LMFDB - Embedded newform 546.2.p.a.281.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(239,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.p (of order $4$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.45474709504.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 38x^{6} + 481x^{4} + 2112x^{2} + 1024 $ x^8 + 38x^6 + 481x^4 + 2112*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.2
Root			$-3.90842i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.a.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(2.47078 - 2.47078i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(2.47078 - 2.47078i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +3.49421i q^{10} +(-0.976570 - 0.976570i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(1.76367 + 3.14475i) q^{13} -1.00000i q^{14} +(1.02343 - 5.96499i) q^{15} -1.00000 q^{16} +5.49421 q^{17} +(1.29289 + 2.70711i) q^{18} +(0.470780 + 0.470780i) q^{19} +(-2.47078 - 2.47078i) q^{20} +(-0.292893 + 1.70711i) q^{21} +1.38108 q^{22} -8.97470 q^{23} +(1.70711 + 0.292893i) q^{24} -7.20950i q^{25} +(-3.47078 - 0.976570i) q^{26} +(-1.41421 - 5.00000i) q^{27} +(0.707107 + 0.707107i) q^{28} -2.03314i q^{29} +(3.49421 + 4.94156i) q^{30} +(0.585786 + 0.585786i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.35765 - 0.404508i) q^{33} +(-3.88499 + 3.88499i) q^{34} +3.49421i q^{35} +(-2.82843 - 1.00000i) q^{36} +(-1.56236 + 1.56236i) q^{37} -0.665783 q^{38} +(5.63896 + 2.68368i) q^{39} +3.49421 q^{40} +(-0.966864 + 0.966864i) q^{41} +(-1.00000 - 1.41421i) q^{42} -10.3889i q^{43} +(-0.976570 + 0.976570i) q^{44} +(-4.51764 - 9.45920i) q^{45} +(6.34607 - 6.34607i) q^{46} +(-4.24264 - 4.24264i) q^{47} +(-1.41421 + 1.00000i) q^{48} -1.00000i q^{49} +(5.09789 + 5.09789i) q^{50} +(7.76999 - 5.49421i) q^{51} +(3.14475 - 1.76367i) q^{52} +13.9464i q^{53} +(4.53553 + 2.53553i) q^{54} -4.82578 q^{55} -1.00000 q^{56} +(1.13656 + 0.195003i) q^{57} +(1.43764 + 1.43764i) q^{58} +(8.81685 + 8.81685i) q^{59} +(-5.96499 - 1.02343i) q^{60} +13.1347 q^{61} -0.828427 q^{62} +(1.29289 + 2.70711i) q^{63} +1.00000i q^{64} +(12.1276 + 3.41234i) q^{65} +(1.95314 - 1.38108i) q^{66} +(4.36735 + 4.36735i) q^{67} -5.49421i q^{68} +(-12.6921 + 8.97470i) q^{69} +(-2.47078 - 2.47078i) q^{70} +(-0.908424 + 0.908424i) q^{71} +(2.70711 - 1.29289i) q^{72} +(-11.0361 + 11.0361i) q^{73} -2.20950i q^{74} +(-7.20950 - 10.1958i) q^{75} +(0.470780 - 0.470780i) q^{76} +1.38108 q^{77} +(-5.88499 + 2.08970i) q^{78} +6.11313 q^{79} +(-2.47078 + 2.47078i) q^{80} +(-7.00000 - 5.65685i) q^{81} -1.36735i q^{82} +(-6.49421 + 6.49421i) q^{83} +(1.70711 + 0.292893i) q^{84} +(13.5750 - 13.5750i) q^{85} +(7.34607 + 7.34607i) q^{86} +(-2.03314 - 2.87529i) q^{87} -1.38108i q^{88} +(-1.74578 - 1.74578i) q^{89} +(9.88312 + 3.49421i) q^{90} +(-3.47078 - 0.976570i) q^{91} +8.97470i q^{92} +(1.41421 + 0.242641i) q^{93} +6.00000 q^{94} +2.32639 q^{95} +(0.292893 - 1.70711i) q^{96} +(5.41421 + 5.41421i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-3.73873 + 1.78559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{6} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^6 + 8 * q^9	$ 8 q - 4 q^{5} - 8 q^{6} + 8 q^{9} - 8 q^{11} - 8 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 20 q^{17} + 16 q^{18} - 20 q^{19} + 4 q^{20} - 8 q^{21} + 12 q^{22} - 12 q^{23} + 8 q^{24} - 4 q^{26} + 4 q^{30} + 16 q^{31} - 20 q^{33} + 4 q^{34} - 24 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{40} - 20 q^{41} - 8 q^{42} - 8 q^{44} - 12 q^{45} + 4 q^{46} + 24 q^{50} - 8 q^{51} + 8 q^{52} + 8 q^{54} - 12 q^{55} - 8 q^{56} - 16 q^{57} + 20 q^{61} + 16 q^{62} + 16 q^{63} + 28 q^{65} + 16 q^{66} + 24 q^{67} - 8 q^{69} + 4 q^{70} + 28 q^{71} + 16 q^{72} + 16 q^{73} - 36 q^{75} - 20 q^{76} + 12 q^{77} - 12 q^{78} + 24 q^{79} + 4 q^{80} - 56 q^{81} - 28 q^{83} + 8 q^{84} + 16 q^{85} + 12 q^{86} - 4 q^{87} - 16 q^{90} - 4 q^{91} + 48 q^{94} + 92 q^{95} + 8 q^{96} + 32 q^{97} - 32 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^6 + 8 * q^9 - 8 * q^11 - 8 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 20 * q^17 + 16 * q^18 - 20 * q^19 + 4 * q^20 - 8 * q^21 + 12 * q^22 - 12 * q^23 + 8 * q^24 - 4 * q^26 + 4 * q^30 + 16 * q^31 - 20 * q^33 + 4 * q^34 - 24 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^40 - 20 * q^41 - 8 * q^42 - 8 * q^44 - 12 * q^45 + 4 * q^46 + 24 * q^50 - 8 * q^51 + 8 * q^52 + 8 * q^54 - 12 * q^55 - 8 * q^56 - 16 * q^57 + 20 * q^61 + 16 * q^62 + 16 * q^63 + 28 * q^65 + 16 * q^66 + 24 * q^67 - 8 * q^69 + 4 * q^70 + 28 * q^71 + 16 * q^72 + 16 * q^73 - 36 * q^75 - 20 * q^76 + 12 * q^77 - 12 * q^78 + 24 * q^79 + 4 * q^80 - 56 * q^81 - 28 * q^83 + 8 * q^84 + 16 * q^85 + 12 * q^86 - 4 * q^87 - 16 * q^90 - 4 * q^91 + 48 * q^94 + 92 * q^95 + 8 * q^96 + 32 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$4$		−	1.00000i		−	0.500000i
$5$	2.47078	−	2.47078i	1.10497	−	1.10497i	0.111164	−	0.993802i	$-0.464542\pi$
$5$	2.47078	−	2.47078i	1.10497	−	1.10497i	0.993802	−	0.111164i	$-0.0354580\pi$
$6$	−0.292893	+	1.70711i	−0.119573	+	0.696923i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$			3.49421i			1.10497i
$11$	−0.976570	−	0.976570i	−0.294447	−	0.294447i	0.544387	−	0.838834i	$-0.316762\pi$
$11$	−0.976570	−	0.976570i	−0.294447	−	0.294447i	−0.838834	+	0.544387i	$0.816762\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	1.76367	+	3.14475i	0.489155	+	0.872197i
$13$	1.76367	+	3.14475i	0.489155	+	0.872197i
$14$		−	1.00000i		−	0.267261i
$15$	1.02343	−	5.96499i	0.264249	−	1.54015i
$16$	−1.00000			−0.250000
$17$	5.49421			1.33254			0.666271	−	0.745710i	$-0.267889\pi$
$17$	5.49421			1.33254			0.666271	+	0.745710i	$0.267889\pi$
$18$	1.29289	+	2.70711i	0.304738	+	0.638071i
$19$	0.470780	+	0.470780i	0.108004	+	0.108004i	0.759044	−	0.651040i	$-0.225667\pi$
$19$	0.470780	+	0.470780i	0.108004	+	0.108004i	−0.651040	+	0.759044i	$0.725667\pi$
$20$	−2.47078	−	2.47078i	−0.552483	−	0.552483i
$21$	−0.292893	+	1.70711i	−0.0639145	+	0.372521i
$22$	1.38108			0.294447
$23$	−8.97470			−1.87135			−0.935677	−	0.352859i	$-0.885210\pi$
$23$	−8.97470			−1.87135			−0.935677	+	0.352859i	$0.885210\pi$
$24$	1.70711	+	0.292893i	0.348462	+	0.0597866i
$25$		−	7.20950i		−	1.44190i
$26$	−3.47078	−	0.976570i	−0.680676	−	0.191521i
$27$	−1.41421	−	5.00000i	−0.272166	−	0.962250i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$		−	2.03314i		−	0.377544i	−0.982021	−	0.188772i	$-0.939549\pi$
$29$		−	2.03314i		−	0.377544i	0.982021	−	0.188772i	$-0.0604507\pi$
$30$	3.49421	+	4.94156i	0.637953	+	0.902201i
$31$	0.585786	+	0.585786i	0.105210	+	0.105210i	0.757752	−	0.652542i	$-0.226297\pi$
$31$	0.585786	+	0.585786i	0.105210	+	0.105210i	−0.652542	+	0.757752i	$0.726297\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−2.35765	−	0.404508i	−0.410414	−	0.0704159i
$34$	−3.88499	+	3.88499i	−0.666271	+	0.666271i
$35$			3.49421i			0.590629i
$36$	−2.82843	−	1.00000i	−0.471405	−	0.166667i
$37$	−1.56236	+	1.56236i	−0.256850	+	0.256850i	−0.823772	−	0.566922i	$-0.808134\pi$
$37$	−1.56236	+	1.56236i	−0.256850	+	0.256850i	0.566922	+	0.823772i	$0.308134\pi$
$38$	−0.665783			−0.108004
$39$	5.63896	+	2.68368i	0.902956	+	0.429732i
$40$	3.49421			0.552483
$41$	−0.966864	+	0.966864i	−0.150999	+	0.150999i	−0.778564	−	0.627565i	$-0.784052\pi$
$41$	−0.966864	+	0.966864i	−0.150999	+	0.150999i	0.627565	+	0.778564i	$0.284052\pi$
$42$	−1.00000	−	1.41421i	−0.154303	−	0.218218i
$43$		−	10.3889i		−	1.58429i	−0.610331	−	0.792147i	$-0.708963\pi$
$43$		−	10.3889i		−	1.58429i	0.610331	−	0.792147i	$-0.291037\pi$
$44$	−0.976570	+	0.976570i	−0.147223	+	0.147223i
$45$	−4.51764	−	9.45920i	−0.673450	−	1.41009i
$46$	6.34607	−	6.34607i	0.935677	−	0.935677i
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	0.326384	−	0.945237i	$-0.394170\pi$
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	−0.945237	+	0.326384i	$0.894170\pi$
$48$	−1.41421	+	1.00000i	−0.204124	+	0.144338i
$49$		−	1.00000i		−	0.142857i
$50$	5.09789	+	5.09789i	0.720950	+	0.720950i
$51$	7.76999	−	5.49421i	1.08802	−	0.769343i
$52$	3.14475	−	1.76367i	0.436098	−	0.244577i
$53$			13.9464i			1.91568i	0.287303	+	0.957840i	$0.407241\pi$
$53$			13.9464i			1.91568i	−0.287303	+	0.957840i	$0.592759\pi$
$54$	4.53553	+	2.53553i	0.617208	+	0.345042i
$55$	−4.82578			−0.650708
$56$	−1.00000			−0.133631
$57$	1.13656	+	0.195003i	0.150541	+	0.0258288i
$58$	1.43764	+	1.43764i	0.188772	+	0.188772i
$59$	8.81685	+	8.81685i	1.14786	+	1.14786i	0.986974	+	0.160882i	$0.0514339\pi$
$59$	8.81685	+	8.81685i	1.14786	+	1.14786i	0.160882	+	0.986974i	$0.448566\pi$
$60$	−5.96499	−	1.02343i	−0.770077	−	0.132124i
$61$	13.1347			1.68172			0.840862	−	0.541249i	$-0.182048\pi$
$61$	13.1347			1.68172			0.840862	+	0.541249i	$0.182048\pi$
$62$	−0.828427			−0.105210
$63$	1.29289	+	2.70711i	0.162889	+	0.341063i
$64$			1.00000i			0.125000i
$65$	12.1276	+	3.41234i	1.50425	+	0.423249i
$66$	1.95314	−	1.38108i	0.240415	−	0.169999i
$67$	4.36735	+	4.36735i	0.533557	+	0.533557i	0.921629	−	0.388072i	$-0.126859\pi$
$67$	4.36735	+	4.36735i	0.533557	+	0.533557i	−0.388072	+	0.921629i	$0.626859\pi$
$68$		−	5.49421i		−	0.666271i
$69$	−12.6921	+	8.97470i	−1.52795	+	1.08043i
$70$	−2.47078	−	2.47078i	−0.295315	−	0.295315i
$71$	−0.908424	+	0.908424i	−0.107810	+	0.107810i	−0.758954	−	0.651144i	$-0.774289\pi$
$71$	−0.908424	+	0.908424i	−0.107810	+	0.107810i	0.651144	+	0.758954i	$0.274289\pi$
$72$	2.70711	−	1.29289i	0.319036	−	0.152369i
$73$	−11.0361	+	11.0361i	−1.29167	+	1.29167i	−0.357921	+	0.933752i	$0.616514\pi$
$73$	−11.0361	+	11.0361i	−1.29167	+	1.29167i	−0.933752	+	0.357921i	$0.883486\pi$
$74$		−	2.20950i		−	0.256850i
$75$	−7.20950	−	10.1958i	−0.832482	−	1.17731i
$76$	0.470780	−	0.470780i	0.0540021	−	0.0540021i
$77$	1.38108			0.157388
$78$	−5.88499	+	2.08970i	−0.666344	+	0.236612i
$79$	6.11313			0.687781			0.343891	−	0.939010i	$-0.388255\pi$
$79$	6.11313			0.687781			0.343891	+	0.939010i	$0.388255\pi$
$80$	−2.47078	+	2.47078i	−0.276242	+	0.276242i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		−	1.36735i		−	0.150999i
$83$	−6.49421	+	6.49421i	−0.712832	+	0.712832i	−0.967127	−	0.254295i	$-0.918157\pi$
$83$	−6.49421	+	6.49421i	−0.712832	+	0.712832i	0.254295	+	0.967127i	$0.418157\pi$
$84$	1.70711	+	0.292893i	0.186261	+	0.0319573i
$85$	13.5750	−	13.5750i	1.47241	−	1.47241i
$86$	7.34607	+	7.34607i	0.792147	+	0.792147i
$87$	−2.03314	−	2.87529i	−0.217975	−	0.308263i
$88$		−	1.38108i		−	0.147223i
$89$	−1.74578	−	1.74578i	−0.185052	−	0.185052i	0.608501	−	0.793553i	$-0.291771\pi$
$89$	−1.74578	−	1.74578i	−0.185052	−	0.185052i	−0.793553	+	0.608501i	$0.791771\pi$
$90$	9.88312	+	3.49421i	1.04177	+	0.368322i
$91$	−3.47078	−	0.976570i	−0.363837	−	0.102372i
$92$			8.97470i			0.935677i
$93$	1.41421	+	0.242641i	0.146647	+	0.0251607i
$94$	6.00000			0.618853
$95$	2.32639			0.238682
$96$	0.292893	−	1.70711i	0.0298933	−	0.174231i
$97$	5.41421	+	5.41421i	0.549730	+	0.549730i	0.926363	−	0.376633i	$-0.122918\pi$
$97$	5.41421	+	5.41421i	0.549730	+	0.549730i	−0.376633	+	0.926363i	$0.622918\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	−3.73873	+	1.78559i	−0.375756	+	0.179458i
$100$	−7.20950			−0.720950
$101$	−8.53214			−0.848980			−0.424490	−	0.905433i	$-0.639547\pi$
$101$	−8.53214			−0.848980			−0.424490	+	0.905433i	$0.639547\pi$
$102$	−1.60922	+	9.37920i	−0.159336	+	0.928680i
$103$		−	11.7563i		−	1.15838i	−0.815193	−	0.579189i	$-0.803369\pi$
$103$		−	11.7563i		−	1.15838i	0.815193	−	0.579189i	$-0.196631\pi$
$104$	−0.976570	+	3.47078i	−0.0957605	+	0.340338i
$105$	3.49421	+	4.94156i	0.341000	+	0.482247i
$106$	−9.86156	−	9.86156i	−0.957840	−	0.957840i
$107$		−	0.828427i		−	0.0800871i	−0.999198	−	0.0400435i	$-0.987250\pi$
$107$		−	0.828427i		−	0.0800871i	0.999198	−	0.0400435i	$-0.0127497\pi$
$108$	−5.00000	+	1.41421i	−0.481125	+	0.136083i
$109$	1.62863	+	1.62863i	0.155994	+	0.155994i	0.780789	−	0.624795i	$-0.214817\pi$
$109$	1.62863	+	1.62863i	0.155994	+	0.155994i	−0.624795	+	0.780789i	$0.714817\pi$
$110$	3.41234	−	3.41234i	0.325354	−	0.325354i
$111$	−0.647149	+	3.77186i	−0.0614247	+	0.358009i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$		−	4.48528i		−	0.421940i	−0.977493	−	0.210970i	$-0.932338\pi$
$113$		−	4.48528i		−	0.421940i	0.977493	−	0.210970i	$-0.0676622\pi$
$114$	−0.941559	+	0.665783i	−0.0881851	+	0.0623563i
$115$	−22.1745	+	22.1745i	−2.06778	+	2.06778i
$116$	−2.03314			−0.188772
$117$	10.6584	−	1.84367i	0.985367	−	0.170447i
$118$	−12.4689			−1.14786
$119$	−3.88499	+	3.88499i	−0.356137	+	0.356137i
$120$	4.94156	−	3.49421i	0.451101	−	0.318976i
$121$		−	9.09262i		−	0.826602i
$122$	−9.28763	+	9.28763i	−0.840862	+	0.840862i
$123$	−0.400488	+	2.33422i	−0.0361108	+	0.210469i
$124$	0.585786	−	0.585786i	0.0526052	−	0.0526052i
$125$	−5.45920	−	5.45920i	−0.488286	−	0.488286i
$126$	−2.82843	−	1.00000i	−0.251976	−	0.0890871i
$127$			19.2437i			1.70760i	0.520600	+	0.853801i	$0.325708\pi$
$127$			19.2437i			1.70760i	−0.520600	+	0.853801i	$0.674292\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−10.3889	−	14.6921i	−0.914692	−	1.29357i
$130$	−10.9884	+	6.16264i	−0.963748	+	0.540500i
$131$		−	0.778915i		−	0.0680542i	−0.999421	−	0.0340271i	$-0.989167\pi$
$131$		−	0.778915i		−	0.0680542i	0.999421	−	0.0340271i	$-0.0108332\pi$
$132$	−0.404508	+	2.35765i	−0.0352079	+	0.205207i
$133$	−0.665783			−0.0577307
$134$	−6.17637			−0.533557
$135$	−15.8481	−	8.85969i	−1.36399	−	0.762521i
$136$	3.88499	+	3.88499i	0.333135	+	0.333135i
$137$	4.82655	+	4.82655i	0.412360	+	0.412360i	0.882560	−	0.470200i	$-0.155818\pi$
$137$	4.82655	+	4.82655i	0.412360	+	0.412360i	−0.470200	+	0.882560i	$0.655818\pi$
$138$	2.62863	−	15.3208i	0.223764	−	1.30419i
$139$	2.18315			0.185173			0.0925863	−	0.995705i	$-0.470487\pi$
$139$	2.18315			0.185173			0.0925863	+	0.995705i	$0.470487\pi$
$140$	3.49421			0.295315
$141$	−10.2426	−	1.75736i	−0.862586	−	0.147996i
$142$		−	1.28471i		−	0.107810i
$143$	1.34872	−	4.79342i	0.112786	−	0.400846i
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	−5.02343	−	5.02343i	−0.417173	−	0.417173i
$146$		−	15.6073i		−	1.29167i
$147$	−1.00000	−	1.41421i	−0.0824786	−	0.116642i
$148$	1.56236	+	1.56236i	0.128425	+	0.128425i
$149$	−10.5020	+	10.5020i	−0.860361	+	0.860361i	−0.991380	−	0.131019i	$-0.958175\pi$
$149$	−10.5020	+	10.5020i	−0.860361	+	0.860361i	0.131019	+	0.991380i	$0.458175\pi$
$150$	12.3074	+	2.11162i	1.00489	+	0.172413i
$151$	−8.12763	+	8.12763i	−0.661417	+	0.661417i	−0.955714	−	0.294297i	$-0.904915\pi$
$151$	−8.12763	+	8.12763i	−0.661417	+	0.661417i	0.294297	+	0.955714i	$0.404915\pi$
$152$			0.665783i			0.0540021i
$153$	5.49421	−	15.5400i	0.444181	−	1.25633i
$154$	−0.976570	+	0.976570i	−0.0786942	+	0.0786942i
$155$	2.89470			0.232508
$156$	2.68368	−	5.63896i	0.214866	−	0.451478i
$157$	−3.22412			−0.257313			−0.128656	−	0.991689i	$-0.541066\pi$
$157$	−3.22412			−0.257313			−0.128656	+	0.991689i	$0.541066\pi$
$158$	−4.32264	+	4.32264i	−0.343891	+	0.343891i
$159$	13.9464	+	19.7231i	1.10602	+	1.56415i
$160$		−	3.49421i		−	0.276242i
$161$	6.34607	−	6.34607i	0.500140	−	0.500140i
$162$	8.94975	−	0.949747i	0.703159	−	0.0746192i
$163$	−14.2973	+	14.2973i	−1.11985	+	1.11985i	−0.128091	+	0.991762i	$0.540885\pi$
$163$	−14.2973	+	14.2973i	−1.11985	+	1.11985i	−0.991762	+	0.128091i	$0.959115\pi$
$164$	0.966864	+	0.966864i	0.0754994	+	0.0754994i
$165$	−6.82468	+	4.82578i	−0.531300	+	0.375686i
$166$		−	9.18420i		−	0.712832i
$167$	8.20763	+	8.20763i	0.635126	+	0.635126i	0.949349	−	0.314224i	$-0.101744\pi$
$167$	8.20763	+	8.20763i	0.635126	+	0.635126i	−0.314224	+	0.949349i	$0.601744\pi$
$168$	−1.41421	+	1.00000i	−0.109109	+	0.0771517i
$169$	−6.77892	+	11.0926i	−0.521455	+	0.853279i
$170$			19.1979i			1.47241i
$171$	1.80235	−	0.860786i	0.137829	−	0.0658260i
$172$	−10.3889			−0.792147
$173$	−1.08744			−0.0826768			−0.0413384	−	0.999145i	$-0.513162\pi$
$173$	−1.08744			−0.0826768			−0.0413384	+	0.999145i	$0.513162\pi$
$174$	3.47078	+	0.595492i	0.263119	+	0.0451441i
$175$	5.09789	+	5.09789i	0.385364	+	0.385364i
$176$	0.976570	+	0.976570i	0.0736117	+	0.0736117i
$177$	21.2858	+	3.65206i	1.59994	+	0.274505i
$178$	2.46891			0.185052
$179$	−5.12471			−0.383039			−0.191519	−	0.981489i	$-0.561342\pi$
$179$	−5.12471			−0.383039			−0.191519	+	0.981489i	$0.561342\pi$
$180$	−9.45920	+	4.51764i	−0.705047	+	0.336725i
$181$		−	14.2895i		−	1.06213i	−0.847331	−	0.531065i	$-0.821792\pi$
$181$		−	14.2895i		−	1.06213i	0.847331	−	0.531065i	$-0.178208\pi$
$182$	3.14475	−	1.76367i	0.233104	−	0.130732i
$183$	18.5753	−	13.1347i	1.37312	−	0.970944i
$184$	−6.34607	−	6.34607i	−0.467838	−	0.467838i
$185$			7.72047i			0.567621i
$186$	−1.17157	+	0.828427i	−0.0859039	+	0.0607432i
$187$	−5.36548	−	5.36548i	−0.392363	−	0.392363i
$188$	−4.24264	+	4.24264i	−0.309426	+	0.309426i
$189$	4.53553	+	2.53553i	0.329912	+	0.184433i
$190$	−1.64500	+	1.64500i	−0.119341	+	0.119341i
$191$		−	17.6200i		−	1.27494i	−0.770477	−	0.637468i	$-0.779982\pi$
$191$		−	17.6200i		−	1.27494i	0.770477	−	0.637468i	$-0.220018\pi$
$192$	1.00000	+	1.41421i	0.0721688	+	0.102062i
$193$	15.2058	−	15.2058i	1.09453	−	1.09453i	0.0994964	−	0.995038i	$-0.468277\pi$
$193$	15.2058	−	15.2058i	1.09453	−	1.09453i	0.995038	−	0.0994964i	$-0.0317232\pi$
$194$	−7.65685			−0.549730
$195$	20.5634	−	7.30186i	1.47258	−	0.522897i
$196$	−1.00000			−0.0714286
$197$	−11.3111	+	11.3111i	−0.805879	+	0.805879i	−0.984007	−	0.178128i	$-0.942996\pi$
$197$	−11.3111	+	11.3111i	−0.805879	+	0.805879i	0.178128	+	0.984007i	$0.442996\pi$
$198$	1.38108	−	3.90628i	0.0981489	−	0.277607i
$199$			13.9394i			0.988139i	0.869422	+	0.494069i	$0.164491\pi$
$199$			13.9394i			0.988139i	−0.869422	+	0.494069i	$0.835509\pi$
$200$	5.09789	−	5.09789i	0.360475	−	0.360475i
$201$	10.5437	+	1.80902i	0.743697	+	0.127598i
$202$	6.03314	−	6.03314i	0.424490	−	0.424490i
$203$	1.43764	+	1.43764i	0.100903	+	0.100903i
$204$	−5.49421	−	7.76999i	−0.384672	−	0.544008i
$205$			4.77782i			0.333697i
$206$	8.31293	+	8.31293i	0.579189	+	0.579189i
$207$	−8.97470	+	25.3843i	−0.623784	+	1.76433i
$208$	−1.76367	−	3.14475i	−0.122289	−	0.218049i
$209$		−	0.919498i		−	0.0636030i
$210$	−5.96499	−	1.02343i	−0.411623	−	0.0706234i
$211$	−8.09637			−0.557377			−0.278689	−	0.960382i	$-0.589900\pi$
$211$	−8.09637			−0.557377			−0.278689	+	0.960382i	$0.589900\pi$
$212$	13.9464			0.957840
$213$	−0.376281	+	2.19313i	−0.0257824	+	0.150271i
$214$	0.585786	+	0.585786i	0.0400435	+	0.0400435i
$215$	−25.6687	−	25.6687i	−1.75059	−	1.75059i
$216$	2.53553	−	4.53553i	0.172521	−	0.308604i
$217$	−0.828427			−0.0562373
$218$	−2.30323			−0.155994
$219$	−4.57128	+	26.6434i	−0.308899	+	1.80039i
$220$			4.82578i			0.325354i
$221$	9.68999	+	17.2779i	0.651819	+	1.16224i
$222$	−2.20950	−	3.12471i	−0.148292	−	0.209717i
$223$	8.52949	+	8.52949i	0.571177	+	0.571177i	0.932457	−	0.361280i	$-0.117660\pi$
$223$	8.52949	+	8.52949i	0.571177	+	0.571177i	−0.361280	+	0.932457i	$0.617660\pi$
$224$			1.00000i			0.0668153i
$225$	−20.3916	−	7.20950i	−1.35944	−	0.480634i
$226$	3.17157	+	3.17157i	0.210970	+	0.210970i
$227$	16.8831	−	16.8831i	1.12057	−	1.12057i	0.128917	−	0.991655i	$-0.458850\pi$
$227$	16.8831	−	16.8831i	1.12057	−	1.12057i	0.991655	−	0.128917i	$-0.0411499\pi$
$228$	0.195003	−	1.13656i	0.0129144	−	0.0752707i
$229$	0.715295	−	0.715295i	0.0472680	−	0.0472680i	−0.683078	−	0.730346i	$-0.739359\pi$
$229$	0.715295	−	0.715295i	0.0472680	−	0.0472680i	0.730346	+	0.683078i	$0.239359\pi$
$230$		−	31.3595i		−	2.06778i
$231$	1.95314	−	1.38108i	0.128507	−	0.0908683i
$232$	1.43764	−	1.43764i	0.0943860	−	0.0943860i
$233$	16.8753			1.10554			0.552768	−	0.833335i	$-0.313571\pi$
$233$	16.8753			1.10554			0.552768	+	0.833335i	$0.313571\pi$
$234$	−6.23294	+	8.84028i	−0.407460	+	0.577907i
$235$	−20.9653			−1.36762
$236$	8.81685	−	8.81685i	0.573928	−	0.573928i
$237$	8.64527	−	6.11313i	0.561571	−	0.397091i
$238$		−	5.49421i		−	0.356137i
$239$	13.8168	−	13.8168i	0.893738	−	0.893738i	−0.101135	−	0.994873i	$-0.532247\pi$
$239$	13.8168	−	13.8168i	0.893738	−	0.893738i	0.994873	+	0.101135i	$0.0322474\pi$
$240$	−1.02343	+	5.96499i	−0.0660622	+	0.385038i
$241$	6.95794	−	6.95794i	0.448200	−	0.448200i	−0.446556	−	0.894756i	$-0.647350\pi$
$241$	6.95794	−	6.95794i	0.448200	−	0.448200i	0.894756	+	0.446556i	$0.147350\pi$
$242$	6.42946	+	6.42946i	0.413301	+	0.413301i
$243$	−15.5563	−	1.00000i	−0.997940	−	0.0641500i
$244$		−	13.1347i		−	0.840862i
$245$	−2.47078	−	2.47078i	−0.157852	−	0.157852i
$246$	−1.36735	−	1.93373i	−0.0871792	−	0.123290i
$247$	−0.650183	+	2.31079i	−0.0413702	+	0.147032i
$248$			0.828427i			0.0526052i
$249$	−2.68999	+	15.6784i	−0.170471	+	0.993579i
$250$	7.72047			0.488286
$251$	−22.7611			−1.43667			−0.718333	−	0.695700i	$-0.755094\pi$
$251$	−22.7611			−1.43667			−0.718333	+	0.695700i	$0.755094\pi$
$252$	2.70711	−	1.29289i	0.170532	−	0.0814446i
$253$	8.76441	+	8.76441i	0.551014	+	0.551014i
$254$	−13.6073	−	13.6073i	−0.853801	−	0.853801i
$255$	5.62294	−	32.7729i	0.352122	−	2.05232i
$256$	1.00000			0.0625000
$257$	−5.59058			−0.348731			−0.174365	−	0.984681i	$-0.555787\pi$
$257$	−5.59058			−0.348731			−0.174365	+	0.984681i	$0.555787\pi$
$258$	17.7350	+	3.04284i	1.10413	+	0.189439i
$259$		−	2.20950i		−	0.137292i
$260$	3.41234	−	12.1276i	0.211624	−	0.752124i
$261$	−5.75058	−	2.03314i	−0.355952	−	0.125848i
$262$	0.550776	+	0.550776i	0.0340271	+	0.0340271i
$263$			12.6052i			0.777270i	0.921392	+	0.388635i	$0.127053\pi$
$263$			12.6052i			0.777270i	−0.921392	+	0.388635i	$0.872947\pi$
$264$	−1.38108	−	1.95314i	−0.0849995	−	0.120207i
$265$	34.4584	+	34.4584i	2.11676	+	2.11676i
$266$	0.470780	−	0.470780i	0.0288654	−	0.0288654i
$267$	−4.21469	−	0.723126i	−0.257935	−	0.0442546i
$268$	4.36735	−	4.36735i	0.266779	−	0.266779i
$269$		−	2.87529i		−	0.175309i	−0.996151	−	0.0876547i	$-0.972063\pi$
$269$		−	2.87529i		−	0.175309i	0.996151	−	0.0876547i	$-0.0279372\pi$
$270$	17.4711	−	4.94156i	1.06325	−	0.300734i
$271$	−0.505790	+	0.505790i	−0.0307245	+	0.0307245i	−0.722302	−	0.691578i	$-0.756916\pi$
$271$	−0.505790	+	0.505790i	−0.0307245	+	0.0307245i	0.691578	+	0.722302i	$0.256916\pi$
$272$	−5.49421			−0.333135
$273$	−5.88499	+	2.08970i	−0.356176	+	0.126475i
$274$	−6.82578			−0.412360
$275$	−7.04058	+	7.04058i	−0.424563	+	0.424563i
$276$	8.97470	+	12.6921i	0.540213	+	0.763977i
$277$			7.68056i			0.461480i	0.973015	+	0.230740i	$0.0741147\pi$
$277$			7.68056i			0.461480i	−0.973015	+	0.230740i	$0.925885\pi$
$278$	−1.54372	+	1.54372i	−0.0925863	+	0.0925863i
$279$	2.24264	−	1.07107i	0.134263	−	0.0641232i
$280$	−2.47078	+	2.47078i	−0.147657	+	0.147657i
$281$	2.76519	+	2.76519i	0.164957	+	0.164957i	0.784759	−	0.619801i	$-0.212787\pi$
$281$	2.76519	+	2.76519i	0.164957	+	0.164957i	−0.619801	+	0.784759i	$0.712787\pi$
$282$	8.48528	−	6.00000i	0.505291	−	0.357295i
$283$		−	32.2500i		−	1.91706i	−0.284989	−	0.958531i	$-0.591990\pi$
$283$		−	32.2500i		−	1.91706i	0.284989	−	0.958531i	$-0.408010\pi$
$284$	0.908424	+	0.908424i	0.0539050	+	0.0539050i
$285$	3.29001	−	2.32639i	0.194883	−	0.137803i
$286$	2.43577	+	4.34315i	0.144030	+	0.256816i
$287$		−	1.36735i		−	0.0807123i
$288$	−1.29289	−	2.70711i	−0.0761845	−	0.159518i
$289$	13.1863			0.775667
$290$	7.10420			0.417173
$291$	13.0711	+	2.24264i	0.766240	+	0.131466i
$292$	11.0361	+	11.0361i	0.645836	+	0.645836i
$293$	−3.19098	−	3.19098i	−0.186419	−	0.186419i	0.607727	−	0.794146i	$-0.292082\pi$
$293$	−3.19098	−	3.19098i	−0.186419	−	0.186419i	−0.794146	+	0.607727i	$0.792082\pi$
$294$	1.70711	+	0.292893i	0.0995605	+	0.0170819i
$295$	43.5690			2.53668
$296$	−2.20950			−0.128425
$297$	−3.50177	+	6.26393i	−0.203193	+	0.363470i
$298$		−	14.8521i		−	0.860361i
$299$	−15.8284	−	28.2232i	−0.915382	−	1.63219i
$300$	−10.1958	+	7.20950i	−0.588654	+	0.416241i
$301$	7.34607	+	7.34607i	0.423420	+	0.423420i
$302$		−	11.4942i		−	0.661417i
$303$	−12.0663	+	8.53214i	−0.693189	+	0.490159i
$304$	−0.470780	−	0.470780i	−0.0270011	−	0.0270011i
$305$	32.4529	−	32.4529i	1.85825	−	1.85825i
$306$	7.10343	+	14.8734i	0.406076	+	0.850256i
$307$	7.47745	−	7.47745i	0.426761	−	0.426761i	−0.460763	−	0.887523i	$-0.652424\pi$
$307$	7.47745	−	7.47745i	0.426761	−	0.426761i	0.887523	+	0.460763i	$0.152424\pi$
$308$		−	1.38108i		−	0.0786942i
$309$	−11.7563	−	16.6259i	−0.668790	−	0.945812i
$310$	−2.04686	+	2.04686i	−0.116254	+	0.116254i
$311$	−8.80902			−0.499514			−0.249757	−	0.968309i	$-0.580351\pi$
$311$	−8.80902			−0.499514			−0.249757	+	0.968309i	$0.580351\pi$
$312$	2.08970	+	5.88499i	0.118306	+	0.333172i
$313$	24.7310			1.39788			0.698938	−	0.715182i	$-0.253656\pi$
$313$	24.7310			1.39788			0.698938	+	0.715182i	$0.253656\pi$
$314$	2.27980	−	2.27980i	0.128656	−	0.128656i
$315$	9.88312	+	3.49421i	0.556851	+	0.196876i
$316$		−	6.11313i		−	0.343891i
$317$	2.05949	−	2.05949i	0.115672	−	0.115672i	−0.646901	−	0.762574i	$-0.723935\pi$
$317$	2.05949	−	2.05949i	0.115672	−	0.115672i	0.762574	+	0.646901i	$0.223935\pi$
$318$	−23.8079	−	4.08479i	−1.33508	−	0.229064i
$319$	−1.98550	+	1.98550i	−0.111167	+	0.111167i
$320$	2.47078	+	2.47078i	0.138121	+	0.138121i
$321$	−0.828427	−	1.17157i	−0.0462383	−	0.0653908i
$322$			8.97470i			0.500140i
$323$	2.58656	+	2.58656i	0.143920	+	0.143920i
$324$	−5.65685	+	7.00000i	−0.314270	+	0.388889i
$325$	22.6721	−	12.7152i	1.25762	−	0.705313i
$326$		−	20.2195i		−	1.11985i
$327$	3.93185	+	0.674600i	0.217432	+	0.0373054i
$328$	−1.36735			−0.0754994
$329$	6.00000			0.330791
$330$	1.41344	−	8.23812i	0.0778072	−	0.453493i
$331$	2.48048	+	2.48048i	0.136340	+	0.136340i	0.771983	−	0.635643i	$-0.219265\pi$
$331$	2.48048	+	2.48048i	0.136340	+	0.136340i	−0.635643	+	0.771983i	$0.719265\pi$
$332$	6.49421	+	6.49421i	0.356416	+	0.356416i
$333$	2.85665	+	5.98137i	0.156544	+	0.327777i
$334$	−11.6073			−0.635126
$335$	21.5815			1.17913
$336$	0.292893	−	1.70711i	0.0159786	−	0.0931303i
$337$		−	4.80207i		−	0.261586i	−0.991410	−	0.130793i	$-0.958248\pi$
$337$		−	4.80207i		−	0.261586i	0.991410	−	0.130793i	$-0.0417523\pi$
$338$	−3.05025	−	12.6371i	−0.165912	−	0.687367i
$339$	−4.48528	−	6.34315i	−0.243607	−	0.344512i
$340$	−13.5750	−	13.5750i	−0.736207	−	0.736207i
$341$		−	1.14412i		−	0.0619577i
$342$	−0.665783	+	1.88312i	−0.0360014	+	0.101827i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	7.34607	−	7.34607i	0.396073	−	0.396073i
$345$	−9.18498	+	53.5340i	−0.494503	+	2.88217i
$346$	0.768939	−	0.768939i	0.0413384	−	0.0413384i
$347$			14.6453i			0.786200i	0.919496	+	0.393100i	$0.128597\pi$
$347$			14.6453i			0.786200i	−0.919496	+	0.393100i	$0.871403\pi$
$348$	−2.87529	+	2.03314i	−0.154132	+	0.108988i
$349$	5.21734	−	5.21734i	0.279278	−	0.279278i	−0.553543	−	0.832821i	$-0.686725\pi$
$349$	5.21734	−	5.21734i	0.279278	−	0.279278i	0.832821	+	0.553543i	$0.186725\pi$
$350$	−7.20950			−0.385364
$351$	13.2295	−	13.2657i	0.706141	−	0.708071i
$352$	−1.38108			−0.0736117
$353$	−8.13734	+	8.13734i	−0.433107	+	0.433107i	−0.889684	−	0.456577i	$-0.849075\pi$
$353$	−8.13734	+	8.13734i	−0.433107	+	0.433107i	0.456577	+	0.889684i	$0.349075\pi$
$354$	−17.6337	+	12.4689i	−0.937220	+	0.662715i
$355$			4.48903i			0.238253i
$356$	−1.74578	+	1.74578i	−0.0925261	+	0.0925261i
$357$	−1.60922	+	9.37920i	−0.0851688	+	0.496400i
$358$	3.62372	−	3.62372i	0.191519	−	0.191519i
$359$	−13.4600	−	13.4600i	−0.710390	−	0.710390i	0.256226	−	0.966617i	$-0.417521\pi$
$359$	−13.4600	−	13.4600i	−0.710390	−	0.710390i	−0.966617	+	0.256226i	$0.917521\pi$
$360$	3.49421	−	9.88312i	0.184161	−	0.520886i
$361$		−	18.5567i		−	0.976670i
$362$	10.1042	+	10.1042i	0.531065	+	0.531065i
$363$	−9.09262	−	12.8589i	−0.477239	−	0.674918i
$364$	−0.976570	+	3.47078i	−0.0511862	+	0.181918i
$365$			54.5353i			2.85451i
$366$	−3.84706	+	22.4223i	−0.201089	+	1.17203i
$367$	−28.1220			−1.46796			−0.733979	−	0.679173i	$-0.762339\pi$
$367$	−28.1220			−1.46796			−0.733979	+	0.679173i	$0.762339\pi$
$368$	8.97470			0.467838
$369$	1.76784	+	3.70157i	0.0920301	+	0.192696i
$370$	−5.45920	−	5.45920i	−0.283810	−	0.283810i
$371$	−9.86156	−	9.86156i	−0.511987	−	0.511987i
$372$	0.242641	−	1.41421i	0.0125803	−	0.0733236i
$373$	−1.28471			−0.0665195			−0.0332598	−	0.999447i	$-0.510589\pi$
$373$	−1.28471			−0.0665195			−0.0332598	+	0.999447i	$0.510589\pi$
$374$	7.58793			0.392363
$375$	−13.1797	−	2.26127i	−0.680595	−	0.116772i
$376$		−	6.00000i		−	0.309426i
$377$	6.39371	−	3.58579i	0.329293	−	0.184677i
$378$	−5.00000	+	1.41421i	−0.257172	+	0.0727393i
$379$	7.53627	+	7.53627i	0.387112	+	0.387112i	0.873656	−	0.486544i	$-0.161743\pi$
$379$	7.53627	+	7.53627i	0.387112	+	0.387112i	−0.486544	+	0.873656i	$0.661743\pi$
$380$		−	2.32639i		−	0.119341i
$381$	19.2437	+	27.2147i	0.985884	+	1.39425i
$382$	12.4592	+	12.4592i	0.637468	+	0.637468i
$383$	2.37137	−	2.37137i	0.121171	−	0.121171i	−0.643921	−	0.765092i	$-0.722693\pi$
$383$	2.37137	−	2.37137i	0.121171	−	0.121171i	0.765092	+	0.643921i	$0.222693\pi$
$384$	−1.70711	−	0.292893i	−0.0871154	−	0.0149466i
$385$	3.41234	−	3.41234i	0.173909	−	0.173909i
$386$			21.5042i			1.09453i
$387$	−29.3843	−	10.3889i	−1.49369	−	0.528098i
$388$	5.41421	−	5.41421i	0.274865	−	0.274865i
$389$	19.0189			0.964297			0.482148	−	0.876090i	$-0.339857\pi$
$389$	19.0189			0.964297			0.482148	+	0.876090i	$0.339857\pi$
$390$	−9.37733	+	19.7037i	−0.474840	+	0.997736i
$391$	−49.3089			−2.49366
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	−0.778915	−	1.10155i	−0.0392911	−	0.0555660i
$394$		−	15.9963i		−	0.805879i
$395$	15.1042	−	15.1042i	0.759975	−	0.759975i
$396$	1.78559	+	3.73873i	0.0897291	+	0.187878i
$397$	−20.6121	+	20.6121i	−1.03449	+	1.03449i	−0.0351102	+	0.999383i	$0.511178\pi$
$397$	−20.6121	+	20.6121i	−1.03449	+	1.03449i	−0.999383	+	0.0351102i	$0.988822\pi$
$398$	−9.85665	−	9.85665i	−0.494069	−	0.494069i
$399$	−0.941559	+	0.665783i	−0.0471369	+	0.0333308i
$400$			7.20950i			0.360475i
$401$	−26.4689	−	26.4689i	−1.32179	−	1.32179i	−0.912323	−	0.409471i	$-0.865713\pi$
$401$	−26.4689	−	26.4689i	−1.32179	−	1.32179i	−0.409471	−	0.912323i	$-0.634287\pi$
$402$	−8.73471	+	6.17637i	−0.435648	+	0.308049i
$403$	−0.809017	+	2.87529i	−0.0403000	+	0.143228i
$404$			8.53214i			0.424490i
$405$	−31.2723	+	3.31862i	−1.55393	+	0.164903i
$406$	−2.03314			−0.100903
$407$	3.05150			0.151257
$408$	9.37920	+	1.60922i	0.464340	+	0.0796681i
$409$	−20.0008	−	20.0008i	−0.988975	−	0.988975i	0.0109651	−	0.999940i	$-0.496510\pi$
$409$	−20.0008	−	20.0008i	−0.988975	−	0.988975i	−0.999940	+	0.0109651i	$0.996510\pi$
$410$	−3.37843	−	3.37843i	−0.166849	−	0.166849i
$411$	11.6523	+	1.99922i	0.574767	+	0.0986144i
$412$	−11.7563			−0.579189
$413$	−12.4689			−0.613555
$414$	−11.6033	−	24.2955i	−0.570272	−	1.19406i
$415$			32.0915i			1.57531i
$416$	3.47078	+	0.976570i	0.170169	+	0.0478803i
$417$	3.08744	−	2.18315i	0.151193	−	0.106909i
$418$	0.650183	+	0.650183i	0.0318015	+	0.0318015i
$419$		−	9.86636i		−	0.482003i	−0.970525	−	0.241002i	$-0.922524\pi$
$419$		−	9.86636i		−	0.482003i	0.970525	−	0.241002i	$-0.0774759\pi$
$420$	4.94156	−	3.49421i	0.241123	−	0.170500i
$421$	−17.4767	−	17.4767i	−0.851764	−	0.851764i	0.138586	−	0.990350i	$-0.455744\pi$
$421$	−17.4767	−	17.4767i	−0.851764	−	0.851764i	−0.990350	+	0.138586i	$0.955744\pi$
$422$	5.72500	−	5.72500i	0.278689	−	0.278689i
$423$	−16.2426	+	7.75736i	−0.789744	+	0.377176i
$424$	−9.86156	+	9.86156i	−0.478920	+	0.478920i
$425$		−	39.6105i		−	1.92139i
$426$	−1.28471	−	1.81685i	−0.0622442	−	0.0880266i
$427$	−9.28763	+	9.28763i	−0.449460	+	0.449460i
$428$	−0.828427			−0.0400435
$429$	−2.88604	−	8.12763i	−0.139339	−	0.392406i
$430$	36.3010			1.75059
$431$	−23.5563	+	23.5563i	−1.13467	+	1.13467i	−0.145279	+	0.989391i	$0.546408\pi$
$431$	−23.5563	+	23.5563i	−1.13467	+	1.13467i	−0.989391	+	0.145279i	$0.953592\pi$
$432$	1.41421	+	5.00000i	0.0680414	+	0.240563i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$	0.585786	−	0.585786i	0.0281186	−	0.0281186i
$435$	−12.1276	−	2.08077i	−0.581476	−	0.0997654i
$436$	1.62863	−	1.62863i	0.0779971	−	0.0779971i
$437$	−4.22510	−	4.22510i	−0.202114	−	0.202114i
$438$	−15.6073	−	22.0721i	−0.745748	−	1.05465i
$439$			3.38996i			0.161794i	0.996722	+	0.0808969i	$0.0257785\pi$
$439$			3.38996i			0.161794i	−0.996722	+	0.0808969i	$0.974222\pi$
$440$	−3.41234	−	3.41234i	−0.162677	−	0.162677i
$441$	−2.82843	−	1.00000i	−0.134687	−	0.0476190i
$442$	−19.0692	−	5.36548i	−0.907029	−	0.255210i
$443$			13.2810i			0.630997i	0.948926	+	0.315499i	$0.102172\pi$
$443$			13.2810i			0.630997i	−0.948926	+	0.315499i	$0.897828\pi$
$444$	3.77186	+	0.647149i	0.179005	+	0.0307123i
$445$	−8.62687			−0.408953
$446$	−12.0625			−0.571177
$447$	−4.35009	+	25.3542i	−0.205752	+	1.19921i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	−5.79556	−	5.79556i	−0.273510	−	0.273510i	0.557002	−	0.830511i	$-0.311952\pi$
$449$	−5.79556	−	5.79556i	−0.273510	−	0.273510i	−0.830511	+	0.557002i	$0.811952\pi$
$450$	19.5169	−	9.32112i	0.920035	−	0.439402i
$451$	1.88842			0.0889222
$452$	−4.48528			−0.210970
$453$	−3.36658	+	19.6218i	−0.158176	+	0.921915i
$454$			23.8763i			1.12057i
$455$	−10.9884	+	6.16264i	−0.515145	+	0.288909i
$456$	0.665783	+	0.941559i	0.0311781	+	0.0440926i
$457$	−17.9211	−	17.9211i	−0.838311	−	0.838311i	0.150325	−	0.988637i	$-0.451968\pi$
$457$	−17.9211	−	17.9211i	−0.838311	−	0.838311i	−0.988637	+	0.150325i	$0.951968\pi$
$458$			1.01158i			0.0472680i
$459$	−7.76999	−	27.4711i	−0.362672	−	1.28224i
$460$	22.1745	+	22.1745i	1.03389	+	1.03389i
$461$	8.77291	−	8.77291i	0.408595	−	0.408595i	−0.472653	−	0.881248i	$-0.656704\pi$
$461$	8.77291	−	8.77291i	0.408595	−	0.408595i	0.881248	+	0.472653i	$0.156704\pi$
$462$	−0.404508	+	2.35765i	−0.0188194	+	0.109688i
$463$	−1.52922	+	1.52922i	−0.0710689	+	0.0710689i	−0.741748	−	0.670679i	$-0.766003\pi$
$463$	−1.52922	+	1.52922i	−0.0710689	+	0.0710689i	0.670679	+	0.741748i	$0.266003\pi$
$464$			2.03314i			0.0943860i
$465$	4.09372	−	2.89470i	0.189842	−	0.134238i
$466$	−11.9326	+	11.9326i	−0.552768	+	0.552768i
$467$	15.8432			0.733136			0.366568	−	0.930391i	$-0.380533\pi$
$467$	15.8432			0.733136			0.366568	+	0.930391i	$0.380533\pi$
$468$	−1.84367	−	10.6584i	−0.0852237	−	0.492683i
$469$	−6.17637			−0.285198
$470$	14.8247	−	14.8247i	0.683811	−	0.683811i
$471$	−4.55959	+	3.22412i	−0.210095	+	0.148560i
$472$			12.4689i			0.573928i
$473$	−10.1455	+	10.1455i	−0.466490	+	0.466490i
$474$	−1.79050	+	10.4358i	−0.0822402	+	0.479331i
$475$	3.39409	−	3.39409i	0.155731	−	0.155731i
$476$	3.88499	+	3.88499i	0.178068	+	0.178068i
$477$	39.4463	+	13.9464i	1.80612	+	0.638560i
$478$			19.5400i			0.893738i
$479$	27.1217	+	27.1217i	1.23922	+	1.23922i	0.960319	+	0.278905i	$0.0899716\pi$
$479$	27.1217	+	27.1217i	1.23922	+	1.23922i	0.278905	+	0.960319i	$0.410028\pi$
$480$	−3.49421	−	4.94156i	−0.159488	−	0.225550i
$481$	−7.66871	−	2.15774i	−0.349663	−	0.0983843i
$482$			9.84001i			0.448200i
$483$	2.62863	−	15.3208i	0.119607	−	0.697119i
$484$	−9.09262			−0.413301
$485$	26.7547			1.21487
$486$	11.7071	−	10.2929i	0.531045	−	0.466895i
$487$	9.05844	+	9.05844i	0.410477	+	0.410477i	0.881905	−	0.471428i	$-0.156261\pi$
$487$	9.05844	+	9.05844i	0.410477	+	0.410477i	−0.471428	+	0.881905i	$0.656261\pi$
$488$	9.28763	+	9.28763i	0.420431	+	0.420431i
$489$	−5.92215	+	34.5168i	−0.267809	+	1.56090i
$490$	3.49421			0.157852
$491$	21.6100			0.975245			0.487623	−	0.873054i	$-0.337864\pi$
$491$	21.6100			0.975245			0.487623	+	0.873054i	$0.337864\pi$
$492$	2.33422	+	0.400488i	0.105235	+	0.0180554i
$493$		−	11.1705i		−	0.503093i
$494$	−1.17422	−	2.09372i	−0.0528308	−	0.0942010i
$495$	−4.82578	+	13.6494i	−0.216903	+	0.613493i
$496$	−0.585786	−	0.585786i	−0.0263026	−	0.0263026i
$497$		−	1.28471i		−	0.0576269i
$498$	−9.18420	−	12.9884i	−0.411554	−	0.582025i
$499$	−22.2779	−	22.2779i	−0.997297	−	0.997297i	0.00269960	−	0.999996i	$-0.499141\pi$
$499$	−22.2779	−	22.2779i	−0.997297	−	0.997297i	−0.999996	+	0.00269960i	$0.999141\pi$
$500$	−5.45920	+	5.45920i	−0.244143	+	0.244143i
$501$	19.8150	+	3.39971i	0.885268	+	0.151888i
$502$	16.0945	−	16.0945i	0.718333	−	0.718333i
$503$			0.485281i			0.0216376i	0.999941	+	0.0108188i	$0.00344380\pi$
$503$			0.485281i			0.0216376i	−0.999941	+	0.0108188i	$0.996556\pi$
$504$	−1.00000	+	2.82843i	−0.0445435	+	0.125988i
$505$	−21.0810	+	21.0810i	−0.938094	+	0.938094i
$506$	−12.3948			−0.551014
$507$	1.50579	+	22.4663i	0.0668745	+	0.997761i
$508$	19.2437			0.853801
$509$	−22.2876	+	22.2876i	−0.987882	+	0.987882i	−0.999927	−	0.0120457i	$-0.996166\pi$
$509$	−22.2876	+	22.2876i	−0.987882	+	0.987882i	0.0120457	+	0.999927i	$0.496166\pi$
$510$	19.1979	+	27.1500i	0.850098	+	1.20222i
$511$		−	15.6073i		−	0.690428i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.68812	−	3.01968i	0.0745321	−	0.133322i
$514$	3.95314	−	3.95314i	0.174365	−	0.174365i
$515$	−29.0471	−	29.0471i	−1.27997	−	1.27997i
$516$	−14.6921	+	10.3889i	−0.646785	+	0.457346i
$517$			8.28647i			0.364438i
$518$	1.56236	+	1.56236i	0.0686460	+	0.0686460i
$519$	−1.53788	+	1.08744i	−0.0675053	+	0.0477335i
$520$	6.16264	+	10.9884i	0.270250	+	0.481874i
$521$			11.5174i			0.504585i	0.967651	+	0.252293i	$0.0811845\pi$
$521$			11.5174i			0.504585i	−0.967651	+	0.252293i	$0.918815\pi$
$522$	5.50392	−	2.62863i	0.240900	−	0.115052i
$523$	−18.5611			−0.811622			−0.405811	−	0.913957i	$-0.633011\pi$
$523$	−18.5611			−0.811622			−0.405811	+	0.913957i	$0.633011\pi$
$524$	−0.778915			−0.0340271
$525$	12.3074	+	2.11162i	0.537139	+	0.0921584i
$526$	−8.91322	−	8.91322i	−0.388635	−	0.388635i
$527$	3.21843	+	3.21843i	0.140197	+	0.140197i
$528$	2.35765	+	0.404508i	0.102603	+	0.0176040i
$529$	57.5452			2.50196
$530$	−48.7315			−2.11676
$531$	33.7547	−	16.1210i	1.46483	−	0.699590i
$532$			0.665783i			0.0288654i
$533$	−4.74578	−	1.33531i	−0.205563	−	0.0578389i
$534$	3.49156	−	2.46891i	0.151095	−	0.106840i
$535$	−2.04686	−	2.04686i	−0.0884935	−	0.0884935i
$536$			6.17637i			0.266779i
$537$	−7.24744	+	5.12471i	−0.312750	+	0.221148i
$538$	2.03314	+	2.03314i	0.0876547	+	0.0876547i
$539$	−0.976570	+	0.976570i	−0.0420638	+	0.0420638i
$540$	−8.85969	+	15.8481i	−0.381260	+	0.681994i
$541$	24.9854	−	24.9854i	1.07421	−	1.07421i	0.0771921	−	0.997016i	$-0.475405\pi$
$541$	24.9854	−	24.9854i	1.07421	−	1.07421i	0.997016	−	0.0771921i	$-0.0245955\pi$
$542$		−	0.715295i		−	0.0307245i
$543$	−14.2895	−	20.2084i	−0.613221	−	0.867226i
$544$	3.88499	−	3.88499i	0.166568	−	0.166568i
$545$	8.04796			0.344737
$546$	2.68368	−	5.63896i	0.114851	−	0.241325i
$547$	−0.0506097			−0.00216391			−0.00108196	−	0.999999i	$-0.500344\pi$
$547$	−0.0506097			−0.00216391			−0.00108196	+	0.999999i	$0.500344\pi$
$548$	4.82655	−	4.82655i	0.206180	−	0.206180i
$549$	13.1347	−	37.1505i	0.560575	−	1.58555i
$550$		−	9.95689i		−	0.424563i
$551$	0.957159	−	0.957159i	0.0407763	−	0.0407763i
$552$	−15.3208	−	2.62863i	−0.652095	−	0.111882i
$553$	−4.32264	+	4.32264i	−0.183817	+	0.183817i
$554$	−5.43097	−	5.43097i	−0.230740	−	0.230740i
$555$	7.72047	+	10.9184i	0.327716	+	0.463460i
$556$		−	2.18315i		−	0.0925863i
$557$	26.0100	+	26.0100i	1.10208	+	1.10208i	0.994160	+	0.107918i	$0.0344185\pi$
$557$	26.0100	+	26.0100i	1.10208	+	1.10208i	0.107918	+	0.994160i	$0.465582\pi$
$558$	−0.828427	+	2.34315i	−0.0350701	+	0.0991933i
$559$	32.6705	−	18.3226i	1.38182	−	0.774965i
$560$		−	3.49421i		−	0.147657i
$561$	−12.9534	−	2.22245i	−0.546893	−	0.0938321i
$562$	−3.91057			−0.164957
$563$	12.5758			0.530007			0.265004	−	0.964247i	$-0.414627\pi$
$563$	12.5758			0.530007			0.265004	+	0.964247i	$0.414627\pi$
$564$	−1.75736	+	10.2426i	−0.0739982	+	0.431293i
$565$	−11.0821	−	11.0821i	−0.466229	−	0.466229i
$566$	22.8042	+	22.8042i	0.958531	+	0.958531i
$567$	8.94975	−	0.949747i	0.375854	−	0.0398856i
$568$	−1.28471			−0.0539050
$569$	−0.972759			−0.0407802			−0.0203901	−	0.999792i	$-0.506491\pi$
$569$	−0.972759			−0.0407802			−0.0203901	+	0.999792i	$0.506491\pi$
$570$	−0.681383	+	3.97139i	−0.0285400	+	0.166343i
$571$		−	18.5790i		−	0.777507i	−0.921342	−	0.388754i	$-0.872906\pi$
$571$		−	18.5790i		−	0.777507i	0.921342	−	0.388754i	$-0.127094\pi$
$572$	−4.79342	−	1.34872i	−0.200423	−	0.0563928i
$573$	−17.6200	−	24.9184i	−0.736085	−	1.04098i
$574$	0.966864	+	0.966864i	0.0403561	+	0.0403561i
$575$			64.7031i			2.69831i
$576$	2.82843	+	1.00000i	0.117851	+	0.0416667i
$577$	−18.8589	−	18.8589i	−0.785107	−	0.785107i	0.195581	−	0.980688i	$-0.437341\pi$
$577$	−18.8589	−	18.8589i	−0.785107	−	0.785107i	−0.980688	+	0.195581i	$0.937341\pi$
$578$	−9.32415	+	9.32415i	−0.387834	+	0.387834i
$579$	6.29843	−	36.7099i	0.261754	−	1.52561i
$580$	−5.02343	+	5.02343i	−0.208587	+	0.208587i
$581$		−	9.18420i		−	0.381025i
$582$	−10.8284	+	7.65685i	−0.448853	+	0.317387i
$583$	13.6196	−	13.6196i	0.564066	−	0.564066i
$584$	−15.6073			−0.645836
$585$	21.7792	−	30.8898i	0.900459	−	1.27714i
$586$	4.51273			0.186419
$587$	24.3800	−	24.3800i	1.00627	−	1.00627i	0.00628924	−	0.999980i	$-0.497998\pi$
$587$	24.3800	−	24.3800i	1.00627	−	1.00627i	0.999980	−	0.00628924i	$-0.00200194\pi$
$588$	−1.41421	+	1.00000i	−0.0583212	+	0.0412393i
$589$			0.551553i			0.0227263i
$590$	−30.8079	+	30.8079i	−1.26834	+	1.26834i
$591$	−4.68519	+	27.3073i	−0.192723	+	1.12327i
$592$	1.56236	−	1.56236i	0.0642124	−	0.0642124i
$593$	−0.273631	−	0.273631i	−0.0112367	−	0.0112367i	0.701466	−	0.712703i	$-0.252529\pi$
$593$	−0.273631	−	0.273631i	−0.0112367	−	0.0112367i	−0.712703	+	0.701466i	$0.752529\pi$
$594$	−1.95314	−	6.90539i	−0.0801383	−	0.283332i
$595$			19.1979i			0.787038i
$596$	10.5020	+	10.5020i	0.430180	+	0.430180i
$597$	13.9394	+	19.7133i	0.570502	+	0.806812i
$598$	31.1492	+	8.76441i	1.27379	+	0.358404i
$599$		−	14.6590i		−	0.598950i	−0.954104	−	0.299475i	$-0.903188\pi$
$599$		−	14.6590i		−	0.598950i	0.954104	−	0.299475i	$-0.0968116\pi$
$600$	2.11162	−	12.3074i	0.0862063	−	0.502447i
$601$	−35.7758			−1.45933			−0.729663	−	0.683807i	$-0.760323\pi$
$601$	−35.7758			−1.45933			−0.729663	+	0.683807i	$0.760323\pi$
$602$	−10.3889			−0.423420
$603$	16.7201	−	7.98539i	0.680895	−	0.325190i
$604$	8.12763	+	8.12763i	0.330709	+	0.330709i
$605$	−22.4659	−	22.4659i	−0.913368	−	0.913368i
$606$	2.49901	−	14.5653i	0.101515	−	0.591674i
$607$	−9.06038			−0.367749			−0.183875	−	0.982950i	$-0.558864\pi$
$607$	−9.06038			−0.367749			−0.183875	+	0.982950i	$0.558864\pi$
$608$	0.665783			0.0270011
$609$	3.47078	+	0.595492i	0.140643	+	0.0241305i
$610$			45.8954i			1.85825i
$611$	5.85942	−	20.8247i	0.237047	−	0.842476i
$612$	−15.5400	−	5.49421i	−0.628166	−	0.222090i
$613$	−19.8823	−	19.8823i	−0.803040	−	0.803040i	0.180529	−	0.983570i	$-0.442219\pi$
$613$	−19.8823	−	19.8823i	−0.803040	−	0.803040i	−0.983570	+	0.180529i	$0.942219\pi$
$614$			10.5747i			0.426761i
$615$	4.77782	+	6.75685i	0.192660	+	0.272463i
$616$	0.976570	+	0.976570i	0.0393471	+	0.0393471i
$617$	10.5728	−	10.5728i	0.425646	−	0.425646i	−0.461496	−	0.887142i	$-0.652687\pi$
$617$	10.5728	−	10.5728i	0.425646	−	0.425646i	0.887142	+	0.461496i	$0.152687\pi$
$618$	20.0692	+	3.44333i	0.807301	+	0.138511i
$619$	13.7555	−	13.7555i	0.552880	−	0.552880i	−0.374391	−	0.927271i	$-0.622148\pi$
$619$	13.7555	−	13.7555i	0.552880	−	0.552880i	0.927271	+	0.374391i	$0.122148\pi$
$620$		−	2.89470i		−	0.116254i
$621$	12.6921	+	44.8735i	0.509318	+	1.80071i
$622$	6.22892	−	6.22892i	0.249757	−	0.249757i
$623$	2.46891			0.0989146
$624$	−5.63896	−	2.68368i	−0.225739	−	0.107433i
$625$	9.07056			0.362823
$626$	−17.4874	+	17.4874i	−0.698938	+	0.698938i
$627$	−0.919498	−	1.30037i	−0.0367212	−	0.0519317i
$628$			3.22412i			0.128656i
$629$	−8.58391	+	8.58391i	−0.342263	+	0.342263i
$630$	−9.45920	+	4.51764i	−0.376864	+	0.179987i
$631$	−8.67334	+	8.67334i	−0.345280	+	0.345280i	−0.858348	−	0.513068i	$-0.828509\pi$
$631$	−8.67334	+	8.67334i	−0.345280	+	0.345280i	0.513068	+	0.858348i	$0.328509\pi$
$632$	4.32264	+	4.32264i	0.171945	+	0.171945i
$633$	−11.4500	+	8.09637i	−0.455097	+	0.321802i
$634$			2.91256i			0.115672i
$635$	47.5469	+	47.5469i	1.88684	+	1.88684i
$636$	19.7231	−	13.9464i	0.782073	−	0.553009i
$637$	3.14475	−	1.76367i	0.124600	−	0.0698793i
$638$		−	2.80792i		−	0.111167i
$639$	1.66099	+	3.47783i	0.0657076	+	0.137581i
$640$	−3.49421			−0.138121
$641$	−15.0449			−0.594237			−0.297118	−	0.954841i	$-0.596026\pi$
$641$	−15.0449			−0.594237			−0.297118	+	0.954841i	$0.596026\pi$
$642$	1.41421	+	0.242641i	0.0558146	+	0.00957626i
$643$	2.63452	+	2.63452i	0.103895	+	0.103895i	0.757144	−	0.653248i	$-0.226594\pi$
$643$	2.63452	+	2.63452i	0.103895	+	0.103895i	−0.653248	+	0.757144i	$0.726594\pi$
$644$	−6.34607	−	6.34607i	−0.250070	−	0.250070i
$645$	−61.9697	−	10.6323i	−2.44006	−	0.418647i
$646$	−3.65795			−0.143920
$647$	9.79315			0.385008			0.192504	−	0.981296i	$-0.438339\pi$
$647$	9.79315			0.385008			0.192504	+	0.981296i	$0.438339\pi$
$648$	−0.949747	−	8.94975i	−0.0373096	−	0.351579i
$649$		−	17.2205i		−	0.675965i
$650$	−7.04058	+	25.0226i	−0.276154	+	0.981467i
$651$	−1.17157	+	0.828427i	−0.0459176	+	0.0324686i
$652$	14.2973	+	14.2973i	0.559927	+	0.559927i
$653$		−	39.9825i		−	1.56464i	−0.622879	−	0.782319i	$-0.714037\pi$
$653$		−	39.9825i		−	1.56464i	0.622879	−	0.782319i	$-0.285963\pi$
$654$	−3.25725	+	2.30323i	−0.127369	+	0.0900633i
$655$	−1.92453	−	1.92453i	−0.0751975	−	0.0751975i
$656$	0.966864	−	0.966864i	0.0377497	−	0.0377497i
$657$	20.1786	+	42.2507i	0.787243	+	1.64836i
$658$	−4.24264	+	4.24264i	−0.165395	+	0.165395i
$659$			12.7294i			0.495867i	0.968777	+	0.247934i	$0.0797515\pi$
$659$			12.7294i			0.495867i	−0.968777	+	0.247934i	$0.920249\pi$
$660$	4.82578	+	6.82468i	0.187843	+	0.265650i
$661$	−23.2601	+	23.2601i	−0.904712	+	0.904712i	−0.995839	−	0.0911276i	$-0.970953\pi$
$661$	−23.2601	+	23.2601i	−0.904712	+	0.904712i	0.0911276	+	0.995839i	$0.470953\pi$
$662$	−3.50794			−0.136340
$663$	30.9816	+	14.7447i	1.20323	+	0.572636i
$664$	−9.18420			−0.356416
$665$	−1.64500	+	1.64500i	−0.0637905	+	0.0637905i
$666$	−6.24942	−	2.20950i	−0.242160	−	0.0856166i
$667$			18.2468i			0.706518i
$668$	8.20763	−	8.20763i	0.317563	−	0.317563i
$669$	20.5920	+	3.53303i	0.796133	+	0.136595i
$670$	−15.2604	+	15.2604i	−0.589563	+	0.589563i
$671$	−12.8269	−	12.8269i	−0.495178	−	0.495178i
$672$	1.00000	+	1.41421i	0.0385758	+	0.0545545i
$673$			49.5336i			1.90938i	0.297604	+	0.954689i	$0.403813\pi$
$673$			49.5336i			1.90938i	−0.297604	+	0.954689i	$0.596187\pi$
$674$	3.39558	+	3.39558i	0.130793	+	0.130793i
$675$	−36.0475	+	10.1958i	−1.38747	+	0.392436i
$676$	11.0926	+	6.77892i	0.426639	+	0.260728i
$677$		−	40.2984i		−	1.54879i	−0.632701	−	0.774396i	$-0.718054\pi$
$677$		−	40.2984i		−	1.54879i	0.632701	−	0.774396i	$-0.281946\pi$
$678$	7.65685	+	1.31371i	0.294060	+	0.0504527i
$679$	−7.65685			−0.293843
$680$	19.1979			0.736207
$681$	6.99322	−	40.7595i	0.267981	−	1.56191i
$682$	0.809017	+	0.809017i	0.0309788	+	0.0309788i
$683$	−23.5944	−	23.5944i	−0.902814	−	0.902814i	0.0928644	−	0.995679i	$-0.470398\pi$
$683$	−23.5944	−	23.5944i	−0.902814	−	0.902814i	−0.995679	+	0.0928644i	$0.970398\pi$
$684$	−0.860786	−	1.80235i	−0.0329130	−	0.0689144i
$685$	23.8507			0.911288
$686$	−1.00000			−0.0381802
$687$	0.296285	−	1.72687i	0.0113040	−	0.0658844i
$688$			10.3889i			0.396073i
$689$	−43.8578	+	24.5968i	−1.67085	+	0.937064i
$690$	−31.3595	−	44.3490i	−1.19383	−	1.68834i
$691$	−29.6768	−	29.6768i	−1.12896	−	1.12896i	−0.990347	−	0.138612i	$-0.955736\pi$
$691$	−29.6768	−	29.6768i	−1.12896	−	1.12896i	−0.138612	−	0.990347i	$-0.544264\pi$
$692$			1.08744i			0.0413384i
$693$	1.38108	−	3.90628i	0.0524628	−	0.148387i
$694$	−10.3558	−	10.3558i	−0.393100	−	0.393100i
$695$	5.39409	−	5.39409i	0.204609	−	0.204609i
$696$	0.595492	−	3.47078i	0.0225721	−	0.131560i
$697$	−5.31216	+	5.31216i	−0.201212	+	0.201212i
$698$			7.37843i			0.279278i
$699$	23.8653	−	16.8753i	0.902667	−	0.638282i
$700$	5.09789	−	5.09789i	0.192682	−	0.192682i
$701$	−6.49261			−0.245222			−0.122611	−	0.992455i	$-0.539127\pi$
$701$	−6.49261			−0.245222			−0.122611	+	0.992455i	$0.539127\pi$
$702$	0.0255762	+	18.7350i	0.000965310	+	0.707106i
$703$	−1.47105			−0.0554817
$704$	0.976570	−	0.976570i	0.0368058	−	0.0368058i
$705$	−29.6494	+	20.9653i	−1.11666	+	0.789597i
$706$		−	11.5079i		−	0.433107i
$707$	6.03314	−	6.03314i	0.226899	−	0.226899i
$708$	3.65206	−	21.2858i	0.137253	−	0.799968i
$709$	32.3795	−	32.3795i	1.21604	−	1.21604i	0.247028	−	0.969008i	$-0.420546\pi$
$709$	32.3795	−	32.3795i	1.21604	−	1.21604i	0.969008	−	0.247028i	$-0.0794541\pi$
$710$	−3.17422	−	3.17422i	−0.119126	−	0.119126i
$711$	6.11313	−	17.2905i	0.229260	−	0.648446i
$712$		−	2.46891i		−	0.0925261i
$713$	−5.25725	−	5.25725i	−0.196886	−	0.196886i
$714$	−5.49421	−	7.76999i	−0.205616	−	0.290784i
$715$	−8.51109	−	15.1759i	−0.318297	−	0.567545i
$716$			5.12471i			0.191519i
$717$	5.72313	−	33.3568i	0.213734	−	1.24573i
$718$	19.0353			0.710390
$719$	36.7955			1.37224			0.686119	−	0.727489i	$-0.259313\pi$
$719$	36.7955			1.37224			0.686119	+	0.727489i	$0.259313\pi$
$720$	4.51764	+	9.45920i	0.168363	+	0.352524i
$721$	8.31293	+	8.31293i	0.309590	+	0.309590i
$722$	13.1216	+	13.1216i	0.488335	+	0.488335i
$723$	2.88207	−	16.7979i	0.107185	−	0.624722i
$724$	−14.2895			−0.531065
$725$	−14.6579			−0.544381
$726$	15.5221	+	2.66317i	0.576078	+	0.0988394i
$727$			26.1269i			0.968992i	0.874794	+	0.484496i	$0.160997\pi$
$727$			26.1269i			0.968992i	−0.874794	+	0.484496i	$0.839003\pi$
$728$	−1.76367	−	3.14475i	−0.0653661	−	0.116552i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$	−38.5623	−	38.5623i	−1.42725	−	1.42725i
$731$		−	57.0788i		−	2.11114i
$732$	−13.1347	−	18.5753i	−0.485472	−	0.686561i
$733$	−27.3747	−	27.3747i	−1.01111	−	1.01111i	−0.999938	−	0.0111692i	$-0.996445\pi$
$733$	−27.3747	−	27.3747i	−1.01111	−	1.01111i	−0.0111692	−	0.999938i	$-0.503555\pi$
$734$	19.8853	−	19.8853i	0.733979	−	0.733979i
$735$	−5.96499	−	1.02343i	−0.220022	−	0.0377498i
$736$	−6.34607	+	6.34607i	−0.233919	+	0.233919i
$737$		−	8.53005i		−	0.314208i
$738$	−3.86746	−	1.36735i	−0.142363	−	0.0503329i
$739$	21.0363	−	21.0363i	0.773834	−	0.773834i	−0.204941	−	0.978774i	$-0.565700\pi$
$739$	21.0363	−	21.0363i	0.773834	−	0.773834i	0.978774	+	0.204941i	$0.0657001\pi$
$740$	7.72047			0.283810
$741$	1.39129	+	3.91813i	0.0511102	+	0.143936i
$742$	13.9464			0.511987
$743$	−11.0752	+	11.0752i	−0.406310	+	0.406310i	−0.880450	−	0.474140i	$-0.842759\pi$
$743$	−11.0752	+	11.0752i	−0.406310	+	0.406310i	0.474140	+	0.880450i	$0.342759\pi$
$744$	0.828427	+	1.17157i	0.0303716	+	0.0429519i
$745$			51.8965i			1.90134i
$746$	0.908424	−	0.908424i	0.0332598	−	0.0332598i
$747$	11.8742	+	24.8626i	0.434454	+	0.909675i
$748$	−5.36548	+	5.36548i	−0.196181	+	0.196181i
$749$	0.585786	+	0.585786i	0.0214042	+	0.0214042i
$750$	10.9184	−	7.72047i	0.398684	−	0.281912i
$751$		−	14.5694i		−	0.531645i	−0.964022	−	0.265823i	$-0.914356\pi$
$751$		−	14.5694i		−	0.531645i	0.964022	−	0.265823i	$-0.0856436\pi$
$752$	4.24264	+	4.24264i	0.154713	+	0.154713i
$753$	−32.1890	+	22.7611i	−1.17303	+	0.829459i
$754$	−1.98550	+	7.05657i	−0.0723076	+	0.256985i
$755$			40.1632i			1.46169i
$756$	2.53553	−	4.53553i	0.0922165	−	0.164956i
$757$	21.8653			0.794706			0.397353	−	0.917666i	$-0.369929\pi$
$757$	21.8653			0.794706			0.397353	+	0.917666i	$0.369929\pi$
$758$	−10.6579			−0.387112
$759$	21.1592	+	3.63034i	0.768029	+	0.131773i
$760$	1.64500	+	1.64500i	0.0596705	+	0.0596705i
$761$	−10.1083	−	10.1083i	−0.366427	−	0.366427i	0.499745	−	0.866172i	$-0.333427\pi$
$761$	−10.1083	−	10.1083i	−0.366427	−	0.366427i	−0.866172	+	0.499745i	$0.833427\pi$
$762$	−32.8510	−	5.63635i	−1.19007	−	0.204183i
$763$	−2.30323			−0.0833824
$764$	−17.6200			−0.637468
$765$	−24.8209	−	51.9708i	−0.897400	−	1.87901i
$766$			3.35363i			0.121171i
$767$	−12.1768	+	43.2768i	−0.439677	+	1.56264i
$768$	1.41421	−	1.00000i	0.0510310	−	0.0360844i
$769$	−15.6851	−	15.6851i	−0.565618	−	0.565618i	0.365279	−	0.930898i	$-0.380973\pi$
$769$	−15.6851	−	15.6851i	−0.565618	−	0.565618i	−0.930898	+	0.365279i	$0.880973\pi$
$770$			4.82578i			0.173909i
$771$	−7.90628	+	5.59058i	−0.284738	+	0.201340i
$772$	−15.2058	−	15.2058i	−0.547267	−	0.547267i
$773$	−20.2229	+	20.2229i	−0.727367	+	0.727367i	−0.970095	−	0.242727i	$-0.921958\pi$
$773$	−20.2229	+	20.2229i	−0.727367	+	0.727367i	0.242727	+	0.970095i	$0.421958\pi$
$774$	28.1239	−	13.4317i	1.01089	−	0.482794i
$775$	4.22323	−	4.22323i	0.151703	−	0.151703i
$776$			7.65685i			0.274865i
$777$	−2.20950	−	3.12471i	−0.0792656	−	0.112098i
$778$	−13.4484	+	13.4484i	−0.482148	+	0.482148i
$779$	−0.910360			−0.0326170
$780$	−7.30186	−	20.5634i	−0.261448	−	0.736288i
$781$	1.77428			0.0634887
$782$	34.8666	−	34.8666i	1.24683	−	1.24683i
$783$	−10.1657	+	2.87529i	−0.363292	+	0.102754i
$784$			1.00000i			0.0357143i
$785$	−7.96609	+	7.96609i	−0.284322	+	0.284322i
$786$	1.32969	+	0.228139i	0.0474285	+	0.00813745i
$787$	16.0851	−	16.0851i	0.573371	−	0.573371i	−0.359698	−	0.933069i	$-0.617120\pi$
$787$	16.0851	−	16.0851i	0.573371	−	0.573371i	0.933069	+	0.359698i	$0.117120\pi$
$788$	11.3111	+	11.3111i	0.402940	+	0.402940i
$789$	12.6052	+	17.8264i	0.448757	+	0.634638i
$790$			21.3606i			0.759975i
$791$	3.17157	+	3.17157i	0.112768	+	0.112768i
$792$	−3.90628	−	1.38108i	−0.138804	−	0.0490745i
$793$	23.1653	+	41.3053i	0.822624	+	1.46680i
$794$		−	29.1500i		−	1.03449i
$795$	83.1899	+	14.2731i	2.95044	+	0.506216i
$796$	13.9394			0.494069
$797$	−12.5984			−0.446259			−0.223129	−	0.974789i	$-0.571627\pi$
$797$	−12.5984			−0.446259			−0.223129	+	0.974789i	$0.571627\pi$
$798$	0.195003	−	1.13656i	0.00690304	−	0.0402339i
$799$	−23.3100	−	23.3100i	−0.824647	−	0.824647i
$800$	−5.09789	−	5.09789i	−0.180238	−	0.180238i
$801$	−6.68359	+	3.19203i	−0.236153	+	0.112785i
$802$	37.4327			1.32179
$803$	21.5550			0.760658
$804$	1.80902	−	10.5437i	0.0637991	−	0.371848i
$805$		−	31.3595i		−	1.10528i
$806$	−1.46107	−	2.60520i	−0.0514642	−	0.0917641i
$807$	−2.87529	−	4.06627i	−0.101215	−	0.143140i
$808$	−6.03314	−	6.03314i	−0.212245	−	0.212245i
$809$		−	49.7721i		−	1.74989i	−0.484219	−	0.874947i	$-0.660896\pi$
$809$		−	49.7721i		−	1.74989i	0.484219	−	0.874947i	$-0.339104\pi$
$810$	19.7662	−	24.4595i	0.694515	−	0.859418i
$811$	−11.7129	−	11.7129i	−0.411296	−	0.411296i	0.470894	−	0.882190i	$-0.343931\pi$
$811$	−11.7129	−	11.7129i	−0.411296	−	0.411296i	−0.882190	+	0.470894i	$0.843931\pi$
$812$	1.43764	−	1.43764i	0.0504514	−	0.0504514i
$813$	−0.209505	+	1.22108i	−0.00734766	+	0.0428253i
$814$	−2.15774	+	2.15774i	−0.0756286	+	0.0756286i
$815$			70.6511i			2.47480i
$816$	−7.76999	+	5.49421i	−0.272004	+	0.192336i
$817$	4.89089	−	4.89089i	0.171111	−	0.171111i
$818$	28.2854			0.988975
$819$	−6.23294	+	8.84028i	−0.217796	+	0.308904i
$820$	4.77782			0.166849
$821$	−12.3789	+	12.3789i	−0.432028	+	0.432028i	−0.889318	−	0.457290i	$-0.848820\pi$
$821$	−12.3789	+	12.3789i	−0.432028	+	0.432028i	0.457290	+	0.889318i	$0.348820\pi$
$822$	−9.65311	+	6.82578i	−0.336691	+	0.238076i
$823$			45.0293i			1.56962i	0.619734	+	0.784812i	$0.287241\pi$
$823$			45.0293i			1.56962i	−0.619734	+	0.784812i	$0.712759\pi$
$824$	8.31293	−	8.31293i	0.289595	−	0.289595i
$825$	−2.91630	+	16.9975i	−0.101533	+	0.591776i
$826$	8.81685	−	8.81685i	0.306777	−	0.306777i
$827$	39.0724	+	39.0724i	1.35868	+	1.35868i	0.875547	+	0.483133i	$0.160501\pi$
$827$	39.0724	+	39.0724i	1.35868	+	1.35868i	0.483133	+	0.875547i	$0.339499\pi$
$828$	25.3843	+	8.97470i	0.882164	+	0.311892i
$829$		−	36.4537i		−	1.26609i	−0.774115	−	0.633045i	$-0.781805\pi$
$829$		−	36.4537i		−	1.26609i	0.774115	−	0.633045i	$-0.218195\pi$
$830$	−22.6921	−	22.6921i	−0.787656	−	0.787656i
$831$	7.68056	+	10.8619i	0.266436	+	0.376797i
$832$	−3.14475	+	1.76367i	−0.109025	+	0.0611444i
$833$		−	5.49421i		−	0.190363i
$834$	−0.639431	+	3.72687i	−0.0221417	+	0.129051i
$835$	40.5585			1.40358
$836$	−0.919498			−0.0318015
$837$	2.10051	−	3.75736i	0.0726041	−	0.129873i
$838$	6.97657	+	6.97657i	0.241002	+	0.241002i
$839$	−26.3654	−	26.3654i	−0.910234	−	0.910234i	0.0860567	−	0.996290i	$-0.472573\pi$
$839$	−26.3654	−	26.3654i	−0.910234	−	0.910234i	−0.996290	+	0.0860567i	$0.972573\pi$
$840$	−1.02343	+	5.96499i	−0.0353117	+	0.205812i
$841$	24.8664			0.857461
$842$	24.7158			0.851764
$843$	6.67576	+	1.14538i	0.229925	+	0.0394490i
$844$			8.09637i			0.278689i
$845$	10.6582	+	44.1566i	0.366654	+	1.51903i
$846$	6.00000	−	16.9706i	0.206284	−	0.583460i
$847$	6.42946	+	6.42946i	0.220919	+	0.220919i
$848$		−	13.9464i		−	0.478920i
$849$	−32.2500	−	45.6083i	−1.10682	−	1.56527i
$850$	28.0089	+	28.0089i	0.960697	+	0.960697i
$851$	14.0217	−	14.0217i	0.480657	−	0.480657i
$852$	2.19313	+	0.376281i	0.0751354	+	0.0128912i
$853$	−19.6599	+	19.6599i	−0.673142	+	0.673142i	−0.958439	−	0.285297i	$-0.907908\pi$
$853$	−19.6599	+	19.6599i	−0.673142	+	0.673142i	0.285297	+	0.958439i	$0.407908\pi$
$854$		−	13.1347i		−	0.449460i
$855$	2.32639	−	6.58001i	0.0795607	−	0.225032i
$856$	0.585786	−	0.585786i	0.0200218	−	0.0200218i
$857$	46.4642			1.58719			0.793594	−	0.608448i	$-0.208208\pi$
$857$	46.4642			1.58719			0.793594	+	0.608448i	$0.208208\pi$
$858$	7.78784	+	3.70637i	0.265873	+	0.126533i
$859$	−4.98788			−0.170184			−0.0850921	−	0.996373i	$-0.527118\pi$
$859$	−4.98788			−0.170184			−0.0850921	+	0.996373i	$0.527118\pi$
$860$	−25.6687	+	25.6687i	−0.875296	+	0.875296i
$861$	−1.36735	−	1.93373i	−0.0465993	−	0.0659013i
$862$		−	33.3137i		−	1.13467i
$863$	17.3237	−	17.3237i	0.589705	−	0.589705i	−0.347846	−	0.937552i	$-0.613087\pi$
$863$	17.3237	−	17.3237i	0.589705	−	0.589705i	0.937552	+	0.347846i	$0.113087\pi$
$864$	−4.53553	−	2.53553i	−0.154302	−	0.0862606i
$865$	−2.68683	+	2.68683i	−0.0913551	+	0.0913551i
$866$	9.89949	+	9.89949i	0.336399	+	0.336399i
$867$	18.6483	−	13.1863i	0.633330	−	0.447832i
$868$			0.828427i			0.0281186i
$869$	−5.96990	−	5.96990i	−0.202515	−	0.202515i
$870$	10.0469	−	7.10420i	0.340620	−	0.240855i
$871$	−6.03165	+	21.4368i	−0.204375	+	0.726359i
$872$			2.30323i			0.0779971i
$873$	20.7279	−	9.89949i	0.701534	−	0.335047i
$874$	5.97520			0.202114
$875$	7.72047			0.261000
$876$	26.6434	+	4.57128i	0.900197	+	0.154449i
$877$	−21.2736	−	21.2736i	−0.718359	−	0.718359i	0.249910	−	0.968269i	$-0.419599\pi$
$877$	−21.2736	−	21.2736i	−0.718359	−	0.718359i	−0.968269	+	0.249910i	$0.919599\pi$
$878$	−2.39706	−	2.39706i	−0.0808969	−	0.0808969i
$879$	−7.70372	−	1.32175i	−0.259840	−	0.0445815i
$880$	4.82578			0.162677
$881$	−48.7163			−1.64129			−0.820647	−	0.571436i	$-0.806387\pi$
$881$	−48.7163			−1.64129			−0.820647	+	0.571436i	$0.806387\pi$
$882$	2.70711	−	1.29289i	0.0911530	−	0.0435340i
$883$			13.5195i			0.454966i	0.973782	+	0.227483i	$0.0730496\pi$
$883$			13.5195i			0.454966i	−0.973782	+	0.227483i	$0.926950\pi$
$884$	17.2779	−	9.68999i	0.581119	−	0.325910i
$885$	61.6158	−	43.5690i	2.07119	−	1.46456i
$886$	−9.39105	−	9.39105i	−0.315499	−	0.315499i
$887$			55.2689i			1.85575i	0.372892	+	0.927875i	$0.378366\pi$
$887$			55.2689i			1.85575i	−0.372892	+	0.927875i	$0.621634\pi$
$888$	−3.12471	+	2.20950i	−0.104858	+	0.0741461i
$889$	−13.6073	−	13.6073i	−0.456376	−	0.456376i
$890$	6.10012	−	6.10012i	0.204477	−	0.204477i
$891$	1.31168	+	12.3603i	0.0439428	+	0.414086i
$892$	8.52949	−	8.52949i	0.285589	−	0.285589i
$893$		−	3.99470i		−	0.133677i
$894$	−14.8521	−	21.0041i	−0.496729	−	0.702482i
$895$	−12.6620	+	12.6620i	−0.423245	+	0.423245i
$896$	1.00000			0.0334077
$897$	−50.6080	−	24.0852i	−1.68975	−	0.804181i
$898$	8.19616			0.273510
$899$	1.19098	−	1.19098i	0.0397215	−	0.0397215i
$900$	−7.20950	+	20.3916i	−0.240317	+	0.679719i
$901$			76.6242i			2.55272i
$902$	−1.33531	+	1.33531i	−0.0444611	+	0.0444611i
$903$	17.7350	+	3.04284i	0.590183	+	0.101259i
$904$	3.17157	−	3.17157i	0.105485	−	0.105485i
$905$	−35.3062	−	35.3062i	−1.17362	−	1.17362i
$906$	−11.4942	−	16.2553i	−0.381870	−	0.540045i
$907$			38.8537i			1.29012i	0.764134	+	0.645058i	$0.223167\pi$
$907$			38.8537i			1.29012i	−0.764134	+	0.645058i	$0.776833\pi$
$908$	−16.8831	−	16.8831i	−0.560286	−	0.560286i
$909$	−8.53214	+	24.1325i	−0.282993	+	0.800426i
$910$	3.41234	−	12.1276i	0.113118	−	0.402027i
$911$			3.45038i			0.114316i	0.998365	+	0.0571582i	$0.0182039\pi$
$911$			3.45038i			0.114316i	−0.998365	+	0.0571582i	$0.981796\pi$
$912$	−1.13656	−	0.195003i	−0.0376354	−	0.00645721i
$913$	12.6841			0.419782
$914$	25.3442			0.838311
$915$	13.4424	−	78.3483i	0.444393	−	2.59011i
$916$	−0.715295	−	0.715295i	−0.0236340	−	0.0236340i
$917$	0.550776	+	0.550776i	0.0181882	+	0.0181882i
$918$	24.9192	+	13.9308i	0.822455	+	0.459783i
$919$	4.34744			0.143409			0.0717044	−	0.997426i	$-0.477156\pi$
$919$	4.34744			0.143409			0.0717044	+	0.997426i	$0.477156\pi$
$920$	−31.3595			−1.03389
$921$	3.09726	−	18.0522i	0.102058	−	0.594839i
$922$			12.4068i			0.408595i
$923$	−4.45893	−	1.25460i	−0.146767	−	0.0412958i
$924$	−1.38108	−	1.95314i	−0.0454341	−	0.0642536i
$925$	11.2638	+	11.2638i	0.370352	+	0.370352i
$926$		−	2.16264i		−	0.0710689i
$927$	−33.2517	−	11.7563i	−1.09213	−	0.386126i
$928$	−1.43764	−	1.43764i	−0.0471930	−	0.0471930i
$929$	−30.9194	+	30.9194i	−1.01443	+	1.01443i	−0.0145399	+	0.999894i	$0.504628\pi$
$929$	−30.9194	+	30.9194i	−1.01443	+	1.01443i	−0.999894	+	0.0145399i	$0.995372\pi$
$930$	−0.847838	+	4.94156i	−0.0278017	+	0.162040i
$931$	0.470780	−	0.470780i	0.0154292	−	0.0154292i
$932$		−	16.8753i		−	0.552768i
$933$	−12.4578	+	8.80902i	−0.407851	+	0.288394i
$934$	−11.2028	+	11.2028i	−0.366568	+	0.366568i
$935$	−26.5138			−0.867095
$936$	8.84028	+	6.23294i	0.288954	+	0.203730i
$937$	22.8867			0.747675			0.373837	−	0.927494i	$-0.378042\pi$
$937$	22.8867			0.747675			0.373837	+	0.927494i	$0.378042\pi$
$938$	4.36735	−	4.36735i	0.142599	−	0.142599i
$939$	34.9749	−	24.7310i	1.14136	−	0.807064i
$940$			20.9653i			0.683811i
$941$	−0.532142	+	0.532142i	−0.0173473	+	0.0173473i	−0.715727	−	0.698380i	$-0.753905\pi$
$941$	−0.532142	+	0.532142i	−0.0173473	+	0.0173473i	0.698380	+	0.715727i	$0.253905\pi$
$942$	0.944323	−	5.50392i	0.0307677	−	0.179327i
$943$	8.67731	−	8.67731i	0.282572	−	0.282572i
$944$	−8.81685	−	8.81685i	−0.286964	−	0.286964i
$945$	17.4711	−	4.94156i	0.568333	−	0.160749i
$946$		−	14.3479i		−	0.466490i
$947$	−16.5909	−	16.5909i	−0.539130	−	0.539130i	0.384143	−	0.923274i	$-0.374497\pi$
$947$	−16.5909	−	16.5909i	−0.539130	−	0.539130i	−0.923274	+	0.384143i	$0.874497\pi$
$948$	−6.11313	−	8.64527i	−0.198545	−	0.280785i
$949$	−54.1696	−	15.2417i	−1.75842	−	0.494765i
$950$			4.79997i			0.155731i
$951$	0.853068	−	4.97204i	0.0276626	−	0.161230i
$952$	−5.49421			−0.178068
$953$	33.1817			1.07486			0.537430	−	0.843308i	$-0.319395\pi$
$953$	33.1817			1.07486			0.537430	+	0.843308i	$0.319395\pi$
$954$	−37.7543	+	18.0311i	−1.22234	+	0.583780i
$955$	−43.5351	−	43.5351i	−1.40876	−	1.40876i
$956$	−13.8168	−	13.8168i	−0.446869	−	0.446869i
$957$	−0.822420	+	4.79342i	−0.0265851	+	0.154949i
$958$	−38.3559			−1.23922
$959$	−6.82578			−0.220416
$960$	5.96499	+	1.02343i	0.192519	+	0.0330311i
$961$		−	30.3137i		−	0.977862i
$962$	6.94834	−	3.89684i	0.224024	−	0.125639i
$963$	−2.34315	−	0.828427i	−0.0755068	−	0.0266957i
$964$	−6.95794	−	6.95794i	−0.224100	−	0.224100i
$965$		−	75.1401i		−	2.41885i
$966$	8.97470	+	12.6921i	0.288756	+	0.408363i
$967$	−8.88979	−	8.88979i	−0.285876	−	0.285876i	0.549571	−	0.835447i	$-0.314791\pi$
$967$	−8.88979	−	8.88979i	−0.285876	−	0.285876i	−0.835447	+	0.549571i	$0.814791\pi$
$968$	6.42946	−	6.42946i	0.206651	−	0.206651i
$969$	6.24452	+	1.07139i	0.200603	+	0.0344180i
$970$	−18.9184	+	18.9184i	−0.607433	+	0.607433i
$971$			25.1915i			0.808435i	0.914663	+	0.404217i	$0.132456\pi$
$971$			25.1915i			0.808435i	−0.914663	+	0.404217i	$0.867544\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$	−1.54372	+	1.54372i	−0.0494895	+	0.0494895i
$974$	−12.8106			−0.410477
$975$	19.3480	−	40.6541i	0.619631	−	1.30197i
$976$	−13.1347			−0.420431
$977$	27.5046	−	27.5046i	0.879949	−	0.879949i	−0.113579	−	0.993529i	$-0.536232\pi$
$977$	27.5046	−	27.5046i	0.879949	−	0.879949i	0.993529	+	0.113579i	$0.0362317\pi$
$978$	−20.2195	−	28.5947i	−0.646548	−	0.914357i
$979$			3.40975i			0.108976i
$980$	−2.47078	+	2.47078i	−0.0789262	+	0.0789262i
$981$	6.23508	−	2.97783i	0.199071	−	0.0950747i
$982$	−15.2806	+	15.2806i	−0.487623	+	0.487623i
$983$	−2.11820	−	2.11820i	−0.0675601	−	0.0675601i	0.672519	−	0.740079i	$-0.265212\pi$
$983$	−2.11820	−	2.11820i	−0.0675601	−	0.0675601i	−0.740079	+	0.672519i	$0.765212\pi$
$984$	−1.93373	+	1.36735i	−0.0616450	+	0.0435896i
$985$			55.8943i			1.78094i
$986$	7.89872	+	7.89872i	0.251546	+	0.251546i
$987$	8.48528	−	6.00000i	0.270089	−	0.190982i
$988$	2.31079	+	0.650183i	0.0735159	+	0.0206851i
$989$			93.2373i			2.96477i
$990$	−6.23921	−	13.0639i	−0.198295	−	0.415198i
$991$	38.9900			1.23856			0.619279	−	0.785171i	$-0.287425\pi$
$991$	38.9900			1.23856			0.619279	+	0.785171i	$0.287425\pi$
$992$	0.828427			0.0263026
$993$	5.98842	+	1.02745i	0.190037	+	0.0326052i
$994$	0.908424	+	0.908424i	0.0288135	+	0.0288135i
$995$	34.4412	+	34.4412i	1.09186	+	1.09186i
$996$	15.6784	+	2.68999i	0.496789	+	0.0852356i
$997$	−40.2114			−1.27351			−0.636755	−	0.771067i	$-0.719724\pi$
$997$	−40.2114			−1.27351			−0.636755	+	0.771067i	$0.719724\pi$
$998$	31.5057			0.997297
$999$	10.0213	+	5.60227i	0.317059	+	0.177248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.a.281.2	yes	8
3.2	odd	2		546.2.p.b.281.3	yes	8
13.5	odd	4		546.2.p.b.239.3	yes	8
39.5	even	4	inner	546.2.p.a.239.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.a.239.2	✓	8	39.5	even	4	inner
546.2.p.a.281.2	yes	8	1.1	even	1	trivial
546.2.p.b.239.3	yes	8	13.5	odd	4
546.2.p.b.281.3	yes	8	3.2	odd	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(2.47078 - 2.47078i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000i q^{4} +(2.47078 - 2.47078i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.82843i) q^{9} +3.49421i q^{10} +(-0.976570 - 0.976570i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(1.76367 + 3.14475i) q^{13} -1.00000i q^{14} +(1.02343 - 5.96499i) q^{15} -1.00000 q^{16} +5.49421 q^{17} +(1.29289 + 2.70711i) q^{18} +(0.470780 + 0.470780i) q^{19} +(-2.47078 - 2.47078i) q^{20} +(-0.292893 + 1.70711i) q^{21} +1.38108 q^{22} -8.97470 q^{23} +(1.70711 + 0.292893i) q^{24} -7.20950i q^{25} +(-3.47078 - 0.976570i) q^{26} +(-1.41421 - 5.00000i) q^{27} +(0.707107 + 0.707107i) q^{28} -2.03314i q^{29} +(3.49421 + 4.94156i) q^{30} +(0.585786 + 0.585786i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.35765 - 0.404508i) q^{33} +(-3.88499 + 3.88499i) q^{34} +3.49421i q^{35} +(-2.82843 - 1.00000i) q^{36} +(-1.56236 + 1.56236i) q^{37} -0.665783 q^{38} +(5.63896 + 2.68368i) q^{39} +3.49421 q^{40} +(-0.966864 + 0.966864i) q^{41} +(-1.00000 - 1.41421i) q^{42} -10.3889i q^{43} +(-0.976570 + 0.976570i) q^{44} +(-4.51764 - 9.45920i) q^{45} +(6.34607 - 6.34607i) q^{46} +(-4.24264 - 4.24264i) q^{47} +(-1.41421 + 1.00000i) q^{48} -1.00000i q^{49} +(5.09789 + 5.09789i) q^{50} +(7.76999 - 5.49421i) q^{51} +(3.14475 - 1.76367i) q^{52} +13.9464i q^{53} +(4.53553 + 2.53553i) q^{54} -4.82578 q^{55} -1.00000 q^{56} +(1.13656 + 0.195003i) q^{57} +(1.43764 + 1.43764i) q^{58} +(8.81685 + 8.81685i) q^{59} +(-5.96499 - 1.02343i) q^{60} +13.1347 q^{61} -0.828427 q^{62} +(1.29289 + 2.70711i) q^{63} +1.00000i q^{64} +(12.1276 + 3.41234i) q^{65} +(1.95314 - 1.38108i) q^{66} +(4.36735 + 4.36735i) q^{67} -5.49421i q^{68} +(-12.6921 + 8.97470i) q^{69} +(-2.47078 - 2.47078i) q^{70} +(-0.908424 + 0.908424i) q^{71} +(2.70711 - 1.29289i) q^{72} +(-11.0361 + 11.0361i) q^{73} -2.20950i q^{74} +(-7.20950 - 10.1958i) q^{75} +(0.470780 - 0.470780i) q^{76} +1.38108 q^{77} +(-5.88499 + 2.08970i) q^{78} +6.11313 q^{79} +(-2.47078 + 2.47078i) q^{80} +(-7.00000 - 5.65685i) q^{81} -1.36735i q^{82} +(-6.49421 + 6.49421i) q^{83} +(1.70711 + 0.292893i) q^{84} +(13.5750 - 13.5750i) q^{85} +(7.34607 + 7.34607i) q^{86} +(-2.03314 - 2.87529i) q^{87} -1.38108i q^{88} +(-1.74578 - 1.74578i) q^{89} +(9.88312 + 3.49421i) q^{90} +(-3.47078 - 0.976570i) q^{91} +8.97470i q^{92} +(1.41421 + 0.242641i) q^{93} +6.00000 q^{94} +2.32639 q^{95} +(0.292893 - 1.70711i) q^{96} +(5.41421 + 5.41421i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-3.73873 + 1.78559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{6} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^6 + 8 * q^9	\( 8 q - 4 q^{5} - 8 q^{6} + 8 q^{9} - 8 q^{11} - 8 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 20 q^{17} + 16 q^{18} - 20 q^{19} + 4 q^{20} - 8 q^{21} + 12 q^{22} - 12 q^{23} + 8 q^{24} - 4 q^{26} + 4 q^{30} + 16 q^{31} - 20 q^{33} + 4 q^{34} - 24 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{40} - 20 q^{41} - 8 q^{42} - 8 q^{44} - 12 q^{45} + 4 q^{46} + 24 q^{50} - 8 q^{51} + 8 q^{52} + 8 q^{54} - 12 q^{55} - 8 q^{56} - 16 q^{57} + 20 q^{61} + 16 q^{62} + 16 q^{63} + 28 q^{65} + 16 q^{66} + 24 q^{67} - 8 q^{69} + 4 q^{70} + 28 q^{71} + 16 q^{72} + 16 q^{73} - 36 q^{75} - 20 q^{76} + 12 q^{77} - 12 q^{78} + 24 q^{79} + 4 q^{80} - 56 q^{81} - 28 q^{83} + 8 q^{84} + 16 q^{85} + 12 q^{86} - 4 q^{87} - 16 q^{90} - 4 q^{91} + 48 q^{94} + 92 q^{95} + 8 q^{96} + 32 q^{97} - 32 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^6 + 8 * q^9 - 8 * q^11 - 8 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 20 * q^17 + 16 * q^18 - 20 * q^19 + 4 * q^20 - 8 * q^21 + 12 * q^22 - 12 * q^23 + 8 * q^24 - 4 * q^26 + 4 * q^30 + 16 * q^31 - 20 * q^33 + 4 * q^34 - 24 * q^37 - 4 * q^38 + 4 * q^39 + 4 * q^40 - 20 * q^41 - 8 * q^42 - 8 * q^44 - 12 * q^45 + 4 * q^46 + 24 * q^50 - 8 * q^51 + 8 * q^52 + 8 * q^54 - 12 * q^55 - 8 * q^56 - 16 * q^57 + 20 * q^61 + 16 * q^62 + 16 * q^63 + 28 * q^65 + 16 * q^66 + 24 * q^67 - 8 * q^69 + 4 * q^70 + 28 * q^71 + 16 * q^72 + 16 * q^73 - 36 * q^75 - 20 * q^76 + 12 * q^77 - 12 * q^78 + 24 * q^79 + 4 * q^80 - 56 * q^81 - 28 * q^83 + 8 * q^84 + 16 * q^85 + 12 * q^86 - 4 * q^87 - 16 * q^90 - 4 * q^91 + 48 * q^94 + 92 * q^95 + 8 * q^96 + 32 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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