LMFDB - Embedded newform 546.2.bm.a.205.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,2,Mod(205,546)] 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("546.205"); 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, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (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			205.5
Root			$1.45057i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.a.277.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.34064 - 1.35137i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.65982 + 2.06034i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.35137 - 2.34064i) q^{10} +(-4.41435 - 2.54863i) 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} +1.00000 q^{16} -5.73328 q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.79715 + 2.19229i) q^{19} +(2.34064 + 1.35137i) q^{20} +(2.61422 - 0.407273i) q^{21} +(2.54863 - 4.41435i) q^{22} +7.46964 q^{23} +(-0.866025 - 0.500000i) q^{24} +(1.15240 + 1.99602i) q^{25} +(3.59192 + 0.313194i) q^{26} -1.00000 q^{27} +(-1.65982 - 2.06034i) q^{28} +(-4.18045 - 7.24074i) q^{29} +(-1.35137 - 2.34064i) q^{30} +(-6.21147 + 3.58619i) q^{31} +1.00000i q^{32} +(-4.41435 + 2.54863i) q^{33} -5.73328i q^{34} +(-1.10075 - 7.06555i) q^{35} +(0.500000 + 0.866025i) q^{36} -6.77410i q^{37} +(-2.19229 - 3.79715i) q^{38} +(-2.95410 - 2.06720i) q^{39} +(-1.35137 + 2.34064i) q^{40} +(3.29661 - 1.90330i) q^{41} +(0.407273 + 2.61422i) q^{42} +(3.10694 - 5.38138i) q^{43} +(4.41435 + 2.54863i) q^{44} +2.70274i q^{45} +7.46964i q^{46} +(-7.44186 - 4.29656i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.49001 + 6.83958i) q^{49} +(-1.99602 + 1.15240i) q^{50} +(-2.86664 + 4.96516i) q^{51} +(-0.313194 + 3.59192i) q^{52} +(3.60339 + 6.24125i) q^{53} -1.00000i q^{54} +(6.88828 + 11.9308i) q^{55} +(2.06034 - 1.65982i) q^{56} +4.38458i q^{57} +(7.24074 - 4.18045i) q^{58} -6.47957i q^{59} +(2.34064 - 1.35137i) q^{60} +(2.32523 + 4.02741i) q^{61} +(-3.58619 - 6.21147i) q^{62} +(0.954400 - 2.46761i) q^{63} -1.00000 q^{64} +(-5.58709 + 7.98416i) q^{65} +(-2.54863 - 4.41435i) q^{66} +(5.25284 + 3.03273i) q^{67} +5.73328 q^{68} +(3.73482 - 6.46890i) q^{69} +(7.06555 - 1.10075i) q^{70} +(0.792408 + 0.457497i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.93963 - 3.42924i) q^{73} +6.77410 q^{74} +2.30480 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} +(-2.34064 - 1.35137i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.90330 + 3.29661i) q^{82} +15.3966i q^{83} +(-2.61422 + 0.407273i) q^{84} +(13.4195 + 7.74778i) q^{85} +(5.38138 + 3.10694i) q^{86} -8.36089 q^{87} +(-2.54863 + 4.41435i) q^{88} +10.3822i q^{89} -2.70274 q^{90} +(7.92043 - 5.31665i) q^{91} -7.46964 q^{92} +7.17238i q^{93} +(4.29656 - 7.44186i) q^{94} +11.8504 q^{95} +(0.866025 + 0.500000i) q^{96} +(-8.20116 - 4.73494i) q^{97} +(-6.83958 - 1.49001i) q^{98} +5.09726i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29}+ \cdots - 60 q^{98}+O(q^{100}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	−2.34064	−	1.35137i	−1.04677	−	0.604351i	−0.125024	−	0.992154i	$-0.539901\pi$
$5$	−2.34064	−	1.35137i	−1.04677	−	0.604351i	−0.921742	+	0.387803i	$0.873234\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	1.65982	+	2.06034i	0.627352	+	0.778736i
$7$	1.65982	+	2.06034i	0.627352	+	0.778736i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.35137	−	2.34064i	0.427341	−	0.740176i
$11$	−4.41435	−	2.54863i	−1.33098	−	0.768440i	−0.345528	−	0.938408i	$-0.612300\pi$
$11$	−4.41435	−	2.54863i	−1.33098	−	0.768440i	−0.985450	+	0.169968i	$0.945633\pi$
$12$	−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
$16$	1.00000			0.250000
$17$	−5.73328			−1.39052			−0.695262	−	0.718756i	$-0.744712\pi$
$17$	−5.73328			−1.39052			−0.695262	+	0.718756i	$0.744712\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−3.79715	+	2.19229i	−0.871127	+	0.502945i	−0.867723	−	0.497049i	$-0.834417\pi$
$19$	−3.79715	+	2.19229i	−0.871127	+	0.502945i	−0.00340438	+	0.999994i	$0.501084\pi$
$20$	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
$23$	7.46964			1.55753			0.778764	−	0.627317i	$-0.215847\pi$
$23$	7.46964			1.55753			0.778764	+	0.627317i	$0.215847\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	1.15240	+	1.99602i	0.230480	+	0.399203i
$26$	3.59192	+	0.313194i	0.704434	+	0.0614224i
$27$	−1.00000			−0.192450
$28$	−1.65982	−	2.06034i	−0.313676	−	0.389368i
$29$	−4.18045	−	7.24074i	−0.776289	−	1.34457i	−0.934067	−	0.357098i	$-0.883766\pi$
$29$	−4.18045	−	7.24074i	−0.776289	−	1.34457i	0.157778	−	0.987475i	$-0.449567\pi$
$30$	−1.35137	−	2.34064i	−0.246725	−	0.427341i
$31$	−6.21147	+	3.58619i	−1.11561	+	0.644099i	−0.940277	−	0.340410i	$-0.889434\pi$
$31$	−6.21147	+	3.58619i	−1.11561	+	0.644099i	−0.175335	+	0.984509i	$0.556101\pi$
$32$			1.00000i			0.176777i
$33$	−4.41435	+	2.54863i	−0.768440	+	0.443659i
$34$		−	5.73328i		−	0.983249i
$35$	−1.10075	−	7.06555i	−0.186061	−	1.19430i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$		−	6.77410i		−	1.11366i	−0.830628	−	0.556828i	$-0.812018\pi$
$37$		−	6.77410i		−	1.11366i	0.830628	−	0.556828i	$-0.187982\pi$
$38$	−2.19229	−	3.79715i	−0.355636	−	0.615980i
$39$	−2.95410	−	2.06720i	−0.473034	−	0.331016i
$40$	−1.35137	+	2.34064i	−0.213670	+	0.370088i
$41$	3.29661	−	1.90330i	0.514843	−	0.297245i	−0.219979	−	0.975505i	$-0.570599\pi$
$41$	3.29661	−	1.90330i	0.514843	−	0.297245i	0.734822	+	0.678260i	$0.237266\pi$
$42$	0.407273	+	2.61422i	0.0628436	+	0.403382i
$43$	3.10694	−	5.38138i	0.473804	−	0.820653i	−0.525746	−	0.850642i	$-0.676214\pi$
$43$	3.10694	−	5.38138i	0.473804	−	0.820653i	0.999550	+	0.0299887i	$0.00954714\pi$
$44$	4.41435	+	2.54863i	0.665489	+	0.384220i
$45$			2.70274i			0.402901i
$46$			7.46964i			1.10134i
$47$	−7.44186	−	4.29656i	−1.08551	−	0.626718i	−0.153130	−	0.988206i	$-0.548935\pi$
$47$	−7.44186	−	4.29656i	−1.08551	−	0.626718i	−0.932377	+	0.361488i	$0.882269\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−1.49001	+	6.83958i	−0.212859	+	0.977083i
$50$	−1.99602	+	1.15240i	−0.282279	+	0.162974i
$51$	−2.86664	+	4.96516i	−0.401410	+	0.695262i
$52$	−0.313194	+	3.59192i	−0.0434322	+	0.498110i
$53$	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	$0.668515\pi$
$54$		−	1.00000i		−	0.136083i
$55$	6.88828	+	11.9308i	0.928815	+	1.60875i
$56$	2.06034	−	1.65982i	0.275325	−	0.221802i
$57$			4.38458i			0.580751i
$58$	7.24074	−	4.18045i	0.950756	−	0.548919i
$59$		−	6.47957i		−	0.843569i	−0.906696	−	0.421784i	$-0.861404\pi$
$59$		−	6.47957i		−	0.843569i	0.906696	−	0.421784i	$-0.138596\pi$
$60$	2.34064	−	1.35137i	0.302175	−	0.174461i
$61$	2.32523	+	4.02741i	0.297715	+	0.515657i	0.975613	−	0.219499i	$-0.0704422\pi$
$61$	2.32523	+	4.02741i	0.297715	+	0.515657i	−0.677898	+	0.735156i	$0.737109\pi$
$62$	−3.58619	−	6.21147i	−0.455447	−	0.788857i
$63$	0.954400	−	2.46761i	0.120243	−	0.310890i
$64$	−1.00000			−0.125000
$65$	−5.58709	+	7.98416i	−0.692993	+	0.990313i
$66$	−2.54863	−	4.41435i	−0.313714	−	0.543369i
$67$	5.25284	+	3.03273i	0.641736	+	0.370507i	0.785283	−	0.619137i	$-0.212517\pi$
$67$	5.25284	+	3.03273i	0.641736	+	0.370507i	−0.143547	+	0.989644i	$0.545851\pi$
$68$	5.73328			0.695262
$69$	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	0.546283	−	0.837601i	$-0.316042\pi$
$71$	0.792408	+	0.457497i	0.0940415	+	0.0542949i	−0.452242	+	0.891895i	$0.649376\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	5.93963	−	3.42924i	0.695181	−	0.401363i	−0.110369	−	0.993891i	$-0.535203\pi$
$73$	5.93963	−	3.42924i	0.695181	−	0.401363i	0.805550	+	0.592528i	$0.201870\pi$
$74$	6.77410			0.787473
$75$	2.30480			0.266135
$76$	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	$0.307816\pi$
$80$	−2.34064	−	1.35137i	−0.261692	−	0.151088i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.90330	+	3.29661i	0.210184	+	0.364049i
$83$			15.3966i			1.69000i	0.534769	+	0.844999i	$0.320399\pi$
$83$			15.3966i			1.69000i	−0.534769	+	0.844999i	$0.679601\pi$
$84$	−2.61422	+	0.407273i	−0.285234	+	0.0444371i
$85$	13.4195	+	7.74778i	1.45555	+	0.840365i
$86$	5.38138	+	3.10694i	0.580289	+	0.335030i
$87$	−8.36089			−0.896382
$88$	−2.54863	+	4.41435i	−0.271685	+	0.470572i
$89$			10.3822i			1.10052i	0.834995	+	0.550258i	$0.185471\pi$
$89$			10.3822i			1.10052i	−0.834995	+	0.550258i	$0.814529\pi$
$90$	−2.70274			−0.284894
$91$	7.92043	−	5.31665i	0.830287	−	0.557336i
$92$	−7.46964			−0.778764
$93$			7.17238i			0.743742i
$94$	4.29656	−	7.44186i	0.443156	−	0.767569i
$95$	11.8504			1.21582
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−8.20116	−	4.73494i	−0.832702	−	0.480761i	0.0220749	−	0.999756i	$-0.492973\pi$
$97$	−8.20116	−	4.73494i	−0.832702	−	0.480761i	−0.854777	+	0.518996i	$0.826306\pi$
$98$	−6.83958	−	1.49001i	−0.690902	−	0.150514i
$99$			5.09726i			0.512293i
$100$	−1.15240	−	1.99602i	−0.115240	−	0.199602i
$101$	1.86105	−	3.22344i	0.185182	−	0.320744i	−0.758456	−	0.651724i	$-0.774046\pi$
$101$	1.86105	−	3.22344i	0.185182	−	0.320744i	0.943638	+	0.330980i	$0.107379\pi$
$102$	−4.96516	−	2.86664i	−0.491625	−	0.283840i
$103$	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
$107$	10.5677			1.02162			0.510810	−	0.859693i	$-0.329345\pi$
$107$	10.5677			1.02162			0.510810	+	0.859693i	$0.329345\pi$
$108$	1.00000			0.0962250
$109$	−3.27729	+	1.89214i	−0.313907	+	0.181235i	−0.648674	−	0.761067i	$-0.724676\pi$
$109$	−3.27729	+	1.89214i	−0.313907	+	0.181235i	0.334766	+	0.942301i	$0.391343\pi$
$110$	−11.9308	+	6.88828i	−1.13756	+	0.656771i
$111$	−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	−0.823294	−	0.567616i	$-0.807866\pi$
$113$	0.849593	−	1.47154i	0.0799230	−	0.138431i	0.903217	+	0.429185i	$0.141199\pi$
$114$	−4.38458			−0.410653
$115$	−17.4838	−	10.0943i	−1.63037	−	0.941294i
$116$	4.18045	+	7.24074i	0.388145	+	0.672286i
$117$	−3.26729	+	1.52473i	−0.302061	+	0.140961i
$118$	6.47957			0.596493
$119$	−9.51619	−	11.8125i	−0.872348	−	1.08285i
$120$	1.35137	+	2.34064i	0.123363	+	0.213670i
$121$	7.49101	+	12.9748i	0.681001	+	1.17953i
$122$	−4.02741	+	2.32523i	−0.364625	+	0.210516i
$123$		−	3.80659i		−	0.343229i
$124$	6.21147	−	3.58619i	0.557806	−	0.322050i
$125$			7.28442i			0.651538i
$126$	2.46761	+	0.954400i	0.219833	+	0.0850247i
$127$	3.11451	+	5.39450i	0.276368	+	0.478684i	0.970479	−	0.241184i	$-0.0775357\pi$
$127$	3.11451	+	5.39450i	0.276368	+	0.478684i	−0.694111	+	0.719868i	$0.744202\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−3.10694	−	5.38138i	−0.273551	−	0.473804i
$130$	−7.98416	−	5.58709i	−0.700257	−	0.490020i
$131$	−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
$133$	−10.8194	−	4.18464i	−0.938165	−	0.362854i
$134$	−3.03273	+	5.25284i	−0.261988	+	0.453776i
$135$	2.34064	+	1.35137i	0.201450	+	0.116307i
$136$			5.73328i			0.491625i
$137$		−	10.0557i		−	0.859120i	−0.903038	−	0.429560i	$-0.858669\pi$
$137$		−	10.0557i		−	0.859120i	0.903038	−	0.429560i	$-0.141331\pi$
$138$	6.46890	+	3.73482i	0.550670	+	0.317929i
$139$	8.84682	−	15.3231i	0.750377	−	1.29969i	−0.197263	−	0.980351i	$-0.563205\pi$
$139$	8.84682	−	15.3231i	0.750377	−	1.29969i	0.947640	−	0.319341i	$-0.103462\pi$
$140$	1.10075	+	7.06555i	0.0930306	+	0.597148i
$141$	−7.44186	+	4.29656i	−0.626718	+	0.361836i
$142$	−0.457497	+	0.792408i	−0.0383923	+	0.0664974i
$143$	−10.5370	+	15.0578i	−0.881150	+	1.25920i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$			22.5973i			1.87660i
$146$	3.42924	+	5.93963i	0.283806	+	0.491567i
$147$	5.17824	+	4.71018i	0.427094	+	0.388489i
$148$			6.77410i			0.556828i
$149$	−20.1710	+	11.6457i	−1.65247	+	0.954055i	−0.676420	+	0.736516i	$0.736469\pi$
$149$	−20.1710	+	11.6457i	−1.65247	+	0.954055i	−0.976052	+	0.217538i	$0.930197\pi$
$150$			2.30480i			0.188186i
$151$	15.8610	−	9.15737i	1.29075	−	0.745216i	0.311964	−	0.950094i	$-0.399013\pi$
$151$	15.8610	−	9.15737i	1.29075	−	0.745216i	0.978788	+	0.204878i	$0.0656798\pi$
$152$	2.19229	+	3.79715i	0.177818	+	0.307990i
$153$	2.86664	+	4.96516i	0.231754	+	0.401410i
$154$	13.3253	−	2.07597i	1.07379	−	0.167287i
$155$	19.3851			1.55705
$156$	2.95410	+	2.06720i	0.236517	+	0.165508i
$157$	−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	$0.882244\pi$
$158$	−6.60504	−	3.81342i	−0.525469	−	0.303380i
$159$	7.20677			0.571534
$160$	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
$163$	9.03020	−	5.21359i	0.707300	−	0.408360i	−0.102761	−	0.994706i	$-0.532768\pi$
$163$	9.03020	−	5.21359i	0.707300	−	0.408360i	0.810061	+	0.586346i	$0.199434\pi$
$164$	−3.29661	+	1.90330i	−0.257422	+	0.148622i
$165$	13.7766			1.07250
$166$	−15.3966			−1.19501
$167$	−1.90573	+	1.10027i	−0.147470	+	0.0851418i	−0.571919	−	0.820310i	$-0.693801\pi$
$167$	−1.90573	+	1.10027i	−0.147470	+	0.0851418i	0.424449	+	0.905452i	$0.360468\pi$
$168$	−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
$171$	3.79715	+	2.19229i	0.290376	+	0.167648i
$172$	−3.10694	+	5.38138i	−0.236902	+	0.410326i
$173$	−10.7383	−	18.5992i	−0.816415	−	1.41407i	−0.908308	−	0.418303i	$-0.862625\pi$
$173$	−10.7383	−	18.5992i	−0.816415	−	1.41407i	0.0918931	−	0.995769i	$-0.470708\pi$
$174$		−	8.36089i		−	0.633838i
$175$	−2.19970	+	5.68736i	−0.166282	+	0.429924i
$176$	−4.41435	−	2.54863i	−0.332744	−	0.192110i
$177$	−5.61147	−	3.23979i	−0.421784	−	0.243517i
$178$	−10.3822			−0.778182
$179$	9.33910	−	16.1758i	0.698037	−	1.20904i	−0.271109	−	0.962549i	$-0.587390\pi$
$179$	9.33910	−	16.1758i	0.698037	−	1.20904i	0.969146	−	0.246487i	$-0.0792763\pi$
$180$		−	2.70274i		−	0.201450i
$181$	1.97032			0.146452			0.0732262	−	0.997315i	$-0.476670\pi$
$181$	1.97032			0.146452			0.0732262	+	0.997315i	$0.476670\pi$
$182$	5.31665	+	7.92043i	0.394096	+	0.587102i
$183$	4.65046			0.343772
$184$		−	7.46964i		−	0.550670i
$185$	−9.15432	+	15.8557i	−0.673039	+	1.16574i
$186$	−7.17238			−0.525905
$187$	25.3087	+	14.6120i	1.85076	+	1.06853i
$188$	7.44186	+	4.29656i	0.542753	+	0.313359i
$189$	−1.65982	−	2.06034i	−0.120734	−	0.149868i
$190$			11.8504i			0.859716i
$191$	−1.85473	−	3.21249i	−0.134204	−	0.232448i	0.791089	−	0.611701i	$-0.209514\pi$
$191$	−1.85473	−	3.21249i	−0.134204	−	0.232448i	−0.925293	+	0.379253i	$0.876181\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	2.58076	+	1.49000i	0.185767	+	0.107253i	0.589999	−	0.807404i	$-0.299128\pi$
$193$	2.58076	+	1.49000i	0.185767	+	0.107253i	−0.404232	+	0.914656i	$0.632461\pi$
$194$	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	−0.883165	−	0.469062i	$-0.844592\pi$
$197$	−12.8922	+	7.44330i	−0.918529	+	0.530313i	−0.0353634	+	0.999375i	$0.511259\pi$
$198$	−5.09726			−0.362246
$199$	−2.66427			−0.188865			−0.0944327	−	0.995531i	$-0.530104\pi$
$199$	−2.66427			−0.188865			−0.0944327	+	0.995531i	$0.530104\pi$
$200$	1.99602	−	1.15240i	0.141140	−	0.0814870i
$201$	5.25284	−	3.03273i	0.370507	−	0.213912i
$202$	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
$205$	−10.2882			−0.718561
$206$	7.88888	+	4.55465i	0.549644	+	0.317337i
$207$	−3.73482	−	6.46890i	−0.259588	−	0.449620i
$208$	0.313194	−	3.59192i	0.0217161	−	0.249055i
$209$	22.3493			1.54593
$210$	2.57949	−	6.66932i	0.178002	−	0.460227i
$211$	−3.24329	−	5.61754i	−0.223277	−	0.386728i	0.732524	−	0.680741i	$-0.238342\pi$
$211$	−3.24329	−	5.61754i	−0.223277	−	0.386728i	−0.955801	+	0.294014i	$0.905009\pi$
$212$	−3.60339	−	6.24125i	−0.247482	−	0.428651i
$213$	0.792408	−	0.457497i	0.0542949	−	0.0313472i
$214$			10.5677i			0.722395i
$215$	−14.5445	+	8.39725i	−0.991925	+	0.572688i
$216$			1.00000i			0.0680414i
$217$	−17.6987	−	6.84532i	−1.20146	−	0.464691i
$218$	−1.89214	−	3.27729i	−0.128152	−	0.221966i
$219$		−	6.85849i		−	0.463454i
$220$	−6.88828	−	11.9308i	−0.464408	−	0.804377i
$221$	−1.79563	+	20.5935i	−0.120787	+	1.38527i
$222$	3.38705	−	5.86654i	0.227324	−	0.393737i
$223$	−22.5859	+	13.0400i	−1.51247	+	0.873223i	−0.512572	+	0.858644i	$0.671307\pi$
$223$	−22.5859	+	13.0400i	−1.51247	+	0.873223i	−0.999894	+	0.0145787i	$0.995359\pi$
$224$	−2.06034	+	1.65982i	−0.137662	+	0.110901i
$225$	1.15240	−	1.99602i	0.0768267	−	0.133068i
$226$	1.47154	+	0.849593i	0.0978852	+	0.0565141i
$227$		−	11.6727i		−	0.774743i	−0.921924	−	0.387372i	$-0.873383\pi$
$227$		−	11.6727i		−	0.774743i	0.921924	−	0.387372i	$-0.126617\pi$
$228$		−	4.38458i		−	0.290376i
$229$	−10.4614	−	6.03988i	−0.691307	−	0.399126i	0.112794	−	0.993618i	$-0.464020\pi$
$229$	−10.4614	−	6.03988i	−0.691307	−	0.399126i	−0.804102	+	0.594492i	$0.797353\pi$
$230$	10.0943	−	17.4838i	0.665595	−	1.15284i
$231$	−12.5781	−	4.86482i	−0.827576	−	0.320082i
$232$	−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	$0.265389\pi$
$234$	−1.52473	−	3.26729i	−0.0996745	−	0.213590i
$235$	11.6125	+	20.1134i	0.757515	+	1.31205i
$236$			6.47957i			0.421784i
$237$	3.81342	+	6.60504i	0.247709	+	0.429044i
$238$	11.8125	−	9.51619i	0.765691	−	0.616843i
$239$		−	16.8139i		−	1.08760i	−0.839215	−	0.543799i	$-0.816985\pi$
$239$		−	16.8139i		−	1.08760i	0.839215	−	0.543799i	$-0.183015\pi$
$240$	−2.34064	+	1.35137i	−0.151088	+	0.0872305i
$241$		−	22.3511i		−	1.43976i	−0.694098	−	0.719881i	$-0.744196\pi$
$241$		−	22.3511i		−	1.43976i	0.694098	−	0.719881i	$-0.255804\pi$
$242$	−12.9748	+	7.49101i	−0.834052	+	0.481540i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.32523	−	4.02741i	−0.148857	−	0.257829i
$245$	12.7304	−	13.9954i	0.813315	−	0.894136i
$246$	3.80659			0.242699
$247$	6.68528	+	14.3257i	0.425374	+	0.911522i
$248$	3.58619	+	6.21147i	0.227723	+	0.394429i
$249$	13.3339	+	7.69830i	0.844999	+	0.487860i
$250$	−7.28442			−0.460707
$251$	3.75155	−	6.49788i	0.236796	−	0.410143i	−0.722997	−	0.690851i	$-0.757236\pi$
$251$	3.75155	−	6.49788i	0.236796	−	0.410143i	0.959793	+	0.280708i	$0.0905694\pi$
$252$	−0.954400	+	2.46761i	−0.0601215	+	0.155445i
$253$	−32.9736	−	19.0373i	−2.07304	−	1.19687i
$254$	−5.39450	+	3.11451i	−0.338481	+	0.195422i
$255$	13.4195	−	7.74778i	0.840365	−	0.485185i
$256$	1.00000			0.0625000
$257$	−7.03753			−0.438989			−0.219494	−	0.975614i	$-0.570441\pi$
$257$	−7.03753			−0.438989			−0.219494	+	0.975614i	$0.570441\pi$
$258$	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
$262$	−0.620884	−	0.358468i	−0.0383583	−	0.0221462i
$263$	11.9643	−	20.7228i	0.737750	−	1.27782i	−0.215757	−	0.976447i	$-0.569222\pi$
$263$	11.9643	−	20.7228i	0.737750	−	1.27782i	0.953506	−	0.301373i	$-0.0974449\pi$
$264$	2.54863	+	4.41435i	0.156857	+	0.271685i
$265$		−	19.4780i		−	1.19653i
$266$	4.18464	−	10.8194i	0.256577	−	0.663383i
$267$	8.99129	+	5.19112i	0.550258	+	0.317692i
$268$	−5.25284	−	3.03273i	−0.320868	−	0.185253i
$269$	−1.59963			−0.0975312			−0.0487656	−	0.998810i	$-0.515529\pi$
$269$	−1.59963			−0.0975312			−0.0487656	+	0.998810i	$0.515529\pi$
$270$	−1.35137	+	2.34064i	−0.0822417	+	0.142447i
$271$		−	20.0012i		−	1.21498i	−0.794326	−	0.607492i	$-0.792176\pi$
$271$		−	20.0012i		−	1.21498i	0.794326	−	0.607492i	$-0.207824\pi$
$272$	−5.73328			−0.347631
$273$	−0.644135	−	9.51762i	−0.0389848	−	0.576033i
$274$	10.0557			0.607490
$275$		−	11.7482i		−	0.708441i
$276$	−3.73482	+	6.46890i	−0.224810	+	0.389382i
$277$	−18.1117			−1.08822			−0.544112	−	0.839012i	$-0.683133\pi$
$277$	−18.1117			−1.08822			−0.544112	+	0.839012i	$0.683133\pi$
$278$	15.3231	+	8.84682i	0.919021	+	0.530597i
$279$	6.21147	+	3.58619i	0.371871	+	0.214700i
$280$	−7.06555	+	1.10075i	−0.422247	+	0.0657826i
$281$			11.0176i			0.657253i	0.944460	+	0.328626i	$0.106586\pi$
$281$			11.0176i			0.657253i	−0.944460	+	0.328626i	$0.893414\pi$
$282$	−4.29656	−	7.44186i	−0.255856	−	0.443156i
$283$	6.74682	−	11.6858i	0.401057	−	0.694651i	−0.592797	−	0.805352i	$-0.701976\pi$
$283$	6.74682	−	11.6858i	0.401057	−	0.694651i	0.993854	+	0.110701i	$0.0353096\pi$
$284$	−0.792408	−	0.457497i	−0.0470208	−	0.0271474i
$285$	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
$289$	15.8705			0.933557
$290$	−22.5973			−1.32696
$291$	−8.20116	+	4.73494i	−0.480761	+	0.277567i
$292$	−5.93963	+	3.42924i	−0.347590	+	0.200681i
$293$	4.13569	+	2.38774i	0.241610	+	0.139494i	0.615916	−	0.787811i	$-0.288786\pi$
$293$	4.13569	+	2.38774i	0.241610	+	0.139494i	−0.374307	+	0.927305i	$0.622119\pi$
$294$	−4.71018	+	5.17824i	−0.274703	+	0.302001i
$295$	−8.75630	+	15.1664i	−0.509811	+	0.883019i
$296$	−6.77410			−0.393737
$297$	4.41435	+	2.54863i	0.256147	+	0.147886i
$298$	−11.6457	−	20.1710i	−0.674619	−	1.16847i
$299$	2.33945	−	26.8304i	0.135294	−	1.55164i
$300$	−2.30480			−0.133068
$301$	16.2444	−	2.53075i	0.936314	−	0.145870i
$302$	9.15737	+	15.8610i	0.526947	+	0.912699i
$303$	−1.86105	−	3.22344i	−0.106915	−	0.185182i
$304$	−3.79715	+	2.19229i	−0.217782	+	0.125736i
$305$		−	12.5690i		−	0.719697i
$306$	−4.96516	+	2.86664i	−0.283840	+	0.163875i
$307$		−	6.26422i		−	0.357518i	−0.983893	−	0.178759i	$-0.942792\pi$
$307$		−	6.26422i		−	0.357518i	0.983893	−	0.178759i	$-0.0572082\pi$
$308$	2.07597	+	13.3253i	0.118290	+	0.759281i
$309$	−4.55465	−	7.88888i	−0.259105	−	0.448783i
$310$			19.3851i			1.10100i
$311$	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	$0.779064\pi$
$312$	−2.06720	+	2.95410i	−0.117032	+	0.167243i
$313$	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
$315$	−5.56857	+	4.48605i	−0.313753	+	0.252760i
$316$	3.81342	−	6.60504i	0.214522	−	0.371563i
$317$	22.2694	+	12.8572i	1.25077	+	0.722134i	0.971263	−	0.238009i	$-0.0764949\pi$
$317$	22.2694	+	12.8572i	1.25077	+	0.722134i	0.279509	+	0.960143i	$0.409828\pi$
$318$			7.20677i			0.404136i
$319$			42.6176i			2.38613i
$320$	2.34064	+	1.35137i	0.130846	+	0.0755439i
$321$	5.28386	−	9.15192i	0.294917	−	0.510810i
$322$	−15.3900	+	12.3982i	−0.857652	+	0.690927i
$323$	21.7701	−	12.5690i	1.21132	−	0.699358i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	7.53046	−	3.51419i	0.417715	−	0.194932i
$326$	5.21359	+	9.03020i	0.288754	+	0.500137i
$327$			3.78429i			0.209272i
$328$	−1.90330	−	3.29661i	−0.105092	−	0.182025i
$329$	−3.49975	−	22.4643i	−0.192947	−	1.23850i
$330$			13.7766i			0.758374i
$331$	−0.762189	+	0.440050i	−0.0418937	+	0.0241873i	−0.520801	−	0.853678i	$-0.674366\pi$
$331$	−0.762189	+	0.440050i	−0.0418937	+	0.0241873i	0.478907	+	0.877866i	$0.341033\pi$
$332$		−	15.3966i		−	0.844999i
$333$	−5.86654	+	3.38705i	−0.321485	+	0.185609i
$334$	−1.10027	−	1.90573i	−0.0602043	−	0.104277i
$335$	−8.19667	−	14.1971i	−0.447832	−	0.775668i
$336$	2.61422	−	0.407273i	0.142617	−	0.0222186i
$337$	16.4964			0.898617			0.449308	−	0.893377i	$-0.351670\pi$
$337$	16.4964			0.898617			0.449308	+	0.893377i	$0.351670\pi$
$338$	2.24994	−	12.8038i	0.122381	−	0.696436i
$339$	−0.849593	−	1.47154i	−0.0461435	−	0.0799230i
$340$	−13.4195	−	7.74778i	−0.727777	−	0.420182i
$341$	36.5595			1.97981
$342$	−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
$345$	−17.4838	+	10.0943i	−0.941294	+	0.543456i
$346$	18.5992	−	10.7383i	0.999900	−	0.577292i
$347$	−5.59149			−0.300167			−0.150084	−	0.988673i	$-0.547954\pi$
$347$	−5.59149			−0.300167			−0.150084	+	0.988673i	$0.547954\pi$
$348$	8.36089			0.448191
$349$	−11.1268	+	6.42408i	−0.595606	+	0.343873i	−0.767311	−	0.641275i	$-0.778406\pi$
$349$	−11.1268	+	6.42408i	−0.595606	+	0.343873i	0.171705	+	0.985148i	$0.445072\pi$
$350$	−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
$353$	15.9755	+	9.22345i	0.850289	+	0.490915i	0.860748	−	0.509031i	$-0.169996\pi$
$353$	15.9755	+	9.22345i	0.850289	+	0.490915i	−0.0104593	+	0.999945i	$0.503329\pi$
$354$	3.23979	−	5.61147i	0.172193	−	0.298247i
$355$	−1.23649	−	2.14167i	−0.0656263	−	0.113668i
$356$		−	10.3822i		−	0.550258i
$357$	−14.9880	+	2.33501i	−0.793251	+	0.123582i
$358$	16.1758	+	9.33910i	0.854917	+	0.493587i
$359$	9.96875	+	5.75546i	0.526130	+	0.303761i	0.739439	−	0.673223i	$-0.235091\pi$
$359$	9.96875	+	5.75546i	0.526130	+	0.303761i	−0.213309	+	0.976985i	$0.568424\pi$
$360$	2.70274			0.142447
$361$	0.112254	−	0.194430i	0.00590811	−	0.0102331i
$362$			1.97032i			0.103557i
$363$	14.9820			0.786352
$364$	−7.92043	+	5.31665i	−0.415143	+	0.278668i
$365$	−18.5367			−0.970256
$366$			4.65046i			0.243083i
$367$	−3.00680	+	5.20794i	−0.156954	+	0.271852i	−0.933769	−	0.357877i	$-0.883501\pi$
$367$	−3.00680	+	5.20794i	−0.156954	+	0.271852i	0.776815	+	0.629729i	$0.216834\pi$
$368$	7.46964			0.389382
$369$	−3.29661	−	1.90330i	−0.171614	−	0.0990816i
$370$	−15.8557	−	9.15432i	−0.824301	−	0.475910i
$371$	−6.87814	+	17.7835i	−0.357095	+	0.923275i
$372$		−	7.17238i		−	0.371871i
$373$	−4.79186	−	8.29975i	−0.248113	−	0.429745i	0.714889	−	0.699238i	$-0.246477\pi$
$373$	−4.79186	−	8.29975i	−0.248113	−	0.429745i	−0.963002	+	0.269493i	$0.913144\pi$
$374$	−14.6120	+	25.3087i	−0.755568	+	1.30868i
$375$	6.30849	+	3.64221i	0.325769	+	0.188083i
$376$	−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	−0.943308	−	0.331919i	$-0.892304\pi$
$379$	−21.9503	+	12.6730i	−1.12751	+	0.650969i	−0.184203	+	0.982888i	$0.558971\pi$
$380$	−11.8504			−0.607911
$381$	6.22903			0.319123
$382$	3.21249	−	1.85473i	0.164365	−	0.0948964i
$383$	−0.247581	+	0.142941i	−0.0126508	+	0.00730394i	−0.506312	−	0.862350i	$-0.668992\pi$
$383$	−0.247581	+	0.142941i	−0.0126508	+	0.00730394i	0.493661	+	0.869654i	$0.335658\pi$
$384$	−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
$387$	−6.21388			−0.315869
$388$	8.20116	+	4.73494i	0.416351	+	0.240380i
$389$	−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	$0.860188\pi$
$390$	−8.83064	+	4.12094i	−0.447157	+	0.208672i
$391$	−42.8255			−2.16578
$392$	6.83958	+	1.49001i	0.345451	+	0.0752571i
$393$	0.358468	+	0.620884i	0.0180823	+	0.0313195i
$394$	−7.44330	−	12.8922i	−0.374988	−	0.649498i
$395$	17.8517	−	10.3067i	0.898217	−	0.518586i
$396$		−	5.09726i		−	0.256147i
$397$	−26.3981	+	15.2409i	−1.32488	+	0.764921i	−0.984503	−	0.175368i	$-0.943889\pi$
$397$	−26.3981	+	15.2409i	−1.32488	+	0.764921i	−0.340378	+	0.940289i	$0.610555\pi$
$398$		−	2.66427i		−	0.133548i
$399$	−9.03372	+	7.27759i	−0.452252	+	0.364335i
$400$	1.15240	+	1.99602i	0.0576200	+	0.0998008i
$401$		−	19.5601i		−	0.976783i	−0.872625	−	0.488392i	$-0.837584\pi$
$401$		−	19.5601i		−	0.976783i	0.872625	−	0.488392i	$-0.162416\pi$
$402$	3.03273	+	5.25284i	0.151259	+	0.261988i
$403$	10.9359	+	23.4343i	0.544757	+	1.16734i
$404$	−1.86105	+	3.22344i	−0.0925908	+	0.160372i
$405$	2.34064	−	1.35137i	0.116307	−	0.0671501i
$406$	20.6315	+	7.97963i	1.02392	+	0.396022i
$407$	−17.2647	+	29.9033i	−0.855778	+	1.48225i
$408$	4.96516	+	2.86664i	0.245812	+	0.141920i
$409$		−	17.0474i		−	0.842942i	−0.906842	−	0.421471i	$-0.861514\pi$
$409$		−	17.0474i		−	0.842942i	0.906842	−	0.421471i	$-0.138486\pi$
$410$		−	10.2882i		−	0.508099i
$411$	−8.70853	−	5.02787i	−0.429560	−	0.248007i
$412$	−4.55465	+	7.88888i	−0.224391	+	0.388657i
$413$	13.3501	−	10.7549i	0.656917	−	0.529214i
$414$	6.46890	−	3.73482i	0.317929	−	0.183557i
$415$	20.8065	−	36.0379i	1.02135	−	1.76903i
$416$	3.59192	+	0.313194i	0.176109	+	0.0153556i
$417$	−8.84682	−	15.3231i	−0.433231	−	0.750377i
$418$			22.3493i			1.09314i
$419$	4.16216	+	7.20908i	0.203335	+	0.352186i	0.949601	−	0.313461i	$-0.101489\pi$
$419$	4.16216	+	7.20908i	0.203335	+	0.352186i	−0.746266	+	0.665648i	$0.768155\pi$
$420$	6.66932	+	2.57949i	0.325429	+	0.125866i
$421$		−	35.9805i		−	1.75358i	−0.480873	−	0.876790i	$-0.659680\pi$
$421$		−	35.9805i		−	1.75358i	0.480873	−	0.876790i	$-0.340320\pi$
$422$	5.61754	−	3.24329i	0.273458	−	0.157881i
$423$			8.59312i			0.417812i
$424$	6.24125	−	3.60339i	0.303102	−	0.174996i
$425$	−6.60703	−	11.4437i	−0.320488	−	0.555102i
$426$	0.457497	+	0.792408i	0.0221658	+	0.0383923i
$427$	−4.43839	+	11.4755i	−0.214789	+	0.555340i
$428$	−10.5677			−0.510810
$429$	7.77192	+	16.6542i	0.375232	+	0.804074i
$430$	−8.39725	−	14.5445i	−0.404951	−	0.701397i
$431$	−5.37734	−	3.10461i	−0.259018	−	0.149544i	0.364869	−	0.931059i	$-0.381114\pi$
$431$	−5.37734	−	3.10461i	−0.259018	−	0.149544i	−0.623886	+	0.781515i	$0.714447\pi$
$432$	−1.00000			−0.0481125
$433$	−3.98578	+	6.90357i	−0.191544	+	0.331764i	−0.945762	−	0.324860i	$-0.894683\pi$
$433$	−3.98578	+	6.90357i	−0.191544	+	0.331764i	0.754218	+	0.656624i	$0.228016\pi$
$434$	6.84532	−	17.6987i	0.328586	−	0.849564i
$435$	19.5698	+	11.2987i	0.938302	+	0.541729i
$436$	3.27729	−	1.89214i	0.156954	−	0.0906173i
$437$	−28.3634	+	16.3756i	−1.35681	+	0.783352i
$438$	6.85849			0.327711
$439$	14.1623			0.675928			0.337964	−	0.941159i	$-0.390262\pi$
$439$	14.1623			0.675928			0.337964	+	0.941159i	$0.390262\pi$
$440$	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	$0.939223\pi$
$444$	5.86654	+	3.38705i	0.278414	+	0.160742i
$445$	14.0303	−	24.3011i	0.665098	−	1.15198i
$446$	−13.0400	−	22.5859i	−0.617462	−	1.06948i
$447$			23.2914i			1.10165i
$448$	−1.65982	−	2.06034i	−0.0784190	−	0.0973420i
$449$	2.53224	+	1.46199i	0.119504	+	0.0689957i	0.558560	−	0.829464i	$-0.311354\pi$
$449$	2.53224	+	1.46199i	0.119504	+	0.0689957i	−0.439056	+	0.898459i	$0.644687\pi$
$450$	1.99602	+	1.15240i	0.0940931	+	0.0543247i
$451$	−19.4032			−0.913660
$452$	−0.849593	+	1.47154i	−0.0399615	+	0.0692153i
$453$		−	18.3147i		−	0.860501i
$454$	11.6727			0.547826
$455$	−25.7236	+	1.74093i	−1.20594	+	0.0816161i
$456$	4.38458			0.205327
$457$			20.9436i			0.979702i	0.871806	+	0.489851i	$0.162949\pi$
$457$			20.9436i			0.979702i	−0.871806	+	0.489851i	$0.837051\pi$
$458$	6.03988	−	10.4614i	0.282225	−	0.488828i
$459$	5.73328			0.267606
$460$	17.4838	+	10.0943i	0.815184	+	0.470647i
$461$	15.9388	+	9.20229i	0.742346	+	0.428593i	0.822922	−	0.568155i	$-0.192343\pi$
$461$	15.9388	+	9.20229i	0.742346	+	0.428593i	−0.0805759	+	0.996748i	$0.525676\pi$
$462$	4.86482	−	12.5781i	0.226332	−	0.585184i
$463$			28.8633i			1.34139i	0.741732	+	0.670697i	$0.234005\pi$
$463$			28.8633i			1.34139i	−0.741732	+	0.670697i	$0.765995\pi$
$464$	−4.18045	−	7.24074i	−0.194072	−	0.336143i
$465$	9.69254	−	16.7880i	0.449481	−	0.778524i
$466$	−8.06902	−	4.65865i	−0.373790	−	0.215808i
$467$	−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
$471$	−3.83550			−0.176731
$472$	−6.47957			−0.298247
$473$	−27.4303	+	15.8369i	−1.26125	+	0.728180i
$474$	−6.60504	+	3.81342i	−0.303380	+	0.175156i
$475$	−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
$478$	16.8139			0.769048
$479$	15.0874	+	8.71070i	0.689360	+	0.398002i	0.803372	−	0.595477i	$-0.203037\pi$
$479$	15.0874	+	8.71070i	0.689360	+	0.398002i	−0.114012	+	0.993479i	$0.536370\pi$
$480$	−1.35137	−	2.34064i	−0.0616813	−	0.106835i
$481$	−24.3321	−	2.12161i	−1.10945	−	0.0967371i
$482$	22.3511			1.01807
$483$	19.5273	−	3.04218i	0.888522	−	0.138424i
$484$	−7.49101	−	12.9748i	−0.340500	−	0.589764i
$485$	12.7973	+	22.1656i	0.581096	+	1.00649i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$		−	38.2660i		−	1.73400i	−0.498312	−	0.866998i	$-0.666046\pi$
$487$		−	38.2660i		−	1.73400i	0.498312	−	0.866998i	$-0.333954\pi$
$488$	4.02741	−	2.32523i	0.182312	−	0.105258i
$489$		−	10.4272i		−	0.471533i
$490$	13.9954	+	12.7304i	0.632250	+	0.575100i
$491$	−18.3883	−	31.8494i	−0.829851	−	1.43734i	−0.898155	−	0.439679i	$-0.855092\pi$
$491$	−18.3883	−	31.8494i	−0.829851	−	1.43734i	0.0683042	−	0.997665i	$-0.478241\pi$
$492$			3.80659i			0.171614i
$493$	23.9677	+	41.5132i	1.07945	+	1.86966i
$494$	−14.3257	+	6.68528i	−0.644544	+	0.300785i
$495$	6.88828	−	11.9308i	0.309605	−	0.536252i
$496$	−6.21147	+	3.58619i	−0.278903	+	0.161025i
$497$	0.372652	+	2.39199i	0.0167157	+	0.107296i
$498$	−7.69830	+	13.3339i	−0.344969	+	0.597504i
$499$	26.0698	+	15.0514i	1.16704	+	0.673793i	0.952982	−	0.303027i	$-0.0979973\pi$
$499$	26.0698	+	15.0514i	1.16704	+	0.673793i	0.214062	+	0.976820i	$0.431331\pi$
$500$		−	7.28442i		−	0.325769i
$501$			2.20055i			0.0983133i
$502$	6.49788	+	3.75155i	0.290015	+	0.167440i
$503$	3.90097	−	6.75668i	0.173936	−	0.301265i	−0.765857	−	0.643011i	$-0.777685\pi$
$503$	3.90097	−	6.75668i	0.173936	−	0.301265i	0.939792	+	0.341746i	$0.111018\pi$
$504$	−2.46761	−	0.954400i	−0.109916	−	0.0425123i
$505$	−8.71211	+	5.02994i	−0.387684	+	0.223829i
$506$	19.0373	−	32.9736i	0.846313	−	1.46586i
$507$	−8.35041	+	9.96346i	−0.370855	+	0.442493i
$508$	−3.11451	−	5.39450i	−0.138184	−	0.239342i
$509$			21.9997i			0.975121i	0.873089	+	0.487561i	$0.162113\pi$
$509$			21.9997i			0.975121i	−0.873089	+	0.487561i	$0.837887\pi$
$510$	7.74778	+	13.4195i	0.343077	+	0.594227i
$511$	16.9241	+	6.54574i	0.748679	+	0.289567i
$512$			1.00000i			0.0441942i
$513$	3.79715	−	2.19229i	0.167648	−	0.0967919i
$514$		−	7.03753i		−	0.310412i
$515$	−21.3216	+	12.3100i	−0.939541	+	0.542444i
$516$	3.10694	+	5.38138i	0.136775	+	0.236902i
$517$	21.9007	+	37.9331i	0.963190	+	1.66829i
$518$	11.2438	+	13.9570i	0.494023	+	0.613234i
$519$	−21.4765			−0.942714
$520$	7.98416	+	5.58709i	0.350129	+	0.245010i
$521$	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	$0.624610\pi$
$522$	−7.24074	−	4.18045i	−0.316919	−	0.182973i
$523$	−9.68552			−0.423518			−0.211759	−	0.977322i	$-0.567919\pi$
$523$	−9.68552			−0.423518			−0.211759	+	0.977322i	$0.567919\pi$
$524$	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
$527$	35.6121	−	20.5606i	1.55129	−	0.895635i
$528$	−4.41435	+	2.54863i	−0.192110	+	0.110915i
$529$	32.7956			1.42590
$530$	19.4780			0.846071
$531$	−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
$535$	−24.7353	−	14.2809i	−1.06940	−	0.617418i
$536$	3.03273	−	5.25284i	0.130994	−	0.226888i
$537$	−9.33910	−	16.1758i	−0.403012	−	0.698037i
$538$		−	1.59963i		−	0.0689649i
$539$	24.0090	−	26.3948i	1.03414	−	1.13691i
$540$	−2.34064	−	1.35137i	−0.100725	−	0.0581537i
$541$	0.964894	+	0.557082i	0.0414840	+	0.0239508i	0.520599	−	0.853802i	$-0.325709\pi$
$541$	0.964894	+	0.557082i	0.0414840	+	0.0239508i	−0.479115	+	0.877752i	$0.659042\pi$
$542$	20.0012			0.859124
$543$	0.985158	−	1.70634i	0.0422772	−	0.0732262i
$544$		−	5.73328i		−	0.245812i
$545$	10.2279			0.438117
$546$	9.51762	−	0.644135i	0.407317	−	0.0275664i
$547$	−18.4164			−0.787430			−0.393715	−	0.919233i	$-0.628810\pi$
$547$	−18.4164			−0.787430			−0.393715	+	0.919233i	$0.628810\pi$
$548$			10.0557i			0.429560i
$549$	2.32523	−	4.02741i	0.0992383	−	0.171886i
$550$	11.7482			0.500943
$551$	31.7476	+	18.3295i	1.35249	+	0.780862i
$552$	−6.46890	−	3.73482i	−0.275335	−	0.158965i
$553$	−19.9382	+	3.10621i	−0.847860	+	0.132089i
$554$		−	18.1117i		−	0.769491i
$555$	9.15432	+	15.8557i	0.388579	+	0.673039i
$556$	−8.84682	+	15.3231i	−0.375189	+	0.649846i
$557$	−29.1335	−	16.8202i	−1.23443	−	0.712696i	−0.266476	−	0.963841i	$-0.585859\pi$
$557$	−29.1335	−	16.8202i	−1.23443	−	0.712696i	−0.967949	+	0.251145i	$0.919193\pi$
$558$	−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
$562$	−11.0176			−0.464748
$563$	−1.55896			−0.0657024			−0.0328512	−	0.999460i	$-0.510459\pi$
$563$	−1.55896			−0.0657024			−0.0328512	+	0.999460i	$0.510459\pi$
$564$	7.44186	−	4.29656i	0.313359	−	0.180918i
$565$	−3.97718	+	2.29623i	−0.167321	+	0.0966030i
$566$	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
$569$	−5.20659			−0.218272			−0.109136	−	0.994027i	$-0.534808\pi$
$569$	−5.20659			−0.218272			−0.109136	+	0.994027i	$0.534808\pi$
$570$	10.2627	+	5.92518i	0.429858	+	0.248179i
$571$	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	$0.752633\pi$
$572$	10.5370	−	15.0578i	0.440575	−	0.629598i
$573$	−3.70946			−0.154965
$574$	−3.63301	+	9.39320i	−0.151639	+	0.392065i
$575$	8.60802	+	14.9095i	0.358979	+	0.621770i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	0.299900	−	0.173147i	0.0124850	−	0.00720821i	−0.493745	−	0.869607i	$-0.664372\pi$
$577$	0.299900	−	0.173147i	0.0124850	−	0.00720821i	0.506230	+	0.862399i	$0.331039\pi$
$578$			15.8705i			0.660125i
$579$	2.58076	−	1.49000i	0.107253	−	0.0619223i
$580$		−	22.5973i		−	0.938302i
$581$	−31.7223	+	25.5556i	−1.31606	+	1.06022i
$582$	−4.73494	−	8.20116i	−0.196270	−	0.339949i
$583$		−	36.7348i		−	1.52140i
$584$	−3.42924	−	5.93963i	−0.141903	−	0.245783i
$585$	9.70803	+	0.846482i	0.401378	+	0.0349977i
$586$	−2.38774	+	4.13569i	−0.0986368	+	0.170844i
$587$	25.5443	−	14.7480i	1.05433	−	0.608715i	0.130468	−	0.991453i	$-0.458352\pi$
$587$	25.5443	−	14.7480i	1.05433	−	0.608715i	0.923857	+	0.382738i	$0.125019\pi$
$588$	−5.17824	−	4.71018i	−0.213547	−	0.194245i
$589$	15.7239	−	27.2347i	0.647893	−	1.12218i
$590$	−15.1664	−	8.75630i	−0.624389	−	0.360491i
$591$			14.8866i			0.612353i
$592$		−	6.77410i		−	0.278414i
$593$	−2.79980	−	1.61647i	−0.114974	−	0.0663803i	0.441410	−	0.897305i	$-0.354478\pi$
$593$	−2.79980	−	1.61647i	−0.114974	−	0.0663803i	−0.556384	+	0.830925i	$0.687812\pi$
$594$	−2.54863	+	4.41435i	−0.104571	+	0.181123i
$595$	6.31092	+	40.5087i	0.258723	+	1.66070i
$596$	20.1710	−	11.6457i	0.826236	−	0.477027i
$597$	−1.33214	+	2.30733i	−0.0545207	+	0.0944327i
$598$	26.8304	+	2.33945i	1.09718	+	0.0956672i
$599$	−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	$0.920791\pi$
$600$		−	2.30480i		−	0.0940931i
$601$	3.58901	+	6.21634i	0.146399	+	0.253570i	0.929894	−	0.367828i	$-0.119898\pi$
$601$	3.58901	+	6.21634i	0.146399	+	0.253570i	−0.783495	+	0.621398i	$0.786565\pi$
$602$	2.53075	+	16.2444i	0.103146	+	0.662074i
$603$		−	6.06546i		−	0.247004i
$604$	−15.8610	+	9.15737i	−0.645376	+	0.372608i
$605$		−	40.4925i		−	1.64625i
$606$	3.22344	−	1.86105i	0.130943	−	0.0756001i
$607$	−20.2069	−	34.9994i	−0.820174	−	1.42058i	−0.905552	−	0.424235i	$-0.860543\pi$
$607$	−20.2069	−	34.9994i	−0.820174	−	1.42058i	0.0853783	−	0.996349i	$-0.472790\pi$
$608$	−2.19229	−	3.79715i	−0.0889090	−	0.153995i
$609$	−13.8775	−	17.2263i	−0.562347	−	0.698045i
$610$	12.5690			0.508903
$611$	−17.7637	+	25.3849i	−0.718641	+	1.02696i
$612$	−2.86664	−	4.96516i	−0.115877	−	0.200705i
$613$	−7.43967	−	4.29529i	−0.300485	−	0.173485i	0.342176	−	0.939636i	$-0.388836\pi$
$613$	−7.43967	−	4.29529i	−0.300485	−	0.173485i	−0.642661	+	0.766151i	$0.722170\pi$
$614$	6.26422			0.252803
$615$	−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	0.976552	−	0.215281i	$-0.0690666\pi$
$617$	31.7545	+	18.3335i	1.27839	+	0.738079i	0.301838	+	0.953359i	$0.402400\pi$
$618$	7.88888	−	4.55465i	0.317337	−	0.183215i
$619$	4.95870	−	2.86291i	0.199307	−	0.115070i	−0.397025	−	0.917808i	$-0.629957\pi$
$619$	4.95870	−	2.86291i	0.199307	−	0.115070i	0.596332	+	0.802738i	$0.296624\pi$
$620$	−19.3851			−0.778524
$621$	−7.46964			−0.299747
$622$	−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
$626$	24.8179	+	14.3286i	0.991923	+	0.572687i
$627$	11.1747	−	19.3551i	0.446273	−	0.772967i
$628$	1.91775	+	3.32164i	0.0765266	+	0.132548i
$629$			38.8378i			1.54856i
$630$	−4.48605	−	5.56857i	−0.178729	−	0.221857i
$631$	−15.3218	−	8.84605i	−0.609952	−	0.352156i	0.162995	−	0.986627i	$-0.447885\pi$
$631$	−15.3218	−	8.84605i	−0.609952	−	0.352156i	−0.772947	+	0.634471i	$0.781218\pi$
$632$	6.60504	+	3.81342i	0.262735	+	0.151690i
$633$	−6.48658			−0.257818
$634$	−12.8572	+	22.2694i	−0.510626	+	0.884430i
$635$		−	16.8354i		−	0.668094i
$636$	−7.20677			−0.285767
$637$	24.1006	+	7.49414i	0.954900	+	0.296928i
$638$	−42.6176			−1.68725
$639$		−	0.914994i		−	0.0361966i
$640$	−1.35137	+	2.34064i	−0.0534176	+	0.0925220i
$641$	23.6951			0.935901			0.467950	−	0.883755i	$-0.344993\pi$
$641$	23.6951			0.935901			0.467950	+	0.883755i	$0.344993\pi$
$642$	9.15192	+	5.28386i	0.361198	+	0.208537i
$643$	−11.0433	−	6.37588i	−0.435507	−	0.251440i	0.266183	−	0.963923i	$-0.414237\pi$
$643$	−11.0433	−	6.37588i	−0.435507	−	0.251440i	−0.701690	+	0.712482i	$0.747571\pi$
$644$	−12.3982	−	15.3900i	−0.488559	−	0.606452i
$645$			16.7945i			0.661283i
$646$	12.5690	+	21.7701i	0.494521	+	0.856535i
$647$	−3.70342	+	6.41451i	−0.145597	+	0.252181i	−0.929595	−	0.368582i	$-0.879843\pi$
$647$	−3.70342	+	6.41451i	−0.145597	+	0.252181i	0.783999	+	0.620762i	$0.213177\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−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
$653$	−40.1506			−1.57121			−0.785606	−	0.618727i	$-0.787649\pi$
$653$	−40.1506			−1.57121			−0.785606	+	0.618727i	$0.787649\pi$
$654$	−3.78429			−0.147977
$655$	1.67809	−	0.968844i	0.0655683	−	0.0378559i
$656$	3.29661	−	1.90330i	0.128711	−	0.0743112i
$657$	−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	−0.317633	−	0.948214i	$-0.602888\pi$
$659$	17.0035	−	29.4509i	0.662361	−	1.14724i	0.979994	−	0.199029i	$-0.0637788\pi$
$660$	−13.7766			−0.536252
$661$	−10.0528	−	5.80401i	−0.391010	−	0.225750i	0.291588	−	0.956544i	$-0.405816\pi$
$661$	−10.0528	−	5.80401i	−0.391010	−	0.225750i	−0.682598	+	0.730794i	$0.739150\pi$
$662$	−0.440050	−	0.762189i	−0.0171030	−	0.0296233i
$663$	16.9367	+	11.8518i	0.657766	+	0.460286i
$664$	15.3966			0.597504
$665$	19.6694	+	24.4158i	0.762748	+	0.946804i
$666$	−3.38705	−	5.86654i	−0.131246	−	0.227324i
$667$	−31.2264	−	54.0858i	−1.20909	−	2.09421i
$668$	1.90573	−	1.10027i	0.0737350	−	0.0425709i
$669$			26.0800i			1.00831i
$670$	14.1971	−	8.19667i	0.548480	−	0.316665i
$671$		−	23.7046i		−	0.915104i
$672$	0.407273	+	2.61422i	0.0157109	+	0.100846i
$673$	−5.22869	−	9.05635i	−0.201551	−	0.349097i	0.747477	−	0.664287i	$-0.231265\pi$
$673$	−5.22869	−	9.05635i	−0.201551	−	0.349097i	−0.949028	+	0.315191i	$0.897932\pi$
$674$			16.4964i			0.635418i
$675$	−1.15240	−	1.99602i	−0.0443559	−	0.0768267i
$676$	12.8038	+	2.24994i	0.492455	+	0.0865361i
$677$	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
$679$	−3.85683	−	24.7563i	−0.148012	−	0.950061i
$680$	7.74778	−	13.4195i	0.297114	−	0.514616i
$681$	−10.1088	−	5.83634i	−0.387372	−	0.223649i
$682$			36.5595i			1.39993i
$683$			16.0329i			0.613481i	0.951793	+	0.306741i	$0.0992384\pi$
$683$			16.0329i			0.613481i	−0.951793	+	0.306741i	$0.900762\pi$
$684$	−3.79715	−	2.19229i	−0.145188	−	0.0838242i
$685$	−13.5890	+	23.5369i	−0.519210	+	0.899298i
$686$	−8.28251	−	16.5650i	−0.316228	−	0.632456i
$687$	−10.4614	+	6.03988i	−0.399126	+	0.230436i
$688$	3.10694	−	5.38138i	0.118451	−	0.205163i
$689$	23.5466	−	10.9884i	0.897056	−	0.418623i
$690$	−10.0943	−	17.4838i	−0.384282	−	0.665595i
$691$		−	36.4604i		−	1.38702i	−0.720447	−	0.693510i	$-0.756063\pi$
$691$		−	36.4604i		−	1.38702i	0.720447	−	0.693510i	$-0.243937\pi$
$692$	10.7383	+	18.5992i	0.408207	+	0.707036i
$693$	−10.5021	+	8.46051i	−0.398941	+	0.321388i
$694$		−	5.59149i		−	0.212250i
$695$	−41.4145	+	23.9106i	−1.57094	+	0.906982i
$696$			8.36089i			0.316919i
$697$	−18.9004	+	10.9121i	−0.715902	+	0.413326i
$698$	−6.42408	−	11.1268i	−0.243155	−	0.421157i
$699$	4.65865	+	8.06902i	0.176206	+	0.305199i
$700$	2.19970	−	5.68736i	0.0831409	−	0.214962i
$701$	11.4738			0.433360			0.216680	−	0.976243i	$-0.430477\pi$
$701$	11.4738			0.433360			0.216680	+	0.976243i	$0.430477\pi$
$702$	−3.59192	−	0.313194i	−0.135568	−	0.0118208i
$703$	14.8508	+	25.7223i	0.560108	+	0.970135i
$704$	4.41435	+	2.54863i	0.166372	+	0.0960550i
$705$	23.2250			0.874703
$706$	−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
$709$	36.2974	−	20.9563i	1.36318	−	0.787030i	0.373131	−	0.927779i	$-0.378284\pi$
$709$	36.2974	−	20.9563i	1.36318	−	0.787030i	0.990045	+	0.140749i	$0.0449509\pi$
$710$	2.14167	−	1.23649i	0.0803755	−	0.0464048i
$711$	7.62685			0.286029
$712$	10.3822			0.389091
$713$	−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
$717$	−14.5612	−	8.40693i	−0.543799	−	0.313963i
$718$	−5.75546	+	9.96875i	−0.214792	+	0.372030i
$719$	18.1215	+	31.3873i	0.675817	+	1.17055i	0.976229	+	0.216739i	$0.0695422\pi$
$719$	18.1215	+	31.3873i	0.675817	+	1.17055i	−0.300413	+	0.953809i	$0.597124\pi$
$720$			2.70274i			0.100725i
$721$	23.8137	−	3.70997i	0.886867	−	0.138166i
$722$	0.194430	+	0.112254i	0.00723593	+	0.00417766i
$723$	−19.3566	−	11.1756i	−0.719881	−	0.415623i
$724$	−1.97032			−0.0732262
$725$	9.63509	−	16.6885i	0.357838	−	0.619794i
$726$			14.9820i			0.556035i
$727$	−6.41054			−0.237754			−0.118877	−	0.992909i	$-0.537929\pi$
$727$	−6.41054			−0.237754			−0.118877	+	0.992909i	$0.537929\pi$
$728$	−5.31665	−	7.92043i	−0.197048	−	0.293551i
$729$	1.00000			0.0370370
$730$		−	18.5367i		−	0.686074i
$731$	−17.8130	+	30.8529i	−0.658836	+	1.14114i
$732$	−4.65046			−0.171886
$733$	−23.5129	−	13.5752i	−0.868469	−	0.501411i	−0.00162955	−	0.999999i	$-0.500519\pi$
$733$	−23.5129	−	13.5752i	−0.868469	−	0.501411i	−0.866839	+	0.498588i	$0.833852\pi$
$734$	−5.20794	−	3.00680i	−0.192228	−	0.110983i
$735$	−5.75521	−	18.0226i	−0.212284	−	0.664772i
$736$			7.46964i			0.275335i
$737$	−15.4586	−	26.7751i	−0.569425	−	0.986272i
$738$	1.90330	−	3.29661i	0.0700613	−	0.121350i
$739$	17.1766	+	9.91693i	0.631853	+	0.364800i	0.781469	−	0.623944i	$-0.214471\pi$
$739$	17.1766	+	9.91693i	0.631853	+	0.364800i	−0.149617	+	0.988744i	$0.547804\pi$
$740$	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	0.204710	−	0.978823i	$-0.434375\pi$
$743$	31.4762	−	18.1728i	1.15475	−	0.666696i	0.950040	+	0.312127i	$0.101041\pi$
$744$	7.17238			0.262952
$745$	62.9507			2.30634
$746$	8.29975	−	4.79186i	0.303875	−	0.175442i
$747$	13.3339	−	7.69830i	0.487860	−	0.281666i
$748$	−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
$751$	0.923620			0.0337034			0.0168517	−	0.999858i	$-0.494636\pi$
$751$	0.923620			0.0337034			0.0168517	+	0.999858i	$0.494636\pi$
$752$	−7.44186	−	4.29656i	−0.271377	−	0.156679i
$753$	−3.75155	−	6.49788i	−0.136714	−	0.236796i
$754$	−12.7481	−	27.3175i	−0.464258	−	0.994844i
$755$	−49.4999			−1.80149
$756$	1.65982	+	2.06034i	0.0603670	+	0.0749339i
$757$	1.33975	+	2.32051i	0.0486940	+	0.0843405i	0.889345	−	0.457237i	$-0.151161\pi$
$757$	1.33975	+	2.32051i	0.0486940	+	0.0843405i	−0.840651	+	0.541577i	$0.817827\pi$
$758$	−12.6730	−	21.9503i	−0.460305	−	0.797271i
$759$	−32.9736	+	19.0373i	−1.19687	+	0.691012i
$760$		−	11.8504i		−	0.429858i
$761$	−13.0650	+	7.54307i	−0.473605	+	0.273436i	−0.717748	−	0.696303i	$-0.754827\pi$
$761$	−13.0650	+	7.54307i	−0.473605	+	0.273436i	0.244143	+	0.969739i	$0.421493\pi$
$762$			6.22903i			0.225654i
$763$	−9.33817	−	3.61172i	−0.338064	−	0.130753i
$764$	1.85473	+	3.21249i	0.0671019	+	0.116224i
$765$		−	15.4956i		−	0.560243i
$766$	−0.142941	−	0.247581i	−0.00516466	−	0.00894546i
$767$	−23.2741	−	2.02936i	−0.840380	−	0.0732761i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	17.7838	−	10.2675i	0.641301	−	0.370256i	−0.143814	−	0.989605i	$-0.545937\pi$
$769$	17.7838	−	10.2675i	0.641301	−	0.370256i	0.785116	+	0.619349i	$0.212603\pi$
$770$	−33.9952	−	13.1483i	−1.22510	−	0.473833i
$771$	−3.51876	+	6.09468i	−0.126725	+	0.219494i
$772$	−2.58076	−	1.49000i	−0.0928834	−	0.0536263i
$773$			18.0867i			0.650532i	0.945623	+	0.325266i	$0.105454\pi$
$773$			18.0867i			0.650532i	−0.945623	+	0.325266i	$0.894546\pi$
$774$		−	6.21388i		−	0.223353i
$775$	−14.3162	−	8.26546i	−0.514253	−	0.296904i
$776$	−4.73494	+	8.20116i	−0.169975	+	0.294405i
$777$	−2.75891	−	17.7090i	−0.0989753	−	0.635306i
$778$	2.87869	−	1.66201i	0.103206	−	0.0595860i
$779$	−8.34515	+	14.4542i	−0.298996	+	0.517876i
$780$	−4.12094	−	8.83064i	−0.147553	−	0.316188i
$781$	−2.33198	−	4.03911i	−0.0834448	−	0.144531i
$782$		−	42.8255i		−	1.53144i
$783$	4.18045	+	7.24074i	0.149397	+	0.258763i
$784$	−1.49001	+	6.83958i	−0.0532148	+	0.244271i
$785$			10.3664i			0.369991i
$786$	−0.620884	+	0.358468i	−0.0221462	+	0.0127861i
$787$			35.0577i			1.24967i	0.780757	+	0.624835i	$0.214834\pi$
$787$			35.0577i			1.24967i	−0.780757	+	0.624835i	$0.785166\pi$
$788$	12.8922	−	7.44330i	0.459264	−	0.265156i
$789$	−11.9643	−	20.7228i	−0.425940	−	0.737750i
$790$	10.3067	+	17.8517i	0.366696	+	0.635135i
$791$	4.44204	−	0.692032i	0.157941	−	0.0246058i
$792$	5.09726			0.181123
$793$	15.1944	−	7.09068i	0.539569	−	0.251797i
$794$	−15.2409	−	26.3981i	−0.540881	−	0.936833i
$795$	−16.8685	−	9.73901i	−0.598263	−	0.345407i
$796$	2.66427			0.0944327
$797$	−8.96425	+	15.5265i	−0.317530	+	0.549978i	−0.979972	−	0.199135i	$-0.936187\pi$
$797$	−8.96425	+	15.5265i	−0.317530	+	0.549978i	0.662442	+	0.749113i	$0.269520\pi$
$798$	−7.27759	−	9.03372i	−0.257624	−	0.319790i
$799$	42.6663	+	24.6334i	1.50942	+	0.871466i
$800$	−1.99602	+	1.15240i	−0.0705698	+	0.0407435i
$801$	8.99129	−	5.19112i	0.317692	−	0.183419i
$802$	19.5601			0.690690
$803$	−34.9595			−1.23369
$804$	−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
$808$	−3.22344	−	1.86105i	−0.113400	−	0.0654716i
$809$	−10.3413	+	17.9116i	−0.363580	+	0.629739i	−0.988547	−	0.150912i	$-0.951779\pi$
$809$	−10.3413	+	17.9116i	−0.363580	+	0.629739i	0.624967	+	0.780651i	$0.285112\pi$
$810$	1.35137	+	2.34064i	0.0474823	+	0.0822417i
$811$		−	16.2377i		−	0.570182i	−0.958500	−	0.285091i	$-0.907976\pi$
$811$		−	16.2377i		−	0.570182i	0.958500	−	0.285091i	$-0.0920239\pi$
$812$	−7.97963	+	20.6315i	−0.280030	+	0.724022i
$813$	−17.3215	−	10.0006i	−0.607492	−	0.350736i
$814$	−29.9033	−	17.2647i	−1.04811	−	0.605126i
$815$	−28.1819			−0.987171
$816$	−2.86664	+	4.96516i	−0.100352	+	0.173816i
$817$			27.2452i			0.953190i
$818$	17.0474			0.596050
$819$	−8.56457	−	4.20097i	−0.299270	−	0.146794i
$820$	10.2882			0.359280
$821$		−	41.5159i		−	1.44891i	−0.689320	−	0.724457i	$-0.742091\pi$
$821$		−	41.5159i		−	1.44891i	0.689320	−	0.724457i	$-0.257909\pi$
$822$	5.02787	−	8.70853i	0.175367	−	0.303745i
$823$	−17.9495			−0.625682			−0.312841	−	0.949806i	$-0.601281\pi$
$823$	−17.9495			−0.625682			−0.312841	+	0.949806i	$0.601281\pi$
$824$	−7.88888	−	4.55465i	−0.274822	−	0.158669i
$825$	−10.1742	−	5.87408i	−0.354220	−	0.204509i
$826$	10.7549	+	13.3501i	0.374211	+	0.464511i
$827$		−	0.0414259i		−	0.00144052i	−1.00000		0.000720261i	$-0.999771\pi$
$827$		−	0.0414259i		−	0.00144052i	1.00000		0.000720261i	$-0.000229266\pi$
$828$	3.73482	+	6.46890i	0.129794	+	0.224810i
$829$	1.75746	−	3.04402i	0.0610393	−	0.105723i	−0.833891	−	0.551929i	$-0.813892\pi$
$829$	1.75746	−	3.04402i	0.0610393	−	0.105723i	0.894930	+	0.446206i	$0.147225\pi$
$830$	36.0379	+	20.8065i	1.25089	+	0.722204i
$831$	−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
$835$	5.94751			0.205822
$836$	−22.3493			−0.772967
$837$	6.21147	−	3.58619i	0.214700	−	0.123957i
$838$	−7.20908	+	4.16216i	−0.249033	+	0.143779i
$839$	−1.59236	−	0.919352i	−0.0549745	−	0.0317395i	0.472261	−	0.881459i	$-0.343438\pi$
$839$	−1.59236	−	0.919352i	−0.0549745	−	0.0317395i	−0.527235	+	0.849719i	$0.676771\pi$
$840$	−2.57949	+	6.66932i	−0.0890010	+	0.230113i
$841$	−20.4523	+	35.4243i	−0.705250	+	1.22153i
$842$	35.9805			1.23997
$843$	9.54149	+	5.50878i	0.328626	+	0.189732i
$844$	3.24329	+	5.61754i	0.111639	+	0.193364i
$845$	26.9286	+	22.5690i	0.926374	+	0.776397i
$846$	−8.59312			−0.295438
$847$	−14.2988	+	36.9698i	−0.491314	+	1.27030i
$848$	3.60339	+	6.24125i	0.123741	+	0.214325i
$849$	−6.74682	−	11.6858i	−0.231550	−	0.401057i
$850$	11.4437	−	6.60703i	0.392516	−	0.226619i
$851$		−	50.6001i		−	1.73455i
$852$	−0.792408	+	0.457497i	−0.0271474	+	0.0156736i
$853$		−	3.88953i		−	0.133175i	−0.997781	−	0.0665875i	$-0.978789\pi$
$853$		−	3.88953i		−	0.133175i	0.997781	−	0.0665875i	$-0.0212111\pi$
$854$	−11.4755	−	4.43839i	−0.392685	−	0.151879i
$855$	−5.92518	−	10.2627i	−0.202637	−	0.350978i
$856$		−	10.5677i		−	0.361198i
$857$	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	$0.799085\pi$
$858$	−16.6542	+	7.77192i	−0.568566	+	0.265329i
$859$	−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
$861$	7.84288	−	6.31825i	0.267285	−	0.215325i
$862$	3.10461	−	5.37734i	0.105743	−	0.183153i
$863$	−11.3137	−	6.53197i	−0.385123	−	0.222351i	0.294922	−	0.955521i	$-0.404706\pi$
$863$	−11.3137	−	6.53197i	−0.385123	−	0.222351i	−0.680045	+	0.733170i	$0.738040\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			58.0454i			1.97360i
$866$	−6.90357	−	3.98578i	−0.234593	−	0.135442i
$867$	7.93524	−	13.7442i	0.269495	−	0.466779i
$868$	17.6987	+	6.84532i	0.600732	+	0.232345i
$869$	33.6676	−	19.4380i	1.14210	−	0.659389i
$870$	−11.2987	+	19.5698i	−0.383060	+	0.663480i
$871$	12.5385	−	17.9180i	0.424850	−	0.607127i
$872$	1.89214	+	3.27729i	0.0640761	+	0.110983i
$873$			9.46989i			0.320507i
$874$	−16.3756	−	28.3634i	−0.553913	−	0.959406i
$875$	−15.0084	+	12.0908i	−0.507376	+	0.408744i
$876$			6.85849i			0.231727i
$877$	−4.28533	+	2.47413i	−0.144705	+	0.0835456i	−0.570605	−	0.821225i	$-0.693291\pi$
$877$	−4.28533	+	2.47413i	−0.144705	+	0.0835456i	0.425899	+	0.904771i	$0.359958\pi$
$878$			14.1623i			0.477953i
$879$	4.13569	−	2.38774i	0.139494	−	0.0805366i
$880$	6.88828	+	11.9308i	0.232204	+	0.402189i
$881$	−5.49446	−	9.51669i	−0.185113	−	0.320625i	0.758501	−	0.651671i	$-0.225932\pi$
$881$	−5.49446	−	9.51669i	−0.185113	−	0.320625i	−0.943615	+	0.331046i	$0.892599\pi$
$882$	2.12940	+	6.66826i	0.0717006	+	0.224532i
$883$	43.0985			1.45038			0.725190	−	0.688549i	$-0.241752\pi$
$883$	43.0985			1.45038			0.725190	+	0.688549i	$0.241752\pi$
$884$	1.79563	−	20.5935i	0.0603936	−	0.692634i
$885$	8.75630	+	15.1664i	0.294340	+	0.509811i
$886$	−23.8880	−	13.7918i	−0.802534	−	0.463343i
$887$	−42.2975			−1.42021			−0.710106	−	0.704095i	$-0.751353\pi$
$887$	−42.2975			−1.42021			−0.710106	+	0.704095i	$0.751353\pi$
$888$	−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
$891$	4.41435	−	2.54863i	0.147886	−	0.0853822i
$892$	22.5859	−	13.0400i	0.756233	−	0.436611i
$893$	37.6772			1.26082
$894$	−23.2914			−0.778983
$895$	−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
$899$	51.9334	+	29.9838i	1.73208	+	1.00001i
$900$	−1.15240	+	1.99602i	−0.0384133	+	0.0665339i
$901$	−20.6592	−	35.7828i	−0.688258	−	1.19210i
$902$		−	19.4032i		−	0.646055i
$903$	5.93053	−	15.3335i	0.197356	−	0.510266i
$904$	−1.47154	−	0.849593i	−0.0489426	−	0.0282570i
$905$	−4.61180	−	2.66262i	−0.153301	−	0.0885086i
$906$	18.3147			0.608466
$907$	−16.5689	+	28.6982i	−0.550162	+	0.952908i	0.448101	+	0.893983i	$0.352101\pi$
$907$	−16.5689	+	28.6982i	−0.550162	+	0.952908i	−0.998262	+	0.0589251i	$0.981233\pi$
$908$			11.6727i			0.387372i
$909$	−3.72210			−0.123454
$910$	−1.74093	−	25.7236i	−0.0577113	−	0.852731i
$911$	−26.0908			−0.864426			−0.432213	−	0.901772i	$-0.642267\pi$
$911$	−26.0908			−0.864426			−0.432213	+	0.901772i	$0.642267\pi$
$912$			4.38458i			0.145188i
$913$	39.2402	−	67.9661i	1.29866	−	2.24935i
$914$	−20.9436			−0.692754
$915$	−10.8850	−	6.28449i	−0.359849	−	0.207759i
$916$	10.4614	+	6.03988i	0.345654	+	0.199563i
$917$	−1.87422	+	0.291988i	−0.0618923	+	0.00964230i
$918$			5.73328i			0.189226i
$919$	23.1004	+	40.0111i	0.762013	+	1.31984i	0.941812	+	0.336141i	$0.109122\pi$
$919$	23.1004	+	40.0111i	0.762013	+	1.31984i	−0.179799	+	0.983703i	$0.557545\pi$
$920$	−10.0943	+	17.4838i	−0.332798	+	0.576422i
$921$	−5.42497	−	3.13211i	−0.178759	−	0.103207i
$922$	−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
$926$	−28.8633			−0.948508
$927$	−9.10929			−0.299188
$928$	7.24074	−	4.18045i	0.237689	−	0.137230i
$929$	2.74803	−	1.58658i	0.0901599	−	0.0520539i	−0.454242	−	0.890878i	$-0.650090\pi$
$929$	2.74803	−	1.58658i	0.0901599	−	0.0520539i	0.544402	+	0.838824i	$0.316757\pi$
$930$	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
$933$	5.98426			0.195916
$934$	−29.2322	−	16.8772i	−0.956505	−	0.552239i
$935$	−39.4924	−	68.4029i	−1.29154	−	2.23701i
$936$	1.52473	+	3.26729i	0.0498373	+	0.106795i
$937$	36.3959			1.18900			0.594501	−	0.804095i	$-0.297350\pi$
$937$	36.3959			1.18900			0.594501	+	0.804095i	$0.297350\pi$
$938$	−15.8564	+	2.47030i	−0.517730	+	0.0806580i
$939$	−14.3286	−	24.8179i	−0.467597	−	0.809902i
$940$	−11.6125	−	20.1134i	−0.378757	−	0.656027i
$941$	25.2928	−	14.6028i	0.824521	−	0.476037i	−0.0274523	−	0.999623i	$-0.508739\pi$
$941$	25.2928	−	14.6028i	0.824521	−	0.476037i	0.851973	+	0.523586i	$0.175406\pi$
$942$		−	3.83550i		−	0.124967i
$943$	24.6245	−	14.2169i	0.801883	−	0.462967i
$944$		−	6.47957i		−	0.210892i
$945$	1.10075	+	7.06555i	0.0358075	+	0.229842i
$946$	−15.8369	−	27.4303i	−0.514901	−	0.891835i
$947$			8.20811i			0.266728i	0.991067	+	0.133364i	$0.0425779\pi$
$947$			8.20811i			0.266728i	−0.991067	+	0.133364i	$0.957422\pi$
$948$	−3.81342	−	6.60504i	−0.123854	−	0.214522i
$949$	−10.4573	−	22.4087i	−0.339459	−	0.727417i
$950$	5.05279	−	8.75168i	0.163934	−	0.283942i
$951$	22.2694	−	12.8572i	0.722134	−	0.416924i
$952$	−11.8125	+	9.51619i	−0.382846	+	0.308422i
$953$	−22.9551	+	39.7595i	−0.743590	+	1.28794i	0.207261	+	0.978286i	$0.433545\pi$
$953$	−22.9551	+	39.7595i	−0.743590	+	1.28794i	−0.950851	+	0.309649i	$0.899788\pi$
$954$	6.24125	+	3.60339i	0.202068	+	0.116664i
$955$			10.0257i			0.324425i
$956$			16.8139i			0.543799i
$957$	36.9079	+	21.3088i	1.19306	+	0.688816i
$958$	−8.71070	+	15.0874i	−0.281430	+	0.487451i
$959$	20.7183	−	16.6907i	0.669028	−	0.538971i
$960$	2.34064	−	1.35137i	0.0755439	−	0.0436153i
$961$	10.2215	−	17.7042i	0.329727	−	0.571105i
$962$	2.12161	−	24.3321i	0.0684034	−	0.784497i
$963$	−5.28386	−	9.15192i	−0.170270	−	0.294917i
$964$			22.3511i			0.719881i
$965$	−4.02708	−	6.97511i	−0.129636	−	0.224537i
$966$	3.04218	+	19.5273i	0.0978807	+	0.628280i
$967$		−	27.1219i		−	0.872182i	−0.899903	−	0.436091i	$-0.856363\pi$
$967$		−	27.1219i		−	0.872182i	0.899903	−	0.436091i	$-0.143637\pi$
$968$	12.9748	−	7.49101i	0.417026	−	0.240770i
$969$		−	25.1380i		−	0.807549i
$970$	−22.1656	+	12.7973i	−0.711695	+	0.410897i
$971$	22.7273	+	39.3648i	0.729353	+	1.26328i	0.957157	+	0.289569i	$0.0935120\pi$
$971$	22.7273	+	39.3648i	0.729353	+	1.26328i	−0.227805	+	0.973707i	$0.573155\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	46.2550	−	7.20614i	1.48287	−	0.231018i
$974$	38.2660			1.22612
$975$	0.721850	−	8.27867i	0.0231177	−	0.265130i
$976$	2.32523	+	4.02741i	0.0744287	+	0.128914i
$977$	−17.8075	−	10.2812i	−0.569714	−	0.328924i	0.187321	−	0.982299i	$-0.440019\pi$
$977$	−17.8075	−	10.2812i	−0.569714	−	0.328924i	−0.757035	+	0.653374i	$0.773353\pi$
$978$	10.4272			0.333424
$979$	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
$982$	31.8494	−	18.3883i	1.01636	−	0.586793i
$983$	13.1471	−	7.59050i	0.419329	−	0.242099i	−0.275461	−	0.961312i	$-0.588831\pi$
$983$	13.1471	−	7.59050i	0.419329	−	0.242099i	0.694790	+	0.719213i	$0.255497\pi$
$984$	−3.80659			−0.121350
$985$	40.2346			1.28198
$986$	−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
$990$	11.9308	+	6.88828i	0.379187	+	0.218924i
$991$	−2.00473	+	3.47230i	−0.0636824	+	0.110301i	−0.896109	−	0.443835i	$-0.853618\pi$
$991$	−2.00473	+	3.47230i	−0.0636824	+	0.110301i	0.832426	+	0.554136i	$0.186951\pi$
$992$	−3.58619	−	6.21147i	−0.113862	−	0.197214i
$993$			0.880100i			0.0279291i
$994$	−2.39199	+	0.372652i	−0.0758694	+	0.0118198i
$995$	6.23611	+	3.60042i	0.197698	+	0.114141i
$996$	−13.3339	−	7.69830i	−0.422499	−	0.243930i
$997$	−34.3896			−1.08913			−0.544565	−	0.838719i	$-0.683305\pi$
$997$	−34.3896			−1.08913			−0.544565	+	0.838719i	$0.683305\pi$
$998$	−15.0514	+	26.0698i	−0.476444	+	0.825224i
$999$			6.77410i			0.214323i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.4	✓	16	13.4	even	6
546.2.bd.a.361.4	yes	16	7.4	even	3
546.2.bm.a.205.5	yes	16	1.1	even	1	trivial
546.2.bm.a.277.1	yes	16	91.4	even	6	inner
1638.2.cr.a.361.5		16	21.11	odd	6
1638.2.cr.a.667.5		16	39.17	odd	6
1638.2.dt.a.1297.4		16	3.2	odd	2
1638.2.dt.a.1369.8		16	273.95	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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-2.34064 - 1.35137i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.65982 + 2.06034i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.35137 - 2.34064i) q^{10} +(-4.41435 - 2.54863i) 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} +1.00000 q^{16} -5.73328 q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.79715 + 2.19229i) q^{19} +(2.34064 + 1.35137i) q^{20} +(2.61422 - 0.407273i) q^{21} +(2.54863 - 4.41435i) q^{22} +7.46964 q^{23} +(-0.866025 - 0.500000i) q^{24} +(1.15240 + 1.99602i) q^{25} +(3.59192 + 0.313194i) q^{26} -1.00000 q^{27} +(-1.65982 - 2.06034i) q^{28} +(-4.18045 - 7.24074i) q^{29} +(-1.35137 - 2.34064i) q^{30} +(-6.21147 + 3.58619i) q^{31} +1.00000i q^{32} +(-4.41435 + 2.54863i) q^{33} -5.73328i q^{34} +(-1.10075 - 7.06555i) q^{35} +(0.500000 + 0.866025i) q^{36} -6.77410i q^{37} +(-2.19229 - 3.79715i) q^{38} +(-2.95410 - 2.06720i) q^{39} +(-1.35137 + 2.34064i) q^{40} +(3.29661 - 1.90330i) q^{41} +(0.407273 + 2.61422i) q^{42} +(3.10694 - 5.38138i) q^{43} +(4.41435 + 2.54863i) q^{44} +2.70274i q^{45} +7.46964i q^{46} +(-7.44186 - 4.29656i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.49001 + 6.83958i) q^{49} +(-1.99602 + 1.15240i) q^{50} +(-2.86664 + 4.96516i) q^{51} +(-0.313194 + 3.59192i) q^{52} +(3.60339 + 6.24125i) q^{53} -1.00000i q^{54} +(6.88828 + 11.9308i) q^{55} +(2.06034 - 1.65982i) q^{56} +4.38458i q^{57} +(7.24074 - 4.18045i) q^{58} -6.47957i q^{59} +(2.34064 - 1.35137i) q^{60} +(2.32523 + 4.02741i) q^{61} +(-3.58619 - 6.21147i) q^{62} +(0.954400 - 2.46761i) q^{63} -1.00000 q^{64} +(-5.58709 + 7.98416i) q^{65} +(-2.54863 - 4.41435i) q^{66} +(5.25284 + 3.03273i) q^{67} +5.73328 q^{68} +(3.73482 - 6.46890i) q^{69} +(7.06555 - 1.10075i) q^{70} +(0.792408 + 0.457497i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.93963 - 3.42924i) q^{73} +6.77410 q^{74} +2.30480 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} +(-2.34064 - 1.35137i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.90330 + 3.29661i) q^{82} +15.3966i q^{83} +(-2.61422 + 0.407273i) q^{84} +(13.4195 + 7.74778i) q^{85} +(5.38138 + 3.10694i) q^{86} -8.36089 q^{87} +(-2.54863 + 4.41435i) q^{88} +10.3822i q^{89} -2.70274 q^{90} +(7.92043 - 5.31665i) q^{91} -7.46964 q^{92} +7.17238i q^{93} +(4.29656 - 7.44186i) q^{94} +11.8504 q^{95} +(0.866025 + 0.500000i) q^{96} +(-8.20116 - 4.73494i) q^{97} +(-6.83958 - 1.49001i) q^{98} +5.09726i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29}+ \cdots - 60 q^{98}+O(q^{100}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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