LMFDB - Embedded newform 546.2.p.c.239.3

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			239.3
Root			$-1.01577 - 1.40293i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.c.281.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} +1.00000i q^{4} +(-1.75112 - 1.75112i) q^{5} +(-1.40293 + 1.01577i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.85010 - 0.936434i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} +1.00000i q^{4} +(-1.75112 - 1.75112i) q^{5} +(-1.40293 + 1.01577i) 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} +(-3.47430 + 2.51550i) q^{15} -1.00000 q^{16} -3.03575 q^{17} +(1.35317 + 2.67749i) q^{18} +(2.63603 - 2.63603i) q^{19} +(1.75112 - 1.75112i) q^{20} +(1.40293 - 1.01577i) q^{21} +3.00237 q^{22} -0.478247 q^{23} +(-1.01577 - 1.40293i) 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} +(3.04971 + 4.21213i) 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} +(0.672986 + 6.20863i) 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} +(3.35106 + 6.63067i) 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} +(4.94970 - 1.58129i) q^{54} +7.43524 q^{55} +1.00000 q^{56} +(-3.78669 - 5.23000i) q^{57} +(4.26874 - 4.26874i) q^{58} +(-3.76763 + 3.76763i) q^{59} +(-2.51550 - 3.47430i) q^{60} +13.2619 q^{61} +2.92963 q^{62} +(-1.35317 - 2.67749i) 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} +(-2.67749 + 1.35317i) 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} +(3.91429 - 4.86604i) 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} +(1.01577 + 1.40293i) 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} +(2.97582 + 4.11007i) q^{93} -9.86025 q^{94} -9.23199 q^{95} +(1.40293 - 1.01577i) q^{96} +(10.7186 - 10.7186i) q^{97} +(0.707107 - 0.707107i) q^{98} +(8.03882 - 4.06272i) 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} - 8 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} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 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} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 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} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 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 - 8 * 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 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * 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 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * 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 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * 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
$3$	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	$-0.436804\pi$
$5$	−1.75112	−	1.75112i	−0.783124	−	0.783124i	−0.980357	+	0.197233i	$0.936804\pi$
$6$	−1.40293	+	1.01577i	−0.572744	+	0.414685i
$7$	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	$-0.899512\pi$
$11$	−2.12300	+	2.12300i	−0.640108	+	0.640108i	0.310474	+	0.950582i	$0.399512\pi$
$12$	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
$15$	−3.47430	+	2.51550i	−0.897059	+	0.649499i
$16$	−1.00000			−0.250000
$17$	−3.03575			−0.736277			−0.368138	−	0.929771i	$-0.620005\pi$
$17$	−3.03575			−0.736277			−0.368138	+	0.929771i	$0.620005\pi$
$18$	1.35317	+	2.67749i	0.318945	+	0.631090i
$19$	2.63603	−	2.63603i	0.604747	−	0.604747i	−0.336822	−	0.941568i	$-0.609352\pi$
$19$	2.63603	−	2.63603i	0.604747	−	0.604747i	0.941568	+	0.336822i	$0.109352\pi$
$20$	1.75112	−	1.75112i	0.391562	−	0.391562i
$21$	1.40293	−	1.01577i	0.306145	−	0.221659i
$22$	3.00237			0.640108
$23$	−0.478247			−0.0997215			−0.0498607	−	0.998756i	$-0.515878\pi$
$23$	−0.478247			−0.0997215			−0.0498607	+	0.998756i	$0.515878\pi$
$24$	−1.01577	−	1.40293i	−0.207343	−	0.286372i
$25$			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	−0.868228	−	0.496165i	$-0.834741\pi$
$31$	−2.07156	+	2.07156i	−0.372064	+	0.372064i	0.496165	+	0.868228i	$0.334741\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.04971	+	4.21213i	0.530887	+	0.733237i
$34$	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	0.270064	−	0.962842i	$-0.412955\pi$
$37$	−4.21400	−	4.21400i	−0.692778	−	0.692778i	−0.962842	+	0.270064i	$0.912955\pi$
$38$	−3.72791			−0.604747
$39$	0.672986	+	6.20863i	0.107764	+	0.994176i
$40$	−2.47645			−0.391562
$41$	−4.84049	−	4.84049i	−0.755957	−	0.755957i	0.219627	−	0.975584i	$-0.429516\pi$
$41$	−4.84049	−	4.84049i	−0.755957	−	0.755957i	−0.975584	+	0.219627i	$0.929516\pi$
$42$	−1.71028	−	0.273767i	−0.263902	−	0.0422431i
$43$			4.59522i			0.700764i	0.936607	+	0.350382i	$0.113948\pi$
$43$			4.59522i			0.700764i	−0.936607	+	0.350382i	$0.886052\pi$
$44$	−2.12300	−	2.12300i	−0.320054	−	0.320054i
$45$	3.35106	+	6.63067i	0.499546	+	0.988442i
$46$	0.338172	+	0.338172i	0.0498607	+	0.0498607i
$47$	6.97225	−	6.97225i	1.01701	−	1.01701i	0.0171544	−	0.999853i	$-0.494539\pi$
$47$	6.97225	−	6.97225i	1.01701	−	1.01701i	0.999853	−	0.0171544i	$-0.00546067\pi$
$48$	−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	$0.867195\pi$
$54$	4.94970	−	1.58129i	0.673569	−	0.215186i
$55$	7.43524			1.00257
$56$	1.00000			0.133631
$57$	−3.78669	−	5.23000i	−0.501559	−	0.692730i
$58$	4.26874	−	4.26874i	0.560513	−	0.560513i
$59$	−3.76763	+	3.76763i	−0.490504	+	0.490504i	−0.908465	−	0.417961i	$-0.862745\pi$
$59$	−3.76763	+	3.76763i	−0.490504	+	0.490504i	0.417961	+	0.908465i	$0.362745\pi$
$60$	−2.51550	−	3.47430i	−0.324750	−	0.448530i
$61$	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
$63$	−1.35317	−	2.67749i	−0.170483	−	0.337332i
$64$		−	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	−0.984276	−	0.176638i	$-0.943478\pi$
$67$	−6.61080	+	6.61080i	−0.807638	+	0.807638i	0.176638	+	0.984276i	$0.443478\pi$
$68$		−	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	$-0.462093\pi$
$71$	−7.36537	−	7.36537i	−0.874109	−	0.874109i	−0.992917	+	0.118808i	$0.962093\pi$
$72$	−2.67749	+	1.35317i	−0.315545	+	0.159472i
$73$	−8.06119	−	8.06119i	−0.943491	−	0.943491i	0.0549955	−	0.998487i	$-0.482486\pi$
$73$	−8.06119	−	8.06119i	−0.943491	−	0.943491i	−0.998487	+	0.0549955i	$0.982486\pi$
$74$			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
$78$	3.91429	−	4.86604i	0.443206	−	0.550970i
$79$	−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	−0.995070	−	0.0991748i	$-0.968380\pi$
$83$	−9.96904	−	9.96904i	−1.09424	−	1.09424i	−0.0991748	−	0.995070i	$-0.531620\pi$
$84$	1.01577	+	1.40293i	0.110829	+	0.153072i
$85$	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	−0.173415	+	0.984849i	$0.555480\pi$
$89$	−10.9270	+	10.9270i	−1.15826	+	1.15826i	−0.984849	+	0.173415i	$0.944520\pi$
$90$	2.31904	−	7.05815i	0.244448	−	0.743994i
$91$	−3.13129	−	1.78746i	−0.328249	−	0.187376i
$92$		−	0.478247i		−	0.0498607i
$93$	2.97582	+	4.11007i	0.308579	+	0.426195i
$94$	−9.86025			−1.01701
$95$	−9.23199			−0.947182
$96$	1.40293	−	1.01577i	0.143186	−	0.103671i
$97$	10.7186	−	10.7186i	1.08831	−	1.08831i	0.0926043	−	0.995703i	$-0.470481\pi$
$97$	10.7186	−	10.7186i	1.08831	−	1.08831i	0.995703	−	0.0926043i	$-0.0295192\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	8.03882	−	4.06272i	0.807932	−	0.408319i
$100$	−1.13282			−0.113282
$101$	5.04608			0.502103			0.251052	−	0.967974i	$-0.419224\pi$
$101$	5.04608			0.502103			0.251052	+	0.967974i	$0.419224\pi$
$102$	4.25894	−	3.08361i	0.421698	−	0.305323i
$103$		−	17.3260i		−	1.70718i	−0.520944	−	0.853591i	$-0.674420\pi$
$103$		−	17.3260i		−	1.70718i	0.520944	−	0.853591i	$-0.325580\pi$
$104$	−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	−0.551588	−	0.834117i	$-0.685978\pi$
$109$	2.94969	−	2.94969i	0.282529	−	0.282529i	0.834117	+	0.551588i	$0.185978\pi$
$110$	−5.25751	−	5.25751i	−0.501284	−	0.501284i
$111$	−8.36077	+	6.05346i	−0.793569	+	0.574569i
$112$	−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
$117$	10.8027	+	0.548722i	0.998712	+	0.0507294i
$118$	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
$123$	−9.60374	+	6.95342i	−0.865940	+	0.626968i
$124$	−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	$0.00736920\pi$
$127$			0.521751i			0.0462979i	−0.999732	+	0.0231490i	$0.992631\pi$
$128$	−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	$-0.145997\pi$
$132$	−4.21213	+	3.04971i	−0.366619	+	0.265443i
$133$	3.72791			0.323251
$134$	9.34908			0.807638
$135$	12.2577	−	3.91599i	1.05498	−	0.337034i
$136$	−2.14660	+	2.14660i	−0.184069	+	0.184069i
$137$	4.06995	−	4.06995i	0.347720	−	0.347720i	−0.511540	−	0.859259i	$-0.670925\pi$
$137$	4.06995	−	4.06995i	0.347720	−	0.347720i	0.859259	+	0.511540i	$0.170925\pi$
$138$	0.670949	−	0.485788i	0.0571149	−	0.0413530i
$139$	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
$141$	−10.0157	−	13.8333i	−0.843476	−	1.16497i
$142$			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	$-0.327071\pi$
$149$	−4.13899	−	4.13899i	−0.339079	−	0.339079i	−0.856021	+	0.516941i	$0.827071\pi$
$150$	−1.15069	−	1.58928i	−0.0939531	−	0.129764i
$151$	−6.75083	−	6.75083i	−0.549375	−	0.549375i	0.376885	−	0.926260i	$-0.376995\pi$
$151$	−6.75083	−	6.75083i	−0.549375	−	0.549375i	−0.926260	+	0.376885i	$0.876995\pi$
$152$		−	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
$156$	−6.20863	+	0.672986i	−0.497088	+	0.0538820i
$157$	−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
$162$	−1.34938	−	8.89827i	−0.106017	−	0.699114i
$163$	−13.3414	−	13.3414i	−1.04498	−	1.04498i	−0.998940	−	0.0460395i	$-0.985340\pi$
$163$	−13.3414	−	13.3414i	−1.04498	−	1.04498i	−0.0460395	−	0.998940i	$-0.514660\pi$
$164$	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	$-0.635239\pi$
$167$	6.44717	−	6.44717i	0.498897	−	0.498897i	0.911095	+	0.412197i	$0.135239\pi$
$168$	0.273767	−	1.71028i	0.0211216	−	0.131951i
$169$	11.1941	−	6.61000i	0.861085	−	0.508462i
$170$		−	7.51789i		−	0.576596i
$171$	−9.98142	+	5.04449i	−0.763299	+	0.385762i
$172$	−4.59522			−0.350382
$173$	−2.65682			−0.201994			−0.100997	−	0.994887i	$-0.532203\pi$
$173$	−2.65682			−0.201994			−0.100997	+	0.994887i	$0.532203\pi$
$174$	−6.13210	−	8.46938i	−0.464873	−	0.642062i
$175$	−0.801028	+	0.801028i	−0.0605520	+	0.0605520i
$176$	2.12300	−	2.12300i	0.160027	−	0.160027i
$177$	5.41225	+	7.47515i	0.406809	+	0.561867i
$178$	15.4532			1.15826
$179$	−3.64878			−0.272723			−0.136361	−	0.990659i	$-0.543541\pi$
$179$	−3.64878			−0.272723			−0.136361	+	0.990659i	$0.543541\pi$
$180$	−6.63067	+	3.35106i	−0.494221	+	0.249773i
$181$			19.5037i			1.44970i	0.688909	+	0.724848i	$0.258090\pi$
$181$			19.5037i			1.44970i	−0.688909	+	0.724848i	$0.741910\pi$
$182$	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
$189$	−4.94970	+	1.58129i	−0.360038	+	0.115022i
$190$	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	−0.980985	−	0.194083i	$-0.937827\pi$
$193$	−16.3246	−	16.3246i	−1.17507	−	1.17507i	−0.194083	−	0.980985i	$-0.562173\pi$
$194$	−15.1584			−1.08831
$195$	9.69356	−	12.0505i	0.694170	−	0.862956i
$196$	−1.00000			−0.0714286
$197$	7.45721	+	7.45721i	0.531304	+	0.531304i	0.920960	−	0.389656i	$-0.127406\pi$
$197$	7.45721	+	7.45721i	0.531304	+	0.531304i	−0.389656	+	0.920960i	$0.627406\pi$
$198$	−8.55708	−	2.81153i	−0.608125	−	0.199807i
$199$		−	0.778109i		−	0.0551587i	−0.999620	−	0.0275793i	$-0.991220\pi$
$199$		−	0.778109i		−	0.0551587i	0.999620	−	0.0275793i	$-0.00877989\pi$
$200$	0.801028	+	0.801028i	0.0566412	+	0.0566412i
$201$	9.49649	+	13.1161i	0.669831	+	0.925140i
$202$	−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
$210$	2.51550	+	3.47430i	0.173586	+	0.239749i
$211$	−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
$213$	−14.6132	+	10.5804i	−1.00128	+	0.724960i
$214$	−5.40784	+	5.40784i	−0.369673	+	0.369673i
$215$	8.04677	−	8.04677i	0.548785	−	0.548785i
$216$	1.58129	+	4.94970i	0.107593	+	0.336784i
$217$	−2.92963			−0.198876
$218$	−4.17149			−0.282529
$219$	−15.9938	+	11.5800i	−1.08076	+	0.782504i
$220$			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	−0.802785	−	0.596269i	$-0.796649\pi$
$223$	−3.08394	+	3.08394i	−0.206516	+	0.206516i	0.596269	+	0.802785i	$0.296649\pi$
$224$			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	0.952637	+	0.304109i	$0.0983588\pi$
$227$	18.9348	+	18.9348i	1.25675	+	1.25675i	0.304109	+	0.952637i	$0.401641\pi$
$228$	5.23000	−	3.78669i	0.346365	−	0.250779i
$229$	12.2479	+	12.2479i	0.809366	+	0.809366i	0.984538	−	0.175172i	$-0.0560482\pi$
$229$	12.2479	+	12.2479i	0.809366	+	0.809366i	−0.175172	+	0.984538i	$0.556048\pi$
$230$		−	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	$-0.330739\pi$
$233$	15.4793			1.01408			0.507041	+	0.861922i	$0.330739\pi$
$234$	−7.25068	−	8.02669i	−0.473992	−	0.524721i
$235$	−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	$-0.0772776\pi$
$239$	11.2898	+	11.2898i	0.730278	+	0.730278i	−0.240397	+	0.970675i	$0.577278\pi$
$240$	3.47430	−	2.51550i	0.224265	−	0.162375i
$241$	−3.14172	−	3.14172i	−0.202376	−	0.202376i	0.598641	−	0.801017i	$-0.295707\pi$
$241$	−3.14172	−	3.14172i	−0.202376	−	0.202376i	−0.801017	+	0.598641i	$0.795707\pi$
$242$	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
$249$	−19.7790	+	14.3206i	−1.25345	+	0.907534i
$250$	9.57688			0.605695
$251$	−18.4294			−1.16326			−0.581628	−	0.813455i	$-0.697584\pi$
$251$	−18.4294			−1.16326			−0.581628	+	0.813455i	$0.697584\pi$
$252$	2.67749	−	1.35317i	0.168666	−	0.0852416i
$253$	1.01532	−	1.01532i	0.0638326	−	0.0638326i
$254$	0.368934	−	0.368934i	0.0231490	−	0.0231490i
$255$	10.5471	−	7.63642i	0.660484	−	0.478211i
$256$	1.00000			0.0625000
$257$	4.35687			0.271774			0.135887	−	0.990724i	$-0.456612\pi$
$257$	4.35687			0.271774			0.135887	+	0.990724i	$0.456612\pi$
$258$	−4.66767	−	6.44678i	−0.290597	−	0.401359i
$259$		−	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
$267$	15.6968	+	21.6797i	0.960630	+	1.32678i
$268$	−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	0.360657	−	0.932699i	$-0.382553\pi$
$271$	−9.41699	−	9.41699i	−0.572042	−	0.572042i	−0.932699	+	0.360657i	$0.882553\pi$
$272$	3.03575			0.184069
$273$	−3.91429	+	4.86604i	−0.236904	+	0.294506i
$274$	−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	$0.209669\pi$
$277$			20.3743i			1.22417i	−0.790792	+	0.612085i	$0.790331\pi$
$278$	−0.122871	−	0.122871i	−0.00736933	−	0.00736933i
$279$	7.84405	−	3.96429i	0.469611	−	0.237336i
$280$	−1.75112	−	1.75112i	−0.104649	−	0.104649i
$281$	−14.5729	+	14.5729i	−0.869346	+	0.869346i	−0.992400	−	0.123054i	$-0.960731\pi$
$281$	−14.5729	+	14.5729i	−0.869346	+	0.869346i	0.123054	+	0.992400i	$0.460731\pi$
$282$	−2.69941	+	16.8638i	−0.160747	+	1.00422i
$283$			17.5244i			1.04171i	0.853644	+	0.520857i	$0.174388\pi$
$283$			17.5244i			1.04171i	−0.853644	+	0.520857i	$0.825612\pi$
$284$	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
$288$	−1.35317	−	2.67749i	−0.0797362	−	0.157772i
$289$	−7.78425			−0.457897
$290$	−14.9501			−0.877903
$291$	−15.3974	−	21.2662i	−0.902610	−	1.24664i
$292$	8.06119	−	8.06119i	0.471746	−	0.471746i
$293$	22.5588	−	22.5588i	1.31790	−	1.31790i	0.402466	−	0.915435i	$-0.368153\pi$
$293$	22.5588	−	22.5588i	1.31790	−	1.31790i	0.915435	−	0.402466i	$-0.131847\pi$
$294$	−1.01577	−	1.40293i	−0.0592407	−	0.0818206i
$295$	13.1951			0.768250
$296$	−5.95950			−0.346389
$297$	−4.74762	−	14.8609i	−0.275485	−	0.862314i
$298$			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
$306$	−4.10788	−	8.12817i	−0.234832	−	0.464657i
$307$	15.0145	+	15.0145i	0.856921	+	0.856921i	0.990974	−	0.134053i	$-0.0427992\pi$
$307$	15.0145	+	15.0145i	0.856921	+	0.856921i	−0.134053	+	0.990974i	$0.542799\pi$
$308$		−	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	$-0.401630\pi$
$311$	10.7272			0.608283			0.304142	+	0.952627i	$0.401630\pi$
$312$	4.86604	+	3.91429i	0.275485	+	0.221603i
$313$	−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	0.993814	+	0.111055i	$0.0354229\pi$
$317$	19.6716	+	19.6716i	1.10487	+	1.10487i	0.111055	+	0.993814i	$0.464577\pi$
$318$	−5.99312	−	8.27742i	−0.336077	−	0.464175i
$319$	−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
$327$	−4.23726	−	5.85232i	−0.234321	−	0.323634i
$328$	−6.84548			−0.377979
$329$	9.86025			0.543613
$330$	−10.4311	+	7.55248i	−0.574215	+	0.415750i
$331$	4.17896	−	4.17896i	0.229697	−	0.229697i	−0.582869	−	0.812566i	$-0.698070\pi$
$331$	4.17896	−	4.17896i	0.229697	−	0.229697i	0.812566	+	0.582869i	$0.198070\pi$
$332$	9.96904	−	9.96904i	0.547122	−	0.547122i
$333$	8.06421	+	15.9565i	0.441916	+	0.874410i
$334$	−9.11768			−0.498897
$335$	23.1526			1.26496
$336$	−1.40293	+	1.01577i	−0.0765362	+	0.0554146i
$337$		−	7.79284i		−	0.424503i	−0.977215	−	0.212251i	$-0.931920\pi$
$337$		−	7.79284i		−	0.424503i	0.977215	−	0.212251i	$-0.0680796\pi$
$338$	−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
$345$	1.66157	−	1.20303i	0.0894561	−	0.0647691i
$346$	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	−0.956850	−	0.290581i	$-0.906151\pi$
$349$	−23.3039	−	23.3039i	−1.24743	−	1.24743i	−0.290581	−	0.956850i	$-0.593849\pi$
$350$	1.13282			0.0605520
$351$	3.89589	−	18.3254i	0.207947	−	0.978140i
$352$	−3.00237			−0.160027
$353$	17.4264	+	17.4264i	0.927516	+	0.927516i	0.997545	−	0.0700290i	$-0.0223092\pi$
$353$	17.4264	+	17.4264i	0.927516	+	0.927516i	−0.0700290	+	0.997545i	$0.522309\pi$
$354$	1.45869	−	9.11277i	0.0775287	−	0.484338i
$355$			25.7953i			1.36907i
$356$	−10.9270	−	10.9270i	−0.579132	−	0.579132i
$357$	−4.25894	+	3.08361i	−0.225407	+	0.163202i
$358$	2.58008	+	2.58008i	0.136361	+	0.136361i
$359$	13.3523	−	13.3523i	0.704707	−	0.704707i	−0.260710	−	0.965417i	$-0.583957\pi$
$359$	13.3523	−	13.3523i	0.704707	−	0.704707i	0.965417	+	0.260710i	$0.0839568\pi$
$360$	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
$366$	−18.6055	+	13.4710i	−0.972528	+	0.704141i
$367$	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
$369$	9.26309	+	18.3287i	0.482217	+	0.954153i
$370$	10.4358	−	10.4358i	0.542531	−	0.542531i
$371$	−4.17199	+	4.17199i	−0.216599	+	0.216599i
$372$	−4.11007	+	2.97582i	−0.213097	+	0.154289i
$373$	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
$375$	9.72788	+	13.4357i	0.502346	+	0.693817i
$376$		−	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	−0.262986	+	0.964800i	$0.584707\pi$
$379$	−23.9024	+	23.9024i	−1.22779	+	1.22779i	−0.964800	+	0.262986i	$0.915293\pi$
$380$		−	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	$-0.330989\pi$
$383$	−6.96614	−	6.96614i	−0.355953	−	0.355953i	−0.862319	+	0.506366i	$0.830989\pi$
$384$	1.01577	+	1.40293i	0.0518356	+	0.0715931i
$385$	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	$-0.171177\pi$
$389$	33.8785			1.71771			0.858854	+	0.512220i	$0.171177\pi$
$390$	−15.3754	+	1.66662i	−0.778563	+	0.0843926i
$391$	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
$396$	4.06272	+	8.03882i	0.204159	+	0.403966i
$397$	1.28835	+	1.28835i	0.0646606	+	0.0646606i	0.738698	−	0.674037i	$-0.235441\pi$
$397$	1.28835	+	1.28835i	0.0646606	+	0.0646606i	−0.674037	+	0.738698i	$0.735441\pi$
$398$	−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	$-0.963205\pi$
$401$	−17.5817	+	17.5817i	−0.877988	+	0.877988i	0.115339	+	0.993326i	$0.463205\pi$
$402$	2.55947	−	15.9895i	0.127655	−	0.797486i
$403$	5.23659	−	9.17354i	0.260853	−	0.456967i
$404$			5.04608i			0.251052i
$405$	−3.34168	−	22.0362i	−0.166049	−	1.09499i
$406$	6.03691			0.299607
$407$	17.8927			0.886906
$408$	3.08361	+	4.25894i	0.152661	+	0.210849i
$409$	21.1765	−	21.1765i	1.04711	−	1.04711i	0.0482783	−	0.998834i	$-0.484627\pi$
$409$	21.1765	−	21.1765i	1.04711	−	1.04711i	0.998834	−	0.0482783i	$-0.0153735\pi$
$410$	11.9872	−	11.9872i	0.592008	−	0.592008i
$411$	−5.84653	−	8.07497i	−0.288388	−	0.398309i
$412$	17.3260			0.853591
$413$	−5.32824			−0.262185
$414$	−0.647149	−	1.28050i	−0.0318057	−	0.0629332i
$415$			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	−0.382915	−	0.923784i	$-0.625080\pi$
$421$	11.0977	−	11.0977i	0.540869	−	0.540869i	0.923784	+	0.382915i	$0.125080\pi$
$422$	3.19074	+	3.19074i	0.155323	+	0.155323i
$423$	−26.4007	+	13.3426i	−1.28365	+	0.648738i
$424$	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
$429$	−14.6097	−	11.7522i	−0.705361	−	0.567400i
$430$	−11.3798			−0.548785
$431$	−0.127561	−	0.127561i	−0.00614442	−	0.00614442i	0.704028	−	0.710172i	$-0.251383\pi$
$431$	−0.127561	−	0.127561i	−0.00614442	−	0.00614442i	−0.710172	+	0.704028i	$0.751383\pi$
$432$	2.38183	−	4.61811i	0.114596	−	0.222189i
$433$			10.1128i			0.485988i	0.970028	+	0.242994i	$0.0781296\pi$
$433$			10.1128i			0.485988i	−0.970028	+	0.242994i	$0.921870\pi$
$434$	2.07156	+	2.07156i	0.0994382	+	0.0994382i
$435$	−15.1859	−	20.9740i	−0.728106	−	1.00563i
$436$	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	$-0.816513\pi$
$439$		−	22.8399i		−	1.09009i	0.838408	−	0.545043i	$-0.183487\pi$
$440$	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	$0.932071\pi$
$444$	−6.05346	−	8.36077i	−0.287285	−	0.396785i
$445$	38.2691			1.81413
$446$	4.36135			0.206516
$447$	−8.21195	+	5.94571i	−0.388412	+	0.281222i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−19.3368	+	19.3368i	−0.912558	+	0.912558i	−0.996473	−	0.0839148i	$-0.973258\pi$
$449$	−19.3368	+	19.3368i	−0.912558	+	0.912558i	0.0839148	+	0.996473i	$0.473258\pi$
$450$	−3.03312	+	1.53290i	−0.142983	+	0.0722617i
$451$	20.5527			0.967789
$452$	4.99755			0.235065
$453$	−13.3940	+	9.69765i	−0.629303	+	0.455635i
$454$		−	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	−0.527669	−	0.849450i	$-0.676934\pi$
$457$	6.87890	−	6.87890i	0.321781	−	0.321781i	0.849450	+	0.527669i	$0.176934\pi$
$458$		−	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	$-0.193319\pi$
$461$	5.37847	+	5.37847i	0.250500	+	0.250500i	−0.570675	+	0.821176i	$0.693319\pi$
$462$	4.21213	−	3.04971i	0.195966	−	0.141886i
$463$	−1.71052	−	1.71052i	−0.0794944	−	0.0794944i	0.666242	−	0.745736i	$-0.267902\pi$
$463$	−1.71052	−	1.71052i	−0.0794944	−	0.0794944i	−0.745736	+	0.666242i	$0.767902\pi$
$464$		−	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	$-0.590397\pi$
$467$	−12.1098			−0.560375			−0.280188	+	0.959945i	$0.590397\pi$
$468$	−0.548722	+	10.8027i	−0.0253647	+	0.499356i
$469$	−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
$474$	16.2771	−	11.7851i	0.747630	−	0.541308i
$475$	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	$-0.755511\pi$
$479$	−0.535810	+	0.535810i	−0.0244818	+	0.0244818i	0.694760	+	0.719242i	$0.255511\pi$
$480$	−4.23543	−	0.677971i	−0.193320	−	0.0309450i
$481$	18.6609	+	10.6523i	0.850866	+	0.485705i
$482$			4.44306i			0.202376i
$483$	−0.670949	+	0.485788i	−0.0305292	+	0.0221041i
$484$	−1.98575			−0.0902612
$485$	−37.5390			−1.70456
$486$	−15.5879	−	0.128235i	−0.707083	−	0.00581687i
$487$	5.52429	−	5.52429i	0.250329	−	0.250329i	−0.570776	−	0.821106i	$-0.693358\pi$
$487$	5.52429	−	5.52429i	0.250329	−	0.250329i	0.821106	+	0.570776i	$0.193358\pi$
$488$	9.37758	−	9.37758i	0.424503	−	0.424503i
$489$	−26.4699	+	19.1651i	−1.19701	+	0.866675i
$490$	−2.47645			−0.111875
$491$	−32.2992			−1.45764			−0.728821	−	0.684704i	$-0.759932\pi$
$491$	−32.2992			−1.45764			−0.728821	+	0.684704i	$0.759932\pi$
$492$	−6.95342	−	9.60374i	−0.313484	−	0.432970i
$493$		−	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	0.102433	−	0.994740i	$-0.467337\pi$
$499$	24.5090	−	24.5090i	1.09717	−	1.09717i	0.994740	−	0.102433i	$-0.0326627\pi$
$500$	−6.77188	−	6.77188i	−0.302848	−	0.302848i
$501$	−9.26144	−	12.7915i	−0.413771	−	0.571481i
$502$	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
$507$	−8.24037	−	20.9546i	−0.365968	−	0.930628i
$508$	−0.521751			−0.0231490
$509$	2.91721	+	2.91721i	0.129303	+	0.129303i	0.768797	−	0.639493i	$-0.220856\pi$
$509$	2.91721	+	2.91721i	0.129303	+	0.129303i	−0.639493	+	0.768797i	$0.720856\pi$
$510$	−12.8577	−	2.05815i	−0.569347	−	0.0911363i
$511$		−	11.4002i		−	0.504317i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	5.89490	+	18.4520i	0.260266	+	0.814677i
$514$	−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	$-0.149762\pi$
$522$	−16.1638	+	8.16896i	−0.707469	+	0.357546i
$523$	−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
$525$	1.15069	+	1.58928i	0.0502201	+	0.0693617i
$526$	1.05816	−	1.05816i	0.0461381	−	0.0461381i
$527$	6.28874	−	6.28874i	0.273942	−	0.273942i
$528$	−3.04971	−	4.21213i	−0.132722	−	0.183309i
$529$	−22.7713			−0.990056
$530$	−14.6113			−0.634674
$531$	14.2663	−	7.21000i	0.619104	−	0.312887i
$532$			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
$540$	3.91599	+	12.2577i	0.168517	+	0.527488i
$541$	−0.860954	−	0.860954i	−0.0370153	−	0.0370153i	0.688357	−	0.725372i	$-0.258332\pi$
$541$	−0.860954	−	0.860954i	−0.0370153	−	0.0370153i	−0.725372	+	0.688357i	$0.758332\pi$
$542$			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
$546$	6.20863	−	0.672986i	0.265705	−	0.0288012i
$547$	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
$552$	0.485788	+	0.670949i	0.0206765	+	0.0285575i
$553$	−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	$-0.758061\pi$
$557$	−0.845111	+	0.845111i	−0.0358085	+	0.0358085i	0.688976	+	0.724784i	$0.258061\pi$
$558$	−8.34976	−	2.74341i	−0.353473	−	0.116138i
$559$	−4.36655	−	15.9825i	−0.184685	−	0.675990i
$560$			2.47645i			0.104649i
$561$	−9.25816	−	12.7869i	−0.390880	−	0.539865i
$562$	20.6092			0.869346
$563$	−42.4619			−1.78955			−0.894777	−	0.446513i	$-0.852666\pi$
$563$	−42.4619			−1.78955			−0.894777	+	0.446513i	$0.852666\pi$
$564$	13.8333	−	10.0157i	0.582485	−	0.421738i
$565$	−8.75130	+	8.75130i	−0.368170	+	0.368170i
$566$	12.3916	−	12.3916i	0.520857	−	0.520857i
$567$	1.34938	+	8.89827i	0.0566686	+	0.373692i
$568$	−10.4162			−0.437055
$569$	13.1702			0.552122			0.276061	−	0.961140i	$-0.410971\pi$
$569$	13.1702			0.552122			0.276061	+	0.961140i	$0.410971\pi$
$570$	12.9519	−	9.37755i	0.542493	−	0.392783i
$571$		−	22.7843i		−	0.953494i	−0.879041	−	0.476747i	$-0.841816\pi$
$571$		−	22.7843i		−	0.953494i	0.879041	−	0.476747i	$-0.158184\pi$
$572$	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	−0.248492	−	0.968634i	$-0.579935\pi$
$577$	17.2984	−	17.2984i	0.720142	−	0.720142i	0.968634	+	0.248492i	$0.0799350\pi$
$578$	5.50429	+	5.50429i	0.228948	+	0.228948i
$579$	−32.3887	+	23.4504i	−1.34603	+	0.974567i
$580$	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
$585$	−17.9560	−	19.8777i	−0.742388	−	0.821843i
$586$	−31.9030			−1.31790
$587$	−21.3846	−	21.3846i	−0.882638	−	0.882638i	0.111164	−	0.993802i	$-0.464542\pi$
$587$	−21.3846	−	21.3846i	−0.882638	−	0.882638i	−0.993802	+	0.111164i	$0.964542\pi$
$588$	−0.273767	+	1.71028i	−0.0112899	+	0.0705307i
$589$			10.9214i			0.450009i
$590$	−9.33037	−	9.33037i	−0.384125	−	0.384125i
$591$	14.7954	−	10.7124i	0.608603	−	0.440648i
$592$	4.21400	+	4.21400i	0.173194	+	0.173194i
$593$	−0.343278	+	0.343278i	−0.0140968	+	0.0140968i	−0.714120	−	0.700023i	$-0.753173\pi$
$593$	−0.343278	+	0.343278i	−0.0140968	+	0.0140968i	0.700023	+	0.714120i	$0.253173\pi$
$594$	−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	$0.733935\pi$
$600$	1.58928	−	1.15069i	0.0648819	−	0.0469766i
$601$	−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
$603$	25.0320	−	12.6509i	1.01938	−	0.515184i
$604$	6.75083	−	6.75083i	0.274687	−	0.274687i
$605$	3.47727	−	3.47727i	0.141371	−	0.141371i
$606$	−7.07930	+	5.12564i	−0.287577	+	0.208215i
$607$	−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
$609$	6.13210	+	8.46938i	0.248485	+	0.343197i
$610$			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	0.181467	−	0.983397i	$-0.441915\pi$
$613$	28.8407	−	28.8407i	1.16486	−	1.16486i	0.983397	−	0.181467i	$-0.0580845\pi$
$614$		−	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	−0.978893	−	0.204373i	$-0.934485\pi$
$617$	−29.3917	−	29.3917i	−1.18327	−	1.18327i	−0.204373	−	0.978893i	$-0.565515\pi$
$618$	17.5992	+	24.3072i	0.707943	+	0.977779i
$619$	−2.81364	−	2.81364i	−0.113090	−	0.113090i	0.648298	−	0.761387i	$-0.275481\pi$
$619$	−2.81364	−	2.81364i	−0.113090	−	0.113090i	−0.761387	+	0.648298i	$0.775481\pi$
$620$			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
$624$	−0.672986	−	6.20863i	−0.0269410	−	0.248544i
$625$	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
$630$	6.63067	−	3.35106i	0.264172	−	0.133509i
$631$	−22.1341	−	22.1341i	−0.881143	−	0.881143i	0.112507	−	0.993651i	$-0.464112\pi$
$631$	−22.1341	−	22.1341i	−0.881143	−	0.881143i	−0.993651	+	0.112507i	$0.964112\pi$
$632$	−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
$639$	14.0949	+	27.8893i	0.557585	+	1.10328i
$640$	2.47645			0.0978904
$641$	22.5807			0.891885			0.445943	−	0.895062i	$-0.352869\pi$
$641$	22.5807			0.891885			0.445943	+	0.895062i	$0.352869\pi$
$642$	7.76843	+	10.7294i	0.306595	+	0.423456i
$643$	−11.9697	+	11.9697i	−0.472039	+	0.472039i	−0.902574	−	0.430535i	$-0.858325\pi$
$643$	−11.9697	+	11.9697i	−0.472039	+	0.472039i	0.430535	+	0.902574i	$0.358325\pi$
$644$	0.338172	−	0.338172i	0.0133258	−	0.0133258i
$645$	−11.5593	−	15.9652i	−0.455146	−	0.628627i
$646$	11.3170			0.445261
$647$	49.1692			1.93304			0.966521	−	0.256586i	$-0.0825978\pi$
$647$	49.1692			1.93304			0.966521	+	0.256586i	$0.0825978\pi$
$648$	8.89827	−	1.34938i	0.349557	−	0.0530086i
$649$		−	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
$657$	15.4265	+	30.5240i	0.601843	+	1.19085i
$658$	−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	0.998440	+	0.0558331i	$0.0177815\pi$
$661$	27.1053	+	27.1053i	1.05427	+	1.05427i	0.0558331	+	0.998440i	$0.482219\pi$
$662$	−5.90994			−0.229697
$663$	−2.04302	−	18.8478i	−0.0793442	−	0.731989i
$664$	−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
$669$	4.43011	+	6.11867i	0.171278	+	0.236561i
$670$	−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	$0.106342\pi$
$673$			17.0132i			0.655809i	−0.944711	+	0.327905i	$0.893658\pi$
$674$	−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	$0.984175\pi$
$678$	5.07635	+	7.01122i	0.194956	+	0.269264i
$679$	15.1584			0.581725
$680$	7.51789			0.288298
$681$	37.5675	−	27.2001i	1.43959	−	1.04231i
$682$	−6.21961	+	6.21961i	−0.238161	+	0.238161i
$683$	−25.9379	+	25.9379i	−0.992486	+	0.992486i	−0.999972	−	0.00748557i	$-0.997617\pi$
$683$	−25.9379	+	25.9379i	−0.992486	+	0.992486i	0.00748557	+	0.999972i	$0.497617\pi$
$684$	−5.04449	−	9.98142i	−0.192881	−	0.381649i
$685$	−14.2539			−0.544615
$686$	1.00000			0.0381802
$687$	24.3004	−	17.5943i	0.927119	−	0.671264i
$688$		−	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	−0.480914	+	0.876768i	$0.659695\pi$
$691$	−35.6892	+	35.6892i	−1.35768	+	1.35768i	−0.876768	+	0.480914i	$0.840305\pi$
$692$		−	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
$696$	8.46938	−	6.13210i	0.321031	−	0.232437i
$697$	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	$-0.319302\pi$
$701$	28.4715			1.07535			0.537676	+	0.843151i	$0.319302\pi$
$702$	−15.7129	+	10.2032i	−0.593044	+	0.385096i
$703$	−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
$708$	−7.47515	+	5.41225i	−0.280933	+	0.203405i
$709$	34.7099	+	34.7099i	1.30356	+	1.30356i	0.925975	+	0.377584i	$0.123245\pi$
$709$	34.7099	+	34.7099i	1.30356	+	1.30356i	0.377584	+	0.925975i	$0.376755\pi$
$710$	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
$717$	22.3995	−	16.2180i	0.836525	−	0.605671i
$718$	−18.8830			−0.704707
$719$	3.99422			0.148959			0.0744797	−	0.997223i	$-0.476270\pi$
$719$	3.99422			0.148959			0.0744797	+	0.997223i	$0.476270\pi$
$720$	−3.35106	−	6.63067i	−0.124887	−	0.247111i
$721$	12.2513	−	12.2513i	0.456263	−	0.456263i
$722$	3.60816	−	3.60816i	0.134282	−	0.134282i
$723$	−6.23331	+	4.51311i	−0.231819	+	0.167844i
$724$	−19.5037			−0.724848
$725$	−6.83877			−0.253985
$726$	−2.01705	−	2.78587i	−0.0748599	−	0.103393i
$727$			31.5807i			1.17126i	0.810577	+	0.585632i	$0.199154\pi$
$727$			31.5807i			1.17126i	−0.810577	+	0.585632i	$0.800846\pi$
$728$	−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	−0.761246	−	0.648463i	$-0.775412\pi$
$733$	−3.05349	+	3.05349i	−0.112783	+	0.112783i	0.648463	+	0.761246i	$0.275412\pi$
$734$	−16.4995	−	16.4995i	−0.609006	−	0.609006i
$735$	−2.51550	−	3.47430i	−0.0927856	−	0.128151i
$736$	−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	0.797861	−	0.602841i	$-0.205965\pi$
$739$	5.30152	+	5.30152i	0.195020	+	0.195020i	−0.602841	+	0.797861i	$0.705965\pi$
$740$	−14.7584			−0.542531
$741$	18.1401	+	14.5921i	0.666395	+	0.536055i
$742$	5.90009			0.216599
$743$	−21.0757	−	21.0757i	−0.773191	−	0.773191i	0.205472	−	0.978663i	$-0.434127\pi$
$743$	−21.0757	−	21.0757i	−0.773191	−	0.773191i	−0.978663	+	0.205472i	$0.934127\pi$
$744$	5.01049	+	0.802036i	0.183693	+	0.0294041i
$745$			14.4957i			0.531082i
$746$	−4.42841	−	4.42841i	−0.162135	−	0.162135i
$747$	19.0775	+	37.7482i	0.698007	+	1.38113i
$748$	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	$0.405861\pi$
$751$			52.4292i			1.91317i	−0.291454	+	0.956585i	$0.594139\pi$
$752$	−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
$756$	−1.58129	−	4.94970i	−0.0575109	−	0.180019i
$757$	−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
$759$	−1.45852	−	2.01444i	−0.0529408	−	0.0731195i
$760$	−6.52800	+	6.52800i	−0.236796	+	0.236796i
$761$	−4.70073	+	4.70073i	−0.170401	+	0.170401i	−0.787156	−	0.616754i	$-0.788447\pi$
$761$	−4.70073	+	4.70073i	−0.170401	+	0.170401i	0.616754	+	0.787156i	$0.288447\pi$
$762$	−0.529978	−	0.731981i	−0.0191991	−	0.0265169i
$763$	4.17149			0.151018
$764$	−0.854794			−0.0309254
$765$	−10.1730	−	20.1290i	−0.367804	−	0.727767i
$766$			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	−0.884596	−	0.466358i	$-0.845566\pi$
$769$	−11.5981	+	11.5981i	−0.418239	+	0.418239i	0.466358	+	0.884596i	$0.345566\pi$
$770$		−	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	$-0.434305\pi$
$773$	−21.5154	−	21.5154i	−0.773854	−	0.773854i	−0.978778	+	0.204924i	$0.934305\pi$
$774$	−12.3036	+	6.21811i	−0.442245	+	0.223505i
$775$	−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
$780$	12.0505	+	9.69356i	0.431478	+	0.347085i
$781$	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
$786$	10.2948	+	14.2187i	0.367202	+	0.507163i
$787$	−16.1871	−	16.1871i	−0.577009	−	0.577009i	0.357069	−	0.934078i	$-0.383776\pi$
$787$	−16.1871	−	16.1871i	−0.577009	−	0.577009i	−0.934078	+	0.357069i	$0.883776\pi$
$788$	−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
$795$	−14.8417	−	20.4987i	−0.526380	−	0.727013i
$796$	0.778109			0.0275793
$797$	−39.4250			−1.39651			−0.698253	−	0.715851i	$-0.746039\pi$
$797$	−39.4250			−1.39651			−0.698253	+	0.715851i	$0.746039\pi$
$798$	−5.23000	+	3.78669i	−0.185140	+	0.134047i
$799$	−21.1660	+	21.1660i	−0.748799	+	0.748799i
$800$	−0.801028	+	0.801028i	−0.0283206	+	0.0283206i
$801$	41.3757	−	20.9107i	1.46194	−	0.738845i
$802$	24.8643			0.877988
$803$	34.2278			1.20787
$804$	−13.1161	+	9.49649i	−0.462570	+	0.334915i
$805$			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	−0.997525	−	0.0703186i	$-0.977598\pi$
$811$	−26.4050	+	26.4050i	−0.927206	+	0.927206i	0.0703186	+	0.997525i	$0.477598\pi$
$812$	−4.26874	−	4.26874i	−0.149804	−	0.149804i
$813$	−18.6837	+	13.5276i	−0.655267	+	0.474434i
$814$	−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
$819$	7.25068	+	8.02669i	0.253359	+	0.280475i
$820$	−16.9525			−0.592008
$821$	−31.8342	−	31.8342i	−1.11102	−	1.11102i	−0.993012	−	0.118010i	$-0.962349\pi$
$821$	−31.8342	−	31.8342i	−1.11102	−	1.11102i	−0.118010	−	0.993012i	$-0.537651\pi$
$822$	−1.57574	+	9.84399i	−0.0549603	+	0.343349i
$823$			29.9746i			1.04485i	0.852685	+	0.522425i	$0.174973\pi$
$823$			29.9746i			1.04485i	−0.852685	+	0.522425i	$0.825027\pi$
$824$	−12.2513	−	12.2513i	−0.426795	−	0.426795i
$825$	−4.77160	+	3.45479i	−0.166126	+	0.120280i
$826$	3.76763	+	3.76763i	0.131093	+	0.131093i
$827$	22.1847	−	22.1847i	0.771436	−	0.771436i	−0.206921	−	0.978358i	$-0.566344\pi$
$827$	22.1847	−	22.1847i	0.771436	−	0.771436i	0.978358	+	0.206921i	$0.0663444\pi$
$828$	−0.447847	+	1.36305i	−0.0155638	+	0.0473694i
$829$			25.2640i			0.877455i	0.898620	+	0.438728i	$0.144571\pi$
$829$			25.2640i			0.877455i	−0.898620	+	0.438728i	$0.855429\pi$
$830$	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
$834$	−0.243782	+	0.176506i	−0.00844148	+	0.00611190i
$835$	−22.5795			−0.781396
$836$	−11.1926			−0.387103
$837$	−4.63259	−	14.5008i	−0.160126	−	0.501221i
$838$	−22.6068	+	22.6068i	−0.780939	+	0.780939i
$839$	21.9032	−	21.9032i	0.756182	−	0.756182i	−0.219443	−	0.975625i	$-0.570424\pi$
$839$	21.9032	−	21.9032i	0.756182	−	0.756182i	0.975625	+	0.219443i	$0.0704240\pi$
$840$	−3.47430	+	2.51550i	−0.119875	+	0.0867930i
$841$	−7.44434			−0.256701
$842$	−15.6945			−0.540869
$843$	20.9341	+	28.9133i	0.721009	+	0.995826i
$844$		−	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
$852$	−10.5804	−	14.6132i	−0.362480	−	0.500641i
$853$	−26.8634	−	26.8634i	−0.919786	−	0.919786i	0.0772278	−	0.997013i	$-0.475393\pi$
$853$	−26.8634	−	26.8634i	−0.919786	−	0.919786i	−0.997013	+	0.0772278i	$0.975393\pi$
$854$		−	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	$-0.577007\pi$
$857$	−14.0267			−0.479144			−0.239572	+	0.970879i	$0.577007\pi$
$858$	2.02056	+	18.6406i	0.0689807	+	0.636381i
$859$	−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	$-0.115865\pi$
$863$	16.9934	+	16.9934i	0.578463	+	0.578463i	−0.356017	+	0.934480i	$0.615865\pi$
$864$	−4.94970	+	1.58129i	−0.168392	+	0.0537965i
$865$	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
$873$	−40.5863	+	20.5118i	−1.37364	+	0.694220i
$874$	1.78286			0.0603062
$875$	−9.57688			−0.323758
$876$	−11.5800	−	15.9938i	−0.391252	−	0.540379i
$877$	−11.7092	+	11.7092i	−0.395392	+	0.395392i	−0.876604	−	0.481212i	$-0.840197\pi$
$877$	−11.7092	+	11.7092i	−0.395392	+	0.395392i	0.481212	+	0.876604i	$0.340197\pi$
$878$	−16.1502	+	16.1502i	−0.545043	+	0.545043i
$879$	−32.4060	−	44.7577i	−1.09303	−	1.50964i
$880$	−7.43524			−0.250642
$881$	−34.9545			−1.17765			−0.588824	−	0.808261i	$-0.700409\pi$
$881$	−34.9545			−1.17765			−0.588824	+	0.808261i	$0.700409\pi$
$882$	−2.67749	+	1.35317i	−0.0901557	+	0.0455636i
$883$		−	38.3261i		−	1.28978i	−0.764277	−	0.644888i	$-0.776904\pi$
$883$		−	38.3261i		−	1.28978i	0.764277	−	0.644888i	$-0.223096\pi$
$884$	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
$891$	−26.7159	+	4.05134i	−0.895018	+	0.135725i
$892$	−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
$897$	−0.321854	−	2.96926i	−0.0107464	−	0.0991408i
$898$	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
$903$	4.66767	+	6.44678i	0.155330	+	0.214535i
$904$	−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	$-0.944162\pi$
$907$		−	10.5119i		−	0.349043i	0.984653	−	0.174522i	$-0.0558379\pi$
$908$	−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	$0.713846\pi$
$912$	3.78669	+	5.23000i	0.125390	+	0.173183i
$913$	42.3286			1.40087
$914$	−9.72824			−0.321781
$915$	−46.0758	+	33.3603i	−1.52322	+	1.10286i
$916$	−12.2479	+	12.2479i	−0.404683	+	0.404683i
$917$	7.16651	−	7.16651i	0.236659	−	0.236659i
$918$	−15.0260	+	4.80039i	−0.495933	+	0.158436i
$919$	−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
$921$	29.7894	−	21.5685i	0.981594	−	0.710705i
$922$		−	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	$-0.134513\pi$
$929$	15.2981	+	15.2981i	0.501914	+	0.501914i	−0.410119	+	0.912032i	$0.634513\pi$
$930$	−10.1784	+	7.36949i	−0.333763	+	0.241655i
$931$	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
$936$	8.02669	−	7.25068i	0.262360	−	0.236996i
$937$	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	0.996989	+	0.0775433i	$0.0247076\pi$
$941$	32.9621	+	32.9621i	1.07453	+	1.07453i	0.0775433	+	0.996989i	$0.475292\pi$
$942$	5.81887	−	4.21304i	0.189589	−	0.137268i
$943$	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	$-0.768558\pi$
$947$	−2.53584	+	2.53584i	−0.0824038	+	0.0824038i	0.664703	+	0.747107i	$0.268558\pi$
$948$	−19.8429	−	3.17629i	−0.644469	−	0.103161i
$949$	35.6975	+	20.3774i	1.15879	+	0.661480i
$950$		−	4.22307i		−	0.137014i
$951$	39.0294	−	28.2585i	1.26562	−	0.916346i
$952$	−3.03575			−0.0983891
$953$	5.10013			0.165209			0.0826047	−	0.996582i	$-0.473676\pi$
$953$	5.10013			0.165209			0.0826047	+	0.996582i	$0.473676\pi$
$954$	−15.7974	+	7.98382i	−0.511460	+	0.258486i
$955$	1.49685	−	1.49685i	0.0484368	−	0.0484368i
$956$	−11.2898	+	11.2898i	−0.365139	+	0.365139i
$957$	−25.4282	+	18.4109i	−0.821979	+	0.595139i
$958$	0.757750			0.0244818
$959$	5.75578			0.185864
$960$	2.51550	+	3.47430i	0.0811874	+	0.112132i
$961$			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	−0.210376	+	0.977621i	$0.567469\pi$
$967$	−36.9427	+	36.9427i	−1.18800	+	1.18800i	−0.977621	+	0.210376i	$0.932531\pi$
$968$	1.40413	+	1.40413i	0.0451306	+	0.0451306i
$969$	11.4954	+	15.8770i	0.369286	+	0.510041i
$970$	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
$975$	−7.03329	+	0.762376i	−0.225246	+	0.0244156i
$976$	−13.2619			−0.424503
$977$	24.4879	+	24.4879i	0.783437	+	0.783437i	0.980409	−	0.196972i	$-0.0631107\pi$
$977$	24.4879	+	24.4879i	0.783437	+	0.783437i	−0.196972	+	0.980409i	$0.563111\pi$
$978$	32.2688	+	5.16532i	1.03184	+	0.165169i
$979$		−	46.3962i		−	1.48283i
$980$	1.75112	+	1.75112i	0.0559374	+	0.0559374i
$981$	−11.1691	+	5.64473i	−0.356602	+	0.180222i
$982$	22.8390	+	22.8390i	0.728821	+	0.728821i
$983$	10.8336	−	10.8336i	0.345537	−	0.345537i	−0.512907	−	0.858444i	$-0.671432\pi$
$983$	10.8336	−	10.8336i	0.345537	−	0.345537i	0.858444	+	0.512907i	$0.171432\pi$
$984$	−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
$990$	10.0611	+	19.9078i	0.319764	+	0.632710i
$991$	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
$993$	−6.00313	−	8.29125i	−0.190503	−	0.263115i
$994$	−7.36537	+	7.36537i	−0.233615	+	0.233615i
$995$	−1.36256	+	1.36256i	−0.0431961	+	0.0431961i
$996$	−14.3206	−	19.7790i	−0.453767	−	0.626723i
$997$	−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
$999$	29.4977	−	9.42368i	0.933267	−	0.298152i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.3	✓	20	1.1	even	1	trivial
546.2.p.c.281.3	yes	20	39.8	even	4	inner
546.2.p.d.239.8	yes	20	3.2	odd	2
546.2.p.d.281.8	yes	20	13.8	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} +1.00000i q^{4} +(-1.75112 - 1.75112i) q^{5} +(-1.40293 + 1.01577i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.85010 - 0.936434i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.273767 - 1.71028i) q^{3} +1.00000i q^{4} +(-1.75112 - 1.75112i) q^{5} +(-1.40293 + 1.01577i) 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} +(-3.47430 + 2.51550i) q^{15} -1.00000 q^{16} -3.03575 q^{17} +(1.35317 + 2.67749i) q^{18} +(2.63603 - 2.63603i) q^{19} +(1.75112 - 1.75112i) q^{20} +(1.40293 - 1.01577i) q^{21} +3.00237 q^{22} -0.478247 q^{23} +(-1.01577 - 1.40293i) 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} +(3.04971 + 4.21213i) 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} +(0.672986 + 6.20863i) 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} +(3.35106 + 6.63067i) 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} +(4.94970 - 1.58129i) q^{54} +7.43524 q^{55} +1.00000 q^{56} +(-3.78669 - 5.23000i) q^{57} +(4.26874 - 4.26874i) q^{58} +(-3.76763 + 3.76763i) q^{59} +(-2.51550 - 3.47430i) q^{60} +13.2619 q^{61} +2.92963 q^{62} +(-1.35317 - 2.67749i) 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} +(-2.67749 + 1.35317i) 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} +(3.91429 - 4.86604i) 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} +(1.01577 + 1.40293i) 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} +(2.97582 + 4.11007i) q^{93} -9.86025 q^{94} -9.23199 q^{95} +(1.40293 - 1.01577i) q^{96} +(10.7186 - 10.7186i) q^{97} +(0.707107 - 0.707107i) q^{98} +(8.03882 - 4.06272i) 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	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 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 - 8 * 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 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * 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 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * 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 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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