LMFDB - Embedded newform 420.2.i.a.139.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(139,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))

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

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

chi := DirichletCharacter("420.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.i (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.9
Character	$\chi$	$=$	420.139
Dual form			420.2.i.a.139.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08769 - 0.903842i) q^{2} -1.00000i q^{3} +(0.366139 + 1.96620i) q^{4} +(-0.660150 - 2.13640i) q^{5} +(-0.903842 + 1.08769i) q^{6} +(-2.64346 - 0.110159i) q^{7} +(1.37889 - 2.46955i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.08769 - 0.903842i) q^{2} -1.00000i q^{3} +(0.366139 + 1.96620i) q^{4} +(-0.660150 - 2.13640i) q^{5} +(-0.903842 + 1.08769i) q^{6} +(-2.64346 - 0.110159i) q^{7} +(1.37889 - 2.46955i) q^{8} -1.00000 q^{9} +(-1.21293 + 2.92041i) q^{10} +2.42837i q^{11} +(1.96620 - 0.366139i) q^{12} -5.02799 q^{13} +(2.77570 + 2.50909i) q^{14} +(-2.13640 + 0.660150i) q^{15} +(-3.73189 + 1.43980i) q^{16} +6.95745 q^{17} +(1.08769 + 0.903842i) q^{18} -1.26188 q^{19} +(3.95888 - 2.08020i) q^{20} +(-0.110159 + 2.64346i) q^{21} +(2.19486 - 2.64131i) q^{22} -6.81927 q^{23} +(-2.46955 - 1.37889i) q^{24} +(-4.12840 + 2.82069i) q^{25} +(5.46890 + 4.54451i) q^{26} +1.00000i q^{27} +(-0.751278 - 5.23790i) q^{28} -4.56347 q^{29} +(2.92041 + 1.21293i) q^{30} -0.903134 q^{31} +(5.36049 + 1.80698i) q^{32} +2.42837 q^{33} +(-7.56755 - 6.28844i) q^{34} +(1.50973 + 5.72020i) q^{35} +(-0.366139 - 1.96620i) q^{36} +8.02957i q^{37} +(1.37253 + 1.14054i) q^{38} +5.02799i q^{39} +(-6.18621 - 1.31559i) q^{40} -3.33664i q^{41} +(2.50909 - 2.77570i) q^{42} +2.06720 q^{43} +(-4.77466 + 0.889120i) q^{44} +(0.660150 + 2.13640i) q^{45} +(7.41725 + 6.16355i) q^{46} -3.31923i q^{47} +(1.43980 + 3.73189i) q^{48} +(6.97573 + 0.582399i) q^{49} +(7.03988 + 0.663393i) q^{50} -6.95745i q^{51} +(-1.84094 - 9.88604i) q^{52} +4.77776i q^{53} +(0.903842 - 1.08769i) q^{54} +(5.18797 - 1.60309i) q^{55} +(-3.91708 + 6.37625i) q^{56} +1.26188i q^{57} +(4.96364 + 4.12465i) q^{58} -8.38831 q^{59} +(-2.08020 - 3.95888i) q^{60} +4.38973i q^{61} +(0.982329 + 0.816290i) q^{62} +(2.64346 + 0.110159i) q^{63} +(-4.19733 - 6.81047i) q^{64} +(3.31923 + 10.7418i) q^{65} +(-2.64131 - 2.19486i) q^{66} -8.25600 q^{67} +(2.54739 + 13.6797i) q^{68} +6.81927i q^{69} +(3.52804 - 7.58637i) q^{70} -11.5725i q^{71} +(-1.37889 + 2.46955i) q^{72} -12.3939 q^{73} +(7.25746 - 8.73368i) q^{74} +(2.82069 + 4.12840i) q^{75} +(-0.462022 - 2.48111i) q^{76} +(0.267506 - 6.41929i) q^{77} +(4.54451 - 5.46890i) q^{78} -8.69070i q^{79} +(5.53960 + 7.02231i) q^{80} +1.00000 q^{81} +(-3.01580 + 3.62923i) q^{82} -9.72136i q^{83} +(-5.23790 + 0.751278i) q^{84} +(-4.59296 - 14.8639i) q^{85} +(-2.24847 - 1.86842i) q^{86} +4.56347i q^{87} +(5.99698 + 3.34846i) q^{88} -13.6598i q^{89} +(1.21293 - 2.92041i) q^{90} +(13.2913 + 0.553877i) q^{91} +(-2.49680 - 13.4081i) q^{92} +0.903134i q^{93} +(-3.00006 + 3.61029i) q^{94} +(0.833029 + 2.69588i) q^{95} +(1.80698 - 5.36049i) q^{96} -1.23014 q^{97} +(-7.06103 - 6.93843i) q^{98} -2.42837i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{9}+O(q^{10}) $ 48 * q - 48 * q^9	$ 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) $ 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.08769	−	0.903842i	−0.769113	−	0.639113i
$2$	−1.08769	−	0.903842i	−0.769113	−	0.639113i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.366139	+	1.96620i	0.183069	+	0.983100i
$5$	−0.660150	−	2.13640i	−0.295228	−	0.955427i
$5$	−0.660150	−	2.13640i	−0.295228	−	0.955427i
$6$	−0.903842	+	1.08769i	−0.368992	+	0.444048i
$7$	−2.64346	−	0.110159i	−0.999133	−	0.0416360i
$7$	−2.64346	−	0.110159i	−0.999133	−	0.0416360i
$8$	1.37889	−	2.46955i	0.487511	−	0.873117i
$9$	−1.00000			−0.333333
$10$	−1.21293	+	2.92041i	−0.383562	+	0.923515i
$11$			2.42837i			0.732181i	0.930579	+	0.366091i	$0.119304\pi$
$11$			2.42837i			0.732181i	−0.930579	+	0.366091i	$0.880696\pi$
$12$	1.96620	−	0.366139i	0.567593	−	0.105695i
$13$	−5.02799			−1.39451			−0.697257	−	0.716821i	$-0.745597\pi$
$13$	−5.02799			−1.39451			−0.697257	+	0.716821i	$0.745597\pi$
$14$	2.77570	+	2.50909i	0.741836	+	0.670582i
$15$	−2.13640	+	0.660150i	−0.551616	+	0.170450i
$16$	−3.73189	+	1.43980i	−0.932971	+	0.359951i
$17$	6.95745			1.68743			0.843715	−	0.536792i	$-0.180364\pi$
$17$	6.95745			1.68743			0.843715	+	0.536792i	$0.180364\pi$
$18$	1.08769	+	0.903842i	0.256371	+	0.213038i
$19$	−1.26188			−0.289495			−0.144747	−	0.989469i	$-0.546237\pi$
$19$	−1.26188			−0.289495			−0.144747	+	0.989469i	$0.546237\pi$
$20$	3.95888	−	2.08020i	0.885233	−	0.465148i
$21$	−0.110159	+	2.64346i	−0.0240386	+	0.576850i
$22$	2.19486	−	2.64131i	0.467947	−	0.563130i
$23$	−6.81927			−1.42192			−0.710958	−	0.703234i	$-0.751739\pi$
$23$	−6.81927			−1.42192			−0.710958	+	0.703234i	$0.751739\pi$
$24$	−2.46955	−	1.37889i	−0.504094	−	0.281465i
$25$	−4.12840	+	2.82069i	−0.825681	+	0.564137i
$26$	5.46890	+	4.54451i	1.07254	+	0.891252i
$27$			1.00000i			0.192450i
$28$	−0.751278	−	5.23790i	−0.141978	−	0.989870i
$29$	−4.56347			−0.847414			−0.423707	−	0.905799i	$-0.639271\pi$
$29$	−4.56347			−0.847414			−0.423707	+	0.905799i	$0.639271\pi$
$30$	2.92041	+	1.21293i	0.533192	+	0.221450i
$31$	−0.903134			−0.162208			−0.0811038	−	0.996706i	$-0.525845\pi$
$31$	−0.903134			−0.162208			−0.0811038	+	0.996706i	$0.525845\pi$
$32$	5.36049	+	1.80698i	0.947609	+	0.319431i
$33$	2.42837			0.422725
$34$	−7.56755	−	6.28844i	−1.29782	−	1.07846i
$35$	1.50973	+	5.72020i	0.255192	+	0.966890i
$36$	−0.366139	−	1.96620i	−0.0610231	−	0.327700i
$37$			8.02957i			1.32005i	0.751242	+	0.660027i	$0.229455\pi$
$37$			8.02957i			1.32005i	−0.751242	+	0.660027i	$0.770545\pi$
$38$	1.37253	+	1.14054i	0.222654	+	0.185020i
$39$			5.02799i			0.805123i
$40$	−6.18621	−	1.31559i	−0.978126	−	0.208013i
$41$		−	3.33664i		−	0.521096i	−0.965461	−	0.260548i	$-0.916097\pi$
$41$		−	3.33664i		−	0.521096i	0.965461	−	0.260548i	$-0.0839033\pi$
$42$	2.50909	−	2.77570i	0.387160	−	0.428299i
$43$	2.06720			0.315245			0.157623	−	0.987499i	$-0.449617\pi$
$43$	2.06720			0.315245			0.157623	+	0.987499i	$0.449617\pi$
$44$	−4.77466	+	0.889120i	−0.719808	+	0.134040i
$45$	0.660150	+	2.13640i	0.0984093	+	0.318476i
$46$	7.41725	+	6.16355i	1.09361	+	0.908765i
$47$		−	3.31923i		−	0.484159i	−0.970256	−	0.242080i	$-0.922170\pi$
$47$		−	3.31923i		−	0.484159i	0.970256	−	0.242080i	$-0.0778295\pi$
$48$	1.43980	+	3.73189i	0.207818	+	0.538651i
$49$	6.97573	+	0.582399i	0.996533	+	0.0831999i
$50$	7.03988	+	0.663393i	0.995589	+	0.0938180i
$51$		−	6.95745i		−	0.974238i
$52$	−1.84094	−	9.88604i	−0.255293	−	1.37095i
$53$			4.77776i			0.656276i	0.944630	+	0.328138i	$0.106421\pi$
$53$			4.77776i			0.656276i	−0.944630	+	0.328138i	$0.893579\pi$
$54$	0.903842	−	1.08769i	0.122997	−	0.148016i
$55$	5.18797	−	1.60309i	0.699546	−	0.216160i
$56$	−3.91708	+	6.37625i	−0.523441	+	0.852062i
$57$			1.26188i			0.167140i
$58$	4.96364	+	4.12465i	0.651757	+	0.541594i
$59$	−8.38831			−1.09207			−0.546033	−	0.837764i	$-0.683863\pi$
$59$	−8.38831			−1.09207			−0.546033	+	0.837764i	$0.683863\pi$
$60$	−2.08020	−	3.95888i	−0.268553	−	0.511089i
$61$			4.38973i			0.562047i	0.959701	+	0.281024i	$0.0906739\pi$
$61$			4.38973i			0.562047i	−0.959701	+	0.281024i	$0.909326\pi$
$62$	0.982329	+	0.816290i	0.124756	+	0.103669i
$63$	2.64346	+	0.110159i	0.333044	+	0.0138787i
$64$	−4.19733	−	6.81047i	−0.524666	−	0.851308i
$65$	3.31923	+	10.7418i	0.411700	+	1.33236i
$66$	−2.64131	−	2.19486i	−0.325123	−	0.270169i
$67$	−8.25600			−1.00863			−0.504315	−	0.863520i	$-0.668255\pi$
$67$	−8.25600			−1.00863			−0.504315	+	0.863520i	$0.668255\pi$
$68$	2.54739	+	13.6797i	0.308916	+	1.65891i
$69$			6.81927i			0.820944i
$70$	3.52804	−	7.58637i	0.421681	−	0.906744i
$71$		−	11.5725i		−	1.37340i	−0.726940	−	0.686701i	$-0.759058\pi$
$71$		−	11.5725i		−	1.37340i	0.726940	−	0.686701i	$-0.240942\pi$
$72$	−1.37889	+	2.46955i	−0.162504	+	0.291039i
$73$	−12.3939			−1.45059			−0.725297	−	0.688436i	$-0.758297\pi$
$73$	−12.3939			−1.45059			−0.725297	+	0.688436i	$0.758297\pi$
$74$	7.25746	−	8.73368i	0.843663	−	1.01527i
$75$	2.82069	+	4.12840i	0.325705	+	0.476707i
$76$	−0.462022	−	2.48111i	−0.0529976	−	0.284602i
$77$	0.267506	−	6.41929i	0.0304851	−	0.731547i
$78$	4.54451	−	5.46890i	0.514565	−	0.619231i
$79$		−	8.69070i		−	0.977780i	−0.872346	−	0.488890i	$-0.837402\pi$
$79$		−	8.69070i		−	0.977780i	0.872346	−	0.488890i	$-0.162598\pi$
$80$	5.53960	+	7.02231i	0.619346	+	0.785118i
$81$	1.00000			0.111111
$82$	−3.01580	+	3.62923i	−0.333039	+	0.400782i
$83$		−	9.72136i		−	1.06706i	−0.845782	−	0.533529i	$-0.820865\pi$
$83$		−	9.72136i		−	1.06706i	0.845782	−	0.533529i	$-0.179135\pi$
$84$	−5.23790	+	0.751278i	−0.571502	+	0.0819711i
$85$	−4.59296	−	14.8639i	−0.498176	−	1.61222i
$86$	−2.24847	−	1.86842i	−0.242459	−	0.201477i
$87$			4.56347i			0.489255i
$88$	5.99698	+	3.34846i	0.639280	+	0.356947i
$89$		−	13.6598i		−	1.44794i	−0.689831	−	0.723970i	$-0.742315\pi$
$89$		−	13.6598i		−	1.44794i	0.689831	−	0.723970i	$-0.257685\pi$
$90$	1.21293	−	2.92041i	0.127854	−	0.307838i
$91$	13.2913	+	0.553877i	1.39331	+	0.0580621i
$92$	−2.49680	−	13.4081i	−0.260309	−	1.39789i
$93$			0.903134i			0.0936506i
$94$	−3.00006	+	3.61029i	−0.309433	+	0.372373i
$95$	0.833029	+	2.69588i	0.0854670	+	0.276591i
$96$	1.80698	−	5.36049i	0.184424	−	0.547103i
$97$	−1.23014			−0.124901			−0.0624507	−	0.998048i	$-0.519892\pi$
$97$	−1.23014			−0.124901			−0.0624507	+	0.998048i	$0.519892\pi$
$98$	−7.06103	−	6.93843i	−0.713272	−	0.700887i
$99$		−	2.42837i		−	0.244060i
$100$	−7.05760	−	7.08451i	−0.705760	−	0.708451i
$101$		−	5.68823i		−	0.566000i	−0.959120	−	0.283000i	$-0.908670\pi$
$101$		−	5.68823i		−	0.566000i	0.959120	−	0.283000i	$-0.0913296\pi$
$102$	−6.28844	+	7.56755i	−0.622648	+	0.749299i
$103$		−	10.0365i		−	0.988925i	−0.869199	−	0.494462i	$-0.835365\pi$
$103$		−	10.0365i		−	0.988925i	0.869199	−	0.494462i	$-0.164635\pi$
$104$	−6.93305	+	12.4169i	−0.679841	+	1.21757i
$105$	5.72020	−	1.50973i	0.558234	−	0.147335i
$106$	4.31834	−	5.19672i	0.419434	−	0.504750i
$107$	10.4278			1.00810			0.504049	−	0.863675i	$-0.331843\pi$
$107$	10.4278			1.00810			0.504049	+	0.863675i	$0.331843\pi$
$108$	−1.96620	+	0.366139i	−0.189198	+	0.0352317i
$109$	−10.8686			−1.04102			−0.520509	−	0.853856i	$-0.674258\pi$
$109$	−10.8686			−1.04102			−0.520509	+	0.853856i	$0.674258\pi$
$110$	−7.09184	−	2.94544i	−0.676181	−	0.280837i
$111$	8.02957			0.762133
$112$	10.0237	−	3.39496i	0.947149	−	0.320793i
$113$		−	5.78750i		−	0.544442i	−0.962235	−	0.272221i	$-0.912242\pi$
$113$		−	5.78750i		−	0.544442i	0.962235	−	0.272221i	$-0.0877582\pi$
$114$	1.14054	−	1.37253i	0.106821	−	0.128549i
$115$	4.50174	+	14.5687i	0.419790	+	1.35854i
$116$	−1.67086	−	8.97269i	−0.155136	−	0.833093i
$117$	5.02799			0.464838
$118$	9.12388	+	7.58171i	0.839922	+	0.697953i
$119$	−18.3917	−	0.766423i	−1.68597	−	0.0702579i
$120$	−1.31559	+	6.18621i	−0.120096	+	0.564721i
$121$	5.10301			0.463910
$122$	3.96762	−	4.77466i	0.359212	−	0.432278i
$123$	−3.33664			−0.300855
$124$	−0.330672	−	1.77574i	−0.0296952	−	0.159466i
$125$	8.75148	+	6.95784i	0.782756	+	0.622329i
$126$	−2.77570	−	2.50909i	−0.247279	−	0.223527i
$127$	7.86714			0.698096			0.349048	−	0.937105i	$-0.386505\pi$
$127$	7.86714			0.698096			0.349048	+	0.937105i	$0.386505\pi$
$128$	−1.59019	+	11.2014i	−0.140555	+	0.990073i
$129$		−	2.06720i		−	0.182007i
$130$	6.09860	−	14.6838i	0.534883	−	1.28786i
$131$	−9.15726			−0.800073			−0.400037	−	0.916499i	$-0.631003\pi$
$131$	−9.15726			−0.800073			−0.400037	+	0.916499i	$0.631003\pi$
$132$	0.889120	+	4.77466i	0.0773880	+	0.415581i
$133$	3.33572	+	0.139007i	0.289244	+	0.0120534i
$134$	8.97997	+	7.46212i	0.775751	+	0.644629i
$135$	2.13640	−	0.660150i	0.183872	−	0.0568167i
$136$	9.59355	−	17.1817i	0.822640	−	1.47332i
$137$		−	13.0458i		−	1.11458i	−0.830318	−	0.557290i	$-0.811841\pi$
$137$		−	13.0458i		−	1.11458i	0.830318	−	0.557290i	$-0.188159\pi$
$138$	6.16355	−	7.41725i	0.524676	−	0.631399i
$139$	−19.4289			−1.64794			−0.823969	−	0.566635i	$-0.808245\pi$
$139$	−19.4289			−1.64794			−0.823969	+	0.566635i	$0.808245\pi$
$140$	−10.6943	+	5.06283i	−0.903832	+	0.427887i
$141$	−3.31923			−0.279530
$142$	−10.4597	+	12.5873i	−0.877759	+	1.05630i
$143$		−	12.2098i		−	1.02104i
$144$	3.73189	−	1.43980i	0.310990	−	0.119984i
$145$	3.01257	+	9.74939i	0.250180	+	0.809643i
$146$	13.4807	+	11.2021i	1.11567	+	0.927093i
$147$	0.582399	−	6.97573i	0.0480355	−	0.575349i
$148$	−15.7877	+	2.93993i	−1.29774	+	0.241661i
$149$	1.00410			0.0822592			0.0411296	−	0.999154i	$-0.486904\pi$
$149$	1.00410			0.0822592			0.0411296	+	0.999154i	$0.486904\pi$
$150$	0.663393	−	7.03988i	0.0541658	−	0.574804i
$151$			18.4558i			1.50191i	0.660352	+	0.750956i	$0.270407\pi$
$151$			18.4558i			1.50191i	−0.660352	+	0.750956i	$0.729593\pi$
$152$	−1.73999	+	3.11627i	−0.141132	+	0.252763i
$153$	−6.95745			−0.562476
$154$	−6.09299	+	6.74042i	−0.490987	+	0.543158i
$155$	0.596204	+	1.92945i	0.0478882	+	0.154978i
$156$	−9.88604	+	1.84094i	−0.791517	+	0.147393i
$157$	4.73711			0.378063			0.189031	−	0.981971i	$-0.439465\pi$
$157$	4.73711			0.378063			0.189031	+	0.981971i	$0.439465\pi$
$158$	−7.85502	+	9.45278i	−0.624912	+	0.752023i
$159$	4.77776			0.378901
$160$	0.321697	−	12.6450i	0.0254324	−	0.999677i
$161$	18.0265	+	0.751201i	1.42068	+	0.0592030i
$162$	−1.08769	−	0.903842i	−0.0854570	−	0.0710126i
$163$	5.51985			0.432348			0.216174	−	0.976355i	$-0.430642\pi$
$163$	5.51985			0.432348			0.216174	+	0.976355i	$0.430642\pi$
$164$	6.56051	−	1.22167i	0.512290	−	0.0953967i
$165$	−1.60309	−	5.18797i	−0.124800	−	0.403883i
$166$	−8.78658	+	10.5738i	−0.681971	+	0.820688i
$167$			19.8651i			1.53721i	0.639724	+	0.768605i	$0.279049\pi$
$167$			19.8651i			1.53721i	−0.639724	+	0.768605i	$0.720951\pi$
$168$	6.37625	+	3.91708i	0.491938	+	0.302209i
$169$	12.2807			0.944671
$170$	−8.43890	+	20.3186i	−0.647234	+	1.55837i
$171$	1.26188			0.0964983
$172$	0.756882	+	4.06453i	0.0577117	+	0.309917i
$173$	−14.4183			−1.09621			−0.548103	−	0.836411i	$-0.684650\pi$
$173$	−14.4183			−1.09621			−0.548103	+	0.836411i	$0.684650\pi$
$174$	4.12465	−	4.96364i	0.312689	−	0.376292i
$175$	11.2240	−	7.00159i	0.848453	−	0.529270i
$176$	−3.49638	−	9.06240i	−0.263549	−	0.683104i
$177$			8.38831i			0.630504i
$178$	−12.3463	+	14.8577i	−0.925397	+	1.11363i
$179$			10.3788i			0.775746i	0.921713	+	0.387873i	$0.126790\pi$
$179$			10.3788i			0.775746i	−0.921713	+	0.387873i	$0.873210\pi$
$180$	−3.95888	+	2.08020i	−0.295078	+	0.155049i
$181$		−	16.2843i		−	1.21040i	−0.796073	−	0.605200i	$-0.793093\pi$
$181$		−	16.2843i		−	1.21040i	0.796073	−	0.605200i	$-0.206907\pi$
$182$	−13.9562	−	12.6157i	−1.03450	−	0.935136i
$183$	4.38973			0.324498
$184$	−9.40302	+	16.8405i	−0.693200	+	1.24150i
$185$	17.1544	−	5.30072i	1.26121	−	0.389717i
$186$	0.816290	−	0.982329i	0.0598533	−	0.0720279i
$187$			16.8953i			1.23550i
$188$	6.52627	−	1.21530i	0.475977	−	0.0886347i
$189$	0.110159	−	2.64346i	0.00801286	−	0.192283i
$190$	1.53057	−	3.68521i	0.111039	−	0.267353i
$191$		−	1.12409i		−	0.0813365i	−0.999173	−	0.0406683i	$-0.987051\pi$
$191$		−	1.12409i		−	0.0813365i	0.999173	−	0.0406683i	$-0.0129487\pi$
$192$	−6.81047	+	4.19733i	−0.491503	+	0.302916i
$193$		−	2.59910i		−	0.187087i	−0.995615	−	0.0935437i	$-0.970181\pi$
$193$		−	2.59910i		−	0.187087i	0.995615	−	0.0935437i	$-0.0298195\pi$
$194$	1.33801	+	1.11185i	0.0960632	+	0.0798260i
$195$	10.7418	−	3.31923i	0.769237	−	0.237695i
$196$	1.40897	+	13.9289i	0.100641	+	0.994923i
$197$		−	10.2716i		−	0.731824i	−0.930649	−	0.365912i	$-0.880757\pi$
$197$		−	10.2716i		−	0.731824i	0.930649	−	0.365912i	$-0.119243\pi$
$198$	−2.19486	+	2.64131i	−0.155982	+	0.187710i
$199$	20.7974			1.47429			0.737144	−	0.675736i	$-0.236174\pi$
$199$	20.7974			1.47429			0.737144	+	0.675736i	$0.236174\pi$
$200$	1.27321	+	14.0847i	0.0900294	+	0.995939i
$201$			8.25600i			0.582333i
$202$	−5.14126	+	6.18703i	−0.361738	+	0.435318i
$203$	12.0633	+	0.502705i	0.846680	+	0.0352830i
$204$	13.6797	−	2.54739i	0.957773	−	0.178353i
$205$	−7.12840	+	2.20269i	−0.497869	+	0.153842i
$206$	−9.07140	+	10.9166i	−0.632035	+	0.760595i
$207$	6.81927			0.473972
$208$	18.7639	−	7.23932i	1.30104	−	0.501957i
$209$		−	3.06431i		−	0.211963i
$210$	−7.58637	−	3.52804i	−0.523509	−	0.243458i
$211$			16.1061i			1.10879i	0.832254	+	0.554394i	$0.187050\pi$
$211$			16.1061i			1.10879i	−0.832254	+	0.554394i	$0.812950\pi$
$212$	−9.39403	+	1.74932i	−0.645185	+	0.120144i
$213$	−11.5725			−0.792934
$214$	−11.3423	−	9.42513i	−0.775341	−	0.644288i
$215$	−1.36466	−	4.41636i	−0.0930692	−	0.301194i
$216$	2.46955	+	1.37889i	0.168031	+	0.0938215i
$217$	2.38740	+	0.0994879i	0.162067	+	0.00675368i
$218$	11.8216	+	9.82346i	0.800661	+	0.665329i
$219$			12.3939i			0.837501i
$220$	5.05151	+	9.61364i	0.340573	+	0.648151i
$221$	−34.9820			−2.35314
$222$	−8.73368	−	7.25746i	−0.586166	−	0.487089i
$223$		−	19.7311i		−	1.32130i	−0.750696	−	0.660648i	$-0.770282\pi$
$223$		−	19.7311i		−	1.32130i	0.750696	−	0.660648i	$-0.229718\pi$
$224$	−13.9712	−	5.36717i	−0.933488	−	0.358609i
$225$	4.12840	−	2.82069i	0.275227	−	0.188046i
$226$	−5.23099	+	6.29500i	−0.347960	+	0.418737i
$227$		−	12.8686i		−	0.854116i	−0.904224	−	0.427058i	$-0.859550\pi$
$227$		−	12.8686i		−	0.854116i	0.904224	−	0.427058i	$-0.140450\pi$
$228$	−2.48111	+	0.462022i	−0.164315	+	0.0305982i
$229$			2.03252i			0.134313i	0.997742	+	0.0671565i	$0.0213927\pi$
$229$			2.03252i			0.134313i	−0.997742	+	0.0671565i	$0.978607\pi$
$230$	8.27130	−	19.9151i	0.545393	−	1.31316i
$231$	−6.41929	−	0.267506i	−0.422359	−	0.0176006i
$232$	−6.29252	+	11.2697i	−0.413124	+	0.739892i
$233$			19.3086i			1.26495i	0.774580	+	0.632476i	$0.217961\pi$
$233$			19.3086i			1.26495i	−0.774580	+	0.632476i	$0.782039\pi$
$234$	−5.46890	−	4.54451i	−0.357513	−	0.297084i
$235$	−7.09120	+	2.19119i	−0.462579	+	0.142937i
$236$	−3.07129	−	16.4931i	−0.199924	−	1.07361i
$237$	−8.69070			−0.564521
$238$	19.3118	+	17.4568i	1.25180	+	1.13156i
$239$			28.1280i			1.81945i	0.415213	+	0.909724i	$0.363707\pi$
$239$			28.1280i			1.81945i	−0.415213	+	0.909724i	$0.636293\pi$
$240$	7.02231	−	5.53960i	0.453288	−	0.357580i
$241$			29.9443i			1.92888i	0.264300	+	0.964441i	$0.414859\pi$
$241$			29.9443i			1.92888i	−0.264300	+	0.964441i	$0.585141\pi$
$242$	−5.55050	−	4.61232i	−0.356799	−	0.296491i
$243$		−	1.00000i		−	0.0641500i
$244$	−8.63108	+	1.60725i	−0.552549	+	0.102894i
$245$	−3.36079	−	15.2874i	−0.214713	−	0.976677i
$246$	3.62923	+	3.01580i	0.231392	+	0.192280i
$247$	6.34472			0.403705
$248$	−1.24532	+	2.23033i	−0.0790780	+	0.141626i
$249$	−9.72136			−0.616066
$250$	−3.23010	−	15.4779i	−0.204290	−	0.978910i
$251$	−5.30422			−0.334799			−0.167400	−	0.985889i	$-0.553537\pi$
$251$	−5.30422			−0.334799			−0.167400	+	0.985889i	$0.553537\pi$
$252$	0.751278	+	5.23790i	0.0473260	+	0.329957i
$253$		−	16.5597i		−	1.04110i
$254$	−8.55701	−	7.11065i	−0.536914	−	0.446162i
$255$	−14.8639	+	4.59296i	−0.930813	+	0.287622i
$256$	11.8539	−	10.7464i	0.740871	−	0.671648i
$257$	−21.5793			−1.34608			−0.673040	−	0.739606i	$-0.735012\pi$
$257$	−21.5793			−1.34608			−0.673040	+	0.739606i	$0.735012\pi$
$258$	−1.86842	+	2.24847i	−0.116323	+	0.139984i
$259$	0.884526	−	21.2258i	0.0549618	−	1.31891i
$260$	−19.9052	+	10.4593i	−1.23447	+	0.648656i
$261$	4.56347			0.282471
$262$	9.96025	+	8.27671i	0.615347	+	0.511337i
$263$	−0.940876			−0.0580169			−0.0290084	−	0.999579i	$-0.509235\pi$
$263$	−0.940876			−0.0580169			−0.0290084	+	0.999579i	$0.509235\pi$
$264$	3.34846	−	5.99698i	0.206083	−	0.369088i
$265$	10.2072	−	3.15404i	0.627023	−	0.193751i
$266$	−3.50259	−	3.16616i	−0.214758	−	0.194130i
$267$	−13.6598			−0.835969
$268$	−3.02284	−	16.2329i	−0.184649	−	0.991585i
$269$			8.65783i			0.527877i	0.964539	+	0.263939i	$0.0850216\pi$
$269$			8.65783i			0.527877i	−0.964539	+	0.263939i	$0.914978\pi$
$270$	−2.92041	−	1.21293i	−0.177731	−	0.0738165i
$271$	−2.31741			−0.140773			−0.0703865	−	0.997520i	$-0.522423\pi$
$271$	−2.31741			−0.140773			−0.0703865	+	0.997520i	$0.522423\pi$
$272$	−25.9644	+	10.0174i	−1.57432	+	0.607391i
$273$	0.553877	−	13.2913i	0.0335222	−	0.804425i
$274$	−11.7914	+	14.1898i	−0.712342	+	0.857238i
$275$	−6.84968	−	10.0253i	−0.413051	−	0.604548i
$276$	−13.4081	+	2.49680i	−0.807070	+	0.150290i
$277$		−	1.45380i		−	0.0873504i	−0.999046	−	0.0436752i	$-0.986093\pi$
$277$		−	1.45380i		−	0.0873504i	0.999046	−	0.0436752i	$-0.0139067\pi$
$278$	21.1326	+	17.5607i	1.26745	+	1.05322i
$279$	0.903134			0.0540692
$280$	16.2081	+	4.15916i	0.968617	+	0.248558i
$281$	4.92911			0.294046			0.147023	−	0.989133i	$-0.453031\pi$
$281$	4.92911			0.294046			0.147023	+	0.989133i	$0.453031\pi$
$282$	3.61029	+	3.00006i	0.214990	+	0.178651i
$283$		−	0.163565i		−	0.00972294i	−0.999988	−	0.00486147i	$-0.998453\pi$
$283$		−	0.163565i		−	0.00972294i	0.999988	−	0.00486147i	$-0.00154746\pi$
$284$	22.7538	−	4.23714i	1.35019	−	0.251428i
$285$	2.69588	−	0.833029i	0.159690	−	0.0493444i
$286$	−11.0358	+	13.2805i	−0.652559	+	0.785293i
$287$	−0.367560	+	8.82028i	−0.0216964	+	0.520644i
$288$	−5.36049	−	1.80698i	−0.315870	−	0.106477i
$289$	31.4061			1.84742
$290$	5.53516	−	13.3272i	0.325036	−	0.782600i
$291$			1.23014i			0.0721118i
$292$	−4.53788	−	24.3688i	−0.265559	−	1.42608i
$293$	2.42869			0.141886			0.0709428	−	0.997480i	$-0.477399\pi$
$293$	2.42869			0.141886			0.0709428	+	0.997480i	$0.477399\pi$
$294$	−6.93843	+	7.06103i	−0.404657	+	0.411808i
$295$	5.53754	+	17.9208i	0.322408	+	1.04339i
$296$	19.8294	+	11.0719i	1.15256	+	0.643540i
$297$	−2.42837			−0.140908
$298$	−1.09215	−	0.907549i	−0.0632666	−	0.0525729i
$299$	34.2873			1.98288
$300$	−7.08451	+	7.05760i	−0.409024	+	0.407471i
$301$	−5.46455	−	0.227720i	−0.314972	−	0.0131256i
$302$	16.6811	−	20.0742i	0.959891	−	1.15514i
$303$	−5.68823			−0.326780
$304$	4.70919	−	1.81686i	0.270090	−	0.104204i
$305$	9.37821	−	2.89788i	0.536995	−	0.165932i
$306$	7.56755	+	6.28844i	0.432608	+	0.359486i
$307$		−	0.689241i		−	0.0393371i	−0.999807	−	0.0196685i	$-0.993739\pi$
$307$		−	0.689241i		−	0.0393371i	0.999807	−	0.0196685i	$-0.00626109\pi$
$308$	12.7196	−	1.82438i	0.724764	−	0.103954i
$309$	−10.0365			−0.570956
$310$	1.09544	−	2.63752i	0.0622167	−	0.149801i
$311$	16.2677			0.922459			0.461230	−	0.887281i	$-0.347408\pi$
$311$	16.2677			0.922459			0.461230	+	0.887281i	$0.347408\pi$
$312$	12.4169	+	6.93305i	0.702967	+	0.392507i
$313$	24.7480			1.39884			0.699419	−	0.714712i	$-0.253442\pi$
$313$	24.7480			1.39884			0.699419	+	0.714712i	$0.253442\pi$
$314$	−5.15251	−	4.28160i	−0.290773	−	0.241625i
$315$	−1.50973	−	5.72020i	−0.0850639	−	0.322297i
$316$	17.0876	−	3.18200i	0.961255	−	0.179001i
$317$		−	21.5126i		−	1.20827i	−0.796883	−	0.604133i	$-0.793520\pi$
$317$		−	21.5126i		−	1.20827i	0.796883	−	0.604133i	$-0.206480\pi$
$318$	−5.19672	−	4.31834i	−0.291418	−	0.242161i
$319$		−	11.0818i		−	0.620461i
$320$	−11.7790	+	13.4631i	−0.658467	+	0.752610i
$321$		−	10.4278i		−	0.582026i
$322$	−18.9282	−	17.1101i	−1.05483	−	0.953511i
$323$	−8.77946			−0.488502
$324$	0.366139	+	1.96620i	0.0203410	+	0.109233i
$325$	20.7576	−	14.1824i	1.15142	−	0.786698i
$326$	−6.00389	−	4.98907i	−0.332524	−	0.276319i
$327$			10.8686i			0.601033i
$328$	−8.24000	−	4.60086i	−0.454978	−	0.254040i
$329$	−0.365642	+	8.77424i	−0.0201585	+	0.483740i
$330$	−2.94544	+	7.09184i	−0.162141	+	0.390393i
$331$		−	10.6160i		−	0.583506i	−0.956494	−	0.291753i	$-0.905762\pi$
$331$		−	10.6160i		−	0.583506i	0.956494	−	0.291753i	$-0.0942385\pi$
$332$	19.1141	−	3.55937i	1.04902	−	0.195346i
$333$		−	8.02957i		−	0.440018i
$334$	17.9549	−	21.6071i	0.982450	−	1.18229i
$335$	5.45020	+	17.6381i	0.297776	+	0.963673i
$336$	−3.39496	−	10.0237i	−0.185210	−	0.546837i
$337$			25.1808i			1.37169i	0.727748	+	0.685844i	$0.240567\pi$
$337$			25.1808i			1.37169i	−0.727748	+	0.685844i	$0.759433\pi$
$338$	−13.3576	−	11.0998i	−0.726559	−	0.603752i
$339$	−5.78750			−0.314334
$340$	27.5437	−	14.4729i	1.49377	−	0.784904i
$341$		−	2.19314i		−	0.118765i
$342$	−1.37253	−	1.14054i	−0.0742181	−	0.0616733i
$343$	−18.3759	−	2.30798i	−0.992205	−	0.124619i
$344$	2.85044	−	5.10505i	0.153685	−	0.275246i
$345$	14.5687	−	4.50174i	0.784352	−	0.242366i
$346$	15.6827	+	13.0319i	0.843106	+	0.700599i
$347$	0.301905			0.0162071			0.00810357	−	0.999967i	$-0.497421\pi$
$347$	0.301905			0.0162071			0.00810357	+	0.999967i	$0.497421\pi$
$348$	−8.97269	+	1.67086i	−0.480987	+	0.0895675i
$349$			22.7065i			1.21545i	0.794147	+	0.607726i	$0.207918\pi$
$349$			22.7065i			1.21545i	−0.794147	+	0.607726i	$0.792082\pi$
$350$	−18.5365	−	2.52915i	−0.990820	−	0.135189i
$351$		−	5.02799i		−	0.268374i
$352$	−4.38801	+	13.0173i	−0.233882	+	0.693822i
$353$	−35.0928			−1.86780			−0.933899	−	0.357536i	$-0.883617\pi$
$353$	−35.0928			−1.86780			−0.933899	+	0.357536i	$0.883617\pi$
$354$	7.58171	−	9.12388i	0.402963	−	0.484929i
$355$	−24.7235	+	7.63958i	−1.31219	+	0.405467i
$356$	26.8580	−	5.00139i	1.42347	−	0.265073i
$357$	−0.766423	+	18.3917i	−0.0405634	+	0.973393i
$358$	9.38077	−	11.2889i	0.495789	−	0.596636i
$359$		−	32.6938i		−	1.72552i	−0.505618	−	0.862758i	$-0.668735\pi$
$359$		−	32.6938i		−	1.72552i	0.505618	−	0.862758i	$-0.331265\pi$
$360$	6.18621	+	1.31559i	0.326042	+	0.0693375i
$361$	−17.4077			−0.916193
$362$	−14.7184	+	17.7122i	−0.773583	+	0.930935i
$363$		−	5.10301i		−	0.267839i
$364$	3.77742	+	26.3361i	0.197991	+	1.38039i
$365$	8.18182	+	26.4783i	0.428256	+	1.38594i
$366$	−4.77466	−	3.96762i	−0.249576	−	0.207391i
$367$			6.26816i			0.327195i	0.986527	+	0.163598i	$0.0523099\pi$
$367$			6.26816i			0.327195i	−0.986527	+	0.163598i	$0.947690\pi$
$368$	25.4487	−	9.81841i	1.32661	−	0.511820i
$369$			3.33664i			0.173699i
$370$	−23.4496	−	9.73930i	−1.21909	−	0.506322i
$371$	0.526311	−	12.6298i	0.0273247	−	0.655707i
$372$	−1.77574	+	0.330672i	−0.0920679	+	0.0171445i
$373$			15.0434i			0.778918i	0.921044	+	0.389459i	$0.127338\pi$
$373$			15.0434i			0.778918i	−0.921044	+	0.389459i	$0.872662\pi$
$374$	15.2707	−	18.3768i	0.789627	−	0.950242i
$375$	6.95784	−	8.75148i	0.359302	−	0.451924i
$376$	−8.19699	−	4.57685i	−0.422728	−	0.236033i
$377$	22.9451			1.18173
$378$	−2.50909	+	2.77570i	−0.129053	+	0.142766i
$379$		−	22.1222i		−	1.13634i	−0.822911	−	0.568171i	$-0.807651\pi$
$379$		−	22.1222i		−	1.13634i	0.822911	−	0.568171i	$-0.192349\pi$
$380$	−4.99563	+	2.62497i	−0.256270	+	0.134658i
$381$		−	7.86714i		−	0.403046i
$382$	−1.01600	+	1.22266i	−0.0519832	+	0.0625570i
$383$		−	19.1338i		−	0.977693i	−0.872370	−	0.488847i	$-0.837418\pi$
$383$		−	19.1338i		−	0.977693i	0.872370	−	0.488847i	$-0.162582\pi$
$384$	11.2014	+	1.59019i	0.571619	+	0.0811493i
$385$	−13.8908	+	3.66620i	−0.707939	+	0.186847i
$386$	−2.34918	+	2.82702i	−0.119570	+	0.143891i
$387$	−2.06720			−0.105082
$388$	−0.450400	−	2.41869i	−0.0228656	−	0.122790i
$389$	−16.6364			−0.843501			−0.421751	−	0.906712i	$-0.638584\pi$
$389$	−16.6364			−0.843501			−0.421751	+	0.906712i	$0.638584\pi$
$390$	−14.6838	−	6.09860i	−0.743544	−	0.308815i
$391$	−47.4447			−2.39938
$392$	11.0570	−	16.4238i	0.558464	−	0.829529i
$393$			9.15726i			0.461922i
$394$	−9.28394	+	11.1724i	−0.467718	+	0.562855i
$395$	−18.5668	+	5.73716i	−0.934197	+	0.288668i
$396$	4.77466	−	0.889120i	0.239936	−	0.0446800i
$397$	7.77915			0.390424			0.195212	−	0.980761i	$-0.437460\pi$
$397$	7.77915			0.390424			0.195212	+	0.980761i	$0.437460\pi$
$398$	−22.6211	−	18.7975i	−1.13389	−	0.942236i
$399$	0.139007	−	3.33572i	0.00695904	−	0.166995i
$400$	11.3455	−	16.4706i	0.567275	−	0.823529i
$401$	23.4144			1.16926			0.584631	−	0.811299i	$-0.301239\pi$
$401$	23.4144			1.16926			0.584631	+	0.811299i	$0.301239\pi$
$402$	7.46212	−	8.97997i	0.372177	−	0.447880i
$403$	4.54095			0.226201
$404$	11.1842	−	2.08268i	0.556434	−	0.103617i
$405$	−0.660150	−	2.13640i	−0.0328031	−	0.106159i
$406$	−12.6668	−	11.4501i	−0.628642	−	0.568261i
$407$	−19.4988			−0.966518
$408$	−17.1817	−	9.59355i	−0.850623	−	0.474952i
$409$		−	28.7795i		−	1.42305i	−0.702659	−	0.711527i	$-0.748004\pi$
$409$		−	28.7795i		−	1.42305i	0.702659	−	0.711527i	$-0.251996\pi$
$410$	9.74437	+	4.04711i	0.481240	+	0.199873i
$411$	−13.0458			−0.643503
$412$	19.7338	−	3.67475i	0.972212	−	0.181042i
$413$	22.1741	+	0.924045i	1.09112	+	0.0454693i
$414$	−7.41725	−	6.16355i	−0.364538	−	0.302922i
$415$	−20.7687	+	6.41756i	−1.01950	+	0.315025i
$416$	−26.9525	−	9.08547i	−1.32146	−	0.445452i
$417$			19.4289i			0.951437i
$418$	−2.76965	+	3.33302i	−0.135468	+	0.163023i
$419$	29.9441			1.46286			0.731432	−	0.681915i	$-0.238852\pi$
$419$	29.9441			1.46286			0.731432	+	0.681915i	$0.238852\pi$
$420$	5.06283	+	10.6943i	0.247041	+	0.521828i
$421$	−12.2568			−0.597360			−0.298680	−	0.954353i	$-0.596546\pi$
$421$	−12.2568			−0.597360			−0.298680	+	0.954353i	$0.596546\pi$
$422$	14.5574	−	17.5184i	0.708641	−	0.852784i
$423$			3.31923i			0.161386i
$424$	11.7989	+	6.58800i	0.573005	+	0.319942i
$425$	−28.7232	+	19.6248i	−1.39328	+	0.951942i
$426$	12.5873	+	10.4597i	0.609856	+	0.506775i
$427$	0.483566	−	11.6041i	0.0234014	−	0.561560i
$428$	3.81804	+	20.5032i	0.184552	+	0.991061i
$429$	−12.2098			−0.589496
$430$	−2.50737	+	6.03707i	−0.120916	+	0.291134i
$431$			13.2857i			0.639948i	0.947426	+	0.319974i	$0.103674\pi$
$431$			13.2857i			0.639948i	−0.947426	+	0.319974i	$0.896326\pi$
$432$	−1.43980	−	3.73189i	−0.0692726	−	0.179550i
$433$	−15.3170			−0.736087			−0.368043	−	0.929809i	$-0.619972\pi$
$433$	−15.3170			−0.736087			−0.368043	+	0.929809i	$0.619972\pi$
$434$	−2.50682	−	2.26604i	−0.120331	−	0.108773i
$435$	9.74939	−	3.01257i	0.467447	−	0.144442i
$436$	−3.97940	−	21.3698i	−0.190579	−	1.02343i
$437$	8.60510			0.411638
$438$	11.2021	−	13.4807i	0.535258	−	0.644133i
$439$	16.4255			0.783948			0.391974	−	0.919976i	$-0.371792\pi$
$439$	16.4255			0.783948			0.391974	+	0.919976i	$0.371792\pi$
$440$	3.19473	−	15.0224i	0.152303	−	0.716166i
$441$	−6.97573	−	0.582399i	−0.332178	−	0.0277333i
$442$	38.0496	+	31.6182i	1.80983	+	1.50393i
$443$	18.5579			0.881712			0.440856	−	0.897578i	$-0.354675\pi$
$443$	18.5579			0.881712			0.440856	+	0.897578i	$0.354675\pi$
$444$	2.93993	+	15.7877i	0.139523	+	0.749253i
$445$	−29.1829	+	9.01754i	−1.38340	+	0.427473i
$446$	−17.8338	+	21.4614i	−0.844457	+	1.01623i
$447$		−	1.00410i		−	0.0474923i
$448$	10.3452	+	18.4655i	0.488766	+	0.872415i
$449$	−15.2449			−0.719451			−0.359726	−	0.933058i	$-0.617130\pi$
$449$	−15.2449			−0.719451			−0.359726	+	0.933058i	$0.617130\pi$
$450$	−7.03988	−	0.663393i	−0.331863	−	0.0312727i
$451$	8.10261			0.381537
$452$	11.3794	−	2.11903i	0.535241	−	0.0996706i
$453$	18.4558			0.867129
$454$	−11.6311	+	13.9970i	−0.545877	+	0.656912i
$455$	−7.59094	−	28.7611i	−0.355869	−	1.34834i
$456$	3.11627	+	1.73999i	0.145933	+	0.0814826i
$457$		−	15.9897i		−	0.747968i	−0.927435	−	0.373984i	$-0.877991\pi$
$457$		−	15.9897i		−	0.747968i	0.927435	−	0.373984i	$-0.122009\pi$
$458$	1.83708	−	2.21076i	0.0858411	−	0.103302i
$459$			6.95745i			0.324746i
$460$	−26.9967	+	14.1855i	−1.25873	+	0.661402i
$461$		−	8.27893i		−	0.385588i	−0.981239	−	0.192794i	$-0.938245\pi$
$461$		−	8.27893i		−	0.385588i	0.981239	−	0.192794i	$-0.0617550\pi$
$462$	6.74042	+	6.09299i	0.313593	+	0.283472i
$463$	−12.0015			−0.557759			−0.278879	−	0.960326i	$-0.589963\pi$
$463$	−12.0015			−0.557759			−0.278879	+	0.960326i	$0.589963\pi$
$464$	17.0303	−	6.57049i	0.790613	−	0.305028i
$465$	1.92945	−	0.596204i	0.0894763	−	0.0276483i
$466$	17.4520	−	21.0018i	0.808447	−	0.972890i
$467$		−	18.4361i		−	0.853122i	−0.904459	−	0.426561i	$-0.859725\pi$
$467$		−	18.4361i		−	0.853122i	0.904459	−	0.426561i	$-0.140275\pi$
$468$	1.84094	+	9.88604i	0.0850976	+	0.456982i
$469$	21.8244	+	0.909469i	1.00776	+	0.0419954i
$470$	9.69352	+	4.02599i	0.447129	+	0.185705i
$471$		−	4.73711i		−	0.218274i
$472$	−11.5666	+	20.7153i	−0.532394	+	0.953501i
$473$			5.01993i			0.230817i
$474$	9.45278	+	7.85502i	0.434181	+	0.360793i
$475$	5.20955	−	3.55937i	0.239030	−	0.163315i
$476$	−5.22698	−	36.4424i	−0.239578	−	1.67034i
$477$		−	4.77776i		−	0.218759i
$478$	25.4233	−	30.5945i	1.16283	−	1.39936i
$479$	−2.49617			−0.114053			−0.0570265	−	0.998373i	$-0.518162\pi$
$479$	−2.49617			−0.114053			−0.0570265	+	0.998373i	$0.518162\pi$
$480$	−12.6450	−	0.321697i	−0.577164	−	0.0146834i
$481$		−	40.3726i		−	1.84083i
$482$	27.0649	−	32.5701i	1.23277	−	1.48353i
$483$	0.751201	−	18.0265i	0.0341809	−	0.820232i
$484$	1.86841	+	10.0335i	0.0849277	+	0.456070i
$485$	0.812073	+	2.62806i	0.0368744	+	0.119334i
$486$	−0.903842	+	1.08769i	−0.0409991	+	0.0493386i
$487$	5.38162			0.243865			0.121932	−	0.992538i	$-0.461091\pi$
$487$	5.38162			0.243865			0.121932	+	0.992538i	$0.461091\pi$
$488$	10.8406	+	6.05295i	0.490733	+	0.274004i
$489$		−	5.51985i		−	0.249616i
$490$	−10.1619	+	19.6656i	−0.459069	+	0.888401i
$491$			5.98485i			0.270093i	0.990839	+	0.135046i	$0.0431183\pi$
$491$			5.98485i			0.270093i	−0.990839	+	0.135046i	$0.956882\pi$
$492$	−1.22167	−	6.56051i	−0.0550773	−	0.295771i
$493$	−31.7501			−1.42995
$494$	−6.90109	−	5.73463i	−0.310495	−	0.258013i
$495$	−5.18797	+	1.60309i	−0.233182	+	0.0720535i
$496$	3.37039	−	1.30033i	0.151335	−	0.0583868i
$497$	−1.27481	+	30.5914i	−0.0571830	+	1.37221i
$498$	10.5738	+	8.78658i	0.473825	+	0.393736i
$499$			12.0965i			0.541516i	0.962647	+	0.270758i	$0.0872743\pi$
$499$			12.0965i			0.541516i	−0.962647	+	0.270758i	$0.912726\pi$
$500$	−10.4763	+	19.7547i	−0.468513	+	0.883457i
$501$	19.8651			0.887508
$502$	5.76935	+	4.79418i	0.257499	+	0.213975i
$503$			40.6529i			1.81262i	0.422612	+	0.906311i	$0.361113\pi$
$503$			40.6529i			1.81262i	−0.422612	+	0.906311i	$0.638887\pi$
$504$	3.91708	−	6.37625i	0.174480	−	0.284021i
$505$	−12.1523	+	3.75508i	−0.540771	+	0.167099i
$506$	−14.9674	+	18.0118i	−0.665381	+	0.800724i
$507$		−	12.2807i		−	0.545406i
$508$	2.88046	+	15.4684i	0.127800	+	0.686298i
$509$			9.39295i			0.416335i	0.978093	+	0.208168i	$0.0667499\pi$
$509$			9.39295i			0.416335i	−0.978093	+	0.208168i	$0.933250\pi$
$510$	20.3186	+	8.43890i	0.899723	+	0.373681i
$511$	32.7627	+	1.36529i	1.44934	+	0.0603970i
$512$	−22.6064	+	0.974622i	−0.999072	+	0.0430726i
$513$		−	1.26188i		−	0.0557133i
$514$	23.4716	+	19.5043i	1.03529	+	0.860297i
$515$	−21.4420	+	6.62559i	−0.944845	+	0.291958i
$516$	4.06453	−	0.756882i	0.178931	−	0.0333199i
$517$	8.06032			0.354493
$518$	−20.1469	+	22.2876i	−0.885203	+	0.979263i
$519$			14.4183i			0.632894i
$520$	31.1042	+	6.61477i	1.36401	+	0.290077i
$521$			35.0857i			1.53713i	0.639769	+	0.768567i	$0.279030\pi$
$521$			35.0857i			1.53713i	−0.639769	+	0.768567i	$0.720970\pi$
$522$	−4.96364	−	4.12465i	−0.217252	−	0.180531i
$523$			40.5211i			1.77186i	0.463814	+	0.885932i	$0.346480\pi$
$523$			40.5211i			1.77186i	−0.463814	+	0.885932i	$0.653520\pi$
$524$	−3.35282	−	18.0050i	−0.146469	−	0.786552i
$525$	−7.00159	−	11.2240i	−0.305574	−	0.489855i
$526$	1.02338	+	0.850403i	0.0446215	+	0.0370793i
$527$	−6.28351			−0.273714
$528$	−9.06240	+	3.49638i	−0.394390	+	0.152160i
$529$	23.5025			1.02185
$530$	−13.9530	−	5.79509i	−0.606081	−	0.251722i
$531$	8.38831			0.364022
$532$	0.948021	+	6.60959i	0.0411019	+	0.286562i
$533$			16.7766i			0.726676i
$534$	14.8577	+	12.3463i	0.642954	+	0.534278i
$535$	−6.88394	−	22.2780i	−0.297619	−	0.963164i
$536$	−11.3841	+	20.3886i	−0.491719	+	0.880652i
$537$	10.3788			0.447877
$538$	7.82531	−	9.41703i	0.337373	−	0.405997i
$539$	−1.41428	+	16.9397i	−0.0609174	+	0.729643i
$540$	2.08020	+	3.95888i	0.0895178	+	0.170363i
$541$	−20.4628			−0.879766			−0.439883	−	0.898055i	$-0.644980\pi$
$541$	−20.4628			−0.879766			−0.439883	+	0.898055i	$0.644980\pi$
$542$	2.52063	+	2.09458i	0.108270	+	0.0899698i
$543$	−16.2843			−0.698825
$544$	37.2953	+	12.5719i	1.59902	+	0.539018i
$545$	7.17488	+	23.2196i	0.307338	+	0.994617i
$546$	−12.6157	+	13.9562i	−0.539901	+	0.597269i
$547$	−19.3311			−0.826538			−0.413269	−	0.910609i	$-0.635613\pi$
$547$	−19.3311			−0.826538			−0.413269	+	0.910609i	$0.635613\pi$
$548$	25.6507	−	4.77658i	1.09574	−	0.204045i
$549$		−	4.38973i		−	0.187349i
$550$	−1.61096	+	17.0954i	−0.0686918	+	0.728952i
$551$	5.75854			0.245322
$552$	16.8405	+	9.40302i	0.716780	+	0.400219i
$553$	−0.957355	+	22.9735i	−0.0407109	+	0.976932i
$554$	−1.31401	+	1.58128i	−0.0558268	+	0.0671823i
$555$	−5.30072	−	17.1544i	−0.225003	−	0.728162i
$556$	−7.11367	−	38.2011i	−0.301687	−	1.62009i
$557$		−	2.17496i		−	0.0921562i	−0.998938	−	0.0460781i	$-0.985328\pi$
$557$		−	2.17496i		−	0.0921562i	0.998938	−	0.0460781i	$-0.0146723\pi$
$558$	−0.982329	−	0.816290i	−0.0415853	−	0.0345563i
$559$	−10.3939			−0.439614
$560$	−13.8701	−	19.1734i	−0.586120	−	0.810225i
$561$	16.8953			0.713319
$562$	−5.36134	−	4.45514i	−0.226155	−	0.187929i
$563$		−	16.2706i		−	0.685723i	−0.939386	−	0.342861i	$-0.888604\pi$
$563$		−	16.2706i		−	0.685723i	0.939386	−	0.342861i	$-0.111396\pi$
$564$	−1.21530	−	6.52627i	−0.0511733	−	0.274806i
$565$	−12.3644	+	3.82062i	−0.520175	+	0.160735i
$566$	−0.147837	+	0.177908i	−0.00621405	+	0.00747803i
$567$	−2.64346	−	0.110159i	−0.111015	−	0.00462623i
$568$	−28.5788	−	15.9572i	−1.19914	−	0.669549i
$569$	−8.46578			−0.354904			−0.177452	−	0.984129i	$-0.556785\pi$
$569$	−8.46578			−0.354904			−0.177452	+	0.984129i	$0.556785\pi$
$570$	−3.68521	−	1.53057i	−0.154356	−	0.0641085i
$571$		−	4.43035i		−	0.185404i	−0.995694	−	0.0927021i	$-0.970450\pi$
$571$		−	4.43035i		−	0.185404i	0.995694	−	0.0927021i	$-0.0295504\pi$
$572$	24.0070	−	4.47049i	1.00378	−	0.186921i
$573$	−1.12409			−0.0469597
$574$	8.37193	−	9.26151i	0.349438	−	0.386568i
$575$	28.1527	−	19.2350i	1.17405	−	0.802156i
$576$	4.19733	+	6.81047i	0.174889	+	0.283769i
$577$	14.0750			0.585950			0.292975	−	0.956120i	$-0.405355\pi$
$577$	14.0750			0.585950			0.292975	+	0.956120i	$0.405355\pi$
$578$	−34.1601	−	28.3862i	−1.42087	−	1.18071i
$579$	−2.59910			−0.108015
$580$	−18.0662	+	9.49294i	−0.750159	+	0.394173i
$581$	−1.07089	+	25.6980i	−0.0444281	+	1.06613i
$582$	1.11185	−	1.33801i	0.0460876	−	0.0554621i
$583$	−11.6022			−0.480513
$584$	−17.0898	+	30.6073i	−0.707180	+	1.26654i
$585$	−3.31923	−	10.7418i	−0.137233	−	0.444119i
$586$	−2.64166	−	2.19515i	−0.109126	−	0.0906809i
$587$			0.686299i			0.0283266i	0.999900	+	0.0141633i	$0.00450847\pi$
$587$			0.686299i			0.0283266i	−0.999900	+	0.0141633i	$0.995492\pi$
$588$	13.9289	−	1.40897i	0.574419	−	0.0581050i
$589$	1.13965			0.0469583
$590$	10.1744	−	24.4973i	0.418875	−	1.00854i
$591$	−10.2716			−0.422519
$592$	−11.5610	−	29.9654i	−0.475154	−	1.23157i
$593$	26.4738			1.08715			0.543574	−	0.839361i	$-0.317071\pi$
$593$	26.4738			1.08715			0.543574	+	0.839361i	$0.317071\pi$
$594$	2.64131	+	2.19486i	0.108374	+	0.0900564i
$595$	10.5039	+	39.7980i	0.430618	+	1.63156i
$596$	0.367640	+	1.97426i	0.0150591	+	0.0808690i
$597$		−	20.7974i		−	0.851180i
$598$	−37.2939	−	30.9903i	−1.52506	−	1.26729i
$599$			12.8228i			0.523927i	0.965078	+	0.261964i	$0.0843701\pi$
$599$			12.8228i			0.523927i	−0.965078	+	0.261964i	$0.915630\pi$
$600$	14.0847	−	1.27321i	0.575006	−	0.0519785i
$601$		−	15.5307i		−	0.633512i	−0.948507	−	0.316756i	$-0.897406\pi$
$601$		−	15.5307i		−	0.633512i	0.948507	−	0.316756i	$-0.102594\pi$
$602$	5.73792	+	5.18678i	0.233860	+	0.211398i
$603$	8.25600			0.336210
$604$	−36.2878	+	6.75738i	−1.47653	+	0.274954i
$605$	−3.36875	−	10.9021i	−0.136959	−	0.443232i
$606$	6.18703	+	5.14126i	0.251331	+	0.208849i
$607$		−	34.3015i		−	1.39226i	−0.717918	−	0.696128i	$-0.754905\pi$
$607$		−	34.3015i		−	1.39226i	0.717918	−	0.696128i	$-0.245095\pi$
$608$	−6.76429	−	2.28018i	−0.274328	−	0.0924737i
$609$	0.502705	−	12.0633i	0.0203706	−	0.488831i
$610$	−12.8198	−	5.32443i	−0.519059	−	0.215580i
$611$			16.6891i			0.675167i
$612$	−2.54739	−	13.6797i	−0.102972	−	0.552971i
$613$		−	31.4527i		−	1.27036i	−0.772363	−	0.635181i	$-0.780925\pi$
$613$		−	31.4527i		−	1.27036i	0.772363	−	0.635181i	$-0.219075\pi$
$614$	−0.622965	+	0.749681i	−0.0251408	+	0.0302547i
$615$	2.20269	+	7.12840i	0.0888208	+	0.287445i
$616$	−15.4839	−	9.51212i	−0.623864	−	0.383254i
$617$		−	18.9888i		−	0.764461i	−0.924067	−	0.382230i	$-0.875156\pi$
$617$		−	18.9888i		−	0.764461i	0.924067	−	0.382230i	$-0.124844\pi$
$618$	10.9166	+	9.07140i	0.439130	+	0.364905i
$619$	5.13881			0.206546			0.103273	−	0.994653i	$-0.467068\pi$
$619$	5.13881			0.206546			0.103273	+	0.994653i	$0.467068\pi$
$620$	−3.57540	+	1.87870i	−0.143592	+	0.0754505i
$621$		−	6.81927i		−	0.273648i
$622$	−17.6943	−	14.7035i	−0.709475	−	0.589556i
$623$	−1.50475	+	36.1092i	−0.0602865	+	1.44668i
$624$	−7.23932	−	18.7639i	−0.289805	−	0.751157i
$625$	9.08745	−	23.2899i	0.363498	−	0.931595i
$626$	−26.9181	−	22.3683i	−1.07586	−	0.894015i
$627$	−3.06431			−0.122377
$628$	1.73444	+	9.31411i	0.0692116	+	0.371673i
$629$			55.8653i			2.22750i
$630$	−3.52804	+	7.58637i	−0.140560	+	0.302248i
$631$		−	26.4530i		−	1.05308i	−0.850152	−	0.526538i	$-0.823490\pi$
$631$		−	26.4530i		−	1.05308i	0.850152	−	0.526538i	$-0.176510\pi$
$632$	−21.4621	−	11.9835i	−0.853716	−	0.476678i
$633$	16.1061			0.640159
$634$	−19.4440	+	23.3990i	−0.772218	+	0.929293i
$635$	−5.19349	−	16.8074i	−0.206097	−	0.666979i
$636$	1.74932	+	9.39403i	0.0693651	+	0.372498i
$637$	−35.0739	−	2.92830i	−1.38968	−	0.116023i
$638$	−10.0162	+	12.0536i	−0.396545	+	0.477205i
$639$			11.5725i			0.457801i
$640$	24.9804	−	3.99731i	0.987438	−	0.158008i
$641$	26.1290			1.03203			0.516017	−	0.856578i	$-0.327414\pi$
$641$	26.1290			1.03203			0.516017	+	0.856578i	$0.327414\pi$
$642$	−9.42513	+	11.3423i	−0.371980	+	0.447643i
$643$			7.94102i			0.313163i	0.987665	+	0.156582i	$0.0500474\pi$
$643$			7.94102i			0.313163i	−0.987665	+	0.156582i	$0.949953\pi$
$644$	5.12317	+	35.7187i	0.201881	+	1.40751i
$645$	−4.41636	+	1.36466i	−0.173894	+	0.0537335i
$646$	9.54933	+	7.93524i	0.375713	+	0.312208i
$647$			13.3597i			0.525224i	0.964901	+	0.262612i	$0.0845839\pi$
$647$			13.3597i			0.525224i	−0.964901	+	0.262612i	$0.915416\pi$
$648$	1.37889	−	2.46955i	0.0541679	−	0.0970130i
$649$		−	20.3699i		−	0.799590i
$650$	−35.3965	−	3.33554i	−1.38836	−	0.130831i
$651$	0.0994879	−	2.38740i	0.00389924	−	0.0935694i
$652$	2.02103	+	10.8531i	0.0791496	+	0.425041i
$653$		−	34.3305i		−	1.34345i	−0.740799	−	0.671727i	$-0.765553\pi$
$653$		−	34.3305i		−	1.34345i	0.740799	−	0.671727i	$-0.234447\pi$
$654$	9.82346	−	11.8216i	0.384128	−	0.462262i
$655$	6.04516	+	19.5636i	0.236204	+	0.764411i
$656$	4.80411	+	12.4520i	0.187569	+	0.486168i
$657$	12.3939			0.483531
$658$	8.32823	−	9.21317i	0.324668	−	0.359167i
$659$		−	8.40189i		−	0.327291i	−0.986519	−	0.163646i	$-0.947675\pi$
$659$		−	8.40189i		−	0.327291i	0.986519	−	0.163646i	$-0.0523254\pi$
$660$	9.61364	−	5.05151i	0.374210	−	0.196630i
$661$			0.695485i			0.0270512i	0.999909	+	0.0135256i	$0.00430547\pi$
$661$			0.695485i			0.0270512i	−0.999909	+	0.0135256i	$0.995695\pi$
$662$	−9.59515	+	11.5469i	−0.372926	+	0.448782i
$663$			34.9820i			1.35859i
$664$	−24.0074	−	13.4047i	−0.931666	−	0.520203i
$665$	−1.90510	−	7.21820i	−0.0738767	−	0.279910i
$666$	−7.25746	+	8.73368i	−0.281221	+	0.338423i
$667$	31.1195			1.20495
$668$	−39.0588	+	7.27339i	−1.51123	+	0.281416i
$669$	−19.7311			−0.762850
$670$	10.0139	−	24.1109i	0.386872	−	0.931486i
$671$	−10.6599			−0.411521
$672$	−5.36717	+	13.9712i	−0.207043	+	0.538949i
$673$			16.9145i			0.652006i	0.945369	+	0.326003i	$0.105702\pi$
$673$			16.9145i			0.652006i	−0.945369	+	0.326003i	$0.894298\pi$
$674$	22.7595	−	27.3890i	0.876664	−	1.05498i
$675$	−2.82069	−	4.12840i	−0.108568	−	0.158902i
$676$	4.49645	+	24.1464i	0.172940	+	0.928707i
$677$	−25.8262			−0.992581			−0.496291	−	0.868156i	$-0.665305\pi$
$677$	−25.8262			−0.992581			−0.496291	+	0.868156i	$0.665305\pi$
$678$	6.29500	+	5.23099i	0.241758	+	0.200895i
$679$	3.25181	+	0.135510i	0.124793	+	0.00520040i
$680$	−43.0403	−	9.15313i	−1.65052	−	0.351007i
$681$	−12.8686			−0.493124
$682$	−1.98226	+	2.38546i	−0.0759045	+	0.0913440i
$683$	−33.6817			−1.28879			−0.644397	−	0.764691i	$-0.722891\pi$
$683$	−33.6817			−1.28879			−0.644397	+	0.764691i	$0.722891\pi$
$684$	0.462022	+	2.48111i	0.0176659	+	0.0948675i
$685$	−27.8711	+	8.61220i	−1.06490	+	0.329055i
$686$	17.9012	+	19.1193i	0.683471	+	0.729977i
$687$	2.03252			0.0775456
$688$	−7.71455	+	2.97636i	−0.294115	+	0.113473i
$689$		−	24.0225i		−	0.915186i
$690$	−19.9151	−	8.27130i	−0.758154	−	0.314883i
$691$	−25.0523			−0.953036			−0.476518	−	0.879165i	$-0.658101\pi$
$691$	−25.0523			−0.953036			−0.476518	+	0.879165i	$0.658101\pi$
$692$	−5.27911	−	28.3493i	−0.200681	−	1.07768i
$693$	−0.267506	+	6.41929i	−0.0101617	+	0.243849i
$694$	−0.328380	−	0.272875i	−0.0124651	−	0.0103582i
$695$	12.8260	+	41.5079i	0.486517	+	1.57448i
$696$	11.2697	+	6.29252i	0.427177	+	0.238517i
$697$		−	23.2145i		−	0.879313i
$698$	20.5231	−	24.6977i	0.776812	−	0.934820i
$699$	19.3086			0.730320
$700$	17.8761	+	19.5050i	0.675651	+	0.737221i
$701$	−21.9049			−0.827338			−0.413669	−	0.910427i	$-0.635753\pi$
$701$	−21.9049			−0.827338			−0.413669	+	0.910427i	$0.635753\pi$
$702$	−4.54451	+	5.46890i	−0.171522	+	0.206410i
$703$		−	10.1323i		−	0.382149i
$704$	16.5383	−	10.1927i	0.623312	−	0.384151i
$705$	2.19119	+	7.09120i	0.0825249	+	0.267070i
$706$	38.1700	+	31.7183i	1.43655	+	1.19373i
$707$	−0.626607	+	15.0366i	−0.0235660	+	0.565509i
$708$	−16.4931	+	3.07129i	−0.619849	+	0.115426i
$709$	12.3158			0.462529			0.231265	−	0.972891i	$-0.425714\pi$
$709$	12.3158			0.462529			0.231265	+	0.972891i	$0.425714\pi$
$710$	33.7964	+	14.0366i	1.26836	+	0.526785i
$711$			8.69070i			0.325927i
$712$	−33.7336	−	18.8354i	−1.26422	−	0.705887i
$713$	6.15871			0.230646
$714$	17.4568	−	19.3118i	0.653306	−	0.722724i
$715$	−26.0851	+	8.06032i	−0.975527	+	0.301439i
$716$	−20.4067	+	3.80007i	−0.762636	+	0.142015i
$717$	28.1280			1.05046
$718$	−29.5501	+	35.5608i	−1.10280	+	1.32712i
$719$	14.7813			0.551250			0.275625	−	0.961265i	$-0.411115\pi$
$719$	14.7813			0.551250			0.275625	+	0.961265i	$0.411115\pi$
$720$	−5.53960	−	7.02231i	−0.206449	−	0.261706i
$721$	−1.10561	+	26.5310i	−0.0411749	+	0.988067i
$722$	18.9341	+	15.7338i	0.704656	+	0.585551i
$723$	29.9443			1.11364
$724$	32.0181	−	5.96230i	1.18994	−	0.221587i
$725$	18.8398	−	12.8721i	0.699694	−	0.478058i
$726$	−4.61232	+	5.55050i	−0.171179	+	0.205998i
$727$		−	40.4563i		−	1.50044i	−0.661187	−	0.750221i	$-0.729947\pi$
$727$		−	40.4563i		−	1.50044i	0.661187	−	0.750221i	$-0.270053\pi$
$728$	19.6950	−	32.0597i	0.729947	−	1.18821i
$729$	−1.00000			−0.0370370
$730$	15.0329	−	36.1952i	0.556393	−	1.33965i
$731$	14.3824			0.531954
$732$	1.60725	+	8.63108i	0.0594056	+	0.319014i
$733$	27.2268			1.00564			0.502822	−	0.864390i	$-0.332295\pi$
$733$	27.2268			1.00564			0.502822	+	0.864390i	$0.332295\pi$
$734$	5.66542	−	6.81781i	0.209115	−	0.251650i
$735$	−15.2874	+	3.36079i	−0.563885	+	0.123965i
$736$	−36.5546	−	12.3223i	−1.34742	−	0.454205i
$737$		−	20.0486i		−	0.738501i
$738$	3.01580	−	3.62923i	0.111013	−	0.133594i
$739$			4.89812i			0.180180i	0.995934	+	0.0900902i	$0.0287155\pi$
$739$			4.89812i			0.180180i	−0.995934	+	0.0900902i	$0.971284\pi$
$740$	16.7031	+	31.7881i	0.614020	+	1.16855i
$741$		−	6.34472i		−	0.233079i
$742$	−11.9878	+	13.2616i	−0.440086	+	0.486849i
$743$	18.5579			0.680823			0.340412	−	0.940277i	$-0.389434\pi$
$743$	18.5579			0.680823			0.340412	+	0.940277i	$0.389434\pi$
$744$	2.23033	+	1.24532i	0.0817679	+	0.0456557i
$745$	−0.662857	−	2.14516i	−0.0242852	−	0.0785926i
$746$	13.5969	−	16.3626i	0.497816	−	0.599076i
$747$			9.72136i			0.355686i
$748$	−33.2195	+	6.18601i	−1.21462	+	0.226183i
$749$	−27.5656	−	1.14872i	−1.00722	−	0.0419732i
$750$	−15.4779	+	3.23010i	−0.565174	+	0.117947i
$751$		−	9.28709i		−	0.338891i	−0.985540	−	0.169445i	$-0.945802\pi$
$751$		−	9.28709i		−	0.338891i	0.985540	−	0.169445i	$-0.0541976\pi$
$752$	4.77904	+	12.3870i	0.174274	+	0.451707i
$753$			5.30422i			0.193297i
$754$	−24.9571	−	20.7387i	−0.908885	−	0.755260i
$755$	39.4290	−	12.1836i	1.43497	−	0.443406i
$756$	5.23790	−	0.751278i	0.190501	−	0.0273237i
$757$			46.9485i			1.70637i	0.521608	+	0.853186i	$0.325333\pi$
$757$			46.9485i			1.70637i	−0.521608	+	0.853186i	$0.674667\pi$
$758$	−19.9950	+	24.0621i	−0.726250	+	0.873975i
$759$	−16.5597			−0.601080
$760$	7.80625	+	1.66011i	0.283162	+	0.0602186i
$761$		−	0.272334i		−	0.00987210i	−0.999988	−	0.00493605i	$-0.998429\pi$
$761$		−	0.272334i		−	0.00987210i	0.999988	−	0.00493605i	$-0.00157120\pi$
$762$	−7.11065	+	8.55701i	−0.257592	+	0.309988i
$763$	28.7306	+	1.19726i	1.04012	+	0.0433439i
$764$	2.21019	−	0.411574i	0.0799619	−	0.0148902i
$765$	4.59296	+	14.8639i	0.166059	+	0.537405i
$766$	−17.2940	+	20.8117i	−0.624856	+	0.751957i
$767$	42.1764			1.52290
$768$	−10.7464	−	11.8539i	−0.387776	−	0.427742i
$769$		−	33.9228i		−	1.22329i	−0.791134	−	0.611643i	$-0.790509\pi$
$769$		−	33.9228i		−	1.22329i	0.791134	−	0.611643i	$-0.209491\pi$
$770$	18.4225	+	8.56738i	0.663901	+	0.308747i
$771$			21.5793i			0.777159i
$772$	5.11036	−	0.951632i	0.183926	−	0.0342500i
$773$	−17.0998			−0.615037			−0.307519	−	0.951542i	$-0.599499\pi$
$773$	−17.0998			−0.615037			−0.307519	+	0.951542i	$0.599499\pi$
$774$	2.24847	+	1.86842i	0.0808197	+	0.0671591i
$775$	3.72850	−	2.54746i	0.133932	−	0.0915074i
$776$	−1.69622	+	3.03788i	−0.0608908	+	0.109053i
$777$	−21.2258	−	0.884526i	−0.761472	−	0.0317322i
$778$	18.0953	+	15.0367i	0.648748	+	0.539093i
$779$			4.21044i			0.150855i
$780$	10.4593	+	19.9052i	0.374502	+	0.712722i
$781$	28.1023			1.00558
$782$	51.6052	+	42.8826i	1.84540	+	1.53348i
$783$		−	4.56347i		−	0.163085i
$784$	−26.8712	+	7.87023i	−0.959684	+	0.281080i
$785$	−3.12720	−	10.1204i	−0.111615	−	0.361211i
$786$	8.27671	−	9.96025i	0.295221	−	0.355270i
$787$			48.8856i			1.74258i	0.490764	+	0.871292i	$0.336718\pi$
$787$			48.8856i			1.74258i	−0.490764	+	0.871292i	$0.663282\pi$
$788$	20.1961	−	3.76084i	0.719456	−	0.133974i
$789$			0.940876i			0.0334961i
$790$	25.3804	+	10.5412i	0.902994	+	0.375039i
$791$	−0.637543	+	15.2990i	−0.0226684	+	0.543970i
$792$	−5.99698	−	3.34846i	−0.213093	−	0.118982i
$793$		−	22.0715i		−	0.783783i
$794$	−8.46130	−	7.03112i	−0.300280	−	0.249525i
$795$	−3.15404	−	10.2072i	−0.111862	−	0.362012i
$796$	7.61472	+	40.8918i	0.269897	+	1.44937i
$797$	−5.35954			−0.189845			−0.0949223	−	0.995485i	$-0.530260\pi$
$797$	−5.35954			−0.189845			−0.0949223	+	0.995485i	$0.530260\pi$
$798$	−3.16616	+	3.50259i	−0.112081	+	0.123990i
$799$		−	23.0934i		−	0.816985i
$800$	−27.2272	+	7.66033i	−0.962626	+	0.270834i
$801$			13.6598i			0.482647i
$802$	−25.4677	−	21.1630i	−0.899294	−	0.747290i
$803$		−	30.0969i		−	1.06210i
$804$	−16.2329	+	3.02284i	−0.572492	+	0.106607i
$805$	−10.2953	−	39.0076i	−0.362861	−	1.37484i
$806$	−4.93915	−	4.10430i	−0.173974	−	0.144568i
$807$	8.65783			0.304770
$808$	−14.0473	−	7.84344i	−0.494184	−	0.275931i
$809$	−0.565476			−0.0198811			−0.00994054	−	0.999951i	$-0.503164\pi$
$809$	−0.565476			−0.0198811			−0.00994054	+	0.999951i	$0.503164\pi$
$810$	−1.21293	+	2.92041i	−0.0426180	+	0.102613i
$811$	−25.0344			−0.879076			−0.439538	−	0.898224i	$-0.644858\pi$
$811$	−25.0344			−0.879076			−0.439538	+	0.898224i	$0.644858\pi$
$812$	3.42843	+	23.9030i	0.120314	+	0.838830i
$813$			2.31741i			0.0812753i
$814$	21.2086	+	17.6238i	0.743362	+	0.617714i
$815$	−3.64393	−	11.7926i	−0.127641	−	0.413077i
$816$	10.0174	+	25.9644i	0.350678	+	0.908936i
$817$	−2.60856			−0.0912618
$818$	−26.0121	+	31.3032i	−0.909492	+	1.09449i
$819$	−13.2913	−	0.553877i	−0.464435	−	0.0193540i
$820$	−6.94090	−	13.2094i	−0.242387	−	0.461292i
$821$	44.7864			1.56306			0.781529	−	0.623869i	$-0.214440\pi$
$821$	44.7864			1.56306			0.781529	+	0.623869i	$0.214440\pi$
$822$	14.1898	+	11.7914i	0.494926	+	0.411271i
$823$	53.8252			1.87623			0.938114	−	0.346326i	$-0.112571\pi$
$823$	53.8252			1.87623			0.938114	+	0.346326i	$0.112571\pi$
$824$	−24.7856	−	13.8392i	−0.863447	−	0.482112i
$825$	−10.0253	+	6.84968i	−0.349036	+	0.238475i
$826$	−23.2834	−	21.0470i	−0.810133	−	0.732319i
$827$	16.2007			0.563353			0.281677	−	0.959509i	$-0.409109\pi$
$827$	16.2007			0.563353			0.281677	+	0.959509i	$0.409109\pi$
$828$	2.49680	+	13.4081i	0.0867697	+	0.465962i
$829$			29.5159i			1.02513i	0.858649	+	0.512564i	$0.171304\pi$
$829$			29.5159i			1.02513i	−0.858649	+	0.512564i	$0.828696\pi$
$830$	28.3904	+	11.7913i	0.985444	+	0.409283i
$831$	−1.45380			−0.0504318
$832$	21.1041	+	34.2430i	0.731654	+	1.18716i
$833$	48.5333	+	4.05201i	1.68158	+	0.140394i
$834$	17.5607	−	21.1326i	0.608076	−	0.731763i
$835$	42.4398	−	13.1140i	1.46869	−	0.453827i
$836$	6.02505	−	1.12196i	0.208381	−	0.0388039i
$837$		−	0.903134i		−	0.0312169i
$838$	−32.5699	−	27.0647i	−1.12511	−	0.934935i
$839$	−22.9604			−0.792681			−0.396341	−	0.918104i	$-0.629720\pi$
$839$	−22.9604			−0.792681			−0.396341	+	0.918104i	$0.629720\pi$
$840$	4.15916	−	16.2081i	0.143505	−	0.559231i
$841$	−8.17477			−0.281889
$842$	13.3316	+	11.0782i	0.459438	+	0.381781i
$843$		−	4.92911i		−	0.169768i
$844$	−31.6678	+	5.89706i	−1.09005	+	0.202985i
$845$	−8.10712	−	26.2365i	−0.278893	−	0.902564i
$846$	3.00006	−	3.61029i	0.103144	−	0.124124i
$847$	−13.4896	−	0.562141i	−0.463508	−	0.0193154i
$848$	−6.87903	−	17.8301i	−0.236227	−	0.612286i
$849$	−0.163565			−0.00561354
$850$	48.9796	+	4.61552i	1.67999	+	0.158311i
$851$		−	54.7558i		−	1.87701i
$852$	−4.23714	−	22.7538i	−0.145162	−	0.779534i
$853$	9.64061			0.330088			0.165044	−	0.986286i	$-0.447223\pi$
$853$	9.64061			0.330088			0.165044	+	0.986286i	$0.447223\pi$
$854$	−11.0142	+	12.1846i	−0.376898	+	0.416947i
$855$	−0.833029	−	2.69588i	−0.0284890	−	0.0921971i
$856$	14.3788	−	25.7521i	0.491459	−	0.880187i
$857$	−26.5550			−0.907101			−0.453551	−	0.891231i	$-0.649843\pi$
$857$	−26.5550			−0.907101			−0.453551	+	0.891231i	$0.649843\pi$
$858$	13.2805	+	11.0358i	0.453389	+	0.376755i
$859$	−29.8048			−1.01693			−0.508464	−	0.861083i	$-0.669786\pi$
$859$	−29.8048			−1.01693			−0.508464	+	0.861083i	$0.669786\pi$
$860$	8.18380	−	4.30020i	0.279065	−	0.146636i
$861$	8.82028	+	0.367560i	0.300594	+	0.0125264i
$862$	12.0081	−	14.4507i	0.408999	−	0.492192i
$863$	−24.8242			−0.845027			−0.422513	−	0.906357i	$-0.638852\pi$
$863$	−24.8242			−0.845027			−0.422513	+	0.906357i	$0.638852\pi$
$864$	−1.80698	+	5.36049i	−0.0614746	+	0.182368i
$865$	9.51826	+	30.8033i	0.323630	+	1.04734i
$866$	16.6601	+	13.8441i	0.566134	+	0.470442i
$867$		−	31.4061i		−	1.06661i
$868$	0.678504	+	4.73052i	0.0230299	+	0.160564i
$869$	21.1042			0.715912
$870$	−13.3272	−	5.53516i	−0.451834	−	0.187660i
$871$	41.5111			1.40655
$872$	−14.9865	+	26.8404i	−0.507508	+	0.908931i
$873$	1.23014			0.0416338
$874$	−9.35968	−	7.77765i	−0.316596	−	0.263083i
$875$	−22.3677	−	19.3568i	−0.756166	−	0.654380i
$876$	−24.3688	+	4.53788i	−0.823347	+	0.153321i
$877$		−	15.6762i		−	0.529347i	−0.964338	−	0.264674i	$-0.914736\pi$
$877$		−	15.6762i		−	0.529347i	0.964338	−	0.264674i	$-0.0852642\pi$
$878$	−17.8659	−	14.8461i	−0.602944	−	0.501031i
$879$		−	2.42869i		−	0.0819176i
$880$	−17.0528	+	13.4522i	−0.574849	+	0.453474i
$881$		−	43.5366i		−	1.46679i	−0.679805	−	0.733393i	$-0.737936\pi$
$881$		−	43.5366i		−	1.46679i	0.679805	−	0.733393i	$-0.262064\pi$
$882$	7.06103	+	6.93843i	0.237757	+	0.233629i
$883$	31.1078			1.04686			0.523430	−	0.852069i	$-0.324652\pi$
$883$	31.1078			1.04686			0.523430	+	0.852069i	$0.324652\pi$
$884$	−12.8083	−	68.7816i	−0.430789	−	2.31338i
$885$	17.9208	−	5.53754i	0.602401	−	0.186143i
$886$	−20.1852	−	16.7734i	−0.678136	−	0.563514i
$887$		−	36.0945i		−	1.21194i	−0.795489	−	0.605968i	$-0.792786\pi$
$887$		−	36.0945i		−	1.21194i	0.795489	−	0.605968i	$-0.207214\pi$
$888$	11.0719	−	19.8294i	0.371548	−	0.665431i
$889$	−20.7964	−	0.866633i	−0.697490	−	0.0290659i
$890$	39.8924	+	16.5684i	1.33719	+	0.555375i
$891$			2.42837i			0.0813535i
$892$	38.7954	−	7.22433i	1.29897	−	0.241889i
$893$			4.18847i			0.140162i
$894$	−0.907549	+	1.09215i	−0.0303530	+	0.0365270i
$895$	22.1732	−	6.85154i	0.741168	−	0.229022i
$896$	5.43754	−	29.4352i	0.181656	−	0.983362i
$897$		−	34.2873i		−	1.14482i
$898$	16.5817	+	13.7790i	0.553339	+	0.459811i
$899$	4.12142			0.137457
$900$	7.05760	+	7.08451i	0.235253	+	0.236150i
$901$			33.2410i			1.10742i
$902$	−8.81313	−	7.32348i	−0.293445	−	0.243845i
$903$	−0.227720	+	5.46455i	−0.00757804	+	0.181849i
$904$	−14.2925	−	7.98032i	−0.475362	−	0.265422i
$905$	−34.7897	+	10.7501i	−1.15645	+	0.357344i
$906$	−20.0742	−	16.6811i	−0.666920	−	0.554193i
$907$	−48.6458			−1.61526			−0.807629	−	0.589691i	$-0.799249\pi$
$907$	−48.6458			−1.61526			−0.807629	+	0.589691i	$0.799249\pi$
$908$	25.3022	−	4.71167i	0.839682	−	0.156362i
$909$			5.68823i			0.188667i
$910$	−17.7389	+	38.1442i	−0.588040	+	1.26447i
$911$		−	15.6640i		−	0.518971i	−0.965747	−	0.259486i	$-0.916447\pi$
$911$		−	15.6640i		−	0.518971i	0.965747	−	0.259486i	$-0.0835530\pi$
$912$	−1.81686	−	4.70919i	−0.0601622	−	0.155937i
$913$	23.6071			0.781280
$914$	−14.4522	+	17.3919i	−0.478036	+	0.575272i
$915$	−2.89788	−	9.37821i	−0.0958009	−	0.310034i
$916$	−3.99635	+	0.744185i	−0.132043	+	0.0245886i
$917$	24.2068	+	1.00875i	0.799379	+	0.0333119i
$918$	6.28844	−	7.56755i	0.207549	−	0.249766i
$919$		−	16.6879i		−	0.550482i	−0.961375	−	0.275241i	$-0.911242\pi$
$919$		−	16.6879i		−	0.550482i	0.961375	−	0.275241i	$-0.0887576\pi$
$920$	42.1855	+	8.97135i	1.39081	+	0.295777i
$921$	−0.689241			−0.0227113
$922$	−7.48285	+	9.00491i	−0.246434	+	0.296561i
$923$			58.1864i			1.91523i
$924$	−1.82438	−	12.7196i	−0.0600177	−	0.418443i
$925$	−22.6489	−	33.1493i	−0.744691	−	1.08994i
$926$	13.0540	+	10.8475i	0.428980	+	0.356471i
$927$			10.0365i			0.329642i
$928$	−24.4624	−	8.24607i	−0.803018	−	0.270691i
$929$		−	1.14435i		−	0.0375450i	−0.999824	−	0.0187725i	$-0.994024\pi$
$929$		−	1.14435i		−	0.0375450i	0.999824	−	0.0187725i	$-0.00597582\pi$
$930$	−2.63752	−	1.09544i	−0.0864877	−	0.0359208i
$931$	−8.80253	−	0.734917i	−0.288491	−	0.0240859i
$932$	−37.9647	+	7.06964i	−1.24357	+	0.231574i
$933$		−	16.2677i		−	0.532582i
$934$	−16.6633	+	20.0528i	−0.545241	+	0.656147i
$935$	36.0950	−	11.1534i	1.18043	−	0.364755i
$936$	6.93305	−	12.4169i	0.226614	−	0.405858i
$937$	−42.6808			−1.39432			−0.697160	−	0.716915i	$-0.745553\pi$
$937$	−42.6808			−1.39432			−0.697160	+	0.716915i	$0.745553\pi$
$938$	−22.9161	−	20.7150i	−0.748238	−	0.676369i
$939$		−	24.7480i		−	0.807619i
$940$	−6.90468	−	13.1404i	−0.225206	−	0.428594i
$941$		−	10.1236i		−	0.330019i	−0.986292	−	0.165010i	$-0.947234\pi$
$941$		−	10.1236i		−	0.330019i	0.986292	−	0.165010i	$-0.0527656\pi$
$942$	−4.28160	+	5.15251i	−0.139502	+	0.167878i
$943$			22.7535i			0.740955i
$944$	31.3042	−	12.0775i	1.01887	−	0.393090i
$945$	−5.72020	+	1.50973i	−0.186078	+	0.0491117i
$946$	4.53722	−	5.46013i	0.147518	−	0.177524i
$947$	18.1681			0.590384			0.295192	−	0.955438i	$-0.404616\pi$
$947$	18.1681			0.590384			0.295192	+	0.955438i	$0.404616\pi$
$948$	−3.18200	−	17.0876i	−0.103347	−	0.554981i
$949$	62.3163			2.02287
$950$	−8.88348	−	0.837122i	−0.288218	−	0.0271598i
$951$	−21.5126			−0.697593
$952$	−27.2529	+	44.3624i	−0.883270	+	1.43779i
$953$		−	16.8056i		−	0.544386i	−0.962243	−	0.272193i	$-0.912251\pi$
$953$		−	16.8056i		−	0.544386i	0.962243	−	0.272193i	$-0.0877490\pi$
$954$	−4.31834	+	5.19672i	−0.139811	+	0.168250i
$955$	−2.40151	+	0.742070i	−0.0777111	+	0.0240128i
$956$	−55.3053	+	10.2987i	−1.78870	+	0.333085i
$957$	−11.0818			−0.358223
$958$	2.71506	+	2.25614i	0.0877196	+	0.0728927i
$959$	−1.43711	+	34.4861i	−0.0464067	+	1.11361i
$960$	13.4631	+	11.7790i	0.434520	+	0.380166i
$961$	−30.1843			−0.973689
$962$	−36.4905	+	43.9129i	−1.17650	+	1.41581i
$963$	−10.4278			−0.336033
$964$	−58.8765	+	10.9638i	−1.89628	+	0.353119i
$965$	−5.55272	+	1.71580i	−0.178748	+	0.0552335i
$966$	−17.1101	+	18.9282i	−0.550510	+	0.609006i
$967$	20.1500			0.647981			0.323991	−	0.946060i	$-0.394975\pi$
$967$	20.1500			0.647981			0.323991	+	0.946060i	$0.394975\pi$
$968$	7.03649	−	12.6021i	0.226161	−	0.405048i
$969$			8.77946i			0.282037i
$970$	1.49207	−	3.59250i	0.0479074	−	0.115348i
$971$	35.2765			1.13208			0.566038	−	0.824379i	$-0.308475\pi$
$971$	35.2765			1.13208			0.566038	+	0.824379i	$0.308475\pi$
$972$	1.96620	−	0.366139i	0.0630659	−	0.0117439i
$973$	51.3594	+	2.14026i	1.64651	+	0.0686136i
$974$	−5.85354	−	4.86414i	−0.187559	−	0.155857i
$975$	−14.1824	−	20.7576i	−0.454200	−	0.664775i
$976$	−6.32035	−	16.3820i	−0.202309	−	0.524374i
$977$			32.8022i			1.04944i	0.851276	+	0.524718i	$0.175829\pi$
$977$			32.8022i			1.04944i	−0.851276	+	0.524718i	$0.824171\pi$
$978$	−4.98907	+	6.00389i	−0.159533	+	0.191983i
$979$	33.1712			1.06016
$980$	28.8276	−	12.2053i	0.920864	−	0.389884i
$981$	10.8686			0.347006
$982$	5.40936	−	6.50966i	0.172620	−	0.207732i
$983$			42.3409i			1.35046i	0.737605	+	0.675232i	$0.235957\pi$
$983$			42.3409i			1.35046i	−0.737605	+	0.675232i	$0.764043\pi$
$984$	−4.60086	+	8.24000i	−0.146670	+	0.262682i
$985$	−21.9443	+	6.78082i	−0.699204	+	0.216055i
$986$	34.5342	+	28.6971i	1.09979	+	0.913901i
$987$	8.77424	+	0.365642i	0.279287	+	0.0116385i
$988$	2.32305	+	12.4750i	0.0739060	+	0.396882i
$989$	−14.0968			−0.448252
$990$	7.09184	+	2.94544i	0.225394	+	0.0936123i
$991$		−	0.426395i		−	0.0135449i	−0.999977	−	0.00677244i	$-0.997844\pi$
$991$		−	0.426395i		−	0.0135449i	0.999977	−	0.00677244i	$-0.00215575\pi$
$992$	−4.84124	−	1.63194i	−0.153709	−	0.0518142i
$993$	−10.6160			−0.336887
$994$	29.0364	−	32.1217i	0.920978	−	1.01884i
$995$	−13.7294	−	44.4315i	−0.435251	−	1.40857i
$996$	−3.55937	−	19.1141i	−0.112783	−	0.605655i
$997$	−7.51623			−0.238041			−0.119021	−	0.992892i	$-0.537976\pi$
$997$	−7.51623			−0.238041			−0.119021	+	0.992892i	$0.537976\pi$
$998$	10.9334	−	13.1573i	0.346090	−	0.416487i
$999$	−8.02957			−0.254044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.i.a.139.9	✓	48
4.3	odd	2	inner	420.2.i.a.139.38	yes	48
5.4	even	2	inner	420.2.i.a.139.40	yes	48
7.6	odd	2	inner	420.2.i.a.139.10	yes	48
20.19	odd	2	inner	420.2.i.a.139.11	yes	48
28.27	even	2	inner	420.2.i.a.139.37	yes	48
35.34	odd	2	inner	420.2.i.a.139.39	yes	48
140.139	even	2	inner	420.2.i.a.139.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.i.a.139.9	✓	48	1.1	even	1	trivial
420.2.i.a.139.10	yes	48	7.6	odd	2	inner
420.2.i.a.139.11	yes	48	20.19	odd	2	inner
420.2.i.a.139.12	yes	48	140.139	even	2	inner
420.2.i.a.139.37	yes	48	28.27	even	2	inner
420.2.i.a.139.38	yes	48	4.3	odd	2	inner
420.2.i.a.139.39	yes	48	35.34	odd	2	inner
420.2.i.a.139.40	yes	48	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08769 - 0.903842i) q^{2} -1.00000i q^{3} +(0.366139 + 1.96620i) q^{4} +(-0.660150 - 2.13640i) q^{5} +(-0.903842 + 1.08769i) q^{6} +(-2.64346 - 0.110159i) q^{7} +(1.37889 - 2.46955i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.08769 - 0.903842i) q^{2} -1.00000i q^{3} +(0.366139 + 1.96620i) q^{4} +(-0.660150 - 2.13640i) q^{5} +(-0.903842 + 1.08769i) q^{6} +(-2.64346 - 0.110159i) q^{7} +(1.37889 - 2.46955i) q^{8} -1.00000 q^{9} +(-1.21293 + 2.92041i) q^{10} +2.42837i q^{11} +(1.96620 - 0.366139i) q^{12} -5.02799 q^{13} +(2.77570 + 2.50909i) q^{14} +(-2.13640 + 0.660150i) q^{15} +(-3.73189 + 1.43980i) q^{16} +6.95745 q^{17} +(1.08769 + 0.903842i) q^{18} -1.26188 q^{19} +(3.95888 - 2.08020i) q^{20} +(-0.110159 + 2.64346i) q^{21} +(2.19486 - 2.64131i) q^{22} -6.81927 q^{23} +(-2.46955 - 1.37889i) q^{24} +(-4.12840 + 2.82069i) q^{25} +(5.46890 + 4.54451i) q^{26} +1.00000i q^{27} +(-0.751278 - 5.23790i) q^{28} -4.56347 q^{29} +(2.92041 + 1.21293i) q^{30} -0.903134 q^{31} +(5.36049 + 1.80698i) q^{32} +2.42837 q^{33} +(-7.56755 - 6.28844i) q^{34} +(1.50973 + 5.72020i) q^{35} +(-0.366139 - 1.96620i) q^{36} +8.02957i q^{37} +(1.37253 + 1.14054i) q^{38} +5.02799i q^{39} +(-6.18621 - 1.31559i) q^{40} -3.33664i q^{41} +(2.50909 - 2.77570i) q^{42} +2.06720 q^{43} +(-4.77466 + 0.889120i) q^{44} +(0.660150 + 2.13640i) q^{45} +(7.41725 + 6.16355i) q^{46} -3.31923i q^{47} +(1.43980 + 3.73189i) q^{48} +(6.97573 + 0.582399i) q^{49} +(7.03988 + 0.663393i) q^{50} -6.95745i q^{51} +(-1.84094 - 9.88604i) q^{52} +4.77776i q^{53} +(0.903842 - 1.08769i) q^{54} +(5.18797 - 1.60309i) q^{55} +(-3.91708 + 6.37625i) q^{56} +1.26188i q^{57} +(4.96364 + 4.12465i) q^{58} -8.38831 q^{59} +(-2.08020 - 3.95888i) q^{60} +4.38973i q^{61} +(0.982329 + 0.816290i) q^{62} +(2.64346 + 0.110159i) q^{63} +(-4.19733 - 6.81047i) q^{64} +(3.31923 + 10.7418i) q^{65} +(-2.64131 - 2.19486i) q^{66} -8.25600 q^{67} +(2.54739 + 13.6797i) q^{68} +6.81927i q^{69} +(3.52804 - 7.58637i) q^{70} -11.5725i q^{71} +(-1.37889 + 2.46955i) q^{72} -12.3939 q^{73} +(7.25746 - 8.73368i) q^{74} +(2.82069 + 4.12840i) q^{75} +(-0.462022 - 2.48111i) q^{76} +(0.267506 - 6.41929i) q^{77} +(4.54451 - 5.46890i) q^{78} -8.69070i q^{79} +(5.53960 + 7.02231i) q^{80} +1.00000 q^{81} +(-3.01580 + 3.62923i) q^{82} -9.72136i q^{83} +(-5.23790 + 0.751278i) q^{84} +(-4.59296 - 14.8639i) q^{85} +(-2.24847 - 1.86842i) q^{86} +4.56347i q^{87} +(5.99698 + 3.34846i) q^{88} -13.6598i q^{89} +(1.21293 - 2.92041i) q^{90} +(13.2913 + 0.553877i) q^{91} +(-2.49680 - 13.4081i) q^{92} +0.903134i q^{93} +(-3.00006 + 3.61029i) q^{94} +(0.833029 + 2.69588i) q^{95} +(1.80698 - 5.36049i) q^{96} -1.23014 q^{97} +(-7.06103 - 6.93843i) q^{98} -2.42837i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{9}+O(q^{10}) \) 48 * q - 48 * q^9	\( 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) \) 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Introduction

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