LMFDB - Embedded newform 240.2.y.f.163.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,2,Mod(163,240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("240.163"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.91640964851$
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} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.3
Root			$-1.09334 + 0.897004i$ of defining polynomial
Character	$\chi$	$=$	240.163
Dual form			240.2.y.f.187.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.897004 + 1.09334i) q^{2} -1.00000 q^{3} +(-0.390769 - 1.96145i) q^{4} +(0.140415 - 2.23165i) q^{5} +(0.897004 - 1.09334i) q^{6} +(-2.83167 + 2.83167i) q^{7} +(2.49505 + 1.33219i) q^{8} +1.00000 q^{9} +(2.31400 + 2.15532i) q^{10} +(4.36026 + 4.36026i) q^{11} +(0.390769 + 1.96145i) q^{12} +4.99276i q^{13} +(-0.555949 - 5.63598i) q^{14} +(-0.140415 + 2.23165i) q^{15} +(-3.69460 + 1.53295i) q^{16} +(2.27272 - 2.27272i) q^{17} +(-0.897004 + 1.09334i) q^{18} +(1.45960 + 1.45960i) q^{19} +(-4.43216 + 0.596643i) q^{20} +(2.83167 - 2.83167i) q^{21} +(-8.67841 + 0.856063i) q^{22} +(1.28911 + 1.28911i) q^{23} +(-2.49505 - 1.33219i) q^{24} +(-4.96057 - 0.626717i) q^{25} +(-5.45876 - 4.47852i) q^{26} -1.00000 q^{27} +(6.66071 + 4.44766i) q^{28} +(-0.965728 + 0.965728i) q^{29} +(-2.31400 - 2.15532i) q^{30} +0.703997i q^{31} +(1.63804 - 5.41450i) q^{32} +(-4.36026 - 4.36026i) q^{33} +(0.446209 + 4.52348i) q^{34} +(5.92169 + 6.71691i) q^{35} +(-0.390769 - 1.96145i) q^{36} +6.29736i q^{37} +(-2.90509 + 0.286567i) q^{38} -4.99276i q^{39} +(3.32333 - 5.38103i) q^{40} +0.772367i q^{41} +(0.555949 + 5.63598i) q^{42} -4.84769i q^{43} +(6.84860 - 10.2563i) q^{44} +(0.140415 - 2.23165i) q^{45} +(-2.56576 + 0.253094i) q^{46} +(-0.450439 - 0.450439i) q^{47} +(3.69460 - 1.53295i) q^{48} -9.03668i q^{49} +(5.13486 - 4.86140i) q^{50} +(-2.27272 + 2.27272i) q^{51} +(9.79306 - 1.95101i) q^{52} +4.17849 q^{53} +(0.897004 - 1.09334i) q^{54} +(10.3428 - 9.11835i) q^{55} +(-10.8375 + 3.29284i) q^{56} +(-1.45960 - 1.45960i) q^{57} +(-0.189604 - 1.92213i) q^{58} +(-2.23629 + 2.23629i) q^{59} +(4.43216 - 0.596643i) q^{60} +(0.794490 + 0.794490i) q^{61} +(-0.769706 - 0.631488i) q^{62} +(-2.83167 + 2.83167i) q^{63} +(4.45055 + 6.64775i) q^{64} +(11.1421 + 0.701060i) q^{65} +(8.67841 - 0.856063i) q^{66} +13.2598i q^{67} +(-5.34594 - 3.56972i) q^{68} +(-1.28911 - 1.28911i) q^{69} +(-12.6556 + 0.449308i) q^{70} -10.8523 q^{71} +(2.49505 + 1.33219i) q^{72} +(10.3838 - 10.3838i) q^{73} +(-6.88513 - 5.64875i) q^{74} +(4.96057 + 0.626717i) q^{75} +(2.29257 - 3.43330i) q^{76} -24.6936 q^{77} +(5.45876 + 4.47852i) q^{78} -4.49087 q^{79} +(2.90224 + 8.46032i) q^{80} +1.00000 q^{81} +(-0.844457 - 0.692816i) q^{82} -7.59721 q^{83} +(-6.66071 - 4.44766i) q^{84} +(-4.75280 - 5.39105i) q^{85} +(5.30015 + 4.34839i) q^{86} +(0.965728 - 0.965728i) q^{87} +(5.07038 + 16.6878i) q^{88} +10.7447 q^{89} +(2.31400 + 2.15532i) q^{90} +(-14.1378 - 14.1378i) q^{91} +(2.02478 - 3.03226i) q^{92} -0.703997i q^{93} +(0.896526 - 0.0884359i) q^{94} +(3.46227 - 3.05237i) q^{95} +(-1.63804 + 5.41450i) q^{96} +(-0.751384 + 0.751384i) q^{97} +(9.88013 + 8.10594i) q^{98} +(4.36026 + 4.36026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 20 q^{9} + 8 q^{10} + 8 q^{11} - 2 q^{12} + 10 q^{14} + 26 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 4 q^{21} - 10 q^{22} - 16 q^{23} - 6 q^{24} + 4 q^{25}+ \cdots + 8 q^{99}+O(q^{100}) $ 20 * q - 20 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 20 * q^9 + 8 * q^10 + 8 * q^11 - 2 * q^12 + 10 * q^14 + 26 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 4 * q^21 - 10 * q^22 - 16 * q^23 - 6 * q^24 + 4 * q^25 - 20 * q^26 - 20 * q^27 + 6 * q^28 - 8 * q^30 - 10 * q^32 - 8 * q^33 + 6 * q^34 - 28 * q^35 + 2 * q^36 - 2 * q^38 + 6 * q^40 - 10 * q^42 + 22 * q^44 - 18 * q^46 - 26 * q^48 - 52 * q^50 - 12 * q^51 + 8 * q^53 - 4 * q^55 - 26 * q^56 - 16 * q^57 - 22 * q^58 - 16 * q^59 + 10 * q^60 - 12 * q^61 + 4 * q^62 - 4 * q^63 + 26 * q^64 + 4 * q^65 + 10 * q^66 + 2 * q^68 + 16 * q^69 - 10 * q^70 + 6 * q^72 - 20 * q^73 - 8 * q^74 - 4 * q^75 + 26 * q^76 + 20 * q^78 + 48 * q^79 - 54 * q^80 + 20 * q^81 - 8 * q^82 - 24 * q^83 - 6 * q^84 + 4 * q^85 + 4 * q^86 + 34 * q^88 + 40 * q^89 + 8 * q^90 - 24 * q^91 + 82 * q^92 + 58 * q^94 - 72 * q^95 + 10 * q^96 - 28 * q^97 + 70 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.897004	+	1.09334i	−0.634277	+	0.773106i
$2$	−0.897004	+	1.09334i	−0.634277	+	0.773106i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.390769	−	1.96145i	−0.195385	−	0.980727i
$5$	0.140415	−	2.23165i	0.0627957	−	0.998026i
$5$	0.140415	−	2.23165i	0.0627957	−	0.998026i
$6$	0.897004	−	1.09334i	0.366200	−	0.446353i
$7$	−2.83167	+	2.83167i	−1.07027	+	1.07027i	−0.0729328	+	0.997337i	$0.523236\pi$
$7$	−2.83167	+	2.83167i	−1.07027	+	1.07027i	−0.997337	+	0.0729328i	$0.976764\pi$
$8$	2.49505	+	1.33219i	0.882133	+	0.471000i
$9$	1.00000			0.333333
$10$	2.31400	+	2.15532i	0.731750	+	0.681573i
$11$	4.36026	+	4.36026i	1.31467	+	1.31467i	0.917933	+	0.396736i	$0.129857\pi$
$11$	4.36026	+	4.36026i	1.31467	+	1.31467i	0.396736	+	0.917933i	$0.370143\pi$
$12$	0.390769	+	1.96145i	0.112805	+	0.566223i
$13$			4.99276i			1.38474i	0.721542	+	0.692371i	$0.243434\pi$
$13$			4.99276i			1.38474i	−0.721542	+	0.692371i	$0.756566\pi$
$14$	−0.555949	−	5.63598i	−0.148584	−	1.50628i
$15$	−0.140415	+	2.23165i	−0.0362551	+	0.576211i
$16$	−3.69460	+	1.53295i	−0.923650	+	0.383238i
$17$	2.27272	−	2.27272i	0.551215	−	0.551215i	−0.375576	−	0.926791i	$-0.622555\pi$
$17$	2.27272	−	2.27272i	0.551215	−	0.551215i	0.926791	+	0.375576i	$0.122555\pi$
$18$	−0.897004	+	1.09334i	−0.211426	+	0.257702i
$19$	1.45960	+	1.45960i	0.334855	+	0.334855i	0.854427	−	0.519572i	$-0.173909\pi$
$19$	1.45960	+	1.45960i	0.334855	+	0.334855i	−0.519572	+	0.854427i	$0.673909\pi$
$20$	−4.43216	+	0.596643i	−0.991060	+	0.133414i
$21$	2.83167	−	2.83167i	0.617920	−	0.617920i
$22$	−8.67841	+	0.856063i	−1.85024	+	0.182513i
$23$	1.28911	+	1.28911i	0.268797	+	0.268797i	0.828615	−	0.559818i	$-0.189129\pi$
$23$	1.28911	+	1.28911i	0.268797	+	0.268797i	−0.559818	+	0.828615i	$0.689129\pi$
$24$	−2.49505	−	1.33219i	−0.509300	−	0.271932i
$25$	−4.96057	−	0.626717i	−0.992113	−	0.125343i
$26$	−5.45876	−	4.47852i	−1.07055	−	0.878310i
$27$	−1.00000			−0.192450
$28$	6.66071	+	4.44766i	1.25876	+	0.840528i
$29$	−0.965728	+	0.965728i	−0.179331	+	0.179331i	−0.791064	−	0.611733i	$-0.790473\pi$
$29$	−0.965728	+	0.965728i	−0.179331	+	0.179331i	0.611733	+	0.791064i	$0.290473\pi$
$30$	−2.31400	−	2.15532i	−0.422476	−	0.393506i
$31$			0.703997i			0.126442i	0.998000	+	0.0632208i	$0.0201372\pi$
$31$			0.703997i			0.126442i	−0.998000	+	0.0632208i	$0.979863\pi$
$32$	1.63804	−	5.41450i	0.289567	−	0.957158i
$33$	−4.36026	−	4.36026i	−0.759024	−	0.759024i
$34$	0.446209	+	4.52348i	0.0765242	+	0.775771i
$35$	5.92169	+	6.71691i	1.00095	+	1.13537i
$36$	−0.390769	−	1.96145i	−0.0651282	−	0.326909i
$37$			6.29736i			1.03528i	0.855599	+	0.517640i	$0.173189\pi$
$37$			6.29736i			1.03528i	−0.855599	+	0.517640i	$0.826811\pi$
$38$	−2.90509	+	0.286567i	−0.471269	+	0.0464873i
$39$		−	4.99276i		−	0.799481i
$40$	3.32333	−	5.38103i	0.525464	−	0.850816i
$41$			0.772367i			0.120624i	0.998180	+	0.0603118i	$0.0192095\pi$
$41$			0.772367i			0.120624i	−0.998180	+	0.0603118i	$0.980791\pi$
$42$	0.555949	+	5.63598i	0.0857848	+	0.869651i
$43$		−	4.84769i		−	0.739265i	−0.929178	−	0.369633i	$-0.879484\pi$
$43$		−	4.84769i		−	0.739265i	0.929178	−	0.369633i	$-0.120516\pi$
$44$	6.84860	−	10.2563i	1.03246	−	1.54620i
$45$	0.140415	−	2.23165i	0.0209319	−	0.332675i
$46$	−2.56576	+	0.253094i	−0.378301	+	0.0373166i
$47$	−0.450439	−	0.450439i	−0.0657033	−	0.0657033i	0.673492	−	0.739195i	$-0.264794\pi$
$47$	−0.450439	−	0.450439i	−0.0657033	−	0.0657033i	−0.739195	+	0.673492i	$0.764794\pi$
$48$	3.69460	−	1.53295i	0.533269	−	0.221262i
$49$		−	9.03668i		−	1.29095i
$50$	5.13486	−	4.86140i	0.726179	−	0.687506i
$51$	−2.27272	+	2.27272i	−0.318244	+	0.318244i
$52$	9.79306	−	1.95101i	1.35805	−	0.270557i
$53$	4.17849			0.573959			0.286980	−	0.957937i	$-0.407349\pi$
$53$	4.17849			0.573959			0.286980	+	0.957937i	$0.407349\pi$
$54$	0.897004	−	1.09334i	0.122067	−	0.148784i
$55$	10.3428	−	9.11835i	1.39463	−	1.22952i
$56$	−10.8375	+	3.29284i	−1.44822	+	0.440024i
$57$	−1.45960	−	1.45960i	−0.193328	−	0.193328i
$58$	−0.189604	−	1.92213i	−0.0248962	−	0.252388i
$59$	−2.23629	+	2.23629i	−0.291140	+	0.291140i	−0.837530	−	0.546391i	$-0.816001\pi$
$59$	−2.23629	+	2.23629i	−0.291140	+	0.291140i	0.546391	+	0.837530i	$0.316001\pi$
$60$	4.43216	−	0.596643i	0.572189	−	0.0770263i
$61$	0.794490	+	0.794490i	0.101724	+	0.101724i	0.756137	−	0.654413i	$-0.227084\pi$
$61$	0.794490	+	0.794490i	0.101724	+	0.101724i	−0.654413	+	0.756137i	$0.727084\pi$
$62$	−0.769706	−	0.631488i	−0.0977528	−	0.0801991i
$63$	−2.83167	+	2.83167i	−0.356757	+	0.356757i
$64$	4.45055	+	6.64775i	0.556318	+	0.830969i
$65$	11.1421	+	0.701060i	1.38201	+	0.0869558i
$66$	8.67841	−	0.856063i	1.06824	−	0.105374i
$67$			13.2598i			1.61994i	0.586470	+	0.809971i	$0.300517\pi$
$67$			13.2598i			1.61994i	−0.586470	+	0.809971i	$0.699483\pi$
$68$	−5.34594	−	3.56972i	−0.648290	−	0.432893i
$69$	−1.28911	−	1.28911i	−0.155190	−	0.155190i
$70$	−12.6556	+	0.449308i	−1.51264	+	0.0537026i
$71$	−10.8523			−1.28793			−0.643967	−	0.765053i	$-0.722713\pi$
$71$	−10.8523			−1.28793			−0.643967	+	0.765053i	$0.722713\pi$
$72$	2.49505	+	1.33219i	0.294044	+	0.157000i
$73$	10.3838	−	10.3838i	1.21533	−	1.21533i	0.246083	−	0.969249i	$-0.420857\pi$
$73$	10.3838	−	10.3838i	1.21533	−	1.21533i	0.969249	−	0.246083i	$-0.0791435\pi$
$74$	−6.88513	−	5.64875i	−0.800380	−	0.656654i
$75$	4.96057	+	0.626717i	0.572797	+	0.0723671i
$76$	2.29257	−	3.43330i	0.262975	−	0.393826i
$77$	−24.6936			−2.81410
$78$	5.45876	+	4.47852i	0.618083	+	0.507093i
$79$	−4.49087			−0.505262			−0.252631	−	0.967563i	$-0.581296\pi$
$79$	−4.49087			−0.505262			−0.252631	+	0.967563i	$0.581296\pi$
$80$	2.90224	+	8.46032i	0.324480	+	0.945893i
$81$	1.00000			0.111111
$82$	−0.844457	−	0.692816i	−0.0932547	−	0.0765088i
$83$	−7.59721			−0.833902			−0.416951	−	0.908929i	$-0.636901\pi$
$83$	−7.59721			−0.833902			−0.416951	+	0.908929i	$0.636901\pi$
$84$	−6.66071	−	4.44766i	−0.726743	−	0.485279i
$85$	−4.75280	−	5.39105i	−0.515513	−	0.584741i
$86$	5.30015	+	4.34839i	0.571530	+	0.468899i
$87$	0.965728	−	0.965728i	0.103537	−	0.103537i
$88$	5.07038	+	16.6878i	0.540504	+	1.77892i
$89$	10.7447			1.13893			0.569467	−	0.822014i	$-0.307150\pi$
$89$	10.7447			1.13893			0.569467	+	0.822014i	$0.307150\pi$
$90$	2.31400	+	2.15532i	0.243917	+	0.227191i
$91$	−14.1378	−	14.1378i	−1.48205	−	1.48205i
$92$	2.02478	−	3.03226i	0.211098	−	0.316135i
$93$		−	0.703997i		−	0.0730011i
$94$	0.896526	−	0.0884359i	0.0924696	−	0.00912147i
$95$	3.46227	−	3.05237i	0.355221	−	0.313166i
$96$	−1.63804	+	5.41450i	−0.167182	+	0.552615i
$97$	−0.751384	+	0.751384i	−0.0762915	+	0.0762915i	−0.744223	−	0.667931i	$-0.767180\pi$
$97$	−0.751384	+	0.751384i	−0.0762915	+	0.0762915i	0.667931	+	0.744223i	$0.267180\pi$
$98$	9.88013	+	8.10594i	0.998044	+	0.818823i
$99$	4.36026	+	4.36026i	0.438223	+	0.438223i
$100$	0.709159	+	9.97482i	0.0709159	+	0.997482i
$101$	5.30053	−	5.30053i	0.527423	−	0.527423i	−0.392380	−	0.919803i	$-0.628348\pi$
$101$	5.30053	−	5.30053i	0.527423	−	0.527423i	0.919803	+	0.392380i	$0.128348\pi$
$102$	−0.446209	−	4.52348i	−0.0441813	−	0.447892i
$103$	−5.38356	−	5.38356i	−0.530458	−	0.530458i	0.390250	−	0.920709i	$-0.372388\pi$
$103$	−5.38356	−	5.38356i	−0.530458	−	0.530458i	−0.920709	+	0.390250i	$0.872388\pi$
$104$	−6.65129	+	12.4572i	−0.652213	+	1.22153i
$105$	−5.92169	−	6.71691i	−0.577898	−	0.655504i
$106$	−3.74812	+	4.56849i	−0.364049	+	0.443731i
$107$	11.9693			1.15711			0.578557	−	0.815642i	$-0.303616\pi$
$107$	11.9693			1.15711			0.578557	+	0.815642i	$0.303616\pi$
$108$	0.390769	+	1.96145i	0.0376018	+	0.188741i
$109$	−3.91485	+	3.91485i	−0.374975	+	0.374975i	−0.869285	−	0.494310i	$-0.835421\pi$
$109$	−3.91485	+	3.91485i	−0.374975	+	0.374975i	0.494310	+	0.869285i	$0.335421\pi$
$110$	0.691854	+	19.4874i	0.0659657	+	1.85805i
$111$		−	6.29736i		−	0.597719i
$112$	6.12107	−	14.8027i	0.578387	−	1.39872i
$113$	−9.13854	−	9.13854i	−0.859681	−	0.859681i	0.131619	−	0.991300i	$-0.457982\pi$
$113$	−9.13854	−	9.13854i	−0.859681	−	0.859681i	−0.991300	+	0.131619i	$0.957982\pi$
$114$	2.90509	−	0.286567i	0.272087	−	0.0268394i
$115$	3.05785	−	2.69583i	0.285146	−	0.251387i
$116$	2.27161	+	1.51685i	0.210913	+	0.140836i
$117$			4.99276i			0.461580i
$118$	−0.439057	−	4.45097i	−0.0404184	−	0.409745i
$119$			12.8712i			1.17990i
$120$	−3.32333	+	5.38103i	−0.303377	+	0.491219i
$121$			27.0238i			2.45671i
$122$	−1.58130	+	0.155984i	−0.143165	+	0.0141222i
$123$		−	0.772367i		−	0.0696420i
$124$	1.38086	−	0.275100i	0.124005	−	0.0247047i
$125$	−2.09516	+	10.9823i	−0.187397	+	0.982284i
$126$	−0.555949	−	5.63598i	−0.0495279	−	0.502093i
$127$	−15.5561	−	15.5561i	−1.38038	−	1.38038i	−0.843931	−	0.536451i	$-0.819765\pi$
$127$	−15.5561	−	15.5561i	−1.38038	−	1.38038i	−0.536451	−	0.843931i	$-0.680235\pi$
$128$	−11.2604	−	1.09712i	−0.995287	−	0.0969723i
$129$			4.84769i			0.426815i
$130$	−10.7610	+	11.5532i	−0.943803	+	1.01328i
$131$	14.4207	−	14.4207i	1.25994	−	1.25994i	0.308818	−	0.951121i	$-0.400067\pi$
$131$	14.4207	−	14.4207i	1.25994	−	1.25994i	0.951121	−	0.308818i	$-0.0999333\pi$
$132$	−6.84860	+	10.2563i	−0.596094	+	0.892697i
$133$	−8.26619			−0.716769
$134$	−14.4974	−	11.8941i	−1.25239	−	1.02749i
$135$	−0.140415	+	2.23165i	−0.0120850	+	0.192070i
$136$	8.69824	−	2.64286i	0.745868	−	0.226623i
$137$	3.54735	+	3.54735i	0.303071	+	0.303071i	0.842214	−	0.539143i	$-0.181252\pi$
$137$	3.54735	+	3.54735i	0.303071	+	0.303071i	−0.539143	+	0.842214i	$0.681252\pi$
$138$	2.56576	−	0.253094i	0.218412	−	0.0215448i
$139$	−4.17152	+	4.17152i	−0.353824	+	0.353824i	−0.861530	−	0.507706i	$-0.830494\pi$
$139$	−4.17152	+	4.17152i	−0.353824	+	0.353824i	0.507706	+	0.861530i	$0.330494\pi$
$140$	10.8609	−	14.2399i	0.917914	−	1.20349i
$141$	0.450439	+	0.450439i	0.0379338	+	0.0379338i
$142$	9.73458	−	11.8652i	0.816908	−	0.995709i
$143$	−21.7697	+	21.7697i	−1.82048	+	1.82048i
$144$	−3.69460	+	1.53295i	−0.307883	+	0.127746i
$145$	2.01957	+	2.29077i	0.167716	+	0.190238i
$146$	2.03868	+	20.6673i	0.168722	+	1.71044i
$147$			9.03668i			0.745333i
$148$	12.3520	−	2.46081i	1.01533	−	0.202278i
$149$	8.42059	+	8.42059i	0.689842	+	0.689842i	0.962197	−	0.272355i	$-0.0878026\pi$
$149$	8.42059	+	8.42059i	0.689842	+	0.689842i	−0.272355	+	0.962197i	$0.587803\pi$
$150$	−5.13486	+	4.86140i	−0.419260	+	0.396932i
$151$	4.96999			0.404452			0.202226	−	0.979339i	$-0.435182\pi$
$151$	4.96999			0.404452			0.202226	+	0.979339i	$0.435182\pi$
$152$	1.69731	+	5.58623i	0.137670	+	0.453103i
$153$	2.27272	−	2.27272i	0.183738	−	0.183738i
$154$	22.1503	−	26.9984i	1.78492	−	2.17560i
$155$	1.57108	+	0.0988521i	0.126192	+	0.00793999i
$156$	−9.79306	+	1.95101i	−0.784072	+	0.156206i
$157$	14.4628			1.15426			0.577129	−	0.816653i	$-0.304173\pi$
$157$	14.4628			1.15426			0.577129	+	0.816653i	$0.304173\pi$
$158$	4.02833	−	4.91003i	0.320476	−	0.390621i
$159$	−4.17849			−0.331376
$160$	−11.8533	−	4.41582i	−0.937085	−	0.349101i
$161$	−7.30064			−0.575371
$162$	−0.897004	+	1.09334i	−0.0704753	+	0.0859006i
$163$	7.70573			0.603559			0.301779	−	0.953378i	$-0.402419\pi$
$163$	7.70573			0.603559			0.301779	+	0.953378i	$0.402419\pi$
$164$	1.51496	−	0.301817i	0.118299	−	0.0235680i
$165$	−10.3428	+	9.11835i	−0.805190	+	0.709863i
$166$	6.81472	−	8.30630i	0.528925	−	0.644694i
$167$	4.64125	−	4.64125i	0.359150	−	0.359150i	−0.504349	−	0.863500i	$-0.668268\pi$
$167$	4.64125	−	4.64125i	0.359150	−	0.359150i	0.863500	+	0.504349i	$0.168268\pi$
$168$	10.8375	−	3.29284i	0.836129	−	0.254048i
$169$	−11.9276			−0.917509
$170$	10.1575	−	0.360618i	0.779045	−	0.0276582i
$171$	1.45960	+	1.45960i	0.111618	+	0.111618i
$172$	−9.50851	+	1.89433i	−0.725017	+	0.144441i
$173$		−	23.9562i		−	1.82136i	−0.413114	−	0.910679i	$-0.635559\pi$
$173$		−	23.9562i		−	1.82136i	0.413114	−	0.910679i	$-0.364441\pi$
$174$	0.189604	+	1.92213i	0.0143738	+	0.145716i
$175$	15.8213	−	12.2720i	1.19598	−	0.927678i
$176$	−22.7935	−	9.42536i	−1.71812	−	0.710463i
$177$	2.23629	−	2.23629i	0.168090	−	0.168090i
$178$	−9.63802	+	11.7475i	−0.722400	+	0.880516i
$179$	1.30724	+	1.30724i	0.0977080	+	0.0977080i	0.754271	−	0.656563i	$-0.227990\pi$
$179$	1.30724	+	1.30724i	0.0977080	+	0.0977080i	−0.656563	+	0.754271i	$0.727990\pi$
$180$	−4.43216	+	0.596643i	−0.330353	+	0.0444712i
$181$	−6.95282	+	6.95282i	−0.516799	+	0.516799i	−0.916601	−	0.399802i	$-0.869079\pi$
$181$	−6.95282	+	6.95282i	−0.516799	+	0.516799i	0.399802	+	0.916601i	$0.369079\pi$
$182$	28.1391	−	2.77572i	2.08581	−	0.205750i
$183$	−0.794490	−	0.794490i	−0.0587304	−	0.0587304i
$184$	1.49905	+	4.93372i	0.110512	+	0.363718i
$185$	14.0535	+	0.884246i	1.03324	+	0.0650111i
$186$	0.769706	+	0.631488i	0.0564376	+	0.0463030i
$187$	19.8193			1.44933
$188$	−0.707497	+	1.05953i	−0.0515995	+	0.0772743i
$189$	2.83167	−	2.83167i	0.205973	−	0.205973i
$190$	0.231598	+	6.52341i	0.0168019	+	0.473258i
$191$			2.42666i			0.175587i	0.996139	+	0.0877936i	$0.0279816\pi$
$191$			2.42666i			0.175587i	−0.996139	+	0.0877936i	$0.972018\pi$
$192$	−4.45055	−	6.64775i	−0.321190	−	0.479760i
$193$	−0.611510	−	0.611510i	−0.0440175	−	0.0440175i	0.684755	−	0.728773i	$-0.259909\pi$
$193$	−0.611510	−	0.611510i	−0.0440175	−	0.0440175i	−0.728773	+	0.684755i	$0.759909\pi$
$194$	−0.147521	−	1.49551i	−0.0105914	−	0.107371i
$195$	−11.1421	−	0.701060i	−0.797903	−	0.0502039i
$196$	−17.7250	+	3.53125i	−1.26607	+	0.252232i
$197$		−	12.6372i		−	0.900363i	−0.892937	−	0.450182i	$-0.851359\pi$
$197$		−	12.6372i		−	0.900363i	0.892937	−	0.450182i	$-0.148641\pi$
$198$	−8.67841	+	0.856063i	−0.616747	+	0.0608377i
$199$		−	10.0036i		−	0.709134i	−0.935031	−	0.354567i	$-0.884628\pi$
$199$		−	10.0036i		−	0.709134i	0.935031	−	0.354567i	$-0.115372\pi$
$200$	−11.5420	−	8.17210i	−0.816139	−	0.577855i
$201$		−	13.2598i		−	0.935274i
$202$	1.04067	+	10.5499i	0.0732211	+	0.742285i
$203$		−	5.46924i		−	0.383865i
$204$	5.34594	+	3.56972i	0.374291	+	0.249931i
$205$	1.72366	+	0.108452i	0.120385	+	0.00757464i
$206$	10.7151	−	1.05697i	0.746558	−	0.0736426i
$207$	1.28911	+	1.28911i	0.0895991	+	0.0895991i
$208$	−7.65365	−	18.4462i	−0.530685	−	1.27902i
$209$			12.7285i			0.880446i
$210$	12.6556	−	0.449308i	0.873321	−	0.0310052i
$211$	9.66719	−	9.66719i	0.665517	−	0.665517i	−0.291158	−	0.956675i	$-0.594041\pi$
$211$	9.66719	−	9.66719i	0.665517	−	0.665517i	0.956675	+	0.291158i	$0.0940405\pi$
$212$	−1.63282	−	8.19591i	−0.112143	−	0.562897i
$213$	10.8523			0.743589
$214$	−10.7365	+	13.0865i	−0.733932	+	0.894572i
$215$	−10.8184	−	0.680690i	−0.737806	−	0.0464227i
$216$	−2.49505	−	1.33219i	−0.169767	−	0.0906440i
$217$	−1.99349	−	1.99349i	−0.135327	−	0.135327i
$218$	−0.768614	−	7.79189i	−0.0520571	−	0.527734i
$219$	−10.3838	+	10.3838i	−0.701672	+	0.701672i
$220$	−21.9269	−	16.7238i	−1.47831	−	1.12752i
$221$	11.3471	+	11.3471i	0.763291	+	0.763291i
$222$	6.88513	+	5.64875i	0.462100	+	0.379120i
$223$	4.29237	−	4.29237i	0.287438	−	0.287438i	−0.548628	−	0.836067i	$-0.684850\pi$
$223$	4.29237	−	4.29237i	0.287438	−	0.287438i	0.836067	+	0.548628i	$0.184850\pi$
$224$	10.6937	+	19.9704i	0.714502	+	1.33433i
$225$	−4.96057	−	0.626717i	−0.330704	−	0.0417812i
$226$	18.1888	−	1.79419i	1.20990	−	0.119348i
$227$		−	13.2703i		−	0.880778i	−0.897807	−	0.440389i	$-0.854841\pi$
$227$		−	13.2703i		−	0.880778i	0.897807	−	0.440389i	$-0.145159\pi$
$228$	−2.29257	+	3.43330i	−0.151829	+	0.227376i
$229$	11.4064	+	11.4064i	0.753758	+	0.753758i	0.975178	−	0.221420i	$-0.0710692\pi$
$229$	11.4064	+	11.4064i	0.753758	+	0.753758i	−0.221420	+	0.975178i	$0.571069\pi$
$230$	0.204546	+	5.76143i	0.0134874	+	0.379897i
$231$	24.6936			1.62472
$232$	−3.69607	+	1.12301i	−0.242659	+	0.0737290i
$233$	−8.19734	+	8.19734i	−0.537026	+	0.537026i	−0.922654	−	0.385629i	$-0.873985\pi$
$233$	−8.19734	+	8.19734i	−0.537026	+	0.537026i	0.385629	+	0.922654i	$0.373985\pi$
$234$	−5.45876	−	4.47852i	−0.356850	−	0.292770i
$235$	−1.06847	+	0.941975i	−0.0696995	+	0.0614477i
$236$	5.26025	+	3.51250i	0.342413	+	0.228644i
$237$	4.49087			0.291713
$238$	−14.0725	−	11.5455i	−0.912186	−	0.748382i
$239$	10.6504			0.688915			0.344458	−	0.938802i	$-0.388063\pi$
$239$	10.6504			0.688915			0.344458	+	0.938802i	$0.388063\pi$
$240$	−2.90224	−	8.46032i	−0.187339	−	0.546111i
$241$	−1.22690			−0.0790315			−0.0395157	−	0.999219i	$-0.512582\pi$
$241$	−1.22690			−0.0790315			−0.0395157	+	0.999219i	$0.512582\pi$
$242$	−29.5461	−	24.2404i	−1.89929	−	1.55823i
$243$	−1.00000			−0.0641500
$244$	1.24789	−	1.86882i	0.0798881	−	0.119639i
$245$	−20.1668	−	1.26889i	−1.28841	−	0.0810664i
$246$	0.844457	+	0.692816i	0.0538406	+	0.0441724i
$247$	−7.28741	+	7.28741i	−0.463687	+	0.463687i
$248$	−0.937857	+	1.75651i	−0.0595540	+	0.111538i
$249$	7.59721			0.481453
$250$	−10.1280	−	12.1419i	−0.640548	−	0.767918i
$251$	−11.5822	−	11.5822i	−0.731061	−	0.731061i	0.239769	−	0.970830i	$-0.422928\pi$
$251$	−11.5822	−	11.5822i	−0.731061	−	0.731061i	−0.970830	+	0.239769i	$0.922928\pi$
$252$	6.66071	+	4.44766i	0.419585	+	0.280176i
$253$			11.2417i			0.706759i
$254$	30.9620	−	3.05418i	1.94273	−	0.191636i
$255$	4.75280	+	5.39105i	0.297632	+	0.337601i
$256$	11.3001	−	11.3273i	0.706258	−	0.707955i
$257$	5.72342	−	5.72342i	0.357017	−	0.357017i	−0.505695	−	0.862712i	$-0.668764\pi$
$257$	5.72342	−	5.72342i	0.357017	−	0.357017i	0.862712	+	0.505695i	$0.168764\pi$
$258$	−5.30015	−	4.34839i	−0.329973	−	0.270719i
$259$	−17.8320	−	17.8320i	−1.10803	−	1.10803i
$260$	−2.97889	−	22.1287i	−0.184743	−	1.37236i
$261$	−0.965728	+	0.965728i	−0.0597771	+	0.0597771i
$262$	2.83125	+	28.7020i	0.174915	+	1.77322i
$263$	6.70033	+	6.70033i	0.413160	+	0.413160i	0.882838	−	0.469678i	$-0.155630\pi$
$263$	6.70033	+	6.70033i	0.413160	+	0.413160i	−0.469678	+	0.882838i	$0.655630\pi$
$264$	−5.07038	−	16.6878i	−0.312060	−	1.02706i
$265$	0.586724	−	9.32494i	0.0360422	−	0.572826i
$266$	7.41480	−	9.03772i	0.454631	−	0.554138i
$267$	−10.7447			−0.657564
$268$	26.0085	−	5.18152i	1.58872	−	0.316512i
$269$	1.08527	−	1.08527i	0.0661699	−	0.0661699i	−0.673247	−	0.739417i	$-0.735101\pi$
$269$	1.08527	−	1.08527i	0.0661699	−	0.0661699i	0.739417	+	0.673247i	$0.235101\pi$
$270$	−2.31400	−	2.15532i	−0.140825	−	0.131169i
$271$		−	3.21705i		−	0.195422i	−0.995215	−	0.0977108i	$-0.968848\pi$
$271$		−	3.21705i		−	0.195422i	0.995215	−	0.0977108i	$-0.0311520\pi$
$272$	−4.91282	+	11.8807i	−0.297883	+	0.720376i
$273$	14.1378	+	14.1378i	0.855660	+	0.855660i
$274$	−7.06044	+	0.696462i	−0.426537	+	0.0420748i
$275$	−18.8967	−	24.3620i	−1.13952	−	1.46909i
$276$	−2.02478	+	3.03226i	−0.121877	+	0.182521i
$277$			28.2079i			1.69485i	0.530915	+	0.847425i	$0.321848\pi$
$277$			28.2079i			1.69485i	−0.530915	+	0.847425i	$0.678152\pi$
$278$	−0.819007	−	8.30275i	−0.0491208	−	0.497966i
$279$			0.703997i			0.0421472i
$280$	5.82672	+	24.6478i	0.348213	+	1.47299i
$281$			24.5928i			1.46709i	0.679643	+	0.733543i	$0.262135\pi$
$281$			24.5928i			1.46709i	−0.679643	+	0.733543i	$0.737865\pi$
$282$	−0.896526	+	0.0884359i	−0.0533874	+	0.00526628i
$283$			15.0862i			0.896779i	0.893838	+	0.448390i	$0.148002\pi$
$283$			15.0862i			0.896779i	−0.893838	+	0.448390i	$0.851998\pi$
$284$	4.24075	+	21.2863i	0.251642	+	1.26311i
$285$	−3.46227	+	3.05237i	−0.205087	+	0.180807i
$286$	−4.27411	−	43.3292i	−0.252734	−	2.56211i
$287$	−2.18709	−	2.18709i	−0.129100	−	0.129100i
$288$	1.63804	−	5.41450i	0.0965223	−	0.319053i
$289$			6.66950i			0.392324i
$290$	−4.31615	+	0.153235i	−0.253453	+	0.00899824i
$291$	0.751384	−	0.751384i	0.0440469	−	0.0440469i
$292$	−24.4250	−	16.3097i	−1.42936	−	0.954451i
$293$	3.49295			0.204060			0.102030	−	0.994781i	$-0.467466\pi$
$293$	3.49295			0.204060			0.102030	+	0.994781i	$0.467466\pi$
$294$	−9.88013	−	8.10594i	−0.576221	−	0.472748i
$295$	4.67661	+	5.30463i	0.272283	+	0.308848i
$296$	−8.38927	+	15.7122i	−0.487616	+	0.913254i
$297$	−4.36026	−	4.36026i	−0.253008	−	0.253008i
$298$	−16.7598	+	1.65324i	−0.970871	+	0.0957695i
$299$	−6.43619	+	6.43619i	−0.372215	+	0.372215i
$300$	−0.709159	−	9.97482i	−0.0409433	−	0.575897i
$301$	13.7270	+	13.7270i	0.791213	+	0.791213i
$302$	−4.45810	+	5.43387i	−0.256535	+	0.312684i
$303$	−5.30053	+	5.30053i	−0.304508	+	0.304508i
$304$	−7.63012	−	3.15514i	−0.437617	−	0.180959i
$305$	1.88458	−	1.66147i	0.107911	−	0.0951354i
$306$	0.446209	+	4.52348i	0.0255081	+	0.258590i
$307$			7.81653i			0.446113i	0.974806	+	0.223056i	$0.0716034\pi$
$307$			7.81653i			0.446113i	−0.974806	+	0.223056i	$0.928397\pi$
$308$	9.64950	+	48.4354i	0.549832	+	2.75986i
$309$	5.38356	+	5.38356i	0.306260	+	0.306260i
$310$	−1.51734	+	1.62905i	−0.0861792	+	0.0925237i
$311$	−6.15295			−0.348902			−0.174451	−	0.984666i	$-0.555815\pi$
$311$	−6.15295			−0.348902			−0.174451	+	0.984666i	$0.555815\pi$
$312$	6.65129	−	12.4572i	0.376555	−	0.705249i
$313$	−9.65621	+	9.65621i	−0.545802	+	0.545802i	−0.925224	−	0.379422i	$-0.876123\pi$
$313$	−9.65621	+	9.65621i	−0.545802	+	0.545802i	0.379422	+	0.925224i	$0.376123\pi$
$314$	−12.9732	+	15.8127i	−0.732119	+	0.892363i
$315$	5.92169	+	6.71691i	0.333650	+	0.378455i
$316$	1.75489	+	8.80863i	0.0987204	+	0.495524i
$317$	−10.5517			−0.592642			−0.296321	−	0.955088i	$-0.595760\pi$
$317$	−10.5517			−0.592642			−0.296321	+	0.955088i	$0.595760\pi$
$318$	3.74812	−	4.56849i	0.210184	−	0.256188i
$319$	−8.42165			−0.471522
$320$	15.4604	−	8.99864i	0.864264	−	0.503039i
$321$	−11.9693			−0.668061
$322$	6.54870	−	7.98206i	0.364945	−	0.444823i
$323$	6.63451			0.369154
$324$	−0.390769	−	1.96145i	−0.0217094	−	0.108970i
$325$	3.12905	−	24.7669i	0.173568	−	1.37382i
$326$	−6.91206	+	8.42495i	−0.382824	+	0.466615i
$327$	3.91485	−	3.91485i	0.216492	−	0.216492i
$328$	−1.02894	+	1.92710i	−0.0568137	+	0.106406i
$329$	2.55099			0.140640
$330$	−0.691854	−	19.4874i	−0.0380853	−	1.07275i
$331$	0.447095	+	0.447095i	0.0245745	+	0.0245745i	0.719287	−	0.694713i	$-0.244469\pi$
$331$	0.447095	+	0.447095i	0.0245745	+	0.0245745i	−0.694713	+	0.719287i	$0.744469\pi$
$332$	2.96875	+	14.9016i	0.162931	+	0.817830i
$333$			6.29736i			0.345093i
$334$	0.911229	+	9.23766i	0.0498602	+	0.505462i
$335$	29.5913	+	1.86188i	1.61675	+	0.101725i
$336$	−6.12107	+	14.8027i	−0.333932	+	0.807553i
$337$	4.17945	−	4.17945i	0.227669	−	0.227669i	−0.584049	−	0.811718i	$-0.698532\pi$
$337$	4.17945	−	4.17945i	0.227669	−	0.227669i	0.811718	+	0.584049i	$0.198532\pi$
$338$	10.6991	−	13.0409i	0.581955	−	0.709331i
$339$	9.13854	+	9.13854i	0.496337	+	0.496337i
$340$	−8.71704	+	11.4290i	−0.472748	+	0.619827i
$341$	−3.06961	+	3.06961i	−0.166229	+	0.166229i
$342$	−2.90509	+	0.286567i	−0.157090	+	0.0154958i
$343$	5.76720	+	5.76720i	0.311400	+	0.311400i
$344$	6.45804	−	12.0952i	0.348194	−	0.652131i
$345$	−3.05785	+	2.69583i	−0.164629	+	0.145139i
$346$	26.1922	+	21.4888i	1.40810	+	1.15525i
$347$	30.4793			1.63622			0.818108	−	0.575064i	$-0.195023\pi$
$347$	30.4793			1.63622			0.818108	+	0.575064i	$0.195023\pi$
$348$	−2.27161	−	1.51685i	−0.121771	−	0.0813119i
$349$	24.1490	−	24.1490i	1.29267	−	1.29267i	0.359535	−	0.933131i	$-0.382935\pi$
$349$	24.1490	−	24.1490i	1.29267	−	1.29267i	0.933131	−	0.359535i	$-0.117065\pi$
$350$	−0.774345	+	28.3061i	−0.0413905	+	1.51302i
$351$		−	4.99276i		−	0.266494i
$352$	30.7509	−	16.4664i	1.63903	−	0.877661i
$353$	−17.3084	−	17.3084i	−0.921233	−	0.921233i	0.0758833	−	0.997117i	$-0.475822\pi$
$353$	−17.3084	−	17.3084i	−0.921233	−	0.921233i	−0.997117	+	0.0758833i	$0.975822\pi$
$354$	0.439057	+	4.45097i	0.0233356	+	0.236567i
$355$	−1.52383	+	24.2186i	−0.0808767	+	1.28539i
$356$	−4.19869	−	21.0752i	−0.222530	−	1.11698i
$357$		−	12.8712i		−	0.681214i
$358$	−2.60186	+	0.256655i	−0.137513	+	0.0135646i
$359$		−	29.4403i		−	1.55380i	−0.629626	−	0.776899i	$-0.716792\pi$
$359$		−	29.4403i		−	1.55380i	0.629626	−	0.776899i	$-0.283208\pi$
$360$	3.32333	−	5.38103i	0.175155	−	0.283605i
$361$		−	14.7392i		−	0.775745i
$362$	−1.36507	−	13.8385i	−0.0717463	−	0.727335i
$363$		−	27.0238i		−	1.41838i
$364$	−22.2061	+	33.2553i	−1.16391	+	1.74305i
$365$	−21.7150	−	24.6311i	−1.13662	−	1.28925i
$366$	1.58130	−	0.155984i	0.0826561	−	0.00815343i
$367$	10.7678	+	10.7678i	0.562076	+	0.562076i	0.929897	−	0.367821i	$-0.119896\pi$
$367$	10.7678	+	10.7678i	0.562076	+	0.562076i	−0.367821	+	0.929897i	$0.619896\pi$
$368$	−6.73887	−	2.78659i	−0.351288	−	0.145261i
$369$			0.772367i			0.0402078i
$370$	−13.5728	+	14.5721i	−0.705619	+	0.757566i
$371$	−11.8321	+	11.8321i	−0.614291	+	0.614291i
$372$	−1.38086	+	0.275100i	−0.0715942	+	0.0142633i
$373$	32.1031			1.66223			0.831117	−	0.556098i	$-0.187702\pi$
$373$	32.1031			1.66223			0.831117	+	0.556098i	$0.187702\pi$
$374$	−17.7780	+	21.6692i	−0.919278	+	1.12049i
$375$	2.09516	−	10.9823i	0.108193	−	0.567122i
$376$	−0.523798	−	1.72394i	−0.0270128	−	0.0889052i
$377$	−4.82164	−	4.82164i	−0.248327	−	0.248327i
$378$	0.555949	+	5.63598i	0.0285949	+	0.289884i
$379$	−23.3329	+	23.3329i	−1.19853	+	1.19853i	−0.223923	+	0.974607i	$0.571887\pi$
$379$	−23.3329	+	23.3329i	−1.19853	+	1.19853i	−0.974607	+	0.223923i	$0.928113\pi$
$380$	−7.34002	−	5.59830i	−0.376535	−	0.287187i
$381$	15.5561	+	15.5561i	0.796964	+	0.796964i
$382$	−2.65316	−	2.17673i	−0.135747	−	0.111371i
$383$	7.02280	−	7.02280i	0.358848	−	0.358848i	−0.504540	−	0.863388i	$-0.668338\pi$
$383$	7.02280	−	7.02280i	0.358848	−	0.358848i	0.863388	+	0.504540i	$0.168338\pi$
$384$	11.2604	+	1.09712i	0.574629	+	0.0559870i
$385$	−3.46737	+	55.1077i	−0.176713	+	2.80855i
$386$	1.21711	−	0.120060i	0.0619495	−	0.00611087i
$387$		−	4.84769i		−	0.246422i
$388$	1.76742	+	1.18019i	0.0897273	+	0.0599149i
$389$	−23.0035	−	23.0035i	−1.16632	−	1.16632i	−0.983065	−	0.183259i	$-0.941335\pi$
$389$	−23.0035	−	23.0035i	−1.16632	−	1.16632i	−0.183259	−	0.983065i	$-0.558665\pi$
$390$	10.7610	−	11.5532i	0.544905	−	0.585020i
$391$	5.85955			0.296330
$392$	12.0386	−	22.5470i	0.608039	−	1.13879i
$393$	−14.4207	+	14.4207i	−0.727426	+	0.727426i
$394$	13.8167	+	11.3356i	0.696076	+	0.571080i
$395$	−0.630587	+	10.0221i	−0.0317283	+	0.504265i
$396$	6.84860	−	10.2563i	0.344155	−	0.515399i
$397$	−25.0560			−1.25753			−0.628763	−	0.777597i	$-0.716438\pi$
$397$	−25.0560			−1.25753			−0.628763	+	0.777597i	$0.716438\pi$
$398$	10.9373	+	8.97323i	0.548235	+	0.449788i
$399$	8.26619			0.413827
$400$	19.2880	−	5.28883i	0.964402	−	0.264442i
$401$	6.21757			0.310491			0.155245	−	0.987876i	$-0.450383\pi$
$401$	6.21757			0.310491			0.155245	+	0.987876i	$0.450383\pi$
$402$	14.4974	+	11.8941i	0.723066	+	0.593223i
$403$	−3.51489			−0.175089
$404$	−12.4680	−	8.32546i	−0.620308	−	0.414207i
$405$	0.140415	−	2.23165i	0.00697730	−	0.110892i
$406$	5.97972	+	4.90593i	0.296768	+	0.243477i
$407$	−27.4581	+	27.4581i	−1.36105	+	1.36105i
$408$	−8.69824	+	2.64286i	−0.430627	+	0.130841i
$409$	13.1629			0.650865			0.325432	−	0.945565i	$-0.394490\pi$
$409$	13.1629			0.650865			0.325432	+	0.945565i	$0.394490\pi$
$410$	−1.66470	+	1.78726i	−0.0822138	+	0.0882663i
$411$	−3.54735	−	3.54735i	−0.174978	−	0.174978i
$412$	−8.45588	+	12.6633i	−0.416591	+	0.623878i
$413$		−	12.6648i		−	0.623196i
$414$	−2.56576	+	0.253094i	−0.126100	+	0.0124389i
$415$	−1.06676	+	16.9543i	−0.0523654	+	0.832256i
$416$	27.0333	+	8.17833i	1.32542	+	0.400975i
$417$	4.17152	−	4.17152i	0.204280	−	0.204280i
$418$	−13.9165	−	11.4175i	−0.680677	−	0.558447i
$419$	−14.7013	−	14.7013i	−0.718208	−	0.718208i	0.250030	−	0.968238i	$-0.419559\pi$
$419$	−14.7013	−	14.7013i	−0.718208	−	0.718208i	−0.968238	+	0.250030i	$0.919559\pi$
$420$	−10.8609	+	14.2399i	−0.529958	+	0.694835i
$421$	17.0481	−	17.0481i	0.830872	−	0.830872i	−0.156764	−	0.987636i	$-0.550106\pi$
$421$	17.0481	−	17.0481i	0.830872	−	0.830872i	0.987636	+	0.156764i	$0.0501063\pi$
$422$	1.89799	+	19.2410i	0.0923926	+	0.936637i
$423$	−0.450439	−	0.450439i	−0.0219011	−	0.0219011i
$424$	10.4255	+	5.56653i	0.506309	+	0.270335i
$425$	−12.6983	+	9.84962i	−0.615959	+	0.477777i
$426$	−9.73458	+	11.8652i	−0.471642	+	0.574873i
$427$	−4.49946			−0.217744
$428$	−4.67723	−	23.4772i	−0.226082	−	1.13481i
$429$	21.7697	−	21.7697i	1.05105	−	1.05105i
$430$	10.4483	−	11.2175i	0.503864	−	0.540957i
$431$		−	18.5363i		−	0.892864i	−0.894818	−	0.446432i	$-0.852694\pi$
$431$		−	18.5363i		−	0.892864i	0.894818	−	0.446432i	$-0.147306\pi$
$432$	3.69460	−	1.53295i	0.177756	−	0.0737541i
$433$	−9.47558	−	9.47558i	−0.455368	−	0.455368i	0.441764	−	0.897131i	$-0.354353\pi$
$433$	−9.47558	−	9.47558i	−0.455368	−	0.455368i	−0.897131	+	0.441764i	$0.854353\pi$
$434$	3.96772	−	0.391387i	0.190456	−	0.0187872i
$435$	−2.01957	−	2.29077i	−0.0968309	−	0.109834i
$436$	9.20861	+	6.14900i	0.441012	+	0.294484i
$437$			3.76315i			0.180016i
$438$	−2.03868	−	20.6673i	−0.0974119	−	0.987521i
$439$			21.7937i			1.04016i	0.854119	+	0.520078i	$0.174097\pi$
$439$			21.7937i			1.04016i	−0.854119	+	0.520078i	$0.825903\pi$
$440$	37.9533	−	8.97212i	1.80935	−	0.427729i
$441$		−	9.03668i		−	0.430318i
$442$	−22.5846	+	2.22781i	−1.07424	+	0.105966i
$443$			26.2733i			1.24828i	0.781312	+	0.624141i	$0.214551\pi$
$443$			26.2733i			1.24828i	−0.781312	+	0.624141i	$0.785449\pi$
$444$	−12.3520	+	2.46081i	−0.586199	+	0.116785i
$445$	1.50872	−	23.9784i	0.0715201	−	1.13669i
$446$	0.842733	+	8.54328i	0.0399046	+	0.404536i
$447$	−8.42059	−	8.42059i	−0.398280	−	0.398280i
$448$	−31.4267	−	6.22176i	−1.48477	−	0.293951i
$449$			29.2615i			1.38093i	0.723364	+	0.690467i	$0.242595\pi$
$449$			29.2615i			1.38093i	−0.723364	+	0.690467i	$0.757405\pi$
$450$	5.13486	−	4.86140i	0.242060	−	0.229169i
$451$	−3.36772	+	3.36772i	−0.158580	+	0.158580i
$452$	−14.3538	+	21.4959i	−0.675144	+	1.01108i
$453$	−4.96999			−0.233510
$454$	14.5088	+	11.9035i	0.680934	+	0.558657i
$455$	−33.5359	+	29.5656i	−1.57219	+	1.38606i
$456$	−1.69731	−	5.58623i	−0.0794837	−	0.261599i
$457$	−18.2488	−	18.2488i	−0.853641	−	0.853641i	0.136938	−	0.990580i	$-0.456274\pi$
$457$	−18.2488	−	18.2488i	−0.853641	−	0.853641i	−0.990580	+	0.136938i	$0.956274\pi$
$458$	−22.7027	+	2.23946i	−1.06083	+	0.104643i
$459$	−2.27272	+	2.27272i	−0.106081	+	0.106081i
$460$	−6.48266	−	4.94438i	−0.302255	−	0.230533i
$461$	5.13473	+	5.13473i	0.239148	+	0.239148i	0.816497	−	0.577349i	$-0.195913\pi$
$461$	5.13473	+	5.13473i	0.239148	+	0.239148i	−0.577349	+	0.816497i	$0.695913\pi$
$462$	−22.1503	+	26.9984i	−1.03052	+	1.25608i
$463$	10.2040	−	10.2040i	0.474220	−	0.474220i	−0.429057	−	0.903277i	$-0.641154\pi$
$463$	10.2040	−	10.2040i	0.474220	−	0.474220i	0.903277	+	0.429057i	$0.141154\pi$
$464$	2.08756	−	5.04839i	0.0969127	−	0.234366i
$465$	−1.57108	−	0.0988521i	−0.0728571	−	0.00458416i
$466$	−1.60941	−	16.3155i	−0.0745543	−	0.755801i
$467$		−	24.2696i		−	1.12306i	−0.827455	−	0.561532i	$-0.810212\pi$
$467$		−	24.2696i		−	1.12306i	0.827455	−	0.561532i	$-0.189788\pi$
$468$	9.79306	−	1.95101i	0.452684	−	0.0901857i
$469$	−37.5473	−	37.5473i	−1.73378	−	1.73378i
$470$	−0.0714723	−	2.01316i	−0.00329677	−	0.0928599i
$471$	−14.4628			−0.666411
$472$	−8.55881	+	2.60049i	−0.393951	+	0.119697i
$473$	21.1372	−	21.1372i	0.971889	−	0.971889i
$474$	−4.02833	+	4.91003i	−0.185027	+	0.225525i
$475$	−6.32567	−	8.15518i	−0.290242	−	0.374186i
$476$	25.2462	−	5.02965i	1.15716	−	0.230534i
$477$	4.17849			0.191320
$478$	−9.55342	+	11.6444i	−0.436963	+	0.532604i
$479$	25.0894			1.14636			0.573182	−	0.819428i	$-0.305709\pi$
$479$	25.0894			1.14636			0.573182	+	0.819428i	$0.305709\pi$
$480$	11.8533	+	4.41582i	0.541026	+	0.201553i
$481$	−31.4412			−1.43359
$482$	1.10053	−	1.34141i	0.0501279	−	0.0610997i
$483$	7.30064			0.332191
$484$	53.0059	−	10.5601i	2.40936	−	0.480003i
$485$	1.57132	+	1.78234i	0.0713502	+	0.0809317i
$486$	0.897004	−	1.09334i	0.0406889	−	0.0495947i
$487$	−0.369801	+	0.369801i	−0.0167573	+	0.0167573i	−0.715436	−	0.698679i	$-0.753772\pi$
$487$	−0.369801	+	0.369801i	−0.0167573	+	0.0167573i	0.698679	+	0.715436i	$0.253772\pi$
$488$	0.923881	+	3.04070i	0.0418221	+	0.137646i
$489$	−7.70573			−0.348465
$490$	19.4770	−	20.9108i	0.879880	−	0.944656i
$491$	−19.2802	−	19.2802i	−0.870104	−	0.870104i	0.122379	−	0.992483i	$-0.460948\pi$
$491$	−19.2802	−	19.2802i	−0.870104	−	0.870104i	−0.992483	+	0.122379i	$0.960948\pi$
$492$	−1.51496	+	0.301817i	−0.0682998	+	0.0136070i
$493$			4.38966i			0.197700i
$494$	−1.43076	−	14.5044i	−0.0643729	−	0.652585i
$495$	10.3428	−	9.11835i	0.464877	−	0.409840i
$496$	−1.07919	−	2.60099i	−0.0484572	−	0.116788i
$497$	30.7302	−	30.7302i	1.37844	−	1.37844i
$498$	−6.81472	+	8.30630i	−0.305375	+	0.372214i
$499$	−17.1262	−	17.1262i	−0.766673	−	0.766673i	0.210847	−	0.977519i	$-0.432378\pi$
$499$	−17.1262	−	17.1262i	−0.766673	−	0.766673i	−0.977519	+	0.210847i	$0.932378\pi$
$500$	22.3599	−	0.181979i	0.999967	−	0.00813834i
$501$	−4.64125	+	4.64125i	−0.207356	+	0.207356i
$502$	23.0525	−	2.27396i	1.02888	−	0.101492i
$503$	5.60127	+	5.60127i	0.249748	+	0.249748i	0.820867	−	0.571119i	$-0.193491\pi$
$503$	5.60127	+	5.60127i	0.249748	+	0.249748i	−0.571119	+	0.820867i	$0.693491\pi$
$504$	−10.8375	+	3.29284i	−0.482739	+	0.146675i
$505$	−11.0847	−	12.5732i	−0.493262	−	0.559501i
$506$	−12.2909	−	10.0838i	−0.546399	−	0.448281i
$507$	11.9276			0.529724
$508$	−24.4338	+	36.5915i	−1.08407	+	1.62348i
$509$	−0.0876457	+	0.0876457i	−0.00388483	+	0.00388483i	−0.709047	−	0.705162i	$-0.750874\pi$
$509$	−0.0876457	+	0.0876457i	−0.00388483	+	0.00388483i	0.705162	+	0.709047i	$0.250874\pi$
$510$	−10.1575	+	0.360618i	−0.449782	+	0.0159684i
$511$			58.8069i			2.60146i
$512$	2.24827	+	22.5154i	0.0993604	+	0.995052i
$513$	−1.45960	−	1.45960i	−0.0644428	−	0.0644428i
$514$	1.12369	+	11.3915i	0.0495640	+	0.502459i
$515$	−12.7702	+	11.2583i	−0.562722	+	0.496101i
$516$	9.50851	−	1.89433i	0.418589	−	0.0833931i
$517$		−	3.92806i		−	0.172756i
$518$	35.4918	−	3.50101i	1.55942	−	0.153826i
$519$			23.9562i			1.05156i
$520$	26.8662	+	16.5926i	1.17816	+	0.727632i
$521$		−	0.327549i		−	0.0143502i	−0.999974	−	0.00717509i	$-0.997716\pi$
$521$		−	0.327549i		−	0.0143502i	0.999974	−	0.00717509i	$-0.00228392\pi$
$522$	−0.189604	−	1.92213i	−0.00829874	−	0.0841292i
$523$		−	21.8823i		−	0.956847i	−0.878129	−	0.478423i	$-0.841208\pi$
$523$		−	21.8823i		−	0.956847i	0.878129	−	0.478423i	$-0.158792\pi$
$524$	−33.9206	−	22.6503i	−1.48183	−	0.989483i
$525$	−15.8213	+	12.2720i	−0.690500	+	0.535595i
$526$	−13.3359	+	1.31549i	−0.581474	+	0.0573582i
$527$	1.59999	+	1.59999i	0.0696966	+	0.0696966i
$528$	22.7935	+	9.42536i	0.991959	+	0.410186i
$529$		−	19.6764i		−	0.855496i
$530$	9.66900	+	9.00599i	0.419995	+	0.391195i
$531$	−2.23629	+	2.23629i	−0.0970466	+	0.0970466i
$532$	3.23017	+	16.2137i	0.140046	+	0.702955i
$533$	−3.85624			−0.167032
$534$	9.63802	−	11.7475i	0.417078	−	0.508366i
$535$	1.68067	−	26.7113i	0.0726618	−	1.15483i
$536$	−17.6646	+	33.0839i	−0.762993	+	1.42901i
$537$	−1.30724	−	1.30724i	−0.0564117	−	0.0564117i
$538$	0.213073	+	2.16005i	0.00918625	+	0.0931264i
$539$	39.4023	−	39.4023i	1.69718	−	1.69718i
$540$	4.43216	−	0.596643i	0.190730	−	0.0256754i
$541$	−21.9852	−	21.9852i	−0.945217	−	0.945217i	0.0533584	−	0.998575i	$-0.483007\pi$
$541$	−21.9852	−	21.9852i	−0.945217	−	0.945217i	−0.998575	+	0.0533584i	$0.983007\pi$
$542$	3.51731	+	2.88570i	0.151082	+	0.123951i
$543$	6.95282	−	6.95282i	0.298374	−	0.298374i
$544$	−8.58284	−	16.0284i	−0.367986	−	0.687214i
$545$	8.18690	+	9.28631i	0.350688	+	0.397782i
$546$	−28.1391	+	2.77572i	−1.20424	+	0.118790i
$547$			28.9503i			1.23783i	0.785459	+	0.618913i	$0.212427\pi$
$547$			28.9503i			1.23783i	−0.785459	+	0.618913i	$0.787573\pi$
$548$	5.57177	−	8.34416i	0.238014	−	0.356445i
$549$	0.794490	+	0.794490i	0.0339080	+	0.0339080i
$550$	43.5863	+	1.19235i	1.85853	+	0.0508421i
$551$	−2.81915			−0.120100
$552$	−1.49905	−	4.93372i	−0.0638039	−	0.209993i
$553$	12.7167	−	12.7167i	0.540767	−	0.540767i
$554$	−30.8408	−	25.3026i	−1.31030	−	1.07500i
$555$	−14.0535	−	0.884246i	−0.596539	−	0.0375342i
$556$	9.81235	+	6.55215i	0.416136	+	0.277873i
$557$	8.55746			0.362591			0.181296	−	0.983429i	$-0.441971\pi$
$557$	8.55746			0.362591			0.181296	+	0.983429i	$0.441971\pi$
$558$	−0.769706	−	0.631488i	−0.0325843	−	0.0267330i
$559$	24.2033			1.02369
$560$	−32.1750	−	15.7386i	−1.35964	−	0.665079i
$561$	−19.8193			−0.836772
$562$	−26.8883	−	22.0599i	−1.13421	−	0.930540i
$563$	19.8277			0.835637			0.417819	−	0.908530i	$-0.362795\pi$
$563$	19.8277			0.835637			0.417819	+	0.908530i	$0.362795\pi$
$564$	0.707497	−	1.05953i	0.0297910	−	0.0446144i
$565$	−21.6773	+	19.1109i	−0.911969	+	0.804000i
$566$	−16.4942	−	13.5323i	−0.693305	−	0.568807i
$567$	−2.83167	+	2.83167i	−0.118919	+	0.118919i
$568$	−27.0771	−	14.4573i	−1.13613	−	0.606617i
$569$	−13.1834			−0.552677			−0.276339	−	0.961060i	$-0.589121\pi$
$569$	−13.1834			−0.552677			−0.276339	+	0.961060i	$0.589121\pi$
$570$	−0.231598	−	6.52341i	−0.00970058	−	0.273235i
$571$	−5.46465	−	5.46465i	−0.228688	−	0.228688i	0.583456	−	0.812145i	$-0.301700\pi$
$571$	−5.46465	−	5.46465i	−0.228688	−	0.228688i	−0.812145	+	0.583456i	$0.801700\pi$
$572$	51.2072	+	34.1934i	2.14108	+	1.42970i
$573$		−	2.42666i		−	0.101375i
$574$	4.35305	−	0.429397i	0.181693	−	0.0179227i
$575$	−5.58679	−	7.20260i	−0.232985	−	0.300369i
$576$	4.45055	+	6.64775i	0.185439	+	0.276990i
$577$	11.0931	−	11.0931i	0.461811	−	0.461811i	−0.437438	−	0.899249i	$-0.644114\pi$
$577$	11.0931	−	11.0931i	0.461811	−	0.461811i	0.899249	+	0.437438i	$0.144114\pi$
$578$	−7.29201	−	5.98257i	−0.303308	−	0.248842i
$579$	0.611510	+	0.611510i	0.0254135	+	0.0254135i
$580$	3.70406	−	4.85645i	0.153803	−	0.201653i
$581$	21.5128	−	21.5128i	0.892500	−	0.892500i
$582$	0.147521	+	1.49551i	0.00611496	+	0.0619909i
$583$	18.2193	+	18.2193i	0.754566	+	0.754566i
$584$	39.7413	−	12.0749i	1.64451	−	0.499663i
$585$	11.1421	+	0.701060i	0.460670	+	0.0289853i
$586$	−3.13319	+	3.81897i	−0.129431	+	0.157760i
$587$	−0.0736360			−0.00303928			−0.00151964	−	0.999999i	$-0.500484\pi$
$587$	−0.0736360			−0.00303928			−0.00151964	+	0.999999i	$0.500484\pi$
$588$	17.7250	−	3.53125i	0.730968	−	0.145626i
$589$	−1.02755	+	1.02755i	−0.0423396	+	0.0423396i
$590$	−9.99469	+	0.354838i	−0.411475	+	0.0146084i
$591$			12.6372i			0.519825i
$592$	−9.65354	−	23.2662i	−0.396758	−	0.956236i
$593$	25.1041	+	25.1041i	1.03090	+	1.03090i	0.999507	+	0.0313952i	$0.00999504\pi$
$593$	25.1041	+	25.1041i	1.03090	+	1.03090i	0.0313952	+	0.999507i	$0.490005\pi$
$594$	8.67841	−	0.856063i	0.356079	−	0.0351247i
$595$	28.7240	+	1.80731i	1.17757	+	0.0740925i
$596$	13.2261	−	19.8071i	0.541762	−	0.811330i
$597$			10.0036i			0.409419i
$598$	−1.26364	−	12.8102i	−0.0516739	−	0.523849i
$599$		−	16.3265i		−	0.667081i	−0.942736	−	0.333541i	$-0.891757\pi$
$599$		−	16.3265i		−	0.667081i	0.942736	−	0.333541i	$-0.108243\pi$
$600$	11.5420	+	8.17210i	0.471198	+	0.333625i
$601$		−	22.5262i		−	0.918862i	−0.888213	−	0.459431i	$-0.848053\pi$
$601$		−	22.5262i		−	0.918862i	0.888213	−	0.459431i	$-0.151947\pi$
$602$	−27.3215	+	2.69507i	−1.11354	+	0.109843i
$603$			13.2598i			0.539981i
$604$	−1.94212	−	9.74840i	−0.0790236	−	0.396657i
$605$	60.3078	+	3.79456i	2.45186	+	0.154271i
$606$	−1.04067	−	10.5499i	−0.0422742	−	0.428559i
$607$	20.2440	+	20.2440i	0.821677	+	0.821677i	0.986348	−	0.164672i	$-0.0526565\pi$
$607$	20.2440	+	20.2440i	0.821677	+	0.821677i	−0.164672	+	0.986348i	$0.552656\pi$
$608$	10.2939	−	5.51212i	0.417471	−	0.223546i
$609$			5.46924i			0.221625i
$610$	0.126064	+	3.55083i	0.00510417	+	0.143769i
$611$	2.24893	−	2.24893i	0.0909820	−	0.0909820i
$612$	−5.34594	−	3.56972i	−0.216097	−	0.144298i
$613$	28.9848			1.17069			0.585343	−	0.810786i	$-0.300960\pi$
$613$	28.9848			1.17069			0.585343	+	0.810786i	$0.300960\pi$
$614$	−8.54609	−	7.01145i	−0.344892	−	0.282959i
$615$	−1.72366	−	0.108452i	−0.0695046	−	0.00437322i
$616$	−61.6118	−	32.8966i	−2.48241	−	1.32544i
$617$	−18.0708	−	18.0708i	−0.727503	−	0.727503i	0.242619	−	0.970122i	$-0.421994\pi$
$617$	−18.0708	−	18.0708i	−0.727503	−	0.727503i	−0.970122	+	0.242619i	$0.921994\pi$
$618$	−10.7151	+	1.05697i	−0.431025	+	0.0425176i
$619$	17.2226	−	17.2226i	0.692236	−	0.692236i	−0.270488	−	0.962723i	$-0.587185\pi$
$619$	17.2226	−	17.2226i	0.692236	−	0.692236i	0.962723	+	0.270488i	$0.0871849\pi$
$620$	−0.420035	−	3.12023i	−0.0168690	−	0.125311i
$621$	−1.28911	−	1.28911i	−0.0517300	−	0.0517300i
$622$	5.51922	−	6.72724i	0.221300	−	0.269738i
$623$	−30.4254	+	30.4254i	−1.21897	+	1.21897i
$624$	7.65365	+	18.4462i	0.306391	+	0.738440i
$625$	24.2145	+	6.21775i	0.968578	+	0.248710i
$626$	−1.89583	−	19.2192i	−0.0757727	−	0.768152i
$627$		−	12.7285i		−	0.508325i
$628$	−5.65161	−	28.3681i	−0.225524	−	1.13201i
$629$	14.3121	+	14.3121i	0.570662	+	0.570662i
$630$	−12.6556	+	0.449308i	−0.504212	+	0.0179009i
$631$	−15.2007			−0.605131			−0.302565	−	0.953129i	$-0.597843\pi$
$631$	−15.2007			−0.605131			−0.302565	+	0.953129i	$0.597843\pi$
$632$	−11.2049	−	5.98269i	−0.445709	−	0.237979i
$633$	−9.66719	+	9.66719i	−0.384236	+	0.384236i
$634$	9.46491	−	11.5366i	0.375900	−	0.458175i
$635$	−36.9002	+	32.5316i	−1.46434	+	1.29098i
$636$	1.63282	+	8.19591i	0.0647456	+	0.324989i
$637$	45.1179			1.78764
$638$	7.55425	−	9.20770i	0.299076	−	0.364536i
$639$	−10.8523			−0.429311
$640$	−4.02952	+	24.9752i	−0.159281	+	0.987233i
$641$	−13.9100			−0.549414			−0.274707	−	0.961528i	$-0.588581\pi$
$641$	−13.9100			−0.549414			−0.274707	+	0.961528i	$0.588581\pi$
$642$	10.7365	−	13.0865i	0.423736	−	0.516481i
$643$	−50.3060			−1.98387			−0.991937	−	0.126735i	$-0.959550\pi$
$643$	−50.3060			−1.98387			−0.991937	+	0.126735i	$0.959550\pi$
$644$	2.85286	+	14.3199i	0.112419	+	0.564282i
$645$	10.8184	+	0.680690i	0.425973	+	0.0268021i
$646$	−5.95118	+	7.25375i	−0.234146	+	0.285395i
$647$	15.4702	−	15.4702i	0.608197	−	0.608197i	−0.334278	−	0.942475i	$-0.608492\pi$
$647$	15.4702	−	15.4702i	0.608197	−	0.608197i	0.942475	+	0.334278i	$0.108492\pi$
$648$	2.49505	+	1.33219i	0.0980148	+	0.0523333i
$649$	−19.5016			−0.765505
$650$	24.2718	+	25.6371i	0.952018	+	1.00557i
$651$	1.99349	+	1.99349i	0.0781309	+	0.0781309i
$652$	−3.01116	−	15.1144i	−0.117926	−	0.591926i
$653$			25.9406i			1.01514i	0.861612	+	0.507568i	$0.169455\pi$
$653$			25.9406i			1.01514i	−0.861612	+	0.507568i	$0.830545\pi$
$654$	0.768614	+	7.79189i	0.0300552	+	0.304687i
$655$	−30.1571	−	34.2068i	−1.17833	−	1.33657i
$656$	−1.18400	−	2.85359i	−0.0462275	−	0.111414i
$657$	10.3838	−	10.3838i	0.405110	−	0.405110i
$658$	−2.28824	+	2.78909i	−0.0892050	+	0.108730i
$659$	12.5270	+	12.5270i	0.487981	+	0.487981i	0.907669	−	0.419687i	$-0.137860\pi$
$659$	12.5270	+	12.5270i	0.487981	+	0.487981i	−0.419687	+	0.907669i	$0.637860\pi$
$660$	21.9269	+	16.7238i	0.853503	+	0.650975i
$661$	−26.5534	+	26.5534i	−1.03281	+	1.03281i	−0.0333644	+	0.999443i	$0.510622\pi$
$661$	−26.5534	+	26.5534i	−1.03281	+	1.03281i	−0.999443	+	0.0333644i	$0.989378\pi$
$662$	−0.889870	+	0.0877793i	−0.0345858	+	0.00341164i
$663$	−11.3471	−	11.3471i	−0.440686	−	0.440686i
$664$	−18.9554	−	10.1209i	−0.735612	−	0.392768i
$665$	−1.16070	+	18.4473i	−0.0450100	+	0.715355i
$666$	−6.88513	−	5.64875i	−0.266793	−	0.218885i
$667$	−2.48985			−0.0964074
$668$	−10.9172	−	7.28993i	−0.422401	−	0.282056i
$669$	−4.29237	+	4.29237i	−0.165953	+	0.165953i
$670$	−28.5792	+	30.6831i	−1.10411	+	1.18539i
$671$			6.92837i			0.267467i
$672$	−10.6937	−	19.9704i	−0.412518	−	0.770377i
$673$	10.4724	+	10.4724i	0.403681	+	0.403681i	0.879528	−	0.475847i	$-0.157858\pi$
$673$	10.4724	+	10.4724i	0.403681	+	0.403681i	−0.475847	+	0.879528i	$0.657858\pi$
$674$	0.820564	+	8.31853i	0.0316069	+	0.320418i
$675$	4.96057	+	0.626717i	0.190932	+	0.0241224i
$676$	4.66094	+	23.3955i	0.179267	+	0.899826i
$677$			23.5614i			0.905539i	0.891628	+	0.452769i	$0.149564\pi$
$677$			23.5614i			0.905539i	−0.891628	+	0.452769i	$0.850436\pi$
$678$	−18.1888	+	1.79419i	−0.698537	+	0.0689056i
$679$		−	4.25534i		−	0.163305i
$680$	−4.67658	−	19.7826i	−0.179338	−	0.758626i
$681$			13.2703i			0.508517i
$682$	−0.602666	−	6.10957i	−0.0230773	−	0.233948i
$683$			30.7873i			1.17804i	0.808117	+	0.589021i	$0.200487\pi$
$683$			30.7873i			1.17804i	−0.808117	+	0.589021i	$0.799513\pi$
$684$	2.29257	−	3.43330i	0.0876585	−	0.131275i
$685$	8.41457	−	7.41837i	0.321504	−	0.283441i
$686$	−11.4787	+	1.13229i	−0.438259	+	0.0432311i
$687$	−11.4064	−	11.4064i	−0.435183	−	0.435183i
$688$	7.43127	+	17.9103i	0.283314	+	0.682822i
$689$			20.8622i			0.794785i
$690$	−0.204546	−	5.76143i	−0.00778693	−	0.219334i
$691$	16.3289	−	16.3289i	0.621182	−	0.621182i	−0.324652	−	0.945834i	$-0.605247\pi$
$691$	16.3289	−	16.3289i	0.621182	−	0.621182i	0.945834	+	0.324652i	$0.105247\pi$
$692$	−46.9890	+	9.36135i	−1.78626	+	0.355865i
$693$	−24.6936			−0.938033
$694$	−27.3401	+	33.3242i	−1.03781	+	1.26497i
$695$	8.72365	+	9.89515i	0.330907	+	0.375344i
$696$	3.69607	−	1.12301i	0.140099	−	0.0425675i
$697$	1.75537	+	1.75537i	0.0664895	+	0.0664895i
$698$	4.74124	+	48.0647i	0.179459	+	1.81928i
$699$	8.19734	−	8.19734i	0.310052	−	0.310052i
$700$	−30.2535	−	26.2373i	−1.14347	−	0.991676i
$701$	−15.1215	−	15.1215i	−0.571130	−	0.571130i	0.361314	−	0.932444i	$-0.382328\pi$
$701$	−15.1215	−	15.1215i	−0.571130	−	0.571130i	−0.932444	+	0.361314i	$0.882328\pi$
$702$	5.45876	+	4.47852i	0.206028	+	0.169031i
$703$	−9.19161	+	9.19161i	−0.346668	+	0.346668i
$704$	−9.58041	+	48.3915i	−0.361075	+	1.82382i
$705$	1.06847	−	0.941975i	0.0402410	−	0.0354768i
$706$	34.4496	−	3.39821i	1.29653	−	0.127893i
$707$			30.0187i			1.12897i
$708$	−5.26025	−	3.51250i	−0.197692	−	0.132008i
$709$	−20.5244	−	20.5244i	−0.770812	−	0.770812i	0.207437	−	0.978248i	$-0.433488\pi$
$709$	−20.5244	−	20.5244i	−0.770812	−	0.770812i	−0.978248	+	0.207437i	$0.933488\pi$
$710$	−25.1122	−	23.3903i	−0.942446	−	0.877822i
$711$	−4.49087			−0.168421
$712$	26.8085	+	14.3139i	1.00469	+	0.536438i
$713$	−0.907527	+	0.907527i	−0.0339872	+	0.0339872i
$714$	14.0725	+	11.5455i	0.526651	+	0.432079i
$715$	45.5257	+	51.6393i	1.70257	+	1.93120i
$716$	2.05327	−	3.07493i	0.0767342	−	0.114915i
$717$	−10.6504			−0.397745
$718$	32.1881	+	26.4080i	1.20125	+	0.985539i
$719$	−13.6873			−0.510451			−0.255225	−	0.966882i	$-0.582150\pi$
$719$	−13.6873			−0.510451			−0.255225	+	0.966882i	$0.582150\pi$
$720$	2.90224	+	8.46032i	0.108160	+	0.315298i
$721$	30.4889			1.13547
$722$	16.1149	+	13.2211i	0.599733	+	0.492037i
$723$	1.22690			0.0456288
$724$	16.3546	+	10.9207i	0.607813	+	0.405864i
$725$	5.39580	−	4.18532i	0.200395	−	0.155439i
$726$	29.5461	+	24.2404i	1.09656	+	0.899647i
$727$	29.3029	−	29.3029i	1.08678	−	1.08678i	0.0909272	−	0.995858i	$-0.471017\pi$
$727$	29.3029	−	29.3029i	1.08678	−	1.08678i	0.995858	−	0.0909272i	$-0.0289831\pi$
$728$	−16.4403	−	54.1088i	−0.609319	−	2.00541i
$729$	1.00000			0.0370370
$730$	46.4085	−	1.64762i	1.71766	−	0.0609813i
$731$	−11.0174	−	11.0174i	−0.407494	−	0.407494i
$732$	−1.24789	+	1.86882i	−0.0461234	+	0.0690734i
$733$			47.2879i			1.74662i	0.487166	+	0.873309i	$0.338031\pi$
$733$			47.2879i			1.74662i	−0.487166	+	0.873309i	$0.661969\pi$
$734$	−21.4316	+	2.11408i	−0.791056	+	0.0780320i
$735$	20.1668	+	1.26889i	0.743862	+	0.0468037i
$736$	9.09147	−	4.86826i	0.335116	−	0.179447i
$737$	−57.8162	+	57.8162i	−2.12969	+	2.12969i
$738$	−0.844457	−	0.692816i	−0.0310849	−	0.0255029i
$739$	−15.3480	−	15.3480i	−0.564587	−	0.564587i	0.366020	−	0.930607i	$-0.380720\pi$
$739$	−15.3480	−	15.3480i	−0.564587	−	0.564587i	−0.930607	+	0.366020i	$0.880720\pi$
$740$	−3.75728	−	27.9109i	−0.138120	−	1.02602i
$741$	7.28741	−	7.28741i	0.267710	−	0.267710i
$742$	−2.32303	−	23.5499i	−0.0852810	−	0.864543i
$743$	16.7906	+	16.7906i	0.615987	+	0.615987i	0.944500	−	0.328513i	$-0.106547\pi$
$743$	16.7906	+	16.7906i	0.615987	+	0.615987i	−0.328513	+	0.944500i	$0.606547\pi$
$744$	0.937857	−	1.75651i	0.0343835	−	0.0643967i
$745$	19.9742	−	17.6095i	0.731799	−	0.645161i
$746$	−28.7966	+	35.0995i	−1.05432	+	1.28508i
$747$	−7.59721			−0.277967
$748$	−7.74477	−	38.8746i	−0.283177	−	1.42140i
$749$	−33.8930	+	33.8930i	−1.23842	+	1.23842i
$750$	10.1280	+	12.1419i	0.369821	+	0.443358i
$751$			37.3096i			1.36145i	0.732540	+	0.680724i	$0.238335\pi$
$751$			37.3096i			1.36145i	−0.732540	+	0.680724i	$0.761665\pi$
$752$	2.35469	+	0.973690i	0.0858668	+	0.0355068i
$753$	11.5822	+	11.5822i	0.422078	+	0.422078i
$754$	9.59671	−	0.946647i	0.349492	−	0.0344748i
$755$	0.697863	−	11.0913i	0.0253978	−	0.403654i
$756$	−6.66071	−	4.44766i	−0.242248	−	0.161760i
$757$			2.73045i			0.0992397i	0.998768	+	0.0496199i	$0.0158010\pi$
$757$			2.73045i			0.0992397i	−0.998768	+	0.0496199i	$0.984199\pi$
$758$	−4.58101	−	46.4404i	−0.166390	−	1.68679i
$759$		−	11.2417i		−	0.408047i
$760$	12.7049	−	3.00341i	0.460854	−	0.108945i
$761$			43.2111i			1.56640i	0.621768	+	0.783201i	$0.286415\pi$
$761$			43.2111i			1.56640i	−0.621768	+	0.783201i	$0.713585\pi$
$762$	−30.9620	+	3.05418i	−1.12163	+	0.110641i
$763$		−	22.1711i		−	0.802649i
$764$	4.75979	−	0.948265i	0.172203	−	0.0343070i
$765$	−4.75280	−	5.39105i	−0.171838	−	0.194914i
$766$	1.37881	+	13.9778i	0.0498183	+	0.505037i
$767$	−11.1652	−	11.1652i	−0.403154	−	0.403154i
$768$	−11.3001	+	11.3273i	−0.407758	+	0.408738i
$769$		−	41.3520i		−	1.49119i	−0.666398	−	0.745596i	$-0.732165\pi$
$769$		−	41.3520i		−	1.49119i	0.666398	−	0.745596i	$-0.267835\pi$
$770$	−57.1410	−	53.2228i	−2.05922	−	1.91802i
$771$	−5.72342	+	5.72342i	−0.206124	+	0.206124i
$772$	−0.960490	+	1.43841i	−0.0345688	+	0.0517695i
$773$	10.4113			0.374469			0.187234	−	0.982315i	$-0.440048\pi$
$773$	10.4113			0.374469			0.187234	+	0.982315i	$0.440048\pi$
$774$	5.30015	+	4.34839i	0.190510	+	0.156300i
$775$	0.441207	−	3.49223i	0.0158486	−	0.125444i
$776$	−2.87573	+	0.873755i	−0.103233	+	0.0313660i
$777$	17.8320	+	17.8320i	0.639720	+	0.639720i
$778$	45.7848	−	4.51634i	1.64146	−	0.161919i
$779$	−1.12735	+	1.12735i	−0.0403913	+	0.0403913i
$780$	2.97889	+	22.1287i	0.106662	+	0.792334i
$781$	−47.3190	−	47.3190i	−1.69321	−	1.69321i
$782$	−5.25604	+	6.40646i	−0.187956	+	0.229095i
$783$	0.965728	−	0.965728i	0.0345123	−	0.0345123i
$784$	13.8528	+	33.3869i	0.494742	+	1.19239i
$785$	2.03080	−	32.2760i	0.0724824	−	1.15198i
$786$	−2.83125	−	28.7020i	−0.100987	−	1.02377i
$787$			9.84332i			0.350877i	0.984490	+	0.175438i	$0.0561342\pi$
$787$			9.84332i			0.350877i	−0.984490	+	0.175438i	$0.943866\pi$
$788$	−24.7873	+	4.93823i	−0.883010	+	0.175917i
$789$	−6.70033	−	6.70033i	−0.238538	−	0.238538i
$790$	−10.3919	−	9.67928i	−0.369726	−	0.344373i
$791$	51.7546			1.84018
$792$	5.07038	+	16.6878i	0.180168	+	0.592974i
$793$	−3.96669	+	3.96669i	−0.140861	+	0.140861i
$794$	22.4753	−	27.3947i	0.797620	−	0.972200i
$795$	−0.586724	+	9.32494i	−0.0208090	+	0.330722i
$796$	−19.6215	+	3.90908i	−0.695467	+	0.138554i
$797$	−13.2854			−0.470592			−0.235296	−	0.971924i	$-0.575606\pi$
$797$	−13.2854			−0.470592			−0.235296	+	0.971924i	$0.575606\pi$
$798$	−7.41480	+	9.03772i	−0.262481	+	0.319932i
$799$	−2.04744			−0.0724333
$800$	−11.5190	+	25.8324i	−0.407257	+	0.913314i
$801$	10.7447			0.379645
$802$	−5.57719	+	6.79790i	−0.196937	+	0.240042i
$803$	90.5522			3.19552
$804$	−26.0085	+	5.18152i	−0.917248	+	0.182738i
$805$	−1.02512	+	16.2925i	−0.0361308	+	0.574235i
$806$	3.15287	−	3.84295i	0.111055	−	0.135362i
$807$	−1.08527	+	1.08527i	−0.0382032	+	0.0382032i
$808$	20.2864	−	6.16378i	0.713673	−	0.216841i
$809$	7.77887			0.273490			0.136745	−	0.990606i	$-0.456336\pi$
$809$	7.77887			0.273490			0.136745	+	0.990606i	$0.456336\pi$
$810$	2.31400	+	2.15532i	0.0813055	+	0.0757304i
$811$	33.4895	+	33.4895i	1.17598	+	1.17598i	0.980760	+	0.195215i	$0.0625405\pi$
$811$	33.4895	+	33.4895i	1.17598	+	1.17598i	0.195215	+	0.980760i	$0.437459\pi$
$812$	−10.7277	+	2.13721i	−0.376467	+	0.0750014i
$813$			3.21705i			0.112827i
$814$	−5.39093	−	54.6510i	−0.188952	−	1.91552i
$815$	1.08200	−	17.1965i	0.0379009	−	0.602368i
$816$	4.91282	−	11.8807i	0.171983	−	0.415909i
$817$	7.07567	−	7.07567i	0.247546	−	0.247546i
$818$	−11.8072	+	14.3915i	−0.412829	+	0.503187i
$819$	−14.1378	−	14.1378i	−0.494016	−	0.494016i
$820$	−0.460828	−	3.42325i	−0.0160928	−	0.119545i
$821$	22.0992	−	22.0992i	0.771267	−	0.771267i	−0.207061	−	0.978328i	$-0.566390\pi$
$821$	22.0992	−	22.0992i	0.771267	−	0.771267i	0.978328	+	0.207061i	$0.0663898\pi$
$822$	7.06044	−	0.696462i	0.246261	−	0.0242919i
$823$	6.47786	+	6.47786i	0.225804	+	0.225804i	0.810937	−	0.585133i	$-0.198958\pi$
$823$	6.47786	+	6.47786i	0.225804	+	0.225804i	−0.585133	+	0.810937i	$0.698958\pi$
$824$	−6.26034	−	20.6042i	−0.218089	−	0.717781i
$825$	18.8967	+	24.3620i	0.657899	+	0.848177i
$826$	13.8469	+	11.3604i	0.481797	+	0.395279i
$827$	−0.819945			−0.0285123			−0.0142561	−	0.999898i	$-0.504538\pi$
$827$	−0.819945			−0.0285123			−0.0142561	+	0.999898i	$0.504538\pi$
$828$	2.02478	−	3.03226i	0.0703659	−	0.105378i
$829$	−27.4647	+	27.4647i	−0.953888	+	0.953888i	−0.998983	−	0.0450945i	$-0.985641\pi$
$829$	−27.4647	+	27.4647i	−0.953888	+	0.953888i	0.0450945	+	0.998983i	$0.485641\pi$
$830$	−17.5799	−	16.3744i	−0.610207	−	0.568365i
$831$		−	28.2079i		−	0.978522i
$832$	−33.1906	+	22.2205i	−1.15068	+	0.770357i
$833$	−20.5378	−	20.5378i	−0.711594	−	0.711594i
$834$	0.819007	+	8.30275i	0.0283599	+	0.287501i
$835$	−9.70595	−	11.0094i	−0.335888	−	0.380995i
$836$	24.9663	−	4.97389i	0.863476	−	0.172025i
$837$		−	0.703997i		−	0.0243337i
$838$	29.2607	−	2.88636i	1.01079	−	0.0997075i
$839$			25.9917i			0.897335i	0.893699	+	0.448667i	$0.148101\pi$
$839$			25.9917i			0.897335i	−0.893699	+	0.448667i	$0.851899\pi$
$840$	−5.82672	−	24.6478i	−0.201041	−	0.850432i
$841$			27.1347i			0.935681i
$842$	3.34709	+	33.9314i	0.115348	+	1.16935i
$843$		−	24.5928i		−	0.847023i
$844$	−22.7394	−	15.1841i	−0.782722	−	0.522659i
$845$	−1.67482	+	26.6183i	−0.0576156	+	0.915698i
$846$	0.896526	−	0.0884359i	0.0308232	−	0.00304049i
$847$	−76.5224	−	76.5224i	−2.62934	−	2.62934i
$848$	−15.4378	+	6.40541i	−0.530137	+	0.219963i
$849$		−	15.0862i		−	0.517756i
$850$	0.621495	−	22.7187i	0.0213171	−	0.779245i
$851$	−8.11796	+	8.11796i	−0.278280	+	0.278280i
$852$	−4.24075	−	21.2863i	−0.145286	−	0.729258i
$853$	13.8457			0.474069			0.237034	−	0.971501i	$-0.423825\pi$
$853$	13.8457			0.474069			0.237034	+	0.971501i	$0.423825\pi$
$854$	4.03603	−	4.91942i	0.138110	−	0.168339i
$855$	3.46227	−	3.05237i	0.118407	−	0.104389i
$856$	29.8640	+	15.9454i	1.02073	+	0.545001i
$857$	27.4340	+	27.4340i	0.937127	+	0.937127i	0.998137	−	0.0610099i	$-0.0194321\pi$
$857$	27.4340	+	27.4340i	0.937127	+	0.937127i	−0.0610099	+	0.998137i	$0.519432\pi$
$858$	4.27411	+	43.3292i	0.145916	+	1.47923i
$859$	3.11480	−	3.11480i	0.106276	−	0.106276i	−0.651969	−	0.758245i	$-0.726057\pi$
$859$	3.11480	−	3.11480i	0.106276	−	0.106276i	0.758245	+	0.651969i	$0.226057\pi$
$860$	2.89234	+	21.4857i	0.0986280	+	0.732657i
$861$	2.18709	+	2.18709i	0.0745357	+	0.0745357i
$862$	20.2665	+	16.6272i	0.690278	+	0.566323i
$863$	18.7075	−	18.7075i	0.636810	−	0.636810i	−0.312957	−	0.949767i	$-0.601320\pi$
$863$	18.7075	−	18.7075i	0.636810	−	0.636810i	0.949767	+	0.312957i	$0.101320\pi$
$864$	−1.63804	+	5.41450i	−0.0557272	+	0.184205i
$865$	−53.4620	−	3.36382i	−1.81776	−	0.114373i
$866$	18.8596	−	1.86037i	0.640877	−	0.0632179i
$867$		−	6.66950i		−	0.226508i
$868$	−3.13114	+	4.68912i	−0.106278	+	0.159159i
$869$	−19.5814	−	19.5814i	−0.664253	−	0.664253i
$870$	4.31615	−	0.153235i	0.146331	−	0.00519514i
$871$	−66.2029			−2.24320
$872$	−14.9831	+	4.55243i	−0.507391	+	0.154165i
$873$	−0.751384	+	0.751384i	−0.0254305	+	0.0254305i
$874$	−4.11439	−	3.37556i	−0.139171	−	0.114180i
$875$	−25.1654	−	37.0309i	−0.850744	−	1.25187i
$876$	24.4250	+	16.3097i	0.825244	+	0.551053i
$877$	−20.1135			−0.679184			−0.339592	−	0.940573i	$-0.610289\pi$
$877$	−20.1135			−0.679184			−0.339592	+	0.940573i	$0.610289\pi$
$878$	−23.8278	−	19.5490i	−0.804150	−	0.659747i
$879$	−3.49295			−0.117814
$880$	−24.2347	+	49.5437i	−0.816952	+	1.67012i
$881$	8.65598			0.291628			0.145814	−	0.989312i	$-0.453420\pi$
$881$	8.65598			0.291628			0.145814	+	0.989312i	$0.453420\pi$
$882$	9.88013	+	8.10594i	0.332681	+	0.272941i
$883$	−15.9095			−0.535399			−0.267699	−	0.963502i	$-0.586263\pi$
$883$	−15.9095			−0.535399			−0.267699	+	0.963502i	$0.586263\pi$
$884$	17.8228	−	26.6910i	0.599444	−	0.897715i
$885$	−4.67661	−	5.30463i	−0.157203	−	0.178313i
$886$	−28.7256	−	23.5673i	−0.965054	−	0.791757i
$887$	19.2454	−	19.2454i	0.646197	−	0.646197i	−0.305875	−	0.952072i	$-0.598949\pi$
$887$	19.2454	−	19.2454i	0.646197	−	0.646197i	0.952072	+	0.305875i	$0.0989489\pi$
$888$	8.38927	−	15.7122i	0.281526	−	0.527268i
$889$	88.0995			2.95476
$890$	24.8631	+	23.1583i	0.833415	+	0.776267i
$891$	4.36026	+	4.36026i	0.146074	+	0.146074i
$892$	−10.0966	−	6.74196i	−0.338060	−	0.225738i
$893$		−	1.31492i		−	0.0440021i
$894$	16.7598	−	1.65324i	0.560533	−	0.0552925i
$895$	3.10087	−	2.73376i	0.103651	−	0.0913795i
$896$	34.9923	−	28.7790i	1.16901	−	0.961439i
$897$	6.43619	−	6.43619i	0.214898	−	0.214898i
$898$	−31.9926	−	26.2476i	−1.06761	−	0.875895i
$899$	−0.679870	−	0.679870i	−0.0226749	−	0.0226749i
$900$	0.709159	+	9.97482i	0.0236386	+	0.332494i
$901$	9.49652	−	9.49652i	0.316375	−	0.316375i
$902$	−0.661195	−	6.70292i	−0.0220154	−	0.223183i
$903$	−13.7270	−	13.7270i	−0.456807	−	0.456807i
$904$	−10.6268	−	34.9754i	−0.353444	−	1.16326i
$905$	14.5400	+	16.4926i	0.483327	+	0.548232i
$906$	4.45810	−	5.43387i	0.148110	−	0.180528i
$907$	−13.9176			−0.462128			−0.231064	−	0.972939i	$-0.574221\pi$
$907$	−13.9176			−0.462128			−0.231064	+	0.972939i	$0.574221\pi$
$908$	−26.0290	+	5.18560i	−0.863802	+	0.172090i
$909$	5.30053	−	5.30053i	0.175808	−	0.175808i
$910$	−2.24329	−	63.1865i	−0.0743642	−	2.09461i
$911$		−	3.79155i		−	0.125620i	−0.998026	−	0.0628098i	$-0.979994\pi$
$911$		−	3.79155i		−	0.125620i	0.998026	−	0.0628098i	$-0.0200062\pi$
$912$	7.63012	+	3.15514i	0.252658	+	0.104477i
$913$	−33.1258	−	33.1258i	−1.09630	−	1.09630i
$914$	36.3212	−	3.58283i	1.20140	−	0.118510i
$915$	−1.88458	+	1.66147i	−0.0623025	+	0.0549264i
$916$	17.9159	−	26.8305i	0.591958	−	0.886504i
$917$			81.6690i			2.69695i
$918$	−0.446209	−	4.52348i	−0.0147271	−	0.149297i
$919$			12.6465i			0.417169i	0.978004	+	0.208584i	$0.0668856\pi$
$919$			12.6465i			0.417169i	−0.978004	+	0.208584i	$0.933114\pi$
$920$	11.2208	−	2.65259i	0.369940	−	0.0874535i
$921$		−	7.81653i		−	0.257563i
$922$	−10.2199	+	1.00812i	−0.336573	+	0.0332005i
$923$		−	54.1830i		−	1.78346i
$924$	−9.64950	−	48.4354i	−0.317445	−	1.59341i
$925$	3.94666	−	31.2385i	0.129766	−	1.02711i
$926$	2.00338	+	20.3094i	0.0658352	+	0.667409i
$927$	−5.38356	−	5.38356i	−0.176819	−	0.176819i
$928$	3.64704	+	6.81083i	0.119720	+	0.223577i
$929$		−	52.7686i		−	1.73128i	−0.500665	−	0.865641i	$-0.666911\pi$
$929$		−	52.7686i		−	1.73128i	0.500665	−	0.865641i	$-0.333089\pi$
$930$	1.51734	−	1.62905i	0.0497556	−	0.0534186i
$931$	13.1899	−	13.1899i	0.432282	−	0.432282i
$932$	19.2820	+	12.8754i	0.631602	+	0.421749i
$933$	6.15295			0.201438
$934$	26.5349	+	21.7700i	0.868248	+	0.712335i
$935$	2.78294	−	44.2298i	0.0910117	−	1.44647i
$936$	−6.65129	+	12.4572i	−0.217404	+	0.407176i
$937$	12.0351	+	12.0351i	0.393168	+	0.393168i	0.875815	−	0.482647i	$-0.160324\pi$
$937$	12.0351	+	12.0351i	0.393168	+	0.393168i	−0.482647	+	0.875815i	$0.660324\pi$
$938$	74.7320	−	7.37177i	2.44009	−	0.240697i
$939$	9.65621	−	9.65621i	0.315119	−	0.315119i
$940$	2.26517	+	1.72766i	0.0738816	+	0.0563502i
$941$	43.1823	+	43.1823i	1.40770	+	1.40770i	0.771626	+	0.636076i	$0.219444\pi$
$941$	43.1823	+	43.1823i	1.40770	+	1.40770i	0.636076	+	0.771626i	$0.280556\pi$
$942$	12.9732	−	15.8127i	0.422689	−	0.515206i
$943$	−0.995664	+	0.995664i	−0.0324233	+	0.0324233i
$944$	4.83407	−	11.6903i	0.157336	−	0.380487i
$945$	−5.92169	−	6.71691i	−0.192633	−	0.218501i
$946$	4.14992	+	42.0702i	0.134926	+	1.36782i
$947$			34.2870i			1.11418i	0.830453	+	0.557089i	$0.188082\pi$
$947$			34.2870i			1.11418i	−0.830453	+	0.557089i	$0.811918\pi$
$948$	−1.75489	−	8.80863i	−0.0569963	−	0.286091i
$949$	51.8438	+	51.8438i	1.68292	+	1.68292i
$950$	14.5905	+	0.399140i	0.473379	+	0.0129498i
$951$	10.5517			0.342162
$952$	−17.1468	+	32.1142i	−0.555732	+	1.04083i
$953$	−8.81942	+	8.81942i	−0.285689	+	0.285689i	−0.835373	−	0.549684i	$-0.814748\pi$
$953$	−8.81942	+	8.81942i	−0.285689	+	0.285689i	0.549684	+	0.835373i	$0.314748\pi$
$954$	−3.74812	+	4.56849i	−0.121350	+	0.147910i
$955$	5.41547	+	0.340741i	0.175241	+	0.0110261i
$956$	−4.16184	−	20.8902i	−0.134603	−	0.675638i
$957$	8.42165			0.272233
$958$	−22.5053	+	27.4311i	−0.727112	+	0.886260i
$959$	−20.0898			−0.648735
$960$	−15.4604	+	8.99864i	−0.498983	+	0.290430i
$961$	30.5044			0.984013
$962$	28.2029	−	34.3758i	0.909296	−	1.10832i
$963$	11.9693			0.385705
$964$	0.479434	+	2.40650i	0.0154415	+	0.0775083i
$965$	−1.45055	+	1.27881i	−0.0466947	+	0.0411665i
$966$	−6.54870	+	7.98206i	−0.210701	+	0.256818i
$967$	1.93099	−	1.93099i	0.0620964	−	0.0620964i	−0.675377	−	0.737473i	$-0.736019\pi$
$967$	1.93099	−	1.93099i	0.0620964	−	0.0620964i	0.737473	+	0.675377i	$0.236019\pi$
$968$	−36.0008	+	67.4257i	−1.15711	+	2.16714i
$969$	−6.63451			−0.213131
$970$	−3.35818	+	0.119224i	−0.107825	+	0.00382806i
$971$	6.98427	+	6.98427i	0.224136	+	0.224136i	0.810238	−	0.586102i	$-0.199338\pi$
$971$	6.98427	+	6.98427i	0.224136	+	0.224136i	−0.586102	+	0.810238i	$0.699338\pi$
$972$	0.390769	+	1.96145i	0.0125339	+	0.0629136i
$973$		−	23.6247i		−	0.757374i
$974$	−0.0726040	−	0.736029i	−0.00232638	−	0.0235839i
$975$	−3.12905	+	24.7669i	−0.100210	+	0.793176i
$976$	−4.15323	−	1.71741i	−0.132942	−	0.0549729i
$977$	28.9284	−	28.9284i	0.925502	−	0.925502i	−0.0719094	−	0.997411i	$-0.522909\pi$
$977$	28.9284	−	28.9284i	0.925502	−	0.925502i	0.997411	+	0.0719094i	$0.0229092\pi$
$978$	6.91206	−	8.42495i	0.221023	−	0.269400i
$979$	46.8496	+	46.8496i	1.49732	+	1.49732i
$980$	5.39168	+	40.0520i	0.172231	+	1.27941i
$981$	−3.91485	+	3.91485i	−0.124992	+	0.124992i
$982$	38.3742	−	3.78534i	1.22457	−	0.120795i
$983$	−23.8805	−	23.8805i	−0.761669	−	0.761669i	0.214955	−	0.976624i	$-0.431039\pi$
$983$	−23.8805	−	23.8805i	−0.761669	−	0.761669i	−0.976624	+	0.214955i	$0.931039\pi$
$984$	1.02894	−	1.92710i	0.0328014	−	0.0614335i
$985$	−28.2019	−	1.77446i	−0.898586	−	0.0565389i
$986$	−4.79937	−	3.93754i	−0.152843	−	0.125397i
$987$	−2.55099			−0.0811988
$988$	17.1416	+	11.4462i	0.545347	+	0.364153i
$989$	6.24918	−	6.24918i	0.198712	−	0.198712i
$990$	0.691854	+	19.4874i	0.0219886	+	0.619351i
$991$			29.1750i			0.926774i	0.886156	+	0.463387i	$0.153366\pi$
$991$			29.1750i			0.926774i	−0.886156	+	0.463387i	$0.846634\pi$
$992$	3.81180	+	1.15317i	0.121025	+	0.0366133i
$993$	−0.447095	−	0.447095i	−0.0141881	−	0.0141881i
$994$	6.03334	+	61.1635i	0.191366	+	1.93999i
$995$	−22.3245	−	1.40465i	−0.707734	−	0.0445305i
$996$	−2.96875	−	14.9016i	−0.0940685	−	0.472174i
$997$		−	42.5940i		−	1.34896i	−0.738291	−	0.674482i	$-0.764367\pi$
$997$		−	42.5940i		−	1.34896i	0.738291	−	0.674482i	$-0.235633\pi$
$998$	34.0869	−	3.36243i	1.07900	−	0.106436i
$999$		−	6.29736i		−	0.199240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.f.163.3	✓	20
3.2	odd	2		720.2.z.h.163.8		20
4.3	odd	2		960.2.y.f.943.6		20
5.2	odd	4		240.2.bc.f.67.2	yes	20
8.3	odd	2		1920.2.y.k.223.5		20
8.5	even	2		1920.2.y.l.223.5		20
15.2	even	4		720.2.bd.h.307.9		20
16.3	odd	4		1920.2.bc.k.1183.1		20
16.5	even	4		960.2.bc.f.463.10		20
16.11	odd	4		240.2.bc.f.43.2	yes	20
16.13	even	4		1920.2.bc.l.1183.1		20
20.7	even	4		960.2.bc.f.367.10		20
40.27	even	4		1920.2.bc.l.607.1		20
40.37	odd	4		1920.2.bc.k.607.1		20
48.11	even	4		720.2.bd.h.523.9		20
80.27	even	4	inner	240.2.y.f.187.3	yes	20
80.37	odd	4		960.2.y.f.847.6		20
80.67	even	4		1920.2.y.l.1567.5		20
80.77	odd	4		1920.2.y.k.1567.5		20
240.107	odd	4		720.2.z.h.667.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.3	✓	20	1.1	even	1	trivial
240.2.y.f.187.3	yes	20	80.27	even	4	inner
240.2.bc.f.43.2	yes	20	16.11	odd	4
240.2.bc.f.67.2	yes	20	5.2	odd	4
720.2.z.h.163.8		20	3.2	odd	2
720.2.z.h.667.8		20	240.107	odd	4
720.2.bd.h.307.9		20	15.2	even	4
720.2.bd.h.523.9		20	48.11	even	4
960.2.y.f.847.6		20	80.37	odd	4
960.2.y.f.943.6		20	4.3	odd	2
960.2.bc.f.367.10		20	20.7	even	4
960.2.bc.f.463.10		20	16.5	even	4
1920.2.y.k.223.5		20	8.3	odd	2
1920.2.y.k.1567.5		20	80.77	odd	4
1920.2.y.l.223.5		20	8.5	even	2
1920.2.y.l.1567.5		20	80.67	even	4
1920.2.bc.k.607.1		20	40.37	odd	4
1920.2.bc.k.1183.1		20	16.3	odd	4
1920.2.bc.l.607.1		20	40.27	even	4
1920.2.bc.l.1183.1		20	16.13	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.897004 + 1.09334i) q^{2} -1.00000 q^{3} +(-0.390769 - 1.96145i) q^{4} +(0.140415 - 2.23165i) q^{5} +(0.897004 - 1.09334i) q^{6} +(-2.83167 + 2.83167i) q^{7} +(2.49505 + 1.33219i) q^{8} +1.00000 q^{9} +(2.31400 + 2.15532i) q^{10} +(4.36026 + 4.36026i) q^{11} +(0.390769 + 1.96145i) q^{12} +4.99276i q^{13} +(-0.555949 - 5.63598i) q^{14} +(-0.140415 + 2.23165i) q^{15} +(-3.69460 + 1.53295i) q^{16} +(2.27272 - 2.27272i) q^{17} +(-0.897004 + 1.09334i) q^{18} +(1.45960 + 1.45960i) q^{19} +(-4.43216 + 0.596643i) q^{20} +(2.83167 - 2.83167i) q^{21} +(-8.67841 + 0.856063i) q^{22} +(1.28911 + 1.28911i) q^{23} +(-2.49505 - 1.33219i) q^{24} +(-4.96057 - 0.626717i) q^{25} +(-5.45876 - 4.47852i) q^{26} -1.00000 q^{27} +(6.66071 + 4.44766i) q^{28} +(-0.965728 + 0.965728i) q^{29} +(-2.31400 - 2.15532i) q^{30} +0.703997i q^{31} +(1.63804 - 5.41450i) q^{32} +(-4.36026 - 4.36026i) q^{33} +(0.446209 + 4.52348i) q^{34} +(5.92169 + 6.71691i) q^{35} +(-0.390769 - 1.96145i) q^{36} +6.29736i q^{37} +(-2.90509 + 0.286567i) q^{38} -4.99276i q^{39} +(3.32333 - 5.38103i) q^{40} +0.772367i q^{41} +(0.555949 + 5.63598i) q^{42} -4.84769i q^{43} +(6.84860 - 10.2563i) q^{44} +(0.140415 - 2.23165i) q^{45} +(-2.56576 + 0.253094i) q^{46} +(-0.450439 - 0.450439i) q^{47} +(3.69460 - 1.53295i) q^{48} -9.03668i q^{49} +(5.13486 - 4.86140i) q^{50} +(-2.27272 + 2.27272i) q^{51} +(9.79306 - 1.95101i) q^{52} +4.17849 q^{53} +(0.897004 - 1.09334i) q^{54} +(10.3428 - 9.11835i) q^{55} +(-10.8375 + 3.29284i) q^{56} +(-1.45960 - 1.45960i) q^{57} +(-0.189604 - 1.92213i) q^{58} +(-2.23629 + 2.23629i) q^{59} +(4.43216 - 0.596643i) q^{60} +(0.794490 + 0.794490i) q^{61} +(-0.769706 - 0.631488i) q^{62} +(-2.83167 + 2.83167i) q^{63} +(4.45055 + 6.64775i) q^{64} +(11.1421 + 0.701060i) q^{65} +(8.67841 - 0.856063i) q^{66} +13.2598i q^{67} +(-5.34594 - 3.56972i) q^{68} +(-1.28911 - 1.28911i) q^{69} +(-12.6556 + 0.449308i) q^{70} -10.8523 q^{71} +(2.49505 + 1.33219i) q^{72} +(10.3838 - 10.3838i) q^{73} +(-6.88513 - 5.64875i) q^{74} +(4.96057 + 0.626717i) q^{75} +(2.29257 - 3.43330i) q^{76} -24.6936 q^{77} +(5.45876 + 4.47852i) q^{78} -4.49087 q^{79} +(2.90224 + 8.46032i) q^{80} +1.00000 q^{81} +(-0.844457 - 0.692816i) q^{82} -7.59721 q^{83} +(-6.66071 - 4.44766i) q^{84} +(-4.75280 - 5.39105i) q^{85} +(5.30015 + 4.34839i) q^{86} +(0.965728 - 0.965728i) q^{87} +(5.07038 + 16.6878i) q^{88} +10.7447 q^{89} +(2.31400 + 2.15532i) q^{90} +(-14.1378 - 14.1378i) q^{91} +(2.02478 - 3.03226i) q^{92} -0.703997i q^{93} +(0.896526 - 0.0884359i) q^{94} +(3.46227 - 3.05237i) q^{95} +(-1.63804 + 5.41450i) q^{96} +(-0.751384 + 0.751384i) q^{97} +(9.88013 + 8.10594i) q^{98} +(4.36026 + 4.36026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 20 q^{9} + 8 q^{10} + 8 q^{11} - 2 q^{12} + 10 q^{14} + 26 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 4 q^{21} - 10 q^{22} - 16 q^{23} - 6 q^{24} + 4 q^{25}+ \cdots + 8 q^{99}+O(q^{100}) \) 20 * q - 20 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 20 * q^9 + 8 * q^10 + 8 * q^11 - 2 * q^12 + 10 * q^14 + 26 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 4 * q^21 - 10 * q^22 - 16 * q^23 - 6 * q^24 + 4 * q^25 - 20 * q^26 - 20 * q^27 + 6 * q^28 - 8 * q^30 - 10 * q^32 - 8 * q^33 + 6 * q^34 - 28 * q^35 + 2 * q^36 - 2 * q^38 + 6 * q^40 - 10 * q^42 + 22 * q^44 - 18 * q^46 - 26 * q^48 - 52 * q^50 - 12 * q^51 + 8 * q^53 - 4 * q^55 - 26 * q^56 - 16 * q^57 - 22 * q^58 - 16 * q^59 + 10 * q^60 - 12 * q^61 + 4 * q^62 - 4 * q^63 + 26 * q^64 + 4 * q^65 + 10 * q^66 + 2 * q^68 + 16 * q^69 - 10 * q^70 + 6 * q^72 - 20 * q^73 - 8 * q^74 - 4 * q^75 + 26 * q^76 + 20 * q^78 + 48 * q^79 - 54 * q^80 + 20 * q^81 - 8 * q^82 - 24 * q^83 - 6 * q^84 + 4 * q^85 + 4 * q^86 + 34 * q^88 + 40 * q^89 + 8 * q^90 - 24 * q^91 + 82 * q^92 + 58 * q^94 - 72 * q^95 + 10 * q^96 - 28 * q^97 + 70 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more