LMFDB - Embedded newform 1920.2.y.k.223.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(223,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, 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("1920.223"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.y (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-20,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$15.3312771881$
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:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.5
Root			$-1.09334 - 0.897004i$ of defining polynomial
Character	$\chi$	$=$	1920.223
Dual form			1920.2.y.k.1567.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{3} +(-0.140415 + 2.23165i) q^{5} +(2.83167 - 2.83167i) q^{7} +1.00000 q^{9} +(4.36026 + 4.36026i) q^{11} -4.99276i q^{13} +(0.140415 - 2.23165i) q^{15} +(2.27272 - 2.27272i) q^{17} +(1.45960 + 1.45960i) q^{19} +(-2.83167 + 2.83167i) q^{21} +(-1.28911 - 1.28911i) q^{23} +(-4.96057 - 0.626717i) q^{25} -1.00000 q^{27} +(0.965728 - 0.965728i) q^{29} -0.703997i q^{31} +(-4.36026 - 4.36026i) q^{33} +(5.92169 + 6.71691i) q^{35} -6.29736i q^{37} +4.99276i q^{39} +0.772367i q^{41} -4.84769i q^{43} +(-0.140415 + 2.23165i) q^{45} +(0.450439 + 0.450439i) q^{47} -9.03668i q^{49} +(-2.27272 + 2.27272i) q^{51} -4.17849 q^{53} +(-10.3428 + 9.11835i) q^{55} +(-1.45960 - 1.45960i) q^{57} +(-2.23629 + 2.23629i) q^{59} +(-0.794490 - 0.794490i) q^{61} +(2.83167 - 2.83167i) q^{63} +(11.1421 + 0.701060i) q^{65} +13.2598i q^{67} +(1.28911 + 1.28911i) q^{69} +10.8523 q^{71} +(10.3838 - 10.3838i) q^{73} +(4.96057 + 0.626717i) q^{75} +24.6936 q^{77} +4.49087 q^{79} +1.00000 q^{81} -7.59721 q^{83} +(4.75280 + 5.39105i) q^{85} +(-0.965728 + 0.965728i) q^{87} +10.7447 q^{89} +(-14.1378 - 14.1378i) q^{91} +0.703997i q^{93} +(-3.46227 + 3.05237i) q^{95} +(-0.751384 + 0.751384i) q^{97} +(4.36026 + 4.36026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{3} + 4 q^{7} + 20 q^{9} + 8 q^{11} + 12 q^{17} + 16 q^{19} - 4 q^{21} + 16 q^{23} + 4 q^{25} - 20 q^{27} - 8 q^{33} - 28 q^{35} - 12 q^{51} - 8 q^{53} + 4 q^{55} - 16 q^{57} - 16 q^{59} + 12 q^{61}+ \cdots + 8 q^{99}+O(q^{100}) $ 20 * q - 20 * q^3 + 4 * q^7 + 20 * q^9 + 8 * q^11 + 12 * q^17 + 16 * q^19 - 4 * q^21 + 16 * q^23 + 4 * q^25 - 20 * q^27 - 8 * q^33 - 28 * q^35 - 12 * q^51 - 8 * q^53 + 4 * q^55 - 16 * q^57 - 16 * q^59 + 12 * q^61 + 4 * q^63 + 4 * q^65 - 16 * q^69 - 20 * q^73 - 4 * q^75 - 48 * q^79 + 20 * q^81 - 24 * q^83 - 4 * q^85 + 40 * q^89 - 24 * q^91 + 72 * q^95 - 28 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−0.140415	+	2.23165i	−0.0627957	+	0.998026i
$5$	−0.140415	+	2.23165i	−0.0627957	+	0.998026i
$6$		0			0
$7$	2.83167	−	2.83167i	1.07027	−	1.07027i	0.0729328	−	0.997337i	$-0.476764\pi$
$7$	2.83167	−	2.83167i	1.07027	−	1.07027i	0.997337	−	0.0729328i	$-0.0232359\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	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			0
$13$		−	4.99276i		−	1.38474i	−0.721542	−	0.692371i	$-0.756566\pi$
$13$		−	4.99276i		−	1.38474i	0.721542	−	0.692371i	$-0.243434\pi$
$14$		0			0
$15$	0.140415	−	2.23165i	0.0362551	−	0.576211i
$16$		0			0
$17$	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			0
$19$	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	$0.673909\pi$
$20$		0			0
$21$	−2.83167	+	2.83167i	−0.617920	+	0.617920i
$22$		0			0
$23$	−1.28911	−	1.28911i	−0.268797	−	0.268797i	0.559818	−	0.828615i	$-0.310871\pi$
$23$	−1.28911	−	1.28911i	−0.268797	−	0.268797i	−0.828615	+	0.559818i	$0.810871\pi$
$24$		0			0
$25$	−4.96057	−	0.626717i	−0.992113	−	0.125343i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.965728	−	0.965728i	0.179331	−	0.179331i	−0.611733	−	0.791064i	$-0.709527\pi$
$29$	0.965728	−	0.965728i	0.179331	−	0.179331i	0.791064	+	0.611733i	$0.209527\pi$
$30$		0			0
$31$		−	0.703997i		−	0.126442i	−0.998000	−	0.0632208i	$-0.979863\pi$
$31$		−	0.703997i		−	0.126442i	0.998000	−	0.0632208i	$-0.0201372\pi$
$32$		0			0
$33$	−4.36026	−	4.36026i	−0.759024	−	0.759024i
$34$		0			0
$35$	5.92169	+	6.71691i	1.00095	+	1.13537i
$36$		0			0
$37$		−	6.29736i		−	1.03528i	−0.855599	−	0.517640i	$-0.826811\pi$
$37$		−	6.29736i		−	1.03528i	0.855599	−	0.517640i	$-0.173189\pi$
$38$		0			0
$39$			4.99276i			0.799481i
$40$		0			0
$41$			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			0
$43$		−	4.84769i		−	0.739265i	−0.929178	−	0.369633i	$-0.879484\pi$
$43$		−	4.84769i		−	0.739265i	0.929178	−	0.369633i	$-0.120516\pi$
$44$		0			0
$45$	−0.140415	+	2.23165i	−0.0209319	+	0.332675i
$46$		0			0
$47$	0.450439	+	0.450439i	0.0657033	+	0.0657033i	0.739195	−	0.673492i	$-0.235206\pi$
$47$	0.450439	+	0.450439i	0.0657033	+	0.0657033i	−0.673492	+	0.739195i	$0.735206\pi$
$48$		0			0
$49$		−	9.03668i		−	1.29095i
$50$		0			0
$51$	−2.27272	+	2.27272i	−0.318244	+	0.318244i
$52$		0			0
$53$	−4.17849			−0.573959			−0.286980	−	0.957937i	$-0.592651\pi$
$53$	−4.17849			−0.573959			−0.286980	+	0.957937i	$0.592651\pi$
$54$		0			0
$55$	−10.3428	+	9.11835i	−1.39463	+	1.22952i
$56$		0			0
$57$	−1.45960	−	1.45960i	−0.193328	−	0.193328i
$58$		0			0
$59$	−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	$0.316001\pi$
$60$		0			0
$61$	−0.794490	−	0.794490i	−0.101724	−	0.101724i	0.654413	−	0.756137i	$-0.272916\pi$
$61$	−0.794490	−	0.794490i	−0.101724	−	0.101724i	−0.756137	+	0.654413i	$0.772916\pi$
$62$		0			0
$63$	2.83167	−	2.83167i	0.356757	−	0.356757i
$64$		0			0
$65$	11.1421	+	0.701060i	1.38201	+	0.0869558i
$66$		0			0
$67$			13.2598i			1.61994i	0.586470	+	0.809971i	$0.300517\pi$
$67$			13.2598i			1.61994i	−0.586470	+	0.809971i	$0.699483\pi$
$68$		0			0
$69$	1.28911	+	1.28911i	0.155190	+	0.155190i
$70$		0			0
$71$	10.8523			1.28793			0.643967	−	0.765053i	$-0.277287\pi$
$71$	10.8523			1.28793			0.643967	+	0.765053i	$0.277287\pi$
$72$		0			0
$73$	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	$-0.0791435\pi$
$74$		0			0
$75$	4.96057	+	0.626717i	0.572797	+	0.0723671i
$76$		0			0
$77$	24.6936			2.81410
$78$		0			0
$79$	4.49087			0.505262			0.252631	−	0.967563i	$-0.418704\pi$
$79$	4.49087			0.505262			0.252631	+	0.967563i	$0.418704\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−7.59721			−0.833902			−0.416951	−	0.908929i	$-0.636901\pi$
$83$	−7.59721			−0.833902			−0.416951	+	0.908929i	$0.636901\pi$
$84$		0			0
$85$	4.75280	+	5.39105i	0.515513	+	0.584741i
$86$		0			0
$87$	−0.965728	+	0.965728i	−0.103537	+	0.103537i
$88$		0			0
$89$	10.7447			1.13893			0.569467	−	0.822014i	$-0.307150\pi$
$89$	10.7447			1.13893			0.569467	+	0.822014i	$0.307150\pi$
$90$		0			0
$91$	−14.1378	−	14.1378i	−1.48205	−	1.48205i
$92$		0			0
$93$			0.703997i			0.0730011i
$94$		0			0
$95$	−3.46227	+	3.05237i	−0.355221	+	0.313166i
$96$		0			0
$97$	−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	$0.267180\pi$
$98$		0			0
$99$	4.36026	+	4.36026i	0.438223	+	0.438223i
$100$		0			0
$101$	−5.30053	+	5.30053i	−0.527423	+	0.527423i	−0.919803	−	0.392380i	$-0.871652\pi$
$101$	−5.30053	+	5.30053i	−0.527423	+	0.527423i	0.392380	+	0.919803i	$0.371652\pi$
$102$		0			0
$103$	5.38356	+	5.38356i	0.530458	+	0.530458i	0.920709	−	0.390250i	$-0.127612\pi$
$103$	5.38356	+	5.38356i	0.530458	+	0.530458i	−0.390250	+	0.920709i	$0.627612\pi$
$104$		0			0
$105$	−5.92169	−	6.71691i	−0.577898	−	0.655504i
$106$		0			0
$107$	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			0
$109$	3.91485	−	3.91485i	0.374975	−	0.374975i	−0.494310	−	0.869285i	$-0.664579\pi$
$109$	3.91485	−	3.91485i	0.374975	−	0.374975i	0.869285	+	0.494310i	$0.164579\pi$
$110$		0			0
$111$			6.29736i			0.597719i
$112$		0			0
$113$	−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	$0.957982\pi$
$114$		0			0
$115$	3.05785	−	2.69583i	0.285146	−	0.251387i
$116$		0			0
$117$		−	4.99276i		−	0.461580i
$118$		0			0
$119$		−	12.8712i		−	1.17990i
$120$		0			0
$121$			27.0238i			2.45671i
$122$		0			0
$123$		−	0.772367i		−	0.0696420i
$124$		0			0
$125$	2.09516	−	10.9823i	0.187397	−	0.982284i
$126$		0			0
$127$	15.5561	+	15.5561i	1.38038	+	1.38038i	0.843931	+	0.536451i	$0.180235\pi$
$127$	15.5561	+	15.5561i	1.38038	+	1.38038i	0.536451	+	0.843931i	$0.319765\pi$
$128$		0			0
$129$			4.84769i			0.426815i
$130$		0			0
$131$	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	$-0.0999333\pi$
$132$		0			0
$133$	8.26619			0.716769
$134$		0			0
$135$	0.140415	−	2.23165i	0.0120850	−	0.192070i
$136$		0			0
$137$	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	$0.681252\pi$
$138$		0			0
$139$	−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	$0.330494\pi$
$140$		0			0
$141$	−0.450439	−	0.450439i	−0.0379338	−	0.0379338i
$142$		0			0
$143$	21.7697	−	21.7697i	1.82048	−	1.82048i
$144$		0			0
$145$	2.01957	+	2.29077i	0.167716	+	0.190238i
$146$		0			0
$147$			9.03668i			0.745333i
$148$		0			0
$149$	−8.42059	−	8.42059i	−0.689842	−	0.689842i	0.272355	−	0.962197i	$-0.412197\pi$
$149$	−8.42059	−	8.42059i	−0.689842	−	0.689842i	−0.962197	+	0.272355i	$0.912197\pi$
$150$		0			0
$151$	−4.96999			−0.404452			−0.202226	−	0.979339i	$-0.564818\pi$
$151$	−4.96999			−0.404452			−0.202226	+	0.979339i	$0.564818\pi$
$152$		0			0
$153$	2.27272	−	2.27272i	0.183738	−	0.183738i
$154$		0			0
$155$	1.57108	+	0.0988521i	0.126192	+	0.00793999i
$156$		0			0
$157$	−14.4628			−1.15426			−0.577129	−	0.816653i	$-0.695827\pi$
$157$	−14.4628			−1.15426			−0.577129	+	0.816653i	$0.695827\pi$
$158$		0			0
$159$	4.17849			0.331376
$160$		0			0
$161$	−7.30064			−0.575371
$162$		0			0
$163$	7.70573			0.603559			0.301779	−	0.953378i	$-0.402419\pi$
$163$	7.70573			0.603559			0.301779	+	0.953378i	$0.402419\pi$
$164$		0			0
$165$	10.3428	−	9.11835i	0.805190	−	0.709863i
$166$		0			0
$167$	−4.64125	+	4.64125i	−0.359150	+	0.359150i	−0.863500	−	0.504349i	$-0.831732\pi$
$167$	−4.64125	+	4.64125i	−0.359150	+	0.359150i	0.504349	+	0.863500i	$0.331732\pi$
$168$		0			0
$169$	−11.9276			−0.917509
$170$		0			0
$171$	1.45960	+	1.45960i	0.111618	+	0.111618i
$172$		0			0
$173$			23.9562i			1.82136i	0.413114	+	0.910679i	$0.364441\pi$
$173$			23.9562i			1.82136i	−0.413114	+	0.910679i	$0.635559\pi$
$174$		0			0
$175$	−15.8213	+	12.2720i	−1.19598	+	0.927678i
$176$		0			0
$177$	2.23629	−	2.23629i	0.168090	−	0.168090i
$178$		0			0
$179$	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	$0.727990\pi$
$180$		0			0
$181$	6.95282	−	6.95282i	0.516799	−	0.516799i	−0.399802	−	0.916601i	$-0.630921\pi$
$181$	6.95282	−	6.95282i	0.516799	−	0.516799i	0.916601	+	0.399802i	$0.130921\pi$
$182$		0			0
$183$	0.794490	+	0.794490i	0.0587304	+	0.0587304i
$184$		0			0
$185$	14.0535	+	0.884246i	1.03324	+	0.0650111i
$186$		0			0
$187$	19.8193			1.44933
$188$		0			0
$189$	−2.83167	+	2.83167i	−0.205973	+	0.205973i
$190$		0			0
$191$		−	2.42666i		−	0.175587i	−0.996139	−	0.0877936i	$-0.972018\pi$
$191$		−	2.42666i		−	0.175587i	0.996139	−	0.0877936i	$-0.0279816\pi$
$192$		0			0
$193$	−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			0
$195$	−11.1421	−	0.701060i	−0.797903	−	0.0502039i
$196$		0			0
$197$			12.6372i			0.900363i	0.892937	+	0.450182i	$0.148641\pi$
$197$			12.6372i			0.900363i	−0.892937	+	0.450182i	$0.851359\pi$
$198$		0			0
$199$			10.0036i			0.709134i	0.935031	+	0.354567i	$0.115372\pi$
$199$			10.0036i			0.709134i	−0.935031	+	0.354567i	$0.884628\pi$
$200$		0			0
$201$		−	13.2598i		−	0.935274i
$202$		0			0
$203$		−	5.46924i		−	0.383865i
$204$		0			0
$205$	−1.72366	−	0.108452i	−0.120385	−	0.00757464i
$206$		0			0
$207$	−1.28911	−	1.28911i	−0.0895991	−	0.0895991i
$208$		0			0
$209$			12.7285i			0.880446i
$210$		0			0
$211$	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	$0.0940405\pi$
$212$		0			0
$213$	−10.8523			−0.743589
$214$		0			0
$215$	10.8184	+	0.680690i	0.737806	+	0.0464227i
$216$		0			0
$217$	−1.99349	−	1.99349i	−0.135327	−	0.135327i
$218$		0			0
$219$	−10.3838	+	10.3838i	−0.701672	+	0.701672i
$220$		0			0
$221$	−11.3471	−	11.3471i	−0.763291	−	0.763291i
$222$		0			0
$223$	−4.29237	+	4.29237i	−0.287438	+	0.287438i	−0.836067	−	0.548628i	$-0.815150\pi$
$223$	−4.29237	+	4.29237i	−0.287438	+	0.287438i	0.548628	+	0.836067i	$0.315150\pi$
$224$		0			0
$225$	−4.96057	−	0.626717i	−0.330704	−	0.0417812i
$226$		0			0
$227$		−	13.2703i		−	0.880778i	−0.897807	−	0.440389i	$-0.854841\pi$
$227$		−	13.2703i		−	0.880778i	0.897807	−	0.440389i	$-0.145159\pi$
$228$		0			0
$229$	−11.4064	−	11.4064i	−0.753758	−	0.753758i	0.221420	−	0.975178i	$-0.428931\pi$
$229$	−11.4064	−	11.4064i	−0.753758	−	0.753758i	−0.975178	+	0.221420i	$0.928931\pi$
$230$		0			0
$231$	−24.6936			−1.62472
$232$		0			0
$233$	−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	$0.373985\pi$
$234$		0			0
$235$	−1.06847	+	0.941975i	−0.0696995	+	0.0614477i
$236$		0			0
$237$	−4.49087			−0.291713
$238$		0			0
$239$	−10.6504			−0.688915			−0.344458	−	0.938802i	$-0.611937\pi$
$239$	−10.6504			−0.688915			−0.344458	+	0.938802i	$0.611937\pi$
$240$		0			0
$241$	−1.22690			−0.0790315			−0.0395157	−	0.999219i	$-0.512582\pi$
$241$	−1.22690			−0.0790315			−0.0395157	+	0.999219i	$0.512582\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	20.1668	+	1.26889i	1.28841	+	0.0810664i
$246$		0			0
$247$	7.28741	−	7.28741i	0.463687	−	0.463687i
$248$		0			0
$249$	7.59721			0.481453
$250$		0			0
$251$	−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	$0.922928\pi$
$252$		0			0
$253$		−	11.2417i		−	0.706759i
$254$		0			0
$255$	−4.75280	−	5.39105i	−0.297632	−	0.337601i
$256$		0			0
$257$	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	$0.168764\pi$
$258$		0			0
$259$	−17.8320	−	17.8320i	−1.10803	−	1.10803i
$260$		0			0
$261$	0.965728	−	0.965728i	0.0597771	−	0.0597771i
$262$		0			0
$263$	−6.70033	−	6.70033i	−0.413160	−	0.413160i	0.469678	−	0.882838i	$-0.344370\pi$
$263$	−6.70033	−	6.70033i	−0.413160	−	0.413160i	−0.882838	+	0.469678i	$0.844370\pi$
$264$		0			0
$265$	0.586724	−	9.32494i	0.0360422	−	0.572826i
$266$		0			0
$267$	−10.7447			−0.657564
$268$		0			0
$269$	−1.08527	+	1.08527i	−0.0661699	+	0.0661699i	−0.739417	−	0.673247i	$-0.764899\pi$
$269$	−1.08527	+	1.08527i	−0.0661699	+	0.0661699i	0.673247	+	0.739417i	$0.264899\pi$
$270$		0			0
$271$			3.21705i			0.195422i	0.995215	+	0.0977108i	$0.0311520\pi$
$271$			3.21705i			0.195422i	−0.995215	+	0.0977108i	$0.968848\pi$
$272$		0			0
$273$	14.1378	+	14.1378i	0.855660	+	0.855660i
$274$		0			0
$275$	−18.8967	−	24.3620i	−1.13952	−	1.46909i
$276$		0			0
$277$		−	28.2079i		−	1.69485i	−0.530915	−	0.847425i	$-0.678152\pi$
$277$		−	28.2079i		−	1.69485i	0.530915	−	0.847425i	$-0.321848\pi$
$278$		0			0
$279$		−	0.703997i		−	0.0421472i
$280$		0			0
$281$			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			0
$283$			15.0862i			0.896779i	0.893838	+	0.448390i	$0.148002\pi$
$283$			15.0862i			0.896779i	−0.893838	+	0.448390i	$0.851998\pi$
$284$		0			0
$285$	3.46227	−	3.05237i	0.205087	−	0.180807i
$286$		0			0
$287$	2.18709	+	2.18709i	0.129100	+	0.129100i
$288$		0			0
$289$			6.66950i			0.392324i
$290$		0			0
$291$	0.751384	−	0.751384i	0.0440469	−	0.0440469i
$292$		0			0
$293$	−3.49295			−0.204060			−0.102030	−	0.994781i	$-0.532534\pi$
$293$	−3.49295			−0.204060			−0.102030	+	0.994781i	$0.532534\pi$
$294$		0			0
$295$	−4.67661	−	5.30463i	−0.272283	−	0.308848i
$296$		0			0
$297$	−4.36026	−	4.36026i	−0.253008	−	0.253008i
$298$		0			0
$299$	−6.43619	+	6.43619i	−0.372215	+	0.372215i
$300$		0			0
$301$	−13.7270	−	13.7270i	−0.791213	−	0.791213i
$302$		0			0
$303$	5.30053	−	5.30053i	0.304508	−	0.304508i
$304$		0			0
$305$	1.88458	−	1.66147i	0.107911	−	0.0951354i
$306$		0			0
$307$			7.81653i			0.446113i	0.974806	+	0.223056i	$0.0716034\pi$
$307$			7.81653i			0.446113i	−0.974806	+	0.223056i	$0.928397\pi$
$308$		0			0
$309$	−5.38356	−	5.38356i	−0.306260	−	0.306260i
$310$		0			0
$311$	6.15295			0.348902			0.174451	−	0.984666i	$-0.444185\pi$
$311$	6.15295			0.348902			0.174451	+	0.984666i	$0.444185\pi$
$312$		0			0
$313$	−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	$0.376123\pi$
$314$		0			0
$315$	5.92169	+	6.71691i	0.333650	+	0.378455i
$316$		0			0
$317$	10.5517			0.592642			0.296321	−	0.955088i	$-0.404240\pi$
$317$	10.5517			0.592642			0.296321	+	0.955088i	$0.404240\pi$
$318$		0			0
$319$	8.42165			0.471522
$320$		0			0
$321$	−11.9693			−0.668061
$322$		0			0
$323$	6.63451			0.369154
$324$		0			0
$325$	−3.12905	+	24.7669i	−0.173568	+	1.37382i
$326$		0			0
$327$	−3.91485	+	3.91485i	−0.216492	+	0.216492i
$328$		0			0
$329$	2.55099			0.140640
$330$		0			0
$331$	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	$0.744469\pi$
$332$		0			0
$333$		−	6.29736i		−	0.345093i
$334$		0			0
$335$	−29.5913	−	1.86188i	−1.61675	−	0.101725i
$336$		0			0
$337$	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	$0.198532\pi$
$338$		0			0
$339$	9.13854	+	9.13854i	0.496337	+	0.496337i
$340$		0			0
$341$	3.06961	−	3.06961i	0.166229	−	0.166229i
$342$		0			0
$343$	−5.76720	−	5.76720i	−0.311400	−	0.311400i
$344$		0			0
$345$	−3.05785	+	2.69583i	−0.164629	+	0.145139i
$346$		0			0
$347$	30.4793			1.63622			0.818108	−	0.575064i	$-0.195023\pi$
$347$	30.4793			1.63622			0.818108	+	0.575064i	$0.195023\pi$
$348$		0			0
$349$	−24.1490	+	24.1490i	−1.29267	+	1.29267i	−0.359535	+	0.933131i	$0.617065\pi$
$349$	−24.1490	+	24.1490i	−1.29267	+	1.29267i	−0.933131	+	0.359535i	$0.882935\pi$
$350$		0			0
$351$			4.99276i			0.266494i
$352$		0			0
$353$	−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			0
$355$	−1.52383	+	24.2186i	−0.0808767	+	1.28539i
$356$		0			0
$357$			12.8712i			0.681214i
$358$		0			0
$359$			29.4403i			1.55380i	0.629626	+	0.776899i	$0.283208\pi$
$359$			29.4403i			1.55380i	−0.629626	+	0.776899i	$0.716792\pi$
$360$		0			0
$361$		−	14.7392i		−	0.775745i
$362$		0			0
$363$		−	27.0238i		−	1.41838i
$364$		0			0
$365$	21.7150	+	24.6311i	1.13662	+	1.28925i
$366$		0			0
$367$	−10.7678	−	10.7678i	−0.562076	−	0.562076i	0.367821	−	0.929897i	$-0.380104\pi$
$367$	−10.7678	−	10.7678i	−0.562076	−	0.562076i	−0.929897	+	0.367821i	$0.880104\pi$
$368$		0			0
$369$			0.772367i			0.0402078i
$370$		0			0
$371$	−11.8321	+	11.8321i	−0.614291	+	0.614291i
$372$		0			0
$373$	−32.1031			−1.66223			−0.831117	−	0.556098i	$-0.812298\pi$
$373$	−32.1031			−1.66223			−0.831117	+	0.556098i	$0.812298\pi$
$374$		0			0
$375$	−2.09516	+	10.9823i	−0.108193	+	0.567122i
$376$		0			0
$377$	−4.82164	−	4.82164i	−0.248327	−	0.248327i
$378$		0			0
$379$	−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	$0.928113\pi$
$380$		0			0
$381$	−15.5561	−	15.5561i	−0.796964	−	0.796964i
$382$		0			0
$383$	−7.02280	+	7.02280i	−0.358848	+	0.358848i	−0.863388	−	0.504540i	$-0.831662\pi$
$383$	−7.02280	+	7.02280i	−0.358848	+	0.358848i	0.504540	+	0.863388i	$0.331662\pi$
$384$		0			0
$385$	−3.46737	+	55.1077i	−0.176713	+	2.80855i
$386$		0			0
$387$		−	4.84769i		−	0.246422i
$388$		0			0
$389$	23.0035	+	23.0035i	1.16632	+	1.16632i	0.983065	+	0.183259i	$0.0586647\pi$
$389$	23.0035	+	23.0035i	1.16632	+	1.16632i	0.183259	+	0.983065i	$0.441335\pi$
$390$		0			0
$391$	−5.85955			−0.296330
$392$		0			0
$393$	−14.4207	+	14.4207i	−0.727426	+	0.727426i
$394$		0			0
$395$	−0.630587	+	10.0221i	−0.0317283	+	0.504265i
$396$		0			0
$397$	25.0560			1.25753			0.628763	−	0.777597i	$-0.283562\pi$
$397$	25.0560			1.25753			0.628763	+	0.777597i	$0.283562\pi$
$398$		0			0
$399$	−8.26619			−0.413827
$400$		0			0
$401$	6.21757			0.310491			0.155245	−	0.987876i	$-0.450383\pi$
$401$	6.21757			0.310491			0.155245	+	0.987876i	$0.450383\pi$
$402$		0			0
$403$	−3.51489			−0.175089
$404$		0			0
$405$	−0.140415	+	2.23165i	−0.00697730	+	0.110892i
$406$		0			0
$407$	27.4581	−	27.4581i	1.36105	−	1.36105i
$408$		0			0
$409$	13.1629			0.650865			0.325432	−	0.945565i	$-0.394490\pi$
$409$	13.1629			0.650865			0.325432	+	0.945565i	$0.394490\pi$
$410$		0			0
$411$	−3.54735	−	3.54735i	−0.174978	−	0.174978i
$412$		0			0
$413$			12.6648i			0.623196i
$414$		0			0
$415$	1.06676	−	16.9543i	0.0523654	−	0.832256i
$416$		0			0
$417$	4.17152	−	4.17152i	0.204280	−	0.204280i
$418$		0			0
$419$	−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	$0.919559\pi$
$420$		0			0
$421$	−17.0481	+	17.0481i	−0.830872	+	0.830872i	−0.987636	−	0.156764i	$-0.949894\pi$
$421$	−17.0481	+	17.0481i	−0.830872	+	0.830872i	0.156764	+	0.987636i	$0.449894\pi$
$422$		0			0
$423$	0.450439	+	0.450439i	0.0219011	+	0.0219011i
$424$		0			0
$425$	−12.6983	+	9.84962i	−0.615959	+	0.477777i
$426$		0			0
$427$	−4.49946			−0.217744
$428$		0			0
$429$	−21.7697	+	21.7697i	−1.05105	+	1.05105i
$430$		0			0
$431$			18.5363i			0.892864i	0.894818	+	0.446432i	$0.147306\pi$
$431$			18.5363i			0.892864i	−0.894818	+	0.446432i	$0.852694\pi$
$432$		0			0
$433$	−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	$0.854353\pi$
$434$		0			0
$435$	−2.01957	−	2.29077i	−0.0968309	−	0.109834i
$436$		0			0
$437$		−	3.76315i		−	0.180016i
$438$		0			0
$439$		−	21.7937i		−	1.04016i	−0.854119	−	0.520078i	$-0.825903\pi$
$439$		−	21.7937i		−	1.04016i	0.854119	−	0.520078i	$-0.174097\pi$
$440$		0			0
$441$		−	9.03668i		−	0.430318i
$442$		0			0
$443$			26.2733i			1.24828i	0.781312	+	0.624141i	$0.214551\pi$
$443$			26.2733i			1.24828i	−0.781312	+	0.624141i	$0.785449\pi$
$444$		0			0
$445$	−1.50872	+	23.9784i	−0.0715201	+	1.13669i
$446$		0			0
$447$	8.42059	+	8.42059i	0.398280	+	0.398280i
$448$		0			0
$449$			29.2615i			1.38093i	0.723364	+	0.690467i	$0.242595\pi$
$449$			29.2615i			1.38093i	−0.723364	+	0.690467i	$0.757405\pi$
$450$		0			0
$451$	−3.36772	+	3.36772i	−0.158580	+	0.158580i
$452$		0			0
$453$	4.96999			0.233510
$454$		0			0
$455$	33.5359	−	29.5656i	1.57219	−	1.38606i
$456$		0			0
$457$	−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	$0.956274\pi$
$458$		0			0
$459$	−2.27272	+	2.27272i	−0.106081	+	0.106081i
$460$		0			0
$461$	−5.13473	−	5.13473i	−0.239148	−	0.239148i	0.577349	−	0.816497i	$-0.304087\pi$
$461$	−5.13473	−	5.13473i	−0.239148	−	0.239148i	−0.816497	+	0.577349i	$0.804087\pi$
$462$		0			0
$463$	−10.2040	+	10.2040i	−0.474220	+	0.474220i	−0.903277	−	0.429057i	$-0.858846\pi$
$463$	−10.2040	+	10.2040i	−0.474220	+	0.474220i	0.429057	+	0.903277i	$0.358846\pi$
$464$		0			0
$465$	−1.57108	−	0.0988521i	−0.0728571	−	0.00458416i
$466$		0			0
$467$		−	24.2696i		−	1.12306i	−0.827455	−	0.561532i	$-0.810212\pi$
$467$		−	24.2696i		−	1.12306i	0.827455	−	0.561532i	$-0.189788\pi$
$468$		0			0
$469$	37.5473	+	37.5473i	1.73378	+	1.73378i
$470$		0			0
$471$	14.4628			0.666411
$472$		0			0
$473$	21.1372	−	21.1372i	0.971889	−	0.971889i
$474$		0			0
$475$	−6.32567	−	8.15518i	−0.290242	−	0.374186i
$476$		0			0
$477$	−4.17849			−0.191320
$478$		0			0
$479$	−25.0894			−1.14636			−0.573182	−	0.819428i	$-0.694291\pi$
$479$	−25.0894			−1.14636			−0.573182	+	0.819428i	$0.694291\pi$
$480$		0			0
$481$	−31.4412			−1.43359
$482$		0			0
$483$	7.30064			0.332191
$484$		0			0
$485$	−1.57132	−	1.78234i	−0.0713502	−	0.0809317i
$486$		0			0
$487$	0.369801	−	0.369801i	0.0167573	−	0.0167573i	−0.698679	−	0.715436i	$-0.746228\pi$
$487$	0.369801	−	0.369801i	0.0167573	−	0.0167573i	0.715436	+	0.698679i	$0.246228\pi$
$488$		0			0
$489$	−7.70573			−0.348465
$490$		0			0
$491$	−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	$0.960948\pi$
$492$		0			0
$493$		−	4.38966i		−	0.197700i
$494$		0			0
$495$	−10.3428	+	9.11835i	−0.464877	+	0.409840i
$496$		0			0
$497$	30.7302	−	30.7302i	1.37844	−	1.37844i
$498$		0			0
$499$	−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	$0.932378\pi$
$500$		0			0
$501$	4.64125	−	4.64125i	0.207356	−	0.207356i
$502$		0			0
$503$	−5.60127	−	5.60127i	−0.249748	−	0.249748i	0.571119	−	0.820867i	$-0.306509\pi$
$503$	−5.60127	−	5.60127i	−0.249748	−	0.249748i	−0.820867	+	0.571119i	$0.806509\pi$
$504$		0			0
$505$	−11.0847	−	12.5732i	−0.493262	−	0.559501i
$506$		0			0
$507$	11.9276			0.529724
$508$		0			0
$509$	0.0876457	−	0.0876457i	0.00388483	−	0.00388483i	−0.705162	−	0.709047i	$-0.749126\pi$
$509$	0.0876457	−	0.0876457i	0.00388483	−	0.00388483i	0.709047	+	0.705162i	$0.249126\pi$
$510$		0			0
$511$		−	58.8069i		−	2.60146i
$512$		0			0
$513$	−1.45960	−	1.45960i	−0.0644428	−	0.0644428i
$514$		0			0
$515$	−12.7702	+	11.2583i	−0.562722	+	0.496101i
$516$		0			0
$517$			3.92806i			0.172756i
$518$		0			0
$519$		−	23.9562i		−	1.05156i
$520$		0			0
$521$		−	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			0
$523$		−	21.8823i		−	0.956847i	−0.878129	−	0.478423i	$-0.841208\pi$
$523$		−	21.8823i		−	0.956847i	0.878129	−	0.478423i	$-0.158792\pi$
$524$		0			0
$525$	15.8213	−	12.2720i	0.690500	−	0.535595i
$526$		0			0
$527$	−1.59999	−	1.59999i	−0.0696966	−	0.0696966i
$528$		0			0
$529$		−	19.6764i		−	0.855496i
$530$		0			0
$531$	−2.23629	+	2.23629i	−0.0970466	+	0.0970466i
$532$		0			0
$533$	3.85624			0.167032
$534$		0			0
$535$	−1.68067	+	26.7113i	−0.0726618	+	1.15483i
$536$		0			0
$537$	−1.30724	−	1.30724i	−0.0564117	−	0.0564117i
$538$		0			0
$539$	39.4023	−	39.4023i	1.69718	−	1.69718i
$540$		0			0
$541$	21.9852	+	21.9852i	0.945217	+	0.945217i	0.998575	−	0.0533584i	$-0.0169926\pi$
$541$	21.9852	+	21.9852i	0.945217	+	0.945217i	−0.0533584	+	0.998575i	$0.516993\pi$
$542$		0			0
$543$	−6.95282	+	6.95282i	−0.298374	+	0.298374i
$544$		0			0
$545$	8.18690	+	9.28631i	0.350688	+	0.397782i
$546$		0			0
$547$			28.9503i			1.23783i	0.785459	+	0.618913i	$0.212427\pi$
$547$			28.9503i			1.23783i	−0.785459	+	0.618913i	$0.787573\pi$
$548$		0			0
$549$	−0.794490	−	0.794490i	−0.0339080	−	0.0339080i
$550$		0			0
$551$	2.81915			0.120100
$552$		0			0
$553$	12.7167	−	12.7167i	0.540767	−	0.540767i
$554$		0			0
$555$	−14.0535	−	0.884246i	−0.596539	−	0.0375342i
$556$		0			0
$557$	−8.55746			−0.362591			−0.181296	−	0.983429i	$-0.558029\pi$
$557$	−8.55746			−0.362591			−0.181296	+	0.983429i	$0.558029\pi$
$558$		0			0
$559$	−24.2033			−1.02369
$560$		0			0
$561$	−19.8193			−0.836772
$562$		0			0
$563$	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			0
$565$	21.6773	−	19.1109i	0.911969	−	0.804000i
$566$		0			0
$567$	2.83167	−	2.83167i	0.118919	−	0.118919i
$568$		0			0
$569$	−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			0
$571$	−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	$0.801700\pi$
$572$		0			0
$573$			2.42666i			0.101375i
$574$		0			0
$575$	5.58679	+	7.20260i	0.232985	+	0.300369i
$576$		0			0
$577$	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	$0.144114\pi$
$578$		0			0
$579$	0.611510	+	0.611510i	0.0254135	+	0.0254135i
$580$		0			0
$581$	−21.5128	+	21.5128i	−0.892500	+	0.892500i
$582$		0			0
$583$	−18.2193	−	18.2193i	−0.754566	−	0.754566i
$584$		0			0
$585$	11.1421	+	0.701060i	0.460670	+	0.0289853i
$586$		0			0
$587$	−0.0736360			−0.00303928			−0.00151964	−	0.999999i	$-0.500484\pi$
$587$	−0.0736360			−0.00303928			−0.00151964	+	0.999999i	$0.500484\pi$
$588$		0			0
$589$	1.02755	−	1.02755i	0.0423396	−	0.0423396i
$590$		0			0
$591$		−	12.6372i		−	0.519825i
$592$		0			0
$593$	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	$0.490005\pi$
$594$		0			0
$595$	28.7240	+	1.80731i	1.17757	+	0.0740925i
$596$		0			0
$597$		−	10.0036i		−	0.409419i
$598$		0			0
$599$			16.3265i			0.667081i	0.942736	+	0.333541i	$0.108243\pi$
$599$			16.3265i			0.667081i	−0.942736	+	0.333541i	$0.891757\pi$
$600$		0			0
$601$		−	22.5262i		−	0.918862i	−0.888213	−	0.459431i	$-0.848053\pi$
$601$		−	22.5262i		−	0.918862i	0.888213	−	0.459431i	$-0.151947\pi$
$602$		0			0
$603$			13.2598i			0.539981i
$604$		0			0
$605$	−60.3078	−	3.79456i	−2.45186	−	0.154271i
$606$		0			0
$607$	−20.2440	−	20.2440i	−0.821677	−	0.821677i	0.164672	−	0.986348i	$-0.447344\pi$
$607$	−20.2440	−	20.2440i	−0.821677	−	0.821677i	−0.986348	+	0.164672i	$0.947344\pi$
$608$		0			0
$609$			5.46924i			0.221625i
$610$		0			0
$611$	2.24893	−	2.24893i	0.0909820	−	0.0909820i
$612$		0			0
$613$	−28.9848			−1.17069			−0.585343	−	0.810786i	$-0.699040\pi$
$613$	−28.9848			−1.17069			−0.585343	+	0.810786i	$0.699040\pi$
$614$		0			0
$615$	1.72366	+	0.108452i	0.0695046	+	0.00437322i
$616$		0			0
$617$	−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	$0.921994\pi$
$618$		0			0
$619$	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			0
$621$	1.28911	+	1.28911i	0.0517300	+	0.0517300i
$622$		0			0
$623$	30.4254	−	30.4254i	1.21897	−	1.21897i
$624$		0			0
$625$	24.2145	+	6.21775i	0.968578	+	0.248710i
$626$		0			0
$627$		−	12.7285i		−	0.508325i
$628$		0			0
$629$	−14.3121	−	14.3121i	−0.570662	−	0.570662i
$630$		0			0
$631$	15.2007			0.605131			0.302565	−	0.953129i	$-0.402157\pi$
$631$	15.2007			0.605131			0.302565	+	0.953129i	$0.402157\pi$
$632$		0			0
$633$	−9.66719	+	9.66719i	−0.384236	+	0.384236i
$634$		0			0
$635$	−36.9002	+	32.5316i	−1.46434	+	1.29098i
$636$		0			0
$637$	−45.1179			−1.78764
$638$		0			0
$639$	10.8523			0.429311
$640$		0			0
$641$	−13.9100			−0.549414			−0.274707	−	0.961528i	$-0.588581\pi$
$641$	−13.9100			−0.549414			−0.274707	+	0.961528i	$0.588581\pi$
$642$		0			0
$643$	−50.3060			−1.98387			−0.991937	−	0.126735i	$-0.959550\pi$
$643$	−50.3060			−1.98387			−0.991937	+	0.126735i	$0.959550\pi$
$644$		0			0
$645$	−10.8184	−	0.680690i	−0.425973	−	0.0268021i
$646$		0			0
$647$	−15.4702	+	15.4702i	−0.608197	+	0.608197i	−0.942475	−	0.334278i	$-0.891508\pi$
$647$	−15.4702	+	15.4702i	−0.608197	+	0.608197i	0.334278	+	0.942475i	$0.391508\pi$
$648$		0			0
$649$	−19.5016			−0.765505
$650$		0			0
$651$	1.99349	+	1.99349i	0.0781309	+	0.0781309i
$652$		0			0
$653$		−	25.9406i		−	1.01514i	−0.861612	−	0.507568i	$-0.830545\pi$
$653$		−	25.9406i		−	1.01514i	0.861612	−	0.507568i	$-0.169455\pi$
$654$		0			0
$655$	30.1571	+	34.2068i	1.17833	+	1.33657i
$656$		0			0
$657$	10.3838	−	10.3838i	0.405110	−	0.405110i
$658$		0			0
$659$	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	$0.637860\pi$
$660$		0			0
$661$	26.5534	−	26.5534i	1.03281	−	1.03281i	0.0333644	−	0.999443i	$-0.489378\pi$
$661$	26.5534	−	26.5534i	1.03281	−	1.03281i	0.999443	−	0.0333644i	$-0.0106222\pi$
$662$		0			0
$663$	11.3471	+	11.3471i	0.440686	+	0.440686i
$664$		0			0
$665$	−1.16070	+	18.4473i	−0.0450100	+	0.715355i
$666$		0			0
$667$	−2.48985			−0.0964074
$668$		0			0
$669$	4.29237	−	4.29237i	0.165953	−	0.165953i
$670$		0			0
$671$		−	6.92837i		−	0.267467i
$672$		0			0
$673$	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			0
$675$	4.96057	+	0.626717i	0.190932	+	0.0241224i
$676$		0			0
$677$		−	23.5614i		−	0.905539i	−0.891628	−	0.452769i	$-0.850436\pi$
$677$		−	23.5614i		−	0.905539i	0.891628	−	0.452769i	$-0.149564\pi$
$678$		0			0
$679$			4.25534i			0.163305i
$680$		0			0
$681$			13.2703i			0.508517i
$682$		0			0
$683$			30.7873i			1.17804i	0.808117	+	0.589021i	$0.200487\pi$
$683$			30.7873i			1.17804i	−0.808117	+	0.589021i	$0.799513\pi$
$684$		0			0
$685$	−8.41457	+	7.41837i	−0.321504	+	0.283441i
$686$		0			0
$687$	11.4064	+	11.4064i	0.435183	+	0.435183i
$688$		0			0
$689$			20.8622i			0.794785i
$690$		0			0
$691$	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	$0.105247\pi$
$692$		0			0
$693$	24.6936			0.938033
$694$		0			0
$695$	−8.72365	−	9.89515i	−0.330907	−	0.375344i
$696$		0			0
$697$	1.75537	+	1.75537i	0.0664895	+	0.0664895i
$698$		0			0
$699$	8.19734	−	8.19734i	0.310052	−	0.310052i
$700$		0			0
$701$	15.1215	+	15.1215i	0.571130	+	0.571130i	0.932444	−	0.361314i	$-0.117672\pi$
$701$	15.1215	+	15.1215i	0.571130	+	0.571130i	−0.361314	+	0.932444i	$0.617672\pi$
$702$		0			0
$703$	9.19161	−	9.19161i	0.346668	−	0.346668i
$704$		0			0
$705$	1.06847	−	0.941975i	0.0402410	−	0.0354768i
$706$		0			0
$707$			30.0187i			1.12897i
$708$		0			0
$709$	20.5244	+	20.5244i	0.770812	+	0.770812i	0.978248	−	0.207437i	$-0.0665122\pi$
$709$	20.5244	+	20.5244i	0.770812	+	0.770812i	−0.207437	+	0.978248i	$0.566512\pi$
$710$		0			0
$711$	4.49087			0.168421
$712$		0			0
$713$	−0.907527	+	0.907527i	−0.0339872	+	0.0339872i
$714$		0			0
$715$	45.5257	+	51.6393i	1.70257	+	1.93120i
$716$		0			0
$717$	10.6504			0.397745
$718$		0			0
$719$	13.6873			0.510451			0.255225	−	0.966882i	$-0.417850\pi$
$719$	13.6873			0.510451			0.255225	+	0.966882i	$0.417850\pi$
$720$		0			0
$721$	30.4889			1.13547
$722$		0			0
$723$	1.22690			0.0456288
$724$		0			0
$725$	−5.39580	+	4.18532i	−0.200395	+	0.155439i
$726$		0			0
$727$	−29.3029	+	29.3029i	−1.08678	+	1.08678i	−0.0909272	+	0.995858i	$0.528983\pi$
$727$	−29.3029	+	29.3029i	−1.08678	+	1.08678i	−0.995858	+	0.0909272i	$0.971017\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−11.0174	−	11.0174i	−0.407494	−	0.407494i
$732$		0			0
$733$		−	47.2879i		−	1.74662i	−0.487166	−	0.873309i	$-0.661969\pi$
$733$		−	47.2879i		−	1.74662i	0.487166	−	0.873309i	$-0.338031\pi$
$734$		0			0
$735$	−20.1668	−	1.26889i	−0.743862	−	0.0468037i
$736$		0			0
$737$	−57.8162	+	57.8162i	−2.12969	+	2.12969i
$738$		0			0
$739$	−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	$0.880720\pi$
$740$		0			0
$741$	−7.28741	+	7.28741i	−0.267710	+	0.267710i
$742$		0			0
$743$	−16.7906	−	16.7906i	−0.615987	−	0.615987i	0.328513	−	0.944500i	$-0.393453\pi$
$743$	−16.7906	−	16.7906i	−0.615987	−	0.615987i	−0.944500	+	0.328513i	$0.893453\pi$
$744$		0			0
$745$	19.9742	−	17.6095i	0.731799	−	0.645161i
$746$		0			0
$747$	−7.59721			−0.277967
$748$		0			0
$749$	33.8930	−	33.8930i	1.23842	−	1.23842i
$750$		0			0
$751$		−	37.3096i		−	1.36145i	−0.732540	−	0.680724i	$-0.761665\pi$
$751$		−	37.3096i		−	1.36145i	0.732540	−	0.680724i	$-0.238335\pi$
$752$		0			0
$753$	11.5822	+	11.5822i	0.422078	+	0.422078i
$754$		0			0
$755$	0.697863	−	11.0913i	0.0253978	−	0.403654i
$756$		0			0
$757$		−	2.73045i		−	0.0992397i	−0.998768	−	0.0496199i	$-0.984199\pi$
$757$		−	2.73045i		−	0.0992397i	0.998768	−	0.0496199i	$-0.0158010\pi$
$758$		0			0
$759$			11.2417i			0.408047i
$760$		0			0
$761$			43.2111i			1.56640i	0.621768	+	0.783201i	$0.286415\pi$
$761$			43.2111i			1.56640i	−0.621768	+	0.783201i	$0.713585\pi$
$762$		0			0
$763$		−	22.1711i		−	0.802649i
$764$		0			0
$765$	4.75280	+	5.39105i	0.171838	+	0.194914i
$766$		0			0
$767$	11.1652	+	11.1652i	0.403154	+	0.403154i
$768$		0			0
$769$		−	41.3520i		−	1.49119i	−0.666398	−	0.745596i	$-0.732165\pi$
$769$		−	41.3520i		−	1.49119i	0.666398	−	0.745596i	$-0.267835\pi$
$770$		0			0
$771$	−5.72342	+	5.72342i	−0.206124	+	0.206124i
$772$		0			0
$773$	−10.4113			−0.374469			−0.187234	−	0.982315i	$-0.559952\pi$
$773$	−10.4113			−0.374469			−0.187234	+	0.982315i	$0.559952\pi$
$774$		0			0
$775$	−0.441207	+	3.49223i	−0.0158486	+	0.125444i
$776$		0			0
$777$	17.8320	+	17.8320i	0.639720	+	0.639720i
$778$		0			0
$779$	−1.12735	+	1.12735i	−0.0403913	+	0.0403913i
$780$		0			0
$781$	47.3190	+	47.3190i	1.69321	+	1.69321i
$782$		0			0
$783$	−0.965728	+	0.965728i	−0.0345123	+	0.0345123i
$784$		0			0
$785$	2.03080	−	32.2760i	0.0724824	−	1.15198i
$786$		0			0
$787$			9.84332i			0.350877i	0.984490	+	0.175438i	$0.0561342\pi$
$787$			9.84332i			0.350877i	−0.984490	+	0.175438i	$0.943866\pi$
$788$		0			0
$789$	6.70033	+	6.70033i	0.238538	+	0.238538i
$790$		0			0
$791$	−51.7546			−1.84018
$792$		0			0
$793$	−3.96669	+	3.96669i	−0.140861	+	0.140861i
$794$		0			0
$795$	−0.586724	+	9.32494i	−0.0208090	+	0.330722i
$796$		0			0
$797$	13.2854			0.470592			0.235296	−	0.971924i	$-0.424394\pi$
$797$	13.2854			0.470592			0.235296	+	0.971924i	$0.424394\pi$
$798$		0			0
$799$	2.04744			0.0724333
$800$		0			0
$801$	10.7447			0.379645
$802$		0			0
$803$	90.5522			3.19552
$804$		0			0
$805$	1.02512	−	16.2925i	0.0361308	−	0.574235i
$806$		0			0
$807$	1.08527	−	1.08527i	0.0382032	−	0.0382032i
$808$		0			0
$809$	7.77887			0.273490			0.136745	−	0.990606i	$-0.456336\pi$
$809$	7.77887			0.273490			0.136745	+	0.990606i	$0.456336\pi$
$810$		0			0
$811$	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	$0.437459\pi$
$812$		0			0
$813$		−	3.21705i		−	0.112827i
$814$		0			0
$815$	−1.08200	+	17.1965i	−0.0379009	+	0.602368i
$816$		0			0
$817$	7.07567	−	7.07567i	0.247546	−	0.247546i
$818$		0			0
$819$	−14.1378	−	14.1378i	−0.494016	−	0.494016i
$820$		0			0
$821$	−22.0992	+	22.0992i	−0.771267	+	0.771267i	−0.978328	−	0.207061i	$-0.933610\pi$
$821$	−22.0992	+	22.0992i	−0.771267	+	0.771267i	0.207061	+	0.978328i	$0.433610\pi$
$822$		0			0
$823$	−6.47786	−	6.47786i	−0.225804	−	0.225804i	0.585133	−	0.810937i	$-0.301042\pi$
$823$	−6.47786	−	6.47786i	−0.225804	−	0.225804i	−0.810937	+	0.585133i	$0.801042\pi$
$824$		0			0
$825$	18.8967	+	24.3620i	0.657899	+	0.848177i
$826$		0			0
$827$	−0.819945			−0.0285123			−0.0142561	−	0.999898i	$-0.504538\pi$
$827$	−0.819945			−0.0285123			−0.0142561	+	0.999898i	$0.504538\pi$
$828$		0			0
$829$	27.4647	−	27.4647i	0.953888	−	0.953888i	−0.0450945	−	0.998983i	$-0.514359\pi$
$829$	27.4647	−	27.4647i	0.953888	−	0.953888i	0.998983	+	0.0450945i	$0.0143589\pi$
$830$		0			0
$831$			28.2079i			0.978522i
$832$		0			0
$833$	−20.5378	−	20.5378i	−0.711594	−	0.711594i
$834$		0			0
$835$	−9.70595	−	11.0094i	−0.335888	−	0.380995i
$836$		0			0
$837$			0.703997i			0.0243337i
$838$		0			0
$839$		−	25.9917i		−	0.897335i	−0.893699	−	0.448667i	$-0.851899\pi$
$839$		−	25.9917i		−	0.897335i	0.893699	−	0.448667i	$-0.148101\pi$
$840$		0			0
$841$			27.1347i			0.935681i
$842$		0			0
$843$		−	24.5928i		−	0.847023i
$844$		0			0
$845$	1.67482	−	26.6183i	0.0576156	−	0.915698i
$846$		0			0
$847$	76.5224	+	76.5224i	2.62934	+	2.62934i
$848$		0			0
$849$		−	15.0862i		−	0.517756i
$850$		0			0
$851$	−8.11796	+	8.11796i	−0.278280	+	0.278280i
$852$		0			0
$853$	−13.8457			−0.474069			−0.237034	−	0.971501i	$-0.576175\pi$
$853$	−13.8457			−0.474069			−0.237034	+	0.971501i	$0.576175\pi$
$854$		0			0
$855$	−3.46227	+	3.05237i	−0.118407	+	0.104389i
$856$		0			0
$857$	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	$0.519432\pi$
$858$		0			0
$859$	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	$0.226057\pi$
$860$		0			0
$861$	−2.18709	−	2.18709i	−0.0745357	−	0.0745357i
$862$		0			0
$863$	−18.7075	+	18.7075i	−0.636810	+	0.636810i	−0.949767	−	0.312957i	$-0.898680\pi$
$863$	−18.7075	+	18.7075i	−0.636810	+	0.636810i	0.312957	+	0.949767i	$0.398680\pi$
$864$		0			0
$865$	−53.4620	−	3.36382i	−1.81776	−	0.114373i
$866$		0			0
$867$		−	6.66950i		−	0.226508i
$868$		0			0
$869$	19.5814	+	19.5814i	0.664253	+	0.664253i
$870$		0			0
$871$	66.2029			2.24320
$872$		0			0
$873$	−0.751384	+	0.751384i	−0.0254305	+	0.0254305i
$874$		0			0
$875$	−25.1654	−	37.0309i	−0.850744	−	1.25187i
$876$		0			0
$877$	20.1135			0.679184			0.339592	−	0.940573i	$-0.389711\pi$
$877$	20.1135			0.679184			0.339592	+	0.940573i	$0.389711\pi$
$878$		0			0
$879$	3.49295			0.117814
$880$		0			0
$881$	8.65598			0.291628			0.145814	−	0.989312i	$-0.453420\pi$
$881$	8.65598			0.291628			0.145814	+	0.989312i	$0.453420\pi$
$882$		0			0
$883$	−15.9095			−0.535399			−0.267699	−	0.963502i	$-0.586263\pi$
$883$	−15.9095			−0.535399			−0.267699	+	0.963502i	$0.586263\pi$
$884$		0			0
$885$	4.67661	+	5.30463i	0.157203	+	0.178313i
$886$		0			0
$887$	−19.2454	+	19.2454i	−0.646197	+	0.646197i	−0.952072	−	0.305875i	$-0.901051\pi$
$887$	−19.2454	+	19.2454i	−0.646197	+	0.646197i	0.305875	+	0.952072i	$0.401051\pi$
$888$		0			0
$889$	88.0995			2.95476
$890$		0			0
$891$	4.36026	+	4.36026i	0.146074	+	0.146074i
$892$		0			0
$893$			1.31492i			0.0440021i
$894$		0			0
$895$	−3.10087	+	2.73376i	−0.103651	+	0.0913795i
$896$		0			0
$897$	6.43619	−	6.43619i	0.214898	−	0.214898i
$898$		0			0
$899$	−0.679870	−	0.679870i	−0.0226749	−	0.0226749i
$900$		0			0
$901$	−9.49652	+	9.49652i	−0.316375	+	0.316375i
$902$		0			0
$903$	13.7270	+	13.7270i	0.456807	+	0.456807i
$904$		0			0
$905$	14.5400	+	16.4926i	0.483327	+	0.548232i
$906$		0			0
$907$	−13.9176			−0.462128			−0.231064	−	0.972939i	$-0.574221\pi$
$907$	−13.9176			−0.462128			−0.231064	+	0.972939i	$0.574221\pi$
$908$		0			0
$909$	−5.30053	+	5.30053i	−0.175808	+	0.175808i
$910$		0			0
$911$			3.79155i			0.125620i	0.998026	+	0.0628098i	$0.0200062\pi$
$911$			3.79155i			0.125620i	−0.998026	+	0.0628098i	$0.979994\pi$
$912$		0			0
$913$	−33.1258	−	33.1258i	−1.09630	−	1.09630i
$914$		0			0
$915$	−1.88458	+	1.66147i	−0.0623025	+	0.0549264i
$916$		0			0
$917$		−	81.6690i		−	2.69695i
$918$		0			0
$919$		−	12.6465i		−	0.417169i	−0.978004	−	0.208584i	$-0.933114\pi$
$919$		−	12.6465i		−	0.417169i	0.978004	−	0.208584i	$-0.0668856\pi$
$920$		0			0
$921$		−	7.81653i		−	0.257563i
$922$		0			0
$923$		−	54.1830i		−	1.78346i
$924$		0			0
$925$	−3.94666	+	31.2385i	−0.129766	+	1.02711i
$926$		0			0
$927$	5.38356	+	5.38356i	0.176819	+	0.176819i
$928$		0			0
$929$		−	52.7686i		−	1.73128i	−0.500665	−	0.865641i	$-0.666911\pi$
$929$		−	52.7686i		−	1.73128i	0.500665	−	0.865641i	$-0.333089\pi$
$930$		0			0
$931$	13.1899	−	13.1899i	0.432282	−	0.432282i
$932$		0			0
$933$	−6.15295			−0.201438
$934$		0			0
$935$	−2.78294	+	44.2298i	−0.0910117	+	1.44647i
$936$		0			0
$937$	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	$0.660324\pi$
$938$		0			0
$939$	9.65621	−	9.65621i	0.315119	−	0.315119i
$940$		0			0
$941$	−43.1823	−	43.1823i	−1.40770	−	1.40770i	−0.771626	−	0.636076i	$-0.780556\pi$
$941$	−43.1823	−	43.1823i	−1.40770	−	1.40770i	−0.636076	−	0.771626i	$-0.719444\pi$
$942$		0			0
$943$	0.995664	−	0.995664i	0.0324233	−	0.0324233i
$944$		0			0
$945$	−5.92169	−	6.71691i	−0.192633	−	0.218501i
$946$		0			0
$947$			34.2870i			1.11418i	0.830453	+	0.557089i	$0.188082\pi$
$947$			34.2870i			1.11418i	−0.830453	+	0.557089i	$0.811918\pi$
$948$		0			0
$949$	−51.8438	−	51.8438i	−1.68292	−	1.68292i
$950$		0			0
$951$	−10.5517			−0.342162
$952$		0			0
$953$	−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	$0.314748\pi$
$954$		0			0
$955$	5.41547	+	0.340741i	0.175241	+	0.0110261i
$956$		0			0
$957$	−8.42165			−0.272233
$958$		0			0
$959$	20.0898			0.648735
$960$		0			0
$961$	30.5044			0.984013
$962$		0			0
$963$	11.9693			0.385705
$964$		0			0
$965$	1.45055	−	1.27881i	0.0466947	−	0.0411665i
$966$		0			0
$967$	−1.93099	+	1.93099i	−0.0620964	+	0.0620964i	−0.737473	−	0.675377i	$-0.763981\pi$
$967$	−1.93099	+	1.93099i	−0.0620964	+	0.0620964i	0.675377	+	0.737473i	$0.263981\pi$
$968$		0			0
$969$	−6.63451			−0.213131
$970$		0			0
$971$	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			0
$973$			23.6247i			0.757374i
$974$		0			0
$975$	3.12905	−	24.7669i	0.100210	−	0.793176i
$976$		0			0
$977$	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	$0.0229092\pi$
$978$		0			0
$979$	46.8496	+	46.8496i	1.49732	+	1.49732i
$980$		0			0
$981$	3.91485	−	3.91485i	0.124992	−	0.124992i
$982$		0			0
$983$	23.8805	+	23.8805i	0.761669	+	0.761669i	0.976624	−	0.214955i	$-0.0689606\pi$
$983$	23.8805	+	23.8805i	0.761669	+	0.761669i	−0.214955	+	0.976624i	$0.568961\pi$
$984$		0			0
$985$	−28.2019	−	1.77446i	−0.898586	−	0.0565389i
$986$		0			0
$987$	−2.55099			−0.0811988
$988$		0			0
$989$	−6.24918	+	6.24918i	−0.198712	+	0.198712i
$990$		0			0
$991$		−	29.1750i		−	0.926774i	−0.886156	−	0.463387i	$-0.846634\pi$
$991$		−	29.1750i		−	0.926774i	0.886156	−	0.463387i	$-0.153366\pi$
$992$		0			0
$993$	−0.447095	−	0.447095i	−0.0141881	−	0.0141881i
$994$		0			0
$995$	−22.3245	−	1.40465i	−0.707734	−	0.0445305i
$996$		0			0
$997$			42.5940i			1.34896i	0.738291	+	0.674482i	$0.235633\pi$
$997$			42.5940i			1.34896i	−0.738291	+	0.674482i	$0.764367\pi$
$998$		0			0
$999$			6.29736i			0.199240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.k.223.5		20
4.3	odd	2		1920.2.y.l.223.5		20
5.2	odd	4		1920.2.bc.l.607.1		20
8.3	odd	2		240.2.y.f.163.3	✓	20
8.5	even	2		960.2.y.f.943.6		20
16.3	odd	4		960.2.bc.f.463.10		20
16.5	even	4		1920.2.bc.k.1183.1		20
16.11	odd	4		1920.2.bc.l.1183.1		20
16.13	even	4		240.2.bc.f.43.2	yes	20
20.7	even	4		1920.2.bc.k.607.1		20
24.11	even	2		720.2.z.h.163.8		20
40.27	even	4		240.2.bc.f.67.2	yes	20
40.37	odd	4		960.2.bc.f.367.10		20
48.29	odd	4		720.2.bd.h.523.9		20
80.27	even	4	inner	1920.2.y.k.1567.5		20
80.37	odd	4		1920.2.y.l.1567.5		20
80.67	even	4		960.2.y.f.847.6		20
80.77	odd	4		240.2.y.f.187.3	yes	20
120.107	odd	4		720.2.bd.h.307.9		20
240.77	even	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	8.3	odd	2
240.2.y.f.187.3	yes	20	80.77	odd	4
240.2.bc.f.43.2	yes	20	16.13	even	4
240.2.bc.f.67.2	yes	20	40.27	even	4
720.2.z.h.163.8		20	24.11	even	2
720.2.z.h.667.8		20	240.77	even	4
720.2.bd.h.307.9		20	120.107	odd	4
720.2.bd.h.523.9		20	48.29	odd	4
960.2.y.f.847.6		20	80.67	even	4
960.2.y.f.943.6		20	8.5	even	2
960.2.bc.f.367.10		20	40.37	odd	4
960.2.bc.f.463.10		20	16.3	odd	4
1920.2.y.k.223.5		20	1.1	even	1	trivial
1920.2.y.k.1567.5		20	80.27	even	4	inner
1920.2.y.l.223.5		20	4.3	odd	2
1920.2.y.l.1567.5		20	80.37	odd	4
1920.2.bc.k.607.1		20	20.7	even	4
1920.2.bc.k.1183.1		20	16.5	even	4
1920.2.bc.l.607.1		20	5.2	odd	4
1920.2.bc.l.1183.1		20	16.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +(-0.140415 + 2.23165i) q^{5} +(2.83167 - 2.83167i) q^{7} +1.00000 q^{9} +(4.36026 + 4.36026i) q^{11} -4.99276i q^{13} +(0.140415 - 2.23165i) q^{15} +(2.27272 - 2.27272i) q^{17} +(1.45960 + 1.45960i) q^{19} +(-2.83167 + 2.83167i) q^{21} +(-1.28911 - 1.28911i) q^{23} +(-4.96057 - 0.626717i) q^{25} -1.00000 q^{27} +(0.965728 - 0.965728i) q^{29} -0.703997i q^{31} +(-4.36026 - 4.36026i) q^{33} +(5.92169 + 6.71691i) q^{35} -6.29736i q^{37} +4.99276i q^{39} +0.772367i q^{41} -4.84769i q^{43} +(-0.140415 + 2.23165i) q^{45} +(0.450439 + 0.450439i) q^{47} -9.03668i q^{49} +(-2.27272 + 2.27272i) q^{51} -4.17849 q^{53} +(-10.3428 + 9.11835i) q^{55} +(-1.45960 - 1.45960i) q^{57} +(-2.23629 + 2.23629i) q^{59} +(-0.794490 - 0.794490i) q^{61} +(2.83167 - 2.83167i) q^{63} +(11.1421 + 0.701060i) q^{65} +13.2598i q^{67} +(1.28911 + 1.28911i) q^{69} +10.8523 q^{71} +(10.3838 - 10.3838i) q^{73} +(4.96057 + 0.626717i) q^{75} +24.6936 q^{77} +4.49087 q^{79} +1.00000 q^{81} -7.59721 q^{83} +(4.75280 + 5.39105i) q^{85} +(-0.965728 + 0.965728i) q^{87} +10.7447 q^{89} +(-14.1378 - 14.1378i) q^{91} +0.703997i q^{93} +(-3.46227 + 3.05237i) q^{95} +(-0.751384 + 0.751384i) q^{97} +(4.36026 + 4.36026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{3} + 4 q^{7} + 20 q^{9} + 8 q^{11} + 12 q^{17} + 16 q^{19} - 4 q^{21} + 16 q^{23} + 4 q^{25} - 20 q^{27} - 8 q^{33} - 28 q^{35} - 12 q^{51} - 8 q^{53} + 4 q^{55} - 16 q^{57} - 16 q^{59} + 12 q^{61}+ \cdots + 8 q^{99}+O(q^{100}) \) 20 * q - 20 * q^3 + 4 * q^7 + 20 * q^9 + 8 * q^11 + 12 * q^17 + 16 * q^19 - 4 * q^21 + 16 * q^23 + 4 * q^25 - 20 * q^27 - 8 * q^33 - 28 * q^35 - 12 * q^51 - 8 * q^53 + 4 * q^55 - 16 * q^57 - 16 * q^59 + 12 * q^61 + 4 * q^63 + 4 * q^65 - 16 * q^69 - 20 * q^73 - 4 * q^75 - 48 * q^79 + 20 * q^81 - 24 * q^83 - 4 * q^85 + 40 * q^89 - 24 * q^91 + 72 * q^95 - 28 * q^97 + 8 * q^99

Introduction

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