LMFDB - Embedded newform 546.2.q.i.335.9

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			335.9
Character	$\chi$	$=$	546.335
Dual form			546.2.q.i.251.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.514158 + 1.65398i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.58412i q^{5} +(1.17531 - 1.27226i) q^{6} +(-2.54363 - 0.727985i) q^{7} +1.00000 q^{8} +(-2.47128 + 1.70081i) q^{9} +O(q^{10})$	\(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} +(-2.54363 - 0.727985i) 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} +(-0.103757 - 4.58140i) 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} +(1.90227 - 1.83885i) 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} +(2.60918 - 9.11666i) 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} +(-3.91573 + 2.38056i) 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} +(5.94008 + 3.70344i) 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} +(-2.54363 - 0.727985i) 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} +(7.52419 - 2.52718i) 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} +(4.01949 + 2.20084i) 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} +(8.90858 - 3.41132i) 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} +(0.237237 - 6.99598i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−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
$7$	−2.54363	−	0.727985i	−0.961401	−	0.275152i
$7$	−2.54363	−	0.727985i	−0.961401	−	0.275152i
$8$	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	0.755120	−	0.655587i	$-0.227579\pi$
$11$	−0.630804	−	1.09258i	−0.190195	−	0.329427i	−0.945315	+	0.326160i	$0.894245\pi$
$12$	−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	$-0.708163\pi$
$17$	1.57988	−	2.73643i	0.383177	−	0.663682i	0.991514	+	0.129996i	$0.0414965\pi$
$18$	2.70859	+	1.28979i	0.638420	+	0.304006i
$19$	0.386956	−	0.670228i	0.0887739	−	0.153761i	−0.818219	−	0.574906i	$-0.805038\pi$
$19$	0.386956	−	0.670228i	0.0887739	−	0.153761i	0.906993	+	0.421145i	$0.138372\pi$
$20$	−3.10394	−	1.79206i	−0.694061	−	0.400716i
$21$	−0.103757	−	4.58140i	−0.0226416	−	0.999744i
$22$	−0.630804	+	1.09258i	−0.134488	+	0.232940i
$23$	7.28626	−	4.20672i	1.51929	−	0.877162i	0.519548	−	0.854441i	$-0.326100\pi$
$23$	7.28626	−	4.20672i	1.51929	−	0.877162i	0.999742	−	0.0227213i	$-0.00723304\pi$
$24$	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
$28$	1.90227	−	1.83885i	0.359495	−	0.347511i
$29$	−6.76234	+	3.90424i	−1.25574	+	0.724999i	−0.972243	−	0.233975i	$-0.924826\pi$
$29$	−6.76234	+	3.90424i	−1.25574	+	0.724999i	−0.283493	+	0.958974i	$0.591493\pi$
$30$	4.55994	+	4.21244i	0.832527	+	0.769083i
$31$	−7.70977			−1.38471			−0.692357	−	0.721555i	$-0.743428\pi$
$31$	−7.70977			−1.38471			−0.692357	+	0.721555i	$0.743428\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.48278	−	1.60510i	0.258118	−	0.279412i
$34$	−3.15976			−0.541894
$35$	2.60918	−	9.11666i	0.441032	−	1.54100i
$36$	−0.237306	−	2.99060i	−0.0395509	−	0.498433i
$37$	−0.424035	+	0.244817i	−0.0697109	+	0.0402476i	−0.534450	−	0.845200i	$-0.679481\pi$
$37$	−0.424035	+	0.244817i	−0.0697109	+	0.0402476i	0.464739	+	0.885447i	$0.346148\pi$
$38$	−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	$-0.632983\pi$
$41$	1.17143	−	0.676327i	0.182947	−	0.105625i	0.588677	+	0.808369i	$0.299649\pi$
$42$	−3.91573	+	2.38056i	−0.604210	+	0.367328i
$43$	0.125032	−	0.216561i	0.0190672	−	0.0330253i	−0.856334	−	0.516422i	$-0.827264\pi$
$43$	0.125032	−	0.216561i	0.0190672	−	0.0330253i	0.875402	+	0.483396i	$0.160597\pi$
$44$	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
$49$	5.94008	+	3.70344i	0.848582	+	0.529063i
$50$	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	$0.315136\pi$
$53$			12.1730i			1.67208i	−0.548665	+	0.836042i	$0.684864\pi$
$54$	−0.740636	+	5.14310i	−0.100788	+	0.699887i
$55$	3.91595	−	2.26088i	0.528027	−	0.304856i
$56$	−2.54363	−	0.727985i	−0.339906	−	0.0972810i
$57$	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	$-0.0462478\pi$
$59$	10.4372	+	6.02594i	1.35881	+	0.784510i	0.369348	+	0.929291i	$0.379581\pi$
$60$	1.36811	−	6.05524i	0.176622	−	0.781728i
$61$	3.27341	+	1.88990i	0.419117	+	0.241977i	0.694699	−	0.719300i	$-0.255537\pi$
$61$	3.27341	+	1.88990i	0.419117	+	0.241977i	−0.275583	+	0.961277i	$0.588871\pi$
$62$	3.85488	+	6.67685i	0.489571	+	0.847961i
$63$	7.52419	−	2.52718i	0.947958	−	0.318394i
$64$	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	−0.977274	−	0.211981i	$-0.932008\pi$
$67$	−10.4963	+	6.06005i	−1.28233	+	0.740353i	−0.305056	+	0.952335i	$0.598675\pi$
$68$	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	−0.870498	−	0.492172i	$-0.836203\pi$
$71$	−0.0759653	+	0.131576i	−0.00901542	+	0.0156152i	0.861482	+	0.507787i	$0.169536\pi$
$72$	−2.47128	+	1.70081i	−0.291243	+	0.200443i
$73$	−10.3607			−1.21263			−0.606315	−	0.795224i	$-0.707353\pi$
$73$	−10.3607			−1.21263			−0.606315	+	0.795224i	$0.707353\pi$
$74$	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	$0.943179\pi$
$84$	4.01949	+	2.20084i	0.438562	+	0.240132i
$85$	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	$-0.780046\pi$
$89$	−5.69791	+	3.28969i	−0.603977	+	0.348706i	0.166627	+	0.986020i	$0.446712\pi$
$90$	−4.62275	+	9.70790i	−0.487280	+	1.02330i
$91$	8.90858	−	3.41132i	0.933873	−	0.357604i
$92$			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	$-0.905506\pi$
$97$	−2.21400	+	3.83477i	−0.224798	+	0.389361i	0.731461	+	0.681883i	$0.238839\pi$
$98$	0.237237	−	6.99598i	0.0239646	−	0.706701i
$99$	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	$-0.151125\pi$
$101$	0.490495	+	0.849562i	0.0488061	+	0.0845346i	−0.840590	+	0.541671i	$0.817792\pi$
$102$	−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
$105$	16.4203	−	0.371877i	1.60246	−	0.0362915i
$106$	10.5421	−	6.08648i	1.02394	−	0.591171i
$107$	4.25464	−	2.45642i	0.411311	−	0.237471i	−0.280042	−	0.959988i	$-0.590348\pi$
$107$	4.25464	−	2.45642i	0.411311	−	0.237471i	0.691353	+	0.722517i	$0.257015\pi$
$108$	4.82437	−	1.93014i	0.464225	−	0.185728i
$109$		−	5.99158i		−	0.573889i	−0.957947	−	0.286945i	$-0.907360\pi$
$109$		−	5.99158i		−	0.573889i	0.957947	−	0.286945i	$-0.0926395\pi$
$110$	−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	−0.313741	−	0.949509i	$-0.601582\pi$
$113$	−13.7438	−	7.93500i	−1.29291	−	0.746462i	−0.979169	+	0.203047i	$0.934916\pi$
$114$	−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
$119$	−6.01071	+	5.81033i	−0.551000	+	0.532633i
$120$	−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
$126$	−5.95069	−	5.25255i	−0.530130	−	0.467934i
$127$	−5.41129	−	9.37263i	−0.480174	−	0.831686i	0.519567	−	0.854430i	$-0.326093\pi$
$127$	−5.41129	−	9.37263i	−0.480174	−	0.831686i	−0.999741	+	0.0227433i	$0.992760\pi$
$128$	−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	$-0.297278\pi$
$131$	13.6129			1.18936			0.594682	+	0.803961i	$0.297278\pi$
$132$	0.648666	+	2.08667i	0.0564591	+	0.181621i
$133$	−1.47219	+	1.42311i	−0.127655	+	0.123399i
$134$	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	−0.909410	−	0.415900i	$-0.863467\pi$
$137$	−1.10639	+	1.91632i	−0.0945251	+	0.163722i	0.814885	+	0.579622i	$0.196800\pi$
$138$	3.21153	−	14.2142i	0.273384	−	1.21000i
$139$	2.92041	+	1.68610i	0.247706	+	0.143013i	0.618713	−	0.785617i	$-0.287654\pi$
$139$	2.92041	+	1.68610i	0.247706	+	0.143013i	−0.371007	+	0.928630i	$0.620988\pi$
$140$	6.59067	+	6.81795i	0.557013	+	0.576222i
$141$	−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
$147$	−3.07127	+	11.7289i	−0.253314	+	0.967384i
$148$		−	0.489633i		−	0.0402476i
$149$	−2.67228	+	4.62852i	−0.218922	+	0.379183i	−0.954479	−	0.298279i	$-0.903587\pi$
$149$	−2.67228	+	4.62852i	−0.218922	+	0.379183i	0.735557	+	0.677463i	$0.236921\pi$
$150$	−9.22134	+	9.98204i	−0.752919	+	0.815030i
$151$		−	13.2645i		−	1.07945i	−0.841842	−	0.539723i	$-0.818529\pi$
$151$		−	13.2645i		−	1.07945i	0.841842	−	0.539723i	$-0.181471\pi$
$152$	0.386956	−	0.670228i	0.0313863	−	0.0543627i
$153$	0.749829	+	9.44958i	0.0606201	+	0.763953i
$154$	2.39991	−	2.31991i	0.193391	−	0.186944i
$155$		−	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	0.974402	−	0.224815i	$-0.0721777\pi$
$163$	16.1748	+	9.33852i	1.26691	+	0.731449i	0.292506	+	0.956264i	$0.405511\pi$
$164$			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	$-0.706560\pi$
$167$	−2.79787	+	1.61535i	−0.216505	+	0.124999i	0.387826	+	0.921733i	$0.373226\pi$
$168$	−0.103757	−	4.58140i	−0.00800502	−	0.353463i
$169$	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	−0.465449	−	0.885075i	$-0.654107\pi$
$173$	7.02069	−	12.1602i	0.533773	−	0.924522i	0.999222	−	0.0394472i	$-0.0125597\pi$
$174$	−2.98061	+	13.1922i	−0.225959	+	1.00009i
$175$	19.9570	+	5.71169i	1.50861	+	0.431763i
$176$	−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	−0.179231	−	0.983807i	$-0.557361\pi$
$179$	7.80209	−	4.50454i	0.583156	−	0.336685i	0.762386	+	0.647122i	$0.224028\pi$
$180$	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	$0.826053\pi$
$182$	−7.40858	−	6.00940i	−0.549161	−	0.445446i
$183$	−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
$189$	8.04852	+	11.1455i	0.585443	+	0.810713i
$190$		−	2.77379i		−	0.201232i
$191$	19.5584	+	11.2921i	1.41520	+	0.817066i	0.995872	−	0.0907692i	$-0.0289326\pi$
$191$	19.5584	+	11.2921i	1.41520	+	0.817066i	0.419328	+	0.907835i	$0.362266\pi$
$192$	0.514158	+	1.65398i	0.0371062	+	0.119366i
$193$	−6.75717	+	3.90126i	−0.486392	+	0.280819i	−0.723076	−	0.690768i	$-0.757273\pi$
$193$	−6.75717	+	3.90126i	−0.486392	+	0.280819i	0.236684	+	0.971587i	$0.423939\pi$
$194$	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	0.986534	+	0.163557i	$0.0522967\pi$
$197$	8.91140	+	15.4350i	0.634911	+	1.09970i	−0.351623	+	0.936142i	$0.614370\pi$
$198$	−0.299387	−	3.77296i	−0.0212765	−	0.268133i
$199$	8.97099	+	5.17941i	0.635937	+	0.367158i	0.783048	−	0.621962i	$-0.213664\pi$
$199$	8.97099	+	5.17941i	0.635937	+	0.367158i	−0.147111	+	0.989120i	$0.546997\pi$
$200$	−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
$210$	−8.53219	−	14.0344i	−0.588777	−	0.968468i
$211$	−1.30125	−	2.25382i	−0.0895814	−	0.155160i	0.817753	−	0.575570i	$-0.195220\pi$
$211$	−1.30125	−	2.25382i	−0.0895814	−	0.155160i	−0.907334	+	0.420410i	$0.861886\pi$
$212$	−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
$217$	19.6108	+	5.61259i	1.33127	+	0.381007i
$218$	−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	$-0.312243\pi$
$223$	−6.59396	−	11.4211i	−0.441564	−	0.764812i	−0.997806	+	0.0662090i	$0.978910\pi$
$224$	1.90227	−	1.83885i	0.127101	−	0.122864i
$225$	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	$-0.603309\pi$
$227$	−19.5736	−	11.3008i	−1.29914	−	0.750060i	−0.980256	+	0.197733i	$0.936642\pi$
$228$	−0.909585	+	0.984620i	−0.0602387	+	0.0652081i
$229$	−0.457707			−0.0302461			−0.0151230	−	0.999886i	$-0.504814\pi$
$229$	−0.457707			−0.0302461			−0.0151230	+	0.999886i	$0.504814\pi$
$230$	15.0774	−	26.1148i	0.994174	−	1.72196i
$231$	−4.94012	+	3.00333i	−0.325036	+	0.197605i
$232$	−6.76234	+	3.90424i	−0.443969	+	0.256326i
$233$			15.7117i			1.02931i	0.857398	+	0.514654i	$0.172079\pi$
$233$			15.7117i			1.02931i	−0.857398	+	0.514654i	$0.827921\pi$
$234$	−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
$238$	8.03725	+	2.30026i	0.520978	+	0.149103i
$239$	−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	−0.379673	−	0.925121i	$-0.623964\pi$
$241$	9.49057	−	16.4382i	0.611341	−	1.05887i	0.991015	−	0.133754i	$-0.0427031\pi$
$242$	−9.40835			−0.604791
$243$	15.5567	+	0.994458i	0.997963	+	0.0637945i
$244$	−3.27341	+	1.88990i	−0.209558	+	0.120989i
$245$	−13.2736	+	21.2899i	−0.848017	+	1.36016i
$246$	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	$-0.788975\pi$
$251$	2.20065	−	3.81164i	0.138904	−	0.240588i	0.927082	+	0.374859i	$0.122309\pi$
$252$	−1.57349	+	7.77972i	−0.0991208	+	0.490077i
$253$	−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	$-0.0786334\pi$
$257$	4.37736	+	7.58182i	0.273052	+	0.472941i	−0.696589	+	0.717470i	$0.745300\pi$
$258$	−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	−0.145151	−	0.989410i	$-0.546367\pi$
$263$	10.3649	−	5.98418i	0.639128	−	0.369000i	0.784278	+	0.620409i	$0.213033\pi$
$264$	1.48278	−	1.60510i	0.0912586	−	0.0987869i
$265$	−43.6293			−2.68013
$266$	1.96855	+	0.563396i	0.120699	+	0.0345441i
$267$	−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	$-0.867498\pi$
$269$	−1.75697	+	3.04316i	−0.107124	+	0.185545i	0.807480	+	0.589895i	$0.200831\pi$
$270$	−18.4335	−	2.65452i	−1.12183	−	0.161549i
$271$	−1.27260	−	2.20420i	−0.0773046	−	0.133896i	0.824782	−	0.565452i	$-0.191298\pi$
$271$	−1.27260	−	2.20420i	−0.0773046	−	0.133896i	−0.902086	+	0.431556i	$0.857965\pi$
$272$	−3.15976			−0.191589
$273$	10.2227	+	12.9806i	0.618704	+	0.785624i
$274$	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	−0.995531	−	0.0944347i	$-0.969896\pi$
$277$	−6.92333	+	11.9916i	−0.415983	+	0.720503i	0.579548	+	0.814938i	$0.303229\pi$
$278$		−	3.37220i		−	0.202251i
$279$	19.0530	−	13.1129i	1.14067	−	0.785047i
$280$	2.60918	−	9.11666i	0.155928	−	0.544824i
$281$	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	$-0.692981\pi$
$283$	−2.40604	+	1.38913i	−0.143024	+	0.0825752i	0.426780	+	0.904355i	$0.359648\pi$
$284$	−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	$-0.374688\pi$
$293$	−3.84106	−	2.21763i	−0.224397	−	0.129556i	−0.607985	+	0.793949i	$0.708022\pi$
$294$	11.6932	−	3.20466i	0.681959	−	0.186899i
$295$	−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
$301$	−0.475688	+	0.459830i	−0.0274182	+	0.0265042i
$302$	−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	$-0.326308\pi$
$307$	18.1869			1.03798			0.518990	+	0.854780i	$0.326308\pi$
$308$	−3.20906	−	0.918431i	−0.182853	−	0.0523325i
$309$	−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	$-0.429838\pi$
$311$	7.71151			0.437279			0.218640	+	0.975806i	$0.429838\pi$
$312$	−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
$315$	9.05770	+	26.9676i	0.510344	+	1.51945i
$316$	−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
$322$	15.4711	+	16.0046i	0.862170	+	0.891903i
$323$	−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
$329$	7.94728	−	27.7683i	0.438148	−	1.53092i
$330$	1.72602	−	7.63934i	0.0950142	−	0.420532i
$331$	−14.2730	−	8.24050i	−0.784513	−	0.452939i	0.0535143	−	0.998567i	$-0.482958\pi$
$331$	−14.2730	−	8.24050i	−0.784513	−	0.452939i	−0.838027	+	0.545628i	$0.816291\pi$
$332$	−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
$336$	−3.91573	+	2.38056i	−0.213621	+	0.129870i
$337$	−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	0.911394	−	0.411536i	$-0.135007\pi$
$347$	18.8271	+	10.8698i	1.01069	+	0.583522i	0.0992964	+	0.995058i	$0.468341\pi$
$348$	12.9150	−	4.01479i	0.692319	−	0.215216i
$349$	13.3083	+	23.0507i	0.712377	+	1.23387i	0.963962	+	0.266038i	$0.0857147\pi$
$349$	13.3083	+	23.0507i	0.712377	+	1.23387i	−0.251585	+	0.967835i	$0.580952\pi$
$350$	−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	$-0.906601\pi$
$353$	−22.2718	+	12.8586i	−1.18541	+	0.684396i	−0.228149	+	0.973626i	$0.573267\pi$
$354$	19.9335	−	6.19657i	1.05946	−	0.329344i
$355$	−0.471583	−	0.272268i	−0.0250290	−	0.0144505i
$356$		−	6.57938i		−	0.348706i
$357$	−12.7006	−	6.95414i	−0.672188	−	0.368052i
$358$	−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
$364$	−1.50000	+	9.42072i	−0.0786213	+	0.493780i
$365$		−	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	$-0.747325\pi$
$367$	−8.31827	+	4.80255i	−0.434210	+	0.250691i	0.266928	+	0.963716i	$0.413991\pi$
$368$	−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
$371$	8.86173	−	30.9635i	0.460078	−	1.60754i
$372$	13.0254	+	2.94293i	0.675335	+	0.152584i
$373$	8.44383	−	14.6251i	0.437205	−	0.757262i	−0.560268	−	0.828312i	$-0.689302\pi$
$373$	8.44383	−	14.6251i	0.437205	−	0.757262i	0.997473	+	0.0710501i	$0.0226350\pi$
$374$	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
$378$	5.62800	−	12.5430i	0.289473	−	0.645140i
$379$	25.2872	−	14.5996i	1.29892	−	0.749930i	0.318700	−	0.947856i	$-0.396754\pi$
$379$	25.2872	−	14.5996i	1.29892	−	0.749930i	0.980217	+	0.197925i	$0.0634203\pi$
$380$	−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	$-0.264124\pi$
$383$	7.31222	+	4.22171i	0.373637	+	0.215719i	−0.301409	+	0.953495i	$0.597457\pi$
$384$	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	$0.00527425\pi$
$389$			0.653576i			0.0331376i	−0.999863	+	0.0165688i	$0.994726\pi$
$390$	−22.2679	−	2.26477i	−1.12758	−	0.114681i
$391$		−	26.5845i		−	1.34443i
$392$	5.94008	+	3.70344i	0.300019	+	0.187052i
$393$	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	$-0.873649\pi$
$397$	−2.51686	+	4.35932i	−0.126317	+	0.218788i	0.795930	+	0.605389i	$0.206982\pi$
$398$		−	10.3588i		−	0.519240i
$399$	−3.11073	−	1.70326i	−0.155731	−	0.0852697i
$400$	3.92295	+	6.79475i	0.196147	+	0.339737i
$401$	−10.4095	−	18.0297i	−0.519824	−	0.900361i	−0.999734	−	0.0230440i	$-0.992664\pi$
$401$	−10.4095	−	18.0297i	−0.519824	−	0.900361i	0.479911	−	0.877317i	$-0.340669\pi$
$402$	−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
$406$	−14.3586	−	14.8538i	−0.712608	−	0.737182i
$407$	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	0.231720	+	0.972783i	$0.425565\pi$
$409$	−14.6945	+	25.4516i	−0.726594	+	1.25850i	−0.958314	+	0.285716i	$0.907769\pi$
$410$	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
$413$	−22.1616	−	22.9259i	−1.09050	−	1.12811i
$414$	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	−0.998156	−	0.0606934i	$-0.980669\pi$
$419$	−11.2918	−	19.5580i	−0.551640	−	0.955469i	0.446516	−	0.894776i	$-0.352665\pi$
$420$	−7.88808	+	14.4063i	−0.384899	+	0.702956i
$421$			28.5241i			1.39018i	0.718922	+	0.695091i	$0.244636\pi$
$421$			28.5241i			1.39018i	−0.718922	+	0.695091i	$0.755364\pi$
$422$	−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
$427$	−6.95050	−	7.19019i	−0.336358	−	0.347958i
$428$			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	0.942399	−	0.334492i	$-0.108565\pi$
$431$	3.76847	+	6.52718i	0.181521	+	0.314403i	−0.760878	+	0.648895i	$0.775231\pi$
$432$	−0.740636	+	5.14310i	−0.0356338	+	0.247447i
$433$	−28.3474	−	16.3664i	−1.36229	−	0.786518i	−0.372361	−	0.928088i	$-0.621452\pi$
$433$	−28.3474	−	16.3664i	−1.36229	−	0.786518i	−0.989928	+	0.141570i	$0.954785\pi$
$434$	−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	$-0.467785\pi$
$439$	21.2278	−	12.2559i	1.01315	−	0.584940i	0.912111	+	0.409943i	$0.134451\pi$
$440$	3.91595	−	2.26088i	0.186686	−	0.107783i
$441$	−20.9785	+	0.950704i	−0.998975	+	0.0452716i
$442$	9.10766	−	6.84424i	0.433207	−	0.325547i
$443$		−	10.7332i		−	0.509951i	−0.966948	−	0.254975i	$-0.917933\pi$
$443$		−	10.7332i		−	0.509951i	0.966948	−	0.254975i	$-0.0820674\pi$
$444$	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
$448$	−2.54363	−	0.727985i	−0.120175	−	0.0343940i
$449$	19.7420	−	34.1941i	0.931683	−	1.61372i	0.151237	−	0.988497i	$-0.451674\pi$
$449$	19.7420	−	34.1941i	0.931683	−	1.61372i	0.780445	−	0.625224i	$-0.214992\pi$
$450$	−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
$455$	12.2266	+	31.9294i	0.573191	+	1.49687i
$456$	1.30750	+	0.295414i	0.0612292	+	0.0138340i
$457$	9.89907	−	5.71523i	0.463059	−	0.267347i	−0.250271	−	0.968176i	$-0.580520\pi$
$457$	9.89907	−	5.71523i	0.463059	−	0.267347i	0.713330	+	0.700829i	$0.247186\pi$
$458$	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	$-0.260580\pi$
$461$	8.42605	+	4.86478i	0.392440	+	0.226576i	−0.290777	+	0.956791i	$0.593914\pi$
$462$	5.07102	+	2.77660i	0.235925	+	0.129179i
$463$		−	26.6572i		−	1.23887i	−0.785050	−	0.619433i	$-0.787363\pi$
$463$		−	26.6572i		−	1.23887i	0.785050	−	0.619433i	$-0.212637\pi$
$464$	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	$-0.544494\pi$
$467$	−6.02179			−0.278655			−0.139328	+	0.990246i	$0.544494\pi$
$468$	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	$-0.601144\pi$
$479$	7.74812	−	4.47338i	0.354021	−	0.204394i	0.666455	+	0.745546i	$0.267811\pi$
$480$	1.36811	−	6.05524i	0.0624454	−	0.276383i
$481$	0.691945	−	1.62414i	0.0315500	−	0.0740545i
$482$	−18.9811			−0.864567
$483$	−20.0287	−	32.9448i	−0.911337	−	1.49904i
$484$	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	0.948942	−	0.315450i	$-0.102155\pi$
$487$	25.3833	+	14.6550i	1.15023	+	0.664083i	0.201284	+	0.979533i	$0.435489\pi$
$488$	3.27341	+	1.88990i	0.148180	+	0.0855518i
$489$	−7.12930	+	31.5542i	−0.322398	+	1.42693i
$490$	25.0744	+	0.850285i	1.13275	+	0.0384120i
$491$	5.50320	−	3.17727i	0.248356	−	0.143388i	−0.370655	−	0.928770i	$-0.620867\pi$
$491$	5.50320	−	3.17727i	0.248356	−	0.143388i	0.619011	+	0.785382i	$0.287534\pi$
$492$	−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
$497$	0.289012	−	0.279378i	0.0129640	−	0.0125318i
$498$	4.11620	+	3.80252i	0.184451	+	0.170395i
$499$		−	5.92485i		−	0.265233i	−0.991167	−	0.132616i	$-0.957662\pi$
$499$		−	5.92485i		−	0.265233i	0.991167	−	0.132616i	$-0.0423378\pi$
$500$	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	−0.0177557	+	0.999842i	$0.505652\pi$
$503$	−19.6190	+	33.9811i	−0.874767	+	1.51514i	−0.857011	+	0.515298i	$0.827681\pi$
$504$	7.52419	−	2.52718i	0.335154	−	0.112569i
$505$	−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	$-0.595001\pi$
$509$	8.72379	−	5.03668i	0.386675	−	0.223247i	0.680718	+	0.732545i	$0.261668\pi$
$510$	18.7312	−	5.82282i	0.829432	−	0.257839i
$511$	26.3538	+	7.54244i	1.16582	+	0.333658i
$512$	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
$518$	−0.900363	−	0.931413i	−0.0395597	−	0.0409239i
$519$	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	$-0.413377\pi$
$521$	12.2704			0.537578			0.268789	+	0.963199i	$0.413377\pi$
$522$	−23.3520	+	1.85300i	−1.02209	+	0.0811034i
$523$	−12.6762	+	7.31862i	−0.554292	+	0.320021i	−0.750851	−	0.660471i	$-0.770357\pi$
$523$	−12.6762	+	7.31862i	−0.554292	+	0.320021i	0.196559	+	0.980492i	$0.437023\pi$
$524$	−6.80645	+	11.7891i	−0.297341	+	0.515010i
$525$	0.814066	+	35.9452i	0.0355288	+	1.56878i
$526$	−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
$539$	0.299300	−	8.82618i	0.0128918	−	0.380171i
$540$	6.91785	+	17.2911i	0.297697	+	0.744091i
$541$			34.8104i			1.49661i	0.663352	+	0.748307i	$0.269133\pi$
$541$			34.8104i			1.49661i	−0.663352	+	0.748307i	$0.730867\pi$
$542$	−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
$546$	6.13022	−	15.3434i	0.262349	−	0.656638i
$547$	−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
$553$	−14.0876	−	4.03187i	−0.599066	−	0.171452i
$554$	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	0.969891	−	0.243541i	$-0.0783091\pi$
$557$	6.46740	+	11.2019i	0.274032	+	0.474638i	−0.695858	+	0.718179i	$0.744976\pi$
$558$	−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	$-0.802020\pi$
$563$	2.33044	−	4.03644i	0.0982162	−	0.170115i	0.910946	+	0.412525i	$0.135353\pi$
$564$	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
$567$	−14.2961	+	19.0426i	−0.600381	+	0.799714i
$568$	−0.0759653	+	0.131576i	−0.00318743	+	0.00552080i
$569$	13.1884	−	7.61435i	0.552888	−	0.319210i	−0.197398	−	0.980323i	$-0.563249\pi$
$569$	13.1884	−	7.61435i	0.552888	−	0.319210i	0.750286	+	0.661113i	$0.229916\pi$
$570$	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
$574$	2.48733	+	2.57311i	0.103819	+	0.107399i
$575$	−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	$-0.438597\pi$
$577$	9.20999			0.383417			0.191709	+	0.981452i	$0.438597\pi$
$578$	3.50796	−	6.07596i	0.145912	−	0.252727i
$579$	−9.92685	−	9.17035i	−0.412546	−	0.381107i
$580$	27.9865			1.16208
$581$	2.35528	−	8.22949i	0.0977133	−	0.341417i
$582$	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	$-0.686945\pi$
$587$	−2.67162	+	1.54246i	−0.110270	+	0.0636642i	0.443851	+	0.896101i	$0.353612\pi$
$588$	−8.62190	−	8.52425i	−0.355561	−	0.351534i
$589$	−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
$595$	−20.8249	−	21.5431i	−0.853739	−	0.883180i
$596$	−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	$0.0930414\pi$
$599$			14.1048i			0.576307i	−0.957584	+	0.288154i	$0.906959\pi$
$600$	−4.03403	−	12.9769i	−0.164689	−	0.529781i
$601$	−18.7865	+	10.8464i	−0.766319	+	0.442435i	−0.831560	−	0.555435i	$-0.812552\pi$
$601$	−18.7865	+	10.8464i	−0.766319	+	0.442435i	0.0652409	+	0.997870i	$0.479218\pi$
$602$	0.636069	+	0.182042i	0.0259242	+	0.00741950i
$603$	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	$-0.199390\pi$
$607$	17.4314	+	10.0640i	0.707518	+	0.408486i	−0.102623	+	0.994720i	$0.532724\pi$
$608$	0.386956	+	0.670228i	0.0156932	+	0.0271813i
$609$	18.5885	+	30.5759i	0.753245	+	1.23900i
$610$	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	0.104184	−	0.994558i	$-0.466777\pi$
$613$	25.1943	−	14.5459i	1.01759	−	0.587505i	0.913404	+	0.407053i	$0.133444\pi$
$614$	−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	−0.506678	−	0.862135i	$-0.669127\pi$
$617$	12.2531	−	21.2230i	0.493292	−	0.854407i	0.999970	+	0.00772817i	$0.00245998\pi$
$618$	19.9524	+	18.4319i	0.802604	+	0.741440i
$619$	−36.1887			−1.45455			−0.727273	−	0.686349i	$-0.759212\pi$
$619$	−36.1887			−1.45455			−0.727273	+	0.686349i	$0.759212\pi$
$620$	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
$630$	18.8257	−	21.3280i	0.750036	−	0.849727i
$631$	10.9062	+	6.29670i	0.434169	+	0.250668i	0.701121	−	0.713042i	$-0.252683\pi$
$631$	10.9062	+	6.29670i	0.434169	+	0.250668i	−0.266952	+	0.963710i	$0.586017\pi$
$632$	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
$637$	−25.1435	+	2.19182i	−0.996222	+	0.0868432i
$638$		−	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	0.365847	−	0.930675i	$-0.380779\pi$
$641$	−6.51225	−	3.75985i	−0.257218	−	0.148505i	−0.623065	+	0.782170i	$0.714113\pi$
$642$	1.87530	−	8.30006i	0.0740121	−	0.327577i
$643$	4.12995	−	7.15328i	0.162869	−	0.282098i	−0.773027	−	0.634373i	$-0.781258\pi$
$643$	4.12995	−	7.15328i	0.162869	−	0.282098i	0.935897	+	0.352275i	$0.114592\pi$
$644$	6.12486	−	21.4007i	0.241353	−	0.843305i
$645$	−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	−0.995445	−	0.0953335i	$-0.969608\pi$
$647$	−14.7602	−	25.5654i	−0.580284	−	1.00508i	0.415161	−	0.909748i	$-0.363725\pi$
$648$	3.21447	−	8.40638i	0.126276	−	0.330234i
$649$		−	15.2047i		−	0.596838i
$650$	−26.0253	−	11.0877i	−1.02080	−	0.434897i
$651$	0.799942	+	35.3215i	0.0313522	+	1.38436i
$652$	−16.1748	+	9.33852i	−0.633454	+	0.365725i
$653$	−4.09902	+	2.36657i	−0.160407	+	0.0926111i	−0.578055	−	0.815998i	$-0.696188\pi$
$653$	−4.09902	+	2.36657i	−0.160407	+	0.0926111i	0.417648	+	0.908609i	$0.362855\pi$
$654$	−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	−0.461385	−	0.887200i	$-0.652647\pi$
$659$	−37.4903	−	21.6450i	−1.46042	−	0.843171i	−0.999030	+	0.0440285i	$0.985981\pi$
$660$	−7.47887	+	2.32490i	−0.291115	+	0.0904964i
$661$	−18.6135	−	32.2396i	−0.723982	−	1.25397i	−0.959392	−	0.282078i	$-0.908976\pi$
$661$	−18.6135	−	32.2396i	−0.723982	−	1.25397i	0.235409	−	0.971896i	$-0.424357\pi$
$662$			16.4810i			0.640552i
$663$	−17.9996	+	8.08659i	−0.699047	+	0.314057i
$664$			3.23534i			0.125555i
$665$	−5.10060	−	5.27650i	−0.197793	−	0.204614i
$666$	−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
$672$	4.01949	+	2.20084i	0.155055	+	0.0848994i
$673$	9.00579	+	15.5985i	0.347148	+	0.601277i	0.985742	−	0.168267i	$-0.0538170\pi$
$673$	9.00579	+	15.5985i	0.347148	+	0.601277i	−0.638594	+	0.769544i	$0.720484\pi$
$674$	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	$-0.812222\pi$
$677$	−43.2431			−1.66197			−0.830984	+	0.556296i	$0.812222\pi$
$678$	−26.2486	+	8.15969i	−1.00807	+	0.313371i
$679$	8.42325	−	8.14245i	0.323255	−	0.312479i
$680$	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	−0.619366	−	0.785103i	$-0.712610\pi$
$683$	9.67584	−	16.7591i	0.370236	−	0.641267i	0.989602	+	0.143835i	$0.0459435\pi$
$684$	−2.09621	−	0.998183i	−0.0801506	−	0.0381665i
$685$	−6.86832	−	3.96543i	−0.262425	−	0.151511i
$686$	−5.69641	+	17.6225i	−0.217490	+	0.672828i
$687$	−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	$-0.158871\pi$
$691$	0.643698	+	1.11492i	0.0244874	+	0.0424135i	−0.853522	+	0.521057i	$0.825538\pi$
$692$	7.02069	+	12.1602i	0.266887	+	0.462261i
$693$	−7.50744	−	6.62666i	−0.285184	−	0.251726i
$694$		−	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
$700$	−14.9250	+	14.4275i	−0.564112	+	0.545306i
$701$			9.09155i			0.343383i	0.985151	+	0.171692i	$0.0549232\pi$
$701$			9.09155i			0.343383i	−0.985151	+	0.171692i	$0.945077\pi$
$702$	−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	−0.244475	−	0.969655i	$-0.578616\pi$
$709$	−32.1245	−	18.5471i	−1.20646	−	0.696550i	−0.961984	+	0.273106i	$0.911949\pi$
$710$			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
$714$	0.327847	+	14.4761i	0.0122694	+	0.541755i
$715$	−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	−0.249325	−	0.968420i	$-0.580209\pi$
$719$	19.1457	−	33.1613i	0.714013	−	1.23671i	0.963339	−	0.268288i	$-0.0864578\pi$
$720$	−4.62275	+	9.70790i	−0.172280	+	0.361792i
$721$	11.4167	−	39.8907i	0.425180	−	1.48561i
$722$	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	$0.770280\pi$
$728$	8.90858	−	3.41132i	0.330174	−	0.126432i
$729$	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	$-0.551774\pi$
$733$	−8.76856			−0.323874			−0.161937	+	0.986801i	$0.551774\pi$
$734$	8.31827	+	4.80255i	0.307033	+	0.177266i
$735$	−42.0378	−	11.0078i	−1.55059	−	0.406029i
$736$			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	−0.592646	−	0.805463i	$-0.701917\pi$
$739$	−5.20359	+	3.00429i	−0.191417	+	0.110515i	0.401229	+	0.915978i	$0.368583\pi$
$740$	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	0.888353	+	0.459160i	$0.151850\pi$
$743$	22.9464	+	39.7443i	0.841821	+	1.45808i	−0.0465322	+	0.998917i	$0.514817\pi$
$744$	−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	−0.922949	−	0.384921i	$-0.874229\pi$
$751$	−21.7817	−	37.7271i	−0.794826	−	1.37668i	0.128123	−	0.991758i	$-0.459105\pi$
$752$	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
$756$	−13.6765	+	1.39749i	−0.497410	+	0.0508261i
$757$	1.39668	+	2.41912i	0.0507632	+	0.0879244i	0.890290	−	0.455393i	$-0.150501\pi$
$757$	1.39668	+	2.41912i	0.0507632	+	0.0879244i	−0.839527	+	0.543318i	$0.817168\pi$
$758$	−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	0.961778	+	0.273829i	$0.0882902\pi$
$761$	46.3396	+	26.7542i	1.67981	+	0.969839i	0.718032	+	0.696010i	$0.245043\pi$
$762$	−18.2844	−	4.13114i	−0.662373	−	0.149655i
$763$	−4.36178	+	15.2403i	−0.157907	+	0.551737i
$764$	−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	$-0.235077\pi$
$769$	−5.91403	−	10.2434i	−0.213265	−	0.369386i	−0.952735	+	0.303804i	$0.901743\pi$
$770$	8.31484	+	8.60158i	0.299646	+	0.309979i
$771$	−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	$-0.138038\pi$
$773$	27.7265	+	16.0079i	0.997251	+	0.575763i	0.0898175	+	0.995958i	$0.471372\pi$
$774$	0.617978	−	0.425311i	0.0222128	−	0.0152875i
$775$	60.4900			2.17287
$776$	−2.21400	+	3.83477i	−0.0794781	+	0.137660i
$777$	1.16560	+	1.91727i	0.0418156	+	0.0687817i
$778$	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
$784$	0.237237	−	6.99598i	0.00847275	−	0.249856i
$785$	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	$-0.911073\pi$
$787$	−6.78351	+	11.7494i	−0.241806	+	0.418820i	0.719423	+	0.694573i	$0.244406\pi$
$788$	−17.8228			−0.634911
$789$	15.2269	+	14.0665i	0.542092	+	0.500781i
$790$	17.1908	−	9.92513i	0.611622	−	0.353120i
$791$	29.1826	+	30.1890i	1.03761	+	1.07340i
$792$	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	0.441089	+	0.897463i	$0.354592\pi$
$797$	−15.7158	+	27.2205i	−0.556682	+	0.964201i	−0.997771	+	0.0667377i	$0.978741\pi$
$798$	0.0802988	+	3.54560i	0.00284255	+	0.125513i
$799$	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	−0.161750	−	0.986832i	$-0.551714\pi$
$809$	17.4070	−	10.0499i	0.611996	−	0.353336i	0.773746	+	0.633496i	$0.218381\pi$
$810$	−5.08720	−	31.8534i	−0.178746	−	1.11921i
$811$	33.5036			1.17647			0.588236	−	0.808689i	$-0.299823\pi$
$811$	33.5036			1.17647			0.588236	+	0.808689i	$0.299823\pi$
$812$	−5.68445	+	19.8619i	−0.199485	+	0.697014i
$813$	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
$819$	−16.2136	+	23.5822i	−0.566549	+	0.824028i
$820$	−4.84807			−0.169302
$821$	7.45863	+	12.9187i	0.260308	+	0.450867i	0.966324	−	0.257329i	$-0.0828425\pi$
$821$	7.45863	+	12.9187i	0.260308	+	0.450867i	−0.706016	+	0.708196i	$0.749509\pi$
$822$	1.13772	+	3.65988i	0.0396825	+	0.127653i
$823$	−4.82700	+	8.36061i	−0.168259	+	0.291433i	−0.937808	−	0.347155i	$-0.887148\pi$
$823$	−4.82700	+	8.36061i	−0.168259	+	0.291433i	0.769549	+	0.638588i	$0.220481\pi$
$824$			15.6826i			0.546330i
$825$	−11.6337	+	12.5934i	−0.405034	+	0.438447i
$826$	−8.77358	+	30.6555i	−0.305272	+	1.06664i
$827$	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	$-0.736327\pi$
$829$	−10.8268	+	6.25083i	−0.376029	+	0.217100i	0.300060	+	0.953920i	$0.402993\pi$
$830$	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	$-0.423431\pi$
$839$	−14.0117	−	8.08964i	−0.483736	−	0.279285i	−0.721972	+	0.691922i	$0.756764\pi$
$840$	16.4203	−	0.371877i	0.566553	−	0.0128310i
$841$	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
$847$	−17.8972	+	17.3006i	−0.614954	+	0.594455i
$848$	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	$-0.342716\pi$
$853$	27.7026			0.948520			0.474260	+	0.880385i	$0.342716\pi$
$854$	−2.75164	+	9.61441i	−0.0941591	+	0.328998i
$855$	−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	$-0.427196\pi$
$857$	13.2750			0.453464			0.226732	+	0.973957i	$0.427196\pi$
$858$	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
$861$	−3.22007	−	5.29663i	−0.109740	−	0.180509i
$862$	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
$868$	−14.6660	+	14.1771i	−0.497797	+	0.481203i
$869$	−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
$875$	−7.42546	+	25.9451i	−0.251026	+	0.877103i
$876$	17.5041	+	3.95484i	0.591408	+	0.133622i
$877$	−39.8280	−	22.9947i	−1.34489	−	0.776475i	−0.357374	−	0.933962i	$-0.616328\pi$
$877$	−39.8280	−	22.9947i	−1.34489	−	0.776475i	−0.987521	+	0.157486i	$0.949661\pi$
$878$	−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	0.986782	+	0.162056i	$0.0518124\pi$
$881$	18.8103	+	32.5804i	0.633735	+	1.09766i	−0.353046	+	0.935606i	$0.614854\pi$
$882$	11.3126	+	17.6925i	0.380914	+	0.595739i
$883$	−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	$-0.252481\pi$
$887$	−7.93228	−	13.7391i	−0.266340	−	0.461314i	−0.967914	+	0.251282i	$0.919148\pi$
$888$	−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
$903$	−1.00513	−	0.550351i	−0.0334486	−	0.0183145i
$904$	−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	0.798633	−	0.601819i	$-0.205557\pi$
$907$	−3.67040	−	6.35732i	−0.121874	−	0.211091i	−0.920507	+	0.390727i	$0.872224\pi$
$908$	19.5736	−	11.3008i	0.649571	−	0.375030i
$909$	−2.65710	−	1.26527i	−0.0881304	−	0.0419663i
$910$	21.5384	−	26.5532i	0.713991	−	0.880231i
$911$			4.10735i			0.136082i	0.997683	+	0.0680412i	$0.0216749\pi$
$911$			4.10735i			0.136082i	−0.997683	+	0.0680412i	$0.978325\pi$
$912$	−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
$917$	−34.6261	−	9.90998i	−1.14346	−	0.327256i
$918$	12.9036	+	10.1522i	0.425883	+	0.335072i
$919$	−19.1541	+	33.1759i	−0.631835	+	1.09437i	0.355341	+	0.934737i	$0.384365\pi$
$919$	−19.1541	+	33.1759i	−0.631835	+	1.09437i	−0.987176	+	0.159634i	$0.948969\pi$
$920$	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
$924$	−0.130901	−	5.77993i	−0.00430631	−	0.190146i
$925$	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	$-0.475853\pi$
$929$	−22.8552	−	13.1955i	−0.749856	−	0.432930i	−0.825642	+	0.564195i	$0.809187\pi$
$930$	−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	$-0.337709\pi$
$938$	−22.2871	−	23.0557i	−0.727699	−	0.752794i
$939$	−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
$945$	−39.9467	+	28.8468i	−1.29946	+	0.938387i
$946$	0.157741	+	0.273216i	0.00512861	+	0.00888301i
$947$	4.57740	+	7.92829i	0.148746	+	0.257635i	0.930764	−	0.365620i	$-0.119143\pi$
$947$	4.57740	+	7.92829i	0.148746	+	0.257635i	−0.782019	+	0.623255i	$0.785810\pi$
$948$	−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
$952$	−6.01071	+	5.81033i	−0.194808	+	0.188314i
$953$	44.8045	+	25.8679i	1.45136	+	0.837943i	0.998559	−	0.0536692i	$-0.0170916\pi$
$953$	44.8045	+	25.8679i	1.45136	+	0.837943i	0.452801	+	0.891612i	$0.350425\pi$
$954$	−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
$959$	4.20929	−	4.06897i	0.135925	−	0.131394i
$960$	−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
$966$	−18.5167	+	33.8177i	−0.595765	+	1.08807i
$967$		−	0.447825i		−	0.0144011i	−0.999974	−	0.00720054i	$-0.997708\pi$
$967$		−	0.447825i		−	0.0144011i	0.999974	−	0.00720054i	$-0.00229202\pi$
$968$	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	0.362025	+	0.932169i	$0.382086\pi$
$971$	−19.5151	+	33.8011i	−0.626269	+	1.08473i	−0.988294	+	0.152562i	$0.951248\pi$
$972$	−8.63958	+	12.9753i	−0.277115	+	0.416182i
$973$	−6.20098	−	6.41482i	−0.198794	−	0.205650i
$974$		−	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	0.957899	−	0.287104i	$-0.0926926\pi$
$977$	7.19880	+	12.4687i	0.230310	+	0.398909i	−0.727589	+	0.686013i	$0.759359\pi$
$978$	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
$987$	50.0144	−	1.13270i	1.59198	−	0.0360541i
$988$	−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	0.926102	−	0.377274i	$-0.123139\pi$
$991$	4.29142	+	7.43296i	0.136322	+	0.236116i	−0.789780	+	0.613390i	$0.789805\pi$
$992$	3.85488	−	6.67685i	0.122393	−	0.211990i
$993$	6.29104	−	27.8441i	0.199640	−	0.883605i
$994$	−0.386455	−	0.110603i	−0.0122576	−	0.00350812i
$995$	−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	$-0.639312\pi$
$997$	−44.8411	−	25.8890i	−1.42013	−	0.819914i	−0.996310	+	0.0858304i	$0.972646\pi$
$998$	−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.335.9	yes	24
3.2	odd	2		546.2.q.j.335.4	yes	24
7.6	odd	2	inner	546.2.q.i.335.4	yes	24
13.4	even	6		546.2.q.j.251.9	yes	24
21.20	even	2		546.2.q.j.335.9	yes	24
39.17	odd	6	inner	546.2.q.i.251.4	✓	24
91.69	odd	6		546.2.q.j.251.4	yes	24
273.251	even	6	inner	546.2.q.i.251.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.4	✓	24	39.17	odd	6	inner
546.2.q.i.251.9	yes	24	273.251	even	6	inner
546.2.q.i.335.4	yes	24	7.6	odd	2	inner
546.2.q.i.335.9	yes	24	1.1	even	1	trivial
546.2.q.j.251.4	yes	24	91.69	odd	6
546.2.q.j.251.9	yes	24	13.4	even	6
546.2.q.j.335.4	yes	24	3.2	odd	2
546.2.q.j.335.9	yes	24	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.514158 + 1.65398i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.58412i q^{5} +(1.17531 - 1.27226i) q^{6} +(-2.54363 - 0.727985i) q^{7} +1.00000 q^{8} +(-2.47128 + 1.70081i) q^{9} +O(q^{10})\)	\(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} +(-2.54363 - 0.727985i) 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} +(-0.103757 - 4.58140i) 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} +(1.90227 - 1.83885i) 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} +(2.60918 - 9.11666i) 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} +(-3.91573 + 2.38056i) 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} +(5.94008 + 3.70344i) 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} +(-2.54363 - 0.727985i) 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} +(7.52419 - 2.52718i) 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} +(4.01949 + 2.20084i) 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} +(8.90858 - 3.41132i) 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} +(0.237237 - 6.99598i) 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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