LMFDB - Embedded newform 675.2.l.g.151.10

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			151.10
Character	$\chi$	$=$	675.151
Dual form			675.2.l.g.76.10

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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	$-0.0237799\pi$
$2$	1.55121	+	1.30162i	1.09687	+	0.920384i	0.0996605	+	0.995022i	$0.468224\pi$
$3$	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	$-0.967078\pi$
$7$	−0.0652816	+	0.370230i	−0.0246741	+	0.139934i	0.969982	+	0.243176i	$0.0781894\pi$
$8$	−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	−0.300539	−	0.953769i	$-0.597167\pi$
$11$	0.272976	−	0.0993552i	0.0823054	−	0.0299567i	0.382845	+	0.923813i	$0.374944\pi$
$12$	2.46395	+	2.67673i	0.711280	+	0.772704i
$13$	0.677752	−	0.568702i	0.187975	−	0.157729i	−0.543944	−	0.839122i	$-0.683070\pi$
$13$	0.677752	−	0.568702i	0.187975	−	0.157729i	0.731919	+	0.681392i	$0.238625\pi$
$14$	−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	0.997158	+	0.0753383i	$0.0240037\pi$
$17$	2.32471	+	4.02651i	0.563824	+	0.976572i	−0.433334	+	0.901233i	$0.642663\pi$
$18$	5.49403	−	2.59227i	1.29495	−	0.611005i
$19$	−1.75100	+	3.03282i	−0.401707	+	0.695777i	−0.993932	−	0.109996i	$-0.964916\pi$
$19$	−1.75100	+	3.03282i	−0.401707	+	0.695777i	0.592225	+	0.805772i	$0.298250\pi$
$20$		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	$-0.0374194\pi$
$23$	0.0948473	+	0.537906i	0.0197770	+	0.112161i	−0.973321	+	0.229447i	$0.926308\pi$
$24$	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	0.0987944	−	0.995108i	$-0.468501\pi$
$29$	−4.65300	−	3.90433i	−0.864040	−	0.725016i	−0.962834	+	0.270092i	$0.912946\pi$
$30$		0			0
$31$	0.953291	+	5.40638i	0.171216	+	0.971015i	0.942421	+	0.334428i	$0.108543\pi$
$31$	0.953291	+	5.40638i	0.171216	+	0.971015i	−0.771205	+	0.636587i	$0.780346\pi$
$32$	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	−0.827598	−	0.561321i	$-0.810293\pi$
$37$	−5.47398	−	9.48122i	−0.899917	−	1.55870i	−0.0723191	−	0.997382i	$-0.523040\pi$
$38$	−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	−0.999384	−	0.0351066i	$-0.988823\pi$
$41$	−7.28901	+	6.11620i	−1.13835	+	0.955190i	−0.138968	+	0.990297i	$0.544378\pi$
$42$	−0.393647	+	1.25842i	−0.0607411	+	0.194179i
$43$	−9.54330	+	3.47348i	−1.45534	+	0.529701i	−0.944077	−	0.329724i	$-0.893044\pi$
$43$	−9.54330	+	3.47348i	−1.45534	+	0.529701i	−0.511263	+	0.859424i	$0.670822\pi$
$44$	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	−0.793275	−	0.608864i	$-0.791626\pi$
$47$	1.09967	−	6.23654i	0.160403	−	0.909693i	0.953678	−	0.300829i	$-0.0972633\pi$
$48$	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	$-0.816809\pi$
$53$	−12.2148			−1.67783			−0.838913	+	0.544265i	$0.816809\pi$
$54$	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	0.263542	−	0.964648i	$-0.415109\pi$
$59$	−1.18778	−	0.432318i	−0.154636	−	0.0562830i	−0.418179	+	0.908365i	$0.637331\pi$
$60$		0			0
$61$	0.499613	−	2.83345i	0.0639690	−	0.362786i	−0.935974	−	0.352070i	$-0.885478\pi$
$61$	0.499613	−	2.83345i	0.0639690	−	0.362786i	0.999943	−	0.0107158i	$-0.00341102\pi$
$62$	−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	$-0.540255\pi$
$67$	6.78495	−	5.69325i	0.828913	−	0.695541i	0.955041	+	0.296473i	$0.0958105\pi$
$68$	−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	0.986054	+	0.166424i	$0.0532219\pi$
$71$	5.36876	+	9.29896i	0.637154	+	1.10358i	−0.348900	+	0.937160i	$0.613445\pi$
$72$	0.352330	+	0.498359i	0.0415225	+	0.0587322i
$73$	−0.389512	+	0.674654i	−0.0455889	+	0.0789623i	−0.887919	−	0.459999i	$-0.847850\pi$
$73$	−0.389512	+	0.674654i	−0.0455889	+	0.0789623i	0.842331	+	0.538961i	$0.181183\pi$
$74$	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	0.890097	−	0.455771i	$-0.150637\pi$
$79$	5.29571	+	4.44363i	0.595813	+	0.499947i	−0.294283	+	0.955718i	$0.595081\pi$
$80$		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	$-0.441902\pi$
$83$	−6.88221	−	5.77486i	−0.755421	−	0.633874i	−0.936931	+	0.349516i	$0.886346\pi$
$84$	−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	−0.982457	−	0.186489i	$-0.940289\pi$
$89$	−3.11061	+	5.38773i	−0.329724	+	0.571099i	0.652733	+	0.757588i	$0.273622\pi$
$90$		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	$-0.359016\pi$
$97$	13.1743	−	4.79504i	1.33765	−	0.486863i	0.909070	+	0.416643i	$0.136794\pi$
$98$	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	0.930145	+	0.367192i	$0.119681\pi$
$101$	−0.698390	+	3.96077i	−0.0694924	+	0.394111i	−0.999638	+	0.0269191i	$0.991430\pi$
$102$	6.27455	+	15.0516i	0.621273	+	1.49033i
$103$	−0.484326	−	0.176280i	−0.0477221	−	0.0173694i	0.318049	−	0.948074i	$-0.396972\pi$
$103$	−0.484326	−	0.176280i	−0.0477221	−	0.0173694i	−0.365771	+	0.930705i	$0.619195\pi$
$104$	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	$-0.834949\pi$
$107$	−17.9687			−1.73710			−0.868552	+	0.495598i	$0.834949\pi$
$108$	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	$-0.248437\pi$
$113$	8.53194	+	3.10537i	0.802618	+	0.292129i	0.0920470	+	0.995755i	$0.470659\pi$
$114$	−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	$-0.674295\pi$
$127$	5.39923	−	9.35175i	0.479105	−	0.829833i	0.999713	+	0.0239622i	$0.00762813\pi$
$128$	−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	0.922350	+	0.386356i	$0.126266\pi$
$131$	2.14908	+	12.1880i	0.187766	+	1.06487i	−0.734584	+	0.678518i	$0.762623\pi$
$132$	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	$-0.526734\pi$
$137$	−12.6386	−	10.6051i	−1.07979	−	0.906052i	−0.995903	+	0.0904234i	$0.971178\pi$
$138$	0.0878978	+	1.91370i	0.00748236	+	0.162905i
$139$	−2.14103	−	12.1424i	−0.181600	−	1.02990i	−0.930247	−	0.366935i	$-0.880407\pi$
$139$	−2.14103	−	12.1424i	−0.181600	−	1.02990i	0.748647	−	0.662969i	$-0.230704\pi$
$140$		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	−0.904173	−	0.427167i	$-0.859512\pi$
$149$	−7.81833	+	6.56036i	−0.640503	+	0.537446i	0.263670	+	0.964613i	$0.415067\pi$
$150$		0			0
$151$	16.7786	−	6.10690i	1.36542	−	0.496972i	0.447695	−	0.894187i	$-0.352245\pi$
$151$	16.7786	−	6.10690i	1.36542	−	0.496972i	0.917726	+	0.397214i	$0.130023\pi$
$152$	−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	$-0.236423\pi$
$157$	10.8531	+	3.95020i	0.866170	+	0.315260i	0.129555	+	0.991572i	$0.458645\pi$
$158$	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	$-0.421132\pi$
$163$	6.26212			0.490487			0.245244	+	0.969461i	$0.421132\pi$
$164$	−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	$-0.181662\pi$
$167$	14.7179	+	5.35688i	1.13891	+	0.414528i	0.297388	+	0.954757i	$0.403884\pi$
$168$	−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	$-0.498402\pi$
$173$	8.57107	−	3.11962i	0.651647	−	0.237180i	0.646626	+	0.762807i	$0.276180\pi$
$174$	−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	0.911165	−	0.412042i	$-0.135184\pi$
$179$	1.32110	+	2.28821i	0.0987437	+	0.171029i	−0.812421	+	0.583071i	$0.801851\pi$
$180$		0			0
$181$	3.54912	−	6.14725i	0.263804	−	0.456922i	−0.703446	−	0.710749i	$-0.748356\pi$
$181$	3.54912	−	6.14725i	0.263804	−	0.456922i	0.967250	+	0.253827i	$0.0816895\pi$
$182$	−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	0.775307	−	0.631585i	$-0.217595\pi$
$191$	3.97951	+	3.33921i	0.287948	+	0.241617i	−0.487359	+	0.873202i	$0.662040\pi$
$192$	13.5089	+	6.99344i	0.974921	+	0.504708i
$193$	−0.681015	−	3.86223i	−0.0490205	−	0.278009i	0.950438	−	0.310914i	$-0.100635\pi$
$193$	−0.681015	−	3.86223i	−0.0490205	−	0.278009i	−0.999458	+	0.0329051i	$0.989524\pi$
$194$	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	$-0.953796\pi$
$197$	−5.18583	+	8.98212i	−0.369475	+	0.639950i	0.620008	+	0.784595i	$0.287129\pi$
$198$	1.24218	−	1.25349i	0.0882780	−	0.0890816i
$199$	−5.95479	−	10.3140i	−0.422124	−	0.731140i	0.574023	−	0.818839i	$-0.305382\pi$
$199$	−5.95479	−	10.3140i	−0.422124	−	0.731140i	−0.996147	+	0.0876991i	$0.972049\pi$
$200$		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	0.261603	−	0.965176i	$-0.415749\pi$
$211$	−2.30091	−	0.837462i	−0.158401	−	0.0576532i	−0.420004	+	0.907522i	$0.637971\pi$
$212$	−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	−0.680639	−	0.732619i	$-0.738298\pi$
$223$	3.12885	−	17.7446i	0.209523	−	1.18826i	0.890162	−	0.455645i	$-0.150591\pi$
$224$	−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	$-0.667890\pi$
$227$	−5.02409	+	1.82862i	−0.333460	+	0.121370i	0.169863	+	0.985468i	$0.445667\pi$
$228$	−12.4324	+	2.78576i	−0.823355	+	0.184491i
$229$	16.5031	−	13.8477i	1.09055	−	0.915083i	0.0937994	−	0.995591i	$-0.470099\pi$
$229$	16.5031	−	13.8477i	1.09055	−	0.915083i	0.996754	+	0.0805082i	$0.0256543\pi$
$230$		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	0.892082	+	0.451874i	$0.149244\pi$
$233$	12.7820	+	22.1390i	0.837375	+	1.45038i	−0.0547064	+	0.998502i	$0.517422\pi$
$234$	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	0.991639	+	0.129043i	$0.0411906\pi$
$239$	1.60685	+	9.11290i	0.103939	+	0.589465i	−0.887700	+	0.460421i	$0.847698\pi$
$240$		0			0
$241$	−22.0268	−	18.4827i	−1.41887	−	1.19058i	−0.951940	−	0.306283i	$-0.900914\pi$
$241$	−22.0268	−	18.4827i	−1.41887	−	1.19058i	−0.466933	−	0.884293i	$-0.654641\pi$
$242$	−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	−0.619557	−	0.784952i	$-0.712688\pi$
$251$	5.86206	−	10.1534i	0.370010	−	0.640876i	0.989567	+	0.144076i	$0.0460210\pi$
$252$	−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	$-0.758925\pi$
$257$	−2.82575	+	2.37109i	−0.176265	+	0.147904i	0.550387	+	0.834910i	$0.314480\pi$
$258$	−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	−0.602099	−	0.798421i	$-0.705669\pi$
$263$	3.83968	−	21.7759i	0.236765	−	1.34276i	0.838864	−	0.544340i	$-0.183220\pi$
$264$	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	0.690360	+	0.723466i	$0.257452\pi$
$277$	−3.42530	+	19.4258i	−0.205806	+	1.16718i	−0.896166	+	0.443719i	$0.853659\pi$
$278$	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	−0.574689	−	0.818372i	$-0.694877\pi$
$281$	−8.19525	+	2.98283i	−0.488887	+	0.177940i	0.0858017	+	0.996312i	$0.472655\pi$
$282$	6.63100	−	21.1982i	0.394870	−	1.26233i
$283$	−5.69001	+	4.77449i	−0.338236	+	0.283814i	−0.796046	−	0.605236i	$-0.793079\pi$
$283$	−5.69001	+	4.77449i	−0.338236	+	0.283814i	0.457810	+	0.889050i	$0.348634\pi$
$284$	−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	$-0.0731700\pi$
$293$	−0.328799	−	1.86471i	−0.0192086	−	0.108937i	−0.992905	+	0.118914i	$0.962059\pi$
$294$	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	$-0.0336247\pi$
$307$	7.11195	+	12.3183i	0.405900	+	0.703040i	−0.588525	+	0.808479i	$0.700291\pi$
$308$	−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	−0.266541	−	0.963824i	$-0.585881\pi$
$311$	11.2222	−	9.41658i	0.636355	−	0.533965i	0.902896	+	0.429858i	$0.141436\pi$
$312$	0.211141	+	0.229375i	0.0119535	+	0.0129858i
$313$	−24.3151	+	8.84996i	−1.37437	+	0.500229i	−0.920466	−	0.390822i	$-0.872191\pi$
$313$	−24.3151	+	8.84996i	−1.37437	+	0.500229i	−0.453902	+	0.891051i	$0.649968\pi$
$314$	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	0.756333	+	0.654187i	$0.226989\pi$
$317$	−3.17156	+	17.9868i	−0.178133	+	1.01024i	−0.934466	+	0.356053i	$0.884122\pi$
$318$	−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	0.336062	+	0.941840i	$0.390905\pi$
$331$	−5.49188	+	31.1460i	−0.301861	+	1.71194i	−0.637923	+	0.770100i	$0.720206\pi$
$332$	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	$-0.789154\pi$
$337$	−5.87047	+	4.92591i	−0.319785	+	0.268332i	0.468737	+	0.883338i	$0.344709\pi$
$338$	−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	$-0.0859351\pi$
$347$	−0.616506	−	3.49638i	−0.0330958	−	0.187695i	−0.996874	+	0.0790102i	$0.974824\pi$
$348$	−1.01391	−	22.0749i	−0.0543515	−	1.18334i
$349$	−3.58455	−	3.00779i	−0.191876	−	0.161003i	0.541788	−	0.840515i	$-0.317747\pi$
$349$	−3.58455	−	3.00779i	−0.191876	−	0.161003i	−0.733665	+	0.679511i	$0.762192\pi$
$350$		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	$-0.414751\pi$
$353$	−12.0080	−	10.0759i	−0.639120	−	0.536286i	−0.903748	+	0.428065i	$0.859195\pi$
$354$	−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	−0.899772	−	0.436360i	$-0.856268\pi$
$359$	−1.36397	+	2.36247i	−0.0719876	+	0.124686i	0.827785	+	0.561046i	$0.189601\pi$
$360$		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	$-0.298031\pi$
$367$	29.9725	−	10.9091i	1.56455	−	0.569450i	0.971773	+	0.235916i	$0.0758091\pi$
$368$	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	$-0.337618\pi$
$373$	5.82118	+	2.11873i	0.301409	+	0.109704i	−0.186888	+	0.982381i	$0.559840\pi$
$374$	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	$-0.450007\pi$
$383$	−7.01885	−	2.55465i	−0.358647	−	0.130537i	−0.515058	+	0.857155i	$0.672230\pi$
$384$	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	−0.914210	−	0.405240i	$-0.867188\pi$
$389$	−26.7061	+	9.72022i	−1.35405	+	0.492835i	−0.439842	+	0.898075i	$0.644966\pi$
$390$		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	−0.230585	−	0.973052i	$-0.574064\pi$
$397$	14.4933	−	25.1031i	0.727396	−	1.25989i	0.957980	−	0.286834i	$-0.0926028\pi$
$398$	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	0.773296	+	0.634046i	$0.218607\pi$
$401$	5.27642	+	29.9241i	0.263492	+	1.49434i	−0.509804	+	0.860291i	$0.670282\pi$
$402$	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	0.961545	−	0.274649i	$-0.0885615\pi$
$409$	−0.726985	−	4.12294i	−0.0359471	−	0.203866i	−0.997492	+	0.0707824i	$0.977450\pi$
$410$		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	−0.963640	−	0.267203i	$-0.913901\pi$
$419$	−17.7641	+	14.9058i	−0.867832	+	0.728197i	0.0958087	+	0.995400i	$0.469456\pi$
$420$		0			0
$421$	6.96568	−	2.53530i	0.339487	−	0.123563i	−0.166651	−	0.986016i	$-0.553295\pi$
$421$	6.96568	−	2.53530i	0.339487	−	0.123563i	0.506137	+	0.862453i	$0.331073\pi$
$422$	−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	$-0.101036\pi$
$433$	39.5383			1.90009			0.950046	+	0.312111i	$0.101036\pi$
$434$	−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	−0.992343	−	0.123516i	$-0.960583\pi$
$439$	−0.368776	+	2.09143i	−0.0176007	+	0.0998186i	0.974742	+	0.223334i	$0.0716942\pi$
$440$		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	$-0.484999\pi$
$443$	15.2652	−	5.55606i	0.725270	−	0.263977i	0.678161	+	0.734913i	$0.262777\pi$
$444$	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	−0.889339	−	0.457249i	$-0.848835\pi$
$449$	−17.8132	−	30.8534i	−0.840658	−	1.45606i	0.0486805	−	0.998814i	$-0.484498\pi$
$450$		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	$-0.483792\pi$
$457$	−19.7485	−	16.5710i	−0.923796	−	0.775157i	−0.974693	+	0.223547i	$0.928236\pi$
$458$	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	−0.998542	−	0.0539762i	$-0.982810\pi$
$461$	−26.3039	−	22.0716i	−1.22509	−	1.02798i	−0.226551	−	0.973999i	$-0.572745\pi$
$462$	0.0175745	+	0.382630i	0.000817639	+	0.0178016i
$463$	5.12509	+	29.0659i	0.238183	+	1.35080i	0.835805	+	0.549026i	$0.185001\pi$
$463$	5.12509	+	29.0659i	0.238183	+	1.35080i	−0.597622	+	0.801778i	$0.703888\pi$
$464$	−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	$-0.707539\pi$
$467$	8.31964	−	14.4100i	0.384987	−	0.666817i	0.991767	+	0.128053i	$0.0408726\pi$
$468$	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	−0.954767	−	0.297356i	$-0.903895\pi$
$479$	0.965663	−	5.47655i	0.0441223	−	0.250230i	0.998889	+	0.0471262i	$0.0150063\pi$
$480$		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	$-0.370170\pi$
$487$	17.5069			0.793314			0.396657	+	0.917967i	$0.370170\pi$
$488$	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	0.841248	−	0.540649i	$-0.181821\pi$
$491$	25.2199	+	9.17930i	1.13816	+	0.414256i	0.296911	+	0.954905i	$0.404044\pi$
$492$	−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	−0.537347	−	0.843361i	$-0.680574\pi$
$499$	4.46524	−	3.74678i	0.199892	−	0.167729i	0.737239	+	0.675632i	$0.236129\pi$
$500$		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	−0.974963	−	0.222369i	$-0.928621\pi$
$503$	−15.2521	−	26.4175i	−0.680059	−	1.17790i	0.294904	−	0.955527i	$-0.404712\pi$
$504$	−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	−0.826980	−	0.562231i	$-0.809943\pi$
$509$	−5.46355	−	30.9853i	−0.242167	−	1.37340i	0.584813	−	0.811168i	$-0.301168\pi$
$510$		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	−0.942365	−	0.334587i	$-0.891403\pi$
$521$	−4.14101	+	7.17245i	−0.181421	+	0.314231i	0.760944	+	0.648818i	$0.224736\pi$
$522$	−35.6848	−	9.38864i	−1.56188	−	0.410930i
$523$	8.91120	+	15.4347i	0.389660	+	0.674910i	0.992404	−	0.123024i	$-0.0392593\pi$
$523$	8.91120	+	15.4347i	0.389660	+	0.674910i	−0.602744	+	0.797935i	$0.705926\pi$
$524$	−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	−0.743069	−	0.669214i	$-0.766631\pi$
$547$	4.30509	−	24.4154i	0.184072	−	1.04393i	0.927142	−	0.374711i	$-0.122258\pi$
$548$	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	−0.980467	−	0.196686i	$-0.936982\pi$
$557$	−15.5900	−	27.0026i	−0.660568	−	1.14414i	0.319898	−	0.947452i	$-0.396351\pi$
$558$	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	−0.997514	−	0.0704615i	$-0.977553\pi$
$563$	−1.99921	−	11.3381i	−0.0842567	−	0.477844i	0.913258	−	0.407382i	$-0.133558\pi$
$564$	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	0.657114	−	0.753791i	$-0.271777\pi$
$569$	0.688909	+	0.578063i	0.0288805	+	0.0242337i	−0.628233	+	0.778025i	$0.716222\pi$
$570$		0			0
$571$	7.41437	+	42.0490i	0.310282	+	1.75969i	0.597538	+	0.801841i	$0.296146\pi$
$571$	7.41437	+	42.0490i	0.310282	+	1.75969i	−0.287256	+	0.957854i	$0.592743\pi$
$572$	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	$-0.0832552\pi$
$577$	6.22274	+	10.7781i	0.259056	+	0.448698i	−0.706933	+	0.707280i	$0.749922\pi$
$578$	−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	−0.919635	−	0.392774i	$-0.871516\pi$
$587$	1.91101	−	10.8379i	0.0788758	−	0.447327i	0.998511	−	0.0545530i	$-0.0173734\pi$
$588$	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	$-0.562986\pi$
$593$	−9.57442			−0.393174			−0.196587	+	0.980486i	$0.562986\pi$
$594$	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	−0.378616	−	0.925554i	$-0.623600\pi$
$599$	−30.9256	−	11.2560i	−1.26359	−	0.459908i	−0.884971	+	0.465646i	$0.845822\pi$
$600$		0			0
$601$	−2.22127	+	12.5974i	−0.0906074	+	0.513860i	0.905398	+	0.424564i	$0.139573\pi$
$601$	−2.22127	+	12.5974i	−0.0906074	+	0.513860i	−0.996005	+	0.0892957i	$0.971538\pi$
$602$	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	$-0.997228\pi$
$607$	−28.7032	+	24.0848i	−1.16503	+	0.977573i	−0.165064	+	0.986283i	$0.552783\pi$
$608$	−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	$-0.850152\pi$
$613$	−1.30760	+	2.26483i	−0.0528136	+	0.0914758i	0.838410	+	0.545040i	$0.183486\pi$
$614$	−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	$-0.0969980\pi$
$617$	−1.11998	−	6.35172i	−0.0450887	−	0.255711i	−0.999017	+	0.0443232i	$0.985887\pi$
$618$	−1.60535	−	0.831075i	−0.0645766	−	0.0334307i
$619$	−0.0522006	−	0.0438015i	−0.00209812	−	0.00176053i	0.641738	−	0.766924i	$-0.278214\pi$
$619$	−0.0522006	−	0.0438015i	−0.00209812	−	0.00176053i	−0.643836	+	0.765163i	$0.722658\pi$
$620$		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	−0.830673	−	0.556761i	$-0.812044\pi$
$631$	−22.5451	−	39.0492i	−0.897506	−	1.55453i	−0.0668329	−	0.997764i	$-0.521289\pi$
$632$	−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	−0.550004	−	0.835162i	$-0.685374\pi$
$641$	6.39211	−	36.2514i	0.252473	−	1.43185i	0.802477	−	0.596683i	$-0.203515\pi$
$642$	−62.5017	−	8.08451i	−2.46675	−	0.319070i
$643$	4.60918	+	1.67760i	0.181768	+	0.0661582i	0.431301	−	0.902208i	$-0.358055\pi$
$643$	4.60918	+	1.67760i	0.181768	+	0.0661582i	−0.249533	+	0.968366i	$0.580277\pi$
$644$	−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	$-0.234766\pi$
$647$	37.6519			1.48025			0.740125	+	0.672469i	$0.234766\pi$
$648$	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	$-0.240853\pi$
$653$	21.5387	+	7.83944i	0.842874	+	0.306781i	0.115743	+	0.993279i	$0.463075\pi$
$654$	−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	−0.254505	−	0.967071i	$-0.581913\pi$
$659$	4.41936	−	1.60852i	0.172154	−	0.0626589i	0.426659	+	0.904412i	$0.359690\pi$
$660$		0			0
$661$	−25.3416	+	21.2641i	−0.985675	+	0.827079i	−0.984936	−	0.172920i	$-0.944680\pi$
$661$	−25.3416	+	21.2641i	−0.985675	+	0.827079i	−0.000739053		1.00000i	$0.500235\pi$
$662$	−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	−0.987678	−	0.156500i	$-0.949979\pi$
$673$	−34.0702	−	28.5883i	−1.31331	−	1.10200i	−0.325631	−	0.945497i	$-0.605577\pi$
$674$	−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	$-0.330470\pi$
$677$	−6.56883	−	5.51191i	−0.252461	−	0.211840i	−0.760231	+	0.649653i	$0.774914\pi$
$678$	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	0.0478347	+	0.998855i	$0.484768\pi$
$683$	−21.9820	+	38.0739i	−0.841117	+	1.45686i	−0.888951	+	0.458002i	$0.848565\pi$
$684$	−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	0.0847628	−	0.996401i	$-0.472987\pi$
$691$	20.7711	−	7.56005i	0.790169	−	0.287598i	0.705406	+	0.708803i	$0.250765\pi$
$692$	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	−0.883080	−	0.469222i	$-0.844535\pi$
$709$	2.85514	−	16.1923i	0.107227	−	0.608115i	0.990307	−	0.138893i	$-0.0443544\pi$
$710$		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	0.969566	+	0.244829i	$0.0787318\pi$
$719$	18.6844	+	32.3624i	0.696811	+	1.20691i	−0.272755	+	0.962083i	$0.587935\pi$
$720$		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	$-0.307759\pi$
$727$	−3.88514	−	3.26002i	−0.144092	−	0.120907i	−0.711984	+	0.702195i	$0.752203\pi$
$728$	−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	−0.953257	−	0.302159i	$-0.902293\pi$
$733$	−4.35439	−	24.6950i	−0.160833	−	0.912129i	0.792424	−	0.609970i	$-0.208819\pi$
$734$	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	−0.880262	−	0.474489i	$-0.842633\pi$
$739$	−23.1354	−	40.0717i	−0.851050	−	1.47406i	0.0292117	−	0.999573i	$-0.490700\pi$
$740$		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	$-0.516963\pi$
$743$	25.1018	−	21.0629i	0.920896	−	0.772723i	0.974160	+	0.225857i	$0.0725183\pi$
$744$	−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	0.548341	−	0.836255i	$-0.315260\pi$
$751$	11.8075	+	4.29756i	0.430860	+	0.156820i	−0.117481	+	0.993075i	$0.537482\pi$
$752$	−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	$-0.722103\pi$
$757$	−35.3551			−1.28500			−0.642501	+	0.766285i	$0.722103\pi$
$758$	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	0.419621	−	0.907699i	$-0.362163\pi$
$761$	4.34791	+	1.58251i	0.157612	+	0.0573660i	−0.262009	+	0.965065i	$0.584385\pi$
$762$	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	−0.808744	−	0.588161i	$-0.799852\pi$
$769$	−10.2592	+	8.60849i	−0.369956	+	0.310430i	0.438788	+	0.898591i	$0.355408\pi$
$770$		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	$-0.304667\pi$
$773$	−11.6796	−	20.2297i	−0.420087	−	0.727612i	−0.995948	+	0.0899361i	$0.971334\pi$
$774$	−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	0.715331	+	0.698786i	$0.246276\pi$
$787$	7.91498	+	44.8881i	0.282139	+	1.60009i	−0.433193	+	0.901301i	$0.642613\pi$
$788$	−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	$-0.898922\pi$
$797$	−22.7960	+	19.1281i	−0.807477	+	0.677553i	0.142528	+	0.989791i	$0.454477\pi$
$798$	−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	−0.247895	−	0.968787i	$-0.579739\pi$
$821$	5.29886	−	1.92863i	0.184932	−	0.0673096i	0.432826	+	0.901477i	$0.357516\pi$
$822$	−39.1902	−	42.5746i	−1.36692	−	1.48496i
$823$	19.1739	−	16.0888i	0.668360	−	0.560821i	−0.244219	−	0.969720i	$-0.578532\pi$
$823$	19.1739	−	16.0888i	0.668360	−	0.560821i	0.912580	+	0.408899i	$0.134087\pi$
$824$	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	$-0.102882\pi$
$827$	5.72413	+	9.91448i	0.199048	+	0.344760i	−0.749172	+	0.662375i	$0.769549\pi$
$828$	−0.284440	+	3.43008i	−0.00988498	+	0.119203i
$829$	−11.2450	+	19.4769i	−0.390555	+	0.676461i	−0.992523	−	0.122059i	$-0.961050\pi$
$829$	−11.2450	+	19.4769i	−0.390555	+	0.676461i	0.601968	+	0.798520i	$0.294383\pi$
$830$		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	0.992548	+	0.121855i	$0.0388844\pi$
$839$	37.2179	+	31.2296i	1.28491	+	1.07816i	0.292358	+	0.956309i	$0.405560\pi$
$840$		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	$-0.605825\pi$
$853$	0.911444	−	0.331738i	0.0312072	−	0.0113585i	0.357577	+	0.933884i	$0.383603\pi$
$854$	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	−0.809759	−	0.586762i	$-0.800402\pi$
$857$	4.44534	−	25.2108i	0.151850	−	0.861184i	0.961609	−	0.274422i	$-0.0884865\pi$
$858$	0.547136	−	0.716396i	0.0186789	−	0.0244573i
$859$	−11.4897	−	4.18192i	−0.392025	−	0.142685i	0.138484	−	0.990365i	$-0.455777\pi$
$859$	−11.4897	−	4.18192i	−0.392025	−	0.142685i	−0.530509	+	0.847679i	$0.677999\pi$
$860$		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	$-0.454384\pi$
$863$	8.39103			0.285634			0.142817	+	0.989749i	$0.454384\pi$
$864$	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	$-0.971264\pi$
$877$	−31.9858	+	26.8393i	−1.08008	+	0.906298i	−0.0841564	+	0.996453i	$0.526820\pi$
$878$	−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	0.945387	−	0.325950i	$-0.105684\pi$
$881$	5.65176	+	9.78914i	0.190413	+	0.329805i	−0.754974	+	0.655754i	$0.772351\pi$
$882$	41.4902	−	3.81941i	1.39705	−	0.128606i
$883$	12.2986	−	21.3019i	0.413882	−	0.716865i	−0.581428	−	0.813598i	$-0.697506\pi$
$883$	12.2986	−	21.3019i	0.413882	−	0.716865i	0.995310	+	0.0967330i	$0.0308393\pi$
$884$	−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	$-0.105519\pi$
$887$	−1.61687	−	9.16975i	−0.0542893	−	0.307890i	−0.999846	+	0.0175685i	$0.994407\pi$
$888$	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	$-0.688380\pi$
$907$	−13.6050	+	4.95182i	−0.451747	+	0.164423i	0.106119	+	0.994353i	$0.466158\pi$
$908$	−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	−0.853189	−	0.521602i	$-0.825335\pi$
$911$	3.83154	−	21.7298i	0.126945	−	0.719939i	0.980134	−	0.198337i	$-0.0635541\pi$
$912$	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	−0.472834	−	0.881151i	$-0.656769\pi$
$929$	−8.18841	+	2.98034i	−0.268653	+	0.0977817i	0.204181	+	0.978933i	$0.434547\pi$
$930$		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	−0.314532	−	0.949247i	$-0.601847\pi$
$937$	20.3500	−	35.2473i	0.664806	−	1.15148i	0.979338	−	0.202231i	$-0.0648192\pi$
$938$	−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	0.851769	+	0.523917i	$0.175530\pi$
$941$	7.07254	+	40.1103i	0.230558	+	1.30756i	−0.621211	+	0.783643i	$0.713359\pi$
$942$	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	$-0.376653\pi$
$947$	−14.4108	−	12.0921i	−0.468288	−	0.392940i	−0.846170	+	0.532914i	$0.821097\pi$
$948$	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	0.317007	+	0.948423i	$0.397322\pi$
$953$	−20.4628	+	35.4426i	−0.662855	+	1.14810i	−0.979862	+	0.199675i	$0.936011\pi$
$954$	−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	$-0.177519\pi$
$967$	36.0183	+	13.1096i	1.15827	+	0.421576i	0.309791	+	0.950805i	$0.399741\pi$
$968$	−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	$-0.493040\pi$
$977$	−18.8800	−	6.87174i	−0.604023	−	0.219847i	−0.625886	+	0.779914i	$0.715263\pi$
$978$	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	$-0.341954\pi$
$983$	44.0962	−	16.0497i	1.40645	−	0.511906i	0.930086	+	0.367342i	$0.119732\pi$
$984$	−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	−0.901840	−	0.432070i	$-0.857783\pi$
$991$	−2.41568	+	4.18408i	−0.0767367	+	0.132912i	0.825103	+	0.564982i	$0.191117\pi$
$992$	−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	$-0.196471\pi$
$997$	12.2229	+	10.2563i	0.387104	+	0.324819i	−0.428380	+	0.903599i	$0.640915\pi$
$998$	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.g.151.10	yes	66
5.2	odd	4		675.2.u.e.124.4		132
5.3	odd	4		675.2.u.e.124.19		132
5.4	even	2		675.2.l.f.151.2	yes	66
27.22	even	9	inner	675.2.l.g.76.10	yes	66
135.22	odd	36		675.2.u.e.49.19		132
135.49	even	18		675.2.l.f.76.2	✓	66
135.103	odd	36		675.2.u.e.49.4		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.2	✓	66	135.49	even	18
675.2.l.f.151.2	yes	66	5.4	even	2
675.2.l.g.76.10	yes	66	27.22	even	9	inner
675.2.l.g.151.10	yes	66	1.1	even	1	trivial
675.2.u.e.49.4		132	135.103	odd	36
675.2.u.e.49.19		132	135.22	odd	36
675.2.u.e.124.4		132	5.2	odd	4
675.2.u.e.124.19		132	5.3	odd	4

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

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Database

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