LMFDB - Embedded newform 546.2.p.d.281.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 8x^18 - 20x^17 + 56x^16 - 140x^15 + 288x^14 - 532x^13 + 1065x^12 - 2080x^11 + 3712x^10 - 6240x^9 + 9585x^8 - 14364x^7 + 23328x^6 - 34020x^5 + 40824x^4 - 43740x^3 + 52488x^2 - 78732*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.8
Root			$-1.01577 + 1.40293i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.d.239.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} -1.00000i q^{4} +(1.75112 - 1.75112i) q^{5} +(-1.01577 - 1.40293i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.85010 - 0.936434i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} -1.00000i q^{4} +(1.75112 - 1.75112i) q^{5} +(-1.01577 - 1.40293i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.85010 - 0.936434i) q^{9} -2.47645i q^{10} +(2.12300 + 2.12300i) q^{11} +(-1.71028 - 0.273767i) q^{12} +(-3.47808 - 0.950237i) q^{13} -1.00000i q^{14} +(-2.51550 - 3.47430i) q^{15} -1.00000 q^{16} +3.03575 q^{17} +(-2.67749 + 1.35317i) q^{18} +(2.63603 + 2.63603i) q^{19} +(-1.75112 - 1.75112i) q^{20} +(-1.01577 - 1.40293i) q^{21} +3.00237 q^{22} +0.478247 q^{23} +(-1.40293 + 1.01577i) q^{24} -1.13282i q^{25} +(-3.13129 + 1.78746i) q^{26} +(-2.38183 + 4.61811i) q^{27} +(-0.707107 - 0.707107i) q^{28} +6.03691i q^{29} +(-4.23543 - 0.677971i) q^{30} +(-2.07156 - 2.07156i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.21213 - 3.04971i) q^{33} +(2.14660 - 2.14660i) q^{34} -2.47645i q^{35} +(-0.936434 + 2.85010i) q^{36} +(-4.21400 + 4.21400i) q^{37} +3.72791 q^{38} +(-2.57735 + 5.68834i) q^{39} -2.47645 q^{40} +(4.84049 - 4.84049i) q^{41} +(-1.71028 - 0.273767i) q^{42} -4.59522i q^{43} +(2.12300 - 2.12300i) q^{44} +(-6.63067 + 3.35106i) q^{45} +(0.338172 - 0.338172i) q^{46} +(-6.97225 - 6.97225i) q^{47} +(-0.273767 + 1.71028i) q^{48} -1.00000i q^{49} +(-0.801028 - 0.801028i) q^{50} +(0.831086 - 5.19197i) q^{51} +(-0.950237 + 3.47808i) q^{52} +5.90009i q^{53} +(1.58129 + 4.94970i) q^{54} +7.43524 q^{55} -1.00000 q^{56} +(5.23000 - 3.78669i) q^{57} +(4.26874 + 4.26874i) q^{58} +(3.76763 + 3.76763i) q^{59} +(-3.47430 + 2.51550i) q^{60} +13.2619 q^{61} -2.92963 q^{62} +(-2.67749 + 1.35317i) q^{63} +1.00000i q^{64} +(-7.75451 + 4.42655i) q^{65} +(0.821950 - 5.13490i) q^{66} +(-6.61080 - 6.61080i) q^{67} -3.03575i q^{68} +(0.130928 - 0.817936i) q^{69} +(-1.75112 - 1.75112i) q^{70} +(7.36537 - 7.36537i) q^{71} +(1.35317 + 2.67749i) q^{72} +(-8.06119 + 8.06119i) q^{73} +5.95950i q^{74} +(-1.93745 - 0.310130i) q^{75} +(2.63603 - 2.63603i) q^{76} +3.00237 q^{77} +(2.19980 + 5.84473i) q^{78} -11.6022 q^{79} +(-1.75112 + 1.75112i) q^{80} +(7.24618 + 5.33787i) q^{81} -6.84548i q^{82} +(9.96904 - 9.96904i) q^{83} +(-1.40293 + 1.01577i) q^{84} +(5.31595 - 5.31595i) q^{85} +(-3.24931 - 3.24931i) q^{86} +(10.3248 + 1.65271i) q^{87} -3.00237i q^{88} +(10.9270 + 10.9270i) q^{89} +(-2.31904 + 7.05815i) q^{90} +(-3.13129 + 1.78746i) q^{91} -0.478247i q^{92} +(-4.11007 + 2.97582i) q^{93} -9.86025 q^{94} +9.23199 q^{95} +(1.01577 + 1.40293i) q^{96} +(10.7186 + 10.7186i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-4.06272 - 8.03882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9	$ 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9 + 16 * q^11 + 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 - 12 * q^17 - 16 * q^18 + 12 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 + 4 * q^23 - 4 * q^24 + 24 * q^27 - 12 * q^30 - 8 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * q^54 + 28 * q^55 - 20 * q^56 + 36 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 - 4 * q^61 - 48 * q^62 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * q^78 - 64 * q^79 - 4 * q^80 + 32 * q^81 + 24 * q^83 - 4 * q^84 + 24 * q^85 - 4 * q^86 + 4 * q^87 + 4 * q^89 + 8 * q^90 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.273767	−	1.71028i	0.158059	−	0.987430i
$3$	0.273767	−	1.71028i	0.158059	−	0.987430i
$4$		−	1.00000i		−	0.500000i
$5$	1.75112	−	1.75112i	0.783124	−	0.783124i	−0.197233	−	0.980357i	$-0.563196\pi$
$5$	1.75112	−	1.75112i	0.783124	−	0.783124i	0.980357	+	0.197233i	$0.0631956\pi$
$6$	−1.01577	−	1.40293i	−0.414685	−	0.572744i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.85010	−	0.936434i	−0.950035	−	0.312145i
$10$		−	2.47645i		−	0.783124i
$11$	2.12300	+	2.12300i	0.640108	+	0.640108i	0.950582	−	0.310474i	$-0.100488\pi$
$11$	2.12300	+	2.12300i	0.640108	+	0.640108i	−0.310474	+	0.950582i	$0.600488\pi$
$12$	−1.71028	−	0.273767i	−0.493715	−	0.0790296i
$13$	−3.47808	−	0.950237i	−0.964646	−	0.263548i
$13$	−3.47808	−	0.950237i	−0.964646	−	0.263548i
$14$		−	1.00000i		−	0.267261i
$15$	−2.51550	−	3.47430i	−0.649499	−	0.897059i
$16$	−1.00000			−0.250000
$17$	3.03575			0.736277			0.368138	−	0.929771i	$-0.379995\pi$
$17$	3.03575			0.736277			0.368138	+	0.929771i	$0.379995\pi$
$18$	−2.67749	+	1.35317i	−0.631090	+	0.318945i
$19$	2.63603	+	2.63603i	0.604747	+	0.604747i	0.941568	−	0.336822i	$-0.109352\pi$
$19$	2.63603	+	2.63603i	0.604747	+	0.604747i	−0.336822	+	0.941568i	$0.609352\pi$
$20$	−1.75112	−	1.75112i	−0.391562	−	0.391562i
$21$	−1.01577	−	1.40293i	−0.221659	−	0.306145i
$22$	3.00237			0.640108
$23$	0.478247			0.0997215			0.0498607	−	0.998756i	$-0.484122\pi$
$23$	0.478247			0.0997215			0.0498607	+	0.998756i	$0.484122\pi$
$24$	−1.40293	+	1.01577i	−0.286372	+	0.207343i
$25$		−	1.13282i		−	0.226565i
$26$	−3.13129	+	1.78746i	−0.614097	+	0.350549i
$27$	−2.38183	+	4.61811i	−0.458383	+	0.888755i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$			6.03691i			1.12103i	0.828145	+	0.560513i	$0.189396\pi$
$29$			6.03691i			1.12103i	−0.828145	+	0.560513i	$0.810604\pi$
$30$	−4.23543	−	0.677971i	−0.773279	−	0.123780i
$31$	−2.07156	−	2.07156i	−0.372064	−	0.372064i	0.496165	−	0.868228i	$-0.334741\pi$
$31$	−2.07156	−	2.07156i	−0.372064	−	0.372064i	−0.868228	+	0.496165i	$0.834741\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	4.21213	−	3.04971i	0.733237	−	0.530887i
$34$	2.14660	−	2.14660i	0.368138	−	0.368138i
$35$		−	2.47645i		−	0.418597i
$36$	−0.936434	+	2.85010i	−0.156072	+	0.475017i
$37$	−4.21400	+	4.21400i	−0.692778	+	0.692778i	−0.962842	−	0.270064i	$-0.912955\pi$
$37$	−4.21400	+	4.21400i	−0.692778	+	0.692778i	0.270064	+	0.962842i	$0.412955\pi$
$38$	3.72791			0.604747
$39$	−2.57735	+	5.68834i	−0.412707	+	0.910864i
$40$	−2.47645			−0.391562
$41$	4.84049	−	4.84049i	0.755957	−	0.755957i	−0.219627	−	0.975584i	$-0.570484\pi$
$41$	4.84049	−	4.84049i	0.755957	−	0.755957i	0.975584	+	0.219627i	$0.0704840\pi$
$42$	−1.71028	−	0.273767i	−0.263902	−	0.0422431i
$43$		−	4.59522i		−	0.700764i	−0.936607	−	0.350382i	$-0.886052\pi$
$43$		−	4.59522i		−	0.700764i	0.936607	−	0.350382i	$-0.113948\pi$
$44$	2.12300	−	2.12300i	0.320054	−	0.320054i
$45$	−6.63067	+	3.35106i	−0.988442	+	0.499546i
$46$	0.338172	−	0.338172i	0.0498607	−	0.0498607i
$47$	−6.97225	−	6.97225i	−1.01701	−	1.01701i	−0.999853	−	0.0171544i	$-0.994539\pi$
$47$	−6.97225	−	6.97225i	−1.01701	−	1.01701i	−0.0171544	−	0.999853i	$-0.505461\pi$
$48$	−0.273767	+	1.71028i	−0.0395148	+	0.246857i
$49$		−	1.00000i		−	0.142857i
$50$	−0.801028	−	0.801028i	−0.113282	−	0.113282i
$51$	0.831086	−	5.19197i	0.116375	−	0.727021i
$52$	−0.950237	+	3.47808i	−0.131774	+	0.482323i
$53$			5.90009i			0.810440i	0.914219	+	0.405220i	$0.132805\pi$
$53$			5.90009i			0.810440i	−0.914219	+	0.405220i	$0.867195\pi$
$54$	1.58129	+	4.94970i	0.215186	+	0.673569i
$55$	7.43524			1.00257
$56$	−1.00000			−0.133631
$57$	5.23000	−	3.78669i	0.692730	−	0.501559i
$58$	4.26874	+	4.26874i	0.560513	+	0.560513i
$59$	3.76763	+	3.76763i	0.490504	+	0.490504i	0.908465	−	0.417961i	$-0.137255\pi$
$59$	3.76763	+	3.76763i	0.490504	+	0.490504i	−0.417961	+	0.908465i	$0.637255\pi$
$60$	−3.47430	+	2.51550i	−0.448530	+	0.324750i
$61$	13.2619			1.69801			0.849007	−	0.528382i	$-0.177201\pi$
$61$	13.2619			1.69801			0.849007	+	0.528382i	$0.177201\pi$
$62$	−2.92963			−0.372064
$63$	−2.67749	+	1.35317i	−0.337332	+	0.170483i
$64$			1.00000i			0.125000i
$65$	−7.75451	+	4.42655i	−0.961828	+	0.549046i
$66$	0.821950	−	5.13490i	0.101175	−	0.632062i
$67$	−6.61080	−	6.61080i	−0.807638	−	0.807638i	0.176638	−	0.984276i	$-0.443478\pi$
$67$	−6.61080	−	6.61080i	−0.807638	−	0.807638i	−0.984276	+	0.176638i	$0.943478\pi$
$68$		−	3.03575i		−	0.368138i
$69$	0.130928	−	0.817936i	0.0157619	−	0.0984680i
$70$	−1.75112	−	1.75112i	−0.209299	−	0.209299i
$71$	7.36537	−	7.36537i	0.874109	−	0.874109i	−0.118808	−	0.992917i	$-0.537907\pi$
$71$	7.36537	−	7.36537i	0.874109	−	0.874109i	0.992917	+	0.118808i	$0.0379073\pi$
$72$	1.35317	+	2.67749i	0.159472	+	0.315545i
$73$	−8.06119	+	8.06119i	−0.943491	+	0.943491i	−0.998487	−	0.0549955i	$-0.982486\pi$
$73$	−8.06119	+	8.06119i	−0.943491	+	0.943491i	0.0549955	+	0.998487i	$0.482486\pi$
$74$			5.95950i			0.692778i
$75$	−1.93745	−	0.310130i	−0.223717	−	0.0358107i
$76$	2.63603	−	2.63603i	0.302373	−	0.302373i
$77$	3.00237			0.342152
$78$	2.19980	+	5.84473i	0.249079	+	0.661785i
$79$	−11.6022			−1.30535			−0.652673	−	0.757640i	$-0.726353\pi$
$79$	−11.6022			−1.30535			−0.652673	+	0.757640i	$0.726353\pi$
$80$	−1.75112	+	1.75112i	−0.195781	+	0.195781i
$81$	7.24618	+	5.33787i	0.805131	+	0.593097i
$82$		−	6.84548i		−	0.755957i
$83$	9.96904	−	9.96904i	1.09424	−	1.09424i	0.0991748	−	0.995070i	$-0.468380\pi$
$83$	9.96904	−	9.96904i	1.09424	−	1.09424i	0.995070	−	0.0991748i	$-0.0316203\pi$
$84$	−1.40293	+	1.01577i	−0.153072	+	0.110829i
$85$	5.31595	−	5.31595i	0.576596	−	0.576596i
$86$	−3.24931	−	3.24931i	−0.350382	−	0.350382i
$87$	10.3248	+	1.65271i	1.10694	+	0.177189i
$88$		−	3.00237i		−	0.320054i
$89$	10.9270	+	10.9270i	1.15826	+	1.15826i	0.984849	+	0.173415i	$0.0554803\pi$
$89$	10.9270	+	10.9270i	1.15826	+	1.15826i	0.173415	+	0.984849i	$0.444520\pi$
$90$	−2.31904	+	7.05815i	−0.244448	+	0.743994i
$91$	−3.13129	+	1.78746i	−0.328249	+	0.187376i
$92$		−	0.478247i		−	0.0498607i
$93$	−4.11007	+	2.97582i	−0.426195	+	0.308579i
$94$	−9.86025			−1.01701
$95$	9.23199			0.947182
$96$	1.01577	+	1.40293i	0.103671	+	0.143186i
$97$	10.7186	+	10.7186i	1.08831	+	1.08831i	0.995703	+	0.0926043i	$0.0295192\pi$
$97$	10.7186	+	10.7186i	1.08831	+	1.08831i	0.0926043	+	0.995703i	$0.470481\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−4.06272	−	8.03882i	−0.408319	−	0.807932i
$100$	−1.13282			−0.113282
$101$	−5.04608			−0.502103			−0.251052	−	0.967974i	$-0.580776\pi$
$101$	−5.04608			−0.502103			−0.251052	+	0.967974i	$0.580776\pi$
$102$	−3.08361	−	4.25894i	−0.305323	−	0.421698i
$103$			17.3260i			1.70718i	0.520944	+	0.853591i	$0.325580\pi$
$103$			17.3260i			1.70718i	−0.520944	+	0.853591i	$0.674420\pi$
$104$	1.78746	+	3.13129i	0.175274	+	0.307049i
$105$	−4.23543	−	0.677971i	−0.413335	−	0.0661632i
$106$	4.17199	+	4.17199i	0.405220	+	0.405220i
$107$		−	7.64785i		−	0.739345i	−0.929162	−	0.369673i	$-0.879470\pi$
$107$		−	7.64785i		−	0.739345i	0.929162	−	0.369673i	$-0.120530\pi$
$108$	4.61811	+	2.38183i	0.444377	+	0.229191i
$109$	2.94969	+	2.94969i	0.282529	+	0.282529i	0.834117	−	0.551588i	$-0.185978\pi$
$109$	2.94969	+	2.94969i	0.282529	+	0.282529i	−0.551588	+	0.834117i	$0.685978\pi$
$110$	5.25751	−	5.25751i	0.501284	−	0.501284i
$111$	6.05346	+	8.36077i	0.574569	+	0.793569i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$		−	4.99755i		−	0.470130i	−0.971980	−	0.235065i	$-0.924470\pi$
$113$		−	4.99755i		−	0.470130i	0.971980	−	0.235065i	$-0.0755303\pi$
$114$	1.02058	−	6.37576i	0.0955858	−	0.597145i
$115$	0.837467	−	0.837467i	0.0780942	−	0.0780942i
$116$	6.03691			0.560513
$117$	9.02306	+	5.96527i	0.834182	+	0.551489i
$118$	5.32824			0.490504
$119$	2.14660	−	2.14660i	0.196778	−	0.196778i
$120$	−0.677971	+	4.23543i	−0.0618900	+	0.386640i
$121$		−	1.98575i		−	0.180522i
$122$	9.37758	−	9.37758i	0.849007	−	0.849007i
$123$	−6.95342	−	9.60374i	−0.626968	−	0.865940i
$124$	−2.07156	+	2.07156i	−0.186032	+	0.186032i
$125$	6.77188	+	6.77188i	0.605695	+	0.605695i
$126$	−0.936434	+	2.85010i	−0.0834242	+	0.253907i
$127$		−	0.521751i		−	0.0462979i	−0.999732	−	0.0231490i	$-0.992631\pi$
$127$		−	0.521751i		−	0.0462979i	0.999732	−	0.0231490i	$-0.00736920\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−7.85910	−	1.25802i	−0.691956	−	0.110762i
$130$	−2.35322	+	8.61331i	−0.206391	+	0.755437i
$131$		−	10.1350i		−	0.885497i	−0.896646	−	0.442748i	$-0.854003\pi$
$131$		−	10.1350i		−	0.885497i	0.896646	−	0.442748i	$-0.145997\pi$
$132$	−3.04971	−	4.21213i	−0.265443	−	0.366619i
$133$	3.72791			0.323251
$134$	−9.34908			−0.807638
$135$	3.91599	+	12.2577i	0.337034	+	1.05498i
$136$	−2.14660	−	2.14660i	−0.184069	−	0.184069i
$137$	−4.06995	−	4.06995i	−0.347720	−	0.347720i	0.511540	−	0.859259i	$-0.329075\pi$
$137$	−4.06995	−	4.06995i	−0.347720	−	0.347720i	−0.859259	+	0.511540i	$0.829075\pi$
$138$	−0.485788	−	0.670949i	−0.0413530	−	0.0571149i
$139$	0.173766			0.0147387			0.00736933	−	0.999973i	$-0.497654\pi$
$139$	0.173766			0.0147387			0.00736933	+	0.999973i	$0.497654\pi$
$140$	−2.47645			−0.209299
$141$	−13.8333	+	10.0157i	−1.16497	+	0.843476i
$142$		−	10.4162i		−	0.874109i
$143$	−5.36661	−	9.40132i	−0.448779	−	0.786178i
$144$	2.85010	+	0.936434i	0.237509	+	0.0780362i
$145$	10.5713	+	10.5713i	0.877903	+	0.877903i
$146$			11.4002i			0.943491i
$147$	−1.71028	−	0.273767i	−0.141061	−	0.0225799i
$148$	4.21400	+	4.21400i	0.346389	+	0.346389i
$149$	4.13899	−	4.13899i	0.339079	−	0.339079i	−0.516941	−	0.856021i	$-0.672929\pi$
$149$	4.13899	−	4.13899i	0.339079	−	0.339079i	0.856021	+	0.516941i	$0.172929\pi$
$150$	−1.58928	+	1.15069i	−0.129764	+	0.0939531i
$151$	−6.75083	+	6.75083i	−0.549375	+	0.549375i	−0.926260	−	0.376885i	$-0.876995\pi$
$151$	−6.75083	+	6.75083i	−0.549375	+	0.549375i	0.376885	+	0.926260i	$0.376995\pi$
$152$		−	3.72791i		−	0.302373i
$153$	−8.65219	−	2.84278i	−0.699488	−	0.229825i
$154$	2.12300	−	2.12300i	0.171076	−	0.171076i
$155$	−7.25510			−0.582744
$156$	5.68834	+	2.57735i	0.455432	+	0.206353i
$157$	−4.14765			−0.331018			−0.165509	−	0.986208i	$-0.552927\pi$
$157$	−4.14765			−0.331018			−0.165509	+	0.986208i	$0.552927\pi$
$158$	−8.20397	+	8.20397i	−0.652673	+	0.652673i
$159$	10.0908	+	1.61525i	0.800252	+	0.128098i
$160$			2.47645i			0.195781i
$161$	0.338172	−	0.338172i	0.0266517	−	0.0266517i
$162$	8.89827	−	1.34938i	0.699114	−	0.106017i
$163$	−13.3414	+	13.3414i	−1.04498	+	1.04498i	−0.0460395	+	0.998940i	$0.514660\pi$
$163$	−13.3414	+	13.3414i	−1.04498	+	1.04498i	−0.998940	+	0.0460395i	$0.985340\pi$
$164$	−4.84049	−	4.84049i	−0.377979	−	0.377979i
$165$	2.03552	−	12.7163i	0.158465	−	0.989965i
$166$		−	14.0984i		−	1.09424i
$167$	−6.44717	−	6.44717i	−0.498897	−	0.498897i	0.412197	−	0.911095i	$-0.364761\pi$
$167$	−6.44717	−	6.44717i	−0.498897	−	0.498897i	−0.911095	+	0.412197i	$0.864761\pi$
$168$	−0.273767	+	1.71028i	−0.0211216	+	0.131951i
$169$	11.1941	+	6.61000i	0.861085	+	0.508462i
$170$		−	7.51789i		−	0.576596i
$171$	−5.04449	−	9.98142i	−0.385762	−	0.763299i
$172$	−4.59522			−0.350382
$173$	2.65682			0.201994			0.100997	−	0.994887i	$-0.467797\pi$
$173$	2.65682			0.201994			0.100997	+	0.994887i	$0.467797\pi$
$174$	8.46938	−	6.13210i	0.642062	−	0.464873i
$175$	−0.801028	−	0.801028i	−0.0605520	−	0.0605520i
$176$	−2.12300	−	2.12300i	−0.160027	−	0.160027i
$177$	7.47515	−	5.41225i	0.561867	−	0.406809i
$178$	15.4532			1.15826
$179$	3.64878			0.272723			0.136361	−	0.990659i	$-0.456459\pi$
$179$	3.64878			0.272723			0.136361	+	0.990659i	$0.456459\pi$
$180$	3.35106	+	6.63067i	0.249773	+	0.494221i
$181$		−	19.5037i		−	1.44970i	−0.688909	−	0.724848i	$-0.741910\pi$
$181$		−	19.5037i		−	1.44970i	0.688909	−	0.724848i	$-0.258090\pi$
$182$	−0.950237	+	3.47808i	−0.0704362	+	0.257813i
$183$	3.63067	−	22.6815i	0.268387	−	1.67667i
$184$	−0.338172	−	0.338172i	−0.0249304	−	0.0249304i
$185$			14.7584i			1.08506i
$186$	−0.802036	+	5.01049i	−0.0588081	+	0.367387i
$187$	6.44489	+	6.44489i	0.471297	+	0.471297i
$188$	−6.97225	+	6.97225i	−0.508504	+	0.508504i
$189$	1.58129	+	4.94970i	0.115022	+	0.360038i
$190$	6.52800	−	6.52800i	0.473591	−	0.473591i
$191$			0.854794i			0.0618508i	0.999522	+	0.0309254i	$0.00984542\pi$
$191$			0.854794i			0.0618508i	−0.999522	+	0.0309254i	$0.990155\pi$
$192$	1.71028	+	0.273767i	0.123429	+	0.0197574i
$193$	−16.3246	+	16.3246i	−1.17507	+	1.17507i	−0.194083	+	0.980985i	$0.562173\pi$
$193$	−16.3246	+	16.3246i	−1.17507	+	1.17507i	−0.980985	+	0.194083i	$0.937827\pi$
$194$	15.1584			1.08831
$195$	5.44771	+	14.4742i	0.390119	+	1.03652i
$196$	−1.00000			−0.0714286
$197$	−7.45721	+	7.45721i	−0.531304	+	0.531304i	−0.920960	−	0.389656i	$-0.872594\pi$
$197$	−7.45721	+	7.45721i	−0.531304	+	0.531304i	0.389656	+	0.920960i	$0.372594\pi$
$198$	−8.55708	−	2.81153i	−0.608125	−	0.199807i
$199$			0.778109i			0.0551587i	0.999620	+	0.0275793i	$0.00877989\pi$
$199$			0.778109i			0.0551587i	−0.999620	+	0.0275793i	$0.991220\pi$
$200$	−0.801028	+	0.801028i	−0.0566412	+	0.0566412i
$201$	−13.1161	+	9.49649i	−0.925140	+	0.669831i
$202$	−3.56811	+	3.56811i	−0.251052	+	0.251052i
$203$	4.26874	+	4.26874i	0.299607	+	0.299607i
$204$	−5.19197	−	0.831086i	−0.363511	−	0.0581877i
$205$		−	16.9525i		−	1.18402i
$206$	12.2513	+	12.2513i	0.853591	+	0.853591i
$207$	−1.36305	−	0.447847i	−0.0947389	−	0.0311275i
$208$	3.47808	+	0.950237i	0.241162	+	0.0658871i
$209$			11.1926i			0.774207i
$210$	−3.47430	+	2.51550i	−0.239749	+	0.173586i
$211$	−4.51239			−0.310646			−0.155323	−	0.987864i	$-0.549642\pi$
$211$	−4.51239			−0.310646			−0.155323	+	0.987864i	$0.549642\pi$
$212$	5.90009			0.405220
$213$	−10.5804	−	14.6132i	−0.724960	−	1.00128i
$214$	−5.40784	−	5.40784i	−0.369673	−	0.369673i
$215$	−8.04677	−	8.04677i	−0.548785	−	0.548785i
$216$	4.94970	−	1.58129i	0.336784	−	0.107593i
$217$	−2.92963			−0.198876
$218$	4.17149			0.282529
$219$	11.5800	+	15.9938i	0.782504	+	1.08076i
$220$		−	7.43524i		−	0.501284i
$221$	−10.5586	−	2.88468i	−0.710246	−	0.194044i
$222$	10.1924	+	1.63151i	0.684069	+	0.109500i
$223$	−3.08394	−	3.08394i	−0.206516	−	0.206516i	0.596269	−	0.802785i	$-0.296649\pi$
$223$	−3.08394	−	3.08394i	−0.206516	−	0.206516i	−0.802785	+	0.596269i	$0.796649\pi$
$224$			1.00000i			0.0668153i
$225$	−1.06082	+	3.22867i	−0.0707211	+	0.215245i
$226$	−3.53380	−	3.53380i	−0.235065	−	0.235065i
$227$	−18.9348	+	18.9348i	−1.25675	+	1.25675i	−0.304109	+	0.952637i	$0.598359\pi$
$227$	−18.9348	+	18.9348i	−1.25675	+	1.25675i	−0.952637	+	0.304109i	$0.901641\pi$
$228$	−3.78669	−	5.23000i	−0.250779	−	0.346365i
$229$	12.2479	−	12.2479i	0.809366	−	0.809366i	−0.175172	−	0.984538i	$-0.556048\pi$
$229$	12.2479	−	12.2479i	0.809366	−	0.809366i	0.984538	+	0.175172i	$0.0560482\pi$
$230$		−	1.18436i		−	0.0780942i
$231$	0.821950	−	5.13490i	0.0540804	−	0.337851i
$232$	4.26874	−	4.26874i	0.280257	−	0.280257i
$233$	−15.4793			−1.01408			−0.507041	−	0.861922i	$-0.669261\pi$
$233$	−15.4793			−1.01408			−0.507041	+	0.861922i	$0.669261\pi$
$234$	10.5983	−	2.16218i	0.692836	−	0.141346i
$235$	−24.4185			−1.59288
$236$	3.76763	−	3.76763i	0.245252	−	0.245252i
$237$	−3.17629	+	19.8429i	−0.206322	+	1.28894i
$238$		−	3.03575i		−	0.196778i
$239$	−11.2898	+	11.2898i	−0.730278	+	0.730278i	−0.970675	−	0.240397i	$-0.922722\pi$
$239$	−11.2898	+	11.2898i	−0.730278	+	0.730278i	0.240397	+	0.970675i	$0.422722\pi$
$240$	2.51550	+	3.47430i	0.162375	+	0.224265i
$241$	−3.14172	+	3.14172i	−0.202376	+	0.202376i	−0.801017	−	0.598641i	$-0.795707\pi$
$241$	−3.14172	+	3.14172i	−0.202376	+	0.202376i	0.598641	+	0.801017i	$0.295707\pi$
$242$	−1.40413	−	1.40413i	−0.0902612	−	0.0902612i
$243$	11.1130	−	10.9317i	0.712900	−	0.701266i
$244$		−	13.2619i		−	0.849007i
$245$	−1.75112	−	1.75112i	−0.111875	−	0.111875i
$246$	−11.7077	−	1.87406i	−0.746454	−	0.119486i
$247$	−6.66347	−	11.6732i	−0.423987	−	0.742746i
$248$			2.92963i			0.186032i
$249$	−14.3206	−	19.7790i	−0.907534	−	1.25345i
$250$	9.57688			0.605695
$251$	18.4294			1.16326			0.581628	−	0.813455i	$-0.302416\pi$
$251$	18.4294			1.16326			0.581628	+	0.813455i	$0.302416\pi$
$252$	1.35317	+	2.67749i	0.0852416	+	0.168666i
$253$	1.01532	+	1.01532i	0.0638326	+	0.0638326i
$254$	−0.368934	−	0.368934i	−0.0231490	−	0.0231490i
$255$	−7.63642	−	10.5471i	−0.478211	−	0.660484i
$256$	1.00000			0.0625000
$257$	−4.35687			−0.271774			−0.135887	−	0.990724i	$-0.543388\pi$
$257$	−4.35687			−0.271774			−0.135887	+	0.990724i	$0.543388\pi$
$258$	−6.44678	+	4.66767i	−0.401359	+	0.290597i
$259$			5.95950i			0.370305i
$260$	4.42655	+	7.75451i	0.274523	+	0.480914i
$261$	5.65317	−	17.2058i	0.349923	−	1.06501i
$262$	−7.16651	−	7.16651i	−0.442748	−	0.442748i
$263$			1.49647i			0.0922762i	0.998935	+	0.0461381i	$0.0146914\pi$
$263$			1.49647i			0.0922762i	−0.998935	+	0.0461381i	$0.985309\pi$
$264$	−5.13490	−	0.821950i	−0.316031	−	0.0505875i
$265$	10.3318	+	10.3318i	0.634674	+	0.634674i
$266$	2.63603	−	2.63603i	0.161625	−	0.161625i
$267$	21.6797	−	15.6968i	1.32678	−	0.960630i
$268$	−6.61080	+	6.61080i	−0.403819	+	0.403819i
$269$			11.0765i			0.675349i	0.941263	+	0.337674i	$0.109640\pi$
$269$			11.0765i			0.675349i	−0.941263	+	0.337674i	$0.890360\pi$
$270$	11.4365	+	5.89849i	0.696005	+	0.358970i
$271$	−9.41699	+	9.41699i	−0.572042	+	0.572042i	−0.932699	−	0.360657i	$-0.882553\pi$
$271$	−9.41699	+	9.41699i	−0.572042	+	0.572042i	0.360657	+	0.932699i	$0.382553\pi$
$272$	−3.03575			−0.184069
$273$	2.19980	+	5.84473i	0.133138	+	0.353739i
$274$	−5.75578			−0.347720
$275$	2.40499	−	2.40499i	0.145026	−	0.145026i
$276$	−0.817936	−	0.130928i	−0.0492340	−	0.00788095i
$277$		−	20.3743i		−	1.22417i	−0.790792	−	0.612085i	$-0.790331\pi$
$277$		−	20.3743i		−	1.22417i	0.790792	−	0.612085i	$-0.209669\pi$
$278$	0.122871	−	0.122871i	0.00736933	−	0.00736933i
$279$	3.96429	+	7.84405i	0.237336	+	0.469611i
$280$	−1.75112	+	1.75112i	−0.104649	+	0.104649i
$281$	14.5729	+	14.5729i	0.869346	+	0.869346i	0.992400	−	0.123054i	$-0.0392690\pi$
$281$	14.5729	+	14.5729i	0.869346	+	0.869346i	−0.123054	+	0.992400i	$0.539269\pi$
$282$	−2.69941	+	16.8638i	−0.160747	+	1.00422i
$283$		−	17.5244i		−	1.04171i	−0.853644	−	0.520857i	$-0.825612\pi$
$283$		−	17.5244i		−	1.04171i	0.853644	−	0.520857i	$-0.174388\pi$
$284$	−7.36537	−	7.36537i	−0.437055	−	0.437055i
$285$	2.52741	−	15.7893i	0.149711	−	0.935276i
$286$	−10.4425	−	2.85297i	−0.617478	−	0.168699i
$287$		−	6.84548i		−	0.404076i
$288$	2.67749	−	1.35317i	0.157772	−	0.0797362i
$289$	−7.78425			−0.457897
$290$	14.9501			0.877903
$291$	21.2662	−	15.3974i	1.24664	−	0.902610i
$292$	8.06119	+	8.06119i	0.471746	+	0.471746i
$293$	−22.5588	−	22.5588i	−1.31790	−	1.31790i	−0.915435	−	0.402466i	$-0.868153\pi$
$293$	−22.5588	−	22.5588i	−1.31790	−	1.31790i	−0.402466	−	0.915435i	$-0.631847\pi$
$294$	−1.40293	+	1.01577i	−0.0818206	+	0.0592407i
$295$	13.1951			0.768250
$296$	5.95950			0.346389
$297$	−14.8609	+	4.74762i	−0.862314	+	0.275485i
$298$		−	5.85342i		−	0.339079i
$299$	−1.66338	−	0.454448i	−0.0961960	−	0.0262814i
$300$	−0.310130	+	1.93745i	−0.0179053	+	0.111858i
$301$	−3.24931	−	3.24931i	−0.187287	−	0.187287i
$302$			9.54712i			0.549375i
$303$	−1.38145	+	8.63019i	−0.0793621	+	0.495792i
$304$	−2.63603	−	2.63603i	−0.151187	−	0.151187i
$305$	23.2232	−	23.2232i	1.32975	−	1.32975i
$306$	−8.12817	+	4.10788i	−0.464657	+	0.234832i
$307$	15.0145	−	15.0145i	0.856921	−	0.856921i	−0.134053	−	0.990974i	$-0.542799\pi$
$307$	15.0145	−	15.0145i	0.856921	−	0.856921i	0.990974	+	0.134053i	$0.0427992\pi$
$308$		−	3.00237i		−	0.171076i
$309$	29.6323	+	4.74328i	1.68572	+	0.269836i
$310$	−5.13013	+	5.13013i	−0.291372	+	0.291372i
$311$	−10.7272			−0.608283			−0.304142	−	0.952627i	$-0.598370\pi$
$311$	−10.7272			−0.608283			−0.304142	+	0.952627i	$0.598370\pi$
$312$	5.84473	−	2.19980i	0.330893	−	0.124539i
$313$	−17.3350			−0.979834			−0.489917	−	0.871769i	$-0.662973\pi$
$313$	−17.3350			−0.979834			−0.489917	+	0.871769i	$0.662973\pi$
$314$	−2.93283	+	2.93283i	−0.165509	+	0.165509i
$315$	−2.31904	+	7.05815i	−0.130663	+	0.397682i
$316$			11.6022i			0.652673i
$317$	−19.6716	+	19.6716i	−1.10487	+	1.10487i	−0.111055	+	0.993814i	$0.535423\pi$
$317$	−19.6716	+	19.6716i	−1.10487	+	1.10487i	−0.993814	+	0.111055i	$0.964577\pi$
$318$	8.27742	−	5.99312i	0.464175	−	0.336077i
$319$	−12.8164	+	12.8164i	−0.717579	+	0.717579i
$320$	1.75112	+	1.75112i	0.0978904	+	0.0978904i
$321$	−13.0799	−	2.09373i	−0.730051	−	0.116860i
$322$		−	0.478247i		−	0.0266517i
$323$	8.00231	+	8.00231i	0.445261	+	0.445261i
$324$	5.33787	−	7.24618i	0.296548	−	0.402566i
$325$	−1.07645	+	3.94006i	−0.0597108	+	0.218555i
$326$			18.8676i			1.04498i
$327$	5.85232	−	4.23726i	0.323634	−	0.234321i
$328$	−6.84548			−0.377979
$329$	−9.86025			−0.543613
$330$	−7.55248	−	10.4311i	−0.415750	−	0.574215i
$331$	4.17896	+	4.17896i	0.229697	+	0.229697i	0.812566	−	0.582869i	$-0.198070\pi$
$331$	4.17896	+	4.17896i	0.229697	+	0.229697i	−0.582869	+	0.812566i	$0.698070\pi$
$332$	−9.96904	−	9.96904i	−0.547122	−	0.547122i
$333$	15.9565	−	8.06421i	0.874410	−	0.441916i
$334$	−9.11768			−0.498897
$335$	−23.1526			−1.26496
$336$	1.01577	+	1.40293i	0.0554146	+	0.0765362i
$337$			7.79284i			0.424503i	0.977215	+	0.212251i	$0.0680796\pi$
$337$			7.79284i			0.424503i	−0.977215	+	0.212251i	$0.931920\pi$
$338$	12.5894	−	3.24145i	0.684773	−	0.176311i
$339$	−8.54720	−	1.36816i	−0.464220	−	0.0743084i
$340$	−5.31595	−	5.31595i	−0.288298	−	0.288298i
$341$		−	8.79586i		−	0.476322i
$342$	−10.6249	−	3.49094i	−0.574530	−	0.188768i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−3.24931	+	3.24931i	−0.175191	+	0.175191i
$345$	−1.20303	−	1.66157i	−0.0647691	−	0.0894561i
$346$	1.87865	−	1.87865i	0.100997	−	0.100997i
$347$		−	10.9288i		−	0.586690i	−0.956007	−	0.293345i	$-0.905232\pi$
$347$		−	10.9288i		−	0.586690i	0.956007	−	0.293345i	$-0.0947684\pi$
$348$	1.65271	−	10.3248i	0.0885944	−	0.553468i
$349$	−23.3039	+	23.3039i	−1.24743	+	1.24743i	−0.290581	+	0.956850i	$0.593849\pi$
$349$	−23.3039	+	23.3039i	−1.24743	+	1.24743i	−0.956850	+	0.290581i	$0.906151\pi$
$350$	−1.13282			−0.0605520
$351$	12.6725	−	13.7988i	0.676407	−	0.736528i
$352$	−3.00237			−0.160027
$353$	−17.4264	+	17.4264i	−0.927516	+	0.927516i	−0.997545	−	0.0700290i	$-0.977691\pi$
$353$	−17.4264	+	17.4264i	−0.927516	+	0.927516i	0.0700290	+	0.997545i	$0.477691\pi$
$354$	1.45869	−	9.11277i	0.0775287	−	0.484338i
$355$		−	25.7953i		−	1.36907i
$356$	10.9270	−	10.9270i	0.579132	−	0.579132i
$357$	−3.08361	−	4.25894i	−0.163202	−	0.225407i
$358$	2.58008	−	2.58008i	0.136361	−	0.136361i
$359$	−13.3523	−	13.3523i	−0.704707	−	0.704707i	0.260710	−	0.965417i	$-0.416043\pi$
$359$	−13.3523	−	13.3523i	−0.704707	−	0.704707i	−0.965417	+	0.260710i	$0.916043\pi$
$360$	7.05815	+	2.31904i	0.371997	+	0.122224i
$361$		−	5.10270i		−	0.268563i
$362$	−13.7912	−	13.7912i	−0.724848	−	0.724848i
$363$	−3.39618	−	0.543631i	−0.178253	−	0.0285332i
$364$	1.78746	+	3.13129i	0.0936882	+	0.164124i
$365$			28.2322i			1.47774i
$366$	−13.4710	−	18.6055i	−0.704141	−	0.972528i
$367$	23.3338			1.21801			0.609006	−	0.793165i	$-0.291568\pi$
$367$	23.3338			1.21801			0.609006	+	0.793165i	$0.291568\pi$
$368$	−0.478247			−0.0249304
$369$	−18.3287	+	9.26309i	−0.954153	+	0.482217i
$370$	10.4358	+	10.4358i	0.542531	+	0.542531i
$371$	4.17199	+	4.17199i	0.216599	+	0.216599i
$372$	2.97582	+	4.11007i	0.154289	+	0.213097i
$373$	6.26271			0.324271			0.162135	−	0.986769i	$-0.448162\pi$
$373$	6.26271			0.324271			0.162135	+	0.986769i	$0.448162\pi$
$374$	9.11445			0.471297
$375$	13.4357	−	9.72788i	0.693817	−	0.502346i
$376$			9.86025i			0.508504i
$377$	5.73650	−	20.9969i	0.295445	−	1.08139i
$378$	4.61811	+	2.38183i	0.237530	+	0.122508i
$379$	−23.9024	−	23.9024i	−1.22779	−	1.22779i	−0.964800	−	0.262986i	$-0.915293\pi$
$379$	−23.9024	−	23.9024i	−1.22779	−	1.22779i	−0.262986	−	0.964800i	$-0.584707\pi$
$380$		−	9.23199i		−	0.473591i
$381$	−0.892340	−	0.142838i	−0.0457160	−	0.00731782i
$382$	0.604431	+	0.604431i	0.0309254	+	0.0309254i
$383$	6.96614	−	6.96614i	0.355953	−	0.355953i	−0.506366	−	0.862319i	$-0.669011\pi$
$383$	6.96614	−	6.96614i	0.355953	−	0.355953i	0.862319	+	0.506366i	$0.169011\pi$
$384$	1.40293	−	1.01577i	0.0715931	−	0.0518356i
$385$	5.25751	−	5.25751i	0.267948	−	0.267948i
$386$			23.0864i			1.17507i
$387$	−4.30312	+	13.0969i	−0.218740	+	0.665750i
$388$	10.7186	−	10.7186i	0.544154	−	0.544154i
$389$	−33.8785			−1.71771			−0.858854	−	0.512220i	$-0.828823\pi$
$389$	−33.8785			−1.71771			−0.858854	+	0.512220i	$0.828823\pi$
$390$	14.0869	+	6.38269i	0.713319	+	0.323200i
$391$	1.45184			0.0734226
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	−17.3336	−	2.77462i	−0.874366	−	0.139961i
$394$			10.5461i			0.531304i
$395$	−20.3168	+	20.3168i	−1.02225	+	1.02225i
$396$	−8.03882	+	4.06272i	−0.403966	+	0.204159i
$397$	1.28835	−	1.28835i	0.0646606	−	0.0646606i	−0.674037	−	0.738698i	$-0.735441\pi$
$397$	1.28835	−	1.28835i	0.0646606	−	0.0646606i	0.738698	+	0.674037i	$0.235441\pi$
$398$	0.550206	+	0.550206i	0.0275793	+	0.0275793i
$399$	1.02058	−	6.37576i	0.0510928	−	0.319187i
$400$			1.13282i			0.0566412i
$401$	17.5817	+	17.5817i	0.877988	+	0.877988i	0.993326	−	0.115339i	$-0.0367953\pi$
$401$	17.5817	+	17.5817i	0.877988	+	0.877988i	−0.115339	+	0.993326i	$0.536795\pi$
$402$	−2.55947	+	15.9895i	−0.127655	+	0.797486i
$403$	5.23659	+	9.17354i	0.260853	+	0.456967i
$404$			5.04608i			0.251052i
$405$	22.0362	−	3.34168i	1.09499	−	0.166049i
$406$	6.03691			0.299607
$407$	−17.8927			−0.886906
$408$	−4.25894	+	3.08361i	−0.210849	+	0.152661i
$409$	21.1765	+	21.1765i	1.04711	+	1.04711i	0.998834	+	0.0482783i	$0.0153735\pi$
$409$	21.1765	+	21.1765i	1.04711	+	1.04711i	0.0482783	+	0.998834i	$0.484627\pi$
$410$	−11.9872	−	11.9872i	−0.592008	−	0.592008i
$411$	−8.07497	+	5.84653i	−0.398309	+	0.288388i
$412$	17.3260			0.853591
$413$	5.32824			0.262185
$414$	−1.28050	+	0.647149i	−0.0629332	+	0.0318057i
$415$		−	34.9139i		−	1.71386i
$416$	3.13129	−	1.78746i	0.153524	−	0.0876372i
$417$	0.0475714	−	0.297189i	0.00232958	−	0.0145534i
$418$	7.91435	+	7.91435i	0.387103	+	0.387103i
$419$		−	31.9709i		−	1.56188i	−0.624607	−	0.780939i	$-0.714741\pi$
$419$		−	31.9709i		−	1.56188i	0.624607	−	0.780939i	$-0.285259\pi$
$420$	−0.677971	+	4.23543i	−0.0330816	+	0.206668i
$421$	11.0977	+	11.0977i	0.540869	+	0.540869i	0.923784	−	0.382915i	$-0.125080\pi$
$421$	11.0977	+	11.0977i	0.540869	+	0.540869i	−0.382915	+	0.923784i	$0.625080\pi$
$422$	−3.19074	+	3.19074i	−0.155323	+	0.155323i
$423$	13.3426	+	26.4007i	0.648738	+	1.28365i
$424$	4.17199	−	4.17199i	0.202610	−	0.202610i
$425$		−	3.43897i		−	0.166814i
$426$	−17.8146	−	2.85161i	−0.863121	−	0.138161i
$427$	9.37758	−	9.37758i	0.453813	−	0.453813i
$428$	−7.64785			−0.369673
$429$	−17.5481	+	6.60463i	−0.847229	+	0.318875i
$430$	−11.3798			−0.548785
$431$	0.127561	−	0.127561i	0.00614442	−	0.00614442i	−0.704028	−	0.710172i	$-0.748617\pi$
$431$	0.127561	−	0.127561i	0.00614442	−	0.00614442i	0.710172	+	0.704028i	$0.248617\pi$
$432$	2.38183	−	4.61811i	0.114596	−	0.222189i
$433$		−	10.1128i		−	0.485988i	−0.970028	−	0.242994i	$-0.921870\pi$
$433$		−	10.1128i		−	0.485988i	0.970028	−	0.242994i	$-0.0781296\pi$
$434$	−2.07156	+	2.07156i	−0.0994382	+	0.0994382i
$435$	20.9740	−	15.1859i	1.00563	−	0.728106i
$436$	2.94969	−	2.94969i	0.141265	−	0.141265i
$437$	1.26067	+	1.26067i	0.0603062	+	0.0603062i
$438$	19.4976	+	3.12101i	0.931631	+	0.149128i
$439$			22.8399i			1.09009i	0.838408	+	0.545043i	$0.183487\pi$
$439$			22.8399i			1.09009i	−0.838408	+	0.545043i	$0.816513\pi$
$440$	−5.25751	−	5.25751i	−0.250642	−	0.250642i
$441$	−0.936434	+	2.85010i	−0.0445921	+	0.135719i
$442$	−9.50581	+	5.42626i	−0.452145	+	0.258101i
$443$			8.91535i			0.423581i	0.977315	+	0.211791i	$0.0679295\pi$
$443$			8.91535i			0.423581i	−0.977315	+	0.211791i	$0.932071\pi$
$444$	8.36077	−	6.05346i	0.396785	−	0.287285i
$445$	38.2691			1.81413
$446$	−4.36135			−0.206516
$447$	−5.94571	−	8.21195i	−0.281222	−	0.388412i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	19.3368	+	19.3368i	0.912558	+	0.912558i	0.996473	−	0.0839148i	$-0.0267424\pi$
$449$	19.3368	+	19.3368i	0.912558	+	0.912558i	−0.0839148	+	0.996473i	$0.526742\pi$
$450$	1.53290	+	3.03312i	0.0722617	+	0.142983i
$451$	20.5527			0.967789
$452$	−4.99755			−0.235065
$453$	9.69765	+	13.3940i	0.455635	+	0.629303i
$454$			26.7778i			1.25675i
$455$	−2.35322	+	8.61331i	−0.110321	+	0.403798i
$456$	−6.37576	−	1.02058i	−0.298572	−	0.0477929i
$457$	6.87890	+	6.87890i	0.321781	+	0.321781i	0.849450	−	0.527669i	$-0.176934\pi$
$457$	6.87890	+	6.87890i	0.321781	+	0.321781i	−0.527669	+	0.849450i	$0.676934\pi$
$458$		−	17.3212i		−	0.809366i
$459$	−7.23062	+	14.0194i	−0.337497	+	0.654369i
$460$	−0.837467	−	0.837467i	−0.0390471	−	0.0390471i
$461$	−5.37847	+	5.37847i	−0.250500	+	0.250500i	−0.821176	−	0.570675i	$-0.806681\pi$
$461$	−5.37847	+	5.37847i	−0.250500	+	0.250500i	0.570675	+	0.821176i	$0.306681\pi$
$462$	−3.04971	−	4.21213i	−0.141886	−	0.195966i
$463$	−1.71052	+	1.71052i	−0.0794944	+	0.0794944i	−0.745736	−	0.666242i	$-0.767902\pi$
$463$	−1.71052	+	1.71052i	−0.0794944	+	0.0794944i	0.666242	+	0.745736i	$0.267902\pi$
$464$		−	6.03691i		−	0.280257i
$465$	−1.98621	+	12.4082i	−0.0921081	+	0.575418i
$466$	−10.9455	+	10.9455i	−0.507041	+	0.507041i
$467$	12.1098			0.560375			0.280188	−	0.959945i	$-0.409603\pi$
$467$	12.1098			0.560375			0.280188	+	0.959945i	$0.409603\pi$
$468$	5.96527	−	9.02306i	0.275745	−	0.417091i
$469$	−9.34908			−0.431701
$470$	−17.2665	+	17.2665i	−0.796442	+	0.796442i
$471$	−1.13549	+	7.09363i	−0.0523205	+	0.326857i
$472$		−	5.32824i		−	0.245252i
$473$	9.75565	−	9.75565i	0.448565	−	0.448565i
$474$	11.7851	+	16.2771i	0.541308	+	0.747630i
$475$	2.98616	−	2.98616i	0.137014	−	0.137014i
$476$	−2.14660	−	2.14660i	−0.0983891	−	0.0983891i
$477$	5.52505	−	16.8159i	0.252975	−	0.769946i
$478$			15.9662i			0.730278i
$479$	0.535810	+	0.535810i	0.0244818	+	0.0244818i	0.719242	−	0.694760i	$-0.244489\pi$
$479$	0.535810	+	0.535810i	0.0244818	+	0.0244818i	−0.694760	+	0.719242i	$0.744489\pi$
$480$	4.23543	+	0.677971i	0.193320	+	0.0309450i
$481$	18.6609	−	10.6523i	0.850866	−	0.485705i
$482$			4.44306i			0.202376i
$483$	−0.485788	−	0.670949i	−0.0221041	−	0.0305292i
$484$	−1.98575			−0.0902612
$485$	37.5390			1.70456
$486$	0.128235	−	15.5879i	0.00581687	−	0.707083i
$487$	5.52429	+	5.52429i	0.250329	+	0.250329i	0.821106	−	0.570776i	$-0.193358\pi$
$487$	5.52429	+	5.52429i	0.250329	+	0.250329i	−0.570776	+	0.821106i	$0.693358\pi$
$488$	−9.37758	−	9.37758i	−0.424503	−	0.424503i
$489$	19.1651	+	26.4699i	0.866675	+	1.19701i
$490$	−2.47645			−0.111875
$491$	32.2992			1.45764			0.728821	−	0.684704i	$-0.240068\pi$
$491$	32.2992			1.45764			0.728821	+	0.684704i	$0.240068\pi$
$492$	−9.60374	+	6.95342i	−0.432970	+	0.313484i
$493$			18.3265i			0.825386i
$494$	−12.9660	−	3.54240i	−0.583366	−	0.159380i
$495$	−21.1912	−	6.96262i	−0.952474	−	0.312946i
$496$	2.07156	+	2.07156i	0.0930159	+	0.0930159i
$497$		−	10.4162i		−	0.467231i
$498$	−24.1121	−	3.85966i	−1.08049	−	0.172956i
$499$	24.5090	+	24.5090i	1.09717	+	1.09717i	0.994740	+	0.102433i	$0.0326627\pi$
$499$	24.5090	+	24.5090i	1.09717	+	1.09717i	0.102433	+	0.994740i	$0.467337\pi$
$500$	6.77188	−	6.77188i	0.302848	−	0.302848i
$501$	−12.7915	+	9.26144i	−0.571481	+	0.413771i
$502$	13.0316	−	13.0316i	0.581628	−	0.581628i
$503$		−	22.3557i		−	0.996792i	−0.866949	−	0.498396i	$-0.833923\pi$
$503$		−	22.3557i		−	0.996792i	0.866949	−	0.498396i	$-0.166077\pi$
$504$	2.85010	+	0.936434i	0.126954	+	0.0417121i
$505$	−8.83627	+	8.83627i	−0.393209	+	0.393209i
$506$	1.43588			0.0638326
$507$	14.3695	−	17.3354i	0.638173	−	0.769893i
$508$	−0.521751			−0.0231490
$509$	−2.91721	+	2.91721i	−0.129303	+	0.129303i	−0.768797	−	0.639493i	$-0.779144\pi$
$509$	−2.91721	+	2.91721i	−0.129303	+	0.129303i	0.639493	+	0.768797i	$0.279144\pi$
$510$	−12.8577	−	2.05815i	−0.569347	−	0.0911363i
$511$			11.4002i			0.504317i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−18.4520	+	5.89490i	−0.814677	+	0.260266i
$514$	−3.08077	+	3.08077i	−0.135887	+	0.135887i
$515$	30.3399	+	30.3399i	1.33693	+	1.33693i
$516$	−1.25802	+	7.85910i	−0.0553812	+	0.345978i
$517$		−	29.6042i		−	1.30199i
$518$	4.21400	+	4.21400i	0.185153	+	0.185153i
$519$	0.727347	−	4.54389i	0.0319270	−	0.199455i
$520$	8.61331	+	2.35322i	0.377719	+	0.103195i
$521$		−	20.6947i		−	0.906651i	−0.891345	−	0.453325i	$-0.850238\pi$
$521$		−	20.6947i		−	0.906651i	0.891345	−	0.453325i	$-0.149762\pi$
$522$	−8.16896	−	16.1638i	−0.357546	−	0.707469i
$523$	−22.5537			−0.986202			−0.493101	−	0.869972i	$-0.664137\pi$
$523$	−22.5537			−0.986202			−0.493101	+	0.869972i	$0.664137\pi$
$524$	−10.1350			−0.442748
$525$	−1.58928	+	1.15069i	−0.0693617	+	0.0502201i
$526$	1.05816	+	1.05816i	0.0461381	+	0.0461381i
$527$	−6.28874	−	6.28874i	−0.273942	−	0.273942i
$528$	−4.21213	+	3.04971i	−0.183309	+	0.132722i
$529$	−22.7713			−0.990056
$530$	14.6113			0.634674
$531$	−7.21000	−	14.2663i	−0.312887	−	0.619104i
$532$		−	3.72791i		−	0.161625i
$533$	−21.4352	+	12.2360i	−0.928462	+	0.530000i
$534$	4.23056	−	26.4292i	0.183074	−	1.14370i
$535$	−13.3923	−	13.3923i	−0.578999	−	0.578999i
$536$			9.34908i			0.403819i
$537$	0.998915	−	6.24043i	0.0431063	−	0.269294i
$538$	7.83230	+	7.83230i	0.337674	+	0.337674i
$539$	2.12300	−	2.12300i	0.0914441	−	0.0914441i
$540$	12.2577	−	3.91599i	0.527488	−	0.168517i
$541$	−0.860954	+	0.860954i	−0.0370153	+	0.0370153i	−0.725372	−	0.688357i	$-0.758332\pi$
$541$	−0.860954	+	0.860954i	−0.0370153	+	0.0370153i	0.688357	+	0.725372i	$0.258332\pi$
$542$			13.3176i			0.572042i
$543$	−33.3567	−	5.33945i	−1.43147	−	0.229138i
$544$	−2.14660	+	2.14660i	−0.0920346	+	0.0920346i
$545$	10.3305			0.442510
$546$	5.68834	+	2.57735i	0.243439	+	0.110300i
$547$	38.4468			1.64387			0.821934	−	0.569582i	$-0.192895\pi$
$547$	38.4468			1.64387			0.821934	+	0.569582i	$0.192895\pi$
$548$	−4.06995	+	4.06995i	−0.173860	+	0.173860i
$549$	−37.7978	−	12.4189i	−1.61317	−	0.530026i
$550$		−	3.40116i		−	0.145026i
$551$	−15.9135	+	15.9135i	−0.677937	+	0.677937i
$552$	−0.670949	+	0.485788i	−0.0285575	+	0.0206765i
$553$	−8.20397	+	8.20397i	−0.348868	+	0.348868i
$554$	−14.4068	−	14.4068i	−0.612085	−	0.612085i
$555$	25.2410	+	4.04037i	1.07142	+	0.171504i
$556$		−	0.173766i		−	0.00736933i
$557$	0.845111	+	0.845111i	0.0358085	+	0.0358085i	0.724784	−	0.688976i	$-0.241939\pi$
$557$	0.845111	+	0.845111i	0.0358085	+	0.0358085i	−0.688976	+	0.724784i	$0.741939\pi$
$558$	8.34976	+	2.74341i	0.353473	+	0.116138i
$559$	−4.36655	+	15.9825i	−0.184685	+	0.675990i
$560$			2.47645i			0.104649i
$561$	12.7869	−	9.25816i	0.539865	−	0.390880i
$562$	20.6092			0.869346
$563$	42.4619			1.78955			0.894777	−	0.446513i	$-0.147334\pi$
$563$	42.4619			1.78955			0.894777	+	0.446513i	$0.147334\pi$
$564$	10.0157	+	13.8333i	0.421738	+	0.582485i
$565$	−8.75130	−	8.75130i	−0.368170	−	0.368170i
$566$	−12.3916	−	12.3916i	−0.520857	−	0.520857i
$567$	8.89827	−	1.34938i	0.373692	−	0.0566686i
$568$	−10.4162			−0.437055
$569$	−13.1702			−0.552122			−0.276061	−	0.961140i	$-0.589029\pi$
$569$	−13.1702			−0.552122			−0.276061	+	0.961140i	$0.589029\pi$
$570$	−9.37755	−	12.9519i	−0.392783	−	0.542493i
$571$			22.7843i			0.953494i	0.879041	+	0.476747i	$0.158184\pi$
$571$			22.7843i			0.953494i	−0.879041	+	0.476747i	$0.841816\pi$
$572$	−9.40132	+	5.36661i	−0.393089	+	0.224389i
$573$	1.46194	+	0.234014i	0.0610733	+	0.00977609i
$574$	−4.84049	−	4.84049i	−0.202038	−	0.202038i
$575$		−	0.541771i		−	0.0225934i
$576$	0.936434	−	2.85010i	0.0390181	−	0.118754i
$577$	17.2984	+	17.2984i	0.720142	+	0.720142i	0.968634	−	0.248492i	$-0.0799350\pi$
$577$	17.2984	+	17.2984i	0.720142	+	0.720142i	−0.248492	+	0.968634i	$0.579935\pi$
$578$	−5.50429	+	5.50429i	−0.228948	+	0.228948i
$579$	23.4504	+	32.3887i	0.974567	+	1.34603i
$580$	10.5713	−	10.5713i	0.438951	−	0.438951i
$581$		−	14.0984i		−	0.584898i
$582$	4.14986	−	25.9250i	0.172017	−	1.07463i
$583$	−12.5259	+	12.5259i	−0.518769	+	0.518769i
$584$	11.4002			0.471746
$585$	26.2463	−	5.35455i	1.08515	−	0.221383i
$586$	−31.9030			−1.31790
$587$	21.3846	−	21.3846i	0.882638	−	0.882638i	−0.111164	−	0.993802i	$-0.535458\pi$
$587$	21.3846	−	21.3846i	0.882638	−	0.882638i	0.993802	+	0.111164i	$0.0354580\pi$
$588$	−0.273767	+	1.71028i	−0.0112899	+	0.0705307i
$589$		−	10.9214i		−	0.450009i
$590$	9.33037	−	9.33037i	0.384125	−	0.384125i
$591$	10.7124	+	14.7954i	0.440648	+	0.608603i
$592$	4.21400	−	4.21400i	0.173194	−	0.173194i
$593$	0.343278	+	0.343278i	0.0140968	+	0.0140968i	0.714120	−	0.700023i	$-0.246827\pi$
$593$	0.343278	+	0.343278i	0.0140968	+	0.0140968i	−0.700023	+	0.714120i	$0.746827\pi$
$594$	−7.15114	+	13.8653i	−0.293415	+	0.568900i
$595$		−	7.51789i		−	0.308203i
$596$	−4.13899	−	4.13899i	−0.169540	−	0.169540i
$597$	1.33078	+	0.213020i	0.0544653	+	0.00871834i
$598$	−1.49753	+	0.854846i	−0.0612387	+	0.0349573i
$599$			36.3142i			1.48376i	0.670534	+	0.741879i	$0.266065\pi$
$599$			36.3142i			1.48376i	−0.670534	+	0.741879i	$0.733935\pi$
$600$	1.15069	+	1.58928i	0.0469766	+	0.0648819i
$601$	−21.1337			−0.862061			−0.431031	−	0.902337i	$-0.641850\pi$
$601$	−21.1337			−0.862061			−0.431031	+	0.902337i	$0.641850\pi$
$602$	−4.59522			−0.187287
$603$	12.6509	+	25.0320i	0.515184	+	1.01938i
$604$	6.75083	+	6.75083i	0.274687	+	0.274687i
$605$	−3.47727	−	3.47727i	−0.141371	−	0.141371i
$606$	5.12564	+	7.07930i	0.208215	+	0.287577i
$607$	−5.09736			−0.206896			−0.103448	−	0.994635i	$-0.532987\pi$
$607$	−5.09736			−0.206896			−0.103448	+	0.994635i	$0.532987\pi$
$608$	−3.72791			−0.151187
$609$	8.46938	−	6.13210i	0.343197	−	0.248485i
$610$		−	32.8425i		−	1.32975i
$611$	17.6248	+	30.8753i	0.713022	+	1.24908i
$612$	−2.84278	+	8.65219i	−0.114912	+	0.349744i
$613$	28.8407	+	28.8407i	1.16486	+	1.16486i	0.983397	+	0.181467i	$0.0580845\pi$
$613$	28.8407	+	28.8407i	1.16486	+	1.16486i	0.181467	+	0.983397i	$0.441915\pi$
$614$		−	21.2337i		−	0.856921i
$615$	−28.9935	−	4.64104i	−1.16913	−	0.187145i
$616$	−2.12300	−	2.12300i	−0.0855381	−	0.0855381i
$617$	29.3917	−	29.3917i	1.18327	−	1.18327i	0.204373	−	0.978893i	$-0.434485\pi$
$617$	29.3917	−	29.3917i	1.18327	−	1.18327i	0.978893	−	0.204373i	$-0.0655155\pi$
$618$	24.3072	−	17.5992i	0.977779	−	0.707943i
$619$	−2.81364	+	2.81364i	−0.113090	+	0.113090i	−0.761387	−	0.648298i	$-0.775481\pi$
$619$	−2.81364	+	2.81364i	−0.113090	+	0.113090i	0.648298	+	0.761387i	$0.275481\pi$
$620$			7.25510i			0.291372i
$621$	−1.13910	+	2.20860i	−0.0457106	+	0.0886280i
$622$	−7.58527	+	7.58527i	−0.304142	+	0.304142i
$623$	15.4532			0.619118
$624$	2.57735	−	5.68834i	0.103177	−	0.227716i
$625$	29.3808			1.17523
$626$	−12.2577	+	12.2577i	−0.489917	+	0.489917i
$627$	19.1424	+	3.06415i	0.764475	+	0.122371i
$628$			4.14765i			0.165509i
$629$	−12.7926	+	12.7926i	−0.510076	+	0.510076i
$630$	3.35106	+	6.63067i	0.133509	+	0.264172i
$631$	−22.1341	+	22.1341i	−0.881143	+	0.881143i	−0.993651	−	0.112507i	$-0.964112\pi$
$631$	−22.1341	+	22.1341i	−0.881143	+	0.881143i	0.112507	+	0.993651i	$0.464112\pi$
$632$	8.20397	+	8.20397i	0.326337	+	0.326337i
$633$	−1.23534	+	7.71744i	−0.0491004	+	0.306741i
$634$			27.8199i			1.10487i
$635$	−0.913648	−	0.913648i	−0.0362570	−	0.0362570i
$636$	1.61525	−	10.0908i	0.0640488	−	0.400126i
$637$	−0.950237	+	3.47808i	−0.0376498	+	0.137807i
$638$			18.1251i			0.717579i
$639$	−27.8893	+	14.0949i	−1.10328	+	0.557585i
$640$	2.47645			0.0978904
$641$	−22.5807			−0.891885			−0.445943	−	0.895062i	$-0.647131\pi$
$641$	−22.5807			−0.891885			−0.445943	+	0.895062i	$0.647131\pi$
$642$	−10.7294	+	7.76843i	−0.423456	+	0.306595i
$643$	−11.9697	−	11.9697i	−0.472039	−	0.472039i	0.430535	−	0.902574i	$-0.358325\pi$
$643$	−11.9697	−	11.9697i	−0.472039	−	0.472039i	−0.902574	+	0.430535i	$0.858325\pi$
$644$	−0.338172	−	0.338172i	−0.0133258	−	0.0133258i
$645$	−15.9652	+	11.5593i	−0.628627	+	0.455146i
$646$	11.3170			0.445261
$647$	−49.1692			−1.93304			−0.966521	−	0.256586i	$-0.917402\pi$
$647$	−49.1692			−1.93304			−0.966521	+	0.256586i	$0.917402\pi$
$648$	−1.34938	−	8.89827i	−0.0530086	−	0.349557i
$649$			15.9974i			0.627951i
$650$	2.02487	+	3.54721i	0.0794221	+	0.139133i
$651$	−0.802036	+	5.01049i	−0.0314343	+	0.196376i
$652$	13.3414	+	13.3414i	0.522490	+	0.522490i
$653$		−	34.8066i		−	1.36209i	−0.732242	−	0.681044i	$-0.761526\pi$
$653$		−	34.8066i		−	1.36209i	0.732242	−	0.681044i	$-0.238474\pi$
$654$	1.14202	−	7.13441i	0.0446563	−	0.278978i
$655$	−17.7475	−	17.7475i	−0.693453	−	0.693453i
$656$	−4.84049	+	4.84049i	−0.188989	+	0.188989i
$657$	30.5240	−	15.4265i	1.19085	−	0.601843i
$658$	−6.97225	+	6.97225i	−0.271807	+	0.271807i
$659$			12.0404i			0.469029i	0.972113	+	0.234514i	$0.0753500\pi$
$659$			12.0404i			0.469029i	−0.972113	+	0.234514i	$0.924650\pi$
$660$	−12.7163	−	2.03552i	−0.494983	−	0.0792326i
$661$	27.1053	−	27.1053i	1.05427	−	1.05427i	0.0558331	−	0.998440i	$-0.482219\pi$
$661$	27.1053	−	27.1053i	1.05427	−	1.05427i	0.998440	−	0.0558331i	$-0.0177815\pi$
$662$	5.90994			0.229697
$663$	−7.82419	+	17.2684i	−0.303866	+	0.670648i
$664$	−14.0984			−0.547122
$665$	6.52800	−	6.52800i	0.253145	−	0.253145i
$666$	5.58068	−	16.9852i	0.216247	−	0.658163i
$667$			2.88714i			0.111790i
$668$	−6.44717	+	6.44717i	−0.249449	+	0.249449i
$669$	−6.11867	+	4.43011i	−0.236561	+	0.171278i
$670$	−16.3713	+	16.3713i	−0.632480	+	0.632480i
$671$	28.1550	+	28.1550i	1.08691	+	1.08691i
$672$	1.71028	+	0.273767i	0.0659754	+	0.0105608i
$673$		−	17.0132i		−	0.655809i	−0.944711	−	0.327905i	$-0.893658\pi$
$673$		−	17.0132i		−	0.655809i	0.944711	−	0.327905i	$-0.106342\pi$
$674$	5.51037	+	5.51037i	0.212251	+	0.212251i
$675$	5.23150	+	2.69819i	0.201361	+	0.103853i
$676$	6.61000	−	11.1941i	0.254231	−	0.430542i
$677$			2.58605i			0.0993901i	0.998764	+	0.0496950i	$0.0158249\pi$
$677$			2.58605i			0.0993901i	−0.998764	+	0.0496950i	$0.984175\pi$
$678$	−7.01122	+	5.07635i	−0.269264	+	0.194956i
$679$	15.1584			0.581725
$680$	−7.51789			−0.288298
$681$	27.2001	+	37.5675i	1.04231	+	1.43959i
$682$	−6.21961	−	6.21961i	−0.238161	−	0.238161i
$683$	25.9379	+	25.9379i	0.992486	+	0.992486i	0.999972	−	0.00748557i	$-0.00238275\pi$
$683$	25.9379	+	25.9379i	0.992486	+	0.992486i	−0.00748557	+	0.999972i	$0.502383\pi$
$684$	−9.98142	+	5.04449i	−0.381649	+	0.192881i
$685$	−14.2539			−0.544615
$686$	−1.00000			−0.0381802
$687$	−17.5943	−	24.3004i	−0.671264	−	0.927119i
$688$			4.59522i			0.175191i
$689$	5.60648	−	20.5210i	0.213590	−	0.781788i
$690$	−2.02558	−	0.324238i	−0.0771126	−	0.0123435i
$691$	−35.6892	−	35.6892i	−1.35768	−	1.35768i	−0.876768	−	0.480914i	$-0.840305\pi$
$691$	−35.6892	−	35.6892i	−1.35768	−	1.35768i	−0.480914	−	0.876768i	$-0.659695\pi$
$692$		−	2.65682i		−	0.100997i
$693$	−8.55708	−	2.81153i	−0.325057	−	0.106801i
$694$	−7.72784	−	7.72784i	−0.293345	−	0.293345i
$695$	0.304285	−	0.304285i	0.0115422	−	0.0115422i
$696$	−6.13210	−	8.46938i	−0.232437	−	0.321031i
$697$	14.6945	−	14.6945i	0.556593	−	0.556593i
$698$			32.9568i			1.24743i
$699$	−4.23771	+	26.4739i	−0.160285	+	1.00133i
$700$	−0.801028	+	0.801028i	−0.0302760	+	0.0302760i
$701$	−28.4715			−1.07535			−0.537676	−	0.843151i	$-0.680698\pi$
$701$	−28.4715			−1.07535			−0.537676	+	0.843151i	$0.680698\pi$
$702$	−0.796461	−	18.7181i	−0.0300605	−	0.706468i
$703$	−22.2165			−0.837910
$704$	−2.12300	+	2.12300i	−0.0800136	+	0.0800136i
$705$	−6.68496	+	41.7624i	−0.251770	+	1.57286i
$706$			24.6447i			0.927516i
$707$	−3.56811	+	3.56811i	−0.134193	+	0.134193i
$708$	−5.41225	−	7.47515i	−0.203405	−	0.280933i
$709$	34.7099	−	34.7099i	1.30356	−	1.30356i	0.377584	−	0.925975i	$-0.376755\pi$
$709$	34.7099	−	34.7099i	1.30356	−	1.30356i	0.925975	−	0.377584i	$-0.123245\pi$
$710$	−18.2400	−	18.2400i	−0.684535	−	0.684535i
$711$	33.0674	+	10.8647i	1.24012	+	0.407457i
$712$		−	15.4532i		−	0.579132i
$713$	−0.990720	−	0.990720i	−0.0371028	−	0.0371028i
$714$	−5.19197	−	0.831086i	−0.194305	−	0.0311026i
$715$	−25.8604	−	7.06524i	−0.967123	−	0.264225i
$716$		−	3.64878i		−	0.136361i
$717$	16.2180	+	22.3995i	0.605671	+	0.836525i
$718$	−18.8830			−0.704707
$719$	−3.99422			−0.148959			−0.0744797	−	0.997223i	$-0.523730\pi$
$719$	−3.99422			−0.148959			−0.0744797	+	0.997223i	$0.523730\pi$
$720$	6.63067	−	3.35106i	0.247111	−	0.124887i
$721$	12.2513	+	12.2513i	0.456263	+	0.456263i
$722$	−3.60816	−	3.60816i	−0.134282	−	0.134282i
$723$	4.51311	+	6.23331i	0.167844	+	0.231819i
$724$	−19.5037			−0.724848
$725$	6.83877			0.253985
$726$	−2.78587	+	2.01705i	−0.103393	+	0.0748599i
$727$		−	31.5807i		−	1.17126i	−0.810577	−	0.585632i	$-0.800846\pi$
$727$		−	31.5807i		−	1.17126i	0.810577	−	0.585632i	$-0.199154\pi$
$728$	3.47808	+	0.950237i	0.128906	+	0.0352181i
$729$	−15.6538	−	21.9991i	−0.579770	−	0.814780i
$730$	19.9632	+	19.9632i	0.738870	+	0.738870i
$731$		−	13.9499i		−	0.515956i
$732$	−22.6815	−	3.63067i	−0.838334	−	0.134193i
$733$	−3.05349	−	3.05349i	−0.112783	−	0.112783i	0.648463	−	0.761246i	$-0.275412\pi$
$733$	−3.05349	−	3.05349i	−0.112783	−	0.112783i	−0.761246	+	0.648463i	$0.775412\pi$
$734$	16.4995	−	16.4995i	0.609006	−	0.609006i
$735$	−3.47430	+	2.51550i	−0.128151	+	0.0927856i
$736$	−0.338172	+	0.338172i	−0.0124652	+	0.0124652i
$737$		−	28.0695i		−	1.03395i
$738$	−6.41035	+	19.5103i	−0.235968	+	0.718185i
$739$	5.30152	−	5.30152i	0.195020	−	0.195020i	−0.602841	−	0.797861i	$-0.705965\pi$
$739$	5.30152	−	5.30152i	0.195020	−	0.195020i	0.797861	+	0.602841i	$0.205965\pi$
$740$	14.7584			0.542531
$741$	−21.7886	+	8.20066i	−0.800425	+	0.301259i
$742$	5.90009			0.216599
$743$	21.0757	−	21.0757i	0.773191	−	0.773191i	−0.205472	−	0.978663i	$-0.565873\pi$
$743$	21.0757	−	21.0757i	0.773191	−	0.773191i	0.978663	+	0.205472i	$0.0658728\pi$
$744$	5.01049	+	0.802036i	0.183693	+	0.0294041i
$745$		−	14.4957i		−	0.531082i
$746$	4.42841	−	4.42841i	0.162135	−	0.162135i
$747$	−37.7482	+	19.0775i	−1.38113	+	0.698007i
$748$	6.44489	−	6.44489i	0.235648	−	0.235648i
$749$	−5.40784	−	5.40784i	−0.197598	−	0.197598i
$750$	2.62183	−	16.3791i	0.0957357	−	0.598081i
$751$		−	52.4292i		−	1.91317i	−0.291454	−	0.956585i	$-0.594139\pi$
$751$		−	52.4292i		−	1.91317i	0.291454	−	0.956585i	$-0.405861\pi$
$752$	6.97225	+	6.97225i	0.254252	+	0.254252i
$753$	5.04536	−	31.5195i	0.183863	−	1.14863i
$754$	−10.7907	−	18.9034i	−0.392975	−	0.688420i
$755$			23.6430i			0.860457i
$756$	4.94970	−	1.58129i	0.180019	−	0.0575109i
$757$	−37.6352			−1.36787			−0.683937	−	0.729541i	$-0.739734\pi$
$757$	−37.6352			−1.36787			−0.683937	+	0.729541i	$0.739734\pi$
$758$	−33.8031			−1.22779
$759$	2.01444	−	1.45852i	0.0731195	−	0.0529408i
$760$	−6.52800	−	6.52800i	−0.236796	−	0.236796i
$761$	4.70073	+	4.70073i	0.170401	+	0.170401i	0.787156	−	0.616754i	$-0.211553\pi$
$761$	4.70073	+	4.70073i	0.170401	+	0.170401i	−0.616754	+	0.787156i	$0.711553\pi$
$762$	−0.731981	+	0.529978i	−0.0265169	+	0.0191991i
$763$	4.17149			0.151018
$764$	0.854794			0.0309254
$765$	−20.1290	+	10.1730i	−0.727767	+	0.367804i
$766$		−	9.85161i		−	0.355953i
$767$	−9.52399	−	16.6843i	−0.343891	−	0.602434i
$768$	0.273767	−	1.71028i	0.00987870	−	0.0617144i
$769$	−11.5981	−	11.5981i	−0.418239	−	0.418239i	0.466358	−	0.884596i	$-0.345566\pi$
$769$	−11.5981	−	11.5981i	−0.418239	−	0.418239i	−0.884596	+	0.466358i	$0.845566\pi$
$770$		−	7.43524i		−	0.267948i
$771$	−1.19277	+	7.45146i	−0.0429564	+	0.268358i
$772$	16.3246	+	16.3246i	0.587534	+	0.587534i
$773$	21.5154	−	21.5154i	0.773854	−	0.773854i	−0.204924	−	0.978778i	$-0.565695\pi$
$773$	21.5154	−	21.5154i	0.773854	−	0.773854i	0.978778	+	0.204924i	$0.0656947\pi$
$774$	6.21811	+	12.3036i	0.223505	+	0.442245i
$775$	−2.34672	+	2.34672i	−0.0842966	+	0.0842966i
$776$		−	15.1584i		−	0.544154i
$777$	10.1924	+	1.63151i	0.365650	+	0.0585302i
$778$	−23.9557	+	23.9557i	−0.858854	+	0.858854i
$779$	25.5193			0.914325
$780$	14.4742	−	5.44771i	0.518260	−	0.195059i
$781$	31.2734			1.11905
$782$	1.02660	−	1.02660i	0.0367113	−	0.0367113i
$783$	−27.8791	−	14.3789i	−0.996318	−	0.513859i
$784$			1.00000i			0.0357143i
$785$	−7.26302	+	7.26302i	−0.259228	+	0.259228i
$786$	−14.2187	+	10.2948i	−0.507163	+	0.367202i
$787$	−16.1871	+	16.1871i	−0.577009	+	0.577009i	−0.934078	−	0.357069i	$-0.883776\pi$
$787$	−16.1871	+	16.1871i	−0.577009	+	0.577009i	0.357069	+	0.934078i	$0.383776\pi$
$788$	7.45721	+	7.45721i	0.265652	+	0.265652i
$789$	2.55938	+	0.409683i	0.0911163	+	0.0145851i
$790$			28.7322i			1.02225i
$791$	−3.53380	−	3.53380i	−0.125648	−	0.125648i
$792$	−2.81153	+	8.55708i	−0.0999033	+	0.304063i
$793$	−46.1260	−	12.6020i	−1.63798	−	0.447508i
$794$		−	1.82201i		−	0.0646606i
$795$	20.4987	−	14.8417i	0.727013	−	0.526380i
$796$	0.778109			0.0275793
$797$	39.4250			1.39651			0.698253	−	0.715851i	$-0.253961\pi$
$797$	39.4250			1.39651			0.698253	+	0.715851i	$0.253961\pi$
$798$	−3.78669	−	5.23000i	−0.134047	−	0.185140i
$799$	−21.1660	−	21.1660i	−0.748799	−	0.748799i
$800$	0.801028	+	0.801028i	0.0283206	+	0.0283206i
$801$	−20.9107	−	41.3757i	−0.738845	−	1.46194i
$802$	24.8643			0.877988
$803$	−34.2278			−1.20787
$804$	9.49649	+	13.1161i	0.334915	+	0.462570i
$805$		−	1.18436i		−	0.0417431i
$806$	10.1895	+	2.78385i	0.358910	+	0.0980568i
$807$	18.9440	+	3.03239i	0.666860	+	0.106745i
$808$	3.56811	+	3.56811i	0.125526	+	0.125526i
$809$			0.405681i			0.0142630i	0.999975	+	0.00713149i	$0.00227004\pi$
$809$			0.405681i			0.0142630i	−0.999975	+	0.00713149i	$0.997730\pi$
$810$	13.2190	−	17.9448i	0.464468	−	0.630517i
$811$	−26.4050	−	26.4050i	−0.927206	−	0.927206i	0.0703186	−	0.997525i	$-0.477598\pi$
$811$	−26.4050	−	26.4050i	−0.927206	−	0.927206i	−0.997525	+	0.0703186i	$0.977598\pi$
$812$	4.26874	−	4.26874i	0.149804	−	0.149804i
$813$	13.5276	+	18.6837i	0.474434	+	0.655267i
$814$	−12.6520	+	12.6520i	−0.443453	+	0.443453i
$815$			46.7247i			1.63670i
$816$	−0.831086	+	5.19197i	−0.0290938	+	0.181755i
$817$	12.1131	−	12.1131i	0.423785	−	0.423785i
$818$	29.9481			1.04711
$819$	10.5983	−	2.16218i	0.370336	−	0.0755528i
$820$	−16.9525			−0.592008
$821$	31.8342	−	31.8342i	1.11102	−	1.11102i	0.118010	−	0.993012i	$-0.462349\pi$
$821$	31.8342	−	31.8342i	1.11102	−	1.11102i	0.993012	−	0.118010i	$-0.0376513\pi$
$822$	−1.57574	+	9.84399i	−0.0549603	+	0.343349i
$823$		−	29.9746i		−	1.04485i	−0.852685	−	0.522425i	$-0.825027\pi$
$823$		−	29.9746i		−	1.04485i	0.852685	−	0.522425i	$-0.174973\pi$
$824$	12.2513	−	12.2513i	0.426795	−	0.426795i
$825$	−3.45479	−	4.77160i	−0.120280	−	0.166126i
$826$	3.76763	−	3.76763i	0.131093	−	0.131093i
$827$	−22.1847	−	22.1847i	−0.771436	−	0.771436i	0.206921	−	0.978358i	$-0.433656\pi$
$827$	−22.1847	−	22.1847i	−0.771436	−	0.771436i	−0.978358	+	0.206921i	$0.933656\pi$
$828$	−0.447847	+	1.36305i	−0.0155638	+	0.0473694i
$829$		−	25.2640i		−	0.877455i	−0.898620	−	0.438728i	$-0.855429\pi$
$829$		−	25.2640i		−	0.877455i	0.898620	−	0.438728i	$-0.144571\pi$
$830$	−24.6879	−	24.6879i	−0.856929	−	0.856929i
$831$	−34.8457	−	5.57779i	−1.20878	−	0.193492i
$832$	0.950237	−	3.47808i	0.0329435	−	0.120581i
$833$		−	3.03575i		−	0.105182i
$834$	−0.176506	−	0.243782i	−0.00611190	−	0.00844148i
$835$	−22.5795			−0.781396
$836$	11.1926			0.387103
$837$	14.5008	−	4.63259i	0.501221	−	0.160126i
$838$	−22.6068	−	22.6068i	−0.780939	−	0.780939i
$839$	−21.9032	−	21.9032i	−0.756182	−	0.756182i	0.219443	−	0.975625i	$-0.429576\pi$
$839$	−21.9032	−	21.9032i	−0.756182	−	0.756182i	−0.975625	+	0.219443i	$0.929576\pi$
$840$	2.51550	+	3.47430i	0.0867930	+	0.119875i
$841$	−7.44434			−0.256701
$842$	15.6945			0.540869
$843$	28.9133	−	20.9341i	0.995826	−	0.721009i
$844$			4.51239i			0.155323i
$845$	31.1771	−	8.02730i	1.07252	−	0.276147i
$846$	28.1027	+	9.23348i	0.966192	+	0.317454i
$847$	−1.40413	−	1.40413i	−0.0482466	−	0.0482466i
$848$		−	5.90009i		−	0.202610i
$849$	−29.9715	−	4.79758i	−1.02862	−	0.164653i
$850$	−2.43172	−	2.43172i	−0.0834072	−	0.0834072i
$851$	−2.01534	+	2.01534i	−0.0690848	+	0.0690848i
$852$	−14.6132	+	10.5804i	−0.500641	+	0.362480i
$853$	−26.8634	+	26.8634i	−0.919786	+	0.919786i	−0.997013	−	0.0772278i	$-0.975393\pi$
$853$	−26.8634	+	26.8634i	−0.919786	+	0.919786i	0.0772278	+	0.997013i	$0.475393\pi$
$854$		−	13.2619i		−	0.453813i
$855$	−26.3121	−	8.64516i	−0.899856	−	0.295658i
$856$	−5.40784	+	5.40784i	−0.184836	+	0.184836i
$857$	14.0267			0.479144			0.239572	−	0.970879i	$-0.422993\pi$
$857$	14.0267			0.479144			0.239572	+	0.970879i	$0.422993\pi$
$858$	−7.73818	+	17.0785i	−0.264177	+	0.583052i
$859$	−8.32911			−0.284185			−0.142093	−	0.989853i	$-0.545383\pi$
$859$	−8.32911			−0.284185			−0.142093	+	0.989853i	$0.545383\pi$
$860$	−8.04677	+	8.04677i	−0.274393	+	0.274393i
$861$	−11.7077	−	1.87406i	−0.398997	−	0.0638680i
$862$		−	0.180399i		−	0.00614442i
$863$	−16.9934	+	16.9934i	−0.578463	+	0.578463i	−0.934480	−	0.356017i	$-0.884135\pi$
$863$	−16.9934	+	16.9934i	−0.578463	+	0.578463i	0.356017	+	0.934480i	$0.384135\pi$
$864$	−1.58129	−	4.94970i	−0.0537965	−	0.168392i
$865$	4.65240	−	4.65240i	0.158186	−	0.158186i
$866$	−7.15080	−	7.15080i	−0.242994	−	0.242994i
$867$	−2.13107	+	13.3132i	−0.0723748	+	0.452141i
$868$			2.92963i			0.0994382i
$869$	−24.6314	−	24.6314i	−0.835563	−	0.835563i
$870$	4.09285	−	25.5689i	0.138761	−	0.866867i
$871$	16.7111	+	29.2747i	0.566233	+	0.991936i
$872$		−	4.17149i		−	0.141265i
$873$	−20.5118	−	40.5863i	−0.694220	−	1.37364i
$874$	1.78286			0.0603062
$875$	9.57688			0.323758
$876$	15.9938	−	11.5800i	0.540379	−	0.391252i
$877$	−11.7092	−	11.7092i	−0.395392	−	0.395392i	0.481212	−	0.876604i	$-0.340197\pi$
$877$	−11.7092	−	11.7092i	−0.395392	−	0.395392i	−0.876604	+	0.481212i	$0.840197\pi$
$878$	16.1502	+	16.1502i	0.545043	+	0.545043i
$879$	−44.7577	+	32.4060i	−1.50964	+	1.09303i
$880$	−7.43524			−0.250642
$881$	34.9545			1.17765			0.588824	−	0.808261i	$-0.299591\pi$
$881$	34.9545			1.17765			0.588824	+	0.808261i	$0.299591\pi$
$882$	1.35317	+	2.67749i	0.0455636	+	0.0901557i
$883$			38.3261i			1.28978i	0.764277	+	0.644888i	$0.223096\pi$
$883$			38.3261i			1.28978i	−0.764277	+	0.644888i	$0.776904\pi$
$884$	−2.88468	+	10.5586i	−0.0970222	+	0.355123i
$885$	3.61239	−	22.5673i	0.121429	−	0.758593i
$886$	6.30410	+	6.30410i	0.211791	+	0.211791i
$887$		−	35.4423i		−	1.19004i	−0.803712	−	0.595018i	$-0.797145\pi$
$887$		−	35.4423i		−	1.19004i	0.803712	−	0.595018i	$-0.202855\pi$
$888$	1.63151	−	10.1924i	0.0547500	−	0.342035i
$889$	−0.368934	−	0.368934i	−0.0123736	−	0.0123736i
$890$	27.0603	−	27.0603i	0.907064	−	0.907064i
$891$	4.05134	+	26.7159i	0.135725	+	0.895018i
$892$	−3.08394	+	3.08394i	−0.103258	+	0.103258i
$893$		−	36.7581i		−	1.23006i
$894$	−10.0110	−	1.60247i	−0.334817	−	0.0535947i
$895$	6.38944	−	6.38944i	0.213576	−	0.213576i
$896$	1.00000			0.0334077
$897$	−1.23261	+	2.72044i	−0.0411557	+	0.0908327i
$898$	27.3463			0.912558
$899$	12.5059	−	12.5059i	0.417093	−	0.417093i
$900$	3.22867	+	1.06082i	0.107622	+	0.0353605i
$901$			17.9112i			0.596708i
$902$	14.5330	−	14.5330i	0.483894	−	0.483894i
$903$	−6.44678	+	4.66767i	−0.214535	+	0.155330i
$904$	−3.53380	+	3.53380i	−0.117533	+	0.117533i
$905$	−34.1532	−	34.1532i	−1.13529	−	1.13529i
$906$	16.3282	+	2.61368i	0.542469	+	0.0868338i
$907$			10.5119i			0.349043i	0.984653	+	0.174522i	$0.0558379\pi$
$907$			10.5119i			0.349043i	−0.984653	+	0.174522i	$0.944162\pi$
$908$	18.9348	+	18.9348i	0.628373	+	0.628373i
$909$	14.3818	+	4.72532i	0.477015	+	0.156729i
$910$	4.42655	+	7.75451i	0.146739	+	0.257059i
$911$			47.2476i			1.56538i	0.622410	+	0.782691i	$0.286154\pi$
$911$			47.2476i			1.56538i	−0.622410	+	0.782691i	$0.713846\pi$
$912$	−5.23000	+	3.78669i	−0.173183	+	0.125390i
$913$	42.3286			1.40087
$914$	9.72824			0.321781
$915$	−33.3603	−	46.0758i	−1.10286	−	1.52322i
$916$	−12.2479	−	12.2479i	−0.404683	−	0.404683i
$917$	−7.16651	−	7.16651i	−0.236659	−	0.236659i
$918$	4.80039	+	15.0260i	0.158436	+	0.495933i
$919$	−55.3266			−1.82506			−0.912529	−	0.409013i	$-0.865873\pi$
$919$	−55.3266			−1.82506			−0.912529	+	0.409013i	$0.865873\pi$
$920$	−1.18436			−0.0390471
$921$	−21.5685	−	29.7894i	−0.710705	−	0.981594i
$922$			7.60631i			0.250500i
$923$	−32.6162	+	18.6185i	−1.07358	+	0.612836i
$924$	−5.13490	−	0.821950i	−0.168926	−	0.0270402i
$925$	4.77373	+	4.77373i	0.156959	+	0.156959i
$926$			2.41903i			0.0794944i
$927$	16.2247	−	49.3809i	0.532888	−	1.62188i
$928$	−4.26874	−	4.26874i	−0.140128	−	0.140128i
$929$	−15.2981	+	15.2981i	−0.501914	+	0.501914i	−0.912032	−	0.410119i	$-0.865487\pi$
$929$	−15.2981	+	15.2981i	−0.501914	+	0.501914i	0.410119	+	0.912032i	$0.365487\pi$
$930$	7.36949	+	10.1784i	0.241655	+	0.333763i
$931$	2.63603	−	2.63603i	0.0863924	−	0.0863924i
$932$			15.4793i			0.507041i
$933$	−2.93675	+	18.3465i	−0.0961448	+	0.600637i
$934$	8.56293	−	8.56293i	0.280188	−	0.280188i
$935$	22.5715			0.738167
$936$	−2.16218	−	10.5983i	−0.0706732	−	0.346418i
$937$	50.3587			1.64515			0.822574	−	0.568658i	$-0.192537\pi$
$937$	50.3587			1.64515			0.822574	+	0.568658i	$0.192537\pi$
$938$	−6.61080	+	6.61080i	−0.215850	+	0.215850i
$939$	−4.74576	+	29.6477i	−0.154872	+	0.967517i
$940$			24.4185i			0.796442i
$941$	−32.9621	+	32.9621i	−1.07453	+	1.07453i	−0.0775433	+	0.996989i	$0.524708\pi$
$941$	−32.9621	+	32.9621i	−1.07453	+	1.07453i	−0.996989	+	0.0775433i	$0.975292\pi$
$942$	4.21304	+	5.81887i	0.137268	+	0.189589i
$943$	2.31495	−	2.31495i	0.0753852	−	0.0753852i
$944$	−3.76763	−	3.76763i	−0.122626	−	0.122626i
$945$	11.4365	+	5.89849i	0.372030	+	0.191878i
$946$		−	13.7966i		−	0.448565i
$947$	2.53584	+	2.53584i	0.0824038	+	0.0824038i	0.747107	−	0.664703i	$-0.231442\pi$
$947$	2.53584	+	2.53584i	0.0824038	+	0.0824038i	−0.664703	+	0.747107i	$0.731442\pi$
$948$	19.8429	+	3.17629i	0.644469	+	0.103161i
$949$	35.6975	−	20.3774i	1.15879	−	0.661480i
$950$		−	4.22307i		−	0.137014i
$951$	28.2585	+	39.0294i	0.916346	+	1.26562i
$952$	−3.03575			−0.0983891
$953$	−5.10013			−0.165209			−0.0826047	−	0.996582i	$-0.526324\pi$
$953$	−5.10013			−0.165209			−0.0826047	+	0.996582i	$0.526324\pi$
$954$	−7.98382	−	15.7974i	−0.258486	−	0.511460i
$955$	1.49685	+	1.49685i	0.0484368	+	0.0484368i
$956$	11.2898	+	11.2898i	0.365139	+	0.365139i
$957$	18.4109	+	25.4282i	0.595139	+	0.821979i
$958$	0.757750			0.0244818
$959$	−5.75578			−0.185864
$960$	3.47430	−	2.51550i	0.112132	−	0.0811874i
$961$		−	22.4173i		−	0.723137i
$962$	5.66294	−	20.7276i	0.182580	−	0.668285i
$963$	−7.16171	+	21.7972i	−0.230783	+	0.702403i
$964$	3.14172	+	3.14172i	0.101188	+	0.101188i
$965$			57.1725i			1.84045i
$966$	−0.817936	−	0.130928i	−0.0263167	−	0.00421255i
$967$	−36.9427	−	36.9427i	−1.18800	−	1.18800i	−0.977621	−	0.210376i	$-0.932531\pi$
$967$	−36.9427	−	36.9427i	−1.18800	−	1.18800i	−0.210376	−	0.977621i	$-0.567469\pi$
$968$	−1.40413	+	1.40413i	−0.0451306	+	0.0451306i
$969$	15.8770	−	11.4954i	0.510041	−	0.369286i
$970$	26.5441	−	26.5441i	0.852279	−	0.852279i
$971$		−	57.2866i		−	1.83842i	−0.393773	−	0.919208i	$-0.628830\pi$
$971$		−	57.2866i		−	1.83842i	0.393773	−	0.919208i	$-0.371170\pi$
$972$	−10.9317	−	11.1130i	−0.350633	−	0.356450i
$973$	0.122871	−	0.122871i	0.00393907	−	0.00393907i
$974$	7.81252			0.250329
$975$	6.44390	+	2.91969i	0.206370	+	0.0935048i
$976$	−13.2619			−0.424503
$977$	−24.4879	+	24.4879i	−0.783437	+	0.783437i	−0.980409	−	0.196972i	$-0.936889\pi$
$977$	−24.4879	+	24.4879i	−0.783437	+	0.783437i	0.196972	+	0.980409i	$0.436889\pi$
$978$	32.2688	+	5.16532i	1.03184	+	0.165169i
$979$			46.3962i			1.48283i
$980$	−1.75112	+	1.75112i	−0.0559374	+	0.0559374i
$981$	−5.64473	−	11.1691i	−0.180222	−	0.356602i
$982$	22.8390	−	22.8390i	0.728821	−	0.728821i
$983$	−10.8336	−	10.8336i	−0.345537	−	0.345537i	0.512907	−	0.858444i	$-0.328568\pi$
$983$	−10.8336	−	10.8336i	−0.345537	−	0.345537i	−0.858444	+	0.512907i	$0.828568\pi$
$984$	−1.87406	+	11.7077i	−0.0597430	+	0.373227i
$985$			26.1169i			0.832154i
$986$	12.9588	+	12.9588i	0.412693	+	0.412693i
$987$	−2.69941	+	16.8638i	−0.0859231	+	0.536780i
$988$	−11.6732	+	6.66347i	−0.371373	+	0.211993i
$989$		−	2.19765i		−	0.0698813i
$990$	−19.9078	+	10.0611i	−0.632710	+	0.319764i
$991$	49.1490			1.56127			0.780635	−	0.624988i	$-0.214896\pi$
$991$	49.1490			1.56127			0.780635	+	0.624988i	$0.214896\pi$
$992$	2.92963			0.0930159
$993$	8.29125	−	6.00313i	0.263115	−	0.190503i
$994$	−7.36537	−	7.36537i	−0.233615	−	0.233615i
$995$	1.36256	+	1.36256i	0.0431961	+	0.0431961i
$996$	−19.7790	+	14.3206i	−0.626723	+	0.453767i
$997$	−3.17797			−0.100647			−0.0503237	−	0.998733i	$-0.516025\pi$
$997$	−3.17797			−0.100647			−0.0503237	+	0.998733i	$0.516025\pi$
$998$	34.6609			1.09717
$999$	−9.42368	−	29.4977i	−0.298152	−	0.933267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.d.281.8	yes	20
3.2	odd	2		546.2.p.c.281.3	yes	20
13.5	odd	4		546.2.p.c.239.3	✓	20
39.5	even	4	inner	546.2.p.d.239.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.3	✓	20	13.5	odd	4
546.2.p.c.281.3	yes	20	3.2	odd	2
546.2.p.d.239.8	yes	20	39.5	even	4	inner
546.2.p.d.281.8	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} -1.00000i q^{4} +(1.75112 - 1.75112i) q^{5} +(-1.01577 - 1.40293i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.85010 - 0.936434i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} -1.00000i q^{4} +(1.75112 - 1.75112i) q^{5} +(-1.01577 - 1.40293i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.85010 - 0.936434i) q^{9} -2.47645i q^{10} +(2.12300 + 2.12300i) q^{11} +(-1.71028 - 0.273767i) q^{12} +(-3.47808 - 0.950237i) q^{13} -1.00000i q^{14} +(-2.51550 - 3.47430i) q^{15} -1.00000 q^{16} +3.03575 q^{17} +(-2.67749 + 1.35317i) q^{18} +(2.63603 + 2.63603i) q^{19} +(-1.75112 - 1.75112i) q^{20} +(-1.01577 - 1.40293i) q^{21} +3.00237 q^{22} +0.478247 q^{23} +(-1.40293 + 1.01577i) q^{24} -1.13282i q^{25} +(-3.13129 + 1.78746i) q^{26} +(-2.38183 + 4.61811i) q^{27} +(-0.707107 - 0.707107i) q^{28} +6.03691i q^{29} +(-4.23543 - 0.677971i) q^{30} +(-2.07156 - 2.07156i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.21213 - 3.04971i) q^{33} +(2.14660 - 2.14660i) q^{34} -2.47645i q^{35} +(-0.936434 + 2.85010i) q^{36} +(-4.21400 + 4.21400i) q^{37} +3.72791 q^{38} +(-2.57735 + 5.68834i) q^{39} -2.47645 q^{40} +(4.84049 - 4.84049i) q^{41} +(-1.71028 - 0.273767i) q^{42} -4.59522i q^{43} +(2.12300 - 2.12300i) q^{44} +(-6.63067 + 3.35106i) q^{45} +(0.338172 - 0.338172i) q^{46} +(-6.97225 - 6.97225i) q^{47} +(-0.273767 + 1.71028i) q^{48} -1.00000i q^{49} +(-0.801028 - 0.801028i) q^{50} +(0.831086 - 5.19197i) q^{51} +(-0.950237 + 3.47808i) q^{52} +5.90009i q^{53} +(1.58129 + 4.94970i) q^{54} +7.43524 q^{55} -1.00000 q^{56} +(5.23000 - 3.78669i) q^{57} +(4.26874 + 4.26874i) q^{58} +(3.76763 + 3.76763i) q^{59} +(-3.47430 + 2.51550i) q^{60} +13.2619 q^{61} -2.92963 q^{62} +(-2.67749 + 1.35317i) q^{63} +1.00000i q^{64} +(-7.75451 + 4.42655i) q^{65} +(0.821950 - 5.13490i) q^{66} +(-6.61080 - 6.61080i) q^{67} -3.03575i q^{68} +(0.130928 - 0.817936i) q^{69} +(-1.75112 - 1.75112i) q^{70} +(7.36537 - 7.36537i) q^{71} +(1.35317 + 2.67749i) q^{72} +(-8.06119 + 8.06119i) q^{73} +5.95950i q^{74} +(-1.93745 - 0.310130i) q^{75} +(2.63603 - 2.63603i) q^{76} +3.00237 q^{77} +(2.19980 + 5.84473i) q^{78} -11.6022 q^{79} +(-1.75112 + 1.75112i) q^{80} +(7.24618 + 5.33787i) q^{81} -6.84548i q^{82} +(9.96904 - 9.96904i) q^{83} +(-1.40293 + 1.01577i) q^{84} +(5.31595 - 5.31595i) q^{85} +(-3.24931 - 3.24931i) q^{86} +(10.3248 + 1.65271i) q^{87} -3.00237i q^{88} +(10.9270 + 10.9270i) q^{89} +(-2.31904 + 7.05815i) q^{90} +(-3.13129 + 1.78746i) q^{91} -0.478247i q^{92} +(-4.11007 + 2.97582i) q^{93} -9.86025 q^{94} +9.23199 q^{95} +(1.01577 + 1.40293i) q^{96} +(10.7186 + 10.7186i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-4.06272 - 8.03882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9 + 16 * q^11 + 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 - 12 * q^17 - 16 * q^18 + 12 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 + 4 * q^23 - 4 * q^24 + 24 * q^27 - 12 * q^30 - 8 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * q^54 + 28 * q^55 - 20 * q^56 + 36 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 - 4 * q^61 - 48 * q^62 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * q^78 - 64 * q^79 - 4 * q^80 + 32 * q^81 + 24 * q^83 - 4 * q^84 + 24 * q^85 - 4 * q^86 + 4 * q^87 + 4 * q^89 + 8 * q^90 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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