LMFDB - Embedded newform 483.2.y.b.331.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(4,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 12]))

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

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

chi := DirichletCharacter("483.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			331.6
Character	$\chi$	$=$	483.331
Dual form			483.2.y.b.340.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.187507 + 0.772913i) q^{2} +(-0.327068 + 0.945001i) q^{3} +(1.21544 + 0.626600i) q^{4} +(2.15041 + 0.860895i) q^{5} +(-0.669076 - 0.429989i) q^{6} +(0.216441 + 2.63688i) q^{7} +(-1.75387 + 2.02408i) q^{8} +(-0.786053 - 0.618159i) q^{9} +O(q^{10})$	\(q+(-0.187507 + 0.772913i) q^{2} +(-0.327068 + 0.945001i) q^{3} +(1.21544 + 0.626600i) q^{4} +(2.15041 + 0.860895i) q^{5} +(-0.669076 - 0.429989i) q^{6} +(0.216441 + 2.63688i) q^{7} +(-1.75387 + 2.02408i) q^{8} +(-0.786053 - 0.618159i) q^{9} +(-1.06861 + 1.50066i) q^{10} +(0.0463658 + 0.191122i) q^{11} +(-0.989668 + 0.943646i) q^{12} +(-0.365286 - 0.799865i) q^{13} +(-2.07867 - 0.327143i) q^{14} +(-1.51688 + 1.75057i) q^{15} +(0.350821 + 0.492660i) q^{16} +(0.361987 - 7.59904i) q^{17} +(0.625173 - 0.491642i) q^{18} +(0.172516 + 3.62155i) q^{19} +(2.07425 + 2.39381i) q^{20} +(-2.56265 - 0.657903i) q^{21} -0.156415 q^{22} +(4.26887 - 2.18558i) q^{23} +(-1.33912 - 2.31942i) q^{24} +(0.264459 + 0.252161i) q^{25} +(0.686720 - 0.132354i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-1.38920 + 3.34058i) q^{28} +(-1.02138 - 0.656400i) q^{29} +(-1.06861 - 1.50066i) q^{30} +(1.47094 + 0.283501i) q^{31} +(-5.41935 + 2.16958i) q^{32} +(-0.195775 - 0.0186943i) q^{33} +(5.80552 + 1.70465i) q^{34} +(-1.80464 + 5.85672i) q^{35} +(-0.568058 - 1.24387i) q^{36} +(-2.16539 - 1.70288i) q^{37} +(-2.83149 - 0.545725i) q^{38} +(0.875347 - 0.0835855i) q^{39} +(-5.51407 + 2.84270i) q^{40} +(-0.172968 - 1.20302i) q^{41} +(0.989015 - 1.85734i) q^{42} +(1.16802 + 1.34797i) q^{43} +(-0.0634027 + 0.261350i) q^{44} +(-1.15817 - 2.00601i) q^{45} +(0.888823 + 3.70927i) q^{46} +(0.751264 - 1.30123i) q^{47} +(-0.580306 + 0.170393i) q^{48} +(-6.90631 + 1.14146i) q^{49} +(-0.244487 + 0.157122i) q^{50} +(7.06271 + 2.82748i) q^{51} +(0.0572141 - 1.20107i) q^{52} +(-10.5330 + 1.00578i) q^{53} +(0.260128 + 0.751589i) q^{54} +(-0.0648307 + 0.450908i) q^{55} +(-5.71687 - 4.18666i) q^{56} +(-3.47879 - 1.02147i) q^{57} +(0.698855 - 0.666357i) q^{58} +(3.76852 - 5.29215i) q^{59} +(-2.94057 + 1.17723i) q^{60} +(4.51254 + 13.0381i) q^{61} +(-0.494933 + 1.08375i) q^{62} +(1.45988 - 2.20653i) q^{63} +(-0.488587 - 3.39819i) q^{64} +(-0.0969158 - 2.03451i) q^{65} +(0.0511583 - 0.147812i) q^{66} +(1.95760 + 1.86656i) q^{67} +(5.20153 - 9.00932i) q^{68} +(0.669166 + 4.74892i) q^{69} +(-4.18835 - 2.49300i) q^{70} +(-0.831265 + 0.244081i) q^{71} +(2.62984 - 0.506860i) q^{72} +(7.83592 + 4.03970i) q^{73} +(1.72220 - 1.35435i) q^{74} +(-0.324789 + 0.167440i) q^{75} +(-2.05958 + 4.50986i) q^{76} +(-0.493932 + 0.163628i) q^{77} +(-0.0995290 + 0.692239i) q^{78} +(2.53186 + 0.241763i) q^{79} +(0.330282 + 1.36144i) q^{80} +(0.235759 + 0.971812i) q^{81} +(0.962261 + 0.0918848i) q^{82} +(1.89350 - 13.1696i) q^{83} +(-2.70249 - 2.40539i) q^{84} +(7.32040 - 16.0294i) q^{85} +(-1.26087 + 0.650024i) q^{86} +(0.954359 - 0.750516i) q^{87} +(-0.468166 - 0.241356i) q^{88} +(7.83798 - 1.51065i) q^{89} +(1.76763 - 0.519023i) q^{90} +(2.03009 - 1.13634i) q^{91} +(6.55802 + 0.0184421i) q^{92} +(-0.749007 + 1.29732i) q^{93} +(0.864869 + 0.824651i) q^{94} +(-2.74680 + 7.93635i) q^{95} +(-0.277759 - 5.83089i) q^{96} +(-1.22151 - 8.49576i) q^{97} +(0.412729 - 5.55200i) q^{98} +(0.0816980 - 0.178894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 2 q^{11} + 18 q^{12} + 18 q^{14} - 18 q^{15} - 8 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 162 q^{20} - 4 q^{21} + 144 q^{22} - 26 q^{23} + 6 q^{24} - 8 q^{25} - 14 q^{26} - 32 q^{27} + 86 q^{28} - 74 q^{29} - 56 q^{31} - 28 q^{32} + 13 q^{33} + 40 q^{34} - 32 q^{35} - 14 q^{36} + 2 q^{37} - 39 q^{38} - 52 q^{40} + 60 q^{41} - 61 q^{42} + 16 q^{43} - 75 q^{44} - 2 q^{45} - 4 q^{46} - 40 q^{47} - 28 q^{48} - 100 q^{49} + 146 q^{50} - 18 q^{51} - 18 q^{52} + 34 q^{53} + 2 q^{54} + 36 q^{55} - 102 q^{56} + 28 q^{57} - 17 q^{58} - 102 q^{59} - 18 q^{60} - 18 q^{61} - 88 q^{62} + 2 q^{63} - 252 q^{64} - 78 q^{65} + 16 q^{66} + 12 q^{67} + 34 q^{68} + 8 q^{69} + 264 q^{70} + 160 q^{71} + 6 q^{72} - 8 q^{73} + 70 q^{74} + 14 q^{75} - 40 q^{76} - 90 q^{77} - 16 q^{78} + 26 q^{79} - 103 q^{80} + 16 q^{81} - 30 q^{82} - 80 q^{83} - 52 q^{84} - 128 q^{85} + 90 q^{86} + 4 q^{87} - 293 q^{88} - 36 q^{89} + 16 q^{91} - 174 q^{92} + 32 q^{93} + 57 q^{94} - 85 q^{95} - 50 q^{96} - 8 q^{97} - 193 q^{98} - 26 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 2 * q^11 + 18 * q^12 + 18 * q^14 - 18 * q^15 - 8 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 162 * q^20 - 4 * q^21 + 144 * q^22 - 26 * q^23 + 6 * q^24 - 8 * q^25 - 14 * q^26 - 32 * q^27 + 86 * q^28 - 74 * q^29 - 56 * q^31 - 28 * q^32 + 13 * q^33 + 40 * q^34 - 32 * q^35 - 14 * q^36 + 2 * q^37 - 39 * q^38 - 52 * q^40 + 60 * q^41 - 61 * q^42 + 16 * q^43 - 75 * q^44 - 2 * q^45 - 4 * q^46 - 40 * q^47 - 28 * q^48 - 100 * q^49 + 146 * q^50 - 18 * q^51 - 18 * q^52 + 34 * q^53 + 2 * q^54 + 36 * q^55 - 102 * q^56 + 28 * q^57 - 17 * q^58 - 102 * q^59 - 18 * q^60 - 18 * q^61 - 88 * q^62 + 2 * q^63 - 252 * q^64 - 78 * q^65 + 16 * q^66 + 12 * q^67 + 34 * q^68 + 8 * q^69 + 264 * q^70 + 160 * q^71 + 6 * q^72 - 8 * q^73 + 70 * q^74 + 14 * q^75 - 40 * q^76 - 90 * q^77 - 16 * q^78 + 26 * q^79 - 103 * q^80 + 16 * q^81 - 30 * q^82 - 80 * q^83 - 52 * q^84 - 128 * q^85 + 90 * q^86 + 4 * q^87 - 293 * q^88 - 36 * q^89 + 16 * q^91 - 174 * q^92 + 32 * q^93 + 57 * q^94 - 85 * q^95 - 50 * q^96 - 8 * q^97 - 193 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.187507	+	0.772913i	−0.132587	+	0.546532i	0.866307	+	0.499512i	$0.166487\pi$
$2$	−0.187507	+	0.772913i	−0.132587	+	0.546532i	−0.998894	+	0.0470196i	$0.985028\pi$
$3$	−0.327068	+	0.945001i	−0.188833	+	0.545596i
$3$	−0.327068	+	0.945001i	−0.188833	+	0.545596i
$4$	1.21544	+	0.626600i	0.607718	+	0.313300i
$5$	2.15041	+	0.860895i	0.961693	+	0.385004i	0.798771	−	0.601635i	$-0.205484\pi$
$5$	2.15041	+	0.860895i	0.961693	+	0.385004i	0.162922	+	0.986639i	$0.447908\pi$
$6$	−0.669076	−	0.429989i	−0.273149	−	0.175542i
$7$	0.216441	+	2.63688i	0.0818071	+	0.996648i
$7$	0.216441	+	2.63688i	0.0818071	+	0.996648i
$8$	−1.75387	+	2.02408i	−0.620088	+	0.715619i
$9$	−0.786053	−	0.618159i	−0.262018	−	0.206053i
$10$	−1.06861	+	1.50066i	−0.337925	+	0.474549i
$11$	0.0463658	+	0.191122i	0.0139798	+	0.0576255i	0.978374	−	0.206843i	$-0.0663188\pi$
$11$	0.0463658	+	0.191122i	0.0139798	+	0.0576255i	−0.964394	+	0.264468i	$0.914804\pi$
$12$	−0.989668	+	0.943646i	−0.285693	+	0.272407i
$13$	−0.365286	−	0.799865i	−0.101312	−	0.221843i	0.852188	−	0.523236i	$-0.175275\pi$
$13$	−0.365286	−	0.799865i	−0.101312	−	0.221843i	−0.953500	+	0.301394i	$0.902548\pi$
$14$	−2.07867	−	0.327143i	−0.555547	−	0.0874326i
$15$	−1.51688	+	1.75057i	−0.391656	+	0.451995i
$16$	0.350821	+	0.492660i	0.0877054	+	0.123165i
$17$	0.361987	−	7.59904i	0.0877947	−	1.84304i	−0.341510	−	0.939878i	$-0.610938\pi$
$17$	0.361987	−	7.59904i	0.0877947	−	1.84304i	0.429304	−	0.903160i	$-0.358759\pi$
$18$	0.625173	−	0.491642i	0.147355	−	0.115881i
$19$	0.172516	+	3.62155i	0.0395778	+	0.830841i	0.928173	+	0.372149i	$0.121379\pi$
$19$	0.172516	+	3.62155i	0.0395778	+	0.830841i	−0.888595	+	0.458692i	$0.848318\pi$
$20$	2.07425	+	2.39381i	0.463816	+	0.535272i
$21$	−2.56265	−	0.657903i	−0.559216	−	0.143566i
$22$	−0.156415			−0.0333477
$23$	4.26887	−	2.18558i	0.890121	−	0.455725i
$23$	4.26887	−	2.18558i	0.890121	−	0.455725i
$24$	−1.33912	−	2.31942i	−0.273347	−	0.473450i
$25$	0.264459	+	0.252161i	0.0528918	+	0.0504323i
$26$	0.686720	−	0.132354i	0.134677	−	0.0259568i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−1.38920	+	3.34058i	−0.262534	+	0.631311i
$29$	−1.02138	−	0.656400i	−0.189665	−	0.121890i	0.442362	−	0.896837i	$-0.354141\pi$
$29$	−1.02138	−	0.656400i	−0.189665	−	0.121890i	−0.632027	+	0.774946i	$0.717777\pi$
$30$	−1.06861	−	1.50066i	−0.195101	−	0.273981i
$31$	1.47094	+	0.283501i	0.264189	+	0.0509183i	0.319626	−	0.947544i	$-0.396443\pi$
$31$	1.47094	+	0.283501i	0.264189	+	0.0509183i	−0.0554364	+	0.998462i	$0.517655\pi$
$32$	−5.41935	+	2.16958i	−0.958014	+	0.383531i
$33$	−0.195775	−	0.0186943i	−0.0340801	−	0.00325426i
$34$	5.80552	+	1.70465i	0.995639	+	0.292346i
$35$	−1.80464	+	5.85672i	−0.305040	+	0.989966i
$36$	−0.568058	−	1.24387i	−0.0946763	−	0.207312i
$37$	−2.16539	−	1.70288i	−0.355987	−	0.279952i	0.424109	−	0.905611i	$-0.360587\pi$
$37$	−2.16539	−	1.70288i	−0.355987	−	0.279952i	−0.780096	+	0.625660i	$0.784830\pi$
$38$	−2.83149	−	0.545725i	−0.459329	−	0.0885284i
$39$	0.875347	−	0.0835855i	0.140168	−	0.0133844i
$40$	−5.51407	+	2.84270i	−0.871851	+	0.449470i
$41$	−0.172968	−	1.20302i	−0.0270131	−	0.187880i	0.971847	−	0.235612i	$-0.0757096\pi$
$41$	−0.172968	−	1.20302i	−0.0270131	−	0.187880i	−0.998860	+	0.0477325i	$0.984801\pi$
$42$	0.989015	−	1.85734i	0.152608	−	0.286594i
$43$	1.16802	+	1.34797i	0.178121	+	0.205563i	0.837788	−	0.545995i	$-0.183848\pi$
$43$	1.16802	+	1.34797i	0.178121	+	0.205563i	−0.659667	+	0.751558i	$0.729303\pi$
$44$	−0.0634027	+	0.261350i	−0.00955832	+	0.0393999i
$45$	−1.15817	−	2.00601i	−0.172649	−	0.299038i
$46$	0.888823	+	3.70927i	0.131050	+	0.546903i
$47$	0.751264	−	1.30123i	0.109583	−	0.189804i	−0.806018	−	0.591891i	$-0.798382\pi$
$47$	0.751264	−	1.30123i	0.109583	−	0.189804i	0.915601	+	0.402087i	$0.131715\pi$
$48$	−0.580306	+	0.170393i	−0.0837600	+	0.0245942i
$49$	−6.90631	+	1.14146i	−0.986615	+	0.163066i
$50$	−0.244487	+	0.157122i	−0.0345756	+	0.0222204i
$51$	7.06271	+	2.82748i	0.988977	+	0.395927i
$52$	0.0572141	−	1.20107i	0.00793417	−	0.166559i
$53$	−10.5330	+	1.00578i	−1.44681	+	0.138154i	−0.788706	−	0.614771i	$-0.789249\pi$
$53$	−10.5330	+	1.00578i	−1.44681	+	0.138154i	−0.658107	+	0.752924i	$0.728643\pi$
$54$	0.260128	+	0.751589i	0.0353989	+	0.102278i
$55$	−0.0648307	+	0.450908i	−0.00874177	+	0.0608004i
$56$	−5.71687	−	4.18666i	−0.763948	−	0.559467i
$57$	−3.47879	−	1.02147i	−0.460778	−	0.135297i
$58$	0.698855	−	0.666357i	0.0917642	−	0.0874970i
$59$	3.76852	−	5.29215i	0.490620	−	0.688979i	−0.492837	−	0.870122i	$-0.664040\pi$
$59$	3.76852	−	5.29215i	0.490620	−	0.688979i	0.983457	+	0.181142i	$0.0579795\pi$
$60$	−2.94057	+	1.17723i	−0.379626	+	0.151979i
$61$	4.51254	+	13.0381i	0.577771	+	1.66936i	0.731984	+	0.681322i	$0.238595\pi$
$61$	4.51254	+	13.0381i	0.577771	+	1.66936i	−0.154213	+	0.988038i	$0.549284\pi$
$62$	−0.494933	+	1.08375i	−0.0628566	+	0.137637i
$63$	1.45988	−	2.20653i	0.183927	−	0.277996i
$64$	−0.488587	−	3.39819i	−0.0610733	−	0.424774i
$65$	−0.0969158	−	2.03451i	−0.0120209	−	0.252350i
$66$	0.0511583	−	0.147812i	0.00629715	−	0.0181944i
$67$	1.95760	+	1.86656i	0.239158	+	0.228037i	0.800174	−	0.599768i	$-0.204741\pi$
$67$	1.95760	+	1.86656i	0.239158	+	0.228037i	−0.561015	+	0.827805i	$0.689589\pi$
$68$	5.20153	−	9.00932i	0.630779	−	1.09254i
$69$	0.669166	+	4.74892i	0.0805581	+	0.571702i
$70$	−4.18835	−	2.49300i	−0.500604	−	0.297971i
$71$	−0.831265	+	0.244081i	−0.0986530	+	0.0289671i	−0.330687	−	0.943741i	$-0.607280\pi$
$71$	−0.831265	+	0.244081i	−0.0986530	+	0.0289671i	0.232034	+	0.972708i	$0.425462\pi$
$72$	2.62984	−	0.506860i	0.309930	−	0.0597340i
$73$	7.83592	+	4.03970i	0.917125	+	0.472811i	0.851098	−	0.525007i	$-0.175937\pi$
$73$	7.83592	+	4.03970i	0.917125	+	0.472811i	0.0660270	+	0.997818i	$0.478968\pi$
$74$	1.72220	−	1.35435i	0.200202	−	0.157440i
$75$	−0.324789	+	0.167440i	−0.0375034	+	0.0193343i
$76$	−2.05958	+	4.50986i	−0.236251	+	0.517317i
$77$	−0.493932	+	0.163628i	−0.0562887	+	0.0186471i
$78$	−0.0995290	+	0.692239i	−0.0112694	+	0.0783807i
$79$	2.53186	+	0.241763i	0.284856	+	0.0272005i	0.236506	−	0.971630i	$-0.423998\pi$
$79$	2.53186	+	0.241763i	0.284856	+	0.0272005i	0.0483501	+	0.998830i	$0.484604\pi$
$80$	0.330282	+	1.36144i	0.0369267	+	0.152214i
$81$	0.235759	+	0.971812i	0.0261954	+	0.107979i
$82$	0.962261	+	0.0918848i	0.106264	+	0.0101470i
$83$	1.89350	−	13.1696i	0.207838	−	1.44555i	−0.572353	−	0.820007i	$-0.693969\pi$
$83$	1.89350	−	13.1696i	0.207838	−	1.44555i	0.780192	−	0.625540i	$-0.215121\pi$
$84$	−2.70249	−	2.40539i	−0.294866	−	0.262450i
$85$	7.32040	−	16.0294i	0.794008	−	1.73864i
$86$	−1.26087	+	0.650024i	−0.135963	+	0.0700939i
$87$	0.954359	−	0.750516i	0.102318	−	0.0804638i
$88$	−0.468166	−	0.241356i	−0.0499067	−	0.0257287i
$89$	7.83798	−	1.51065i	0.830824	−	0.160128i	0.243931	−	0.969793i	$-0.421563\pi$
$89$	7.83798	−	1.51065i	0.830824	−	0.160128i	0.586893	+	0.809664i	$0.300351\pi$
$90$	1.76763	−	0.519023i	0.186325	−	0.0547099i
$91$	2.03009	−	1.13634i	0.212811	−	0.119121i
$92$	6.55802	+	0.0184421i	0.683721	+	0.00192272i
$93$	−0.749007	+	1.29732i	−0.0776684	+	0.134526i
$94$	0.864869	+	0.824651i	0.0892044	+	0.0850562i
$95$	−2.74680	+	7.93635i	−0.281815	+	0.814252i
$96$	−0.277759	−	5.83089i	−0.0283487	−	0.595112i
$97$	−1.22151	−	8.49576i	−0.124025	−	0.862614i	−0.952923	−	0.303213i	$-0.901940\pi$
$97$	−1.22151	−	8.49576i	−0.124025	−	0.862614i	0.828898	−	0.559401i	$-0.188969\pi$
$98$	0.412729	−	5.55200i	0.0416919	−	0.560837i
$99$	0.0816980	−	0.178894i	0.00821096	−	0.0179795i
$100$	0.163429	+	0.472196i	0.0163429	+	0.0472196i
$101$	9.04591	−	3.62144i	0.900102	−	0.360346i	0.124981	−	0.992159i	$-0.460113\pi$
$101$	9.04591	−	3.62144i	0.900102	−	0.360346i	0.775121	+	0.631813i	$0.217689\pi$
$102$	−3.50970	+	4.92868i	−0.347512	+	0.488012i
$103$	13.8119	−	13.1696i	1.36093	−	1.29764i	0.445435	−	0.895314i	$-0.353049\pi$
$103$	13.8119	−	13.1696i	1.36093	−	1.29764i	0.915495	−	0.402329i	$-0.131799\pi$
$104$	2.25965	+	0.663494i	0.221577	+	0.0650610i
$105$	−4.94436	−	3.62093i	−0.482520	−	0.353367i
$106$	1.19762	−	8.32965i	0.116323	−	0.809047i
$107$	2.97712	+	8.60182i	0.287809	+	0.831569i	0.992521	+	0.122076i	$0.0389551\pi$
$107$	2.97712	+	8.60182i	0.287809	+	0.831569i	−0.704712	+	0.709494i	$0.748924\pi$
$108$	1.36126	−	0.129984i	0.130987	−	0.0125077i
$109$	−0.730901	+	15.3435i	−0.0700076	+	1.46964i	0.641587	+	0.767050i	$0.278276\pi$
$109$	−0.730901	+	15.3435i	−0.0700076	+	1.46964i	−0.711595	+	0.702590i	$0.752027\pi$
$110$	−0.336356	−	0.134657i	−0.0320703	−	0.0128390i
$111$	2.31745	−	1.48934i	0.219963	−	0.141361i
$112$	−1.22315	+	1.03171i	−0.115577	+	0.0974872i
$113$	−7.49163	+	2.19974i	−0.704753	+	0.206934i	−0.614422	−	0.788978i	$-0.710611\pi$
$113$	−7.49163	+	2.19974i	−0.704753	+	0.206934i	−0.0903312	+	0.995912i	$0.528793\pi$
$114$	1.44180	−	2.49727i	0.135037	−	0.233891i
$115$	11.0614	−	1.02485i	1.03148	−	0.0955680i
$116$	−0.830119	−	1.43781i	−0.0770746	−	0.133497i
$117$	−0.207309	+	0.854541i	−0.0191658	+	0.0790024i
$118$	3.38375	+	3.90505i	0.311499	+	0.359489i
$119$	20.1161	−	0.690229i	1.84404	−	0.0632732i
$120$	−0.882878	−	6.14055i	−0.0805954	−	0.560553i
$121$	9.74281	−	5.02277i	0.885710	−	0.456615i
$122$	−10.9235	+	1.04306i	−0.988963	+	0.0944345i
$123$	1.19343	+	0.230014i	0.107608	+	0.0207397i
$124$	1.61019	+	1.26627i	0.144600	+	0.113714i
$125$	−4.45959	−	9.76514i	−0.398878	−	0.873421i
$126$	1.43171	+	1.54210i	0.127547	+	0.137381i
$127$	−17.7798	−	5.22063i	−1.57770	−	0.463256i	−0.628472	−	0.777832i	$-0.716319\pi$
$127$	−17.7798	−	5.22063i	−1.57770	−	0.463256i	−0.949232	+	0.314576i	$0.898138\pi$
$128$	−8.90401	−	0.850230i	−0.787011	−	0.0751504i
$129$	−1.65585	+	0.662903i	−0.145790	+	0.0583653i
$130$	1.59067	+	0.306577i	0.139511	+	0.0268886i
$131$	−0.596203	−	0.837249i	−0.0520905	−	0.0731508i	0.787709	−	0.616047i	$-0.211267\pi$
$131$	−0.596203	−	0.837249i	−0.0520905	−	0.0731508i	−0.839800	+	0.542896i	$0.817328\pi$
$132$	−0.226239	−	0.145395i	−0.0196915	−	0.0126550i
$133$	−9.51227	+	1.23876i	−0.824819	+	0.107414i
$134$	−1.80975	+	1.16306i	−0.156339	+	0.100473i
$135$	2.27448	−	0.438369i	0.195756	−	0.0377288i
$136$	14.7462	+	14.0604i	1.26447	+	1.20567i
$137$	−1.93201	−	3.34634i	−0.165063	−	0.285897i	0.771615	−	0.636090i	$-0.219449\pi$
$137$	−1.93201	−	3.34634i	−0.165063	−	0.285897i	−0.936678	+	0.350193i	$0.886116\pi$
$138$	−3.79597	−	0.373246i	−0.323135	−	0.0317728i
$139$	6.70678			0.568862			0.284431	−	0.958697i	$-0.408195\pi$
$139$	6.70678			0.568862			0.284431	+	0.958697i	$0.408195\pi$
$140$	−5.86325	+	5.98767i	−0.495535	+	0.506051i
$141$	0.983947	+	1.13554i	0.0828633	+	0.0956293i
$142$	−0.0327860	−	0.688262i	−0.00275134	−	0.0577577i
$143$	0.135935	−	0.106901i	0.0113675	−	0.00893948i
$144$	0.0287778	−	0.604120i	0.00239815	−	0.0503434i
$145$	−1.63129	−	2.29083i	−0.135471	−	0.190243i
$146$	−4.59162	+	5.29901i	−0.380005	+	0.438549i
$147$	1.18015	−	6.89980i	0.0973372	−	0.569086i
$148$	−1.56486	−	3.42657i	−0.128631	−	0.281662i
$149$	−3.72918	+	3.55577i	−0.305506	+	0.291300i	−0.827286	−	0.561780i	$-0.810117\pi$
$149$	−3.72918	+	3.55577i	−0.305506	+	0.291300i	0.521780	+	0.853080i	$0.325268\pi$
$150$	−0.0685167	−	0.282430i	−0.00559436	−	0.0230603i
$151$	−6.14079	+	8.62353i	−0.499730	+	0.701773i	−0.984993	−	0.172595i	$-0.944785\pi$
$151$	−6.14079	+	8.62353i	−0.499730	+	0.701773i	0.485262	+	0.874369i	$0.338724\pi$
$152$	−7.63287	−	6.00256i	−0.619108	−	0.486872i
$153$	−4.98196	+	5.74948i	−0.402767	+	0.464818i
$154$	−0.0338546	−	0.412447i	−0.00272808	−	0.0332360i
$155$	2.91907	+	1.87597i	0.234465	+	0.150682i
$156$	1.11630	+	0.446900i	0.0893757	+	0.0357806i
$157$	−18.7470	−	9.66474i	−1.49617	−	0.771330i	−0.500631	−	0.865661i	$-0.666899\pi$
$157$	−18.7470	−	9.66474i	−1.49617	−	0.771330i	−0.995541	+	0.0943302i	$0.969929\pi$
$158$	−0.661602	+	1.91157i	−0.0526342	+	0.152077i
$159$	2.49453	−	10.2826i	0.197829	−	0.815464i
$160$	−13.5216			−1.06898
$161$	6.68708	+	10.7835i	0.527016	+	0.849855i
$162$	−0.795332			−0.0624872
$163$	3.34169	−	13.7746i	0.261741	−	1.07891i	−0.677464	−	0.735556i	$-0.736921\pi$
$163$	3.34169	−	13.7746i	0.261741	−	1.07891i	0.939205	−	0.343357i	$-0.111564\pi$
$164$	0.543581	−	1.57057i	0.0424465	−	0.122641i
$165$	−0.404904	−	0.208743i	−0.0315217	−	0.0162506i
$166$	9.82388	+	3.93289i	0.762481	+	0.305251i
$167$	13.9202	+	8.94598i	1.07718	+	0.692261i	0.953904	−	0.300111i	$-0.0970239\pi$
$167$	13.9202	+	8.94598i	1.07718	+	0.692261i	0.123275	+	0.992373i	$0.460660\pi$
$168$	5.82621	−	4.03312i	0.449502	−	0.311162i
$169$	8.00684	−	9.24039i	0.615911	−	0.710799i
$170$	11.0167	+	8.66365i	0.844945	+	0.664472i
$171$	2.10309	−	2.95337i	0.160827	−	0.225850i
$172$	0.575016	+	2.37025i	0.0438445	+	0.180730i
$173$	−9.13333	+	8.70861i	−0.694394	+	0.662104i	−0.952684	−	0.303964i	$-0.901690\pi$
$173$	−9.13333	+	8.70861i	−0.694394	+	0.662104i	0.258289	+	0.966068i	$0.416841\pi$
$174$	0.401135	+	0.878363i	0.0304100	+	0.0665885i
$175$	−0.607680	+	0.751926i	−0.0459363	+	0.0568403i
$176$	−0.0778922	+	0.0898923i	−0.00587134	+	0.00677589i
$177$	3.76852	+	5.29215i	0.283260	+	0.397782i
$178$	−0.302075	+	6.34133i	−0.0226415	+	0.475303i
$179$	0.363327	−	0.285724i	0.0271564	−	0.0213560i	−0.604489	−	0.796614i	$-0.706622\pi$
$179$	0.363327	−	0.285724i	0.0271564	−	0.0213560i	0.631645	+	0.775258i	$0.282380\pi$
$180$	−0.150714	−	3.16388i	−0.0112336	−	0.235822i
$181$	6.94493	+	8.01488i	0.516213	+	0.595741i	0.952679	−	0.303980i	$-0.0983155\pi$
$181$	6.94493	+	8.01488i	0.516213	+	0.595741i	−0.436466	+	0.899721i	$0.643770\pi$
$182$	0.497637	+	1.78215i	0.0368873	+	0.132102i
$183$	−13.7969			−1.01990
$184$	−3.06327	+	12.4738i	−0.225827	+	0.919577i
$185$	−3.19047	−	5.52606i	−0.234568	−	0.406284i
$186$	−0.862270	−	0.822173i	−0.0632247	−	0.0602846i
$187$	1.46913	−	0.283152i	0.107433	−	0.0207061i
$188$	1.72846	−	1.11082i	0.126061	−	0.0810146i
$189$	1.60769	+	2.10127i	0.116942	+	0.152845i
$190$	−5.61906	−	3.61115i	−0.407650	−	0.261980i
$191$	3.25852	+	4.57595i	0.235778	+	0.331104i	0.915464	−	0.402399i	$-0.131823\pi$
$191$	3.25852	+	4.57595i	0.235778	+	0.331104i	−0.679686	+	0.733503i	$0.737884\pi$
$192$	3.37110	+	0.649726i	0.243288	+	0.0468899i
$193$	−0.0607922	+	0.0243375i	−0.00437592	+	0.00175185i	−0.373849	−	0.927489i	$-0.621962\pi$
$193$	−0.0607922	+	0.0243375i	−0.00437592	+	0.00175185i	0.369473	+	0.929241i	$0.379538\pi$
$194$	6.79552	+	0.648894i	0.487890	+	0.0465879i
$195$	1.95431	+	0.573838i	0.139951	+	0.0410934i
$196$	−9.10941	−	2.94012i	−0.650672	−	0.210009i
$197$	−0.541418	−	1.18554i	−0.0385745	−	0.0844663i	0.889364	−	0.457200i	$-0.151148\pi$
$197$	−0.541418	−	1.18554i	−0.0385745	−	0.0844663i	−0.927938	+	0.372734i	$0.878420\pi$
$198$	0.122950	+	0.0966892i	0.00873770	+	0.00687140i
$199$	−17.8013	−	3.43093i	−1.26190	−	0.243212i	−0.485941	−	0.873991i	$-0.661523\pi$
$199$	−17.8013	−	3.43093i	−1.26190	−	0.243212i	−0.775962	+	0.630780i	$0.782735\pi$
$200$	−0.974222	+	0.0930269i	−0.0688879	+	0.00657800i
$201$	−2.40417	+	1.23944i	−0.169577	+	0.0874231i
$202$	1.10289	+	7.67074i	0.0775988	+	0.539712i
$203$	1.50978	−	2.83533i	0.105966	−	0.199001i
$204$	6.81256	+	7.86211i	0.476975	+	0.550458i
$205$	0.663720	−	2.73589i	0.0463562	−	0.191083i
$206$	7.58916	+	13.1448i	0.528762	+	0.915842i
$207$	−4.70659	−	0.920856i	−0.327131	−	0.0640039i
$208$	0.265911	−	0.460572i	0.0184376	−	0.0319349i
$209$	−0.684161	+	0.200888i	−0.0473244	+	0.0138957i
$210$	3.72577	−	3.14261i	0.257102	−	0.216861i
$211$	−7.84565	+	5.04209i	−0.540117	+	0.347112i	−0.782085	−	0.623172i	$-0.785844\pi$
$211$	−7.84565	+	5.04209i	−0.540117	+	0.347112i	0.241968	+	0.970284i	$0.422207\pi$
$212$	−13.4323	−	5.37750i	−0.922537	−	0.369328i
$213$	0.0412230	−	0.865377i	0.00282455	−	0.0592947i
$214$	−7.20669	+	0.688155i	−0.492639	+	0.0470413i
$215$	1.35126	+	3.90422i	0.0921555	+	0.266266i
$216$	−0.381153	+	2.65098i	−0.0259342	+	0.180376i
$217$	−0.429186	+	3.94007i	−0.0291351	+	0.267469i
$218$	−11.7221	−	3.44193i	−0.793923	−	0.233117i
$219$	−6.38039	+	6.08369i	−0.431147	+	0.411098i
$220$	−0.361336	+	0.507426i	−0.0243613	+	0.0342107i
$221$	−6.21044	+	2.48628i	−0.417759	+	0.167246i
$222$	0.716589	+	2.07045i	0.0480943	+	0.138959i
$223$	2.50405	−	5.48310i	0.167683	−	0.367176i	−0.807071	−	0.590454i	$-0.798949\pi$
$223$	2.50405	−	5.48310i	0.167683	−	0.367176i	0.974755	+	0.223279i	$0.0716759\pi$
$224$	−6.89390	−	13.8206i	−0.460618	−	0.923427i
$225$	−0.0520032	−	0.361690i	−0.00346688	−	0.0241127i
$226$	−0.295478	−	6.20284i	−0.0196549	−	0.412607i
$227$	4.77477	−	13.7958i	0.316913	−	0.915660i	−0.668235	−	0.743950i	$-0.732950\pi$
$227$	4.77477	−	13.7958i	0.316913	−	0.915660i	0.985148	−	0.171709i	$-0.0549289\pi$
$228$	−3.58820	−	3.42134i	−0.237634	−	0.226584i
$229$	10.5023	−	18.1905i	0.694010	−	1.20206i	−0.276504	−	0.961013i	$-0.589176\pi$
$229$	10.5023	−	18.1905i	0.694010	−	1.20206i	0.970513	−	0.241047i	$-0.0774909\pi$
$230$	−1.28196	+	8.74165i	−0.0845300	+	0.576407i
$231$	0.00692077	−	0.520283i	0.000455353	−	0.0342321i
$232$	3.11997	−	0.916107i	0.204836	−	0.0601454i
$233$	7.95236	−	1.53269i	0.520976	−	0.100410i	0.0780176	−	0.996952i	$-0.475141\pi$
$233$	7.95236	−	1.53269i	0.520976	−	0.100410i	0.442959	+	0.896542i	$0.353929\pi$
$234$	−0.621614	−	0.320464i	−0.0406362	−	0.0209494i
$235$	2.73575	−	2.15142i	0.178461	−	0.140343i
$236$	7.89646	−	4.07091i	0.514016	−	0.264994i
$237$	−1.05656	+	2.31354i	−0.0686307	+	0.150280i
$238$	−3.23842	+	15.6774i	−0.209916	+	1.01622i
$239$	−3.82046	+	26.5719i	−0.247125	+	1.71879i	0.367544	+	0.930006i	$0.380199\pi$
$239$	−3.82046	+	26.5719i	−0.247125	+	1.71879i	−0.614669	+	0.788785i	$0.710710\pi$
$240$	−1.39459	−	0.133167i	−0.0900203	−	0.00859590i
$241$	−3.65812	−	15.0790i	−0.235640	−	0.971322i	−0.959575	−	0.281454i	$-0.909183\pi$
$241$	−3.65812	−	15.0790i	−0.235640	−	0.971322i	0.723935	−	0.689869i	$-0.242332\pi$
$242$	2.05532	+	8.47215i	0.132121	+	0.544610i
$243$	−0.995472	−	0.0950560i	−0.0638596	−	0.00609785i
$244$	−2.68499	+	18.6745i	−0.171889	+	1.19552i
$245$	−15.8341	−	3.49099i	−1.01160	−	0.223031i
$246$	−0.401556	+	0.879285i	−0.0256023	+	0.0560612i
$247$	2.83374	−	1.46089i	0.180306	−	0.0929544i
$248$	−3.15368	+	2.48008i	−0.200259	+	0.157485i
$249$	11.8259	+	6.09670i	0.749439	+	0.386363i
$250$	8.38381	−	1.61585i	0.530238	−	0.102195i
$251$	−12.7718	+	3.75015i	−0.806152	+	0.236707i	−0.658743	−	0.752368i	$-0.728911\pi$
$251$	−12.7718	+	3.75015i	−0.806152	+	0.236707i	−0.147409	+	0.989076i	$0.547093\pi$
$252$	3.15700	−	1.76713i	0.198872	−	0.111319i
$253$	0.615643	+	0.714540i	0.0387051	+	0.0449227i
$254$	7.36893	−	12.7634i	0.462368	−	0.800844i
$255$	12.7536	+	12.1605i	0.798659	+	0.761520i
$256$	4.57245	−	13.2112i	0.285778	−	0.825702i
$257$	0.544136	+	11.4228i	0.0339422	+	0.712535i	0.950143	+	0.311815i	$0.100937\pi$
$257$	0.544136	+	11.4228i	0.0339422	+	0.712535i	−0.916200	+	0.400720i	$0.868760\pi$
$258$	−0.201883	−	1.40413i	−0.0125687	−	0.0874171i
$259$	4.02161	−	6.07845i	0.249891	−	0.377696i
$260$	1.15703	−	2.53355i	0.0717560	−	0.157124i
$261$	0.397098	+	1.14734i	0.0245798	+	0.0710185i
$262$	0.758913	−	0.303823i	0.0468858	−	0.0187702i
$263$	−10.1669	+	14.2774i	−0.626915	+	0.880379i	−0.998853	−	0.0478782i	$-0.984754\pi$
$263$	−10.1669	+	14.2774i	−0.626915	+	0.880379i	0.371938	+	0.928258i	$0.378693\pi$
$264$	0.381204	−	0.363477i	0.0234615	−	0.0223705i
$265$	−23.5161	−	6.90494i	−1.44458	−	0.424167i
$266$	0.826162	−	7.58443i	0.0506553	−	0.465031i
$267$	−1.13599	+	7.90098i	−0.0695215	+	0.483532i
$268$	1.20974	+	3.49532i	0.0738967	+	0.213511i
$269$	−21.9478	+	2.09576i	−1.33818	+	0.127781i	−0.739472	−	0.673188i	$-0.764925\pi$
$269$	−21.9478	+	2.09576i	−1.33818	+	0.127781i	−0.598707	+	0.800968i	$0.704319\pi$
$270$	−0.0876581	+	1.84017i	−0.00533470	+	0.111989i
$271$	18.9378	+	7.58157i	1.15039	+	0.460547i	0.866927	−	0.498435i	$-0.166092\pi$
$271$	18.9378	+	7.58157i	1.15039	+	0.460547i	0.283465	+	0.958983i	$0.408516\pi$
$272$	3.87073	−	2.48757i	0.234698	−	0.150831i
$273$	0.409866	+	2.29010i	0.0248062	+	0.138603i
$274$	2.94869	−	0.865814i	0.178137	−	0.0523058i
$275$	−0.0359318	+	0.0622357i	−0.00216677	+	0.00375295i
$276$	−2.16235	+	6.19130i	−0.130158	+	0.372673i
$277$	2.09887	+	3.63536i	0.126109	+	0.218427i	0.922166	−	0.386794i	$-0.126418\pi$
$277$	2.09887	+	3.63536i	0.126109	+	0.218427i	−0.796057	+	0.605222i	$0.793084\pi$
$278$	−1.25757	+	5.18376i	−0.0754238	+	0.310901i
$279$	−0.980990	−	1.13212i	−0.0587304	−	0.0677785i
$280$	−8.68934	−	13.9247i	−0.519287	−	0.832158i
$281$	−4.01801	−	27.9458i	−0.239694	−	1.66711i	−0.653638	−	0.756807i	$-0.726758\pi$
$281$	−4.01801	−	27.9458i	−0.239694	−	1.66711i	0.413944	−	0.910302i	$-0.364151\pi$
$282$	−1.06217	+	0.547585i	−0.0632511	+	0.0326082i
$283$	−29.2428	+	2.79235i	−1.73830	+	0.165988i	−0.915495	−	0.402329i	$-0.868201\pi$
$283$	−29.2428	+	2.79235i	−1.73830	+	0.165988i	−0.822809	+	0.568317i	$0.807595\pi$
$284$	−1.16329	−	0.224206i	−0.0690286	−	0.0133042i
$285$	−6.60146	−	5.19145i	−0.391037	−	0.307515i
$286$	0.0571361	+	0.125111i	0.00337853	+	0.00739795i
$287$	3.13478	−	0.716479i	0.185040	−	0.0422924i
$288$	5.60104	+	1.64461i	0.330044	+	0.0969098i
$289$	−40.6914	−	3.88555i	−2.39361	−	0.228562i
$290$	2.07649	−	0.831301i	0.121936	−	0.0488157i
$291$	8.42802	+	1.62437i	0.494059	+	0.0952221i
$292$	6.99278	+	9.81998i	0.409221	+	0.574671i
$293$	−1.19804	−	0.769933i	−0.0699902	−	0.0449800i	0.505178	−	0.863015i	$-0.331427\pi$
$293$	−1.19804	−	0.769933i	−0.0699902	−	0.0449800i	−0.575168	+	0.818035i	$0.695063\pi$
$294$	5.11166	+	2.20591i	0.298118	+	0.128651i
$295$	12.6599	−	8.13600i	0.737086	−	0.473696i
$296$	7.24457	−	1.39628i	0.421082	−	0.0811570i
$297$	0.142334	+	0.135715i	0.00825905	+	0.00787499i
$298$	−2.04905	−	3.54906i	−0.118698	−	0.205592i
$299$	−3.30753	−	2.61616i	−0.191279	−	0.151296i
$300$	−0.499678			−0.0288489
$301$	−3.30162	+	3.37169i	−0.190302	+	0.194341i
$302$	−5.51380	−	6.36327i	−0.317284	−	0.366165i
$303$	0.463633	+	9.73285i	0.0266350	+	0.559138i
$304$	−1.72367	+	1.35551i	−0.0988593	+	0.0777438i
$305$	−1.52064	+	31.9221i	−0.0870715	+	1.82786i
$306$	−3.50970	−	4.92868i	−0.200636	−	0.281754i
$307$	−13.7162	+	15.8293i	−0.782824	+	0.903427i	−0.997310	−	0.0732999i	$-0.976647\pi$
$307$	−13.7162	+	15.8293i	−0.782824	+	0.903427i	0.214486	+	0.976727i	$0.431192\pi$
$308$	−0.702871	−	0.110619i	−0.0400498	−	0.00630309i
$309$	7.92789	+	17.3597i	0.451002	+	0.987556i
$310$	−1.99731	+	1.90443i	−0.113439	+	0.108164i
$311$	4.26792	+	17.5926i	0.242011	+	0.997584i	0.955046	+	0.296456i	$0.0958048\pi$
$311$	4.26792	+	17.5926i	0.242011	+	0.997584i	−0.713035	+	0.701128i	$0.752680\pi$
$312$	−1.36606	+	1.91837i	−0.0773381	+	0.108606i
$313$	7.43879	+	5.84993i	0.420465	+	0.330658i	0.805873	−	0.592089i	$-0.201697\pi$
$313$	7.43879	+	5.84993i	0.420465	+	0.330658i	−0.385407	+	0.922747i	$0.625939\pi$
$314$	10.9852	−	12.6776i	0.619930	−	0.715437i
$315$	5.03893	−	3.48814i	0.283911	−	0.196534i
$316$	2.92582	+	1.88031i	0.164590	+	0.105776i
$317$	−2.88041	−	1.15314i	−0.161780	−	0.0647668i	0.289359	−	0.957221i	$-0.406558\pi$
$317$	−2.88041	−	1.15314i	−0.161780	−	0.0647668i	−0.451139	+	0.892454i	$0.648982\pi$
$318$	7.47982	+	3.85611i	0.419447	+	0.216240i
$319$	0.0780957	−	0.225643i	0.00437252	−	0.0126336i
$320$	1.87483	−	7.72814i	0.104806	−	0.432016i
$321$	−9.10245			−0.508049
$322$	−9.58854	+	3.14656i	−0.534349	+	0.175351i
$323$	27.5828			1.53475
$324$	−0.322388	+	1.32890i	−0.0179104	+	0.0738278i
$325$	0.105092	−	0.303643i	0.00582944	−	0.0168431i
$326$	10.0200	+	5.16567i	0.554957	+	0.286100i
$327$	−14.2606	−	5.70907i	−0.788611	−	0.315712i
$328$	2.73837	+	1.75984i	0.151201	+	0.0971710i
$329$	3.59379	+	1.69936i	0.198132	+	0.0936886i
$330$	0.237262	−	0.273815i	0.0130608	−	0.0150730i
$331$	25.8370	+	20.3184i	1.42013	+	1.11680i	0.975223	+	0.221222i	$0.0710046\pi$
$331$	25.8370	+	20.3184i	1.42013	+	1.11680i	0.444904	+	0.895578i	$0.353238\pi$
$332$	10.5535	−	14.8203i	0.579197	−	0.813369i
$333$	0.649459	+	2.67711i	0.0355901	+	0.146705i
$334$	−9.52460	+	9.08169i	−0.521163	+	0.496928i
$335$	2.60272	+	5.69917i	0.142202	+	0.311379i
$336$	−0.574910	−	1.49332i	−0.0313639	−	0.0814673i
$337$	0.669198	−	0.772295i	0.0364535	−	0.0420696i	−0.737230	−	0.675642i	$-0.763867\pi$
$337$	0.669198	−	0.772295i	0.0364535	−	0.0420696i	0.773684	+	0.633572i	$0.218412\pi$
$338$	5.64068	+	7.92122i	0.306812	+	0.430858i
$339$	0.371515	−	7.79906i	0.0201779	−	0.423587i
$340$	18.9415	−	14.8958i	1.02725	−	0.807837i
$341$	0.0140180	+	0.294275i	0.000759119	+	0.0159359i
$342$	1.88836	+	2.17928i	0.102111	+	0.117842i
$343$	−4.50471	−	17.9641i	−0.243231	−	0.969968i
$344$	−4.77695			−0.257556
$345$	−2.64934	+	10.7882i	−0.142635	+	0.580818i
$346$	−5.01844	−	8.69219i	−0.269793	−	0.467295i
$347$	4.33882	+	4.13706i	0.232920	+	0.222089i	0.797546	−	0.603258i	$-0.206131\pi$
$347$	4.33882	+	4.13706i	0.232920	+	0.222089i	−0.564626	+	0.825347i	$0.690980\pi$
$348$	1.63024	−	0.314202i	0.0873898	−	0.0168430i
$349$	4.08502	−	2.62529i	0.218666	−	0.140528i	−0.426722	−	0.904383i	$-0.640332\pi$
$349$	4.08502	−	2.62529i	0.218666	−	0.140528i	0.645389	+	0.763854i	$0.276695\pi$
$350$	−0.467229	−	0.610675i	−0.0249745	−	0.0326419i
$351$	−0.739738	−	0.475401i	−0.0394843	−	0.0253750i
$352$	−0.665927	−	0.935164i	−0.0354940	−	0.0498444i
$353$	16.3211	+	3.14564i	0.868686	+	0.167426i	0.604073	−	0.796929i	$-0.293544\pi$
$353$	16.3211	+	3.14564i	0.868686	+	0.167426i	0.264613	+	0.964355i	$0.414756\pi$
$354$	−4.79699	+	1.92043i	−0.254957	+	0.102070i
$355$	−1.99769	−	0.190756i	−0.106026	−	0.0101243i
$356$	10.4731	+	3.07519i	0.555075	+	0.162985i
$357$	−5.92708	+	19.2355i	−0.313694	+	1.01805i
$358$	0.152713	+	0.334395i	0.00807115	+	0.0176733i
$359$	−15.9310	−	12.5283i	−0.840809	−	0.661219i	0.101915	−	0.994793i	$-0.467503\pi$
$359$	−15.9310	−	12.5283i	−0.840809	−	0.661219i	−0.942724	+	0.333574i	$0.891745\pi$
$360$	6.09159	+	1.17406i	0.321055	+	0.0618783i
$361$	5.82809	−	0.556515i	0.306741	−	0.0292902i
$362$	−7.49702	+	3.86498i	−0.394035	+	0.203139i
$363$	1.55996	+	10.8498i	0.0818766	+	0.569464i
$364$	3.17947	−	0.109095i	0.166650	−	0.00571811i
$365$	13.3727	+	15.4329i	0.699959	+	0.807796i
$366$	2.58702	−	10.6638i	0.135226	−	0.557407i
$367$	−10.1442	−	17.5702i	−0.529522	−	0.917159i	−0.999407	−	0.0344315i	$-0.989038\pi$
$367$	−10.1442	−	17.5702i	−0.529522	−	0.917159i	0.469885	−	0.882728i	$-0.344295\pi$
$368$	2.57436	+	1.33635i	0.134198	+	0.0696621i
$369$	−0.607695	+	1.05256i	−0.0316353	+	0.0547940i
$370$	4.86940	−	1.42978i	0.253148	−	0.0743309i
$371$	−4.93188	−	27.5565i	−0.256050	−	1.43066i
$372$	−1.72327	+	1.10748i	−0.0893474	+	0.0574201i
$373$	−28.6220	−	11.4585i	−1.48199	−	0.593300i	−0.517095	−	0.855928i	$-0.672987\pi$
$373$	−28.6220	−	11.4585i	−1.48199	−	0.593300i	−0.964897	+	0.262627i	$0.915411\pi$
$374$	−0.0566201	+	1.18860i	−0.00292776	+	0.0614612i
$375$	10.6867	−	1.02045i	0.551857	−	0.0526959i
$376$	1.31616	+	3.80281i	0.0678760	+	0.196115i
$377$	−0.151936	+	1.05674i	−0.00782511	+	0.0544248i
$378$	−1.92555	+	0.848601i	−0.0990397	+	0.0436473i
$379$	−30.8793	−	9.06699i	−1.58617	−	0.465740i	−0.634512	−	0.772913i	$-0.718799\pi$
$379$	−30.8793	−	9.06699i	−1.58617	−	0.465740i	−0.951654	+	0.307173i	$0.900617\pi$
$380$	−8.31147	+	7.92497i	−0.426369	+	0.406542i
$381$	10.7487	−	15.0945i	0.550673	−	0.773312i
$382$	−4.14781	+	1.66053i	−0.212220	+	0.0849601i
$383$	10.4058	+	30.0656i	0.531711	+	1.53628i	0.816300	+	0.577628i	$0.196022\pi$
$383$	10.4058	+	30.0656i	0.531711	+	1.53628i	−0.284589	+	0.958650i	$0.591857\pi$
$384$	3.71568	−	8.13621i	0.189615	−	0.415199i
$385$	−1.20302	−	0.0733560i	−0.0613117	−	0.00373857i
$386$	−0.00741185	−	0.0515505i	−0.000377253	−	0.00262385i
$387$	−0.0848678	−	1.78159i	−0.00431407	−	0.0905635i
$388$	3.83879	−	11.0914i	0.194885	−	0.563083i
$389$	−20.3764	−	19.4288i	−1.03312	−	0.985080i	−0.0332257	−	0.999448i	$-0.510578\pi$
$389$	−20.3764	−	19.4288i	−1.03312	−	0.985080i	−0.999897	+	0.0143676i	$0.995426\pi$
$390$	−0.809974	+	1.40292i	−0.0410146	+	0.0710394i
$391$	−15.0630	−	33.2305i	−0.761771	−	1.68054i
$392$	9.80238	−	15.9809i	0.495095	−	0.807156i
$393$	0.986200	−	0.289574i	0.0497472	−	0.0146071i
$394$	1.01784	−	0.196172i	0.0512780	−	0.00988302i
$395$	5.23640	+	2.69955i	0.263472	+	0.135829i
$396$	0.211394	−	0.166242i	0.0106229	−	0.00835396i
$397$	−3.14419	+	1.62094i	−0.157802	+	0.0813527i	−0.535319	−	0.844650i	$-0.679808\pi$
$397$	−3.14419	+	1.62094i	−0.157802	+	0.0813527i	0.377516	+	0.926003i	$0.376778\pi$
$398$	5.98968	−	13.1156i	0.300235	−	0.657424i
$399$	1.94053	−	9.39426i	0.0971481	−	0.470301i
$400$	−0.0314518	+	0.218752i	−0.00157259	+	0.0109376i
$401$	−9.09716	−	0.868673i	−0.454291	−	0.0433795i	−0.134597	−	0.990900i	$-0.542974\pi$
$401$	−9.09716	−	0.868673i	−0.454291	−	0.0433795i	−0.319694	+	0.947521i	$0.603580\pi$
$402$	−0.507178	−	2.09062i	−0.0252958	−	0.104271i
$403$	−0.310552	−	1.28011i	−0.0154697	−	0.0637671i
$404$	13.2639	+	1.26655i	0.659904	+	0.0630132i
$405$	−0.329649	+	2.29276i	−0.0163804	+	0.113928i
$406$	1.90837	+	1.69857i	0.0947107	+	0.0842988i
$407$	0.225058	−	0.492809i	0.0111557	−	0.0244276i
$408$	−18.1101	+	9.33642i	−0.896585	+	0.462222i
$409$	−10.1085	+	7.94945i	−0.499835	+	0.393075i	−0.836001	−	0.548728i	$-0.815112\pi$
$409$	−10.1085	+	7.94945i	−0.499835	+	0.393075i	0.336166	+	0.941803i	$0.390870\pi$
$410$	1.99015	+	1.02600i	0.0982867	+	0.0506703i
$411$	3.79419	−	0.731270i	0.187154	−	0.0360709i
$412$	25.0396	−	7.35229i	1.23361	−	0.362221i
$413$	14.7704	+	8.79172i	0.726806	+	0.432612i
$414$	1.59426	−	3.46512i	0.0783536	−	0.170301i
$415$	15.4094	−	26.6899i	0.756418	−	1.31015i
$416$	3.71498	+	3.54223i	0.182142	+	0.173672i
$417$	−2.19357	+	6.33791i	−0.107420	+	0.310369i
$418$	−0.0269840	−	0.566464i	−0.00131983	−	0.0277067i
$419$	3.50921	+	24.4071i	0.171436	+	1.19236i	0.875853	+	0.482577i	$0.160299\pi$
$419$	3.50921	+	24.4071i	0.171436	+	1.19236i	−0.704417	+	0.709786i	$0.748792\pi$
$420$	−3.74067	−	7.49915i	−0.182526	−	0.365921i
$421$	15.1470	−	33.1672i	0.738218	−	1.61647i	−0.0482463	−	0.998835i	$-0.515363\pi$
$421$	15.1470	−	33.1672i	0.738218	−	1.61647i	0.786464	−	0.617636i	$-0.211909\pi$
$422$	−2.42599	−	7.00943i	−0.118095	−	0.341214i
$423$	−1.39490	+	0.558434i	−0.0678223	+	0.0271520i
$424$	16.4377	−	23.0835i	0.798285	−	1.12103i
$425$	2.01191	−	1.91836i	0.0975922	−	0.0930540i
$426$	0.661131	+	0.194126i	0.0320319	+	0.00940542i
$427$	−33.4033	+	14.7210i	−1.61650	+	0.712400i
$428$	−1.77141	+	12.3204i	−0.0856243	+	0.595530i
$429$	0.0565612	+	0.163423i	0.00273080	+	0.00789012i
$430$	−3.27100	+	0.312342i	−0.157741	+	0.0150625i
$431$	1.42233	−	29.8584i	0.0685114	−	1.43823i	−0.659004	−	0.752139i	$-0.729022\pi$
$431$	1.42233	−	29.8584i	0.0685114	−	1.43823i	0.727516	−	0.686091i	$-0.240675\pi$
$432$	0.561482	+	0.224783i	0.0270143	+	0.0108149i
$433$	8.04312	−	5.16900i	0.386528	−	0.248406i	−0.332917	−	0.942956i	$-0.608033\pi$
$433$	8.04312	−	5.16900i	0.386528	−	0.248406i	0.719444	+	0.694550i	$0.244396\pi$
$434$	−2.96485	−	1.07051i	−0.142317	−	0.0513862i
$435$	2.69838	−	0.792316i	0.129377	−	0.0379886i
$436$	−10.5026	+	18.1910i	−0.502984	+	0.871193i
$437$	8.65164	+	15.0829i	0.413864	+	0.721512i
$438$	−3.50580	−	6.07222i	−0.167514	−	0.290142i
$439$	−3.10760	+	12.8097i	−0.148318	+	0.611375i	0.848323	+	0.529479i	$0.177613\pi$
$439$	−3.10760	+	12.8097i	−0.148318	+	0.611375i	−0.996641	+	0.0818956i	$0.973903\pi$
$440$	−0.798967	−	0.922057i	−0.0380893	−	0.0439573i
$441$	6.13433	+	3.37195i	0.292111	+	0.160569i
$442$	−0.757183	−	5.26632i	−0.0360155	−	0.250493i
$443$	25.6915	−	13.2449i	1.22064	−	0.629283i	0.277195	−	0.960814i	$-0.410595\pi$
$443$	25.6915	−	13.2449i	1.22064	−	0.629283i	0.943444	+	0.331531i	$0.107565\pi$
$444$	3.74993	−	0.358075i	0.177964	−	0.0169935i
$445$	18.1554	+	3.49917i	0.860648	+	0.165876i
$446$	3.76843	+	2.96353i	0.178440	+	0.140327i
$447$	−2.14051	−	4.68706i	−0.101242	−	0.221690i
$448$	8.85489	−	2.02385i	0.418354	−	0.0956182i
$449$	−13.6432	−	4.00599i	−0.643860	−	0.189054i	−0.0565288	−	0.998401i	$-0.518003\pi$
$449$	−13.6432	−	4.00599i	−0.643860	−	0.189054i	−0.587331	+	0.809347i	$0.699821\pi$
$450$	0.289306	+	0.0276254i	0.0136380	+	0.00130227i
$451$	0.221904	−	0.0888369i	0.0104490	−	0.00418317i
$452$	−10.4840	−	2.02062i	−0.493124	−	0.0950418i
$453$	−6.14079	−	8.62353i	−0.288520	−	0.405169i
$454$	9.76765	+	6.27729i	0.458419	+	0.294608i
$455$	5.34379	−	0.695908i	0.250521	−	0.0326247i
$456$	8.16889	−	5.24983i	0.382543	−	0.245846i
$457$	−14.4572	+	2.78640i	−0.676281	+	0.130342i	−0.515816	−	0.856699i	$-0.672511\pi$
$457$	−14.4572	+	2.78640i	−0.676281	+	0.130342i	−0.160464	+	0.987042i	$0.551299\pi$
$458$	12.0904	+	11.5282i	0.564947	+	0.538676i
$459$	−3.80383	−	6.58842i	−0.177548	−	0.307521i
$460$	14.0866	+	5.68542i	0.656789	+	0.265084i
$461$	26.4986			1.23416			0.617081	−	0.786900i	$-0.288315\pi$
$461$	26.4986			1.23416			0.617081	+	0.786900i	$0.288315\pi$
$462$	0.400836	+	0.102906i	0.0186486	+	0.00478761i
$463$	21.4245	+	24.7252i	0.995681	+	1.14908i	0.988822	+	0.149100i	$0.0476377\pi$
$463$	21.4245	+	24.7252i	0.995681	+	1.14908i	0.00685847	+	0.999976i	$0.497817\pi$
$464$	−0.0349396	−	0.733471i	−0.00162203	−	0.0340506i
$465$	−2.72753	+	2.14495i	−0.126486	+	0.0994697i
$466$	−0.306483	+	6.43387i	−0.0141975	+	0.298043i
$467$	−6.78680	−	9.53073i	−0.314056	−	0.441029i	0.627132	−	0.778913i	$-0.284228\pi$
$467$	−6.78680	−	9.53073i	−0.314056	−	0.441029i	−0.941188	+	0.337883i	$0.890289\pi$
$468$	−0.787427	+	0.908740i	−0.0363988	+	0.0420065i
$469$	−4.49821	+	5.56596i	−0.207708	+	0.257012i
$470$	1.14989	+	2.51790i	0.0530403	+	0.116142i
$471$	15.2647	−	14.5549i	0.703362	−	0.670654i
$472$	4.10221	+	16.9095i	0.188820	+	0.778325i
$473$	−0.203470	+	0.285734i	−0.00935557	+	0.0131381i
$474$	−1.59005	−	1.25043i	−0.0730334	−	0.0574341i
$475$	−0.867592	+	1.00125i	−0.0398079	+	0.0459407i
$476$	24.8824	+	11.7658i	1.14048	+	0.539287i
$477$	8.90119	+	5.72045i	0.407558	+	0.261921i
$478$	−19.8214	−	7.93528i	−0.906609	−	0.362951i
$479$	−14.6068	−	7.53032i	−0.667401	−	0.344069i	0.0910062	−	0.995850i	$-0.470992\pi$
$479$	−14.6068	−	7.53032i	−0.667401	−	0.344069i	−0.758407	+	0.651781i	$0.774022\pi$
$480$	4.42248	−	12.7779i	0.201858	−	0.583230i
$481$	−0.571088	+	2.35406i	−0.0260394	+	0.107336i
$482$	12.3407			0.562101
$483$	−12.3775	+	2.79237i	−0.563196	+	0.127057i
$484$	14.9890			0.681319
$485$	4.68722	−	19.3210i	0.212836	−	0.877320i
$486$	0.260128	−	0.751589i	0.0117996	−	0.0340928i
$487$	−22.4814	−	11.5900i	−1.01873	−	0.525192i	−0.133846	−	0.991002i	$-0.542733\pi$
$487$	−22.4814	−	11.5900i	−1.01873	−	0.525192i	−0.884885	+	0.465810i	$0.845763\pi$
$488$	−34.3046	−	13.7335i	−1.55289	−	0.621685i
$489$	11.9241	+	7.66314i	0.539226	+	0.346539i
$490$	5.66723	−	11.5838i	0.256019	−	0.523302i
$491$	−7.80303	+	9.00517i	−0.352146	+	0.406398i	−0.903993	−	0.427547i	$-0.859378\pi$
$491$	−7.80303	+	9.00517i	−0.352146	+	0.406398i	0.551847	+	0.833945i	$0.313923\pi$
$492$	1.30641	+	1.02737i	0.0588973	+	0.0463174i
$493$	−5.35774	+	7.52389i	−0.241300	+	0.338859i
$494$	0.597798	+	2.46416i	0.0268962	+	0.110868i
$495$	0.329693	−	0.314362i	0.0148186	−	0.0141295i
$496$	0.376369	+	0.824133i	0.0168995	+	0.0370046i
$497$	−0.823534	−	2.13912i	−0.0369405	−	0.0959526i
$498$	−6.92966	+	7.99725i	−0.310526	+	0.358366i
$499$	−0.563918	−	0.791912i	−0.0252444	−	0.0354508i	0.801761	−	0.597645i	$-0.203897\pi$
$499$	−0.563918	−	0.791912i	−0.0252444	−	0.0354508i	−0.827005	+	0.562194i	$0.809957\pi$
$500$	0.698498	−	14.6633i	0.0312378	−	0.655762i
$501$	−13.0068	+	10.2287i	−0.581102	+	0.456984i
$502$	−0.503735	−	10.5747i	−0.0224828	−	0.471972i
$503$	−19.4424	−	22.4378i	−0.866896	−	1.00045i	−0.999956	−	0.00934324i	$-0.997026\pi$
$503$	−19.4424	−	22.4378i	−0.866896	−	1.00045i	0.133060	−	0.991108i	$-0.457520\pi$
$504$	1.90574	+	6.82487i	0.0848882	+	0.304004i
$505$	22.5701			1.00436
$506$	−0.667714	+	0.341857i	−0.0296835	+	0.0151974i
$507$	6.11339	+	10.5887i	0.271505	+	0.470261i
$508$	−18.3390	−	17.4862i	−0.813661	−	0.775824i
$509$	−15.3188	+	2.95246i	−0.678994	+	0.130865i	−0.517077	−	0.855939i	$-0.672980\pi$
$509$	−15.3188	+	2.95246i	−0.678994	+	0.130865i	−0.161917	+	0.986804i	$0.551768\pi$
$510$	−11.7904	+	7.57722i	−0.522087	+	0.335525i
$511$	−8.95619	+	21.5368i	−0.396199	+	0.952730i
$512$	−5.69543	−	3.66023i	−0.251705	−	0.161761i
$513$	2.10309	+	2.95337i	0.0928536	+	0.130395i
$514$	−8.93087	−	1.72128i	−0.393924	−	0.0759226i
$515$	41.0390	−	16.4295i	1.80839	−	0.723972i
$516$	−2.42795	−	0.231842i	−0.106885	−	0.0102063i
$517$	0.283527	+	0.0832509i	0.0124695	+	0.00366137i
$518$	3.94403	+	4.24811i	0.173291	+	0.186651i
$519$	−5.24243	−	11.4793i	−0.230117	−	0.503886i
$520$	4.28799	+	3.37211i	0.188041	+	0.147877i
$521$	19.6195	+	3.78135i	0.859546	+	0.165664i	0.599935	−	0.800049i	$-0.295193\pi$
$521$	19.6195	+	3.78135i	0.859546	+	0.165664i	0.259612	+	0.965713i	$0.416405\pi$
$522$	−0.961252	+	0.0917885i	−0.0420729	+	0.00401747i
$523$	−0.354939	+	0.182984i	−0.0155204	+	0.00800131i	−0.465969	−	0.884801i	$-0.654294\pi$
$523$	−0.354939	+	0.182984i	−0.0155204	+	0.00800131i	0.450449	+	0.892802i	$0.351264\pi$
$524$	−0.200025	−	1.39120i	−0.00873812	−	0.0607750i
$525$	−0.511818	−	0.820189i	−0.0223376	−	0.0357960i
$526$	−9.12880	−	10.5352i	−0.398034	−	0.459356i
$527$	2.68680	−	11.0751i	0.117039	−	0.482440i
$528$	−0.0594723	−	0.103009i	−0.00258820	−	0.00448289i
$529$	13.4465	−	18.6599i	0.584629	−	0.811301i
$530$	9.74633	−	16.8811i	0.423354	−	0.733270i
$531$	−6.23365	+	1.83036i	−0.270517	+	0.0794311i
$532$	−12.3378	−	4.45476i	−0.534910	−	0.193139i
$533$	−0.899070	+	0.577797i	−0.0389430	+	0.0250272i
$534$	−5.89377	−	2.35951i	−0.255048	−	0.102106i
$535$	−1.00323	+	21.0604i	−0.0433735	+	0.910522i
$536$	−7.21145	+	0.688610i	−0.311487	+	0.0297434i
$537$	0.151176	+	0.436796i	0.00652374	+	0.0188491i
$538$	2.49551	−	17.3567i	0.107589	−	0.748300i
$539$	−0.538375	−	1.26702i	−0.0231894	−	0.0545746i
$540$	3.03916	+	0.892378i	0.130785	+	0.0384018i
$541$	12.8310	−	12.2343i	0.551646	−	0.525994i	−0.362175	−	0.932110i	$-0.617966\pi$
$541$	12.8310	−	12.2343i	0.551646	−	0.525994i	0.913821	+	0.406116i	$0.133117\pi$
$542$	−9.41086	+	13.2157i	−0.404231	+	0.567663i
$543$	−9.84553	+	3.94156i	−0.422512	+	0.169148i
$544$	14.5250	+	41.9672i	0.622754	+	1.79933i
$545$	−14.7809	+	32.3656i	−0.633143	+	1.38639i
$546$	−1.84690	−	0.112617i	−0.0790399	−	0.00481957i
$547$	5.54058	+	38.5356i	0.236898	+	1.64766i	0.667128	+	0.744943i	$0.267523\pi$
$547$	5.54058	+	38.5356i	0.236898	+	1.64766i	−0.430230	+	0.902719i	$0.641568\pi$
$548$	−0.251415	−	5.27786i	−0.0107399	−	0.225459i
$549$	4.51254	−	13.0381i	0.192590	−	0.556453i
$550$	−0.0413653	−	0.0394417i	−0.00176382	−	0.00168180i
$551$	2.20098	−	3.81222i	0.0937651	−	0.162406i
$552$	−10.7858	−	6.97455i	−0.459075	−	0.296857i
$553$	−0.0895026	+	6.72854i	−0.00380604	+	0.286127i
$554$	−3.20337	+	0.940594i	−0.136098	+	0.0399620i
$555$	6.26563	−	1.20760i	0.265961	−	0.0512598i
$556$	8.15166	+	4.20247i	0.345707	+	0.178224i
$557$	−3.33718	+	2.62439i	−0.141401	+	0.111199i	−0.686354	−	0.727268i	$-0.740790\pi$
$557$	−3.33718	+	2.62439i	−0.141401	+	0.111199i	0.544953	+	0.838467i	$0.316547\pi$
$558$	1.05897	−	0.545939i	0.0448300	−	0.0231115i
$559$	0.651530	−	1.42665i	0.0275568	−	0.0603409i
$560$	−3.51848	+	1.16559i	−0.148683	+	0.0492551i
$561$	−0.212927	+	1.48094i	−0.00898978	+	0.0625253i
$562$	22.3531	+	2.13446i	0.942909	+	0.0900369i
$563$	−3.54146	−	14.5981i	−0.149255	−	0.615237i	−0.996467	−	0.0839824i	$-0.973236\pi$
$563$	−3.54146	−	14.5981i	−0.149255	−	0.615237i	0.847212	−	0.531254i	$-0.178279\pi$
$564$	0.484397	+	1.99671i	0.0203968	+	0.0840767i
$565$	−18.0038	−	1.71916i	−0.757427	−	0.0723255i
$566$	3.32498	−	23.1257i	0.139759	−	0.972047i
$567$	−2.51153	+	0.832009i	−0.105474	+	0.0349411i
$568$	0.963893	−	2.11063i	0.0404441	−	0.0885602i
$569$	−40.7738	+	21.0203i	−1.70933	+	0.881218i	−0.728825	+	0.684700i	$0.759933\pi$
$569$	−40.7738	+	21.0203i	−1.70933	+	0.881218i	−0.980500	+	0.196518i	$0.937037\pi$
$570$	5.25036	−	4.12893i	0.219913	−	0.172942i
$571$	34.3443	+	17.7057i	1.43727	+	0.740962i	0.988291	−	0.152583i	$-0.0487591\pi$
$571$	34.3443	+	17.7057i	1.43727	+	0.740962i	0.448974	+	0.893545i	$0.351789\pi$
$572$	0.232205	−	0.0447538i	0.00970896	−	0.00187125i
$573$	−5.39003	+	1.58266i	−0.225172	+	0.0661164i
$574$	−0.0340165	+	2.55726i	−0.00141982	+	0.106738i
$575$	1.68006	+	0.498446i	0.0700634	+	0.0207867i
$576$	−1.71657	+	2.97318i	−0.0715237	+	0.123883i
$577$	−25.8326	−	24.6313i	−1.07542	−	1.02542i	−0.999600	−	0.0282942i	$-0.990992\pi$
$577$	−25.8326	−	24.6313i	−1.07542	−	1.02542i	−0.0758250	−	0.997121i	$-0.524159\pi$
$578$	10.6331	−	30.7223i	0.442278	−	1.27788i
$579$	−0.00311580	−	0.0654087i	−0.000129488	−	0.00271829i
$580$	−0.547296	−	3.80652i	−0.0227252	−	0.158057i
$581$	35.1364	+	2.14249i	1.45770	+	0.0888857i
$582$	−2.83580	+	6.20954i	−0.117548	+	0.257394i
$583$	−0.680595	−	1.96645i	−0.0281874	−	0.0814420i
$584$	−21.9199	+	8.77539i	−0.907051	+	0.363128i
$585$	−1.18147	+	1.65914i	−0.0488478	+	0.0685972i
$586$	0.819732	−	0.781613i	0.0338628	−	0.0322881i
$587$	−18.7670	−	5.51048i	−0.774596	−	0.227442i	−0.129537	−	0.991575i	$-0.541349\pi$
$587$	−18.7670	−	5.51048i	−0.774596	−	0.227442i	−0.645059	+	0.764133i	$0.723167\pi$
$588$	5.75781	−	7.64678i	0.237448	−	0.315348i
$589$	−0.772953	+	5.37600i	−0.0318490	+	0.221514i
$590$	3.91461	+	11.3105i	0.161162	+	0.465647i
$591$	1.29742	−	0.123888i	0.0533686	−	0.00509609i
$592$	0.0792759	−	1.66421i	0.00325822	−	0.0683984i
$593$	−44.7119	−	17.8999i	−1.83610	−	0.735063i	−0.973309	−	0.229499i	$-0.926291\pi$
$593$	−44.7119	−	17.8999i	−1.83610	−	0.735063i	−0.862789	−	0.505564i	$-0.831285\pi$
$594$	−0.131584	+	0.0845642i	−0.00539898	+	0.00346971i
$595$	43.8522	+	15.8336i	1.79776	+	0.649114i
$596$	−6.76062	+	1.98510i	−0.276926	+	0.0813128i
$597$	9.06448	−	15.7001i	0.370984	−	0.642564i
$598$	2.64224	−	2.06588i	0.108049	−	0.0844803i
$599$	−13.0637	−	22.6270i	−0.533769	−	0.924514i	−0.999222	−	0.0394418i	$-0.987442\pi$
$599$	−13.0637	−	22.6270i	−0.533769	−	0.924514i	0.465453	−	0.885072i	$-0.345891\pi$
$600$	0.230726	−	0.951067i	0.00941936	−	0.0388271i
$601$	−14.7340	−	17.0039i	−0.601011	−	0.693603i	0.370975	−	0.928643i	$-0.379024\pi$
$601$	−14.7340	−	17.0039i	−0.601011	−	0.693603i	−0.971986	+	0.235039i	$0.924478\pi$
$602$	−1.98694	−	3.18408i	−0.0809818	−	0.129773i
$603$	−0.384941	−	2.67732i	−0.0156760	−	0.109029i
$604$	−12.8672	+	6.63353i	−0.523561	+	0.269914i
$605$	25.2751	−	2.41348i	1.02758	−	0.0981220i
$606$	−7.60958	−	1.46663i	−0.309118	−	0.0595776i
$607$	28.9932	+	22.8005i	1.17680	+	0.925444i	0.998288	−	0.0584942i	$-0.0186299\pi$
$607$	28.9932	+	22.8005i	1.17680	+	0.925444i	0.178510	+	0.983938i	$0.442872\pi$
$608$	−8.79217	−	19.2522i	−0.356569	−	0.780778i
$609$	2.18559	+	2.35409i	0.0885644	+	0.0953926i
$610$	−24.3879	−	7.16093i	−0.987437	−	0.289938i
$611$	−1.31523	−	0.125590i	−0.0532086	−	0.00508081i
$612$	−9.65788	+	3.86643i	−0.390396	+	0.156291i
$613$	27.4724	+	5.29488i	1.10960	+	0.213858i	0.710948	−	0.703244i	$-0.248266\pi$
$613$	27.4724	+	5.29488i	1.10960	+	0.213858i	0.398652	+	0.917102i	$0.369478\pi$
$614$	−9.66281	−	13.5695i	−0.389959	−	0.547621i
$615$	2.36834	+	1.52204i	0.0955007	+	0.0613745i
$616$	0.535098	−	1.28674i	0.0215597	−	0.0518442i
$617$	−38.7726	+	24.9177i	−1.56093	+	1.00315i	−0.578680	+	0.815554i	$0.696432\pi$
$617$	−38.7726	+	24.9177i	−1.56093	+	1.00315i	−0.982247	+	0.187593i	$0.939932\pi$
$618$	−14.9040	+	2.87252i	−0.599528	+	0.115550i
$619$	18.5609	+	17.6978i	0.746028	+	0.711336i	0.964376	−	0.264535i	$-0.0852185\pi$
$619$	18.5609	+	17.6978i	0.746028	+	0.711336i	−0.218349	+	0.975871i	$0.570067\pi$
$620$	2.37245	+	4.10921i	0.0952800	+	0.165030i
$621$	2.40959	−	4.14655i	0.0966934	−	0.166395i
$622$	−14.3978			−0.577299
$623$	5.67986	+	20.3409i	0.227559	+	0.814940i
$624$	0.348270	+	0.401925i	0.0139419	+	0.0160899i
$625$	−1.27013	−	26.6633i	−0.0508052	−	1.06653i
$626$	−5.91631	+	4.65264i	−0.236463	+	0.185957i
$627$	0.0339280	−	0.712236i	0.00135495	−	0.0284440i
$628$	−16.7298	−	23.4937i	−0.667592	−	0.937502i
$629$	−13.7241	+	15.8384i	−0.547215	+	0.631520i
$630$	1.75119	+	4.54870i	0.0697692	+	0.181225i
$631$	7.01531	+	15.3614i	0.279275	+	0.611527i	0.996340	−	0.0854794i	$-0.0272422\pi$
$631$	7.01531	+	15.3614i	0.279275	+	0.611527i	−0.717065	+	0.697006i	$0.754515\pi$
$632$	−4.92991	+	4.70066i	−0.196101	+	0.186982i
$633$	−2.19872	−	9.06325i	−0.0873913	−	0.360232i
$634$	1.43137	−	2.01008i	0.0568471	−	0.0798305i
$635$	−33.7395	−	26.5331i	−1.33891	−	1.05293i
$636$	9.47503	−	10.9348i	0.375710	−	0.433592i
$637$	3.43579	+	5.10715i	0.136131	+	0.202353i
$638$	0.159759	+	0.102671i	0.00632491	+	0.00406477i
$639$	0.804299	+	0.321993i	0.0318176	+	0.0127378i
$640$	−18.4153	−	9.49376i	−0.727930	−	0.375274i
$641$	8.12354	−	23.4714i	0.320860	−	0.927065i	−0.663077	−	0.748551i	$-0.730750\pi$
$641$	8.12354	−	23.4714i	0.320860	−	0.927065i	0.983937	−	0.178514i	$-0.0571290\pi$
$642$	1.70677	−	7.03540i	0.0673608	−	0.277665i
$643$	22.5143			0.887878			0.443939	−	0.896057i	$-0.353581\pi$
$643$	22.5143			0.887878			0.443939	+	0.896057i	$0.353581\pi$
$644$	1.37080	+	17.2967i	0.0540169	+	0.681586i
$645$	−4.13145			−0.162676
$646$	−5.17195	+	21.3191i	−0.203488	+	0.838788i
$647$	−10.1125	+	29.2183i	−0.397565	+	1.14869i	0.551654	+	0.834073i	$0.313997\pi$
$647$	−10.1125	+	29.2183i	−0.397565	+	1.14869i	−0.949219	+	0.314616i	$0.898124\pi$
$648$	−2.38051	−	1.22724i	−0.0935154	−	0.0482105i
$649$	1.18618	+	0.474874i	0.0465616	+	0.0186404i
$650$	0.214984	+	0.138162i	0.00843236	+	0.00541915i
$651$	−3.58299	−	1.69425i	−0.140429	−	0.0664029i
$652$	12.6928	−	14.6483i	0.497089	−	0.573671i
$653$	26.0026	+	20.4487i	1.01756	+	0.800218i	0.979984	−	0.199076i	$-0.0637940\pi$
$653$	26.0026	+	20.4487i	1.01756	+	0.800218i	0.0375758	+	0.999294i	$0.488036\pi$
$654$	7.08656	−	9.95169i	0.277107	−	0.389142i
$655$	−0.561297	−	2.31370i	−0.0219317	−	0.0904037i
$656$	0.531998	−	0.507259i	0.0207710	−	0.0198051i
$657$	−3.66227	−	8.01926i	−0.142879	−	0.312861i
$658$	−1.98731	+	2.45905i	−0.0774736	+	0.0958636i
$659$	−17.3228	+	19.9916i	−0.674801	+	0.778761i	−0.985119	−	0.171871i	$-0.945019\pi$
$659$	−17.3228	+	19.9916i	−0.674801	+	0.778761i	0.310319	+	0.950633i	$0.399564\pi$
$660$	−0.361336	−	0.507426i	−0.0140650	−	0.0197515i
$661$	−0.768552	+	16.1339i	−0.0298932	+	0.627536i	0.933360	+	0.358941i	$0.116862\pi$
$661$	−0.768552	+	16.1339i	−0.0298932	+	0.627536i	−0.963253	+	0.268595i	$0.913441\pi$
$662$	−20.5490	+	16.1599i	−0.798658	+	0.628071i
$663$	−0.318305	−	6.68205i	−0.0123620	−	0.259509i
$664$	23.3353	+	26.9303i	0.905584	+	1.04510i
$665$	−21.5217	−	5.52523i	−0.834577	−	0.214259i
$666$	−2.19095			−0.0848975
$667$	−5.79475	−	0.569780i	−0.224373	−	0.0220620i
$668$	11.3136	+	19.5957i	0.437735	+	0.758180i
$669$	4.36254	+	4.15967i	0.168666	+	0.160822i
$670$	−4.89299	+	0.943046i	−0.189033	+	0.0364330i
$671$	−2.28265	+	1.46697i	−0.0881206	+	0.0566317i
$672$	15.3152	−	1.99446i	0.590798	−	0.0769381i
$673$	−8.52921	−	5.48139i	−0.328777	−	0.211292i	0.365830	−	0.930682i	$-0.380785\pi$
$673$	−8.52921	−	5.48139i	−0.328777	−	0.211292i	−0.694607	+	0.719390i	$0.744422\pi$
$674$	0.471438	+	0.662042i	0.0181591	+	0.0255009i
$675$	0.358806	+	0.0691542i	0.0138104	+	0.00266175i
$676$	15.5218	−	6.21400i	0.596993	−	0.239000i
$677$	−32.2784	−	3.08221i	−1.24056	−	0.118459i	−0.545932	−	0.837829i	$-0.683824\pi$
$677$	−32.2784	−	3.08221i	−1.24056	−	0.118459i	−0.694627	+	0.719370i	$0.744430\pi$
$678$	5.95833	+	1.74952i	0.228828	+	0.0671901i
$679$	22.1379	−	5.05980i	0.849576	−	0.194177i
$680$	19.6058	+	42.9306i	0.751847	+	1.64631i
$681$	11.4754	+	9.02433i	0.439737	+	0.345813i
$682$	−0.230077	−	0.0443437i	−0.00881011	−	0.00169801i
$683$	−9.56875	+	0.913705i	−0.366138	+	0.0349620i	−0.276504	−	0.961013i	$-0.589176\pi$
$683$	−9.56875	+	0.913705i	−0.366138	+	0.0349620i	−0.0896343	+	0.995975i	$0.528570\pi$
$684$	4.40675	−	2.27184i	0.168496	−	0.0868660i
$685$	−1.27377	−	8.85926i	−0.0486682	−	0.338495i
$686$	14.7293	−	0.113366i	0.562368	−	0.00432832i
$687$	13.7551	+	15.8742i	0.524788	+	0.605638i
$688$	−0.254322	+	1.04833i	−0.00969595	+	0.0399673i
$689$	4.65203	+	8.05755i	0.177228	+	0.306968i
$690$	−7.84158	−	4.07057i	−0.298524	−	0.154964i
$691$	−10.3723	+	17.9653i	−0.394580	+	0.683433i	−0.993048	−	0.117714i	$-0.962443\pi$
$691$	−10.3723	+	17.9653i	−0.394580	+	0.683433i	0.598467	+	0.801147i	$0.295777\pi$
$692$	−16.5578	+	4.86181i	−0.629433	+	0.184818i
$693$	0.489405	+	0.176708i	0.0185909	+	0.00671259i
$694$	−4.01114	+	2.57781i	−0.152261	+	0.0978522i
$695$	14.4223	+	5.77383i	0.547070	+	0.219014i
$696$	−0.154722	+	3.24801i	−0.00586471	+	0.123115i
$697$	−9.20440	+	0.878914i	−0.348642	+	0.0332912i
$698$	1.26315	+	3.64963i	0.0478109	+	0.138140i
$699$	−1.15257	+	8.01628i	−0.0435941	+	0.303203i
$700$	−1.20975	+	0.533145i	−0.0457244	+	0.0201510i
$701$	17.4067	+	5.11108i	0.657443	+	0.193043i	0.593404	−	0.804905i	$-0.297784\pi$
$701$	17.4067	+	5.11108i	0.657443	+	0.193043i	0.0640390	+	0.997947i	$0.479602\pi$
$702$	0.506149	−	0.482612i	0.0191034	−	0.0182150i
$703$	5.79350	−	8.13584i	0.218506	−	0.306849i
$704$	0.626817	−	0.250940i	0.0236240	−	0.00945764i
$705$	1.13831	+	3.28894i	0.0428714	+	0.123869i
$706$	−5.49163	+	12.0250i	−0.206680	+	0.452566i
$707$	11.5072	+	23.0692i	0.432773	+	0.867606i
$708$	1.26433	+	8.79363i	0.0475165	+	0.330485i
$709$	1.51539	+	31.8120i	0.0569117	+	1.19472i	0.829015	+	0.559227i	$0.188902\pi$
$709$	1.51539	+	31.8120i	0.0569117	+	1.19472i	−0.772103	+	0.635497i	$0.780795\pi$
$710$	0.522018	−	1.50827i	0.0195910	−	0.0566044i
$711$	−1.84073	−	1.75513i	−0.0690327	−	0.0658225i
$712$	−10.6892	+	18.5142i	−0.400593	+	0.693848i
$713$	6.89888	−	2.00464i	0.258365	−	0.0750742i
$714$	−13.7560	−	8.18790i	−0.514806	−	0.306424i
$715$	0.384347	−	0.112854i	0.0143738	−	0.00422052i
$716$	0.620635	−	0.119618i	0.0231942	−	0.00447032i
$717$	−23.8609	−	12.3011i	−0.891101	−	0.459395i
$718$	12.6705	−	9.96417i	0.472858	−	0.371859i
$719$	−17.0359	+	8.78259i	−0.635330	+	0.327535i	−0.745627	−	0.666363i	$-0.767850\pi$
$719$	−17.0359	+	8.78259i	−0.635330	+	0.327535i	0.110297	+	0.993899i	$0.464820\pi$
$720$	0.581968	−	1.27433i	0.0216887	−	0.0474916i
$721$	37.7163	+	33.5700i	1.40463	+	1.25021i
$722$	−0.662667	+	4.60895i	−0.0246619	+	0.171527i
$723$	15.4461	+	1.47492i	0.574446	+	0.0548530i
$724$	3.41899	+	14.0933i	0.127066	+	0.523772i
$725$	−0.104594	−	0.431143i	−0.00388453	−	0.0160123i
$726$	−8.67842	−	0.828688i	−0.322086	−	0.0307555i
$727$	5.04150	−	35.0644i	0.186979	−	1.30047i	−0.652797	−	0.757533i	$-0.726405\pi$
$727$	5.04150	−	35.0644i	0.186979	−	1.30047i	0.839776	−	0.542933i	$-0.182686\pi$
$728$	−1.26047	+	6.10205i	−0.0467163	+	0.226157i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−14.4358	+	7.44215i	−0.534292	+	0.275446i
$731$	10.6661	−	8.38788i	0.394498	−	0.310237i
$732$	−16.7693	−	8.64517i	−0.619811	−	0.319535i
$733$	−1.32440	+	0.255257i	−0.0489178	+	0.00942813i	−0.213651	−	0.976910i	$-0.568536\pi$
$733$	−1.32440	+	0.255257i	−0.0489178	+	0.00942813i	0.164734	+	0.986338i	$0.447324\pi$
$734$	15.4824	−	4.54603i	0.571465	−	0.167797i
$735$	8.47781	−	13.8214i	0.312709	−	0.509811i
$736$	−18.3927	+	21.1061i	−0.677963	+	0.777980i
$737$	−0.265977	+	0.460685i	−0.00979737	+	0.0169695i
$738$	−0.699589	−	0.667057i	−0.0257522	−	0.0245547i
$739$	−10.6388	+	30.7387i	−0.391353	+	1.13074i	0.561544	+	0.827447i	$0.310208\pi$
$739$	−10.6388	+	30.7387i	−0.391353	+	1.13074i	−0.952897	+	0.303294i	$0.901914\pi$
$740$	−0.415181	−	8.71572i	−0.0152624	−	0.320396i
$741$	0.453720	+	3.15569i	0.0166678	+	0.115927i
$742$	22.2235	+	1.35511i	0.815851	+	0.0497477i
$743$	9.06072	−	19.8402i	0.332406	−	0.727867i	−0.667454	−	0.744651i	$-0.732616\pi$
$743$	9.06072	−	19.8402i	0.332406	−	0.727867i	0.999859	+	0.0167847i	$0.00534299\pi$
$744$	−1.31221	−	3.79138i	−0.0481079	−	0.138999i
$745$	−11.0804	+	4.43593i	−0.405955	+	0.162520i
$746$	14.2233	−	19.9738i	0.520751	−	0.731292i
$747$	−9.62927	+	9.18149i	−0.352317	+	0.335933i
$748$	1.96306	+	0.576405i	0.0717764	+	0.0210755i
$749$	−22.0376	+	9.71210i	−0.805237	+	0.354873i
$750$	−1.21510	+	8.45120i	−0.0443691	+	0.308594i
$751$	9.38197	+	27.1074i	0.342353	+	0.989164i	0.976419	+	0.215885i	$0.0692636\pi$
$751$	9.38197	+	27.1074i	0.342353	+	0.989164i	−0.634066	+	0.773279i	$0.718615\pi$
$752$	0.904622	−	0.0863810i	0.0329882	−	0.00314999i
$753$	0.633364	−	13.2960i	0.0230811	−	0.484532i
$754$	−0.788278	−	0.315579i	−0.0287074	−	0.0114927i
$755$	−20.6292	+	13.2576i	−0.750773	+	0.482492i
$756$	0.637385	+	3.56134i	0.0231815	+	0.129525i
$757$	29.7137	−	8.72473i	1.07996	−	0.317106i	0.307099	−	0.951678i	$-0.400642\pi$
$757$	29.7137	−	8.72473i	1.07996	−	0.317106i	0.772864	+	0.634572i	$0.218823\pi$
$758$	12.7981	−	22.1669i	0.464847	−	0.805139i
$759$	−0.876598	+	0.348080i	−0.0318185	+	0.0126345i
$760$	−11.2462	−	19.4791i	−0.407944	−	0.706580i
$761$	6.37126	−	26.2627i	0.230958	−	0.952021i	−0.731770	−	0.681551i	$-0.761306\pi$
$761$	6.37126	−	26.2627i	0.230958	−	0.952021i	0.962728	−	0.270470i	$-0.0871792\pi$
$762$	9.65124	+	11.1381i	0.349628	+	0.403492i
$763$	−40.6172	+	1.39367i	−1.47044	+	0.0504541i
$764$	1.09323	+	7.60356i	0.0395516	+	0.275087i
$765$	−15.6630	+	8.07482i	−0.566295	+	0.291946i
$766$	−25.1892	+	2.40528i	−0.910123	+	0.0869062i
$767$	−5.60960	−	1.08116i	−0.202551	−	0.0390385i
$768$	10.9891	+	8.64194i	0.396536	+	0.311839i
$769$	−5.89285	−	12.9036i	−0.212502	−	0.465314i	0.773125	−	0.634254i	$-0.218693\pi$
$769$	−5.89285	−	12.9036i	−0.212502	−	0.465314i	−0.985626	+	0.168940i	$0.945965\pi$
$770$	0.282273	−	0.916077i	0.0101724	−	0.0330131i
$771$	−10.9725	−	3.22183i	−0.395166	−	0.116031i
$772$	−0.0891389	−	0.00851173i	−0.00320818	−	0.000306344i
$773$	−1.54297	+	0.617711i	−0.0554967	+	0.0222175i	−0.399245	−	0.916844i	$-0.630728\pi$
$773$	−1.54297	+	0.617711i	−0.0554967	+	0.0222175i	0.343748	+	0.939062i	$0.388303\pi$
$774$	1.39293	+	0.268465i	0.0500679	+	0.00964979i
$775$	0.317516	+	0.445889i	0.0114055	+	0.0160168i
$776$	19.3384	+	12.4281i	0.694210	+	0.446142i
$777$	4.42879	+	5.78849i	0.158882	+	0.207661i
$778$	18.8375	−	12.1061i	0.675357	−	0.434025i
$779$	4.32696	−	0.833952i	0.155029	−	0.0298794i
$780$	2.01577	+	1.92204i	0.0721763	+	0.0688200i
$781$	−0.0851916	−	0.147556i	−0.00304840	−	0.00527998i
$782$	28.5087	−	5.41149i	1.01947	−	0.193515i
$783$	−1.21412			−0.0433889
$784$	−2.98523	−	3.00201i	−0.106615	−	0.107215i
$785$	−31.9934	−	36.9224i	−1.14189	−	1.31782i
$786$	0.0388968	+	0.816544i	0.00138740	+	0.0291252i
$787$	−15.9211	+	12.5205i	−0.567528	+	0.446309i	−0.860238	−	0.509892i	$-0.829685\pi$
$787$	−15.9211	+	12.5205i	−0.567528	+	0.446309i	0.292711	+	0.956201i	$0.405443\pi$
$788$	0.0848014	−	1.78020i	0.00302093	−	0.0634170i
$789$	−10.1669	−	14.2774i	−0.361950	−	0.508287i
$790$	−3.06838	+	3.54110i	−0.109168	+	0.125987i
$791$	−7.42196	−	19.2784i	−0.263894	−	0.685462i
$792$	0.218807	+	0.479120i	0.00777496	+	0.0170248i
$793$	8.78037	−	8.37206i	0.311800	−	0.297301i
$794$	−0.663290	−	2.73412i	−0.0235393	−	0.0970302i
$795$	14.2165	−	19.9643i	0.504208	−	0.708061i
$796$	−19.4866	−	15.3244i	−0.690683	−	0.543159i
$797$	−28.5683	+	32.9696i	−1.01194	+	1.16784i	−0.0261869	+	0.999657i	$0.508336\pi$
$797$	−28.5683	+	32.9696i	−1.01194	+	1.16784i	−0.985755	+	0.168186i	$0.946209\pi$
$798$	6.89708	+	3.26135i	0.244154	+	0.115451i
$799$	−9.61614	−	6.17992i	−0.340194	−	0.218630i
$800$	−1.98028	−	0.792784i	−0.0700135	−	0.0280292i
$801$	−7.09489	−	3.65767i	−0.250686	−	0.129237i
$802$	2.37719	−	6.86843i	0.0839414	−	0.242533i
$803$	−0.408758	+	1.68492i	−0.0144247	+	0.0594596i
$804$	−3.69875			−0.130445
$805$	5.09655	+	28.9457i	0.179630	+	1.02020i
$806$	1.04765			0.0369018
$807$	5.19792	−	21.4261i	0.182975	−	0.754235i
$808$	−8.53531	+	24.6612i	−0.300271	+	0.867577i
$809$	−6.69358	−	3.45078i	−0.235334	−	0.121323i	0.336527	−	0.941674i	$-0.390748\pi$
$809$	−6.69358	−	3.45078i	−0.235334	−	0.121323i	−0.571860	+	0.820351i	$0.693778\pi$
$810$	−1.71029	−	0.684697i	−0.0600935	−	0.0240578i
$811$	10.9131	+	7.01340i	0.383209	+	0.246274i	0.718036	−	0.696006i	$-0.245041\pi$
$811$	10.9131	+	7.01340i	0.383209	+	0.246274i	−0.334827	+	0.942280i	$0.608678\pi$
$812$	3.61166	−	2.50013i	0.126744	−	0.0877373i
$813$	−13.3585	+	15.4166i	−0.468505	+	0.540683i
$814$	0.338698	+	0.266355i	0.0118714	+	0.00933575i
$815$	19.0445	−	26.7443i	0.667101	−	0.936812i
$816$	1.08476	+	4.47145i	0.0379743	+	0.156532i
$817$	−4.68023	+	4.46259i	−0.163740	+	0.156126i
$818$	−4.24881	−	9.30360i	−0.148556	−	0.325293i
$819$	−2.29820	−	0.361693i	−0.0803055	−	0.0126386i
$820$	2.52102	−	2.90941i	0.0880379	−	0.101601i
$821$	16.8135	+	23.6112i	0.586795	+	0.824038i	0.996088	−	0.0883650i	$-0.0281642\pi$
$821$	16.8135	+	23.6112i	0.586795	+	0.824038i	−0.409294	+	0.912403i	$0.634225\pi$
$822$	−0.146228	+	3.06970i	−0.00510028	+	0.107068i
$823$	40.9236	−	32.1827i	1.42651	−	1.12182i	0.453442	−	0.891286i	$-0.350196\pi$
$823$	40.9236	−	32.1827i	1.42651	−	1.12182i	0.973065	−	0.230531i	$-0.0740464\pi$
$824$	2.43202	+	51.0543i	0.0847233	+	1.77856i
$825$	−0.0470606	−	0.0543109i	−0.00163844	−	0.00189086i
$826$	−9.56479	+	9.76776i	−0.332802	+	0.339864i
$827$	22.8288			0.793835			0.396917	−	0.917854i	$-0.370080\pi$
$827$	22.8288			0.793835			0.396917	+	0.917854i	$0.370080\pi$
$828$	−5.14355	−	4.06840i	−0.178751	−	0.141387i
$829$	−3.92268	−	6.79429i	−0.136240	−	0.235975i	0.789830	−	0.613326i	$-0.210169\pi$
$829$	−3.92268	−	6.79429i	−0.136240	−	0.235975i	−0.926071	+	0.377350i	$0.876835\pi$
$830$	17.7396	+	16.9147i	0.615750	+	0.587116i
$831$	−4.12189	+	0.794429i	−0.142987	+	0.0275585i
$832$	−2.53962	+	1.63212i	−0.0880456	+	0.0565835i
$833$	6.17401	+	52.8945i	0.213917	+	1.83269i
$834$	−4.48734	−	2.88384i	−0.155384	−	0.0998592i
$835$	22.2327	+	31.2214i	0.769393	+	1.08046i
$836$	−0.957429	−	0.184529i	−0.0331134	−	0.00638208i
$837$	1.39071	−	0.556755i	0.0480699	−	0.0192443i
$838$	−19.5225	−	1.86418i	−0.674395	−	0.0643969i
$839$	−22.1742	−	6.51094i	−0.765539	−	0.224783i	−0.124426	−	0.992229i	$-0.539709\pi$
$839$	−22.1742	−	6.51094i	−0.765539	−	0.224783i	−0.641113	+	0.767446i	$0.721527\pi$
$840$	16.0008	−	3.65712i	0.552081	−	0.126182i
$841$	−11.4347	−	25.0385i	−0.394299	−	0.863395i
$842$	22.7952	+	17.9264i	0.785575	+	0.617783i
$843$	27.7230	+	5.34317i	0.954831	+	0.184029i
$844$	−12.6953	+	1.21225i	−0.436989	+	0.0417274i
$845$	25.1730	−	12.9776i	0.865977	−	0.446442i
$846$	−0.170068	−	1.18285i	−0.00584704	−	0.0406671i
$847$	15.3532	+	24.6035i	0.527542	+	0.845387i
$848$	−4.19069	−	4.83632i	−0.143909	−	0.166080i
$849$	6.92561	−	28.5478i	0.237686	−	0.979757i
$850$	1.10548	+	1.91474i	0.0379175	+	0.0656750i
$851$	−12.9655	−	2.53674i	−0.444453	−	0.0869582i
$852$	0.592350	−	1.02598i	0.0202936	−	0.0351495i
$853$	−10.3707	+	3.04510i	−0.355085	+	0.104262i	−0.454410	−	0.890793i	$-0.650150\pi$
$853$	−10.3707	+	3.04510i	−0.355085	+	0.104262i	0.0993249	+	0.995055i	$0.468332\pi$
$854$	−5.11472	−	28.5781i	−0.175022	−	0.977923i
$855$	7.06505	−	4.54043i	0.241620	−	0.155280i
$856$	−22.6322	−	9.06058i	−0.773554	−	0.309684i
$857$	2.26266	−	47.4991i	0.0772911	−	1.62254i	−0.544087	−	0.839029i	$-0.683124\pi$
$857$	2.26266	−	47.4991i	0.0772911	−	1.62254i	0.621378	−	0.783511i	$-0.286573\pi$
$858$	−0.136917	+	0.0130740i	−0.00467427	+	0.000446339i
$859$	−6.23394	−	18.0118i	−0.212699	−	0.614555i	0.787299	−	0.616572i	$-0.211479\pi$
$859$	−6.23394	−	18.0118i	−0.212699	−	0.614555i	−0.999998	+	0.00201741i	$0.999358\pi$
$860$	−0.804013	+	5.59203i	−0.0274166	+	0.190687i
$861$	−0.348213	+	3.19671i	−0.0118671	+	0.108944i
$862$	22.8113	+	6.69799i	0.776955	+	0.228135i
$863$	−5.51999	+	5.26330i	−0.187903	+	0.179165i	−0.778191	−	0.628028i	$-0.783862\pi$
$863$	−5.51999	+	5.26330i	−0.187903	+	0.179165i	0.590288	+	0.807192i	$0.299014\pi$
$864$	−3.38608	+	4.75509i	−0.115197	+	0.161771i
$865$	−27.1376	+	10.8643i	−0.922707	+	0.369396i
$866$	2.48705	+	7.18585i	0.0845133	+	0.244185i
$867$	16.9807	−	37.1825i	0.576695	−	1.26279i
$868$	−2.99050	+	4.51997i	−0.101504	+	0.153418i
$869$	0.0711852	+	0.495104i	0.00241479	+	0.0167953i
$870$	0.106427	+	2.23418i	0.00360821	+	0.0757457i
$871$	0.777917	−	2.24764i	0.0263587	−	0.0761585i
$872$	−29.7745	−	28.3900i	−1.00829	−	0.961405i
$873$	−4.29156	+	7.43321i	−0.145247	+	0.251576i
$874$	−13.2800	+	3.85883i	−0.449203	+	0.130527i
$875$	24.7843	−	13.8730i	0.837862	−	0.468993i
$876$	−11.5670	+	3.39638i	−0.390813	+	0.114753i
$877$	37.0216	−	7.13533i	1.25013	−	0.240943i	0.479111	−	0.877754i	$-0.340959\pi$
$877$	37.0216	−	7.13533i	1.25013	−	0.240943i	0.771019	+	0.636812i	$0.219747\pi$
$878$	−9.31810	−	4.80381i	−0.314471	−	0.162121i
$879$	1.11943	−	0.880328i	0.0377574	−	0.0296927i
$880$	−0.244888	+	0.126249i	−0.00825517	+	0.00425584i
$881$	3.55266	−	7.77924i	0.119692	−	0.262089i	−0.840297	−	0.542126i	$-0.817619\pi$
$881$	3.55266	−	7.77924i	0.119692	−	0.262089i	0.959989	+	0.280037i	$0.0903467\pi$
$882$	−3.75645	+	4.10904i	−0.126486	+	0.138359i
$883$	3.84836	−	26.7659i	0.129508	−	0.900745i	−0.816672	−	0.577102i	$-0.804183\pi$
$883$	3.84836	−	26.7659i	0.129508	−	0.900745i	0.946179	−	0.323643i	$-0.104908\pi$
$884$	−9.10629	−	0.869545i	−0.306278	−	0.0292460i
$885$	3.54789	+	14.6246i	0.119261	+	0.491601i
$886$	5.41981	+	22.3408i	0.182082	+	0.750553i
$887$	9.21752	+	0.880167i	0.309494	+	0.0295531i	0.248648	−	0.968594i	$-0.420014\pi$
$887$	9.21752	+	0.880167i	0.309494	+	0.0295531i	0.0608466	+	0.998147i	$0.480620\pi$
$888$	−1.04998	+	7.30280i	−0.0352352	+	0.245066i
$889$	9.91790	−	48.0133i	0.332636	−	1.61031i
$890$	−6.10881	+	13.3764i	−0.204768	+	0.448379i
$891$	−0.174804	+	0.0901176i	−0.00585614	+	0.00301905i
$892$	6.47922	−	5.09532i	0.216940	−	0.170604i
$893$	4.84207	+	2.49626i	0.162034	+	0.0835342i
$894$	4.02404	−	0.775571i	0.134584	−	0.0259390i
$895$	1.02728	−	0.301637i	0.0343382	−	0.0100826i
$896$	0.314762	−	23.6629i	0.0105154	−	0.790521i
$897$	3.55406	−	2.26996i	0.118666	−	0.0757916i
$898$	5.65446	−	9.79382i	0.188692	−	0.326824i
$899$	−1.31630	−	1.25509i	−0.0439010	−	0.0418596i
$900$	0.163429	−	0.472196i	0.00544762	−	0.0157399i
$901$	3.83014	+	80.4044i	0.127600	+	2.67866i
$902$	0.0270547	+	0.188170i	0.000900825	+	0.00626537i
$903$	−2.10639	−	4.22281i	−0.0700963	−	0.140526i
$904$	8.68692	−	19.0217i	0.288923	−	0.632653i
$905$	8.03449	+	23.2141i	0.267076	+	0.771664i
$906$	7.81668	−	3.12933i	0.259692	−	0.103965i
$907$	−25.7388	+	36.1450i	−0.854641	+	1.20018i	0.123523	+	0.992342i	$0.460581\pi$
$907$	−25.7388	+	36.1450i	−0.854641	+	1.20018i	−0.978164	+	0.207834i	$0.933359\pi$
$908$	14.4479	−	13.7760i	0.479470	−	0.457174i
$909$	−9.34919	−	2.74517i	−0.310093	−	0.0910515i
$910$	−0.464121	+	4.26077i	−0.0153855	+	0.141243i
$911$	4.89858	−	34.0704i	0.162297	−	1.12880i	−0.731992	−	0.681313i	$-0.761409\pi$
$911$	4.89858	−	34.0704i	0.162297	−	1.12880i	0.894289	−	0.447489i	$-0.147682\pi$
$912$	−0.717200	−	2.07221i	−0.0237489	−	0.0686179i
$913$	2.60479	−	0.248727i	0.0862060	−	0.00823167i
$914$	0.557180	−	11.6966i	0.0184299	−	0.386891i
$915$	−29.6691	−	11.8777i	−0.980830	−	0.392665i
$916$	24.1630	−	15.5286i	0.798368	−	0.513080i
$917$	2.07869	−	1.75333i	0.0686443	−	0.0579001i
$918$	5.80552	−	1.70465i	0.191611	−	0.0562620i
$919$	1.24301	−	2.15295i	0.0410030	−	0.0710193i	−0.844796	−	0.535089i	$-0.820278\pi$
$919$	1.24301	−	2.15295i	0.0410030	−	0.0710193i	0.885799	+	0.464070i	$0.153611\pi$
$920$	−17.3259	+	24.1865i	−0.571217	+	0.797407i
$921$	−10.4726	−	18.1391i	−0.345084	−	0.597703i
$922$	−4.96866	+	20.4811i	−0.163634	+	0.674509i
$923$	0.498882	+	0.575740i	0.0164209	+	0.0189507i
$924$	0.334421	−	0.628034i	0.0110017	−	0.0206608i
$925$	−0.143256	−	0.996369i	−0.00471024	−	0.0327604i
$926$	−23.1276	+	11.9231i	−0.760022	+	0.391818i
$927$	−18.9978	+	1.81407i	−0.623971	+	0.0595820i
$928$	6.95932	+	1.34130i	0.228451	+	0.0440303i
$929$	4.78836	+	3.76561i	0.157101	+	0.123546i	0.693615	−	0.720346i	$-0.256017\pi$
$929$	4.78836	+	3.76561i	0.157101	+	0.123546i	−0.536514	+	0.843891i	$0.680259\pi$
$930$	−1.14643	−	2.51033i	−0.0375930	−	0.0823171i
$931$	−5.32531	−	24.8146i	−0.174530	−	0.813267i
$932$	10.6260	+	3.12006i	0.348065	+	0.102201i
$933$	−18.0209	−	1.72079i	−0.589978	−	0.0563361i
$934$	8.63899	−	3.45853i	0.282676	−	0.113167i
$935$	3.40300	+	0.655874i	0.111290	+	0.0214494i
$936$	−1.36606	−	1.91837i	−0.0446512	−	0.0627038i
$937$	−51.1270	−	32.8573i	−1.67025	−	1.07340i	−0.900275	−	0.435321i	$-0.856635\pi$
$937$	−51.1270	−	32.8573i	−1.67025	−	1.07340i	−0.769970	−	0.638080i	$-0.779729\pi$
$938$	−3.45855	−	4.52038i	−0.112926	−	0.147596i
$939$	−7.96118	+	5.11634i	−0.259803	+	0.166965i
$940$	4.67320	−	0.900686i	0.152423	−	0.0293771i
$941$	−13.7689	−	13.1286i	−0.448853	−	0.427981i	0.431635	−	0.902048i	$-0.357937\pi$
$941$	−13.7689	−	13.1286i	−0.448853	−	0.427981i	−0.880489	+	0.474067i	$0.842785\pi$
$942$	8.38742	+	14.5274i	0.273277	+	0.473330i
$943$	−3.36767	−	4.75749i	−0.109667	−	0.154925i
$944$	3.92931			0.127888
$945$	1.64822	+	5.90265i	0.0536166	+	0.192013i
$946$	−0.182695	−	0.210842i	−0.00593994	−	0.00685506i
$947$	−2.44820	−	51.3941i	−0.0795559	−	1.67008i	−0.587903	−	0.808931i	$-0.700046\pi$
$947$	−2.44820	−	51.3941i	−0.0795559	−	1.67008i	0.508348	−	0.861152i	$-0.330257\pi$
$948$	−2.73384	+	2.14991i	−0.0887909	+	0.0698260i
$949$	0.368860	−	7.74332i	0.0119737	−	0.251359i
$950$	−0.611203	−	0.858315i	−0.0198301	−	0.0278474i
$951$	2.03181	−	2.34483i	0.0658859	−	0.0760364i
$952$	−33.8841	+	41.9272i	−1.09819	+	1.35887i
$953$	21.0487	+	46.0903i	0.681835	+	1.49301i	0.860687	+	0.509135i	$0.170034\pi$
$953$	21.0487	+	46.0903i	0.681835	+	1.49301i	−0.178852	+	0.983876i	$0.557238\pi$
$954$	−6.09044	+	5.80722i	−0.197185	+	0.188016i
$955$	3.06775	+	12.6454i	0.0992699	+	0.409196i
$956$	−21.2935	+	29.9025i	−0.688680	+	0.967116i
$957$	0.187690	+	0.147601i	0.00606715	+	0.00477126i
$958$	8.55915	−	9.87778i	0.276534	−	0.319137i
$959$	8.40574	−	5.81877i	0.271435	−	0.187898i
$960$	6.68990	+	4.29934i	0.215916	+	0.138761i
$961$	−26.6961	−	10.6875i	−0.861165	−	0.344758i
$962$	−1.71240	−	0.882802i	−0.0552099	−	0.0284627i
$963$	2.97712	−	8.60182i	0.0959363	−	0.277190i
$964$	5.00228	−	20.6197i	0.161113	−	0.664116i
$965$	−0.151680			−0.00488276
$966$	0.162602	−	10.0903i	0.00523164	−	0.324651i
$967$	−33.4653			−1.07617			−0.538086	−	0.842890i	$-0.680852\pi$
$967$	−33.4653			−1.07617			−0.538086	+	0.842890i	$0.680852\pi$
$968$	−6.92118	+	28.5295i	−0.222455	+	0.916973i
$969$	−9.02144	+	26.0657i	−0.289810	+	0.837352i
$970$	14.0545	+	7.24562i	0.451264	+	0.232643i
$971$	−6.22792	−	2.49328i	−0.199863	−	0.0800132i	0.269571	−	0.962980i	$-0.413118\pi$
$971$	−6.22792	−	2.49328i	−0.199863	−	0.0800132i	−0.469435	+	0.882967i	$0.655542\pi$
$972$	−1.15037	−	0.739298i	−0.0368981	−	0.0237130i
$973$	1.45162	+	17.6850i	0.0465369	+	0.566955i
$974$	13.1735	−	15.2030i	0.422105	−	0.487135i
$975$	0.252570	+	0.198624i	0.00808873	+	0.00636105i
$976$	−4.84026	+	6.79720i	−0.154933	+	0.217573i
$977$	11.2829	+	46.5087i	0.360971	+	1.48794i	0.805725	+	0.592290i	$0.201776\pi$
$977$	11.2829	+	46.5087i	0.360971	+	1.48794i	−0.444753	+	0.895653i	$0.646709\pi$
$978$	−8.15879	+	7.77939i	−0.260889	+	0.248757i
$979$	0.652132	+	1.42797i	0.0208422	+	0.0456381i
$980$	−17.0578	−	14.1647i	−0.544893	−	0.452475i
$981$	10.0592	−	11.6090i	0.321167	−	0.370647i
$982$	−5.49709	−	7.71959i	−0.175419	−	0.246342i
$983$	1.15347	−	24.2143i	0.0367900	−	0.772316i	−0.902810	−	0.430040i	$-0.858499\pi$
$983$	1.15347	−	24.2143i	0.0367900	−	0.772316i	0.939600	−	0.342276i	$-0.111198\pi$
$984$	−2.55868	+	2.01217i	−0.0815679	+	0.0641457i
$985$	−0.143646	−	3.01550i	−0.00457695	−	0.0960820i
$986$	−4.81070	−	5.55184i	−0.153204	−	0.176807i
$987$	−2.78131	+	2.84033i	−0.0885300	+	0.0904087i
$988$	4.35962			0.138698
$989$	7.93221	+	3.20149i	0.252230	+	0.101801i
$990$	0.181155	+	0.313769i	0.00575747	+	0.00997223i
$991$	20.3457	+	19.3996i	0.646304	+	0.616249i	0.940621	−	0.339458i	$-0.110244\pi$
$991$	20.3457	+	19.3996i	0.646304	+	0.616249i	−0.294317	+	0.955708i	$0.595092\pi$
$992$	−8.58663	+	1.65494i	−0.272626	+	0.0525443i
$993$	−27.6513	+	17.7704i	−0.877489	+	0.563928i
$994$	1.80777	−	0.235421i	0.0573390	−	0.00746710i
$995$	−35.3265	−	22.7030i	−1.11993	−	0.719733i
$996$	10.5535	+	14.8203i	0.334400	+	0.469599i
$997$	41.2521	+	7.95069i	1.30647	+	0.251801i	0.794532	−	0.607223i	$-0.207716\pi$
$997$	41.2521	+	7.95069i	1.30647	+	0.251801i	0.511936	+	0.859024i	$0.328929\pi$
$998$	0.717817	−	0.287371i	0.0227221	−	0.00909656i
$999$	−2.74229	−	0.261856i	−0.0867621	−	0.00828477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.b.331.6	yes	320
7.4	even	3	inner	483.2.y.b.193.6	✓	320
23.18	even	11	inner	483.2.y.b.478.6	yes	320
161.18	even	33	inner	483.2.y.b.340.6	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.b.193.6	✓	320	7.4	even	3	inner
483.2.y.b.331.6	yes	320	1.1	even	1	trivial
483.2.y.b.340.6	yes	320	161.18	even	33	inner
483.2.y.b.478.6	yes	320	23.18	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.187507 + 0.772913i) q^{2} +(-0.327068 + 0.945001i) q^{3} +(1.21544 + 0.626600i) q^{4} +(2.15041 + 0.860895i) q^{5} +(-0.669076 - 0.429989i) q^{6} +(0.216441 + 2.63688i) q^{7} +(-1.75387 + 2.02408i) q^{8} +(-0.786053 - 0.618159i) q^{9} +O(q^{10})\)	\(q+(-0.187507 + 0.772913i) q^{2} +(-0.327068 + 0.945001i) q^{3} +(1.21544 + 0.626600i) q^{4} +(2.15041 + 0.860895i) q^{5} +(-0.669076 - 0.429989i) q^{6} +(0.216441 + 2.63688i) q^{7} +(-1.75387 + 2.02408i) q^{8} +(-0.786053 - 0.618159i) q^{9} +(-1.06861 + 1.50066i) q^{10} +(0.0463658 + 0.191122i) q^{11} +(-0.989668 + 0.943646i) q^{12} +(-0.365286 - 0.799865i) q^{13} +(-2.07867 - 0.327143i) q^{14} +(-1.51688 + 1.75057i) q^{15} +(0.350821 + 0.492660i) q^{16} +(0.361987 - 7.59904i) q^{17} +(0.625173 - 0.491642i) q^{18} +(0.172516 + 3.62155i) q^{19} +(2.07425 + 2.39381i) q^{20} +(-2.56265 - 0.657903i) q^{21} -0.156415 q^{22} +(4.26887 - 2.18558i) q^{23} +(-1.33912 - 2.31942i) q^{24} +(0.264459 + 0.252161i) q^{25} +(0.686720 - 0.132354i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-1.38920 + 3.34058i) q^{28} +(-1.02138 - 0.656400i) q^{29} +(-1.06861 - 1.50066i) q^{30} +(1.47094 + 0.283501i) q^{31} +(-5.41935 + 2.16958i) q^{32} +(-0.195775 - 0.0186943i) q^{33} +(5.80552 + 1.70465i) q^{34} +(-1.80464 + 5.85672i) q^{35} +(-0.568058 - 1.24387i) q^{36} +(-2.16539 - 1.70288i) q^{37} +(-2.83149 - 0.545725i) q^{38} +(0.875347 - 0.0835855i) q^{39} +(-5.51407 + 2.84270i) q^{40} +(-0.172968 - 1.20302i) q^{41} +(0.989015 - 1.85734i) q^{42} +(1.16802 + 1.34797i) q^{43} +(-0.0634027 + 0.261350i) q^{44} +(-1.15817 - 2.00601i) q^{45} +(0.888823 + 3.70927i) q^{46} +(0.751264 - 1.30123i) q^{47} +(-0.580306 + 0.170393i) q^{48} +(-6.90631 + 1.14146i) q^{49} +(-0.244487 + 0.157122i) q^{50} +(7.06271 + 2.82748i) q^{51} +(0.0572141 - 1.20107i) q^{52} +(-10.5330 + 1.00578i) q^{53} +(0.260128 + 0.751589i) q^{54} +(-0.0648307 + 0.450908i) q^{55} +(-5.71687 - 4.18666i) q^{56} +(-3.47879 - 1.02147i) q^{57} +(0.698855 - 0.666357i) q^{58} +(3.76852 - 5.29215i) q^{59} +(-2.94057 + 1.17723i) q^{60} +(4.51254 + 13.0381i) q^{61} +(-0.494933 + 1.08375i) q^{62} +(1.45988 - 2.20653i) q^{63} +(-0.488587 - 3.39819i) q^{64} +(-0.0969158 - 2.03451i) q^{65} +(0.0511583 - 0.147812i) q^{66} +(1.95760 + 1.86656i) q^{67} +(5.20153 - 9.00932i) q^{68} +(0.669166 + 4.74892i) q^{69} +(-4.18835 - 2.49300i) q^{70} +(-0.831265 + 0.244081i) q^{71} +(2.62984 - 0.506860i) q^{72} +(7.83592 + 4.03970i) q^{73} +(1.72220 - 1.35435i) q^{74} +(-0.324789 + 0.167440i) q^{75} +(-2.05958 + 4.50986i) q^{76} +(-0.493932 + 0.163628i) q^{77} +(-0.0995290 + 0.692239i) q^{78} +(2.53186 + 0.241763i) q^{79} +(0.330282 + 1.36144i) q^{80} +(0.235759 + 0.971812i) q^{81} +(0.962261 + 0.0918848i) q^{82} +(1.89350 - 13.1696i) q^{83} +(-2.70249 - 2.40539i) q^{84} +(7.32040 - 16.0294i) q^{85} +(-1.26087 + 0.650024i) q^{86} +(0.954359 - 0.750516i) q^{87} +(-0.468166 - 0.241356i) q^{88} +(7.83798 - 1.51065i) q^{89} +(1.76763 - 0.519023i) q^{90} +(2.03009 - 1.13634i) q^{91} +(6.55802 + 0.0184421i) q^{92} +(-0.749007 + 1.29732i) q^{93} +(0.864869 + 0.824651i) q^{94} +(-2.74680 + 7.93635i) q^{95} +(-0.277759 - 5.83089i) q^{96} +(-1.22151 - 8.49576i) q^{97} +(0.412729 - 5.55200i) q^{98} +(0.0816980 - 0.178894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 2 q^{11} + 18 q^{12} + 18 q^{14} - 18 q^{15} - 8 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 162 q^{20} - 4 q^{21} + 144 q^{22} - 26 q^{23} + 6 q^{24} - 8 q^{25} - 14 q^{26} - 32 q^{27} + 86 q^{28} - 74 q^{29} - 56 q^{31} - 28 q^{32} + 13 q^{33} + 40 q^{34} - 32 q^{35} - 14 q^{36} + 2 q^{37} - 39 q^{38} - 52 q^{40} + 60 q^{41} - 61 q^{42} + 16 q^{43} - 75 q^{44} - 2 q^{45} - 4 q^{46} - 40 q^{47} - 28 q^{48} - 100 q^{49} + 146 q^{50} - 18 q^{51} - 18 q^{52} + 34 q^{53} + 2 q^{54} + 36 q^{55} - 102 q^{56} + 28 q^{57} - 17 q^{58} - 102 q^{59} - 18 q^{60} - 18 q^{61} - 88 q^{62} + 2 q^{63} - 252 q^{64} - 78 q^{65} + 16 q^{66} + 12 q^{67} + 34 q^{68} + 8 q^{69} + 264 q^{70} + 160 q^{71} + 6 q^{72} - 8 q^{73} + 70 q^{74} + 14 q^{75} - 40 q^{76} - 90 q^{77} - 16 q^{78} + 26 q^{79} - 103 q^{80} + 16 q^{81} - 30 q^{82} - 80 q^{83} - 52 q^{84} - 128 q^{85} + 90 q^{86} + 4 q^{87} - 293 q^{88} - 36 q^{89} + 16 q^{91} - 174 q^{92} + 32 q^{93} + 57 q^{94} - 85 q^{95} - 50 q^{96} - 8 q^{97} - 193 q^{98} - 26 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 2 * q^11 + 18 * q^12 + 18 * q^14 - 18 * q^15 - 8 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 162 * q^20 - 4 * q^21 + 144 * q^22 - 26 * q^23 + 6 * q^24 - 8 * q^25 - 14 * q^26 - 32 * q^27 + 86 * q^28 - 74 * q^29 - 56 * q^31 - 28 * q^32 + 13 * q^33 + 40 * q^34 - 32 * q^35 - 14 * q^36 + 2 * q^37 - 39 * q^38 - 52 * q^40 + 60 * q^41 - 61 * q^42 + 16 * q^43 - 75 * q^44 - 2 * q^45 - 4 * q^46 - 40 * q^47 - 28 * q^48 - 100 * q^49 + 146 * q^50 - 18 * q^51 - 18 * q^52 + 34 * q^53 + 2 * q^54 + 36 * q^55 - 102 * q^56 + 28 * q^57 - 17 * q^58 - 102 * q^59 - 18 * q^60 - 18 * q^61 - 88 * q^62 + 2 * q^63 - 252 * q^64 - 78 * q^65 + 16 * q^66 + 12 * q^67 + 34 * q^68 + 8 * q^69 + 264 * q^70 + 160 * q^71 + 6 * q^72 - 8 * q^73 + 70 * q^74 + 14 * q^75 - 40 * q^76 - 90 * q^77 - 16 * q^78 + 26 * q^79 - 103 * q^80 + 16 * q^81 - 30 * q^82 - 80 * q^83 - 52 * q^84 - 128 * q^85 + 90 * q^86 + 4 * q^87 - 293 * q^88 - 36 * q^89 + 16 * q^91 - 174 * q^92 + 32 * q^93 + 57 * q^94 - 85 * q^95 - 50 * q^96 - 8 * q^97 - 193 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

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