LMFDB - Embedded newform 675.2.l.f.76.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] 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("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,-6] 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.2
Character	$\chi$	$=$	675.76
Dual form			675.2.l.f.151.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55121 + 1.30162i) q^{2} +(-1.45868 - 0.933937i) q^{3} +(0.364742 - 2.06856i) q^{4} +(3.47836 - 0.449921i) q^{6} +(0.0652816 + 0.370230i) q^{7} +(0.101721 + 0.176186i) q^{8} +(1.25552 + 2.72464i) q^{9} +(0.272976 + 0.0993552i) q^{11} +(-2.46395 + 2.67673i) q^{12} +(-0.677752 - 0.568702i) q^{13} +(-0.583165 - 0.489333i) q^{14} +(3.56047 + 1.29590i) q^{16} +(-2.32471 + 4.02651i) q^{17} +(-5.49403 - 2.59227i) q^{18} +(-1.75100 - 3.03282i) q^{19} +(0.250547 - 0.601018i) q^{21} +(-0.552766 + 0.201190i) q^{22} +(-0.0948473 + 0.537906i) q^{23} +(0.0161677 - 0.352001i) q^{24} +1.79157 q^{26} +(0.713228 - 5.14697i) q^{27} +0.789653 q^{28} +(-4.65300 + 3.90433i) q^{29} +(0.953291 - 5.40638i) q^{31} +(-7.59216 + 2.76332i) q^{32} +(-0.305395 - 0.399870i) q^{33} +(-1.63488 - 9.27184i) q^{34} +(6.09401 - 1.60333i) q^{36} +(5.47398 - 9.48122i) q^{37} +(6.66375 + 2.42541i) q^{38} +(0.457496 + 1.46253i) q^{39} +(-7.28901 - 6.11620i) q^{41} +(0.393647 + 1.25842i) q^{42} +(9.54330 + 3.47348i) q^{43} +(0.305088 - 0.528427i) q^{44} +(-0.553021 - 0.957860i) q^{46} +(-1.09967 - 6.23654i) q^{47} +(-3.98331 - 5.21557i) q^{48} +(6.44504 - 2.34580i) q^{49} +(7.15152 - 3.70228i) q^{51} +(-1.42360 + 1.19454i) q^{52} +12.2148 q^{53} +(5.59303 + 8.91238i) q^{54} +(-0.0585889 + 0.0491619i) q^{56} +(-0.278306 + 6.05925i) q^{57} +(2.13583 - 12.1129i) q^{58} +(-1.18778 + 0.432318i) q^{59} +(0.499613 + 2.83345i) q^{61} +(5.55830 + 9.62726i) q^{62} +(-0.926782 + 0.642702i) q^{63} +(4.39127 - 7.60590i) q^{64} +(0.994211 + 0.222775i) q^{66} +(-6.78495 - 5.69325i) q^{67} +(7.48114 + 6.27742i) q^{68} +(0.640723 - 0.696054i) q^{69} +(5.36876 - 9.29896i) q^{71} +(-0.352330 + 0.498359i) q^{72} +(0.389512 + 0.674654i) q^{73} +(3.84964 + 21.8324i) q^{74} +(-6.91222 + 2.51584i) q^{76} +(-0.0189640 + 0.107550i) q^{77} +(-2.61334 - 1.67321i) q^{78} +(5.29571 - 4.44363i) q^{79} +(-5.84732 + 6.84170i) q^{81} +19.2678 q^{82} +(6.88221 - 5.77486i) q^{83} +(-1.15186 - 0.737486i) q^{84} +(-19.3248 + 7.03366i) q^{86} +(10.4337 - 1.34958i) q^{87} +(0.0102624 + 0.0582011i) q^{88} +(-3.11061 - 5.38773i) q^{89} +(0.166306 - 0.288050i) q^{91} +(1.07809 + 0.392394i) q^{92} +(-6.43977 + 6.99589i) q^{93} +(9.82342 + 8.24283i) q^{94} +(13.6553 + 3.05978i) q^{96} +(-13.1743 - 4.79504i) q^{97} +(-6.94427 + 12.0278i) q^{98} +(0.0720209 + 0.868504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−1.55121	+	1.30162i	−1.09687	+	0.920384i	−0.997211	−	0.0746373i	$-0.976220\pi$
$2$	−1.55121	+	1.30162i	−1.09687	+	0.920384i	−0.0996605	+	0.995022i	$0.531776\pi$
$3$	−1.45868	−	0.933937i	−0.842172	−	0.539209i
$3$	−1.45868	−	0.933937i	−0.842172	−	0.539209i
$4$	0.364742	−	2.06856i	0.182371	−	1.03428i
$5$		0			0
$5$		0			0
$6$	3.47836	−	0.449921i	1.42003	−	0.183679i
$7$	0.0652816	+	0.370230i	0.0246741	+	0.139934i	0.994656	−	0.103242i	$-0.0329217\pi$
$7$	0.0652816	+	0.370230i	0.0246741	+	0.139934i	−0.969982	+	0.243176i	$0.921811\pi$
$8$	0.101721	+	0.176186i	0.0359638	+	0.0622912i
$9$	1.25552	+	2.72464i	0.418508	+	0.908213i
$10$		0			0
$11$	0.272976	+	0.0993552i	0.0823054	+	0.0299567i	0.382845	−	0.923813i	$-0.374944\pi$
$11$	0.272976	+	0.0993552i	0.0823054	+	0.0299567i	−0.300539	+	0.953769i	$0.597167\pi$
$12$	−2.46395	+	2.67673i	−0.711280	+	0.772704i
$13$	−0.677752	−	0.568702i	−0.187975	−	0.157729i	0.543944	−	0.839122i	$-0.316930\pi$
$13$	−0.677752	−	0.568702i	−0.187975	−	0.157729i	−0.731919	+	0.681392i	$0.761375\pi$
$14$	−0.583165	−	0.489333i	−0.155857	−	0.130780i
$15$		0			0
$16$	3.56047	+	1.29590i	0.890117	+	0.323976i
$17$	−2.32471	+	4.02651i	−0.563824	+	0.976572i	0.433334	+	0.901233i	$0.357337\pi$
$17$	−2.32471	+	4.02651i	−0.563824	+	0.976572i	−0.997158	+	0.0753383i	$0.975996\pi$
$18$	−5.49403	−	2.59227i	−1.29495	−	0.611005i
$19$	−1.75100	−	3.03282i	−0.401707	−	0.695777i	0.592225	−	0.805772i	$-0.298250\pi$
$19$	−1.75100	−	3.03282i	−0.401707	−	0.695777i	−0.993932	+	0.109996i	$0.964916\pi$
$20$		0			0
$21$	0.250547	−	0.601018i	0.0546737	−	0.131153i
$22$	−0.552766	+	0.201190i	−0.117850	+	0.0428939i
$23$	−0.0948473	+	0.537906i	−0.0197770	+	0.112161i	−0.993098	−	0.117286i	$-0.962581\pi$
$23$	−0.0948473	+	0.537906i	−0.0197770	+	0.112161i	0.973321	+	0.229447i	$0.0736918\pi$
$24$	0.0161677	−	0.352001i	0.00330021	−	0.0718519i
$25$		0			0
$26$	1.79157			0.351356
$27$	0.713228	−	5.14697i	0.137261	−	0.990535i
$28$	0.789653			0.149230
$29$	−4.65300	+	3.90433i	−0.864040	+	0.725016i	−0.962834	−	0.270092i	$-0.912946\pi$
$29$	−4.65300	+	3.90433i	−0.864040	+	0.725016i	0.0987944	+	0.995108i	$0.468501\pi$
$30$		0			0
$31$	0.953291	−	5.40638i	0.171216	−	0.971015i	−0.771205	−	0.636587i	$-0.780346\pi$
$31$	0.953291	−	5.40638i	0.171216	−	0.971015i	0.942421	−	0.334428i	$-0.108543\pi$
$32$	−7.59216	+	2.76332i	−1.34212	+	0.488490i
$33$	−0.305395	−	0.399870i	−0.0531624	−	0.0696085i
$34$	−1.63488	−	9.27184i	−0.280379	−	1.59011i
$35$		0			0
$36$	6.09401	−	1.60333i	1.01567	−	0.267222i
$37$	5.47398	−	9.48122i	0.899917	−	1.55870i	0.0723191	−	0.997382i	$-0.476960\pi$
$37$	5.47398	−	9.48122i	0.899917	−	1.55870i	0.827598	−	0.561321i	$-0.189707\pi$
$38$	6.66375	+	2.42541i	1.08100	+	0.393453i
$39$	0.457496	+	1.46253i	0.0732579	+	0.234193i
$40$		0			0
$41$	−7.28901	−	6.11620i	−1.13835	−	0.955190i	−0.138968	−	0.990297i	$-0.544378\pi$
$41$	−7.28901	−	6.11620i	−1.13835	−	0.955190i	−0.999384	+	0.0351066i	$0.988823\pi$
$42$	0.393647	+	1.25842i	0.0607411	+	0.194179i
$43$	9.54330	+	3.47348i	1.45534	+	0.529701i	0.944077	−	0.329724i	$-0.106956\pi$
$43$	9.54330	+	3.47348i	1.45534	+	0.529701i	0.511263	+	0.859424i	$0.329178\pi$
$44$	0.305088	−	0.528427i	0.0459937	−	0.0796634i
$45$		0			0
$46$	−0.553021	−	0.957860i	−0.0815385	−	0.141229i
$47$	−1.09967	−	6.23654i	−0.160403	−	0.909693i	−0.953678	−	0.300829i	$-0.902737\pi$
$47$	−1.09967	−	6.23654i	−0.160403	−	0.909693i	0.793275	−	0.608864i	$-0.208374\pi$
$48$	−3.98331	−	5.21557i	−0.574941	−	0.752803i
$49$	6.44504	−	2.34580i	0.920720	−	0.335115i
$50$		0			0
$51$	7.15152	−	3.70228i	1.00141	−	0.518423i
$52$	−1.42360	+	1.19454i	−0.197417	+	0.165653i
$53$	12.2148			1.67783			0.838913	−	0.544265i	$-0.183191\pi$
$53$	12.2148			1.67783			0.838913	+	0.544265i	$0.183191\pi$
$54$	5.59303	+	8.91238i	0.761115	+	1.21282i
$55$		0			0
$56$	−0.0585889	+	0.0491619i	−0.00782927	+	0.00656954i
$57$	−0.278306	+	6.05925i	−0.0368625	+	0.802567i
$58$	2.13583	−	12.1129i	0.280448	−	1.59050i
$59$	−1.18778	+	0.432318i	−0.154636	+	0.0562830i	−0.418179	−	0.908365i	$-0.637331\pi$
$59$	−1.18778	+	0.432318i	−0.154636	+	0.0562830i	0.263542	+	0.964648i	$0.415109\pi$
$60$		0			0
$61$	0.499613	+	2.83345i	0.0639690	+	0.362786i	0.999943	+	0.0107158i	$0.00341102\pi$
$61$	0.499613	+	2.83345i	0.0639690	+	0.362786i	−0.935974	+	0.352070i	$0.885478\pi$
$62$	5.55830	+	9.62726i	0.705905	+	1.22266i
$63$	−0.926782	+	0.642702i	−0.116764	+	0.0809728i
$64$	4.39127	−	7.60590i	0.548909	−	0.950737i
$65$		0			0
$66$	0.994211	+	0.222775i	0.122379	+	0.0274217i
$67$	−6.78495	−	5.69325i	−0.828913	−	0.695541i	0.126128	−	0.992014i	$-0.459745\pi$
$67$	−6.78495	−	5.69325i	−0.828913	−	0.695541i	−0.955041	+	0.296473i	$0.904189\pi$
$68$	7.48114	+	6.27742i	0.907222	+	0.761249i
$69$	0.640723	−	0.696054i	0.0771339	−	0.0837951i
$70$		0			0
$71$	5.36876	−	9.29896i	0.637154	−	1.10358i	−0.348900	−	0.937160i	$-0.613445\pi$
$71$	5.36876	−	9.29896i	0.637154	−	1.10358i	0.986054	−	0.166424i	$-0.0532219\pi$
$72$	−0.352330	+	0.498359i	−0.0415225	+	0.0587322i
$73$	0.389512	+	0.674654i	0.0455889	+	0.0789623i	0.887919	−	0.459999i	$-0.152150\pi$
$73$	0.389512	+	0.674654i	0.0455889	+	0.0789623i	−0.842331	+	0.538961i	$0.818817\pi$
$74$	3.84964	+	21.8324i	0.447512	+	2.53797i
$75$		0			0
$76$	−6.91222	+	2.51584i	−0.792886	+	0.288587i
$77$	−0.0189640	+	0.107550i	−0.00216115	+	0.0122565i
$78$	−2.61334	−	1.67321i	−0.295902	−	0.189454i
$79$	5.29571	−	4.44363i	0.595813	−	0.499947i	−0.294283	−	0.955718i	$-0.595081\pi$
$79$	5.29571	−	4.44363i	0.595813	−	0.499947i	0.890097	+	0.455771i	$0.150637\pi$
$80$		0			0
$81$	−5.84732	+	6.84170i	−0.649702	+	0.760189i
$82$	19.2678			2.12777
$83$	6.88221	−	5.77486i	0.755421	−	0.633874i	−0.181509	−	0.983389i	$-0.558098\pi$
$83$	6.88221	−	5.77486i	0.755421	−	0.633874i	0.936931	+	0.349516i	$0.113654\pi$
$84$	−1.15186	−	0.737486i	−0.125678	−	0.0804664i
$85$		0			0
$86$	−19.3248	+	7.03366i	−2.08385	+	0.758459i
$87$	10.4337	−	1.34958i	1.11861	−	0.144690i
$88$	0.0102624	+	0.0582011i	0.00109398	+	0.00620426i
$89$	−3.11061	−	5.38773i	−0.329724	−	0.571099i	0.652733	−	0.757588i	$-0.273622\pi$
$89$	−3.11061	−	5.38773i	−0.329724	−	0.571099i	−0.982457	+	0.186489i	$0.940289\pi$
$90$		0			0
$91$	0.166306	−	0.288050i	0.0174336	−	0.0301959i
$92$	1.07809	+	0.392394i	0.112399	+	0.0409099i
$93$	−6.43977	+	6.99589i	−0.667773	+	0.725440i
$94$	9.82342	+	8.24283i	1.01321	+	0.850183i
$95$		0			0
$96$	13.6553	+	3.05978i	1.39369	+	0.312288i
$97$	−13.1743	−	4.79504i	−1.33765	−	0.486863i	−0.428575	−	0.903506i	$-0.640984\pi$
$97$	−13.1743	−	4.79504i	−1.33765	−	0.486863i	−0.909070	+	0.416643i	$0.863206\pi$
$98$	−6.94427	+	12.0278i	−0.701477	+	1.21499i
$99$	0.0720209	+	0.868504i	0.00723838	+	0.0872880i
$100$		0			0
$101$	−0.698390	−	3.96077i	−0.0694924	−	0.394111i	−0.999638	−	0.0269191i	$-0.991430\pi$
$101$	−0.698390	−	3.96077i	−0.0694924	−	0.394111i	0.930145	−	0.367192i	$-0.119681\pi$
$102$	−6.27455	+	15.0516i	−0.621273	+	1.49033i
$103$	0.484326	−	0.176280i	0.0477221	−	0.0173694i	−0.318049	−	0.948074i	$-0.603028\pi$
$103$	0.484326	−	0.176280i	0.0477221	−	0.0173694i	0.365771	+	0.930705i	$0.380805\pi$
$104$	0.0312556	−	0.177260i	0.00306487	−	0.0173817i
$105$		0			0
$106$	−18.9477	+	15.8990i	−1.84036	+	1.54425i
$107$	17.9687			1.73710			0.868552	−	0.495598i	$-0.165051\pi$
$107$	17.9687			1.73710			0.868552	+	0.495598i	$0.165051\pi$
$108$	−10.3867	−	3.35267i	−0.999456	−	0.322611i
$109$	−1.10502			−0.105842			−0.0529209	−	0.998599i	$-0.516853\pi$
$109$	−1.10502			−0.105842			−0.0529209	+	0.998599i	$0.516853\pi$
$110$		0			0
$111$	−16.8397	+	8.71775i	−1.59835	+	0.827453i
$112$	−0.247350	+	1.40279i	−0.0233724	+	0.132551i
$113$	−8.53194	+	3.10537i	−0.802618	+	0.292129i	−0.710571	−	0.703626i	$-0.751563\pi$
$113$	−8.53194	+	3.10537i	−0.802618	+	0.292129i	−0.0920470	+	0.995755i	$0.529341\pi$
$114$	−7.45513	−	9.76142i	−0.698237	−	0.914241i
$115$		0			0
$116$	6.37918	+	11.0491i	0.592292	+	1.02588i
$117$	0.698573	−	2.56065i	0.0645831	−	0.236732i
$118$	1.27979	−	2.21666i	0.117814	−	0.204060i
$119$	−1.64250	−	0.597820i	−0.150567	−	0.0548020i
$120$		0			0
$121$	−8.36184	−	7.01642i	−0.760168	−	0.637856i
$122$	−4.46308	−	3.74497i	−0.404068	−	0.339053i
$123$	4.92022	+	15.7291i	0.443641	+	1.41824i
$124$	−10.8357	−	3.94387i	−0.973074	−	0.354170i
$125$		0			0
$126$	0.601080	−	2.20328i	0.0535484	−	0.196284i
$127$	−5.39923	−	9.35175i	−0.479105	−	0.829833i	0.520608	−	0.853796i	$-0.325705\pi$
$127$	−5.39923	−	9.35175i	−0.479105	−	0.829833i	−0.999713	+	0.0239622i	$0.992372\pi$
$128$	0.282262	+	1.60079i	0.0249487	+	0.141491i
$129$	−10.6767	−	13.9796i	−0.940028	−	1.23083i
$130$		0			0
$131$	2.14908	−	12.1880i	0.187766	−	1.06487i	−0.734584	−	0.678518i	$-0.762623\pi$
$131$	2.14908	−	12.1880i	0.187766	−	1.06487i	0.922350	−	0.386356i	$-0.126266\pi$
$132$	−0.938545	+	0.485876i	−0.0816898	+	0.0422901i
$133$	1.00853	−	0.846260i	0.0874510	−	0.0733801i
$134$	17.9353			1.54938
$135$		0			0
$136$	−0.945886			−0.0811091
$137$	12.6386	−	10.6051i	1.07979	−	0.906052i	0.0838872	−	0.996475i	$-0.473266\pi$
$137$	12.6386	−	10.6051i	1.07979	−	0.906052i	0.995903	+	0.0904234i	$0.0288220\pi$
$138$	−0.0878978	+	1.91370i	−0.00748236	+	0.162905i
$139$	−2.14103	+	12.1424i	−0.181600	+	1.02990i	0.748647	+	0.662969i	$0.230704\pi$
$139$	−2.14103	+	12.1424i	−0.181600	+	1.02990i	−0.930247	+	0.366935i	$0.880407\pi$
$140$		0			0
$141$	−4.22046	+	10.1242i	−0.355427	+	0.852609i
$142$	3.77564	+	21.4127i	0.316845	+	1.79692i
$143$	−0.128507	−	0.222580i	−0.0107463	−	0.0186131i
$144$	0.939380	+	11.3280i	0.0782817	+	0.944003i
$145$		0			0
$146$	−1.48236	−	0.539534i	−0.122681	−	0.0446522i
$147$	−11.5921	−	2.59747i	−0.956101	−	0.214236i
$148$	−17.6158	−	14.7814i	−1.44801	−	1.21503i
$149$	−7.81833	−	6.56036i	−0.640503	−	0.537446i	0.263670	−	0.964613i	$-0.415067\pi$
$149$	−7.81833	−	6.56036i	−0.640503	−	0.537446i	−0.904173	+	0.427167i	$0.859512\pi$
$150$		0			0
$151$	16.7786	+	6.10690i	1.36542	+	0.496972i	0.917726	−	0.397214i	$-0.130023\pi$
$151$	16.7786	+	6.10690i	1.36542	+	0.496972i	0.447695	+	0.894187i	$0.352245\pi$
$152$	0.356227	−	0.617003i	0.0288938	−	0.0500456i
$153$	−13.8895	−	1.27861i	−1.12290	−	0.103369i
$154$	−0.110572	−	0.191517i	−0.00891016	−	0.0154329i
$155$		0			0
$156$	3.19220	−	0.412907i	0.255581	−	0.0330590i
$157$	−10.8531	+	3.95020i	−0.866170	+	0.315260i	−0.736615	−	0.676312i	$-0.763577\pi$
$157$	−10.8531	+	3.95020i	−0.866170	+	0.315260i	−0.129555	+	0.991572i	$0.541355\pi$
$158$	−2.43084	+	13.7860i	−0.193387	+	1.09675i
$159$	−17.8175	−	11.4078i	−1.41302	−	0.904699i
$160$		0			0
$161$	−0.205341			−0.0161831
$162$	0.165131	−	18.2239i	0.0129739	−	1.43180i
$163$	−6.26212			−0.490487			−0.245244	−	0.969461i	$-0.578868\pi$
$163$	−6.26212			−0.490487			−0.245244	+	0.969461i	$0.578868\pi$
$164$	−15.3103	+	12.8469i	−1.19553	+	1.00317i
$165$		0			0
$166$	−3.15908	+	17.9161i	−0.245192	+	1.39056i
$167$	−14.7179	+	5.35688i	−1.13891	+	0.414528i	−0.841518	−	0.540229i	$-0.818338\pi$
$167$	−14.7179	+	5.35688i	−1.13891	+	0.414528i	−0.297388	+	0.954757i	$0.596116\pi$
$168$	0.131377	−	0.0169934i	0.0101360	−	0.00131107i
$169$	−2.12150	−	12.0316i	−0.163192	−	0.925509i
$170$		0			0
$171$	6.06492	−	8.57862i	0.463796	−	0.656023i
$172$	10.6659	−	18.4739i	0.813270	−	1.40862i
$173$	−8.57107	−	3.11962i	−0.651647	−	0.237180i	−0.00502090	−	0.999987i	$-0.501598\pi$
$173$	−8.57107	−	3.11962i	−0.651647	−	0.237180i	−0.646626	+	0.762807i	$0.723820\pi$
$174$	−14.4282	+	15.6741i	−1.09380	+	1.18825i
$175$		0			0
$176$	0.843168	+	0.707502i	0.0635562	+	0.0533300i
$177$	2.13636	+	0.478700i	0.160579	+	0.0359813i
$178$	11.8380	+	4.30868i	0.887295	+	0.322949i
$179$	1.32110	−	2.28821i	0.0987437	−	0.171029i	−0.812421	−	0.583071i	$-0.801851\pi$
$179$	1.32110	−	2.28821i	0.0987437	−	0.171029i	0.911165	+	0.412042i	$0.135184\pi$
$180$		0			0
$181$	3.54912	+	6.14725i	0.263804	+	0.456922i	0.967250	−	0.253827i	$-0.0816895\pi$
$181$	3.54912	+	6.14725i	0.263804	+	0.456922i	−0.703446	+	0.710749i	$0.748356\pi$
$182$	0.116957	+	0.663294i	0.00866940	+	0.0491666i
$183$	1.91748	−	4.59972i	0.141744	−	0.340021i
$184$	−0.104420	+	0.0380056i	−0.00769791	+	0.00280181i
$185$		0			0
$186$	0.883443	−	19.2342i	0.0647772	−	1.41032i
$187$	−1.03464	+	0.868169i	−0.0756606	+	0.0634868i
$188$	−13.3017			−0.970128
$189$	1.95213	−	0.0719439i	0.141996	−	0.00523315i
$190$		0			0
$191$	3.97951	−	3.33921i	0.287948	−	0.241617i	−0.487359	−	0.873202i	$-0.662040\pi$
$191$	3.97951	−	3.33921i	0.287948	−	0.241617i	0.775307	+	0.631585i	$0.217595\pi$
$192$	−13.5089	+	6.99344i	−0.974921	+	0.504708i
$193$	0.681015	−	3.86223i	0.0490205	−	0.278009i	−0.950438	−	0.310914i	$-0.899365\pi$
$193$	0.681015	−	3.86223i	0.0490205	−	0.278009i	0.999458	+	0.0329051i	$0.0104759\pi$
$194$	26.6774	−	9.70978i	1.91533	−	0.697121i
$195$		0			0
$196$	−2.50165	−	14.1875i	−0.178689	−	1.01340i
$197$	5.18583	+	8.98212i	0.369475	+	0.639950i	0.989484	−	0.144646i	$-0.0462042\pi$
$197$	5.18583	+	8.98212i	0.369475	+	0.639950i	−0.620008	+	0.784595i	$0.712871\pi$
$198$	−1.24218	−	1.25349i	−0.0882780	−	0.0890816i
$199$	−5.95479	+	10.3140i	−0.422124	+	0.731140i	−0.996147	−	0.0876991i	$-0.972049\pi$
$199$	−5.95479	+	10.3140i	−0.422124	+	0.731140i	0.574023	+	0.818839i	$0.305382\pi$
$200$		0			0
$201$	4.57997	+	14.6414i	0.323046	+	1.03272i
$202$	6.23876	+	5.23494i	0.438958	+	0.368329i
$203$	−1.74926	−	1.46780i	−0.122774	−	0.103019i
$204$	−5.04991	−	16.1437i	−0.353565	−	1.13028i
$205$		0			0
$206$	−0.521842	+	0.903856i	−0.0363584	+	0.0629747i
$207$	−1.58468	+	0.416929i	−0.110143	+	0.0289786i
$208$	−1.67613	−	2.90315i	−0.116219	−	0.201297i
$209$	−0.176655	−	1.00186i	−0.0122195	−	0.0693000i
$210$		0			0
$211$	−2.30091	+	0.837462i	−0.158401	+	0.0576532i	−0.420004	−	0.907522i	$-0.637971\pi$
$211$	−2.30091	+	0.837462i	−0.158401	+	0.0576532i	0.261603	+	0.965176i	$0.415749\pi$
$212$	4.45524	−	25.2669i	0.305987	−	1.73534i
$213$	−16.5160	+	8.55017i	−1.13166	+	0.585848i
$214$	−27.8733	+	23.3885i	−1.90538	+	1.59880i
$215$		0			0
$216$	0.979375	−	0.397895i	0.0666380	−	0.0270733i
$217$	2.06384			0.140103
$218$	1.71412	−	1.43832i	0.116095	−	0.0974152i
$219$	0.0619094	−	1.34789i	0.00418345	−	0.0910818i
$220$		0			0
$221$	3.86546	−	1.40691i	0.260019	−	0.0946391i
$222$	14.7747	−	35.4419i	0.991611	−	2.37871i
$223$	−3.12885	−	17.7446i	−0.209523	−	1.18826i	−0.890162	−	0.455645i	$-0.849409\pi$
$223$	−3.12885	−	17.7446i	−0.209523	−	1.18826i	0.680639	−	0.732619i	$-0.261702\pi$
$224$	−1.51869	−	2.63045i	−0.101472	−	0.175755i
$225$		0			0
$226$	9.19282	−	15.9224i	0.611497	−	1.05914i
$227$	5.02409	+	1.82862i	0.333460	+	0.121370i	0.503324	−	0.864098i	$-0.332110\pi$
$227$	5.02409	+	1.82862i	0.333460	+	0.121370i	−0.169863	+	0.985468i	$0.554333\pi$
$228$	12.4324	+	2.78576i	0.823355	+	0.184491i
$229$	16.5031	+	13.8477i	1.09055	+	0.915083i	0.996754	−	0.0805082i	$-0.0256543\pi$
$229$	16.5031	+	13.8477i	1.09055	+	0.915083i	0.0937994	+	0.995591i	$0.470099\pi$
$230$		0			0
$231$	0.128107	−	0.139171i	0.00842885	−	0.00915675i
$232$	−1.16120	−	0.422641i	−0.0762363	−	0.0277477i
$233$	−12.7820	+	22.1390i	−0.837375	+	1.45038i	0.0547064	+	0.998502i	$0.482578\pi$
$233$	−12.7820	+	22.1390i	−0.837375	+	1.45038i	−0.892082	+	0.451874i	$0.850756\pi$
$234$	2.24936	+	4.88138i	0.147045	+	0.319106i
$235$		0			0
$236$	0.461039	+	2.61468i	0.0300111	+	0.170201i
$237$	−11.8748	+	1.53599i	−0.771353	+	0.0997735i
$238$	3.32599	−	1.21056i	0.215592	−	0.0784691i
$239$	1.60685	−	9.11290i	0.103939	−	0.589465i	−0.887700	−	0.460421i	$-0.847698\pi$
$239$	1.60685	−	9.11290i	0.103939	−	0.589465i	0.991639	−	0.129043i	$-0.0411906\pi$
$240$		0			0
$241$	−22.0268	+	18.4827i	−1.41887	+	1.19058i	−0.466933	+	0.884293i	$0.654641\pi$
$241$	−22.0268	+	18.4827i	−1.41887	+	1.19058i	−0.951940	+	0.306283i	$0.900914\pi$
$242$	22.1037			1.42088
$243$	14.9191	−	4.51886i	0.957062	−	0.289885i
$244$	6.04338			0.386888
$245$		0			0
$246$	−28.1056	−	17.9949i	−1.79195	−	1.14731i
$247$	−0.538026	+	3.05130i	−0.0342338	+	0.194149i
$248$	1.04950	−	0.381986i	0.0666432	−	0.0242562i
$249$	−15.4323	+	1.99615i	−0.977985	+	0.126501i
$250$		0			0
$251$	5.86206	+	10.1534i	0.370010	+	0.640876i	0.989567	−	0.144076i	$-0.0460210\pi$
$251$	5.86206	+	10.1534i	0.370010	+	0.640876i	−0.619557	+	0.784952i	$0.712688\pi$
$252$	0.991429	+	2.15152i	0.0624541	+	0.135533i
$253$	−0.0793348	+	0.137412i	−0.00498774	+	0.00863901i
$254$	20.5478	+	7.47878i	1.28928	+	0.469260i
$255$		0			0
$256$	10.9342	+	9.17485i	0.683385	+	0.573428i
$257$	2.82575	+	2.37109i	0.176265	+	0.147904i	0.726652	−	0.687006i	$-0.241075\pi$
$257$	2.82575	+	2.37109i	0.176265	+	0.147904i	−0.550387	+	0.834910i	$0.685520\pi$
$258$	34.7578	+	7.78827i	2.16393	+	0.484876i
$259$	3.86758	+	1.40769i	0.240320	+	0.0874693i
$260$		0			0
$261$	−16.4798	−	7.77576i	−1.02008	−	0.481308i
$262$	12.5305	+	21.7035i	0.774138	+	1.34085i
$263$	−3.83968	−	21.7759i	−0.236765	−	1.34276i	−0.838864	−	0.544340i	$-0.816780\pi$
$263$	−3.83968	−	21.7759i	−0.236765	−	1.34276i	0.602099	−	0.798421i	$-0.294331\pi$
$264$	0.0393865	−	0.0944815i	0.00242407	−	0.00581494i
$265$		0			0
$266$	−0.462939	+	2.62546i	−0.0283846	+	0.160977i
$267$	−0.494404	+	10.7641i	−0.0302570	+	0.658754i
$268$	−14.2516	+	11.9585i	−0.870553	+	0.730480i
$269$	25.3331			1.54459			0.772294	−	0.635265i	$-0.219109\pi$
$269$	25.3331			1.54459			0.772294	+	0.635265i	$0.219109\pi$
$270$		0			0
$271$	28.7783			1.74816			0.874079	−	0.485783i	$-0.161466\pi$
$271$	28.7783			1.74816			0.874079	+	0.485783i	$0.161466\pi$
$272$	−13.4950	+	11.3237i	−0.818255	+	0.686598i
$273$	−0.511609	+	0.264855i	−0.0309640	+	0.0160298i
$274$	−5.80140	+	32.9014i	−0.350475	+	1.98764i
$275$		0			0
$276$	−1.20613	−	1.57925i	−0.0726004	−	0.0950598i
$277$	3.42530	+	19.4258i	0.205806	+	1.16718i	0.896166	+	0.443719i	$0.146341\pi$
$277$	3.42530	+	19.4258i	0.205806	+	1.16718i	−0.690360	+	0.723466i	$0.742548\pi$
$278$	−12.4836	−	21.6222i	−0.748715	−	1.29681i
$279$	15.9273	−	4.19047i	0.953544	−	0.250877i
$280$		0			0
$281$	−8.19525	−	2.98283i	−0.488887	−	0.177940i	0.0858017	−	0.996312i	$-0.472655\pi$
$281$	−8.19525	−	2.98283i	−0.488887	−	0.177940i	−0.574689	+	0.818372i	$0.694877\pi$
$282$	−6.63100	−	21.1982i	−0.394870	−	1.26233i
$283$	5.69001	+	4.77449i	0.338236	+	0.283814i	0.796046	−	0.605236i	$-0.206921\pi$
$283$	5.69001	+	4.77449i	0.338236	+	0.283814i	−0.457810	+	0.889050i	$0.651366\pi$
$284$	−17.2772	−	14.4973i	−1.02521	−	0.860257i
$285$		0			0
$286$	0.489056	+	0.178002i	0.0289185	+	0.0105255i
$287$	1.78857	−	3.09789i	0.105576	−	0.182862i
$288$	−17.0612	−	17.2165i	−1.00534	−	1.01449i
$289$	−2.30851	−	3.99846i	−0.135795	−	0.235204i
$290$		0			0
$291$	14.7389	+	19.2984i	0.864007	+	1.13129i
$292$	1.53763	−	0.559652i	0.0899831	−	0.0327512i
$293$	0.328799	−	1.86471i	0.0192086	−	0.108937i	−0.973696	−	0.227851i	$-0.926830\pi$
$293$	0.328799	−	1.86471i	0.0192086	−	0.108937i	0.992905	+	0.118914i	$0.0379412\pi$
$294$	21.3627	−	11.0593i	1.24590	−	0.644991i
$295$		0			0
$296$	2.22728			0.129458
$297$	0.706072	−	1.33414i	0.0409705	−	0.0774145i
$298$	20.6670			1.19721
$299$	0.370191	−	0.310627i	0.0214087	−	0.0179640i
$300$		0			0
$301$	−0.662985	+	3.75998i	−0.0382138	+	0.216721i
$302$	−33.9759	+	12.3662i	−1.95510	+	0.711597i
$303$	−2.68037	+	6.42976i	−0.153983	+	0.369380i
$304$	−2.30413	−	13.0674i	−0.132151	−	0.749466i
$305$		0			0
$306$	23.2098	−	16.0955i	1.32682	−	0.920117i
$307$	−7.11195	+	12.3183i	−0.405900	+	0.703040i	−0.994426	−	0.105439i	$-0.966375\pi$
$307$	−7.11195	+	12.3183i	−0.405900	+	0.703040i	0.588525	+	0.808479i	$0.299709\pi$
$308$	0.215556	+	0.0784561i	0.0122825	+	0.00447045i
$309$	−0.871114	−	0.195193i	−0.0495559	−	0.0111041i
$310$		0			0
$311$	11.2222	+	9.41658i	0.636355	+	0.533965i	0.902896	−	0.429858i	$-0.141436\pi$
$311$	11.2222	+	9.41658i	0.636355	+	0.533965i	−0.266541	+	0.963824i	$0.585881\pi$
$312$	−0.211141	+	0.229375i	−0.0119535	+	0.0129858i
$313$	24.3151	+	8.84996i	1.37437	+	0.500229i	0.920466	−	0.390822i	$-0.127809\pi$
$313$	24.3151	+	8.84996i	1.37437	+	0.500229i	0.453902	+	0.891051i	$0.350032\pi$
$314$	11.6938	−	20.2542i	0.659917	−	1.14301i
$315$		0			0
$316$	−7.26032	−	12.5752i	−0.408425	−	0.707413i
$317$	3.17156	+	17.9868i	0.178133	+	1.01024i	0.934466	+	0.356053i	$0.115878\pi$
$317$	3.17156	+	17.9868i	0.178133	+	1.01024i	−0.756333	+	0.654187i	$0.773011\pi$
$318$	42.4873	−	5.49568i	2.38257	−	0.308182i
$319$	−1.65807	+	0.603489i	−0.0928342	+	0.0337889i
$320$		0			0
$321$	−26.2107	−	16.7817i	−1.46294	−	0.936661i
$322$	0.318527	−	0.267276i	0.0177508	−	0.0148947i
$323$	16.2822			0.905968
$324$	12.0197	+	14.5910i	0.667760	+	0.810609i
$325$		0			0
$326$	9.71387	−	8.15090i	0.538001	−	0.451437i
$327$	1.61188	+	1.03202i	0.0891371	+	0.0570709i
$328$	0.336144	−	1.90637i	0.0185605	−	0.105262i
$329$	2.23717	−	0.814263i	0.123339	−	0.0448918i
$330$		0			0
$331$	−5.49188	−	31.1460i	−0.301861	−	1.71194i	−0.637923	−	0.770100i	$-0.720206\pi$
$331$	−5.49188	−	31.1460i	−0.301861	−	1.71194i	0.336062	−	0.941840i	$-0.390905\pi$
$332$	−9.43539	−	16.3426i	−0.517835	−	0.896916i
$333$	32.7056	+	3.01074i	1.79226	+	0.164987i
$334$	15.8580	−	27.4668i	0.867709	−	1.50292i
$335$		0			0
$336$	1.67093	−	1.81522i	0.0911565	−	0.0990285i
$337$	5.87047	+	4.92591i	0.319785	+	0.268332i	0.788522	−	0.615006i	$-0.210846\pi$
$337$	5.87047	+	4.92591i	0.319785	+	0.268332i	−0.468737	+	0.883338i	$0.655291\pi$
$338$	18.9515	+	15.9022i	1.03083	+	0.864965i
$339$	15.3456	+	3.43854i	0.833461	+	0.186756i
$340$		0			0
$341$	0.797378	−	1.38110i	0.0431804	−	0.0747907i
$342$	1.75814	+	21.2015i	0.0950691	+	1.14644i
$343$	2.60503	+	4.51204i	0.140658	+	0.243627i
$344$	0.358777	+	2.03472i	0.0193439	+	0.109705i
$345$		0			0
$346$	17.3561	−	6.31710i	0.933069	−	0.339609i
$347$	0.616506	−	3.49638i	0.0330958	−	0.187695i	−0.963778	−	0.266706i	$-0.914065\pi$
$347$	0.616506	−	3.49638i	0.0330958	−	0.187695i	0.996874	+	0.0790102i	$0.0251760\pi$
$348$	1.01391	−	22.0749i	0.0543515	−	1.18334i
$349$	−3.58455	+	3.00779i	−0.191876	+	0.161003i	−0.733665	−	0.679511i	$-0.762192\pi$
$349$	−3.58455	+	3.00779i	−0.191876	+	0.161003i	0.541788	+	0.840515i	$0.317747\pi$
$350$		0			0
$351$	−3.41048	+	3.08276i	−0.182038	+	0.164545i
$352$	−2.34703			−0.125097
$353$	12.0080	−	10.0759i	0.639120	−	0.536286i	−0.264628	−	0.964351i	$-0.585249\pi$
$353$	12.0080	−	10.0759i	0.639120	−	0.536286i	0.903748	+	0.428065i	$0.140805\pi$
$354$	−3.93703	+	2.03817i	−0.209251	+	0.108327i
$355$		0			0
$356$	−12.2794	+	4.46934i	−0.650807	+	0.236874i
$357$	1.83756	+	2.40602i	0.0972539	+	0.127340i
$358$	0.929080	+	5.26907i	0.0491034	+	0.278479i
$359$	−1.36397	−	2.36247i	−0.0719876	−	0.124686i	0.827785	−	0.561046i	$-0.189601\pi$
$359$	−1.36397	−	2.36247i	−0.0719876	−	0.124686i	−0.899772	+	0.436360i	$0.856268\pi$
$360$		0			0
$361$	3.36800	−	5.83355i	0.177263	−	0.307029i
$362$	−13.5068	−	4.91608i	−0.709902	−	0.258383i
$363$	5.64440	+	18.0442i	0.296254	+	0.947074i
$364$	−0.535189	−	0.449077i	−0.0280516	−	0.0235380i
$365$		0			0
$366$	3.01266	+	9.63096i	0.157474	+	0.503418i
$367$	−29.9725	−	10.9091i	−1.56455	−	0.569450i	−0.592778	−	0.805366i	$-0.701969\pi$
$367$	−29.9725	−	10.9091i	−1.56455	−	0.569450i	−0.971773	+	0.235916i	$0.924191\pi$
$368$	−1.03478	+	1.79228i	−0.0539414	+	0.0934293i
$369$	7.51293	−	27.5390i	0.391107	−	1.43362i
$370$		0			0
$371$	0.797399	+	4.52228i	0.0413989	+	0.234785i
$372$	12.1225	+	15.8727i	0.628525	+	0.822962i
$373$	−5.82118	+	2.11873i	−0.301409	+	0.109704i	−0.488298	−	0.872677i	$-0.662382\pi$
$373$	−5.82118	+	2.11873i	−0.301409	+	0.109704i	0.186888	+	0.982381i	$0.440160\pi$
$374$	0.474924	−	2.69343i	0.0245577	−	0.139274i
$375$		0			0
$376$	0.986932	−	0.828134i	0.0508971	−	0.0427078i
$377$	5.37398			0.276774
$378$	−2.93451	+	2.65253i	−0.150935	+	0.136431i
$379$	24.4506			1.25595			0.627973	−	0.778235i	$-0.283885\pi$
$379$	24.4506			1.25595			0.627973	+	0.778235i	$0.283885\pi$
$380$		0			0
$381$	−0.858161	+	18.6838i	−0.0439649	+	0.957200i
$382$	−1.82668	+	10.3596i	−0.0934612	+	0.530045i
$383$	7.01885	−	2.55465i	0.358647	−	0.130537i	−0.156411	−	0.987692i	$-0.549993\pi$
$383$	7.01885	−	2.55465i	0.358647	−	0.130537i	0.515058	+	0.857155i	$0.327770\pi$
$384$	1.08330	−	2.59866i	0.0552821	−	0.132612i
$385$		0			0
$386$	3.97075	+	6.87755i	0.202106	+	0.350058i
$387$	2.51787	+	30.3631i	0.127990	+	1.54344i
$388$	−14.7240	+	25.5028i	−0.747500	+	1.29471i
$389$	−26.7061	−	9.72022i	−1.35405	−	0.492835i	−0.439842	−	0.898075i	$-0.644966\pi$
$389$	−26.7061	−	9.72022i	−1.35405	−	0.492835i	−0.914210	+	0.405240i	$0.867188\pi$
$390$		0			0
$391$	−1.94539	−	1.63238i	−0.0983826	−	0.0825528i
$392$	1.06889	+	0.896909i	0.0539873	+	0.0453007i
$393$	−14.5177	+	15.7714i	−0.732320	+	0.795562i
$394$	−19.7356	−	7.18318i	−0.994266	−	0.361883i
$395$		0			0
$396$	1.82282	+	0.167801i	0.0916001	+	0.00843231i
$397$	−14.4933	−	25.1031i	−0.727396	−	1.25989i	−0.957980	−	0.286834i	$-0.907397\pi$
$397$	−14.4933	−	25.1031i	−0.727396	−	1.25989i	0.230585	−	0.973052i	$-0.425936\pi$
$398$	−4.18777	−	23.7501i	−0.209914	−	1.19048i
$399$	−2.26149	+	0.292520i	−0.113216	+	0.0146443i
$400$		0			0
$401$	5.27642	−	29.9241i	0.263492	−	1.49434i	−0.509804	−	0.860291i	$-0.670282\pi$
$401$	5.27642	−	29.9241i	0.263492	−	1.49434i	0.773296	−	0.634046i	$-0.218607\pi$
$402$	−26.1620	−	16.7505i	−1.30484	−	0.835437i
$403$	−3.72071	+	3.12205i	−0.185342	+	0.155520i
$404$	−8.44780			−0.420294
$405$		0			0
$406$	4.62398			0.229484
$407$	2.43627	−	2.04428i	0.120762	−	0.101331i
$408$	1.37975	+	0.883398i	0.0683078	+	0.0437347i
$409$	−0.726985	+	4.12294i	−0.0359471	+	0.203866i	−0.997492	−	0.0707824i	$-0.977450\pi$
$409$	−0.726985	+	4.12294i	−0.0359471	+	0.203866i	0.961545	+	0.274649i	$0.0885615\pi$
$410$		0			0
$411$	−28.3402	+	3.66577i	−1.39792	+	0.180819i
$412$	−0.187992	−	1.06615i	−0.00926168	−	0.0525256i
$413$	−0.237598	−	0.411531i	−0.0116914	−	0.0202501i
$414$	1.91549	−	2.70940i	0.0941414	−	0.133160i
$415$		0			0
$416$	6.71711	+	2.44483i	0.329333	+	0.119868i
$417$	14.4633	−	15.7123i	0.708271	−	0.769436i
$418$	1.57807	+	1.32416i	0.0771858	+	0.0647666i
$419$	−17.7641	−	14.9058i	−0.867832	−	0.728197i	0.0958087	−	0.995400i	$-0.469456\pi$
$419$	−17.7641	−	14.9058i	−0.867832	−	0.728197i	−0.963640	+	0.267203i	$0.913901\pi$
$420$		0			0
$421$	6.96568	+	2.53530i	0.339487	+	0.123563i	0.506137	−	0.862453i	$-0.331073\pi$
$421$	6.96568	+	2.53530i	0.339487	+	0.123563i	−0.166651	+	0.986016i	$0.553295\pi$
$422$	2.47913	−	4.29399i	0.120682	−	0.209028i
$423$	15.6117	−	10.8263i	0.759065	−	0.526394i
$424$	1.24250	+	2.15207i	0.0603411	+	0.104514i
$425$		0			0
$426$	14.4907	−	34.7606i	0.702075	−	1.68416i
$427$	−1.01641	+	0.369944i	−0.0491877	+	0.0179029i
$428$	6.55396	−	37.1694i	0.316798	−	1.79665i
$429$	−0.0204250	+	0.444692i	−0.000986129	+	0.0214699i
$430$		0			0
$431$	3.55875			0.171419			0.0857095	−	0.996320i	$-0.472684\pi$
$431$	3.55875			0.171419			0.0857095	+	0.996320i	$0.472684\pi$
$432$	9.20941	−	17.4014i	0.443088	−	0.837223i
$433$	−39.5383			−1.90009			−0.950046	−	0.312111i	$-0.898964\pi$
$433$	−39.5383			−1.90009			−0.950046	+	0.312111i	$0.898964\pi$
$434$	−3.20145	+	2.68633i	−0.153674	+	0.128948i
$435$		0			0
$436$	−0.403048	+	2.28580i	−0.0193025	+	0.109470i
$437$	1.79745	−	0.654218i	0.0859837	−	0.0312955i
$438$	1.65840	+	2.17144i	0.0792415	+	0.103755i
$439$	−0.368776	−	2.09143i	−0.0176007	−	0.0998186i	0.974742	−	0.223334i	$-0.0716942\pi$
$439$	−0.368776	−	2.09143i	−0.0176007	−	0.0998186i	−0.992343	+	0.123516i	$0.960583\pi$
$440$		0			0
$441$	14.4834	+	14.6152i	0.689684	+	0.695962i
$442$	−4.16487	+	7.21377i	−0.198103	+	0.343124i
$443$	−15.2652	−	5.55606i	−0.725270	−	0.263977i	−0.0471084	−	0.998890i	$-0.515001\pi$
$443$	−15.2652	−	5.55606i	−0.725270	−	0.263977i	−0.678161	+	0.734913i	$0.737223\pi$
$444$	11.8910	+	38.0136i	0.564323	+	1.80404i
$445$		0			0
$446$	27.9502	+	23.4530i	1.32348	+	1.11053i
$447$	5.27752	+	16.8713i	0.249618	+	0.797987i
$448$	3.10260	+	1.12926i	0.146584	+	0.0533523i
$449$	−17.8132	+	30.8534i	−0.840658	+	1.45606i	0.0486805	+	0.998814i	$0.484498\pi$
$449$	−17.8132	+	30.8534i	−0.840658	+	1.45606i	−0.889339	+	0.457249i	$0.848835\pi$
$450$		0			0
$451$	−1.38205	−	2.39378i	−0.0650781	−	0.112719i
$452$	3.31168	+	18.7815i	0.155768	+	0.883406i
$453$	−18.7712	−	24.5782i	−0.881947	−	1.15478i
$454$	−10.1736	+	3.70288i	−0.477470	+	0.173785i
$455$		0			0
$456$	−1.09587	+	0.567320i	−0.0513186	+	0.0265672i
$457$	19.7485	−	16.5710i	0.923796	−	0.775157i	−0.0508970	−	0.998704i	$-0.516208\pi$
$457$	19.7485	−	16.5710i	0.923796	−	0.775157i	0.974693	+	0.223547i	$0.0717636\pi$
$458$	−43.6242			−2.03842
$459$	19.0663	+	14.8370i	0.889938	+	0.692532i
$460$		0			0
$461$	−26.3039	+	22.0716i	−1.22509	+	1.02798i	−0.226551	+	0.973999i	$0.572745\pi$
$461$	−26.3039	+	22.0716i	−1.22509	+	1.02798i	−0.998542	+	0.0539762i	$0.982810\pi$
$462$	−0.0175745	+	0.382630i	−0.000817639	+	0.0178016i
$463$	−5.12509	+	29.0659i	−0.238183	+	1.35080i	0.597622	+	0.801778i	$0.296112\pi$
$463$	−5.12509	+	29.0659i	−0.238183	+	1.35080i	−0.835805	+	0.549026i	$0.814999\pi$
$464$	−21.6265	+	7.87140i	−1.00398	+	0.365421i
$465$		0			0
$466$	−8.98908	−	50.9796i	−0.416411	−	2.36158i
$467$	−8.31964	−	14.4100i	−0.384987	−	0.666817i	0.606780	−	0.794869i	$-0.292461\pi$
$467$	−8.31964	−	14.4100i	−0.384987	−	0.666817i	−0.991767	+	0.128053i	$0.959127\pi$
$468$	−5.04205	−	2.37902i	−0.233069	−	0.109970i
$469$	1.66488	−	2.88366i	0.0768770	−	0.133155i
$470$		0			0
$471$	19.5205	+	4.37400i	0.899455	+	0.201543i
$472$	−0.196991	−	0.165295i	−0.00906725	−	0.00760833i
$473$	2.25999	+	1.89635i	0.103914	+	0.0871944i
$474$	16.4211	−	17.8392i	0.754245	−	0.819380i
$475$		0			0
$476$	−1.83571	+	3.17955i	−0.0841397	+	0.145734i
$477$	15.3359	+	33.2808i	0.702184	+	1.52382i
$478$	9.36897	+	16.2275i	0.428527	+	0.742230i
$479$	0.965663	+	5.47655i	0.0441223	+	0.250230i	0.998889	−	0.0471262i	$-0.0150063\pi$
$479$	0.965663	+	5.47655i	0.0441223	+	0.250230i	−0.954767	+	0.297356i	$0.903895\pi$
$480$		0			0
$481$	−9.10199	+	3.31285i	−0.415015	+	0.151053i
$482$	10.1108	−	57.3411i	0.460534	−	2.61182i
$483$	0.299528	+	0.191775i	0.0136290	+	0.00872609i
$484$	−17.5638	+	14.7378i	−0.798354	+	0.669898i
$485$		0			0
$486$	−17.2608	+	26.4287i	−0.782968	+	1.19883i
$487$	−17.5069			−0.793314			−0.396657	−	0.917967i	$-0.629830\pi$
$487$	−17.5069			−0.793314			−0.396657	+	0.917967i	$0.629830\pi$
$488$	−0.448393	+	0.376246i	−0.0202978	+	0.0170319i
$489$	9.13446	+	5.84843i	0.413075	+	0.264475i
$490$		0			0
$491$	25.2199	−	9.17930i	1.13816	−	0.414256i	0.296911	−	0.954905i	$-0.404044\pi$
$491$	25.2199	−	9.17930i	1.13816	−	0.414256i	0.841248	+	0.540649i	$0.181821\pi$
$492$	34.3311	−	4.44068i	1.54777	−	0.200201i
$493$	−4.90396	−	27.8118i	−0.220863	−	1.25258i
$494$	−3.13704	−	5.43351i	−0.141142	−	0.244465i
$495$		0			0
$496$	10.4003	−	18.0139i	0.466988	−	0.808847i
$497$	3.79324	+	1.38063i	0.170150	+	0.0619295i
$498$	21.3406	−	23.1835i	0.956294	−	1.03888i
$499$	4.46524	+	3.74678i	0.199892	+	0.167729i	0.737239	−	0.675632i	$-0.236129\pi$
$499$	4.46524	+	3.74678i	0.199892	+	0.167729i	−0.537347	+	0.843361i	$0.680574\pi$
$500$		0			0
$501$	26.4718	+	5.93160i	1.18267	+	0.265004i
$502$	−22.3091	−	8.11986i	−0.995705	−	0.362407i
$503$	15.2521	−	26.4175i	0.680059	−	1.17790i	−0.294904	−	0.955527i	$-0.595288\pi$
$503$	15.2521	−	26.4175i	0.680059	−	1.17790i	0.974963	−	0.222369i	$-0.0713790\pi$
$504$	−0.207508	−	0.0979097i	−0.00924316	−	0.00436124i
$505$		0			0
$506$	−0.0557931	−	0.316419i	−0.00248031	−	0.0140665i
$507$	−8.14218	+	19.5317i	−0.361607	+	0.867433i
$508$	−21.3139	+	7.75764i	−0.945654	+	0.344190i
$509$	−5.46355	+	30.9853i	−0.242167	+	1.37340i	0.584813	+	0.811168i	$0.301168\pi$
$509$	−5.46355	+	30.9853i	−0.242167	+	1.37340i	−0.826980	+	0.562231i	$0.809943\pi$
$510$		0			0
$511$	−0.224349	+	0.188252i	−0.00992464	+	0.00832776i
$512$	−32.1543			−1.42103
$513$	−16.8587	+	6.84925i	−0.744330	+	0.302402i
$514$	−7.46958			−0.329469
$515$		0			0
$516$	−32.8117	+	16.9863i	−1.44446	+	0.747782i
$517$	0.319449	−	1.81168i	0.0140493	−	0.0796778i
$518$	−7.83171	+	2.85051i	−0.344106	+	0.125244i
$519$	9.58897	+	12.5554i	0.420909	+	0.551120i
$520$		0			0
$521$	−4.14101	−	7.17245i	−0.181421	−	0.314231i	0.760944	−	0.648818i	$-0.224736\pi$
$521$	−4.14101	−	7.17245i	−0.181421	−	0.314231i	−0.942365	+	0.334587i	$0.891403\pi$
$522$	35.6848	−	9.38864i	1.56188	−	0.410930i
$523$	−8.91120	+	15.4347i	−0.389660	+	0.674910i	−0.992404	−	0.123024i	$-0.960741\pi$
$523$	−8.91120	+	15.4347i	−0.389660	+	0.674910i	0.602744	+	0.797935i	$0.294074\pi$
$524$	−24.4278	−	8.89098i	−1.06713	−	0.388404i
$525$		0			0
$526$	34.3001	+	28.7812i	1.49556	+	1.25492i
$527$	19.5527	+	16.4067i	0.851730	+	0.714686i
$528$	−0.569154	−	1.81949i	−0.0247693	−	0.0791831i
$529$	21.3326	+	7.76443i	0.927504	+	0.337584i
$530$		0			0
$531$	−2.66920	−	2.69350i	−0.115834	−	0.116888i
$532$	−1.38268	−	2.39488i	−0.0599469	−	0.103831i
$533$	1.46185	+	8.29054i	0.0633196	+	0.359103i
$534$	−13.2439	−	17.3409i	−0.573118	−	0.750416i
$535$		0			0
$536$	0.312899	−	1.77454i	0.0135152	−	0.0766483i
$537$	−4.06412	+	2.10396i	−0.175380	+	0.0907925i
$538$	−39.2970	+	32.9741i	−1.69421	+	1.42161i
$539$	1.99241			0.0858191
$540$		0			0
$541$	−34.8916			−1.50011			−0.750054	−	0.661376i	$-0.769973\pi$
$541$	−34.8916			−1.50011			−0.750054	+	0.661376i	$0.769973\pi$
$542$	−44.6412	+	37.4584i	−1.91750	+	1.60898i
$543$	0.564101	−	12.2816i	0.0242079	−	0.527052i
$544$	6.52300	−	36.9938i	0.279671	−	1.58610i
$545$		0			0
$546$	0.448872	−	1.07677i	0.0192099	−	0.0460814i
$547$	−4.30509	−	24.4154i	−0.184072	−	1.04393i	−0.927142	−	0.374711i	$-0.877742\pi$
$547$	−4.30509	−	24.4154i	−0.184072	−	1.04393i	0.743069	−	0.669214i	$-0.233369\pi$
$548$	−17.3273	−	30.0118i	−0.740187	−	1.28204i
$549$	−7.09285	+	4.91873i	−0.302715	+	0.209926i
$550$		0			0
$551$	19.9885	+	7.27523i	0.851540	+	0.309935i
$552$	0.187810	+	0.0420831i	0.00799373	+	0.00179117i
$553$	1.99088	+	1.67054i	0.0846607	+	0.0710388i
$554$	−30.5984	−	25.6751i	−1.30000	−	1.09083i
$555$		0			0
$556$	24.3363	+	8.85768i	1.03209	+	0.375649i
$557$	15.5900	−	27.0026i	0.660568	−	1.14414i	−0.319898	−	0.947452i	$-0.603649\pi$
$557$	15.5900	−	27.0026i	0.660568	−	1.14414i	0.980467	−	0.196686i	$-0.0630180\pi$
$558$	−19.2522	+	27.2316i	−0.815012	+	1.15281i
$559$	−4.49262	−	7.78145i	−0.190018	−	0.329120i
$560$		0			0
$561$	2.32003	−	0.300093i	0.0979519	−	0.0126699i
$562$	16.5951	−	6.04011i	0.700020	−	0.254787i
$563$	1.99921	−	11.3381i	0.0842567	−	0.477844i	−0.913258	−	0.407382i	$-0.866442\pi$
$563$	1.99921	−	11.3381i	0.0842567	−	0.477844i	0.997514	−	0.0704615i	$-0.0224472\pi$
$564$	19.4030	+	12.4230i	0.817015	+	0.523102i
$565$		0			0
$566$	−15.0410			−0.632219
$567$	−2.91473	−	1.71822i	−0.122407	−	0.0721584i
$568$	2.18446			0.0916580
$569$	0.688909	−	0.578063i	0.0288805	−	0.0242337i	−0.628233	−	0.778025i	$-0.716222\pi$
$569$	0.688909	−	0.578063i	0.0288805	−	0.0242337i	0.657114	+	0.753791i	$0.271777\pi$
$570$		0			0
$571$	7.41437	−	42.0490i	0.310282	−	1.75969i	−0.287256	−	0.957854i	$-0.592743\pi$
$571$	7.41437	−	42.0490i	0.310282	−	1.75969i	0.597538	−	0.801841i	$-0.296146\pi$
$572$	−0.507292	+	0.184639i	−0.0212109	+	0.00772015i
$573$	−8.92347	+	1.15424i	−0.372783	+	0.0482190i
$574$	1.25783	+	7.13351i	0.0525008	+	0.297747i
$575$		0			0
$576$	26.2367	+	2.41524i	1.09319	+	0.100635i
$577$	−6.22274	+	10.7781i	−0.259056	+	0.448698i	−0.965989	−	0.258582i	$-0.916745\pi$
$577$	−6.22274	+	10.7781i	−0.259056	+	0.448698i	0.706933	+	0.707280i	$0.250078\pi$
$578$	8.78546	+	3.19765i	0.365427	+	0.133005i
$579$	−4.60046	+	4.99775i	−0.191189	+	0.207699i
$580$		0			0
$581$	2.58731	+	2.17101i	0.107340	+	0.0900688i
$582$	−47.9822	−	10.7515i	−1.98893	−	0.445664i
$583$	3.33434	+	1.21360i	0.138094	+	0.0502622i
$584$	−0.0792431	+	0.137253i	−0.00327910	+	0.00567957i
$585$		0			0
$586$	1.91711	+	3.32053i	0.0791950	+	0.137170i
$587$	−1.91101	−	10.8379i	−0.0788758	−	0.447327i	−0.998511	−	0.0545530i	$-0.982627\pi$
$587$	−1.91101	−	10.8379i	−0.0788758	−	0.447327i	0.919635	−	0.392774i	$-0.128484\pi$
$588$	−9.60115	+	23.0315i	−0.395945	+	0.949804i
$589$	−18.0658	+	6.57541i	−0.744388	+	0.270935i
$590$		0			0
$591$	0.824242	−	17.9453i	0.0339048	−	0.738172i
$592$	31.7767	−	26.6638i	1.30601	−	1.09588i
$593$	9.57442			0.393174			0.196587	−	0.980486i	$-0.437014\pi$
$593$	9.57442			0.393174			0.196587	+	0.980486i	$0.437014\pi$
$594$	0.641273	+	2.98856i	0.0263117	+	0.122622i
$595$		0			0
$596$	−16.4222	+	13.7798i	−0.672678	+	0.564444i
$597$	18.3188	−	9.48348i	0.749738	−	0.388133i
$598$	−0.169926	+	0.963696i	−0.00694878	+	0.0394085i
$599$	−30.9256	+	11.2560i	−1.26359	+	0.459908i	−0.884971	−	0.465646i	$-0.845822\pi$
$599$	−30.9256	+	11.2560i	−1.26359	+	0.459908i	−0.378616	+	0.925554i	$0.623600\pi$
$600$		0			0
$601$	−2.22127	−	12.5974i	−0.0906074	−	0.513860i	−0.996005	−	0.0892957i	$-0.971538\pi$
$601$	−2.22127	−	12.5974i	−0.0906074	−	0.513860i	0.905398	−	0.424564i	$-0.139573\pi$
$602$	−3.86563	−	6.69547i	−0.157551	−	0.272887i
$603$	6.99338	−	25.6345i	0.284793	−	1.04392i
$604$	18.7523	−	32.4800i	0.763021	−	1.32159i
$605$		0			0
$606$	−4.21128	−	13.4627i	−0.171072	−	0.546886i
$607$	28.7032	+	24.0848i	1.16503	+	0.977573i	0.999962	−	0.00870958i	$-0.00277238\pi$
$607$	28.7032	+	24.0848i	1.16503	+	0.977573i	0.165064	+	0.986283i	$0.447217\pi$
$608$	21.6745	+	18.1871i	0.879018	+	0.737583i
$609$	1.18078	+	3.77475i	0.0478477	+	0.152961i
$610$		0			0
$611$	−2.80143	+	4.85221i	−0.113334	+	0.196300i
$612$	−7.71096	+	28.2649i	−0.311697	+	1.14254i
$613$	1.30760	+	2.26483i	0.0528136	+	0.0914758i	0.891224	−	0.453564i	$-0.149848\pi$
$613$	1.30760	+	2.26483i	0.0528136	+	0.0914758i	−0.838410	+	0.545040i	$0.816514\pi$
$614$	−5.00156	−	28.3653i	−0.201847	−	1.14473i
$615$		0			0
$616$	−0.0208779	+	0.00759892i	−0.000841193	+	0.000306169i
$617$	1.11998	−	6.35172i	0.0450887	−	0.255711i	−0.953929	−	0.300034i	$-0.903002\pi$
$617$	1.11998	−	6.35172i	0.0450887	−	0.255711i	0.999017	+	0.0443232i	$0.0141131\pi$
$618$	1.60535	−	0.831075i	0.0645766	−	0.0334307i
$619$	−0.0522006	+	0.0438015i	−0.00209812	+	0.00176053i	−0.643836	−	0.765163i	$-0.722658\pi$
$619$	−0.0522006	+	0.0438015i	−0.00209812	+	0.00176053i	0.641738	+	0.766924i	$0.278214\pi$
$620$		0			0
$621$	2.70094	+	0.871826i	0.108385	+	0.0349852i
$622$	−29.6649			−1.18945
$623$	1.79164	−	1.50336i	0.0717804	−	0.0602309i
$624$	−0.266407	+	5.80018i	−0.0106648	+	0.232193i
$625$		0			0
$626$	−49.2370	+	17.9208i	−1.96791	+	0.716260i
$627$	−0.677989	+	1.62638i	−0.0270763	+	0.0649514i
$628$	4.21263	+	23.8910i	0.168102	+	0.953355i
$629$	25.4508	+	44.0821i	1.01479	+	1.75767i
$630$		0			0
$631$	−22.5451	+	39.0492i	−0.897506	+	1.55453i	−0.0668329	+	0.997764i	$0.521289\pi$
$631$	−22.5451	+	39.0492i	−0.897506	+	1.55453i	−0.830673	+	0.556761i	$0.812044\pi$
$632$	1.32159	+	0.481019i	0.0525700	+	0.0191339i
$633$	4.13843	+	0.927309i	0.164488	+	0.0368572i
$634$	−28.3317	−	23.7732i	−1.12520	−	0.944153i
$635$		0			0
$636$	−30.0965	+	32.6956i	−1.19340	+	1.29646i
$637$	−5.70220	−	2.07543i	−0.225930	−	0.0822316i
$638$	1.78651	−	3.09432i	0.0707284	−	0.122505i
$639$	32.0769	+	2.95286i	1.26894	+	0.116813i
$640$		0			0
$641$	6.39211	+	36.2514i	0.252473	+	1.43185i	0.802477	+	0.596683i	$0.203515\pi$
$641$	6.39211	+	36.2514i	0.252473	+	1.43185i	−0.550004	+	0.835162i	$0.685374\pi$
$642$	62.5017	−	8.08451i	2.46675	−	0.319070i
$643$	−4.60918	+	1.67760i	−0.181768	+	0.0661582i	−0.431301	−	0.902208i	$-0.641945\pi$
$643$	−4.60918	+	1.67760i	−0.181768	+	0.0661582i	0.249533	+	0.968366i	$0.419723\pi$
$644$	−0.0748965	+	0.424759i	−0.00295134	+	0.0167379i
$645$		0			0
$646$	−25.2572	+	21.1933i	−0.993730	+	0.833838i
$647$	−37.6519			−1.48025			−0.740125	−	0.672469i	$-0.765234\pi$
$647$	−37.6519			−1.48025			−0.740125	+	0.672469i	$0.765234\pi$
$648$	−1.80021	−	0.334271i	−0.0707188	−	0.0131314i
$649$	−0.367190			−0.0144135
$650$		0			0
$651$	−3.01049	−	1.92750i	−0.117990	−	0.0755445i
$652$	−2.28406	+	12.9536i	−0.0894507	+	0.507300i
$653$	−21.5387	+	7.83944i	−0.842874	+	0.306781i	−0.727132	−	0.686498i	$-0.759147\pi$
$653$	−21.5387	+	7.83944i	−0.842874	+	0.306781i	−0.115743	+	0.993279i	$0.536925\pi$
$654$	−3.84366	+	0.497172i	−0.150299	+	0.0194410i
$655$		0			0
$656$	−18.0263	−	31.2224i	−0.703807	−	1.21903i
$657$	−1.34915	+	1.90832i	−0.0526353	+	0.0744508i
$658$	−2.41046	+	4.17504i	−0.0939694	+	0.162760i
$659$	4.41936	+	1.60852i	0.172154	+	0.0626589i	0.426659	−	0.904412i	$-0.359690\pi$
$659$	4.41936	+	1.60852i	0.172154	+	0.0626589i	−0.254505	+	0.967071i	$0.581913\pi$
$660$		0			0
$661$	−25.3416	−	21.2641i	−0.985675	−	0.827079i	−0.000739053	−	1.00000i	$-0.500235\pi$
$661$	−25.3416	−	21.2641i	−0.985675	−	0.827079i	−0.984936	+	0.172920i	$0.944680\pi$
$662$	49.0593	+	41.1657i	1.90675	+	1.59995i
$663$	−6.95245	−	1.55785i	−0.270011	−	0.0605020i
$664$	1.71752	+	0.625125i	0.0666526	+	0.0242596i
$665$		0			0
$666$	−54.6521	+	37.9000i	−2.11773	+	1.46859i
$667$	−1.65884	−	2.87319i	−0.0642304	−	0.111250i
$668$	5.71277	+	32.3987i	0.221034	+	1.25354i
$669$	−12.0083	+	28.8059i	−0.464268	+	1.11370i
$670$		0			0
$671$	−0.145135	+	0.823103i	−0.00560288	+	0.0317755i
$672$	−0.241383	+	5.25537i	−0.00931155	+	0.202730i
$673$	34.0702	−	28.5883i	1.31331	−	1.10200i	0.325631	−	0.945497i	$-0.394423\pi$
$673$	34.0702	−	28.5883i	1.31331	−	1.10200i	0.987678	−	0.156500i	$-0.0500212\pi$
$674$	−15.5180			−0.597731
$675$		0			0
$676$	−25.6619			−0.986996
$677$	6.56883	−	5.51191i	0.252461	−	0.211840i	−0.507770	−	0.861492i	$-0.669530\pi$
$677$	6.56883	−	5.51191i	0.252461	−	0.211840i	0.760231	+	0.649653i	$0.225086\pi$
$678$	−28.2800	+	14.6403i	−1.08609	+	0.562257i
$679$	0.915233	−	5.19055i	0.0351234	−	0.199195i
$680$		0			0
$681$	−5.62075	−	7.35956i	−0.215388	−	0.282019i
$682$	0.560765	+	3.18026i	0.0214728	+	0.121778i
$683$	21.9820	+	38.0739i	0.841117	+	1.45686i	0.888951	+	0.458002i	$0.151435\pi$
$683$	21.9820	+	38.0739i	0.841117	+	1.45686i	−0.0478347	+	0.998855i	$0.515232\pi$
$684$	−15.5332	−	15.6746i	−0.593928	−	0.599334i
$685$		0			0
$686$	−9.91390	−	3.60836i	−0.378514	−	0.137768i
$687$	−11.1399	−	35.6123i	−0.425013	−	1.35869i
$688$	29.4773	+	24.7344i	1.12381	+	0.942991i
$689$	−8.27859	−	6.94656i	−0.315389	−	0.264643i
$690$		0			0
$691$	20.7711	+	7.56005i	0.790169	+	0.287598i	0.705406	−	0.708803i	$-0.250765\pi$
$691$	20.7711	+	7.56005i	0.790169	+	0.287598i	0.0847628	+	0.996401i	$0.472987\pi$
$692$	−9.57933	+	16.5919i	−0.364152	+	0.630729i
$693$	−0.316845	+	0.0833617i	−0.0120359	+	0.00316665i
$694$	3.59462	+	6.22607i	0.136450	+	0.236338i
$695$		0			0
$696$	1.29910	+	1.70098i	0.0492423	+	0.0644756i
$697$	41.5717	−	15.1309i	1.57464	−	0.573123i
$698$	1.64538	−	9.33144i	0.0622787	−	0.353200i
$699$	39.3213	−	20.3563i	1.48727	−	0.769947i
$700$		0			0
$701$	−0.728282			−0.0275068			−0.0137534	−	0.999905i	$-0.504378\pi$
$701$	−0.728282			−0.0275068			−0.0137534	+	0.999905i	$0.504378\pi$
$702$	1.27780	−	9.22116i	0.0482274	−	0.348030i
$703$	−38.3398			−1.44601
$704$	1.95440	−	1.63993i	0.0736591	−	0.0618073i
$705$		0			0
$706$	−5.51192	+	31.2596i	−0.207444	+	1.17647i
$707$	1.42080	−	0.517130i	0.0534348	−	0.0194487i
$708$	1.76944	−	4.24458i	0.0664996	−	0.159521i
$709$	2.85514	+	16.1923i	0.107227	+	0.608115i	0.990307	+	0.138893i	$0.0443544\pi$
$709$	2.85514	+	16.1923i	0.107227	+	0.608115i	−0.883080	+	0.469222i	$0.844535\pi$
$710$		0			0
$711$	18.7562	+	8.84981i	0.703411	+	0.331894i
$712$	0.632829	−	1.09609i	0.0237163	−	0.0410778i
$713$	2.81771	+	1.02556i	0.105524	+	0.0384076i
$714$	−5.98216	−	1.34044i	−0.223877	−	0.0501646i
$715$		0			0
$716$	−4.25144	−	3.56738i	−0.158884	−	0.133319i
$717$	−10.8548	+	11.7922i	−0.405379	+	0.440386i
$718$	5.19084	+	1.88931i	0.193720	+	0.0705085i
$719$	18.6844	−	32.3624i	0.696811	−	1.20691i	−0.272755	−	0.962083i	$-0.587935\pi$
$719$	18.6844	−	32.3624i	0.696811	−	1.20691i	0.969566	−	0.244829i	$-0.0787318\pi$
$720$		0			0
$721$	0.0968819	+	0.167804i	0.00360807	+	0.00624936i
$722$	2.36859	+	13.4329i	0.0881497	+	0.499922i
$723$	49.3919	−	6.38878i	1.83690	−	0.237601i
$724$	14.0105	−	5.09939i	0.520694	−	0.189517i
$725$		0			0
$726$	−32.2423	−	20.6435i	−1.19662	−	0.766150i
$727$	3.88514	−	3.26002i	0.144092	−	0.120907i	−0.567893	−	0.823103i	$-0.692241\pi$
$727$	3.88514	−	3.26002i	0.144092	−	0.120907i	0.711984	+	0.702195i	$0.247797\pi$
$728$	0.0676673			0.00250792
$729$	−25.9826	−	7.34192i	−0.962319	−	0.271923i
$730$		0			0
$731$	−36.1714	+	30.3514i	−1.33785	+	1.12259i
$732$	−8.81539	−	5.64413i	−0.325826	−	0.208613i
$733$	4.35439	−	24.6950i	0.160833	−	0.912129i	−0.792424	−	0.609970i	$-0.791181\pi$
$733$	4.35439	−	24.6950i	0.160833	−	0.912129i	0.953257	−	0.302159i	$-0.0977075\pi$
$734$	60.6931	−	22.0905i	2.24022	−	0.815375i
$735$		0			0
$736$	−0.766310	−	4.34596i	−0.0282466	−	0.160194i
$737$	−1.28647	−	2.22824i	−0.0473879	−	0.0820783i
$738$	24.1911	+	52.4977i	0.890487	+	1.93247i
$739$	−23.1354	+	40.0717i	−0.851050	+	1.47406i	0.0292117	+	0.999573i	$0.490700\pi$
$739$	−23.1354	+	40.0717i	−0.851050	+	1.47406i	−0.880262	+	0.474489i	$0.842633\pi$
$740$		0			0
$741$	3.63453	−	3.94840i	0.133518	−	0.145048i
$742$	−7.12322	−	5.97709i	−0.261502	−	0.219426i
$743$	−25.1018	−	21.0629i	−0.920896	−	0.772723i	0.0532649	−	0.998580i	$-0.483037\pi$
$743$	−25.1018	−	21.0629i	−0.920896	−	0.772723i	−0.974160	+	0.225857i	$0.927482\pi$
$744$	−1.88764	−	0.422968i	−0.0692042	−	0.0155068i
$745$		0			0
$746$	6.27208	−	10.8636i	0.229637	−	0.397743i
$747$	24.3752	+	11.5011i	0.891842	+	0.420802i
$748$	1.41848	+	2.45688i	0.0518647	+	0.0898323i
$749$	1.17303	+	6.65257i	0.0428615	+	0.243080i
$750$		0			0
$751$	11.8075	−	4.29756i	0.430860	−	0.156820i	−0.117481	−	0.993075i	$-0.537482\pi$
$751$	11.8075	−	4.29756i	0.430860	−	0.156820i	0.548341	+	0.836255i	$0.315260\pi$
$752$	4.16662	−	23.6301i	0.151941	−	0.861700i
$753$	0.931722	−	20.2854i	0.0339538	−	0.739240i
$754$	−8.33617	+	6.99488i	−0.303585	+	0.254738i
$755$		0			0
$756$	0.563203	−	4.06432i	0.0204835	−	0.147818i
$757$	35.3551			1.28500			0.642501	−	0.766285i	$-0.277897\pi$
$757$	35.3551			1.28500			0.642501	+	0.766285i	$0.277897\pi$
$758$	−37.9281	+	31.8254i	−1.37761	+	1.15595i
$759$	0.244059	−	0.126347i	0.00885876	−	0.00458611i
$760$		0			0
$761$	4.34791	−	1.58251i	0.157612	−	0.0573660i	−0.262009	−	0.965065i	$-0.584385\pi$
$761$	4.34791	−	1.58251i	0.157612	−	0.0573660i	0.419621	+	0.907699i	$0.362163\pi$
$762$	−22.9880	−	30.0995i	−0.832768	−	1.09039i
$763$	−0.0721376	−	0.409113i	−0.00261156	−	0.0148109i
$764$	−5.45584	−	9.44980i	−0.197386	−	0.341882i
$765$		0			0
$766$	−7.56253	+	13.0987i	−0.273245	+	0.473275i
$767$	1.05088	+	0.382490i	0.0379452	+	0.0138109i
$768$	−7.38076	−	23.5950i	−0.266330	−	0.851412i
$769$	−10.2592	−	8.60849i	−0.369956	−	0.310430i	0.438788	−	0.898591i	$-0.355408\pi$
$769$	−10.2592	−	8.60849i	−0.369956	−	0.310430i	−0.808744	+	0.588161i	$0.799852\pi$
$770$		0			0
$771$	−1.90743	−	6.09774i	−0.0686946	−	0.219605i
$772$	−7.74084	−	2.81744i	−0.278599	−	0.101402i
$773$	11.6796	−	20.2297i	0.420087	−	0.727612i	−0.575861	−	0.817548i	$-0.695333\pi$
$773$	11.6796	−	20.2297i	0.420087	−	0.727612i	0.995948	+	0.0899361i	$0.0286663\pi$
$774$	−43.4270	−	43.8222i	−1.56095	−	1.57516i
$775$		0			0
$776$	−0.495282	−	2.80888i	−0.0177796	−	0.100833i
$777$	−4.32690	−	5.66545i	−0.155227	−	0.203247i
$778$	54.0788	−	19.6831i	1.93882	−	0.705672i
$779$	−5.78629	+	32.8157i	−0.207316	+	1.17574i
$780$		0			0
$781$	2.38944	−	2.00498i	0.0855010	−	0.0717438i
$782$	5.14244			0.183893
$783$	16.7768	+	26.7335i	0.599555	+	0.955378i
$784$	25.9873			0.928118
$785$		0			0
$786$	1.99161	−	43.3613i	0.0710385	−	1.54664i
$787$	−7.91498	+	44.8881i	−0.282139	+	1.60009i	0.433193	+	0.901301i	$0.357387\pi$
$787$	−7.91498	+	44.8881i	−0.282139	+	1.60009i	−0.715331	+	0.698786i	$0.753724\pi$
$788$	20.4715	−	7.45102i	0.729267	−	0.265432i
$789$	−14.7365	+	35.3503i	−0.524632	+	1.25850i
$790$		0			0
$791$	−1.70668	−	2.95606i	−0.0606827	−	0.105105i
$792$	−0.145692	+	0.101034i	−0.00517695	+	0.00359010i
$793$	1.27277	−	2.20451i	0.0451975	−	0.0782844i
$794$	55.1567	+	20.0754i	1.95744	+	0.712449i
$795$		0			0
$796$	19.1631	+	16.0798i	0.679219	+	0.569932i
$797$	22.7960	+	19.1281i	0.807477	+	0.677553i	0.950004	−	0.312238i	$-0.101078\pi$
$797$	22.7960	+	19.1281i	0.807477	+	0.677553i	−0.142528	+	0.989791i	$0.545523\pi$
$798$	3.12729	−	3.39736i	0.110705	−	0.120265i
$799$	27.6679	+	10.0703i	0.978820	+	0.356261i
$800$		0			0
$801$	10.7742	−	15.2397i	0.380687	−	0.538469i
$802$	30.7649	+	53.2864i	1.08635	+	1.88161i
$803$	0.0392970	+	0.222864i	0.00138676	+	0.00786472i
$804$	31.9570	−	4.13360i	1.12704	−	0.145781i
$805$		0			0
$806$	1.70789	−	9.68591i	0.0601578	−	0.341172i
$807$	−36.9531	−	23.6595i	−1.30081	−	0.832855i
$808$	0.626791	−	0.525940i	0.0220504	−	0.0185025i
$809$	6.39776			0.224933			0.112467	−	0.993656i	$-0.464125\pi$
$809$	6.39776			0.224933			0.112467	+	0.993656i	$0.464125\pi$
$810$		0			0
$811$	6.93453			0.243504			0.121752	−	0.992561i	$-0.461149\pi$
$811$	6.93453			0.243504			0.121752	+	0.992561i	$0.461149\pi$
$812$	−3.67426	+	3.08307i	−0.128941	+	0.108194i
$813$	−41.9785	−	26.8771i	−1.47225	−	0.942622i
$814$	−1.11830	+	6.34221i	−0.0391965	+	0.222294i
$815$		0			0
$816$	30.2606	−	3.91416i	1.05933	−	0.137023i
$817$	−6.17588	−	35.0252i	−0.216067	−	1.22538i
$818$	−4.23879	−	7.34180i	−0.148206	−	0.256700i
$819$	0.993634	+	0.0914697i	0.0347204	+	0.00319621i
$820$		0			0
$821$	5.29886	+	1.92863i	0.184932	+	0.0673096i	0.432826	−	0.901477i	$-0.357516\pi$
$821$	5.29886	+	1.92863i	0.184932	+	0.0673096i	−0.247895	+	0.968787i	$0.579739\pi$
$822$	39.1902	−	42.5746i	1.36692	−	1.48496i
$823$	−19.1739	−	16.0888i	−0.668360	−	0.560821i	0.244219	−	0.969720i	$-0.421468\pi$
$823$	−19.1739	−	16.0888i	−0.668360	−	0.560821i	−0.912580	+	0.408899i	$0.865913\pi$
$824$	0.0803243	+	0.0674001i	0.00279823	+	0.00234799i
$825$		0			0
$826$	0.904222	+	0.329110i	0.0314619	+	0.0114512i
$827$	−5.72413	+	9.91448i	−0.199048	+	0.344760i	−0.948220	−	0.317615i	$-0.897118\pi$
$827$	−5.72413	+	9.91448i	−0.199048	+	0.344760i	0.749172	+	0.662375i	$0.230451\pi$
$828$	0.284440	+	3.43008i	0.00988498	+	0.119203i
$829$	−11.2450	−	19.4769i	−0.390555	−	0.676461i	0.601968	−	0.798520i	$-0.294383\pi$
$829$	−11.2450	−	19.4769i	−0.390555	−	0.676461i	−0.992523	+	0.122059i	$0.961050\pi$
$830$		0			0
$831$	13.1461	−	31.5352i	0.456032	−	1.09394i
$832$	−7.30168	+	2.65759i	−0.253140	+	0.0921355i
$833$	−5.53743	+	31.4043i	−0.191860	+	1.08809i
$834$	−1.98415	+	43.1988i	−0.0687057	+	1.49585i
$835$		0			0
$836$	−2.13683			−0.0739039
$837$	−27.1466	−	8.76254i	−0.938323	−	0.302878i
$838$	46.9575			1.62212
$839$	37.2179	−	31.2296i	1.28491	−	1.07816i	0.292358	−	0.956309i	$-0.405560\pi$
$839$	37.2179	−	31.2296i	1.28491	−	1.07816i	0.992548	−	0.121855i	$-0.0388844\pi$
$840$		0			0
$841$	1.37081	−	7.77424i	0.0472693	−	0.268077i
$842$	−14.1052	+	5.13389i	−0.486099	+	0.176925i
$843$	9.16851	+	12.0048i	0.315780	+	0.413469i
$844$	0.893098	+	5.06501i	0.0307417	+	0.174345i
$845$		0			0
$846$	−10.1252	+	37.1144i	−0.348112	+	1.27602i
$847$	2.05182	−	3.55385i	0.0705013	−	0.122112i
$848$	43.4903	+	15.8292i	1.49346	+	0.543576i
$849$	−3.84087	−	12.2786i	−0.131818	−	0.421400i
$850$		0			0
$851$	4.58081	+	3.84376i	0.157028	+	0.131762i
$852$	11.6624	+	37.2828i	0.399549	+	1.27729i
$853$	−0.911444	−	0.331738i	−0.0312072	−	0.0113585i	0.326369	−	0.945242i	$-0.394175\pi$
$853$	−0.911444	−	0.331738i	−0.0312072	−	0.0113585i	−0.357577	+	0.933884i	$0.616397\pi$
$854$	1.09514	−	1.89684i	0.0374751	−	0.0649087i
$855$		0			0
$856$	1.82780	+	3.16584i	0.0624729	+	0.108206i
$857$	−4.44534	−	25.2108i	−0.151850	−	0.861184i	−0.961609	−	0.274422i	$-0.911514\pi$
$857$	−4.44534	−	25.2108i	−0.151850	−	0.861184i	0.809759	−	0.586762i	$-0.199598\pi$
$858$	−0.547136	−	0.716396i	−0.0186789	−	0.0244573i
$859$	−11.4897	+	4.18192i	−0.392025	+	0.142685i	−0.530509	−	0.847679i	$-0.677999\pi$
$859$	−11.4897	+	4.18192i	−0.392025	+	0.142685i	0.138484	+	0.990365i	$0.455777\pi$
$860$		0			0
$861$	−5.50219	+	2.84843i	−0.187514	+	0.0970744i
$862$	−5.52037	+	4.63214i	−0.188025	+	0.157771i
$863$	−8.39103			−0.285634			−0.142817	−	0.989749i	$-0.545616\pi$
$863$	−8.39103			−0.285634			−0.142817	+	0.989749i	$0.545616\pi$
$864$	8.80779	+	41.0475i	0.299647	+	1.39646i
$865$		0			0
$866$	61.3323	−	51.4639i	2.08416	−	1.74881i
$867$	−0.366918	+	7.98850i	−0.0124612	+	0.271304i
$868$	0.752769	−	4.26917i	0.0255507	−	0.144905i
$869$	1.88710	−	0.686848i	0.0640154	−	0.0232997i
$870$		0			0
$871$	1.36075	+	7.71722i	0.0461074	+	0.261488i
$872$	−0.112404	−	0.194689i	−0.00380648	−	0.00659302i
$873$	−3.47585	−	41.9154i	−0.117640	−	1.41862i
$874$	−1.93668	+	3.35443i	−0.0655091	+	0.113465i
$875$		0			0
$876$	−2.76560	−	0.619695i	−0.0934409	−	0.0209375i
$877$	31.9858	+	26.8393i	1.08008	+	0.906298i	0.995928	−	0.0901543i	$-0.0287360\pi$
$877$	31.9858	+	26.8393i	1.08008	+	0.906298i	0.0841564	+	0.996453i	$0.473180\pi$
$878$	3.29430	+	2.76425i	0.111177	+	0.0932888i
$879$	−2.22113	+	2.41295i	−0.0749170	+	0.0813867i
$880$		0			0
$881$	5.65176	−	9.78914i	0.190413	−	0.329805i	−0.754974	−	0.655754i	$-0.772351\pi$
$881$	5.65176	−	9.78914i	0.190413	−	0.329805i	0.945387	+	0.325950i	$0.105684\pi$
$882$	−41.4902	−	3.81941i	−1.39705	−	0.128606i
$883$	−12.2986	−	21.3019i	−0.413882	−	0.716865i	0.581428	−	0.813598i	$-0.302494\pi$
$883$	−12.2986	−	21.3019i	−0.413882	−	0.716865i	−0.995310	+	0.0967330i	$0.969161\pi$
$884$	−1.50038	−	8.50908i	−0.0504632	−	0.286191i
$885$		0			0
$886$	30.9113	−	11.2508i	1.03849	−	0.377978i
$887$	1.61687	−	9.16975i	0.0542893	−	0.307890i	−0.945556	−	0.325458i	$-0.894481\pi$
$887$	1.61687	−	9.16975i	0.0542893	−	0.307890i	0.999846	+	0.0175685i	$0.00559251\pi$
$888$	−3.24890	−	2.08014i	−0.109026	−	0.0698048i
$889$	3.10983	−	2.60946i	0.104300	−	0.0875184i
$890$		0			0
$891$	−2.27594	+	1.28666i	−0.0762468	+	0.0431047i
$892$	−37.8468			−1.26721
$893$	−16.9888	+	14.2553i	−0.568508	+	0.477035i
$894$	−30.1466	−	19.3017i	−1.00825	−	0.645544i
$895$		0			0
$896$	−0.574234	+	0.209004i	−0.0191838	+	0.00698234i
$897$	−0.830099	+	0.107372i	−0.0277162	+	0.00358505i
$898$	−12.5274	−	71.0462i	−0.418043	−	2.37084i
$899$	16.6726	+	28.8778i	0.556063	+	0.963130i
$900$		0			0
$901$	−28.3957	+	49.1828i	−0.945999	+	1.63852i
$902$	5.25964	+	1.91435i	0.175127	+	0.0637409i
$903$	4.47867	−	4.86543i	0.149041	−	0.161911i
$904$	−1.41500	−	1.18733i	−0.0470623	−	0.0394899i
$905$		0			0
$906$	61.1095	+	13.6930i	2.03023	+	0.454918i
$907$	13.6050	+	4.95182i	0.451747	+	0.164423i	0.557866	−	0.829931i	$-0.311620\pi$
$907$	13.6050	+	4.95182i	0.451747	+	0.164423i	−0.106119	+	0.994353i	$0.533842\pi$
$908$	5.61510	−	9.72563i	0.186344	−	0.322757i
$909$	9.91481	−	6.87570i	0.328854	−	0.228052i
$910$		0			0
$911$	3.83154	+	21.7298i	0.126945	+	0.719939i	0.980134	+	0.198337i	$0.0635541\pi$
$911$	3.83154	+	21.7298i	0.126945	+	0.719939i	−0.853189	+	0.521602i	$0.825335\pi$
$912$	−8.84311	+	21.2131i	−0.292825	+	0.702437i
$913$	2.45244	−	0.892616i	0.0811640	−	0.0295413i
$914$	−9.06499	+	51.4101i	−0.299843	+	1.70049i
$915$		0			0
$916$	34.6642	−	29.0867i	1.14534	−	0.961051i
$917$	4.65267			0.153645
$918$	−48.8879	+	1.80172i	−1.61354	+	0.0594657i
$919$	−23.3762			−0.771109			−0.385554	−	0.922685i	$-0.625990\pi$
$919$	−23.3762			−0.771109			−0.385554	+	0.922685i	$0.625990\pi$
$920$		0			0
$921$	21.8786	−	11.3263i	0.720923	−	0.373216i
$922$	12.0740	−	68.4753i	0.397637	−	2.25511i
$923$	−8.92702	+	3.24917i	−0.293837	+	0.106948i
$924$	−0.241156	−	0.315759i	−0.00793345	−	0.0103877i
$925$		0			0
$926$	−29.8826	−	51.7582i	−0.982003	−	1.70088i
$927$	1.08838	+	1.09829i	0.0357472	+	0.0360726i
$928$	24.5374	−	42.5000i	0.805479	−	1.39513i
$929$	−8.18841	−	2.98034i	−0.268653	−	0.0977817i	0.204181	−	0.978933i	$-0.434547\pi$
$929$	−8.18841	−	2.98034i	−0.268653	−	0.0977817i	−0.472834	+	0.881151i	$0.656769\pi$
$930$		0			0
$931$	−18.3997	−	15.4391i	−0.603024	−	0.505998i
$932$	41.1337	+	34.5153i	1.34738	+	1.13059i
$933$	−7.57523	−	24.2167i	−0.248002	−	0.792819i
$934$	31.6619	+	11.5240i	1.03601	+	0.377076i
$935$		0			0
$936$	0.522210	−	0.137393i	0.0170690	−	0.00449084i
$937$	−20.3500	−	35.2473i	−0.664806	−	1.15148i	−0.979338	−	0.202231i	$-0.935181\pi$
$937$	−20.3500	−	35.2473i	−0.664806	−	1.15148i	0.314532	−	0.949247i	$-0.398153\pi$
$938$	1.17085	+	6.64020i	0.0382295	+	0.216810i
$939$	−27.2027	−	35.6180i	−0.887727	−	1.16235i
$940$		0			0
$941$	7.07254	−	40.1103i	0.230558	−	1.30756i	−0.621211	−	0.783643i	$-0.713359\pi$
$941$	7.07254	−	40.1103i	0.230558	−	1.30756i	0.851769	−	0.523917i	$-0.175530\pi$
$942$	−35.9736	+	18.6232i	−1.17208	+	0.606778i
$943$	3.98129	−	3.34069i	0.129648	−	0.108788i
$944$	−4.78931			−0.155879
$945$		0			0
$946$	−5.97404			−0.194233
$947$	14.4108	−	12.0921i	0.468288	−	0.392940i	−0.377882	−	0.925854i	$-0.623347\pi$
$947$	14.4108	−	12.0921i	0.468288	−	0.392940i	0.846170	+	0.532914i	$0.178903\pi$
$948$	−1.15396	+	25.1240i	−0.0374790	+	0.815990i
$949$	0.119684	−	0.678764i	0.00388512	−	0.0220336i
$950$		0			0
$951$	12.1722	−	29.1991i	0.394712	−	0.946847i
$952$	−0.0617490	−	0.350196i	−0.00200130	−	0.0113499i
$953$	20.4628	+	35.4426i	0.662855	+	1.14810i	0.979862	+	0.199675i	$0.0639887\pi$
$953$	20.4628	+	35.4426i	0.662855	+	1.14810i	−0.317007	+	0.948423i	$0.602678\pi$
$954$	−67.1082	−	31.6640i	−2.17271	−	1.02516i
$955$		0			0
$956$	−18.2645	−	6.64772i	−0.590715	−	0.215003i
$957$	2.98223	+	0.668235i	0.0964017	+	0.0216010i
$958$	−8.62633	−	7.23835i	−0.278704	−	0.233860i
$959$	4.75139	+	3.98689i	0.153430	+	0.128743i
$960$		0			0
$961$	0.810279	+	0.294918i	0.0261380	+	0.00951347i
$962$	9.80702	−	16.9863i	0.316191	−	0.547659i
$963$	22.5602	+	48.9583i	0.726992	+	1.57766i
$964$	30.1984	+	52.3052i	0.972625	+	1.68464i
$965$		0			0
$966$	−0.714249	+	0.0923872i	−0.0229806	+	0.00297251i
$967$	−36.0183	+	13.1096i	−1.15827	+	0.421576i	−0.848479	−	0.529229i	$-0.822481\pi$
$967$	−36.0183	+	13.1096i	−1.15827	+	0.421576i	−0.309791	+	0.950805i	$0.600259\pi$
$968$	0.385620	−	2.18696i	0.0123943	−	0.0702915i
$969$	−23.7506	−	15.2066i	−0.762981	−	0.488506i
$970$		0			0
$971$	50.2132			1.61142			0.805709	−	0.592312i	$-0.201785\pi$
$971$	50.2132			1.61142			0.805709	+	0.592312i	$0.201785\pi$
$972$	−3.90588	−	32.5092i	−0.125281	−	1.04273i
$973$	−4.63525			−0.148599
$974$	27.1569	−	22.7874i	0.870164	−	0.730154i
$975$		0			0
$976$	−1.89302	+	10.7359i	−0.0605941	+	0.343646i
$977$	18.8800	−	6.87174i	0.604023	−	0.219847i	−0.0218628	−	0.999761i	$-0.506960\pi$
$977$	18.8800	−	6.87174i	0.604023	−	0.219847i	0.625886	+	0.779914i	$0.284737\pi$
$978$	−21.7819	+	2.81746i	−0.696508	+	0.0900924i
$979$	−0.313823	−	1.77978i	−0.0100298	−	0.0568820i
$980$		0			0
$981$	−1.38738	−	3.01079i	−0.0442957	−	0.0961270i
$982$	−27.1734	+	47.0658i	−0.867139	+	1.50193i
$983$	−44.0962	−	16.0497i	−1.40645	−	0.511906i	−0.476364	−	0.879248i	$-0.658046\pi$
$983$	−44.0962	−	16.0497i	−1.40645	−	0.511906i	−0.930086	+	0.367342i	$0.880268\pi$
$984$	−2.27076	+	2.46685i	−0.0723891	+	0.0786404i
$985$		0			0
$986$	43.8074	+	36.7588i	1.39511	+	1.17064i
$987$	−4.02379	−	0.901621i	−0.128079	−	0.0286989i
$988$	6.11554	+	2.22587i	0.194561	+	0.0708145i
$989$	−2.77356	+	4.80395i	−0.0881941	+	0.152757i
$990$		0			0
$991$	−2.41568	−	4.18408i	−0.0767367	−	0.132912i	0.825103	−	0.564982i	$-0.191117\pi$
$991$	−2.41568	−	4.18408i	−0.0767367	−	0.132912i	−0.901840	+	0.432070i	$0.857783\pi$
$992$	7.70202	+	43.6803i	0.244539	+	1.38685i
$993$	−21.0775	+	50.5613i	−0.668874	+	1.60451i
$994$	−7.68116	+	2.79571i	−0.243632	+	0.0886747i
$995$		0			0
$996$	−1.49967	+	32.6507i	−0.0475190	+	1.03458i
$997$	−12.2229	+	10.2563i	−0.387104	+	0.324819i	−0.815484	−	0.578780i	$-0.803529\pi$
$997$	−12.2229	+	10.2563i	−0.387104	+	0.324819i	0.428380	+	0.903599i	$0.359085\pi$
$998$	−11.8034			−0.373630
$999$	−44.8953	−	34.9367i	−1.42043	−	1.10535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.f.76.2	✓	66
5.2	odd	4		675.2.u.e.49.4		132
5.3	odd	4		675.2.u.e.49.19		132
5.4	even	2		675.2.l.g.76.10	yes	66
27.16	even	9	inner	675.2.l.f.151.2	yes	66
135.43	odd	36		675.2.u.e.124.4		132
135.97	odd	36		675.2.u.e.124.19		132
135.124	even	18		675.2.l.g.151.10	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.2	✓	66	1.1	even	1	trivial
675.2.l.f.151.2	yes	66	27.16	even	9	inner
675.2.l.g.76.10	yes	66	5.4	even	2
675.2.l.g.151.10	yes	66	135.124	even	18
675.2.u.e.49.4		132	5.2	odd	4
675.2.u.e.49.19		132	5.3	odd	4
675.2.u.e.124.4		132	135.43	odd	36
675.2.u.e.124.19		132	135.97	odd	36

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55121 + 1.30162i) q^{2} +(-1.45868 - 0.933937i) q^{3} +(0.364742 - 2.06856i) q^{4} +(3.47836 - 0.449921i) q^{6} +(0.0652816 + 0.370230i) q^{7} +(0.101721 + 0.176186i) q^{8} +(1.25552 + 2.72464i) q^{9} +(0.272976 + 0.0993552i) q^{11} +(-2.46395 + 2.67673i) q^{12} +(-0.677752 - 0.568702i) q^{13} +(-0.583165 - 0.489333i) q^{14} +(3.56047 + 1.29590i) q^{16} +(-2.32471 + 4.02651i) q^{17} +(-5.49403 - 2.59227i) q^{18} +(-1.75100 - 3.03282i) q^{19} +(0.250547 - 0.601018i) q^{21} +(-0.552766 + 0.201190i) q^{22} +(-0.0948473 + 0.537906i) q^{23} +(0.0161677 - 0.352001i) q^{24} +1.79157 q^{26} +(0.713228 - 5.14697i) q^{27} +0.789653 q^{28} +(-4.65300 + 3.90433i) q^{29} +(0.953291 - 5.40638i) q^{31} +(-7.59216 + 2.76332i) q^{32} +(-0.305395 - 0.399870i) q^{33} +(-1.63488 - 9.27184i) q^{34} +(6.09401 - 1.60333i) q^{36} +(5.47398 - 9.48122i) q^{37} +(6.66375 + 2.42541i) q^{38} +(0.457496 + 1.46253i) q^{39} +(-7.28901 - 6.11620i) q^{41} +(0.393647 + 1.25842i) q^{42} +(9.54330 + 3.47348i) q^{43} +(0.305088 - 0.528427i) q^{44} +(-0.553021 - 0.957860i) q^{46} +(-1.09967 - 6.23654i) q^{47} +(-3.98331 - 5.21557i) q^{48} +(6.44504 - 2.34580i) q^{49} +(7.15152 - 3.70228i) q^{51} +(-1.42360 + 1.19454i) q^{52} +12.2148 q^{53} +(5.59303 + 8.91238i) q^{54} +(-0.0585889 + 0.0491619i) q^{56} +(-0.278306 + 6.05925i) q^{57} +(2.13583 - 12.1129i) q^{58} +(-1.18778 + 0.432318i) q^{59} +(0.499613 + 2.83345i) q^{61} +(5.55830 + 9.62726i) q^{62} +(-0.926782 + 0.642702i) q^{63} +(4.39127 - 7.60590i) q^{64} +(0.994211 + 0.222775i) q^{66} +(-6.78495 - 5.69325i) q^{67} +(7.48114 + 6.27742i) q^{68} +(0.640723 - 0.696054i) q^{69} +(5.36876 - 9.29896i) q^{71} +(-0.352330 + 0.498359i) q^{72} +(0.389512 + 0.674654i) q^{73} +(3.84964 + 21.8324i) q^{74} +(-6.91222 + 2.51584i) q^{76} +(-0.0189640 + 0.107550i) q^{77} +(-2.61334 - 1.67321i) q^{78} +(5.29571 - 4.44363i) q^{79} +(-5.84732 + 6.84170i) q^{81} +19.2678 q^{82} +(6.88221 - 5.77486i) q^{83} +(-1.15186 - 0.737486i) q^{84} +(-19.3248 + 7.03366i) q^{86} +(10.4337 - 1.34958i) q^{87} +(0.0102624 + 0.0582011i) q^{88} +(-3.11061 - 5.38773i) q^{89} +(0.166306 - 0.288050i) q^{91} +(1.07809 + 0.392394i) q^{92} +(-6.43977 + 6.99589i) q^{93} +(9.82342 + 8.24283i) q^{94} +(13.6553 + 3.05978i) q^{96} +(-13.1743 - 4.79504i) q^{97} +(-6.94427 + 12.0278i) q^{98} +(0.0720209 + 0.868504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more