LMFDB - Embedded newform 875.2.bb.a.857.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			857.2
Character	$\chi$	$=$	875.857
Dual form			875.2.bb.a.243.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.58550 + 0.135500i) q^{2} +(-1.53862 + 1.90004i) q^{3} +(4.67742 - 0.491617i) q^{4} +(3.72066 - 5.12104i) q^{6} +(0.791332 - 2.52464i) q^{7} +(-6.91252 + 1.09484i) q^{8} +(-0.619060 - 2.91245i) q^{9} +(-5.30433 - 1.12747i) q^{11} +(-6.26269 + 9.64370i) q^{12} +(0.247532 - 0.126124i) q^{13} +(-1.70390 + 6.63468i) q^{14} +(8.52317 - 1.81165i) q^{16} +(-1.62286 + 4.22770i) q^{17} +(1.99522 + 7.44626i) q^{18} +(-0.00214840 + 0.0204407i) q^{19} +(3.57935 + 5.38803i) q^{21} +(13.8671 + 2.19634i) q^{22} +(-0.285728 - 5.45201i) q^{23} +(8.55552 - 14.8186i) q^{24} +(-0.622904 + 0.359634i) q^{26} +(-0.0489845 - 0.0249589i) q^{27} +(2.46024 - 12.1978i) q^{28} +(0.413497 + 0.569129i) q^{29} +(1.64234 + 3.68876i) q^{31} +(-8.27077 + 2.21615i) q^{32} +(10.3036 - 8.34369i) q^{33} +(3.62306 - 11.1506i) q^{34} +(-4.32741 - 13.3184i) q^{36} +(0.0199223 + 0.0129377i) q^{37} +(0.00278498 - 0.0531405i) q^{38} +(-0.141218 + 0.664377i) q^{39} +(5.37154 + 1.74532i) q^{41} +(-9.98451 - 13.4458i) q^{42} +(4.35752 - 4.35752i) q^{43} +(-25.3649 - 2.66596i) q^{44} +(1.47750 + 14.0575i) q^{46} +(3.21600 - 1.23451i) q^{47} +(-9.67172 + 18.9818i) q^{48} +(-5.74759 - 3.99565i) q^{49} +(-5.53583 - 9.58833i) q^{51} +(1.09581 - 0.711624i) q^{52} +(2.89407 + 2.34357i) q^{53} +(0.130032 + 0.0578938i) q^{54} +(-2.70603 + 18.3180i) q^{56} +(-0.0355325 - 0.0355325i) q^{57} +(-1.14621 - 1.41546i) q^{58} +(3.75527 + 4.17065i) q^{59} +(1.43060 + 1.28812i) q^{61} +(-4.74610 - 9.31476i) q^{62} +(-7.84276 - 0.741811i) q^{63} +(4.50960 - 1.46526i) q^{64} +(-25.5094 + 22.9688i) q^{66} +(14.1898 + 5.44695i) q^{67} +(-5.51240 + 20.5725i) q^{68} +(10.7987 + 7.84569i) q^{69} +(1.09682 - 0.796887i) q^{71} +(7.46791 + 19.4546i) q^{72} +(4.47058 + 6.88409i) q^{73} +(-0.0532622 - 0.0307510i) q^{74} +0.0966658i q^{76} +(-7.04394 + 12.4993i) q^{77} +(0.275095 - 1.73688i) q^{78} +(1.03233 - 2.31865i) q^{79} +(8.28307 - 3.68786i) q^{81} +(-14.1246 - 3.78468i) q^{82} +(1.06897 + 6.74923i) q^{83} +(19.3910 + 23.4424i) q^{84} +(-10.6759 + 11.8568i) q^{86} +(-1.71758 - 0.0900148i) q^{87} +(37.9007 + 1.98629i) q^{88} +(5.48864 - 6.09575i) q^{89} +(-0.122537 - 0.724733i) q^{91} +(-4.01677 - 25.3609i) q^{92} +(-9.53573 - 2.55509i) q^{93} +(-8.14770 + 3.62759i) q^{94} +(8.51483 - 19.1246i) q^{96} +(-2.19595 + 13.8647i) q^{97} +(15.4018 + 9.55197i) q^{98} +16.1466i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.58550	+	0.135500i	−1.82823	+	0.0958133i	−0.935185	−	0.354160i	$-0.884767\pi$
$2$	−2.58550	+	0.135500i	−1.82823	+	0.0958133i	−0.893042	+	0.449974i	$0.851433\pi$
$3$	−1.53862	+	1.90004i	−0.888324	+	1.09699i	0.106392	+	0.994324i	$0.466070\pi$
$3$	−1.53862	+	1.90004i	−0.888324	+	1.09699i	−0.994716	+	0.102665i	$0.967263\pi$
$4$	4.67742	−	0.491617i	2.33871	−	0.245808i
$5$		0			0
$5$		0			0
$6$	3.72066	−	5.12104i	1.51895	−	2.09066i
$7$	0.791332	−	2.52464i	0.299095	−	0.954223i
$7$	0.791332	−	2.52464i	0.299095	−	0.954223i
$8$	−6.91252	+	1.09484i	−2.44394	+	0.387083i
$9$	−0.619060	−	2.91245i	−0.206353	−	0.970816i
$10$		0			0
$11$	−5.30433	−	1.12747i	−1.59932	−	0.339945i	−0.679922	−	0.733284i	$-0.737987\pi$
$11$	−5.30433	−	1.12747i	−1.59932	−	0.339945i	−0.919394	+	0.393339i	$0.871320\pi$
$12$	−6.26269	+	9.64370i	−1.80788	+	2.78390i
$13$	0.247532	−	0.126124i	0.0686529	−	0.0349804i	−0.419327	−	0.907835i	$-0.637734\pi$
$13$	0.247532	−	0.126124i	0.0686529	−	0.0349804i	0.487980	+	0.872855i	$0.337734\pi$
$14$	−1.70390	+	6.63468i	−0.455387	+	1.77319i
$15$		0			0
$16$	8.52317	−	1.81165i	2.13079	−	0.452914i
$17$	−1.62286	+	4.22770i	−0.393602	+	1.02537i	0.583409	+	0.812178i	$0.301718\pi$
$17$	−1.62286	+	4.22770i	−0.393602	+	1.02537i	−0.977011	+	0.213189i	$0.931615\pi$
$18$	1.99522	+	7.44626i	0.470278	+	1.75510i
$19$	−0.00214840	+	0.0204407i	−0.000492877	+	0.00468941i	−0.994766	−	0.102183i	$-0.967417\pi$
$19$	−0.00214840	+	0.0204407i	−0.000492877	+	0.00468941i	0.994273	+	0.106873i	$0.0340838\pi$
$20$		0			0
$21$	3.57935	+	5.38803i	0.781079	+	1.17576i
$22$	13.8671	+	2.19634i	2.95648	+	0.468261i
$23$	−0.285728	−	5.45201i	−0.0595784	−	1.13682i	−0.850867	−	0.525380i	$-0.823923\pi$
$23$	−0.285728	−	5.45201i	−0.0595784	−	1.13682i	0.791289	−	0.611442i	$-0.209410\pi$
$24$	8.55552	−	14.8186i	1.74639	−	3.02483i
$25$		0			0
$26$	−0.622904	+	0.359634i	−0.122162	+	0.0705300i
$27$	−0.0489845	−	0.0249589i	−0.00942707	−	0.00480333i
$28$	2.46024	−	12.1978i	0.464941	−	2.30517i
$29$	0.413497	+	0.569129i	0.0767844	+	0.105685i	0.845682	−	0.533688i	$-0.179194\pi$
$29$	0.413497	+	0.569129i	0.0767844	+	0.105685i	−0.768897	+	0.639372i	$0.779194\pi$
$30$		0			0
$31$	1.64234	+	3.68876i	0.294973	+	0.662520i	0.998857	−	0.0477944i	$-0.0152192\pi$
$31$	1.64234	+	3.68876i	0.294973	+	0.662520i	−0.703884	+	0.710315i	$0.748553\pi$
$32$	−8.27077	+	2.21615i	−1.46208	+	0.391763i
$33$	10.3036	−	8.34369i	1.79363	−	1.45245i
$34$	3.62306	−	11.1506i	0.621349	−	1.91232i
$35$		0			0
$36$	−4.32741	−	13.3184i	−0.721235	−	2.21973i
$37$	0.0199223	+	0.0129377i	0.00327521	+	0.00212694i	0.546276	−	0.837605i	$-0.316045\pi$
$37$	0.0199223	+	0.0129377i	0.00327521	+	0.00212694i	−0.543000	+	0.839732i	$0.682712\pi$
$38$	0.00278498	−	0.0531405i	0.000451783	−	0.00862053i
$39$	−0.141218	+	0.664377i	−0.0226129	+	0.106385i
$40$		0			0
$41$	5.37154	+	1.74532i	0.838894	+	0.272573i	0.696787	−	0.717278i	$-0.254612\pi$
$41$	5.37154	+	1.74532i	0.838894	+	0.272573i	0.142107	+	0.989851i	$0.454612\pi$
$42$	−9.98451	−	13.4458i	−1.54064	−	2.07472i
$43$	4.35752	−	4.35752i	0.664515	−	0.664515i	−0.291926	−	0.956441i	$-0.594296\pi$
$43$	4.35752	−	4.35752i	0.664515	−	0.664515i	0.956441	+	0.291926i	$0.0942961\pi$
$44$	−25.3649	−	2.66596i	−3.82390	−	0.401908i
$45$		0			0
$46$	1.47750	+	14.0575i	0.217845	+	2.07266i
$47$	3.21600	−	1.23451i	0.469102	−	0.180071i	−0.112323	−	0.993672i	$-0.535829\pi$
$47$	3.21600	−	1.23451i	0.469102	−	0.180071i	0.581424	+	0.813600i	$0.302496\pi$
$48$	−9.67172	+	18.9818i	−1.39599	+	2.73979i
$49$	−5.74759	−	3.99565i	−0.821084	−	0.570807i
$50$		0			0
$51$	−5.53583	−	9.58833i	−0.775171	−	1.34264i
$52$	1.09581	−	0.711624i	0.151961	−	0.0986845i
$53$	2.89407	+	2.34357i	0.397531	+	0.321914i	0.807154	−	0.590341i	$-0.201007\pi$
$53$	2.89407	+	2.34357i	0.397531	+	0.321914i	−0.409624	+	0.912255i	$0.634340\pi$
$54$	0.130032	+	0.0578938i	0.0176950	+	0.00787834i
$55$		0			0
$56$	−2.70603	+	18.3180i	−0.361609	+	2.44784i
$57$	−0.0355325	−	0.0355325i	−0.00470640	−	0.00470640i
$58$	−1.14621	−	1.41546i	−0.150505	−	0.185859i
$59$	3.75527	+	4.17065i	0.488894	+	0.542972i	0.936227	−	0.351396i	$-0.114293\pi$
$59$	3.75527	+	4.17065i	0.488894	+	0.542972i	−0.447333	+	0.894367i	$0.647626\pi$
$60$		0			0
$61$	1.43060	+	1.28812i	0.183169	+	0.164926i	0.755614	−	0.655017i	$-0.227338\pi$
$61$	1.43060	+	1.28812i	0.183169	+	0.164926i	−0.572445	+	0.819943i	$0.694005\pi$
$62$	−4.74610	−	9.31476i	−0.602756	−	1.18298i
$63$	−7.84276	−	0.741811i	−0.988094	−	0.0934594i
$64$	4.50960	−	1.46526i	0.563700	−	0.183157i
$65$		0			0
$66$	−25.5094	+	22.9688i	−3.13999	+	2.82726i
$67$	14.1898	+	5.44695i	1.73356	+	0.665451i	0.999901	−	0.0140668i	$-0.00447773\pi$
$67$	14.1898	+	5.44695i	1.73356	+	0.665451i	0.733659	+	0.679518i	$0.237811\pi$
$68$	−5.51240	+	20.5725i	−0.668476	+	2.49479i
$69$	10.7987	+	7.84569i	1.30001	+	0.944510i
$70$		0			0
$71$	1.09682	−	0.796887i	0.130169	−	0.0945731i	−0.520796	−	0.853681i	$-0.674365\pi$
$71$	1.09682	−	0.796887i	0.130169	−	0.0945731i	0.650964	+	0.759108i	$0.274365\pi$
$72$	7.46791	+	19.4546i	0.880102	+	2.29274i
$73$	4.47058	+	6.88409i	0.523242	+	0.805722i	0.997196	−	0.0748276i	$-0.0238407\pi$
$73$	4.47058	+	6.88409i	0.523242	+	0.805722i	−0.473955	+	0.880549i	$0.657174\pi$
$74$	−0.0532622	−	0.0307510i	−0.00619161	−	0.00357473i
$75$		0			0
$76$			0.0966658i			0.0110883i
$77$	−7.04394	+	12.4993i	−0.802731	+	1.42443i
$78$	0.275095	−	1.73688i	0.0311484	−	0.196663i
$79$	1.03233	−	2.31865i	0.116146	−	0.260869i	−0.846113	−	0.533004i	$-0.821063\pi$
$79$	1.03233	−	2.31865i	0.116146	−	0.260869i	0.962259	+	0.272135i	$0.0877298\pi$
$80$		0			0
$81$	8.28307	−	3.68786i	0.920342	−	0.409762i
$82$	−14.1246	−	3.78468i	−1.55980	−	0.417948i
$83$	1.06897	+	6.74923i	0.117335	+	0.740825i	0.974267	+	0.225396i	$0.0723675\pi$
$83$	1.06897	+	6.74923i	0.117335	+	0.740825i	−0.856932	+	0.515429i	$0.827633\pi$
$84$	19.3910	+	23.4424i	2.11573	+	2.55778i
$85$		0			0
$86$	−10.6759	+	11.8568i	−1.15121	+	1.27855i
$87$	−1.71758	−	0.0900148i	−0.184144	−	0.00965060i
$88$	37.9007	+	1.98629i	4.04023	+	0.211739i
$89$	5.48864	−	6.09575i	0.581794	−	0.646148i	−0.378347	−	0.925664i	$-0.623507\pi$
$89$	5.48864	−	6.09575i	0.581794	−	0.646148i	0.960141	+	0.279516i	$0.0901740\pi$
$90$		0			0
$91$	−0.122537	−	0.724733i	−0.0128454	−	0.0759727i
$92$	−4.01677	−	25.3609i	−0.418777	−	2.64405i
$93$	−9.53573	−	2.55509i	−0.988809	−	0.264951i
$94$	−8.14770	+	3.62759i	−0.840371	+	0.374157i
$95$		0			0
$96$	8.51483	−	19.1246i	0.869041	−	1.95190i
$97$	−2.19595	+	13.8647i	−0.222965	+	1.40775i	0.581404	+	0.813615i	$0.302504\pi$
$97$	−2.19595	+	13.8647i	−0.222965	+	1.40775i	−0.804369	+	0.594130i	$0.797496\pi$
$98$	15.4018	+	9.55197i	1.55582	+	0.964894i
$99$			16.1466i			1.62279i
$100$		0			0
$101$	−1.86039	−	1.07409i	−0.185115	−	0.106876i	0.404579	−	0.914503i	$-0.367418\pi$
$101$	−1.86039	−	1.07409i	−0.185115	−	0.106876i	−0.589694	+	0.807627i	$0.700752\pi$
$102$	15.6121	+	24.0406i	1.54583	+	2.38037i
$103$	−3.65021	−	9.50912i	−0.359666	−	0.936962i	−0.987359	−	0.158501i	$-0.949334\pi$
$103$	−3.65021	−	9.50912i	−0.359666	−	0.936962i	0.627693	−	0.778461i	$-0.283999\pi$
$104$	−1.57298	+	1.14284i	−0.154244	+	0.112065i
$105$		0			0
$106$	−7.80017	−	5.66716i	−0.757620	−	0.550443i
$107$	−1.63621	+	6.10643i	−0.158179	+	0.590331i	0.840633	+	0.541605i	$0.182183\pi$
$107$	−1.63621	+	6.10643i	−0.158179	+	0.590331i	−0.998812	+	0.0487267i	$0.984484\pi$
$108$	−0.241391	−	0.0926614i	−0.0232279	−	0.00891635i
$109$	−12.5165	+	11.2699i	−1.19886	+	1.07946i	−0.203920	+	0.978988i	$0.565368\pi$
$109$	−12.5165	+	11.2699i	−1.19886	+	1.07946i	−0.994940	+	0.100471i	$0.967965\pi$
$110$		0			0
$111$	−0.0552351	+	0.0179470i	−0.00524268	+	0.00170345i
$112$	2.17088	−	22.9515i	0.205129	−	2.16872i
$113$	0.964975	+	1.89387i	0.0907772	+	0.178160i	0.931931	−	0.362636i	$-0.118123\pi$
$113$	0.964975	+	1.89387i	0.0907772	+	0.178160i	−0.841154	+	0.540796i	$0.818123\pi$
$114$	0.0966841	+	0.0870547i	0.00905529	+	0.00815342i
$115$		0			0
$116$	2.21389	+	2.45878i	0.205555	+	0.228292i
$117$	−0.520566	−	0.642845i	−0.0481263	−	0.0594310i
$118$	−10.2744	−	10.2744i	−0.945833	−	0.945833i
$119$	9.38918	+	7.44265i	0.860705	+	0.682266i
$120$		0			0
$121$	16.8157	+	7.48685i	1.52870	+	0.680623i
$122$	−3.87335	−	3.13658i	−0.350677	−	0.283973i
$123$	−11.5810	+	7.52076i	−1.04422	+	0.678124i
$124$	9.49537	+	16.4465i	0.852710	+	1.47694i
$125$		0			0
$126$	20.3780	+	0.855257i	1.81542	+	0.0761923i
$127$	4.74461	−	9.31183i	0.421016	−	0.826291i	−0.578924	−	0.815381i	$-0.696527\pi$
$127$	4.74461	−	9.31183i	0.421016	−	0.826291i	0.999940	−	0.0109096i	$-0.00347270\pi$
$128$	4.52658	−	1.73759i	0.400097	−	0.153583i
$129$	1.57488	+	14.9840i	0.138661	+	1.31927i
$130$		0			0
$131$	18.4422	+	1.93835i	1.61130	+	0.169354i	0.866935	−	0.498421i	$-0.166087\pi$
$131$	18.4422	+	1.93835i	1.61130	+	0.169354i	0.744363	+	0.667775i	$0.232753\pi$
$132$	44.0924	−	44.0924i	3.83775	−	3.83775i
$133$	0.0499052	+	0.0215993i	0.00432733	+	0.00187289i
$134$	−37.4258	−	12.1604i	−3.23310	−	1.05050i
$135$		0			0
$136$	6.58943	−	31.0008i	0.565039	−	2.65830i
$137$	−0.576801	+	11.0060i	−0.0492794	+	0.940308i	0.856392	+	0.516327i	$0.172701\pi$
$137$	−0.576801	+	11.0060i	−0.0492794	+	0.940308i	−0.905671	+	0.423981i	$0.860632\pi$
$138$	−28.9831	−	18.8218i	−2.46720	−	1.60222i
$139$	−1.73378	−	5.33603i	−0.147058	−	0.452597i	0.850212	−	0.526440i	$-0.176474\pi$
$139$	−1.73378	−	5.33603i	−0.147058	−	0.452597i	−0.997270	+	0.0738434i	$0.976474\pi$
$140$		0			0
$141$	−2.60260	+	8.00997i	−0.219178	+	0.674561i
$142$	−2.72785	+	2.20897i	−0.228916	+	0.185373i
$143$	−1.45519	+	0.389917i	−0.121689	+	0.0326065i
$144$	−10.5527	−	23.7018i	−0.879392	−	1.97515i
$145$		0			0
$146$	−12.4915	−	17.1931i	−1.03380	−	1.42291i
$147$	16.4353	−	4.77285i	1.35556	−	0.393658i
$148$	0.0995454	+	0.0507209i	0.00818258	+	0.00416923i
$149$	−2.27766	+	1.31501i	−0.186593	+	0.107730i	−0.590387	−	0.807121i	$-0.701025\pi$
$149$	−2.27766	+	1.31501i	−0.186593	+	0.107730i	0.403794	+	0.914850i	$0.367691\pi$
$150$		0			0
$151$	2.52619	−	4.37549i	0.205579	−	0.356073i	−0.744738	−	0.667357i	$-0.767426\pi$
$151$	2.52619	−	4.37549i	0.205579	−	0.356073i	0.950317	+	0.311284i	$0.100759\pi$
$152$	−0.00752830	−	0.143649i	−0.000610626	−	0.0116514i
$153$	13.3176	+	2.10930i	1.07666	+	0.170527i
$154$	16.5185	−	33.2715i	1.33110	−	2.68109i
$155$		0			0
$156$	−0.333916	+	3.17700i	−0.0267346	+	0.254363i
$157$	1.62461	+	6.06312i	0.129658	+	0.483890i	0.999963	−	0.00862335i	$-0.00274493\pi$
$157$	1.62461	+	6.06312i	0.129658	+	0.483890i	−0.870305	+	0.492513i	$0.836078\pi$
$158$	−2.35492	+	6.13476i	−0.187347	+	0.488056i
$159$	−8.90575	+	1.89298i	−0.706272	+	0.150123i
$160$		0			0
$161$	−13.9905	−	3.59299i	−1.10260	−	0.283167i
$162$	−20.9162	+	10.6573i	−1.64333	+	0.837320i
$163$	−10.6353	+	16.3769i	−0.833018	+	1.28274i	0.123876	+	0.992298i	$0.460468\pi$
$163$	−10.6353	+	16.3769i	−0.833018	+	1.28274i	−0.956894	+	0.290438i	$0.906199\pi$
$164$	25.9830	+	5.52285i	2.02893	+	0.431262i
$165$		0			0
$166$	−3.67836	−	17.3053i	−0.285496	−	1.34315i
$167$	−17.6942	+	2.80249i	−1.36922	+	0.216863i	−0.797367	−	0.603494i	$-0.793775\pi$
$167$	−17.6942	+	2.80249i	−1.36922	+	0.216863i	−0.571852	+	0.820357i	$0.693775\pi$
$168$	−30.6413	−	33.3260i	−2.36403	−	2.57116i
$169$	−7.59584	+	10.4548i	−0.584296	+	0.804214i
$170$		0			0
$171$	0.0608624	−	0.00639689i	0.00465426	−	0.000489183i
$172$	18.2397	−	22.5242i	1.39076	−	1.71745i
$173$	15.3805	−	0.806056i	1.16935	−	0.0612833i	0.542249	−	0.840218i	$-0.317573\pi$
$173$	15.3805	−	0.806056i	1.16935	−	0.0612833i	0.627105	+	0.778934i	$0.284240\pi$
$174$	4.45302			0.337582
$175$		0			0
$176$	−47.2523			−3.56177
$177$	−13.7023	+	0.718109i	−1.02993	+	0.0539764i
$178$	−13.3649	+	16.5043i	−1.00174	+	1.23705i
$179$	0.501141	−	0.0526720i	0.0374570	−	0.00393689i	−0.0857814	−	0.996314i	$-0.527339\pi$
$179$	0.501141	−	0.0526720i	0.0374570	−	0.00393689i	0.123238	+	0.992377i	$0.460672\pi$
$180$		0			0
$181$	7.22957	−	9.95064i	0.537369	−	0.739625i	−0.450862	−	0.892594i	$-0.648883\pi$
$181$	7.22957	−	9.95064i	0.537369	−	0.739625i	0.988231	+	0.152968i	$0.0488832\pi$
$182$	0.415021	+	1.85720i	0.0307634	+	0.137665i
$183$	−4.64862	+	0.736269i	−0.343636	+	0.0544266i
$184$	7.94415	+	37.3743i	0.585651	+	2.75527i
$185$		0			0
$186$	25.0009	+	5.31410i	1.83315	+	0.389649i
$187$	13.3748	−	20.5954i	0.978062	−	1.50608i
$188$	14.4357	−	7.35535i	1.05283	−	0.536444i
$189$	−0.101775	+	0.103917i	−0.00740305	+	0.00755888i
$190$		0			0
$191$	13.0831	−	2.78090i	0.946659	−	0.201219i	0.291382	−	0.956607i	$-0.405885\pi$
$191$	13.0831	−	2.78090i	0.946659	−	0.201219i	0.655277	+	0.755388i	$0.272552\pi$
$192$	−4.15452	+	10.8229i	−0.299827	+	0.781076i
$193$	0.646732	+	2.41364i	0.0465528	+	0.173737i	0.985288	−	0.170902i	$-0.0546680\pi$
$193$	0.646732	+	2.41364i	0.0465528	+	0.173737i	−0.938735	+	0.344639i	$0.888001\pi$
$194$	3.79896	−	36.1447i	0.272750	−	2.59504i
$195$		0			0
$196$	−28.8482	−	15.8637i	−2.06059	−	1.13312i
$197$	−25.4720	−	4.03436i	−1.81480	−	0.287436i	−0.845621	−	0.533784i	$-0.820769\pi$
$197$	−25.4720	−	4.03436i	−1.81480	−	0.287436i	−0.969181	+	0.246348i	$0.920769\pi$
$198$	−2.18787	−	41.7470i	−0.155485	−	2.96683i
$199$	9.50790	−	16.4682i	0.673997	−	1.16740i	−0.302764	−	0.953066i	$-0.597909\pi$
$199$	9.50790	−	16.4682i	0.673997	−	1.16740i	0.976761	−	0.214332i	$-0.0687573\pi$
$200$		0			0
$201$	−32.1822	+	18.5804i	−2.26996	+	1.31056i
$202$	4.95557	+	2.52499i	0.348673	+	0.177658i
$203$	1.76406	−	0.593559i	0.123813	−	0.0416597i
$204$	−30.6072	−	42.1272i	−2.14293	−	2.94949i
$205$		0			0
$206$	10.7261	+	24.0913i	0.747324	+	1.67852i
$207$	−15.7018	+	4.20729i	−1.09135	+	0.292427i
$208$	1.88126	−	1.52342i	0.130442	−	0.105630i
$209$	0.0344421	−	0.106002i	0.00238241	−	0.00733230i
$210$		0			0
$211$	1.55379	+	4.78206i	0.106967	+	0.329211i	0.990187	−	0.139748i	$-0.0446293\pi$
$211$	1.55379	+	4.78206i	0.106967	+	0.329211i	−0.883220	+	0.468959i	$0.844629\pi$
$212$	14.6889	+	9.53909i	1.00884	+	0.655147i
$213$	−0.173476	+	3.31011i	−0.0118864	+	0.226805i
$214$	3.40301	−	16.0099i	0.232625	−	1.09442i
$215$		0			0
$216$	0.365932	+	0.118899i	0.0248985	+	0.00809002i
$217$	10.6124	−	1.22728i	0.720417	−	0.0833135i
$218$	30.8343	−	30.8343i	2.08836	−	2.08836i
$219$	−19.9586	−	2.09773i	−1.34868	−	0.141752i
$220$		0			0
$221$	0.131503	+	1.25117i	0.00884587	+	0.0841628i
$222$	0.140379	−	0.0538863i	0.00942159	−	0.00361661i
$223$	12.4361	−	24.4072i	0.832782	−	1.63443i	0.0613496	−	0.998116i	$-0.480460\pi$
$223$	12.4361	−	24.4072i	0.832782	−	1.63443i	0.771433	−	0.636311i	$-0.219540\pi$
$224$	−0.949958	+	22.6344i	−0.0634717	+	1.51232i
$225$		0			0
$226$	−2.75157	−	4.76585i	−0.183031	−	0.317020i
$227$	9.58871	−	6.22698i	0.636425	−	0.413299i	−0.185700	−	0.982607i	$-0.559455\pi$
$227$	9.58871	−	6.22698i	0.636425	−	0.413299i	0.822125	+	0.569307i	$0.192789\pi$
$228$	−0.183669	−	0.148732i	−0.0121638	−	0.00985003i
$229$	9.83654	+	4.37951i	0.650017	+	0.289406i	0.705134	−	0.709074i	$-0.250887\pi$
$229$	9.83654	+	4.37951i	0.650017	+	0.289406i	−0.0551173	+	0.998480i	$0.517553\pi$
$230$		0			0
$231$	−12.9112	−	32.6155i	−0.849497	−	2.14594i
$232$	−3.48141	−	3.48141i	−0.228566	−	0.228566i
$233$	−4.36556	−	5.39101i	−0.285997	−	0.353177i	0.613819	−	0.789447i	$-0.289633\pi$
$233$	−4.36556	−	5.39101i	−0.285997	−	0.353177i	−0.899816	+	0.436270i	$0.856299\pi$
$234$	1.43303	+	1.59154i	0.0936801	+	0.104042i
$235$		0			0
$236$	19.6153	+	17.6617i	1.27685	+	1.14968i
$237$	2.81717	+	5.52900i	0.182995	+	0.359147i
$238$	−25.2842	−	17.9707i	−1.63893	−	1.16487i
$239$	16.7344	−	5.43732i	1.08246	−	0.351711i	0.287129	−	0.957892i	$-0.407299\pi$
$239$	16.7344	−	5.43732i	1.08246	−	0.351711i	0.795327	+	0.606181i	$0.207299\pi$
$240$		0			0
$241$	−0.793839	+	0.714776i	−0.0511357	+	0.0460427i	−0.694302	−	0.719683i	$-0.744287\pi$
$241$	−0.793839	+	0.714776i	−0.0511357	+	0.0460427i	0.643167	+	0.765726i	$0.277620\pi$
$242$	−44.4916	−	17.0787i	−2.86003	−	1.09786i
$243$	−5.69475	+	21.2531i	−0.365318	+	1.36339i
$244$	7.32476	+	5.32175i	0.468920	+	0.340690i
$245$		0			0
$246$	28.9235	−	21.0142i	1.84410	−	1.33981i
$247$	0.00204625	+	0.00533068i	0.000130200	+	0.000339183i
$248$	−15.3913	−	23.7005i	−0.977348	−	1.50498i
$249$	−14.4686	−	8.35343i	−0.916908	−	0.529377i
$250$		0			0
$251$			20.3040i			1.28158i	0.767716	+	0.640790i	$0.221393\pi$
$251$			20.3040i			1.28158i	−0.767716	+	0.640790i	$0.778607\pi$
$252$	−37.0486	+	0.385870i	−2.33384	+	0.0243075i
$253$	−4.63139	+	29.2414i	−0.291173	+	1.83839i
$254$	−11.0055	+	24.7186i	−0.690543	+	1.55099i
$255$		0			0
$256$	−20.1315	+	8.96313i	−1.25822	+	0.560196i
$257$	22.1448	+	5.93369i	1.38136	+	0.370133i	0.871613	−	0.490194i	$-0.163074\pi$
$257$	22.1448	+	5.93369i	1.38136	+	0.370133i	0.509742	+	0.860327i	$0.329741\pi$
$258$	−6.10221	−	38.5278i	−0.379907	−	2.39864i
$259$	0.0484281	−	0.0400586i	0.00300918	−	0.00248912i
$260$		0			0
$261$	1.40158	−	1.55661i	0.0867557	−	0.0963519i
$262$	−47.9449	−	2.51268i	−2.96204	−	0.155234i
$263$	−23.7468	−	1.24452i	−1.46429	−	0.0767401i	−0.696553	−	0.717506i	$-0.745284\pi$
$263$	−23.7468	−	1.24452i	−1.46429	−	0.0767401i	−0.767737	+	0.640766i	$0.778617\pi$
$264$	−62.0889	+	68.9567i	−3.82131	+	4.24399i
$265$		0			0
$266$	−0.131957	−	0.0490828i	−0.00809078	−	0.00300946i
$267$	3.13723	+	19.8077i	0.191995	+	1.21221i
$268$	69.0495	+	18.5017i	4.21787	+	1.13017i
$269$	5.31165	−	2.36490i	0.323857	−	0.144190i	−0.238368	−	0.971175i	$-0.576612\pi$
$269$	5.31165	−	2.36490i	0.323857	−	0.144190i	0.562225	+	0.826985i	$0.309946\pi$
$270$		0			0
$271$	6.85867	−	15.4048i	0.416635	−	0.935777i	−0.576314	−	0.817229i	$-0.695509\pi$
$271$	6.85867	−	15.4048i	0.416635	−	0.935777i	0.992948	−	0.118548i	$-0.0378240\pi$
$272$	−6.17279	+	38.9734i	−0.374280	+	2.36311i
$273$	1.56556	+	0.882266i	0.0947521	+	0.0533972i
$274$		−	28.5343i		−	1.72382i
$275$		0			0
$276$	54.3670	+	31.3888i	3.27251	+	1.88938i
$277$	11.3638	+	17.4987i	0.682782	+	1.05139i	0.994853	+	0.101333i	$0.0323108\pi$
$277$	11.3638	+	17.4987i	0.682782	+	1.05139i	−0.312071	+	0.950059i	$0.601023\pi$
$278$	5.20574	+	13.5614i	0.312219	+	0.813359i
$279$	9.72661	−	7.06679i	0.582317	−	0.423078i
$280$		0			0
$281$	−10.0464	−	7.29912i	−0.599316	−	0.435429i	0.246320	−	0.969189i	$-0.420779\pi$
$281$	−10.0464	−	7.29912i	−0.599316	−	0.435429i	−0.845636	+	0.533760i	$0.820779\pi$
$282$	5.64367	−	21.0625i	0.336076	−	1.25425i
$283$	4.63100	+	1.77767i	0.275284	+	0.105672i	0.492094	−	0.870542i	$-0.336232\pi$
$283$	4.63100	+	1.77767i	0.275284	+	0.105672i	−0.216809	+	0.976214i	$0.569565\pi$
$284$	4.73853	−	4.26659i	0.281180	−	0.253176i
$285$		0			0
$286$	3.70957	−	1.20531i	0.219351	−	0.0712715i
$287$	8.65697	−	12.1801i	0.511005	−	0.718967i
$288$	11.5745	+	22.7163i	0.682035	+	1.33857i
$289$	−2.60629	−	2.34672i	−0.153311	−	0.138042i
$290$		0			0
$291$	−22.9647	−	25.5049i	−1.34622	−	1.49512i
$292$	24.2951	+	30.0020i	1.42176	+	1.75573i
$293$	7.51221	+	7.51221i	0.438868	+	0.438868i	0.891631	−	0.452763i	$-0.149562\pi$
$293$	7.51221	+	7.51221i	0.438868	+	0.438868i	−0.452763	+	0.891631i	$0.649562\pi$
$294$	−41.8467	+	14.5672i	−2.44055	+	0.849577i
$295$		0			0
$296$	−0.151878	−	0.0676204i	−0.00882773	−	0.00393036i
$297$	0.231690	+	0.187619i	0.0134440	+	0.0108867i
$298$	5.71071	−	3.70858i	0.330812	−	0.214832i
$299$	−0.758354	−	1.31351i	−0.0438568	−	0.0759621i
$300$		0			0
$301$	−7.55291	−	14.4494i	−0.435342	−	0.832849i
$302$	−5.93860	+	11.6552i	−0.341728	+	0.670679i
$303$	4.90325	−	1.88218i	0.281685	−	0.108129i
$304$	0.0187203	+	0.178111i	0.00107368	+	0.0102154i
$305$		0			0
$306$	−34.7185	−	3.64906i	−1.98472	−	0.208603i
$307$	−2.99332	+	2.99332i	−0.170838	+	0.170838i	−0.787347	−	0.616510i	$-0.788546\pi$
$307$	−2.99332	+	2.99332i	−0.170838	+	0.170838i	0.616510	+	0.787347i	$0.288546\pi$
$308$	−26.8026	+	61.9274i	−1.52722	+	3.52864i
$309$	23.6840	+	7.69540i	1.34734	+	0.437776i
$310$		0			0
$311$	−0.840907	+	3.95616i	−0.0476835	+	0.224333i	−0.995537	−	0.0943736i	$-0.969915\pi$
$311$	−0.840907	+	3.95616i	−0.0476835	+	0.224333i	0.947853	+	0.318707i	$0.103248\pi$
$312$	0.248786	−	4.74713i	0.0140848	−	0.268753i
$313$	12.0326	+	7.81404i	0.680121	+	0.441676i	0.837918	−	0.545796i	$-0.183773\pi$
$313$	12.0326	+	7.81404i	0.680121	+	0.441676i	−0.157797	+	0.987472i	$0.550439\pi$
$314$	−5.02199	−	15.4561i	−0.283407	−	0.872238i
$315$		0			0
$316$	3.68876	−	11.3528i	0.207509	−	0.638646i
$317$	17.7724	−	14.3918i	0.998195	−	0.808322i	0.0167098	−	0.999860i	$-0.494681\pi$
$317$	17.7724	−	14.3918i	0.998195	−	0.808322i	0.981485	+	0.191538i	$0.0613475\pi$
$318$	22.7693	−	6.10103i	1.27684	−	0.342129i
$319$	−1.55165	−	3.48506i	−0.0868756	−	0.195126i
$320$		0			0
$321$	−9.08496	−	12.5044i	−0.507073	−	0.697926i
$322$	36.6592	+	7.39397i	2.04294	+	0.412050i
$323$	−0.0829304	−	0.0422552i	−0.00461437	−	0.00235114i
$324$	36.9304	−	21.3218i	2.05169	−	1.18454i
$325$		0			0
$326$	25.2784	−	43.7835i	1.40004	−	2.42494i
$327$	−2.15511	−	41.1219i	−0.119178	−	2.27405i
$328$	−39.0417	−	6.18360i	−2.15572	−	0.341432i
$329$	−0.571759	−	9.09614i	−0.0315221	−	0.501486i
$330$		0			0
$331$	−3.52843	+	33.5708i	−0.193940	+	1.84522i	0.274337	+	0.961634i	$0.411542\pi$
$331$	−3.52843	+	33.5708i	−0.193940	+	1.84522i	−0.468277	+	0.883582i	$0.655125\pi$
$332$	8.31808	+	31.0435i	0.456514	+	1.70373i
$333$	0.0253473	−	0.0660319i	0.00138902	−	0.00361852i
$334$	45.3687	−	9.64341i	2.48246	−	0.527664i
$335$		0			0
$336$	40.2687	+	39.4385i	2.19684	+	2.15155i
$337$	22.6851	−	11.5586i	1.23574	−	0.629640i	0.290766	−	0.956794i	$-0.406090\pi$
$337$	22.6851	−	11.5586i	1.23574	−	0.629640i	0.944971	+	0.327155i	$0.106090\pi$
$338$	18.2224	−	28.0601i	0.991170	−	1.52627i
$339$	−5.08316	−	1.08046i	−0.276080	−	0.0586825i
$340$		0			0
$341$	−4.55255	−	21.4181i	−0.246535	−	1.15985i
$342$	−0.156493	+	0.0247861i	−0.00846217	+	0.00134028i
$343$	−14.6358	+	11.3487i	−0.790260	+	0.612772i
$344$	−25.3506	+	34.8922i	−1.36682	+	1.88126i
$345$		0			0
$346$	−39.6570	+	4.16812i	−2.13197	+	0.224079i
$347$	−0.139330	+	0.172059i	−0.00747964	+	0.00923659i	−0.780872	−	0.624691i	$-0.785225\pi$
$347$	−0.139330	+	0.172059i	−0.00747964	+	0.00923659i	0.773392	+	0.633928i	$0.218558\pi$
$348$	−8.07812	+	0.423356i	−0.433033	+	0.0226943i
$349$	−9.15927			−0.490285			−0.245142	−	0.969487i	$-0.578835\pi$
$349$	−9.15927			−0.490285			−0.245142	+	0.969487i	$0.578835\pi$
$350$		0			0
$351$	−0.0152731			−0.000815219
$352$	46.3695	−	2.43013i	2.47151	−	0.129526i
$353$	12.4551	−	15.3807i	0.662917	−	0.818634i	−0.329159	−	0.944274i	$-0.606765\pi$
$353$	12.4551	−	15.3807i	0.662917	−	0.818634i	0.992076	+	0.125641i	$0.0400986\pi$
$354$	35.3301	−	3.71334i	1.87777	−	0.197362i
$355$		0			0
$356$	22.6759	−	31.2107i	1.20182	−	1.65416i
$357$	−28.5877	+	6.38840i	−1.51302	+	0.338110i
$358$	−1.28856	+	0.204089i	−0.0681027	+	0.0107864i
$359$	−1.99733	−	9.39672i	−0.105415	−	0.495940i	−0.998902	−	0.0468502i	$-0.985082\pi$
$359$	−1.99733	−	9.39672i	−0.105415	−	0.495940i	0.893487	−	0.449090i	$-0.148252\pi$
$360$		0			0
$361$	18.5844	+	3.95023i	0.978126	+	0.207907i
$362$	−17.3437	+	26.7070i	−0.911567	+	1.40369i
$363$	−40.0984	+	20.4311i	−2.10462	+	1.07236i
$364$	−0.929448	−	3.32964i	−0.0487163	−	0.174521i
$365$		0			0
$366$	11.9193	−	2.53352i	0.623029	−	0.132429i
$367$	−5.79588	+	15.0988i	−0.302543	+	0.788151i	0.695060	+	0.718952i	$0.255378\pi$
$367$	−5.79588	+	15.0988i	−0.302543	+	0.788151i	−0.997603	+	0.0691990i	$0.977956\pi$
$368$	−12.3125	−	45.9507i	−0.641832	−	2.39535i
$369$	1.75785	−	16.7248i	0.0915098	−	0.870658i
$370$		0			0
$371$	8.20683	−	5.45193i	0.426077	−	0.283050i
$372$	−45.8588	−	7.26331i	−2.37767	−	0.376585i
$373$	−0.762331	−	14.5461i	−0.0394720	−	0.753171i	−0.944638	−	0.328113i	$-0.893587\pi$
$373$	−0.762331	−	14.5461i	−0.0394720	−	0.753171i	0.905166	−	0.425057i	$-0.139746\pi$
$374$	−31.7899	+	55.0617i	−1.64382	+	2.84717i
$375$		0			0
$376$	−20.8791	+	12.0545i	−1.07676	+	0.621665i
$377$	0.174134	+	0.0887258i	0.00896837	+	0.00456961i
$378$	0.249059	−	0.282469i	0.0128102	−	0.0145286i
$379$	12.1419	+	16.7119i	0.623687	+	0.858432i	0.997615	−	0.0690260i	$-0.0219891\pi$
$379$	12.1419	+	16.7119i	0.623687	+	0.858432i	−0.373928	+	0.927458i	$0.621989\pi$
$380$		0			0
$381$	10.3927	+	23.3423i	0.532433	+	1.19586i
$382$	−33.4496	+	8.96278i	−1.71143	+	0.458576i
$383$	26.6178	−	21.5547i	1.36011	−	1.10139i	0.375458	−	0.926840i	$-0.377486\pi$
$383$	26.6178	−	21.5547i	1.36011	−	1.10139i	0.984648	−	0.174552i	$-0.0558478\pi$
$384$	−3.66321	+	11.2742i	−0.186937	+	0.575333i
$385$		0			0
$386$	−1.99918	−	6.15283i	−0.101755	−	0.313171i
$387$	−15.3886	−	9.99347i	−0.782247	−	0.507997i
$388$	−3.45527	+	65.9305i	−0.175415	+	3.34711i
$389$	0.617880	−	2.90689i	0.0313277	−	0.147385i	−0.959704	−	0.281014i	$-0.909329\pi$
$389$	0.617880	−	2.90689i	0.0313277	−	0.147385i	0.991032	+	0.133628i	$0.0426628\pi$
$390$		0			0
$391$	23.5131	+	7.63989i	1.18911	+	0.386366i
$392$	44.1049	+	21.3274i	2.22763	+	1.07719i
$393$	−32.0585	+	32.0585i	−1.61713	+	1.61713i
$394$	66.4045	+	6.97939i	3.34541	+	0.351617i
$395$		0			0
$396$	7.93792	+	75.5242i	0.398895	+	3.79524i
$397$	−16.9274	+	6.49782i	−0.849562	+	0.326116i	−0.743904	−	0.668286i	$-0.767028\pi$
$397$	−16.9274	+	6.49782i	−0.849562	+	0.326116i	−0.105658	+	0.994403i	$0.533695\pi$
$398$	−22.3513	+	43.8668i	−1.12037	+	2.19884i
$399$	−0.117825	+	0.0615887i	−0.00589861	+	0.00308329i
$400$		0			0
$401$	14.8272	+	25.6815i	0.740436	+	1.28247i	0.952297	+	0.305172i	$0.0987141\pi$
$401$	14.8272	+	25.6815i	0.740436	+	1.28247i	−0.211862	+	0.977300i	$0.567953\pi$
$402$	80.6895	−	52.4003i	4.02442	−	2.61349i
$403$	0.871771	+	0.705946i	0.0434260	+	0.0351657i
$404$	−9.22985	−	4.10939i	−0.459202	−	0.204450i
$405$		0			0
$406$	−4.48055	+	1.77368i	−0.222366	+	0.0880262i
$407$	−0.0910876	−	0.0910876i	−0.00451505	−	0.00451505i
$408$	48.7642	+	60.2187i	2.41419	+	2.98127i
$409$	5.99960	+	6.66323i	0.296661	+	0.329476i	0.872986	−	0.487745i	$-0.162180\pi$
$409$	5.99960	+	6.66323i	0.296661	+	0.329476i	−0.576325	+	0.817221i	$0.695514\pi$
$410$		0			0
$411$	−20.0244	−	18.0301i	−0.987731	−	0.889357i
$412$	−21.7484	−	42.6837i	−1.07147	−	2.10287i
$413$	13.5010	−	6.18032i	0.664342	−	0.304114i
$414$	40.0270	−	13.0056i	1.96722	−	0.639188i
$415$		0			0
$416$	−1.76777	+	1.59171i	−0.0866720	+	0.0780398i
$417$	12.8063	+	4.91589i	0.627128	+	0.240732i
$418$	−0.0746868	+	0.278735i	−0.00365305	+	0.0136334i
$419$	13.9434	+	10.1305i	0.681179	+	0.494905i	0.873748	−	0.486378i	$-0.161682\pi$
$419$	13.9434	+	10.1305i	0.681179	+	0.494905i	−0.192570	+	0.981283i	$0.561682\pi$
$420$		0			0
$421$	−9.71469	+	7.05813i	−0.473465	+	0.343992i	−0.798790	−	0.601610i	$-0.794526\pi$
$421$	−9.71469	+	7.05813i	−0.473465	+	0.343992i	0.325325	+	0.945602i	$0.394526\pi$
$422$	−4.66529	−	12.1535i	−0.227103	−	0.591623i
$423$	−5.58633	−	8.60220i	−0.271617	−	0.418253i
$424$	−22.5711	−	13.0314i	−1.09615	−	0.632863i
$425$		0			0
$426$		−	8.58181i		−	0.415790i
$427$	4.38410	−	2.59241i	0.212162	−	0.125456i
$428$	−4.65124	+	29.3668i	−0.224826	+	1.41950i
$429$	1.49813	−	3.36486i	0.0723304	−	0.162457i
$430$		0			0
$431$	−20.7997	+	9.26062i	−1.00189	+	0.446068i	−0.841076	−	0.540917i	$-0.818077\pi$
$431$	−20.7997	+	9.26062i	−1.00189	+	0.446068i	−0.160810	+	0.986985i	$0.551411\pi$
$432$	−0.462720	−	0.123985i	−0.0222626	−	0.00596525i
$433$	0.661050	+	4.17371i	0.0317680	+	0.200576i	0.998468	−	0.0553382i	$-0.0176237\pi$
$433$	0.661050	+	4.17371i	0.0317680	+	0.200576i	−0.966700	+	0.255914i	$0.917624\pi$
$434$	−27.2721	+	4.61113i	−1.30910	+	0.221341i
$435$		0			0
$436$	−53.0043	+	58.8673i	−2.53845	+	2.81923i
$437$	0.112057	+	0.00587264i	0.00536039	+	0.000280926i
$438$	51.8872	+	2.71929i	2.47927	+	0.129933i
$439$	−8.37528	+	9.30169i	−0.399730	+	0.443945i	−0.909085	−	0.416612i	$-0.863218\pi$
$439$	−8.37528	+	9.30169i	−0.399730	+	0.443945i	0.509355	+	0.860557i	$0.329884\pi$
$440$		0			0
$441$	−8.07903	+	19.2131i	−0.384716	+	0.914909i
$442$	−0.509536	−	3.21709i	−0.0242362	−	0.153021i
$443$	16.0567	+	4.30238i	0.762877	+	0.204412i	0.619223	−	0.785216i	$-0.287448\pi$
$443$	16.0567	+	4.30238i	0.762877	+	0.204412i	0.143655	+	0.989628i	$0.454115\pi$
$444$	−0.249535	+	0.111100i	−0.0118424	+	0.00527257i
$445$		0			0
$446$	−28.8464	+	64.7900i	−1.36591	+	3.06789i
$447$	1.00589	−	6.35094i	0.0475770	−	0.300389i
$448$	−0.130655	−	12.5446i	−0.00617288	−	0.592677i
$449$		−	30.5962i		−	1.44392i	−0.691934	−	0.721961i	$-0.743241\pi$
$449$		−	30.5962i		−	1.44392i	0.691934	−	0.721961i	$-0.256759\pi$
$450$		0			0
$451$	−26.5246	−	15.3140i	−1.24900	−	0.721108i
$452$	5.44465	+	8.38403i	0.256095	+	0.394352i
$453$	4.42676	+	11.5321i	0.207987	+	0.541825i
$454$	−23.9479	+	17.3991i	−1.12393	+	0.816582i
$455$		0			0
$456$	0.284521	+	0.206717i	0.0133239	+	0.00968041i
$457$	7.33215	−	27.3640i	0.342984	−	1.28003i	−0.551967	−	0.833866i	$-0.686122\pi$
$457$	7.33215	−	27.3640i	0.342984	−	1.28003i	0.894950	−	0.446166i	$-0.147211\pi$
$458$	−26.0258	−	9.99038i	−1.21611	−	0.466820i
$459$	0.185014	−	0.166587i	0.00863569	−	0.00777561i
$460$		0			0
$461$	−5.27336	+	1.71342i	−0.245605	+	0.0798018i	−0.429233	−	0.903194i	$-0.641216\pi$
$461$	−5.27336	+	1.71342i	−0.245605	+	0.0798018i	0.183628	+	0.982996i	$0.441216\pi$
$462$	37.8014	+	82.5780i	1.75868	+	3.84187i
$463$	−17.6164	−	34.5741i	−0.818703	−	1.60680i	−0.794637	−	0.607085i	$-0.792339\pi$
$463$	−17.6164	−	34.5741i	−0.818703	−	1.60680i	−0.0240660	−	0.999710i	$-0.507661\pi$
$464$	4.55537	+	4.10167i	0.211478	+	0.190415i
$465$		0			0
$466$	12.0176	+	13.3469i	0.556706	+	0.618285i
$467$	−11.8632	−	14.6499i	−0.548966	−	0.677916i	0.424848	−	0.905265i	$-0.360328\pi$
$467$	−11.8632	−	14.6499i	−0.548966	−	0.677916i	−0.973813	+	0.227349i	$0.926994\pi$
$468$	−2.75094	−	2.75094i	−0.127162	−	0.127162i
$469$	24.9804	−	31.5138i	1.15349	−	1.45517i
$470$		0			0
$471$	−14.0198	−	6.24204i	−0.646000	−	0.287618i
$472$	−30.5245	−	24.7183i	−1.40500	−	1.13775i
$473$	−28.0267	+	18.2007i	−1.28867	+	0.836871i
$474$	−8.03298	−	13.9135i	−0.368967	−	0.639069i
$475$		0			0
$476$	47.5761	+	30.1965i	2.18065	+	1.38406i
$477$	5.03392	−	9.87963i	0.230487	−	0.452357i
$478$	−42.5300	+	16.3257i	−1.94528	+	0.746722i
$479$	−2.02979	−	19.3122i	−0.0927436	−	0.882396i	−0.937673	−	0.347519i	$-0.887024\pi$
$479$	−2.02979	−	19.3122i	−0.0927436	−	0.882396i	0.844930	−	0.534878i	$-0.179642\pi$
$480$		0			0
$481$	0.00656315		0.000689815i	0.000299254		3.14529e-5i
$482$	1.95562	−	1.95562i	0.0890760	−	0.0890760i
$483$	28.3529	−	21.0542i	1.29010	−	0.957998i
$484$	82.3349	+	26.7522i	3.74250	+	1.21601i
$485$		0			0
$486$	11.8440	−	55.7216i	0.537254	−	2.52758i
$487$	−0.0615003	+	1.17349i	−0.00278684	+	0.0531761i	−0.999669	−	0.0257293i	$-0.991809\pi$
$487$	−0.0615003	+	1.17349i	−0.00278684	+	0.0531761i	0.996882	+	0.0789055i	$0.0251425\pi$
$488$	−11.2993	−	7.33785i	−0.511495	−	0.332169i
$489$	−14.7531	−	45.4052i	−0.667156	−	2.05330i
$490$		0			0
$491$	4.11148	−	12.6538i	0.185548	−	0.571059i	−0.814409	−	0.580291i	$-0.802939\pi$
$491$	4.11148	−	12.6538i	0.185548	−	0.571059i	0.999957	+	0.00923217i	$0.00293873\pi$
$492$	−50.4717	+	40.8711i	−2.27544	+	1.84261i
$493$	−3.07716	+	0.824521i	−0.138588	+	0.0371346i
$494$	−0.00601291	−	0.0135052i	−0.000270533	−	0.000607628i
$495$		0			0
$496$	20.6807	+	28.4645i	0.928591	+	1.27810i
$497$	−1.14390	−	3.39968i	−0.0513110	−	0.152496i
$498$	38.5404	+	19.6373i	1.72704	+	0.879969i
$499$	−31.8592	+	18.3939i	−1.42621	+	0.823426i	−0.996820	−	0.0796912i	$-0.974607\pi$
$499$	−31.8592	+	18.3939i	−1.42621	+	0.823426i	−0.429395	+	0.903117i	$0.641273\pi$
$500$		0			0
$501$	21.8999	−	37.9317i	0.978414	−	1.69466i
$502$	−2.75121	−	52.4962i	−0.122792	−	2.34302i
$503$	−13.5703	−	2.14933i	−0.605072	−	0.0958339i	−0.153621	−	0.988130i	$-0.549093\pi$
$503$	−13.5703	−	2.14933i	−0.605072	−	0.0958339i	−0.451451	+	0.892296i	$0.649093\pi$
$504$	55.0254	−	3.45875i	2.45102	−	0.154065i
$505$		0			0
$506$	8.01223	−	76.2313i	0.356187	−	3.38890i
$507$	−8.17737	−	30.5184i	−0.363170	−	1.35537i
$508$	17.6147	−	45.8879i	0.781526	−	2.03594i
$509$	−25.4376	+	5.40692i	−1.12750	+	0.239658i	−0.733657	−	0.679520i	$-0.762188\pi$
$509$	−25.4376	+	5.40692i	−1.12750	+	0.239658i	−0.393843	+	0.919178i	$0.628855\pi$
$510$		0			0
$511$	20.9175	−	5.83899i	0.925337	−	0.258302i
$512$	42.1953	−	21.4996i	1.86479	−	0.950156i
$513$	0.000615414	0	0.000947654i	2.71712e−5	0	4.18400e-5i
$514$	−58.0595	−	12.3409i	−2.56090	−	0.544335i
$515$		0			0
$516$	14.7328	+	69.3124i	0.648575	+	3.05131i
$517$	−18.4506	+	2.92229i	−0.811456	+	0.128522i
$518$	−0.119783	+	0.110134i	−0.00526297	+	0.00483899i
$519$	−22.1332	+	30.4637i	−0.971539	+	1.33721i
$520$		0			0
$521$	37.6789	−	3.96021i	1.65074	−	0.173500i	0.767056	−	0.641580i	$-0.221721\pi$
$521$	37.6789	−	3.96021i	1.65074	−	0.173500i	0.883686	+	0.468081i	$0.155054\pi$
$522$	−3.41287	+	4.21454i	−0.149377	+	0.184466i
$523$	6.86781	−	0.359926i	0.300308	−	0.0157385i	0.0984131	−	0.995146i	$-0.468623\pi$
$523$	6.86781	−	0.359926i	0.300308	−	0.0157385i	0.201895	+	0.979407i	$0.435290\pi$
$524$	87.2146			3.80999
$525$		0			0
$526$	61.5660			2.68441
$527$	−18.2602	+	0.956979i	−0.795429	+	0.0416867i
$528$	72.7034	−	89.7813i	3.16401	−	3.90723i
$529$	−6.76877	+	0.711426i	−0.294294	+	0.0309316i
$530$		0			0
$531$	9.82205	−	13.5189i	0.426241	−	0.586670i
$532$	0.244046	+	0.0764947i	0.0105807	+	0.00331647i
$533$	1.54975	−	0.245457i	0.0671272	−	0.0106319i
$534$	−10.7953	−	50.7877i	−0.467157	−	2.19780i
$535$		0			0
$536$	−104.051	−	22.1167i	−4.49431	−	0.955295i
$537$	−0.670988	+	1.03323i	−0.0289553	+	0.0445872i
$538$	−13.4128	+	6.83419i	−0.578269	+	0.294643i
$539$	25.9821	+	27.6745i	1.11913	+	1.19202i
$540$		0			0
$541$	−30.6338	+	6.51141i	−1.31705	+	0.279947i	−0.812260	−	0.583296i	$-0.801763\pi$
$541$	−30.6338	+	6.51141i	−1.31705	+	0.279947i	−0.504789	+	0.863243i	$0.668430\pi$
$542$	−15.6458	+	40.7586i	−0.672043	+	1.75073i
$543$	7.78305	+	29.0468i	0.334003	+	1.24652i
$544$	4.05312	−	38.5628i	0.173776	−	1.65337i
$545$		0			0
$546$	−4.16731	−	2.06897i	−0.178344	−	0.0885436i
$547$	−34.9599	−	5.53710i	−1.49478	−	0.236749i	−0.645119	−	0.764082i	$-0.723192\pi$
$547$	−34.9599	−	5.53710i	−1.49478	−	0.236749i	−0.849659	+	0.527333i	$0.823192\pi$
$548$	2.71280	+	51.7634i	0.115885	+	2.21122i
$549$	2.86594	−	4.96396i	0.122315	−	0.211857i
$550$		0			0
$551$	−0.0125217	+	0.00722943i	−0.000533444	+	0.000307984i
$552$	−83.2357	−	42.4107i	−3.54275	−	1.80512i
$553$	−5.03684	−	4.44108i	−0.214188	−	0.188854i
$554$	−31.7521	−	43.7030i	−1.34902	−	1.85676i
$555$		0			0
$556$	−10.7329	−	24.1065i	−0.455177	−	1.02234i
$557$	1.98966	−	0.533128i	0.0843046	−	0.0225893i	−0.216420	−	0.976300i	$-0.569438\pi$
$557$	1.98966	−	0.533128i	0.0843046	−	0.0225893i	0.300725	+	0.953711i	$0.402771\pi$
$558$	−24.1906	+	19.5892i	−1.02407	+	0.829276i
$559$	0.529037	−	1.62821i	0.0223759	−	0.0688659i
$560$		0			0
$561$	18.5533	+	57.1012i	0.783321	+	2.41081i
$562$	26.9640	+	17.5106i	1.13741	+	0.738640i
$563$	1.72346	−	32.8856i	0.0726352	−	1.38596i	−0.682736	−	0.730665i	$-0.739210\pi$
$563$	1.72346	−	32.8856i	0.0726352	−	1.38596i	0.755371	−	0.655297i	$-0.227457\pi$
$564$	−8.23561	+	38.7455i	−0.346782	+	1.63148i
$565$		0			0
$566$	−12.2143	−	3.96868i	−0.513407	−	0.166816i
$567$	−2.75586	−	23.8301i	−0.115735	−	1.00077i
$568$	−6.70933	+	6.70933i	−0.281517	+	0.281517i
$569$	9.03713	+	0.949841i	0.378856	+	0.0398194i	0.292043	−	0.956405i	$-0.405665\pi$
$569$	9.03713	+	0.949841i	0.378856	+	0.0398194i	0.0868133	+	0.996225i	$0.472332\pi$
$570$		0			0
$571$	−3.95668	−	37.6453i	−0.165582	−	1.57541i	−0.689912	−	0.723893i	$-0.742351\pi$
$571$	−3.95668	−	37.6453i	−0.165582	−	1.57541i	0.524330	−	0.851515i	$-0.324316\pi$
$572$	−6.61485	+	2.53920i	−0.276581	+	0.106169i
$573$	−14.8461	+	29.1372i	−0.620206	+	1.21722i
$574$	−20.7322	+	32.6646i	−0.865346	+	1.36339i
$575$		0			0
$576$	−7.05920	−	12.2269i	−0.294133	−	0.509454i
$577$	−14.9280	+	9.69437i	−0.621462	+	0.403582i	−0.816608	−	0.577192i	$-0.804148\pi$
$577$	−14.9280	+	9.69437i	−0.621462	+	0.403582i	0.195147	+	0.980774i	$0.437482\pi$
$578$	7.05656	+	5.71429i	0.293514	+	0.237683i
$579$	−5.58109	−	2.48486i	−0.231942	−	0.103267i
$580$		0			0
$581$	17.8853	+	2.64211i	0.742007	+	0.109613i
$582$	62.8313	+	62.8313i	2.60444	+	2.60444i
$583$	−12.7088	−	15.6940i	−0.526344	−	0.649981i
$584$	−38.4399	−	42.6918i	−1.59065	−	1.76660i
$585$		0			0
$586$	−20.4408	−	18.4049i	−0.844400	−	0.760301i
$587$	18.6280	+	36.5596i	0.768861	+	1.50898i	0.858394	+	0.512991i	$0.171463\pi$
$587$	18.6280	+	36.5596i	0.768861	+	1.50898i	−0.0895323	+	0.995984i	$0.528537\pi$
$588$	74.5282	−	30.4045i	3.07349	−	1.25386i
$589$	−0.0789291	+	0.0256456i	−0.00325222	+	0.00105671i
$590$		0			0
$591$	46.8572	−	42.1904i	1.92745	−	1.73548i
$592$	0.193240	+	0.0741778i	0.00794210	+	0.00304869i
$593$	0.682938	−	2.54876i	0.0280449	−	0.104665i	−0.950485	−	0.310771i	$-0.899413\pi$
$593$	0.682938	−	2.54876i	0.0280449	−	0.104665i	0.978530	+	0.206106i	$0.0660793\pi$
$594$	−0.624457	−	0.453694i	−0.0256218	−	0.0186153i
$595$		0			0
$596$	−10.0071	+	7.27057i	−0.409906	+	0.297814i
$597$	16.6611	+	43.4037i	0.681894	+	1.77639i
$598$	2.13871	+	3.29332i	0.0874583	+	0.134674i
$599$	15.2314	+	8.79385i	0.622338	+	0.359307i	0.777779	−	0.628538i	$-0.216346\pi$
$599$	15.2314	+	8.79385i	0.622338	+	0.359307i	−0.155441	+	0.987845i	$0.549680\pi$
$600$		0			0
$601$			4.58675i			0.187097i	0.995615	+	0.0935487i	$0.0298211\pi$
$601$			4.58675i			0.187097i	−0.995615	+	0.0935487i	$0.970179\pi$
$602$	21.4860	+	36.3355i	0.875702	+	1.48092i
$603$	7.07963	−	44.6990i	0.288305	−	1.82029i
$604$	9.66500	−	21.7079i	0.393263	−	0.883284i
$605$		0			0
$606$	−12.4223	+	5.53078i	−0.504623	+	0.224673i
$607$	0.509336	+	0.136476i	0.0206733	+	0.00553939i	0.269141	−	0.963101i	$-0.413260\pi$
$607$	0.509336	+	0.136476i	0.0206733	+	0.00553939i	−0.248468	+	0.968640i	$0.579927\pi$
$608$	−0.0275306	−	0.173821i	−0.00111651	−	0.00704938i
$609$	−1.58643	+	4.26505i	−0.0642855	+	0.172828i
$610$		0			0
$611$	0.640361	−	0.711193i	0.0259062	−	0.0287718i
$612$	63.3290	+	3.31893i	2.55992	+	0.134160i
$613$	−1.63130	−	0.0854926i	−0.0658874	−	0.00345301i	0.0193637	−	0.999813i	$-0.493836\pi$
$613$	−1.63130	−	0.0854926i	−0.0658874	−	0.00345301i	−0.0852512	+	0.996359i	$0.527169\pi$
$614$	7.33364	−	8.14483i	0.295962	−	0.328699i
$615$		0			0
$616$	35.0067	−	94.1137i	1.41046	−	3.79195i
$617$	0.578692	+	3.65372i	0.0232973	+	0.147093i	0.996595	−	0.0824536i	$-0.0262756\pi$
$617$	0.578692	+	3.65372i	0.0232973	+	0.147093i	−0.973298	+	0.229547i	$0.926276\pi$
$618$	−62.2778	−	16.6873i	−2.50518	−	0.671261i
$619$	−12.2539	+	5.45579i	−0.492526	+	0.219287i	−0.637943	−	0.770084i	$-0.720214\pi$
$619$	−12.2539	+	5.45579i	−0.492526	+	0.219287i	0.145417	+	0.989371i	$0.453548\pi$
$620$		0			0
$621$	−0.122080	+	0.274195i	−0.00489889	+	0.0110031i
$622$	1.63811	−	10.3426i	0.0656821	−	0.414700i
$623$	−11.0462	−	18.6806i	−0.442558	−	0.748421i
$624$			5.91843i			0.236927i
$625$		0			0
$626$	−32.1690	−	18.5728i	−1.28573	−	0.742318i
$627$	0.148414	+	0.228538i	0.00592710	+	0.00912693i
$628$	10.5797	+	27.5611i	0.422177	+	1.09981i
$629$	−0.0870278	+	0.0632294i	−0.00347003	+	0.00252112i
$630$		0			0
$631$	−2.90402	−	2.10989i	−0.115607	−	0.0839935i	0.528479	−	0.848946i	$-0.322762\pi$
$631$	−2.90402	−	2.10989i	−0.115607	−	0.0839935i	−0.644087	+	0.764953i	$0.722762\pi$
$632$	−4.59746	+	17.1580i	−0.182877	+	0.682507i
$633$	−11.4768	−	4.40553i	−0.456162	−	0.175104i
$634$	−44.0004	+	39.6181i	−1.74748	+	1.57344i
$635$		0			0
$636$	−40.7253	+	13.2325i	−1.61486	+	0.524701i
$637$	−1.92666	−	0.264143i	−0.0763369	−	0.0104657i
$638$	4.48401	+	8.80037i	0.177524	+	0.348410i
$639$	−2.99989	−	2.70111i	−0.118674	−	0.106854i
$640$		0			0
$641$	19.9539	+	22.1611i	0.788133	+	0.875310i	0.994668	−	0.103129i	$-0.0328854\pi$
$641$	19.9539	+	22.1611i	0.788133	+	0.875310i	−0.206535	+	0.978439i	$0.566219\pi$
$642$	25.1835	+	31.0991i	0.993915	+	1.22738i
$643$	30.4036	+	30.4036i	1.19900	+	1.19900i	0.974466	+	0.224535i	$0.0720863\pi$
$643$	30.4036	+	30.4036i	1.19900	+	1.19900i	0.224535	+	0.974466i	$0.427914\pi$
$644$	−67.2056	−	9.92798i	−2.64827	−	0.391217i
$645$		0			0
$646$	0.220142	+	0.0980137i	0.00866139	+	0.00385630i
$647$	−27.3639	−	22.1589i	−1.07579	−	0.871155i	−0.0836728	−	0.996493i	$-0.526665\pi$
$647$	−27.3639	−	22.1589i	−1.07579	−	0.871155i	−0.992114	+	0.125338i	$0.959998\pi$
$648$	−53.2193	+	34.5610i	−2.09065	+	1.35768i
$649$	−15.2169	−	26.3564i	−0.597315	−	1.03458i
$650$		0			0
$651$	−13.9966	+	22.0523i	−0.548570	+	0.864299i
$652$	−41.6945	+	81.8300i	−1.63288	+	3.20471i
$653$	−6.98754	+	2.68227i	−0.273444	+	0.104965i	−0.491226	−	0.871032i	$-0.663451\pi$
$653$	−6.98754	+	2.68227i	−0.273444	+	0.104965i	0.217782	+	0.975997i	$0.430118\pi$
$654$	11.1441	+	106.029i	0.435767	+	4.14605i
$655$		0			0
$656$	48.9445	+	5.14427i	1.91096	+	0.200850i
$657$	17.2820	−	17.2820i	0.674235	−	0.674235i
$658$	2.71082	+	23.4406i	0.105679	+	0.913810i
$659$	−18.3227	−	5.95342i	−0.713753	−	0.231912i	−0.0704403	−	0.997516i	$-0.522440\pi$
$659$	−18.3227	−	5.95342i	−0.713753	−	0.231912i	−0.643313	+	0.765604i	$0.722440\pi$
$660$		0			0
$661$	4.30614	−	20.2588i	0.167489	−	0.787975i	−0.811547	−	0.584288i	$-0.801374\pi$
$661$	4.30614	−	20.2588i	0.167489	−	0.787975i	0.979036	−	0.203687i	$-0.0652926\pi$
$662$	4.57391	−	87.2754i	0.177770	−	3.39205i
$663$	−2.57961	−	1.67522i	−0.100184	−	0.0650601i
$664$	−14.7786	−	45.4839i	−0.573521	−	1.76512i
$665$		0			0
$666$	−0.0565881	+	0.174160i	−0.00219274	+	0.00674857i
$667$	2.98475	−	2.41700i	0.115570	−	0.0935868i
$668$	−81.3855	+	21.8072i	−3.14890	+	0.843745i
$669$	27.2402	+	61.1826i	1.05317	+	2.36545i
$670$		0			0
$671$	−6.13605	−	8.44555i	−0.236880	−	0.326037i
$672$	−41.5447	−	36.6308i	−1.60262	−	1.41306i
$673$	−27.6449	−	14.0858i	−1.06563	−	0.542968i	−0.168944	−	0.985626i	$-0.554036\pi$
$673$	−27.6449	−	14.0858i	−1.06563	−	0.542968i	−0.896691	+	0.442658i	$0.854036\pi$
$674$	−57.0862	+	32.9588i	−2.19888	+	1.26952i
$675$		0			0
$676$	−30.3892	+	52.6357i	−1.16882	+	2.02445i
$677$	1.41235	+	26.9492i	0.0542809	+	1.03574i	0.880997	+	0.473122i	$0.156873\pi$
$677$	1.41235	+	26.9492i	0.0542809	+	1.03574i	−0.826716	+	0.562620i	$0.809794\pi$
$678$	13.2889	+	2.10476i	0.510359	+	0.0808329i
$679$	33.2656	+	16.5155i	1.27662	+	0.633808i
$680$		0			0
$681$	−2.92189	+	27.7999i	−0.111967	+	1.06529i
$682$	14.6728	+	54.7596i	0.561851	+	2.09685i
$683$	11.6045	−	30.2309i	0.444036	−	1.15675i	−0.510821	−	0.859687i	$-0.670659\pi$
$683$	11.6045	−	30.2309i	0.444036	−	1.15675i	0.954857	−	0.297066i	$-0.0960080\pi$
$684$	0.281534	−	0.0598419i	0.0107647	−	0.00228811i
$685$		0			0
$686$	36.3032	−	31.3252i	1.38606	−	1.19600i
$687$	−23.4560	+	11.9514i	−0.894901	+	0.455975i
$688$	29.2455	−	45.0341i	1.11497	−	1.71691i
$689$	1.01195	+	0.215097i	0.0385523	+	0.00819455i
$690$		0			0
$691$	3.76383	+	17.7074i	0.143183	+	0.673622i	0.989922	+	0.141614i	$0.0452291\pi$
$691$	3.76383	+	17.7074i	0.143183	+	0.673622i	−0.846739	+	0.532008i	$0.821438\pi$
$692$	71.5446	−	11.3316i	2.71972	−	0.430761i
$693$	40.7642	+	12.7773i	1.54850	+	0.485369i
$694$	0.336925	−	0.463737i	0.0127895	−	0.0176032i
$695$		0			0
$696$	11.9714	−	1.25824i	0.453774	−	0.0476936i
$697$	−16.0960	+	19.8768i	−0.609678	+	0.752889i
$698$	23.6813	−	1.24109i	0.896351	−	0.0469758i
$699$	16.9601			0.641489
$700$		0			0
$701$	−8.89063			−0.335794			−0.167897	−	0.985805i	$-0.553698\pi$
$701$	−8.89063			−0.335794			−0.167897	+	0.985805i	$0.553698\pi$
$702$	0.0394887	−	0.00206951i	0.00149040	−	7.81088e-5i
$703$	−0.000307256	0	0.000379430i	−1.15884e−5	0	1.43105e-5i
$704$	−25.5725	+	2.68777i	−0.963798	+	0.101299i
$705$		0			0
$706$	−30.1185	+	41.4546i	−1.13353	+	1.56016i
$707$	−4.18388	+	3.84683i	−0.157351	+	0.144675i
$708$	−63.7385	+	10.0952i	−2.39544	+	0.379401i
$709$	1.90273	+	8.95164i	0.0714585	+	0.336186i	0.999325	−	0.0367258i	$-0.0116928\pi$
$709$	1.90273	+	8.95164i	0.0714585	+	0.336186i	−0.927867	+	0.372912i	$0.878359\pi$
$710$		0			0
$711$	−7.39203	−	1.57122i	−0.277223	−	0.0589255i
$712$	−31.2665	+	48.1461i	−1.17176	+	1.80435i
$713$	19.6419	−	10.0080i	0.735594	−	0.374804i
$714$	73.0481	−	20.3909i	2.73375	−	0.763110i
$715$		0			0
$716$	2.31815	−	0.492739i	0.0866334	−	0.0184145i
$717$	−15.4167	+	40.1620i	−0.575748	+	1.49988i
$718$	6.43738	+	24.0246i	0.240241	+	0.896591i
$719$	4.94586	−	47.0567i	0.184450	−	1.75492i	−0.375897	−	0.926662i	$-0.622665\pi$
$719$	4.94586	−	47.0567i	0.184450	−	1.75492i	0.560346	−	0.828258i	$-0.310668\pi$
$720$		0			0
$721$	−26.8956	+	1.69059i	−1.00164	+	0.0629607i
$722$	−48.5853	−	7.69515i	−1.80816	−	0.286384i
$723$	−0.136685	−	2.60810i	−0.00508335	−	0.0969961i
$724$	28.9238	−	50.0975i	1.07495	−	1.86186i
$725$		0			0
$726$	100.906	−	58.2581i	3.74498	−	2.16216i
$727$	34.9809	+	17.8237i	1.29737	+	0.661043i	0.959913	−	0.280298i	$-0.0904333\pi$
$727$	34.9809	+	17.8237i	1.29737	+	0.661043i	0.337457	+	0.941341i	$0.390433\pi$
$728$	1.64050	+	4.87557i	0.0608011	+	0.180701i
$729$	−15.6314	−	21.5148i	−0.578941	−	0.796844i
$730$		0			0
$731$	11.3506	+	25.4939i	0.419818	+	0.942926i
$732$	−21.3816	+	5.72918i	−0.790286	+	0.211757i
$733$	8.56030	−	6.93199i	0.316182	−	0.256039i	−0.458071	−	0.888916i	$-0.651459\pi$
$733$	8.56030	−	6.93199i	0.316182	−	0.256039i	0.774253	+	0.632877i	$0.218126\pi$
$734$	12.9394	−	39.8233i	0.477601	−	1.46991i
$735$		0			0
$736$	14.4456	+	44.4591i	0.532473	+	1.63878i
$737$	−69.1261	−	44.8910i	−2.54629	−	1.65358i
$738$	−2.27870	+	43.4802i	−0.0838801	+	1.60053i
$739$	−6.86091	+	32.2780i	−0.252383	+	1.18737i	0.651184	+	0.758920i	$0.274273\pi$
$739$	−6.86091	+	32.2780i	−0.252383	+	1.18737i	−0.903567	+	0.428447i	$0.859061\pi$
$740$		0			0
$741$	−0.0132769	−	0.00431393i	−0.000487740	−	0.000158476i
$742$	−20.4800	+	15.2080i	−0.751846	+	0.558303i
$743$	2.10074	−	2.10074i	0.0770687	−	0.0770687i	−0.667522	−	0.744590i	$-0.732645\pi$
$743$	2.10074	−	2.10074i	0.0770687	−	0.0770687i	0.744590	+	0.667522i	$0.232645\pi$
$744$	68.7133	+	7.22206i	2.51915	+	0.264774i
$745$		0			0
$746$	3.94202	+	37.5058i	0.144328	+	1.37318i
$747$	18.9950	−	7.29151i	0.694992	−	0.266782i
$748$	52.4345	−	102.909i	1.91720	−	3.76271i
$749$	14.1217	+	8.96306i	0.515997	+	0.327503i
$750$		0			0
$751$	−9.49836	−	16.4516i	−0.346600	−	0.600329i	0.639043	−	0.769171i	$-0.279331\pi$
$751$	−9.49836	−	16.4516i	−0.346600	−	0.600329i	−0.985643	+	0.168842i	$0.945997\pi$
$752$	25.1740	−	16.3482i	0.918001	−	0.596157i
$753$	−38.5785	−	31.2403i	−1.40588	−	1.13846i
$754$	−0.462247	−	0.205806i	−0.0168340	−	0.00749500i
$755$		0			0
$756$	−0.424957	+	0.536100i	−0.0154555	+	0.0194978i
$757$	17.4136	+	17.4136i	0.632909	+	0.632909i	0.948797	−	0.315887i	$-0.102302\pi$
$757$	17.4136	+	17.4136i	0.632909	+	0.632909i	−0.315887	+	0.948797i	$0.602302\pi$
$758$	−33.6574	−	41.5634i	−1.22249	−	1.50965i
$759$	−48.4339	−	53.7913i	−1.75804	−	1.95250i
$760$		0			0
$761$	24.5170	+	22.0752i	0.888741	+	0.800226i	0.980696	−	0.195537i	$-0.0626449\pi$
$761$	24.5170	+	22.0752i	0.888741	+	0.800226i	−0.0919551	+	0.995763i	$0.529312\pi$
$762$	−30.0332	−	58.9435i	−1.08799	−	2.13530i
$763$	18.5477	+	40.5177i	0.671471	+	1.46684i
$764$	59.8280	−	19.4393i	2.16450	−	0.703289i
$765$		0			0
$766$	−65.8997	+	59.3364i	−2.38105	+	2.14391i
$767$	1.45556	+	0.558739i	0.0525574	+	0.0201749i
$768$	13.9445	−	52.0416i	0.503179	−	1.87789i
$769$	−11.2664	−	8.18549i	−0.406275	−	0.295176i	0.365817	−	0.930687i	$-0.380790\pi$
$769$	−11.2664	−	8.18549i	−0.406275	−	0.295176i	−0.772092	+	0.635511i	$0.780790\pi$
$770$		0			0
$771$	−45.3468	+	32.9464i	−1.63312	+	1.18653i
$772$	4.21162	+	10.9717i	0.151580	+	0.394878i
$773$	3.25938	+	5.01900i	0.117232	+	0.180521i	0.892415	−	0.451215i	$-0.149009\pi$
$773$	3.25938	+	5.01900i	0.117232	+	0.180521i	−0.775184	+	0.631736i	$0.782343\pi$
$774$	41.1414	+	23.7530i	1.47880	+	0.853784i
$775$		0			0
$776$		−	98.2441i		−	3.52676i
$777$	0.00160031	+	0.153650i	5.74107e−5	+	0.00551218i
$778$	−1.20364	+	7.59951i	−0.0431527	+	0.272456i
$779$	−0.0472157	+	0.106048i	−0.00169168	+	0.00379957i
$780$		0			0
$781$	−6.71637	+	2.99032i	−0.240330	+	0.107002i
$782$	−61.8285	−	16.5669i	−2.21098	−	0.592431i
$783$	−0.00605012	−	0.0381989i	−0.000216214	−	0.00136512i
$784$	−56.2264	−	23.6430i	−2.00809	−	0.844391i
$785$		0			0
$786$	78.5433	−	87.2311i	2.80155	−	3.11143i
$787$	4.95092	+	0.259467i	0.176481	+	0.00924899i	0.140372	−	0.990099i	$-0.455170\pi$
$787$	4.95092	+	0.259467i	0.176481	+	0.00924899i	0.0361094	+	0.999348i	$0.488504\pi$
$788$	−121.126	−	6.34797i	−4.31495	−	0.226137i
$789$	38.9020	−	43.2050i	1.38495	−	1.53814i
$790$		0			0
$791$	5.54495	−	0.937533i	0.197156	−	0.0333348i
$792$	−17.6778	−	111.613i	−0.628154	−	3.96601i
$793$	0.516580	+	0.138417i	0.0183443	+	0.00491534i
$794$	42.8854	−	19.0938i	1.52195	−	0.677614i
$795$		0			0
$796$	36.3764	−	81.7028i	1.28933	−	2.89588i
$797$	6.03107	−	38.0787i	0.213632	−	1.34882i	−0.614781	−	0.788698i	$-0.710756\pi$
$797$	6.03107	−	38.0787i	0.213632	−	1.34882i	0.828412	−	0.560119i	$-0.189244\pi$
$798$	0.296291	−	0.175203i	0.0104886	−	0.00620212i
$799$			15.5997i			0.551878i
$800$		0			0
$801$	−21.1513	−	12.2117i	−0.747346	−	0.431480i
$802$	−41.8156	−	64.3904i	−1.47656	−	2.27371i
$803$	−15.9518	−	41.5559i	−0.562928	−	1.46648i
$804$	−141.395	+	102.730i	−4.98662	+	3.62299i
$805$		0			0
$806$	−2.34962	−	1.70710i	−0.0827619	−	0.0601301i
$807$	−3.67922	+	13.7310i	−0.129515	+	0.483356i
$808$	14.0359	+	5.38788i	0.493781	+	0.189545i
$809$	23.3940	−	21.0641i	0.822490	−	0.740574i	−0.146091	−	0.989271i	$-0.546669\pi$
$809$	23.3940	−	21.0641i	0.822490	−	0.740574i	0.968581	+	0.248698i	$0.0800025\pi$
$810$		0			0
$811$	−20.5598	+	6.68028i	−0.721952	+	0.234576i	−0.646869	−	0.762601i	$-0.723922\pi$
$811$	−20.5598	+	6.68028i	−0.721952	+	0.234576i	−0.0750826	+	0.997177i	$0.523922\pi$
$812$	7.95944	−	3.64357i	0.279322	−	0.127864i
$813$	18.7169	+	36.7340i	0.656430	+	1.28832i
$814$	0.247850	+	0.223165i	0.00868713	+	0.00782193i
$815$		0			0
$816$	−64.5535	−	71.6940i	−2.25983	−	2.50979i
$817$	0.0797088	+	0.0984322i	0.00278866	+	0.00344371i
$818$	−16.4149	−	16.4149i	−0.573932	−	0.573932i
$819$	−2.03489	+	0.805536i	−0.0711048	+	0.0281477i
$820$		0			0
$821$	5.44192	+	2.42290i	0.189924	+	0.0845597i	0.499495	−	0.866317i	$-0.333519\pi$
$821$	5.44192	+	2.42290i	0.189924	+	0.0845597i	−0.309571	+	0.950876i	$0.600185\pi$
$822$	54.2162	+	43.9035i	1.89101	+	1.53131i
$823$	30.1026	−	19.5489i	1.04931	−	0.681431i	0.0997500	−	0.995013i	$-0.468196\pi$
$823$	30.1026	−	19.5489i	1.04931	−	0.681431i	0.949561	+	0.313582i	$0.101529\pi$
$824$	35.6431	+	61.7356i	1.24169	+	2.15066i
$825$		0			0
$826$	−34.0695	+	17.8086i	−1.18543	+	0.619642i
$827$	9.72304	−	19.0825i	0.338103	−	0.663565i	−0.657878	−	0.753124i	$-0.728546\pi$
$827$	9.72304	−	19.0825i	0.338103	−	0.663565i	0.995981	+	0.0895595i	$0.0285459\pi$
$828$	−71.3756	+	27.3985i	−2.48047	+	0.952165i
$829$	−2.22744	−	21.1927i	−0.0773622	−	0.736052i	−0.962602	−	0.270918i	$-0.912673\pi$
$829$	−2.22744	−	21.1927i	−0.0773622	−	0.736052i	0.885240	−	0.465134i	$-0.153994\pi$
$830$		0			0
$831$	−50.7327	−	5.33222i	−1.75990	−	0.184973i
$832$	0.931465	−	0.931465i	0.0322928	−	0.0322928i
$833$	26.2199	−	17.8147i	0.908467	−	0.617242i
$834$	−33.7769	−	10.9748i	−1.16960	−	0.380025i
$835$		0			0
$836$	0.108988	−	0.512747i	0.00376942	−	0.0177337i
$837$	0.0116179	−	0.221683i	0.000401574	−	0.00766248i
$838$	−37.4233	−	24.3030i	−1.29277	−	0.839533i
$839$	12.8534	+	39.5588i	0.443750	+	1.36572i	0.883849	+	0.467773i	$0.154943\pi$
$839$	12.8534	+	39.5588i	0.443750	+	1.36572i	−0.440099	+	0.897949i	$0.645057\pi$
$840$		0			0
$841$	8.80856	−	27.1100i	0.303744	−	0.934827i
$842$	24.1610	−	19.5652i	0.832642	−	0.674260i
$843$	29.3262	−	7.85793i	1.01005	−	0.270641i
$844$	9.61865	+	21.6038i	0.331088	+	0.743635i
$845$		0			0
$846$	15.6091	+	21.4841i	0.536651	+	0.738637i
$847$	32.2084	−	36.5291i	1.10669	−	1.25515i
$848$	28.9124	+	14.7316i	0.992854	+	0.505884i
$849$	−10.5030	+	6.06392i	−0.360462	+	0.208113i
$850$		0			0
$851$	0.0648441	−	0.112313i	0.00222283	−	0.00385005i
$852$	0.815888	+	15.5681i	0.0279519	+	0.533353i
$853$	36.3011	+	5.74952i	1.24292	+	0.196860i	0.743049	−	0.669237i	$-0.233379\pi$
$853$	36.3011	+	5.74952i	1.24292	+	0.196860i	0.499876	+	0.866097i	$0.333379\pi$
$854$	−10.9838	+	7.29674i	−0.375859	+	0.249689i
$855$		0			0
$856$	4.62482	−	44.0022i	0.158073	−	1.50397i
$857$	1.40103	+	5.22871i	0.0478582	+	0.178609i	0.985718	−	0.168406i	$-0.0538619\pi$
$857$	1.40103	+	5.22871i	0.0478582	+	0.178609i	−0.937860	+	0.347015i	$0.887195\pi$
$858$	−3.41748	+	8.90284i	−0.116671	+	0.303938i
$859$	−20.0684	+	4.26566i	−0.684723	+	0.145542i	−0.537122	−	0.843504i	$-0.680489\pi$
$859$	−20.0684	+	4.26566i	−0.684723	+	0.145542i	−0.147601	+	0.989047i	$0.547155\pi$
$860$		0			0
$861$	9.82281	+	35.1891i	0.334761	+	1.19924i
$862$	52.5228	−	26.7617i	1.78894	−	0.911508i
$863$	1.11554	−	1.71778i	0.0379733	−	0.0584738i	−0.819174	−	0.573545i	$-0.805568\pi$
$863$	1.11554	−	1.71778i	0.0379733	−	0.0584738i	0.857147	+	0.515071i	$0.172234\pi$
$864$	0.460452	+	0.0978721i	0.0156649	+	0.00332968i
$865$		0			0
$866$	−2.27469	−	10.7016i	−0.0772970	−	0.363654i
$867$	8.46896	−	1.34135i	0.287621	−	0.0455547i
$868$	49.0354	−	10.9578i	1.66437	−	0.371931i
$869$	−8.09004	+	11.1350i	−0.274436	+	0.377728i
$870$		0			0
$871$	4.19941	−	0.441376i	0.142292	−	0.0149555i
$872$	74.1816	−	91.6067i	2.51211	−	3.10219i
$873$	41.7396	−	2.18748i	1.41267	−	0.0740350i
$874$	−0.290518			−0.00982693
$875$		0			0
$876$	−94.3860			−3.18901
$877$	26.7720	−	1.40306i	0.904025	−	0.0473779i	0.405345	−	0.914164i	$-0.367152\pi$
$877$	26.7720	−	1.40306i	0.904025	−	0.0473779i	0.498680	+	0.866786i	$0.333818\pi$
$878$	20.3939	−	25.1844i	0.688261	−	0.849932i
$879$	−25.8320	+	2.71505i	−0.871291	+	0.0915764i
$880$		0			0
$881$	−1.86581	+	2.56806i	−0.0628607	+	0.0865203i	−0.839290	−	0.543684i	$-0.817029\pi$
$881$	−1.86581	+	2.56806i	−0.0628607	+	0.0865203i	0.776429	+	0.630204i	$0.217029\pi$
$882$	18.2850	−	50.7702i	0.615687	−	1.70952i
$883$	2.39702	−	0.379650i	0.0806661	−	0.0127763i	−0.115971	−	0.993253i	$-0.536998\pi$
$883$	2.39702	−	0.379650i	0.0806661	−	0.0127763i	0.196637	+	0.980476i	$0.436998\pi$
$884$	1.23019	+	5.78760i	0.0413759	+	0.194658i
$885$		0			0
$886$	−42.0976	−	8.94813i	−1.41430	−	0.300618i
$887$	2.87223	−	4.42285i	0.0964401	−	0.148505i	−0.787157	−	0.616753i	$-0.788448\pi$
$887$	2.87223	−	4.42285i	0.0964401	−	0.148505i	0.883597	+	0.468248i	$0.155115\pi$
$888$	0.362164	−	0.184532i	0.0121534	−	0.00619249i
$889$	−19.7544	−	19.3472i	−0.662542	−	0.648883i
$890$		0			0
$891$	−48.0941	+	10.2227i	−1.61121	+	0.342474i
$892$	46.1698	−	120.277i	1.54588	−	4.02716i
$893$	0.0183249	+	0.0683894i	0.000613219	+	0.00228856i
$894$	−1.74018	+	16.5567i	−0.0582002	+	0.553738i
$895$		0			0
$896$	−0.804762	−	12.8030i	−0.0268852	−	0.427718i
$897$	3.66254	+	0.580089i	0.122289	+	0.0193686i
$898$	4.14579	+	79.1065i	0.138347	+	2.63982i
$899$	−1.42028	+	2.45999i	−0.0473689	+	0.0820454i
$900$		0			0
$901$	−14.6046	+	8.43195i	−0.486549	+	0.280909i
$902$	70.6546	+	36.0003i	2.35254	+	1.19868i
$903$	39.0755	+	7.88132i	1.30035	+	0.262274i
$904$	−8.74389	−	12.0349i	−0.290817	−	0.400276i
$905$		0			0
$906$	−13.0080	−	29.2165i	−0.432162	−	0.970652i
$907$	14.3895	−	3.85565i	0.477795	−	0.128025i	−0.0118806	−	0.999929i	$-0.503782\pi$
$907$	14.3895	−	3.85565i	0.477795	−	0.128025i	0.489676	+	0.871905i	$0.337115\pi$
$908$	41.7891	−	33.8402i	1.38682	−	1.12303i
$909$	−1.97655	+	6.08321i	−0.0655581	+	0.201767i
$910$		0			0
$911$	9.35146	+	28.7808i	0.309828	+	0.953551i	0.977831	+	0.209394i	$0.0671490\pi$
$911$	9.35146	+	28.7808i	0.309828	+	0.953551i	−0.668004	+	0.744158i	$0.732851\pi$
$912$	−0.367222	−	0.238477i	−0.0121599	−	0.00789676i
$913$	1.93937	−	37.0054i	0.0641838	−	1.22470i
$914$	−15.2495	+	71.7431i	−0.504408	+	2.37305i
$915$		0			0
$916$	48.1627	+	15.6490i	1.59134	+	0.517058i
$917$	19.4875	−	45.0259i	0.643534	−	1.48689i
$918$	−0.455780	+	0.455780i	−0.0150430	+	0.0150430i
$919$	−54.4821	−	5.72630i	−1.79720	−	0.188893i	−0.853810	−	0.520584i	$-0.825714\pi$
$919$	−54.4821	−	5.72630i	−1.79720	−	0.188893i	−0.943388	+	0.331691i	$0.892381\pi$
$920$		0			0
$921$	−1.08184	−	10.2930i	−0.0356478	−	0.339166i
$922$	13.4021	−	5.14459i	0.441375	−	0.169428i
$923$	0.170992	−	0.335590i	0.00562825	−	0.0110461i
$924$	−76.4256	−	146.209i	−2.51422	−	4.80992i
$925$		0			0
$926$	50.2320	+	87.0044i	1.65073	+	2.85914i
$927$	−25.4351	+	16.5178i	−0.835399	+	0.542515i
$928$	−4.68121	−	3.79077i	−0.153668	−	0.124438i
$929$	51.4693	+	22.9156i	1.68865	+	0.751837i	0.999633	+	0.0270962i	$0.00862604\pi$
$929$	51.4693	+	22.9156i	1.68865	+	0.751837i	0.689021	+	0.724741i	$0.258041\pi$
$930$		0			0
$931$	0.0940219	−	0.108900i	0.00308144	−	0.00356906i
$932$	−23.0698	−	23.0698i	−0.755678	−	0.755678i
$933$	−6.22302	−	7.68479i	−0.203733	−	0.251589i
$934$	32.6575	+	36.2699i	1.06859	+	1.18679i
$935$		0			0
$936$	4.30223	+	3.87374i	0.140623	+	0.126617i
$937$	8.84942	+	17.3680i	0.289098	+	0.567387i	0.989185	−	0.146670i	$-0.0468557\pi$
$937$	8.84942	+	17.3680i	0.289098	+	0.567387i	−0.700087	+	0.714057i	$0.746856\pi$
$938$	−60.3168	+	84.8637i	−1.96941	+	2.77090i
$939$	−33.3606	+	10.8395i	−1.08868	+	0.353734i
$940$		0			0
$941$	26.4414	−	23.8079i	0.861964	−	0.776116i	−0.114130	−	0.993466i	$-0.536408\pi$
$941$	26.4414	−	23.8079i	0.861964	−	0.776116i	0.976094	+	0.217350i	$0.0697413\pi$
$942$	37.0941	+	14.2391i	1.20859	+	0.463935i
$943$	7.98070	−	29.7844i	0.259887	−	0.969913i
$944$	39.5625	+	28.7439i	1.28765	+	0.935533i
$945$		0			0
$946$	69.9968	−	50.8557i	2.27579	−	1.65346i
$947$	8.87912	+	23.1309i	0.288533	+	0.751653i	0.998858	+	0.0477796i	$0.0152145\pi$
$947$	8.87912	+	23.1309i	0.288533	+	0.751653i	−0.710325	+	0.703874i	$0.751452\pi$
$948$	15.8952	+	24.4765i	0.516253	+	0.794960i
$949$	1.97486	+	1.14018i	0.0641065	+	0.0370119i
$950$		0			0
$951$			55.9117i			1.81306i
$952$	−73.0514	−	41.1678i	−2.36761	−	1.33426i
$953$	−1.31208	+	8.28414i	−0.0425024	+	0.268350i	−0.999783	−	0.0208095i	$-0.993376\pi$
$953$	−1.31208	+	8.28414i	−0.0425024	+	0.268350i	0.957281	+	0.289159i	$0.0933757\pi$
$954$	−11.6765	+	26.2259i	−0.378041	+	0.849095i
$955$		0			0
$956$	75.6006	−	33.6595i	2.44510	−	1.08863i
$957$	9.00915	+	2.41399i	0.291224	+	0.0780333i
$958$	7.86484	+	49.6567i	0.254102	+	1.60433i
$959$	27.3298	+	10.1656i	0.882524	+	0.328265i
$960$		0			0
$961$	9.83340	−	10.9211i	0.317206	−	0.352293i
$962$	−0.0170625		0.000894208i	−0.000550118		2.88304e-5i
$963$	18.7976	+	0.985140i	0.605744	+	0.0317457i
$964$	−3.36172	+	3.73357i	−0.108274	+	0.120250i
$965$		0			0
$966$	−70.4535	+	58.2775i	−2.26681	+	1.87505i
$967$	5.16582	+	32.6157i	0.166121	+	1.04885i	0.920024	+	0.391863i	$0.128169\pi$
$967$	5.16582	+	32.6157i	0.166121	+	1.04885i	−0.753902	+	0.656987i	$0.771831\pi$
$968$	−124.436	−	33.3425i	−3.99952	−	1.07167i
$969$	0.207885	−	0.0925564i	0.00667823	−	0.00297334i
$970$		0			0
$971$	−7.08660	+	15.9168i	−0.227420	+	0.510793i	−0.990829	−	0.135122i	$-0.956857\pi$
$971$	−7.08660	+	15.9168i	−0.227420	+	0.510793i	0.763409	+	0.645915i	$0.223524\pi$
$972$	−16.1884	+	102.209i	−0.519242	+	3.27836i
$973$	−14.8436	+	0.154599i	−0.475862	+	0.00495622i
$974$		−	3.04241i		−	0.0974850i
$975$		0			0
$976$	14.5268	+	8.38707i	0.464993	+	0.268464i
$977$	−12.5495	−	19.3245i	−0.401493	−	0.618245i	0.578876	−	0.815416i	$-0.303491\pi$
$977$	−12.5495	−	19.3245i	−0.401493	−	0.618245i	−0.980369	+	0.197170i	$0.936825\pi$
$978$	44.2965	+	115.396i	1.41645	+	3.68997i
$979$	−35.9863	+	26.1456i	−1.15013	+	0.835617i
$980$		0			0
$981$	40.5714	+	29.4768i	1.29534	+	0.941123i
$982$	−8.91563	+	33.2736i	−0.284509	+	1.06180i
$983$	−21.8734	−	8.39643i	−0.697654	−	0.267804i	−0.0164151	−	0.999865i	$-0.505225\pi$
$983$	−21.8734	−	8.39643i	−0.697654	−	0.267804i	−0.681239	+	0.732061i	$0.738559\pi$
$984$	71.8196	−	64.6666i	2.28952	−	2.06150i
$985$		0			0
$986$	7.84427	−	2.54876i	0.249812	−	0.0811690i
$987$	18.1628	+	12.9092i	0.578127	+	0.410903i
$988$	0.0121918	+	0.0239278i	0.000387874	+	0.000761246i
$989$	−25.0023	−	22.5122i	−0.795026	−	0.715845i
$990$		0			0
$991$	24.9088	+	27.6641i	0.791255	+	0.878778i	0.994962	−	0.100254i	$-0.0319655\pi$
$991$	24.9088	+	27.6641i	0.791255	+	0.878778i	−0.203706	+	0.979032i	$0.565299\pi$
$992$	−21.7583	−	26.8692i	−0.690825	−	0.853098i
$993$	−58.3569	−	58.3569i	−1.85190	−	1.85190i
$994$	3.41822	+	8.63487i	0.108419	+	0.273882i
$995$		0			0
$996$	−71.7823	−	31.9595i	−2.27451	−	1.01268i
$997$	20.8290	+	16.8670i	0.659660	+	0.534182i	0.899660	−	0.436591i	$-0.143814\pi$
$997$	20.8290	+	16.8670i	0.659660	+	0.534182i	−0.240000	+	0.970773i	$0.577148\pi$
$998$	79.8797	−	51.8745i	2.52855	−	1.64206i
$999$	−0.000652974	−	0.00113098i	−2.06592e−5	−	3.57828e-5i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.857.2		288
5.2	odd	4		175.2.x.a.108.2	yes	288
5.3	odd	4		875.2.bb.c.143.17		288
5.4	even	2		875.2.bb.b.857.17		288
7.5	odd	6	inner	875.2.bb.a.607.17		288
25.3	odd	20	inner	875.2.bb.a.493.17		288
25.4	even	10		175.2.x.a.122.2	yes	288
25.21	even	5		875.2.bb.c.507.17		288
25.22	odd	20		875.2.bb.b.493.2		288
35.12	even	12		175.2.x.a.33.2	✓	288
35.19	odd	6		875.2.bb.b.607.2		288
35.33	even	12		875.2.bb.c.768.17		288
175.47	even	60		875.2.bb.b.243.17		288
175.54	odd	30		175.2.x.a.47.2	yes	288
175.96	odd	30		875.2.bb.c.257.17		288
175.103	even	60	inner	875.2.bb.a.243.2		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.2	✓	288	35.12	even	12
175.2.x.a.47.2	yes	288	175.54	odd	30
175.2.x.a.108.2	yes	288	5.2	odd	4
175.2.x.a.122.2	yes	288	25.4	even	10
875.2.bb.a.243.2		288	175.103	even	60	inner
875.2.bb.a.493.17		288	25.3	odd	20	inner
875.2.bb.a.607.17		288	7.5	odd	6	inner
875.2.bb.a.857.2		288	1.1	even	1	trivial
875.2.bb.b.243.17		288	175.47	even	60
875.2.bb.b.493.2		288	25.22	odd	20
875.2.bb.b.607.2		288	35.19	odd	6
875.2.bb.b.857.17		288	5.4	even	2
875.2.bb.c.143.17		288	5.3	odd	4
875.2.bb.c.257.17		288	175.96	odd	30
875.2.bb.c.507.17		288	25.21	even	5
875.2.bb.c.768.17		288	35.33	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.58550 + 0.135500i) q^{2} +(-1.53862 + 1.90004i) q^{3} +(4.67742 - 0.491617i) q^{4} +(3.72066 - 5.12104i) q^{6} +(0.791332 - 2.52464i) q^{7} +(-6.91252 + 1.09484i) q^{8} +(-0.619060 - 2.91245i) q^{9} +(-5.30433 - 1.12747i) q^{11} +(-6.26269 + 9.64370i) q^{12} +(0.247532 - 0.126124i) q^{13} +(-1.70390 + 6.63468i) q^{14} +(8.52317 - 1.81165i) q^{16} +(-1.62286 + 4.22770i) q^{17} +(1.99522 + 7.44626i) q^{18} +(-0.00214840 + 0.0204407i) q^{19} +(3.57935 + 5.38803i) q^{21} +(13.8671 + 2.19634i) q^{22} +(-0.285728 - 5.45201i) q^{23} +(8.55552 - 14.8186i) q^{24} +(-0.622904 + 0.359634i) q^{26} +(-0.0489845 - 0.0249589i) q^{27} +(2.46024 - 12.1978i) q^{28} +(0.413497 + 0.569129i) q^{29} +(1.64234 + 3.68876i) q^{31} +(-8.27077 + 2.21615i) q^{32} +(10.3036 - 8.34369i) q^{33} +(3.62306 - 11.1506i) q^{34} +(-4.32741 - 13.3184i) q^{36} +(0.0199223 + 0.0129377i) q^{37} +(0.00278498 - 0.0531405i) q^{38} +(-0.141218 + 0.664377i) q^{39} +(5.37154 + 1.74532i) q^{41} +(-9.98451 - 13.4458i) q^{42} +(4.35752 - 4.35752i) q^{43} +(-25.3649 - 2.66596i) q^{44} +(1.47750 + 14.0575i) q^{46} +(3.21600 - 1.23451i) q^{47} +(-9.67172 + 18.9818i) q^{48} +(-5.74759 - 3.99565i) q^{49} +(-5.53583 - 9.58833i) q^{51} +(1.09581 - 0.711624i) q^{52} +(2.89407 + 2.34357i) q^{53} +(0.130032 + 0.0578938i) q^{54} +(-2.70603 + 18.3180i) q^{56} +(-0.0355325 - 0.0355325i) q^{57} +(-1.14621 - 1.41546i) q^{58} +(3.75527 + 4.17065i) q^{59} +(1.43060 + 1.28812i) q^{61} +(-4.74610 - 9.31476i) q^{62} +(-7.84276 - 0.741811i) q^{63} +(4.50960 - 1.46526i) q^{64} +(-25.5094 + 22.9688i) q^{66} +(14.1898 + 5.44695i) q^{67} +(-5.51240 + 20.5725i) q^{68} +(10.7987 + 7.84569i) q^{69} +(1.09682 - 0.796887i) q^{71} +(7.46791 + 19.4546i) q^{72} +(4.47058 + 6.88409i) q^{73} +(-0.0532622 - 0.0307510i) q^{74} +0.0966658i q^{76} +(-7.04394 + 12.4993i) q^{77} +(0.275095 - 1.73688i) q^{78} +(1.03233 - 2.31865i) q^{79} +(8.28307 - 3.68786i) q^{81} +(-14.1246 - 3.78468i) q^{82} +(1.06897 + 6.74923i) q^{83} +(19.3910 + 23.4424i) q^{84} +(-10.6759 + 11.8568i) q^{86} +(-1.71758 - 0.0900148i) q^{87} +(37.9007 + 1.98629i) q^{88} +(5.48864 - 6.09575i) q^{89} +(-0.122537 - 0.724733i) q^{91} +(-4.01677 - 25.3609i) q^{92} +(-9.53573 - 2.55509i) q^{93} +(-8.14770 + 3.62759i) q^{94} +(8.51483 - 19.1246i) q^{96} +(-2.19595 + 13.8647i) q^{97} +(15.4018 + 9.55197i) q^{98} +16.1466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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