LMFDB - Embedded newform 441.2.o.e.146.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(146,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.2
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.34591 - 1.35441i) q^{2} +(1.70185 - 0.322036i) q^{3} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +(-4.42857 - 1.54954i) q^{6} -9.04141i q^{8} +(2.79259 - 1.09611i) q^{9} +O(q^{10})$	\(q+(-2.34591 - 1.35441i) q^{2} +(1.70185 - 0.322036i) q^{3} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +(-4.42857 - 1.54954i) q^{6} -9.04141i q^{8} +(2.79259 - 1.09611i) q^{9} +3.25853i q^{10} +(-2.15351 - 1.24333i) q^{11} +(6.03068 + 7.00755i) q^{12} +(-1.63211 + 0.942300i) q^{13} +(-1.35909 - 1.57924i) q^{15} +(-6.90806 + 11.9651i) q^{16} +1.20373 q^{17} +(-8.03576 - 1.21093i) q^{18} -7.47013i q^{19} +(3.21047 - 5.56070i) q^{20} +(3.36797 + 5.83350i) q^{22} +(2.63359 - 1.52050i) q^{23} +(-2.91166 - 15.3871i) q^{24} +(1.77648 - 3.07696i) q^{25} +5.10506 q^{26} +(4.39957 - 2.76473i) q^{27} +(-0.173847 - 0.100371i) q^{29} +(1.04936 + 5.54553i) q^{30} +(3.03381 - 1.75157i) q^{31} +(16.7513 - 9.67135i) q^{32} +(-4.06535 - 1.42246i) q^{33} +(-2.82384 - 1.63034i) q^{34} +(12.5200 + 9.98370i) q^{36} +1.73092 q^{37} +(-10.1177 + 17.5243i) q^{38} +(-2.47416 + 2.12925i) q^{39} +(-9.41904 + 5.43809i) q^{40} +(-3.36029 - 5.82020i) q^{41} +(0.00656005 - 0.0113623i) q^{43} -13.2732i q^{44} +(-2.82153 - 2.24995i) q^{45} -8.23756 q^{46} +(0.717403 - 1.24258i) q^{47} +(-7.90329 + 22.5875i) q^{48} +(-8.33495 + 4.81219i) q^{50} +(2.04856 - 0.387643i) q^{51} +(-8.71182 - 5.02977i) q^{52} +9.90831i q^{53} +(-14.0656 + 0.526983i) q^{54} +2.99128i q^{55} +(-2.40565 - 12.7130i) q^{57} +(0.271887 + 0.470923i) q^{58} +(-6.10954 - 10.5820i) q^{59} +(3.67299 - 10.4974i) q^{60} +(-9.73903 - 5.62283i) q^{61} -9.48942 q^{62} -24.7638 q^{64} +(1.96331 + 1.13352i) q^{65} +(7.61038 + 8.84314i) q^{66} +(2.57932 + 4.46752i) q^{67} +(3.21260 + 5.56438i) q^{68} +(3.99231 - 3.43578i) q^{69} +12.0452i q^{71} +(-9.91041 - 25.2489i) q^{72} +8.67204i q^{73} +(-4.06058 - 2.34438i) q^{74} +(2.03241 - 5.80861i) q^{75} +(34.5317 - 19.9369i) q^{76} +(8.68805 - 1.64401i) q^{78} +(-2.74801 + 4.75969i) q^{79} +16.6198 q^{80} +(6.59707 - 6.12198i) q^{81} +18.2049i q^{82} +(-1.60854 + 2.78607i) q^{83} +(-0.723998 - 1.25400i) q^{85} +(-0.0307786 + 0.0177700i) q^{86} +(-0.328185 - 0.114831i) q^{87} +(-11.2415 + 19.4708i) q^{88} +7.96728 q^{89} +(3.57172 + 9.09972i) q^{90} +(14.0574 + 8.11607i) q^{92} +(4.59902 - 3.95791i) q^{93} +(-3.36593 + 1.94332i) q^{94} +(-7.78214 + 4.49302i) q^{95} +(25.3936 - 21.8537i) q^{96} +(-2.06260 - 1.19084i) q^{97} +(-7.37671 - 1.11162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 + 16 * q^9	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.34591	−	1.35441i	−1.65881	−	0.957716i	−0.973264	−	0.229689i	$-0.926229\pi$
$2$	−2.34591	−	1.35441i	−1.65881	−	0.957716i	−0.685548	−	0.728027i	$-0.740437\pi$
$3$	1.70185	−	0.322036i	0.982563	−	0.185928i
$3$	1.70185	−	0.322036i	0.982563	−	0.185928i
$4$	2.66888	+	4.62263i	1.33444	+	2.31132i
$5$	−0.601464	−	1.04177i	−0.268983	−	0.465892i	0.699616	−	0.714519i	$-0.253354\pi$
$5$	−0.601464	−	1.04177i	−0.268983	−	0.465892i	−0.968599	+	0.248626i	$0.920021\pi$
$6$	−4.42857	−	1.54954i	−1.80795	−	0.632598i
$7$		0			0
$7$		0			0
$8$		−	9.04141i		−	3.19662i
$9$	2.79259	−	1.09611i	0.930862	−	0.365371i
$10$			3.25853i			1.03044i
$11$	−2.15351	−	1.24333i	−0.649309	−	0.374879i	0.138882	−	0.990309i	$-0.455649\pi$
$11$	−2.15351	−	1.24333i	−0.649309	−	0.374879i	−0.788191	+	0.615430i	$0.788982\pi$
$12$	6.03068	+	7.00755i	1.74091	+	2.02291i
$13$	−1.63211	+	0.942300i	−0.452666	+	0.261347i	−0.708956	−	0.705253i	$-0.750833\pi$
$13$	−1.63211	+	0.942300i	−0.452666	+	0.261347i	0.256289	+	0.966600i	$0.417500\pi$
$14$		0			0
$15$	−1.35909	−	1.57924i	−0.350915	−	0.407757i
$16$	−6.90806	+	11.9651i	−1.72702	+	2.99128i
$17$	1.20373			0.291947			0.145973	−	0.989289i	$-0.453369\pi$
$17$	1.20373			0.291947			0.145973	+	0.989289i	$0.453369\pi$
$18$	−8.03576	−	1.21093i	−1.89405	−	0.285419i
$19$		−	7.47013i		−	1.71377i	−0.515511	−	0.856883i	$-0.672398\pi$
$19$		−	7.47013i		−	1.71377i	0.515511	−	0.856883i	$-0.327602\pi$
$20$	3.21047	−	5.56070i	0.717883	−	1.24341i
$21$		0			0
$22$	3.36797	+	5.83350i	0.718054	+	1.24371i
$23$	2.63359	−	1.52050i	0.549141	−	0.317047i	−0.199634	−	0.979870i	$-0.563975\pi$
$23$	2.63359	−	1.52050i	0.549141	−	0.317047i	0.748775	+	0.662824i	$0.230642\pi$
$24$	−2.91166	−	15.3871i	−0.594340	−	3.14088i
$25$	1.77648	−	3.07696i	0.355296	−	0.615391i
$26$	5.10506			1.00118
$27$	4.39957	−	2.76473i	0.846698	−	0.532073i
$28$		0			0
$29$	−0.173847	−	0.100371i	−0.0322826	−	0.0186384i	0.483772	−	0.875194i	$-0.339266\pi$
$29$	−0.173847	−	0.100371i	−0.0322826	−	0.0186384i	−0.516054	+	0.856556i	$0.672600\pi$
$30$	1.04936	+	5.54553i	0.191587	+	1.01247i
$31$	3.03381	−	1.75157i	0.544889	−	0.314592i	−0.202169	−	0.979351i	$-0.564799\pi$
$31$	3.03381	−	1.75157i	0.544889	−	0.314592i	0.747058	+	0.664759i	$0.231466\pi$
$32$	16.7513	−	9.67135i	2.96124	−	1.70967i
$33$	−4.06535	−	1.42246i	−0.707687	−	0.247618i
$34$	−2.82384	−	1.63034i	−0.484285	−	0.279602i
$35$		0			0
$36$	12.5200	+	9.98370i	2.08667	+	1.66395i
$37$	1.73092			0.284561			0.142280	−	0.989826i	$-0.454557\pi$
$37$	1.73092			0.284561			0.142280	+	0.989826i	$0.454557\pi$
$38$	−10.1177	+	17.5243i	−1.64130	+	2.84282i
$39$	−2.47416	+	2.12925i	−0.396182	+	0.340953i
$40$	−9.41904	+	5.43809i	−1.48928	+	0.859837i
$41$	−3.36029	−	5.82020i	−0.524790	−	0.908963i	−0.999583	−	0.0288655i	$-0.990811\pi$
$41$	−3.36029	−	5.82020i	−0.524790	−	0.908963i	0.474793	−	0.880097i	$-0.342523\pi$
$42$		0			0
$43$	0.00656005	−	0.0113623i	0.00100040	−	0.00173274i	−0.865525	−	0.500866i	$-0.833015\pi$
$43$	0.00656005	−	0.0113623i	0.00100040	−	0.00173274i	0.866525	+	0.499133i	$0.166348\pi$
$44$		−	13.2732i		−	2.00101i
$45$	−2.82153	−	2.24995i	−0.420610	−	0.335403i
$46$	−8.23756			−1.21456
$47$	0.717403	−	1.24258i	0.104644	−	0.181249i	−0.808949	−	0.587879i	$-0.799963\pi$
$47$	0.717403	−	1.24258i	0.104644	−	0.181249i	0.913593	+	0.406631i	$0.133296\pi$
$48$	−7.90329	+	22.5875i	−1.14074	+	3.26022i
$49$		0			0
$50$	−8.33495	+	4.81219i	−1.17874	+	0.680546i
$51$	2.04856	−	0.387643i	0.286856	−	0.0542809i
$52$	−8.71182	−	5.02977i	−1.20811	−	0.697504i
$53$			9.90831i			1.36101i	0.732743	+	0.680506i	$0.238240\pi$
$53$			9.90831i			1.36101i	−0.732743	+	0.680506i	$0.761760\pi$
$54$	−14.0656	+	0.526983i	−1.91409	+	0.0717133i
$55$			2.99128i			0.403344i
$56$		0			0
$57$	−2.40565	−	12.7130i	−0.318636	−	1.68388i
$58$	0.271887	+	0.470923i	0.0357005	+	0.0618352i
$59$	−6.10954	−	10.5820i	−0.795394	−	1.37766i	−0.922588	−	0.385786i	$-0.873930\pi$
$59$	−6.10954	−	10.5820i	−0.795394	−	1.37766i	0.127194	−	0.991878i	$-0.459403\pi$
$60$	3.67299	−	10.4974i	0.474181	−	1.35520i
$61$	−9.73903	−	5.62283i	−1.24696	−	0.719930i	−0.276454	−	0.961027i	$-0.589159\pi$
$61$	−9.73903	−	5.62283i	−1.24696	−	0.719930i	−0.970501	+	0.241097i	$0.922493\pi$
$62$	−9.48942			−1.20516
$63$		0			0
$64$	−24.7638			−3.09548
$65$	1.96331	+	1.13352i	0.243519	+	0.140596i
$66$	7.61038	+	8.84314i	0.936773	+	1.08851i
$67$	2.57932	+	4.46752i	0.315115	+	0.545794i	0.979462	−	0.201630i	$-0.0646237\pi$
$67$	2.57932	+	4.46752i	0.315115	+	0.545794i	−0.664347	+	0.747424i	$0.731290\pi$
$68$	3.21260	+	5.56438i	0.389585	+	0.674781i
$69$	3.99231	−	3.43578i	0.480618	−	0.413619i
$70$		0			0
$71$			12.0452i			1.42950i	0.699379	+	0.714751i	$0.253460\pi$
$71$			12.0452i			1.42950i	−0.699379	+	0.714751i	$0.746540\pi$
$72$	−9.91041	−	25.2489i	−1.16795	−	2.97561i
$73$			8.67204i			1.01499i	0.861656	+	0.507493i	$0.169428\pi$
$73$			8.67204i			1.01499i	−0.861656	+	0.507493i	$0.830572\pi$
$74$	−4.06058	−	2.34438i	−0.472033	−	0.272528i
$75$	2.03241	−	5.80861i	0.234683	−	0.670720i
$76$	34.5317	−	19.9369i	3.96106	−	2.28692i
$77$		0			0
$78$	8.68805	−	1.64401i	0.983728	−	0.186148i
$79$	−2.74801	+	4.75969i	−0.309175	+	0.535507i	−0.978182	−	0.207749i	$-0.933386\pi$
$79$	−2.74801	+	4.75969i	−0.309175	+	0.535507i	0.669007	+	0.743256i	$0.266719\pi$
$80$	16.6198			1.85815
$81$	6.59707	−	6.12198i	0.733008	−	0.680220i
$82$			18.2049i			2.01040i
$83$	−1.60854	+	2.78607i	−0.176560	+	0.305811i	−0.940700	−	0.339239i	$-0.889830\pi$
$83$	−1.60854	+	2.78607i	−0.176560	+	0.305811i	0.764140	+	0.645051i	$0.223164\pi$
$84$		0			0
$85$	−0.723998	−	1.25400i	−0.0785286	−	0.136016i
$86$	−0.0307786	+	0.0177700i	−0.00331894	+	0.00191619i
$87$	−0.328185	−	0.114831i	−0.0351851	−	0.0123112i
$88$	−11.2415	+	19.4708i	−1.19835	+	2.07559i
$89$	7.96728			0.844530			0.422265	−	0.906473i	$-0.361235\pi$
$89$	7.96728			0.844530			0.422265	+	0.906473i	$0.361235\pi$
$90$	3.57172	+	9.09972i	0.376492	+	0.959195i
$91$		0			0
$92$	14.0574	+	8.11607i	1.46559	+	0.846159i
$93$	4.59902	−	3.95791i	0.476896	−	0.410416i
$94$	−3.36593	+	1.94332i	−0.347170	+	0.200438i
$95$	−7.78214	+	4.49302i	−0.798430	+	0.460974i
$96$	25.3936	−	21.8537i	2.59173	−	2.23043i
$97$	−2.06260	−	1.19084i	−0.209425	−	0.120912i	0.391619	−	0.920128i	$-0.371915\pi$
$97$	−2.06260	−	1.19084i	−0.209425	−	0.120912i	−0.601044	+	0.799216i	$0.705249\pi$
$98$		0			0
$99$	−7.37671	−	1.11162i	−0.741387	−	0.111722i
$100$	18.9648			1.89648
$101$	4.73272	−	8.19730i	0.470923	−	0.815662i	−0.528524	−	0.848918i	$-0.677254\pi$
$101$	4.73272	−	8.19730i	0.470923	−	0.815662i	0.999447	+	0.0332561i	$0.0105877\pi$
$102$	−5.33078	−	1.86522i	−0.527826	−	0.184685i
$103$	14.9460	−	8.62908i	1.47267	−	0.850249i	0.473147	−	0.880984i	$-0.343118\pi$
$103$	14.9460	−	8.62908i	1.47267	−	0.850249i	0.999528	+	0.0307347i	$0.00978469\pi$
$104$	8.51973	+	14.7566i	0.835428	+	1.44700i
$105$		0			0
$106$	13.4200	−	23.2441i	1.30346	−	2.25766i
$107$			9.88349i			0.955473i	0.878503	+	0.477737i	$0.158543\pi$
$107$			9.88349i			0.955473i	−0.878503	+	0.477737i	$0.841457\pi$
$108$	24.5223	+	12.9589i	2.35966	+	1.24697i
$109$	10.4136			0.997438			0.498719	−	0.866764i	$-0.333804\pi$
$109$	10.4136			0.997438			0.498719	+	0.866764i	$0.333804\pi$
$110$	4.05143	−	7.01729i	0.386289	−	0.669072i
$111$	2.94576	−	0.557417i	0.279599	−	0.0529077i
$112$		0			0
$113$	−9.56137	+	5.52026i	−0.899458	+	0.519303i	−0.877024	−	0.480446i	$-0.840475\pi$
$113$	−9.56137	+	5.52026i	−0.899458	+	0.519303i	−0.0224339	+	0.999748i	$0.507142\pi$
$114$	−11.5753	+	33.0820i	−1.08412	+	3.09841i
$115$	−3.16802	−	1.82906i	−0.295419	−	0.170560i
$116$		−	1.07151i		−	0.0994871i
$117$	−3.52494	+	4.42043i	−0.325881	+	0.408669i
$118$			33.0994i			3.04705i
$119$		0			0
$120$	−14.2785	+	12.2881i	−1.30345	+	1.12174i
$121$	−2.40825	−	4.17121i	−0.218932	−	0.379201i
$122$	15.2313	+	26.3814i	1.37898	+	2.38846i
$123$	−7.59303	−	8.82297i	−0.684641	−	0.795541i
$124$	16.1937	+	9.34946i	1.45424	+	0.839607i
$125$	−10.2886			−0.920241
$126$		0			0
$127$	13.8634			1.23018			0.615090	−	0.788457i	$-0.289119\pi$
$127$	13.8634			1.23018			0.615090	+	0.788457i	$0.289119\pi$
$128$	24.5913	+	14.1978i	2.17359	+	1.25492i
$129$	0.00750514	−	0.0214496i	0.000660790	−	0.00188853i
$130$	−3.07051	−	5.31828i	−0.269302	−	0.466444i
$131$	6.17975	+	10.7036i	0.539927	+	0.935181i	0.998907	+	0.0467344i	$0.0148814\pi$
$131$	6.17975	+	10.7036i	0.539927	+	0.935181i	−0.458981	+	0.888446i	$0.651785\pi$
$132$	−4.27445	−	22.5890i	−0.372043	−	1.96612i
$133$		0			0
$134$		−	13.9739i		−	1.20716i
$135$	−5.52639	−	2.92044i	−0.475636	−	0.251352i
$136$		−	10.8834i		−	0.933243i
$137$	10.0991	+	5.83070i	0.862822	+	0.498150i	0.864956	−	0.501847i	$-0.167346\pi$
$137$	10.0991	+	5.83070i	0.862822	+	0.498150i	−0.00213432	+	0.999998i	$0.500679\pi$
$138$	−14.0191	+	2.65279i	−1.19338	+	0.225821i
$139$	−8.73893	+	5.04543i	−0.741227	+	0.427947i	−0.822515	−	0.568743i	$-0.807430\pi$
$139$	−8.73893	+	5.04543i	−0.741227	+	0.427947i	0.0812884	+	0.996691i	$0.474097\pi$
$140$		0			0
$141$	0.820757	−	2.34571i	0.0691202	−	0.197545i
$142$	16.3142	−	28.2570i	1.36906	−	2.37128i
$143$	4.68637			0.391894
$144$	−6.17623	+	40.9856i	−0.514686	+	3.41547i
$145$			0.241478i			0.0200536i
$146$	11.7455	−	20.3439i	0.972067	−	1.68367i
$147$		0			0
$148$	4.61960	+	8.00138i	0.379729	+	0.657710i
$149$	4.15010	−	2.39606i	0.339990	−	0.196293i	−0.320278	−	0.947324i	$-0.603776\pi$
$149$	4.15010	−	2.39606i	0.339990	−	0.196293i	0.660267	+	0.751031i	$0.270443\pi$
$150$	−12.6351	+	10.8738i	−1.03165	+	0.887840i
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	−0.538446	−	0.842660i	$-0.680988\pi$
$151$	5.65924	−	9.80209i	0.460542	−	0.797683i	0.998988	+	0.0449774i	$0.0143216\pi$
$152$	−67.5406			−5.47826
$153$	3.36151	−	1.31942i	0.271762	−	0.106669i
$154$		0			0
$155$	−3.64946	−	2.10702i	−0.293132	−	0.169240i
$156$	−16.4460	−	5.75439i	−1.31673	−	0.460720i
$157$	12.7580	−	7.36581i	1.01820	−	0.587856i	0.104615	−	0.994513i	$-0.466639\pi$
$157$	12.7580	−	7.36581i	1.01820	−	0.587856i	0.913581	+	0.406657i	$0.133306\pi$
$158$	12.8932	−	7.44388i	1.02573	−	0.592203i
$159$	3.19083	+	16.8625i	0.253049	+	1.33728i
$160$	−20.1506	−	11.6339i	−1.59304	−	0.919744i
$161$		0			0
$162$	−23.7679	+	5.42648i	−1.86738	+	0.426345i
$163$	−18.1580			−1.42224			−0.711122	−	0.703069i	$-0.751813\pi$
$163$	−18.1580			−1.42224			−0.711122	+	0.703069i	$0.751813\pi$
$164$	17.9364	−	31.0668i	1.40060	−	2.42591i
$165$	0.963299	+	5.09071i	0.0749927	+	0.396311i
$166$	7.54700	−	4.35726i	0.585761	−	0.338189i
$167$	−0.599436	−	1.03825i	−0.0463857	−	0.0803425i	0.841900	−	0.539633i	$-0.181437\pi$
$167$	−0.599436	−	1.03825i	−0.0463857	−	0.0803425i	−0.888286	+	0.459291i	$0.848104\pi$
$168$		0			0
$169$	−4.72414	+	8.18245i	−0.363395	+	0.629419i
$170$			3.92238i			0.300833i
$171$	−8.18811	−	20.8610i	−0.626161	−	1.59528i
$172$	0.0700319			0.00533988
$173$	−9.00403	+	15.5954i	−0.684564	+	1.18570i	0.289010	+	0.957326i	$0.406674\pi$
$173$	−9.00403	+	15.5954i	−0.684564	+	1.18570i	−0.973574	+	0.228373i	$0.926660\pi$
$174$	0.614365	+	0.713882i	0.0465749	+	0.0541193i
$175$		0			0
$176$	29.7532	−	17.1780i	2.24273	−	1.29484i
$177$	−13.8053	−	16.0415i	−1.03767	−	1.20576i
$178$	−18.6906	−	10.7910i	−1.40092	−	0.808819i
$179$		−	15.1424i		−	1.13179i	−0.824476	−	0.565897i	$-0.808530\pi$
$179$		−	15.1424i		−	1.13179i	0.824476	−	0.565897i	$-0.191470\pi$
$180$	2.87036	−	19.0478i	0.213944	−	1.41974i
$181$			7.98716i			0.593681i	0.954927	+	0.296840i	$0.0959329\pi$
$181$			7.98716i			0.593681i	−0.954927	+	0.296840i	$0.904067\pi$
$182$		0			0
$183$	−18.3851	−	6.43290i	−1.35907	−	0.475534i
$184$	−13.7475	−	23.8114i	−1.01348	−	1.75540i
$185$	−1.04108	−	1.80321i	−0.0765420	−	0.132575i
$186$	−16.1496	+	3.05593i	−1.18414	+	0.224072i
$187$	−2.59224	−	1.49663i	−0.189563	−	0.109445i
$188$	7.65865			0.558564
$189$		0			0
$190$	24.3416			1.76593
$191$	13.8711	+	8.00848i	1.00368	+	0.579473i	0.909334	−	0.416067i	$-0.136592\pi$
$191$	13.8711	+	8.00848i	1.00368	+	0.579473i	0.0943426	+	0.995540i	$0.469925\pi$
$192$	−42.1443	+	7.97485i	−3.04151	+	0.575535i
$193$	6.85468	+	11.8726i	0.493410	+	0.854612i	0.999971	−	0.00759239i	$-0.00241676\pi$
$193$	6.85468	+	11.8726i	0.493410	+	0.854612i	−0.506561	+	0.862204i	$0.669083\pi$
$194$	3.22579	+	5.58724i	0.231598	+	0.401140i
$195$	3.70630	+	1.29682i	0.265414	+	0.0928674i
$196$		0			0
$197$			18.9248i			1.34834i	0.738577	+	0.674170i	$0.235498\pi$
$197$			18.9248i			1.34834i	−0.738577	+	0.674170i	$0.764502\pi$
$198$	15.7995	+	12.5989i	1.12282	+	0.895363i
$199$			24.8325i			1.76033i	0.474672	+	0.880163i	$0.342567\pi$
$199$			24.8325i			1.76033i	−0.474672	+	0.880163i	$0.657433\pi$
$200$	−27.8200	−	16.0619i	−1.96717	−	1.13575i
$201$	5.82832	+	6.77241i	0.411098	+	0.477689i
$202$	−22.2051	+	12.8201i	−1.56235	+	0.902020i
$203$		0			0
$204$	7.25929	+	8.43517i	0.508252	+	0.590580i
$205$	−4.04219	+	7.00129i	−0.282319	+	0.488991i
$206$	−46.7494			−3.25719
$207$	5.68788	−	7.13285i	0.395335	−	0.495767i
$208$		−	26.0379i		−	1.80540i
$209$	−9.28786	+	16.0870i	−0.642454	+	1.11276i
$210$		0			0
$211$	3.60761	+	6.24857i	0.248358	+	0.430169i	0.963070	−	0.269250i	$-0.0867757\pi$
$211$	3.60761	+	6.24857i	0.248358	+	0.430169i	−0.714712	+	0.699419i	$0.753442\pi$
$212$	−45.8025	+	26.4441i	−3.14573	+	1.81619i
$213$	3.87899	+	20.4991i	0.265784	+	1.40458i
$214$	13.3863	−	23.1858i	0.915072	−	1.58495i
$215$	−0.0157825			−0.00107636
$216$	−24.9971	−	39.7784i	−1.70084	−	2.70657i
$217$		0			0
$218$	−24.4293	−	14.1043i	−1.65456	−	0.955262i
$219$	2.79271	+	14.7585i	0.188714	+	0.997287i
$220$	−13.8276	+	7.98336i	−0.932255	+	0.538238i
$221$	−1.96462	+	1.13427i	−0.132154	+	0.0762994i
$222$	−7.66547	−	2.68212i	−0.514473	−	0.180012i
$223$	21.0706	+	12.1651i	1.41099	+	0.814635i	0.995482	−	0.0949545i	$-0.0302705\pi$
$223$	21.0706	+	12.1651i	1.41099	+	0.814635i	0.415508	+	0.909590i	$0.363604\pi$
$224$		0			0
$225$	1.58828	−	10.5399i	0.105886	−	0.702659i
$226$	29.9069			1.98938
$227$	0.240288	−	0.416192i	0.0159485	−	0.0276236i	−0.857941	−	0.513748i	$-0.828257\pi$
$227$	0.240288	−	0.416192i	0.0159485	−	0.0276236i	0.873890	+	0.486125i	$0.161590\pi$
$228$	52.3473	−	45.0500i	3.46679	−	2.98351i
$229$	−7.80442	+	4.50588i	−0.515730	+	0.297757i	−0.735186	−	0.677865i	$-0.762905\pi$
$229$	−7.80442	+	4.50588i	−0.515730	+	0.297757i	0.219456	+	0.975622i	$0.429572\pi$
$230$	4.95460	+	8.58162i	0.326697	+	0.565855i
$231$		0			0
$232$	−0.907493	+	1.57182i	−0.0595799	+	0.103195i
$233$		−	11.1168i		−	0.728285i	−0.931343	−	0.364143i	$-0.881362\pi$
$233$		−	11.1168i		−	0.728285i	0.931343	−	0.364143i	$-0.118638\pi$
$234$	14.2563	−	5.59573i	0.931965	−	0.365804i
$235$	−1.72597			−0.112590
$236$	32.6112	−	56.4843i	2.12281	−	3.67682i
$237$	−3.14390	+	8.98523i	−0.204219	+	0.583653i
$238$		0			0
$239$	12.0446	−	6.95395i	0.779100	−	0.449813i	−0.0570114	−	0.998374i	$-0.518157\pi$
$239$	12.0446	−	6.95395i	0.779100	−	0.449813i	0.836111	+	0.548560i	$0.184824\pi$
$240$	28.2844	−	5.35218i	1.82575	−	0.345482i
$241$	−10.7181	−	6.18807i	−0.690411	−	0.398609i	0.113355	−	0.993555i	$-0.463840\pi$
$241$	−10.7181	−	6.18807i	−0.690411	−	0.398609i	−0.803766	+	0.594946i	$0.797173\pi$
$242$			13.0471i			0.838698i
$243$	9.25573	−	12.5432i	0.593755	−	0.804646i
$244$		−	60.0266i		−	3.84281i
$245$		0			0
$246$	5.86264	+	30.9821i	0.373788	+	1.97534i
$247$	7.03911	+	12.1921i	0.447888	+	0.775764i
$248$	−15.8367	−	27.4299i	−1.00563	−	1.74180i
$249$	−1.84028	+	5.25949i	−0.116623	+	0.333306i
$250$	24.1362	+	13.9350i	1.52651	+	0.881329i
$251$	19.7147			1.24438			0.622191	−	0.782866i	$-0.286243\pi$
$251$	19.7147			1.24438			0.622191	+	0.782866i	$0.286243\pi$
$252$		0			0
$253$	−7.56196			−0.475416
$254$	−32.5224	−	18.7768i	−2.04064	−	1.17816i
$255$	−1.63597	−	1.90097i	−0.102448	−	0.119043i
$256$	−13.6956	−	23.7214i	−0.855973	−	1.48259i
$257$	5.62025	+	9.73456i	0.350581	+	0.607225i	0.986351	−	0.164654i	$-0.0526506\pi$
$257$	5.62025	+	9.73456i	0.350581	+	0.607225i	−0.635770	+	0.771879i	$0.719317\pi$
$258$	−0.0466580	+	0.0401538i	−0.00290480	+	0.00249987i
$259$		0			0
$260$			12.1009i			0.750466i
$261$	−0.595501	−	0.0897376i	−0.0368606	−	0.00555462i
$262$		−	33.4797i		−	2.06839i
$263$	−2.82146	−	1.62897i	−0.173979	−	0.100447i	0.410482	−	0.911869i	$-0.365360\pi$
$263$	−2.82146	−	1.62897i	−0.173979	−	0.100447i	−0.584461	+	0.811422i	$0.698694\pi$
$264$	−12.8610	+	36.7565i	−0.791540	+	2.26221i
$265$	10.3221	−	5.95949i	0.634084	−	0.366089i
$266$		0			0
$267$	13.5591	−	2.56575i	0.829804	−	0.157021i
$268$	−13.7678	+	23.8465i	−0.841002	+	1.45666i
$269$	−0.242293			−0.0147729			−0.00738644	−	0.999973i	$-0.502351\pi$
$269$	−0.242293			−0.0147729			−0.00738644	+	0.999973i	$0.502351\pi$
$270$	9.00896	+	14.3361i	0.548268	+	0.872469i
$271$		−	1.07305i		−	0.0651830i	−0.999469	−	0.0325915i	$-0.989624\pi$
$271$		−	1.07305i		−	0.0651830i	0.999469	−	0.0325915i	$-0.0103760\pi$
$272$	−8.31542	+	14.4027i	−0.504196	+	0.873294i
$273$		0			0
$274$	−15.7944	−	27.3567i	−0.954173	−	1.65268i
$275$	−7.65136	+	4.41751i	−0.461394	+	0.266386i
$276$	26.5373	+	9.28533i	1.59736	+	0.558911i
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	−0.782959	−	0.622074i	$-0.786290\pi$
$277$	2.45076	−	4.24485i	0.147252	−	0.255048i	0.930211	+	0.367025i	$0.119624\pi$
$278$	27.3344			1.63941
$279$	6.55226	−	8.21682i	0.392273	−	0.491928i
$280$		0			0
$281$	11.5613	+	6.67494i	0.689691	+	0.398194i	0.803496	−	0.595310i	$-0.202971\pi$
$281$	11.5613	+	6.67494i	0.689691	+	0.398194i	−0.113805	+	0.993503i	$0.536304\pi$
$282$	−5.10249	+	4.39119i	−0.303849	+	0.261492i
$283$	3.25329	−	1.87829i	0.193388	−	0.111653i	−0.400180	−	0.916437i	$-0.631052\pi$
$283$	3.25329	−	1.87829i	0.193388	−	0.111653i	0.593568	+	0.804784i	$0.297719\pi$
$284$	−55.6805	+	32.1472i	−3.30403	+	1.90758i
$285$	−11.7971	+	10.1526i	−0.698801	+	0.601386i
$286$	−10.9938	−	6.34729i	−0.650078	−	0.375323i
$287$		0			0
$288$	36.1785	−	45.3694i	2.13184	−	2.67342i
$289$	−15.5510			−0.914767
$290$	0.327061	−	0.566486i	0.0192057	−	0.0332652i
$291$	−3.89373	−	1.36241i	−0.228255	−	0.0798656i
$292$	−40.0876	+	23.1446i	−2.34595	+	1.35444i
$293$	−6.38430	−	11.0579i	−0.372975	−	0.646011i	0.617047	−	0.786926i	$-0.288329\pi$
$293$	−6.38430	−	11.0579i	−0.372975	−	0.646011i	−0.990022	+	0.140915i	$0.954995\pi$
$294$		0			0
$295$	−7.34934	+	12.7294i	−0.427895	+	0.741136i
$296$		−	15.6499i		−	0.909633i
$297$	−12.9120	+	0.483762i	−0.749232	+	0.0280707i
$298$	−12.9810			−0.751972
$299$	−2.86554	+	4.96326i	−0.165718	+	0.287033i
$300$	32.2753	−	6.10736i	1.86342	−	0.352609i
$301$		0			0
$302$	−26.5522	+	15.3299i	−1.52791	+	0.882137i
$303$	5.41455	−	15.4747i	0.311058	−	0.888997i
$304$	89.3810	+	51.6042i	5.12635	+	2.95970i
$305$			13.5277i			0.774596i
$306$	−9.67286	−	1.45763i	−0.552960	−	0.0833271i
$307$		−	10.7257i		−	0.612148i	−0.952008	−	0.306074i	$-0.900984\pi$
$307$		−	10.7257i		−	0.612148i	0.952008	−	0.306074i	$-0.0990155\pi$
$308$		0			0
$309$	22.6570	−	19.4986i	1.28891	−	1.10923i
$310$	5.70755	+	9.88576i	0.324167	+	0.561473i
$311$	9.41743	+	16.3115i	0.534013	+	0.924938i	0.999210	+	0.0397310i	$0.0126501\pi$
$311$	9.41743	+	16.3115i	0.534013	+	0.924938i	−0.465197	+	0.885207i	$0.654017\pi$
$312$	19.2514	+	22.3699i	1.08990	+	1.26644i
$313$	−22.5774	−	13.0351i	−1.27615	−	0.736787i	−0.300013	−	0.953935i	$-0.596991\pi$
$313$	−22.5774	−	13.0351i	−1.27615	−	0.736787i	−0.976139	+	0.217148i	$0.930324\pi$
$314$	−39.9054			−2.25199
$315$		0			0
$316$	−29.3364			−1.65030
$317$	12.0290	+	6.94495i	0.675616	+	0.390067i	0.798201	−	0.602391i	$-0.205785\pi$
$317$	12.0290	+	6.94495i	0.675616	+	0.390067i	−0.122585	+	0.992458i	$0.539118\pi$
$318$	15.3533	−	43.8796i	0.860972	−	2.46065i
$319$	0.249588	+	0.432300i	0.0139743	+	0.0242041i
$320$	14.8946	+	25.7981i	0.832631	+	1.44216i
$321$	3.18284	+	16.8202i	0.177649	+	0.938813i
$322$		0			0
$323$		−	8.99200i		−	0.500328i
$324$	45.9064	+	14.1570i	2.55036	+	0.786500i
$325$			6.69592i			0.371423i
$326$	42.5971	+	24.5935i	2.35924	+	1.36211i
$327$	17.7223	−	3.35354i	0.980046	−	0.185451i
$328$	−52.6228	+	30.3818i	−2.90561	+	1.67755i
$329$		0			0
$330$	4.63511	−	13.2471i	0.255154	−	0.729227i
$331$	−2.24230	+	3.88378i	−0.123248	+	0.213472i	−0.921047	−	0.389452i	$-0.872664\pi$
$331$	−2.24230	+	3.88378i	−0.123248	+	0.213472i	0.797799	+	0.602924i	$0.205998\pi$
$332$	−17.1720			−0.942435
$333$	4.83373	−	1.89728i	0.264887	−	0.103970i
$334$			3.24754i			0.177697i
$335$	3.10274	−	5.37411i	0.169521	−	0.293619i
$336$		0			0
$337$	−16.4010	−	28.4074i	−0.893420	−	1.54745i	−0.835748	−	0.549113i	$-0.814965\pi$
$337$	−16.4010	−	28.4074i	−0.893420	−	1.54745i	−0.0576723	−	0.998336i	$-0.518368\pi$
$338$	22.1649	−	12.7969i	1.20561	−	0.696059i
$339$	−14.4943	+	12.4738i	−0.787222	+	0.677482i
$340$	3.86453	−	6.69356i	0.209583	−	0.363009i
$341$	−8.71114			−0.471735
$342$	−9.04581	+	60.0282i	−0.489141	+	3.24595i
$343$		0			0
$344$	−0.102732	−	0.0593121i	−0.00553891	−	0.00319789i
$345$	−5.98051	−	2.09256i	−0.321980	−	0.112660i
$346$	42.2454	−	24.3904i	2.27112	−	1.31123i
$347$	11.6112	−	6.70374i	0.623323	−	0.359876i	−0.154839	−	0.987940i	$-0.549486\pi$
$347$	11.6112	−	6.70374i	0.623323	−	0.359876i	0.778162	+	0.628064i	$0.216152\pi$
$348$	−0.345064	−	1.82355i	−0.0184974	−	0.0977524i
$349$	−19.3276	−	11.1588i	−1.03458	−	0.597316i	−0.116288	−	0.993215i	$-0.537100\pi$
$349$	−19.3276	−	11.1588i	−1.03458	−	0.597316i	−0.918294	+	0.395899i	$0.870433\pi$
$350$		0			0
$351$	−4.57539	+	8.65807i	−0.244216	+	0.462134i
$352$	−48.0988			−2.56368
$353$	−8.60842	+	14.9102i	−0.458180	+	0.793591i	−0.998865	−	0.0476341i	$-0.984832\pi$
$353$	−8.60842	+	14.9102i	−0.458180	+	0.793591i	0.540685	+	0.841225i	$0.318165\pi$
$354$	10.6592	+	56.3302i	0.566530	+	2.99392i
$355$	12.5483	−	7.24476i	0.665994	−	0.384512i
$356$	21.2637	+	36.8298i	1.12697	+	1.95198i
$357$		0			0
$358$	−20.5090	+	35.5227i	−1.08394	+	1.87743i
$359$		−	6.49943i		−	0.343027i	−0.985182	−	0.171513i	$-0.945134\pi$
$359$		−	6.49943i		−	0.343027i	0.985182	−	0.171513i	$-0.0548656\pi$
$360$	−20.3427	+	25.5107i	−1.07216	+	1.34453i
$361$	−36.8029			−1.93699
$362$	10.8179	−	18.7372i	0.568577	−	0.984805i
$363$	−5.44176	−	6.32324i	−0.285619	−	0.331884i
$364$		0			0
$365$	9.03424	−	5.21592i	0.472874	−	0.273014i
$366$	34.4171	+	39.9921i	1.79901	+	2.09042i
$367$	7.79734	+	4.50180i	0.407018	+	0.234992i	0.689508	−	0.724278i	$-0.257827\pi$
$367$	7.79734	+	4.50180i	0.407018	+	0.234992i	−0.282490	+	0.959270i	$0.591160\pi$
$368$			42.0149i			2.19018i
$369$	−15.7635	−	12.5701i	−0.820616	−	0.654376i
$370$			5.64024i			0.293222i
$371$		0			0
$372$	30.5702	+	10.6964i	1.58499	+	0.554583i
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	0.677767	−	0.735277i	$-0.262948\pi$
$373$	−5.75312	−	9.96470i	−0.297885	−	0.515953i	−0.975652	+	0.219324i	$0.929615\pi$
$374$	4.05412	+	7.02194i	0.209633	+	0.363096i
$375$	−17.5097	+	3.31330i	−0.904195	+	0.171098i
$376$	−11.2347	−	6.48634i	−0.579384	−	0.334507i
$377$	0.378318			0.0194844
$378$		0			0
$379$	17.0982			0.878275			0.439138	−	0.898420i	$-0.355284\pi$
$379$	17.0982			0.878275			0.439138	+	0.898420i	$0.355284\pi$
$380$	−41.5391	−	23.9826i	−2.13091	−	1.23028i
$381$	23.5935	−	4.46452i	1.20873	−	0.228724i
$382$	−21.6936	−	37.5744i	−1.10994	−	1.92247i
$383$	−8.10778	−	14.0431i	−0.414288	−	0.717569i	0.581065	−	0.813857i	$-0.302636\pi$
$383$	−8.10778	−	14.0431i	−0.414288	−	0.717569i	−0.995353	+	0.0962885i	$0.969303\pi$
$384$	46.4229	+	16.2432i	2.36901	+	0.828909i
$385$		0			0
$386$		−	37.1363i		−	1.89019i
$387$	0.00586509	−	0.0389209i	0.000298139	−	0.00197846i
$388$		−	12.7129i		−	0.645398i
$389$	−16.2358	−	9.37376i	−0.823189	−	0.475269i	0.0283257	−	0.999599i	$-0.490982\pi$
$389$	−16.2358	−	9.37376i	−0.823189	−	0.475269i	−0.851515	+	0.524330i	$0.824316\pi$
$390$	−6.93823	−	8.06210i	−0.351331	−	0.408240i
$391$	3.17012	−	1.83027i	0.160320	−	0.0925607i
$392$		0			0
$393$	13.9640	+	16.2259i	0.704388	+	0.818487i
$394$	25.6321	−	44.3961i	1.29133	−	2.23664i
$395$	6.61131			0.332651
$396$	−14.5489	−	37.0666i	−0.731112	−	1.86266i
$397$			30.9709i			1.55438i	0.629264	+	0.777192i	$0.283357\pi$
$397$			30.9709i			1.55438i	−0.629264	+	0.777192i	$0.716643\pi$
$398$	33.6334	−	58.2548i	1.68589	−	2.92005i
$399$		0			0
$400$	24.5441	+	42.5116i	1.22720	+	2.12558i
$401$	−0.801065	+	0.462495i	−0.0400033	+	0.0230959i	−0.519868	−	0.854246i	$-0.674019\pi$
$401$	−0.801065	+	0.462495i	−0.0400033	+	0.0230959i	0.479865	+	0.877342i	$0.340686\pi$
$402$	−4.50010	−	23.7815i	−0.224444	−	1.18611i
$403$	−3.30101	+	5.71752i	−0.164435	+	0.284810i
$404$	50.5242			2.51367
$405$	−10.3456	−	3.19045i	−0.514076	−	0.158535i
$406$		0			0
$407$	−3.72755	−	2.15210i	−0.184768	−	0.106676i
$408$	−3.50484	−	18.5219i	−0.173515	−	0.916970i
$409$	−6.56585	+	3.79079i	−0.324660	+	0.187443i	−0.653468	−	0.756954i	$-0.726687\pi$
$409$	−6.56585	+	3.79079i	−0.324660	+	0.187443i	0.328808	+	0.944397i	$0.393353\pi$
$410$	18.9653	−	10.9496i	0.936629	−	0.540763i
$411$	19.0648	+	6.67072i	0.940397	+	0.329042i
$412$	79.7782	+	46.0599i	3.93039	+	2.26921i
$413$		0			0
$414$	−23.0041	+	9.02931i	−1.13059	+	0.443766i
$415$	3.86992			0.189967
$416$	−18.2266	+	31.5695i	−0.893635	+	1.54782i
$417$	−13.2475	+	11.4008i	−0.648735	+	0.558300i
$418$	43.5770	−	25.1592i	2.13142	−	1.23058i
$419$	−2.85061	−	4.93740i	−0.139262	−	0.241208i	0.787956	−	0.615732i	$-0.211140\pi$
$419$	−2.85061	−	4.93740i	−0.139262	−	0.241208i	−0.927217	+	0.374524i	$0.877806\pi$
$420$		0			0
$421$	−5.86189	+	10.1531i	−0.285691	+	0.494832i	−0.972777	−	0.231745i	$-0.925557\pi$
$421$	−5.86189	+	10.1531i	−0.285691	+	0.494832i	0.687085	+	0.726577i	$0.258890\pi$
$422$		−	19.5448i		−	0.951426i
$423$	0.641403	−	4.25636i	0.0311861	−	0.206951i
$424$	89.5851			4.35064
$425$	2.13840	−	3.70381i	0.103728	−	0.179661i
$426$	18.6645	−	53.3430i	0.904300	−	2.58447i
$427$		0			0
$428$	−45.6877	+	26.3778i	−2.20840	+	1.27502i
$429$	7.97549	−	1.50918i	0.385061	−	0.0728638i
$430$	0.0370245	+	0.0213761i	0.00178548	+	0.00103085i
$431$		−	26.9014i		−	1.29579i	−0.761728	−	0.647897i	$-0.775649\pi$
$431$		−	26.9014i		−	1.29579i	0.761728	−	0.647897i	$-0.224351\pi$
$432$	2.68783	+	71.7404i	0.129318	+	3.45161i
$433$		−	28.1028i		−	1.35053i	−0.737574	−	0.675266i	$-0.764029\pi$
$433$		−	28.1028i		−	1.35053i	0.737574	−	0.675266i	$-0.235971\pi$
$434$		0			0
$435$	0.0777645	+	0.410959i	0.00372852	+	0.0197040i
$436$	27.7925	+	48.1381i	1.33102	+	2.30539i
$437$	−11.3584	−	19.6733i	−0.543344	−	0.941099i
$438$	13.4377	−	38.4047i	0.642077	−	1.83505i
$439$	−8.07680	−	4.66314i	−0.385485	−	0.222560i	0.294717	−	0.955585i	$-0.404775\pi$
$439$	−8.07680	−	4.66314i	−0.385485	−	0.222560i	−0.680202	+	0.733025i	$0.738108\pi$
$440$	27.0454			1.28934
$441$		0			0
$442$	6.14510			0.292292
$443$	9.82131	+	5.67034i	0.466624	+	0.269406i	0.714826	−	0.699303i	$-0.246506\pi$
$443$	9.82131	+	5.67034i	0.466624	+	0.269406i	−0.248201	+	0.968709i	$0.579839\pi$
$444$	10.4386	+	12.1295i	0.495394	+	0.575640i
$445$	−4.79203	−	8.30004i	−0.227164	−	0.393460i
$446$	−32.9532	−	57.0766i	−1.56038	−	2.70265i
$447$	6.29123	−	5.41422i	0.297565	−	0.256084i
$448$		0			0
$449$		−	15.3295i		−	0.723444i	−0.932286	−	0.361722i	$-0.882189\pi$
$449$		−	15.3295i		−	0.723444i	0.932286	−	0.361722i	$-0.117811\pi$
$450$	−18.0014	+	22.5745i	−0.848592	+	1.06417i
$451$			16.7118i			0.786930i
$452$	−51.0363	−	29.4658i	−2.40054	−	1.38596i
$453$	6.47455	−	18.5042i	0.304201	−	0.869402i
$454$	−1.12739	+	0.650900i	−0.0529111	+	0.0305483i
$455$		0			0
$456$	−114.944	+	21.7505i	−5.38274	+	1.01856i
$457$	4.58649	−	7.94404i	0.214547	−	0.371606i	−0.738585	−	0.674160i	$-0.764506\pi$
$457$	4.58649	−	7.94404i	0.214547	−	0.371606i	0.953132	+	0.302554i	$0.0978391\pi$
$458$	24.4113			1.14067
$459$	5.29588	−	3.32798i	0.247191	−	0.155337i
$460$		−	19.5261i		−	0.910410i
$461$	−16.5365	+	28.6420i	−0.770181	+	1.33399i	0.167283	+	0.985909i	$0.446501\pi$
$461$	−16.5365	+	28.6420i	−0.770181	+	1.33399i	−0.937464	+	0.348083i	$0.886833\pi$
$462$		0			0
$463$	3.91594	+	6.78260i	0.181989	+	0.315214i	0.942558	−	0.334043i	$-0.108413\pi$
$463$	3.91594	+	6.78260i	0.181989	+	0.315214i	−0.760569	+	0.649257i	$0.775080\pi$
$464$	2.40190	−	1.38674i	0.111505	−	0.0643776i
$465$	−6.88936	−	2.41057i	−0.319487	−	0.111787i
$466$	−15.0567	+	26.0790i	−0.697490	+	1.20809i
$467$	−20.6770			−0.956816			−0.478408	−	0.878138i	$-0.658786\pi$
$467$	−20.6770			−0.956816			−0.478408	+	0.878138i	$0.658786\pi$
$468$	−29.8417	−	4.49692i	−1.37943	−	0.207870i
$469$		0			0
$470$	4.04898	+	2.33768i	0.186765	+	0.107829i
$471$	19.3401	−	16.6440i	0.891144	−	0.766916i
$472$	−95.6765	+	55.2389i	−4.40387	+	2.54257i
$473$	−0.0282543	+	0.0163126i	−0.00129913	+	0.000750056i
$474$	19.5451	−	16.8204i	0.897734	−	0.772588i
$475$	−22.9853	−	13.2706i	−1.05464	−	0.608895i
$476$		0			0
$477$	10.8606	+	27.6698i	0.497274	+	1.26691i
$478$	−37.6741			−1.72317
$479$	1.32999	−	2.30361i	0.0607688	−	0.105255i	−0.834040	−	0.551703i	$-0.813978\pi$
$479$	1.32999	−	2.30361i	0.0607688	−	0.105255i	0.894809	+	0.446449i	$0.147311\pi$
$480$	−38.0398	−	13.3100i	−1.73627	−	0.607516i
$481$	−2.82505	+	1.63104i	−0.128811	+	0.0743691i
$482$	16.7624	+	29.0334i	0.763508	+	1.32243i
$483$		0			0
$484$	12.8547	−	22.2649i	0.584303	−	1.01204i
$485$			2.86500i			0.130093i
$486$	−38.7018	+	16.8892i	−1.75555	+	0.766108i
$487$	−1.04380			−0.0472991			−0.0236495	−	0.999720i	$-0.507529\pi$
$487$	−1.04380			−0.0472991			−0.0236495	+	0.999720i	$0.507529\pi$
$488$	−50.8383	+	88.0546i	−2.30134	+	3.98604i
$489$	−30.9022	+	5.84753i	−1.39745	+	0.264434i
$490$		0			0
$491$	36.0415	−	20.8085i	1.62653	−	0.939076i	0.641410	−	0.767198i	$-0.278350\pi$
$491$	36.0415	−	20.8085i	1.62653	−	0.939076i	0.985118	−	0.171878i	$-0.0549835\pi$
$492$	20.5205	−	58.6472i	0.925135	−	2.64402i
$493$	−0.209265	−	0.120819i	−0.00942480	−	0.00544141i
$494$		−	38.1355i		−	1.71580i
$495$	3.27878	+	8.35340i	0.147370	+	0.375458i
$496$			48.3999i			2.17322i
$497$		0			0
$498$	11.4407	−	9.84581i	0.512668	−	0.441201i
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	0.959898	+	0.280348i	$0.0904499\pi$
$499$	16.1447	+	27.9635i	0.722738	+	1.25182i	−0.237161	+	0.971470i	$0.576217\pi$
$500$	−27.4590	−	47.5604i	−1.22800	−	2.12697i
$501$	−1.35450	−	1.57391i	−0.0605148	−	0.0703172i
$502$	−46.2490	−	26.7019i	−2.06420	−	1.19176i
$503$	39.9702			1.78218			0.891091	−	0.453825i	$-0.149941\pi$
$503$	39.9702			1.78218			0.891091	+	0.453825i	$0.149941\pi$
$504$		0			0
$505$	−11.3862			−0.506681
$506$	17.7397	+	10.2420i	0.788626	+	0.455314i
$507$	−5.40473	+	15.4466i	−0.240033	+	0.686010i
$508$	36.9998	+	64.0856i	1.64160	+	2.84334i
$509$	−11.3631	−	19.6815i	−0.503661	−	0.872367i	−0.999991	−	0.00423260i	$-0.998653\pi$
$509$	−11.3631	−	19.6815i	−0.503661	−	0.872367i	0.496330	−	0.868134i	$-0.334681\pi$
$510$	1.26315	+	6.67529i	0.0559330	+	0.295587i
$511$		0			0
$512$			17.4067i			0.769277i
$513$	−20.6529	−	32.8654i	−0.911849	−	1.45104i
$514$		−	30.4486i		−	1.34303i
$515$	−17.9790	−	10.3802i	−0.792249	−	0.457405i
$516$	0.119184	−	0.0225528i	0.00524677	−	0.000992831i
$517$	−3.08988	+	1.78394i	−0.135893	+	0.0784576i
$518$		0			0
$519$	−10.3012	+	29.4407i	−0.452173	+	1.29230i
$520$	10.2486	−	17.7511i	0.449432	−	0.778439i
$521$	30.0359			1.31590			0.657948	−	0.753063i	$-0.271425\pi$
$521$	30.0359			1.31590			0.657948	+	0.753063i	$0.271425\pi$
$522$	1.27545	+	1.01707i	0.0558251	+	0.0445160i
$523$		−	0.779769i		−	0.0340969i	−0.999855	−	0.0170485i	$-0.994573\pi$
$523$		−	0.779769i		−	0.0340969i	0.999855	−	0.0170485i	$-0.00542696\pi$
$524$	−32.9860	+	57.1334i	−1.44100	+	2.49588i
$525$		0			0
$526$	4.41260	+	7.64285i	0.192399	+	0.333244i
$527$	3.65188	−	2.10841i	0.159078	−	0.0918439i
$528$	45.1036	−	38.8160i	1.96288	−	1.68925i
$529$	−6.87614	+	11.9098i	−0.298963	+	0.517819i
$530$	−32.2865			−1.40244
$531$	−28.6605	−	22.8545i	−1.24376	−	0.991800i
$532$		0			0
$533$	10.9688	+	6.33281i	0.475110	+	0.274305i
$534$	−35.2836	−	12.3456i	−1.52687	−	0.534248i
$535$	10.2963	−	5.94457i	0.445147	−	0.257006i
$536$	40.3927	−	23.3207i	1.74470	−	1.00730i
$537$	−4.87638	−	25.7700i	−0.210432	−	1.11206i
$538$	0.568399	+	0.328165i	0.0245054	+	0.0141482i
$539$		0			0
$540$	−1.24915	−	33.3408i	−0.0537547	−	1.43476i
$541$	2.04030			0.0877196			0.0438598	−	0.999038i	$-0.486035\pi$
$541$	2.04030			0.0877196			0.0438598	+	0.999038i	$0.486035\pi$
$542$	−1.45335	+	2.51728i	−0.0624268	+	0.108126i
$543$	2.57215	+	13.5929i	0.110382	+	0.583329i
$544$	20.1640	−	11.6417i	0.864522	−	0.499132i
$545$	−6.26338	−	10.8485i	−0.268294	−	0.464699i
$546$		0			0
$547$	−8.93590	+	15.4774i	−0.382071	+	0.661767i	−0.991358	−	0.131183i	$-0.958123\pi$
$547$	−8.93590	+	15.4774i	−0.382071	+	0.661767i	0.609287	+	0.792950i	$0.291456\pi$
$548$			62.2457i			2.65901i
$549$	−33.3603	−	5.02716i	−1.42378	−	0.214554i
$550$	23.9326			1.02049
$551$	−0.749783	+	1.29866i	−0.0319418	+	0.0553249i
$552$	−31.0643	−	36.0962i	−1.32218	−	1.53635i
$553$		0			0
$554$	−11.4986	+	6.63870i	−0.488527	+	0.282051i
$555$	−2.35247	−	2.73353i	−0.0998566	−	0.116032i
$556$	−46.6463	−	26.9313i	−1.97824	−	1.14214i
$557$			42.9605i			1.82029i	0.414285	+	0.910147i	$0.364032\pi$
$557$			42.9605i			1.82029i	−0.414285	+	0.910147i	$0.635968\pi$
$558$	−26.5000	+	10.4015i	−1.12183	+	0.440330i
$559$			0.0247261i			0.00104580i
$560$		0			0
$561$	−4.89357	−	1.71225i	−0.206607	−	0.0722911i
$562$	−18.0813	−	31.3177i	−0.762713	−	1.32106i
$563$	0.773739	+	1.34016i	0.0326092	+	0.0564808i	0.881869	−	0.471494i	$-0.156285\pi$
$563$	0.773739	+	1.34016i	0.0326092	+	0.0564808i	−0.849260	+	0.527975i	$0.822952\pi$
$564$	13.0339	−	2.46636i	0.548825	−	0.103852i
$565$	11.5016	+	6.64048i	0.483878	+	0.279367i
$566$	−10.1759			−0.427726
$567$		0			0
$568$	108.906			4.56958
$569$	−8.65905	−	4.99931i	−0.363006	−	0.209582i	0.307392	−	0.951583i	$-0.400544\pi$
$569$	−8.65905	−	4.99931i	−0.363006	−	0.209582i	−0.670399	+	0.742001i	$0.733877\pi$
$570$	41.4258	−	7.83888i	1.73514	−	0.328335i
$571$	1.39715	+	2.41994i	0.0584689	+	0.101271i	0.893778	−	0.448509i	$-0.148045\pi$
$571$	1.39715	+	2.41994i	0.0584689	+	0.101271i	−0.835309	+	0.549780i	$0.814711\pi$
$572$	12.5073	+	21.6634i	0.522958	+	0.905790i
$573$	26.1855	+	9.16224i	1.09392	+	0.382758i
$574$		0			0
$575$		−	10.8046i		−	0.450582i
$576$	−69.1551	+	27.1440i	−2.88146	+	1.13100i
$577$			3.73764i			0.155600i	0.996969	+	0.0778000i	$0.0247896\pi$
$577$			3.73764i			0.155600i	−0.996969	+	0.0778000i	$0.975210\pi$
$578$	36.4814	+	21.0626i	1.51743	+	0.876087i
$579$	15.4890	+	17.9980i	0.643703	+	0.747972i
$580$	−1.11626	+	0.644475i	−0.0463503	+	0.0267604i
$581$		0			0
$582$	7.28910	+	8.46981i	0.302143	+	0.351085i
$583$	12.3193	−	21.3377i	0.510214	−	0.883717i
$584$	78.4074			3.24452
$585$	6.72519	+	1.01344i	0.278052	+	0.0419004i
$586$			34.5879i			1.42881i
$587$	13.1249	−	22.7331i	0.541725	−	0.938295i	−0.457081	−	0.889425i	$-0.651105\pi$
$587$	13.1249	−	22.7331i	0.541725	−	0.938295i	0.998805	−	0.0488692i	$-0.0155618\pi$
$588$		0			0
$589$	−13.0845	−	22.6630i	−0.539136	−	0.933812i
$590$	34.4819	−	19.9081i	1.41960	−	0.819604i
$591$	6.09448	+	32.2072i	0.250693	+	1.32483i
$592$	−11.9573	+	20.7106i	−0.491441	+	0.851201i
$593$	3.59667			0.147698			0.0738488	−	0.997269i	$-0.476472\pi$
$593$	3.59667			0.147698			0.0738488	+	0.997269i	$0.476472\pi$
$594$	30.9457	+	16.3534i	1.26972	+	0.670987i
$595$		0			0
$596$	22.1522	+	12.7896i	0.907391	+	0.523882i
$597$	7.99694	+	42.2611i	0.327293	+	1.72963i
$598$	13.4446	−	7.76226i	0.549792	−	0.317422i
$599$	20.6400	−	11.9165i	0.843326	−	0.486895i	−0.0150672	−	0.999886i	$-0.504796\pi$
$599$	20.6400	−	11.9165i	0.843326	−	0.486895i	0.858394	+	0.512992i	$0.171463\pi$
$600$	−52.5180	−	18.3759i	−2.14404	−	0.750193i
$601$	14.6034	+	8.43126i	0.595684	+	0.343918i	0.767342	−	0.641238i	$-0.221579\pi$
$601$	14.6034	+	8.43126i	0.595684	+	0.343918i	−0.171658	+	0.985157i	$0.554912\pi$
$602$		0			0
$603$	12.0999	+	9.64870i	0.492746	+	0.392925i
$604$	60.4153			2.45826
$605$	−2.89695	+	5.01767i	−0.117778	+	0.203997i
$606$	−33.6612	+	28.9688i	−1.36739	+	1.17678i
$607$	9.07737	−	5.24082i	0.368439	−	0.212718i	−0.304337	−	0.952564i	$-0.598435\pi$
$607$	9.07737	−	5.24082i	0.368439	−	0.212718i	0.672776	+	0.739846i	$0.265102\pi$
$608$	−72.2463	−	125.134i	−2.92997	−	5.07487i
$609$		0			0
$610$	18.3222	−	31.7349i	0.741842	−	1.28491i
$611$			2.70404i			0.109394i
$612$	15.0707	+	12.0176i	0.609195	+	0.485785i
$613$	−47.9001			−1.93467			−0.967333	−	0.253510i	$-0.918415\pi$
$613$	−47.9001			−1.93467			−0.967333	+	0.253510i	$0.918415\pi$
$614$	−14.5270	+	25.1616i	−0.586264	+	1.01544i
$615$	−4.62454	+	13.2169i	−0.186480	+	0.532956i
$616$		0			0
$617$	4.69477	−	2.71053i	0.189004	−	0.109122i	−0.402512	−	0.915415i	$-0.631863\pi$
$617$	4.69477	−	2.71053i	0.189004	−	0.109122i	0.591516	+	0.806293i	$0.298530\pi$
$618$	−79.5605	+	15.0550i	−3.20039	+	0.605601i
$619$	−27.9729	−	16.1501i	−1.12432	−	0.649129i	−0.181823	−	0.983331i	$-0.558200\pi$
$619$	−27.9729	−	16.1501i	−1.12432	−	0.649129i	−0.942501	+	0.334202i	$0.891533\pi$
$620$		−	22.4935i		−	0.903359i
$621$	7.38288	−	13.9707i	0.296265	−	0.560626i
$622$		−	51.0204i		−	2.04573i
$623$		0			0
$624$	−8.38513	−	44.3126i	−0.335674	−	1.77392i
$625$	−2.69418	−	4.66646i	−0.107767	−	0.186658i
$626$	35.3098	+	61.1584i	1.41126	+	2.44438i
$627$	−10.6259	+	30.3687i	−0.424359	+	1.21281i
$628$	68.0989	+	39.3169i	2.71744	+	1.56892i
$629$	2.08355			0.0830765
$630$		0			0
$631$	−18.3539			−0.730656			−0.365328	−	0.930879i	$-0.619043\pi$
$631$	−18.3539			−0.730656			−0.365328	+	0.930879i	$0.619043\pi$
$632$	43.0343	+	24.8459i	1.71181	+	0.988315i
$633$	8.15187	+	9.47234i	0.324008	+	0.376492i
$634$	−18.8127	−	32.5845i	−0.747147	−	1.29410i
$635$	−8.33836	−	14.4425i	−0.330898	−	0.573132i
$636$	−69.4330	+	59.7539i	−2.75320	+	2.36940i
$637$		0			0
$638$		−	1.35218i		−	0.0535335i
$639$	13.2029	+	33.6373i	0.522299	+	1.33067i
$640$		−	34.1579i		−	1.35021i
$641$	9.07003	+	5.23658i	0.358245	+	0.206833i	0.668310	−	0.743882i	$-0.267018\pi$
$641$	9.07003	+	5.23658i	0.358245	+	0.206833i	−0.310066	+	0.950715i	$0.600351\pi$
$642$	15.3149	−	43.7697i	0.604430	−	1.72745i
$643$	−3.37572	+	1.94897i	−0.133125	+	0.0768600i	−0.565084	−	0.825034i	$-0.691156\pi$
$643$	−3.37572	+	1.94897i	−0.133125	+	0.0768600i	0.431958	+	0.901894i	$0.357823\pi$
$644$		0			0
$645$	−0.0268595	+	0.00508254i	−0.00105759	+	0.000200125i
$646$	−12.1789	+	21.0945i	−0.479172	+	0.829950i
$647$	−12.4054			−0.487706			−0.243853	−	0.969812i	$-0.578411\pi$
$647$	−12.4054			−0.487706			−0.243853	+	0.969812i	$0.578411\pi$
$648$	−55.3514	−	59.6468i	−2.17441	−	2.34315i
$649$			30.3847i			1.19271i
$650$	9.06905	−	15.7081i	0.355717	−	0.616120i
$651$		0			0
$652$	−48.4615	−	83.9377i	−1.89790	−	3.28726i
$653$	−12.2749	+	7.08690i	−0.480353	+	0.277332i	−0.720564	−	0.693389i	$-0.756117\pi$
$653$	−12.2749	+	7.08690i	−0.480353	+	0.277332i	0.240211	+	0.970721i	$0.422784\pi$
$654$	−46.1171	−	16.1362i	−1.80332	−	0.630977i
$655$	7.43379	−	12.8757i	0.290462	−	0.503095i
$656$	92.8525			3.62528
$657$	9.50554	+	24.2174i	0.370846	+	0.944811i
$658$		0			0
$659$	−17.2962	−	9.98594i	−0.673763	−	0.388997i	0.123738	−	0.992315i	$-0.460512\pi$
$659$	−17.2962	−	9.98594i	−0.673763	−	0.388997i	−0.797501	+	0.603318i	$0.793845\pi$
$660$	−20.9615	+	18.0395i	−0.815927	+	0.702185i
$661$	21.0493	−	12.1528i	0.818721	−	0.472689i	−0.0312540	−	0.999511i	$-0.509950\pi$
$661$	21.0493	−	12.1528i	0.818721	−	0.472689i	0.849975	+	0.526823i	$0.176617\pi$
$662$	10.5205	−	6.07401i	0.408891	−	0.236073i
$663$	−2.97821	+	2.56304i	−0.115664	+	0.0995401i
$664$	25.1900	+	14.5435i	0.977563	+	0.564396i
$665$		0			0
$666$	−13.9092	−	2.09602i	−0.538971	−	0.0812190i
$667$	−0.610456			−0.0236370
$668$	3.19964	−	5.54194i	0.123798	−	0.214424i
$669$	39.7765	+	13.9177i	1.53785	+	0.538089i
$670$	−14.5575	+	8.40480i	−0.562407	+	0.324706i
$671$	13.9821	+	24.2177i	0.539773	+	0.934914i
$672$		0			0
$673$	−1.82521	+	3.16135i	−0.0703566	+	0.121861i	−0.899058	−	0.437830i	$-0.855747\pi$
$673$	−1.82521	+	3.16135i	−0.0703566	+	0.121861i	0.828701	+	0.559692i	$0.189080\pi$
$674$			88.8551i			3.42257i
$675$	−0.691203	−	18.4488i	−0.0266044	−	0.710094i
$676$	−50.4326			−1.93972
$677$	0.968676	−	1.67780i	0.0372292	−	0.0644829i	−0.846810	−	0.531895i	$-0.821480\pi$
$677$	0.968676	−	1.67780i	0.0372292	−	0.0644829i	0.884040	+	0.467412i	$0.154813\pi$
$678$	50.8970	−	9.63109i	1.95469	−	0.369880i
$679$		0			0
$680$	−11.3379	+	6.54597i	−0.434790	+	0.251026i
$681$	0.274906	−	0.785677i	0.0105344	−	0.0301072i
$682$	20.4356	+	11.7985i	0.782519	+	0.451788i
$683$		−	19.4931i		−	0.745884i	−0.927855	−	0.372942i	$-0.878349\pi$
$683$		−	19.4931i		−	0.745884i	0.927855	−	0.372942i	$-0.121651\pi$
$684$	74.5796	−	93.5261i	2.85162	−	3.57606i
$685$		−	14.0278i		−	0.535976i
$686$		0			0
$687$	−11.8309	+	10.1816i	−0.451377	+	0.388454i
$688$	0.0906345	+	0.156983i	0.00345541	+	0.00598494i
$689$	−9.33660	−	16.1715i	−0.355696	−	0.616084i
$690$	11.1956	+	13.0091i	0.426208	+	0.495247i
$691$	35.7855	+	20.6608i	1.36134	+	0.785972i	0.989803	−	0.142444i	$-0.0454960\pi$
$691$	35.7855	+	20.6608i	1.36134	+	0.785972i	0.371541	+	0.928416i	$0.378829\pi$
$692$	−96.1226			−3.65403
$693$		0			0
$694$	−36.3186			−1.37863
$695$	10.5123	+	6.06929i	0.398755	+	0.230221i
$696$	−1.03823	+	2.96726i	−0.0393541	+	0.112474i
$697$	−4.04488	−	7.00593i	−0.153211	−	0.265369i
$698$	30.2273	+	52.3552i	1.14412	+	1.98167i
$699$	−3.58001	−	18.9191i	−0.135408	−	0.715586i
$700$		0			0
$701$			27.3333i			1.03236i	0.856479	+	0.516182i	$0.172647\pi$
$701$			27.3333i			1.03236i	−0.856479	+	0.516182i	$0.827353\pi$
$702$	22.4601	−	14.1141i	0.847702	−	0.532704i
$703$		−	12.9302i		−	0.487671i
$704$	53.3293	+	30.7897i	2.00992	+	1.16043i
$705$	−2.93734	+	0.555824i	−0.110627	+	0.0209335i
$706$	40.3893	−	23.3187i	1.52007	−	0.877613i
$707$		0			0
$708$	37.3094	−	106.630i	1.40217	−	4.00739i
$709$	−1.35635	+	2.34926i	−0.0509387	+	0.0882283i	−0.890370	−	0.455237i	$-0.849555\pi$
$709$	−1.35635	+	2.34926i	−0.0509387	+	0.0882283i	0.839432	+	0.543465i	$0.182888\pi$
$710$	−39.2496			−1.47301
$711$	−2.45689	+	16.3040i	−0.0921404	+	0.611446i
$712$		−	72.0354i		−	2.69964i
$713$	5.32654	−	9.22584i	0.199480	−	0.345510i
$714$		0			0
$715$	−2.81868	−	4.88210i	−0.105413	−	0.182580i
$716$	69.9976	−	40.4131i	2.61593	−	1.51031i
$717$	18.2587	−	15.7134i	0.681882	−	0.586826i
$718$	−8.80292	+	15.2471i	−0.328522	+	0.569017i
$719$	−16.2786			−0.607090			−0.303545	−	0.952817i	$-0.598170\pi$
$719$	−16.2786			−0.607090			−0.303545	+	0.952817i	$0.598170\pi$
$720$	46.4123	−	18.2172i	1.72968	−	0.678915i
$721$		0			0
$722$	86.3365	+	49.8464i	3.21311	+	1.85509i
$723$	−20.2333	−	7.07957i	−0.752484	−	0.263292i
$724$	−36.9217	+	21.3167i	−1.37218	+	0.792231i
$725$	−0.617673	+	0.356614i	−0.0229398	+	0.0132443i
$726$	4.20163	+	22.2042i	0.155937	+	0.824074i
$727$	0.980123	+	0.565874i	0.0363508	+	0.0209871i	0.518065	−	0.855341i	$-0.326652\pi$
$727$	0.980123	+	0.565874i	0.0363508	+	0.0209871i	−0.481714	+	0.876328i	$0.659986\pi$
$728$		0			0
$729$	11.7125	−	24.3273i	0.433796	−	0.901011i
$730$	−28.2581			−1.04588
$731$	0.00789650	−	0.0136771i	0.000292063	−	0.000505867i
$732$	−19.3307	−	102.156i	−0.714484	−	3.77580i
$733$	−33.2085	+	19.1729i	−1.22658	+	0.708169i	−0.966314	−	0.257367i	$-0.917145\pi$
$733$	−33.2085	+	19.1729i	−1.22658	+	0.708169i	−0.260270	+	0.965536i	$0.583812\pi$
$734$	−12.1946	−	21.1217i	−0.450111	−	0.779615i
$735$		0			0
$736$	29.4106	−	50.9407i	1.08409	−	1.87770i
$737$		−	12.8278i		−	0.472519i
$738$	19.9547	+	50.8388i	0.734542	+	1.87140i
$739$	10.7298			0.394701			0.197351	−	0.980333i	$-0.436766\pi$
$739$	10.7298			0.394701			0.197351	+	0.980333i	$0.436766\pi$
$740$	5.55705	−	9.62509i	0.204281	−	0.353825i
$741$	15.9058	+	18.4823i	0.584314	+	0.678963i
$742$		0			0
$743$	−11.3308	+	6.54185i	−0.415687	+	0.239997i	−0.693230	−	0.720716i	$-0.743813\pi$
$743$	−11.3308	+	6.54185i	−0.415687	+	0.239997i	0.277543	+	0.960713i	$0.410480\pi$
$744$	−35.7851	−	41.5816i	−1.31194	−	1.52446i
$745$	−4.99228	−	2.88229i	−0.182903	−	0.105599i
$746$			31.1685i			1.14116i
$747$	−1.43813	+	9.54349i	−0.0526186	+	0.349178i
$748$		−	15.9773i		−	0.584188i
$749$		0			0
$750$	45.5637	+	15.9426i	1.66375	+	0.582142i
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	0.519254	−	0.854620i	$-0.326210\pi$
$751$	−13.1677	−	22.8071i	−0.480495	−	0.832242i	−0.999750	+	0.0223774i	$0.992876\pi$
$752$	9.91173	+	17.1676i	0.361444	+	0.626039i
$753$	33.5515	−	6.34884i	1.22268	−	0.231365i
$754$	−0.887501	−	0.512399i	−0.0323209	−	0.0186605i
$755$	−13.6153			−0.495512
$756$		0			0
$757$	−32.6280			−1.18588			−0.592942	−	0.805245i	$-0.702034\pi$
$757$	−32.6280			−1.18588			−0.592942	+	0.805245i	$0.702034\pi$
$758$	−40.1109	−	23.1580i	−1.45689	−	0.841138i
$759$	−12.8693	+	2.43522i	−0.467127	+	0.0883930i
$760$	40.6232	+	70.3615i	1.47356	+	2.55228i
$761$	12.6727	+	21.9498i	0.459385	+	0.795679i	0.998929	−	0.0462793i	$-0.0147364\pi$
$761$	12.6727	+	21.9498i	0.459385	+	0.795679i	−0.539543	+	0.841958i	$0.681403\pi$
$762$	−61.3951	−	21.4820i	−2.22411	−	0.778210i
$763$		0			0
$764$			85.4946i			3.09309i
$765$	−3.39636	−	2.70832i	−0.122796	−	0.0979196i
$766$			43.9252i			1.58708i
$767$	19.9429	+	11.5140i	0.720097	+	0.415748i
$768$	−30.9470	−	35.9598i	−1.11670	−	1.29759i
$769$	11.4964	−	6.63744i	0.414570	−	0.239352i	−0.278181	−	0.960529i	$-0.589732\pi$
$769$	11.4964	−	6.63744i	0.414570	−	0.239352i	0.692752	+	0.721176i	$0.256398\pi$
$770$		0			0
$771$	12.6997	+	14.7568i	0.457368	+	0.531454i
$772$	−36.5886	+	63.3733i	−1.31685	+	2.28085i
$773$	16.0136			0.575969			0.287985	−	0.957635i	$-0.407015\pi$
$773$	16.0136			0.575969			0.287985	+	0.957635i	$0.407015\pi$
$774$	−0.0664740	+	0.0833613i	−0.00238936	+	0.00299636i
$775$		−	12.4465i		−	0.447093i
$776$	−10.7669	+	18.6488i	−0.386509	+	0.669454i
$777$		0			0
$778$	25.3919	+	43.9801i	0.910344	+	1.57676i
$779$	−43.4777	+	25.1019i	−1.55775	+	0.899367i
$780$	3.89693	+	20.5939i	0.139532	+	0.737381i
$781$	14.9762	−	25.9395i	0.535890	−	0.928189i
$782$	−9.91577			−0.354587
$783$	−1.04235	+	0.0390528i	−0.0372506	+	0.00139563i
$784$		0			0
$785$	−15.3469	−	8.86054i	−0.547755	−	0.316246i
$786$	−10.7817	−	56.9775i	−0.384570	−	2.03232i
$787$	−4.24659	+	2.45177i	−0.151375	+	0.0873961i	−0.573774	−	0.819014i	$-0.694521\pi$
$787$	−4.24659	+	2.45177i	−0.151375	+	0.0873961i	0.422400	+	0.906410i	$0.361188\pi$
$788$	−87.4826	+	50.5081i	−3.11644	+	1.79928i
$789$	−5.32629	−	1.86365i	−0.189621	−	0.0663478i
$790$	−15.5096	−	8.95445i	−0.551806	−	0.318585i
$791$		0			0
$792$	−10.0506	+	66.6958i	−0.357131	+	2.36993i
$793$	21.1936			0.752606
$794$	41.9474	−	72.6551i	1.48866	−	2.57843i
$795$	15.6476	−	13.4663i	0.554962	−	0.477599i
$796$	−114.791	+	66.2748i	−4.06867	+	2.34905i
$797$	21.3994	+	37.0649i	0.758006	+	1.31290i	0.943866	+	0.330328i	$0.107159\pi$
$797$	21.3994	+	37.0649i	0.758006	+	1.31290i	−0.185860	+	0.982576i	$0.559507\pi$
$798$		0			0
$799$	0.863557	−	1.49572i	0.0305505	−	0.0529149i
$800$		−	68.7239i		−	2.42976i
$801$	22.2493	−	8.73304i	0.786141	−	0.308567i
$802$	2.50564			0.0884772
$803$	10.7822	−	18.6754i	0.380496	−	0.659039i
$804$	−15.7513	+	45.0169i	−0.555505	+	1.58763i
$805$		0			0
$806$	15.4878	−	8.94188i	0.545534	−	0.314964i
$807$	−0.412347	+	0.0780271i	−0.0145153	+	0.00274668i
$808$	−74.1152	−	42.7904i	−2.60736	−	1.50536i
$809$		−	35.2933i		−	1.24085i	−0.784267	−	0.620424i	$-0.786961\pi$
$809$		−	35.2933i		−	1.24085i	0.784267	−	0.620424i	$-0.213039\pi$
$810$	19.9486	+	21.4967i	0.700924	+	0.755318i
$811$			21.0223i			0.738193i	0.929391	+	0.369096i	$0.120333\pi$
$811$			21.0223i			0.738193i	−0.929391	+	0.369096i	$0.879667\pi$
$812$		0			0
$813$	−0.345560	−	1.82617i	−0.0121193	−	0.0640465i
$814$	5.82968	+	10.0973i	0.204330	+	0.353910i
$815$	10.9214	+	18.9164i	0.382559	+	0.662612i
$816$	−9.51340	+	27.1891i	−0.333036	+	0.951810i
$817$	−0.0848782	−	0.0490044i	−0.00296951	−	0.00171445i
$818$	20.5372			0.718067
$819$		0			0
$820$	−43.1525			−1.50695
$821$	−29.8623	−	17.2410i	−1.04220	−	0.601716i	−0.121746	−	0.992561i	$-0.538849\pi$
$821$	−29.8623	−	17.2410i	−1.04220	−	0.601716i	−0.920456	+	0.390845i	$0.872183\pi$
$822$	−35.6895	−	41.4706i	−1.24481	−	1.44645i
$823$	19.4950	+	33.7663i	0.679552	+	1.17702i	0.975116	+	0.221695i	$0.0711590\pi$
$823$	19.4950	+	33.7663i	0.679552	+	1.17702i	−0.295564	+	0.955323i	$0.595508\pi$
$824$	−78.0191	−	135.133i	−2.71792	−	4.70758i
$825$	−11.5989	+	9.98195i	−0.403820	+	0.347527i
$826$		0			0
$827$		−	47.2537i		−	1.64317i	−0.570086	−	0.821585i	$-0.693090\pi$
$827$		−	47.2537i		−	1.64317i	0.570086	−	0.821585i	$-0.306910\pi$
$828$	48.1528	+	7.25627i	1.67342	+	0.252173i
$829$		−	49.1426i		−	1.70679i	−0.521262	−	0.853397i	$-0.674538\pi$
$829$		−	49.1426i		−	1.70679i	0.521262	−	0.853397i	$-0.325462\pi$
$830$	−9.07850	−	5.24147i	−0.315119	−	0.181934i
$831$	2.80384	−	8.01332i	0.0972641	−	0.277979i
$832$	40.4174	−	23.3350i	1.40122	−	0.808995i
$833$		0			0
$834$	46.5190	−	8.80266i	1.61082	−	0.304811i
$835$	−0.721079	+	1.24894i	−0.0249540	+	0.0432215i
$836$	−99.1526			−3.42926
$837$	8.50485	−	16.0938i	0.293971	−	0.556285i
$838$			15.4436i			0.533492i
$839$	−26.0780	+	45.1684i	−0.900312	+	1.55939i	−0.0732219	+	0.997316i	$0.523328\pi$
$839$	−26.0780	+	45.1684i	−0.900312	+	1.55939i	−0.827090	+	0.562070i	$0.810005\pi$
$840$		0			0
$841$	−14.4799	−	25.0798i	−0.499305	−	0.864822i
$842$	27.5030	−	15.8789i	0.947816	−	0.547222i
$843$	21.8252	+	7.63658i	0.751701	+	0.263018i
$844$	−19.2565	+	33.3533i	−0.662838	+	1.14807i
$845$	11.3656			0.390989
$846$	−7.26956	+	9.11634i	−0.249932	+	0.313426i
$847$		0			0
$848$	−118.554	−	68.4472i	−4.07116	−	2.35049i
$849$	4.93173	−	4.24424i	0.169257	−	0.145662i
$850$	−10.0330	+	5.79255i	−0.344129	+	0.198683i
$851$	4.55852	−	2.63186i	0.156264	−	0.0902190i
$852$	−84.4074	+	72.6408i	−2.89175	+	2.48863i
$853$	13.4028	+	7.73808i	0.458902	+	0.264947i	0.711582	−	0.702603i	$-0.247979\pi$
$853$	13.4028	+	7.73808i	0.458902	+	0.264947i	−0.252681	+	0.967550i	$0.581312\pi$
$854$		0			0
$855$	−16.8074	+	21.0772i	−0.574802	+	0.720827i
$856$	89.3607			3.05429
$857$	−24.4356	+	42.3238i	−0.834706	+	1.44575i	0.0595642	+	0.998224i	$0.481029\pi$
$857$	−24.4356	+	42.3238i	−0.834706	+	1.44575i	−0.894270	+	0.447528i	$0.852304\pi$
$858$	−20.7539	−	7.26172i	−0.708526	−	0.247911i
$859$	8.45000	−	4.87861i	0.288310	−	0.166456i	−0.348869	−	0.937171i	$-0.613434\pi$
$859$	8.45000	−	4.87861i	0.288310	−	0.166456i	0.637180	+	0.770715i	$0.280101\pi$
$860$	−0.0421217	−	0.0729569i	−0.00143634	−	0.00248781i
$861$		0			0
$862$	−36.4356	+	63.1083i	−1.24100	+	2.14948i
$863$		−	27.6507i		−	0.941241i	−0.882336	−	0.470620i	$-0.844030\pi$
$863$		−	27.6507i		−	0.941241i	0.882336	−	0.470620i	$-0.155970\pi$
$864$	46.9598	−	88.8627i	1.59760	−	3.02317i
$865$	21.6624			0.736544
$866$	−38.0628	+	65.9267i	−1.29343	+	2.24028i
$867$	−26.4655	+	5.00799i	−0.898817	+	0.170080i
$868$		0			0
$869$	11.8357	−	6.83337i	0.401500	−	0.231806i
$870$	0.374180	−	1.06940i	0.0126859	−	0.0362560i
$871$	−8.41949	−	4.86100i	−0.285284	−	0.164709i
$872$		−	94.1533i		−	3.18843i
$873$	−7.06529	−	1.06469i	−0.239124	−	0.0360342i
$874$			61.5357i			2.08148i
$875$		0			0
$876$	−60.7697	+	52.2983i	−2.05322	+	1.76700i
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	0.881342	−	0.472479i	$-0.156641\pi$
$877$	0.932622	+	1.61535i	0.0314924	+	0.0545465i	−0.849850	+	0.527025i	$0.823307\pi$
$878$	12.6317	+	21.8787i	0.426298	+	0.738370i
$879$	−14.4262	−	16.7630i	−0.486582	−	0.565401i
$880$	−35.7910	−	20.6639i	−1.20651	−	0.696581i
$881$	−0.0273875			−0.000922707			−0.000461353	−	1.00000i	$-0.500147\pi$
$881$	−0.0273875			−0.000922707			−0.000461353		1.00000i	$0.500147\pi$
$882$		0			0
$883$	36.2074			1.21848			0.609239	−	0.792987i	$-0.291475\pi$
$883$	36.2074			1.21848			0.609239	+	0.792987i	$0.291475\pi$
$884$	−10.4866	−	6.05447i	−0.352704	−	0.203634i
$885$	−8.40814	+	24.0303i	−0.282637	+	0.807771i
$886$	−15.3600	−	26.6043i	−0.516028	−	0.893787i
$887$	12.6626	+	21.9323i	0.425170	+	0.736415i	0.996436	−	0.0843491i	$-0.0268811\pi$
$887$	12.6626	+	21.9323i	0.425170	+	0.736415i	−0.571267	+	0.820765i	$0.693548\pi$
$888$	−5.03984	−	26.6338i	−0.169126	−	0.893772i
$889$		0			0
$890$			25.9616i			0.870235i
$891$	−21.8185	+	4.98143i	−0.730949	+	0.166884i
$892$			129.869i			4.34832i
$893$	−9.28223	−	5.35910i	−0.310618	−	0.179335i
$894$	−22.0918	+	4.18036i	−0.738860	+	0.139812i
$895$	−15.7748	+	9.10759i	−0.527294	+	0.304433i
$896$		0			0
$897$	−3.27837	+	9.36953i	−0.109462	+	0.312840i
$898$	−20.7625	+	35.9617i	−0.692854	+	1.20006i
$899$	−0.703226			−0.0234539
$900$	52.9610	−	20.7876i	1.76537	−	0.692921i
$901$			11.9269i			0.397342i
$902$	22.6348	−	39.2046i	0.753655	−	1.30537i
$903$		0			0
$904$	49.9110	+	86.4483i	1.66001	+	2.87523i
$905$	8.32075	−	4.80399i	0.276591	−	0.159690i
$906$	−40.2511	+	34.6400i	−1.33725	+	1.15084i
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	−0.340081	−	0.940396i	$-0.610455\pi$
$907$	19.4060	−	33.6122i	0.644366	−	1.11608i	0.984447	−	0.175679i	$-0.0562121\pi$
$908$	2.56520			0.0851292
$909$	4.23134	−	28.0793i	0.140345	−	0.931331i
$910$		0			0
$911$	−43.6110	−	25.1788i	−1.44490	−	0.834211i	−0.446725	−	0.894671i	$-0.647410\pi$
$911$	−43.6110	−	25.1788i	−1.44490	−	0.834211i	−0.998171	+	0.0604602i	$0.980743\pi$
$912$	168.731	+	59.0386i	5.58726	+	1.95496i
$913$	6.92803	−	3.99990i	0.229284	−	0.132377i
$914$	−21.5190	+	12.4240i	−0.711787	+	0.410950i
$915$	4.35642	+	23.0222i	0.144019	+	0.761089i
$916$	−41.6581	−	24.0513i	−1.37642	−	0.794677i
$917$		0			0
$918$	−16.9312	+	0.634343i	−0.558812	+	0.0209364i
$919$	−2.99690			−0.0988585			−0.0494293	−	0.998778i	$-0.515740\pi$
$919$	−2.99690			−0.0988585			−0.0494293	+	0.998778i	$0.515740\pi$
$920$	−16.5372	+	28.6434i	−0.545217	+	0.944343i
$921$	−3.45406	−	18.2535i	−0.113815	−	0.601474i
$922$	77.5863	−	44.7945i	2.55517	−	1.47523i
$923$	−11.3502	−	19.6591i	−0.373596	−	0.647088i
$924$		0			0
$925$	3.07494	−	5.32595i	0.101103	−	0.175116i
$926$		−	21.2152i		−	0.697175i
$927$	32.2796	−	40.4800i	1.06020	−	1.32954i
$928$	−3.88289			−0.127462
$929$	16.1108	−	27.9047i	0.528577	−	0.915522i	−0.470868	−	0.882204i	$-0.656059\pi$
$929$	16.1108	−	27.9047i	0.528577	−	0.915522i	0.999445	−	0.0333184i	$-0.0106075\pi$
$930$	12.8970	+	14.9860i	0.422908	+	0.491412i
$931$		0			0
$932$	51.3888	−	29.6694i	1.68330	−	0.971852i
$933$	21.2799	+	24.7269i	0.696673	+	0.809523i
$934$	48.5064	+	28.0052i	1.58718	+	0.916358i
$935$			3.60068i			0.117755i
$936$	39.9670	+	31.8705i	1.30636	+	1.04172i
$937$			3.07038i			0.100305i	0.998742	+	0.0501525i	$0.0159708\pi$
$937$			3.07038i			0.100305i	−0.998742	+	0.0501525i	$0.984029\pi$
$938$		0			0
$939$	−42.6212	−	14.9130i	−1.39089	−	0.486668i
$940$	−4.60640	−	7.97852i	−0.150244	−	0.260231i
$941$	−19.4136	−	33.6253i	−0.632865	−	1.09615i	−0.986963	−	0.160946i	$-0.948546\pi$
$941$	−19.4136	−	33.6253i	−0.632865	−	1.09615i	0.354099	−	0.935208i	$-0.384788\pi$
$942$	−67.9131	+	12.8510i	−2.21273	+	0.418708i
$943$	−17.6993	−	10.2187i	−0.576367	−	0.332766i
$944$	168.820			5.49464
$945$		0			0
$946$	0.0883763			0.00287336
$947$	16.2391	+	9.37567i	0.527701	+	0.304668i	0.740080	−	0.672519i	$-0.234788\pi$
$947$	16.2391	+	9.37567i	0.527701	+	0.304668i	−0.212379	+	0.977187i	$0.568121\pi$
$948$	−49.9261	+	9.44737i	−1.62152	+	0.306836i
$949$	−8.17166	−	14.1537i	−0.265263	−	0.459450i
$950$	35.9477	+	62.2632i	1.16630	+	2.02008i
$951$	22.7081	+	7.94549i	0.736360	+	0.257650i
$952$		0			0
$953$			47.6453i			1.54338i	0.635997	+	0.771692i	$0.280589\pi$
$953$			47.6453i			1.54338i	−0.635997	+	0.771692i	$0.719411\pi$
$954$	11.9983	−	79.6208i	0.388458	−	2.57782i
$955$		−	19.2672i		−	0.623474i
$956$	64.2911	+	37.1185i	2.07932	+	1.20050i
$957$	0.563978	+	0.655333i	0.0182308	+	0.0211839i
$958$	−6.24009	+	3.60272i	−0.201608	+	0.116398i
$959$		0			0
$960$	33.6562	+	39.1080i	1.08625	+	1.26220i
$961$	−9.36399	+	16.2189i	−0.302064	+	0.523191i
$962$	8.83643			0.284898
$963$	10.8334	+	27.6005i	0.349102	+	0.889414i
$964$		−	66.0608i		−	2.12768i
$965$	8.24569	−	14.2819i	0.265438	−	0.459752i
$966$		0			0
$967$	25.8005	+	44.6878i	0.829689	+	1.43706i	0.898282	+	0.439419i	$0.144815\pi$
$967$	25.8005	+	44.6878i	0.829689	+	1.43706i	−0.0685936	+	0.997645i	$0.521851\pi$
$968$	−37.7137	+	21.7740i	−1.21216	+	0.699843i
$969$	−2.89575	−	15.3030i	−0.0930248	−	0.491604i
$970$	3.88040	−	6.72104i	0.124592	−	0.215800i
$971$	−28.3866			−0.910971			−0.455485	−	0.890243i	$-0.650534\pi$
$971$	−28.3866			−0.910971			−0.455485	+	0.890243i	$0.650534\pi$
$972$	82.6849	+	9.30958i	2.65212	+	0.298605i
$973$		0			0
$974$	2.44867	+	1.41374i	0.0784603	+	0.0452991i
$975$	2.15633	+	11.3954i	0.0690577	+	0.364946i
$976$	134.556	−	77.6858i	4.30702	−	2.48666i
$977$	35.6722	−	20.5954i	1.14126	−	0.658904i	0.194515	−	0.980900i	$-0.437687\pi$
$977$	35.6722	−	20.5954i	1.14126	−	0.658904i	0.946741	+	0.321995i	$0.104353\pi$
$978$	80.4139	+	28.1366i	2.57135	+	0.899708i
$979$	−17.1576	−	9.90597i	−0.548361	−	0.316596i
$980$		0			0
$981$	29.0808	−	11.4144i	0.928477	−	0.364435i
$982$	−112.734			−3.59747
$983$	26.4017	−	45.7291i	0.842085	−	1.45853i	−0.0460447	−	0.998939i	$-0.514662\pi$
$983$	26.4017	−	45.7291i	0.842085	−	1.45853i	0.888129	−	0.459594i	$-0.152005\pi$
$984$	−79.7721	+	68.6517i	−2.54304	+	2.18854i
$985$	19.7153	−	11.3826i	0.628181	−	0.362680i
$986$	0.327278	+	0.566862i	0.0104227	+	0.0180526i
$987$		0			0
$988$	−37.5731	+	65.0784i	−1.19536	+	2.07042i
$989$		−	0.0398983i		−	0.00126869i
$990$	3.62223	−	24.0372i	0.115122	−	0.763952i
$991$	16.4897			0.523813			0.261907	−	0.965093i	$-0.415649\pi$
$991$	16.4897			0.523813			0.261907	+	0.965093i	$0.415649\pi$
$992$	33.8801	−	58.6821i	1.07570	−	1.86316i
$993$	−2.56534	+	7.33171i	−0.0814087	+	0.232665i
$994$		0			0
$995$	25.8696	−	14.9358i	0.820122	−	0.473498i
$996$	−29.2241	+	5.53000i	−0.926003	+	0.175225i
$997$	42.4857	+	24.5291i	1.34553	+	0.776845i	0.987613	−	0.156907i	$-0.0501523\pi$
$997$	42.4857	+	24.5291i	1.34553	+	0.776845i	0.357921	+	0.933752i	$0.383486\pi$
$998$		−	87.4667i		−	2.76871i
$999$	7.61529	−	4.78552i	0.240937	−	0.151407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.146.2	yes	48
3.2	odd	2		1323.2.o.e.440.24		48
7.2	even	3		441.2.i.d.227.23		48
7.3	odd	6		441.2.s.d.362.24		48
7.4	even	3		441.2.s.d.362.23		48
7.5	odd	6		441.2.i.d.227.24		48
7.6	odd	2	inner	441.2.o.e.146.1	✓	48
9.4	even	3		1323.2.o.e.881.23		48
9.5	odd	6	inner	441.2.o.e.293.1	yes	48
21.2	odd	6		1323.2.i.d.521.21		48
21.5	even	6		1323.2.i.d.521.6		48
21.11	odd	6		1323.2.s.d.656.2		48
21.17	even	6		1323.2.s.d.656.1		48
21.20	even	2		1323.2.o.e.440.23		48
63.4	even	3		1323.2.i.d.1097.6		48
63.5	even	6		441.2.s.d.374.23		48
63.13	odd	6		1323.2.o.e.881.24		48
63.23	odd	6		441.2.s.d.374.24		48
63.31	odd	6		1323.2.i.d.1097.21		48
63.32	odd	6		441.2.i.d.68.2		48
63.40	odd	6		1323.2.s.d.962.2		48
63.41	even	6	inner	441.2.o.e.293.2	yes	48
63.58	even	3		1323.2.s.d.962.1		48
63.59	even	6		441.2.i.d.68.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.1		48	63.59	even	6
441.2.i.d.68.2		48	63.32	odd	6
441.2.i.d.227.23		48	7.2	even	3
441.2.i.d.227.24		48	7.5	odd	6
441.2.o.e.146.1	✓	48	7.6	odd	2	inner
441.2.o.e.146.2	yes	48	1.1	even	1	trivial
441.2.o.e.293.1	yes	48	9.5	odd	6	inner
441.2.o.e.293.2	yes	48	63.41	even	6	inner
441.2.s.d.362.23		48	7.4	even	3
441.2.s.d.362.24		48	7.3	odd	6
441.2.s.d.374.23		48	63.5	even	6
441.2.s.d.374.24		48	63.23	odd	6
1323.2.i.d.521.6		48	21.5	even	6
1323.2.i.d.521.21		48	21.2	odd	6
1323.2.i.d.1097.6		48	63.4	even	3
1323.2.i.d.1097.21		48	63.31	odd	6
1323.2.o.e.440.23		48	21.20	even	2
1323.2.o.e.440.24		48	3.2	odd	2
1323.2.o.e.881.23		48	9.4	even	3
1323.2.o.e.881.24		48	63.13	odd	6
1323.2.s.d.656.1		48	21.17	even	6
1323.2.s.d.656.2		48	21.11	odd	6
1323.2.s.d.962.1		48	63.58	even	3
1323.2.s.d.962.2		48	63.40	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.34591 - 1.35441i) q^{2} +(1.70185 - 0.322036i) q^{3} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +(-4.42857 - 1.54954i) q^{6} -9.04141i q^{8} +(2.79259 - 1.09611i) q^{9} +O(q^{10})\)	\(q+(-2.34591 - 1.35441i) q^{2} +(1.70185 - 0.322036i) q^{3} +(2.66888 + 4.62263i) q^{4} +(-0.601464 - 1.04177i) q^{5} +(-4.42857 - 1.54954i) q^{6} -9.04141i q^{8} +(2.79259 - 1.09611i) q^{9} +3.25853i q^{10} +(-2.15351 - 1.24333i) q^{11} +(6.03068 + 7.00755i) q^{12} +(-1.63211 + 0.942300i) q^{13} +(-1.35909 - 1.57924i) q^{15} +(-6.90806 + 11.9651i) q^{16} +1.20373 q^{17} +(-8.03576 - 1.21093i) q^{18} -7.47013i q^{19} +(3.21047 - 5.56070i) q^{20} +(3.36797 + 5.83350i) q^{22} +(2.63359 - 1.52050i) q^{23} +(-2.91166 - 15.3871i) q^{24} +(1.77648 - 3.07696i) q^{25} +5.10506 q^{26} +(4.39957 - 2.76473i) q^{27} +(-0.173847 - 0.100371i) q^{29} +(1.04936 + 5.54553i) q^{30} +(3.03381 - 1.75157i) q^{31} +(16.7513 - 9.67135i) q^{32} +(-4.06535 - 1.42246i) q^{33} +(-2.82384 - 1.63034i) q^{34} +(12.5200 + 9.98370i) q^{36} +1.73092 q^{37} +(-10.1177 + 17.5243i) q^{38} +(-2.47416 + 2.12925i) q^{39} +(-9.41904 + 5.43809i) q^{40} +(-3.36029 - 5.82020i) q^{41} +(0.00656005 - 0.0113623i) q^{43} -13.2732i q^{44} +(-2.82153 - 2.24995i) q^{45} -8.23756 q^{46} +(0.717403 - 1.24258i) q^{47} +(-7.90329 + 22.5875i) q^{48} +(-8.33495 + 4.81219i) q^{50} +(2.04856 - 0.387643i) q^{51} +(-8.71182 - 5.02977i) q^{52} +9.90831i q^{53} +(-14.0656 + 0.526983i) q^{54} +2.99128i q^{55} +(-2.40565 - 12.7130i) q^{57} +(0.271887 + 0.470923i) q^{58} +(-6.10954 - 10.5820i) q^{59} +(3.67299 - 10.4974i) q^{60} +(-9.73903 - 5.62283i) q^{61} -9.48942 q^{62} -24.7638 q^{64} +(1.96331 + 1.13352i) q^{65} +(7.61038 + 8.84314i) q^{66} +(2.57932 + 4.46752i) q^{67} +(3.21260 + 5.56438i) q^{68} +(3.99231 - 3.43578i) q^{69} +12.0452i q^{71} +(-9.91041 - 25.2489i) q^{72} +8.67204i q^{73} +(-4.06058 - 2.34438i) q^{74} +(2.03241 - 5.80861i) q^{75} +(34.5317 - 19.9369i) q^{76} +(8.68805 - 1.64401i) q^{78} +(-2.74801 + 4.75969i) q^{79} +16.6198 q^{80} +(6.59707 - 6.12198i) q^{81} +18.2049i q^{82} +(-1.60854 + 2.78607i) q^{83} +(-0.723998 - 1.25400i) q^{85} +(-0.0307786 + 0.0177700i) q^{86} +(-0.328185 - 0.114831i) q^{87} +(-11.2415 + 19.4708i) q^{88} +7.96728 q^{89} +(3.57172 + 9.09972i) q^{90} +(14.0574 + 8.11607i) q^{92} +(4.59902 - 3.95791i) q^{93} +(-3.36593 + 1.94332i) q^{94} +(-7.78214 + 4.49302i) q^{95} +(25.3936 - 21.8537i) q^{96} +(-2.06260 - 1.19084i) q^{97} +(-7.37671 - 1.11162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 + 16 * q^9	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

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