LMFDB - Embedded newform 875.2.bb.b.493.11

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			493.11
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.b.607.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.226901 - 0.349398i) q^{2} +(0.446713 - 1.16373i) q^{3} +(0.742879 + 1.66853i) q^{4} +(-0.305244 - 0.420132i) q^{6} +(2.40197 + 1.10931i) q^{7} +(1.57450 + 0.249376i) q^{8} +(1.07473 + 0.967688i) q^{9} +(-2.78759 - 3.09593i) q^{11} +(2.27357 - 0.119153i) q^{12} +(0.406529 + 0.207137i) q^{13} +(0.932599 - 0.587538i) q^{14} +(-1.99986 + 2.22107i) q^{16} +(0.713032 - 0.880521i) q^{17} +(0.581965 - 0.155937i) q^{18} +(0.247218 + 0.110068i) q^{19} +(2.36392 - 2.29969i) q^{21} +(-1.71422 + 0.271506i) q^{22} +(7.54118 + 4.89730i) q^{23} +(0.993556 - 1.72089i) q^{24} +(0.164615 - 0.0950407i) q^{26} +(4.93819 - 2.51613i) q^{27} +(-0.0665460 + 4.83184i) q^{28} +(-1.26059 + 1.73505i) q^{29} +(-6.75621 + 0.710106i) q^{31} +(1.14745 + 4.28233i) q^{32} +(-4.84808 + 1.86100i) q^{33} +(-0.145864 - 0.448923i) q^{34} +(-0.816228 + 2.51209i) q^{36} +(0.0958050 + 1.82807i) q^{37} +(0.0945518 - 0.0614026i) q^{38} +(0.422653 - 0.380558i) q^{39} +(6.60977 - 2.14764i) q^{41} +(-0.267130 - 1.34775i) q^{42} +(-6.90254 - 6.90254i) q^{43} +(3.09483 - 6.95109i) q^{44} +(3.42221 - 1.52367i) q^{46} +(-0.0134006 + 0.0108516i) q^{47} +(1.69136 + 3.31947i) q^{48} +(4.53888 + 5.32903i) q^{49} +(-0.706165 - 1.22311i) q^{51} +(-0.0436130 + 0.832185i) q^{52} +(6.32342 + 2.42733i) q^{53} +(0.241352 - 2.29631i) q^{54} +(3.50526 + 2.34560i) q^{56} +(0.238525 - 0.238525i) q^{57} +(0.320193 + 0.834132i) q^{58} +(10.5132 + 2.23464i) q^{59} +(-2.23943 - 10.5357i) q^{61} +(-1.28488 + 2.52173i) q^{62} +(1.50799 + 3.51655i) q^{63} +(-3.92834 - 1.27640i) q^{64} +(-0.449806 + 2.11617i) q^{66} +(1.46122 + 1.18327i) q^{67} +(1.99887 + 0.535597i) q^{68} +(9.06786 - 6.58819i) q^{69} +(-7.24631 - 5.26475i) q^{71} +(1.45084 + 1.79164i) q^{72} +(-5.20142 - 0.272595i) q^{73} +(0.660461 + 0.381317i) q^{74} +0.494259i q^{76} +(-3.26136 - 10.5286i) q^{77} +(-0.0370656 - 0.234023i) q^{78} +(-14.7078 - 1.54585i) q^{79} +(-0.268636 - 2.55590i) q^{81} +(0.749384 - 2.79674i) q^{82} +(2.10145 - 13.2680i) q^{83} +(5.59322 + 2.23589i) q^{84} +(-3.97793 + 0.845535i) q^{86} +(1.45600 + 2.24205i) q^{87} +(-3.61701 - 5.56971i) q^{88} +(-3.99599 + 0.849374i) q^{89} +(0.746691 + 0.948502i) q^{91} +(-2.56912 + 16.2208i) q^{92} +(-2.19171 + 8.17959i) q^{93} +(0.000750902 + 0.00714436i) q^{94} +(5.49604 + 0.577657i) q^{96} +(-1.29756 - 8.19248i) q^{97} +(2.89183 - 0.376707i) q^{98} -6.02480i 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.226901	−	0.349398i	0.160444	−	0.247061i	−0.749301	−	0.662229i	$-0.769610\pi$
$2$	0.226901	−	0.349398i	0.160444	−	0.247061i	0.909745	+	0.415168i	$0.136277\pi$
$3$	0.446713	−	1.16373i	0.257910	−	0.671878i	−0.742089	−	0.670301i	$-0.766165\pi$
$3$	0.446713	−	1.16373i	0.257910	−	0.671878i	0.999999	−	0.00157664i	$-0.000501860\pi$
$4$	0.742879	+	1.66853i	0.371439	+	0.834267i
$5$		0			0
$5$		0			0
$6$	−0.305244	−	0.420132i	−0.124615	−	0.171518i
$7$	2.40197	+	1.10931i	0.907858	+	0.419279i
$7$	2.40197	+	1.10931i	0.907858	+	0.419279i
$8$	1.57450	+	0.249376i	0.556670	+	0.0881679i
$9$	1.07473	+	0.967688i	0.358242	+	0.322563i
$10$		0			0
$11$	−2.78759	−	3.09593i	−0.840491	−	0.933459i	0.158052	−	0.987431i	$-0.449479\pi$
$11$	−2.78759	−	3.09593i	−0.840491	−	0.933459i	−0.998542	+	0.0539714i	$0.982812\pi$
$12$	2.27357	−	0.119153i	0.656323	−	0.0343964i
$13$	0.406529	+	0.207137i	0.112751	+	0.0574495i	0.509456	−	0.860497i	$-0.329847\pi$
$13$	0.406529	+	0.207137i	0.112751	+	0.0574495i	−0.396705	+	0.917946i	$0.629847\pi$
$14$	0.932599	−	0.587538i	0.249247	−	0.157026i
$15$		0			0
$16$	−1.99986	+	2.22107i	−0.499965	+	0.555268i
$17$	0.713032	−	0.880521i	0.172936	−	0.213558i	−0.683308	−	0.730131i	$-0.739459\pi$
$17$	0.713032	−	0.880521i	0.172936	−	0.213558i	0.856243	+	0.516573i	$0.172793\pi$
$18$	0.581965	−	0.155937i	0.137170	−	0.0367547i
$19$	0.247218	+	0.110068i	0.0567157	+	0.0252514i	0.434898	−	0.900479i	$-0.356784\pi$
$19$	0.247218	+	0.110068i	0.0567157	+	0.0252514i	−0.378183	+	0.925731i	$0.623451\pi$
$20$		0			0
$21$	2.36392	−	2.29969i	0.515850	−	0.501834i
$22$	−1.71422	+	0.271506i	−0.365473	+	0.0578853i
$23$	7.54118	+	4.89730i	1.57244	+	1.02116i	0.975803	+	0.218649i	$0.0701651\pi$
$23$	7.54118	+	4.89730i	1.57244	+	1.02116i	0.596641	+	0.802508i	$0.296502\pi$
$24$	0.993556	−	1.72089i	0.202809	−	0.351275i
$25$		0			0
$26$	0.164615	−	0.0950407i	0.0322837	−	0.0186390i
$27$	4.93819	−	2.51613i	0.950356	−	0.484230i
$28$	−0.0665460	+	4.83184i	−0.0125760	+	0.913132i
$29$	−1.26059	+	1.73505i	−0.234085	+	0.322191i	−0.909858	−	0.414919i	$-0.863810\pi$
$29$	−1.26059	+	1.73505i	−0.234085	+	0.322191i	0.675773	+	0.737110i	$0.263810\pi$
$30$		0			0
$31$	−6.75621	+	0.710106i	−1.21345	+	0.127539i	−0.689548	−	0.724240i	$-0.742191\pi$
$31$	−6.75621	+	0.710106i	−1.21345	+	0.127539i	−0.523902	+	0.851779i	$0.675524\pi$
$32$	1.14745	+	4.28233i	0.202842	+	0.757016i
$33$	−4.84808	+	1.86100i	−0.843942	+	0.323959i
$34$	−0.145864	−	0.448923i	−0.0250155	−	0.0769897i
$35$		0			0
$36$	−0.816228	+	2.51209i	−0.136038	+	0.418682i
$37$	0.0958050	+	1.82807i	0.0157502	+	0.300532i	0.995134	+	0.0985262i	$0.0314128\pi$
$37$	0.0958050	+	1.82807i	0.0157502	+	0.300532i	−0.979384	+	0.202006i	$0.935254\pi$
$38$	0.0945518	−	0.0614026i	0.0153383	−	0.00996082i
$39$	0.422653	−	0.380558i	0.0676786	−	0.0609381i
$40$		0			0
$41$	6.60977	−	2.14764i	1.03227	−	0.335406i	0.256584	−	0.966522i	$-0.417403\pi$
$41$	6.60977	−	2.14764i	1.03227	−	0.335406i	0.775688	+	0.631116i	$0.217403\pi$
$42$	−0.267130	−	1.34775i	−0.0412190	−	0.207962i
$43$	−6.90254	−	6.90254i	−1.05263	−	1.05263i	−0.998536	−	0.0540922i	$-0.982774\pi$
$43$	−6.90254	−	6.90254i	−1.05263	−	1.05263i	−0.0540922	−	0.998536i	$-0.517226\pi$
$44$	3.09483	−	6.95109i	0.466563	−	1.04792i
$45$		0			0
$46$	3.42221	−	1.52367i	0.504577	−	0.224652i
$47$	−0.0134006	+	0.0108516i	−0.00195467	+	0.00158286i	−0.630297	−	0.776354i	$-0.717067\pi$
$47$	−0.0134006	+	0.0108516i	−0.00195467	+	0.00158286i	0.628343	+	0.777937i	$0.283734\pi$
$48$	1.69136	+	3.31947i	0.244126	+	0.479125i
$49$	4.53888	+	5.32903i	0.648411	+	0.761291i
$50$		0			0
$51$	−0.706165	−	1.22311i	−0.0988829	−	0.171270i
$52$	−0.0436130	+	0.832185i	−0.00604803	+	0.115403i
$53$	6.32342	+	2.42733i	0.868588	+	0.333420i	0.751525	−	0.659705i	$-0.229319\pi$
$53$	6.32342	+	2.42733i	0.868588	+	0.333420i	0.117063	+	0.993124i	$0.462652\pi$
$54$	0.241352	−	2.29631i	0.0328438	−	0.312488i
$55$		0			0
$56$	3.50526	+	2.34560i	0.468410	+	0.313444i
$57$	0.238525	−	0.238525i	0.0315934	−	0.0315934i
$58$	0.320193	+	0.834132i	0.0420434	+	0.109527i
$59$	10.5132	+	2.23464i	1.36870	+	0.290926i	0.832901	−	0.553421i	$-0.186678\pi$
$59$	10.5132	+	2.23464i	1.36870	+	0.290926i	0.535797	+	0.844347i	$0.320011\pi$
$60$		0			0
$61$	−2.23943	−	10.5357i	−0.286730	−	1.34896i	−0.851779	−	0.523901i	$-0.824476\pi$
$61$	−2.23943	−	10.5357i	−0.286730	−	1.34896i	0.565050	−	0.825057i	$-0.308857\pi$
$62$	−1.28488	+	2.52173i	−0.163180	+	0.320259i
$63$	1.50799	+	3.51655i	0.189989	+	0.443044i
$64$	−3.92834	−	1.27640i	−0.491043	−	0.159549i
$65$		0			0
$66$	−0.449806	+	2.11617i	−0.0553673	+	0.260483i
$67$	1.46122	+	1.18327i	0.178516	+	0.144560i	0.714414	−	0.699723i	$-0.246693\pi$
$67$	1.46122	+	1.18327i	0.178516	+	0.144560i	−0.535898	+	0.844283i	$0.680027\pi$
$68$	1.99887	+	0.535597i	0.242399	+	0.0649507i
$69$	9.06786	−	6.58819i	1.09164	−	0.793125i
$70$		0			0
$71$	−7.24631	−	5.26475i	−0.859979	−	0.624811i	0.0679005	−	0.997692i	$-0.478370\pi$
$71$	−7.24631	−	5.26475i	−0.859979	−	0.624811i	−0.927879	+	0.372881i	$0.878370\pi$
$72$	1.45084	+	1.79164i	0.170983	+	0.211147i
$73$	−5.20142	−	0.272595i	−0.608780	−	0.0319048i	−0.254545	−	0.967061i	$-0.581926\pi$
$73$	−5.20142	−	0.272595i	−0.608780	−	0.0319048i	−0.354236	+	0.935156i	$0.615259\pi$
$74$	0.660461	+	0.381317i	0.0767770	+	0.0443272i
$75$		0			0
$76$			0.494259i			0.0566954i
$77$	−3.26136	−	10.5286i	−0.371666	−	1.19985i
$78$	−0.0370656	−	0.234023i	−0.00419685	−	0.0264979i
$79$	−14.7078	−	1.54585i	−1.65476	−	0.173922i	−0.769379	−	0.638792i	$-0.779434\pi$
$79$	−14.7078	−	1.54585i	−1.65476	−	0.173922i	−0.885379	+	0.464870i	$0.846101\pi$
$80$		0			0
$81$	−0.268636	−	2.55590i	−0.0298485	−	0.283989i
$82$	0.749384	−	2.79674i	0.0827557	−	0.308848i
$83$	2.10145	−	13.2680i	0.230664	−	1.45635i	−0.551967	−	0.833866i	$-0.686122\pi$
$83$	2.10145	−	13.2680i	0.230664	−	1.45635i	0.782630	−	0.622487i	$-0.213878\pi$
$84$	5.59322	+	2.23589i	0.610270	+	0.243955i
$85$		0			0
$86$	−3.97793	+	0.845535i	−0.428951	+	0.0911764i
$87$	1.45600	+	2.24205i	0.156100	+	0.240373i
$88$	−3.61701	−	5.56971i	−0.385575	−	0.593733i
$89$	−3.99599	+	0.849374i	−0.423574	+	0.0900335i	−0.414767	−	0.909928i	$-0.636137\pi$
$89$	−3.99599	+	0.849374i	−0.423574	+	0.0900335i	−0.00880734	+	0.999961i	$0.502803\pi$
$90$		0			0
$91$	0.746691	+	0.948502i	0.0782745	+	0.0994300i
$92$	−2.56912	+	16.2208i	−0.267850	+	1.69114i
$93$	−2.19171	+	8.17959i	−0.227270	+	0.848184i
$94$	0.000750902		0.00714436i	7.74496e−5		0.000736884i
$95$		0			0
$96$	5.49604	+	0.577657i	0.560937	+	0.0589569i
$97$	−1.29756	−	8.19248i	−0.131747	−	0.831820i	−0.961724	−	0.274022i	$-0.911646\pi$
$97$	−1.29756	−	8.19248i	−0.131747	−	0.831820i	0.829976	−	0.557799i	$-0.188354\pi$
$98$	2.89183	−	0.376707i	0.292119	−	0.0380532i
$99$		−	6.02480i		−	0.605515i
$100$		0			0
$101$	−4.33946	−	2.50539i	−0.431793	−	0.249296i	0.268317	−	0.963331i	$-0.413532\pi$
$101$	−4.33946	−	2.50539i	−0.431793	−	0.249296i	−0.700110	+	0.714035i	$0.746866\pi$
$102$	−0.587583	−	0.0307939i	−0.0581794	−	0.00304905i
$103$	−2.91528	−	3.60007i	−0.287251	−	0.354726i	0.613011	−	0.790075i	$-0.289958\pi$
$103$	−2.91528	−	3.60007i	−0.287251	−	0.354726i	−0.900262	+	0.435349i	$0.856625\pi$
$104$	0.588426	+	0.427516i	0.0576999	+	0.0419214i
$105$		0			0
$106$	2.28290	−	1.65862i	0.221735	−	0.161100i
$107$	7.29067	+	1.95353i	0.704816	+	0.188855i	0.593387	−	0.804918i	$-0.297791\pi$
$107$	7.29067	+	1.95353i	0.704816	+	0.188855i	0.111429	+	0.993772i	$0.464457\pi$
$108$	7.86673	+	6.37035i	0.756977	+	0.612988i
$109$	−3.20334	+	15.0705i	−0.306824	+	1.44350i	0.506779	+	0.862076i	$0.330836\pi$
$109$	−3.20334	+	15.0705i	−0.306824	+	1.44350i	−0.813604	+	0.581420i	$0.802497\pi$
$110$		0			0
$111$	2.17017	+	0.705131i	0.205983	+	0.0669280i
$112$	−7.26745	+	3.11648i	−0.686709	+	0.294479i
$113$	−1.51479	+	2.97293i	−0.142499	+	0.279670i	−0.951215	−	0.308530i	$-0.900163\pi$
$113$	−1.51479	+	2.97293i	−0.142499	+	0.279670i	0.808716	+	0.588200i	$0.200163\pi$
$114$	−0.0292184	−	0.137462i	−0.00273655	−	0.0128745i
$115$		0			0
$116$	−3.83146	−	0.814401i	−0.355742	−	0.0756152i
$117$	0.236464	+	0.616009i	0.0218611	+	0.0569501i
$118$	3.16623	−	3.16623i	0.291475	−	0.291475i
$119$	2.68945	−	1.32401i	0.246541	−	0.121372i
$120$		0			0
$121$	−0.664329	+	6.32067i	−0.0603935	+	0.574606i
$122$	−4.18928	−	1.60811i	−0.379279	−	0.145592i
$123$	0.453398	−	8.65134i	0.0408815	−	0.780065i
$124$	−6.20388	−	10.7454i	−0.557125	−	0.964968i
$125$		0			0
$126$	1.57084	+	0.271022i	0.139942	+	0.0241446i
$127$	−0.625655	−	1.22792i	−0.0555179	−	0.108960i	0.861580	−	0.507621i	$-0.169475\pi$
$127$	−0.625655	−	1.22792i	−0.0555179	−	0.108960i	−0.917098	+	0.398661i	$0.869475\pi$
$128$	−8.22810	+	6.66299i	−0.727268	+	0.588930i
$129$	−11.1161	+	4.94922i	−0.978721	+	0.435755i
$130$		0			0
$131$	1.56157	−	3.50735i	0.136435	−	0.306438i	−0.832387	−	0.554194i	$-0.813026\pi$
$131$	1.56157	−	3.50735i	0.136435	−	0.306438i	0.968822	+	0.247756i	$0.0796931\pi$
$132$	−6.70668	−	6.70668i	−0.583741	−	0.583741i
$133$	0.471709	+	0.538621i	0.0409024	+	0.0467044i
$134$	0.744985	−	0.242060i	0.0643569	−	0.0209108i
$135$		0			0
$136$	1.34225	−	1.20857i	0.115097	−	0.103634i
$137$	2.63997	−	1.71442i	0.225548	−	0.146473i	−0.426919	−	0.904290i	$-0.640401\pi$
$137$	2.63997	−	1.71442i	0.225548	−	0.146473i	0.652467	+	0.757817i	$0.273734\pi$
$138$	−0.244386	−	4.66316i	−0.0208035	−	0.396954i
$139$	−2.03657	+	6.26792i	−0.172740	+	0.531638i	−0.999523	−	0.0308825i	$-0.990168\pi$
$139$	−2.03657	+	6.26792i	−0.172740	+	0.531638i	0.826783	+	0.562520i	$0.190168\pi$
$140$		0			0
$141$	0.00664205	+	0.0204421i	0.000559361	+	0.00172154i
$142$	−3.48369	+	1.33726i	−0.292345	+	0.112221i
$143$	−0.491955	−	1.83600i	−0.0411394	−	0.153534i
$144$	−4.29861	+	0.451802i	−0.358217	+	0.0376502i
$145$		0			0
$146$	−1.27545	+	1.75551i	−0.105557	+	0.145287i
$147$	8.22912	−	2.90146i	0.678726	−	0.239309i
$148$	−2.97902	+	1.51789i	−0.244874	+	0.124770i
$149$	−13.4928	+	7.79005i	−1.10537	+	0.638186i	−0.937626	−	0.347645i	$-0.886982\pi$
$149$	−13.4928	+	7.79005i	−1.10537	+	0.638186i	−0.167744	+	0.985831i	$0.553648\pi$
$150$		0			0
$151$	−8.07317	+	13.9831i	−0.656985	+	1.13793i	0.324407	+	0.945918i	$0.394835\pi$
$151$	−8.07317	+	13.9831i	−0.656985	+	1.13793i	−0.981392	+	0.192014i	$0.938498\pi$
$152$	0.361796	+	0.234953i	0.0293456	+	0.0190572i
$153$	1.61838	−	0.256327i	0.130839	−	0.0207228i
$154$	−4.41868	−	1.24945i	−0.356068	−	0.100683i
$155$		0			0
$156$	0.948954	+	0.422502i	0.0759771	+	0.0338272i
$157$	11.9442	−	3.20043i	0.953248	−	0.255422i	0.251508	−	0.967855i	$-0.419073\pi$
$157$	11.9442	−	3.20043i	0.953248	−	0.255422i	0.701740	+	0.712433i	$0.252407\pi$
$158$	−3.87734	+	4.78812i	−0.308465	+	0.380922i
$159$	5.64951	−	6.27441i	0.448035	−	0.497593i
$160$		0			0
$161$	12.6810	+	20.1286i	0.999406	+	1.58636i
$162$	−0.953980	−	0.486077i	−0.0749518	−	0.0381898i
$163$	5.52743	−	0.289680i	0.432942	−	0.0226895i	0.165379	−	0.986230i	$-0.447115\pi$
$163$	5.52743	−	0.289680i	0.432942	−	0.0226895i	0.267562	+	0.963541i	$0.413782\pi$
$164$	8.49367	+	9.43318i	0.663244	+	0.736607i
$165$		0			0
$166$	−4.15899	−	3.74477i	−0.322800	−	0.290651i
$167$	−21.8387	−	3.45892i	−1.68993	−	0.267659i	−0.763963	−	0.645260i	$-0.776749\pi$
$167$	−21.8387	−	3.45892i	−1.68993	−	0.267659i	−0.925968	+	0.377601i	$0.876749\pi$
$168$	4.29548	−	3.03136i	0.331404	−	0.233874i
$169$	−7.51885	−	10.3488i	−0.578373	−	0.796062i
$170$		0			0
$171$	0.159180	+	0.357523i	0.0121728	+	0.0273405i
$172$	6.38937	−	16.6449i	0.487185	−	1.26916i
$173$	2.09630	−	3.22802i	0.159379	−	0.245421i	−0.749955	−	0.661488i	$-0.769925\pi$
$173$	2.09630	−	3.22802i	0.159379	−	0.245421i	0.909334	+	0.416067i	$0.136592\pi$
$174$	1.11374			0.0844322
$175$		0			0
$176$	12.4511			0.938536
$177$	7.29688	−	11.2362i	0.548467	−	0.844566i
$178$	−0.609927	+	1.58891i	−0.0457159	+	0.119094i
$179$	−9.09796	−	20.4344i	−0.680014	−	1.52734i	−0.841382	−	0.540441i	$-0.818257\pi$
$179$	−9.09796	−	20.4344i	−0.680014	−	1.52734i	0.161368	−	0.986894i	$-0.448409\pi$
$180$		0			0
$181$	12.0280	+	16.5551i	0.894031	+	1.23053i	0.972333	+	0.233598i	$0.0750501\pi$
$181$	12.0280	+	16.5551i	0.894031	+	1.23053i	−0.0783022	+	0.996930i	$0.524950\pi$
$182$	0.500829	−	0.0456756i	0.0371239	−	0.00338570i
$183$	−13.2611	−	2.10035i	−0.980286	−	0.155262i
$184$	10.6523	+	9.59140i	0.785300	+	0.707087i
$185$		0			0
$186$	2.36063	+	2.62174i	0.173090	+	0.192235i
$187$	−4.71368	+	0.247033i	−0.344698	+	0.0180649i
$188$	−0.0280612	−	0.0142979i	−0.00204657	−	0.00104278i
$189$	14.6525	−	0.565698i	1.06581	−	0.0411485i
$190$		0			0
$191$	−3.38394	+	3.75825i	−0.244853	+	0.271937i	−0.853027	−	0.521867i	$-0.825236\pi$
$191$	−3.38394	+	3.75825i	−0.244853	+	0.271937i	0.608174	+	0.793804i	$0.291902\pi$
$192$	−3.24022	+	4.00133i	−0.233842	+	0.288771i
$193$	−9.13540	+	2.44782i	−0.657581	+	0.176198i	−0.572154	−	0.820146i	$-0.693892\pi$
$193$	−9.13540	+	2.44782i	−0.657581	+	0.176198i	−0.0854268	+	0.996344i	$0.527225\pi$
$194$	−3.15685	−	1.40552i	−0.226649	−	0.100911i
$195$		0			0
$196$	−5.51983	+	11.5321i	−0.394274	+	0.823721i
$197$	−14.6050	+	2.31321i	−1.04056	+	0.164809i	−0.653253	−	0.757140i	$-0.726596\pi$
$197$	−14.6050	+	2.31321i	−1.04056	+	0.164809i	−0.387311	+	0.921949i	$0.626596\pi$
$198$	−2.10505	−	1.36704i	−0.149599	−	0.0971510i
$199$	−9.48990	+	16.4370i	−0.672721	+	1.16519i	0.304408	+	0.952542i	$0.401541\pi$
$199$	−9.48990	+	16.4370i	−0.672721	+	1.16519i	−0.977129	+	0.212645i	$0.931792\pi$
$200$		0			0
$201$	2.02975	−	1.17188i	0.143168	−	0.0826579i
$202$	−1.86001	+	0.947721i	−0.130870	+	0.0666814i
$203$	−4.95259	+	2.76915i	−0.347604	+	0.194356i
$204$	1.51621	−	2.08689i	0.106156	−	0.146111i
$205$		0			0
$206$	−1.91934	+	0.201731i	−0.133727	+	0.0140552i
$207$	3.36565	+	12.5608i	0.233929	+	0.873034i
$208$	−1.27307	+	0.488685i	−0.0882714	+	0.0338842i
$209$	−0.348378	−	1.07220i	−0.0240978	−	0.0741654i
$210$		0			0
$211$	5.14512	−	15.8351i	0.354205	−	1.09013i	−0.602264	−	0.798297i	$-0.705735\pi$
$211$	5.14512	−	15.8351i	0.354205	−	1.09013i	0.956469	−	0.291834i	$-0.0942654\pi$
$212$	0.647448	+	12.3540i	0.0444669	+	0.848480i
$213$	−9.36375	+	6.08089i	−0.641594	+	0.416656i
$214$	2.33682	−	2.10408i	0.159742	−	0.143832i
$215$		0			0
$216$	8.40265	−	2.73019i	0.571728	−	0.185766i
$217$	−17.0159	−	5.78906i	−1.15511	−	0.392987i
$218$	4.53877	+	4.53877i	0.307404	+	0.307404i
$219$	−2.64077	+	5.93126i	−0.178447	+	0.400798i
$220$		0			0
$221$	0.472257	−	0.210262i	0.0317674	−	0.0141438i
$222$	0.738785	−	0.598257i	0.0495840	−	0.0401524i
$223$	−8.88764	−	17.4430i	−0.595160	−	1.16807i	−0.970482	−	0.241173i	$-0.922468\pi$
$223$	−8.88764	−	17.4430i	−0.595160	−	1.16807i	0.375322	−	0.926895i	$-0.377532\pi$
$224$	−1.99429	+	11.5589i	−0.133249	+	0.772310i
$225$		0			0
$226$	0.695029	+	1.20383i	0.0462326	+	0.0800773i
$227$	0.0129867	−	0.247801i	0.000861959	−	0.0164472i	−0.998165	−	0.0605578i	$-0.980712\pi$
$227$	0.0129867	−	0.247801i	0.000861959	−	0.0164472i	0.999027	+	0.0441106i	$0.0140454\pi$
$228$	0.575182	+	0.220792i	0.0380924	+	0.0146223i
$229$	−2.78762	+	26.5224i	−0.184211	+	1.75265i	0.378139	+	0.925749i	$0.376564\pi$
$229$	−2.78762	+	26.5224i	−0.184211	+	1.75265i	−0.562349	+	0.826900i	$0.690102\pi$
$230$		0			0
$231$	−13.7093	−	0.907942i	−0.902008	−	0.0597382i
$232$	−2.41748	+	2.41748i	−0.158715	+	0.158715i
$233$	−4.98713	−	12.9919i	−0.326717	−	0.851128i	−0.994303	−	0.106595i	$-0.966005\pi$
$233$	−4.98713	−	12.9919i	−0.326717	−	0.851128i	0.667585	−	0.744534i	$-0.267328\pi$
$234$	0.268886	+	0.0571535i	0.0175776	+	0.00373624i
$235$		0			0
$236$	4.08143	+	19.2016i	0.265679	+	1.24992i
$237$	−8.36912	+	16.4253i	−0.543633	+	1.06694i
$238$	0.147633	−	1.24011i	0.00956964	−	0.0803841i
$239$	−7.25153	−	2.35616i	−0.469062	−	0.152408i	0.0649425	−	0.997889i	$-0.479314\pi$
$239$	−7.25153	−	2.35616i	−0.469062	−	0.152408i	−0.534005	+	0.845481i	$0.679314\pi$
$240$		0			0
$241$	−1.39977	+	6.58538i	−0.0901668	+	0.424201i	0.909791	+	0.415066i	$0.136241\pi$
$241$	−1.39977	+	6.58538i	−0.0901668	+	0.424201i	−0.999958	+	0.00913580i	$0.997092\pi$
$242$	2.05769	+	1.66628i	0.132273	+	0.107113i
$243$	12.9659	+	3.47419i	0.831761	+	0.222870i
$244$	15.9155	−	11.5633i	1.01889	−	0.740265i
$245$		0			0
$246$	−2.91988	−	2.12142i	−0.186165	−	0.135257i
$247$	0.0777020	+	0.0959540i	0.00494406	+	0.00610541i
$248$	−10.8147	−	0.566776i	−0.686736	−	0.0359903i
$249$	−14.5016	−	8.37250i	−0.919001	−	0.530586i
$250$		0			0
$251$		−	8.11241i		−	0.512051i	−0.966670	−	0.256025i	$-0.917587\pi$
$251$		−	8.11241i		−	0.512051i	0.966670	−	0.256025i	$-0.0824130\pi$
$252$	−4.74723	+	5.12851i	−0.299048	+	0.323066i
$253$	−5.86001	−	36.9987i	−0.368416	−	2.32609i
$254$	−0.570993	−	0.0600138i	−0.0358273	−	0.00376560i
$255$		0			0
$256$	−0.402447	−	3.82903i	−0.0251529	−	0.239314i
$257$	−1.82750	+	6.82034i	−0.113997	+	0.425441i	−0.999210	−	0.0397443i	$-0.987346\pi$
$257$	−1.82750	+	6.82034i	−0.113997	+	0.425441i	0.885213	+	0.465185i	$0.154012\pi$
$258$	−0.793021	+	5.00694i	−0.0493713	+	0.311718i
$259$	−1.79777	+	4.49723i	−0.111708	+	0.279444i
$260$		0			0
$261$	−3.03378	+	0.644849i	−0.187786	+	0.0399152i
$262$	−0.871136	−	1.34143i	−0.0538189	−	0.0828739i
$263$	−0.467232	−	0.719474i	−0.0288107	−	0.0443646i	0.823972	−	0.566631i	$-0.191753\pi$
$263$	−0.467232	−	0.719474i	−0.0288107	−	0.0443646i	−0.852783	+	0.522266i	$0.825087\pi$
$264$	−8.09739	+	1.72115i	−0.498360	+	0.105930i
$265$		0			0
$266$	0.295224	−	0.0426001i	0.0181014	−	0.00261198i
$267$	−0.796621	+	5.02967i	−0.0487524	+	0.307811i
$268$	−0.888820	+	3.31712i	−0.0542933	+	0.202625i
$269$	−2.78061	−	26.4558i	−0.169537	−	1.61304i	−0.666664	−	0.745358i	$-0.732278\pi$
$269$	−2.78061	−	26.4558i	−0.169537	−	1.61304i	0.497127	−	0.867678i	$-0.334388\pi$
$270$		0			0
$271$	−22.8456	−	2.40117i	−1.38777	−	0.145861i	−0.619003	−	0.785389i	$-0.712463\pi$
$271$	−22.8456	−	2.40117i	−1.38777	−	0.145861i	−0.768767	+	0.639528i	$0.779130\pi$
$272$	0.529735	+	3.34461i	0.0321199	+	0.202797i
$273$	1.43735	−	0.445236i	0.0869926	−	0.0269469i
$274$		−	1.31140i		−	0.0792248i
$275$		0			0
$276$	17.7289	+	10.2358i	1.06716	+	0.616123i
$277$	−7.97110	−	0.417748i	−0.478937	−	0.0251000i	−0.188660	−	0.982043i	$-0.560414\pi$
$277$	−7.97110	−	0.417748i	−0.478937	−	0.0251000i	−0.290278	+	0.956943i	$0.593748\pi$
$278$	1.72790	+	2.13377i	0.103632	+	0.127975i
$279$	−7.94823	−	5.77473i	−0.475848	−	0.345724i
$280$		0			0
$281$	3.83031	−	2.78288i	0.228497	−	0.166013i	−0.467646	−	0.883916i	$-0.654898\pi$
$281$	3.83031	−	2.78288i	0.228497	−	0.166013i	0.696143	+	0.717903i	$0.254898\pi$
$282$	0.00864952	+	0.00231763i	0.000515071	+	0.000138013i
$283$	23.1794	+	18.7703i	1.37787	+	1.11578i	0.980147	+	0.198272i	$0.0635330\pi$
$283$	23.1794	+	18.7703i	1.37787	+	1.11578i	0.397724	+	0.917505i	$0.369800\pi$
$284$	3.40128	−	16.0018i	0.201829	−	0.949531i
$285$		0			0
$286$	−0.753120	−	0.244703i	−0.0445329	−	0.0144696i
$287$	18.2588	+	2.17369i	1.07778	+	0.128309i
$288$	−2.91077	+	5.71270i	−0.171519	+	0.336624i
$289$	3.26760	+	15.3728i	0.192212	+	0.904284i
$290$		0			0
$291$	−10.1134	−	2.14968i	−0.592861	−	0.126016i
$292$	−3.40919	−	8.88125i	−0.199508	−	0.519736i
$293$	18.8350	−	18.8350i	1.10035	−	1.10035i	0.105985	−	0.994368i	$-0.466200\pi$
$293$	18.8350	−	18.8350i	1.10035	−	1.10035i	0.994368	−	0.105985i	$-0.0337997\pi$
$294$	0.853433	−	3.53358i	0.0497732	−	0.206083i
$295$		0			0
$296$	−0.305032	+	2.90219i	−0.0177296	+	0.168686i
$297$	−21.5555	−	8.27436i	−1.25077	−	0.480127i
$298$	−0.339703	+	6.48191i	−0.0196785	+	0.375487i
$299$	2.05130	+	3.55295i	0.118630	+	0.205473i
$300$		0			0
$301$	−8.92263	−	24.2367i	−0.514292	−	1.39698i
$302$	3.05386	+	5.99354i	0.175730	+	0.344890i
$303$	−4.85408	+	3.93076i	−0.278860	+	0.225816i
$304$	−0.738872	+	0.328967i	−0.0423772	+	0.0188675i
$305$		0			0
$306$	0.277654	−	0.623620i	0.0158724	−	0.0356500i
$307$	−14.2537	−	14.2537i	−0.813499	−	0.813499i	0.171658	−	0.985157i	$-0.445088\pi$
$307$	−14.2537	−	14.2537i	−0.813499	−	0.813499i	−0.985157	+	0.171658i	$0.945088\pi$
$308$	15.1446	−	13.2632i	0.862942	−	0.755740i
$309$	−5.49180	+	1.78439i	−0.312417	+	0.101511i
$310$		0			0
$311$	13.8102	−	12.4348i	0.783105	−	0.705111i	−0.177166	−	0.984181i	$-0.556693\pi$
$311$	13.8102	−	12.4348i	0.783105	−	0.705111i	0.960271	+	0.279070i	$0.0900261\pi$
$312$	0.760370	−	0.493790i	0.0430475	−	0.0279553i
$313$	−0.341836	−	6.52263i	−0.0193217	−	0.368681i	−0.991129	−	0.132904i	$-0.957570\pi$
$313$	−0.341836	−	6.52263i	−0.0193217	−	0.368681i	0.971807	−	0.235777i	$-0.0757634\pi$
$314$	1.59193	−	4.89945i	0.0898376	−	0.276492i
$315$		0			0
$316$	−8.34682	−	25.6889i	−0.469545	−	1.44511i
$317$	10.2564	−	3.93708i	0.576059	−	0.221128i	−0.0528566	−	0.998602i	$-0.516833\pi$
$317$	10.2564	−	3.93708i	0.576059	−	0.221128i	0.628915	+	0.777474i	$0.283499\pi$
$318$	−0.910383	−	3.39760i	−0.0510518	−	0.190528i
$319$	8.88561	−	0.933915i	0.497499	−	0.0522892i
$320$		0			0
$321$	5.53021	−	7.61168i	0.308666	−	0.424843i
$322$	9.91024	+	0.136488i	0.552276	+	0.00760617i
$323$	0.273192	−	0.139198i	0.0152008	−	0.00774519i
$324$	4.06505	−	2.34695i	0.225836	−	0.130386i
$325$		0			0
$326$	1.15297	−	1.99700i	0.0638570	−	0.110604i
$327$	16.1070	+	10.4600i	0.890720	+	0.578440i
$328$	10.9427	−	1.73315i	0.604207	−	0.0956970i
$329$	−0.0442254	+	0.0111997i	−0.00243822	+	0.000617461i
$330$		0			0
$331$	2.10579	+	0.937559i	0.115745	+	0.0515329i	0.463792	−	0.885944i	$-0.346488\pi$
$331$	2.10579	+	0.937559i	0.115745	+	0.0515329i	−0.348047	+	0.937477i	$0.613155\pi$
$332$	23.6992	−	6.35019i	1.30066	−	0.348512i
$333$	−1.66604	+	2.05738i	−0.0912982	+	0.112744i
$334$	−6.16378	+	6.84557i	−0.337267	+	0.374573i
$335$		0			0
$336$	0.380265	+	9.84950i	0.0207451	+	0.537334i
$337$	13.9482	+	7.10695i	0.759806	+	0.387140i	0.790558	−	0.612387i	$-0.209790\pi$
$337$	13.9482	+	7.10695i	0.759806	+	0.387140i	−0.0307527	+	0.999527i	$0.509790\pi$
$338$	−5.32189	+	0.278908i	−0.289472	+	0.0151706i
$339$	2.78301	+	3.09085i	0.151152	+	0.167872i
$340$		0			0
$341$	21.0320	+	18.9373i	1.13895	+	1.02551i
$342$	0.161036	+	0.0255056i	0.00870782	+	0.00137918i
$343$	4.99069	+	17.8352i	0.269472	+	0.963008i
$344$	−9.14673	−	12.5894i	−0.493159	−	0.678775i
$345$		0			0
$346$	−0.652208	−	1.46488i	−0.0350629	−	0.0787526i
$347$	−1.30103	+	3.38931i	−0.0698431	+	0.181947i	−0.964059	−	0.265689i	$-0.914401\pi$
$347$	−1.30103	+	3.38931i	−0.0698431	+	0.181947i	0.894216	+	0.447636i	$0.147734\pi$
$348$	−2.65930	+	4.09496i	−0.142553	+	0.219513i
$349$	10.3897			0.556148			0.278074	−	0.960560i	$-0.410304\pi$
$349$	10.3897			0.556148			0.278074	+	0.960560i	$0.410304\pi$
$350$		0			0
$351$	2.52870			0.134972
$352$	10.0592	−	15.4898i	0.536157	−	0.825610i
$353$	−1.27877	+	3.33131i	−0.0680621	+	0.177308i	−0.963393	−	0.268095i	$-0.913606\pi$
$353$	−1.27877	+	3.33131i	−0.0680621	+	0.177308i	0.895331	+	0.445402i	$0.146939\pi$
$354$	−2.27023	−	5.09903i	−0.120662	−	0.271010i
$355$		0			0
$356$	−4.38575	−	6.03646i	−0.232444	−	0.319932i
$357$	−0.339376	−	3.72123i	−0.0179617	−	0.196949i
$358$	−9.20406	−	1.45778i	−0.486450	−	0.0770460i
$359$	15.0820	+	13.5799i	0.795997	+	0.716719i	0.963077	−	0.269224i	$-0.0867673\pi$
$359$	15.0820	+	13.5799i	0.795997	+	0.716719i	−0.167081	+	0.985943i	$0.553434\pi$
$360$		0			0
$361$	−12.6645	−	14.0653i	−0.666552	−	0.740281i
$362$	8.51346	−	0.446172i	0.447458	−	0.0234503i
$363$	7.05877	+	3.59662i	0.370489	+	0.188774i
$364$	−1.02791	+	1.95050i	−0.0538769	+	0.102234i
$365$		0			0
$366$	−3.74281	+	4.15681i	−0.195640	+	0.217280i
$367$	15.0156	−	18.5427i	0.783805	−	0.967919i	−0.216159	−	0.976358i	$-0.569353\pi$
$367$	15.0156	−	18.5427i	0.783805	−	0.967919i	0.999964	+	0.00843913i	$0.00268629\pi$
$368$	−25.9586	+	6.95558i	−1.35318	+	0.362585i
$369$	9.18194	+	4.08806i	0.477993	+	0.212816i
$370$		0			0
$371$	12.4960	+	12.8450i	0.648759	+	0.666878i
$372$	−15.2761	+	2.41950i	−0.792029	+	0.125445i
$373$	6.02409	+	3.91209i	0.311915	+	0.202560i	0.691097	−	0.722762i	$-0.257128\pi$
$373$	6.02409	+	3.91209i	0.311915	+	0.202560i	−0.379182	+	0.925322i	$0.623794\pi$
$374$	−0.983227	+	1.70300i	−0.0508415	+	0.0880600i
$375$		0			0
$376$	−0.0238053	+	0.0137440i	−0.00122767	+	0.000708793i
$377$	−0.871859	+	0.444235i	−0.0449030	+	0.0228792i
$378$	3.12703	−	5.24792i	0.160837	−	0.269924i
$379$	12.3615	−	17.0141i	0.634966	−	0.873956i	−0.363368	−	0.931646i	$-0.618373\pi$
$379$	12.3615	−	17.0141i	0.634966	−	0.873956i	0.998335	+	0.0576896i	$0.0183734\pi$
$380$		0			0
$381$	−1.70845	+	0.179565i	−0.0875264	+	0.00919940i
$382$	0.545301	+	2.03509i	0.0279000	+	0.104124i
$383$	−25.9228	+	9.95083i	−1.32459	+	0.508464i	−0.914871	−	0.403747i	$-0.867708\pi$
$383$	−25.9228	+	9.95083i	−1.32459	+	0.508464i	−0.409722	+	0.912210i	$0.634374\pi$
$384$	4.07830	+	12.5517i	0.208120	+	0.640527i
$385$		0			0
$386$	−1.21757	+	3.74730i	−0.0619728	+	0.190733i
$387$	−0.738837	−	14.0979i	−0.0375572	−	0.716634i
$388$	12.7055	−	8.25105i	0.645024	−	0.418883i
$389$	−11.4543	+	10.3135i	−0.580754	+	0.522913i	−0.906312	−	0.422609i	$-0.861114\pi$
$389$	−11.4543	+	10.3135i	−0.580754	+	0.522913i	0.325558	+	0.945522i	$0.394448\pi$
$390$		0			0
$391$	9.68928	−	3.14824i	0.490008	−	0.159213i
$392$	5.81753	+	9.52246i	0.293830	+	0.480957i
$393$	−3.38402	−	3.38402i	−0.170701	−	0.170701i
$394$	−2.50567	+	5.62783i	−0.126234	+	0.283526i
$395$		0			0
$396$	10.0526	−	4.47570i	0.505161	−	0.224912i
$397$	−16.8875	+	13.6752i	−0.847558	+	0.686339i	−0.951301	−	0.308265i	$-0.900252\pi$
$397$	−16.8875	+	13.6752i	−0.847558	+	0.686339i	0.103742	+	0.994604i	$0.466918\pi$
$398$	3.58977	+	7.04532i	0.179939	+	0.353150i
$399$	0.837527	−	0.308332i	0.0419288	−	0.0154359i
$400$		0			0
$401$	−4.12035	−	7.13665i	−0.205760	−	0.356387i	0.744614	−	0.667495i	$-0.232633\pi$
$401$	−4.12035	−	7.13665i	−0.205760	−	0.356387i	−0.950375	+	0.311107i	$0.899300\pi$
$402$	0.0511024	−	0.975091i	0.00254875	−	0.0486331i
$403$	−2.89368	−	1.11078i	−0.144145	−	0.0553320i
$404$	0.956631	−	9.10174i	0.0475942	−	0.452828i
$405$		0			0
$406$	−0.156215	+	2.35875i	−0.00775283	+	0.117063i
$407$	5.39251	−	5.39251i	0.267297	−	0.267297i
$408$	−0.806842	−	2.10190i	−0.0399446	−	0.104059i
$409$	−10.1930	−	2.16659i	−0.504011	−	0.107131i	−0.0511126	−	0.998693i	$-0.516277\pi$
$409$	−10.1930	−	2.16659i	−0.504011	−	0.107131i	−0.452899	+	0.891562i	$0.649610\pi$
$410$		0			0
$411$	−0.815804	−	3.83806i	−0.0402407	−	0.189317i
$412$	3.84114	−	7.53866i	0.189239	−	0.371403i
$413$	22.7734	+	17.0299i	1.12060	+	0.837985i
$414$	5.15237	+	1.67411i	0.253225	+	0.0822779i
$415$		0			0
$416$	−0.420558	+	1.97857i	−0.0206196	+	0.0970074i
$417$	6.38438	+	5.16997i	0.312645	+	0.253175i
$418$	−0.453670	−	0.121561i	−0.0221897	−	0.00594572i
$419$	22.9552	−	16.6779i	1.12143	−	0.814769i	0.137008	−	0.990570i	$-0.456251\pi$
$419$	22.9552	−	16.6779i	1.12143	−	0.814769i	0.984426	+	0.175801i	$0.0562515\pi$
$420$		0			0
$421$	−1.40395	−	1.02003i	−0.0684242	−	0.0497131i	0.553047	−	0.833150i	$-0.313465\pi$
$421$	−1.40395	−	1.02003i	−0.0684242	−	0.0497131i	−0.621472	+	0.783437i	$0.713465\pi$
$422$	−4.36530	−	5.39069i	−0.212499	−	0.262415i
$423$	−0.0249029	−	0.00130510i	−0.00121082	−	6.34563e-5i
$424$	9.35091	+	5.39875i	0.454120	+	0.262187i
$425$		0			0
$426$			4.65144i			0.225363i
$427$	6.30828	−	27.7906i	0.305279	−	1.34488i
$428$	2.15656	+	13.6160i	0.104241	+	0.658152i
$429$	−2.35637	−	0.247664i	−0.113766	−	0.0119573i
$430$		0			0
$431$	−1.30039	−	12.3724i	−0.0626377	−	0.595958i	−0.980151	−	0.198253i	$-0.936473\pi$
$431$	−1.30039	−	12.3724i	−0.0626377	−	0.595958i	0.917513	−	0.397705i	$-0.130193\pi$
$432$	−4.28719	+	16.0000i	−0.206267	+	0.769800i
$433$	−3.04572	+	19.2299i	−0.146368	+	0.924130i	0.799756	+	0.600325i	$0.204962\pi$
$433$	−3.04572	+	19.2299i	−0.146368	+	0.924130i	−0.946124	+	0.323805i	$0.895038\pi$
$434$	−5.88361	+	4.63177i	−0.282422	+	0.222332i
$435$		0			0
$436$	−27.5254	+	5.85070i	−1.31823	+	0.280198i
$437$	1.32528	+	2.04075i	0.0633966	+	0.0976221i
$438$	1.47317	+	2.26849i	0.0703910	+	0.108393i
$439$	6.34586	−	1.34885i	0.302871	−	0.0643773i	−0.0539693	−	0.998543i	$-0.517187\pi$
$439$	6.34586	−	1.34885i	0.302871	−	0.0643773i	0.356840	+	0.934165i	$0.383854\pi$
$440$		0			0
$441$	−0.278792	+	10.1195i	−0.0132758	+	0.481880i
$442$	0.0336906	−	0.212714i	0.00160250	−	0.0101178i
$443$	−5.41131	+	20.1953i	−0.257099	+	0.959506i	0.709812	+	0.704391i	$0.248780\pi$
$443$	−5.41131	+	20.1953i	−0.257099	+	0.959506i	−0.966911	+	0.255115i	$0.917887\pi$
$444$	0.435639	+	4.14483i	0.0206745	+	0.196705i
$445$		0			0
$446$	−8.11115	−	0.852516i	−0.384074	−	0.0403678i
$447$	3.03810	+	19.1818i	0.143697	+	0.907269i
$448$	−8.01982	−	7.42359i	−0.378901	−	0.350732i
$449$			10.1728i			0.480082i	0.970763	+	0.240041i	$0.0771610\pi$
$449$			10.1728i			0.480082i	−0.970763	+	0.240041i	$0.922839\pi$
$450$		0			0
$451$	−25.0743	−	14.4767i	−1.18070	−	0.681679i
$452$	−6.08574	−	0.318940i	−0.286249	−	0.0150017i
$453$	12.6662	+	15.6414i	0.595108	+	0.734898i
$454$	−0.0836345	−	0.0607640i	−0.00392516	−	0.00285180i
$455$		0			0
$456$	0.435041	−	0.316075i	0.0203726	−	0.0148016i
$457$	23.4285	+	6.27766i	1.09594	+	0.293656i	0.761111	−	0.648622i	$-0.224654\pi$
$457$	23.4285	+	6.27766i	1.09594	+	0.293656i	0.334830	+	0.942278i	$0.391321\pi$
$458$	8.63434	+	6.99195i	0.403456	+	0.326713i
$459$	1.30558	−	6.14227i	0.0609392	−	0.286696i
$460$		0			0
$461$	−9.74059	−	3.16491i	−0.453664	−	0.147405i	0.0732669	−	0.997312i	$-0.476658\pi$
$461$	−9.74059	−	3.16491i	−0.453664	−	0.147405i	−0.526931	+	0.849908i	$0.676658\pi$
$462$	−3.42790	+	4.58400i	−0.159480	+	0.213267i
$463$	1.15985	−	2.27633i	0.0539027	−	0.105790i	−0.862484	−	0.506085i	$-0.831092\pi$
$463$	1.15985	−	2.27633i	0.0539027	−	0.105790i	0.916386	+	0.400295i	$0.131092\pi$
$464$	−1.33267	−	6.26972i	−0.0618677	−	0.291064i
$465$		0			0
$466$	−5.67093	−	1.20539i	−0.262701	−	0.0558387i
$467$	4.07743	+	10.6221i	0.188681	+	0.491531i	0.994991	−	0.0999621i	$-0.0318722\pi$
$467$	4.07743	+	10.6221i	0.188681	+	0.491531i	−0.806310	+	0.591493i	$0.798539\pi$
$468$	−0.852168	+	0.852168i	−0.0393915	+	0.0393915i
$469$	2.19719	+	4.46312i	0.101457	+	0.206088i
$470$		0			0
$471$	1.61119	−	15.3294i	0.0742396	−	0.706343i
$472$	15.9957	+	6.14019i	0.736263	+	0.282625i
$473$	−2.12835	+	40.6113i	−0.0978616	+	1.86731i
$474$	3.84000	+	6.65108i	0.176377	+	0.305494i
$475$		0			0
$476$	4.20709	+	3.50385i	0.192831	+	0.160599i
$477$	4.44704	+	8.72782i	0.203616	+	0.399619i
$478$	−2.46862	+	1.99905i	−0.112912	+	0.0914344i
$479$	17.1840	−	7.65082i	0.785158	−	0.349575i	0.0253132	−	0.999680i	$-0.491942\pi$
$479$	17.1840	−	7.65082i	0.785158	−	0.349575i	0.759845	+	0.650105i	$0.225275\pi$
$480$		0			0
$481$	−0.339713	+	0.763008i	−0.0154896	+	0.0347902i
$482$	1.98331	+	1.98331i	0.0903371	+	0.0903371i
$483$	29.0890	−	5.76556i	1.32360	−	0.262342i
$484$	−11.0398	+	3.58703i	−0.501807	+	0.163047i
$485$		0			0
$486$	4.15585	−	3.74194i	0.188513	−	0.169738i
$487$	−1.80137	+	1.16982i	−0.0816278	+	0.0530097i	−0.584808	−	0.811172i	$-0.698830\pi$
$487$	−1.80137	+	1.16982i	−0.0816278	+	0.0530097i	0.503180	+	0.864182i	$0.332163\pi$
$488$	−0.898632	−	17.1469i	−0.0406792	−	0.776205i
$489$	2.13206	−	6.56182i	0.0964153	−	0.296736i
$490$		0			0
$491$	0.270800	+	0.833436i	0.0122210	+	0.0376124i	0.956981	−	0.290150i	$-0.0937053\pi$
$491$	0.270800	+	0.833436i	0.0122210	+	0.0376124i	−0.944760	+	0.327763i	$0.893705\pi$
$492$	14.7719	−	5.67039i	0.665968	−	0.255641i
$493$	0.628909	+	2.34712i	0.0283246	+	0.105709i
$494$	0.0511568	−	0.00537680i	0.00230165	−	0.000241914i
$495$		0			0
$496$	11.9343	−	16.4261i	0.535865	−	0.737555i
$497$	−11.5652	−	20.6841i	−0.518768	−	0.927810i
$498$	−6.21576	+	3.16709i	−0.278535	+	0.141921i
$499$	17.9979	−	10.3911i	0.805696	−	0.465169i	−0.0397630	−	0.999209i	$-0.512660\pi$
$499$	17.9979	−	10.3911i	0.805696	−	0.465169i	0.845459	+	0.534040i	$0.179327\pi$
$500$		0			0
$501$	−13.7809	+	23.8692i	−0.615684	+	1.06640i
$502$	−2.83446	−	1.84072i	−0.126508	−	0.0821552i
$503$	37.8153	−	5.98936i	1.68610	−	0.267052i	0.761549	−	0.648107i	$-0.224439\pi$
$503$	37.8153	−	5.98936i	1.68610	−	0.267052i	0.924553	+	0.381055i	$0.124439\pi$
$504$	1.49739	+	5.91288i	0.0666991	+	0.263381i
$505$		0			0
$506$	−14.2569	−	6.34758i	−0.633796	−	0.282184i
$507$	−15.4020	+	4.12694i	−0.684025	+	0.183284i
$508$	1.58403	−	1.95612i	0.0702801	−	0.0867887i
$509$	21.4267	−	23.7968i	0.949723	−	1.05477i	−0.0487098	−	0.998813i	$-0.515511\pi$
$509$	21.4267	−	23.7968i	0.949723	−	1.05477i	0.998433	−	0.0559614i	$-0.0178224\pi$
$510$		0			0
$511$	−12.1912	−	6.42474i	−0.539309	−	0.284214i
$512$	−20.2964	−	10.3415i	−0.896982	−	0.457035i
$513$	1.49776	−	0.0784941i	0.0661276	−	0.00346560i
$514$	1.96835	+	2.18607i	0.0868201	+	0.0964234i
$515$		0			0
$516$	−16.5159	−	14.8710i	−0.727071	−	0.654658i
$517$	0.0709510	+	0.0112375i	0.00312042	+	0.000494226i
$518$	1.16341	+	1.64856i	0.0511171	+	0.0724338i
$519$	−2.82009	−	3.88151i	−0.123788	−	0.170380i
$520$		0			0
$521$	8.94936	+	20.1006i	0.392079	+	0.880623i	0.996471	+	0.0839365i	$0.0267493\pi$
$521$	8.94936	+	20.1006i	0.392079	+	0.880623i	−0.604392	+	0.796687i	$0.706584\pi$
$522$	−0.463059	+	1.20631i	−0.0202676	+	0.0527988i
$523$	7.60202	−	11.7061i	0.332413	−	0.511871i	−0.632458	−	0.774595i	$-0.717954\pi$
$523$	7.60202	−	11.7061i	0.332413	−	0.511871i	0.964871	+	0.262723i	$0.0846206\pi$
$524$	7.01218			0.306329
$525$		0			0
$526$	−0.357398			−0.0155833
$527$	−4.19213	+	6.45531i	−0.182612	+	0.281198i
$528$	5.56206	−	14.4897i	0.242058	−	0.630582i
$529$	23.5309	+	52.8513i	1.02308	+	2.29788i
$530$		0			0
$531$	9.13634	+	12.5751i	0.396484	+	0.545713i
$532$	−0.548285	+	1.18719i	−0.0237712	+	0.0514713i
$533$	3.13192	+	0.496047i	0.135659	+	0.0214862i
$534$	1.57660	+	1.41958i	0.0682261	+	0.0614311i
$535$		0			0
$536$	2.00561	+	2.22746i	0.0866293	+	0.0962115i
$537$	−27.8442	+	1.45925i	−1.20157	+	0.0629714i
$538$	−9.87450	−	5.03131i	−0.425720	−	0.216915i
$539$	3.84580	−	28.9072i	0.165651	−	1.24512i
$540$		0			0
$541$	−2.25446	+	2.50383i	−0.0969266	+	0.107648i	−0.789656	−	0.613549i	$-0.789741\pi$
$541$	−2.25446	+	2.50383i	−0.0969266	+	0.107648i	0.692730	+	0.721197i	$0.256408\pi$
$542$	−6.02266	+	7.43736i	−0.258695	+	0.319462i
$543$	24.6386	−	6.60190i	1.05734	−	0.283315i
$544$	4.58885	+	2.04309i	0.196745	+	0.0875966i
$545$		0			0
$546$	0.170573	−	0.603233i	0.00729986	−	0.0258160i
$547$	28.1940	−	4.46548i	1.20549	−	0.190930i	0.478815	−	0.877916i	$-0.341066\pi$
$547$	28.1940	−	4.46548i	1.20549	−	0.190930i	0.726671	+	0.686985i	$0.241066\pi$
$548$	4.82174	+	3.13128i	0.205975	+	0.133761i
$549$	7.78849	−	13.4901i	0.332405	−	0.575742i
$550$		0			0
$551$	−0.502614	+	0.290185i	−0.0214121	+	0.0123623i
$552$	15.9203	−	8.11180i	0.677613	−	0.345261i
$553$	−33.6128	−	20.0286i	−1.42936	−	0.851701i
$554$	−1.95461	+	2.69030i	−0.0830436	+	0.114300i
$555$		0			0
$556$	−11.9712	+	1.25822i	−0.507690	+	0.0533604i
$557$	7.56621	+	28.2375i	0.320591	+	1.19646i	0.918671	+	0.395024i	$0.129264\pi$
$557$	7.56621	+	28.2375i	0.320591	+	1.19646i	−0.598080	+	0.801436i	$0.704070\pi$
$558$	−3.82114	+	1.46680i	−0.161762	+	0.0620946i
$559$	−1.37631	−	4.23586i	−0.0582119	−	0.179158i
$560$		0			0
$561$	−1.81818	+	5.59579i	−0.0767637	+	0.236254i
$562$	−0.103230	−	1.96974i	−0.00435449	−	0.0830886i
$563$	−11.9263	+	7.74505i	−0.502635	+	0.326415i	−0.770928	−	0.636922i	$-0.780207\pi$
$563$	−11.9263	+	7.74505i	−0.502635	+	0.326415i	0.268293	+	0.963337i	$0.413540\pi$
$564$	−0.0291741	+	0.0262685i	−0.00122845	+	0.00110610i
$565$		0			0
$566$	11.8177	−	3.83981i	0.496736	−	0.161399i
$567$	2.19003	−	6.43719i	0.0919724	−	0.270337i
$568$	−10.0964	−	10.0964i	−0.423636	−	0.423636i
$569$	−12.5011	+	28.0778i	−0.524071	+	1.17708i	0.436666	+	0.899624i	$0.356159\pi$
$569$	−12.5011	+	28.0778i	−0.524071	+	1.17708i	−0.960737	+	0.277460i	$0.910508\pi$
$570$		0			0
$571$	29.9939	−	13.3541i	1.25521	−	0.558854i	0.332044	−	0.943264i	$-0.392262\pi$
$571$	29.9939	−	13.3541i	1.25521	−	0.558854i	0.923162	+	0.384410i	$0.125595\pi$
$572$	2.69797	−	2.18477i	0.112808	−	0.0913498i
$573$	2.86192	+	5.61684i	0.119559	+	0.234647i
$574$	4.90244	−	5.88638i	0.204624	−	0.245693i
$575$		0			0
$576$	−2.98674	−	5.17318i	−0.124447	−	0.215549i
$577$	−2.14884	+	41.0024i	−0.0894575	+	1.70695i	0.473769	+	0.880649i	$0.342893\pi$
$577$	−2.14884	+	41.0024i	−0.0894575	+	1.70695i	−0.563227	+	0.826302i	$0.690440\pi$
$578$	6.11265	+	2.34643i	0.254253	+	0.0975985i
$579$	−1.23230	+	11.7246i	−0.0512128	+	0.487257i
$580$		0			0
$581$	19.7659	−	29.5381i	0.820027	−	1.22545i
$582$	−3.04585	+	3.04585i	−0.126255	+	0.126255i
$583$	−10.1122	−	26.3433i	−0.418807	−	1.09103i
$584$	−8.12166	−	1.72631i	−0.336077	−	0.0714353i
$585$		0			0
$586$	−2.30722	−	10.8546i	−0.0953102	−	0.448399i
$587$	10.7855	−	21.1676i	0.445163	−	0.873682i	−0.553989	−	0.832524i	$-0.686895\pi$
$587$	10.7855	−	21.1676i	0.445163	−	0.873682i	0.999153	−	0.0411584i	$-0.0131048\pi$
$588$	10.9544	+	11.5751i	0.451753	+	0.477350i
$589$	−1.74841	−	0.568094i	−0.0720422	−	0.0234079i
$590$		0			0
$591$	−3.83231	+	18.0296i	−0.157640	+	0.741638i
$592$	−4.25187	−	3.44309i	−0.174751	−	0.141510i
$593$	−17.4687	−	4.68072i	−0.717353	−	0.192214i	−0.118363	−	0.992970i	$-0.537765\pi$
$593$	−17.4687	−	4.68072i	−0.717353	−	0.192214i	−0.598990	+	0.800756i	$0.704431\pi$
$594$	−7.78201	+	5.65396i	−0.319300	+	0.231985i
$595$		0			0
$596$	−23.0215	−	16.7261i	−0.942996	−	0.685126i
$597$	14.8889	+	18.3863i	0.609362	+	0.752500i
$598$	1.70684	+	0.0894515i	0.0697977	+	0.00365794i
$599$	−4.39041	−	2.53480i	−0.179387	−	0.103569i	0.407617	−	0.913153i	$-0.366360\pi$
$599$	−4.39041	−	2.53480i	−0.179387	−	0.103569i	−0.587005	+	0.809583i	$0.699693\pi$
$600$		0			0
$601$			14.7165i			0.600300i	0.953892	+	0.300150i	$0.0970368\pi$
$601$			14.7165i			0.600300i	−0.953892	+	0.300150i	$0.902963\pi$
$602$	−10.4928	−	2.38180i	−0.427655	−	0.0970749i
$603$	0.425373	+	2.68570i	0.0173225	+	0.109370i
$604$	−29.3287	−	3.08257i	−1.19337	−	0.125428i
$605$		0			0
$606$	0.271999	+	2.58790i	0.0110492	+	0.105126i
$607$	8.91332	−	33.2650i	0.361781	−	1.35018i	−0.509952	−	0.860203i	$-0.670337\pi$
$607$	8.91332	−	33.2650i	0.361781	−	1.35018i	0.871733	−	0.489981i	$-0.162996\pi$
$608$	−0.187680	+	1.18497i	−0.00761144	+	0.0480567i
$609$	1.01015	+	7.00048i	0.0409334	+	0.283674i
$610$		0			0
$611$	−0.00769548	+	0.00163572i	−0.000311326	+	6.61743e-5i
$612$	1.62995	+	2.50991i	0.0658869	+	0.101457i
$613$	−5.17312	−	7.96591i	−0.208941	−	0.321740i	0.718627	−	0.695396i	$-0.244771\pi$
$613$	−5.17312	−	7.96591i	−0.208941	−	0.321740i	−0.927568	+	0.373656i	$0.878104\pi$
$614$	−8.21437	+	1.74602i	−0.331505	+	0.0704635i
$615$		0			0
$616$	−2.50942	−	17.3906i	−0.101107	−	0.700689i
$617$	1.41008	−	8.90288i	0.0567676	−	0.358416i	−0.942911	−	0.333046i	$-0.891924\pi$
$617$	1.41008	−	8.90288i	0.0567676	−	0.358416i	0.999678	−	0.0253702i	$-0.00807646\pi$
$618$	−0.622634	+	2.32370i	−0.0250460	+	0.0934730i
$619$	−0.543979	−	5.17561i	−0.0218643	−	0.208025i	−1.00000		5.74497e-5i	$-0.999982\pi$
$619$	−0.543979	−	5.17561i	−0.0218643	−	0.208025i	0.978136	−	0.207968i	$-0.0666850\pi$
$620$		0			0
$621$	49.5621	+	5.20918i	1.98886	+	0.209037i
$622$	−1.21112	−	7.64672i	−0.0485616	−	0.306606i
$623$	−10.5404	−	2.39261i	−0.422294	−	0.0958580i
$624$			1.69981i			0.0680467i
$625$		0			0
$626$	−2.35655	−	1.36056i	−0.0941868	−	0.0543788i
$627$	−1.40337	−	0.0735474i	−0.0560452	−	0.00293720i
$628$	14.2131	+	17.5517i	0.567164	+	0.700389i
$629$	1.67796	+	1.21911i	0.0669048	+	0.0486092i
$630$		0			0
$631$	21.0020	−	15.2589i	0.836078	−	0.607446i	−0.0851944	−	0.996364i	$-0.527151\pi$
$631$	21.0020	−	15.2589i	0.836078	−	0.607446i	0.921272	+	0.388918i	$0.127151\pi$
$632$	−22.7720	−	6.10173i	−0.905820	−	0.242714i
$633$	−16.1293	−	13.0612i	−0.641082	−	0.519138i
$634$	0.951595	−	4.47690i	0.0377927	−	0.177800i
$635$		0			0
$636$	14.6660	+	4.76526i	0.581543	+	0.188955i
$637$	0.741346	+	3.10658i	0.0293732	+	0.123087i
$638$	1.68985	−	3.31652i	0.0669018	−	0.131302i
$639$	−2.69316	−	12.6703i	−0.106540	−	0.501231i
$640$		0			0
$641$	9.87232	+	2.09843i	0.389933	+	0.0828829i	0.398706	−	0.917079i	$-0.369459\pi$
$641$	9.87232	+	2.09843i	0.389933	+	0.0828829i	−0.00877310	+	0.999962i	$0.502793\pi$
$642$	−1.40469	−	3.65935i	−0.0554387	−	0.144423i
$643$	−21.1590	+	21.1590i	−0.834431	+	0.834431i	−0.988119	−	0.153688i	$-0.950885\pi$
$643$	−21.1590	+	21.1590i	−0.834431	+	0.834431i	0.153688	+	0.988119i	$0.450885\pi$
$644$	−24.1648	+	36.1119i	−0.952227	+	1.42301i
$645$		0			0
$646$	0.0133521	−	0.127037i	0.000525332	−	0.00499820i
$647$	−0.997603	−	0.382944i	−0.0392198	−	0.0150551i	0.338679	−	0.940902i	$-0.390020\pi$
$647$	−0.997603	−	0.382944i	−0.0392198	−	0.0150551i	−0.377899	+	0.925847i	$0.623353\pi$
$648$	0.214414	−	4.09126i	0.00842298	−	0.160720i
$649$	−22.3881	−	38.7774i	−0.878811	−	1.52214i
$650$		0			0
$651$	−14.3381	+	17.2158i	−0.561954	+	0.674741i
$652$	4.58955	+	9.00750i	0.179741	+	0.352761i
$653$	−23.1459	+	18.7432i	−0.905769	+	0.733477i	−0.964301	−	0.264808i	$-0.914691\pi$
$653$	−23.1459	+	18.7432i	−0.905769	+	0.733477i	0.0585321	+	0.998286i	$0.481358\pi$
$654$	7.30941	−	3.25436i	0.285821	−	0.127256i
$655$		0			0
$656$	−8.44855	+	18.9758i	−0.329860	+	0.740879i
$657$	−5.32632	−	5.32632i	−0.207799	−	0.207799i
$658$	−0.00612164	+	0.0179935i	−0.000238646	+	0.000701459i
$659$	8.35402	−	2.71439i	0.325426	−	0.105737i	−0.141748	−	0.989903i	$-0.545272\pi$
$659$	8.35402	−	2.71439i	0.325426	−	0.105737i	0.467174	+	0.884165i	$0.345272\pi$
$660$		0			0
$661$	8.13739	−	7.32694i	0.316508	−	0.284985i	−0.495529	−	0.868592i	$-0.665026\pi$
$661$	8.13739	−	7.32694i	0.316508	−	0.284985i	0.812036	+	0.583607i	$0.198359\pi$
$662$	0.805388	−	0.523025i	0.0313023	−	0.0203280i
$663$	−0.0337247	−	0.643505i	−0.00130976	−	0.0249917i
$664$	6.61746	−	20.3664i	0.256807	−	0.790371i
$665$		0			0
$666$	0.340819	+	1.04893i	0.0132065	+	0.0406453i
$667$	−18.0034	+	6.91085i	−0.697094	+	0.267589i
$668$	−10.4522	−	39.0082i	−0.404408	−	1.50927i
$669$	−24.2691	+	2.55078i	−0.938297	+	0.0986190i
$670$		0			0
$671$	−26.3752	+	36.3024i	−1.01820	+	1.40144i
$672$	12.5605	+	7.48431i	0.484532	+	0.288713i
$673$	25.3164	−	12.8993i	0.975875	−	0.497233i	0.108073	−	0.994143i	$-0.465532\pi$
$673$	25.3164	−	12.8993i	0.975875	−	0.497233i	0.867802	+	0.496910i	$0.165532\pi$
$674$	5.64801	−	3.26088i	0.217553	−	0.125604i
$675$		0			0
$676$	11.6817	−	20.2334i	0.449297	−	0.778206i
$677$	10.5744	+	6.86709i	0.406407	+	0.263924i	0.731614	−	0.681719i	$-0.238767\pi$
$677$	10.5744	+	6.86709i	0.406407	+	0.263924i	−0.325207	+	0.945643i	$0.605434\pi$
$678$	1.71140	−	0.271060i	0.0657260	−	0.0104100i
$679$	5.97128	−	21.1174i	0.229157	−	0.810413i
$680$		0			0
$681$	−0.282572	−	0.125809i	−0.0108282	−	0.00482101i
$682$	11.3888	−	3.05163i	0.436101	−	0.116853i
$683$	21.3113	−	26.3173i	0.815455	−	1.00700i	−0.184254	−	0.982879i	$-0.558987\pi$
$683$	21.3113	−	26.3173i	0.815455	−	1.00700i	0.999709	−	0.0241242i	$-0.00767971\pi$
$684$	−0.478288	+	0.531193i	−0.0182878	+	0.0203107i
$685$		0			0
$686$	7.36396	+	2.30309i	0.281157	+	0.0879323i
$687$	29.6196	+	15.0919i	1.13006	+	0.575793i
$688$	29.1352	−	1.52691i	1.11077	−	0.0582129i
$689$	2.06786	+	2.29660i	0.0787794	+	0.0874933i
$690$		0			0
$691$	−13.9555	−	12.5656i	−0.530892	−	0.478017i	0.359543	−	0.933129i	$-0.382933\pi$
$691$	−13.9555	−	12.5656i	−0.530892	−	0.478017i	−0.890434	+	0.455112i	$0.849599\pi$
$692$	6.94335	+	1.09972i	0.263946	+	0.0418050i
$693$	6.68335	−	14.4714i	0.253880	−	0.549722i
$694$	0.889009	+	1.22362i	0.0337463	+	0.0464478i
$695$		0			0
$696$	1.73337	+	3.89320i	0.0657031	+	0.147572i
$697$	2.82193	−	7.35138i	0.106888	−	0.278453i
$698$	2.35744	−	3.63014i	0.0892304	−	0.137403i
$699$	−17.3468			−0.656118
$700$		0			0
$701$	3.28420			0.124042			0.0620212	−	0.998075i	$-0.480245\pi$
$701$	3.28420			0.124042			0.0620212	+	0.998075i	$0.480245\pi$
$702$	0.573767	−	0.883523i	0.0216554	−	0.0333464i
$703$	−0.177528	+	0.462476i	−0.00669559	+	0.0174426i
$704$	6.99898	+	15.7200i	0.263784	+	0.592468i
$705$		0			0
$706$	0.873797	+	1.20268i	0.0328858	+	0.0452634i
$707$	−7.64399	−	10.8317i	−0.287482	−	0.407366i
$708$	24.1687	+	3.82795i	0.908315	+	0.143863i
$709$	−17.6687	−	15.9089i	−0.663560	−	0.597472i	0.266962	−	0.963707i	$-0.413980\pi$
$709$	−17.6687	−	15.9089i	−0.663560	−	0.597472i	−0.930523	+	0.366235i	$0.880647\pi$
$710$		0			0
$711$	−14.3110	−	15.8939i	−0.536703	−	0.596069i
$712$	−6.50351	+	0.340834i	−0.243729	+	0.0127733i
$713$	−54.4274	−	27.7321i	−2.03832	−	1.03858i
$714$	−1.37719	−	0.725776i	−0.0515402	−	0.0271615i
$715$		0			0
$716$	27.3367	−	30.3605i	1.02162	−	1.13463i
$717$	−5.98128	+	7.38627i	−0.223375	+	0.275845i
$718$	8.16690	−	2.18832i	0.304786	−	0.0816672i
$719$	12.9986	+	5.78736i	0.484767	+	0.215832i	0.634542	−	0.772888i	$-0.281189\pi$
$719$	12.9986	+	5.78736i	0.484767	+	0.215832i	−0.149776	+	0.988720i	$0.547855\pi$
$720$		0			0
$721$	−3.00882	−	11.8812i	−0.112054	−	0.442479i
$722$	−7.78798	+	1.23350i	−0.289839	+	0.0459059i
$723$	7.03829	+	4.57072i	0.261757	+	0.169987i
$724$	−18.6874	+	32.3675i	−0.694510	+	1.20293i
$725$		0			0
$726$	2.85829	−	1.65024i	0.106081	−	0.0612460i
$727$	−34.2694	+	17.4611i	−1.27098	+	0.647597i	−0.953707	−	0.300737i	$-0.902767\pi$
$727$	−34.2694	+	17.4611i	−1.27098	+	0.647597i	−0.317273	+	0.948334i	$0.602767\pi$
$728$	0.939132	+	1.67962i	0.0348065	+	0.0622510i
$729$	14.3668	−	19.7742i	0.532105	−	0.732379i
$730$		0			0
$731$	−10.9996	+	1.15610i	−0.406834	+	0.0427599i
$732$	−6.34686	−	23.6868i	−0.234587	−	0.875490i
$733$	−45.7718	+	17.5701i	−1.69062	+	0.648968i	−0.997421	−	0.0717788i	$-0.977132\pi$
$733$	−45.7718	+	17.5701i	−1.69062	+	0.648968i	−0.693199	+	0.720747i	$0.743799\pi$
$734$	−3.07171	−	9.45375i	−0.113379	−	0.348944i
$735$		0			0
$736$	−12.3187	+	37.9132i	−0.454075	+	1.39750i
$737$	−0.409951	−	7.82232i	−0.0151007	−	0.288139i
$738$	3.51176	−	2.28056i	0.129269	−	0.0839486i
$739$	−8.30887	+	7.48134i	−0.305647	+	0.275205i	−0.807653	−	0.589659i	$-0.799262\pi$
$739$	−8.30887	+	7.48134i	−0.305647	+	0.275205i	0.502006	+	0.864864i	$0.332596\pi$
$740$		0			0
$741$	0.146375	−	0.0475601i	0.00537721	−	0.00174716i
$742$	7.32336	−	1.45152i	0.268849	−	0.0532869i
$743$	13.0550	+	13.0550i	0.478941	+	0.478941i	0.904793	−	0.425852i	$-0.140026\pi$
$743$	13.0550	+	13.0550i	0.478941	+	0.478941i	−0.425852	+	0.904793i	$0.640026\pi$
$744$	−5.49066	+	12.3322i	−0.201297	+	0.452121i
$745$		0			0
$746$	2.73375	−	1.21714i	0.100090	−	0.0445628i
$747$	15.0978	−	12.2259i	0.552399	−	0.447324i
$748$	−3.91387	−	7.68141i	−0.143105	−	0.280860i
$749$	15.3449	+	12.7799i	0.560690	+	0.466967i
$750$		0			0
$751$	23.9092	+	41.4119i	0.872458	+	1.51114i	0.859446	+	0.511227i	$0.170809\pi$
$751$	23.9092	+	41.4119i	0.872458	+	1.51114i	0.0130124	+	0.999915i	$0.495858\pi$
$752$	0.00269718	−	0.0514652i	9.83559e−5	−	0.00187674i
$753$	−9.44063	−	3.62392i	−0.344036	−	0.132063i
$754$	−0.0426117	+	0.405423i	−0.00155183	+	0.0147646i
$755$		0			0
$756$	11.8289	+	24.0280i	0.430214	+	0.873890i
$757$	−25.0469	+	25.0469i	−0.910346	+	0.910346i	−0.996299	−	0.0859530i	$-0.972607\pi$
$757$	−25.0469	+	25.0469i	−0.910346	+	0.910346i	0.0859530	+	0.996299i	$0.472607\pi$
$758$	−3.13985	−	8.17959i	−0.114045	−	0.297096i
$759$	−45.6741	−	9.70833i	−1.65786	−	0.352390i
$760$		0			0
$761$	0.0356015	+	0.167492i	0.00129055	+	0.00607158i	0.978788	−	0.204875i	$-0.0656788\pi$
$761$	0.0356015	+	0.167492i	0.00129055	+	0.00607158i	−0.977498	+	0.210946i	$0.932345\pi$
$762$	−0.324910	+	0.637671i	−0.0117702	+	0.0231004i
$763$	−24.4122	+	32.6454i	−0.883780	+	1.18184i
$764$	−8.78462	−	2.85429i	−0.317816	−	0.103265i
$765$		0			0
$766$	−2.40512	+	11.3152i	−0.0869007	+	0.408836i
$767$	3.81103	+	3.08611i	0.137608	+	0.111433i
$768$	−4.63572	−	1.24214i	−0.167277	−	0.0448218i
$769$	−27.2261	+	19.7809i	−0.981797	+	0.713317i	−0.958109	−	0.286403i	$-0.907541\pi$
$769$	−27.2261	+	19.7809i	−0.981797	+	0.713317i	−0.0236871	+	0.999719i	$0.507541\pi$
$770$		0			0
$771$	7.12064	+	5.17345i	0.256444	+	0.186317i
$772$	−10.8708	−	13.4243i	−0.391248	−	0.483151i
$773$	37.1749	+	1.94825i	1.33709	+	0.0700738i	0.707422	−	0.706792i	$-0.249858\pi$
$773$	37.1749	+	1.94825i	1.33709	+	0.0700738i	0.629667	+	0.776865i	$0.283191\pi$
$774$	−5.09340	−	2.94068i	−0.183078	−	0.105700i
$775$		0			0
$776$		−	13.2227i		−	0.474666i
$777$	4.43047	+	4.10108i	0.158942	+	0.147126i
$778$	1.00451	+	6.34223i	0.0360135	+	0.227380i
$779$	1.87044	+	0.196591i	0.0670155	+	0.00704361i
$780$		0			0
$781$	3.90043	+	37.1101i	0.139568	+	1.32790i
$782$	1.09852	−	4.09975i	0.0392832	−	0.146607i
$783$	−1.85941	+	11.7398i	−0.0664497	+	0.419547i
$784$	−20.9133	−	0.576162i	−0.746903	−	0.0205772i
$785$		0			0
$786$	−1.95021	+	0.414529i	−0.0695616	+	0.0147858i
$787$	−18.6167	−	28.6672i	−0.663613	−	1.02187i	−0.996872	−	0.0790392i	$-0.974815\pi$
$787$	−18.6167	−	28.6672i	−0.663613	−	1.02187i	0.333258	−	0.942836i	$-0.391852\pi$
$788$	−14.7094	−	22.6505i	−0.524001	−	0.806892i
$789$	−1.04599	+	0.222332i	−0.0372382	+	0.00791522i
$790$		0			0
$791$	−6.93636	+	5.46052i	−0.246629	+	0.194154i
$792$	1.50244	−	9.48606i	0.0533870	−	0.337072i
$793$	1.27194	−	4.74694i	0.0451679	−	0.168569i
$794$	0.946292	+	9.00337i	0.0335827	+	0.319518i
$795$		0			0
$796$	−34.4755	−	3.62352i	−1.22195	−	0.128432i
$797$	3.49859	+	22.0892i	0.123926	+	0.782441i	0.968867	+	0.247581i	$0.0796356\pi$
$797$	3.49859	+	22.0892i	0.123926	+	0.782441i	−0.844941	+	0.534860i	$0.820364\pi$
$798$	0.0823057	−	0.362591i	0.00291359	−	0.0128356i
$799$			0.0195370i			0.000691168i
$800$		0			0
$801$	−5.11653	−	2.95403i	−0.180784	−	0.104375i
$802$	−3.42844	−	0.179677i	−0.121063	−	0.00634462i
$803$	13.6555	+	16.8631i	0.481892	+	0.595087i
$804$	3.46318	+	2.51615i	0.122137	+	0.0887376i
$805$		0			0
$806$	−1.04469	+	0.759008i	−0.0367975	+	0.0267349i
$807$	−32.0294	−	8.58226i	−1.12749	−	0.302110i
$808$	−6.20770	−	5.02690i	−0.218386	−	0.176846i
$809$	−1.17058	+	5.50714i	−0.0411553	+	0.193621i	−0.993923	−	0.110081i	$-0.964889\pi$
$809$	−1.17058	+	5.50714i	−0.0411553	+	0.193621i	0.952767	+	0.303701i	$0.0982225\pi$
$810$		0			0
$811$	19.3958	+	6.30209i	0.681080	+	0.221296i	0.629068	−	0.777350i	$-0.283437\pi$
$811$	19.3958	+	6.30209i	0.681080	+	0.221296i	0.0520120	+	0.998646i	$0.483437\pi$
$812$	−8.29960	−	6.20642i	−0.291259	−	0.217803i
$813$	−12.9997	+	25.5134i	−0.455920	+	0.894793i
$814$	−0.660562	−	3.10770i	−0.0231527	−	0.108925i
$815$		0			0
$816$	4.12886	+	0.877616i	0.144539	+	0.0307227i
$817$	−0.946680	−	2.46618i	−0.0331201	−	0.0862809i
$818$	−3.06981	+	3.06981i	−0.107333	+	0.107333i
$819$	−0.115365	+	1.74194i	−0.00403119	+	0.0608684i
$820$		0			0
$821$	−2.09632	+	19.9451i	−0.0731620	+	0.696090i	0.895051	+	0.445963i	$0.147139\pi$
$821$	−2.09632	+	19.9451i	−0.0731620	+	0.696090i	−0.968213	+	0.250126i	$0.919528\pi$
$822$	−1.52612	−	0.585821i	−0.0532294	−	0.0204328i
$823$	1.36145	−	25.9779i	0.0474570	−	0.905534i	−0.866363	−	0.499415i	$-0.833548\pi$
$823$	1.36145	−	25.9779i	0.0474570	−	0.905534i	0.913820	−	0.406119i	$-0.133118\pi$
$824$	−3.69234	−	6.39532i	−0.128629	−	0.222792i
$825$		0			0
$826$	11.1175	−	4.09286i	0.386827	−	0.142409i
$827$	−12.3384	−	24.2154i	−0.429047	−	0.842052i	−0.999781	−	0.0209175i	$-0.993341\pi$
$827$	−12.3384	−	24.2154i	−0.429047	−	0.842052i	0.570734	−	0.821135i	$-0.306659\pi$
$828$	−18.4578	+	14.9468i	−0.641453	+	0.519438i
$829$	21.9606	−	9.77747i	0.762722	−	0.339586i	0.0117598	−	0.999931i	$-0.496257\pi$
$829$	21.9606	−	9.77747i	0.762722	−	0.339586i	0.750962	+	0.660345i	$0.229590\pi$
$830$		0			0
$831$	−4.04694	+	9.08957i	−0.140387	+	0.315314i
$832$	−1.33260	−	1.33260i	−0.0461995	−	0.0461995i
$833$	7.92869	−	0.196805i	0.274713	−	0.00681890i
$834$	3.25500	−	1.05761i	0.112712	−	0.0366222i
$835$		0			0
$836$	1.53019	−	1.37779i	0.0529228	−	0.0476519i
$837$	−31.5767	+	20.5062i	−1.09145	+	0.708797i
$838$	−0.618659	−	11.8047i	−0.0213712	−	0.407787i
$839$	−17.2942	+	53.2260i	−0.597061	+	1.83757i	−0.0528742	+	0.998601i	$0.516838\pi$
$839$	−17.2942	+	53.2260i	−0.597061	+	1.83757i	−0.544187	+	0.838964i	$0.683162\pi$
$840$		0			0
$841$	7.54017	+	23.2063i	0.260006	+	0.800216i
$842$	−0.674953	+	0.259090i	−0.0232604	+	0.00892884i
$843$	−1.52747	−	5.70059i	−0.0526088	−	0.196339i
$844$	30.2435	−	3.17872i	1.04103	−	0.109416i
$845$		0			0
$846$	−0.00610649	+	0.00840487i	−0.000209946	+	0.000288965i
$847$	−8.60725	+	14.4451i	−0.295749	+	0.496339i
$848$	−18.0372	+	9.19043i	−0.619401	+	0.315601i
$849$	32.1980	−	18.5895i	1.10503	−	0.637991i
$850$		0			0
$851$	−8.23011	+	14.2550i	−0.282125	+	0.488654i
$852$	−17.1023	−	11.1064i	−0.585915	−	0.380498i
$853$	−12.9033	+	2.04369i	−0.441802	+	0.0699745i	−0.373373	−	0.927681i	$-0.621799\pi$
$853$	−12.9033	+	2.04369i	−0.441802	+	0.0699745i	−0.0684291	+	0.997656i	$0.521799\pi$
$854$	−8.27861	−	8.50983i	−0.283288	−	0.291200i
$855$		0			0
$856$	10.9920	+	4.89396i	0.375699	+	0.167272i
$857$	−37.7085	+	10.1040i	−1.28810	+	0.345145i	−0.836938	−	0.547298i	$-0.815656\pi$
$857$	−37.7085	+	10.1040i	−1.28810	+	0.345145i	−0.451161	+	0.892443i	$0.648990\pi$
$858$	−0.621196	+	0.767114i	−0.0212073	+	0.0261888i
$859$	15.8004	−	17.5481i	0.539101	−	0.598732i	−0.410629	−	0.911803i	$-0.634691\pi$
$859$	15.8004	−	17.5481i	0.539101	−	0.598732i	0.949730	+	0.313070i	$0.101358\pi$
$860$		0			0
$861$	10.6860	−	20.2773i	0.364179	−	0.691048i
$862$	−4.61795	−	2.35296i	−0.157288	−	0.0801423i
$863$	45.3747	−	2.37799i	1.54457	−	0.0809476i	0.739106	−	0.673589i	$-0.235248\pi$
$863$	45.3747	−	2.37799i	1.54457	−	0.0809476i	0.805466	+	0.592642i	$0.201915\pi$
$864$	16.4412	+	18.2598i	0.559342	+	0.621212i
$865$		0			0
$866$	6.02780	+	5.42746i	0.204833	+	0.184433i
$867$	19.3495	+	3.06465i	0.657142	+	0.104081i
$868$	−2.98152	−	32.6922i	−0.101199	−	1.10964i
$869$	36.2135	+	49.8436i	1.22846	+	1.69083i
$870$		0			0
$871$	0.348929	+	0.783708i	0.0118230	+	0.0265549i
$872$	−8.80190	+	22.9297i	−0.298070	+	0.776499i
$873$	6.53324	−	10.0603i	0.221117	−	0.340490i
$874$	1.01374			0.0342902
$875$		0			0
$876$	−11.8583			−0.400654
$877$	−31.3438	+	48.2652i	−1.05841	+	1.62980i	−0.330947	+	0.943649i	$0.607368\pi$
$877$	−31.3438	+	48.2652i	−1.05841	+	1.62980i	−0.727458	+	0.686152i	$0.759299\pi$
$878$	0.968598	−	2.52328i	0.0326886	−	0.0851567i
$879$	−13.5050	−	30.3327i	−0.455511	−	1.02309i
$880$		0			0
$881$	−10.2302	−	14.0806i	−0.344663	−	0.474388i	0.601133	−	0.799149i	$-0.294716\pi$
$881$	−10.2302	−	14.0806i	−0.344663	−	0.474388i	−0.945796	+	0.324761i	$0.894716\pi$
$882$	3.47246	+	2.39353i	0.116924	+	0.0805944i
$883$	0.518382	+	0.0821037i	0.0174450	+	0.00276301i	0.165151	−	0.986268i	$-0.447189\pi$
$883$	0.518382	+	0.0821037i	0.0174450	+	0.00276301i	−0.147706	+	0.989031i	$0.547189\pi$
$884$	0.701659	+	0.631777i	0.0235994	+	0.0212490i
$885$		0			0
$886$	5.82835	+	6.47303i	0.195807	+	0.217466i
$887$	32.4077	−	1.69842i	1.08815	−	0.0570273i	0.500186	−	0.865918i	$-0.333265\pi$
$887$	32.4077	−	1.69842i	1.08815	−	0.0570273i	0.587959	+	0.808891i	$0.299932\pi$
$888$	3.24109	+	1.65142i	0.108764	+	0.0554180i
$889$	−0.140665	−	3.64346i	−0.00471774	−	0.122198i
$890$		0			0
$891$	−7.16406	+	7.95650i	−0.240005	+	0.266553i
$892$	22.5017	−	27.7873i	0.753414	−	0.930389i
$893$	−0.00450727	+	0.00120772i	−0.000150830	+	4.04148e-5i
$894$	7.39143	+	3.29088i	0.247206	+	0.110063i
$895$		0			0
$896$	−27.1549	+	6.87677i	−0.907182	+	0.229737i
$897$	5.05101	−	0.800001i	0.168648	−	0.0267113i
$898$	3.55434	+	2.30822i	0.118610	+	0.0770261i
$899$	7.28472	−	12.6175i	0.242959	−	0.420818i
$900$		0			0
$901$	6.64612	−	3.83714i	0.221414	−	0.127834i
$902$	−10.7475	+	5.47613i	−0.357853	+	0.182335i
$903$	−32.1908	−	0.443344i	−1.07124	−	0.0147536i
$904$	−3.12641	+	4.30314i	−0.103983	+	0.143120i
$905$		0			0
$906$	8.33904	−	0.876469i	0.277046	−	0.0291187i
$907$	−3.10385	−	11.5837i	−0.103062	−	0.384631i	0.895056	−	0.445953i	$-0.147135\pi$
$907$	−3.10385	−	11.5837i	−0.103062	−	0.384631i	−0.998118	+	0.0613217i	$0.980468\pi$
$908$	0.423112	−	0.162418i	0.0140415	−	0.00539002i
$909$	−2.23930	−	6.89185i	−0.0742729	−	0.228588i
$910$		0			0
$911$	1.11500	−	3.43163i	0.0369417	−	0.113695i	−0.930885	−	0.365312i	$-0.880962\pi$
$911$	1.11500	−	3.43163i	0.0369417	−	0.113695i	0.967827	+	0.251617i	$0.0809623\pi$
$912$	0.0527641	+	1.00680i	0.00174719	+	0.0333384i
$913$	−46.9349	+	30.4799i	−1.55332	+	1.00874i
$914$	7.50937	−	6.76147i	0.248388	−	0.223649i
$915$		0			0
$916$	−46.3243	+	15.0517i	−1.53060	+	0.497322i
$917$	7.64156	−	6.69226i	0.252347	−	0.220998i
$918$	−1.84985	−	1.84985i	−0.0610543	−	0.0610543i
$919$	−18.6364	+	41.8581i	−0.614758	+	1.38077i	0.290897	+	0.956754i	$0.406046\pi$
$919$	−18.6364	+	41.8581i	−0.614758	+	1.38077i	−0.905655	+	0.424015i	$0.860620\pi$
$920$		0			0
$921$	−22.9547	+	10.2201i	−0.756382	+	0.336763i
$922$	−3.31597	+	2.68522i	−0.109206	+	0.0884329i
$923$	−1.85531	−	3.64125i	−0.0610683	−	0.119853i
$924$	−8.66944	−	23.5490i	−0.285204	−	0.774704i
$925$		0			0
$926$	−0.532173	−	0.921751i	−0.0174883	−	0.0302906i
$927$	0.350617	−	6.69018i	0.0115158	−	0.219734i
$928$	−8.87652	−	3.40738i	−0.291386	−	0.111853i
$929$	−1.50534	+	14.3224i	−0.0493886	+	0.469902i	0.941676	+	0.336520i	$0.109250\pi$
$929$	−1.50534	+	14.3224i	−0.0493886	+	0.469902i	−0.991065	+	0.133381i	$0.957417\pi$
$930$		0			0
$931$	0.535533	+	1.81702i	0.0175514	+	0.0595504i
$932$	17.9726	−	17.9726i	0.588712	−	0.588712i
$933$	−8.30148	−	21.6261i	−0.271778	−	0.708006i
$934$	4.63650	+	0.985518i	0.151711	+	0.0322471i
$935$		0			0
$936$	0.218694	+	1.02888i	0.00714825	+	0.0336299i
$937$	14.7123	−	28.8746i	0.480631	−	0.943291i	−0.515623	−	0.856816i	$-0.672439\pi$
$937$	14.7123	−	28.8746i	0.480631	−	0.943291i	0.996254	−	0.0864758i	$-0.0275605\pi$
$938$	2.05795	+	0.244997i	0.0671944	+	0.00799942i
$939$	−7.74326	−	2.51594i	−0.252692	−	0.0821045i
$940$		0			0
$941$	1.27970	−	6.02053i	0.0417171	−	0.196264i	−0.952354	−	0.304995i	$-0.901345\pi$
$941$	1.27970	−	6.02053i	0.0417171	−	0.196264i	0.994071	+	0.108731i	$0.0346787\pi$
$942$	−4.99048	−	4.04121i	−0.162599	−	0.131670i
$943$	60.3631	+	16.1742i	1.96569	+	0.526706i
$944$	−25.9882	+	18.8815i	−0.845843	+	0.614541i
$945$		0			0
$946$	13.7066	+	9.95840i	0.445639	+	0.323776i
$947$	9.62964	+	11.8916i	0.312921	+	0.386426i	0.909205	−	0.416348i	$-0.136690\pi$
$947$	9.62964	+	11.8916i	0.312921	+	0.386426i	−0.596284	+	0.802774i	$0.703357\pi$
$948$	−33.6234	−	1.76213i	−1.09204	−	0.0572313i
$949$	−2.05807	−	1.18822i	−0.0668076	−	0.0385714i
$950$		0			0
$951$		−	13.6944i		−	0.444072i
$952$	4.56471	−	1.41397i	0.147943	−	0.0458270i
$953$	−2.86067	−	18.0615i	−0.0926660	−	0.585070i	−0.989705	−	0.143120i	$-0.954287\pi$
$953$	−2.86067	−	18.0615i	−0.0926660	−	0.585070i	0.897039	−	0.441951i	$-0.145713\pi$
$954$	4.05852	+	0.426568i	0.131399	+	0.0138106i
$955$		0			0
$956$	−1.45567	−	13.8498i	−0.0470797	−	0.447933i
$957$	2.88250	−	10.7576i	0.0931778	−	0.347744i
$958$	1.22590	−	7.74004i	0.0396071	−	0.250069i
$959$	8.24293	−	1.18943i	0.266178	−	0.0384088i
$960$		0			0
$961$	14.8195	−	3.14998i	0.478048	−	0.101612i
$962$	0.189512	+	0.291822i	0.00611010	+	0.00940873i
$963$	5.94507	+	9.15461i	0.191577	+	0.295003i
$964$	−12.0278	+	2.55658i	−0.387389	+	0.0823420i
$965$		0			0
$966$	4.58587	−	11.4718i	0.147548	−	0.369101i
$967$	0.926476	−	5.84954i	0.0297934	−	0.188108i	−0.968303	−	0.249778i	$-0.919642\pi$
$967$	0.926476	−	5.84954i	0.0297934	−	0.188108i	0.998097	+	0.0616694i	$0.0196424\pi$
$968$	−2.62221	+	9.78623i	−0.0842811	+	0.314541i
$969$	−0.0399504	−	0.380102i	−0.00128339	−	0.0122106i
$970$		0			0
$971$	−37.3654	−	3.92726i	−1.19911	−	0.126032i	−0.516159	−	0.856493i	$-0.672638\pi$
$971$	−37.3654	−	3.92726i	−1.19911	−	0.126032i	−0.682954	+	0.730461i	$0.739305\pi$
$972$	3.83526	+	24.2149i	0.123016	+	0.776693i
$973$	−11.8448	+	12.7961i	−0.379727	+	0.410226i
$974$			0.894828i			0.0286721i
$975$		0			0
$976$	27.8791	+	16.0960i	0.892388	+	0.515220i
$977$	7.37944	+	0.386740i	0.236089	+	0.0123729i	0.170014	−	0.985442i	$-0.445619\pi$
$977$	7.37944	+	0.386740i	0.236089	+	0.0123729i	0.0660755	+	0.997815i	$0.478952\pi$
$978$	−1.80892	−	2.23382i	−0.0578427	−	0.0714298i
$979$	13.7688	+	10.0036i	0.440053	+	0.319717i
$980$		0			0
$981$	−18.0263	+	13.0969i	−0.575535	+	0.418151i
$982$	0.352645	+	0.0944910i	0.0112534	+	0.00301533i
$983$	38.5837	+	31.2444i	1.23063	+	0.996543i	0.999722	+	0.0235670i	$0.00750229\pi$
$983$	38.5837	+	31.2444i	1.23063	+	0.996543i	0.230906	+	0.972976i	$0.425831\pi$
$984$	2.87132	−	13.5085i	0.0915343	−	0.430635i
$985$		0			0
$986$	0.962779	+	0.312826i	0.0306611	+	0.00996240i
$987$	−0.00672262	+	0.0564693i	−0.000213983	+	0.00179744i
$988$	−0.102379	+	0.200931i	−0.00325712	+	0.00639246i
$989$	−18.2495	−	85.8572i	−0.580300	−	2.73010i
$990$		0			0
$991$	36.1772	+	7.68971i	1.14921	+	0.244272i	0.742860	−	0.669447i	$-0.233469\pi$
$991$	36.1772	+	7.68971i	1.14921	+	0.244272i	0.406348	+	0.913718i	$0.366802\pi$
$992$	−10.7933	−	28.1175i	−0.342687	−	0.892731i
$993$	2.03175	−	2.03175i	0.0644756	−	0.0644756i
$994$	−9.85114	−	0.652421i	−0.312459	−	0.0206935i
$995$		0			0
$996$	3.19687	−	30.4161i	0.101297	−	0.963772i
$997$	−6.84900	−	2.62908i	−0.216910	−	0.0832639i	0.247487	−	0.968891i	$-0.420395\pi$
$997$	−6.84900	−	2.62908i	−0.216910	−	0.0832639i	−0.464397	+	0.885627i	$0.653729\pi$
$998$	0.453127	−	8.64617i	0.0143435	−	0.273690i
$999$	5.07277	+	8.78629i	0.160495	+	0.277986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.493.11		288
5.2	odd	4		175.2.x.a.122.11	yes	288
5.3	odd	4		875.2.bb.c.507.8		288
5.4	even	2		875.2.bb.a.493.8		288
7.5	odd	6	inner	875.2.bb.b.243.8		288
25.6	even	5		175.2.x.a.108.11	yes	288
25.8	odd	20		875.2.bb.a.857.11		288
25.17	odd	20	inner	875.2.bb.b.857.8		288
25.19	even	10		875.2.bb.c.143.8		288
35.12	even	12		175.2.x.a.47.11	yes	288
35.19	odd	6		875.2.bb.a.243.11		288
35.33	even	12		875.2.bb.c.257.8		288
175.19	odd	30		875.2.bb.c.768.8		288
175.33	even	60		875.2.bb.a.607.8		288
175.117	even	60	inner	875.2.bb.b.607.11		288
175.131	odd	30		175.2.x.a.33.11	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.11	✓	288	175.131	odd	30
175.2.x.a.47.11	yes	288	35.12	even	12
175.2.x.a.108.11	yes	288	25.6	even	5
175.2.x.a.122.11	yes	288	5.2	odd	4
875.2.bb.a.243.11		288	35.19	odd	6
875.2.bb.a.493.8		288	5.4	even	2
875.2.bb.a.607.8		288	175.33	even	60
875.2.bb.a.857.11		288	25.8	odd	20
875.2.bb.b.243.8		288	7.5	odd	6	inner
875.2.bb.b.493.11		288	1.1	even	1	trivial
875.2.bb.b.607.11		288	175.117	even	60	inner
875.2.bb.b.857.8		288	25.17	odd	20	inner
875.2.bb.c.143.8		288	25.19	even	10
875.2.bb.c.257.8		288	35.33	even	12
875.2.bb.c.507.8		288	5.3	odd	4
875.2.bb.c.768.8		288	175.19	odd	30

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+(0.226901 - 0.349398i) q^{2} +(0.446713 - 1.16373i) q^{3} +(0.742879 + 1.66853i) q^{4} +(-0.305244 - 0.420132i) q^{6} +(2.40197 + 1.10931i) q^{7} +(1.57450 + 0.249376i) q^{8} +(1.07473 + 0.967688i) q^{9} +(-2.78759 - 3.09593i) q^{11} +(2.27357 - 0.119153i) q^{12} +(0.406529 + 0.207137i) q^{13} +(0.932599 - 0.587538i) q^{14} +(-1.99986 + 2.22107i) q^{16} +(0.713032 - 0.880521i) q^{17} +(0.581965 - 0.155937i) q^{18} +(0.247218 + 0.110068i) q^{19} +(2.36392 - 2.29969i) q^{21} +(-1.71422 + 0.271506i) q^{22} +(7.54118 + 4.89730i) q^{23} +(0.993556 - 1.72089i) q^{24} +(0.164615 - 0.0950407i) q^{26} +(4.93819 - 2.51613i) q^{27} +(-0.0665460 + 4.83184i) q^{28} +(-1.26059 + 1.73505i) q^{29} +(-6.75621 + 0.710106i) q^{31} +(1.14745 + 4.28233i) q^{32} +(-4.84808 + 1.86100i) q^{33} +(-0.145864 - 0.448923i) q^{34} +(-0.816228 + 2.51209i) q^{36} +(0.0958050 + 1.82807i) q^{37} +(0.0945518 - 0.0614026i) q^{38} +(0.422653 - 0.380558i) q^{39} +(6.60977 - 2.14764i) q^{41} +(-0.267130 - 1.34775i) q^{42} +(-6.90254 - 6.90254i) q^{43} +(3.09483 - 6.95109i) q^{44} +(3.42221 - 1.52367i) q^{46} +(-0.0134006 + 0.0108516i) q^{47} +(1.69136 + 3.31947i) q^{48} +(4.53888 + 5.32903i) q^{49} +(-0.706165 - 1.22311i) q^{51} +(-0.0436130 + 0.832185i) q^{52} +(6.32342 + 2.42733i) q^{53} +(0.241352 - 2.29631i) q^{54} +(3.50526 + 2.34560i) q^{56} +(0.238525 - 0.238525i) q^{57} +(0.320193 + 0.834132i) q^{58} +(10.5132 + 2.23464i) q^{59} +(-2.23943 - 10.5357i) q^{61} +(-1.28488 + 2.52173i) q^{62} +(1.50799 + 3.51655i) q^{63} +(-3.92834 - 1.27640i) q^{64} +(-0.449806 + 2.11617i) q^{66} +(1.46122 + 1.18327i) q^{67} +(1.99887 + 0.535597i) q^{68} +(9.06786 - 6.58819i) q^{69} +(-7.24631 - 5.26475i) q^{71} +(1.45084 + 1.79164i) q^{72} +(-5.20142 - 0.272595i) q^{73} +(0.660461 + 0.381317i) q^{74} +0.494259i q^{76} +(-3.26136 - 10.5286i) q^{77} +(-0.0370656 - 0.234023i) q^{78} +(-14.7078 - 1.54585i) q^{79} +(-0.268636 - 2.55590i) q^{81} +(0.749384 - 2.79674i) q^{82} +(2.10145 - 13.2680i) q^{83} +(5.59322 + 2.23589i) q^{84} +(-3.97793 + 0.845535i) q^{86} +(1.45600 + 2.24205i) q^{87} +(-3.61701 - 5.56971i) q^{88} +(-3.99599 + 0.849374i) q^{89} +(0.746691 + 0.948502i) q^{91} +(-2.56912 + 16.2208i) q^{92} +(-2.19171 + 8.17959i) q^{93} +(0.000750902 + 0.00714436i) q^{94} +(5.49604 + 0.577657i) q^{96} +(-1.29756 - 8.19248i) q^{97} +(2.89183 - 0.376707i) q^{98} -6.02480i 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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