LMFDB - Embedded newform 546.2.q.i.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.4
Character	$\chi$	$=$	546.251
Dual form			546.2.q.i.335.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.514158 + 1.65398i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.58412i q^{5} +(-1.17531 - 1.27226i) q^{6} +(-1.90227 + 1.83885i) q^{7} +1.00000 q^{8} +(-2.47128 - 1.70081i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.514158 + 1.65398i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.58412i q^{5} +(-1.17531 - 1.27226i) q^{6} +(-1.90227 + 1.83885i) q^{7} +1.00000 q^{8} +(-2.47128 - 1.70081i) q^{9} +(-3.10394 - 1.79206i) q^{10} +(-0.630804 + 1.09258i) q^{11} +(1.68947 - 0.381715i) q^{12} +(2.88239 + 2.16606i) q^{13} +(-0.641360 - 2.56684i) q^{14} +(-5.92805 - 1.84280i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.57988 - 2.73643i) q^{17} +(2.70859 - 1.28979i) q^{18} +(-0.386956 - 0.670228i) q^{19} +(3.10394 - 1.79206i) q^{20} +(-2.06336 - 4.09177i) q^{21} +(-0.630804 - 1.09258i) q^{22} +(7.28626 + 4.20672i) q^{23} +(-0.514158 + 1.65398i) q^{24} -7.84590 q^{25} +(-3.31706 + 1.41319i) q^{26} +(4.08374 - 3.21296i) q^{27} +(2.54363 + 0.727985i) q^{28} +(-6.76234 - 3.90424i) q^{29} +(4.55994 - 4.21244i) q^{30} +7.70977 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.48278 - 1.60510i) q^{33} +3.15976 q^{34} +(-6.59067 - 6.81795i) q^{35} +(-0.237306 + 2.99060i) q^{36} +(-0.424035 - 0.244817i) q^{37} +0.773913 q^{38} +(-5.06463 + 3.65371i) q^{39} +3.58412i q^{40} +(-1.17143 - 0.676327i) q^{41} +(4.57525 + 0.258966i) q^{42} +(0.125032 + 0.216561i) q^{43} +1.26161 q^{44} +(6.09591 - 8.85737i) q^{45} +(-7.28626 + 4.20672i) q^{46} +10.9168i q^{47} +(-1.17531 - 1.27226i) q^{48} +(0.237237 - 6.99598i) q^{49} +(3.92295 - 6.79475i) q^{50} +(5.33831 - 1.20613i) q^{51} +(0.434672 - 3.57925i) q^{52} -12.1730i q^{53} +(0.740636 + 5.14310i) q^{54} +(-3.91595 - 2.26088i) q^{55} +(-1.90227 + 1.83885i) q^{56} +(1.30750 - 0.295414i) q^{57} +(6.76234 - 3.90424i) q^{58} +(-10.4372 + 6.02594i) q^{59} +(1.36811 + 6.05524i) q^{60} +(-3.27341 + 1.88990i) q^{61} +(-3.85488 + 6.67685i) q^{62} +(7.82858 - 1.30893i) q^{63} +1.00000 q^{64} +(-7.76343 + 10.3308i) q^{65} +(2.13144 - 0.481574i) q^{66} +(-10.4963 - 6.06005i) q^{67} +(-1.57988 + 2.73643i) q^{68} +(-10.7041 + 9.88839i) q^{69} +(9.19985 - 2.29871i) q^{70} +(-0.0759653 - 0.131576i) q^{71} +(-2.47128 - 1.70081i) q^{72} +10.3607 q^{73} +(0.424035 - 0.244817i) q^{74} +(4.03403 - 12.9769i) q^{75} +(-0.386956 + 0.670228i) q^{76} +(-0.809145 - 3.23834i) q^{77} +(-0.631890 - 6.21295i) q^{78} +5.53840 q^{79} +(-3.10394 - 1.79206i) q^{80} +(3.21447 + 8.40638i) q^{81} +(1.17143 - 0.676327i) q^{82} +3.23534i q^{83} +(-2.51190 + 3.83280i) q^{84} +(9.80769 - 5.66247i) q^{85} -0.250064 q^{86} +(9.93444 - 9.17736i) q^{87} +(-0.630804 + 1.09258i) q^{88} +(5.69791 + 3.28969i) q^{89} +(4.62275 + 9.70790i) q^{90} +(-9.46615 + 1.17986i) q^{91} -8.41345i q^{92} +(-3.96404 + 12.7518i) q^{93} +(-9.45425 - 5.45842i) q^{94} +(2.40218 - 1.38690i) q^{95} +(1.68947 - 0.381715i) q^{96} +(2.21400 + 3.83477i) q^{97} +(5.94008 + 3.70344i) q^{98} +(3.41718 - 1.62721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 q^{93} + 36 q^{95} - 36 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * q^93 + 36 * q^95 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.514158	+	1.65398i	−0.296849	+	0.954924i
$3$	−0.514158	+	1.65398i	−0.296849	+	0.954924i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$			3.58412i			1.60287i	0.598085	+	0.801433i	$0.295929\pi$
$5$			3.58412i			1.60287i	−0.598085	+	0.801433i	$0.704071\pi$
$6$	−1.17531	−	1.27226i	−0.479817	−	0.519399i
$7$	−1.90227	+	1.83885i	−0.718989	+	0.695021i
$7$	−1.90227	+	1.83885i	−0.718989	+	0.695021i
$8$	1.00000			0.353553
$9$	−2.47128	−	1.70081i	−0.823761	−	0.566938i
$10$	−3.10394	−	1.79206i	−0.981551	−	0.566699i
$11$	−0.630804	+	1.09258i	−0.190195	+	0.329427i	−0.945315	−	0.326160i	$-0.894245\pi$
$11$	−0.630804	+	1.09258i	−0.190195	+	0.329427i	0.755120	+	0.655587i	$0.227579\pi$
$12$	1.68947	−	0.381715i	0.487707	−	0.110191i
$13$	2.88239	+	2.16606i	0.799431	+	0.600758i
$13$	2.88239	+	2.16606i	0.799431	+	0.600758i
$14$	−0.641360	−	2.56684i	−0.171411	−	0.686016i
$15$	−5.92805	−	1.84280i	−1.53062	−	0.475810i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.57988	−	2.73643i	−0.383177	−	0.663682i	0.608337	−	0.793679i	$-0.291837\pi$
$17$	−1.57988	−	2.73643i	−0.383177	−	0.663682i	−0.991514	+	0.129996i	$0.958503\pi$
$18$	2.70859	−	1.28979i	0.638420	−	0.304006i
$19$	−0.386956	−	0.670228i	−0.0887739	−	0.153761i	0.818219	−	0.574906i	$-0.194962\pi$
$19$	−0.386956	−	0.670228i	−0.0887739	−	0.153761i	−0.906993	+	0.421145i	$0.861628\pi$
$20$	3.10394	−	1.79206i	0.694061	−	0.400716i
$21$	−2.06336	−	4.09177i	−0.450261	−	0.892897i
$22$	−0.630804	−	1.09258i	−0.134488	−	0.232940i
$23$	7.28626	+	4.20672i	1.51929	+	0.877162i	0.999742	+	0.0227213i	$0.00723304\pi$
$23$	7.28626	+	4.20672i	1.51929	+	0.877162i	0.519548	+	0.854441i	$0.326100\pi$
$24$	−0.514158	+	1.65398i	−0.104952	+	0.337617i
$25$	−7.84590			−1.56918
$26$	−3.31706	+	1.41319i	−0.650529	+	0.277149i
$27$	4.08374	−	3.21296i	0.785915	−	0.618334i
$28$	2.54363	+	0.727985i	0.480700	+	0.137576i
$29$	−6.76234	−	3.90424i	−1.25574	−	0.724999i	−0.283493	−	0.958974i	$-0.591493\pi$
$29$	−6.76234	−	3.90424i	−1.25574	−	0.724999i	−0.972243	+	0.233975i	$0.924826\pi$
$30$	4.55994	−	4.21244i	0.832527	−	0.769083i
$31$	7.70977			1.38471			0.692357	−	0.721555i	$-0.256572\pi$
$31$	7.70977			1.38471			0.692357	+	0.721555i	$0.256572\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.48278	−	1.60510i	−0.258118	−	0.279412i
$34$	3.15976			0.541894
$35$	−6.59067	−	6.81795i	−1.11403	−	1.15244i
$36$	−0.237306	+	2.99060i	−0.0395509	+	0.498433i
$37$	−0.424035	−	0.244817i	−0.0697109	−	0.0402476i	0.464739	−	0.885447i	$-0.346148\pi$
$37$	−0.424035	−	0.244817i	−0.0697109	−	0.0402476i	−0.534450	+	0.845200i	$0.679481\pi$
$38$	0.773913			0.125545
$39$	−5.06463	+	3.65371i	−0.810989	+	0.585061i
$40$			3.58412i			0.566699i
$41$	−1.17143	−	0.676327i	−0.182947	−	0.105625i	0.405730	−	0.913993i	$-0.367017\pi$
$41$	−1.17143	−	0.676327i	−0.182947	−	0.105625i	−0.588677	+	0.808369i	$0.700351\pi$
$42$	4.57525	+	0.258966i	0.705977	+	0.0399593i
$43$	0.125032	+	0.216561i	0.0190672	+	0.0330253i	0.875402	−	0.483396i	$-0.160597\pi$
$43$	0.125032	+	0.216561i	0.0190672	+	0.0330253i	−0.856334	+	0.516422i	$0.827264\pi$
$44$	1.26161			0.190195
$45$	6.09591	−	8.85737i	0.908725	−	1.32038i
$46$	−7.28626	+	4.20672i	−1.07430	+	0.620248i
$47$			10.9168i			1.59238i	0.605044	+	0.796192i	$0.293155\pi$
$47$			10.9168i			1.59238i	−0.605044	+	0.796192i	$0.706845\pi$
$48$	−1.17531	−	1.27226i	−0.169641	−	0.183635i
$49$	0.237237	−	6.99598i	0.0338910	−	0.999426i
$50$	3.92295	−	6.79475i	0.554789	−	0.960922i
$51$	5.33831	−	1.20613i	0.747512	−	0.168891i
$52$	0.434672	−	3.57925i	0.0602781	−	0.496353i
$53$		−	12.1730i		−	1.67208i	−0.548665	−	0.836042i	$-0.684864\pi$
$53$		−	12.1730i		−	1.67208i	0.548665	−	0.836042i	$-0.315136\pi$
$54$	0.740636	+	5.14310i	0.100788	+	0.699887i
$55$	−3.91595	−	2.26088i	−0.528027	−	0.304856i
$56$	−1.90227	+	1.83885i	−0.254201	+	0.245727i
$57$	1.30750	−	0.295414i	0.173182	−	0.0391285i
$58$	6.76234	−	3.90424i	0.887939	−	0.512652i
$59$	−10.4372	+	6.02594i	−1.35881	+	0.784510i	−0.989464	−	0.144781i	$-0.953752\pi$
$59$	−10.4372	+	6.02594i	−1.35881	+	0.784510i	−0.369348	+	0.929291i	$0.620419\pi$
$60$	1.36811	+	6.05524i	0.176622	+	0.781728i
$61$	−3.27341	+	1.88990i	−0.419117	+	0.241977i	−0.694699	−	0.719300i	$-0.744463\pi$
$61$	−3.27341	+	1.88990i	−0.419117	+	0.241977i	0.275583	+	0.961277i	$0.411129\pi$
$62$	−3.85488	+	6.67685i	−0.489571	+	0.847961i
$63$	7.82858	−	1.30893i	0.986309	−	0.164909i
$64$	1.00000			0.125000
$65$	−7.76343	+	10.3308i	−0.962935	+	1.28138i
$66$	2.13144	−	0.481574i	0.262363	−	0.0592777i
$67$	−10.4963	−	6.06005i	−1.28233	−	0.740353i	−0.305056	−	0.952335i	$-0.598675\pi$
$67$	−10.4963	−	6.06005i	−1.28233	−	0.740353i	−0.977274	+	0.211981i	$0.932008\pi$
$68$	−1.57988	+	2.73643i	−0.191589	+	0.331841i
$69$	−10.7041	+	9.88839i	−1.28862	+	1.19042i
$70$	9.19985	−	2.29871i	1.09959	−	0.274748i
$71$	−0.0759653	−	0.131576i	−0.00901542	−	0.0156152i	0.861482	−	0.507787i	$-0.169536\pi$
$71$	−0.0759653	−	0.131576i	−0.00901542	−	0.0156152i	−0.870498	+	0.492172i	$0.836203\pi$
$72$	−2.47128	−	1.70081i	−0.291243	−	0.200443i
$73$	10.3607			1.21263			0.606315	−	0.795224i	$-0.292647\pi$
$73$	10.3607			1.21263			0.606315	+	0.795224i	$0.292647\pi$
$74$	0.424035	−	0.244817i	0.0492930	−	0.0284593i
$75$	4.03403	−	12.9769i	0.465810	−	1.49845i
$76$	−0.386956	+	0.670228i	−0.0443869	+	0.0768804i
$77$	−0.809145	−	3.23834i	−0.0922107	−	0.369043i
$78$	−0.631890	−	6.21295i	−0.0715475	−	0.703478i
$79$	5.53840			0.623118			0.311559	−	0.950227i	$-0.399149\pi$
$79$	5.53840			0.623118			0.311559	+	0.950227i	$0.399149\pi$
$80$	−3.10394	−	1.79206i	−0.347031	−	0.200358i
$81$	3.21447	+	8.40638i	0.357164	+	0.934042i
$82$	1.17143	−	0.676327i	0.129363	−	0.0746878i
$83$			3.23534i			0.355125i	0.984110	+	0.177562i	$0.0568211\pi$
$83$			3.23534i			0.355125i	−0.984110	+	0.177562i	$0.943179\pi$
$84$	−2.51190	+	3.83280i	−0.274070	+	0.418193i
$85$	9.80769	−	5.66247i	1.06379	−	0.614182i
$86$	−0.250064			−0.0269651
$87$	9.93444	−	9.17736i	1.06508	−	0.983916i
$88$	−0.630804	+	1.09258i	−0.0672439	+	0.116470i
$89$	5.69791	+	3.28969i	0.603977	+	0.348706i	0.770605	−	0.637314i	$-0.219954\pi$
$89$	5.69791	+	3.28969i	0.603977	+	0.348706i	−0.166627	+	0.986020i	$0.553288\pi$
$90$	4.62275	+	9.70790i	0.487280	+	1.02330i
$91$	−9.46615	+	1.17986i	−0.992322	+	0.123683i
$92$		−	8.41345i		−	0.877162i
$93$	−3.96404	+	12.7518i	−0.411052	+	1.32230i
$94$	−9.45425	−	5.45842i	−0.975132	−	0.562993i
$95$	2.40218	−	1.38690i	0.246458	−	0.142293i
$96$	1.68947	−	0.381715i	0.172430	−	0.0389586i
$97$	2.21400	+	3.83477i	0.224798	+	0.389361i	0.956259	−	0.292522i	$-0.0944945\pi$
$97$	2.21400	+	3.83477i	0.224798	+	0.389361i	−0.731461	+	0.681883i	$0.761161\pi$
$98$	5.94008	+	3.70344i	0.600038	+	0.374104i
$99$	3.41718	−	1.62721i	0.343439	−	0.163540i
$100$	3.92295	+	6.79475i	0.392295	+	0.679475i
$101$	−0.490495	+	0.849562i	−0.0488061	+	0.0845346i	−0.889396	−	0.457137i	$-0.848875\pi$
$101$	−0.490495	+	0.849562i	−0.0488061	+	0.0845346i	0.840590	+	0.541671i	$0.182208\pi$
$102$	−1.62462	+	5.22617i	−0.160861	+	0.517468i
$103$			15.6826i			1.54525i	0.634860	+	0.772627i	$0.281058\pi$
$103$			15.6826i			1.54525i	−0.634860	+	0.772627i	$0.718942\pi$
$104$	2.88239	+	2.16606i	0.282642	+	0.212400i
$105$	14.6654	−	7.39531i	1.43119	−	0.721708i
$106$	10.5421	+	6.08648i	1.02394	+	0.591171i
$107$	4.25464	+	2.45642i	0.411311	+	0.237471i	0.691353	−	0.722517i	$-0.257015\pi$
$107$	4.25464	+	2.45642i	0.411311	+	0.237471i	−0.280042	+	0.959988i	$0.590348\pi$
$108$	−4.82437	−	1.93014i	−0.464225	−	0.185728i
$109$			5.99158i			0.573889i	0.957947	+	0.286945i	$0.0926395\pi$
$109$			5.99158i			0.573889i	−0.957947	+	0.286945i	$0.907360\pi$
$110$	3.91595	−	2.26088i	0.373371	−	0.215566i
$111$	0.622942	−	0.575469i	0.0591270	−	0.0546211i
$112$	−0.641360	−	2.56684i	−0.0606029	−	0.242543i
$113$	−13.7438	+	7.93500i	−1.29291	+	0.746462i	−0.979169	−	0.203047i	$-0.934916\pi$
$113$	−13.7438	+	7.93500i	−1.29291	+	0.746462i	−0.313741	+	0.949509i	$0.601582\pi$
$114$	−0.397914	+	1.28003i	−0.0372680	+	0.119886i
$115$	−15.0774	+	26.1148i	−1.40597	+	2.43522i
$116$			7.80848i			0.724999i
$117$	−3.43913	−	10.2554i	−0.317948	−	0.948108i
$118$		−	12.0519i		−	1.10946i
$119$	8.03725	+	2.30026i	0.736774	+	0.210864i
$120$	−5.92805	−	1.84280i	−0.541154	−	0.168224i
$121$	4.70417	+	8.14787i	0.427652	+	0.740715i
$122$		−	3.77980i		−	0.342207i
$123$	1.72093	−	1.58978i	0.155171	−	0.143346i
$124$	−3.85488	−	6.67685i	−0.346179	−	0.599599i
$125$		−	10.2000i		−	0.912318i
$126$	−2.78073	+	7.43422i	−0.247727	+	0.662293i
$127$	−5.41129	+	9.37263i	−0.480174	+	0.831686i	−0.999741	−	0.0227433i	$-0.992760\pi$
$127$	−5.41129	+	9.37263i	−0.480174	+	0.831686i	0.519567	+	0.854430i	$0.326093\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−0.422474	+	0.0954529i	−0.0371967	+	0.00840416i
$130$	−5.06504	−	11.8887i	−0.444233	−	1.04271i
$131$	−13.6129			−1.18936			−0.594682	−	0.803961i	$-0.702722\pi$
$131$	−13.6129			−1.18936			−0.594682	+	0.803961i	$0.702722\pi$
$132$	−0.648666	+	2.08667i	−0.0564591	+	0.181621i
$133$	1.96855	+	0.563396i	0.170695	+	0.0488527i
$134$	10.4963	−	6.06005i	0.906744	−	0.523509i
$135$	11.5156	+	14.6366i	0.991107	+	1.25972i
$136$	−1.57988	−	2.73643i	−0.135474	−	0.234647i
$137$	−1.10639	−	1.91632i	−0.0945251	−	0.163722i	0.814885	−	0.579622i	$-0.196800\pi$
$137$	−1.10639	−	1.91632i	−0.0945251	−	0.163722i	−0.909410	+	0.415900i	$0.863467\pi$
$138$	−3.21153	−	14.2142i	−0.273384	−	1.21000i
$139$	−2.92041	+	1.68610i	−0.247706	+	0.143013i	−0.618713	−	0.785617i	$-0.712346\pi$
$139$	−2.92041	+	1.68610i	−0.247706	+	0.143013i	0.371007	+	0.928630i	$0.379012\pi$
$140$	−2.60918	+	9.11666i	−0.220516	+	0.770498i
$141$	−18.0562	−	5.61298i	−1.52061	−	0.472698i
$142$	0.151931			0.0127497
$143$	−4.18483	+	1.78289i	−0.349953	+	0.149093i
$144$	2.70859	−	1.28979i	0.225716	−	0.107482i
$145$	13.9933	−	24.2370i	1.16208	−	2.01277i
$146$	−5.18036	+	8.97264i	−0.428730	+	0.742581i
$147$	11.4492	+	3.98943i	0.944315	+	0.329042i
$148$			0.489633i			0.0402476i
$149$	−2.67228	−	4.62852i	−0.218922	−	0.379183i	0.735557	−	0.677463i	$-0.236921\pi$
$149$	−2.67228	−	4.62852i	−0.218922	−	0.379183i	−0.954479	+	0.298279i	$0.903587\pi$
$150$	9.22134	+	9.98204i	0.752919	+	0.815030i
$151$			13.2645i			1.07945i	0.841842	+	0.539723i	$0.181471\pi$
$151$			13.2645i			1.07945i	−0.841842	+	0.539723i	$0.818529\pi$
$152$	−0.386956	−	0.670228i	−0.0313863	−	0.0543627i
$153$	−0.749829	+	9.44958i	−0.0606201	+	0.763953i
$154$	3.20906	+	0.918431i	0.258593	+	0.0740093i
$155$			27.6327i			2.21951i
$156$	5.69652	+	2.55924i	0.456086	+	0.204903i
$157$		−	5.83056i		−	0.465329i	−0.972557	−	0.232665i	$-0.925256\pi$
$157$		−	5.83056i		−	0.465329i	0.972557	−	0.232665i	$-0.0747444\pi$
$158$	−2.76920	+	4.79639i	−0.220306	+	0.381581i
$159$	20.1338	+	6.25883i	1.59671	+	0.496358i
$160$	3.10394	−	1.79206i	0.245388	−	0.141675i
$161$	−21.5960	+	5.39605i	−1.70200	+	0.425268i
$162$	−8.88737	−	1.41937i	−0.698258	−	0.111516i
$163$	16.1748	−	9.33852i	1.26691	−	0.731449i	0.292506	−	0.956264i	$-0.405511\pi$
$163$	16.1748	−	9.33852i	1.26691	−	0.731449i	0.974402	+	0.224815i	$0.0721777\pi$
$164$			1.35265i			0.105625i
$165$	5.75286	−	5.31445i	0.447859	−	0.413729i
$166$	−2.80189	−	1.61767i	−0.217468	−	0.125555i
$167$	2.79787	+	1.61535i	0.216505	+	0.124999i	0.604331	−	0.796733i	$-0.293440\pi$
$167$	2.79787	+	1.61535i	0.216505	+	0.124999i	−0.387826	+	0.921733i	$0.626774\pi$
$168$	−2.06336	−	4.09177i	−0.159191	−	0.315687i
$169$	3.61634	+	12.4869i	0.278180	+	0.960529i
$170$			11.3249i			0.868584i
$171$	−0.183654	+	2.31446i	−0.0140444	+	0.176991i
$172$	0.125032	−	0.216561i	0.00953359	−	0.0165127i
$173$	−7.02069	−	12.1602i	−0.533773	−	0.924522i	−0.999222	−	0.0394472i	$-0.987440\pi$
$173$	−7.02069	−	12.1602i	−0.533773	−	0.924522i	0.465449	−	0.885075i	$-0.345893\pi$
$174$	2.98061	+	13.1922i	0.225959	+	1.00009i
$175$	14.9250	−	14.4275i	1.12822	−	1.09061i
$176$	−0.630804	−	1.09258i	−0.0475486	−	0.0823567i
$177$	−4.60038	−	20.3612i	−0.345785	−	1.53044i
$178$	−5.69791	+	3.28969i	−0.427076	+	0.246573i
$179$	7.80209	+	4.50454i	0.583156	+	0.336685i	0.762386	−	0.647122i	$-0.224028\pi$
$179$	7.80209	+	4.50454i	0.583156	+	0.336685i	−0.179231	+	0.983807i	$0.557361\pi$
$180$	−10.7187	−	0.850531i	−0.798922	−	0.0633949i
$181$			13.9831i			1.03935i	0.854363	+	0.519676i	$0.173947\pi$
$181$			13.9831i			1.03935i	−0.854363	+	0.519676i	$0.826053\pi$
$182$	3.71128	−	8.78785i	0.275099	−	0.651399i
$183$	−1.44281	−	6.38585i	−0.106655	−	0.472055i
$184$	7.28626	+	4.20672i	0.537150	+	0.310124i
$185$	0.877451	−	1.51979i	0.0645115	−	0.111737i
$186$	−9.06134	−	9.80885i	−0.664410	−	0.719220i
$187$	3.98638			0.291513
$188$	9.45425	−	5.45842i	0.689522	−	0.398096i
$189$	−1.86020	+	13.6213i	−0.135309	+	0.990803i
$190$			2.77379i			0.201232i
$191$	19.5584	−	11.2921i	1.41520	−	0.817066i	0.419328	−	0.907835i	$-0.362266\pi$
$191$	19.5584	−	11.2921i	1.41520	−	0.817066i	0.995872	+	0.0907692i	$0.0289326\pi$
$192$	−0.514158	+	1.65398i	−0.0371062	+	0.119366i
$193$	−6.75717	−	3.90126i	−0.486392	−	0.280819i	0.236684	−	0.971587i	$-0.423939\pi$
$193$	−6.75717	−	3.90126i	−0.486392	−	0.280819i	−0.723076	+	0.690768i	$0.757273\pi$
$194$	−4.42801			−0.317912
$195$	−13.0953	−	18.1522i	−0.937775	−	1.29991i
$196$	−6.17731	+	3.29254i	−0.441237	+	0.235181i
$197$	8.91140	−	15.4350i	0.634911	−	1.09970i	−0.351623	−	0.936142i	$-0.614370\pi$
$197$	8.91140	−	15.4350i	0.634911	−	1.09970i	0.986534	−	0.163557i	$-0.0522967\pi$
$198$	−0.299387	+	3.77296i	−0.0212765	+	0.268133i
$199$	−8.97099	+	5.17941i	−0.635937	+	0.367158i	−0.783048	−	0.621962i	$-0.786336\pi$
$199$	−8.97099	+	5.17941i	−0.635937	+	0.367158i	0.147111	+	0.989120i	$0.453003\pi$
$200$	−7.84590			−0.554789
$201$	15.4200	−	14.2448i	1.08764	−	1.00475i
$202$	−0.490495	−	0.849562i	−0.0345111	−	0.0597750i
$203$	20.0431	−	5.00805i	1.40675	−	0.351496i
$204$	−3.71369	−	4.02005i	−0.260010	−	0.281459i
$205$	2.42403	−	4.19855i	0.169302	−	0.293240i
$206$	−13.5815	−	7.84131i	−0.946271	−	0.546330i
$207$	−10.8516	−	22.7886i	−0.754235	−	1.58391i
$208$	−3.31706	+	1.41319i	−0.229997	+	0.0979871i
$209$	0.976374			0.0675372
$210$	−0.928163	+	16.3982i	−0.0640493	+	1.13159i
$211$	−1.30125	+	2.25382i	−0.0895814	+	0.155160i	−0.907334	−	0.420410i	$-0.861886\pi$
$211$	−1.30125	+	2.25382i	−0.0895814	+	0.155160i	0.817753	+	0.575570i	$0.195220\pi$
$212$	−10.5421	+	6.08648i	−0.724034	+	0.418021i
$213$	0.256681	−	0.0579941i	0.0175875	−	0.00397369i
$214$	−4.25464	+	2.45642i	−0.290841	+	0.167917i
$215$	−0.776182	+	0.448129i	−0.0529351	+	0.0305621i
$216$	4.08374	−	3.21296i	0.277863	−	0.218614i
$217$	−14.6660	+	14.1771i	−0.995595	+	0.962406i
$218$	−5.18886	−	2.99579i	−0.351434	−	0.202900i
$219$	−5.32705	+	17.1364i	−0.359969	+	1.15797i
$220$			4.52175i			0.304856i
$221$	1.37346	−	11.3096i	0.0923888	−	0.760765i
$222$	0.186900	+	0.827218i	0.0125439	+	0.0555193i
$223$	6.59396	−	11.4211i	0.441564	−	0.764812i	−0.556242	−	0.831021i	$-0.687757\pi$
$223$	6.59396	−	11.4211i	0.441564	−	0.764812i	0.997806	+	0.0662090i	$0.0210904\pi$
$224$	2.54363	+	0.727985i	0.169953	+	0.0486405i
$225$	19.3894	+	13.3444i	1.29263	+	0.889627i
$226$		−	15.8700i		−	1.05566i
$227$	19.5736	−	11.3008i	1.29914	−	0.750060i	0.318886	−	0.947793i	$-0.396691\pi$
$227$	19.5736	−	11.3008i	1.29914	−	0.750060i	0.980256	+	0.197733i	$0.0633578\pi$
$228$	−0.909585	−	0.984620i	−0.0602387	−	0.0652081i
$229$	0.457707			0.0302461			0.0151230	−	0.999886i	$-0.495186\pi$
$229$	0.457707			0.0302461			0.0151230	+	0.999886i	$0.495186\pi$
$230$	−15.0774	−	26.1148i	−0.994174	−	1.72196i
$231$	5.77217	+	0.326713i	0.379781	+	0.0214961i
$232$	−6.76234	−	3.90424i	−0.443969	−	0.256326i
$233$		−	15.7117i		−	1.02931i	−0.857398	−	0.514654i	$-0.827921\pi$
$233$		−	15.7117i		−	1.02931i	0.857398	−	0.514654i	$-0.172079\pi$
$234$	10.6010	+	2.14931i	0.693007	+	0.140505i
$235$	−39.1272			−2.55238
$236$	10.4372	+	6.02594i	0.679406	+	0.392255i
$237$	−2.84761	+	9.16038i	−0.184972	+	0.595031i
$238$	−6.01071	+	5.81033i	−0.389616	+	0.376628i
$239$	−18.8837			−1.22148			−0.610741	−	0.791830i	$-0.709128\pi$
$239$	−18.8837			−1.22148			−0.610741	+	0.791830i	$0.709128\pi$
$240$	4.55994	−	4.21244i	0.294343	−	0.271912i
$241$	−9.49057	−	16.4382i	−0.611341	−	1.05887i	−0.991015	−	0.133754i	$-0.957297\pi$
$241$	−9.49057	−	16.4382i	−0.611341	−	1.05887i	0.379673	−	0.925121i	$-0.376036\pi$
$242$	−9.40835			−0.604791
$243$	−15.5567	+	0.994458i	−0.997963	+	0.0637945i
$244$	3.27341	+	1.88990i	0.209558	+	0.120989i
$245$	25.0744	+	0.850285i	1.60195	+	0.0543227i
$246$	0.516328	+	2.28526i	0.0329198	+	0.145703i
$247$	0.336398	−	2.77003i	0.0214045	−	0.176253i
$248$	7.70977			0.489571
$249$	−5.35118	−	1.66348i	−0.339117	−	0.105419i
$250$	8.83348	+	5.10001i	0.558678	+	0.322553i
$251$	−2.20065	−	3.81164i	−0.138904	−	0.240588i	0.788178	−	0.615447i	$-0.211025\pi$
$251$	−2.20065	−	3.81164i	−0.138904	−	0.240588i	−0.927082	+	0.374859i	$0.877691\pi$
$252$	−5.04786	−	6.12529i	−0.317985	−	0.385857i
$253$	−9.19240	+	5.30724i	−0.577921	+	0.333663i
$254$	−5.41129	−	9.37263i	−0.339535	−	0.588091i
$255$	4.32290	+	19.1331i	0.270710	+	1.19816i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.37736	+	7.58182i	−0.273052	+	0.472941i	−0.969642	−	0.244529i	$-0.921367\pi$
$257$	−4.37736	+	7.58182i	−0.273052	+	0.472941i	0.696589	+	0.717470i	$0.254700\pi$
$258$	0.128572	−	0.413600i	0.00800456	−	0.0257496i
$259$	1.25681	−	0.314031i	0.0780943	−	0.0195130i
$260$	12.8285	+	1.55791i	0.795588	+	0.0966177i
$261$	10.0713	+	21.1500i	0.623396	+	1.30915i
$262$	6.80645	−	11.7891i	0.420504	−	0.728334i
$263$	10.3649	+	5.98418i	0.639128	+	0.369000i	0.784278	−	0.620409i	$-0.213033\pi$
$263$	10.3649	+	5.98418i	0.639128	+	0.369000i	−0.145151	+	0.989410i	$0.546367\pi$
$264$	−1.48278	−	1.60510i	−0.0912586	−	0.0987869i
$265$	43.6293			2.68013
$266$	−1.47219	+	1.42311i	−0.0902657	+	0.0872566i
$267$	−8.37070	+	7.73279i	−0.512279	+	0.473239i
$268$			12.1201i			0.740353i
$269$	1.75697	+	3.04316i	0.107124	+	0.185545i	0.914604	−	0.404350i	$-0.132502\pi$
$269$	1.75697	+	3.04316i	0.107124	+	0.185545i	−0.807480	+	0.589895i	$0.799169\pi$
$270$	−18.4335	+	2.65452i	−1.12183	+	0.161549i
$271$	1.27260	−	2.20420i	0.0773046	−	0.133896i	−0.824782	−	0.565452i	$-0.808702\pi$
$271$	1.27260	−	2.20420i	0.0773046	−	0.133896i	0.902086	+	0.431556i	$0.142035\pi$
$272$	3.15976			0.191589
$273$	2.91564	−	16.2634i	0.176462	−	0.984307i
$274$	2.21278			0.133679
$275$	4.94922	−	8.57230i	0.298449	−	0.516929i
$276$	13.9157	+	4.32584i	0.837624	+	0.260385i
$277$	−6.92333	−	11.9916i	−0.415983	−	0.720503i	0.579548	−	0.814938i	$-0.303229\pi$
$277$	−6.92333	−	11.9916i	−0.415983	−	0.720503i	−0.995531	+	0.0944347i	$0.969896\pi$
$278$		−	3.37220i		−	0.202251i
$279$	−19.0530	−	13.1129i	−1.14067	−	0.785047i
$280$	−6.59067	−	6.81795i	−0.393868	−	0.407450i
$281$	15.0793			0.899556			0.449778	−	0.893140i	$-0.351503\pi$
$281$	15.0793			0.899556			0.449778	+	0.893140i	$0.351503\pi$
$282$	13.8891	−	12.8306i	0.827083	−	0.764053i
$283$	2.40604	+	1.38913i	0.143024	+	0.0825752i	0.569805	−	0.821780i	$-0.307019\pi$
$283$	2.40604	+	1.38913i	0.143024	+	0.0825752i	−0.426780	+	0.904355i	$0.640352\pi$
$284$	−0.0759653	+	0.131576i	−0.00450771	+	0.00780758i
$285$	1.05880	+	4.68623i	0.0627177	+	0.277588i
$286$	0.548385	−	4.51562i	0.0324267	−	0.267014i
$287$	3.47204	−	0.867538i	0.204948	−	0.0512092i
$288$	−0.237306	+	2.99060i	−0.0139834	+	0.176223i
$289$	3.50796	−	6.07596i	0.206351	−	0.357410i
$290$	13.9933	+	24.2370i	0.821712	+	1.42325i
$291$	−7.48096	+	1.69023i	−0.438542	+	0.0990833i
$292$	−5.18036	−	8.97264i	−0.303158	−	0.525084i
$293$	3.84106	−	2.21763i	0.224397	−	0.129556i	−0.383588	−	0.923504i	$-0.625312\pi$
$293$	3.84106	−	2.21763i	0.224397	−	0.129556i	0.607985	+	0.793949i	$0.291978\pi$
$294$	−9.17955	+	7.92060i	−0.535362	+	0.461939i
$295$	−21.5977	−	37.4083i	−1.25746	−	2.17799i
$296$	−0.424035	−	0.244817i	−0.0246465	−	0.0142297i
$297$	0.934392	+	6.48857i	0.0542189	+	0.376505i
$298$	5.34456			0.309602
$299$	11.8898	+	27.9079i	0.687605	+	1.61396i
$300$	−13.2554	+	2.99489i	−0.765299	+	0.172910i
$301$	−0.636069	−	0.182042i	−0.0366624	−	0.0104928i
$302$	−11.4874	−	6.63223i	−0.661024	−	0.381642i
$303$	−1.15296	−	1.24808i	−0.0662361	−	0.0717001i
$304$	0.773913			0.0443869
$305$	−6.77363	−	11.7323i	−0.387857	−	0.671788i
$306$	−7.80866	−	5.37416i	−0.446391	−	0.307220i
$307$	−18.1869			−1.03798			−0.518990	−	0.854780i	$-0.673692\pi$
$307$	−18.1869			−1.03798			−0.518990	+	0.854780i	$0.673692\pi$
$308$	−2.39991	+	2.31991i	−0.136748	+	0.132189i
$309$	−25.9387	−	8.06335i	−1.47560	−	0.458708i
$310$	−23.9306	−	13.8164i	−1.35917	−	0.784716i
$311$	−7.71151			−0.437279			−0.218640	−	0.975806i	$-0.570162\pi$
$311$	−7.71151			−0.437279			−0.218640	+	0.975806i	$0.570162\pi$
$312$	−5.06463	+	3.65371i	−0.286728	+	0.206850i
$313$			15.8942i			0.898391i	0.893433	+	0.449196i	$0.148289\pi$
$313$			15.8942i			0.898391i	−0.893433	+	0.449196i	$0.851711\pi$
$314$	5.04941	+	2.91528i	0.284955	+	0.164519i
$315$	4.69135	+	28.0586i	0.264327	+	1.58092i
$316$	−2.76920	−	4.79639i	−0.155780	−	0.269818i
$317$	6.00739			0.337409			0.168704	−	0.985667i	$-0.446042\pi$
$317$	6.00739			0.337409			0.168704	+	0.985667i	$0.446042\pi$
$318$	−15.4872	+	14.3070i	−0.868479	+	0.802295i
$319$	8.53142	−	4.92562i	0.477668	−	0.275782i
$320$			3.58412i			0.200358i
$321$	−6.25041	+	5.77409i	−0.348864	+	0.322278i
$322$	6.12486	−	21.4007i	0.341325	−	1.19261i
$323$	−1.22269	+	2.11776i	−0.0680322	+	0.117835i
$324$	5.67290	−	6.98700i	0.315161	−	0.388167i
$325$	−22.6149	−	16.9947i	−1.25445	−	0.942697i
$326$			18.6770i			1.03443i
$327$	−9.90993	−	3.08062i	−0.548021	−	0.170359i
$328$	−1.17143	−	0.676327i	−0.0646815	−	0.0373439i
$329$	−20.0744	−	20.7667i	−1.10674	−	1.14491i
$330$	1.72602	+	7.63934i	0.0950142	+	0.420532i
$331$	−14.2730	+	8.24050i	−0.784513	+	0.452939i	−0.838027	−	0.545628i	$-0.816291\pi$
$331$	−14.2730	+	8.24050i	−0.784513	+	0.452939i	0.0535143	+	0.998567i	$0.482958\pi$
$332$	2.80189	−	1.61767i	0.153773	−	0.0887811i
$333$	0.631522	+	1.32621i	0.0346072	+	0.0726761i
$334$	−2.79787	+	1.61535i	−0.153092	+	0.0883880i
$335$	21.7199	−	37.6200i	1.18669	−	2.05540i
$336$	4.57525	+	0.258966i	0.249600	+	0.0141277i
$337$	−28.6451			−1.56040			−0.780200	−	0.625530i	$-0.784883\pi$
$337$	−28.6451			−1.56040			−0.780200	+	0.625530i	$0.784883\pi$
$338$	−12.6221	−	3.11160i	−0.686553	−	0.169249i
$339$	−6.05781	−	26.8118i	−0.329015	−	1.45622i
$340$	−9.80769	−	5.66247i	−0.531897	−	0.307091i
$341$	−4.86335	+	8.42357i	−0.263365	+	0.456162i
$342$	−1.91256	−	1.31628i	−0.103419	−	0.0711763i
$343$	12.4133	+	13.7445i	0.670255	+	0.742131i
$344$	0.125032	+	0.216561i	0.00674126	+	0.0116762i
$345$	−35.4411	−	38.3648i	−1.90809	−	2.06549i
$346$	14.0414			0.754869
$347$	18.8271	−	10.8698i	1.01069	−	0.583522i	0.0992964	−	0.995058i	$-0.468341\pi$
$347$	18.8271	−	10.8698i	1.01069	−	0.583522i	0.911394	+	0.411536i	$0.135007\pi$
$348$	−12.9150	−	4.01479i	−0.692319	−	0.215216i
$349$	−13.3083	+	23.0507i	−0.712377	+	1.23387i	0.251585	+	0.967835i	$0.419048\pi$
$349$	−13.3083	+	23.0507i	−0.712377	+	1.23387i	−0.963962	+	0.266038i	$0.914285\pi$
$350$	5.03205	+	20.1391i	0.268974	+	1.07648i
$351$	18.7304	−	0.415364i	0.999754	−	0.0221705i
$352$	1.26161			0.0672439
$353$	22.2718	+	12.8586i	1.18541	+	0.684396i	0.957259	−	0.289231i	$-0.0933995\pi$
$353$	22.2718	+	12.8586i	1.18541	+	0.684396i	0.228149	+	0.973626i	$0.426733\pi$
$354$	19.9335	+	6.19657i	1.05946	+	0.329344i
$355$	0.471583	−	0.272268i	0.0250290	−	0.0144505i
$356$		−	6.57938i		−	0.348706i
$357$	−7.93699	+	12.1107i	−0.420070	+	0.640968i
$358$	−7.80209	+	4.50454i	−0.412353	+	0.238072i
$359$	−9.32911			−0.492372			−0.246186	−	0.969223i	$-0.579177\pi$
$359$	−9.32911			−0.492372			−0.246186	+	0.969223i	$0.579177\pi$
$360$	6.09591	−	8.85737i	0.321283	−	0.466824i
$361$	9.20053	−	15.9358i	0.484238	−	0.838726i
$362$	−12.1097	−	6.99153i	−0.636470	−	0.367466i
$363$	−15.8951	+	3.59130i	−0.834275	+	0.188494i
$364$	5.75486	+	7.60799i	0.301637	+	0.398767i
$365$			37.1340i			1.94368i
$366$	6.25171	+	1.94342i	0.326782	+	0.101584i
$367$	8.31827	+	4.80255i	0.434210	+	0.250691i	0.701139	−	0.713025i	$-0.252675\pi$
$367$	8.31827	+	4.80255i	0.434210	+	0.250691i	−0.266928	+	0.963716i	$0.586009\pi$
$368$	−7.28626	+	4.20672i	−0.379822	+	0.219291i
$369$	1.74464	+	3.66378i	0.0908221	+	0.190729i
$370$	0.877451	+	1.51979i	0.0456165	+	0.0790101i
$371$	22.3843	+	23.1562i	1.16213	+	1.20221i
$372$	13.0254	−	2.94293i	0.675335	−	0.152584i
$373$	8.44383	+	14.6251i	0.437205	+	0.757262i	0.997473	−	0.0710501i	$-0.0226350\pi$
$373$	8.44383	+	14.6251i	0.437205	+	0.757262i	−0.560268	+	0.828312i	$0.689302\pi$
$374$	−1.99319	+	3.45230i	−0.103065	+	0.178514i
$375$	16.8706	+	5.24443i	0.871195	+	0.270821i
$376$			10.9168i			0.562993i
$377$	−11.0349	−	25.9012i	−0.568325	−	1.33398i
$378$	−10.8663	−	8.42162i	−0.558902	−	0.433162i
$379$	25.2872	+	14.5996i	1.29892	+	0.749930i	0.980217	−	0.197925i	$-0.0634203\pi$
$379$	25.2872	+	14.5996i	1.29892	+	0.749930i	0.318700	+	0.947856i	$0.396754\pi$
$380$	−2.40218	−	1.38690i	−0.123229	−	0.0711463i
$381$	−12.7199	−	13.7692i	−0.651658	−	0.705416i
$382$			22.5841i			1.15551i
$383$	−7.31222	+	4.22171i	−0.373637	+	0.215719i	−0.675046	−	0.737775i	$-0.735876\pi$
$383$	−7.31222	+	4.22171i	−0.373637	+	0.215719i	0.301409	+	0.953495i	$0.402543\pi$
$384$	−1.17531	−	1.27226i	−0.0599771	−	0.0649249i
$385$	11.6066	−	2.90007i	0.591527	−	0.147801i
$386$	6.75717	−	3.90126i	0.343931	−	0.198569i
$387$	0.0593415	−	0.747840i	0.00301650	−	0.0380149i
$388$	2.21400	−	3.83477i	0.112399	−	0.194681i
$389$		−	0.653576i		−	0.0331376i	−0.999863	−	0.0165688i	$-0.994726\pi$
$389$		−	0.653576i		−	0.0331376i	0.999863	−	0.0165688i	$-0.00527425\pi$
$390$	22.2679	−	2.26477i	1.12758	−	0.114681i
$391$		−	26.5845i		−	1.34443i
$392$	0.237237	−	6.99598i	0.0119823	−	0.353350i
$393$	6.99918	−	22.5154i	0.353062	−	1.13575i
$394$	8.91140	+	15.4350i	0.448950	+	0.777604i
$395$			19.8503i			0.998775i
$396$	−3.11779	−	2.14576i	−0.156675	−	0.107828i
$397$	2.51686	+	4.35932i	0.126317	+	0.218788i	0.922247	−	0.386601i	$-0.126351\pi$
$397$	2.51686	+	4.35932i	0.126317	+	0.218788i	−0.795930	+	0.605389i	$0.793018\pi$
$398$		−	10.3588i		−	0.519240i
$399$	−1.94399	+	2.96625i	−0.0973212	+	0.148498i
$400$	3.92295	−	6.79475i	0.196147	−	0.339737i
$401$	−10.4095	+	18.0297i	−0.519824	+	0.900361i	0.479911	+	0.877317i	$0.340669\pi$
$401$	−10.4095	+	18.0297i	−0.519824	+	0.900361i	−0.999734	+	0.0230440i	$0.992664\pi$
$402$	4.62642	+	20.4765i	0.230745	+	1.02127i
$403$	22.2225	+	16.6998i	1.10698	+	0.831878i
$404$	0.980990			0.0488061
$405$	−30.1294	+	11.5211i	−1.49714	+	0.572486i
$406$	−5.68445	+	19.8619i	−0.282115	+	0.985727i
$407$	0.534966	−	0.308863i	0.0265173	−	0.0153097i
$408$	5.33831	−	1.20613i	0.264286	−	0.0597121i
$409$	14.6945	+	25.4516i	0.726594	+	1.25850i	0.958314	+	0.285716i	$0.0922314\pi$
$409$	14.6945	+	25.4516i	0.726594	+	1.25850i	−0.231720	+	0.972783i	$0.574435\pi$
$410$	2.42403	+	4.19855i	0.119715	+	0.207352i
$411$	3.73841	−	0.844649i	0.184402	−	0.0416635i
$412$	13.5815	−	7.84131i	0.669115	−	0.386314i
$413$	8.77358	−	30.6555i	0.431720	−	1.50846i
$414$	25.1613	+	1.99656i	1.23661	+	0.0981255i
$415$	−11.5958			−0.569217
$416$	0.434672	−	3.57925i	0.0213115	−	0.175487i
$417$	−1.28722	−	5.69722i	−0.0630353	−	0.278994i
$418$	−0.488187	+	0.845565i	−0.0238780	+	0.0413579i
$419$	11.2918	−	19.5580i	0.551640	−	0.955469i	−0.446516	−	0.894776i	$-0.647335\pi$
$419$	11.2918	−	19.5580i	0.551640	−	0.955469i	0.998156	−	0.0606934i	$-0.0193312\pi$
$420$	−13.7372	−	9.00293i	−0.670307	−	0.439298i
$421$		−	28.5241i		−	1.39018i	−0.718922	−	0.695091i	$-0.755364\pi$
$421$		−	28.5241i		−	1.39018i	0.718922	−	0.695091i	$-0.244636\pi$
$422$	−1.30125	−	2.25382i	−0.0633436	−	0.109714i
$423$	18.5675	−	26.9786i	0.902782	−	1.31174i
$424$		−	12.1730i		−	0.591171i
$425$	12.3956	+	21.4698i	0.601274	+	1.04144i
$426$	−0.0781164	+	0.251290i	−0.00378475	+	0.0121750i
$427$	2.75164	−	9.61441i	0.133161	−	0.465274i
$428$		−	4.91283i		−	0.237471i
$429$	−0.797198	−	7.83830i	−0.0384891	−	0.378437i
$430$		−	0.896257i		−	0.0432214i
$431$	3.76847	−	6.52718i	0.181521	−	0.314403i	−0.760878	−	0.648895i	$-0.775231\pi$
$431$	3.76847	−	6.52718i	0.181521	−	0.314403i	0.942399	+	0.334492i	$0.108565\pi$
$432$	0.740636	+	5.14310i	0.0356338	+	0.247447i
$433$	28.3474	−	16.3664i	1.36229	−	0.786518i	0.372361	−	0.928088i	$-0.378548\pi$
$433$	28.3474	−	16.3664i	1.36229	−	0.786518i	0.989928	+	0.141570i	$0.0452150\pi$
$434$	−4.94474	−	19.7897i	−0.237355	−	0.949937i
$435$	32.8927	+	35.6062i	1.57709	+	1.70719i
$436$	5.18886	−	2.99579i	0.248501	−	0.143472i
$437$		−	6.51127i		−	0.311476i
$438$	−12.1770	−	13.1816i	−0.581841	−	0.629839i
$439$	−21.2278	−	12.2559i	−1.01315	−	0.584940i	−0.101035	−	0.994883i	$-0.532215\pi$
$439$	−21.2278	−	12.2559i	−1.01315	−	0.584940i	−0.912111	+	0.409943i	$0.865549\pi$
$440$	−3.91595	−	2.26088i	−0.186686	−	0.107783i
$441$	−12.4851	+	16.8855i	−0.594530	+	0.804074i
$442$	9.10766	+	6.84424i	0.433207	+	0.325547i
$443$			10.7332i			0.509951i	0.966948	+	0.254975i	$0.0820674\pi$
$443$			10.7332i			0.509951i	−0.966948	+	0.254975i	$0.917933\pi$
$444$	−0.809842	−	0.251749i	−0.0384334	−	0.0119475i
$445$	−11.7906	+	20.4220i	−0.558930	+	0.968095i
$446$	6.59396	+	11.4211i	0.312233	+	0.540803i
$447$	9.02945	−	2.04010i	0.427078	−	0.0964932i
$448$	−1.90227	+	1.83885i	−0.0898737	+	0.0868777i
$449$	19.7420	+	34.1941i	0.931683	+	1.61372i	0.780445	+	0.625224i	$0.214992\pi$
$449$	19.7420	+	34.1941i	0.931683	+	1.61372i	0.151237	+	0.988497i	$0.451674\pi$
$450$	−21.2513	+	10.1195i	−1.00180	+	0.477040i
$451$	1.47789	−	0.853259i	0.0695910	−	0.0401784i
$452$	13.7438	+	7.93500i	0.646455	+	0.373231i
$453$	−21.9391	−	6.82004i	−1.03079	−	0.320433i
$454$			22.6016i			1.06075i
$455$	−4.22876	−	33.9278i	−0.198247	−	1.59056i
$456$	1.30750	−	0.295414i	0.0612292	−	0.0138340i
$457$	9.89907	+	5.71523i	0.463059	+	0.267347i	0.713330	−	0.700829i	$-0.247186\pi$
$457$	9.89907	+	5.71523i	0.463059	+	0.267347i	−0.250271	+	0.968176i	$0.580520\pi$
$458$	−0.228853	+	0.396385i	−0.0106936	+	0.0185219i
$459$	−15.2439	−	6.09878i	−0.711522	−	0.284667i
$460$	30.1548			1.40597
$461$	−8.42605	+	4.86478i	−0.392440	+	0.226576i	−0.683217	−	0.730215i	$-0.739420\pi$
$461$	−8.42605	+	4.86478i	−0.392440	+	0.226576i	0.290777	+	0.956791i	$0.406086\pi$
$462$	−3.16903	+	4.83549i	−0.147437	+	0.224968i
$463$			26.6572i			1.23887i	0.785050	+	0.619433i	$0.212637\pi$
$463$			26.6572i			1.23887i	−0.785050	+	0.619433i	$0.787363\pi$
$464$	6.76234	−	3.90424i	0.313934	−	0.181250i
$465$	−45.7039	−	14.2076i	−2.11947	−	0.658861i
$466$	13.6067	+	7.85585i	0.630319	+	0.363915i
$467$	6.02179			0.278655			0.139328	−	0.990246i	$-0.455506\pi$
$467$	6.02179			0.278655			0.139328	+	0.990246i	$0.455506\pi$
$468$	−7.16184	+	8.10605i	−0.331056	+	0.374702i
$469$	31.1103	−	7.77335i	1.43654	−	0.358940i
$470$	19.5636	−	33.8851i	0.902402	−	1.56301i
$471$	9.64361	+	2.99783i	0.444354	+	0.138133i
$472$	−10.4372	+	6.02594i	−0.480412	+	0.277366i
$473$	−0.315482			−0.0145059
$474$	−6.50932	−	7.04630i	−0.298983	−	0.323647i
$475$	3.03602	+	5.25854i	0.139302	+	0.241278i
$476$	−2.02654	−	8.11059i	−0.0928865	−	0.371748i
$477$	−20.7039	+	30.0828i	−0.947968	+	1.37740i
$478$	9.44183	−	16.3537i	0.431859	−	0.748002i
$479$	−7.74812	−	4.47338i	−0.354021	−	0.204394i	0.312434	−	0.949939i	$-0.398856\pi$
$479$	−7.74812	−	4.47338i	−0.354021	−	0.204394i	−0.666455	+	0.745546i	$0.732189\pi$
$480$	1.36811	+	6.05524i	0.0624454	+	0.276383i
$481$	−0.691945	−	1.62414i	−0.0315500	−	0.0740545i
$482$	18.9811			0.864567
$483$	2.17879	−	38.4936i	0.0991385	−	1.75152i
$484$	4.70417	−	8.14787i	0.213826	−	0.370358i
$485$	−13.7442	+	7.93525i	−0.624094	+	0.360321i
$486$	6.91713	−	13.9697i	0.313767	−	0.633680i
$487$	25.3833	−	14.6550i	1.15023	−	0.664083i	0.201284	−	0.979533i	$-0.435489\pi$
$487$	25.3833	−	14.6550i	1.15023	−	0.664083i	0.948942	+	0.315450i	$0.102155\pi$
$488$	−3.27341	+	1.88990i	−0.148180	+	0.0855518i
$489$	7.12930	+	31.5542i	0.322398	+	1.42693i
$490$	−13.2736	+	21.2899i	−0.599639	+	0.961781i
$491$	5.50320	+	3.17727i	0.248356	+	0.143388i	0.619011	−	0.785382i	$-0.287534\pi$
$491$	5.50320	+	3.17727i	0.248356	+	0.143388i	−0.370655	+	0.928770i	$0.620867\pi$
$492$	−2.23726	−	0.695478i	−0.100863	−	0.0313546i
$493$			24.6729i			1.11121i
$494$	2.23072	+	1.67634i	0.100365	+	0.0754223i
$495$	5.83210	+	12.2476i	0.262133	+	0.550487i
$496$	−3.85488	+	6.67685i	−0.173089	+	0.299800i
$497$	0.386455	+	0.110603i	0.0173349	+	0.00496123i
$498$	4.11620	−	3.80252i	0.184451	−	0.170395i
$499$			5.92485i			0.265233i	0.991167	+	0.132616i	$0.0423378\pi$
$499$			5.92485i			0.265233i	−0.991167	+	0.132616i	$0.957662\pi$
$500$	−8.83348	+	5.10001i	−0.395045	+	0.228080i
$501$	−4.11030	+	3.79706i	−0.183635	+	0.169640i
$502$	4.40130			0.196440
$503$	19.6190	+	33.9811i	0.874767	+	1.51514i	0.857011	+	0.515298i	$0.172319\pi$
$503$	19.6190	+	33.9811i	0.874767	+	1.51514i	0.0177557	+	0.999842i	$0.494348\pi$
$504$	7.82858	−	1.30893i	0.348713	−	0.0583042i
$505$	−3.04493	−	1.75799i	−0.135498	−	0.0782296i
$506$		−	10.6145i		−	0.471871i
$507$	−22.5124	−	0.438896i	−0.999810	−	0.0194921i
$508$	10.8226			0.480174
$509$	−8.72379	−	5.03668i	−0.386675	−	0.223247i	0.294043	−	0.955792i	$-0.404999\pi$
$509$	−8.72379	−	5.03668i	−0.386675	−	0.223247i	−0.680718	+	0.732545i	$0.738332\pi$
$510$	−18.7312	−	5.82282i	−0.829432	−	0.257839i
$511$	−19.7088	+	19.0518i	−0.871868	+	0.842804i
$512$	1.00000			0.0441942
$513$	−3.73364	−	1.49376i	−0.164844	−	0.0659511i
$514$	−4.37736	−	7.58182i	−0.193077	−	0.334420i
$515$	−56.2083			−2.47684
$516$	0.293902	+	0.318147i	0.0129383	+	0.0140056i
$517$	−11.9276	−	6.88638i	−0.524573	−	0.302863i
$518$	−0.356445	+	1.24544i	−0.0156613	+	0.0547217i
$519$	23.7224	−	5.35980i	1.04130	−	0.235269i
$520$	−7.76343	+	10.3308i	−0.340449	+	0.453036i
$521$	−12.2704			−0.537578			−0.268789	−	0.963199i	$-0.586623\pi$
$521$	−12.2704			−0.537578			−0.268789	+	0.963199i	$0.586623\pi$
$522$	−23.3520	−	1.85300i	−1.02209	−	0.0811034i
$523$	12.6762	+	7.31862i	0.554292	+	0.320021i	0.750851	−	0.660471i	$-0.229643\pi$
$523$	12.6762	+	7.31862i	0.554292	+	0.320021i	−0.196559	+	0.980492i	$0.562977\pi$
$524$	6.80645	+	11.7891i	0.297341	+	0.515010i
$525$	16.1889	+	32.1036i	0.706540	+	1.40112i
$526$	−10.3649	+	5.98418i	−0.451931	+	0.260923i
$527$	−12.1805	−	21.0973i	−0.530591	−	0.919011i
$528$	2.13144	−	0.481574i	0.0927592	−	0.0209578i
$529$	23.8930	+	41.3840i	1.03883	+	1.79930i
$530$	−21.8147	+	37.7841i	−0.947568	+	1.64124i
$531$	36.0423	+	2.85998i	1.56410	+	0.124112i
$532$	−0.496357	−	1.98651i	−0.0215198	−	0.0861261i
$533$	−1.91156	−	4.48683i	−0.0827987	−	0.194346i
$534$	−2.51144	−	11.1156i	−0.108681	−	0.481021i
$535$	−8.80408	+	15.2491i	−0.380634	+	0.659277i
$536$	−10.4963	−	6.06005i	−0.453372	−	0.261754i
$537$	−11.4619	+	10.5884i	−0.494618	+	0.456925i
$538$	−3.51394			−0.151497
$539$	7.49405	+	4.67229i	0.322791	+	0.201250i
$540$	6.91785	−	17.2911i	0.297697	−	0.744091i
$541$		−	34.8104i		−	1.49661i	−0.663352	−	0.748307i	$-0.730867\pi$
$541$		−	34.8104i		−	1.49661i	0.663352	−	0.748307i	$-0.269133\pi$
$542$	1.27260	+	2.20420i	0.0546626	+	0.0946785i
$543$	−23.1276	−	7.18950i	−0.992502	−	0.308531i
$544$	−1.57988	+	2.73643i	−0.0677368	+	0.117324i
$545$	−21.4745			−0.919867
$546$	12.6267	+	10.6567i	0.540374	+	0.456066i
$547$	−27.0523			−1.15667			−0.578336	−	0.815799i	$-0.696298\pi$
$547$	−27.0523			−1.15667			−0.578336	+	0.815799i	$0.696298\pi$
$548$	−1.10639	+	1.91632i	−0.0472626	+	0.0818612i
$549$	11.3039	+	0.896968i	0.482438	+	0.0382817i
$550$	4.94922	+	8.57230i	0.211036	+	0.365524i
$551$			6.04308i			0.257444i
$552$	−10.7041	+	9.88839i	−0.455597	+	0.420878i
$553$	−10.5355	+	10.1843i	−0.448015	+	0.433081i
$554$	13.8467			0.588288
$555$	2.06255	+	2.23270i	0.0875504	+	0.0947727i
$556$	2.92041	+	1.68610i	0.123853	+	0.0715066i
$557$	6.46740	−	11.2019i	0.274032	−	0.474638i	−0.695858	−	0.718179i	$-0.744976\pi$
$557$	6.46740	−	11.2019i	0.274032	−	0.474638i	0.969891	+	0.243541i	$0.0783091\pi$
$558$	20.8826	−	9.94396i	0.884030	−	0.420961i
$559$	−0.108696	+	0.895041i	−0.00459733	+	0.0378562i
$560$	9.19985	−	2.29871i	0.388765	−	0.0971383i
$561$	−2.04963	+	6.59338i	−0.0865354	+	0.278373i
$562$	−7.53965	+	13.0591i	−0.318041	+	0.550863i
$563$	−2.33044	−	4.03644i	−0.0982162	−	0.170115i	0.812730	−	0.582640i	$-0.197980\pi$
$563$	−2.33044	−	4.03644i	−0.0982162	−	0.170115i	−0.910946	+	0.412525i	$0.864647\pi$
$564$	4.16711	+	18.4436i	0.175467	+	0.776616i
$565$	−28.4400	−	49.2595i	−1.19648	−	2.07236i
$566$	−2.40604	+	1.38913i	−0.101134	+	0.0583895i
$567$	−21.5729	−	10.0802i	−0.905976	−	0.423330i
$568$	−0.0759653	−	0.131576i	−0.00318743	−	0.00552080i
$569$	13.1884	+	7.61435i	0.552888	+	0.319210i	0.750286	−	0.661113i	$-0.229916\pi$
$569$	13.1884	+	7.61435i	0.552888	+	0.319210i	−0.197398	+	0.980323i	$0.563249\pi$
$570$	−4.58779	−	1.42617i	−0.192161	−	0.0597357i
$571$	35.0542			1.46697			0.733487	−	0.679703i	$-0.237891\pi$
$571$	35.0542			1.46697			0.733487	+	0.679703i	$0.237891\pi$
$572$	3.63645	+	2.73272i	0.152047	+	0.114261i
$573$	8.62070	+	38.1551i	0.360135	+	1.59395i
$574$	−0.984711	+	3.44065i	−0.0411010	+	0.143610i
$575$	−57.1672	−	33.0055i	−2.38404	−	1.37643i
$576$	−2.47128	−	1.70081i	−0.102970	−	0.0708672i
$577$	−9.20999			−0.383417			−0.191709	−	0.981452i	$-0.561403\pi$
$577$	−9.20999			−0.383417			−0.191709	+	0.981452i	$0.561403\pi$
$578$	3.50796	+	6.07596i	0.145912	+	0.252727i
$579$	9.92685	−	9.17035i	0.412546	−	0.381107i
$580$	−27.9865			−1.16208
$581$	−5.94931	−	6.15448i	−0.246819	−	0.255331i
$582$	2.27670	−	7.32382i	0.0943721	−	0.303582i
$583$	13.3000	+	7.67875i	0.550829	+	0.318021i
$584$	10.3607			0.428730
$585$	36.7564	−	12.3262i	1.51969	−	0.509627i
$586$			4.43527i			0.183219i
$587$	2.67162	+	1.54246i	0.110270	+	0.0636642i	0.554120	−	0.832436i	$-0.313055\pi$
$587$	2.67162	+	1.54246i	0.110270	+	0.0636642i	−0.443851	+	0.896101i	$0.646388\pi$
$588$	−2.26966	−	11.9100i	−0.0935993	−	0.491161i
$589$	−2.98334	−	5.16730i	−0.122926	−	0.212915i
$590$	43.1953			1.77832
$591$	20.9473	+	22.6753i	0.861656	+	0.932737i
$592$	0.424035	−	0.244817i	0.0174277	−	0.0100619i
$593$			6.04376i			0.248187i	0.992271	+	0.124094i	$0.0396023\pi$
$593$			6.04376i			0.248187i	−0.992271	+	0.124094i	$0.960398\pi$
$594$	−6.08647	−	2.43508i	−0.249731	−	0.0999125i
$595$	−8.24439	+	28.8064i	−0.337987	+	1.18095i
$596$	−2.67228	+	4.62852i	−0.109461	+	0.189592i
$597$	−3.95411	−	17.5009i	−0.161831	−	0.716262i
$598$	−30.1139	−	3.65709i	−1.23145	−	0.149549i
$599$		−	14.1048i		−	0.576307i	−0.957584	−	0.288154i	$-0.906959\pi$
$599$		−	14.1048i		−	0.576307i	0.957584	−	0.288154i	$-0.0930414\pi$
$600$	4.03403	−	12.9769i	0.164689	−	0.529781i
$601$	18.7865	+	10.8464i	0.766319	+	0.442435i	0.831560	−	0.555435i	$-0.187448\pi$
$601$	18.7865	+	10.8464i	0.766319	+	0.442435i	−0.0652409	+	0.997870i	$0.520782\pi$
$602$	0.475688	−	0.459830i	0.0193876	−	0.0187413i
$603$	15.6324	+	32.8284i	0.636599	+	1.33687i
$604$	11.4874	−	6.63223i	0.467414	−	0.269862i
$605$	−29.2029	+	16.8603i	−1.18727	+	0.685469i
$606$	1.65735	−	0.374458i	0.0673252	−	0.0152113i
$607$	−17.4314	+	10.0640i	−0.707518	+	0.408486i	−0.810141	−	0.586235i	$-0.800610\pi$
$607$	−17.4314	+	10.0640i	−0.707518	+	0.408486i	0.102623	+	0.994720i	$0.467276\pi$
$608$	−0.386956	+	0.670228i	−0.0156932	+	0.0271813i
$609$	−2.02213	+	35.7258i	−0.0819407	+	1.44768i
$610$	13.5473			0.548512
$611$	−23.6466	+	31.4666i	−0.956637	+	1.27300i
$612$	8.55849	−	4.07542i	0.345956	−	0.164739i
$613$	25.1943	+	14.5459i	1.01759	+	0.587505i	0.913404	−	0.407053i	$-0.133444\pi$
$613$	25.1943	+	14.5459i	1.01759	+	0.587505i	0.104184	+	0.994558i	$0.466777\pi$
$614$	9.09344	−	15.7503i	0.366981	−	0.635630i
$615$	5.69797	+	6.16802i	0.229764	+	0.248719i
$616$	−0.809145	−	3.23834i	−0.0326014	−	0.130477i
$617$	12.2531	+	21.2230i	0.493292	+	0.854407i	0.999970	−	0.00772817i	$-0.00245998\pi$
$617$	12.2531	+	21.2230i	0.493292	+	0.854407i	−0.506678	+	0.862135i	$0.669127\pi$
$618$	19.9524	−	18.4319i	0.802604	−	0.741440i
$619$	36.1887			1.45455			0.727273	−	0.686349i	$-0.240788\pi$
$619$	36.1887			1.45455			0.727273	+	0.686349i	$0.240788\pi$
$620$	23.9306	−	13.8164i	0.961077	−	0.554878i
$621$	43.2712	−	6.23130i	1.73641	−	0.250053i
$622$	3.85575	−	6.67836i	0.154602	−	0.267778i
$623$	−16.8882	+	4.21975i	−0.676612	+	0.169061i
$624$	−0.631890	−	6.21295i	−0.0252959	−	0.248717i
$625$	−2.67139			−0.106856
$626$	−13.7648	−	7.94708i	−0.550150	−	0.317629i
$627$	−0.502011	+	1.61490i	−0.0200484	+	0.0644929i
$628$	−5.04941	+	2.91528i	−0.201493	+	0.116332i
$629$			1.54712i			0.0616878i
$630$	−26.6451	−	9.96645i	−1.06157	−	0.397073i
$631$	10.9062	−	6.29670i	0.434169	−	0.250668i	−0.266952	−	0.963710i	$-0.586017\pi$
$631$	10.9062	−	6.29670i	0.434169	−	0.250668i	0.701121	+	0.713042i	$0.252683\pi$
$632$	5.53840			0.220306
$633$	−3.05873	−	3.31105i	−0.121573	−	0.131603i
$634$	−3.00370	+	5.20256i	−0.119292	+	0.206620i
$635$	−33.5926	−	19.3947i	−1.33308	−	0.769655i
$636$	−4.64660	−	20.5658i	−0.184250	−	0.815487i
$637$	15.8375	−	19.6513i	0.627506	−	0.778611i
$638$			9.85124i			0.390014i
$639$	−0.0360540	+	0.454364i	−0.00142627	+	0.0179743i
$640$	−3.10394	−	1.79206i	−0.122694	−	0.0708373i
$641$	−6.51225	+	3.75985i	−0.257218	+	0.148505i	−0.623065	−	0.782170i	$-0.714113\pi$
$641$	−6.51225	+	3.75985i	−0.257218	+	0.148505i	0.365847	+	0.930675i	$0.380779\pi$
$642$	−1.87530	−	8.30006i	−0.0740121	−	0.327577i
$643$	−4.12995	−	7.15328i	−0.162869	−	0.282098i	0.773027	−	0.634373i	$-0.218742\pi$
$643$	−4.12995	−	7.15328i	−0.162869	−	0.282098i	−0.935897	+	0.352275i	$0.885408\pi$
$644$	15.4711	+	16.0046i	0.609647	+	0.630670i
$645$	−0.342114	−	1.51420i	−0.0134707	−	0.0596214i
$646$	−1.22269	−	2.11776i	−0.0481061	−	0.0833221i
$647$	14.7602	−	25.5654i	0.580284	−	1.00508i	−0.415161	−	0.909748i	$-0.636275\pi$
$647$	14.7602	−	25.5654i	0.580284	−	1.00508i	0.995445	−	0.0953335i	$-0.0303918\pi$
$648$	3.21447	+	8.40638i	0.126276	+	0.330234i
$649$		−	15.2047i		−	0.596838i
$650$	26.0253	−	11.0877i	1.02080	−	0.434897i
$651$	−15.9080	−	31.5466i	−0.623483	−	1.23641i
$652$	−16.1748	−	9.33852i	−0.633454	−	0.365725i
$653$	−4.09902	−	2.36657i	−0.160407	−	0.0926111i	0.417648	−	0.908609i	$-0.362855\pi$
$653$	−4.09902	−	2.36657i	−0.160407	−	0.0926111i	−0.578055	+	0.815998i	$0.696188\pi$
$654$	7.62286	−	7.04194i	0.298077	−	0.275362i
$655$		−	48.7902i		−	1.90639i
$656$	1.17143	−	0.676327i	0.0457368	−	0.0264061i
$657$	−25.6043	−	17.6216i	−0.998917	−	0.687486i
$658$	28.0217	−	7.00162i	1.09240	−	0.272952i
$659$	−37.4903	+	21.6450i	−1.46042	+	0.843171i	−0.999030	−	0.0440285i	$-0.985981\pi$
$659$	−37.4903	+	21.6450i	−1.46042	+	0.843171i	−0.461385	+	0.887200i	$0.652647\pi$
$660$	−7.47887	−	2.32490i	−0.291115	−	0.0904964i
$661$	18.6135	−	32.2396i	0.723982	−	1.25397i	−0.235409	−	0.971896i	$-0.575643\pi$
$661$	18.6135	−	32.2396i	0.723982	−	1.25397i	0.959392	−	0.282078i	$-0.0910236\pi$
$662$		−	16.4810i		−	0.640552i
$663$	17.9996	+	8.08659i	0.699047	+	0.314057i
$664$			3.23534i			0.125555i
$665$	−2.01928	+	7.05550i	−0.0783043	+	0.273600i
$666$	−1.46430	−	0.116193i	−0.0567403	−	0.00450238i
$667$	−32.8481	−	56.8946i	−1.27188	−	2.20297i
$668$		−	3.23070i		−	0.124999i
$669$	15.4999	+	16.7785i	0.599259	+	0.648694i
$670$	21.7199	+	37.6200i	0.839114	+	1.45339i
$671$		−	4.76863i		−	0.184091i
$672$	−2.51190	+	3.83280i	−0.0968985	+	0.147854i
$673$	9.00579	−	15.5985i	0.347148	−	0.601277i	−0.638594	−	0.769544i	$-0.720484\pi$
$673$	9.00579	−	15.5985i	0.347148	−	0.601277i	0.985742	+	0.168267i	$0.0538170\pi$
$674$	14.3226	−	24.8074i	0.551685	−	0.955546i
$675$	−32.0406	+	25.2085i	−1.23324	+	0.970277i
$676$	9.00579	−	9.37528i	0.346376	−	0.360588i
$677$	43.2431			1.66197			0.830984	−	0.556296i	$-0.187778\pi$
$677$	43.2431			1.66197			0.830984	+	0.556296i	$0.187778\pi$
$678$	26.2486	+	8.15969i	1.00807	+	0.313371i
$679$	−11.2632	−	3.22352i	−0.432242	−	0.123707i
$680$	9.80769	−	5.66247i	0.376108	−	0.217146i
$681$	8.62736	+	38.1846i	0.330601	+	1.46324i
$682$	−4.86335	−	8.42357i	−0.186227	−	0.322555i
$683$	9.67584	+	16.7591i	0.370236	+	0.641267i	0.989602	−	0.143835i	$-0.0459435\pi$
$683$	9.67584	+	16.7591i	0.370236	+	0.641267i	−0.619366	+	0.785103i	$0.712610\pi$
$684$	2.09621	−	0.998183i	0.0801506	−	0.0381665i
$685$	6.86832	−	3.96543i	0.262425	−	0.151511i
$686$	−18.1097	+	3.87799i	−0.691431	+	0.148063i
$687$	−0.235334	+	0.757036i	−0.00897854	+	0.0288827i
$688$	−0.250064			−0.00953359
$689$	26.3674	−	35.0872i	1.00452	−	1.33672i
$690$	50.9455	−	11.5105i	1.93946	−	0.438198i
$691$	−0.643698	+	1.11492i	−0.0244874	+	0.0424135i	−0.878009	−	0.478643i	$-0.841129\pi$
$691$	−0.643698	+	1.11492i	−0.0244874	+	0.0424135i	0.853522	+	0.521057i	$0.174462\pi$
$692$	−7.02069	+	12.1602i	−0.266887	+	0.462261i
$693$	−3.50819	+	9.37906i	−0.133265	+	0.356281i
$694$			21.7396i			0.825225i
$695$	−6.04318	−	10.4671i	−0.229231	−	0.397040i
$696$	9.93444	−	9.17736i	0.376564	−	0.347867i
$697$			4.27406i			0.161892i
$698$	−13.3083	−	23.0507i	−0.503727	−	0.872480i
$699$	25.9868	+	8.07830i	0.982911	+	0.305549i
$700$	−19.9570	−	5.71169i	−0.754305	−	0.215882i
$701$		−	9.09155i		−	0.343383i	−0.985151	−	0.171692i	$-0.945077\pi$
$701$		−	9.09155i		−	0.343383i	0.985151	−	0.171692i	$-0.0549232\pi$
$702$	−9.00548	+	16.4287i	−0.339890	+	0.620060i
$703$			0.378933i			0.0142917i
$704$	−0.630804	+	1.09258i	−0.0237743	+	0.0411783i
$705$	20.1176	−	64.7155i	0.757672	−	2.43733i
$706$	−22.2718	+	12.8586i	−0.838210	+	0.483941i
$707$	−0.629168	−	2.51804i	−0.0236623	−	0.0947007i
$708$	−15.3332	+	14.1647i	−0.576255	+	0.532340i
$709$	−32.1245	+	18.5471i	−1.20646	+	0.696550i	−0.961984	−	0.273106i	$-0.911949\pi$
$709$	−32.1245	+	18.5471i	−1.20646	+	0.696550i	−0.244475	+	0.969655i	$0.578616\pi$
$710$			0.544537i			0.0204361i
$711$	−13.6869	−	9.41978i	−0.513301	−	0.353269i
$712$	5.69791	+	3.28969i	0.213538	+	0.123286i
$713$	56.1753	+	32.4329i	2.10378	+	1.21462i
$714$	−6.51971	−	12.9290i	−0.243994	−	0.483856i
$715$	−6.39009	−	14.9989i	−0.238976	−	0.560928i
$716$		−	9.00908i		−	0.336685i
$717$	9.70919	−	31.2331i	0.362596	−	1.16642i
$718$	4.66456	−	8.07925i	0.174080	−	0.301515i
$719$	−19.1457	−	33.1613i	−0.714013	−	1.23671i	−0.963339	−	0.268288i	$-0.913542\pi$
$719$	−19.1457	−	33.1613i	−0.714013	−	1.23671i	0.249325	−	0.968420i	$-0.419791\pi$
$720$	4.62275	+	9.70790i	0.172280	+	0.361792i
$721$	−28.8380	−	29.8325i	−1.07398	−	1.11102i
$722$	9.20053	+	15.9358i	0.342408	+	0.593068i
$723$	32.0680	−	7.24538i	1.19262	−	0.269459i
$724$	12.1097	−	6.99153i	0.450053	−	0.259838i
$725$	53.0566	+	30.6323i	1.97047	+	1.13765i
$726$	4.83738	−	15.5612i	0.179532	−	0.577530i
$727$			35.6262i			1.32130i	0.750693	+	0.660651i	$0.229720\pi$
$727$			35.6262i			1.32130i	−0.750693	+	0.660651i	$0.770280\pi$
$728$	−9.46615	+	1.17986i	−0.350839	+	0.0437285i
$729$	6.35380	−	26.2417i	0.235326	−	0.971917i
$730$	−32.1590	−	18.5670i	−1.19026	−	0.687196i
$731$	0.395070	−	0.684282i	0.0146122	−	0.0253091i
$732$	−4.80890	+	4.44243i	−0.177742	+	0.164197i
$733$	8.76856			0.323874			0.161937	−	0.986801i	$-0.448226\pi$
$733$	8.76856			0.323874			0.161937	+	0.986801i	$0.448226\pi$
$734$	−8.31827	+	4.80255i	−0.307033	+	0.177266i
$735$	−14.2986	+	41.0353i	−0.527411	+	1.51361i
$736$		−	8.41345i		−	0.310124i
$737$	13.2422	−	7.64541i	0.487784	−	0.281622i
$738$	−4.04525	−	0.320992i	−0.148908	−	0.0118159i
$739$	−5.20359	−	3.00429i	−0.191417	−	0.110515i	0.401229	−	0.915978i	$-0.368583\pi$
$739$	−5.20359	−	3.00429i	−0.191417	−	0.110515i	−0.592646	+	0.805463i	$0.701917\pi$
$740$	−1.75490			−0.0645115
$741$	4.40861	+	1.98063i	0.161954	+	0.0727602i
$742$	−31.2460	+	7.80726i	−1.14708	+	0.286613i
$743$	22.9464	−	39.7443i	0.841821	−	1.45808i	−0.0465322	−	0.998917i	$-0.514817\pi$
$743$	22.9464	−	39.7443i	0.841821	−	1.45808i	0.888353	−	0.459160i	$-0.151850\pi$
$744$	−3.96404	+	12.7518i	−0.145329	+	0.467503i
$745$	16.5892	−	9.57776i	0.607780	−	0.350902i
$746$	−16.8877			−0.618301
$747$	5.50270	−	7.99544i	0.201333	−	0.292538i
$748$	−1.99319	−	3.45230i	−0.0728782	−	0.126229i
$749$	−12.6104	+	3.15089i	−0.460775	+	0.115131i
$750$	−12.9771	+	11.9882i	−0.473857	+	0.437746i
$751$	−21.7817	+	37.7271i	−0.794826	+	1.37668i	0.128123	+	0.991758i	$0.459105\pi$
$751$	−21.7817	+	37.7271i	−0.794826	+	1.37668i	−0.922949	+	0.384921i	$0.874229\pi$
$752$	−9.45425	−	5.45842i	−0.344761	−	0.199048i
$753$	7.43584	−	1.68004i	0.270977	−	0.0612241i
$754$	27.9485	+	3.39412i	1.01783	+	0.123607i
$755$	−47.5414			−1.73021
$756$	12.7265	−	5.19967i	0.462858	−	0.189110i
$757$	1.39668	−	2.41912i	0.0507632	−	0.0879244i	−0.839527	−	0.543318i	$-0.817168\pi$
$757$	1.39668	−	2.41912i	0.0507632	−	0.0879244i	0.890290	+	0.455393i	$0.150501\pi$
$758$	−25.2872	+	14.5996i	−0.918473	+	0.530281i
$759$	−4.05170	−	17.9328i	−0.147067	−	0.650919i
$760$	2.40218	−	1.38690i	0.0871361	−	0.0503080i
$761$	−46.3396	+	26.7542i	−1.67981	+	0.969839i	−0.718032	+	0.696010i	$0.754957\pi$
$761$	−46.3396	+	26.7542i	−1.67981	+	0.969839i	−0.961778	+	0.273829i	$0.911710\pi$
$762$	18.2844	−	4.13114i	0.662373	−	0.149655i
$763$	−11.0176	−	11.3976i	−0.398865	−	0.412620i
$764$	−19.5584	−	11.2921i	−0.707600	−	0.408533i
$765$	−33.8684	−	2.68747i	−1.22451	−	0.0971658i
$766$		−	8.44343i		−	0.305073i
$767$	−43.1367	−	5.23861i	−1.55758	−	0.189155i
$768$	1.68947	−	0.381715i	0.0609633	−	0.0137739i
$769$	5.91403	−	10.2434i	0.213265	−	0.369386i	−0.739469	−	0.673190i	$-0.764923\pi$
$769$	5.91403	−	10.2434i	0.213265	−	0.369386i	0.952735	+	0.303804i	$0.0982568\pi$
$770$	−3.29176	+	11.5016i	−0.118627	+	0.414491i
$771$	−10.2895	−	11.1383i	−0.370567	−	0.401137i
$772$			7.80251i			0.280819i
$773$	−27.7265	+	16.0079i	−0.997251	+	0.575763i	−0.907434	−	0.420195i	$-0.861962\pi$
$773$	−27.7265	+	16.0079i	−0.997251	+	0.575763i	−0.0898175	+	0.995958i	$0.528628\pi$
$774$	0.617978	+	0.425311i	0.0222128	+	0.0152875i
$775$	−60.4900			−2.17287
$776$	2.21400	+	3.83477i	0.0794781	+	0.137660i
$777$	−0.126798	+	2.24020i	−0.00454886	+	0.0803666i
$778$	0.566013	+	0.326788i	0.0202926	+	0.0117159i
$779$			1.04684i			0.0375068i
$780$	−9.17262	+	20.4170i	−0.328432	+	0.731045i
$781$	0.191677			0.00685874
$782$	23.0228	+	13.2922i	0.823295	+	0.475329i
$783$	−40.1598	+	5.78324i	−1.43519	+	0.206676i
$784$	5.94008	+	3.70344i	0.212146	+	0.132266i
$785$	20.8974			0.745860
$786$	15.9993	+	17.3192i	0.570677	+	0.617755i
$787$	6.78351	+	11.7494i	0.241806	+	0.418820i	0.961229	−	0.275752i	$-0.0889269\pi$
$787$	6.78351	+	11.7494i	0.241806	+	0.418820i	−0.719423	+	0.694573i	$0.755594\pi$
$788$	−17.8228			−0.634911
$789$	−15.2269	+	14.0665i	−0.542092	+	0.500781i
$790$	−17.1908	−	9.92513i	−0.611622	−	0.353120i
$791$	11.5531	−	40.3674i	0.410782	−	1.43530i
$792$	3.41718	−	1.62721i	0.121424	−	0.0578202i
$793$	−13.5289	−	1.64297i	−0.480424	−	0.0583437i
$794$	−5.03371			−0.178640
$795$	−22.4324	+	72.1619i	−0.795595	+	2.55932i
$796$	8.97099	+	5.17941i	0.317968	+	0.183579i
$797$	15.7158	+	27.2205i	0.556682	+	0.964201i	0.997771	+	0.0667377i	$0.0212591\pi$
$797$	15.7158	+	27.2205i	0.556682	+	0.964201i	−0.441089	+	0.897463i	$0.645408\pi$
$798$	−1.59686	−	3.16667i	−0.0565281	−	0.112099i
$799$	29.8732	−	17.2473i	1.05684	−	0.610165i
$800$	3.92295	+	6.79475i	0.138697	+	0.240231i
$801$	−8.48600	−	17.8208i	−0.299838	−	0.629668i
$802$	−10.4095	−	18.0297i	−0.367571	−	0.636652i
$803$	−6.53558	+	11.3200i	−0.230636	+	0.399473i
$804$	−20.0464	−	6.23165i	−0.706981	−	0.219773i
$805$	−19.3401	−	77.4024i	−0.681648	−	2.72808i
$806$	−25.5738	+	10.8954i	−0.900797	+	0.383773i
$807$	−5.93668	+	1.34132i	−0.208981	+	0.0472168i
$808$	−0.490495	+	0.849562i	−0.0172556	+	0.0298875i
$809$	17.4070	+	10.0499i	0.611996	+	0.353336i	0.773746	−	0.633496i	$-0.218381\pi$
$809$	17.4070	+	10.0499i	0.611996	+	0.353336i	−0.161750	+	0.986832i	$0.551714\pi$
$810$	5.08720	−	31.8534i	0.178746	−	1.11921i
$811$	−33.5036			−1.17647			−0.588236	−	0.808689i	$-0.700177\pi$
$811$	−33.5036			−1.17647			−0.588236	+	0.808689i	$0.700177\pi$
$812$	−14.3586	−	14.8538i	−0.503890	−	0.521266i
$813$	2.99138	+	3.23815i	0.104912	+	0.113567i
$814$			0.617725i			0.0216513i
$815$	33.4703	+	57.9723i	1.17241	+	2.03068i
$816$	−1.62462	+	5.22617i	−0.0568730	+	0.182953i
$817$	0.0967637	−	0.167600i	0.00338533	−	0.00586357i
$818$	−29.3889			−1.02756
$819$	25.4002	+	13.1844i	0.887556	+	0.460699i
$820$	−4.84807			−0.169302
$821$	7.45863	−	12.9187i	0.260308	−	0.450867i	−0.706016	−	0.708196i	$-0.749509\pi$
$821$	7.45863	−	12.9187i	0.260308	−	0.450867i	0.966324	+	0.257329i	$0.0828425\pi$
$822$	−1.13772	+	3.65988i	−0.0396825	+	0.127653i
$823$	−4.82700	−	8.36061i	−0.168259	−	0.291433i	0.769549	−	0.638588i	$-0.220481\pi$
$823$	−4.82700	−	8.36061i	−0.168259	−	0.291433i	−0.937808	+	0.347155i	$0.887148\pi$
$824$			15.6826i			0.546330i
$825$	11.6337	+	12.5934i	0.405034	+	0.438447i
$826$	22.1616	+	22.9259i	0.771102	+	0.797693i
$827$	7.56315			0.262996			0.131498	−	0.991316i	$-0.458021\pi$
$827$	7.56315			0.262996			0.131498	+	0.991316i	$0.458021\pi$
$828$	−14.3097	+	20.7920i	−0.497296	+	0.722572i
$829$	10.8268	+	6.25083i	0.376029	+	0.217100i	0.676089	−	0.736820i	$-0.263673\pi$
$829$	10.8268	+	6.25083i	0.376029	+	0.217100i	−0.300060	+	0.953920i	$0.597007\pi$
$830$	5.79792	−	10.0423i	0.201249	−	0.348573i
$831$	23.3935	−	5.28547i	0.811510	−	0.183351i
$832$	2.88239	+	2.16606i	0.0999289	+	0.0750948i
$833$	−19.5188	+	10.4036i	−0.676287	+	0.360464i
$834$	5.57754	+	1.73384i	0.193135	+	0.0600381i
$835$	−5.78960	+	10.0279i	−0.200357	+	0.347029i
$836$	−0.488187	−	0.845565i	−0.0168843	−	0.0292445i
$837$	31.4846	−	24.7712i	1.08827	−	0.856216i
$838$	11.2918	+	19.5580i	0.390069	+	0.675619i
$839$	14.0117	−	8.08964i	0.483736	−	0.279285i	−0.238236	−	0.971207i	$-0.576569\pi$
$839$	14.0117	−	8.08964i	0.483736	−	0.279285i	0.721972	+	0.691922i	$0.243236\pi$
$840$	14.6654	−	7.39531i	0.506004	−	0.255162i
$841$	15.9862	+	27.6888i	0.551247	+	0.954788i
$842$	24.7026	+	14.2621i	0.851309	+	0.491503i
$843$	−7.75315	+	24.9408i	−0.267033	+	0.859008i
$844$	2.60249			0.0895814
$845$	−44.7544	+	12.9614i	−1.53960	+	0.445885i
$846$	14.0804	+	29.5692i	0.484094	+	1.01661i
$847$	−23.9313	−	6.84913i	−0.822290	−	0.235339i
$848$	10.5421	+	6.08648i	0.362017	+	0.209011i
$849$	−3.53468	+	3.26531i	−0.121310	+	0.112065i
$850$	−24.7911			−0.850329
$851$	−2.05975	−	3.56759i	−0.0706074	−	0.122296i
$852$	−0.178565	−	0.193296i	−0.00611754	−	0.00662220i
$853$	−27.7026			−0.948520			−0.474260	−	0.880385i	$-0.657284\pi$
$853$	−27.7026			−0.948520			−0.474260	+	0.880385i	$0.657284\pi$
$854$	6.95050	+	7.19019i	0.237841	+	0.246043i
$855$	−8.29531	−	0.658237i	−0.283693	−	0.0225112i
$856$	4.25464	+	2.45642i	0.145420	+	0.0839585i
$857$	−13.2750			−0.453464			−0.226732	−	0.973957i	$-0.572804\pi$
$857$	−13.2750			−0.453464			−0.226732	+	0.973957i	$0.572804\pi$
$858$	7.18677	+	3.22876i	0.245352	+	0.110228i
$859$		−	51.4810i		−	1.75651i	−0.478194	−	0.878254i	$-0.658708\pi$
$859$		−	51.4810i		−	1.75651i	0.478194	−	0.878254i	$-0.341292\pi$
$860$	0.776182	+	0.448129i	0.0264676	+	0.0152811i
$861$	−0.350291	+	6.18873i	−0.0119379	+	0.210911i
$862$	3.76847	+	6.52718i	0.128354	+	0.222316i
$863$	14.4211			0.490900			0.245450	−	0.969409i	$-0.421064\pi$
$863$	14.4211			0.490900			0.245450	+	0.969409i	$0.421064\pi$
$864$	−4.82437	−	1.93014i	−0.164128	−	0.0656647i
$865$	43.5836	−	25.1630i	1.48189	−	0.855567i
$866$			32.7328i			1.11230i
$867$	8.24586	+	8.92609i	0.280044	+	0.303146i
$868$	19.6108	+	5.61259i	0.665633	+	0.190504i
$869$	−3.49364	+	6.05117i	−0.118514	+	0.205272i
$870$	−47.2822	+	10.6829i	−1.60302	+	0.362183i
$871$	−17.1280	−	40.2031i	−0.580361	−	1.36223i
$872$			5.99158i			0.202900i
$873$	1.05079	−	13.2424i	0.0355639	−	0.448187i
$874$	5.63893	+	3.25564i	0.190740	+	0.110124i
$875$	18.7564	+	19.4032i	0.634080	+	0.655947i
$876$	17.5041	−	3.95484i	0.591408	−	0.133622i
$877$	−39.8280	+	22.9947i	−1.34489	+	0.776475i	−0.987521	−	0.157486i	$-0.949661\pi$
$877$	−39.8280	+	22.9947i	−1.34489	+	0.776475i	−0.357374	+	0.933962i	$0.616328\pi$
$878$	21.2278	−	12.2559i	0.716403	−	0.413615i
$879$	1.69301	+	7.49323i	0.0571037	+	0.252741i
$880$	3.91595	−	2.26088i	0.132007	−	0.0762141i
$881$	−18.8103	+	32.5804i	−0.633735	+	1.09766i	0.353046	+	0.935606i	$0.385146\pi$
$881$	−18.8103	+	32.5804i	−0.633735	+	1.09766i	−0.986782	+	0.162056i	$0.948188\pi$
$882$	−8.38075	−	19.2552i	−0.282194	−	0.648357i
$883$	−23.2787			−0.783389			−0.391695	−	0.920095i	$-0.628111\pi$
$883$	−23.2787			−0.783389			−0.391695	+	0.920095i	$0.628111\pi$
$884$	−10.4811	+	4.46534i	−0.352518	+	0.150186i
$885$	72.9770	−	16.4883i	2.45310	−	0.554248i
$886$	−9.29525	−	5.36661i	−0.312280	−	0.180295i
$887$	7.93228	−	13.7391i	0.266340	−	0.461314i	−0.701574	−	0.712597i	$-0.747519\pi$
$887$	7.93228	−	13.7391i	0.266340	−	0.461314i	0.967914	+	0.251282i	$0.0808523\pi$
$888$	0.622942	−	0.575469i	0.0209046	−	0.0193115i
$889$	−6.94117	−	27.7798i	−0.232800	−	0.931705i
$890$	−11.7906	−	20.4220i	−0.395223	−	0.684546i
$891$	−11.2124	−	1.79069i	−0.375629	−	0.0599904i
$892$	−13.1879			−0.441564
$893$	7.31677	−	4.22434i	0.244846	−	0.141362i
$894$	−2.74795	+	8.83978i	−0.0919052	+	0.295646i
$895$	−16.1448	+	27.9636i	−0.539661	+	0.934720i
$896$	−0.641360	−	2.56684i	−0.0214263	−	0.0857520i
$897$	−52.2723	+	5.31638i	−1.74532	+	0.177509i
$898$	−39.4840			−1.31760
$899$	−52.1361	−	30.1008i	−1.73883	−	1.00392i
$900$	1.86188	−	23.4639i	0.0620625	−	0.782131i
$901$	−33.3105	+	19.2318i	−1.10973	+	0.640705i
$902$			1.70652i			0.0568209i
$903$	0.628134	−	0.958444i	0.0209030	−	0.0318950i
$904$	−13.7438	+	7.93500i	−0.457113	+	0.263914i
$905$	−50.1169			−1.66594
$906$	16.8759	−	15.5898i	0.560664	−	0.517937i
$907$	−3.67040	+	6.35732i	−0.121874	+	0.211091i	−0.920507	−	0.390727i	$-0.872224\pi$
$907$	−3.67040	+	6.35732i	−0.121874	+	0.211091i	0.798633	+	0.601819i	$0.205557\pi$
$908$	−19.5736	−	11.3008i	−0.649571	−	0.375030i
$909$	2.65710	−	1.26527i	0.0881304	−	0.0419663i
$910$	31.4967	+	13.3017i	1.04411	+	0.440946i
$911$		−	4.10735i		−	0.136082i	−0.997683	−	0.0680412i	$-0.978325\pi$
$911$		−	4.10735i		−	0.136082i	0.997683	−	0.0680412i	$-0.0216749\pi$
$912$	−0.397914	+	1.28003i	−0.0131762	+	0.0423862i
$913$	−3.53488	−	2.04086i	−0.116987	−	0.0675428i
$914$	−9.89907	+	5.71523i	−0.327432	+	0.189043i
$915$	22.8876	−	5.17118i	0.756641	−	0.170954i
$916$	−0.228853	−	0.396385i	−0.00756152	−	0.0130969i
$917$	25.8954	−	25.0321i	0.855140	−	0.826633i
$918$	12.9036	−	10.1522i	0.425883	−	0.335072i
$919$	−19.1541	−	33.1759i	−0.631835	−	1.09437i	−0.987176	−	0.159634i	$-0.948969\pi$
$919$	−19.1541	−	33.1759i	−0.631835	−	1.09437i	0.355341	−	0.934737i	$-0.384365\pi$
$920$	−15.0774	+	26.1148i	−0.497087	+	0.860980i
$921$	9.35094	−	30.0807i	0.308124	−	0.991192i
$922$		−	9.72957i		−	0.320426i
$923$	0.0660399	−	0.543798i	0.00217373	−	0.0178993i
$924$	−2.60315	−	5.16221i	−0.0856372	−	0.169824i
$925$	3.32693	+	1.92081i	0.109389	+	0.0631557i
$926$	−23.0858	−	13.3286i	−0.758647	−	0.438005i
$927$	26.6732	−	38.7562i	0.876063	−	1.27292i
$928$			7.80848i			0.256326i
$929$	22.8552	−	13.1955i	0.749856	−	0.432930i	−0.0757859	−	0.997124i	$-0.524147\pi$
$929$	22.8552	−	13.1955i	0.749856	−	0.432930i	0.825642	+	0.564195i	$0.190813\pi$
$930$	35.1561	−	32.4769i	1.15281	−	1.06496i
$931$	−4.78070	+	2.54814i	−0.156681	+	0.0835118i
$932$	−13.6067	+	7.85585i	−0.445703	+	0.257327i
$933$	3.96493	−	12.7547i	0.129806	−	0.417569i
$934$	−3.01089	+	5.21502i	−0.0985194	+	0.170641i
$935$			14.2876i			0.467256i
$936$	−3.43913	−	10.2554i	−0.112411	−	0.335207i
$937$		−	53.4346i		−	1.74563i	−0.488049	−	0.872816i	$-0.662291\pi$
$937$		−	53.4346i		−	1.74563i	0.488049	−	0.872816i	$-0.337709\pi$
$938$	−8.82325	+	30.8290i	−0.288089	+	1.00660i
$939$	−26.2886	−	8.17212i	−0.857896	−	0.266687i
$940$	19.5636	+	33.8851i	0.638094	+	1.10521i
$941$			11.0561i			0.360419i	0.983628	+	0.180209i	$0.0576775\pi$
$941$			11.0561i			0.360419i	−0.983628	+	0.180209i	$0.942322\pi$
$942$	−7.41800	+	6.85270i	−0.241692	+	0.223273i
$943$	−5.69024	−	9.85578i	−0.185300	−	0.320949i
$944$		−	12.0519i		−	0.392255i
$945$	−48.8203	−	6.66716i	−1.58813	−	0.216883i
$946$	0.157741	−	0.273216i	0.00512861	−	0.00888301i
$947$	4.57740	−	7.92829i	0.148746	−	0.257635i	−0.782019	−	0.623255i	$-0.785810\pi$
$947$	4.57740	−	7.92829i	0.148746	−	0.257635i	0.930764	+	0.365620i	$0.119143\pi$
$948$	9.35693	−	2.11409i	0.303899	−	0.0686623i
$949$	29.8636	+	22.4420i	0.969414	+	0.728497i
$950$	−6.07204			−0.197003
$951$	−3.08875	+	9.93609i	−0.100160	+	0.322200i
$952$	8.03725	+	2.30026i	0.260489	+	0.0745517i
$953$	44.8045	−	25.8679i	1.45136	−	0.837943i	0.452801	−	0.891612i	$-0.350425\pi$
$953$	44.8045	−	25.8679i	1.45136	−	0.837943i	0.998559	+	0.0536692i	$0.0170916\pi$
$954$	−15.7005	−	32.9715i	−0.508323	−	1.06749i
$955$	40.4721	+	70.0998i	1.30965	+	2.26838i
$956$	9.44183	+	16.3537i	0.305371	+	0.528917i
$957$	3.76036	+	16.6433i	0.121555	+	0.538002i
$958$	7.74812	−	4.47338i	0.250330	−	0.144528i
$959$	5.62848	+	1.61087i	0.181753	+	0.0520176i
$960$	−5.92805	−	1.84280i	−0.191327	−	0.0594762i
$961$	28.4405			0.917435
$962$	1.75252	+	0.212830i	0.0565036	+	0.00686190i
$963$	−6.33651	−	13.3068i	−0.204191	−	0.428807i
$964$	−9.49057	+	16.4382i	−0.305671	+	0.529437i
$965$	13.9826	−	24.2185i	0.450114	−	0.779621i
$966$	32.2471	+	21.1337i	1.03753	+	0.679966i
$967$			0.447825i			0.0144011i	0.999974	+	0.00720054i	$0.00229202\pi$
$967$			0.447825i			0.0144011i	−0.999974	+	0.00720054i	$0.997708\pi$
$968$	4.70417	+	8.14787i	0.151198	+	0.261882i
$969$	−2.87407	−	3.11116i	−0.0923284	−	0.0999450i
$970$		−	15.8705i		−	0.509571i
$971$	19.5151	+	33.8011i	0.626269	+	1.08473i	0.988294	+	0.152562i	$0.0487523\pi$
$971$	19.5151	+	33.8011i	0.626269	+	1.08473i	−0.362025	+	0.932169i	$0.617914\pi$
$972$	8.63958	+	12.9753i	0.277115	+	0.416182i
$973$	2.45491	−	8.57762i	0.0787008	−	0.274986i
$974$			29.3101i			0.939155i
$975$	39.7365	−	28.6666i	1.27259	−	0.918066i
$976$		−	3.77980i		−	0.120989i
$977$	7.19880	−	12.4687i	0.230310	−	0.398909i	−0.727589	−	0.686013i	$-0.759359\pi$
$977$	7.19880	−	12.4687i	0.230310	−	0.398909i	0.957899	+	0.287104i	$0.0926926\pi$
$978$	−30.8914	−	9.60295i	−0.987798	−	0.307069i
$979$	−7.18853	+	4.15030i	−0.229746	+	0.132644i
$980$	−11.8008	−	22.1402i	−0.376964	−	0.707243i
$981$	10.1905	−	14.8069i	0.325359	−	0.472747i
$982$	−5.50320	+	3.17727i	−0.175614	+	0.101391i
$983$			55.8894i			1.78259i	0.453420	+	0.891297i	$0.350204\pi$
$983$			55.8894i			1.78259i	−0.453420	+	0.891297i	$0.649796\pi$
$984$	1.72093	−	1.58978i	0.0548613	−	0.0506805i
$985$	55.3209	+	31.9395i	1.76267	+	1.01768i
$986$	−21.3674	−	12.3365i	−0.680476	−	0.392873i
$987$	44.6691	−	22.5253i	1.42183	−	0.716988i
$988$	−2.56712	+	1.09369i	−0.0816708	+	0.0347948i
$989$			2.10390i			0.0669000i
$990$	−13.5227	−	1.07304i	−0.429781	−	0.0341034i
$991$	4.29142	−	7.43296i	0.136322	−	0.236116i	−0.789780	−	0.613390i	$-0.789805\pi$
$991$	4.29142	−	7.43296i	0.136322	−	0.236116i	0.926102	+	0.377274i	$0.123139\pi$
$992$	−3.85488	−	6.67685i	−0.122393	−	0.211990i
$993$	−6.29104	−	27.8441i	−0.199640	−	0.883605i
$994$	−0.289012	+	0.279378i	−0.00916692	+	0.00886133i
$995$	−18.5636	−	32.1531i	−0.588506	−	1.01932i
$996$	1.23498	+	5.46599i	0.0391317	+	0.173197i
$997$	44.8411	−	25.8890i	1.42013	−	0.819914i	0.423824	−	0.905745i	$-0.360688\pi$
$997$	44.8411	−	25.8890i	1.42013	−	0.819914i	0.996310	+	0.0858304i	$0.0273543\pi$
$998$	−5.13107	−	2.96242i	−0.162421	−	0.0937739i
$999$	−2.51823	+	0.362640i	−0.0796733	+	0.0114734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.i.251.4	✓	24
3.2	odd	2		546.2.q.j.251.9	yes	24
7.6	odd	2	inner	546.2.q.i.251.9	yes	24
13.10	even	6		546.2.q.j.335.4	yes	24
21.20	even	2		546.2.q.j.251.4	yes	24
39.23	odd	6	inner	546.2.q.i.335.9	yes	24
91.62	odd	6		546.2.q.j.335.9	yes	24
273.62	even	6	inner	546.2.q.i.335.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.4	✓	24	1.1	even	1	trivial
546.2.q.i.251.9	yes	24	7.6	odd	2	inner
546.2.q.i.335.4	yes	24	273.62	even	6	inner
546.2.q.i.335.9	yes	24	39.23	odd	6	inner
546.2.q.j.251.4	yes	24	21.20	even	2
546.2.q.j.251.9	yes	24	3.2	odd	2
546.2.q.j.335.4	yes	24	13.10	even	6
546.2.q.j.335.9	yes	24	91.62	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.514158 + 1.65398i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.58412i q^{5} +(-1.17531 - 1.27226i) q^{6} +(-1.90227 + 1.83885i) q^{7} +1.00000 q^{8} +(-2.47128 - 1.70081i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.514158 + 1.65398i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.58412i q^{5} +(-1.17531 - 1.27226i) q^{6} +(-1.90227 + 1.83885i) q^{7} +1.00000 q^{8} +(-2.47128 - 1.70081i) q^{9} +(-3.10394 - 1.79206i) q^{10} +(-0.630804 + 1.09258i) q^{11} +(1.68947 - 0.381715i) q^{12} +(2.88239 + 2.16606i) q^{13} +(-0.641360 - 2.56684i) q^{14} +(-5.92805 - 1.84280i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.57988 - 2.73643i) q^{17} +(2.70859 - 1.28979i) q^{18} +(-0.386956 - 0.670228i) q^{19} +(3.10394 - 1.79206i) q^{20} +(-2.06336 - 4.09177i) q^{21} +(-0.630804 - 1.09258i) q^{22} +(7.28626 + 4.20672i) q^{23} +(-0.514158 + 1.65398i) q^{24} -7.84590 q^{25} +(-3.31706 + 1.41319i) q^{26} +(4.08374 - 3.21296i) q^{27} +(2.54363 + 0.727985i) q^{28} +(-6.76234 - 3.90424i) q^{29} +(4.55994 - 4.21244i) q^{30} +7.70977 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.48278 - 1.60510i) q^{33} +3.15976 q^{34} +(-6.59067 - 6.81795i) q^{35} +(-0.237306 + 2.99060i) q^{36} +(-0.424035 - 0.244817i) q^{37} +0.773913 q^{38} +(-5.06463 + 3.65371i) q^{39} +3.58412i q^{40} +(-1.17143 - 0.676327i) q^{41} +(4.57525 + 0.258966i) q^{42} +(0.125032 + 0.216561i) q^{43} +1.26161 q^{44} +(6.09591 - 8.85737i) q^{45} +(-7.28626 + 4.20672i) q^{46} +10.9168i q^{47} +(-1.17531 - 1.27226i) q^{48} +(0.237237 - 6.99598i) q^{49} +(3.92295 - 6.79475i) q^{50} +(5.33831 - 1.20613i) q^{51} +(0.434672 - 3.57925i) q^{52} -12.1730i q^{53} +(0.740636 + 5.14310i) q^{54} +(-3.91595 - 2.26088i) q^{55} +(-1.90227 + 1.83885i) q^{56} +(1.30750 - 0.295414i) q^{57} +(6.76234 - 3.90424i) q^{58} +(-10.4372 + 6.02594i) q^{59} +(1.36811 + 6.05524i) q^{60} +(-3.27341 + 1.88990i) q^{61} +(-3.85488 + 6.67685i) q^{62} +(7.82858 - 1.30893i) q^{63} +1.00000 q^{64} +(-7.76343 + 10.3308i) q^{65} +(2.13144 - 0.481574i) q^{66} +(-10.4963 - 6.06005i) q^{67} +(-1.57988 + 2.73643i) q^{68} +(-10.7041 + 9.88839i) q^{69} +(9.19985 - 2.29871i) q^{70} +(-0.0759653 - 0.131576i) q^{71} +(-2.47128 - 1.70081i) q^{72} +10.3607 q^{73} +(0.424035 - 0.244817i) q^{74} +(4.03403 - 12.9769i) q^{75} +(-0.386956 + 0.670228i) q^{76} +(-0.809145 - 3.23834i) q^{77} +(-0.631890 - 6.21295i) q^{78} +5.53840 q^{79} +(-3.10394 - 1.79206i) q^{80} +(3.21447 + 8.40638i) q^{81} +(1.17143 - 0.676327i) q^{82} +3.23534i q^{83} +(-2.51190 + 3.83280i) q^{84} +(9.80769 - 5.66247i) q^{85} -0.250064 q^{86} +(9.93444 - 9.17736i) q^{87} +(-0.630804 + 1.09258i) q^{88} +(5.69791 + 3.28969i) q^{89} +(4.62275 + 9.70790i) q^{90} +(-9.46615 + 1.17986i) q^{91} -8.41345i q^{92} +(-3.96404 + 12.7518i) q^{93} +(-9.45425 - 5.45842i) q^{94} +(2.40218 - 1.38690i) q^{95} +(1.68947 - 0.381715i) q^{96} +(2.21400 + 3.83477i) q^{97} +(5.94008 + 3.70344i) q^{98} +(3.41718 - 1.62721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 q^{93} + 36 q^{95} - 36 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * q^93 + 36 * q^95 - 36 * q^99

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