LMFDB - Embedded newform 546.2.bd.a.121.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,2,Mod(121,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.4
Root			$1.45057i$ of defining polynomial
Character	$\chi$	$=$	546.121
Dual form			546.2.bd.a.361.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(2.34064 + 1.35137i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.61422 - 0.407273i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -2.70274 q^{10} -5.09726i q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.313194 + 3.59192i) q^{13} +(-2.06034 + 1.65982i) q^{14} +(-2.34064 - 1.35137i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.86664 - 4.96516i) q^{17} +(-0.866025 + 0.500000i) q^{18} +4.38458i q^{19} +(2.34064 - 1.35137i) q^{20} +(-2.61422 + 0.407273i) q^{21} +(2.54863 + 4.41435i) q^{22} +(-3.73482 - 6.46890i) q^{23} -1.00000i q^{24} +(1.15240 + 1.99602i) q^{25} +(-2.06720 - 2.95410i) q^{26} -1.00000 q^{27} +(0.954400 - 2.46761i) q^{28} +(-4.18045 + 7.24074i) q^{29} +2.70274 q^{30} +(6.21147 - 3.58619i) q^{31} +(0.866025 + 0.500000i) q^{32} +5.09726i q^{33} +5.73328i q^{34} +(6.66932 + 2.57949i) q^{35} +(0.500000 - 0.866025i) q^{36} +(5.86654 - 3.38705i) q^{37} +(-2.19229 - 3.79715i) q^{38} +(-0.313194 - 3.59192i) q^{39} +(-1.35137 + 2.34064i) q^{40} +(3.29661 + 1.90330i) q^{41} +(2.06034 - 1.65982i) q^{42} +(3.10694 + 5.38138i) q^{43} +(-4.41435 - 2.54863i) q^{44} +(2.34064 + 1.35137i) q^{45} +(6.46890 + 3.73482i) q^{46} +(7.44186 + 4.29656i) q^{47} +(0.500000 + 0.866025i) q^{48} +(6.66826 - 2.12940i) q^{49} +(-1.99602 - 1.15240i) q^{50} +(-2.86664 + 4.96516i) q^{51} +(3.26729 + 1.52473i) q^{52} +(3.60339 + 6.24125i) q^{53} +(0.866025 - 0.500000i) q^{54} +(6.88828 - 11.9308i) q^{55} +(0.407273 + 2.61422i) q^{56} -4.38458i q^{57} -8.36089i q^{58} +(-5.61147 - 3.23979i) q^{59} +(-2.34064 + 1.35137i) q^{60} -4.65046 q^{61} +(-3.58619 + 6.21147i) q^{62} +(2.61422 - 0.407273i) q^{63} -1.00000 q^{64} +(-4.12094 + 8.83064i) q^{65} +(-2.54863 - 4.41435i) q^{66} +6.06546i q^{67} +(-2.86664 - 4.96516i) q^{68} +(3.73482 + 6.46890i) q^{69} +(-7.06555 + 1.10075i) q^{70} +(0.792408 - 0.457497i) q^{71} +1.00000i q^{72} +(-5.93963 + 3.42924i) q^{73} +(-3.38705 + 5.86654i) q^{74} +(-1.15240 - 1.99602i) q^{75} +(3.79715 + 2.19229i) q^{76} +(-2.07597 - 13.3253i) q^{77} +(2.06720 + 2.95410i) q^{78} +(-3.81342 + 6.60504i) q^{79} -2.70274i q^{80} +1.00000 q^{81} -3.80659 q^{82} -15.3966i q^{83} +(-0.954400 + 2.46761i) q^{84} +(13.4195 - 7.74778i) q^{85} +(-5.38138 - 3.10694i) q^{86} +(4.18045 - 7.24074i) q^{87} +5.09726 q^{88} +(-8.99129 + 5.19112i) q^{89} -2.70274 q^{90} +(2.28165 + 9.26251i) q^{91} -7.46964 q^{92} +(-6.21147 + 3.58619i) q^{93} -8.59312 q^{94} +(-5.92518 + 10.2627i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(-8.20116 + 4.73494i) q^{97} +(-4.71018 + 5.17824i) q^{98} -5.09726i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31}+ \cdots - 12 q^{98}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.34064	+	1.35137i	1.04677	+	0.604351i	0.921742	−	0.387803i	$-0.126766\pi$
$5$	2.34064	+	1.35137i	1.04677	+	0.604351i	0.125024	+	0.992154i	$0.460099\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	2.61422	−	0.407273i	0.988081	−	0.153935i
$7$	2.61422	−	0.407273i	0.988081	−	0.153935i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−2.70274			−0.854681
$11$		−	5.09726i		−	1.53688i	−0.639922	−	0.768440i	$-0.721033\pi$
$11$		−	5.09726i		−	1.53688i	0.639922	−	0.768440i	$-0.278967\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.313194	+	3.59192i	0.0868644	+	0.996220i
$13$	0.313194	+	3.59192i	0.0868644	+	0.996220i
$14$	−2.06034	+	1.65982i	−0.550649	+	0.443605i
$15$	−2.34064	−	1.35137i	−0.604351	−	0.348922i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.86664	−	4.96516i	0.695262	−	1.20423i	−0.274830	−	0.961493i	$-0.588622\pi$
$17$	2.86664	−	4.96516i	0.695262	−	1.20423i	0.970092	−	0.242736i	$-0.0780450\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$			4.38458i			1.00589i	0.864318	+	0.502945i	$0.167750\pi$
$19$			4.38458i			1.00589i	−0.864318	+	0.502945i	$0.832250\pi$
$20$	2.34064	−	1.35137i	0.523383	−	0.302175i
$21$	−2.61422	+	0.407273i	−0.570469	+	0.0888742i
$22$	2.54863	+	4.41435i	0.543369	+	0.941143i
$23$	−3.73482	−	6.46890i	−0.778764	−	1.34886i	−0.932654	−	0.360771i	$-0.882513\pi$
$23$	−3.73482	−	6.46890i	−0.778764	−	1.34886i	0.153890	−	0.988088i	$-0.450820\pi$
$24$		−	1.00000i		−	0.204124i
$25$	1.15240	+	1.99602i	0.230480	+	0.399203i
$26$	−2.06720	−	2.95410i	−0.405410	−	0.579347i
$27$	−1.00000			−0.192450
$28$	0.954400	−	2.46761i	0.180365	−	0.466335i
$29$	−4.18045	+	7.24074i	−0.776289	+	1.34457i	0.157778	+	0.987475i	$0.449567\pi$
$29$	−4.18045	+	7.24074i	−0.776289	+	1.34457i	−0.934067	+	0.357098i	$0.883766\pi$
$30$	2.70274			0.493450
$31$	6.21147	−	3.58619i	1.11561	−	0.644099i	0.175335	−	0.984509i	$-0.443899\pi$
$31$	6.21147	−	3.58619i	1.11561	−	0.644099i	0.940277	+	0.340410i	$0.110566\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$			5.09726i			0.887318i
$34$			5.73328i			0.983249i
$35$	6.66932	+	2.57949i	1.12732	+	0.436014i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	5.86654	−	3.38705i	0.964454	−	0.556828i	0.0669130	−	0.997759i	$-0.478685\pi$
$37$	5.86654	−	3.38705i	0.964454	−	0.556828i	0.897541	+	0.440931i	$0.145352\pi$
$38$	−2.19229	−	3.79715i	−0.355636	−	0.615980i
$39$	−0.313194	−	3.59192i	−0.0501512	−	0.575168i
$40$	−1.35137	+	2.34064i	−0.213670	+	0.370088i
$41$	3.29661	+	1.90330i	0.514843	+	0.297245i	0.734822	−	0.678260i	$-0.237266\pi$
$41$	3.29661	+	1.90330i	0.514843	+	0.297245i	−0.219979	+	0.975505i	$0.570599\pi$
$42$	2.06034	−	1.65982i	0.317918	−	0.256115i
$43$	3.10694	+	5.38138i	0.473804	+	0.820653i	0.999550	−	0.0299887i	$-0.00954714\pi$
$43$	3.10694	+	5.38138i	0.473804	+	0.820653i	−0.525746	+	0.850642i	$0.676214\pi$
$44$	−4.41435	−	2.54863i	−0.665489	−	0.384220i
$45$	2.34064	+	1.35137i	0.348922	+	0.201450i
$46$	6.46890	+	3.73482i	0.953788	+	0.550670i
$47$	7.44186	+	4.29656i	1.08551	+	0.626718i	0.932377	−	0.361488i	$-0.117731\pi$
$47$	7.44186	+	4.29656i	1.08551	+	0.626718i	0.153130	+	0.988206i	$0.451065\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	6.66826	−	2.12940i	0.952608	−	0.304200i
$50$	−1.99602	−	1.15240i	−0.282279	−	0.162974i
$51$	−2.86664	+	4.96516i	−0.401410	+	0.695262i
$52$	3.26729	+	1.52473i	0.453092	+	0.211442i
$53$	3.60339	+	6.24125i	0.494963	+	0.857301i	0.999983	−	0.00580635i	$-0.00184823\pi$
$53$	3.60339	+	6.24125i	0.494963	+	0.857301i	−0.505020	+	0.863108i	$0.668515\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	6.88828	−	11.9308i	0.928815	−	1.60875i
$56$	0.407273	+	2.61422i	0.0544241	+	0.349339i
$57$		−	4.38458i		−	0.580751i
$58$		−	8.36089i		−	1.09784i
$59$	−5.61147	−	3.23979i	−0.730552	−	0.421784i	0.0880722	−	0.996114i	$-0.471929\pi$
$59$	−5.61147	−	3.23979i	−0.730552	−	0.421784i	−0.818624	+	0.574330i	$0.805263\pi$
$60$	−2.34064	+	1.35137i	−0.302175	+	0.174461i
$61$	−4.65046			−0.595430			−0.297715	−	0.954655i	$-0.596224\pi$
$61$	−4.65046			−0.595430			−0.297715	+	0.954655i	$0.596224\pi$
$62$	−3.58619	+	6.21147i	−0.455447	+	0.788857i
$63$	2.61422	−	0.407273i	0.329360	−	0.0513116i
$64$	−1.00000			−0.125000
$65$	−4.12094	+	8.83064i	−0.511140	+	1.09531i
$66$	−2.54863	−	4.41435i	−0.313714	−	0.543369i
$67$			6.06546i			0.741013i	0.928830	+	0.370507i	$0.120816\pi$
$67$			6.06546i			0.741013i	−0.928830	+	0.370507i	$0.879184\pi$
$68$	−2.86664	−	4.96516i	−0.347631	−	0.602115i
$69$	3.73482	+	6.46890i	0.449620	+	0.778764i
$70$	−7.06555	+	1.10075i	−0.844494	+	0.131565i
$71$	0.792408	−	0.457497i	0.0940415	−	0.0542949i	−0.452242	−	0.891895i	$-0.649376\pi$
$71$	0.792408	−	0.457497i	0.0940415	−	0.0542949i	0.546283	+	0.837601i	$0.316042\pi$
$72$			1.00000i			0.117851i
$73$	−5.93963	+	3.42924i	−0.695181	+	0.401363i	−0.805550	−	0.592528i	$-0.798130\pi$
$73$	−5.93963	+	3.42924i	−0.695181	+	0.401363i	0.110369	+	0.993891i	$0.464797\pi$
$74$	−3.38705	+	5.86654i	−0.393737	+	0.681972i
$75$	−1.15240	−	1.99602i	−0.133068	−	0.230480i
$76$	3.79715	+	2.19229i	0.435563	+	0.251473i
$77$	−2.07597	−	13.3253i	−0.236579	−	1.51856i
$78$	2.06720	+	2.95410i	0.234064	+	0.334486i
$79$	−3.81342	+	6.60504i	−0.429044	+	0.743126i	−0.996789	−	0.0800791i	$-0.974483\pi$
$79$	−3.81342	+	6.60504i	−0.429044	+	0.743126i	0.567745	+	0.823205i	$0.307816\pi$
$80$		−	2.70274i		−	0.302175i
$81$	1.00000			0.111111
$82$	−3.80659			−0.420368
$83$		−	15.3966i		−	1.69000i	−0.534769	−	0.844999i	$-0.679601\pi$
$83$		−	15.3966i		−	1.69000i	0.534769	−	0.844999i	$-0.320399\pi$
$84$	−0.954400	+	2.46761i	−0.104134	+	0.269239i
$85$	13.4195	−	7.74778i	1.45555	−	0.840365i
$86$	−5.38138	−	3.10694i	−0.580289	−	0.335030i
$87$	4.18045	−	7.24074i	0.448191	−	0.776289i
$88$	5.09726			0.543369
$89$	−8.99129	+	5.19112i	−0.953075	+	0.550258i	−0.894035	−	0.447998i	$-0.852137\pi$
$89$	−8.99129	+	5.19112i	−0.953075	+	0.550258i	−0.0590402	+	0.998256i	$0.518804\pi$
$90$	−2.70274			−0.284894
$91$	2.28165	+	9.26251i	0.239182	+	0.970975i
$92$	−7.46964			−0.778764
$93$	−6.21147	+	3.58619i	−0.644099	+	0.371871i
$94$	−8.59312			−0.886313
$95$	−5.92518	+	10.2627i	−0.607911	+	1.05293i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	−8.20116	+	4.73494i	−0.832702	+	0.480761i	−0.854777	−	0.518996i	$-0.826306\pi$
$97$	−8.20116	+	4.73494i	−0.832702	+	0.480761i	0.0220749	+	0.999756i	$0.492973\pi$
$98$	−4.71018	+	5.17824i	−0.475800	+	0.523082i
$99$		−	5.09726i		−	0.512293i
$100$	2.30480			0.230480
$101$	−3.72210			−0.370363			−0.185182	−	0.982704i	$-0.559287\pi$
$101$	−3.72210			−0.370363			−0.185182	+	0.982704i	$0.559287\pi$
$102$		−	5.73328i		−	0.567679i
$103$	4.55465	−	7.88888i	0.448783	−	0.777314i	−0.549525	−	0.835478i	$-0.685191\pi$
$103$	4.55465	−	7.88888i	0.448783	−	0.777314i	0.998307	+	0.0581634i	$0.0185244\pi$
$104$	−3.59192	+	0.313194i	−0.352217	+	0.0307112i
$105$	−6.66932	−	2.57949i	−0.650859	−	0.251733i
$106$	−6.24125	−	3.60339i	−0.606204	−	0.349992i
$107$	−5.28386	−	9.15192i	−0.510810	−	0.884750i	−0.999922	−	0.0125282i	$-0.996012\pi$
$107$	−5.28386	−	9.15192i	−0.510810	−	0.884750i	0.489111	−	0.872222i	$-0.337321\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	3.27729	−	1.89214i	0.313907	−	0.181235i	−0.334766	−	0.942301i	$-0.608657\pi$
$109$	3.27729	−	1.89214i	0.313907	−	0.181235i	0.648674	+	0.761067i	$0.275324\pi$
$110$			13.7766i			1.31354i
$111$	−5.86654	+	3.38705i	−0.556828	+	0.321485i
$112$	−1.65982	−	2.06034i	−0.156838	−	0.194684i
$113$	0.849593	+	1.47154i	0.0799230	+	0.138431i	0.903217	−	0.429185i	$-0.141199\pi$
$113$	0.849593	+	1.47154i	0.0799230	+	0.138431i	−0.823294	+	0.567616i	$0.807866\pi$
$114$	2.19229	+	3.79715i	0.205327	+	0.355636i
$115$		−	20.1885i		−	1.88259i
$116$	4.18045	+	7.24074i	0.388145	+	0.672286i
$117$	0.313194	+	3.59192i	0.0289548	+	0.332073i
$118$	6.47957			0.596493
$119$	5.47184	−	14.1475i	0.501603	−	1.29690i
$120$	1.35137	−	2.34064i	0.123363	−	0.213670i
$121$	−14.9820			−1.36200
$122$	4.02741	−	2.32523i	0.364625	−	0.210516i
$123$	−3.29661	−	1.90330i	−0.297245	−	0.171614i
$124$		−	7.17238i		−	0.644099i
$125$		−	7.28442i		−	0.651538i
$126$	−2.06034	+	1.65982i	−0.183550	+	0.147868i
$127$	3.11451	−	5.39450i	0.276368	−	0.478684i	−0.694111	−	0.719868i	$-0.744202\pi$
$127$	3.11451	−	5.39450i	0.276368	−	0.478684i	0.970479	+	0.241184i	$0.0775357\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.10694	−	5.38138i	−0.273551	−	0.473804i
$130$	−0.846482	−	9.70803i	−0.0742414	−	0.851451i
$131$	−0.358468	+	0.620884i	−0.0313195	+	0.0542469i	−0.881260	−	0.472631i	$-0.843304\pi$
$131$	−0.358468	+	0.620884i	−0.0313195	+	0.0542469i	0.849941	+	0.526878i	$0.176638\pi$
$132$	4.41435	+	2.54863i	0.384220	+	0.221830i
$133$	1.78572	+	11.4622i	0.154841	+	0.993902i
$134$	−3.03273	−	5.25284i	−0.261988	−	0.453776i
$135$	−2.34064	−	1.35137i	−0.201450	−	0.116307i
$136$	4.96516	+	2.86664i	0.425759	+	0.245812i
$137$	−8.70853	−	5.02787i	−0.744020	−	0.429560i	0.0795091	−	0.996834i	$-0.474665\pi$
$137$	−8.70853	−	5.02787i	−0.744020	−	0.429560i	−0.823529	+	0.567274i	$0.807998\pi$
$138$	−6.46890	−	3.73482i	−0.550670	−	0.317929i
$139$	8.84682	+	15.3231i	0.750377	+	1.29969i	0.947640	+	0.319341i	$0.103462\pi$
$139$	8.84682	+	15.3231i	0.750377	+	1.29969i	−0.197263	+	0.980351i	$0.563205\pi$
$140$	5.56857	−	4.48605i	0.470630	−	0.379141i
$141$	−7.44186	−	4.29656i	−0.626718	−	0.361836i
$142$	−0.457497	+	0.792408i	−0.0383923	+	0.0664974i
$143$	18.3089	−	1.59643i	1.53107	−	0.133500i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−19.5698	+	11.2987i	−1.62519	+	0.938302i
$146$	3.42924	−	5.93963i	0.283806	−	0.491567i
$147$	−6.66826	+	2.12940i	−0.549989	+	0.175630i
$148$		−	6.77410i		−	0.556828i
$149$			23.2914i			1.90811i	0.299632	+	0.954055i	$0.403136\pi$
$149$			23.2914i			1.90811i	−0.299632	+	0.954055i	$0.596864\pi$
$150$	1.99602	+	1.15240i	0.162974	+	0.0940931i
$151$	−15.8610	+	9.15737i	−1.29075	+	0.745216i	−0.978788	−	0.204878i	$-0.934320\pi$
$151$	−15.8610	+	9.15737i	−1.29075	+	0.745216i	−0.311964	+	0.950094i	$0.600987\pi$
$152$	−4.38458			−0.355636
$153$	2.86664	−	4.96516i	0.231754	−	0.401410i
$154$	8.46051	+	10.5021i	0.681767	+	0.846282i
$155$	19.3851			1.55705
$156$	−3.26729	−	1.52473i	−0.261593	−	0.122076i
$157$	−1.91775	−	3.32164i	−0.153053	−	0.265096i	0.779295	−	0.626657i	$-0.215577\pi$
$157$	−1.91775	−	3.32164i	−0.153053	−	0.265096i	−0.932348	+	0.361561i	$0.882244\pi$
$158$		−	7.62685i		−	0.606759i
$159$	−3.60339	−	6.24125i	−0.285767	−	0.494963i
$160$	1.35137	+	2.34064i	0.106835	+	0.185044i
$161$	−12.3982	−	15.3900i	−0.977118	−	1.21290i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$		−	10.4272i		−	0.816720i	−0.912821	−	0.408360i	$-0.866101\pi$
$163$		−	10.4272i		−	0.816720i	0.912821	−	0.408360i	$-0.133899\pi$
$164$	3.29661	−	1.90330i	0.257422	−	0.148622i
$165$	−6.88828	+	11.9308i	−0.536252	+	0.928815i
$166$	7.69830	+	13.3339i	0.597504	+	1.03491i
$167$	−1.90573	−	1.10027i	−0.147470	−	0.0851418i	0.424449	−	0.905452i	$-0.360468\pi$
$167$	−1.90573	−	1.10027i	−0.147470	−	0.0851418i	−0.571919	+	0.820310i	$0.693801\pi$
$168$	−0.407273	−	2.61422i	−0.0314218	−	0.201691i
$169$	−12.8038	+	2.24994i	−0.984909	+	0.173072i
$170$	−7.74778	+	13.4195i	−0.594227	+	1.02923i
$171$			4.38458i			0.335297i
$172$	6.21388			0.473804
$173$	21.4765			1.63283			0.816415	−	0.577466i	$-0.195958\pi$
$173$	21.4765			1.63283			0.816415	+	0.577466i	$0.195958\pi$
$174$			8.36089i			0.633838i
$175$	3.82555	+	4.74868i	0.289184	+	0.358966i
$176$	−4.41435	+	2.54863i	−0.332744	+	0.192110i
$177$	5.61147	+	3.23979i	0.421784	+	0.243517i
$178$	5.19112	−	8.99129i	0.389091	−	0.673926i
$179$	−18.6782			−1.39607			−0.698037	−	0.716062i	$-0.745943\pi$
$179$	−18.6782			−1.39607			−0.698037	+	0.716062i	$0.745943\pi$
$180$	2.34064	−	1.35137i	0.174461	−	0.100725i
$181$	1.97032			0.146452			0.0732262	−	0.997315i	$-0.476670\pi$
$181$	1.97032			0.146452			0.0732262	+	0.997315i	$0.476670\pi$
$182$	−6.60722	−	6.88074i	−0.489760	−	0.510035i
$183$	4.65046			0.343772
$184$	6.46890	−	3.73482i	0.476894	−	0.275335i
$185$	18.3086			1.34608
$186$	3.58619	−	6.21147i	0.262952	−	0.455447i
$187$	−25.3087	−	14.6120i	−1.85076	−	1.06853i
$188$	7.44186	−	4.29656i	0.542753	−	0.313359i
$189$	−2.61422	+	0.407273i	−0.190156	+	0.0296247i
$190$		−	11.8504i		−	0.859716i
$191$	3.70946			0.268407			0.134204	−	0.990954i	$-0.457152\pi$
$191$	3.70946			0.268407			0.134204	+	0.990954i	$0.457152\pi$
$192$	1.00000			0.0721688
$193$			2.98000i			0.214505i	0.994232	+	0.107253i	$0.0342053\pi$
$193$			2.98000i			0.214505i	−0.994232	+	0.107253i	$0.965795\pi$
$194$	4.73494	−	8.20116i	0.339949	−	0.588809i
$195$	4.12094	−	8.83064i	0.295107	−	0.632375i
$196$	1.49001	−	6.83958i	0.106430	−	0.488541i
$197$	−12.8922	−	7.44330i	−0.918529	−	0.530313i	−0.0353634	−	0.999375i	$-0.511259\pi$
$197$	−12.8922	−	7.44330i	−0.918529	−	0.530313i	−0.883165	+	0.469062i	$0.844592\pi$
$198$	2.54863	+	4.41435i	0.181123	+	0.313714i
$199$	1.33214	−	2.30733i	0.0944327	−	0.163562i	−0.814939	−	0.579547i	$-0.803230\pi$
$199$	1.33214	−	2.30733i	0.0944327	−	0.163562i	0.909372	+	0.415985i	$0.136563\pi$
$200$	−1.99602	+	1.15240i	−0.141140	+	0.0814870i
$201$		−	6.06546i		−	0.427824i
$202$	3.22344	−	1.86105i	0.226800	−	0.130943i
$203$	−7.97963	+	20.6315i	−0.560060	+	1.44804i
$204$	2.86664	+	4.96516i	0.200705	+	0.347631i
$205$	5.14411	+	8.90987i	0.359280	+	0.622292i
$206$			9.10929i			0.634674i
$207$	−3.73482	−	6.46890i	−0.259588	−	0.449620i
$208$	2.95410	−	2.06720i	0.204830	−	0.143334i
$209$	22.3493			1.54593
$210$	7.06555	−	1.10075i	0.487569	−	0.0759591i
$211$	−3.24329	+	5.61754i	−0.223277	+	0.386728i	−0.955801	−	0.294014i	$-0.905009\pi$
$211$	−3.24329	+	5.61754i	−0.223277	+	0.386728i	0.732524	+	0.680741i	$0.238342\pi$
$212$	7.20677			0.494963
$213$	−0.792408	+	0.457497i	−0.0542949	+	0.0313472i
$214$	9.15192	+	5.28386i	0.625612	+	0.361198i
$215$			16.7945i			1.14538i
$216$		−	1.00000i		−	0.0680414i
$217$	14.7776	−	11.9048i	1.00317	−	0.808154i
$218$	−1.89214	+	3.27729i	−0.128152	+	0.221966i
$219$	5.93963	−	3.42924i	0.401363	−	0.231727i
$220$	−6.88828	−	11.9308i	−0.464408	−	0.804377i
$221$	18.7323	+	8.74168i	1.26007	+	0.588029i
$222$	3.38705	−	5.86654i	0.227324	−	0.393737i
$223$	−22.5859	−	13.0400i	−1.51247	−	0.873223i	−0.999894	−	0.0145787i	$-0.995359\pi$
$223$	−22.5859	−	13.0400i	−1.51247	−	0.873223i	−0.512572	−	0.858644i	$-0.671307\pi$
$224$	2.46761	+	0.954400i	0.164874	+	0.0637685i
$225$	1.15240	+	1.99602i	0.0768267	+	0.133068i
$226$	−1.47154	−	0.849593i	−0.0978852	−	0.0565141i
$227$	−10.1088	−	5.83634i	−0.670947	−	0.387372i	0.125488	−	0.992095i	$-0.459950\pi$
$227$	−10.1088	−	5.83634i	−0.670947	−	0.387372i	−0.796436	+	0.604723i	$0.793284\pi$
$228$	−3.79715	−	2.19229i	−0.251473	−	0.145188i
$229$	10.4614	+	6.03988i	0.691307	+	0.399126i	0.804102	−	0.594492i	$-0.202647\pi$
$229$	10.4614	+	6.03988i	0.691307	+	0.399126i	−0.112794	+	0.993618i	$0.535980\pi$
$230$	10.0943	+	17.4838i	0.665595	+	1.15284i
$231$	2.07597	+	13.3253i	0.136589	+	0.876742i
$232$	−7.24074	−	4.18045i	−0.475378	−	0.274460i
$233$	−4.65865	+	8.06902i	−0.305199	+	0.528619i	−0.977306	−	0.211835i	$-0.932056\pi$
$233$	−4.65865	+	8.06902i	−0.305199	+	0.528619i	0.672107	+	0.740454i	$0.265389\pi$
$234$	−2.06720	−	2.95410i	−0.135137	−	0.193116i
$235$	11.6125	+	20.1134i	0.757515	+	1.31205i
$236$	−5.61147	+	3.23979i	−0.365276	+	0.210892i
$237$	3.81342	−	6.60504i	0.247709	−	0.429044i
$238$	2.33501	+	14.9880i	0.151356	+	0.971530i
$239$			16.8139i			1.08760i	0.839215	+	0.543799i	$0.183015\pi$
$239$			16.8139i			1.08760i	−0.839215	+	0.543799i	$0.816985\pi$
$240$			2.70274i			0.174461i
$241$	−19.3566	−	11.1756i	−1.24687	−	0.719881i	−0.276386	−	0.961047i	$-0.589137\pi$
$241$	−19.3566	−	11.1756i	−1.24687	−	0.719881i	−0.970484	+	0.241166i	$0.922470\pi$
$242$	12.9748	−	7.49101i	0.834052	−	0.481540i
$243$	−1.00000			−0.0641500
$244$	−2.32523	+	4.02741i	−0.148857	+	0.257829i
$245$	18.4856	+	4.02712i	1.18100	+	0.257283i
$246$	3.80659			0.242699
$247$	−15.7491	+	1.37322i	−1.00209	+	0.0873761i
$248$	3.58619	+	6.21147i	0.227723	+	0.394429i
$249$			15.3966i			0.975720i
$250$	3.64221	+	6.30849i	0.230354	+	0.398984i
$251$	3.75155	+	6.49788i	0.236796	+	0.410143i	0.959793	−	0.280708i	$-0.0905694\pi$
$251$	3.75155	+	6.49788i	0.236796	+	0.410143i	−0.722997	+	0.690851i	$0.757236\pi$
$252$	0.954400	−	2.46761i	0.0601215	−	0.155445i
$253$	−32.9736	+	19.0373i	−2.07304	+	1.19687i
$254$			6.22903i			0.390844i
$255$	−13.4195	+	7.74778i	−0.840365	+	0.485185i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.51876	+	6.09468i	0.219494	+	0.380175i	0.954654	−	0.297719i	$-0.0962259\pi$
$257$	3.51876	+	6.09468i	0.219494	+	0.380175i	−0.735159	+	0.677895i	$0.762893\pi$
$258$	5.38138	+	3.10694i	0.335030	+	0.193430i
$259$	13.9570	−	11.2438i	0.867244	−	0.698654i
$260$	5.58709	+	7.98416i	0.346497	+	0.495157i
$261$	−4.18045	+	7.24074i	−0.258763	+	0.448191i
$262$		−	0.716935i		−	0.0442924i
$263$	−23.9286			−1.47550			−0.737750	−	0.675074i	$-0.764112\pi$
$263$	−23.9286			−1.47550			−0.737750	+	0.675074i	$0.764112\pi$
$264$	−5.09726			−0.313714
$265$			19.4780i			1.19653i
$266$	−7.27759	−	9.03372i	−0.446218	−	0.553893i
$267$	8.99129	−	5.19112i	0.550258	−	0.317692i
$268$	5.25284	+	3.03273i	0.320868	+	0.185253i
$269$	0.799815	−	1.38532i	0.0487656	−	0.0844645i	−0.840612	−	0.541637i	$-0.817805\pi$
$269$	0.799815	−	1.38532i	0.0487656	−	0.0844645i	0.889378	+	0.457173i	$0.151138\pi$
$270$	2.70274			0.164483
$271$	17.3215	−	10.0006i	1.05221	−	0.607492i	0.128941	−	0.991652i	$-0.458842\pi$
$271$	17.3215	−	10.0006i	1.05221	−	0.607492i	0.923267	+	0.384160i	$0.125509\pi$
$272$	−5.73328			−0.347631
$273$	−2.28165	−	9.26251i	−0.138092	−	0.560593i
$274$	10.0557			0.607490
$275$	10.1742	−	5.87408i	0.613528	−	0.354220i
$276$	7.46964			0.449620
$277$	9.05583	−	15.6852i	0.544112	−	0.942430i	−0.454550	−	0.890721i	$-0.650200\pi$
$277$	9.05583	−	15.6852i	0.544112	−	0.942430i	0.998662	−	0.0517090i	$-0.0164668\pi$
$278$	−15.3231	−	8.84682i	−0.919021	−	0.530597i
$279$	6.21147	−	3.58619i	0.371871	−	0.214700i
$280$	−2.57949	+	6.66932i	−0.154154	+	0.398568i
$281$		−	11.0176i		−	0.657253i	−0.944460	−	0.328626i	$-0.893414\pi$
$281$		−	11.0176i		−	0.657253i	0.944460	−	0.328626i	$-0.106586\pi$
$282$	8.59312			0.511713
$283$	−13.4936			−0.802114			−0.401057	−	0.916053i	$-0.631357\pi$
$283$	−13.4936			−0.802114			−0.401057	+	0.916053i	$0.631357\pi$
$284$		−	0.914994i		−	0.0542949i
$285$	5.92518	−	10.2627i	0.350978	−	0.607911i
$286$	−15.0578	+	10.5370i	−0.890386	+	0.623067i
$287$	9.39320	+	3.63301i	0.554463	+	0.214450i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−7.93524	−	13.7442i	−0.466779	−	0.808484i
$290$	11.2987	−	19.5698i	0.663480	−	1.14918i
$291$	8.20116	−	4.73494i	0.480761	−	0.277567i
$292$			6.85849i			0.401363i
$293$	4.13569	−	2.38774i	0.241610	−	0.139494i	−0.374307	−	0.927305i	$-0.622119\pi$
$293$	4.13569	−	2.38774i	0.241610	−	0.139494i	0.615916	+	0.787811i	$0.288786\pi$
$294$	4.71018	−	5.17824i	0.274703	−	0.302001i
$295$	−8.75630	−	15.1664i	−0.509811	−	0.883019i
$296$	3.38705	+	5.86654i	0.196868	+	0.340986i
$297$			5.09726i			0.295773i
$298$	−11.6457	−	20.1710i	−0.674619	−	1.16847i
$299$	22.0661	−	15.4412i	1.27611	−	0.892989i
$300$	−2.30480			−0.133068
$301$	10.3139	+	12.8027i	0.594484	+	0.737937i
$302$	9.15737	−	15.8610i	0.526947	−	0.912699i
$303$	3.72210			0.213829
$304$	3.79715	−	2.19229i	0.217782	−	0.125736i
$305$	−10.8850	−	6.28449i	−0.623276	−	0.359849i
$306$			5.73328i			0.327750i
$307$			6.26422i			0.357518i	0.983893	+	0.178759i	$0.0572082\pi$
$307$			6.26422i			0.357518i	−0.983893	+	0.178759i	$0.942792\pi$
$308$	−12.5781	−	4.86482i	−0.716702	−	0.277199i
$309$	−4.55465	+	7.88888i	−0.259105	+	0.448783i
$310$	−16.7880	+	9.69254i	−0.953493	+	0.550499i
$311$	2.99213	+	5.18252i	0.169668	+	0.293874i	0.938303	−	0.345814i	$-0.112397\pi$
$311$	2.99213	+	5.18252i	0.169668	+	0.293874i	−0.768635	+	0.639688i	$0.779064\pi$
$312$	3.59192	−	0.313194i	0.203353	−	0.0177311i
$313$	14.3286	−	24.8179i	0.809902	−	1.40279i	−0.103030	−	0.994678i	$-0.532854\pi$
$313$	14.3286	−	24.8179i	0.809902	−	1.40279i	0.912931	−	0.408113i	$-0.133813\pi$
$314$	3.32164	+	1.91775i	0.187451	+	0.108225i
$315$	6.66932	+	2.57949i	0.375774	+	0.145338i
$316$	3.81342	+	6.60504i	0.214522	+	0.371563i
$317$	−22.2694	−	12.8572i	−1.25077	−	0.722134i	−0.279509	−	0.960143i	$-0.590172\pi$
$317$	−22.2694	−	12.8572i	−1.25077	−	0.722134i	−0.971263	+	0.238009i	$0.923505\pi$
$318$	6.24125	+	3.60339i	0.349992	+	0.202068i
$319$	36.9079	+	21.3088i	2.06645	+	1.19306i
$320$	−2.34064	−	1.35137i	−0.130846	−	0.0755439i
$321$	5.28386	+	9.15192i	0.294917	+	0.510810i
$322$	18.4322	+	7.12903i	1.02719	+	0.397285i
$323$	21.7701	+	12.5690i	1.21132	+	0.699358i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−6.80861	+	4.76447i	−0.377674	+	0.264285i
$326$	5.21359	+	9.03020i	0.288754	+	0.500137i
$327$	−3.27729	+	1.89214i	−0.181235	+	0.104636i
$328$	−1.90330	+	3.29661i	−0.105092	+	0.182025i
$329$	21.2045	+	8.20127i	1.16904	+	0.452151i
$330$		−	13.7766i		−	0.758374i
$331$			0.880100i			0.0483747i	0.999707	+	0.0241873i	$0.00769982\pi$
$331$			0.880100i			0.0483747i	−0.999707	+	0.0241873i	$0.992300\pi$
$332$	−13.3339	−	7.69830i	−0.731790	−	0.422499i
$333$	5.86654	−	3.38705i	0.321485	−	0.185609i
$334$	2.20055			0.120409
$335$	−8.19667	+	14.1971i	−0.447832	+	0.775668i
$336$	1.65982	+	2.06034i	0.0905504	+	0.112401i
$337$	16.4964			0.898617			0.449308	−	0.893377i	$-0.351670\pi$
$337$	16.4964			0.898617			0.449308	+	0.893377i	$0.351670\pi$
$338$	9.96346	−	8.35041i	0.541941	−	0.454203i
$339$	−0.849593	−	1.47154i	−0.0461435	−	0.0799230i
$340$		−	15.4956i		−	0.840365i
$341$	−18.2797	−	31.6614i	−0.989903	−	1.71456i
$342$	−2.19229	−	3.79715i	−0.118545	−	0.205327i
$343$	16.5650	−	8.28251i	0.894427	−	0.447214i
$344$	−5.38138	+	3.10694i	−0.290145	+	0.167515i
$345$			20.1885i			1.08691i
$346$	−18.5992	+	10.7383i	−0.999900	+	0.577292i
$347$	2.79575	−	4.84237i	0.150084	−	0.259952i	−0.781174	−	0.624313i	$-0.785379\pi$
$347$	2.79575	−	4.84237i	0.150084	−	0.259952i	0.931258	+	0.364361i	$0.118712\pi$
$348$	−4.18045	−	7.24074i	−0.224095	−	0.388145i
$349$	−11.1268	−	6.42408i	−0.595606	−	0.343873i	0.171705	−	0.985148i	$-0.445072\pi$
$349$	−11.1268	−	6.42408i	−0.595606	−	0.343873i	−0.767311	+	0.641275i	$0.778406\pi$
$350$	−5.68736	−	2.19970i	−0.304002	−	0.117579i
$351$	−0.313194	−	3.59192i	−0.0167171	−	0.191723i
$352$	2.54863	−	4.41435i	0.135842	−	0.235286i
$353$			18.4469i			0.981829i	0.871208	+	0.490915i	$0.163337\pi$
$353$			18.4469i			0.981829i	−0.871208	+	0.490915i	$0.836663\pi$
$354$	−6.47957			−0.344385
$355$	2.47299			0.131253
$356$			10.3822i			0.550258i
$357$	−5.47184	+	14.1475i	−0.289600	+	0.748766i
$358$	16.1758	−	9.33910i	0.854917	−	0.493587i
$359$	−9.96875	−	5.75546i	−0.526130	−	0.303761i	0.213309	−	0.976985i	$-0.431576\pi$
$359$	−9.96875	−	5.75546i	−0.526130	−	0.303761i	−0.739439	+	0.673223i	$0.764909\pi$
$360$	−1.35137	+	2.34064i	−0.0712234	+	0.123363i
$361$	−0.224508			−0.0118162
$362$	−1.70634	+	0.985158i	−0.0896834	+	0.0517787i
$363$	14.9820			0.786352
$364$	9.16239	+	2.65529i	0.480240	+	0.139175i
$365$	−18.5367			−0.970256
$366$	−4.02741	+	2.32523i	−0.210516	+	0.121542i
$367$	6.01361			0.313908			0.156954	−	0.987606i	$-0.449833\pi$
$367$	6.01361			0.313908			0.156954	+	0.987606i	$0.449833\pi$
$368$	−3.73482	+	6.46890i	−0.194691	+	0.337215i
$369$	3.29661	+	1.90330i	0.171614	+	0.0990816i
$370$	−15.8557	+	9.15432i	−0.824301	+	0.475910i
$371$	11.9619	+	14.8484i	0.621032	+	0.770891i
$372$			7.17238i			0.371871i
$373$	9.58372			0.496226			0.248113	−	0.968731i	$-0.420190\pi$
$373$	9.58372			0.496226			0.248113	+	0.968731i	$0.420190\pi$
$374$	29.2240			1.51114
$375$			7.28442i			0.376166i
$376$	−4.29656	+	7.44186i	−0.221578	+	0.383785i
$377$	−27.3175	−	12.7481i	−1.40692	−	0.656559i
$378$	2.06034	−	1.65982i	0.105973	−	0.0853718i
$379$	−21.9503	−	12.6730i	−1.12751	−	0.650969i	−0.184203	−	0.982888i	$-0.558971\pi$
$379$	−21.9503	−	12.6730i	−1.12751	−	0.650969i	−0.943308	+	0.331919i	$0.892304\pi$
$380$	5.92518	+	10.2627i	0.303956	+	0.526466i
$381$	−3.11451	+	5.39450i	−0.159561	+	0.276368i
$382$	−3.21249	+	1.85473i	−0.164365	+	0.0948964i
$383$			0.285882i			0.0146079i	0.999973	+	0.00730394i	$0.00232494\pi$
$383$			0.285882i			0.0146079i	−0.999973	+	0.00730394i	$0.997675\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	13.1483	−	33.9952i	0.670101	−	1.73256i
$386$	−1.49000	−	2.58076i	−0.0758390	−	0.131357i
$387$	3.10694	+	5.38138i	0.157935	+	0.273551i
$388$			9.46989i			0.480761i
$389$	−1.66201	−	2.87869i	−0.0842674	−	0.145955i	0.820811	−	0.571199i	$-0.193522\pi$
$389$	−1.66201	−	2.87869i	−0.0842674	−	0.145955i	−0.905079	+	0.425244i	$0.860188\pi$
$390$	0.846482	+	9.70803i	0.0428633	+	0.491585i
$391$	−42.8255			−2.16578
$392$	2.12940	+	6.66826i	0.107551	+	0.336798i
$393$	0.358468	−	0.620884i	0.0180823	−	0.0313195i
$394$	14.8866			0.749976
$395$	−17.8517	+	10.3067i	−0.898217	+	0.518586i
$396$	−4.41435	−	2.54863i	−0.221830	−	0.128073i
$397$			30.4819i			1.52984i	0.644125	+	0.764921i	$0.277222\pi$
$397$			30.4819i			1.52984i	−0.644125	+	0.764921i	$0.722778\pi$
$398$			2.66427i			0.133548i
$399$	−1.78572	−	11.4622i	−0.0893978	−	0.573829i
$400$	1.15240	−	1.99602i	0.0576200	−	0.0998008i
$401$	16.9395	−	9.78003i	0.845919	−	0.488392i	−0.0133528	−	0.999911i	$-0.504250\pi$
$401$	16.9395	−	9.78003i	0.845919	−	0.488392i	0.859272	+	0.511519i	$0.170917\pi$
$402$	3.03273	+	5.25284i	0.151259	+	0.261988i
$403$	14.8267	+	21.1879i	0.738572	+	1.05545i
$404$	−1.86105	+	3.22344i	−0.0925908	+	0.160372i
$405$	2.34064	+	1.35137i	0.116307	+	0.0671501i
$406$	−3.40516	−	21.8572i	−0.168995	−	1.08475i
$407$	−17.2647	−	29.9033i	−0.855778	−	1.48225i
$408$	−4.96516	−	2.86664i	−0.245812	−	0.141920i
$409$	−14.7635	−	8.52372i	−0.730009	−	0.421471i	0.0884163	−	0.996084i	$-0.471819\pi$
$409$	−14.7635	−	8.52372i	−0.730009	−	0.421471i	−0.818426	+	0.574613i	$0.805153\pi$
$410$	−8.90987	−	5.14411i	−0.440027	−	0.254050i
$411$	8.70853	+	5.02787i	0.429560	+	0.248007i
$412$	−4.55465	−	7.88888i	−0.224391	−	0.388657i
$413$	−15.9891	−	6.18410i	−0.786772	−	0.304300i
$414$	6.46890	+	3.73482i	0.317929	+	0.183557i
$415$	20.8065	−	36.0379i	1.02135	−	1.76903i
$416$	−1.52473	+	3.26729i	−0.0747559	+	0.160192i
$417$	−8.84682	−	15.3231i	−0.433231	−	0.750377i
$418$	−19.3551	+	11.1747i	−0.946687	+	0.546570i
$419$	4.16216	−	7.20908i	0.203335	−	0.352186i	−0.746266	−	0.665648i	$-0.768155\pi$
$419$	4.16216	−	7.20908i	0.203335	−	0.352186i	0.949601	+	0.313461i	$0.101489\pi$
$420$	−5.56857	+	4.48605i	−0.271718	+	0.218897i
$421$			35.9805i			1.75358i	0.480873	+	0.876790i	$0.340320\pi$
$421$			35.9805i			1.75358i	−0.480873	+	0.876790i	$0.659680\pi$
$422$		−	6.48658i		−	0.315762i
$423$	7.44186	+	4.29656i	0.361836	+	0.208906i
$424$	−6.24125	+	3.60339i	−0.303102	+	0.174996i
$425$	13.2141			0.640976
$426$	0.457497	−	0.792408i	0.0221658	−	0.0383923i
$427$	−12.1573	+	1.89400i	−0.588333	+	0.0916573i
$428$	−10.5677			−0.510810
$429$	−18.3089	+	1.59643i	−0.883964	+	0.0770764i
$430$	−8.39725	−	14.5445i	−0.404951	−	0.701397i
$431$		−	6.20922i		−	0.299088i	−0.988755	−	0.149544i	$-0.952219\pi$
$431$		−	6.20922i		−	0.299088i	0.988755	−	0.149544i	$-0.0477805\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−3.98578	−	6.90357i	−0.191544	−	0.331764i	0.754218	−	0.656624i	$-0.228016\pi$
$433$	−3.98578	−	6.90357i	−0.191544	−	0.331764i	−0.945762	+	0.324860i	$0.894683\pi$
$434$	−6.84532	+	17.6987i	−0.328586	+	0.849564i
$435$	19.5698	−	11.2987i	0.938302	−	0.541729i
$436$		−	3.78429i		−	0.181235i
$437$	28.3634	−	16.3756i	1.35681	−	0.783352i
$438$	−3.42924	+	5.93963i	−0.163856	+	0.283806i
$439$	−7.08113	−	12.2649i	−0.337964	−	0.585371i	0.646086	−	0.763265i	$-0.276405\pi$
$439$	−7.08113	−	12.2649i	−0.337964	−	0.585371i	−0.984050	+	0.177894i	$0.943072\pi$
$440$	11.9308	+	6.88828i	0.568781	+	0.328386i
$441$	6.66826	−	2.12940i	0.317536	−	0.101400i
$442$	−20.5935	+	1.79563i	−0.979532	+	0.0854094i
$443$	−13.7918	+	23.8880i	−0.655267	+	1.13495i	0.326560	+	0.945176i	$0.394110\pi$
$443$	−13.7918	+	23.8880i	−0.655267	+	1.13495i	−0.981827	+	0.189779i	$0.939223\pi$
$444$			6.77410i			0.321485i
$445$	−28.0605			−1.33020
$446$	26.0800			1.23492
$447$		−	23.2914i		−	1.10165i
$448$	−2.61422	+	0.407273i	−0.123510	+	0.0192418i
$449$	2.53224	−	1.46199i	0.119504	−	0.0689957i	−0.439056	−	0.898459i	$-0.644687\pi$
$449$	2.53224	−	1.46199i	0.119504	−	0.0689957i	0.558560	+	0.829464i	$0.311354\pi$
$450$	−1.99602	−	1.15240i	−0.0940931	−	0.0543247i
$451$	9.70159	−	16.8036i	0.456830	−	0.791253i
$452$	1.69919			0.0799230
$453$	15.8610	−	9.15737i	0.745216	−	0.430251i
$454$	11.6727			0.547826
$455$	−7.17655	+	24.7636i	−0.336442	+	1.16093i
$456$	4.38458			0.205327
$457$	−18.1377	+	10.4718i	−0.848447	+	0.489851i	−0.860126	−	0.510081i	$-0.829615\pi$
$457$	−18.1377	+	10.4718i	−0.848447	+	0.489851i	0.0116798	+	0.999932i	$0.496282\pi$
$458$	−12.0798			−0.564450
$459$	−2.86664	+	4.96516i	−0.133803	+	0.231754i
$460$	−17.4838	−	10.0943i	−0.815184	−	0.470647i
$461$	15.9388	−	9.20229i	0.742346	−	0.428593i	−0.0805759	−	0.996748i	$-0.525676\pi$
$461$	15.9388	−	9.20229i	0.742346	−	0.428593i	0.822922	+	0.568155i	$0.192343\pi$
$462$	−8.46051	−	10.5021i	−0.393619	−	0.488601i
$463$		−	28.8633i		−	1.34139i	−0.741732	−	0.670697i	$-0.765995\pi$
$463$		−	28.8633i		−	1.34139i	0.741732	−	0.670697i	$-0.234005\pi$
$464$	8.36089			0.388145
$465$	−19.3851			−0.898962
$466$		−	9.31731i		−	0.431616i
$467$	−16.8772	+	29.2322i	−0.780983	+	1.35270i	0.150386	+	0.988627i	$0.451948\pi$
$467$	−16.8772	+	29.2322i	−0.780983	+	1.35270i	−0.931369	+	0.364075i	$0.881385\pi$
$468$	3.26729	+	1.52473i	0.151031	+	0.0704805i
$469$	2.47030	+	15.8564i	0.114068	+	0.732181i
$470$	−20.1134	−	11.6125i	−0.927762	−	0.535644i
$471$	1.91775	+	3.32164i	0.0883653	+	0.153053i
$472$	3.23979	−	5.61147i	0.149123	−	0.258289i
$473$	27.4303	−	15.8369i	1.26125	−	0.728180i
$474$			7.62685i			0.350313i
$475$	−8.75168	+	5.05279i	−0.401555	+	0.231838i
$476$	−9.51619	−	11.8125i	−0.436174	−	0.541426i
$477$	3.60339	+	6.24125i	0.164988	+	0.285767i
$478$	−8.40693	−	14.5612i	−0.384524	−	0.666015i
$479$			17.4214i			0.796004i	0.917384	+	0.398002i	$0.130296\pi$
$479$			17.4214i			0.796004i	−0.917384	+	0.398002i	$0.869704\pi$
$480$	−1.35137	−	2.34064i	−0.0616813	−	0.106835i
$481$	14.0034	+	20.0114i	0.638500	+	0.912440i
$482$	22.3511			1.01807
$483$	12.3982	+	15.3900i	0.564140	+	0.700270i
$484$	−7.49101	+	12.9748i	−0.340500	+	0.589764i
$485$	−25.5946			−1.16219
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−33.1393	−	19.1330i	−1.50168	−	0.866998i	−0.999998	−	0.00194838i	$-0.999380\pi$
$487$	−33.1393	−	19.1330i	−1.50168	−	0.866998i	−0.501686	−	0.865050i	$-0.667287\pi$
$488$		−	4.65046i		−	0.210516i
$489$			10.4272i			0.471533i
$490$	−18.0226	+	5.75521i	−0.814176	+	0.259994i
$491$	−18.3883	+	31.8494i	−0.829851	+	1.43734i	0.0683042	+	0.997665i	$0.478241\pi$
$491$	−18.3883	+	31.8494i	−0.829851	+	1.43734i	−0.898155	+	0.439679i	$0.855092\pi$
$492$	−3.29661	+	1.90330i	−0.148622	+	0.0858072i
$493$	23.9677	+	41.5132i	1.07945	+	1.86966i
$494$	12.9525	−	9.06378i	0.582759	−	0.407799i
$495$	6.88828	−	11.9308i	0.309605	−	0.536252i
$496$	−6.21147	−	3.58619i	−0.278903	−	0.161025i
$497$	1.88520	−	1.51872i	0.0845628	−	0.0681240i
$498$	−7.69830	−	13.3339i	−0.344969	−	0.597504i
$499$	−26.0698	−	15.0514i	−1.16704	−	0.673793i	−0.214062	−	0.976820i	$-0.568669\pi$
$499$	−26.0698	−	15.0514i	−1.16704	−	0.673793i	−0.952982	+	0.303027i	$0.902003\pi$
$500$	−6.30849	−	3.64221i	−0.282124	−	0.162885i
$501$	1.90573	+	1.10027i	0.0851418	+	0.0491566i
$502$	−6.49788	−	3.75155i	−0.290015	−	0.167440i
$503$	3.90097	+	6.75668i	0.173936	+	0.301265i	0.939792	−	0.341746i	$-0.111018\pi$
$503$	3.90097	+	6.75668i	0.173936	+	0.301265i	−0.765857	+	0.643011i	$0.777685\pi$
$504$	0.407273	+	2.61422i	0.0181414	+	0.116446i
$505$	−8.71211	−	5.02994i	−0.387684	−	0.223829i
$506$	19.0373	−	32.9736i	0.846313	−	1.46586i
$507$	12.8038	−	2.24994i	0.568638	−	0.0999233i
$508$	−3.11451	−	5.39450i	−0.138184	−	0.239342i
$509$	−19.0523	+	10.9999i	−0.844480	+	0.487561i	−0.858784	−	0.512337i	$-0.828780\pi$
$509$	−19.0523	+	10.9999i	−0.844480	+	0.487561i	0.0143047	+	0.999898i	$0.495447\pi$
$510$	7.74778	−	13.4195i	0.343077	−	0.594227i
$511$	−14.1308	+	11.3838i	−0.625111	+	0.503591i
$512$		−	1.00000i		−	0.0441942i
$513$		−	4.38458i		−	0.193584i
$514$	−6.09468	−	3.51876i	−0.268825	−	0.155206i
$515$	21.3216	−	12.3100i	0.939541	−	0.542444i
$516$	−6.21388			−0.273551
$517$	21.9007	−	37.9331i	0.963190	−	1.66829i
$518$	−6.46520	+	16.7159i	−0.284065	+	0.734453i
$519$	−21.4765			−0.942714
$520$	−8.83064	−	4.12094i	−0.387249	−	0.180715i
$521$	13.9174	+	24.1056i	0.609732	+	1.05609i	0.991284	+	0.131740i	$0.0420563\pi$
$521$	13.9174	+	24.1056i	0.609732	+	1.05609i	−0.381552	+	0.924347i	$0.624610\pi$
$522$		−	8.36089i		−	0.365946i
$523$	4.84276	+	8.38790i	0.211759	+	0.366777i	0.952265	−	0.305272i	$-0.0987475\pi$
$523$	4.84276	+	8.38790i	0.211759	+	0.366777i	−0.740506	+	0.672050i	$0.765414\pi$
$524$	0.358468	+	0.620884i	0.0156597	+	0.0271234i
$525$	−3.82555	−	4.74868i	−0.166961	−	0.207249i
$526$	20.7228	−	11.9643i	0.903555	−	0.521668i
$527$		−	41.1213i		−	1.79127i
$528$	4.41435	−	2.54863i	0.192110	−	0.110915i
$529$	−16.3978	+	28.4018i	−0.712948	+	1.23486i
$530$	−9.73901	−	16.8685i	−0.423036	−	0.732719i
$531$	−5.61147	−	3.23979i	−0.243517	−	0.140595i
$532$	10.8194	+	4.18464i	0.469082	+	0.181427i
$533$	−5.80402	+	12.4373i	−0.251400	+	0.538717i
$534$	−5.19112	+	8.99129i	−0.224642	+	0.389091i
$535$		−	28.5618i		−	1.23484i
$536$	−6.06546			−0.261988
$537$	18.6782			0.806024
$538$			1.59963i			0.0689649i
$539$	−10.8541	−	33.9898i	−0.467519	−	1.46404i
$540$	−2.34064	+	1.35137i	−0.100725	+	0.0581537i
$541$	−0.964894	−	0.557082i	−0.0414840	−	0.0239508i	0.479115	−	0.877752i	$-0.340958\pi$
$541$	−0.964894	−	0.557082i	−0.0414840	−	0.0239508i	−0.520599	+	0.853802i	$0.674291\pi$
$542$	−10.0006	+	17.3215i	−0.429562	+	0.744023i
$543$	−1.97032			−0.0845543
$544$	4.96516	−	2.86664i	0.212880	−	0.122906i
$545$	10.2279			0.438117
$546$	6.60722	+	6.88074i	0.282763	+	0.294469i
$547$	−18.4164			−0.787430			−0.393715	−	0.919233i	$-0.628810\pi$
$547$	−18.4164			−0.787430			−0.393715	+	0.919233i	$0.628810\pi$
$548$	−8.70853	+	5.02787i	−0.372010	+	0.214780i
$549$	−4.65046			−0.198477
$550$	−5.87408	+	10.1742i	−0.250472	+	0.433830i
$551$	−31.7476	−	18.3295i	−1.35249	−	0.780862i
$552$	−6.46890	+	3.73482i	−0.275335	+	0.158965i
$553$	−7.27906	+	18.8201i	−0.309537	+	0.800313i
$554$			18.1117i			0.769491i
$555$	−18.3086			−0.777158
$556$	17.6936			0.750377
$557$		−	33.6405i		−	1.42539i	−0.701473	−	0.712696i	$-0.747474\pi$
$557$		−	33.6405i		−	1.42539i	0.701473	−	0.712696i	$-0.252526\pi$
$558$	−3.58619	+	6.21147i	−0.151816	+	0.262952i
$559$	−18.3564	+	12.8453i	−0.776394	+	0.543299i
$560$	−1.10075	−	7.06555i	−0.0465153	−	0.298574i
$561$	25.3087	+	14.6120i	1.06853	+	0.616919i
$562$	5.50878	+	9.54149i	0.232374	+	0.402483i
$563$	0.779481	−	1.35010i	0.0328512	−	0.0568999i	−0.849132	−	0.528180i	$-0.822875\pi$
$563$	0.779481	−	1.35010i	0.0328512	−	0.0568999i	0.881984	+	0.471280i	$0.156208\pi$
$564$	−7.44186	+	4.29656i	−0.313359	+	0.180918i
$565$			4.59246i			0.193206i
$566$	11.6858	−	6.74682i	0.491193	−	0.283590i
$567$	2.61422	−	0.407273i	0.109787	−	0.0171039i
$568$	0.457497	+	0.792408i	0.0191961	+	0.0332487i
$569$	2.60329	+	4.50904i	0.109136	+	0.189029i	0.915420	−	0.402499i	$-0.131858\pi$
$569$	2.60329	+	4.50904i	0.109136	+	0.189029i	−0.806285	+	0.591528i	$0.798525\pi$
$570$			11.8504i			0.496357i
$571$	5.99348	+	10.3810i	0.250819	+	0.434432i	0.963752	−	0.266801i	$-0.0859666\pi$
$571$	5.99348	+	10.3810i	0.250819	+	0.434432i	−0.712932	+	0.701233i	$0.752633\pi$
$572$	7.77192	−	16.6542i	0.324960	−	0.696348i
$573$	−3.70946			−0.154965
$574$	−9.95126	+	1.55032i	−0.415357	+	0.0647092i
$575$	8.60802	−	14.9095i	0.358979	−	0.621770i
$576$	−1.00000			−0.0416667
$577$	−0.299900	+	0.173147i	−0.0124850	+	0.00720821i	−0.506230	−	0.862399i	$-0.668961\pi$
$577$	−0.299900	+	0.173147i	−0.0124850	+	0.00720821i	0.493745	+	0.869607i	$0.335628\pi$
$578$	13.7442	+	7.93524i	0.571685	+	0.330062i
$579$		−	2.98000i		−	0.123845i
$580$			22.5973i			0.938302i
$581$	−6.27062	−	40.2501i	−0.260149	−	1.66985i
$582$	−4.73494	+	8.20116i	−0.196270	+	0.339949i
$583$	31.8132	−	18.3674i	1.31757	−	0.760699i
$584$	−3.42924	−	5.93963i	−0.141903	−	0.245783i
$585$	−4.12094	+	8.83064i	−0.170380	+	0.365102i
$586$	−2.38774	+	4.13569i	−0.0986368	+	0.170844i
$587$	25.5443	+	14.7480i	1.05433	+	0.608715i	0.923857	−	0.382738i	$-0.125019\pi$
$587$	25.5443	+	14.7480i	1.05433	+	0.608715i	0.130468	+	0.991453i	$0.458352\pi$
$588$	−1.49001	+	6.83958i	−0.0614472	+	0.282060i
$589$	15.7239	+	27.2347i	0.647893	+	1.12218i
$590$	15.1664	+	8.75630i	0.624389	+	0.360491i
$591$	12.8922	+	7.44330i	0.530313	+	0.306176i
$592$	−5.86654	−	3.38705i	−0.241113	−	0.139207i
$593$	2.79980	+	1.61647i	0.114974	+	0.0663803i	0.556384	−	0.830925i	$-0.312188\pi$
$593$	2.79980	+	1.61647i	0.114974	+	0.0663803i	−0.441410	+	0.897305i	$0.645522\pi$
$594$	−2.54863	−	4.41435i	−0.104571	−	0.181123i
$595$	31.9261	−	25.7198i	1.30884	−	1.05441i
$596$	20.1710	+	11.6457i	0.826236	+	0.477027i
$597$	−1.33214	+	2.30733i	−0.0545207	+	0.0944327i
$598$	−11.3892	+	24.4055i	−0.465738	+	0.998016i
$599$	−6.64023	−	11.5012i	−0.271312	−	0.469927i	0.697886	−	0.716209i	$-0.254124\pi$
$599$	−6.64023	−	11.5012i	−0.271312	−	0.469927i	−0.969198	+	0.246282i	$0.920791\pi$
$600$	1.99602	−	1.15240i	0.0814870	−	0.0470465i
$601$	3.58901	−	6.21634i	0.146399	−	0.253570i	−0.783495	−	0.621398i	$-0.786565\pi$
$601$	3.58901	−	6.21634i	0.146399	−	0.253570i	0.929894	+	0.367828i	$0.119898\pi$
$602$	−15.3335	−	5.93053i	−0.624945	−	0.241710i
$603$			6.06546i			0.247004i
$604$			18.3147i			0.745216i
$605$	−35.0675	−	20.2462i	−1.42570	−	0.823127i
$606$	−3.22344	+	1.86105i	−0.130943	+	0.0756001i
$607$	40.4139			1.64035			0.820174	−	0.572114i	$-0.193877\pi$
$607$	40.4139			1.64035			0.820174	+	0.572114i	$0.193877\pi$
$608$	−2.19229	+	3.79715i	−0.0889090	+	0.153995i
$609$	7.97963	−	20.6315i	0.323351	−	0.836029i
$610$	12.5690			0.508903
$611$	−13.1022	+	28.0762i	−0.530057	+	1.13584i
$612$	−2.86664	−	4.96516i	−0.115877	−	0.200705i
$613$		−	8.59059i		−	0.346971i	−0.984836	−	0.173485i	$-0.944497\pi$
$613$		−	8.59059i		−	0.346971i	0.984836	−	0.173485i	$-0.0555029\pi$
$614$	−3.13211	−	5.42497i	−0.126402	−	0.218934i
$615$	−5.14411	−	8.90987i	−0.207431	−	0.359280i
$616$	13.3253	−	2.07597i	0.536893	−	0.0836434i
$617$	31.7545	−	18.3335i	1.27839	−	0.738079i	0.301838	−	0.953359i	$-0.402400\pi$
$617$	31.7545	−	18.3335i	1.27839	−	0.738079i	0.976552	+	0.215281i	$0.0690666\pi$
$618$		−	9.10929i		−	0.366429i
$619$	−4.95870	+	2.86291i	−0.199307	+	0.115070i	−0.596332	−	0.802738i	$-0.703376\pi$
$619$	−4.95870	+	2.86291i	−0.199307	+	0.115070i	0.397025	+	0.917808i	$0.370043\pi$
$620$	9.69254	−	16.7880i	0.389262	−	0.674221i
$621$	3.73482	+	6.46890i	0.149873	+	0.259588i
$622$	−5.18252	−	2.99213i	−0.207800	−	0.119974i
$623$	−21.3910	+	17.2326i	−0.857011	+	0.690411i
$624$	−2.95410	+	2.06720i	−0.118259	+	0.0827541i
$625$	15.6059	−	27.0303i	0.624238	−	1.08121i
$626$			28.6573i			1.14537i
$627$	−22.3493			−0.892545
$628$	−3.83550			−0.153053
$629$		−	38.8378i		−	1.54856i
$630$	−7.06555	+	1.10075i	−0.281498	+	0.0438550i
$631$	−15.3218	+	8.84605i	−0.609952	+	0.352156i	−0.772947	−	0.634471i	$-0.781218\pi$
$631$	−15.3218	+	8.84605i	−0.609952	+	0.352156i	0.162995	+	0.986627i	$0.447885\pi$
$632$	−6.60504	−	3.81342i	−0.262735	−	0.151690i
$633$	3.24329	−	5.61754i	0.128909	−	0.223277i
$634$	25.7145			1.02125
$635$	14.5799	−	8.41772i	0.578586	−	0.334047i
$636$	−7.20677			−0.285767
$637$	9.73710	+	23.2850i	0.385798	+	0.922583i
$638$	−42.6176			−1.68725
$639$	0.792408	−	0.457497i	0.0313472	−	0.0180983i
$640$	2.70274			0.106835
$641$	−11.8476	+	20.5206i	−0.467950	+	0.810514i	−0.999329	−	0.0366205i	$-0.988341\pi$
$641$	−11.8476	+	20.5206i	−0.467950	+	0.810514i	0.531379	+	0.847134i	$0.321674\pi$
$642$	−9.15192	−	5.28386i	−0.361198	−	0.208537i
$643$	−11.0433	+	6.37588i	−0.435507	+	0.251440i	−0.701690	−	0.712482i	$-0.747571\pi$
$643$	−11.0433	+	6.37588i	−0.435507	+	0.251440i	0.266183	+	0.963923i	$0.414237\pi$
$644$	−19.5273	+	3.04218i	−0.769482	+	0.119879i
$645$		−	16.7945i		−	0.661283i
$646$	−25.1380			−0.989041
$647$	7.40684			0.291193			0.145597	−	0.989344i	$-0.453490\pi$
$647$	7.40684			0.291193			0.145597	+	0.989344i	$0.453490\pi$
$648$			1.00000i			0.0392837i
$649$	−16.5140	+	28.6031i	−0.648232	+	1.12277i
$650$	3.51419	−	7.53046i	0.137838	−	0.295369i
$651$	−14.7776	+	11.9048i	−0.579178	+	0.466588i
$652$	−9.03020	−	5.21359i	−0.353650	−	0.204180i
$653$	20.0753	+	34.7714i	0.785606	+	1.36071i	0.928636	+	0.370992i	$0.120982\pi$
$653$	20.0753	+	34.7714i	0.785606	+	1.36071i	−0.143030	+	0.989718i	$0.545684\pi$
$654$	1.89214	−	3.27729i	0.0739887	−	0.128152i
$655$	−1.67809	+	0.968844i	−0.0655683	+	0.0378559i
$656$		−	3.80659i		−	0.148622i
$657$	−5.93963	+	3.42924i	−0.231727	+	0.133788i
$658$	−22.4643	+	3.49975i	−0.875749	+	0.136434i
$659$	17.0035	+	29.4509i	0.662361	+	1.14724i	0.979994	+	0.199029i	$0.0637788\pi$
$659$	17.0035	+	29.4509i	0.662361	+	1.14724i	−0.317633	+	0.948214i	$0.602888\pi$
$660$	6.88828	+	11.9308i	0.268126	+	0.464408i
$661$		−	11.6080i		−	0.451499i	−0.974185	−	0.225750i	$-0.927517\pi$
$661$		−	11.6080i		−	0.451499i	0.974185	−	0.225750i	$-0.0724831\pi$
$662$	−0.440050	−	0.762189i	−0.0171030	−	0.0296233i
$663$	−18.7323	−	8.74168i	−0.727502	−	0.339499i
$664$	15.3966			0.597504
$665$	−11.3100	+	29.2421i	−0.438582	+	1.13396i
$666$	−3.38705	+	5.86654i	−0.131246	+	0.227324i
$667$	62.4529			2.41819
$668$	−1.90573	+	1.10027i	−0.0737350	+	0.0425709i
$669$	22.5859	+	13.0400i	0.873223	+	0.504155i
$670$		−	16.3933i		−	0.633330i
$671$			23.7046i			0.915104i
$672$	−2.46761	−	0.954400i	−0.0951903	−	0.0368168i
$673$	−5.22869	+	9.05635i	−0.201551	+	0.349097i	−0.949028	−	0.315191i	$-0.897932\pi$
$673$	−5.22869	+	9.05635i	−0.201551	+	0.349097i	0.747477	+	0.664287i	$0.231265\pi$
$674$	−14.2863	+	8.24820i	−0.550288	+	0.317709i
$675$	−1.15240	−	1.99602i	−0.0443559	−	0.0768267i
$676$	−4.45341	+	12.2134i	−0.171285	+	0.469746i
$677$	2.49022	−	4.31318i	0.0957068	−	0.165769i	−0.814197	−	0.580589i	$-0.802822\pi$
$677$	2.49022	−	4.31318i	0.0957068	−	0.165769i	0.909903	+	0.414820i	$0.136156\pi$
$678$	1.47154	+	0.849593i	0.0565141	+	0.0326284i
$679$	−19.5112	+	15.7183i	−0.748771	+	0.603212i
$680$	7.74778	+	13.4195i	0.297114	+	0.514616i
$681$	10.1088	+	5.83634i	0.387372	+	0.223649i
$682$	31.6614	+	18.2797i	1.21238	+	0.699967i
$683$	13.8849	+	8.01644i	0.531290	+	0.306741i	0.741542	−	0.670907i	$-0.234095\pi$
$683$	13.8849	+	8.01644i	0.531290	+	0.306741i	−0.210251	+	0.977647i	$0.567428\pi$
$684$	3.79715	+	2.19229i	0.145188	+	0.0838242i
$685$	−13.5890	−	23.5369i	−0.519210	−	0.899298i
$686$	−10.2045	+	15.4554i	−0.389609	+	0.590089i
$687$	−10.4614	−	6.03988i	−0.399126	−	0.230436i
$688$	3.10694	−	5.38138i	0.118451	−	0.205163i
$689$	−21.2895	+	14.8978i	−0.811066	+	0.567561i
$690$	−10.0943	−	17.4838i	−0.384282	−	0.665595i
$691$	31.5756	−	18.2302i	1.20119	−	0.693510i	0.240373	−	0.970681i	$-0.422730\pi$
$691$	31.5756	−	18.2302i	1.20119	−	0.693510i	0.960821	+	0.277171i	$0.0893968\pi$
$692$	10.7383	−	18.5992i	0.408207	−	0.707036i
$693$	−2.07597	−	13.3253i	−0.0788597	−	0.506187i
$694$			5.59149i			0.212250i
$695$			47.8213i			1.81396i
$696$	7.24074	+	4.18045i	0.274460	+	0.158459i
$697$	18.9004	−	10.9121i	0.715902	−	0.413326i
$698$	12.8482			0.486310
$699$	4.65865	−	8.06902i	0.176206	−	0.305199i
$700$	6.02525	−	0.938683i	0.227733	−	0.0354789i
$701$	11.4738			0.433360			0.216680	−	0.976243i	$-0.430477\pi$
$701$	11.4738			0.433360			0.216680	+	0.976243i	$0.430477\pi$
$702$	2.06720	+	2.95410i	0.0780213	+	0.111495i
$703$	14.8508	+	25.7223i	0.560108	+	0.970135i
$704$			5.09726i			0.192110i
$705$	−11.6125	−	20.1134i	−0.437351	−	0.757515i
$706$	−9.22345	−	15.9755i	−0.347129	−	0.601245i
$707$	−9.73039	+	1.51591i	−0.365949	+	0.0570117i
$708$	5.61147	−	3.23979i	0.210892	−	0.121759i
$709$		−	41.9126i		−	1.57406i	−0.616915	−	0.787030i	$-0.711618\pi$
$709$		−	41.9126i		−	1.57406i	0.616915	−	0.787030i	$-0.288382\pi$
$710$	−2.14167	+	1.23649i	−0.0803755	+	0.0464048i
$711$	−3.81342	+	6.60504i	−0.143015	+	0.247709i
$712$	−5.19112	−	8.99129i	−0.194546	−	0.336963i
$713$	−46.3975	−	26.7876i	−1.73760	−	1.00320i
$714$	−2.33501	−	14.9880i	−0.0873855	−	0.560913i
$715$	45.0120	+	21.0055i	1.68336	+	0.785561i
$716$	−9.33910	+	16.1758i	−0.349019	+	0.604518i
$717$		−	16.8139i		−	0.627925i
$718$	11.5109			0.429584
$719$	−36.2429			−1.35163			−0.675817	−	0.737070i	$-0.736209\pi$
$719$	−36.2429			−1.35163			−0.675817	+	0.737070i	$0.736209\pi$
$720$		−	2.70274i		−	0.100725i
$721$	8.69390	−	22.4782i	0.323778	−	0.837133i
$722$	0.194430	−	0.112254i	0.00723593	−	0.00417766i
$723$	19.3566	+	11.1756i	0.719881	+	0.415623i
$724$	0.985158	−	1.70634i	0.0366131	−	0.0634157i
$725$	−19.2702			−0.715677
$726$	−12.9748	+	7.49101i	−0.481540	+	0.278017i
$727$	−6.41054			−0.237754			−0.118877	−	0.992909i	$-0.537929\pi$
$727$	−6.41054			−0.237754			−0.118877	+	0.992909i	$0.537929\pi$
$728$	−9.26251	+	2.28165i	−0.343291	+	0.0845636i
$729$	1.00000			0.0370370
$730$	16.0533	−	9.26836i	0.594158	−	0.343037i
$731$	35.6259			1.31767
$732$	2.32523	−	4.02741i	0.0859429	−	0.148857i
$733$	23.5129	+	13.5752i	0.868469	+	0.501411i	0.866839	−	0.498588i	$-0.166148\pi$
$733$	23.5129	+	13.5752i	0.868469	+	0.501411i	0.00162955	+	0.999999i	$0.499481\pi$
$734$	−5.20794	+	3.00680i	−0.192228	+	0.110983i
$735$	−18.4856	−	4.02712i	−0.681852	−	0.148543i
$736$		−	7.46964i		−	0.275335i
$737$	30.9172			1.13885
$738$	−3.80659			−0.140123
$739$			19.8339i			0.729601i	0.931086	+	0.364800i	$0.118863\pi$
$739$			19.8339i			0.729601i	−0.931086	+	0.364800i	$0.881137\pi$
$740$	9.15432	−	15.8557i	0.336519	−	0.582869i
$741$	15.7491	−	1.37322i	0.578556	−	0.0504466i
$742$	−17.7835	−	6.87814i	−0.652854	−	0.252504i
$743$	31.4762	+	18.1728i	1.15475	+	0.666696i	0.950040	−	0.312127i	$-0.101041\pi$
$743$	31.4762	+	18.1728i	1.15475	+	0.666696i	0.204710	+	0.978823i	$0.434375\pi$
$744$	−3.58619	−	6.21147i	−0.131476	−	0.227723i
$745$	−31.4754	+	54.5169i	−1.15317	+	1.99735i
$746$	−8.29975	+	4.79186i	−0.303875	+	0.175442i
$747$		−	15.3966i		−	0.563332i
$748$	−25.3087	+	14.6120i	−0.925378	+	0.534267i
$749$	−17.5405	−	21.7731i	−0.640916	−	0.795573i
$750$	−3.64221	−	6.30849i	−0.132995	−	0.230354i
$751$	−0.461810	−	0.799878i	−0.0168517	−	0.0291880i	0.857477	−	0.514523i	$-0.172031\pi$
$751$	−0.461810	−	0.799878i	−0.0168517	−	0.0291880i	−0.874328	+	0.485335i	$0.838698\pi$
$752$		−	8.59312i		−	0.313359i
$753$	−3.75155	−	6.49788i	−0.136714	−	0.236796i
$754$	30.0317	−	2.61858i	1.09369	−	0.0953632i
$755$	−49.4999			−1.80149
$756$	−0.954400	+	2.46761i	−0.0347112	+	0.0897463i
$757$	1.33975	−	2.32051i	0.0486940	−	0.0843405i	−0.840651	−	0.541577i	$-0.817827\pi$
$757$	1.33975	−	2.32051i	0.0486940	−	0.0843405i	0.889345	+	0.457237i	$0.151161\pi$
$758$	25.3460			0.920609
$759$	32.9736	−	19.0373i	1.19687	−	0.691012i
$760$	−10.2627	−	5.92518i	−0.372268	−	0.214929i
$761$			15.0861i			0.546872i	0.961890	+	0.273436i	$0.0881602\pi$
$761$			15.0861i			0.546872i	−0.961890	+	0.273436i	$0.911840\pi$
$762$		−	6.22903i		−	0.225654i
$763$	7.79693	−	6.28123i	0.282268	−	0.227396i
$764$	1.85473	−	3.21249i	0.0671019	−	0.116224i
$765$	13.4195	−	7.74778i	0.485185	−	0.280122i
$766$	−0.142941	−	0.247581i	−0.00516466	−	0.00894546i
$767$	9.87958	−	21.1707i	0.356731	−	0.764428i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	17.7838	+	10.2675i	0.641301	+	0.370256i	0.785116	−	0.619349i	$-0.212603\pi$
$769$	17.7838	+	10.2675i	0.641301	+	0.370256i	−0.143814	+	0.989605i	$0.545937\pi$
$770$	5.61082	+	36.0149i	0.202200	+	1.29789i
$771$	−3.51876	−	6.09468i	−0.126725	−	0.219494i
$772$	2.58076	+	1.49000i	0.0928834	+	0.0536263i
$773$	15.6635	+	9.04334i	0.563378	+	0.325266i	0.754500	−	0.656300i	$-0.227879\pi$
$773$	15.6635	+	9.04334i	0.563378	+	0.325266i	−0.191122	+	0.981566i	$0.561213\pi$
$774$	−5.38138	−	3.10694i	−0.193430	−	0.111677i
$775$	14.3162	+	8.26546i	0.514253	+	0.296904i
$776$	−4.73494	−	8.20116i	−0.169975	−	0.294405i
$777$	−13.9570	+	11.2438i	−0.500703	+	0.403368i
$778$	2.87869	+	1.66201i	0.103206	+	0.0595860i
$779$	−8.34515	+	14.4542i	−0.298996	+	0.517876i
$780$	−5.58709	−	7.98416i	−0.200050	−	0.285879i
$781$	−2.33198	−	4.03911i	−0.0834448	−	0.144531i
$782$	37.0880	−	21.4128i	1.32626	−	0.765719i
$783$	4.18045	−	7.24074i	0.149397	−	0.258763i
$784$	−5.17824	−	4.71018i	−0.184937	−	0.168221i
$785$		−	10.3664i		−	0.369991i
$786$			0.716935i			0.0255722i
$787$	30.3608	+	17.5288i	1.08225	+	0.624835i	0.931501	−	0.363738i	$-0.118499\pi$
$787$	30.3608	+	17.5288i	1.08225	+	0.624835i	0.150745	+	0.988573i	$0.451833\pi$
$788$	−12.8922	+	7.44330i	−0.459264	+	0.265156i
$789$	23.9286			0.851880
$790$	10.3067	−	17.8517i	0.366696	−	0.635135i
$791$	2.82034	+	3.50090i	0.100280	+	0.124478i
$792$	5.09726			0.181123
$793$	−1.45650	−	16.7041i	−0.0517217	−	0.593179i
$794$	−15.2409	−	26.3981i	−0.540881	−	0.936833i
$795$		−	19.4780i		−	0.690814i
$796$	−1.33214	−	2.30733i	−0.0472163	−	0.0817811i
$797$	−8.96425	−	15.5265i	−0.317530	−	0.549978i	0.662442	−	0.749113i	$-0.269520\pi$
$797$	−8.96425	−	15.5265i	−0.317530	−	0.549978i	−0.979972	+	0.199135i	$0.936187\pi$
$798$	7.27759	+	9.03372i	0.257624	+	0.319790i
$799$	42.6663	−	24.6334i	1.50942	−	0.871466i
$800$			2.30480i			0.0814870i
$801$	−8.99129	+	5.19112i	−0.317692	+	0.183419i
$802$	−9.78003	+	16.9395i	−0.345345	+	0.598155i
$803$	17.4797	+	30.2758i	0.616847	+	1.06841i
$804$	−5.25284	−	3.03273i	−0.185253	−	0.106956i
$805$	−8.22223	−	52.7771i	−0.289796	−	1.86015i
$806$	−23.4343	−	10.9359i	−0.825437	−	0.385202i
$807$	−0.799815	+	1.38532i	−0.0281548	+	0.0487656i
$808$		−	3.72210i		−	0.130943i
$809$	20.6825			0.727160			0.363580	−	0.931563i	$-0.381554\pi$
$809$	20.6825			0.727160			0.363580	+	0.931563i	$0.381554\pi$
$810$	−2.70274			−0.0949646
$811$			16.2377i			0.570182i	0.958500	+	0.285091i	$0.0920239\pi$
$811$			16.2377i			0.570182i	−0.958500	+	0.285091i	$0.907976\pi$
$812$	13.8775	+	17.2263i	0.487007	+	0.604524i
$813$	−17.3215	+	10.0006i	−0.607492	+	0.350736i
$814$	29.9033	+	17.2647i	1.04811	+	0.605126i
$815$	14.0910	−	24.4063i	0.493585	−	0.854915i
$816$	5.73328			0.200705
$817$	−23.5951	+	13.6226i	−0.825487	+	0.476595i
$818$	17.0474			0.596050
$819$	2.28165	+	9.26251i	0.0797273	+	0.323658i
$820$	10.2882			0.359280
$821$	35.9538	−	20.7579i	1.25480	−	0.724457i	0.282738	−	0.959197i	$-0.408757\pi$
$821$	35.9538	−	20.7579i	1.25480	−	0.724457i	0.972058	+	0.234740i	$0.0754240\pi$
$822$	−10.0557			−0.350734
$823$	8.97477	−	15.5448i	0.312841	−	0.541856i	−0.666135	−	0.745831i	$-0.732053\pi$
$823$	8.97477	−	15.5448i	0.312841	−	0.541856i	0.978976	+	0.203975i	$0.0653860\pi$
$824$	7.88888	+	4.55465i	0.274822	+	0.158669i
$825$	−10.1742	+	5.87408i	−0.354220	+	0.204509i
$826$	16.9390	−	2.63895i	0.589383	−	0.0918210i
$827$			0.0414259i			0.00144052i	1.00000		0.000720261i	$0.000229266\pi$
$827$			0.0414259i			0.00144052i	−1.00000		0.000720261i	$0.999771\pi$
$828$	−7.46964			−0.259588
$829$	−3.51493			−0.122079			−0.0610393	−	0.998135i	$-0.519441\pi$
$829$	−3.51493			−0.122079			−0.0610393	+	0.998135i	$0.519441\pi$
$830$			41.6130i			1.44441i
$831$	−9.05583	+	15.6852i	−0.314143	+	0.544112i
$832$	−0.313194	−	3.59192i	−0.0108581	−	0.124528i
$833$	8.54267	−	39.2132i	0.295986	−	1.35866i
$834$	15.3231	+	8.84682i	0.530597	+	0.306340i
$835$	−2.97376	−	5.15070i	−0.102911	−	0.178247i
$836$	11.1747	−	19.3551i	0.386483	−	0.669409i
$837$	−6.21147	+	3.58619i	−0.214700	+	0.123957i
$838$			8.32432i			0.287559i
$839$	−1.59236	+	0.919352i	−0.0549745	+	0.0317395i	−0.527235	−	0.849719i	$-0.676771\pi$
$839$	−1.59236	+	0.919352i	−0.0549745	+	0.0317395i	0.472261	+	0.881459i	$0.343438\pi$
$840$	2.57949	−	6.66932i	0.0890010	−	0.230113i
$841$	−20.4523	−	35.4243i	−0.705250	−	1.22153i
$842$	−17.9902	−	31.1600i	−0.619984	−	1.07384i
$843$			11.0176i			0.379465i
$844$	3.24329	+	5.61754i	0.111639	+	0.193364i
$845$	−33.0096	−	12.0364i	−1.13557	−	0.414065i
$846$	−8.59312			−0.295438
$847$	−39.1662	+	6.10177i	−1.34577	+	0.209659i
$848$	3.60339	−	6.24125i	0.123741	−	0.214325i
$849$	13.4936			0.463101
$850$	−11.4437	+	6.60703i	−0.392516	+	0.226619i
$851$	−43.8210	−	25.3001i	−1.50216	−	0.867275i
$852$			0.914994i			0.0313472i
$853$			3.88953i			0.133175i	0.997781	+	0.0665875i	$0.0212111\pi$
$853$			3.88953i			0.133175i	−0.997781	+	0.0665875i	$0.978789\pi$
$854$	9.58153	−	7.71891i	0.327873	−	0.264136i
$855$	−5.92518	+	10.2627i	−0.202637	+	0.350978i
$856$	9.15192	−	5.28386i	0.312806	−	0.180599i
$857$	3.14373	+	5.44510i	0.107388	+	0.186001i	0.914711	−	0.404108i	$-0.132418\pi$
$857$	3.14373	+	5.44510i	0.107388	+	0.186001i	−0.807323	+	0.590109i	$0.799085\pi$
$858$	15.0578	−	10.5370i	0.514065	−	0.359728i
$859$	−3.28045	+	5.68190i	−0.111927	+	0.193864i	−0.916547	−	0.399926i	$-0.869036\pi$
$859$	−3.28045	+	5.68190i	−0.111927	+	0.193864i	0.804620	+	0.593790i	$0.202369\pi$
$860$	14.5445	+	8.39725i	0.495962	+	0.286344i
$861$	−9.39320	−	3.63301i	−0.320119	−	0.123813i
$862$	3.10461	+	5.37734i	0.105743	+	0.183153i
$863$	11.3137	+	6.53197i	0.385123	+	0.222351i	0.680045	−	0.733170i	$-0.261960\pi$
$863$	11.3137	+	6.53197i	0.385123	+	0.222351i	−0.294922	+	0.955521i	$0.595294\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	50.2688	+	29.0227i	1.70919	+	0.986802i
$866$	6.90357	+	3.98578i	0.234593	+	0.135442i
$867$	7.93524	+	13.7442i	0.269495	+	0.466779i
$868$	−2.92112	−	18.7502i	−0.0991492	−	0.636422i
$869$	33.6676	+	19.4380i	1.14210	+	0.659389i
$870$	−11.2987	+	19.5698i	−0.383060	+	0.663480i
$871$	−21.7867	+	1.89967i	−0.738213	+	0.0643677i
$872$	1.89214	+	3.27729i	0.0640761	+	0.110983i
$873$	−8.20116	+	4.73494i	−0.277567	+	0.160254i
$874$	−16.3756	+	28.3634i	−0.553913	+	0.959406i
$875$	−2.96675	−	19.0431i	−0.100294	−	0.643773i
$876$		−	6.85849i		−	0.231727i
$877$			4.94827i			0.167091i	0.996504	+	0.0835456i	$0.0266244\pi$
$877$			4.94827i			0.167091i	−0.996504	+	0.0835456i	$0.973376\pi$
$878$	12.2649	+	7.08113i	0.413920	+	0.238977i
$879$	−4.13569	+	2.38774i	−0.139494	+	0.0805366i
$880$	−13.7766			−0.464408
$881$	−5.49446	+	9.51669i	−0.185113	+	0.320625i	−0.943615	−	0.331046i	$-0.892599\pi$
$881$	−5.49446	+	9.51669i	−0.185113	+	0.320625i	0.758501	+	0.651671i	$0.225932\pi$
$882$	−4.71018	+	5.17824i	−0.158600	+	0.174361i
$883$	43.0985			1.45038			0.725190	−	0.688549i	$-0.241752\pi$
$883$	43.0985			1.45038			0.725190	+	0.688549i	$0.241752\pi$
$884$	16.9367	−	11.8518i	0.569642	−	0.398619i
$885$	8.75630	+	15.1664i	0.294340	+	0.509811i
$886$		−	27.5835i		−	0.926687i
$887$	21.1488	+	36.6307i	0.710106	+	1.22994i	0.964817	+	0.262923i	$0.0846864\pi$
$887$	21.1488	+	36.6307i	0.710106	+	1.22994i	−0.254711	+	0.967017i	$0.581980\pi$
$888$	−3.38705	−	5.86654i	−0.113662	−	0.196868i
$889$	5.94498	−	15.3708i	0.199388	−	0.515521i
$890$	24.3011	−	14.0303i	0.814575	−	0.470295i
$891$		−	5.09726i		−	0.170764i
$892$	−22.5859	+	13.0400i	−0.756233	+	0.436611i
$893$	−18.8386	+	32.6294i	−0.630410	+	1.09190i
$894$	11.6457	+	20.1710i	0.389491	+	0.674619i
$895$	−43.7190	−	25.2412i	−1.46136	−	0.843719i
$896$	2.06034	−	1.65982i	0.0688312	−	0.0554506i
$897$	−22.0661	+	15.4412i	−0.736765	+	0.515567i
$898$	−1.46199	+	2.53224i	−0.0487873	+	0.0845021i
$899$			59.9675i			2.00003i
$900$	2.30480			0.0768267
$901$	41.3184			1.37652
$902$			19.4032i			0.646055i
$903$	−10.3139	−	12.8027i	−0.343225	−	0.426048i
$904$	−1.47154	+	0.849593i	−0.0489426	+	0.0282570i
$905$	4.61180	+	2.66262i	0.153301	+	0.0885086i
$906$	−9.15737	+	15.8610i	−0.304233	+	0.526947i
$907$	33.1378			1.10032			0.550162	−	0.835058i	$-0.314566\pi$
$907$	33.1378			1.10032			0.550162	+	0.835058i	$0.314566\pi$
$908$	−10.1088	+	5.83634i	−0.335474	+	0.193686i
$909$	−3.72210			−0.123454
$910$	−6.16671	−	25.0341i	−0.204424	−	0.829874i
$911$	−26.0908			−0.864426			−0.432213	−	0.901772i	$-0.642267\pi$
$911$	−26.0908			−0.864426			−0.432213	+	0.901772i	$0.642267\pi$
$912$	−3.79715	+	2.19229i	−0.125736	+	0.0725939i
$913$	−78.4804			−2.59732
$914$	10.4718	−	18.1377i	0.346377	−	0.599942i
$915$	10.8850	+	6.28449i	0.359849	+	0.207759i
$916$	10.4614	−	6.03988i	0.345654	−	0.199563i
$917$	−0.684243	+	1.76912i	−0.0225957	+	0.0584215i
$918$		−	5.73328i		−	0.189226i
$919$	−46.2008			−1.52403			−0.762013	−	0.647562i	$-0.775789\pi$
$919$	−46.2008			−1.52403			−0.762013	+	0.647562i	$0.775789\pi$
$920$	20.1885			0.665595
$921$		−	6.26422i		−	0.206413i
$922$	−9.20229	+	15.9388i	−0.303061	+	0.524918i
$923$	1.89147	+	2.70298i	0.0622585	+	0.0889698i
$924$	12.5781	+	4.86482i	0.413788	+	0.160041i
$925$	13.5212	+	7.80648i	0.444575	+	0.256675i
$926$	14.4317	+	24.9964i	0.474254	+	0.821432i
$927$	4.55465	−	7.88888i	0.149594	−	0.259105i
$928$	−7.24074	+	4.18045i	−0.237689	+	0.137230i
$929$		−	3.17315i		−	0.104108i	−0.998644	−	0.0520539i	$-0.983423\pi$
$929$		−	3.17315i		−	0.104108i	0.998644	−	0.0520539i	$-0.0165768\pi$
$930$	16.7880	−	9.69254i	0.550499	−	0.317831i
$931$	9.33651	+	29.2375i	0.305992	+	0.958220i
$932$	4.65865	+	8.06902i	0.152599	+	0.264310i
$933$	−2.99213	−	5.18252i	−0.0979580	−	0.169668i
$934$		−	33.7544i		−	1.10448i
$935$	−39.4924	−	68.4029i	−1.29154	−	2.23701i
$936$	−3.59192	+	0.313194i	−0.117406	+	0.0102371i
$937$	36.3959			1.18900			0.594501	−	0.804095i	$-0.297350\pi$
$937$	36.3959			1.18900			0.594501	+	0.804095i	$0.297350\pi$
$938$	−10.0675	−	12.4969i	−0.328717	−	0.408039i
$939$	−14.3286	+	24.8179i	−0.467597	+	0.809902i
$940$	23.2250			0.757515
$941$	−25.2928	+	14.6028i	−0.824521	+	0.476037i	−0.851973	−	0.523586i	$-0.824594\pi$
$941$	−25.2928	+	14.6028i	−0.824521	+	0.476037i	0.0274523	+	0.999623i	$0.491261\pi$
$942$	−3.32164	−	1.91775i	−0.108225	−	0.0624837i
$943$		−	28.4339i		−	0.925935i
$944$			6.47957i			0.210892i
$945$	−6.66932	−	2.57949i	−0.216953	−	0.0839109i
$946$	−15.8369	+	27.4303i	−0.514901	+	0.891835i
$947$	−7.10843	+	4.10406i	−0.230993	+	0.133364i	−0.611030	−	0.791607i	$-0.709245\pi$
$947$	−7.10843	+	4.10406i	−0.230993	+	0.133364i	0.380037	+	0.924971i	$0.375911\pi$
$948$	−3.81342	−	6.60504i	−0.123854	−	0.214522i
$949$	−14.1778	−	20.2607i	−0.460232	−	0.657689i
$950$	5.05279	−	8.75168i	0.163934	−	0.283942i
$951$	22.2694	+	12.8572i	0.722134	+	0.416924i
$952$	14.1475	+	5.47184i	0.458524	+	0.177343i
$953$	−22.9551	−	39.7595i	−0.743590	−	1.28794i	−0.950851	−	0.309649i	$-0.899788\pi$
$953$	−22.9551	−	39.7595i	−0.743590	−	1.28794i	0.207261	−	0.978286i	$-0.433545\pi$
$954$	−6.24125	−	3.60339i	−0.202068	−	0.116664i
$955$	8.68253	+	5.01286i	0.280960	+	0.162212i
$956$	14.5612	+	8.40693i	0.470944	+	0.271900i
$957$	−36.9079	−	21.3088i	−1.19306	−	0.688816i
$958$	−8.71070	−	15.0874i	−0.281430	−	0.487451i
$959$	−24.8137	−	9.59720i	−0.801276	−	0.309910i
$960$	2.34064	+	1.35137i	0.0755439	+	0.0436153i
$961$	10.2215	−	17.7042i	0.329727	−	0.571105i
$962$	−22.1330	−	10.3287i	−0.713596	−	0.333009i
$963$	−5.28386	−	9.15192i	−0.170270	−	0.294917i
$964$	−19.3566	+	11.1756i	−0.623435	+	0.359940i
$965$	−4.02708	+	6.97511i	−0.129636	+	0.224537i
$966$	−18.4322	−	7.12903i	−0.593046	−	0.229373i
$967$			27.1219i			0.872182i	0.899903	+	0.436091i	$0.143637\pi$
$967$			27.1219i			0.872182i	−0.899903	+	0.436091i	$0.856363\pi$
$968$		−	14.9820i		−	0.481540i
$969$	−21.7701	−	12.5690i	−0.699358	−	0.403774i
$970$	22.1656	−	12.7973i	0.711695	−	0.410897i
$971$	−45.4545			−1.45871			−0.729353	−	0.684138i	$-0.760179\pi$
$971$	−45.4545			−1.45871			−0.729353	+	0.684138i	$0.760179\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	29.3682	+	36.4549i	0.941501	+	1.16869i
$974$	38.2660			1.22612
$975$	6.80861	−	4.76447i	0.218050	−	0.152585i
$976$	2.32523	+	4.02741i	0.0744287	+	0.128914i
$977$		−	20.5624i		−	0.657849i	−0.944356	−	0.328924i	$-0.893314\pi$
$977$		−	20.5624i		−	0.657849i	0.944356	−	0.328924i	$-0.106686\pi$
$978$	−5.21359	−	9.03020i	−0.166712	−	0.288754i
$979$	26.4605	+	45.8309i	0.845681	+	1.46476i
$980$	12.7304	−	13.9954i	0.406657	−	0.447068i
$981$	3.27729	−	1.89214i	0.104636	−	0.0604115i
$982$		−	36.7765i		−	1.17359i
$983$	−13.1471	+	7.59050i	−0.419329	+	0.242099i	−0.694790	−	0.719213i	$-0.744503\pi$
$983$	−13.1471	+	7.59050i	−0.419329	+	0.242099i	0.275461	+	0.961312i	$0.411169\pi$
$984$	1.90330	−	3.29661i	0.0606749	−	0.105092i
$985$	−20.1173	−	34.8442i	−0.640990	−	1.11023i
$986$	−41.5132	−	23.9677i	−1.32205	−	0.763286i
$987$	−21.2045	−	8.20127i	−0.674947	−	0.261049i
$988$	−6.68528	+	14.3257i	−0.212687	+	0.455761i
$989$	23.2077	−	40.1970i	0.737963	−	1.27819i
$990$			13.7766i			0.437848i
$991$	4.00946			0.127365			0.0636824	−	0.997970i	$-0.479716\pi$
$991$	4.00946			0.127365			0.0636824	+	0.997970i	$0.479716\pi$
$992$	7.17238			0.227723
$993$		−	0.880100i		−	0.0279291i
$994$	−0.873270	+	2.25785i	−0.0276984	+	0.0716147i
$995$	6.23611	−	3.60042i	0.197698	−	0.114141i
$996$	13.3339	+	7.69830i	0.422499	+	0.243930i
$997$	17.1948	−	29.7823i	0.544565	−	0.943214i	−0.454070	−	0.890966i	$-0.650028\pi$
$997$	17.1948	−	29.7823i	0.544565	−	0.943214i	0.998634	−	0.0522474i	$-0.0166384\pi$
$998$	30.1028			0.952887
$999$	−5.86654	+	3.38705i	−0.185609	+	0.107162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.a.121.4	✓	16
3.2	odd	2		1638.2.cr.a.667.5		16
7.4	even	3		546.2.bm.a.277.1	yes	16
13.10	even	6		546.2.bm.a.205.5	yes	16
21.11	odd	6		1638.2.dt.a.1369.8		16
39.23	odd	6		1638.2.dt.a.1297.4		16
91.88	even	6	inner	546.2.bd.a.361.4	yes	16
273.179	odd	6		1638.2.cr.a.361.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.4	✓	16	1.1	even	1	trivial
546.2.bd.a.361.4	yes	16	91.88	even	6	inner
546.2.bm.a.205.5	yes	16	13.10	even	6
546.2.bm.a.277.1	yes	16	7.4	even	3
1638.2.cr.a.361.5		16	273.179	odd	6
1638.2.cr.a.667.5		16	3.2	odd	2
1638.2.dt.a.1297.4		16	39.23	odd	6
1638.2.dt.a.1369.8		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(2.34064 + 1.35137i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.61422 - 0.407273i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -2.70274 q^{10} -5.09726i q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.313194 + 3.59192i) q^{13} +(-2.06034 + 1.65982i) q^{14} +(-2.34064 - 1.35137i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.86664 - 4.96516i) q^{17} +(-0.866025 + 0.500000i) q^{18} +4.38458i q^{19} +(2.34064 - 1.35137i) q^{20} +(-2.61422 + 0.407273i) q^{21} +(2.54863 + 4.41435i) q^{22} +(-3.73482 - 6.46890i) q^{23} -1.00000i q^{24} +(1.15240 + 1.99602i) q^{25} +(-2.06720 - 2.95410i) q^{26} -1.00000 q^{27} +(0.954400 - 2.46761i) q^{28} +(-4.18045 + 7.24074i) q^{29} +2.70274 q^{30} +(6.21147 - 3.58619i) q^{31} +(0.866025 + 0.500000i) q^{32} +5.09726i q^{33} +5.73328i q^{34} +(6.66932 + 2.57949i) q^{35} +(0.500000 - 0.866025i) q^{36} +(5.86654 - 3.38705i) q^{37} +(-2.19229 - 3.79715i) q^{38} +(-0.313194 - 3.59192i) q^{39} +(-1.35137 + 2.34064i) q^{40} +(3.29661 + 1.90330i) q^{41} +(2.06034 - 1.65982i) q^{42} +(3.10694 + 5.38138i) q^{43} +(-4.41435 - 2.54863i) q^{44} +(2.34064 + 1.35137i) q^{45} +(6.46890 + 3.73482i) q^{46} +(7.44186 + 4.29656i) q^{47} +(0.500000 + 0.866025i) q^{48} +(6.66826 - 2.12940i) q^{49} +(-1.99602 - 1.15240i) q^{50} +(-2.86664 + 4.96516i) q^{51} +(3.26729 + 1.52473i) q^{52} +(3.60339 + 6.24125i) q^{53} +(0.866025 - 0.500000i) q^{54} +(6.88828 - 11.9308i) q^{55} +(0.407273 + 2.61422i) q^{56} -4.38458i q^{57} -8.36089i q^{58} +(-5.61147 - 3.23979i) q^{59} +(-2.34064 + 1.35137i) q^{60} -4.65046 q^{61} +(-3.58619 + 6.21147i) q^{62} +(2.61422 - 0.407273i) q^{63} -1.00000 q^{64} +(-4.12094 + 8.83064i) q^{65} +(-2.54863 - 4.41435i) q^{66} +6.06546i q^{67} +(-2.86664 - 4.96516i) q^{68} +(3.73482 + 6.46890i) q^{69} +(-7.06555 + 1.10075i) q^{70} +(0.792408 - 0.457497i) q^{71} +1.00000i q^{72} +(-5.93963 + 3.42924i) q^{73} +(-3.38705 + 5.86654i) q^{74} +(-1.15240 - 1.99602i) q^{75} +(3.79715 + 2.19229i) q^{76} +(-2.07597 - 13.3253i) q^{77} +(2.06720 + 2.95410i) q^{78} +(-3.81342 + 6.60504i) q^{79} -2.70274i q^{80} +1.00000 q^{81} -3.80659 q^{82} -15.3966i q^{83} +(-0.954400 + 2.46761i) q^{84} +(13.4195 - 7.74778i) q^{85} +(-5.38138 - 3.10694i) q^{86} +(4.18045 - 7.24074i) q^{87} +5.09726 q^{88} +(-8.99129 + 5.19112i) q^{89} -2.70274 q^{90} +(2.28165 + 9.26251i) q^{91} -7.46964 q^{92} +(-6.21147 + 3.58619i) q^{93} -8.59312 q^{94} +(-5.92518 + 10.2627i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(-8.20116 + 4.73494i) q^{97} +(-4.71018 + 5.17824i) q^{98} -5.09726i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31}+ \cdots - 12 q^{98}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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