LMFDB - Embedded newform 825.2.cw.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(7,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 14]))

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

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

chi := DirichletCharacter("825.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cw (of order $20$, degree $8$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	825.7
Dual form			825.2.cw.b.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13992 + 0.338930i) q^{2} +(0.453990 + 0.891007i) q^{3} +(2.56227 - 0.832532i) q^{4} +(-1.27349 - 1.75281i) q^{6} +(0.770101 + 0.392386i) q^{7} +(-1.33999 + 0.682757i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-2.13992 + 0.338930i) q^{2} +(0.453990 + 0.891007i) q^{3} +(2.56227 - 0.832532i) q^{4} +(-1.27349 - 1.75281i) q^{6} +(0.770101 + 0.392386i) q^{7} +(-1.33999 + 0.682757i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.59884 - 2.06059i) q^{11} +(1.90504 + 1.90504i) q^{12} +(0.604046 + 3.81380i) q^{13} +(-1.78095 - 0.578664i) q^{14} +(-1.72314 + 1.25193i) q^{16} +(0.752203 - 4.74922i) q^{17} +(0.983613 - 1.93045i) q^{18} +(-0.838408 + 2.58036i) q^{19} +0.864305i q^{21} +(6.25970 + 3.52868i) q^{22} +(-4.79338 + 4.79338i) q^{23} +(-1.21668 - 0.883971i) q^{24} +(-2.58522 - 7.95649i) q^{26} +(-0.987688 - 0.156434i) q^{27} +(2.29988 + 0.364266i) q^{28} +(1.50081 + 4.61903i) q^{29} +(0.834544 + 0.606332i) q^{31} +(5.38990 - 5.38990i) q^{32} +(0.656154 - 3.25107i) q^{33} +10.4179i q^{34} +(-0.832532 + 2.56227i) q^{36} +(-1.97230 + 3.87086i) q^{37} +(0.919567 - 5.80592i) q^{38} +(-3.12389 + 2.26964i) q^{39} +(3.96986 + 1.28989i) q^{41} +(-0.292939 - 1.84954i) q^{42} +(7.22637 + 7.22637i) q^{43} +(-8.37444 - 3.11618i) q^{44} +(8.63283 - 11.8821i) q^{46} +(-6.70751 + 3.41765i) q^{47} +(-1.89777 - 0.966963i) q^{48} +(-3.67541 - 5.05877i) q^{49} +(4.57308 - 1.48588i) q^{51} +(4.72284 + 9.26910i) q^{52} +(-6.46794 + 1.02442i) q^{53} +2.16659 q^{54} -1.29983 q^{56} +(-2.67974 + 0.424430i) q^{57} +(-4.77715 - 9.37568i) q^{58} +(7.48114 - 2.43077i) q^{59} +(0.304083 + 0.418534i) q^{61} +(-1.99136 - 1.01465i) q^{62} +(-0.770101 + 0.392386i) q^{63} +(-7.20329 + 9.91448i) q^{64} +(-0.302231 + 7.17942i) q^{66} +(4.30527 + 4.30527i) q^{67} +(-2.02653 - 12.7950i) q^{68} +(-6.44708 - 2.09478i) q^{69} +(-13.0228 + 9.46160i) q^{71} +(0.235262 - 1.48539i) q^{72} +(-0.974881 + 1.91331i) q^{73} +(2.90862 - 8.95180i) q^{74} +7.30957i q^{76} +(-1.19282 - 2.60661i) q^{77} +(5.91562 - 5.91562i) q^{78} +(-3.33797 - 2.42518i) q^{79} +(-0.309017 - 0.951057i) q^{81} +(-8.93237 - 1.41475i) q^{82} +(-13.4534 - 2.13082i) q^{83} +(0.719562 + 2.21458i) q^{84} +(-17.9131 - 13.0146i) q^{86} +(-3.43423 + 3.43423i) q^{87} +(4.88929 + 0.986791i) q^{88} +4.64987i q^{89} +(-1.03130 + 3.17403i) q^{91} +(-8.29130 + 16.2726i) q^{92} +(-0.161370 + 1.01885i) q^{93} +(13.1952 - 9.58687i) q^{94} +(7.24940 + 2.35547i) q^{96} +(-1.43336 - 9.04989i) q^{97} +(9.57965 + 9.57965i) q^{98} +(3.19461 - 0.891318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 20 q^{7}+O(q^{10}) $ 96 * q + 20 * q^7	$ 96 q + 20 q^{7} + 8 q^{11} + 16 q^{12} + 8 q^{16} + 20 q^{17} + 32 q^{22} - 32 q^{23} + 60 q^{28} + 16 q^{31} + 16 q^{33} + 24 q^{36} - 8 q^{37} - 56 q^{38} - 120 q^{41} - 12 q^{42} - 200 q^{46} - 60 q^{47} - 48 q^{48} + 40 q^{51} - 40 q^{52} - 36 q^{53} - 80 q^{56} - 40 q^{57} - 44 q^{58} + 40 q^{61} - 80 q^{62} - 20 q^{63} + 56 q^{66} + 48 q^{67} - 80 q^{68} + 32 q^{71} + 60 q^{73} + 24 q^{77} + 96 q^{78} + 24 q^{81} - 32 q^{82} + 200 q^{83} - 80 q^{86} + 144 q^{88} + 56 q^{91} - 20 q^{92} + 72 q^{93} - 32 q^{97}+O(q^{100}) $ 96 * q + 20 * q^7 + 8 * q^11 + 16 * q^12 + 8 * q^16 + 20 * q^17 + 32 * q^22 - 32 * q^23 + 60 * q^28 + 16 * q^31 + 16 * q^33 + 24 * q^36 - 8 * q^37 - 56 * q^38 - 120 * q^41 - 12 * q^42 - 200 * q^46 - 60 * q^47 - 48 * q^48 + 40 * q^51 - 40 * q^52 - 36 * q^53 - 80 * q^56 - 40 * q^57 - 44 * q^58 + 40 * q^61 - 80 * q^62 - 20 * q^63 + 56 * q^66 + 48 * q^67 - 80 * q^68 + 32 * q^71 + 60 * q^73 + 24 * q^77 + 96 * q^78 + 24 * q^81 - 32 * q^82 + 200 * q^83 - 80 * q^86 + 144 * q^88 + 56 * q^91 - 20 * q^92 + 72 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.13992	+	0.338930i	−1.51315	+	0.239660i	−0.857137	−	0.515088i	$-0.827759\pi$
$2$	−2.13992	+	0.338930i	−1.51315	+	0.239660i	−0.656015	+	0.754748i	$0.727759\pi$
$3$	0.453990	+	0.891007i	0.262112	+	0.514423i
$3$	0.453990	+	0.891007i	0.262112	+	0.514423i
$4$	2.56227	−	0.832532i	1.28114	−	0.416266i
$5$		0			0
$5$		0			0
$6$	−1.27349	−	1.75281i	−0.519901	−	0.715582i
$7$	0.770101	+	0.392386i	0.291071	+	0.148308i	0.593429	−	0.804886i	$-0.297774\pi$
$7$	0.770101	+	0.392386i	0.291071	+	0.148308i	−0.302358	+	0.953194i	$0.597774\pi$
$8$	−1.33999	+	0.682757i	−0.473757	+	0.241391i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$		0			0
$11$	−2.59884	−	2.06059i	−0.783579	−	0.621292i
$11$	−2.59884	−	2.06059i	−0.783579	−	0.621292i
$12$	1.90504	+	1.90504i	0.549937	+	0.549937i
$13$	0.604046	+	3.81380i	0.167532	+	1.05776i	0.917922	+	0.396761i	$0.129866\pi$
$13$	0.604046	+	3.81380i	0.167532	+	1.05776i	−0.750390	+	0.660996i	$0.770134\pi$
$14$	−1.78095	−	0.578664i	−0.475978	−	0.154655i
$15$		0			0
$16$	−1.72314	+	1.25193i	−0.430785	+	0.312984i
$17$	0.752203	−	4.74922i	0.182436	−	1.15186i	−0.711176	−	0.703014i	$-0.751837\pi$
$17$	0.752203	−	4.74922i	0.182436	−	1.15186i	0.893612	−	0.448841i	$-0.148163\pi$
$18$	0.983613	−	1.93045i	0.231840	−	0.455011i
$19$	−0.838408	+	2.58036i	−0.192344	+	0.591974i	0.807653	+	0.589658i	$0.200737\pi$
$19$	−0.838408	+	2.58036i	−0.192344	+	0.591974i	−0.999997	+	0.00231648i	$0.999263\pi$
$20$		0			0
$21$			0.864305i			0.188607i
$22$	6.25970	+	3.52868i	1.33457	+	0.752317i
$23$	−4.79338	+	4.79338i	−0.999489	+	0.999489i	−1.00000		0.000510925i	$-0.999837\pi$
$23$	−4.79338	+	4.79338i	−0.999489	+	0.999489i	0.000510925		1.00000i	$0.499837\pi$
$24$	−1.21668	−	0.883971i	−0.248354	−	0.180440i
$25$		0			0
$26$	−2.58522	−	7.95649i	−0.507004	−	1.56040i
$27$	−0.987688	−	0.156434i	−0.190081	−	0.0301058i
$28$	2.29988	+	0.364266i	0.434637	+	0.0688397i
$29$	1.50081	+	4.61903i	0.278694	+	0.857732i	0.988218	+	0.153051i	$0.0489100\pi$
$29$	1.50081	+	4.61903i	0.278694	+	0.857732i	−0.709524	+	0.704681i	$0.751090\pi$
$30$		0			0
$31$	0.834544	+	0.606332i	0.149889	+	0.108900i	0.660202	−	0.751088i	$-0.270471\pi$
$31$	0.834544	+	0.606332i	0.149889	+	0.108900i	−0.510314	+	0.859988i	$0.670471\pi$
$32$	5.38990	−	5.38990i	0.952809	−	0.952809i
$33$	0.656154	−	3.25107i	0.114222	−	0.565939i
$34$			10.4179i			1.78665i
$35$		0			0
$36$	−0.832532	+	2.56227i	−0.138755	+	0.427045i
$37$	−1.97230	+	3.87086i	−0.324244	+	0.636365i	−0.994380	−	0.105874i	$-0.966236\pi$
$37$	−1.97230	+	3.87086i	−0.324244	+	0.636365i	0.670135	+	0.742239i	$0.266236\pi$
$38$	0.919567	−	5.80592i	0.149173	−	0.941844i
$39$	−3.12389	+	2.26964i	−0.500222	+	0.363433i
$40$		0			0
$41$	3.96986	+	1.28989i	0.619988	+	0.201446i	0.602135	−	0.798394i	$-0.294317\pi$
$41$	3.96986	+	1.28989i	0.619988	+	0.201446i	0.0178531	+	0.999841i	$0.494317\pi$
$42$	−0.292939	−	1.84954i	−0.0452014	−	0.285391i
$43$	7.22637	+	7.22637i	1.10201	+	1.10201i	0.994168	+	0.107843i	$0.0343945\pi$
$43$	7.22637	+	7.22637i	1.10201	+	1.10201i	0.107843	+	0.994168i	$0.465606\pi$
$44$	−8.37444	−	3.11618i	−1.26249	−	0.469782i
$45$		0			0
$46$	8.63283	−	11.8821i	1.27284	−	1.75192i
$47$	−6.70751	+	3.41765i	−0.978391	+	0.498515i	−0.868640	−	0.495444i	$-0.835005\pi$
$47$	−6.70751	+	3.41765i	−0.978391	+	0.498515i	−0.109751	+	0.993959i	$0.535005\pi$
$48$	−1.89777	−	0.966963i	−0.273920	−	0.139569i
$49$	−3.67541	−	5.05877i	−0.525058	−	0.722681i
$50$		0			0
$51$	4.57308	−	1.48588i	0.640359	−	0.208065i
$52$	4.72284	+	9.26910i	0.654940	+	1.28539i
$53$	−6.46794	+	1.02442i	−0.888440	+	0.140715i	−0.583940	−	0.811797i	$-0.698490\pi$
$53$	−6.46794	+	1.02442i	−0.888440	+	0.140715i	−0.304501	+	0.952512i	$0.598490\pi$
$54$	2.16659			0.294836
$55$		0			0
$56$	−1.29983			−0.173697
$57$	−2.67974	+	0.424430i	−0.354941	+	0.0562171i
$58$	−4.77715	−	9.37568i	−0.627271	−	1.23109i
$59$	7.48114	−	2.43077i	0.973962	−	0.316459i	0.221548	−	0.975150i	$-0.428889\pi$
$59$	7.48114	−	2.43077i	0.973962	−	0.316459i	0.752414	+	0.658690i	$0.228889\pi$
$60$		0			0
$61$	0.304083	+	0.418534i	0.0389338	+	0.0535878i	0.828040	−	0.560669i	$-0.189456\pi$
$61$	0.304083	+	0.418534i	0.0389338	+	0.0535878i	−0.789106	+	0.614257i	$0.789456\pi$
$62$	−1.99136	−	1.01465i	−0.252903	−	0.128861i
$63$	−0.770101	+	0.392386i	−0.0970236	+	0.0494360i
$64$	−7.20329	+	9.91448i	−0.900411	+	1.23931i
$65$		0			0
$66$	−0.302231	+	7.17942i	−0.0372021	+	0.883726i
$67$	4.30527	+	4.30527i	0.525972	+	0.525972i	0.919369	−	0.393397i	$-0.128700\pi$
$67$	4.30527	+	4.30527i	0.525972	+	0.525972i	−0.393397	+	0.919369i	$0.628700\pi$
$68$	−2.02653	−	12.7950i	−0.245753	−	1.55162i
$69$	−6.44708	−	2.09478i	−0.776138	−	0.252182i
$70$		0			0
$71$	−13.0228	+	9.46160i	−1.54552	+	1.12289i	−0.598766	+	0.800924i	$0.704342\pi$
$71$	−13.0228	+	9.46160i	−1.54552	+	1.12289i	−0.946753	+	0.321961i	$0.895658\pi$
$72$	0.235262	−	1.48539i	0.0277259	−	0.175054i
$73$	−0.974881	+	1.91331i	−0.114101	+	0.223936i	−0.940994	−	0.338424i	$-0.890106\pi$
$73$	−0.974881	+	1.91331i	−0.114101	+	0.223936i	0.826893	+	0.562360i	$0.190106\pi$
$74$	2.90862	−	8.95180i	0.338120	−	1.04063i
$75$		0			0
$76$			7.30957i			0.838466i
$77$	−1.19282	−	2.60661i	−0.135934	−	0.297051i
$78$	5.91562	−	5.91562i	0.669812	−	0.669812i
$79$	−3.33797	−	2.42518i	−0.375551	−	0.272854i	0.383958	−	0.923351i	$-0.374561\pi$
$79$	−3.33797	−	2.42518i	−0.375551	−	0.272854i	−0.759509	+	0.650497i	$0.774561\pi$
$80$		0			0
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	−8.93237	−	1.41475i	−0.986415	−	0.156233i
$83$	−13.4534	−	2.13082i	−1.47671	−	0.233887i	−0.634450	−	0.772964i	$-0.718773\pi$
$83$	−13.4534	−	2.13082i	−1.47671	−	0.233887i	−0.842257	+	0.539076i	$0.818773\pi$
$84$	0.719562	+	2.21458i	0.0785106	+	0.241631i
$85$		0			0
$86$	−17.9131	−	13.0146i	−1.93162	−	1.40340i
$87$	−3.43423	+	3.43423i	−0.368188	+	0.368188i
$88$	4.88929	+	0.986791i	0.521200	+	0.105192i
$89$			4.64987i			0.492885i	0.969157	+	0.246443i	$0.0792617\pi$
$89$			4.64987i			0.492885i	−0.969157	+	0.246443i	$0.920738\pi$
$90$		0			0
$91$	−1.03130	+	3.17403i	−0.108110	+	0.332729i
$92$	−8.29130	+	16.2726i	−0.864427	+	1.69653i
$93$	−0.161370	+	1.01885i	−0.0167333	+	0.105650i
$94$	13.1952	−	9.58687i	1.36098	−	0.988810i
$95$		0			0
$96$	7.24940	+	2.35547i	0.739889	+	0.240405i
$97$	−1.43336	−	9.04989i	−0.145536	−	0.918877i	−0.947093	−	0.320959i	$-0.895995\pi$
$97$	−1.43336	−	9.04989i	−0.145536	−	0.918877i	0.801557	−	0.597918i	$-0.204005\pi$
$98$	9.57965	+	9.57965i	0.967690	+	0.967690i
$99$	3.19461	−	0.891318i	0.321071	−	0.0895808i
$100$		0			0
$101$	−6.69495	+	9.21481i	−0.666172	+	0.916908i	−0.999666	−	0.0258448i	$-0.991772\pi$
$101$	−6.69495	+	9.21481i	−0.666172	+	0.916908i	0.333494	+	0.942752i	$0.391772\pi$
$102$	−9.28241	+	4.72963i	−0.919096	+	0.468303i
$103$	−13.7754	−	7.01893i	−1.35733	−	0.691596i	−0.384505	−	0.923123i	$-0.625628\pi$
$103$	−13.7754	−	7.01893i	−1.35733	−	0.691596i	−0.972829	+	0.231527i	$0.925628\pi$
$104$	−3.41331	−	4.69802i	−0.334703	−	0.460679i
$105$		0			0
$106$	13.4937	−	4.38436i	1.31062	−	0.425847i
$107$	2.13168	+	4.18366i	0.206078	+	0.404450i	0.970793	−	0.239918i	$-0.0771205\pi$
$107$	2.13168	+	4.18366i	0.206078	+	0.404450i	−0.764716	+	0.644368i	$0.777121\pi$
$108$	−2.66096	+	0.421455i	−0.256051	+	0.0405545i
$109$	−7.54711			−0.722882			−0.361441	−	0.932395i	$-0.617715\pi$
$109$	−7.54711			−0.722882			−0.361441	+	0.932395i	$0.617715\pi$
$110$		0			0
$111$	−4.34437			−0.412349
$112$	−1.81823	+	0.287980i	−0.171807	+	0.0272115i
$113$	7.58585	+	14.8881i	0.713617	+	1.40055i	0.907722	+	0.419572i	$0.137820\pi$
$113$	7.58585	+	14.8881i	0.713617	+	1.40055i	−0.194105	+	0.980981i	$0.562180\pi$
$114$	5.59058	−	1.81649i	0.523606	−	0.170130i
$115$		0			0
$116$	7.69099	+	10.5857i	0.714090	+	0.982861i
$117$	−3.44048	−	1.75301i	−0.318072	−	0.162066i
$118$	−15.1852	+	7.73724i	−1.39791	+	0.712271i
$119$	2.44280	−	3.36223i	0.223931	−	0.308215i
$120$		0			0
$121$	2.50792	+	10.7103i	0.227992	+	0.973663i
$122$	−0.792567	−	0.792567i	−0.0717556	−	0.0717556i
$123$	0.652982	+	4.12277i	0.0588774	+	0.371737i
$124$	2.64312	+	0.858802i	0.237359	+	0.0771227i
$125$		0			0
$126$	1.51496	−	1.10069i	0.134964	−	0.0980568i
$127$	−0.245254	+	1.54847i	−0.0217627	+	0.137404i	−0.996177	−	0.0873533i	$-0.972159\pi$
$127$	−0.245254	+	1.54847i	−0.0217627	+	0.137404i	0.974415	+	0.224758i	$0.0721591\pi$
$128$	5.13309	−	10.0743i	0.453705	−	0.890447i
$129$	−3.15804	+	9.71945i	−0.278050	+	0.855750i
$130$		0			0
$131$		−	7.80413i		−	0.681850i	−0.940090	−	0.340925i	$-0.889260\pi$
$131$		−	7.80413i		−	0.681850i	0.940090	−	0.340925i	$-0.110740\pi$
$132$	−1.02538	−	8.87640i	−0.0892477	−	0.772591i
$133$	−1.65815	+	1.65815i	−0.143780	+	0.143780i
$134$	−10.6721	−	7.75374i	−0.921930	−	0.669821i
$135$		0			0
$136$	2.23462	+	6.87746i	0.191617	+	0.589737i
$137$	−21.1656	−	3.35231i	−1.80830	−	0.286407i	−0.841188	−	0.540743i	$-0.818143\pi$
$137$	−21.1656	−	3.35231i	−1.80830	−	0.286407i	−0.967116	+	0.254336i	$0.918143\pi$
$138$	14.5062	+	2.29756i	1.23485	+	0.195581i
$139$	3.78913	+	11.6617i	0.321390	+	0.989136i	0.973044	+	0.230620i	$0.0740754\pi$
$139$	3.78913	+	11.6617i	0.321390	+	0.989136i	−0.651654	+	0.758516i	$0.725925\pi$
$140$		0			0
$141$	−6.09029	−	4.42486i	−0.512895	−	0.372640i
$142$	24.6609	−	24.6609i	2.06949	−	2.06949i
$143$	6.28886	−	11.1561i	0.525901	−	0.932923i
$144$		−	2.12992i		−	0.177493i
$145$		0			0
$146$	1.43769	−	4.42475i	0.118984	−	0.366195i
$147$	2.83879	−	5.57144i	0.234140	−	0.459525i
$148$	−1.83095	+	11.5602i	−0.150504	+	0.950242i
$149$	7.63358	−	5.54612i	0.625367	−	0.454356i	−0.229425	−	0.973326i	$-0.573685\pi$
$149$	7.63358	−	5.54612i	0.625367	−	0.454356i	0.854792	+	0.518971i	$0.173685\pi$
$150$		0			0
$151$	−12.3035	−	3.99764i	−1.00124	−	0.325323i	−0.237880	−	0.971295i	$-0.576452\pi$
$151$	−12.3035	−	3.99764i	−1.00124	−	0.325323i	−0.763361	+	0.645972i	$0.776452\pi$
$152$	−0.638300	−	4.03007i	−0.0517730	−	0.326882i
$153$	3.40007	+	3.40007i	0.274879	+	0.274879i
$154$	3.43600	+	5.17366i	0.276881	+	0.416905i
$155$		0			0
$156$	−6.11470	+	8.41616i	−0.489568	+	0.673832i
$157$	1.18944	−	0.606051i	0.0949278	−	0.0483682i	−0.405882	−	0.913925i	$-0.633036\pi$
$157$	1.18944	−	0.606051i	0.0949278	−	0.0483682i	0.500810	+	0.865557i	$0.333036\pi$
$158$	7.96495	+	4.05835i	0.633657	+	0.322865i
$159$	−3.84915	−	5.29790i	−0.305258	−	0.420151i
$160$		0			0
$161$	−5.57224	+	1.81053i	−0.439154	+	0.142690i
$162$	0.983613	+	1.93045i	0.0772800	+	0.151670i
$163$	5.14399	−	0.814729i	0.402909	−	0.0638145i	0.0483085	−	0.998832i	$-0.484617\pi$
$163$	5.14399	−	0.814729i	0.402909	−	0.0638145i	0.354600	+	0.935018i	$0.384617\pi$
$164$	11.2457			0.878144
$165$		0			0
$166$	29.5115			2.29054
$167$	24.0103	−	3.80285i	1.85797	−	0.294274i	0.875858	−	0.482570i	$-0.160296\pi$
$167$	24.0103	−	3.80285i	1.85797	−	0.294274i	0.982112	+	0.188296i	$0.0602964\pi$
$168$	−0.590110	−	1.15816i	−0.0455280	−	0.0893537i
$169$	−1.81644	+	0.590198i	−0.139726	+	0.0453998i
$170$		0			0
$171$	−1.59475	−	2.19498i	−0.121953	−	0.167854i
$172$	24.5321	+	12.4997i	1.87056	+	0.953096i
$173$	18.8644	−	9.61191i	1.43424	−	0.730780i	0.447679	−	0.894195i	$-0.352251\pi$
$173$	18.8644	−	9.61191i	1.43424	−	0.730780i	0.986557	+	0.163415i	$0.0522509\pi$
$174$	6.18502	−	8.51294i	0.468885	−	0.645365i
$175$		0			0
$176$	7.05789	+	0.297115i	0.532008	+	0.0223959i
$177$	5.56220	+	5.56220i	0.418081	+	0.418081i
$178$	−1.57598	−	9.95035i	−0.118125	−	0.745811i
$179$	−1.88959	−	0.613966i	−0.141235	−	0.0458900i	0.237547	−	0.971376i	$-0.423657\pi$
$179$	−1.88959	−	0.613966i	−0.141235	−	0.0458900i	−0.378781	+	0.925486i	$0.623657\pi$
$180$		0			0
$181$	0.514109	−	0.373522i	0.0382134	−	0.0277637i	−0.568515	−	0.822673i	$-0.692482\pi$
$181$	0.514109	−	0.373522i	0.0382134	−	0.0277637i	0.606728	+	0.794910i	$0.292482\pi$
$182$	1.13114	−	7.14171i	0.0838453	−	0.529379i
$183$	−0.234866	+	0.460950i	−0.0173618	+	0.0340744i
$184$	3.15035	−	9.69578i	0.232247	−	0.714782i
$185$		0			0
$186$		−	2.23496i		−	0.163875i
$187$	−11.7411	+	10.7925i	−0.858592	+	0.789224i
$188$	−14.3412	+	14.3412i	−1.04594	+	1.04594i
$189$	−0.699237	−	0.508025i	−0.0508620	−	0.0369534i
$190$		0			0
$191$	5.29545	+	16.2977i	0.383165	+	1.17926i	0.937802	+	0.347169i	$0.112857\pi$
$191$	5.29545	+	16.2977i	0.383165	+	1.17926i	−0.554637	+	0.832092i	$0.687143\pi$
$192$	−12.1041	−	1.91710i	−0.873537	−	0.138355i
$193$	20.4582	+	3.24026i	1.47261	+	0.233239i	0.840574	−	0.541697i	$-0.182218\pi$
$193$	20.4582	+	3.24026i	1.47261	+	0.233239i	0.632040	+	0.774936i	$0.282218\pi$
$194$	6.13456	+	18.8802i	0.440436	+	1.35552i
$195$		0			0
$196$	−13.6290	−	9.90203i	−0.973498	−	0.707288i
$197$	15.1802	−	15.1802i	1.08154	−	1.08154i	0.0851750	−	0.996366i	$-0.472855\pi$
$197$	15.1802	−	15.1802i	1.08154	−	1.08154i	0.996366	−	0.0851750i	$-0.0271449\pi$
$198$	−6.53412	+	2.99010i	−0.464360	+	0.212497i
$199$			6.97596i			0.494513i	0.968950	+	0.247256i	$0.0795290\pi$
$199$			6.97596i			0.494513i	−0.968950	+	0.247256i	$0.920471\pi$
$200$		0			0
$201$	−1.88147	+	5.79057i	−0.132709	+	0.408435i
$202$	11.2035	−	21.9881i	0.788274	−	1.54708i
$203$	−0.656665	+	4.14602i	−0.0460888	+	0.290993i
$204$	10.4804	−	7.61447i	0.733777	−	0.533120i
$205$		0			0
$206$	31.8573	+	10.3510i	2.21960	+	0.721192i
$207$	−1.06045	−	6.69540i	−0.0737062	−	0.465363i
$208$	−5.81548	−	5.81548i	−0.403231	−	0.403231i
$209$	7.49595	−	4.97831i	0.518506	−	0.344357i
$210$		0			0
$211$	12.2002	−	16.7921i	0.839896	−	1.15602i	−0.146103	−	0.989269i	$-0.546673\pi$
$211$	12.2002	−	16.7921i	0.839896	−	1.15602i	0.985999	−	0.166749i	$-0.0533269\pi$
$212$	−15.7198	+	8.00962i	−1.07964	+	0.550103i
$213$	−14.3426	−	7.30790i	−0.982736	−	0.500729i
$214$	−5.97960	−	8.23021i	−0.408757	−	0.562606i
$215$		0			0
$216$	1.43030	−	0.464731i	0.0973193	−	0.0316209i
$217$	0.404767	+	0.794400i	0.0274774	+	0.0539274i
$218$	16.1502	−	2.55794i	1.09383	−	0.173246i
$219$	−2.14736			−0.145105
$220$		0			0
$221$	18.5669			1.24895
$222$	9.29659	−	1.47244i	0.623947	−	0.0988234i
$223$	1.80034	+	3.53336i	0.120559	+	0.236611i	0.943397	−	0.331665i	$-0.107610\pi$
$223$	1.80034	+	3.53336i	0.120559	+	0.236611i	−0.822838	+	0.568276i	$0.807610\pi$
$224$	6.26569	−	2.03585i	0.418644	−	0.136026i
$225$		0			0
$226$	−21.2791	−	29.2882i	−1.41547	−	1.94822i
$227$	6.34326	+	3.23205i	0.421017	+	0.214519i	0.651647	−	0.758523i	$-0.274079\pi$
$227$	6.34326	+	3.23205i	0.421017	+	0.214519i	−0.230630	+	0.973042i	$0.574079\pi$
$228$	−6.51288	+	3.31848i	−0.431326	+	0.219772i
$229$	15.4505	−	21.2658i	1.02100	−	1.40529i	0.109500	−	0.993987i	$-0.465075\pi$
$229$	15.4505	−	21.2658i	1.02100	−	1.40529i	0.911500	−	0.411300i	$-0.134925\pi$
$230$		0			0
$231$	1.78098	−	2.24619i	0.117180	−	0.147788i
$232$	−5.16474	−	5.16474i	−0.339082	−	0.339082i
$233$	−0.0653864	−	0.412834i	−0.00428361	−	0.0270456i	0.985454	−	0.169943i	$-0.0543582\pi$
$233$	−0.0653864	−	0.412834i	−0.00428361	−	0.0270456i	−0.989738	+	0.142897i	$0.954358\pi$
$234$	7.95649	+	2.58522i	0.520132	+	0.169001i
$235$		0			0
$236$	17.1450	−	12.4566i	1.11605	−	0.810855i
$237$	0.645442	−	4.07516i	0.0419259	−	0.264710i
$238$	−4.08784	+	8.02283i	−0.264975	+	0.520043i
$239$	−2.76541	+	8.51105i	−0.178879	+	0.550534i	−0.999789	−	0.0205236i	$-0.993467\pi$
$239$	−2.76541	+	8.51105i	−0.178879	+	0.550534i	0.820910	+	0.571058i	$0.193467\pi$
$240$		0			0
$241$		−	5.14635i		−	0.331506i	−0.986167	−	0.165753i	$-0.946995\pi$
$241$		−	5.14635i		−	0.331506i	0.986167	−	0.165753i	$-0.0530054\pi$
$242$	−8.99678	−	22.0692i	−0.578335	−	1.41866i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	1.12759	+	0.819239i	0.0721863	+	0.0524464i
$245$		0			0
$246$	−2.79466	−	8.60108i	−0.178181	−	0.548385i
$247$	−10.3474	−	1.63887i	−0.658389	−	0.104279i
$248$	−1.53225	−	0.242685i	−0.0972983	−	0.0154105i
$249$	−4.20916	−	12.9545i	−0.266745	−	0.820956i
$250$		0			0
$251$	−10.2950	−	7.47972i	−0.649812	−	0.472116i	0.213395	−	0.976966i	$-0.431548\pi$
$251$	−10.2950	−	7.47972i	−0.649812	−	0.472116i	−0.863207	+	0.504850i	$0.831548\pi$
$252$	−1.64653	+	1.64653i	−0.103722	+	0.103722i
$253$	22.3344	−	2.58001i	1.40415	−	0.162204i
$254$		−	3.39673i		−	0.213130i
$255$		0			0
$256$	0.00405212	−	0.0124712i	0.000253258	−	0.000779447i
$257$	1.50904	−	2.96165i	0.0941312	−	0.184743i	−0.839140	−	0.543916i	$-0.816941\pi$
$257$	1.50904	−	2.96165i	0.0941312	−	0.184743i	0.933271	+	0.359173i	$0.116941\pi$
$258$	3.46374	−	21.8692i	0.215643	−	1.36152i
$259$	−3.03774	+	2.20705i	−0.188756	+	0.137139i
$260$		0			0
$261$	−4.61903	−	1.50081i	−0.285911	−	0.0928981i
$262$	2.64506	+	16.7002i	0.163412	+	1.03174i
$263$	1.88137	+	1.88137i	0.116010	+	0.116010i	0.762729	−	0.646719i	$-0.223859\pi$
$263$	1.88137	+	1.88137i	0.116010	+	0.116010i	−0.646719	+	0.762729i	$0.723859\pi$
$264$	1.34045	+	4.80438i	0.0824993	+	0.295689i
$265$		0			0
$266$	2.98632	−	4.11032i	0.183103	−	0.252020i
$267$	−4.14307	+	2.11100i	−0.253552	+	0.129191i
$268$	14.6155	+	7.44699i	0.892786	+	0.454897i
$269$	5.92437	+	8.15420i	0.361215	+	0.497170i	0.950487	−	0.310765i	$-0.100585\pi$
$269$	5.92437	+	8.15420i	0.361215	+	0.497170i	−0.589272	+	0.807935i	$0.700585\pi$
$270$		0			0
$271$	−18.8796	+	6.13437i	−1.14686	+	0.372636i	−0.819958	−	0.572423i	$-0.806004\pi$
$271$	−18.8796	+	6.13437i	−1.14686	+	0.372636i	−0.326899	+	0.945059i	$0.606004\pi$
$272$	4.64956	+	9.12528i	0.281921	+	0.553302i
$273$	−3.29628	+	0.522080i	−0.199500	+	0.0315977i
$274$	46.4290			2.80488
$275$		0			0
$276$	−18.2632			−1.09931
$277$	−18.3708	+	2.90964i	−1.10379	+	0.174823i	−0.681630	−	0.731697i	$-0.738729\pi$
$277$	−18.3708	+	2.90964i	−1.10379	+	0.174823i	−0.422162	+	0.906520i	$0.638729\pi$
$278$	−12.0610	−	23.6710i	−0.723368	−	1.41969i
$279$	−0.981066	+	0.318768i	−0.0587349	+	0.0190841i
$280$		0			0
$281$	12.9374	+	17.8068i	0.771779	+	1.06226i	0.996142	+	0.0877573i	$0.0279700\pi$
$281$	12.9374	+	17.8068i	0.771779	+	1.06226i	−0.224363	+	0.974506i	$0.572030\pi$
$282$	14.5325	+	7.40466i	0.865395	+	0.440941i
$283$	−13.6893	+	6.97507i	−0.813747	+	0.414625i	−0.810766	−	0.585371i	$-0.800949\pi$
$283$	−13.6893	+	6.97507i	−0.813747	+	0.414625i	−0.00298147	+	0.999996i	$0.500949\pi$
$284$	−25.4908	+	35.0851i	−1.51260	+	2.08192i
$285$		0			0
$286$	−9.67652	+	26.0047i	−0.572185	+	1.53769i
$287$	2.55106	+	2.55106i	0.150584	+	0.150584i
$288$	1.19242	+	7.52863i	0.0702639	+	0.443629i
$289$	−5.82133	−	1.89147i	−0.342431	−	0.111263i
$290$		0			0
$291$	7.41278	−	5.38570i	0.434545	−	0.315715i
$292$	−0.905015	+	5.71404i	−0.0529620	+	0.334389i
$293$	−9.93247	+	19.4936i	−0.580261	+	1.13883i	0.395188	+	0.918600i	$0.370680\pi$
$293$	−9.93247	+	19.4936i	−0.580261	+	1.13883i	−0.975449	+	0.220226i	$0.929320\pi$
$294$	−4.18646	+	12.8846i	−0.244159	+	0.751445i
$295$		0			0
$296$		−	6.53350i		−	0.379752i
$297$	2.24449	+	2.44177i	0.130239	+	0.141686i
$298$	−14.4555	+	14.4555i	−0.837385	+	0.837385i
$299$	−21.1764	−	15.3856i	−1.22466	−	0.889770i
$300$		0			0
$301$	2.72951	+	8.40056i	0.157326	+	0.484200i
$302$	27.6833	+	4.38461i	1.59300	+	0.252306i
$303$	−11.2499	−	1.78181i	−0.646290	−	0.102362i
$304$	−1.78574	−	5.49595i	−0.102419	−	0.315214i
$305$		0			0
$306$	−8.42826	−	6.12349i	−0.481811	−	0.350056i
$307$	1.44060	−	1.44060i	0.0822191	−	0.0822191i	−0.664801	−	0.747020i	$-0.731484\pi$
$307$	1.44060	−	1.44060i	0.0822191	−	0.0822191i	0.747020	+	0.664801i	$0.231484\pi$
$308$	−5.22642	−	5.68579i	−0.297803	−	0.323978i
$309$		−	15.4605i		−	0.879519i
$310$		0			0
$311$	−4.96363	+	15.2765i	−0.281462	+	0.866250i	0.705975	+	0.708236i	$0.250509\pi$
$311$	−4.96363	+	15.2765i	−0.281462	+	0.866250i	−0.987437	+	0.158013i	$0.949491\pi$
$312$	2.63635	−	5.17414i	0.149254	−	0.292928i
$313$	1.26973	−	8.01675i	0.0717693	−	0.453134i	−0.925466	−	0.378830i	$-0.876327\pi$
$313$	1.26973	−	8.01675i	0.0717693	−	0.453134i	0.997236	−	0.0743038i	$-0.0236735\pi$
$314$	−2.33990	+	1.70004i	−0.132048	+	0.0959387i
$315$		0			0
$316$	−10.5718	−	3.43499i	−0.594711	−	0.193233i
$317$	0.982650	+	6.20421i	0.0551911	+	0.348463i	0.999795	+	0.0202502i	$0.00644628\pi$
$317$	0.982650	+	6.20421i	0.0551911	+	0.348463i	−0.944604	+	0.328213i	$0.893554\pi$
$318$	10.0325	+	10.0325i	0.562594	+	0.562594i
$319$	5.61757	−	15.0967i	0.314523	−	0.845252i
$320$		0			0
$321$	−2.75991	+	3.79869i	−0.154043	+	0.212022i
$322$	11.3105	−	5.76299i	0.630310	−	0.321159i
$323$	11.6240	+	5.92274i	0.646778	+	0.329550i
$324$	−1.58357	−	2.17960i	−0.0879762	−	0.121089i
$325$		0			0
$326$	−10.7316	+	3.48691i	−0.594368	+	0.193122i
$327$	−3.42632	−	6.72453i	−0.189476	−	0.371867i
$328$	−6.20024	+	0.982021i	−0.342351	+	0.0542230i
$329$	−6.50650			−0.358715
$330$		0			0
$331$	12.6157			0.693420			0.346710	−	0.937972i	$-0.387299\pi$
$331$	12.6157			0.693420			0.346710	+	0.937972i	$0.387299\pi$
$332$	−36.2453	+	5.74070i	−1.98922	+	0.315062i
$333$	−1.97230	−	3.87086i	−0.108081	−	0.212122i
$334$	−50.0911	+	16.2756i	−2.74087	+	0.890561i
$335$		0			0
$336$	−1.08205	−	1.48932i	−0.0590308	−	0.0812490i
$337$	8.65746	+	4.41119i	0.471602	+	0.240293i	0.673605	−	0.739092i	$-0.264745\pi$
$337$	8.65746	+	4.41119i	0.471602	+	0.240293i	−0.202003	+	0.979385i	$0.564745\pi$
$338$	3.68701	−	1.87862i	0.200547	−	0.102184i
$339$	−9.82147	+	13.5181i	−0.533429	+	0.734202i
$340$		0			0
$341$	−0.919442	−	3.29541i	−0.0497906	−	0.178457i
$342$	4.15658	+	4.15658i	0.224762	+	0.224762i
$343$	−1.79190	−	11.3136i	−0.0967533	−	0.610876i
$344$	−14.6171	−	4.74938i	−0.788101	−	0.256069i
$345$		0			0
$346$	−37.1106	+	26.9624i	−1.99508	+	1.44951i
$347$	−1.26537	+	7.98922i	−0.0679285	+	0.428884i	0.930164	+	0.367145i	$0.119665\pi$
$347$	−1.26537	+	7.98922i	−0.0679285	+	0.428884i	−0.998092	+	0.0617391i	$0.980335\pi$
$348$	−5.94032	+	11.6585i	−0.318435	+	0.624963i
$349$	6.69962	−	20.6193i	0.358622	−	1.10373i	−0.595257	−	0.803535i	$-0.702950\pi$
$349$	6.69962	−	20.6193i	0.358622	−	1.10373i	0.953879	−	0.300191i	$-0.0970503\pi$
$350$		0			0
$351$		−	3.86134i		−	0.206103i
$352$	−25.1139	+	2.90109i	−1.33857	+	0.154628i
$353$	3.46607	−	3.46607i	0.184480	−	0.184480i	−0.608825	−	0.793305i	$-0.708359\pi$
$353$	3.46607	−	3.46607i	0.184480	−	0.184480i	0.793305	+	0.608825i	$0.208359\pi$
$354$	−13.7879	−	10.0175i	−0.732817	−	0.532422i
$355$		0			0
$356$	3.87117	+	11.9142i	0.205172	+	0.631453i
$357$	4.10477	+	0.650132i	0.217248	+	0.0344086i
$358$	4.25167	+	0.673398i	0.224708	+	0.0355902i
$359$	7.66946	+	23.6042i	0.404778	+	1.24578i	0.921080	+	0.389373i	$0.127308\pi$
$359$	7.66946	+	23.6042i	0.404778	+	1.24578i	−0.516302	+	0.856407i	$0.672692\pi$
$360$		0			0
$361$	9.41602	+	6.84114i	0.495580	+	0.360060i
$362$	−0.973554	+	0.973554i	−0.0511689	+	0.0511689i
$363$	−8.40437	+	7.09694i	−0.441115	+	0.372493i
$364$			8.99132i			0.471273i
$365$		0			0
$366$	0.346364	−	1.06600i	0.0181048	−	0.0557207i
$367$	−8.06905	+	15.8364i	−0.421201	+	0.826653i	0.578737	+	0.815514i	$0.303546\pi$
$367$	−8.06905	+	15.8364i	−0.421201	+	0.826653i	−0.999938	+	0.0111390i	$0.996454\pi$
$368$	2.25867	−	14.2607i	0.117741	−	0.743389i
$369$	−3.37697	+	2.45351i	−0.175798	+	0.127725i
$370$		0			0
$371$	−5.38294	−	1.74902i	−0.279468	−	0.0908047i
$372$	0.434753	+	2.74492i	0.0225409	+	0.142318i
$373$	−2.68094	−	2.68094i	−0.138814	−	0.138814i	0.634285	−	0.773099i	$-0.281294\pi$
$373$	−2.68094	−	2.68094i	−0.138814	−	0.138814i	−0.773099	+	0.634285i	$0.781294\pi$
$374$	21.4670	−	27.0744i	1.11003	−	1.39999i
$375$		0			0
$376$	6.65455	−	9.15920i	0.343182	−	0.472350i
$377$	−16.7095	+	8.51391i	−0.860582	+	0.438489i
$378$	1.66850	+	0.850141i	0.0858182	+	0.0437266i
$379$	−16.4337	−	22.6190i	−0.844142	−	1.16186i	−0.985123	−	0.171849i	$-0.945026\pi$
$379$	−16.4337	−	22.6190i	−0.844142	−	1.16186i	0.140982	−	0.990012i	$-0.454974\pi$
$380$		0			0
$381$	−1.49104	+	0.484468i	−0.0763883	+	0.0248201i
$382$	−16.8556	−	33.0810i	−0.862409	−	1.69257i
$383$	−5.32993	+	0.844178i	−0.272347	+	0.0431355i	−0.291114	−	0.956688i	$-0.594026\pi$
$383$	−5.32993	+	0.844178i	−0.272347	+	0.0431355i	0.0187671	+	0.999824i	$0.494026\pi$
$384$	11.3066			0.576988
$385$		0			0
$386$	−44.8771			−2.28419
$387$	−10.0938	+	1.59870i	−0.513097	+	0.0812666i
$388$	−11.2070	−	21.9950i	−0.568949	−	1.11662i
$389$	−23.4661	+	7.62459i	−1.18978	+	0.386582i	−0.835991	−	0.548744i	$-0.815106\pi$
$389$	−23.4661	+	7.62459i	−1.18978	+	0.386582i	−0.353787	+	0.935326i	$0.615106\pi$
$390$		0			0
$391$	19.1592	+	26.3704i	0.968924	+	1.33361i
$392$	8.37890	+	4.26926i	0.423198	+	0.215630i
$393$	6.95353	−	3.54300i	0.350759	−	0.178721i
$394$	−27.3393	+	37.6293i	−1.37733	+	1.89574i
$395$		0			0
$396$	7.44341	−	4.94342i	0.374046	−	0.248416i
$397$	19.9092	+	19.9092i	0.999213	+	0.999213i	1.00000		0.000786386i	$-0.000250315\pi$
$397$	19.9092	+	19.9092i	0.999213	+	0.999213i	−0.000786386		1.00000i	$0.500250\pi$
$398$	−2.36436	−	14.9280i	−0.118515	−	0.748273i
$399$	−2.23021	−	0.724640i	−0.111650	−	0.0362774i
$400$		0			0
$401$	29.8989	−	21.7228i	1.49308	−	1.08479i	0.520041	−	0.854141i	$-0.325917\pi$
$401$	29.8989	−	21.7228i	1.49308	−	1.08479i	0.973038	−	0.230644i	$-0.0740833\pi$
$402$	2.06360	−	13.0290i	0.102923	−	0.649830i
$403$	−1.80832	+	3.54903i	−0.0900790	+	0.176790i
$404$	−9.48265	+	29.1846i	−0.471779	+	1.45199i
$405$		0			0
$406$		−	9.09471i		−	0.451363i
$407$	13.1020	−	5.99562i	0.649440	−	0.297192i
$408$	−5.11337	+	5.11337i	−0.253149	+	0.253149i
$409$	23.5917	+	17.1404i	1.16653	+	0.847536i	0.990590	−	0.136864i	$-0.0437024\pi$
$409$	23.5917	+	17.1404i	1.16653	+	0.847536i	0.175943	+	0.984400i	$0.443702\pi$
$410$		0			0
$411$	−6.62207	−	20.3806i	−0.326643	−	1.00530i
$412$	−41.1399	−	6.51592i	−2.02682	−	0.321016i
$413$	6.71504	+	1.06356i	0.330425	+	0.0523342i
$414$	4.53855	+	13.9682i	0.223057	+	0.686500i
$415$		0			0
$416$	23.8117	+	17.3002i	1.16747	+	0.848214i
$417$	−8.67046	+	8.67046i	−0.424594	+	0.424594i
$418$	−14.3534	+	13.1938i	−0.702049	+	0.645329i
$419$			3.99414i			0.195126i	0.995229	+	0.0975632i	$0.0311048\pi$
$419$			3.99414i			0.195126i	−0.995229	+	0.0975632i	$0.968895\pi$
$420$		0			0
$421$	3.84749	−	11.8414i	0.187515	−	0.577113i	−0.812467	−	0.583007i	$-0.801876\pi$
$421$	3.84749	−	11.8414i	0.187515	−	0.577113i	0.999983	+	0.00589398i	$0.00187612\pi$
$422$	−20.4161	+	40.0688i	−0.993840	+	1.95052i
$423$	1.17764	−	7.43533i	0.0572589	−	0.361518i
$424$	7.96752	−	5.78874i	0.386937	−	0.281126i
$425$		0			0
$426$	33.1688	+	10.7772i	1.60703	+	0.522157i
$427$	0.0699475	+	0.441631i	0.00338500	+	0.0213720i
$428$	8.94499	+	8.94499i	0.432372	+	0.432372i
$429$	12.7953	+	0.538641i	0.617762	+	0.0260058i
$430$		0			0
$431$	1.02475	−	1.41044i	0.0493603	−	0.0679386i	−0.783623	−	0.621236i	$-0.786631\pi$
$431$	1.02475	−	1.41044i	0.0493603	−	0.0679386i	0.832984	+	0.553298i	$0.186631\pi$
$432$	1.89777	−	0.966963i	0.0913066	−	0.0465230i
$433$	−12.6248	−	6.43267i	−0.606711	−	0.309135i	0.123513	−	0.992343i	$-0.460584\pi$
$433$	−12.6248	−	6.43267i	−0.606711	−	0.309135i	−0.730223	+	0.683208i	$0.760584\pi$
$434$	−1.13542	−	1.56277i	−0.0545017	−	0.0750151i
$435$		0			0
$436$	−19.3378	+	6.28322i	−0.926111	+	0.300912i
$437$	−8.34982	−	16.3874i	−0.399426	−	0.783917i
$438$	4.59518	−	0.727805i	0.219566	−	0.0347758i
$439$	3.06567			0.146316			0.0731582	−	0.997320i	$-0.476692\pi$
$439$	3.06567			0.146316			0.0731582	+	0.997320i	$0.476692\pi$
$440$		0			0
$441$	6.25298			0.297761
$442$	−39.7317	+	6.29289i	−1.88985	+	0.299322i
$443$	−0.929947	−	1.82512i	−0.0441831	−	0.0867143i	0.867859	−	0.496810i	$-0.165495\pi$
$443$	−0.929947	−	1.82512i	−0.0441831	−	0.0867143i	−0.912043	+	0.410096i	$0.865495\pi$
$444$	−11.1314	+	3.61682i	−0.528275	+	0.171647i
$445$		0			0
$446$	−5.05014	−	6.95092i	−0.239131	−	0.329136i
$447$	8.40720	+	4.28368i	0.397647	+	0.202611i
$448$	−9.43756	+	4.80868i	−0.445883	+	0.227189i
$449$	17.9978	−	24.7719i	0.849370	−	1.16906i	−0.134631	−	0.990896i	$-0.542985\pi$
$449$	17.9978	−	24.7719i	0.849370	−	1.16906i	0.984001	−	0.178162i	$-0.0570152\pi$
$450$		0			0
$451$	−7.65909	−	11.5325i	−0.360653	−	0.543043i
$452$	31.8318	+	31.8318i	1.49724	+	1.49724i
$453$	−2.02373	−	12.7773i	−0.0950833	−	0.600332i
$454$	−14.6695	−	4.76641i	−0.688474	−	0.223699i
$455$		0			0
$456$	3.30104	−	2.39834i	0.154585	−	0.112313i
$457$	1.97017	−	12.4392i	0.0921607	−	0.581880i	−0.897785	−	0.440433i	$-0.854825\pi$
$457$	1.97017	−	12.4392i	0.0921607	−	0.581880i	0.989946	−	0.141446i	$-0.0451752\pi$
$458$	−25.8553	+	50.7439i	−1.20814	+	2.37110i
$459$	−1.48588	+	4.57308i	−0.0693551	+	0.213453i
$460$		0			0
$461$		−	34.8146i		−	1.62148i	−0.585409	−	0.810738i	$-0.699066\pi$
$461$		−	34.8146i		−	1.62148i	0.585409	−	0.810738i	$-0.300934\pi$
$462$	−3.04985	+	5.41029i	−0.141892	+	0.251709i
$463$	26.7521	−	26.7521i	1.24327	−	1.24327i	0.284639	−	0.958635i	$-0.408126\pi$
$463$	26.7521	−	26.7521i	1.24327	−	1.24327i	0.958635	−	0.284639i	$-0.0918739\pi$
$464$	−8.36884	−	6.08032i	−0.388513	−	0.282272i
$465$		0			0
$466$	0.279843	+	0.861269i	0.0129635	+	0.0398975i
$467$	32.2491	+	5.10776i	1.49231	+	0.236359i	0.848652	−	0.528952i	$-0.177415\pi$
$467$	32.2491	+	5.10776i	1.49231	+	0.236359i	0.643661	+	0.765311i	$0.277415\pi$
$468$	−10.2749	−	1.62738i	−0.474956	−	0.0752257i
$469$	1.62616	+	5.00482i	0.0750893	+	0.231101i
$470$		0			0
$471$	1.07999	+	0.784659i	0.0497634	+	0.0361552i
$472$	−8.36500	+	8.36500i	−0.385030	+	0.385030i
$473$	−3.88956	−	33.6708i	−0.178842	−	1.54818i
$474$			8.93927i			0.410594i
$475$		0			0
$476$	3.45995	−	10.6486i	0.158587	−	0.488080i
$477$	2.97299	−	5.83482i	0.136124	−	0.267158i
$478$	3.03310	−	19.1502i	0.138731	−	0.875912i
$479$	−17.2715	+	12.5485i	−0.789155	+	0.573355i	−0.907713	−	0.419592i	$-0.862173\pi$
$479$	−17.2715	+	12.5485i	−0.789155	+	0.573355i	0.118557	+	0.992947i	$0.462173\pi$
$480$		0			0
$481$	−15.9540	−	5.18378i	−0.727441	−	0.236360i
$482$	1.74425	+	11.0128i	0.0794485	+	0.501618i
$483$	−4.14294	−	4.14294i	−0.188510	−	0.188510i
$484$	15.3426	+	25.3548i	0.697392	+	1.15249i
$485$		0			0
$486$	−1.27349	+	1.75281i	−0.0577668	+	0.0795092i
$487$	−7.08841	+	3.61173i	−0.321207	+	0.163663i	−0.607158	−	0.794581i	$-0.707690\pi$
$487$	−7.08841	+	3.61173i	−0.321207	+	0.163663i	0.285951	+	0.958244i	$0.407690\pi$
$488$	−0.693224	−	0.353215i	−0.0313808	−	0.0159893i
$489$	3.06125	+	4.21345i	0.138435	+	0.190539i
$490$		0			0
$491$	−14.1432	+	4.59541i	−0.638275	+	0.207388i	−0.610237	−	0.792219i	$-0.708926\pi$
$491$	−14.1432	+	4.59541i	−0.638275	+	0.207388i	−0.0280376	+	0.999607i	$0.508926\pi$
$492$	5.10546	+	10.0200i	0.230172	+	0.451737i
$493$	23.0657	−	3.65325i	1.03883	−	0.164534i
$494$	22.6981			1.02123
$495$		0			0
$496$	−2.19712			−0.0986538
$497$	−13.7415	+	2.17643i	−0.616388	+	0.0976263i
$498$	13.3979	+	26.2949i	0.600376	+	1.17830i
$499$	−3.20365	+	1.04093i	−0.143415	+	0.0465985i	−0.379845	−	0.925050i	$-0.624023\pi$
$499$	−3.20365	+	1.04093i	−0.143415	+	0.0465985i	0.236430	+	0.971649i	$0.424023\pi$
$500$		0			0
$501$	14.2888	+	19.6668i	0.638376	+	0.878650i
$502$	24.5655	+	12.5167i	1.09641	+	0.558649i
$503$	8.11747	−	4.13606i	0.361940	−	0.184418i	−0.263558	−	0.964644i	$-0.584896\pi$
$503$	8.11747	−	4.13606i	0.361940	−	0.184418i	0.625498	+	0.780226i	$0.284896\pi$
$504$	0.764020	−	1.05158i	0.0340322	−	0.0468413i
$505$		0			0
$506$	−46.9194	+	13.0908i	−2.08582	+	0.581958i
$507$	−1.35052	−	1.35052i	−0.0599786	−	0.0599786i
$508$	0.660745	+	4.17178i	0.0293158	+	0.185093i
$509$	0.588312	+	0.191154i	0.0260765	+	0.00847276i	0.322026	−	0.946731i	$-0.395636\pi$
$509$	0.588312	+	0.191154i	0.0260765	+	0.00847276i	−0.295950	+	0.955204i	$0.595636\pi$
$510$		0			0
$511$	−1.50151	+	1.09091i	−0.0664230	+	0.0482592i
$512$	−3.54193	+	22.3629i	−0.156533	+	0.988308i
$513$	1.23174	−	2.41743i	0.0543828	−	0.106732i
$514$	−2.22543	+	6.84916i	−0.0981594	+	0.302104i
$515$		0			0
$516$			27.5330i			1.21207i
$517$	24.4741	+	4.93954i	1.07637	+	0.217241i
$518$	5.75249	−	5.75249i	0.252750	−	0.252750i
$519$	17.1285	+	12.4446i	0.751860	+	0.546258i
$520$		0			0
$521$	−1.47759	−	4.54754i	−0.0647342	−	0.199231i	0.913458	−	0.406933i	$-0.133402\pi$
$521$	−1.47759	−	4.54754i	−0.0647342	−	0.199231i	−0.978192	+	0.207702i	$0.933402\pi$
$522$	10.3930	+	1.64609i	0.454890	+	0.0720476i
$523$	−6.91964	−	1.09596i	−0.302575	−	0.0479231i	0.00330118	−	0.999995i	$-0.498949\pi$
$523$	−6.91964	−	1.09596i	−0.302575	−	0.0479231i	−0.305876	+	0.952071i	$0.598949\pi$
$524$	−6.49719	−	19.9963i	−0.283831	−	0.873543i
$525$		0			0
$526$	−4.66363	−	3.38833i	−0.203344	−	0.147738i
$527$	3.50735	−	3.50735i	0.152783	−	0.152783i
$528$	2.93948	+	6.42351i	0.127925	+	0.279548i
$529$		−	22.9530i		−	0.997956i
$530$		0			0
$531$	−2.43077	+	7.48114i	−0.105486	+	0.324654i
$532$	−2.86817	+	5.62911i	−0.124351	+	0.244053i
$533$	−2.52138	+	15.9194i	−0.109213	+	0.689545i
$534$	8.15035	−	5.92158i	0.352700	−	0.256252i
$535$		0			0
$536$	−8.70845	−	2.82955i	−0.376148	−	0.122218i
$537$	−0.310810	−	1.96237i	−0.0134124	−	0.0846827i
$538$	−15.4414	−	15.4414i	−0.665725	−	0.665725i
$539$	−0.872266	+	20.7204i	−0.0375711	+	0.892492i
$540$		0			0
$541$	10.5952	−	14.5831i	0.455524	−	0.626975i	−0.518049	−	0.855351i	$-0.673342\pi$
$541$	10.5952	−	14.5831i	0.455524	−	0.626975i	0.973573	+	0.228376i	$0.0733415\pi$
$542$	38.3218	−	19.5259i	1.64606	−	0.838711i
$543$	0.566211	+	0.288499i	0.0242984	+	0.0123807i
$544$	−21.5435	−	29.6521i	−0.923672	−	1.27132i
$545$		0			0
$546$	6.87683	−	2.23442i	0.294301	−	0.0956243i
$547$	5.68228	+	11.1521i	0.242957	+	0.476830i	0.979995	−	0.199021i	$-0.0637763\pi$
$547$	5.68228	+	11.1521i	0.242957	+	0.476830i	−0.737038	+	0.675851i	$0.763776\pi$
$548$	−57.0230	+	9.03156i	−2.43590	+	0.385809i
$549$	−0.517337			−0.0220794
$550$		0			0
$551$	−13.1770			−0.561361
$552$	10.0692	−	1.59481i	0.428575	−	0.0678796i
$553$	−1.61897	−	3.17740i	−0.0688455	−	0.135117i
$554$	38.3258	−	12.4528i	1.62831	−	0.529069i
$555$		0			0
$556$	19.4176	+	26.7260i	0.823488	+	1.13343i
$557$	−17.5893	−	8.96222i	−0.745285	−	0.379741i	0.0397367	−	0.999210i	$-0.487348\pi$
$557$	−17.5893	−	8.96222i	−0.745285	−	0.379741i	−0.785021	+	0.619469i	$0.787348\pi$
$558$	1.99136	−	1.01465i	0.0843011	−	0.0429535i
$559$	−23.1948	+	31.9250i	−0.981038	+	1.35028i
$560$		0			0
$561$	−14.9465	−	5.56168i	−0.631041	−	0.234814i
$562$	−33.7202	−	33.7202i	−1.42240	−	1.42240i
$563$	3.47414	+	21.9349i	0.146418	+	0.924445i	0.946065	+	0.323976i	$0.105020\pi$
$563$	3.47414	+	21.9349i	0.146418	+	0.924445i	−0.799648	+	0.600469i	$0.794980\pi$
$564$	−19.2888	−	6.26732i	−0.812206	−	0.263902i
$565$		0			0
$566$	26.9301	−	19.5658i	1.13195	−	0.822413i
$567$	0.135207	−	0.853664i	0.00567816	−	0.0358505i
$568$	10.9904	−	21.5698i	0.461145	−	0.905049i
$569$	12.9364	−	39.8142i	0.542323	−	1.66910i	−0.184947	−	0.982748i	$-0.559211\pi$
$569$	12.9364	−	39.8142i	0.542323	−	1.66910i	0.727271	−	0.686351i	$-0.240789\pi$
$570$		0			0
$571$		−	17.1045i		−	0.715801i	−0.933760	−	0.357901i	$-0.883493\pi$
$571$		−	17.1045i		−	0.715801i	0.933760	−	0.357901i	$-0.116507\pi$
$572$	6.82594	−	33.8207i	0.285407	−	1.41412i
$573$	−12.1173	+	12.1173i	−0.506207	+	0.506207i
$574$	−6.32370	−	4.59443i	−0.263946	−	0.191768i
$575$		0			0
$576$	−3.78699	−	11.6552i	−0.157791	−	0.485632i
$577$	−1.22406	−	0.193873i	−0.0509584	−	0.00807102i	0.130903	−	0.991395i	$-0.458212\pi$
$577$	−1.22406	−	0.193873i	−0.0509584	−	0.00807102i	−0.181862	+	0.983324i	$0.558212\pi$
$578$	13.0983	+	2.07456i	0.544816	+	0.0862903i
$579$	6.40074	+	19.6994i	0.266006	+	0.818681i
$580$		0			0
$581$	−9.52441	−	6.91989i	−0.395139	−	0.287085i
$582$	−14.0374	+	14.0374i	−0.581868	+	0.581868i
$583$	18.9200	+	10.6655i	0.783588	+	0.441719i
$584$		−	3.22942i		−	0.133634i
$585$		0			0
$586$	14.6477	−	45.0811i	0.605092	−	1.86228i
$587$	16.9627	−	33.2912i	0.700126	−	1.37407i	−0.217275	−	0.976110i	$-0.569717\pi$
$587$	16.9627	−	33.2912i	0.700126	−	1.37407i	0.917401	−	0.397964i	$-0.130283\pi$
$588$	2.63535	−	16.6389i	0.108680	−	0.686178i
$589$	−2.26424	+	1.64507i	−0.0932964	+	0.0677838i
$590$		0			0
$591$	20.4173	+	6.63397i	0.839854	+	0.272885i
$592$	−1.44751	−	9.13922i	−0.0594923	−	0.375620i
$593$	−19.7192	−	19.7192i	−0.809770	−	0.809770i	0.174829	−	0.984599i	$-0.444063\pi$
$593$	−19.7192	−	19.7192i	−0.809770	−	0.809770i	−0.984599	+	0.174829i	$0.944063\pi$
$594$	−5.63063	−	4.46447i	−0.231027	−	0.183179i
$595$		0			0
$596$	14.9420	−	20.5659i	0.612047	−	0.842410i
$597$	−6.21562	+	3.16702i	−0.254389	+	0.129617i
$598$	50.5304	+	25.7465i	2.06634	+	1.05285i
$599$	11.2303	+	15.4572i	0.458859	+	0.631566i	0.974272	−	0.225377i	$-0.0723613\pi$
$599$	11.2303	+	15.4572i	0.458859	+	0.631566i	−0.515412	+	0.856942i	$0.672361\pi$
$600$		0			0
$601$	−20.1867	+	6.55907i	−0.823434	+	0.267550i	−0.690277	−	0.723545i	$-0.742511\pi$
$601$	−20.1867	+	6.55907i	−0.823434	+	0.267550i	−0.133157	+	0.991095i	$0.542511\pi$
$602$	−8.68813	−	17.0514i	−0.354102	−	0.694964i
$603$	−6.01361	+	0.952462i	−0.244893	+	0.0387872i
$604$	−34.8530			−1.41815
$605$		0			0
$606$	24.6778			1.00247
$607$	21.4858	−	3.40302i	0.872082	−	0.138124i	0.295677	−	0.955288i	$-0.404455\pi$
$607$	21.4858	−	3.40302i	0.872082	−	0.138124i	0.576405	+	0.817164i	$0.304455\pi$
$608$	9.38893	+	18.4268i	0.380771	+	0.747306i
$609$	−3.99225	+	1.29716i	−0.161774	+	0.0525636i
$610$		0			0
$611$	−17.0859	−	23.5167i	−0.691220	−	0.951383i
$612$	11.5426	+	5.88123i	0.466580	+	0.237735i
$613$	−25.4981	+	12.9919i	−1.02986	+	0.524740i	−0.885429	−	0.464775i	$-0.846135\pi$
$613$	−25.4981	+	12.9919i	−1.02986	+	0.524740i	−0.144431	+	0.989515i	$0.546135\pi$
$614$	−2.59450	+	3.57102i	−0.104705	+	0.144115i
$615$		0			0
$616$	3.37804	+	2.67842i	0.136105	+	0.107917i
$617$	−3.05678	−	3.05678i	−0.123061	−	0.123061i	0.642894	−	0.765955i	$-0.277734\pi$
$617$	−3.05678	−	3.05678i	−0.123061	−	0.123061i	−0.765955	+	0.642894i	$0.777734\pi$
$618$	5.24004	+	33.0843i	0.210785	+	1.33085i
$619$	32.8210	+	10.6642i	1.31919	+	0.428629i	0.882215	−	0.470846i	$-0.156051\pi$
$619$	32.8210	+	10.6642i	1.31919	+	0.428629i	0.436971	+	0.899476i	$0.356051\pi$
$620$		0			0
$621$	5.48422	−	3.98452i	0.220074	−	0.159893i
$622$	5.44411	−	34.3728i	0.218289	−	1.37822i
$623$	−1.82454	+	3.58087i	−0.0730988	+	0.143465i
$624$	2.54146	−	7.82180i	0.101740	−	0.313123i
$625$		0			0
$626$			17.5856i			0.702860i
$627$	7.83879	+	4.41884i	0.313051	+	0.176471i
$628$	2.54312	−	2.54312i	0.101481	−	0.101481i
$629$	16.9000	+	12.2786i	0.673847	+	0.489578i
$630$		0			0
$631$	7.36128	+	22.6557i	0.293048	+	0.901908i	0.983870	+	0.178884i	$0.0572487\pi$
$631$	7.36128	+	22.6557i	0.293048	+	0.901908i	−0.690822	+	0.723025i	$0.742751\pi$
$632$	6.12864	+	0.970681i	0.243784	+	0.0386116i
$633$	20.5007	+	3.24699i	0.814829	+	0.129056i
$634$	−4.20558	−	12.9435i	−0.167025	−	0.514050i
$635$		0			0
$636$	−14.2732	−	10.3701i	−0.565971	−	0.411202i
$637$	17.0730	−	17.0730i	0.676456	−	0.676456i
$638$	−6.90443	+	34.2096i	−0.273349	+	1.35437i
$639$		−	16.0970i		−	0.636789i
$640$		0			0
$641$	−7.69272	+	23.6758i	−0.303844	+	0.935137i	0.676262	+	0.736662i	$0.263599\pi$
$641$	−7.69272	+	23.6758i	−0.303844	+	0.935137i	−0.980106	+	0.198475i	$0.936401\pi$
$642$	4.61849	−	9.06430i	0.182277	−	0.357740i
$643$	0.0163360	−	0.103141i	0.000644228	−	0.00406749i	−0.987364	−	0.158468i	$-0.949345\pi$
$643$	0.0163360	−	0.103141i	0.000644228	−	0.00406749i	0.988008	+	0.154400i	$0.0493446\pi$
$644$	−12.7703	+	9.27815i	−0.503219	+	0.365610i
$645$		0			0
$646$	−26.8819	−	8.73445i	−1.05765	−	0.343652i
$647$	3.10582	+	19.6094i	0.122102	+	0.770924i	0.970418	+	0.241433i	$0.0776173\pi$
$647$	3.10582	+	19.6094i	0.122102	+	0.770924i	−0.848315	+	0.529492i	$0.822383\pi$
$648$	1.06342	+	1.06342i	0.0417750	+	0.0417750i
$649$	−24.4511	−	9.09841i	−0.959790	−	0.357144i
$650$		0			0
$651$	−0.524055	+	0.721300i	−0.0205394	+	0.0282700i
$652$	12.5020	−	6.37010i	0.489617	−	0.249472i
$653$	−20.3785	−	10.3834i	−0.797474	−	0.406333i	0.00725675	−	0.999974i	$-0.497690\pi$
$653$	−20.3785	−	10.3834i	−0.797474	−	0.406333i	−0.804730	+	0.593641i	$0.797690\pi$
$654$	9.61119	+	13.2287i	0.375827	+	0.517282i
$655$		0			0
$656$	−8.45548	+	2.74735i	−0.330131	+	0.107266i
$657$	−0.974881	−	1.91331i	−0.0380337	−	0.0746454i
$658$	13.9234	−	2.20525i	0.542790	−	0.0859695i
$659$	15.2005			0.592126			0.296063	−	0.955168i	$-0.404326\pi$
$659$	15.2005			0.592126			0.296063	+	0.955168i	$0.404326\pi$
$660$		0			0
$661$	9.56894			0.372189			0.186094	−	0.982532i	$-0.440417\pi$
$661$	9.56894			0.372189			0.186094	+	0.982532i	$0.440417\pi$
$662$	−26.9965	+	4.27583i	−1.04925	+	0.166185i
$663$	8.42921	+	16.5433i	0.327363	+	0.642487i
$664$	19.4823	−	6.33017i	0.756058	−	0.245658i
$665$		0			0
$666$	5.53252	+	7.61485i	0.214381	+	0.295070i
$667$	−29.3347	−	14.9468i	−1.13585	−	0.578742i
$668$	58.3548	−	29.7333i	2.25782	−	1.15041i
$669$	−2.33091	+	3.20822i	−0.0901182	+	0.124037i
$670$		0			0
$671$	0.0721664	−	1.71429i	0.00278595	−	0.0661796i
$672$	4.65852	+	4.65852i	0.179706	+	0.179706i
$673$	0.506604	+	3.19857i	0.0195282	+	0.123296i	0.995527	−	0.0944815i	$-0.0301193\pi$
$673$	0.506604	+	3.19857i	0.0195282	+	0.123296i	−0.975998	+	0.217777i	$0.930119\pi$
$674$	−20.0214	−	6.50533i	−0.771194	−	0.250576i
$675$		0			0
$676$	−4.16286	+	3.02449i	−0.160110	+	0.116327i
$677$	−0.896704	+	5.66156i	−0.0344631	+	0.217592i	−0.998910	−	0.0466867i	$-0.985134\pi$
$677$	−0.896704	+	5.66156i	−0.0344631	+	0.217592i	0.964446	+	0.264278i	$0.0851337\pi$
$678$	16.4355	−	32.2564i	0.631200	−	1.23880i
$679$	2.44722	−	7.53176i	0.0939156	−	0.289042i
$680$		0			0
$681$			7.11921i			0.272809i
$682$	3.08445	+	6.74030i	0.118110	+	0.258099i
$683$	−5.04567	+	5.04567i	−0.193067	+	0.193067i	−0.797020	−	0.603953i	$-0.793592\pi$
$683$	−5.04567	+	5.04567i	−0.193067	+	0.193067i	0.603953	+	0.797020i	$0.293592\pi$
$684$	−5.91357	−	4.29646i	−0.226111	−	0.164279i
$685$		0			0
$686$	7.66903	+	23.6028i	0.292805	+	0.901161i
$687$	25.9624	+	4.11204i	0.990527	+	0.156884i
$688$	−21.4990	−	3.40511i	−0.819641	−	0.129818i
$689$	−7.81387	−	24.0486i	−0.297685	−	0.916180i
$690$		0			0
$691$	14.3602	+	10.4333i	0.546289	+	0.396903i	0.826416	−	0.563061i	$-0.190376\pi$
$691$	14.3602	+	10.4333i	0.546289	+	0.396903i	−0.280126	+	0.959963i	$0.590376\pi$
$692$	40.3336	−	40.3336i	1.53325	−	1.53325i
$693$	2.80992	+	0.567117i	0.106740	+	0.0215430i
$694$		−	17.5252i		−	0.665246i
$695$		0			0
$696$	2.25708	−	6.94657i	0.0855543	−	0.263309i
$697$	9.11209	−	17.8835i	0.345145	−	0.677385i
$698$	−7.34815	+	46.3944i	−0.278131	+	1.75605i
$699$	0.338153	−	0.245682i	0.0127901	−	0.00929256i
$700$		0			0
$701$	−7.00098	−	2.27476i	−0.264423	−	0.0859164i	0.173805	−	0.984780i	$-0.444394\pi$
$701$	−7.00098	−	2.27476i	−0.264423	−	0.0859164i	−0.438228	+	0.898864i	$0.644394\pi$
$702$	1.30872	+	8.26295i	0.0493946	+	0.311865i
$703$	−8.33460	−	8.33460i	−0.314345	−	0.314345i
$704$	39.1499	−	10.9231i	1.47552	−	0.411679i
$705$		0			0
$706$	−6.24235	+	8.59186i	−0.234934	+	0.323359i
$707$	−8.77155	+	4.46933i	−0.329888	+	0.168086i
$708$	18.8826	+	9.62116i	0.709651	+	0.361585i
$709$	−5.88349	−	8.09792i	−0.220959	−	0.304124i	0.684118	−	0.729371i	$-0.260187\pi$
$709$	−5.88349	−	8.09792i	−0.220959	−	0.304124i	−0.905077	+	0.425247i	$0.860187\pi$
$710$		0			0
$711$	3.92402	−	1.27499i	0.147162	−	0.0478159i
$712$	−3.17473	−	6.23076i	−0.118978	−	0.233508i
$713$	−6.90667	+	1.09391i	−0.258657	+	0.0409672i
$714$	−9.00424			−0.336975
$715$		0			0
$716$	−5.35280			−0.200043
$717$	−8.83887	+	1.39994i	−0.330094	+	0.0522817i
$718$	−24.4122	−	47.9116i	−0.911054	−	1.78805i
$719$	−19.0499	+	6.18968i	−0.710440	+	0.230836i	−0.641873	−	0.766811i	$-0.721843\pi$
$719$	−19.0499	+	6.18968i	−0.710440	+	0.230836i	−0.0685666	+	0.997647i	$0.521843\pi$
$720$		0			0
$721$	−7.85434	−	10.8106i	−0.292511	−	0.402607i
$722$	−22.4682	−	11.4481i	−0.836179	−	0.426055i
$723$	4.58543	−	2.33639i	0.170534	−	0.0868914i
$724$	1.00632	−	1.38508i	0.0373995	−	0.0514760i
$725$		0			0
$726$	15.5793	−	18.0354i	0.578203	−	0.669356i
$727$	−0.469364	−	0.469364i	−0.0174077	−	0.0174077i	0.698349	−	0.715757i	$-0.253918\pi$
$727$	−0.469364	−	0.469364i	−0.0174077	−	0.0174077i	−0.715757	+	0.698349i	$0.753918\pi$
$728$	−0.785157	−	4.95728i	−0.0290998	−	0.183729i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$		0			0
$731$	39.7553	−	28.8839i	1.47040	−	1.06831i
$732$	−0.218034	+	1.37661i	−0.00805877	+	0.0508811i
$733$	4.98837	−	9.79023i	0.184250	−	0.361610i	−0.780344	−	0.625350i	$-0.784956\pi$
$733$	4.98837	−	9.79023i	0.184250	−	0.361610i	0.964594	+	0.263740i	$0.0849561\pi$
$734$	11.8997	−	36.6235i	0.439225	−	1.35180i
$735$		0			0
$736$			51.6717i			1.90464i
$737$	−2.31729	−	20.0601i	−0.0853584	−	0.738923i
$738$	6.39487	−	6.39487i	0.235398	−	0.235398i
$739$	−6.41880	−	4.66353i	−0.236119	−	0.171551i	0.463433	−	0.886132i	$-0.346617\pi$
$739$	−6.41880	−	4.66353i	−0.236119	−	0.171551i	−0.699553	+	0.714581i	$0.746617\pi$
$740$		0			0
$741$	−3.23738	−	9.96362i	−0.118928	−	0.366023i
$742$	12.1119	+	1.91833i	0.444640	+	0.0704241i
$743$	−16.0963	−	2.54941i	−0.590518	−	0.0935288i	−0.145978	−	0.989288i	$-0.546633\pi$
$743$	−16.0963	−	2.54941i	−0.590518	−	0.0935288i	−0.444540	+	0.895759i	$0.646633\pi$
$744$	−0.479395	−	1.47543i	−0.0175755	−	0.0540917i
$745$		0			0
$746$	6.64564	+	4.82834i	0.243314	+	0.176778i
$747$	9.63160	−	9.63160i	0.352402	−	0.352402i
$748$	−21.0987	+	37.4281i	−0.771445	+	1.36851i
$749$			4.05829i			0.148287i
$750$		0			0
$751$	−5.73752	+	17.6583i	−0.209365	+	0.644360i	0.790141	+	0.612926i	$0.210007\pi$
$751$	−5.73752	+	17.6583i	−0.209365	+	0.644360i	−0.999506	+	0.0314342i	$0.989993\pi$
$752$	7.27931	−	14.2864i	0.265449	−	0.520973i
$753$	1.99067	−	12.5686i	0.0725440	−	0.458025i
$754$	32.8713	−	23.8824i	1.19710	−	0.869747i
$755$		0			0
$756$	−2.21458	−	0.719562i	−0.0805436	−	0.0261702i
$757$	6.75295	+	42.6364i	0.245440	+	1.54965i	0.735237	+	0.677811i	$0.237071\pi$
$757$	6.75295	+	42.6364i	0.245440	+	1.54965i	−0.489796	+	0.871837i	$0.662929\pi$
$758$	42.8330	+	42.8330i	1.55577	+	1.55577i
$759$	12.4384	+	18.7288i	0.451486	+	0.679813i
$760$		0			0
$761$	−1.53149	+	2.10792i	−0.0555166	+	0.0764120i	−0.835873	−	0.548923i	$-0.815038\pi$
$761$	−1.53149	+	2.10792i	−0.0555166	+	0.0764120i	0.780356	+	0.625335i	$0.215038\pi$
$762$	3.02650	−	1.54208i	0.109639	−	0.0558637i
$763$	−5.81204	−	2.96138i	−0.210410	−	0.107209i
$764$	27.1368	+	37.3505i	0.981773	+	1.35130i
$765$		0			0
$766$	11.1195	−	3.61295i	0.401764	−	0.130541i
$767$	13.7894	+	27.0633i	0.497907	+	0.977198i
$768$	0.0129515	−	0.00205132i	0.000467347	−	7.40205e-5i
$769$	53.6748			1.93556			0.967781	−	0.251793i	$-0.0810203\pi$
$769$	53.6748			1.93556			0.967781	+	0.251793i	$0.0810203\pi$
$770$		0			0
$771$	3.32394			0.119709
$772$	55.1171	−	8.72969i	1.98371	−	0.314188i
$773$	1.21726	+	2.38902i	0.0437820	+	0.0859269i	0.911861	−	0.410499i	$-0.134645\pi$
$773$	1.21726	+	2.38902i	0.0437820	+	0.0859269i	−0.868079	+	0.496426i	$0.834645\pi$
$774$	21.0581	−	6.84219i	0.756918	−	0.245937i
$775$		0			0
$776$	8.09956	+	11.1481i	0.290757	+	0.400193i
$777$	−3.34560	−	1.70467i	−0.120023	−	0.0611546i
$778$	47.6313	−	24.2694i	1.70767	−	0.870099i
$779$	−6.65673	+	9.16220i	−0.238502	+	0.328270i
$780$		0			0
$781$	53.3406	+	2.24547i	1.90868	+	0.0803493i
$782$	−49.9369	−	49.9369i	−1.78574	−	1.78574i
$783$	−0.759761	−	4.79694i	−0.0271516	−	0.171429i
$784$	12.6665	+	4.11559i	0.452375	+	0.146985i
$785$		0			0
$786$	−13.6792	+	9.93850i	−0.487920	+	0.354495i
$787$	−0.511018	+	3.22644i	−0.0182158	+	0.115010i	−0.995121	−	0.0986640i	$-0.968543\pi$
$787$	−0.511018	+	3.22644i	−0.0182158	+	0.115010i	0.976905	+	0.213674i	$0.0685431\pi$
$788$	26.2577	−	51.5336i	0.935392	−	1.83581i
$789$	−0.822188	+	2.53044i	−0.0292707	+	0.0900859i
$790$		0			0
$791$			14.4419i			0.513495i
$792$	−3.67218	+	3.37550i	−0.130485	+	0.119943i
$793$	−1.41252	+	1.41252i	−0.0501602	+	0.0501602i
$794$	−49.3519	−	35.8562i	−1.75143	−	1.27249i
$795$		0			0
$796$	5.80771	+	17.8743i	0.205849	+	0.633538i
$797$	−4.37329	−	0.692661i	−0.154910	−	0.0245353i	0.0784978	−	0.996914i	$-0.474988\pi$
$797$	−4.37329	−	0.692661i	−0.154910	−	0.0245353i	−0.233408	+	0.972379i	$0.574988\pi$
$798$	5.01808	+	0.794786i	0.177638	+	0.0281351i
$799$	11.1858	+	34.4262i	0.395724	+	1.21791i
$800$		0			0
$801$	−3.76183	−	2.73313i	−0.132918	−	0.0965703i
$802$	−56.6187	+	56.6187i	−1.99928	+	1.99928i
$803$	6.47611	−	2.96355i	0.228537	−	0.104582i
$804$			16.4034i			0.578503i
$805$		0			0
$806$	2.66679	−	8.20755i	0.0939338	−	0.289098i
$807$	−4.57583	+	8.98058i	−0.161077	+	0.316131i
$808$	2.67966	−	16.9187i	0.0942703	−	0.595199i
$809$	−0.650906	+	0.472911i	−0.0228846	+	0.0166267i	−0.599169	−	0.800623i	$-0.704502\pi$
$809$	−0.650906	+	0.472911i	−0.0228846	+	0.0166267i	0.576284	+	0.817249i	$0.304502\pi$
$810$		0			0
$811$	−26.9792	−	8.76606i	−0.947367	−	0.307818i	−0.205722	−	0.978611i	$-0.565954\pi$
$811$	−26.9792	−	8.76606i	−0.947367	−	0.307818i	−0.741645	+	0.670792i	$0.765954\pi$
$812$	1.76914	+	11.1699i	0.0620847	+	0.391987i
$813$	−14.0369	−	14.0369i	−0.492297	−	0.492297i
$814$	−26.0050	+	17.2708i	−0.911476	+	0.605341i
$815$		0			0
$816$	−6.01983	+	8.28558i	−0.210736	+	0.290053i
$817$	−24.7053	+	12.5880i	−0.864328	+	0.440397i
$818$	−56.2937	−	28.6831i	−1.96826	−	1.00288i
$819$	−1.96166	−	2.69999i	−0.0685459	−	0.0943453i
$820$		0			0
$821$	17.9704	−	5.83895i	0.627173	−	0.203781i	0.0218505	−	0.999761i	$-0.493044\pi$
$821$	17.9704	−	5.83895i	0.627173	−	0.203781i	0.605322	+	0.795980i	$0.293044\pi$
$822$	21.0783	+	41.3685i	0.735191	+	1.44289i
$823$	22.1101	−	3.50190i	0.770710	−	0.122068i	0.241318	−	0.970446i	$-0.422420\pi$
$823$	22.1101	−	3.50190i	0.770710	−	0.122068i	0.529392	+	0.848378i	$0.322420\pi$
$824$	23.2511			0.809991
$825$		0			0
$826$	−14.7301			−0.512526
$827$	13.8406	−	2.19213i	0.481284	−	0.0762280i	0.0889219	−	0.996039i	$-0.471658\pi$
$827$	13.8406	−	2.19213i	0.481284	−	0.0762280i	0.392363	+	0.919811i	$0.371658\pi$
$828$	−8.29130	−	16.2726i	−0.288142	−	0.565511i
$829$	30.3401	−	9.85809i	1.05375	−	0.342385i	0.269613	−	0.962969i	$-0.413104\pi$
$829$	30.3401	−	9.85809i	1.05375	−	0.342385i	0.784141	+	0.620583i	$0.213104\pi$
$830$		0			0
$831$	−10.9327	−	15.0475i	−0.379250	−	0.521993i
$832$	−42.1629	−	21.4831i	−1.46174	−	0.744792i
$833$	−26.7898	+	13.6501i	−0.928213	+	0.472948i
$834$	15.6154	−	21.4928i	0.540718	−	0.744234i
$835$		0			0
$836$	15.0621	−	18.9964i	0.520932	−	0.657004i
$837$	−0.729418	−	0.729418i	−0.0252124	−	0.0252124i
$838$	−1.35373	−	8.54713i	−0.0467639	−	0.295256i
$839$	14.8731	+	4.83255i	0.513475	+	0.166838i	0.554282	−	0.832329i	$-0.312993\pi$
$839$	14.8731	+	4.83255i	0.513475	+	0.166838i	−0.0408068	+	0.999167i	$0.512993\pi$
$840$		0			0
$841$	4.37849	−	3.18116i	0.150983	−	0.109695i
$842$	−4.21993	+	26.6436i	−0.145428	+	0.918199i
$843$	−9.99250	+	19.6114i	−0.344160	+	0.675452i
$844$	17.2802	−	53.1831i	0.594810	−	1.83064i
$845$		0			0
$846$			16.3102i			0.560755i
$847$	−2.27122	+	9.23208i	−0.0780401	+	0.317218i
$848$	9.86266	−	9.86266i	0.338685	−	0.338685i
$849$	−12.4297	−	9.03068i	−0.426585	−	0.309932i
$850$		0			0
$851$	−9.10051	−	28.0085i	−0.311961	−	0.960118i
$852$	−42.8336	−	6.78418i	−1.46745	−	0.232422i
$853$	10.0374	+	1.58977i	0.343675	+	0.0544328i	0.325886	−	0.945409i	$-0.394337\pi$
$853$	10.0374	+	1.58977i	0.343675	+	0.0544328i	0.0177890	+	0.999842i	$0.494337\pi$
$854$	−0.299364	−	0.921349i	−0.0102440	−	0.0315279i
$855$		0			0
$856$	−5.71285	−	4.15063i	−0.195261	−	0.141866i
$857$	−22.7332	+	22.7332i	−0.776550	+	0.776550i	−0.979243	−	0.202692i	$-0.935031\pi$
$857$	−22.7332	+	22.7332i	−0.776550	+	0.776550i	0.202692	+	0.979243i	$0.435031\pi$
$858$	−27.5634	+	3.18405i	−0.941000	+	0.108702i
$859$			45.0738i			1.53790i	0.639310	+	0.768949i	$0.279220\pi$
$859$			45.0738i			1.53790i	−0.639310	+	0.768949i	$0.720780\pi$
$860$		0			0
$861$	−1.11485	+	3.43117i	−0.0379941	+	0.116934i
$862$	−1.71483	+	3.36555i	−0.0584075	+	0.114631i
$863$	−3.91752	+	24.7343i	−0.133354	+	0.841964i	0.826801	+	0.562495i	$0.190158\pi$
$863$	−3.91752	+	24.7343i	−0.133354	+	0.841964i	−0.960155	+	0.279469i	$0.909842\pi$
$864$	−6.16671	+	4.48038i	−0.209796	+	0.152426i
$865$		0			0
$866$	29.1964	+	9.48647i	0.992133	+	0.322363i
$867$	−0.957521	−	6.04555i	−0.0325191	−	0.205318i
$868$	1.69849	+	1.69849i	0.0576504	+	0.0576504i
$869$	3.67754	+	13.1808i	0.124752	+	0.447129i
$870$		0			0
$871$	−13.8188	+	19.0200i	−0.468233	+	0.644468i
$872$	10.1130	−	5.15285i	0.342470	−	0.174497i
$873$	8.16402	+	4.15978i	0.276310	+	0.140787i
$874$	23.4221	+	32.2378i	0.792266	+	1.09046i
$875$		0			0
$876$	−5.50212	+	1.78775i	−0.185899	+	0.0604023i
$877$	−25.8347	−	50.7034i	−0.872374	−	1.71213i	−0.683259	−	0.730176i	$-0.739438\pi$
$877$	−25.8347	−	50.7034i	−0.872374	−	1.71213i	−0.189116	−	0.981955i	$-0.560562\pi$
$878$	−6.56029	+	1.03905i	−0.221399	+	0.0350662i
$879$	−21.8781			−0.737932
$880$		0			0
$881$	−2.85135			−0.0960644			−0.0480322	−	0.998846i	$-0.515295\pi$
$881$	−2.85135			−0.0960644			−0.0480322	+	0.998846i	$0.515295\pi$
$882$	−13.3809	+	2.11932i	−0.450557	+	0.0713613i
$883$	10.7230	+	21.0450i	0.360857	+	0.708221i	0.998046	−	0.0624865i	$-0.0199031\pi$
$883$	10.7230	+	21.0450i	0.360857	+	0.708221i	−0.637189	+	0.770707i	$0.719903\pi$
$884$	47.5735	−	15.4576i	1.60007	−	0.519894i
$885$		0			0
$886$	2.60860	+	3.59043i	0.0876377	+	0.120623i
$887$	−46.0666	−	23.4721i	−1.54676	−	0.788116i	−0.547937	−	0.836520i	$-0.684587\pi$
$887$	−46.0666	−	23.4721i	−1.54676	−	0.788116i	−0.998828	+	0.0484036i	$0.984587\pi$
$888$	5.82139	−	2.96615i	0.195353	−	0.0995373i
$889$	−0.796468	+	1.09624i	−0.0267127	+	0.0367668i
$890$		0			0
$891$	−1.15666	+	3.10840i	−0.0387494	+	0.104135i
$892$	7.55459	+	7.55459i	0.252946	+	0.252946i
$893$	−3.19511	−	20.1731i	−0.106920	−	0.675069i
$894$	−19.4426	−	6.31728i	−0.650258	−	0.211282i
$895$		0			0
$896$	7.90600	−	5.74404i	0.264121	−	0.191895i
$897$	4.09475	−	25.8532i	0.136720	−	0.863214i
$898$	−30.1180	+	59.1099i	−1.00505	+	1.97252i
$899$	−1.54817	+	4.76478i	−0.0516343	+	0.158914i
$900$		0			0
$901$			31.4883i			1.04903i
$902$	20.2985	+	22.0827i	0.675868	+	0.735272i
$903$	−6.24578	+	6.24578i	−0.207847	+	0.207847i
$904$	−20.3299	−	14.7705i	−0.676162	−	0.491260i
$905$		0			0
$906$	8.66125	+	26.6566i	0.287751	+	0.885606i
$907$	−40.5647	−	6.42481i	−1.34693	−	0.213332i	−0.559035	−	0.829144i	$-0.688828\pi$
$907$	−40.5647	−	6.42481i	−1.34693	−	0.213332i	−0.787893	+	0.615812i	$0.788828\pi$
$908$	18.9439	+	3.00043i	0.628677	+	0.0995726i
$909$	−3.51974	−	10.8327i	−0.116743	−	0.359296i
$910$		0			0
$911$	−10.8571	−	7.88817i	−0.359713	−	0.261347i	0.393220	−	0.919445i	$-0.371361\pi$
$911$	−10.8571	−	7.88817i	−0.359713	−	0.261347i	−0.752932	+	0.658098i	$0.771361\pi$
$912$	4.08622	−	4.08622i	0.135308	−	0.135308i
$913$	30.5726	+	33.2597i	1.01180	+	1.10074i
$914$			27.2866i			0.902559i
$915$		0			0
$916$	21.8840	−	67.3519i	0.723067	−	2.22537i
$917$	3.06223	−	6.00997i	0.101124	−	0.198467i
$918$	1.62972	−	10.2896i	0.0537887	−	0.339609i
$919$	−6.41832	+	4.66318i	−0.211721	+	0.153824i	−0.688592	−	0.725149i	$-0.741771\pi$
$919$	−6.41832	+	4.66318i	−0.211721	+	0.153824i	0.476871	+	0.878973i	$0.341771\pi$
$920$		0			0
$921$	1.93760	+	0.629563i	0.0638460	+	0.0207448i
$922$	11.7997	+	74.5004i	0.388603	+	2.45354i
$923$	−43.9510	−	43.9510i	−1.44666	−	1.44666i
$924$	2.69333	−	7.23806i	0.0886040	−	0.238115i
$925$		0			0
$926$	−48.1802	+	66.3144i	−1.58330	+	2.17923i
$927$	13.7754	−	7.01893i	0.452445	−	0.230532i
$928$	32.9854	+	16.8069i	1.08280	+	0.551713i
$929$	−2.16567	−	2.98079i	−0.0710533	−	0.0977965i	0.772011	−	0.635609i	$-0.219251\pi$
$929$	−2.16567	−	2.98079i	−0.0710533	−	0.0977965i	−0.843065	+	0.537812i	$0.819251\pi$
$930$		0			0
$931$	16.1349	−	5.24255i	0.528800	−	0.171818i
$932$	−0.511235	−	1.00336i	−0.0167461	−	0.0328660i
$933$	−15.8649	+	2.51275i	−0.519393	+	0.0822638i
$934$	−70.7418			−2.31474
$935$		0			0
$936$	5.80707			0.189810
$937$	31.6531	−	5.01336i	1.03406	−	0.163779i	0.383742	−	0.923440i	$-0.374635\pi$
$937$	31.6531	−	5.01336i	1.03406	−	0.163779i	0.650319	+	0.759661i	$0.274635\pi$
$938$	−5.17614	−	10.1588i	−0.169007	−	0.331695i
$939$	7.71943	−	2.50819i	0.251914	−	0.0818518i
$940$		0			0
$941$	14.1350	+	19.4552i	0.460788	+	0.634221i	0.974672	−	0.223639i	$-0.0717937\pi$
$941$	14.1350	+	19.4552i	0.460788	+	0.634221i	−0.513884	+	0.857860i	$0.671794\pi$
$942$	−2.57704	−	1.31307i	−0.0839645	−	0.0427820i
$943$	−25.2120	+	12.8461i	−0.821015	+	0.418328i
$944$	−9.84789	+	13.5545i	−0.320522	+	0.441160i
$945$		0			0
$946$	19.7354	+	70.7345i	0.641652	+	2.29978i
$947$	−14.0245	−	14.0245i	−0.455736	−	0.455736i	0.441517	−	0.897253i	$-0.354441\pi$
$947$	−14.0245	−	14.0245i	−0.455736	−	0.455736i	−0.897253	+	0.441517i	$0.854441\pi$
$948$	−1.73890	−	10.9790i	−0.0564770	−	0.356582i
$949$	−7.88585	−	2.56227i	−0.255986	−	0.0831748i
$950$		0			0
$951$	−5.08187	+	3.69220i	−0.164791	+	0.119728i
$952$	−0.977735	+	6.17318i	−0.0316886	+	0.200074i
$953$	4.26631	−	8.37310i	0.138199	−	0.271231i	−0.811526	−	0.584317i	$-0.801363\pi$
$953$	4.26631	−	8.37310i	0.138199	−	0.271231i	0.949725	+	0.313085i	$0.101363\pi$
$954$	−4.38436	+	13.4937i	−0.141949	+	0.436874i
$955$		0			0
$956$			24.1099i			0.779770i
$957$	16.0016	−	1.84846i	0.517257	−	0.0597521i
$958$	32.7066	−	32.7066i	1.05670	−	1.05670i
$959$	−14.9843	−	10.8867i	−0.483868	−	0.351551i
$960$		0			0
$961$	−9.25070	−	28.4707i	−0.298410	−	0.918411i
$962$	35.8973	+	5.68557i	1.15737	+	0.183310i
$963$	−4.63763	−	0.734528i	−0.149445	−	0.0236698i
$964$	−4.28450	−	13.1863i	−0.137995	−	0.424704i
$965$		0			0
$966$	10.2697	+	7.46140i	0.330423	+	0.240066i
$967$	−25.7543	+	25.7543i	−0.828201	+	0.828201i	−0.987268	−	0.159067i	$-0.949151\pi$
$967$	−25.7543	+	25.7543i	−0.828201	+	0.828201i	0.159067	+	0.987268i	$0.449151\pi$
$968$	−10.6731	−	12.6393i	−0.343046	−	0.406244i
$969$			13.0460i			0.419096i
$970$		0			0
$971$	−2.81437	+	8.66173i	−0.0903173	+	0.277968i	−0.986005	−	0.166715i	$-0.946684\pi$
$971$	−2.81437	+	8.66173i	−0.0903173	+	0.277968i	0.895688	+	0.444684i	$0.146684\pi$
$972$	1.22311	−	2.40049i	0.0392313	−	0.0769957i
$973$	−1.65789	+	10.4675i	−0.0531496	+	0.335573i
$974$	13.9445	−	10.1313i	0.446811	−	0.324627i
$975$		0			0
$976$	−1.04795	−	0.340501i	−0.0335442	−	0.0108992i
$977$	6.42933	+	40.5932i	0.205693	+	1.29869i	0.847076	+	0.531471i	$0.178361\pi$
$977$	6.42933	+	40.5932i	0.205693	+	1.29869i	−0.641384	+	0.767220i	$0.721639\pi$
$978$	−7.97890	−	7.97890i	−0.255137	−	0.255137i
$979$	9.58149	−	12.0843i	0.306226	−	0.386215i
$980$		0			0
$981$	4.43608	−	6.10574i	0.141633	−	0.194941i
$982$	28.7078	−	14.6274i	0.916104	−	0.466778i
$983$	1.69244	+	0.862341i	0.0539804	+	0.0275044i	0.480772	−	0.876845i	$-0.340356\pi$
$983$	1.69244	+	0.862341i	0.0539804	+	0.0275044i	−0.426792	+	0.904350i	$0.640356\pi$
$984$	−3.68984	−	5.07862i	−0.117628	−	0.161901i
$985$		0			0
$986$	−48.1206	+	15.6353i	−1.53247	+	0.497930i
$987$	−2.95389	−	5.79733i	−0.0940233	−	0.184531i
$988$	−27.8772	+	4.41532i	−0.886893	+	0.140470i
$989$	−69.2775			−2.20290
$990$		0			0
$991$	−47.5039			−1.50901			−0.754506	−	0.656294i	$-0.772123\pi$
$991$	−47.5039			−1.50901			−0.754506	+	0.656294i	$0.772123\pi$
$992$	7.76618	−	1.23004i	0.246576	−	0.0390539i
$993$	5.72739	+	11.2406i	0.181753	+	0.356711i
$994$	28.6679	−	9.31478i	0.909292	−	0.295447i
$995$		0			0
$996$	−21.5700	−	29.6886i	−0.683473	−	0.940720i
$997$	5.65684	+	2.88231i	0.179154	+	0.0912835i	0.541267	−	0.840851i	$-0.317945\pi$
$997$	5.65684	+	2.88231i	0.179154	+	0.0912835i	−0.362113	+	0.932134i	$0.617945\pi$
$998$	6.50276	−	3.31332i	0.205841	−	0.104881i
$999$	2.55355	−	3.51467i	0.0807909	−	0.111199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cw.b.7.2		96
5.2	odd	4		165.2.w.a.73.2	yes	96
5.3	odd	4	inner	825.2.cw.b.568.11		96
5.4	even	2		165.2.w.a.7.11	✓	96
11.8	odd	10	inner	825.2.cw.b.382.11		96
15.2	even	4		495.2.bj.c.73.11		96
15.14	odd	2		495.2.bj.c.172.2		96
55.8	even	20	inner	825.2.cw.b.118.2		96
55.19	odd	10		165.2.w.a.52.2	yes	96
55.52	even	20		165.2.w.a.118.11	yes	96
165.74	even	10		495.2.bj.c.217.11		96
165.107	odd	20		495.2.bj.c.118.2		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.w.a.7.11	✓	96	5.4	even	2
165.2.w.a.52.2	yes	96	55.19	odd	10
165.2.w.a.73.2	yes	96	5.2	odd	4
165.2.w.a.118.11	yes	96	55.52	even	20
495.2.bj.c.73.11		96	15.2	even	4
495.2.bj.c.118.2		96	165.107	odd	20
495.2.bj.c.172.2		96	15.14	odd	2
495.2.bj.c.217.11		96	165.74	even	10
825.2.cw.b.7.2		96	1.1	even	1	trivial
825.2.cw.b.118.2		96	55.8	even	20	inner
825.2.cw.b.382.11		96	11.8	odd	10	inner
825.2.cw.b.568.11		96	5.3	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cw (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.13992 + 0.338930i) q^{2} +(0.453990 + 0.891007i) q^{3} +(2.56227 - 0.832532i) q^{4} +(-1.27349 - 1.75281i) q^{6} +(0.770101 + 0.392386i) q^{7} +(-1.33999 + 0.682757i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-2.13992 + 0.338930i) q^{2} +(0.453990 + 0.891007i) q^{3} +(2.56227 - 0.832532i) q^{4} +(-1.27349 - 1.75281i) q^{6} +(0.770101 + 0.392386i) q^{7} +(-1.33999 + 0.682757i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.59884 - 2.06059i) q^{11} +(1.90504 + 1.90504i) q^{12} +(0.604046 + 3.81380i) q^{13} +(-1.78095 - 0.578664i) q^{14} +(-1.72314 + 1.25193i) q^{16} +(0.752203 - 4.74922i) q^{17} +(0.983613 - 1.93045i) q^{18} +(-0.838408 + 2.58036i) q^{19} +0.864305i q^{21} +(6.25970 + 3.52868i) q^{22} +(-4.79338 + 4.79338i) q^{23} +(-1.21668 - 0.883971i) q^{24} +(-2.58522 - 7.95649i) q^{26} +(-0.987688 - 0.156434i) q^{27} +(2.29988 + 0.364266i) q^{28} +(1.50081 + 4.61903i) q^{29} +(0.834544 + 0.606332i) q^{31} +(5.38990 - 5.38990i) q^{32} +(0.656154 - 3.25107i) q^{33} +10.4179i q^{34} +(-0.832532 + 2.56227i) q^{36} +(-1.97230 + 3.87086i) q^{37} +(0.919567 - 5.80592i) q^{38} +(-3.12389 + 2.26964i) q^{39} +(3.96986 + 1.28989i) q^{41} +(-0.292939 - 1.84954i) q^{42} +(7.22637 + 7.22637i) q^{43} +(-8.37444 - 3.11618i) q^{44} +(8.63283 - 11.8821i) q^{46} +(-6.70751 + 3.41765i) q^{47} +(-1.89777 - 0.966963i) q^{48} +(-3.67541 - 5.05877i) q^{49} +(4.57308 - 1.48588i) q^{51} +(4.72284 + 9.26910i) q^{52} +(-6.46794 + 1.02442i) q^{53} +2.16659 q^{54} -1.29983 q^{56} +(-2.67974 + 0.424430i) q^{57} +(-4.77715 - 9.37568i) q^{58} +(7.48114 - 2.43077i) q^{59} +(0.304083 + 0.418534i) q^{61} +(-1.99136 - 1.01465i) q^{62} +(-0.770101 + 0.392386i) q^{63} +(-7.20329 + 9.91448i) q^{64} +(-0.302231 + 7.17942i) q^{66} +(4.30527 + 4.30527i) q^{67} +(-2.02653 - 12.7950i) q^{68} +(-6.44708 - 2.09478i) q^{69} +(-13.0228 + 9.46160i) q^{71} +(0.235262 - 1.48539i) q^{72} +(-0.974881 + 1.91331i) q^{73} +(2.90862 - 8.95180i) q^{74} +7.30957i q^{76} +(-1.19282 - 2.60661i) q^{77} +(5.91562 - 5.91562i) q^{78} +(-3.33797 - 2.42518i) q^{79} +(-0.309017 - 0.951057i) q^{81} +(-8.93237 - 1.41475i) q^{82} +(-13.4534 - 2.13082i) q^{83} +(0.719562 + 2.21458i) q^{84} +(-17.9131 - 13.0146i) q^{86} +(-3.43423 + 3.43423i) q^{87} +(4.88929 + 0.986791i) q^{88} +4.64987i q^{89} +(-1.03130 + 3.17403i) q^{91} +(-8.29130 + 16.2726i) q^{92} +(-0.161370 + 1.01885i) q^{93} +(13.1952 - 9.58687i) q^{94} +(7.24940 + 2.35547i) q^{96} +(-1.43336 - 9.04989i) q^{97} +(9.57965 + 9.57965i) q^{98} +(3.19461 - 0.891318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 20 q^{7}+O(q^{10}) \) 96 * q + 20 * q^7	\( 96 q + 20 q^{7} + 8 q^{11} + 16 q^{12} + 8 q^{16} + 20 q^{17} + 32 q^{22} - 32 q^{23} + 60 q^{28} + 16 q^{31} + 16 q^{33} + 24 q^{36} - 8 q^{37} - 56 q^{38} - 120 q^{41} - 12 q^{42} - 200 q^{46} - 60 q^{47} - 48 q^{48} + 40 q^{51} - 40 q^{52} - 36 q^{53} - 80 q^{56} - 40 q^{57} - 44 q^{58} + 40 q^{61} - 80 q^{62} - 20 q^{63} + 56 q^{66} + 48 q^{67} - 80 q^{68} + 32 q^{71} + 60 q^{73} + 24 q^{77} + 96 q^{78} + 24 q^{81} - 32 q^{82} + 200 q^{83} - 80 q^{86} + 144 q^{88} + 56 q^{91} - 20 q^{92} + 72 q^{93} - 32 q^{97}+O(q^{100}) \) 96 * q + 20 * q^7 + 8 * q^11 + 16 * q^12 + 8 * q^16 + 20 * q^17 + 32 * q^22 - 32 * q^23 + 60 * q^28 + 16 * q^31 + 16 * q^33 + 24 * q^36 - 8 * q^37 - 56 * q^38 - 120 * q^41 - 12 * q^42 - 200 * q^46 - 60 * q^47 - 48 * q^48 + 40 * q^51 - 40 * q^52 - 36 * q^53 - 80 * q^56 - 40 * q^57 - 44 * q^58 + 40 * q^61 - 80 * q^62 - 20 * q^63 + 56 * q^66 + 48 * q^67 - 80 * q^68 + 32 * q^71 + 60 * q^73 + 24 * q^77 + 96 * q^78 + 24 * q^81 - 32 * q^82 + 200 * q^83 - 80 * q^86 + 144 * q^88 + 56 * q^91 - 20 * q^92 + 72 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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