LMFDB - Embedded newform 670.2.w.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(7,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(132))

chi = DirichletCharacter(H, H._module([33, 46]))

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

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

chi := DirichletCharacter("670.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.w (of order $132$, degree $40$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$34$ over $\Q(\zeta_{132})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{132}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	670.7
Dual form			670.2.w.a.383.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.304486 + 0.952517i) q^{2} +(-0.0909985 - 0.166651i) q^{3} +(-0.814576 - 0.580057i) q^{4} +(-0.579530 + 2.15966i) q^{5} +(0.186446 - 0.0359345i) q^{6} +(3.19533 + 3.51498i) q^{7} +(0.800541 - 0.599278i) q^{8} +(1.60243 - 2.49343i) q^{9} +O(q^{10})$	\(q+(-0.304486 + 0.952517i) q^{2} +(-0.0909985 - 0.166651i) q^{3} +(-0.814576 - 0.580057i) q^{4} +(-0.579530 + 2.15966i) q^{5} +(0.186446 - 0.0359345i) q^{6} +(3.19533 + 3.51498i) q^{7} +(0.800541 - 0.599278i) q^{8} +(1.60243 - 2.49343i) q^{9} +(-1.88066 - 1.20960i) q^{10} +(0.982868 - 5.09960i) q^{11} +(-0.0225420 + 0.188534i) q^{12} +(1.85570 + 4.33347i) q^{13} +(-4.32101 + 1.97334i) q^{14} +(0.412647 - 0.0999466i) q^{15} +(0.327068 + 0.945001i) q^{16} +(-0.00615002 + 0.0365728i) q^{17} +(1.88712 + 2.28556i) q^{18} +(0.370467 - 0.0176475i) q^{19} +(1.72480 - 1.42305i) q^{20} +(0.295006 - 0.852363i) q^{21} +(4.55819 + 2.48896i) q^{22} +(-0.113423 + 4.76477i) q^{23} +(-0.172718 - 0.0788779i) q^{24} +(-4.32829 - 2.50318i) q^{25} +(-4.69274 + 0.448103i) q^{26} +(-1.12953 - 0.0807858i) q^{27} +(-0.563949 - 4.71669i) q^{28} +(2.70879 - 1.56392i) q^{29} +(-0.0304447 + 0.423486i) q^{30} +(0.830182 + 2.07369i) q^{31} +(-0.999717 + 0.0237977i) q^{32} +(-0.939295 + 0.300260i) q^{33} +(-0.0329636 - 0.0169939i) q^{34} +(-9.44296 + 4.86379i) q^{35} +(-2.75163 + 1.10159i) q^{36} +(-6.40339 + 1.71578i) q^{37} +(-0.0959926 + 0.358249i) q^{38} +(0.553313 - 0.703595i) q^{39} +(0.830300 + 2.07620i) q^{40} +(0.790653 + 8.28009i) q^{41} +(0.722064 + 0.540531i) q^{42} +(5.36692 - 2.00176i) q^{43} +(-3.75868 + 3.58389i) q^{44} +(4.45631 + 4.90573i) q^{45} +(-4.50398 - 1.55884i) q^{46} +(-1.06932 + 1.75433i) q^{47} +(0.127723 - 0.140500i) q^{48} +(-1.47956 + 15.4947i) q^{49} +(3.70223 - 3.36058i) q^{50} +(0.00665454 - 0.00230316i) q^{51} +(1.00205 - 4.60636i) q^{52} +(1.72507 - 4.62509i) q^{53} +(0.420877 - 1.05130i) q^{54} +(10.4438 + 5.07804i) q^{55} +(4.66444 + 0.898997i) q^{56} +(-0.0366529 - 0.0601329i) q^{57} +(0.664871 + 3.05636i) q^{58} +(-1.94465 - 0.279599i) q^{59} +(-0.394107 - 0.157945i) q^{60} +(0.521057 + 2.70350i) q^{61} +(-2.22801 + 0.159350i) q^{62} +(13.8846 - 2.33482i) q^{63} +(0.281733 - 0.959493i) q^{64} +(-10.4343 + 1.49631i) q^{65} -0.986119i q^{66} +(-5.09441 + 6.40679i) q^{67} +(0.0262240 - 0.0262240i) q^{68} +(0.804376 - 0.414684i) q^{69} +(-1.75759 - 10.4755i) q^{70} +(2.40029 - 3.37073i) q^{71} +(-0.211446 - 2.95639i) q^{72} +(-1.87756 + 2.77409i) q^{73} +(0.315434 - 6.62177i) q^{74} +(-0.0232906 + 0.949101i) q^{75} +(-0.312010 - 0.200517i) q^{76} +(21.0656 - 12.8401i) q^{77} +(0.501709 + 0.741275i) q^{78} +(1.57435 - 1.23808i) q^{79} +(-2.23043 + 0.158700i) q^{80} +(-3.60448 - 7.89271i) q^{81} +(-8.12767 - 1.76807i) q^{82} +(-1.42357 - 0.691525i) q^{83} +(-0.734723 + 0.523194i) q^{84} +(-0.0754208 - 0.0344770i) q^{85} +(0.272553 + 5.72159i) q^{86} +(-0.507125 - 0.309109i) q^{87} +(-2.26925 - 4.67145i) q^{88} +(-3.19493 - 10.8809i) q^{89} +(-6.02968 + 2.75098i) q^{90} +(-9.30249 + 20.3696i) q^{91} +(2.85623 - 3.81547i) q^{92} +(0.270038 - 0.327054i) q^{93} +(-1.34543 - 1.55271i) q^{94} +(-0.176584 + 0.810311i) q^{95} +(0.0949386 + 0.164439i) q^{96} +(-4.45085 - 16.6108i) q^{97} +(-14.3084 - 6.12723i) q^{98} +(-11.1405 - 10.6225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 4 q^{6}+O(q^{10}) $ 1360 * q - 4 * q^6	$ 1360 q - 4 q^{6} + 8 q^{15} - 68 q^{16} + 12 q^{20} - 24 q^{21} - 36 q^{23} - 24 q^{25} + 88 q^{31} - 44 q^{33} + 12 q^{35} + 64 q^{36} + 24 q^{37} - 24 q^{38} + 12 q^{41} + 88 q^{43} + 12 q^{46} - 108 q^{47} + 44 q^{48} - 72 q^{50} + 48 q^{51} - 288 q^{55} + 4 q^{56} + 36 q^{57} - 164 q^{60} + 20 q^{61} - 32 q^{62} - 352 q^{65} + 68 q^{67} - 484 q^{70} + 88 q^{71} - 16 q^{73} - 704 q^{75} - 32 q^{76} + 456 q^{77} - 60 q^{78} - 56 q^{81} + 48 q^{82} - 16 q^{83} - 96 q^{85} + 4 q^{86} + 96 q^{87} - 32 q^{90} - 128 q^{91} + 16 q^{92} + 80 q^{93} + 60 q^{95} + 4 q^{96} + 120 q^{97} + 48 q^{98}+O(q^{100}) $ 1360 * q - 4 * q^6 + 8 * q^15 - 68 * q^16 + 12 * q^20 - 24 * q^21 - 36 * q^23 - 24 * q^25 + 88 * q^31 - 44 * q^33 + 12 * q^35 + 64 * q^36 + 24 * q^37 - 24 * q^38 + 12 * q^41 + 88 * q^43 + 12 * q^46 - 108 * q^47 + 44 * q^48 - 72 * q^50 + 48 * q^51 - 288 * q^55 + 4 * q^56 + 36 * q^57 - 164 * q^60 + 20 * q^61 - 32 * q^62 - 352 * q^65 + 68 * q^67 - 484 * q^70 + 88 * q^71 - 16 * q^73 - 704 * q^75 - 32 * q^76 + 456 * q^77 - 60 * q^78 - 56 * q^81 + 48 * q^82 - 16 * q^83 - 96 * q^85 + 4 * q^86 + 96 * q^87 - 32 * q^90 - 128 * q^91 + 16 * q^92 + 80 * q^93 + 60 * q^95 + 4 * q^96 + 120 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.304486	+	0.952517i	−0.215304	+	0.673531i
$2$	−0.304486	+	0.952517i	−0.215304	+	0.673531i
$3$	−0.0909985	−	0.166651i	−0.0525380	−	0.0962162i	0.850091	−	0.526637i	$-0.176547\pi$
$3$	−0.0909985	−	0.166651i	−0.0525380	−	0.0962162i	−0.902629	+	0.430420i	$0.858365\pi$
$4$	−0.814576	−	0.580057i	−0.407288	−	0.290028i
$5$	−0.579530	+	2.15966i	−0.259174	+	0.965831i
$5$	−0.579530	+	2.15966i	−0.259174	+	0.965831i
$6$	0.186446	−	0.0359345i	0.0761162	−	0.0146702i
$7$	3.19533	+	3.51498i	1.20772	+	1.32854i	0.929859	+	0.367915i	$0.119928\pi$
$7$	3.19533	+	3.51498i	1.20772	+	1.32854i	0.277860	+	0.960621i	$0.410375\pi$
$8$	0.800541	−	0.599278i	0.283034	−	0.211877i
$9$	1.60243	−	2.49343i	0.534144	−	0.831144i
$10$	−1.88066	−	1.20960i	−0.594716	−	0.382509i
$11$	0.982868	−	5.09960i	0.296346	−	1.53759i	−0.462679	−	0.886526i	$-0.653112\pi$
$11$	0.982868	−	5.09960i	0.296346	−	1.53759i	0.759025	−	0.651062i	$-0.225676\pi$
$12$	−0.0225420	+	0.188534i	−0.00650733	+	0.0544252i
$13$	1.85570	+	4.33347i	0.514679	+	1.20189i	0.952972	+	0.303057i	$0.0980074\pi$
$13$	1.85570	+	4.33347i	0.514679	+	1.20189i	−0.438293	+	0.898832i	$0.644417\pi$
$14$	−4.32101	+	1.97334i	−1.15484	+	0.527397i
$15$	0.412647	−	0.0999466i	0.106545	−	0.0258061i
$16$	0.327068	+	0.945001i	0.0817670	+	0.236250i
$17$	−0.00615002	+	0.0365728i	−0.00149160	+	0.00887020i	−0.986890	−	0.161393i	$-0.948401\pi$
$17$	−0.00615002	+	0.0365728i	−0.00149160	+	0.00887020i	0.985399	+	0.170263i	$0.0544619\pi$
$18$	1.88712	+	2.28556i	0.444797	+	0.538711i
$19$	0.370467	−	0.0176475i	0.0849909	−	0.00404862i	−0.00504337	−	0.999987i	$-0.501605\pi$
$19$	0.370467	−	0.0176475i	0.0849909	−	0.00404862i	0.0900343	+	0.995939i	$0.471302\pi$
$20$	1.72480	−	1.42305i	0.385677	−	0.318203i
$21$	0.295006	−	0.852363i	0.0643755	−	0.186001i
$22$	4.55819	+	2.48896i	0.971808	+	0.530648i
$23$	−0.113423	+	4.76477i	−0.0236502	+	0.993523i	0.855736	+	0.517413i	$0.173105\pi$
$23$	−0.113423	+	4.76477i	−0.0236502	+	0.993523i	−0.879386	+	0.476109i	$0.842047\pi$
$24$	−0.172718	−	0.0788779i	−0.0352560	−	0.0161009i
$25$	−4.32829	−	2.50318i	−0.865658	−	0.500636i
$26$	−4.69274	+	0.448103i	−0.920322	+	0.0878801i
$27$	−1.12953	−	0.0807858i	−0.217379	−	0.0155472i
$28$	−0.563949	−	4.71669i	−0.106576	−	0.891370i
$29$	2.70879	−	1.56392i	0.503010	−	0.290413i	−0.226946	−	0.973907i	$-0.572874\pi$
$29$	2.70879	−	1.56392i	0.503010	−	0.290413i	0.729956	+	0.683495i	$0.239541\pi$
$30$	−0.0304447	+	0.423486i	−0.00555841	+	0.0773175i
$31$	0.830182	+	2.07369i	0.149105	+	0.372446i	0.984051	−	0.177885i	$-0.0569256\pi$
$31$	0.830182	+	2.07369i	0.149105	+	0.372446i	−0.834946	+	0.550332i	$0.814501\pi$
$32$	−0.999717	+	0.0237977i	−0.176727	+	0.00420688i
$33$	−0.939295	+	0.300260i	−0.163510	+	0.0522685i
$34$	−0.0329636	−	0.0169939i	−0.00565321	−	0.00291443i
$35$	−9.44296	+	4.86379i	−1.59615	+	0.822131i
$36$	−2.75163	+	1.10159i	−0.458606	+	0.183598i
$37$	−6.40339	+	1.71578i	−1.05271	+	0.282073i	−0.743371	−	0.668879i	$-0.766775\pi$
$37$	−6.40339	+	1.71578i	−1.05271	+	0.282073i	−0.309339	+	0.950952i	$0.600108\pi$
$38$	−0.0959926	+	0.358249i	−0.0155721	+	0.0581157i
$39$	0.553313	−	0.703595i	0.0886010	−	0.112665i
$40$	0.830300	+	2.07620i	0.131282	+	0.328276i
$41$	0.790653	+	8.28009i	0.123479	+	1.29313i	0.818652	+	0.574290i	$0.194722\pi$
$41$	0.790653	+	8.28009i	0.123479	+	1.29313i	−0.695173	+	0.718843i	$0.744672\pi$
$42$	0.722064	+	0.540531i	0.111417	+	0.0834057i
$43$	5.36692	−	2.00176i	0.818448	−	0.305265i	0.0948538	−	0.995491i	$-0.469762\pi$
$43$	5.36692	−	2.00176i	0.818448	−	0.305265i	0.723594	+	0.690226i	$0.242489\pi$
$44$	−3.75868	+	3.58389i	−0.566642	+	0.540292i
$45$	4.45631	+	4.90573i	0.664308	+	0.731303i
$46$	−4.50398	−	1.55884i	−0.664076	−	0.229839i
$47$	−1.06932	+	1.75433i	−0.155976	+	0.255895i	−0.922229	−	0.386644i	$-0.873634\pi$
$47$	−1.06932	+	1.75433i	−0.155976	+	0.255895i	0.766253	+	0.642539i	$0.222119\pi$
$48$	0.127723	−	0.140500i	0.0184352	−	0.0202794i
$49$	−1.47956	+	15.4947i	−0.211366	+	2.21353i
$50$	3.70223	−	3.36058i	0.523574	−	0.475258i
$51$	0.00665454	−	0.00230316i	0.000931823	−	0.000322507i
$52$	1.00205	−	4.60636i	0.138960	−	0.638787i
$53$	1.72507	−	4.62509i	0.236956	−	0.635305i	−0.762982	−	0.646420i	$-0.776265\pi$
$53$	1.72507	−	4.62509i	0.236956	−	0.635305i	0.999938	+	0.0111152i	$0.00353816\pi$
$54$	0.420877	−	1.05130i	0.0572741	−	0.143064i
$55$	10.4438	+	5.07804i	1.40824	+	0.684722i
$56$	4.66444	+	0.898997i	0.623312	+	0.120133i
$57$	−0.0366529	−	0.0601329i	−0.00485480	−	0.00796479i
$58$	0.664871	+	3.05636i	0.0873018	+	0.401320i
$59$	−1.94465	−	0.279599i	−0.253172	−	0.0364007i	0.0145602	−	0.999894i	$-0.495365\pi$
$59$	−1.94465	−	0.279599i	−0.253172	−	0.0364007i	−0.267732	+	0.963493i	$0.586274\pi$
$60$	−0.394107	−	0.157945i	−0.0508790	−	0.0203906i
$61$	0.521057	+	2.70350i	0.0667145	+	0.346148i	0.999913	−	0.0132144i	$-0.00420638\pi$
$61$	0.521057	+	2.70350i	0.0667145	+	0.346148i	−0.933198	+	0.359362i	$0.882994\pi$
$62$	−2.22801	+	0.159350i	−0.282957	+	0.0202375i
$63$	13.8846	−	2.33482i	1.74930	−	0.294159i
$64$	0.281733	−	0.959493i	0.0352166	−	0.119937i
$65$	−10.4343	+	1.49631i	−1.29421	+	0.185594i
$66$		−	0.986119i		−	0.121383i
$67$	−5.09441	+	6.40679i	−0.622381	+	0.782715i
$67$	−5.09441	+	6.40679i	−0.622381	+	0.782715i
$68$	0.0262240	−	0.0262240i	0.00318012	−	0.00318012i
$69$	0.804376	−	0.414684i	0.0968355	−	0.0499221i
$70$	−1.75759	−	10.4755i	−0.210072	−	1.25207i
$71$	2.40029	−	3.37073i	0.284862	−	0.400032i	−0.647207	−	0.762314i	$-0.724063\pi$
$71$	2.40029	−	3.37073i	0.284862	−	0.400032i	0.932068	+	0.362282i	$0.118002\pi$
$72$	−0.211446	−	2.95639i	−0.0249191	−	0.348414i
$73$	−1.87756	+	2.77409i	−0.219751	+	0.324682i	−0.921957	−	0.387292i	$-0.873411\pi$
$73$	−1.87756	+	2.77409i	−0.219751	+	0.324682i	0.702206	+	0.711974i	$0.252199\pi$
$74$	0.315434	−	6.62177i	0.0366684	−	0.769765i
$75$	−0.0232906	+	0.949101i	−0.00268937	+	0.109593i
$76$	−0.312010	−	0.200517i	−0.0357900	−	0.0230008i
$77$	21.0656	−	12.8401i	2.40064	−	1.46327i
$78$	0.501709	+	0.741275i	0.0568074	+	0.0839328i
$79$	1.57435	−	1.23808i	0.177128	−	0.139295i	−0.525659	−	0.850695i	$-0.676181\pi$
$79$	1.57435	−	1.23808i	0.177128	−	0.139295i	0.702787	+	0.711400i	$0.251939\pi$
$80$	−2.23043	+	0.158700i	−0.249370	+	0.0177432i
$81$	−3.60448	−	7.89271i	−0.400498	−	0.876968i
$82$	−8.12767	−	1.76807i	−0.897551	−	0.195250i
$83$	−1.42357	−	0.691525i	−0.156257	−	0.0759048i	0.357165	−	0.934041i	$-0.383743\pi$
$83$	−1.42357	−	0.691525i	−0.156257	−	0.0759048i	−0.513421	+	0.858137i	$0.671622\pi$
$84$	−0.734723	+	0.523194i	−0.0801649	+	0.0570852i
$85$	−0.0754208	−	0.0344770i	−0.00818053	−	0.00373956i
$86$	0.272553	+	5.72159i	0.0293901	+	0.616975i
$87$	−0.507125	−	0.309109i	−0.0543695	−	0.0331400i
$88$	−2.26925	−	4.67145i	−0.241903	−	0.497978i
$89$	−3.19493	−	10.8809i	−0.338662	−	1.15338i	−0.936180	−	0.351521i	$-0.885665\pi$
$89$	−3.19493	−	10.8809i	−0.338662	−	1.15338i	0.597518	−	0.801855i	$-0.296154\pi$
$90$	−6.02968	+	2.75098i	−0.635584	+	0.289979i
$91$	−9.30249	+	20.3696i	−0.975166	+	2.13532i
$92$	2.85623	−	3.81547i	0.297782	−	0.397791i
$93$	0.270038	−	0.327054i	0.0280017	−	0.0339139i
$94$	−1.34543	−	1.55271i	−0.138771	−	0.160150i
$95$	−0.176584	+	0.810311i	−0.0181172	+	0.0831361i
$96$	0.0949386	+	0.164439i	0.00968963	+	0.0167829i
$97$	−4.45085	−	16.6108i	−0.451916	−	1.68657i	−0.697001	−	0.717070i	$-0.745483\pi$
$97$	−4.45085	−	16.6108i	−0.451916	−	1.68657i	0.245085	−	0.969501i	$-0.421184\pi$
$98$	−14.3084	−	6.12723i	−1.44537	−	0.618944i
$99$	−11.1405	−	10.6225i	−1.11966	−	1.06760i
$100$	2.07373	+	4.54968i	0.207373	+	0.454968i
$101$	4.56714	−	8.85902i	0.454448	−	0.881506i	−0.544635	−	0.838673i	$-0.683332\pi$
$101$	4.56714	−	8.85902i	0.454448	−	0.881506i	0.999082	−	0.0428322i	$-0.0136381\pi$
$102$	0.000167580		0.00703984i	1.65928e−5		0.000697049i
$103$	−5.35195	+	12.4980i	−0.527344	+	1.23146i	0.418907	+	0.908029i	$0.362413\pi$
$103$	−5.35195	+	12.4980i	−0.527344	+	1.23146i	−0.946250	+	0.323435i	$0.895162\pi$
$104$	4.08252	+	2.35704i	0.400324	+	0.231127i
$105$	1.66985	+	1.13108i	0.162961	+	0.110382i
$106$	3.88021	+	3.05143i	0.376880	+	0.296381i
$107$	1.44544	−	20.2099i	0.139736	−	1.95377i	−0.131643	−	0.991297i	$-0.542025\pi$
$107$	1.44544	−	20.2099i	0.139736	−	1.95377i	0.271380	−	0.962472i	$-0.412520\pi$
$108$	0.873230	+	0.720999i	0.0840266	+	0.0693782i
$109$	0.794106	+	5.52313i	0.0760616	+	0.529020i	0.991855	+	0.127371i	$0.0406538\pi$
$109$	0.794106	+	5.52313i	0.0760616	+	0.529020i	−0.915794	+	0.401649i	$0.868437\pi$
$110$	−8.01692	+	8.40172i	−0.764383	+	0.801072i
$111$	0.868636	+	0.910999i	0.0824473	+	0.0864682i
$112$	−2.27657	+	4.16922i	−0.215115	+	0.393954i
$113$	−9.45803	+	4.59443i	−0.889736	+	0.432207i	−0.824631	−	0.565671i	$-0.808617\pi$
$113$	−9.45803	+	4.59443i	−0.889736	+	0.432207i	−0.0651055	+	0.997878i	$0.520738\pi$
$114$	0.0684379	−	0.0166029i	0.00640980	−	0.00155500i
$115$	−10.2246	−	3.00628i	−0.953445	−	0.280337i
$116$	−3.11368	−	0.297320i	−0.289098	−	0.0276055i
$117$	13.7788	+	2.31703i	1.27386	+	0.214209i
$118$	0.858443	−	1.76718i	0.0790261	−	0.162682i
$119$	−0.148204	+	0.0952448i	−0.0135858	+	0.00873108i
$120$	0.270445	−	0.327301i	0.0246882	−	0.0298784i
$121$	−14.8279	−	5.93618i	−1.34799	−	0.539653i
$122$	−2.73378	−	0.326864i	−0.247505	−	0.0295929i
$123$	1.30794	−	0.885239i	0.117933	−	0.0798193i
$124$	0.526614	−	2.17073i	0.0472914	−	0.194938i
$125$	7.91440	−	7.89698i	0.707886	−	0.706327i
$126$	−2.00373	+	13.9363i	−0.178507	+	1.24154i
$127$	0.666463	−	0.605855i	0.0591390	−	0.0537609i	−0.642554	−	0.766241i	$-0.722125\pi$
$127$	0.666463	−	0.605855i	0.0591390	−	0.0537609i	0.701693	+	0.712480i	$0.252428\pi$
$128$	0.828149	+	0.560508i	0.0731987	+	0.0495423i
$129$	−0.821977	−	0.712247i	−0.0723710	−	0.0627099i
$130$	1.75184	−	10.3944i	0.153646	−	0.911652i
$131$	14.2898	+	4.19586i	1.24850	+	0.366594i	0.838204	−	0.545357i	$-0.183606\pi$
$131$	14.2898	+	4.19586i	1.24850	+	0.366594i	0.410300	+	0.911951i	$0.365424\pi$
$132$	0.939295	+	0.300260i	0.0817551	+	0.0261343i
$133$	1.24579	+	1.24579i	0.108024	+	0.108024i
$134$	−4.55140	−	6.80329i	−0.393181	−	0.587715i
$135$	0.829069	−	2.39259i	0.0713549	−	0.205922i
$136$	0.0169939	+	0.0329636i	0.00145722	+	0.00282660i
$137$	19.7379	−	10.7777i	1.68633	−	0.920804i	0.710086	−	0.704115i	$-0.248656\pi$
$137$	19.7379	−	10.7777i	1.68633	−	0.920804i	0.976241	−	0.216689i	$-0.0695258\pi$
$138$	0.150072	+	0.892447i	0.0127750	+	0.0759701i
$139$	7.77507	−	8.97291i	0.659473	−	0.761073i	−0.323218	−	0.946325i	$-0.604765\pi$
$139$	7.77507	−	8.97291i	0.659473	−	0.761073i	0.982691	+	0.185252i	$0.0593101\pi$
$140$	10.5133	+	1.51552i	0.888534	+	0.128085i
$141$	0.389667	+	0.0185621i	0.0328159	+	0.00156321i
$142$	2.47982	+	3.31266i	0.208102	+	0.277992i
$143$	23.9229	−	5.20411i	2.00053	−	0.435189i
$144$	2.88040	+	0.698777i	0.240033	+	0.0582314i
$145$	1.80772	+	6.75642i	0.150123	+	0.561090i
$146$	−2.07067	−	2.63308i	−0.171370	−	0.217915i
$147$	2.71685	−	1.16342i	0.224082	−	0.0959575i
$148$	6.21130	+	2.31669i	0.510566	+	0.190431i
$149$	−11.3747	−	17.6994i	−0.931852	−	1.44999i	−0.892646	−	0.450758i	$-0.851154\pi$
$149$	−11.3747	−	17.6994i	−0.931852	−	1.44999i	−0.0392057	−	0.999231i	$-0.512483\pi$
$150$	−0.896942	−	0.311173i	−0.0732350	−	0.0254072i
$151$	7.60986	+	10.6866i	0.619282	+	0.869659i	0.998449	−	0.0556687i	$-0.0177291\pi$
$151$	7.60986	+	10.6866i	0.619282	+	0.869659i	−0.379168	+	0.925328i	$0.623790\pi$
$152$	0.285998	−	0.236140i	0.0231975	−	0.0191535i
$153$	0.0813367	+	0.0739400i	0.00657569	+	0.00597769i
$154$	5.81626	+	23.9749i	0.468688	+	1.93196i
$155$	−4.95959	+	0.591144i	−0.398364	+	0.0474818i
$156$	−0.858840	+	0.252178i	−0.0687623	+	0.0201904i
$157$	7.94323	+	0.189084i	0.633938	+	0.0150905i	0.339539	−	0.940592i	$-0.389729\pi$
$157$	7.94323	+	0.189084i	0.633938	+	0.0150905i	0.294399	+	0.955683i	$0.404880\pi$
$158$	0.699925	+	1.87657i	0.0556831	+	0.149292i
$159$	−0.927755	+	0.133391i	−0.0735758	+	0.0105786i
$160$	0.527971	−	2.17284i	0.0417398	−	0.171778i
$161$	−17.1105	+	14.8263i	−1.34849	+	1.16848i
$162$	8.61546	−	1.03010i	0.676894	−	0.0809326i
$163$	17.0732	+	4.57474i	1.33727	+	0.358321i	0.855422	−	0.517932i	$-0.173298\pi$
$163$	17.0732	+	4.57474i	1.33727	+	0.358321i	0.481851	+	0.876253i	$0.339964\pi$
$164$	4.15888	−	7.20339i	0.324754	−	0.562490i
$165$	−0.104110	−	2.20257i	−0.00810497	−	0.171470i
$166$	1.09215	−	1.14541i	0.0847670	−	0.0889010i
$167$	6.33306	+	19.8115i	0.490067	+	1.53306i	0.810469	+	0.585782i	$0.199212\pi$
$167$	6.33306	+	19.8115i	0.490067	+	1.53306i	−0.320402	+	0.947282i	$0.603818\pi$
$168$	−0.274638	−	0.859142i	−0.0211888	−	0.0662842i
$169$	−6.36434	+	6.67473i	−0.489565	+	0.513440i
$170$	0.0558045	−	0.0613418i	0.00428001	−	0.00470470i
$171$	0.549645	−	0.952012i	0.0420324	−	0.0728022i
$172$	−5.53290	−	1.48254i	−0.421879	−	0.113042i
$173$	−16.4821	+	1.97068i	−1.25311	+	0.149828i	−0.718654	−	0.695368i	$-0.755241\pi$
$173$	−16.4821	+	1.97068i	−1.25311	+	0.149828i	−0.534457	+	0.845196i	$0.679484\pi$
$174$	0.448844	−	0.388926i	0.0340268	−	0.0294844i
$175$	−5.03167	−	23.2123i	−0.380358	−	1.75469i
$176$	5.14059	−	0.739106i	0.387487	−	0.0557122i
$177$	0.130365	+	0.349522i	0.00979883	+	0.0262717i
$178$	11.3371	+	0.269873i	0.849750	+	0.0202278i
$179$	−8.09386	+	2.37657i	−0.604964	+	0.177633i	−0.569848	−	0.821750i	$-0.692998\pi$
$179$	−8.09386	+	2.37657i	−0.604964	+	0.177633i	−0.0351153	+	0.999383i	$0.511180\pi$
$180$	−0.784403	−	6.58100i	−0.0584659	−	0.490519i
$181$	0.0625473	+	0.257823i	0.00464910	+	0.0191639i	0.974089	−	0.226166i	$-0.0726190\pi$
$181$	0.0625473	+	0.257823i	0.00464910	+	0.0191639i	−0.969440	+	0.245329i	$0.921104\pi$
$182$	−16.5699	−	15.0630i	−1.22824	−	1.11655i
$183$	0.403127	−	0.332849i	0.0298000	−	0.0246049i
$184$	2.76462	+	3.88236i	0.203810	+	0.286212i
$185$	0.00544614	−	14.8235i	0.000400408	−	1.08985i
$186$	0.229301	+	0.356800i	0.0168132	+	0.0261618i
$187$	0.180462	+	0.0673088i	0.0131967	+	0.00492211i
$188$	1.88865	−	0.808767i	0.137744	−	0.0589854i
$189$	−3.32526	−	4.22842i	−0.241877	−	0.307572i
$190$	−0.718067	−	0.414928i	−0.0520941	−	0.0301020i
$191$	−14.9042	−	3.61571i	−1.07843	−	0.261624i	−0.343075	−	0.939308i	$-0.611469\pi$
$191$	−14.9042	−	3.61571i	−1.07843	−	0.261624i	−0.735353	+	0.677684i	$0.762984\pi$
$192$	−0.185538	+	0.0403613i	−0.0133900	+	0.00291283i
$193$	−12.1524	−	16.2337i	−0.874751	−	1.16853i	−0.984642	−	0.174587i	$-0.944141\pi$
$193$	−12.1524	−	16.2337i	−0.874751	−	1.16853i	0.109891	−	0.993944i	$-0.464950\pi$
$194$	17.1773	+	0.818255i	1.23326	+	0.0587473i
$195$	1.19887	+	1.60272i	0.0858525	+	0.114773i
$196$	10.1930	−	11.7634i	0.728073	−	0.840241i
$197$	−4.27571	−	25.4267i	−0.304632	−	1.81158i	−0.542246	−	0.840220i	$-0.682426\pi$
$197$	−4.27571	−	25.4267i	−0.304632	−	1.81158i	0.237614	−	0.971360i	$-0.423635\pi$
$198$	13.5102	−	7.37714i	0.960129	−	0.524270i
$199$	1.42471	+	2.76354i	0.100995	+	0.195902i	0.933919	−	0.357484i	$-0.116365\pi$
$199$	1.42471	+	2.76354i	0.100995	+	0.195902i	−0.832924	+	0.553387i	$0.813335\pi$
$200$	−4.96507	+	0.589947i	−0.351084	+	0.0417156i
$201$	1.53128	+	0.265981i	0.108008	+	0.0187608i
$202$	7.04773	+	7.04773i	0.495877	+	0.495877i
$203$	14.1526	+	4.52410i	0.993319	+	0.317530i
$204$	−0.00675660	−	0.00198392i	−0.000473056	−	0.000138902i
$205$	−18.3404	−	3.09102i	−1.28095	−	0.215886i
$206$	−10.2750	−	8.90330i	−0.715890	−	0.620322i
$207$	11.6989	+	7.91802i	0.813127	+	0.550340i
$208$	−3.48820	+	3.17098i	−0.241863	+	0.219868i
$209$	0.274125	−	1.90658i	0.0189616	−	0.131881i
$210$	−1.58582	+	1.24616i	−0.109432	+	0.0859933i
$211$	5.25117	−	21.6456i	0.361505	−	1.49014i	−0.443175	−	0.896435i	$-0.646148\pi$
$211$	5.25117	−	21.6456i	0.361505	−	1.49014i	0.804680	−	0.593709i	$-0.202337\pi$
$212$	−4.08801	+	2.76685i	−0.280766	+	0.190028i
$213$	−0.780159	−	0.0932794i	−0.0534556	−	0.00639140i
$214$	18.8102	+	7.53047i	1.28584	+	0.514772i
$215$	1.21283	+	12.7508i	0.0827142	+	0.869599i
$216$	−0.952650	+	0.612231i	−0.0648197	+	0.0416571i
$217$	−4.63628	+	9.54420i	−0.314731	+	0.647902i
$218$	−5.50267	−	0.925319i	−0.372688	−	0.0626705i
$219$	0.633160	+	0.0604594i	0.0427850	+	0.00408547i
$220$	−5.56173	−	10.1945i	−0.374972	−	0.687310i
$221$	−0.169900	+	0.0412172i	−0.0114287	+	0.00277257i
$222$	−1.13223	+	0.550003i	−0.0759903	+	0.0369138i
$223$	−3.22263	+	5.90180i	−0.215803	+	0.395214i	−0.963046	−	0.269337i	$-0.913195\pi$
$223$	−3.22263	+	5.90180i	−0.215803	+	0.395214i	0.747243	+	0.664551i	$0.231377\pi$
$224$	−3.27807	−	3.43794i	−0.219025	−	0.229707i
$225$	−13.1773	+	6.78111i	−0.878486	+	0.452074i
$226$	−1.49643	−	10.4079i	−0.0995408	−	0.692321i
$227$	16.8291	+	13.8953i	1.11699	+	0.922261i	0.997506	−	0.0705752i	$-0.0224835\pi$
$227$	16.8291	+	13.8953i	1.11699	+	0.922261i	0.119480	+	0.992837i	$0.461877\pi$
$228$	−0.00502392	+	0.0702436i	−0.000332717	+	0.00465199i
$229$	−5.17729	−	4.07147i	−0.342125	−	0.269050i	0.432281	−	0.901739i	$-0.357709\pi$
$229$	−5.17729	−	4.07147i	−0.342125	−	0.269050i	−0.774406	+	0.632689i	$0.781951\pi$
$230$	5.97677	−	8.82369i	0.394097	−	0.581817i
$231$	−4.05676	−	2.34217i	−0.266915	−	0.154104i
$232$	1.23128	−	2.87530i	0.0808372	−	0.188773i
$233$	0.339025	+	14.2421i	0.0222103	+	0.933031i	0.895298	+	0.445468i	$0.146963\pi$
$233$	0.339025	+	14.2421i	0.0222103	+	0.933031i	−0.873088	+	0.487563i	$0.837886\pi$
$234$	−6.40248	+	12.4191i	−0.418543	+	0.811861i
$235$	−3.16905	−	3.32605i	−0.206726	−	0.216968i
$236$	1.42188	+	1.35576i	0.0925567	+	0.0882527i
$237$	−0.349591	−	0.149704i	−0.0227084	−	0.00972430i
$238$	−0.0455962	−	0.170167i	−0.00295556	−	0.0110303i
$239$	14.1775	+	24.5562i	0.917067	+	1.58841i	0.803847	+	0.594836i	$0.202783\pi$
$239$	14.1775	+	24.5562i	0.917067	+	1.58841i	0.113220	+	0.993570i	$0.463883\pi$
$240$	0.229413	+	0.357262i	0.0148086	+	0.0230612i
$241$	17.8527	+	20.6031i	1.14999	+	1.32716i	0.936683	+	0.350177i	$0.113879\pi$
$241$	17.8527	+	20.6031i	1.14999	+	1.32716i	0.213309	+	0.976985i	$0.431576\pi$
$242$	10.1692	−	12.3163i	0.653700	−	0.791721i
$243$	−3.02323	+	4.03856i	−0.193940	+	0.259074i
$244$	1.14374	−	2.50445i	0.0732207	−	0.160331i
$245$	−32.6059	−	12.1750i	−2.08311	−	0.777833i
$246$	0.444955	+	1.51538i	0.0283693	+	0.0966169i
$247$	0.763951	+	1.57266i	0.0486090	+	0.100066i
$248$	1.90731	+	1.16257i	0.121114	+	0.0738231i
$249$	0.0142987	+	0.300167i	0.000906144	+	0.0190223i
$250$	5.11217	+	9.94312i	0.323322	+	0.628858i
$251$	3.50737	−	2.49758i	0.221383	−	0.157646i	−0.463985	−	0.885843i	$-0.653581\pi$
$251$	3.50737	−	2.49758i	0.221383	−	0.157646i	0.685368	+	0.728197i	$0.259641\pi$
$252$	−12.6644	−	6.15200i	−0.797783	−	0.387539i
$253$	24.1869	+	5.26154i	1.52062	+	0.330790i
$254$	0.374158	+	0.819292i	0.0234768	+	0.0514069i
$255$	0.00111754	+	0.0157063i	6.99830e−5	+	0.000983568i
$256$	−0.786053	+	0.618159i	−0.0491283	+	0.0386349i
$257$	−4.69416	−	6.93562i	−0.292814	−	0.432632i	0.652992	−	0.757365i	$-0.273514\pi$
$257$	−4.69416	−	6.93562i	−0.292814	−	0.432632i	−0.945806	+	0.324733i	$0.894726\pi$
$258$	0.928708	−	0.566077i	0.0578188	−	0.0352424i
$259$	−26.4919	−	17.0253i	−1.64612	−	1.05790i
$260$	9.36746	+	4.83362i	0.580945	+	0.299768i
$261$	0.441120	−	9.26026i	0.0273047	−	0.573196i
$262$	−8.34767	+	12.3337i	−0.515721	+	0.761977i
$263$	−1.39458	−	19.4987i	−0.0859933	−	1.20234i	−0.838926	−	0.544246i	$-0.816816\pi$
$263$	−1.39458	−	19.4987i	−0.0859933	−	1.20234i	0.752932	−	0.658098i	$-0.228639\pi$
$264$	−0.572005	+	0.803269i	−0.0352045	+	0.0494378i
$265$	8.98890	+	6.40595i	0.552184	+	0.393514i
$266$	−1.56597	+	0.807311i	−0.0960155	+	0.0494994i
$267$	−1.52259	+	1.52259i	−0.0931808	+	0.0931808i
$268$	7.86609	−	2.26378i	0.480498	−	0.138282i
$269$		−	15.5504i		−	0.948127i	−0.880491	−	0.474063i	$-0.842787\pi$
$269$		−	15.5504i		−	0.948127i	0.880491	−	0.474063i	$-0.157213\pi$
$270$	2.02654	+	1.51821i	0.123332	+	0.0923955i
$271$	1.58883	−	5.41106i	0.0965145	−	0.328698i	−0.897055	−	0.441918i	$-0.854298\pi$
$271$	1.58883	−	5.41106i	0.0965145	−	0.328698i	0.993570	+	0.113220i	$0.0361164\pi$
$272$	−0.0365728	+	0.00615002i	−0.00221755	+	0.000372900i
$273$	4.24113	−	0.303332i	0.256685	−	0.0183585i
$274$	4.25603	+	22.0824i	0.257116	+	1.33405i
$275$	−17.0194	+	19.6123i	−1.02631	+	1.18266i
$276$	−0.895766	−	0.128792i	−0.0539188	−	0.00775235i
$277$	−3.66486	−	16.8471i	−0.220200	−	1.01224i	−0.945957	−	0.324292i	$-0.894874\pi$
$277$	−3.66486	−	16.8471i	−0.220200	−	1.01224i	0.725757	−	0.687951i	$-0.241490\pi$
$278$	6.17945	+	10.1380i	0.370618	+	0.608038i
$279$	6.50092	+	1.25295i	0.389200	+	0.0750121i
$280$	−4.64471	+	9.55262i	−0.277575	+	0.570878i
$281$	2.16361	−	5.40445i	0.129070	−	0.322402i	−0.849730	−	0.527218i	$-0.823235\pi$
$281$	2.16361	−	5.40445i	0.129070	−	0.322402i	0.978801	+	0.204815i	$0.0656594\pi$
$282$	−0.136329	+	0.365513i	−0.00811828	+	0.0217660i
$283$	−4.33059	+	19.9074i	−0.257427	+	1.18337i	0.648927	+	0.760851i	$0.275218\pi$
$283$	−4.33059	+	19.9074i	−0.257427	+	1.18337i	−0.906353	+	0.422520i	$0.861145\pi$
$284$	−3.91043	+	1.35341i	−0.232041	+	0.0803103i
$285$	0.151108	−	0.0443091i	0.00895088	−	0.00262464i
$286$	−2.32720	+	24.3715i	−0.137610	+	1.44112i
$287$	−26.5779	+	29.2367i	−1.56885	+	1.72579i
$288$	−1.54264	+	2.53086i	−0.0909009	+	0.149132i
$289$	16.0637	+	5.55971i	0.944924	+	0.327042i
$290$	−6.98602	−	0.335358i	−0.410233	−	0.0196929i
$291$	−2.36319	+	2.25330i	−0.138533	+	0.132091i
$292$	3.13854	−	1.17061i	0.183669	−	0.0685051i
$293$	−10.0517	−	7.52458i	−0.587225	−	0.439591i	0.263903	−	0.964549i	$-0.414990\pi$
$293$	−10.0517	−	7.52458i	−0.587225	−	0.439591i	−0.851128	+	0.524958i	$0.824081\pi$
$294$	0.280936	+	2.94209i	0.0163845	+	0.171586i
$295$	1.73082	−	4.03776i	0.100772	−	0.235087i
$296$	−4.09795	+	5.21096i	−0.238188	+	0.302881i
$297$	−1.52216	+	5.68076i	−0.0883245	+	0.329631i
$298$	20.3224	−	5.44537i	1.17724	−	0.315442i
$299$	−20.8585	+	8.35047i	−1.20628	+	0.482920i
$300$	0.569504	−	0.759605i	0.0328803	−	0.0438558i
$301$	24.1852	+	12.4683i	1.39401	+	0.718663i
$302$	−12.4962	+	3.99461i	−0.719077	+	0.229864i
$303$	−1.89197	+	0.0450373i	−0.108691	+	0.00258732i
$304$	0.137845	+	0.344320i	0.00790594	+	0.0197481i
$305$	−6.14062	−	0.441453i	−0.351611	−	0.0252776i
$306$	−0.0951950	+	0.0549609i	−0.00544194	+	0.00314190i
$307$	−2.36868	−	19.8108i	−0.135187	−	1.13066i	−0.883869	−	0.467735i	$-0.845070\pi$
$307$	−2.36868	−	19.8108i	−0.135187	−	1.13066i	0.748681	−	0.662930i	$-0.230687\pi$
$308$	−24.6075	−	1.75996i	−1.40214	−	0.100283i
$309$	2.56983	−	0.245389i	0.146192	−	0.0139597i
$310$	0.947055	−	4.90409i	0.0537891	−	0.278534i
$311$	15.4589	+	7.05982i	0.876591	+	0.400326i	0.802307	−	0.596911i	$-0.203606\pi$
$311$	15.4589	+	7.05982i	0.876591	+	0.400326i	0.0742841	+	0.997237i	$0.476333\pi$
$312$	0.0213013	−	0.894845i	0.00120595	−	0.0506606i
$313$	−21.8888	−	11.9522i	−1.23723	−	0.675576i	−0.278644	−	0.960395i	$-0.589885\pi$
$313$	−21.8888	−	11.9522i	−1.23723	−	0.675576i	−0.958582	+	0.284818i	$0.908067\pi$
$314$	−2.59871	+	7.50848i	−0.146654	+	0.423728i
$315$	−3.00415	+	31.3392i	−0.169265	+	1.76577i
$316$	−2.00058	+	0.0952996i	−0.112542	+	0.00536102i
$317$	12.3590	+	14.9684i	0.694150	+	0.840712i	0.993547	−	0.113417i	$-0.0361796\pi$
$317$	12.3590	+	14.9684i	0.694150	+	0.840712i	−0.299397	+	0.954128i	$0.596786\pi$
$318$	0.155432	−	0.924318i	0.00871618	−	0.0518332i
$319$	−5.31299	−	15.3509i	−0.297470	−	0.859484i
$320$	1.90891	+	1.16450i	0.106711	+	0.0650977i
$321$	−3.49955	+	1.59819i	−0.195326	+	0.0892022i
$322$	−8.91240	−	20.8124i	−0.496668	−	1.15983i
$323$	−0.00163296	+	0.0136575i	−9.08603e−5	+	0.000759926i
$324$	−1.64210	+	8.52002i	−0.0912277	+	0.473334i
$325$	2.81546	−	23.4017i	0.156173	−	1.29809i
$326$	−9.55607	+	14.8695i	−0.529262	+	0.823547i
$327$	0.848174	−	0.634935i	0.0469041	−	0.0351120i
$328$	5.59502	+	6.15473i	0.308933	+	0.339838i
$329$	−9.58324	+	1.84702i	−0.528341	+	0.101829i
$330$	2.12968	+	0.571486i	0.117235	+	0.0314593i
$331$	11.5827	+	8.24800i	0.636643	+	0.453351i	0.852254	−	0.523128i	$-0.175235\pi$
$331$	11.5827	+	8.24800i	0.636643	+	0.453351i	−0.215612	+	0.976479i	$0.569174\pi$
$332$	0.758478	+	1.38905i	0.0416269	+	0.0762340i
$333$	−5.98280	+	18.7158i	−0.327855	+	1.02562i
$334$	−20.7992			−1.13808
$335$	−10.8842	−	14.7151i	−0.594665	−	0.803974i
$336$	0.901970			0.0492065
$337$	2.50852	−	7.84734i	0.136648	−	0.427472i	−0.859903	−	0.510458i	$-0.829476\pi$
$337$	2.50852	−	7.84734i	0.136648	−	0.427472i	0.996551	+	0.0829859i	$0.0264456\pi$
$338$	−4.41993	−	8.09450i	−0.240413	−	0.440283i
$339$	1.62633	+	1.15811i	0.0883303	+	0.0628997i
$340$	0.0414373	+	0.0718325i	0.00224725	+	0.00389566i
$341$	11.3910	−	2.19543i	0.616856	−	0.118889i
$342$	0.739448	+	0.813421i	0.0399848	+	0.0439847i
$343$	−32.5716	+	24.3828i	−1.75870	+	1.31655i
$344$	3.09683	−	4.81877i	0.166970	−	0.259810i
$345$	0.429419	+	1.97750i	0.0231191	+	0.106465i
$346$	3.14147	−	16.2995i	0.168887	−	0.876267i
$347$	1.33282	−	11.1473i	0.0715497	−	0.598419i	−0.910998	−	0.412410i	$-0.864687\pi$
$347$	1.33282	−	11.1473i	0.0715497	−	0.598419i	0.982548	−	0.186009i	$-0.0595553\pi$
$348$	0.233791	+	0.545954i	0.0125325	+	0.0292662i
$349$	−11.6528	+	5.32164i	−0.623758	+	0.284861i	−0.702114	−	0.712065i	$-0.747760\pi$
$349$	−11.6528	+	5.32164i	−0.623758	+	0.284861i	0.0783557	+	0.996925i	$0.475033\pi$
$350$	23.6422	+	2.27509i	1.26373	+	0.121609i
$351$	−1.74599	−	5.04471i	−0.0931942	−	0.269267i
$352$	−0.861230	+	5.12155i	−0.0459037	+	0.272979i
$353$	−14.1979	−	17.1956i	−0.755676	−	0.915228i	0.242819	−	0.970072i	$-0.421928\pi$
$353$	−14.1979	−	17.1956i	−0.755676	−	0.915228i	−0.998495	+	0.0548435i	$0.982534\pi$
$354$	−0.372620	+	0.0177501i	−0.0198045	+	0.000943405i
$355$	5.88860	+	7.13725i	0.312535	+	0.378806i
$356$	−3.70904	+	10.7166i	−0.196579	+	0.567978i
$357$	0.0293590	+	0.0160312i	0.00155384	+	0.000848462i
$358$	0.200747	−	8.43317i	0.0106098	−	0.445707i
$359$	−11.0774	−	5.05887i	−0.584642	−	0.266997i	0.101059	−	0.994880i	$-0.467777\pi$
$359$	−11.0774	−	5.05887i	−0.584642	−	0.266997i	−0.685701	+	0.727883i	$0.740504\pi$
$360$	6.50736	+	1.25667i	0.342968	+	0.0662323i
$361$	−18.7770	+	1.79299i	−0.988265	+	0.0943679i
$362$	−0.264626	−	0.0189264i	−0.0139084	−	0.000994750i
$363$	0.360041	+	3.01126i	0.0188972	+	0.158050i
$364$	19.3931	−	11.1966i	1.01648	−	0.586862i
$365$	−4.90299	−	5.66256i	−0.256634	−	0.296392i
$366$	0.194298	+	0.485333i	0.0101561	+	0.0253688i
$367$	−21.3201	+	0.507513i	−1.11290	+	0.0264919i	−0.576220	−	0.817294i	$-0.695473\pi$
$367$	−21.3201	+	0.507513i	−1.11290	+	0.0264919i	−0.536679	+	0.843786i	$0.680321\pi$
$368$	−4.53981	+	1.45122i	−0.236654	+	0.0756500i
$369$	21.9128	+	11.2968i	1.14073	+	0.588089i
$370$	14.1180	+	4.51875i	0.733959	+	0.234918i
$371$	21.7692	−	8.71509i	1.13020	−	0.452465i
$372$	−0.409677	+	0.109773i	−0.0212407	+	0.00569144i
$373$	4.57946	−	17.0908i	0.237115	−	0.884926i	−0.740069	−	0.672531i	$-0.765207\pi$
$373$	4.57946	−	17.0908i	0.237115	−	0.884926i	0.977184	−	0.212395i	$-0.0681263\pi$
$374$	−0.119061	+	0.151398i	−0.00615650	+	0.00782863i
$375$	−2.03624	−	0.600333i	−0.105151	−	0.0310010i
$376$	0.195296	+	2.04523i	0.0100716	+	0.105475i
$377$	11.8039	+	8.83630i	0.607933	+	0.455093i
$378$	5.04014	−	1.87987i	0.259237	−	0.0966903i
$379$	9.68483	−	9.23447i	0.497476	−	0.474343i	−0.399304	−	0.916819i	$-0.630748\pi$
$379$	9.68483	−	9.23447i	0.497476	−	0.474343i	0.896780	+	0.442476i	$0.145900\pi$
$380$	0.613868	−	0.557631i	0.0314907	−	0.0286059i
$381$	−0.161614	−	0.0559350i	−0.00827972	−	0.00286564i
$382$	7.98215	−	13.0955i	0.408402	−	0.670026i
$383$	−17.2545	+	18.9806i	−0.881663	+	0.969863i	−0.999732	−	0.0231429i	$-0.992633\pi$
$383$	−17.2545	+	18.9806i	−0.881663	+	0.969863i	0.118069	+	0.993005i	$0.462330\pi$
$384$	0.0180490	−	0.189017i	0.000921058	−	0.00964576i
$385$	15.5222	+	52.9358i	0.791086	+	2.69786i
$386$	19.1632	−	6.63244i	0.975380	−	0.337582i
$387$	3.60887	−	16.5897i	0.183449	−	0.843303i
$388$	−6.00966	+	16.1125i	−0.305094	+	0.817989i
$389$	−2.77468	+	6.93082i	−0.140682	+	0.351406i	−0.981930	−	0.189242i	$-0.939397\pi$
$389$	−2.77468	+	6.93082i	−0.140682	+	0.351406i	0.841249	+	0.540649i	$0.181821\pi$
$390$	−1.89166	+	0.653932i	−0.0957879	+	0.0331131i
$391$	−0.173563	−	0.0334516i	−0.00877747	−	0.00169172i
$392$	8.10117	+	13.2908i	0.409171	+	0.671287i
$393$	−0.601103	−	2.76323i	−0.0303216	−	0.139386i
$394$	25.5213	+	3.66941i	1.28574	+	0.184862i
$395$	1.76146	+	4.11757i	0.0886285	+	0.207177i
$396$	2.91317	+	15.1149i	0.146392	+	0.759555i
$397$	−16.2706	+	1.16370i	−0.816600	+	0.0584044i	−0.473388	−	0.880854i	$-0.656969\pi$
$397$	−16.2706	+	1.16370i	−0.816600	+	0.0584044i	−0.343211	+	0.939258i	$0.611515\pi$
$398$	−3.06613	+	0.515594i	−0.153691	+	0.0258444i
$399$	0.0942477	−	0.320978i	0.00471829	−	0.0160690i
$400$	0.949864	−	4.90895i	0.0474932	−	0.245447i
$401$		−	9.25886i		−	0.462365i	−0.972910	−	0.231183i	$-0.925740\pi$
$401$		−	9.25886i		−	0.462365i	0.972910	−	0.231183i	$-0.0742595\pi$
$402$	−0.719606	+	1.37759i	−0.0358907	+	0.0687077i
$403$	−7.44573	+	7.44573i	−0.370898	+	0.370898i
$404$	−8.85902	+	4.56714i	−0.440753	+	0.227224i
$405$	19.1345	−	3.21040i	0.950801	−	0.159526i
$406$	−8.61856	+	12.1031i	−0.427732	+	0.600666i
$407$	2.45613	+	34.3411i	0.121746	+	1.70223i
$408$	0.00394700	−	0.00583169i	0.000195406	−	0.000288712i
$409$	1.28446	−	26.9641i	0.0635123	−	1.33329i	−0.712100	−	0.702078i	$-0.752256\pi$
$409$	1.28446	−	26.9641i	0.0635123	−	1.33329i	0.775613	−	0.631209i	$-0.217441\pi$
$410$	8.52866	−	16.5284i	0.421200	−	0.816278i
$411$	−3.59225	−	2.30860i	−0.177192	−	0.113875i
$412$	11.6091	−	7.07613i	0.571940	−	0.348616i
$413$	−5.23101	−	7.72882i	−0.257401	−	0.380310i
$414$	−11.1042	+	8.73243i	−0.545741	+	0.429176i
$415$	2.31846	−	2.67366i	0.113809	−	0.131245i
$416$	−1.95830	−	4.28809i	−0.0960137	−	0.210241i
$417$	−2.20287	−	0.479204i	−0.107875	−	0.0234667i
$418$	1.73258	+	0.841636i	0.0847433	+	0.0411657i
$419$	−22.8582	+	16.2773i	−1.11670	+	0.795196i	−0.980701	−	0.195513i	$-0.937363\pi$
$419$	−22.8582	+	16.2773i	−1.11670	+	0.795196i	−0.135996	+	0.990709i	$0.543423\pi$
$420$	−0.704128	−	1.88996i	−0.0343580	−	0.0922207i
$421$	0.887867	+	18.6386i	0.0432720	+	0.908391i	0.911267	+	0.411817i	$0.135106\pi$
$421$	0.887867	+	18.6386i	0.0432720	+	0.908391i	−0.867995	+	0.496574i	$0.834591\pi$
$422$	19.0189	+	11.5926i	0.925825	+	0.564320i
$423$	2.66079	+	5.47746i	0.129372	+	0.266323i
$424$	−1.39072	−	4.73637i	−0.0675395	−	0.230018i
$425$	0.118167	−	0.142903i	0.00573196	−	0.00693181i
$426$	0.326398	−	0.714712i	0.0158140	−	0.0346279i
$427$	−7.83780	+	10.4701i	−0.379298	+	0.506682i
$428$	−12.9003	+	15.6241i	−0.623562	+	0.755219i
$429$	−3.04422	−	3.51322i	−0.146976	−	0.169620i
$430$	−12.5147	−	2.72721i	−0.603510	−	0.131518i
$431$	−7.71328	−	13.3598i	−0.371536	−	0.643518i	0.618266	−	0.785969i	$-0.287835\pi$
$431$	−7.71328	−	13.3598i	−0.371536	−	0.643518i	−0.989802	+	0.142450i	$0.954502\pi$
$432$	−0.293091	−	1.09383i	−0.0141014	−	0.0526270i
$433$	25.8202	+	11.0569i	1.24084	+	0.531358i	0.910894	−	0.412641i	$-0.135394\pi$
$433$	25.8202	+	11.0569i	1.24084	+	0.531358i	0.329946	+	0.944000i	$0.392969\pi$
$434$	−7.67932	−	7.32222i	−0.368619	−	0.351478i
$435$	0.961466	−	0.916082i	0.0460988	−	0.0439228i
$436$	2.55687	−	4.95963i	0.122452	−	0.237523i
$437$	0.0420670	+	1.76719i	0.00201234	+	0.0845362i
$438$	−0.250377	+	0.584686i	−0.0119635	+	0.0279374i
$439$	−28.2783	−	16.3265i	−1.34965	−	0.779221i	−0.361451	−	0.932391i	$-0.617719\pi$
$439$	−28.2783	−	16.3265i	−1.34965	−	0.779221i	−0.988200	+	0.153170i	$0.951052\pi$
$440$	11.4039	−	2.19357i	0.543658	−	0.104574i
$441$	36.2640	+	28.5184i	1.72686	+	1.35802i
$442$	0.0124721	−	0.174382i	0.000593236	−	0.00829453i
$443$	−11.3871	−	9.40200i	−0.541018	−	0.446702i	0.325719	−	0.945466i	$-0.394394\pi$
$443$	−11.3871	−	9.40200i	−0.541018	−	0.446702i	−0.866738	+	0.498764i	$0.833787\pi$
$444$	−0.179139	−	1.24594i	−0.00850154	−	0.0591295i
$445$	25.3507	−	0.594140i	1.20174	−	0.0281649i
$446$	−4.64032	−	4.86662i	−0.219725	−	0.230441i
$447$	−1.91454	+	3.50622i	−0.0905548	+	0.165839i
$448$	4.27282	−	2.07561i	0.201872	−	0.0980633i
$449$	−13.3838	+	3.24688i	−0.631623	+	0.153230i	−0.538774	−	0.842450i	$-0.681112\pi$
$449$	−13.3838	+	3.24688i	−0.631623	+	0.153230i	−0.0928485	+	0.995680i	$0.529597\pi$
$450$	−2.44682	−	14.6163i	−0.115344	−	0.689021i
$451$	43.0023	+	4.10622i	2.02490	+	0.193354i
$452$	10.3693	+	1.74369i	0.487731	+	0.0820161i
$453$	1.08844	−	2.24065i	0.0511395	−	0.105275i
$454$	−18.3597	+	11.7991i	−0.861664	+	0.553758i
$455$	−38.6004	−	31.8951i	−1.80962	−	1.49526i
$456$	−0.0653785	−	0.0261736i	−0.00306163	−	0.00122569i
$457$	19.1502	+	2.28969i	0.895810	+	0.107107i	0.553859	−	0.832611i	$-0.313155\pi$
$457$	19.1502	+	2.28969i	0.895810	+	0.107107i	0.341951	+	0.939718i	$0.388912\pi$
$458$	5.45456	−	3.69175i	0.254875	−	0.172504i
$459$	0.00990120	−	0.0408133i	0.000462149	−	0.00190500i
$460$	6.58486	+	8.37967i	0.307021	+	0.390704i
$461$	0.224184	−	1.55924i	0.0104413	−	0.0726209i	−0.983935	−	0.178530i	$-0.942866\pi$
$461$	0.224184	−	1.55924i	0.0104413	−	0.0726209i	0.994376	+	0.105909i	$0.0337751\pi$
$462$	3.46618	−	3.15097i	0.161262	−	0.146596i
$463$	17.9223	+	12.1302i	0.832921	+	0.563737i	0.900938	−	0.433947i	$-0.142880\pi$
$463$	17.9223	+	12.1302i	0.832921	+	0.563737i	−0.0680177	+	0.997684i	$0.521667\pi$
$464$	2.36387	+	2.04830i	0.109740	+	0.0950900i
$465$	0.549830	+	0.772730i	0.0254978	+	0.0358345i
$466$	−13.6691	−	4.01360i	−0.633207	−	0.185926i
$467$	9.58657	+	3.06449i	0.443614	+	0.141808i	0.517923	−	0.855427i	$-0.326705\pi$
$467$	9.58657	+	3.06449i	0.443614	+	0.141808i	−0.0743092	+	0.997235i	$0.523675\pi$
$468$	−9.87991	−	9.87991i	−0.456699	−	0.456699i
$469$	−38.7980	+	2.56507i	−1.79153	+	0.118444i
$470$	4.13306	−	2.00584i	0.190644	−	0.0925224i
$471$	−0.691310	−	1.34095i	−0.0318539	−	0.0617879i
$472$	−1.72433	+	0.941556i	−0.0793688	+	0.0433386i
$473$	−4.93319	−	29.3366i	−0.226829	−	1.34890i
$474$	0.249041	−	0.287409i	0.0114388	−	0.0132011i
$475$	−1.64766	−	0.850962i	−0.0755999	−	0.0390448i
$476$	0.175971	+	0.00838252i	0.00806560	+	0.000384212i
$477$	−8.76803	−	11.7127i	−0.401461	−	0.536289i
$478$	−27.7070	+	6.02729i	−1.26729	+	0.275682i
$479$	22.9708	+	5.57264i	1.04956	+	0.254621i	0.723210	−	0.690628i	$-0.242666\pi$
$479$	22.9708	+	5.57264i	1.04956	+	0.254621i	0.326350	+	0.945249i	$0.394181\pi$
$480$	−0.410152	+	0.109738i	−0.0187208	+	0.00500885i
$481$	−19.3181	−	24.5649i	−0.880829	−	1.12006i
$482$	−25.0607	+	10.7316i	−1.14148	+	0.488812i
$483$	4.02785	+	1.50231i	0.183273	+	0.0683575i
$484$	8.63510	+	13.4365i	0.392504	+	0.610749i
$485$	38.4531	+	0.0141276i	1.74607	+	0.000641502i
$486$	−2.92626	−	4.10936i	−0.132738	−	0.186404i
$487$	−7.62501	+	6.29574i	−0.345522	+	0.285287i	−0.793267	−	0.608874i	$-0.791621\pi$
$487$	−7.62501	+	6.29574i	−0.345522	+	0.285287i	0.447745	+	0.894162i	$0.352227\pi$
$488$	2.03728	+	1.85201i	0.0922231	+	0.0838364i
$489$	−0.791246	−	3.26156i	−0.0357814	−	0.147493i
$490$	21.5249	−	27.3505i	0.972398	−	1.23557i
$491$	8.75252	−	2.56997i	0.394995	−	0.115981i	−0.0782020	−	0.996938i	$-0.524918\pi$
$491$	8.75252	−	2.56997i	0.394995	−	0.115981i	0.473197	+	0.880956i	$0.343100\pi$
$492$	−1.57890	−	0.0375849i	−0.0711825	−	0.00169446i
$493$	0.0405378	+	0.108686i	0.00182573	+	0.00489498i
$494$	−1.73060	+	0.248822i	−0.0778633	+	0.0111950i
$495$	29.3972	−	17.9037i	1.32131	−	0.804713i
$496$	−1.68812	+	1.46276i	−0.0757987	+	0.0656799i
$497$	19.5177	−	2.33363i	0.875490	−	0.104678i
$498$	−0.290268	−	0.0777770i	−0.0130072	−	0.00348527i
$499$	−6.82773	+	11.8260i	−0.305651	+	0.529403i	−0.977406	−	0.211370i	$-0.932207\pi$
$499$	−6.82773	+	11.8260i	−0.305651	+	0.529403i	0.671755	+	0.740773i	$0.265541\pi$
$500$	−11.0276	+	1.84188i	−0.493168	+	0.0823715i
$501$	2.72532	−	2.85823i	0.121758	−	0.127696i
$502$	1.31104	+	4.10131i	0.0585148	+	0.183050i
$503$	−5.42075	−	16.9576i	−0.241699	−	0.756101i	−0.995130	−	0.0985732i	$-0.968572\pi$
$503$	−5.42075	−	16.9576i	−0.241699	−	0.756101i	0.753431	−	0.657527i	$-0.228398\pi$
$504$	9.71602	−	10.1899i	0.432786	−	0.453893i
$505$	16.4857	+	14.9976i	0.733604	+	0.667383i
$506$	−12.3763	+	21.4364i	−0.550194	+	0.952964i
$507$	1.69150	+	0.453235i	0.0751220	+	0.0201289i
$508$	−0.894315	+	0.106928i	−0.0396788	+	0.00474418i
$509$	13.5067	−	11.7036i	0.598674	−	0.518754i	−0.301967	−	0.953318i	$-0.597643\pi$
$509$	13.5067	−	11.7036i	0.598674	−	0.518754i	0.900641	+	0.434564i	$0.143098\pi$
$510$	−0.0153008	−	0.00371789i	−0.000677531	−	0.000164631i
$511$	−15.7503	+	2.26454i	−0.696750	+	0.100178i
$512$	−0.349464	−	0.936950i	−0.0154443	−	0.0414077i
$513$	−0.419880	−	0.00999501i	−0.0185382	−	0.000441290i
$514$	8.03560	−	2.35947i	0.354435	−	0.104072i
$515$	−23.8898	−	18.8014i	−1.05271	−	0.828488i
$516$	0.256419	+	1.05697i	0.0112882	+	0.0465306i
$517$	7.89537	+	7.17737i	0.347238	+	0.315660i
$518$	24.2833	−	20.0500i	1.06695	−	0.880945i
$519$	1.82826	+	2.56743i	0.0802517	+	0.112698i
$520$	−7.45637	+	7.45089i	−0.326983	+	0.326743i
$521$	−20.2175	−	31.4591i	−0.885747	−	1.37825i	−0.925382	−	0.379035i	$-0.876256\pi$
$521$	−20.2175	−	31.4591i	−0.885747	−	1.37825i	0.0396357	−	0.999214i	$-0.487380\pi$
$522$	8.68623	+	3.23980i	0.380186	+	0.141802i
$523$	31.0308	−	13.2882i	1.35688	−	0.581052i	0.412820	−	0.910813i	$-0.364544\pi$
$523$	31.0308	−	13.2882i	1.35688	−	0.581052i	0.944064	+	0.329761i	$0.106968\pi$
$524$	−9.20627	−	11.7067i	−0.402178	−	0.511411i
$525$	−3.41049	+	2.95082i	−0.148846	+	0.128784i
$526$	18.9975	+	4.60875i	0.828331	+	0.200951i
$527$	−0.0809464	+	0.0176088i	−0.00352608	+	0.000767052i
$528$	−0.590959	−	0.789429i	−0.0257182	−	0.0343555i
$529$	0.283812	+	0.0135196i	0.0123397	+	0.000587810i
$530$	−8.83877	+	6.61155i	−0.383932	+	0.287188i
$531$	−3.81333	+	4.40082i	−0.165484	+	0.190979i
$532$	−0.292162	−	1.73742i	−0.0126668	−	0.0753269i
$533$	−34.4143	+	18.7916i	−1.49065	+	0.813957i
$534$	−0.986682	−	1.91390i	−0.0426979	−	0.0828224i
$535$	42.8090	+	14.8340i	1.85079	+	0.641328i
$536$	−0.238834	+	8.18187i	−0.0103160	+	0.353403i
$537$	1.13259	+	1.13259i	0.0488748	+	0.0488748i
$538$	14.8120	+	4.73490i	0.638593	+	0.204136i
$539$	77.5625	+	22.7744i	3.34086	+	0.980964i
$540$	−2.06318	+	1.46804i	−0.0887851	+	0.0631744i
$541$	−8.13039	−	7.04502i	−0.349553	−	0.302889i	0.462332	−	0.886707i	$-0.347013\pi$
$541$	−8.13039	−	7.04502i	−0.349553	−	0.302889i	−0.811885	+	0.583818i	$0.801558\pi$
$542$	4.67034	+	3.16098i	0.200608	+	0.135776i
$543$	0.0372749	−	0.0338851i	0.00159962	−	0.00145415i
$544$	0.00527793	−	0.0367088i	0.000226289	−	0.00157388i
$545$	−12.3883	−	1.48582i	−0.530657	−	0.0636455i
$546$	−1.00244	+	4.13211i	−0.0429004	+	0.176838i
$547$	2.13105	−	1.44233i	0.0911170	−	0.0616698i	−0.514100	−	0.857730i	$-0.671874\pi$
$547$	2.13105	−	1.44233i	0.0911170	−	0.0616698i	0.605217	+	0.796060i	$0.293086\pi$
$548$	−22.3298	−	2.66985i	−0.953880	−	0.114050i
$549$	7.57595	+	3.03295i	0.323334	+	0.129443i
$550$	−13.4988	−	22.1829i	−0.575592	−	0.945882i
$551$	0.975918	−	0.627184i	0.0415755	−	0.0267190i
$552$	0.395425	−	0.814016i	0.0168304	−	0.0346468i
$553$	9.38239	+	1.57773i	0.398980	+	0.0670917i
$554$	17.1630	+	1.63887i	0.729187	+	0.0696289i
$555$	−2.47085	+	1.34801i	−0.104882	+	0.0572198i
$556$	−11.5382	+	2.79913i	−0.489328	+	0.118710i
$557$	−37.8045	+	18.3643i	−1.60183	+	0.778119i	−0.999793	−	0.0203510i	$-0.993522\pi$
$557$	−37.8045	+	18.3643i	−1.60183	+	0.778119i	−0.602034	+	0.798470i	$0.705643\pi$
$558$	−3.17290	+	5.81073i	−0.134319	+	0.245988i
$559$	18.6340	+	19.5427i	0.788133	+	0.826570i
$560$	−7.68477	−	7.33281i	−0.324741	−	0.309868i
$561$	−0.00520466	−	0.0361992i	−0.000219741	−	0.00152833i
$562$	4.48904	+	3.70646i	0.189359	+	0.156348i
$563$	0.631561	−	8.83038i	0.0266171	−	0.372156i	−0.966633	−	0.256165i	$-0.917541\pi$
$563$	0.631561	−	8.83038i	0.0266171	−	0.372156i	0.993250	−	0.115991i	$-0.0370044\pi$
$564$	−0.306646	−	0.241149i	−0.0129121	−	0.0101542i
$565$	−4.44120	−	23.0888i	−0.186843	−	0.971352i
$566$	−17.6435	−	10.1865i	−0.741612	−	0.428170i
$567$	16.2252	−	37.8895i	0.681395	−	1.59121i
$568$	−0.0984753	−	4.13685i	−0.00413193	−	0.173578i
$569$	−15.6818	+	30.4184i	−0.657415	+	1.27521i	0.290558	+	0.956857i	$0.406159\pi$
$569$	−15.6818	+	30.4184i	−0.657415	+	1.27521i	−0.947973	+	0.318350i	$0.896871\pi$
$570$	−0.00380528	+	0.157425i	−0.000159385	+	0.00659379i
$571$	−27.1733	−	25.9096i	−1.13717	−	1.08428i	−0.995538	−	0.0943648i	$-0.969918\pi$
$571$	−27.1733	−	25.9096i	−1.13717	−	1.08428i	−0.141628	−	0.989920i	$-0.545234\pi$
$572$	−22.5057	−	9.63750i	−0.941010	−	0.402964i
$573$	0.753694	+	2.81282i	0.0314860	+	0.117507i
$574$	−19.7558	−	34.2181i	−0.824593	−	1.42824i
$575$	12.4180	−	20.3394i	0.517866	−	0.848210i
$576$	−1.94097	−	2.24000i	−0.0808738	−	0.0933334i
$577$	−2.04351	+	2.47498i	−0.0850726	+	0.103035i	−0.811933	−	0.583750i	$-0.801585\pi$
$577$	−2.04351	+	2.47498i	−0.0850726	+	0.103035i	0.726861	+	0.686785i	$0.240979\pi$
$578$	−10.1869	+	13.6081i	−0.423719	+	0.566022i
$579$	−1.59952	+	3.50246i	−0.0664739	+	0.145557i
$580$	2.44658	−	6.55219i	0.101589	−	0.272065i
$581$	−2.11806	−	7.21345i	−0.0878719	−	0.299264i
$582$	−1.42674	−	2.93708i	−0.0591404	−	0.121746i
$583$	−21.8906	−	13.3430i	−0.906616	−	0.552611i
$584$	0.159387	+	3.34595i	0.00659549	+	0.138456i
$585$	−12.9893	+	28.4149i	−0.537040	+	1.17481i
$586$	10.2279	−	7.28324i	0.422510	−	0.300868i
$587$	−30.3947	−	14.7648i	−1.25452	−	0.609410i	−0.314092	−	0.949392i	$-0.601700\pi$
$587$	−30.3947	−	14.7648i	−1.25452	−	0.609410i	−0.940432	+	0.339982i	$0.889579\pi$
$588$	−2.88793	−	0.628231i	−0.119096	−	0.0259078i
$589$	0.344150	+	0.753584i	0.0141805	+	0.0310509i
$590$	3.31902	+	2.87808i	0.136642	+	0.118489i
$591$	−3.84831	+	3.02635i	−0.158298	+	0.124487i
$592$	−3.71576	−	5.49003i	−0.152717	−	0.225639i
$593$	13.2827	−	8.09622i	0.545454	−	0.332472i	−0.220479	−	0.975392i	$-0.570762\pi$
$593$	13.2827	−	8.09622i	0.545454	−	0.332472i	0.765933	+	0.642920i	$0.222277\pi$
$594$	−4.94755	−	3.17959i	−0.203000	−	0.130460i
$595$	−0.119808	−	0.375268i	−0.00491165	−	0.0153845i
$596$	−1.00109	+	21.0155i	−0.0410062	+	0.860827i
$597$	0.330902	−	0.488907i	0.0135429	−	0.0200096i
$598$	−1.60284	−	22.4106i	−0.0655450	−	0.916439i
$599$	−2.75667	+	3.87120i	−0.112634	+	0.158173i	−0.867045	−	0.498230i	$-0.833983\pi$
$599$	−2.75667	+	3.87120i	−0.112634	+	0.158173i	0.754410	+	0.656403i	$0.227923\pi$
$600$	0.550130	+	0.773752i	0.0224589	+	0.0315883i
$601$	−2.27320	+	1.17191i	−0.0927256	+	0.0478034i	−0.503966	−	0.863724i	$-0.668126\pi$
$601$	−2.27320	+	1.17191i	−0.0927256	+	0.0478034i	0.411240	+	0.911527i	$0.365096\pi$
$602$	−19.2404	+	19.2404i	−0.784179	+	0.784179i
$603$	7.81147	+	22.9690i	0.318107	+	0.935370i
$604$		−	13.1192i		−	0.533811i
$605$	21.4133	−	28.5830i	0.870576	−	1.16206i
$606$	0.533181	−	1.81585i	0.0216590	−	0.0737637i
$607$	−9.67976	+	1.62773i	−0.392890	+	0.0660676i	−0.358951	−	0.933356i	$-0.616866\pi$
$607$	−9.67976	+	1.62773i	−0.392890	+	0.0660676i	−0.0339383	+	0.999424i	$0.510805\pi$
$608$	−0.369942	+	0.0264588i	−0.0150031	+	0.00107304i
$609$	−0.533920	−	2.77024i	−0.0216355	−	0.112256i
$610$	2.29023	−	5.71463i	0.0927286	−	0.231378i
$611$	−9.58667	−	1.37835i	−0.387835	−	0.0557623i
$612$	−0.0233655	−	0.107410i	−0.000944496	−	0.00434178i
$613$	5.55038	+	9.10598i	0.224178	+	0.367787i	0.945933	−	0.324361i	$-0.105149\pi$
$613$	5.55038	+	9.10598i	0.224178	+	0.367787i	−0.721755	+	0.692148i	$0.756664\pi$
$614$	19.5914	+	3.77593i	0.790644	+	0.152384i
$615$	1.15383	+	3.33773i	0.0465268	+	0.134590i
$616$	9.16905	−	22.9032i	0.369432	−	0.922795i
$617$	5.97838	−	16.0287i	0.240681	−	0.645289i	−0.759305	−	0.650735i	$-0.774461\pi$
$617$	5.97838	−	16.0287i	0.240681	−	0.645289i	0.999985	+	0.00544585i	$0.00173348\pi$
$618$	−0.548741	+	2.52252i	−0.0220736	+	0.101471i
$619$	22.0697	−	7.63840i	0.887057	−	0.307013i	0.154722	−	0.987958i	$-0.450552\pi$
$619$	22.0697	−	7.63840i	0.887057	−	0.307013i	0.732335	+	0.680945i	$0.238431\pi$
$620$	4.38286	+	2.39532i	0.176020	+	0.0961982i
$621$	0.513040	−	5.37280i	0.0205876	−	0.215603i
$622$	−11.4316	+	12.5752i	−0.458366	+	0.504219i
$623$	28.0374	−	45.9982i	1.12329	−	1.84288i
$624$	0.845868	+	0.292758i	0.0338618	+	0.0117197i
$625$	12.4682	+	21.6690i	0.498727	+	0.866759i
$626$	18.0495	−	17.2101i	0.721402	−	0.687855i
$627$	−0.342679	+	0.127813i	−0.0136853	+	0.00510434i
$628$	−6.36068	−	4.76155i	−0.253819	−	0.190006i
$629$	−0.0233700	−	0.244742i	−0.000931824	−	0.00975850i
$630$	−28.9364	−	12.4039i	−1.15285	−	0.494182i
$631$	17.2206	−	21.8978i	0.685541	−	0.871736i	−0.311369	−	0.950289i	$-0.600787\pi$
$631$	17.2206	−	21.8978i	0.685541	−	0.871736i	0.996910	+	0.0785527i	$0.0250299\pi$
$632$	0.518377	−	1.93461i	0.0206199	−	0.0769546i
$633$	−4.08511	+	1.09460i	−0.162369	+	0.0435066i
$634$	−18.0208	+	7.21445i	−0.715699	+	0.286523i
$635$	0.922207	+	1.79045i	0.0365967	+	0.0710517i
$636$	0.833102	+	0.429494i	0.0330346	+	0.0170305i
$637$	−69.8915	+	22.3419i	−2.76920	+	0.885217i
$638$	16.2397	−	0.386577i	0.642936	−	0.0153047i
$639$	−4.55839	−	11.3863i	−0.180327	−	0.450435i
$640$	−1.69045	+	1.46369i	−0.0668207	+	0.0578575i
$641$	−11.5022	+	6.64080i	−0.454310	+	0.262296i	−0.709649	−	0.704556i	$-0.751146\pi$
$641$	−11.5022	+	6.64080i	−0.454310	+	0.262296i	0.255339	+	0.966852i	$0.417813\pi$
$642$	−0.456737	−	3.82000i	−0.0180260	−	0.150764i
$643$	23.9639	+	1.71393i	0.945045	+	0.0675909i	0.535349	−	0.844631i	$-0.320180\pi$
$643$	23.9639	+	1.71393i	0.945045	+	0.0675909i	0.409696	+	0.912222i	$0.365635\pi$
$644$	22.5379	−	2.15211i	0.888117	−	0.0848049i
$645$	2.01457	−	1.36242i	0.0793238	−	0.0536454i
$646$	−0.0125118	−	0.00571396i	−0.000492271	−	0.000224813i
$647$	−0.0837300	+	3.51741i	−0.00329177	+	0.138284i	0.995677	+	0.0928826i	$0.0296081\pi$
$647$	−0.0837300	+	3.51741i	−0.00329177	+	0.138284i	−0.998969	+	0.0454012i	$0.985543\pi$
$648$	−7.61546	−	4.15836i	−0.299164	−	0.163356i
$649$	−3.33718	+	9.64214i	−0.130996	+	0.378487i
$650$	21.4332	+	9.80727i	0.840680	+	0.384673i
$651$	2.01245	−	0.0958647i	0.0788740	−	0.00375723i
$652$	−11.2538	−	13.6299i	−0.440732	−	0.533787i
$653$	−1.59972	+	9.51318i	−0.0626018	+	0.372279i	0.937127	+	0.348989i	$0.113475\pi$
$653$	−1.59972	+	9.51318i	−0.0626018	+	0.372279i	−0.999729	+	0.0232905i	$0.992586\pi$
$654$	0.346529	+	1.00123i	0.0135503	+	0.0391512i
$655$	−17.3430	+	28.4295i	−0.677647	+	1.11083i
$656$	−7.56609	+	3.45532i	−0.295406	+	0.134908i
$657$	3.90834	+	9.12684i	0.152479	+	0.356072i
$658$	1.15865	−	9.69059i	0.0451689	−	0.377778i
$659$	−0.266654	+	1.38353i	−0.0103874	+	0.0538947i	−0.986753	−	0.162233i	$-0.948131\pi$
$659$	−0.266654	+	1.38353i	−0.0103874	+	0.0538947i	0.976365	+	0.216127i	$0.0693426\pi$
$660$	−1.19281	+	1.85455i	−0.0464301	+	0.0721883i
$661$	−0.865974	+	1.34748i	−0.0336825	+	0.0524109i	−0.857687	−	0.514173i	$-0.828099\pi$
$661$	−0.865974	+	1.34748i	−0.0336825	+	0.0524109i	0.824004	+	0.566584i	$0.191735\pi$
$662$	−11.3831	+	8.52131i	−0.442418	+	0.331190i
$663$	0.0223295	+	0.0245633i	0.000867207	+	0.000953960i
$664$	−1.55404	+	0.299516i	−0.0603084	+	0.0116235i
$665$	−3.41247	+	1.96852i	−0.132330	+	0.0763359i
$666$	−16.0055	−	11.3974i	−0.620199	−	0.441642i
$667$	7.14448	+	13.0841i	0.276635	+	0.506620i
$668$	6.33306	−	19.8115i	0.245034	−	0.766532i
$669$	1.27680			0.0493638
$670$	17.3305	−	5.88678i	0.669535	−	0.227426i
$671$	14.2989			0.552003
$672$	−0.274638	+	0.859142i	−0.0105944	+	0.0331421i
$673$	23.8661	+	43.7076i	0.919972	+	1.68480i	0.706319	+	0.707893i	$0.250354\pi$
$673$	23.8661	+	43.7076i	0.919972	+	1.68480i	0.213653	+	0.976910i	$0.431464\pi$
$674$	6.71091	+	4.77882i	0.258495	+	0.184073i
$675$	4.68672	+	3.17709i	0.180392	+	0.122286i
$676$	9.05596	−	1.74539i	0.348306	−	0.0671305i
$677$	−18.0249	−	19.8281i	−0.692754	−	0.762055i	0.287931	−	0.957651i	$-0.407033\pi$
$677$	−18.0249	−	19.8281i	−0.692754	−	0.762055i	−0.980684	+	0.195596i	$0.937336\pi$
$678$	−1.59831	+	1.19648i	−0.0613828	+	0.0459506i
$679$	44.1647	−	68.7216i	1.69488	−	2.63729i
$680$	−0.0810387	+	0.0175977i	−0.00310769	+	0.000674842i
$681$	0.784243	−	4.06904i	0.0300522	−	0.155926i
$682$	−1.37721	+	11.5186i	−0.0527362	+	0.441069i
$683$	−2.32323	−	5.42525i	−0.0888958	−	0.207591i	0.868934	−	0.494929i	$-0.164806\pi$
$683$	−2.32323	−	5.42525i	−0.0888958	−	0.207591i	−0.957830	+	0.287337i	$0.907230\pi$
$684$	−0.999949	+	0.456661i	−0.0382340	+	0.0174609i
$685$	11.8375	+	48.8733i	0.452289	+	1.86735i
$686$	−13.3074	−	38.4492i	−0.508079	−	1.46800i
$687$	−0.207390	+	1.23330i	−0.00791241	+	0.0470533i
$688$	3.64701	+	4.41703i	0.139041	+	0.168398i
$689$	23.2439	−	1.10724i	0.885522	−	0.0421826i
$690$	−2.01436	−	0.193095i	−0.0766852	−	0.00735098i
$691$	6.85614	−	19.8095i	0.260820	−	0.753590i	−0.736223	−	0.676739i	$-0.763392\pi$
$691$	6.85614	−	19.8095i	0.260820	−	0.753590i	0.997043	−	0.0768504i	$-0.0244864\pi$
$692$	14.5690	+	7.95529i	0.553831	+	0.302415i
$693$	1.74013	−	73.1009i	0.0661020	−	2.77688i
$694$	10.2122	+	4.66374i	0.387649	+	0.177033i
$695$	14.8726	+	21.9916i	0.564149	+	0.834190i
$696$	−0.591217	+	0.0564544i	−0.0224100	+	0.00213990i
$697$	−0.307688	−	0.0220063i	−0.0116545	−	0.000833549i
$698$	−1.52084	−	12.7198i	−0.0575647	−	0.481452i
$699$	2.34261	−	1.35251i	0.0886057	−	0.0511565i
$700$	−9.36579	+	21.8268i	−0.353993	+	0.824977i
$701$	12.1696	+	30.3981i	0.459638	+	1.14812i	0.959423	+	0.281971i	$0.0909881\pi$
$701$	12.1696	+	30.3981i	0.459638	+	1.14812i	−0.499785	+	0.866149i	$0.666588\pi$
$702$	5.33680	−	0.127040i	0.201425	−	0.00479480i
$703$	−2.34196	+	0.748645i	−0.0883289	+	0.0282357i
$704$	−4.61613	−	2.37978i	−0.173977	−	0.0896913i
$705$	−0.265912	+	0.830793i	−0.0100148	+	0.0312895i
$706$	20.7021	−	8.28788i	0.779135	−	0.311919i
$707$	45.7328	−	12.2541i	1.71996	−	0.460861i
$708$	0.0965504	−	0.360331i	0.00362859	−	0.0135421i
$709$	10.1556	−	12.9140i	0.381403	−	0.484994i	−0.557011	−	0.830505i	$-0.688052\pi$
$709$	10.1556	−	12.9140i	0.381403	−	0.484994i	0.938415	+	0.345511i	$0.112294\pi$
$710$	−8.59135	+	3.43580i	−0.322428	+	0.128943i
$711$	−0.564286	−	5.90947i	−0.0211624	−	0.221622i
$712$	−9.07837	−	6.79598i	−0.340226	−	0.254690i
$713$	−9.97483	+	3.72042i	−0.373560	+	0.139331i
$714$	−0.0242094	+	0.0230836i	−0.000906015	+	0.000863883i
$715$	−2.62493	+	54.6813i	−0.0981668	+	2.04497i
$716$	7.97161	+	2.75900i	0.297913	+	0.103109i
$717$	2.80218	−	4.59727i	0.104649	−	0.171688i
$718$	8.19158	−	9.01104i	0.305707	−	0.336289i
$719$	0.707897	−	7.41344i	0.0264001	−	0.276475i	−0.972627	−	0.232372i	$-0.925351\pi$
$719$	0.707897	−	7.41344i	0.0264001	−	0.276475i	0.999027	−	0.0441022i	$-0.0140427\pi$
$720$	−3.17840	+	5.81573i	−0.118452	+	0.216739i
$721$	−61.0314	+	21.1232i	−2.27293	+	0.786668i
$722$	4.00950	−	18.4314i	0.149218	−	0.685945i
$723$	1.80897	−	4.85002i	0.0672761	−	0.180374i
$724$	0.0986027	−	0.246298i	0.00366454	−	0.00915358i
$725$	−15.6392	−	0.0114916i	−0.580826	−	0.000426789i
$726$	−2.97791	−	0.573945i	−0.110521	−	0.0213011i
$727$	0.624278	+	1.02419i	0.0231532	+	0.0379852i	0.865247	−	0.501346i	$-0.167162\pi$
$727$	0.624278	+	1.02419i	0.0231532	+	0.0379852i	−0.842093	+	0.539332i	$0.818677\pi$
$728$	4.76003	+	21.8815i	0.176418	+	0.810982i
$729$	−24.8174	−	3.56820i	−0.919162	−	0.132156i
$730$	6.88657	−	2.94601i	0.254884	−	0.109037i
$731$	0.0402032	+	0.208594i	0.00148697	+	0.00771513i
$732$	−0.521449	+	0.0372947i	−0.0192733	+	0.00137845i
$733$	−20.6287	+	3.46889i	−0.761938	+	0.128126i	−0.533925	−	0.845532i	$-0.679284\pi$
$733$	−20.6287	+	3.46889i	−0.761938	+	0.128126i	−0.228013	+	0.973658i	$0.573223\pi$
$734$	6.00826	−	20.4623i	0.221769	−	0.755276i
$735$	0.938104	+	6.54172i	0.0346025	+	0.241295i
$736$		−	4.76612i		−	0.175681i
$737$	27.6650	+	32.2765i	1.01905	+	1.18892i
$738$	−17.4326	+	17.4326i	−0.641702	+	0.641702i
$739$	−6.50526	+	3.35370i	−0.239300	+	0.123368i	−0.573706	−	0.819061i	$-0.694495\pi$
$739$	−6.50526	+	3.35370i	−0.239300	+	0.123368i	0.334406	+	0.942429i	$0.391464\pi$
$740$	−8.60292	+	12.0717i	−0.316250	+	0.443765i
$741$	0.192567	−	0.270423i	0.00707414	−	0.00993424i
$742$	1.67283	+	23.3892i	0.0614114	+	0.858644i
$743$	−29.9690	+	44.2791i	−1.09946	+	1.62444i	−0.388091	+	0.921621i	$0.626865\pi$
$743$	−29.9690	+	44.2791i	−1.09946	+	1.62444i	−0.711365	+	0.702823i	$0.751923\pi$
$744$	0.0201808	−	0.423648i	0.000739866	−	0.0155317i
$745$	44.8167	−	14.3082i	1.64196	−	0.524211i
$746$	14.8849	+	9.56592i	0.544973	+	0.350233i
$747$	−4.00544	+	2.44144i	−0.146551	+	0.0893276i
$748$	−0.107957	−	0.159506i	−0.00394730	−	0.00583213i
$749$	75.6562	−	59.4967i	2.76442	−	2.17396i
$750$	1.19183	−	1.75676i	0.0435196	−	0.0641478i
$751$	−14.4873	−	31.7228i	−0.528649	−	1.15758i	−0.966060	−	0.258318i	$-0.916832\pi$
$751$	−14.4873	−	31.7228i	−0.528649	−	1.15758i	0.437411	−	0.899262i	$-0.355896\pi$
$752$	−2.00758	−	0.436722i	−0.0732089	−	0.0159256i
$753$	−0.735391	−	0.357231i	−0.0267991	−	0.0130182i
$754$	−12.0109	+	8.55289i	−0.437410	+	0.311478i
$755$	−27.4895	+	10.2415i	−1.00045	+	0.372728i
$756$	0.255958	+	5.37321i	0.00930909	+	0.195422i
$757$	−20.3745	−	12.4189i	−0.740525	−	0.451373i	0.0987282	−	0.995114i	$-0.468523\pi$
$757$	−20.3745	−	12.4189i	−0.740525	−	0.451373i	−0.839253	+	0.543741i	$0.817007\pi$
$758$	5.84709	+	12.0367i	0.212376	+	0.437194i
$759$	−1.32413	−	4.50958i	−0.0480629	−	0.163687i
$760$	0.344238	+	0.754510i	0.0124868	+	0.0273690i
$761$	18.7813	−	41.1253i	0.680821	−	1.49079i	−0.180949	−	0.983492i	$-0.557917\pi$
$761$	18.7813	−	41.1253i	0.680821	−	1.49079i	0.861771	−	0.507298i	$-0.169356\pi$
$762$	0.102488	−	0.136908i	0.00371276	−	0.00495966i
$763$	−16.8762	+	20.4395i	−0.610961	+	0.739958i
$764$	10.0433	+	11.5905i	0.363352	+	0.419331i
$765$	−0.206823	+	0.132809i	−0.00747769	+	0.00480174i
$766$	−12.8256	−	22.2145i	−0.463406	−	0.802643i
$767$	−2.39706	−	8.94595i	−0.0865528	−	0.323020i
$768$	0.174547	+	0.0747452i	0.00629841	+	0.00269714i
$769$	1.13036	+	1.07780i	0.0407619	+	0.0388664i	0.710186	−	0.704014i	$-0.248611\pi$
$769$	1.13036	+	1.07780i	0.0407619	+	0.0388664i	−0.669424	+	0.742880i	$0.733459\pi$
$770$	−55.1485	−	1.33305i	−1.98741	−	0.0480399i
$771$	−0.728668	+	1.41342i	−0.0262423	+	0.0509030i
$772$	0.482581	+	20.2727i	0.0173685	+	0.729631i
$773$	0.0105321	−	0.0245949i	0.000378814	−	0.000884615i	−0.919071	−	0.394092i	$-0.871059\pi$
$773$	0.0105321	−	0.0245949i	0.000378814	−	0.000884615i	0.919450	+	0.393208i	$0.128635\pi$
$774$	14.7031	+	8.48886i	0.528493	+	0.305126i
$775$	1.59756	−	11.0536i	0.0573862	−	0.397058i
$776$	−13.5176	−	10.6303i	−0.485253	−	0.381607i
$777$	−0.426566	+	5.96418i	−0.0153030	+	0.213964i
$778$	−5.75687	−	4.75327i	−0.206394	−	0.170413i
$779$	0.439034	+	3.05355i	0.0157300	+	0.109405i
$780$	−0.0468959	−	2.00095i	−0.00167914	−	0.0716455i
$781$	−14.8302	−	15.5535i	−0.530667	−	0.556548i
$782$	0.0847108	−	0.155136i	0.00302925	−	0.00554766i
$783$	−3.18601	+	1.54767i	−0.113859	+	0.0553091i
$784$	−15.1264	+	3.66963i	−0.540229	+	0.131058i
$785$	−5.01170	+	17.0451i	−0.178875	+	0.608366i
$786$	2.81505	+	0.268804i	0.100409	+	0.00958793i
$787$	−16.2589	−	2.73407i	−0.579567	−	0.0974589i	−0.131275	−	0.991346i	$-0.541907\pi$
$787$	−16.2589	−	2.73407i	−0.579567	−	0.0974589i	−0.448292	+	0.893887i	$0.647968\pi$
$788$	−11.2661	+	23.1922i	−0.401337	+	0.826186i
$789$	−3.12259	+	2.00676i	−0.111167	+	0.0714427i
$790$	−4.45839	+	0.424072i	−0.158622	+	0.0150878i
$791$	−46.3708	−	18.5641i	−1.64876	−	0.660062i
$792$	−15.2843	−	1.82746i	−0.543102	−	0.0649358i
$793$	−10.7486	+	7.27488i	−0.381695	+	0.258339i
$794$	3.84575	−	15.8524i	0.136480	−	0.562580i
$795$	0.249583	−	2.08094i	0.00885179	−	0.0738035i
$796$	0.442482	−	3.07753i	0.0156833	−	0.109080i
$797$	−28.9569	+	26.3236i	−1.02571	+	0.932428i	−0.997741	−	0.0671805i	$-0.978600\pi$
$797$	−28.9569	+	26.3236i	−1.02571	+	0.932428i	−0.0279650	+	0.999609i	$0.508903\pi$
$798$	0.277040	+	0.187506i	0.00980711	+	0.00663764i
$799$	−0.0575843	−	0.0498971i	−0.00203719	−	0.00176523i
$800$	4.38663	+	2.39947i	0.155091	+	0.0848340i
$801$	−32.2505	−	9.46960i	−1.13951	−	0.334592i
$802$	8.81922	+	2.81920i	0.311417	+	0.0995493i
$803$	12.3013	+	12.3013i	0.434105	+	0.434105i
$804$	−1.09306	−	1.10489i	−0.0385494	−	0.0389666i
$805$	−22.1038	−	45.5451i	−0.779056	−	1.60526i
$806$	−4.82506	−	9.35930i	−0.169955	−	0.329667i
$807$	−2.59150	+	1.41507i	−0.0912251	+	0.0498127i
$808$	−1.65283	−	9.82900i	−0.0581463	−	0.345783i
$809$	−14.5079	+	16.7430i	−0.510070	+	0.588652i	−0.951116	−	0.308832i	$-0.900062\pi$
$809$	−14.5079	+	16.7430i	−0.510070	+	0.588652i	0.441047	+	0.897484i	$0.354607\pi$
$810$	−2.76824	+	19.2035i	−0.0972661	+	0.674741i
$811$	49.2957	+	2.34825i	1.73101	+	0.0824580i	0.889257	−	0.457408i	$-0.151222\pi$
$811$	49.2957	+	2.34825i	1.73101	+	0.0824580i	0.841751	+	0.539866i	$0.181525\pi$
$812$	−8.90415	−	11.8945i	−0.312474	−	0.417417i
$813$	−1.04634	+	0.227617i	−0.0366968	+	0.00798289i
$814$	−33.4583	−	8.11691i	−1.17271	−	0.284497i
$815$	−19.7743	+	34.2211i	−0.692664	+	1.19871i
$816$	0.00435298	+	0.00553526i	0.000152385	+	0.000193773i
$817$	1.95294	−	0.836298i	0.0683247	−	0.0292584i
$818$	25.2926	+	9.43366i	0.884336	+	0.329840i
$819$	35.8836	+	55.8360i	1.25388	+	1.95107i
$820$	13.1467	+	13.1564i	0.459102	+	0.459440i
$821$	28.3420	+	39.8008i	0.989143	+	1.38906i	0.920205	+	0.391436i	$0.128022\pi$
$821$	28.3420	+	39.8008i	0.989143	+	1.38906i	0.0689378	+	0.997621i	$0.478039\pi$
$822$	3.29277	−	2.71874i	0.114848	−	0.0948269i
$823$	7.22150	+	6.56478i	0.251726	+	0.228834i	0.788721	−	0.614752i	$-0.210744\pi$
$823$	7.22150	+	6.56478i	0.251726	+	0.228834i	−0.536995	+	0.843585i	$0.680441\pi$
$824$	3.20531	+	13.2125i	0.111662	+	0.460278i
$825$	4.81714	+	1.05161i	0.167711	+	0.0366125i
$826$	8.95460	−	2.62931i	0.311570	−	0.0914853i
$827$	28.6624	+	0.682293i	0.996691	+	0.0237257i	0.518976	−	0.854789i	$-0.326314\pi$
$827$	28.6624	+	0.682293i	0.996691	+	0.0237257i	0.477715	+	0.878515i	$0.341465\pi$
$828$	−4.93671	−	13.2358i	−0.171563	−	0.459977i
$829$	−28.1501	+	4.04738i	−0.977694	+	0.140571i	−0.612595	−	0.790397i	$-0.709874\pi$
$829$	−28.1501	+	4.04738i	−0.977694	+	0.140571i	−0.365100	+	0.930968i	$0.618965\pi$
$830$	1.84077	+	3.02247i	0.0638940	+	0.104911i
$831$	−2.47409	+	2.14381i	−0.0858252	+	0.0743680i
$832$	4.68075	−	0.559652i	0.162276	−	0.0194024i
$833$	−0.557585	−	0.149404i	−0.0193192	−	0.00517656i
$834$	1.12719	−	1.95236i	0.0390315	−	0.0676046i
$835$	−46.4565	+	2.19589i	−1.60769	+	0.0759918i
$836$	−1.32922	+	1.39405i	−0.0459720	+	0.0482141i
$837$	−0.770192	−	2.40937i	−0.0266217	−	0.0832800i
$838$	−8.54434	−	26.7290i	−0.295159	−	0.923339i
$839$	30.1974	−	31.6701i	1.04253	−	1.09337i	0.0470016	−	0.998895i	$-0.485033\pi$
$839$	30.1974	−	31.6701i	1.04253	−	1.09337i	0.995527	−	0.0944776i	$-0.0301181\pi$
$840$	2.01462	−	0.0952262i	0.0695109	−	0.00328562i
$841$	−9.60830	+	16.6421i	−0.331321	+	0.573864i
$842$	−18.0239	−	4.82950i	−0.621146	−	0.166436i
$843$	−1.09754	+	0.131227i	−0.0378014	+	0.00451971i
$844$	−16.8332	+	14.5860i	−0.579421	+	0.502071i
$845$	−10.7268	−	17.6130i	−0.369014	−	0.605907i
$846$	−6.02754	+	0.866630i	−0.207231	+	0.0297954i
$847$	−26.5143	−	71.0876i	−0.911042	−	2.44260i
$848$	4.93493	+	0.117473i	0.169466	+	0.00403404i
$849$	3.71167	−	1.08984i	0.127384	−	0.0374034i
$850$	0.100137	+	0.156068i	0.00343467	+	0.00535310i
$851$	−7.44902	−	30.7053i	−0.255349	−	1.05256i
$852$	0.581391	+	0.528520i	0.0199181	+	0.0181068i
$853$	22.2857	−	18.4006i	0.763049	−	0.630026i	−0.171776	−	0.985136i	$-0.554951\pi$
$853$	22.2857	−	18.4006i	0.763049	−	0.630026i	0.934825	+	0.355110i	$0.115557\pi$
$854$	−7.58641	−	10.6536i	−0.259602	−	0.364560i
$855$	1.73749	+	1.73877i	0.0594209	+	0.0594646i
$856$	−10.9542	−	17.0451i	−0.374408	−	0.582590i
$857$	39.1688	+	14.6092i	1.33798	+	0.499041i	0.913663	−	0.406472i	$-0.133241\pi$
$857$	39.1688	+	14.6092i	1.33798	+	0.499041i	0.424318	+	0.905513i	$0.360514\pi$
$858$	4.27332	−	1.82994i	0.145889	−	0.0624732i
$859$	−31.8268	−	40.4710i	−1.08592	−	1.38085i	−0.918711	−	0.394931i	$-0.870768\pi$
$859$	−31.8268	−	40.4710i	−1.08592	−	1.38085i	−0.167205	−	0.985922i	$-0.553474\pi$
$860$	6.40826	−	11.0900i	0.218520	−	0.378167i
$861$	7.29089	+	1.76875i	0.248473	+	0.0602788i
$862$	15.0740	−	3.27915i	0.513423	−	0.111688i
$863$	−16.3423	−	21.8307i	−0.556298	−	0.743127i	0.430940	−	0.902381i	$-0.358182\pi$
$863$	−16.3423	−	21.8307i	−0.556298	−	0.743127i	−0.987238	+	0.159254i	$0.949091\pi$
$864$	1.13114	+	0.0538826i	0.0384820	+	0.00183312i
$865$	5.29588	−	36.7378i	0.180065	−	1.24912i
$866$	−18.3937	+	21.2275i	−0.625045	+	0.721340i
$867$	−0.535242	−	3.18296i	−0.0181778	−	0.108099i
$868$	9.31278	−	5.08516i	0.316096	−	0.172602i
$869$	−4.76635	−	9.24542i	−0.161687	−	0.313629i
$870$	0.579830	+	1.19475i	0.0196581	+	0.0405057i
$871$	−37.2174	−	10.1874i	−1.26106	−	0.345186i
$872$	3.94560	+	3.94560i	0.133615	+	0.133615i
$873$	−48.5501	−	15.5198i	−1.64317	−	0.525265i
$874$	−1.69609	−	0.498016i	−0.0573710	−	0.0168456i
$875$	53.0468	+	2.58553i	1.79331	+	0.0874070i
$876$	−0.480687	−	0.416518i	−0.0162409	−	0.0140728i
$877$	38.1533	+	25.8229i	1.28834	+	0.871976i	0.996426	−	0.0844672i	$-0.0269188\pi$
$877$	38.1533	+	25.8229i	1.28834	+	0.871976i	0.291918	+	0.956443i	$0.405707\pi$
$878$	24.1616	−	21.9644i	0.815416	−	0.741262i
$879$	−0.339295	+	2.35985i	−0.0114441	+	0.0795957i
$880$	−1.38291	+	11.5303i	−0.0466179	+	0.388686i
$881$	−10.7717	+	44.4017i	−0.362909	+	1.49593i	0.439001	+	0.898486i	$0.355332\pi$
$881$	−10.7717	+	44.4017i	−0.362909	+	1.49593i	−0.801910	+	0.597445i	$0.796183\pi$
$882$	−38.2061	+	25.8587i	−1.28647	+	0.870706i
$883$	−4.93383	−	0.589912i	−0.166037	−	0.0198521i	0.0352850	−	0.999377i	$-0.488766\pi$
$883$	−4.93383	−	0.589912i	−0.166037	−	0.0198521i	−0.201322	+	0.979525i	$0.564524\pi$
$884$	0.162305	+	0.0649770i	0.00545890	+	0.00218541i
$885$	−0.830400	+	0.0789857i	−0.0279136	+	0.00265508i
$886$	12.4228	−	7.98364i	0.417352	−	0.268216i
$887$	−15.4311	+	31.7663i	−0.518127	+	1.06661i	0.465275	+	0.885166i	$0.345955\pi$
$887$	−15.4311	+	31.7663i	−0.518127	+	1.06661i	−0.983402	+	0.181443i	$0.941923\pi$
$888$	1.24132	+	0.208738i	0.0416560	+	0.00700480i
$889$	4.25913	+	0.406698i	0.142847	+	0.0136402i
$890$	−7.15302	+	24.3279i	−0.239770	+	0.815472i
$891$	−43.7924	+	10.6239i	−1.46710	+	0.355915i
$892$	6.04845	−	2.93816i	0.202517	−	0.0983768i
$893$	−0.365187	+	0.668791i	−0.0122205	+	0.0223802i
$894$	−2.75678	−	2.89123i	−0.0922007	−	0.0966973i
$895$	−0.441956	−	18.8573i	−0.0147729	−	0.630330i
$896$	0.676036	+	4.70193i	0.0225848	+	0.157080i
$897$	3.28971	+	2.71621i	0.109840	+	0.0906916i
$898$	0.982487	−	13.7370i	0.0327860	−	0.458408i
$899$	5.49188	+	4.31886i	0.183165	+	0.144042i
$900$	14.6673	+	2.11985i	0.488911	+	0.0706615i
$901$	0.158543	+	0.0915349i	0.00528184	+	0.00304947i
$902$	−17.0048	+	39.7101i	−0.566200	+	1.32220i
$903$	−0.122952	−	5.16509i	−0.00409159	−	0.171884i
$904$	−4.81820	+	9.34601i	−0.160251	+	0.310844i
$905$	−0.593060	−	0.0143355i	−0.0197140	−	0.000476527i
$906$	1.80284	+	1.71901i	0.0598954	+	0.0571102i
$907$	24.0381	+	10.2937i	0.798171	+	0.341797i	0.753704	−	0.657214i	$-0.228265\pi$
$907$	24.0381	+	10.2937i	0.798171	+	0.341797i	0.0444668	+	0.999011i	$0.485841\pi$
$908$	−5.64853	−	21.0806i	−0.187453	−	0.699584i
$909$	−14.7708	−	25.5838i	−0.489917	−	0.848562i
$910$	42.1339	−	27.0559i	1.39672	−	0.896895i
$911$	0.929777	+	1.07302i	0.0308049	+	0.0355507i	0.770943	−	0.636904i	$-0.219785\pi$
$911$	0.929777	+	1.07302i	0.0308049	+	0.0355507i	−0.740138	+	0.672455i	$0.765240\pi$
$912$	0.0448376	−	0.0543046i	0.00148472	−	0.00179820i
$913$	−4.92568	+	6.57994i	−0.163016	+	0.217764i
$914$	−8.01195	+	17.5437i	−0.265012	+	0.580295i
$915$	0.485218	+	1.06351i	0.0160408	+	0.0351587i
$916$	1.85562	+	6.31965i	0.0613113	+	0.208807i
$917$	30.9122	+	63.6354i	1.02081	+	2.10142i
$918$	0.0358606	+	0.0218582i	0.00118358	+	0.000721427i
$919$	2.78745	+	58.5157i	0.0919494	+	1.93026i	0.303394	+	0.952865i	$0.401880\pi$
$919$	2.78745	+	58.5157i	0.0919494	+	1.93026i	−0.211444	+	0.977390i	$0.567817\pi$
$920$	−9.98678	+	3.72070i	−0.329254	+	0.122668i
$921$	−3.08596	+	2.19750i	−0.101686	+	0.0724101i
$922$	1.41694	+	0.688306i	0.0466644	+	0.0226682i
$923$	19.0612	+	4.14651i	0.627407	+	0.136484i
$924$	1.94595	+	4.26103i	0.0640169	+	0.140177i
$925$	32.0106	+	8.60244i	1.05250	+	0.282846i
$926$	−17.0113	+	13.3778i	−0.559026	+	0.439623i
$927$	22.5868	+	33.3719i	0.741846	+	1.09608i
$928$	−2.67081	+	1.62794i	−0.0876735	+	0.0534398i
$929$	10.6020	+	6.81350i	0.347841	+	0.223544i	0.702881	−	0.711307i	$-0.251897\pi$
$929$	10.6020	+	6.81350i	0.347841	+	0.223544i	−0.355040	+	0.934851i	$0.615533\pi$
$930$	−0.903454	+	0.288437i	−0.0296254	+	0.00945822i
$931$	−0.274687	+	5.76638i	−0.00900249	+	0.188986i
$932$	7.98506	−	11.7979i	0.261559	−	0.386454i
$933$	−0.230204	−	3.21867i	−0.00753654	−	0.105375i
$934$	−5.83796	+	8.19827i	−0.191024	+	0.268256i
$935$	−0.249948	+	0.350730i	−0.00817416	+	0.0114701i
$936$	12.4191	−	6.40248i	0.405930	−	0.209272i
$937$	27.0747	−	27.0747i	0.884492	−	0.884492i	−0.109495	−	0.993987i	$-0.534923\pi$
$937$	27.0747	−	27.0747i	0.884492	−	0.884492i	0.993987	+	0.109495i	$0.0349234\pi$
$938$	9.37020	−	37.7368i	0.305948	−	1.23215i
$939$			4.73542i			0.154534i
$940$	0.652134	+	4.54755i	0.0212703	+	0.148325i
$941$	−6.55099	+	22.3106i	−0.213556	+	0.727305i	0.781132	+	0.624366i	$0.214643\pi$
$941$	−6.55099	+	22.3106i	−0.213556	+	0.727305i	−0.994688	+	0.102939i	$0.967175\pi$
$942$	1.48778	−	0.250182i	0.0484744	−	0.00815137i
$943$	−39.5424	+	2.82813i	−1.28768	+	0.0920965i
$944$	−0.371812	−	1.92915i	−0.0121015	−	0.0627883i
$945$	11.0590	−	4.73095i	0.359751	−	0.153898i
$946$	29.4457	+	4.23365i	0.957363	+	0.137648i
$947$	2.53416	+	11.6494i	0.0823492	+	0.378553i	0.999814	−	0.0192628i	$-0.00613192\pi$
$947$	2.53416	+	11.6494i	0.0823492	+	0.378553i	−0.917465	+	0.397816i	$0.869768\pi$
$948$	0.197932	+	0.324728i	0.00642853	+	0.0105467i
$949$	−15.5056	−	2.98846i	−0.503334	−	0.0970096i
$950$	1.31225	−	1.31032i	0.0425749	−	0.0425124i
$951$	1.36986	−	3.42175i	0.0444208	−	0.110958i
$952$	−0.0615652	+	0.165063i	−0.00199534	+	0.00534971i
$953$	−1.30139	+	5.98238i	−0.0421560	+	0.193788i	−0.993409	−	0.114624i	$-0.963434\pi$
$953$	−1.30139	+	5.98238i	−0.0421560	+	0.193788i	0.951253	+	0.308412i	$0.0997974\pi$
$954$	13.8263	−	4.78533i	0.447643	−	0.154931i
$955$	16.4461	−	30.0926i	0.532185	−	0.973773i
$956$	2.69532	−	28.2266i	0.0871727	−	0.912914i
$957$	−2.07477	+	2.28232i	−0.0670678	+	0.0737770i
$958$	−12.3023	+	20.1832i	−0.397470	+	0.652090i
$959$	100.953	+	34.9401i	3.25993	+	1.12827i
$960$	0.0203581	−	0.424090i	0.000657054	−	0.0136874i
$961$	18.8248	−	17.9494i	0.607250	−	0.579012i
$962$	29.2806	−	10.9211i	0.944045	−	0.352110i
$963$	−48.0759	−	35.9892i	−1.54922	−	1.15973i
$964$	−2.59140	−	27.1384i	−0.0834633	−	0.874068i
$965$	42.1021	−	16.8372i	1.35532	−	0.542009i
$966$	−2.65740	+	3.37916i	−0.0855005	+	0.108723i
$967$	−10.2049	+	38.0853i	−0.328168	+	1.22474i	0.582921	+	0.812529i	$0.301910\pi$
$967$	−10.2049	+	38.0853i	−0.328168	+	1.22474i	−0.911089	+	0.412210i	$0.864757\pi$
$968$	−15.4277	+	4.13385i	−0.495866	+	0.132867i
$969$	0.00242464		0.000970681i	7.78908e−5		3.11828e-5i
$970$	−11.7219	+	36.6230i	−0.376368	+	1.17589i
$971$	14.0974	+	7.26770i	0.452406	+	0.233232i	0.669342	−	0.742954i	$-0.266576\pi$
$971$	14.0974	+	7.26770i	0.452406	+	0.233232i	−0.216936	+	0.976186i	$0.569606\pi$
$972$	4.80524	−	1.53607i	0.154128	−	0.0492694i
$973$	56.3835	−	1.34218i	1.80757	−	0.0430282i
$974$	−3.67508	−	9.17992i	−0.117757	−	0.294143i
$975$	−4.15612	+	1.66032i	−0.133102	+	0.0531727i
$976$	−2.38439	+	1.37663i	−0.0763225	+	0.0440648i
$977$	0.600514	+	5.02250i	0.0192121	+	0.160684i	0.999278	−	0.0379877i	$-0.0120948\pi$
$977$	0.600514	+	5.02250i	0.0192121	+	0.160684i	−0.980066	+	0.198672i	$0.936337\pi$
$978$	3.34761	+	0.239426i	0.107045	+	0.00765600i
$979$	−58.6286	+	5.59835i	−1.87378	+	0.178924i
$980$	19.4978	+	28.8307i	0.622833	+	0.920964i
$981$	15.0440	+	6.87038i	0.480319	+	0.219354i
$982$	−0.217083	+	9.11944i	−0.00692740	+	0.291013i
$983$	35.0114	+	19.1177i	1.11669	+	0.609759i	0.928113	−	0.372299i	$-0.121431\pi$
$983$	35.0114	+	19.1177i	1.11669	+	0.609759i	0.188577	+	0.982058i	$0.439612\pi$
$984$	0.516555	−	1.49249i	0.0164672	−	0.0475788i
$985$	57.3911	+	5.50146i	1.82863	+	0.175291i
$986$	−0.115869	+	0.00551950i	−0.00369001	+	0.000175777i
$987$	1.17987	+	1.42898i	0.0375556	+	0.0454850i
$988$	0.289936	−	1.72419i	0.00922410	−	0.0548537i
$989$	8.92918	+	25.7992i	0.283931	+	0.820366i
$990$	8.10255	+	33.4528i	0.257516	+	1.06320i
$991$	−21.0362	+	9.60692i	−0.668238	+	0.305174i	−0.720495	−	0.693460i	$-0.756086\pi$
$991$	−21.0362	+	9.60692i	−0.668238	+	0.305174i	0.0522576	+	0.998634i	$0.483358\pi$
$992$	−0.879296	−	2.05335i	−0.0279177	−	0.0651939i
$993$	0.320532	−	2.68083i	0.0101718	−	0.0850735i
$994$	−3.72007	+	19.3015i	−0.117993	+	0.612207i
$995$	−6.79398	+	1.47533i	−0.215384	+	0.0467710i
$996$	0.162466	−	0.252803i	0.00514795	−	0.00801036i
$997$	−14.6234	+	10.9469i	−0.463127	+	0.346693i	−0.805223	−	0.592973i	$-0.797954\pi$
$997$	−14.6234	+	10.9469i	−0.463127	+	0.346693i	0.342096	+	0.939665i	$0.388863\pi$
$998$	−9.18548	−	10.1044i	−0.290761	−	0.319848i
$999$	7.37145	−	1.42073i	0.233222	−	0.0449499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.w.a.7.8	✓	1360
5.3	odd	4	inner	670.2.w.a.543.27	yes	1360
67.48	odd	66	inner	670.2.w.a.517.27	yes	1360
335.48	even	132	inner	670.2.w.a.383.8	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.w.a.7.8	✓	1360	1.1	even	1	trivial
670.2.w.a.383.8	yes	1360	335.48	even	132	inner
670.2.w.a.517.27	yes	1360	67.48	odd	66	inner
670.2.w.a.543.27	yes	1360	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.w (of order \(132\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.304486 + 0.952517i) q^{2} +(-0.0909985 - 0.166651i) q^{3} +(-0.814576 - 0.580057i) q^{4} +(-0.579530 + 2.15966i) q^{5} +(0.186446 - 0.0359345i) q^{6} +(3.19533 + 3.51498i) q^{7} +(0.800541 - 0.599278i) q^{8} +(1.60243 - 2.49343i) q^{9} +O(q^{10})\)	\(q+(-0.304486 + 0.952517i) q^{2} +(-0.0909985 - 0.166651i) q^{3} +(-0.814576 - 0.580057i) q^{4} +(-0.579530 + 2.15966i) q^{5} +(0.186446 - 0.0359345i) q^{6} +(3.19533 + 3.51498i) q^{7} +(0.800541 - 0.599278i) q^{8} +(1.60243 - 2.49343i) q^{9} +(-1.88066 - 1.20960i) q^{10} +(0.982868 - 5.09960i) q^{11} +(-0.0225420 + 0.188534i) q^{12} +(1.85570 + 4.33347i) q^{13} +(-4.32101 + 1.97334i) q^{14} +(0.412647 - 0.0999466i) q^{15} +(0.327068 + 0.945001i) q^{16} +(-0.00615002 + 0.0365728i) q^{17} +(1.88712 + 2.28556i) q^{18} +(0.370467 - 0.0176475i) q^{19} +(1.72480 - 1.42305i) q^{20} +(0.295006 - 0.852363i) q^{21} +(4.55819 + 2.48896i) q^{22} +(-0.113423 + 4.76477i) q^{23} +(-0.172718 - 0.0788779i) q^{24} +(-4.32829 - 2.50318i) q^{25} +(-4.69274 + 0.448103i) q^{26} +(-1.12953 - 0.0807858i) q^{27} +(-0.563949 - 4.71669i) q^{28} +(2.70879 - 1.56392i) q^{29} +(-0.0304447 + 0.423486i) q^{30} +(0.830182 + 2.07369i) q^{31} +(-0.999717 + 0.0237977i) q^{32} +(-0.939295 + 0.300260i) q^{33} +(-0.0329636 - 0.0169939i) q^{34} +(-9.44296 + 4.86379i) q^{35} +(-2.75163 + 1.10159i) q^{36} +(-6.40339 + 1.71578i) q^{37} +(-0.0959926 + 0.358249i) q^{38} +(0.553313 - 0.703595i) q^{39} +(0.830300 + 2.07620i) q^{40} +(0.790653 + 8.28009i) q^{41} +(0.722064 + 0.540531i) q^{42} +(5.36692 - 2.00176i) q^{43} +(-3.75868 + 3.58389i) q^{44} +(4.45631 + 4.90573i) q^{45} +(-4.50398 - 1.55884i) q^{46} +(-1.06932 + 1.75433i) q^{47} +(0.127723 - 0.140500i) q^{48} +(-1.47956 + 15.4947i) q^{49} +(3.70223 - 3.36058i) q^{50} +(0.00665454 - 0.00230316i) q^{51} +(1.00205 - 4.60636i) q^{52} +(1.72507 - 4.62509i) q^{53} +(0.420877 - 1.05130i) q^{54} +(10.4438 + 5.07804i) q^{55} +(4.66444 + 0.898997i) q^{56} +(-0.0366529 - 0.0601329i) q^{57} +(0.664871 + 3.05636i) q^{58} +(-1.94465 - 0.279599i) q^{59} +(-0.394107 - 0.157945i) q^{60} +(0.521057 + 2.70350i) q^{61} +(-2.22801 + 0.159350i) q^{62} +(13.8846 - 2.33482i) q^{63} +(0.281733 - 0.959493i) q^{64} +(-10.4343 + 1.49631i) q^{65} -0.986119i q^{66} +(-5.09441 + 6.40679i) q^{67} +(0.0262240 - 0.0262240i) q^{68} +(0.804376 - 0.414684i) q^{69} +(-1.75759 - 10.4755i) q^{70} +(2.40029 - 3.37073i) q^{71} +(-0.211446 - 2.95639i) q^{72} +(-1.87756 + 2.77409i) q^{73} +(0.315434 - 6.62177i) q^{74} +(-0.0232906 + 0.949101i) q^{75} +(-0.312010 - 0.200517i) q^{76} +(21.0656 - 12.8401i) q^{77} +(0.501709 + 0.741275i) q^{78} +(1.57435 - 1.23808i) q^{79} +(-2.23043 + 0.158700i) q^{80} +(-3.60448 - 7.89271i) q^{81} +(-8.12767 - 1.76807i) q^{82} +(-1.42357 - 0.691525i) q^{83} +(-0.734723 + 0.523194i) q^{84} +(-0.0754208 - 0.0344770i) q^{85} +(0.272553 + 5.72159i) q^{86} +(-0.507125 - 0.309109i) q^{87} +(-2.26925 - 4.67145i) q^{88} +(-3.19493 - 10.8809i) q^{89} +(-6.02968 + 2.75098i) q^{90} +(-9.30249 + 20.3696i) q^{91} +(2.85623 - 3.81547i) q^{92} +(0.270038 - 0.327054i) q^{93} +(-1.34543 - 1.55271i) q^{94} +(-0.176584 + 0.810311i) q^{95} +(0.0949386 + 0.164439i) q^{96} +(-4.45085 - 16.6108i) q^{97} +(-14.3084 - 6.12723i) q^{98} +(-11.1405 - 10.6225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 4 q^{6}+O(q^{10}) \) 1360 * q - 4 * q^6	\( 1360 q - 4 q^{6} + 8 q^{15} - 68 q^{16} + 12 q^{20} - 24 q^{21} - 36 q^{23} - 24 q^{25} + 88 q^{31} - 44 q^{33} + 12 q^{35} + 64 q^{36} + 24 q^{37} - 24 q^{38} + 12 q^{41} + 88 q^{43} + 12 q^{46} - 108 q^{47} + 44 q^{48} - 72 q^{50} + 48 q^{51} - 288 q^{55} + 4 q^{56} + 36 q^{57} - 164 q^{60} + 20 q^{61} - 32 q^{62} - 352 q^{65} + 68 q^{67} - 484 q^{70} + 88 q^{71} - 16 q^{73} - 704 q^{75} - 32 q^{76} + 456 q^{77} - 60 q^{78} - 56 q^{81} + 48 q^{82} - 16 q^{83} - 96 q^{85} + 4 q^{86} + 96 q^{87} - 32 q^{90} - 128 q^{91} + 16 q^{92} + 80 q^{93} + 60 q^{95} + 4 q^{96} + 120 q^{97} + 48 q^{98}+O(q^{100}) \) 1360 * q - 4 * q^6 + 8 * q^15 - 68 * q^16 + 12 * q^20 - 24 * q^21 - 36 * q^23 - 24 * q^25 + 88 * q^31 - 44 * q^33 + 12 * q^35 + 64 * q^36 + 24 * q^37 - 24 * q^38 + 12 * q^41 + 88 * q^43 + 12 * q^46 - 108 * q^47 + 44 * q^48 - 72 * q^50 + 48 * q^51 - 288 * q^55 + 4 * q^56 + 36 * q^57 - 164 * q^60 + 20 * q^61 - 32 * q^62 - 352 * q^65 + 68 * q^67 - 484 * q^70 + 88 * q^71 - 16 * q^73 - 704 * q^75 - 32 * q^76 + 456 * q^77 - 60 * q^78 - 56 * q^81 + 48 * q^82 - 16 * q^83 - 96 * q^85 + 4 * q^86 + 96 * q^87 - 32 * q^90 - 128 * q^91 + 16 * q^92 + 80 * q^93 + 60 * q^95 + 4 * q^96 + 120 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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