LMFDB - Embedded newform 546.2.o.a.265.2

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:	8.0.7442857984.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
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			265.2
Root			$2.73923i$ of defining polynomial
Character	$\chi$	$=$	546.265
Dual form			546.2.o.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(0.0951965 + 0.0951965i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.64404 - 0.0951965i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(0.0951965 + 0.0951965i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.64404 - 0.0951965i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -0.134628 q^{10} +(-3.64404 - 3.64404i) q^{11} +1.00000 q^{12} +(2.00000 - 3.00000i) q^{13} +(1.93693 - 1.80230i) q^{14} +(-0.0951965 + 0.0951965i) q^{15} -1.00000 q^{16} +5.98188 q^{17} +(0.707107 - 0.707107i) q^{18} +(-4.19288 - 4.19288i) q^{19} +(0.0951965 - 0.0951965i) q^{20} +(0.0951965 - 2.64404i) q^{21} +5.15345 q^{22} +4.69380i q^{23} +(-0.707107 + 0.707107i) q^{24} -4.98188i q^{25} +(0.707107 + 3.53553i) q^{26} -1.00000i q^{27} +(-0.0951965 + 2.64404i) q^{28} -4.59428 q^{29} -0.134628i q^{30} +(-0.739235 - 0.739235i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.64404 - 3.64404i) q^{33} +(-4.22982 + 4.22982i) q^{34} +(-0.242641 - 0.260765i) q^{35} +1.00000i q^{36} +(-4.83443 - 4.83443i) q^{37} +5.92963 q^{38} +(3.00000 + 2.00000i) q^{39} +0.134628i q^{40} +(3.04544 + 3.04544i) q^{41} +(1.80230 + 1.93693i) q^{42} -8.78467i q^{43} +(-3.64404 + 3.64404i) q^{44} +(-0.0951965 - 0.0951965i) q^{45} +(-3.31902 - 3.31902i) q^{46} +(3.28808 - 3.28808i) q^{47} -1.00000i q^{48} +(6.98188 + 0.503406i) q^{49} +(3.52272 + 3.52272i) q^{50} +5.98188i q^{51} +(-3.00000 - 2.00000i) q^{52} +1.09768 q^{53} +(0.707107 + 0.707107i) q^{54} -0.693799i q^{55} +(-1.80230 - 1.93693i) q^{56} +(4.19288 - 4.19288i) q^{57} +(3.24864 - 3.24864i) q^{58} +(1.30620 - 1.30620i) q^{59} +(0.0951965 + 0.0951965i) q^{60} +5.98188i q^{61} +1.04544 q^{62} +(2.64404 + 0.0951965i) q^{63} +1.00000i q^{64} +(0.475982 - 0.0951965i) q^{65} +5.15345i q^{66} +(-0.0454356 + 0.0454356i) q^{67} -5.98188i q^{68} -4.69380 q^{69} +(0.355962 + 0.0128161i) q^{70} +(8.69380 - 8.69380i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(-4.83443 + 4.83443i) q^{73} +6.83692 q^{74} +4.98188 q^{75} +(-4.19288 + 4.19288i) q^{76} +(9.28808 + 9.98188i) q^{77} +(-3.53553 + 0.707107i) q^{78} -11.5780 q^{79} +(-0.0951965 - 0.0951965i) q^{80} +1.00000 q^{81} -4.30690 q^{82} +(-1.28808 - 1.28808i) q^{83} +(-2.64404 - 0.0951965i) q^{84} +(0.569453 + 0.569453i) q^{85} +(6.21170 + 6.21170i) q^{86} -4.59428i q^{87} -5.15345i q^{88} +(-9.21770 + 9.21770i) q^{89} +0.134628 q^{90} +(-5.57367 + 7.74172i) q^{91} +4.69380 q^{92} +(0.739235 - 0.739235i) q^{93} +4.65004i q^{94} -0.798295i q^{95} +(0.707107 + 0.707107i) q^{96} +(-9.97506 - 9.97506i) q^{97} +(-5.29289 + 4.58097i) q^{98} +(3.64404 + 3.64404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^9	$ 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 12 q^{17} + 4 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{28} - 12 q^{29} + 20 q^{31} + 8 q^{33} - 24 q^{34} + 32 q^{35} - 8 q^{37} + 12 q^{38} + 24 q^{39} + 16 q^{41} + 4 q^{42} - 8 q^{44} + 4 q^{45} - 20 q^{46} - 16 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{52} - 24 q^{53} - 4 q^{56} - 4 q^{57} - 16 q^{58} + 28 q^{59} - 4 q^{60} - 20 q^{65} + 8 q^{67} - 20 q^{69} + 24 q^{70} + 52 q^{71} - 8 q^{73} - 4 q^{74} - 20 q^{75} + 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 32 q^{83} + 20 q^{85} - 20 q^{86} + 4 q^{89} - 4 q^{90} + 12 q^{91} + 20 q^{92} - 20 q^{93} - 36 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 12 * q^17 + 4 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^28 - 12 * q^29 + 20 * q^31 + 8 * q^33 - 24 * q^34 + 32 * q^35 - 8 * q^37 + 12 * q^38 + 24 * q^39 + 16 * q^41 + 4 * q^42 - 8 * q^44 + 4 * q^45 - 20 * q^46 - 16 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^52 - 24 * q^53 - 4 * q^56 - 4 * q^57 - 16 * q^58 + 28 * q^59 - 4 * q^60 - 20 * q^65 + 8 * q^67 - 20 * q^69 + 24 * q^70 + 52 * q^71 - 8 * q^73 - 4 * q^74 - 20 * q^75 + 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 32 * q^83 + 20 * q^85 - 20 * q^86 + 4 * q^89 - 4 * q^90 + 12 * q^91 + 20 * q^92 - 20 * q^93 - 36 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.0951965	+	0.0951965i	0.0425731	+	0.0425731i	0.728073	−	0.685500i	$-0.240416\pi$
$5$	0.0951965	+	0.0951965i	0.0425731	+	0.0425731i	−0.685500	+	0.728073i	$0.740416\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−2.64404	−	0.0951965i	−0.999352	−	0.0359809i
$7$	−2.64404	−	0.0951965i	−0.999352	−	0.0359809i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−0.134628			−0.0425731
$11$	−3.64404	−	3.64404i	−1.09872	−	1.09872i	−0.994561	−	0.104158i	$-0.966785\pi$
$11$	−3.64404	−	3.64404i	−1.09872	−	1.09872i	−0.104158	−	0.994561i	$-0.533215\pi$
$12$	1.00000			0.288675
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$	1.93693	−	1.80230i	0.517667	−	0.481686i
$15$	−0.0951965	+	0.0951965i	−0.0245796	+	0.0245796i
$16$	−1.00000			−0.250000
$17$	5.98188			1.45082			0.725409	−	0.688318i	$-0.241651\pi$
$17$	5.98188			1.45082			0.725409	+	0.688318i	$0.241651\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−4.19288	−	4.19288i	−0.961913	−	0.961913i	0.0373882	−	0.999301i	$-0.488096\pi$
$19$	−4.19288	−	4.19288i	−0.961913	−	0.961913i	−0.999301	+	0.0373882i	$0.988096\pi$
$20$	0.0951965	−	0.0951965i	0.0212866	−	0.0212866i
$21$	0.0951965	−	2.64404i	0.0207736	−	0.576976i
$22$	5.15345			1.09872
$23$			4.69380i			0.978725i	0.872081	+	0.489362i	$0.162770\pi$
$23$			4.69380i			0.978725i	−0.872081	+	0.489362i	$0.837230\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$		−	4.98188i		−	0.996375i
$26$	0.707107	+	3.53553i	0.138675	+	0.693375i
$27$		−	1.00000i		−	0.192450i
$28$	−0.0951965	+	2.64404i	−0.0179904	+	0.499676i
$29$	−4.59428			−0.853136			−0.426568	−	0.904456i	$-0.640277\pi$
$29$	−4.59428			−0.853136			−0.426568	+	0.904456i	$0.640277\pi$
$30$		−	0.134628i		−	0.0245796i
$31$	−0.739235	−	0.739235i	−0.132770	−	0.132770i	0.637598	−	0.770369i	$-0.279928\pi$
$31$	−0.739235	−	0.739235i	−0.132770	−	0.132770i	−0.770369	+	0.637598i	$0.779928\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.64404	−	3.64404i	0.634346	−	0.634346i
$34$	−4.22982	+	4.22982i	−0.725409	+	0.725409i
$35$	−0.242641	−	0.260765i	−0.0410138	−	0.0440774i
$36$			1.00000i			0.166667i
$37$	−4.83443	−	4.83443i	−0.794776	−	0.794776i	0.187491	−	0.982266i	$-0.439965\pi$
$37$	−4.83443	−	4.83443i	−0.794776	−	0.794776i	−0.982266	+	0.187491i	$0.939965\pi$
$38$	5.92963			0.961913
$39$	3.00000	+	2.00000i	0.480384	+	0.320256i
$40$			0.134628i			0.0212866i
$41$	3.04544	+	3.04544i	0.475617	+	0.475617i	0.903727	−	0.428110i	$-0.140820\pi$
$41$	3.04544	+	3.04544i	0.475617	+	0.475617i	−0.428110	+	0.903727i	$0.640820\pi$
$42$	1.80230	+	1.93693i	0.278101	+	0.298875i
$43$		−	8.78467i		−	1.33965i	−0.742519	−	0.669825i	$-0.766369\pi$
$43$		−	8.78467i		−	1.33965i	0.742519	−	0.669825i	$-0.233631\pi$
$44$	−3.64404	+	3.64404i	−0.549359	+	0.549359i
$45$	−0.0951965	−	0.0951965i	−0.0141910	−	0.0141910i
$46$	−3.31902	−	3.31902i	−0.489362	−	0.489362i
$47$	3.28808	−	3.28808i	0.479615	−	0.479615i	−0.425393	−	0.905009i	$-0.639864\pi$
$47$	3.28808	−	3.28808i	0.479615	−	0.479615i	0.905009	+	0.425393i	$0.139864\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.98188	+	0.503406i	0.997411	+	0.0719152i
$50$	3.52272	+	3.52272i	0.498188	+	0.498188i
$51$			5.98188i			0.837630i
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	1.09768			0.150778			0.0753892	−	0.997154i	$-0.475980\pi$
$53$	1.09768			0.150778			0.0753892	+	0.997154i	$0.475980\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$		−	0.693799i		−	0.0935518i
$56$	−1.80230	−	1.93693i	−0.240843	−	0.258833i
$57$	4.19288	−	4.19288i	0.555360	−	0.555360i
$58$	3.24864	−	3.24864i	0.426568	−	0.426568i
$59$	1.30620	−	1.30620i	0.170053	−	0.170053i	−0.616950	−	0.787003i	$-0.711632\pi$
$59$	1.30620	−	1.30620i	0.170053	−	0.170053i	0.787003	+	0.616950i	$0.211632\pi$
$60$	0.0951965	+	0.0951965i	0.0122898	+	0.0122898i
$61$			5.98188i			0.765901i	0.923769	+	0.382950i	$0.125092\pi$
$61$			5.98188i			0.765901i	−0.923769	+	0.382950i	$0.874908\pi$
$62$	1.04544			0.132770
$63$	2.64404	+	0.0951965i	0.333117	+	0.0119936i
$64$			1.00000i			0.125000i
$65$	0.475982	−	0.0951965i	0.0590383	−	0.0118077i
$66$			5.15345i			0.634346i
$67$	−0.0454356	+	0.0454356i	−0.00555084	+	0.00555084i	−0.709877	−	0.704326i	$-0.751249\pi$
$67$	−0.0454356	+	0.0454356i	−0.00555084	+	0.00555084i	0.704326	+	0.709877i	$0.251249\pi$
$68$		−	5.98188i		−	0.725409i
$69$	−4.69380			−0.565067
$70$	0.355962	+	0.0128161i	0.0425456	+	0.00153182i
$71$	8.69380	−	8.69380i	1.03176	−	1.03176i	0.0322854	−	0.999479i	$-0.489721\pi$
$71$	8.69380	−	8.69380i	1.03176	−	1.03176i	0.999479	−	0.0322854i	$-0.0102786\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−4.83443	+	4.83443i	−0.565827	+	0.565827i	−0.930957	−	0.365129i	$-0.881025\pi$
$73$	−4.83443	+	4.83443i	−0.565827	+	0.565827i	0.365129	+	0.930957i	$0.381025\pi$
$74$	6.83692			0.794776
$75$	4.98188			0.575257
$76$	−4.19288	+	4.19288i	−0.480956	+	0.480956i
$77$	9.28808	+	9.98188i	1.05847	+	1.13754i
$78$	−3.53553	+	0.707107i	−0.400320	+	0.0800641i
$79$	−11.5780			−1.30263			−0.651313	−	0.758809i	$-0.725781\pi$
$79$	−11.5780			−1.30263			−0.651313	+	0.758809i	$0.725781\pi$
$80$	−0.0951965	−	0.0951965i	−0.0106433	−	0.0106433i
$81$	1.00000			0.111111
$82$	−4.30690			−0.475617
$83$	−1.28808	−	1.28808i	−0.141385	−	0.141385i	0.632872	−	0.774257i	$-0.281876\pi$
$83$	−1.28808	−	1.28808i	−0.141385	−	0.141385i	−0.774257	+	0.632872i	$0.781876\pi$
$84$	−2.64404	−	0.0951965i	−0.288488	−	0.0103868i
$85$	0.569453	+	0.569453i	0.0617659	+	0.0617659i
$86$	6.21170	+	6.21170i	0.669825	+	0.669825i
$87$		−	4.59428i		−	0.492558i
$88$		−	5.15345i		−	0.549359i
$89$	−9.21770	+	9.21770i	−0.977075	+	0.977075i	−0.999743	−	0.0226684i	$-0.992784\pi$
$89$	−9.21770	+	9.21770i	−0.977075	+	0.977075i	0.0226684	+	0.999743i	$0.492784\pi$
$90$	0.134628			0.0141910
$91$	−5.57367	+	7.74172i	−0.584279	+	0.811553i
$92$	4.69380			0.489362
$93$	0.739235	−	0.739235i	0.0766551	−	0.0766551i
$94$			4.65004i			0.479615i
$95$		−	0.798295i		−	0.0819033i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−9.97506	−	9.97506i	−1.01281	−	1.01281i	−0.999917	−	0.0128974i	$-0.995895\pi$
$97$	−9.97506	−	9.97506i	−1.01281	−	1.01281i	−0.0128974	−	0.999917i	$-0.504105\pi$
$98$	−5.29289	+	4.58097i	−0.534663	+	0.462748i
$99$	3.64404	+	3.64404i	0.366240	+	0.366240i
$100$	−4.98188			−0.498188
$101$	−3.09271			−0.307736			−0.153868	−	0.988091i	$-0.549173\pi$
$101$	−3.09271			−0.307736			−0.153868	+	0.988091i	$0.549173\pi$
$102$	−4.22982	−	4.22982i	−0.418815	−	0.418815i
$103$	−8.31301			−0.819106			−0.409553	−	0.912286i	$-0.634315\pi$
$103$	−8.31301			−0.819106			−0.409553	+	0.912286i	$0.634315\pi$
$104$	3.53553	−	0.707107i	0.346688	−	0.0693375i
$105$	0.260765	−	0.242641i	0.0254481	−	0.0236793i
$106$	−0.776179	+	0.776179i	−0.0753892	+	0.0753892i
$107$	−18.9569			−1.83264			−0.916318	−	0.400451i	$-0.868853\pi$
$107$	−18.9569			−1.83264			−0.916318	+	0.400451i	$0.868853\pi$
$108$	−1.00000			−0.0962250
$109$	11.3197	−	11.3197i	1.08423	−	1.08423i	0.0881221	−	0.996110i	$-0.471913\pi$
$109$	11.3197	−	11.3197i	1.08423	−	1.08423i	0.996110	−	0.0881221i	$-0.0280866\pi$
$110$	0.490590	+	0.490590i	0.0467759	+	0.0467759i
$111$	4.83443	−	4.83443i	0.458864	−	0.458864i
$112$	2.64404	+	0.0951965i	0.249838	+	0.00899522i
$113$	−0.716898			−0.0674400			−0.0337200	−	0.999431i	$-0.510735\pi$
$113$	−0.716898			−0.0674400			−0.0337200	+	0.999431i	$0.510735\pi$
$114$			5.92963i			0.555360i
$115$	−0.446833	+	0.446833i	−0.0416674	+	0.0416674i
$116$			4.59428i			0.426568i
$117$	−2.00000	+	3.00000i	−0.184900	+	0.277350i
$118$			1.84725i			0.170053i
$119$	−15.8163	−	0.569453i	−1.44988	−	0.0522017i
$120$	−0.134628			−0.0122898
$121$			15.5580i			1.41437i
$122$	−4.22982	−	4.22982i	−0.382950	−	0.382950i
$123$	−3.04544	+	3.04544i	−0.274598	+	0.274598i
$124$	−0.739235	+	0.739235i	−0.0663852	+	0.0663852i
$125$	0.950239	−	0.950239i	0.0849920	−	0.0849920i
$126$	−1.93693	+	1.80230i	−0.172556	+	0.160562i
$127$			2.28126i			0.202429i	0.994865	+	0.101215i	$0.0322729\pi$
$127$			2.28126i			0.202429i	−0.994865	+	0.101215i	$0.967727\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	8.78467			0.773447
$130$	−0.269256	+	0.403884i	−0.0236153	+	0.0354230i
$131$			7.79148i			0.680745i	0.940291	+	0.340372i	$0.110553\pi$
$131$			7.79148i			0.680745i	−0.940291	+	0.340372i	$0.889447\pi$
$132$	−3.64404	−	3.64404i	−0.317173	−	0.317173i
$133$	10.6870	+	11.4853i	0.926679	+	0.995900i
$134$		−	0.0642556i		−	0.00555084i
$135$	0.0951965	−	0.0951965i	0.00819321	−	0.00819321i
$136$	4.22982	+	4.22982i	0.362704	+	0.362704i
$137$	1.90480	+	1.90480i	0.162738	+	0.162738i	0.783779	−	0.621040i	$-0.213290\pi$
$137$	1.90480	+	1.90480i	0.162738	+	0.162738i	−0.621040	+	0.783779i	$0.713290\pi$
$138$	3.31902	−	3.31902i	0.282533	−	0.282533i
$139$		−	0.716898i		−	0.0608065i	−0.999538	−	0.0304032i	$-0.990321\pi$
$139$		−	0.716898i		−	0.0608065i	0.999538	−	0.0304032i	$-0.00967914\pi$
$140$	−0.260765	+	0.242641i	−0.0220387	+	0.0205069i
$141$	3.28808	+	3.28808i	0.276906	+	0.276906i
$142$			12.2949i			1.03176i
$143$	−18.2202	+	3.64404i	−1.52365	+	0.304730i
$144$	1.00000			0.0833333
$145$	−0.437359	−	0.437359i	−0.0363207	−	0.0363207i
$146$		−	6.83692i		−	0.565827i
$147$	−0.503406	+	6.98188i	−0.0415202	+	0.575855i
$148$	−4.83443	+	4.83443i	−0.397388	+	0.397388i
$149$	−8.22452	+	8.22452i	−0.673779	+	0.673779i	−0.958585	−	0.284806i	$-0.908071\pi$
$149$	−8.22452	+	8.22452i	−0.673779	+	0.673779i	0.284806	+	0.958585i	$0.408071\pi$
$150$	−3.52272	+	3.52272i	−0.287629	+	0.287629i
$151$	13.6713	+	13.6713i	1.11256	+	1.11256i	0.992803	+	0.119755i	$0.0382110\pi$
$151$	13.6713	+	13.6713i	1.11256	+	1.11256i	0.119755	+	0.992803i	$0.461789\pi$
$152$		−	5.92963i		−	0.480956i
$153$	−5.98188			−0.483606
$154$	−13.6259	−	0.490590i	−1.09801	−	0.0395329i
$155$		−	0.140745i		−	0.0113049i
$156$	2.00000	−	3.00000i	0.160128	−	0.240192i
$157$		−	12.3627i		−	0.986648i	−0.869846	−	0.493324i	$-0.835782\pi$
$157$		−	12.3627i		−	0.986648i	0.869846	−	0.493324i	$-0.164218\pi$
$158$	8.18688	−	8.18688i	0.651313	−	0.651313i
$159$			1.09768i			0.0870520i
$160$	0.134628			0.0106433
$161$	0.446833	−	12.4106i	0.0352154	−	0.978091i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	8.72111	+	8.72111i	0.683090	+	0.683090i	0.960695	−	0.277605i	$-0.0895407\pi$
$163$	8.72111	+	8.72111i	0.683090	+	0.683090i	−0.277605	+	0.960695i	$0.589541\pi$
$164$	3.04544	−	3.04544i	0.237809	−	0.237809i
$165$	0.693799			0.0540122
$166$	1.82161			0.141385
$167$	−13.3129	+	13.3129i	−1.03018	+	1.03018i	−0.0306531	+	0.999530i	$0.509759\pi$
$167$	−13.3129	+	13.3129i	−1.03018	+	1.03018i	−0.999530	+	0.0306531i	$0.990241\pi$
$168$	1.93693	−	1.80230i	0.149437	−	0.139051i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−0.805329			−0.0617659
$171$	4.19288	+	4.19288i	0.320638	+	0.320638i
$172$	−8.78467			−0.669825
$173$	9.58296			0.728579			0.364290	−	0.931286i	$-0.381312\pi$
$173$	9.58296			0.728579			0.364290	+	0.931286i	$0.381312\pi$
$174$	3.24864	+	3.24864i	0.246279	+	0.246279i
$175$	−0.474257	+	13.1723i	−0.0358504	+	0.995730i
$176$	3.64404	+	3.64404i	0.274680	+	0.274680i
$177$	1.30620	+	1.30620i	0.0981801	+	0.0981801i
$178$		−	13.0358i		−	0.977075i
$179$		−	6.90729i		−	0.516275i	−0.966108	−	0.258138i	$-0.916891\pi$
$179$		−	6.90729i		−	0.516275i	0.966108	−	0.258138i	$-0.0831088\pi$
$180$	−0.0951965	+	0.0951965i	−0.00709552	+	0.00709552i
$181$	22.3445			1.66086			0.830428	−	0.557126i	$-0.188096\pi$
$181$	22.3445			1.66086			0.830428	+	0.557126i	$0.188096\pi$
$182$	−1.53305	−	9.41540i	−0.113637	−	0.697916i
$183$	−5.98188			−0.442193
$184$	−3.31902	+	3.31902i	−0.244681	+	0.244681i
$185$		−	0.920441i		−	0.0676722i
$186$			1.04544i			0.0766551i
$187$	−21.7982	−	21.7982i	−1.59404	−	1.59404i
$188$	−3.28808	−	3.28808i	−0.239808	−	0.239808i
$189$	−0.0951965	+	2.64404i	−0.00692452	+	0.192325i
$190$	0.564480	+	0.564480i	0.0409516	+	0.0409516i
$191$	12.0315			0.870570			0.435285	−	0.900293i	$-0.356648\pi$
$191$	12.0315			0.870570			0.435285	+	0.900293i	$0.356648\pi$
$192$	−1.00000			−0.0721688
$193$	−14.2700	−	14.2700i	−1.02717	−	1.02717i	−0.999620	−	0.0275533i	$-0.991228\pi$
$193$	−14.2700	−	14.2700i	−1.02717	−	1.02717i	−0.0275533	−	0.999620i	$-0.508772\pi$
$194$	14.1069			1.01281
$195$	0.0951965	+	0.475982i	0.00681716	+	0.0340858i
$196$	0.503406	−	6.98188i	0.0359576	−	0.498705i
$197$	−5.54884	+	5.54884i	−0.395339	+	0.395339i	−0.876585	−	0.481247i	$-0.840184\pi$
$197$	−5.54884	+	5.54884i	−0.395339	+	0.395339i	0.481247	+	0.876585i	$0.340184\pi$
$198$	−5.15345			−0.366240
$199$	9.16546			0.649722			0.324861	−	0.945762i	$-0.394682\pi$
$199$	9.16546			0.649722			0.324861	+	0.945762i	$0.394682\pi$
$200$	3.52272	−	3.52272i	0.249094	−	0.249094i
$201$	−0.0454356	−	0.0454356i	−0.00320478	−	0.00320478i
$202$	2.18688	−	2.18688i	0.153868	−	0.153868i
$203$	12.1474	+	0.437359i	0.852583	+	0.0306966i
$204$	5.98188			0.418815
$205$			0.579829i			0.0404970i
$206$	5.87819	−	5.87819i	0.409553	−	0.409553i
$207$		−	4.69380i		−	0.326242i
$208$	−2.00000	+	3.00000i	−0.138675	+	0.208013i
$209$			30.5580i			2.11374i
$210$	−0.0128161	+	0.355962i	−0.000884396	+	0.0245637i
$211$	0.784670			0.0540189			0.0270095	−	0.999635i	$-0.491402\pi$
$211$	0.784670			0.0540189			0.0270095	+	0.999635i	$0.491402\pi$
$212$		−	1.09768i		−	0.0753892i
$213$	8.69380	+	8.69380i	0.595689	+	0.595689i
$214$	13.4046	−	13.4046i	0.916318	−	0.916318i
$215$	0.836269	−	0.836269i	0.0570331	−	0.0570331i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	1.88419	+	2.02494i	0.127907	+	0.137462i
$218$			16.0085i			1.08423i
$219$	−4.83443	−	4.83443i	−0.326681	−	0.326681i
$220$	−0.693799			−0.0467759
$221$	11.9638	−	17.9456i	0.804769	−	1.20715i
$222$			6.83692i			0.458864i
$223$	19.2064	+	19.2064i	1.28616	+	1.28616i	0.937104	+	0.349052i	$0.113496\pi$
$223$	19.2064	+	19.2064i	1.28616	+	1.28616i	0.349052	+	0.937104i	$0.386504\pi$
$224$	−1.93693	+	1.80230i	−0.129417	+	0.120421i
$225$			4.98188i			0.332125i
$226$	0.506923	−	0.506923i	0.0337200	−	0.0337200i
$227$	−11.9819	−	11.9819i	−0.795265	−	0.795265i	0.187080	−	0.982345i	$-0.440098\pi$
$227$	−11.9819	−	11.9819i	−0.795265	−	0.795265i	−0.982345	+	0.187080i	$0.940098\pi$
$228$	−4.19288	−	4.19288i	−0.277680	−	0.277680i
$229$	−8.98188	+	8.98188i	−0.593539	+	0.593539i	−0.938586	−	0.345047i	$-0.887863\pi$
$229$	−8.98188	+	8.98188i	−0.593539	+	0.593539i	0.345047	+	0.938586i	$0.387863\pi$
$230$		−	0.631917i		−	0.0416674i
$231$	−9.98188	+	9.28808i	−0.656759	+	0.611111i
$232$	−3.24864	−	3.24864i	−0.213284	−	0.213284i
$233$		−	13.1473i		−	0.861310i	−0.902517	−	0.430655i	$-0.858283\pi$
$233$		−	13.1473i		−	0.861310i	0.902517	−	0.430655i	$-0.141717\pi$
$234$	−0.707107	−	3.53553i	−0.0462250	−	0.231125i
$235$	0.626026			0.0408375
$236$	−1.30620	−	1.30620i	−0.0850264	−	0.0850264i
$237$		−	11.5780i		−	0.752071i
$238$	11.5865	−	10.7812i	0.751040	−	0.698838i
$239$	17.4834	−	17.4834i	1.13091	−	1.13091i	0.140884	−	0.990026i	$-0.455006\pi$
$239$	17.4834	−	17.4834i	1.13091	−	1.13091i	0.990026	−	0.140884i	$-0.0449944\pi$
$240$	0.0951965	−	0.0951965i	0.00614490	−	0.00614490i
$241$	−5.69380	+	5.69380i	−0.366770	+	0.366770i	−0.866298	−	0.499528i	$-0.833507\pi$
$241$	−5.69380	+	5.69380i	−0.366770	+	0.366770i	0.499528	+	0.866298i	$0.333507\pi$
$242$	−11.0012	−	11.0012i	−0.707183	−	0.707183i
$243$			1.00000i			0.0641500i
$244$	5.98188			0.382950
$245$	0.616727	+	0.712572i	0.0394013	+	0.0455246i
$246$		−	4.30690i		−	0.274598i
$247$	−20.9644	+	4.19288i	−1.33393	+	0.266787i
$248$		−	1.04544i		−	0.0663852i
$249$	1.28808	−	1.28808i	0.0816285	−	0.0816285i
$250$			1.34384i			0.0849920i
$251$	−12.4585			−0.786374			−0.393187	−	0.919459i	$-0.628627\pi$
$251$	−12.4585			−0.786374			−0.393187	+	0.919459i	$0.628627\pi$
$252$	0.0951965	−	2.64404i	0.00599681	−	0.166559i
$253$	17.1044	−	17.1044i	1.07534	−	1.07534i
$254$	−1.61310	−	1.61310i	−0.101215	−	0.101215i
$255$	−0.569453	+	0.569453i	−0.0356605	+	0.0356605i
$256$	1.00000			0.0625000
$257$	31.6738			1.97576			0.987880	−	0.155221i	$-0.0496089\pi$
$257$	31.6738			1.97576			0.987880	+	0.155221i	$0.0496089\pi$
$258$	−6.21170	+	6.21170i	−0.386724	+	0.386724i
$259$	12.3222	+	13.2426i	0.765664	+	0.822858i
$260$	−0.0951965	−	0.475982i	−0.00590383	−	0.0295192i
$261$	4.59428			0.284379
$262$	−5.50941	−	5.50941i	−0.340372	−	0.340372i
$263$	23.4422			1.44551			0.722755	−	0.691105i	$-0.242876\pi$
$263$	23.4422			1.44551			0.722755	+	0.691105i	$0.242876\pi$
$264$	5.15345			0.317173
$265$	0.104496	+	0.104496i	0.00641911	+	0.00641911i
$266$	−15.6782	−	0.564480i	−0.961290	−	0.0346105i
$267$	−9.21770	−	9.21770i	−0.564114	−	0.564114i
$268$	0.0454356	+	0.0454356i	0.00277542	+	0.00277542i
$269$			16.2813i			0.992686i	0.868126	+	0.496343i	$0.165324\pi$
$269$			16.2813i			0.992686i	−0.868126	+	0.496343i	$0.834676\pi$
$270$			0.134628i			0.00819321i
$271$	−10.1499	+	10.1499i	−0.616564	+	0.616564i	−0.944649	−	0.328084i	$-0.893597\pi$
$271$	−10.1499	+	10.1499i	−0.616564	+	0.616564i	0.328084	+	0.944649i	$0.393597\pi$
$272$	−5.98188			−0.362704
$273$	−7.74172	−	5.57367i	−0.468550	−	0.337334i
$274$	−2.69380			−0.162738
$275$	−18.1541	+	18.1541i	−1.09474	+	1.09474i
$276$			4.69380i			0.282533i
$277$			1.09271i			0.0656546i	0.999461	+	0.0328273i	$0.0104511\pi$
$277$			1.09271i			0.0656546i	−0.999461	+	0.0328273i	$0.989549\pi$
$278$	0.506923	+	0.506923i	0.0304032	+	0.0304032i
$279$	0.739235	+	0.739235i	0.0442568	+	0.0442568i
$280$	0.0128161	−	0.355962i	0.000765910	−	0.0212728i
$281$	−22.6284	−	22.6284i	−1.34990	−	1.34990i	−0.885767	−	0.464130i	$-0.846367\pi$
$281$	−22.6284	−	22.6284i	−1.34990	−	1.34990i	−0.464130	−	0.885767i	$-0.653633\pi$
$282$	−4.65004			−0.276906
$283$	30.7167			1.82592			0.912958	−	0.408053i	$-0.133792\pi$
$283$	30.7167			1.82592			0.912958	+	0.408053i	$0.133792\pi$
$284$	−8.69380	−	8.69380i	−0.515882	−	0.515882i
$285$	0.798295			0.0472869
$286$	10.3069	−	15.4603i	0.609460	−	0.914189i
$287$	−7.76233	−	8.34216i	−0.458196	−	0.492422i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	18.7828			1.10487
$290$	0.618519			0.0363207
$291$	9.97506	−	9.97506i	0.584749	−	0.584749i
$292$	4.83443	+	4.83443i	0.282914	+	0.282914i
$293$	15.5804	−	15.5804i	0.910215	−	0.910215i	−0.0860741	−	0.996289i	$-0.527432\pi$
$293$	15.5804	−	15.5804i	0.910215	−	0.910215i	0.996289	+	0.0860741i	$0.0274322\pi$
$294$	−4.58097	−	5.29289i	−0.267168	−	0.308688i
$295$	0.248691			0.0144794
$296$		−	6.83692i		−	0.397388i
$297$	−3.64404	+	3.64404i	−0.211449	+	0.211449i
$298$		−	11.6312i		−	0.673779i
$299$	14.0814	+	9.38760i	0.814348	+	0.542899i
$300$		−	4.98188i		−	0.287629i
$301$	−0.836269	+	23.2270i	−0.0482018	+	1.33878i
$302$	−19.3342			−1.11256
$303$		−	3.09271i		−	0.177672i
$304$	4.19288	+	4.19288i	0.240478	+	0.240478i
$305$	−0.569453	+	0.569453i	−0.0326068	+	0.0326068i
$306$	4.22982	−	4.22982i	0.241803	−	0.241803i
$307$	23.5058	−	23.5058i	1.34155	−	1.34155i	0.447024	−	0.894522i	$-0.352484\pi$
$307$	23.5058	−	23.5058i	1.34155	−	1.34155i	0.894522	−	0.447024i	$-0.147516\pi$
$308$	9.98188	−	9.28808i	0.568770	−	0.529237i
$309$		−	8.31301i		−	0.472911i
$310$	0.0995218	+	0.0995218i	0.00565246	+	0.00565246i
$311$	−33.9687			−1.92619			−0.963095	−	0.269162i	$-0.913253\pi$
$311$	−33.9687			−1.92619			−0.963095	+	0.269162i	$0.913253\pi$
$312$	0.707107	+	3.53553i	0.0400320	+	0.200160i
$313$		−	29.8779i		−	1.68880i	−0.535716	−	0.844398i	$-0.679958\pi$
$313$		−	29.8779i		−	1.68880i	0.535716	−	0.844398i	$-0.320042\pi$
$314$	8.74172	+	8.74172i	0.493324	+	0.493324i
$315$	0.242641	+	0.260765i	0.0136713	+	0.0146925i
$316$			11.5780i			0.651313i
$317$	15.1450	−	15.1450i	0.850626	−	0.850626i	−0.139585	−	0.990210i	$-0.544577\pi$
$317$	15.1450	−	15.1450i	0.850626	−	0.850626i	0.990210	+	0.139585i	$0.0445767\pi$
$318$	−0.776179	−	0.776179i	−0.0435260	−	0.0435260i
$319$	16.7417	+	16.7417i	0.937356	+	0.937356i
$320$	−0.0951965	+	0.0951965i	−0.00532164	+	0.00532164i
$321$		−	18.9569i		−	1.05807i
$322$	8.45965	+	9.09157i	0.471438	+	0.506653i
$323$	−25.0813	−	25.0813i	−1.39556	−	1.39556i
$324$		−	1.00000i		−	0.0555556i
$325$	−14.9456	−	9.96375i	−0.829034	−	0.552689i
$326$	−12.3335			−0.683090
$327$	11.3197	+	11.3197i	0.625982	+	0.625982i
$328$			4.30690i			0.237809i
$329$	−9.00681	+	8.38079i	−0.496562	+	0.462048i
$330$	−0.490590	+	0.490590i	−0.0270061	+	0.0270061i
$331$	10.2408	−	10.2408i	0.562885	−	0.562885i	−0.367241	−	0.930126i	$-0.619697\pi$
$331$	10.2408	−	10.2408i	0.562885	−	0.562885i	0.930126	+	0.367241i	$0.119697\pi$
$332$	−1.28808	+	1.28808i	−0.0706924	+	0.0706924i
$333$	4.83443	+	4.83443i	0.264925	+	0.264925i
$334$		−	18.8273i		−	1.03018i
$335$	−0.00865061			−0.000472633
$336$	−0.0951965	+	2.64404i	−0.00519339	+	0.144244i
$337$		−	4.59428i		−	0.250266i	−0.992140	−	0.125133i	$-0.960064\pi$
$337$		−	4.59428i		−	0.250266i	0.992140	−	0.125133i	$-0.0399358\pi$
$338$	12.0208	+	4.94975i	0.653846	+	0.269231i
$339$		−	0.716898i		−	0.0389365i
$340$	0.569453	−	0.569453i	0.0308829	−	0.0308829i
$341$			5.38760i			0.291755i
$342$	−5.92963			−0.320638
$343$	−18.4124	−	1.99567i	−0.994177	−	0.107756i
$344$	6.21170	−	6.21170i	0.334912	−	0.334912i
$345$	−0.446833	−	0.446833i	−0.0240567	−	0.0240567i
$346$	−6.77618	+	6.77618i	−0.364290	+	0.364290i
$347$	−12.2500			−0.657614			−0.328807	−	0.944397i	$-0.606647\pi$
$347$	−12.2500			−0.657614			−0.328807	+	0.944397i	$0.606647\pi$
$348$	−4.59428			−0.246279
$349$	−1.38576	+	1.38576i	−0.0741780	+	0.0741780i	−0.743222	−	0.669044i	$-0.766704\pi$
$349$	−1.38576	+	1.38576i	−0.0741780	+	0.0741780i	0.669044	+	0.743222i	$0.266704\pi$
$350$	−8.97885	−	9.64955i	−0.479940	−	0.515790i
$351$	−3.00000	−	2.00000i	−0.160128	−	0.106752i
$352$	−5.15345			−0.274680
$353$	4.31041	+	4.31041i	0.229420	+	0.229420i	0.812450	−	0.583030i	$-0.198133\pi$
$353$	4.31041	+	4.31041i	0.229420	+	0.229420i	−0.583030	+	0.812450i	$0.698133\pi$
$354$	−1.84725			−0.0981801
$355$	1.65524			0.0878509
$356$	9.21770	+	9.21770i	0.488537	+	0.488537i
$357$	0.569453	−	15.8163i	0.0301387	−	0.837088i
$358$	4.88419	+	4.88419i	0.258138	+	0.258138i
$359$	0.213491	+	0.213491i	0.0112676	+	0.0112676i	0.712718	−	0.701451i	$-0.247464\pi$
$359$	0.213491	+	0.213491i	0.0112676	+	0.0112676i	−0.701451	+	0.712718i	$0.747464\pi$
$360$		−	0.134628i		−	0.00709552i
$361$			16.1605i			0.850552i
$362$	−15.8000	+	15.8000i	−0.830428	+	0.830428i
$363$	−15.5580			−0.816585
$364$	7.74172	+	5.57367i	0.405776	+	0.292139i
$365$	−0.920441			−0.0481781
$366$	4.22982	−	4.22982i	0.221096	−	0.221096i
$367$		−	1.09768i		−	0.0572986i	−0.999590	−	0.0286493i	$-0.990879\pi$
$367$		−	1.09768i		−	0.0572986i	0.999590	−	0.0286493i	$-0.00912060\pi$
$368$		−	4.69380i		−	0.244681i
$369$	−3.04544	−	3.04544i	−0.158539	−	0.158539i
$370$	0.650850	+	0.650850i	0.0338361	+	0.0338361i
$371$	−2.90232	−	0.104496i	−0.150681	−	0.00542514i
$372$	−0.739235	−	0.739235i	−0.0383275	−	0.0383275i
$373$	21.0565			1.09026			0.545131	−	0.838351i	$-0.316480\pi$
$373$	21.0565			1.09026			0.545131	+	0.838351i	$0.316480\pi$
$374$	30.8273			1.59404
$375$	0.950239	+	0.950239i	0.0490701	+	0.0490701i
$376$	4.65004			0.239808
$377$	−9.18855	+	13.7828i	−0.473235	+	0.709852i
$378$	−1.80230	−	1.93693i	−0.0927005	−	0.0996250i
$379$	−7.22452	+	7.22452i	−0.371098	+	0.371098i	−0.867877	−	0.496779i	$-0.834516\pi$
$379$	−7.22452	+	7.22452i	−0.371098	+	0.371098i	0.496779	+	0.867877i	$0.334516\pi$
$380$	−0.798295			−0.0409516
$381$	−2.28126			−0.116873
$382$	−8.50757	+	8.50757i	−0.435285	+	0.435285i
$383$	5.97518	+	5.97518i	0.305317	+	0.305317i	0.843090	−	0.537773i	$-0.180734\pi$
$383$	5.97518	+	5.97518i	0.305317	+	0.305317i	−0.537773	+	0.843090i	$0.680734\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−0.0660472	+	1.83443i	−0.00336608	+	0.0934913i
$386$	20.1808			1.02717
$387$			8.78467i			0.446550i
$388$	−9.97506	+	9.97506i	−0.506407	+	0.506407i
$389$			25.0614i			1.27067i	0.772239	+	0.635333i	$0.219137\pi$
$389$			25.0614i			1.27067i	−0.772239	+	0.635333i	$0.780863\pi$
$390$	−0.403884	−	0.269256i	−0.0204515	−	0.0136343i
$391$			28.0777i			1.41995i
$392$	4.58097	+	5.29289i	0.231374	+	0.267331i
$393$	−7.79148			−0.393028
$394$		−	7.84725i		−	0.395339i
$395$	−1.10218	−	1.10218i	−0.0554569	−	0.0554569i
$396$	3.64404	−	3.64404i	0.183120	−	0.183120i
$397$	7.28624	−	7.28624i	0.365686	−	0.365686i	−0.500215	−	0.865901i	$-0.666746\pi$
$397$	7.28624	−	7.28624i	0.365686	−	0.365686i	0.865901	+	0.500215i	$0.166746\pi$
$398$	−6.48096	+	6.48096i	−0.324861	+	0.324861i
$399$	−11.4853	+	10.6870i	−0.574983	+	0.535019i
$400$			4.98188i			0.249094i
$401$	11.1450	+	11.1450i	0.556553	+	0.556553i	0.928324	−	0.371772i	$-0.121250\pi$
$401$	11.1450	+	11.1450i	0.556553	+	0.556553i	−0.371772	+	0.928324i	$0.621250\pi$
$402$	0.0642556			0.00320478
$403$	−3.69617	+	0.739235i	−0.184119	+	0.0368239i
$404$			3.09271i			0.153868i
$405$	0.0951965	+	0.0951965i	0.00473035	+	0.00473035i
$406$	−8.89880	+	8.28028i	−0.441640	+	0.410943i
$407$			35.2337i			1.74647i
$408$	−4.22982	+	4.22982i	−0.209408	+	0.209408i
$409$	14.6028	+	14.6028i	0.722063	+	0.722063i	0.969025	−	0.246962i	$-0.0794324\pi$
$409$	14.6028	+	14.6028i	0.722063	+	0.722063i	−0.246962	+	0.969025i	$0.579432\pi$
$410$	−0.410001	−	0.410001i	−0.0202485	−	0.0202485i
$411$	−1.90480	+	1.90480i	−0.0939570	+	0.0939570i
$412$			8.31301i			0.409553i
$413$	−3.57799	+	3.32930i	−0.176061	+	0.163824i
$414$	3.31902	+	3.31902i	0.163121	+	0.163121i
$415$		−	0.245241i		−	0.0120384i
$416$	−0.707107	−	3.53553i	−0.0346688	−	0.173344i
$417$	0.716898			0.0351066
$418$	−21.6078	−	21.6078i	−1.05687	−	1.05687i
$419$		−	16.5630i		−	0.809156i	−0.914504	−	0.404578i	$-0.867418\pi$
$419$		−	16.5630i		−	0.809156i	0.914504	−	0.404578i	$-0.132582\pi$
$420$	−0.242641	−	0.260765i	−0.0118397	−	0.0127240i
$421$	−12.1655	+	12.1655i	−0.592908	+	0.592908i	−0.938416	−	0.345508i	$-0.887707\pi$
$421$	−12.1655	+	12.1655i	−0.592908	+	0.592908i	0.345508	+	0.938416i	$0.387707\pi$
$422$	−0.554846	+	0.554846i	−0.0270095	+	0.0270095i
$423$	−3.28808	+	3.28808i	−0.159872	+	0.159872i
$424$	0.776179	+	0.776179i	0.0376946	+	0.0376946i
$425$		−	29.8010i		−	1.44556i
$426$	−12.2949			−0.595689
$427$	0.569453	−	15.8163i	0.0275578	−	0.765405i
$428$			18.9569i			0.916318i
$429$	−3.64404	−	18.2202i	−0.175936	−	0.879679i
$430$			1.18266i			0.0570331i
$431$	5.80961	−	5.80961i	0.279839	−	0.279839i	−0.553206	−	0.833045i	$-0.686596\pi$
$431$	5.80961	−	5.80961i	0.279839	−	0.279839i	0.833045	+	0.553206i	$0.186596\pi$
$432$			1.00000i			0.0481125i
$433$	30.1229			1.44761			0.723806	−	0.690003i	$-0.242391\pi$
$433$	30.1229			1.44761			0.723806	+	0.690003i	$0.242391\pi$
$434$	−2.76417	−	0.0995218i	−0.132684	−	0.00477720i
$435$	0.437359	−	0.437359i	0.0209698	−	0.0209698i
$436$	−11.3197	−	11.3197i	−0.542116	−	0.542116i
$437$	19.6805	−	19.6805i	0.941448	−	0.941448i
$438$	6.83692			0.326681
$439$	−8.65755			−0.413202			−0.206601	−	0.978425i	$-0.566240\pi$
$439$	−8.65755			−0.413202			−0.206601	+	0.978425i	$0.566240\pi$
$440$	0.490590	−	0.490590i	0.0233880	−	0.0233880i
$441$	−6.98188	−	0.503406i	−0.332470	−	0.0239717i
$442$	4.22982	+	21.1491i	0.201192	+	1.00596i
$443$	15.3839			0.730912			0.365456	−	0.930829i	$-0.380913\pi$
$443$	15.3839			0.730912			0.365456	+	0.930829i	$0.380913\pi$
$444$	−4.83443	−	4.83443i	−0.229432	−	0.229432i
$445$	−1.75499			−0.0831943
$446$	−27.1619			−1.28616
$447$	−8.22452	−	8.22452i	−0.389006	−	0.389006i
$448$	0.0951965	−	2.64404i	0.00449761	−	0.124919i
$449$	2.29056	+	2.29056i	0.108098	+	0.108098i	0.759087	−	0.650989i	$-0.225646\pi$
$449$	2.29056	+	2.29056i	0.108098	+	0.108098i	−0.650989	+	0.759087i	$0.725646\pi$
$450$	−3.52272	−	3.52272i	−0.166063	−	0.166063i
$451$		−	22.1954i		−	1.04514i
$452$			0.716898i			0.0337200i
$453$	−13.6713	+	13.6713i	−0.642336	+	0.642336i
$454$	16.9449			0.795265
$455$	−1.26758	+	0.206391i	−0.0594250	+	0.00967577i
$456$	5.92963			0.277680
$457$	9.79829	−	9.79829i	0.458345	−	0.458345i	−0.439767	−	0.898112i	$-0.644939\pi$
$457$	9.79829	−	9.79829i	0.458345	−	0.458345i	0.898112	+	0.439767i	$0.144939\pi$
$458$		−	12.7023i		−	0.593539i
$459$		−	5.98188i		−	0.279210i
$460$	0.446833	+	0.446833i	0.0208337	+	0.0208337i
$461$	−7.71441	−	7.71441i	−0.359296	−	0.359296i	0.504257	−	0.863553i	$-0.331766\pi$
$461$	−7.71441	−	7.71441i	−0.359296	−	0.359296i	−0.863553	+	0.504257i	$0.831766\pi$
$462$	0.490590	−	13.6259i	0.0228243	−	0.633935i
$463$	10.0521	+	10.0521i	0.467162	+	0.467162i	0.900994	−	0.433832i	$-0.142839\pi$
$463$	10.0521	+	10.0521i	0.467162	+	0.467162i	−0.433832	+	0.900994i	$0.642839\pi$
$464$	4.59428			0.213284
$465$	0.140745			0.00652689
$466$	9.29657	+	9.29657i	0.430655	+	0.430655i
$467$	−9.63711			−0.445952			−0.222976	−	0.974824i	$-0.571577\pi$
$467$	−9.63711			−0.445952			−0.222976	+	0.974824i	$0.571577\pi$
$468$	3.00000	+	2.00000i	0.138675	+	0.0924500i
$469$	0.124459	−	0.115808i	0.00574697	−	0.00534752i
$470$	−0.442668	+	0.442668i	−0.0204187	+	0.0204187i
$471$	12.3627			0.569641
$472$	1.84725			0.0850264
$473$	−32.0117	+	32.0117i	−1.47190	+	1.47190i
$474$	8.18688	+	8.18688i	0.376036	+	0.376036i
$475$	−20.8884	+	20.8884i	−0.958426	+	0.958426i
$476$	−0.569453	+	15.8163i	−0.0261008	+	0.724939i
$477$	−1.09768			−0.0502595
$478$			24.7253i			1.13091i
$479$	10.2288	−	10.2288i	0.467368	−	0.467368i	−0.433693	−	0.901061i	$-0.642790\pi$
$479$	10.2288	−	10.2288i	0.467368	−	0.467368i	0.901061	+	0.433693i	$0.142790\pi$
$480$			0.134628i			0.00614490i
$481$	−24.1722	+	4.83443i	−1.10216	+	0.220431i
$482$		−	8.05225i		−	0.366770i
$483$	12.4106	+	0.446833i	0.564701	+	0.0203316i
$484$	15.5580			0.707183
$485$		−	1.89918i		−	0.0862374i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	1.05675	−	1.05675i	0.0478858	−	0.0478858i	−0.682758	−	0.730644i	$-0.739220\pi$
$487$	1.05675	−	1.05675i	0.0478858	−	0.0478858i	0.730644	+	0.682758i	$0.239220\pi$
$488$	−4.22982	+	4.22982i	−0.191475	+	0.191475i
$489$	−8.72111	+	8.72111i	−0.394382	+	0.394382i
$490$	−0.939957	−	0.0677726i	−0.0424629	−	0.00306165i
$491$			1.19721i			0.0540291i	0.999635	+	0.0270146i	$0.00860005\pi$
$491$			1.19721i			0.0540291i	−0.999635	+	0.0270146i	$0.991400\pi$
$492$	3.04544	+	3.04544i	0.137299	+	0.137299i
$493$	−27.4824			−1.23774
$494$	11.8593	−	17.7889i	0.533573	−	0.800360i
$495$			0.693799i			0.0311839i
$496$	0.739235	+	0.739235i	0.0331926	+	0.0331926i
$497$	−23.8144	+	22.1591i	−1.06822	+	0.993972i
$498$			1.82161i			0.0816285i
$499$	−4.14128	+	4.14128i	−0.185389	+	0.185389i	−0.793699	−	0.608310i	$-0.791848\pi$
$499$	−4.14128	+	4.14128i	−0.185389	+	0.185389i	0.608310	+	0.793699i	$0.291848\pi$
$500$	−0.950239	−	0.950239i	−0.0424960	−	0.0424960i
$501$	−13.3129	−	13.3129i	−0.594777	−	0.594777i
$502$	8.80949	−	8.80949i	0.393187	−	0.393187i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$	1.80230	+	1.93693i	0.0802810	+	0.0862778i
$505$	−0.294415	−	0.294415i	−0.0131013	−	0.0131013i
$506$			24.1892i			1.07534i
$507$	12.0000	−	5.00000i	0.532939	−	0.222058i
$508$	2.28126			0.101215
$509$	7.43292	+	7.43292i	0.329458	+	0.329458i	0.852380	−	0.522922i	$-0.175158\pi$
$509$	7.43292	+	7.43292i	0.329458	+	0.329458i	−0.522922	+	0.852380i	$0.675158\pi$
$510$		−	0.805329i		−	0.0356605i
$511$	13.2426	−	12.3222i	0.585820	−	0.545102i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.19288	+	4.19288i	−0.185120	+	0.185120i
$514$	−22.3968	+	22.3968i	−0.987880	+	0.987880i
$515$	−0.791369	−	0.791369i	−0.0348719	−	0.0348719i
$516$		−	8.78467i		−	0.386724i
$517$	−23.9638			−1.05392
$518$	−18.0771	−	0.650850i	−0.794261	−	0.0285967i
$519$			9.58296i			0.420645i
$520$	0.403884	+	0.269256i	0.0177115	+	0.0118077i
$521$			32.0002i			1.40196i	0.713183	+	0.700978i	$0.247253\pi$
$521$			32.0002i			1.40196i	−0.713183	+	0.700978i	$0.752747\pi$
$522$	−3.24864	+	3.24864i	−0.142189	+	0.142189i
$523$			1.89550i			0.0828846i	0.999141	+	0.0414423i	$0.0131953\pi$
$523$			1.89550i			0.0828846i	−0.999141	+	0.0414423i	$0.986805\pi$
$524$	7.79148			0.340372
$525$	−13.1723	−	0.474257i	−0.574885	−	0.0206983i
$526$	−16.5762	+	16.5762i	−0.722755	+	0.722755i
$527$	−4.42201	−	4.42201i	−0.192626	−	0.192626i
$528$	−3.64404	+	3.64404i	−0.158586	+	0.158586i
$529$	0.968251			0.0420979
$530$	−0.147779			−0.00641911
$531$	−1.30620	+	1.30620i	−0.0566843	+	0.0566843i
$532$	11.4853	−	10.6870i	0.497950	−	0.463340i
$533$	15.2272	−	3.04544i	0.659562	−	0.131912i
$534$	13.0358			0.564114
$535$	−1.80463	−	1.80463i	−0.0780211	−	0.0780211i
$536$	−0.0642556			−0.00277542
$537$	6.90729			0.298072
$538$	−11.5126	−	11.5126i	−0.496343	−	0.496343i
$539$	−23.6078	−	27.2767i	−1.01686	−	1.17489i
$540$	−0.0951965	−	0.0951965i	−0.00409660	−	0.00409660i
$541$	−4.11753	−	4.11753i	−0.177027	−	0.177027i	0.613032	−	0.790058i	$-0.289950\pi$
$541$	−4.11753	−	4.11753i	−0.177027	−	0.177027i	−0.790058	+	0.613032i	$0.789950\pi$
$542$		−	14.3542i		−	0.616564i
$543$			22.3445i			0.958896i
$544$	4.22982	−	4.22982i	0.181352	−	0.181352i
$545$	2.15519			0.0923183
$546$	9.41540	−	1.53305i	0.402942	−	0.0656084i
$547$	−44.5000			−1.90268			−0.951341	−	0.308141i	$-0.900293\pi$
$547$	−44.5000			−1.90268			−0.951341	+	0.308141i	$0.900293\pi$
$548$	1.90480	−	1.90480i	0.0813692	−	0.0813692i
$549$		−	5.98188i		−	0.255300i
$550$		−	25.6738i		−	1.09474i
$551$	19.2633	+	19.2633i	0.820642	+	0.820642i
$552$	−3.31902	−	3.31902i	−0.141267	−	0.141267i
$553$	30.6126	+	1.10218i	1.30178	+	0.0468696i
$554$	−0.772662	−	0.772662i	−0.0328273	−	0.0328273i
$555$	0.920441			0.0390706
$556$	−0.716898			−0.0304032
$557$	−9.50762	−	9.50762i	−0.402851	−	0.402851i	0.476386	−	0.879236i	$-0.341947\pi$
$557$	−9.50762	−	9.50762i	−0.402851	−	0.402851i	−0.879236	+	0.476386i	$0.841947\pi$
$558$	−1.04544			−0.0442568
$559$	−26.3540	−	17.5693i	−1.11466	−	0.743104i
$560$	0.242641	+	0.260765i	0.0102534	+	0.0110194i
$561$	21.7982	−	21.7982i	0.920320	−	0.920320i
$562$	32.0014			1.34990
$563$	16.3640			0.689659			0.344829	−	0.938665i	$-0.387937\pi$
$563$	16.3640			0.689659			0.344829	+	0.938665i	$0.387937\pi$
$564$	3.28808	−	3.28808i	0.138453	−	0.138453i
$565$	−0.0682461	−	0.0682461i	−0.00287114	−	0.00287114i
$566$	−21.7200	+	21.7200i	−0.912958	+	0.912958i
$567$	−2.64404	−	0.0951965i	−0.111039	−	0.00399788i
$568$	12.2949			0.515882
$569$		−	26.8760i		−	1.12670i	−0.826218	−	0.563351i	$-0.809512\pi$
$569$		−	26.8760i		−	1.12670i	0.826218	−	0.563351i	$-0.190488\pi$
$570$	−0.564480	+	0.564480i	−0.0236434	+	0.0236434i
$571$		−	26.1591i		−	1.09472i	−0.836896	−	0.547362i	$-0.815632\pi$
$571$		−	26.1591i		−	1.09472i	0.836896	−	0.547362i	$-0.184368\pi$
$572$	3.64404	+	18.2202i	0.152365	+	0.761824i
$573$			12.0315i			0.502624i
$574$	11.3876	+	0.410001i	0.475309	+	0.0171131i
$575$	23.3839			0.975177
$576$		−	1.00000i		−	0.0416667i
$577$	3.83454	+	3.83454i	0.159634	+	0.159634i	0.782405	−	0.622770i	$-0.213993\pi$
$577$	3.83454	+	3.83454i	0.159634	+	0.159634i	−0.622770	+	0.782405i	$0.713993\pi$
$578$	−13.2815	+	13.2815i	−0.552436	+	0.552436i
$579$	14.2700	−	14.2700i	0.593039	−	0.593039i
$580$	−0.437359	+	0.437359i	−0.0181603	+	0.0181603i
$581$	3.28310	+	3.52834i	0.136206	+	0.146380i
$582$			14.1069i			0.584749i
$583$	−4.00000	−	4.00000i	−0.165663	−	0.165663i
$584$	−6.83692			−0.282914
$585$	−0.475982	+	0.0951965i	−0.0196794	+	0.00393589i
$586$			22.0340i			0.910215i
$587$	−15.5599	−	15.5599i	−0.642224	−	0.642224i	0.308877	−	0.951102i	$-0.400047\pi$
$587$	−15.5599	−	15.5599i	−0.642224	−	0.642224i	−0.951102	+	0.308877i	$0.900047\pi$
$588$	6.98188	+	0.503406i	0.287928	+	0.0207601i
$589$			6.19904i			0.255427i
$590$	−0.175851	+	0.175851i	−0.00723969	+	0.00723969i
$591$	−5.54884	−	5.54884i	−0.228249	−	0.228249i
$592$	4.83443	+	4.83443i	0.198694	+	0.198694i
$593$	−0.351637	+	0.351637i	−0.0144400	+	0.0144400i	−0.714290	−	0.699850i	$-0.753250\pi$
$593$	−0.351637	+	0.351637i	−0.0144400	+	0.0144400i	0.699850	+	0.714290i	$0.253250\pi$
$594$		−	5.15345i		−	0.211449i
$595$	−1.45145	−	1.55987i	−0.0595035	−	0.0639483i
$596$	8.22452	+	8.22452i	0.336889	+	0.336889i
$597$			9.16546i			0.375117i
$598$	−16.5951	+	3.31902i	−0.678624	+	0.135725i
$599$	34.9302			1.42721			0.713604	−	0.700549i	$-0.247062\pi$
$599$	34.9302			1.42721			0.713604	+	0.700549i	$0.247062\pi$
$600$	3.52272	+	3.52272i	0.143814	+	0.143814i
$601$			0.993188i			0.0405130i	0.999795	+	0.0202565i	$0.00644828\pi$
$601$			0.993188i			0.0405130i	−0.999795	+	0.0202565i	$0.993552\pi$
$602$	−15.8326	−	17.0153i	−0.645290	−	0.693492i
$603$	0.0454356	−	0.0454356i	0.00185028	−	0.00185028i
$604$	13.6713	−	13.6713i	0.556279	−	0.556279i
$605$	−1.48107	+	1.48107i	−0.0602140	+	0.0602140i
$606$	2.18688	+	2.18688i	0.0888358	+	0.0888358i
$607$		−	20.6029i		−	0.836247i	−0.908390	−	0.418124i	$-0.862688\pi$
$607$		−	20.6029i		−	0.836247i	0.908390	−	0.418124i	$-0.137312\pi$
$608$	−5.92963			−0.240478
$609$	−0.437359	+	12.1474i	−0.0177227	+	0.492239i
$610$		−	0.805329i		−	0.0326068i
$611$	−3.28808	−	16.4404i	−0.133021	−	0.665107i
$612$			5.98188i			0.241803i
$613$	−30.3315	+	30.3315i	−1.22508	+	1.22508i	−0.259274	+	0.965804i	$0.583483\pi$
$613$	−30.3315	+	30.3315i	−1.22508	+	1.22508i	−0.965804	+	0.259274i	$0.916517\pi$
$614$			33.2422i			1.34155i
$615$	−0.579829			−0.0233810
$616$	−0.490590	+	13.6259i	−0.0197664	+	0.549004i
$617$	−22.7622	+	22.7622i	−0.916372	+	0.916372i	−0.996763	−	0.0803909i	$-0.974383\pi$
$617$	−22.7622	+	22.7622i	−0.916372	+	0.916372i	0.0803909	+	0.996763i	$0.474383\pi$
$618$	5.87819	+	5.87819i	0.236455	+	0.236455i
$619$	−9.96126	+	9.96126i	−0.400377	+	0.400377i	−0.878366	−	0.477989i	$-0.841366\pi$
$619$	−9.96126	+	9.96126i	−0.400377	+	0.400377i	0.477989	+	0.878366i	$0.341366\pi$
$620$	−0.140745			−0.00565246
$621$	4.69380			0.188356
$622$	24.0195	−	24.0195i	0.963095	−	0.963095i
$623$	25.2495	−	23.4945i	1.01160	−	0.941286i
$624$	−3.00000	−	2.00000i	−0.120096	−	0.0800641i
$625$	−24.7285			−0.989138
$626$	21.1268	+	21.1268i	0.844398	+	0.844398i
$627$	−30.5580			−1.22037
$628$	−12.3627			−0.493324
$629$	−28.9190	−	28.9190i	−1.15307	−	1.15307i
$630$	−0.355962	−	0.0128161i	−0.0141819	−	0.000510606i
$631$	8.24750	+	8.24750i	0.328328	+	0.328328i	0.851950	−	0.523623i	$-0.175420\pi$
$631$	8.24750	+	8.24750i	0.328328	+	0.328328i	−0.523623	+	0.851950i	$0.675420\pi$
$632$	−8.18688	−	8.18688i	−0.325656	−	0.325656i
$633$			0.784670i			0.0311878i
$634$			21.4182i			0.850626i
$635$	−0.217168	+	0.217168i	−0.00861806	+	0.00861806i
$636$	1.09768			0.0435260
$637$	15.4740	−	19.9388i	0.613101	−	0.790005i
$638$	−23.6764			−0.937356
$639$	−8.69380	+	8.69380i	−0.343921	+	0.343921i
$640$		−	0.134628i		−	0.00532164i
$641$			27.4472i			1.08410i	0.840347	+	0.542049i	$0.182351\pi$
$641$			27.4472i			1.08410i	−0.840347	+	0.542049i	$0.817649\pi$
$642$	13.4046	+	13.4046i	0.529037	+	0.529037i
$643$	27.7346	+	27.7346i	1.09375	+	1.09375i	0.995125	+	0.0986217i	$0.0314434\pi$
$643$	27.7346	+	27.7346i	1.09375	+	1.09375i	0.0986217	+	0.995125i	$0.468557\pi$
$644$	−12.4106	−	0.446833i	−0.489046	−	0.0176077i
$645$	0.836269	+	0.836269i	0.0329281	+	0.0329281i
$646$	35.4703			1.39556
$647$	−14.6620			−0.576425			−0.288212	−	0.957567i	$-0.593061\pi$
$647$	−14.6620			−0.576425			−0.288212	+	0.957567i	$0.593061\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−9.51969			−0.373681
$650$	17.6136	−	3.52272i	0.690862	−	0.138172i
$651$	−2.02494	+	1.88419i	−0.0793635	+	0.0738473i
$652$	8.72111	−	8.72111i	0.341545	−	0.341545i
$653$	15.7965			0.618163			0.309082	−	0.951036i	$-0.399978\pi$
$653$	15.7965			0.618163			0.309082	+	0.951036i	$0.399978\pi$
$654$	−16.0085			−0.625982
$655$	−0.741721	+	0.741721i	−0.0289815	+	0.0289815i
$656$	−3.04544	−	3.04544i	−0.118904	−	0.118904i
$657$	4.83443	−	4.83443i	0.188609	−	0.188609i
$658$	0.442668	−	12.2949i	0.0172570	−	0.479305i
$659$	8.06825			0.314294			0.157147	−	0.987575i	$-0.449770\pi$
$659$	8.06825			0.314294			0.157147	+	0.987575i	$0.449770\pi$
$660$		−	0.693799i		−	0.0270061i
$661$	30.7552	−	30.7552i	1.19624	−	1.19624i	0.220956	−	0.975284i	$-0.429082\pi$
$661$	30.7552	−	30.7552i	1.19624	−	1.19624i	0.975284	−	0.220956i	$-0.0709178\pi$
$662$			14.4827i			0.562885i
$663$	17.9456	+	11.9638i	0.696950	+	0.464634i
$664$		−	1.82161i		−	0.0706924i
$665$	−0.0759948	+	2.11072i	−0.00294695	+	0.0818503i
$666$	−6.83692			−0.264925
$667$		−	21.5646i		−	0.834985i
$668$	13.3129	+	13.3129i	0.515092	+	0.515092i
$669$	−19.2064	+	19.2064i	−0.742562	+	0.742562i
$670$	0.00611691	−	0.00611691i	0.000236317	−	0.000236317i
$671$	21.7982	−	21.7982i	0.841509	−	0.841509i
$672$	−1.80230	−	1.93693i	−0.0695254	−	0.0747187i
$673$		−	43.5286i		−	1.67790i	−0.544206	−	0.838952i	$-0.683169\pi$
$673$		−	43.5286i		−	1.67790i	0.544206	−	0.838952i	$-0.316831\pi$
$674$	3.24864	+	3.24864i	0.125133	+	0.125133i
$675$	−4.98188			−0.191752
$676$	−12.0000	+	5.00000i	−0.461538	+	0.192308i
$677$		−	13.3826i		−	0.514336i	−0.966367	−	0.257168i	$-0.917211\pi$
$677$		−	13.3826i		−	0.514336i	0.966367	−	0.257168i	$-0.0827894\pi$
$678$	0.506923	+	0.506923i	0.0194683	+	0.0194683i
$679$	25.4249	+	27.3240i	0.975716	+	1.04860i
$680$			0.805329i			0.0308829i
$681$	11.9819	−	11.9819i	0.459146	−	0.459146i
$682$	−3.80961	−	3.80961i	−0.145877	−	0.145877i
$683$	11.4536	+	11.4536i	0.438262	+	0.438262i	0.891427	−	0.453165i	$-0.149705\pi$
$683$	11.4536	+	11.4536i	0.438262	+	0.438262i	−0.453165	+	0.891427i	$0.649705\pi$
$684$	4.19288	−	4.19288i	0.160319	−	0.160319i
$685$			0.362661i			0.0138566i
$686$	14.4307	−	11.6084i	0.550967	−	0.443211i
$687$	−8.98188	−	8.98188i	−0.342680	−	0.342680i
$688$			8.78467i			0.334912i
$689$	2.19537	−	3.29305i	0.0836368	−	0.125455i
$690$	0.631917			0.0240567
$691$	−1.55068	−	1.55068i	−0.0589907	−	0.0589907i	0.676996	−	0.735987i	$-0.263281\pi$
$691$	−1.55068	−	1.55068i	−0.0589907	−	0.0589907i	−0.735987	+	0.676996i	$0.763281\pi$
$692$		−	9.58296i		−	0.364290i
$693$	−9.28808	−	9.98188i	−0.352825	−	0.379180i
$694$	8.66205	−	8.66205i	0.328807	−	0.328807i
$695$	0.0682461	−	0.0682461i	0.00258872	−	0.00258872i
$696$	3.24864	−	3.24864i	0.123140	−	0.123140i
$697$	18.2174	+	18.2174i	0.690034	+	0.690034i
$698$		−	1.95976i		−	0.0741780i
$699$	13.1473			0.497278
$700$	13.1723	+	0.474257i	0.497865	+	0.0179252i
$701$		−	8.43541i		−	0.318601i	−0.987230	−	0.159300i	$-0.949076\pi$
$701$		−	8.43541i		−	0.318601i	0.987230	−	0.159300i	$-0.0509239\pi$
$702$	3.53553	−	0.707107i	0.133440	−	0.0266880i
$703$			40.5404i			1.52901i
$704$	3.64404	−	3.64404i	0.137340	−	0.137340i
$705$			0.626026i			0.0235775i
$706$	−6.09584			−0.229420
$707$	8.17724	+	0.294415i	0.307537	+	0.0110726i
$708$	1.30620	−	1.30620i	0.0490900	−	0.0490900i
$709$	−19.8616	−	19.8616i	−0.745917	−	0.745917i	0.227793	−	0.973710i	$-0.426849\pi$
$709$	−19.8616	−	19.8616i	−0.745917	−	0.745917i	−0.973710	+	0.227793i	$0.926849\pi$
$710$	−1.17043	+	1.17043i	−0.0439254	+	0.0439254i
$711$	11.5780			0.434209
$712$	−13.0358			−0.488537
$713$	3.46982	−	3.46982i	0.129946	−	0.129946i
$714$	10.7812	+	11.5865i	0.403475	+	0.433613i
$715$	−2.08140	−	1.38760i	−0.0778398	−	0.0518932i
$716$	−6.90729			−0.258138
$717$	17.4834	+	17.4834i	0.652931	+	0.652931i
$718$	−0.301922			−0.0112676
$719$	3.21983			0.120079			0.0600397	−	0.998196i	$-0.480877\pi$
$719$	3.21983			0.120079			0.0600397	+	0.998196i	$0.480877\pi$
$720$	0.0951965	+	0.0951965i	0.00354776	+	0.00354776i
$721$	21.9799	+	0.791369i	0.818575	+	0.0294721i
$722$	−11.4272	−	11.4272i	−0.425276	−	0.425276i
$723$	−5.69380	−	5.69380i	−0.211755	−	0.211755i
$724$		−	22.3445i		−	0.830428i
$725$			22.8881i			0.850043i
$726$	11.0012	−	11.0012i	0.408292	−	0.408292i
$727$	13.4007			0.497006			0.248503	−	0.968631i	$-0.420061\pi$
$727$	13.4007			0.497006			0.248503	+	0.968631i	$0.420061\pi$
$728$	−9.41540	+	1.53305i	−0.348958	+	0.0568185i
$729$	−1.00000			−0.0370370
$730$	0.650850	−	0.650850i	0.0240891	−	0.0240891i
$731$		−	52.5488i		−	1.94359i
$732$			5.98188i			0.221096i
$733$	−28.6644	−	28.6644i	−1.05874	−	1.05874i	−0.998163	−	0.0605789i	$-0.980705\pi$
$733$	−28.6644	−	28.6644i	−1.05874	−	1.05874i	−0.0605789	−	0.998163i	$-0.519295\pi$
$734$	0.776179	+	0.776179i	0.0286493	+	0.0286493i
$735$	−0.712572	+	0.616727i	−0.0262836	+	0.0227483i
$736$	3.31902	+	3.31902i	0.122341	+	0.122341i
$737$	0.331138			0.0121976
$738$	4.30690			0.158539
$739$	5.76417	+	5.76417i	0.212038	+	0.212038i	0.805133	−	0.593094i	$-0.202094\pi$
$739$	5.76417	+	5.76417i	0.212038	+	0.212038i	−0.593094	+	0.805133i	$0.702094\pi$
$740$	−0.920441			−0.0338361
$741$	−4.19288	−	20.9644i	−0.154029	−	0.770146i
$742$	2.12614	−	1.97836i	0.0780530	−	0.0726278i
$743$	15.4107	−	15.4107i	0.565364	−	0.565364i	−0.365462	−	0.930826i	$-0.619089\pi$
$743$	15.4107	−	15.4107i	0.565364	−	0.565364i	0.930826	+	0.365462i	$0.119089\pi$
$744$	1.04544			0.0383275
$745$	−1.56589			−0.0573698
$746$	−14.8892	+	14.8892i	−0.545131	+	0.545131i
$747$	1.28808	+	1.28808i	0.0471282	+	0.0471282i
$748$	−21.7982	+	21.7982i	−0.797020	+	0.797020i
$749$	50.1229	+	1.80463i	1.83145	+	0.0659399i
$750$	−1.34384			−0.0490701
$751$			4.11812i			0.150272i	0.997173	+	0.0751362i	$0.0239391\pi$
$751$			4.11812i			0.150272i	−0.997173	+	0.0751362i	$0.976061\pi$
$752$	−3.28808	+	3.28808i	−0.119904	+	0.119904i
$753$		−	12.4585i		−	0.454013i
$754$	−3.24864	−	16.2432i	−0.118309	−	0.591543i
$755$			2.60293i			0.0947302i
$756$	2.64404	+	0.0951965i	0.0961627	+	0.00346226i
$757$	−18.1229			−0.658687			−0.329343	−	0.944210i	$-0.606827\pi$
$757$	−18.1229			−0.658687			−0.329343	+	0.944210i	$0.606827\pi$
$758$		−	10.2170i		−	0.371098i
$759$	17.1044	+	17.1044i	0.620850	+	0.620850i
$760$	0.564480	−	0.564480i	0.0204758	−	0.0204758i
$761$	21.1268	−	21.1268i	0.765847	−	0.765847i	−0.211525	−	0.977372i	$-0.567843\pi$
$761$	21.1268	−	21.1268i	0.765847	−	0.765847i	0.977372	+	0.211525i	$0.0678431\pi$
$762$	1.61310	−	1.61310i	0.0584363	−	0.0584363i
$763$	−31.0073	+	28.8522i	−1.12254	+	1.04452i
$764$		−	12.0315i		−	0.435285i
$765$	−0.569453	−	0.569453i	−0.0205886	−	0.0205886i
$766$	−8.45018			−0.305317
$767$	−1.30620	−	6.53100i	−0.0471642	−	0.235821i
$768$			1.00000i			0.0360844i
$769$	−2.12748	−	2.12748i	−0.0767189	−	0.0767189i	0.667706	−	0.744425i	$-0.267276\pi$
$769$	−2.12748	−	2.12748i	−0.0767189	−	0.0767189i	−0.744425	+	0.667706i	$0.767276\pi$
$770$	−1.25044	−	1.34384i	−0.0450626	−	0.0484287i
$771$			31.6738i			1.14071i
$772$	−14.2700	+	14.2700i	−0.513587	+	0.513587i
$773$	3.62354	+	3.62354i	0.130330	+	0.130330i	0.769263	−	0.638933i	$-0.220624\pi$
$773$	3.62354	+	3.62354i	0.130330	+	0.130330i	−0.638933	+	0.769263i	$0.720624\pi$
$774$	−6.21170	−	6.21170i	−0.223275	−	0.223275i
$775$	−3.68277	+	3.68277i	−0.132289	+	0.132289i
$776$		−	14.1069i		−	0.506407i
$777$	−13.2426	+	12.3222i	−0.475077	+	0.442056i
$778$	−17.7211	−	17.7211i	−0.635333	−	0.635333i
$779$		−	25.5383i		−	0.915004i
$780$	0.475982	−	0.0951965i	0.0170429	−	0.00340858i
$781$	−63.3611			−2.26724
$782$	−19.8539	−	19.8539i	−0.709976	−	0.709976i
$783$			4.59428i			0.164186i
$784$	−6.98188	−	0.503406i	−0.249353	−	0.0179788i
$785$	1.17688	−	1.17688i	0.0420047	−	0.0420047i
$786$	5.50941	−	5.50941i	0.196514	−	0.196514i
$787$	1.94787	−	1.94787i	0.0694339	−	0.0694339i	−0.671537	−	0.740971i	$-0.734366\pi$
$787$	1.94787	−	1.94787i	0.0694339	−	0.0694339i	0.740971	+	0.671537i	$0.234366\pi$
$788$	5.54884	+	5.54884i	0.197669	+	0.197669i
$789$			23.4422i			0.834565i
$790$	1.55872			0.0554569
$791$	1.89550	+	0.0682461i	0.0673964	+	0.00242655i
$792$			5.15345i			0.183120i
$793$	17.9456	+	11.9638i	0.637268	+	0.424845i
$794$			10.3043i			0.365686i
$795$	−0.104496	+	0.104496i	−0.00370608	+	0.00370608i
$796$		−	9.16546i		−	0.324861i
$797$	37.8727			1.34152			0.670759	−	0.741675i	$-0.265968\pi$
$797$	37.8727			1.34152			0.670759	+	0.741675i	$0.265968\pi$
$798$	0.564480	−	15.6782i	0.0199824	−	0.555001i
$799$	19.6689	−	19.6689i	0.695834	−	0.695834i
$800$	−3.52272	−	3.52272i	−0.124547	−	0.124547i
$801$	9.21770	−	9.21770i	0.325692	−	0.325692i
$802$	−15.7613			−0.556553
$803$	35.2337			1.24337
$804$	−0.0454356	+	0.0454356i	−0.00160239	+	0.00160239i
$805$	1.22398	−	1.13891i	0.0431396	−	0.0401412i
$806$	2.09087	−	3.13631i	0.0736478	−	0.110472i
$807$	−16.2813			−0.573128
$808$	−2.18688	−	2.18688i	−0.0769340	−	0.0769340i
$809$	−30.9619			−1.08856			−0.544281	−	0.838903i	$-0.683198\pi$
$809$	−30.9619			−1.08856			−0.544281	+	0.838903i	$0.683198\pi$
$810$	−0.134628			−0.00473035
$811$	10.3882	+	10.3882i	0.364781	+	0.364781i	0.865569	−	0.500789i	$-0.166957\pi$
$811$	10.3882	+	10.3882i	0.364781	+	0.364781i	−0.500789	+	0.865569i	$0.666957\pi$
$812$	0.437359	−	12.1474i	0.0153483	−	0.426292i
$813$	−10.1499	−	10.1499i	−0.355974	−	0.355974i
$814$	−24.9140	−	24.9140i	−0.873235	−	0.873235i
$815$			1.66044i			0.0581626i
$816$		−	5.98188i		−	0.209408i
$817$	−36.8331	+	36.8331i	−1.28863	+	1.28863i
$818$	−20.6515			−0.722063
$819$	5.57367	−	7.74172i	0.194760	−	0.270518i
$820$	0.579829			0.0202485
$821$	−28.9593	+	28.9593i	−1.01069	+	1.01069i	−0.0107447	+	0.999942i	$0.503420\pi$
$821$	−28.9593	+	28.9593i	−1.01069	+	1.01069i	−0.999942	+	0.0107447i	$0.996580\pi$
$822$		−	2.69380i		−	0.0939570i
$823$		−	1.99480i		−	0.0695344i	−0.999395	−	0.0347672i	$-0.988931\pi$
$823$		−	1.99480i		−	0.0695344i	0.999395	−	0.0347672i	$-0.0110690\pi$
$824$	−5.87819	−	5.87819i	−0.204776	−	0.204776i
$825$	−18.1541	−	18.1541i	−0.632046	−	0.632046i
$826$	0.175851	−	4.88419i	0.00611865	−	0.169943i
$827$	−25.3675	−	25.3675i	−0.882115	−	0.882115i	0.111634	−	0.993749i	$-0.464392\pi$
$827$	−25.3675	−	25.3675i	−0.882115	−	0.882115i	−0.993749	+	0.111634i	$0.964392\pi$
$828$	−4.69380			−0.163121
$829$	−25.3522			−0.880517			−0.440259	−	0.897871i	$-0.645113\pi$
$829$	−25.3522			−0.880517			−0.440259	+	0.897871i	$0.645113\pi$
$830$	0.173411	+	0.173411i	0.00601919	+	0.00601919i
$831$	−1.09271			−0.0379057
$832$	3.00000	+	2.00000i	0.104006	+	0.0693375i
$833$	41.7647	+	3.01131i	1.44706	+	0.104336i
$834$	−0.506923	+	0.506923i	−0.0175533	+	0.0175533i
$835$	−2.53468			−0.0877163
$836$	30.5580			1.05687
$837$	−0.739235	+	0.739235i	−0.0255517	+	0.0255517i
$838$	11.7118	+	11.7118i	0.404578	+	0.404578i
$839$	−34.3545	+	34.3545i	−1.18605	+	1.18605i	−0.207898	+	0.978151i	$0.566662\pi$
$839$	−34.3545	+	34.3545i	−1.18605	+	1.18605i	−0.978151	+	0.207898i	$0.933338\pi$
$840$	0.355962	+	0.0128161i	0.0122819	+	0.000442198i
$841$	−7.89262			−0.272159
$842$		−	17.2046i		−	0.592908i
$843$	22.6284	−	22.6284i	0.779364	−	0.779364i
$844$		−	0.784670i		−	0.0270095i
$845$	0.666375	−	1.61834i	0.0229240	−	0.0556726i
$846$		−	4.65004i		−	0.159872i
$847$	1.48107	−	41.1360i	0.0508901	−	1.41345i
$848$	−1.09768			−0.0376946
$849$			30.7167i			1.05419i
$850$	21.0725	+	21.0725i	0.722779	+	0.722779i
$851$	22.6918	−	22.6918i	0.777867	−	0.777867i
$852$	8.69380	−	8.69380i	0.297845	−	0.297845i
$853$	−15.6489	+	15.6489i	−0.535808	+	0.535808i	−0.922295	−	0.386487i	$-0.873688\pi$
$853$	−15.6489	+	15.6489i	−0.535808	+	0.535808i	0.386487	+	0.922295i	$0.373688\pi$
$854$	10.7812	+	11.5865i	0.368923	+	0.396481i
$855$			0.798295i			0.0273011i
$856$	−13.4046	−	13.4046i	−0.458159	−	0.458159i
$857$	−44.8434			−1.53182			−0.765911	−	0.642946i	$-0.777712\pi$
$857$	−44.8434			−1.53182			−0.765911	+	0.642946i	$0.777712\pi$
$858$	15.4603	+	10.3069i	0.527807	+	0.351872i
$859$		−	55.8416i		−	1.90529i	−0.304083	−	0.952645i	$-0.598350\pi$
$859$		−	55.8416i		−	1.90529i	0.304083	−	0.952645i	$-0.401650\pi$
$860$	−0.836269	−	0.836269i	−0.0285166	−	0.0285166i
$861$	8.34216	−	7.76233i	0.284300	−	0.264540i
$862$			8.21603i			0.279839i
$863$	28.7122	−	28.7122i	0.977374	−	0.977374i	−0.0223760	−	0.999750i	$-0.507123\pi$
$863$	28.7122	−	28.7122i	0.977374	−	0.977374i	0.999750	+	0.0223760i	$0.00712308\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	0.912264	+	0.912264i	0.0310179	+	0.0310179i
$866$	−21.3001	+	21.3001i	−0.723806	+	0.723806i
$867$			18.7828i			0.637898i
$868$	2.02494	−	1.88419i	0.0687308	−	0.0639536i
$869$	42.1906	+	42.1906i	1.43122	+	1.43122i
$870$			0.618519i			0.0209698i
$871$	0.0454356	+	0.227178i	0.00153953	+	0.00769763i
$872$	16.0085			0.542116
$873$	9.97506	+	9.97506i	0.337605	+	0.337605i
$874$			27.8325i			0.941448i
$875$	−2.60293	+	2.42201i	−0.0879950	+	0.0818789i
$876$	−4.83443	+	4.83443i	−0.163340	+	0.163340i
$877$	25.4259	−	25.4259i	0.858573	−	0.858573i	−0.132597	−	0.991170i	$-0.542332\pi$
$877$	25.4259	−	25.4259i	0.858573	−	0.858573i	0.991170	+	0.132597i	$0.0423317\pi$
$878$	6.12181	−	6.12181i	0.206601	−	0.206601i
$879$	15.5804	+	15.5804i	0.525513	+	0.525513i
$880$			0.693799i			0.0233880i
$881$	−32.2182			−1.08546			−0.542730	−	0.839907i	$-0.682609\pi$
$881$	−32.2182			−1.08546			−0.542730	+	0.839907i	$0.682609\pi$
$882$	5.29289	−	4.58097i	0.178221	−	0.154249i
$883$		−	16.0777i		−	0.541058i	−0.962712	−	0.270529i	$-0.912801\pi$
$883$		−	16.0777i		−	0.541058i	0.962712	−	0.270529i	$-0.0871987\pi$
$884$	−17.9456	−	11.9638i	−0.603577	−	0.402384i
$885$			0.248691i			0.00835967i
$886$	−10.8781	+	10.8781i	−0.365456	+	0.365456i
$887$		−	48.6804i		−	1.63453i	−0.576263	−	0.817264i	$-0.695490\pi$
$887$		−	48.6804i		−	1.63453i	0.576263	−	0.817264i	$-0.304510\pi$
$888$	6.83692			0.229432
$889$	0.217168	−	6.03175i	0.00728359	−	0.202298i
$890$	1.24096	−	1.24096i	0.0415971	−	0.0415971i
$891$	−3.64404	−	3.64404i	−0.122080	−	0.122080i
$892$	19.2064	−	19.2064i	0.643078	−	0.643078i
$893$	−27.5730			−0.922696
$894$	11.6312			0.389006
$895$	0.657550	−	0.657550i	0.0219795	−	0.0219795i
$896$	1.80230	+	1.93693i	0.0602107	+	0.0647083i
$897$	−9.38760	+	14.0814i	−0.313443	+	0.470164i
$898$	−3.23935			−0.108098
$899$	3.39625	+	3.39625i	0.113271	+	0.113271i
$900$	4.98188			0.166063
$901$	6.56620			0.218752
$902$	15.6945	+	15.6945i	0.522569	+	0.522569i
$903$	−23.2270	−	0.836269i	−0.772946	−	0.0278293i
$904$	−0.506923	−	0.506923i	−0.0168600	−	0.0168600i
$905$	2.12712	+	2.12712i	0.0707079	+	0.0707079i
$906$		−	19.3342i		−	0.642336i
$907$		−	9.60559i		−	0.318948i	−0.987202	−	0.159474i	$-0.949020\pi$
$907$		−	9.60559i		−	0.318948i	0.987202	−	0.159474i	$-0.0509799\pi$
$908$	−11.9819	+	11.9819i	−0.397632	+	0.397632i
$909$	3.09271			0.102579
$910$	0.750372	−	1.04225i	0.0248746	−	0.0345504i
$911$	−20.1412			−0.667308			−0.333654	−	0.942696i	$-0.608282\pi$
$911$	−20.1412			−0.667308			−0.333654	+	0.942696i	$0.608282\pi$
$912$	−4.19288	+	4.19288i	−0.138840	+	0.138840i
$913$			9.38760i			0.310684i
$914$			13.8569i			0.458345i
$915$	−0.569453	−	0.569453i	−0.0188255	−	0.0188255i
$916$	8.98188	+	8.98188i	0.296770	+	0.296770i
$917$	0.741721	−	20.6010i	0.0244938	−	0.680304i
$918$	4.22982	+	4.22982i	0.139605	+	0.139605i
$919$	−48.6806			−1.60583			−0.802913	−	0.596096i	$-0.796718\pi$
$919$	−48.6806			−1.60583			−0.802913	+	0.596096i	$0.796718\pi$
$920$	−0.631917			−0.0208337
$921$	23.5058	+	23.5058i	0.774542	+	0.774542i
$922$	10.9098			0.359296
$923$	−8.69380	−	43.4690i	−0.286160	−	1.43080i
$924$	9.28808	+	9.98188i	0.305555	+	0.328380i
$925$	−24.0845	+	24.0845i	−0.791895	+	0.791895i
$926$	−14.2159			−0.467162
$927$	8.31301			0.273035
$928$	−3.24864	+	3.24864i	−0.106642	+	0.106642i
$929$	35.6667	+	35.6667i	1.17019	+	1.17019i	0.982165	+	0.188023i	$0.0602080\pi$
$929$	35.6667	+	35.6667i	1.17019	+	1.17019i	0.188023	+	0.982165i	$0.439792\pi$
$930$	−0.0995218	+	0.0995218i	−0.00326345	+	0.00326345i
$931$	−27.1634	−	31.3849i	−0.890246	−	1.02860i
$932$	−13.1473			−0.430655
$933$		−	33.9687i		−	1.11209i
$934$	6.81447	−	6.81447i	0.222976	−	0.222976i
$935$		−	4.15022i		−	0.135727i
$936$	−3.53553	+	0.707107i	−0.115563	+	0.0231125i
$937$		−	38.9567i		−	1.27266i	−0.771417	−	0.636330i	$-0.780452\pi$
$937$		−	38.9567i		−	1.27266i	0.771417	−	0.636330i	$-0.219548\pi$
$938$	−0.00611691	+	0.169894i	−0.000199724	+	0.00554724i
$939$	29.8779			0.975027
$940$		−	0.626026i		−	0.0204187i
$941$	23.3041	+	23.3041i	0.759691	+	0.759691i	0.976266	−	0.216575i	$-0.0694885\pi$
$941$	23.3041	+	23.3041i	0.759691	+	0.759691i	−0.216575	+	0.976266i	$0.569489\pi$
$942$	−8.74172	+	8.74172i	−0.284821	+	0.284821i
$943$	−14.2947	+	14.2947i	−0.465498	+	0.465498i
$944$	−1.30620	+	1.30620i	−0.0425132	+	0.0425132i
$945$	−0.260765	+	0.242641i	−0.00848270	+	0.00789310i
$946$		−	45.2713i		−	1.47190i
$947$	5.45365	+	5.45365i	0.177220	+	0.177220i	0.790143	−	0.612923i	$-0.210006\pi$
$947$	5.45365	+	5.45365i	0.177220	+	0.177220i	−0.612923	+	0.790143i	$0.710006\pi$
$948$	−11.5780			−0.376036
$949$	4.83443	+	24.1722i	0.156932	+	0.784661i
$950$		−	29.5407i		−	0.958426i
$951$	15.1450	+	15.1450i	0.491109	+	0.491109i
$952$	−10.7812	−	11.5865i	−0.349419	−	0.375520i
$953$			5.73711i			0.185843i	0.995673	+	0.0929216i	$0.0296206\pi$
$953$			5.73711i			0.185843i	−0.995673	+	0.0929216i	$0.970379\pi$
$954$	0.776179	−	0.776179i	0.0251297	−	0.0251297i
$955$	1.14536	+	1.14536i	0.0370629	+	0.0370629i
$956$	−17.4834	−	17.4834i	−0.565455	−	0.565455i
$957$	−16.7417	+	16.7417i	−0.541183	+	0.541183i
$958$			14.4658i			0.467368i
$959$	−4.85504	−	5.21770i	−0.156778	−	0.168488i
$960$	−0.0951965	−	0.0951965i	−0.00307245	−	0.00307245i
$961$		−	29.9071i		−	0.964744i
$962$	13.6738	−	20.5108i	0.440862	−	0.661293i
$963$	18.9569			0.610879
$964$	5.69380	+	5.69380i	0.183385	+	0.183385i
$965$		−	2.71690i		−	0.0874600i
$966$	−9.09157	+	8.45965i	−0.292516	+	0.272185i
$967$	13.7260	−	13.7260i	0.441397	−	0.441397i	−0.451084	−	0.892481i	$-0.648963\pi$
$967$	13.7260	−	13.7260i	0.441397	−	0.441397i	0.892481	+	0.451084i	$0.148963\pi$
$968$	−11.0012	+	11.0012i	−0.353592	+	0.353592i
$969$	25.0813	−	25.0813i	0.805727	−	0.805727i
$970$	1.34292	+	1.34292i	0.0431187	+	0.0431187i
$971$			43.6460i			1.40067i	0.713816	+	0.700334i	$0.246965\pi$
$971$			43.6460i			1.40067i	−0.713816	+	0.700334i	$0.753035\pi$
$972$	1.00000			0.0320750
$973$	−0.0682461	+	1.89550i	−0.00218787	+	0.0607671i
$974$			1.49447i			0.0478858i
$975$	9.96375	−	14.9456i	0.319095	−	0.478643i
$976$		−	5.98188i		−	0.191475i
$977$	−34.3951	+	34.3951i	−1.10040	+	1.10040i	−0.106033	+	0.994363i	$0.533815\pi$
$977$	−34.3951	+	34.3951i	−1.10040	+	1.10040i	−0.994363	+	0.106033i	$0.966185\pi$
$978$		−	12.3335i		−	0.394382i
$979$	67.1793			2.14706
$980$	0.712572	−	0.616727i	0.0227623	−	0.0197006i
$981$	−11.3197	+	11.3197i	−0.361411	+	0.361411i
$982$	−0.846552	−	0.846552i	−0.0270146	−	0.0270146i
$983$	−34.2785	+	34.2785i	−1.09331	+	1.09331i	−0.0981415	+	0.995172i	$0.531290\pi$
$983$	−34.2785	+	34.2785i	−1.09331	+	1.09331i	−0.995172	+	0.0981415i	$0.968710\pi$
$984$	−4.30690			−0.137299
$985$	−1.05646			−0.0336616
$986$	19.4330	−	19.4330i	0.618872	−	0.618872i
$987$	−8.38079	−	9.00681i	−0.266763	−	0.286690i
$988$	4.19288	+	20.9644i	0.133393	+	0.666966i
$989$	41.2335			1.31115
$990$	−0.490590	−	0.490590i	−0.0155920	−	0.0155920i
$991$	56.0596			1.78079			0.890396	−	0.455187i	$-0.150428\pi$
$991$	56.0596			1.78079			0.890396	+	0.455187i	$0.150428\pi$
$992$	−1.04544			−0.0331926
$993$	10.2408	+	10.2408i	0.324982	+	0.324982i
$994$	1.17043	−	32.5082i	0.0371238	−	1.03110i
$995$	0.872519	+	0.872519i	0.0276607	+	0.0276607i
$996$	−1.28808	−	1.28808i	−0.0408143	−	0.0408143i
$997$			12.1817i			0.385800i	0.981218	+	0.192900i	$0.0617892\pi$
$997$			12.1817i			0.385800i	−0.981218	+	0.192900i	$0.938211\pi$
$998$		−	5.85666i		−	0.185389i
$999$	−4.83443	+	4.83443i	−0.152955	+	0.152955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.a.265.2	✓	8
3.2	odd	2		1638.2.x.d.811.3		8
7.6	odd	2		546.2.o.d.265.1	yes	8
13.8	odd	4		546.2.o.d.307.1	yes	8
21.20	even	2		1638.2.x.b.811.4		8
39.8	even	4		1638.2.x.b.307.4		8
91.34	even	4	inner	546.2.o.a.307.2	yes	8
273.125	odd	4		1638.2.x.d.307.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.2	✓	8	1.1	even	1	trivial
546.2.o.a.307.2	yes	8	91.34	even	4	inner
546.2.o.d.265.1	yes	8	7.6	odd	2
546.2.o.d.307.1	yes	8	13.8	odd	4
1638.2.x.b.307.4		8	39.8	even	4
1638.2.x.b.811.4		8	21.20	even	2
1638.2.x.d.307.3		8	273.125	odd	4
1638.2.x.d.811.3		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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(0.0951965 + 0.0951965i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.64404 - 0.0951965i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{3} -1.00000i q^{4} +(0.0951965 + 0.0951965i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.64404 - 0.0951965i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -0.134628 q^{10} +(-3.64404 - 3.64404i) q^{11} +1.00000 q^{12} +(2.00000 - 3.00000i) q^{13} +(1.93693 - 1.80230i) q^{14} +(-0.0951965 + 0.0951965i) q^{15} -1.00000 q^{16} +5.98188 q^{17} +(0.707107 - 0.707107i) q^{18} +(-4.19288 - 4.19288i) q^{19} +(0.0951965 - 0.0951965i) q^{20} +(0.0951965 - 2.64404i) q^{21} +5.15345 q^{22} +4.69380i q^{23} +(-0.707107 + 0.707107i) q^{24} -4.98188i q^{25} +(0.707107 + 3.53553i) q^{26} -1.00000i q^{27} +(-0.0951965 + 2.64404i) q^{28} -4.59428 q^{29} -0.134628i q^{30} +(-0.739235 - 0.739235i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.64404 - 3.64404i) q^{33} +(-4.22982 + 4.22982i) q^{34} +(-0.242641 - 0.260765i) q^{35} +1.00000i q^{36} +(-4.83443 - 4.83443i) q^{37} +5.92963 q^{38} +(3.00000 + 2.00000i) q^{39} +0.134628i q^{40} +(3.04544 + 3.04544i) q^{41} +(1.80230 + 1.93693i) q^{42} -8.78467i q^{43} +(-3.64404 + 3.64404i) q^{44} +(-0.0951965 - 0.0951965i) q^{45} +(-3.31902 - 3.31902i) q^{46} +(3.28808 - 3.28808i) q^{47} -1.00000i q^{48} +(6.98188 + 0.503406i) q^{49} +(3.52272 + 3.52272i) q^{50} +5.98188i q^{51} +(-3.00000 - 2.00000i) q^{52} +1.09768 q^{53} +(0.707107 + 0.707107i) q^{54} -0.693799i q^{55} +(-1.80230 - 1.93693i) q^{56} +(4.19288 - 4.19288i) q^{57} +(3.24864 - 3.24864i) q^{58} +(1.30620 - 1.30620i) q^{59} +(0.0951965 + 0.0951965i) q^{60} +5.98188i q^{61} +1.04544 q^{62} +(2.64404 + 0.0951965i) q^{63} +1.00000i q^{64} +(0.475982 - 0.0951965i) q^{65} +5.15345i q^{66} +(-0.0454356 + 0.0454356i) q^{67} -5.98188i q^{68} -4.69380 q^{69} +(0.355962 + 0.0128161i) q^{70} +(8.69380 - 8.69380i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(-4.83443 + 4.83443i) q^{73} +6.83692 q^{74} +4.98188 q^{75} +(-4.19288 + 4.19288i) q^{76} +(9.28808 + 9.98188i) q^{77} +(-3.53553 + 0.707107i) q^{78} -11.5780 q^{79} +(-0.0951965 - 0.0951965i) q^{80} +1.00000 q^{81} -4.30690 q^{82} +(-1.28808 - 1.28808i) q^{83} +(-2.64404 - 0.0951965i) q^{84} +(0.569453 + 0.569453i) q^{85} +(6.21170 + 6.21170i) q^{86} -4.59428i q^{87} -5.15345i q^{88} +(-9.21770 + 9.21770i) q^{89} +0.134628 q^{90} +(-5.57367 + 7.74172i) q^{91} +4.69380 q^{92} +(0.739235 - 0.739235i) q^{93} +4.65004i q^{94} -0.798295i q^{95} +(0.707107 + 0.707107i) q^{96} +(-9.97506 - 9.97506i) q^{97} +(-5.29289 + 4.58097i) q^{98} +(3.64404 + 3.64404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^9	\( 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 12 q^{17} + 4 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{28} - 12 q^{29} + 20 q^{31} + 8 q^{33} - 24 q^{34} + 32 q^{35} - 8 q^{37} + 12 q^{38} + 24 q^{39} + 16 q^{41} + 4 q^{42} - 8 q^{44} + 4 q^{45} - 20 q^{46} - 16 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{52} - 24 q^{53} - 4 q^{56} - 4 q^{57} - 16 q^{58} + 28 q^{59} - 4 q^{60} - 20 q^{65} + 8 q^{67} - 20 q^{69} + 24 q^{70} + 52 q^{71} - 8 q^{73} - 4 q^{74} - 20 q^{75} + 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 32 q^{83} + 20 q^{85} - 20 q^{86} + 4 q^{89} - 4 q^{90} + 12 q^{91} + 20 q^{92} - 20 q^{93} - 36 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 12 * q^17 + 4 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^28 - 12 * q^29 + 20 * q^31 + 8 * q^33 - 24 * q^34 + 32 * q^35 - 8 * q^37 + 12 * q^38 + 24 * q^39 + 16 * q^41 + 4 * q^42 - 8 * q^44 + 4 * q^45 - 20 * q^46 - 16 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^52 - 24 * q^53 - 4 * q^56 - 4 * q^57 - 16 * q^58 + 28 * q^59 - 4 * q^60 - 20 * q^65 + 8 * q^67 - 20 * q^69 + 24 * q^70 + 52 * q^71 - 8 * q^73 - 4 * q^74 - 20 * q^75 + 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 32 * q^83 + 20 * q^85 - 20 * q^86 + 4 * q^89 - 4 * q^90 + 12 * q^91 + 20 * q^92 - 20 * q^93 - 36 * q^97 - 48 * q^98 + 8 * q^99

Introduction

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