LMFDB - Embedded newform 605.2.m.f.118.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.3
Character	$\chi$	$=$	605.118
Dual form			605.2.m.f.282.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83377 - 0.290440i) q^{2} +(0.700818 - 1.37543i) q^{3} +(1.37624 + 0.447166i) q^{4} +(-1.62810 - 1.53273i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-1.83912 + 0.937080i) q^{7} +(0.914708 + 0.466067i) q^{8} +(0.362685 + 0.499192i) q^{9} +O(q^{10})$	\(q+(-1.83377 - 0.290440i) q^{2} +(0.700818 - 1.37543i) q^{3} +(1.37624 + 0.447166i) q^{4} +(-1.62810 - 1.53273i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-1.83912 + 0.937080i) q^{7} +(0.914708 + 0.466067i) q^{8} +(0.362685 + 0.499192i) q^{9} +(2.54040 + 3.28355i) q^{10} +(1.57954 - 1.57954i) q^{12} +(-0.471357 + 2.97603i) q^{13} +(3.64469 - 1.18423i) q^{14} +(-3.24918 + 1.16518i) q^{15} +(-3.88339 - 2.82145i) q^{16} +(1.07677 + 6.79848i) q^{17} +(-0.520094 - 1.02074i) q^{18} +(-1.26002 - 3.87793i) q^{19} +(-1.55527 - 2.83744i) q^{20} +3.18632i q^{21} +(5.40871 + 5.40871i) q^{23} +(1.28209 - 0.931492i) q^{24} +(0.301449 + 4.99090i) q^{25} +(1.72872 - 5.32045i) q^{26} +(5.51482 - 0.873462i) q^{27} +(-2.95010 + 0.467250i) q^{28} +(1.58644 - 4.88256i) q^{29} +(6.29666 - 1.19298i) q^{30} +(-2.22412 + 1.61592i) q^{31} +(4.84994 + 4.84994i) q^{32} -12.7796i q^{34} +(4.43058 + 1.29322i) q^{35} +(0.275918 + 0.849187i) q^{36} +(-2.17288 - 4.26452i) q^{37} +(1.18427 + 7.47719i) q^{38} +(3.76300 + 2.73398i) q^{39} +(-0.774883 - 2.16081i) q^{40} +(-7.18688 + 2.33516i) q^{41} +(0.925435 - 5.84296i) q^{42} +(2.58034 - 2.58034i) q^{43} +(0.174641 - 1.36864i) q^{45} +(-8.34742 - 11.4892i) q^{46} +(0.394842 + 0.201182i) q^{47} +(-6.60227 + 3.36402i) q^{48} +(-1.61024 + 2.21631i) q^{49} +(0.896772 - 9.23971i) q^{50} +(10.1055 + 3.28347i) q^{51} +(-1.97948 + 3.88495i) q^{52} +(7.23977 + 1.14667i) q^{53} -10.3666 q^{54} -2.11900 q^{56} +(-6.21688 - 0.984657i) q^{57} +(-4.32725 + 8.49271i) q^{58} +(12.3338 + 4.00750i) q^{59} +(-4.99267 + 0.150641i) q^{60} +(3.14797 - 4.33281i) q^{61} +(4.54785 - 2.31725i) q^{62} +(-1.13481 - 0.578212i) q^{63} +(-1.84216 - 2.53551i) q^{64} +(5.32888 - 4.12282i) q^{65} +(-3.40871 + 3.40871i) q^{67} +(-1.55816 + 9.83782i) q^{68} +(11.2299 - 3.64880i) q^{69} +(-7.74905 - 3.65829i) q^{70} +(3.54451 + 2.57524i) q^{71} +(0.0990933 + 0.625651i) q^{72} +(4.08198 + 8.01134i) q^{73} +(2.74597 + 8.45123i) q^{74} +(7.07592 + 3.08309i) q^{75} -5.90039i q^{76} +(-6.10640 - 6.10640i) q^{78} +(10.2736 - 7.46420i) q^{79} +(1.99804 + 10.5458i) q^{80} +(2.09148 - 6.43690i) q^{81} +(13.8573 - 2.19478i) q^{82} +(-1.10302 + 0.174702i) q^{83} +(-1.42481 + 4.38513i) q^{84} +(8.66717 - 12.7191i) q^{85} +(-5.48119 + 3.98231i) q^{86} +(-5.60383 - 5.60383i) q^{87} +13.5666i q^{89} +(-0.717759 + 2.45904i) q^{90} +(-1.92190 - 5.91499i) q^{91} +(5.02507 + 9.86226i) q^{92} +(0.663884 + 4.19160i) q^{93} +(-0.665617 - 0.483599i) q^{94} +(-3.89240 + 8.24495i) q^{95} +(10.0697 - 3.27185i) q^{96} +(-1.31883 + 8.32676i) q^{97} +(3.59651 - 3.59651i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^5	$ 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.83377	−	0.290440i	−1.29667	−	0.205372i	−0.530321	−	0.847797i	$-0.677929\pi$
$2$	−1.83377	−	0.290440i	−1.29667	−	0.205372i	−0.766349	+	0.642425i	$0.777929\pi$
$3$	0.700818	−	1.37543i	0.404618	−	0.794107i	−0.595338	−	0.803475i	$-0.702982\pi$
$3$	0.700818	−	1.37543i	0.404618	−	0.794107i	0.999956	+	0.00936808i	$0.00298200\pi$
$4$	1.37624	+	0.447166i	0.688118	+	0.223583i
$5$	−1.62810	−	1.53273i	−0.728111	−	0.685460i
$5$	−1.62810	−	1.53273i	−0.728111	−	0.685460i
$6$	−1.68462	+	2.31868i	−0.687743	+	0.946597i
$7$	−1.83912	+	0.937080i	−0.695123	+	0.354183i	−0.765588	−	0.643331i	$-0.777552\pi$
$7$	−1.83912	+	0.937080i	−0.695123	+	0.354183i	0.0704646	+	0.997514i	$0.477552\pi$
$8$	0.914708	+	0.466067i	0.323398	+	0.164780i
$9$	0.362685	+	0.499192i	0.120895	+	0.166397i
$10$	2.54040	+	3.28355i	0.803345	+	1.03835i
$11$		0			0
$11$		0			0
$12$	1.57954	−	1.57954i	0.455974	−	0.455974i
$13$	−0.471357	+	2.97603i	−0.130731	+	0.825402i	0.831967	+	0.554825i	$0.187215\pi$
$13$	−0.471357	+	2.97603i	−0.130731	+	0.825402i	−0.962698	+	0.270577i	$0.912785\pi$
$14$	3.64469	−	1.18423i	0.974085	−	0.316499i
$15$	−3.24918	+	1.16518i	−0.838935	+	0.300848i
$16$	−3.88339	−	2.82145i	−0.970848	−	0.705362i
$17$	1.07677	+	6.79848i	0.261156	+	1.64887i	0.674482	+	0.738291i	$0.264367\pi$
$17$	1.07677	+	6.79848i	0.261156	+	1.64887i	−0.413326	+	0.910583i	$0.635633\pi$
$18$	−0.520094	−	1.02074i	−0.122587	−	0.240591i
$19$	−1.26002	−	3.87793i	−0.289068	−	0.889659i	−0.985150	−	0.171697i	$-0.945075\pi$
$19$	−1.26002	−	3.87793i	−0.289068	−	0.889659i	0.696082	−	0.717962i	$-0.254925\pi$
$20$	−1.55527	−	2.83744i	−0.347769	−	0.634471i
$21$			3.18632i			0.695311i
$22$		0			0
$23$	5.40871	+	5.40871i	1.12779	+	1.12779i	0.990535	+	0.137259i	$0.0438294\pi$
$23$	5.40871	+	5.40871i	1.12779	+	1.12779i	0.137259	+	0.990535i	$0.456171\pi$
$24$	1.28209	−	0.931492i	0.261705	−	0.190140i
$25$	0.301449	+	4.99090i	0.0602899	+	0.998181i
$26$	1.72872	−	5.32045i	0.339029	−	1.04343i
$27$	5.51482	−	0.873462i	1.06133	−	0.168098i
$28$	−2.95010	+	0.467250i	−0.557517	+	0.0883020i
$29$	1.58644	−	4.88256i	0.294594	−	0.906668i	−0.688763	−	0.724986i	$-0.741846\pi$
$29$	1.58644	−	4.88256i	0.294594	−	0.906668i	0.983357	−	0.181682i	$-0.0581540\pi$
$30$	6.29666	−	1.19298i	1.14961	−	0.217807i
$31$	−2.22412	+	1.61592i	−0.399464	+	0.290228i	−0.769323	−	0.638860i	$-0.779406\pi$
$31$	−2.22412	+	1.61592i	−0.399464	+	0.290228i	0.369859	+	0.929088i	$0.379406\pi$
$32$	4.84994	+	4.84994i	0.857357	+	0.857357i
$33$		0			0
$34$		−	12.7796i		−	2.19168i
$35$	4.43058	+	1.29322i	0.748905	+	0.218595i
$36$	0.275918	+	0.849187i	0.0459863	+	0.141531i
$37$	−2.17288	−	4.26452i	−0.357220	−	0.701083i	0.640544	−	0.767921i	$-0.278709\pi$
$37$	−2.17288	−	4.26452i	−0.357220	−	0.701083i	−0.997764	+	0.0668384i	$0.978709\pi$
$38$	1.18427	+	7.47719i	0.192114	+	1.21296i
$39$	3.76300	+	2.73398i	0.602562	+	0.437787i
$40$	−0.774883	−	2.16081i	−0.122520	−	0.341654i
$41$	−7.18688	+	2.33516i	−1.12240	+	0.364690i	−0.810684	−	0.585484i	$-0.800904\pi$
$41$	−7.18688	+	2.33516i	−1.12240	+	0.364690i	−0.311718	+	0.950175i	$0.600904\pi$
$42$	0.925435	−	5.84296i	0.142798	−	0.901589i
$43$	2.58034	−	2.58034i	0.393499	−	0.393499i	−0.482434	−	0.875932i	$-0.660247\pi$
$43$	2.58034	−	2.58034i	0.393499	−	0.393499i	0.875932	+	0.482434i	$0.160247\pi$
$44$		0			0
$45$	0.174641	−	1.36864i	0.0260340	−	0.204024i
$46$	−8.34742	−	11.4892i	−1.23076	−	1.69400i
$47$	0.394842	+	0.201182i	0.0575936	+	0.0293454i	0.482550	−	0.875868i	$-0.339711\pi$
$47$	0.394842	+	0.201182i	0.0575936	+	0.0293454i	−0.424957	+	0.905214i	$0.639711\pi$
$48$	−6.60227	+	3.36402i	−0.952955	+	0.485555i
$49$	−1.61024	+	2.21631i	−0.230034	+	0.316615i
$50$	0.896772	−	9.23971i	0.126823	−	1.30669i
$51$	10.1055	+	3.28347i	1.41505	+	0.459778i
$52$	−1.97948	+	3.88495i	−0.274504	+	0.538745i
$53$	7.23977	+	1.14667i	0.994458	+	0.157507i	0.632394	−	0.774647i	$-0.282072\pi$
$53$	7.23977	+	1.14667i	0.994458	+	0.157507i	0.362064	+	0.932153i	$0.382072\pi$
$54$	−10.3666			−1.41071
$55$		0			0
$56$	−2.11900			−0.283164
$57$	−6.21688	−	0.984657i	−0.823446	−	0.130421i
$58$	−4.32725	+	8.49271i	−0.568196	+	1.11515i
$59$	12.3338	+	4.00750i	1.60573	+	0.521732i	0.968515	−	0.248956i	$-0.0800875\pi$
$59$	12.3338	+	4.00750i	1.60573	+	0.521732i	0.637212	+	0.770688i	$0.280087\pi$
$60$	−4.99267	+	0.150641i	−0.644551	+	0.0194476i
$61$	3.14797	−	4.33281i	0.403056	−	0.554759i	−0.558452	−	0.829537i	$-0.688604\pi$
$61$	3.14797	−	4.33281i	0.403056	−	0.554759i	0.961508	+	0.274778i	$0.0886044\pi$
$62$	4.54785	−	2.31725i	0.577578	−	0.294291i
$63$	−1.13481	−	0.578212i	−0.142972	−	0.0728479i
$64$	−1.84216	−	2.53551i	−0.230269	−	0.316939i
$65$	5.32888	−	4.12282i	0.660966	−	0.511373i
$66$		0			0
$67$	−3.40871	+	3.40871i	−0.416441	+	0.416441i	−0.883975	−	0.467534i	$-0.845142\pi$
$67$	−3.40871	+	3.40871i	−0.416441	+	0.416441i	0.467534	+	0.883975i	$0.345142\pi$
$68$	−1.55816	+	9.83782i	−0.188954	+	1.19301i
$69$	11.2299	−	3.64880i	1.35192	−	0.439264i
$70$	−7.74905	−	3.65829i	−0.926189	−	0.437250i
$71$	3.54451	+	2.57524i	0.420656	+	0.305625i	0.777902	−	0.628386i	$-0.216284\pi$
$71$	3.54451	+	2.57524i	0.420656	+	0.305625i	−0.357246	+	0.934011i	$0.616284\pi$
$72$	0.0990933	+	0.625651i	0.0116783	+	0.0737336i
$73$	4.08198	+	8.01134i	0.477760	+	0.937656i	0.996569	+	0.0827663i	$0.0263755\pi$
$73$	4.08198	+	8.01134i	0.477760	+	0.937656i	−0.518809	+	0.854890i	$0.673625\pi$
$74$	2.74597	+	8.45123i	0.319213	+	0.982436i
$75$	7.07592	+	3.08309i	0.817057	+	0.356005i
$76$		−	5.90039i		−	0.676821i
$77$		0			0
$78$	−6.10640	−	6.10640i	−0.691414	−	0.691414i
$79$	10.2736	−	7.46420i	1.15587	−	0.839788i	0.166619	−	0.986021i	$-0.446715\pi$
$79$	10.2736	−	7.46420i	1.15587	−	0.839788i	0.989250	+	0.146234i	$0.0467151\pi$
$80$	1.99804	+	10.5458i	0.223387	+	1.17906i
$81$	2.09148	−	6.43690i	0.232386	−	0.715211i
$82$	13.8573	−	2.19478i	1.53028	−	0.242373i
$83$	−1.10302	+	0.174702i	−0.121073	+	0.0191760i	−0.216677	−	0.976243i	$-0.569522\pi$
$83$	−1.10302	+	0.174702i	−0.121073	+	0.0191760i	0.0956041	+	0.995419i	$0.469522\pi$
$84$	−1.42481	+	4.38513i	−0.155460	+	0.478456i
$85$	8.66717	−	12.7191i	0.940087	−	1.37957i
$86$	−5.48119	+	3.98231i	−0.591051	+	0.429424i
$87$	−5.60383	−	5.60383i	−0.600793	−	0.600793i
$88$		0			0
$89$			13.5666i			1.43806i	0.694981	+	0.719028i	$0.255413\pi$
$89$			13.5666i			1.43806i	−0.694981	+	0.719028i	$0.744587\pi$
$90$	−0.717759	+	2.45904i	−0.0756584	+	0.259206i
$91$	−1.92190	−	5.91499i	−0.201469	−	0.620059i
$92$	5.02507	+	9.86226i	0.523900	+	1.02821i
$93$	0.663884	+	4.19160i	0.0688415	+	0.434648i
$94$	−0.665617	−	0.483599i	−0.0686532	−	0.0498795i
$95$	−3.89240	+	8.24495i	−0.399352	+	0.845914i
$96$	10.0697	−	3.27185i	1.02774	−	0.333931i
$97$	−1.31883	+	8.32676i	−0.133907	+	0.845454i	0.825700	+	0.564110i	$0.190780\pi$
$97$	−1.31883	+	8.32676i	−0.133907	+	0.845454i	−0.959607	+	0.281345i	$0.909220\pi$
$98$	3.59651	−	3.59651i	0.363303	−	0.363303i
$99$		0			0
$100$	−1.81690	+	7.00346i	−0.181690	+	0.700346i
$101$	0.876896	+	1.20694i	0.0872544	+	0.120095i	0.850413	−	0.526116i	$-0.176352\pi$
$101$	0.876896	+	1.20694i	0.0872544	+	0.120095i	−0.763158	+	0.646212i	$0.776352\pi$
$102$	−17.5775	−	8.95617i	−1.74043	−	0.886793i
$103$	−6.31735	+	3.21885i	−0.622467	+	0.317163i	−0.736627	−	0.676300i	$-0.763582\pi$
$103$	−6.31735	+	3.21885i	−0.622467	+	0.317163i	0.114160	+	0.993462i	$0.463582\pi$
$104$	−1.81818	+	2.50251i	−0.178288	+	0.245392i
$105$	4.88378	−	5.18766i	0.476608	−	0.506263i
$106$	−12.9430	−	4.20544i	−1.25714	−	0.408468i
$107$	−6.88905	+	13.5205i	−0.665990	+	1.30708i	0.272628	+	0.962119i	$0.412107\pi$
$107$	−6.88905	+	13.5205i	−0.665990	+	1.30708i	−0.938618	+	0.344959i	$0.887893\pi$
$108$	7.98028	+	1.26395i	0.767903	+	0.121624i
$109$	−1.85686			−0.177855			−0.0889275	−	0.996038i	$-0.528344\pi$
$109$	−1.85686			−0.177855			−0.0889275	+	0.996038i	$0.528344\pi$
$110$		0			0
$111$	−7.38836			−0.701272
$112$	9.78596	+	1.54994i	0.924687	+	0.146456i
$113$	3.81054	−	7.47860i	0.358465	−	0.703528i	−0.639397	−	0.768877i	$-0.720816\pi$
$113$	3.81054	−	7.47860i	0.358465	−	0.703528i	0.997862	+	0.0653490i	$0.0208161\pi$
$114$	11.1143	+	3.61127i	1.04095	+	0.338226i
$115$	−0.515829	−	17.0961i	−0.0481013	−	1.59422i
$116$	4.36663	−	6.01015i	0.405432	−	0.558029i
$117$	−1.65657	+	0.844062i	−0.153149	+	0.0780336i
$118$	−21.4534	−	10.9311i	−1.97495	−	1.00629i
$119$	−8.35105	−	11.4942i	−0.765539	−	1.05367i
$120$	−3.51510	−	0.448535i	−0.320884	−	0.0409455i
$121$		0			0
$122$	−7.03106	+	7.03106i	−0.636563	+	0.636563i
$123$	−1.82484	+	11.5216i	−0.164540	+	1.03887i
$124$	−3.78350	+	1.22933i	−0.339769	+	0.110398i
$125$	7.15894	−	8.58776i	0.640315	−	0.768112i
$126$	1.91303	+	1.38990i	0.170427	+	0.123822i
$127$	0.207561	+	1.31049i	0.0184181	+	0.116287i	0.995184	−	0.0980197i	$-0.0312508\pi$
$127$	0.207561	+	1.31049i	0.0184181	+	0.116287i	−0.976766	+	0.214307i	$0.931251\pi$
$128$	−3.58604	−	7.03800i	−0.316964	−	0.622077i
$129$	−1.74074	−	5.35744i	−0.153263	−	0.471696i
$130$	−10.9694	+	6.01258i	−0.962077	+	0.527338i
$131$			9.41359i			0.822469i	0.911530	+	0.411235i	$0.134902\pi$
$131$			9.41359i			0.822469i	−0.911530	+	0.411235i	$0.865098\pi$
$132$		0			0
$133$	5.95126	+	5.95126i	0.516040	+	0.516040i
$134$	7.24082	−	5.26076i	0.625511	−	0.454461i
$135$	−10.3175	−	7.03067i	−0.887988	−	0.605104i
$136$	−2.18362	+	6.72048i	−0.187243	+	0.576276i
$137$	−12.0534	+	1.90908i	−1.02979	+	0.163103i	−0.648393	−	0.761306i	$-0.724559\pi$
$137$	−12.0534	+	1.90908i	−1.02979	+	0.163103i	−0.381402	+	0.924409i	$0.624559\pi$
$138$	−21.6527	+	3.42945i	−1.84320	+	0.291934i
$139$	−2.16939	+	6.67668i	−0.184005	+	0.566309i	−0.999930	−	0.0118491i	$-0.996228\pi$
$139$	−2.16939	+	6.67668i	−0.184005	+	0.566309i	0.815925	+	0.578158i	$0.196228\pi$
$140$	5.51924	+	3.76099i	0.466461	+	0.317862i
$141$	0.553425	−	0.402087i	0.0466068	−	0.0338618i
$142$	−5.75186	−	5.75186i	−0.482686	−	0.482686i
$143$		0			0
$144$		−	2.96186i		−	0.246821i
$145$	−10.0666	+	5.51772i	−0.835982	+	0.458222i
$146$	−5.15859	−	15.8765i	−0.426928	−	1.31395i
$147$	1.91990	+	3.76801i	0.158350	+	0.310780i
$148$	−1.08345	−	6.84063i	−0.0890590	−	0.562296i
$149$	−1.08836	−	0.790739i	−0.0891618	−	0.0647798i	0.542311	−	0.840178i	$-0.317549\pi$
$149$	−1.08836	−	0.790739i	−0.0891618	−	0.0647798i	−0.631473	+	0.775398i	$0.717549\pi$
$150$	−12.0801	−	7.70881i	−0.986339	−	0.629422i
$151$	−2.80475	+	0.911319i	−0.228247	+	0.0741621i	−0.420908	−	0.907103i	$-0.638288\pi$
$151$	−2.80475	+	0.911319i	−0.228247	+	0.0741621i	0.192660	+	0.981265i	$0.438288\pi$
$152$	0.654829	−	4.13443i	0.0531137	−	0.335346i
$153$	−3.00322	+	3.00322i	−0.242796	+	0.242796i
$154$		0			0
$155$	6.09788	+	0.778103i	0.489793	+	0.0624987i
$156$	3.95623	+	5.44528i	0.316752	+	0.435972i
$157$	−2.20759	−	1.12482i	−0.176185	−	0.0897705i	0.363674	−	0.931526i	$-0.381522\pi$
$157$	−2.20759	−	1.12482i	−0.176185	−	0.0897705i	−0.539858	+	0.841756i	$0.681522\pi$
$158$	−21.0073	+	10.7037i	−1.67125	+	0.851544i
$159$	6.65093	−	9.15421i	0.527453	−	0.725976i
$160$	−0.462539	−	15.3299i	−0.0365670	−	1.21193i
$161$	−15.0157	−	4.87889i	−1.18340	−	0.384511i
$162$	−5.70482	+	11.1963i	−0.448213	+	0.879667i
$163$	−9.43258	−	1.49397i	−0.738816	−	0.117017i	−0.224327	−	0.974514i	$-0.572018\pi$
$163$	−9.43258	−	1.49397i	−0.738816	−	0.117017i	−0.514489	+	0.857497i	$0.672018\pi$
$164$	−10.9350			−0.853884
$165$		0			0
$166$	2.07343			0.160929
$167$	7.57923	+	1.20043i	0.586498	+	0.0928922i	0.442629	−	0.896705i	$-0.354046\pi$
$167$	7.57923	+	1.20043i	0.586498	+	0.0928922i	0.143869	+	0.989597i	$0.454046\pi$
$168$	−1.48504	+	2.91455i	−0.114573	+	0.224862i
$169$	3.72916	+	1.21168i	0.286859	+	0.0932060i
$170$	−19.5877	+	20.8065i	−1.50231	+	1.59579i
$171$	1.47885	−	2.03546i	0.113090	−	0.155655i
$172$	4.70501	−	2.39732i	0.358753	−	0.182794i
$173$	12.2013	+	6.21685i	0.927644	+	0.472658i	0.851451	−	0.524435i	$-0.175723\pi$
$173$	12.2013	+	6.21685i	0.927644	+	0.472658i	0.0761935	+	0.997093i	$0.475723\pi$
$174$	8.64854	+	11.9037i	0.655644	+	0.902417i
$175$	−5.23128	−	8.89641i	−0.395448	−	0.672505i
$176$		0			0
$177$	14.1558	−	14.1558i	1.06402	−	1.06402i
$178$	3.94029	−	24.8780i	0.295337	−	1.86468i
$179$	−13.2716	+	4.31220i	−0.991966	+	0.322309i	−0.759651	−	0.650331i	$-0.774630\pi$
$179$	−13.2716	+	4.31220i	−0.991966	+	0.322309i	−0.232315	+	0.972641i	$0.574630\pi$
$180$	0.852356	−	1.80547i	0.0635309	−	0.134572i
$181$	−16.0147	−	11.6354i	−1.19037	−	0.864852i	−0.197063	−	0.980391i	$-0.563140\pi$
$181$	−16.0147	−	11.6354i	−1.19037	−	0.864852i	−0.993303	+	0.115539i	$0.963140\pi$
$182$	1.80636	+	11.4049i	0.133896	+	0.845388i
$183$	−3.75333	−	7.36633i	−0.277454	−	0.544535i
$184$	2.42657	+	7.46822i	0.178889	+	0.550564i
$185$	−2.99870	+	10.2735i	−0.220469	+	0.755325i
$186$		−	7.87924i		−	0.577734i
$187$		0			0
$188$	0.453434	+	0.453434i	0.0330701	+	0.0330701i
$189$	−9.32394	+	6.77424i	−0.678217	+	0.492753i
$190$	9.53243	−	13.9888i	0.691555	−	1.01486i
$191$	−0.169695	+	0.522269i	−0.0122787	+	0.0377900i	−0.957008	−	0.290061i	$-0.906324\pi$
$191$	−0.169695	+	0.522269i	−0.0122787	+	0.0377900i	0.944729	+	0.327851i	$0.106324\pi$
$192$	−4.77844	+	0.756831i	−0.344854	+	0.0546196i
$193$	−4.99642	+	0.791355i	−0.359650	+	0.0569630i	−0.333645	−	0.942699i	$-0.608279\pi$
$193$	−4.99642	+	0.791355i	−0.359650	+	0.0569630i	−0.0260052	+	0.999662i	$0.508279\pi$
$194$	4.83685	−	14.8863i	0.347266	−	1.06877i
$195$	−1.93609	−	10.2189i	−0.138646	−	0.731789i
$196$	−3.20713	+	2.33012i	−0.229081	+	0.166437i
$197$	−5.33112	−	5.33112i	−0.379827	−	0.379827i	0.491213	−	0.871040i	$-0.336554\pi$
$197$	−5.33112	−	5.33112i	−0.379827	−	0.379827i	−0.871040	+	0.491213i	$0.836554\pi$
$198$		0			0
$199$		−	5.88702i		−	0.417320i	−0.977988	−	0.208660i	$-0.933090\pi$
$199$		−	5.88702i		−	0.417320i	0.977988	−	0.208660i	$-0.0669102\pi$
$200$	−2.05036	+	4.70572i	−0.144982	+	0.332744i
$201$	2.29957	+	7.07735i	0.162199	+	0.499198i
$202$	−1.25748	−	2.46794i	−0.0884759	−	0.173644i
$203$	1.65769	+	10.4662i	0.116347	+	0.734586i
$204$	12.4393	+	9.03767i	0.870924	+	0.632763i
$205$	15.2802	+	7.21369i	1.06721	+	0.503826i
$206$	12.5194	−	4.06781i	0.872270	−	0.283418i
$207$	−0.738332	+	4.66164i	−0.0513176	+	0.324007i
$208$	10.2272	−	10.2272i	0.709127	−	0.709127i
$209$		0			0
$210$	−10.4624	+	8.09451i	−0.721975	+	0.558574i
$211$	8.91493	+	12.2703i	0.613729	+	0.844725i	0.996878	−	0.0789613i	$-0.0251604\pi$
$211$	8.91493	+	12.2703i	0.613729	+	0.844725i	−0.383149	+	0.923687i	$0.625160\pi$
$212$	9.45088	+	4.81547i	0.649089	+	0.330728i
$213$	6.02613	−	3.07047i	0.412904	−	0.210385i
$214$	16.5598	−	22.7926i	1.13201	−	1.55807i
$215$	−8.15605	+	0.246087i	−0.556238	+	0.0167830i
$216$	5.45154	+	1.77131i	0.370931	+	0.120523i
$217$	2.57619	−	5.05606i	0.174883	−	0.343227i
$218$	3.40505	+	0.539307i	0.230619	+	0.0365265i
$219$	13.8798			0.937910
$220$		0			0
$221$	−20.7400			−1.39513
$222$	13.5485	+	2.14588i	0.909319	+	0.144022i
$223$	−1.36205	+	2.67317i	−0.0912095	+	0.179009i	−0.932104	−	0.362190i	$-0.882029\pi$
$223$	−1.36205	+	2.67317i	−0.0912095	+	0.179009i	0.840895	+	0.541198i	$0.182029\pi$
$224$	−13.4644	−	4.37486i	−0.899630	−	0.292308i
$225$	−2.38209	+	1.96061i	−0.158806	+	0.130707i
$226$	−9.15973	+	12.6073i	−0.609296	+	0.838624i
$227$	0.668764	−	0.340752i	0.0443874	−	0.0226165i	−0.431656	−	0.902038i	$-0.642071\pi$
$227$	0.668764	−	0.340752i	0.0443874	−	0.0226165i	0.476043	+	0.879422i	$0.342071\pi$
$228$	−8.11560	−	4.13510i	−0.537468	−	0.273854i
$229$	−4.74155	−	6.52618i	−0.313330	−	0.431262i	0.623086	−	0.782153i	$-0.285879\pi$
$229$	−4.74155	−	6.52618i	−0.313330	−	0.431262i	−0.936416	+	0.350891i	$0.885879\pi$
$230$	−4.01948	+	31.5000i	−0.265037	+	2.07705i
$231$		0			0
$232$	3.72673	−	3.72673i	0.244672	−	0.244672i
$233$	0.261825	−	1.65310i	0.0171527	−	0.108298i	−0.977627	−	0.210348i	$-0.932540\pi$
$233$	0.261825	−	1.65310i	0.0171527	−	0.108298i	0.994779	+	0.102050i	$0.0325402\pi$
$234$	3.28291	−	1.06668i	0.214610	−	0.0697311i
$235$	−0.334486	−	0.932734i	−0.0218194	−	0.0608448i
$236$	15.1822	+	11.0305i	0.988280	+	0.718027i
$237$	−3.06659	−	19.3617i	−0.199196	−	1.25768i
$238$	11.9755	+	23.5032i	0.776256	+	1.52349i
$239$	5.09940	+	15.6943i	0.329853	+	1.01518i	0.969202	+	0.246266i	$0.0792037\pi$
$239$	5.09940	+	15.6943i	0.329853	+	1.01518i	−0.639350	+	0.768916i	$0.720796\pi$
$240$	15.9053	+	4.64254i	1.02669	+	0.299675i
$241$			21.2562i			1.36923i	0.728903	+	0.684617i	$0.240030\pi$
$241$			21.2562i			1.36923i	−0.728903	+	0.684617i	$0.759970\pi$
$242$		0			0
$243$	4.45674	+	4.45674i	0.285900	+	0.285900i
$244$	6.26983	−	4.55530i	0.401385	−	0.291623i
$245$	6.01865	−	1.14031i	0.384517	−	0.0728515i
$246$	6.69267	−	20.5979i	0.426709	−	1.31328i
$247$	12.1348	−	1.92196i	0.772116	−	0.122291i
$248$	−2.78755	+	0.441504i	−0.177010	+	0.0280356i
$249$	−0.532729	+	1.63957i	−0.0337603	+	0.103904i
$250$	−15.6221	+	13.6687i	−0.988026	+	0.864485i
$251$	21.0751	−	15.3119i	1.33025	−	0.966481i	0.330505	−	0.943804i	$-0.392781\pi$
$251$	21.0751	−	15.3119i	1.33025	−	0.966481i	0.999743	−	0.0226769i	$-0.00721890\pi$
$252$	−1.30320	−	1.30320i	−0.0820941	−	0.0820941i
$253$		0			0
$254$		−	2.46342i		−	0.154568i
$255$	−11.4201	−	20.8349i	−0.715154	−	1.30473i
$256$	6.46880	+	19.9089i	0.404300	+	1.24431i
$257$	1.11540	+	2.18909i	0.0695766	+	0.136552i	0.923175	−	0.384380i	$-0.125585\pi$
$257$	1.11540	+	2.18909i	0.0695766	+	0.136552i	−0.853598	+	0.520932i	$0.825585\pi$
$258$	1.63609	+	10.3299i	0.101859	+	0.643111i
$259$	7.99240	+	5.80682i	0.496623	+	0.360818i
$260$	9.17739	−	3.29108i	0.569158	−	0.204104i
$261$	3.01271	−	0.978890i	0.186482	−	0.0605917i
$262$	2.73409	−	17.2623i	0.168912	−	1.06647i
$263$	14.2199	−	14.2199i	0.876839	−	0.876839i	−0.116367	−	0.993206i	$-0.537125\pi$
$263$	14.2199	−	14.2199i	0.876839	−	0.876839i	0.993206	+	0.116367i	$0.0371250\pi$
$264$		0			0
$265$	−10.0296	−	12.9635i	−0.616111	−	0.796344i
$266$	−9.18475	−	12.6417i	−0.563153	−	0.775113i
$267$	18.6599	+	9.50772i	1.14197	+	0.581863i
$268$	−6.21546	+	3.16693i	−0.379670	+	0.193451i
$269$	−1.31547	+	1.81059i	−0.0802055	+	0.110393i	−0.847235	−	0.531219i	$-0.821734\pi$
$269$	−1.31547	+	1.81059i	−0.0802055	+	0.110393i	0.767029	+	0.641612i	$0.221734\pi$
$270$	16.8779	+	15.8892i	1.02716	+	0.966988i
$271$	2.81475	+	0.914566i	0.170984	+	0.0555559i	0.393258	−	0.919428i	$-0.371348\pi$
$271$	2.81475	+	0.914566i	0.170984	+	0.0555559i	−0.222274	+	0.974984i	$0.571348\pi$
$272$	15.0000	−	29.4392i	0.909511	−	1.78502i
$273$	−9.48257	−	1.50189i	−0.573911	−	0.0908986i
$274$	22.6577			1.36880
$275$		0			0
$276$	17.0866			1.02849
$277$	−27.3016	−	4.32414i	−1.64039	−	0.259813i	−0.733040	−	0.680185i	$-0.761899\pi$
$277$	−27.3016	−	4.32414i	−1.64039	−	0.259813i	−0.907352	+	0.420373i	$0.861899\pi$
$278$	5.91733	−	11.6134i	0.354898	−	0.696526i
$279$	−1.61331	−	0.524196i	−0.0965863	−	0.0313828i
$280$	3.44996	+	3.24787i	0.206175	+	0.194097i
$281$	17.4272	−	23.9864i	1.03962	−	1.43091i	0.142142	−	0.989846i	$-0.454601\pi$
$281$	17.4272	−	23.9864i	1.03962	−	1.43091i	0.897475	−	0.441064i	$-0.145399\pi$
$282$	−1.13164	+	0.576597i	−0.0673879	+	0.0343359i
$283$	−8.14498	−	4.15007i	−0.484169	−	0.246696i	0.194828	−	0.980837i	$-0.437585\pi$
$283$	−8.14498	−	4.15007i	−0.484169	−	0.246696i	−0.678997	+	0.734141i	$0.737585\pi$
$284$	3.72653	+	5.12913i	0.221129	+	0.304358i
$285$	8.61251	+	11.1320i	0.510161	+	0.659400i
$286$		0			0
$287$	11.0293	−	11.0293i	0.651040	−	0.651040i
$288$	−0.662056	+	4.18006i	−0.0390120	+	0.246312i
$289$	−28.8920	+	9.38757i	−1.69953	+	0.552210i
$290$	20.0623	−	7.19449i	1.17810	−	0.422475i
$291$	10.5286	+	7.64951i	0.617200	+	0.448422i
$292$	2.03537	+	12.8508i	0.119111	+	0.752038i
$293$	0.800320	+	1.57072i	0.0467552	+	0.0917622i	0.913202	−	0.407507i	$-0.133602\pi$
$293$	0.800320	+	1.57072i	0.0467552	+	0.0917622i	−0.866447	+	0.499269i	$0.833602\pi$
$294$	−2.42626	−	7.46727i	−0.141502	−	0.435500i
$295$	−13.9383	−	25.4291i	−0.811520	−	1.48054i
$296$		−	4.91350i		−	0.285591i
$297$		0			0
$298$	1.76613	+	1.76613i	0.102309	+	0.102309i
$299$	−18.6459	+	13.5471i	−1.07832	+	0.783446i
$300$	8.35948	+	7.40718i	0.482635	+	0.427654i
$301$	−2.32758	+	7.16356i	−0.134160	+	0.412901i
$302$	5.40795	−	0.856535i	0.311192	−	0.0492880i
$303$	2.27461	−	0.360264i	0.130673	−	0.0206966i
$304$	−6.04825	+	18.6146i	−0.346891	+	1.06762i
$305$	−11.7663	+	2.22926i	−0.673734	+	0.127647i
$306$	6.37947	−	4.63496i	0.364690	−	0.264963i
$307$	−10.6721	−	10.6721i	−0.609087	−	0.609087i	0.333621	−	0.942707i	$-0.391730\pi$
$307$	−10.6721	−	10.6721i	−0.609087	−	0.609087i	−0.942707	+	0.333621i	$0.891730\pi$
$308$		0			0
$309$			10.9449i			0.622635i
$310$	−10.9561	−	3.19793i	−0.622265	−	0.181630i
$311$	8.43735	+	25.9675i	0.478438	+	1.47248i	0.841264	+	0.540624i	$0.181812\pi$
$311$	8.43735	+	25.9675i	0.478438	+	1.47248i	−0.362826	+	0.931857i	$0.618188\pi$
$312$	2.16783	+	4.25460i	0.122729	+	0.240869i
$313$	4.19572	+	26.4908i	0.237156	+	1.49735i	0.762796	+	0.646639i	$0.223826\pi$
$313$	4.19572	+	26.4908i	0.237156	+	1.49735i	−0.525640	+	0.850707i	$0.676174\pi$
$314$	3.72151	+	2.70383i	0.210017	+	0.152586i
$315$	0.961336	+	2.68074i	0.0541651	+	0.151043i
$316$	17.4766	−	5.67850i	0.983137	−	0.319441i
$317$	−0.307559	+	1.94185i	−0.0172742	+	0.109065i	−0.994819	−	0.101663i	$-0.967584\pi$
$317$	−0.307559	+	1.94185i	−0.0172742	+	0.109065i	0.977545	+	0.210728i	$0.0675836\pi$
$318$	−14.8550	+	14.8550i	−0.833027	+	0.833027i
$319$		0			0
$320$	−0.887041	+	6.95161i	−0.0495871	+	0.388607i
$321$	13.7686	+	18.9509i	0.768489	+	1.05773i
$322$	26.1183	+	13.3079i	1.45551	+	0.741621i
$323$	25.0073	−	12.7419i	1.39144	−	0.708976i
$324$	5.75673	−	7.92346i	0.319819	−	0.440192i
$325$	−14.9952	−	1.45537i	−0.831782	−	0.0807296i
$326$	16.8632	+	5.47920i	0.933969	+	0.303465i
$327$	−1.30132	+	2.55399i	−0.0719633	+	0.141236i
$328$	−7.66223	−	1.21358i	−0.423076	−	0.0670087i
$329$	−0.914687			−0.0504283
$330$		0			0
$331$	24.3840			1.34027			0.670133	−	0.742241i	$-0.266237\pi$
$331$	24.3840			1.34027			0.670133	+	0.742241i	$0.266237\pi$
$332$	−1.59614	−	0.252804i	−0.0875997	−	0.0138744i
$333$	1.34075	−	2.63136i	0.0734724	−	0.144198i
$334$	−13.5499	−	4.40263i	−0.741417	−	0.240901i
$335$	10.7744	−	0.325089i	0.588668	−	0.0177615i
$336$	8.99003	−	12.3737i	0.490446	−	0.675041i
$337$	7.18976	−	3.66337i	0.391651	−	0.199556i	−0.247065	−	0.968999i	$-0.579466\pi$
$337$	7.18976	−	3.66337i	0.391651	−	0.199556i	0.638716	+	0.769443i	$0.279466\pi$
$338$	−6.48650	−	3.30504i	−0.352819	−	0.179770i
$339$	−7.61582	−	10.4823i	−0.413635	−	0.569319i
$340$	17.6156	−	13.6288i	0.955341	−	0.739123i
$341$		0			0
$342$	−3.30304	+	3.30304i	−0.178608	+	0.178608i
$343$	3.14485	−	19.8558i	0.169806	−	1.07211i
$344$	3.56287	−	1.15765i	0.192097	−	0.0624162i
$345$	−23.8760	−	11.2718i	−1.28544	−	0.606851i
$346$	−20.5686	−	14.9440i	−1.10578	−	0.803394i
$347$	4.53644	+	28.6419i	0.243529	+	1.53758i	0.741837	+	0.670580i	$0.233955\pi$
$347$	4.53644	+	28.6419i	0.243529	+	1.53758i	−0.498308	+	0.867000i	$0.666045\pi$
$348$	−5.20635	−	10.2180i	−0.279090	−	0.547744i
$349$	1.06444	+	3.27600i	0.0569780	+	0.175360i	0.975495	−	0.220021i	$-0.0706125\pi$
$349$	1.06444	+	3.27600i	0.0569780	+	0.175360i	−0.918517	+	0.395381i	$0.870613\pi$
$350$	7.00908	+	17.8333i	0.374651	+	0.953231i
$351$			16.8240i			0.897998i
$352$		0			0
$353$	−7.44497	−	7.44497i	−0.396256	−	0.396256i	0.480654	−	0.876910i	$-0.340399\pi$
$353$	−7.44497	−	7.44497i	−0.396256	−	0.396256i	−0.876910	+	0.480654i	$0.840399\pi$
$354$	−30.0699	+	21.8471i	−1.59820	+	1.16116i
$355$	−1.82368	−	9.62556i	−0.0967909	−	0.510872i
$356$	−6.06652	+	18.6708i	−0.321525	+	0.989553i
$357$	−21.6621	+	3.43094i	−1.14648	+	0.181585i
$358$	25.5895	−	4.05297i	1.35245	−	0.214206i
$359$	4.66630	−	14.3614i	0.246278	−	0.757965i	−0.749146	−	0.662405i	$-0.769536\pi$
$359$	4.66630	−	14.3614i	0.246278	−	0.757965i	0.995424	−	0.0955602i	$-0.0304642\pi$
$360$	0.797622	−	1.17051i	0.0420384	−	0.0616912i
$361$	1.92061	−	1.39540i	0.101085	−	0.0734423i
$362$	25.9879	+	25.9879i	1.36590	+	1.36590i
$363$		0			0
$364$		−	8.99983i		−	0.471719i
$365$	5.63336	−	19.2999i	0.294864	−	1.01020i
$366$	4.74326	+	14.5983i	0.247934	+	0.763063i
$367$	15.1871	+	29.8064i	0.792762	+	1.55588i	0.830777	+	0.556605i	$0.187896\pi$
$367$	15.1871	+	29.8064i	0.792762	+	1.55588i	−0.0380157	+	0.999277i	$0.512104\pi$
$368$	−5.74374	−	36.2646i	−0.299413	−	1.89042i
$369$	−3.77226	−	2.74071i	−0.196376	−	0.142676i
$370$	8.48277	−	17.9683i	0.440998	−	0.934130i
$371$	−14.3893	+	4.67538i	−0.747058	+	0.242734i
$372$	−0.960680	+	6.06550i	−0.0498090	+	0.314481i
$373$	−0.821903	+	0.821903i	−0.0425565	+	0.0425565i	−0.728065	−	0.685508i	$-0.759580\pi$
$373$	−0.821903	+	0.821903i	−0.0425565	+	0.0425565i	0.685508	+	0.728065i	$0.259580\pi$
$374$		0			0
$375$	−6.79477	−	15.8651i	−0.350881	−	0.819271i
$376$	0.267401	+	0.368046i	0.0137902	+	0.0189805i
$377$	13.7829	+	7.02271i	0.709853	+	0.361688i
$378$	19.0654	−	9.71433i	0.980621	−	0.499651i
$379$	−7.02572	+	9.67008i	−0.360887	+	0.496719i	−0.950396	−	0.311044i	$-0.899321\pi$
$379$	−7.02572	+	9.67008i	−0.360887	+	0.496719i	0.589508	+	0.807762i	$0.299321\pi$
$380$	−9.04373	+	9.60645i	−0.463934	+	0.492801i
$381$	1.94795	+	0.632928i	0.0997966	+	0.0324259i
$382$	0.462870	−	0.908433i	0.0236825	−	0.0464795i
$383$	19.3881	+	3.07077i	0.990684	+	0.156909i	0.630681	−	0.776042i	$-0.282776\pi$
$383$	19.3881	+	3.07077i	0.990684	+	0.156909i	0.360003	+	0.932951i	$0.382776\pi$
$384$	−12.1935			−0.622245
$385$		0			0
$386$	9.39212			0.478046
$387$	2.22394	+	0.352237i	0.113049	+	0.0179052i
$388$	−5.53847	+	10.8699i	−0.281173	+	0.551833i
$389$	−33.6777	−	10.9425i	−1.70753	−	0.554809i	−0.717607	−	0.696448i	$-0.754763\pi$
$389$	−33.6777	−	10.9425i	−1.70753	−	0.554809i	−0.989918	+	0.141639i	$0.954763\pi$
$390$	0.582368	+	19.3014i	0.0294894	+	0.977362i
$391$	−30.9471	+	42.5950i	−1.56506	+	2.15412i
$392$	−2.50585	+	1.27679i	−0.126564	+	0.0644878i
$393$	12.9478	+	6.59722i	0.653129	+	0.332786i
$394$	8.22766	+	11.3244i	0.414504	+	0.570515i
$395$	−28.1671	−	3.59419i	−1.41724	−	0.180843i
$396$		0			0
$397$	−13.8345	+	13.8345i	−0.694333	+	0.694333i	−0.963182	−	0.268849i	$-0.913357\pi$
$397$	−13.8345	+	13.8345i	−0.694333	+	0.694333i	0.268849	+	0.963182i	$0.413357\pi$
$398$	−1.70983	+	10.7954i	−0.0857059	+	0.541126i
$399$	12.3563	−	4.01481i	0.618590	−	0.200992i
$400$	12.9109	−	20.2322i	0.645547	−	1.01161i
$401$	−5.37959	−	3.90850i	−0.268644	−	0.195181i	0.445305	−	0.895379i	$-0.353095\pi$
$401$	−5.37959	−	3.90850i	−0.268644	−	0.195181i	−0.713949	+	0.700198i	$0.753095\pi$
$402$	−2.16133	−	13.6461i	−0.107797	−	0.680606i
$403$	−3.76067	−	7.38073i	−0.187332	−	0.367660i
$404$	0.667111	+	2.05316i	0.0331900	+	0.102148i
$405$	−13.2712	+	7.27427i	−0.659451	+	0.361461i
$406$		−	19.6741i		−	0.976411i
$407$		0			0
$408$	7.71325	+	7.71325i	0.381863	+	0.381863i
$409$	23.6337	−	17.1709i	1.16861	−	0.849047i	0.177771	−	0.984072i	$-0.443111\pi$
$409$	23.6337	−	17.1709i	1.16861	−	0.849047i	0.990842	+	0.135025i	$0.0431115\pi$
$410$	−25.9251	−	17.6662i	−1.28035	−	0.872472i
$411$	−5.82146	+	17.9166i	−0.287152	+	0.883762i
$412$	−10.1335	+	1.60499i	−0.499243	+	0.0790723i
$413$	−26.4388	+	4.18749i	−1.30097	+	0.206053i
$414$	2.70786	−	8.33393i	0.133084	−	0.409591i
$415$	2.06361	+	1.40621i	0.101299	+	0.0690281i
$416$	−16.7196	+	12.1475i	−0.819747	+	0.595581i
$417$	7.66299	+	7.66299i	0.375258	+	0.375258i
$418$		0			0
$419$		−	19.2755i		−	0.941672i	−0.882221	−	0.470836i	$-0.843952\pi$
$419$		−	19.2755i		−	0.941672i	0.882221	−	0.470836i	$-0.156048\pi$
$420$	9.04098	−	4.95558i	0.441155	−	0.241808i
$421$	−11.2868	−	34.7372i	−0.550085	−	1.69299i	−0.708582	−	0.705629i	$-0.750665\pi$
$421$	−11.2868	−	34.7372i	−0.550085	−	1.69299i	0.158497	−	0.987359i	$-0.449335\pi$
$422$	−12.7841	−	25.0902i	−0.622320	−	1.22137i
$423$	0.0427745	+	0.270068i	0.00207977	+	0.0131311i
$424$	6.08785	+	4.42308i	0.295652	+	0.214804i
$425$	−33.6060	+	7.42347i	−1.63013	+	0.360091i
$426$	−11.9423	+	3.88029i	−0.578607	+	0.188001i
$427$	−1.72931	+	10.9185i	−0.0836874	+	0.528381i
$428$	−15.5269	+	15.5269i	−0.750520	+	0.750520i
$429$		0			0
$430$	15.0278	+	1.91758i	0.724704	+	0.0924738i
$431$	7.12379	+	9.80505i	0.343141	+	0.472293i	0.945355	−	0.326041i	$-0.105715\pi$
$431$	7.12379	+	9.80505i	0.343141	+	0.472293i	−0.602215	+	0.798334i	$0.705715\pi$
$432$	−23.8806	−	12.1678i	−1.14896	−	0.585423i
$433$	4.21842	−	2.14939i	0.202725	−	0.103293i	−0.349681	−	0.936869i	$-0.613710\pi$
$433$	4.21842	−	2.14939i	0.202725	−	0.103293i	0.552406	+	0.833576i	$0.313710\pi$
$434$	−6.19262	+	8.52340i	−0.297255	+	0.409136i
$435$	0.534437	+	17.7128i	0.0256243	+	0.849264i
$436$	−2.55548	−	0.830326i	−0.122385	−	0.0397654i
$437$	14.1596	−	27.7897i	0.677343	−	1.32936i
$438$	−25.4523	−	4.03125i	−1.21616	−	0.192621i
$439$	26.1692			1.24899			0.624494	−	0.781029i	$-0.285305\pi$
$439$	26.1692			1.24899			0.624494	+	0.781029i	$0.285305\pi$
$440$		0			0
$441$	−1.69037			−0.0804939
$442$	38.0324	+	6.02374i	1.80902	+	0.286520i
$443$	12.9785	−	25.4718i	0.616629	−	1.21020i	−0.345708	−	0.938342i	$-0.612361\pi$
$443$	12.9785	−	25.4718i	0.616629	−	1.21020i	0.962337	−	0.271860i	$-0.0876388\pi$
$444$	−10.1681	−	3.30383i	−0.482558	−	0.156793i
$445$	20.7940	−	22.0878i	0.985729	−	1.04706i
$446$	3.27408	−	4.50638i	0.155032	−	0.213383i
$447$	−1.85035	+	0.942801i	−0.0875186	+	0.0445929i
$448$	5.76393	+	2.93687i	0.272320	+	0.138754i
$449$	2.78863	+	3.83822i	0.131603	+	0.181137i	0.869733	−	0.493522i	$-0.164291\pi$
$449$	2.78863	+	3.83822i	0.131603	+	0.181137i	−0.738130	+	0.674659i	$0.764291\pi$
$450$	4.93764	−	2.90344i	0.232763	−	0.136869i
$451$		0			0
$452$	8.58838	−	8.58838i	0.403963	−	0.403963i
$453$	−0.712163	+	4.49642i	−0.0334603	+	0.211260i
$454$	−1.32533	+	0.430625i	−0.0622007	+	0.0202102i
$455$	−5.93706	+	12.5760i	−0.278333	+	0.589571i
$456$	−5.22772	−	3.79816i	−0.244810	−	0.177865i
$457$	−5.29572	−	33.4359i	−0.247724	−	1.56406i	−0.727147	−	0.686481i	$-0.759154\pi$
$457$	−5.29572	−	33.4359i	−0.247724	−	1.56406i	0.479424	−	0.877584i	$-0.340846\pi$
$458$	6.79943	+	13.3446i	0.317716	+	0.623554i
$459$	11.8764	+	36.5519i	0.554344	+	1.70610i
$460$	6.93489	−	23.7589i	0.323341	−	1.10776i
$461$		−	28.3761i		−	1.32161i	−0.750559	−	0.660803i	$-0.770216\pi$
$461$		−	28.3761i		−	1.32161i	0.750559	−	0.660803i	$-0.229784\pi$
$462$		0			0
$463$	−16.0155	−	16.0155i	−0.744304	−	0.744304i	0.229099	−	0.973403i	$-0.426422\pi$
$463$	−16.0155	−	16.0155i	−0.744304	−	0.744304i	−0.973403	+	0.229099i	$0.926422\pi$
$464$	−19.9367	+	14.4848i	−0.925536	+	0.672441i
$465$	5.34373	−	7.84192i	0.247810	−	0.363660i
$466$	−0.960252	+	2.95535i	−0.0444828	+	0.136904i
$467$	4.35537	−	0.689823i	0.201543	−	0.0319212i	−0.0548469	−	0.998495i	$-0.517467\pi$
$467$	4.35537	−	0.689823i	0.201543	−	0.0319212i	0.256389	+	0.966574i	$0.417467\pi$
$468$	−2.65726	+	0.420869i	−0.122832	+	0.0194547i
$469$	3.07481	−	9.46328i	0.141981	−	0.436974i
$470$	0.342465	+	1.80757i	0.0157967	+	0.0833768i
$471$	−3.09423	+	2.24809i	−0.142575	+	0.103587i
$472$	9.41408	+	9.41408i	0.433318	+	0.433318i
$473$		0			0
$474$			36.3955i			1.67170i
$475$	18.9746	−	7.45762i	0.870612	−	0.342179i
$476$	−6.35318	−	19.5531i	−0.291198	−	0.896214i
$477$	2.05334	+	4.02991i	0.0940162	+	0.184517i
$478$	−4.79285	−	30.2608i	−0.219220	−	1.38410i
$479$	−14.1416	−	10.2744i	−0.646144	−	0.469451i	0.215811	−	0.976435i	$-0.430760\pi$
$479$	−14.1416	−	10.2744i	−0.646144	−	0.469451i	−0.861956	+	0.506984i	$0.830760\pi$
$480$	−21.4094	−	10.1073i	−0.977201	−	0.461332i
$481$	13.7155	−	4.45645i	0.625375	−	0.203197i
$482$	6.17366	−	38.9790i	0.281203	−	1.77544i
$483$	−17.2339	+	17.2339i	−0.784168	+	0.784168i
$484$		0			0
$485$	14.9099	−	11.5354i	0.677024	−	0.523797i
$486$	−6.87822	−	9.46705i	−0.312002	−	0.429434i
$487$	−16.4551	−	8.38431i	−0.745653	−	0.379929i	0.0395092	−	0.999219i	$-0.487421\pi$
$487$	−16.4551	−	8.38431i	−0.745653	−	0.379929i	−0.785162	+	0.619290i	$0.787421\pi$
$488$	4.89885	−	2.49609i	0.221760	−	0.112993i
$489$	−8.66539	+	11.9269i	−0.391862	+	0.539352i
$490$	−11.3680	+	0.342999i	−0.513554	+	0.0154951i
$491$	−12.6037	−	4.09521i	−0.568799	−	0.184814i	0.0104775	−	0.999945i	$-0.496665\pi$
$491$	−12.6037	−	4.09521i	−0.568799	−	0.184814i	−0.579277	+	0.815131i	$0.696665\pi$
$492$	−7.66348	+	15.0404i	−0.345497	+	0.678075i
$493$	34.9022	+	5.52797i	1.57192	+	0.248967i
$494$	−22.8105			−1.02629
$495$		0			0
$496$	13.1964			0.592534
$497$	−8.93200	−	1.41469i	−0.400655	−	0.0634575i
$498$	1.45310	−	2.85186i	0.0651149	−	0.127795i
$499$	−11.0332	−	3.58490i	−0.493913	−	0.160482i	0.0514608	−	0.998675i	$-0.483612\pi$
$499$	−11.0332	−	3.58490i	−0.493913	−	0.160482i	−0.545374	+	0.838193i	$0.683612\pi$
$500$	13.6926	−	8.61755i	0.612350	−	0.385389i
$501$	6.96278	−	9.58344i	0.311074	−	0.428156i
$502$	−43.0940	+	21.9575i	−1.92338	+	0.980011i
$503$	−3.75999	−	1.91581i	−0.167650	−	0.0854218i	0.368152	−	0.929766i	$-0.379991\pi$
$503$	−3.75999	−	1.91581i	−0.167650	−	0.0854218i	−0.535802	+	0.844344i	$0.679991\pi$
$504$	−0.768530	−	1.05779i	−0.0342330	−	0.0471177i
$505$	0.422246	−	3.30908i	0.0187897	−	0.147252i
$506$		0			0
$507$	4.28005	−	4.28005i	0.190084	−	0.190084i
$508$	−0.300353	+	1.89636i	−0.0133260	+	0.0841372i
$509$	−25.8090	+	8.38584i	−1.14396	+	0.371696i	−0.818866	−	0.573985i	$-0.805397\pi$
$509$	−25.8090	+	8.38584i	−1.14396	+	0.371696i	−0.325097	+	0.945681i	$0.605397\pi$
$510$	14.8905	+	41.5232i	0.659364	+	1.83868i
$511$	−15.0145	−	10.9087i	−0.664204	−	0.482572i
$512$	−3.60860	−	22.7838i	−0.159479	−	1.00691i
$513$	−10.3360	−	20.2855i	−0.456345	−	0.895628i
$514$	−1.40958	−	4.33824i	−0.0621739	−	0.191352i
$515$	15.2189	+	4.44219i	0.670627	+	0.195746i
$516$		−	8.15151i		−	0.358850i
$517$		0			0
$518$	−12.9697	−	12.9697i	−0.569855	−	0.569855i
$519$	17.1017	−	12.4251i	0.750683	−	0.545403i
$520$	6.79588	−	1.28756i	0.298019	−	0.0564634i
$521$	3.57064	−	10.9893i	0.156433	−	0.481450i	−0.841871	−	0.539679i	$-0.818545\pi$
$521$	3.57064	−	10.9893i	0.156433	−	0.481450i	0.998303	+	0.0582294i	$0.0185455\pi$
$522$	−5.80892	+	0.920043i	−0.254250	+	0.0402692i
$523$	28.1755	−	4.46255i	1.23203	−	0.195134i	0.493733	−	0.869613i	$-0.335632\pi$
$523$	28.1755	−	4.46255i	1.23203	−	0.195134i	0.738294	+	0.674480i	$0.235632\pi$
$524$	−4.20944	+	12.9553i	−0.183890	+	0.565956i
$525$	−15.9026	+	0.960513i	−0.694046	+	0.0419202i
$526$	−30.2061	+	21.9460i	−1.31705	+	0.956892i
$527$	−13.3807	−	13.3807i	−0.582871	−	0.582871i
$528$		0			0
$529$			35.5083i			1.54384i
$530$	14.6268	+	26.6851i	0.635346	+	1.15913i
$531$	2.47277	+	7.61041i	0.107309	+	0.330264i
$532$	5.52914	+	10.8515i	0.239719	+	0.470474i
$533$	−3.56192	−	22.4890i	−0.154284	−	0.974109i
$534$	−31.4566	−	22.8545i	−1.36126	−	0.989013i
$535$	31.9395	−	11.4537i	1.38086	−	0.495188i
$536$	−4.70667	+	1.52929i	−0.203297	+	0.0660552i
$537$	−3.36983	+	21.2763i	−0.145419	+	0.918139i
$538$	2.93813	−	2.93813i	0.126672	−	0.126672i
$539$		0			0
$540$	−11.0554	−	14.2895i	−0.475750	−	0.614922i
$541$	−12.5833	−	17.3194i	−0.540996	−	0.744618i	0.447760	−	0.894154i	$-0.352222\pi$
$541$	−12.5833	−	17.3194i	−0.540996	−	0.744618i	−0.988756	+	0.149536i	$0.952222\pi$
$542$	−4.89596	−	2.49462i	−0.210300	−	0.107153i
$543$	−27.2271	+	13.8729i	−1.16843	+	0.595344i
$544$	−27.7500	+	38.1946i	−1.18977	+	1.63758i
$545$	3.02316	+	2.84608i	0.129498	+	0.121912i
$546$	16.9526	+	5.50824i	0.725505	+	0.235731i
$547$	−2.06513	+	4.05305i	−0.0882987	+	0.173296i	−0.930933	−	0.365191i	$-0.881004\pi$
$547$	−2.06513	+	4.05305i	−0.0882987	+	0.173296i	0.842634	+	0.538487i	$0.181004\pi$
$548$	−17.4421	−	2.76255i	−0.745088	−	0.118010i
$549$	3.30462			0.141038
$550$		0			0
$551$	−20.9332			−0.891783
$552$	11.9726	+	1.89628i	0.509589	+	0.0807109i
$553$	−11.8998	+	23.3548i	−0.506033	+	0.993145i
$554$	48.8088	+	15.8590i	2.07369	+	0.673782i
$555$	12.0290	+	11.3244i	0.510604	+	0.480694i
$556$	−5.97118	+	8.21862i	−0.253234	+	0.348547i
$557$	8.42203	−	4.29124i	0.356853	−	0.181826i	−0.266368	−	0.963871i	$-0.585824\pi$
$557$	8.42203	−	4.29124i	0.356853	−	0.181826i	0.623221	+	0.782046i	$0.285824\pi$
$558$	2.80619	+	1.42982i	0.118795	+	0.0605293i
$559$	6.46291	+	8.89544i	0.273352	+	0.376237i
$560$	−13.5569	−	17.5228i	−0.572884	−	0.740472i
$561$		0			0
$562$	−38.9240	+	38.9240i	−1.64191	+	1.64191i
$563$	−5.21103	+	32.9011i	−0.219619	+	1.38662i	0.593647	+	0.804726i	$0.297688\pi$
$563$	−5.21103	+	32.9011i	−0.219619	+	1.38662i	−0.813266	+	0.581892i	$0.802312\pi$
$564$	0.941444	−	0.305894i	0.0396419	−	0.0128804i
$565$	−17.6667	+	6.33540i	−0.743242	+	0.266532i
$566$	13.7306	+	9.97590i	0.577142	+	0.419318i
$567$	2.18541	+	13.7981i	0.0917786	+	0.579467i
$568$	2.04196	+	4.00757i	0.0856788	+	0.168154i
$569$	−11.7947	−	36.3003i	−0.494459	−	1.52179i	−0.817798	−	0.575506i	$-0.804805\pi$
$569$	−11.7947	−	36.3003i	−0.494459	−	1.52179i	0.323338	−	0.946283i	$-0.395195\pi$
$570$	−12.5602	−	22.9148i	−0.526088	−	0.959797i
$571$		−	0.631817i		−	0.0264407i	−0.999913	−	0.0132204i	$-0.995792\pi$
$571$		−	0.631817i		−	0.0264407i	0.999913	−	0.0132204i	$-0.00420829\pi$
$572$		0			0
$573$	0.599420	+	0.599420i	0.0250411	+	0.0250411i
$574$	−23.4286	+	17.0219i	−0.977890	+	0.710479i
$575$	−25.3639	+	28.6248i	−1.05775	+	1.19374i
$576$	0.597586	−	1.83918i	0.0248994	−	0.0766325i
$577$	−9.67233	+	1.53195i	−0.402665	+	0.0637758i	−0.354482	−	0.935063i	$-0.615343\pi$
$577$	−9.67233	+	1.53195i	−0.402665	+	0.0637758i	−0.0481823	+	0.998839i	$0.515343\pi$
$578$	55.7077	−	8.82323i	2.31714	−	0.366998i
$579$	−2.41313	+	7.42684i	−0.100286	+	0.308649i
$580$	−16.3213	+	3.09227i	−0.677705	+	0.128400i
$581$	1.86489	−	1.35492i	0.0773685	−	0.0562115i
$582$	−17.0854	−	17.0854i	−0.708211	−	0.708211i
$583$		0			0
$584$			9.23051i			0.381961i
$585$	3.99078	+	1.16485i	0.164999	+	0.0481608i
$586$	−1.01140	−	3.11277i	−0.0417806	−	0.128588i
$587$	−6.17797	−	12.1249i	−0.254992	−	0.500450i	0.727653	−	0.685945i	$-0.240611\pi$
$587$	−6.17797	−	12.1249i	−0.254992	−	0.500450i	−0.982645	+	0.185495i	$0.940611\pi$
$588$	0.957304	+	6.04418i	0.0394786	+	0.249258i
$589$	9.06885	+	6.58891i	0.373676	+	0.271491i
$590$	18.1740	+	50.6793i	0.748212	+	2.08644i
$591$	−11.0687	+	3.59645i	−0.455307	+	0.147938i
$592$	−3.59398	+	22.6915i	−0.147712	+	0.932614i
$593$	−6.27189	+	6.27189i	−0.257555	+	0.257555i	−0.824059	−	0.566504i	$-0.808296\pi$
$593$	−6.27189	+	6.27189i	−0.257555	+	0.257555i	0.566504	+	0.824059i	$0.308296\pi$
$594$		0			0
$595$	−4.02123	+	31.5137i	−0.164854	+	1.29194i
$596$	−1.14425	−	1.57492i	−0.0468702	−	0.0645113i
$597$	−8.09721	−	4.12573i	−0.331397	−	0.168855i
$598$	38.1269	−	19.4266i	1.55913	−	0.794414i
$599$	14.2632	−	19.6316i	0.582779	−	0.802126i	−0.411218	−	0.911537i	$-0.634896\pi$
$599$	14.2632	−	19.6316i	0.582779	−	0.802126i	0.993997	+	0.109411i	$0.0348965\pi$
$600$	5.03547	+	6.11798i	0.205572	+	0.249766i
$601$	−22.2254	−	7.22146i	−0.906592	−	0.294570i	−0.181637	−	0.983366i	$-0.558140\pi$
$601$	−22.2254	−	7.22146i	−0.906592	−	0.294570i	−0.724955	+	0.688796i	$0.758140\pi$
$602$	6.34883	−	12.4603i	0.258759	−	0.507843i
$603$	−2.93789	−	0.465316i	−0.119640	−	0.0189491i
$604$	−4.26751			−0.173643
$605$		0			0
$606$	−4.27575			−0.173691
$607$	−17.7079	−	2.80466i	−0.718743	−	0.113838i	−0.213660	−	0.976908i	$-0.568538\pi$
$607$	−17.7079	−	2.80466i	−0.718743	−	0.113838i	−0.505084	+	0.863070i	$0.668538\pi$
$608$	12.6967	−	24.9188i	0.514921	−	1.01059i
$609$	15.5574	+	5.05490i	0.630416	+	0.204835i
$610$	22.2241	−	0.670553i	0.899826	−	0.0271499i
$611$	−0.784835	+	1.08023i	−0.0317510	+	0.0437016i
$612$	−5.47609	+	2.79020i	−0.221358	+	0.112787i
$613$	34.0219	+	17.3350i	1.37413	+	0.700156i	0.976122	−	0.217225i	$-0.0697006\pi$
$613$	34.0219	+	17.3350i	1.37413	+	0.700156i	0.398011	+	0.917381i	$0.369701\pi$
$614$	16.4705	+	22.6697i	0.664695	+	0.914874i
$615$	20.6306	−	15.9614i	0.831905	−	0.643624i
$616$		0			0
$617$	−9.02298	+	9.02298i	−0.363252	+	0.363252i	−0.865009	−	0.501757i	$-0.832687\pi$
$617$	−9.02298	+	9.02298i	−0.363252	+	0.363252i	0.501757	+	0.865009i	$0.332687\pi$
$618$	3.17885	−	20.0704i	0.127872	−	0.807352i
$619$	38.0001	−	12.3470i	1.52735	−	0.496267i	0.579498	−	0.814973i	$-0.303249\pi$
$619$	38.0001	−	12.3470i	1.52735	−	0.496267i	0.947853	+	0.318707i	$0.103249\pi$
$620$	8.04418	+	3.79762i	0.323062	+	0.152516i
$621$	34.5524	+	25.1038i	1.38654	+	1.00738i
$622$	−7.93013	−	50.0689i	−0.317969	−	2.00758i
$623$	−12.7130	−	24.9506i	−0.509335	−	0.999626i
$624$	−6.89941	−	21.2342i	−0.276197	−	0.850048i
$625$	−24.8183	+	3.00901i	−0.992730	+	0.120360i
$626$		−	49.7965i		−	1.99027i
$627$		0			0
$628$	−2.53518	−	2.53518i	−0.101165	−	0.101165i
$629$	26.6526	−	19.3642i	1.06271	−	0.772102i
$630$	−0.984271	−	5.19508i	−0.0392143	−	0.206977i
$631$	−2.70001	+	8.30977i	−0.107486	+	0.330807i	−0.990306	−	0.138904i	$-0.955642\pi$
$631$	−2.70001	+	8.30977i	−0.107486	+	0.330807i	0.882820	+	0.469711i	$0.155642\pi$
$632$	12.8762	−	2.03938i	0.512186	−	0.0811223i
$633$	23.1248	−	3.66261i	0.919128	−	0.145576i
$634$	1.12798	−	3.47157i	0.0447979	−	0.137874i
$635$	1.67070	−	2.45175i	0.0662997	−	0.0972946i
$636$	13.2467	−	9.62430i	0.525266	−	0.381628i
$637$	−5.83679	−	5.83679i	−0.231262	−	0.231262i
$638$		0			0
$639$			2.70339i			0.106945i
$640$	−4.94894	+	16.9551i	−0.195624	+	0.670207i
$641$	6.80796	+	20.9528i	0.268898	+	0.827584i	0.990770	+	0.135557i	$0.0432823\pi$
$641$	6.80796	+	20.9528i	0.268898	+	0.827584i	−0.721871	+	0.692027i	$0.756718\pi$
$642$	−19.7443	−	38.7504i	−0.779247	−	1.52936i
$643$	6.88955	+	43.4989i	0.271697	+	1.71543i	0.625597	+	0.780146i	$0.284855\pi$
$643$	6.88955	+	43.4989i	0.271697	+	1.71543i	−0.353900	+	0.935283i	$0.615145\pi$
$644$	−18.4835	−	13.4290i	−0.728351	−	0.529178i
$645$	−5.37743	+	11.3906i	−0.211736	+	0.448503i
$646$	−49.5583	+	16.1025i	−1.94985	+	0.633544i
$647$	−5.93893	+	37.4969i	−0.233484	+	1.47416i	0.540711	+	0.841209i	$0.318155\pi$
$647$	−5.93893	+	37.4969i	−0.233484	+	1.47416i	−0.774194	+	0.632948i	$0.781845\pi$
$648$	4.91312	−	4.91312i	0.193006	−	0.193006i
$649$		0			0
$650$	27.0750	+	7.02402i	1.06197	+	0.275505i
$651$	−5.14883	−	7.08675i	−0.201798	−	0.277752i
$652$	−12.3134	−	6.27399i	−0.482230	−	0.245709i
$653$	7.23650	−	3.68718i	0.283186	−	0.144290i	−0.306628	−	0.951829i	$-0.599201\pi$
$653$	7.23650	−	3.68718i	0.283186	−	0.144290i	0.589814	+	0.807539i	$0.299201\pi$
$654$	3.12811	−	4.30547i	0.122319	−	0.168357i
$655$	14.4285	−	15.3263i	0.563770	−	0.598848i
$656$	34.4980	+	11.2091i	1.34692	+	0.437641i
$657$	−2.51873	+	4.94328i	−0.0982650	+	0.192856i
$658$	1.67732	+	0.265662i	0.0653889	+	0.0103566i
$659$	−35.1688			−1.36998			−0.684990	−	0.728552i	$-0.740194\pi$
$659$	−35.1688			−1.36998			−0.684990	+	0.728552i	$0.740194\pi$
$660$		0			0
$661$	−40.3405			−1.56906			−0.784531	−	0.620090i	$-0.787096\pi$
$661$	−40.3405			−1.56906			−0.784531	+	0.620090i	$0.787096\pi$
$662$	−44.7146	−	7.08210i	−1.73788	−	0.275254i
$663$	−14.5350	+	28.5265i	−0.564492	+	1.10788i
$664$	−1.09037	−	0.354282i	−0.0423145	−	0.0137488i
$665$	−0.567572	−	18.8110i	−0.0220095	−	0.729458i
$666$	−3.22287	+	4.43590i	−0.124884	+	0.171888i
$667$	34.9889	−	17.8278i	1.35478	−	0.690293i
$668$	9.89402	+	5.04125i	0.382811	+	0.195052i
$669$	2.72222	+	3.74681i	0.105247	+	0.144860i
$670$	−19.8522	−	2.53318i	−0.766956	−	0.0978653i
$671$		0			0
$672$	−15.4535	+	15.4535i	−0.596130	+	0.596130i
$673$	4.67604	−	29.5233i	0.180248	−	1.13804i	−0.717183	−	0.696885i	$-0.754569\pi$
$673$	4.67604	−	29.5233i	0.180248	−	1.13804i	0.897431	−	0.441155i	$-0.145431\pi$
$674$	−14.2483	+	4.62957i	−0.548826	+	0.178324i
$675$	6.02181	+	27.2606i	0.231779	+	1.04926i
$676$	4.59039	+	3.33511i	0.176553	+	0.128274i
$677$	1.96819	+	12.4267i	0.0756438	+	0.477596i	0.996208	+	0.0870046i	$0.0277295\pi$
$677$	1.96819	+	12.4267i	0.0756438	+	0.477596i	−0.920564	+	0.390591i	$0.872271\pi$
$678$	10.9212	+	21.4340i	0.419425	+	0.823168i
$679$	−5.37735	−	16.5498i	−0.206364	−	0.635123i
$680$	13.8559	−	7.59474i	0.531348	−	0.291245i
$681$		−	1.15865i		−	0.0443994i
$682$		0			0
$683$	1.03200	+	1.03200i	0.0394883	+	0.0394883i	0.726575	−	0.687087i	$-0.241111\pi$
$683$	1.03200	+	1.03200i	0.0394883	+	0.0394883i	−0.687087	+	0.726575i	$0.741111\pi$
$684$	2.94543	−	2.13998i	0.112621	−	0.0818242i
$685$	22.5504	+	15.3665i	0.861605	+	0.587125i
$686$	−11.5338	+	35.4975i	−0.440364	+	1.35530i
$687$	−12.2993	+	1.94802i	−0.469247	+	0.0743214i
$688$	−17.3008	+	2.74018i	−0.659586	+	0.104468i
$689$	−6.82503	+	21.0053i	−0.260013	+	0.800237i
$690$	40.5093	+	27.6043i	1.54216	+	1.05088i
$691$	32.0075	−	23.2548i	1.21762	−	0.884654i	0.221722	−	0.975110i	$-0.428832\pi$
$691$	32.0075	−	23.2548i	1.21762	−	0.884654i	0.995900	+	0.0904558i	$0.0288324\pi$
$692$	14.0118	+	14.0118i	0.532651	+	0.532651i
$693$		0			0
$694$		−	53.8402i		−	2.04375i
$695$	13.7656	−	7.54524i	0.522158	−	0.286207i
$696$	−2.51411	−	7.73763i	−0.0952970	−	0.293294i
$697$	−23.6142	−	46.3454i	−0.894451	−	1.75546i
$698$	−1.00045	−	6.31658i	−0.0378675	−	0.239086i
$699$	−2.09023	−	1.51864i	−0.0790599	−	0.0574404i
$700$	−3.22131	−	14.5828i	−0.121754	−	0.551179i
$701$	1.11844	−	0.363404i	0.0422430	−	0.0137256i	−0.287819	−	0.957685i	$-0.592930\pi$
$701$	1.11844	−	0.363404i	0.0422430	−	0.0137256i	0.330062	+	0.943959i	$0.392930\pi$
$702$	4.88636	−	30.8513i	0.184424	−	1.16441i
$703$	−13.7997	+	13.7997i	−0.520464	+	0.520464i
$704$		0			0
$705$	−1.51733	−	0.193614i	−0.0571458	−	0.00729194i
$706$	11.4900	+	15.8147i	0.432433	+	0.595193i
$707$	−2.74372	−	1.39800i	−0.103188	−	0.0525771i
$708$	25.8118	−	13.1518i	0.970066	−	0.494273i
$709$	−17.3156	+	23.8329i	−0.650301	+	0.895063i	−0.999112	−	0.0421305i	$-0.986585\pi$
$709$	−17.3156	+	23.8329i	−0.650301	+	0.895063i	0.348811	+	0.937193i	$0.386585\pi$
$710$	0.548555	+	18.1807i	0.0205869	+	0.682310i
$711$	7.45214	+	2.42135i	0.279477	+	0.0908076i
$712$	−6.32294	+	12.4095i	−0.236962	+	0.465065i
$713$	−20.7697	−	3.28959i	−0.777830	−	0.123196i
$714$	40.7198			1.52390
$715$		0			0
$716$	−20.1931			−0.754653
$717$	25.1603	+	3.98499i	0.939627	+	0.148822i
$718$	−12.7280	+	24.9802i	−0.475006	+	0.932252i
$719$	−14.4170	−	4.68435i	−0.537662	−	0.174697i	0.0275840	−	0.999619i	$-0.491219\pi$
$719$	−14.4170	−	4.68435i	−0.537662	−	0.174697i	−0.565246	+	0.824923i	$0.691219\pi$
$720$	−4.53974	+	4.82221i	−0.169186	+	0.179713i
$721$	8.60206	−	11.8397i	0.320358	−	0.440934i
$722$	−3.92723	+	2.00102i	−0.146156	+	0.0744704i
$723$	29.2365	+	14.8967i	1.08732	+	0.554016i
$724$	−16.8371	−	23.1743i	−0.625747	−	0.861266i
$725$	24.8466	+	6.44592i	0.922780	+	0.239395i
$726$		0			0
$727$	6.89315	−	6.89315i	0.255653	−	0.255653i	−0.567631	−	0.823283i	$-0.692140\pi$
$727$	6.89315	−	6.89315i	0.255653	−	0.255653i	0.823283	+	0.567631i	$0.192140\pi$
$728$	0.998807	−	6.30622i	0.0370182	−	0.233724i
$729$	28.5640	−	9.28102i	1.05793	−	0.343741i
$730$	−15.9358	+	33.7554i	−0.589809	+	1.24934i
$731$	20.3209	+	14.7640i	0.751594	+	0.546065i
$732$	−1.87150	−	11.8162i	−0.0691726	−	0.436739i
$733$	4.08198	+	8.01134i	0.150771	+	0.295906i	0.954022	−	0.299735i	$-0.0968983\pi$
$733$	4.08198	+	8.01134i	0.150771	+	0.295906i	−0.803251	+	0.595641i	$0.796898\pi$
$734$	−19.1927	−	59.0690i	−0.708415	−	2.18028i
$735$	2.64956	−	9.07740i	0.0977306	−	0.334825i
$736$			52.4639i			1.93385i
$737$		0			0
$738$	6.12144	+	6.12144i	0.225333	+	0.225333i
$739$	−7.29302	+	5.29869i	−0.268278	+	0.194915i	−0.713788	−	0.700361i	$-0.753022\pi$
$739$	−7.29302	+	5.29869i	−0.268278	+	0.194915i	0.445511	+	0.895277i	$0.353022\pi$
$740$	−8.72090	+	12.7979i	−0.320587	+	0.470460i
$741$	5.86074	−	18.0375i	0.215300	−	0.662624i
$742$	27.7446	−	4.39432i	1.01854	−	0.161321i
$743$	35.4064	−	5.60782i	1.29894	−	0.205731i	0.531610	−	0.846989i	$-0.321587\pi$
$743$	35.4064	−	5.60782i	1.29894	−	0.205731i	0.767325	+	0.641258i	$0.221587\pi$
$744$	−1.34631	+	4.14350i	−0.0493580	+	0.151908i
$745$	0.559969	+	2.95557i	0.0205157	+	0.108284i
$746$	1.74589	−	1.26847i	0.0639217	−	0.0464419i
$747$	−0.487259	−	0.487259i	−0.0178279	−	0.0178279i
$748$		0			0
$749$		−	31.3215i		−	1.14446i
$750$	7.85217	+	31.0664i	0.286721	+	1.13438i
$751$	−8.62499	−	26.5450i	−0.314730	−	0.968640i	−0.975865	−	0.218373i	$-0.929925\pi$
$751$	−8.62499	−	26.5450i	−0.314730	−	0.968640i	0.661135	−	0.750267i	$-0.270075\pi$
$752$	−0.965702	−	1.89530i	−0.0352155	−	0.0691143i
$753$	−6.29076	−	39.7183i	−0.229248	−	1.44741i
$754$	−23.2349	−	16.8811i	−0.846164	−	0.614774i
$755$	5.96324	+	2.81522i	0.217025	+	0.102456i
$756$	−15.8612	+	5.15360i	−0.576865	+	0.187435i
$757$	6.79448	−	42.8987i	0.246950	−	1.55918i	−0.482965	−	0.875640i	$-0.660440\pi$
$757$	6.79448	−	42.8987i	0.246950	−	1.55918i	0.729915	−	0.683538i	$-0.239560\pi$
$758$	15.6921	−	15.6921i	0.569964	−	0.569964i
$759$		0			0
$760$	−7.40311	+	5.72760i	−0.268539	+	0.207762i
$761$	1.89773	+	2.61200i	0.0687925	+	0.0946848i	0.842027	−	0.539436i	$-0.181362\pi$
$761$	1.89773	+	2.61200i	0.0687925	+	0.0946848i	−0.773234	+	0.634120i	$0.781362\pi$
$762$	−3.38826	−	1.72641i	−0.122744	−	0.0625411i
$763$	3.41500	−	1.74003i	0.123631	−	0.0629933i
$764$	−0.467082	+	0.642883i	−0.0168984	+	0.0232587i
$765$	9.49270	−	0.286417i	0.343209	−	0.0103554i
$766$	−34.6613	−	11.2622i	−1.25236	−	0.406918i
$767$	−17.7401	+	34.8169i	−0.640557	+	1.25716i
$768$	31.9169	+	5.05514i	1.15170	+	0.182412i
$769$	5.00727			0.180567			0.0902834	−	0.995916i	$-0.471223\pi$
$769$	5.00727			0.180567			0.0902834	+	0.995916i	$0.471223\pi$
$770$		0			0
$771$	3.79264			0.136589
$772$	−7.23012	−	1.14514i	−0.260218	−	0.0412145i
$773$	3.83395	−	7.52455i	0.137898	−	0.270639i	−0.811722	−	0.584044i	$-0.801470\pi$
$773$	3.83395	−	7.52455i	0.137898	−	0.270639i	0.949620	+	0.313405i	$0.101470\pi$
$774$	−3.97588	−	1.29184i	−0.142910	−	0.0464343i
$775$	−8.73536	−	10.6133i	−0.313783	−	0.381240i
$776$	−5.08717	+	7.00189i	−0.182619	+	0.251353i
$777$	13.5881	−	6.92349i	0.487471	−	0.248379i
$778$	58.5789	+	29.8474i	2.10015	+	1.07008i
$779$	18.1112	+	24.9279i	0.648900	+	0.893134i
$780$	1.90502	−	14.9293i	0.0682106	−	0.534556i
$781$		0			0
$782$	69.1211	−	69.1211i	2.47176	−	2.47176i
$783$	4.48420	−	28.3121i	0.160252	−	1.01179i
$784$	12.5064	−	4.06357i	0.446657	−	0.145128i
$785$	1.87013	+	5.21497i	0.0667477	+	0.186130i
$786$	−21.8271	−	15.8583i	−0.778547	−	0.565648i
$787$	−1.78753	−	11.2860i	−0.0637184	−	0.402302i	−0.998848	−	0.0479951i	$-0.984717\pi$
$787$	−1.78753	−	11.2860i	−0.0637184	−	0.402302i	0.935129	−	0.354307i	$-0.115283\pi$
$788$	−4.95299	−	9.72078i	−0.176443	−	0.346288i
$789$	−9.59298	−	29.5242i	−0.341519	−	1.05109i
$790$	50.6080	+	14.7718i	1.80055	+	0.525556i
$791$			17.3249i			0.616001i
$792$		0			0
$793$	11.4107	+	11.4107i	0.405207	+	0.405207i
$794$	29.3873	−	21.3511i	1.04292	−	0.757724i
$795$	−24.8594	+	4.70991i	−0.881671	+	0.167043i
$796$	2.63248	−	8.10193i	0.0933057	−	0.287165i
$797$	−18.5254	+	2.93414i	−0.656204	+	0.103933i	−0.475653	−	0.879633i	$-0.657788\pi$
$797$	−18.5254	+	2.93414i	−0.656204	+	0.103933i	−0.180551	+	0.983566i	$0.557788\pi$
$798$	−23.8247	+	3.77346i	−0.843385	+	0.133579i
$799$	−0.942577	+	2.90096i	−0.0333460	+	0.102628i
$800$	−22.7436	+	25.6676i	−0.804108	+	0.907488i
$801$	−6.77234	+	4.92039i	−0.239289	+	0.173854i
$802$	8.72973	+	8.72973i	0.308258	+	0.308258i
$803$		0			0
$804$			10.7684i			0.379772i
$805$	16.9691	+	30.9584i	0.598081	+	1.09114i
$806$	4.75253	+	14.6268i	0.167401	+	0.515207i
$807$	1.56844	+	3.07823i	0.0552116	+	0.108359i
$808$	0.239587	+	1.51269i	0.00842864	+	0.0532164i
$809$	−41.0380	−	29.8158i	−1.44282	−	1.04827i	−0.987444	−	0.157970i	$-0.949505\pi$
$809$	−41.0380	−	29.8158i	−1.44282	−	1.04827i	−0.455375	−	0.890300i	$-0.650495\pi$
$810$	26.4491	−	9.48484i	0.929325	−	0.333263i
$811$	34.3089	−	11.1476i	1.20475	−	0.391446i	0.363242	−	0.931695i	$-0.381670\pi$
$811$	34.3089	−	11.1476i	1.20475	−	0.391446i	0.841506	+	0.540248i	$0.181670\pi$
$812$	−2.39878	+	15.1453i	−0.0841807	+	0.531496i
$813$	3.23055	−	3.23055i	0.113300	−	0.113300i
$814$		0			0
$815$	13.0674	+	16.8900i	0.457730	+	0.591630i
$816$	−29.9794	−	41.2631i	−1.04949	−	1.44450i
$817$	−13.2577	−	6.75512i	−0.463827	−	0.236332i
$818$	−48.3259	+	24.6233i	−1.68968	+	0.860933i
$819$	2.25567	−	3.10467i	0.0788196	−	0.108486i
$820$	17.8034	+	16.7605i	0.621722	+	0.585303i
$821$	−9.80876	−	3.18706i	−0.342328	−	0.111229i	0.132807	−	0.991142i	$-0.457601\pi$
$821$	−9.80876	−	3.18706i	−0.342328	−	0.111229i	−0.475135	+	0.879913i	$0.657601\pi$
$822$	15.8789	−	31.1641i	0.553841	−	1.08697i
$823$	−54.3097	−	8.60181i	−1.89312	−	0.299840i	−0.901885	−	0.431976i	$-0.857817\pi$
$823$	−54.3097	−	8.60181i	−1.89312	−	0.299840i	−0.991232	+	0.132136i	$0.957817\pi$
$824$	−7.27873			−0.253567
$825$		0			0
$826$	49.6988			1.72924
$827$	−26.6290	−	4.21763i	−0.925983	−	0.146661i	−0.324809	−	0.945780i	$-0.605300\pi$
$827$	−26.6290	−	4.21763i	−0.925983	−	0.146661i	−0.601174	+	0.799118i	$0.705300\pi$
$828$	−3.10065	+	6.08537i	−0.107755	+	0.211481i
$829$	−4.90606	−	1.59408i	−0.170395	−	0.0553645i	0.222577	−	0.974915i	$-0.428553\pi$
$829$	−4.90606	−	1.59408i	−0.170395	−	0.0553645i	−0.392972	+	0.919551i	$0.628553\pi$
$830$	−3.37576	−	3.17802i	−0.117174	−	0.110311i
$831$	−25.0810	+	34.5211i	−0.870051	+	1.19752i
$832$	8.41406	−	4.28718i	0.291705	−	0.148631i
$833$	−16.8014	−	8.56073i	−0.582133	−	0.296612i
$834$	−11.8265	−	16.2778i	−0.409518	−	0.563654i
$835$	−10.4998	−	13.5714i	−0.363362	−	0.469657i
$836$		0			0
$837$	−10.8542	+	10.8542i	−0.375176	+	0.375176i
$838$	−5.59839	+	35.3469i	−0.193393	+	1.22104i
$839$	46.1151	−	14.9837i	1.59207	−	0.517295i	0.626941	−	0.779066i	$-0.284307\pi$
$839$	46.1151	−	14.9837i	1.59207	−	0.517295i	0.965130	+	0.261771i	$0.0843065\pi$
$840$	6.88503	−	2.46902i	0.237556	−	0.0851894i
$841$	2.13892	+	1.55402i	0.0737559	+	0.0535868i
$842$	10.6083	+	66.9781i	0.365586	+	2.30822i
$843$	−20.7785	−	40.7800i	−0.715649	−	1.40454i
$844$	6.78216	+	20.8734i	0.233452	+	0.718490i
$845$	−4.21428	−	7.68855i	−0.144976	−	0.264494i
$846$		−	0.507665i		−	0.0174539i
$847$		0			0
$848$	−24.8796	−	24.8796i	−0.854369	−	0.854369i
$849$	−11.4163	+	8.29443i	−0.391806	+	0.284664i
$850$	63.7817	−	3.85240i	2.18769	−	0.132136i
$851$	11.3131	−	34.8181i	0.387807	−	1.19355i
$852$	9.66639	−	1.53101i	0.331165	−	0.0524514i
$853$	−13.8916	+	2.20022i	−0.475640	+	0.0753341i	−0.389652	−	0.920962i	$-0.627405\pi$
$853$	−13.8916	+	2.20022i	−0.475640	+	0.0753341i	−0.0859883	+	0.996296i	$0.527405\pi$
$854$	6.34232	−	19.5197i	0.217030	−	0.667949i
$855$	−5.52753	+	1.04726i	−0.189038	+	0.0358155i
$856$	−12.6029	+	9.15657i	−0.430760	+	0.312965i
$857$	25.9087	+	25.9087i	0.885023	+	0.885023i	0.994040	−	0.109017i	$-0.0347702\pi$
$857$	25.9087	+	25.9087i	0.885023	+	0.885023i	−0.109017	+	0.994040i	$0.534770\pi$
$858$		0			0
$859$		−	12.2122i		−	0.416675i	−0.978057	−	0.208337i	$-0.933195\pi$
$859$		−	12.2122i		−	0.416675i	0.978057	−	0.208337i	$-0.0668052\pi$
$860$	−11.3347	−	3.30844i	−0.386510	−	0.112817i
$861$	−7.44055	−	22.8997i	−0.253573	−	0.780418i
$862$	−10.2156	−	20.0492i	−0.347944	−	0.682879i
$863$	−1.31634	−	8.31104i	−0.0448087	−	0.282911i	0.955102	−	0.296277i	$-0.0957453\pi$
$863$	−1.31634	−	8.31104i	−0.0448087	−	0.282911i	−0.999911	+	0.0133663i	$0.995745\pi$
$864$	30.9828	+	22.5103i	1.05406	+	0.765817i
$865$	−10.3361	−	28.8230i	−0.351439	−	0.980010i
$866$	−8.35988	+	2.71629i	−0.284080	+	0.0923033i
$867$	−7.33605	+	46.3180i	−0.249145	+	1.57304i
$868$	5.80634	−	5.80634i	0.197080	−	0.197080i
$869$		0			0
$870$	4.16448	−	32.6364i	0.141189	−	1.10648i
$871$	−8.53771	−	11.7511i	−0.289289	−	0.398172i
$872$	−1.69849	−	0.865422i	−0.0575180	−	0.0293069i
$873$	−4.63497	+	2.36164i	−0.156870	+	0.0799293i
$874$	−34.0366	+	46.8473i	−1.15130	+	1.58463i
$875$	−5.11876	+	22.5024i	−0.173046	+	0.760722i
$876$	19.1019	+	6.20658i	0.645393	+	0.209701i
$877$	12.4471	−	24.4288i	0.420308	−	0.824900i	−0.579642	−	0.814871i	$-0.696808\pi$
$877$	12.4471	−	24.4288i	0.420308	−	0.824900i	0.999950	−	0.0100291i	$-0.00319241\pi$
$878$	−47.9883	−	7.60059i	−1.61953	−	0.256508i
$879$	2.72129			0.0917870
$880$		0			0
$881$	13.9259			0.469176			0.234588	−	0.972095i	$-0.424626\pi$
$881$	13.9259			0.469176			0.234588	+	0.972095i	$0.424626\pi$
$882$	3.09975	+	0.490952i	0.104374	+	0.0165312i
$883$	−1.34544	+	2.64057i	−0.0452776	+	0.0888623i	−0.912537	−	0.408995i	$-0.865879\pi$
$883$	−1.34544	+	2.64057i	−0.0452776	+	0.0888623i	0.867259	+	0.497857i	$0.165879\pi$
$884$	−28.5432	−	9.27425i	−0.960011	−	0.311927i
$885$	−44.7443	+	1.35004i	−1.50406	+	0.0453812i
$886$	−31.1977	+	42.9399i	−1.04811	+	1.44259i
$887$	−32.3064	+	16.4609i	−1.08474	+	0.552703i	−0.902561	−	0.430562i	$-0.858315\pi$
$887$	−32.3064	+	16.4609i	−1.08474	+	0.552703i	−0.182180	+	0.983265i	$0.558315\pi$
$888$	−6.75819	−	3.44347i	−0.226790	−	0.115555i
$889$	−1.60976	−	2.21565i	−0.0539897	−	0.0743105i
$890$	−44.5465	+	34.4645i	−1.49320	+	1.15525i
$891$		0			0
$892$	−3.06985	+	3.06985i	−0.102786	+	0.102786i
$893$	0.282663	−	1.78466i	0.00945896	−	0.0597215i
$894$	3.66694	−	1.19146i	0.122641	−	0.0398484i
$895$	28.2170	+	13.3211i	0.943191	+	0.445276i
$896$	13.1903	+	9.58335i	0.440659	+	0.320157i
$897$	5.56567	+	35.1403i	0.185832	+	1.17330i
$898$	−3.99892	−	7.84833i	−0.133446	−	0.261902i
$899$	4.36138	+	13.4230i	0.145460	+	0.447681i
$900$	−4.15504	+	1.63307i	−0.138501	+	0.0544355i
$901$			50.4541i			1.68087i
$902$		0			0
$903$	8.22179	+	8.22179i	0.273604	+	0.273604i
$904$	6.97106	−	5.06477i	0.231854	−	0.168452i
$905$	8.23971	+	43.4900i	0.273897	+	1.44566i
$906$	2.61188	−	8.03855i	0.0867740	−	0.267063i
$907$	−20.6208	+	3.26601i	−0.684703	+	0.108446i	−0.489088	−	0.872235i	$-0.662670\pi$
$907$	−20.6208	+	3.26601i	−0.684703	+	0.108446i	−0.195615	+	0.980681i	$0.562670\pi$
$908$	1.07275	−	0.169907i	0.0356005	−	0.00563856i
$909$	−0.284460	+	0.875479i	−0.00943496	+	0.0290378i
$910$	14.5398	−	21.3371i	0.481988	−	0.707316i
$911$	−5.53607	+	4.02219i	−0.183418	+	0.133261i	−0.675706	−	0.737172i	$-0.736161\pi$
$911$	−5.53607	+	4.02219i	−0.183418	+	0.133261i	0.492287	+	0.870433i	$0.336161\pi$
$912$	21.3644	+	21.3644i	0.707447	+	0.707447i
$913$		0			0
$914$			62.8518i			2.07895i
$915$	−5.17981	+	17.7460i	−0.171239	+	0.586665i
$916$	−3.60720	−	11.1018i	−0.119185	−	0.366815i
$917$	−8.82129	−	17.3128i	−0.291305	−	0.571718i
$918$	−11.1625	−	70.4771i	−0.368417	−	2.32609i
$919$	22.4253	+	16.2930i	0.739744	+	0.537455i	0.892631	−	0.450788i	$-0.148857\pi$
$919$	22.4253	+	16.2930i	0.739744	+	0.537455i	−0.152887	+	0.988244i	$0.548857\pi$
$920$	7.49608	−	15.8783i	0.247139	−	0.523493i
$921$	−22.1579	+	7.19954i	−0.730128	+	0.237233i
$922$	−8.24156	+	52.0352i	−0.271421	+	1.71369i
$923$	−9.33472	+	9.33472i	−0.307256	+	0.307256i
$924$		0			0
$925$	20.6288	−	12.1302i	0.678271	−	0.398838i
$926$	24.7172	+	34.0203i	0.812258	+	1.11798i
$927$	−3.89803	−	1.98615i	−0.128028	−	0.0652336i
$928$	31.3743	−	15.9860i	1.02991	−	0.524766i
$929$	20.4219	−	28.1083i	0.670020	−	0.922204i	−0.329740	−	0.944072i	$-0.606961\pi$
$929$	20.4219	−	28.1083i	0.670020	−	0.922204i	0.999761	+	0.0218676i	$0.00696122\pi$
$930$	−12.0768	+	12.8282i	−0.396013	+	0.420654i
$931$	10.6236	+	3.45182i	0.348175	+	0.113129i
$932$	1.09954	−	2.15797i	0.0360167	−	0.0706868i
$933$	41.6296	+	6.59348i	1.36289	+	0.215861i
$934$	−8.18709			−0.267890
$935$		0			0
$936$	−1.90866			−0.0623866
$937$	−45.0200	−	7.13046i	−1.47074	−	0.232942i	−0.630936	−	0.775835i	$-0.717329\pi$
$937$	−45.0200	−	7.13046i	−1.47074	−	0.232942i	−0.839802	+	0.542893i	$0.817329\pi$
$938$	−8.38700	+	16.4604i	−0.273845	+	0.537452i
$939$	39.3767	+	12.7943i	1.28501	+	0.417525i
$940$	−0.0432441	−	1.43323i	−0.00141047	−	0.0467469i
$941$	5.13895	−	7.07316i	0.167525	−	0.230578i	−0.716998	−	0.697076i	$-0.754484\pi$
$941$	5.13895	−	7.07316i	0.167525	−	0.230578i	0.884523	+	0.466497i	$0.154484\pi$
$942$	6.32704	−	3.22379i	0.206146	−	0.105037i
$943$	−51.5019	−	26.2416i	−1.67713	−	0.854542i
$944$	−36.5901	−	50.3620i	−1.19091	−	1.63914i
$945$	25.5634	+	3.26195i	0.831579	+	0.106111i
$946$		0			0
$947$	−8.84044	+	8.84044i	−0.287276	+	0.287276i	−0.836002	−	0.548726i	$-0.815113\pi$
$947$	−8.84044	+	8.84044i	−0.287276	+	0.287276i	0.548726	+	0.836002i	$0.315113\pi$
$948$	4.43754	−	28.0175i	0.144125	−	0.909967i
$949$	−25.7660	+	8.37190i	−0.836401	+	0.271763i
$950$	−36.9609	+	8.16457i	−1.19917	+	0.264894i
$951$	2.45534	+	1.78391i	0.0796199	+	0.0578473i
$952$	−2.28169	−	14.4060i	−0.0739499	−	0.466902i
$953$	7.23507	+	14.1996i	0.234367	+	0.459971i	0.977997	−	0.208621i	$-0.0668975\pi$
$953$	7.23507	+	14.1996i	0.234367	+	0.459971i	−0.743630	+	0.668592i	$0.766897\pi$
$954$	−2.59491	−	7.98630i	−0.0840132	−	0.258566i
$955$	1.07678	−	0.590210i	0.0348438	−	0.0190988i
$956$			23.8794i			0.772315i
$957$		0			0
$958$	22.9482	+	22.9482i	0.741424	+	0.741424i
$959$	20.3788	−	14.8061i	0.658066	−	0.478113i
$960$	8.93982	+	6.09188i	0.288532	+	0.196615i
$961$	−7.24400	+	22.2948i	−0.233678	+	0.719186i
$962$	−26.4455	+	4.18855i	−0.852636	+	0.135044i
$963$	−9.24789	+	1.46472i	−0.298009	+	0.0472000i
$964$	−9.50507	+	29.2536i	−0.306138	+	0.942195i
$965$	9.34763	+	6.36978i	0.300911	+	0.205050i
$966$	36.6083	−	26.5975i	1.17785	−	0.855761i
$967$	−12.0840	−	12.0840i	−0.388597	−	0.388597i	0.485590	−	0.874187i	$-0.338605\pi$
$967$	−12.0840	−	12.0840i	−0.388597	−	0.388597i	−0.874187	+	0.485590i	$0.838605\pi$
$968$		0			0
$969$		−	43.3256i		−	1.39182i
$970$	−30.6917	+	16.8229i	−0.985450	+	0.540149i
$971$	−11.7573	−	36.1853i	−0.377310	−	1.16124i	−0.941907	−	0.335874i	$-0.890968\pi$
$971$	−11.7573	−	36.1853i	−0.377310	−	1.16124i	0.564596	−	0.825367i	$-0.309032\pi$
$972$	4.14063	+	8.12644i	0.132811	+	0.260656i
$973$	−2.26682	−	14.3121i	−0.0726709	−	0.458826i
$974$	27.7398	+	20.1541i	0.888839	+	0.645779i
$975$	−12.5107	+	19.6049i	−0.400662	+	0.627859i
$976$	−24.4496	+	7.94415i	−0.782612	+	0.254286i
$977$	4.48535	−	28.3194i	0.143499	−	0.906017i	−0.805924	−	0.592018i	$-0.798331\pi$
$977$	4.48535	−	28.3194i	0.143499	−	0.906017i	0.949423	−	0.313999i	$-0.101669\pi$
$978$	19.3544	−	19.3544i	0.618884	−	0.618884i
$979$		0			0
$980$	8.79299	+	1.12201i	0.280882	+	0.0358412i
$981$	−0.673455	−	0.926931i	−0.0215018	−	0.0295946i
$982$	21.9229	+	11.1703i	0.699589	+	0.356458i
$983$	1.66195	−	0.846804i	0.0530079	−	0.0270089i	−0.427286	−	0.904117i	$-0.640530\pi$
$983$	1.66195	−	0.846804i	0.0530079	−	0.0270089i	0.480294	+	0.877108i	$0.340530\pi$
$984$	−7.03903	+	9.68840i	−0.224396	+	0.308855i
$985$	0.508429	+	16.8508i	0.0161999	+	0.536912i
$986$	−62.3970	−	20.2740i	−1.98713	−	0.645656i
$987$	−0.641030	+	1.25809i	−0.0204042	+	0.0400455i
$988$	17.5597	+	2.78119i	0.558650	+	0.0884814i
$989$	27.9127			0.887571
$990$		0			0
$991$	44.4865			1.41316			0.706580	−	0.707634i	$-0.250237\pi$
$991$	44.4865			1.41316			0.706580	+	0.707634i	$0.250237\pi$
$992$	−18.6240	−	2.94975i	−0.591312	−	0.0936546i
$993$	17.0888	−	33.5386i	0.542296	−	1.06432i
$994$	15.9683	+	5.18843i	0.506485	+	0.164567i
$995$	−9.02324	+	9.58469i	−0.286056	+	0.303855i
$996$	−1.46632	+	2.01822i	−0.0464622	+	0.0639497i
$997$	7.42150	−	3.78144i	0.235041	−	0.119759i	−0.332504	−	0.943102i	$-0.607893\pi$
$997$	7.42150	−	3.78144i	0.235041	−	0.119759i	0.567545	+	0.823343i	$0.307893\pi$
$998$	19.1911	+	9.77835i	0.607483	+	0.309528i
$999$	−15.7080	−	21.6201i	−0.496978	−	0.684031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.f.118.3		80
5.2	odd	4	inner	605.2.m.f.602.8		80
11.2	odd	10		605.2.e.a.483.3	yes	20
11.3	even	5	inner	605.2.m.f.578.3		80
11.4	even	5	inner	605.2.m.f.403.3		80
11.5	even	5	inner	605.2.m.f.233.8		80
11.6	odd	10	inner	605.2.m.f.233.3		80
11.7	odd	10	inner	605.2.m.f.403.8		80
11.8	odd	10	inner	605.2.m.f.578.8		80
11.9	even	5		605.2.e.a.483.8	yes	20
11.10	odd	2	inner	605.2.m.f.118.8		80
55.2	even	20		605.2.e.a.362.8	yes	20
55.7	even	20	inner	605.2.m.f.282.3		80
55.17	even	20	inner	605.2.m.f.112.3		80
55.27	odd	20	inner	605.2.m.f.112.8		80
55.32	even	4	inner	605.2.m.f.602.3		80
55.37	odd	20	inner	605.2.m.f.282.8		80
55.42	odd	20		605.2.e.a.362.3	✓	20
55.47	odd	20	inner	605.2.m.f.457.3		80
55.52	even	20	inner	605.2.m.f.457.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.3	✓	20	55.42	odd	20
605.2.e.a.362.8	yes	20	55.2	even	20
605.2.e.a.483.3	yes	20	11.2	odd	10
605.2.e.a.483.8	yes	20	11.9	even	5
605.2.m.f.112.3		80	55.17	even	20	inner
605.2.m.f.112.8		80	55.27	odd	20	inner
605.2.m.f.118.3		80	1.1	even	1	trivial
605.2.m.f.118.8		80	11.10	odd	2	inner
605.2.m.f.233.3		80	11.6	odd	10	inner
605.2.m.f.233.8		80	11.5	even	5	inner
605.2.m.f.282.3		80	55.7	even	20	inner
605.2.m.f.282.8		80	55.37	odd	20	inner
605.2.m.f.403.3		80	11.4	even	5	inner
605.2.m.f.403.8		80	11.7	odd	10	inner
605.2.m.f.457.3		80	55.47	odd	20	inner
605.2.m.f.457.8		80	55.52	even	20	inner
605.2.m.f.578.3		80	11.3	even	5	inner
605.2.m.f.578.8		80	11.8	odd	10	inner
605.2.m.f.602.3		80	55.32	even	4	inner
605.2.m.f.602.8		80	5.2	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.83377 - 0.290440i) q^{2} +(0.700818 - 1.37543i) q^{3} +(1.37624 + 0.447166i) q^{4} +(-1.62810 - 1.53273i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-1.83912 + 0.937080i) q^{7} +(0.914708 + 0.466067i) q^{8} +(0.362685 + 0.499192i) q^{9} +O(q^{10})\)	\(q+(-1.83377 - 0.290440i) q^{2} +(0.700818 - 1.37543i) q^{3} +(1.37624 + 0.447166i) q^{4} +(-1.62810 - 1.53273i) q^{5} +(-1.68462 + 2.31868i) q^{6} +(-1.83912 + 0.937080i) q^{7} +(0.914708 + 0.466067i) q^{8} +(0.362685 + 0.499192i) q^{9} +(2.54040 + 3.28355i) q^{10} +(1.57954 - 1.57954i) q^{12} +(-0.471357 + 2.97603i) q^{13} +(3.64469 - 1.18423i) q^{14} +(-3.24918 + 1.16518i) q^{15} +(-3.88339 - 2.82145i) q^{16} +(1.07677 + 6.79848i) q^{17} +(-0.520094 - 1.02074i) q^{18} +(-1.26002 - 3.87793i) q^{19} +(-1.55527 - 2.83744i) q^{20} +3.18632i q^{21} +(5.40871 + 5.40871i) q^{23} +(1.28209 - 0.931492i) q^{24} +(0.301449 + 4.99090i) q^{25} +(1.72872 - 5.32045i) q^{26} +(5.51482 - 0.873462i) q^{27} +(-2.95010 + 0.467250i) q^{28} +(1.58644 - 4.88256i) q^{29} +(6.29666 - 1.19298i) q^{30} +(-2.22412 + 1.61592i) q^{31} +(4.84994 + 4.84994i) q^{32} -12.7796i q^{34} +(4.43058 + 1.29322i) q^{35} +(0.275918 + 0.849187i) q^{36} +(-2.17288 - 4.26452i) q^{37} +(1.18427 + 7.47719i) q^{38} +(3.76300 + 2.73398i) q^{39} +(-0.774883 - 2.16081i) q^{40} +(-7.18688 + 2.33516i) q^{41} +(0.925435 - 5.84296i) q^{42} +(2.58034 - 2.58034i) q^{43} +(0.174641 - 1.36864i) q^{45} +(-8.34742 - 11.4892i) q^{46} +(0.394842 + 0.201182i) q^{47} +(-6.60227 + 3.36402i) q^{48} +(-1.61024 + 2.21631i) q^{49} +(0.896772 - 9.23971i) q^{50} +(10.1055 + 3.28347i) q^{51} +(-1.97948 + 3.88495i) q^{52} +(7.23977 + 1.14667i) q^{53} -10.3666 q^{54} -2.11900 q^{56} +(-6.21688 - 0.984657i) q^{57} +(-4.32725 + 8.49271i) q^{58} +(12.3338 + 4.00750i) q^{59} +(-4.99267 + 0.150641i) q^{60} +(3.14797 - 4.33281i) q^{61} +(4.54785 - 2.31725i) q^{62} +(-1.13481 - 0.578212i) q^{63} +(-1.84216 - 2.53551i) q^{64} +(5.32888 - 4.12282i) q^{65} +(-3.40871 + 3.40871i) q^{67} +(-1.55816 + 9.83782i) q^{68} +(11.2299 - 3.64880i) q^{69} +(-7.74905 - 3.65829i) q^{70} +(3.54451 + 2.57524i) q^{71} +(0.0990933 + 0.625651i) q^{72} +(4.08198 + 8.01134i) q^{73} +(2.74597 + 8.45123i) q^{74} +(7.07592 + 3.08309i) q^{75} -5.90039i q^{76} +(-6.10640 - 6.10640i) q^{78} +(10.2736 - 7.46420i) q^{79} +(1.99804 + 10.5458i) q^{80} +(2.09148 - 6.43690i) q^{81} +(13.8573 - 2.19478i) q^{82} +(-1.10302 + 0.174702i) q^{83} +(-1.42481 + 4.38513i) q^{84} +(8.66717 - 12.7191i) q^{85} +(-5.48119 + 3.98231i) q^{86} +(-5.60383 - 5.60383i) q^{87} +13.5666i q^{89} +(-0.717759 + 2.45904i) q^{90} +(-1.92190 - 5.91499i) q^{91} +(5.02507 + 9.86226i) q^{92} +(0.663884 + 4.19160i) q^{93} +(-0.665617 - 0.483599i) q^{94} +(-3.89240 + 8.24495i) q^{95} +(10.0697 - 3.27185i) q^{96} +(-1.31883 + 8.32676i) q^{97} +(3.59651 - 3.59651i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^5	\( 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

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