LMFDB - Embedded newform 441.2.f.e.295.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(148,441)] 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("441.148"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,2,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	441.295
Dual form			441.2.f.e.148.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02682 + 1.77851i) q^{2} +(0.608729 + 1.62156i) q^{3} +(-1.10873 - 1.92038i) q^{4} +(0.0731228 + 0.126652i) q^{5} +(-3.50901 - 0.582422i) q^{6} +0.446582 q^{8} +(-2.25890 + 1.97418i) q^{9} -0.300337 q^{10} +(-0.832020 + 1.44110i) q^{11} +(2.43908 - 2.96686i) q^{12} +(0.0999454 + 0.173111i) q^{13} +(-0.160862 + 0.195670i) q^{15} +(1.75890 - 3.04650i) q^{16} -6.27110 q^{17} +(-1.19161 - 6.04460i) q^{18} -6.91758 q^{19} +(0.162147 - 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(3.09092 + 5.35363i) q^{23} +(0.271848 + 0.724159i) q^{24} +(2.48931 - 4.31160i) q^{25} -0.410505 q^{26} +(-4.57630 - 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-0.182824 - 0.487013i) q^{30} +(1.25890 + 2.18047i) q^{31} +(4.05873 + 7.02993i) q^{32} +(-2.84330 - 0.471928i) q^{33} +(6.43931 - 11.1532i) q^{34} +(6.29567 + 2.14910i) q^{36} +7.00046 q^{37} +(7.10312 - 12.3030i) q^{38} +(-0.219869 + 0.267445i) q^{39} +(0.0326554 + 0.0565608i) q^{40} +(1.15895 + 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +3.68994 q^{44} +(-0.415212 - 0.141737i) q^{45} -12.6953 q^{46} +(0.905887 - 1.56904i) q^{47} +(6.01077 + 0.997660i) q^{48} +(5.11215 + 8.85451i) q^{50} +(-3.81740 - 10.1690i) q^{51} +(0.221625 - 0.383865i) q^{52} +5.34614 q^{53} +(9.07630 - 5.61178i) q^{54} -0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 - 8.77720i) q^{58} +(2.28549 + 3.95859i) q^{59} +(0.554112 + 0.0919709i) q^{60} +(0.339138 - 0.587404i) q^{61} -5.17066 q^{62} -9.63481 q^{64} +(-0.0146166 + 0.0253167i) q^{65} +(3.75890 - 4.57226i) q^{66} +(3.09342 + 5.35796i) q^{67} +(6.95296 + 12.0429i) q^{68} +(-6.79968 + 8.27101i) q^{69} +1.27749 q^{71} +(-1.00878 + 0.881633i) q^{72} +1.55721 q^{73} +(-7.18823 + 12.4504i) q^{74} +(8.50683 + 1.41195i) q^{75} +(7.66972 + 13.2843i) q^{76} +(-0.249886 - 0.665657i) q^{78} +(-6.39787 + 11.0814i) q^{79} +0.514462 q^{80} +(1.20524 - 8.91894i) q^{81} -4.76015 q^{82} +(3.75687 - 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 - 3.34713i) q^{86} +(-8.43256 - 1.39963i) q^{87} +(-0.371566 + 0.643571i) q^{88} -9.06788 q^{89} +(0.678430 - 0.592918i) q^{90} +(6.85398 - 11.8714i) q^{92} +(-2.76944 + 3.36869i) q^{93} +(1.86037 + 3.22226i) q^{94} +(-0.505833 - 0.876128i) q^{95} +(-8.92877 + 10.8608i) q^{96} +(-3.98514 + 6.90246i) q^{97} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9} + 14 q^{10} + 4 q^{11} - 2 q^{12} - 8 q^{13} - 19 q^{15} + 2 q^{16} - 24 q^{17} - 2 q^{18} - 2 q^{19} + 5 q^{20} - q^{22} + 3 q^{23}+ \cdots + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^8 - 7 * q^9 + 14 * q^10 + 4 * q^11 - 2 * q^12 - 8 * q^13 - 19 * q^15 + 2 * q^16 - 24 * q^17 - 2 * q^18 - 2 * q^19 + 5 * q^20 - q^22 + 3 * q^23 - 9 * q^24 - q^25 - 22 * q^26 - 7 * q^27 + 7 * q^29 + 10 * q^30 - 3 * q^31 - 2 * q^32 - 13 * q^33 + 3 * q^34 + 34 * q^36 + 20 * q^38 - 22 * q^39 - 3 * q^40 + 5 * q^41 - 7 * q^43 + 20 * q^44 + 17 * q^45 - 6 * q^46 + 27 * q^47 - 5 * q^48 + 19 * q^50 - 15 * q^51 - 10 * q^52 + 42 * q^53 + 52 * q^54 + 4 * q^55 - 4 * q^57 - 10 * q^58 + 30 * q^59 + 31 * q^60 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 + 22 * q^66 - 2 * q^67 + 27 * q^68 + 15 * q^69 - 6 * q^71 - 12 * q^72 - 30 * q^73 - 36 * q^74 - 17 * q^75 + 5 * q^76 - 20 * q^78 - 4 * q^79 - 40 * q^80 - 31 * q^81 + 10 * q^82 + 9 * q^83 - 6 * q^85 - 8 * q^86 - 34 * q^87 - 18 * q^88 - 56 * q^89 + 28 * q^90 + 27 * q^92 + 18 * q^93 - 3 * q^94 - 14 * q^95 - 58 * q^96 - 12 * q^97 + 35 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.02682	+	1.77851i	−0.726073	+	1.25760i	0.232458	+	0.972607i	$0.425323\pi$
$2$	−1.02682	+	1.77851i	−0.726073	+	1.25760i	−0.958531	+	0.284989i	$0.908010\pi$
$3$	0.608729	+	1.62156i	0.351450	+	0.936207i
$3$	0.608729	+	1.62156i	0.351450	+	0.936207i
$4$	−1.10873	−	1.92038i	−0.554365	−	0.960188i
$5$	0.0731228	+	0.126652i	0.0327015	+	0.0566407i	0.881913	−	0.471412i	$-0.156256\pi$
$5$	0.0731228	+	0.126652i	0.0327015	+	0.0566407i	−0.849211	+	0.528053i	$0.822922\pi$
$6$	−3.50901	−	0.582422i	−1.43255	−	0.237773i
$7$		0			0
$7$		0			0
$8$	0.446582			0.157891
$9$	−2.25890	+	1.97418i	−0.752966	+	0.658060i
$10$	−0.300337			−0.0949748
$11$	−0.832020	+	1.44110i	−0.250864	+	0.434508i	−0.963764	−	0.266757i	$-0.914048\pi$
$11$	−0.832020	+	1.44110i	−0.250864	+	0.434508i	0.712900	+	0.701265i	$0.247381\pi$
$12$	2.43908	−	2.96686i	0.704103	−	0.856458i
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	0.879553	−	0.475802i	$-0.157842\pi$
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	−0.851833	+	0.523814i	$0.824509\pi$
$14$		0			0
$15$	−0.160862	+	0.195670i	−0.0415345	+	0.0505218i
$16$	1.75890	−	3.04650i	0.439724	−	0.761625i
$17$	−6.27110			−1.52097			−0.760483	−	0.649358i	$-0.775038\pi$
$17$	−6.27110			−1.52097			−0.760483	+	0.649358i	$0.775038\pi$
$18$	−1.19161	−	6.04460i	−0.280865	−	1.42473i
$19$	−6.91758			−1.58700			−0.793500	−	0.608570i	$-0.791744\pi$
$19$	−6.91758			−1.58700			−0.793500	+	0.608570i	$0.791744\pi$
$20$	0.162147	−	0.280847i	0.0362571	−	0.0627992i
$21$		0			0
$22$	−1.70867	−	2.95951i	−0.364291	−	0.630970i
$23$	3.09092	+	5.35363i	0.644501	+	1.11631i	0.984417	+	0.175852i	$0.0562682\pi$
$23$	3.09092	+	5.35363i	0.644501	+	1.11631i	−0.339916	+	0.940456i	$0.610399\pi$
$24$	0.271848	+	0.724159i	0.0554907	+	0.147818i
$25$	2.48931	−	4.31160i	0.497861	−	0.862321i
$26$	−0.410505			−0.0805066
$27$	−4.57630	−	2.46119i	−0.880710	−	0.473657i
$28$		0			0
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	−0.998867	−	0.0475930i	$-0.984845\pi$
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	0.540650	+	0.841248i	$0.318178\pi$
$30$	−0.182824	−	0.487013i	−0.0333789	−	0.0889160i
$31$	1.25890	+	2.18047i	0.226105	+	0.391625i	0.956650	−	0.291239i	$-0.0940675\pi$
$31$	1.25890	+	2.18047i	0.226105	+	0.391625i	−0.730546	+	0.682864i	$0.760734\pi$
$32$	4.05873	+	7.02993i	0.717490	+	1.24273i
$33$	−2.84330	−	0.471928i	−0.494956	−	0.0821522i
$34$	6.43931	−	11.1532i	1.10433	−	1.91276i
$35$		0			0
$36$	6.29567	+	2.14910i	1.04928	+	0.358184i
$37$	7.00046			1.15087			0.575434	−	0.817848i	$-0.304833\pi$
$37$	7.00046			1.15087			0.575434	+	0.817848i	$0.304833\pi$
$38$	7.10312	−	12.3030i	1.15228	−	1.99581i
$39$	−0.219869	+	0.267445i	−0.0352072	+	0.0428254i
$40$	0.0326554	+	0.0565608i	0.00516327	+	0.00894304i
$41$	1.15895	+	2.00736i	0.180998	+	0.313498i	0.942221	−	0.334993i	$-0.108734\pi$
$41$	1.15895	+	2.00736i	0.180998	+	0.313498i	−0.761223	+	0.648491i	$0.775401\pi$
$42$		0			0
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	−0.928812	−	0.370550i	$-0.879169\pi$
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	0.785312	+	0.619100i	$0.212502\pi$
$44$	3.68994			0.556280
$45$	−0.415212	−	0.141737i	−0.0618961	−	0.0211290i
$46$	−12.6953			−1.87182
$47$	0.905887	−	1.56904i	0.132137	−	0.228868i	−0.792363	−	0.610050i	$-0.791149\pi$
$47$	0.905887	−	1.56904i	0.132137	−	0.228868i	0.924500	+	0.381181i	$0.124483\pi$
$48$	6.01077	+	0.997660i	0.867579	+	0.144000i
$49$		0			0
$50$	5.11215	+	8.85451i	0.722967	+	1.25222i
$51$	−3.81740	−	10.1690i	−0.534543	−	1.42394i
$52$	0.221625	−	0.383865i	0.0307338	−	0.0532325i
$53$	5.34614			0.734348			0.367174	−	0.930152i	$-0.380325\pi$
$53$	5.34614			0.734348			0.367174	+	0.930152i	$0.380325\pi$
$54$	9.07630	−	5.61178i	1.23513	−	0.763667i
$55$	−0.243359			−0.0328145
$56$		0			0
$57$	−4.21093	−	11.2172i	−0.557751	−	1.48576i
$58$	−5.06752	−	8.77720i	−0.665398	−	1.15250i
$59$	2.28549	+	3.95859i	0.297546	+	0.515364i	0.975574	−	0.219672i	$-0.0704986\pi$
$59$	2.28549	+	3.95859i	0.297546	+	0.515364i	−0.678028	+	0.735036i	$0.737165\pi$
$60$	0.554112	+	0.0919709i	0.0715356	+	0.0118734i
$61$	0.339138	−	0.587404i	0.0434221	−	0.0752094i	−0.843498	−	0.537133i	$-0.819507\pi$
$61$	0.339138	−	0.587404i	0.0434221	−	0.0752094i	0.886920	+	0.461924i	$0.152841\pi$
$62$	−5.17066			−0.656674
$63$		0			0
$64$	−9.63481			−1.20435
$65$	−0.0146166	+	0.0253167i	−0.00181296	+	0.00314015i
$66$	3.75890	−	4.57226i	0.462688	−	0.562806i
$67$	3.09342	+	5.35796i	0.377921	+	0.654579i	0.990760	−	0.135630i	$-0.0433057\pi$
$67$	3.09342	+	5.35796i	0.377921	+	0.654579i	−0.612838	+	0.790208i	$0.709972\pi$
$68$	6.95296	+	12.0429i	0.843170	+	1.46041i
$69$	−6.79968	+	8.27101i	−0.818586	+	0.995713i
$70$		0			0
$71$	1.27749			0.151611			0.0758053	−	0.997123i	$-0.475847\pi$
$71$	1.27749			0.151611			0.0758053	+	0.997123i	$0.475847\pi$
$72$	−1.00878	+	0.881633i	−0.118886	+	0.103901i
$73$	1.55721			0.182257			0.0911286	−	0.995839i	$-0.470953\pi$
$73$	1.55721			0.182257			0.0911286	+	0.995839i	$0.470953\pi$
$74$	−7.18823	+	12.4504i	−0.835614	+	1.44733i
$75$	8.50683	+	1.41195i	0.982284	+	0.163038i
$76$	7.66972	+	13.2843i	0.879777	+	1.52382i
$77$		0			0
$78$	−0.249886	−	0.665657i	−0.0282940	−	0.0753708i
$79$	−6.39787	+	11.0814i	−0.719817	+	1.24676i	0.241255	+	0.970462i	$0.422441\pi$
$79$	−6.39787	+	11.0814i	−0.719817	+	1.24676i	−0.961072	+	0.276298i	$0.910892\pi$
$80$	0.514462			0.0575186
$81$	1.20524	−	8.91894i	0.133915	−	0.990993i
$82$	−4.76015			−0.525671
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	−0.582778	−	0.812631i	$-0.698034\pi$
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	0.995148	+	0.0983854i	$0.0313678\pi$
$84$		0			0
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$	−1.93247	−	3.34713i	−0.208383	−	0.360930i
$87$	−8.43256	−	1.39963i	−0.904065	−	0.150056i
$88$	−0.371566	+	0.643571i	−0.0396090	+	0.0686048i
$89$	−9.06788			−0.961193			−0.480597	−	0.876942i	$-0.659580\pi$
$89$	−9.06788			−0.961193			−0.480597	+	0.876942i	$0.659580\pi$
$90$	0.678430	−	0.592918i	0.0715128	−	0.0624991i
$91$		0			0
$92$	6.85398	−	11.8714i	0.714577	−	1.23768i
$93$	−2.76944	+	3.36869i	−0.287177	+	0.349317i
$94$	1.86037	+	3.22226i	0.191883	+	0.332350i
$95$	−0.505833	−	0.876128i	−0.0518973	−	0.0898888i
$96$	−8.92877	+	10.8608i	−0.911289	+	1.10848i
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	−0.994278	−	0.106821i	$-0.965933\pi$
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	0.589649	+	0.807660i	$0.299266\pi$
$98$		0			0
$99$	−0.965543	−	4.89786i	−0.0970408	−	0.492253i
$100$	−11.0399			−1.10399
$101$	−7.42150	+	12.8544i	−0.738467	+	1.27906i	0.214719	+	0.976676i	$0.431117\pi$
$101$	−7.42150	+	12.8544i	−0.738467	+	1.27906i	−0.953186	+	0.302386i	$0.902217\pi$
$102$	22.0054	+	3.65243i	2.17886	+	0.361644i
$103$	0.101974	+	0.176624i	0.0100478	+	0.0174033i	0.871006	−	0.491273i	$-0.163468\pi$
$103$	0.101974	+	0.176624i	0.0100478	+	0.0174033i	−0.860958	+	0.508676i	$0.830135\pi$
$104$	0.0446339	+	0.0773081i	0.00437671	+	0.00758068i
$105$		0			0
$106$	−5.48953	+	9.50815i	−0.533191	+	0.923513i
$107$	−6.96889			−0.673708			−0.336854	−	0.941557i	$-0.609363\pi$
$107$	−6.96889			−0.673708			−0.336854	+	0.941557i	$0.609363\pi$
$108$	0.347467	+	11.5170i	0.0334350	+	1.10822i
$109$	−6.66116			−0.638024			−0.319012	−	0.947751i	$-0.603351\pi$
$109$	−6.66116			−0.638024			−0.319012	+	0.947751i	$0.603351\pi$
$110$	0.249886	−	0.432816i	0.0238257	−	0.0412674i
$111$	4.26138	+	11.3516i	0.404472	+	1.07745i
$112$		0			0
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	0.865115	−	0.501573i	$-0.167245\pi$
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	−0.866933	+	0.498425i	$0.833912\pi$
$114$	24.2739	+	4.02895i	2.27345	+	0.377345i
$115$	−0.452033	+	0.782945i	−0.0421523	+	0.0730100i
$116$	10.9435			1.01608
$117$	−0.567518	−	0.193729i	−0.0524670	−	0.0179102i
$118$	−9.38718			−0.864160
$119$		0			0
$120$	−0.0718382	+	0.0873827i	−0.00655790	+	0.00797692i
$121$	4.11548	+	7.12823i	0.374135	+	0.648021i
$122$	0.696469	+	1.20632i	0.0630553	+	0.109215i
$123$	−2.54957	+	3.10125i	−0.229887	+	0.279630i
$124$	2.79155	−	4.83511i	0.250689	−	0.434206i
$125$	1.45933			0.130526
$126$		0			0
$127$	13.4788			1.19605			0.598027	−	0.801476i	$-0.295952\pi$
$127$	13.4788			1.19605			0.598027	+	0.801476i	$0.295952\pi$
$128$	1.77577	−	3.07572i	0.156957	−	0.271858i
$129$	−3.21570	−	0.533739i	−0.283127	−	0.0469931i
$130$	−0.0300173	−	0.0519914i	−0.00263269	−	0.00455995i
$131$	9.91665	+	17.1761i	0.866422	+	1.50069i	0.865628	+	0.500687i	$0.166919\pi$
$131$	9.91665	+	17.1761i	0.866422	+	1.50069i	0.000793988		1.00000i	$0.499747\pi$
$132$	2.24617	+	5.98345i	0.195504	+	0.520793i
$133$		0			0
$134$	−12.7056			−1.09759
$135$	−0.0229161	−	0.759569i	−0.00197230	−	0.0653733i
$136$	−2.80056			−0.240146
$137$	3.22255	−	5.58162i	0.275321	−	0.476870i	−0.694895	−	0.719111i	$-0.744549\pi$
$137$	3.22255	−	5.58162i	0.275321	−	0.476870i	0.970216	+	0.242241i	$0.0778826\pi$
$138$	−7.72800	−	20.5862i	−0.657851	−	1.75241i
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	0.999328	+	0.0366611i	$0.0116722\pi$
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	−0.467914	+	0.883774i	$0.654994\pi$
$140$		0			0
$141$	3.09573	+	0.513826i	0.260708	+	0.0432720i
$142$	−1.31176	+	2.27203i	−0.110080	+	0.190665i
$143$	−0.332626			−0.0278156
$144$	2.04117	+	10.3541i	0.170097	+	0.862842i
$145$	−0.721743			−0.0599375
$146$	−1.59897	+	2.76950i	−0.132332	+	0.229206i
$147$		0			0
$148$	−7.76161	−	13.4435i	−0.638000	−	1.10505i
$149$	−8.88364	−	15.3869i	−0.727776	−	1.26054i	−0.957821	−	0.287365i	$-0.907221\pi$
$149$	−8.88364	−	15.3869i	−0.727776	−	1.26054i	0.230045	−	0.973180i	$-0.426113\pi$
$150$	−11.2462	+	13.6796i	−0.918246	+	1.11694i
$151$	−4.23300	+	7.33177i	−0.344476	+	0.596651i	−0.985259	−	0.171072i	$-0.945277\pi$
$151$	−4.23300	+	7.33177i	−0.344476	+	0.596651i	0.640782	+	0.767723i	$0.278610\pi$
$152$	−3.08927			−0.250573
$153$	14.1658	−	12.3803i	1.14524	−	1.00089i
$154$		0			0
$155$	−0.184108	+	0.318885i	−0.0147879	+	0.0256135i
$156$	0.757369	+	0.125707i	0.0606381	+	0.0100646i
$157$	−2.84968	−	4.93579i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$157$	−2.84968	−	4.93579i	−0.227429	−	0.393919i	−0.957045	+	0.289938i	$0.906365\pi$
$158$	−13.1390	−	22.7573i	−1.04528	−	1.81048i
$159$	3.25435	+	8.66907i	0.258087	+	0.687502i
$160$	−0.593572	+	1.02810i	−0.0469260	+	0.0812782i
$161$		0			0
$162$	14.6248	+	11.3017i	1.14904	+	0.887944i
$163$	2.12535			0.166470			0.0832349	−	0.996530i	$-0.473475\pi$
$163$	2.12535			0.166470			0.0832349	+	0.996530i	$0.473475\pi$
$164$	2.56993	−	4.45125i	0.200678	−	0.347584i
$165$	−0.148140	−	0.394620i	−0.0115326	−	0.0307211i
$166$	7.71528	+	13.3632i	0.598821	+	1.03719i
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	0.550415	−	0.834891i	$-0.314470\pi$
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	−0.998244	+	0.0592278i	$0.981136\pi$
$168$		0			0
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$	1.88344			0.144453
$171$	15.6261	−	13.6565i	1.19496	−	1.04434i
$172$	4.17323			0.318206
$173$	7.95546	−	13.7793i	0.604842	−	1.04762i	−0.387234	−	0.921981i	$-0.626570\pi$
$173$	7.95546	−	13.7793i	0.604842	−	1.04762i	0.992076	−	0.125636i	$-0.0400971\pi$
$174$	11.1480	−	13.5602i	0.845127	−	1.02800i
$175$		0			0
$176$	2.92688	+	5.06950i	0.220622	+	0.382128i
$177$	−5.02783	+	6.11577i	−0.377915	+	0.459689i
$178$	9.31110	−	16.1273i	0.697897	−	1.20879i
$179$	−7.75331			−0.579509			−0.289755	−	0.957101i	$-0.593574\pi$
$179$	−7.75331			−0.579509			−0.289755	+	0.957101i	$0.593574\pi$
$180$	0.188168	+	0.954510i	0.0140252	+	0.0711450i
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$		0			0
$183$	1.15895	+	0.192362i	0.0856722	+	0.0142198i
$184$	1.38035	+	2.39084i	0.101761	+	0.176255i
$185$	0.511893	+	0.886625i	0.0376351	+	0.0651860i
$186$	−3.14753	−	8.38452i	−0.230788	−	0.614783i
$187$	5.21769	−	9.03730i	0.381555	−	0.660873i
$188$	−4.01754			−0.293009
$189$		0			0
$190$	2.07760			0.150725
$191$	2.48383	−	4.30211i	0.179723	−	0.311290i	−0.762062	−	0.647504i	$-0.775813\pi$
$191$	2.48383	−	4.30211i	0.179723	−	0.311290i	0.941786	+	0.336214i	$0.109146\pi$
$192$	−5.86499	−	15.6234i	−0.423269	−	1.12752i
$193$	7.45221	+	12.9076i	0.536422	+	0.929110i	0.999093	+	0.0425800i	$0.0135577\pi$
$193$	7.45221	+	12.9076i	0.536422	+	0.929110i	−0.462671	+	0.886530i	$0.653109\pi$
$194$	−8.18406	−	14.1752i	−0.587581	−	1.01772i
$195$	−0.0499500	−	0.00829064i	−0.00357699	−	0.000593705i
$196$		0			0
$197$	−21.2608			−1.51477			−0.757386	−	0.652968i	$-0.773524\pi$
$197$	−21.2608			−1.51477			−0.757386	+	0.652968i	$0.773524\pi$
$198$	9.70233	+	3.31200i	0.689514	+	0.235374i
$199$	19.9442			1.41380			0.706902	−	0.707311i	$-0.250092\pi$
$199$	19.9442			1.41380			0.706902	+	0.707311i	$0.250092\pi$
$200$	1.11168	−	1.92549i	0.0786077	−	0.136152i
$201$	−6.80518	+	8.27770i	−0.480001	+	0.583864i
$202$	−15.2411	−	26.3984i	−1.07236	−	1.85739i
$203$		0			0
$204$	−15.2957	+	18.6055i	−1.07092	+	1.30264i
$205$	−0.169492	+	0.293568i	−0.0118378	+	0.0205037i
$206$	−0.418838			−0.0291818
$207$	−17.5511	−	5.99127i	−1.21988	−	0.416422i
$208$	0.703175			0.0487564
$209$	5.75556	−	9.96893i	0.398121	−	0.689565i
$210$		0			0
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	0.913293	+	0.407303i	$0.133531\pi$
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	−0.103912	+	0.994587i	$0.533136\pi$
$212$	−5.92742	−	10.2666i	−0.407097	−	0.705112i
$213$	0.777647	+	2.07153i	0.0532835	+	0.141939i
$214$	7.15581	−	12.3942i	0.489161	−	0.847252i
$215$	−0.275232			−0.0187707
$216$	−2.04370	−	1.09912i	−0.139056	−	0.0747860i
$217$		0			0
$218$	6.83983	−	11.8469i	0.463252	−	0.802376i
$219$	0.947916	+	2.52510i	0.0640543	+	0.170630i
$220$	0.269819	+	0.467340i	0.0181912	+	0.0315081i
$221$	−0.626768	−	1.08559i	−0.0421610	−	0.0730250i
$222$	−24.5647	−	4.07722i	−1.64867	−	0.273645i
$223$	2.03052	−	3.51696i	0.135974	−	0.235513i	−0.789995	−	0.613113i	$-0.789917\pi$
$223$	2.03052	−	3.51696i	0.135974	−	0.235513i	0.925969	+	0.377600i	$0.123250\pi$
$224$		0			0
$225$	2.88879	+	14.6538i	0.192586	+	0.976921i
$226$	0.0793667			0.00527940
$227$	1.92643	−	3.33667i	0.127861	−	0.221462i	−0.794986	−	0.606627i	$-0.792522\pi$
$227$	1.92643	−	3.33667i	0.127861	−	0.221462i	0.922848	+	0.385165i	$0.125855\pi$
$228$	−16.8725	+	20.5235i	−1.11741	+	1.35920i
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	0.563788	−	0.825919i	$-0.309343\pi$
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	−0.997161	+	0.0752952i	$0.976010\pi$
$230$	−0.928316	−	1.60789i	−0.0612113	−	0.106021i
$231$		0			0
$232$	−1.10197	+	1.90868i	−0.0723481	+	0.125311i
$233$	17.5023			1.14661			0.573307	−	0.819340i	$-0.305660\pi$
$233$	17.5023			1.14661			0.573307	+	0.819340i	$0.305660\pi$
$234$	0.927288	−	0.810410i	0.0606187	−	0.0529781i
$235$	0.264964			0.0172844
$236$	5.06798	−	8.77801i	0.329898	−	0.571400i
$237$	−21.8638	−	3.62892i	−1.42020	−	0.235724i
$238$		0			0
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	0.959752	−	0.280849i	$-0.0906161\pi$
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	−0.723099	+	0.690745i	$0.757283\pi$
$240$	0.313168	+	0.834230i	0.0202149	+	0.0538493i
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	−0.948751	−	0.316026i	$-0.897651\pi$
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	0.748062	+	0.663629i	$0.230985\pi$
$242$	−16.9035			−1.08660
$243$	15.1962	−	3.47486i	0.974839	−	0.222912i
$244$	−1.50405			−0.0962868
$245$		0			0
$246$	−2.89764	−	7.71886i	−0.184747	−	0.492137i
$247$	−0.691380	−	1.19751i	−0.0439915	−	0.0761954i
$248$	0.562201	+	0.973761i	0.0356998	+	0.0618339i
$249$	12.8385	+	2.13092i	0.813609	+	0.135042i
$250$	−1.49847	+	2.59543i	−0.0947717	+	0.164149i
$251$	5.65283			0.356803			0.178402	−	0.983958i	$-0.442907\pi$
$251$	5.65283			0.356803			0.178402	+	0.983958i	$0.442907\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$	−13.8404	+	23.9722i	−0.868422	+	1.50415i
$255$	1.00878	−	1.22707i	0.0631725	−	0.0768419i
$256$	−5.98801	−	10.3715i	−0.374250	−	0.648221i
$257$	−5.90082	−	10.2205i	−0.368083	−	0.637539i	0.621183	−	0.783666i	$-0.286653\pi$
$257$	−5.90082	−	10.2205i	−0.368083	−	0.637539i	−0.989266	+	0.146127i	$0.953319\pi$
$258$	4.25121	−	5.17110i	0.264669	−	0.321939i
$259$		0			0
$260$	0.0648233			0.00402017
$261$	−2.86357	−	14.5259i	−0.177250	−	0.899129i
$262$	−40.7306			−2.51634
$263$	11.1200	−	19.2605i	0.685691	−	1.18765i	−0.287528	−	0.957772i	$-0.592834\pi$
$263$	11.1200	−	19.2605i	0.685691	−	1.18765i	0.973219	−	0.229879i	$-0.0738331\pi$
$264$	−1.26977	−	0.210755i	−0.0781489	−	0.0129711i
$265$	0.390925	+	0.677101i	0.0240143	+	0.0415940i
$266$		0			0
$267$	−5.51988	−	14.7041i	−0.337811	−	0.899876i
$268$	6.85953	−	11.8810i	0.419012	−	0.725750i
$269$	2.38884			0.145650			0.0728251	−	0.997345i	$-0.476799\pi$
$269$	2.38884			0.145650			0.0728251	+	0.997345i	$0.476799\pi$
$270$	1.37443	+	0.739186i	0.0836452	+	0.0449854i
$271$	23.2258			1.41087			0.705435	−	0.708775i	$-0.250752\pi$
$271$	23.2258			1.41087			0.705435	+	0.708775i	$0.250752\pi$
$272$	−11.0302	+	19.1049i	−0.668806	+	1.15841i
$273$		0			0
$274$	6.61797	+	11.4627i	0.399806	+	0.692484i
$275$	4.14231	+	7.17469i	0.249790	+	0.432650i
$276$	23.4224	+	3.88763i	1.40987	+	0.234008i
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	−0.788283	−	0.615312i	$-0.789030\pi$
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	0.927018	+	0.375017i	$0.122363\pi$
$278$	−25.7333			−1.54338
$279$	−7.14837	−	2.44018i	−0.427962	−	0.146090i
$280$		0			0
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	−0.634215	−	0.773157i	$-0.718676\pi$
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	0.986681	+	0.162668i	$0.0520098\pi$
$282$	−4.09261	+	4.97818i	−0.243712	+	0.296446i
$283$	−7.92483	−	13.7262i	−0.471082	−	0.815939i	0.528370	−	0.849014i	$-0.322803\pi$
$283$	−7.92483	−	13.7262i	−0.471082	−	0.815939i	−0.999453	+	0.0330753i	$0.989470\pi$
$284$	−1.41639	−	2.45327i	−0.0840475	−	0.145575i
$285$	1.11278	−	1.35356i	0.0659152	−	0.0801781i
$286$	0.341548	−	0.591579i	0.0201962	−	0.0349808i
$287$		0			0
$288$	−23.0466	−	7.86723i	−1.35803	−	0.463581i
$289$	22.3267			1.31334
$290$	0.741102	−	1.28363i	0.0435190	−	0.0753772i
$291$	−13.6186	−	2.26040i	−0.798337	−	0.132507i
$292$	−1.72652	−	2.99042i	−0.101037	−	0.175001i
$293$	7.04804	+	12.2076i	0.411751	+	0.713173i	0.995081	−	0.0990615i	$-0.0315841\pi$
$293$	7.04804	+	12.2076i	0.411751	+	0.713173i	−0.583330	+	0.812235i	$0.698251\pi$
$294$		0			0
$295$	−0.334243	+	0.578927i	−0.0194604	+	0.0337064i
$296$	3.12628			0.181711
$297$	7.35440	−	4.54715i	0.426746	−	0.263853i
$298$	36.4877			2.11367
$299$	−0.617846	+	1.07014i	−0.0357310	+	0.0618878i
$300$	−6.72029	−	17.9018i	−0.387996	−	1.03356i
$301$		0			0
$302$	−8.69307	−	15.0568i	−0.500230	−	0.866424i
$303$	−25.3619	−	4.20953i	−1.45700	−	0.241831i
$304$	−12.1673	+	21.0744i	−0.697843	+	1.20870i
$305$	0.0991949			0.00567988
$306$	7.47269	+	37.9063i	0.427185	+	2.16696i
$307$	27.3916			1.56332			0.781660	−	0.623704i	$-0.214373\pi$
$307$	27.3916			1.56332			0.781660	+	0.623704i	$0.214373\pi$
$308$		0			0
$309$	−0.224332	+	0.272873i	−0.0127618	+	0.0155232i
$310$	−0.378093	−	0.654877i	−0.0214742	−	0.0371945i
$311$	7.02785	+	12.1726i	0.398513	+	0.690244i	0.993543	−	0.113459i	$-0.0361931\pi$
$311$	7.02785	+	12.1726i	0.398513	+	0.690244i	−0.595030	+	0.803704i	$0.702860\pi$
$312$	−0.0981896	+	0.119436i	−0.00555889	+	0.00676174i
$313$	−10.8723	+	18.8314i	−0.614540	+	1.06441i	0.375925	+	0.926650i	$0.377325\pi$
$313$	−10.8723	+	18.8314i	−0.614540	+	1.06441i	−0.990465	+	0.137764i	$0.956008\pi$
$314$	11.7045			0.660520
$315$		0			0
$316$	28.3740			1.59616
$317$	−4.28148	+	7.41575i	−0.240472	+	0.416510i	−0.960849	−	0.277073i	$-0.910636\pi$
$317$	−4.28148	+	7.41575i	−0.240472	+	0.416510i	0.720377	+	0.693583i	$0.243969\pi$
$318$	−18.7597	−	3.11371i	−1.05199	−	0.174608i
$319$	−4.10614	−	7.11204i	−0.229900	−	0.398198i
$320$	−0.704524	−	1.22027i	−0.0393841	−	0.0682153i
$321$	−4.24217	−	11.3005i	−0.236775	−	0.630730i
$322$		0			0
$323$	43.3808			2.41377
$324$	−18.4640	+	7.57418i	−1.02578	+	0.420788i
$325$	0.995179			0.0552026
$326$	−2.18235	+	3.77995i	−0.120869	+	0.209352i
$327$	−4.05484	−	10.8015i	−0.224233	−	0.597322i
$328$	0.517568	+	0.896453i	0.0285779	+	0.0494984i
$329$		0			0
$330$	0.853949	+	0.141737i	0.0470083	+	0.00780239i
$331$	−5.42360	+	9.39396i	−0.298108	+	0.516339i	−0.975703	−	0.219097i	$-0.929689\pi$
$331$	−5.42360	+	9.39396i	−0.298108	+	0.516339i	0.677595	+	0.735435i	$0.263022\pi$
$332$	−16.6614			−0.914413
$333$	−15.8133	+	13.8201i	−0.866564	+	0.757340i
$334$	23.7698			1.30063
$335$	−0.452399	+	0.783578i	−0.0247172	+	0.0428114i
$336$		0			0
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$	13.3077	+	23.0496i	0.723842	+	1.25373i
$339$	0.0425093	−	0.0517076i	0.00230879	−	0.00280837i
$340$	−1.01684	+	1.76122i	−0.0551459	+	0.0955154i
$341$	−4.18971			−0.226886
$342$	8.24304	+	41.8140i	0.445732	+	2.26104i
$343$		0			0
$344$	−0.420231	+	0.727861i	−0.0226573	+	0.0392437i
$345$	−1.54476	−	0.256397i	−0.0831669	−	0.0138039i
$346$	16.3377	+	28.2977i	0.878319	+	1.52129i
$347$	5.76652	+	9.98790i	0.309563	+	0.536178i	0.978267	−	0.207350i	$-0.0664840\pi$
$347$	5.76652	+	9.98790i	0.309563	+	0.536178i	−0.668704	+	0.743529i	$0.733151\pi$
$348$	6.66161	+	17.7455i	0.357100	+	0.951257i
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	−0.960186	−	0.279362i	$-0.909877\pi$
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	0.722027	+	0.691865i	$0.243211\pi$
$350$		0			0
$351$	−0.0313221	−	1.03819i	−0.00167185	−	0.0554145i
$352$	−13.5078			−0.719968
$353$	1.32349	−	2.29236i	0.0704424	−	0.122010i	−0.828653	−	0.559763i	$-0.810892\pi$
$353$	1.32349	−	2.29236i	0.0704424	−	0.122010i	0.899095	+	0.437753i	$0.144226\pi$
$354$	−5.71425	−	15.2219i	−0.303709	−	0.809032i
$355$	0.0934139	+	0.161798i	0.00495790	+	0.00858733i
$356$	10.0538	+	17.4137i	0.532852	+	0.922926i
$357$		0			0
$358$	7.96127	−	13.7893i	0.420766	−	0.728789i
$359$	25.9671			1.37049			0.685245	−	0.728312i	$-0.259695\pi$
$359$	25.9671			1.37049			0.685245	+	0.728312i	$0.259695\pi$
$360$	−0.185426	−	0.0632974i	−0.00977282	−	0.00333607i
$361$	28.8529			1.51857
$362$	12.4880	−	21.6299i	0.656357	−	1.13684i
$363$	−9.05362	+	11.0127i	−0.475192	+	0.578014i
$364$		0			0
$365$	0.113867	+	0.197224i	0.00596009	+	0.0103232i
$366$	−1.53215	+	1.86369i	−0.0800870	+	0.0974164i
$367$	−8.79371	+	15.2312i	−0.459028	+	0.795060i	−0.998910	−	0.0466808i	$-0.985136\pi$
$367$	−8.79371	+	15.2312i	−0.459028	+	0.795060i	0.539882	+	0.841741i	$0.318469\pi$
$368$	21.7464			1.13361
$369$	−6.58085	−	2.24645i	−0.342585	−	0.116946i
$370$	−2.10249			−0.109303
$371$		0			0
$372$	9.53971	+	1.58339i	0.494611	+	0.0820950i
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	0.855282	−	0.518163i	$-0.173384\pi$
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	−0.876383	+	0.481614i	$0.840051\pi$
$374$	10.7153	+	18.5594i	0.554074	+	0.959684i
$375$	0.888336	+	2.36639i	0.0458735	+	0.122200i
$376$	0.404553	−	0.700707i	0.0208632	−	0.0361362i
$377$	−0.986490			−0.0508068
$378$		0			0
$379$	−20.4312			−1.04948			−0.524741	−	0.851262i	$-0.675838\pi$
$379$	−20.4312			−1.04948			−0.524741	+	0.851262i	$0.675838\pi$
$380$	−1.12166	+	1.94278i	−0.0575401	+	0.0996624i
$381$	8.20496	+	21.8567i	0.420353	+	1.11975i
$382$	5.10090	+	8.83501i	0.260985	+	0.452039i
$383$	−8.94638	−	15.4956i	−0.457139	−	0.791788i	0.541670	−	0.840591i	$-0.317792\pi$
$383$	−8.94638	−	15.4956i	−0.457139	−	0.791788i	−0.998808	+	0.0488039i	$0.984459\pi$
$384$	6.06843	+	1.00723i	0.309678	+	0.0514000i
$385$		0			0
$386$	−30.6084			−1.55793
$387$	−1.09200	−	5.53935i	−0.0555097	−	0.281581i
$388$	17.6738			0.897249
$389$	−7.81392	+	13.5341i	−0.396181	+	0.686206i	−0.993251	−	0.115983i	$-0.962998\pi$
$389$	−7.81392	+	13.5341i	−0.396181	+	0.686206i	0.597070	+	0.802189i	$0.296331\pi$
$390$	0.0660347	−	0.0803234i	0.00334380	−	0.00406734i
$391$	−19.3835	−	33.5731i	−0.980264	−	1.69787i
$392$		0			0
$393$	−21.8156	+	26.5360i	−1.10045	+	1.33857i
$394$	21.8311	−	37.8126i	1.09984	−	1.90497i
$395$	−1.87132			−0.0941564
$396$	−8.33520	+	7.28460i	−0.418860	+	0.366065i
$397$	−19.2613			−0.966696			−0.483348	−	0.875428i	$-0.660579\pi$
$397$	−19.2613			−0.966696			−0.483348	+	0.875428i	$0.660579\pi$
$398$	−20.4791	+	35.4709i	−1.02653	+	1.77799i
$399$		0			0
$400$	−8.75687	−	15.1673i	−0.437843	−	0.758367i
$401$	−7.15064	−	12.3853i	−0.357086	−	0.618491i	0.630387	−	0.776281i	$-0.282896\pi$
$401$	−7.15064	−	12.3853i	−0.357086	−	0.618491i	−0.987473	+	0.157790i	$0.949563\pi$
$402$	−7.73425	−	20.6028i	−0.385749	−	1.02757i
$403$	−0.251642	+	0.435857i	−0.0125352	+	0.0217116i
$404$	32.9137			1.63752
$405$	1.21774	−	0.499532i	0.0605098	−	0.0248219i
$406$		0			0
$407$	−5.82452	+	10.0884i	−0.288711	+	0.500062i
$408$	−1.70479	−	4.54128i	−0.0843994	−	0.224827i
$409$	−15.9305	−	27.5924i	−0.787712	−	1.36436i	−0.927366	−	0.374156i	$-0.877932\pi$
$409$	−15.9305	−	27.5924i	−0.787712	−	1.36436i	0.139654	−	0.990200i	$-0.455401\pi$
$410$	−0.348076	−	0.602885i	−0.0171902	−	0.0297744i
$411$	11.0126	+	1.82785i	0.543210	+	0.0901614i
$412$	0.226124	−	0.391657i	0.0111403	−	0.0192956i
$413$		0			0
$414$	28.6774	−	25.0628i	1.40942	−	1.23177i
$415$	1.09885			0.0539405
$416$	−0.811304	+	1.40522i	−0.0397774	+	0.0688965i
$417$	−13.7829	+	16.7653i	−0.674952	+	0.821000i
$418$	11.8199	+	20.4726i	0.578130	+	1.00135i
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	0.995036	+	0.0995110i	$0.0317278\pi$
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	−0.411339	+	0.911482i	$0.634939\pi$
$420$		0			0
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$	−48.2892			−2.35068
$423$	1.05126	+	5.33269i	0.0511142	+	0.259284i
$424$	2.38749			0.115947
$425$	−15.6107	+	27.0385i	−0.757230	+	1.31156i
$426$	−4.48274	−	0.744039i	−0.217189	−	0.0360488i
$427$		0			0
$428$	7.72661	+	13.3829i	0.373480	+	0.646886i
$429$	−0.202479	−	0.539373i	−0.00977580	−	0.0260412i
$430$	0.282615	−	0.489503i	0.0136289	−	0.0236059i
$431$	−4.92764			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$431$	−4.92764			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$432$	−15.5473	+	9.61272i	−0.748018	+	0.462492i
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$		0			0
$435$	−0.439346	−	1.17035i	−0.0210650	−	0.0561139i
$436$	7.38543	+	12.7919i	0.353698	+	0.612622i
$437$	−21.3817	−	37.0341i	−1.02282	−	1.77158i
$438$	−5.46425	−	0.906950i	−0.261092	−	0.0433358i
$439$	−1.22411	+	2.12022i	−0.0584235	+	0.101192i	−0.893758	−	0.448550i	$-0.851941\pi$
$439$	−1.22411	+	2.12022i	−0.0584235	+	0.101192i	0.835334	+	0.549742i	$0.185274\pi$
$440$	−0.108680			−0.00518110
$441$		0			0
$442$	2.57432			0.122448
$443$	13.1475	−	22.7722i	0.624657	−	1.08194i	−0.363950	−	0.931419i	$-0.618572\pi$
$443$	13.1475	−	22.7722i	0.624657	−	1.08194i	0.988607	−	0.150520i	$-0.0480946\pi$
$444$	17.0747	−	20.7693i	0.810329	−	0.985670i
$445$	−0.663069	−	1.14847i	−0.0314325	−	0.0544427i
$446$	4.16996	+	7.22259i	0.197453	+	0.341999i
$447$	19.5430	−	23.7718i	0.924354	−	1.12437i
$448$		0			0
$449$	−38.7077			−1.82673			−0.913365	−	0.407141i	$-0.866526\pi$
$449$	−38.7077			−1.82673			−0.913365	+	0.407141i	$0.866526\pi$
$450$	−29.0282	−	9.90912i	−1.36840	−	0.467120i
$451$	−3.85709			−0.181623
$452$	−0.0428488	+	0.0742163i	−0.00201544	+	0.00349084i
$453$	−14.4656	−	2.40099i	−0.679655	−	0.112808i
$454$	3.95620	+	6.85233i	0.185673	+	0.321596i
$455$		0			0
$456$	−1.88053	−	5.00943i	−0.0880638	−	0.234588i
$457$	4.57756	−	7.92856i	0.214129	−	0.370882i	−0.738874	−	0.673844i	$-0.764642\pi$
$457$	4.57756	−	7.92856i	0.214129	−	0.370882i	0.953003	+	0.302961i	$0.0979754\pi$
$458$	26.9361			1.25864
$459$	28.6985	+	15.4344i	1.33953	+	0.720416i
$460$	2.00473			0.0934710
$461$	14.6152	−	25.3143i	0.680698	−	1.17900i	−0.294070	−	0.955784i	$-0.595010\pi$
$461$	14.6152	−	25.3143i	0.680698	−	1.17900i	0.974768	−	0.223220i	$-0.0716568\pi$
$462$		0			0
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	0.609721	−	0.792616i	$-0.291282\pi$
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	−0.991286	+	0.131726i	$0.957948\pi$
$464$	8.68041	+	15.0349i	0.402978	+	0.697978i
$465$	−0.629162	−	0.104428i	−0.0291767	−	0.00484272i
$466$	−17.9718	+	31.1280i	−0.832526	+	1.44198i
$467$	−15.3726			−0.711361			−0.355680	−	0.934608i	$-0.615751\pi$
$467$	−15.3726			−0.711361			−0.355680	+	0.934608i	$0.615751\pi$
$468$	0.257191	+	1.30464i	0.0118887	+	0.0603070i
$469$		0			0
$470$	−0.272071	+	0.471241i	−0.0125497	+	0.0217367i
$471$	6.26898	−	7.62547i	0.288859	−	0.351363i
$472$	1.02066	+	1.76784i	0.0469797	+	0.0813713i
$473$	−1.56585	−	2.71213i	−0.0719979	−	0.124704i
$474$	28.9043	−	35.1586i	1.32762	−	1.61489i
$475$	−17.2200	+	29.8259i	−0.790106	+	1.36850i
$476$		0			0
$477$	−12.0764	+	10.5542i	−0.552939	+	0.483245i
$478$	−15.0268			−0.687310
$479$	18.9646	−	32.8476i	0.866513	−	1.50084i	0.000975329	−	1.00000i	$-0.499690\pi$
$479$	18.9646	−	32.8476i	0.866513	−	1.50084i	0.865537	−	0.500844i	$-0.166977\pi$
$480$	−2.02844	−	0.336679i	−0.0925854	−	0.0153672i
$481$	0.699663	+	1.21185i	0.0319019	+	0.0552557i
$482$	−6.39820	−	11.0820i	−0.291430	−	0.504772i
$483$		0			0
$484$	9.12591	−	15.8065i	0.414814	−	0.718479i
$485$	−1.16562			−0.0529280
$486$	−9.42377	+	30.5947i	−0.427471	+	1.38780i
$487$	−4.60495			−0.208670			−0.104335	−	0.994542i	$-0.533271\pi$
$487$	−4.60495			−0.208670			−0.104335	+	0.994542i	$0.533271\pi$
$488$	0.151453	−	0.262324i	0.00685595	−	0.0118749i
$489$	1.29376	+	3.44637i	0.0585058	+	0.155850i
$490$		0			0
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	−0.973309	−	0.229497i	$-0.926292\pi$
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	0.287904	−	0.957659i	$-0.407042\pi$
$492$	8.78234	+	1.45768i	0.395939	+	0.0657174i
$493$	15.4744	−	26.8024i	0.696932	−	1.20712i
$494$	2.83970			0.127764
$495$	0.549722	−	0.480434i	0.0247082	−	0.0215939i
$496$	8.85709			0.397695
$497$		0			0
$498$	−16.9728	+	20.6454i	−0.760568	+	0.925141i
$499$	−4.63436	−	8.02694i	−0.207462	−	0.359335i	0.743452	−	0.668789i	$-0.233187\pi$
$499$	−4.63436	−	8.02694i	−0.207462	−	0.359335i	−0.950914	+	0.309454i	$0.899854\pi$
$500$	−1.61800	−	2.80246i	−0.0723592	−	0.125330i
$501$	12.7313	−	15.4861i	0.568792	−	0.691868i
$502$	−5.80445	+	10.0536i	−0.259065	+	0.448715i
$503$	−22.4230			−0.999791			−0.499896	−	0.866086i	$-0.666628\pi$
$503$	−22.4230			−0.999791			−0.499896	+	0.866086i	$0.666628\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$	10.5627	−	18.2952i	0.469571	−	0.813321i
$507$	22.1445	+	3.67552i	0.983472	+	0.163235i
$508$	−14.9444	−	25.8844i	−0.663050	−	1.14844i
$509$	18.8207	+	32.5984i	0.834213	+	1.44490i	0.894670	+	0.446728i	$0.147411\pi$
$509$	18.8207	+	32.5984i	0.834213	+	1.44490i	−0.0604572	+	0.998171i	$0.519256\pi$
$510$	1.14651	+	3.05411i	0.0507682	+	0.135238i
$511$		0			0
$512$	31.6976			1.40085
$513$	31.6569	+	17.0255i	1.39769	+	0.751694i
$514$	24.2364			1.06902
$515$	−0.0149133	+	0.0258306i	−0.000657158	+	0.00113823i
$516$	2.54036	+	6.76713i	0.111833	+	0.297906i
$517$	1.50743	+	2.61095i	0.0662969	+	0.114830i
$518$		0			0
$519$	27.1866	+	4.51240i	1.19336	+	0.198072i
$520$	−0.00652751	+	0.0113060i	−0.000286250	+	0.000495800i
$521$	−34.9283			−1.53023			−0.765117	−	0.643891i	$-0.777319\pi$
$521$	−34.9283			−1.53023			−0.765117	+	0.643891i	$0.777319\pi$
$522$	28.7748	+	9.82260i	1.25944	+	0.429924i
$523$	23.7471			1.03839			0.519194	−	0.854656i	$-0.326232\pi$
$523$	23.7471			1.03839			0.519194	+	0.854656i	$0.326232\pi$
$524$	21.9898	−	38.0874i	0.960628	−	1.66386i
$525$		0			0
$526$	22.8366	+	39.5542i	0.995723	+	1.72464i
$527$	−7.89468	−	13.6740i	−0.343898	−	0.595648i
$528$	−6.43881	+	7.83205i	−0.280213	+	0.340846i
$529$	−7.60755	+	13.1767i	−0.330763	+	0.572898i
$530$	−1.60564			−0.0697446
$531$	−12.9777	−	4.43008i	−0.563182	−	0.192249i
$532$		0			0
$533$	−0.231664	+	0.401254i	−0.0100345	+	0.0173802i
$534$	31.8193	+	5.28133i	1.37696	+	0.228545i
$535$	−0.509585	−	0.882627i	−0.0220313	−	0.0381593i
$536$	1.38147	+	2.39277i	0.0596702	+	0.103352i
$537$	−4.71967	−	12.5724i	−0.203669	−	0.542541i
$538$	−2.45292	+	4.24857i	−0.105753	+	0.183169i
$539$		0			0
$540$	−1.43325	+	0.886164i	−0.0616773	+	0.0381344i
$541$	−17.1708			−0.738232			−0.369116	−	0.929383i	$-0.620340\pi$
$541$	−17.1708			−0.738232			−0.369116	+	0.929383i	$0.620340\pi$
$542$	−23.8488	+	41.3074i	−1.02439	+	1.77430i
$543$	−7.40327	−	19.7211i	−0.317705	−	0.846314i
$544$	−25.4527	−	44.0854i	−1.09128	−	1.89015i
$545$	−0.487083	−	0.843653i	−0.0208643	−	0.0361381i
$546$		0			0
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	−0.996674	−	0.0814901i	$-0.974032\pi$
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	0.568910	+	0.822400i	$0.307365\pi$
$548$	−14.2917			−0.610512
$549$	0.393563	+	1.99640i	0.0167968	+	0.0852044i
$550$	−17.0137			−0.725465
$551$	17.0696	−	29.5654i	0.727190	−	1.25953i
$552$	−3.03662	+	3.69369i	−0.129247	+	0.157214i
$553$		0			0
$554$	4.74187	+	8.21316i	0.201463	+	0.348944i
$555$	−1.12611	+	1.36978i	−0.0478007	+	0.0581439i
$556$	13.8930	−	24.0633i	0.589193	−	1.02051i
$557$	0.245481			0.0104014			0.00520068	−	0.999986i	$-0.498345\pi$
$557$	0.245481			0.0104014			0.00520068	+	0.999986i	$0.498345\pi$
$558$	11.6800	−	10.2078i	0.494453	−	0.432131i
$559$	−0.376192			−0.0159112
$560$		0			0
$561$	17.8307	+	2.95951i	0.752811	+	0.124951i
$562$	12.1338	+	21.0163i	0.511833	+	0.886520i
$563$	22.1255	+	38.3224i	0.932477	+	1.61510i	0.779073	+	0.626934i	$0.215690\pi$
$563$	22.1255	+	38.3224i	0.932477	+	1.61510i	0.153404	+	0.988164i	$0.450976\pi$
$564$	−2.44559	−	6.51466i	−0.102978	−	0.274317i
$565$	0.00282596	−	0.00489471i	0.000118889	−	0.000205922i
$566$	32.5496			1.36816
$567$		0			0
$568$	0.570506			0.0239379
$569$	2.76767	−	4.79374i	0.116027	−	0.200964i	−0.802163	−	0.597105i	$-0.796318\pi$
$569$	2.76767	−	4.79374i	0.116027	−	0.200964i	0.918190	+	0.396141i	$0.129651\pi$
$570$	1.26470	+	3.36895i	0.0529723	+	0.141110i
$571$	2.05191	+	3.55400i	0.0858696	+	0.148730i	0.905761	−	0.423788i	$-0.139300\pi$
$571$	2.05191	+	3.55400i	0.0858696	+	0.148730i	−0.819892	+	0.572518i	$0.805966\pi$
$572$	0.368793	+	0.638768i	0.0154200	+	0.0267082i
$573$	8.48810	+	1.40884i	0.354595	+	0.0588553i
$574$		0			0
$575$	30.7770			1.28349
$576$	21.7640	−	19.0208i	0.906835	−	0.792535i
$577$	5.64550			0.235025			0.117513	−	0.993071i	$-0.462508\pi$
$577$	5.64550			0.235025			0.117513	+	0.993071i	$0.462508\pi$
$578$	−22.9256	+	39.7083i	−0.953579	+	1.65165i
$579$	−16.3941	+	19.9414i	−0.681314	+	0.828737i
$580$	0.800218	+	1.38602i	0.0332272	+	0.0575513i
$581$		0			0
$582$	18.0040	−	21.8998i	0.746292	−	0.907776i
$583$	−4.44809	+	7.70433i	−0.184221	+	0.319081i
$584$	0.695420			0.0287767
$585$	−0.0169623	−	0.0860435i	−0.000701303	−	0.00355746i
$586$	−28.9483			−1.19585
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	−0.605394	−	0.795926i	$-0.706985\pi$
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	0.991989	+	0.126324i	$0.0403180\pi$
$588$		0			0
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$	−0.686417	−	1.18891i	−0.0282594	−	0.0489466i
$591$	−12.9421	−	34.4757i	−0.532366	−	1.41814i
$592$	12.3131	−	21.3269i	0.506065	−	0.876530i
$593$	18.8703			0.774912			0.387456	−	0.921888i	$-0.373354\pi$
$593$	18.8703			0.774912			0.387456	+	0.921888i	$0.373354\pi$
$594$	0.535484	+	17.7490i	0.0219712	+	0.728250i
$595$		0			0
$596$	−19.6991	+	34.1198i	−0.806906	+	1.39760i
$597$	12.1406	+	32.3406i	0.496882	+	1.32361i
$598$	−1.26884	−	2.19769i	−0.0518866	−	0.0898702i
$599$	−1.33726	−	2.31620i	−0.0546388	−	0.0946372i	0.837412	−	0.546572i	$-0.184067\pi$
$599$	−1.33726	−	2.31620i	−0.0546388	−	0.0946372i	−0.892051	+	0.451934i	$0.850734\pi$
$600$	3.79900	+	0.630553i	0.155094	+	0.0257422i
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	−0.968736	−	0.248095i	$-0.920196\pi$
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	0.699224	+	0.714902i	$0.253529\pi$
$602$		0			0
$603$	−17.5653	−	5.99612i	−0.715313	−	0.244181i
$604$	18.7730			0.763862
$605$	−0.601872	+	1.04247i	−0.0244696	+	0.0423825i
$606$	33.5288	−	40.7838i	1.36201	−	1.65673i
$607$	−12.9026	−	22.3480i	−0.523701	−	0.907076i	−0.999619	−	0.0275869i	$-0.991218\pi$
$607$	−12.9026	−	22.3480i	−0.523701	−	0.907076i	0.475919	−	0.879489i	$-0.342116\pi$
$608$	−28.0766	−	48.6301i	−1.13866	−	1.97221i
$609$		0			0
$610$	−0.101856	+	0.176419i	−0.00412401	+	0.00714299i
$611$	0.362157			0.0146513
$612$	−39.4808	−	13.4772i	−1.59592	−	0.544785i
$613$	−26.9533			−1.08863			−0.544316	−	0.838880i	$-0.683211\pi$
$613$	−26.9533			−1.08863			−0.544316	+	0.838880i	$0.683211\pi$
$614$	−28.1263	+	48.7162i	−1.13509	+	1.96603i
$615$	−0.579212	−	0.0961370i	−0.0233561	−	0.00387662i
$616$		0			0
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	0.754002	−	0.656872i	$-0.228121\pi$
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	−0.945869	+	0.324549i	$0.894788\pi$
$618$	−0.254959	−	0.679169i	−0.0102559	−	0.0273202i
$619$	−17.3536	+	30.0573i	−0.697499	+	1.20810i	0.271832	+	0.962345i	$0.412370\pi$
$619$	−17.3536	+	30.0573i	−0.697499	+	1.20810i	−0.969331	+	0.245759i	$0.920963\pi$
$620$	0.816505			0.0327916
$621$	−0.968668	−	32.1072i	−0.0388713	−	1.28842i
$622$	−28.8654			−1.15740
$623$		0			0
$624$	0.428043	+	1.14024i	0.0171354	+	0.0456461i
$625$	−12.3398	−	21.3732i	−0.493593	−	0.854928i
$626$	−22.3279	−	38.6730i	−0.892402	−	1.54568i
$627$	19.6688	+	3.26460i	0.785495	+	0.130376i
$628$	−6.31904	+	10.9449i	−0.252157	+	0.436749i
$629$	−43.9006			−1.75043
$630$		0			0
$631$	−36.7963			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$631$	−36.7963			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$632$	−2.85718	+	4.94877i	−0.113652	+	0.196852i
$633$	−25.8640	+	31.4605i	−1.02800	+	1.25044i
$634$	−8.79265	−	15.2293i	−0.349201	−	0.604833i
$635$	0.985611	+	1.70713i	0.0391128	+	0.0677453i
$636$	13.0397	−	15.8612i	0.517057	−	0.628938i
$637$		0			0
$638$	16.8651			0.667696
$639$	−2.88573	+	2.52200i	−0.114158	+	0.0997688i
$640$	0.519397			0.0205310
$641$	22.0922	−	38.2648i	0.872590	−	1.51137i	0.0132813	−	0.999912i	$-0.495772\pi$
$641$	22.0922	−	38.2648i	0.872590	−	1.51137i	0.859308	−	0.511458i	$-0.170894\pi$
$642$	24.4539	+	4.05883i	0.965119	+	0.160189i
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	0.972741	−	0.231895i	$-0.0744926\pi$
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	−0.687197	+	0.726471i	$0.741159\pi$
$644$		0			0
$645$	−0.167542	−	0.446305i	−0.00659696	−	0.0175732i
$646$	−44.5444	+	77.1532i	−1.75258	+	3.03555i
$647$	33.3071			1.30944			0.654719	−	0.755872i	$-0.272787\pi$
$647$	33.3071			1.30944			0.654719	+	0.755872i	$0.272787\pi$
$648$	0.538237	−	3.98304i	0.0211440	−	0.156469i
$649$	−7.60631			−0.298574
$650$	−1.02187	+	1.76993i	−0.0400811	+	0.0694225i
$651$		0			0
$652$	−2.35643	−	4.08146i	−0.0922850	−	0.159842i
$653$	4.53322	+	7.85176i	0.177398	+	0.307263i	0.940989	−	0.338438i	$-0.109899\pi$
$653$	4.53322	+	7.85176i	0.177398	+	0.307263i	−0.763590	+	0.645701i	$0.776565\pi$
$654$	23.3741	+	3.87961i	0.913999	+	0.151705i
$655$	−1.45027	+	2.51194i	−0.0566666	+	0.0981495i
$656$	8.15391			0.318357
$657$	−3.51757	+	3.07420i	−0.137233	+	0.119936i
$658$		0			0
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	−0.357184	−	0.934034i	$-0.616263\pi$
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	0.987489	−	0.157686i	$-0.0504035\pi$
$660$	−0.593572	+	0.722010i	−0.0231048	+	0.0281042i
$661$	4.32958	+	7.49905i	0.168401	+	0.291679i	0.937858	−	0.347020i	$-0.112806\pi$
$661$	4.32958	+	7.49905i	0.168401	+	0.291679i	−0.769457	+	0.638699i	$0.779473\pi$
$662$	−11.1382	−	19.2919i	−0.432897	−	0.749799i
$663$	1.37882	−	1.67717i	0.0535490	−	0.0651360i
$664$	1.67775	−	2.90595i	0.0651094	−	0.112773i
$665$		0			0
$666$	−8.34179	−	42.3150i	−0.323238	−	1.63967i
$667$	−30.5083			−1.18128
$668$	−12.8329	+	22.2273i	−0.496522	+	0.860001i
$669$	6.93899	+	1.15173i	0.268277	+	0.0445283i
$670$	−0.929067	−	1.60919i	−0.0358930	−	0.0621685i
$671$	0.564339	+	0.977464i	0.0217861	+	0.0377346i
$672$		0			0
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$	−6.87605			−0.264856
$675$	−22.0035	+	13.6045i	−0.846915	+	0.523639i
$676$	−28.7384			−1.10532
$677$	−19.1657	+	33.1960i	−0.736600	+	1.27583i	0.217418	+	0.976078i	$0.430236\pi$
$677$	−19.1657	+	33.1960i	−0.736600	+	1.27583i	−0.954018	+	0.299749i	$0.903097\pi$
$678$	0.0483128	+	0.128698i	0.00185544	+	0.00494260i
$679$		0			0
$680$	−0.204785	−	0.354698i	−0.00785315	−	0.0136021i
$681$	6.58327	+	1.09268i	0.252271	+	0.0418717i
$682$	4.30209	−	7.45144i	0.164736	−	0.285330i
$683$	6.63318			0.253812			0.126906	−	0.991915i	$-0.459495\pi$
$683$	6.63318			0.253812			0.126906	+	0.991915i	$0.459495\pi$
$684$	−43.5508	−	14.8666i	−1.66521	−	0.568438i
$685$	0.942567			0.0360136
$686$		0			0
$687$	14.4272	−	17.5489i	0.550430	−	0.669534i
$688$	3.31022	+	5.73347i	0.126201	+	0.218587i
$689$	0.534322	+	0.925472i	0.0203560	+	0.0352577i
$690$	2.04219	−	2.48409i	0.0777450	−	0.0945676i
$691$	11.6938	−	20.2542i	0.444852	−	0.770506i	−0.553190	−	0.833055i	$-0.686590\pi$
$691$	11.6938	−	20.2542i	0.444852	−	0.770506i	0.998042	+	0.0625490i	$0.0199230\pi$
$692$	−35.2818			−1.34121
$693$		0			0
$694$	−23.6848			−0.899061
$695$	−0.916269	+	1.58702i	−0.0347561	+	0.0601992i
$696$	−3.76583	−	0.625048i	−0.142743	−	0.0236924i
$697$	−7.26791	−	12.5884i	−0.275292	−	0.476819i
$698$	−9.13702	−	15.8258i	−0.345841	−	0.599015i
$699$	10.6542	+	28.3810i	0.402978	+	1.07347i
$700$		0			0
$701$	9.26736			0.350023			0.175012	−	0.984566i	$-0.444004\pi$
$701$	9.26736			0.350023			0.175012	+	0.984566i	$0.444004\pi$
$702$	1.87859	+	1.01033i	0.0709029	+	0.0381325i
$703$	−48.4262			−1.82643
$704$	8.01636	−	13.8847i	0.302128	−	0.523301i
$705$	0.161291	+	0.429655i	0.00607459	+	0.0161817i
$706$	2.71799	+	4.70769i	0.102293	+	0.177176i
$707$		0			0
$708$	17.3191	+	2.87460i	0.650891	+	0.108034i
$709$	−7.11775	+	12.3283i	−0.267313	+	0.462999i	−0.968167	−	0.250305i	$-0.919469\pi$
$709$	−7.11775	+	12.3283i	−0.267313	+	0.462999i	0.700854	+	0.713305i	$0.252802\pi$
$710$	−0.383678			−0.0143992
$711$	−7.42460	−	37.6624i	−0.278444	−	1.41245i
$712$	−4.04956			−0.151763
$713$	−7.78230	+	13.4793i	−0.291449	+	0.504805i
$714$		0			0
$715$	−0.0243226	−	0.0421280i	−0.000909613	−	0.00157550i
$716$	8.59632	+	14.8893i	0.321260	+	0.556438i
$717$	−8.04846	+	9.79000i	−0.300575	+	0.365614i
$718$	−26.6636	+	46.1827i	−0.995077	+	1.72352i
$719$	−13.8570			−0.516777			−0.258389	−	0.966041i	$-0.583192\pi$
$719$	−13.8570			−0.516777			−0.258389	+	0.966041i	$0.583192\pi$
$720$	−1.16212	+	1.01564i	−0.0433096	+	0.0378507i
$721$		0			0
$722$	−29.6268	+	51.3151i	−1.10259	+	1.90975i
$723$	−10.6469	−	1.76715i	−0.395961	−	0.0657212i
$724$	13.4842	+	23.3553i	0.501136	+	0.867993i
$725$	12.2851	+	21.2784i	0.456257	+	0.790260i
$726$	−10.2896	−	27.4100i	−0.381885	−	1.01728i
$727$	15.7000	−	27.1932i	0.582280	−	1.00854i	−0.412928	−	0.910764i	$-0.635494\pi$
$727$	15.7000	−	27.1932i	0.582280	−	1.00854i	0.995208	−	0.0977755i	$-0.0311727\pi$
$728$		0			0
$729$	14.8851	+	22.5263i	0.551299	+	0.834308i
$730$	−0.467686			−0.0173098
$731$	5.90107	−	10.2209i	0.218259	−	0.378035i
$732$	−0.915558	−	2.43890i	−0.0338400	−	0.0901443i
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	0.999949	−	0.0100658i	$-0.00320409\pi$
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	−0.508692	+	0.860949i	$0.669871\pi$
$734$	−18.0592	−	31.2794i	−0.666576	−	1.15454i
$735$		0			0
$736$	−25.0904	+	43.4579i	−0.924845	+	1.60188i
$737$	−10.2951			−0.379227
$738$	10.7527	−	9.39739i	0.395812	−	0.345923i
$739$	−33.0039			−1.21407			−0.607034	−	0.794676i	$-0.707641\pi$
$739$	−33.0039			−1.21407			−0.607034	+	0.794676i	$0.707641\pi$
$740$	1.13510	−	1.96605i	0.0417272	−	0.0722736i
$741$	1.52096	−	1.85007i	0.0558739	−	0.0679640i
$742$		0			0
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	0.965570	+	0.260144i	$0.0837701\pi$
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	−0.257493	+	0.966280i	$0.582897\pi$
$744$	−1.23678	+	1.50440i	−0.0453426	+	0.0551539i
$745$	1.29919	−	2.25027i	0.0475988	−	0.0824435i
$746$	1.67388			0.0612849
$747$	4.35977	+	22.1156i	0.159516	+	0.809167i
$748$	−23.1400			−0.846082
$749$		0			0
$750$	−5.12080	−	0.849945i	−0.186985	−	0.0310356i
$751$	18.9498	+	32.8220i	0.691487	+	1.19769i	0.971351	+	0.237651i	$0.0763776\pi$
$751$	18.9498	+	32.8220i	0.691487	+	1.19769i	−0.279863	+	0.960040i	$0.590289\pi$
$752$	−3.18673	−	5.51957i	−0.116208	−	0.201278i
$753$	3.44104	+	9.16639i	0.125399	+	0.334042i
$754$	1.01295	−	1.75448i	0.0368895	−	0.0638944i
$755$	−1.23811			−0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$	20.9793	−	36.3371i	0.762001	−	1.31982i
$759$	−6.26189	−	16.6807i	−0.227292	−	0.605470i
$760$	−0.225896	−	0.391263i	−0.00819411	−	0.0141926i
$761$	−13.8735	−	24.0296i	−0.502913	−	0.871072i	−0.999994	−	0.00336738i	$-0.998928\pi$
$761$	−13.8735	−	24.0296i	−0.502913	−	0.871072i	0.497081	−	0.867704i	$-0.334405\pi$
$762$	−47.2974	−	7.85037i	−1.71340	−	0.284389i
$763$		0			0
$764$	−11.0156			−0.398529
$765$	2.60383	+	0.888850i	0.0941418	+	0.0321364i
$766$	36.7454			1.32766
$767$	−0.456849	+	0.791286i	−0.0164959	+	0.0285717i
$768$	13.1730	−	16.0233i	0.475338	−	0.578193i
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	0.735412	−	0.677621i	$-0.236989\pi$
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	−0.954542	+	0.298075i	$0.903655\pi$
$770$		0			0
$771$	12.9812	−	15.7901i	0.467505	−	0.568665i
$772$	16.5250	−	28.6221i	0.594747	−	1.03013i
$773$	41.5591			1.49478			0.747388	−	0.664388i	$-0.231308\pi$
$773$	41.5591			1.49478			0.747388	+	0.664388i	$0.231308\pi$
$774$	10.9731	+	3.74579i	0.394419	+	0.134640i
$775$	12.5351			0.450275
$776$	−1.77969	+	3.08252i	−0.0638873	+	0.110656i
$777$		0			0
$778$	−16.0470	−	27.7942i	−0.575313	−	0.996472i
$779$	−8.01714	−	13.8861i	−0.287244	−	0.497521i
$780$	0.0394598	+	0.105115i	0.00141289	+	0.00376371i
$781$	−1.06290	+	1.84100i	−0.0380336	+	0.0658761i
$782$	79.6135			2.84697
$783$	21.8114	−	13.4858i	0.779476	−	0.481942i
$784$		0			0
$785$	0.416753	−	0.721837i	0.0148746	−	0.0257635i
$786$	−24.7939	−	66.0470i	−0.884369	−	2.35582i
$787$	10.4484	+	18.0972i	0.372446	+	0.645096i	0.989941	−	0.141479i	$-0.0451857\pi$
$787$	10.4484	+	18.0972i	0.372446	+	0.645096i	−0.617495	+	0.786575i	$0.711852\pi$
$788$	23.5725	+	40.8288i	0.839736	+	1.45447i
$789$	38.0010	+	6.30737i	1.35287	+	0.224548i
$790$	1.92152	−	3.32816i	0.0683645	−	0.118411i
$791$		0			0
$792$	−0.431195	−	2.18730i	−0.0153218	−	0.0777222i
$793$	0.135581			0.00481462
$794$	19.7779	−	34.2564i	0.701892	−	1.21571i
$795$	−0.859992	+	1.04608i	−0.0305008	+	0.0371006i
$796$	−22.1127	−	38.3003i	−0.783763	−	1.35752i
$797$	−0.319383	−	0.553188i	−0.0113131	−	0.0195949i	0.860313	−	0.509765i	$-0.170268\pi$
$797$	−0.319383	−	0.553188i	−0.0113131	−	0.0195949i	−0.871627	+	0.490171i	$0.836934\pi$
$798$		0			0
$799$	−5.68091	+	9.83963i	−0.200976	+	0.348101i
$800$	40.4137			1.42884
$801$	20.4834	−	17.9016i	0.723746	−	0.632523i
$802$	29.3698			1.03708
$803$	−1.29563	+	2.24409i	−0.0457217	+	0.0791923i
$804$	23.4414	+	3.89078i	0.826714	+	0.137217i
$805$		0			0
$806$	−0.516783	−	0.895095i	−0.0182029	−	0.0315284i
$807$	1.45416	+	3.87364i	0.0511888	+	0.136359i
$808$	−3.31431	+	5.74055i	−0.116597	+	0.201952i
$809$	−50.5592			−1.77757			−0.888783	−	0.458327i	$-0.848449\pi$
$809$	−50.5592			−1.77757			−0.888783	+	0.458327i	$0.848449\pi$
$810$	−0.361977	+	2.67868i	−0.0127186	+	0.0941193i
$811$	−0.784071			−0.0275325			−0.0137662	−	0.999905i	$-0.504382\pi$
$811$	−0.784071			−0.0275325			−0.0137662	+	0.999905i	$0.504382\pi$
$812$		0			0
$813$	14.1382	+	37.6620i	0.495850	+	1.32087i
$814$	−11.9615	−	20.7179i	−0.419250	−	0.726163i
$815$	0.155411	+	0.269180i	0.00544382	+	0.00942897i
$816$	−37.6941	−	6.25643i	−1.31956	−	0.219019i
$817$	6.50939	−	11.2746i	0.227735	−	0.394448i
$818$	65.4311			2.28775
$819$		0			0
$820$	0.751682			0.0262499
$821$	−21.7207	+	37.6213i	−0.758056	+	1.31299i	0.185784	+	0.982591i	$0.440517\pi$
$821$	−21.7207	+	37.6213i	−0.758056	+	1.31299i	−0.943841	+	0.330401i	$0.892816\pi$
$822$	−14.5588	+	17.7091i	−0.507797	+	0.617675i
$823$	−1.98273	−	3.43419i	−0.0691136	−	0.119708i	0.829398	−	0.558659i	$-0.188684\pi$
$823$	−1.98273	−	3.43419i	−0.0691136	−	0.119708i	−0.898511	+	0.438950i	$0.855350\pi$
$824$	0.0455399	+	0.0788774i	0.00158646	+	0.00274782i
$825$	−9.11262	+	11.0844i	−0.317261	+	0.385910i
$826$		0			0
$827$	29.3159			1.01941			0.509707	−	0.860348i	$-0.329754\pi$
$827$	29.3159			1.01941			0.509707	+	0.860348i	$0.329754\pi$
$828$	7.95391	+	40.3474i	0.276418	+	1.40217i
$829$	35.0427			1.21708			0.608541	−	0.793522i	$-0.291755\pi$
$829$	35.0427			1.21708			0.608541	+	0.793522i	$0.291755\pi$
$830$	−1.12833	+	1.95432i	−0.0391648	+	0.0678353i
$831$	7.89067	+	1.30968i	0.273724	+	0.0454324i
$832$	−0.962955	−	1.66789i	−0.0333844	−	0.0578236i
$833$		0			0
$834$	−15.6646	−	41.7280i	−0.542421	−	1.44492i
$835$	0.846358	−	1.46593i	0.0292894	−	0.0507308i
$836$	−25.5255			−0.882816
$837$	−0.394528	−	13.0769i	−0.0136369	−	0.452004i
$838$	−49.0738			−1.69523
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	0.334639	+	0.942347i	$0.391386\pi$
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	−0.983415	+	0.181368i	$0.941948\pi$
$840$		0			0
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$	−2.51060	−	4.34848i	−0.0865208	−	0.149858i
$843$	20.1911	+	3.35130i	0.695419	+	0.115425i
$844$	26.0705	−	45.1555i	0.897385	−	1.55432i
$845$	1.89535			0.0652020
$846$	−10.5637	−	3.60604i	−0.363188	−	0.123978i
$847$		0			0
$848$	9.40331	−	16.2870i	0.322911	−	0.559298i
$849$	17.4338	−	21.2061i	0.598325	−	0.727792i
$850$	−32.0588	−	55.5275i	−1.09961	−	1.90458i
$851$	21.6378	+	37.4778i	0.741735	+	1.28472i
$852$	3.11591	−	3.79014i	0.106749	−	0.129848i
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	−0.436400	−	0.899753i	$-0.643747\pi$
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	0.997409	−	0.0719434i	$-0.0229201\pi$
$854$		0			0
$855$	2.87226	+	0.980479i	0.0982291	+	0.0335317i
$856$	−3.11218			−0.106372
$857$	−13.7673	+	23.8457i	−0.470283	+	0.814554i	−0.999422	−	0.0339808i	$-0.989181\pi$
$857$	−13.7673	+	23.8457i	−0.470283	+	0.814554i	0.529139	+	0.848535i	$0.322515\pi$
$858$	1.16719	+	0.193729i	0.0398472	+	0.00661379i
$859$	23.2550	+	40.2789i	0.793451	+	1.37430i	0.923818	+	0.382832i	$0.125051\pi$
$859$	23.2550	+	40.2789i	0.793451	+	1.37430i	−0.130366	+	0.991466i	$0.541615\pi$
$860$	0.305158	+	0.528549i	0.0104058	+	0.0180234i
$861$		0			0
$862$	5.05981	−	8.76384i	0.172338	−	0.298498i
$863$	−4.88014			−0.166122			−0.0830610	−	0.996544i	$-0.526470\pi$
$863$	−4.88014			−0.166122			−0.0830610	+	0.996544i	$0.526470\pi$
$864$	−1.27197	−	42.1604i	−0.0432734	−	1.43433i
$865$	2.32690			0.0791170
$866$	−31.6814	+	54.8739i	−1.07658	+	1.86469i
$867$	13.5909	+	36.2041i	0.461572	+	1.22956i
$868$		0			0
$869$	−10.6463	−	18.4400i	−0.361152	−	0.625533i
$870$	2.53261	+	0.420359i	0.0858634	+	0.0142515i
$871$	−0.618346	+	1.07101i	−0.0209518	+	0.0362897i
$872$	−2.97476			−0.100738
$873$	−4.62468	−	23.4593i	−0.156522	−	0.793978i
$874$	87.8207			2.97058
$875$		0			0
$876$	3.79815	−	4.62001i	0.128328	−	0.156096i
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	−0.979729	−	0.200326i	$-0.935800\pi$
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	0.316378	−	0.948633i	$-0.397533\pi$
$878$	−2.51388	−	4.35418i	−0.0848395	−	0.146946i
$879$	−15.5049	+	18.8599i	−0.522968	+	0.636129i
$880$	−0.428043	+	0.741392i	−0.0144293	+	0.0249923i
$881$	47.3713			1.59598			0.797990	−	0.602670i	$-0.205897\pi$
$881$	47.3713			1.59598			0.797990	+	0.602670i	$0.205897\pi$
$882$		0			0
$883$	−2.67206			−0.0899221			−0.0449610	−	0.998989i	$-0.514316\pi$
$883$	−2.67206			−0.0899221			−0.0449610	+	0.998989i	$0.514316\pi$
$884$	−1.38983	+	2.40726i	−0.0467451	+	0.0809649i
$885$	−1.14223	−	0.189585i	−0.0383955	−	0.00637284i
$886$	27.0003	+	46.7659i	0.907094	+	1.57113i
$887$	11.4800	+	19.8840i	0.385461	+	0.667638i	0.991833	−	0.127543i	$-0.0407091\pi$
$887$	11.4800	+	19.8840i	0.385461	+	0.667638i	−0.606372	+	0.795181i	$0.707376\pi$
$888$	1.90306	+	5.06944i	0.0638624	+	0.170119i
$889$		0			0
$890$	2.72342			0.0912891
$891$	11.8503	+	9.15760i	0.397000	+	0.306791i
$892$	−9.00518			−0.301516
$893$	−6.26655	+	10.8540i	−0.209702	+	0.363214i
$894$	22.2111	+	59.1669i	0.742851	+	1.97884i
$895$	−0.566944	−	0.981976i	−0.0189508	−	0.0328238i
$896$		0			0
$897$	−2.11140	−	0.350447i	−0.0704975	−	0.0117011i
$898$	39.7460	−	68.8420i	1.32634	−	2.29729i
$899$	−12.4257			−0.414420
$900$	24.9379	−	21.7947i	0.831264	−	0.726489i
$901$	−33.5262			−1.11692
$902$	3.96054	−	6.85986i	0.131872	−	0.228408i
$903$		0			0
$904$	−0.00862948	−	0.0149467i	−0.000287012	−	0.000497120i
$905$	−0.889308	−	1.54033i	−0.0295616	−	0.0512022i
$906$	19.1238	−	23.2619i	0.635346	−	0.772824i
$907$	13.9491	−	24.1606i	0.463173	−	0.802238i	−0.535944	−	0.844253i	$-0.680044\pi$
$907$	13.9491	−	24.1606i	0.463173	−	0.802238i	0.999117	+	0.0420148i	$0.0133777\pi$
$908$	−8.54354			−0.283527
$909$	−8.61250	−	43.6882i	−0.285659	−	1.44905i
$910$		0			0
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	0.368513	+	0.929623i	$0.379867\pi$
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	−0.989333	+	0.145670i	$0.953466\pi$
$912$	−41.5799	−	6.90139i	−1.37685	−	0.228528i
$913$	6.25158	+	10.8281i	0.206897	+	0.358356i
$914$	9.40068	+	16.2825i	0.310947	+	0.538576i
$915$	0.0603828	+	0.160850i	0.00199619	+	0.00531754i
$916$	−14.5424	+	25.1881i	−0.480493	+	0.832239i
$917$		0			0
$918$	−56.9184	+	35.1921i	−1.87859	+	1.16151i
$919$	30.2147			0.996691			0.498345	−	0.866979i	$-0.333941\pi$
$919$	30.2147			0.996691			0.498345	+	0.866979i	$0.333941\pi$
$920$	−0.201870	+	0.349649i	−0.00665546	+	0.0115276i
$921$	16.6741	+	44.4170i	0.549429	+	1.46359i
$922$	30.0145	+	51.9866i	0.988474	+	1.71209i
$923$	0.127680	+	0.221147i	0.00420262	+	0.00727916i
$924$		0			0
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$	33.7221			1.10818
$927$	−0.579037	−	0.197661i	−0.0190181	−	0.00649205i
$928$	−40.0609			−1.31506
$929$	22.9675	−	39.7809i	0.753540	−	1.30517i	−0.192556	−	0.981286i	$-0.561678\pi$
$929$	22.9675	−	39.7809i	0.753540	−	1.30517i	0.946097	−	0.323884i	$-0.104989\pi$
$930$	0.831764	−	1.01174i	0.0272746	−	0.0331763i
$931$		0			0
$932$	−19.4053	−	33.6110i	−0.635642	−	1.10096i
$933$	−15.4605	+	18.8059i	−0.506154	+	0.615677i
$934$	15.7850	−	27.3404i	0.516500	−	0.894604i
$935$	1.52613			0.0499097
$936$	−0.253443	−	0.0865159i	−0.00828405	−	0.00282786i
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$		0			0
$939$	−37.1545	−	6.16686i	−1.21249	−	0.201248i
$940$	−0.293774	−	0.508831i	−0.00958184	−	0.0165962i
$941$	−24.7002	−	42.7819i	−0.805202	−	1.39465i	−0.916154	−	0.400825i	$-0.868723\pi$
$941$	−24.7002	−	42.7819i	−0.805202	−	1.39465i	0.110952	−	0.993826i	$-0.464610\pi$
$942$	7.12484	+	18.9794i	0.232140	+	0.618384i
$943$	−7.16445	+	12.4092i	−0.233307	+	0.404099i
$944$	16.0798			0.523353
$945$		0			0
$946$	6.43141			0.209103
$947$	−15.8253	+	27.4102i	−0.514252	+	0.890711i	0.485611	+	0.874175i	$0.338597\pi$
$947$	−15.8253	+	27.4102i	−0.514252	+	0.890711i	−0.999863	+	0.0165357i	$0.994736\pi$
$948$	17.2721	+	46.0101i	0.560972	+	1.49434i
$949$	0.155636	+	0.269569i	0.00505214	+	0.00875057i
$950$	−35.3637	−	61.2517i	−1.14735	−	1.98727i
$951$	−14.6313	−	2.42849i	−0.474453	−	0.0787492i
$952$		0			0
$953$	−19.1237			−0.619477			−0.309739	−	0.950822i	$-0.600242\pi$
$953$	−19.1237			−0.619477			−0.309739	+	0.950822i	$0.600242\pi$
$954$	−6.37050	−	32.3153i	−0.206252	−	1.04625i
$955$	0.726498			0.0235089
$956$	8.11273	−	14.0517i	0.262384	−	0.454463i
$957$	9.03306	−	10.9877i	0.291997	−	0.355180i
$958$	38.9465	+	67.4573i	1.25830	+	2.17945i
$959$		0			0
$960$	1.54988	−	1.88524i	0.0500221	−	0.0608459i
$961$	12.3304	−	21.3568i	0.397753	−	0.688929i
$962$	−2.87372			−0.0926525
$963$	15.7420	−	13.7578i	0.507279	−	0.443340i
$964$	13.8171			0.445020
$965$	−1.08985	+	1.88768i	−0.0350836	+	0.0607666i
$966$		0			0
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	0.934982	−	0.354696i	$-0.115416\pi$
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	−0.774667	+	0.632370i	$0.782082\pi$
$968$	1.83790	+	3.18334i	0.0590724	+	0.102316i
$969$	26.4072	+	70.3445i	0.848321	+	2.25979i
$970$	1.19688	−	2.07306i	0.0384296	−	0.0665621i
$971$	−1.04511			−0.0335391			−0.0167695	−	0.999859i	$-0.505338\pi$
$971$	−1.04511			−0.0335391			−0.0167695	+	0.999859i	$0.505338\pi$
$972$	−23.5215	−	25.3298i	−0.754453	−	0.812453i
$973$		0			0
$974$	4.72847	−	8.18994i	0.151510	−	0.262423i
$975$	0.605794	+	1.61374i	0.0194009	+	0.0516810i
$976$	−1.19302	−	2.06637i	−0.0381875	−	0.0661428i
$977$	9.44308	+	16.3559i	0.302111	+	0.523272i	0.976614	−	0.215001i	$-0.0689753\pi$
$977$	9.44308	+	16.3559i	0.302111	+	0.523272i	−0.674503	+	0.738272i	$0.735642\pi$
$978$	−7.45786	−	1.23785i	−0.238476	−	0.0395820i
$979$	7.54466	−	13.0677i	0.241128	−	0.417647i
$980$		0			0
$981$	15.0469	−	13.1503i	0.480410	−	0.419858i
$982$	62.3797			1.99062
$983$	−1.14446	+	1.98226i	−0.0365025	+	0.0632242i	−0.883700	−	0.468055i	$-0.844955\pi$
$983$	−1.14446	+	1.98226i	−0.0365025	+	0.0632242i	0.847197	+	0.531279i	$0.178288\pi$
$984$	−1.13859	+	1.38496i	−0.0362970	+	0.0441510i
$985$	−1.55465	−	2.69274i	−0.0495353	−	0.0857977i
$986$	31.7789	+	55.0427i	1.01205	+	1.75292i
$987$		0			0
$988$	−1.53311	+	2.65542i	−0.0487746	+	0.0844801i
$989$	−11.6341			−0.369944
$990$	0.289988	+	1.47101i	0.00921643	+	0.0467517i
$991$	19.0698			0.605773			0.302886	−	0.953027i	$-0.402050\pi$
$991$	19.0698			0.605773			0.302886	+	0.953027i	$0.402050\pi$
$992$	−10.2191	+	17.6999i	−0.324455	+	0.561973i
$993$	−18.5343	−	3.07631i	−0.588170	−	0.0976237i
$994$		0			0
$995$	1.45837	+	2.52598i	0.0462336	+	0.0800789i
$996$	−10.1423	−	27.0174i	−0.321370	−	0.856080i
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	0.408593	+	0.912717i	$0.366020\pi$
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	−0.994732	+	0.102507i	$0.967314\pi$
$998$	19.0346			0.602531
$999$	−32.0362	−	17.2295i	−1.01358	−	0.545116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.e.295.1		10
3.2	odd	2		1323.2.f.e.883.5		10
7.2	even	3		63.2.h.b.25.5	yes	10
7.3	odd	6		441.2.g.f.79.1		10
7.4	even	3		63.2.g.b.16.1	yes	10
7.5	odd	6		441.2.h.f.214.5		10
7.6	odd	2		441.2.f.f.295.1		10
9.2	odd	6		3969.2.a.bc.1.1		5
9.4	even	3	inner	441.2.f.e.148.1		10
9.5	odd	6		1323.2.f.e.442.5		10
9.7	even	3		3969.2.a.z.1.5		5
21.2	odd	6		189.2.h.b.46.1		10
21.5	even	6		1323.2.h.f.802.1		10
21.11	odd	6		189.2.g.b.100.5		10
21.17	even	6		1323.2.g.f.667.5		10
21.20	even	2		1323.2.f.f.883.5		10
28.11	odd	6		1008.2.t.i.961.2		10
28.23	odd	6		1008.2.q.i.529.5		10
63.2	odd	6		567.2.e.e.487.5		10
63.4	even	3		63.2.h.b.58.5	yes	10
63.5	even	6		1323.2.g.f.361.5		10
63.11	odd	6		567.2.e.e.163.5		10
63.13	odd	6		441.2.f.f.148.1		10
63.16	even	3		567.2.e.f.487.1		10
63.20	even	6		3969.2.a.bb.1.1		5
63.23	odd	6		189.2.g.b.172.5		10
63.25	even	3		567.2.e.f.163.1		10
63.31	odd	6		441.2.h.f.373.5		10
63.32	odd	6		189.2.h.b.37.1		10
63.34	odd	6		3969.2.a.ba.1.5		5
63.40	odd	6		441.2.g.f.67.1		10
63.41	even	6		1323.2.f.f.442.5		10
63.58	even	3		63.2.g.b.4.1	✓	10
63.59	even	6		1323.2.h.f.226.1		10
84.11	even	6		3024.2.t.i.289.3		10
84.23	even	6		3024.2.q.i.2881.3		10
252.23	even	6		3024.2.t.i.1873.3		10
252.67	odd	6		1008.2.q.i.625.5		10
252.95	even	6		3024.2.q.i.2305.3		10
252.247	odd	6		1008.2.t.i.193.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	63.58	even	3
63.2.g.b.16.1	yes	10	7.4	even	3
63.2.h.b.25.5	yes	10	7.2	even	3
63.2.h.b.58.5	yes	10	63.4	even	3
189.2.g.b.100.5		10	21.11	odd	6
189.2.g.b.172.5		10	63.23	odd	6
189.2.h.b.37.1		10	63.32	odd	6
189.2.h.b.46.1		10	21.2	odd	6
441.2.f.e.148.1		10	9.4	even	3	inner
441.2.f.e.295.1		10	1.1	even	1	trivial
441.2.f.f.148.1		10	63.13	odd	6
441.2.f.f.295.1		10	7.6	odd	2
441.2.g.f.67.1		10	63.40	odd	6
441.2.g.f.79.1		10	7.3	odd	6
441.2.h.f.214.5		10	7.5	odd	6
441.2.h.f.373.5		10	63.31	odd	6
567.2.e.e.163.5		10	63.11	odd	6
567.2.e.e.487.5		10	63.2	odd	6
567.2.e.f.163.1		10	63.25	even	3
567.2.e.f.487.1		10	63.16	even	3
1008.2.q.i.529.5		10	28.23	odd	6
1008.2.q.i.625.5		10	252.67	odd	6
1008.2.t.i.193.2		10	252.247	odd	6
1008.2.t.i.961.2		10	28.11	odd	6
1323.2.f.e.442.5		10	9.5	odd	6
1323.2.f.e.883.5		10	3.2	odd	2
1323.2.f.f.442.5		10	63.41	even	6
1323.2.f.f.883.5		10	21.20	even	2
1323.2.g.f.361.5		10	63.5	even	6
1323.2.g.f.667.5		10	21.17	even	6
1323.2.h.f.226.1		10	63.59	even	6
1323.2.h.f.802.1		10	21.5	even	6
3024.2.q.i.2305.3		10	252.95	even	6
3024.2.q.i.2881.3		10	84.23	even	6
3024.2.t.i.289.3		10	84.11	even	6
3024.2.t.i.1873.3		10	252.23	even	6
3969.2.a.z.1.5		5	9.7	even	3
3969.2.a.ba.1.5		5	63.34	odd	6
3969.2.a.bb.1.1		5	63.20	even	6
3969.2.a.bc.1.1		5	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02682 + 1.77851i) q^{2} +(0.608729 + 1.62156i) q^{3} +(-1.10873 - 1.92038i) q^{4} +(0.0731228 + 0.126652i) q^{5} +(-3.50901 - 0.582422i) q^{6} +0.446582 q^{8} +(-2.25890 + 1.97418i) q^{9} -0.300337 q^{10} +(-0.832020 + 1.44110i) q^{11} +(2.43908 - 2.96686i) q^{12} +(0.0999454 + 0.173111i) q^{13} +(-0.160862 + 0.195670i) q^{15} +(1.75890 - 3.04650i) q^{16} -6.27110 q^{17} +(-1.19161 - 6.04460i) q^{18} -6.91758 q^{19} +(0.162147 - 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(3.09092 + 5.35363i) q^{23} +(0.271848 + 0.724159i) q^{24} +(2.48931 - 4.31160i) q^{25} -0.410505 q^{26} +(-4.57630 - 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-0.182824 - 0.487013i) q^{30} +(1.25890 + 2.18047i) q^{31} +(4.05873 + 7.02993i) q^{32} +(-2.84330 - 0.471928i) q^{33} +(6.43931 - 11.1532i) q^{34} +(6.29567 + 2.14910i) q^{36} +7.00046 q^{37} +(7.10312 - 12.3030i) q^{38} +(-0.219869 + 0.267445i) q^{39} +(0.0326554 + 0.0565608i) q^{40} +(1.15895 + 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +3.68994 q^{44} +(-0.415212 - 0.141737i) q^{45} -12.6953 q^{46} +(0.905887 - 1.56904i) q^{47} +(6.01077 + 0.997660i) q^{48} +(5.11215 + 8.85451i) q^{50} +(-3.81740 - 10.1690i) q^{51} +(0.221625 - 0.383865i) q^{52} +5.34614 q^{53} +(9.07630 - 5.61178i) q^{54} -0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 - 8.77720i) q^{58} +(2.28549 + 3.95859i) q^{59} +(0.554112 + 0.0919709i) q^{60} +(0.339138 - 0.587404i) q^{61} -5.17066 q^{62} -9.63481 q^{64} +(-0.0146166 + 0.0253167i) q^{65} +(3.75890 - 4.57226i) q^{66} +(3.09342 + 5.35796i) q^{67} +(6.95296 + 12.0429i) q^{68} +(-6.79968 + 8.27101i) q^{69} +1.27749 q^{71} +(-1.00878 + 0.881633i) q^{72} +1.55721 q^{73} +(-7.18823 + 12.4504i) q^{74} +(8.50683 + 1.41195i) q^{75} +(7.66972 + 13.2843i) q^{76} +(-0.249886 - 0.665657i) q^{78} +(-6.39787 + 11.0814i) q^{79} +0.514462 q^{80} +(1.20524 - 8.91894i) q^{81} -4.76015 q^{82} +(3.75687 - 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 - 3.34713i) q^{86} +(-8.43256 - 1.39963i) q^{87} +(-0.371566 + 0.643571i) q^{88} -9.06788 q^{89} +(0.678430 - 0.592918i) q^{90} +(6.85398 - 11.8714i) q^{92} +(-2.76944 + 3.36869i) q^{93} +(1.86037 + 3.22226i) q^{94} +(-0.505833 - 0.876128i) q^{95} +(-8.92877 + 10.8608i) q^{96} +(-3.98514 + 6.90246i) q^{97} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9} + 14 q^{10} + 4 q^{11} - 2 q^{12} - 8 q^{13} - 19 q^{15} + 2 q^{16} - 24 q^{17} - 2 q^{18} - 2 q^{19} + 5 q^{20} - q^{22} + 3 q^{23}+ \cdots + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^8 - 7 * q^9 + 14 * q^10 + 4 * q^11 - 2 * q^12 - 8 * q^13 - 19 * q^15 + 2 * q^16 - 24 * q^17 - 2 * q^18 - 2 * q^19 + 5 * q^20 - q^22 + 3 * q^23 - 9 * q^24 - q^25 - 22 * q^26 - 7 * q^27 + 7 * q^29 + 10 * q^30 - 3 * q^31 - 2 * q^32 - 13 * q^33 + 3 * q^34 + 34 * q^36 + 20 * q^38 - 22 * q^39 - 3 * q^40 + 5 * q^41 - 7 * q^43 + 20 * q^44 + 17 * q^45 - 6 * q^46 + 27 * q^47 - 5 * q^48 + 19 * q^50 - 15 * q^51 - 10 * q^52 + 42 * q^53 + 52 * q^54 + 4 * q^55 - 4 * q^57 - 10 * q^58 + 30 * q^59 + 31 * q^60 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 + 22 * q^66 - 2 * q^67 + 27 * q^68 + 15 * q^69 - 6 * q^71 - 12 * q^72 - 30 * q^73 - 36 * q^74 - 17 * q^75 + 5 * q^76 - 20 * q^78 - 4 * q^79 - 40 * q^80 - 31 * q^81 + 10 * q^82 + 9 * q^83 - 6 * q^85 - 8 * q^86 - 34 * q^87 - 18 * q^88 - 56 * q^89 + 28 * q^90 + 27 * q^92 + 18 * q^93 - 3 * q^94 - 14 * q^95 - 58 * q^96 - 12 * q^97 + 35 * q^99

Introduction

L-functions

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