LMFDB - Embedded newform 132.2.j.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,2,Mod(7,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("132.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.j (of order $10$, degree $4$, 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:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	132.7
Dual form			132.2.j.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.655516 + 1.25312i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.14060 - 1.64288i) q^{4} +(2.66345 - 1.93511i) q^{5} +(1.01067 - 0.989218i) q^{6} +(1.40437 + 4.32221i) q^{7} +(2.80639 - 0.352368i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.655516 + 1.25312i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.14060 - 1.64288i) q^{4} +(2.66345 - 1.93511i) q^{5} +(1.01067 - 0.989218i) q^{6} +(1.40437 + 4.32221i) q^{7} +(2.80639 - 0.352368i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.678982 + 4.60611i) q^{10} +(1.46412 - 2.97596i) q^{11} +(0.577096 + 1.91493i) q^{12} +(-0.838793 + 1.15450i) q^{13} +(-6.33681 - 1.07344i) q^{14} +(-3.13108 + 1.01735i) q^{15} +(-1.39808 + 3.74772i) q^{16} +(1.93604 + 2.66473i) q^{17} +(-1.26689 + 0.628489i) q^{18} +(0.989336 - 3.04486i) q^{19} +(-6.21707 - 2.16854i) q^{20} -4.54464i q^{21} +(2.76947 + 3.78550i) q^{22} -3.51482i q^{23} +(-2.77793 - 0.532101i) q^{24} +(1.80424 - 5.55287i) q^{25} +(-0.896879 - 1.80790i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(5.49903 - 7.23710i) q^{28} +(-3.38012 + 1.09827i) q^{29} +(0.777617 - 4.59049i) q^{30} +(-1.57372 + 2.16604i) q^{31} +(-3.77986 - 4.20864i) q^{32} +(-2.31208 + 2.37787i) q^{33} +(-4.60833 + 0.679308i) q^{34} +(12.1044 + 8.79438i) q^{35} +(0.0428958 - 1.99954i) q^{36} +(0.140713 + 0.433070i) q^{37} +(3.16704 + 3.23571i) q^{38} +(1.15450 - 0.838793i) q^{39} +(6.79282 - 6.36920i) q^{40} +(-8.53807 - 2.77419i) q^{41} +(5.69496 + 2.97909i) q^{42} -10.5057 q^{43} +(-6.55910 + 0.989014i) q^{44} +3.29221 q^{45} +(4.40448 + 2.30402i) q^{46} +(-3.26990 - 1.06246i) q^{47} +(2.48776 - 3.13226i) q^{48} +(-11.0461 + 8.02547i) q^{49} +(5.77569 + 5.90092i) q^{50} +(-1.01784 - 3.13258i) q^{51} +(2.85342 + 0.0612140i) q^{52} +(1.87204 + 1.36012i) q^{53} +(1.39909 - 0.206239i) q^{54} +(-1.85922 - 10.7596i) q^{55} +(5.46422 + 11.6350i) q^{56} +(-1.88183 + 2.59011i) q^{57} +(0.839467 - 4.95561i) q^{58} +(2.50457 - 0.813785i) q^{59} +(5.24267 + 3.98358i) q^{60} +(0.697794 + 0.960431i) q^{61} +(-1.68270 - 3.39193i) q^{62} +(-1.40437 + 4.32221i) q^{63} +(7.75167 - 1.97776i) q^{64} +4.69811i q^{65} +(-1.46414 - 4.45604i) q^{66} +6.30893i q^{67} +(2.16958 - 6.22006i) q^{68} +(-1.08614 + 3.34279i) q^{69} +(-18.9550 + 9.40339i) q^{70} +(-0.379984 - 0.523003i) q^{71} +(2.47754 + 1.36448i) q^{72} +(6.49205 - 2.10940i) q^{73} +(-0.634926 - 0.107555i) q^{74} +(-3.43187 + 4.72356i) q^{75} +(-6.13076 + 1.84760i) q^{76} +(14.9189 + 2.14886i) q^{77} +(0.294311 + 1.99656i) q^{78} +(7.83975 + 5.69591i) q^{79} +(3.52853 + 12.6873i) q^{80} +(0.309017 + 0.951057i) q^{81} +(9.07322 - 8.88066i) q^{82} +(0.906427 - 0.658558i) q^{83} +(-7.46628 + 5.18360i) q^{84} +(10.3131 + 3.35093i) q^{85} +(6.88668 - 13.1649i) q^{86} +3.55406 q^{87} +(3.06025 - 8.86763i) q^{88} -16.2562 q^{89} +(-2.15810 + 4.12552i) q^{90} +(-6.16797 - 2.00409i) q^{91} +(-5.77441 + 4.00899i) q^{92} +(2.16604 - 1.57372i) q^{93} +(3.47485 - 3.40111i) q^{94} +(-3.25710 - 10.0243i) q^{95} +(2.29432 + 5.17070i) q^{96} +(-9.60184 - 6.97614i) q^{97} +(-2.81593 - 19.1029i) q^{98} +(2.93372 - 1.54702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) $ 48 * q - 4 * q^4 + 12 * q^9	$ 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

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 $

$2$	−0.655516	+	1.25312i	−0.463520	+	0.886086i
$2$	−0.655516	+	1.25312i	−0.463520	+	0.886086i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−1.14060	−	1.64288i	−0.570298	−	0.821438i
$5$	2.66345	−	1.93511i	1.19113	−	0.865408i	0.197749	−	0.980253i	$-0.436637\pi$
$5$	2.66345	−	1.93511i	1.19113	−	0.865408i	0.993383	+	0.114844i	$0.0366370\pi$
$6$	1.01067	−	0.989218i	0.412603	−	0.403847i
$7$	1.40437	+	4.32221i	0.530802	+	1.63364i	0.752548	+	0.658537i	$0.228824\pi$
$7$	1.40437	+	4.32221i	0.530802	+	1.63364i	−0.221746	+	0.975104i	$0.571176\pi$
$8$	2.80639	−	0.352368i	0.992209	−	0.124581i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.678982	+	4.60611i	0.214713	+	1.45658i
$11$	1.46412	−	2.97596i	0.441448	−	0.897287i
$11$	1.46412	−	2.97596i	0.441448	−	0.897287i
$12$	0.577096	+	1.91493i	0.166593	+	0.552793i
$13$	−0.838793	+	1.15450i	−0.232639	+	0.320201i	−0.909337	−	0.416060i	$-0.863410\pi$
$13$	−0.838793	+	1.15450i	−0.232639	+	0.320201i	0.676698	+	0.736261i	$0.263410\pi$
$14$	−6.33681	−	1.07344i	−1.69359	−	0.286889i
$15$	−3.13108	+	1.01735i	−0.808440	+	0.262678i
$16$	−1.39808	+	3.74772i	−0.349520	+	0.936929i
$17$	1.93604	+	2.66473i	0.469559	+	0.646293i	0.976457	−	0.215714i	$-0.0692078\pi$
$17$	1.93604	+	2.66473i	0.469559	+	0.646293i	−0.506898	+	0.862006i	$0.669208\pi$
$18$	−1.26689	+	0.628489i	−0.298608	+	0.148136i
$19$	0.989336	−	3.04486i	0.226969	−	0.698539i	−0.771117	−	0.636694i	$-0.780301\pi$
$19$	0.989336	−	3.04486i	0.226969	−	0.698539i	0.998086	−	0.0618453i	$-0.0196985\pi$
$20$	−6.21707	−	2.16854i	−1.39018	−	0.484900i
$21$		−	4.54464i		−	0.991722i
$22$	2.76947	+	3.78550i	0.590454	+	0.807071i
$23$		−	3.51482i		−	0.732891i	−0.930439	−	0.366446i	$-0.880575\pi$
$23$		−	3.51482i		−	0.732891i	0.930439	−	0.366446i	$-0.119425\pi$
$24$	−2.77793	−	0.532101i	−0.567042	−	0.108615i
$25$	1.80424	−	5.55287i	0.360848	−	1.11057i
$26$	−0.896879	−	1.80790i	−0.175892	−	0.354558i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	5.49903	−	7.23710i	1.03922	−	1.36768i
$29$	−3.38012	+	1.09827i	−0.627672	+	0.203943i	−0.605543	−	0.795812i	$-0.707044\pi$
$29$	−3.38012	+	1.09827i	−0.627672	+	0.203943i	−0.0221282	+	0.999755i	$0.507044\pi$
$30$	0.777617	−	4.59049i	0.141973	−	0.838105i
$31$	−1.57372	+	2.16604i	−0.282649	+	0.389033i	−0.926609	−	0.376026i	$-0.877290\pi$
$31$	−1.57372	+	2.16604i	−0.282649	+	0.389033i	0.643960	+	0.765059i	$0.277290\pi$
$32$	−3.77986	−	4.20864i	−0.668191	−	0.743990i
$33$	−2.31208	+	2.37787i	−0.402482	+	0.413935i
$34$	−4.60833	+	0.679308i	−0.790321	+	0.116500i
$35$	12.1044	+	8.79438i	2.04602	+	1.48652i
$36$	0.0428958	−	1.99954i	0.00714929	−	0.333257i
$37$	0.140713	+	0.433070i	0.0231331	+	0.0711962i	0.961957	−	0.273202i	$-0.0880829\pi$
$37$	0.140713	+	0.433070i	0.0231331	+	0.0711962i	−0.938824	+	0.344399i	$0.888083\pi$
$38$	3.16704	+	3.23571i	0.513761	+	0.524901i
$39$	1.15450	−	0.838793i	0.184868	−	0.134314i
$40$	6.79282	−	6.36920i	1.07404	−	1.00706i
$41$	−8.53807	−	2.77419i	−1.33342	−	0.433255i	−0.446339	−	0.894864i	$-0.647272\pi$
$41$	−8.53807	−	2.77419i	−1.33342	−	0.433255i	−0.887084	+	0.461609i	$0.847272\pi$
$42$	5.69496	+	2.97909i	0.878751	+	0.459683i
$43$	−10.5057			−1.60211			−0.801055	−	0.598591i	$-0.795727\pi$
$43$	−10.5057			−1.60211			−0.801055	+	0.598591i	$0.795727\pi$
$44$	−6.55910	+	0.989014i	−0.988822	+	0.149100i
$45$	3.29221			0.490773
$46$	4.40448	+	2.30402i	0.649405	+	0.339710i
$47$	−3.26990	−	1.06246i	−0.476964	−	0.154975i	0.0606621	−	0.998158i	$-0.480679\pi$
$47$	−3.26990	−	1.06246i	−0.476964	−	0.154975i	−0.537626	+	0.843183i	$0.680679\pi$
$48$	2.48776	−	3.13226i	0.359077	−	0.452103i
$49$	−11.0461	+	8.02547i	−1.57802	+	1.14650i
$50$	5.77569	+	5.90092i	0.816805	+	0.834516i
$51$	−1.01784	−	3.13258i	−0.142526	−	0.438649i
$52$	2.85342	+	0.0612140i	0.395699	+	0.00848885i
$53$	1.87204	+	1.36012i	0.257145	+	0.186827i	0.708887	−	0.705322i	$-0.249197\pi$
$53$	1.87204	+	1.36012i	0.257145	+	0.186827i	−0.451743	+	0.892148i	$0.649197\pi$
$54$	1.39909	−	0.206239i	0.190393	−	0.0280656i
$55$	−1.85922	−	10.7596i	−0.250697	−	1.45082i
$56$	5.46422	+	11.6350i	0.730187	+	1.55479i
$57$	−1.88183	+	2.59011i	−0.249254	+	0.343069i
$58$	0.839467	−	4.95561i	0.110227	−	0.650703i
$59$	2.50457	−	0.813785i	0.326067	−	0.105946i	−0.141409	−	0.989951i	$-0.545163\pi$
$59$	2.50457	−	0.813785i	0.326067	−	0.105946i	0.467476	+	0.884006i	$0.345163\pi$
$60$	5.24267	+	3.98358i	0.676826	+	0.514278i
$61$	0.697794	+	0.960431i	0.0893434	+	0.122971i	0.851349	−	0.524600i	$-0.175785\pi$
$61$	0.697794	+	0.960431i	0.0893434	+	0.122971i	−0.762005	+	0.647571i	$0.775785\pi$
$62$	−1.68270	−	3.39193i	−0.213703	−	0.430776i
$63$	−1.40437	+	4.32221i	−0.176934	+	0.544547i
$64$	7.75167	−	1.97776i	0.968959	−	0.247221i
$65$			4.69811i			0.582729i
$66$	−1.46414	−	4.45604i	−0.180224	−	0.548501i
$67$			6.30893i			0.770759i	0.922758	+	0.385379i	$0.125929\pi$
$67$			6.30893i			0.770759i	−0.922758	+	0.385379i	$0.874071\pi$
$68$	2.16958	−	6.22006i	0.263100	−	0.754293i
$69$	−1.08614	+	3.34279i	−0.130756	+	0.402425i
$70$	−18.9550	+	9.40339i	−2.26556	+	1.12392i
$71$	−0.379984	−	0.523003i	−0.0450958	−	0.0620690i	0.785874	−	0.618387i	$-0.212214\pi$
$71$	−0.379984	−	0.523003i	−0.0450958	−	0.0620690i	−0.830969	+	0.556318i	$0.812214\pi$
$72$	2.47754	+	1.36448i	0.291980	+	0.160806i
$73$	6.49205	−	2.10940i	0.759837	−	0.246886i	0.0966285	−	0.995321i	$-0.469194\pi$
$73$	6.49205	−	2.10940i	0.759837	−	0.246886i	0.663209	+	0.748434i	$0.269194\pi$
$74$	−0.634926	−	0.107555i	−0.0738087	−	0.0125030i
$75$	−3.43187	+	4.72356i	−0.396278	+	0.545429i
$76$	−6.13076	+	1.84760i	−0.703247	+	0.211935i
$77$	14.9189	+	2.14886i	1.70017	+	0.244885i
$78$	0.294311	+	1.99656i	0.0333242	+	0.226066i
$79$	7.83975	+	5.69591i	0.882041	+	0.640840i	0.933791	−	0.357820i	$-0.116480\pi$
$79$	7.83975	+	5.69591i	0.882041	+	0.640840i	−0.0517498	+	0.998660i	$0.516480\pi$
$80$	3.52853	+	12.6873i	0.394502	+	1.41848i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	9.07322	−	8.88066i	1.00197	−	0.980705i
$83$	0.906427	−	0.658558i	0.0994933	−	0.0722861i	−0.536926	−	0.843629i	$-0.680415\pi$
$83$	0.906427	−	0.658558i	0.0994933	−	0.0722861i	0.636420	+	0.771343i	$0.280415\pi$
$84$	−7.46628	+	5.18360i	−0.814637	+	0.565577i
$85$	10.3131	+	3.35093i	1.11861	+	0.363460i
$86$	6.88668	−	13.1649i	0.742610	−	1.41961i
$87$	3.55406			0.381036
$88$	3.06025	−	8.86763i	0.326224	−	0.945293i
$89$	−16.2562			−1.72316			−0.861579	−	0.507624i	$-0.830524\pi$
$89$	−16.2562			−1.72316			−0.861579	+	0.507624i	$0.830524\pi$
$90$	−2.15810	+	4.12552i	−0.227483	+	0.434868i
$91$	−6.16797	−	2.00409i	−0.646579	−	0.210086i
$92$	−5.77441	+	4.00899i	−0.602024	+	0.417967i
$93$	2.16604	−	1.57372i	0.224608	−	0.163187i
$94$	3.47485	−	3.40111i	0.358404	−	0.350797i
$95$	−3.25710	−	10.0243i	−0.334171	−	1.02847i
$96$	2.29432	+	5.17070i	0.234163	+	0.527732i
$97$	−9.60184	−	6.97614i	−0.974919	−	0.708320i	−0.0183516	−	0.999832i	$-0.505842\pi$
$97$	−9.60184	−	6.97614i	−0.974919	−	0.708320i	−0.956567	+	0.291512i	$0.905842\pi$
$98$	−2.81593	−	19.1029i	−0.284452	−	1.92968i
$99$	2.93372	−	1.54702i	0.294850	−	0.155481i
$100$	−11.1806	+	3.36945i	−1.11806	+	0.336945i
$101$	5.24907	−	7.22473i	0.522302	−	0.718887i	−0.463631	−	0.886028i	$-0.653454\pi$
$101$	5.24907	−	7.22473i	0.522302	−	0.718887i	0.985933	+	0.167141i	$0.0534536\pi$
$102$	4.59270	+	0.777991i	0.454745	+	0.0770325i
$103$	16.7188	−	5.43226i	1.64735	−	0.535256i	0.669187	−	0.743094i	$-0.266643\pi$
$103$	16.7188	−	5.43226i	1.64735	−	0.535256i	0.978163	+	0.207838i	$0.0666427\pi$
$104$	−1.94717	+	3.53554i	−0.190936	+	0.346689i
$105$	−8.79438	−	12.1044i	−0.858244	−	1.18127i
$106$	−2.93154	+	1.45431i	−0.284736	+	0.141255i
$107$	−0.159322	+	0.490341i	−0.0154022	+	0.0474031i	−0.958462	−	0.285219i	$-0.907934\pi$
$107$	−0.159322	+	0.490341i	−0.0154022	+	0.0474031i	0.943060	+	0.332623i	$0.107934\pi$
$108$	−0.658688	+	1.88842i	−0.0633823	+	0.181713i
$109$		−	1.15068i		−	0.110215i	−0.998480	−	0.0551077i	$-0.982450\pi$
$109$		−	1.15068i		−	0.110215i	0.998480	−	0.0551077i	$-0.0175502\pi$
$110$	14.7017	+	4.72326i	1.40175	+	0.450345i
$111$		−	0.455357i		−	0.0432205i
$112$	−18.1618	−	0.779604i	−1.71613	−	0.0736656i
$113$	−2.25825	+	6.95019i	−0.212439	+	0.653819i	0.786887	+	0.617097i	$0.211692\pi$
$113$	−2.25825	+	6.95019i	−0.212439	+	0.653819i	−0.999326	+	0.0367218i	$0.988308\pi$
$114$	−2.01214	−	4.05601i	−0.188454	−	0.379880i
$115$	−6.80157	−	9.36156i	−0.634250	−	0.872970i
$116$	5.65966	+	4.30043i	0.525486	+	0.399285i
$117$	−1.35720	+	0.440980i	−0.125473	+	0.0407686i
$118$	−0.622022	+	3.67197i	−0.0572617	+	0.338032i
$119$	−8.79861	+	12.1103i	−0.806567	+	1.11014i
$120$	−8.42855	+	3.95837i	−0.769418	+	0.361348i
$121$	−6.71273	−	8.71432i	−0.610248	−	0.792211i
$122$	−1.66095	+	0.244838i	−0.150375	+	0.0221666i
$123$	7.26292	+	5.27682i	0.654875	+	0.475795i
$124$	5.35352	+	0.114848i	0.480760	+	0.0103137i
$125$	−0.853187	−	2.62584i	−0.0763113	−	0.234862i
$126$	−4.49564	−	4.59312i	−0.400503	−	0.409187i
$127$	−9.54190	+	6.93260i	−0.846707	+	0.615168i	−0.924236	−	0.381822i	$-0.875297\pi$
$127$	−9.54190	+	6.93260i	−0.846707	+	0.615168i	0.0775294	+	0.996990i	$0.475297\pi$
$128$	−2.60298	+	11.0102i	−0.230073	+	0.973173i
$129$	9.99154	+	3.24645i	0.879706	+	0.285834i
$130$	−5.88728	−	3.07969i	−0.516349	−	0.270107i
$131$	−1.62443			−0.141927			−0.0709635	−	0.997479i	$-0.522607\pi$
$131$	−1.62443			−0.141927			−0.0709635	+	0.997479i	$0.522607\pi$
$132$	6.54370	+	1.08627i	0.569556	+	0.0945473i
$133$	14.5499			1.26164
$134$	−7.90582	−	4.13561i	−0.682959	−	0.357262i
$135$	−3.13108	−	1.01735i	−0.269480	−	0.0875594i
$136$	6.37226	+	6.79609i	0.546417	+	0.582760i
$137$	8.56610	−	6.22364i	0.731852	−	0.531721i	−0.158297	−	0.987392i	$-0.550600\pi$
$137$	8.56610	−	6.22364i	0.731852	−	0.531721i	0.890149	+	0.455670i	$0.150600\pi$
$138$	−3.47693	−	3.55232i	−0.295976	−	0.302393i
$139$	−2.31508	−	7.12509i	−0.196363	−	0.604342i	−0.999958	−	0.00916624i	$-0.997082\pi$
$139$	−2.31508	−	7.12509i	−0.196363	−	0.604342i	0.803595	−	0.595176i	$-0.202918\pi$
$140$	0.641802	−	29.9169i	0.0542422	−	2.52844i
$141$	2.78154	+	2.02091i	0.234248	+	0.170191i
$142$	0.904468	−	0.133327i	0.0759013	−	0.0111885i
$143$	2.20766	+	4.18654i	0.184614	+	0.350096i
$144$	−3.33392	+	2.21020i	−0.277827	+	0.184183i
$145$	−6.87751	+	9.46608i	−0.571146	+	0.786115i
$146$	−1.61233	+	9.51803i	−0.133437	+	0.787718i
$147$	12.9855	−	4.21924i	1.07102	−	0.347997i
$148$	0.550983	−	0.725132i	0.0452905	−	0.0596055i
$149$	−1.52127	−	2.09385i	−0.124628	−	0.171535i	0.742144	−	0.670240i	$-0.233809\pi$
$149$	−1.52127	−	2.09385i	−0.124628	−	0.171535i	−0.866772	+	0.498705i	$0.833809\pi$
$150$	−3.66952	−	7.39689i	−0.299615	−	0.603954i
$151$	−2.79066	+	8.58877i	−0.227101	+	0.698944i	0.770971	+	0.636870i	$0.219771\pi$
$151$	−2.79066	+	8.58877i	−0.227101	+	0.698944i	−0.998072	+	0.0620737i	$0.980229\pi$
$152$	1.70355	−	8.89369i	0.138176	−	0.721373i
$153$			3.29379i			0.266287i
$154$	−12.4724	+	17.2865i	−1.00505	+	1.39299i
$155$			8.81448i			0.707996i
$156$	−2.69485	−	0.939974i	−0.215761	−	0.0752582i
$157$	5.48646	−	16.8856i	0.437867	−	1.34762i	−0.452252	−	0.891890i	$-0.649379\pi$
$157$	5.48646	−	16.8856i	0.437867	−	1.34762i	0.890120	−	0.455727i	$-0.150621\pi$
$158$	−12.2767	+	6.09035i	−0.976683	+	0.484522i
$159$	−1.36012	−	1.87204i	−0.107864	−	0.148463i
$160$	−18.2117	−	3.89507i	−1.43976	−	0.307933i
$161$	15.1918	−	4.93611i	1.19728	−	0.389020i
$162$	−1.39435	−	0.236199i	−0.109550	−	0.0185576i
$163$	−5.78224	+	7.95857i	−0.452900	+	0.623363i	−0.973017	−	0.230731i	$-0.925888\pi$
$163$	−5.78224	+	7.95857i	−0.452900	+	0.623363i	0.520118	+	0.854095i	$0.325888\pi$
$164$	5.18085	+	17.1912i	0.404556	+	1.34241i
$165$	−1.55667	+	10.8075i	−0.121186	+	0.841362i
$166$	0.231071	+	1.56755i	0.0179346	+	0.121666i
$167$	−6.02021	−	4.37394i	−0.465858	−	0.338466i	0.329967	−	0.943993i	$-0.392962\pi$
$167$	−6.02021	−	4.37394i	−0.465858	−	0.338466i	−0.795825	+	0.605527i	$0.792962\pi$
$168$	−1.60138	−	12.7540i	−0.123549	−	0.983996i
$169$	3.38793	+	10.4270i	0.260610	+	0.802074i
$170$	−10.9595	+	10.7269i	−0.840557	+	0.822718i
$171$	2.59011	−	1.88183i	0.198071	−	0.143907i
$172$	11.9828	+	17.2596i	0.913680	+	1.31603i
$173$	−6.78760	−	2.20542i	−0.516052	−	0.167675i	0.0394011	−	0.999223i	$-0.487455\pi$
$173$	−6.78760	−	2.20542i	−0.516052	−	0.167675i	−0.555453	+	0.831548i	$0.687455\pi$
$174$	−2.32975	+	4.45365i	−0.176618	+	0.337630i
$175$	26.5345			2.00582
$176$	9.10612	+	9.64772i	0.686400	+	0.727225i
$177$	−2.63346			−0.197943
$178$	10.6562	−	20.3709i	0.798718	−	1.52687i
$179$	−21.7851	−	7.07840i	−1.62829	−	0.529064i	−0.654414	−	0.756136i	$-0.727085\pi$
$179$	−21.7851	−	7.07840i	−1.62829	−	0.529064i	−0.973878	+	0.227072i	$0.927085\pi$
$180$	−3.75508	−	5.40869i	−0.279887	−	0.403140i
$181$	8.57223	−	6.22809i	0.637169	−	0.462930i	−0.221707	−	0.975113i	$-0.571163\pi$
$181$	8.57223	−	6.22809i	0.637169	−	0.462930i	0.858876	+	0.512183i	$0.171163\pi$
$182$	6.55456	−	6.41546i	0.485857	−	0.475545i
$183$	−0.366852	−	1.12905i	−0.0271185	−	0.0834621i
$184$	−1.23851	−	9.86397i	−0.0913042	−	0.727182i
$185$	1.21282	+	0.881166i	0.0891683	+	0.0647846i
$186$	0.552179	+	3.74590i	0.0404877	+	0.274663i
$187$	10.7647	−	1.86011i	0.787196	−	0.136025i
$188$	1.98416	+	6.58387i	0.144709	+	0.480178i
$189$	2.67127	−	3.67669i	0.194306	−	0.267440i
$190$	14.6967	+	2.48958i	1.06621	+	0.180613i
$191$	10.1007	−	3.28193i	0.730863	−	0.237472i	0.0801365	−	0.996784i	$-0.474464\pi$
$191$	10.1007	−	3.28193i	0.730863	−	0.237472i	0.650727	+	0.759312i	$0.274464\pi$
$192$	−7.98344	−	0.514433i	−0.576155	−	0.0371260i
$193$	14.9881	+	20.6293i	1.07887	+	1.48493i	0.860764	+	0.509005i	$0.169986\pi$
$193$	14.9881	+	20.6293i	1.07887	+	1.48493i	0.218102	+	0.975926i	$0.430014\pi$
$194$	15.0361	−	7.45924i	1.07953	−	0.535542i
$195$	1.45180	−	4.46817i	0.103965	−	0.319972i
$196$	25.7840	+	8.99356i	1.84171	+	0.642397i
$197$		−	7.36121i		−	0.524464i	−0.965005	−	0.262232i	$-0.915541\pi$
$197$		−	7.36121i		−	0.524464i	0.965005	−	0.262232i	$-0.0844586\pi$
$198$	0.0154910	+	4.69039i	0.00110090	+	0.333332i
$199$		−	15.2259i		−	1.07934i	−0.841878	−	0.539668i	$-0.818550\pi$
$199$		−	15.2259i		−	1.07934i	0.841878	−	0.539668i	$-0.181450\pi$
$200$	3.10675	−	16.2193i	0.219680	−	1.14688i
$201$	1.94957	−	6.00015i	0.137512	−	0.423218i
$202$	5.61257	+	11.3136i	0.394899	+	0.796023i
$203$	−9.49387	−	13.0672i	−0.666339	−	0.917137i
$204$	−3.98550	+	5.24519i	−0.279041	+	0.367237i
$205$	−28.1091	+	9.13320i	−1.96323	+	0.637891i
$206$	−4.15218	+	24.5115i	−0.289296	+	1.70780i
$207$	2.06596	−	2.84355i	0.143594	−	0.197640i
$208$	−3.15404	−	4.75764i	−0.218693	−	0.329883i
$209$	−7.61290	−	7.40226i	−0.526595	−	0.512025i
$210$	20.9331	−	3.08573i	1.44452	−	0.212935i
$211$	11.6671	+	8.47664i	0.803196	+	0.583556i	0.911850	−	0.410524i	$-0.134654\pi$
$211$	11.6671	+	8.47664i	0.803196	+	0.583556i	−0.108654	+	0.994080i	$0.534654\pi$
$212$	0.0992596	−	4.62688i	0.00681717	−	0.317775i
$213$	0.199769	+	0.614827i	0.0136880	+	0.0421272i
$214$	−0.510017	−	0.521075i	−0.0348640	−	0.0356200i
$215$	−27.9815	+	20.3298i	−1.90832	+	1.38648i
$216$	−1.93463	−	2.06330i	−0.131635	−	0.140390i
$217$	−11.5722	−	3.76003i	−0.785571	−	0.255247i
$218$	1.44194	+	0.754291i	0.0976603	+	0.0510870i
$219$	−6.82615			−0.461268
$220$	−15.5560	+	15.3268i	−1.04879	+	1.03333i
$221$	−4.70037			−0.316181
$222$	0.570614	+	0.298494i	0.0382971	+	0.0200336i
$223$	20.9700	+	6.81357i	1.40425	+	0.456270i	0.910564	−	0.413368i	$-0.135648\pi$
$223$	20.9700	+	6.81357i	1.40425	+	0.456270i	0.493691	+	0.869638i	$0.335648\pi$
$224$	12.8823	−	22.2478i	0.860736	−	1.48650i
$225$	4.72356	−	3.43187i	0.314904	−	0.228791i
$226$	−7.22907	−	7.38582i	−0.480871	−	0.491297i
$227$	7.04025	+	21.6676i	0.467278	+	1.43813i	0.856095	+	0.516818i	$0.172884\pi$
$227$	7.04025	+	21.6676i	0.467278	+	1.43813i	−0.388818	+	0.921315i	$0.627116\pi$
$228$	6.40164	+	0.137333i	0.423959	+	0.00909512i
$229$	5.40049	+	3.92369i	0.356875	+	0.259285i	0.751747	−	0.659451i	$-0.229211\pi$
$229$	5.40049	+	3.92369i	0.356875	+	0.259285i	−0.394873	+	0.918736i	$0.629211\pi$
$230$	16.1897	−	2.38650i	1.06751	−	0.157361i
$231$	−13.5247	−	6.65388i	−0.889859	−	0.437793i
$232$	−9.09894	+	4.27321i	−0.597374	+	0.280550i
$233$	−2.93304	+	4.03698i	−0.192150	+	0.264471i	−0.894212	−	0.447645i	$-0.852263\pi$
$233$	−2.93304	+	4.03698i	−0.192150	+	0.264471i	0.702062	+	0.712116i	$0.252263\pi$
$234$	0.337066	−	1.98979i	0.0220347	−	0.130077i
$235$	−10.7652	+	3.49782i	−0.702244	+	0.228173i
$236$	−4.19365	−	3.18650i	−0.272984	−	0.207423i
$237$	−5.69591	−	7.83975i	−0.369989	−	0.509246i
$238$	−9.40791	−	18.9641i	−0.609824	−	1.22926i
$239$	0.333992	−	1.02792i	0.0216042	−	0.0664908i	−0.939673	−	0.342074i	$-0.888871\pi$
$239$	0.333992	−	1.02792i	0.0216042	−	0.0664908i	0.961277	+	0.275583i	$0.0888708\pi$
$240$	0.564757	−	13.1567i	0.0364549	−	0.849263i
$241$			1.92559i			0.124038i	0.998075	+	0.0620192i	$0.0197540\pi$
$241$			1.92559i			0.124038i	−0.998075	+	0.0620192i	$0.980246\pi$
$242$	15.3203	−	2.69945i	0.984829	−	0.173527i
$243$		−	1.00000i		−	0.0641500i
$244$	0.781967	−	2.24185i	0.0500603	−	0.143520i
$245$	−13.8906	+	42.7509i	−0.887439	+	2.73126i
$246$	−11.3734	+	5.64223i	−0.725143	+	0.359736i
$247$	2.68544	+	3.69620i	0.170871	+	0.235183i
$248$	−3.65324	+	6.63330i	−0.231981	+	0.421215i
$249$	−1.06557	+	0.346224i	−0.0675277	+	0.0219411i
$250$	3.84976	+	0.652139i	0.243480	+	0.0412449i
$251$	7.31555	−	10.0690i	0.461754	−	0.635549i	−0.513118	−	0.858318i	$-0.671510\pi$
$251$	7.31555	−	10.0690i	0.461754	−	0.635549i	0.974871	+	0.222769i	$0.0715095\pi$
$252$	8.70267	−	2.62269i	0.548217	−	0.165214i
$253$	−10.4600	−	5.14611i	−0.657614	−	0.323533i
$254$	−2.43247	−	16.5015i	−0.152627	−	1.03540i
$255$	−8.77286	−	6.37385i	−0.549378	−	0.399146i
$256$	−12.0908	−	10.4792i	−0.755672	−	0.654950i
$257$	2.72942	+	8.40029i	0.170257	+	0.523996i	0.999385	−	0.0350621i	$-0.0111629\pi$
$257$	2.72942	+	8.40029i	0.170257	+	0.523996i	−0.829129	+	0.559058i	$0.811163\pi$
$258$	−10.6178	+	10.3925i	−0.661035	+	0.647006i
$259$	−1.67421	+	1.21638i	−0.104030	+	0.0755822i
$260$	7.71842	−	5.35865i	0.478676	−	0.332330i
$261$	−3.38012	−	1.09827i	−0.209224	−	0.0679810i
$262$	1.06484	−	2.03560i	0.0657861	−	0.125760i
$263$	−1.43738			−0.0886326			−0.0443163	−	0.999018i	$-0.514111\pi$
$263$	−1.43738			−0.0886326			−0.0443163	+	0.999018i	$0.514111\pi$
$264$	−5.65072	+	7.48795i	−0.347778	+	0.460851i
$265$	7.61808			0.467975
$266$	−9.53771	+	18.2327i	−0.584795	+	1.11792i
$267$	15.4606	+	5.02345i	0.946173	+	0.307430i
$268$	10.3648	−	7.19594i	0.633130	−	0.439562i
$269$	1.66385	−	1.20886i	0.101447	−	0.0737055i	−0.535905	−	0.844278i	$-0.680030\pi$
$269$	1.66385	−	1.20886i	0.101447	−	0.0737055i	0.637352	+	0.770573i	$0.280030\pi$
$270$	3.32733	−	3.25671i	0.202495	−	0.198197i
$271$	−2.13419	−	6.56835i	−0.129643	−	0.398999i	0.865076	−	0.501641i	$-0.167270\pi$
$271$	−2.13419	−	6.56835i	−0.129643	−	0.398999i	−0.994718	+	0.102642i	$0.967270\pi$
$272$	−12.6934	+	3.53023i	−0.769651	+	0.214052i
$273$	5.24679	+	3.81201i	0.317550	+	0.230714i
$274$	2.18372	+	14.8140i	0.131923	+	0.894947i
$275$	−13.8835	−	13.4994i	−0.837209	−	0.814045i
$276$	6.73064	−	2.02839i	0.405137	−	0.122095i
$277$	−11.0982	+	15.2753i	−0.666824	+	0.917804i	−0.999683	−	0.0251724i	$-0.991987\pi$
$277$	−11.0982	+	15.2753i	−0.666824	+	0.917804i	0.332859	+	0.942976i	$0.391987\pi$
$278$	10.4461	+	1.76955i	0.626518	+	0.106130i
$279$	−2.54634	+	0.827355i	−0.152445	+	0.0495324i
$280$	37.0686	+	20.4153i	2.21528	+	1.22005i
$281$	−7.98872	−	10.9955i	−0.476567	−	0.655938i	0.501274	−	0.865289i	$-0.332865\pi$
$281$	−7.98872	−	10.9955i	−0.476567	−	0.655938i	−0.977841	+	0.209350i	$0.932865\pi$
$282$	−4.35578	+	2.16086i	−0.259383	+	0.128677i
$283$	−5.97209	+	18.3802i	−0.355004	+	1.09259i	0.601003	+	0.799247i	$0.294768\pi$
$283$	−5.97209	+	18.3802i	−0.355004	+	1.09259i	−0.956007	+	0.293344i	$0.905232\pi$
$284$	−0.425820	+	1.22080i	−0.0252678	+	0.0724412i
$285$			10.5402i			0.624347i
$286$	−6.69338	+	0.0221063i	−0.395788	+	0.00130717i
$287$		−	40.7993i		−	2.40831i
$288$	−0.584191	−	5.62661i	−0.0344238	−	0.331551i
$289$	1.90074	−	5.84989i	0.111809	−	0.344111i
$290$	−7.35377	−	14.8235i	−0.431828	−	0.870465i
$291$	6.97614	+	9.60184i	0.408949	+	0.562870i
$292$	−10.8703	−	8.25966i	−0.636135	−	0.483360i
$293$	15.0360	−	4.88550i	0.878414	−	0.285414i	0.165115	−	0.986274i	$-0.447200\pi$
$293$	15.0360	−	4.88550i	0.878414	−	0.285414i	0.713298	+	0.700860i	$0.247200\pi$
$294$	−3.22500	+	19.0381i	−0.188086	+	1.11032i
$295$	5.09604	−	7.01410i	0.296703	−	0.408377i
$296$	0.547495	+	1.16578i	0.0318225	+	0.0677596i
$297$	−3.26819	+	0.564733i	−0.189640	+	0.0327691i
$298$	3.62106	−	0.533776i	0.209762	−	0.0309208i
$299$	4.05786	+	2.94821i	0.234672	+	0.170499i
$300$	11.6746	+	0.250453i	0.674033	+	0.0144599i
$301$	−14.7539	−	45.4080i	−0.850403	−	2.61727i
$302$	−8.93340	−	9.12710i	−0.514059	−	0.525205i
$303$	−7.22473	+	5.24907i	−0.415050	+	0.301551i
$304$	10.0281	+	7.96470i	0.575152	+	0.456807i
$305$	3.71708	+	1.20775i	0.212840	+	0.0691558i
$306$	−4.12750	−	2.15913i	−0.235954	−	0.123429i
$307$	−25.7118			−1.46745			−0.733725	−	0.679446i	$-0.762220\pi$
$307$	−25.7118			−1.46745			−0.733725	+	0.679446i	$0.762220\pi$
$308$	−13.4861	−	26.9609i	−0.768444	−	1.53624i
$309$	−17.5792			−1.00004
$310$	−11.0456	−	5.77804i	−0.627346	−	0.328170i
$311$	29.4939	+	9.58316i	1.67245	+	0.543411i	0.983423	−	0.181326i	$-0.0580390\pi$
$311$	29.4939	+	9.58316i	1.67245	+	0.543411i	0.689025	+	0.724738i	$0.258039\pi$
$312$	2.94442	−	2.76079i	0.166695	−	0.156299i
$313$	−9.77635	+	7.10293i	−0.552592	+	0.401481i	−0.828740	−	0.559634i	$-0.810942\pi$
$313$	−9.77635	+	7.10293i	−0.552592	+	0.401481i	0.276148	+	0.961115i	$0.410942\pi$
$314$	17.5631	+	17.9440i	0.991145	+	1.01264i
$315$	4.62348	+	14.2296i	0.260504	+	0.801748i
$316$	0.415680	−	19.3765i	0.0233838	−	1.09001i
$317$	−27.1151	−	19.7003i	−1.52294	−	1.10648i	−0.960008	−	0.279974i	$-0.909674\pi$
$317$	−27.1151	−	19.7003i	−1.52294	−	1.10648i	−0.562929	−	0.826505i	$-0.690326\pi$
$318$	3.23746	−	0.477231i	0.181548	−	0.0267618i
$319$	−1.68048	+	11.6671i	−0.0940889	+	0.653232i
$320$	16.8190	−	20.2680i	0.940212	−	1.13302i
$321$	0.303048	−	0.417109i	0.0169145	−	0.0232808i
$322$	−3.77295	+	22.2728i	−0.210258	+	1.24121i
$323$	10.0291	−	3.25866i	0.558036	−	0.181317i
$324$	1.21000	−	1.59245i	0.0672224	−	0.0884693i
$325$	4.89741	+	6.74071i	0.271659	+	0.373907i
$326$	−6.18265	−	12.4628i	−0.342426	−	0.690250i
$327$	−0.355580	+	1.09436i	−0.0196636	+	0.0605184i
$328$	−24.9387	−	4.77692i	−1.37701	−	0.263761i
$329$		−	15.6253i		−	0.861449i
$330$	−12.5226	−	9.03517i	−0.689347	−	0.497370i
$331$		−	24.0830i		−	1.32372i	−0.749626	−	0.661861i	$-0.769767\pi$
$331$		−	24.0830i		−	1.32372i	0.749626	−	0.661861i	$-0.230233\pi$
$332$	−2.11580	−	0.737997i	−0.116119	−	0.0405029i
$333$	−0.140713	+	0.433070i	−0.00771102	+	0.0237321i
$334$	9.42740	−	4.67683i	0.515845	−	0.255905i
$335$	12.2085	+	16.8035i	0.667021	+	0.918075i
$336$	17.0320	+	6.35376i	0.929173	+	0.346626i
$337$	−8.75821	+	2.84572i	−0.477090	+	0.155016i	−0.537684	−	0.843147i	$-0.680701\pi$
$337$	−8.75821	+	2.84572i	−0.477090	+	0.155016i	0.0605937	+	0.998163i	$0.480701\pi$
$338$	−15.2870	−	2.58958i	−0.831505	−	0.140855i
$339$	4.29546	−	5.91219i	0.233297	−	0.321106i
$340$	−6.25794	−	20.7652i	−0.339384	−	1.12615i
$341$	4.14195	+	7.85468i	0.224299	+	0.425355i
$342$	0.660286	+	4.47928i	0.0357042	+	0.242212i
$343$	−24.4638	−	17.7740i	−1.32092	−	0.959704i
$344$	−29.4832	+	3.70188i	−1.58963	+	0.199592i
$345$	3.57580	+	11.0052i	0.192515	+	0.592499i
$346$	7.21303	−	7.05995i	0.387775	−	0.379545i
$347$	27.8132	−	20.2074i	1.49309	−	1.08479i	0.520054	−	0.854133i	$-0.325912\pi$
$347$	27.8132	−	20.2074i	1.49309	−	1.08479i	0.973035	−	0.230659i	$-0.0740883\pi$
$348$	−4.05375	−	5.83888i	−0.217304	−	0.312997i
$349$	16.7485	+	5.44191i	0.896525	+	0.291299i	0.720802	−	0.693141i	$-0.243774\pi$
$349$	16.7485	+	5.44191i	0.896525	+	0.291299i	0.175723	+	0.984440i	$0.443774\pi$
$350$	−17.3938	+	33.2508i	−0.929738	+	1.77733i
$351$	1.42704			0.0761698
$352$	−18.0589	+	5.08678i	−0.962544	+	0.271126i
$353$	28.4766			1.51565			0.757827	−	0.652455i	$-0.226261\pi$
$353$	28.4766			1.51565			0.757827	+	0.652455i	$0.226261\pi$
$354$	1.72628	−	3.30003i	0.0917506	−	0.175395i
$355$	−2.02414	−	0.657682i	−0.107430	−	0.0349061i
$356$	18.5418	+	26.7070i	0.982714	+	1.41547i
$357$	12.1103	−	8.79861i	0.640942	−	0.465672i
$358$	23.1505	−	22.6592i	1.22354	−	1.19758i
$359$	6.72849	+	20.7082i	0.355116	+	1.09294i	0.955942	+	0.293556i	$0.0948386\pi$
$359$	6.72849	+	20.7082i	0.355116	+	1.09294i	−0.600826	+	0.799380i	$0.705161\pi$
$360$	9.23923	−	1.16007i	0.486950	−	0.0611410i
$361$	7.07892	+	5.14314i	0.372575	+	0.270692i
$362$	2.18528	+	14.8246i	0.114856	+	0.779164i
$363$	3.69131	+	10.3622i	0.193744	+	0.543872i
$364$	3.74269	+	12.4191i	0.196170	+	0.650936i
$365$	13.2094	−	18.1811i	0.691409	−	0.951643i
$366$	1.65531	+	0.280406i	0.0865246	+	0.0146570i
$367$	−27.1565	+	8.82369i	−1.41756	+	0.460593i	−0.914826	−	0.403848i	$-0.867672\pi$
$367$	−27.1565	+	8.82369i	−1.41756	+	0.460593i	−0.502734	+	0.864441i	$0.667672\pi$
$368$	13.1726	+	4.91400i	0.686667	+	0.256160i
$369$	−5.27682	−	7.26292i	−0.274700	−	0.378092i
$370$	−1.89923	+	0.942186i	−0.0987361	+	0.0489819i
$371$	−3.24967	+	10.0015i	−0.168715	+	0.519250i
$372$	−5.05601	−	1.76356i	−0.262142	−	0.0914361i
$373$			32.5424i			1.68498i	0.538712	+	0.842490i	$0.318911\pi$
$373$			32.5424i			1.68498i	−0.538712	+	0.842490i	$0.681089\pi$
$374$	−4.72553	+	14.7088i	−0.244351	+	0.760574i
$375$			2.76097i			0.142576i
$376$	−9.55100	−	1.82946i	−0.492555	−	0.0943471i
$377$	1.56727	−	4.82356i	0.0807185	−	0.248426i
$378$	2.85626	+	5.75754i	0.146910	+	0.296136i
$379$	−9.49522	−	13.0690i	−0.487737	−	0.671312i	0.492232	−	0.870464i	$-0.336181\pi$
$379$	−9.49522	−	13.0690i	−0.487737	−	0.671312i	−0.979969	+	0.199152i	$0.936181\pi$
$380$	−12.7537	+	16.7847i	−0.654250	+	0.861038i
$381$	11.2172	−	3.64468i	0.574673	−	0.186723i
$382$	−2.50856	+	14.8087i	−0.128349	+	0.757681i
$383$	−10.2544	+	14.1139i	−0.523974	+	0.721188i	−0.986197	−	0.165575i	$-0.947052\pi$
$383$	−10.2544	+	14.1139i	−0.523974	+	0.721188i	0.462223	+	0.886764i	$0.347052\pi$
$384$	5.87792	−	9.66696i	0.299956	−	0.493315i
$385$	43.8941	−	23.1464i	2.23705	−	1.17965i
$386$	−35.6758	+	5.25894i	−1.81585	+	0.267673i
$387$	−8.49932	−	6.17511i	−0.432044	−	0.313899i
$388$	−0.509109	+	23.7316i	−0.0258461	+	1.20479i
$389$	10.7040	+	32.9437i	0.542717	+	1.67031i	0.726358	+	0.687317i	$0.241211\pi$
$389$	10.7040	+	32.9437i	0.542717	+	1.67031i	−0.183641	+	0.982993i	$0.558789\pi$
$390$	4.64746	+	4.74823i	0.235333	+	0.240436i
$391$	9.36606	−	6.80484i	0.473662	−	0.344136i
$392$	−28.1718	+	26.4149i	−1.42289	+	1.33415i
$393$	1.54492	+	0.501976i	0.0779311	+	0.0253214i
$394$	9.22444	+	4.82539i	0.464721	+	0.243100i
$395$	31.9030			1.60522
$396$	−5.88776	−	3.05522i	−0.295871	−	0.153530i
$397$	34.3247			1.72271			0.861354	−	0.508005i	$-0.169617\pi$
$397$	34.3247			1.72271			0.861354	+	0.508005i	$0.169617\pi$
$398$	19.0798	+	9.98083i	0.956385	+	0.500294i
$399$	−13.8378	−	4.49617i	−0.692756	−	0.225090i
$400$	18.2881	+	14.5251i	0.914407	+	0.726256i
$401$	−18.7900	+	13.6517i	−0.938329	+	0.681736i	−0.948018	−	0.318217i	$-0.896916\pi$
$401$	−18.7900	+	13.6517i	−0.938329	+	0.681736i	0.00968917	+	0.999953i	$0.496916\pi$
$402$	6.24091	+	6.37623i	0.311268	+	0.318017i
$403$	−1.18067	−	3.63372i	−0.0588133	−	0.181009i
$404$	−17.8564	−	0.383070i	−0.888389	−	0.0190584i
$405$	2.66345	+	1.93511i	0.132348	+	0.0961565i
$406$	22.5981	−	3.33116i	1.12152	−	0.165323i
$407$	1.49482	+	0.215308i	0.0740955	+	0.0106724i
$408$	−3.96027	−	8.43260i	−0.196063	−	0.417476i
$409$	18.0110	−	24.7900i	0.890588	−	1.22579i	−0.0827865	−	0.996567i	$-0.526382\pi$
$409$	18.0110	−	24.7900i	0.890588	−	1.22579i	0.973374	−	0.229222i	$-0.0736181\pi$
$410$	6.98102	−	41.2109i	0.344768	−	2.03526i
$411$	−10.0701	+	3.27196i	−0.496719	+	0.161394i
$412$	−27.9939	−	21.2708i	−1.37916	−	1.04794i
$413$	7.03470	+	9.68243i	0.346155	+	0.476441i
$414$	2.20903	+	4.45288i	0.108568	+	0.218847i
$415$	1.13984	−	3.50807i	0.0559527	−	0.172205i
$416$	8.02940	−	0.833664i	0.393674	−	0.0408737i
$417$			7.49177i			0.366873i
$418$	14.2663	−	4.68754i	0.697786	−	0.229275i
$419$			19.7469i			0.964701i	0.875978	+	0.482350i	$0.160217\pi$
$419$			19.7469i			0.964701i	−0.875978	+	0.482350i	$0.839783\pi$
$420$	−9.85523	+	28.2544i	−0.480886	+	1.37867i
$421$	6.95732	−	21.4124i	0.339079	−	1.04358i	−0.625599	−	0.780145i	$-0.715145\pi$
$421$	6.95732	−	21.4124i	0.339079	−	1.04358i	0.964678	−	0.263433i	$-0.0848548\pi$
$422$	−18.2702	+	9.06364i	−0.889378	+	0.441211i
$423$	−2.02091	−	2.78154i	−0.0982600	−	0.135243i
$424$	5.73295	+	3.15738i	0.278416	+	0.153336i
$425$	18.2900	−	5.94278i	0.887196	−	0.288267i
$426$	−0.901401	−	0.152695i	−0.0436730	−	0.00739809i
$427$	−3.17122	+	4.36481i	−0.153466	+	0.211228i
$428$	0.987292	−	0.297536i	0.0477225	−	0.0143820i
$429$	−0.805897	−	4.66384i	−0.0389091	−	0.225172i
$430$	−7.13320	−	48.3906i	−0.343993	−	2.33360i
$431$	−5.38269	−	3.91076i	−0.259275	−	0.188374i	0.450552	−	0.892750i	$-0.351227\pi$
$431$	−5.38269	−	3.91076i	−0.259275	−	0.188374i	−0.709827	+	0.704376i	$0.751227\pi$
$432$	3.85374	−	1.07178i	0.185413	−	0.0515662i
$433$	−5.78193	−	17.7950i	−0.277862	−	0.855171i	−0.988448	−	0.151561i	$-0.951570\pi$
$433$	−5.78193	−	17.7950i	−0.277862	−	0.855171i	0.710586	−	0.703610i	$-0.248430\pi$
$434$	12.2975	−	12.0365i	0.590299	−	0.577771i
$435$	9.46608	−	6.87751i	0.453864	−	0.329751i
$436$	−1.89043	+	1.31246i	−0.0905350	+	0.0628556i
$437$	−10.7021	−	3.47734i	−0.511953	−	0.166344i
$438$	4.47465	−	8.55395i	0.213807	−	0.408724i
$439$	35.7973			1.70851			0.854256	−	0.519853i	$-0.174013\pi$
$439$	35.7973			1.70851			0.854256	+	0.519853i	$0.174013\pi$
$440$	−9.00902	−	29.5404i	−0.429488	−	1.40829i
$441$	−13.6537			−0.650178
$442$	3.08117	−	5.89011i	0.146556	−	0.280164i
$443$	1.11072	+	0.360895i	0.0527719	+	0.0171466i	0.335284	−	0.942117i	$-0.391168\pi$
$443$	1.11072	+	0.360895i	0.0527719	+	0.0171466i	−0.282512	+	0.959264i	$0.591168\pi$
$444$	−0.748094	+	0.519378i	−0.0355030	+	0.0246486i
$445$	−43.2977	+	31.4576i	−2.05251	+	1.49123i
$446$	−22.2844	+	21.8114i	−1.05520	+	1.03280i
$447$	0.799780	+	2.46147i	0.0378283	+	0.116424i
$448$	19.4345	+	30.7268i	0.918195	+	1.45171i
$449$	10.6588	+	7.74407i	0.503020	+	0.365465i	0.810169	−	0.586196i	$-0.199375\pi$
$449$	10.6588	+	7.74407i	0.503020	+	0.365465i	−0.307149	+	0.951661i	$0.599375\pi$
$450$	1.20415	+	8.16881i	0.0567644	+	0.385081i
$451$	−20.7566	+	21.3473i	−0.977391	+	1.00520i
$452$	13.9941	−	4.21734i	0.658225	−	0.198367i
$453$	5.30815	−	7.30604i	0.249399	−	0.343268i
$454$	−31.7671	−	5.38126i	−1.49090	−	0.252555i
$455$	−20.3062	+	6.59789i	−0.951971	+	0.309314i
$456$	−4.36848	+	7.93197i	−0.204573	+	0.371449i
$457$	−4.63542	−	6.38011i	−0.216836	−	0.298449i	0.686718	−	0.726924i	$-0.259051\pi$
$457$	−4.63542	−	6.38011i	−0.216836	−	0.298449i	−0.903554	+	0.428475i	$0.859051\pi$
$458$	−8.45695	+	4.19540i	−0.395167	+	0.196038i
$459$	1.01784	−	3.13258i	0.0475086	−	0.146216i
$460$	−7.62203	+	21.8519i	−0.355379	+	1.01885i
$461$		−	15.7440i		−	0.733269i	−0.930365	−	0.366635i	$-0.880510\pi$
$461$		−	15.7440i		−	0.733269i	0.930365	−	0.366635i	$-0.119490\pi$
$462$	17.2037	−	12.5863i	0.800390	−	0.585566i
$463$			28.0352i			1.30291i	0.758688	+	0.651454i	$0.225841\pi$
$463$			28.0352i			1.30291i	−0.758688	+	0.651454i	$0.774159\pi$
$464$	0.609677	−	14.2032i	0.0283035	−	0.659366i
$465$	2.72382	−	8.38307i	0.126314	−	0.388756i
$466$	−3.13615	−	6.32174i	−0.145279	−	0.292849i
$467$	−1.46797	−	2.02049i	−0.0679297	−	0.0934973i	0.773700	−	0.633552i	$-0.218404\pi$
$467$	−1.46797	−	2.02049i	−0.0679297	−	0.0934973i	−0.841630	+	0.540054i	$0.818404\pi$
$468$	2.27249	+	1.72672i	0.105046	+	0.0798178i
$469$	−27.2685	+	8.86008i	−1.25914	+	0.409120i
$470$	2.67358	−	15.7829i	0.123323	−	0.728012i
$471$	−10.4359	+	14.3637i	−0.480859	+	0.661846i
$472$	6.74206	−	3.16633i	0.310328	−	0.145742i
$473$	−15.3816	+	31.2647i	−0.707247	+	1.43755i
$474$	13.5579	−	1.99855i	0.622734	−	0.0917965i
$475$	−15.1227	−	10.9873i	−0.693879	−	0.504132i
$476$	29.9313	+	0.642111i	1.37190	+	0.0294311i
$477$	0.715056	+	2.20072i	0.0327402	+	0.100764i
$478$	1.06917	+	1.09235i	0.0489026	+	0.0499630i
$479$	5.94112	−	4.31647i	0.271457	−	0.197225i	−0.443726	−	0.896163i	$-0.646344\pi$
$479$	5.94112	−	4.31647i	0.271457	−	0.197225i	0.715182	+	0.698938i	$0.246344\pi$
$480$	16.1167	+	9.33215i	0.735622	+	0.425952i
$481$	−0.618008	−	0.200803i	−0.0281787	−	0.00915583i
$482$	−2.41299	−	1.26226i	−0.109909	−	0.0574943i
$483$	−15.9736			−0.726824
$484$	−6.66002	+	20.9677i	−0.302728	+	0.953077i
$485$	−39.0737			−1.77424
$486$	1.25312	+	0.655516i	0.0568425	+	0.0297348i
$487$	−16.4772	−	5.35378i	−0.746655	−	0.242603i	−0.0891135	−	0.996021i	$-0.528403\pi$
$487$	−16.4772	−	5.35378i	−0.746655	−	0.242603i	−0.657541	+	0.753419i	$0.728403\pi$
$488$	2.29671	+	2.44947i	0.103967	+	0.110882i
$489$	7.95857	−	5.78224i	0.359899	−	0.261482i
$490$	−44.4663	−	45.4305i	−2.00878	−	2.05234i
$491$	−3.30378	−	10.1680i	−0.149098	−	0.458875i	0.848418	−	0.529328i	$-0.177556\pi$
$491$	−3.30378	−	10.1680i	−0.149098	−	0.458875i	−0.997515	+	0.0704524i	$0.977556\pi$
$492$	0.385095	−	17.9508i	0.0173614	−	0.809284i
$493$	−9.47063	−	6.88082i	−0.426536	−	0.309896i
$494$	−6.39211	+	0.942254i	−0.287595	+	0.0423940i
$495$	4.82018	−	9.79750i	0.216651	−	0.440365i
$496$	−5.91753	−	8.92616i	−0.265705	−	0.400797i
$497$	1.72689	−	2.37686i	0.0774616	−	0.106617i
$498$	0.264639	−	1.56224i	0.0118587	−	0.0700055i
$499$	36.1595	−	11.7489i	1.61872	−	0.525955i	0.647083	−	0.762420i	$-0.275989\pi$
$499$	36.1595	−	11.7489i	1.61872	−	0.525955i	0.971640	+	0.236465i	$0.0759888\pi$
$500$	−3.34078	+	4.39670i	−0.149404	+	0.196626i
$501$	4.37394	+	6.02021i	0.195413	+	0.268963i
$502$	7.82215	+	15.7676i	0.349120	+	0.703744i
$503$	13.5200	−	41.6103i	0.602828	−	1.85531i	0.0917431	−	0.995783i	$-0.470756\pi$
$503$	13.5200	−	41.6103i	0.602828	−	1.85531i	0.511085	−	0.859530i	$-0.329244\pi$
$504$	−2.41821	+	12.6247i	−0.107716	+	0.562347i
$505$		−	29.4003i		−	1.30829i
$506$	13.3054	−	9.73421i	0.591495	−	0.432738i
$507$		−	10.9636i		−	0.486909i
$508$	22.2728	+	7.76886i	0.988198	+	0.344687i
$509$	9.53129	−	29.3343i	0.422467	−	1.30022i	−0.482932	−	0.875658i	$-0.660428\pi$
$509$	9.53129	−	29.3343i	0.422467	−	1.30022i	0.905399	−	0.424562i	$-0.139572\pi$
$510$	13.7379	−	6.81524i	0.608326	−	0.301784i
$511$	18.2345	+	25.0976i	0.806647	+	1.11025i
$512$	21.0573	−	8.28182i	0.930612	−	0.366008i
$513$	−3.04486	+	0.989336i	−0.134434	+	0.0436802i
$514$	−12.3157	−	2.08625i	−0.543223	−	0.0920205i
$515$	34.0176	−	46.8213i	1.49900	−	2.06319i
$516$	−6.06281	−	20.1178i	−0.266900	−	0.885635i
$517$	−7.94934	+	8.17555i	−0.349612	+	0.359560i
$518$	−0.426797	−	2.89533i	−0.0187524	−	0.127213i
$519$	5.77388	+	4.19497i	0.253445	+	0.184139i
$520$	1.65546	+	13.1848i	0.0725969	+	0.578190i
$521$	−5.30038	−	16.3129i	−0.232214	−	0.714681i	−0.997479	−	0.0709652i	$-0.977392\pi$
$521$	−5.30038	−	16.3129i	−0.232214	−	0.714681i	0.765265	−	0.643715i	$-0.222608\pi$
$522$	3.59197	−	3.51574i	0.157216	−	0.153880i
$523$	5.52497	−	4.01412i	0.241590	−	0.175525i	−0.460401	−	0.887711i	$-0.652295\pi$
$523$	5.52497	−	4.01412i	0.241590	−	0.175525i	0.701991	+	0.712186i	$0.252295\pi$
$524$	1.85282	+	2.66874i	0.0809408	+	0.116584i
$525$	−25.2358	−	8.19961i	−1.10138	−	0.357860i
$526$	0.942225	−	1.80120i	0.0410830	−	0.0785361i
$527$	−8.81872			−0.384149
$528$	−5.67912	−	11.9895i	−0.247152	−	0.521775i
$529$	10.6460			0.462871
$530$	−4.99377	+	9.54633i	−0.216916	+	0.414666i
$531$	2.50457	+	0.813785i	0.108689	+	0.0353153i
$532$	−16.5956	−	23.9037i	−0.719510	−	1.03636i
$533$	10.3645	−	7.53023i	0.448935	−	0.326170i
$534$	−16.4296	+	16.0810i	−0.710980	+	0.695891i
$535$	0.524520	+	1.61431i	0.0226770	+	0.0697925i
$536$	2.22306	+	17.7053i	0.0960217	+	0.764754i
$537$	18.5315	+	13.4639i	0.799692	+	0.581011i
$538$	0.424158	+	2.87743i	0.0182868	+	0.124055i
$539$	7.71072	+	44.6231i	0.332124	+	1.92205i
$540$	1.89992	+	6.30435i	0.0817595	+	0.271296i
$541$	−16.6098	+	22.8614i	−0.714111	+	0.982890i	0.285588	+	0.958353i	$0.407811\pi$
$541$	−16.6098	+	22.8614i	−0.714111	+	0.982890i	−0.999699	+	0.0245371i	$0.992189\pi$
$542$	9.62990	+	1.63128i	0.413640	+	0.0700695i
$543$	−10.0773	+	3.27430i	−0.432457	+	0.140514i
$544$	3.89695	−	18.2204i	0.167080	−	0.781194i
$545$	−2.22670	−	3.06479i	−0.0953813	−	0.131281i
$546$	−8.21625	+	4.07599i	−0.351623	+	0.174436i
$547$	5.25161	−	16.1628i	0.224543	−	0.691071i	−0.773795	−	0.633436i	$-0.781644\pi$
$547$	5.25161	−	16.1628i	0.224543	−	0.691071i	0.998338	−	0.0576351i	$-0.0183560\pi$
$548$	−19.9951	−	6.97438i	−0.854150	−	0.297931i
$549$			1.18716i			0.0506667i
$550$	26.0172	−	8.54860i	1.10938	−	0.364514i
$551$			11.3785i			0.484742i
$552$	−1.87024	+	9.76391i	−0.0796028	+	0.415580i
$553$	−13.6090	+	41.8842i	−0.578714	+	1.78110i
$554$	−11.8667	−	23.9205i	−0.504168	−	1.01628i
$555$	−0.881166	−	1.21282i	−0.0374034	−	0.0514814i
$556$	−9.06506	+	11.9302i	−0.384444	+	0.505955i
$557$	−23.7257	+	7.70896i	−1.00529	+	0.326639i	−0.764978	−	0.644056i	$-0.777250\pi$
$557$	−23.7257	+	7.70896i	−1.00529	+	0.326639i	−0.240314	+	0.970695i	$0.577250\pi$
$558$	0.632394	−	3.73320i	0.0267714	−	0.158039i
$559$	8.81214	−	12.1289i	0.372714	−	0.512996i
$560$	−49.8818	+	33.0687i	−2.10789	+	1.39741i
$561$	−10.8127	−	1.55742i	−0.456512	−	0.0657542i
$562$	19.0154	−	2.80304i	0.802117	−	0.118239i
$563$	−17.5519	−	12.7522i	−0.739724	−	0.537441i	0.152900	−	0.988242i	$-0.451139\pi$
$563$	−17.5519	−	12.7522i	−0.739724	−	0.537441i	−0.892625	+	0.450800i	$0.851139\pi$
$564$	0.147483	−	6.87477i	0.00621016	−	0.289480i
$565$	7.43465	+	22.8815i	0.312778	+	0.962631i
$566$	−19.1177	−	19.5323i	−0.803578	−	0.821002i
$567$	−3.67669	+	2.67127i	−0.154406	+	0.112183i
$568$	−1.25067	−	1.33386i	−0.0524771	−	0.0559674i
$569$	26.6537	+	8.66031i	1.11738	+	0.363059i	0.808768	−	0.588128i	$-0.200135\pi$
$569$	26.6537	+	8.66031i	1.11738	+	0.363059i	0.308614	+	0.951187i	$0.400135\pi$
$570$	−13.2081	−	6.90927i	−0.553226	−	0.289397i
$571$	−30.5486			−1.27842			−0.639209	−	0.769033i	$-0.720738\pi$
$571$	−30.5486			−1.27842			−0.639209	+	0.769033i	$0.720738\pi$
$572$	4.35992	−	8.40206i	0.182297	−	0.351308i
$573$	−10.6205			−0.443679
$574$	51.1262	+	26.7446i	2.13397	+	1.11630i
$575$	−19.5174	−	6.34158i	−0.813930	−	0.264462i
$576$	7.43374	+	2.95627i	0.309739	+	0.123178i
$577$	10.7807	−	7.83261i	0.448805	−	0.326076i	−0.340319	−	0.940310i	$-0.610535\pi$
$577$	10.7807	−	7.83261i	0.448805	−	0.326076i	0.789124	+	0.614234i	$0.210535\pi$
$578$	6.08462	+	6.21655i	0.253087	+	0.258574i
$579$	−7.87970	−	24.2512i	−0.327469	−	1.00785i
$580$	23.3961	+	0.501911i	0.971468	+	0.0208407i
$581$	4.11938	+	2.99291i	0.170901	+	0.124167i
$582$	−16.6052	+	2.44775i	−0.688307	+	0.101463i
$583$	6.78855	−	3.57976i	0.281153	−	0.148258i
$584$	17.4760	−	8.20738i	0.723160	−	0.339624i
$585$	−2.76148	+	3.80085i	−0.114173	+	0.157146i
$586$	−3.73426	+	22.0444i	−0.154261	+	0.910645i
$587$	−28.4389	+	9.24035i	−1.17380	+	0.381390i	−0.830059	−	0.557675i	$-0.811694\pi$
$587$	−28.4389	+	9.24035i	−1.17380	+	0.381390i	−0.343739	+	0.939065i	$0.611694\pi$
$588$	−21.7429	−	16.5211i	−0.896662	−	0.681318i
$589$	5.03836	+	6.93471i	0.207602	+	0.285740i
$590$	5.44894	+	10.9838i	0.224329	+	0.452196i
$591$	−2.27474	+	7.00092i	−0.0935702	+	0.287980i
$592$	−1.81975	−	0.0781135i	−0.0747913	−	0.00321044i
$593$			22.1335i			0.908914i	0.890769	+	0.454457i	$0.150167\pi$
$593$			22.1335i			0.908914i	−0.890769	+	0.454457i	$0.849833\pi$
$594$	1.43468	−	4.46561i	0.0588655	−	0.183226i
$595$			49.2814i			2.02034i
$596$	−1.70478	+	4.88750i	−0.0698305	+	0.200200i
$597$	−4.70506	+	14.4807i	−0.192565	+	0.592655i
$598$	−6.35444	+	3.15237i	−0.259852	+	0.128910i
$599$	21.8597	+	30.0873i	0.893162	+	1.22933i	0.972598	+	0.232492i	$0.0746881\pi$
$599$	21.8597	+	30.0873i	0.893162	+	1.22933i	−0.0794359	+	0.996840i	$0.525312\pi$
$600$	−7.96673	+	14.4654i	−0.325240	+	0.590549i
$601$	−6.83308	+	2.22020i	−0.278727	+	0.0905640i	−0.445045	−	0.895508i	$-0.646812\pi$
$601$	−6.83308	+	2.22020i	−0.278727	+	0.0905640i	0.166318	+	0.986072i	$0.446812\pi$
$602$	66.5729	+	11.2773i	2.71331	+	0.459627i
$603$	−3.70830	+	5.10403i	−0.151013	+	0.207852i
$604$	17.2933	−	5.21161i	0.703654	−	0.212058i
$605$	−34.7422	−	10.2203i	−1.41247	−	0.415514i
$606$	−1.84177	−	12.4943i	−0.0748166	−	0.507545i
$607$	2.80811	+	2.04021i	0.113978	+	0.0828098i	0.643314	−	0.765602i	$-0.277559\pi$
$607$	2.80811	+	2.04021i	0.113978	+	0.0828098i	−0.529336	+	0.848412i	$0.677559\pi$
$608$	−16.5543	+	7.34539i	−0.671365	+	0.297895i
$609$	4.99122	+	15.3614i	0.202255	+	0.622476i
$610$	−3.95006	+	3.86623i	−0.159933	+	0.156539i
$611$	3.96937	−	2.88392i	0.160584	−	0.116671i
$612$	5.41129	−	3.75689i	0.218738	−	0.151863i
$613$	−25.6464	−	8.33301i	−1.03585	−	0.336567i	−0.258748	−	0.965945i	$-0.583310\pi$
$613$	−25.6464	−	8.33301i	−1.03585	−	0.336567i	−0.777100	+	0.629378i	$0.783310\pi$
$614$	16.8545	−	32.2199i	0.680193	−	1.30029i
$615$	29.5557			1.19180
$616$	42.6255	+	0.773602i	1.71743	+	0.0311693i
$617$	−2.41944			−0.0974030			−0.0487015	−	0.998813i	$-0.515508\pi$
$617$	−2.41944			−0.0974030			−0.0487015	+	0.998813i	$0.515508\pi$
$618$	11.5234	−	22.0287i	0.463540	−	0.886125i
$619$	−4.31562	−	1.40223i	−0.173459	−	0.0563604i	0.221000	−	0.975274i	$-0.429068\pi$
$619$	−4.31562	−	1.40223i	−0.173459	−	0.0563604i	−0.394459	+	0.918913i	$0.629068\pi$
$620$	14.4811	−	10.0538i	0.581575	−	0.403769i
$621$	−2.84355	+	2.06596i	−0.114108	+	0.0829041i
$622$	−31.3426	+	30.6774i	−1.25672	+	1.23005i
$623$	−22.8298	−	70.2628i	−0.914656	−	2.81502i
$624$	1.52948	+	5.49944i	0.0612281	+	0.220154i
$625$	16.2641	+	11.8165i	0.650563	+	0.472662i
$626$	−2.49224	−	16.9070i	−0.0996099	−	0.675739i
$627$	4.95287	+	9.39248i	0.197799	+	0.375100i
$628$	−33.9988	+	10.2461i	−1.35670	+	0.408863i
$629$	−0.881589	+	1.21340i	−0.0351513	+	0.0483816i
$630$	−20.8621	−	3.53399i	−0.831167	−	0.140797i
$631$	8.11153	−	2.63559i	0.322915	−	0.104921i	−0.143074	−	0.989712i	$-0.545699\pi$
$631$	8.11153	−	2.63559i	0.322915	−	0.104921i	0.465989	+	0.884791i	$0.345699\pi$
$632$	24.0085	+	13.2225i	0.955006	+	0.525962i
$633$	−8.47664	−	11.6671i	−0.336916	−	0.463725i
$634$	42.4611	−	21.0645i	1.68635	−	0.836579i
$635$	−11.9991	+	36.9293i	−0.476168	+	1.46549i
$636$	−1.52419	+	4.36975i	−0.0604379	+	0.173272i
$637$		−	19.4844i		−	0.772002i
$638$	−13.5186	−	9.75381i	−0.535208	−	0.386157i
$639$		−	0.646467i		−	0.0255738i
$640$	14.3730	+	34.3622i	0.568145	+	1.35829i
$641$	−2.68980	+	8.27836i	−0.106241	+	0.326976i	−0.990020	−	0.140929i	$-0.954991\pi$
$641$	−2.68980	+	8.27836i	−0.106241	+	0.326976i	0.883779	+	0.467905i	$0.154991\pi$
$642$	0.324033	+	0.653176i	0.0127886	+	0.0257788i
$643$	2.43194	+	3.34728i	0.0959065	+	0.132004i	0.854273	−	0.519824i	$-0.174002\pi$
$643$	2.43194	+	3.34728i	0.0959065	+	0.132004i	−0.758367	+	0.651828i	$0.774002\pi$
$644$	−25.4371	−	19.3281i	−1.00236	−	0.761634i
$645$	32.8942	−	10.6880i	1.29521	−	0.420839i
$646$	−2.49078	+	14.7038i	−0.0979985	+	0.578512i
$647$	5.69838	−	7.84315i	0.224027	−	0.308346i	−0.682178	−	0.731186i	$-0.738967\pi$
$647$	5.69838	−	7.84315i	0.224027	−	0.308346i	0.906204	+	0.422840i	$0.138967\pi$
$648$	1.20234	+	2.56015i	0.0472326	+	0.100572i
$649$	1.24519	−	8.64499i	0.0488780	−	0.339346i
$650$	−11.6572	+	1.71838i	−0.457234	+	0.0674003i
$651$	9.84389	+	7.15200i	0.385812	+	0.280309i
$652$	19.6701	+	0.421980i	0.770342	+	0.0165260i
$653$	7.76856	+	23.9092i	0.304007	+	0.935638i	0.980046	+	0.198772i	$0.0636953\pi$
$653$	7.76856	+	23.9092i	0.304007	+	0.935638i	−0.676039	+	0.736866i	$0.736305\pi$
$654$	−1.13828	−	1.16296i	−0.0445101	−	0.0454752i
$655$	−4.32659	+	3.14345i	−0.169054	+	0.122825i
$656$	22.3338	−	28.1197i	0.871987	−	1.09789i
$657$	6.49205	+	2.10940i	0.253279	+	0.0822954i
$658$	19.5803	+	10.2426i	0.763319	+	0.399299i
$659$	−32.9528			−1.28366			−0.641830	−	0.766847i	$-0.721825\pi$
$659$	−32.9528			−1.28366			−0.641830	+	0.766847i	$0.721825\pi$
$660$	19.5309	−	9.76957i	0.760239	−	0.380280i
$661$	−17.1205			−0.665910			−0.332955	−	0.942943i	$-0.608046\pi$
$661$	−17.1205			−0.665910			−0.332955	+	0.942943i	$0.608046\pi$
$662$	30.1788	+	15.7868i	1.17293	+	0.613572i
$663$	4.47032	+	1.45249i	0.173613	+	0.0564102i
$664$	2.31173	−	2.16757i	0.0897127	−	0.0841179i
$665$	38.7530	−	28.1557i	1.50278	−	1.09183i
$666$	−0.450447	−	0.460214i	−0.0174545	−	0.0178329i
$667$	3.86021	+	11.8805i	0.149468	+	0.460015i
$668$	−0.319204	+	14.8794i	−0.0123504	+	0.575700i
$669$	−17.8381	−	12.9602i	−0.689663	−	0.501069i
$670$	−29.0596	+	4.28365i	−1.12267	+	0.165492i
$671$	3.87986	−	0.670427i	0.149780	−	0.0258816i
$672$	−19.1268	+	17.1781i	−0.737831	+	0.662659i
$673$	−11.4758	+	15.7951i	−0.442359	+	0.608855i	−0.970734	−	0.240156i	$-0.922801\pi$
$673$	−11.4758	+	15.7951i	−0.442359	+	0.608855i	0.528375	+	0.849011i	$0.322801\pi$
$674$	2.17514	−	12.8405i	0.0837833	−	0.494596i
$675$	−5.55287	+	1.80424i	−0.213730	+	0.0694452i
$676$	13.2659	−	17.4589i	0.510229	−	0.671496i
$677$	−7.60174	−	10.4629i	−0.292159	−	0.402122i	0.637555	−	0.770405i	$-0.279946\pi$
$677$	−7.60174	−	10.4629i	−0.292159	−	0.402122i	−0.929714	+	0.368283i	$0.879946\pi$
$678$	4.59291	+	9.25824i	0.176390	+	0.355560i
$679$	16.6678	−	51.2982i	0.639652	−	1.96865i
$680$	30.1234	+	5.77002i	1.15518	+	0.221270i
$681$		−	22.7827i		−	0.873035i
$682$	−12.5579	+	0.0414753i	−0.480868	+	0.00158817i
$683$			33.9625i			1.29954i	0.760132	+	0.649769i	$0.225134\pi$
$683$			33.9625i			1.29954i	−0.760132	+	0.649769i	$0.774866\pi$
$684$	−6.04588	−	2.10883i	−0.231170	−	0.0806330i
$685$	10.7720	−	33.1527i	0.411576	−	1.26670i
$686$	38.3092	−	19.0048i	1.46265	−	0.725607i
$687$	−3.92369	−	5.40049i	−0.149698	−	0.206042i
$688$	14.6878	−	39.3725i	0.559969	−	1.50106i
$689$	−3.14051	+	1.02041i	−0.119644	+	0.0388747i
$690$	−16.1348	−	2.73318i	−0.614240	−	0.104051i
$691$	8.46306	−	11.6484i	0.321950	−	0.443126i	−0.617111	−	0.786876i	$-0.711697\pi$
$691$	8.46306	−	11.6484i	0.321950	−	0.443126i	0.939061	+	0.343750i	$0.111697\pi$
$692$	4.11868	+	13.6667i	0.156569	+	0.519529i
$693$	10.8066	+	10.5076i	0.410508	+	0.399150i
$694$	7.09028	+	48.0994i	0.269143	+	1.82583i
$695$	−19.9540	−	14.4974i	−0.756897	−	0.549918i
$696$	9.97410	−	1.25234i	0.378067	−	0.0474697i
$697$	−9.13759	−	28.1226i	−0.346111	−	1.06522i
$698$	−17.7982	+	17.4205i	−0.673673	+	0.659376i
$699$	4.03698	−	2.93304i	0.152693	−	0.110938i
$700$	−30.2652	−	43.5929i	−1.14392	−	1.64766i
$701$	13.7481	+	4.46702i	0.519257	+	0.168717i	0.556908	−	0.830574i	$-0.311987\pi$
$701$	13.7481	+	4.46702i	0.519257	+	0.168717i	−0.0376508	+	0.999291i	$0.511987\pi$
$702$	−0.935448	+	1.78825i	−0.0353062	+	0.0674930i
$703$	1.45785			0.0549839
$704$	5.46360	−	25.9644i	0.205917	−	0.978569i
$705$	11.3192			0.426306
$706$	−18.6668	+	35.6844i	−0.702536	+	1.34300i
$707$	38.5984	+	12.5414i	1.45164	+	0.471667i
$708$	3.00372	+	4.32645i	0.112887	+	0.162598i
$709$	11.2242	−	8.15483i	0.421532	−	0.306261i	−0.356722	−	0.934211i	$-0.616106\pi$
$709$	11.2242	−	8.15483i	0.421532	−	0.306261i	0.778254	+	0.627950i	$0.216106\pi$
$710$	2.15101	−	2.10536i	0.0807258	−	0.0790126i
$711$	2.99452	+	9.21618i	0.112303	+	0.345634i
$712$	−45.6214	+	5.72817i	−1.70973	+	0.214672i
$713$	7.61326	+	5.53135i	0.285119	+	0.207151i
$714$	3.08721	+	20.9432i	0.115536	+	0.783779i
$715$	13.9814	+	6.87859i	0.522875	+	0.257245i
$716$	13.2190	+	43.8637i	0.494019	+	1.63926i
$717$	−0.635291	+	0.874403i	−0.0237254	+	0.0326552i
$718$	−30.3604	−	5.14297i	−1.13304	−	0.191934i
$719$	−40.9937	+	13.3196i	−1.52881	+	0.496739i	−0.948262	−	0.317490i	$-0.897160\pi$
$719$	−40.9937	+	13.3196i	−1.52881	+	0.496739i	−0.580544	+	0.814229i	$0.697160\pi$
$720$	−4.60277	+	12.3383i	−0.171535	+	0.459820i
$721$	46.9587	+	64.6331i	1.74883	+	2.40706i
$722$	−11.0853	+	5.49930i	−0.412552	+	0.204663i
$723$	0.595041	−	1.83135i	0.0221298	−	0.0681086i
$724$	−20.0094	−	6.97937i	−0.743645	−	0.259386i
$725$			20.7509i			0.770669i
$726$	−15.4047	−	2.16692i	−0.571722	−	0.0804220i
$727$			53.1309i			1.97052i	0.171070	+	0.985259i	$0.445278\pi$
$727$			53.1309i			1.97052i	−0.171070	+	0.985259i	$0.554722\pi$
$728$	−18.0159	−	3.45088i	−0.667714	−	0.127898i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	14.1241	+	28.4709i	0.522756	+	1.05375i
$731$	−20.3395	−	27.9950i	−0.752285	−	1.03543i
$732$	−1.43647	+	1.89049i	−0.0530933	+	0.0698744i
$733$	32.2964	−	10.4937i	1.19290	−	0.387595i	0.355753	−	0.934580i	$-0.384224\pi$
$733$	32.2964	−	10.4937i	1.19290	−	0.387595i	0.837143	+	0.546985i	$0.184224\pi$
$734$	6.74445	−	39.8144i	0.248942	−	1.46957i
$735$	26.4215	−	36.3661i	0.974573	−	1.34138i
$736$	−14.7926	+	13.2855i	−0.545264	+	0.489711i
$737$	18.7752	+	9.23701i	0.691592	+	0.340250i
$738$	12.5603	−	1.85150i	0.462351	−	0.0681547i
$739$	−19.0365	−	13.8309i	−0.700271	−	0.508776i	0.179750	−	0.983712i	$-0.442471\pi$
$739$	−19.0365	−	13.8309i	−0.700271	−	0.508776i	−0.880020	+	0.474936i	$0.842471\pi$
$740$	0.0643063	−	2.99757i	0.00236395	−	0.110193i
$741$	−1.41182	−	4.34514i	−0.0518646	−	0.159623i
$742$	−10.4028	−	10.6283i	−0.381898	−	0.390179i
$743$	9.47180	−	6.88167i	0.347487	−	0.252464i	−0.400327	−	0.916372i	$-0.631104\pi$
$743$	9.47180	−	6.88167i	0.347487	−	0.252464i	0.747814	+	0.663908i	$0.231104\pi$
$744$	5.52424	−	5.17973i	0.202528	−	0.189898i
$745$	−8.10368	−	2.63304i	−0.296896	−	0.0964673i
$746$	−40.7793	−	21.3320i	−1.49304	−	0.781022i
$747$	1.12040			0.0409935
$748$	−15.3342	−	15.5635i	−0.560672	−	0.569058i
$749$	−2.34310			−0.0856152
$750$	−3.45981	−	1.80986i	−0.126335	−	0.0660868i
$751$	12.9484	+	4.20718i	0.472493	+	0.153522i	0.535578	−	0.844486i	$-0.320094\pi$
$751$	12.9484	+	4.20718i	0.472493	+	0.153522i	−0.0630847	+	0.998008i	$0.520094\pi$
$752$	8.55336	−	10.7693i	0.311909	−	0.392715i
$753$	−10.0690	+	7.31555i	−0.366935	+	0.266594i
$754$	5.01711	+	5.12589i	0.182712	+	0.186674i
$755$	9.18744	+	28.2760i	0.334365	+	1.02907i
$756$	−9.08719	−	0.194946i	−0.330498	−	0.00709011i
$757$	−3.81262	−	2.77003i	−0.138572	−	0.100678i	0.516340	−	0.856384i	$-0.327294\pi$
$757$	−3.81262	−	2.77003i	−0.138572	−	0.100678i	−0.654912	+	0.755705i	$0.727294\pi$
$758$	22.6013	−	3.33163i	0.820916	−	0.121010i
$759$	8.35780	+	8.12655i	0.303369	+	0.294975i
$760$	−12.6729	−	26.9845i	−0.459696	−	0.978830i
$761$	−5.49260	+	7.55992i	−0.199107	+	0.274047i	−0.896882	−	0.442270i	$-0.854173\pi$
$761$	−5.49260	+	7.55992i	−0.199107	+	0.274047i	0.697775	+	0.716317i	$0.254173\pi$
$762$	−2.78584	+	16.4456i	−0.100920	+	0.595760i
$763$	4.97349	−	1.61598i	0.180052	−	0.0585026i
$764$	−16.9127	−	12.8509i	−0.611878	−	0.464929i
$765$	6.37385	+	8.77286i	0.230447	+	0.317183i
$766$	−10.9645	−	22.1018i	−0.396163	−	0.798572i
$767$	−1.16130	+	3.57412i	−0.0419322	+	0.129054i
$768$	8.26074	+	13.7026i	0.298084	+	0.494449i
$769$		−	24.7915i		−	0.894004i	−0.894533	−	0.447002i	$-0.852492\pi$
$769$		−	24.7915i		−	0.894004i	0.894533	−	0.447002i	$-0.147508\pi$
$770$	0.231775	+	70.1772i	0.00835259	+	2.52901i
$771$		−	8.83259i		−	0.318098i
$772$	16.7960	−	48.1533i	0.604503	−	1.73307i
$773$	8.40986	−	25.8829i	0.302482	−	0.930943i	−0.678123	−	0.734948i	$-0.737206\pi$
$773$	8.40986	−	25.8829i	0.302482	−	0.930943i	0.980605	−	0.195995i	$-0.0627936\pi$
$774$	13.3096	−	6.60274i	0.478403	−	0.237330i
$775$	9.18840	+	12.6467i	0.330057	+	0.454284i
$776$	−29.4047	−	16.1944i	−1.05557	−	0.581346i
$777$	1.96815	−	0.639489i	0.0706068	−	0.0229416i
$778$	−48.2989	−	8.18170i	−1.73160	−	0.293328i
$779$	−16.8940	+	23.2526i	−0.605292	+	0.833112i
$780$	−8.99656	+	2.71126i	−0.322129	+	0.0970787i
$781$	−2.11278	+	0.365081i	−0.0756011	+	0.0130636i
$782$	2.38765	+	16.1974i	0.0853821	+	0.579219i
$783$	2.87530	+	2.08903i	0.102755	+	0.0746557i
$784$	−14.6339	−	52.6179i	−0.522638	−	1.87921i
$785$	−18.0626	−	55.5909i	−0.644681	−	1.98412i
$786$	−1.64176	+	1.60692i	−0.0585596	+	0.0573168i
$787$	16.6876	−	12.1242i	0.594848	−	0.432183i	−0.249198	−	0.968452i	$-0.580167\pi$
$787$	16.6876	−	12.1242i	0.594848	−	0.432183i	0.844047	+	0.536270i	$0.180167\pi$
$788$	−12.0935	+	8.39617i	−0.430815	+	0.299101i
$789$	1.36703	+	0.444174i	0.0486675	+	0.0158130i
$790$	−20.9130	+	39.9782i	−0.744050	+	1.42236i
$791$	−33.2116			−1.18087
$792$	7.68806	−	5.37529i	0.273183	−	0.191003i
$793$	−1.69412			−0.0601600
$794$	−22.5004	+	43.0128i	−0.798510	+	1.52647i
$795$	−7.24522	−	2.35411i	−0.256961	−	0.0834918i
$796$	−25.0143	+	17.3666i	−0.886607	+	0.615543i
$797$	−13.0728	+	9.49798i	−0.463064	+	0.336436i	−0.794732	−	0.606960i	$-0.792389\pi$
$797$	−13.0728	+	9.49798i	−0.463064	+	0.336436i	0.331668	+	0.943396i	$0.392389\pi$
$798$	14.7051	−	14.3930i	0.520556	−	0.509508i
$799$	−3.49951	−	10.7704i	−0.123804	−	0.381028i
$800$	−30.1898	+	13.3957i	−1.06737	+	0.473609i
$801$	−13.1516	−	9.55518i	−0.464688	−	0.337616i
$802$	−4.79005	−	32.4950i	−0.169143	−	1.14744i
$803$	3.22763	−	22.4085i	0.113901	−	0.790779i
$804$	−12.0812	+	3.64086i	−0.426070	+	0.128403i
$805$	30.9107	−	42.5449i	1.08946	−	1.49951i
$806$	5.32742	+	0.902452i	0.187651	+	0.0317875i
$807$	−1.95598	+	0.635536i	−0.0688537	+	0.0223719i
$808$	12.1852	−	22.1250i	0.428674	−	0.778356i
$809$	−29.6885	−	40.8627i	−1.04379	−	1.43666i	−0.894070	−	0.447928i	$-0.852162\pi$
$809$	−29.6885	−	40.8627i	−1.04379	−	1.43666i	−0.149722	−	0.988728i	$-0.547838\pi$
$810$	−4.17086	+	2.06912i	−0.146549	+	0.0727013i
$811$	7.20764	−	22.1828i	0.253095	−	0.778945i	−0.741105	−	0.671390i	$-0.765698\pi$
$811$	7.20764	−	22.1828i	0.253095	−	0.778945i	0.994199	−	0.107555i	$-0.0343023\pi$
$812$	−10.6391	+	30.5016i	−0.373359	+	1.07040i
$813$			6.90638i			0.242217i
$814$	−1.24968	+	1.73204i	−0.0438014	+	0.0607081i
$815$			32.3866i			1.13445i
$816$	13.1630	+	0.565029i	0.460799	+	0.0197800i
$817$	−10.3937	+	31.9885i	−0.363629	+	1.11914i
$818$	19.2583	+	38.8202i	0.673350	+	1.35732i
$819$	−3.81201	−	5.24679i	−0.133203	−	0.183338i
$820$	47.0659	+	35.7625i	1.64361	+	1.24888i
$821$	15.0235	−	4.88144i	0.524325	−	0.170363i	−0.0348825	−	0.999391i	$-0.511106\pi$
$821$	15.0235	−	4.88144i	0.524325	−	0.170363i	0.559207	+	0.829028i	$0.311106\pi$
$822$	2.50094	−	14.7638i	0.0872304	−	0.514946i
$823$	6.21791	−	8.55821i	0.216743	−	0.298321i	−0.686776	−	0.726869i	$-0.740975\pi$
$823$	6.21791	−	8.55821i	0.216743	−	0.298321i	0.903519	+	0.428548i	$0.140975\pi$
$824$	45.0053	−	21.1362i	1.56783	−	0.736315i
$825$	9.03249	+	17.1289i	0.314471	+	0.596353i
$826$	−16.7446	+	2.46830i	−0.582618	+	0.0858830i
$827$	3.28348	+	2.38559i	0.114178	+	0.0829550i	0.643409	−	0.765523i	$-0.277520\pi$
$827$	3.28348	+	2.38559i	0.114178	+	0.0829550i	−0.529231	+	0.848478i	$0.677520\pi$
$828$	−7.02803	−	0.150771i	−0.244241	−	0.00523965i
$829$	4.59857	+	14.1529i	0.159715	+	0.491552i	0.998608	−	0.0527441i	$-0.0167968\pi$
$829$	4.59857	+	14.1529i	0.159715	+	0.491552i	−0.838893	+	0.544296i	$0.816797\pi$
$830$	3.64884	+	3.72795i	0.126653	+	0.129399i
$831$	15.2753	−	11.0982i	0.529894	−	0.384991i
$832$	−4.21872	+	10.6082i	−0.146258	+	0.367775i
$833$	−42.7715	−	13.8973i	−1.48194	−	0.481513i
$834$	−9.38805	−	4.91097i	−0.325081	−	0.170053i
$835$	−24.4986			−0.847810
$836$	−3.47774	+	20.9500i	−0.120280	+	0.724572i
$837$	2.67738			0.0925437
$838$	−24.7452	−	12.9444i	−0.854808	−	0.447158i
$839$	−12.3827	−	4.02337i	−0.427497	−	0.138902i	0.0873629	−	0.996177i	$-0.472156\pi$
$839$	−12.3827	−	4.02337i	−0.427497	−	0.138902i	−0.514860	+	0.857274i	$0.672156\pi$
$840$	−28.9457	−	30.8709i	−0.998722	−	1.06515i
$841$	−13.2425	+	9.62124i	−0.456638	+	0.331767i
$842$	22.2716	+	22.7545i	0.767531	+	0.784173i
$843$	4.19992	+	12.9260i	0.144653	+	0.445196i
$844$	0.618614	−	28.8360i	0.0212936	−	0.992576i
$845$	29.2009	+	21.2157i	1.00454	+	0.729842i
$846$	4.81033	−	0.709086i	0.165383	−	0.0243789i
$847$	28.2379	−	41.2519i	0.970267	−	1.41743i
$848$	−7.71460	+	5.11433i	−0.264920	+	0.175627i
$849$	11.3596	−	15.6351i	0.389860	−	0.536597i
$850$	−4.54240	+	26.8151i	−0.155803	+	0.919750i
$851$	1.52216	−	0.494581i	0.0521791	−	0.0169540i
$852$	0.782227	−	1.02947i	0.0267987	−	0.0352689i
$853$	−12.1213	−	16.6835i	−0.415025	−	0.571233i	0.549410	−	0.835553i	$-0.314852\pi$
$853$	−12.1213	−	16.6835i	−0.415025	−	0.571233i	−0.964435	+	0.264320i	$0.914852\pi$
$854$	−3.39083	−	6.83511i	−0.116032	−	0.233893i
$855$	3.25710	−	10.0243i	0.111390	−	0.342825i
$856$	−0.274338	+	1.43223i	−0.00937669	+	0.0489526i
$857$			26.3263i			0.899290i	0.893207	+	0.449645i	$0.148450\pi$
$857$			26.3263i			0.899290i	−0.893207	+	0.449645i	$0.851550\pi$
$858$	6.37261	+	2.04734i	0.217557	+	0.0698951i
$859$		−	50.2269i		−	1.71372i	−0.515550	−	0.856860i	$-0.672412\pi$
$859$		−	50.2269i		−	1.71372i	0.515550	−	0.856860i	$-0.327588\pi$
$860$	65.3149	+	22.7821i	2.22722	+	0.776863i
$861$	−12.6077	+	38.8024i	−0.429669	+	1.32238i
$862$	8.42907	−	4.18157i	0.287095	−	0.142425i
$863$	11.9210	+	16.4079i	0.405796	+	0.558531i	0.962187	−	0.272390i	$-0.0878141\pi$
$863$	11.9210	+	16.4079i	0.405796	+	0.558531i	−0.556391	+	0.830921i	$0.687814\pi$
$864$	−1.18312	+	5.53175i	−0.0402505	+	0.188194i
$865$	−22.3462	+	7.26072i	−0.759793	+	0.246872i
$866$	26.0893	+	4.41946i	0.886550	+	0.150179i
$867$	−3.61543	+	4.97621i	−0.122786	+	0.169001i
$868$	7.02193	+	23.3003i	0.238340	+	0.790865i
$869$	28.4291	−	14.9913i	0.964392	−	0.508546i
$870$	2.41314	+	16.3704i	0.0818132	+	0.555009i
$871$	−7.28366	−	5.29189i	−0.246797	−	0.179309i
$872$	−0.405463	−	3.22926i	−0.0137307	−	0.109357i
$873$	−3.66758	−	11.2876i	−0.124129	−	0.382029i
$874$	11.3729	−	11.1316i	0.384695	−	0.376531i
$875$	10.1512	−	7.37530i	0.343174	−	0.249331i
$876$	7.78588	+	11.2145i	0.263061	+	0.378903i
$877$	48.9484	+	15.9043i	1.65287	+	0.537050i	0.979359	−	0.202128i	$-0.0647855\pi$
$877$	48.9484	+	15.9043i	1.65287	+	0.537050i	0.673511	+	0.739178i	$0.264786\pi$
$878$	−23.4657	+	44.8581i	−0.791929	+	1.51389i
$879$	−15.8098			−0.533252
$880$	42.9231	+	8.07490i	1.44694	+	0.272205i
$881$	6.44252			0.217054			0.108527	−	0.994094i	$-0.465387\pi$
$881$	6.44252			0.217054			0.108527	+	0.994094i	$0.465387\pi$
$882$	8.95025	−	17.1097i	0.301371	−	0.576114i
$883$	37.8694	+	12.3045i	1.27441	+	0.414080i	0.866607	−	0.498992i	$-0.166296\pi$
$883$	37.8694	+	12.3045i	1.27441	+	0.414080i	0.407800	+	0.913071i	$0.366296\pi$
$884$	5.36123	+	7.72213i	0.180318	+	0.259723i
$885$	−7.01410	+	5.09604i	−0.235777	+	0.171302i
$886$	−1.18034	+	1.15529i	−0.0396543	+	0.0388127i
$887$	10.0922	+	31.0606i	0.338863	+	1.04291i	0.964788	+	0.263030i	$0.0847219\pi$
$887$	10.0922	+	31.0606i	0.338863	+	1.04291i	−0.625924	+	0.779884i	$0.715278\pi$
$888$	−0.160453	−	1.27791i	−0.00538445	−	0.0428838i
$889$	−43.3645	−	31.5061i	−1.45440	−	1.05668i
$890$	−11.0377	−	74.8780i	−0.369984	−	2.50992i
$891$	3.28275	+	0.472834i	0.109976	+	0.0158405i
$892$	−12.7245	−	42.2226i	−0.426047	−	1.41372i
$893$	−6.47006	+	8.90527i	−0.216512	+	0.298004i
$894$	−3.60878	−	0.611317i	−0.120696	−	0.0204455i
$895$	−71.7210	+	23.3036i	−2.39737	+	0.778952i
$896$	−51.2439	+	4.21177i	−1.71194	+	0.140705i
$897$	−2.94821	−	4.05786i	−0.0984378	−	0.135488i
$898$	−16.6912	+	8.28034i	−0.556994	+	0.276319i
$899$	2.94047	−	9.04984i	0.0980702	−	0.301829i
$900$	−11.0258	−	3.84584i	−0.367527	−	0.128195i
$901$			7.62174i			0.253917i
$902$	−13.1443	−	40.0039i	−0.437657	−	1.33198i
$903$			47.7448i			1.58885i
$904$	−3.88852	+	20.3007i	−0.129330	+	0.675191i
$905$	10.7797	−	33.1765i	0.358329	−	1.10282i
$906$	5.67574	+	11.4410i	0.188564	+	0.380100i
$907$	−12.5516	−	17.2757i	−0.416768	−	0.573632i	0.548085	−	0.836423i	$-0.315357\pi$
$907$	−12.5516	−	17.2757i	−0.416768	−	0.573632i	−0.964853	+	0.262791i	$0.915357\pi$
$908$	27.5672	−	36.2803i	0.914848	−	1.20400i
$909$	8.49318	−	2.75960i	0.281701	−	0.0915302i
$910$	5.04314	−	29.7711i	0.167179	−	0.986902i
$911$	−14.5327	+	20.0025i	−0.481489	+	0.662713i	−0.978790	−	0.204865i	$-0.934324\pi$
$911$	−14.5327	+	20.0025i	−0.481489	+	0.662713i	0.497301	+	0.867578i	$0.334324\pi$
$912$	−7.07607	−	10.6737i	−0.234312	−	0.353443i
$913$	−0.632730	−	3.66170i	−0.0209403	−	0.121185i
$914$	11.0336	−	1.62645i	0.364960	−	0.0537983i
$915$	−3.16194	−	2.29728i	−0.104530	−	0.0759458i
$916$	0.286345	−	13.3477i	0.00946112	−	0.441020i
$917$	−2.28130	−	7.02112i	−0.0753352	−	0.231858i
$918$	3.25828	+	3.32893i	0.107539	+	0.109871i
$919$	−25.1196	+	18.2505i	−0.828621	+	0.602028i	−0.919169	−	0.393864i	$-0.871138\pi$
$919$	−25.1196	+	18.2505i	−0.828621	+	0.602028i	0.0905481	+	0.995892i	$0.471138\pi$
$920$	−22.3866	−	23.8756i	−0.738064	−	0.787154i
$921$	24.4534	+	7.94539i	0.805766	+	0.261809i
$922$	19.7290	+	10.3204i	0.649740	+	0.339885i
$923$	0.922534			0.0303656
$924$	4.49471	+	29.8088i	0.147865	+	0.980636i
$925$	2.65866			0.0874163
$926$	−35.1314	−	18.3776i	−1.15449	−	0.603924i
$927$	16.7188	+	5.43226i	0.549117	+	0.178419i
$928$	17.3986	+	10.0744i	0.571136	+	0.330709i
$929$	−18.7373	+	13.6135i	−0.614752	+	0.446643i	−0.851084	−	0.525029i	$-0.824055\pi$
$929$	−18.7373	+	13.6135i	−0.614752	+	0.446643i	0.236333	+	0.971672i	$0.424055\pi$
$930$	8.71944	+	8.90851i	0.285922	+	0.292121i
$931$	13.5081	+	41.5738i	0.442711	+	1.36253i
$932$	9.97766	+	0.214049i	0.326829	+	0.00701141i
$933$	−25.0890	−	18.2283i	−0.821378	−	0.596766i
$934$	3.49419	−	0.515075i	0.114333	−	0.0168538i
$935$	25.0719	−	25.7853i	0.819937	−	0.843269i
$936$	−3.65344	+	1.71579i	−0.119416	+	0.0560825i
$937$	−5.74761	+	7.91091i	−0.187766	+	0.258438i	−0.892514	−	0.451020i	$-0.851060\pi$
$937$	−5.74761	+	7.91091i	−0.187766	+	0.258438i	0.704748	+	0.709458i	$0.251060\pi$
$938$	6.77226	−	39.9785i	0.221122	−	1.30535i
$939$	11.4928	−	3.73423i	0.375053	−	0.121862i
$940$	18.0252	+	13.6963i	0.587918	+	0.446723i
$941$	−4.80526	−	6.61387i	−0.156647	−	0.215606i	0.723479	−	0.690347i	$-0.242542\pi$
$941$	−4.80526	−	6.61387i	−0.156647	−	0.215606i	−0.880126	+	0.474740i	$0.842542\pi$
$942$	−11.1585	−	22.4930i	−0.363565	−	0.732862i
$943$	−9.75077	+	30.0098i	−0.317529	+	0.977253i
$944$	−0.451754	+	10.5242i	−0.0147033	+	0.342532i
$945$		−	14.9619i		−	0.486711i
$946$	−29.0954	−	39.7694i	−0.945972	−	1.29302i
$947$		−	51.1326i		−	1.66159i	−0.556581	−	0.830794i	$-0.687887\pi$
$947$		−	51.1326i		−	1.66159i	0.556581	−	0.830794i	$-0.312113\pi$
$948$	−6.38299	+	18.2997i	−0.207310	+	0.594346i
$949$	−3.01019	+	9.26442i	−0.0977150	+	0.300736i
$950$	23.6816	−	11.7482i	0.768332	−	0.381161i
$951$	19.7003	+	27.1151i	0.638826	+	0.879268i
$952$	−20.4251	+	37.0865i	−0.661981	+	1.20198i
$953$	−36.1108	+	11.7331i	−1.16974	+	0.380073i	−0.828547	−	0.559920i	$-0.810832\pi$
$953$	−36.1108	+	11.7331i	−1.16974	+	0.380073i	−0.341196	+	0.939992i	$0.610832\pi$
$954$	−3.22648	−	0.546558i	−0.104461	−	0.0176955i
$955$	20.5519	−	28.2873i	0.665045	−	0.915355i
$956$	−2.06970	+	0.623737i	−0.0669388	+	0.0201731i
$957$	5.20356	−	10.5768i	0.168207	−	0.341898i
$958$	1.51454	+	10.2744i	0.0489326	+	0.331952i
$959$	38.9298	+	28.2842i	1.25711	+	0.913344i
$960$	−22.2590	+	14.0787i	−0.718406	+	0.454388i
$961$	7.36439	+	22.6653i	0.237561	+	0.731137i
$962$	0.656744	−	0.642806i	0.0211743	−	0.0207249i
$963$	−0.417109	+	0.303048i	−0.0134412	+	0.00976557i
$964$	3.16351	−	2.19633i	0.101890	−	0.0707389i
$965$	79.8401	+	25.9416i	2.57014	+	0.835090i
$966$	10.4710	−	20.0168i	0.336897	−	0.644029i
$967$	−31.7381			−1.02063			−0.510314	−	0.859988i	$-0.670471\pi$
$967$	−31.7381			−1.02063			−0.510314	+	0.859988i	$0.670471\pi$
$968$	−21.9092	−	22.0904i	−0.704188	−	0.710014i
$969$	−10.5453			−0.338763
$970$	25.6134	−	48.9638i	0.822397	−	1.57213i
$971$	−26.3894	−	8.57442i	−0.846875	−	0.275166i	−0.146738	−	0.989175i	$-0.546878\pi$
$971$	−26.3894	−	8.57442i	−0.846875	−	0.275166i	−0.700137	+	0.714009i	$0.746878\pi$
$972$	−1.64288	+	1.14060i	−0.0526952	+	0.0365847i
$973$	27.5449	−	20.0125i	0.883049	−	0.641573i
$974$	17.5100	−	17.1384i	0.561056	−	0.549149i
$975$	−2.57472	−	7.92418i	−0.0824570	−	0.253777i
$976$	−4.57499	+	1.27238i	−0.146442	+	0.0407278i
$977$	35.5201	+	25.8069i	1.13639	+	0.825636i	0.986612	−	0.163084i	$-0.0521442\pi$
$977$	35.5201	+	25.8069i	1.13639	+	0.825636i	0.149778	+	0.988720i	$0.452144\pi$
$978$	2.02884	+	13.7634i	0.0648752	+	0.440104i
$979$	−23.8010	+	48.3780i	−0.760684	+	1.54617i
$980$	86.0780	−	25.9410i	2.74966	−	0.828655i
$981$	0.676354	−	0.930921i	0.0215943	−	0.0297220i
$982$	14.9074	+	2.52527i	0.475713	+	0.0805845i
$983$	14.9235	−	4.84893i	0.475985	−	0.154657i	−0.0611928	−	0.998126i	$-0.519490\pi$
$983$	14.9235	−	4.84893i	0.475985	−	0.154657i	0.537178	+	0.843469i	$0.319490\pi$
$984$	22.2420	+	12.2496i	0.709048	+	0.390503i
$985$	−14.2448	−	19.6062i	−0.453876	−	0.624706i
$986$	14.8306	−	7.35731i	0.472303	−	0.234304i
$987$	−4.82848	+	14.8605i	−0.153692	+	0.473016i
$988$	3.00938	−	8.62772i	0.0957412	−	0.274484i
$989$			36.9258i			1.17417i
$990$	9.11769	+	12.4627i	0.289779	+	0.396089i
$991$		−	27.8527i		−	0.884770i	−0.896825	−	0.442385i	$-0.854133\pi$
$991$		−	27.8527i		−	0.884770i	0.896825	−	0.442385i	$-0.145867\pi$
$992$	15.0645	−	1.56410i	0.478300	−	0.0496602i
$993$	−7.44206	+	22.9043i	−0.236167	+	0.726846i
$994$	1.84647	+	3.72206i	0.0585666	+	0.118057i
$995$	−29.4638	−	40.5535i	−0.934066	−	1.28563i
$996$	1.78419	+	1.35569i	0.0565341	+	0.0429568i
$997$	44.8898	−	14.5856i	1.42167	−	0.461930i	0.505540	−	0.862803i	$-0.331293\pi$
$997$	44.8898	−	14.5856i	1.42167	−	0.461930i	0.916134	+	0.400873i	$0.131293\pi$
$998$	−8.98038	+	53.0137i	−0.284269	+	1.67812i
$999$	0.267652	−	0.368391i	0.00846813	−	0.0116554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.j.a.7.6	yes	48
3.2	odd	2		396.2.r.b.271.7		48
4.3	odd	2	inner	132.2.j.a.7.4	✓	48
11.8	odd	10	inner	132.2.j.a.19.4	yes	48
12.11	even	2		396.2.r.b.271.9		48
33.8	even	10		396.2.r.b.19.9		48
44.19	even	10	inner	132.2.j.a.19.6	yes	48
132.107	odd	10		396.2.r.b.19.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.4	✓	48	4.3	odd	2	inner
132.2.j.a.7.6	yes	48	1.1	even	1	trivial
132.2.j.a.19.4	yes	48	11.8	odd	10	inner
132.2.j.a.19.6	yes	48	44.19	even	10	inner
396.2.r.b.19.7		48	132.107	odd	10
396.2.r.b.19.9		48	33.8	even	10
396.2.r.b.271.7		48	3.2	odd	2
396.2.r.b.271.9		48	12.11	even	2

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.655516 + 1.25312i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.14060 - 1.64288i) q^{4} +(2.66345 - 1.93511i) q^{5} +(1.01067 - 0.989218i) q^{6} +(1.40437 + 4.32221i) q^{7} +(2.80639 - 0.352368i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.655516 + 1.25312i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.14060 - 1.64288i) q^{4} +(2.66345 - 1.93511i) q^{5} +(1.01067 - 0.989218i) q^{6} +(1.40437 + 4.32221i) q^{7} +(2.80639 - 0.352368i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.678982 + 4.60611i) q^{10} +(1.46412 - 2.97596i) q^{11} +(0.577096 + 1.91493i) q^{12} +(-0.838793 + 1.15450i) q^{13} +(-6.33681 - 1.07344i) q^{14} +(-3.13108 + 1.01735i) q^{15} +(-1.39808 + 3.74772i) q^{16} +(1.93604 + 2.66473i) q^{17} +(-1.26689 + 0.628489i) q^{18} +(0.989336 - 3.04486i) q^{19} +(-6.21707 - 2.16854i) q^{20} -4.54464i q^{21} +(2.76947 + 3.78550i) q^{22} -3.51482i q^{23} +(-2.77793 - 0.532101i) q^{24} +(1.80424 - 5.55287i) q^{25} +(-0.896879 - 1.80790i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(5.49903 - 7.23710i) q^{28} +(-3.38012 + 1.09827i) q^{29} +(0.777617 - 4.59049i) q^{30} +(-1.57372 + 2.16604i) q^{31} +(-3.77986 - 4.20864i) q^{32} +(-2.31208 + 2.37787i) q^{33} +(-4.60833 + 0.679308i) q^{34} +(12.1044 + 8.79438i) q^{35} +(0.0428958 - 1.99954i) q^{36} +(0.140713 + 0.433070i) q^{37} +(3.16704 + 3.23571i) q^{38} +(1.15450 - 0.838793i) q^{39} +(6.79282 - 6.36920i) q^{40} +(-8.53807 - 2.77419i) q^{41} +(5.69496 + 2.97909i) q^{42} -10.5057 q^{43} +(-6.55910 + 0.989014i) q^{44} +3.29221 q^{45} +(4.40448 + 2.30402i) q^{46} +(-3.26990 - 1.06246i) q^{47} +(2.48776 - 3.13226i) q^{48} +(-11.0461 + 8.02547i) q^{49} +(5.77569 + 5.90092i) q^{50} +(-1.01784 - 3.13258i) q^{51} +(2.85342 + 0.0612140i) q^{52} +(1.87204 + 1.36012i) q^{53} +(1.39909 - 0.206239i) q^{54} +(-1.85922 - 10.7596i) q^{55} +(5.46422 + 11.6350i) q^{56} +(-1.88183 + 2.59011i) q^{57} +(0.839467 - 4.95561i) q^{58} +(2.50457 - 0.813785i) q^{59} +(5.24267 + 3.98358i) q^{60} +(0.697794 + 0.960431i) q^{61} +(-1.68270 - 3.39193i) q^{62} +(-1.40437 + 4.32221i) q^{63} +(7.75167 - 1.97776i) q^{64} +4.69811i q^{65} +(-1.46414 - 4.45604i) q^{66} +6.30893i q^{67} +(2.16958 - 6.22006i) q^{68} +(-1.08614 + 3.34279i) q^{69} +(-18.9550 + 9.40339i) q^{70} +(-0.379984 - 0.523003i) q^{71} +(2.47754 + 1.36448i) q^{72} +(6.49205 - 2.10940i) q^{73} +(-0.634926 - 0.107555i) q^{74} +(-3.43187 + 4.72356i) q^{75} +(-6.13076 + 1.84760i) q^{76} +(14.9189 + 2.14886i) q^{77} +(0.294311 + 1.99656i) q^{78} +(7.83975 + 5.69591i) q^{79} +(3.52853 + 12.6873i) q^{80} +(0.309017 + 0.951057i) q^{81} +(9.07322 - 8.88066i) q^{82} +(0.906427 - 0.658558i) q^{83} +(-7.46628 + 5.18360i) q^{84} +(10.3131 + 3.35093i) q^{85} +(6.88668 - 13.1649i) q^{86} +3.55406 q^{87} +(3.06025 - 8.86763i) q^{88} -16.2562 q^{89} +(-2.15810 + 4.12552i) q^{90} +(-6.16797 - 2.00409i) q^{91} +(-5.77441 + 4.00899i) q^{92} +(2.16604 - 1.57372i) q^{93} +(3.47485 - 3.40111i) q^{94} +(-3.25710 - 10.0243i) q^{95} +(2.29432 + 5.17070i) q^{96} +(-9.60184 - 6.97614i) q^{97} +(-2.81593 - 19.1029i) q^{98} +(2.93372 - 1.54702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) \) 48 * q - 4 * q^4 + 12 * q^9	\( 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Introduction

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