LMFDB - Embedded newform 490.2.l.c.313.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(117,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("490.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.l (of order $12$, degree $4$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			313.4
Root			$1.01089 + 0.750919i$ of defining polynomial
Character	$\chi$	$=$	490.313
Dual form			490.2.l.c.227.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.279864 + 0.0749894i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +(-2.52538 - 1.45803i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.279864 + 0.0749894i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +(-2.52538 - 1.45803i) q^{9} +(1.82591 - 1.29076i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(-0.279864 + 0.0749894i) q^{12} +(-1.42962 + 1.42962i) q^{13} +(-0.0593598 - 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.37400 - 5.12784i) q^{17} +(0.754730 - 2.81669i) q^{18} +(-1.94590 + 3.37040i) q^{19} +(1.71936 + 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(1.08562 - 0.290892i) q^{23} +(-0.144868 - 0.250919i) q^{24} +(-3.80124 + 3.24817i) q^{25} +(-1.75092 - 1.01089i) q^{26} +(-1.21205 - 1.21205i) q^{27} +3.15502i q^{29} +(0.607800 - 0.224313i) q^{30} +(3.33287 - 1.92423i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.421872 - 1.57445i) q^{33} +5.30873 q^{34} +2.91605 q^{36} +(-1.30444 - 4.86824i) q^{37} +(-3.75919 - 1.00727i) q^{38} +(-0.507306 + 0.292893i) q^{39} +(-0.935904 + 2.03078i) q^{40} -7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} +(4.87205 + 2.81288i) q^{44} +(-1.10346 + 6.42644i) q^{45} +(0.561961 + 0.973344i) q^{46} +(5.69475 - 1.52590i) q^{47} +(0.204875 - 0.204875i) q^{48} +(-4.12132 - 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(0.523277 - 1.95290i) q^{52} +(-0.357978 + 1.33599i) q^{53} +(0.857049 - 1.48445i) q^{54} +(-8.04270 + 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(-3.04751 + 0.816578i) q^{58} +(2.73923 + 4.74448i) q^{59} +(0.373980 + 0.529033i) q^{60} +(3.99172 + 2.30462i) q^{61} +(2.72127 + 2.72127i) q^{62} +1.00000i q^{64} +(4.10581 + 1.89220i) q^{65} +(1.41161 - 0.814995i) q^{66} +(-0.816193 - 0.218698i) q^{67} +(1.37400 + 5.12784i) q^{68} +0.325641 q^{69} +4.77710 q^{71} +(0.754730 + 2.81669i) q^{72} +(-5.42104 - 1.45256i) q^{73} +(4.36475 - 2.51999i) q^{74} +(-1.30741 + 0.623993i) q^{75} -3.89180i q^{76} +(-0.414214 - 0.414214i) q^{78} +(-5.41079 - 3.12392i) q^{79} +(-2.20382 - 0.378409i) q^{80} +(4.12576 + 7.14603i) q^{81} +(6.96481 - 1.86622i) q^{82} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(-0.236593 + 0.882976i) q^{87} +(-1.45605 + 5.43407i) q^{88} +(-5.96090 + 10.3246i) q^{89} +(-6.49307 + 0.597426i) q^{90} +(-0.794732 + 0.794732i) q^{92} +(1.07705 - 0.288594i) q^{93} +(2.94782 + 5.10577i) q^{94} +(8.57682 + 1.47269i) q^{95} +(0.250919 + 0.144868i) q^{96} +(-6.63103 - 6.63103i) q^{97} +16.4050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5}+O(q^{10}) $ 16 * q + 12 * q^5	$ 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) $ 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.279864	+	0.0749894i	0.161580	+	0.0432952i	0.338702	−	0.940894i	$-0.390012\pi$
$3$	0.279864	+	0.0749894i	0.161580	+	0.0432952i	−0.177122	+	0.984189i	$0.556679\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.774197	−	2.09777i	−0.346231	−	0.938149i
$5$	−0.774197	−	2.09777i	−0.346231	−	0.938149i
$6$			0.289737i			0.118285i
$7$		0			0
$7$		0			0
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.52538	−	1.45803i	−0.841792	−	0.486009i
$10$	1.82591	−	1.29076i	0.577403	−	0.408174i
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	−0.882888	−	0.469583i	$-0.844404\pi$
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	0.0347729	−	0.999395i	$-0.488929\pi$
$12$	−0.279864	+	0.0749894i	−0.0807899	+	0.0216476i
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	−0.876998	−	0.480493i	$-0.840458\pi$
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	0.480493	+	0.876998i	$0.340458\pi$
$14$		0			0
$15$	−0.0593598	−	0.645146i	−0.0153266	−	0.166576i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.37400	−	5.12784i	0.333244	−	1.24368i	−0.572516	−	0.819893i	$-0.694033\pi$
$17$	1.37400	−	5.12784i	0.333244	−	1.24368i	0.905760	−	0.423790i	$-0.139301\pi$
$18$	0.754730	−	2.81669i	0.177892	−	0.663900i
$19$	−1.94590	+	3.37040i	−0.446420	+	0.773223i	−0.998150	−	0.0608002i	$-0.980635\pi$
$19$	−1.94590	+	3.37040i	−0.446420	+	0.773223i	0.551729	+	0.834023i	$0.313968\pi$
$20$	1.71936	+	1.42962i	0.384460	+	0.319673i
$21$		0			0
$22$	3.97801	−	3.97801i	0.848115	−	0.848115i
$23$	1.08562	−	0.290892i	0.226368	−	0.0606552i	−0.143852	−	0.989599i	$-0.545949\pi$
$23$	1.08562	−	0.290892i	0.226368	−	0.0606552i	0.370220	+	0.928944i	$0.379282\pi$
$24$	−0.144868	−	0.250919i	−0.0295711	−	0.0512187i
$25$	−3.80124	+	3.24817i	−0.760248	+	0.649633i
$26$	−1.75092	−	1.01089i	−0.343384	−	0.198253i
$27$	−1.21205	−	1.21205i	−0.233259	−	0.233259i
$28$		0			0
$29$			3.15502i			0.585872i	0.956132	+	0.292936i	$0.0946322\pi$
$29$			3.15502i			0.585872i	−0.956132	+	0.292936i	$0.905368\pi$
$30$	0.607800	−	0.224313i	0.110969	−	0.0409538i
$31$	3.33287	−	1.92423i	0.598601	−	0.345602i	−0.169890	−	0.985463i	$-0.554341\pi$
$31$	3.33287	−	1.92423i	0.598601	−	0.345602i	0.768491	+	0.639861i	$0.221008\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−0.421872	−	1.57445i	−0.0734386	−	0.274076i
$34$	5.30873			0.910440
$35$		0			0
$36$	2.91605			0.486009
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	−0.986360	−	0.164603i	$-0.947366\pi$
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	0.771911	−	0.635731i	$-0.219301\pi$
$38$	−3.75919	−	1.00727i	−0.609822	−	0.163401i
$39$	−0.507306	+	0.292893i	−0.0812340	+	0.0469005i
$40$	−0.935904	+	2.03078i	−0.147979	+	0.321095i
$41$		−	7.21050i		−	1.12609i	−0.826426	−	0.563046i	$-0.809629\pi$
$41$		−	7.21050i		−	1.12609i	0.826426	−	0.563046i	$-0.190371\pi$
$42$		0			0
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	0.834361	−	0.551218i	$-0.185837\pi$
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	−0.551218	+	0.834361i	$0.685837\pi$
$44$	4.87205	+	2.81288i	0.734489	+	0.424058i
$45$	−1.10346	+	6.42644i	−0.164494	+	0.957998i
$46$	0.561961	+	0.973344i	0.0828566	+	0.143512i
$47$	5.69475	−	1.52590i	0.830665	−	0.222576i	0.181661	−	0.983361i	$-0.441853\pi$
$47$	5.69475	−	1.52590i	0.830665	−	0.222576i	0.649004	+	0.760785i	$0.275186\pi$
$48$	0.204875	−	0.204875i	0.0295711	−	0.0295711i
$49$		0			0
$50$	−4.12132	−	2.83103i	−0.582843	−	0.400368i
$51$	0.769067	−	1.33206i	0.107691	−	0.186526i
$52$	0.523277	−	1.95290i	0.0725655	−	0.270818i
$53$	−0.357978	+	1.33599i	−0.0491720	+	0.183512i	−0.986144	−	0.165892i	$-0.946950\pi$
$53$	−0.357978	+	1.33599i	−0.0491720	+	0.183512i	0.936972	+	0.349405i	$0.113616\pi$
$54$	0.857049	−	1.48445i	0.116630	−	0.202008i
$55$	−8.04270	+	9.67269i	−1.08448	+	1.30426i
$56$		0			0
$57$	−0.797333	+	0.797333i	−0.105609	+	0.105609i
$58$	−3.04751	+	0.816578i	−0.400158	+	0.107222i
$59$	2.73923	+	4.74448i	0.356617	+	0.617679i	0.987393	−	0.158286i	$-0.0505968\pi$
$59$	2.73923	+	4.74448i	0.356617	+	0.617679i	−0.630776	+	0.775965i	$0.717263\pi$
$60$	0.373980	+	0.529033i	0.0482806	+	0.0682979i
$61$	3.99172	+	2.30462i	0.511088	+	0.295077i	0.733281	−	0.679926i	$-0.237988\pi$
$61$	3.99172	+	2.30462i	0.511088	+	0.295077i	−0.222193	+	0.975003i	$0.571322\pi$
$62$	2.72127	+	2.72127i	0.345602	+	0.345602i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.10581	+	1.89220i	0.509264	+	0.234699i
$66$	1.41161	−	0.814995i	0.173758	−	0.100319i
$67$	−0.816193	−	0.218698i	−0.0997138	−	0.0267182i	0.208617	−	0.977997i	$-0.433104\pi$
$67$	−0.816193	−	0.218698i	−0.0997138	−	0.0267182i	−0.308331	+	0.951279i	$0.599770\pi$
$68$	1.37400	+	5.12784i	0.166622	+	0.621842i
$69$	0.325641			0.0392026
$70$		0			0
$71$	4.77710			0.566937			0.283469	−	0.958982i	$-0.408515\pi$
$71$	4.77710			0.566937			0.283469	+	0.958982i	$0.408515\pi$
$72$	0.754730	+	2.81669i	0.0889458	+	0.331950i
$73$	−5.42104	−	1.45256i	−0.634485	−	0.170010i	−0.0727807	−	0.997348i	$-0.523187\pi$
$73$	−5.42104	−	1.45256i	−0.634485	−	0.170010i	−0.561704	+	0.827338i	$0.689854\pi$
$74$	4.36475	−	2.51999i	0.507391	−	0.292943i
$75$	−1.30741	+	0.623993i	−0.150967	+	0.0720525i
$76$		−	3.89180i		−	0.446420i
$77$		0			0
$78$	−0.414214	−	0.414214i	−0.0469005	−	0.0469005i
$79$	−5.41079	−	3.12392i	−0.608761	−	0.351469i	0.163719	−	0.986507i	$-0.447651\pi$
$79$	−5.41079	−	3.12392i	−0.608761	−	0.351469i	−0.772481	+	0.635038i	$0.780984\pi$
$80$	−2.20382	−	0.378409i	−0.246394	−	0.0423074i
$81$	4.12576	+	7.14603i	0.458418	+	0.794003i
$82$	6.96481	−	1.86622i	0.769135	−	0.206089i
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	−0.323542	−	0.946214i	$-0.604874\pi$
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	0.946214	+	0.323542i	$0.104874\pi$
$84$		0			0
$85$	−11.8207	+	1.08763i	−1.28214	+	0.117970i
$86$	−1.31288	+	2.27397i	−0.141571	+	0.245209i
$87$	−0.236593	+	0.882976i	−0.0253654	+	0.0946650i
$88$	−1.45605	+	5.43407i	−0.155216	+	0.579273i
$89$	−5.96090	+	10.3246i	−0.631855	+	1.09440i	0.355318	+	0.934746i	$0.384373\pi$
$89$	−5.96090	+	10.3246i	−0.631855	+	1.09440i	−0.987172	+	0.159659i	$0.948961\pi$
$90$	−6.49307	+	0.597426i	−0.684429	+	0.0629742i
$91$		0			0
$92$	−0.794732	+	0.794732i	−0.0828566	+	0.0828566i
$93$	1.07705	−	0.288594i	0.111685	−	0.0299258i
$94$	2.94782	+	5.10577i	0.304044	+	0.526620i
$95$	8.57682	+	1.47269i	0.879963	+	0.151095i
$96$	0.250919	+	0.144868i	0.0256094	+	0.0147856i
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	0.285191	−	0.958471i	$-0.407943\pi$
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	−0.958471	+	0.285191i	$0.907943\pi$
$98$		0			0
$99$			16.4050i			1.64877i
$100$	1.66789	−	4.71361i	0.166789	−	0.471361i
$101$	−13.9423	+	8.04960i	−1.38731	+	0.800965i	−0.993012	−	0.118016i	$-0.962347\pi$
$101$	−13.9423	+	8.04960i	−1.38731	+	0.800965i	−0.394301	+	0.918981i	$0.629013\pi$
$102$	1.48572	+	0.398099i	0.147109	+	0.0394176i
$103$	−5.09084	−	18.9993i	−0.501616	−	1.87206i	−0.489271	−	0.872132i	$-0.662737\pi$
$103$	−5.09084	−	18.9993i	−0.501616	−	1.87206i	−0.0123445	−	0.999924i	$-0.503929\pi$
$104$	2.02179			0.198253
$105$		0			0
$106$	−1.38312			−0.134340
$107$	0.724955	+	2.70557i	0.0700840	+	0.261557i	0.992074	−	0.125657i	$-0.0401040\pi$
$107$	0.724955	+	2.70557i	0.0700840	+	0.261557i	−0.921990	+	0.387214i	$0.873437\pi$
$108$	1.65569	+	0.443641i	0.159319	+	0.0426894i
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	−0.234395	−	0.972141i	$-0.575311\pi$
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	0.724701	+	0.689063i	$0.241978\pi$
$110$	−11.4247	−	5.26517i	−1.08930	−	0.502015i
$111$		−	1.46027i		−	0.138602i
$112$		0			0
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.941970	−	0.335697i	$-0.891028\pi$
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.335697	−	0.941970i	$-0.608972\pi$
$114$	−0.976529	−	0.563800i	−0.0914604	−	0.0528047i
$115$	−1.45071	−	2.05218i	−0.135279	−	0.191367i
$116$	−1.57751	−	2.73232i	−0.146468	−	0.253690i
$117$	5.69475	−	1.52590i	0.526480	−	0.141070i
$118$	−3.87385	+	3.87385i	−0.356617	+	0.356617i
$119$		0			0
$120$	−0.414214	+	0.498161i	−0.0378124	+	0.0454757i
$121$	−10.3246	+	17.8827i	−0.938599	+	1.62570i
$122$	−1.19296	+	4.45219i	−0.108006	+	0.403082i
$123$	0.540712	−	2.01796i	0.0487543	−	0.181954i
$124$	−1.92423	+	3.33287i	−0.172801	+	0.299300i
$125$	9.75680	+	5.45939i	0.872674	+	0.488303i
$126$		0			0
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	−0.470906	−	0.882184i	$-0.656073\pi$
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	0.882184	+	0.470906i	$0.156073\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	0.380390	+	0.658854i	0.0334915	+	0.0580089i
$130$	−0.765062	+	4.45565i	−0.0671004	+	0.390786i
$131$	6.66437	+	3.84768i	0.582269	+	0.336173i	0.762035	−	0.647536i	$-0.224201\pi$
$131$	6.66437	+	3.84768i	0.582269	+	0.336173i	−0.179766	+	0.983709i	$0.557534\pi$
$132$	1.15258	+	1.15258i	0.100319	+	0.100319i
$133$		0			0
$134$		−	0.844985i		−	0.0729956i
$135$	−1.60423	+	3.48096i	−0.138070	+	0.299594i
$136$	−4.59749	+	2.65436i	−0.394232	+	0.227610i
$137$	8.53471	+	2.28687i	0.729170	+	0.195380i	0.604259	−	0.796788i	$-0.293469\pi$
$137$	8.53471	+	2.28687i	0.729170	+	0.195380i	0.124910	+	0.992168i	$0.460136\pi$
$138$	0.0842822	+	0.314545i	0.00717458	+	0.0267759i
$139$	11.0631			0.938361			0.469180	−	0.883102i	$-0.344549\pi$
$139$	11.0631			0.938361			0.469180	+	0.883102i	$0.344549\pi$
$140$		0			0
$141$	1.70818			0.143855
$142$	1.23640	+	4.61432i	0.103757	+	0.387225i
$143$	10.9865	+	2.94383i	0.918740	+	0.246176i
$144$	−2.52538	+	1.45803i	−0.210448	+	0.121502i
$145$	6.61848	−	2.44260i	0.549635	−	0.202847i
$146$		−	5.61227i		−	0.464475i
$147$		0			0
$148$	3.56380	+	3.56380i	0.292943	+	0.292943i
$149$	4.37243	+	2.52443i	0.358204	+	0.206809i	0.668293	−	0.743899i	$-0.267025\pi$
$149$	4.37243	+	2.52443i	0.358204	+	0.206809i	−0.310089	+	0.950708i	$0.600359\pi$
$150$	−0.941113	−	1.10136i	−0.0768416	−	0.0899256i
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	−0.998479	−	0.0551270i	$-0.982444\pi$
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	0.451498	−	0.892272i	$-0.350890\pi$
$152$	3.75919	−	1.00727i	0.304911	−	0.0817006i
$153$	−10.9464	+	10.9464i	−0.884963	+	0.884963i
$154$		0			0
$155$	−6.61688	−	5.50184i	−0.531481	−	0.441918i
$156$	0.292893	−	0.507306i	0.0234502	−	0.0406170i
$157$	0.285443	−	1.06529i	0.0227808	−	0.0850191i	−0.953600	−	0.301078i	$-0.902654\pi$
$157$	0.285443	−	1.06529i	0.0227808	−	0.0850191i	0.976380	+	0.216059i	$0.0693203\pi$
$158$	1.61706	−	6.03495i	0.128646	−	0.480115i
$159$	−0.200370	+	0.347052i	−0.0158904	+	0.0275230i
$160$	−0.204875	−	2.22666i	−0.0161968	−	0.176033i
$161$		0			0
$162$	−5.83471	+	5.83471i	−0.458418	+	0.458418i
$163$	12.7899	−	3.42705i	1.00179	−	0.268428i	0.279592	−	0.960119i	$-0.409801\pi$
$163$	12.7899	−	3.42705i	1.00179	−	0.268428i	0.722193	+	0.691691i	$0.243134\pi$
$164$	3.60525	+	6.24448i	0.281523	+	0.487612i
$165$	−2.97621	+	2.10392i	−0.231698	+	0.163790i
$166$	6.94775	+	4.01128i	0.539250	+	0.311336i
$167$	−4.70680	−	4.70680i	−0.364223	−	0.364223i	0.501142	−	0.865365i	$-0.332913\pi$
$167$	−4.70680	−	4.70680i	−0.364223	−	0.364223i	−0.865365	+	0.501142i	$0.832913\pi$
$168$		0			0
$169$			8.91237i			0.685567i
$170$	−4.11000	−	11.1365i	−0.315223	−	0.854128i
$171$	9.82827	−	5.67435i	0.751586	−	0.433929i
$172$	−2.53629	−	0.679597i	−0.193390	−	0.0518188i
$173$	1.82586	+	6.81421i	0.138818	+	0.518075i	0.999953	+	0.00969875i	$0.00308726\pi$
$173$	1.82586	+	6.81421i	0.138818	+	0.518075i	−0.861135	+	0.508376i	$0.830246\pi$
$174$	−0.914124			−0.0692996
$175$		0			0
$176$	−5.62576			−0.424058
$177$	0.410826	+	1.53322i	0.0308796	+	0.115244i
$178$	−11.5156	−	3.08559i	−0.863129	−	0.231275i
$179$	−1.91075	+	1.10317i	−0.142816	+	0.0824550i	−0.569706	−	0.821849i	$-0.692943\pi$
$179$	−1.91075	+	1.10317i	−0.142816	+	0.0824550i	0.426889	+	0.904304i	$0.359609\pi$
$180$	−2.25760	−	6.11719i	−0.168271	−	0.455949i
$181$			4.11867i			0.306139i	0.988215	+	0.153069i	$0.0489158\pi$
$181$			4.11867i			0.306139i	−0.988215	+	0.153069i	$0.951084\pi$
$182$		0			0
$183$	0.944318	+	0.944318i	0.0698060	+	0.0698060i
$184$	−0.973344	−	0.561961i	−0.0717559	−	0.0414283i
$185$	−9.20253	+	6.50539i	−0.676584	+	0.478286i
$186$	0.557521	+	0.965654i	0.0408794	+	0.0708052i
$187$	−28.8480	+	7.72980i	−2.10957	+	0.565259i
$188$	−4.16885	+	4.16885i	−0.304044	+	0.304044i
$189$		0			0
$190$	0.797333	+	8.66573i	0.0578446	+	0.628678i
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	−0.366686	−	0.930345i	$-0.619508\pi$
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	0.989045	−	0.147613i	$-0.0471589\pi$
$192$	−0.0749894	+	0.279864i	−0.00541190	+	0.0201975i
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	0.757659	+	0.652650i	$0.226343\pi$
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	−0.982477	+	0.186382i	$0.940324\pi$
$194$	4.68885	−	8.12132i	0.336640	−	0.583077i
$195$	1.00718	+	0.837452i	0.0721254	+	0.0599712i
$196$		0			0
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.0199932	−	0.999800i	$-0.493636\pi$
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.999800	−	0.0199932i	$-0.00636444\pi$
$198$	−15.8460	+	4.24593i	−1.12613	+	0.301745i
$199$	−3.76653	−	6.52383i	−0.267002	−	0.462462i	0.701084	−	0.713079i	$-0.252700\pi$
$199$	−3.76653	−	6.52383i	−0.267002	−	0.462462i	−0.968086	+	0.250617i	$0.919367\pi$
$200$	4.98468	+	0.391082i	0.352470	+	0.0276537i
$201$	−0.212023	−	0.122412i	−0.0149550	−	0.00863425i
$202$	−11.3839	−	11.3839i	−0.800965	−	0.800965i
$203$		0			0
$204$			1.53813i			0.107691i
$205$	−15.1259	+	5.58235i	−1.05644	+	0.389888i
$206$	17.0343	−	9.83476i	1.18684	−	0.685220i
$207$	−3.16574	−	0.848257i	−0.220034	−	0.0589579i
$208$	0.523277	+	1.95290i	0.0362827	+	0.135409i
$209$	21.8944			1.51446
$210$		0			0
$211$	19.5766			1.34771			0.673854	−	0.738865i	$-0.264638\pi$
$211$	19.5766			1.34771			0.673854	+	0.738865i	$0.264638\pi$
$212$	−0.357978	−	1.33599i	−0.0245860	−	0.0917562i
$213$	1.33694	+	0.358232i	0.0916056	+	0.0245456i
$214$	−2.42575	+	1.40051i	−0.165821	+	0.0957366i
$215$	2.45746	−	5.33235i	0.167597	−	0.363663i
$216$			1.71410i			0.116630i
$217$		0			0
$218$	4.17960	+	4.17960i	0.283078	+	0.283078i
$219$	−1.40823	−	0.813041i	−0.0951593	−	0.0549402i
$220$	2.12884	−	12.3981i	0.143526	−	0.835883i
$221$	5.36656	+	9.29516i	0.360994	+	0.625260i
$222$	1.41051	−	0.377945i	0.0946672	−	0.0253660i
$223$	1.46027	−	1.46027i	0.0977867	−	0.0977867i	−0.656521	−	0.754308i	$-0.727973\pi$
$223$	1.46027	−	1.46027i	0.0977867	−	0.0977867i	0.754308	+	0.656521i	$0.227973\pi$
$224$		0			0
$225$	14.3355	−	2.66053i	0.955698	−	0.177369i
$226$	9.60377	−	16.6342i	0.638833	−	1.10649i
$227$	4.82525	−	18.0081i	0.320263	−	1.19524i	−0.598726	−	0.800954i	$-0.704326\pi$
$227$	4.82525	−	18.0081i	0.320263	−	1.19524i	0.918989	−	0.394283i	$-0.129007\pi$
$228$	0.291844	−	1.08918i	0.0193278	−	0.0721325i
$229$	−2.00384	+	3.47074i	−0.132417	+	0.229353i	−0.924608	−	0.380920i	$-0.875607\pi$
$229$	−2.00384	+	3.47074i	−0.132417	+	0.229353i	0.792191	+	0.610274i	$0.208941\pi$
$230$	1.60678	−	1.93242i	0.105948	−	0.127420i
$231$		0			0
$232$	2.23093	−	2.23093i	0.146468	−	0.146468i
$233$	13.2637	−	3.55400i	0.868934	−	0.232830i	0.203307	−	0.979115i	$-0.434831\pi$
$233$	13.2637	−	3.55400i	0.868934	−	0.232830i	0.665627	+	0.746285i	$0.268164\pi$
$234$	2.94782	+	5.10577i	0.192705	+	0.333775i
$235$	−7.60984	−	10.7649i	−0.496412	−	0.702225i
$236$	−4.74448	−	2.73923i	−0.308839	−	0.178308i
$237$	−1.28003	−	1.28003i	−0.0831466	−	0.0831466i
$238$		0			0
$239$		−	19.6621i		−	1.27183i	−0.771758	−	0.635916i	$-0.780622\pi$
$239$		−	19.6621i		−	1.27183i	0.771758	−	0.635916i	$-0.219378\pi$
$240$	−0.588393	−	0.271166i	−0.0379806	−	0.0175037i
$241$	5.09667	−	2.94256i	0.328305	−	0.189547i	−0.326783	−	0.945099i	$-0.605965\pi$
$241$	5.09667	−	2.94256i	0.328305	−	0.189547i	0.655088	+	0.755552i	$0.272631\pi$
$242$	−19.9456	−	5.34440i	−1.28215	−	0.343551i
$243$	1.94970	+	7.27638i	0.125073	+	0.466780i
$244$	−4.60924			−0.295077
$245$		0			0
$246$	2.08915			0.133199
$247$	−2.03649	−	7.60029i	−0.129579	−	0.483595i
$248$	−3.71733	−	0.996056i	−0.236051	−	0.0632496i
$249$	2.01302	−	1.16222i	0.127570	−	0.0736525i
$250$	−2.74812	+	10.8373i	−0.173806	+	0.685413i
$251$			7.09950i			0.448116i	0.974576	+	0.224058i	$0.0719306\pi$
$251$			7.09950i			0.448116i	−0.974576	+	0.224058i	$0.928069\pi$
$252$		0			0
$253$	−4.47097	−	4.47097i	−0.281088	−	0.281088i
$254$	5.67653	+	3.27735i	0.356177	+	0.205639i
$255$	−3.38977	−	0.582044i	−0.212275	−	0.0364490i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.54998	−	2.55891i	0.595711	−	0.159620i	0.0516491	−	0.998665i	$-0.483552\pi$
$257$	9.54998	−	2.55891i	0.595711	−	0.159620i	0.544062	+	0.839045i	$0.316886\pi$
$258$	−0.537952	+	0.537952i	−0.0334915	+	0.0334915i
$259$		0			0
$260$	−4.50184	+	0.414214i	−0.279192	+	0.0256884i
$261$	4.60010	−	7.96760i	0.284739	−	0.493182i
$262$	−1.99170	+	7.43314i	−0.123048	+	0.459221i
$263$	3.55829	−	13.2797i	0.219413	−	0.818861i	−0.765153	−	0.643849i	$-0.777337\pi$
$263$	3.55829	−	13.2797i	0.219413	−	0.818861i	0.984566	−	0.175013i	$-0.0559967\pi$
$264$	−0.814995	+	1.41161i	−0.0501595	+	0.0868788i
$265$	3.07974	−	0.283366i	0.189187	−	0.0174071i
$266$		0			0
$267$	−2.44248	+	2.44248i	−0.149477	+	0.149477i
$268$	0.816193	−	0.218698i	0.0498569	−	0.0133591i
$269$	−13.2510	−	22.9514i	−0.807928	−	1.39937i	−0.914296	−	0.405046i	$-0.867255\pi$
$269$	−13.2510	−	22.9514i	−0.807928	−	1.39937i	0.106368	−	0.994327i	$-0.466078\pi$
$270$	−3.77756	−	0.648630i	−0.229895	−	0.0394744i
$271$	11.0824	+	6.39844i	0.673209	+	0.388678i	0.797292	−	0.603594i	$-0.206265\pi$
$271$	11.0824	+	6.39844i	0.673209	+	0.388678i	−0.124082	+	0.992272i	$0.539599\pi$
$272$	−3.75384	−	3.75384i	−0.227610	−	0.227610i
$273$		0			0
$274$			8.83578i			0.533789i
$275$	26.5177	+	9.38313i	1.59908	+	0.565824i
$276$	−0.282014	+	0.162821i	−0.0169752	+	0.00980065i
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.377083	−	0.926180i	$-0.623073\pi$
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.789653	+	0.613554i	$0.789739\pi$
$278$	2.86334	+	10.6861i	0.171732	+	0.640912i
$279$	−11.2223			−0.671863
$280$		0			0
$281$	−14.1498			−0.844107			−0.422054	−	0.906571i	$-0.638691\pi$
$281$	−14.1498			−0.844107			−0.422054	+	0.906571i	$0.638691\pi$
$282$	0.442111	+	1.64998i	0.0263273	+	0.0982548i
$283$	26.1454	+	7.00563i	1.55418	+	0.416442i	0.930816	−	0.365489i	$-0.119098\pi$
$283$	26.1454	+	7.00563i	1.55418	+	0.416442i	0.623366	+	0.781930i	$0.285765\pi$
$284$	−4.13709	+	2.38855i	−0.245491	+	0.141734i
$285$	2.28991	+	1.05532i	0.135643	+	0.0625121i
$286$			11.3741i			0.672564i
$287$		0			0
$288$	−2.06196	−	2.06196i	−0.121502	−	0.121502i
$289$	−9.68442	−	5.59130i	−0.569672	−	0.328900i
$290$	4.07236	+	5.76077i	0.239137	+	0.338284i
$291$	−1.35853	−	2.35305i	−0.0796385	−	0.137938i
$292$	5.42104	−	1.45256i	0.317242	−	0.0850048i
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	0.000106876	−	1.00000i	$-0.499966\pi$
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	1.00000		0.000106876i	$-3.40197e-5\pi$
$294$		0			0
$295$	7.83211	−	9.41941i	0.456003	−	0.548420i
$296$	−2.51999	+	4.36475i	−0.146471	+	0.253696i
$297$	−2.49582	+	9.31453i	−0.144822	+	0.540484i
$298$	−1.30674	+	4.87682i	−0.0756974	+	0.282506i
$299$	−1.13616	+	1.96790i	−0.0657061	+	0.113806i
$300$	0.820253	−	1.19410i	0.0473573	−	0.0689413i
$301$		0			0
$302$	9.50552	−	9.50552i	0.546981	−	0.546981i
$303$	−4.50559	+	1.20727i	−0.258840	+	0.0693558i
$304$	1.94590	+	3.37040i	0.111605	+	0.193306i
$305$	1.74418	−	10.1579i	0.0998713	−	0.581641i
$306$	−13.4065	−	7.74027i	−0.766401	−	0.442482i
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	0.999919	−	0.0127019i	$-0.00404326\pi$
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	−0.0127019	+	0.999919i	$0.504043\pi$
$308$		0			0
$309$		−	5.69898i		−	0.324204i
$310$	3.60179	−	7.81540i	0.204568	−	0.443885i
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	−0.205486	−	0.978660i	$-0.565877\pi$
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	0.744802	+	0.667286i	$0.232544\pi$
$312$	0.565826	+	0.151613i	0.0320336	+	0.00858338i
$313$	−7.61212	−	28.4088i	−0.430262	−	1.60576i	−0.752156	−	0.658985i	$-0.770986\pi$
$313$	−7.61212	−	28.4088i	−0.430262	−	1.60576i	0.321893	−	0.946776i	$-0.395681\pi$
$314$	1.10287			0.0622383
$315$		0			0
$316$	6.24784			0.351469
$317$	1.11136	+	4.14766i	0.0624203	+	0.232956i	0.990087	−	0.140453i	$-0.0448558\pi$
$317$	1.11136	+	4.14766i	0.0624203	+	0.232956i	−0.927667	+	0.373408i	$0.878189\pi$
$318$	−0.387086	−	0.103719i	−0.0217067	−	0.00581629i
$319$	15.3714	−	8.87468i	0.860633	−	0.496887i
$320$	2.09777	−	0.774197i	0.117269	−	0.0432789i
$321$			0.811556i			0.0452966i
$322$		0			0
$323$	14.6092	+	14.6092i	0.812878	+	0.812878i
$324$	−7.14603	−	4.12576i	−0.397001	−	0.229209i
$325$	0.790684	−	10.0780i	0.0438593	−	0.559025i
$326$	6.62056	+	11.4671i	0.366679	+	0.635106i
$327$	1.65424	−	0.443251i	0.0914795	−	0.0245119i
$328$	−5.09860	+	5.09860i	−0.281523	+	0.281523i
$329$		0			0
$330$	−2.80253	−	2.33027i	−0.154274	−	0.128277i
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.291863	+	0.956460i	$0.594275\pi$
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.682387	+	0.730991i	$0.739058\pi$
$332$	−2.07639	+	7.74921i	−0.113957	+	0.425293i
$333$	−3.80382	+	14.1960i	−0.208448	+	0.777939i
$334$	3.32821	−	5.76463i	0.182112	−	0.315426i
$335$	0.173116	+	1.88150i	0.00945835	+	0.102797i
$336$		0			0
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	−0.955782	−	0.294075i	$-0.904989\pi$
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	0.294075	+	0.955782i	$0.404989\pi$
$338$	−8.60869	+	2.30669i	−0.468251	+	0.125468i
$339$	−2.78257	−	4.81955i	−0.151128	−	0.261762i
$340$	9.69326	−	6.85229i	0.525691	−	0.371617i
$341$	−18.7499	−	10.8253i	−1.01536	−	0.586221i
$342$	8.02475	+	8.02475i	0.433929	+	0.433929i
$343$		0			0
$344$		−	2.62576i		−	0.141571i
$345$	−0.252110	−	0.683119i	−0.0135732	−	0.0367779i
$346$	−6.10945	+	3.52729i	−0.328446	+	0.189628i
$347$	−8.67040	−	2.32323i	−0.465452	−	0.124717i	0.0184687	−	0.999829i	$-0.494121\pi$
$347$	−8.67040	−	2.32323i	−0.465452	−	0.124717i	−0.483920	+	0.875112i	$0.660788\pi$
$348$	−0.236593	−	0.882976i	−0.0126827	−	0.0473325i
$349$	−26.0251			−1.39309			−0.696546	−	0.717512i	$-0.745281\pi$
$349$	−26.0251			−1.39309			−0.696546	+	0.717512i	$0.745281\pi$
$350$		0			0
$351$	3.46554			0.184977
$352$	−1.45605	−	5.43407i	−0.0776079	−	0.289637i
$353$	−9.62659	−	2.57944i	−0.512372	−	0.137290i	−0.00663577	−	0.999978i	$-0.502112\pi$
$353$	−9.62659	−	2.57944i	−0.512372	−	0.137290i	−0.505736	+	0.862688i	$0.668779\pi$
$354$	−1.37465	+	0.793655i	−0.0730619	+	0.0421823i
$355$	−3.69841	−	10.0212i	−0.196291	−	0.531872i
$356$		−	11.9218i		−	0.631855i
$357$		0			0
$358$	−1.56012	−	1.56012i	−0.0824550	−	0.0824550i
$359$	−10.0235	−	5.78705i	−0.529019	−	0.305429i	0.211598	−	0.977357i	$-0.432133\pi$
$359$	−10.0235	−	5.78705i	−0.529019	−	0.305429i	−0.740617	+	0.671928i	$0.765467\pi$
$360$	5.32445	−	3.76392i	0.280623	−	0.198376i
$361$	1.92693	+	3.33754i	0.101417	+	0.175660i
$362$	−3.97833	+	1.06599i	−0.209097	+	0.0560273i
$363$	−4.23050	+	4.23050i	−0.222044	+	0.222044i
$364$		0			0
$365$	1.14981	+	12.4966i	0.0601840	+	0.654104i
$366$	−0.667734	+	1.15655i	−0.0349030	+	0.0604538i
$367$	−4.32083	+	16.1256i	−0.225545	+	0.841747i	0.756640	+	0.653832i	$0.226840\pi$
$367$	−4.32083	+	16.1256i	−0.225545	+	0.841747i	−0.982185	+	0.187915i	$0.939827\pi$
$368$	0.290892	−	1.08562i	0.0151638	−	0.0565921i
$369$	−10.5131	+	18.2092i	−0.547290	+	0.947935i
$370$	−8.66551	−	7.20525i	−0.450499	−	0.374583i
$371$		0			0
$372$	−0.788454	+	0.788454i	−0.0408794	+	0.0408794i
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	−0.337436	−	0.941348i	$-0.609560\pi$
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	0.178446	+	0.983950i	$0.442893\pi$
$374$	−14.9328	−	25.8644i	−0.772158	−	1.33742i
$375$	2.32118	+	2.25954i	0.119865	+	0.116682i
$376$	−5.10577	−	2.94782i	−0.263310	−	0.152022i
$377$	−4.51047	−	4.51047i	−0.232301	−	0.232301i
$378$		0			0
$379$		−	7.15349i		−	0.367450i	−0.982978	−	0.183725i	$-0.941184\pi$
$379$		−	7.15349i		−	0.367450i	0.982978	−	0.183725i	$-0.0588156\pi$
$380$	−8.16409	+	3.01302i	−0.418809	+	0.154565i
$381$	1.64470	−	0.949568i	0.0842605	−	0.0486478i
$382$	16.6162	+	4.45229i	0.850158	+	0.227799i
$383$	3.77704	+	14.0961i	0.192998	+	0.720278i	0.992776	+	0.119982i	$0.0382837\pi$
$383$	3.77704	+	14.0961i	0.192998	+	0.720278i	−0.799778	+	0.600296i	$0.795050\pi$
$384$	−0.289737			−0.0147856
$385$		0			0
$386$	−12.0674			−0.614214
$387$	−1.98174	−	7.39595i	−0.100737	−	0.375957i
$388$	9.05816	+	2.42713i	0.459858	+	0.123219i
$389$	−5.36634	+	3.09826i	−0.272084	+	0.157088i	−0.629834	−	0.776729i	$-0.716877\pi$
$389$	−5.36634	+	3.09826i	−0.272084	+	0.157088i	0.357750	+	0.933817i	$0.383544\pi$
$390$	−0.548240	+	1.18961i	−0.0277612	+	0.0602380i
$391$		−	5.96659i		−	0.301744i
$392$		0			0
$393$	1.57658	+	1.57658i	0.0795282	+	0.0795282i
$394$	17.5304	+	10.1212i	0.883167	+	0.509897i
$395$	−2.36424	+	13.7691i	−0.118958	+	0.692798i
$396$	−8.20251	−	14.2072i	−0.412191	−	0.713937i
$397$	−2.81652	+	0.754685i	−0.141357	+	0.0378766i	−0.328804	−	0.944398i	$-0.606646\pi$
$397$	−2.81652	+	0.754685i	−0.141357	+	0.0378766i	0.187447	+	0.982275i	$0.439979\pi$
$398$	5.32668	−	5.32668i	0.267002	−	0.267002i
$399$		0			0
$400$	0.912375	+	4.91605i	0.0456187	+	0.245803i
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	−0.501358	−	0.865240i	$-0.667166\pi$
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	0.999999	+	0.00156835i	$0.000499221\pi$
$402$	0.0633649	−	0.236481i	0.00316035	−	0.0117946i
$403$	−2.01381	+	7.51565i	−0.100315	+	0.374381i
$404$	8.04960	−	13.9423i	0.400483	−	0.693656i
$405$	11.7965	−	14.1873i	0.586175	−	0.704973i
$406$		0			0
$407$	−20.0491	+	20.0491i	−0.993796	+	0.993796i
$408$	−1.48572	+	0.398099i	−0.0735543	+	0.0197088i
$409$	17.1791	+	29.7550i	0.849451	+	1.47129i	0.881699	+	0.471812i	$0.156400\pi$
$409$	17.1791	+	29.7550i	0.849451	+	1.47129i	−0.0322484	+	0.999480i	$0.510267\pi$
$410$	−9.30702	−	13.1657i	−0.459641	−	0.650209i
$411$	2.21707	+	1.28003i	0.109360	+	0.0631390i
$412$	13.9084	+	13.9084i	0.685220	+	0.685220i
$413$		0			0
$414$		−	3.27741i		−	0.161076i
$415$	−16.2921	−	7.50836i	−0.799748	−	0.368571i
$416$	−1.75092	+	1.01089i	−0.0858459	+	0.0495631i
$417$	3.09617	+	0.829616i	0.151620	+	0.0406265i
$418$	5.66668	+	21.1483i	0.277166	+	1.03440i
$419$	−31.1360			−1.52109			−0.760547	−	0.649283i	$-0.775069\pi$
$419$	−31.1360			−1.52109			−0.760547	+	0.649283i	$0.775069\pi$
$420$		0			0
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	5.06679	+	18.9095i	0.246648	+	0.920501i
$423$	−16.6062	−	4.44962i	−0.807421	−	0.216348i
$424$	1.19782	−	0.691560i	0.0581711	−	0.0335851i
$425$	11.4332	+	23.9551i	0.554590	+	1.16199i
$426$			1.38410i			0.0670599i
$427$		0			0
$428$	−1.98061	−	1.98061i	−0.0957366	−	0.0957366i
$429$	2.85398	+	1.64775i	0.137792	+	0.0795540i
$430$	5.78669	+	0.993610i	0.279059	+	0.0479162i
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	0.987141	−	0.159849i	$-0.0511008\pi$
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	−0.632004	+	0.774965i	$0.717767\pi$
$432$	−1.65569	+	0.443641i	−0.0796595	+	0.0213447i
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	−0.905046	−	0.425315i	$-0.860163\pi$
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	0.425315	+	0.905046i	$0.360163\pi$
$434$		0			0
$435$	2.03545	−	0.187281i	0.0975922	−	0.00897944i
$436$	−2.95543	+	5.11895i	−0.141539	+	0.245153i
$437$	−1.13210	+	4.22504i	−0.0541555	+	0.202111i
$438$	0.420861	−	1.57067i	0.0201095	−	0.0750498i
$439$	19.2142	−	33.2800i	0.917046	−	1.58837i	0.113167	−	0.993576i	$-0.463900\pi$
$439$	19.2142	−	33.2800i	0.917046	−	1.58837i	0.803878	−	0.594794i	$-0.202766\pi$
$440$	12.5267	−	1.15258i	0.597186	−	0.0549470i
$441$		0			0
$442$	−7.58946	+	7.58946i	−0.360994	+	0.360994i
$443$	−5.54016	+	1.48448i	−0.263221	+	0.0705299i	−0.388016	−	0.921653i	$-0.626839\pi$
$443$	−5.54016	+	1.48448i	−0.263221	+	0.0705299i	0.124795	+	0.992183i	$0.460173\pi$
$444$	0.730133	+	1.26463i	0.0346506	+	0.0600166i
$445$	26.2735	+	4.51132i	1.24548	+	0.213857i
$446$	1.78845	+	1.03256i	0.0846857	+	0.0488933i
$447$	1.03438	+	1.03438i	0.0489247	+	0.0489247i
$448$		0			0
$449$		−	7.30267i		−	0.344635i	−0.985042	−	0.172317i	$-0.944875\pi$
$449$		−	7.30267i		−	0.344635i	0.985042	−	0.172317i	$-0.0551254\pi$
$450$	6.28017	+	13.1584i	0.296050	+	0.620293i
$451$	−35.1299	+	20.2823i	−1.65420	+	0.955055i
$452$	18.5531	+	4.97128i	0.872663	+	0.233829i
$453$	−1.00807	−	3.76217i	−0.0473633	−	0.176762i
$454$	18.6433			0.874974
$455$		0			0
$456$	1.12760			0.0528047
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	0.990055	−	0.140683i	$-0.0449299\pi$
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	−0.927754	+	0.373192i	$0.878263\pi$
$458$	−3.87111	−	1.03726i	−0.180885	−	0.0484680i
$459$	−7.88056	+	4.54984i	−0.367833	+	0.212368i
$460$	2.28244	+	1.05188i	0.106419	+	0.0490443i
$461$			29.4110i			1.36981i	0.728634	+	0.684903i	$0.240155\pi$
$461$			29.4110i			1.36981i	−0.728634	+	0.684903i	$0.759845\pi$
$462$		0			0
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	0.606805	−	0.794851i	$-0.292451\pi$
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	−0.794851	+	0.606805i	$0.792451\pi$
$464$	2.73232	+	1.57751i	0.126845	+	0.0732340i
$465$	−1.43925	−	2.03596i	−0.0667436	−	0.0944156i
$466$	6.86580	+	11.8919i	0.318052	+	0.550882i
$467$	−16.0757	+	4.30747i	−0.743894	+	0.199326i	−0.610808	−	0.791779i	$-0.709155\pi$
$467$	−16.0757	+	4.30747i	−0.743894	+	0.199326i	−0.133086	+	0.991105i	$0.542489\pi$
$468$	−4.16885	+	4.16885i	−0.192705	+	0.192705i
$469$		0			0
$470$	8.42852	−	10.1367i	0.388779	−	0.467571i
$471$	0.159770	−	0.276731i	0.00736184	−	0.0127511i
$472$	1.41793	−	5.29178i	0.0652654	−	0.243574i
$473$	3.82325	−	14.2686i	0.175793	−	0.656069i
$474$	0.905115	−	1.56771i	0.0415733	−	0.0720071i
$475$	−3.55078	−	19.1323i	−0.162921	−	0.877851i
$476$		0			0
$477$	2.85194	−	2.85194i	0.130581	−	0.130581i
$478$	18.9921	−	5.08891i	0.868678	−	0.232762i
$479$	7.69460	+	13.3274i	0.351575	+	0.608946i	0.986526	−	0.163607i	$-0.0523128\pi$
$479$	7.69460	+	13.3274i	0.351575	+	0.608946i	−0.634950	+	0.772553i	$0.718979\pi$
$480$	0.109639	−	0.638527i	0.00500431	−	0.0291446i
$481$	8.82459	+	5.09488i	0.402367	+	0.232306i
$482$	4.16141	+	4.16141i	0.189547	+	0.189547i
$483$		0			0
$484$		−	20.6492i		−	0.938599i
$485$	−8.77662	+	19.0441i	−0.398526	+	0.864747i
$486$	−6.52383	+	3.76653i	−0.295927	+	0.170853i
$487$	34.7656	+	9.31541i	1.57538	+	0.422122i	0.937492	−	0.348007i	$-0.113142\pi$
$487$	34.7656	+	9.31541i	1.57538	+	0.422122i	0.637888	+	0.770129i	$0.279808\pi$
$488$	−1.19296	−	4.45219i	−0.0540028	−	0.201541i
$489$	3.83644			0.173490
$490$		0			0
$491$	−15.2823			−0.689680			−0.344840	−	0.938661i	$-0.612067\pi$
$491$	−15.2823			−0.689680			−0.344840	+	0.938661i	$0.612067\pi$
$492$	0.540712	+	2.01796i	0.0243772	+	0.0909768i
$493$	16.1784	+	4.33499i	0.728639	+	0.195238i
$494$	6.81423	−	3.93420i	0.306587	−	0.177008i
$495$	34.4139	−	12.7007i	1.54679	−	0.570854i
$496$		−	3.84846i		−	0.172801i
$497$		0			0
$498$	1.64362	+	1.64362i	0.0736525	+	0.0736525i
$499$	27.3534	+	15.7925i	1.22451	+	0.706969i	0.965875	−	0.259008i	$-0.0833955\pi$
$499$	27.3534	+	15.7925i	1.22451	+	0.706969i	0.258630	+	0.965976i	$0.416729\pi$
$500$	−11.1793	+	0.150429i	−0.499955	+	0.00672739i
$501$	−0.964305	−	1.67023i	−0.0430820	−	0.0746202i
$502$	−6.85759	+	1.83749i	−0.306069	+	0.0820110i
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	−0.218778	−	0.975775i	$-0.570207\pi$
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	0.975775	+	0.218778i	$0.0702070\pi$
$504$		0			0
$505$	27.6803	+	23.0157i	1.23176	+	1.02419i
$506$	3.16146	−	5.47580i	0.140544	−	0.243429i
$507$	−0.668334	+	2.49426i	−0.0296817	+	0.110774i
$508$	−1.69648	+	6.33135i	−0.0752691	+	0.280908i
$509$	10.7571	−	18.6318i	0.476799	−	0.825840i	−0.522848	−	0.852426i	$-0.675130\pi$
$509$	10.7571	−	18.6318i	0.476799	−	0.825840i	0.999647	+	0.0265865i	$0.00846373\pi$
$510$	−0.315125	−	3.42491i	−0.0139540	−	0.151657i
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	6.44363	−	1.72657i	0.284493	−	0.0762297i
$514$	4.94343	+	8.56228i	0.218045	+	0.377666i
$515$	−35.9147	+	25.3886i	−1.58259	+	1.11875i
$516$	−0.658854	−	0.380390i	−0.0290044	−	0.0167457i
$517$	−23.4529	−	23.4529i	−1.03146	−	1.03146i
$518$		0			0
$519$			2.04397i			0.0897205i
$520$	−1.56526	−	4.24124i	−0.0686412	−	0.185991i
$521$	−11.4657	+	6.61973i	−0.502322	+	0.290016i	−0.729672	−	0.683798i	$-0.760327\pi$
$521$	−11.4657	+	6.61973i	−0.502322	+	0.290016i	0.227350	+	0.973813i	$0.426994\pi$
$522$	8.88670	+	2.38118i	0.388960	+	0.104222i
$523$	6.97006	+	26.0126i	0.304779	+	1.13745i	0.933135	+	0.359526i	$0.117062\pi$
$523$	6.97006	+	26.0126i	0.304779	+	1.13745i	−0.628356	+	0.777926i	$0.716272\pi$
$524$	−7.69535			−0.336173
$525$		0			0
$526$	13.7482			0.599448
$527$	−5.28779	−	19.7343i	−0.230340	−	0.859640i
$528$	−1.57445	−	0.421872i	−0.0685191	−	0.0183596i
$529$	−18.8246	+	10.8684i	−0.818462	+	0.472539i
$530$	1.07081	+	2.90146i	0.0465129	+	0.126031i
$531$		−	15.9755i		−	0.693276i
$532$		0			0
$533$	10.3083	+	10.3083i	0.446501	+	0.446501i
$534$	−2.99141	−	1.72709i	−0.129451	−	0.0747386i
$535$	5.11439	−	3.61543i	0.221114	−	0.156309i
$536$	0.422492	+	0.731778i	0.0182489	+	0.0316080i
$537$	−0.617477	+	0.165453i	−0.0266461	+	0.00713980i
$538$	18.7398	−	18.7398i	0.807928	−	0.807928i
$539$		0			0
$540$	−0.351176	−	3.81672i	−0.0151122	−	0.164245i
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	−0.718171	−	0.695867i	$-0.755020\pi$
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	0.961724	+	0.274020i	$0.0883536\pi$
$542$	−3.31208	+	12.3608i	−0.142266	+	0.530943i
$543$	−0.308857	+	1.15267i	−0.0132543	+	0.0494658i
$544$	2.65436	−	4.59749i	0.113805	−	0.197116i
$545$	−10.1629	−	8.45027i	−0.435329	−	0.361970i
$546$		0			0
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.409527	+	0.912298i	$0.634306\pi$
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.912298	+	0.409527i	$0.865694\pi$
$548$	−8.53471	+	2.28687i	−0.364585	+	0.0976902i
$549$	−6.72040	−	11.6401i	−0.286820	−	0.496786i
$550$	−2.20013	+	28.0426i	−0.0938140	+	1.19574i
$551$	−10.6337	−	6.13935i	−0.453009	−	0.261545i
$552$	−0.230263	−	0.230263i	−0.00980065	−	0.00980065i
$553$		0			0
$554$		−	20.1034i		−	0.854110i
$555$	−3.06330	+	1.13053i	−0.130030	+	0.0479885i
$556$	−9.58094	+	5.53156i	−0.406322	+	0.234590i
$557$	25.5003	+	6.83277i	1.08048	+	0.289514i	0.754793	−	0.655963i	$-0.227737\pi$
$557$	25.5003	+	6.83277i	1.08048	+	0.289514i	0.325688	+	0.945477i	$0.394404\pi$
$558$	−2.90455	−	10.8399i	−0.122959	−	0.458891i
$559$	−5.30873			−0.224535
$560$		0			0
$561$	−8.65318			−0.365337
$562$	−3.66224	−	13.6677i	−0.154482	−	0.576536i
$563$	−19.5055	−	5.22648i	−0.822058	−	0.220270i	−0.176812	−	0.984245i	$-0.556578\pi$
$563$	−19.5055	−	5.22648i	−0.822058	−	0.220270i	−0.645246	+	0.763975i	$0.723245\pi$
$564$	−1.47933	+	0.854092i	−0.0622911	+	0.0359638i
$565$	−17.9764	+	39.0064i	−0.756274	+	1.64101i
$566$			27.0677i			1.13774i
$567$		0			0
$568$	−3.37792	−	3.37792i	−0.141734	−	0.141734i
$569$	−21.4890	−	12.4067i	−0.900867	−	0.520116i	−0.0233856	−	0.999727i	$-0.507445\pi$
$569$	−21.4890	−	12.4067i	−0.900867	−	0.520116i	−0.877481	+	0.479611i	$0.840778\pi$
$570$	−0.426693	+	2.48502i	−0.0178722	+	0.104086i
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	0.814116	−	0.580703i	$-0.197222\pi$
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	−0.909961	+	0.414693i	$0.863889\pi$
$572$	−10.9865	+	2.94383i	−0.459370	+	0.123088i
$573$	3.52433	−	3.52433i	0.147231	−	0.147231i
$574$		0			0
$575$	−3.18185	+	4.63204i	−0.132692	+	0.193169i
$576$	1.45803	−	2.52538i	0.0607511	−	0.105224i
$577$	5.11957	−	19.1065i	0.213131	−	0.795414i	−0.773686	−	0.633570i	$-0.781589\pi$
$577$	5.11957	−	19.1065i	0.213131	−	0.795414i	0.986816	−	0.161845i	$-0.0517444\pi$
$578$	2.89427	−	10.8016i	0.120386	−	0.449286i
$579$	−1.74818	+	3.02794i	−0.0726520	+	0.125837i
$580$	−4.51047	+	5.42460i	−0.187287	+	0.225244i
$581$		0			0
$582$	1.92125	−	1.92125i	0.0796385	−	0.0796385i
$583$	7.51596	−	2.01390i	0.311279	−	0.0834071i
$584$	2.80614	+	4.86037i	0.116119	+	0.201124i
$585$	−7.60984	−	10.7649i	−0.314628	−	0.445074i
$586$	20.9665	+	12.1050i	0.866118	+	0.500053i
$587$	19.3782	+	19.3782i	0.799824	+	0.799824i	0.983068	−	0.183244i	$-0.0586597\pi$
$587$	19.3782	+	19.3782i	0.799824	+	0.799824i	−0.183244	+	0.983068i	$0.558660\pi$
$588$		0			0
$589$			14.9775i			0.617136i
$590$	11.1256	+	5.12731i	0.458032	+	0.211088i
$591$	5.07919	−	2.93247i	0.208930	−	0.120626i
$592$	−4.86824	−	1.30444i	−0.200083	−	0.0536122i
$593$	−0.837988	−	3.12741i	−0.0344121	−	0.128428i	0.946583	−	0.322460i	$-0.104510\pi$
$593$	−0.837988	−	3.12741i	−0.0344121	−	0.128428i	−0.980995	+	0.194033i	$0.937843\pi$
$594$	−9.64311			−0.395661
$595$		0			0
$596$	−5.04885			−0.206809
$597$	−0.564900	−	2.10824i	−0.0231198	−	0.0862844i
$598$	−2.19490	−	0.588122i	−0.0897562	−	0.0240501i
$599$	−6.75802	+	3.90174i	−0.276125	+	0.159421i	−0.631668	−	0.775239i	$-0.717629\pi$
$599$	−6.75802	+	3.90174i	−0.276125	+	0.159421i	0.355543	+	0.934660i	$0.384296\pi$
$600$	1.36571	+	0.483248i	0.0557548	+	0.0197285i
$601$			31.7170i			1.29377i	0.762590	+	0.646883i	$0.223928\pi$
$601$			31.7170i			1.29377i	−0.762590	+	0.646883i	$0.776072\pi$
$602$		0			0
$603$	1.74233	+	1.74233i	0.0709530	+	0.0709530i
$604$	11.6418	+	6.72142i	0.473699	+	0.273491i
$605$	45.5070	+	7.81383i	1.85012	+	0.317677i
$606$	−2.33227	−	4.03960i	−0.0947418	−	0.164098i
$607$	−0.743495	+	0.199219i	−0.0301775	+	0.00808604i	−0.273876	−	0.961765i	$-0.588306\pi$
$607$	−0.743495	+	0.199219i	−0.0301775	+	0.00808604i	0.243699	+	0.969851i	$0.421639\pi$
$608$	−2.75192	+	2.75192i	−0.111605	+	0.111605i
$609$		0			0
$610$	10.2632	−	0.944318i	0.415546	−	0.0382343i
$611$	−5.95987	+	10.3228i	−0.241110	+	0.417615i
$612$	4.00666	−	14.9530i	0.161960	−	0.604441i
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	−0.500323	−	0.865839i	$-0.666786\pi$
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	0.866212	−	0.499676i	$-0.166548\pi$
$614$	−12.2311	+	21.1850i	−0.493609	+	0.854955i
$615$	−4.65183	+	0.428014i	−0.187580	+	0.0172592i
$616$		0			0
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	−0.124980	−	0.992159i	$-0.539887\pi$
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	0.992159	+	0.124980i	$0.0398866\pi$
$618$	5.50479	−	1.47501i	0.221435	−	0.0593334i
$619$	−21.6707	−	37.5348i	−0.871021	−	1.50865i	−0.860942	−	0.508703i	$-0.830125\pi$
$619$	−21.6707	−	37.5348i	−0.871021	−	1.50865i	−0.0100783	−	0.999949i	$-0.503208\pi$
$620$	8.48131	+	1.45629i	0.340617	+	0.0584861i
$621$	−1.66841	−	0.963256i	−0.0669509	−	0.0386541i
$622$	7.76566	+	7.76566i	0.311374	+	0.311374i
$623$		0			0
$624$			0.585786i			0.0234502i
$625$	3.89884	−	24.6941i	0.155953	−	0.987764i
$626$	25.4707	−	14.7055i	1.01801	−	0.587749i
$627$	6.12745	+	1.64184i	0.244707	+	0.0655690i
$628$	0.285443	+	1.06529i	0.0113904	+	0.0425096i
$629$	−26.7559			−1.06683
$630$		0			0
$631$	7.53463			0.299949			0.149974	−	0.988690i	$-0.452081\pi$
$631$	7.53463			0.299949			0.149974	+	0.988690i	$0.452081\pi$
$632$	1.61706	+	6.03495i	0.0643232	+	0.240058i
$633$	5.47879	+	1.46804i	0.217762	+	0.0583492i
$634$	−3.71869	+	2.14699i	−0.147688	+	0.0852677i
$635$	−13.3112	−	6.13457i	−0.528237	−	0.243443i
$636$		−	0.400741i		−	0.0158904i
$637$		0			0
$638$	12.5507	+	12.5507i	0.496887	+	0.496887i
$639$	−12.0640	−	6.96513i	−0.477243	−	0.275536i
$640$	1.29076	+	1.82591i	0.0510217	+	0.0721754i
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	0.519233	−	0.854633i	$-0.326218\pi$
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	−0.999750	+	0.0223521i	$0.992885\pi$
$642$	−0.783903	+	0.210046i	−0.0309382	+	0.00828986i
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	−0.818989	−	0.573809i	$-0.805465\pi$
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	0.573809	+	0.818989i	$0.305465\pi$
$644$		0			0
$645$	1.08763	−	1.30805i	0.0428252	−	0.0515045i
$646$	−10.3303	+	17.8925i	−0.406439	+	0.703973i
$647$	−5.33869	+	19.9243i	−0.209886	+	0.783304i	0.778019	+	0.628241i	$0.216225\pi$
$647$	−5.33869	+	19.9243i	−0.209886	+	0.783304i	−0.987905	+	0.155063i	$0.950442\pi$
$648$	2.13565	−	7.97036i	0.0838963	−	0.313105i
$649$	15.4102	−	26.6913i	0.604905	−	1.04773i
$650$	9.93921	−	1.84463i	0.389848	−	0.0723523i
$651$		0			0
$652$	−9.36288	+	9.36288i	−0.366679	+	0.366679i
$653$	−25.2490	+	6.76544i	−0.988069	+	0.264752i	−0.716439	−	0.697650i	$-0.754229\pi$
$653$	−25.2490	+	6.76544i	−0.988069	+	0.264752i	−0.271630	+	0.962402i	$0.587563\pi$
$654$	0.856296	+	1.48315i	0.0334838	+	0.0579957i
$655$	2.91199	−	16.9591i	0.113781	−	0.662649i
$656$	−6.24448	−	3.60525i	−0.243806	−	0.140761i
$657$	11.5723	+	11.5723i	0.451478	+	0.451478i
$658$		0			0
$659$		−	24.2448i		−	0.944443i	−0.881480	−	0.472222i	$-0.843452\pi$
$659$		−	24.2448i		−	0.944443i	0.881480	−	0.472222i	$-0.156548\pi$
$660$	1.52551	−	3.31016i	0.0593806	−	0.128848i
$661$	−15.5301	+	8.96630i	−0.604050	+	0.348749i	−0.770633	−	0.637279i	$-0.780060\pi$
$661$	−15.5301	+	8.96630i	−0.604050	+	0.348749i	0.166583	+	0.986027i	$0.446727\pi$
$662$	−34.2419	−	9.17510i	−1.33085	−	0.356600i
$663$	0.804871	+	3.00382i	0.0312586	+	0.116659i
$664$	−8.02257			−0.311336
$665$		0			0
$666$	−14.6968			−0.569491
$667$	0.917769	+	3.42516i	0.0355362	+	0.132623i
$668$	6.42961	+	1.72281i	0.248769	+	0.0666574i
$669$	0.518181	−	0.299172i	0.0200340	−	0.0115667i
$670$	−1.77258	+	0.654184i	−0.0684807	+	0.0252733i
$671$		−	25.9305i		−	1.00104i
$672$		0			0
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	0.607340	−	0.794442i	$-0.292237\pi$
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	−0.794442	+	0.607340i	$0.792237\pi$
$674$	−14.8774	−	8.58946i	−0.573056	−	0.330854i
$675$	8.54424	+	0.670353i	0.328868	+	0.0258019i
$676$	−4.45619	−	7.71834i	−0.171392	−	0.296859i
$677$	17.8506	−	4.78306i	0.686055	−	0.183828i	0.101079	−	0.994878i	$-0.467771\pi$
$677$	17.8506	−	4.78306i	0.686055	−	0.183828i	0.584976	+	0.811051i	$0.301104\pi$
$678$	3.93514	−	3.93514i	0.151128	−	0.151128i
$679$		0			0
$680$	9.12760	+	7.58946i	0.350027	+	0.291043i
$681$	2.70083	−	4.67797i	0.103496	−	0.179260i
$682$	5.60357	−	20.9128i	0.214572	−	0.800793i
$683$	−6.93661	+	25.8878i	−0.265422	+	0.990569i	0.696569	+	0.717489i	$0.254709\pi$
$683$	−6.93661	+	25.8878i	−0.265422	+	0.990569i	−0.961992	+	0.273079i	$0.911958\pi$
$684$	−5.67435	+	9.82827i	−0.216964	+	0.375793i
$685$	−1.81023	−	19.6743i	−0.0691653	−	0.751717i
$686$		0			0
$687$	−0.821071	+	0.821071i	−0.0313258	+	0.0313258i
$688$	2.53629	−	0.679597i	0.0966951	−	0.0259094i
$689$	−1.39819	−	2.42173i	−0.0532667	−	0.0922606i
$690$	0.594591	−	0.420324i	0.0226357	−	0.0160015i
$691$	−25.1773	−	14.5361i	−0.957790	−	0.552980i	−0.0622976	−	0.998058i	$-0.519843\pi$
$691$	−25.1773	−	14.5361i	−0.957790	−	0.552980i	−0.895492	+	0.445077i	$0.853176\pi$
$692$	−4.98835	−	4.98835i	−0.189628	−	0.189628i
$693$		0			0
$694$		−	8.97626i		−	0.340734i
$695$	−8.56502	−	23.2078i	−0.324890	−	0.880323i
$696$	0.791655	−	0.457062i	0.0300076	−	0.0173249i
$697$	−36.9743	−	9.90723i	−1.40050	−	0.375263i
$698$	−6.73580	−	25.1383i	−0.254954	−	0.951500i
$699$	3.97855			0.150483
$700$		0			0
$701$	25.4462			0.961089			0.480545	−	0.876970i	$-0.340439\pi$
$701$	25.4462			0.961089			0.480545	+	0.876970i	$0.340439\pi$
$702$	0.896949	+	3.34746i	0.0338531	+	0.126342i
$703$	18.9462	+	5.07663i	0.714571	+	0.191469i
$704$	4.87205	−	2.81288i	0.183622	−	0.106014i
$705$	−1.32247	−	3.58337i	−0.0498071	−	0.134957i
$706$		−	9.96618i		−	0.375082i
$707$		0			0
$708$	−1.12240	−	1.12240i	−0.0421823	−	0.0421823i
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.914537	−	0.404503i	$-0.132555\pi$
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.106958	+	0.994263i	$0.465889\pi$
$710$	8.72254	−	6.16608i	0.327351	−	0.231409i
$711$	9.10952	+	15.7781i	0.341634	+	0.591727i
$712$	11.5156	−	3.08559i	0.431565	−	0.115637i
$713$	3.05850	−	3.05850i	0.114542	−	0.114542i
$714$		0			0
$715$	−2.33027	−	25.3263i	−0.0871470	−	0.947149i
$716$	1.10317	−	1.91075i	0.0412275	−	0.0714081i
$717$	1.47445	−	5.50271i	0.0550642	−	0.205502i
$718$	2.99560	−	11.1797i	0.111795	−	0.417224i
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	−0.949001	−	0.315273i	$-0.897904\pi$
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	0.747535	+	0.664222i	$0.231237\pi$
$720$	5.01373	+	4.16885i	0.186851	+	0.155364i
$721$		0			0
$722$	−2.72509	+	2.72509i	−0.101417	+	0.101417i
$723$	1.64704	−	0.441322i	0.0612539	−	0.0164129i
$724$	−2.05934	−	3.56688i	−0.0765347	−	0.132562i
$725$	−10.2480	−	11.9930i	−0.380602	−	0.445408i
$726$	−5.18128	−	2.99141i	−0.192295	−	0.111022i
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.957231	+	0.289326i	$0.0934311\pi$
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.289326	+	0.957231i	$0.406569\pi$
$728$		0			0
$729$		−	22.5720i		−	0.835998i
$730$	−11.7732	+	4.34500i	−0.435747	+	0.160816i
$731$	12.0719	−	6.96972i	0.446496	−	0.257785i
$732$	−1.28996	−	0.345644i	−0.0476784	−	0.0127754i
$733$	−6.66658	−	24.8800i	−0.246236	−	0.918964i	−0.972758	−	0.231822i	$-0.925531\pi$
$733$	−6.66658	−	24.8800i	−0.246236	−	0.918964i	0.726523	−	0.687143i	$-0.241135\pi$
$734$	−16.6944			−0.616202
$735$		0			0
$736$	1.12392			0.0414283
$737$	1.23034	+	4.59170i	0.0453203	+	0.169138i
$738$	−20.3098	−	5.44198i	−0.747613	−	0.200322i
$739$	−10.4948	+	6.05920i	−0.386059	+	0.222891i	−0.680451	−	0.732793i	$-0.738216\pi$
$739$	−10.4948	+	6.05920i	−0.386059	+	0.222891i	0.294392	+	0.955685i	$0.404883\pi$
$740$	4.71693	−	10.2351i	0.173398	−	0.376250i
$741$		−	2.27977i		−	0.0837493i
$742$		0			0
$743$	23.2618	+	23.2618i	0.853393	+	0.853393i	0.990549	−	0.137157i	$-0.0437964\pi$
$743$	23.2618	+	23.2618i	0.853393	+	0.853393i	−0.137157	+	0.990549i	$0.543796\pi$
$744$	−0.965654	−	0.557521i	−0.0354026	−	0.0204397i
$745$	1.91053	−	11.1267i	0.0699964	−	0.407652i
$746$	−1.58946	−	2.75303i	−0.0581944	−	0.100796i
$747$	−22.5971	+	6.05487i	−0.826784	+	0.221536i
$748$	21.1182	−	21.1182i	0.772158	−	0.772158i
$749$		0			0
$750$	−1.58179	+	2.82690i	−0.0577587	+	0.103224i
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	−0.964903	−	0.262607i	$-0.915418\pi$
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	0.709875	+	0.704327i	$0.248751\pi$
$752$	1.52590	−	5.69475i	0.0556440	−	0.207666i
$753$	−0.532387	+	1.98690i	−0.0194013	+	0.0724065i
$754$	3.18939	−	5.52418i	0.116151	−	0.201179i
$755$	−19.2181	+	23.1130i	−0.699420	+	0.841169i
$756$		0			0
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	−0.312035	−	0.950071i	$-0.601010\pi$
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	0.950071	+	0.312035i	$0.101010\pi$
$758$	6.90974	−	1.85146i	0.250973	−	0.0672481i
$759$	−0.915990	−	1.58654i	−0.0332483	−	0.0575878i
$760$	−5.02338	−	7.10608i	−0.182217	−	0.257765i
$761$	−18.9372	−	10.9334i	−0.686471	−	0.396334i	0.115817	−	0.993271i	$-0.463051\pi$
$761$	−18.9372	−	10.9334i	−0.686471	−	0.396334i	−0.802289	+	0.596936i	$0.796385\pi$
$762$	1.34289	+	1.34289i	0.0486478	+	0.0486478i
$763$		0			0
$764$			17.2023i			0.622359i
$765$	31.4376	+	14.4883i	1.13663	+	0.523826i
$766$	−12.6382	+	7.29669i	−0.456638	+	0.263640i
$767$	−10.6989	−	2.86675i	−0.386313	−	0.103512i
$768$	−0.0749894	−	0.279864i	−0.00270595	−	0.0100987i
$769$	31.0506			1.11971			0.559857	−	0.828589i	$-0.310856\pi$
$769$	31.0506			1.11971			0.559857	+	0.828589i	$0.310856\pi$
$770$		0			0
$771$	2.86459			0.103166
$772$	−3.12327	−	11.6562i	−0.112409	−	0.419516i
$773$	5.86173	+	1.57065i	0.210832	+	0.0564922i	0.362689	−	0.931910i	$-0.381859\pi$
$773$	5.86173	+	1.57065i	0.210832	+	0.0564922i	−0.151857	+	0.988402i	$0.548525\pi$
$774$	6.63103	−	3.82843i	0.238347	−	0.137610i
$775$	−6.41880	+	18.1402i	−0.230570	+	0.651614i
$776$			9.37769i			0.336640i
$777$		0			0
$778$	−4.38160	−	4.38160i	−0.157088	−	0.157088i
$779$	24.3023	+	14.0309i	0.870720	+	0.502710i
$780$	−1.29097	−	0.221667i	−0.0462240	−	0.00793694i
$781$	−13.4374	−	23.2743i	−0.480828	−	0.832819i
$782$	5.76329	−	1.54427i	0.206095	−	0.0552229i
$783$	3.82404	−	3.82404i	0.136660	−	0.136660i
$784$		0			0
$785$	−2.45571	+	0.225950i	−0.0876481	+	0.00806449i
$786$	−1.11481	+	1.93091i	−0.0397641	+	0.0688734i
$787$	5.78752	−	21.5993i	0.206303	−	0.769932i	−0.782746	−	0.622342i	$-0.786182\pi$
$787$	5.78752	−	21.5993i	0.206303	−	0.769932i	0.989049	−	0.147591i	$-0.0471518\pi$
$788$	−5.23910	+	19.5526i	−0.186635	+	0.696532i
$789$	1.99167	−	3.44968i	0.0709055	−	0.122812i
$790$	−13.9118	+	1.28003i	−0.494961	+	0.0455413i
$791$		0			0
$792$	11.6001	−	11.6001i	0.412191	−	0.412191i
$793$	−9.00138	+	2.41191i	−0.319648	+	0.0856495i
$794$	−1.45794	−	2.52523i	−0.0517403	−	0.0896169i
$795$	0.883159	+	0.151644i	0.0313224	+	0.00537825i
$796$	6.52383	+	3.76653i	0.231231	+	0.133501i
$797$	16.5528	+	16.5528i	0.586330	+	0.586330i	0.936636	−	0.350305i	$-0.113922\pi$
$797$	16.5528	+	16.5528i	0.586330	+	0.586330i	−0.350305	+	0.936636i	$0.613922\pi$
$798$		0			0
$799$		−	31.2984i		−	1.10726i
$800$	−4.51240	+	2.15365i	−0.159538	+	0.0761432i
$801$	30.1070	−	17.3823i	1.06378	−	0.614174i
$802$	19.2901	+	5.16876i	0.681156	+	0.182515i
$803$	8.17177	+	30.4975i	0.288376	+	1.07623i
$804$	0.244823			0.00863425
$805$		0			0
$806$	−7.78078			−0.274066
$807$	−1.98737	−	7.41697i	−0.0699588	−	0.261090i
$808$	15.5506	+	4.16678i	0.547069	+	0.146587i
$809$	−2.84139	+	1.64048i	−0.0998980	+	0.0576762i	−0.549117	−	0.835746i	$-0.685036\pi$
$809$	−2.84139	+	1.64048i	−0.0998980	+	0.0576762i	0.449219	+	0.893422i	$0.351702\pi$
$810$	16.7571	+	7.72263i	0.588783	+	0.271346i
$811$		−	17.8693i		−	0.627476i	−0.949510	−	0.313738i	$-0.898419\pi$
$811$		−	17.8693i		−	0.627476i	0.949510	−	0.313738i	$-0.101581\pi$
$812$		0			0
$813$	2.62176	+	2.62176i	0.0919491	+	0.0919491i
$814$	−24.5550	−	14.1768i	−0.860653	−	0.496898i
$815$	−17.0911	−	24.1771i	−0.598674	−	0.846886i
$816$	−0.769067	−	1.33206i	−0.0269227	−	0.0466316i
$817$	−9.87074	+	2.64486i	−0.345333	+	0.0925318i
$818$	−24.2949	+	24.2949i	−0.849451	+	0.849451i
$819$		0			0
$820$	10.3083	−	12.3974i	0.359981	−	0.432937i
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	−0.744312	−	0.667832i	$-0.767222\pi$
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	0.950516	+	0.310677i	$0.100556\pi$
$822$	−0.662590	+	2.47282i	−0.0231105	+	0.0862495i
$823$	9.13692	−	34.0995i	0.318493	−	1.18863i	−0.602200	−	0.798345i	$-0.705709\pi$
$823$	9.13692	−	34.0995i	0.318493	−	1.18863i	0.920693	−	0.390287i	$-0.127624\pi$
$824$	−9.83476	+	17.0343i	−0.342610	+	0.593418i
$825$	6.71771	+	4.61455i	0.233881	+	0.160658i
$826$		0			0
$827$	−17.2835	+	17.2835i	−0.601005	+	0.601005i	−0.940579	−	0.339574i	$-0.889717\pi$
$827$	−17.2835	+	17.2835i	−0.601005	+	0.601005i	0.339574	+	0.940579i	$0.389717\pi$
$828$	3.16574	−	0.848257i	0.110017	−	0.0294790i
$829$	17.2877	+	29.9431i	0.600426	+	1.03997i	0.992756	+	0.120144i	$0.0383357\pi$
$829$	17.2877	+	29.9431i	0.600426	+	1.03997i	−0.392330	+	0.919824i	$0.628331\pi$
$830$	3.03581	−	17.6803i	0.105374	−	0.613691i
$831$	−5.04433	−	2.91234i	−0.174986	−	0.101028i
$832$	−1.42962	−	1.42962i	−0.0495631	−	0.0495631i
$833$		0			0
$834$			3.20539i			0.110994i
$835$	−6.22977	+	13.5177i	−0.215590	+	0.467801i
$836$	−18.9611	+	10.9472i	−0.655782	+	0.378616i
$837$	−6.37187	−	1.70734i	−0.220244	−	0.0590142i
$838$	−8.05859	−	30.0751i	−0.278379	−	1.03893i
$839$	−50.1328			−1.73078			−0.865388	−	0.501102i	$-0.832928\pi$
$839$	−50.1328			−1.73078			−0.865388	+	0.501102i	$0.832928\pi$
$840$		0			0
$841$	19.0459			0.656754
$842$	−8.71515	−	32.5254i	−0.300344	−	1.12090i
$843$	−3.96003	−	1.06109i	−0.136391	−	0.0365458i
$844$	−16.9538	+	9.78829i	−0.583575	+	0.336927i
$845$	18.6961	−	6.89993i	0.643164	−	0.237365i
$846$		−	17.1920i		−	0.591073i
$847$		0			0
$848$	0.978013	+	0.978013i	0.0335851	+	0.0335851i
$849$	6.79181	+	3.92125i	0.233094	+	0.134577i
$850$	−20.1797	+	17.2436i	−0.692160	+	0.591452i
$851$	−2.83227	−	4.90563i	−0.0970888	−	0.168163i
$852$	−1.33694	+	0.358232i	−0.0458028	+	0.0122728i
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	−0.746596	−	0.665278i	$-0.768313\pi$
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	0.665278	+	0.746596i	$0.268313\pi$
$854$		0			0
$855$	−19.5125	−	16.2243i	−0.667312	−	0.554860i
$856$	1.40051	−	2.42575i	0.0478683	−	0.0829103i
$857$	10.8545	−	40.5097i	0.370784	−	1.38378i	−0.488624	−	0.872494i	$-0.662501\pi$
$857$	10.8545	−	40.5097i	0.370784	−	1.38378i	0.859408	−	0.511290i	$-0.170832\pi$
$858$	−0.852937	+	3.18320i	−0.0291188	+	0.108673i
$859$	−1.17847	+	2.04117i	−0.0402090	+	0.0696440i	−0.885430	−	0.464774i	$-0.846136\pi$
$859$	−1.17847	+	2.04117i	−0.0402090	+	0.0696440i	0.845221	+	0.534418i	$0.179469\pi$
$860$	0.537952	+	5.84668i	0.0183440	+	0.199370i
$861$		0			0
$862$	−10.4268	+	10.4268i	−0.355137	+	0.355137i
$863$	−46.7022	+	12.5138i	−1.58976	+	0.425975i	−0.941930	−	0.335808i	$-0.890991\pi$
$863$	−46.7022	+	12.5138i	−1.58976	+	0.425975i	−0.647831	+	0.761784i	$0.724324\pi$
$864$	−0.857049	−	1.48445i	−0.0291574	−	0.0505021i
$865$	12.8810	−	9.10577i	0.437968	−	0.309605i
$866$	−12.2261	−	7.05873i	−0.415459	−	0.239865i
$867$	−2.29104	−	2.29104i	−0.0778076	−	0.0778076i
$868$		0			0
$869$			35.1489i			1.19234i
$870$	0.707712	+	1.91762i	0.0239937	+	0.0650133i
$871$	1.47950	−	0.854190i	0.0501310	−	0.0289431i
$872$	−5.70944	−	1.52984i	−0.193346	−	0.0518069i
$873$	7.07763	+	26.4141i	0.239541	+	0.893980i
$874$	−4.37408			−0.147955
$875$		0			0
$876$	1.62608			0.0549402
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	0.879194	−	0.476465i	$-0.158082\pi$
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	−0.999636	+	0.0269665i	$0.991415\pi$
$878$	37.1191	+	9.94602i	1.25271	+	0.335662i
$879$	6.07477	−	3.50727i	0.204897	−	0.118297i
$880$	4.35544	+	11.8015i	0.146822	+	0.397829i
$881$		−	3.32542i		−	0.112036i	−0.998430	−	0.0560181i	$-0.982160\pi$
$881$		−	3.32542i		−	0.112036i	0.998430	−	0.0560181i	$-0.0178405\pi$
$882$		0			0
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.959358	−	0.282191i	$-0.908939\pi$
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.282191	−	0.959358i	$-0.591061\pi$
$884$	−9.29516	−	5.36656i	−0.312630	−	0.180497i
$885$	2.89828	−	2.04883i	0.0974247	−	0.0688708i
$886$	−2.86780	−	4.96718i	−0.0963456	−	0.166876i
$887$	34.6001	−	9.27107i	1.16176	−	0.311292i	0.374090	−	0.927392i	$-0.377955\pi$
$887$	34.6001	−	9.27107i	1.16176	−	0.311292i	0.787668	+	0.616101i	$0.211289\pi$
$888$	−1.03256	+	1.03256i	−0.0346506	+	0.0346506i
$889$		0			0
$890$	2.44248	+	26.5458i	0.0818721	+	0.889819i
$891$	23.2105	−	40.2018i	0.777582	−	1.34681i
$892$	−0.534495	+	1.99476i	−0.0178962	+	0.0667895i
$893$	−5.93852	+	22.1628i	−0.198725	+	0.741651i
$894$	−0.731419	+	1.26686i	−0.0244623	+	0.0423700i
$895$	3.79349	+	3.15423i	0.126803	+	0.105434i
$896$		0			0
$897$	−0.465543	+	0.465543i	−0.0155440	+	0.0155440i
$898$	7.05384	−	1.89007i	0.235390	−	0.0630725i
$899$	6.07098	+	10.5152i	0.202479	+	0.350703i
$900$	−11.0846	+	9.47182i	−0.369487	+	0.315727i
$901$	6.35888	+	3.67130i	0.211845	+	0.122309i
$902$	−28.6835	−	28.6835i	−0.955055	−	0.955055i
$903$		0			0
$904$			19.2075i			0.638833i
$905$	8.64001	−	3.18866i	0.287204	−	0.105995i
$906$	3.37307	−	1.94744i	0.112063	−	0.0646994i
$907$	16.6696	+	4.46661i	0.553506	+	0.148312i	0.524721	−	0.851274i	$-0.324170\pi$
$907$	16.6696	+	4.46661i	0.553506	+	0.148312i	0.0287849	+	0.999586i	$0.490836\pi$
$908$	4.82525	+	18.0081i	0.160131	+	0.597618i
$909$	46.9461			1.55710
$910$		0			0
$911$	5.56820			0.184483			0.0922414	−	0.995737i	$-0.470597\pi$
$911$	5.56820			0.184483			0.0922414	+	0.995737i	$0.470597\pi$
$912$	0.291844	+	1.08918i	0.00966392	+	0.0360663i
$913$	−43.5952	−	11.6813i	−1.44279	−	0.386594i
$914$	−4.45641	+	2.57291i	−0.147405	+	0.0851042i
$915$	1.24987	−	2.71205i	0.0413194	−	0.0896575i
$916$		−	4.00767i		−	0.132417i
$917$		0			0
$918$	−6.43445	−	6.43445i	−0.212368	−	0.212368i
$919$	−5.37964	−	3.10593i	−0.177458	−	0.102455i	0.408640	−	0.912696i	$-0.366003\pi$
$919$	−5.37964	−	3.10593i	−0.177458	−	0.102455i	−0.586098	+	0.810240i	$0.699337\pi$
$920$	−0.425302	+	2.47692i	−0.0140218	+	0.0816615i
$921$	3.54381	+	6.13806i	0.116773	+	0.202256i
$922$	−28.4088	+	7.61212i	−0.935595	+	0.250692i
$923$	−6.82943	+	6.82943i	−0.224794	+	0.224794i
$924$		0			0
$925$	20.7713	+	14.2683i	0.682958	+	0.469139i
$926$	2.86113	−	4.95563i	0.0940226	−	0.162852i
$927$	−14.8452	+	55.4029i	−0.487579	+	1.81967i
$928$	−0.816578	+	3.04751i	−0.0268055	+	0.100039i
$929$	0.0947297	−	0.164077i	0.00310798	−	0.00538318i	−0.864467	−	0.502689i	$-0.832344\pi$
$929$	0.0947297	−	0.164077i	0.00310798	−	0.00538318i	0.867575	+	0.497306i	$0.165677\pi$
$930$	1.59409	−	1.91715i	0.0522721	−	0.0628660i
$931$		0			0
$932$	−9.70971	+	9.70971i	−0.318052	+	0.318052i
$933$	3.07355	−	0.823556i	0.100624	−	0.0269620i
$934$	−8.32139	−	14.4131i	−0.272284	−	0.471610i
$935$	38.5493	+	54.5319i	1.26070	+	1.78338i
$936$	−5.10577	−	2.94782i	−0.166887	−	0.0963525i
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.992131	−	0.125208i	$-0.960040\pi$
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.125208	−	0.992131i	$-0.539960\pi$
$938$		0			0
$939$		−	8.52144i		−	0.278087i
$940$	11.9728	+	5.51775i	0.390509	+	0.179969i
$941$	16.3826	−	9.45851i	0.534058	−	0.308339i	−0.208609	−	0.977999i	$-0.566894\pi$
$941$	16.3826	−	9.45851i	0.534058	−	0.308339i	0.742667	+	0.669660i	$0.233560\pi$
$942$	0.308653	+	0.0827033i	0.0100565	+	0.00269462i
$943$	−2.09748	−	7.82790i	−0.0683033	−	0.254911i
$944$	5.47845			0.178308
$945$		0			0
$946$	14.7719			0.480276
$947$	12.2033	+	45.5435i	0.396555	+	1.47996i	0.819115	+	0.573629i	$0.194465\pi$
$947$	12.2033	+	45.5435i	0.396555	+	1.47996i	−0.422560	+	0.906335i	$0.638869\pi$
$948$	1.74855	+	0.468522i	0.0567902	+	0.0152169i
$949$	9.82664	−	5.67341i	0.318986	−	0.184167i
$950$	17.5614	−	8.38160i	0.569767	−	0.271935i
$951$			1.24412i			0.0403434i
$952$		0			0
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	0.943047	−	0.332658i	$-0.107946\pi$
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	−0.332658	+	0.943047i	$0.607946\pi$
$954$	3.49290	+	2.01662i	0.113087	+	0.0652906i
$955$	−37.9108	−	6.50952i	−1.22677	−	0.210643i
$956$	9.83103	+	17.0278i	0.317958	+	0.550720i
$957$	4.96741	−	1.33101i	0.160574	−	0.0430256i
$958$	−10.8818	+	10.8818i	−0.351575	+	0.351575i
$959$		0			0
$960$	0.645146	−	0.0593598i	0.0208220	−	0.00191583i
$961$	−8.09467	+	14.0204i	−0.261118	+	0.452270i
$962$	−2.63730	+	9.84255i	−0.0850301	+	0.317337i
$963$	2.11401	−	7.88958i	0.0681229	−	0.254238i
$964$	−2.94256	+	5.09667i	−0.0947735	+	0.164153i
$965$	26.8700	−	2.47231i	0.864976	−	0.0795863i
$966$		0			0
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	−0.113383	−	0.993551i	$-0.536169\pi$
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	0.993551	+	0.113383i	$0.0361687\pi$
$968$	19.9456	−	5.34440i	0.641075	−	0.171776i
$969$	2.99306	+	5.18413i	0.0961509	+	0.166538i
$970$	−20.6667	−	3.54860i	−0.663568	−	0.113939i
$971$	27.8750	+	16.0936i	0.894550	+	0.516469i	0.875428	−	0.483348i	$-0.160580\pi$
$971$	27.8750	+	16.0936i	0.894550	+	0.516469i	0.0191221	+	0.999817i	$0.493913\pi$
$972$	−5.32668	−	5.32668i	−0.170853	−	0.170853i
$973$		0			0
$974$			35.9920i			1.15326i
$975$	0.977025	−	2.76117i	0.0312899	−	0.0884282i
$976$	3.99172	−	2.30462i	0.127772	−	0.0737691i
$977$	22.4848	+	6.02479i	0.719353	+	0.192750i	0.599883	−	0.800088i	$-0.295214\pi$
$977$	22.4848	+	6.02479i	0.719353	+	0.192750i	0.119470	+	0.992838i	$0.461881\pi$
$978$	0.992944	+	3.70572i	0.0317508	+	0.118496i
$979$	67.0692			2.14354
$980$		0			0
$981$	−17.2364			−0.550314
$982$	−3.95535	−	14.7616i	−0.126220	−	0.471060i
$983$	−55.0964	−	14.7630i	−1.75730	−	0.470868i	−0.771143	−	0.636662i	$-0.780315\pi$
$983$	−55.0964	−	14.7630i	−1.75730	−	0.470868i	−0.986160	+	0.165793i	$0.946981\pi$
$984$	−1.80926	+	1.04457i	−0.0576770	+	0.0332998i
$985$	−41.1078	−	18.9449i	−1.30980	−	0.603634i
$986$			16.7491i			0.533401i
$987$		0			0
$988$	5.56380	+	5.56380i	0.177008	+	0.177008i
$989$	2.55577	+	1.47557i	0.0812687	+	0.0469205i
$990$	21.1749	+	29.9541i	0.672983	+	0.952002i
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.808478	+	0.588526i	$0.200292\pi$
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.105440	+	0.994426i	$0.466375\pi$
$992$	3.71733	−	0.996056i	0.118025	−	0.0316248i
$993$	−7.26279	+	7.26279i	−0.230478	+	0.230478i
$994$		0			0
$995$	−10.7694	+	12.9520i	−0.341414	+	0.410607i
$996$	−1.16222	+	2.01302i	−0.0368262	+	0.0637849i
$997$	−6.27762	+	23.4284i	−0.198814	+	0.741985i	0.792432	+	0.609960i	$0.208815\pi$
$997$	−6.27762	+	23.4284i	−0.198814	+	0.741985i	−0.991246	+	0.132025i	$0.957852\pi$
$998$	−8.17479	+	30.5087i	−0.258768	+	0.965737i
$999$	−4.31951	+	7.48160i	−0.136663	+	0.236707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.c.313.4		16
5.2	odd	4	inner	490.2.l.c.117.2		16
7.2	even	3		490.2.g.c.293.6		16
7.3	odd	6	inner	490.2.l.c.423.2		16
7.4	even	3		70.2.k.a.3.1	✓	16
7.5	odd	6		490.2.g.c.293.7		16
7.6	odd	2		70.2.k.a.33.3	yes	16
21.11	odd	6		630.2.bv.c.73.3		16
21.20	even	2		630.2.bv.c.523.1		16
28.11	odd	6		560.2.ci.c.353.3		16
28.27	even	2		560.2.ci.c.33.3		16
35.2	odd	12		490.2.g.c.97.7		16
35.4	even	6		350.2.o.c.143.4		16
35.12	even	12		490.2.g.c.97.6		16
35.13	even	4		350.2.o.c.257.4		16
35.17	even	12	inner	490.2.l.c.227.4		16
35.18	odd	12		350.2.o.c.157.2		16
35.27	even	4		70.2.k.a.47.1	yes	16
35.32	odd	12		70.2.k.a.17.3	yes	16
35.34	odd	2		350.2.o.c.243.2		16
105.32	even	12		630.2.bv.c.577.1		16
105.62	odd	4		630.2.bv.c.397.3		16
140.27	odd	4		560.2.ci.c.257.3		16
140.67	even	12		560.2.ci.c.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	7.4	even	3
70.2.k.a.17.3	yes	16	35.32	odd	12
70.2.k.a.33.3	yes	16	7.6	odd	2
70.2.k.a.47.1	yes	16	35.27	even	4
350.2.o.c.143.4		16	35.4	even	6
350.2.o.c.157.2		16	35.18	odd	12
350.2.o.c.243.2		16	35.34	odd	2
350.2.o.c.257.4		16	35.13	even	4
490.2.g.c.97.6		16	35.12	even	12
490.2.g.c.97.7		16	35.2	odd	12
490.2.g.c.293.6		16	7.2	even	3
490.2.g.c.293.7		16	7.5	odd	6
490.2.l.c.117.2		16	5.2	odd	4	inner
490.2.l.c.227.4		16	35.17	even	12	inner
490.2.l.c.313.4		16	1.1	even	1	trivial
490.2.l.c.423.2		16	7.3	odd	6	inner
560.2.ci.c.17.3		16	140.67	even	12
560.2.ci.c.33.3		16	28.27	even	2
560.2.ci.c.257.3		16	140.27	odd	4
560.2.ci.c.353.3		16	28.11	odd	6
630.2.bv.c.73.3		16	21.11	odd	6
630.2.bv.c.397.3		16	105.62	odd	4
630.2.bv.c.523.1		16	21.20	even	2
630.2.bv.c.577.1		16	105.32	even	12

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.279864 + 0.0749894i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +(-2.52538 - 1.45803i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.279864 + 0.0749894i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +(-2.52538 - 1.45803i) q^{9} +(1.82591 - 1.29076i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(-0.279864 + 0.0749894i) q^{12} +(-1.42962 + 1.42962i) q^{13} +(-0.0593598 - 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.37400 - 5.12784i) q^{17} +(0.754730 - 2.81669i) q^{18} +(-1.94590 + 3.37040i) q^{19} +(1.71936 + 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(1.08562 - 0.290892i) q^{23} +(-0.144868 - 0.250919i) q^{24} +(-3.80124 + 3.24817i) q^{25} +(-1.75092 - 1.01089i) q^{26} +(-1.21205 - 1.21205i) q^{27} +3.15502i q^{29} +(0.607800 - 0.224313i) q^{30} +(3.33287 - 1.92423i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.421872 - 1.57445i) q^{33} +5.30873 q^{34} +2.91605 q^{36} +(-1.30444 - 4.86824i) q^{37} +(-3.75919 - 1.00727i) q^{38} +(-0.507306 + 0.292893i) q^{39} +(-0.935904 + 2.03078i) q^{40} -7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} +(4.87205 + 2.81288i) q^{44} +(-1.10346 + 6.42644i) q^{45} +(0.561961 + 0.973344i) q^{46} +(5.69475 - 1.52590i) q^{47} +(0.204875 - 0.204875i) q^{48} +(-4.12132 - 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(0.523277 - 1.95290i) q^{52} +(-0.357978 + 1.33599i) q^{53} +(0.857049 - 1.48445i) q^{54} +(-8.04270 + 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(-3.04751 + 0.816578i) q^{58} +(2.73923 + 4.74448i) q^{59} +(0.373980 + 0.529033i) q^{60} +(3.99172 + 2.30462i) q^{61} +(2.72127 + 2.72127i) q^{62} +1.00000i q^{64} +(4.10581 + 1.89220i) q^{65} +(1.41161 - 0.814995i) q^{66} +(-0.816193 - 0.218698i) q^{67} +(1.37400 + 5.12784i) q^{68} +0.325641 q^{69} +4.77710 q^{71} +(0.754730 + 2.81669i) q^{72} +(-5.42104 - 1.45256i) q^{73} +(4.36475 - 2.51999i) q^{74} +(-1.30741 + 0.623993i) q^{75} -3.89180i q^{76} +(-0.414214 - 0.414214i) q^{78} +(-5.41079 - 3.12392i) q^{79} +(-2.20382 - 0.378409i) q^{80} +(4.12576 + 7.14603i) q^{81} +(6.96481 - 1.86622i) q^{82} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(-0.236593 + 0.882976i) q^{87} +(-1.45605 + 5.43407i) q^{88} +(-5.96090 + 10.3246i) q^{89} +(-6.49307 + 0.597426i) q^{90} +(-0.794732 + 0.794732i) q^{92} +(1.07705 - 0.288594i) q^{93} +(2.94782 + 5.10577i) q^{94} +(8.57682 + 1.47269i) q^{95} +(0.250919 + 0.144868i) q^{96} +(-6.63103 - 6.63103i) q^{97} +16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5}+O(q^{10}) \) 16 * q + 12 * q^5	\( 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) \) 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

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