LMFDB - Embedded newform 546.2.o.c.265.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(265,546)]

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([0, 2, 3]))

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

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

chi := DirichletCharacter("546.265");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.o (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:	8.0.836829184.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
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			265.4
Root			$-2.63640i$ of defining polynomial
Character	$\chi$	$=$	546.265
Dual form			546.2.o.c.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.63640 q^{10} +(1.37930 + 1.37930i) q^{11} +1.00000 q^{12} +(1.50062 + 3.27843i) q^{13} +(0.222191 + 2.63640i) q^{14} +(-1.15711 + 1.15711i) q^{15} -1.00000 q^{16} +1.50625 q^{17} +(-0.707107 + 0.707107i) q^{18} +(0.934922 + 0.934922i) q^{19} +(1.15711 - 1.15711i) q^{20} +(-2.02133 - 1.70711i) q^{21} +1.95063 q^{22} +4.19327i q^{23} +(0.707107 - 0.707107i) q^{24} -2.32218i q^{25} +(3.37930 + 1.25710i) q^{26} -1.00000i q^{27} +(2.02133 + 1.70711i) q^{28} -0.406261 q^{29} +1.63640i q^{30} +(2.31423 + 2.31423i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.37930 + 1.37930i) q^{33} +(1.06508 - 1.06508i) q^{34} +(-4.31423 + 0.363595i) q^{35} +1.00000i q^{36} +(0.257101 + 0.257101i) q^{37} +1.32218 q^{38} +(-3.27843 + 1.50062i) q^{39} -1.63640i q^{40} +(-3.60624 - 3.60624i) q^{41} +(-2.63640 + 0.222191i) q^{42} -2.46483i q^{43} +(1.37930 - 1.37930i) q^{44} +(-1.15711 - 1.15711i) q^{45} +(2.96509 + 2.96509i) q^{46} +(1.41421 - 1.41421i) q^{47} -1.00000i q^{48} +(-1.17157 - 6.90126i) q^{49} +(-1.64203 - 1.64203i) q^{50} +1.50625i q^{51} +(3.27843 - 1.50062i) q^{52} +13.4456 q^{53} +(-0.707107 - 0.707107i) q^{54} +3.19202i q^{55} +(2.63640 - 0.222191i) q^{56} +(-0.934922 + 0.934922i) q^{57} +(-0.287270 + 0.287270i) q^{58} +(-8.75986 + 8.75986i) q^{59} +(1.15711 + 1.15711i) q^{60} -11.7394i q^{61} +3.27281 q^{62} +(1.70711 - 2.02133i) q^{63} +1.00000i q^{64} +(-2.05713 + 5.52991i) q^{65} +1.95063i q^{66} +(11.1012 - 11.1012i) q^{67} -1.50625i q^{68} -4.19327 q^{69} +(-2.79352 + 3.30772i) q^{70} +(-5.18078 + 5.18078i) q^{71} +(0.707107 + 0.707107i) q^{72} +(2.56008 - 2.56008i) q^{73} +0.363595 q^{74} +2.32218 q^{75} +(0.934922 - 0.934922i) q^{76} +(-5.14265 + 0.433413i) q^{77} +(-1.25710 + 3.37930i) q^{78} +1.42546 q^{79} +(-1.15711 - 1.15711i) q^{80} +1.00000 q^{81} -5.09999 q^{82} +(-4.90797 - 4.90797i) q^{83} +(-1.70711 + 2.02133i) q^{84} +(1.74290 + 1.74290i) q^{85} +(-1.74290 - 1.74290i) q^{86} -0.406261i q^{87} -1.95063i q^{88} +(-2.03017 + 2.03017i) q^{89} -1.63640 q^{90} +(-9.18853 - 2.56337i) q^{91} +4.19327 q^{92} +(-2.31423 + 2.31423i) q^{93} -2.00000i q^{94} +2.16362i q^{95} +(-0.707107 - 0.707107i) q^{96} +(-10.2741 - 10.2741i) q^{97} +(-5.70836 - 4.05150i) q^{98} +(-1.37930 - 1.37930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9	$ 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 4 q^{17} + 8 q^{19} + 4 q^{20} - 12 q^{22} + 16 q^{26} + 12 q^{29} + 8 q^{31} + 8 q^{34} - 24 q^{35} - 4 q^{37} + 4 q^{38} - 4 q^{39} - 12 q^{41} - 4 q^{42} - 4 q^{45} + 24 q^{46} - 32 q^{49} - 8 q^{50} + 4 q^{52} + 40 q^{53} + 4 q^{56} - 8 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} - 8 q^{62} + 8 q^{63} - 12 q^{65} + 32 q^{67} + 28 q^{69} - 12 q^{71} - 20 q^{73} + 20 q^{74} + 12 q^{75} + 8 q^{76} - 8 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 40 q^{82} - 44 q^{83} - 8 q^{84} + 20 q^{85} - 20 q^{86} - 16 q^{89} + 4 q^{90} - 12 q^{91} - 28 q^{92} - 8 q^{93} + 8 q^{97} + 16 q^{98}+O(q^{100}) $ 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 4 * q^17 + 8 * q^19 + 4 * q^20 - 12 * q^22 + 16 * q^26 + 12 * q^29 + 8 * q^31 + 8 * q^34 - 24 * q^35 - 4 * q^37 + 4 * q^38 - 4 * q^39 - 12 * q^41 - 4 * q^42 - 4 * q^45 + 24 * q^46 - 32 * q^49 - 8 * q^50 + 4 * q^52 + 40 * q^53 + 4 * q^56 - 8 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 - 8 * q^62 + 8 * q^63 - 12 * q^65 + 32 * q^67 + 28 * q^69 - 12 * q^71 - 20 * q^73 + 20 * q^74 + 12 * q^75 + 8 * q^76 - 8 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 40 * q^82 - 44 * q^83 - 8 * q^84 + 20 * q^85 - 20 * q^86 - 16 * q^89 + 4 * q^90 - 12 * q^91 - 28 * q^92 - 8 * q^93 + 8 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		−	1.00000i		−	0.500000i
$5$	1.15711	+	1.15711i	0.517477	+	0.517477i	0.916807	−	0.399330i	$-0.130757\pi$
$5$	1.15711	+	1.15711i	0.517477	+	0.517477i	−0.399330	+	0.916807i	$0.630757\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−1.70711	+	2.02133i	−0.645226	+	0.763992i
$7$	−1.70711	+	2.02133i	−0.645226	+	0.763992i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	1.63640			0.517477
$11$	1.37930	+	1.37930i	0.415876	+	0.415876i	0.883780	−	0.467904i	$-0.154991\pi$
$11$	1.37930	+	1.37930i	0.415876	+	0.415876i	−0.467904	+	0.883780i	$0.654991\pi$
$12$	1.00000			0.288675
$13$	1.50062	+	3.27843i	0.416198	+	0.909274i
$13$	1.50062	+	3.27843i	0.416198	+	0.909274i
$14$	0.222191	+	2.63640i	0.0593831	+	0.704609i
$15$	−1.15711	+	1.15711i	−0.298765	+	0.298765i
$16$	−1.00000			−0.250000
$17$	1.50625			0.365319			0.182659	−	0.983176i	$-0.441529\pi$
$17$	1.50625			0.365319			0.182659	+	0.983176i	$0.441529\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	0.934922	+	0.934922i	0.214486	+	0.214486i	0.806170	−	0.591684i	$-0.201537\pi$
$19$	0.934922	+	0.934922i	0.214486	+	0.214486i	−0.591684	+	0.806170i	$0.701537\pi$
$20$	1.15711	−	1.15711i	0.258738	−	0.258738i
$21$	−2.02133	−	1.70711i	−0.441091	−	0.372521i
$22$	1.95063			0.415876
$23$			4.19327i			0.874358i	0.899375	+	0.437179i	$0.144022\pi$
$23$			4.19327i			0.874358i	−0.899375	+	0.437179i	$0.855978\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$		−	2.32218i		−	0.464436i
$26$	3.37930	+	1.25710i	0.662736	+	0.246538i
$27$		−	1.00000i		−	0.192450i
$28$	2.02133	+	1.70711i	0.381996	+	0.322613i
$29$	−0.406261			−0.0754407			−0.0377204	−	0.999288i	$-0.512010\pi$
$29$	−0.406261			−0.0754407			−0.0377204	+	0.999288i	$0.512010\pi$
$30$			1.63640i			0.298765i
$31$	2.31423	+	2.31423i	0.415647	+	0.415647i	0.883700	−	0.468053i	$-0.155044\pi$
$31$	2.31423	+	2.31423i	0.415647	+	0.415647i	−0.468053	+	0.883700i	$0.655044\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.37930	+	1.37930i	−0.240106	+	0.240106i
$34$	1.06508	−	1.06508i	0.182659	−	0.182659i
$35$	−4.31423	+	0.363595i	−0.729237	+	0.0614588i
$36$			1.00000i			0.166667i
$37$	0.257101	+	0.257101i	0.0422671	+	0.0422671i	0.727924	−	0.685657i	$-0.240485\pi$
$37$	0.257101	+	0.257101i	0.0422671	+	0.0422671i	−0.685657	+	0.727924i	$0.740485\pi$
$38$	1.32218			0.214486
$39$	−3.27843	+	1.50062i	−0.524969	+	0.240292i
$40$		−	1.63640i		−	0.258738i
$41$	−3.60624	−	3.60624i	−0.563199	−	0.563199i	0.367015	−	0.930215i	$-0.380380\pi$
$41$	−3.60624	−	3.60624i	−0.563199	−	0.563199i	−0.930215	+	0.367015i	$0.880380\pi$
$42$	−2.63640	+	0.222191i	−0.406806	+	0.0342849i
$43$		−	2.46483i		−	0.375883i	−0.982180	−	0.187942i	$-0.939818\pi$
$43$		−	2.46483i		−	0.375883i	0.982180	−	0.187942i	$-0.0601816\pi$
$44$	1.37930	−	1.37930i	0.207938	−	0.207938i
$45$	−1.15711	−	1.15711i	−0.172492	−	0.172492i
$46$	2.96509	+	2.96509i	0.437179	+	0.437179i
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	−0.596402	−	0.802686i	$-0.703403\pi$
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	0.802686	+	0.596402i	$0.203403\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.17157	−	6.90126i	−0.167368	−	0.985895i
$50$	−1.64203	−	1.64203i	−0.232218	−	0.232218i
$51$			1.50625i			0.210917i
$52$	3.27843	−	1.50062i	0.454637	−	0.208099i
$53$	13.4456			1.84690			0.923450	−	0.383719i	$-0.125357\pi$
$53$	13.4456			1.84690			0.923450	+	0.383719i	$0.125357\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$			3.19202i			0.430412i
$56$	2.63640	−	0.222191i	0.352304	−	0.0296916i
$57$	−0.934922	+	0.934922i	−0.123833	+	0.123833i
$58$	−0.287270	+	0.287270i	−0.0377204	+	0.0377204i
$59$	−8.75986	+	8.75986i	−1.14044	+	1.14044i	−0.152066	+	0.988370i	$0.548593\pi$
$59$	−8.75986	+	8.75986i	−1.14044	+	1.14044i	−0.988370	+	0.152066i	$0.951407\pi$
$60$	1.15711	+	1.15711i	0.149383	+	0.149383i
$61$		−	11.7394i		−	1.50308i	−0.659689	−	0.751539i	$-0.729312\pi$
$61$		−	11.7394i		−	1.50308i	0.659689	−	0.751539i	$-0.270688\pi$
$62$	3.27281			0.415647
$63$	1.70711	−	2.02133i	0.215075	−	0.254664i
$64$			1.00000i			0.125000i
$65$	−2.05713	+	5.52991i	−0.255155	+	0.685901i
$66$			1.95063i			0.240106i
$67$	11.1012	−	11.1012i	1.35623	−	1.35623i	0.477720	−	0.878512i	$-0.341464\pi$
$67$	11.1012	−	11.1012i	1.35623	−	1.35623i	0.878512	−	0.477720i	$-0.158536\pi$
$68$		−	1.50625i		−	0.182659i
$69$	−4.19327			−0.504811
$70$	−2.79352	+	3.30772i	−0.333889	+	0.395348i
$71$	−5.18078	+	5.18078i	−0.614845	+	0.614845i	−0.944205	−	0.329360i	$-0.893167\pi$
$71$	−5.18078	+	5.18078i	−0.614845	+	0.614845i	0.329360	+	0.944205i	$0.393167\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	2.56008	−	2.56008i	0.299635	−	0.299635i	−0.541236	−	0.840871i	$-0.682043\pi$
$73$	2.56008	−	2.56008i	0.299635	−	0.299635i	0.840871	+	0.541236i	$0.182043\pi$
$74$	0.363595			0.0422671
$75$	2.32218			0.268142
$76$	0.934922	−	0.934922i	0.107243	−	0.107243i
$77$	−5.14265	+	0.433413i	−0.586060	+	0.0493920i
$78$	−1.25710	+	3.37930i	−0.142339	+	0.382631i
$79$	1.42546			0.160377			0.0801884	−	0.996780i	$-0.474448\pi$
$79$	1.42546			0.160377			0.0801884	+	0.996780i	$0.474448\pi$
$80$	−1.15711	−	1.15711i	−0.129369	−	0.129369i
$81$	1.00000			0.111111
$82$	−5.09999			−0.563199
$83$	−4.90797	−	4.90797i	−0.538719	−	0.538719i	0.384434	−	0.923153i	$-0.374397\pi$
$83$	−4.90797	−	4.90797i	−0.538719	−	0.538719i	−0.923153	+	0.384434i	$0.874397\pi$
$84$	−1.70711	+	2.02133i	−0.186261	+	0.220545i
$85$	1.74290	+	1.74290i	0.189044	+	0.189044i
$86$	−1.74290	−	1.74290i	−0.187942	−	0.187942i
$87$		−	0.406261i		−	0.0435557i
$88$		−	1.95063i		−	0.207938i
$89$	−2.03017	+	2.03017i	−0.215198	+	0.215198i	−0.806471	−	0.591274i	$-0.798625\pi$
$89$	−2.03017	+	2.03017i	−0.215198	+	0.215198i	0.591274	+	0.806471i	$0.298625\pi$
$90$	−1.63640			−0.172492
$91$	−9.18853	−	2.56337i	−0.963220	−	0.268715i
$92$	4.19327			0.437179
$93$	−2.31423	+	2.31423i	−0.239974	+	0.239974i
$94$		−	2.00000i		−	0.206284i
$95$			2.16362i			0.221983i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−10.2741	−	10.2741i	−1.04317	−	1.04317i	−0.999025	−	0.0441477i	$-0.985943\pi$
$97$	−10.2741	−	10.2741i	−1.04317	−	1.04317i	−0.0441477	−	0.999025i	$-0.514057\pi$
$98$	−5.70836	−	4.05150i	−0.576631	−	0.409264i
$99$	−1.37930	−	1.37930i	−0.138625	−	0.138625i
$100$	−2.32218			−0.232218
$101$	1.93018			0.192060			0.0960301	−	0.995378i	$-0.469385\pi$
$101$	1.93018			0.192060			0.0960301	+	0.995378i	$0.469385\pi$
$102$	1.06508	+	1.06508i	0.105458	+	0.105458i
$103$	−7.94886			−0.783225			−0.391612	−	0.920130i	$-0.628083\pi$
$103$	−7.94886			−0.783225			−0.391612	+	0.920130i	$0.628083\pi$
$104$	1.25710	−	3.37930i	0.123269	−	0.331368i
$105$	−0.363595	−	4.31423i	−0.0354832	−	0.421025i
$106$	9.50750	−	9.50750i	0.923450	−	0.923450i
$107$	−3.33315			−0.322228			−0.161114	−	0.986936i	$-0.551509\pi$
$107$	−3.33315			−0.322228			−0.161114	+	0.986936i	$0.551509\pi$
$108$	−1.00000			−0.0962250
$109$	9.58382	−	9.58382i	0.917964	−	0.917964i	−0.0789174	−	0.996881i	$-0.525146\pi$
$109$	9.58382	−	9.58382i	0.917964	−	0.917964i	0.996881	+	0.0789174i	$0.0251463\pi$
$110$	2.25710	+	2.25710i	0.215206	+	0.215206i
$111$	−0.257101	+	0.257101i	−0.0244029	+	0.0244029i
$112$	1.70711	−	2.02133i	0.161306	−	0.190998i
$113$	−10.3865			−0.977084			−0.488542	−	0.872540i	$-0.662471\pi$
$113$	−10.3865			−0.977084			−0.488542	+	0.872540i	$0.662471\pi$
$114$			1.32218i			0.123833i
$115$	−4.85209	+	4.85209i	−0.452460	+	0.452460i
$116$			0.406261i			0.0377204i
$117$	−1.50062	−	3.27843i	−0.138733	−	0.303091i
$118$			12.3883i			1.14044i
$119$	−2.57133	+	3.04463i	−0.235713	+	0.279101i
$120$	1.63640			0.149383
$121$		−	7.19504i		−	0.654094i
$122$	−8.30102	−	8.30102i	−0.751539	−	0.751539i
$123$	3.60624	−	3.60624i	0.325163	−	0.325163i
$124$	2.31423	−	2.31423i	0.207824	−	0.207824i
$125$	8.47259	−	8.47259i	0.757811	−	0.757811i
$126$	−0.222191	−	2.63640i	−0.0197944	−	0.234870i
$127$		−	9.12016i		−	0.809283i	−0.914475	−	0.404642i	$-0.867396\pi$
$127$		−	9.12016i		−	0.809283i	0.914475	−	0.404642i	$-0.132604\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	2.46483			0.217016
$130$	2.45563	+	5.36484i	0.215373	+	0.470528i
$131$			3.98205i			0.347913i	0.984753	+	0.173957i	$0.0556553\pi$
$131$			3.98205i			0.347913i	−0.984753	+	0.173957i	$0.944345\pi$
$132$	1.37930	+	1.37930i	0.120053	+	0.120053i
$133$	−3.48580	+	0.293777i	−0.302257	+	0.0254737i
$134$		−	15.6995i		−	1.35623i
$135$	1.15711	−	1.15711i	0.0995884	−	0.0995884i
$136$	−1.06508	−	1.06508i	−0.0913297	−	0.0913297i
$137$	13.8868	+	13.8868i	1.18643	+	1.18643i	0.978047	+	0.208382i	$0.0668197\pi$
$137$	13.8868	+	13.8868i	1.18643	+	1.18643i	0.208382	+	0.978047i	$0.433180\pi$
$138$	−2.96509	+	2.96509i	−0.252405	+	0.252405i
$139$			7.37155i			0.625247i	0.949877	+	0.312623i	$0.101208\pi$
$139$			7.37155i			0.625247i	−0.949877	+	0.312623i	$0.898792\pi$
$140$	0.363595	+	4.31423i	0.0307294	+	0.364619i
$141$	1.41421	+	1.41421i	0.119098	+	0.119098i
$142$			7.32672i			0.614845i
$143$	−2.45214	+	6.59178i	−0.205058	+	0.551232i
$144$	1.00000			0.0833333
$145$	−0.470090	−	0.470090i	−0.0390388	−	0.0390388i
$146$		−	3.62050i		−	0.299635i
$147$	6.90126	−	1.17157i	0.569206	−	0.0966297i
$148$	0.257101	−	0.257101i	0.0211335	−	0.0211335i
$149$	−11.7376	+	11.7376i	−0.961585	+	0.961585i	−0.999289	−	0.0377039i	$-0.987996\pi$
$149$	−11.7376	+	11.7376i	−0.961585	+	0.961585i	0.0377039	+	0.999289i	$0.487996\pi$
$150$	1.64203	−	1.64203i	0.134071	−	0.134071i
$151$	2.79529	+	2.79529i	0.227477	+	0.227477i	0.811638	−	0.584161i	$-0.198576\pi$
$151$	2.79529	+	2.79529i	0.227477	+	0.227477i	−0.584161	+	0.811638i	$0.698576\pi$
$152$		−	1.32218i		−	0.107243i
$153$	−1.50625			−0.121773
$154$	−3.32994	+	3.94287i	−0.268334	+	0.317726i
$155$			5.35564i			0.430176i
$156$	1.50062	+	3.27843i	0.120146	+	0.262485i
$157$		−	10.4472i		−	0.833774i	−0.908958	−	0.416887i	$-0.863121\pi$
$157$		−	10.4472i		−	0.833774i	0.908958	−	0.416887i	$-0.136879\pi$
$158$	1.00795	−	1.00795i	0.0801884	−	0.0801884i
$159$			13.4456i			1.06631i
$160$	−1.63640			−0.129369
$161$	−8.47600	−	7.15836i	−0.668002	−	0.564158i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	9.07232	+	9.07232i	0.710599	+	0.710599i	0.966660	−	0.256062i	$-0.0824250\pi$
$163$	9.07232	+	9.07232i	0.710599	+	0.710599i	−0.256062	+	0.966660i	$0.582425\pi$
$164$	−3.60624	+	3.60624i	−0.281600	+	0.281600i
$165$	−3.19202			−0.248499
$166$	−6.94091			−0.538719
$167$	9.04741	−	9.04741i	0.700109	−	0.700109i	−0.264325	−	0.964434i	$-0.585149\pi$
$167$	9.04741	−	9.04741i	0.700109	−	0.700109i	0.964434	+	0.264325i	$0.0851490\pi$
$168$	0.222191	+	2.63640i	0.0171424	+	0.203403i
$169$	−8.49625	+	9.83940i	−0.653558	+	0.756877i
$170$	2.46483			0.189044
$171$	−0.934922	−	0.934922i	−0.0714952	−	0.0714952i
$172$	−2.46483			−0.187942
$173$	0.0159057			0.00120928			0.000604642	−	1.00000i	$-0.499808\pi$
$173$	0.0159057			0.00120928			0.000604642		1.00000i	$0.499808\pi$
$174$	−0.287270	−	0.287270i	−0.0217779	−	0.0217779i
$175$	4.69390	+	3.96421i	0.354825	+	0.299666i
$176$	−1.37930	−	1.37930i	−0.103969	−	0.103969i
$177$	−8.75986	−	8.75986i	−0.658431	−	0.658431i
$178$			2.87109i			0.215198i
$179$		−	10.3710i		−	0.775167i	−0.921835	−	0.387584i	$-0.873310\pi$
$179$		−	10.3710i		−	0.775167i	0.921835	−	0.387584i	$-0.126690\pi$
$180$	−1.15711	+	1.15711i	−0.0862461	+	0.0862461i
$181$	−1.42973			−0.106271			−0.0531354	−	0.998587i	$-0.516921\pi$
$181$	−1.42973			−0.106271			−0.0531354	+	0.998587i	$0.516921\pi$
$182$	−8.30985	+	4.68469i	−0.615967	+	0.347253i
$183$	11.7394			0.867802
$184$	2.96509	−	2.96509i	0.218589	−	0.218589i
$185$			0.594989i			0.0437444i
$186$			3.27281i			0.239974i
$187$	2.07757	+	2.07757i	0.151927	+	0.151927i
$188$	−1.41421	−	1.41421i	−0.103142	−	0.103142i
$189$	2.02133	+	1.70711i	0.147030	+	0.124174i
$190$	1.52991	+	1.52991i	0.110991	+	0.110991i
$191$	−23.1833			−1.67748			−0.838741	−	0.544530i	$-0.816708\pi$
$191$	−23.1833			−1.67748			−0.838741	+	0.544530i	$0.816708\pi$
$192$	−1.00000			−0.0721688
$193$	13.6264	+	13.6264i	0.980850	+	0.980850i	0.999820	−	0.0189698i	$-0.00603863\pi$
$193$	13.6264	+	13.6264i	0.980850	+	0.980850i	−0.0189698	+	0.999820i	$0.506039\pi$
$194$	−14.5297			−1.04317
$195$	−5.52991	−	2.05713i	−0.396005	−	0.147314i
$196$	−6.90126	+	1.17157i	−0.492947	+	0.0836838i
$197$	10.1950	−	10.1950i	0.726366	−	0.726366i	−0.243528	−	0.969894i	$-0.578305\pi$
$197$	10.1950	−	10.1950i	0.726366	−	0.726366i	0.969894	+	0.243528i	$0.0783046\pi$
$198$	−1.95063			−0.138625
$199$	1.42518			0.101029			0.0505143	−	0.998723i	$-0.483914\pi$
$199$	1.42518			0.101029			0.0505143	+	0.998723i	$0.483914\pi$
$200$	−1.64203	+	1.64203i	−0.116109	+	0.116109i
$201$	11.1012	+	11.1012i	0.783021	+	0.783021i
$202$	1.36484	−	1.36484i	0.0960301	−	0.0960301i
$203$	0.693530	−	0.821188i	0.0486763	−	0.0576361i
$204$	1.50625			0.105458
$205$		−	8.34564i		−	0.582885i
$206$	−5.62070	+	5.62070i	−0.391612	+	0.391612i
$207$		−	4.19327i		−	0.291453i
$208$	−1.50062	−	3.27843i	−0.104050	−	0.227318i
$209$			2.57908i			0.178399i
$210$	−3.30772	−	2.79352i	−0.228254	−	0.192771i
$211$	5.45234			0.375354			0.187677	−	0.982231i	$-0.439904\pi$
$211$	5.45234			0.375354			0.187677	+	0.982231i	$0.439904\pi$
$212$		−	13.4456i		−	0.923450i
$213$	−5.18078	−	5.18078i	−0.354981	−	0.354981i
$214$	−2.35689	+	2.35689i	−0.161114	+	0.161114i
$215$	2.85209	−	2.85209i	0.194511	−	0.194511i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−8.62845	+	0.727190i	−0.585737	+	0.0493649i
$218$		−	13.5536i		−	0.917964i
$219$	2.56008	+	2.56008i	0.172994	+	0.172994i
$220$	3.19202			0.215206
$221$	2.26031	+	4.93813i	0.152045	+	0.332175i
$222$			0.363595i			0.0244029i
$223$	18.3548	+	18.3548i	1.22913	+	1.22913i	0.964293	+	0.264839i	$0.0853187\pi$
$223$	18.3548	+	18.3548i	1.22913	+	1.22913i	0.264839	+	0.964293i	$0.414681\pi$
$224$	−0.222191	−	2.63640i	−0.0148458	−	0.176152i
$225$			2.32218i			0.154812i
$226$	−7.34440	+	7.34440i	−0.488542	+	0.488542i
$227$	6.91251	+	6.91251i	0.458799	+	0.458799i	0.898261	−	0.439462i	$-0.144831\pi$
$227$	6.91251	+	6.91251i	0.458799	+	0.458799i	−0.439462	+	0.898261i	$0.644831\pi$
$228$	0.934922	+	0.934922i	0.0619167	+	0.0619167i
$229$	2.96035	−	2.96035i	0.195625	−	0.195625i	−0.602496	−	0.798122i	$-0.705827\pi$
$229$	2.96035	−	2.96035i	0.195625	−	0.195625i	0.798122	+	0.602496i	$0.205827\pi$
$230$			6.86189i			0.452460i
$231$	−0.433413	−	5.14265i	−0.0285165	−	0.338362i
$232$	0.287270	+	0.287270i	0.0188602	+	0.0188602i
$233$		−	6.59953i		−	0.432350i	−0.976355	−	0.216175i	$-0.930642\pi$
$233$		−	6.59953i		−	0.432350i	0.976355	−	0.216175i	$-0.0693581\pi$
$234$	−3.37930	−	1.25710i	−0.220912	−	0.0821792i
$235$	3.27281			0.213495
$236$	8.75986	+	8.75986i	0.570218	+	0.570218i
$237$			1.42546i			0.0925936i
$238$	0.334675	+	3.97108i	0.0216938	+	0.257407i
$239$	−10.9611	+	10.9611i	−0.709014	+	0.709014i	−0.966328	−	0.257314i	$-0.917162\pi$
$239$	−10.9611	+	10.9611i	−0.709014	+	0.709014i	0.257314	+	0.966328i	$0.417162\pi$
$240$	1.15711	−	1.15711i	0.0746913	−	0.0746913i
$241$	20.1598	−	20.1598i	1.29861	−	1.29861i	0.369295	−	0.929312i	$-0.379599\pi$
$241$	20.1598	−	20.1598i	1.29861	−	1.29861i	0.929312	−	0.369295i	$-0.120401\pi$
$242$	−5.08766	−	5.08766i	−0.327047	−	0.327047i
$243$			1.00000i			0.0641500i
$244$	−11.7394			−0.751539
$245$	6.62990	−	9.34118i	0.423569	−	0.596786i
$246$		−	5.09999i		−	0.325163i
$247$	−1.66211	+	4.46804i	−0.105758	+	0.284295i
$248$		−	3.27281i		−	0.207824i
$249$	4.90797	−	4.90797i	0.311030	−	0.311030i
$250$		−	11.9820i		−	0.757811i
$251$	6.62641			0.418255			0.209128	−	0.977888i	$-0.432938\pi$
$251$	6.62641			0.418255			0.209128	+	0.977888i	$0.432938\pi$
$252$	−2.02133	−	1.70711i	−0.127332	−	0.107538i
$253$	−5.78380	+	5.78380i	−0.363624	+	0.363624i
$254$	−6.44893	−	6.44893i	−0.404642	−	0.404642i
$255$	−1.74290	+	1.74290i	−0.109145	+	0.109145i
$256$	1.00000			0.0625000
$257$	10.5297			0.656826			0.328413	−	0.944534i	$-0.393486\pi$
$257$	10.5297			0.656826			0.328413	+	0.944534i	$0.393486\pi$
$258$	1.74290	−	1.74290i	0.108508	−	0.108508i
$259$	−0.958584	+	0.0807877i	−0.0595635	+	0.00501990i
$260$	5.52991	+	2.05713i	0.342950	+	0.127578i
$261$	0.406261			0.0251469
$262$	2.81573	+	2.81573i	0.173957	+	0.173957i
$263$	11.3310			0.698699			0.349349	−	0.936993i	$-0.386403\pi$
$263$	11.3310			0.698699			0.349349	+	0.936993i	$0.386403\pi$
$264$	1.95063			0.120053
$265$	15.5581	+	15.5581i	0.955727	+	0.955727i
$266$	−2.25710	+	2.67256i	−0.138392	+	0.163865i
$267$	−2.03017	−	2.03017i	−0.124244	−	0.124244i
$268$	−11.1012	−	11.1012i	−0.678116	−	0.678116i
$269$			11.6504i			0.710339i	0.934802	+	0.355170i	$0.115577\pi$
$269$			11.6504i			0.710339i	−0.934802	+	0.355170i	$0.884423\pi$
$270$		−	1.63640i		−	0.0995884i
$271$	9.41876	−	9.41876i	0.572149	−	0.572149i	−0.360580	−	0.932728i	$-0.617421\pi$
$271$	9.41876	−	9.41876i	0.572149	−	0.572149i	0.932728	+	0.360580i	$0.117421\pi$
$272$	−1.50625			−0.0913297
$273$	2.56337	−	9.18853i	0.155142	−	0.556115i
$274$	19.6389			1.18643
$275$	3.20299	−	3.20299i	0.193148	−	0.193148i
$276$			4.19327i			0.252405i
$277$			5.99357i			0.360119i	0.983656	+	0.180059i	$0.0576290\pi$
$277$			5.99357i			0.360119i	−0.983656	+	0.180059i	$0.942371\pi$
$278$	5.21247	+	5.21247i	0.312623	+	0.312623i
$279$	−2.31423	−	2.31423i	−0.138549	−	0.138549i
$280$	3.30772	+	2.79352i	0.197674	+	0.166945i
$281$	12.4581	+	12.4581i	0.743190	+	0.743190i	0.973190	−	0.230001i	$-0.0738729\pi$
$281$	12.4581	+	12.4581i	0.743190	+	0.743190i	−0.230001	+	0.973190i	$0.573873\pi$
$282$	2.00000			0.119098
$283$	−12.9995			−0.772739			−0.386370	−	0.922344i	$-0.626271\pi$
$283$	−12.9995			−0.772739			−0.386370	+	0.922344i	$0.626271\pi$
$284$	5.18078	+	5.18078i	0.307422	+	0.307422i
$285$	−2.16362			−0.128162
$286$	2.92717	+	6.39501i	0.173087	+	0.378145i
$287$	13.4456	−	1.13317i	0.793671	−	0.0668891i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	−14.7312			−0.866542
$290$	−0.664807			−0.0390388
$291$	10.2741	−	10.2741i	0.602276	−	0.602276i
$292$	−2.56008	−	2.56008i	−0.149817	−	0.149817i
$293$	1.51545	−	1.51545i	0.0885336	−	0.0885336i	−0.661453	−	0.749987i	$-0.730060\pi$
$293$	1.51545	−	1.51545i	0.0885336	−	0.0885336i	0.749987	+	0.661453i	$0.230060\pi$
$294$	4.05150	−	5.70836i	0.236288	−	0.332918i
$295$	−20.2723			−1.18030
$296$		−	0.363595i		−	0.0211335i
$297$	1.37930	−	1.37930i	0.0800354	−	0.0800354i
$298$			16.5995i			0.961585i
$299$	−13.7474	+	6.29253i	−0.795030	+	0.363906i
$300$		−	2.32218i		−	0.134071i
$301$	4.98225	+	4.20773i	0.287172	+	0.242530i
$302$	3.95313			0.227477
$303$			1.93018i			0.110886i
$304$	−0.934922	−	0.934922i	−0.0536214	−	0.0536214i
$305$	13.5838	−	13.5838i	0.777807	−	0.777807i
$306$	−1.06508	+	1.06508i	−0.0608865	+	0.0608865i
$307$	−4.87286	+	4.87286i	−0.278109	+	0.278109i	−0.832354	−	0.554245i	$-0.813007\pi$
$307$	−4.87286	+	4.87286i	−0.278109	+	0.278109i	0.554245	+	0.832354i	$0.313007\pi$
$308$	0.433413	+	5.14265i	0.0246960	+	0.293030i
$309$		−	7.94886i		−	0.452195i
$310$	3.78701	+	3.78701i	0.215088	+	0.215088i
$311$	26.8179			1.52070			0.760352	−	0.649511i	$-0.225026\pi$
$311$	26.8179			1.52070			0.760352	+	0.649511i	$0.225026\pi$
$312$	3.37930	+	1.25710i	0.191315	+	0.0711693i
$313$		−	1.96858i		−	0.111271i	−0.998451	−	0.0556354i	$-0.982282\pi$
$313$		−	1.96858i		−	0.111271i	0.998451	−	0.0556354i	$-0.0177184\pi$
$314$	−7.38726	−	7.38726i	−0.416887	−	0.416887i
$315$	4.31423	−	0.363595i	0.243079	−	0.0204863i
$316$		−	1.42546i		−	0.0801884i
$317$	9.47705	−	9.47705i	0.532284	−	0.532284i	−0.388967	−	0.921252i	$-0.627168\pi$
$317$	9.47705	−	9.47705i	0.532284	−	0.532284i	0.921252	+	0.388967i	$0.127168\pi$
$318$	9.50750	+	9.50750i	0.533154	+	0.533154i
$319$	−0.560357	−	0.560357i	−0.0313740	−	0.0313740i
$320$	−1.15711	+	1.15711i	−0.0646846	+	0.0646846i
$321$		−	3.33315i		−	0.186038i
$322$	−11.0552	+	0.931709i	−0.616080	+	0.0519221i
$323$	1.40822	+	1.40822i	0.0783557	+	0.0783557i
$324$		−	1.00000i		−	0.0555556i
$325$	7.61311	−	3.48472i	0.422299	−	0.193297i
$326$	12.8302			0.710599
$327$	9.58382	+	9.58382i	0.529987	+	0.529987i
$328$			5.09999i			0.281600i
$329$	0.444383	+	5.27281i	0.0244996	+	0.290699i
$330$	−2.25710	+	2.25710i	−0.124249	+	0.124249i
$331$	−13.2853	+	13.2853i	−0.730226	+	0.730226i	−0.970664	−	0.240438i	$-0.922709\pi$
$331$	−13.2853	+	13.2853i	−0.730226	+	0.730226i	0.240438	+	0.970664i	$0.422709\pi$
$332$	−4.90797	+	4.90797i	−0.269360	+	0.269360i
$333$	−0.257101	−	0.257101i	−0.0140890	−	0.0140890i
$334$		−	12.7950i		−	0.700109i
$335$	25.6908			1.40364
$336$	2.02133	+	1.70711i	0.110273	+	0.0931303i
$337$			10.6200i			0.578507i	0.957252	+	0.289254i	$0.0934071\pi$
$337$			10.6200i			0.578507i	−0.957252	+	0.289254i	$0.906593\pi$
$338$	0.949747	+	12.9653i	0.0516595	+	0.705217i
$339$		−	10.3865i		−	0.564120i
$340$	1.74290	−	1.74290i	0.0945220	−	0.0945220i
$341$			6.38404i			0.345715i
$342$	−1.32218			−0.0714952
$343$	15.9497	+	9.41305i	0.861205	+	0.508257i
$344$	−1.74290	+	1.74290i	−0.0939708	+	0.0939708i
$345$	−4.85209	−	4.85209i	−0.261228	−	0.261228i
$346$	0.0112470	−	0.0112470i	0.000604642	−	0.000604642i
$347$	−33.6050			−1.80401			−0.902007	−	0.431722i	$-0.857906\pi$
$347$	−33.6050			−1.80401			−0.902007	+	0.431722i	$0.857906\pi$
$348$	−0.406261			−0.0217779
$349$	−22.5833	+	22.5833i	−1.20886	+	1.20886i	−0.237462	+	0.971397i	$0.576316\pi$
$349$	−22.5833	+	22.5833i	−1.20886	+	1.20886i	−0.971397	+	0.237462i	$0.923684\pi$
$350$	6.12220	−	0.515968i	0.327246	−	0.0275797i
$351$	3.27843	−	1.50062i	0.174990	−	0.0800974i
$352$	−1.95063			−0.103969
$353$	−10.4681	−	10.4681i	−0.557162	−	0.557162i	0.371336	−	0.928498i	$-0.378900\pi$
$353$	−10.4681	−	10.4681i	−0.557162	−	0.557162i	−0.928498	+	0.371336i	$0.878900\pi$
$354$	−12.3883			−0.658431
$355$	−11.9895			−0.636336
$356$	2.03017	+	2.03017i	0.107599	+	0.107599i
$357$	−3.04463	−	2.57133i	−0.161139	−	0.136089i
$358$	−7.33343	−	7.33343i	−0.387584	−	0.387584i
$359$	−2.68248	−	2.68248i	−0.141576	−	0.141576i	0.632767	−	0.774343i	$-0.281919\pi$
$359$	−2.68248	−	2.68248i	−0.141576	−	0.141576i	−0.774343	+	0.632767i	$0.781919\pi$
$360$			1.63640i			0.0862461i
$361$		−	17.2518i		−	0.907992i
$362$	−1.01097	+	1.01097i	−0.0531354	+	0.0531354i
$363$	7.19504			0.377642
$364$	−2.56337	+	9.18853i	−0.134357	+	0.481610i
$365$	5.92460			0.310108
$366$	8.30102	−	8.30102i	0.433901	−	0.433901i
$367$		−	8.08749i		−	0.422164i	−0.977468	−	0.211082i	$-0.932301\pi$
$367$		−	8.08749i		−	0.422164i	0.977468	−	0.211082i	$-0.0676986\pi$
$368$		−	4.19327i		−	0.218589i
$369$	3.60624	+	3.60624i	0.187733	+	0.187733i
$370$	0.420721	+	0.420721i	0.0218722	+	0.0218722i
$371$	−22.9531	+	27.1781i	−1.19167	+	1.41102i
$372$	2.31423	+	2.31423i	0.119987	+	0.119987i
$373$	−27.5920			−1.42866			−0.714331	−	0.699808i	$-0.753269\pi$
$373$	−27.5920			−1.42866			−0.714331	+	0.699808i	$0.753269\pi$
$374$	2.93813			0.151927
$375$	8.47259	+	8.47259i	0.437523	+	0.437523i
$376$	−2.00000			−0.103142
$377$	−0.609645	−	1.33190i	−0.0313983	−	0.0685963i
$378$	2.63640	−	0.222191i	0.135602	−	0.0114283i
$379$	−7.79457	+	7.79457i	−0.400380	+	0.400380i	−0.878367	−	0.477987i	$-0.841367\pi$
$379$	−7.79457	+	7.79457i	−0.400380	+	0.400380i	0.477987	+	0.878367i	$0.341367\pi$
$380$	2.16362			0.110991
$381$	9.12016			0.467240
$382$	−16.3931	+	16.3931i	−0.838741	+	0.838741i
$383$	11.3366	+	11.3366i	0.579275	+	0.579275i	0.934704	−	0.355428i	$-0.115665\pi$
$383$	11.3366	+	11.3366i	0.579275	+	0.579275i	−0.355428	+	0.934704i	$0.615665\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−6.45214	−	5.44912i	−0.328831	−	0.277713i
$386$	19.2707			0.980850
$387$			2.46483i			0.125294i
$388$	−10.2741	+	10.2741i	−0.521586	+	0.521586i
$389$		−	17.5669i		−	0.890675i	−0.895363	−	0.445338i	$-0.853084\pi$
$389$		−	17.5669i		−	0.890675i	0.895363	−	0.445338i	$-0.146916\pi$
$390$	−5.36484	+	2.45563i	−0.271659	+	0.124346i
$391$			6.31611i			0.319419i
$392$	−4.05150	+	5.70836i	−0.204632	+	0.288316i
$393$	−3.98205			−0.200868
$394$		−	14.4180i		−	0.726366i
$395$	1.64942	+	1.64942i	0.0829913	+	0.0829913i
$396$	−1.37930	+	1.37930i	−0.0693127	+	0.0693127i
$397$	24.6394	−	24.6394i	1.23662	−	1.23662i	0.275242	−	0.961375i	$-0.411242\pi$
$397$	24.6394	−	24.6394i	1.23662	−	1.23662i	0.961375	−	0.275242i	$-0.0887580\pi$
$398$	1.00776	−	1.00776i	0.0505143	−	0.0505143i
$399$	−0.293777	−	3.48580i	−0.0147072	−	0.174508i
$400$			2.32218i			0.116109i
$401$	20.8486	+	20.8486i	1.04113	+	1.04113i	0.999117	+	0.0420122i	$0.0133769\pi$
$401$	20.8486	+	20.8486i	1.04113	+	1.04113i	0.0420122	+	0.999117i	$0.486623\pi$
$402$	15.6995			0.783021
$403$	−4.11425	+	11.0598i	−0.204945	+	0.550929i
$404$		−	1.93018i		−	0.0960301i
$405$	1.15711	+	1.15711i	0.0574974	+	0.0574974i
$406$	−0.0902676	−	1.07107i	−0.00447991	−	0.0531562i
$407$			0.709240i			0.0351557i
$408$	1.06508	−	1.06508i	0.0527292	−	0.0527292i
$409$	−13.8170	−	13.8170i	−0.683206	−	0.683206i	0.277515	−	0.960721i	$-0.410489\pi$
$409$	−13.8170	−	13.8170i	−0.683206	−	0.683206i	−0.960721	+	0.277515i	$0.910489\pi$
$410$	−5.90126	−	5.90126i	−0.291443	−	0.291443i
$411$	−13.8868	+	13.8868i	−0.684985	+	0.684985i
$412$			7.94886i			0.391612i
$413$	−2.75258	−	32.6606i	−0.135445	−	1.60712i
$414$	−2.96509	−	2.96509i	−0.145726	−	0.145726i
$415$		−	11.3581i		−	0.557549i
$416$	−3.37930	−	1.25710i	−0.165684	−	0.0616344i
$417$	−7.37155			−0.360986
$418$	1.82369	+	1.82369i	0.0891995	+	0.0891995i
$419$			16.3845i			0.800435i	0.916420	+	0.400218i	$0.131065\pi$
$419$			16.3845i			0.800435i	−0.916420	+	0.400218i	$0.868935\pi$
$420$	−4.31423	+	0.363595i	−0.210513	+	0.0177416i
$421$	−17.2214	+	17.2214i	−0.839319	+	0.839319i	−0.988769	−	0.149450i	$-0.952250\pi$
$421$	−17.2214	+	17.2214i	−0.839319	+	0.839319i	0.149450	+	0.988769i	$0.452250\pi$
$422$	3.85538	−	3.85538i	0.187677	−	0.187677i
$423$	−1.41421	+	1.41421i	−0.0687614	+	0.0687614i
$424$	−9.50750	−	9.50750i	−0.461725	−	0.461725i
$425$		−	3.49778i		−	0.169667i
$426$	−7.32672			−0.354981
$427$	23.7293	+	20.0404i	1.14834	+	0.969824i
$428$			3.33315i			0.161114i
$429$	−6.59178	−	2.45214i	−0.318254	−	0.118390i
$430$		−	4.03346i		−	0.194511i
$431$	22.5749	−	22.5749i	1.08739	−	1.08739i	0.0915975	−	0.995796i	$-0.470803\pi$
$431$	22.5749	−	22.5749i	1.08739	−	1.08739i	0.995796	−	0.0915975i	$-0.0291973\pi$
$432$			1.00000i			0.0481125i
$433$	−35.8075			−1.72080			−0.860400	−	0.509620i	$-0.829786\pi$
$433$	−35.8075			−1.72080			−0.860400	+	0.509620i	$0.829786\pi$
$434$	−5.58704	+	6.61544i	−0.268186	+	0.317551i
$435$	0.470090	−	0.470090i	0.0225391	−	0.0225391i
$436$	−9.58382	−	9.58382i	−0.458982	−	0.458982i
$437$	−3.92038	+	3.92038i	−0.187537	+	0.187537i
$438$	3.62050			0.172994
$439$	−9.78979			−0.467241			−0.233621	−	0.972328i	$-0.575057\pi$
$439$	−9.78979			−0.467241			−0.233621	+	0.972328i	$0.575057\pi$
$440$	2.25710	−	2.25710i	0.107603	−	0.107603i
$441$	1.17157	+	6.90126i	0.0557892	+	0.328632i
$442$	5.09007	+	1.89351i	0.242110	+	0.0900649i
$443$	−2.71378			−0.128936			−0.0644679	−	0.997920i	$-0.520535\pi$
$443$	−2.71378			−0.128936			−0.0644679	+	0.997920i	$0.520535\pi$
$444$	0.257101	+	0.257101i	0.0122015	+	0.0122015i
$445$	−4.69827			−0.222719
$446$	25.9577			1.22913
$447$	−11.7376	−	11.7376i	−0.555171	−	0.555171i
$448$	−2.02133	−	1.70711i	−0.0954990	−	0.0806532i
$449$	14.7825	+	14.7825i	0.697632	+	0.697632i	0.963899	−	0.266268i	$-0.0857905\pi$
$449$	14.7825	+	14.7825i	0.697632	+	0.697632i	−0.266268	+	0.963899i	$0.585790\pi$
$450$	1.64203	+	1.64203i	0.0774060	+	0.0774060i
$451$		−	9.94819i		−	0.468442i
$452$			10.3865i			0.488542i
$453$	−2.79529	+	2.79529i	−0.131334	+	0.131334i
$454$	9.77576			0.458799
$455$	−7.66606	−	13.5983i	−0.359390	−	0.637497i
$456$	1.32218			0.0619167
$457$	−17.9920	+	17.9920i	−0.841632	+	0.841632i	−0.989071	−	0.147439i	$-0.952897\pi$
$457$	−17.9920	+	17.9920i	−0.841632	+	0.841632i	0.147439	+	0.989071i	$0.452897\pi$
$458$		−	4.18657i		−	0.195625i
$459$		−	1.50625i		−	0.0703056i
$460$	4.85209	+	4.85209i	0.226230	+	0.226230i
$461$	−23.4424	−	23.4424i	−1.09182	−	1.09182i	−0.995334	−	0.0964882i	$-0.969239\pi$
$461$	−23.4424	−	23.4424i	−1.09182	−	1.09182i	−0.0964882	−	0.995334i	$-0.530761\pi$
$462$	−3.94287	−	3.32994i	−0.183439	−	0.154923i
$463$	12.4486	+	12.4486i	0.578536	+	0.578536i	0.934500	−	0.355964i	$-0.115847\pi$
$463$	12.4486	+	12.4486i	0.578536	+	0.578536i	−0.355964	+	0.934500i	$0.615847\pi$
$464$	0.406261			0.0188602
$465$	−5.35564			−0.248362
$466$	−4.66657	−	4.66657i	−0.216175	−	0.216175i
$467$	−27.6932			−1.28149			−0.640744	−	0.767754i	$-0.721374\pi$
$467$	−27.6932			−1.28149			−0.640744	+	0.767754i	$0.721374\pi$
$468$	−3.27843	+	1.50062i	−0.151546	+	0.0693664i
$469$	3.48830	+	41.3903i	0.161075	+	1.91123i
$470$	2.31423	−	2.31423i	0.106747	−	0.106747i
$471$	10.4472			0.481380
$472$	12.3883			0.570218
$473$	3.39975	−	3.39975i	0.156321	−	0.156321i
$474$	1.00795	+	1.00795i	0.0462968	+	0.0462968i
$475$	2.17106	−	2.17106i	0.0996148	−	0.0996148i
$476$	3.04463	+	2.57133i	0.139550	+	0.117857i
$477$	−13.4456			−0.615633
$478$			15.5013i			0.709014i
$479$	−7.69426	+	7.69426i	−0.351560	+	0.351560i	−0.860690	−	0.509130i	$-0.829967\pi$
$479$	−7.69426	+	7.69426i	−0.351560	+	0.351560i	0.509130	+	0.860690i	$0.329967\pi$
$480$		−	1.63640i		−	0.0746913i
$481$	−0.457076	+	1.22870i	−0.0208409	+	0.0560238i
$482$		−	28.5103i		−	1.29861i
$483$	7.15836	−	8.47600i	0.325717	−	0.385671i
$484$	−7.19504			−0.327047
$485$		−	23.7765i		−	1.07964i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−3.65436	+	3.65436i	−0.165595	+	0.165595i	−0.785040	−	0.619445i	$-0.787358\pi$
$487$	−3.65436	+	3.65436i	−0.165595	+	0.165595i	0.619445	+	0.785040i	$0.287358\pi$
$488$	−8.30102	+	8.30102i	−0.375769	+	0.375769i
$489$	−9.07232	+	9.07232i	−0.410264	+	0.410264i
$490$	−1.91717	−	11.2933i	−0.0866088	−	0.510177i
$491$			12.9652i			0.585110i	0.956249	+	0.292555i	$0.0945055\pi$
$491$			12.9652i			0.585110i	−0.956249	+	0.292555i	$0.905495\pi$
$492$	−3.60624	−	3.60624i	−0.162582	−	0.162582i
$493$	−0.611930			−0.0275599
$494$	1.98409	+	4.33468i	0.0892686	+	0.195026i
$495$		−	3.19202i		−	0.143471i
$496$	−2.31423	−	2.31423i	−0.103912	−	0.103912i
$497$	−1.62793	−	19.3162i	−0.0730228	−	0.866450i
$498$		−	6.94091i		−	0.311030i
$499$	15.8982	−	15.8982i	0.711703	−	0.711703i	−0.255188	−	0.966891i	$-0.582137\pi$
$499$	15.8982	−	15.8982i	0.711703	−	0.711703i	0.966891	+	0.255188i	$0.0821374\pi$
$500$	−8.47259	−	8.47259i	−0.378906	−	0.378906i
$501$	9.04741	+	9.04741i	0.404208	+	0.404208i
$502$	4.68558	−	4.68558i	0.209128	−	0.209128i
$503$		−	7.72073i		−	0.344250i	−0.985075	−	0.172125i	$-0.944937\pi$
$503$		−	7.72073i		−	0.344250i	0.985075	−	0.172125i	$-0.0550633\pi$
$504$	−2.63640	+	0.222191i	−0.117435	+	0.00989719i
$505$	2.23344	+	2.23344i	0.0993867	+	0.0993867i
$506$			8.17953i			0.363624i
$507$	−9.83940	−	8.49625i	−0.436983	−	0.377332i
$508$	−9.12016			−0.404642
$509$	−23.7432	−	23.7432i	−1.05240	−	1.05240i	−0.998549	−	0.0538516i	$-0.982850\pi$
$509$	−23.7432	−	23.7432i	−1.05240	−	1.05240i	−0.0538516	−	0.998549i	$-0.517150\pi$
$510$			2.46483i			0.109145i
$511$	0.804444	+	9.54510i	0.0355865	+	0.422250i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	0.934922	−	0.934922i	0.0412778	−	0.0412778i
$514$	7.44563	−	7.44563i	0.328413	−	0.328413i
$515$	−9.19773	−	9.19773i	−0.405301	−	0.405301i
$516$		−	2.46483i		−	0.108508i
$517$	3.90126			0.171577
$518$	−0.620696	+	0.734947i	−0.0272718	+	0.0322917i
$519$			0.0159057i			0.000698181i
$520$	5.36484	−	2.45563i	0.235264	−	0.107686i
$521$			11.2520i			0.492958i	0.969148	+	0.246479i	$0.0792736\pi$
$521$			11.2520i			0.492958i	−0.969148	+	0.246479i	$0.920726\pi$
$522$	0.287270	−	0.287270i	0.0125735	−	0.0125735i
$523$		−	39.7356i		−	1.73752i	−0.495237	−	0.868758i	$-0.664919\pi$
$523$		−	39.7356i		−	1.73752i	0.495237	−	0.868758i	$-0.335081\pi$
$524$	3.98205			0.173957
$525$	−3.96421	+	4.69390i	−0.173012	+	0.204858i
$526$	8.01222	−	8.01222i	0.349349	−	0.349349i
$527$	3.48580	+	3.48580i	0.151844	+	0.151844i
$528$	1.37930	−	1.37930i	0.0600265	−	0.0600265i
$529$	5.41647			0.235499
$530$	22.0025			0.955727
$531$	8.75986	−	8.75986i	0.380145	−	0.380145i
$532$	0.293777	+	3.48580i	0.0127368	+	0.151129i
$533$	6.41120	−	17.2344i	0.277700	−	0.746505i
$534$	−2.87109			−0.124244
$535$	−3.85683	−	3.85683i	−0.166745	−	0.166745i
$536$	−15.6995			−0.678116
$537$	10.3710			0.447543
$538$	8.23810	+	8.23810i	0.355170	+	0.355170i
$539$	7.90299	−	11.1349i	0.340406	−	0.479614i
$540$	−1.15711	−	1.15711i	−0.0497942	−	0.0497942i
$541$	−10.4751	−	10.4751i	−0.450359	−	0.450359i	0.445114	−	0.895474i	$-0.353163\pi$
$541$	−10.4751	−	10.4751i	−0.450359	−	0.450359i	−0.895474	+	0.445114i	$0.853163\pi$
$542$		−	13.3201i		−	0.572149i
$543$		−	1.42973i		−	0.0613554i
$544$	−1.06508	+	1.06508i	−0.0456649	+	0.0456649i
$545$	22.1791			0.950050
$546$	−4.68469	−	8.30985i	−0.200486	−	0.355629i
$547$	17.4124			0.744502			0.372251	−	0.928132i	$-0.378586\pi$
$547$	17.4124			0.744502			0.372251	+	0.928132i	$0.378586\pi$
$548$	13.8868	−	13.8868i	0.593215	−	0.593215i
$549$			11.7394i			0.501026i
$550$		−	4.52971i		−	0.193148i
$551$	−0.379822	−	0.379822i	−0.0161810	−	0.0161810i
$552$	2.96509	+	2.96509i	0.126203	+	0.126203i
$553$	−2.43341	+	2.88133i	−0.103479	+	0.122527i
$554$	4.23810	+	4.23810i	0.180059	+	0.180059i
$555$	−0.594989			−0.0252559
$556$	7.37155			0.312623
$557$	6.23417	+	6.23417i	0.264150	+	0.264150i	0.826738	−	0.562587i	$-0.190194\pi$
$557$	6.23417	+	6.23417i	0.264150	+	0.264150i	−0.562587	+	0.826738i	$0.690194\pi$
$558$	−3.27281			−0.138549
$559$	8.08079	−	3.69879i	0.341781	−	0.156442i
$560$	4.31423	−	0.363595i	0.182309	−	0.0153647i
$561$	−2.07757	+	2.07757i	−0.0877153	+	0.0877153i
$562$	17.6185			0.743190
$563$	−32.2131			−1.35762			−0.678809	−	0.734315i	$-0.737504\pi$
$563$	−32.2131			−1.35762			−0.678809	+	0.734315i	$0.737504\pi$
$564$	1.41421	−	1.41421i	0.0595491	−	0.0595491i
$565$	−12.0184	−	12.0184i	−0.505618	−	0.505618i
$566$	−9.19202	+	9.19202i	−0.386370	+	0.386370i
$567$	−1.70711	+	2.02133i	−0.0716917	+	0.0848880i
$568$	7.32672			0.307422
$569$		−	25.5422i		−	1.07079i	−0.844603	−	0.535393i	$-0.820164\pi$
$569$		−	25.5422i		−	1.07079i	0.844603	−	0.535393i	$-0.179836\pi$
$570$	−1.52991	+	1.52991i	−0.0640809	+	0.0640809i
$571$		−	34.8620i		−	1.45893i	−0.684020	−	0.729464i	$-0.739770\pi$
$571$		−	34.8620i		−	1.45893i	0.684020	−	0.729464i	$-0.260230\pi$
$572$	6.59178	+	2.45214i	0.275616	+	0.102529i
$573$		−	23.1833i		−	0.968495i
$574$	8.70622	−	10.3088i	0.363391	−	0.430280i
$575$	9.73753			0.406083
$576$		−	1.00000i		−	0.0416667i
$577$	−11.7404	−	11.7404i	−0.488760	−	0.488760i	0.419155	−	0.907915i	$-0.362326\pi$
$577$	−11.7404	−	11.7404i	−0.488760	−	0.488760i	−0.907915	+	0.419155i	$0.862326\pi$
$578$	−10.4165	+	10.4165i	−0.433271	+	0.433271i
$579$	−13.6264	+	13.6264i	−0.566294	+	0.566294i
$580$	−0.470090	+	0.470090i	−0.0195194	+	0.0195194i
$581$	18.2991	−	1.54221i	0.759173	−	0.0639817i
$582$		−	14.5297i		−	0.602276i
$583$	18.5456	+	18.5456i	0.768081	+	0.768081i
$584$	−3.62050			−0.149817
$585$	2.05713	−	5.52991i	0.0850517	−	0.228634i
$586$		−	2.14317i		−	0.0885336i
$587$	−25.6920	−	25.6920i	−1.06042	−	1.06042i	−0.998053	−	0.0623701i	$-0.980134\pi$
$587$	−25.6920	−	25.6920i	−1.06042	−	1.06042i	−0.0623701	−	0.998053i	$-0.519866\pi$
$588$	−1.17157	−	6.90126i	−0.0483149	−	0.284603i
$589$			4.32724i			0.178301i
$590$	−14.3347	+	14.3347i	−0.590149	+	0.590149i
$591$	10.1950	+	10.1950i	0.419368	+	0.419368i
$592$	−0.257101	−	0.257101i	−0.0105668	−	0.0105668i
$593$	−6.06857	+	6.06857i	−0.249206	+	0.249206i	−0.820645	−	0.571439i	$-0.806386\pi$
$593$	−6.06857	+	6.06857i	−0.249206	+	0.249206i	0.571439	+	0.820645i	$0.306386\pi$
$594$		−	1.95063i		−	0.0800354i
$595$	−6.49830	+	0.547664i	−0.266404	+	0.0224521i
$596$	11.7376	+	11.7376i	0.480793	+	0.480793i
$597$			1.42518i			0.0583289i
$598$	−5.27136	+	14.1703i	−0.215562	+	0.579468i
$599$	−42.6492			−1.74260			−0.871300	−	0.490750i	$-0.836723\pi$
$599$	−42.6492			−1.74260			−0.871300	+	0.490750i	$0.836723\pi$
$600$	−1.64203	−	1.64203i	−0.0670355	−	0.0670355i
$601$			4.02249i			0.164081i	0.996629	+	0.0820405i	$0.0261437\pi$
$601$			4.02249i			0.164081i	−0.996629	+	0.0820405i	$0.973856\pi$
$602$	6.49830	−	0.547664i	0.264851	−	0.0223211i
$603$	−11.1012	+	11.1012i	−0.452077	+	0.452077i
$604$	2.79529	−	2.79529i	0.113739	−	0.113739i
$605$	8.32547	−	8.32547i	0.338479	−	0.338479i
$606$	1.36484	+	1.36484i	0.0554430	+	0.0554430i
$607$		−	39.1674i		−	1.58975i	−0.606770	−	0.794877i	$-0.707535\pi$
$607$		−	39.1674i		−	1.58975i	0.606770	−	0.794877i	$-0.292465\pi$
$608$	−1.32218			−0.0536214
$609$	0.821188	+	0.693530i	0.0332762	+	0.0281033i
$610$		−	19.2104i		−	0.777807i
$611$	6.75861	+	2.51420i	0.273424	+	0.101714i
$612$			1.50625i			0.0608865i
$613$	−15.7609	+	15.7609i	−0.636577	+	0.636577i	−0.949710	−	0.313132i	$-0.898622\pi$
$613$	−15.7609	+	15.7609i	−0.636577	+	0.636577i	0.313132	+	0.949710i	$0.398622\pi$
$614$			6.89126i			0.278109i
$615$	8.34564			0.336529
$616$	3.94287	+	3.32994i	0.158863	+	0.134167i
$617$	−19.4135	+	19.4135i	−0.781558	+	0.781558i	−0.980094	−	0.198536i	$-0.936381\pi$
$617$	−19.4135	+	19.4135i	−0.781558	+	0.781558i	0.198536	+	0.980094i	$0.436381\pi$
$618$	−5.62070	−	5.62070i	−0.226098	−	0.226098i
$619$	−28.9913	+	28.9913i	−1.16526	+	1.16526i	−0.181953	+	0.983307i	$0.558242\pi$
$619$	−28.9913	+	28.9913i	−1.16526	+	1.16526i	−0.983307	+	0.181953i	$0.941758\pi$
$620$	5.35564			0.215088
$621$	4.19327			0.168270
$622$	18.9631	−	18.9631i	0.760352	−	0.760352i
$623$	−0.637932	−	7.56936i	−0.0255582	−	0.303260i
$624$	3.27843	−	1.50062i	0.131242	−	0.0600731i
$625$	7.99659			0.319864
$626$	−1.39200	−	1.39200i	−0.0556354	−	0.0556354i
$627$	−2.57908			−0.102999
$628$	−10.4472			−0.416887
$629$	0.387257	+	0.387257i	0.0154410	+	0.0154410i
$630$	2.79352	−	3.30772i	0.111296	−	0.131783i
$631$	−14.3025	−	14.3025i	−0.569375	−	0.569375i	0.362578	−	0.931953i	$-0.381897\pi$
$631$	−14.3025	−	14.3025i	−0.569375	−	0.569375i	−0.931953	+	0.362578i	$0.881897\pi$
$632$	−1.00795	−	1.00795i	−0.0400942	−	0.0400942i
$633$			5.45234i			0.216711i
$634$		−	13.4026i		−	0.532284i
$635$	10.5531	−	10.5531i	0.418785	−	0.418785i
$636$	13.4456			0.533154
$637$	20.8672	−	14.1971i	0.826790	−	0.562511i
$638$	−0.792465			−0.0313740
$639$	5.18078	−	5.18078i	0.204948	−	0.204948i
$640$			1.63640i			0.0646846i
$641$			41.5501i			1.64113i	0.571553	+	0.820565i	$0.306341\pi$
$641$			41.5501i			1.64113i	−0.571553	+	0.820565i	$0.693659\pi$
$642$	−2.35689	−	2.35689i	−0.0930191	−	0.0930191i
$643$	−23.7094	−	23.7094i	−0.935009	−	0.935009i	0.0630044	−	0.998013i	$-0.479932\pi$
$643$	−23.7094	−	23.7094i	−0.935009	−	0.935009i	−0.998013	+	0.0630044i	$0.979932\pi$
$644$	−7.15836	+	8.47600i	−0.282079	+	0.334001i
$645$	2.85209	+	2.85209i	0.112301	+	0.112301i
$646$	1.99153			0.0783557
$647$	26.3735			1.03685			0.518425	−	0.855123i	$-0.326518\pi$
$647$	26.3735			1.03685			0.518425	+	0.855123i	$0.326518\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−24.1650			−0.948560
$650$	2.91921	−	7.84735i	0.114501	−	0.307798i
$651$	−0.727190	−	8.62845i	−0.0285008	−	0.338176i
$652$	9.07232	−	9.07232i	0.355299	−	0.355299i
$653$	−12.3520			−0.483369			−0.241685	−	0.970355i	$-0.577700\pi$
$653$	−12.3520			−0.483369			−0.241685	+	0.970355i	$0.577700\pi$
$654$	13.5536			0.529987
$655$	−4.60768	+	4.60768i	−0.180037	+	0.180037i
$656$	3.60624	+	3.60624i	0.140800	+	0.140800i
$657$	−2.56008	+	2.56008i	−0.0998782	+	0.0998782i
$658$	4.04267	+	3.41421i	0.157600	+	0.133100i
$659$	−40.1732			−1.56492			−0.782462	−	0.622698i	$-0.786036\pi$
$659$	−40.1732			−1.56492			−0.782462	+	0.622698i	$0.786036\pi$
$660$			3.19202i			0.124249i
$661$	−26.5576	+	26.5576i	−1.03297	+	1.03297i	−0.0335333	+	0.999438i	$0.510676\pi$
$661$	−26.5576	+	26.5576i	−1.03297	+	1.03297i	−0.999438	+	0.0335333i	$0.989324\pi$
$662$			18.7883i			0.730226i
$663$	−4.93813	+	2.26031i	−0.191781	+	0.0877833i
$664$			6.94091i			0.269360i
$665$	−4.37340	−	3.69353i	−0.169593	−	0.143229i
$666$	−0.363595			−0.0140890
$667$		−	1.70356i		−	0.0659622i
$668$	−9.04741	−	9.04741i	−0.350055	−	0.350055i
$669$	−18.3548	+	18.3548i	−0.709639	+	0.709639i
$670$	18.1661	−	18.1661i	0.701818	−	0.701818i
$671$	16.1922	−	16.1922i	0.625094	−	0.625094i
$672$	2.63640	−	0.222191i	0.101702	−	0.00857122i
$673$		−	3.49388i		−	0.134679i	−0.997730	−	0.0673395i	$-0.978549\pi$
$673$		−	3.49388i		−	0.134679i	0.997730	−	0.0673395i	$-0.0214511\pi$
$674$	7.50946	+	7.50946i	0.289254	+	0.289254i
$675$	−2.32218			−0.0893807
$676$	9.83940	+	8.49625i	0.378438	+	0.326779i
$677$			25.1586i			0.966922i	0.875366	+	0.483461i	$0.160620\pi$
$677$			25.1586i			0.966922i	−0.875366	+	0.483461i	$0.839380\pi$
$678$	−7.34440	−	7.34440i	−0.282060	−	0.282060i
$679$	38.3062	−	3.22838i	1.47006	−	0.123894i
$680$		−	2.46483i		−	0.0945220i
$681$	−6.91251	+	6.91251i	−0.264888	+	0.264888i
$682$	4.51420	+	4.51420i	0.172858	+	0.172858i
$683$	−26.5689	−	26.5689i	−1.01663	−	1.01663i	−0.999859	−	0.0167709i	$-0.994661\pi$
$683$	−26.5689	−	26.5689i	−1.01663	−	1.01663i	−0.0167709	−	0.999859i	$-0.505339\pi$
$684$	−0.934922	+	0.934922i	−0.0357476	+	0.0357476i
$685$			32.1372i			1.22790i
$686$	17.9342	−	4.62214i	0.684731	−	0.176474i
$687$	2.96035	+	2.96035i	0.112944	+	0.112944i
$688$			2.46483i			0.0939708i
$689$	20.1768	+	44.0806i	0.768677	+	1.67934i
$690$	−6.86189			−0.261228
$691$	1.14265	+	1.14265i	0.0434686	+	0.0434686i	0.728507	−	0.685038i	$-0.240215\pi$
$691$	1.14265	+	1.14265i	0.0434686	+	0.0434686i	−0.685038	+	0.728507i	$0.740215\pi$
$692$		−	0.0159057i		−	0.000604642i
$693$	5.14265	−	0.433413i	0.195353	−	0.0164640i
$694$	−23.7624	+	23.7624i	−0.902007	+	0.902007i
$695$	−8.52971	+	8.52971i	−0.323550	+	0.323550i
$696$	−0.287270	+	0.287270i	−0.0108889	+	0.0108889i
$697$	−5.43189	−	5.43189i	−0.205747	−	0.205747i
$698$			31.9377i			1.20886i
$699$	6.59953			0.249617
$700$	3.96421	−	4.69390i	0.149833	−	0.177413i
$701$		−	21.5853i		−	0.815264i	−0.913146	−	0.407632i	$-0.866355\pi$
$701$		−	21.5853i		−	0.815264i	0.913146	−	0.407632i	$-0.133645\pi$
$702$	1.25710	−	3.37930i	0.0474462	−	0.127544i
$703$			0.480738i			0.0181314i
$704$	−1.37930	+	1.37930i	−0.0519845	+	0.0519845i
$705$			3.27281i			0.123261i
$706$	−14.8042			−0.557162
$707$	−3.29503	+	3.90154i	−0.123922	+	0.146732i
$708$	−8.75986	+	8.75986i	−0.329216	+	0.329216i
$709$	29.2210	+	29.2210i	1.09742	+	1.09742i	0.994712	+	0.102706i	$0.0327501\pi$
$709$	29.2210	+	29.2210i	1.09742	+	1.09742i	0.102706	+	0.994712i	$0.467250\pi$
$710$	−8.47785	+	8.47785i	−0.318168	+	0.318168i
$711$	−1.42546			−0.0534589
$712$	2.87109			0.107599
$713$	−9.70418	+	9.70418i	−0.363424	+	0.363424i
$714$	−3.97108	+	0.334675i	−0.148614	+	0.0125249i
$715$	−10.4648	+	4.79003i	−0.391363	+	0.179137i
$716$	−10.3710			−0.387584
$717$	−10.9611	−	10.9611i	−0.409349	−	0.409349i
$718$	−3.79360			−0.141576
$719$	13.2373			0.493668			0.246834	−	0.969058i	$-0.420610\pi$
$719$	13.2373			0.493668			0.246834	+	0.969058i	$0.420610\pi$
$720$	1.15711	+	1.15711i	0.0431231	+	0.0431231i
$721$	13.5696	−	16.0673i	0.505357	−	0.598378i
$722$	−12.1989	−	12.1989i	−0.453996	−	0.453996i
$723$	20.1598	+	20.1598i	0.749751	+	0.749751i
$724$			1.42973i			0.0531354i
$725$			0.943410i			0.0350374i
$726$	5.08766	−	5.08766i	0.188821	−	0.188821i
$727$	17.2911			0.641291			0.320646	−	0.947199i	$-0.396100\pi$
$727$	17.2911			0.641291			0.320646	+	0.947199i	$0.396100\pi$
$728$	4.68469	+	8.30985i	0.173626	+	0.307984i
$729$	−1.00000			−0.0370370
$730$	4.18933	−	4.18933i	0.155054	−	0.155054i
$731$		−	3.71265i		−	0.137317i
$732$		−	11.7394i		−	0.433901i
$733$	14.5279	+	14.5279i	0.536602	+	0.536602i	0.922529	−	0.385927i	$-0.126118\pi$
$733$	14.5279	+	14.5279i	0.536602	+	0.536602i	−0.385927	+	0.922529i	$0.626118\pi$
$734$	−5.71872	−	5.71872i	−0.211082	−	0.211082i
$735$	9.34118	+	6.62990i	0.344555	+	0.244547i
$736$	−2.96509	−	2.96509i	−0.109295	−	0.109295i
$737$	30.6240			1.12805
$738$	5.09999			0.187733
$739$	−12.3646	−	12.3646i	−0.454838	−	0.454838i	0.442119	−	0.896957i	$-0.354227\pi$
$739$	−12.3646	−	12.3646i	−0.454838	−	0.454838i	−0.896957	+	0.442119i	$0.854227\pi$
$740$	0.594989			0.0218722
$741$	−4.46804	−	1.66211i	−0.164138	−	0.0610592i
$742$	2.98750	+	35.4481i	0.109675	+	1.30134i
$743$	−12.6873	+	12.6873i	−0.465452	+	0.465452i	−0.900437	−	0.434986i	$-0.856753\pi$
$743$	−12.6873	+	12.6873i	−0.465452	+	0.465452i	0.434986	+	0.900437i	$0.356753\pi$
$744$	3.27281			0.119987
$745$	−27.1636			−0.995196
$746$	−19.5105	+	19.5105i	−0.714331	+	0.714331i
$747$	4.90797	+	4.90797i	0.179573	+	0.179573i
$748$	2.07757	−	2.07757i	0.0759637	−	0.0759637i
$749$	5.69004	−	6.73740i	0.207910	−	0.246179i
$750$	11.9820			0.437523
$751$		−	15.8031i		−	0.576663i	−0.957531	−	0.288331i	$-0.906900\pi$
$751$		−	15.8031i		−	0.576663i	0.957531	−	0.288331i	$-0.0931004\pi$
$752$	−1.41421	+	1.41421i	−0.0515711	+	0.0515711i
$753$			6.62641i			0.241480i
$754$	−1.37288	−	0.510711i	−0.0499973	−	0.0185990i
$755$			6.46892i			0.235428i
$756$	1.70711	−	2.02133i	0.0620869	−	0.0735152i
$757$	36.8200			1.33825			0.669123	−	0.743152i	$-0.266670\pi$
$757$	36.8200			1.33825			0.669123	+	0.743152i	$0.266670\pi$
$758$			11.0232i			0.400380i
$759$	−5.78380	−	5.78380i	−0.209939	−	0.209939i
$760$	1.52991	−	1.52991i	0.0554957	−	0.0554957i
$761$	−29.9773	+	29.9773i	−1.08668	+	1.08668i	−0.0908090	+	0.995868i	$0.528945\pi$
$761$	−29.9773	+	29.9773i	−1.08668	+	1.08668i	−0.995868	+	0.0908090i	$0.971055\pi$
$762$	6.44893	−	6.44893i	0.233620	−	0.233620i
$763$	3.01149	+	35.7327i	0.109023	+	1.29361i
$764$			23.1833i			0.838741i
$765$	−1.74290	−	1.74290i	−0.0630147	−	0.0630147i
$766$	16.0324			0.579275
$767$	−41.8639	−	15.5734i	−1.51162	−	0.562321i
$768$			1.00000i			0.0360844i
$769$	28.6613	+	28.6613i	1.03355	+	1.03355i	0.999417	+	0.0341363i	$0.0108680\pi$
$769$	28.6613	+	28.6613i	1.03355	+	1.03355i	0.0341363	+	0.999417i	$0.489132\pi$
$770$	−8.41546	+	0.709240i	−0.303272	+	0.0255592i
$771$			10.5297i			0.379218i
$772$	13.6264	−	13.6264i	0.490425	−	0.490425i
$773$	31.7211	+	31.7211i	1.14093	+	1.14093i	0.988280	+	0.152650i	$0.0487806\pi$
$773$	31.7211	+	31.7211i	1.14093	+	1.14093i	0.152650	+	0.988280i	$0.451219\pi$
$774$	1.74290	+	1.74290i	0.0626472	+	0.0626472i
$775$	5.37405	−	5.37405i	0.193041	−	0.193041i
$776$			14.5297i			0.521586i
$777$	−0.0807877	−	0.958584i	−0.00289824	−	0.0343890i
$778$	−12.4216	−	12.4216i	−0.445338	−	0.445338i
$779$		−	6.74310i		−	0.241596i
$780$	−2.05713	+	5.52991i	−0.0736569	+	0.198003i
$781$	−14.2917			−0.511398
$782$	4.46616	+	4.46616i	0.159710	+	0.159710i
$783$			0.406261i			0.0145186i
$784$	1.17157	+	6.90126i	0.0418419	+	0.246474i
$785$	12.0885	−	12.0885i	0.431459	−	0.431459i
$786$	−2.81573	+	2.81573i	−0.100434	+	0.100434i
$787$	33.6855	−	33.6855i	1.20076	−	1.20076i	0.226823	−	0.973936i	$-0.427166\pi$
$787$	33.6855	−	33.6855i	1.20076	−	1.20076i	0.973936	−	0.226823i	$-0.0728339\pi$
$788$	−10.1950	−	10.1950i	−0.363183	−	0.363183i
$789$			11.3310i			0.403394i
$790$	2.33263			0.0829913
$791$	17.7309	−	20.9947i	0.630440	−	0.746484i
$792$			1.95063i			0.0693127i
$793$	38.4869	−	17.6164i	1.36671	−	0.625578i
$794$		−	34.8454i		−	1.23662i
$795$	−15.5581	+	15.5581i	−0.551790	+	0.551790i
$796$		−	1.42518i		−	0.0505143i
$797$	36.5386			1.29426			0.647132	−	0.762378i	$-0.275968\pi$
$797$	36.5386			1.29426			0.647132	+	0.762378i	$0.275968\pi$
$798$	−2.67256	−	2.25710i	−0.0946077	−	0.0799005i
$799$	2.13016	−	2.13016i	0.0753595	−	0.0753595i
$800$	1.64203	+	1.64203i	0.0580545	+	0.0580545i
$801$	2.03017	−	2.03017i	0.0717325	−	0.0717325i
$802$	29.4844			1.04113
$803$	7.06226			0.249222
$804$	11.1012	−	11.1012i	0.391510	−	0.391510i
$805$	−1.52465	−	18.0907i	−0.0537370	−	0.637614i
$806$	4.91126	+	10.7297i	0.172992	+	0.377937i
$807$	−11.6504			−0.410115
$808$	−1.36484	−	1.36484i	−0.0480151	−	0.0480151i
$809$	19.7133			0.693082			0.346541	−	0.938035i	$-0.387356\pi$
$809$	19.7133			0.693082			0.346541	+	0.938035i	$0.387356\pi$
$810$	1.63640			0.0574974
$811$	0.988834	+	0.988834i	0.0347227	+	0.0347227i	0.724255	−	0.689532i	$-0.242184\pi$
$811$	0.988834	+	0.988834i	0.0347227	+	0.0347227i	−0.689532	+	0.724255i	$0.742184\pi$
$812$	−0.821188	−	0.693530i	−0.0288181	−	0.0243381i
$813$	9.41876	+	9.41876i	0.330330	+	0.330330i
$814$	0.501508	+	0.501508i	0.0175779	+	0.0175779i
$815$			20.9954i			0.735437i
$816$		−	1.50625i		−	0.0527292i
$817$	2.30442	−	2.30442i	0.0806216	−	0.0806216i
$818$	−19.5402			−0.683206
$819$	9.18853	+	2.56337i	0.321073	+	0.0895715i
$820$	−8.34564			−0.291443
$821$	−7.22975	+	7.22975i	−0.252320	+	0.252320i	−0.821921	−	0.569601i	$-0.807098\pi$
$821$	−7.22975	+	7.22975i	−0.252320	+	0.252320i	0.569601	+	0.821921i	$0.307098\pi$
$822$			19.6389i			0.684985i
$823$		−	1.41848i		−	0.0494451i	−0.999694	−	0.0247225i	$-0.992130\pi$
$823$		−	1.41848i		−	0.0494451i	0.999694	−	0.0247225i	$-0.00787023\pi$
$824$	5.62070	+	5.62070i	0.195806	+	0.195806i
$825$	3.20299	+	3.20299i	0.111514	+	0.111514i
$826$	−25.0409	−	21.1482i	−0.871284	−	0.735839i
$827$	−18.4680	−	18.4680i	−0.642197	−	0.642197i	0.308898	−	0.951095i	$-0.400040\pi$
$827$	−18.4680	−	18.4680i	−0.642197	−	0.642197i	−0.951095	+	0.308898i	$0.900040\pi$
$828$	−4.19327			−0.145726
$829$	−2.23560			−0.0776455			−0.0388228	−	0.999246i	$-0.512361\pi$
$829$	−2.23560			−0.0776455			−0.0388228	+	0.999246i	$0.512361\pi$
$830$	−8.03142	−	8.03142i	−0.278775	−	0.278775i
$831$	−5.99357			−0.207915
$832$	−3.27843	+	1.50062i	−0.113659	+	0.0520248i
$833$	−1.76468	−	10.3950i	−0.0611425	−	0.360166i
$834$	−5.21247	+	5.21247i	−0.180493	+	0.180493i
$835$	20.9377			0.724580
$836$	2.57908			0.0891995
$837$	2.31423	−	2.31423i	0.0799914	−	0.0799914i
$838$	11.5856	+	11.5856i	0.400218	+	0.400218i
$839$	−18.5594	+	18.5594i	−0.640740	+	0.640740i	−0.950738	−	0.309997i	$-0.899672\pi$
$839$	−18.5594	+	18.5594i	−0.640740	+	0.640740i	0.309997	+	0.950738i	$0.399672\pi$
$840$	−2.79352	+	3.30772i	−0.0963855	+	0.114127i
$841$	−28.8350			−0.994309
$842$			24.3547i			0.839319i
$843$	−12.4581	+	12.4581i	−0.429081	+	0.429081i
$844$		−	5.45234i		−	0.187677i
$845$	−21.2164	+	1.55417i	−0.729867	+	0.0534651i
$846$			2.00000i			0.0687614i
$847$	14.5436	+	12.2827i	0.499723	+	0.422039i
$848$	−13.4456			−0.461725
$849$		−	12.9995i		−	0.446141i
$850$	−2.47330	−	2.47330i	−0.0848336	−	0.0848336i
$851$	−1.07809	+	1.07809i	−0.0369565	+	0.0369565i
$852$	−5.18078	+	5.18078i	−0.177490	+	0.177490i
$853$	14.9138	−	14.9138i	0.510637	−	0.510637i	−0.404084	−	0.914722i	$-0.632410\pi$
$853$	14.9138	−	14.9138i	0.510637	−	0.510637i	0.914722	+	0.404084i	$0.132410\pi$
$854$	30.9498	−	2.60840i	1.05908	−	0.0892575i
$855$		−	2.16362i		−	0.0739942i
$856$	2.35689	+	2.35689i	0.0805569	+	0.0805569i
$857$	54.4574			1.86023			0.930115	−	0.367268i	$-0.119707\pi$
$857$	54.4574			1.86023			0.930115	+	0.367268i	$0.119707\pi$
$858$	−6.39501	+	2.92717i	−0.218322	+	0.0999318i
$859$			39.4294i			1.34531i	0.739954	+	0.672657i	$0.234847\pi$
$859$			39.4294i			1.34531i	−0.739954	+	0.672657i	$0.765153\pi$
$860$	−2.85209	−	2.85209i	−0.0972554	−	0.0972554i
$861$	1.13317	+	13.4456i	0.0386184	+	0.458226i
$862$		−	31.9257i		−	1.08739i
$863$	18.5773	−	18.5773i	0.632379	−	0.632379i	−0.316285	−	0.948664i	$-0.602436\pi$
$863$	18.5773	−	18.5773i	0.632379	−	0.632379i	0.948664	+	0.316285i	$0.102436\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	0.0184046	+	0.0184046i	0.000625776	+	0.000625776i
$866$	−25.3197	+	25.3197i	−0.860400	+	0.860400i
$867$		−	14.7312i		−	0.500298i
$868$	0.727190	+	8.62845i	0.0246824	+	0.292869i
$869$	1.96614	+	1.96614i	0.0666969	+	0.0666969i
$870$		−	0.664807i		−	0.0225391i
$871$	53.0535	+	19.7359i	1.79765	+	0.668725i
$872$	−13.5536			−0.458982
$873$	10.2741	+	10.2741i	0.347724	+	0.347724i
$874$			5.54426i			0.187537i
$875$	2.66231	+	31.5895i	0.0900024	+	1.06792i
$876$	2.56008	−	2.56008i	0.0864971	−	0.0864971i
$877$	5.10175	−	5.10175i	0.172274	−	0.172274i	−0.615704	−	0.787978i	$-0.711128\pi$
$877$	5.10175	−	5.10175i	0.172274	−	0.172274i	0.787978	+	0.615704i	$0.211128\pi$
$878$	−6.92243	+	6.92243i	−0.233621	+	0.233621i
$879$	1.51545	+	1.51545i	0.0511149	+	0.0511149i
$880$		−	3.19202i		−	0.107603i
$881$	−3.68123			−0.124024			−0.0620119	−	0.998075i	$-0.519752\pi$
$881$	−3.68123			−0.124024			−0.0620119	+	0.998075i	$0.519752\pi$
$882$	5.70836	+	4.05150i	0.192210	+	0.136421i
$883$		−	51.2530i		−	1.72480i	−0.506226	−	0.862401i	$-0.668960\pi$
$883$		−	51.2530i		−	1.72480i	0.506226	−	0.862401i	$-0.331040\pi$
$884$	4.93813	−	2.26031i	0.166087	−	0.0760226i
$885$		−	20.2723i		−	0.681446i
$886$	−1.91893	+	1.91893i	−0.0644679	+	0.0644679i
$887$		−	35.1063i		−	1.17875i	−0.807858	−	0.589377i	$-0.799373\pi$
$887$		−	35.1063i		−	1.17875i	0.807858	−	0.589377i	$-0.200627\pi$
$888$	0.363595			0.0122015
$889$	18.4349	+	15.5691i	0.618286	+	0.522170i
$890$	−3.32218	+	3.32218i	−0.111360	+	0.111360i
$891$	1.37930	+	1.37930i	0.0462084	+	0.0462084i
$892$	18.3548	−	18.3548i	0.614566	−	0.614566i
$893$	2.64436			0.0884901
$894$	−16.5995			−0.555171
$895$	12.0005	−	12.0005i	0.401131	−	0.401131i
$896$	−2.63640	+	0.222191i	−0.0880761	+	0.00742289i
$897$	−6.29253	−	13.7474i	−0.210101	−	0.459011i
$898$	20.9057			0.697632
$899$	−0.940179	−	0.940179i	−0.0313567	−	0.0313567i
$900$	2.32218			0.0774060
$901$	20.2525			0.674707
$902$	−7.03444	−	7.03444i	−0.234221	−	0.234221i
$903$	−4.20773	+	4.98225i	−0.140025	+	0.165799i
$904$	7.34440	+	7.34440i	0.244271	+	0.244271i
$905$	−1.65436	−	1.65436i	−0.0549926	−	0.0549926i
$906$			3.95313i			0.131334i
$907$			39.1741i			1.30075i	0.759612	+	0.650377i	$0.225389\pi$
$907$			39.1741i			1.30075i	−0.759612	+	0.650377i	$0.774611\pi$
$908$	6.91251	−	6.91251i	0.229400	−	0.229400i
$909$	−1.93018			−0.0640201
$910$	−15.0362	−	4.19472i	−0.498444	−	0.139054i
$911$	−36.7864			−1.21879			−0.609394	−	0.792868i	$-0.708587\pi$
$911$	−36.7864			−1.21879			−0.609394	+	0.792868i	$0.708587\pi$
$912$	0.934922	−	0.934922i	0.0309583	−	0.0309583i
$913$		−	13.5392i		−	0.448081i
$914$			25.4446i			0.841632i
$915$	13.5838	+	13.5838i	0.449067	+	0.449067i
$916$	−2.96035	−	2.96035i	−0.0978127	−	0.0978127i
$917$	−8.04905	−	6.79778i	−0.265803	−	0.224483i
$918$	−1.06508	−	1.06508i	−0.0351528	−	0.0351528i
$919$	38.3072			1.26364			0.631820	−	0.775115i	$-0.282308\pi$
$919$	38.3072			1.26364			0.631820	+	0.775115i	$0.282308\pi$
$920$	6.86189			0.226230
$921$	−4.87286	−	4.87286i	−0.160566	−	0.160566i
$922$	−33.1526			−1.09182
$923$	−24.7592	−	9.21043i	−0.814960	−	0.303165i
$924$	−5.14265	+	0.433413i	−0.169181	+	0.0142583i
$925$	0.597033	−	0.597033i	0.0196303	−	0.0196303i
$926$	17.6050			0.578536
$927$	7.94886			0.261075
$928$	0.287270	−	0.287270i	0.00943009	−	0.00943009i
$929$	30.8995	+	30.8995i	1.01378	+	1.01378i	0.999904	+	0.0138758i	$0.00441695\pi$
$929$	30.8995	+	30.8995i	1.01378	+	1.01378i	0.0138758	+	0.999904i	$0.495583\pi$
$930$	−3.78701	+	3.78701i	−0.124181	+	0.124181i
$931$	5.35681	−	7.54747i	0.175562	−	0.247358i
$932$	−6.59953			−0.216175
$933$			26.8179i			0.877979i
$934$	−19.5821	+	19.5821i	−0.640744	+	0.640744i
$935$			4.80798i			0.157238i
$936$	−1.25710	+	3.37930i	−0.0410896	+	0.110456i
$937$			23.1904i			0.757596i	0.925479	+	0.378798i	$0.123663\pi$
$937$			23.1904i			0.757596i	−0.925479	+	0.378798i	$0.876337\pi$
$938$	31.7340	+	26.8008i	1.03615	+	0.875076i
$939$	1.96858			0.0642422
$940$		−	3.27281i		−	0.106747i
$941$	−21.8417	−	21.8417i	−0.712018	−	0.712018i	0.254939	−	0.966957i	$-0.417944\pi$
$941$	−21.8417	−	21.8417i	−0.712018	−	0.712018i	−0.966957	+	0.254939i	$0.917944\pi$
$942$	7.38726	−	7.38726i	0.240690	−	0.240690i
$943$	15.1219	−	15.1219i	0.492438	−	0.492438i
$944$	8.75986	−	8.75986i	0.285109	−	0.285109i
$945$	0.363595	+	4.31423i	0.0118277	+	0.140342i
$946$		−	4.80798i		−	0.156321i
$947$	18.1943	+	18.1943i	0.591236	+	0.591236i	0.937965	−	0.346729i	$-0.112708\pi$
$947$	18.1943	+	18.1943i	0.591236	+	0.591236i	−0.346729	+	0.937965i	$0.612708\pi$
$948$	1.42546			0.0462968
$949$	12.2348	+	4.55133i	0.397157	+	0.147742i
$950$		−	3.07034i		−	0.0996148i
$951$	9.47705	+	9.47705i	0.307314	+	0.307314i
$952$	3.97108	−	0.334675i	0.128703	−	0.0108469i
$953$		−	10.2539i		−	0.332156i	−0.986113	−	0.166078i	$-0.946890\pi$
$953$		−	10.2539i		−	0.332156i	0.986113	−	0.166078i	$-0.0531104\pi$
$954$	−9.50750	+	9.50750i	−0.307817	+	0.307817i
$955$	−26.8257	−	26.8257i	−0.868058	−	0.868058i
$956$	10.9611	+	10.9611i	0.354507	+	0.354507i
$957$	0.560357	−	0.560357i	0.0181138	−	0.0181138i
$958$			10.8813i			0.351560i
$959$	−51.7761	+	4.36360i	−1.67194	+	0.140908i
$960$	−1.15711	−	1.15711i	−0.0373457	−	0.0373457i
$961$		−	20.2887i		−	0.654475i
$962$	0.545620	+	1.19202i	0.0175915	+	0.0384323i
$963$	3.33315			0.107409
$964$	−20.1598	−	20.1598i	−0.649304	−	0.649304i
$965$			31.5346i			1.01513i
$966$	−0.931709	−	11.0552i	−0.0299772	−	0.355694i
$967$	21.4696	−	21.4696i	0.690417	−	0.690417i	−0.271907	−	0.962324i	$-0.587654\pi$
$967$	21.4696	−	21.4696i	0.690417	−	0.690417i	0.962324	+	0.271907i	$0.0876542\pi$
$968$	−5.08766	+	5.08766i	−0.163524	+	0.163524i
$969$	−1.40822	+	1.40822i	−0.0452387	+	0.0452387i
$970$	−16.8125	−	16.8125i	−0.539818	−	0.539818i
$971$		−	43.1357i		−	1.38429i	−0.721759	−	0.692145i	$-0.756666\pi$
$971$		−	43.1357i		−	1.38429i	0.721759	−	0.692145i	$-0.243334\pi$
$972$	1.00000			0.0320750
$973$	−14.9004	−	12.5840i	−0.477683	−	0.403425i
$974$			5.16804i			0.165595i
$975$	3.48472	+	7.61311i	0.111600	+	0.243815i
$976$			11.7394i			0.375769i
$977$	−17.7281	+	17.7281i	−0.567173	+	0.567173i	−0.931335	−	0.364163i	$-0.881355\pi$
$977$	−17.7281	+	17.7281i	−0.567173	+	0.567173i	0.364163	+	0.931335i	$0.381355\pi$
$978$			12.8302i			0.410264i
$979$	−5.60044			−0.178991
$980$	−9.34118	−	6.62990i	−0.298393	−	0.211784i
$981$	−9.58382	+	9.58382i	−0.305988	+	0.305988i
$982$	9.16776	+	9.16776i	0.292555	+	0.292555i
$983$	30.2120	−	30.2120i	0.963613	−	0.963613i	−0.0357478	−	0.999361i	$-0.511381\pi$
$983$	30.2120	−	30.2120i	0.963613	−	0.963613i	0.999361	+	0.0357478i	$0.0113813\pi$
$984$	−5.09999			−0.162582
$985$	23.5936			0.751755
$986$	−0.432700	+	0.432700i	−0.0137800	+	0.0137800i
$987$	−5.27281	+	0.444383i	−0.167835	+	0.0141449i
$988$	4.46804	+	1.66211i	0.142147	+	0.0528788i
$989$	10.3357			0.328656
$990$	−2.25710	−	2.25710i	−0.0717354	−	0.0717354i
$991$	−45.3635			−1.44102			−0.720510	−	0.693445i	$-0.756092\pi$
$991$	−45.3635			−1.44102			−0.720510	+	0.693445i	$0.756092\pi$
$992$	−3.27281			−0.103912
$993$	−13.2853	−	13.2853i	−0.421596	−	0.421596i
$994$	−14.8097	−	12.5075i	−0.469737	−	0.396714i
$995$	1.64910	+	1.64910i	0.0522799	+	0.0522799i
$996$	−4.90797	−	4.90797i	−0.155515	−	0.155515i
$997$			29.1744i			0.923963i	0.886890	+	0.461981i	$0.152861\pi$
$997$			29.1744i			0.923963i	−0.886890	+	0.461981i	$0.847139\pi$
$998$		−	22.4835i		−	0.711703i
$999$	0.257101	−	0.257101i	0.00813430	−	0.00813430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.c.265.4	yes	8
3.2	odd	2		1638.2.x.a.811.1		8
7.6	odd	2		546.2.o.b.265.3	✓	8
13.8	odd	4		546.2.o.b.307.3	yes	8
21.20	even	2		1638.2.x.c.811.2		8
39.8	even	4		1638.2.x.c.307.2		8
91.34	even	4	inner	546.2.o.c.307.4	yes	8
273.125	odd	4		1638.2.x.a.307.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.b.265.3	✓	8	7.6	odd	2
546.2.o.b.307.3	yes	8	13.8	odd	4
546.2.o.c.265.4	yes	8	1.1	even	1	trivial
546.2.o.c.307.4	yes	8	91.34	even	4	inner
1638.2.x.a.307.1		8	273.125	odd	4
1638.2.x.a.811.1		8	3.2	odd	2
1638.2.x.c.307.2		8	39.8	even	4
1638.2.x.c.811.2		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.63640 q^{10} +(1.37930 + 1.37930i) q^{11} +1.00000 q^{12} +(1.50062 + 3.27843i) q^{13} +(0.222191 + 2.63640i) q^{14} +(-1.15711 + 1.15711i) q^{15} -1.00000 q^{16} +1.50625 q^{17} +(-0.707107 + 0.707107i) q^{18} +(0.934922 + 0.934922i) q^{19} +(1.15711 - 1.15711i) q^{20} +(-2.02133 - 1.70711i) q^{21} +1.95063 q^{22} +4.19327i q^{23} +(0.707107 - 0.707107i) q^{24} -2.32218i q^{25} +(3.37930 + 1.25710i) q^{26} -1.00000i q^{27} +(2.02133 + 1.70711i) q^{28} -0.406261 q^{29} +1.63640i q^{30} +(2.31423 + 2.31423i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.37930 + 1.37930i) q^{33} +(1.06508 - 1.06508i) q^{34} +(-4.31423 + 0.363595i) q^{35} +1.00000i q^{36} +(0.257101 + 0.257101i) q^{37} +1.32218 q^{38} +(-3.27843 + 1.50062i) q^{39} -1.63640i q^{40} +(-3.60624 - 3.60624i) q^{41} +(-2.63640 + 0.222191i) q^{42} -2.46483i q^{43} +(1.37930 - 1.37930i) q^{44} +(-1.15711 - 1.15711i) q^{45} +(2.96509 + 2.96509i) q^{46} +(1.41421 - 1.41421i) q^{47} -1.00000i q^{48} +(-1.17157 - 6.90126i) q^{49} +(-1.64203 - 1.64203i) q^{50} +1.50625i q^{51} +(3.27843 - 1.50062i) q^{52} +13.4456 q^{53} +(-0.707107 - 0.707107i) q^{54} +3.19202i q^{55} +(2.63640 - 0.222191i) q^{56} +(-0.934922 + 0.934922i) q^{57} +(-0.287270 + 0.287270i) q^{58} +(-8.75986 + 8.75986i) q^{59} +(1.15711 + 1.15711i) q^{60} -11.7394i q^{61} +3.27281 q^{62} +(1.70711 - 2.02133i) q^{63} +1.00000i q^{64} +(-2.05713 + 5.52991i) q^{65} +1.95063i q^{66} +(11.1012 - 11.1012i) q^{67} -1.50625i q^{68} -4.19327 q^{69} +(-2.79352 + 3.30772i) q^{70} +(-5.18078 + 5.18078i) q^{71} +(0.707107 + 0.707107i) q^{72} +(2.56008 - 2.56008i) q^{73} +0.363595 q^{74} +2.32218 q^{75} +(0.934922 - 0.934922i) q^{76} +(-5.14265 + 0.433413i) q^{77} +(-1.25710 + 3.37930i) q^{78} +1.42546 q^{79} +(-1.15711 - 1.15711i) q^{80} +1.00000 q^{81} -5.09999 q^{82} +(-4.90797 - 4.90797i) q^{83} +(-1.70711 + 2.02133i) q^{84} +(1.74290 + 1.74290i) q^{85} +(-1.74290 - 1.74290i) q^{86} -0.406261i q^{87} -1.95063i q^{88} +(-2.03017 + 2.03017i) q^{89} -1.63640 q^{90} +(-9.18853 - 2.56337i) q^{91} +4.19327 q^{92} +(-2.31423 + 2.31423i) q^{93} -2.00000i q^{94} +2.16362i q^{95} +(-0.707107 - 0.707107i) q^{96} +(-10.2741 - 10.2741i) q^{97} +(-5.70836 - 4.05150i) q^{98} +(-1.37930 - 1.37930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9	\( 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 4 q^{17} + 8 q^{19} + 4 q^{20} - 12 q^{22} + 16 q^{26} + 12 q^{29} + 8 q^{31} + 8 q^{34} - 24 q^{35} - 4 q^{37} + 4 q^{38} - 4 q^{39} - 12 q^{41} - 4 q^{42} - 4 q^{45} + 24 q^{46} - 32 q^{49} - 8 q^{50} + 4 q^{52} + 40 q^{53} + 4 q^{56} - 8 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} - 8 q^{62} + 8 q^{63} - 12 q^{65} + 32 q^{67} + 28 q^{69} - 12 q^{71} - 20 q^{73} + 20 q^{74} + 12 q^{75} + 8 q^{76} - 8 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 40 q^{82} - 44 q^{83} - 8 q^{84} + 20 q^{85} - 20 q^{86} - 16 q^{89} + 4 q^{90} - 12 q^{91} - 28 q^{92} - 8 q^{93} + 8 q^{97} + 16 q^{98}+O(q^{100}) \) 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 4 * q^17 + 8 * q^19 + 4 * q^20 - 12 * q^22 + 16 * q^26 + 12 * q^29 + 8 * q^31 + 8 * q^34 - 24 * q^35 - 4 * q^37 + 4 * q^38 - 4 * q^39 - 12 * q^41 - 4 * q^42 - 4 * q^45 + 24 * q^46 - 32 * q^49 - 8 * q^50 + 4 * q^52 + 40 * q^53 + 4 * q^56 - 8 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 - 8 * q^62 + 8 * q^63 - 12 * q^65 + 32 * q^67 + 28 * q^69 - 12 * q^71 - 20 * q^73 + 20 * q^74 + 12 * q^75 + 8 * q^76 - 8 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 40 * q^82 - 44 * q^83 - 8 * q^84 + 20 * q^85 - 20 * q^86 - 16 * q^89 + 4 * q^90 - 12 * q^91 - 28 * q^92 - 8 * q^93 + 8 * q^97 + 16 * q^98

Introduction

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