LMFDB - Embedded newform 668.2.e.a.21.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			21.5
Character	$\chi$	$=$	668.21
Dual form			668.2.e.a.509.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +O(q^{10})$	\(q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +(3.97566 - 3.75611i) q^{11} +(0.411828 - 3.09047i) q^{13} +(1.00851 + 1.64924i) q^{15} +(-3.90237 + 5.87032i) q^{17} +(4.29909 + 0.993475i) q^{19} +(5.23254 - 5.33251i) q^{21} +(1.11800 + 5.29258i) q^{23} +(0.633303 - 3.68213i) q^{25} +(4.70218 + 2.29586i) q^{27} +(0.0318815 - 0.150927i) q^{29} +(9.99434 - 1.91437i) q^{31} +(-7.73247 + 5.35398i) q^{33} +(4.87020 - 0.369385i) q^{35} +(4.21572 - 1.31704i) q^{37} +(-1.50161 + 5.14674i) q^{39} +(8.59220 - 3.41695i) q^{41} +(-0.170641 - 0.0604876i) q^{43} +(0.0187143 + 0.0445825i) q^{45} +(0.0288402 - 0.114848i) q^{47} +(-3.75518 - 11.2663i) q^{49} +(8.15621 - 8.96697i) q^{51} +(0.180465 + 0.135337i) q^{53} +(-6.10906 - 0.696690i) q^{55} +(-7.05044 - 2.80382i) q^{57} +(0.557327 + 0.838386i) q^{59} +(-0.548065 - 0.702708i) q^{61} +(0.149493 - 0.112109i) q^{63} +(-2.95510 + 1.88479i) q^{65} +(1.41050 - 1.67380i) q^{67} +(-0.527839 - 9.28692i) q^{69} +(0.759892 + 8.00647i) q^{71} +(-0.447602 + 0.798365i) q^{73} +(-2.03154 + 6.09506i) q^{75} +(3.13877 + 23.5542i) q^{77} +(5.29749 + 0.200609i) q^{79} +(-7.29180 - 5.04886i) q^{81} +(2.99997 - 0.813991i) q^{83} +(7.87346 - 0.897906i) q^{85} +(-0.0933398 + 0.248295i) q^{87} +(-6.10917 + 9.99046i) q^{89} +(9.84619 + 9.30246i) q^{91} +(-17.4861 + 0.662173i) q^{93} +(-2.26032 - 4.41545i) q^{95} +(17.0247 + 3.26100i) q^{97} +(-0.211385 + 0.103210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{23}{83}\right)$	$1$

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			0
$2$		0			0
$3$	−1.69992	−	0.259356i	−0.981449	−	0.149739i	−0.359795	−	0.933031i	$-0.617153\pi$
$3$	−1.69992	−	0.259356i	−0.981449	−	0.149739i	−0.621654	+	0.783292i	$0.713539\pi$
$4$		0			0
$5$	−0.724427	−	0.859660i	−0.323973	−	0.384452i	0.578150	−	0.815931i	$-0.303775\pi$
$5$	−0.724427	−	0.859660i	−0.323973	−	0.384452i	−0.902123	+	0.431479i	$0.857992\pi$
$6$		0			0
$7$	−2.54038	+	3.52451i	−0.960172	+	1.33214i	−0.0169925	+	0.999856i	$0.505409\pi$
$7$	−2.54038	+	3.52451i	−0.960172	+	1.33214i	−0.943180	+	0.332283i	$0.892181\pi$
$8$		0			0
$9$	−0.0410528	−	0.0128253i	−0.0136843	−	0.00427512i
$10$		0			0
$11$	3.97566	−	3.75611i	1.19871	−	1.13251i	0.210789	−	0.977532i	$-0.432397\pi$
$11$	3.97566	−	3.75611i	1.19871	−	1.13251i	0.987918	−	0.154979i	$-0.0495310\pi$
$12$		0			0
$13$	0.411828	−	3.09047i	0.114221	−	0.857143i	−0.836690	−	0.547677i	$-0.815512\pi$
$13$	0.411828	−	3.09047i	0.114221	−	0.857143i	0.950910	−	0.309466i	$-0.100150\pi$
$14$		0			0
$15$	1.00851	+	1.64924i	0.260396	+	0.425831i
$16$		0			0
$17$	−3.90237	+	5.87032i	−0.946463	+	1.42376i	−0.0410853	+	0.999156i	$0.513082\pi$
$17$	−3.90237	+	5.87032i	−0.946463	+	1.42376i	−0.905378	+	0.424607i	$0.860412\pi$
$18$		0			0
$19$	4.29909	+	0.993475i	0.986278	+	0.227919i	0.687326	−	0.726349i	$-0.258784\pi$
$19$	4.29909	+	0.993475i	0.986278	+	0.227919i	0.298952	+	0.954268i	$0.403363\pi$
$20$		0			0
$21$	5.23254	−	5.33251i	1.14183	−	1.16365i
$22$		0			0
$23$	1.11800	+	5.29258i	0.233118	+	1.10358i	0.924527	+	0.381116i	$0.124460\pi$
$23$	1.11800	+	5.29258i	0.233118	+	1.10358i	−0.691409	+	0.722463i	$0.743010\pi$
$24$		0			0
$25$	0.633303	−	3.68213i	0.126661	−	0.736425i
$26$		0			0
$27$	4.70218	+	2.29586i	0.904935	+	0.441838i
$28$		0			0
$29$	0.0318815	−	0.150927i	0.00592025	−	0.0280264i	−0.975349	−	0.220669i	$-0.929176\pi$
$29$	0.0318815	−	0.150927i	0.00592025	−	0.0280264i	0.981269	+	0.192643i	$0.0617059\pi$
$30$		0			0
$31$	9.99434	−	1.91437i	1.79504	−	0.343830i	0.821124	−	0.570750i	$-0.193348\pi$
$31$	9.99434	−	1.91437i	1.79504	−	0.343830i	0.973913	+	0.226920i	$0.0728657\pi$
$32$		0			0
$33$	−7.73247	+	5.35398i	−1.34605	+	0.932008i
$34$		0			0
$35$	4.87020	−	0.369385i	0.823213	−	0.0624374i
$36$		0			0
$37$	4.21572	−	1.31704i	0.693059	−	0.216520i	0.0686776	−	0.997639i	$-0.478122\pi$
$37$	4.21572	−	1.31704i	0.693059	−	0.216520i	0.624382	+	0.781119i	$0.285351\pi$
$38$		0			0
$39$	−1.50161	+	5.14674i	−0.240450	+	0.824139i
$40$		0			0
$41$	8.59220	−	3.41695i	1.34188	−	0.533638i	0.415280	−	0.909694i	$-0.363684\pi$
$41$	8.59220	−	3.41695i	1.34188	−	0.533638i	0.926597	+	0.376056i	$0.122720\pi$
$42$		0			0
$43$	−0.170641	−	0.0604876i	−0.0260224	−	0.00922427i	0.321061	−	0.947058i	$-0.395961\pi$
$43$	−0.170641	−	0.0604876i	−0.0260224	−	0.00922427i	−0.347084	+	0.937834i	$0.612828\pi$
$44$		0			0
$45$	0.0187143	+	0.0445825i	0.00278976	+	0.00664596i
$46$		0			0
$47$	0.0288402	−	0.114848i	0.00420677	−	0.0167523i	−0.967748	−	0.251921i	$-0.918938\pi$
$47$	0.0288402	−	0.114848i	0.00420677	−	0.0167523i	0.971955	+	0.235169i	$0.0755642\pi$
$48$		0			0
$49$	−3.75518	−	11.2663i	−0.536454	−	1.60947i
$50$		0			0
$51$	8.15621	−	8.96697i	1.14210	−	1.25563i
$52$		0			0
$53$	0.180465	+	0.135337i	0.0247887	+	0.0185899i	0.612288	−	0.790634i	$-0.290249\pi$
$53$	0.180465	+	0.135337i	0.0247887	+	0.0185899i	−0.587500	+	0.809224i	$0.699888\pi$
$54$		0			0
$55$	−6.10906	−	0.696690i	−0.823745	−	0.0939416i
$56$		0			0
$57$	−7.05044	−	2.80382i	−0.933853	−	0.371375i
$58$		0			0
$59$	0.557327	+	0.838386i	0.0725579	+	0.109149i	0.867270	−	0.497837i	$-0.165872\pi$
$59$	0.557327	+	0.838386i	0.0725579	+	0.109149i	−0.794713	+	0.606986i	$0.792378\pi$
$60$		0			0
$61$	−0.548065	−	0.702708i	−0.0701725	−	0.0899726i	0.752158	−	0.658983i	$-0.229013\pi$
$61$	−0.548065	−	0.702708i	−0.0701725	−	0.0899726i	−0.822330	+	0.569010i	$0.807326\pi$
$62$		0			0
$63$	0.149493	−	0.112109i	0.0188343	−	0.0141245i
$64$		0			0
$65$	−2.95510	+	1.88479i	−0.366535	+	0.233779i
$66$		0			0
$67$	1.41050	−	1.67380i	0.172319	−	0.204488i	−0.671665	−	0.740855i	$-0.734421\pi$
$67$	1.41050	−	1.67380i	0.172319	−	0.204488i	0.843985	+	0.536367i	$0.180204\pi$
$68$		0			0
$69$	−0.527839	−	9.28692i	−0.0635444	−	1.11801i
$70$		0			0
$71$	0.759892	+	8.00647i	0.0901826	+	0.950194i	0.919937	+	0.392065i	$0.128239\pi$
$71$	0.759892	+	8.00647i	0.0901826	+	0.950194i	−0.829755	+	0.558128i	$0.811520\pi$
$72$		0			0
$73$	−0.447602	+	0.798365i	−0.0523879	+	0.0934415i	−0.897207	−	0.441611i	$-0.854407\pi$
$73$	−0.447602	+	0.798365i	−0.0523879	+	0.0934415i	0.844819	+	0.535053i	$0.179708\pi$
$74$		0			0
$75$	−2.03154	+	6.09506i	−0.234583	+	0.703797i
$76$		0			0
$77$	3.13877	+	23.5542i	0.357696	+	2.68425i
$78$		0			0
$79$	5.29749	+	0.200609i	0.596014	+	0.0225702i	0.334127	−	0.942528i	$-0.391559\pi$
$79$	5.29749	+	0.200609i	0.596014	+	0.0225702i	0.261888	+	0.965098i	$0.415655\pi$
$80$		0			0
$81$	−7.29180	−	5.04886i	−0.810200	−	0.560984i
$82$		0			0
$83$	2.99997	−	0.813991i	0.329290	−	0.0893471i	−0.0933808	−	0.995630i	$-0.529767\pi$
$83$	2.99997	−	0.813991i	0.329290	−	0.0893471i	0.422671	+	0.906283i	$0.361093\pi$
$84$		0			0
$85$	7.87346	−	0.897906i	0.853997	−	0.0973916i
$86$		0			0
$87$	−0.0933398	+	0.248295i	−0.0100071	+	0.0266200i
$88$		0			0
$89$	−6.10917	+	9.99046i	−0.647570	+	1.05899i	0.345150	+	0.938547i	$0.387828\pi$
$89$	−6.10917	+	9.99046i	−0.647570	+	1.05899i	−0.992721	+	0.120439i	$0.961570\pi$
$90$		0			0
$91$	9.84619	+	9.30246i	1.03216	+	0.975163i
$92$		0			0
$93$	−17.4861	+	0.662173i	−1.81322	+	0.0686642i
$94$		0			0
$95$	−2.26032	−	4.41545i	−0.231904	−	0.453016i
$96$		0			0
$97$	17.0247	+	3.26100i	1.72860	+	0.331104i	0.953650	−	0.300920i	$-0.0972936\pi$
$97$	17.0247	+	3.26100i	1.72860	+	0.331104i	0.774949	+	0.632024i	$0.217776\pi$
$98$		0			0
$99$	−0.211385	+	0.103210i	−0.0212450	+	0.0103730i
$100$		0			0
$101$	−5.24763	+	1.86015i	−0.522159	+	0.185092i	−0.582111	−	0.813110i	$-0.697773\pi$
$101$	−5.24763	+	1.86015i	−0.522159	+	0.185092i	0.0599514	+	0.998201i	$0.480905\pi$
$102$		0			0
$103$	−0.253172	+	13.3759i	−0.0249458	+	1.31797i	0.739447	+	0.673215i	$0.235087\pi$
$103$	−0.253172	+	13.3759i	−0.0249458	+	1.31797i	−0.764393	+	0.644751i	$0.776961\pi$
$104$		0			0
$105$	−8.37474	−	0.635190i	−0.817291	−	0.0619882i
$106$		0			0
$107$	−0.362987	−	19.1777i	−0.0350913	−	1.85398i	−0.392152	−	0.919900i	$-0.628269\pi$
$107$	−0.362987	−	19.1777i	−0.0350913	−	1.85398i	0.357061	−	0.934081i	$-0.383779\pi$
$108$		0			0
$109$	−5.98037	+	11.6824i	−0.572816	+	1.11897i	0.405931	+	0.913904i	$0.366947\pi$
$109$	−5.98037	+	11.6824i	−0.572816	+	1.11897i	−0.978747	+	0.205071i	$0.934258\pi$
$110$		0			0
$111$	−7.50796	+	1.14549i	−0.712624	+	0.108725i
$112$		0			0
$113$	−9.13471	−	7.99819i	−0.859321	−	0.752407i	0.111104	−	0.993809i	$-0.464561\pi$
$113$	−9.13471	−	7.99819i	−0.859321	−	0.752407i	−0.970425	+	0.241402i	$0.922393\pi$
$114$		0			0
$115$	3.73992	−	4.79518i	0.348749	−	0.447153i
$116$		0			0
$117$	−0.0565431	+	0.121591i	−0.00522741	+	0.0112411i
$118$		0			0
$119$	−10.7765	−	28.6668i	−0.987880	−	2.62788i
$120$		0			0
$121$	1.07329	−	18.8838i	0.0975722	−	1.71671i
$122$		0			0
$123$	−15.4923	+	3.58010i	−1.39689	+	0.322807i
$124$		0			0
$125$	−8.47423	+	4.96414i	−0.757958	+	0.444006i
$126$		0			0
$127$	−0.0565232	+	0.595546i	−0.00501562	+	0.0528462i	−0.997683	−	0.0680287i	$-0.978329\pi$
$127$	−0.0565232	+	0.595546i	−0.00501562	+	0.0528462i	0.992668	+	0.120875i	$0.0385700\pi$
$128$		0			0
$129$	0.274387	+	0.147081i	0.0241585	+	0.0129497i
$130$		0			0
$131$	−2.50237	−	2.75111i	−0.218633	−	0.240366i	0.620614	−	0.784116i	$-0.286883\pi$
$131$	−2.50237	−	2.75111i	−0.218633	−	0.240366i	−0.839247	+	0.543750i	$0.817004\pi$
$132$		0			0
$133$	−14.4228	+	12.6284i	−1.25062	+	1.09502i
$134$		0			0
$135$	−1.43273	−	5.70546i	−0.123310	−	0.491048i
$136$		0			0
$137$	−4.07494	−	13.9668i	−0.348145	−	1.19326i	−0.926126	−	0.377214i	$-0.876882\pi$
$137$	−4.07494	−	13.9668i	−0.348145	−	1.19326i	0.577981	−	0.816050i	$-0.303841\pi$
$138$		0			0
$139$	−12.7574	+	5.64142i	−1.08207	+	0.478499i	−0.867106	−	0.498124i	$-0.834023\pi$
$139$	−12.7574	+	5.64142i	−1.08207	+	0.478499i	−0.214961	+	0.976623i	$0.568962\pi$
$140$		0			0
$141$	−0.0788125	+	0.187753i	−0.00663721	+	0.0158116i
$142$		0			0
$143$	−9.97088	−	13.8335i	−0.833807	−	1.15682i
$144$		0			0
$145$	−0.152842	+	0.0819281i	−0.0126928	+	0.00680376i
$146$		0			0
$147$	3.46151	+	20.1258i	0.285500	+	1.65995i
$148$		0			0
$149$	14.0286	+	8.94759i	1.14927	+	0.733016i	0.968132	−	0.250442i	$-0.0805760\pi$
$149$	14.0286	+	8.94759i	1.14927	+	0.733016i	0.181139	+	0.983458i	$0.442022\pi$
$150$		0			0
$151$	2.42211	+	4.32019i	0.197108	+	0.351572i	0.952922	−	0.303214i	$-0.0980599\pi$
$151$	2.42211	+	4.32019i	0.197108	+	0.351572i	−0.755814	+	0.654786i	$0.772759\pi$
$152$		0			0
$153$	0.235492	−	0.190944i	0.0190384	−	0.0154369i
$154$		0			0
$155$	−8.88587	−	7.20492i	−0.713730	−	0.578713i
$156$		0			0
$157$	−4.93351	−	10.6091i	−0.393737	−	0.846695i	−0.998726	−	0.0504609i	$-0.983931\pi$
$157$	−4.93351	−	10.6091i	−0.393737	−	0.846695i	0.604989	−	0.796234i	$-0.293177\pi$
$158$		0			0
$159$	−0.271675	−	0.276866i	−0.0215452	−	0.0219569i
$160$		0			0
$161$	−21.4939	−	9.50477i	−1.69395	−	0.749081i
$162$		0			0
$163$	18.5886	+	10.8891i	1.45597	+	0.852899i	0.999325	−	0.0367480i	$-0.0116999\pi$
$163$	18.5886	+	10.8891i	1.45597	+	0.852899i	0.456650	+	0.889647i	$0.349049\pi$
$164$		0			0
$165$	10.2042	+	2.76874i	0.794397	+	0.215546i
$166$		0			0
$167$	−3.88125	+	12.3262i	−0.300340	+	0.953832i
$167$	−3.88125	+	12.3262i	−0.300340	+	0.953832i
$168$		0			0
$169$	3.16494	+	0.858752i	0.243457	+	0.0660578i
$170$		0			0
$171$	−0.163748	−	0.0959222i	−0.0125221	−	0.00733535i
$172$		0			0
$173$	5.91298	+	2.61477i	0.449556	+	0.198797i	0.616803	−	0.787118i	$-0.288428\pi$
$173$	5.91298	+	2.61477i	0.449556	+	0.198797i	−0.167247	+	0.985915i	$0.553488\pi$
$174$		0			0
$175$	11.3688	+	11.5861i	0.859404	+	0.875824i
$176$		0			0
$177$	−0.729971	−	1.56973i	−0.0548680	−	0.117989i
$178$		0			0
$179$	5.95683	+	4.82997i	0.445234	+	0.361009i	0.826007	−	0.563660i	$-0.190607\pi$
$179$	5.95683	+	4.82997i	0.445234	+	0.361009i	−0.380773	+	0.924669i	$0.624342\pi$
$180$		0			0
$181$	11.2305	−	9.10601i	0.834756	−	0.676844i	−0.113783	−	0.993506i	$-0.536297\pi$
$181$	11.2305	−	9.10601i	0.834756	−	0.676844i	0.948539	+	0.316661i	$0.102562\pi$
$182$		0			0
$183$	0.749414	+	1.33669i	0.0553983	+	0.0988111i
$184$		0			0
$185$	−4.18618	−	2.66999i	−0.307774	−	0.196301i
$186$		0			0
$187$	6.53510	+	37.9961i	0.477894	+	2.77855i
$188$		0			0
$189$	−20.0371	+	10.7405i	−1.45748	+	0.781258i
$190$		0			0
$191$	−3.81289	−	5.28999i	−0.275891	−	0.382770i	0.650392	−	0.759599i	$-0.274605\pi$
$191$	−3.81289	−	5.28999i	−0.275891	−	0.382770i	−0.926283	+	0.376829i	$0.877014\pi$
$192$		0			0
$193$	8.10430	−	19.3066i	0.583360	−	1.38972i	−0.314423	−	0.949283i	$-0.601811\pi$
$193$	8.10430	−	19.3066i	0.583360	−	1.38972i	0.897783	−	0.440439i	$-0.145177\pi$
$194$		0			0
$195$	5.51226	−	2.43757i	0.394741	−	0.174558i
$196$		0			0
$197$	−6.79435	−	23.2876i	−0.484077	−	1.65917i	−0.725095	−	0.688649i	$-0.758204\pi$
$197$	−6.79435	−	23.2876i	−0.484077	−	1.65917i	0.241017	−	0.970521i	$-0.422519\pi$
$198$		0			0
$199$	−2.13212	−	8.49061i	−0.151142	−	0.601883i	−0.997588	−	0.0694088i	$-0.977889\pi$
$199$	−2.13212	−	8.49061i	−0.151142	−	0.601883i	0.846446	−	0.532475i	$-0.178738\pi$
$200$		0			0
$201$	−2.83184	+	2.47951i	−0.199743	+	0.174891i
$202$		0			0
$203$	0.450952	+	0.495778i	0.0316506	+	0.0347968i
$204$		0			0
$205$	−9.16184	−	4.91105i	−0.639890	−	0.343002i
$206$		0			0
$207$	0.0219824	−	0.231614i	0.00152788	−	0.0160983i
$208$		0			0
$209$	20.8233	−	12.1981i	1.44038	−	0.843763i
$210$		0			0
$211$	−21.9127	+	5.06379i	−1.50853	+	0.348606i	−0.896791	−	0.442454i	$-0.854108\pi$
$211$	−21.9127	+	5.06379i	−1.50853	+	0.348606i	−0.611739	+	0.791060i	$0.709530\pi$
$212$		0			0
$213$	0.784772	−	13.8074i	0.0537717	−	0.946070i
$214$		0			0
$215$	0.0716178	+	0.190512i	0.00488429	+	0.0129928i
$216$		0			0
$217$	−18.6422	+	40.0883i	−1.26552	+	2.72137i
$218$		0			0
$219$	0.967948	−	1.24107i	0.0654079	−	0.0838636i
$220$		0			0
$221$	16.5350	+	14.4777i	1.11226	+	0.973877i
$222$		0			0
$223$	25.6470	−	3.91295i	1.71745	−	0.262031i	0.784006	−	0.620753i	$-0.213173\pi$
$223$	25.6470	−	3.91295i	1.71745	−	0.262031i	0.933444	+	0.358723i	$0.116788\pi$
$224$		0			0
$225$	−0.0732234	+	0.143039i	−0.00488156	+	0.00953594i
$226$		0			0
$227$	0.502403	+	26.5435i	0.0333457	+	1.76176i	0.489638	+	0.871926i	$0.337129\pi$
$227$	0.502403	+	26.5435i	0.0333457	+	1.76176i	−0.456293	+	0.889830i	$0.650823\pi$
$228$		0			0
$229$	19.3624	+	1.46856i	1.27950	+	0.0970451i	0.697762	−	0.716330i	$-0.254179\pi$
$229$	19.3624	+	1.46856i	1.27950	+	0.0970451i	0.581740	+	0.813375i	$0.302372\pi$
$230$		0			0
$231$	0.773270	−	40.8543i	0.0508774	−	2.68801i
$232$		0			0
$233$	6.76873	−	2.39934i	0.443434	−	0.157186i	−0.103012	−	0.994680i	$-0.532848\pi$
$233$	6.76873	−	2.39934i	0.443434	−	0.157186i	0.546446	+	0.837494i	$0.315980\pi$
$234$		0			0
$235$	−0.119623	+	0.0584063i	−0.00780335	+	0.00381001i
$236$		0			0
$237$	−8.95328	−	1.71495i	−0.581578	−	0.111398i
$238$		0			0
$239$	1.59414	+	3.11409i	0.103116	+	0.201434i	0.935988	−	0.352033i	$-0.114509\pi$
$239$	1.59414	+	3.11409i	0.103116	+	0.201434i	−0.832871	+	0.553467i	$0.813305\pi$
$240$		0			0
$241$	17.2838	−	0.654514i	1.11335	−	0.0421610i	0.525248	−	0.850949i	$-0.323972\pi$
$241$	17.2838	−	0.654514i	1.11335	−	0.0421610i	0.588100	+	0.808788i	$0.299876\pi$
$242$		0			0
$243$	−0.324872	−	0.306932i	−0.0208406	−	0.0196897i
$244$		0			0
$245$	−6.96486	+	11.3898i	−0.444969	+	0.727668i
$246$		0			0
$247$	4.84079	−	12.8771i	0.308012	−	0.819349i
$248$		0			0
$249$	−5.31082	+	0.605658i	−0.336560	+	0.0383820i
$250$		0			0
$251$	−3.56203	+	0.966496i	−0.224834	+	0.0610047i	−0.372499	−	0.928033i	$-0.621499\pi$
$251$	−3.56203	+	0.966496i	−0.224834	+	0.0610047i	0.147665	+	0.989037i	$0.452824\pi$
$252$		0			0
$253$	24.3243	+	16.8422i	1.52926	+	1.05886i
$254$		0			0
$255$	−13.6171	−	0.515662i	−0.852738	−	0.0322920i
$256$		0			0
$257$	2.08825	+	15.6708i	0.130261	+	0.977517i	0.927492	+	0.373842i	$0.121960\pi$
$257$	2.08825	+	15.6708i	0.130261	+	0.977517i	−0.797231	+	0.603674i	$0.793703\pi$
$258$		0			0
$259$	−6.06760	+	18.2041i	−0.377022	+	1.13115i
$260$		0			0
$261$	−0.00324451	+	0.00578707i	−0.000200830	+	0.000358211i
$262$		0			0
$263$	−2.44048	−	25.7137i	−0.150487	−	1.58558i	−0.677372	−	0.735640i	$-0.736881\pi$
$263$	−2.44048	−	25.7137i	−0.150487	−	1.58558i	0.526886	−	0.849936i	$-0.323360\pi$
$264$		0			0
$265$	−0.0143899	−	0.253180i	−0.000883968	−	0.0155527i
$266$		0			0
$267$	12.9762	−	15.3985i	0.794129	−	0.942375i
$268$		0			0
$269$	8.26750	−	5.27309i	0.504078	−	0.321506i	−0.261114	−	0.965308i	$-0.584090\pi$
$269$	8.26750	−	5.27309i	0.504078	−	0.321506i	0.765192	+	0.643802i	$0.222644\pi$
$270$		0			0
$271$	−11.7338	+	8.79958i	−0.712778	+	0.534536i	−0.893536	−	0.448991i	$-0.851783\pi$
$271$	−11.7338	+	8.79958i	−0.712778	+	0.534536i	0.180758	+	0.983528i	$0.442145\pi$
$272$		0			0
$273$	−14.3251	−	18.3671i	−0.866994	−	1.11163i
$274$		0			0
$275$	−11.3127	−	17.0176i	−0.682180	−	1.02620i
$276$		0			0
$277$	−2.26907	−	0.902366i	−0.136335	−	0.0542179i	0.300368	−	0.953823i	$-0.402890\pi$
$277$	−2.26907	−	0.902366i	−0.136335	−	0.0542179i	−0.436704	+	0.899605i	$0.643854\pi$
$278$		0			0
$279$	−0.434848	−	0.0495910i	−0.0260337	−	0.00296893i
$280$		0			0
$281$	3.68087	+	2.76041i	0.219582	+	0.164672i	0.704081	−	0.710120i	$-0.251359\pi$
$281$	3.68087	+	2.76041i	0.219582	+	0.164672i	−0.484499	+	0.874792i	$0.660998\pi$
$282$		0			0
$283$	20.1125	−	22.1117i	1.19556	−	1.31441i	0.258184	−	0.966096i	$-0.416876\pi$
$283$	20.1125	−	22.1117i	1.19556	−	1.31441i	0.937379	−	0.348310i	$-0.113244\pi$
$284$		0			0
$285$	2.69719	+	8.09214i	0.159768	+	0.479337i
$286$		0			0
$287$	−9.78437	+	38.9636i	−0.577553	+	2.29995i
$288$		0			0
$289$	−12.6523	−	30.1413i	−0.744256	−	1.77302i
$290$		0			0
$291$	−28.0949	−	9.95890i	−1.64695	−	0.583801i
$292$		0			0
$293$	3.39053	−	1.34835i	0.198077	−	0.0787713i	−0.268388	−	0.963311i	$-0.586491\pi$
$293$	3.39053	−	1.34835i	0.198077	−	0.0787713i	0.466465	+	0.884539i	$0.345527\pi$
$294$		0			0
$295$	0.316985	−	1.08646i	0.0184556	−	0.0632562i
$296$		0			0
$297$	27.3178	−	8.53438i	1.58514	−	0.495215i
$298$		0			0
$299$	16.8170	−	1.27550i	0.972552	−	0.0737641i
$300$		0			0
$301$	0.646680	−	0.447763i	0.0372740	−	0.0258086i
$302$		0			0
$303$	9.40300	−	1.80110i	0.540188	−	0.103470i
$304$		0			0
$305$	−0.207058	+	0.980210i	−0.0118561	+	0.0561267i
$306$		0			0
$307$	0.897746	+	0.438327i	0.0512371	+	0.0250167i	0.464189	−	0.885736i	$-0.346346\pi$
$307$	0.897746	+	0.438327i	0.0512371	+	0.0250167i	−0.412952	+	0.910753i	$0.635502\pi$
$308$		0			0
$309$	3.89949	−	22.6723i	0.221834	−	1.28978i
$310$		0			0
$311$	4.77983	+	22.6277i	0.271039	+	1.28310i	0.874235	+	0.485503i	$0.161364\pi$
$311$	4.77983	+	22.6277i	0.271039	+	1.28310i	−0.603196	+	0.797593i	$0.706106\pi$
$312$		0			0
$313$	8.25408	−	8.41178i	0.466548	−	0.475462i	−0.439739	−	0.898126i	$-0.644929\pi$
$313$	8.25408	−	8.41178i	0.466548	−	0.475462i	0.906287	+	0.422664i	$0.138905\pi$
$314$		0			0
$315$	−0.204672	−	0.0472977i	−0.0115320	−	0.00266492i
$316$		0			0
$317$	−4.14208	+	6.23091i	−0.232642	+	0.349963i	−0.930512	−	0.366262i	$-0.880637\pi$
$317$	−4.14208	+	6.23091i	−0.232642	+	0.349963i	0.697870	+	0.716225i	$0.254131\pi$
$318$		0			0
$319$	−0.440148	−	0.719784i	−0.0246436	−	0.0403002i
$320$		0			0
$321$	−4.35681	+	32.6947i	−0.243174	+	1.82484i
$322$		0			0
$323$	−22.6086	+	21.3601i	−1.25798	+	1.18851i
$324$		0			0
$325$	−11.1187	−	3.47361i	−0.616754	−	0.192681i
$326$		0			0
$327$	13.1961	−	18.3081i	0.729744	−	1.01244i
$328$		0			0
$329$	0.331518	+	0.393405i	0.0182772	+	0.0216891i
$330$		0			0
$331$	17.0057	+	2.59455i	0.934718	+	0.142610i	0.600263	−	0.799802i	$-0.295062\pi$
$331$	17.0057	+	2.59455i	0.934718	+	0.142610i	0.334454	+	0.942412i	$0.391448\pi$
$332$		0			0
$333$	−0.189958			−0.0104096
$334$		0			0
$335$	−2.46070			−0.134443
$336$		0			0
$337$	−24.1738	−	3.68819i	−1.31683	−	0.200909i	−0.545914	−	0.837841i	$-0.683817\pi$
$337$	−24.1738	−	3.68819i	−1.31683	−	0.200909i	−0.770919	+	0.636933i	$0.780203\pi$
$338$		0			0
$339$	13.4539	+	15.9654i	0.730715	+	0.867123i
$340$		0			0
$341$	32.5435	−	45.1507i	1.76233	−	2.44505i
$342$		0			0
$343$	20.2191	+	6.31669i	1.09173	+	0.341069i
$344$		0			0
$345$	−7.60121	+	7.18145i	−0.409236	+	0.386636i
$346$		0			0
$347$	1.62901	−	12.2245i	0.0874496	−	0.656246i	−0.891629	−	0.452766i	$-0.850437\pi$
$347$	1.62901	−	12.2245i	0.0874496	−	0.656246i	0.979079	−	0.203480i	$-0.0652253\pi$
$348$		0			0
$349$	12.4654	+	20.3850i	0.667259	+	1.09118i	0.989501	+	0.144527i	$0.0461661\pi$
$349$	12.4654	+	20.3850i	0.667259	+	1.09118i	−0.322241	+	0.946658i	$0.604436\pi$
$350$		0			0
$351$	9.03177	−	13.5865i	0.482080	−	0.725192i
$352$		0			0
$353$	−3.91764	−	0.905325i	−0.208515	−	0.0481856i	0.119606	−	0.992821i	$-0.461837\pi$
$353$	−3.91764	−	0.905325i	−0.208515	−	0.0481856i	−0.328121	+	0.944636i	$0.606415\pi$
$354$		0			0
$355$	6.33236	−	6.45335i	0.336087	−	0.342508i
$356$		0			0
$357$	10.8843	+	51.5261i	0.576057	+	2.72705i
$358$		0			0
$359$	−0.743703	+	4.32401i	−0.0392512	+	0.228213i	−0.998527	−	0.0542586i	$-0.982720\pi$
$359$	−0.743703	+	4.32401i	−0.0392512	+	0.228213i	0.959276	+	0.282471i	$0.0911542\pi$
$360$		0			0
$361$	0.421578	+	0.205837i	0.0221883	+	0.0108335i
$362$		0			0
$363$	−6.72214	+	31.8225i	−0.352821	+	1.67025i
$364$		0			0
$365$	1.01058	−	0.193571i	0.0528960	−	0.0101320i
$366$		0			0
$367$	−24.7729	+	17.1528i	−1.29313	+	0.895368i	−0.998190	−	0.0601460i	$-0.980843\pi$
$367$	−24.7729	+	17.1528i	−1.29313	+	0.895368i	−0.294945	+	0.955514i	$0.595301\pi$
$368$		0			0
$369$	−0.396557	+	0.0300773i	−0.0206439	+	0.00156576i
$370$		0			0
$371$	−0.935444	+	0.292243i	−0.0485658	+	0.0151725i
$372$		0			0
$373$	−6.93563	+	23.7718i	−0.359113	+	1.23086i	0.557194	+	0.830382i	$0.311878\pi$
$373$	−6.93563	+	23.7718i	−0.359113	+	1.23086i	−0.916308	+	0.400475i	$0.868845\pi$
$374$		0			0
$375$	15.6930	−	6.24079i	0.810382	−	0.322273i
$376$		0			0
$377$	−0.453306	−	0.160685i	−0.0233464	−	0.00827569i
$378$		0			0
$379$	−8.26649	−	19.6930i	−0.424621	−	1.01156i	−0.983269	−	0.182158i	$-0.941692\pi$
$379$	−8.26649	−	19.6930i	−0.424621	−	1.01156i	0.558648	−	0.829405i	$-0.311320\pi$
$380$		0			0
$381$	0.250543	−	0.997721i	0.0128357	−	0.0511148i
$382$		0			0
$383$	−0.851737	−	2.55539i	−0.0435217	−	0.130574i	0.924680	−	0.380745i	$-0.124332\pi$
$383$	−0.851737	−	2.55539i	−0.0435217	−	0.130574i	−0.968202	+	0.250171i	$0.919513\pi$
$384$		0			0
$385$	17.9748	−	19.7616i	0.916080	−	1.00714i
$386$		0			0
$387$	0.00622949	+	0.00467171i	0.000316663	+	0.000237476i
$388$		0			0
$389$	4.74278	+	0.540877i	0.240469	+	0.0274236i	0.232709	−	0.972546i	$-0.425241\pi$
$389$	4.74278	+	0.540877i	0.240469	+	0.0274236i	0.00775940	+	0.999970i	$0.497530\pi$
$390$		0			0
$391$	−35.4320	−	14.0906i	−1.79187	−	0.712592i
$392$		0			0
$393$	3.54031	+	5.32568i	0.178585	+	0.268645i
$394$		0			0
$395$	−3.66519	−	4.69937i	−0.184416	−	0.236451i
$396$		0			0
$397$	−9.11239	+	6.83369i	−0.457338	+	0.342973i	−0.803605	−	0.595163i	$-0.797088\pi$
$397$	−9.11239	+	6.83369i	−0.457338	+	0.342973i	0.346267	+	0.938136i	$0.387449\pi$
$398$		0			0
$399$	27.7929	−	17.7265i	1.39138	−	0.887437i
$400$		0			0
$401$	−19.3822	+	23.0004i	−0.967901	+	1.14859i	0.0209657	+	0.999780i	$0.493326\pi$
$401$	−19.3822	+	23.0004i	−0.967901	+	1.14859i	−0.988867	+	0.148805i	$0.952457\pi$
$402$		0			0
$403$	−1.80034	−	31.6756i	−0.0896815	−	1.57788i
$404$		0			0
$405$	0.942074	+	9.92600i	0.0468120	+	0.493227i
$406$		0			0
$407$	11.8133	−	21.0708i	0.585564	−	1.04444i
$408$		0			0
$409$	3.26876	−	9.80698i	0.161630	−	0.484924i	−0.836368	−	0.548168i	$-0.815325\pi$
$409$	3.26876	−	9.80698i	0.161630	−	0.484924i	0.997998	+	0.0632442i	$0.0201447\pi$
$410$		0			0
$411$	3.30469	+	24.7993i	0.163008	+	1.22326i
$412$		0			0
$413$	−4.37072	−	0.165513i	−0.215069	−	0.00814436i
$414$		0			0
$415$	−2.87302	−	1.98928i	−0.141031	−	0.0976500i
$416$		0			0
$417$	23.1496	−	6.28126i	1.13364	−	0.307594i
$418$		0			0
$419$	−8.64432	+	0.985817i	−0.422303	+	0.0481603i	−0.321871	−	0.946784i	$-0.604312\pi$
$419$	−8.64432	+	0.985817i	−0.422303	+	0.0481603i	−0.100432	+	0.994944i	$0.532022\pi$
$420$		0			0
$421$	1.38513	−	3.68461i	0.0675072	−	0.179577i	−0.897975	−	0.440047i	$-0.854962\pi$
$421$	1.38513	−	3.68461i	0.0675072	−	0.179577i	0.965482	+	0.260470i	$0.0838775\pi$
$422$		0			0
$423$	−0.00265694	+	0.00434495i	−0.000129185	+	0.000211259i
$424$		0			0
$425$	19.1439	+	18.0867i	0.928615	+	0.877334i
$426$		0			0
$427$	3.86899	−	0.146513i	0.187234	−	0.00709028i
$428$		0			0
$429$	13.3619	+	26.1019i	0.645117	+	1.26021i
$430$		0			0
$431$	−14.0396	−	2.68921i	−0.676262	−	0.129535i	−0.161507	−	0.986872i	$-0.551635\pi$
$431$	−14.0396	−	2.68921i	−0.676262	−	0.129535i	−0.514755	+	0.857337i	$0.672117\pi$
$432$		0			0
$433$	−11.3423	+	5.53791i	−0.545075	+	0.266135i	−0.690621	−	0.723217i	$-0.742663\pi$
$433$	−11.3423	+	5.53791i	−0.545075	+	0.266135i	0.145546	+	0.989352i	$0.453506\pi$
$434$		0			0
$435$	0.281067	−	0.0996308i	0.0134761	−	0.00477693i
$436$		0			0
$437$	−0.451686	+	23.8640i	−0.0216071	+	1.14157i
$438$		0			0
$439$	25.1248	+	1.90561i	1.19914	+	0.0909500i	0.660000	−	0.751266i	$-0.270556\pi$
$439$	25.1248	+	1.90561i	1.19914	+	0.0909500i	0.539141	+	0.842216i	$0.318749\pi$
$440$		0			0
$441$	0.00966581	+	0.510675i	0.000460277	+	0.0243179i
$442$		0			0
$443$	4.18149	−	8.16838i	0.198669	−	0.388091i	−0.769404	−	0.638763i	$-0.779447\pi$
$443$	4.18149	−	8.16838i	0.198669	−	0.388091i	0.968072	+	0.250671i	$0.0806513\pi$
$444$		0			0
$445$	13.0140	−	1.98555i	0.616925	−	0.0941240i
$446$		0			0
$447$	−21.5269	−	18.8486i	−1.01819	−	0.891508i
$448$		0			0
$449$	−1.45182	+	1.86147i	−0.0685155	+	0.0878481i	−0.821562	−	0.570120i	$-0.806897\pi$
$449$	−1.45182	+	1.86147i	−0.0685155	+	0.0878481i	0.753046	+	0.657968i	$0.228584\pi$
$450$		0			0
$451$	21.3252	−	45.8579i	1.00417	−	2.15937i
$452$		0			0
$453$	−2.99692	−	7.97215i	−0.140808	−	0.374565i
$454$		0			0
$455$	0.864109	−	15.2033i	0.0405101	−	0.712743i
$456$		0			0
$457$	−6.23312	+	1.44041i	−0.291573	+	0.0673795i	−0.368408	−	0.929664i	$-0.620097\pi$
$457$	−6.23312	+	1.44041i	−0.291573	+	0.0673795i	0.0768347	+	0.997044i	$0.475519\pi$
$458$		0			0
$459$	−31.8271	+	18.6440i	−1.48556	+	0.870229i
$460$		0			0
$461$	1.77021	−	18.6515i	0.0824470	−	0.868689i	−0.854554	−	0.519362i	$-0.826169\pi$
$461$	1.77021	−	18.6515i	0.0824470	−	0.868689i	0.937001	−	0.349326i	$-0.113590\pi$
$462$		0			0
$463$	24.8760	+	13.3344i	1.15609	+	0.619700i	0.934683	−	0.355482i	$-0.115683\pi$
$463$	24.8760	+	13.3344i	1.15609	+	0.619700i	0.221403	+	0.975182i	$0.428936\pi$
$464$		0			0
$465$	13.2366	+	14.5524i	0.613834	+	0.674851i
$466$		0			0
$467$	3.72059	−	3.25768i	0.172168	−	0.150748i	−0.568342	−	0.822792i	$-0.692415\pi$
$467$	3.72059	−	3.25768i	0.172168	−	0.150748i	0.740511	+	0.672045i	$0.234584\pi$
$468$		0			0
$469$	2.31614	+	9.22339i	0.106949	+	0.425897i
$470$		0			0
$471$	5.63505	+	19.3141i	0.259649	+	0.889945i
$472$		0			0
$473$	−0.905607	+	0.400467i	−0.0416399	+	0.0184135i
$474$		0			0
$475$	6.38072	−	15.2006i	0.292768	−	0.697452i
$476$		0			0
$477$	−0.00567284	−	0.00787047i	−0.000259741	−	0.000360364i
$478$		0			0
$479$	−8.28183	+	4.43933i	−0.378406	+	0.202838i	−0.650628	−	0.759396i	$-0.725494\pi$
$479$	−8.28183	+	4.43933i	−0.378406	+	0.202838i	0.272222	+	0.962234i	$0.412241\pi$
$480$		0			0
$481$	−2.33412	−	13.5709i	−0.106427	−	0.618782i
$482$		0			0
$483$	34.0727	+	21.7319i	1.55036	+	0.988836i
$484$		0			0
$485$	−9.52981	−	16.9978i	−0.432726	−	0.771832i
$486$		0			0
$487$	11.2279	−	9.10388i	0.508783	−	0.412536i	−0.340684	−	0.940178i	$-0.610659\pi$
$487$	11.2279	−	9.10388i	0.508783	−	0.412536i	0.849467	+	0.527642i	$0.176924\pi$
$488$		0			0
$489$	−28.7750	−	23.3316i	−1.30125	−	1.05509i
$490$		0			0
$491$	8.72505	+	18.7624i	0.393756	+	0.846735i	0.998725	+	0.0504863i	$0.0160771\pi$
$491$	8.72505	+	18.7624i	0.393756	+	0.846735i	−0.604969	+	0.796249i	$0.706814\pi$
$492$		0			0
$493$	0.761576	+	0.776127i	0.0342996	+	0.0349550i
$494$		0			0
$495$	0.241858	+	0.106952i	0.0108707	+	0.00480713i
$496$		0			0
$497$	−30.1493	−	17.6612i	−1.35238	−	0.792214i
$498$		0			0
$499$	8.02173	+	2.17656i	0.359102	+	0.0974362i	0.436844	−	0.899537i	$-0.356096\pi$
$499$	8.02173	+	2.17656i	0.359102	+	0.0974362i	−0.0777417	+	0.996974i	$0.524771\pi$
$500$		0			0
$501$	9.79469	−	19.9470i	0.437595	−	0.891165i
$502$		0			0
$503$	−3.03912	−	0.824612i	−0.135508	−	0.0367676i	0.193465	−	0.981107i	$-0.438028\pi$
$503$	−3.03912	−	0.824612i	−0.135508	−	0.0367676i	−0.328972	+	0.944340i	$0.606702\pi$
$504$		0			0
$505$	5.40062	+	3.16364i	0.240325	+	0.140780i
$506$		0			0
$507$	−5.15742	−	2.28065i	−0.229049	−	0.101287i
$508$		0			0
$509$	9.31439	+	9.49236i	0.412853	+	0.420741i	0.888487	−	0.458902i	$-0.151757\pi$
$509$	9.31439	+	9.49236i	0.412853	+	0.420741i	−0.475634	+	0.879643i	$0.657781\pi$
$510$		0			0
$511$	−1.67676	−	3.60572i	−0.0741757	−	0.159508i
$512$		0			0
$513$	17.9342	+	14.5416i	0.791815	+	0.642026i
$514$		0			0
$515$	11.6821	−	9.47221i	0.514776	−	0.417396i
$516$		0			0
$517$	−0.316724	−	0.564924i	−0.0139295	−	0.0248453i
$518$		0			0
$519$	−9.37344	−	5.97847i	−0.411448	−	0.262426i
$520$		0			0
$521$	−6.06561	−	35.2665i	−0.265739	−	1.54505i	−0.744810	−	0.667276i	$-0.767460\pi$
$521$	−6.06561	−	35.2665i	−0.265739	−	1.54505i	0.479071	−	0.877776i	$-0.340974\pi$
$522$		0			0
$523$	20.5508	−	11.0159i	0.898624	−	0.481692i	0.0428733	−	0.999081i	$-0.486349\pi$
$523$	20.5508	−	11.0159i	0.898624	−	0.481692i	0.855751	+	0.517389i	$0.173096\pi$
$524$		0			0
$525$	−16.3212	−	22.6440i	−0.712316	−	0.988263i
$526$		0			0
$527$	−27.7637	+	66.1406i	−1.20940	+	2.88113i
$528$		0			0
$529$	−5.72640	+	2.53226i	−0.248974	+	0.110098i
$530$		0			0
$531$	−0.0121272	−	0.0415660i	−0.000526277	−	0.00180381i
$532$		0			0
$533$	−7.02148	−	27.9612i	−0.304134	−	1.21113i
$534$		0			0
$535$	−16.2234	+	14.2049i	−0.701398	+	0.614132i
$536$		0			0
$537$	−8.87345	−	9.75550i	−0.382918	−	0.420981i
$538$		0			0
$539$	−57.2469	−	30.6862i	−2.46580	−	1.32175i
$540$		0			0
$541$	−2.86426	+	30.1787i	−0.123144	+	1.29749i	0.693548	+	0.720411i	$0.256047\pi$
$541$	−2.86426	+	30.1787i	−0.123144	+	1.29749i	−0.816692	+	0.577074i	$0.804194\pi$
$542$		0			0
$543$	−21.4526	+	12.5668i	−0.920620	+	0.539292i
$544$		0			0
$545$	14.3753	−	3.32198i	0.615769	−	0.142298i
$546$		0			0
$547$	0.132164	−	2.32532i	0.00565091	−	0.0994234i	−0.994325	−	0.106387i	$-0.966072\pi$
$547$	0.132164	−	2.32532i	0.00565091	−	0.0994234i	0.999976	+	0.00696320i	$0.00221647\pi$
$548$		0			0
$549$	0.0134871	+	0.0358772i	0.000575615	+	0.00153120i
$550$		0			0
$551$	0.287003	−	0.617174i	0.0122268	−	0.0262925i
$552$		0			0
$553$	−14.1647	+	18.1614i	−0.602343	+	0.772302i
$554$		0			0
$555$	6.42369	+	5.62447i	0.272671	+	0.238746i
$556$		0			0
$557$	11.2179	−	1.71151i	0.475317	−	0.0725190i	0.0912578	−	0.995827i	$-0.470911\pi$
$557$	11.2179	−	1.71151i	0.475317	−	0.0725190i	0.384060	+	0.923308i	$0.374526\pi$
$558$		0			0
$559$	−0.257210	+	0.502450i	−0.0108788	+	0.0212514i
$560$		0			0
$561$	−1.25462	−	66.2853i	−0.0529699	−	2.79857i
$562$		0			0
$563$	−46.3977	−	3.51908i	−1.95543	−	0.148311i	−0.962860	−	0.270001i	$-0.912976\pi$
$563$	−46.3977	−	3.51908i	−1.95543	−	0.148311i	−0.992568	+	0.121690i	$0.961169\pi$
$564$		0			0
$565$	−0.258301	+	13.6469i	−0.0108668	+	0.574127i
$566$		0			0
$567$	36.3187	−	12.8740i	1.52524	−	0.540657i
$568$		0			0
$569$	−8.46771	+	4.13439i	−0.354985	+	0.173323i	−0.607598	−	0.794245i	$-0.707867\pi$
$569$	−8.46771	+	4.13439i	−0.354985	+	0.173323i	0.252613	+	0.967567i	$0.418710\pi$
$570$		0			0
$571$	−22.8941	−	4.38525i	−0.958088	−	0.183517i	−0.314815	−	0.949153i	$-0.601942\pi$
$571$	−22.8941	−	4.38525i	−0.958088	−	0.183517i	−0.643274	+	0.765636i	$0.722424\pi$
$572$		0			0
$573$	5.10962	+	9.98144i	0.213457	+	0.416981i
$574$		0			0
$575$	20.1960	−	0.764793i	0.842230	−	0.0318941i
$576$		0			0
$577$	−2.97414	−	2.80990i	−0.123815	−	0.116978i	0.622349	−	0.782740i	$-0.286179\pi$
$577$	−2.97414	−	2.80990i	−0.123815	−	0.116978i	−0.746164	+	0.665763i	$0.768106\pi$
$578$		0			0
$579$	−18.7839	+	30.7178i	−0.780634	+	1.27659i
$580$		0			0
$581$	−4.75215	+	12.6413i	−0.197152	+	0.524448i
$582$		0			0
$583$	1.22581	−	0.139794i	0.0507677	−	0.00578966i
$584$		0			0
$585$	0.145488	−	0.0394756i	0.00601519	−	0.00163212i
$586$		0			0
$587$	35.9399	+	24.8849i	1.48340	+	1.02711i	0.987304	+	0.158839i	$0.0507751\pi$
$587$	35.9399	+	24.8849i	1.48340	+	1.02711i	0.496094	+	0.868269i	$0.334767\pi$
$588$		0			0
$589$	44.8684	+	1.69910i	1.84877	+	0.0700104i
$590$		0			0
$591$	5.51007	+	41.3491i	0.226654	+	1.70088i
$592$		0			0
$593$	−6.44363	+	19.3323i	−0.264608	+	0.793881i	0.729352	+	0.684139i	$0.239822\pi$
$593$	−6.44363	+	19.3323i	−0.264608	+	0.793881i	−0.993960	+	0.109742i	$0.964998\pi$
$594$		0			0
$595$	−16.8369	+	30.0311i	−0.690245	+	1.23115i
$596$		0			0
$597$	1.42235	+	14.9863i	0.0582128	+	0.613350i
$598$		0			0
$599$	−0.0653149	−	1.14916i	−0.00266869	−	0.0469536i	0.996778	−	0.0802064i	$-0.0255579\pi$
$599$	−0.0653149	−	1.14916i	−0.00266869	−	0.0469536i	−0.999447	+	0.0332528i	$0.989413\pi$
$600$		0			0
$601$	10.3476	−	12.2793i	0.422087	−	0.500881i	−0.511474	−	0.859299i	$-0.670900\pi$
$601$	10.3476	−	12.2793i	0.422087	−	0.500881i	0.933561	+	0.358418i	$0.116684\pi$
$602$		0			0
$603$	−0.0793718	+	0.0506241i	−0.00323227	+	0.00206157i
$604$		0			0
$605$	−17.0112	+	12.7572i	−0.691602	+	0.518656i
$606$		0			0
$607$	26.1737	+	33.5589i	1.06236	+	1.36212i	0.928592	+	0.371103i	$0.121020\pi$
$607$	26.1737	+	33.5589i	1.06236	+	1.36212i	0.133766	+	0.991013i	$0.457293\pi$
$608$		0			0
$609$	−0.637998	−	0.959739i	−0.0258530	−	0.0388906i
$610$		0			0
$611$	−0.343058	−	0.136427i	−0.0138786	−	0.00551927i
$612$		0			0
$613$	−42.3561	−	4.83038i	−1.71075	−	0.195097i	−0.797730	−	0.603015i	$-0.793966\pi$
$613$	−42.3561	−	4.83038i	−1.71075	−	0.195097i	−0.913019	+	0.407918i	$0.866255\pi$
$614$		0			0
$615$	14.3007	+	10.7246i	0.576659	+	0.432456i
$616$		0			0
$617$	29.1406	−	32.0373i	1.17316	−	1.28977i	0.224136	−	0.974558i	$-0.428044\pi$
$617$	29.1406	−	32.0373i	1.17316	−	1.28977i	0.949020	−	0.315215i	$-0.102077\pi$
$618$		0			0
$619$	−12.4233	−	37.2724i	−0.499333	−	1.49810i	−0.831846	−	0.555006i	$-0.812716\pi$
$619$	−12.4233	−	37.2724i	−0.499333	−	1.49810i	0.332514	−	0.943098i	$-0.392103\pi$
$620$		0			0
$621$	−6.89398	+	27.4534i	−0.276646	+	1.10167i
$622$		0			0
$623$	−19.6919	−	46.9113i	−0.788938	−	1.87946i
$624$		0			0
$625$	−7.20104	−	2.55258i	−0.288042	−	0.102103i
$626$		0			0
$627$	−38.5616	+	15.3352i	−1.54000	+	0.612429i
$628$		0			0
$629$	−8.71984	+	29.8872i	−0.347683	+	1.19168i
$630$		0			0
$631$	−34.1169	+	10.6585i	−1.35817	+	0.424308i	−0.888639	−	0.458607i	$-0.848348\pi$
$631$	−34.1169	+	10.6585i	−1.35817	+	0.424308i	−0.469532	+	0.882915i	$0.655577\pi$
$632$		0			0
$633$	38.5631	−	2.92485i	1.53274	−	0.116253i
$634$		0			0
$635$	0.552915	−	0.382839i	0.0219417	−	0.0151925i
$636$		0			0
$637$	−36.3648	+	6.96548i	−1.44082	+	0.275982i
$638$		0			0
$639$	0.0714901	−	0.338434i	0.00282811	−	0.0133882i
$640$		0			0
$641$	−14.2526	−	6.95889i	−0.562944	−	0.274859i	0.135198	−	0.990819i	$-0.456833\pi$
$641$	−14.2526	−	6.95889i	−0.562944	−	0.274859i	−0.698142	+	0.715959i	$0.745990\pi$
$642$		0			0
$643$	−0.478272	+	2.78075i	−0.0188612	+	0.109662i	−0.993433	−	0.114411i	$-0.963502\pi$
$643$	−0.478272	+	2.78075i	−0.0188612	+	0.109662i	0.974572	+	0.224073i	$0.0719356\pi$
$644$		0			0
$645$	−0.0723341	−	0.342429i	−0.00284815	−	0.0134831i
$646$		0			0
$647$	−25.5993	+	26.0884i	−1.00641	+	1.02564i	−0.00674061	+	0.999977i	$0.502146\pi$
$647$	−25.5993	+	26.0884i	−1.00641	+	1.02564i	−0.999671	+	0.0256631i	$0.991830\pi$
$648$		0			0
$649$	5.36482	+	1.23975i	0.210588	+	0.0486646i
$650$		0			0
$651$	42.0874	−	63.3120i	1.64954	−	2.48139i
$652$		0			0
$653$	1.28593	+	2.10291i	0.0503224	+	0.0822934i	0.877303	−	0.479938i	$-0.159341\pi$
$653$	1.28593	+	2.10291i	0.0503224	+	0.0822934i	−0.826980	+	0.562231i	$0.809943\pi$
$654$		0			0
$655$	−0.552240	+	4.14417i	−0.0215778	+	0.161926i
$656$		0			0
$657$	0.0286146	−	0.0270344i	0.00111636	−	0.00105471i
$658$		0			0
$659$	−42.2943	−	13.2132i	−1.64755	−	0.514714i	−0.673145	−	0.739511i	$-0.735057\pi$
$659$	−42.2943	−	13.2132i	−1.64755	−	0.514714i	−0.974406	+	0.224797i	$0.927828\pi$
$660$		0			0
$661$	24.8920	−	34.5351i	0.968188	−	1.34326i	0.0291027	−	0.999576i	$-0.490735\pi$
$661$	24.8920	−	34.5351i	0.968188	−	1.34326i	0.939086	−	0.343683i	$-0.111675\pi$
$662$		0			0
$663$	−24.3532	−	28.8994i	−0.945801	−	1.12236i
$664$		0			0
$665$	21.3044	+	3.25040i	0.826148	+	0.126045i
$666$		0			0
$667$	0.834436			0.0323095
$668$		0			0
$669$	−44.6127			−1.72483
$670$		0			0
$671$	−4.81837	−	0.735137i	−0.186011	−	0.0283796i
$672$		0			0
$673$	−1.57957	−	1.87443i	−0.0608878	−	0.0722541i	0.733393	−	0.679805i	$-0.237935\pi$
$673$	−1.57957	−	1.87443i	−0.0608878	−	0.0722541i	−0.794281	+	0.607550i	$0.792152\pi$
$674$		0			0
$675$	11.4315	−	15.8600i	0.440000	−	0.610453i
$676$		0			0
$677$	−25.5706	−	7.98854i	−0.982757	−	0.307024i	−0.235730	−	0.971818i	$-0.575748\pi$
$677$	−25.5706	−	7.98854i	−0.982757	−	0.307024i	−0.747027	+	0.664794i	$0.768519\pi$
$678$		0			0
$679$	−54.7426	+	51.7196i	−2.10083	+	1.98482i
$680$		0			0
$681$	6.03018	−	45.2521i	0.231077	−	1.73407i
$682$		0			0
$683$	−17.6330	−	28.8357i	−0.674709	−	1.10337i	−0.988110	−	0.153747i	$-0.950866\pi$
$683$	−17.6330	−	28.8357i	−0.674709	−	1.10337i	0.313401	−	0.949621i	$-0.398532\pi$
$684$		0			0
$685$	−9.05472	+	13.6210i	−0.345963	+	0.520431i
$686$		0			0
$687$	−32.5336	−	7.51818i	−1.24123	−	0.286836i
$688$		0			0
$689$	0.492575	−	0.501986i	0.0187656	−	0.0191241i
$690$		0			0
$691$	2.49949	+	11.8326i	0.0950852	+	0.450133i	0.999714	+	0.0239314i	$0.00761831\pi$
$691$	2.49949	+	11.8326i	0.0950852	+	0.450133i	−0.904628	+	0.426201i	$0.859852\pi$
$692$		0			0
$693$	0.173236	−	1.00722i	0.00658068	−	0.0382611i
$694$		0			0
$695$	14.0915	+	6.88022i	0.534521	+	0.260981i
$696$		0			0
$697$	−13.4713	+	63.7732i	−0.510263	+	2.41558i
$698$		0			0
$699$	−12.1286	+	2.32317i	−0.458745	+	0.0878702i
$700$		0			0
$701$	−35.3826	+	24.4990i	−1.33638	+	0.925314i	−0.999866	−	0.0163632i	$-0.994791\pi$
$701$	−35.3826	+	24.4990i	−1.33638	+	0.925314i	−0.336517	+	0.941677i	$0.609249\pi$
$702$		0			0
$703$	19.4322	−	1.47385i	0.732898	−	0.0555874i
$704$		0			0
$705$	0.218498	−	0.0682611i	0.00822909	−	0.00257086i
$706$		0			0
$707$	6.77487	−	23.2208i	0.254795	−	0.873308i
$708$		0			0
$709$	20.8149	−	8.27769i	0.781721	−	0.310875i	0.0556101	−	0.998453i	$-0.482290\pi$
$709$	20.8149	−	8.27769i	0.781721	−	0.310875i	0.726111	+	0.687577i	$0.241326\pi$
$710$		0			0
$711$	−0.214904	−	0.0761777i	−0.00805952	−	0.00285689i
$712$		0			0
$713$	21.3056	+	50.7556i	0.797899	+	1.90081i
$714$		0			0
$715$	−4.66898	+	18.5930i	−0.174610	+	0.695337i
$716$		0			0
$717$	−1.90225	−	5.70715i	−0.0710408	−	0.213138i
$718$		0			0
$719$	2.45184	−	2.69557i	0.0914383	−	0.100528i	−0.692330	−	0.721581i	$-0.743416\pi$
$719$	2.45184	−	2.69557i	0.0914383	−	0.100528i	0.783768	+	0.621054i	$0.213295\pi$
$720$		0			0
$721$	−46.5003	−	34.8721i	−1.73176	−	1.29871i
$722$		0			0
$723$	−29.5509	−	3.37004i	−1.09901	−	0.125333i
$724$		0			0
$725$	−0.535541	−	0.212974i	−0.0198895	−	0.00790966i
$726$		0			0
$727$	−0.559928	−	0.842298i	−0.0207666	−	0.0312391i	0.822252	−	0.569124i	$-0.192718\pi$
$727$	−0.559928	−	0.842298i	−0.0207666	−	0.0312391i	−0.843018	+	0.537885i	$0.819224\pi$
$728$		0			0
$729$	16.8361	+	21.5867i	0.623561	+	0.799507i
$730$		0			0
$731$	1.02098	−	0.765670i	0.0377624	−	0.0283193i
$732$		0			0
$733$	13.2342	−	8.44089i	0.488816	−	0.311771i	−0.270245	−	0.962792i	$-0.587105\pi$
$733$	13.2342	−	8.44089i	0.488816	−	0.311771i	0.759060	+	0.651020i	$0.225659\pi$
$734$		0			0
$735$	14.7937	−	17.5554i	0.545674	−	0.647539i
$736$		0			0
$737$	−0.679340	−	11.9525i	−0.0250238	−	0.440274i
$738$		0			0
$739$	−4.18215	−	44.0645i	−0.153843	−	1.62094i	−0.655033	−	0.755601i	$-0.727345\pi$
$739$	−4.18215	−	44.0645i	−0.153843	−	1.62094i	0.501190	−	0.865337i	$-0.332896\pi$
$740$		0			0
$741$	−11.5687	+	20.6345i	−0.424987	+	0.758027i
$742$		0			0
$743$	−9.19392	+	27.5837i	−0.337292	+	1.01195i	0.633852	+	0.773455i	$0.281473\pi$
$743$	−9.19392	+	27.5837i	−0.337292	+	1.01195i	−0.971144	+	0.238494i	$0.923346\pi$
$744$		0			0
$745$	−2.47082	−	18.5417i	−0.0905239	−	0.679317i
$746$		0			0
$747$	−0.133597	−	0.00505913i	−0.00488805	−	0.000185104i
$748$		0			0
$749$	68.5142	+	47.4393i	2.50345	+	1.73340i
$750$		0			0
$751$	−41.5790	+	11.2818i	−1.51724	+	0.411677i	−0.920495	−	0.390754i	$-0.872214\pi$
$751$	−41.5790	+	11.2818i	−1.51724	+	0.411677i	−0.596745	+	0.802431i	$0.703540\pi$
$752$		0			0
$753$	6.30583	−	0.719131i	0.229797	−	0.0262066i
$754$		0			0
$755$	1.95925	−	5.21185i	0.0713046	−	0.189679i
$756$		0			0
$757$	−0.255296	+	0.417492i	−0.00927890	+	0.0151740i	−0.857740	−	0.514084i	$-0.828132\pi$
$757$	−0.255296	+	0.417492i	−0.00927890	+	0.0151740i	0.848461	+	0.529258i	$0.177530\pi$
$758$		0			0
$759$	−36.9812	−	34.9390i	−1.34233	−	1.26821i
$760$		0			0
$761$	−31.8648	+	1.20667i	−1.15510	+	0.0437419i	−0.608430	−	0.793608i	$-0.708200\pi$
$761$	−31.8648	+	1.20667i	−1.15510	+	0.0437419i	−0.546667	+	0.837350i	$0.684104\pi$
$762$		0			0
$763$	−25.9824	−	50.7557i	−0.940626	−	1.83748i
$764$		0			0
$765$	−0.334743	−	0.0641184i	−0.0121027	−	0.00231820i
$766$		0			0
$767$	2.82053	−	1.37713i	0.101844	−	0.0497254i
$768$		0			0
$769$	−15.4122	+	5.46321i	−0.555778	+	0.197008i	−0.597142	−	0.802136i	$-0.703697\pi$
$769$	−15.4122	+	5.46321i	−0.555778	+	0.197008i	0.0413642	+	0.999144i	$0.486830\pi$
$770$		0			0
$771$	0.514462	−	27.1807i	0.0185279	−	0.978888i
$772$		0			0
$773$	22.3872	+	1.69798i	0.805211	+	0.0610720i	0.471796	−	0.881708i	$-0.343606\pi$
$773$	22.3872	+	1.69798i	0.805211	+	0.0610720i	0.333416	+	0.942780i	$0.391799\pi$
$774$		0			0
$775$	−0.719488	−	38.0128i	−0.0258448	−	1.36546i
$776$		0			0
$777$	15.0358	−	29.3718i	0.539405	−	1.05371i
$778$		0			0
$779$	40.3333	−	6.15363i	1.44509	−	0.220477i
$780$		0			0
$781$	33.0943	+	28.9768i	1.18421	+	1.03687i
$782$		0			0
$783$	0.496419	−	0.636490i	0.0177406	−	0.0227463i
$784$		0			0
$785$	−5.54622	+	11.9266i	−0.197953	+	0.425679i
$786$		0			0
$787$	−5.94201	−	15.8064i	−0.211810	−	0.563439i	0.786739	−	0.617285i	$-0.211768\pi$
$787$	−5.94201	−	15.8064i	−0.211810	−	0.563439i	−0.998549	+	0.0538464i	$0.982852\pi$
$788$		0			0
$789$	−2.52039	+	44.3442i	−0.0897281	+	1.57870i
$790$		0			0
$791$	51.3953	−	11.8769i	1.82741	−	0.422295i
$792$		0			0
$793$	−2.39741	+	1.40438i	−0.0851345	+	0.0498712i
$794$		0			0
$795$	−0.0412020	+	0.434117i	−0.00146128	+	0.0153966i
$796$		0			0
$797$	11.8495	+	6.35170i	0.419730	+	0.224989i	0.668716	−	0.743518i	$-0.266844\pi$
$797$	11.8495	+	6.35170i	0.419730	+	0.224989i	−0.248986	+	0.968507i	$0.580097\pi$
$798$		0			0
$799$	0.561651	+	0.617481i	0.0198698	+	0.0218449i
$800$		0			0
$801$	0.378929	−	0.331784i	0.0133888	−	0.0117230i
$802$		0			0
$803$	1.21923	+	4.85527i	0.0430258	+	0.171339i
$804$		0			0
$805$	7.39985	+	25.3629i	0.260811	+	0.893926i
$806$		0			0
$807$	−15.4217	+	6.81960i	−0.542869	+	0.240061i
$808$		0			0
$809$	7.29624	−	17.3816i	0.256522	−	0.611105i	−0.741699	−	0.670733i	$-0.765980\pi$
$809$	7.29624	−	17.3816i	0.256522	−	0.611105i	0.998221	+	0.0596283i	$0.0189916\pi$
$810$		0			0
$811$	−17.5182	−	24.3046i	−0.615147	−	0.853451i	0.382361	−	0.924013i	$-0.375111\pi$
$811$	−17.5182	−	24.3046i	−0.615147	−	0.853451i	−0.997507	+	0.0705619i	$0.977521\pi$
$812$		0			0
$813$	22.2287	−	11.9153i	0.779596	−	0.417889i
$814$		0			0
$815$	−4.10519	−	23.8683i	−0.143799	−	0.836068i
$816$		0			0
$817$	−0.673506	−	0.429568i	−0.0235630	−	0.0150287i
$818$		0			0
$819$	−0.284906	−	0.508172i	−0.00995543	−	0.0177570i
$820$		0			0
$821$	24.5144	−	19.8770i	0.855560	−	0.693713i	−0.0979121	−	0.995195i	$-0.531216\pi$
$821$	24.5144	−	19.8770i	0.855560	−	0.693713i	0.953472	+	0.301482i	$0.0974815\pi$
$822$		0			0
$823$	23.4672	+	19.0279i	0.818014	+	0.663270i	0.944432	−	0.328707i	$-0.106613\pi$
$823$	23.4672	+	19.0279i	0.818014	+	0.663270i	−0.126418	+	0.991977i	$0.540348\pi$
$824$		0			0
$825$	14.8170	+	31.8626i	0.515862	+	1.10931i
$826$		0			0
$827$	−3.12276	−	3.18242i	−0.108589	−	0.110664i	0.657324	−	0.753608i	$-0.271688\pi$
$827$	−3.12276	−	3.18242i	−0.108589	−	0.110664i	−0.765913	+	0.642945i	$0.777713\pi$
$828$		0			0
$829$	4.08009	+	1.80425i	0.141708	+	0.0626643i	0.474068	−	0.880488i	$-0.342785\pi$
$829$	4.08009	+	1.80425i	0.141708	+	0.0626643i	−0.332361	+	0.943152i	$0.607845\pi$
$830$		0			0
$831$	3.62321	+	2.12245i	0.125688	+	0.0736269i
$832$		0			0
$833$	80.7910	+	21.9212i	2.79924	+	0.759526i
$834$		0			0
$835$	13.4081	−	5.59289i	0.464005	−	0.193550i
$836$		0			0
$837$	51.3903	+	13.9439i	1.77631	+	0.481971i
$838$		0			0
$839$	−3.59740	−	2.10733i	−0.124196	−	0.0727532i	0.442045	−	0.896993i	$-0.354253\pi$
$839$	−3.59740	−	2.10733i	−0.124196	−	0.0727532i	−0.566241	+	0.824240i	$0.691603\pi$
$840$		0			0
$841$	26.5007	+	11.7189i	0.913818	+	0.404098i
$842$		0			0
$843$	−5.54125	−	5.64712i	−0.190851	−	0.194497i
$844$		0			0
$845$	−1.55453	−	3.34288i	−0.0534775	−	0.114998i
$846$		0			0
$847$	63.8294	+	51.7548i	2.19321	+	1.77831i
$848$		0			0
$849$	−39.9244	+	32.3719i	−1.37020	+	1.11100i
$850$		0			0
$851$	11.6837	+	20.8396i	0.400511	+	0.714371i
$852$		0			0
$853$	−1.25838	−	0.802608i	−0.0430862	−	0.0274808i	0.516024	−	0.856574i	$-0.327411\pi$
$853$	−1.25838	−	0.802608i	−0.0430862	−	0.0274808i	−0.559110	+	0.829093i	$0.688857\pi$
$854$		0			0
$855$	0.0361627	+	0.210256i	0.00123674	+	0.00719060i
$856$		0			0
$857$	−40.3164	+	21.6109i	−1.37718	+	0.738214i	−0.983479	−	0.181023i	$-0.942059\pi$
$857$	−40.3164	+	21.6109i	−1.37718	+	0.738214i	−0.393703	+	0.919238i	$0.628806\pi$
$858$		0			0
$859$	29.7823	+	41.3198i	1.01616	+	1.40981i	0.909590	+	0.415507i	$0.136396\pi$
$859$	29.7823	+	41.3198i	1.01616	+	1.40981i	0.106568	+	0.994305i	$0.466014\pi$
$860$		0			0
$861$	26.7381	−	63.6974i	0.911232	−	2.17080i
$862$		0			0
$863$	23.2009	−	10.2596i	0.789769	−	0.349242i	0.0300951	−	0.999547i	$-0.490419\pi$
$863$	23.2009	−	10.2596i	0.789769	−	0.349242i	0.759674	+	0.650305i	$0.225359\pi$
$864$		0			0
$865$	−2.03571	−	6.97737i	−0.0692161	−	0.237238i
$866$		0			0
$867$	13.6906	+	54.5193i	0.464958	+	1.85157i
$868$		0			0
$869$	21.8145	−	19.1004i	0.740007	−	0.647938i
$870$		0			0
$871$	−4.59196	−	5.04842i	−0.155593	−	0.171059i
$872$		0			0
$873$	−0.657088	−	0.352221i	−0.0222391	−	0.0119209i
$874$		0			0
$875$	4.03160	−	42.4783i	0.136293	−	1.43603i
$876$		0			0
$877$	16.5169	−	9.67547i	0.557736	−	0.326717i	−0.199459	−	0.979906i	$-0.563919\pi$
$877$	16.5169	−	9.67547i	0.557736	−	0.326717i	0.757195	+	0.653189i	$0.226569\pi$
$878$		0			0
$879$	−6.11333	+	1.41273i	−0.206197	+	0.0476501i
$880$		0			0
$881$	−1.56859	+	27.5981i	−0.0528471	+	0.929803i	0.857119	+	0.515119i	$0.172252\pi$
$881$	−1.56859	+	27.5981i	−0.0528471	+	0.929803i	−0.909966	+	0.414684i	$0.863892\pi$
$882$		0			0
$883$	10.5947	+	28.1830i	0.356539	+	0.948434i	0.985300	+	0.170836i	$0.0546467\pi$
$883$	10.5947	+	28.1830i	0.356539	+	0.948434i	−0.628761	+	0.777599i	$0.716438\pi$
$884$		0			0
$885$	−0.820628	+	1.76468i	−0.0275851	+	0.0593192i
$886$		0			0
$887$	−13.8935	+	17.8138i	−0.466499	+	0.598127i	−0.962864	−	0.269986i	$-0.912981\pi$
$887$	−13.8935	+	17.8138i	−0.466499	+	0.598127i	0.496365	+	0.868114i	$0.334668\pi$
$888$		0			0
$889$	−1.95542	−	1.71213i	−0.0655826	−	0.0574230i
$890$		0			0
$891$	−47.9538	+	7.31629i	−1.60651	+	0.245105i
$892$		0			0
$893$	0.238085	−	0.465090i	0.00796722	−	0.0155637i
$894$		0			0
$895$	−0.163152	−	8.61981i	−0.00545356	−	0.288128i
$896$		0			0
$897$	−28.9183	−	2.19334i	−0.965555	−	0.0732335i
$898$		0			0
$899$	0.0297057	−	1.56945i	0.000990742	−	0.0523440i
$900$		0			0
$901$	−1.49871	+	0.531253i	−0.0499293	+	0.0176986i
$902$		0			0
$903$	−1.21543	+	0.593440i	−0.0404471	+	0.0197484i
$904$		0			0
$905$	−15.9637	−	3.05777i	−0.530653	−	0.101644i
$906$		0			0
$907$	−8.60133	−	16.8024i	−0.285602	−	0.557913i	0.702505	−	0.711679i	$-0.252065\pi$
$907$	−8.60133	−	16.8024i	−0.285602	−	0.557913i	−0.988107	+	0.153765i	$0.950860\pi$
$908$		0			0
$909$	0.239287	−	0.00906146i	0.00793665	−	0.000300550i
$910$		0			0
$911$	4.19693	+	3.96517i	0.139051	+	0.131372i	0.753128	−	0.657874i	$-0.228544\pi$
$911$	4.19693	+	3.96517i	0.139051	+	0.131372i	−0.614077	+	0.789246i	$0.710472\pi$
$912$		0			0
$913$	8.86943	−	14.5044i	0.293535	−	0.480025i
$914$		0			0
$915$	0.606205	−	1.61258i	0.0200405	−	0.0533101i
$916$		0			0
$917$	16.0533	−	1.83075i	0.530126	−	0.0604567i
$918$		0			0
$919$	−12.6919	+	3.44373i	−0.418667	+	0.113598i	−0.464964	−	0.885330i	$-0.653933\pi$
$919$	−12.6919	+	3.44373i	−0.418667	+	0.113598i	0.0462969	+	0.998928i	$0.485258\pi$
$920$		0			0
$921$	−1.41241	−	0.977957i	−0.0465406	−	0.0322248i
$922$		0			0
$923$	25.0567	+	0.948864i	0.824753	+	0.0312322i
$924$		0			0
$925$	−2.17967	−	16.3569i	−0.0716672	−	0.537811i
$926$		0			0
$927$	0.181944	−	0.545870i	0.00597582	−	0.0179287i
$928$		0			0
$929$	−21.5799	+	38.4910i	−0.708015	+	1.26285i	0.247781	+	0.968816i	$0.420299\pi$
$929$	−21.5799	+	38.4910i	−0.708015	+	1.26285i	−0.955795	+	0.294033i	$0.905002\pi$
$930$		0			0
$931$	−4.95102	−	52.1656i	−0.162263	−	1.70966i
$932$		0			0
$933$	−2.25670	−	39.7049i	−0.0738810	−	1.29988i
$934$		0			0
$935$	27.9296	−	33.1434i	0.913395	−	1.08390i
$936$		0			0
$937$	−21.1652	+	13.4994i	−0.691436	+	0.441005i	−0.836173	−	0.548466i	$-0.815212\pi$
$937$	−21.1652	+	13.4994i	−0.691436	+	0.441005i	0.144737	+	0.989470i	$0.453766\pi$
$938$		0			0
$939$	−16.2129	+	12.1586i	−0.529088	+	0.396781i
$940$		0			0
$941$	−21.3391	−	27.3602i	−0.695634	−	0.891917i	0.302489	−	0.953153i	$-0.402183\pi$
$941$	−21.3391	−	27.3602i	−0.695634	−	0.891917i	−0.998123	+	0.0612360i	$0.980496\pi$
$942$		0			0
$943$	27.6905	+	41.6548i	0.901728	+	1.35647i
$944$		0			0
$945$	23.7486	+	9.44435i	0.772542	+	0.307225i
$946$		0			0
$947$	−20.6749	−	2.35781i	−0.671844	−	0.0766185i	−0.229287	−	0.973359i	$-0.573639\pi$
$947$	−20.6749	−	2.35781i	−0.671844	−	0.0766185i	−0.442557	+	0.896740i	$0.645929\pi$
$948$		0			0
$949$	2.28299	+	1.71209i	0.0741090	+	0.0555768i
$950$		0			0
$951$	8.65722	−	9.51778i	0.280730	−	0.308635i
$952$		0			0
$953$	−8.91269	−	26.7400i	−0.288710	−	0.866192i	−0.988417	−	0.151762i	$-0.951505\pi$
$953$	−8.91269	−	26.7400i	−0.288710	−	0.866192i	0.699707	−	0.714430i	$-0.253314\pi$
$954$		0			0
$955$	−1.78543	+	7.11000i	−0.0577752	+	0.230074i
$956$		0			0
$957$	0.561536	+	1.33773i	0.0181519	+	0.0432427i
$958$		0			0
$959$	59.5780	+	21.1188i	1.92387	+	0.681962i
$960$		0			0
$961$	67.4163	−	26.8102i	2.17472	−	0.864844i
$962$		0			0
$963$	−0.231060	+	0.791954i	−0.00744579	+	0.0255204i
$964$		0			0
$965$	−22.4681	+	7.01929i	−0.723274	+	0.225959i
$966$		0			0
$967$	−28.4736	+	2.15961i	−0.915650	+	0.0694483i	−0.525011	−	0.851096i	$-0.675939\pi$
$967$	−28.4736	+	2.15961i	−0.915650	+	0.0694483i	−0.390639	+	0.920544i	$0.627746\pi$
$968$		0			0
$969$	43.9727	−	30.4468i	1.41261	−	0.978092i
$970$		0			0
$971$	11.3663	−	2.17716i	0.364762	−	0.0698683i	−0.00247188	−	0.999997i	$-0.500787\pi$
$971$	11.3663	−	2.17716i	0.364762	−	0.0698683i	0.367234	+	0.930129i	$0.380305\pi$
$972$		0			0
$973$	12.5253	−	59.2948i	0.401544	−	1.90090i
$974$		0			0
$975$	18.0000	+	8.78855i	0.576461	+	0.281459i
$976$		0			0
$977$	3.90138	−	22.6833i	0.124816	−	0.725701i	−0.853893	−	0.520449i	$-0.825765\pi$
$977$	3.90138	−	22.6833i	0.124816	−	0.725701i	0.978709	−	0.205253i	$-0.0658016\pi$
$978$		0			0
$979$	13.2373	+	62.6654i	0.423067	+	2.00279i
$980$		0			0
$981$	0.395342	−	0.402896i	0.0126223	−	0.0128635i
$982$		0			0
$983$	−36.2486	−	8.37668i	−1.15615	−	0.267175i	−0.396831	−	0.917892i	$-0.629890\pi$
$983$	−36.2486	−	8.37668i	−1.15615	−	0.267175i	−0.759320	+	0.650717i	$0.774468\pi$
$984$		0			0
$985$	−15.0974	+	22.7110i	−0.481043	+	0.723631i
$986$		0			0
$987$	−0.461522	−	0.754738i	−0.0146904	−	0.0240236i
$988$		0			0
$989$	0.129360	−	0.970754i	0.00411341	−	0.0308682i
$990$		0			0
$991$	30.7059	−	29.0103i	0.975406	−	0.921541i	−0.0215298	−	0.999768i	$-0.506854\pi$
$991$	30.7059	−	29.0103i	0.975406	−	0.921541i	0.996936	+	0.0782272i	$0.0249260\pi$
$992$		0			0
$993$	−28.2354	−	8.82106i	−0.896023	−	0.279928i
$994$		0			0
$995$	−5.75447	+	7.98373i	−0.182429	+	0.253101i
$996$		0			0
$997$	−40.3316	−	47.8606i	−1.27731	−	1.51576i	−0.740495	−	0.672062i	$-0.765409\pi$
$997$	−40.3316	−	47.8606i	−1.27731	−	1.51576i	−0.536819	−	0.843697i	$-0.680374\pi$
$998$		0			0
$999$	22.8468	+	3.48573i	0.722840	+	0.110283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.21.5	✓	1148
167.8	even	83	inner	668.2.e.a.509.5	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.21.5	✓	1148	1.1	even	1	trivial
668.2.e.a.509.5	yes	1148	167.8	even	83	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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +O(q^{10})\)	\(q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +(3.97566 - 3.75611i) q^{11} +(0.411828 - 3.09047i) q^{13} +(1.00851 + 1.64924i) q^{15} +(-3.90237 + 5.87032i) q^{17} +(4.29909 + 0.993475i) q^{19} +(5.23254 - 5.33251i) q^{21} +(1.11800 + 5.29258i) q^{23} +(0.633303 - 3.68213i) q^{25} +(4.70218 + 2.29586i) q^{27} +(0.0318815 - 0.150927i) q^{29} +(9.99434 - 1.91437i) q^{31} +(-7.73247 + 5.35398i) q^{33} +(4.87020 - 0.369385i) q^{35} +(4.21572 - 1.31704i) q^{37} +(-1.50161 + 5.14674i) q^{39} +(8.59220 - 3.41695i) q^{41} +(-0.170641 - 0.0604876i) q^{43} +(0.0187143 + 0.0445825i) q^{45} +(0.0288402 - 0.114848i) q^{47} +(-3.75518 - 11.2663i) q^{49} +(8.15621 - 8.96697i) q^{51} +(0.180465 + 0.135337i) q^{53} +(-6.10906 - 0.696690i) q^{55} +(-7.05044 - 2.80382i) q^{57} +(0.557327 + 0.838386i) q^{59} +(-0.548065 - 0.702708i) q^{61} +(0.149493 - 0.112109i) q^{63} +(-2.95510 + 1.88479i) q^{65} +(1.41050 - 1.67380i) q^{67} +(-0.527839 - 9.28692i) q^{69} +(0.759892 + 8.00647i) q^{71} +(-0.447602 + 0.798365i) q^{73} +(-2.03154 + 6.09506i) q^{75} +(3.13877 + 23.5542i) q^{77} +(5.29749 + 0.200609i) q^{79} +(-7.29180 - 5.04886i) q^{81} +(2.99997 - 0.813991i) q^{83} +(7.87346 - 0.897906i) q^{85} +(-0.0933398 + 0.248295i) q^{87} +(-6.10917 + 9.99046i) q^{89} +(9.84619 + 9.30246i) q^{91} +(-17.4861 + 0.662173i) q^{93} +(-2.26032 - 4.41545i) q^{95} +(17.0247 + 3.26100i) q^{97} +(-0.211385 + 0.103210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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