LMFDB - Embedded newform 720.2.bd.h.307.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(307,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-2,0,-2,-8,0,-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:	$5.74922894553$
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:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.9
Root			$-1.09334 - 0.897004i$ of defining polynomial
Character	$\chi$	$=$	720.307
Dual form			720.2.bd.h.523.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09334 + 0.897004i) q^{2} +(0.390769 + 1.96145i) q^{4} +(-2.23165 + 0.140415i) q^{5} +(-2.83167 - 2.83167i) q^{7} +(-1.33219 + 2.49505i) q^{8} +(-2.56590 - 1.84828i) q^{10} +(-4.36026 - 4.36026i) q^{11} +4.99276 q^{13} +(-0.555949 - 5.63598i) q^{14} +(-3.69460 + 1.53295i) q^{16} +(-2.27272 - 2.27272i) q^{17} +(-1.45960 - 1.45960i) q^{19} +(-1.14748 - 4.32242i) q^{20} +(-0.856063 - 8.67841i) q^{22} +(-1.28911 + 1.28911i) q^{23} +(4.96057 - 0.626717i) q^{25} +(5.45876 + 4.47852i) q^{26} +(4.44766 - 6.66071i) q^{28} +(-0.965728 + 0.965728i) q^{29} +0.703997i q^{31} +(-5.41450 - 1.63804i) q^{32} +(-0.446209 - 4.52348i) q^{34} +(6.71691 + 5.92169i) q^{35} -6.29736 q^{37} +(-0.286567 - 2.90509i) q^{38} +(2.62264 - 5.75515i) q^{40} -0.772367i q^{41} -4.84769 q^{43} +(6.84860 - 10.2563i) q^{44} +(-2.56576 + 0.253094i) q^{46} +(-0.450439 + 0.450439i) q^{47} +9.03668i q^{49} +(5.98574 + 3.76443i) q^{50} +(1.95101 + 9.79306i) q^{52} +4.17849i q^{53} +(10.3428 + 9.11835i) q^{55} +(10.8375 - 3.29284i) q^{56} +(-1.92213 + 0.189604i) q^{58} +(-2.23629 + 2.23629i) q^{59} +(0.794490 + 0.794490i) q^{61} +(-0.631488 + 0.769706i) q^{62} +(-4.45055 - 6.64775i) q^{64} +(-11.1421 + 0.701060i) q^{65} -13.2598 q^{67} +(3.56972 - 5.34594i) q^{68} +(2.03207 + 12.4995i) q^{70} +10.8523 q^{71} +(-10.3838 - 10.3838i) q^{73} +(-6.88513 - 5.64875i) q^{74} +(2.29257 - 3.43330i) q^{76} +24.6936i q^{77} +4.49087 q^{79} +(8.02982 - 3.93980i) q^{80} +(0.692816 - 0.844457i) q^{82} -7.59721i q^{83} +(5.39105 + 4.75280i) q^{85} +(-5.30015 - 4.34839i) q^{86} +(16.6878 - 5.07038i) q^{88} +10.7447 q^{89} +(-14.1378 - 14.1378i) q^{91} +(-3.03226 - 2.02478i) q^{92} +(-0.896526 + 0.0884359i) q^{94} +(3.46227 + 3.05237i) q^{95} +(-0.751384 - 0.751384i) q^{97} +(-8.10594 + 9.88013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{13} + 10 q^{14} + 26 q^{16} - 12 q^{17} - 16 q^{19} + 4 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 20 q^{26} + 22 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 2 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^13 + 10 * q^14 + 26 * q^16 - 12 * q^17 - 16 * q^19 + 4 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 20 * q^26 + 22 * q^28 - 12 * q^32 - 6 * q^34 + 12 * q^35 + 24 * q^37 + 22 * q^38 - 10 * q^40 - 8 * q^43 + 22 * q^44 - 18 * q^46 + 18 * q^50 + 24 * q^52 - 4 * q^55 + 26 * q^56 - 2 * q^58 - 16 * q^59 - 12 * q^61 - 12 * q^62 - 26 * q^64 - 4 * q^65 - 16 * q^67 + 2 * q^68 - 10 * q^70 + 20 * q^73 - 8 * q^74 + 26 * q^76 - 48 * q^79 + 16 * q^80 + 80 * q^82 + 4 * q^85 - 4 * q^86 + 94 * q^88 + 40 * q^89 - 24 * q^91 + 30 * q^92 - 58 * q^94 - 72 * q^95 - 28 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.09334	+	0.897004i	0.773106	+	0.634277i
$2$	1.09334	+	0.897004i	0.773106	+	0.634277i
$3$		0			0
$3$		0			0
$4$	0.390769	+	1.96145i	0.195385	+	0.980727i
$5$	−2.23165	+	0.140415i	−0.998026	+	0.0627957i
$5$	−2.23165	+	0.140415i	−0.998026	+	0.0627957i
$6$		0			0
$7$	−2.83167	−	2.83167i	−1.07027	−	1.07027i	−0.997337	−	0.0729328i	$-0.976764\pi$
$7$	−2.83167	−	2.83167i	−1.07027	−	1.07027i	−0.0729328	−	0.997337i	$-0.523236\pi$
$8$	−1.33219	+	2.49505i	−0.471000	+	0.882133i
$9$		0			0
$10$	−2.56590	−	1.84828i	−0.811410	−	0.584478i
$11$	−4.36026	−	4.36026i	−1.31467	−	1.31467i	−0.917933	−	0.396736i	$-0.870143\pi$
$11$	−4.36026	−	4.36026i	−1.31467	−	1.31467i	−0.396736	−	0.917933i	$-0.629857\pi$
$12$		0			0
$13$	4.99276			1.38474			0.692371	−	0.721542i	$-0.256566\pi$
$13$	4.99276			1.38474			0.692371	+	0.721542i	$0.256566\pi$
$14$	−0.555949	−	5.63598i	−0.148584	−	1.50628i
$15$		0			0
$16$	−3.69460	+	1.53295i	−0.923650	+	0.383238i
$17$	−2.27272	−	2.27272i	−0.551215	−	0.551215i	0.375576	−	0.926791i	$-0.377445\pi$
$17$	−2.27272	−	2.27272i	−0.551215	−	0.551215i	−0.926791	+	0.375576i	$0.877445\pi$
$18$		0			0
$19$	−1.45960	−	1.45960i	−0.334855	−	0.334855i	0.519572	−	0.854427i	$-0.326091\pi$
$19$	−1.45960	−	1.45960i	−0.334855	−	0.334855i	−0.854427	+	0.519572i	$0.826091\pi$
$20$	−1.14748	−	4.32242i	−0.256584	−	0.966522i
$21$		0			0
$22$	−0.856063	−	8.67841i	−0.182513	−	1.85024i
$23$	−1.28911	+	1.28911i	−0.268797	+	0.268797i	−0.828615	−	0.559818i	$-0.810871\pi$
$23$	−1.28911	+	1.28911i	−0.268797	+	0.268797i	0.559818	+	0.828615i	$0.310871\pi$
$24$		0			0
$25$	4.96057	−	0.626717i	0.992113	−	0.125343i
$26$	5.45876	+	4.47852i	1.07055	+	0.878310i
$27$		0			0
$28$	4.44766	−	6.66071i	0.840528	−	1.25876i
$29$	−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	$0.290473\pi$
$30$		0			0
$31$			0.703997i			0.126442i	0.998000	+	0.0632208i	$0.0201372\pi$
$31$			0.703997i			0.126442i	−0.998000	+	0.0632208i	$0.979863\pi$
$32$	−5.41450	−	1.63804i	−0.957158	−	0.289567i
$33$		0			0
$34$	−0.446209	−	4.52348i	−0.0765242	−	0.775771i
$35$	6.71691	+	5.92169i	1.13537	+	1.00095i
$36$		0			0
$37$	−6.29736			−1.03528			−0.517640	−	0.855599i	$-0.673189\pi$
$37$	−6.29736			−1.03528			−0.517640	+	0.855599i	$0.673189\pi$
$38$	−0.286567	−	2.90509i	−0.0464873	−	0.471269i
$39$		0			0
$40$	2.62264	−	5.75515i	0.414676	−	0.909969i
$41$		−	0.772367i		−	0.120624i	−0.998180	−	0.0603118i	$-0.980791\pi$
$41$		−	0.772367i		−	0.120624i	0.998180	−	0.0603118i	$-0.0192095\pi$
$42$		0			0
$43$	−4.84769			−0.739265			−0.369633	−	0.929178i	$-0.620516\pi$
$43$	−4.84769			−0.739265			−0.369633	+	0.929178i	$0.620516\pi$
$44$	6.84860	−	10.2563i	1.03246	−	1.54620i
$45$		0			0
$46$	−2.56576	+	0.253094i	−0.378301	+	0.0373166i
$47$	−0.450439	+	0.450439i	−0.0657033	+	0.0657033i	−0.739195	−	0.673492i	$-0.764794\pi$
$47$	−0.450439	+	0.450439i	−0.0657033	+	0.0657033i	0.673492	+	0.739195i	$0.264794\pi$
$48$		0			0
$49$			9.03668i			1.29095i
$50$	5.98574	+	3.76443i	0.846511	+	0.532371i
$51$		0			0
$52$	1.95101	+	9.79306i	0.270557	+	1.35805i
$53$			4.17849i			0.573959i	0.957937	+	0.286980i	$0.0926512\pi$
$53$			4.17849i			0.573959i	−0.957937	+	0.286980i	$0.907349\pi$
$54$		0			0
$55$	10.3428	+	9.11835i	1.39463	+	1.22952i
$56$	10.8375	−	3.29284i	1.44822	−	0.440024i
$57$		0			0
$58$	−1.92213	+	0.189604i	−0.252388	+	0.0248962i
$59$	−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	0.756137	−	0.654413i	$-0.227084\pi$
$61$	0.794490	+	0.794490i	0.101724	+	0.101724i	−0.654413	+	0.756137i	$0.727084\pi$
$62$	−0.631488	+	0.769706i	−0.0801991	+	0.0977528i
$63$		0			0
$64$	−4.45055	−	6.64775i	−0.556318	−	0.830969i
$65$	−11.1421	+	0.701060i	−1.38201	+	0.0869558i
$66$		0			0
$67$	−13.2598			−1.61994			−0.809971	−	0.586470i	$-0.800517\pi$
$67$	−13.2598			−1.61994			−0.809971	+	0.586470i	$0.800517\pi$
$68$	3.56972	−	5.34594i	0.432893	−	0.648290i
$69$		0			0
$70$	2.03207	+	12.4995i	0.242878	+	1.49398i
$71$	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	−0.969249	−	0.246083i	$-0.920857\pi$
$73$	−10.3838	−	10.3838i	−1.21533	−	1.21533i	−0.246083	−	0.969249i	$-0.579143\pi$
$74$	−6.88513	−	5.64875i	−0.800380	−	0.656654i
$75$		0			0
$76$	2.29257	−	3.43330i	0.262975	−	0.393826i
$77$			24.6936i			2.81410i
$78$		0			0
$79$	4.49087			0.505262			0.252631	−	0.967563i	$-0.418704\pi$
$79$	4.49087			0.505262			0.252631	+	0.967563i	$0.418704\pi$
$80$	8.02982	−	3.93980i	0.897761	−	0.440482i
$81$		0			0
$82$	0.692816	−	0.844457i	0.0765088	−	0.0932547i
$83$		−	7.59721i		−	0.833902i	−0.908929	−	0.416951i	$-0.863099\pi$
$83$		−	7.59721i		−	0.833902i	0.908929	−	0.416951i	$-0.136901\pi$
$84$		0			0
$85$	5.39105	+	4.75280i	0.584741	+	0.515513i
$86$	−5.30015	−	4.34839i	−0.571530	−	0.468899i
$87$		0			0
$88$	16.6878	−	5.07038i	1.77892	−	0.540504i
$89$	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
$92$	−3.03226	−	2.02478i	−0.316135	−	0.211098i
$93$		0			0
$94$	−0.896526	+	0.0884359i	−0.0924696	+	0.00912147i
$95$	3.46227	+	3.05237i	0.355221	+	0.313166i
$96$		0			0
$97$	−0.751384	−	0.751384i	−0.0762915	−	0.0762915i	0.667931	−	0.744223i	$-0.267180\pi$
$97$	−0.751384	−	0.751384i	−0.0762915	−	0.0762915i	−0.744223	+	0.667931i	$0.767180\pi$
$98$	−8.10594	+	9.88013i	−0.818823	+	0.998044i
$99$		0			0
$100$	3.16771	+	9.48502i	0.316771	+	0.948502i
$101$	−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	$-0.872388\pi$
$103$	−5.38356	+	5.38356i	−0.530458	+	0.530458i	0.390250	+	0.920709i	$0.372388\pi$
$104$	−6.65129	+	12.4572i	−0.652213	+	1.22153i
$105$		0			0
$106$	−3.74812	+	4.56849i	−0.364049	+	0.443731i
$107$		−	11.9693i		−	1.15711i	−0.815642	−	0.578557i	$-0.803616\pi$
$107$		−	11.9693i		−	1.15711i	0.815642	−	0.578557i	$-0.196384\pi$
$108$		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	$0.164579\pi$
$110$	3.12902	+	19.2470i	0.298340	+	1.83513i
$111$		0			0
$112$	14.8027	+	6.12107i	1.39872	+	0.578387i
$113$	9.13854	−	9.13854i	0.859681	−	0.859681i	−0.131619	−	0.991300i	$-0.542018\pi$
$113$	9.13854	−	9.13854i	0.859681	−	0.859681i	0.991300	+	0.131619i	$0.0420176\pi$
$114$		0			0
$115$	2.69583	−	3.05785i	0.251387	−	0.285146i
$116$	−2.27161	−	1.51685i	−0.210913	−	0.140836i
$117$		0			0
$118$	−4.45097	+	0.439057i	−0.409745	+	0.0404184i
$119$			12.8712i			1.17990i
$120$		0			0
$121$			27.0238i			2.45671i
$122$	0.155984	+	1.58130i	0.0141222	+	0.143165i
$123$		0			0
$124$	−1.38086	+	0.275100i	−0.124005	+	0.0247047i
$125$	−10.9823	+	2.09516i	−0.982284	+	0.187397i
$126$		0			0
$127$	15.5561	−	15.5561i	1.38038	−	1.38038i	0.536451	−	0.843931i	$-0.319765\pi$
$127$	15.5561	−	15.5561i	1.38038	−	1.38038i	0.843931	−	0.536451i	$-0.180235\pi$
$128$	1.09712	−	11.2604i	0.0969723	−	0.995287i
$129$		0			0
$130$	−12.8109	−	9.22802i	−1.12359	−	0.809351i
$131$	−14.4207	+	14.4207i	−1.25994	+	1.25994i	−0.308818	+	0.951121i	$0.599933\pi$
$131$	−14.4207	+	14.4207i	−1.25994	+	1.25994i	−0.951121	+	0.308818i	$0.900067\pi$
$132$		0			0
$133$			8.26619i			0.716769i
$134$	−14.4974	−	11.8941i	−1.25239	−	1.02749i
$135$		0			0
$136$	8.69824	−	2.64286i	0.745868	−	0.226623i
$137$	3.54735	−	3.54735i	0.303071	−	0.303071i	−0.539143	−	0.842214i	$-0.681252\pi$
$137$	3.54735	−	3.54735i	0.303071	−	0.303071i	0.842214	+	0.539143i	$0.181252\pi$
$138$		0			0
$139$	4.17152	−	4.17152i	0.353824	−	0.353824i	−0.507706	−	0.861530i	$-0.669506\pi$
$139$	4.17152	−	4.17152i	0.353824	−	0.353824i	0.861530	+	0.507706i	$0.169506\pi$
$140$	−8.99037	+	15.4889i	−0.759825	+	1.30905i
$141$		0			0
$142$	11.8652	+	9.73458i	0.995709	+	0.816908i
$143$	−21.7697	−	21.7697i	−1.82048	−	1.82048i
$144$		0			0
$145$	2.01957	−	2.29077i	0.167716	−	0.190238i
$146$	−2.03868	−	20.6673i	−0.168722	−	1.71044i
$147$		0			0
$148$	−2.46081	−	12.3520i	−0.202278	−	1.01533i
$149$	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	$0.587803\pi$
$150$		0			0
$151$	4.96999			0.404452			0.202226	−	0.979339i	$-0.435182\pi$
$151$	4.96999			0.404452			0.202226	+	0.979339i	$0.435182\pi$
$152$	5.58623	−	1.69731i	0.453103	−	0.137670i
$153$		0			0
$154$	−22.1503	+	26.9984i	−1.78492	+	2.17560i
$155$	−0.0988521	−	1.57108i	−0.00793999	−	0.126192i
$156$		0			0
$157$			14.4628i			1.15426i	0.816653	+	0.577129i	$0.195827\pi$
$157$			14.4628i			1.15426i	−0.816653	+	0.577129i	$0.804173\pi$
$158$	4.91003	+	4.02833i	0.390621	+	0.320476i
$159$		0			0
$160$	12.3133	+	2.89526i	0.973452	+	0.228890i
$161$	7.30064			0.575371
$162$		0			0
$163$		−	7.70573i		−	0.603559i	−0.953378	−	0.301779i	$-0.902419\pi$
$163$		−	7.70573i		−	0.603559i	0.953378	−	0.301779i	$-0.0975806\pi$
$164$	1.51496	−	0.301817i	0.118299	−	0.0235680i
$165$		0			0
$166$	6.81472	−	8.30630i	0.528925	−	0.644694i
$167$	−4.64125	−	4.64125i	−0.359150	−	0.359150i	0.504349	−	0.863500i	$-0.331732\pi$
$167$	−4.64125	−	4.64125i	−0.359150	−	0.359150i	−0.863500	+	0.504349i	$0.831732\pi$
$168$		0			0
$169$	11.9276			0.917509
$170$	1.63095	+	10.0322i	0.125088	+	0.769434i
$171$		0			0
$172$	−1.89433	−	9.50851i	−0.144441	−	0.725017i
$173$	23.9562			1.82136			0.910679	−	0.413114i	$-0.135559\pi$
$173$	23.9562			1.82136			0.910679	+	0.413114i	$0.135559\pi$
$174$		0			0
$175$	−15.8213	−	12.2720i	−1.19598	−	0.927678i
$176$	22.7935	+	9.42536i	1.71812	+	0.710463i
$177$		0			0
$178$	11.7475	+	9.63802i	0.880516	+	0.722400i
$179$	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	−0.916601	−	0.399802i	$-0.869079\pi$
$181$	−6.95282	+	6.95282i	−0.516799	+	0.516799i	0.399802	+	0.916601i	$0.369079\pi$
$182$	−2.77572	−	28.1391i	−0.205750	−	2.08581i
$183$		0			0
$184$	−1.49905	−	4.93372i	−0.110512	−	0.363718i
$185$	14.0535	−	0.884246i	1.03324	−	0.0650111i
$186$		0			0
$187$			19.8193i			1.44933i
$188$	−1.05953	−	0.707497i	−0.0772743	−	0.0515995i
$189$		0			0
$190$	1.04744	+	6.44293i	0.0759892	+	0.467419i
$191$		−	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	−0.728773	−	0.684755i	$-0.759909\pi$
$193$	−0.611510	+	0.611510i	−0.0440175	+	0.0440175i	0.684755	+	0.728773i	$0.259909\pi$
$194$	−0.147521	−	1.49551i	−0.0105914	−	0.107371i
$195$		0			0
$196$	−17.7250	+	3.53125i	−1.26607	+	0.252232i
$197$	−12.6372			−0.900363			−0.450182	−	0.892937i	$-0.648641\pi$
$197$	−12.6372			−0.900363			−0.450182	+	0.892937i	$0.648641\pi$
$198$		0			0
$199$			10.0036i			0.709134i	0.935031	+	0.354567i	$0.115372\pi$
$199$			10.0036i			0.709134i	−0.935031	+	0.354567i	$0.884628\pi$
$200$	−5.04472	+	13.2118i	−0.356716	+	0.934213i
$201$		0			0
$202$	−10.5499	+	1.04067i	−0.742285	+	0.0732211i
$203$	5.46924			0.383865
$204$		0			0
$205$	0.108452	+	1.72366i	0.00757464	+	0.120385i
$206$	−10.7151	+	1.05697i	−0.746558	+	0.0736426i
$207$		0			0
$208$	−18.4462	+	7.65365i	−1.27902	+	0.530685i
$209$			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	$0.0940405\pi$
$212$	−8.19591	+	1.63282i	−0.562897	+	0.112143i
$213$		0			0
$214$	10.7365	−	13.0865i	0.733932	−	0.894572i
$215$	10.8184	−	0.680690i	0.737806	−	0.0464227i
$216$		0			0
$217$	1.99349	−	1.99349i	0.135327	−	0.135327i
$218$	7.79189	−	0.768614i	0.527734	−	0.0520571i
$219$		0			0
$220$	−13.8436	+	23.8502i	−0.933333	+	1.60798i
$221$	−11.3471	−	11.3471i	−0.763291	−	0.763291i
$222$		0			0
$223$	−4.29237	−	4.29237i	−0.287438	−	0.287438i	0.548628	−	0.836067i	$-0.315150\pi$
$223$	−4.29237	−	4.29237i	−0.287438	−	0.287438i	−0.836067	+	0.548628i	$0.815150\pi$
$224$	10.6937	+	19.9704i	0.714502	+	1.33433i
$225$		0			0
$226$	18.1888	−	1.79419i	1.20990	−	0.119348i
$227$	−13.2703			−0.880778			−0.440389	−	0.897807i	$-0.645159\pi$
$227$	−13.2703			−0.880778			−0.440389	+	0.897807i	$0.645159\pi$
$228$		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	$0.928931\pi$
$230$	5.69035	−	0.925090i	0.375211	−	0.0609986i
$231$		0			0
$232$	−1.12301	−	3.69607i	−0.0737290	−	0.242659i
$233$	−8.19734	−	8.19734i	−0.537026	−	0.537026i	0.385629	−	0.922654i	$-0.373985\pi$
$233$	−8.19734	−	8.19734i	−0.537026	−	0.537026i	−0.922654	+	0.385629i	$0.873985\pi$
$234$		0			0
$235$	0.941975	−	1.06847i	0.0614477	−	0.0696995i
$236$	−5.26025	−	3.51250i	−0.342413	−	0.228644i
$237$		0			0
$238$	−11.5455	+	14.0725i	−0.748382	+	0.912186i
$239$	10.6504			0.688915			0.344458	−	0.938802i	$-0.388063\pi$
$239$	10.6504			0.688915			0.344458	+	0.938802i	$0.388063\pi$
$240$		0			0
$241$	−1.22690			−0.0790315			−0.0395157	−	0.999219i	$-0.512582\pi$
$241$	−1.22690			−0.0790315			−0.0395157	+	0.999219i	$0.512582\pi$
$242$	−24.2404	+	29.5461i	−1.55823	+	1.89929i
$243$		0			0
$244$	−1.24789	+	1.86882i	−0.0798881	+	0.119639i
$245$	−1.26889	−	20.1668i	−0.0810664	−	1.28841i
$246$		0			0
$247$	−7.28741	−	7.28741i	−0.463687	−	0.463687i
$248$	−1.75651	−	0.937857i	−0.111538	−	0.0595540i
$249$		0			0
$250$	−13.8867	−	7.56043i	−0.878271	−	0.478163i
$251$	11.5822	+	11.5822i	0.731061	+	0.731061i	0.970830	−	0.239769i	$-0.0770717\pi$
$251$	11.5822	+	11.5822i	0.731061	+	0.731061i	−0.239769	+	0.970830i	$0.577072\pi$
$252$		0			0
$253$	11.2417			0.706759
$254$	30.9620	−	3.05418i	1.94273	−	0.191636i
$255$		0			0
$256$	11.3001	−	11.3273i	0.706258	−	0.707955i
$257$	−5.72342	−	5.72342i	−0.357017	−	0.357017i	0.505695	−	0.862712i	$-0.331236\pi$
$257$	−5.72342	−	5.72342i	−0.357017	−	0.357017i	−0.862712	+	0.505695i	$0.831236\pi$
$258$		0			0
$259$	17.8320	+	17.8320i	1.10803	+	1.10803i
$260$	−5.72909	−	21.5808i	−0.355303	−	1.33838i
$261$		0			0
$262$	−28.7020	+	2.83125i	−1.77322	+	0.174915i
$263$	−6.70033	+	6.70033i	−0.413160	+	0.413160i	−0.882838	−	0.469678i	$-0.844370\pi$
$263$	−6.70033	+	6.70033i	−0.413160	+	0.413160i	0.469678	+	0.882838i	$0.344370\pi$
$264$		0			0
$265$	−0.586724	−	9.32494i	−0.0360422	−	0.572826i
$266$	−7.41480	+	9.03772i	−0.454631	+	0.554138i
$267$		0			0
$268$	−5.18152	−	26.0085i	−0.316512	−	1.58872i
$269$	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	$0.235101\pi$
$270$		0			0
$271$		−	3.21705i		−	0.195422i	−0.995215	−	0.0977108i	$-0.968848\pi$
$271$		−	3.21705i		−	0.195422i	0.995215	−	0.0977108i	$-0.0311520\pi$
$272$	11.8807	+	4.91282i	0.720376	+	0.297883i
$273$		0			0
$274$	7.06044	−	0.696462i	0.426537	−	0.0420748i
$275$	−24.3620	−	18.8967i	−1.46909	−	1.13952i
$276$		0			0
$277$	−28.2079			−1.69485			−0.847425	−	0.530915i	$-0.821848\pi$
$277$	−28.2079			−1.69485			−0.847425	+	0.530915i	$0.821848\pi$
$278$	8.30275	−	0.819007i	0.497966	−	0.0491208i
$279$		0			0
$280$	−23.7231	+	8.87022i	−1.41773	+	0.530097i
$281$		−	24.5928i		−	1.46709i	−0.679643	−	0.733543i	$-0.737865\pi$
$281$		−	24.5928i		−	1.46709i	0.679643	−	0.733543i	$-0.262135\pi$
$282$		0			0
$283$	15.0862			0.896779			0.448390	−	0.893838i	$-0.351998\pi$
$283$	15.0862			0.896779			0.448390	+	0.893838i	$0.351998\pi$
$284$	4.24075	+	21.2863i	0.251642	+	1.26311i
$285$		0			0
$286$	−4.27411	−	43.3292i	−0.252734	−	2.56211i
$287$	−2.18709	+	2.18709i	−0.129100	+	0.129100i
$288$		0			0
$289$		−	6.66950i		−	0.392324i
$290$	4.26290	−	0.693027i	0.250326	−	0.0406959i
$291$		0			0
$292$	16.3097	−	24.4250i	0.954451	−	1.42936i
$293$			3.49295i			0.204060i	0.994781	+	0.102030i	$0.0325338\pi$
$293$			3.49295i			0.204060i	−0.994781	+	0.102030i	$0.967466\pi$
$294$		0			0
$295$	4.67661	−	5.30463i	0.272283	−	0.308848i
$296$	8.38927	−	15.7122i	0.487616	−	0.913254i
$297$		0			0
$298$	1.65324	+	16.7598i	0.0957695	+	0.970871i
$299$	−6.43619	+	6.43619i	−0.372215	+	0.372215i
$300$		0			0
$301$	13.7270	+	13.7270i	0.791213	+	0.791213i
$302$	5.43387	+	4.45810i	0.312684	+	0.256535i
$303$		0			0
$304$	7.63012	+	3.15514i	0.437617	+	0.180959i
$305$	−1.88458	−	1.66147i	−0.107911	−	0.0951354i
$306$		0			0
$307$	−7.81653			−0.446113			−0.223056	−	0.974806i	$-0.571603\pi$
$307$	−7.81653			−0.446113			−0.223056	+	0.974806i	$0.571603\pi$
$308$	−48.4354	+	9.64950i	−2.75986	+	0.549832i
$309$		0			0
$310$	1.30119	−	1.80639i	0.0739023	−	0.102596i
$311$	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	$-0.123877\pi$
$313$	9.65621	+	9.65621i	0.545802	+	0.545802i	−0.379422	+	0.925224i	$0.623877\pi$
$314$	−12.9732	+	15.8127i	−0.732119	+	0.892363i
$315$		0			0
$316$	1.75489	+	8.80863i	0.0987204	+	0.495524i
$317$			10.5517i			0.592642i	0.955088	+	0.296321i	$0.0957599\pi$
$317$			10.5517i			0.592642i	−0.955088	+	0.296321i	$0.904240\pi$
$318$		0			0
$319$	8.42165			0.471522
$320$	10.8655	+	14.2106i	0.607402	+	0.794395i
$321$		0			0
$322$	7.98206	+	6.54870i	0.444823	+	0.364945i
$323$			6.63451i			0.369154i
$324$		0			0
$325$	24.7669	−	3.12905i	1.37382	−	0.173568i
$326$	6.91206	−	8.42495i	0.382824	−	0.466615i
$327$		0			0
$328$	1.92710	+	1.02894i	0.106406	+	0.0568137i
$329$	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	$0.744469\pi$
$332$	14.9016	−	2.96875i	0.817830	−	0.162931i
$333$		0			0
$334$	−0.911229	−	9.23766i	−0.0498602	−	0.505462i
$335$	29.5913	−	1.86188i	1.61675	−	0.101725i
$336$		0			0
$337$	4.17945	+	4.17945i	0.227669	+	0.227669i	0.811718	−	0.584049i	$-0.198532\pi$
$337$	4.17945	+	4.17945i	0.227669	+	0.227669i	−0.584049	+	0.811718i	$0.698532\pi$
$338$	13.0409	+	10.6991i	0.709331	+	0.581955i
$339$		0			0
$340$	−7.21574	+	12.4315i	−0.391328	+	0.674195i
$341$	3.06961	−	3.06961i	0.166229	−	0.166229i
$342$		0			0
$343$	5.76720	−	5.76720i	0.311400	−	0.311400i
$344$	6.45804	−	12.0952i	0.348194	−	0.652131i
$345$		0			0
$346$	26.1922	+	21.4888i	1.40810	+	1.15525i
$347$		−	30.4793i		−	1.63622i	−0.575064	−	0.818108i	$-0.695023\pi$
$347$		−	30.4793i		−	1.63622i	0.575064	−	0.818108i	$-0.304977\pi$
$348$		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	$0.882935\pi$
$350$	−6.28999	−	27.6092i	−0.336214	−	1.47578i
$351$		0			0
$352$	16.4664	+	30.7509i	0.877661	+	1.63903i
$353$	17.3084	−	17.3084i	0.921233	−	0.921233i	−0.0758833	−	0.997117i	$-0.524178\pi$
$353$	17.3084	−	17.3084i	0.921233	−	0.921233i	0.997117	+	0.0758833i	$0.0241777\pi$
$354$		0			0
$355$	−24.2186	+	1.52383i	−1.28539	+	0.0808767i
$356$	4.19869	+	21.0752i	0.222530	+	1.11698i
$357$		0			0
$358$	0.256655	+	2.60186i	0.0135646	+	0.137513i
$359$		−	29.4403i		−	1.55380i	−0.629626	−	0.776899i	$-0.716792\pi$
$359$		−	29.4403i		−	1.55380i	0.629626	−	0.776899i	$-0.283208\pi$
$360$		0			0
$361$		−	14.7392i		−	0.775745i
$362$	−13.8385	+	1.36507i	−0.727335	+	0.0717463i
$363$		0			0
$364$	22.2061	−	33.2553i	1.16391	−	1.74305i
$365$	24.6311	+	21.7150i	1.28925	+	1.13662i
$366$		0			0
$367$	−10.7678	+	10.7678i	−0.562076	+	0.562076i	−0.929897	−	0.367821i	$-0.880104\pi$
$367$	−10.7678	+	10.7678i	−0.562076	+	0.562076i	0.367821	+	0.929897i	$0.380104\pi$
$368$	2.78659	−	6.73887i	0.145261	−	0.351288i
$369$		0			0
$370$	16.1584	+	11.6393i	0.840036	+	0.605098i
$371$	11.8321	−	11.8321i	0.614291	−	0.614291i
$372$		0			0
$373$		−	32.1031i		−	1.66223i	−0.556098	−	0.831117i	$-0.687702\pi$
$373$		−	32.1031i		−	1.66223i	0.556098	−	0.831117i	$-0.312298\pi$
$374$	−17.7780	+	21.6692i	−0.919278	+	1.12049i
$375$		0			0
$376$	−0.523798	−	1.72394i	−0.0270128	−	0.0889052i
$377$	−4.82164	+	4.82164i	−0.248327	+	0.248327i
$378$		0			0
$379$	23.3329	−	23.3329i	1.19853	−	1.19853i	0.223923	−	0.974607i	$-0.428113\pi$
$379$	23.3329	−	23.3329i	1.19853	−	1.19853i	0.974607	−	0.223923i	$-0.0718865\pi$
$380$	−4.63413	+	7.98385i	−0.237726	+	0.409563i
$381$		0			0
$382$	2.17673	−	2.65316i	0.111371	−	0.135747i
$383$	7.02280	+	7.02280i	0.358848	+	0.358848i	0.863388	−	0.504540i	$-0.168338\pi$
$383$	7.02280	+	7.02280i	0.358848	+	0.358848i	−0.504540	+	0.863388i	$0.668338\pi$
$384$		0			0
$385$	−3.46737	−	55.1077i	−0.176713	−	2.80855i
$386$	−1.21711	+	0.120060i	−0.0619495	+	0.00611087i
$387$		0			0
$388$	1.18019	−	1.76742i	0.0599149	−	0.0897273i
$389$	−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	$-0.558665\pi$
$390$		0			0
$391$	5.85955			0.296330
$392$	−22.5470	−	12.0386i	−1.13879	−	0.608039i
$393$		0			0
$394$	−13.8167	−	11.3356i	−0.696076	−	0.571080i
$395$	−10.0221	+	0.630587i	−0.504265	+	0.0317283i
$396$		0			0
$397$		−	25.0560i		−	1.25753i	−0.777597	−	0.628763i	$-0.783562\pi$
$397$		−	25.0560i		−	1.25753i	0.777597	−	0.628763i	$-0.216438\pi$
$398$	−8.97323	+	10.9373i	−0.449788	+	0.548235i
$399$		0			0
$400$	−17.3666	+	9.91977i	−0.868329	+	0.495989i
$401$	−6.21757			−0.310491			−0.155245	−	0.987876i	$-0.549617\pi$
$401$	−6.21757			−0.310491			−0.155245	+	0.987876i	$0.549617\pi$
$402$		0			0
$403$			3.51489i			0.175089i
$404$	−12.4680	−	8.32546i	−0.620308	−	0.414207i
$405$		0			0
$406$	5.97972	+	4.90593i	0.296768	+	0.243477i
$407$	27.4581	+	27.4581i	1.36105	+	1.36105i
$408$		0			0
$409$	−13.1629			−0.650865			−0.325432	−	0.945565i	$-0.605510\pi$
$409$	−13.1629			−0.650865			−0.325432	+	0.945565i	$0.605510\pi$
$410$	−1.42755	+	1.98182i	−0.0705018	+	0.0978751i
$411$		0			0
$412$	−12.6633	−	8.45588i	−0.623878	−	0.416591i
$413$	12.6648			0.623196
$414$		0			0
$415$	1.06676	+	16.9543i	0.0523654	+	0.832256i
$416$	−27.0333	−	8.17833i	−1.32542	−	0.400975i
$417$		0			0
$418$	−11.4175	+	13.9165i	−0.558447	+	0.680677i
$419$	−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	−0.156764	−	0.987636i	$-0.550106\pi$
$421$	17.0481	−	17.0481i	0.830872	−	0.830872i	0.987636	+	0.156764i	$0.0501063\pi$
$422$	19.2410	−	1.89799i	0.936637	−	0.0923926i
$423$		0			0
$424$	−10.4255	−	5.56653i	−0.506309	−	0.270335i
$425$	−12.6983	−	9.84962i	−0.615959	−	0.477777i
$426$		0			0
$427$		−	4.49946i		−	0.217744i
$428$	23.4772	−	4.67723i	1.13481	−	0.226082i
$429$		0			0
$430$	12.4387	+	8.95989i	0.599847	+	0.432084i
$431$			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	−0.897131	−	0.441764i	$-0.854353\pi$
$433$	−9.47558	+	9.47558i	−0.455368	+	0.455368i	0.441764	+	0.897131i	$0.354353\pi$
$434$	3.96772	−	0.391387i	0.190456	−	0.0187872i
$435$		0			0
$436$	9.20861	+	6.14900i	0.441012	+	0.294484i
$437$	3.76315			0.180016
$438$		0			0
$439$		−	21.7937i		−	1.04016i	−0.854119	−	0.520078i	$-0.825903\pi$
$439$		−	21.7937i		−	1.04016i	0.854119	−	0.520078i	$-0.174097\pi$
$440$	−36.5294	+	13.6586i	−1.74147	+	0.651146i
$441$		0			0
$442$	−2.22781	−	22.5846i	−0.105966	−	1.07424i
$443$	−26.2733			−1.24828			−0.624141	−	0.781312i	$-0.714551\pi$
$443$	−26.2733			−1.24828			−0.624141	+	0.781312i	$0.714551\pi$
$444$		0			0
$445$	−23.9784	+	1.50872i	−1.13669	+	0.0715201i
$446$	−0.842733	−	8.54328i	−0.0399046	−	0.404536i
$447$		0			0
$448$	−6.22176	+	31.4267i	−0.293951	+	1.48477i
$449$			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
$452$	21.4959	+	14.3538i	1.01108	+	0.675144i
$453$		0			0
$454$	−14.5088	−	11.9035i	−0.680934	−	0.558657i
$455$	33.5359	+	29.5656i	1.57219	+	1.38606i
$456$		0			0
$457$	18.2488	−	18.2488i	0.853641	−	0.853641i	−0.136938	−	0.990580i	$-0.543726\pi$
$457$	18.2488	−	18.2488i	0.853641	−	0.853641i	0.990580	+	0.136938i	$0.0437262\pi$
$458$	−2.23946	−	22.7027i	−0.104643	−	1.06083i
$459$		0			0
$460$	7.05128	+	4.09283i	0.328768	+	0.190829i
$461$	−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	0.429057	−	0.903277i	$-0.358846\pi$
$463$	−10.2040	−	10.2040i	−0.474220	−	0.474220i	−0.903277	+	0.429057i	$0.858846\pi$
$464$	2.08756	−	5.04839i	0.0969127	−	0.234366i
$465$		0			0
$466$	−1.60941	−	16.3155i	−0.0745543	−	0.755801i
$467$	−24.2696			−1.12306			−0.561532	−	0.827455i	$-0.689788\pi$
$467$	−24.2696			−1.12306			−0.561532	+	0.827455i	$0.689788\pi$
$468$		0			0
$469$	37.5473	+	37.5473i	1.73378	+	1.73378i
$470$	1.98832	−	0.323245i	0.0917143	−	0.0149102i
$471$		0			0
$472$	−2.60049	−	8.55881i	−0.119697	−	0.393951i
$473$	21.1372	+	21.1372i	0.971889	+	0.971889i
$474$		0			0
$475$	−8.15518	−	6.32567i	−0.374186	−	0.290242i
$476$	−25.2462	+	5.02965i	−1.15716	+	0.230534i
$477$		0			0
$478$	11.6444	+	9.55342i	0.532604	+	0.436963i
$479$	25.0894			1.14636			0.573182	−	0.819428i	$-0.305709\pi$
$479$	25.0894			1.14636			0.573182	+	0.819428i	$0.305709\pi$
$480$		0			0
$481$	−31.4412			−1.43359
$482$	−1.34141	−	1.10053i	−0.0610997	−	0.0501279i
$483$		0			0
$484$	−53.0059	+	10.5601i	−2.40936	+	0.480003i
$485$	1.78234	+	1.57132i	0.0809317	+	0.0713502i
$486$		0			0
$487$	−0.369801	−	0.369801i	−0.0167573	−	0.0167573i	0.698679	−	0.715436i	$-0.253772\pi$
$487$	−0.369801	−	0.369801i	−0.0167573	−	0.0167573i	−0.715436	+	0.698679i	$0.753772\pi$
$488$	−3.04070	+	0.923881i	−0.137646	+	0.0418221i
$489$		0			0
$490$	16.7023	−	23.1872i	0.754534	−	1.04749i
$491$	19.2802	+	19.2802i	0.870104	+	0.870104i	0.992483	−	0.122379i	$-0.0390524\pi$
$491$	19.2802	+	19.2802i	0.870104	+	0.870104i	−0.122379	+	0.992483i	$0.539052\pi$
$492$		0			0
$493$	4.38966			0.197700
$494$	−1.43076	−	14.5044i	−0.0643729	−	0.652585i
$495$		0			0
$496$	−1.07919	−	2.60099i	−0.0484572	−	0.116788i
$497$	−30.7302	−	30.7302i	−1.37844	−	1.37844i
$498$		0			0
$499$	17.1262	+	17.1262i	0.766673	+	0.766673i	0.977519	−	0.210847i	$-0.0676220\pi$
$499$	17.1262	+	17.1262i	0.766673	+	0.766673i	−0.210847	+	0.977519i	$0.567622\pi$
$500$	−8.40109	−	20.7225i	−0.375708	−	0.926738i
$501$		0			0
$502$	2.27396	+	23.0525i	0.101492	+	1.02888i
$503$	−5.60127	+	5.60127i	−0.249748	+	0.249748i	−0.820867	−	0.571119i	$-0.806509\pi$
$503$	−5.60127	+	5.60127i	−0.249748	+	0.249748i	0.571119	+	0.820867i	$0.306509\pi$
$504$		0			0
$505$	11.0847	−	12.5732i	0.493262	−	0.559501i
$506$	12.2909	+	10.0838i	0.546399	+	0.448281i
$507$		0			0
$508$	36.5915	+	24.4338i	1.62348	+	1.08407i
$509$	−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	$0.250874\pi$
$510$		0			0
$511$			58.8069i			2.60146i
$512$	22.5154	−	2.24827i	0.995052	−	0.0993604i
$513$		0			0
$514$	−1.12369	−	11.3915i	−0.0495640	−	0.502459i
$515$	11.2583	−	12.7702i	0.496101	−	0.562722i
$516$		0			0
$517$	3.92806			0.172756
$518$	3.50101	+	35.4918i	0.153826	+	1.55942i
$519$		0			0
$520$	13.0942	−	28.7341i	0.574219	−	1.26007i
$521$			0.327549i			0.0143502i	0.999974	+	0.00717509i	$0.00228392\pi$
$521$			0.327549i			0.0143502i	−0.999974	+	0.00717509i	$0.997716\pi$
$522$		0			0
$523$	−21.8823			−0.956847			−0.478423	−	0.878129i	$-0.658792\pi$
$523$	−21.8823			−0.956847			−0.478423	+	0.878129i	$0.658792\pi$
$524$	−33.9206	−	22.6503i	−1.48183	−	0.989483i
$525$		0			0
$526$	−13.3359	+	1.31549i	−0.581474	+	0.0573582i
$527$	1.59999	−	1.59999i	0.0696966	−	0.0696966i
$528$		0			0
$529$			19.6764i			0.855496i
$530$	7.72302	−	10.7216i	0.335466	−	0.465716i
$531$		0			0
$532$	−16.2137	+	3.23017i	−0.702955	+	0.140046i
$533$		−	3.85624i		−	0.167032i
$534$		0			0
$535$	1.68067	+	26.7113i	0.0726618	+	1.15483i
$536$	17.6646	−	33.0839i	0.762993	−	1.42901i
$537$		0			0
$538$	2.16005	−	0.213073i	0.0931264	−	0.00918625i
$539$	39.4023	−	39.4023i	1.69718	−	1.69718i
$540$		0			0
$541$	−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	$0.983007\pi$
$542$	2.88570	−	3.51731i	0.123951	−	0.151082i
$543$		0			0
$544$	8.58284	+	16.0284i	0.367986	+	0.687214i
$545$	−8.18690	+	9.28631i	−0.350688	+	0.397782i
$546$		0			0
$547$	−28.9503			−1.23783			−0.618913	−	0.785459i	$-0.712427\pi$
$547$	−28.9503			−1.23783			−0.618913	+	0.785459i	$0.712427\pi$
$548$	8.34416	+	5.57177i	0.356445	+	0.238014i
$549$		0			0
$550$	−9.68546	−	42.5133i	−0.412990	−	1.81277i
$551$	2.81915			0.120100
$552$		0			0
$553$	−12.7167	−	12.7167i	−0.540767	−	0.540767i
$554$	−30.8408	−	25.3026i	−1.31030	−	1.07500i
$555$		0			0
$556$	9.81235	+	6.55215i	0.416136	+	0.277873i
$557$		−	8.55746i		−	0.362591i	−0.983429	−	0.181296i	$-0.941971\pi$
$557$		−	8.55746i		−	0.362591i	0.983429	−	0.181296i	$-0.0580291\pi$
$558$		0			0
$559$	−24.2033			−1.02369
$560$	−33.8940	−	11.5816i	−1.43228	−	0.489412i
$561$		0			0
$562$	22.0599	−	26.8883i	0.930540	−	1.13421i
$563$			19.8277i			0.835637i	0.908530	+	0.417819i	$0.137205\pi$
$563$			19.8277i			0.835637i	−0.908530	+	0.417819i	$0.862795\pi$
$564$		0			0
$565$	−19.1109	+	21.6773i	−0.804000	+	0.911969i
$566$	16.4942	+	13.5323i	0.693305	+	0.568807i
$567$		0			0
$568$	−14.4573	+	27.0771i	−0.606617	+	1.13613i
$569$	−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	$0.801700\pi$
$572$	34.1934	−	51.2072i	1.42970	−	2.14108i
$573$		0			0
$574$	−4.35305	+	0.429397i	−0.181693	+	0.0179227i
$575$	−5.58679	+	7.20260i	−0.232985	+	0.300369i
$576$		0			0
$577$	11.0931	+	11.0931i	0.461811	+	0.461811i	0.899249	−	0.437438i	$-0.144114\pi$
$577$	11.0931	+	11.0931i	0.461811	+	0.461811i	−0.437438	+	0.899249i	$0.644114\pi$
$578$	5.98257	−	7.29201i	0.248842	−	0.303308i
$579$		0			0
$580$	5.28243	+	3.06613i	0.219341	+	0.127314i
$581$	−21.5128	+	21.5128i	−0.892500	+	0.892500i
$582$		0			0
$583$	18.2193	−	18.2193i	0.754566	−	0.754566i
$584$	39.7413	−	12.0749i	1.64451	−	0.499663i
$585$		0			0
$586$	−3.13319	+	3.81897i	−0.129431	+	0.157760i
$587$			0.0736360i			0.00303928i	0.999999	+	0.00151964i	$0.000483717\pi$
$587$			0.0736360i			0.00303928i	−0.999999	+	0.00151964i	$0.999516\pi$
$588$		0			0
$589$	1.02755	−	1.02755i	0.0423396	−	0.0423396i
$590$	9.87139	−	1.60481i	0.406399	−	0.0660689i
$591$		0			0
$592$	23.2662	−	9.65354i	0.956236	−	0.396758i
$593$	−25.1041	+	25.1041i	−1.03090	+	1.03090i	−0.0313952	+	0.999507i	$0.509995\pi$
$593$	−25.1041	+	25.1041i	−1.03090	+	1.03090i	−0.999507	+	0.0313952i	$0.990005\pi$
$594$		0			0
$595$	−1.80731	−	28.7240i	−0.0740925	−	1.17757i
$596$	−13.2261	+	19.8071i	−0.541762	+	0.811330i
$597$		0			0
$598$	−12.8102	+	1.26364i	−0.523849	+	0.0516739i
$599$		−	16.3265i		−	0.667081i	−0.942736	−	0.333541i	$-0.891757\pi$
$599$		−	16.3265i		−	0.667081i	0.942736	−	0.333541i	$-0.108243\pi$
$600$		0			0
$601$		−	22.5262i		−	0.918862i	−0.888213	−	0.459431i	$-0.848053\pi$
$601$		−	22.5262i		−	0.918862i	0.888213	−	0.459431i	$-0.151947\pi$
$602$	2.69507	+	27.3215i	0.109843	+	1.11354i
$603$		0			0
$604$	1.94212	+	9.74840i	0.0790236	+	0.396657i
$605$	−3.79456	−	60.3078i	−0.154271	−	2.45186i
$606$		0			0
$607$	−20.2440	+	20.2440i	−0.821677	+	0.821677i	−0.986348	−	0.164672i	$-0.947344\pi$
$607$	−20.2440	+	20.2440i	−0.821677	+	0.821677i	0.164672	+	0.986348i	$0.447344\pi$
$608$	5.51212	+	10.2939i	0.223546	+	0.417471i
$609$		0			0
$610$	−0.570143	−	3.50702i	−0.0230844	−	0.141995i
$611$	−2.24893	+	2.24893i	−0.0909820	+	0.0909820i
$612$		0			0
$613$		−	28.9848i		−	1.17069i	−0.810786	−	0.585343i	$-0.800960\pi$
$613$		−	28.9848i		−	1.17069i	0.810786	−	0.585343i	$-0.199040\pi$
$614$	−8.54609	−	7.01145i	−0.344892	−	0.282959i
$615$		0			0
$616$	−61.6118	−	32.8966i	−2.48241	−	1.32544i
$617$	−18.0708	+	18.0708i	−0.727503	+	0.727503i	−0.970122	−	0.242619i	$-0.921994\pi$
$617$	−18.0708	+	18.0708i	−0.727503	+	0.727503i	0.242619	+	0.970122i	$0.421994\pi$
$618$		0			0
$619$	−17.2226	+	17.2226i	−0.692236	+	0.692236i	−0.962723	−	0.270488i	$-0.912815\pi$
$619$	−17.2226	+	17.2226i	−0.692236	+	0.692236i	0.270488	+	0.962723i	$0.412815\pi$
$620$	3.04297	−	0.807823i	0.122209	−	0.0324429i
$621$		0			0
$622$	6.72724	+	5.51922i	0.269738	+	0.221300i
$623$	−30.4254	−	30.4254i	−1.21897	−	1.21897i
$624$		0			0
$625$	24.2145	−	6.21775i	0.968578	−	0.248710i
$626$	1.89583	+	19.2192i	0.0757727	+	0.768152i
$627$		0			0
$628$	−28.3681	+	5.65161i	−1.13201	+	0.225524i
$629$	14.3121	+	14.3121i	0.570662	+	0.570662i
$630$		0			0
$631$	−15.2007			−0.605131			−0.302565	−	0.953129i	$-0.597843\pi$
$631$	−15.2007			−0.605131			−0.302565	+	0.953129i	$0.597843\pi$
$632$	−5.98269	+	11.2049i	−0.237979	+	0.445709i
$633$		0			0
$634$	−9.46491	+	11.5366i	−0.375900	+	0.458175i
$635$	−32.5316	+	36.9002i	−1.29098	+	1.46434i
$636$		0			0
$637$			45.1179i			1.78764i
$638$	9.20770	+	7.55425i	0.364536	+	0.299076i
$639$		0			0
$640$	−0.867252	+	25.2834i	−0.0342812	+	0.999412i
$641$	13.9100			0.549414			0.274707	−	0.961528i	$-0.411419\pi$
$641$	13.9100			0.549414			0.274707	+	0.961528i	$0.411419\pi$
$642$		0			0
$643$			50.3060i			1.98387i	0.126735	+	0.991937i	$0.459550\pi$
$643$			50.3060i			1.98387i	−0.126735	+	0.991937i	$0.540450\pi$
$644$	2.85286	+	14.3199i	0.112419	+	0.564282i
$645$		0			0
$646$	−5.95118	+	7.25375i	−0.234146	+	0.285395i
$647$	−15.4702	−	15.4702i	−0.608197	−	0.608197i	0.334278	−	0.942475i	$-0.391508\pi$
$647$	−15.4702	−	15.4702i	−0.608197	−	0.608197i	−0.942475	+	0.334278i	$0.891508\pi$
$648$		0			0
$649$	19.5016			0.765505
$650$	29.8853	+	18.7949i	1.17220	+	0.737197i
$651$		0			0
$652$	15.1144	−	3.01116i	0.591926	−	0.117926i
$653$	−25.9406			−1.01514			−0.507568	−	0.861612i	$-0.669455\pi$
$653$	−25.9406			−1.01514			−0.507568	+	0.861612i	$0.669455\pi$
$654$		0			0
$655$	30.1571	−	34.2068i	1.17833	−	1.33657i
$656$	1.18400	+	2.85359i	0.0462275	+	0.111414i
$657$		0			0
$658$	2.78909	+	2.28824i	0.108730	+	0.0892050i
$659$	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	$0.510622\pi$
$661$	−26.5534	+	26.5534i	−1.03281	+	1.03281i	−0.999443	+	0.0333644i	$0.989378\pi$
$662$	0.0877793	+	0.889870i	0.00341164	+	0.0345858i
$663$		0			0
$664$	18.9554	+	10.1209i	0.735612	+	0.392768i
$665$	−1.16070	−	18.4473i	−0.0450100	−	0.715355i
$666$		0			0
$667$		−	2.48985i		−	0.0964074i
$668$	7.28993	−	10.9172i	0.282056	−	0.422401i
$669$		0			0
$670$	34.0234	+	24.5078i	1.31444	+	0.946820i
$671$		−	6.92837i		−	0.267467i
$672$		0			0
$673$	10.4724	−	10.4724i	0.403681	−	0.403681i	−0.475847	−	0.879528i	$-0.657858\pi$
$673$	10.4724	−	10.4724i	0.403681	−	0.403681i	0.879528	+	0.475847i	$0.157858\pi$
$674$	0.820564	+	8.31853i	0.0316069	+	0.320418i
$675$		0			0
$676$	4.66094	+	23.3955i	0.179267	+	0.899826i
$677$	23.5614			0.905539			0.452769	−	0.891628i	$-0.350436\pi$
$677$	23.5614			0.905539			0.452769	+	0.891628i	$0.350436\pi$
$678$		0			0
$679$			4.25534i			0.163305i
$680$	−19.0404	+	7.11931i	−0.730165	+	0.273013i
$681$		0			0
$682$	6.10957	−	0.602666i	0.233948	−	0.0230773i
$683$	−30.7873			−1.17804			−0.589021	−	0.808117i	$-0.700487\pi$
$683$	−30.7873			−1.17804			−0.589021	+	0.808117i	$0.700487\pi$
$684$		0			0
$685$	−7.41837	+	8.41457i	−0.283441	+	0.321504i
$686$	11.4787	−	1.13229i	0.438259	−	0.0432311i
$687$		0			0
$688$	17.9103	−	7.43127i	0.682822	−	0.283314i
$689$			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	$0.105247\pi$
$692$	9.36135	+	46.9890i	0.355865	+	1.78626i
$693$		0			0
$694$	27.3401	−	33.3242i	1.03781	−	1.26497i
$695$	−8.72365	+	9.89515i	−0.330907	+	0.375344i
$696$		0			0
$697$	−1.75537	+	1.75537i	−0.0664895	+	0.0664895i
$698$	−48.0647	+	4.74124i	−1.81928	+	0.179459i
$699$		0			0
$700$	17.8885	−	35.8283i	0.676122	−	1.35418i
$701$	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
$704$	−9.58041	+	48.3915i	−0.361075	+	1.82382i
$705$		0			0
$706$	34.4496	−	3.39821i	1.29653	−	0.127893i
$707$	30.0187			1.12897
$708$		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	$0.566512\pi$
$710$	−27.8460	−	20.0582i	−1.04504	−	0.752769i
$711$		0			0
$712$	−14.3139	+	26.8085i	−0.536438	+	1.00469i
$713$	−0.907527	−	0.907527i	−0.0339872	−	0.0339872i
$714$		0			0
$715$	51.6393	+	45.5257i	1.93120	+	1.70257i
$716$	−2.05327	+	3.07493i	−0.0767342	+	0.114915i
$717$		0			0
$718$	26.4080	−	32.1881i	0.985539	−	1.20125i
$719$	−13.6873			−0.510451			−0.255225	−	0.966882i	$-0.582150\pi$
$719$	−13.6873			−0.510451			−0.255225	+	0.966882i	$0.582150\pi$
$720$		0			0
$721$	30.4889			1.13547
$722$	13.2211	−	16.1149i	0.492037	−	0.599733i
$723$		0			0
$724$	−16.3546	−	10.9207i	−0.607813	−	0.405864i
$725$	−4.18532	+	5.39580i	−0.155439	+	0.200395i
$726$		0			0
$727$	29.3029	+	29.3029i	1.08678	+	1.08678i	0.995858	+	0.0909272i	$0.0289831\pi$
$727$	29.3029	+	29.3029i	1.08678	+	1.08678i	0.0909272	+	0.995858i	$0.471017\pi$
$728$	54.1088	−	16.4403i	2.00541	−	0.609319i
$729$		0			0
$730$	7.45164	+	45.8360i	0.275797	+	1.69647i
$731$	11.0174	+	11.0174i	0.407494	+	0.407494i
$732$		0			0
$733$	47.2879			1.74662			0.873309	−	0.487166i	$-0.161969\pi$
$733$	47.2879			1.74662			0.873309	+	0.487166i	$0.161969\pi$
$734$	−21.4316	+	2.11408i	−0.791056	+	0.0780320i
$735$		0			0
$736$	9.09147	−	4.86826i	0.335116	−	0.179447i
$737$	57.8162	+	57.8162i	2.12969	+	2.12969i
$738$		0			0
$739$	15.3480	+	15.3480i	0.564587	+	0.564587i	0.930607	−	0.366020i	$-0.119280\pi$
$739$	15.3480	+	15.3480i	0.564587	+	0.564587i	−0.366020	+	0.930607i	$0.619280\pi$
$740$	7.22609	+	27.2198i	0.265636	+	1.00062i
$741$		0			0
$742$	23.5499	−	2.32303i	0.864543	−	0.0852810i
$743$	−16.7906	+	16.7906i	−0.615987	+	0.615987i	−0.944500	−	0.328513i	$-0.893453\pi$
$743$	−16.7906	+	16.7906i	−0.615987	+	0.615987i	0.328513	+	0.944500i	$0.393453\pi$
$744$		0			0
$745$	−19.9742	−	17.6095i	−0.731799	−	0.645161i
$746$	28.7966	−	35.0995i	1.05432	−	1.28508i
$747$		0			0
$748$	−38.8746	+	7.74477i	−1.42140	+	0.283177i
$749$	−33.8930	+	33.8930i	−1.23842	+	1.23842i
$750$		0			0
$751$			37.3096i			1.36145i	0.732540	+	0.680724i	$0.238335\pi$
$751$			37.3096i			1.36145i	−0.732540	+	0.680724i	$0.761665\pi$
$752$	0.973690	−	2.35469i	0.0355068	−	0.0858668i
$753$		0			0
$754$	−9.59671	+	0.946647i	−0.349492	+	0.0344748i
$755$	−11.0913	+	0.697863i	−0.403654	+	0.0253978i
$756$		0			0
$757$	−2.73045			−0.0992397			−0.0496199	−	0.998768i	$-0.515801\pi$
$757$	−2.73045			−0.0992397			−0.0496199	+	0.998768i	$0.515801\pi$
$758$	46.4404	−	4.58101i	1.68679	−	0.166390i
$759$		0			0
$760$	−12.2282	+	4.57220i	−0.443563	+	0.165851i
$761$		−	43.2111i		−	1.56640i	−0.621768	−	0.783201i	$-0.713585\pi$
$761$		−	43.2111i		−	1.56640i	0.621768	−	0.783201i	$-0.286415\pi$
$762$		0			0
$763$	−22.1711			−0.802649
$764$	4.75979	−	0.948265i	0.172203	−	0.0343070i
$765$		0			0
$766$	1.37881	+	13.9778i	0.0498183	+	0.505037i
$767$	−11.1652	+	11.1652i	−0.403154	+	0.403154i
$768$		0			0
$769$			41.3520i			1.49119i	0.666398	+	0.745596i	$0.267835\pi$
$769$			41.3520i			1.49119i	−0.666398	+	0.745596i	$0.732165\pi$
$770$	45.6408	−	63.3614i	1.64478	−	2.28339i
$771$		0			0
$772$	−1.43841	−	0.960490i	−0.0517695	−	0.0345688i
$773$			10.4113i			0.374469i	0.982315	+	0.187234i	$0.0599523\pi$
$773$			10.4113i			0.374469i	−0.982315	+	0.187234i	$0.940048\pi$
$774$		0			0
$775$	0.441207	+	3.49223i	0.0158486	+	0.125444i
$776$	2.87573	−	0.873755i	0.103233	−	0.0313660i
$777$		0			0
$778$	−4.51634	−	45.7848i	−0.161919	−	1.64146i
$779$	−1.12735	+	1.12735i	−0.0403913	+	0.0403913i
$780$		0			0
$781$	−47.3190	−	47.3190i	−1.69321	−	1.69321i
$782$	6.40646	+	5.25604i	0.229095	+	0.187956i
$783$		0			0
$784$	−13.8528	−	33.3869i	−0.494742	−	1.19239i
$785$	−2.03080	−	32.2760i	−0.0724824	−	1.15198i
$786$		0			0
$787$	−9.84332			−0.350877			−0.175438	−	0.984490i	$-0.556134\pi$
$787$	−9.84332			−0.350877			−0.175438	+	0.984490i	$0.556134\pi$
$788$	−4.93823	−	24.7873i	−0.175917	−	0.883010i
$789$		0			0
$790$	−11.5231	−	8.30039i	−0.409975	−	0.295315i
$791$	−51.7546			−1.84018
$792$		0			0
$793$	3.96669	+	3.96669i	0.140861	+	0.140861i
$794$	22.4753	−	27.3947i	0.797620	−	0.972200i
$795$		0			0
$796$	−19.6215	+	3.90908i	−0.695467	+	0.138554i
$797$			13.2854i			0.470592i	0.971924	+	0.235296i	$0.0756060\pi$
$797$			13.2854i			0.470592i	−0.971924	+	0.235296i	$0.924394\pi$
$798$		0			0
$799$	2.04744			0.0724333
$800$	−27.8856	−	4.73224i	−0.985904	−	0.167310i
$801$		0			0
$802$	−6.79790	−	5.57719i	−0.240042	−	0.196937i
$803$			90.5522i			3.19552i
$804$		0			0
$805$	−16.2925	+	1.02512i	−0.574235	+	0.0361308i
$806$	−3.15287	+	3.84295i	−0.111055	+	0.135362i
$807$		0			0
$808$	−6.16378	−	20.2864i	−0.216841	−	0.713673i
$809$	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	$0.437459\pi$
$812$	2.13721	+	10.7277i	0.0750014	+	0.376467i
$813$		0			0
$814$	5.39093	+	54.6510i	0.188952	+	1.91552i
$815$	1.08200	+	17.1965i	0.0379009	+	0.602368i
$816$		0			0
$817$	7.07567	+	7.07567i	0.247546	+	0.247546i
$818$	−14.3915	−	11.8072i	−0.503187	−	0.412829i
$819$		0			0
$820$	−3.33849	+	0.886276i	−0.116585	+	0.0309501i
$821$	−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	$-0.698958\pi$
$823$	6.47786	−	6.47786i	0.225804	−	0.225804i	0.810937	+	0.585133i	$0.198958\pi$
$824$	−6.26034	−	20.6042i	−0.218089	−	0.717781i
$825$		0			0
$826$	13.8469	+	11.3604i	0.481797	+	0.395279i
$827$			0.819945i			0.0285123i	0.999898	+	0.0142561i	$0.00453803\pi$
$827$			0.819945i			0.0285123i	−0.999898	+	0.0142561i	$0.995462\pi$
$828$		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	$0.0143589\pi$
$830$	−14.0418	+	19.4937i	−0.487397	+	0.676636i
$831$		0			0
$832$	−22.2205	−	33.1906i	−0.770357	−	1.15068i
$833$	20.5378	−	20.5378i	0.711594	−	0.711594i
$834$		0			0
$835$	11.0094	+	9.70595i	0.380995	+	0.335888i
$836$	−24.9663	+	4.97389i	−0.863476	+	0.172025i
$837$		0			0
$838$	−2.88636	−	29.2607i	−0.0997075	−	1.01079i
$839$			25.9917i			0.897335i	0.893699	+	0.448667i	$0.148101\pi$
$839$			25.9917i			0.897335i	−0.893699	+	0.448667i	$0.851899\pi$
$840$		0			0
$841$			27.1347i			0.935681i
$842$	33.9314	−	3.34709i	1.16935	−	0.115348i
$843$		0			0
$844$	22.7394	+	15.1841i	0.782722	+	0.522659i
$845$	−26.6183	+	1.67482i	−0.915698	+	0.0576156i
$846$		0			0
$847$	76.5224	−	76.5224i	2.62934	−	2.62934i
$848$	−6.40541	−	15.4378i	−0.219963	−	0.530137i
$849$		0			0
$850$	−5.04840	−	22.1594i	−0.173159	−	0.760061i
$851$	8.11796	−	8.11796i	0.278280	−	0.278280i
$852$		0			0
$853$		−	13.8457i		−	0.474069i	−0.971501	−	0.237034i	$-0.923825\pi$
$853$		−	13.8457i		−	0.474069i	0.971501	−	0.237034i	$-0.0761754\pi$
$854$	4.03603	−	4.91942i	0.138110	−	0.168339i
$855$		0			0
$856$	29.8640	+	15.9454i	1.02073	+	0.545001i
$857$	27.4340	−	27.4340i	0.937127	−	0.937127i	−0.0610099	−	0.998137i	$-0.519432\pi$
$857$	27.4340	−	27.4340i	0.937127	−	0.937127i	0.998137	+	0.0610099i	$0.0194321\pi$
$858$		0			0
$859$	−3.11480	+	3.11480i	−0.106276	+	0.106276i	−0.758245	−	0.651969i	$-0.773943\pi$
$859$	−3.11480	+	3.11480i	−0.106276	+	0.106276i	0.651969	+	0.758245i	$0.273943\pi$
$860$	5.56262	+	20.9537i	0.189684	+	0.714516i
$861$		0			0
$862$	−16.6272	+	20.2665i	−0.566323	+	0.690278i
$863$	18.7075	+	18.7075i	0.636810	+	0.636810i	0.949767	−	0.312957i	$-0.101320\pi$
$863$	18.7075	+	18.7075i	0.636810	+	0.636810i	−0.312957	+	0.949767i	$0.601320\pi$
$864$		0			0
$865$	−53.4620	+	3.36382i	−1.81776	+	0.114373i
$866$	−18.8596	+	1.86037i	−0.640877	+	0.0632179i
$867$		0			0
$868$	4.68912	+	3.13114i	0.159159	+	0.106278i
$869$	−19.5814	−	19.5814i	−0.664253	−	0.664253i
$870$		0			0
$871$	−66.2029			−2.24320
$872$	4.55243	+	14.9831i	0.154165	+	0.507391i
$873$		0			0
$874$	4.11439	+	3.37556i	0.139171	+	0.114180i
$875$	37.0309	+	25.1654i	1.25187	+	0.850744i
$876$		0			0
$877$		−	20.1135i		−	0.679184i	−0.940573	−	0.339592i	$-0.889711\pi$
$877$		−	20.1135i		−	0.679184i	0.940573	−	0.339592i	$-0.110289\pi$
$878$	19.5490	−	23.8278i	0.659747	−	0.804150i
$879$		0			0
$880$	−52.1907	−	17.8336i	−1.75935	−	0.601170i
$881$	−8.65598			−0.291628			−0.145814	−	0.989312i	$-0.546580\pi$
$881$	−8.65598			−0.291628			−0.145814	+	0.989312i	$0.546580\pi$
$882$		0			0
$883$			15.9095i			0.535399i	0.963502	+	0.267699i	$0.0862634\pi$
$883$			15.9095i			0.535399i	−0.963502	+	0.267699i	$0.913737\pi$
$884$	17.8228	−	26.6910i	0.599444	−	0.897715i
$885$		0			0
$886$	−28.7256	−	23.5673i	−0.965054	−	0.791757i
$887$	−19.2454	−	19.2454i	−0.646197	−	0.646197i	0.305875	−	0.952072i	$-0.401051\pi$
$887$	−19.2454	−	19.2454i	−0.646197	−	0.646197i	−0.952072	+	0.305875i	$0.901051\pi$
$888$		0			0
$889$	−88.0995			−2.95476
$890$	−27.5698	−	19.8592i	−0.924142	−	0.665681i
$891$		0			0
$892$	6.74196	−	10.0966i	0.225738	−	0.338060i
$893$	1.31492			0.0440021
$894$		0			0
$895$	−3.10087	−	2.73376i	−0.103651	−	0.0913795i
$896$	−34.9923	+	28.7790i	−1.16901	+	0.961439i
$897$		0			0
$898$	−26.2476	+	31.9926i	−0.875895	+	1.06761i
$899$	−0.679870	−	0.679870i	−0.0226749	−	0.0226749i
$900$		0			0
$901$	9.49652	−	9.49652i	0.316375	−	0.316375i
$902$	−6.70292	+	0.661195i	−0.223183	+	0.0220154i
$903$		0			0
$904$	10.6268	+	34.9754i	0.353444	+	1.16326i
$905$	14.5400	−	16.4926i	0.483327	−	0.548232i
$906$		0			0
$907$		−	13.9176i		−	0.462128i	−0.972939	−	0.231064i	$-0.925779\pi$
$907$		−	13.9176i		−	0.462128i	0.972939	−	0.231064i	$-0.0742206\pi$
$908$	−5.18560	−	26.0290i	−0.172090	−	0.863802i
$909$		0			0
$910$	10.1456	+	62.4070i	0.336324	+	2.06877i
$911$			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
$914$	36.3212	−	3.58283i	1.20140	−	0.118510i
$915$		0			0
$916$	17.9159	−	26.8305i	0.591958	−	0.886504i
$917$	81.6690			2.69695
$918$		0			0
$919$		−	12.6465i		−	0.417169i	−0.978004	−	0.208584i	$-0.933114\pi$
$919$		−	12.6465i		−	0.417169i	0.978004	−	0.208584i	$-0.0668856\pi$
$920$	4.03813	+	10.7999i	0.133133	+	0.356061i
$921$		0			0
$922$	−1.00812	−	10.2199i	−0.0332005	−	0.336573i
$923$	54.1830			1.78346
$924$		0			0
$925$	−31.2385	+	3.94666i	−1.02711	+	0.129766i
$926$	−2.00338	−	20.3094i	−0.0658352	−	0.667409i
$927$		0			0
$928$	6.81083	−	3.64704i	0.223577	−	0.119720i
$929$		−	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
$932$	12.8754	−	19.2820i	0.421749	−	0.631602i
$933$		0			0
$934$	−26.5349	−	21.7700i	−0.868248	−	0.712335i
$935$	−2.78294	−	44.2298i	−0.0910117	−	1.44647i
$936$		0			0
$937$	−12.0351	+	12.0351i	−0.393168	+	0.393168i	−0.875815	−	0.482647i	$-0.839676\pi$
$937$	−12.0351	+	12.0351i	−0.393168	+	0.393168i	0.482647	+	0.875815i	$0.339676\pi$
$938$	7.37177	+	74.7320i	0.240697	+	2.44009i
$939$		0			0
$940$	2.46385	+	1.43011i	0.0803621	+	0.0466452i
$941$	−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
$944$	4.83407	−	11.6903i	0.157336	−	0.380487i
$945$		0			0
$946$	4.14992	+	42.0702i	0.134926	+	1.36782i
$947$	34.2870			1.11418			0.557089	−	0.830453i	$-0.311918\pi$
$947$	34.2870			1.11418			0.557089	+	0.830453i	$0.311918\pi$
$948$		0			0
$949$	−51.8438	−	51.8438i	−1.68292	−	1.68292i
$950$	−3.24221	−	14.2313i	−0.105191	−	0.461725i
$951$		0			0
$952$	−32.1142	−	17.1468i	−1.04083	−	0.555732i
$953$	−8.81942	−	8.81942i	−0.285689	−	0.285689i	0.549684	−	0.835373i	$-0.314748\pi$
$953$	−8.81942	−	8.81942i	−0.285689	−	0.285689i	−0.835373	+	0.549684i	$0.814748\pi$
$954$		0			0
$955$	0.340741	+	5.41547i	0.0110261	+	0.175241i
$956$	4.16184	+	20.8902i	0.134603	+	0.675638i
$957$		0			0
$958$	27.4311	+	22.5053i	0.886260	+	0.727112i
$959$	−20.0898			−0.648735
$960$		0			0
$961$	30.5044			0.984013
$962$	−34.3758	−	28.2029i	−1.10832	−	0.909296i
$963$		0			0
$964$	−0.479434	−	2.40650i	−0.0154415	−	0.0775083i
$965$	1.27881	−	1.45055i	0.0411665	−	0.0466947i
$966$		0			0
$967$	1.93099	+	1.93099i	0.0620964	+	0.0620964i	0.737473	−	0.675377i	$-0.236019\pi$
$967$	1.93099	+	1.93099i	0.0620964	+	0.0620964i	−0.675377	+	0.737473i	$0.736019\pi$
$968$	−67.4257	−	36.0008i	−2.16714	−	1.15711i
$969$		0			0
$970$	0.539209	+	3.31675i	0.0173130	+	0.106494i
$971$	−6.98427	−	6.98427i	−0.224136	−	0.224136i	0.586102	−	0.810238i	$-0.300662\pi$
$971$	−6.98427	−	6.98427i	−0.224136	−	0.224136i	−0.810238	+	0.586102i	$0.800662\pi$
$972$		0			0
$973$	−23.6247			−0.757374
$974$	−0.0726040	−	0.736029i	−0.00232638	−	0.0235839i
$975$		0			0
$976$	−4.15323	−	1.71741i	−0.132942	−	0.0549729i
$977$	−28.9284	−	28.9284i	−0.925502	−	0.925502i	0.0719094	−	0.997411i	$-0.477091\pi$
$977$	−28.9284	−	28.9284i	−0.925502	−	0.925502i	−0.997411	+	0.0719094i	$0.977091\pi$
$978$		0			0
$979$	−46.8496	−	46.8496i	−1.49732	−	1.49732i
$980$	39.0603	−	10.3694i	1.24774	−	0.331239i
$981$		0			0
$982$	3.78534	+	38.3742i	0.120795	+	1.22457i
$983$	23.8805	−	23.8805i	0.761669	−	0.761669i	−0.214955	−	0.976624i	$-0.568961\pi$
$983$	23.8805	−	23.8805i	0.761669	−	0.761669i	0.976624	+	0.214955i	$0.0689606\pi$
$984$		0			0
$985$	28.2019	−	1.77446i	0.898586	−	0.0565389i
$986$	4.79937	+	3.93754i	0.152843	+	0.125397i
$987$		0			0
$988$	11.4462	−	17.1416i	0.364153	−	0.545347i
$989$	6.24918	−	6.24918i	0.198712	−	0.198712i
$990$		0			0
$991$			29.1750i			0.926774i	0.886156	+	0.463387i	$0.153366\pi$
$991$			29.1750i			0.926774i	−0.886156	+	0.463387i	$0.846634\pi$
$992$	1.15317	−	3.81180i	0.0366133	−	0.121025i
$993$		0			0
$994$	−6.03334	−	61.1635i	−0.191366	−	1.93999i
$995$	−1.40465	−	22.3245i	−0.0445305	−	0.707734i
$996$		0			0
$997$	42.5940			1.34896			0.674482	−	0.738291i	$-0.264367\pi$
$997$	42.5940			1.34896			0.674482	+	0.738291i	$0.264367\pi$
$998$	3.36243	+	34.0869i	0.106436	+	1.07900i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bd.h.307.9		20
3.2	odd	2		240.2.bc.f.67.2	yes	20
5.3	odd	4		720.2.z.h.163.8		20
12.11	even	2		960.2.bc.f.367.10		20
15.8	even	4		240.2.y.f.163.3	✓	20
16.11	odd	4		720.2.z.h.667.8		20
24.5	odd	2		1920.2.bc.k.607.1		20
24.11	even	2		1920.2.bc.l.607.1		20
48.5	odd	4		960.2.y.f.847.6		20
48.11	even	4		240.2.y.f.187.3	yes	20
48.29	odd	4		1920.2.y.k.1567.5		20
48.35	even	4		1920.2.y.l.1567.5		20
60.23	odd	4		960.2.y.f.943.6		20
80.43	even	4	inner	720.2.bd.h.523.9		20
120.53	even	4		1920.2.y.l.223.5		20
120.83	odd	4		1920.2.y.k.223.5		20
240.53	even	4		960.2.bc.f.463.10		20
240.83	odd	4		1920.2.bc.k.1183.1		20
240.173	even	4		1920.2.bc.l.1183.1		20
240.203	odd	4		240.2.bc.f.43.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.3	✓	20	15.8	even	4
240.2.y.f.187.3	yes	20	48.11	even	4
240.2.bc.f.43.2	yes	20	240.203	odd	4
240.2.bc.f.67.2	yes	20	3.2	odd	2
720.2.z.h.163.8		20	5.3	odd	4
720.2.z.h.667.8		20	16.11	odd	4
720.2.bd.h.307.9		20	1.1	even	1	trivial
720.2.bd.h.523.9		20	80.43	even	4	inner
960.2.y.f.847.6		20	48.5	odd	4
960.2.y.f.943.6		20	60.23	odd	4
960.2.bc.f.367.10		20	12.11	even	2
960.2.bc.f.463.10		20	240.53	even	4
1920.2.y.k.223.5		20	120.83	odd	4
1920.2.y.k.1567.5		20	48.29	odd	4
1920.2.y.l.223.5		20	120.53	even	4
1920.2.y.l.1567.5		20	48.35	even	4
1920.2.bc.k.607.1		20	24.5	odd	2
1920.2.bc.k.1183.1		20	240.83	odd	4
1920.2.bc.l.607.1		20	24.11	even	2
1920.2.bc.l.1183.1		20	240.173	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09334 + 0.897004i) q^{2} +(0.390769 + 1.96145i) q^{4} +(-2.23165 + 0.140415i) q^{5} +(-2.83167 - 2.83167i) q^{7} +(-1.33219 + 2.49505i) q^{8} +(-2.56590 - 1.84828i) q^{10} +(-4.36026 - 4.36026i) q^{11} +4.99276 q^{13} +(-0.555949 - 5.63598i) q^{14} +(-3.69460 + 1.53295i) q^{16} +(-2.27272 - 2.27272i) q^{17} +(-1.45960 - 1.45960i) q^{19} +(-1.14748 - 4.32242i) q^{20} +(-0.856063 - 8.67841i) q^{22} +(-1.28911 + 1.28911i) q^{23} +(4.96057 - 0.626717i) q^{25} +(5.45876 + 4.47852i) q^{26} +(4.44766 - 6.66071i) q^{28} +(-0.965728 + 0.965728i) q^{29} +0.703997i q^{31} +(-5.41450 - 1.63804i) q^{32} +(-0.446209 - 4.52348i) q^{34} +(6.71691 + 5.92169i) q^{35} -6.29736 q^{37} +(-0.286567 - 2.90509i) q^{38} +(2.62264 - 5.75515i) q^{40} -0.772367i q^{41} -4.84769 q^{43} +(6.84860 - 10.2563i) q^{44} +(-2.56576 + 0.253094i) q^{46} +(-0.450439 + 0.450439i) q^{47} +9.03668i q^{49} +(5.98574 + 3.76443i) q^{50} +(1.95101 + 9.79306i) q^{52} +4.17849i q^{53} +(10.3428 + 9.11835i) q^{55} +(10.8375 - 3.29284i) q^{56} +(-1.92213 + 0.189604i) q^{58} +(-2.23629 + 2.23629i) q^{59} +(0.794490 + 0.794490i) q^{61} +(-0.631488 + 0.769706i) q^{62} +(-4.45055 - 6.64775i) q^{64} +(-11.1421 + 0.701060i) q^{65} -13.2598 q^{67} +(3.56972 - 5.34594i) q^{68} +(2.03207 + 12.4995i) q^{70} +10.8523 q^{71} +(-10.3838 - 10.3838i) q^{73} +(-6.88513 - 5.64875i) q^{74} +(2.29257 - 3.43330i) q^{76} +24.6936i q^{77} +4.49087 q^{79} +(8.02982 - 3.93980i) q^{80} +(0.692816 - 0.844457i) q^{82} -7.59721i q^{83} +(5.39105 + 4.75280i) q^{85} +(-5.30015 - 4.34839i) q^{86} +(16.6878 - 5.07038i) q^{88} +10.7447 q^{89} +(-14.1378 - 14.1378i) q^{91} +(-3.03226 - 2.02478i) q^{92} +(-0.896526 + 0.0884359i) q^{94} +(3.46227 + 3.05237i) q^{95} +(-0.751384 - 0.751384i) q^{97} +(-8.10594 + 9.88013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{13} + 10 q^{14} + 26 q^{16} - 12 q^{17} - 16 q^{19} + 4 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 20 q^{26} + 22 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 2 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^13 + 10 * q^14 + 26 * q^16 - 12 * q^17 - 16 * q^19 + 4 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 20 * q^26 + 22 * q^28 - 12 * q^32 - 6 * q^34 + 12 * q^35 + 24 * q^37 + 22 * q^38 - 10 * q^40 - 8 * q^43 + 22 * q^44 - 18 * q^46 + 18 * q^50 + 24 * q^52 - 4 * q^55 + 26 * q^56 - 2 * q^58 - 16 * q^59 - 12 * q^61 - 12 * q^62 - 26 * q^64 - 4 * q^65 - 16 * q^67 + 2 * q^68 - 10 * q^70 + 20 * q^73 - 8 * q^74 + 26 * q^76 - 48 * q^79 + 16 * q^80 + 80 * q^82 + 4 * q^85 - 4 * q^86 + 94 * q^88 + 40 * q^89 - 24 * q^91 + 30 * q^92 - 58 * q^94 - 72 * q^95 - 28 * q^97 - 4 * q^98

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