LMFDB - Embedded newform 1050.2.u.f.899.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,2,Mod(299,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.299"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-6,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.1
Root			$-1.21252 + 1.23685i$ of defining polynomial
Character	$\chi$	$=$	1050.899
Dual form			1050.2.u.f.299.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.21252 + 1.23685i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.67740 + 0.431645i) q^{6} +(2.62736 + 0.311378i) q^{7} +1.00000 q^{8} +(-0.0596020 - 2.99941i) q^{9} +(-4.44749 - 2.56776i) q^{11} +(-0.464886 - 1.66850i) q^{12} +5.00256 q^{13} +(-1.04402 - 2.43105i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.25579 - 1.87973i) q^{17} +(-2.56776 + 1.55132i) q^{18} +(-2.33193 + 1.34634i) q^{19} +(-3.57085 + 2.87211i) q^{21} +5.13552i q^{22} +(1.24302 + 2.15298i) q^{23} +(-1.21252 + 1.23685i) q^{24} +(-2.50128 - 4.33235i) q^{26} +(3.78209 + 3.56312i) q^{27} +(-1.58334 + 2.11968i) q^{28} -6.18694i q^{29} +(-4.13446 - 2.38703i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(8.56861 - 2.38743i) q^{33} +3.75947i q^{34} +(2.62736 + 1.44809i) q^{36} +(-0.0453927 + 0.0262075i) q^{37} +(2.33193 + 1.34634i) q^{38} +(-6.06570 + 6.18743i) q^{39} +6.55478 q^{41} +(4.27275 + 1.65640i) q^{42} -9.45088i q^{43} +(4.44749 - 2.56776i) q^{44} +(1.24302 - 2.15298i) q^{46} +(2.65776 - 1.53446i) q^{47} +(1.67740 + 0.431645i) q^{48} +(6.80609 + 1.63621i) q^{49} +(6.27266 - 1.74772i) q^{51} +(-2.50128 + 4.33235i) q^{52} +(0.556019 - 0.963053i) q^{53} +(1.19470 - 5.05694i) q^{54} +(2.62736 + 0.311378i) q^{56} +(1.16228 - 4.51670i) q^{57} +(-5.35804 + 3.09347i) q^{58} +(6.63079 - 11.4849i) q^{59} +(3.59330 - 2.07459i) q^{61} +4.77406i q^{62} +(0.777354 - 7.89910i) q^{63} +1.00000 q^{64} +(-6.35188 - 6.22691i) q^{66} +(-0.776110 - 0.448087i) q^{67} +(3.25579 - 1.87973i) q^{68} +(-4.17010 - 1.07309i) q^{69} +13.4240i q^{71} +(-0.0596020 - 2.99941i) q^{72} +(3.49014 - 6.04511i) q^{73} +(0.0453927 + 0.0262075i) q^{74} -2.69268i q^{76} +(-10.8856 - 8.13130i) q^{77} +(8.39132 + 2.15933i) q^{78} +(-8.37381 - 14.5039i) q^{79} +(-8.99290 + 0.357541i) q^{81} +(-3.27739 - 5.67661i) q^{82} -1.37724i q^{83} +(-0.701891 - 4.52850i) q^{84} +(-8.18470 + 4.72544i) q^{86} +(7.65232 + 7.50177i) q^{87} +(-4.44749 - 2.56776i) q^{88} +(-2.67056 - 4.62555i) q^{89} +(13.1436 + 1.55769i) q^{91} -2.48605 q^{92} +(7.96551 - 2.21939i) q^{93} +(-2.65776 - 1.53446i) q^{94} +(-0.464886 - 1.66850i) q^{96} +0.633608 q^{97} +(-1.98605 - 6.71235i) q^{98} +(-7.43669 + 13.4929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} - 12 q^{11} - 2 q^{12} + 8 q^{13} - 12 q^{14} - 6 q^{16} + 12 q^{17} - 18 q^{21} + 2 q^{23} + 4 q^{24} - 4 q^{26} + 28 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 - 12 * q^11 - 2 * q^12 + 8 * q^13 - 12 * q^14 - 6 * q^16 + 12 * q^17 - 18 * q^21 + 2 * q^23 + 4 * q^24 - 4 * q^26 + 28 * q^27 + 6 * q^28 + 12 * q^31 - 6 * q^32 + 14 * q^33 + 6 * q^36 - 30 * q^39 - 4 * q^41 + 6 * q^42 + 12 * q^44 + 2 * q^46 + 24 * q^47 - 2 * q^48 + 14 * q^49 + 4 * q^51 - 4 * q^52 + 8 * q^53 + 4 * q^54 + 6 * q^56 - 20 * q^57 - 18 * q^58 - 12 * q^59 - 30 * q^61 - 38 * q^63 + 12 * q^64 - 34 * q^66 + 6 * q^67 - 12 * q^68 - 50 * q^69 - 6 * q^72 - 20 * q^77 - 12 * q^78 + 4 * q^79 + 50 * q^81 + 2 * q^82 + 12 * q^84 - 54 * q^86 - 34 * q^87 - 12 * q^88 - 26 * q^89 + 28 * q^91 - 4 * q^92 + 60 * q^93 - 24 * q^94 - 2 * q^96 - 72 * q^97 + 2 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.21252	+	1.23685i	−0.700047	+	0.714096i
$3$	−1.21252	+	1.23685i	−0.700047	+	0.714096i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.67740	+	0.431645i	0.684797	+	0.176219i
$7$	2.62736	+	0.311378i	0.993050	+	0.117690i
$7$	2.62736	+	0.311378i	0.993050	+	0.117690i
$8$	1.00000			0.353553
$9$	−0.0596020	−	2.99941i	−0.0198673	−	0.999803i
$10$		0			0
$11$	−4.44749	−	2.56776i	−1.34097	−	0.774210i	−0.354020	−	0.935238i	$-0.615186\pi$
$11$	−4.44749	−	2.56776i	−1.34097	−	0.774210i	−0.986950	+	0.161028i	$0.948519\pi$
$12$	−0.464886	−	1.66850i	−0.134201	−	0.481654i
$13$	5.00256			1.38746			0.693731	−	0.720234i	$-0.255966\pi$
$13$	5.00256			1.38746			0.693731	+	0.720234i	$0.255966\pi$
$14$	−1.04402	−	2.43105i	−0.279026	−	0.649726i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.25579	−	1.87973i	−0.789646	−	0.455902i	0.0501922	−	0.998740i	$-0.484017\pi$
$17$	−3.25579	−	1.87973i	−0.789646	−	0.455902i	−0.839838	+	0.542837i	$0.817350\pi$
$18$	−2.56776	+	1.55132i	−0.605227	+	0.365650i
$19$	−2.33193	+	1.34634i	−0.534981	+	0.308871i	−0.743042	−	0.669245i	$-0.766618\pi$
$19$	−2.33193	+	1.34634i	−0.534981	+	0.308871i	0.208062	+	0.978116i	$0.433285\pi$
$20$		0			0
$21$	−3.57085	+	2.87211i	−0.779224	+	0.626745i
$22$			5.13552i			1.09490i
$23$	1.24302	+	2.15298i	0.259188	+	0.448927i	0.966025	−	0.258450i	$-0.0832116\pi$
$23$	1.24302	+	2.15298i	0.259188	+	0.448927i	−0.706836	+	0.707377i	$0.749878\pi$
$24$	−1.21252	+	1.23685i	−0.247504	+	0.252471i
$25$		0			0
$26$	−2.50128	−	4.33235i	−0.490542	−	0.849643i
$27$	3.78209	+	3.56312i	0.727864	+	0.685722i
$28$	−1.58334	+	2.11968i	−0.299224	+	0.400581i
$29$		−	6.18694i		−	1.14889i	−0.818545	−	0.574443i	$-0.805219\pi$
$29$		−	6.18694i		−	1.14889i	0.818545	−	0.574443i	$-0.194781\pi$
$30$		0			0
$31$	−4.13446	−	2.38703i	−0.742571	−	0.428724i	0.0804322	−	0.996760i	$-0.474370\pi$
$31$	−4.13446	−	2.38703i	−0.742571	−	0.428724i	−0.823003	+	0.568036i	$0.807703\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	8.56861	−	2.38743i	1.49160	−	0.415599i
$34$			3.75947i			0.644743i
$35$		0			0
$36$	2.62736	+	1.44809i	0.437894	+	0.241348i
$37$	−0.0453927	+	0.0262075i	−0.00746252	+	0.00430849i	−0.503727	−	0.863863i	$-0.668038\pi$
$37$	−0.0453927	+	0.0262075i	−0.00746252	+	0.00430849i	0.496264	+	0.868172i	$0.334705\pi$
$38$	2.33193	+	1.34634i	0.378288	+	0.218405i
$39$	−6.06570	+	6.18743i	−0.971289	+	0.990781i
$40$		0			0
$41$	6.55478			1.02369			0.511843	−	0.859079i	$-0.328963\pi$
$41$	6.55478			1.02369			0.511843	+	0.859079i	$0.328963\pi$
$42$	4.27275	+	1.65640i	0.659299	+	0.255588i
$43$		−	9.45088i		−	1.44125i	−0.693327	−	0.720623i	$-0.743856\pi$
$43$		−	9.45088i		−	1.44125i	0.693327	−	0.720623i	$-0.256144\pi$
$44$	4.44749	−	2.56776i	0.670485	−	0.387105i
$45$		0			0
$46$	1.24302	−	2.15298i	0.183274	−	0.317440i
$47$	2.65776	−	1.53446i	0.387674	−	0.223824i	−0.293478	−	0.955966i	$-0.594813\pi$
$47$	2.65776	−	1.53446i	0.387674	−	0.223824i	0.681152	+	0.732142i	$0.261479\pi$
$48$	1.67740	+	0.431645i	0.242112	+	0.0623027i
$49$	6.80609	+	1.63621i	0.972298	+	0.233744i
$50$		0			0
$51$	6.27266	−	1.74772i	0.878347	−	0.244730i
$52$	−2.50128	+	4.33235i	−0.346865	+	0.600788i
$53$	0.556019	−	0.963053i	0.0763751	−	0.132286i	−0.825308	−	0.564682i	$-0.808999\pi$
$53$	0.556019	−	0.963053i	0.0763751	−	0.132286i	0.901683	+	0.432397i	$0.142332\pi$
$54$	1.19470	−	5.05694i	0.162579	−	0.688163i
$55$		0			0
$56$	2.62736	+	0.311378i	0.351096	+	0.0416096i
$57$	1.16228	−	4.51670i	0.153948	−	0.598252i
$58$	−5.35804	+	3.09347i	−0.703546	+	0.406192i
$59$	6.63079	−	11.4849i	0.863255	−	1.49520i	−0.00551419	−	0.999985i	$-0.501755\pi$
$59$	6.63079	−	11.4849i	0.863255	−	1.49520i	0.868769	−	0.495217i	$-0.164911\pi$
$60$		0			0
$61$	3.59330	−	2.07459i	0.460075	−	0.265624i	−0.252001	−	0.967727i	$-0.581089\pi$
$61$	3.59330	−	2.07459i	0.460075	−	0.265624i	0.712076	+	0.702103i	$0.247755\pi$
$62$			4.77406i			0.606307i
$63$	0.777354	−	7.89910i	0.0979373	−	0.995193i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.35188	−	6.22691i	−0.781862	−	0.766480i
$67$	−0.776110	−	0.448087i	−0.0948169	−	0.0547426i	0.451842	−	0.892098i	$-0.350767\pi$
$67$	−0.776110	−	0.448087i	−0.0948169	−	0.0547426i	−0.546659	+	0.837356i	$0.684100\pi$
$68$	3.25579	−	1.87973i	0.394823	−	0.227951i
$69$	−4.17010	−	1.07309i	−0.502021	−	0.129185i
$70$		0			0
$71$			13.4240i			1.59313i	0.604551	+	0.796567i	$0.293353\pi$
$71$			13.4240i			1.59313i	−0.604551	+	0.796567i	$0.706647\pi$
$72$	−0.0596020	−	2.99941i	−0.00702416	−	0.353484i
$73$	3.49014	−	6.04511i	0.408490	−	0.707526i	−0.586230	−	0.810144i	$-0.699389\pi$
$73$	3.49014	−	6.04511i	0.408490	−	0.707526i	0.994721	+	0.102618i	$0.0327220\pi$
$74$	0.0453927	+	0.0262075i	0.00527680	+	0.00304656i
$75$		0			0
$76$		−	2.69268i		−	0.308871i
$77$	−10.8856	−	8.13130i	−1.24053	−	0.926648i
$78$	8.39132	+	2.15933i	0.950130	+	0.244496i
$79$	−8.37381	−	14.5039i	−0.942127	−	1.63181i	−0.761403	−	0.648279i	$-0.775489\pi$
$79$	−8.37381	−	14.5039i	−0.942127	−	1.63181i	−0.180724	−	0.983534i	$-0.557844\pi$
$80$		0			0
$81$	−8.99290	+	0.357541i	−0.999211	+	0.0397268i
$82$	−3.27739	−	5.67661i	−0.361927	−	0.626877i
$83$		−	1.37724i		−	0.151172i	−0.997139	−	0.0755861i	$-0.975917\pi$
$83$		−	1.37724i		−	0.151172i	0.997139	−	0.0755861i	$-0.0240828\pi$
$84$	−0.701891	−	4.52850i	−0.0765826	−	0.494100i
$85$		0			0
$86$	−8.18470	+	4.72544i	−0.882579	+	0.509557i
$87$	7.65232	+	7.50177i	0.820415	+	0.804274i
$88$	−4.44749	−	2.56776i	−0.474105	−	0.273724i
$89$	−2.67056	−	4.62555i	−0.283079	−	0.490307i	0.689062	−	0.724702i	$-0.258023\pi$
$89$	−2.67056	−	4.62555i	−0.283079	−	0.490307i	−0.972142	+	0.234395i	$0.924689\pi$
$90$		0			0
$91$	13.1436	+	1.55769i	1.37782	+	0.163290i
$92$	−2.48605			−0.259188
$93$	7.96551	−	2.21939i	0.825985	−	0.230141i
$94$	−2.65776	−	1.53446i	−0.274127	−	0.158267i
$95$		0			0
$96$	−0.464886	−	1.66850i	−0.0474472	−	0.170290i
$97$	0.633608			0.0643331			0.0321666	−	0.999483i	$-0.489759\pi$
$97$	0.633608			0.0643331			0.0321666	+	0.999483i	$0.489759\pi$
$98$	−1.98605	−	6.71235i	−0.200621	−	0.678050i
$99$	−7.43669	+	13.4929i	−0.747415	+	1.35609i
$100$		0			0
$101$	8.81430	−	15.2668i	0.877056	−	1.51910i	0.0224989	−	0.999747i	$-0.492838\pi$
$101$	8.81430	−	15.2668i	0.877056	−	1.51910i	0.854557	−	0.519358i	$-0.173829\pi$
$102$	−4.64990	−	4.55842i	−0.460409	−	0.451351i
$103$	7.35823	+	12.7448i	0.725028	+	1.25579i	0.958962	+	0.283533i	$0.0915066\pi$
$103$	7.35823	+	12.7448i	0.725028	+	1.25579i	−0.233934	+	0.972252i	$0.575160\pi$
$104$	5.00256			0.490542
$105$		0			0
$106$	−1.11204			−0.108011
$107$	−2.35501	−	4.07900i	−0.227667	−	0.394331i	0.729449	−	0.684035i	$-0.239777\pi$
$107$	−2.35501	−	4.07900i	−0.227667	−	0.394331i	−0.957116	+	0.289704i	$0.906443\pi$
$108$	−4.97679	+	1.49383i	−0.478892	+	0.143744i
$109$	4.31181	−	7.46828i	0.412997	−	0.715331i	−0.582219	−	0.813032i	$-0.697815\pi$
$109$	4.31181	−	7.46828i	0.412997	−	0.715331i	0.995216	+	0.0977007i	$0.0311488\pi$
$110$		0			0
$111$	0.0226247	−	0.0879211i	0.00214744	−	0.00834510i
$112$	−1.04402	−	2.43105i	−0.0986507	−	0.229713i
$113$	15.3809			1.44691			0.723455	−	0.690372i	$-0.242553\pi$
$113$	15.3809			1.44691			0.723455	+	0.690372i	$0.242553\pi$
$114$	−4.49272	+	1.25179i	−0.420782	+	0.117241i
$115$		0			0
$116$	5.35804	+	3.09347i	0.497482	+	0.287221i
$117$	−0.298163	−	15.0047i	−0.0275652	−	1.38719i
$118$	−13.2616			−1.22083
$119$	−7.96885	−	5.95252i	−0.730503	−	0.545667i
$120$		0			0
$121$	7.68681	+	13.3139i	0.698801	+	1.21036i
$122$	−3.59330	−	2.07459i	−0.325322	−	0.187825i
$123$	−7.94779	+	8.10729i	−0.716628	+	0.731010i
$124$	4.13446	−	2.38703i	0.371286	−	0.214362i
$125$		0			0
$126$	−7.22949	+	3.27634i	−0.644055	+	0.291880i
$127$			1.78518i			0.158409i	0.996858	+	0.0792047i	$0.0252381\pi$
$127$			1.78518i			0.158409i	−0.996858	+	0.0792047i	$0.974762\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	11.6893	+	11.4594i	1.02919	+	1.00894i
$130$		0			0
$131$	−1.55132	−	2.68697i	−0.135540	−	0.234761i	0.790264	−	0.612767i	$-0.209943\pi$
$131$	−1.55132	−	2.68697i	−0.135540	−	0.234761i	−0.925803	+	0.378005i	$0.876610\pi$
$132$	−2.21673	+	8.61435i	−0.192941	+	0.749783i
$133$	−6.54604	+	2.81121i	−0.567614	+	0.243763i
$134$			0.896174i			0.0774177i
$135$		0			0
$136$	−3.25579	−	1.87973i	−0.279182	−	0.161186i
$137$	−4.87855	+	8.44989i	−0.416803	+	0.721923i	−0.995616	−	0.0935370i	$-0.970183\pi$
$137$	−4.87855	+	8.44989i	−0.416803	+	0.721923i	0.578813	+	0.815460i	$0.303516\pi$
$138$	1.15573	+	4.14796i	0.0983821	+	0.353098i
$139$			4.26248i			0.361539i	0.983526	+	0.180769i	$0.0578588\pi$
$139$			4.26248i			0.361539i	−0.983526	+	0.180769i	$0.942141\pi$
$140$		0			0
$141$	−1.32468	+	5.14781i	−0.111558	+	0.433524i
$142$	11.6255	−	6.71199i	0.975591	−	0.563258i
$143$	−22.2489	−	12.8454i	−1.86054	−	1.07419i
$144$	−2.56776	+	1.55132i	−0.213980	+	0.129277i
$145$		0			0
$146$	−6.98029			−0.577693
$147$	−10.2762	+	6.43419i	−0.847570	+	0.530683i
$148$		−	0.0524150i		−	0.00430849i
$149$	−7.77014	+	4.48609i	−0.636554	+	0.367515i	−0.783286	−	0.621662i	$-0.786458\pi$
$149$	−7.77014	+	4.48609i	−0.636554	+	0.367515i	0.146732	+	0.989176i	$0.453125\pi$
$150$		0			0
$151$	−6.61328	+	11.4545i	−0.538181	+	0.932157i	0.460821	+	0.887493i	$0.347555\pi$
$151$	−6.61328	+	11.4545i	−0.538181	+	0.932157i	−0.999002	+	0.0446642i	$0.985778\pi$
$152$	−2.33193	+	1.34634i	−0.189144	+	0.109202i
$153$	−5.44403	+	9.87748i	−0.440124	+	0.798547i
$154$	−1.59909	+	13.4929i	−0.128858	+	1.08729i
$155$		0			0
$156$	−2.32562	−	8.34676i	−0.186199	−	0.668276i
$157$	4.28200	−	7.41664i	0.341741	−	0.591912i	−0.643015	−	0.765853i	$-0.722317\pi$
$157$	4.28200	−	7.41664i	0.341741	−	0.591912i	0.984756	+	0.173941i	$0.0556502\pi$
$158$	−8.37381	+	14.5039i	−0.666185	+	1.15387i
$159$	0.516971	+	1.85543i	0.0409985	+	0.147145i
$160$		0			0
$161$	2.59549	+	6.04371i	0.204553	+	0.476311i
$162$	4.80609	+	7.60931i	0.377602	+	0.597843i
$163$	9.59085	−	5.53728i	0.751213	−	0.433713i	−0.0749190	−	0.997190i	$-0.523870\pi$
$163$	9.59085	−	5.53728i	0.751213	−	0.433713i	0.826132	+	0.563477i	$0.190536\pi$
$164$	−3.27739	+	5.67661i	−0.255921	+	0.443269i
$165$		0			0
$166$	−1.19273	+	0.688622i	−0.0925737	+	0.0534474i
$167$		−	2.95799i		−	0.228896i	−0.993429	−	0.114448i	$-0.963490\pi$
$167$		−	2.95799i		−	0.228896i	0.993429	−	0.114448i	$-0.0365099\pi$
$168$	−3.57085	+	2.87211i	−0.275497	+	0.221588i
$169$	12.0256			0.925049
$170$		0			0
$171$	4.17720	+	6.91415i	0.319439	+	0.528738i
$172$	8.18470	+	4.72544i	0.624078	+	0.360311i
$173$	−17.9628	+	10.3708i	−1.36568	+	0.788478i	−0.990374	−	0.138421i	$-0.955797\pi$
$173$	−17.9628	+	10.3708i	−1.36568	+	0.788478i	−0.375311	+	0.926899i	$0.622464\pi$
$174$	2.67056	−	10.3780i	0.202455	−	0.786753i
$175$		0			0
$176$			5.13552i			0.387105i
$177$	6.16512	+	22.1269i	0.463399	+	1.66316i
$178$	−2.67056	+	4.62555i	−0.200167	+	0.346700i
$179$	21.2335	+	12.2592i	1.58707	+	0.916294i	0.993787	+	0.111298i	$0.0355009\pi$
$179$	21.2335	+	12.2592i	1.58707	+	0.916294i	0.593281	+	0.804996i	$0.297832\pi$
$180$		0			0
$181$		−	18.6533i		−	1.38649i	−0.720704	−	0.693243i	$-0.756181\pi$
$181$		−	18.6533i		−	1.38649i	0.720704	−	0.693243i	$-0.243819\pi$
$182$	−5.22278	−	12.1615i	−0.387138	−	0.901470i
$183$	−1.79098	+	6.95985i	−0.132393	+	0.514487i
$184$	1.24302	+	2.15298i	0.0916369	+	0.158720i
$185$		0			0
$186$	−5.90481	−	5.78864i	−0.432962	−	0.424444i
$187$	9.65341	+	16.7202i	0.705927	+	1.22270i
$188$			3.06892i			0.223824i
$189$	8.82745	+	10.5393i	0.642103	+	0.766619i
$190$		0			0
$191$	−6.29976	+	3.63717i	−0.455835	+	0.263176i	−0.710291	−	0.703908i	$-0.751437\pi$
$191$	−6.29976	+	3.63717i	−0.455835	+	0.263176i	0.254457	+	0.967084i	$0.418103\pi$
$192$	−1.21252	+	1.23685i	−0.0875059	+	0.0892620i
$193$	9.58185	+	5.53208i	0.689716	+	0.398208i	0.803506	−	0.595297i	$-0.202966\pi$
$193$	9.58185	+	5.53208i	0.689716	+	0.398208i	−0.113789	+	0.993505i	$0.536299\pi$
$194$	−0.316804	−	0.548721i	−0.0227452	−	0.0393958i
$195$		0			0
$196$	−4.82004	+	5.07614i	−0.344289	+	0.362582i
$197$	−8.86701			−0.631748			−0.315874	−	0.948801i	$-0.602298\pi$
$197$	−8.86701			−0.631748			−0.315874	+	0.948801i	$0.602298\pi$
$198$	15.4035	−	0.306087i	1.09468	−	0.0217527i
$199$	−16.0911	−	9.29018i	−1.14066	−	0.658563i	−0.194070	−	0.980988i	$-0.562169\pi$
$199$	−16.0911	−	9.29018i	−1.14066	−	0.658563i	−0.946595	+	0.322425i	$0.895502\pi$
$200$		0			0
$201$	1.49526	−	0.416619i	0.105468	−	0.0293860i
$202$	−17.6286			−1.24034
$203$	1.92648	−	16.2553i	0.135212	−	1.14090i
$204$	−1.62276	+	6.30614i	−0.113616	+	0.441518i
$205$		0			0
$206$	7.35823	−	12.7448i	0.512672	−	0.887974i
$207$	6.38358	−	3.85666i	0.443689	−	0.268056i
$208$	−2.50128	−	4.33235i	−0.173433	−	0.300394i
$209$	13.8283			0.956524
$210$		0			0
$211$	−7.36879			−0.507288			−0.253644	−	0.967298i	$-0.581629\pi$
$211$	−7.36879			−0.507288			−0.253644	+	0.967298i	$0.581629\pi$
$212$	0.556019	+	0.963053i	0.0381876	+	0.0661428i
$213$	−16.6035	−	16.2768i	−1.13765	−	1.11527i
$214$	−2.35501	+	4.07900i	−0.160985	+	0.278834i
$215$		0			0
$216$	3.78209	+	3.56312i	0.257339	+	0.242439i
$217$	−10.1195	−	7.55898i	−0.686954	−	0.513137i
$218$	−8.62362			−0.584065
$219$	3.24504	+	11.6466i	0.219279	+	0.787003i
$220$		0			0
$221$	−16.2873	−	9.40348i	−1.09560	−	0.632547i
$222$	−0.0874543	+	0.0243670i	−0.00586955	+	0.00163541i
$223$	5.79472			0.388043			0.194021	−	0.980997i	$-0.437847\pi$
$223$	5.79472			0.388043			0.194021	+	0.980997i	$0.437847\pi$
$224$	−1.58334	+	2.11968i	−0.105792	+	0.141627i
$225$		0			0
$226$	−7.69043	−	13.3202i	−0.511560	−	0.886047i
$227$	−9.24746	−	5.33902i	−0.613775	−	0.354363i	0.160666	−	0.987009i	$-0.448636\pi$
$227$	−9.24746	−	5.33902i	−0.613775	−	0.354363i	−0.774442	+	0.632645i	$0.781969\pi$
$228$	3.33044	+	3.26492i	0.220564	+	0.216224i
$229$	7.46827	−	4.31181i	0.493517	−	0.284932i	−0.232515	−	0.972593i	$-0.574696\pi$
$229$	7.46827	−	4.31181i	0.493517	−	0.284932i	0.726032	+	0.687661i	$0.241362\pi$
$230$		0			0
$231$	23.2562	−	3.60458i	1.53015	−	0.237164i
$232$		−	6.18694i		−	0.406192i
$233$	−8.03272	−	13.9131i	−0.526241	−	0.911476i	−0.999533	−	0.0305704i	$-0.990268\pi$
$233$	−8.03272	−	13.9131i	−0.526241	−	0.911476i	0.473292	−	0.880906i	$-0.343066\pi$
$234$	−12.8454	+	7.76058i	−0.839730	+	0.507325i
$235$		0			0
$236$	6.63079	+	11.4849i	0.431628	+	0.747601i
$237$	28.0925	+	7.22904i	1.82481	+	0.469576i
$238$	−1.17061	+	9.87748i	−0.0758797	+	0.640262i
$239$			11.0070i			0.711981i	0.934490	+	0.355990i	$0.115856\pi$
$239$			11.0070i			0.711981i	−0.934490	+	0.355990i	$0.884144\pi$
$240$		0			0
$241$	8.40789	+	4.85430i	0.541600	+	0.312693i	0.745727	−	0.666252i	$-0.232102\pi$
$241$	8.40789	+	4.85430i	0.541600	+	0.312693i	−0.204127	+	0.978944i	$0.565436\pi$
$242$	7.68681	−	13.3139i	0.494127	−	0.855853i
$243$	10.4618	−	11.5564i	0.671126	−	0.741343i
$244$			4.14918i			0.265624i
$245$		0			0
$246$	10.9950	+	2.82934i	0.701017	+	0.180392i
$247$	−11.6656	+	6.73514i	−0.742265	+	0.428547i
$248$	−4.13446	−	2.38703i	−0.262539	−	0.151577i
$249$	1.70345	+	1.66993i	0.107951	+	0.105828i
$250$		0			0
$251$	−4.59082			−0.289770			−0.144885	−	0.989449i	$-0.546281\pi$
$251$	−4.59082			−0.289770			−0.144885	+	0.989449i	$0.546281\pi$
$252$	6.45214	+	4.62276i	0.406447	+	0.291206i
$253$		−	12.7672i		−	0.802664i
$254$	1.54601	−	0.892591i	0.0970055	−	0.0560062i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.1694	−	5.87132i	0.634352	−	0.366243i	−0.148084	−	0.988975i	$-0.547311\pi$
$257$	10.1694	−	5.87132i	0.634352	−	0.366243i	0.782435	+	0.622732i	$0.213977\pi$
$258$	4.07943	−	15.8529i	0.253974	−	0.986961i
$259$	−0.127424	+	0.0547224i	−0.00791772	+	0.00340028i
$260$		0			0
$261$	−18.5571	+	0.368754i	−1.14866	+	0.0228253i
$262$	−1.55132	+	2.68697i	−0.0958409	+	0.166001i
$263$	−11.4564	+	19.8431i	−0.706432	+	1.22358i	0.259740	+	0.965679i	$0.416363\pi$
$263$	−11.4564	+	19.8431i	−0.706432	+	1.22358i	−0.966172	+	0.257898i	$0.916970\pi$
$264$	8.56861	−	2.38743i	0.527361	−	0.146936i
$265$		0			0
$266$	5.70760	+	4.26343i	0.349955	+	0.261408i
$267$	8.95922	+	2.30547i	0.548295	+	0.141093i
$268$	0.776110	−	0.448087i	0.0474084	−	0.0273713i
$269$	−4.06200	+	7.03559i	−0.247665	+	0.428968i	−0.962877	−	0.269939i	$-0.912996\pi$
$269$	−4.06200	+	7.03559i	−0.247665	+	0.428968i	0.715213	+	0.698907i	$0.246330\pi$
$270$		0			0
$271$	−9.47446	+	5.47008i	−0.575533	+	0.332284i	−0.759356	−	0.650675i	$-0.774486\pi$
$271$	−9.47446	+	5.47008i	−0.575533	+	0.332284i	0.183823	+	0.982959i	$0.441153\pi$
$272$			3.75947i			0.227951i
$273$	−17.8634	+	14.3679i	−1.08114	+	0.869585i
$274$	9.75710			0.589448
$275$		0			0
$276$	3.01438	−	3.07487i	0.181444	−	0.185085i
$277$	4.14209	+	2.39144i	0.248874	+	0.143688i	0.619249	−	0.785195i	$-0.287437\pi$
$277$	4.14209	+	2.39144i	0.248874	+	0.143688i	−0.370374	+	0.928883i	$0.620771\pi$
$278$	3.69142	−	2.13124i	0.221396	−	0.127823i
$279$	−6.91326	+	12.5432i	−0.413886	+	0.750942i
$280$		0			0
$281$			21.1040i			1.25896i	0.777018	+	0.629479i	$0.216732\pi$
$281$			21.1040i			1.25896i	−0.777018	+	0.629479i	$0.783268\pi$
$282$	5.12048	−	1.42670i	0.304920	−	0.0849585i
$283$	−11.0026	+	19.0570i	−0.654035	+	1.13282i	0.328100	+	0.944643i	$0.393592\pi$
$283$	−11.0026	+	19.0570i	−0.654035	+	1.13282i	−0.982135	+	0.188178i	$0.939742\pi$
$284$	−11.6255	−	6.71199i	−0.689847	−	0.398283i
$285$		0			0
$286$			25.6908i			1.51913i
$287$	17.2218	+	2.04102i	1.01657	+	0.120477i
$288$	2.62736	+	1.44809i	0.154819	+	0.0853294i
$289$	−1.43321	−	2.48239i	−0.0843065	−	0.146023i
$290$		0			0
$291$	−0.768261	+	0.783679i	−0.0450362	+	0.0459401i
$292$	3.49014	+	6.04511i	0.204245	+	0.353763i
$293$			11.2905i			0.659598i	0.944051	+	0.329799i	$0.106981\pi$
$293$			11.2905i			0.659598i	−0.944051	+	0.329799i	$0.893019\pi$
$294$	10.7103	+	5.68240i	0.624637	+	0.331404i
$295$		0			0
$296$	−0.0453927	+	0.0262075i	−0.00263840	+	0.00152328i
$297$	−7.67159	−	25.5584i	−0.445151	−	1.48305i
$298$	7.77014	+	4.48609i	0.450112	+	0.259872i
$299$	6.21830	+	10.7704i	0.359614	+	0.622869i
$300$		0			0
$301$	2.94280	−	24.8309i	0.169620	−	1.43123i
$302$	13.2266			0.761103
$303$	8.19529	+	29.4133i	0.470807	+	1.68975i
$304$	2.33193	+	1.34634i	0.133745	+	0.0772178i
$305$		0			0
$306$	11.2762	−	0.224072i	0.644616	−	0.0128093i
$307$	2.12162			0.121087			0.0605436	−	0.998166i	$-0.480717\pi$
$307$	2.12162			0.121087			0.0605436	+	0.998166i	$0.480717\pi$
$308$	12.4847	−	5.36160i	0.711384	−	0.305505i
$309$	−24.6854	−	6.35229i	−1.40431	−	0.361369i
$310$		0			0
$311$	5.50229	−	9.53025i	0.312006	−	0.540411i	−0.666790	−	0.745245i	$-0.732332\pi$
$311$	5.50229	−	9.53025i	0.312006	−	0.540411i	0.978797	+	0.204835i	$0.0656656\pi$
$312$	−6.06570	+	6.18743i	−0.343402	+	0.350294i
$313$	−3.71718	−	6.43835i	−0.210108	−	0.363917i	0.741640	−	0.670798i	$-0.234048\pi$
$313$	−3.71718	−	6.43835i	−0.210108	−	0.363917i	−0.951748	+	0.306881i	$0.900715\pi$
$314$	−8.56400			−0.483294
$315$		0			0
$316$	16.7476			0.942127
$317$	2.23730	+	3.87512i	0.125659	+	0.217648i	0.921990	−	0.387213i	$-0.126562\pi$
$317$	2.23730	+	3.87512i	0.125659	+	0.217648i	−0.796331	+	0.604861i	$0.793229\pi$
$318$	1.34837	−	1.37543i	0.0756126	−	0.0771301i
$319$	−15.8866	+	27.5164i	−0.889478	+	1.54062i
$320$		0			0
$321$	7.90060	+	2.03306i	0.440969	+	0.113474i
$322$	3.93627	−	5.26961i	0.219360	−	0.293664i
$323$	10.1230			0.563260
$324$	4.18681	−	7.96685i	0.232600	−	0.442603i
$325$		0			0
$326$	−9.59085	−	5.53728i	−0.531188	−	0.306681i
$327$	4.00900	+	14.3885i	0.221698	+	0.795685i
$328$	6.55478			0.361927
$329$	7.46070	−	3.20401i	0.411322	−	0.176643i
$330$		0			0
$331$	−8.48598	−	14.6981i	−0.466432	−	0.807883i	0.532833	−	0.846220i	$-0.321127\pi$
$331$	−8.48598	−	14.6981i	−0.466432	−	0.807883i	−0.999265	+	0.0383371i	$0.987794\pi$
$332$	1.19273	+	0.688622i	0.0654595	+	0.0377930i
$333$	0.0813125	+	0.134589i	0.00445590	+	0.00737545i
$334$	−2.56169	+	1.47899i	−0.140169	+	0.0809269i
$335$		0			0
$336$	4.27275	+	1.65640i	0.233097	+	0.0903638i
$337$		−	30.7045i		−	1.67258i	−0.548287	−	0.836290i	$-0.684720\pi$
$337$		−	30.7045i		−	1.67258i	0.548287	−	0.836290i	$-0.315280\pi$
$338$	−6.01282	−	10.4145i	−0.327054	−	0.566475i
$339$	−18.6496	+	19.0238i	−1.01291	+	1.03323i
$340$		0			0
$341$	12.2587	+	21.2326i	0.663844	+	1.14981i
$342$	3.89923	−	7.07464i	0.210846	−	0.382553i
$343$	17.3726	+	6.41818i	0.938032	+	0.346549i
$344$		−	9.45088i		−	0.509557i
$345$		0			0
$346$	17.9628	+	10.3708i	0.965685	+	0.557538i
$347$	−16.6003	+	28.7525i	−0.891149	+	1.54352i	−0.0526494	+	0.998613i	$0.516767\pi$
$347$	−16.6003	+	28.7525i	−0.891149	+	1.54352i	−0.838500	+	0.544902i	$0.816567\pi$
$348$	−10.3229	+	2.87622i	−0.553365	+	0.154181i
$349$		−	21.5465i		−	1.15336i	−0.816972	−	0.576678i	$-0.804349\pi$
$349$		−	21.5465i		−	1.15336i	0.816972	−	0.576678i	$-0.195651\pi$
$350$		0			0
$351$	18.9201	+	17.8247i	1.00988	+	0.951413i
$352$	4.44749	−	2.56776i	0.237052	−	0.136862i
$353$	−4.77779	−	2.75846i	−0.254296	−	0.146818i	0.367434	−	0.930050i	$-0.380237\pi$
$353$	−4.77779	−	2.75846i	−0.254296	−	0.146818i	−0.621730	+	0.783232i	$0.713570\pi$
$354$	16.0799	−	16.4026i	0.854637	−	0.871788i
$355$		0			0
$356$	5.34113			0.283079
$357$	17.0248	−	2.63874i	0.901045	−	0.139657i
$358$		−	24.5184i		−	1.29584i
$359$	−16.7632	+	9.67826i	−0.884730	+	0.510799i	−0.872215	−	0.489122i	$-0.837317\pi$
$359$	−16.7632	+	9.67826i	−0.884730	+	0.510799i	−0.0125151	+	0.999922i	$0.503984\pi$
$360$		0			0
$361$	−5.87475	+	10.1754i	−0.309197	+	0.535545i
$362$	−16.1542	+	9.32664i	−0.849046	+	0.490197i
$363$	−25.7878	−	6.63595i	−1.35351	−	0.348297i
$364$	−7.92078	+	10.6038i	−0.415161	+	0.555791i
$365$		0			0
$366$	6.92290	−	1.92890i	0.361866	−	0.100825i
$367$	−7.01628	+	12.1526i	−0.366247	+	0.634358i	−0.988975	−	0.148080i	$-0.952691\pi$
$367$	−7.01628	+	12.1526i	−0.366247	+	0.634358i	0.622728	+	0.782438i	$0.286024\pi$
$368$	1.24302	−	2.15298i	0.0647971	−	0.112232i
$369$	−0.390678	−	19.6605i	−0.0203379	−	1.02348i
$370$		0			0
$371$	1.76074	−	2.35716i	0.0914130	−	0.122378i
$372$	−2.06070	+	8.00803i	−0.106842	+	0.415197i
$373$	−1.15907	+	0.669190i	−0.0600144	+	0.0346493i	−0.529707	−	0.848181i	$-0.677698\pi$
$373$	−1.15907	+	0.669190i	−0.0600144	+	0.0346493i	0.469693	+	0.882830i	$0.344365\pi$
$374$	9.65341	−	16.7202i	0.499166	−	0.864581i
$375$		0			0
$376$	2.65776	−	1.53446i	0.137063	−	0.0791336i
$377$		−	30.9505i		−	1.59403i
$378$	4.71354	−	12.9144i	0.242439	−	0.664247i
$379$	−8.07964			−0.415023			−0.207512	−	0.978233i	$-0.566536\pi$
$379$	−8.07964			−0.415023			−0.207512	+	0.978233i	$0.566536\pi$
$380$		0			0
$381$	−2.20801	−	2.16457i	−0.113120	−	0.110894i
$382$	6.29976	+	3.63717i	0.322324	+	0.186094i
$383$	20.1734	−	11.6471i	1.03081	−	0.595141i	0.113596	−	0.993527i	$-0.463763\pi$
$383$	20.1734	−	11.6471i	1.03081	−	0.595141i	0.917218	+	0.398386i	$0.130430\pi$
$384$	1.67740	+	0.431645i	0.0855996	+	0.0220273i
$385$		0			0
$386$		−	11.0642i		−	0.563151i
$387$	−28.3470	+	0.563291i	−1.44096	+	0.0286337i
$388$	−0.316804	+	0.548721i	−0.0160833	+	0.0278571i
$389$	−10.1748	−	5.87442i	−0.515882	−	0.297845i	0.219366	−	0.975643i	$-0.429601\pi$
$389$	−10.1748	−	5.87442i	−0.515882	−	0.297845i	−0.735248	+	0.677798i	$0.762934\pi$
$390$		0			0
$391$		−	9.34621i		−	0.472658i
$392$	6.80609	+	1.63621i	0.343759	+	0.0826409i
$393$	5.20438	+	1.33924i	0.262526	+	0.0675558i
$394$	4.43350	+	7.67905i	0.223357	+	0.386865i
$395$		0			0
$396$	−7.96685	−	13.1868i	−0.400349	−	0.662662i
$397$	−8.61072	−	14.9142i	−0.432160	−	0.748522i	0.564899	−	0.825160i	$-0.308915\pi$
$397$	−8.61072	−	14.9142i	−0.432160	−	0.748522i	−0.997059	+	0.0766373i	$0.975582\pi$
$398$			18.5804i			0.931349i
$399$	4.46014	−	11.5051i	0.223286	−	0.575976i
$400$		0			0
$401$	−7.31712	+	4.22454i	−0.365400	+	0.210964i	−0.671447	−	0.741053i	$-0.734327\pi$
$401$	−7.31712	+	4.22454i	−0.365400	+	0.210964i	0.306047	+	0.952016i	$0.400993\pi$
$402$	−1.10843	−	1.08663i	−0.0552837	−	0.0541960i
$403$	−20.6829	−	11.9413i	−1.03029	−	0.594838i
$404$	8.81430	+	15.2668i	0.438528	+	0.759552i
$405$		0			0
$406$	−15.0408	+	6.45929i	−0.746461	+	0.320569i
$407$	0.269179			0.0133427
$408$	6.27266	−	1.74772i	0.310543	−	0.0865251i
$409$	25.2043	+	14.5517i	1.24627	+	0.719535i	0.970364	−	0.241649i	$-0.0776882\pi$
$409$	25.2043	+	14.5517i	1.24627	+	0.719535i	0.275908	+	0.961184i	$0.411021\pi$
$410$		0			0
$411$	−4.53594	−	16.2797i	−0.223741	−	0.803018i
$412$	−14.7165			−0.725028
$413$	20.9976	−	28.1102i	1.03323	−	1.38321i
$414$	−6.53175	−	3.60001i	−0.321018	−	0.176931i
$415$		0			0
$416$	−2.50128	+	4.33235i	−0.122635	+	0.212411i
$417$	−5.27205	−	5.16833i	−0.258174	−	0.253094i
$418$	−6.91415	−	11.9757i	−0.338182	−	0.585749i
$419$	−2.07947			−0.101589			−0.0507944	−	0.998709i	$-0.516175\pi$
$419$	−2.07947			−0.101589			−0.0507944	+	0.998709i	$0.516175\pi$
$420$		0			0
$421$	−32.8371			−1.60038			−0.800190	−	0.599746i	$-0.795268\pi$
$421$	−32.8371			−1.60038			−0.800190	+	0.599746i	$0.795268\pi$
$422$	3.68439	+	6.38156i	0.179354	+	0.310649i
$423$	−4.76087	−	7.88025i	−0.231482	−	0.383151i
$424$	0.556019	−	0.963053i	0.0270027	−	0.0467700i
$425$		0			0
$426$	−5.79440	+	22.5174i	−0.280740	+	1.09097i
$427$	10.0869	−	4.33183i	0.488138	−	0.209632i
$428$	4.71002			0.227667
$429$	42.8650	−	11.9433i	2.06954	−	0.576627i
$430$		0			0
$431$	7.57956	+	4.37606i	0.365094	+	0.210787i	0.671313	−	0.741174i	$-0.265731\pi$
$431$	7.57956	+	4.37606i	0.365094	+	0.210787i	−0.306219	+	0.951961i	$0.599064\pi$
$432$	1.19470	−	5.05694i	0.0574802	−	0.243302i
$433$	12.3440			0.593214			0.296607	−	0.955000i	$-0.404145\pi$
$433$	12.3440			0.593214			0.296607	+	0.955000i	$0.404145\pi$
$434$	−1.48654	+	12.5432i	−0.0713561	+	0.602093i
$435$		0			0
$436$	4.31181	+	7.46828i	0.206498	+	0.357666i
$437$	−5.79728	−	3.34706i	−0.277321	−	0.160112i
$438$	8.46372	−	8.63358i	0.404412	−	0.412528i
$439$	9.72433	−	5.61435i	0.464117	−	0.267958i	−0.249657	−	0.968334i	$-0.580318\pi$
$439$	9.72433	−	5.61435i	0.464117	−	0.267958i	0.713774	+	0.700376i	$0.246984\pi$
$440$		0			0
$441$	4.50200	−	20.5118i	0.214381	−	0.976750i
$442$			18.8070i			0.894556i
$443$	16.7161	+	28.9532i	0.794208	+	1.37561i	0.923341	+	0.383981i	$0.125447\pi$
$443$	16.7161	+	28.9532i	0.794208	+	1.37561i	−0.129133	+	0.991627i	$0.541220\pi$
$444$	0.0648296	+	0.0635541i	0.00307667	+	0.00301614i
$445$		0			0
$446$	−2.89736	−	5.01837i	−0.137194	−	0.237627i
$447$	3.87280	−	15.0500i	0.183177	−	0.711839i
$448$	2.62736	+	0.311378i	0.124131	+	0.0147112i
$449$		−	27.8343i		−	1.31358i	−0.754073	−	0.656791i	$-0.771914\pi$
$449$		−	27.8343i		−	1.31358i	0.754073	−	0.656791i	$-0.228086\pi$
$450$		0			0
$451$	−29.1524	−	16.8311i	−1.37273	−	0.792547i
$452$	−7.69043	+	13.3202i	−0.361727	+	0.626530i
$453$	−6.14884	−	22.0685i	−0.288898	−	1.03687i
$454$			10.6780i			0.501146i
$455$		0			0
$456$	1.16228	−	4.51670i	0.0544288	−	0.211514i
$457$	−24.5277	+	14.1611i	−1.14736	+	0.662427i	−0.948242	−	0.317550i	$-0.897140\pi$
$457$	−24.5277	+	14.1611i	−1.14736	+	0.662427i	−0.199115	+	0.979976i	$0.563807\pi$
$458$	−7.46827	−	4.31181i	−0.348969	−	0.201477i
$459$	−5.61599	−	18.7101i	−0.262132	−	0.873312i
$460$		0			0
$461$	−35.5758			−1.65693			−0.828466	−	0.560040i	$-0.810786\pi$
$461$	−35.5758			−1.65693			−0.828466	+	0.560040i	$0.810786\pi$
$462$	−14.7498	−	18.3382i	−0.686222	−	0.853171i
$463$			18.8371i			0.875434i	0.899113	+	0.437717i	$0.144213\pi$
$463$			18.8371i			0.875434i	−0.899113	+	0.437717i	$0.855787\pi$
$464$	−5.35804	+	3.09347i	−0.248741	+	0.143611i
$465$		0			0
$466$	−8.03272	+	13.9131i	−0.372109	+	0.644511i
$467$	10.8853	−	6.28462i	0.503711	−	0.290818i	−0.226534	−	0.974003i	$-0.572739\pi$
$467$	10.8853	−	6.28462i	0.503711	−	0.290818i	0.730245	+	0.683186i	$0.239406\pi$
$468$	13.1436	+	7.24415i	0.607561	+	0.334861i
$469$	−1.89960	−	1.41895i	−0.0877153	−	0.0655211i
$470$		0			0
$471$	3.98128	+	14.2890i	0.183448	+	0.658403i
$472$	6.63079	−	11.4849i	0.305207	−	0.528634i
$473$	−24.2676	+	42.0327i	−1.11583	+	1.93267i
$474$	−7.78573	−	27.9434i	−0.357611	−	1.28348i
$475$		0			0
$476$	9.13946	−	3.92496i	0.418906	−	0.179900i
$477$	−2.92173	−	1.61033i	−0.133777	−	0.0737319i
$478$	9.53230	−	5.50348i	0.435997	−	0.251723i
$479$	10.7038	−	18.5395i	0.489069	−	0.847093i	−0.510852	−	0.859669i	$-0.670670\pi$
$479$	10.7038	−	18.5395i	0.489069	−	0.847093i	0.999921	+	0.0125762i	$0.00400322\pi$
$480$		0			0
$481$	−0.227080	+	0.131105i	−0.0103540	+	0.00597786i
$482$		−	9.70859i		−	0.442214i
$483$	−10.6222	−	4.11788i	−0.483329	−	0.187370i
$484$	−15.3736			−0.698801
$485$		0			0
$486$	−15.2390	−	3.28200i	−0.691257	−	0.148875i
$487$	2.17886	+	1.25796i	0.0987335	+	0.0570038i	0.548554	−	0.836115i	$-0.315179\pi$
$487$	2.17886	+	1.25796i	0.0987335	+	0.0570038i	−0.449820	+	0.893119i	$0.648512\pi$
$488$	3.59330	−	2.07459i	0.162661	−	0.0939123i
$489$	−4.78028	+	18.5765i	−0.216172	+	0.840058i
$490$		0			0
$491$		−	34.7105i		−	1.56646i	−0.621729	−	0.783232i	$-0.713570\pi$
$491$		−	34.7105i		−	1.56646i	0.621729	−	0.783232i	$-0.286430\pi$
$492$	−3.04723	−	10.9366i	−0.137380	−	0.493062i
$493$	−11.6298	+	20.1434i	−0.523779	+	0.907212i
$494$	11.6656	+	6.73514i	0.524861	+	0.303028i
$495$		0			0
$496$			4.77406i			0.214362i
$497$	−4.17993	+	35.2697i	−0.187496	+	1.58206i
$498$	0.594481	−	2.31019i	0.0266393	−	0.103522i
$499$	−3.07500	−	5.32606i	−0.137656	−	0.238427i	0.788953	−	0.614454i	$-0.210624\pi$
$499$	−3.07500	−	5.32606i	−0.137656	−	0.238427i	−0.926609	+	0.376026i	$0.877290\pi$
$500$		0			0
$501$	3.65859	+	3.58661i	0.163454	+	0.160238i
$502$	2.29541	+	3.97576i	0.102449	+	0.177447i
$503$			5.99378i			0.267249i	0.991032	+	0.133625i	$0.0426617\pi$
$503$			5.99378i			0.267249i	−0.991032	+	0.133625i	$0.957338\pi$
$504$	0.777354	−	7.89910i	0.0346261	−	0.351854i
$505$		0			0
$506$	−11.0567	+	6.38358i	−0.491529	+	0.283785i
$507$	−14.5813	+	14.8739i	−0.647578	+	0.660574i
$508$	−1.54601	−	0.892591i	−0.0685933	−	0.0396023i
$509$	7.71953	+	13.3706i	0.342162	+	0.592642i	0.984834	−	0.173499i	$-0.0555075\pi$
$509$	7.71953	+	13.3706i	0.342162	+	0.592642i	−0.642672	+	0.766142i	$0.722174\pi$
$510$		0			0
$511$	11.0522	−	14.7959i	0.488920	−	0.654534i
$512$	1.00000			0.0441942
$513$	−13.6167	−	3.21695i	−0.601193	−	0.142032i
$514$	−10.1694	−	5.87132i	−0.448554	−	0.258973i
$515$		0			0
$516$	−15.7688	+	4.39358i	−0.694181	+	0.193417i
$517$	−15.7605			−0.693146
$518$	0.111103	+	0.0829910i	0.00488158	+	0.00364641i
$519$	8.95303	−	34.7921i	0.392994	−	1.52720i
$520$		0			0
$521$	21.0358	−	36.4350i	0.921594	−	1.59625i	0.124646	−	0.992201i	$-0.460221\pi$
$521$	21.0358	−	36.4350i	0.921594	−	1.59625i	0.796949	−	0.604047i	$-0.206446\pi$
$522$	9.59792	+	15.8866i	0.420090	+	0.695337i
$523$	8.91333	+	15.4383i	0.389753	+	0.675071i	0.992416	−	0.122924i	$-0.0392272\pi$
$523$	8.91333	+	15.4383i	0.389753	+	0.675071i	−0.602663	+	0.797996i	$0.705894\pi$
$524$	3.10264			0.135540
$525$		0			0
$526$	22.9128			0.999046
$527$	8.97396	+	15.5434i	0.390912	+	0.677080i
$528$	−6.35188	−	6.22691i	−0.276430	−	0.270992i
$529$	8.40979	−	14.5662i	0.365643	−	0.633312i
$530$		0			0
$531$	−34.8430	−	19.2039i	−1.51206	−	0.833379i
$532$	0.838440	−	7.07464i	0.0363510	−	0.306725i
$533$	32.7907			1.42032
$534$	−2.48301	−	8.91165i	−0.107450	−	0.385645i
$535$		0			0
$536$	−0.776110	−	0.448087i	−0.0335228	−	0.0193544i
$537$	−40.9088	+	11.3982i	−1.76534	+	0.491870i
$538$	8.12400			0.350251
$539$	−26.0686	−	24.7534i	−1.12286	−	1.06621i
$540$		0			0
$541$	17.7195	+	30.6912i	0.761823	+	1.31952i	0.941910	+	0.335865i	$0.109029\pi$
$541$	17.7195	+	30.6912i	0.761823	+	1.31952i	−0.180087	+	0.983651i	$0.557638\pi$
$542$	9.47446	+	5.47008i	0.406963	+	0.234960i
$543$	23.0713	+	22.6174i	0.990085	+	0.970606i
$544$	3.25579	−	1.87973i	0.139591	−	0.0805929i
$545$		0			0
$546$	21.3747	+	8.28623i	0.914752	+	0.354618i
$547$		−	33.9313i		−	1.45080i	−0.688329	−	0.725399i	$-0.741655\pi$
$547$		−	33.9313i		−	1.45080i	0.688329	−	0.725399i	$-0.258345\pi$
$548$	−4.87855	−	8.44989i	−0.208401	−	0.360962i
$549$	−6.43671	−	10.6541i	−0.274712	−	0.454706i
$550$		0			0
$551$	8.32971	+	14.4275i	0.354857	+	0.614631i
$552$	−4.17010	−	1.07309i	−0.177491	−	0.0456738i
$553$	−17.4849	−	40.7144i	−0.743532	−	1.73135i
$554$		−	4.78288i		−	0.203205i
$555$		0			0
$556$	−3.69142	−	2.13124i	−0.156551	−	0.0903847i
$557$	3.39140	−	5.87408i	0.143698	−	0.248893i	−0.785188	−	0.619257i	$-0.787434\pi$
$557$	3.39140	−	5.87408i	0.143698	−	0.248893i	0.928887	+	0.370364i	$0.120767\pi$
$558$	14.3194	−	0.284544i	0.606187	−	0.0120457i
$559$		−	47.2786i		−	1.99967i
$560$		0			0
$561$	−32.3853	−	8.33370i	−1.36731	−	0.351849i
$562$	18.2766	−	10.5520i	0.770951	−	0.445109i
$563$	16.8803	+	9.74586i	0.711421	+	0.410739i	0.811587	−	0.584232i	$-0.198604\pi$
$563$	16.8803	+	9.74586i	0.711421	+	0.410739i	−0.100166	+	0.994971i	$0.531937\pi$
$564$	−3.79579	−	3.72111i	−0.159832	−	0.156687i
$565$		0			0
$566$	22.0051			0.924944
$567$	−23.7389	−	1.86080i	−0.996942	−	0.0781462i
$568$			13.4240i			0.563258i
$569$	−24.4915	+	14.1402i	−1.02674	+	0.592788i	−0.916049	−	0.401067i	$-0.868639\pi$
$569$	−24.4915	+	14.1402i	−1.02674	+	0.592788i	−0.110690	+	0.993855i	$0.535306\pi$
$570$		0			0
$571$	9.87150	−	17.0979i	0.413110	−	0.715527i	−0.582118	−	0.813104i	$-0.697776\pi$
$571$	9.87150	−	17.0979i	0.413110	−	0.715527i	0.995228	+	0.0975773i	$0.0311093\pi$
$572$	22.2489	−	12.8454i	0.930272	−	0.537093i
$573$	3.13993	−	12.2020i	0.131173	−	0.509746i
$574$	−6.84333	−	15.9350i	−0.285635	−	0.665115i
$575$		0			0
$576$	−0.0596020	−	2.99941i	−0.00248342	−	0.124975i
$577$	−10.0431	+	17.3952i	−0.418101	+	0.724172i	−0.995748	−	0.0921142i	$-0.970638\pi$
$577$	−10.0431	+	17.3952i	−0.418101	+	0.724172i	0.577647	+	0.816286i	$0.303971\pi$
$578$	−1.43321	+	2.48239i	−0.0596137	+	0.103254i
$579$	−18.4605	+	5.14357i	−0.767193	+	0.213760i
$580$		0			0
$581$	0.428843	−	3.61852i	0.0177914	−	0.150122i
$582$	1.06282	+	0.273494i	0.0440551	+	0.0113367i
$583$	−4.94579	+	2.85545i	−0.204833	+	0.118261i
$584$	3.49014	−	6.04511i	0.144423	−	0.250148i
$585$		0			0
$586$	9.77786	−	5.64525i	0.403920	−	0.233203i
$587$			31.1052i			1.28385i	0.766767	+	0.641925i	$0.221864\pi$
$587$			31.1052i			1.28385i	−0.766767	+	0.641925i	$0.778136\pi$
$588$	−0.434047	−	12.1166i	−0.0178998	−	0.499679i
$589$	12.8550			0.529681
$590$		0			0
$591$	10.7514	−	10.9672i	0.442254	−	0.451129i
$592$	0.0453927	+	0.0262075i	0.00186563	+	0.00107712i
$593$	−7.73070	+	4.46332i	−0.317462	+	0.183287i	−0.650261	−	0.759711i	$-0.725340\pi$
$593$	−7.73070	+	4.46332i	−0.317462	+	0.183287i	0.332799	+	0.942998i	$0.392007\pi$
$594$	−18.2985	+	19.4230i	−0.750795	+	0.796936i
$595$		0			0
$596$		−	8.97218i		−	0.367515i
$597$	31.0013	−	8.63774i	1.26880	−	0.353519i
$598$	6.21830	−	10.7704i	0.254285	−	0.440435i
$599$	4.30419	+	2.48502i	0.175864	+	0.101535i	0.585348	−	0.810782i	$-0.300958\pi$
$599$	4.30419	+	2.48502i	0.175864	+	0.101535i	−0.409484	+	0.912317i	$0.634291\pi$
$600$		0			0
$601$			25.0660i			1.02246i	0.859442	+	0.511232i	$0.170811\pi$
$601$			25.0660i			1.02246i	−0.859442	+	0.511232i	$0.829189\pi$
$602$	−22.9756	+	9.86692i	−0.936415	+	0.402146i
$603$	−1.29774	+	2.35458i	−0.0528480	+	0.0958858i
$604$	−6.61328	−	11.4545i	−0.269091	−	0.466079i
$605$		0			0
$606$	21.3750	−	21.8040i	0.868300	−	0.885725i
$607$	11.5970	+	20.0866i	0.470709	+	0.815291i	0.999439	−	0.0334986i	$-0.0106649\pi$
$607$	11.5970	+	20.0866i	0.470709	+	0.815291i	−0.528730	+	0.848790i	$0.677332\pi$
$608$		−	2.69268i		−	0.109202i
$609$	17.7695	+	22.0926i	0.720058	+	0.895239i
$610$		0			0
$611$	13.2956	−	7.67622i	0.537883	−	0.310547i
$612$	−5.83214	−	9.65341i	−0.235750	−	0.390216i
$613$	−3.72873	−	2.15278i	−0.150602	−	0.0869500i	0.422805	−	0.906221i	$-0.361045\pi$
$613$	−3.72873	−	2.15278i	−0.150602	−	0.0869500i	−0.573407	+	0.819270i	$0.694379\pi$
$614$	−1.06081	−	1.83737i	−0.0428108	−	0.0741504i
$615$		0			0
$616$	−10.8856	−	8.13130i	−0.438595	−	0.327619i
$617$	36.2107			1.45779			0.728895	−	0.684626i	$-0.240034\pi$
$617$	36.2107			1.45779			0.728895	+	0.684626i	$0.240034\pi$
$618$	6.84147	+	24.5544i	0.275204	+	0.987722i
$619$	−17.5269	−	10.1191i	−0.704464	−	0.406723i	0.104544	−	0.994520i	$-0.466662\pi$
$619$	−17.5269	−	10.1191i	−0.704464	−	0.406723i	−0.809008	+	0.587798i	$0.799995\pi$
$620$		0			0
$621$	−2.97009	+	12.5718i	−0.119186	+	0.504489i
$622$	−11.0046			−0.441244
$623$	−5.57625	−	12.9846i	−0.223408	−	0.520215i
$624$	8.39132	+	2.15933i	0.335922	+	0.0864425i
$625$		0			0
$626$	−3.71718	+	6.43835i	−0.148569	+	0.257328i
$627$	−16.7671	+	17.1036i	−0.669612	+	0.683050i
$628$	4.28200	+	7.41664i	0.170870	+	0.295956i
$629$	0.197052			0.00785699
$630$		0			0
$631$	−16.1847			−0.644304			−0.322152	−	0.946688i	$-0.604406\pi$
$631$	−16.1847			−0.644304			−0.322152	+	0.946688i	$0.604406\pi$
$632$	−8.37381	−	14.5039i	−0.333092	−	0.576933i
$633$	8.93479	−	9.11410i	0.355126	−	0.362253i
$634$	2.23730	−	3.87512i	0.0888545	−	0.153901i
$635$		0			0
$636$	−1.86534	−	0.480006i	−0.0739654	−	0.0190335i
$637$	34.0479	+	8.18523i	1.34903	+	0.324311i
$638$	31.7732			1.25791
$639$	40.2640	−	0.800096i	1.59282	−	0.0316513i
$640$		0			0
$641$	−5.57645	−	3.21957i	−0.220257	−	0.127165i	0.385812	−	0.922577i	$-0.373921\pi$
$641$	−5.57645	−	3.21957i	−0.220257	−	0.127165i	−0.606069	+	0.795412i	$0.707255\pi$
$642$	−2.18962	−	7.85865i	−0.0864174	−	0.310156i
$643$	−35.5764			−1.40299			−0.701497	−	0.712672i	$-0.747485\pi$
$643$	−35.5764			−1.40299			−0.701497	+	0.712672i	$0.747485\pi$
$644$	−6.53175	−	0.774100i	−0.257387	−	0.0305038i
$645$		0			0
$646$	−5.06151	−	8.76679i	−0.199142	−	0.344925i
$647$	11.8748	+	6.85590i	0.466845	+	0.269533i	0.714918	−	0.699208i	$-0.246464\pi$
$647$	11.8748	+	6.85590i	0.466845	+	0.269533i	−0.248073	+	0.968741i	$0.579797\pi$
$648$	−8.99290	+	0.357541i	−0.353274	+	0.0140455i
$649$	−58.9808	+	34.0526i	−2.31520	+	1.33668i
$650$		0			0
$651$	21.6194	−	3.35087i	0.847330	−	0.131331i
$652$			11.0746i			0.433713i
$653$	−0.930370	−	1.61145i	−0.0364082	−	0.0630608i	0.847247	−	0.531199i	$-0.178258\pi$
$653$	−0.930370	−	1.61145i	−0.0364082	−	0.0630608i	−0.883655	+	0.468138i	$0.844925\pi$
$654$	10.4563	−	10.6661i	0.408873	−	0.417079i
$655$		0			0
$656$	−3.27739	−	5.67661i	−0.127961	−	0.221634i
$657$	−18.3398	−	10.1081i	−0.715502	−	0.394353i
$658$	−6.50511	−	4.85915i	−0.253595	−	0.189429i
$659$		−	13.8786i		−	0.540633i	−0.962771	−	0.270317i	$-0.912872\pi$
$659$		−	13.8786i		−	0.540633i	0.962771	−	0.270317i	$-0.0871284\pi$
$660$		0			0
$661$	19.0521	+	10.9997i	0.741041	+	0.427840i	0.822448	−	0.568841i	$-0.192608\pi$
$661$	19.0521	+	10.9997i	0.741041	+	0.427840i	−0.0814067	+	0.996681i	$0.525941\pi$
$662$	−8.48598	+	14.6981i	−0.329817	+	0.571260i
$663$	31.3794	−	8.74309i	1.21867	−	0.339553i
$664$		−	1.37724i		−	0.0534474i
$665$		0			0
$666$	0.0759015	−	0.137713i	0.00294112	−	0.00533628i
$667$	13.3203	−	7.69051i	0.515766	−	0.297778i
$668$	2.56169	+	1.47899i	0.0991148	+	0.0572240i
$669$	−7.02620	+	7.16720i	−0.271648	+	0.277100i
$670$		0			0
$671$	−21.3082			−0.822595
$672$	−0.701891	−	4.52850i	−0.0270760	−	0.174691i
$673$			13.4735i			0.519366i	0.965694	+	0.259683i	$0.0836181\pi$
$673$			13.4735i			0.519366i	−0.965694	+	0.259683i	$0.916382\pi$
$674$	−26.5909	+	15.3523i	−1.02424	+	0.591347i
$675$		0			0
$676$	−6.01282	+	10.4145i	−0.231262	+	0.400558i
$677$	−1.10725	+	0.639271i	−0.0425551	+	0.0245692i	−0.521127	−	0.853479i	$-0.674488\pi$
$677$	−1.10725	+	0.639271i	−0.0425551	+	0.0245692i	0.478572	+	0.878049i	$0.341155\pi$
$678$	25.7999	+	6.63908i	0.990839	+	0.254972i
$679$	1.66472	+	0.197292i	0.0638860	+	0.00757136i
$680$		0			0
$681$	17.8163	−	4.96407i	0.682721	−	0.190224i
$682$	12.2587	−	21.2326i	0.469409	−	0.813039i
$683$	20.0122	−	34.6622i	0.765747	−	1.32631i	−0.174104	−	0.984727i	$-0.555703\pi$
$683$	20.0122	−	34.6622i	0.765747	−	1.32631i	0.939851	−	0.341585i	$-0.110964\pi$
$684$	−8.07643	+	0.160489i	−0.308810	+	0.00613644i
$685$		0			0
$686$	−3.12799	−	18.2542i	−0.119427	−	0.696948i
$687$	−3.72234	+	14.4653i	−0.142016	+	0.551885i
$688$	−8.18470	+	4.72544i	−0.312039	+	0.180156i
$689$	2.78152	−	4.81774i	0.105968	−	0.183541i
$690$		0			0
$691$	21.6787	−	12.5162i	0.824696	−	0.476138i	−0.0273375	−	0.999626i	$-0.508703\pi$
$691$	21.6787	−	12.5162i	0.824696	−	0.476138i	0.852033	+	0.523488i	$0.175370\pi$
$692$		−	20.7416i		−	0.788478i
$693$	−23.7403	+	33.1351i	−0.901819	+	1.25870i
$694$	33.2005			1.26027
$695$		0			0
$696$	7.65232	+	7.50177i	0.290060	+	0.284354i
$697$	−21.3410	−	12.3212i	−0.808348	−	0.466700i
$698$	−18.6598	+	10.7732i	−0.706283	+	0.407773i
$699$	26.9482	+	6.93458i	1.01928	+	0.262290i
$700$		0			0
$701$		−	7.09535i		−	0.267988i	−0.990982	−	0.133994i	$-0.957220\pi$
$701$		−	7.09535i		−	0.267988i	0.990982	−	0.133994i	$-0.0427802\pi$
$702$	5.97658	−	25.2977i	0.225572	−	0.954800i
$703$	0.0705683	−	0.122228i	0.00266153	−	0.00460991i
$704$	−4.44749	−	2.56776i	−0.167621	−	0.0967762i
$705$		0			0
$706$			5.51692i			0.207632i
$707$	27.9121	−	37.3669i	1.04974	−	1.40533i
$708$	−22.2450	−	5.72430i	−0.836019	−	0.215132i
$709$	13.9611	+	24.1814i	0.524320	+	0.908150i	0.999599	+	0.0283143i	$0.00901394\pi$
$709$	13.9611	+	24.1814i	0.524320	+	0.908150i	−0.475279	+	0.879835i	$0.657653\pi$
$710$		0			0
$711$	−43.0039	+	25.9809i	−1.61277	+	0.974361i
$712$	−2.67056	−	4.62555i	−0.100084	−	0.173350i
$713$		−	11.8685i		−	0.444481i
$714$	−10.7976	−	13.4245i	−0.404090	−	0.502399i
$715$		0			0
$716$	−21.2335	+	12.2592i	−0.793534	+	0.458147i
$717$	−13.6140	−	13.3461i	−0.508423	−	0.498420i
$718$	16.7632	+	9.67826i	0.625599	+	0.361190i
$719$	12.0025	+	20.7889i	0.447618	+	0.775296i	0.998230	−	0.0594644i	$-0.0189393\pi$
$719$	12.0025	+	20.7889i	0.447618	+	0.775296i	−0.550613	+	0.834761i	$0.685606\pi$
$720$		0			0
$721$	15.3643	+	35.7765i	0.572196	+	1.33239i
$722$	11.7495			0.437271
$723$	−16.1988	+	4.51339i	−0.602438	+	0.167855i
$724$	16.1542	+	9.32664i	0.600366	+	0.346622i
$725$		0			0
$726$	7.14698	+	25.6508i	0.265249	+	0.951991i
$727$	12.3007			0.456206			0.228103	−	0.973637i	$-0.426748\pi$
$727$	12.3007			0.456206			0.228103	+	0.973637i	$0.426748\pi$
$728$	13.1436	+	1.55769i	0.487133	+	0.0577318i
$729$	1.60841	+	26.9521i	0.0595706	+	0.998224i
$730$		0			0
$731$	−17.7651	+	30.7701i	−0.657067	+	1.13807i
$732$	−5.13192	−	5.03096i	−0.189681	−	0.185949i
$733$	−10.7803	−	18.6720i	−0.398178	−	0.689665i	0.595323	−	0.803486i	$-0.297024\pi$
$733$	−10.7803	−	18.6720i	−0.398178	−	0.689665i	−0.993501	+	0.113822i	$0.963691\pi$
$734$	14.0326			0.517951
$735$		0			0
$736$	−2.48605			−0.0916369
$737$	2.30116	+	3.98573i	0.0847644	+	0.146816i
$738$	−16.8311	+	10.1686i	−0.619562	+	0.374310i
$739$	0.411063	−	0.711982i	0.0151212	−	0.0261907i	−0.858366	−	0.513038i	$-0.828520\pi$
$739$	0.411063	−	0.711982i	0.0151212	−	0.0261907i	0.873487	+	0.486847i	$0.161853\pi$
$740$		0			0
$741$	5.81439	−	22.5951i	0.213597	−	0.830052i
$742$	−2.92173	−	0.346264i	−0.107260	−	0.0127118i
$743$	10.6722			0.391526			0.195763	−	0.980651i	$-0.437282\pi$
$743$	10.6722			0.391526			0.195763	+	0.980651i	$0.437282\pi$
$744$	7.96551	−	2.21939i	0.292030	−	0.0813670i
$745$		0			0
$746$	1.15907	+	0.669190i	0.0424366	+	0.0245008i
$747$	−4.13092	+	0.0820865i	−0.151142	+	0.00300339i
$748$	−19.3068			−0.705927
$749$	−4.91736	−	11.4503i	−0.179676	−	0.418385i
$750$		0			0
$751$	13.4066	+	23.2209i	0.489213	+	0.847342i	0.999923	−	0.0124115i	$-0.00395079\pi$
$751$	13.4066	+	23.2209i	0.489213	+	0.847342i	−0.510710	+	0.859753i	$0.670617\pi$
$752$	−2.65776	−	1.53446i	−0.0969185	−	0.0559559i
$753$	5.56644	−	5.67816i	0.202853	−	0.206923i
$754$	−26.8040	+	15.4753i	−0.976142	+	0.563576i
$755$		0			0
$756$	−13.5410	+	2.37517i	−0.492481	+	0.0863839i
$757$			14.2502i			0.517934i	0.965886	+	0.258967i	$0.0833821\pi$
$757$			14.2502i			0.517934i	−0.965886	+	0.258967i	$0.916618\pi$
$758$	4.03982	+	6.99717i	0.146733	+	0.254149i
$759$	15.7911	+	15.4804i	0.573180	+	0.561903i
$760$		0			0
$761$	13.6118	+	23.5763i	0.493428	+	0.854642i	0.999971	−	0.00757262i	$-0.00241046\pi$
$761$	13.6118	+	23.5763i	0.493428	+	0.854642i	−0.506544	+	0.862214i	$0.669077\pi$
$762$	−0.770566	+	2.99447i	−0.0279147	+	0.108478i
$763$	13.6542	−	18.2793i	0.494314	−	0.661754i
$764$		−	7.27434i		−	0.263176i
$765$		0			0
$766$	−20.1734	−	11.6471i	−0.728896	−	0.420828i
$767$	33.1709	−	57.4538i	1.19773	−	2.07453i
$768$	−0.464886	−	1.66850i	−0.0167751	−	0.0602067i
$769$			6.31431i			0.227700i	0.993498	+	0.113850i	$0.0363183\pi$
$769$			6.31431i			0.227700i	−0.993498	+	0.113850i	$0.963682\pi$
$770$		0			0
$771$	−5.06866	+	19.6972i	−0.182543	+	0.709376i
$772$	−9.58185	+	5.53208i	−0.344858	+	0.199104i
$773$	36.7341	+	21.2084i	1.32123	+	0.762814i	0.983925	−	0.178580i	$-0.0571505\pi$
$773$	36.7341	+	21.2084i	1.32123	+	0.762814i	0.337308	+	0.941395i	$0.390484\pi$
$774$	14.6613	+	24.2676i	0.526991	+	0.872282i
$775$		0			0
$776$	0.633608			0.0227452
$777$	0.0868200	−	0.223956i	0.00311465	−	0.00803437i
$778$			11.7488i			0.421216i
$779$	−15.2853	+	8.82495i	−0.547652	+	0.316187i
$780$		0			0
$781$	34.4696	−	59.7031i	1.23342	−	2.13634i
$782$	−8.09405	+	4.67310i	−0.289443	+	0.167110i
$783$	22.0448	−	23.3995i	0.787816	−	0.836232i
$784$	−1.98605	−	6.71235i	−0.0709302	−	0.239727i
$785$		0			0
$786$	−1.44237	−	5.17675i	−0.0514478	−	0.184648i
$787$	−19.9571	+	34.5667i	−0.711393	+	1.23217i	0.252941	+	0.967482i	$0.418602\pi$
$787$	−19.9571	+	34.5667i	−0.711393	+	1.23217i	−0.964334	+	0.264687i	$0.914731\pi$
$788$	4.43350	−	7.67905i	0.157937	−	0.273555i
$789$	−10.6518	−	38.2300i	−0.379216	−	1.36102i
$790$		0			0
$791$	40.4111	+	4.78926i	1.43685	+	0.170287i
$792$	−7.43669	+	13.4929i	−0.264251	+	0.479449i
$793$	17.9757	−	10.3783i	0.638336	−	0.368543i
$794$	−8.61072	+	14.9142i	−0.305583	+	0.529285i
$795$		0			0
$796$	16.0911	−	9.29018i	0.570332	−	0.329282i
$797$			17.5658i			0.622211i	0.950375	+	0.311105i	$0.100699\pi$
$797$			17.5658i			0.622211i	−0.950375	+	0.311105i	$0.899301\pi$
$798$	−12.1938	+	1.88997i	−0.431656	+	0.0669041i
$799$	−11.5375			−0.408167
$800$		0			0
$801$	−13.7147	+	8.28580i	−0.484587	+	0.292764i
$802$	7.31712	+	4.22454i	0.258377	+	0.149174i
$803$	−31.0448	+	17.9237i	−1.09555	+	0.632514i
$804$	−0.386830	+	1.50325i	−0.0136424	+	0.0530154i
$805$		0			0
$806$			23.8826i			0.841227i
$807$	−3.77673	−	13.5549i	−0.132947	−	0.477154i
$808$	8.81430	−	15.2668i	0.310086	−	0.537085i
$809$	−16.6120	−	9.59095i	−0.584047	−	0.337200i	0.178693	−	0.983905i	$-0.442813\pi$
$809$	−16.6120	−	9.59095i	−0.584047	−	0.337200i	−0.762740	+	0.646705i	$0.776146\pi$
$810$		0			0
$811$		−	45.4972i		−	1.59762i	−0.601582	−	0.798811i	$-0.705463\pi$
$811$		−	45.4972i		−	1.59762i	0.601582	−	0.798811i	$-0.294537\pi$
$812$	13.1143	+	9.79604i	0.460222	+	0.343774i
$813$	4.72227	−	18.3511i	0.165617	−	0.643600i
$814$	−0.134589	−	0.233115i	−0.00471735	−	0.00817069i
$815$		0			0
$816$	−4.64990	−	4.55842i	−0.162779	−	0.159577i
$817$	12.7241	+	22.0388i	0.445159	+	0.771038i
$818$		−	29.1034i		−	1.01758i
$819$	3.88876	−	39.5157i	0.135884	−	1.38079i
$820$		0			0
$821$	−2.21615	+	1.27949i	−0.0773441	+	0.0446546i	−0.538173	−	0.842834i	$-0.680885\pi$
$821$	−2.21615	+	1.27949i	−0.0773441	+	0.0446546i	0.460829	+	0.887489i	$0.347552\pi$
$822$	−11.8307	+	12.0681i	−0.412641	+	0.420923i
$823$	30.7738	+	17.7673i	1.07271	+	0.619328i	0.928920	−	0.370281i	$-0.120739\pi$
$823$	30.7738	+	17.7673i	1.07271	+	0.619328i	0.143787	+	0.989609i	$0.454072\pi$
$824$	7.35823	+	12.7448i	0.256336	+	0.443987i
$825$		0			0
$826$	−34.8430	−	4.12936i	−1.21234	−	0.143679i
$827$	1.85721			0.0645814			0.0322907	−	0.999479i	$-0.489720\pi$
$827$	1.85721			0.0645814			0.0322907	+	0.999479i	$0.489720\pi$
$828$	0.148173	+	7.45667i	0.00514938	+	0.259137i
$829$	46.4027	+	26.7906i	1.61163	+	0.930477i	0.988992	+	0.147970i	$0.0472738\pi$
$829$	46.4027	+	26.7906i	1.61163	+	0.930477i	0.622641	+	0.782507i	$0.286060\pi$
$830$		0			0
$831$	−7.98021	+	2.22349i	−0.276831	+	0.0771320i
$832$	5.00256			0.173433
$833$	−19.0836	−	18.1208i	−0.661207	−	0.627848i
$834$	−1.83988	+	7.14990i	−0.0637098	+	0.247581i
$835$		0			0
$836$	−6.91415	+	11.9757i	−0.239131	+	0.414187i
$837$	−7.13163	−	23.7595i	−0.246505	−	0.821250i
$838$	1.03974	+	1.80088i	0.0359171	+	0.0622102i
$839$	−6.41502			−0.221471			−0.110736	−	0.993850i	$-0.535321\pi$
$839$	−6.41502			−0.221471			−0.110736	+	0.993850i	$0.535321\pi$
$840$		0			0
$841$	−9.27817			−0.319937
$842$	16.4185	+	28.4377i	0.565820	+	0.980029i
$843$	−26.1025	−	25.5889i	−0.899017	−	0.881330i
$844$	3.68439	−	6.38156i	0.126822	−	0.219662i
$845$		0			0
$846$	−4.44406	+	8.06316i	−0.152790	+	0.277217i
$847$	16.0504	+	37.3741i	0.551497	+	1.28419i
$848$	−1.11204			−0.0381876
$849$	−10.2299	−	36.7155i	−0.351088	−	1.26007i
$850$		0			0
$851$	−0.112848	−	0.0651531i	−0.00386839	−	0.00223342i
$852$	22.3979	−	6.24062i	0.767338	−	0.213800i
$853$	40.7419			1.39498			0.697488	−	0.716596i	$-0.254301\pi$
$853$	40.7419			1.39498			0.697488	+	0.716596i	$0.254301\pi$
$854$	−8.79492	−	6.56958i	−0.300956	−	0.224806i
$855$		0			0
$856$	−2.35501	−	4.07900i	−0.0804926	−	0.139417i
$857$	6.99524	+	4.03870i	0.238953	+	0.137959i	0.614695	−	0.788765i	$-0.289279\pi$
$857$	6.99524	+	4.03870i	0.238953	+	0.137959i	−0.375743	+	0.926724i	$0.622612\pi$
$858$	−31.7757	−	31.1505i	−1.08480	−	1.06346i
$859$	11.3048	−	6.52683i	0.385715	−	0.222693i	−0.294587	−	0.955625i	$-0.595182\pi$
$859$	11.3048	−	6.52683i	0.385715	−	0.222693i	0.680302	+	0.732932i	$0.261849\pi$
$860$		0			0
$861$	−23.4062	+	18.8260i	−0.797680	+	0.641590i
$862$		−	8.75212i		−	0.298098i
$863$	−27.0946	−	46.9292i	−0.922310	−	1.59749i	−0.795831	−	0.605518i	$-0.792966\pi$
$863$	−27.0946	−	46.9292i	−0.922310	−	1.59749i	−0.126479	−	0.991969i	$-0.540368\pi$
$864$	−4.97679	+	1.49383i	−0.169314	+	0.0508211i
$865$		0			0
$866$	−6.17199	−	10.6902i	−0.209733	−	0.363268i
$867$	4.80815	+	1.23728i	0.163293	+	0.0420202i
$868$	11.6060	−	4.98422i	0.393934	−	0.169176i
$869$			86.0078i			2.91762i
$870$		0			0
$871$	−3.88254	−	2.24158i	−0.131555	−	0.0759532i
$872$	4.31181	−	7.46828i	0.146016	−	0.252908i
$873$	−0.0377643	−	1.90045i	−0.00127813	−	0.0643204i
$874$			6.69412i			0.226432i
$875$		0			0
$876$	−11.7088	−	3.01301i	−0.395602	−	0.101800i
$877$	16.2332	−	9.37226i	0.548157	−	0.316479i	−0.200221	−	0.979751i	$-0.564166\pi$
$877$	16.2332	−	9.37226i	0.548157	−	0.316479i	0.748378	+	0.663272i	$0.230833\pi$
$878$	−9.72433	−	5.61435i	−0.328180	−	0.189475i
$879$	−13.9647	−	13.6899i	−0.471017	−	0.461750i
$880$		0			0
$881$	36.3542			1.22480			0.612402	−	0.790546i	$-0.290203\pi$
$881$	36.3542			1.22480			0.612402	+	0.790546i	$0.290203\pi$
$882$	−20.0147	+	6.35703i	−0.673930	+	0.214052i
$883$		−	22.9059i		−	0.770845i	−0.922740	−	0.385422i	$-0.874056\pi$
$883$		−	22.9059i		−	0.770845i	0.922740	−	0.385422i	$-0.125944\pi$
$884$	16.2873	−	9.40348i	0.547801	−	0.316273i
$885$		0			0
$886$	16.7161	−	28.9532i	0.561590	−	0.972702i
$887$	−44.9860	+	25.9727i	−1.51048	+	0.872077i	−0.510557	+	0.859844i	$0.670561\pi$
$887$	−44.9860	+	25.9727i	−1.51048	+	0.872077i	−0.999925	+	0.0122334i	$0.996106\pi$
$888$	0.0226247	−	0.0879211i	0.000759235	−	0.00295044i
$889$	−0.555867	+	4.69033i	−0.0186432	+	0.157308i
$890$		0			0
$891$	40.9139	+	21.5015i	1.37067	+	0.720326i
$892$	−2.89736	+	5.01837i	−0.0970107	+	0.168028i
$893$	−4.13180	+	7.15648i	−0.138265	+	0.239483i
$894$	−14.9701	+	4.17104i	−0.500673	+	0.139500i
$895$		0			0
$896$	−1.04402	−	2.43105i	−0.0348783	−	0.0812158i
$897$	−20.8612	−	5.36821i	−0.696535	−	0.179239i
$898$	−24.1052	+	13.9171i	−0.804401	+	0.464421i
$899$	−14.7684	+	25.5796i	−0.492554	+	0.853129i
$900$		0			0
$901$	−3.62057	+	2.09033i	−0.120619	+	0.0696391i
$902$			33.6622i			1.12083i
$903$	27.1439	+	33.7477i	0.903294	+	1.12305i
$904$	15.3809			0.511560
$905$		0			0
$906$	−16.0374	+	16.3593i	−0.532808	+	0.543501i
$907$	−2.87864	−	1.66199i	−0.0955838	−	0.0551853i	0.451446	−	0.892298i	$-0.350908\pi$
$907$	−2.87864	−	1.66199i	−0.0955838	−	0.0551853i	−0.547030	+	0.837113i	$0.684242\pi$
$908$	9.24746	−	5.33902i	0.306888	−	0.177182i
$909$	−46.3168	−	25.5277i	−1.53623	−	0.846702i
$910$		0			0
$911$		−	0.497610i		−	0.0164866i	−0.999966	−	0.00824328i	$-0.997376\pi$
$911$		−	0.497610i		−	0.0164866i	0.999966	−	0.00824328i	$-0.00262395\pi$
$912$	−4.49272	+	1.25179i	−0.148769	+	0.0414508i
$913$	−3.53644	+	6.12529i	−0.117039	+	0.202717i
$914$	24.5277	+	14.1611i	0.811304	+	0.468406i
$915$		0			0
$916$			8.62361i			0.284932i
$917$	−3.23922	−	7.54269i	−0.106969	−	0.249081i
$918$	−13.3954	+	14.2186i	−0.442114	+	0.469285i
$919$	24.7546	+	42.8762i	0.816579	+	1.41436i	0.908189	+	0.418561i	$0.137465\pi$
$919$	24.7546	+	42.8762i	0.816579	+	1.41436i	−0.0916101	+	0.995795i	$0.529201\pi$
$920$		0			0
$921$	−2.57250	+	2.62413i	−0.0847667	+	0.0864679i
$922$	17.7879	+	30.8096i	0.585814	+	1.01466i
$923$			67.1543i			2.21041i
$924$	−8.50647	+	21.9428i	−0.279842	+	0.721865i
$925$		0			0
$926$	16.3134	−	9.41855i	0.536092	−	0.309513i
$927$	37.7884	−	22.8300i	1.24113	−	0.749834i
$928$	5.35804	+	3.09347i	0.175886	+	0.101548i
$929$	26.4197	+	45.7602i	0.866802	+	1.50134i	0.865247	+	0.501346i	$0.167162\pi$
$929$	26.4197	+	45.7602i	0.866802	+	1.50134i	0.00155503	+	0.999999i	$0.499505\pi$
$930$		0			0
$931$	−18.0742	+	5.34778i	−0.592357	+	0.175266i
$932$	16.0654			0.526241
$933$	5.11587	+	18.3611i	0.167486	+	0.601116i
$934$	−10.8853	−	6.28462i	−0.356177	−	0.205639i
$935$		0			0
$936$	−0.298163	−	15.0047i	−0.00974575	−	0.490445i
$937$	55.7017			1.81970			0.909848	−	0.414941i	$-0.136198\pi$
$937$	55.7017			1.81970			0.909848	+	0.414941i	$0.136198\pi$
$938$	−0.279049	+	2.35458i	−0.00911127	+	0.0768796i
$939$	12.4704	+	3.20901i	0.406957	+	0.104722i
$940$		0			0
$941$	−0.110773	+	0.191865i	−0.00361110	+	0.00625461i	−0.867825	−	0.496869i	$-0.834483\pi$
$941$	−0.110773	+	0.191865i	−0.00361110	+	0.00625461i	0.864214	+	0.503124i	$0.167816\pi$
$942$	10.3840	−	10.5924i	0.338329	−	0.345119i
$943$	8.14775	+	14.1123i	0.265327	+	0.459560i
$944$	−13.2616			−0.431628
$945$		0			0
$946$	48.5352			1.57802
$947$	8.67143	+	15.0194i	0.281784	+	0.488064i	0.971824	−	0.235707i	$-0.0757406\pi$
$947$	8.67143	+	15.0194i	0.281784	+	0.488064i	−0.690041	+	0.723771i	$0.742407\pi$
$948$	−20.3068	+	20.7143i	−0.659534	+	0.672770i
$949$	17.4597	−	30.2410i	0.566765	−	0.981665i
$950$		0			0
$951$	−7.50571	−	1.93144i	−0.243389	−	0.0626312i
$952$	−7.96885	−	5.95252i	−0.258272	−	0.192922i
$953$	−47.2619			−1.53096			−0.765482	−	0.643458i	$-0.777499\pi$
$953$	−47.2619			−1.53096			−0.765482	+	0.643458i	$0.777499\pi$
$954$	0.0662797	+	3.33546i	0.00214588	+	0.107989i
$955$		0			0
$956$	−9.53230	−	5.50348i	−0.308297	−	0.177995i
$957$	−14.7709	−	53.0134i	−0.477475	−	1.71368i
$958$	−21.4076			−0.691648
$959$	−15.4488	+	20.6819i	−0.498869	+	0.667853i
$960$		0			0
$961$	−4.10415	−	7.10860i	−0.132392	−	0.229310i
$962$	0.227080	+	0.131105i	0.00732135	+	0.00422698i
$963$	−12.0942	+	7.30675i	−0.389730	+	0.235457i
$964$	−8.40789	+	4.85430i	−0.270800	+	0.156346i
$965$		0			0
$966$	1.74493	+	11.2581i	0.0561423	+	0.362223i
$967$		−	56.9397i		−	1.83106i	−0.402254	−	0.915528i	$-0.631773\pi$
$967$		−	56.9397i		−	1.83106i	0.402254	−	0.915528i	$-0.368227\pi$
$968$	7.68681	+	13.3139i	0.247063	+	0.427926i
$969$	−12.2743	+	12.5207i	−0.394309	+	0.402222i
$970$		0			0
$971$	−0.585122	−	1.01346i	−0.0187775	−	0.0325235i	0.856484	−	0.516174i	$-0.172644\pi$
$971$	−0.585122	−	1.01346i	−0.0187775	−	0.0325235i	−0.875261	+	0.483650i	$0.839311\pi$
$972$	4.77723	+	14.8384i	0.153230	+	0.475942i
$973$	−1.32724	+	11.1991i	−0.0425494	+	0.359026i
$974$		−	2.51593i		−	0.0806155i
$975$		0			0
$976$	−3.59330	−	2.07459i	−0.115019	−	0.0664060i
$977$	−16.2443	+	28.1359i	−0.519700	+	0.900146i	0.480038	+	0.877248i	$0.340623\pi$
$977$	−16.2443	+	28.1359i	−0.519700	+	0.900146i	−0.999738	+	0.0228986i	$0.992711\pi$
$978$	18.4779	−	5.14840i	0.590857	−	0.164628i
$979$			27.4295i			0.876650i
$980$		0			0
$981$	−22.6574	−	12.4878i	−0.723395	−	0.398703i
$982$	−30.0602	+	17.3553i	−0.959260	+	0.553829i
$983$	21.4685	+	12.3949i	0.684740	+	0.395335i	0.801638	−	0.597809i	$-0.203962\pi$
$983$	21.4685	+	12.3949i	0.684740	+	0.395335i	−0.116899	+	0.993144i	$0.537295\pi$
$984$	−7.94779	+	8.10729i	−0.253366	+	0.258451i
$985$		0			0
$986$	23.2596			0.740736
$987$	−5.08334	+	13.1127i	−0.161805	+	0.417382i
$988$		−	13.4703i		−	0.428547i
$989$	20.3476	−	11.7477i	0.647015	−	0.373554i
$990$		0			0
$991$	−17.7444	+	30.7343i	−0.563671	+	0.976307i	0.433501	+	0.901153i	$0.357278\pi$
$991$	−17.7444	+	30.7343i	−0.563671	+	0.976307i	−0.997172	+	0.0751537i	$0.976055\pi$
$992$	4.13446	−	2.38703i	0.131269	−	0.0757884i
$993$	28.4688	+	7.32587i	0.903431	+	0.232479i
$994$	32.6344	−	14.0149i	1.03510	−	0.444526i
$995$		0			0
$996$	−2.29793	+	0.640261i	−0.0728126	+	0.0202875i
$997$	−19.4263	+	33.6474i	−0.615238	+	1.06562i	0.375105	+	0.926982i	$0.377607\pi$
$997$	−19.4263	+	33.6474i	−0.615238	+	1.06562i	−0.990343	+	0.138641i	$0.955727\pi$
$998$	−3.07500	+	5.32606i	−0.0973375	+	0.168593i
$999$	−0.265060	−	0.0626204i	−0.00838612	−	0.00198122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.u.f.899.1		12
3.2	odd	2		1050.2.u.h.899.4		12
5.2	odd	4		210.2.r.a.101.6	✓	12
5.3	odd	4		1050.2.s.g.101.1		12
5.4	even	2		1050.2.u.g.899.6		12
7.5	odd	6		1050.2.u.e.299.3		12
15.2	even	4		210.2.r.b.101.3	yes	12
15.8	even	4		1050.2.s.f.101.4		12
15.14	odd	2		1050.2.u.e.899.3		12
21.5	even	6		1050.2.u.g.299.6		12
35.12	even	12		210.2.r.b.131.3	yes	12
35.17	even	12		1470.2.b.a.881.10		12
35.19	odd	6		1050.2.u.h.299.4		12
35.32	odd	12		1470.2.b.b.881.9		12
35.33	even	12		1050.2.s.f.551.4		12
105.17	odd	12		1470.2.b.b.881.3		12
105.32	even	12		1470.2.b.a.881.4		12
105.47	odd	12		210.2.r.a.131.6	yes	12
105.68	odd	12		1050.2.s.g.551.1		12
105.89	even	6	inner	1050.2.u.f.299.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.6	✓	12	5.2	odd	4
210.2.r.a.131.6	yes	12	105.47	odd	12
210.2.r.b.101.3	yes	12	15.2	even	4
210.2.r.b.131.3	yes	12	35.12	even	12
1050.2.s.f.101.4		12	15.8	even	4
1050.2.s.f.551.4		12	35.33	even	12
1050.2.s.g.101.1		12	5.3	odd	4
1050.2.s.g.551.1		12	105.68	odd	12
1050.2.u.e.299.3		12	7.5	odd	6
1050.2.u.e.899.3		12	15.14	odd	2
1050.2.u.f.299.1		12	105.89	even	6	inner
1050.2.u.f.899.1		12	1.1	even	1	trivial
1050.2.u.g.299.6		12	21.5	even	6
1050.2.u.g.899.6		12	5.4	even	2
1050.2.u.h.299.4		12	35.19	odd	6
1050.2.u.h.899.4		12	3.2	odd	2
1470.2.b.a.881.4		12	105.32	even	12
1470.2.b.a.881.10		12	35.17	even	12
1470.2.b.b.881.3		12	105.17	odd	12
1470.2.b.b.881.9		12	35.32	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.21252 + 1.23685i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.67740 + 0.431645i) q^{6} +(2.62736 + 0.311378i) q^{7} +1.00000 q^{8} +(-0.0596020 - 2.99941i) q^{9} +(-4.44749 - 2.56776i) q^{11} +(-0.464886 - 1.66850i) q^{12} +5.00256 q^{13} +(-1.04402 - 2.43105i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.25579 - 1.87973i) q^{17} +(-2.56776 + 1.55132i) q^{18} +(-2.33193 + 1.34634i) q^{19} +(-3.57085 + 2.87211i) q^{21} +5.13552i q^{22} +(1.24302 + 2.15298i) q^{23} +(-1.21252 + 1.23685i) q^{24} +(-2.50128 - 4.33235i) q^{26} +(3.78209 + 3.56312i) q^{27} +(-1.58334 + 2.11968i) q^{28} -6.18694i q^{29} +(-4.13446 - 2.38703i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(8.56861 - 2.38743i) q^{33} +3.75947i q^{34} +(2.62736 + 1.44809i) q^{36} +(-0.0453927 + 0.0262075i) q^{37} +(2.33193 + 1.34634i) q^{38} +(-6.06570 + 6.18743i) q^{39} +6.55478 q^{41} +(4.27275 + 1.65640i) q^{42} -9.45088i q^{43} +(4.44749 - 2.56776i) q^{44} +(1.24302 - 2.15298i) q^{46} +(2.65776 - 1.53446i) q^{47} +(1.67740 + 0.431645i) q^{48} +(6.80609 + 1.63621i) q^{49} +(6.27266 - 1.74772i) q^{51} +(-2.50128 + 4.33235i) q^{52} +(0.556019 - 0.963053i) q^{53} +(1.19470 - 5.05694i) q^{54} +(2.62736 + 0.311378i) q^{56} +(1.16228 - 4.51670i) q^{57} +(-5.35804 + 3.09347i) q^{58} +(6.63079 - 11.4849i) q^{59} +(3.59330 - 2.07459i) q^{61} +4.77406i q^{62} +(0.777354 - 7.89910i) q^{63} +1.00000 q^{64} +(-6.35188 - 6.22691i) q^{66} +(-0.776110 - 0.448087i) q^{67} +(3.25579 - 1.87973i) q^{68} +(-4.17010 - 1.07309i) q^{69} +13.4240i q^{71} +(-0.0596020 - 2.99941i) q^{72} +(3.49014 - 6.04511i) q^{73} +(0.0453927 + 0.0262075i) q^{74} -2.69268i q^{76} +(-10.8856 - 8.13130i) q^{77} +(8.39132 + 2.15933i) q^{78} +(-8.37381 - 14.5039i) q^{79} +(-8.99290 + 0.357541i) q^{81} +(-3.27739 - 5.67661i) q^{82} -1.37724i q^{83} +(-0.701891 - 4.52850i) q^{84} +(-8.18470 + 4.72544i) q^{86} +(7.65232 + 7.50177i) q^{87} +(-4.44749 - 2.56776i) q^{88} +(-2.67056 - 4.62555i) q^{89} +(13.1436 + 1.55769i) q^{91} -2.48605 q^{92} +(7.96551 - 2.21939i) q^{93} +(-2.65776 - 1.53446i) q^{94} +(-0.464886 - 1.66850i) q^{96} +0.633608 q^{97} +(-1.98605 - 6.71235i) q^{98} +(-7.43669 + 13.4929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 4 q^{3} - 6 q^{4} - 2 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} - 12 q^{11} - 2 q^{12} + 8 q^{13} - 12 q^{14} - 6 q^{16} + 12 q^{17} - 18 q^{21} + 2 q^{23} + 4 q^{24} - 4 q^{26} + 28 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 4 * q^3 - 6 * q^4 - 2 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 - 12 * q^11 - 2 * q^12 + 8 * q^13 - 12 * q^14 - 6 * q^16 + 12 * q^17 - 18 * q^21 + 2 * q^23 + 4 * q^24 - 4 * q^26 + 28 * q^27 + 6 * q^28 + 12 * q^31 - 6 * q^32 + 14 * q^33 + 6 * q^36 - 30 * q^39 - 4 * q^41 + 6 * q^42 + 12 * q^44 + 2 * q^46 + 24 * q^47 - 2 * q^48 + 14 * q^49 + 4 * q^51 - 4 * q^52 + 8 * q^53 + 4 * q^54 + 6 * q^56 - 20 * q^57 - 18 * q^58 - 12 * q^59 - 30 * q^61 - 38 * q^63 + 12 * q^64 - 34 * q^66 + 6 * q^67 - 12 * q^68 - 50 * q^69 - 6 * q^72 - 20 * q^77 - 12 * q^78 + 4 * q^79 + 50 * q^81 + 2 * q^82 + 12 * q^84 - 54 * q^86 - 34 * q^87 - 12 * q^88 - 26 * q^89 + 28 * q^91 - 4 * q^92 + 60 * q^93 - 24 * q^94 - 2 * q^96 - 72 * q^97 + 2 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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