LMFDB - Embedded newform 675.2.u.e.49.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); 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, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30162 - 1.55121i) q^{2} +(-0.933937 + 1.45868i) q^{3} +(-0.364742 + 2.06856i) q^{4} +(3.47836 - 0.449921i) q^{6} +(-0.370230 + 0.0652816i) q^{7} +(0.176186 - 0.101721i) q^{8} +(-1.25552 - 2.72464i) q^{9} +(0.272976 + 0.0993552i) q^{11} +(-2.67673 - 2.46395i) q^{12} +(-0.568702 + 0.677752i) q^{13} +(0.583165 + 0.489333i) q^{14} +(3.56047 + 1.29590i) q^{16} +(-4.02651 - 2.32471i) q^{17} +(-2.59227 + 5.49403i) q^{18} +(1.75100 + 3.03282i) q^{19} +(0.250547 - 0.601018i) q^{21} +(-0.201190 - 0.552766i) q^{22} +(0.537906 + 0.0948473i) q^{23} +(-0.0161677 + 0.352001i) q^{24} +1.79157 q^{26} +(5.14697 + 0.713228i) q^{27} -0.789653i q^{28} +(4.65300 - 3.90433i) q^{29} +(0.953291 - 5.40638i) q^{31} +(-2.76332 - 7.59216i) q^{32} +(-0.399870 + 0.305395i) q^{33} +(1.63488 + 9.27184i) q^{34} +(6.09401 - 1.60333i) q^{36} +(9.48122 + 5.47398i) q^{37} +(2.42541 - 6.66375i) q^{38} +(-0.457496 - 1.46253i) q^{39} +(-7.28901 - 6.11620i) q^{41} +(-1.25842 + 0.393647i) q^{42} +(3.47348 - 9.54330i) q^{43} +(-0.305088 + 0.528427i) q^{44} +(-0.553021 - 0.957860i) q^{46} +(6.23654 - 1.09967i) q^{47} +(-5.21557 + 3.98331i) q^{48} +(-6.44504 + 2.34580i) q^{49} +(7.15152 - 3.70228i) q^{51} +(-1.19454 - 1.42360i) q^{52} -12.2148i q^{53} +(-5.59303 - 8.91238i) q^{54} +(-0.0585889 + 0.0491619i) q^{56} +(-6.05925 - 0.278306i) q^{57} +(-12.1129 - 2.13583i) q^{58} +(1.18778 - 0.432318i) q^{59} +(0.499613 + 2.83345i) q^{61} +(-9.62726 + 5.55830i) q^{62} +(0.642702 + 0.926782i) q^{63} +(-4.39127 + 7.60590i) q^{64} +(0.994211 + 0.222775i) q^{66} +(5.69325 - 6.78495i) q^{67} +(6.27742 - 7.48114i) q^{68} +(-0.640723 + 0.696054i) q^{69} +(5.36876 - 9.29896i) q^{71} +(-0.498359 - 0.352330i) q^{72} +(0.674654 - 0.389512i) q^{73} +(-3.84964 - 21.8324i) q^{74} +(-6.91222 + 2.51584i) q^{76} +(-0.107550 - 0.0189640i) q^{77} +(-1.67321 + 2.61334i) q^{78} +(-5.29571 + 4.44363i) q^{79} +(-5.84732 + 6.84170i) q^{81} +19.2678i q^{82} +(-5.77486 - 6.88221i) q^{83} +(1.15186 + 0.737486i) q^{84} +(-19.3248 + 7.03366i) q^{86} +(1.34958 + 10.4337i) q^{87} +(0.0582011 - 0.0102624i) q^{88} +(3.11061 + 5.38773i) q^{89} +(0.166306 - 0.288050i) q^{91} +(-0.392394 + 1.07809i) q^{92} +(6.99589 + 6.43977i) q^{93} +(-9.82342 - 8.24283i) q^{94} +(13.6553 + 3.05978i) q^{96} +(4.79504 - 13.1743i) q^{97} +(12.0278 + 6.94427i) q^{98} +(-0.0720209 - 0.868504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * 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 $

$2$	−1.30162	−	1.55121i	−0.920384	−	1.09687i	−0.995022	−	0.0996605i	$-0.968224\pi$
$2$	−1.30162	−	1.55121i	−0.920384	−	1.09687i	0.0746373	−	0.997211i	$-0.476220\pi$
$3$	−0.933937	+	1.45868i	−0.539209	+	0.842172i
$3$	−0.933937	+	1.45868i	−0.539209	+	0.842172i
$4$	−0.364742	+	2.06856i	−0.182371	+	1.03428i
$5$		0			0
$5$		0			0
$6$	3.47836	−	0.449921i	1.42003	−	0.183679i
$7$	−0.370230	+	0.0652816i	−0.139934	+	0.0246741i	−0.243176	−	0.969982i	$-0.578189\pi$
$7$	−0.370230	+	0.0652816i	−0.139934	+	0.0246741i	0.103242	+	0.994656i	$0.467078\pi$
$8$	0.176186	−	0.101721i	0.0622912	−	0.0359638i
$9$	−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	$0.597167\pi$
$12$	−2.67673	−	2.46395i	−0.772704	−	0.711280i
$13$	−0.568702	+	0.677752i	−0.157729	+	0.187975i	−0.839122	−	0.543944i	$-0.816930\pi$
$13$	−0.568702	+	0.677752i	−0.157729	+	0.187975i	0.681392	+	0.731919i	$0.261375\pi$
$14$	0.583165	+	0.489333i	0.155857	+	0.130780i
$15$		0			0
$16$	3.56047	+	1.29590i	0.890117	+	0.323976i
$17$	−4.02651	−	2.32471i	−0.976572	−	0.563824i	−0.0753383	−	0.997158i	$-0.524004\pi$
$17$	−4.02651	−	2.32471i	−0.976572	−	0.563824i	−0.901233	+	0.433334i	$0.857337\pi$
$18$	−2.59227	+	5.49403i	−0.611005	+	1.29495i
$19$	1.75100	+	3.03282i	0.401707	+	0.695777i	0.993932	−	0.109996i	$-0.0350838\pi$
$19$	1.75100	+	3.03282i	0.401707	+	0.695777i	−0.592225	+	0.805772i	$0.701750\pi$
$20$		0			0
$21$	0.250547	−	0.601018i	0.0546737	−	0.131153i
$22$	−0.201190	−	0.552766i	−0.0428939	−	0.117850i
$23$	0.537906	+	0.0948473i	0.112161	+	0.0197770i	0.229447	−	0.973321i	$-0.426308\pi$
$23$	0.537906	+	0.0948473i	0.112161	+	0.0197770i	−0.117286	+	0.993098i	$0.537419\pi$
$24$	−0.0161677	+	0.352001i	−0.00330021	+	0.0718519i
$25$		0			0
$26$	1.79157			0.351356
$27$	5.14697	+	0.713228i	0.990535	+	0.137261i
$28$		−	0.789653i		−	0.149230i
$29$	4.65300	−	3.90433i	0.864040	−	0.725016i	−0.0987944	−	0.995108i	$-0.531499\pi$
$29$	4.65300	−	3.90433i	0.864040	−	0.725016i	0.962834	+	0.270092i	$0.0870542\pi$
$30$		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	$-0.108543\pi$
$32$	−2.76332	−	7.59216i	−0.488490	−	1.34212i
$33$	−0.399870	+	0.305395i	−0.0696085	+	0.0531624i
$34$	1.63488	+	9.27184i	0.280379	+	1.59011i
$35$		0			0
$36$	6.09401	−	1.60333i	1.01567	−	0.267222i
$37$	9.48122	+	5.47398i	1.55870	+	0.899917i	0.997382	+	0.0723191i	$0.0230400\pi$
$37$	9.48122	+	5.47398i	1.55870	+	0.899917i	0.561321	+	0.827598i	$0.310293\pi$
$38$	2.42541	−	6.66375i	0.393453	−	1.08100i
$39$	−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	$0.988823\pi$
$42$	−1.25842	+	0.393647i	−0.194179	+	0.0607411i
$43$	3.47348	−	9.54330i	0.529701	−	1.45534i	−0.329724	−	0.944077i	$-0.606956\pi$
$43$	3.47348	−	9.54330i	0.529701	−	1.45534i	0.859424	−	0.511263i	$-0.170822\pi$
$44$	−0.305088	+	0.528427i	−0.0459937	+	0.0796634i
$45$		0			0
$46$	−0.553021	−	0.957860i	−0.0815385	−	0.141229i
$47$	6.23654	−	1.09967i	0.909693	−	0.160403i	0.300829	−	0.953678i	$-0.402737\pi$
$47$	6.23654	−	1.09967i	0.909693	−	0.160403i	0.608864	+	0.793275i	$0.291626\pi$
$48$	−5.21557	+	3.98331i	−0.752803	+	0.574941i
$49$	−6.44504	+	2.34580i	−0.920720	+	0.335115i
$50$		0			0
$51$	7.15152	−	3.70228i	1.00141	−	0.518423i
$52$	−1.19454	−	1.42360i	−0.165653	−	0.197417i
$53$		−	12.2148i		−	1.67783i	−0.544265	−	0.838913i	$-0.683191\pi$
$53$		−	12.2148i		−	1.67783i	0.544265	−	0.838913i	$-0.316809\pi$
$54$	−5.59303	−	8.91238i	−0.761115	−	1.21282i
$55$		0			0
$56$	−0.0585889	+	0.0491619i	−0.00782927	+	0.00656954i
$57$	−6.05925	−	0.278306i	−0.802567	−	0.0368625i
$58$	−12.1129	−	2.13583i	−1.59050	−	0.280448i
$59$	1.18778	−	0.432318i	0.154636	−	0.0562830i	−0.263542	−	0.964648i	$-0.584891\pi$
$59$	1.18778	−	0.432318i	0.154636	−	0.0562830i	0.418179	+	0.908365i	$0.362669\pi$
$60$		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	$0.885478\pi$
$62$	−9.62726	+	5.55830i	−1.22266	+	0.705905i
$63$	0.642702	+	0.926782i	0.0809728	+	0.116764i
$64$	−4.39127	+	7.60590i	−0.548909	+	0.950737i
$65$		0			0
$66$	0.994211	+	0.222775i	0.122379	+	0.0274217i
$67$	5.69325	−	6.78495i	0.695541	−	0.828913i	−0.296473	−	0.955041i	$-0.595811\pi$
$67$	5.69325	−	6.78495i	0.695541	−	0.828913i	0.992014	+	0.126128i	$0.0402550\pi$
$68$	6.27742	−	7.48114i	0.761249	−	0.907222i
$69$	−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	$-0.0532219\pi$
$72$	−0.498359	−	0.352330i	−0.0587322	−	0.0415225i
$73$	0.674654	−	0.389512i	0.0789623	−	0.0455889i	−0.459999	−	0.887919i	$-0.652150\pi$
$73$	0.674654	−	0.389512i	0.0789623	−	0.0455889i	0.538961	+	0.842331i	$0.318817\pi$
$74$	−3.84964	−	21.8324i	−0.447512	−	2.53797i
$75$		0			0
$76$	−6.91222	+	2.51584i	−0.792886	+	0.288587i
$77$	−0.107550	−	0.0189640i	−0.0122565	−	0.00216115i
$78$	−1.67321	+	2.61334i	−0.189454	+	0.295902i
$79$	−5.29571	+	4.44363i	−0.595813	+	0.499947i	−0.890097	−	0.455771i	$-0.849363\pi$
$79$	−5.29571	+	4.44363i	−0.595813	+	0.499947i	0.294283	+	0.955718i	$0.404919\pi$
$80$		0			0
$81$	−5.84732	+	6.84170i	−0.649702	+	0.760189i
$82$			19.2678i			2.12777i
$83$	−5.77486	−	6.88221i	−0.633874	−	0.755421i	0.349516	−	0.936931i	$-0.386346\pi$
$83$	−5.77486	−	6.88221i	−0.633874	−	0.755421i	−0.983389	+	0.181509i	$0.941902\pi$
$84$	1.15186	+	0.737486i	0.125678	+	0.0804664i
$85$		0			0
$86$	−19.3248	+	7.03366i	−2.08385	+	0.758459i
$87$	1.34958	+	10.4337i	0.144690	+	1.11861i
$88$	0.0582011	−	0.0102624i	0.00620426	−	0.00109398i
$89$	3.11061	+	5.38773i	0.329724	+	0.571099i	0.982457	−	0.186489i	$-0.0597110\pi$
$89$	3.11061	+	5.38773i	0.329724	+	0.571099i	−0.652733	+	0.757588i	$0.726378\pi$
$90$		0			0
$91$	0.166306	−	0.288050i	0.0174336	−	0.0301959i
$92$	−0.392394	+	1.07809i	−0.0409099	+	0.112399i
$93$	6.99589	+	6.43977i	0.725440	+	0.667773i
$94$	−9.82342	−	8.24283i	−1.01321	−	0.850183i
$95$		0			0
$96$	13.6553	+	3.05978i	1.39369	+	0.312288i
$97$	4.79504	−	13.1743i	0.486863	−	1.33765i	−0.416643	−	0.909070i	$-0.636794\pi$
$97$	4.79504	−	13.1743i	0.486863	−	1.33765i	0.903506	−	0.428575i	$-0.140984\pi$
$98$	12.0278	+	6.94427i	1.21499	+	0.701477i
$99$	−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	$-0.119681\pi$
$102$	−15.0516	−	6.27455i	−1.49033	−	0.621273i
$103$	−0.176280	−	0.484326i	−0.0173694	−	0.0477221i	0.930705	−	0.365771i	$-0.119195\pi$
$103$	−0.176280	−	0.484326i	−0.0173694	−	0.0477221i	−0.948074	+	0.318049i	$0.896972\pi$
$104$	−0.0312556	+	0.177260i	−0.00306487	+	0.0173817i
$105$		0			0
$106$	−18.9477	+	15.8990i	−1.84036	+	1.54425i
$107$			17.9687i			1.73710i	0.495598	+	0.868552i	$0.334949\pi$
$107$			17.9687i			1.73710i	−0.495598	+	0.868552i	$0.665051\pi$
$108$	−3.35267	+	10.3867i	−0.322611	+	0.999456i
$109$	1.10502			0.105842			0.0529209	−	0.998599i	$-0.483147\pi$
$109$	1.10502			0.105842			0.0529209	+	0.998599i	$0.483147\pi$
$110$		0			0
$111$	−16.8397	+	8.71775i	−1.59835	+	0.827453i
$112$	−1.40279	−	0.247350i	−0.132551	−	0.0233724i
$113$	3.10537	+	8.53194i	0.292129	+	0.802618i	0.995755	+	0.0920470i	$0.0293410\pi$
$113$	3.10537	+	8.53194i	0.292129	+	0.802618i	−0.703626	+	0.710571i	$0.748437\pi$
$114$	7.45513	+	9.76142i	0.698237	+	0.914241i
$115$		0			0
$116$	6.37918	+	11.0491i	0.592292	+	1.02588i
$117$	2.56065	+	0.698573i	0.236732	+	0.0645831i
$118$	−2.21666	−	1.27979i	−0.204060	−	0.117814i
$119$	1.64250	+	0.597820i	0.150567	+	0.0548020i
$120$		0			0
$121$	−8.36184	−	7.01642i	−0.760168	−	0.637856i
$122$	3.74497	−	4.46308i	0.339053	−	0.404068i
$123$	15.7291	−	4.92022i	1.41824	−	0.443641i
$124$	10.8357	+	3.94387i	0.973074	+	0.354170i
$125$		0			0
$126$	0.601080	−	2.20328i	0.0535484	−	0.196284i
$127$	9.35175	−	5.39923i	0.829833	−	0.479105i	−0.0239622	−	0.999713i	$-0.507628\pi$
$127$	9.35175	−	5.39923i	0.829833	−	0.479105i	0.853796	+	0.520608i	$0.174295\pi$
$128$	1.60079	−	0.282262i	0.141491	−	0.0249487i
$129$	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	$-0.126266\pi$
$132$	−0.485876	−	0.938545i	−0.0422901	−	0.0816898i
$133$	−0.846260	−	1.00853i	−0.0733801	−	0.0874510i
$134$	−17.9353			−1.54938
$135$		0			0
$136$	−0.945886			−0.0811091
$137$	10.6051	+	12.6386i	0.906052	+	1.07979i	0.996475	+	0.0838872i	$0.0267335\pi$
$137$	10.6051	+	12.6386i	0.906052	+	1.07979i	−0.0904234	+	0.995903i	$0.528822\pi$
$138$	1.91370	+	0.0878978i	0.162905	+	0.00748236i
$139$	2.14103	−	12.1424i	0.181600	−	1.02990i	−0.748647	−	0.662969i	$-0.769296\pi$
$139$	2.14103	−	12.1424i	0.181600	−	1.02990i	0.930247	−	0.366935i	$-0.119593\pi$
$140$		0			0
$141$	−4.22046	+	10.1242i	−0.355427	+	0.852609i
$142$	−21.4127	+	3.77564i	−1.79692	+	0.316845i
$143$	−0.222580	+	0.128507i	−0.0186131	+	0.0107463i
$144$	−0.939380	−	11.3280i	−0.0782817	−	0.944003i
$145$		0			0
$146$	−1.48236	−	0.539534i	−0.122681	−	0.0446522i
$147$	2.59747	−	11.5921i	0.214236	−	0.956101i
$148$	−14.7814	+	17.6158i	−1.21503	+	1.44801i
$149$	7.81833	+	6.56036i	0.640503	+	0.537446i	0.904173	−	0.427167i	$-0.140488\pi$
$149$	7.81833	+	6.56036i	0.640503	+	0.537446i	−0.263670	+	0.964613i	$0.584933\pi$
$150$		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	$0.352245\pi$
$152$	0.617003	+	0.356227i	0.0500456	+	0.0288938i
$153$	−1.27861	+	13.8895i	−0.103369	+	1.12290i
$154$	0.110572	+	0.191517i	0.00891016	+	0.0154329i
$155$		0			0
$156$	3.19220	−	0.412907i	0.255581	−	0.0330590i
$157$	−3.95020	−	10.8531i	−0.315260	−	0.866170i	−0.991572	−	0.129555i	$-0.958645\pi$
$157$	−3.95020	−	10.8531i	−0.315260	−	0.866170i	0.676312	−	0.736615i	$-0.263577\pi$
$158$	13.7860	+	2.43084i	1.09675	+	0.193387i
$159$	17.8175	+	11.4078i	1.41302	+	0.904699i
$160$		0			0
$161$	−0.205341			−0.0161831
$162$	18.2239	+	0.165131i	1.43180	+	0.0129739i
$163$			6.26212i			0.490487i	0.969461	+	0.245244i	$0.0788679\pi$
$163$			6.26212i			0.490487i	−0.969461	+	0.245244i	$0.921132\pi$
$164$	15.3103	−	12.8469i	1.19553	−	1.00317i
$165$		0			0
$166$	−3.15908	+	17.9161i	−0.245192	+	1.39056i
$167$	−5.35688	−	14.7179i	−0.414528	−	1.13891i	−0.954757	−	0.297388i	$-0.903884\pi$
$167$	−5.35688	−	14.7179i	−0.414528	−	1.13891i	0.540229	−	0.841518i	$-0.318338\pi$
$168$	−0.0169934	−	0.131377i	−0.00131107	−	0.0101360i
$169$	2.12150	+	12.0316i	0.163192	+	0.925509i
$170$		0			0
$171$	6.06492	−	8.57862i	0.463796	−	0.656023i
$172$	18.4739	+	10.6659i	1.40862	+	0.813270i
$173$	−3.11962	+	8.57107i	−0.237180	+	0.651647i	0.762807	+	0.646626i	$0.223820\pi$
$173$	−3.11962	+	8.57107i	−0.237180	+	0.651647i	−0.999987	+	0.00502090i	$0.998402\pi$
$174$	14.4282	−	15.6741i	1.09380	−	1.18825i
$175$		0			0
$176$	0.843168	+	0.707502i	0.0635562	+	0.0533300i
$177$	−0.478700	+	2.13636i	−0.0359813	+	0.160579i
$178$	4.30868	−	11.8380i	0.322949	−	0.887295i
$179$	−1.32110	+	2.28821i	−0.0987437	+	0.171029i	−0.911165	−	0.412042i	$-0.864816\pi$
$179$	−1.32110	+	2.28821i	−0.0987437	+	0.171029i	0.812421	+	0.583071i	$0.198149\pi$
$180$		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	$0.748356\pi$
$182$	−0.663294	+	0.116957i	−0.0491666	+	0.00866940i
$183$	−4.59972	−	1.91748i	−0.340021	−	0.141744i
$184$	0.104420	−	0.0380056i	0.00769791	−	0.00280181i
$185$		0			0
$186$	0.883443	−	19.2342i	0.0647772	−	1.41032i
$187$	−0.868169	−	1.03464i	−0.0634868	−	0.0756606i
$188$			13.3017i			0.970128i
$189$	−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	$0.217595\pi$
$192$	−6.99344	−	13.5089i	−0.504708	−	0.974921i
$193$	−3.86223	−	0.681015i	−0.278009	−	0.0490205i	0.0329051	−	0.999458i	$-0.489524\pi$
$193$	−3.86223	−	0.681015i	−0.278009	−	0.0490205i	−0.310914	+	0.950438i	$0.600635\pi$
$194$	−26.6774	+	9.70978i	−1.91533	+	0.697121i
$195$		0			0
$196$	−2.50165	−	14.1875i	−0.178689	−	1.01340i
$197$	−8.98212	+	5.18583i	−0.639950	+	0.369475i	−0.784595	−	0.620008i	$-0.787129\pi$
$197$	−8.98212	+	5.18583i	−0.639950	+	0.369475i	0.144646	+	0.989484i	$0.453796\pi$
$198$	−1.25349	+	1.24218i	−0.0890816	+	0.0882780i
$199$	5.95479	−	10.3140i	0.422124	−	0.731140i	−0.574023	−	0.818839i	$-0.694618\pi$
$199$	5.95479	−	10.3140i	0.422124	−	0.731140i	0.996147	+	0.0876991i	$0.0279514\pi$
$200$		0			0
$201$	4.57997	+	14.6414i	0.323046	+	1.03272i
$202$	−5.23494	+	6.23876i	−0.368329	+	0.438958i
$203$	−1.46780	+	1.74926i	−0.103019	+	0.122774i
$204$	5.04991	+	16.1437i	0.353565	+	1.13028i
$205$		0			0
$206$	−0.521842	+	0.903856i	−0.0363584	+	0.0629747i
$207$	−0.416929	−	1.58468i	−0.0289786	−	0.110143i
$208$	−2.90315	+	1.67613i	−0.201297	+	0.116219i
$209$	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	$0.415749\pi$
$212$	25.2669	+	4.45524i	1.73534	+	0.305987i
$213$	8.55017	+	16.5160i	0.585848	+	1.13166i
$214$	27.8733	−	23.3885i	1.90538	−	1.59880i
$215$		0			0
$216$	0.979375	−	0.397895i	0.0666380	−	0.0270733i
$217$			2.06384i			0.140103i
$218$	−1.43832	−	1.71412i	−0.0974152	−	0.116095i
$219$	−0.0619094	+	1.34789i	−0.00418345	+	0.0910818i
$220$		0			0
$221$	3.86546	−	1.40691i	0.260019	−	0.0946391i
$222$	35.4419	+	14.7747i	2.37871	+	0.991611i
$223$	−17.7446	+	3.12885i	−1.18826	+	0.209523i	−0.732619	−	0.680639i	$-0.761702\pi$
$223$	−17.7446	+	3.12885i	−1.18826	+	0.209523i	−0.455645	+	0.890162i	$0.650591\pi$
$224$	1.51869	+	2.63045i	0.101472	+	0.175755i
$225$		0			0
$226$	9.19282	−	15.9224i	0.611497	−	1.05914i
$227$	−1.82862	+	5.02409i	−0.121370	+	0.333460i	−0.985468	−	0.169863i	$-0.945667\pi$
$227$	−1.82862	+	5.02409i	−0.121370	+	0.333460i	0.864098	+	0.503324i	$0.167890\pi$
$228$	2.78576	−	12.4324i	0.184491	−	0.823355i
$229$	−16.5031	−	13.8477i	−1.09055	−	0.915083i	−0.0937994	−	0.995591i	$-0.529901\pi$
$229$	−16.5031	−	13.8477i	−1.09055	−	0.915083i	−0.996754	+	0.0805082i	$0.974346\pi$
$230$		0			0
$231$	0.128107	−	0.139171i	0.00842885	−	0.00915675i
$232$	0.422641	−	1.16120i	0.0277477	−	0.0762363i
$233$	22.1390	+	12.7820i	1.45038	+	0.837375i	0.998502	−	0.0547064i	$-0.0174223\pi$
$233$	22.1390	+	12.7820i	1.45038	+	0.837375i	0.451874	+	0.892082i	$0.350756\pi$
$234$	−2.24936	−	4.88138i	−0.147045	−	0.319106i
$235$		0			0
$236$	0.461039	+	2.61468i	0.0300111	+	0.170201i
$237$	−1.53599	−	11.8748i	−0.0997735	−	0.771353i
$238$	−1.21056	−	3.32599i	−0.0784691	−	0.215592i
$239$	−1.60685	+	9.11290i	−0.103939	+	0.589465i	0.887700	+	0.460421i	$0.152302\pi$
$239$	−1.60685	+	9.11290i	−0.103939	+	0.589465i	−0.991639	+	0.129043i	$0.958809\pi$
$240$		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	$0.900914\pi$
$242$			22.1037i			1.42088i
$243$	−4.51886	−	14.9191i	−0.289885	−	0.957062i
$244$	−6.04338			−0.386888
$245$		0			0
$246$	−28.1056	−	17.9949i	−1.79195	−	1.14731i
$247$	−3.05130	−	0.538026i	−0.194149	−	0.0342338i
$248$	−0.381986	−	1.04950i	−0.0242562	−	0.0666432i
$249$	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	$0.712688\pi$
$252$	−2.15152	+	0.991429i	−0.135533	+	0.0624541i
$253$	0.137412	+	0.0793348i	0.00863901	+	0.00498774i
$254$	−20.5478	−	7.47878i	−1.28928	−	0.469260i
$255$		0			0
$256$	10.9342	+	9.17485i	0.683385	+	0.573428i
$257$	−2.37109	+	2.82575i	−0.147904	+	0.176265i	−0.834910	−	0.550387i	$-0.814480\pi$
$257$	−2.37109	+	2.82575i	−0.147904	+	0.176265i	0.687006	+	0.726652i	$0.258925\pi$
$258$	7.78827	−	34.7578i	0.484876	−	2.16393i
$259$	−3.86758	−	1.40769i	−0.240320	−	0.0874693i
$260$		0			0
$261$	−16.4798	−	7.77576i	−1.02008	−	0.481308i
$262$	−21.7035	+	12.5305i	−1.34085	+	0.774138i
$263$	−21.7759	+	3.83968i	−1.34276	+	0.236765i	−0.798421	−	0.602099i	$-0.794331\pi$
$263$	−21.7759	+	3.83968i	−1.34276	+	0.236765i	−0.544340	+	0.838864i	$0.683220\pi$
$264$	−0.0393865	+	0.0944815i	−0.00242407	+	0.00581494i
$265$		0			0
$266$	−0.462939	+	2.62546i	−0.0283846	+	0.160977i
$267$	−10.7641	−	0.494404i	−0.658754	−	0.0302570i
$268$	11.9585	+	14.2516i	0.730480	+	0.870553i
$269$	−25.3331			−1.54459			−0.772294	−	0.635265i	$-0.780891\pi$
$269$	−25.3331			−1.54459			−0.772294	+	0.635265i	$0.780891\pi$
$270$		0			0
$271$	28.7783			1.74816			0.874079	−	0.485783i	$-0.161466\pi$
$271$	28.7783			1.74816			0.874079	+	0.485783i	$0.161466\pi$
$272$	−11.3237	−	13.4950i	−0.686598	−	0.818255i
$273$	0.264855	+	0.511609i	0.0160298	+	0.0309640i
$274$	5.80140	−	32.9014i	0.350475	−	1.98764i
$275$		0			0
$276$	−1.20613	−	1.57925i	−0.0726004	−	0.0950598i
$277$	−19.4258	+	3.42530i	−1.16718	+	0.205806i	−0.723466	−	0.690360i	$-0.757452\pi$
$277$	−19.4258	+	3.42530i	−1.16718	+	0.205806i	−0.443719	+	0.896166i	$0.646341\pi$
$278$	−21.6222	+	12.4836i	−1.29681	+	0.748715i
$279$	−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	$0.694877\pi$
$282$	21.1982	−	6.63100i	1.26233	−	0.394870i
$283$	4.77449	−	5.69001i	0.283814	−	0.338236i	−0.605236	−	0.796046i	$-0.706921\pi$
$283$	4.77449	−	5.69001i	0.283814	−	0.338236i	0.889050	+	0.457810i	$0.151366\pi$
$284$	17.2772	+	14.4973i	1.02521	+	0.860257i
$285$		0			0
$286$	0.489056	+	0.178002i	0.0289185	+	0.0105255i
$287$	3.09789	+	1.78857i	0.182862	+	0.105576i
$288$	−17.2165	+	17.0612i	−1.01449	+	1.00534i
$289$	2.30851	+	3.99846i	0.135795	+	0.235204i
$290$		0			0
$291$	14.7389	+	19.2984i	0.864007	+	1.13129i
$292$	0.559652	+	1.53763i	0.0327512	+	0.0899831i
$293$	−1.86471	−	0.328799i	−0.108937	−	0.0192086i	0.118914	−	0.992905i	$-0.462059\pi$
$293$	−1.86471	−	0.328799i	−0.108937	−	0.0192086i	−0.227851	+	0.973696i	$0.573170\pi$
$294$	−21.3627	+	11.0593i	−1.24590	+	0.644991i
$295$		0			0
$296$	2.22728			0.129458
$297$	1.33414	+	0.706072i	0.0774145	+	0.0409705i
$298$		−	20.6670i		−	1.19721i
$299$	−0.370191	+	0.310627i	−0.0214087	+	0.0179640i
$300$		0			0
$301$	−0.662985	+	3.75998i	−0.0382138	+	0.216721i
$302$	−12.3662	−	33.9759i	−0.711597	−	1.95510i
$303$	6.42976	+	2.68037i	0.369380	+	0.153983i
$304$	2.30413	+	13.0674i	0.132151	+	0.749466i
$305$		0			0
$306$	23.2098	−	16.0955i	1.32682	−	0.920117i
$307$	−12.3183	−	7.11195i	−0.703040	−	0.405900i	0.105439	−	0.994426i	$-0.466375\pi$
$307$	−12.3183	−	7.11195i	−0.703040	−	0.405900i	−0.808479	+	0.588525i	$0.799709\pi$
$308$	0.0784561	−	0.215556i	0.00447045	−	0.0122825i
$309$	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	$0.585881\pi$
$312$	−0.229375	−	0.211141i	−0.0129858	−	0.0119535i
$313$	8.84996	−	24.3151i	0.500229	−	1.37437i	−0.390822	−	0.920466i	$-0.627809\pi$
$313$	8.84996	−	24.3151i	0.500229	−	1.37437i	0.891051	−	0.453902i	$-0.149968\pi$
$314$	−11.6938	+	20.2542i	−0.659917	+	1.14301i
$315$		0			0
$316$	−7.26032	−	12.5752i	−0.408425	−	0.707413i
$317$	−17.9868	+	3.17156i	−1.01024	+	0.178133i	−0.654187	−	0.756333i	$-0.726989\pi$
$317$	−17.9868	+	3.17156i	−1.01024	+	0.178133i	−0.356053	+	0.934466i	$0.615878\pi$
$318$	−5.49568	−	42.4873i	−0.308182	−	2.38257i
$319$	1.65807	−	0.603489i	0.0928342	−	0.0337889i
$320$		0			0
$321$	−26.2107	−	16.7817i	−1.46294	−	0.936661i
$322$	0.267276	+	0.318527i	0.0148947	+	0.0177508i
$323$		−	16.2822i		−	0.905968i
$324$	−12.0197	−	14.5910i	−0.667760	−	0.810609i
$325$		0			0
$326$	9.71387	−	8.15090i	0.538001	−	0.451437i
$327$	−1.03202	+	1.61188i	−0.0570709	+	0.0891371i
$328$	−1.90637	−	0.336144i	−0.105262	−	0.0185605i
$329$	−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	$-0.390905\pi$
$332$	16.3426	−	9.43539i	0.896916	−	0.517835i
$333$	3.01074	−	32.7056i	0.164987	−	1.79226i
$334$	−15.8580	+	27.4668i	−0.867709	+	1.50292i
$335$		0			0
$336$	1.67093	−	1.81522i	0.0911565	−	0.0990285i
$337$	−4.92591	+	5.87047i	−0.268332	+	0.319785i	−0.883338	−	0.468737i	$-0.844709\pi$
$337$	−4.92591	+	5.87047i	−0.268332	+	0.319785i	0.615006	+	0.788522i	$0.289154\pi$
$338$	15.9022	−	18.9515i	0.864965	−	1.03083i
$339$	−15.3456	−	3.43854i	−0.833461	−	0.186756i
$340$		0			0
$341$	0.797378	−	1.38110i	0.0431804	−	0.0747907i
$342$	−21.2015	+	1.75814i	−1.14644	+	0.0950691i
$343$	4.51204	−	2.60503i	0.243627	−	0.140658i
$344$	−0.358777	−	2.03472i	−0.0193439	−	0.109705i
$345$		0			0
$346$	17.3561	−	6.31710i	0.933069	−	0.339609i
$347$	3.49638	+	0.616506i	0.187695	+	0.0330958i	0.266706	−	0.963778i	$-0.414065\pi$
$347$	3.49638	+	0.616506i	0.187695	+	0.0330958i	−0.0790102	+	0.996874i	$0.525176\pi$
$348$	−22.0749	−	1.01391i	−1.18334	−	0.0543515i
$349$	3.58455	−	3.00779i	0.191876	−	0.161003i	−0.541788	−	0.840515i	$-0.682253\pi$
$349$	3.58455	−	3.00779i	0.191876	−	0.161003i	0.733665	+	0.679511i	$0.237808\pi$
$350$		0			0
$351$	−3.41048	+	3.08276i	−0.182038	+	0.164545i
$352$		−	2.34703i		−	0.125097i
$353$	−10.0759	−	12.0080i	−0.536286	−	0.639120i	0.428065	−	0.903748i	$-0.359195\pi$
$353$	−10.0759	−	12.0080i	−0.536286	−	0.639120i	−0.964351	+	0.264628i	$0.914751\pi$
$354$	3.93703	−	2.03817i	0.209251	−	0.108327i
$355$		0			0
$356$	−12.2794	+	4.46934i	−0.650807	+	0.236874i
$357$	−2.40602	+	1.83756i	−0.127340	+	0.0972539i
$358$	5.26907	−	0.929080i	0.278479	−	0.0491034i
$359$	1.36397	+	2.36247i	0.0719876	+	0.124686i	0.899772	−	0.436360i	$-0.143732\pi$
$359$	1.36397	+	2.36247i	0.0719876	+	0.124686i	−0.827785	+	0.561046i	$0.810399\pi$
$360$		0			0
$361$	3.36800	−	5.83355i	0.177263	−	0.307029i
$362$	4.91608	−	13.5068i	0.258383	−	0.709902i
$363$	18.0442	−	5.64440i	0.947074	−	0.296254i
$364$	0.535189	+	0.449077i	0.0280516	+	0.0235380i
$365$		0			0
$366$	3.01266	+	9.63096i	0.157474	+	0.503418i
$367$	10.9091	−	29.9725i	0.569450	−	1.56455i	−0.235916	−	0.971773i	$-0.575809\pi$
$367$	10.9091	−	29.9725i	0.569450	−	1.56455i	0.805366	−	0.592778i	$-0.201969\pi$
$368$	1.79228	+	1.03478i	0.0934293	+	0.0539414i
$369$	−7.51293	+	27.5390i	−0.391107	+	1.43362i
$370$		0			0
$371$	0.797399	+	4.52228i	0.0413989	+	0.234785i
$372$	−15.8727	+	12.1225i	−0.822962	+	0.628525i
$373$	2.11873	+	5.82118i	0.109704	+	0.301409i	0.982381	−	0.186888i	$-0.0598403\pi$
$373$	2.11873	+	5.82118i	0.109704	+	0.301409i	−0.872677	+	0.488298i	$0.837618\pi$
$374$	−0.474924	+	2.69343i	−0.0245577	+	0.139274i
$375$		0			0
$376$	0.986932	−	0.828134i	0.0508971	−	0.0427078i
$377$			5.37398i			0.276774i
$378$	2.65253	+	2.93451i	0.136431	+	0.150935i
$379$	−24.4506			−1.25595			−0.627973	−	0.778235i	$-0.716115\pi$
$379$	−24.4506			−1.25595			−0.627973	+	0.778235i	$0.716115\pi$
$380$		0			0
$381$	−0.858161	+	18.6838i	−0.0439649	+	0.957200i
$382$	−10.3596	−	1.82668i	−0.530045	−	0.0934612i
$383$	−2.55465	−	7.01885i	−0.130537	−	0.358647i	0.857155	−	0.515058i	$-0.172230\pi$
$383$	−2.55465	−	7.01885i	−0.130537	−	0.358647i	−0.987692	+	0.156411i	$0.950007\pi$
$384$	−1.08330	+	2.59866i	−0.0552821	+	0.132612i
$385$		0			0
$386$	3.97075	+	6.87755i	0.202106	+	0.350058i
$387$	−30.3631	+	2.51787i	−1.54344	+	0.127990i
$388$	25.5028	+	14.7240i	1.29471	+	0.747500i
$389$	26.7061	+	9.72022i	1.35405	+	0.492835i	0.914210	−	0.405240i	$-0.132812\pi$
$389$	26.7061	+	9.72022i	1.35405	+	0.492835i	0.439842	+	0.898075i	$0.355034\pi$
$390$		0			0
$391$	−1.94539	−	1.63238i	−0.0983826	−	0.0825528i
$392$	−0.896909	+	1.06889i	−0.0453007	+	0.0539873i
$393$	15.7714	+	14.5177i	0.795562	+	0.732320i
$394$	19.7356	+	7.18318i	0.994266	+	0.361883i
$395$		0			0
$396$	1.82282	+	0.167801i	0.0916001	+	0.00843231i
$397$	25.1031	−	14.4933i	1.25989	−	0.727396i	0.286834	−	0.957980i	$-0.407397\pi$
$397$	25.1031	−	14.4933i	1.25989	−	0.727396i	0.973052	+	0.230585i	$0.0740639\pi$
$398$	−23.7501	+	4.18777i	−1.19048	+	0.209914i
$399$	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	$-0.218607\pi$
$402$	16.7505	−	26.1620i	0.835437	−	1.30484i
$403$	3.12205	+	3.72071i	0.155520	+	0.185342i
$404$	8.44780			0.420294
$405$		0			0
$406$	4.62398			0.229484
$407$	2.04428	+	2.43627i	0.101331	+	0.120762i
$408$	0.883398	−	1.37975i	0.0437347	−	0.0683078i
$409$	0.726985	−	4.12294i	0.0359471	−	0.203866i	−0.961545	−	0.274649i	$-0.911438\pi$
$409$	0.726985	−	4.12294i	0.0359471	−	0.203866i	0.997492	+	0.0707824i	$0.0225496\pi$
$410$		0			0
$411$	−28.3402	+	3.66577i	−1.39792	+	0.180819i
$412$	1.06615	−	0.187992i	0.0525256	−	0.00926168i
$413$	−0.411531	+	0.237598i	−0.0202501	+	0.0116914i
$414$	−1.91549	+	2.70940i	−0.0941414	+	0.133160i
$415$		0			0
$416$	6.71711	+	2.44483i	0.329333	+	0.119868i
$417$	15.7123	+	14.4633i	0.769436	+	0.708271i
$418$	1.32416	−	1.57807i	0.0647666	−	0.0771858i
$419$	17.7641	+	14.9058i	0.867832	+	0.728197i	0.963640	−	0.267203i	$-0.0860993\pi$
$419$	17.7641	+	14.9058i	0.867832	+	0.728197i	−0.0958087	+	0.995400i	$0.530544\pi$
$420$		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	$0.553295\pi$
$422$	4.29399	+	2.47913i	0.209028	+	0.120682i
$423$	−10.8263	−	15.6117i	−0.526394	−	0.759065i
$424$	−1.24250	−	2.15207i	−0.0603411	−	0.104514i
$425$		0			0
$426$	14.4907	−	34.7606i	0.702075	−	1.68416i
$427$	−0.369944	−	1.01641i	−0.0179029	−	0.0491877i
$428$	−37.1694	−	6.55396i	−1.79665	−	0.316798i
$429$	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	$0.472684\pi$
$432$	17.4014	+	9.20941i	0.837223	+	0.443088i
$433$			39.5383i			1.90009i	0.312111	+	0.950046i	$0.398964\pi$
$433$			39.5383i			1.90009i	−0.312111	+	0.950046i	$0.601036\pi$
$434$	3.20145	−	2.68633i	0.153674	−	0.128948i
$435$		0			0
$436$	−0.403048	+	2.28580i	−0.0193025	+	0.109470i
$437$	0.654218	+	1.79745i	0.0312955	+	0.0859837i
$438$	2.17144	−	1.65840i	0.103755	−	0.0792415i
$439$	0.368776	+	2.09143i	0.0176007	+	0.0998186i	0.992343	−	0.123516i	$-0.0394169\pi$
$439$	0.368776	+	2.09143i	0.0176007	+	0.0998186i	−0.974742	+	0.223334i	$0.928306\pi$
$440$		0			0
$441$	14.4834	+	14.6152i	0.689684	+	0.695962i
$442$	−7.21377	−	4.16487i	−0.343124	−	0.198103i
$443$	−5.55606	+	15.2652i	−0.263977	+	0.725270i	0.734913	+	0.678161i	$0.237223\pi$
$443$	−5.55606	+	15.2652i	−0.263977	+	0.725270i	−0.998890	+	0.0471084i	$0.984999\pi$
$444$	−11.8910	−	38.0136i	−0.564323	−	1.80404i
$445$		0			0
$446$	27.9502	+	23.4530i	1.32348	+	1.11053i
$447$	−16.8713	+	5.27752i	−0.797987	+	0.249618i
$448$	1.12926	−	3.10260i	0.0533523	−	0.146584i
$449$	17.8132	−	30.8534i	0.840658	−	1.45606i	−0.0486805	−	0.998814i	$-0.515502\pi$
$449$	17.8132	−	30.8534i	0.840658	−	1.45606i	0.889339	−	0.457249i	$-0.151165\pi$
$450$		0			0
$451$	−1.38205	−	2.39378i	−0.0650781	−	0.112719i
$452$	−18.7815	+	3.31168i	−0.883406	+	0.155768i
$453$	−24.5782	+	18.7712i	−1.15478	+	0.881947i
$454$	10.1736	−	3.70288i	0.477470	−	0.173785i
$455$		0			0
$456$	−1.09587	+	0.567320i	−0.0513186	+	0.0265672i
$457$	16.5710	+	19.7485i	0.775157	+	0.923796i	0.998704	−	0.0508970i	$-0.0162080\pi$
$457$	16.5710	+	19.7485i	0.775157	+	0.923796i	−0.223547	+	0.974693i	$0.571764\pi$
$458$			43.6242i			2.03842i
$459$	−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	$0.982810\pi$
$462$	−0.382630	−	0.0175745i	−0.0178016	−	0.000817639i
$463$	29.0659	+	5.12509i	1.35080	+	0.238183i	0.801778	−	0.597622i	$-0.203888\pi$
$463$	29.0659	+	5.12509i	1.35080	+	0.238183i	0.549026	+	0.835805i	$0.314999\pi$
$464$	21.6265	−	7.87140i	1.00398	−	0.365421i
$465$		0			0
$466$	−8.98908	−	50.9796i	−0.416411	−	2.36158i
$467$	14.4100	−	8.31964i	0.666817	−	0.384987i	−0.128053	−	0.991767i	$-0.540873\pi$
$467$	14.4100	−	8.31964i	0.666817	−	0.384987i	0.794869	+	0.606780i	$0.207539\pi$
$468$	−2.37902	+	5.04205i	−0.109970	+	0.233069i
$469$	−1.66488	+	2.88366i	−0.0768770	+	0.133155i
$470$		0			0
$471$	19.5205	+	4.37400i	0.899455	+	0.201543i
$472$	0.165295	−	0.196991i	0.00760833	−	0.00906725i
$473$	1.89635	−	2.25999i	0.0871944	−	0.103914i
$474$	−16.4211	+	17.8392i	−0.754245	+	0.819380i
$475$		0			0
$476$	−1.83571	+	3.17955i	−0.0841397	+	0.145734i
$477$	−33.2808	+	15.3359i	−1.52382	+	0.702184i
$478$	16.2275	−	9.36897i	0.742230	−	0.428527i
$479$	−0.965663	−	5.47655i	−0.0441223	−	0.250230i	0.954767	−	0.297356i	$-0.0961048\pi$
$479$	−0.965663	−	5.47655i	−0.0441223	−	0.250230i	−0.998889	+	0.0471262i	$0.984994\pi$
$480$		0			0
$481$	−9.10199	+	3.31285i	−0.415015	+	0.151053i
$482$	57.3411	+	10.1108i	2.61182	+	0.460534i
$483$	0.191775	−	0.299528i	0.00872609	−	0.0136290i
$484$	17.5638	−	14.7378i	0.798354	−	0.669898i
$485$		0			0
$486$	−17.2608	+	26.4287i	−0.782968	+	1.19883i
$487$		−	17.5069i		−	0.793314i	−0.917967	−	0.396657i	$-0.870170\pi$
$487$		−	17.5069i		−	0.793314i	0.917967	−	0.396657i	$-0.129830\pi$
$488$	0.376246	+	0.448393i	0.0170319	+	0.0202978i
$489$	−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	$0.181821\pi$
$492$	4.44068	+	34.3311i	0.200201	+	1.54777i
$493$	−27.8118	+	4.90396i	−1.25258	+	0.220863i
$494$	3.13704	+	5.43351i	0.141142	+	0.244465i
$495$		0			0
$496$	10.4003	−	18.0139i	0.466988	−	0.808847i
$497$	−1.38063	+	3.79324i	−0.0619295	+	0.170150i
$498$	−23.1835	−	21.3406i	−1.03888	−	0.956294i
$499$	−4.46524	−	3.74678i	−0.199892	−	0.167729i	0.537347	−	0.843361i	$-0.319426\pi$
$499$	−4.46524	−	3.74678i	−0.199892	−	0.167729i	−0.737239	+	0.675632i	$0.763871\pi$
$500$		0			0
$501$	26.4718	+	5.93160i	1.18267	+	0.265004i
$502$	8.11986	−	22.3091i	0.362407	−	0.995705i
$503$	−26.4175	−	15.2521i	−1.17790	−	0.680059i	−0.222369	−	0.974963i	$-0.571379\pi$
$503$	−26.4175	−	15.2521i	−1.17790	−	0.680059i	−0.955527	+	0.294904i	$0.904712\pi$
$504$	0.207508	+	0.0979097i	0.00924316	+	0.00436124i
$505$		0			0
$506$	−0.0557931	−	0.316419i	−0.00248031	−	0.0140665i
$507$	−19.5317	−	8.14218i	−0.867433	−	0.361607i
$508$	7.75764	+	21.3139i	0.344190	+	0.945654i
$509$	5.46355	−	30.9853i	0.242167	−	1.37340i	−0.584813	−	0.811168i	$-0.698832\pi$
$509$	5.46355	−	30.9853i	0.242167	−	1.37340i	0.826980	−	0.562231i	$-0.190057\pi$
$510$		0			0
$511$	−0.224349	+	0.188252i	−0.00992464	+	0.00832776i
$512$		−	32.1543i		−	1.42103i
$513$	6.84925	+	16.8587i	0.302402	+	0.744330i
$514$	7.46958			0.329469
$515$		0			0
$516$	−32.8117	+	16.9863i	−1.44446	+	0.747782i
$517$	1.81168	+	0.319449i	0.0796778	+	0.0140493i
$518$	2.85051	+	7.83171i	0.125244	+	0.344106i
$519$	−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	$0.891403\pi$
$522$	9.38864	+	35.6848i	0.410930	+	1.56188i
$523$	15.4347	+	8.91120i	0.674910	+	0.389660i	0.797935	−	0.602744i	$-0.205926\pi$
$523$	15.4347	+	8.91120i	0.674910	+	0.389660i	−0.123024	+	0.992404i	$0.539259\pi$
$524$	24.4278	+	8.89098i	1.06713	+	0.388404i
$525$		0			0
$526$	34.3001	+	28.7812i	1.49556	+	1.25492i
$527$	−16.4067	+	19.5527i	−0.714686	+	0.851730i
$528$	−1.81949	+	0.569154i	−0.0791831	+	0.0247693i
$529$	−21.3326	−	7.76443i	−0.927504	−	0.337584i
$530$		0			0
$531$	−2.66920	−	2.69350i	−0.115834	−	0.116888i
$532$	2.39488	−	1.38268i	0.103831	−	0.0599469i
$533$	8.29054	−	1.46185i	0.359103	−	0.0633196i
$534$	13.2439	+	17.3409i	0.573118	+	0.750416i
$535$		0			0
$536$	0.312899	−	1.77454i	0.0135152	−	0.0766483i
$537$	−2.10396	−	4.06412i	−0.0907925	−	0.175380i
$538$	32.9741	+	39.2970i	1.42161	+	1.69421i
$539$	−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	$0.769973\pi$
$542$	−37.4584	−	44.6412i	−1.60898	−	1.91750i
$543$	−12.2816	−	0.564101i	−0.527052	−	0.0242079i
$544$	−6.52300	+	36.9938i	−0.279671	+	1.58610i
$545$		0			0
$546$	0.448872	−	1.07677i	0.0192099	−	0.0460814i
$547$	24.4154	−	4.30509i	1.04393	−	0.184072i	0.374711	−	0.927142i	$-0.377742\pi$
$547$	24.4154	−	4.30509i	1.04393	−	0.184072i	0.669214	+	0.743069i	$0.266631\pi$
$548$	−30.0118	+	17.3273i	−1.28204	+	0.740187i
$549$	7.09285	−	4.91873i	0.302715	−	0.209926i
$550$		0			0
$551$	19.9885	+	7.27523i	0.851540	+	0.309935i
$552$	−0.0420831	+	0.187810i	−0.00179117	+	0.00799373i
$553$	1.67054	−	1.99088i	0.0710388	−	0.0846607i
$554$	30.5984	+	25.6751i	1.30000	+	1.09083i
$555$		0			0
$556$	24.3363	+	8.85768i	1.03209	+	0.375649i
$557$	27.0026	+	15.5900i	1.14414	+	0.660568i	0.947452	−	0.319898i	$-0.103649\pi$
$557$	27.0026	+	15.5900i	1.14414	+	0.660568i	0.196686	+	0.980467i	$0.436982\pi$
$558$	27.2316	+	19.2522i	1.15281	+	0.815012i
$559$	4.49262	+	7.78145i	0.190018	+	0.329120i
$560$		0			0
$561$	2.32003	−	0.300093i	0.0979519	−	0.0126699i
$562$	6.04011	+	16.5951i	0.254787	+	0.700020i
$563$	−11.3381	−	1.99921i	−0.477844	−	0.0842567i	−0.0704615	−	0.997514i	$-0.522447\pi$
$563$	−11.3381	−	1.99921i	−0.477844	−	0.0842567i	−0.407382	+	0.913258i	$0.633558\pi$
$564$	−19.4030	−	12.4230i	−0.817015	−	0.523102i
$565$		0			0
$566$	−15.0410			−0.632219
$567$	1.71822	−	2.91473i	0.0721584	−	0.122407i
$568$		−	2.18446i		−	0.0916580i
$569$	−0.688909	+	0.578063i	−0.0288805	+	0.0242337i	−0.657114	−	0.753791i	$-0.728223\pi$
$569$	−0.688909	+	0.578063i	−0.0288805	+	0.0242337i	0.628233	+	0.778025i	$0.283778\pi$
$570$		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	$-0.296146\pi$
$572$	−0.184639	−	0.507292i	−0.00772015	−	0.0212109i
$573$	1.15424	+	8.92347i	0.0482190	+	0.372783i
$574$	−1.25783	−	7.13351i	−0.0525008	−	0.297747i
$575$		0			0
$576$	26.2367	+	2.41524i	1.09319	+	0.100635i
$577$	−10.7781	−	6.22274i	−0.448698	−	0.259056i	0.258582	−	0.965989i	$-0.416745\pi$
$577$	−10.7781	−	6.22274i	−0.448698	−	0.259056i	−0.707280	+	0.706933i	$0.750078\pi$
$578$	3.19765	−	8.78546i	0.133005	−	0.365427i
$579$	4.60046	−	4.99775i	0.191189	−	0.207699i
$580$		0			0
$581$	2.58731	+	2.17101i	0.107340	+	0.0900688i
$582$	10.7515	−	47.9822i	0.445664	−	1.98893i
$583$	1.21360	−	3.33434i	0.0502622	−	0.138094i
$584$	0.0792431	−	0.137253i	0.00327910	−	0.00567957i
$585$		0			0
$586$	1.91711	+	3.32053i	0.0791950	+	0.137170i
$587$	10.8379	−	1.91101i	0.447327	−	0.0788758i	0.0545530	−	0.998511i	$-0.482627\pi$
$587$	10.8379	−	1.91101i	0.447327	−	0.0788758i	0.392774	+	0.919635i	$0.371516\pi$
$588$	23.0315	+	9.60115i	0.949804	+	0.395945i
$589$	18.0658	−	6.57541i	0.744388	−	0.270935i
$590$		0			0
$591$	0.824242	−	17.9453i	0.0339048	−	0.738172i
$592$	26.6638	+	31.7767i	1.09588	+	1.30601i
$593$		−	9.57442i		−	0.393174i	−0.980486	−	0.196587i	$-0.937014\pi$
$593$		−	9.57442i		−	0.393174i	0.980486	−	0.196587i	$-0.0629859\pi$
$594$	−0.641273	−	2.98856i	−0.0263117	−	0.122622i
$595$		0			0
$596$	−16.4222	+	13.7798i	−0.672678	+	0.564444i
$597$	9.48348	+	18.3188i	0.388133	+	0.749738i
$598$	0.963696	+	0.169926i	0.0394085	+	0.00694878i
$599$	30.9256	−	11.2560i	1.26359	−	0.459908i	0.378616	−	0.925554i	$-0.376400\pi$
$599$	30.9256	−	11.2560i	1.26359	−	0.459908i	0.884971	+	0.465646i	$0.154178\pi$
$600$		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	$-0.139573\pi$
$602$	6.69547	−	3.86563i	0.272887	−	0.157551i
$603$	−25.6345	−	6.99338i	−1.04392	−	0.284793i
$604$	−18.7523	+	32.4800i	−0.763021	+	1.32159i
$605$		0			0
$606$	−4.21128	−	13.4627i	−0.171072	−	0.546886i
$607$	−24.0848	+	28.7032i	−0.977573	+	1.16503i	0.00870958	+	0.999962i	$0.497228\pi$
$607$	−24.0848	+	28.7032i	−0.977573	+	1.16503i	−0.986283	+	0.165064i	$0.947217\pi$
$608$	18.1871	−	21.6745i	0.737583	−	0.879018i
$609$	−1.18078	−	3.77475i	−0.0478477	−	0.152961i
$610$		0			0
$611$	−2.80143	+	4.85221i	−0.113334	+	0.196300i
$612$	−28.2649	−	7.71096i	−1.14254	−	0.311697i
$613$	2.26483	−	1.30760i	0.0914758	−	0.0528136i	−0.453564	−	0.891224i	$-0.649848\pi$
$613$	2.26483	−	1.30760i	0.0914758	−	0.0528136i	0.545040	+	0.838410i	$0.316514\pi$
$614$	5.00156	+	28.3653i	0.201847	+	1.14473i
$615$		0			0
$616$	−0.0208779	+	0.00759892i	−0.000841193	+	0.000306169i
$617$	6.35172	+	1.11998i	0.255711	+	0.0450887i	0.300034	−	0.953929i	$-0.403002\pi$
$617$	6.35172	+	1.11998i	0.255711	+	0.0450887i	−0.0443232	+	0.999017i	$0.514113\pi$
$618$	−0.831075	−	1.60535i	−0.0334307	−	0.0645766i
$619$	0.0522006	−	0.0438015i	0.00209812	−	0.00176053i	−0.641738	−	0.766924i	$-0.721786\pi$
$619$	0.0522006	−	0.0438015i	0.00209812	−	0.00176053i	0.643836	+	0.765163i	$0.277342\pi$
$620$		0			0
$621$	2.70094	+	0.871826i	0.108385	+	0.0349852i
$622$		−	29.6649i		−	1.18945i
$623$	−1.50336	−	1.79164i	−0.0602309	−	0.0717804i
$624$	0.266407	−	5.80018i	0.0106648	−	0.232193i
$625$		0			0
$626$	−49.2370	+	17.9208i	−1.96791	+	0.716260i
$627$	−1.62638	−	0.677989i	−0.0649514	−	0.0270763i
$628$	23.8910	−	4.21263i	0.953355	−	0.168102i
$629$	−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	$0.812044\pi$
$632$	−0.481019	+	1.32159i	−0.0191339	+	0.0525700i
$633$	0.927309	−	4.13843i	0.0368572	−	0.164488i
$634$	28.3317	+	23.7732i	1.12520	+	0.944153i
$635$		0			0
$636$	−30.0965	+	32.6956i	−1.19340	+	1.29646i
$637$	2.07543	−	5.70220i	0.0822316	−	0.225930i
$638$	−3.09432	−	1.78651i	−0.122505	−	0.0707284i
$639$	−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	$0.685374\pi$
$642$	8.08451	+	62.5017i	0.319070	+	2.46675i
$643$	1.67760	+	4.60918i	0.0661582	+	0.181768i	0.968366	−	0.249533i	$-0.0802770\pi$
$643$	1.67760	+	4.60918i	0.0661582	+	0.181768i	−0.902208	+	0.431301i	$0.858055\pi$
$644$	0.0748965	−	0.424759i	0.00295134	−	0.0167379i
$645$		0			0
$646$	−25.2572	+	21.1933i	−0.993730	+	0.833838i
$647$		−	37.6519i		−	1.48025i	−0.672469	−	0.740125i	$-0.734766\pi$
$647$		−	37.6519i		−	1.48025i	0.672469	−	0.740125i	$-0.265234\pi$
$648$	−0.334271	+	1.80021i	−0.0131314	+	0.0707188i
$649$	0.367190			0.0144135
$650$		0			0
$651$	−3.01049	−	1.92750i	−0.117990	−	0.0755445i
$652$	−12.9536	−	2.28406i	−0.507300	−	0.0894507i
$653$	7.83944	+	21.5387i	0.306781	+	0.842874i	0.993279	+	0.115743i	$0.0369247\pi$
$653$	7.83944	+	21.5387i	0.306781	+	0.842874i	−0.686498	+	0.727132i	$0.740853\pi$
$654$	3.84366	−	0.497172i	0.150299	−	0.0194410i
$655$		0			0
$656$	−18.0263	−	31.2224i	−0.703807	−	1.21903i
$657$	−1.90832	−	1.34915i	−0.0744508	−	0.0526353i
$658$	4.17504	+	2.41046i	0.162760	+	0.0939694i
$659$	−4.41936	−	1.60852i	−0.172154	−	0.0626589i	0.254505	−	0.967071i	$-0.418087\pi$
$659$	−4.41936	−	1.60852i	−0.172154	−	0.0626589i	−0.426659	+	0.904412i	$0.640310\pi$
$660$		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	$0.944680\pi$
$662$	−41.1657	+	49.0593i	−1.59995	+	1.90675i
$663$	−1.55785	+	6.95245i	−0.0605020	+	0.270011i
$664$	−1.71752	−	0.625125i	−0.0666526	−	0.0242596i
$665$		0			0
$666$	−54.6521	+	37.9000i	−2.11773	+	1.46859i
$667$	2.87319	−	1.65884i	0.111250	−	0.0642304i
$668$	32.3987	−	5.71277i	1.25354	−	0.221034i
$669$	12.0083	−	28.8059i	0.464268	−	1.11370i
$670$		0			0
$671$	−0.145135	+	0.823103i	−0.00560288	+	0.0317755i
$672$	−5.25537	−	0.241383i	−0.202730	−	0.00931155i
$673$	−28.5883	−	34.0702i	−1.10200	−	1.31331i	−0.945497	−	0.325631i	$-0.894423\pi$
$673$	−28.5883	−	34.0702i	−1.10200	−	1.31331i	−0.156500	−	0.987678i	$-0.550021\pi$
$674$	15.5180			0.597731
$675$		0			0
$676$	−25.6619			−0.986996
$677$	5.51191	+	6.56883i	0.211840	+	0.252461i	0.861492	−	0.507770i	$-0.169530\pi$
$677$	5.51191	+	6.56883i	0.211840	+	0.252461i	−0.649653	+	0.760231i	$0.725086\pi$
$678$	14.6403	+	28.2800i	0.562257	+	1.08609i
$679$	−0.915233	+	5.19055i	−0.0351234	+	0.199195i
$680$		0			0
$681$	−5.62075	−	7.35956i	−0.215388	−	0.282019i
$682$	−3.18026	+	0.560765i	−0.121778	+	0.0214728i
$683$	38.0739	−	21.9820i	1.45686	−	0.841117i	0.458002	−	0.888951i	$-0.348565\pi$
$683$	38.0739	−	21.9820i	1.45686	−	0.841117i	0.998855	+	0.0478347i	$0.0152321\pi$
$684$	15.5332	+	15.6746i	0.593928	+	0.599334i
$685$		0			0
$686$	−9.91390	−	3.60836i	−0.378514	−	0.137768i
$687$	35.6123	−	11.1399i	1.35869	−	0.425013i
$688$	24.7344	−	29.4773i	0.942991	−	1.12381i
$689$	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	$0.472987\pi$
$692$	−16.5919	−	9.57933i	−0.630729	−	0.364152i
$693$	0.0833617	+	0.316845i	0.00316665	+	0.0120359i
$694$	−3.59462	−	6.22607i	−0.136450	−	0.236338i
$695$		0			0
$696$	1.29910	+	1.70098i	0.0492423	+	0.0644756i
$697$	15.1309	+	41.5717i	0.573123	+	1.57464i
$698$	−9.33144	−	1.64538i	−0.353200	−	0.0622787i
$699$	−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	$0.504378\pi$
$702$	9.22116	+	1.27780i	0.348030	+	0.0482274i
$703$			38.3398i			1.44601i
$704$	−1.95440	+	1.63993i	−0.0736591	+	0.0618073i
$705$		0			0
$706$	−5.51192	+	31.2596i	−0.207444	+	1.17647i
$707$	0.517130	+	1.42080i	0.0194487	+	0.0534348i
$708$	−4.24458	−	1.76944i	−0.159521	−	0.0664996i
$709$	−2.85514	−	16.1923i	−0.107227	−	0.608115i	−0.990307	−	0.138893i	$-0.955646\pi$
$709$	−2.85514	−	16.1923i	−0.107227	−	0.608115i	0.883080	−	0.469222i	$-0.155465\pi$
$710$		0			0
$711$	18.7562	+	8.84981i	0.703411	+	0.331894i
$712$	1.09609	+	0.632829i	0.0410778	+	0.0237163i
$713$	1.02556	−	2.81771i	0.0384076	−	0.105524i
$714$	5.98216	+	1.34044i	0.223877	+	0.0501646i
$715$		0			0
$716$	−4.25144	−	3.56738i	−0.158884	−	0.133319i
$717$	−11.7922	−	10.8548i	−0.440386	−	0.405379i
$718$	1.88931	−	5.19084i	0.0705085	−	0.193720i
$719$	−18.6844	+	32.3624i	−0.696811	+	1.20691i	0.272755	+	0.962083i	$0.412065\pi$
$719$	−18.6844	+	32.3624i	−0.696811	+	1.20691i	−0.969566	+	0.244829i	$0.921268\pi$
$720$		0			0
$721$	0.0968819	+	0.167804i	0.00360807	+	0.00624936i
$722$	−13.4329	+	2.36859i	−0.499922	+	0.0881497i
$723$	−6.38878	−	49.3919i	−0.237601	−	1.83690i
$724$	−14.0105	+	5.09939i	−0.520694	+	0.189517i
$725$		0			0
$726$	−32.2423	−	20.6435i	−1.19662	−	0.766150i
$727$	3.26002	+	3.88514i	0.120907	+	0.144092i	0.823103	−	0.567893i	$-0.192241\pi$
$727$	3.26002	+	3.88514i	0.120907	+	0.144092i	−0.702195	+	0.711984i	$0.747797\pi$
$728$		−	0.0676673i		−	0.00250792i
$729$	25.9826	+	7.34192i	0.962319	+	0.271923i
$730$		0			0
$731$	−36.1714	+	30.3514i	−1.33785	+	1.12259i
$732$	5.64413	−	8.81539i	0.208613	−	0.325826i
$733$	−24.6950	−	4.35439i	−0.912129	−	0.160833i	−0.302159	−	0.953257i	$-0.597707\pi$
$733$	−24.6950	−	4.35439i	−0.912129	−	0.160833i	−0.609970	+	0.792424i	$0.708819\pi$
$734$	−60.6931	+	22.0905i	−2.24022	+	0.815375i
$735$		0			0
$736$	−0.766310	−	4.34596i	−0.0282466	−	0.160194i
$737$	2.22824	−	1.28647i	0.0820783	−	0.0473879i
$738$	52.4977	−	24.1911i	1.93247	−	0.890487i
$739$	23.1354	−	40.0717i	0.851050	−	1.47406i	−0.0292117	−	0.999573i	$-0.509300\pi$
$739$	23.1354	−	40.0717i	0.851050	−	1.47406i	0.880262	−	0.474489i	$-0.157367\pi$
$740$		0			0
$741$	3.63453	−	3.94840i	0.133518	−	0.145048i
$742$	5.97709	−	7.12322i	0.219426	−	0.261502i
$743$	−21.0629	+	25.1018i	−0.772723	+	0.920896i	−0.998580	−	0.0532649i	$-0.983037\pi$
$743$	−21.0629	+	25.1018i	−0.772723	+	0.920896i	0.225857	+	0.974160i	$0.427482\pi$
$744$	1.88764	+	0.422968i	0.0692042	+	0.0155068i
$745$		0			0
$746$	6.27208	−	10.8636i	0.229637	−	0.397743i
$747$	−11.5011	+	24.3752i	−0.420802	+	0.891842i
$748$	2.45688	−	1.41848i	0.0898323	−	0.0518647i
$749$	−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	$0.315260\pi$
$752$	23.6301	+	4.16662i	0.861700	+	0.151941i
$753$	−20.2854	−	0.931722i	−0.739240	−	0.0339538i
$754$	8.33617	−	6.99488i	0.303585	−	0.254738i
$755$		0			0
$756$	0.563203	−	4.06432i	0.0204835	−	0.147818i
$757$			35.3551i			1.28500i	0.766285	+	0.642501i	$0.222103\pi$
$757$			35.3551i			1.28500i	−0.766285	+	0.642501i	$0.777897\pi$
$758$	31.8254	+	37.9281i	1.15595	+	1.37761i
$759$	−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	$0.362163\pi$
$762$	30.0995	−	22.9880i	1.09039	−	0.832768i
$763$	−0.409113	+	0.0721376i	−0.0148109	+	0.00261156i
$764$	5.45584	+	9.44980i	0.197386	+	0.341882i
$765$		0			0
$766$	−7.56253	+	13.0987i	−0.273245	+	0.473275i
$767$	−0.382490	+	1.05088i	−0.0138109	+	0.0379452i
$768$	−23.5950	+	7.38076i	−0.851412	+	0.266330i
$769$	10.2592	+	8.60849i	0.369956	+	0.310430i	0.808744	−	0.588161i	$-0.200148\pi$
$769$	10.2592	+	8.60849i	0.369956	+	0.310430i	−0.438788	+	0.898591i	$0.644592\pi$
$770$		0			0
$771$	−1.90743	−	6.09774i	−0.0686946	−	0.219605i
$772$	2.81744	−	7.74084i	0.101402	−	0.278599i
$773$	−20.2297	−	11.6796i	−0.727612	−	0.420087i	0.0899361	−	0.995948i	$-0.471334\pi$
$773$	−20.2297	−	11.6796i	−0.727612	−	0.420087i	−0.817548	+	0.575861i	$0.804667\pi$
$774$	43.4270	+	43.8222i	1.56095	+	1.57516i
$775$		0			0
$776$	−0.495282	−	2.80888i	−0.0177796	−	0.100833i
$777$	5.66545	−	4.32690i	0.203247	−	0.155227i
$778$	−19.6831	−	54.0788i	−0.705672	−	1.93882i
$779$	5.78629	−	32.8157i	0.207316	−	1.17574i
$780$		0			0
$781$	2.38944	−	2.00498i	0.0855010	−	0.0717438i
$782$			5.14244i			0.183893i
$783$	26.7335	−	16.7768i	0.955378	−	0.599555i
$784$	−25.9873			−0.928118
$785$		0			0
$786$	1.99161	−	43.3613i	0.0710385	−	1.54664i
$787$	−44.8881	−	7.91498i	−1.60009	−	0.282139i	−0.698786	−	0.715331i	$-0.746276\pi$
$787$	−44.8881	−	7.91498i	−1.60009	−	0.282139i	−0.901301	+	0.433193i	$0.857387\pi$
$788$	−7.45102	−	20.4715i	−0.265432	−	0.729267i
$789$	14.7365	−	35.3503i	0.524632	−	1.25850i
$790$		0			0
$791$	−1.70668	−	2.95606i	−0.0606827	−	0.105105i
$792$	−0.101034	−	0.145692i	−0.00359010	−	0.00517695i
$793$	−2.20451	−	1.27277i	−0.0782844	−	0.0451975i
$794$	−55.1567	−	20.0754i	−1.95744	−	0.712449i
$795$		0			0
$796$	19.1631	+	16.0798i	0.679219	+	0.569932i
$797$	−19.1281	+	22.7960i	−0.677553	+	0.807477i	−0.989791	−	0.142528i	$-0.954477\pi$
$797$	−19.1281	+	22.7960i	−0.677553	+	0.807477i	0.312238	+	0.950004i	$0.398922\pi$
$798$	−3.39736	−	3.12729i	−0.120265	−	0.110705i
$799$	−27.6679	−	10.0703i	−0.978820	−	0.356261i
$800$		0			0
$801$	10.7742	−	15.2397i	0.380687	−	0.538469i
$802$	−53.2864	+	30.7649i	−1.88161	+	1.08635i
$803$	0.222864	−	0.0392970i	0.00786472	−	0.00138676i
$804$	−31.9570	+	4.13360i	−1.12704	+	0.145781i
$805$		0			0
$806$	1.70789	−	9.68591i	0.0601578	−	0.341172i
$807$	23.6595	−	36.9531i	0.832855	−	1.30081i
$808$	−0.525940	−	0.626791i	−0.0185025	−	0.0220504i
$809$	−6.39776			−0.224933			−0.112467	−	0.993656i	$-0.535875\pi$
$809$	−6.39776			−0.224933			−0.112467	+	0.993656i	$0.535875\pi$
$810$		0			0
$811$	6.93453			0.243504			0.121752	−	0.992561i	$-0.461149\pi$
$811$	6.93453			0.243504			0.121752	+	0.992561i	$0.461149\pi$
$812$	−3.08307	−	3.67426i	−0.108194	−	0.128941i
$813$	−26.8771	+	41.9785i	−0.942622	+	1.47225i
$814$	1.11830	−	6.34221i	0.0391965	−	0.222294i
$815$		0			0
$816$	30.2606	−	3.91416i	1.05933	−	0.137023i
$817$	35.0252	−	6.17588i	1.22538	−	0.216067i
$818$	−7.34180	+	4.23879i	−0.256700	+	0.148206i
$819$	−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	$0.579739\pi$
$822$	42.5746	+	39.1902i	1.48496	+	1.36692i
$823$	−16.0888	+	19.1739i	−0.560821	+	0.668360i	−0.969720	−	0.244219i	$-0.921468\pi$
$823$	−16.0888	+	19.1739i	−0.560821	+	0.668360i	0.408899	+	0.912580i	$0.365913\pi$
$824$	−0.0803243	−	0.0674001i	−0.00279823	−	0.00234799i
$825$		0			0
$826$	0.904222	+	0.329110i	0.0314619	+	0.0114512i
$827$	−9.91448	−	5.72413i	−0.344760	−	0.199048i	0.317615	−	0.948220i	$-0.397118\pi$
$827$	−9.91448	−	5.72413i	−0.344760	−	0.199048i	−0.662375	+	0.749172i	$0.730451\pi$
$828$	3.43008	−	0.284440i	0.119203	−	0.00988498i
$829$	11.2450	+	19.4769i	0.390555	+	0.676461i	0.992523	−	0.122059i	$-0.0389498\pi$
$829$	11.2450	+	19.4769i	0.390555	+	0.676461i	−0.601968	+	0.798520i	$0.705617\pi$
$830$		0			0
$831$	13.1461	−	31.5352i	0.456032	−	1.09394i
$832$	−2.65759	−	7.30168i	−0.0921355	−	0.253140i
$833$	31.4043	+	5.53743i	1.08809	+	0.191860i
$834$	1.98415	−	43.1988i	0.0687057	−	1.49585i
$835$		0			0
$836$	−2.13683			−0.0739039
$837$	8.76254	−	27.1466i	0.302878	−	0.938323i
$838$		−	46.9575i		−	1.62212i
$839$	−37.2179	+	31.2296i	−1.28491	+	1.07816i	−0.292358	+	0.956309i	$0.594440\pi$
$839$	−37.2179	+	31.2296i	−1.28491	+	1.07816i	−0.992548	+	0.121855i	$0.961116\pi$
$840$		0			0
$841$	1.37081	−	7.77424i	0.0472693	−	0.268077i
$842$	−5.13389	−	14.1052i	−0.176925	−	0.486099i
$843$	12.0048	−	9.16851i	0.413469	−	0.315780i
$844$	−0.893098	−	5.06501i	−0.0307417	−	0.174345i
$845$		0			0
$846$	−10.1252	+	37.1144i	−0.348112	+	1.27602i
$847$	3.55385	+	2.05182i	0.122112	+	0.0705013i
$848$	15.8292	−	43.4903i	0.543576	−	1.49346i
$849$	3.84087	+	12.2786i	0.131818	+	0.421400i
$850$		0			0
$851$	4.58081	+	3.84376i	0.157028	+	0.131762i
$852$	−37.2828	+	11.6624i	−1.27729	+	0.399549i
$853$	−0.331738	+	0.911444i	−0.0113585	+	0.0312072i	−0.945242	−	0.326369i	$-0.894175\pi$
$853$	−0.331738	+	0.911444i	−0.0113585	+	0.0312072i	0.933884	+	0.357577i	$0.116397\pi$
$854$	−1.09514	+	1.89684i	−0.0374751	+	0.0649087i
$855$		0			0
$856$	1.82780	+	3.16584i	0.0624729	+	0.108206i
$857$	25.2108	−	4.44534i	0.861184	−	0.151850i	0.274422	−	0.961609i	$-0.411514\pi$
$857$	25.2108	−	4.44534i	0.861184	−	0.151850i	0.586762	+	0.809759i	$0.300402\pi$
$858$	−0.716396	+	0.547136i	−0.0244573	+	0.0186789i
$859$	11.4897	−	4.18192i	0.392025	−	0.142685i	−0.138484	−	0.990365i	$-0.544223\pi$
$859$	11.4897	−	4.18192i	0.392025	−	0.142685i	0.530509	+	0.847679i	$0.322001\pi$
$860$		0			0
$861$	−5.50219	+	2.84843i	−0.187514	+	0.0970744i
$862$	−4.63214	−	5.52037i	−0.157771	−	0.188025i
$863$			8.39103i			0.285634i	0.989749	+	0.142817i	$0.0456161\pi$
$863$			8.39103i			0.285634i	−0.989749	+	0.142817i	$0.954384\pi$
$864$	−8.80779	−	41.0475i	−0.299647	−	1.39646i
$865$		0			0
$866$	61.3323	−	51.4639i	2.08416	−	1.74881i
$867$	−7.98850	−	0.366918i	−0.271304	−	0.0124612i
$868$	−4.26917	−	0.752769i	−0.144905	−	0.0255507i
$869$	−1.88710	+	0.686848i	−0.0640154	+	0.0232997i
$870$		0			0
$871$	1.36075	+	7.71722i	0.0461074	+	0.261488i
$872$	0.194689	−	0.112404i	0.00659302	−	0.00380648i
$873$	−41.9154	+	3.47585i	−1.41862	+	0.117640i
$874$	1.93668	−	3.35443i	0.0655091	−	0.113465i
$875$		0			0
$876$	−2.76560	−	0.619695i	−0.0934409	−	0.0209375i
$877$	−26.8393	+	31.9858i	−0.906298	+	1.08008i	0.0901543	+	0.995928i	$0.471264\pi$
$877$	−26.8393	+	31.9858i	−0.906298	+	1.08008i	−0.996453	+	0.0841564i	$0.973180\pi$
$878$	2.76425	−	3.29430i	0.0932888	−	0.111177i
$879$	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	$0.105684\pi$
$882$	3.81941	−	41.4902i	0.128606	−	1.39705i
$883$	−21.3019	+	12.2986i	−0.716865	+	0.413882i	−0.813598	−	0.581428i	$-0.802494\pi$
$883$	−21.3019	+	12.2986i	−0.716865	+	0.413882i	0.0967330	+	0.995310i	$0.469161\pi$
$884$	1.50038	+	8.50908i	0.0504632	+	0.286191i
$885$		0			0
$886$	30.9113	−	11.2508i	1.03849	−	0.377978i
$887$	9.16975	+	1.61687i	0.307890	+	0.0542893i	0.325458	−	0.945556i	$-0.394481\pi$
$887$	9.16975	+	1.61687i	0.307890	+	0.0542893i	−0.0175685	+	0.999846i	$0.505593\pi$
$888$	−2.08014	+	3.24890i	−0.0698048	+	0.109026i
$889$	−3.10983	+	2.60946i	−0.104300	+	0.0875184i
$890$		0			0
$891$	−2.27594	+	1.28666i	−0.0762468	+	0.0431047i
$892$		−	37.8468i		−	1.26721i
$893$	14.2553	+	16.9888i	0.477035	+	0.568508i
$894$	30.1466	+	19.3017i	1.00825	+	0.645544i
$895$		0			0
$896$	−0.574234	+	0.209004i	−0.0191838	+	0.00698234i
$897$	−0.107372	−	0.830099i	−0.00358505	−	0.0277162i
$898$	−71.0462	+	12.5274i	−2.37084	+	0.418043i
$899$	−16.6726	−	28.8778i	−0.556063	−	0.963130i
$900$		0			0
$901$	−28.3957	+	49.1828i	−0.945999	+	1.63852i
$902$	−1.91435	+	5.25964i	−0.0637409	+	0.175127i
$903$	−4.86543	−	4.47867i	−0.161911	−	0.149041i
$904$	1.41500	+	1.18733i	0.0470623	+	0.0394899i
$905$		0			0
$906$	61.1095	+	13.6930i	2.03023	+	0.454918i
$907$	−4.95182	+	13.6050i	−0.164423	+	0.451747i	−0.994353	−	0.106119i	$-0.966158\pi$
$907$	−4.95182	+	13.6050i	−0.164423	+	0.451747i	0.829931	+	0.557866i	$0.188380\pi$
$908$	−9.72563	−	5.61510i	−0.322757	−	0.186344i
$909$	−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	$0.825335\pi$
$912$	−21.2131	−	8.84311i	−0.702437	−	0.292825i
$913$	−0.892616	−	2.45244i	−0.0295413	−	0.0811640i
$914$	9.06499	−	51.4101i	0.299843	−	1.70049i
$915$		0			0
$916$	34.6642	−	29.0867i	1.14534	−	0.961051i
$917$			4.65267i			0.153645i
$918$	1.80172	+	48.8879i	0.0594657	+	1.61354i
$919$	23.3762			0.771109			0.385554	−	0.922685i	$-0.374010\pi$
$919$	23.3762			0.771109			0.385554	+	0.922685i	$0.374010\pi$
$920$		0			0
$921$	21.8786	−	11.3263i	0.720923	−	0.373216i
$922$	68.4753	+	12.0740i	2.25511	+	0.397637i
$923$	3.24917	+	8.92702i	0.106948	+	0.293837i
$924$	0.241156	+	0.315759i	0.00793345	+	0.0103877i
$925$		0			0
$926$	−29.8826	−	51.7582i	−0.982003	−	1.70088i
$927$	−1.09829	+	1.08838i	−0.0360726	+	0.0357472i
$928$	−42.5000	−	24.5374i	−1.39513	−	0.805479i
$929$	8.18841	+	2.98034i	0.268653	+	0.0977817i	0.472834	−	0.881151i	$-0.343231\pi$
$929$	8.18841	+	2.98034i	0.268653	+	0.0977817i	−0.204181	+	0.978933i	$0.565453\pi$
$930$		0			0
$931$	−18.3997	−	15.4391i	−0.603024	−	0.505998i
$932$	−34.5153	+	41.1337i	−1.13059	+	1.34738i
$933$	−24.2167	+	7.57523i	−0.792819	+	0.248002i
$934$	−31.6619	−	11.5240i	−1.03601	−	0.377076i
$935$		0			0
$936$	0.522210	−	0.137393i	0.0170690	−	0.00449084i
$937$	35.2473	−	20.3500i	1.15148	−	0.664806i	0.202231	−	0.979338i	$-0.435181\pi$
$937$	35.2473	−	20.3500i	1.15148	−	0.664806i	0.949247	+	0.314532i	$0.101847\pi$
$938$	6.64020	−	1.17085i	0.216810	−	0.0382295i
$939$	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	$-0.175530\pi$
$942$	−18.6232	−	35.9736i	−0.606778	−	1.17208i
$943$	−3.34069	−	3.98129i	−0.108788	−	0.129648i
$944$	4.78931			0.155879
$945$		0			0
$946$	−5.97404			−0.194233
$947$	12.0921	+	14.4108i	0.392940	+	0.468288i	0.925854	−	0.377882i	$-0.123347\pi$
$947$	12.0921	+	14.4108i	0.392940	+	0.468288i	−0.532914	+	0.846170i	$0.678903\pi$
$948$	25.1240	+	1.15396i	0.815990	+	0.0374790i
$949$	−0.119684	+	0.678764i	−0.00388512	+	0.0220336i
$950$		0			0
$951$	12.1722	−	29.1991i	0.394712	−	0.946847i
$952$	0.350196	−	0.0617490i	0.0113499	−	0.00200130i
$953$	35.4426	−	20.4628i	1.14810	−	0.662855i	0.199675	−	0.979862i	$-0.436011\pi$
$953$	35.4426	−	20.4628i	1.14810	−	0.662855i	0.948423	+	0.317007i	$0.102678\pi$
$954$	67.1082	+	31.6640i	2.17271	+	1.02516i
$955$		0			0
$956$	−18.2645	−	6.64772i	−0.590715	−	0.215003i
$957$	−0.668235	+	2.98223i	−0.0216010	+	0.0964017i
$958$	−7.23835	+	8.62633i	−0.233860	+	0.278704i
$959$	−4.75139	−	3.98689i	−0.153430	−	0.128743i
$960$		0			0
$961$	0.810279	+	0.294918i	0.0261380	+	0.00951347i
$962$	16.9863	+	9.80702i	0.547659	+	0.316191i
$963$	48.9583	−	22.5602i	1.57766	−	0.726992i
$964$	−30.1984	−	52.3052i	−0.972625	−	1.68464i
$965$		0			0
$966$	−0.714249	+	0.0923872i	−0.0229806	+	0.00297251i
$967$	−13.1096	−	36.0183i	−0.421576	−	1.15827i	−0.950805	−	0.309791i	$-0.899741\pi$
$967$	−13.1096	−	36.0183i	−0.421576	−	1.15827i	0.529229	−	0.848479i	$-0.322481\pi$
$968$	−2.18696	−	0.385620i	−0.0702915	−	0.0123943i
$969$	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	$0.201785\pi$
$972$	32.5092	−	3.90588i	1.04273	−	0.125281i
$973$			4.63525i			0.148599i
$974$	−27.1569	+	22.7874i	−0.870164	+	0.730154i
$975$		0			0
$976$	−1.89302	+	10.7359i	−0.0605941	+	0.343646i
$977$	6.87174	+	18.8800i	0.219847	+	0.604023i	0.999761	−	0.0218628i	$-0.00695969\pi$
$977$	6.87174	+	18.8800i	0.219847	+	0.604023i	−0.779914	+	0.625886i	$0.784737\pi$
$978$	2.81746	+	21.7819i	0.0900924	+	0.696508i
$979$	0.313823	+	1.77978i	0.0100298	+	0.0568820i
$980$		0			0
$981$	−1.38738	−	3.01079i	−0.0442957	−	0.0961270i
$982$	−47.0658	−	27.1734i	−1.50193	−	0.867139i
$983$	−16.0497	+	44.0962i	−0.511906	+	1.40645i	0.367342	+	0.930086i	$0.380268\pi$
$983$	−16.0497	+	44.0962i	−0.511906	+	1.40645i	−0.879248	+	0.476364i	$0.841954\pi$
$984$	2.27076	−	2.46685i	0.0723891	−	0.0786404i
$985$		0			0
$986$	43.8074	+	36.7588i	1.39511	+	1.17064i
$987$	0.901621	−	4.02379i	0.0286989	−	0.128079i
$988$	2.22587	−	6.11554i	0.0708145	−	0.194561i
$989$	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	$0.857783\pi$
$992$	−43.6803	+	7.70202i	−1.38685	+	0.244539i
$993$	50.5613	+	21.0775i	1.60451	+	0.668874i
$994$	7.68116	−	2.79571i	0.243632	−	0.0886747i
$995$		0			0
$996$	−1.49967	+	32.6507i	−0.0475190	+	1.03458i
$997$	−10.2563	−	12.2229i	−0.324819	−	0.387104i	0.578780	−	0.815484i	$-0.303529\pi$
$997$	−10.2563	−	12.2229i	−0.324819	−	0.387104i	−0.903599	+	0.428380i	$0.859085\pi$
$998$			11.8034i			0.373630i
$999$	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.u.e.49.4		132
5.2	odd	4		675.2.l.g.76.10	yes	66
5.3	odd	4		675.2.l.f.76.2	✓	66
5.4	even	2	inner	675.2.u.e.49.19		132
27.16	even	9	inner	675.2.u.e.124.19		132
135.43	odd	36		675.2.l.f.151.2	yes	66
135.97	odd	36		675.2.l.g.151.10	yes	66
135.124	even	18	inner	675.2.u.e.124.4		132

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

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30162 - 1.55121i) q^{2} +(-0.933937 + 1.45868i) q^{3} +(-0.364742 + 2.06856i) q^{4} +(3.47836 - 0.449921i) q^{6} +(-0.370230 + 0.0652816i) q^{7} +(0.176186 - 0.101721i) q^{8} +(-1.25552 - 2.72464i) q^{9} +(0.272976 + 0.0993552i) q^{11} +(-2.67673 - 2.46395i) q^{12} +(-0.568702 + 0.677752i) q^{13} +(0.583165 + 0.489333i) q^{14} +(3.56047 + 1.29590i) q^{16} +(-4.02651 - 2.32471i) q^{17} +(-2.59227 + 5.49403i) q^{18} +(1.75100 + 3.03282i) q^{19} +(0.250547 - 0.601018i) q^{21} +(-0.201190 - 0.552766i) q^{22} +(0.537906 + 0.0948473i) q^{23} +(-0.0161677 + 0.352001i) q^{24} +1.79157 q^{26} +(5.14697 + 0.713228i) q^{27} -0.789653i q^{28} +(4.65300 - 3.90433i) q^{29} +(0.953291 - 5.40638i) q^{31} +(-2.76332 - 7.59216i) q^{32} +(-0.399870 + 0.305395i) q^{33} +(1.63488 + 9.27184i) q^{34} +(6.09401 - 1.60333i) q^{36} +(9.48122 + 5.47398i) q^{37} +(2.42541 - 6.66375i) q^{38} +(-0.457496 - 1.46253i) q^{39} +(-7.28901 - 6.11620i) q^{41} +(-1.25842 + 0.393647i) q^{42} +(3.47348 - 9.54330i) q^{43} +(-0.305088 + 0.528427i) q^{44} +(-0.553021 - 0.957860i) q^{46} +(6.23654 - 1.09967i) q^{47} +(-5.21557 + 3.98331i) q^{48} +(-6.44504 + 2.34580i) q^{49} +(7.15152 - 3.70228i) q^{51} +(-1.19454 - 1.42360i) q^{52} -12.2148i q^{53} +(-5.59303 - 8.91238i) q^{54} +(-0.0585889 + 0.0491619i) q^{56} +(-6.05925 - 0.278306i) q^{57} +(-12.1129 - 2.13583i) q^{58} +(1.18778 - 0.432318i) q^{59} +(0.499613 + 2.83345i) q^{61} +(-9.62726 + 5.55830i) q^{62} +(0.642702 + 0.926782i) q^{63} +(-4.39127 + 7.60590i) q^{64} +(0.994211 + 0.222775i) q^{66} +(5.69325 - 6.78495i) q^{67} +(6.27742 - 7.48114i) q^{68} +(-0.640723 + 0.696054i) q^{69} +(5.36876 - 9.29896i) q^{71} +(-0.498359 - 0.352330i) q^{72} +(0.674654 - 0.389512i) q^{73} +(-3.84964 - 21.8324i) q^{74} +(-6.91222 + 2.51584i) q^{76} +(-0.107550 - 0.0189640i) q^{77} +(-1.67321 + 2.61334i) q^{78} +(-5.29571 + 4.44363i) q^{79} +(-5.84732 + 6.84170i) q^{81} +19.2678i q^{82} +(-5.77486 - 6.88221i) q^{83} +(1.15186 + 0.737486i) q^{84} +(-19.3248 + 7.03366i) q^{86} +(1.34958 + 10.4337i) q^{87} +(0.0582011 - 0.0102624i) q^{88} +(3.11061 + 5.38773i) q^{89} +(0.166306 - 0.288050i) q^{91} +(-0.392394 + 1.07809i) q^{92} +(6.99589 + 6.43977i) q^{93} +(-9.82342 - 8.24283i) q^{94} +(13.6553 + 3.05978i) q^{96} +(4.79504 - 13.1743i) q^{97} +(12.0278 + 6.94427i) q^{98} +(-0.0720209 - 0.868504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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