LMFDB - Embedded newform 675.2.ba.b.518.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] 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("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] 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:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			518.16
Character	$\chi$	$=$	675.518
Dual form			675.2.ba.b.632.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.71476 + 0.237511i) q^{2} +(-1.47097 - 0.914466i) q^{3} +(5.34392 + 0.942278i) q^{4} +(-3.77614 - 2.83193i) q^{6} +(1.29639 + 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +(1.32750 + 2.69030i) q^{9} +(0.162954 - 0.447712i) q^{11} +(-6.99907 - 6.27290i) q^{12} +(-0.242081 - 2.76700i) q^{13} +(3.30380 + 2.77222i) q^{14} +(13.7126 + 4.99098i) q^{16} +(-3.35386 + 0.898665i) q^{17} +(2.96488 + 7.61884i) q^{18} +(-1.97319 + 1.13922i) q^{19} +(-1.07685 - 2.52077i) q^{21} +(0.548719 - 1.17673i) q^{22} +(0.230790 + 0.329603i) q^{23} +(-11.0569 - 11.8025i) q^{24} -7.56924i q^{26} +(0.507474 - 5.17131i) q^{27} +(6.07248 + 6.07248i) q^{28} +(4.29568 - 3.60450i) q^{29} +(0.908475 - 5.15222i) q^{31} +(19.1162 + 8.91403i) q^{32} +(-0.649118 + 0.509556i) q^{33} +(-9.31839 + 1.64308i) q^{34} +(4.55906 + 15.6276i) q^{36} +(0.387140 + 1.44483i) q^{37} +(-5.62733 + 2.62407i) q^{38} +(-2.17423 + 4.29154i) q^{39} +(-4.99389 + 5.95149i) q^{41} +(-2.32469 - 7.09907i) q^{42} +(0.501128 + 1.07467i) q^{43} +(1.29268 - 2.23899i) q^{44} +(0.548257 + 0.949609i) q^{46} +(-6.94767 + 9.92230i) q^{47} +(-15.6068 - 19.8813i) q^{48} +(-1.53751 - 4.22426i) q^{49} +(5.75523 + 1.74508i) q^{51} +(1.31362 - 15.0147i) q^{52} +(0.274270 - 0.274270i) q^{53} +(2.60592 - 13.9184i) q^{54} +(9.49862 + 11.3200i) q^{56} +(3.94428 + 0.128655i) q^{57} +(12.5179 - 8.76510i) q^{58} +(-3.33385 + 1.21342i) q^{59} +(-1.59716 - 9.05792i) q^{61} +(3.69001 - 13.7713i) q^{62} +(-0.721141 + 4.69272i) q^{63} +(24.5036 + 14.1471i) q^{64} +(-1.88323 + 1.22915i) q^{66} +(-13.1561 + 1.15101i) q^{67} +(-18.7696 + 1.64212i) q^{68} +(-0.0380751 - 0.695886i) q^{69} +(-13.8198 - 7.97886i) q^{71} +(5.47136 + 27.4723i) q^{72} +(-2.07381 + 7.73957i) q^{73} +(0.707832 + 4.01431i) q^{74} +(-11.6180 + 4.22862i) q^{76} +(0.617661 - 0.432491i) q^{77} +(-6.92182 + 11.1341i) q^{78} +(-2.85683 - 3.40464i) q^{79} +(-5.47547 + 7.14278i) q^{81} +(-14.9708 + 14.9708i) q^{82} +(-0.253902 + 2.90211i) q^{83} +(-3.37935 - 14.4855i) q^{84} +(1.10520 + 3.03651i) q^{86} +(-9.61501 + 1.37386i) q^{87} +(2.55168 - 3.64417i) q^{88} +(3.50126 + 6.06435i) q^{89} +(2.19789 - 3.80686i) q^{91} +(0.922748 + 1.97884i) q^{92} +(-6.04787 + 6.74799i) q^{93} +(-21.2179 + 25.2866i) q^{94} +(-19.9678 - 30.5934i) q^{96} +(6.86175 - 3.19969i) q^{97} +(-3.17066 - 11.8331i) q^{98} +(1.42080 - 0.155944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.71476	+	0.237511i	1.91963	+	0.167946i	0.983153	−	0.182786i	$-0.0585116\pi$
$2$	2.71476	+	0.237511i	1.91963	+	0.167946i	0.936476	+	0.350732i	$0.114067\pi$
$3$	−1.47097	−	0.914466i	−0.849265	−	0.527967i
$3$	−1.47097	−	0.914466i	−0.849265	−	0.527967i
$4$	5.34392	+	0.942278i	2.67196	+	0.471139i
$5$		0			0
$5$		0			0
$6$	−3.77614	−	2.83193i	−1.54160	−	1.15613i
$7$	1.29639	+	0.907744i	0.489990	+	0.343095i	0.792317	−	0.610109i	$-0.208874\pi$
$7$	1.29639	+	0.907744i	0.489990	+	0.343095i	−0.302327	+	0.953204i	$0.597763\pi$
$8$	9.01913	+	2.41667i	3.18874	+	0.854422i
$9$	1.32750	+	2.69030i	0.442501	+	0.896768i
$10$		0			0
$11$	0.162954	−	0.447712i	0.0491325	−	0.134990i	−0.912699	−	0.408632i	$-0.866006\pi$
$11$	0.162954	−	0.447712i	0.0491325	−	0.134990i	0.961832	+	0.273642i	$0.0882282\pi$
$12$	−6.99907	−	6.27290i	−2.02046	−	1.81083i
$13$	−0.242081	−	2.76700i	−0.0671411	−	0.767427i	−0.952901	−	0.303282i	$-0.901917\pi$
$13$	−0.242081	−	2.76700i	−0.0671411	−	0.767427i	0.885760	−	0.464144i	$-0.153638\pi$
$14$	3.30380	+	2.77222i	0.882978	+	0.740907i
$15$		0			0
$16$	13.7126	+	4.99098i	3.42815	+	1.24775i
$17$	−3.35386	+	0.898665i	−0.813431	+	0.217958i	−0.641473	−	0.767146i	$-0.721676\pi$
$17$	−3.35386	+	0.898665i	−0.813431	+	0.217958i	−0.171959	+	0.985104i	$0.555010\pi$
$18$	2.96488	+	7.61884i	0.698830	+	1.79578i
$19$	−1.97319	+	1.13922i	−0.452681	+	0.261356i	−0.708962	−	0.705247i	$-0.750836\pi$
$19$	−1.97319	+	1.13922i	−0.452681	+	0.261356i	0.256281	+	0.966602i	$0.417503\pi$
$20$		0			0
$21$	−1.07685	−	2.52077i	−0.234989	−	0.550077i
$22$	0.548719	−	1.17673i	0.116987	−	0.250880i
$23$	0.230790	+	0.329603i	0.0481231	+	0.0687269i	0.842493	−	0.538708i	$-0.181087\pi$
$23$	0.230790	+	0.329603i	0.0481231	+	0.0687269i	−0.794369	+	0.607435i	$0.792199\pi$
$24$	−11.0569	−	11.8025i	−2.25698	−	2.40918i
$25$		0			0
$26$		−	7.56924i		−	1.48445i
$27$	0.507474	−	5.17131i	0.0976633	−	0.995220i
$28$	6.07248	+	6.07248i	1.14759	+	1.14759i
$29$	4.29568	−	3.60450i	0.797687	−	0.669339i	−0.149948	−	0.988694i	$-0.547911\pi$
$29$	4.29568	−	3.60450i	0.797687	−	0.669339i	0.947635	+	0.319355i	$0.103466\pi$
$30$		0			0
$31$	0.908475	−	5.15222i	0.163167	−	0.925366i	−0.787767	−	0.615973i	$-0.788763\pi$
$31$	0.908475	−	5.15222i	0.163167	−	0.925366i	0.950934	−	0.309393i	$-0.100126\pi$
$32$	19.1162	+	8.91403i	3.37930	+	1.57579i
$33$	−0.649118	+	0.509556i	−0.112997	+	0.0887022i
$34$	−9.31839	+	1.64308i	−1.59809	+	0.281787i
$35$		0			0
$36$	4.55906	+	15.6276i	0.759844	+	2.60461i
$37$	0.387140	+	1.44483i	0.0636454	+	0.237528i	0.990420	−	0.138091i	$-0.0440967\pi$
$37$	0.387140	+	1.44483i	0.0636454	+	0.237528i	−0.926774	+	0.375619i	$0.877430\pi$
$38$	−5.62733	+	2.62407i	−0.912873	+	0.425680i
$39$	−2.17423	+	4.29154i	−0.348156	+	0.687197i
$40$		0			0
$41$	−4.99389	+	5.95149i	−0.779915	+	0.929467i	−0.998930	−	0.0462550i	$-0.985271\pi$
$41$	−4.99389	+	5.95149i	−0.779915	+	0.929467i	0.219015	+	0.975722i	$0.429716\pi$
$42$	−2.32469	−	7.09907i	−0.358708	−	1.09541i
$43$	0.501128	+	1.07467i	0.0764213	+	0.163886i	0.940806	−	0.338944i	$-0.110070\pi$
$43$	0.501128	+	1.07467i	0.0764213	+	0.163886i	−0.864385	+	0.502830i	$0.832292\pi$
$44$	1.29268	−	2.23899i	0.194879	−	0.337541i
$45$		0			0
$46$	0.548257	+	0.949609i	0.0808361	+	0.140012i
$47$	−6.94767	+	9.92230i	−1.01342	+	1.44732i	−0.122876	+	0.992422i	$0.539212\pi$
$47$	−6.94767	+	9.92230i	−1.01342	+	1.44732i	−0.890546	+	0.454894i	$0.849677\pi$
$48$	−15.6068	−	19.8813i	−2.25264	−	2.86962i
$49$	−1.53751	−	4.22426i	−0.219644	−	0.603466i
$50$		0			0
$51$	5.75523	+	1.74508i	0.805893	+	0.244361i
$52$	1.31362	−	15.0147i	0.182166	−	2.08217i
$53$	0.274270	−	0.274270i	0.0376738	−	0.0376738i	−0.688019	−	0.725693i	$-0.741519\pi$
$53$	0.274270	−	0.274270i	0.0376738	−	0.0376738i	0.725693	+	0.688019i	$0.241519\pi$
$54$	2.60592	−	13.9184i	0.354620	−	1.89405i
$55$		0			0
$56$	9.49862	+	11.3200i	1.26931	+	1.51270i
$57$	3.94428	+	0.128655i	0.522433	+	0.0170407i
$58$	12.5179	−	8.76510i	1.64368	−	1.15091i
$59$	−3.33385	+	1.21342i	−0.434031	+	0.157974i	−0.549790	−	0.835303i	$-0.685292\pi$
$59$	−3.33385	+	1.21342i	−0.434031	+	0.157974i	0.115759	+	0.993277i	$0.463070\pi$
$60$		0			0
$61$	−1.59716	−	9.05792i	−0.204495	−	1.15975i	−0.898233	−	0.439520i	$-0.855149\pi$
$61$	−1.59716	−	9.05792i	−0.204495	−	1.15975i	0.693738	−	0.720228i	$-0.255963\pi$
$62$	3.69001	−	13.7713i	0.468631	−	1.74896i
$63$	−0.721141	+	4.69272i	−0.0908552	+	0.591228i
$64$	24.5036	+	14.1471i	3.06294	+	1.76839i
$65$		0			0
$66$	−1.88323	+	1.22915i	−0.231809	+	0.151298i
$67$	−13.1561	+	1.15101i	−1.60727	+	0.140618i	−0.855142	−	0.518394i	$-0.826530\pi$
$67$	−13.1561	+	1.15101i	−1.60727	+	0.140618i	−0.752132	+	0.659012i	$0.770975\pi$
$68$	−18.7696	+	1.64212i	−2.27614	+	0.199137i
$69$	−0.0380751	−	0.695886i	−0.00458370	−	0.0837748i
$70$		0			0
$71$	−13.8198	−	7.97886i	−1.64011	−	0.946916i	−0.980794	−	0.195047i	$-0.937514\pi$
$71$	−13.8198	−	7.97886i	−1.64011	−	0.946916i	−0.659313	−	0.751869i	$-0.729153\pi$
$72$	5.47136	+	27.4723i	0.644806	+	3.23765i
$73$	−2.07381	+	7.73957i	−0.242721	+	0.905849i	0.731794	+	0.681526i	$0.238683\pi$
$73$	−2.07381	+	7.73957i	−0.242721	+	0.905849i	−0.974515	+	0.224322i	$0.927983\pi$
$74$	0.707832	+	4.01431i	0.0822838	+	0.466655i
$75$		0			0
$76$	−11.6180	+	4.22862i	−1.33268	+	0.485056i
$77$	0.617661	−	0.432491i	0.0703890	−	0.0492869i
$78$	−6.92182	+	11.1341i	−0.783741	+	1.26069i
$79$	−2.85683	−	3.40464i	−0.321418	−	0.383051i	0.581006	−	0.813899i	$-0.302659\pi$
$79$	−2.85683	−	3.40464i	−0.321418	−	0.383051i	−0.902425	+	0.430848i	$0.858215\pi$
$80$		0			0
$81$	−5.47547	+	7.14278i	−0.608385	+	0.793642i
$82$	−14.9708	+	14.9708i	−1.65325	+	1.65325i
$83$	−0.253902	+	2.90211i	−0.0278694	+	0.318548i	0.969445	+	0.245309i	$0.0788893\pi$
$83$	−0.253902	+	2.90211i	−0.0278694	+	0.318548i	−0.997314	+	0.0732395i	$0.976666\pi$
$84$	−3.37935	−	14.4855i	−0.368718	−	1.58050i
$85$		0			0
$86$	1.10520	+	3.03651i	0.119177	+	0.327435i
$87$	−9.61501	+	1.37386i	−1.03084	+	0.147293i
$88$	2.55168	−	3.64417i	0.272010	−	0.388470i
$89$	3.50126	+	6.06435i	0.371132	+	0.642820i	0.989740	−	0.142880i	$-0.0456363\pi$
$89$	3.50126	+	6.06435i	0.371132	+	0.642820i	−0.618608	+	0.785700i	$0.712303\pi$
$90$		0			0
$91$	2.19789	−	3.80686i	0.230402	−	0.399068i
$92$	0.922748	+	1.97884i	0.0962031	+	0.206308i
$93$	−6.04787	+	6.74799i	−0.627135	+	0.699734i
$94$	−21.2179	+	25.2866i	−2.18846	+	2.60811i
$95$		0			0
$96$	−19.9678	−	30.5934i	−2.03795	−	3.12242i
$97$	6.86175	−	3.19969i	0.696705	−	0.324879i	−0.0418007	−	0.999126i	$-0.513309\pi$
$97$	6.86175	−	3.19969i	0.696705	−	0.324879i	0.738506	+	0.674247i	$0.235532\pi$
$98$	−3.17066	−	11.8331i	−0.320285	−	1.19532i
$99$	1.42080	−	0.155944i	0.142796	−	0.0156730i
$100$		0			0
$101$	5.72678	−	1.00979i	0.569836	−	0.100477i	0.118696	−	0.992931i	$-0.462129\pi$
$101$	5.72678	−	1.00979i	0.569836	−	0.100477i	0.451140	+	0.892453i	$0.351017\pi$
$102$	15.2096	+	6.10443i	1.50598	+	0.604428i
$103$	4.05522	+	1.89098i	0.399573	+	0.186324i	0.612009	−	0.790851i	$-0.290362\pi$
$103$	4.05522	+	1.89098i	0.399573	+	0.186324i	−0.212436	+	0.977175i	$0.568140\pi$
$104$	4.50356	−	25.5409i	0.441610	−	2.50450i
$105$		0			0
$106$	0.809720	−	0.679435i	0.0786469	−	0.0659926i
$107$	−0.577939	−	0.577939i	−0.0558714	−	0.0558714i	0.678619	−	0.734490i	$-0.262579\pi$
$107$	−0.577939	−	0.577939i	−0.0558714	−	0.0558714i	−0.734490	+	0.678619i	$0.762579\pi$
$108$	7.58471	−	27.1569i	0.729839	−	2.61317i
$109$			8.45996i			0.810317i	0.914246	+	0.405159i	$0.132784\pi$
$109$			8.45996i			0.810317i	−0.914246	+	0.405159i	$0.867216\pi$
$110$		0			0
$111$	0.751773	−	2.47932i	0.0713552	−	0.235327i
$112$	13.2464	+	18.9178i	1.25167	+	1.78757i
$113$	0.921497	−	1.97616i	0.0866871	−	0.185901i	−0.858185	−	0.513340i	$-0.828408\pi$
$113$	0.921497	−	1.97616i	0.0866871	−	0.185901i	0.944872	+	0.327439i	$0.106186\pi$
$114$	10.6772	+	1.28608i	1.00002	+	0.120452i
$115$		0			0
$116$	26.3522	−	15.2145i	2.44674	−	1.41263i
$117$	7.12270	−	4.32447i	0.658494	−	0.399797i
$118$	−9.33883	+	2.50233i	−0.859709	+	0.230358i
$119$	−5.16368	−	1.87943i	−0.473354	−	0.172287i
$120$		0			0
$121$	8.25260	+	6.92475i	0.750236	+	0.629523i
$122$	−2.18454	−	24.9695i	−0.197779	−	2.26063i
$123$	12.7883	−	4.18772i	1.15308	−	0.377594i
$124$	9.70964	−	26.6770i	0.871952	−	2.39567i
$125$		0			0
$126$	−3.07230	+	12.5684i	−0.273702	+	1.11968i
$127$	3.44795	+	0.923874i	0.305956	+	0.0819806i	0.408530	−	0.912745i	$-0.366041\pi$
$127$	3.44795	+	0.923874i	0.305956	+	0.0819806i	−0.102575	+	0.994725i	$0.532708\pi$
$128$	28.6056	+	20.0298i	2.52840	+	1.77040i
$129$	0.245607	−	2.03908i	0.0216245	−	0.179531i
$130$		0			0
$131$	−3.02885	−	0.534068i	−0.264632	−	0.0466617i	0.0397579	−	0.999209i	$-0.487341\pi$
$131$	−3.02885	−	0.534068i	−0.264632	−	0.0466617i	−0.304390	+	0.952548i	$0.598452\pi$
$132$	−3.94898	+	2.11138i	−0.343715	+	0.183772i
$133$	−3.59215	−	0.314273i	−0.311479	−	0.0272509i
$134$	−35.9891			−3.10899
$135$		0			0
$136$	−32.4207			−2.78005
$137$	−2.06926	−	0.181036i	−0.176788	−	0.0154670i	−0.00158226	−	0.999999i	$-0.500504\pi$
$137$	−2.06926	−	0.181036i	−0.176788	−	0.0154670i	−0.175206	+	0.984532i	$0.556059\pi$
$138$	0.0619158	−	1.89821i	0.00527062	−	0.161586i
$139$	15.2015	+	2.68044i	1.28938	+	0.227352i	0.775957	−	0.630785i	$-0.217267\pi$
$139$	15.2015	+	2.68044i	1.28938	+	0.227352i	0.513420	+	0.858137i	$0.328378\pi$
$140$		0			0
$141$	19.2934	−	8.24199i	1.62480	−	0.694101i
$142$	−35.6224	−	24.9431i	−2.98937	−	2.09318i
$143$	−1.27827	−	0.342511i	−0.106894	−	0.0286422i
$144$	4.77629	+	43.5167i	0.398024	+	3.62639i
$145$		0			0
$146$	−7.46815	+	20.5186i	−0.618068	+	1.69813i
$147$	−1.60132	+	7.61976i	−0.132075	+	0.628467i
$148$	0.707419	+	8.08583i	0.0581495	+	0.664651i
$149$	12.0609	+	10.1203i	0.988065	+	0.829085i	0.985286	−	0.170911i	$-0.0546712\pi$
$149$	12.0609	+	10.1203i	0.988065	+	0.829085i	0.00277827	+	0.999996i	$0.499116\pi$
$150$		0			0
$151$	−1.00956	−	0.367451i	−0.0821571	−	0.0299027i	0.300615	−	0.953746i	$-0.402808\pi$
$151$	−1.00956	−	0.367451i	−0.0821571	−	0.0299027i	−0.382772	+	0.923843i	$0.625030\pi$
$152$	−20.5496	+	5.50625i	−1.66679	+	0.446616i
$153$	−6.86995	−	7.82993i	−0.555402	−	0.633012i
$154$	1.77953	−	1.02741i	0.143398	−	0.0827910i
$155$		0			0
$156$	−15.6627	+	20.8849i	−1.25402	+	1.67213i
$157$	7.27543	−	15.6022i	0.580643	−	1.24519i	−0.368289	−	0.929711i	$-0.620056\pi$
$157$	7.27543	−	15.6022i	0.580643	−	1.24519i	0.948932	−	0.315481i	$-0.102166\pi$
$158$	−6.94698	−	9.92131i	−0.552672	−	0.789297i
$159$	−0.654253	+	0.152632i	−0.0518856	+	0.0121045i
$160$		0			0
$161$			0.636793i			0.0501863i
$162$	−16.5611	+	18.0905i	−1.30116	+	1.42132i
$163$	−2.47310	−	2.47310i	−0.193708	−	0.193708i	0.603588	−	0.797296i	$-0.293737\pi$
$163$	−2.47310	−	2.47310i	−0.193708	−	0.193708i	−0.797296	+	0.603588i	$0.793737\pi$
$164$	−32.2949	+	27.0987i	−2.52181	+	2.11605i
$165$		0			0
$166$	−1.37857	+	7.81825i	−0.106998	+	0.606814i
$167$	5.97097	+	2.78431i	0.462048	+	0.215456i	0.639681	−	0.768640i	$-0.279066\pi$
$167$	5.97097	+	2.78431i	0.462048	+	0.215456i	−0.177634	+	0.984097i	$0.556844\pi$
$168$	−3.62041	−	25.3376i	−0.279321	−	1.95484i
$169$	5.20483	−	0.917752i	0.400372	−	0.0705963i
$170$		0			0
$171$	−5.68427	−	3.79616i	−0.434687	−	0.290300i
$172$	1.66535	+	6.21517i	0.126982	+	0.473902i
$173$	9.69016	−	4.51859i	0.736729	−	0.343542i	−0.0177714	−	0.999842i	$-0.505657\pi$
$173$	9.69016	−	4.51859i	0.736729	−	0.343542i	0.754500	+	0.656300i	$0.227879\pi$
$174$	−26.4288	+	1.44604i	−2.00356	+	0.109624i
$175$		0			0
$176$	4.46905	−	5.32601i	0.336867	−	0.401463i
$177$	6.01363	+	1.26379i	0.452012	+	0.0949920i
$178$	8.06473	+	17.2949i	0.604477	+	1.29631i
$179$	−3.31311	+	5.73847i	−0.247633	+	0.428913i	−0.962869	−	0.269970i	$-0.912986\pi$
$179$	−3.31311	+	5.73847i	−0.247633	+	0.428913i	0.715235	+	0.698884i	$0.246319\pi$
$180$		0			0
$181$	−4.36897	−	7.56727i	−0.324743	−	0.562471i	0.656717	−	0.754137i	$-0.271944\pi$
$181$	−4.36897	−	7.56727i	−0.324743	−	0.562471i	−0.981460	+	0.191666i	$0.938611\pi$
$182$	6.87094	−	9.81271i	0.509308	−	0.727367i
$183$	−5.93379	+	14.7845i	−0.438639	+	1.09290i
$184$	1.28499	+	3.53048i	0.0947306	+	0.260270i
$185$		0			0
$186$	−18.0213	+	16.8828i	−1.32138	+	1.23790i
$187$	−0.144182	+	1.64801i	−0.0105436	+	0.120514i
$188$	−46.4773	+	46.4773i	−3.38971	+	3.38971i
$189$	5.35211	−	6.24340i	0.389309	−	0.454140i
$190$		0			0
$191$	−12.9658	−	15.4521i	−0.938176	−	1.11807i	−0.992826	−	0.119569i	$-0.961849\pi$
$191$	−12.9658	−	15.4521i	−0.938176	−	1.11807i	0.0546500	−	0.998506i	$-0.482596\pi$
$192$	−23.1069	−	43.2177i	−1.66760	−	3.11897i
$193$	15.3824	−	10.7709i	1.10725	−	0.775303i	0.130875	−	0.991399i	$-0.458221\pi$
$193$	15.3824	−	10.7709i	1.10725	−	0.775303i	0.976372	+	0.216096i	$0.0693323\pi$
$194$	19.3880	−	7.05665i	1.39198	−	0.506638i
$195$		0			0
$196$	−4.23588	−	24.0229i	−0.302563	−	1.71592i
$197$	1.29693	−	4.84019i	0.0924021	−	0.344849i	−0.904211	−	0.427087i	$-0.859540\pi$
$197$	1.29693	−	4.84019i	0.0924021	−	0.344849i	0.996613	+	0.0822373i	$0.0262066\pi$
$198$	3.89419	−	0.0858949i	0.276748	−	0.00610428i
$199$	−14.4356	−	8.33443i	−1.02332	−	0.590812i	−0.108253	−	0.994123i	$-0.534526\pi$
$199$	−14.4356	−	8.33443i	−1.02332	−	0.590812i	−0.915063	+	0.403312i	$0.867859\pi$
$200$		0			0
$201$	20.4048	+	10.3377i	1.43924	+	0.729166i
$202$	15.7867	−	1.38116i	1.11075	−	0.0971779i
$203$	8.84085	−	0.773474i	0.620506	−	0.0542872i
$204$	29.1111	+	14.7486i	2.03819	+	1.03261i
$205$		0			0
$206$	10.5599	+	6.09673i	0.735740	+	0.424779i
$207$	−0.580357	+	1.05845i	−0.0403376	+	0.0735670i
$208$	10.4905	−	39.1510i	0.727384	−	2.71463i
$209$	0.188505	+	1.06906i	0.0130391	+	0.0739486i
$210$		0			0
$211$	9.81899	−	3.57382i	0.675967	−	0.246032i	0.0188522	−	0.999822i	$-0.493999\pi$
$211$	9.81899	−	3.57382i	0.675967	−	0.246032i	0.657115	+	0.753790i	$0.271777\pi$
$212$	1.72411	−	1.20724i	0.118413	−	0.0829134i
$213$	13.0321	+	24.3744i	0.892944	+	1.67010i
$214$	−1.43170	−	1.70623i	−0.0978690	−	0.116636i
$215$		0			0
$216$	17.0743	−	45.4144i	1.16176	−	3.09006i
$217$	5.85464	−	5.85464i	0.397439	−	0.397439i
$218$	−2.00934	+	22.9668i	−0.136089	+	1.55551i
$219$	10.1281	−	9.48825i	0.684393	−	0.641156i
$220$		0			0
$221$	3.29851	+	9.06258i	0.221882	+	0.609615i
$222$	2.62975	−	6.55222i	0.176498	−	0.439756i
$223$	13.4550	−	19.2158i	0.901015	−	1.28678i	−0.0565006	−	0.998403i	$-0.517994\pi$
$223$	13.4550	−	19.2158i	0.901015	−	1.28678i	0.957516	−	0.288381i	$-0.0931168\pi$
$224$	16.6904	+	28.9087i	1.11518	+	1.93154i
$225$		0			0
$226$	2.97101	−	5.14593i	0.197628	−	0.342302i
$227$	8.45994	+	18.1424i	0.561506	+	1.20415i	0.958173	+	0.286191i	$0.0923891\pi$
$227$	8.45994	+	18.1424i	0.561506	+	1.20415i	−0.396667	+	0.917963i	$0.629833\pi$
$228$	20.9567	+	4.40413i	1.38789	+	0.291671i
$229$	14.1827	−	16.9023i	0.937218	−	1.11693i	−0.0557370	−	0.998445i	$-0.517751\pi$
$229$	14.1827	−	16.9023i	0.937218	−	1.11693i	0.992955	−	0.118488i	$-0.0378047\pi$
$230$		0			0
$231$	−1.30406	+	0.0713510i	−0.0858007	+	0.00469455i
$232$	47.4542	−	22.1282i	3.11552	−	1.45279i
$233$	−4.83296	−	18.0369i	−0.316618	−	1.18163i	−0.922474	−	0.386059i	$-0.873836\pi$
$233$	−4.83296	−	18.0369i	−0.316618	−	1.18163i	0.605856	−	0.795574i	$-0.292831\pi$
$234$	20.3636	−	10.0482i	1.33121	−	0.656871i
$235$		0			0
$236$	−18.9592	+	3.34302i	−1.23414	+	0.217612i
$237$	1.08888	+	7.62059i	0.0707306	+	0.495010i
$238$	−13.5718	−	6.32863i	−0.879729	−	0.410224i
$239$	−3.38846	+	19.2169i	−0.219181	+	1.24304i	0.654320	+	0.756218i	$0.272955\pi$
$239$	−3.38846	+	19.2169i	−0.219181	+	1.24304i	−0.873502	+	0.486821i	$0.838156\pi$
$240$		0			0
$241$	−3.76991	+	3.16333i	−0.242841	+	0.203768i	−0.756082	−	0.654476i	$-0.772889\pi$
$241$	−3.76991	+	3.16333i	−0.242841	+	0.203768i	0.513241	+	0.858244i	$0.328445\pi$
$242$	20.7592	+	20.7592i	1.33445	+	1.33445i
$243$	14.5861	−	5.49968i	0.935697	−	0.352805i
$244$		−	49.9098i		−	3.19515i
$245$		0			0
$246$	35.7119	−	8.33130i	2.27690	−	0.531184i
$247$	3.62990	+	5.18403i	0.230965	+	0.329852i
$248$	20.6449	−	44.2731i	1.31095	−	2.81134i
$249$	3.02737	−	4.03673i	0.191851	−	0.255818i
$250$		0			0
$251$	−18.1080	+	10.4546i	−1.14297	+	0.659892i	−0.947163	−	0.320752i	$-0.896065\pi$
$251$	−18.1080	+	10.4546i	−1.14297	+	0.659892i	−0.195803	+	0.980643i	$0.562731\pi$
$252$	−8.27557	+	24.3980i	−0.521312	+	1.53693i
$253$	0.185175	−	0.0496176i	0.0116419	−	0.00311943i
$254$	9.14093	+	3.32703i	0.573553	+	0.208756i
$255$		0			0
$256$	29.5507	+	24.7960i	1.84692	+	1.54975i
$257$	1.27235	+	14.5430i	0.0793667	+	0.907166i	0.926626	+	0.375986i	$0.122696\pi$
$257$	1.27235	+	14.5430i	0.0793667	+	0.907166i	−0.847259	+	0.531180i	$0.821749\pi$
$258$	1.15107	−	5.47728i	0.0716625	−	0.341000i
$259$	−0.809647	+	2.22449i	−0.0503090	+	0.138223i
$260$		0			0
$261$	15.3997	+	6.77169i	0.953219	+	0.419157i
$262$	−8.09576	−	2.16925i	−0.500158	−	0.134017i
$263$	−25.0799	−	17.5612i	−1.54650	−	1.08287i	−0.962561	−	0.271067i	$-0.912624\pi$
$263$	−25.0799	−	17.5612i	−1.54650	−	1.08287i	−0.583935	−	0.811801i	$-0.698488\pi$
$264$	−7.08591	+	3.02704i	−0.436108	+	0.186302i
$265$		0			0
$266$	−9.67721	−	1.70635i	−0.593348	−	0.104623i
$267$	0.395404	−	12.1223i	0.0241983	−	0.741870i
$268$	−71.3898	−	6.24580i	−4.36083	−	0.381523i
$269$	23.6912			1.44448			0.722239	−	0.691643i	$-0.243113\pi$
$269$	23.6912			1.44448			0.722239	+	0.691643i	$0.243113\pi$
$270$		0			0
$271$	20.1164			1.22198			0.610991	−	0.791638i	$-0.290771\pi$
$271$	20.1164			1.22198			0.610991	+	0.791638i	$0.290771\pi$
$272$	−50.4755	−	4.41603i	−3.06052	−	0.267761i
$273$	−6.71428	+	3.58988i	−0.406367	+	0.217269i
$274$	−5.57454	−	0.982943i	−0.336771	−	0.0593817i
$275$		0			0
$276$	0.452247	−	3.75464i	0.0272221	−	0.226002i
$277$	12.4565	+	8.72217i	0.748441	+	0.524064i	0.884445	−	0.466644i	$-0.154537\pi$
$277$	12.4565	+	8.72217i	0.748441	+	0.524064i	−0.136004	+	0.990708i	$0.543426\pi$
$278$	40.6320	+	10.8873i	2.43694	+	0.652977i
$279$	15.0670	−	4.39552i	0.902040	−	0.263153i
$280$		0			0
$281$	−8.16607	+	22.4361i	−0.487147	+	1.33842i	0.416106	+	0.909316i	$0.363394\pi$
$281$	−8.16607	+	22.4361i	−0.487147	+	1.33842i	−0.903253	+	0.429108i	$0.858828\pi$
$282$	54.3346	−	17.7927i	3.23558	−	1.05954i
$283$	0.0248657	+	0.284217i	0.00147811	+	0.0168949i	0.996898	−	0.0787051i	$-0.0250786\pi$
$283$	0.0248657	+	0.284217i	0.00147811	+	0.0168949i	−0.995420	+	0.0956001i	$0.969523\pi$
$284$	−66.3335	−	55.6605i	−3.93617	−	3.30284i
$285$		0			0
$286$	−3.38884	−	1.23344i	−0.200387	−	0.0729347i
$287$	−11.8765	+	3.18229i	−0.701046	+	0.187845i
$288$	1.39538	+	63.2618i	0.0822234	+	3.72774i
$289$	−4.28164	+	2.47200i	−0.251861	+	0.145412i
$290$		0			0
$291$	−13.0194	−	1.56820i	−0.763213	−	0.0919292i
$292$	−18.3751	+	39.4056i	−1.07532	+	2.30604i
$293$	8.91694	+	12.7347i	0.520933	+	0.743969i	0.990287	−	0.139041i	$-0.0444019\pi$
$293$	8.91694	+	12.7347i	0.520933	+	0.743969i	−0.469354	+	0.883010i	$0.655513\pi$
$294$	−6.15698	+	20.3055i	−0.359083	+	1.18424i
$295$		0			0
$296$			13.9667i			0.811796i
$297$	−2.23257	−	1.06989i	−0.129547	−	0.0620812i
$298$	30.3387	+	30.3387i	1.75748	+	1.75748i
$299$	0.856140	−	0.718387i	0.0495119	−	0.0415454i
$300$		0			0
$301$	−0.325869	+	1.84809i	−0.0187828	+	0.106522i
$302$	−2.65345	−	1.23733i	−0.152689	−	0.0712001i
$303$	−9.34734	−	3.75158i	−0.536990	−	0.215523i
$304$	−32.7435	+	5.77355i	−1.87797	+	0.331136i
$305$		0			0
$306$	−16.7906	−	22.8881i	−0.959854	−	1.30843i
$307$	−2.72426	−	10.1671i	−0.155482	−	0.580267i	−0.999064	−	0.0432656i	$-0.986224\pi$
$307$	−2.72426	−	10.1671i	−0.155482	−	0.580267i	0.843582	−	0.537001i	$-0.180443\pi$
$308$	3.70826	−	1.72919i	0.211298	−	0.0985297i
$309$	−4.23587	−	6.48994i	−0.240970	−	0.369200i
$310$		0			0
$311$	2.06659	−	2.46287i	0.117186	−	0.139657i	−0.704262	−	0.709940i	$-0.748722\pi$
$311$	2.06659	−	2.46287i	0.117186	−	0.139657i	0.821448	+	0.570283i	$0.193167\pi$
$312$	−29.9809	+	33.4516i	−1.69734	+	1.89382i
$313$	−10.2775	−	22.0403i	−0.580921	−	1.24579i	−0.948789	−	0.315911i	$-0.897690\pi$
$313$	−10.2775	−	22.0403i	−0.580921	−	1.24579i	0.367868	−	0.929878i	$-0.380088\pi$
$314$	23.4568	−	40.6283i	1.32374	−	2.29279i
$315$		0			0
$316$	−12.0586	−	20.8860i	−0.678347	−	1.17493i
$317$	−11.9128	+	17.0133i	−0.669092	+	0.955562i	0.330838	+	0.943688i	$0.392669\pi$
$317$	−11.9128	+	17.0133i	−0.669092	+	0.955562i	−0.999929	+	0.0118742i	$0.996220\pi$
$318$	−1.81239	+	0.258968i	−0.101634	+	0.0145222i
$319$	−0.913782	−	2.51060i	−0.0511620	−	0.140566i
$320$		0			0
$321$	0.321625	+	1.37864i	0.0179514	+	0.0769479i
$322$	−0.151246	+	1.72874i	−0.00842858	+	0.0963391i
$323$	5.59403	−	5.59403i	0.311260	−	0.311260i
$324$	−35.9909	+	33.0110i	−1.99950	+	1.83395i
$325$		0			0
$326$	−6.12650	−	7.30128i	−0.339315	−	0.404380i
$327$	7.73635	−	12.4443i	0.427821	−	0.688174i
$328$	−59.4234	+	41.6087i	−3.28111	+	2.29746i
$329$	−18.0138	+	6.55649i	−0.993134	+	0.361471i
$330$		0			0
$331$	1.03458	+	5.86738i	0.0568655	+	0.322500i	0.999949	−	0.0100545i	$-0.00320050\pi$
$331$	1.03458	+	5.86738i	0.0568655	+	0.322500i	−0.943084	+	0.332555i	$0.892089\pi$
$332$	−4.09143	+	15.2694i	−0.224546	+	0.838018i
$333$	−3.37309	+	2.95954i	−0.184844	+	0.162182i
$334$	15.5485	+	8.97692i	0.850775	+	0.491195i
$335$		0			0
$336$	−2.18535	−	39.9409i	−0.119221	−	2.17896i
$337$	11.1098	−	0.971978i	0.605187	−	0.0529470i	0.219556	−	0.975600i	$-0.429539\pi$
$337$	11.1098	−	0.971978i	0.605187	−	0.0529470i	0.385631	+	0.922653i	$0.373984\pi$
$338$	14.3479	−	1.25528i	0.780421	−	0.0682780i
$339$	−3.16262	+	2.06419i	−0.171770	+	0.112111i
$340$		0			0
$341$	−2.15867	−	1.24631i	−0.116899	−	0.0674915i
$342$	−14.5298	−	11.6558i	−0.785683	−	0.630271i
$343$	4.70859	−	17.5727i	0.254240	−	0.948837i
$344$	1.92261	+	10.9037i	0.103660	+	0.587887i
$345$		0			0
$346$	27.3797	−	9.96540i	1.47194	−	0.535743i
$347$	19.4431	−	13.6142i	1.04376	−	0.730851i	0.0797793	−	0.996813i	$-0.474578\pi$
$347$	19.4431	−	13.6142i	1.04376	−	0.730851i	0.963984	+	0.265962i	$0.0856896\pi$
$348$	−52.6764	−	1.71820i	−2.82375	−	0.0921051i
$349$	−4.82633	−	5.75179i	−0.258347	−	0.307886i	0.621243	−	0.783618i	$-0.286628\pi$
$349$	−4.82633	−	5.75179i	−0.258347	−	0.307886i	−0.879591	+	0.475731i	$0.842183\pi$
$350$		0			0
$351$	−14.4319	−	0.152302i	−0.770315	−	0.00812929i
$352$	7.10598	−	7.10598i	0.378750	−	0.378750i
$353$	−0.451688	+	5.16281i	−0.0240409	+	0.274789i	0.974654	+	0.223717i	$0.0718192\pi$
$353$	−0.451688	+	5.16281i	−0.0240409	+	0.274789i	−0.998695	+	0.0510716i	$0.983736\pi$
$354$	16.0254	+	4.85919i	0.851742	+	0.258263i
$355$		0			0
$356$	12.9961	+	35.7066i	0.688793	+	1.89244i
$357$	5.87695	+	7.48659i	0.311041	+	0.396232i
$358$	−10.3573	+	14.7917i	−0.547398	+	0.781765i
$359$	6.82697	+	11.8247i	0.360314	+	0.624082i	0.988012	−	0.154375i	$-0.0493363\pi$
$359$	6.82697	+	11.8247i	0.360314	+	0.624082i	−0.627699	+	0.778457i	$0.716003\pi$
$360$		0			0
$361$	−6.90435	+	11.9587i	−0.363387	+	0.629404i
$362$	−10.0634	−	21.5810i	−0.528921	−	1.13427i
$363$	−5.80687	−	17.7328i	−0.304782	−	0.930732i
$364$	15.3325	−	18.2725i	0.803641	−	0.957742i
$365$		0			0
$366$	−19.6203	+	38.7270i	−1.02557	+	2.02429i
$367$	−19.5461	+	9.11448i	−1.02030	+	0.475772i	−0.859457	−	0.511208i	$-0.829198\pi$
$367$	−19.5461	+	9.11448i	−1.02030	+	0.475772i	−0.160840	+	0.986981i	$0.551420\pi$
$368$	1.51970	+	5.67159i	0.0792197	+	0.295652i
$369$	−22.6407	−	5.53446i	−1.17863	−	0.288113i
$370$		0			0
$371$	0.604528	−	0.106595i	0.0313855	−	0.00553411i
$372$	−38.6778	+	30.3620i	−2.00535	+	1.57419i
$373$	11.9942	+	5.59299i	0.621037	+	0.289594i	0.707557	−	0.706656i	$-0.249797\pi$
$373$	11.9942	+	5.59299i	0.621037	+	0.289594i	−0.0865206	+	0.996250i	$0.527575\pi$
$374$	−0.782840	+	4.43971i	−0.0404797	+	0.229572i
$375$		0			0
$376$	−86.6408	+	72.7003i	−4.46816	+	3.74923i
$377$	−11.0135	−	11.0135i	−0.567226	−	0.567226i
$378$	16.0126	−	15.6782i	0.823600	−	0.806398i
$379$			27.4089i			1.40790i	0.710249	+	0.703951i	$0.248583\pi$
$379$			27.4089i			1.40790i	−0.710249	+	0.703951i	$0.751417\pi$
$380$		0			0
$381$	−4.22697	−	4.51202i	−0.216554	−	0.231158i
$382$	−31.5292	−	45.0283i	−1.61317	−	2.30385i
$383$	−15.2701	+	32.7469i	−0.780267	+	1.67329i	−0.0416793	+	0.999131i	$0.513271\pi$
$383$	−15.2701	+	32.7469i	−0.780267	+	1.67329i	−0.738588	+	0.674157i	$0.764507\pi$
$384$	−23.7613	−	55.6221i	−1.21256	−	2.83845i
$385$		0			0
$386$	44.3177	−	25.5869i	2.25571	−	1.30234i
$387$	−2.22595	+	2.77482i	−0.113151	+	0.141052i
$388$	39.6836	−	10.6332i	2.01463	−	0.539819i
$389$	−17.3733	−	6.32335i	−0.880860	−	0.320607i	−0.138303	−	0.990390i	$-0.544165\pi$
$389$	−17.3733	−	6.32335i	−0.880860	−	0.320607i	−0.742557	+	0.669783i	$0.766387\pi$
$390$		0			0
$391$	−1.07024	−	0.898039i	−0.0541244	−	0.0454158i
$392$	−3.65832	−	41.8148i	−0.184773	−	2.11197i
$393$	3.96696	+	3.55538i	0.200106	+	0.179345i
$394$	4.67045	−	12.8320i	0.235294	−	0.646464i
$395$		0			0
$396$	7.73961	+	0.505439i	0.388930	+	0.0253992i
$397$	29.1350	+	7.80671i	1.46224	+	0.391807i	0.900265	−	0.435343i	$-0.143373\pi$
$397$	29.1350	+	7.80671i	1.46224	+	0.391807i	0.561980	+	0.827151i	$0.310040\pi$
$398$	−37.2099	−	26.0546i	−1.86516	−	1.30600i
$399$	4.99656	+	3.74719i	0.250141	+	0.187594i
$400$		0			0
$401$	34.2820	+	6.04485i	1.71196	+	0.301865i	0.941848	−	0.336040i	$-0.109088\pi$
$401$	34.2820	+	6.04485i	1.71196	+	0.301865i	0.770115	+	0.637905i	$0.220199\pi$
$402$	52.9389	+	32.9108i	2.64035	+	1.64144i
$403$	−14.4761	−	1.26649i	−0.721106	−	0.0630886i
$404$	31.5550			1.56992
$405$		0			0
$406$	24.1845			1.20026
$407$	0.709953	+	0.0621128i	0.0351911	+	0.00307882i
$408$	47.6899	+	29.6476i	2.36100	+	1.46778i
$409$	−21.8207	−	3.84758i	−1.07897	−	0.190251i	−0.394208	−	0.919021i	$-0.628981\pi$
$409$	−21.8207	−	3.84758i	−1.07897	−	0.190251i	−0.684758	+	0.728771i	$0.740092\pi$
$410$		0			0
$411$	2.87826	+	2.15856i	0.141974	+	0.106474i
$412$	19.8890	+	13.9264i	0.979859	+	0.686105i
$413$	−5.42346	−	1.45321i	−0.266871	−	0.0715079i
$414$	−1.82692	+	2.73559i	−0.0897884	+	0.134447i
$415$		0			0
$416$	20.0374	−	55.0524i	0.982415	−	2.69916i
$417$	−19.9098	−	17.8441i	−0.974989	−	0.873831i
$418$	0.257831	+	2.94703i	0.0126109	+	0.144144i
$419$	−3.82900	−	3.21291i	−0.187059	−	0.156961i	0.544449	−	0.838794i	$-0.316739\pi$
$419$	−3.82900	−	3.21291i	−0.187059	−	0.156961i	−0.731508	+	0.681833i	$0.761183\pi$
$420$		0			0
$421$	12.3825	+	4.50685i	0.603485	+	0.219651i	0.625650	−	0.780104i	$-0.284834\pi$
$421$	12.3825	+	4.50685i	0.603485	+	0.219651i	−0.0221653	+	0.999754i	$0.507056\pi$
$422$	27.5051	−	7.36996i	1.33893	−	0.358764i
$423$	−35.9170	−	5.51945i	−1.74635	−	0.268365i
$424$	3.13649	−	1.81086i	0.152322	−	0.0879429i
$425$		0			0
$426$	29.5899	+	69.2660i	1.43363	+	3.35595i
$427$	6.15173	−	13.1924i	0.297703	−	0.638426i
$428$	−2.54388	−	3.63304i	−0.122963	−	0.175609i
$429$	1.56708	+	1.67275i	0.0756592	+	0.0807613i
$430$		0			0
$431$			14.5168i			0.699251i	0.936890	+	0.349625i	$0.113691\pi$
$431$			14.5168i			0.699251i	−0.936890	+	0.349625i	$0.886309\pi$
$432$	32.7687	−	68.3794i	1.57659	−	3.28991i
$433$	16.6348	+	16.6348i	0.799416	+	0.799416i	0.983003	−	0.183587i	$-0.0587710\pi$
$433$	16.6348	+	16.6348i	0.799416	+	0.799416i	−0.183587	+	0.983003i	$0.558771\pi$
$434$	17.2845	−	14.5034i	0.829683	−	0.696187i
$435$		0			0
$436$	−7.97163	+	45.2094i	−0.381772	+	2.16514i
$437$	−0.830884	−	0.387448i	−0.0397466	−	0.0185341i
$438$	29.7490	−	23.3528i	1.42146	−	1.11584i
$439$	−21.2894	+	3.75390i	−1.01609	+	0.179164i	−0.656801	−	0.754064i	$-0.728091\pi$
$439$	−21.2894	+	3.75390i	−1.01609	+	0.179164i	−0.359287	+	0.933227i	$0.616980\pi$
$440$		0			0
$441$	9.32350	−	9.74408i	0.443976	−	0.464004i
$442$	6.80221	+	25.3862i	0.323548	+	1.20750i
$443$	−10.8788	+	5.07285i	−0.516866	+	0.241018i	−0.663505	−	0.748172i	$-0.730932\pi$
$443$	−10.8788	+	5.07285i	−0.516866	+	0.241018i	0.146640	+	0.989190i	$0.453154\pi$
$444$	6.35363	−	12.5409i	0.301530	−	0.595166i
$445$		0			0
$446$	41.0912	−	48.9706i	1.94572	−	2.31882i
$447$	−8.48653	−	25.9159i	−0.401399	−	1.22578i
$448$	18.9243	+	40.5832i	0.894087	+	1.91738i
$449$	15.1373	−	26.2186i	0.714374	−	1.23733i	−0.248826	−	0.968548i	$-0.580045\pi$
$449$	15.1373	−	26.2186i	0.714374	−	1.23733i	0.963200	−	0.268784i	$-0.0866218\pi$
$450$		0			0
$451$	1.85078	+	3.20565i	0.0871499	+	0.150948i
$452$	6.78649	−	9.69212i	0.319210	−	0.455879i
$453$	1.14902	+	1.46372i	0.0539855	+	0.0687716i
$454$	18.6577	+	51.2617i	0.875651	+	2.40583i
$455$		0			0
$456$	35.2631	+	10.6924i	1.65135	+	0.500717i
$457$	−3.62673	+	41.4537i	−0.169651	+	1.93912i	0.143990	+	0.989579i	$0.454007\pi$
$457$	−3.62673	+	41.4537i	−0.169651	+	1.93912i	−0.313642	+	0.949541i	$0.601549\pi$
$458$	42.5171	−	42.5171i	1.98670	−	1.98670i
$459$	2.94528	+	17.7999i	0.137474	+	0.830829i
$460$		0			0
$461$	−11.0916	−	13.2184i	−0.516586	−	0.615643i	0.443184	−	0.896431i	$-0.353849\pi$
$461$	−11.0916	−	13.2184i	−0.516586	−	0.615643i	−0.959770	+	0.280788i	$0.909404\pi$
$462$	−3.55716	−	0.116027i	−0.165494	−	0.00539808i
$463$	13.5021	−	9.45428i	0.627496	−	0.439378i	−0.216088	−	0.976374i	$-0.569330\pi$
$463$	13.5021	−	9.45428i	0.627496	−	0.439378i	0.843585	+	0.536996i	$0.180441\pi$
$464$	76.8950	−	27.9875i	3.56976	−	1.29929i
$465$		0			0
$466$	−8.83640	−	50.1137i	−0.409338	−	2.32147i
$467$	−1.03012	+	3.84448i	−0.0476685	+	0.177901i	−0.985656	−	0.168769i	$-0.946021\pi$
$467$	−1.03012	+	3.84448i	−0.0476685	+	0.177901i	0.937987	+	0.346670i	$0.112688\pi$
$468$	42.1380	−	16.3981i	1.94783	−	0.758001i
$469$	−18.1003	−	10.4502i	−0.835795	−	0.482546i
$470$		0			0
$471$	−24.9696	+	16.2972i	−1.15054	+	0.750937i
$472$	−33.0009	+	2.88720i	−1.51899	+	0.132894i
$473$	0.562805	−	0.0492391i	0.0258778	−	0.00226402i
$474$	1.14609	+	20.9467i	0.0526417	+	0.962115i
$475$		0			0
$476$	−25.8234	−	14.9091i	−1.18361	−	0.683359i
$477$	1.10196	+	0.373775i	0.0504554	+	0.0171140i
$478$	−13.7631	+	51.3646i	−0.629510	+	2.34936i
$479$	−0.246236	−	1.39648i	−0.0112508	−	0.0638066i	0.978665	−	0.205460i	$-0.0658692\pi$
$479$	−0.246236	−	1.39648i	−0.0112508	−	0.0638066i	−0.989916	+	0.141654i	$0.954758\pi$
$480$		0			0
$481$	3.90411	−	1.42098i	0.178012	−	0.0647911i
$482$	−10.9857	+	7.69230i	−0.500387	+	0.350375i
$483$	0.582326	−	0.936704i	0.0264967	−	0.0426215i
$484$	37.5762	+	44.7816i	1.70801	+	2.03553i
$485$		0			0
$486$	40.9040	−	11.4660i	1.85544	−	0.520107i
$487$	5.92999	−	5.92999i	0.268714	−	0.268714i	−0.559868	−	0.828582i	$-0.689148\pi$
$487$	5.92999	−	5.92999i	0.268714	−	0.268714i	0.828582	+	0.559868i	$0.189148\pi$
$488$	7.48504	−	85.5544i	0.338832	−	3.87286i
$489$	1.37629	+	5.89942i	0.0622380	+	0.266781i
$490$		0			0
$491$	−9.16760	−	25.1878i	−0.413728	−	1.13671i	−0.955193	−	0.295985i	$-0.904352\pi$
$491$	−9.16760	−	25.1878i	−0.413728	−	1.13671i	0.541464	−	0.840724i	$-0.317870\pi$
$492$	72.2857	−	10.3287i	3.25889	−	0.465654i
$493$	−11.1679	+	15.9494i	−0.502976	+	0.718324i
$494$	8.62305	+	14.9356i	0.387969	+	0.671983i
$495$		0			0
$496$	38.1722	−	66.1162i	1.71398	−	2.96871i
$497$	−10.6731	−	22.8886i	−0.478754	−	1.02669i
$498$	9.17735	−	10.2398i	0.411247	−	0.458854i
$499$	7.19594	−	8.57579i	0.322134	−	0.383905i	−0.580538	−	0.814233i	$-0.697158\pi$
$499$	7.19594	−	8.57579i	0.322134	−	0.383905i	0.902672	+	0.430328i	$0.141602\pi$
$500$		0			0
$501$	−6.23696	−	9.55588i	−0.278647	−	0.426925i
$502$	−51.6420	+	24.0811i	−2.30490	+	1.07479i
$503$	−3.44372	−	12.8521i	−0.153548	−	0.573049i	−0.999225	−	0.0393543i	$-0.987470\pi$
$503$	−3.44372	−	12.8521i	−0.153548	−	0.573049i	0.845677	−	0.533694i	$-0.179197\pi$
$504$	−17.8448	+	40.5815i	−0.794872	+	1.80765i
$505$		0			0
$506$	0.514493	−	0.0907189i	0.0228720	−	0.00403295i
$507$	−8.49540	−	3.40966i	−0.377294	−	0.151428i
$508$	17.5550	+	8.18603i	0.778877	+	0.363197i
$509$	−1.12261	+	6.36664i	−0.0497588	+	0.282196i	−0.999527	−	0.0307584i	$-0.990208\pi$
$509$	−1.12261	+	6.36664i	−0.0497588	+	0.282196i	0.949768	+	0.312955i	$0.101319\pi$
$510$		0			0
$511$	−9.71403	+	8.15104i	−0.429723	+	0.360581i
$512$	24.9482	+	24.9482i	1.10257	+	1.10257i
$513$	4.88993	+	10.7821i	0.215896	+	0.476042i
$514$			39.7830i			1.75475i
$515$		0			0
$516$	3.23388	−	10.6652i	0.142364	−	0.469511i
$517$	3.31019	+	4.72744i	0.145582	+	0.207912i
$518$	−2.72634	+	5.84666i	−0.119789	+	0.256887i
$519$	−18.3860	−	2.21460i	−0.807057	−	0.0972103i
$520$		0			0
$521$	−6.34977	+	3.66604i	−0.278188	+	0.160612i	−0.632603	−	0.774476i	$-0.718013\pi$
$521$	−6.34977	+	3.66604i	−0.278188	+	0.160612i	0.354415	+	0.935088i	$0.384680\pi$
$522$	40.1983	+	22.0411i	1.75943	+	0.964715i
$523$	−12.5860	+	3.37240i	−0.550346	+	0.147465i	−0.523268	−	0.852168i	$-0.675287\pi$
$523$	−12.5860	+	3.37240i	−0.550346	+	0.147465i	−0.0270787	+	0.999633i	$0.508620\pi$
$524$	−15.6827	−	5.70803i	−0.685101	−	0.249356i
$525$		0			0
$526$	−63.9152	−	53.6312i	−2.78683	−	2.33843i
$527$	1.58322	+	18.0963i	0.0689660	+	0.788285i
$528$	−11.4443	+	3.74760i	−0.498049	+	0.163093i
$529$	7.81109	−	21.4608i	0.339613	−	0.933078i
$530$		0			0
$531$	−7.69018	−	7.35825i	−0.333725	−	0.319321i
$532$	−18.9001	−	5.06425i	−0.819421	−	0.219563i
$533$	17.6767	+	12.3773i	0.765662	+	0.536122i
$534$	3.95260	−	32.8152i	0.171046	−	1.42005i
$535$		0			0
$536$	−121.438	−	21.4128i	−5.24534	−	0.924894i
$537$	10.1211	−	5.41139i	0.436758	−	0.233519i
$538$	64.3161	+	5.62693i	2.77286	+	0.242594i
$539$	−2.14180			−0.0922537
$540$		0			0
$541$	−19.4815			−0.837576			−0.418788	−	0.908084i	$-0.637545\pi$
$541$	−19.4815			−0.837576			−0.418788	+	0.908084i	$0.637545\pi$
$542$	54.6112	+	4.77786i	2.34575	+	0.205227i
$543$	−0.493396	+	15.1265i	−0.0211737	+	0.649140i
$544$	−72.1238	−	12.7174i	−3.09228	−	0.545253i
$545$		0			0
$546$	−19.0803	+	8.15097i	−0.816563	+	0.348829i
$547$	−11.7626	−	8.23625i	−0.502932	−	0.352157i	0.294415	−	0.955678i	$-0.404875\pi$
$547$	−11.7626	−	8.23625i	−0.502932	−	0.352157i	−0.797347	+	0.603521i	$0.793764\pi$
$548$	−10.8874	−	2.91726i	−0.465085	−	0.124619i
$549$	22.2483	−	16.3213i	0.949535	−	0.696574i
$550$		0			0
$551$	−4.36986	+	12.0061i	−0.186162	+	0.511477i
$552$	1.33832	−	6.36830i	0.0569627	−	0.271053i
$553$	−0.613034	−	7.00702i	−0.0260689	−	0.297969i
$554$	31.7450	+	26.6372i	1.34871	+	1.13171i
$555$		0			0
$556$	78.7101	+	28.6481i	3.33805	+	1.21495i
$557$	−22.3886	+	5.99902i	−0.948637	+	0.254187i	−0.699784	−	0.714355i	$-0.746720\pi$
$557$	−22.3886	+	5.99902i	−0.948637	+	0.254187i	−0.248853	+	0.968541i	$0.580054\pi$
$558$	41.9475	−	8.35420i	1.77578	−	0.353662i
$559$	2.85230	−	1.64678i	0.120640	−	0.0696513i
$560$		0			0
$561$	1.71913	−	2.29232i	0.0725819	−	0.0967818i
$562$	−27.4978	+	58.9691i	−1.15992	+	2.48746i
$563$	17.2788	+	24.6767i	0.728214	+	1.04000i	0.997046	+	0.0768099i	$0.0244735\pi$
$563$	17.2788	+	24.6767i	0.728214	+	1.04000i	−0.268832	+	0.963187i	$0.586638\pi$
$564$	110.869	−	25.8648i	4.66842	−	1.08911i
$565$		0			0
$566$			0.777487i			0.0326802i
$567$	−13.5822	+	4.28952i	−0.570398	+	0.180143i
$568$	−105.360	−	105.360i	−4.42082	−	4.42082i
$569$	14.2448	−	11.9528i	0.597173	−	0.501088i	−0.293362	−	0.956001i	$-0.594774\pi$
$569$	14.2448	−	11.9528i	0.597173	−	0.501088i	0.890536	+	0.454913i	$0.150330\pi$
$570$		0			0
$571$	6.82003	−	38.6783i	0.285409	−	1.61864i	−0.418410	−	0.908258i	$-0.637412\pi$
$571$	6.82003	−	38.6783i	0.285409	−	1.61864i	0.703819	−	0.710379i	$-0.251476\pi$
$572$	−6.50822	−	3.03483i	−0.272122	−	0.126893i
$573$	4.94195	+	34.5864i	0.206453	+	1.44487i
$574$	−32.9977	+	5.81838i	−1.37730	+	0.242854i
$575$		0			0
$576$	−5.53153	+	84.7024i	−0.230480	+	3.52927i
$577$	−11.3255	−	42.2673i	−0.471486	−	1.75961i	−0.634436	−	0.772975i	$-0.718768\pi$
$577$	−11.3255	−	42.2673i	−0.471486	−	1.75961i	0.162950	−	0.986634i	$-0.447899\pi$
$578$	−12.2108	+	5.69397i	−0.507901	+	0.236838i
$579$	−32.4766	+	1.77694i	−1.34968	+	0.0738472i
$580$		0			0
$581$	−2.96353	+	3.53180i	−0.122948	+	0.146524i
$582$	−34.9722	−	7.34954i	−1.44965	−	0.304648i
$583$	−0.0781006	−	0.167487i	−0.00323460	−	0.00693661i
$584$	−37.4080	+	64.7925i	−1.54795	+	2.68113i
$585$		0			0
$586$	21.1828	+	36.6896i	0.875051	+	1.51563i
$587$	11.6046	−	16.5731i	0.478974	−	0.684046i	−0.504845	−	0.863210i	$-0.668450\pi$
$587$	11.6046	−	16.5731i	0.478974	−	0.684046i	0.983819	+	0.179164i	$0.0573394\pi$
$588$	−15.7373	+	39.2105i	−0.648993	+	1.61701i
$589$	4.07693	+	11.2013i	0.167987	+	0.461540i
$590$		0			0
$591$	−6.33393	+	5.93378i	−0.260543	+	0.244083i
$592$	−1.90240	+	21.7446i	−0.0781883	+	0.893696i
$593$	2.27116	−	2.27116i	0.0932652	−	0.0932652i	−0.658935	−	0.752200i	$-0.728993\pi$
$593$	2.27116	−	2.27116i	0.0932652	−	0.0932652i	0.752200	+	0.658935i	$0.228993\pi$
$594$	−5.80678	−	3.43475i	−0.238255	−	0.140930i
$595$		0			0
$596$	54.9162	+	65.4466i	2.24946	+	2.68080i
$597$	13.6129	+	25.4606i	0.557137	+	1.04203i
$598$	2.49484	−	1.74691i	0.102022	−	0.0714364i
$599$	11.3910	−	4.14598i	0.465423	−	0.169400i	−0.0986548	−	0.995122i	$-0.531454\pi$
$599$	11.3910	−	4.14598i	0.465423	−	0.169400i	0.564078	+	0.825722i	$0.309232\pi$
$600$		0			0
$601$	2.78962	+	15.8207i	0.113791	+	0.645340i	0.987342	+	0.158607i	$0.0507003\pi$
$601$	2.78962	+	15.8207i	0.113791	+	0.645340i	−0.873551	+	0.486733i	$0.838189\pi$
$602$	−1.32360	+	4.93974i	−0.0539459	+	0.201329i
$603$	−20.5614	−	33.8660i	−0.837323	−	1.37913i
$604$	−5.04879	−	2.91492i	−0.205432	−	0.118606i
$605$		0			0
$606$	−24.4848	−	12.4048i	−0.994626	−	0.503909i
$607$	12.6491	−	1.10665i	0.513412	−	0.0449177i	0.172494	−	0.985011i	$-0.444818\pi$
$607$	12.6491	−	1.10665i	0.513412	−	0.0449177i	0.340918	+	0.940093i	$0.389262\pi$
$608$	−47.8750	+	4.18852i	−1.94159	+	0.169867i
$609$	−13.7119	−	6.94690i	−0.555636	−	0.281503i
$610$		0			0
$611$	29.1369	+	16.8222i	1.17875	+	0.680552i
$612$	−29.3345	−	48.3159i	−1.18578	−	1.95306i
$613$	−3.15725	+	11.7830i	−0.127520	+	0.475912i	−0.999917	−	0.0128866i	$-0.995898\pi$
$613$	−3.15725	+	11.7830i	−0.127520	+	0.475912i	0.872397	+	0.488798i	$0.162565\pi$
$614$	−4.98094	−	28.2483i	−0.201014	−	1.14001i
$615$		0			0
$616$	6.61595	−	2.40801i	0.266564	−	0.0970215i
$617$	−7.63591	+	5.34672i	−0.307410	+	0.215251i	−0.717094	−	0.696977i	$-0.754528\pi$
$617$	−7.63591	+	5.34672i	−0.307410	+	0.215251i	0.409684	+	0.912228i	$0.365639\pi$
$618$	−9.95797	−	18.6247i	−0.400568	−	0.749197i
$619$	10.1944	+	12.1492i	0.409748	+	0.488319i	0.930967	−	0.365104i	$-0.118967\pi$
$619$	10.1944	+	12.1492i	0.409748	+	0.488319i	−0.521218	+	0.853423i	$0.674522\pi$
$620$		0			0
$621$	1.82160	−	1.02622i	0.0730982	−	0.0411810i
$622$	6.19528	−	6.19528i	0.248408	−	0.248408i
$623$	−0.965877	+	11.0400i	−0.0386971	+	0.442309i
$624$	−51.2334	+	47.9967i	−2.05098	+	1.92141i
$625$		0			0
$626$	−22.6663	−	62.2751i	−0.905927	−	2.48901i
$627$	0.700337	−	1.74494i	0.0279688	−	0.0696862i
$628$	53.5809	−	76.5215i	2.13811	−	3.05354i
$629$	−2.59683	−	4.49784i	−0.103542	−	0.179341i
$630$		0			0
$631$	−12.2239	+	21.1724i	−0.486626	+	0.842861i	−0.999882	−	0.0153745i	$-0.995106\pi$
$631$	−12.2239	+	21.1724i	−0.486626	+	0.842861i	0.513256	+	0.858236i	$0.328439\pi$
$632$	−17.5382	−	37.6109i	−0.697634	−	1.49608i
$633$	−17.7116	−	3.72215i	−0.703972	−	0.147942i
$634$	−36.3814	+	43.3577i	−1.44489	+	1.72195i
$635$		0			0
$636$	−3.64010	+	0.199166i	−0.144339	+	0.00789745i
$637$	−11.3163	+	5.27689i	−0.448369	+	0.209078i
$638$	−1.88441	−	7.03271i	−0.0746045	−	0.278428i
$639$	3.11973	−	47.7714i	0.123415	−	1.88981i
$640$		0			0
$641$	−5.87001	+	1.03504i	−0.231852	+	0.0408817i	−0.288367	−	0.957520i	$-0.593112\pi$
$641$	−5.87001	+	1.03504i	−0.231852	+	0.0408817i	0.0565151	+	0.998402i	$0.482001\pi$
$642$	0.545695	+	3.81906i	0.0215369	+	0.150726i
$643$	29.1651	+	13.5999i	1.15016	+	0.536328i	0.901720	−	0.432320i	$-0.142305\pi$
$643$	29.1651	+	13.5999i	1.15016	+	0.536328i	0.248438	+	0.968648i	$0.420083\pi$
$644$	−0.600036	+	3.40297i	−0.0236447	+	0.134096i
$645$		0			0
$646$	16.5151	−	13.8578i	0.649779	−	0.545229i
$647$	5.43613	+	5.43613i	0.213717	+	0.213717i	0.805844	−	0.592128i	$-0.201712\pi$
$647$	5.43613	+	5.43613i	0.213717	+	0.213717i	−0.592128	+	0.805844i	$0.701712\pi$
$648$	−66.6457	+	51.1892i	−2.61809	+	2.01090i
$649$			1.69034i			0.0663516i
$650$		0			0
$651$	−13.9659	+	3.25813i	−0.547365	+	0.127696i
$652$	−10.8857	−	15.5464i	−0.426317	−	0.608844i
$653$	6.80729	−	14.5983i	0.266390	−	0.571275i	−0.726924	−	0.686717i	$-0.759051\pi$
$653$	6.80729	−	14.5983i	0.266390	−	0.571275i	0.993314	+	0.115443i	$0.0368287\pi$
$654$	23.9580	−	31.9460i	0.936833	−	1.24919i
$655$		0			0
$656$	−98.1831	+	56.6861i	−3.83341	+	2.21322i
$657$	−23.5748	+	4.69513i	−0.919740	+	0.183174i
$658$	−50.4605	+	13.5209i	−1.96716	+	0.527098i
$659$	−31.0994	−	11.3193i	−1.21146	−	0.440936i	−0.344250	−	0.938878i	$-0.611867\pi$
$659$	−31.0994	−	11.3193i	−1.21146	−	0.440936i	−0.867210	+	0.497942i	$0.834089\pi$
$660$		0			0
$661$	22.7885	+	19.1218i	0.886369	+	0.743752i	0.967478	−	0.252954i	$-0.0814020\pi$
$661$	22.7885	+	19.1218i	0.886369	+	0.743752i	−0.0811098	+	0.996705i	$0.525846\pi$
$662$	1.41507	+	16.1743i	0.0549981	+	0.628631i
$663$	3.43541	−	16.3472i	0.133420	−	0.634871i
$664$	−9.30342	+	25.5609i	−0.361043	+	0.991957i
$665$		0			0
$666$	−9.86008	+	7.23330i	−0.382070	+	0.280285i
$667$	2.17945	+	0.583983i	0.0843888	+	0.0226119i
$668$	29.2848	+	20.5054i	1.13306	+	0.793379i
$669$	−37.3641	+	15.9617i	−1.44458	+	0.617113i
$670$		0			0
$671$	−4.31561	−	0.760958i	−0.166602	−	0.0293764i
$672$	1.88488	−	57.7867i	0.0727110	−	2.22917i
$673$	−34.6064	−	3.02767i	−1.33398	−	0.116708i	−0.602252	−	0.798306i	$-0.705730\pi$
$673$	−34.6064	−	3.02767i	−1.33398	−	0.116708i	−0.731727	+	0.681598i	$0.761285\pi$
$674$	30.3912			1.17063
$675$		0			0
$676$	28.6790			1.10304
$677$	17.3173	+	1.51507i	0.665560	+	0.0582289i	0.414929	−	0.909854i	$-0.363806\pi$
$677$	17.3173	+	1.51507i	0.665560	+	0.0582289i	0.250631	+	0.968083i	$0.419362\pi$
$678$	−9.07604	+	4.85263i	−0.348563	+	0.186364i
$679$	11.8000	+	2.08066i	0.452843	+	0.0798485i
$680$		0			0
$681$	4.14629	−	34.4233i	0.158886	−	1.31910i
$682$	−5.56428	−	3.89615i	−0.213067	−	0.149191i
$683$	10.9763	+	2.94108i	0.419995	+	0.112537i	0.462626	−	0.886554i	$-0.346907\pi$
$683$	10.9763	+	2.94108i	0.419995	+	0.112537i	−0.0426308	+	0.999091i	$0.513574\pi$
$684$	−26.7993	−	25.6425i	−1.02470	−	0.980467i
$685$		0			0
$686$	16.9564	−	46.5874i	0.647400	−	1.77872i
$687$	−36.3189	+	11.8931i	−1.38565	+	0.453752i
$688$	1.50810	+	17.2377i	0.0574959	+	0.657181i
$689$	−0.825299	−	0.692508i	−0.0314414	−	0.0263824i
$690$		0			0
$691$	−22.0909	−	8.04044i	−0.840378	−	0.305873i	−0.114267	−	0.993450i	$-0.536452\pi$
$691$	−22.0909	−	8.04044i	−0.840378	−	0.305873i	−0.726111	+	0.687577i	$0.758674\pi$
$692$	56.0412	−	15.0162i	2.13037	−	0.570830i
$693$	1.98348	+	1.08756i	0.0753461	+	0.0413131i
$694$	56.0171	−	32.3415i	2.12638	−	1.22767i
$695$		0			0
$696$	−90.0392	−	10.8453i	−3.41293	−	0.411088i
$697$	11.4004	−	24.4483i	0.431822	−	0.926046i
$698$	−11.7362	−	16.7611i	−0.444223	−	0.634416i
$699$	−9.38495	+	30.9512i	−0.354971	+	1.17068i
$700$		0			0
$701$		−	44.6039i		−	1.68467i	−0.538956	−	0.842334i	$-0.681181\pi$
$701$		−	44.6039i		−	1.68467i	0.538956	−	0.842334i	$-0.318819\pi$
$702$	−39.1429	−	3.84119i	−1.47735	−	0.144976i
$703$	−2.40988	−	2.40988i	−0.0908903	−	0.0908903i
$704$	10.3268	−	8.66522i	0.389206	−	0.326583i
$705$		0			0
$706$	−2.45245	+	13.9085i	−0.0922992	+	0.523455i
$707$	8.34079	+	3.88937i	0.313688	+	0.146275i
$708$	30.9455	+	12.4201i	1.16300	+	0.466775i
$709$	36.4781	−	6.43207i	1.36996	−	0.241562i	0.560219	−	0.828344i	$-0.310717\pi$
$709$	36.4781	−	6.43207i	1.36996	−	0.241562i	0.809744	+	0.586783i	$0.199606\pi$
$710$		0			0
$711$	5.36705	−	12.2054i	0.201280	−	0.457738i
$712$	16.9228	+	63.1566i	0.634207	+	2.36689i
$713$	1.90785	−	0.889647i	0.0714497	−	0.0333175i
$714$	14.1764	+	21.7202i	0.530538	+	0.812857i
$715$		0			0
$716$	−23.1122	+	27.5441i	−0.863744	+	1.02937i
$717$	22.5575	−	25.1689i	0.842427	−	0.939949i
$718$	15.7251	+	33.7227i	0.586857	+	1.25852i
$719$	−19.2483	+	33.3390i	−0.717839	+	1.24333i	0.244016	+	0.969771i	$0.421535\pi$
$719$	−19.2483	+	33.3390i	−0.717839	+	1.24333i	−0.961854	+	0.273562i	$0.911798\pi$
$720$		0			0
$721$	3.54064	+	6.13256i	0.131860	+	0.228389i
$722$	−21.5840	+	30.8251i	−0.803273	+	1.14719i
$723$	8.43818	−	1.20571i	0.313819	−	0.0448408i
$724$	−16.2169	−	44.5557i	−0.602698	−	1.65590i
$725$		0			0
$726$	−11.5525	−	49.5196i	−0.428755	−	1.83785i
$727$	2.27381	−	25.9897i	0.0843308	−	0.963906i	−0.829686	−	0.558230i	$-0.811481\pi$
$727$	2.27381	−	25.9897i	0.0843308	−	0.963906i	0.914017	−	0.405676i	$-0.132964\pi$
$728$	29.0230	−	29.0230i	1.07566	−	1.07566i
$729$	−26.4849	−	5.24861i	−0.980924	−	0.194393i
$730$		0			0
$731$	−2.64649	−	3.15396i	−0.0978838	−	0.116653i
$732$	−45.6408	+	73.4158i	−1.68693	+	2.71352i
$733$	−39.9276	+	27.9576i	−1.47476	+	1.03264i	−0.487571	+	0.873083i	$0.662117\pi$
$733$	−39.9276	+	27.9576i	−1.47476	+	1.03264i	−0.987189	+	0.159555i	$0.948994\pi$
$734$	−55.2278	+	20.1013i	−2.03849	+	0.741951i
$735$		0			0
$736$	1.47374	+	8.35802i	0.0543230	+	0.308081i
$737$	−1.62852	+	6.07772i	−0.0599873	+	0.223876i
$738$	−60.1498	−	20.4022i	−2.21414	−	0.751015i
$739$	11.7531	+	6.78566i	0.432345	+	0.249614i	0.700345	−	0.713804i	$-0.253029\pi$
$739$	11.7531	+	6.78566i	0.432345	+	0.249614i	−0.268000	+	0.963419i	$0.586363\pi$
$740$		0			0
$741$	−0.598849	−	10.9450i	−0.0219993	−	0.402073i
$742$	1.66647	−	0.145797i	0.0611780	−	0.00535238i
$743$	1.23767	−	0.108282i	0.0454055	−	0.00397247i	−0.0644303	−	0.997922i	$-0.520523\pi$
$743$	1.23767	−	0.108282i	0.0454055	−	0.00397247i	0.109836	+	0.993950i	$0.464967\pi$
$744$	−70.8542	+	46.2453i	−2.59764	+	1.69544i
$745$		0			0
$746$	31.2331	+	18.0324i	1.14352	+	0.660214i
$747$	−8.14462	+	3.16949i	−0.297996	+	0.115966i
$748$	−2.32338	+	8.67096i	−0.0849511	+	0.317042i
$749$	−0.224615	−	1.27386i	−0.00820726	−	0.0465457i
$750$		0			0
$751$	−8.15950	+	2.96982i	−0.297745	+	0.108370i	−0.486573	−	0.873640i	$-0.661753\pi$
$751$	−8.15950	+	2.96982i	−0.297745	+	0.108370i	0.188828	+	0.982010i	$0.439531\pi$
$752$	−144.793	+	101.385i	−5.28005	+	3.69713i
$753$	36.1967	+	1.18066i	1.31908	+	0.0430258i
$754$	−27.2833	−	32.5150i	−0.993601	−	1.18413i
$755$		0			0
$756$	34.4843	−	28.3210i	1.25418	−	1.03003i
$757$	−29.4262	+	29.4262i	−1.06951	+	1.06951i	−0.0721170	+	0.997396i	$0.522975\pi$
$757$	−29.4262	+	29.4262i	−1.06951	+	1.06951i	−0.997396	+	0.0721170i	$0.977025\pi$
$758$	−6.50993	+	74.4088i	−0.236451	+	2.70265i
$759$	−0.317761	−	0.0963507i	−0.0115340	−	0.00349731i
$760$		0			0
$761$	14.0169	+	38.5111i	0.508112	+	1.39603i	0.883183	+	0.469029i	$0.155396\pi$
$761$	14.0169	+	38.5111i	0.508112	+	1.39603i	−0.375071	+	0.926996i	$0.622382\pi$
$762$	−10.4036	−	13.2530i	−0.376882	−	0.480107i
$763$	−7.67948	+	10.9674i	−0.278016	+	0.397048i
$764$	−54.7283	−	94.7922i	−1.98000	−	3.42946i
$765$		0			0
$766$	−49.2326	+	85.2733i	−1.77884	+	3.08105i
$767$	4.16460	+	8.93101i	0.150375	+	0.322480i
$768$	−20.7931	−	63.4973i	−0.750307	−	2.29126i
$769$	−3.94057	+	4.69619i	−0.142100	+	0.169349i	−0.832401	−	0.554174i	$-0.813034\pi$
$769$	−3.94057	+	4.69619i	−0.142100	+	0.169349i	0.690300	+	0.723523i	$0.257479\pi$
$770$		0			0
$771$	11.4275	−	22.5558i	0.411550	−	0.812327i
$772$	92.3513	−	43.0641i	3.32380	−	1.54991i
$773$	2.46257	+	9.19044i	0.0885726	+	0.330557i	0.995967	−	0.0897234i	$-0.0285983\pi$
$773$	2.46257	+	9.19044i	0.0885726	+	0.330557i	−0.907394	+	0.420281i	$0.861932\pi$
$774$	−6.70197	+	7.00429i	−0.240897	+	0.251764i
$775$		0			0
$776$	69.6196	−	12.2758i	2.49920	−	0.440676i
$777$	3.22518	−	2.53176i	0.115703	−	0.0908263i
$778$	−45.6625	−	21.2928i	−1.63708	−	0.763382i
$779$	3.07383	−	17.4326i	0.110132	−	0.624587i
$780$		0			0
$781$	−5.82422	+	4.88710i	−0.208407	+	0.174874i
$782$	−2.69216	−	2.69216i	−0.0962714	−	0.0962714i
$783$	−16.4601	−	24.0435i	−0.588235	−	0.859244i
$784$		−	65.5994i		−	2.34283i
$785$		0			0
$786$	9.92491	+	10.5942i	0.354010	+	0.377883i
$787$	−4.85971	−	6.94038i	−0.173230	−	0.247398i	0.723143	−	0.690698i	$-0.242697\pi$
$787$	−4.85971	−	6.94038i	−0.173230	−	0.247398i	−0.896373	+	0.443300i	$0.853808\pi$
$788$	11.4915	−	24.6435i	0.409367	−	0.877890i
$789$	20.8327	+	48.7667i	0.741665	+	1.73614i
$790$		0			0
$791$	2.98847	−	1.72539i	0.106258	−	0.0613479i
$792$	13.1913	+	2.02713i	0.468732	+	0.0720310i
$793$	−24.6766	+	6.61207i	−0.876291	+	0.234802i
$794$	77.2406	+	28.1133i	2.74116	+	0.997702i
$795$		0			0
$796$	−69.2896	−	58.1409i	−2.45591	−	2.06075i
$797$	−2.46530	−	28.1786i	−0.0873256	−	0.998136i	−0.905832	−	0.423638i	$-0.860753\pi$
$797$	−2.46530	−	28.1786i	−0.0873256	−	0.998136i	0.818506	−	0.574498i	$-0.194803\pi$
$798$	12.6745	+	11.3595i	0.448672	+	0.402121i
$799$	14.3847	−	39.5216i	0.508894	−	1.39818i
$800$		0			0
$801$	−11.6670	+	17.4699i	−0.412234	+	0.617268i
$802$	91.6319	+	24.5527i	3.23564	+	0.866986i
$803$	3.12717	+	2.18967i	0.110355	+	0.0772716i
$804$	99.3006	+	74.4709i	3.50206	+	2.62639i
$805$		0			0
$806$	−38.9984	−	6.87647i	−1.37366	−	0.242213i
$807$	−34.8490	−	21.6648i	−1.22674	−	0.762637i
$808$	54.0909	+	4.73234i	1.90291	+	0.166483i
$809$	−2.28591			−0.0803683			−0.0401841	−	0.999192i	$-0.512794\pi$
$809$	−2.28591			−0.0803683			−0.0401841	+	0.999192i	$0.512794\pi$
$810$		0			0
$811$	21.6606			0.760605			0.380303	−	0.924862i	$-0.375820\pi$
$811$	21.6606			0.760605			0.380303	+	0.924862i	$0.375820\pi$
$812$	47.9736	+	4.19715i	1.68354	+	0.147291i
$813$	−29.5906	−	18.3957i	−1.03779	−	0.645166i
$814$	1.91260	+	0.337243i	0.0670367	+	0.0118204i
$815$		0			0
$816$	70.2096	+	52.6539i	2.45783	+	1.84326i
$817$	−2.21311	−	1.54964i	−0.0774270	−	0.0542150i
$818$	−58.3243	−	15.6279i	−2.03926	−	0.546418i
$819$	13.1593	+	0.859376i	0.459824	+	0.0300290i
$820$		0			0
$821$	7.91413	−	21.7439i	0.276205	−	0.758867i	−0.721579	−	0.692332i	$-0.756583\pi$
$821$	7.91413	−	21.7439i	0.276205	−	0.758867i	0.997784	−	0.0665351i	$-0.0211944\pi$
$822$	7.30112	+	6.54361i	0.254656	+	0.228235i
$823$	0.569178	+	6.50574i	0.0198403	+	0.226776i	0.999641	+	0.0267986i	$0.00853127\pi$
$823$	0.569178	+	6.50574i	0.0198403	+	0.226776i	−0.979801	+	0.199977i	$0.935913\pi$
$824$	32.0047	+	26.8552i	1.11494	+	0.935544i
$825$		0			0
$826$	−14.3783	−	5.23326i	−0.500284	−	0.182088i
$827$	−8.94494	+	2.39679i	−0.311046	+	0.0833445i	−0.410965	−	0.911651i	$-0.634808\pi$
$827$	−8.94494	+	2.39679i	−0.311046	+	0.0833445i	0.0999193	+	0.994996i	$0.468142\pi$
$828$	−4.09873	+	5.10939i	−0.142441	+	0.177564i
$829$	2.45210	−	1.41572i	0.0851648	−	0.0491699i	−0.456813	−	0.889563i	$-0.651009\pi$
$829$	2.45210	−	1.41572i	0.0851648	−	0.0491699i	0.541978	+	0.840393i	$0.317676\pi$
$830$		0			0
$831$	−10.3471	−	24.2211i	−0.358936	−	0.840222i
$832$	33.2132	−	71.2260i	1.15146	−	2.46932i
$833$	8.95278	+	12.7859i	0.310195	+	0.443005i
$834$	−49.8123	−	53.1715i	−1.72486	−	1.84118i
$835$		0			0
$836$			5.89061i			0.203731i
$837$	−26.1827	−	7.31263i	−0.905007	−	0.252761i
$838$	−9.63173	−	9.63173i	−0.332723	−	0.332723i
$839$	−32.4518	+	27.2303i	−1.12036	+	0.940095i	−0.998623	−	0.0524668i	$-0.983292\pi$
$839$	−32.4518	+	27.2303i	−1.12036	+	0.940095i	−0.121739	+	0.992562i	$0.538847\pi$
$840$		0			0
$841$	0.424617	−	2.40812i	0.0146420	−	0.0830387i
$842$	32.5451	+	15.1760i	1.12158	+	0.523000i
$843$	32.5291	−	25.5352i	1.12036	−	0.879479i
$844$	55.8394	−	9.84600i	1.92207	−	0.338913i
$845$		0			0
$846$	−96.1954	−	23.5147i	−3.30727	−	0.808452i
$847$	4.41271	+	16.4684i	0.151622	+	0.565862i
$848$	5.12983	−	2.39208i	0.176159	−	0.0821443i
$849$	0.223330	−	0.440813i	0.00766466	−	0.0151287i
$850$		0			0
$851$	−0.386871	+	0.461054i	−0.0132618	+	0.0158047i
$852$	46.6750	+	142.535i	1.59906	+	4.88316i
$853$	−14.0780	−	30.1905i	−0.482023	−	1.03370i	−0.985497	−	0.169691i	$-0.945723\pi$
$853$	−14.0780	−	30.1905i	−0.482023	−	1.03370i	0.503474	−	0.864010i	$-0.332055\pi$
$854$	19.8339	−	34.3532i	0.678701	−	1.17554i
$855$		0			0
$856$	−3.81582	−	6.60919i	−0.130422	−	0.225897i
$857$	17.6306	−	25.1791i	0.602249	−	0.860100i	−0.396061	−	0.918224i	$-0.629623\pi$
$857$	17.6306	−	25.1791i	0.602249	−	0.860100i	0.998309	+	0.0581240i	$0.0185119\pi$
$858$	3.85695	+	4.91333i	0.131674	+	0.167738i
$859$	17.6716	+	48.5522i	0.602946	+	1.65658i	0.745272	+	0.666760i	$0.232320\pi$
$859$	17.6716	+	48.5522i	0.602946	+	1.65658i	−0.142326	+	0.989820i	$0.545458\pi$
$860$		0			0
$861$	20.3800	+	6.17958i	0.694550	+	0.210600i
$862$	−3.44791	+	39.4098i	−0.117436	+	1.34230i
$863$	31.9076	−	31.9076i	1.08615	−	1.08615i	0.0902264	−	0.995921i	$-0.471241\pi$
$863$	31.9076	−	31.9076i	1.08615	−	1.08615i	0.995921	−	0.0902264i	$-0.0287591\pi$
$864$	55.7982	−	94.3322i	1.89829	−	3.20925i
$865$		0			0
$866$	41.2086	+	49.1104i	1.40032	+	1.66884i
$867$	8.55872	+	0.279168i	0.290669	+	0.00948105i
$868$	36.8034	−	25.7700i	1.24919	−	0.874692i
$869$	−1.98983	+	0.724239i	−0.0675003	+	0.0245681i
$870$		0			0
$871$	6.36968	+	36.1243i	0.215829	+	1.22402i
$872$	−20.4449	+	76.3015i	−0.692353	+	2.58390i
$873$	17.7171	+	14.2126i	0.599634	+	0.481023i
$874$	−2.16363	−	1.24917i	−0.0731860	−	0.0422539i
$875$		0			0
$876$	63.0643	−	41.1610i	2.13074	−	1.39070i
$877$	−39.1615	+	3.42618i	−1.32239	+	0.115694i	−0.726385	−	0.687288i	$-0.758801\pi$
$877$	−39.1615	+	3.42618i	−1.32239	+	0.115694i	−0.596003	+	0.802982i	$0.703245\pi$
$878$	−58.6873	+	5.13448i	−1.98060	+	0.173280i
$879$	−1.47109	−	26.8866i	−0.0496186	−	0.906863i
$880$		0			0
$881$	−34.0163	−	19.6393i	−1.14604	−	0.661666i	−0.198120	−	0.980178i	$-0.563484\pi$
$881$	−34.0163	−	19.6393i	−1.14604	−	0.661666i	−0.947919	+	0.318512i	$0.896817\pi$
$882$	27.6254	−	24.2385i	0.930197	−	0.816151i
$883$	4.64284	−	17.3273i	0.156244	−	0.583111i	−0.842752	−	0.538303i	$-0.819066\pi$
$883$	4.64284	−	17.3273i	0.156244	−	0.583111i	0.998996	−	0.0448081i	$-0.0142676\pi$
$884$	9.08751	+	51.5378i	0.305646	+	1.73340i
$885$		0			0
$886$	−30.7381	+	11.1878i	−1.03267	+	0.375860i
$887$	14.2556	−	9.98188i	0.478656	−	0.335159i	−0.309222	−	0.950990i	$-0.600069\pi$
$887$	14.2556	−	9.98188i	0.478656	−	0.335159i	0.787878	+	0.615831i	$0.211180\pi$
$888$	12.7720	−	20.5446i	0.428602	−	0.689430i
$889$	3.63125	+	4.32756i	0.121788	+	0.145142i
$890$		0			0
$891$	2.30566	+	3.61538i	0.0772425	+	0.121120i
$892$	90.0092	−	90.0092i	3.01373	−	3.01373i
$893$	2.40537	−	27.4935i	0.0804927	−	0.920036i
$894$	−16.8836	−	72.3711i	−0.564673	−	2.42045i
$895$		0			0
$896$	18.9021	+	51.9330i	0.631474	+	1.73496i
$897$	−1.91630	+	0.273814i	−0.0639833	+	0.00914239i
$898$	47.3215	−	67.5821i	1.57914	−	2.25524i
$899$	−14.6687	−	25.4069i	−0.489227	−	0.847367i
$900$		0			0
$901$	−0.673386	+	1.16634i	−0.0224337	+	0.0388564i
$902$	4.26306	+	9.14216i	0.141944	+	0.304401i
$903$	2.16936	−	2.42050i	0.0721919	−	0.0805490i
$904$	13.0868	−	15.5963i	0.435261	−	0.518724i
$905$		0			0
$906$	2.77166	+	4.24656i	0.0920821	+	0.141083i
$907$	17.8896	−	8.34207i	0.594015	−	0.276994i	−0.102273	−	0.994756i	$-0.532611\pi$
$907$	17.8896	−	8.34207i	0.594015	−	0.276994i	0.696288	+	0.717763i	$0.254834\pi$
$908$	28.1141	+	104.923i	0.932999	+	3.48200i
$909$	10.3190	+	14.0663i	0.342258	+	0.466549i
$910$		0			0
$911$	29.7171	−	5.23993i	0.984571	−	0.173606i	0.341890	−	0.939740i	$-0.388933\pi$
$911$	29.7171	−	5.23993i	0.984571	−	0.173606i	0.642681	+	0.766134i	$0.277822\pi$
$912$	53.4443	+	21.4501i	1.76972	+	0.710282i
$913$	1.25794	+	0.586586i	0.0416317	+	0.0194132i
$914$	−19.6914	+	111.676i	−0.651334	+	3.69390i
$915$		0			0
$916$	91.7178	−	76.9604i	3.03044	−	2.54284i
$917$	−3.44178	−	3.44178i	−0.113658	−	0.113658i
$918$	3.76806	+	49.0221i	0.124365	+	1.61797i
$919$			5.90514i			0.194793i	0.995246	+	0.0973964i	$0.0310515\pi$
$919$			5.90514i			0.194793i	−0.995246	+	0.0973964i	$0.968949\pi$
$920$		0			0
$921$	−5.29015	+	17.4467i	−0.174316	+	0.574889i
$922$	−26.9715	−	38.5192i	−0.888258	−	1.26856i
$923$	−18.7320	+	40.1708i	−0.616570	+	1.32224i
$924$	−7.03602	−	0.847491i	−0.231468	−	0.0278804i
$925$		0			0
$926$	38.9006	−	22.4592i	1.27835	−	0.738057i
$927$	0.296009	+	13.4201i	0.00972221	+	0.440773i
$928$	114.248	−	30.6126i	3.75036	−	1.00491i
$929$	−6.36097	−	2.31520i	−0.208697	−	0.0759593i	0.235557	−	0.971861i	$-0.424309\pi$
$929$	−6.36097	−	2.31520i	−0.208697	−	0.0759593i	−0.444253	+	0.895901i	$0.646531\pi$
$930$		0			0
$931$	7.84617	+	6.58371i	0.257148	+	0.215773i
$932$	−8.83124	−	100.942i	−0.289277	−	3.30645i
$933$	−5.29211	+	1.73298i	−0.173256	+	0.0567352i
$934$	−3.70965	+	10.1922i	−0.121383	+	0.333498i
$935$		0			0
$936$	74.6914	−	21.7898i	2.44136	−	0.712220i
$937$	−6.08835	−	1.63137i	−0.198898	−	0.0532945i	0.157995	−	0.987440i	$-0.449497\pi$
$937$	−6.08835	−	1.63137i	−0.198898	−	0.0532945i	−0.356892	+	0.934145i	$0.616164\pi$
$938$	−46.6560	−	32.6689i	−1.52337	−	1.06668i
$939$	−5.03711	+	41.8190i	−0.164380	+	1.36471i
$940$		0			0
$941$	26.7793	+	4.72192i	0.872981	+	0.153930i	0.592151	−	0.805827i	$-0.298279\pi$
$941$	26.7793	+	4.72192i	0.872981	+	0.153930i	0.280831	+	0.959757i	$0.409390\pi$
$942$	−71.6575	+	38.3126i	−2.33473	+	1.24829i
$943$	−3.11417	−	0.272455i	−0.101411	−	0.00887234i
$944$	−51.7720			−1.68504
$945$		0			0
$946$	1.53958			0.0500560
$947$	−48.0728	−	4.20583i	−1.56216	−	0.136671i	−0.726982	−	0.686656i	$-0.759078\pi$
$947$	−48.0728	−	4.20583i	−1.56216	−	0.136671i	−0.835174	+	0.549985i	$0.814633\pi$
$948$	−1.36180	+	41.7499i	−0.0442291	+	1.35597i
$949$	21.9174	+	3.86463i	0.711469	+	0.125451i
$950$		0			0
$951$	33.0815	−	14.1322i	1.07274	−	0.458267i
$952$	−42.0300	−	29.4297i	−1.36220	−	0.953822i
$953$	18.9362	+	5.07394i	0.613404	+	0.164361i	0.552128	−	0.833760i	$-0.313816\pi$
$953$	18.9362	+	5.07394i	0.613404	+	0.164361i	0.0612767	+	0.998121i	$0.480483\pi$
$954$	2.90279	+	1.27644i	0.0939814	+	0.0413262i
$955$		0			0
$956$	−36.2153	+	99.5008i	−1.17129	+	3.21809i
$957$	−0.951709	+	4.52863i	−0.0307644	+	0.146390i
$958$	−0.336795	−	3.84959i	−0.0108814	−	0.124375i
$959$	−2.51823	−	2.11305i	−0.0813180	−	0.0682339i
$960$		0			0
$961$	3.41043	+	1.24130i	0.110014	+	0.0400418i
$962$	10.9362	−	2.93036i	0.352599	−	0.0944785i
$963$	0.787615	−	2.32205i	0.0253805	−	0.0748269i
$964$	−23.1268	+	13.3523i	−0.744865	+	0.430048i
$965$		0			0
$966$	1.80336	−	2.40462i	0.0580220	−	0.0773674i
$967$	1.83617	−	3.93769i	0.0590474	−	0.126628i	−0.874570	−	0.484900i	$-0.838856\pi$
$967$	1.83617	−	3.93769i	0.0590474	−	0.126628i	0.933617	+	0.358272i	$0.116634\pi$
$968$	57.6964	+	82.3990i	1.85443	+	2.64841i
$969$	−13.3442	+	3.11310i	−0.428678	+	0.100007i
$970$		0			0
$971$			17.3753i			0.557601i	0.960349	+	0.278800i	$0.0899367\pi$
$971$			17.3753i			0.557601i	−0.960349	+	0.278800i	$0.910063\pi$
$972$	83.1291	−	15.6457i	2.66637	−	0.501837i
$973$	17.2740	+	17.2740i	0.553779	+	0.553779i
$974$	17.5070	−	14.6901i	0.560960	−	0.470701i
$975$		0			0
$976$	23.3068	−	132.179i	0.746031	−	4.23095i
$977$	−21.9259	−	10.2242i	−0.701470	−	0.327101i	0.0389538	−	0.999241i	$-0.487597\pi$
$977$	−21.9259	−	10.2242i	−0.701470	−	0.327101i	−0.740424	+	0.672140i	$0.765375\pi$
$978$	2.33512	+	16.3424i	0.0746690	+	0.522573i
$979$	3.28563	−	0.579345i	0.105009	−	0.0185159i
$980$		0			0
$981$	−22.7599	+	11.2306i	−0.726667	+	0.358566i
$982$	−18.9055	−	70.5563i	−0.603299	−	2.25154i
$983$	−22.0159	+	10.2662i	−0.702199	+	0.327441i	−0.740717	−	0.671817i	$-0.765514\pi$
$983$	−22.0159	+	10.2662i	−0.702199	+	0.327441i	0.0385180	+	0.999258i	$0.487736\pi$
$984$	125.460	−	6.86447i	3.99951	−	0.218831i
$985$		0			0
$986$	−34.1063	+	40.6463i	−1.08617	+	1.29444i
$987$	32.4935	+	6.82862i	1.03428	+	0.217357i
$988$	14.5131	+	31.1234i	0.461723	+	0.990168i
$989$	−0.238560	+	0.413197i	−0.00758575	+	0.0131389i
$990$		0			0
$991$	−18.0498	−	31.2632i	−0.573372	−	0.993110i	−0.996216	−	0.0869073i	$-0.972302\pi$
$991$	−18.0498	−	31.2632i	−0.573372	−	0.993110i	0.422844	−	0.906202i	$-0.361032\pi$
$992$	63.2936	−	90.3927i	2.00957	−	2.86997i
$993$	3.84369	−	9.57682i	0.121976	−	0.303911i
$994$	−23.5387	−	64.6720i	−0.746602	−	2.05127i
$995$		0			0
$996$	19.9817	−	18.7194i	0.633145	−	0.593146i
$997$	−1.73962	+	19.8840i	−0.0550944	+	0.629732i	0.917579	+	0.397554i	$0.130141\pi$
$997$	−1.73962	+	19.8840i	−0.0550944	+	0.629732i	−0.972673	+	0.232178i	$0.925415\pi$
$998$	21.5721	−	21.5721i	0.682854	−	0.682854i
$999$	7.66811	−	1.26881i	0.242608	−	0.0401434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.518.16		192
5.2	odd	4	inner	675.2.ba.b.32.1		192
5.3	odd	4		135.2.q.a.32.16	✓	192
5.4	even	2		135.2.q.a.113.1	yes	192
15.8	even	4		405.2.r.a.287.1		192
15.14	odd	2		405.2.r.a.368.16		192
27.11	odd	18	inner	675.2.ba.b.443.1		192
135.38	even	36		135.2.q.a.92.1	yes	192
135.43	odd	36		405.2.r.a.197.16		192
135.92	even	36	inner	675.2.ba.b.632.16		192
135.119	odd	18		135.2.q.a.38.16	yes	192
135.124	even	18		405.2.r.a.278.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.16	✓	192	5.3	odd	4
135.2.q.a.38.16	yes	192	135.119	odd	18
135.2.q.a.92.1	yes	192	135.38	even	36
135.2.q.a.113.1	yes	192	5.4	even	2
405.2.r.a.197.16		192	135.43	odd	36
405.2.r.a.278.1		192	135.124	even	18
405.2.r.a.287.1		192	15.8	even	4
405.2.r.a.368.16		192	15.14	odd	2
675.2.ba.b.32.1		192	5.2	odd	4	inner
675.2.ba.b.443.1		192	27.11	odd	18	inner
675.2.ba.b.518.16		192	1.1	even	1	trivial
675.2.ba.b.632.16		192	135.92	even	36	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.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.71476 + 0.237511i) q^{2} +(-1.47097 - 0.914466i) q^{3} +(5.34392 + 0.942278i) q^{4} +(-3.77614 - 2.83193i) q^{6} +(1.29639 + 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +(1.32750 + 2.69030i) q^{9} +(0.162954 - 0.447712i) q^{11} +(-6.99907 - 6.27290i) q^{12} +(-0.242081 - 2.76700i) q^{13} +(3.30380 + 2.77222i) q^{14} +(13.7126 + 4.99098i) q^{16} +(-3.35386 + 0.898665i) q^{17} +(2.96488 + 7.61884i) q^{18} +(-1.97319 + 1.13922i) q^{19} +(-1.07685 - 2.52077i) q^{21} +(0.548719 - 1.17673i) q^{22} +(0.230790 + 0.329603i) q^{23} +(-11.0569 - 11.8025i) q^{24} -7.56924i q^{26} +(0.507474 - 5.17131i) q^{27} +(6.07248 + 6.07248i) q^{28} +(4.29568 - 3.60450i) q^{29} +(0.908475 - 5.15222i) q^{31} +(19.1162 + 8.91403i) q^{32} +(-0.649118 + 0.509556i) q^{33} +(-9.31839 + 1.64308i) q^{34} +(4.55906 + 15.6276i) q^{36} +(0.387140 + 1.44483i) q^{37} +(-5.62733 + 2.62407i) q^{38} +(-2.17423 + 4.29154i) q^{39} +(-4.99389 + 5.95149i) q^{41} +(-2.32469 - 7.09907i) q^{42} +(0.501128 + 1.07467i) q^{43} +(1.29268 - 2.23899i) q^{44} +(0.548257 + 0.949609i) q^{46} +(-6.94767 + 9.92230i) q^{47} +(-15.6068 - 19.8813i) q^{48} +(-1.53751 - 4.22426i) q^{49} +(5.75523 + 1.74508i) q^{51} +(1.31362 - 15.0147i) q^{52} +(0.274270 - 0.274270i) q^{53} +(2.60592 - 13.9184i) q^{54} +(9.49862 + 11.3200i) q^{56} +(3.94428 + 0.128655i) q^{57} +(12.5179 - 8.76510i) q^{58} +(-3.33385 + 1.21342i) q^{59} +(-1.59716 - 9.05792i) q^{61} +(3.69001 - 13.7713i) q^{62} +(-0.721141 + 4.69272i) q^{63} +(24.5036 + 14.1471i) q^{64} +(-1.88323 + 1.22915i) q^{66} +(-13.1561 + 1.15101i) q^{67} +(-18.7696 + 1.64212i) q^{68} +(-0.0380751 - 0.695886i) q^{69} +(-13.8198 - 7.97886i) q^{71} +(5.47136 + 27.4723i) q^{72} +(-2.07381 + 7.73957i) q^{73} +(0.707832 + 4.01431i) q^{74} +(-11.6180 + 4.22862i) q^{76} +(0.617661 - 0.432491i) q^{77} +(-6.92182 + 11.1341i) q^{78} +(-2.85683 - 3.40464i) q^{79} +(-5.47547 + 7.14278i) q^{81} +(-14.9708 + 14.9708i) q^{82} +(-0.253902 + 2.90211i) q^{83} +(-3.37935 - 14.4855i) q^{84} +(1.10520 + 3.03651i) q^{86} +(-9.61501 + 1.37386i) q^{87} +(2.55168 - 3.64417i) q^{88} +(3.50126 + 6.06435i) q^{89} +(2.19789 - 3.80686i) q^{91} +(0.922748 + 1.97884i) q^{92} +(-6.04787 + 6.74799i) q^{93} +(-21.2179 + 25.2866i) q^{94} +(-19.9678 - 30.5934i) q^{96} +(6.86175 - 3.19969i) q^{97} +(-3.17066 - 11.8331i) q^{98} +(1.42080 - 0.155944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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Database

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