136311i
$779$	−12.7905	+	7.38459i	−0.458267	+	0.264580i
$780$	−0.320223	+	0.287654i	−0.0114658	+	0.0102997i
$781$	4.05547	−	7.02429i	0.145116	−	0.251349i
$782$	13.6963	−	23.7228i	0.489780	−	0.848324i
$783$	−8.67191	+	19.2955i	−0.309909	+	0.689564i
$784$		0			0
$785$	−0.400742	+	0.231368i	−0.0143031	+	0.00825789i
$786$	−2.78348	−	0.907998i	−0.0992834	−	0.0323872i
$787$			47.3534i			1.68797i	0.536369	+	0.843983i	$0.319795\pi$
$787$			47.3534i			1.68797i	−0.536369	+	0.843983i	$0.680205\pi$
$788$			23.6424i			0.842224i
$789$	1.03812	+	4.91213i	0.0369580	+	0.174876i
$790$	−0.254023	+	0.146660i	−0.00903775	+	0.00521795i
$791$		0			0
$792$	−5.85554	−	4.27520i	−0.208068	−	0.151913i
$793$	6.67436	−	11.5603i	0.237014	−	0.410520i
$794$	2.49462	−	4.32082i	0.0885309	−	0.153340i
$795$	−0.117580	−	0.556362i	−0.00417014	−	0.0197321i
$796$	−13.0766	+	7.54980i	−0.463489	+	0.267596i
$797$	−4.42781	+	7.66919i	−0.156841	+	0.271657i	−0.933728	−	0.357984i	$-0.883464\pi$
$797$	−4.42781	+	7.66919i	−0.156841	+	0.271657i	0.776887	+	0.629640i	$0.216798\pi$
$798$		0			0
$799$	−30.8925	−	53.5074i	−1.09290	−	1.89296i
$800$	24.9191	+	14.3871i	0.881023	+	0.508659i
$801$	−29.2003	−	21.3195i	−1.03174	−	0.753287i
$802$	2.10404	+	3.64430i	0.0742962	+	0.128685i
$803$	−11.1420			−0.393191
$804$	−23.0569	−	25.6674i	−0.813154	−	0.905220i
$805$		0			0
$806$	−10.7534	−	6.20848i	−0.378772	−	0.218684i
$807$	11.7603	−	36.0515i	0.413984	−	1.26907i
$808$	0.929170	+	0.536456i	0.0326881	+	0.0188725i
$809$	−6.40871	+	3.70007i	−0.225318	+	0.130087i	−0.608410	−	0.793623i	$-0.708192\pi$
$809$	−6.40871	+	3.70007i	−0.225318	+	0.130087i	0.383092	+	0.923710i	$0.374859\pi$
$810$	−0.161180	+	0.0515404i	−0.00566328	+	0.00181095i
$811$		−	25.0843i		−	0.880829i	−0.897794	−	0.440415i	$-0.854831\pi$
$811$		−	25.0843i		−	0.880829i	0.897794	−	0.440415i	$-0.145169\pi$
$812$		0			0
$813$	3.21732	+	15.2236i	0.112836	+	0.533914i
$814$	0.839587	+	1.45421i	0.0294275	+	0.0509699i
$815$	0.293105			0.0102670
$816$	−4.71894	+	14.4660i	−0.165196	+	0.506411i
$817$		−	4.85492i		−	0.169852i
$818$	−22.2483			−0.777893
$819$		0			0
$820$	0.311353			0.0108729
$821$			21.2212i			0.740627i	0.928907	+	0.370313i	$0.120750\pi$
$821$			21.2212i			0.740627i	−0.928907	+	0.370313i	$0.879250\pi$
$822$	12.7718	−	2.69917i	0.445468	−	0.0941442i
$823$	16.9538			0.590972			0.295486	−	0.955347i	$-0.404518\pi$
$823$	16.9538			0.590972			0.295486	+	0.955347i	$0.404518\pi$
$824$	6.25546	+	10.8348i	0.217919	+	0.377447i
$825$	−8.41538	−	2.74518i	−0.292986	−	0.0955749i
$826$		0			0
$827$		−	25.3052i		−	0.879949i	−0.898010	−	0.439975i	$-0.854987\pi$
$827$		−	25.3052i		−	0.879949i	0.898010	−	0.439975i	$-0.145013\pi$
$828$	13.7383	+	31.0515i	0.477439	+	1.07911i
$829$	−35.9640	+	20.7638i	−1.24908	+	0.721158i	−0.970927	−	0.239378i	$-0.923057\pi$
$829$	−35.9640	+	20.7638i	−1.24908	+	0.721158i	−0.278156	+	0.960536i	$0.589723\pi$
$830$	−0.100111	−	0.0577990i	−0.00347490	−	0.00200623i
$831$	26.9475	−	5.69504i	0.934800	−	0.197559i
$832$	−3.55896	−	2.05477i	−0.123385	−	0.0712362i
$833$		0			0
$834$	−3.96323	+	0.837580i	−0.137235	+	0.0290030i
$835$	−0.166595			−0.00576527
$836$	1.66733	+	2.88791i	0.0576659	+	0.0998803i
$837$	10.0856	+	13.9843i	0.348611	+	0.483369i
$838$	1.03146	+	0.595515i	0.0356312	+	0.0205717i
$839$	6.61780	+	11.4624i	0.228472	+	0.395725i	0.957355	−	0.288913i	$-0.0932938\pi$
$839$	6.61780	+	11.4624i	0.228472	+	0.395725i	−0.728884	+	0.684638i	$0.759960\pi$
$840$		0			0
$841$	−6.21265	+	10.7606i	−0.214229	+	0.371056i
$842$	−2.18914	+	1.26390i	−0.0754428	+	0.0435569i
$843$	8.56242	+	2.79314i	0.294905	+	0.0962009i
$844$	−11.0036	+	19.0588i	−0.378759	+	0.656030i
$845$	0.265099	−	0.459164i	0.00911967	−	0.0157957i
$846$	−21.5584	−	2.31673i	−0.741193	−	0.0796509i
$847$		0			0
$848$	−15.5403	+	8.97217i	−0.533654	+	0.308106i
$849$	−24.1904	+	21.7301i	−0.830213	+	0.745776i
$850$		−	18.8590i		−	0.646859i
$851$		−	17.9547i		−	0.615479i
$852$	−15.9351	+	14.3144i	−0.545928	+	0.490404i
$853$	−15.3814	+	8.88048i	−0.526651	+	0.304062i	−0.739651	−	0.672990i	$-0.765010\pi$
$853$	−15.3814	+	8.88048i	−0.526651	+	0.304062i	0.213001	+	0.977052i	$0.431676\pi$
$854$		0			0
$855$	0.176681	+	0.0189867i	0.00604237	+	0.000649332i
$856$	10.7180	−	18.5642i	0.366334	−	0.634510i
$857$	9.17157	−	15.8856i	0.313295	−	0.542643i	−0.665779	−	0.746149i	$-0.731900\pi$
$857$	9.17157	−	15.8856i	0.313295	−	0.542643i	0.979074	+	0.203507i	$0.0652338\pi$
$858$	6.29921	+	2.05486i	0.215052	+	0.0701519i
$859$	2.69126	−	1.55380i	0.0918246	−	0.0530150i	−0.453385	−	0.891315i	$-0.649784\pi$
$859$	2.69126	−	1.55380i	0.0918246	−	0.0530150i	0.545209	+	0.838300i	$0.316450\pi$
$860$	−0.0511739	+	0.0886358i	−0.00174502	+	0.00302246i
$861$		0			0
$862$	−0.441616	−	0.764902i	−0.0150415	−	0.0260527i
$863$	−35.8587	−	20.7030i	−1.22064	−	0.704739i	−0.255589	−	0.966786i	$-0.582269\pi$
$863$	−35.8587	−	20.7030i	−1.22064	−	0.704739i	−0.965055	+	0.262047i	$0.915603\pi$
$864$	17.4946	+	24.2572i	0.595177	+	0.825247i
$865$	−0.0688566	−	0.119263i	−0.00234119	−	0.00405507i
$866$	−24.8641			−0.844917
$867$	25.8409	−	5.46115i	0.877602	−	0.185471i
$868$		0			0
$869$	−13.8114	−	7.97399i	−0.468518	−	0.270499i
$870$	0.129719	−	0.0274146i	0.00439789	−	0.000929441i
$871$	62.3460	+	35.9955i	2.11251	+	1.21966i
$872$	9.68438	−	5.59128i	0.327954	−	0.189345i
$873$	−9.49669	−	21.4645i	−0.321414	−	0.726464i
$874$			10.0947i			0.341459i
$875$		0			0
$876$	27.9742	+	9.12545i	0.945161	+	0.308320i
$877$	11.3979	+	19.7417i	0.384878	+	0.666628i	0.991752	−	0.128170i	$-0.0409102\pi$
$877$	11.3979	+	19.7417i	0.384878	+	0.666628i	−0.606874	+	0.794798i	$0.707577\pi$
$878$	15.7696			0.532199
$879$	−38.7054	+	8.17993i	−1.30550	+	0.275902i
$880$		−	0.0447618i		−	0.00150892i
$881$	−43.4050			−1.46235			−0.731175	−	0.682190i	$-0.761028\pi$
$881$	−43.4050			−1.46235			−0.731175	+	0.682190i	$0.761028\pi$
$882$		0			0
$883$	−29.9309			−1.00725			−0.503627	−	0.863921i	$-0.668001\pi$
$883$	−29.9309			−1.00725			−0.503627	+	0.863921i	$0.668001\pi$
$884$		−	49.8623i		−	1.67705i
$885$	0.0915592	−	0.280676i	0.00307773	−	0.00943483i
$886$	−7.47363			−0.251082
$887$	19.4788	+	33.7382i	0.654033	+	1.13282i	0.982135	+	0.188176i	$0.0602576\pi$
$887$	19.4788	+	33.7382i	0.654033	+	1.13282i	−0.328102	+	0.944642i	$0.606409\pi$
$888$	−2.09347	−	9.90579i	−0.0702522	−	0.332417i
$889$		0			0
$890$			0.226597i			0.00759556i
$891$	−6.80855	−	6.18820i	−0.228095	−	0.207313i
$892$	4.03358	−	2.32879i	0.135054	−	0.0779736i
$893$	19.7185	+	11.3845i	0.659853	+	0.380966i
$894$	5.67803	−	17.4061i	0.189902	−	0.582147i
$895$	0.00496721	+	0.00286782i	0.000166035	+	9.58606e-5i
$896$		0			0
$897$	−47.3451	−	52.7055i	−1.58081	−	1.75979i
$898$	−9.56277			−0.319114
$899$	−6.75453	−	11.6992i	−0.225276	−	0.390190i
$900$	18.8802	+	13.7847i	0.629340	+	0.459489i
$901$	57.0460	+	32.9355i	1.90048	+	1.09724i
$902$	−2.39632	−	4.15054i	−0.0797886	−	0.138198i
$903$		0			0
$904$	11.2071	−	19.4113i	0.372743	−	0.645611i
$905$	0.153512	−	0.0886299i	0.00510290	−	0.00294616i
$906$	0.823206	+	3.89521i	0.0273492	+	0.129410i
$907$	14.0526	−	24.3399i	0.466610	−	0.808192i	−0.532663	−	0.846328i	$-0.678809\pi$
$907$	14.0526	−	24.3399i	0.466610	−	0.808192i	0.999273	+	0.0381355i	$0.0121419\pi$
$908$	22.4246	−	38.8406i	0.744187	−	1.28897i
$909$	1.09964	+	0.802861i	0.0364728	+	0.0266292i
$910$		0			0
$911$	32.3883	−	18.6994i	1.07307	−	0.619538i	0.144052	−	0.989570i	$-0.453987\pi$
$911$	32.3883	−	18.6994i	1.07307	−	0.619538i	0.929019	+	0.370032i	$0.120653\pi$
$912$	−1.15946	−	5.48627i	−0.0383935	−	0.181669i
$913$		−	6.28511i		−	0.208007i
$914$		−	13.7024i		−	0.453235i
$915$	0.110443	+	0.0360275i	0.00365113	+	0.00119103i
$916$	−11.9616	+	6.90601i	−0.395221	+	0.228181i
$917$		0			0
$918$	8.03546	−	17.8793i	0.265210	−	0.590105i
$919$	12.9115	−	22.3634i	0.425911	−	0.737699i	−0.570594	−	0.821232i	$-0.693287\pi$
$919$	12.9115	−	22.3634i	0.425911	−	0.737699i	0.996505	+	0.0835328i	$0.0266203\pi$
$920$	0.242933	−	0.420773i	0.00800928	−	0.0138725i
$921$	−24.0083	+	21.5665i	−0.791100	+	0.710641i
$922$	0.957884	−	0.553034i	0.0315462	−	0.0182132i
$923$	22.3471	−	38.7063i	0.735563	−	1.27403i
$924$		0			0
$925$	−6.18063	−	10.7052i	−0.203218	−	0.351983i
$926$	0.695162	+	0.401352i	0.0228444	+	0.0131892i
$927$	6.42372	+	14.5190i	0.210983	+	0.476865i
$928$	−11.7164	−	20.2934i	−0.384610	−	0.666164i
$929$	−15.9419			−0.523036			−0.261518	−	0.965199i	$-0.584223\pi$
$929$	−15.9419			−0.523036			−0.261518	+	0.965199i	$0.584223\pi$
$930$	0.0335127	−	0.102734i	0.00109893	−	0.00336877i
$931$		0			0
$932$	−17.4246	−	10.0601i	−0.570762	−	0.329529i
$933$	−23.7854	−	26.4783i	−0.778697	−	0.866862i
$934$	5.31568	+	3.06901i	0.173934	+	0.100421i
$935$	−0.142300	+	0.0821570i	−0.00465371	+	0.00268682i
$936$	−32.2661	−	23.5579i	−1.05465	−	0.770013i
$937$			15.0698i			0.492308i	0.969231	+	0.246154i	$0.0791668\pi$
$937$			15.0698i			0.492308i	−0.969231	+	0.246154i	$0.920833\pi$
$938$		0			0
$939$	−0.929112	+	0.834616i	−0.0303204	+	0.0272367i
$940$	−0.239999	−	0.415690i	−0.00782789	−	0.0135583i
$941$	−11.5372			−0.376102			−0.188051	−	0.982159i	$-0.560217\pi$
$941$	−11.5372			−0.376102			−0.188051	+	0.982159i	$0.560217\pi$
$942$	−12.5706	−	13.9939i	−0.409574	−	0.455946i
$943$			51.2456i			1.66879i
$944$	−9.31636			−0.303222
$945$		0			0
$946$	1.57543			0.0512218
$947$		−	28.3321i		−	0.920671i	−0.887745	−	0.460336i	$-0.847729\pi$
$947$		−	28.3321i		−	0.920671i	0.887745	−	0.460336i	$-0.152271\pi$
$948$	28.1454	+	31.3321i	0.914121	+	1.01762i
$949$	−61.3961			−1.99300
$950$	3.47495	+	6.01879i	0.112742	+	0.195275i
$951$	−28.2565	+	25.3826i	−0.916278	+	0.823088i
$952$		0			0
$953$			29.8498i			0.966931i	0.875364	+	0.483465i	$0.160622\pi$
$953$			29.8498i			0.966931i	−0.875364	+	0.483465i	$0.839378\pi$
$954$	21.1398	−	9.35303i	0.684427	−	0.302816i
$955$	0.338347	−	0.195345i	0.0109486	−	0.00632120i
$956$	−7.57084	−	4.37102i	−0.244858	−	0.141369i
$957$	4.81729	+	5.36271i	0.155721	+	0.173352i
$958$	−10.0935	−	5.82748i	−0.326106	−	0.188277i
$959$		0			0
$960$	0.0110914	−	0.0340009i	0.000357974	−	0.00109737i
$961$	19.9896			0.644824
$962$	4.62642	+	8.01319i	0.149162	+	0.258356i
$963$	16.0406	−	21.9700i	0.516901	−	0.707975i
$964$	−14.8308	−	8.56258i	−0.477669	−	0.275782i
$965$	0.298287	+	0.516648i	0.00960219	+	0.0166315i
$966$		0			0
$967$	8.17864	−	14.1658i	0.263007	−	0.455542i	−0.704032	−	0.710168i	$-0.748619\pi$
$967$	8.17864	−	14.1658i	0.263007	−	0.455542i	0.967040	+	0.254626i	$0.0819523\pi$
$968$	20.3809	−	11.7669i	0.655068	−	0.378203i
$969$	−15.3131	+	13.7556i	−0.491926	+	0.441895i
$970$	−0.0735528	+	0.127397i	−0.00236164	+	0.00409048i
$971$	−10.7315	+	18.5875i	−0.344390	+	0.596500i	−0.985243	−	0.171163i	$-0.945247\pi$
$971$	−10.7315	+	18.5875i	−0.344390	+	0.596500i	0.640853	+	0.767663i	$0.278581\pi$
$972$	12.0260	+	21.1131i	0.385735	+	0.677202i
$973$		0			0
$974$	−24.8470	+	14.3454i	−0.796148	+	0.459657i
$975$	−46.3717	−	15.1269i	−1.48508	−	0.484448i
$976$		−	3.66588i		−	0.117342i
$977$			21.5027i			0.687932i	0.938982	+	0.343966i	$0.111770\pi$
$977$			21.5027i			0.687932i	−0.938982	+	0.343966i	$0.888230\pi$
$978$	2.46370	+	11.6577i	0.0787806	+	0.372771i
$979$	−10.6696	+	6.16010i	−0.341002	+	0.196878i
$980$		0			0
$981$	12.9774	−	5.74167i	0.414336	−	0.183318i
$982$	−8.82301	+	15.2819i	−0.281554	+	0.487665i
$983$	−12.7097	+	22.0138i	−0.405376	+	0.702131i	−0.994365	−	0.106009i	$-0.966193\pi$
$983$	−12.7097	+	22.0138i	−0.405376	+	0.702131i	0.588989	+	0.808141i	$0.299526\pi$
$984$	5.97510	+	28.2727i	0.190479	+	0.901302i
$985$	0.371794	−	0.214656i	0.0118464	−	0.00683949i
$986$	−7.67912	+	13.3006i	−0.244553	+	0.423578i
$987$		0			0
$988$	9.18759	+	15.9134i	0.292296	+	0.506272i
$989$	−14.5886	−	8.42273i	−0.463890	−	0.267827i
$990$	−0.00616123	+	0.0573334i	−0.000195817	+	0.00182218i
$991$	−11.8768	−	20.5713i	−0.377280	−	0.653468i	0.613385	−	0.789784i	$-0.289807\pi$
$991$	−11.8768	−	20.5713i	−0.377280	−	0.653468i	−0.990665	+	0.136315i	$0.956474\pi$
$992$	−19.0987			−0.606384
$993$	−25.0795	−	27.9191i	−0.795875	−	0.885985i
$994$		0			0
$995$	0.237453	+	0.137093i	0.00752776	+	0.00434615i
$996$	−5.14761	+	15.7801i	−0.163108	+	0.500011i
$997$	−10.5366	−	6.08329i	−0.333697	−	0.192660i	0.323785	−	0.946131i	$-0.395045\pi$
$997$	−10.5366	−	6.08329i	−0.333697	−	0.192660i	−0.657481	+	0.753471i	$0.728378\pi$
$998$	3.05781	−	1.76543i	0.0967934	−	0.0558837i
$999$	−1.29829	−	12.7825i	−0.0410762	−	0.404420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.15		48
3.2	odd	2		1323.2.i.d.1097.10		48
7.2	even	3		441.2.o.e.293.16	yes	48
7.3	odd	6		441.2.s.d.374.10		48
7.4	even	3		441.2.s.d.374.9		48
7.5	odd	6		441.2.o.e.293.15	yes	48
7.6	odd	2	inner	441.2.i.d.68.16		48
9.2	odd	6		441.2.s.d.362.10		48
9.7	even	3		1323.2.s.d.656.15		48
21.2	odd	6		1323.2.o.e.881.10		48
21.5	even	6		1323.2.o.e.881.9		48
21.11	odd	6		1323.2.s.d.962.16		48
21.17	even	6		1323.2.s.d.962.15		48
21.20	even	2		1323.2.i.d.1097.9		48
63.2	odd	6		441.2.o.e.146.15	✓	48
63.11	odd	6	inner	441.2.i.d.227.10		48
63.16	even	3		1323.2.o.e.440.9		48
63.20	even	6		441.2.s.d.362.9		48
63.25	even	3		1323.2.i.d.521.9		48
63.34	odd	6		1323.2.s.d.656.16		48
63.38	even	6	inner	441.2.i.d.227.9		48
63.47	even	6		441.2.o.e.146.16	yes	48
63.52	odd	6		1323.2.i.d.521.10		48
63.61	odd	6		1323.2.o.e.440.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.15		48	1.1	even	1	trivial
441.2.i.d.68.16		48	7.6	odd	2	inner
441.2.i.d.227.9		48	63.38	even	6	inner
441.2.i.d.227.10		48	63.11	odd	6	inner
441.2.o.e.146.15	✓	48	63.2	odd	6
441.2.o.e.146.16	yes	48	63.47	even	6
441.2.o.e.293.15	yes	48	7.5	odd	6
441.2.o.e.293.16	yes	48	7.2	even	3
441.2.s.d.362.9		48	63.20	even	6
441.2.s.d.362.10		48	9.2	odd	6
441.2.s.d.374.9		48	7.4	even	3
441.2.s.d.374.10		48	7.3	odd	6
1323.2.i.d.521.9		48	63.25	even	3
1323.2.i.d.521.10		48	63.52	odd	6
1323.2.i.d.1097.9		48	21.20	even	2
1323.2.i.d.1097.10		48	3.2	odd	2
1323.2.o.e.440.9		48	63.16	even	3
1323.2.o.e.440.10		48	63.61	odd	6
1323.2.o.e.881.9		48	21.5	even	6
1323.2.o.e.881.10		48	21.2	odd	6
1323.2.s.d.656.15		48	9.7	even	3
1323.2.s.d.656.16		48	63.34	odd	6
1323.2.s.d.962.15		48	21.17	even	6
1323.2.s.d.962.16		48	21.11	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.664297i q^{2} +(-1.15747 - 1.28852i) q^{3} +1.55871 q^{4} +(-0.0141520 - 0.0245119i) q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(-0.320544 + 2.98283i) q^{9} +O(q^{10})\)	\(q+0.664297i q^{2} +(-1.15747 - 1.28852i) q^{3} +1.55871 q^{4} +(-0.0141520 - 0.0245119i) q^{5} +(0.855956 - 0.768901i) q^{6} +2.36404i q^{8} +(-0.320544 + 2.98283i) q^{9} +(0.0162832 - 0.00940110i) q^{10} +(0.885324 + 0.511142i) q^{11} +(-1.80415 - 2.00842i) q^{12} +(4.87844 + 2.81657i) q^{13} +(-0.0152036 + 0.0466067i) q^{15} +1.54700 q^{16} +(-2.83940 - 4.91798i) q^{17} +(-1.98148 - 0.212936i) q^{18} +(1.81237 + 1.04637i) q^{19} +(-0.0220588 - 0.0382070i) q^{20} +(-0.339550 + 0.588118i) q^{22} +(6.28849 - 3.63066i) q^{23} +(3.04610 - 2.73630i) q^{24} +(2.49960 - 4.32943i) q^{25} +(-1.87104 + 3.24073i) q^{26} +(4.21444 - 3.03949i) q^{27} +(-3.52577 + 2.03560i) q^{29} +(-0.0309607 - 0.0100997i) q^{30} +3.31820i q^{31} +5.75574i q^{32} +(-0.366118 - 1.73238i) q^{33} +(3.26700 - 1.88620i) q^{34} +(-0.499635 + 4.64936i) q^{36} +(1.23632 - 2.14137i) q^{37} +(-0.695101 + 1.20395i) q^{38} +(-2.01744 - 9.54604i) q^{39} +(0.0579471 - 0.0334558i) q^{40} +(-3.52867 + 6.11183i) q^{41} +(-1.15994 - 2.00908i) q^{43} +(1.37996 + 0.796722i) q^{44} +(0.0776511 - 0.0343557i) q^{45} +(2.41184 + 4.17742i) q^{46} +10.8799 q^{47} +(-1.79060 - 1.99333i) q^{48} +(2.87603 + 1.66048i) q^{50} +(-3.05039 + 9.35101i) q^{51} +(7.60408 + 4.39022i) q^{52} +(-10.0454 + 5.79973i) q^{53} +(2.01913 + 2.79964i) q^{54} -0.0289346i q^{55} +(-0.749489 - 3.54640i) q^{57} +(-1.35224 - 2.34215i) q^{58} -6.02222 q^{59} +(-0.0236979 + 0.0726464i) q^{60} -2.36968i q^{61} -2.20427 q^{62} -0.729528 q^{64} -0.159440i q^{65} +(1.15082 - 0.243211i) q^{66} +12.7799 q^{67} +(-4.42580 - 7.66571i) q^{68} +(-11.9569 - 3.90045i) q^{69} -7.93415i q^{71} +(-7.05152 - 0.757778i) q^{72} +(-9.43889 + 5.44955i) q^{73} +(1.42251 + 0.821285i) q^{74} +(-8.47174 + 1.79040i) q^{75} +(2.82496 + 1.63099i) q^{76} +(6.34140 - 1.34018i) q^{78} -15.6004 q^{79} +(-0.0218930 - 0.0379198i) q^{80} +(-8.79450 - 1.91225i) q^{81} +(-4.06007 - 2.34408i) q^{82} +(-3.07406 - 5.32442i) q^{83} +(-0.0803661 + 0.139198i) q^{85} +(1.33463 - 0.770546i) q^{86} +(6.70386 + 2.18686i) q^{87} +(-1.20836 + 2.09294i) q^{88} +(-6.02582 + 10.4370i) q^{89} +(0.0228224 + 0.0515834i) q^{90} +(9.80194 - 5.65915i) q^{92} +(4.27555 - 3.84070i) q^{93} +7.22751i q^{94} -0.0592328i q^{95} +(7.41636 - 6.66208i) q^{96} +(-6.77565 + 3.91192i) q^{97} +(-1.80843 + 2.47692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^9	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

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