LMFDB - Embedded newform 650.2.w.a.357.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(193,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,6,-2,0,-6,6] 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.357
Dual form			650.2.w.a.193.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.633975 + 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.36603 - 0.633975i) q^{6} +(3.23205 - 1.86603i) q^{7} +1.00000 q^{8} +(-2.59808 + 1.50000i) q^{9} +(1.86603 - 0.500000i) q^{11} +(1.73205 - 1.73205i) q^{12} +(3.50000 - 0.866025i) q^{13} +3.73205i q^{14} +(-0.500000 + 0.866025i) q^{16} +(5.09808 + 1.36603i) q^{17} -3.00000i q^{18} +(-1.33013 + 4.96410i) q^{19} +(6.46410 + 6.46410i) q^{21} +(-0.500000 + 1.86603i) q^{22} +(-3.36603 + 0.901924i) q^{23} +(0.633975 + 2.36603i) q^{24} +(-1.00000 + 3.46410i) q^{26} +(-3.23205 - 1.86603i) q^{28} +(-8.19615 - 4.73205i) q^{29} +(3.00000 - 3.00000i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.36603 + 4.09808i) q^{33} +(-3.73205 + 3.73205i) q^{34} +(2.59808 + 1.50000i) q^{36} +(-3.23205 - 1.86603i) q^{37} +(-3.63397 - 3.63397i) q^{38} +(4.26795 + 7.73205i) q^{39} +(-0.0980762 - 0.366025i) q^{41} +(-8.83013 + 2.36603i) q^{42} +(2.19615 - 8.19615i) q^{43} +(-1.36603 - 1.36603i) q^{44} +(0.901924 - 3.36603i) q^{46} +7.00000i q^{47} +(-2.36603 - 0.633975i) q^{48} +(3.46410 - 6.00000i) q^{49} +12.9282i q^{51} +(-2.50000 - 2.59808i) q^{52} +(-6.36603 + 6.36603i) q^{53} +(3.23205 - 1.86603i) q^{56} -12.5885 q^{57} +(8.19615 - 4.73205i) q^{58} +(0.633975 + 0.169873i) q^{59} +(-6.36603 - 11.0263i) q^{61} +(1.09808 + 4.09808i) q^{62} +(-5.59808 + 9.69615i) q^{63} +1.00000 q^{64} -4.73205 q^{66} +(0.464102 - 0.803848i) q^{67} +(-1.36603 - 5.09808i) q^{68} +(-4.26795 - 7.39230i) q^{69} +(-10.4641 - 2.80385i) q^{71} +(-2.59808 + 1.50000i) q^{72} +4.73205 q^{73} +(3.23205 - 1.86603i) q^{74} +(4.96410 - 1.33013i) q^{76} +(5.09808 - 5.09808i) q^{77} +(-8.83013 - 0.169873i) q^{78} +11.1244i q^{79} +(-4.50000 + 7.79423i) q^{81} +(0.366025 + 0.0980762i) q^{82} +2.73205i q^{83} +(2.36603 - 8.83013i) q^{84} +(6.00000 + 6.00000i) q^{86} +(6.00000 - 22.3923i) q^{87} +(1.86603 - 0.500000i) q^{88} +(3.89230 + 14.5263i) q^{89} +(9.69615 - 9.33013i) q^{91} +(2.46410 + 2.46410i) q^{92} +(9.00000 + 5.19615i) q^{93} +(-6.06218 - 3.50000i) q^{94} +(1.73205 - 1.73205i) q^{96} +(8.09808 + 14.0263i) q^{97} +(3.46410 + 6.00000i) q^{98} +(-4.09808 + 4.09808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 6 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{11} + 14 q^{13} - 2 q^{16} + 10 q^{17} + 12 q^{19} + 12 q^{21} - 2 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{26} - 6 q^{28} - 12 q^{29}+ \cdots - 6 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 6 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^11 + 14 * q^13 - 2 * q^16 + 10 * q^17 + 12 * q^19 + 12 * q^21 - 2 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^26 - 6 * q^28 - 12 * q^29 + 12 * q^31 - 2 * q^32 + 6 * q^33 - 8 * q^34 - 6 * q^37 - 18 * q^38 + 24 * q^39 + 10 * q^41 - 18 * q^42 - 12 * q^43 - 2 * q^44 + 14 * q^46 - 6 * q^48 - 10 * q^52 - 22 * q^53 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 6 * q^59 - 22 * q^61 - 6 * q^62 - 12 * q^63 + 4 * q^64 - 12 * q^66 - 12 * q^67 - 2 * q^68 - 24 * q^69 - 28 * q^71 + 12 * q^73 + 6 * q^74 + 6 * q^76 + 10 * q^77 - 18 * q^78 - 18 * q^81 - 2 * q^82 + 6 * q^84 + 24 * q^86 + 24 * q^87 + 4 * q^88 - 26 * q^89 + 18 * q^91 - 4 * q^92 + 36 * q^93 + 22 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.633975	+	2.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$3$	0.633975	+	2.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−2.36603	−	0.633975i	−0.965926	−	0.258819i
$7$	3.23205	−	1.86603i	1.22160	−	0.705291i	0.256341	−	0.966586i	$-0.417483\pi$
$7$	3.23205	−	1.86603i	1.22160	−	0.705291i	0.965259	+	0.261295i	$0.0841495\pi$
$8$	1.00000			0.353553
$9$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$10$		0			0
$11$	1.86603	−	0.500000i	0.562628	−	0.150756i	0.0337145	−	0.999432i	$-0.489266\pi$
$11$	1.86603	−	0.500000i	0.562628	−	0.150756i	0.528913	+	0.848676i	$0.322600\pi$
$12$	1.73205	−	1.73205i	0.500000	−	0.500000i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$			3.73205i			0.997433i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.09808	+	1.36603i	1.23647	+	0.331310i	0.817094	−	0.576505i	$-0.195584\pi$
$17$	5.09808	+	1.36603i	1.23647	+	0.331310i	0.419371	+	0.907815i	$0.362251\pi$
$18$		−	3.00000i		−	0.707107i
$19$	−1.33013	+	4.96410i	−0.305152	+	1.13884i	0.627662	+	0.778486i	$0.284012\pi$
$19$	−1.33013	+	4.96410i	−0.305152	+	1.13884i	−0.932814	+	0.360357i	$0.882655\pi$
$20$		0			0
$21$	6.46410	+	6.46410i	1.41058	+	1.41058i
$22$	−0.500000	+	1.86603i	−0.106600	+	0.397838i
$23$	−3.36603	+	0.901924i	−0.701865	+	0.188064i	−0.592066	−	0.805890i	$-0.701687\pi$
$23$	−3.36603	+	0.901924i	−0.701865	+	0.188064i	−0.109799	+	0.993954i	$0.535021\pi$
$24$	0.633975	+	2.36603i	0.129410	+	0.482963i
$25$		0			0
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$		0			0
$28$	−3.23205	−	1.86603i	−0.610800	−	0.352646i
$29$	−8.19615	−	4.73205i	−1.52199	−	0.878720i	−0.999663	−	0.0259731i	$-0.991732\pi$
$29$	−8.19615	−	4.73205i	−1.52199	−	0.878720i	−0.522325	−	0.852747i	$-0.674935\pi$
$30$		0			0
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	−0.384365	−	0.923181i	$-0.625580\pi$
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	0.923181	+	0.384365i	$0.125580\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.36603	+	4.09808i	0.411872	+	0.713384i
$34$	−3.73205	+	3.73205i	−0.640041	+	0.640041i
$35$		0			0
$36$	2.59808	+	1.50000i	0.433013	+	0.250000i
$37$	−3.23205	−	1.86603i	−0.531346	−	0.306773i	0.210218	−	0.977654i	$-0.432582\pi$
$37$	−3.23205	−	1.86603i	−0.531346	−	0.306773i	−0.741564	+	0.670882i	$0.765916\pi$
$38$	−3.63397	−	3.63397i	−0.589509	−	0.589509i
$39$	4.26795	+	7.73205i	0.683419	+	1.23812i
$40$		0			0
$41$	−0.0980762	−	0.366025i	−0.0153169	−	0.0571636i	0.957844	−	0.287287i	$-0.0927535\pi$
$41$	−0.0980762	−	0.366025i	−0.0153169	−	0.0571636i	−0.973161	+	0.230124i	$0.926087\pi$
$42$	−8.83013	+	2.36603i	−1.36252	+	0.365086i
$43$	2.19615	−	8.19615i	0.334910	−	1.24990i	−0.569056	−	0.822298i	$-0.692691\pi$
$43$	2.19615	−	8.19615i	0.334910	−	1.24990i	0.903967	−	0.427603i	$-0.140642\pi$
$44$	−1.36603	−	1.36603i	−0.205936	−	0.205936i
$45$		0			0
$46$	0.901924	−	3.36603i	0.132981	−	0.496293i
$47$			7.00000i			1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$			7.00000i			1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$	−2.36603	−	0.633975i	−0.341506	−	0.0915064i
$49$	3.46410	−	6.00000i	0.494872	−	0.857143i
$50$		0			0
$51$			12.9282i			1.81031i
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	−6.36603	+	6.36603i	−0.874441	+	0.874441i	−0.992953	−	0.118512i	$-0.962188\pi$
$53$	−6.36603	+	6.36603i	−0.874441	+	0.874441i	0.118512	+	0.992953i	$0.462188\pi$
$54$		0			0
$55$		0			0
$56$	3.23205	−	1.86603i	0.431901	−	0.249358i
$57$	−12.5885			−1.66738
$58$	8.19615	−	4.73205i	1.07621	−	0.621349i
$59$	0.633975	+	0.169873i	0.0825365	+	0.0221156i	0.299851	−	0.953986i	$-0.403063\pi$
$59$	0.633975	+	0.169873i	0.0825365	+	0.0221156i	−0.217314	+	0.976102i	$0.569730\pi$
$60$		0			0
$61$	−6.36603	−	11.0263i	−0.815086	−	1.41177i	−0.909266	−	0.416215i	$-0.863356\pi$
$61$	−6.36603	−	11.0263i	−0.815086	−	1.41177i	0.0941801	−	0.995555i	$-0.469977\pi$
$62$	1.09808	+	4.09808i	0.139456	+	0.520456i
$63$	−5.59808	+	9.69615i	−0.705291	+	1.22160i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.73205			−0.582475
$67$	0.464102	−	0.803848i	0.0566990	−	0.0982056i	−0.836283	−	0.548298i	$-0.815276\pi$
$67$	0.464102	−	0.803848i	0.0566990	−	0.0982056i	0.892982	+	0.450093i	$0.148609\pi$
$68$	−1.36603	−	5.09808i	−0.165655	−	0.618233i
$69$	−4.26795	−	7.39230i	−0.513801	−	0.889929i
$70$		0			0
$71$	−10.4641	−	2.80385i	−1.24186	−	0.332755i	−0.422673	−	0.906282i	$-0.638908\pi$
$71$	−10.4641	−	2.80385i	−1.24186	−	0.332755i	−0.819187	+	0.573527i	$0.805575\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$	4.73205			0.553845			0.276922	−	0.960892i	$-0.410686\pi$
$73$	4.73205			0.553845			0.276922	+	0.960892i	$0.410686\pi$
$74$	3.23205	−	1.86603i	0.375718	−	0.216921i
$75$		0			0
$76$	4.96410	−	1.33013i	0.569422	−	0.152576i
$77$	5.09808	−	5.09808i	0.580980	−	0.580980i
$78$	−8.83013	−	0.169873i	−0.999815	−	0.0192343i
$79$			11.1244i			1.25159i	0.779988	+	0.625794i	$0.215225\pi$
$79$			11.1244i			1.25159i	−0.779988	+	0.625794i	$0.784775\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	0.366025	+	0.0980762i	0.0404207	+	0.0108307i
$83$			2.73205i			0.299882i	0.988695	+	0.149941i	$0.0479083\pi$
$83$			2.73205i			0.299882i	−0.988695	+	0.149941i	$0.952092\pi$
$84$	2.36603	−	8.83013i	0.258155	−	0.963446i
$85$		0			0
$86$	6.00000	+	6.00000i	0.646997	+	0.646997i
$87$	6.00000	−	22.3923i	0.643268	−	2.40071i
$88$	1.86603	−	0.500000i	0.198919	−	0.0533002i
$89$	3.89230	+	14.5263i	0.412583	+	1.53978i	0.789627	+	0.613587i	$0.210274\pi$
$89$	3.89230	+	14.5263i	0.412583	+	1.53978i	−0.377044	+	0.926196i	$0.623059\pi$
$90$		0			0
$91$	9.69615	−	9.33013i	1.01643	−	0.978063i
$92$	2.46410	+	2.46410i	0.256900	+	0.256900i
$93$	9.00000	+	5.19615i	0.933257	+	0.538816i
$94$	−6.06218	−	3.50000i	−0.625266	−	0.360997i
$95$		0			0
$96$	1.73205	−	1.73205i	0.176777	−	0.176777i
$97$	8.09808	+	14.0263i	0.822235	+	1.42415i	0.904014	+	0.427502i	$0.140606\pi$
$97$	8.09808	+	14.0263i	0.822235	+	1.42415i	−0.0817791	+	0.996650i	$0.526060\pi$
$98$	3.46410	+	6.00000i	0.349927	+	0.606092i
$99$	−4.09808	+	4.09808i	−0.411872	+	0.411872i
$100$		0			0
$101$	−5.36603	−	3.09808i	−0.533939	−	0.308270i	0.208680	−	0.977984i	$-0.433083\pi$
$101$	−5.36603	−	3.09808i	−0.533939	−	0.308270i	−0.742619	+	0.669714i	$0.766417\pi$
$102$	−11.1962	−	6.46410i	−1.10858	−	0.640041i
$103$	2.16987	+	2.16987i	0.213804	+	0.213804i	0.805881	−	0.592077i	$-0.201692\pi$
$103$	2.16987	+	2.16987i	0.213804	+	0.213804i	−0.592077	+	0.805881i	$0.701692\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	−2.33013	−	8.69615i	−0.226322	−	0.844645i
$107$	12.5622	−	3.36603i	1.21443	−	0.325406i	0.405932	−	0.913903i	$-0.366947\pi$
$107$	12.5622	−	3.36603i	1.21443	−	0.325406i	0.808499	+	0.588497i	$0.200280\pi$
$108$		0			0
$109$	−14.1962	−	14.1962i	−1.35974	−	1.35974i	−0.874227	−	0.485518i	$-0.838631\pi$
$109$	−14.1962	−	14.1962i	−1.35974	−	1.35974i	−0.485518	−	0.874227i	$-0.661369\pi$
$110$		0			0
$111$	2.36603	−	8.83013i	0.224573	−	0.838119i
$112$			3.73205i			0.352646i
$113$	2.73205	+	0.732051i	0.257010	+	0.0688655i	0.385023	−	0.922907i	$-0.374193\pi$
$113$	2.73205	+	0.732051i	0.257010	+	0.0688655i	−0.128014	+	0.991772i	$0.540860\pi$
$114$	6.29423	−	10.9019i	0.589509	−	1.02106i
$115$		0			0
$116$			9.46410i			0.878720i
$117$	−7.79423	+	7.50000i	−0.720577	+	0.693375i
$118$	−0.464102	+	0.464102i	−0.0427240	+	0.0427240i
$119$	19.0263	−	5.09808i	1.74414	−	0.467340i
$120$		0			0
$121$	−6.29423	+	3.63397i	−0.572203	+	0.330361i
$122$	12.7321			1.15271
$123$	0.803848	−	0.464102i	0.0724805	−	0.0418466i
$124$	−4.09808	−	1.09808i	−0.368018	−	0.0986102i
$125$		0			0
$126$	−5.59808	−	9.69615i	−0.498716	−	0.863802i
$127$	−2.57180	−	9.59808i	−0.228210	−	0.851692i	−0.981093	−	0.193537i	$-0.938004\pi$
$127$	−2.57180	−	9.59808i	−0.228210	−	0.851692i	0.752883	−	0.658154i	$-0.228663\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	20.7846			1.82998
$130$		0			0
$131$	1.39230			0.121646			0.0608231	−	0.998149i	$-0.480627\pi$
$131$	1.39230			0.121646			0.0608231	+	0.998149i	$0.480627\pi$
$132$	2.36603	−	4.09808i	0.205936	−	0.356692i
$133$	4.96410	+	18.5263i	0.430442	+	1.60643i
$134$	0.464102	+	0.803848i	0.0400923	+	0.0694419i
$135$		0			0
$136$	5.09808	+	1.36603i	0.437156	+	0.117136i
$137$	−17.8301	+	10.2942i	−1.52333	+	0.879495i	−0.523711	+	0.851896i	$0.675453\pi$
$137$	−17.8301	+	10.2942i	−1.52333	+	0.879495i	−0.999619	+	0.0275996i	$0.991214\pi$
$138$	8.53590			0.726624
$139$	12.0622	−	6.96410i	1.02310	−	0.590687i	0.108100	−	0.994140i	$-0.465523\pi$
$139$	12.0622	−	6.96410i	1.02310	−	0.590687i	0.915001	+	0.403453i	$0.132190\pi$
$140$		0			0
$141$	−16.5622	+	4.43782i	−1.39479	+	0.373732i
$142$	7.66025	−	7.66025i	0.642834	−	0.642834i
$143$	6.09808	−	3.36603i	0.509947	−	0.281481i
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	−2.36603	+	4.09808i	−0.195814	+	0.339159i
$147$	16.3923	+	4.39230i	1.35201	+	0.362271i
$148$			3.73205i			0.306773i
$149$	2.26795	−	8.46410i	0.185798	−	0.693406i	−0.808661	−	0.588275i	$-0.799807\pi$
$149$	2.26795	−	8.46410i	0.185798	−	0.693406i	0.994458	−	0.105131i	$-0.0335262\pi$
$150$		0			0
$151$	1.53590	+	1.53590i	0.124990	+	0.124990i	0.766835	−	0.641845i	$-0.221831\pi$
$151$	1.53590	+	1.53590i	0.124990	+	0.124990i	−0.641845	+	0.766835i	$0.721831\pi$
$152$	−1.33013	+	4.96410i	−0.107888	+	0.402642i
$153$	−15.2942	+	4.09808i	−1.23647	+	0.331310i
$154$	1.86603	+	6.96410i	0.150369	+	0.561183i
$155$		0			0
$156$	4.56218	−	7.56218i	0.365267	−	0.605459i
$157$	11.3660	+	11.3660i	0.907108	+	0.907108i	0.996038	−	0.0889303i	$-0.0283448\pi$
$157$	11.3660	+	11.3660i	0.907108	+	0.907108i	−0.0889303	+	0.996038i	$0.528345\pi$
$158$	−9.63397	−	5.56218i	−0.766438	−	0.442503i
$159$	−19.0981	−	11.0263i	−1.51458	−	0.874441i
$160$		0			0
$161$	−9.19615	+	9.19615i	−0.724758	+	0.724758i
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−9.56218	−	16.5622i	−0.748968	−	1.29725i	−0.948318	−	0.317322i	$-0.897217\pi$
$163$	−9.56218	−	16.5622i	−0.748968	−	1.29725i	0.199350	−	0.979928i	$-0.436117\pi$
$164$	−0.267949	+	0.267949i	−0.0209233	+	0.0209233i
$165$		0			0
$166$	−2.36603	−	1.36603i	−0.183639	−	0.106024i
$167$	−15.8660	−	9.16025i	−1.22775	−	0.708842i	−0.261191	−	0.965287i	$-0.584115\pi$
$167$	−15.8660	−	9.16025i	−1.22775	−	0.708842i	−0.966559	+	0.256445i	$0.917449\pi$
$168$	6.46410	+	6.46410i	0.498716	+	0.498716i
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	−3.99038	−	14.8923i	−0.305152	−	1.13884i
$172$	−8.19615	+	2.19615i	−0.624951	+	0.167455i
$173$	4.16025	−	15.5263i	0.316298	−	1.18044i	−0.606477	−	0.795101i	$-0.707418\pi$
$173$	4.16025	−	15.5263i	0.316298	−	1.18044i	0.922775	−	0.385340i	$-0.125916\pi$
$174$	16.3923	+	16.3923i	1.24270	+	1.24270i
$175$		0			0
$176$	−0.500000	+	1.86603i	−0.0376889	+	0.140657i
$177$			1.60770i			0.120842i
$178$	−14.5263	−	3.89230i	−1.08879	−	0.291741i
$179$	11.3923	−	19.7321i	0.851501	−	1.47484i	−0.0283528	−	0.999598i	$-0.509026\pi$
$179$	11.3923	−	19.7321i	0.851501	−	1.47484i	0.879854	−	0.475245i	$-0.157640\pi$
$180$		0			0
$181$		−	10.5885i		−	0.787034i	−0.919317	−	0.393517i	$-0.871258\pi$
$181$		−	10.5885i		−	0.787034i	0.919317	−	0.393517i	$-0.128742\pi$
$182$	3.23205	+	13.0622i	0.239576	+	0.968233i
$183$	22.0526	−	22.0526i	1.63017	−	1.63017i
$184$	−3.36603	+	0.901924i	−0.248147	+	0.0664907i
$185$		0			0
$186$	−9.00000	+	5.19615i	−0.659912	+	0.381000i
$187$	10.1962			0.745617
$188$	6.06218	−	3.50000i	0.442130	−	0.255264i
$189$		0			0
$190$		0			0
$191$	5.56218	+	9.63397i	0.402465	+	0.697090i	0.994023	−	0.109173i	$-0.0348202\pi$
$191$	5.56218	+	9.63397i	0.402465	+	0.697090i	−0.591558	+	0.806263i	$0.701487\pi$
$192$	0.633975	+	2.36603i	0.0457532	+	0.170753i
$193$	1.19615	−	2.07180i	0.0861009	−	0.149131i	−0.819759	−	0.572709i	$-0.805893\pi$
$193$	1.19615	−	2.07180i	0.0861009	−	0.149131i	0.905860	+	0.423578i	$0.139226\pi$
$194$	−16.1962			−1.16282
$195$		0			0
$196$	−6.92820			−0.494872
$197$	−4.06218	+	7.03590i	−0.289418	+	0.501287i	−0.973671	−	0.227958i	$-0.926795\pi$
$197$	−4.06218	+	7.03590i	−0.289418	+	0.501287i	0.684253	+	0.729245i	$0.260128\pi$
$198$	−1.50000	−	5.59808i	−0.106600	−	0.397838i
$199$	−9.46410	−	16.3923i	−0.670892	−	1.16202i	−0.977651	−	0.210232i	$-0.932578\pi$
$199$	−9.46410	−	16.3923i	−0.670892	−	1.16202i	0.306759	−	0.951787i	$-0.400755\pi$
$200$		0			0
$201$	2.19615	+	0.588457i	0.154905	+	0.0415066i
$202$	5.36603	−	3.09808i	0.377552	−	0.217980i
$203$	−35.3205			−2.47901
$204$	11.1962	−	6.46410i	0.783887	−	0.452578i
$205$		0			0
$206$	−2.96410	+	0.794229i	−0.206519	+	0.0553365i
$207$	7.39230	−	7.39230i	0.513801	−	0.513801i
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$			9.92820i			0.686748i
$210$		0			0
$211$	10.3301	−	17.8923i	0.711155	−	1.23176i	−0.253269	−	0.967396i	$-0.581506\pi$
$211$	10.3301	−	17.8923i	0.711155	−	1.23176i	0.964424	−	0.264361i	$-0.0851611\pi$
$212$	8.69615	+	2.33013i	0.597254	+	0.160034i
$213$		−	26.5359i		−	1.81821i
$214$	−3.36603	+	12.5622i	−0.230097	+	0.858733i
$215$		0			0
$216$		0			0
$217$	4.09808	−	15.2942i	0.278196	−	1.03824i
$218$	19.3923	−	5.19615i	1.31341	−	0.351928i
$219$	3.00000	+	11.1962i	0.202721	+	0.756566i
$220$		0			0
$221$	19.0263	+	0.366025i	1.27985	+	0.0246215i
$222$	6.46410	+	6.46410i	0.433842	+	0.433842i
$223$	−3.40192	−	1.96410i	−0.227810	−	0.131526i	0.381752	−	0.924265i	$-0.375321\pi$
$223$	−3.40192	−	1.96410i	−0.227810	−	0.131526i	−0.609561	+	0.792739i	$0.708654\pi$
$224$	−3.23205	−	1.86603i	−0.215950	−	0.124679i
$225$		0			0
$226$	−2.00000	+	2.00000i	−0.133038	+	0.133038i
$227$	0.928203	+	1.60770i	0.0616070	+	0.106706i	0.895184	−	0.445697i	$-0.147044\pi$
$227$	0.928203	+	1.60770i	0.0616070	+	0.106706i	−0.833577	+	0.552403i	$0.813711\pi$
$228$	6.29423	+	10.9019i	0.416845	+	0.721998i
$229$	−13.5885	+	13.5885i	−0.897951	+	0.897951i	−0.995255	−	0.0973042i	$-0.968978\pi$
$229$	−13.5885	+	13.5885i	−0.897951	+	0.897951i	0.0973042	+	0.995255i	$0.468978\pi$
$230$		0			0
$231$	15.2942	+	8.83013i	1.00629	+	0.580980i
$232$	−8.19615	−	4.73205i	−0.538104	−	0.310674i
$233$	−8.85641	−	8.85641i	−0.580202	−	0.580202i	0.354756	−	0.934959i	$-0.384564\pi$
$233$	−8.85641	−	8.85641i	−0.580202	−	0.580202i	−0.934959	+	0.354756i	$0.884564\pi$
$234$	−2.59808	−	10.5000i	−0.169842	−	0.686406i
$235$		0			0
$236$	−0.169873	−	0.633975i	−0.0110578	−	0.0412682i
$237$	−26.3205	+	7.05256i	−1.70970	+	0.458113i
$238$	−5.09808	+	19.0263i	−0.330459	+	1.23329i
$239$	5.73205	+	5.73205i	0.370776	+	0.370776i	0.867760	−	0.496984i	$-0.165559\pi$
$239$	5.73205	+	5.73205i	0.370776	+	0.370776i	−0.496984	+	0.867760i	$0.665559\pi$
$240$		0			0
$241$	1.66987	−	6.23205i	0.107566	−	0.401442i	−0.891058	−	0.453890i	$-0.850036\pi$
$241$	1.66987	−	6.23205i	0.107566	−	0.401442i	0.998624	+	0.0524484i	$0.0167025\pi$
$242$		−	7.26795i		−	0.467201i
$243$	−21.2942	−	5.70577i	−1.36603	−	0.366025i
$244$	−6.36603	+	11.0263i	−0.407543	+	0.705885i
$245$		0			0
$246$			0.928203i			0.0591801i
$247$	−0.356406	+	18.5263i	−0.0226776	+	1.17880i
$248$	3.00000	−	3.00000i	0.190500	−	0.190500i
$249$	−6.46410	+	1.73205i	−0.409646	+	0.109764i
$250$		0			0
$251$	−9.23205	+	5.33013i	−0.582722	+	0.336435i	−0.762214	−	0.647325i	$-0.775888\pi$
$251$	−9.23205	+	5.33013i	−0.582722	+	0.336435i	0.179492	+	0.983759i	$0.442554\pi$
$252$	11.1962			0.705291
$253$	−5.83013	+	3.36603i	−0.366537	+	0.211620i
$254$	9.59808	+	2.57180i	0.602237	+	0.161369i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.19615	−	8.19615i	−0.136992	−	0.511262i	−0.999982	−	0.00604014i	$-0.998077\pi$
$257$	−2.19615	−	8.19615i	−0.136992	−	0.511262i	0.862990	−	0.505222i	$-0.168589\pi$
$258$	−10.3923	+	18.0000i	−0.646997	+	1.12063i
$259$	−13.9282			−0.865456
$260$		0			0
$261$	28.3923			1.75744
$262$	−0.696152	+	1.20577i	−0.0430084	+	0.0744928i
$263$	3.52628	+	13.1603i	0.217440	+	0.811496i	0.985293	+	0.170871i	$0.0546581\pi$
$263$	3.52628	+	13.1603i	0.217440	+	0.811496i	−0.767854	+	0.640625i	$0.778675\pi$
$264$	2.36603	+	4.09808i	0.145619	+	0.252219i
$265$		0			0
$266$	−18.5263	−	4.96410i	−1.13592	−	0.304369i
$267$	−31.9019	+	18.4186i	−1.95237	+	1.12720i
$268$	−0.928203			−0.0566990
$269$	−9.75833	+	5.63397i	−0.594976	+	0.343509i	−0.767063	−	0.641572i	$-0.778282\pi$
$269$	−9.75833	+	5.63397i	−0.594976	+	0.343509i	0.172087	+	0.985082i	$0.444949\pi$
$270$		0			0
$271$	−6.73205	+	1.80385i	−0.408943	+	0.109576i	−0.457425	−	0.889248i	$-0.651228\pi$
$271$	−6.73205	+	1.80385i	−0.408943	+	0.109576i	0.0484822	+	0.998824i	$0.484562\pi$
$272$	−3.73205	+	3.73205i	−0.226289	+	0.226289i
$273$	28.2224	+	17.0263i	1.70810	+	1.03048i
$274$		−	20.5885i		−	1.24379i
$275$		0			0
$276$	−4.26795	+	7.39230i	−0.256900	+	0.444964i
$277$	−19.4282	−	5.20577i	−1.16733	−	0.312784i	−0.377439	−	0.926035i	$-0.623195\pi$
$277$	−19.4282	−	5.20577i	−1.16733	−	0.312784i	−0.789889	+	0.613250i	$0.789862\pi$
$278$			13.9282i			0.835358i
$279$	−3.29423	+	12.2942i	−0.197220	+	0.736036i
$280$		0			0
$281$	8.66025	+	8.66025i	0.516627	+	0.516627i	0.916549	−	0.399922i	$-0.130963\pi$
$281$	8.66025	+	8.66025i	0.516627	+	0.516627i	−0.399922	+	0.916549i	$0.630963\pi$
$282$	4.43782	−	16.5622i	0.264268	−	0.986263i
$283$	8.46410	−	2.26795i	0.503139	−	0.134816i	0.00168236	−	0.999999i	$-0.499464\pi$
$283$	8.46410	−	2.26795i	0.503139	−	0.134816i	0.501456	+	0.865183i	$0.332798\pi$
$284$	2.80385	+	10.4641i	0.166378	+	0.620930i
$285$		0			0
$286$	−0.133975	+	6.96410i	−0.00792208	+	0.411796i
$287$	−1.00000	−	1.00000i	−0.0590281	−	0.0590281i
$288$	2.59808	+	1.50000i	0.153093	+	0.0883883i
$289$	9.40192	+	5.42820i	0.553054	+	0.319306i
$290$		0			0
$291$	−28.0526	+	28.0526i	−1.64447	+	1.64447i
$292$	−2.36603	−	4.09808i	−0.138461	−	0.239822i
$293$	13.9641	+	24.1865i	0.815792	+	1.41299i	0.908758	+	0.417323i	$0.137032\pi$
$293$	13.9641	+	24.1865i	0.815792	+	1.41299i	−0.0929666	+	0.995669i	$0.529635\pi$
$294$	−12.0000	+	12.0000i	−0.699854	+	0.699854i
$295$		0			0
$296$	−3.23205	−	1.86603i	−0.187859	−	0.108461i
$297$		0			0
$298$	6.19615	+	6.19615i	0.358933	+	0.358933i
$299$	−11.0000	+	6.07180i	−0.636146	+	0.351141i
$300$		0			0
$301$	−8.19615	−	30.5885i	−0.472418	−	1.76309i
$302$	−2.09808	+	0.562178i	−0.120731	+	0.0323497i
$303$	3.92820	−	14.6603i	0.225669	−	0.842210i
$304$	−3.63397	−	3.63397i	−0.208423	−	0.208423i
$305$		0			0
$306$	4.09808	−	15.2942i	0.234271	−	0.874313i
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$	−6.96410	−	1.86603i	−0.396817	−	0.106327i
$309$	−3.75833	+	6.50962i	−0.213804	+	0.370319i
$310$		0			0
$311$			5.66025i			0.320964i	0.987039	+	0.160482i	$0.0513048\pi$
$311$			5.66025i			0.320964i	−0.987039	+	0.160482i	$0.948695\pi$
$312$	4.26795	+	7.73205i	0.241625	+	0.437741i
$313$	8.53590	−	8.53590i	0.482478	−	0.482478i	−0.423445	−	0.905922i	$-0.639179\pi$
$313$	8.53590	−	8.53590i	0.482478	−	0.482478i	0.905922	+	0.423445i	$0.139179\pi$
$314$	−15.5263	+	4.16025i	−0.876199	+	0.234777i
$315$		0			0
$316$	9.63397	−	5.56218i	0.541953	−	0.312897i
$317$	−1.39230			−0.0781996			−0.0390998	−	0.999235i	$-0.512449\pi$
$317$	−1.39230			−0.0781996			−0.0390998	+	0.999235i	$0.512449\pi$
$318$	19.0981	−	11.0263i	1.07097	−	0.618323i
$319$	−17.6603	−	4.73205i	−0.988784	−	0.264944i
$320$		0			0
$321$	15.9282	+	27.5885i	0.889026	+	1.53984i
$322$	−3.36603	−	12.5622i	−0.187581	−	0.700063i
$323$	−13.5622	+	23.4904i	−0.754620	+	1.30704i
$324$	9.00000			0.500000
$325$		0			0
$326$	19.1244			1.05920
$327$	24.5885	−	42.5885i	1.35974	−	2.35515i
$328$	−0.0980762	−	0.366025i	−0.00541535	−	0.0202104i
$329$	13.0622	+	22.6244i	0.720141	+	1.24732i
$330$		0			0
$331$	18.2942	+	4.90192i	1.00554	+	0.269434i	0.723765	−	0.690046i	$-0.242410\pi$
$331$	18.2942	+	4.90192i	1.00554	+	0.269434i	0.281776	+	0.959480i	$0.409076\pi$
$332$	2.36603	−	1.36603i	0.129853	−	0.0749704i
$333$	11.1962			0.613545
$334$	15.8660	−	9.16025i	0.868150	−	0.501227i
$335$		0			0
$336$	−8.83013	+	2.36603i	−0.481723	+	0.129077i
$337$	−4.26795	+	4.26795i	−0.232490	+	0.232490i	−0.813731	−	0.581241i	$-0.802567\pi$
$337$	−4.26795	+	4.26795i	−0.232490	+	0.232490i	0.581241	+	0.813731i	$0.302567\pi$
$338$	−0.500000	+	12.9904i	−0.0271964	+	0.706584i
$339$			6.92820i			0.376288i
$340$		0			0
$341$	4.09808	−	7.09808i	0.221923	−	0.384382i
$342$	14.8923	+	3.99038i	0.805284	+	0.215775i
$343$			0.267949i			0.0144679i
$344$	2.19615	−	8.19615i	0.118409	−	0.441907i
$345$		0			0
$346$	11.3660	+	11.3660i	0.611041	+	0.611041i
$347$	7.63397	−	28.4904i	0.409813	−	1.52944i	−0.385189	−	0.922838i	$-0.625864\pi$
$347$	7.63397	−	28.4904i	0.409813	−	1.52944i	0.795002	−	0.606606i	$-0.207470\pi$
$348$	−22.3923	+	6.00000i	−1.20035	+	0.321634i
$349$	−3.09808	−	11.5622i	−0.165836	−	0.618909i	−0.997932	−	0.0642773i	$-0.979526\pi$
$349$	−3.09808	−	11.5622i	−0.165836	−	0.618909i	0.832096	−	0.554632i	$-0.187141\pi$
$350$		0			0
$351$		0			0
$352$	−1.36603	−	1.36603i	−0.0728094	−	0.0728094i
$353$	−4.22243	−	2.43782i	−0.224737	−	0.129752i	0.383405	−	0.923581i	$-0.374752\pi$
$353$	−4.22243	−	2.43782i	−0.224737	−	0.129752i	−0.608142	+	0.793828i	$0.708085\pi$
$354$	−1.39230	−	0.803848i	−0.0740002	−	0.0427240i
$355$		0			0
$356$	10.6340	−	10.6340i	0.563600	−	0.563600i
$357$	24.1244	+	41.7846i	1.27680	+	2.21148i
$358$	11.3923	+	19.7321i	0.602102	+	1.04287i
$359$	23.6603	−	23.6603i	1.24874	−	1.24874i	0.292464	−	0.956277i	$-0.405525\pi$
$359$	23.6603	−	23.6603i	1.24874	−	1.24874i	0.956277	−	0.292464i	$-0.0944751\pi$
$360$		0			0
$361$	−6.41858	−	3.70577i	−0.337820	−	0.195041i
$362$	9.16987	+	5.29423i	0.481958	+	0.278258i
$363$	−12.5885	−	12.5885i	−0.660723	−	0.660723i
$364$	−12.9282	−	3.73205i	−0.677622	−	0.195613i
$365$		0			0
$366$	8.07180	+	30.1244i	0.421920	+	1.57463i
$367$	17.2942	−	4.63397i	0.902751	−	0.241892i	0.222554	−	0.974920i	$-0.428561\pi$
$367$	17.2942	−	4.63397i	0.902751	−	0.241892i	0.680198	+	0.733029i	$0.261894\pi$
$368$	0.901924	−	3.36603i	0.0470160	−	0.175466i
$369$	0.803848	+	0.803848i	0.0418466	+	0.0418466i
$370$		0			0
$371$	−8.69615	+	32.4545i	−0.451482	+	1.68495i
$372$		−	10.3923i		−	0.538816i
$373$	−14.5622	−	3.90192i	−0.754001	−	0.202034i	−0.138709	−	0.990333i	$-0.544295\pi$
$373$	−14.5622	−	3.90192i	−0.754001	−	0.202034i	−0.615292	+	0.788299i	$0.710962\pi$
$374$	−5.09808	+	8.83013i	−0.263615	+	0.456595i
$375$		0			0
$376$			7.00000i			0.360997i
$377$	−32.7846	−	9.46410i	−1.68849	−	0.487426i
$378$		0			0
$379$	−17.8923	+	4.79423i	−0.919066	+	0.246263i	−0.687186	−	0.726481i	$-0.741154\pi$
$379$	−17.8923	+	4.79423i	−0.919066	+	0.246263i	−0.231880	+	0.972744i	$0.574488\pi$
$380$		0			0
$381$	21.0788	−	12.1699i	1.07990	−	0.623481i
$382$	−11.1244			−0.569172
$383$	−6.92820	+	4.00000i	−0.354015	+	0.204390i	−0.666452	−	0.745548i	$-0.732188\pi$
$383$	−6.92820	+	4.00000i	−0.354015	+	0.204390i	0.312437	+	0.949938i	$0.398855\pi$
$384$	−2.36603	−	0.633975i	−0.120741	−	0.0323524i
$385$		0			0
$386$	1.19615	+	2.07180i	0.0608826	+	0.105452i
$387$	6.58846	+	24.5885i	0.334910	+	1.24990i
$388$	8.09808	−	14.0263i	0.411118	−	0.712076i
$389$	2.87564			0.145801			0.0729005	−	0.997339i	$-0.476774\pi$
$389$	2.87564			0.145801			0.0729005	+	0.997339i	$0.476774\pi$
$390$		0			0
$391$	−18.3923			−0.930139
$392$	3.46410	−	6.00000i	0.174964	−	0.303046i
$393$	0.882686	+	3.29423i	0.0445256	+	0.166172i
$394$	−4.06218	−	7.03590i	−0.204650	−	0.354463i
$395$		0			0
$396$	5.59808	+	1.50000i	0.281314	+	0.0753778i
$397$	−15.0622	+	8.69615i	−0.755949	+	0.436447i	−0.827839	−	0.560965i	$-0.810430\pi$
$397$	−15.0622	+	8.69615i	−0.755949	+	0.436447i	0.0718904	+	0.997413i	$0.477097\pi$
$398$	18.9282			0.948785
$399$	−40.6865	+	23.4904i	−2.03687	+	1.17599i
$400$		0			0
$401$	−5.33013	+	1.42820i	−0.266174	+	0.0713211i	−0.389438	−	0.921053i	$-0.627331\pi$
$401$	−5.33013	+	1.42820i	−0.266174	+	0.0713211i	0.123264	+	0.992374i	$0.460664\pi$
$402$	−1.60770	+	1.60770i	−0.0801845	+	0.0801845i
$403$	7.90192	−	13.0981i	0.393623	−	0.652462i
$404$			6.19615i			0.308270i
$405$		0			0
$406$	17.6603	−	30.5885i	0.876464	−	1.51808i
$407$	−6.96410	−	1.86603i	−0.345198	−	0.0924954i
$408$			12.9282i			0.640041i
$409$	−7.66987	+	28.6244i	−0.379251	+	1.41538i	0.467783	+	0.883844i	$0.345053\pi$
$409$	−7.66987	+	28.6244i	−0.379251	+	1.41538i	−0.847033	+	0.531540i	$0.821614\pi$
$410$		0			0
$411$	−35.6603	−	35.6603i	−1.75899	−	1.75899i
$412$	0.794229	−	2.96410i	0.0391288	−	0.146031i
$413$	2.36603	−	0.633975i	0.116424	−	0.0311959i
$414$	2.70577	+	10.0981i	0.132981	+	0.496293i
$415$		0			0
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	24.1244	+	24.1244i	1.18137	+	1.18137i
$418$	−8.59808	−	4.96410i	−0.420546	−	0.242802i
$419$	14.7846	+	8.53590i	0.722275	+	0.417006i	0.815590	−	0.578631i	$-0.196413\pi$
$419$	14.7846	+	8.53590i	0.722275	+	0.417006i	−0.0933142	+	0.995637i	$0.529746\pi$
$420$		0			0
$421$	2.46410	−	2.46410i	0.120093	−	0.120093i	−0.644506	−	0.764599i	$-0.722937\pi$
$421$	2.46410	−	2.46410i	0.120093	−	0.120093i	0.764599	+	0.644506i	$0.222937\pi$
$422$	10.3301	+	17.8923i	0.502863	+	0.870984i
$423$	−10.5000	−	18.1865i	−0.510527	−	0.884260i
$424$	−6.36603	+	6.36603i	−0.309162	+	0.309162i
$425$		0			0
$426$	22.9808	+	13.2679i	1.11342	+	0.642834i
$427$	−41.1506	−	23.7583i	−1.99142	−	1.14975i
$428$	−9.19615	−	9.19615i	−0.444513	−	0.444513i
$429$	11.8301	+	12.2942i	0.571164	+	0.593571i
$430$		0			0
$431$	0.222432	+	0.830127i	0.0107142	+	0.0399858i	0.971076	−	0.238771i	$-0.0767444\pi$
$431$	0.222432	+	0.830127i	0.0107142	+	0.0399858i	−0.960362	+	0.278757i	$0.910078\pi$
$432$		0			0
$433$	−1.41154	+	5.26795i	−0.0678344	+	0.253161i	−0.991513	−	0.130006i	$-0.958500\pi$
$433$	−1.41154	+	5.26795i	−0.0678344	+	0.253161i	0.923679	+	0.383168i	$0.125167\pi$
$434$	11.1962	+	11.1962i	0.537433	+	0.537433i
$435$		0			0
$436$	−5.19615	+	19.3923i	−0.248851	+	0.928723i
$437$		−	17.9090i		−	0.856702i
$438$	−11.1962	−	3.00000i	−0.534973	−	0.143346i
$439$	−6.02628	+	10.4378i	−0.287619	+	0.498170i	−0.973241	−	0.229787i	$-0.926197\pi$
$439$	−6.02628	+	10.4378i	−0.287619	+	0.498170i	0.685622	+	0.727958i	$0.259530\pi$
$440$		0			0
$441$			20.7846i			0.989743i
$442$	−9.83013	+	16.2942i	−0.467571	+	0.775037i
$443$	1.80385	−	1.80385i	0.0857034	−	0.0857034i	−0.662955	−	0.748659i	$-0.730698\pi$
$443$	1.80385	−	1.80385i	0.0857034	−	0.0857034i	0.748659	+	0.662955i	$0.230698\pi$
$444$	−8.83013	+	2.36603i	−0.419059	+	0.112287i
$445$		0			0
$446$	3.40192	−	1.96410i	0.161086	−	0.0930029i
$447$	21.4641			1.01522
$448$	3.23205	−	1.86603i	0.152700	−	0.0881614i
$449$	−4.76795	−	1.27757i	−0.225013	−	0.0602922i	0.144551	−	0.989497i	$-0.453826\pi$
$449$	−4.76795	−	1.27757i	−0.225013	−	0.0602922i	−0.369564	+	0.929205i	$0.620493\pi$
$450$		0			0
$451$	−0.366025	−	0.633975i	−0.0172355	−	0.0298527i
$452$	−0.732051	−	2.73205i	−0.0344328	−	0.128505i
$453$	−2.66025	+	4.60770i	−0.124990	+	0.216488i
$454$	−1.85641			−0.0871255
$455$		0			0
$456$	−12.5885			−0.589509
$457$	−3.56218	+	6.16987i	−0.166632	+	0.288614i	−0.937234	−	0.348702i	$-0.886622\pi$
$457$	−3.56218	+	6.16987i	−0.166632	+	0.288614i	0.770602	+	0.637317i	$0.219956\pi$
$458$	−4.97372	−	18.5622i	−0.232407	−	0.867354i
$459$		0			0
$460$		0			0
$461$	9.09808	+	2.43782i	0.423740	+	0.113541i	0.464386	−	0.885633i	$-0.346275\pi$
$461$	9.09808	+	2.43782i	0.423740	+	0.113541i	−0.0406464	+	0.999174i	$0.512942\pi$
$462$	−15.2942	+	8.83013i	−0.711552	+	0.410815i
$463$	33.1769			1.54186			0.770931	−	0.636919i	$-0.219791\pi$
$463$	33.1769			1.54186			0.770931	+	0.636919i	$0.219791\pi$
$464$	8.19615	−	4.73205i	0.380497	−	0.219680i
$465$		0			0
$466$	12.0981	−	3.24167i	0.560433	−	0.150167i
$467$	−6.53590	+	6.53590i	−0.302445	+	0.302445i	−0.841970	−	0.539525i	$-0.818604\pi$
$467$	−6.53590	+	6.53590i	−0.302445	+	0.302445i	0.539525	+	0.841970i	$0.318604\pi$
$468$	10.3923	+	3.00000i	0.480384	+	0.138675i
$469$		−	3.46410i		−	0.159957i
$470$		0			0
$471$	−19.6865	+	34.0981i	−0.907108	+	1.57116i
$472$	0.633975	+	0.169873i	0.0291810	+	0.00781904i
$473$		−	16.3923i		−	0.753719i
$474$	7.05256	−	26.3205i	0.323935	−	1.20894i
$475$		0			0
$476$	−13.9282	−	13.9282i	−0.638398	−	0.638398i
$477$	6.99038	−	26.0885i	0.320068	−	1.19451i
$478$	−7.83013	+	2.09808i	−0.358142	+	0.0959638i
$479$	−6.90192	−	25.7583i	−0.315357	−	1.17693i	−0.923657	−	0.383221i	$-0.874815\pi$
$479$	−6.90192	−	25.7583i	−0.315357	−	1.17693i	0.608300	−	0.793707i	$-0.291852\pi$
$480$		0			0
$481$	−12.9282	−	3.73205i	−0.589475	−	0.170167i
$482$	4.56218	+	4.56218i	0.207802	+	0.207802i
$483$	−27.5885	−	15.9282i	−1.25532	−	0.724758i
$484$	6.29423	+	3.63397i	0.286101	+	0.165181i
$485$		0			0
$486$	15.5885	−	15.5885i	0.707107	−	0.707107i
$487$	6.16025	+	10.6699i	0.279148	+	0.483498i	0.971173	−	0.238375i	$-0.0766147\pi$
$487$	6.16025	+	10.6699i	0.279148	+	0.483498i	−0.692025	+	0.721873i	$0.743281\pi$
$488$	−6.36603	−	11.0263i	−0.288176	−	0.499136i
$489$	33.1244	−	33.1244i	1.49794	−	1.49794i
$490$		0			0
$491$	0.741670	+	0.428203i	0.0334711	+	0.0193245i	0.516642	−	0.856201i	$-0.327182\pi$
$491$	0.741670	+	0.428203i	0.0334711	+	0.0193245i	−0.483171	+	0.875526i	$0.660515\pi$
$492$	−0.803848	−	0.464102i	−0.0362402	−	0.0209233i
$493$	−35.3205	−	35.3205i	−1.59076	−	1.59076i
$494$	−15.8660	−	9.57180i	−0.713846	−	0.430655i
$495$		0			0
$496$	1.09808	+	4.09808i	0.0493051	+	0.184009i
$497$	−39.0526	+	10.4641i	−1.75175	+	0.469379i
$498$	1.73205	−	6.46410i	0.0776151	−	0.289663i
$499$	−20.1244	−	20.1244i	−0.900890	−	0.900890i	0.0946233	−	0.995513i	$-0.469835\pi$
$499$	−20.1244	−	20.1244i	−0.900890	−	0.900890i	−0.995513	+	0.0946233i	$0.969835\pi$
$500$		0			0
$501$	11.6147	−	43.3468i	0.518908	−	1.93659i
$502$		−	10.6603i		−	0.475790i
$503$	9.06218	+	2.42820i	0.404063	+	0.108268i	0.455126	−	0.890427i	$-0.349594\pi$
$503$	9.06218	+	2.42820i	0.404063	+	0.108268i	−0.0510632	+	0.998695i	$0.516261\pi$
$504$	−5.59808	+	9.69615i	−0.249358	+	0.431901i
$505$		0			0
$506$		−	6.73205i		−	0.299276i
$507$	21.6340	+	23.3660i	0.960799	+	1.03772i
$508$	−7.02628	+	7.02628i	−0.311741	+	0.311741i
$509$	0.732051	−	0.196152i	0.0324476	−	0.00869430i	−0.242559	−	0.970137i	$-0.577987\pi$
$509$	0.732051	−	0.196152i	0.0324476	−	0.00869430i	0.275006	+	0.961442i	$0.411320\pi$
$510$		0			0
$511$	15.2942	−	8.83013i	0.676577	−	0.390622i
$512$	1.00000			0.0441942
$513$		0			0
$514$	8.19615	+	2.19615i	0.361517	+	0.0968681i
$515$		0			0
$516$	−10.3923	−	18.0000i	−0.457496	−	0.792406i
$517$	3.50000	+	13.0622i	0.153930	+	0.574474i
$518$	6.96410	−	12.0622i	0.305985	−	0.529982i
$519$	39.3731			1.72829
$520$		0			0
$521$	−40.7128			−1.78366			−0.891830	−	0.452370i	$-0.850579\pi$
$521$	−40.7128			−1.78366			−0.891830	+	0.452370i	$0.850579\pi$
$522$	−14.1962	+	24.5885i	−0.621349	+	1.07621i
$523$	3.53590	+	13.1962i	0.154614	+	0.577027i	0.999138	+	0.0415098i	$0.0132168\pi$
$523$	3.53590	+	13.1962i	0.154614	+	0.577027i	−0.844524	+	0.535518i	$0.820117\pi$
$524$	−0.696152	−	1.20577i	−0.0304116	−	0.0526744i
$525$		0			0
$526$	−13.1603	−	3.52628i	−0.573814	−	0.153753i
$527$	19.3923	−	11.1962i	0.844742	−	0.487712i
$528$	−4.73205			−0.205936
$529$	−9.40192	+	5.42820i	−0.408779	+	0.236009i
$530$		0			0
$531$	−1.90192	+	0.509619i	−0.0825365	+	0.0221156i
$532$	13.5622	−	13.5622i	0.587995	−	0.587995i
$533$	−0.660254	−	1.19615i	−0.0285988	−	0.0518111i
$534$		−	36.8372i		−	1.59410i
$535$		0			0
$536$	0.464102	−	0.803848i	0.0200461	−	0.0347209i
$537$	53.9090	+	14.4449i	2.32634	+	0.623342i
$538$		−	11.2679i		−	0.485796i
$539$	3.46410	−	12.9282i	0.149209	−	0.556857i
$540$		0			0
$541$	5.53590	+	5.53590i	0.238007	+	0.238007i	0.816024	−	0.578018i	$-0.196173\pi$
$541$	5.53590	+	5.53590i	0.238007	+	0.238007i	−0.578018	+	0.816024i	$0.696173\pi$
$542$	1.80385	−	6.73205i	0.0774819	−	0.289166i
$543$	25.0526	−	6.71281i	1.07511	−	0.288074i
$544$	−1.36603	−	5.09808i	−0.0585679	−	0.218578i
$545$		0			0
$546$	−28.8564	+	15.9282i	−1.23494	+	0.681664i
$547$	−8.53590	−	8.53590i	−0.364969	−	0.364969i	0.500670	−	0.865638i	$-0.333087\pi$
$547$	−8.53590	−	8.53590i	−0.364969	−	0.364969i	−0.865638	+	0.500670i	$0.833087\pi$
$548$	17.8301	+	10.2942i	0.761665	+	0.439748i
$549$	33.0788	+	19.0981i	1.41177	+	0.815086i
$550$		0			0
$551$	34.3923	−	34.3923i	1.46516	−	1.46516i
$552$	−4.26795	−	7.39230i	−0.181656	−	0.314637i
$553$	20.7583	+	35.9545i	0.882734	+	1.52894i
$554$	14.2224	−	14.2224i	0.604253	−	0.604253i
$555$		0			0
$556$	−12.0622	−	6.96410i	−0.511550	−	0.295344i
$557$	−22.7942	−	13.1603i	−0.965822	−	0.557618i	−0.0678623	−	0.997695i	$-0.521618\pi$
$557$	−22.7942	−	13.1603i	−0.965822	−	0.557618i	−0.897960	+	0.440077i	$0.854951\pi$
$558$	−9.00000	−	9.00000i	−0.381000	−	0.381000i
$559$	0.588457	−	30.5885i	0.0248891	−	1.29375i
$560$		0			0
$561$	6.46410	+	24.1244i	0.272915	+	1.01853i
$562$	−11.8301	+	3.16987i	−0.499024	+	0.133713i
$563$	1.33975	−	5.00000i	0.0564636	−	0.210725i	−0.931930	−	0.362637i	$-0.881876\pi$
$563$	1.33975	−	5.00000i	0.0564636	−	0.210725i	0.988394	+	0.151912i	$0.0485431\pi$
$564$	12.1244	+	12.1244i	0.510527	+	0.510527i
$565$		0			0
$566$	−2.26795	+	8.46410i	−0.0953290	+	0.355773i
$567$			33.5885i			1.41058i
$568$	−10.4641	−	2.80385i	−0.439064	−	0.117647i
$569$	−11.8923	+	20.5981i	−0.498551	+	0.863516i	−0.999999	−	0.00167195i	$-0.999468\pi$
$569$	−11.8923	+	20.5981i	−0.498551	+	0.863516i	0.501447	+	0.865188i	$0.332801\pi$
$570$		0			0
$571$		−	41.9808i		−	1.75684i	−0.477889	−	0.878420i	$-0.658598\pi$
$571$		−	41.9808i		−	1.75684i	0.477889	−	0.878420i	$-0.341402\pi$
$572$	−5.96410	−	3.59808i	−0.249372	−	0.150443i
$573$	−19.2679	+	19.2679i	−0.804930	+	0.804930i
$574$	1.36603	−	0.366025i	0.0570168	−	0.0152776i
$575$		0			0
$576$	−2.59808	+	1.50000i	−0.108253	+	0.0625000i
$577$	28.3397			1.17980			0.589900	−	0.807477i	$-0.299167\pi$
$577$	28.3397			1.17980			0.589900	+	0.807477i	$0.299167\pi$
$578$	−9.40192	+	5.42820i	−0.391068	+	0.225783i
$579$	5.66025	+	1.51666i	0.235232	+	0.0630303i
$580$		0			0
$581$	5.09808	+	8.83013i	0.211504	+	0.366335i
$582$	−10.2679	−	38.3205i	−0.425620	−	1.58844i
$583$	−8.69615	+	15.0622i	−0.360158	+	0.623812i
$584$	4.73205			0.195814
$585$		0			0
$586$	−27.9282			−1.15370
$587$	11.8564	−	20.5359i	0.489366	−	0.847607i	−0.510559	−	0.859843i	$-0.670561\pi$
$587$	11.8564	−	20.5359i	0.489366	−	0.847607i	0.999925	+	0.0122356i	$0.00389480\pi$
$588$	−4.39230	−	16.3923i	−0.181136	−	0.676007i
$589$	10.9019	+	18.8827i	0.449206	+	0.778048i
$590$		0			0
$591$	−19.2224	−	5.15064i	−0.790705	−	0.211869i
$592$	3.23205	−	1.86603i	0.132836	−	0.0766932i
$593$	−15.7128			−0.645248			−0.322624	−	0.946527i	$-0.604565\pi$
$593$	−15.7128			−0.645248			−0.322624	+	0.946527i	$0.604565\pi$
$594$		0			0
$595$		0			0
$596$	−8.46410	+	2.26795i	−0.346703	+	0.0928988i
$597$	32.7846	−	32.7846i	1.34178	−	1.34178i
$598$	0.241670	−	12.5622i	0.00988261	−	0.513706i
$599$			15.0718i			0.615817i	0.951416	+	0.307908i	$0.0996291\pi$
$599$			15.0718i			0.615817i	−0.951416	+	0.307908i	$0.900371\pi$
$600$		0			0
$601$	13.8660	−	24.0167i	0.565607	−	0.979660i	−0.431386	−	0.902167i	$-0.641975\pi$
$601$	13.8660	−	24.0167i	0.565607	−	0.979660i	0.996993	−	0.0774925i	$-0.0246914\pi$
$602$	30.5885	+	8.19615i	1.24669	+	0.334050i
$603$			2.78461i			0.113398i
$604$	0.562178	−	2.09808i	0.0228747	−	0.0853695i
$605$		0			0
$606$	10.7321	+	10.7321i	0.435960	+	0.435960i
$607$	−1.45448	+	5.42820i	−0.0590356	+	0.220324i	−0.989141	−	0.146968i	$-0.953048\pi$
$607$	−1.45448	+	5.42820i	−0.0590356	+	0.220324i	0.930106	+	0.367292i	$0.119715\pi$
$608$	4.96410	−	1.33013i	0.201321	−	0.0539438i
$609$	−22.3923	−	83.5692i	−0.907382	−	3.38640i
$610$		0			0
$611$	6.06218	+	24.5000i	0.245249	+	0.991164i
$612$	11.1962	+	11.1962i	0.452578	+	0.452578i
$613$	31.1147	+	17.9641i	1.25671	+	0.725563i	0.972434	−	0.233179i	$-0.0749127\pi$
$613$	31.1147	+	17.9641i	1.25671	+	0.725563i	0.284278	+	0.958742i	$0.408246\pi$
$614$	−1.73205	−	1.00000i	−0.0698999	−	0.0403567i
$615$		0			0
$616$	5.09808	−	5.09808i	0.205407	−	0.205407i
$617$	−12.1244	−	21.0000i	−0.488108	−	0.845428i	0.511798	−	0.859106i	$-0.328980\pi$
$617$	−12.1244	−	21.0000i	−0.488108	−	0.845428i	−0.999906	+	0.0136775i	$0.995646\pi$
$618$	−3.75833	−	6.50962i	−0.151182	−	0.261855i
$619$	31.7583	−	31.7583i	1.27648	−	1.27648i	0.333848	−	0.942627i	$-0.391653\pi$
$619$	31.7583	−	31.7583i	1.27648	−	1.27648i	0.942627	−	0.333848i	$-0.108347\pi$
$620$		0			0
$621$		0			0
$622$	−4.90192	−	2.83013i	−0.196549	−	0.113478i
$623$	39.6865	+	39.6865i	1.59001	+	1.59001i
$624$	−8.83013	−	0.169873i	−0.353488	−	0.00680036i
$625$		0			0
$626$	3.12436	+	11.6603i	0.124874	+	0.466037i
$627$	−23.4904	+	6.29423i	−0.938115	+	0.251367i
$628$	4.16025	−	15.5263i	0.166012	−	0.619566i
$629$	−13.9282	−	13.9282i	−0.555354	−	0.555354i
$630$		0			0
$631$	−5.87564	+	21.9282i	−0.233906	+	0.872948i	0.744733	+	0.667362i	$0.232577\pi$
$631$	−5.87564	+	21.9282i	−0.233906	+	0.872948i	−0.978639	+	0.205586i	$0.934090\pi$
$632$			11.1244i			0.442503i
$633$	48.8827	+	13.0981i	1.94291	+	0.520602i
$634$	0.696152	−	1.20577i	0.0276477	−	0.0478873i
$635$		0			0
$636$			22.0526i			0.874441i
$637$	6.92820	−	24.0000i	0.274505	−	0.950915i
$638$	12.9282	−	12.9282i	0.511832	−	0.511832i
$639$	31.3923	−	8.41154i	1.24186	−	0.332755i
$640$		0			0
$641$	−27.1865	+	15.6962i	−1.07380	+	0.619961i	−0.929218	−	0.369532i	$-0.879518\pi$
$641$	−27.1865	+	15.6962i	−1.07380	+	0.619961i	−0.144585	+	0.989492i	$0.546185\pi$
$642$	−31.8564			−1.25727
$643$	−25.3468	+	14.6340i	−0.999580	+	0.577108i	−0.908124	−	0.418702i	$-0.862485\pi$
$643$	−25.3468	+	14.6340i	−0.999580	+	0.577108i	−0.0914558	+	0.995809i	$0.529152\pi$
$644$	12.5622	+	3.36603i	0.495019	+	0.132640i
$645$		0			0
$646$	−13.5622	−	23.4904i	−0.533597	−	0.924217i
$647$	−2.86603	−	10.6962i	−0.112675	−	0.420509i	0.886427	−	0.462868i	$-0.153179\pi$
$647$	−2.86603	−	10.6962i	−0.112675	−	0.420509i	−0.999102	+	0.0423585i	$0.986513\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	1.26795			0.0497714
$650$		0			0
$651$	38.7846			1.52009
$652$	−9.56218	+	16.5622i	−0.374484	+	0.648625i
$653$	−0.186533	−	0.696152i	−0.00729962	−	0.0272425i	0.962180	−	0.272415i	$-0.0878222\pi$
$653$	−0.186533	−	0.696152i	−0.00729962	−	0.0272425i	−0.969480	+	0.245172i	$0.921156\pi$
$654$	24.5885	+	42.5885i	0.961485	+	1.66534i
$655$		0			0
$656$	0.366025	+	0.0980762i	0.0142909	+	0.00382923i
$657$	−12.2942	+	7.09808i	−0.479644	+	0.276922i
$658$	−26.1244			−1.01843
$659$	−34.3923	+	19.8564i	−1.33973	+	0.773496i	−0.986768	−	0.162140i	$-0.948160\pi$
$659$	−34.3923	+	19.8564i	−1.33973	+	0.773496i	−0.352966	+	0.935636i	$0.614827\pi$
$660$		0			0
$661$	4.63397	−	1.24167i	0.180241	−	0.0482954i	−0.167570	−	0.985860i	$-0.553592\pi$
$661$	4.63397	−	1.24167i	0.180241	−	0.0482954i	0.347810	+	0.937565i	$0.386925\pi$
$662$	−13.3923	+	13.3923i	−0.520507	+	0.520507i
$663$	11.1962	+	45.2487i	0.434823	+	1.75731i
$664$			2.73205i			0.106024i
$665$		0			0
$666$	−5.59808	+	9.69615i	−0.216921	+	0.375718i
$667$	31.8564	+	8.53590i	1.23348	+	0.330511i
$668$			18.3205i			0.708842i
$669$	2.49038	−	9.29423i	0.0962837	−	0.359336i
$670$		0			0
$671$	−17.3923	−	17.3923i	−0.671422	−	0.671422i
$672$	2.36603	−	8.83013i	0.0912714	−	0.340630i
$673$	−27.8564	+	7.46410i	−1.07379	+	0.287720i	−0.752048	−	0.659109i	$-0.770934\pi$
$673$	−27.8564	+	7.46410i	−1.07379	+	0.287720i	−0.321738	+	0.946829i	$0.604267\pi$
$674$	−1.56218	−	5.83013i	−0.0601728	−	0.224568i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	18.6603	+	18.6603i	0.717172	+	0.717172i	0.968025	−	0.250853i	$-0.0807112\pi$
$677$	18.6603	+	18.6603i	0.717172	+	0.717172i	−0.250853	+	0.968025i	$0.580711\pi$
$678$	−6.00000	−	3.46410i	−0.230429	−	0.133038i
$679$	52.3468	+	30.2224i	2.00889	+	1.15983i
$680$		0			0
$681$	−3.21539	+	3.21539i	−0.123214	+	0.123214i
$682$	4.09808	+	7.09808i	0.156923	+	0.271799i
$683$	1.53590	+	2.66025i	0.0587695	+	0.101792i	0.893913	−	0.448240i	$-0.147949\pi$
$683$	1.53590	+	2.66025i	0.0587695	+	0.101792i	−0.835144	+	0.550032i	$0.814616\pi$
$684$	−10.9019	+	10.9019i	−0.416845	+	0.416845i
$685$		0			0
$686$	−0.232051	−	0.133975i	−0.00885974	−	0.00511517i
$687$	−40.7654	−	23.5359i	−1.55530	−	0.897951i
$688$	6.00000	+	6.00000i	0.228748	+	0.228748i
$689$	−16.7679	+	27.7942i	−0.638808	+	1.05888i
$690$		0			0
$691$	10.8205	+	40.3827i	0.411632	+	1.53623i	0.791488	+	0.611184i	$0.209307\pi$
$691$	10.8205	+	40.3827i	0.411632	+	1.53623i	−0.379857	+	0.925045i	$0.624027\pi$
$692$	−15.5263	+	4.16025i	−0.590221	+	0.158149i
$693$	−5.59808	+	20.8923i	−0.212653	+	0.793633i
$694$	20.8564	+	20.8564i	0.791698	+	0.791698i
$695$		0			0
$696$	6.00000	−	22.3923i	0.227429	−	0.848778i
$697$		−	2.00000i		−	0.0757554i
$698$	11.5622	+	3.09808i	0.437635	+	0.117264i
$699$	15.3397	−	26.5692i	0.580202	−	1.00494i
$700$		0			0
$701$		−	23.9090i		−	0.903029i	−0.892264	−	0.451515i	$-0.850884\pi$
$701$		−	23.9090i		−	0.903029i	0.892264	−	0.451515i	$-0.149116\pi$
$702$		0			0
$703$	13.5622	−	13.5622i	0.511507	−	0.511507i
$704$	1.86603	−	0.500000i	0.0703285	−	0.0188445i
$705$		0			0
$706$	4.22243	−	2.43782i	0.158913	−	0.0917486i
$707$	−23.1244			−0.869681
$708$	1.39230	−	0.803848i	0.0523260	−	0.0302104i
$709$	−1.90192	−	0.509619i	−0.0714282	−	0.0191391i	0.222928	−	0.974835i	$-0.428439\pi$
$709$	−1.90192	−	0.509619i	−0.0714282	−	0.0191391i	−0.294356	+	0.955696i	$0.595105\pi$
$710$		0			0
$711$	−16.6865	−	28.9019i	−0.625794	−	1.08391i
$712$	3.89230	+	14.5263i	0.145870	+	0.544395i
$713$	−7.39230	+	12.8038i	−0.276844	+	0.479508i
$714$	−48.2487			−1.80566
$715$		0			0
$716$	−22.7846			−0.851501
$717$	−9.92820	+	17.1962i	−0.370776	+	0.642202i
$718$	8.66025	+	32.3205i	0.323198	+	1.20619i
$719$	−22.2487	−	38.5359i	−0.829737	−	1.43715i	−0.898245	−	0.439496i	$-0.855157\pi$
$719$	−22.2487	−	38.5359i	−0.829737	−	1.43715i	0.0685077	−	0.997651i	$-0.478176\pi$
$720$		0			0
$721$	11.0622	+	2.96410i	0.411977	+	0.110389i
$722$	6.41858	−	3.70577i	0.238875	−	0.137915i
$723$	15.8038			0.587751
$724$	−9.16987	+	5.29423i	−0.340796	+	0.196758i
$725$		0			0
$726$	17.1962	−	4.60770i	0.638209	−	0.171008i
$727$	4.90192	−	4.90192i	0.181802	−	0.181802i	−0.610338	−	0.792141i	$-0.708967\pi$
$727$	4.90192	−	4.90192i	0.181802	−	0.181802i	0.792141	+	0.610338i	$0.208967\pi$
$728$	9.69615	−	9.33013i	0.359363	−	0.345798i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	22.3923	−	38.7846i	0.828209	−	1.43450i
$732$	−30.1244	−	8.07180i	−1.11343	−	0.298342i
$733$			24.5167i			0.905544i	0.891626	+	0.452772i	$0.149565\pi$
$733$			24.5167i			0.905544i	−0.891626	+	0.452772i	$0.850435\pi$
$734$	−4.63397	+	17.2942i	−0.171043	+	0.638342i
$735$		0			0
$736$	2.46410	+	2.46410i	0.0908280	+	0.0908280i
$737$	0.464102	−	1.73205i	0.0170954	−	0.0638009i
$738$	−1.09808	+	0.294229i	−0.0404207	+	0.0108307i
$739$	−1.83975	−	6.86603i	−0.0676761	−	0.252571i	0.923797	−	0.382883i	$-0.125069\pi$
$739$	−1.83975	−	6.86603i	−0.0676761	−	0.252571i	−0.991473	+	0.130312i	$0.958402\pi$
$740$		0			0
$741$	−44.0596	+	10.9019i	−1.61857	+	0.400492i
$742$	−23.7583	−	23.7583i	−0.872196	−	0.872196i
$743$	19.1769	+	11.0718i	0.703533	+	0.406185i	0.808662	−	0.588274i	$-0.200192\pi$
$743$	19.1769	+	11.0718i	0.703533	+	0.406185i	−0.105129	+	0.994459i	$0.533526\pi$
$744$	9.00000	+	5.19615i	0.329956	+	0.190500i
$745$		0			0
$746$	10.6603	−	10.6603i	0.390300	−	0.390300i
$747$	−4.09808	−	7.09808i	−0.149941	−	0.259705i
$748$	−5.09808	−	8.83013i	−0.186404	−	0.322861i
$749$	34.3205	−	34.3205i	1.25404	−	1.25404i
$750$		0			0
$751$	29.6603	+	17.1244i	1.08232	+	0.624877i	0.931521	−	0.363688i	$-0.118483\pi$
$751$	29.6603	+	17.1244i	1.08232	+	0.624877i	0.150797	+	0.988565i	$0.451816\pi$
$752$	−6.06218	−	3.50000i	−0.221065	−	0.127632i
$753$	−18.4641	−	18.4641i	−0.672869	−	0.672869i
$754$	24.5885	−	23.6603i	0.895459	−	0.861656i
$755$		0			0
$756$		0			0
$757$	13.0622	−	3.50000i	0.474753	−	0.127210i	−0.0135054	−	0.999909i	$-0.504299\pi$
$757$	13.0622	−	3.50000i	0.474753	−	0.127210i	0.488258	+	0.872699i	$0.337632\pi$
$758$	4.79423	−	17.8923i	0.174134	−	0.649878i
$759$	−11.6603	−	11.6603i	−0.423240	−	0.423240i
$760$		0			0
$761$	−1.62436	+	6.06218i	−0.0588828	+	0.219754i	−0.989097	−	0.147262i	$-0.952954\pi$
$761$	−1.62436	+	6.06218i	−0.0588828	+	0.219754i	0.930215	+	0.367016i	$0.119621\pi$
$762$			24.3397i			0.881736i
$763$	−72.3731	−	19.3923i	−2.62008	−	0.702049i
$764$	5.56218	−	9.63397i	0.201233	−	0.348545i
$765$		0			0
$766$		−	8.00000i		−	0.289052i
$767$	2.36603	+	0.0455173i	0.0854322	+	0.00164354i
$768$	1.73205	−	1.73205i	0.0625000	−	0.0625000i
$769$	22.9545	−	6.15064i	0.827760	−	0.221798i	0.180024	−	0.983662i	$-0.442383\pi$
$769$	22.9545	−	6.15064i	0.827760	−	0.221798i	0.647736	+	0.761865i	$0.275716\pi$
$770$		0			0
$771$	18.0000	−	10.3923i	0.648254	−	0.374270i
$772$	−2.39230			−0.0861009
$773$	32.5070	−	18.7679i	1.16920	−	0.675036i	0.215706	−	0.976458i	$-0.430795\pi$
$773$	32.5070	−	18.7679i	1.16920	−	0.675036i	0.953491	+	0.301422i	$0.0974613\pi$
$774$	−24.5885	−	6.58846i	−0.883814	−	0.236817i
$775$		0			0
$776$	8.09808	+	14.0263i	0.290704	+	0.503514i
$777$	−8.83013	−	32.9545i	−0.316779	−	1.18224i
$778$	−1.43782	+	2.49038i	−0.0515484	+	0.0892845i
$779$	1.94744			0.0697743
$780$		0			0
$781$	−20.9282			−0.748870
$782$	9.19615	−	15.9282i	0.328854	−	0.569591i
$783$		0			0
$784$	3.46410	+	6.00000i	0.123718	+	0.214286i
$785$		0			0
$786$	−3.29423	−	0.882686i	−0.117501	−	0.0314844i
$787$	−2.95448	+	1.70577i	−0.105316	+	0.0608042i	−0.551733	−	0.834021i	$-0.686033\pi$
$787$	−2.95448	+	1.70577i	−0.105316	+	0.0608042i	0.446417	+	0.894825i	$0.352700\pi$
$788$	8.12436			0.289418
$789$	−28.9019	+	16.6865i	−1.02894	+	0.594056i
$790$		0			0
$791$	10.1962	−	2.73205i	0.362533	−	0.0971405i
$792$	−4.09808	+	4.09808i	−0.145619	+	0.145619i
$793$	−31.8301	−	33.0788i	−1.13032	−	1.17466i
$794$		−	17.3923i		−	0.617230i
$795$		0			0
$796$	−9.46410	+	16.3923i	−0.335446	+	0.581010i
$797$	−23.5622	−	6.31347i	−0.834615	−	0.223634i	−0.183889	−	0.982947i	$-0.558869\pi$
$797$	−23.5622	−	6.31347i	−0.834615	−	0.223634i	−0.650726	+	0.759313i	$0.725535\pi$
$798$		−	46.9808i		−	1.66310i
$799$	−9.56218	+	35.6865i	−0.338286	+	1.26250i
$800$		0			0
$801$	−31.9019	−	31.9019i	−1.12720	−	1.12720i
$802$	1.42820	−	5.33013i	0.0504316	−	0.188213i
$803$	8.83013	−	2.36603i	0.311608	−	0.0834952i
$804$	−0.588457	−	2.19615i	−0.0207533	−	0.0774523i
$805$		0			0
$806$	7.39230	+	13.3923i	0.260383	+	0.471724i
$807$	−19.5167	−	19.5167i	−0.687019	−	0.687019i
$808$	−5.36603	−	3.09808i	−0.188776	−	0.108990i
$809$	−30.8038	−	17.7846i	−1.08301	−	0.625274i	−0.151300	−	0.988488i	$-0.548346\pi$
$809$	−30.8038	−	17.7846i	−1.08301	−	0.625274i	−0.931706	+	0.363214i	$0.881679\pi$
$810$		0			0
$811$	−24.4186	+	24.4186i	−0.857452	+	0.857452i	−0.991037	−	0.133585i	$-0.957351\pi$
$811$	−24.4186	+	24.4186i	−0.857452	+	0.857452i	0.133585	+	0.991037i	$0.457351\pi$
$812$	17.6603	+	30.5885i	0.619753	+	1.07344i
$813$	−8.53590	−	14.7846i	−0.299367	−	0.518519i
$814$	5.09808	−	5.09808i	0.178687	−	0.178687i
$815$		0			0
$816$	−11.1962	−	6.46410i	−0.391944	−	0.226289i
$817$	37.7654	+	21.8038i	1.32124	+	0.762820i
$818$	−20.9545	−	20.9545i	−0.732656	−	0.732656i
$819$	−11.1962	+	38.7846i	−0.391225	+	1.35524i
$820$		0			0
$821$	5.68653	+	21.2224i	0.198461	+	0.740668i	0.991344	+	0.131293i	$0.0419129\pi$
$821$	5.68653	+	21.2224i	0.198461	+	0.740668i	−0.792882	+	0.609375i	$0.791420\pi$
$822$	48.7128	−	13.0526i	1.69905	−	0.455260i
$823$	0.160254	−	0.598076i	0.00558610	−	0.0208476i	−0.963077	−	0.269228i	$-0.913232\pi$
$823$	0.160254	−	0.598076i	0.00558610	−	0.0208476i	0.968663	+	0.248380i	$0.0798982\pi$
$824$	2.16987	+	2.16987i	0.0755911	+	0.0755911i
$825$		0			0
$826$	−0.633975	+	2.36603i	−0.0220588	+	0.0823246i
$827$			53.3731i			1.85596i	0.372626	+	0.927982i	$0.378458\pi$
$827$			53.3731i			1.85596i	−0.372626	+	0.927982i	$0.621542\pi$
$828$	−10.0981	−	2.70577i	−0.350932	−	0.0940321i
$829$	−12.5885	+	21.8038i	−0.437215	+	0.757279i	−0.997474	−	0.0710390i	$-0.977369\pi$
$829$	−12.5885	+	21.8038i	−0.437215	+	0.757279i	0.560258	+	0.828318i	$0.310702\pi$
$830$		0			0
$831$		−	49.2679i		−	1.70909i
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	25.8564	−	25.8564i	0.895871	−	0.895871i
$834$	−32.9545	+	8.83013i	−1.14112	+	0.305762i
$835$		0			0
$836$	8.59808	−	4.96410i	0.297371	−	0.171687i
$837$		0			0
$838$	−14.7846	+	8.53590i	−0.510726	+	0.294868i
$839$	39.2224	+	10.5096i	1.35411	+	0.362832i	0.861650	−	0.507503i	$-0.169432\pi$
$839$	39.2224	+	10.5096i	1.35411	+	0.362832i	0.492459	+	0.870336i	$0.336098\pi$
$840$		0			0
$841$	30.2846	+	52.4545i	1.04430	+	1.80878i
$842$	0.901924	+	3.36603i	0.0310823	+	0.116001i
$843$	−15.0000	+	25.9808i	−0.516627	+	0.894825i
$844$	−20.6603			−0.711155
$845$		0			0
$846$	21.0000			0.721995
$847$	−13.5622	+	23.4904i	−0.466002	+	0.807139i
$848$	−2.33013	−	8.69615i	−0.0800169	−	0.298627i
$849$	10.7321	+	18.5885i	0.368323	+	0.637954i
$850$		0			0
$851$	12.5622	+	3.36603i	0.430626	+	0.115386i
$852$	−22.9808	+	13.2679i	−0.787308	+	0.454552i
$853$	29.8564			1.02226			0.511132	−	0.859502i	$-0.329226\pi$
$853$	29.8564			1.02226			0.511132	+	0.859502i	$0.329226\pi$
$854$	41.1506	−	23.7583i	1.40815	−	0.812993i
$855$		0			0
$856$	12.5622	−	3.36603i	0.429366	−	0.115048i
$857$	35.5885	−	35.5885i	1.21568	−	1.21568i	0.246548	−	0.969131i	$-0.420704\pi$
$857$	35.5885	−	35.5885i	1.21568	−	1.21568i	0.969131	−	0.246548i	$-0.0792963\pi$
$858$	−16.5622	+	4.09808i	−0.565423	+	0.139906i
$859$			19.8756i			0.678148i	0.940760	+	0.339074i	$0.110114\pi$
$859$			19.8756i			0.678148i	−0.940760	+	0.339074i	$0.889886\pi$
$860$		0			0
$861$	1.73205	−	3.00000i	0.0590281	−	0.102240i
$862$	−0.830127	−	0.222432i	−0.0282742	−	0.00757606i
$863$			11.0718i			0.376888i	0.982084	+	0.188444i	$0.0603445\pi$
$863$			11.0718i			0.376888i	−0.982084	+	0.188444i	$0.939656\pi$
$864$		0			0
$865$		0			0
$866$	−3.85641	−	3.85641i	−0.131046	−	0.131046i
$867$	−6.88269	+	25.6865i	−0.233748	+	0.872360i
$868$	−15.2942	+	4.09808i	−0.519120	+	0.139098i
$869$	5.56218	+	20.7583i	0.188684	+	0.704178i
$870$		0			0
$871$	0.928203	−	3.21539i	0.0314510	−	0.108949i
$872$	−14.1962	−	14.1962i	−0.480742	−	0.480742i
$873$	−42.0788	−	24.2942i	−1.42415	−	0.822235i
$874$	15.5096	+	8.95448i	0.524621	+	0.302890i
$875$		0			0
$876$	8.19615	−	8.19615i	0.276922	−	0.276922i
$877$	17.1962	+	29.7846i	0.580673	+	1.00575i	0.995400	+	0.0958089i	$0.0305438\pi$
$877$	17.1962	+	29.7846i	0.580673	+	1.00575i	−0.414727	+	0.909946i	$0.636123\pi$
$878$	−6.02628	−	10.4378i	−0.203377	−	0.352259i
$879$	−48.3731	+	48.3731i	−1.63158	+	1.63158i
$880$		0			0
$881$	−32.2583	−	18.6244i	−1.08681	−	0.627470i	−0.154085	−	0.988058i	$-0.549243\pi$
$881$	−32.2583	−	18.6244i	−1.08681	−	0.627470i	−0.932726	+	0.360587i	$0.882576\pi$
$882$	−18.0000	−	10.3923i	−0.606092	−	0.349927i
$883$	19.5885	+	19.5885i	0.659204	+	0.659204i	0.955192	−	0.295988i	$-0.0956487\pi$
$883$	19.5885	+	19.5885i	0.659204	+	0.659204i	−0.295988	+	0.955192i	$0.595649\pi$
$884$	−9.19615	−	16.6603i	−0.309300	−	0.560345i
$885$		0			0
$886$	0.660254	+	2.46410i	0.0221817	+	0.0827831i
$887$	26.1865	−	7.01666i	0.879258	−	0.235596i	0.209171	−	0.977879i	$-0.432924\pi$
$887$	26.1865	−	7.01666i	0.879258	−	0.235596i	0.670087	+	0.742283i	$0.266257\pi$
$888$	2.36603	−	8.83013i	0.0793986	−	0.296320i
$889$	−26.2224	−	26.2224i	−0.879472	−	0.879472i
$890$		0			0
$891$	−4.50000	+	16.7942i	−0.150756	+	0.562628i
$892$			3.92820i			0.131526i
$893$	−34.7487	−	9.31089i	−1.16282	−	0.311577i
$894$	−10.7321	+	18.5885i	−0.358933	+	0.621691i
$895$		0			0
$896$			3.73205i			0.124679i
$897$	−21.3397	−	22.1769i	−0.712513	−	0.740466i
$898$	3.49038	−	3.49038i	0.116476	−	0.116476i
$899$	−38.7846	+	10.3923i	−1.29354	+	0.346603i
$900$		0			0
$901$	−41.1506	+	23.7583i	−1.37093	+	0.791505i
$902$	0.732051			0.0243746
$903$	67.1769	−	38.7846i	2.23551	−	1.29067i
$904$	2.73205	+	0.732051i	0.0908667	+	0.0243476i
$905$		0			0
$906$	−2.66025	−	4.60770i	−0.0883810	−	0.153080i
$907$	12.8109	+	47.8109i	0.425379	+	1.58753i	0.763095	+	0.646287i	$0.223679\pi$
$907$	12.8109	+	47.8109i	0.425379	+	1.58753i	−0.337716	+	0.941248i	$0.609654\pi$
$908$	0.928203	−	1.60770i	0.0308035	−	0.0533532i
$909$	18.5885			0.616540
$910$		0			0
$911$	27.1769			0.900411			0.450206	−	0.892925i	$-0.351351\pi$
$911$	27.1769			0.900411			0.450206	+	0.892925i	$0.351351\pi$
$912$	6.29423	−	10.9019i	0.208423	−	0.360999i
$913$	1.36603	+	5.09808i	0.0452088	+	0.168722i
$914$	−3.56218	−	6.16987i	−0.117826	−	0.204081i
$915$		0			0
$916$	18.5622	+	4.97372i	0.613312	+	0.164336i
$917$	4.50000	−	2.59808i	0.148603	−	0.0857960i
$918$		0			0
$919$	−1.51666	+	0.875644i	−0.0500300	+	0.0288848i	−0.524806	−	0.851222i	$-0.675862\pi$
$919$	−1.51666	+	0.875644i	−0.0500300	+	0.0288848i	0.474776	+	0.880106i	$0.342529\pi$
$920$		0			0
$921$	−4.73205	+	1.26795i	−0.155926	+	0.0417803i
$922$	−6.66025	+	6.66025i	−0.219344	+	0.219344i
$923$	−39.0526	−	0.751289i	−1.28543	−	0.0247290i
$924$		−	17.6603i		−	0.580980i
$925$		0			0
$926$	−16.5885	+	28.7321i	−0.545131	+	0.944194i
$927$	−8.89230	−	2.38269i	−0.292062	−	0.0782577i
$928$			9.46410i			0.310674i
$929$	−2.75833	+	10.2942i	−0.0904979	+	0.337743i	−0.996298	−	0.0859616i	$-0.972604\pi$
$929$	−2.75833	+	10.2942i	−0.0904979	+	0.337743i	0.905801	+	0.423704i	$0.139270\pi$
$930$		0			0
$931$	25.1769	+	25.1769i	0.825140	+	0.825140i
$932$	−3.24167	+	12.0981i	−0.106184	+	0.396286i
$933$	−13.3923	+	3.58846i	−0.438444	+	0.117481i
$934$	−2.39230	−	8.92820i	−0.0782786	−	0.292140i
$935$		0			0
$936$	−7.79423	+	7.50000i	−0.254762	+	0.245145i
$937$	−11.6077	−	11.6077i	−0.379207	−	0.379207i	0.491609	−	0.870816i	$-0.336409\pi$
$937$	−11.6077	−	11.6077i	−0.379207	−	0.379207i	−0.870816	+	0.491609i	$0.836409\pi$
$938$	3.00000	+	1.73205i	0.0979535	+	0.0565535i
$939$	25.6077	+	14.7846i	0.835676	+	0.482478i
$940$		0			0
$941$	1.41154	−	1.41154i	0.0460150	−	0.0460150i	−0.683725	−	0.729740i	$-0.739641\pi$
$941$	1.41154	−	1.41154i	0.0460150	−	0.0460150i	0.729740	+	0.683725i	$0.239641\pi$
$942$	−19.6865	−	34.0981i	−0.641422	−	1.11098i
$943$	0.660254	+	1.14359i	0.0215008	+	0.0372405i
$944$	−0.464102	+	0.464102i	−0.0151052	+	0.0151052i
$945$		0			0
$946$	14.1962	+	8.19615i	0.461557	+	0.266480i
$947$	21.7583	+	12.5622i	0.707051	+	0.408216i	0.809968	−	0.586474i	$-0.199484\pi$
$947$	21.7583	+	12.5622i	0.707051	+	0.408216i	−0.102917	+	0.994690i	$0.532818\pi$
$948$	19.2679	+	19.2679i	0.625794	+	0.625794i
$949$	16.5622	−	4.09808i	0.537631	−	0.133029i
$950$		0			0
$951$	−0.882686	−	3.29423i	−0.0286231	−	0.106823i
$952$	19.0263	−	5.09808i	0.616645	−	0.165230i
$953$	8.09808	−	30.2224i	0.262322	−	0.979001i	−0.701547	−	0.712624i	$-0.747507\pi$
$953$	8.09808	−	30.2224i	0.262322	−	0.979001i	0.963869	−	0.266377i	$-0.0858266\pi$
$954$	19.0981	+	19.0981i	0.618323	+	0.618323i
$955$		0			0
$956$	2.09808	−	7.83013i	0.0678566	−	0.253244i
$957$		−	44.7846i		−	1.44768i
$958$	25.7583	+	6.90192i	0.832214	+	0.222991i
$959$	−38.4186	+	66.5429i	−1.24060	+	2.14878i
$960$		0			0
$961$			13.0000i			0.419355i
$962$	9.69615	−	9.33013i	0.312617	−	0.300815i
$963$	−27.5885	+	27.5885i	−0.889026	+	0.889026i
$964$	−6.23205	+	1.66987i	−0.200721	+	0.0537830i
$965$		0			0
$966$	27.5885	−	15.9282i	0.887644	−	0.512482i
$967$	−2.66025			−0.0855480			−0.0427740	−	0.999085i	$-0.513620\pi$
$967$	−2.66025			−0.0855480			−0.0427740	+	0.999085i	$0.513620\pi$
$968$	−6.29423	+	3.63397i	−0.202304	+	0.116800i
$969$	−64.1769	−	17.1962i	−2.06166	−	0.552420i
$970$		0			0
$971$	0.473721	+	0.820508i	0.0152024	+	0.0263314i	0.873527	−	0.486777i	$-0.161827\pi$
$971$	0.473721	+	0.820508i	0.0152024	+	0.0263314i	−0.858324	+	0.513108i	$0.828494\pi$
$972$	5.70577	+	21.2942i	0.183013	+	0.683013i
$973$	25.9904	−	45.0167i	0.833213	−	1.44317i
$974$	−12.3205			−0.394775
$975$		0			0
$976$	12.7321			0.407543
$977$	−1.46410	+	2.53590i	−0.0468408	+	0.0811306i	−0.888495	−	0.458886i	$-0.848249\pi$
$977$	−1.46410	+	2.53590i	−0.0468408	+	0.0811306i	0.841654	+	0.540016i	$0.181582\pi$
$978$	12.1244	+	45.2487i	0.387694	+	1.44689i
$979$	14.5263	+	25.1603i	0.464262	+	0.804125i
$980$		0			0
$981$	58.1769	+	15.5885i	1.85745	+	0.497701i
$982$	−0.741670	+	0.428203i	−0.0236676	+	0.0136645i
$983$	3.33975			0.106521			0.0532607	−	0.998581i	$-0.483039\pi$
$983$	3.33975			0.106521			0.0532607	+	0.998581i	$0.483039\pi$
$984$	0.803848	−	0.464102i	0.0256257	−	0.0147950i
$985$		0			0
$986$	48.2487	−	12.9282i	1.53655	−	0.411718i
$987$	−45.2487	+	45.2487i	−1.44028	+	1.44028i
$988$	16.2224	−	8.95448i	0.516104	−	0.284880i
$989$			29.5692i			0.940246i
$990$		0			0
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	−4.09808	−	1.09808i	−0.130114	−	0.0348640i
$993$			46.3923i			1.47222i
$994$	10.4641	−	39.0526i	0.331901	−	1.23867i
$995$		0			0
$996$	4.73205	+	4.73205i	0.149941	+	0.149941i
$997$	−1.17949	+	4.40192i	−0.0373549	+	0.139410i	−0.982085	−	0.188439i	$-0.939657\pi$
$997$	−1.17949	+	4.40192i	−0.0373549	+	0.139410i	0.944730	+	0.327849i	$0.106324\pi$
$998$	27.4904	−	7.36603i	0.870193	−	0.233167i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.w.a.357.1	yes	4
5.2	odd	4		650.2.t.b.643.1	yes	4
5.3	odd	4		650.2.t.a.643.1	yes	4
5.4	even	2		650.2.w.b.357.1	yes	4
13.11	odd	12		650.2.t.a.557.1	✓	4
65.24	odd	12		650.2.t.b.557.1	yes	4
65.37	even	12		650.2.w.b.193.1	yes	4
65.63	even	12	inner	650.2.w.a.193.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.a.557.1	✓	4	13.11	odd	12
650.2.t.a.643.1	yes	4	5.3	odd	4
650.2.t.b.557.1	yes	4	65.24	odd	12
650.2.t.b.643.1	yes	4	5.2	odd	4
650.2.w.a.193.1	yes	4	65.63	even	12	inner
650.2.w.a.357.1	yes	4	1.1	even	1	trivial
650.2.w.b.193.1	yes	4	65.37	even	12
650.2.w.b.357.1	yes	4	5.4	even	2

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.633975 + 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.36603 - 0.633975i) q^{6} +(3.23205 - 1.86603i) q^{7} +1.00000 q^{8} +(-2.59808 + 1.50000i) q^{9} +(1.86603 - 0.500000i) q^{11} +(1.73205 - 1.73205i) q^{12} +(3.50000 - 0.866025i) q^{13} +3.73205i q^{14} +(-0.500000 + 0.866025i) q^{16} +(5.09808 + 1.36603i) q^{17} -3.00000i q^{18} +(-1.33013 + 4.96410i) q^{19} +(6.46410 + 6.46410i) q^{21} +(-0.500000 + 1.86603i) q^{22} +(-3.36603 + 0.901924i) q^{23} +(0.633975 + 2.36603i) q^{24} +(-1.00000 + 3.46410i) q^{26} +(-3.23205 - 1.86603i) q^{28} +(-8.19615 - 4.73205i) q^{29} +(3.00000 - 3.00000i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.36603 + 4.09808i) q^{33} +(-3.73205 + 3.73205i) q^{34} +(2.59808 + 1.50000i) q^{36} +(-3.23205 - 1.86603i) q^{37} +(-3.63397 - 3.63397i) q^{38} +(4.26795 + 7.73205i) q^{39} +(-0.0980762 - 0.366025i) q^{41} +(-8.83013 + 2.36603i) q^{42} +(2.19615 - 8.19615i) q^{43} +(-1.36603 - 1.36603i) q^{44} +(0.901924 - 3.36603i) q^{46} +7.00000i q^{47} +(-2.36603 - 0.633975i) q^{48} +(3.46410 - 6.00000i) q^{49} +12.9282i q^{51} +(-2.50000 - 2.59808i) q^{52} +(-6.36603 + 6.36603i) q^{53} +(3.23205 - 1.86603i) q^{56} -12.5885 q^{57} +(8.19615 - 4.73205i) q^{58} +(0.633975 + 0.169873i) q^{59} +(-6.36603 - 11.0263i) q^{61} +(1.09808 + 4.09808i) q^{62} +(-5.59808 + 9.69615i) q^{63} +1.00000 q^{64} -4.73205 q^{66} +(0.464102 - 0.803848i) q^{67} +(-1.36603 - 5.09808i) q^{68} +(-4.26795 - 7.39230i) q^{69} +(-10.4641 - 2.80385i) q^{71} +(-2.59808 + 1.50000i) q^{72} +4.73205 q^{73} +(3.23205 - 1.86603i) q^{74} +(4.96410 - 1.33013i) q^{76} +(5.09808 - 5.09808i) q^{77} +(-8.83013 - 0.169873i) q^{78} +11.1244i q^{79} +(-4.50000 + 7.79423i) q^{81} +(0.366025 + 0.0980762i) q^{82} +2.73205i q^{83} +(2.36603 - 8.83013i) q^{84} +(6.00000 + 6.00000i) q^{86} +(6.00000 - 22.3923i) q^{87} +(1.86603 - 0.500000i) q^{88} +(3.89230 + 14.5263i) q^{89} +(9.69615 - 9.33013i) q^{91} +(2.46410 + 2.46410i) q^{92} +(9.00000 + 5.19615i) q^{93} +(-6.06218 - 3.50000i) q^{94} +(1.73205 - 1.73205i) q^{96} +(8.09808 + 14.0263i) q^{97} +(3.46410 + 6.00000i) q^{98} +(-4.09808 + 4.09808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 6 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{11} + 14 q^{13} - 2 q^{16} + 10 q^{17} + 12 q^{19} + 12 q^{21} - 2 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{26} - 6 q^{28} - 12 q^{29}+ \cdots - 6 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 6 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^11 + 14 * q^13 - 2 * q^16 + 10 * q^17 + 12 * q^19 + 12 * q^21 - 2 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^26 - 6 * q^28 - 12 * q^29 + 12 * q^31 - 2 * q^32 + 6 * q^33 - 8 * q^34 - 6 * q^37 - 18 * q^38 + 24 * q^39 + 10 * q^41 - 18 * q^42 - 12 * q^43 - 2 * q^44 + 14 * q^46 - 6 * q^48 - 10 * q^52 - 22 * q^53 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 6 * q^59 - 22 * q^61 - 6 * q^62 - 12 * q^63 + 4 * q^64 - 12 * q^66 - 12 * q^67 - 2 * q^68 - 24 * q^69 - 28 * q^71 + 12 * q^73 + 6 * q^74 + 6 * q^76 + 10 * q^77 - 18 * q^78 - 18 * q^81 - 2 * q^82 + 6 * q^84 + 24 * q^86 + 24 * q^87 + 4 * q^88 - 26 * q^89 + 18 * q^91 - 4 * q^92 + 36 * q^93 + 22 * q^97 - 6 * q^99

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