LMFDB - Embedded newform 845.2.n.c.529.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(484,845)] 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("845.484"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-6,0,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.3
Root			$0.228425 + 1.39564i$ of defining polynomial
Character	$\chi$	$=$	845.529
Dual form			845.2.n.c.484.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395644 + 0.228425i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.895644 - 1.55130i) q^{4} +(-0.456850 - 2.18890i) q^{5} +(-0.228425 - 0.395644i) q^{6} +(-1.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.319250 - 0.970381i) q^{10} +(1.32288 - 2.29129i) q^{11} +1.79129i q^{12} -0.791288 q^{14} +(-0.698807 + 2.12407i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-3.96863 + 2.29129i) q^{17} -0.913701i q^{18} +(0.866025 + 1.50000i) q^{19} +(-2.98647 + 2.66919i) q^{20} +1.73205 q^{21} +(1.04678 - 0.604356i) q^{22} +(3.96863 + 2.29129i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(-4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +(2.68693 + 1.55130i) q^{28} +(2.29129 - 3.96863i) q^{29} +(-0.761669 + 0.680750i) q^{30} +6.20520 q^{31} +(-4.10436 + 2.36965i) q^{32} +(-2.29129 + 1.32288i) q^{33} -2.09355 q^{34} +(2.58092 + 2.88771i) q^{35} +(-1.79129 + 3.10260i) q^{36} +(-6.87386 - 3.96863i) q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +(1.32288 - 2.29129i) q^{41} +(0.685275 + 0.395644i) q^{42} +(-9.16478 + 5.29129i) q^{43} -4.73930 q^{44} +(-3.33444 + 2.98019i) q^{45} +(1.04678 + 1.81307i) q^{46} -1.82740i q^{47} +(2.41733 - 1.39564i) q^{48} +(-2.00000 + 3.46410i) q^{49} +(-2.26992 - 0.255488i) q^{50} +4.58258 q^{51} +7.58258i q^{53} +(-1.14213 + 1.97822i) q^{54} +(-5.61976 - 1.84887i) q^{55} +(1.50000 + 2.59808i) q^{56} -1.73205i q^{57} +(1.81307 - 1.04678i) q^{58} +(-6.97588 - 12.0826i) q^{59} +(3.92095 - 0.818350i) q^{60} +(0.708712 + 1.22753i) q^{61} +(2.45505 + 1.41742i) q^{62} +(3.00000 + 1.73205i) q^{63} +3.41742 q^{64} -1.20871 q^{66} +(-0.873864 - 0.504525i) q^{67} +(7.10895 + 4.10436i) q^{68} +(-2.29129 - 3.96863i) q^{69} +(0.361500 + 1.73205i) q^{70} +(-3.51178 - 6.08258i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-1.81307 - 3.14033i) q^{74} +(4.96863 + 0.559237i) q^{75} +(1.55130 - 2.68693i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(5.92889 + 1.95057i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.04678 - 0.604356i) q^{82} -6.01450i q^{83} +(-1.55130 - 2.68693i) q^{84} +(6.82847 + 7.64016i) q^{85} -4.83465 q^{86} +(-3.96863 + 2.29129i) q^{87} +(-3.96863 - 2.29129i) q^{88} +(-4.78698 + 8.29129i) q^{89} +(-2.00000 + 0.417424i) q^{90} -8.20871i q^{92} +(-5.37386 - 3.10260i) q^{93} +(0.417424 - 0.723000i) q^{94} +(2.88771 - 2.58092i) q^{95} +4.73930 q^{96} +(9.87386 - 5.70068i) q^{97} +(-1.58258 + 0.913701i) q^{98} -5.29150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + 2 q^{4} - 12 q^{7} - 8 q^{9} + 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 18 q^{20} - 6 q^{28} + 10 q^{30} - 42 q^{32} + 6 q^{35} + 4 q^{36} - 12 q^{40} - 12 q^{45} - 16 q^{49} - 42 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 + 2 * q^4 - 12 * q^7 - 8 * q^9 + 4 * q^10 + 12 * q^14 - 6 * q^15 - 2 * q^16 - 18 * q^20 - 6 * q^28 + 10 * q^30 - 42 * q^32 + 6 * q^35 + 4 * q^36 - 12 * q^40 - 12 * q^45 - 16 * q^49 - 42 * q^50 - 14 * q^55 + 12 * q^56 + 42 * q^58 + 24 * q^61 + 24 * q^63 + 64 * q^64 - 28 * q^66 + 48 * q^67 - 24 * q^72 - 42 * q^74 + 8 * q^75 + 48 * q^79 + 24 * q^80 - 4 * q^81 + 42 * q^85 - 16 * q^90 + 12 * q^93 + 40 * q^94 + 6 * q^95 + 24 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.395644	+	0.228425i	0.279763	+	0.161521i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	0.395644	+	0.228425i	0.279763	+	0.161521i	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	0.228714	−	0.973494i	$-0.426548\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	−0.728714	+	0.684819i	$0.759881\pi$
$4$	−0.895644	−	1.55130i	−0.447822	−	0.775650i
$5$	−0.456850	−	2.18890i	−0.204310	−	0.978906i
$5$	−0.456850	−	2.18890i	−0.204310	−	0.978906i
$6$	−0.228425	−	0.395644i	−0.0932542	−	0.161521i
$7$	−1.50000	+	0.866025i	−0.566947	+	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−1.50000	+	0.866025i	−0.566947	+	0.327327i	0.188982	+	0.981981i	$0.439481\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	0.319250	−	0.970381i	0.100956	−	0.306862i
$11$	1.32288	−	2.29129i	0.398862	−	0.690849i	−0.594724	−	0.803930i	$-0.702739\pi$
$11$	1.32288	−	2.29129i	0.398862	−	0.690849i	0.993586	+	0.113081i	$0.0360719\pi$
$12$			1.79129i			0.517100i
$13$		0			0
$13$		0			0
$14$	−0.791288			−0.211481
$15$	−0.698807	+	2.12407i	−0.180431	+	0.548432i
$16$	−1.39564	+	2.41733i	−0.348911	+	0.604332i
$17$	−3.96863	+	2.29129i	−0.962533	+	0.555719i	−0.896952	−	0.442128i	$-0.854224\pi$
$17$	−3.96863	+	2.29129i	−0.962533	+	0.555719i	−0.0655816	+	0.997847i	$0.520890\pi$
$18$		−	0.913701i		−	0.215361i
$19$	0.866025	+	1.50000i	0.198680	+	0.344124i	0.948101	−	0.317970i	$-0.103001\pi$
$19$	0.866025	+	1.50000i	0.198680	+	0.344124i	−0.749421	+	0.662094i	$0.769668\pi$
$20$	−2.98647	+	2.66919i	−0.667795	+	0.596849i
$21$	1.73205			0.377964
$22$	1.04678	−	0.604356i	0.223173	−	0.128849i
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	0.853001	−	0.521909i	$-0.174780\pi$
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	−0.0254855	+	0.999675i	$0.508113\pi$
$24$	−0.866025	+	1.50000i	−0.176777	+	0.306186i
$25$	−4.58258	+	2.00000i	−0.916515	+	0.400000i
$26$		0			0
$27$			5.00000i			0.962250i
$28$	2.68693	+	1.55130i	0.507782	+	0.293168i
$29$	2.29129	−	3.96863i	0.425481	−	0.736956i	−0.570984	−	0.820961i	$-0.693438\pi$
$29$	2.29129	−	3.96863i	0.425481	−	0.736956i	0.996465	+	0.0840058i	$0.0267714\pi$
$30$	−0.761669	+	0.680750i	−0.139061	+	0.124287i
$31$	6.20520			1.11449			0.557244	−	0.830349i	$-0.311859\pi$
$31$	6.20520			1.11449			0.557244	+	0.830349i	$0.311859\pi$
$32$	−4.10436	+	2.36965i	−0.725555	+	0.418899i
$33$	−2.29129	+	1.32288i	−0.398862	+	0.230283i
$34$	−2.09355			−0.359041
$35$	2.58092	+	2.88771i	0.436255	+	0.488112i
$36$	−1.79129	+	3.10260i	−0.298548	+	0.517100i
$37$	−6.87386	−	3.96863i	−1.13006	−	0.652438i	−0.186107	−	0.982529i	$-0.559587\pi$
$37$	−6.87386	−	3.96863i	−1.13006	−	0.652438i	−0.943949	+	0.330091i	$0.892920\pi$
$38$			0.791288i			0.128364i
$39$		0			0
$40$	−3.79129	+	0.791288i	−0.599455	+	0.125114i
$41$	1.32288	−	2.29129i	0.206598	−	0.357839i	−0.744042	−	0.668132i	$-0.767094\pi$
$41$	1.32288	−	2.29129i	0.206598	−	0.357839i	0.950641	+	0.310293i	$0.100427\pi$
$42$	0.685275	+	0.395644i	0.105740	+	0.0610492i
$43$	−9.16478	+	5.29129i	−1.39762	+	0.806914i	−0.994142	−	0.108078i	$-0.965531\pi$
$43$	−9.16478	+	5.29129i	−1.39762	+	0.806914i	−0.403473	+	0.914991i	$0.632197\pi$
$44$	−4.73930			−0.714477
$45$	−3.33444	+	2.98019i	−0.497069	+	0.444260i
$46$	1.04678	+	1.81307i	0.154339	+	0.267322i
$47$		−	1.82740i		−	0.266554i	−0.991079	−	0.133277i	$-0.957450\pi$
$47$		−	1.82740i		−	0.266554i	0.991079	−	0.133277i	$-0.0425500\pi$
$48$	2.41733	−	1.39564i	0.348911	−	0.201444i
$49$	−2.00000	+	3.46410i	−0.285714	+	0.494872i
$50$	−2.26992	−	0.255488i	−0.321015	−	0.0361314i
$51$	4.58258			0.641689
$52$		0			0
$53$			7.58258i			1.04155i	0.853695	+	0.520773i	$0.174356\pi$
$53$			7.58258i			1.04155i	−0.853695	+	0.520773i	$0.825644\pi$
$54$	−1.14213	+	1.97822i	−0.155424	+	0.269202i
$55$	−5.61976	−	1.84887i	−0.757768	−	0.249301i
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$		−	1.73205i		−	0.229416i
$58$	1.81307	−	1.04678i	0.238068	−	0.137448i
$59$	−6.97588	−	12.0826i	−0.908182	−	1.57302i	−0.816588	−	0.577221i	$-0.804137\pi$
$59$	−6.97588	−	12.0826i	−0.908182	−	1.57302i	−0.0915940	−	0.995796i	$-0.529196\pi$
$60$	3.92095	−	0.818350i	0.506193	−	0.105649i
$61$	0.708712	+	1.22753i	0.0907413	+	0.157169i	0.907823	−	0.419353i	$-0.137743\pi$
$61$	0.708712	+	1.22753i	0.0907413	+	0.157169i	−0.817082	+	0.576522i	$0.804410\pi$
$62$	2.45505	+	1.41742i	0.311792	+	0.180013i
$63$	3.00000	+	1.73205i	0.377964	+	0.218218i
$64$	3.41742			0.427178
$65$		0			0
$66$	−1.20871			−0.148782
$67$	−0.873864	−	0.504525i	−0.106759	−	0.0616376i	0.445670	−	0.895198i	$-0.352966\pi$
$67$	−0.873864	−	0.504525i	−0.106759	−	0.0616376i	−0.552429	+	0.833560i	$0.686299\pi$
$68$	7.10895	+	4.10436i	0.862087	+	0.497726i
$69$	−2.29129	−	3.96863i	−0.275839	−	0.477767i
$70$	0.361500	+	1.73205i	0.0432075	+	0.207020i
$71$	−3.51178	−	6.08258i	−0.416771	−	0.721869i	0.578841	−	0.815440i	$-0.303505\pi$
$71$	−3.51178	−	6.08258i	−0.416771	−	0.721869i	−0.995613	+	0.0935712i	$0.970172\pi$
$72$	−3.00000	+	1.73205i	−0.353553	+	0.204124i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−1.81307	−	3.14033i	−0.210765	−	0.365056i
$75$	4.96863	+	0.559237i	0.573728	+	0.0645751i
$76$	1.55130	−	2.68693i	0.177946	−	0.308212i
$77$			4.58258i			0.522233i
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	5.92889	+	1.95057i	0.662870	+	0.218080i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.04678	−	0.604356i	0.115597	−	0.0667400i
$83$		−	6.01450i		−	0.660177i	−0.943950	−	0.330089i	$-0.892921\pi$
$83$		−	6.01450i		−	0.660177i	0.943950	−	0.330089i	$-0.107079\pi$
$84$	−1.55130	−	2.68693i	−0.169261	−	0.293168i
$85$	6.82847	+	7.64016i	0.740652	+	0.828691i
$86$	−4.83465			−0.521334
$87$	−3.96863	+	2.29129i	−0.425481	+	0.245652i
$88$	−3.96863	−	2.29129i	−0.423057	−	0.244252i
$89$	−4.78698	+	8.29129i	−0.507419	+	0.878875i	0.492545	+	0.870287i	$0.336067\pi$
$89$	−4.78698	+	8.29129i	−0.507419	+	0.878875i	−0.999963	+	0.00858752i	$0.997266\pi$
$90$	−2.00000	+	0.417424i	−0.210819	+	0.0440004i
$91$		0			0
$92$		−	8.20871i		−	0.855817i
$93$	−5.37386	−	3.10260i	−0.557244	−	0.321725i
$94$	0.417424	−	0.723000i	0.0430540	−	0.0745718i
$95$	2.88771	−	2.58092i	0.296273	−	0.264797i
$96$	4.73930			0.483703
$97$	9.87386	−	5.70068i	1.00254	−	0.578816i	0.0935404	−	0.995615i	$-0.470182\pi$
$97$	9.87386	−	5.70068i	1.00254	−	0.578816i	0.908999	+	0.416799i	$0.136848\pi$
$98$	−1.58258	+	0.913701i	−0.159864	+	0.0922977i
$99$	−5.29150			−0.531816
$100$	7.20696	+	5.31767i	0.720696	+	0.531767i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	1.81307	+	1.04678i	0.179521	+	0.103646i
$103$		−	3.16515i		−	0.311872i	−0.987767	−	0.155936i	$-0.950161\pi$
$103$		−	3.16515i		−	0.311872i	0.987767	−	0.155936i	$-0.0498393\pi$
$104$		0			0
$105$	−0.791288	−	3.79129i	−0.0772218	−	0.369992i
$106$	−1.73205	+	3.00000i	−0.168232	+	0.291386i
$107$	−9.16478	−	5.29129i	−0.885993	−	0.511528i	−0.0133631	−	0.999911i	$-0.504254\pi$
$107$	−9.16478	−	5.29129i	−0.885993	−	0.511528i	−0.872630	+	0.488383i	$0.837587\pi$
$108$	7.75650	−	4.47822i	0.746370	−	0.430917i
$109$	−13.1334			−1.25795			−0.628976	−	0.777425i	$-0.716526\pi$
$109$	−13.1334			−1.25795			−0.628976	+	0.777425i	$0.716526\pi$
$110$	−1.80110	−	2.01519i	−0.171728	−	0.192141i
$111$	3.96863	+	6.87386i	0.376685	+	0.652438i
$112$		−	4.83465i		−	0.456832i
$113$	−6.42368	+	3.70871i	−0.604289	+	0.348886i	−0.770727	−	0.637166i	$-0.780107\pi$
$113$	−6.42368	+	3.70871i	−0.604289	+	0.348886i	0.166438	+	0.986052i	$0.446773\pi$
$114$	0.395644	−	0.685275i	0.0370554	−	0.0641819i
$115$	3.20233	−	9.73371i	0.298619	−	0.907673i
$116$	−8.20871			−0.762160
$117$		0			0
$118$		−	6.37386i		−	0.586762i
$119$	3.96863	−	6.87386i	0.363803	−	0.630126i
$120$	3.67900	+	1.21037i	0.335845	+	0.110491i
$121$	2.00000	+	3.46410i	0.181818	+	0.314918i
$122$			0.647551i			0.0586265i
$123$	−2.29129	+	1.32288i	−0.206598	+	0.119280i
$124$	−5.55765	−	9.62614i	−0.499092	−	0.864453i
$125$	6.47135	+	9.11710i	0.578815	+	0.815459i
$126$	0.791288	+	1.37055i	0.0704935	+	0.122098i
$127$	−15.3700	−	8.87386i	−1.36387	−	0.787428i	−0.373729	−	0.927538i	$-0.621921\pi$
$127$	−15.3700	−	8.87386i	−1.36387	−	0.787428i	−0.990136	+	0.140110i	$0.955254\pi$
$128$	9.56080	+	5.51993i	0.845063	+	0.487897i
$129$	10.5826			0.931744
$130$		0			0
$131$	−7.58258			−0.662493			−0.331246	−	0.943544i	$-0.607469\pi$
$131$	−7.58258			−0.662493			−0.331246	+	0.943544i	$0.607469\pi$
$132$	4.10436	+	2.36965i	0.357238	+	0.206252i
$133$	−2.59808	−	1.50000i	−0.225282	−	0.130066i
$134$	−0.230493	−	0.399225i	−0.0199115	−	0.0344878i
$135$	10.9445	−	2.28425i	0.941953	−	0.196597i
$136$	3.96863	+	6.87386i	0.340307	+	0.589429i
$137$	9.08258	−	5.24383i	0.775977	−	0.448010i	−0.0590258	−	0.998256i	$-0.518799\pi$
$137$	9.08258	−	5.24383i	0.775977	−	0.448010i	0.835003	+	0.550246i	$0.185466\pi$
$138$		−	2.09355i		−	0.178215i
$139$	−10.8739	−	18.8341i	−0.922309	−	1.59749i	−0.795833	−	0.605517i	$-0.792967\pi$
$139$	−10.8739	−	18.8341i	−0.922309	−	1.59749i	−0.126476	−	0.991970i	$-0.540367\pi$
$140$	2.16812	−	6.59014i	0.183239	−	0.556968i
$141$	−0.913701	+	1.58258i	−0.0769475	+	0.133277i
$142$		−	3.20871i		−	0.269269i
$143$		0			0
$144$	5.58258			0.465215
$145$	−9.73371	−	3.20233i	−0.808340	−	0.265939i
$146$		0			0
$147$	3.46410	−	2.00000i	0.285714	−	0.164957i
$148$			14.2179i			1.16870i
$149$	8.34643	+	14.4564i	0.683766	+	1.18432i	0.973823	+	0.227308i	$0.0729925\pi$
$149$	8.34643	+	14.4564i	0.683766	+	1.18432i	−0.290057	+	0.957009i	$0.593674\pi$
$150$	1.83806	+	1.35622i	0.150077	+	0.110735i
$151$	9.66930			0.786877			0.393438	−	0.919351i	$-0.371285\pi$
$151$	9.66930			0.786877			0.393438	+	0.919351i	$0.371285\pi$
$152$	2.59808	−	1.50000i	0.210732	−	0.121666i
$153$	7.93725	+	4.58258i	0.641689	+	0.370479i
$154$	−1.04678	+	1.81307i	−0.0843516	+	0.146101i
$155$	−2.83485	−	13.5826i	−0.227701	−	1.09098i
$156$		0			0
$157$		−	9.16515i		−	0.731459i	−0.930721	−	0.365729i	$-0.880820\pi$
$157$		−	9.16515i		−	0.731459i	0.930721	−	0.365729i	$-0.119180\pi$
$158$	2.37386	+	1.37055i	0.188854	+	0.109035i
$159$	3.79129	−	6.56670i	0.300669	−	0.520773i
$160$	7.06201	+	7.90145i	0.558301	+	0.624665i
$161$	−7.93725			−0.625543
$162$	−0.395644	+	0.228425i	−0.0310847	+	0.0179468i
$163$	18.2477	−	10.5353i	1.42927	−	0.825191i	0.432209	−	0.901773i	$-0.357734\pi$
$163$	18.2477	−	10.5353i	1.42927	−	0.825191i	0.997063	+	0.0765827i	$0.0244009\pi$
$164$	−4.73930			−0.370077
$165$	3.94242	+	4.41105i	0.306917	+	0.343399i
$166$	1.37386	−	2.37960i	0.106632	−	0.184693i
$167$	8.29129	+	4.78698i	0.641599	+	0.370427i	0.785230	−	0.619204i	$-0.212545\pi$
$167$	8.29129	+	4.78698i	0.641599	+	0.370427i	−0.143631	+	0.989631i	$0.545878\pi$
$168$		−	3.00000i		−	0.231455i
$169$		0			0
$170$	0.956439	+	4.58258i	0.0733555	+	0.351468i
$171$	1.73205	−	3.00000i	0.132453	−	0.229416i
$172$	16.4168	+	9.47822i	1.25177	+	0.722707i
$173$	14.3609	−	8.29129i	1.09184	−	0.630375i	0.157775	−	0.987475i	$-0.449568\pi$
$173$	14.3609	−	8.29129i	1.09184	−	0.630375i	0.934066	+	0.357100i	$0.116234\pi$
$174$	−2.09355			−0.158712
$175$	5.14181	−	6.96863i	0.388685	−	0.526779i
$176$	3.69253	+	6.39564i	0.278335	+	0.482090i
$177$			13.9518i			1.04868i
$178$	−3.78788	+	2.18693i	−0.283913	+	0.163917i
$179$	−9.08258	+	15.7315i	−0.678864	+	1.17583i	0.296460	+	0.955045i	$0.404194\pi$
$179$	−9.08258	+	15.7315i	−0.678864	+	1.17583i	−0.975323	+	0.220781i	$0.929139\pi$
$180$	7.60964	+	2.50353i	0.567189	+	0.186602i
$181$	−8.74773			−0.650213			−0.325107	−	0.945677i	$-0.605400\pi$
$181$	−8.74773			−0.650213			−0.325107	+	0.945677i	$0.605400\pi$
$182$		0			0
$183$		−	1.41742i		−	0.104779i
$184$	3.96863	−	6.87386i	0.292571	−	0.506748i
$185$	−5.54661	+	16.8593i	−0.407795	+	1.23952i
$186$	−1.41742	−	2.45505i	−0.103931	−	0.180013i
$187$			12.1244i			0.886621i
$188$	−2.83485	+	1.63670i	−0.206753	+	0.119369i
$189$	−4.33013	−	7.50000i	−0.314970	−	0.545545i
$190$	1.73205	−	0.361500i	0.125656	−	0.0262260i
$191$	8.29129	+	14.3609i	0.599937	+	1.03912i	0.992830	+	0.119536i	$0.0381408\pi$
$191$	8.29129	+	14.3609i	0.599937	+	1.03912i	−0.392893	+	0.919584i	$0.628526\pi$
$192$	−2.95958	−	1.70871i	−0.213589	−	0.123316i
$193$	−12.8739	−	7.43273i	−0.926681	−	0.535020i	−0.0409206	−	0.999162i	$-0.513029\pi$
$193$	−12.8739	−	7.43273i	−0.926681	−	0.535020i	−0.885760	+	0.464143i	$0.846362\pi$
$194$	5.20871			0.373964
$195$		0			0
$196$	7.16515			0.511797
$197$	−12.7087	−	7.33738i	−0.905458	−	0.522767i	−0.0264912	−	0.999649i	$-0.508433\pi$
$197$	−12.7087	−	7.33738i	−0.905458	−	0.522767i	−0.878967	+	0.476882i	$0.841767\pi$
$198$	−2.09355	−	1.20871i	−0.148782	−	0.0858994i
$199$	−5.29129	−	9.16478i	−0.375089	−	0.649674i	0.615251	−	0.788331i	$-0.289055\pi$
$199$	−5.29129	−	9.16478i	−0.375089	−	0.649674i	−0.990340	+	0.138657i	$0.955721\pi$
$200$	3.46410	+	7.93725i	0.244949	+	0.561249i
$201$	0.504525	+	0.873864i	0.0355865	+	0.0616376i
$202$	3.56080	−	2.05583i	0.250537	−	0.144647i
$203$			7.93725i			0.557086i
$204$	−4.10436	−	7.10895i	−0.287362	−	0.497726i
$205$	−5.61976	−	1.84887i	−0.392501	−	0.129131i
$206$	0.723000	−	1.25227i	0.0503738	−	0.0872500i
$207$		−	9.16515i		−	0.637022i
$208$		0			0
$209$	4.58258			0.316983
$210$	0.552957	−	1.68075i	0.0381577	−	0.115983i
$211$	0.0825757	−	0.143025i	0.00568475	−	0.00984627i	−0.863169	−	0.504915i	$-0.831524\pi$
$211$	0.0825757	−	0.143025i	0.00568475	−	0.00984627i	0.868854	+	0.495069i	$0.164857\pi$
$212$	11.7629	−	6.79129i	0.807876	−	0.466428i
$213$			7.02355i			0.481246i
$214$	−2.41733	−	4.18693i	−0.165245	−	0.286213i
$215$	15.7690	+	17.6435i	1.07544	+	1.20327i
$216$	8.66025			0.589256
$217$	−9.30780	+	5.37386i	−0.631855	+	0.364802i
$218$	−5.19615	−	3.00000i	−0.351928	−	0.203186i
$219$		0			0
$220$	2.16515	+	10.3739i	0.145974	+	0.699406i
$221$		0			0
$222$			3.62614i			0.243370i
$223$	−7.50000	−	4.33013i	−0.502237	−	0.289967i	0.227400	−	0.973801i	$-0.426978\pi$
$223$	−7.50000	−	4.33013i	−0.502237	−	0.289967i	−0.729637	+	0.683835i	$0.760311\pi$
$224$	4.10436	−	7.10895i	0.274234	−	0.474987i
$225$	8.04668	+	5.93725i	0.536445	+	0.395817i
$226$	−3.38865			−0.225410
$227$	−0.708712	+	0.409175i	−0.0470389	+	0.0271579i	−0.523335	−	0.852127i	$-0.675312\pi$
$227$	−0.708712	+	0.409175i	−0.0470389	+	0.0271579i	0.476296	+	0.879285i	$0.341979\pi$
$228$	−2.68693	+	1.55130i	−0.177946	+	0.102737i
$229$	−26.2668			−1.73576			−0.867880	−	0.496774i	$-0.834518\pi$
$229$	−26.2668			−1.73576			−0.867880	+	0.496774i	$0.834518\pi$
$230$	3.49041	−	3.11959i	0.230151	−	0.205700i
$231$	2.29129	−	3.96863i	0.150756	−	0.261116i
$232$	−6.87386	−	3.96863i	−0.451291	−	0.260553i
$233$		−	2.83485i		−	0.185717i	−0.995679	−	0.0928586i	$-0.970400\pi$
$233$		−	2.83485i		−	0.185717i	0.995679	−	0.0928586i	$-0.0296004\pi$
$234$		0			0
$235$	−4.00000	+	0.834849i	−0.260931	+	0.0544595i
$236$	−12.4958	+	21.6434i	−0.813408	+	1.40886i
$237$	−5.19615	−	3.00000i	−0.337526	−	0.194871i
$238$	3.14033	−	1.81307i	0.203557	−	0.117524i
$239$	0.190700			0.0123354			0.00616769	−	0.999981i	$-0.498037\pi$
$239$	0.190700			0.0123354			0.00616769	+	0.999981i	$0.498037\pi$
$240$	−4.15928	−	4.65369i	−0.268481	−	0.300394i
$241$	−0.866025	−	1.50000i	−0.0557856	−	0.0966235i	0.836784	−	0.547533i	$-0.184433\pi$
$241$	−0.866025	−	1.50000i	−0.0557856	−	0.0966235i	−0.892570	+	0.450910i	$0.851100\pi$
$242$			1.82740i			0.117470i
$243$	13.8564	−	8.00000i	0.888889	−	0.513200i
$244$	1.26951	−	2.19885i	0.0812719	−	0.140767i
$245$	8.49628	+	2.79523i	0.542807	+	0.178580i
$246$	−1.20871			−0.0770647
$247$		0			0
$248$		−	10.7477i		−	0.682481i
$249$	−3.00725	+	5.20871i	−0.190577	+	0.330089i
$250$	0.477776	+	5.08535i	0.0302172	+	0.321626i
$251$	−0.0825757	−	0.143025i	−0.00521213	−	0.00902768i	0.863408	−	0.504507i	$-0.168326\pi$
$251$	−0.0825757	−	0.143025i	−0.00521213	−	0.00902768i	−0.868620	+	0.495479i	$0.834992\pi$
$252$		−	6.20520i		−	0.390891i
$253$	10.5000	−	6.06218i	0.660129	−	0.381126i
$254$	−4.05403	−	7.02178i	−0.254372	−	0.440586i
$255$	−2.09355	−	10.0308i	−0.131103	−	0.628153i
$256$	−0.895644	−	1.55130i	−0.0559777	−	0.0969563i
$257$	15.7315	+	9.08258i	0.981303	+	0.566556i	0.902663	−	0.430348i	$-0.141609\pi$
$257$	15.7315	+	9.08258i	0.981303	+	0.566556i	0.0786397	+	0.996903i	$0.474942\pi$
$258$	4.18693	+	2.41733i	0.260667	+	0.150496i
$259$	13.7477			0.854242
$260$		0			0
$261$	−9.16515			−0.567309
$262$	−3.00000	−	1.73205i	−0.185341	−	0.107006i
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	0.240059	−	0.970758i	$-0.422833\pi$
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	−0.720672	+	0.693276i	$0.756167\pi$
$264$	2.29129	+	3.96863i	0.141019	+	0.244252i
$265$	16.5975	−	3.46410i	1.01958	−	0.212798i
$266$	−0.685275	−	1.18693i	−0.0420169	−	0.0727755i
$267$	8.29129	−	4.78698i	0.507419	−	0.292958i
$268$			1.80750i			0.110411i
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$	4.85191	+	1.59625i	0.295278	+	0.0971447i
$271$	−4.33013	+	7.50000i	−0.263036	+	0.455593i	−0.967047	−	0.254597i	$-0.918057\pi$
$271$	−4.33013	+	7.50000i	−0.263036	+	0.455593i	0.704011	+	0.710189i	$0.251391\pi$
$272$		−	12.7913i		−	0.775586i
$273$		0			0
$274$	4.79129			0.289452
$275$	−1.47960	+	13.1458i	−0.0892234	+	0.792719i
$276$	−4.10436	+	7.10895i	−0.247053	+	0.427909i
$277$	−6.42368	+	3.70871i	−0.385961	+	0.222835i	−0.680409	−	0.732833i	$-0.738198\pi$
$277$	−6.42368	+	3.70871i	−0.385961	+	0.222835i	0.294447	+	0.955668i	$0.404864\pi$
$278$		−	9.93545i		−	0.595889i
$279$	−6.20520	−	10.7477i	−0.371496	−	0.643450i
$280$	5.00166	−	4.47028i	0.298906	−	0.267151i
$281$	−3.65480			−0.218027			−0.109014	−	0.994040i	$-0.534769\pi$
$281$	−3.65480			−0.218027			−0.109014	+	0.994040i	$0.534769\pi$
$282$	−0.723000	+	0.417424i	−0.0430540	+	0.0248573i
$283$	−24.0302	−	13.8739i	−1.42845	−	0.824716i	−0.431451	−	0.902136i	$-0.641998\pi$
$283$	−24.0302	−	13.8739i	−1.42845	−	0.824716i	−0.996998	+	0.0774209i	$0.975331\pi$
$284$	−6.29060	+	10.8956i	−0.373279	+	0.646538i
$285$	−3.79129	+	0.791288i	−0.224577	+	0.0468718i
$286$		0			0
$287$			4.58258i			0.270501i
$288$	8.20871	+	4.73930i	0.483703	+	0.279266i
$289$	2.00000	−	3.46410i	0.117647	−	0.203771i
$290$	−3.11959	−	3.49041i	−0.183189	−	0.204964i
$291$	−11.4014			−0.668359
$292$		0			0
$293$	−15.7087	+	9.06943i	−0.917713	+	0.529842i	−0.882905	−	0.469552i	$-0.844415\pi$
$293$	−15.7087	+	9.06943i	−0.917713	+	0.529842i	−0.0348081	+	0.999394i	$0.511082\pi$
$294$	1.82740			0.106576
$295$	−23.2606	+	20.7894i	−1.35429	+	1.21041i
$296$	−6.87386	+	11.9059i	−0.399535	+	0.692015i
$297$	11.4564	+	6.61438i	0.664770	+	0.383805i
$298$			7.62614i			0.441770i
$299$		0			0
$300$	−3.58258	−	8.20871i	−0.206840	−	0.473930i
$301$	9.16478	−	15.8739i	0.528249	−	0.914954i
$302$	3.82560	+	2.20871i	0.220139	+	0.127097i
$303$	−7.79423	+	4.50000i	−0.447767	+	0.258518i
$304$	−4.83465			−0.277286
$305$	2.36316	−	2.11210i	0.135314	−	0.120938i
$306$	2.09355	+	3.62614i	0.119680	+	0.207292i
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$	7.10895	−	4.10436i	0.405070	−	0.233867i
$309$	−1.58258	+	2.74110i	−0.0900296	+	0.155936i
$310$	1.98101	−	6.02141i	0.112514	−	0.341993i
$311$	−7.58258			−0.429968			−0.214984	−	0.976618i	$-0.568970\pi$
$311$	−7.58258			−0.429968			−0.214984	+	0.976618i	$0.568970\pi$
$312$		0			0
$313$		−	3.25227i		−	0.183829i	−0.995767	−	0.0919147i	$-0.970701\pi$
$313$		−	3.25227i		−	0.183829i	0.995767	−	0.0919147i	$-0.0292987\pi$
$314$	2.09355	−	3.62614i	0.118146	−	0.204635i
$315$	2.42074	−	7.35799i	0.136393	−	0.414576i
$316$	−5.37386	−	9.30780i	−0.302303	−	0.523605i
$317$		−	0.190700i		−	0.0107108i	−0.999986	−	0.00535540i	$-0.998295\pi$
$317$		−	0.190700i		−	0.0107108i	0.999986	−	0.00535540i	$-0.00170469\pi$
$318$	3.00000	−	1.73205i	0.168232	−	0.0971286i
$319$	−6.06218	−	10.5000i	−0.339417	−	0.587887i
$320$	−1.56125	−	7.48040i	−0.0872766	−	0.418167i
$321$	5.29129	+	9.16478i	0.295331	+	0.511528i
$322$	−3.14033	−	1.81307i	−0.175004	−	0.101038i
$323$	−6.87386	−	3.96863i	−0.382472	−	0.220820i
$324$	1.79129			0.0995160
$325$		0			0
$326$	9.62614			0.533142
$327$	11.3739	+	6.56670i	0.628976	+	0.363140i
$328$	−3.96863	−	2.29129i	−0.219131	−	0.126515i
$329$	1.58258	+	2.74110i	0.0872502	+	0.151122i
$330$	0.552200	+	2.64575i	0.0303976	+	0.145644i
$331$	2.23658	+	3.87386i	0.122933	+	0.212927i	0.920923	−	0.389744i	$-0.127437\pi$
$331$	2.23658	+	3.87386i	0.122933	+	0.212927i	−0.797990	+	0.602671i	$0.794103\pi$
$332$	−9.33030	+	5.38685i	−0.512067	+	0.295642i
$333$			15.8745i			0.869918i
$334$	2.18693	+	3.78788i	0.119664	+	0.207263i
$335$	−0.705131	+	2.14329i	−0.0385254	+	0.117101i
$336$	−2.41733	+	4.18693i	−0.131876	+	0.228416i
$337$			30.7477i			1.67494i	0.546487	+	0.837468i	$0.315965\pi$
$337$			30.7477i			1.67494i	−0.546487	+	0.837468i	$0.684035\pi$
$338$		0			0
$339$	7.41742			0.402859
$340$	5.73630	−	17.4359i	0.311095	−	0.945593i
$341$	8.20871	−	14.2179i	0.444527	−	0.769943i
$342$	1.37055	−	0.791288i	0.0741109	−	0.0427879i
$343$		−	19.0526i		−	1.02874i
$344$	9.16478	+	15.8739i	0.494132	+	0.855861i
$345$	−7.64016	+	6.82847i	−0.411332	+	0.367633i
$346$	7.57575			0.407275
$347$	18.4726	−	10.6652i	0.991660	−	0.572535i	0.0858901	−	0.996305i	$-0.472627\pi$
$347$	18.4726	−	10.6652i	0.991660	−	0.572535i	0.905770	+	0.423769i	$0.139293\pi$
$348$	7.10895	+	4.10436i	0.381080	+	0.220017i
$349$	−1.22753	+	2.12614i	−0.0657079	+	0.113809i	−0.897008	−	0.442015i	$-0.854264\pi$
$349$	−1.22753	+	2.12614i	−0.0657079	+	0.113809i	0.831300	+	0.555824i	$0.187597\pi$
$350$	3.62614	−	1.58258i	0.193825	−	0.0845922i
$351$		0			0
$352$			12.5390i			0.668332i
$353$	5.91742	+	3.41643i	0.314953	+	0.181838i	0.649141	−	0.760668i	$-0.275129\pi$
$353$	5.91742	+	3.41643i	0.314953	+	0.181838i	−0.334188	+	0.942506i	$0.608462\pi$
$354$	−3.18693	+	5.51993i	−0.169384	+	0.293381i
$355$	−11.7098	+	10.4658i	−0.621492	+	0.555465i
$356$	17.1497			0.908933
$357$	−6.87386	+	3.96863i	−0.363803	+	0.210042i
$358$	−7.18693	+	4.14938i	−0.379841	+	0.219301i
$359$	19.5293			1.03072			0.515359	−	0.856975i	$-0.327659\pi$
$359$	19.5293			1.03072			0.515359	+	0.856975i	$0.327659\pi$
$360$	5.16184	+	5.77542i	0.272053	+	0.304391i
$361$	8.00000	−	13.8564i	0.421053	−	0.729285i
$362$	−3.46099	−	1.99820i	−0.181905	−	0.105023i
$363$		−	4.00000i		−	0.209946i
$364$		0			0
$365$		0			0
$366$	0.323775	−	0.560795i	0.0169240	−	0.0293132i
$367$	−1.51358	−	0.873864i	−0.0790080	−	0.0456153i	0.459976	−	0.887932i	$-0.347858\pi$
$367$	−1.51358	−	0.873864i	−0.0790080	−	0.0456153i	−0.538984	+	0.842316i	$0.681192\pi$
$368$	−11.0776	+	6.39564i	−0.577459	+	0.333396i
$369$	−5.29150			−0.275465
$370$	−6.04556	+	5.40329i	−0.314294	+	0.280903i
$371$	−6.56670	−	11.3739i	−0.340926	−	0.590502i
$372$			11.1153i			0.576302i
$373$	−11.2583	+	6.50000i	−0.582934	+	0.336557i	−0.762299	−	0.647225i	$-0.775929\pi$
$373$	−11.2583	+	6.50000i	−0.582934	+	0.336557i	0.179364	+	0.983783i	$0.442596\pi$
$374$	−2.76951	+	4.79693i	−0.143208	+	0.248043i
$375$	−1.04580	−	11.1313i	−0.0540051	−	0.574819i
$376$	−3.16515			−0.163230
$377$		0			0
$378$		−	3.95644i		−	0.203497i
$379$	−5.33918	+	9.24773i	−0.274255	+	0.475024i	−0.969947	−	0.243317i	$-0.921765\pi$
$379$	−5.33918	+	9.24773i	−0.274255	+	0.475024i	0.695692	+	0.718340i	$0.255098\pi$
$380$	−6.59014	−	2.16812i	−0.338067	−	0.111222i
$381$	8.87386	+	15.3700i	0.454622	+	0.787428i
$382$			7.57575i			0.387609i
$383$	−20.4564	+	11.8105i	−1.04528	+	0.603490i	−0.921323	−	0.388798i	$-0.872890\pi$
$383$	−20.4564	+	11.8105i	−1.04528	+	0.603490i	−0.123952	+	0.992288i	$0.539557\pi$
$384$	−5.51993	−	9.56080i	−0.281688	−	0.487897i
$385$	10.0308	−	2.09355i	0.511217	−	0.106697i
$386$	−3.39564	−	5.88143i	−0.172834	−	0.299357i
$387$	18.3296	+	10.5826i	0.931744	+	0.537943i
$388$	−17.6869	−	10.2116i	−0.897918	−	0.518413i
$389$	−3.16515			−0.160480			−0.0802398	−	0.996776i	$-0.525569\pi$
$389$	−3.16515			−0.160480			−0.0802398	+	0.996776i	$0.525569\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	6.00000	+	3.46410i	0.303046	+	0.174964i
$393$	6.56670	+	3.79129i	0.331246	+	0.191245i
$394$	−3.35208	−	5.80598i	−0.168876	−	0.292501i
$395$	−2.74110	−	13.1334i	−0.137920	−	0.660813i
$396$	4.73930	+	8.20871i	0.238159	+	0.412503i
$397$	−17.6216	+	10.1738i	−0.884402	+	0.510610i	−0.872107	−	0.489315i	$-0.837247\pi$
$397$	−17.6216	+	10.1738i	−0.884402	+	0.510610i	−0.0122949	+	0.999924i	$0.503914\pi$
$398$		−	4.83465i		−	0.242339i
$399$	1.50000	+	2.59808i	0.0750939	+	0.130066i
$400$	1.56099	−	13.8689i	0.0780496	−	0.693443i
$401$	14.9131	−	25.8303i	0.744726	−	1.28990i	−0.205596	−	0.978637i	$-0.565913\pi$
$401$	14.9131	−	25.8303i	0.744726	−	1.28990i	0.950323	−	0.311267i	$-0.100753\pi$
$402$			0.460985i			0.0229918i
$403$		0			0
$404$	−16.1216			−0.802079
$405$	2.12407	+	0.698807i	0.105546	+	0.0347240i
$406$	−1.81307	+	3.14033i	−0.0899811	+	0.155852i
$407$	−18.1865	+	10.5000i	−0.901473	+	0.520466i
$408$		−	7.93725i		−	0.392953i
$409$	−4.33013	−	7.50000i	−0.214111	−	0.370851i	0.738886	−	0.673830i	$-0.235352\pi$
$409$	−4.33013	−	7.50000i	−0.214111	−	0.370851i	−0.952997	+	0.302979i	$0.902019\pi$
$410$	−1.80110	−	2.01519i	−0.0889498	−	0.0995230i
$411$	−10.4877			−0.517318
$412$	−4.91010	+	2.83485i	−0.241903	+	0.139663i
$413$	20.9276	+	12.0826i	1.02978	+	0.594545i
$414$	2.09355	−	3.62614i	0.102892	−	0.178215i
$415$	−13.1652	+	2.74773i	−0.646252	+	0.134881i
$416$		0			0
$417$			21.7477i			1.06499i
$418$	1.81307	+	1.04678i	0.0886801	+	0.0511995i
$419$	−2.91742	+	5.05313i	−0.142526	+	0.246861i	−0.928447	−	0.371465i	$-0.878856\pi$
$419$	−2.91742	+	5.05313i	−0.142526	+	0.246861i	0.785922	+	0.618326i	$0.212189\pi$
$420$	−5.17272	+	4.62317i	−0.252403	+	0.225588i
$421$	5.48220			0.267186			0.133593	−	0.991036i	$-0.457348\pi$
$421$	5.48220			0.267186			0.133593	+	0.991036i	$0.457348\pi$
$422$	0.0653411	−	0.0377247i	0.00318076	−	0.00183641i
$423$	−3.16515	+	1.82740i	−0.153895	+	0.0888513i
$424$	13.1334			0.637815
$425$	13.6040	−	18.4373i	0.659889	−	0.894338i
$426$	−1.60436	+	2.77883i	−0.0777313	+	0.134635i
$427$	−2.12614	−	1.22753i	−0.102891	−	0.0594041i
$428$			18.9564i			0.916294i
$429$		0			0
$430$	2.20871	+	10.5826i	0.106514	+	0.510337i
$431$	4.23478	−	7.33485i	0.203982	−	0.353307i	−0.745826	−	0.666141i	$-0.767945\pi$
$431$	4.23478	−	7.33485i	0.203982	−	0.353307i	0.949808	+	0.312834i	$0.101278\pi$
$432$	−12.0866	−	6.97822i	−0.581518	−	0.335740i
$433$	−8.44178	+	4.87386i	−0.405686	+	0.234223i	−0.688934	−	0.724824i	$-0.741921\pi$
$433$	−8.44178	+	4.87386i	−0.405686	+	0.234223i	0.283248	+	0.959047i	$0.408588\pi$
$434$	−4.91010			−0.235692
$435$	6.82847	+	7.64016i	0.327400	+	0.366317i
$436$	11.7629	+	20.3739i	0.563339	+	0.975731i
$437$			7.93725i			0.379690i
$438$		0			0
$439$	7.24773	−	12.5534i	0.345915	−	0.599143i	−0.639604	−	0.768704i	$-0.720902\pi$
$439$	7.24773	−	12.5534i	0.345915	−	0.599143i	0.985520	+	0.169562i	$0.0542352\pi$
$440$	−3.20233	+	9.73371i	−0.152665	+	0.464036i
$441$	8.00000			0.380952
$442$		0			0
$443$			19.9129i			0.946089i	0.881038	+	0.473045i	$0.156845\pi$
$443$			19.9129i			0.946089i	−0.881038	+	0.473045i	$0.843155\pi$
$444$	7.10895	−	12.3131i	0.337376	−	0.584352i
$445$	20.3357	+	6.69034i	0.964007	+	0.317153i
$446$	−1.97822	−	3.42638i	−0.0936714	−	0.162244i
$447$		−	16.6929i		−	0.789545i
$448$	−5.12614	+	2.95958i	−0.242187	+	0.139827i
$449$	5.50998	+	9.54356i	0.260032	+	0.450388i	0.966250	−	0.257606i	$-0.0829336\pi$
$449$	5.50998	+	9.54356i	0.260032	+	0.450388i	−0.706218	+	0.707994i	$0.749600\pi$
$450$	1.82740	+	4.18710i	0.0861445	+	0.197382i
$451$	−3.50000	−	6.06218i	−0.164809	−	0.285457i
$452$	11.5067	+	6.64337i	0.541228	+	0.312478i
$453$	−8.37386	−	4.83465i	−0.393438	−	0.227152i
$454$	−0.373864			−0.0175463
$455$		0			0
$456$	−3.00000			−0.140488
$457$	1.50000	+	0.866025i	0.0701670	+	0.0405110i	0.534673	−	0.845059i	$-0.320435\pi$
$457$	1.50000	+	0.866025i	0.0701670	+	0.0405110i	−0.464506	+	0.885570i	$0.653768\pi$
$458$	−10.3923	−	6.00000i	−0.485601	−	0.280362i
$459$	−11.4564	−	19.8431i	−0.534741	−	0.926198i
$460$	−17.9681	+	3.75015i	−0.837765	+	0.174852i
$461$	−17.9204	−	31.0390i	−0.834635	−	1.44563i	−0.894327	−	0.447414i	$-0.852345\pi$
$461$	−17.9204	−	31.0390i	−0.834635	−	1.44563i	0.0596914	−	0.998217i	$-0.480988\pi$
$462$	1.81307	−	1.04678i	0.0843516	−	0.0487004i
$463$		−	39.4002i		−	1.83108i	−0.402223	−	0.915542i	$-0.631762\pi$
$463$		−	39.4002i		−	1.83108i	0.402223	−	0.915542i	$-0.368238\pi$
$464$	6.39564	+	11.0776i	0.296910	+	0.514264i
$465$	−4.33624	+	13.1803i	−0.201088	+	0.611221i
$466$	0.647551	−	1.12159i	0.0299972	−	0.0519567i
$467$		−	24.3303i		−	1.12587i	−0.826500	−	0.562936i	$-0.809672\pi$
$467$		−	24.3303i		−	1.12587i	0.826500	−	0.562936i	$-0.190328\pi$
$468$		0			0
$469$	1.74773			0.0807025
$470$	−1.77328	−	0.583398i	−0.0817951	−	0.0269101i
$471$	−4.58258	+	7.93725i	−0.211154	+	0.365729i
$472$	−20.9276	+	12.0826i	−0.963272	+	0.556146i
$473$			27.9989i			1.28739i
$474$	−1.37055	−	2.37386i	−0.0629515	−	0.109035i
$475$	−6.96863	−	5.14181i	−0.319743	−	0.235923i
$476$	−14.2179			−0.651677
$477$	13.1334	−	7.58258i	0.601337	−	0.347182i
$478$	0.0754495	+	0.0435608i	0.00345098	+	0.00199242i
$479$	−2.33193	+	4.03901i	−0.106548	+	0.184547i	−0.914370	−	0.404880i	$-0.867313\pi$
$479$	−2.33193	+	4.03901i	−0.106548	+	0.184547i	0.807821	+	0.589427i	$0.200647\pi$
$480$	−2.16515	−	10.3739i	−0.0988252	−	0.473500i
$481$		0			0
$482$		−	0.791288i		−	0.0360422i
$483$	6.87386	+	3.96863i	0.312772	+	0.180579i
$484$	3.58258	−	6.20520i	0.162844	−	0.282055i
$485$	−16.9891	−	19.0086i	−0.771435	−	0.863134i
$486$	7.30960			0.331570
$487$	−9.24773	+	5.33918i	−0.419055	+	0.241941i	−0.694673	−	0.719326i	$-0.744451\pi$
$487$	−9.24773	+	5.33918i	−0.419055	+	0.241941i	0.275618	+	0.961267i	$0.411117\pi$
$488$	2.12614	−	1.22753i	0.0962457	−	0.0555675i
$489$	−21.0707			−0.952848
$490$	2.72300	+	3.04668i	0.123013	+	0.137635i
$491$	9.70871	−	16.8160i	0.438148	−	0.758895i	−0.559399	−	0.828899i	$-0.688968\pi$
$491$	9.70871	−	16.8160i	0.438148	−	0.758895i	0.997547	+	0.0700041i	$0.0223012\pi$
$492$	4.10436	+	2.36965i	0.185039	+	0.106832i
$493$			21.0000i			0.945792i
$494$		0			0
$495$	2.41742	+	11.5826i	0.108655	+	0.520598i
$496$	−8.66025	+	15.0000i	−0.388857	+	0.673520i
$497$	10.5353	+	6.08258i	0.472574	+	0.272841i
$498$	−2.37960	+	1.37386i	−0.106632	+	0.0615643i
$499$	0.723000			0.0323659			0.0161830	−	0.999869i	$-0.494849\pi$
$499$	0.723000			0.0323659			0.0161830	+	0.999869i	$0.494849\pi$
$500$	8.34734	−	18.2047i	0.373305	−	0.814139i
$501$	−4.78698	−	8.29129i	−0.213866	−	0.370427i
$502$		−	0.0754495i		−	0.00336747i
$503$	0.143025	−	0.0825757i	0.00637718	−	0.00368187i	−0.496808	−	0.867860i	$-0.665495\pi$
$503$	0.143025	−	0.0825757i	0.00637718	−	0.00368187i	0.503185	+	0.864179i	$0.332161\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$	−19.1166	−	6.28926i	−0.850678	−	0.279868i
$506$	5.53901			0.246239
$507$		0			0
$508$			31.7913i			1.41051i
$509$	−4.23478	+	7.33485i	−0.187703	+	0.325111i	−0.944484	−	0.328557i	$-0.893438\pi$
$509$	−4.23478	+	7.33485i	−0.187703	+	0.325111i	0.756781	+	0.653669i	$0.226771\pi$
$510$	1.46299	−	4.44685i	0.0647822	−	0.196910i
$511$		0			0
$512$		−	22.8981i		−	1.01196i
$513$	−7.50000	+	4.33013i	−0.331133	+	0.191180i
$514$	4.14938	+	7.18693i	0.183021	+	0.317002i
$515$	−6.92820	+	1.44600i	−0.305293	+	0.0637184i
$516$	−9.47822	−	16.4168i	−0.417255	−	0.722707i
$517$	−4.18710	−	2.41742i	−0.184149	−	0.106318i
$518$	5.43920	+	3.14033i	0.238985	+	0.137978i
$519$	−16.5826			−0.727894
$520$		0			0
$521$	27.4955			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$521$	27.4955			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$522$	−3.62614	−	2.09355i	−0.158712	−	0.0916322i
$523$	−0.143025	−	0.0825757i	−0.00625406	−	0.00361078i	0.496870	−	0.867825i	$-0.334483\pi$
$523$	−0.143025	−	0.0825757i	−0.00625406	−	0.00361078i	−0.503124	+	0.864214i	$0.667816\pi$
$524$	6.79129	+	11.7629i	0.296679	+	0.513863i
$525$	−7.93725	+	3.46410i	−0.346410	+	0.151186i
$526$	−2.05583	−	3.56080i	−0.0896383	−	0.155258i
$527$	−24.6261	+	14.2179i	−1.07273	+	0.619342i
$528$		−	7.38505i		−	0.321393i
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$	7.35799	+	2.42074i	0.319611	+	0.105150i
$531$	−13.9518	+	24.1652i	−0.605455	+	1.04868i
$532$			5.37386i			0.232987i
$533$		0			0
$534$	4.37386			0.189276
$535$	−7.39517	+	22.4781i	−0.319721	+	0.971814i
$536$	−0.873864	+	1.51358i	−0.0377452	+	0.0653765i
$537$	15.7315	−	9.08258i	0.678864	−	0.391942i
$538$		−	6.85275i		−	0.295443i
$539$	5.29150	+	9.16515i	0.227921	+	0.394771i
$540$	−13.3459	−	14.9323i	−0.574318	−	0.642586i
$541$	10.3923			0.446800			0.223400	−	0.974727i	$-0.428284\pi$
$541$	10.3923			0.446800			0.223400	+	0.974727i	$0.428284\pi$
$542$	−3.42638	+	1.97822i	−0.147175	+	0.0849718i
$543$	7.57575	+	4.37386i	0.325107	+	0.187700i
$544$	10.8591	−	18.8085i	0.465580	−	0.806409i
$545$	6.00000	+	28.7477i	0.257012	+	1.23142i
$546$		0			0
$547$		−	28.7477i		−	1.22916i	−0.788853	−	0.614582i	$-0.789325\pi$
$547$		−	28.7477i		−	1.22916i	0.788853	−	0.614582i	$-0.210675\pi$
$548$	−16.2695	−	9.39320i	−0.694999	−	0.401258i
$549$	1.41742	−	2.45505i	0.0604942	−	0.104779i
$550$	−3.58822	+	4.86306i	−0.153002	+	0.207362i
$551$	7.93725			0.338138
$552$	−6.87386	+	3.96863i	−0.292571	+	0.168916i
$553$	−9.00000	+	5.19615i	−0.382719	+	0.220963i
$554$	−3.38865			−0.143970
$555$	13.2331	−	11.8273i	0.561715	−	0.502039i
$556$	−19.4782	+	33.7373i	−0.826061	+	1.43078i
$557$	−6.70871	−	3.87328i	−0.284257	−	0.164116i	0.351092	−	0.936341i	$-0.385810\pi$
$557$	−6.70871	−	3.87328i	−0.284257	−	0.164116i	−0.635349	+	0.772225i	$0.719144\pi$
$558$		−	5.66970i		−	0.240017i
$559$		0			0
$560$	−10.5826	+	2.20871i	−0.447195	+	0.0933351i
$561$	6.06218	−	10.5000i	0.255945	−	0.443310i
$562$	−1.44600	−	0.834849i	−0.0609958	−	0.0352160i
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	−0.326682	−	0.945134i	$-0.605931\pi$
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	0.655169	+	0.755482i	$0.272597\pi$
$564$	3.27340			0.137835
$565$	11.0527	+	12.3665i	0.464989	+	0.520261i
$566$	−6.33828	−	10.9782i	−0.266418	−	0.461449i
$567$		−	1.73205i		−	0.0727393i
$568$	−10.5353	+	6.08258i	−0.442053	+	0.255219i
$569$	−3.87386	+	6.70973i	−0.162401	+	0.281286i	−0.935729	−	0.352719i	$-0.885257\pi$
$569$	−3.87386	+	6.70973i	−0.162401	+	0.281286i	0.773328	+	0.634006i	$0.218590\pi$
$570$	−1.68075	−	0.552957i	−0.0703989	−	0.0231608i
$571$	35.0780			1.46797			0.733985	−	0.679166i	$-0.237658\pi$
$571$	35.0780			1.46797			0.733985	+	0.679166i	$0.237658\pi$
$572$		0			0
$573$		−	16.5826i		−	0.692747i
$574$	−1.04678	+	1.81307i	−0.0436916	+	0.0756760i
$575$	−22.7691	−	2.56275i	−0.949537	−	0.106874i
$576$	−3.41742	−	5.91915i	−0.142393	−	0.246631i
$577$		−	6.92820i		−	0.288425i	−0.989547	−	0.144212i	$-0.953935\pi$
$577$		−	6.92820i		−	0.288425i	0.989547	−	0.144212i	$-0.0460649\pi$
$578$	1.58258	−	0.913701i	0.0658265	−	0.0380049i
$579$	7.43273	+	12.8739i	0.308894	+	0.535020i
$580$	3.75015	+	17.9681i	0.155717	+	0.746083i
$581$	5.20871	+	9.02175i	0.216094	+	0.374285i
$582$	−4.51088	−	2.60436i	−0.186982	−	0.107954i
$583$	17.3739	+	10.0308i	0.719552	+	0.415433i
$584$		0			0
$585$		0			0
$586$	−8.28674			−0.342322
$587$	34.2042	+	19.7478i	1.41176	+	0.815078i	0.995554	−	0.0941934i	$-0.0300272\pi$
$587$	34.2042	+	19.7478i	1.41176	+	0.815078i	0.416203	+	0.909272i	$0.363361\pi$
$588$	−6.20520	−	3.58258i	−0.255898	−	0.147743i
$589$	5.37386	+	9.30780i	0.221426	+	0.383521i
$590$	−13.9518	+	2.91190i	−0.574385	+	0.119881i
$591$	7.33738	+	12.7087i	0.301819	+	0.522767i
$592$	19.1869	−	11.0776i	0.788578	−	0.455286i
$593$			21.1660i			0.869184i	0.900627	+	0.434592i	$0.143107\pi$
$593$			21.1660i			0.869184i	−0.900627	+	0.434592i	$0.856893\pi$
$594$	3.02178	+	5.23388i	0.123985	+	0.214749i
$595$	−16.8593	−	5.54661i	−0.691163	−	0.227389i
$596$	14.9509	−	25.8956i	0.612411	−	1.06073i
$597$			10.5826i			0.433116i
$598$		0			0
$599$	−15.4955			−0.633127			−0.316564	−	0.948571i	$-0.602529\pi$
$599$	−15.4955			−0.633127			−0.316564	+	0.948571i	$0.602529\pi$
$600$	0.968627	−	8.60591i	0.0395440	−	0.351335i
$601$	−8.45644	+	14.6470i	−0.344945	+	0.597463i	−0.985344	−	0.170580i	$-0.945436\pi$
$601$	−8.45644	+	14.6470i	−0.344945	+	0.597463i	0.640398	+	0.768043i	$0.278769\pi$
$602$	7.25198	−	4.18693i	0.295569	−	0.170647i
$603$			2.01810i			0.0821834i
$604$	−8.66025	−	15.0000i	−0.352381	−	0.610341i
$605$	6.66888	−	5.96038i	0.271128	−	0.242324i
$606$	−4.11165			−0.167024
$607$	−6.70973	+	3.87386i	−0.272339	+	0.157235i	−0.629950	−	0.776635i	$-0.716925\pi$
$607$	−6.70973	+	3.87386i	−0.272339	+	0.157235i	0.357611	+	0.933871i	$0.383591\pi$
$608$	−7.10895	−	4.10436i	−0.288306	−	0.166454i
$609$	3.96863	−	6.87386i	0.160817	−	0.278543i
$610$	1.41742	−	0.295834i	0.0573898	−	0.0119780i
$611$		0			0
$612$		−	16.4174i		−	0.663635i
$613$	−5.12614	−	2.95958i	−0.207043	−	0.119536i	0.392894	−	0.919584i	$-0.371474\pi$
$613$	−5.12614	−	2.95958i	−0.207043	−	0.119536i	−0.599936	+	0.800048i	$0.704807\pi$
$614$	5.53901	−	9.59386i	0.223536	−	0.387176i
$615$	3.94242	+	4.41105i	0.158974	+	0.177871i
$616$	7.93725			0.319801
$617$	12.0826	−	6.97588i	0.486426	−	0.280838i	−0.236664	−	0.971591i	$-0.576054\pi$
$617$	12.0826	−	6.97588i	0.486426	−	0.280838i	0.723091	+	0.690753i	$0.242721\pi$
$618$	−1.25227	+	0.723000i	−0.0503738	+	0.0290833i
$619$	29.7309			1.19499			0.597493	−	0.801874i	$-0.296164\pi$
$619$	29.7309			1.19499			0.597493	+	0.801874i	$0.296164\pi$
$620$	−18.5316	+	16.5629i	−0.744249	+	0.665180i
$621$	−11.4564	+	19.8431i	−0.459731	+	0.796278i
$622$	−3.00000	−	1.73205i	−0.120289	−	0.0694489i
$623$		−	16.5826i		−	0.664367i
$624$		0			0
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$	0.742901	−	1.28674i	0.0296923	−	0.0514286i
$627$	−3.96863	−	2.29129i	−0.158492	−	0.0915052i
$628$	−14.2179	+	8.20871i	−0.567356	+	0.327563i
$629$	36.3731			1.45029
$630$	2.63850	−	2.35819i	0.105120	−	0.0939524i
$631$	−2.95958	−	5.12614i	−0.117819	−	0.204068i	0.801084	−	0.598552i	$-0.204257\pi$
$631$	−2.95958	−	5.12614i	−0.117819	−	0.204068i	−0.918903	+	0.394483i	$0.870924\pi$
$632$		−	10.3923i		−	0.413384i
$633$	−0.143025	+	0.0825757i	−0.00568475	+	0.00328209i
$634$	0.0435608	−	0.0754495i	0.00173002	−	0.00299648i
$635$	−12.4022	+	37.6974i	−0.492167	+	1.49598i
$636$	−13.5826			−0.538584
$637$		0			0
$638$		−	5.53901i		−	0.219292i
$639$	−7.02355	+	12.1652i	−0.277847	+	0.481246i
$640$	7.71472	−	23.4494i	0.304951	−	0.926920i
$641$	9.08258	+	15.7315i	0.358740	+	0.621356i	0.987751	−	0.156041i	$-0.0498731\pi$
$641$	9.08258	+	15.7315i	0.358740	+	0.621356i	−0.629010	+	0.777397i	$0.716540\pi$
$642$			4.83465i			0.190809i
$643$	18.8739	−	10.8968i	0.744313	−	0.429729i	−0.0793227	−	0.996849i	$-0.525276\pi$
$643$	18.8739	−	10.8968i	0.744313	−	0.429729i	0.823635	+	0.567120i	$0.191942\pi$
$644$	7.10895	+	12.3131i	0.280132	+	0.485203i
$645$	−4.83465	−	23.1642i	−0.190364	−	0.912090i
$646$	−1.81307	−	3.14033i	−0.0713342	−	0.123554i
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.0358667	−	0.999357i	$-0.511419\pi$
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.883402	+	0.468617i	$0.844753\pi$
$648$	1.50000	+	0.866025i	0.0589256	+	0.0340207i
$649$	−36.9129			−1.44896
$650$		0			0
$651$	10.7477			0.421237
$652$	−32.6869	−	18.8718i	−1.28012	−	0.739077i
$653$	37.0882	+	21.4129i	1.45137	+	0.837951i	0.998560	−	0.0536545i	$-0.0170870\pi$
$653$	37.0882	+	21.4129i	1.45137	+	0.837951i	0.452814	+	0.891605i	$0.350420\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$	3.46410	+	16.5975i	0.135354	+	0.648518i
$656$	3.69253	+	6.39564i	0.144169	+	0.249708i
$657$		0			0
$658$			1.44600i			0.0563710i
$659$	15.2477	+	26.4098i	0.593967	+	1.02878i	0.993692	+	0.112146i	$0.0357724\pi$
$659$	15.2477	+	26.4098i	0.593967	+	1.02878i	−0.399725	+	0.916635i	$0.630894\pi$
$660$	3.31186	−	10.0666i	0.128914	−	0.391842i
$661$	−9.16478	+	15.8739i	−0.356469	+	0.617422i	−0.987368	−	0.158443i	$-0.949353\pi$
$661$	−9.16478	+	15.8739i	−0.356469	+	0.617422i	0.630900	+	0.775865i	$0.282686\pi$
$662$			2.04356i			0.0794252i
$663$		0			0
$664$	−10.4174			−0.404274
$665$	−2.09642	+	6.37221i	−0.0812957	+	0.247104i
$666$	−3.62614	+	6.28065i	−0.140510	+	0.243370i
$667$	18.1865	−	10.5000i	0.704185	−	0.406562i
$668$		−	17.1497i		−	0.663542i
$669$	4.33013	+	7.50000i	0.167412	+	0.289967i
$670$	−0.768563	+	0.686911i	−0.0296922	+	0.0265377i
$671$	3.75015			0.144773
$672$	−7.10895	+	4.10436i	−0.274234	+	0.158329i
$673$	−20.9276	−	12.0826i	−0.806701	−	0.465749i	0.0391079	−	0.999235i	$-0.487548\pi$
$673$	−20.9276	−	12.0826i	−0.806701	−	0.465749i	−0.845809	+	0.533486i	$0.820882\pi$
$674$	−7.02355	+	12.1652i	−0.270537	+	0.468584i
$675$	−10.0000	−	22.9129i	−0.384900	−	0.881917i
$676$		0			0
$677$			2.83485i			0.108952i	0.998515	+	0.0544760i	$0.0173489\pi$
$677$			2.83485i			0.108952i	−0.998515	+	0.0544760i	$0.982651\pi$
$678$	2.93466	+	1.69433i	0.112705	+	0.0650702i
$679$	−9.87386	+	17.1020i	−0.378924	+	0.656316i
$680$	13.2331	−	11.8273i	0.507468	−	0.453555i
$681$	0.818350			0.0313593
$682$	6.49545	−	3.75015i	0.248724	−	0.143601i
$683$	28.6652	−	16.5498i	1.09684	−	0.633262i	0.161452	−	0.986881i	$-0.448382\pi$
$683$	28.6652	−	16.5498i	1.09684	−	0.633262i	0.935390	+	0.353619i	$0.115049\pi$
$684$	−6.20520			−0.237262
$685$	−15.6276	−	17.4852i	−0.597100	−	0.668076i
$686$	4.35208	−	7.53803i	0.166163	−	0.287803i
$687$	22.7477	+	13.1334i	0.867880	+	0.501071i
$688$		−	29.5390i		−	1.12616i
$689$		0			0
$690$	−4.58258	+	0.956439i	−0.174456	+	0.0364110i
$691$	9.88778	−	17.1261i	0.376149	−	0.651509i	−0.614349	−	0.789034i	$-0.710581\pi$
$691$	9.88778	−	17.1261i	0.376149	−	0.651509i	0.990498	+	0.137525i	$0.0439148\pi$
$692$	−25.7246	−	14.8521i	−0.977901	−	0.564591i
$693$	7.93725	−	4.58258i	0.301511	−	0.174078i
$694$	9.74475			0.369906
$695$	−36.2582	+	32.4062i	−1.37535	+	1.22924i
$696$	3.96863	+	6.87386i	0.150430	+	0.260553i
$697$			12.1244i			0.459243i
$698$	−0.971326	+	0.560795i	−0.0367652	+	0.0212264i
$699$	−1.41742	+	2.45505i	−0.0536119	+	0.0928586i
$700$	−15.4157	−	1.73509i	−0.582658	−	0.0655802i
$701$	21.1652			0.799397			0.399698	−	0.916647i	$-0.369115\pi$
$701$	21.1652			0.799397			0.399698	+	0.916647i	$0.369115\pi$
$702$		0			0
$703$		−	13.7477i		−	0.518505i
$704$	4.52083	−	7.83030i	0.170385	−	0.295116i
$705$	3.88153	+	1.27700i	0.146187	+	0.0480946i
$706$	1.56080	+	2.70338i	0.0587413	+	0.101743i
$707$			15.5885i			0.586264i
$708$	21.6434	−	12.4958i	0.813408	−	0.469621i
$709$	18.1865	+	31.5000i	0.683010	+	1.18301i	0.974058	+	0.226299i	$0.0726626\pi$
$709$	18.1865	+	31.5000i	0.683010	+	1.18301i	−0.291048	+	0.956708i	$0.594004\pi$
$710$	−7.02355	+	1.46590i	−0.263589	+	0.0550143i
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$	14.3609	+	8.29129i	0.538199	+	0.310729i
$713$	24.6261	+	14.2179i	0.922256	+	0.532465i
$714$	−3.62614			−0.135705
$715$		0			0
$716$	32.5390			1.21604
$717$	−0.165151	−	0.0953502i	−0.00616769	−	0.00356092i
$718$	7.72665	+	4.46099i	0.288356	+	0.166482i
$719$	12.2477	+	21.2137i	0.456763	+	0.791137i	0.998788	−	0.0492257i	$-0.0156754\pi$
$719$	12.2477	+	21.2137i	0.456763	+	0.791137i	−0.542025	+	0.840363i	$0.682342\pi$
$720$	−2.55040	−	12.2197i	−0.0950478	−	0.455402i
$721$	2.74110	+	4.74773i	0.102084	+	0.176815i
$722$	6.33030	−	3.65480i	0.235589	−	0.136018i
$723$			1.73205i			0.0644157i
$724$	7.83485	+	13.5704i	0.291180	+	0.504338i
$725$	−2.56275	+	22.7691i	−0.0951780	+	0.845623i
$726$	0.913701	−	1.58258i	0.0339106	−	0.0587349i
$727$		−	15.2523i		−	0.565675i	−0.959168	−	0.282838i	$-0.908724\pi$
$727$		−	15.2523i		−	0.565675i	0.959168	−	0.282838i	$-0.0912758\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	24.2477	−	41.9983i	0.896835	−	1.55336i
$732$	−2.19885	+	1.26951i	−0.0812719	+	0.0469223i
$733$			22.8027i			0.842237i	0.907006	+	0.421119i	$0.138362\pi$
$733$			22.8027i			0.842237i	−0.907006	+	0.421119i	$0.861638\pi$
$734$	−0.399225	−	0.691478i	−0.0147357	−	0.0255229i
$735$	−5.96038	−	6.66888i	−0.219852	−	0.245985i
$736$	−21.7182			−0.800544
$737$	−2.31203	+	1.33485i	−0.0851646	+	0.0491698i
$738$	−2.09355	−	1.20871i	−0.0770647	−	0.0444933i
$739$	8.51723	−	14.7523i	0.313311	−	0.542671i	−0.665766	−	0.746161i	$-0.731895\pi$
$739$	8.51723	−	14.7523i	0.313311	−	0.542671i	0.979077	+	0.203490i	$0.0652283\pi$
$740$	31.1216	−	6.49545i	1.14405	−	0.238778i
$741$		0			0
$742$		−	6.00000i		−	0.220267i
$743$	4.96099	+	2.86423i	0.182001	+	0.105078i	0.588232	−	0.808692i	$-0.299824\pi$
$743$	4.96099	+	2.86423i	0.182001	+	0.105078i	−0.406232	+	0.913770i	$0.633157\pi$
$744$	−5.37386	+	9.30780i	−0.197015	+	0.341241i
$745$	27.8306	−	24.8739i	1.01964	−	0.911310i
$746$	−5.93905			−0.217444
$747$	−10.4174	+	6.01450i	−0.381154	+	0.220059i
$748$	18.8085	−	10.8591i	0.687708	−	0.397048i
$749$	18.3296			0.669748
$750$	2.12891	−	4.64293i	0.0777367	−	0.169536i
$751$	5.87386	−	10.1738i	0.214340	−	0.371248i	−0.738728	−	0.674004i	$-0.764573\pi$
$751$	5.87386	−	10.1738i	0.214340	−	0.371248i	0.953068	+	0.302755i	$0.0979065\pi$
$752$	4.41742	+	2.55040i	0.161087	+	0.0930036i
$753$			0.165151i			0.00601845i
$754$		0			0
$755$	−4.41742	−	21.1652i	−0.160767	−	0.770279i
$756$	−7.75650	+	13.4347i	−0.282101	+	0.488614i
$757$	8.44178	+	4.87386i	0.306822	+	0.177144i	0.645503	−	0.763757i	$-0.276648\pi$
$757$	8.44178	+	4.87386i	0.306822	+	0.177144i	−0.338682	+	0.940901i	$0.609981\pi$
$758$	−4.22483	+	2.43920i	−0.153453	+	0.0885959i
$759$	−12.1244			−0.440086
$760$	−4.47028	−	5.00166i	−0.162154	−	0.181429i
$761$	−17.7297	−	30.7087i	−0.642701	−	1.11319i	−0.984827	−	0.173536i	$-0.944481\pi$
$761$	−17.7297	−	30.7087i	−0.642701	−	1.11319i	0.342127	−	0.939654i	$-0.388853\pi$
$762$			8.10805i			0.293724i
$763$	19.7001	−	11.3739i	0.713192	−	0.411762i
$764$	14.8521	−	25.7246i	0.537330	−	0.930682i
$765$	6.40467	−	19.4674i	0.231561	−	0.703846i
$766$	−10.7913			−0.389905
$767$		0			0
$768$			1.79129i			0.0646375i
$769$	−7.79423	+	13.5000i	−0.281067	+	0.486822i	−0.971648	−	0.236433i	$-0.924022\pi$
$769$	−7.79423	+	13.5000i	−0.281067	+	0.486822i	0.690581	+	0.723255i	$0.257355\pi$
$770$	4.44685	+	1.46299i	0.160253	+	0.0527224i
$771$	−9.08258	−	15.7315i	−0.327101	−	0.566556i
$772$			26.6283i			0.958374i
$773$	20.9174	−	12.0767i	0.752347	−	0.434368i	−0.0741940	−	0.997244i	$-0.523638\pi$
$773$	20.9174	−	12.0767i	0.752347	−	0.434368i	0.826541	+	0.562876i	$0.190305\pi$
$774$	4.83465	+	8.37386i	0.173778	+	0.300992i
$775$	−28.4358	+	12.4104i	−1.02144	+	0.445795i
$776$	−9.87386	−	17.1020i	−0.354451	−	0.613927i
$777$	−11.9059	−	6.87386i	−0.427121	−	0.246598i
$778$	−1.25227	−	0.723000i	−0.0448962	−	0.0259208i
$779$	4.58258			0.164188
$780$		0			0
$781$	−18.5826			−0.664937
$782$	−8.30852	−	4.79693i	−0.297112	−	0.171538i
$783$	19.8431	+	11.4564i	0.709136	+	0.409420i
$784$	−5.58258	−	9.66930i	−0.199378	−	0.345332i
$785$	−20.0616	+	4.18710i	−0.716030	+	0.149444i
$786$	1.73205	+	3.00000i	0.0617802	+	0.107006i
$787$	14.1261	−	8.15573i	0.503542	−	0.290720i	−0.226633	−	0.973980i	$-0.572772\pi$
$787$	14.1261	−	8.15573i	0.503542	−	0.290720i	0.730175	+	0.683260i	$0.239438\pi$
$788$			26.2867i			0.936425i
$789$	4.50000	+	7.79423i	0.160204	+	0.277482i
$790$	1.91550	−	5.82229i	0.0681504	−	0.207148i
$791$	6.42368	−	11.1261i	0.228400	−	0.395600i
$792$			9.16515i			0.325669i
$793$		0			0
$794$	−9.29583			−0.329897
$795$	−16.1059	−	5.29875i	−0.571218	−	0.187927i
$796$	−9.47822	+	16.4168i	−0.335947	+	0.581877i
$797$	38.1727	−	22.0390i	1.35215	−	0.780662i	0.363596	−	0.931557i	$-0.381549\pi$
$797$	38.1727	−	22.0390i	1.35215	−	0.780662i	0.988550	+	0.150895i	$0.0482154\pi$
$798$			1.37055i			0.0485170i
$799$	4.18710	+	7.25227i	0.148129	+	0.256567i
$800$	14.0692	−	19.0678i	0.497422	−	0.674149i
$801$	19.1479			0.676558
$802$	11.8006	−	6.81307i	0.416693	−	0.240578i
$803$		0			0
$804$	0.903750	−	1.56534i	0.0318728	−	0.0552053i
$805$	3.62614	+	17.3739i	0.127805	+	0.612348i
$806$		0			0
$807$			15.0000i			0.528025i
$808$	−13.5000	−	7.79423i	−0.474928	−	0.274200i
$809$	−27.4129	+	47.4805i	−0.963785	+	1.66933i	−0.250942	+	0.968002i	$0.580740\pi$
$809$	−27.4129	+	47.4805i	−0.963785	+	1.66933i	−0.712843	+	0.701323i	$0.752593\pi$
$810$	0.680750	+	0.761669i	0.0239191	+	0.0267623i
$811$	−50.5155			−1.77384			−0.886920	−	0.461923i	$-0.847160\pi$
$811$	−50.5155			−1.77384			−0.886920	+	0.461923i	$0.847160\pi$
$812$	12.3131	−	7.10895i	0.432104	−	0.249475i
$813$	7.50000	−	4.33013i	0.263036	−	0.151864i
$814$	−9.59386			−0.336264
$815$	−31.3973	−	35.1294i	−1.09980	−	1.23053i
$816$	−6.39564	+	11.0776i	−0.223892	+	0.387793i
$817$	−15.8739	−	9.16478i	−0.555356	−	0.320635i
$818$		−	3.95644i		−	0.138334i
$819$		0			0
$820$	2.16515	+	10.3739i	0.0756104	+	0.362271i
$821$	9.06943	−	15.7087i	0.316525	−	0.548238i	−0.663235	−	0.748411i	$-0.730817\pi$
$821$	9.06943	−	15.7087i	0.316525	−	0.548238i	0.979761	+	0.200173i	$0.0641505\pi$
$822$	−4.14938	−	2.39564i	−0.144726	−	0.0835577i
$823$	27.2083	−	15.7087i	0.948421	−	0.547571i	0.0558311	−	0.998440i	$-0.482219\pi$
$823$	27.2083	−	15.7087i	0.948421	−	0.547571i	0.892590	+	0.450869i	$0.148886\pi$
$824$	−5.48220			−0.190982
$825$	7.85425	−	10.6448i	0.273450	−	0.370603i
$826$	5.51993	+	9.56080i	0.192063	+	0.332663i
$827$		−	10.7737i		−	0.374638i	−0.982299	−	0.187319i	$-0.940020\pi$
$827$		−	10.7737i		−	0.374638i	0.982299	−	0.187319i	$-0.0599799\pi$
$828$	−14.2179	+	8.20871i	−0.494106	+	0.285272i
$829$	16.6652	−	28.8649i	0.578805	−	1.00252i	−0.416812	−	0.908993i	$-0.636853\pi$
$829$	16.6652	−	28.8649i	0.578805	−	1.00252i	0.995617	−	0.0935264i	$-0.0298139\pi$
$830$	−5.83636	−	1.92013i	−0.202583	−	0.0666487i
$831$	7.41742			0.257308
$832$		0			0
$833$		−	18.3303i		−	0.635107i
$834$	−4.96773	+	8.60436i	−0.172018	+	0.297944i
$835$	6.69034	−	20.3357i	0.231529	−	0.703747i
$836$	−4.10436	−	7.10895i	−0.141952	−	0.245868i
$837$			31.0260i			1.07242i
$838$	−2.30852	+	1.33283i	−0.0797466	+	0.0460417i
$839$	21.8413	+	37.8303i	0.754047	+	1.30605i	0.945847	+	0.324613i	$0.105234\pi$
$839$	21.8413	+	37.8303i	0.754047	+	1.30605i	−0.191800	+	0.981434i	$0.561433\pi$
$840$	−6.56670	+	1.37055i	−0.226573	+	0.0472885i
$841$	4.00000	+	6.92820i	0.137931	+	0.238904i
$842$	2.16900	+	1.25227i	0.0747487	+	0.0431562i
$843$	3.16515	+	1.82740i	0.109014	+	0.0629390i
$844$	−0.295834			−0.0101830
$845$		0			0
$846$	−1.66970			−0.0574054
$847$	−6.00000	−	3.46410i	−0.206162	−	0.119028i
$848$	−18.3296	−	10.5826i	−0.629440	−	0.363407i
$849$	13.8739	+	24.0302i	0.476150	+	0.824716i
$850$	9.59386	−	4.18710i	0.329067	−	0.143616i
$851$	−18.1865	−	31.5000i	−0.623426	−	1.07981i
$852$	10.8956	−	6.29060i	0.373279	−	0.215513i
$853$			5.63310i			0.192874i	0.995339	+	0.0964369i	$0.0307446\pi$
$853$			5.63310i			0.192874i	−0.995339	+	0.0964369i	$0.969255\pi$
$854$	−0.560795	−	0.971326i	−0.0191900	−	0.0332381i
$855$	−7.35799	−	2.42074i	−0.251638	−	0.0827875i
$856$	−9.16478	+	15.8739i	−0.313246	+	0.542557i
$857$		−	4.74773i		−	0.162179i	−0.996707	−	0.0810896i	$-0.974160\pi$
$857$		−	4.74773i		−	0.162179i	0.996707	−	0.0810896i	$-0.0258400\pi$
$858$		0			0
$859$	44.2432			1.50956			0.754779	−	0.655979i	$-0.227744\pi$
$859$	44.2432			1.50956			0.754779	+	0.655979i	$0.227744\pi$
$860$	13.2469	−	40.2648i	0.451715	−	1.37302i
$861$	2.29129	−	3.96863i	0.0780869	−	0.135250i
$862$	3.35093	−	1.93466i	0.114133	−	0.0658947i
$863$			13.6657i			0.465186i	0.972574	+	0.232593i	$0.0747210\pi$
$863$			13.6657i			0.465186i	−0.972574	+	0.232593i	$0.925279\pi$
$864$	−11.8483	−	20.5218i	−0.403086	−	0.698165i
$865$	−24.7096	−	27.6468i	−0.840152	−	0.940019i
$866$	−4.45325			−0.151328
$867$	−3.46410	+	2.00000i	−0.117647	+	0.0679236i
$868$	16.6730	+	9.62614i	0.565917	+	0.326732i
$869$	7.93725	−	13.7477i	0.269253	−	0.466360i
$870$	0.956439	+	4.58258i	0.0324263	+	0.155364i
$871$		0			0
$872$			22.7477i			0.770335i
$873$	−19.7477	−	11.4014i	−0.668359	−	0.385877i
$874$	−1.81307	+	3.14033i	−0.0613279	+	0.106223i
$875$	−17.6027	−	8.07130i	−0.595079	−	0.272860i
$876$		0			0
$877$	6.87386	−	3.96863i	0.232114	−	0.134011i	−0.379433	−	0.925219i	$-0.623881\pi$
$877$	6.87386	−	3.96863i	0.232114	−	0.134011i	0.611547	+	0.791208i	$0.290548\pi$
$878$	5.73504	−	3.31113i	0.193548	−	0.111745i
$879$	18.1389			0.611809
$880$	12.3125	−	11.0044i	0.415054	−	0.370959i
$881$	18.2477	−	31.6060i	0.614782	−	1.06483i	−0.375641	−	0.926765i	$-0.622578\pi$
$881$	18.2477	−	31.6060i	0.614782	−	1.06483i	0.990423	−	0.138068i	$-0.0440892\pi$
$882$	3.16515	+	1.82740i	0.106576	+	0.0615318i
$883$		−	36.2432i		−	1.21968i	−0.792524	−	0.609840i	$-0.791234\pi$
$883$		−	36.2432i		−	1.21968i	0.792524	−	0.609840i	$-0.208766\pi$
$884$		0			0
$885$	30.5390	−	6.37386i	1.02656	−	0.214255i
$886$	−4.54860	+	7.87841i	−0.152813	+	0.264680i
$887$	47.1944	+	27.2477i	1.58463	+	0.914889i	0.994170	+	0.107826i	$0.0343888\pi$
$887$	47.1944	+	27.2477i	1.58463	+	0.914889i	0.590465	+	0.807064i	$0.298945\pi$
$888$	11.9059	−	6.87386i	0.399535	−	0.230672i
$889$	30.7400			1.03099
$890$	6.51747	+	7.29219i	0.218466	+	0.244435i
$891$	1.32288	+	2.29129i	0.0443180	+	0.0767610i
$892$			15.5130i			0.519414i
$893$	2.74110	−	1.58258i	0.0917275	−	0.0529589i
$894$	3.81307	−	6.60443i	0.127528	−	0.220885i
$895$	38.5840	+	12.6939i	1.28972	+	0.424311i
$896$	−19.1216			−0.638808
$897$		0			0
$898$			5.03447i			0.168002i
$899$	14.2179	−	24.6261i	0.474194	−	0.821328i
$900$	2.00351	−	17.8005i	0.0667836	−	0.593349i
$901$	−17.3739	−	30.0924i	−0.578807	−	1.00252i
$902$		−	3.19795i		−	0.106480i
$903$	−15.8739	+	9.16478i	−0.528249	+	0.304985i
$904$	6.42368	+	11.1261i	0.213648	+	0.370050i
$905$	3.99640	+	19.1479i	0.132845	+	0.636498i
$906$	−2.20871	−	3.82560i	−0.0733795	−	0.127097i
$907$	5.41463	+	3.12614i	0.179790	+	0.103802i	0.587194	−	0.809446i	$-0.300233\pi$
$907$	5.41463	+	3.12614i	0.179790	+	0.103802i	−0.407404	+	0.913248i	$0.633566\pi$
$908$	1.26951	+	0.732950i	0.0421301	+	0.0243238i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−7.91288			−0.262165			−0.131083	−	0.991371i	$-0.541845\pi$
$911$	−7.91288			−0.262165			−0.131083	+	0.991371i	$0.541845\pi$
$912$	4.18693	+	2.41733i	0.138643	+	0.0800457i
$913$	−13.7810	−	7.95644i	−0.456083	−	0.263320i
$914$	0.395644	+	0.685275i	0.0130867	+	0.0226669i
$915$	−3.10260	+	0.647551i	−0.102569	+	0.0214074i
$916$	23.5257	+	40.7477i	0.777311	+	1.34634i
$917$	11.3739	−	6.56670i	0.375598	−	0.216852i
$918$		−	10.4678i		−	0.345487i
$919$	27.0826	+	46.9084i	0.893372	+	1.54737i	0.835807	+	0.549023i	$0.185000\pi$
$919$	27.0826	+	46.9084i	0.893372	+	1.54737i	0.0575648	+	0.998342i	$0.481666\pi$
$920$	−16.8593	−	5.54661i	−0.555834	−	0.182866i
$921$	−12.1244	+	21.0000i	−0.399511	+	0.691974i
$922$		−	16.3739i		−	0.539244i
$923$		0			0
$924$	−8.20871			−0.270047
$925$	39.4373	+	4.43881i	1.29669	+	0.145947i
$926$	9.00000	−	15.5885i	0.295758	−	0.512268i
$927$	−5.48220	+	3.16515i	−0.180059	+	0.103957i
$928$			21.7182i			0.712935i
$929$	−13.1811	−	22.8303i	−0.432457	−	0.749038i	0.564627	−	0.825346i	$-0.309020\pi$
$929$	−13.1811	−	22.8303i	−0.432457	−	0.749038i	−0.997084	+	0.0763082i	$0.975687\pi$
$930$	−4.72631	+	4.22419i	−0.154982	+	0.138517i
$931$	−6.92820			−0.227063
$932$	−4.39770	+	2.53901i	−0.144052	+	0.0831682i
$933$	6.56670	+	3.79129i	0.214984	+	0.124121i
$934$	5.55765	−	9.62614i	0.181852	−	0.314977i
$935$	26.5390	−	5.53901i	0.867919	−	0.181145i
$936$		0			0
$937$		−	31.4955i		−	1.02891i	−0.857517	−	0.514456i	$-0.827994\pi$
$937$		−	31.4955i		−	1.02891i	0.857517	−	0.514456i	$-0.172006\pi$
$938$	0.691478	+	0.399225i	0.0225775	+	0.0130352i
$939$	−1.62614	+	2.81655i	−0.0530670	+	0.0919147i
$940$	4.87768	+	5.45748i	0.159092	+	0.178003i
$941$	−26.4575			−0.862490			−0.431245	−	0.902235i	$-0.641926\pi$
$941$	−26.4575			−0.862490			−0.431245	+	0.902235i	$0.641926\pi$
$942$	−3.62614	+	2.09355i	−0.118146	+	0.0682116i
$943$	10.5000	−	6.06218i	0.341927	−	0.197412i
$944$	38.9434			1.26750
$945$	−14.4385	+	12.9046i	−0.469686	+	0.419787i
$946$	−6.39564	+	11.0776i	−0.207940	+	0.360163i
$947$	−12.4129	−	7.16658i	−0.403364	−	0.232883i	0.284570	−	0.958655i	$-0.408149\pi$
$947$	−12.4129	−	7.16658i	−0.403364	−	0.232883i	−0.687935	+	0.725773i	$0.741482\pi$
$948$			10.7477i			0.349070i
$949$		0			0
$950$	−1.58258	−	3.62614i	−0.0513455	−	0.117647i
$951$	−0.0953502	+	0.165151i	−0.00309194	+	0.00535540i
$952$	−11.9059	−	6.87386i	−0.385872	−	0.222783i
$953$	6.99578	−	4.03901i	0.226616	−	0.130837i	−0.382394	−	0.923999i	$-0.624900\pi$
$953$	6.99578	−	4.03901i	0.226616	−	0.130837i	0.609010	+	0.793163i	$0.291567\pi$
$954$	6.92820			0.224309
$955$	27.6468	−	24.7096i	0.894629	−	0.799584i
$956$	−0.170800	−	0.295834i	−0.00552406	−	0.00956794i
$957$			12.1244i			0.391925i
$958$	−1.84522	+	1.06534i	−0.0596165	+	0.0344196i
$959$	−9.08258	+	15.7315i	−0.293292	+	0.507996i
$960$	−2.38812	+	7.25885i	−0.0770762	+	0.234278i
$961$	7.50455			0.242082
$962$		0			0
$963$			21.1652i			0.682037i
$964$	−1.55130	+	2.68693i	−0.0499640	+	0.0865402i
$965$	−10.3881	+	31.5753i	−0.334404	+	1.01644i
$966$	1.81307	+	3.14033i	0.0583345	+	0.101038i
$967$		−	37.3821i		−	1.20213i	−0.799201	−	0.601064i	$-0.794744\pi$
$967$		−	37.3821i		−	1.20213i	0.799201	−	0.601064i	$-0.205256\pi$
$968$	6.00000	−	3.46410i	0.192847	−	0.111340i
$969$	3.96863	+	6.87386i	0.127491	+	0.220820i
$970$	−2.37960	−	11.4014i	−0.0764044	−	0.366075i
$971$	9.24773	+	16.0175i	0.296774	+	0.514027i	0.975396	−	0.220460i	$-0.0707560\pi$
$971$	9.24773	+	16.0175i	0.296774	+	0.514027i	−0.678622	+	0.734487i	$0.737423\pi$
$972$	−24.8208	−	14.3303i	−0.796128	−	0.459645i
$973$	32.6216	+	18.8341i	1.04580	+	0.603793i
$974$	−4.87841			−0.156314
$975$		0			0
$976$	−3.95644			−0.126643
$977$	−30.5780	−	17.6542i	−0.978278	−	0.564809i	−0.0765281	−	0.997067i	$-0.524383\pi$
$977$	−30.5780	−	17.6542i	−0.978278	−	0.564809i	−0.901750	+	0.432258i	$0.857717\pi$
$978$	−8.33648	−	4.81307i	−0.266571	−	0.153905i
$979$	12.6652	+	21.9367i	0.404780	+	0.701100i
$980$	−3.27340	−	15.6838i	−0.104565	−	0.501001i
$981$	13.1334	+	22.7477i	0.419317	+	0.726279i
$982$	7.68239	−	4.43543i	0.245155	−	0.141540i
$983$		−	55.0840i		−	1.75691i	−0.477827	−	0.878454i	$-0.658576\pi$
$983$		−	55.0840i		−	1.75691i	0.477827	−	0.878454i	$-0.341424\pi$
$984$	2.29129	+	3.96863i	0.0730436	+	0.126515i
$985$	−10.2548	+	31.1702i	−0.326746	+	0.993165i
$986$	−4.79693	+	8.30852i	−0.152765	+	0.264597i
$987$		−	3.16515i		−	0.100748i
$988$		0			0
$989$	−48.4955			−1.54207
$990$	−1.68931	+	5.13478i	−0.0536899	+	0.163194i
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	−25.4684	+	14.7042i	−0.808621	+	0.466858i
$993$		−	4.47315i		−	0.141951i
$994$	2.77883	+	4.81307i	0.0881390	+	0.152661i
$995$	−17.6435	+	15.7690i	−0.559336	+	0.499912i
$996$	10.7737			0.341378
$997$	−0.143025	+	0.0825757i	−0.00452966	+	0.00261520i	−0.502263	−	0.864715i	$-0.667499\pi$
$997$	−0.143025	+	0.0825757i	−0.00452966	+	0.00261520i	0.497733	+	0.867330i	$0.334166\pi$
$998$	0.286051	+	0.165151i	0.00905477	+	0.00522778i
$999$	19.8431	−	34.3693i	0.627809	−	1.08740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.c.529.3		8
5.4	even	2		845.2.n.d.529.2		8
13.2	odd	12		65.2.l.a.49.3	yes	8
13.3	even	3		845.2.n.d.484.2		8
13.4	even	6		845.2.b.f.339.6		8
13.5	odd	4		845.2.l.c.654.3		8
13.6	odd	12		845.2.d.c.844.4		8
13.7	odd	12		845.2.d.c.844.6		8
13.8	odd	4		65.2.l.a.4.2	✓	8
13.9	even	3		845.2.b.f.339.4		8
13.10	even	6	inner	845.2.n.c.484.4		8
13.11	odd	12		845.2.l.c.699.2		8
13.12	even	2		845.2.n.d.529.1		8
39.2	even	12		585.2.bf.a.244.2		8
39.8	even	4		585.2.bf.a.199.3		8
52.15	even	12		1040.2.df.b.49.1		8
52.47	even	4		1040.2.df.b.849.4		8
65.2	even	12		325.2.n.c.101.1		4
65.4	even	6		845.2.b.f.339.3		8
65.8	even	4		325.2.n.b.251.2		4
65.9	even	6		845.2.b.f.339.5		8
65.17	odd	12		4225.2.a.bk.1.2		4
65.19	odd	12		845.2.d.c.844.5		8
65.22	odd	12		4225.2.a.bk.1.3		4
65.24	odd	12		845.2.l.c.699.3		8
65.28	even	12		325.2.n.b.101.2		4
65.29	even	6	inner	845.2.n.c.484.3		8
65.34	odd	4		65.2.l.a.4.3	yes	8
65.43	odd	12		4225.2.a.bj.1.3		4
65.44	odd	4		845.2.l.c.654.2		8
65.47	even	4		325.2.n.c.251.1		4
65.48	odd	12		4225.2.a.bj.1.2		4
65.49	even	6		845.2.n.d.484.1		8
65.54	odd	12		65.2.l.a.49.2	yes	8
65.59	odd	12		845.2.d.c.844.3		8
65.64	even	2	inner	845.2.n.c.529.4		8
195.119	even	12		585.2.bf.a.244.3		8
195.164	even	4		585.2.bf.a.199.2		8
260.99	even	4		1040.2.df.b.849.1		8
260.119	even	12		1040.2.df.b.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	13.8	odd	4
65.2.l.a.4.3	yes	8	65.34	odd	4
65.2.l.a.49.2	yes	8	65.54	odd	12
65.2.l.a.49.3	yes	8	13.2	odd	12
325.2.n.b.101.2		4	65.28	even	12
325.2.n.b.251.2		4	65.8	even	4
325.2.n.c.101.1		4	65.2	even	12
325.2.n.c.251.1		4	65.47	even	4
585.2.bf.a.199.2		8	195.164	even	4
585.2.bf.a.199.3		8	39.8	even	4
585.2.bf.a.244.2		8	39.2	even	12
585.2.bf.a.244.3		8	195.119	even	12
845.2.b.f.339.3		8	65.4	even	6
845.2.b.f.339.4		8	13.9	even	3
845.2.b.f.339.5		8	65.9	even	6
845.2.b.f.339.6		8	13.4	even	6
845.2.d.c.844.3		8	65.59	odd	12
845.2.d.c.844.4		8	13.6	odd	12
845.2.d.c.844.5		8	65.19	odd	12
845.2.d.c.844.6		8	13.7	odd	12
845.2.l.c.654.2		8	65.44	odd	4
845.2.l.c.654.3		8	13.5	odd	4
845.2.l.c.699.2		8	13.11	odd	12
845.2.l.c.699.3		8	65.24	odd	12
845.2.n.c.484.3		8	65.29	even	6	inner
845.2.n.c.484.4		8	13.10	even	6	inner
845.2.n.c.529.3		8	1.1	even	1	trivial
845.2.n.c.529.4		8	65.64	even	2	inner
845.2.n.d.484.1		8	65.49	even	6
845.2.n.d.484.2		8	13.3	even	3
845.2.n.d.529.1		8	13.12	even	2
845.2.n.d.529.2		8	5.4	even	2
1040.2.df.b.49.1		8	52.15	even	12
1040.2.df.b.49.4		8	260.119	even	12
1040.2.df.b.849.1		8	260.99	even	4
1040.2.df.b.849.4		8	52.47	even	4
4225.2.a.bj.1.2		4	65.48	odd	12
4225.2.a.bj.1.3		4	65.43	odd	12
4225.2.a.bk.1.2		4	65.17	odd	12
4225.2.a.bk.1.3		4	65.22	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.395644 + 0.228425i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.895644 - 1.55130i) q^{4} +(-0.456850 - 2.18890i) q^{5} +(-0.228425 - 0.395644i) q^{6} +(-1.50000 + 0.866025i) q^{7} -1.73205i q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.319250 - 0.970381i) q^{10} +(1.32288 - 2.29129i) q^{11} +1.79129i q^{12} -0.791288 q^{14} +(-0.698807 + 2.12407i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-3.96863 + 2.29129i) q^{17} -0.913701i q^{18} +(0.866025 + 1.50000i) q^{19} +(-2.98647 + 2.66919i) q^{20} +1.73205 q^{21} +(1.04678 - 0.604356i) q^{22} +(3.96863 + 2.29129i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(-4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +(2.68693 + 1.55130i) q^{28} +(2.29129 - 3.96863i) q^{29} +(-0.761669 + 0.680750i) q^{30} +6.20520 q^{31} +(-4.10436 + 2.36965i) q^{32} +(-2.29129 + 1.32288i) q^{33} -2.09355 q^{34} +(2.58092 + 2.88771i) q^{35} +(-1.79129 + 3.10260i) q^{36} +(-6.87386 - 3.96863i) q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +(1.32288 - 2.29129i) q^{41} +(0.685275 + 0.395644i) q^{42} +(-9.16478 + 5.29129i) q^{43} -4.73930 q^{44} +(-3.33444 + 2.98019i) q^{45} +(1.04678 + 1.81307i) q^{46} -1.82740i q^{47} +(2.41733 - 1.39564i) q^{48} +(-2.00000 + 3.46410i) q^{49} +(-2.26992 - 0.255488i) q^{50} +4.58258 q^{51} +7.58258i q^{53} +(-1.14213 + 1.97822i) q^{54} +(-5.61976 - 1.84887i) q^{55} +(1.50000 + 2.59808i) q^{56} -1.73205i q^{57} +(1.81307 - 1.04678i) q^{58} +(-6.97588 - 12.0826i) q^{59} +(3.92095 - 0.818350i) q^{60} +(0.708712 + 1.22753i) q^{61} +(2.45505 + 1.41742i) q^{62} +(3.00000 + 1.73205i) q^{63} +3.41742 q^{64} -1.20871 q^{66} +(-0.873864 - 0.504525i) q^{67} +(7.10895 + 4.10436i) q^{68} +(-2.29129 - 3.96863i) q^{69} +(0.361500 + 1.73205i) q^{70} +(-3.51178 - 6.08258i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-1.81307 - 3.14033i) q^{74} +(4.96863 + 0.559237i) q^{75} +(1.55130 - 2.68693i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(5.92889 + 1.95057i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.04678 - 0.604356i) q^{82} -6.01450i q^{83} +(-1.55130 - 2.68693i) q^{84} +(6.82847 + 7.64016i) q^{85} -4.83465 q^{86} +(-3.96863 + 2.29129i) q^{87} +(-3.96863 - 2.29129i) q^{88} +(-4.78698 + 8.29129i) q^{89} +(-2.00000 + 0.417424i) q^{90} -8.20871i q^{92} +(-5.37386 - 3.10260i) q^{93} +(0.417424 - 0.723000i) q^{94} +(2.88771 - 2.58092i) q^{95} +4.73930 q^{96} +(9.87386 - 5.70068i) q^{97} +(-1.58258 + 0.913701i) q^{98} -5.29150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 2 q^{4} - 12 q^{7} - 8 q^{9} + 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 18 q^{20} - 6 q^{28} + 10 q^{30} - 42 q^{32} + 6 q^{35} + 4 q^{36} - 12 q^{40} - 12 q^{45} - 16 q^{49} - 42 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 + 2 * q^4 - 12 * q^7 - 8 * q^9 + 4 * q^10 + 12 * q^14 - 6 * q^15 - 2 * q^16 - 18 * q^20 - 6 * q^28 + 10 * q^30 - 42 * q^32 + 6 * q^35 + 4 * q^36 - 12 * q^40 - 12 * q^45 - 16 * q^49 - 42 * q^50 - 14 * q^55 + 12 * q^56 + 42 * q^58 + 24 * q^61 + 24 * q^63 + 64 * q^64 - 28 * q^66 + 48 * q^67 - 24 * q^72 - 42 * q^74 + 8 * q^75 + 48 * q^79 + 24 * q^80 - 4 * q^81 + 42 * q^85 - 16 * q^90 + 12 * q^93 + 40 * q^94 + 6 * q^95 + 24 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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