LMFDB - Embedded newform 546.2.u.a.425.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (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:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.2
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.59603 - 0.672816i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.07511 - 1.86215i) q^{5} +(1.71861 - 0.215340i) q^{6} +(0.447408 - 2.60765i) q^{7} +1.00000i q^{8} +(2.09464 + 2.14767i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.59603 - 0.672816i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.07511 - 1.86215i) q^{5} +(1.71861 - 0.215340i) q^{6} +(0.447408 - 2.60765i) q^{7} +1.00000i q^{8} +(2.09464 + 2.14767i) q^{9} +2.15023i q^{10} +0.832434i q^{11} +(-1.38069 + 1.04580i) q^{12} +(1.46072 - 3.29641i) q^{13} +(0.916357 + 2.48199i) q^{14} +(-2.96880 + 2.24870i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.36171 - 2.35856i) q^{17} +(-2.88784 - 0.812620i) q^{18} +2.56816i q^{19} +(-1.07511 - 1.86215i) q^{20} +(-2.46855 + 3.86087i) q^{21} +(-0.416217 - 0.720909i) q^{22} +(-2.15206 + 1.24249i) q^{23} +(0.672816 - 1.59603i) q^{24} +(0.188263 + 0.326081i) q^{25} +(0.383182 + 3.58513i) q^{26} +(-1.89812 - 4.83706i) q^{27} +(-2.03458 - 1.69129i) q^{28} +(-7.62813 - 4.40410i) q^{29} +(1.44671 - 3.43183i) q^{30} +(-2.06419 + 1.19176i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.560075 - 1.32859i) q^{33} +2.72343i q^{34} +(-4.37482 - 3.63666i) q^{35} +(2.90726 - 0.740172i) q^{36} +(0.0899619 + 0.155819i) q^{37} +(-1.28408 - 2.22409i) q^{38} +(-4.54923 + 4.27837i) q^{39} +(1.86215 + 1.07511i) q^{40} +(5.93979 - 10.2880i) q^{41} +(0.207390 - 4.57788i) q^{42} +(-3.89154 - 6.74035i) q^{43} +(0.720909 + 0.416217i) q^{44} +(6.25126 - 1.59154i) q^{45} +(1.24249 - 2.15206i) q^{46} +(0.425408 - 0.736829i) q^{47} +(0.215340 + 1.71861i) q^{48} +(-6.59965 - 2.33337i) q^{49} +(-0.326081 - 0.188263i) q^{50} +(-3.76022 + 2.84815i) q^{51} +(-2.12441 - 2.91322i) q^{52} +(10.3882 - 5.99761i) q^{53} +(4.06235 + 3.23996i) q^{54} +(1.55012 + 0.894961i) q^{55} +(2.60765 + 0.447408i) q^{56} +(1.72790 - 4.09887i) q^{57} +8.80820 q^{58} +(1.26178 - 2.18546i) q^{59} +(0.463030 + 3.69541i) q^{60} +3.65506i q^{61} +(1.19176 - 2.06419i) q^{62} +(6.53753 - 4.50119i) q^{63} -1.00000 q^{64} +(-4.56797 - 6.26409i) q^{65} +(0.179257 + 1.43063i) q^{66} -6.61431 q^{67} +(-1.36171 - 2.35856i) q^{68} +(4.27073 - 0.535117i) q^{69} +(5.60703 + 0.962029i) q^{70} +(-7.48494 + 4.32143i) q^{71} +(-2.14767 + 2.09464i) q^{72} +(-10.9421 + 6.31743i) q^{73} +(-0.155819 - 0.0899619i) q^{74} +(-0.0810812 - 0.647102i) q^{75} +(2.22409 + 1.28408i) q^{76} +(2.17070 + 0.372438i) q^{77} +(1.80056 - 5.97980i) q^{78} +(-3.10814 + 5.38345i) q^{79} -2.15023 q^{80} +(-0.224993 + 8.99719i) q^{81} +11.8796i q^{82} -0.930821 q^{83} +(2.10933 + 4.06826i) q^{84} +(-2.92799 - 5.07144i) q^{85} +(6.74035 + 3.89154i) q^{86} +(9.21158 + 12.1614i) q^{87} -0.832434 q^{88} +(0.572948 + 0.992375i) q^{89} +(-4.61798 + 4.50394i) q^{90} +(-7.94233 - 5.28388i) q^{91} +2.48498i q^{92} +(4.09635 - 0.513268i) q^{93} +0.850817i q^{94} +(4.78231 + 2.76107i) q^{95} +(-1.04580 - 1.38069i) q^{96} +(7.08918 - 4.09294i) q^{97} +(6.88215 - 1.27907i) q^{98} +(-1.78780 + 1.74365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.59603	−	0.672816i	−0.921470	−	0.388451i
$3$	−1.59603	−	0.672816i	−0.921470	−	0.388451i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.07511	−	1.86215i	0.480805	−	0.832779i	−0.518952	−	0.854803i	$-0.673678\pi$
$5$	1.07511	−	1.86215i	0.480805	−	0.832779i	0.999757	+	0.0220241i	$0.00701107\pi$
$6$	1.71861	−	0.215340i	0.701621	−	0.0879122i
$7$	0.447408	−	2.60765i	0.169104	−	0.985598i
$7$	0.447408	−	2.60765i	0.169104	−	0.985598i
$8$			1.00000i			0.353553i
$9$	2.09464	+	2.14767i	0.698212	+	0.715891i
$10$			2.15023i			0.679961i
$11$			0.832434i			0.250988i	0.992094	+	0.125494i	$0.0400516\pi$
$11$			0.832434i			0.250988i	−0.992094	+	0.125494i	$0.959948\pi$
$12$	−1.38069	+	1.04580i	−0.398571	+	0.301895i
$13$	1.46072	−	3.29641i	0.405131	−	0.914259i
$13$	1.46072	−	3.29641i	0.405131	−	0.914259i
$14$	0.916357	+	2.48199i	0.244907	+	0.663341i
$15$	−2.96880	+	2.24870i	−0.766541	+	0.580612i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.36171	−	2.35856i	0.330264	−	0.572035i	−0.652299	−	0.757962i	$-0.726195\pi$
$17$	1.36171	−	2.35856i	0.330264	−	0.572035i	0.982564	+	0.185927i	$0.0595288\pi$
$18$	−2.88784	−	0.812620i	−0.680672	−	0.191536i
$19$			2.56816i			0.589177i	0.955624	+	0.294589i	$0.0951826\pi$
$19$			2.56816i			0.589177i	−0.955624	+	0.294589i	$0.904817\pi$
$20$	−1.07511	−	1.86215i	−0.240403	−	0.416390i
$21$	−2.46855	+	3.86087i	−0.538681	+	0.842510i
$22$	−0.416217	−	0.720909i	−0.0887378	−	0.153698i
$23$	−2.15206	+	1.24249i	−0.448736	+	0.259078i	−0.707296	−	0.706917i	$-0.750085\pi$
$23$	−2.15206	+	1.24249i	−0.448736	+	0.259078i	0.258560	+	0.965995i	$0.416752\pi$
$24$	0.672816	−	1.59603i	0.137338	−	0.325789i
$25$	0.188263	+	0.326081i	0.0376526	+	0.0652162i
$26$	0.383182	+	3.58513i	0.0751482	+	0.703102i
$27$	−1.89812	−	4.83706i	−0.365293	−	0.930893i
$28$	−2.03458	−	1.69129i	−0.384500	−	0.319624i
$29$	−7.62813	−	4.40410i	−1.41651	−	0.817821i	−0.420517	−	0.907285i	$-0.638151\pi$
$29$	−7.62813	−	4.40410i	−1.41651	−	0.817821i	−0.995990	+	0.0894637i	$0.971485\pi$
$30$	1.44671	−	3.43183i	0.264131	−	0.626564i
$31$	−2.06419	+	1.19176i	−0.370740	+	0.214047i	−0.673782	−	0.738931i	$-0.735331\pi$
$31$	−2.06419	+	1.19176i	−0.370740	+	0.214047i	0.303042	+	0.952977i	$0.401998\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.560075	−	1.32859i	0.0974966	−	0.231278i
$34$			2.72343i			0.467064i
$35$	−4.37482	−	3.63666i	−0.739479	−	0.614707i
$36$	2.90726	−	0.740172i	0.484543	−	0.123362i
$37$	0.0899619	+	0.155819i	0.0147896	+	0.0256164i	0.873326	−	0.487137i	$-0.161959\pi$
$37$	0.0899619	+	0.155819i	0.0147896	+	0.0256164i	−0.858536	+	0.512754i	$0.828625\pi$
$38$	−1.28408	−	2.22409i	−0.208306	−	0.360796i
$39$	−4.54923	+	4.27837i	−0.728460	+	0.685088i
$40$	1.86215	+	1.07511i	0.294432	+	0.169990i
$41$	5.93979	−	10.2880i	0.927640	−	1.60672i	0.140381	−	0.990098i	$-0.455167\pi$
$41$	5.93979	−	10.2880i	0.927640	−	1.60672i	0.787259	−	0.616622i	$-0.211499\pi$
$42$	0.207390	−	4.57788i	0.0320010	−	0.706382i
$43$	−3.89154	−	6.74035i	−0.593454	−	1.02789i	−0.993763	−	0.111513i	$-0.964430\pi$
$43$	−3.89154	−	6.74035i	−0.593454	−	1.02789i	0.400309	−	0.916380i	$-0.368903\pi$
$44$	0.720909	+	0.416217i	0.108681	+	0.0627471i
$45$	6.25126	−	1.59154i	0.931883	−	0.237253i
$46$	1.24249	−	2.15206i	0.183196	−	0.317304i
$47$	0.425408	−	0.736829i	0.0620522	−	0.107478i	−0.833330	−	0.552775i	$-0.813569\pi$
$47$	0.425408	−	0.736829i	0.0620522	−	0.107478i	0.895383	+	0.445298i	$0.146902\pi$
$48$	0.215340	+	1.71861i	0.0310817	+	0.248060i
$49$	−6.59965	−	2.33337i	−0.942807	−	0.333338i
$50$	−0.326081	−	0.188263i	−0.0461148	−	0.0266244i
$51$	−3.76022	+	2.84815i	−0.526536	+	0.398821i
$52$	−2.12441	−	2.91322i	−0.294603	−	0.403992i
$53$	10.3882	−	5.99761i	1.42692	−	0.823835i	0.430047	−	0.902807i	$-0.358497\pi$
$53$	10.3882	−	5.99761i	1.42692	−	0.823835i	0.996877	+	0.0789721i	$0.0251638\pi$
$54$	4.06235	+	3.23996i	0.552816	+	0.440902i
$55$	1.55012	+	0.894961i	0.209018	+	0.120677i
$56$	2.60765	+	0.447408i	0.348462	+	0.0597875i
$57$	1.72790	−	4.09887i	0.228866	−	0.542909i
$58$	8.80820			1.15657
$59$	1.26178	−	2.18546i	0.164270	−	0.284523i	−0.772126	−	0.635469i	$-0.780807\pi$
$59$	1.26178	−	2.18546i	0.164270	−	0.284523i	0.936396	+	0.350946i	$0.114140\pi$
$60$	0.463030	+	3.69541i	0.0597769	+	0.477075i
$61$			3.65506i			0.467983i	0.972239	+	0.233991i	$0.0751788\pi$
$61$			3.65506i			0.467983i	−0.972239	+	0.233991i	$0.924821\pi$
$62$	1.19176	−	2.06419i	0.151354	−	0.262153i
$63$	6.53753	−	4.50119i	0.823651	−	0.567096i
$64$	−1.00000			−0.125000
$65$	−4.56797	−	6.26409i	−0.566586	−	0.776965i
$66$	0.179257	+	1.43063i	0.0220650	+	0.176099i
$67$	−6.61431			−0.808067			−0.404033	−	0.914744i	$-0.632392\pi$
$67$	−6.61431			−0.808067			−0.404033	+	0.914744i	$0.632392\pi$
$68$	−1.36171	−	2.35856i	−0.165132	−	0.286017i
$69$	4.27073	−	0.535117i	0.514135	−	0.0644205i
$70$	5.60703	+	0.962029i	0.670169	+	0.114985i
$71$	−7.48494	+	4.32143i	−0.888299	+	0.512859i	−0.873386	−	0.487029i	$-0.838080\pi$
$71$	−7.48494	+	4.32143i	−0.888299	+	0.512859i	−0.0149130	+	0.999889i	$0.504747\pi$
$72$	−2.14767	+	2.09464i	−0.253106	+	0.246855i
$73$	−10.9421	+	6.31743i	−1.28068	+	0.739399i	−0.976972	−	0.213367i	$-0.931557\pi$
$73$	−10.9421	+	6.31743i	−1.28068	+	0.739399i	−0.303704	+	0.952766i	$0.598224\pi$
$74$	−0.155819	−	0.0899619i	−0.0181135	−	0.0104579i
$75$	−0.0810812	−	0.647102i	−0.00936245	−	0.0747209i
$76$	2.22409	+	1.28408i	0.255121	+	0.147294i
$77$	2.17070	+	0.372438i	0.247374	+	0.0424433i
$78$	1.80056	−	5.97980i	0.203874	−	0.677079i
$79$	−3.10814	+	5.38345i	−0.349693	+	0.605686i	−0.986195	−	0.165589i	$-0.947047\pi$
$79$	−3.10814	+	5.38345i	−0.349693	+	0.605686i	0.636502	+	0.771275i	$0.280381\pi$
$80$	−2.15023			−0.240403
$81$	−0.224993	+	8.99719i	−0.0249993	+	0.999687i
$82$			11.8796i			1.31188i
$83$	−0.930821			−0.102171			−0.0510854	−	0.998694i	$-0.516268\pi$
$83$	−0.930821			−0.102171			−0.0510854	+	0.998694i	$0.516268\pi$
$84$	2.10933	+	4.06826i	0.230147	+	0.443883i
$85$	−2.92799	−	5.07144i	−0.317586	−	0.550074i
$86$	6.74035	+	3.89154i	0.726830	+	0.419636i
$87$	9.21158	+	12.1614i	0.987585	+	1.30384i
$88$	−0.832434			−0.0887378
$89$	0.572948	+	0.992375i	0.0607324	+	0.105192i	0.894793	−	0.446481i	$-0.147323\pi$
$89$	0.572948	+	0.992375i	0.0607324	+	0.105192i	−0.834061	+	0.551673i	$0.813990\pi$
$90$	−4.61798	+	4.50394i	−0.486778	+	0.474757i
$91$	−7.94233	−	5.28388i	−0.832582	−	0.553902i
$92$			2.48498i			0.259078i
$93$	4.09635	−	0.513268i	0.424772	−	0.0532234i
$94$			0.850817i			0.0877550i
$95$	4.78231	+	2.76107i	0.490654	+	0.283279i
$96$	−1.04580	−	1.38069i	−0.106736	−	0.140916i
$97$	7.08918	−	4.09294i	0.719797	−	0.415575i	−0.0948811	−	0.995489i	$-0.530247\pi$
$97$	7.08918	−	4.09294i	0.719797	−	0.415575i	0.814678	+	0.579914i	$0.196914\pi$
$98$	6.88215	−	1.27907i	0.695202	−	0.129206i
$99$	−1.78780	+	1.74365i	−0.179680	+	0.175243i
$100$	0.376526			0.0376526
$101$	−13.3676			−1.33013			−0.665064	−	0.746786i	$-0.731596\pi$
$101$	−13.3676			−1.33013			−0.665064	+	0.746786i	$0.731596\pi$
$102$	1.83237	−	4.34668i	0.181431	−	0.430385i
$103$	12.8325	+	7.40885i	1.26442	+	0.730015i	0.973927	−	0.226861i	$-0.0728462\pi$
$103$	12.8325	+	7.40885i	1.26442	+	0.730015i	0.290497	+	0.956876i	$0.406180\pi$
$104$	3.29641	+	1.46072i	0.323239	+	0.143235i
$105$	4.53555	+	8.74767i	0.442624	+	0.853685i
$106$	−5.99761	+	10.3882i	−0.582539	+	1.00899i
$107$	−1.21334	+	0.700521i	−0.117298	+	0.0677219i	−0.557501	−	0.830176i	$-0.688240\pi$
$107$	−1.21334	+	0.700521i	−0.117298	+	0.0677219i	0.440203	+	0.897898i	$0.354906\pi$
$108$	−5.13808	−	0.774711i	−0.494412	−	0.0745466i
$109$	4.04758	+	7.01062i	0.387688	+	0.671496i	0.992138	−	0.125147i	$-0.0399404\pi$
$109$	4.04758	+	7.01062i	0.387688	+	0.671496i	−0.604450	+	0.796643i	$0.706607\pi$
$110$	−1.78992			−0.170662
$111$	−0.0387448	−	0.309219i	−0.00367749	−	0.0293498i
$112$	−2.48199	+	0.916357i	−0.234526	+	0.0865876i
$113$	−3.15285	+	1.82030i	−0.296595	+	0.171239i	−0.640912	−	0.767614i	$-0.721444\pi$
$113$	−3.15285	+	1.82030i	−0.296595	+	0.171239i	0.344317	+	0.938853i	$0.388111\pi$
$114$	0.553029	+	4.41368i	0.0517959	+	0.413379i
$115$			5.34328i			0.498263i
$116$	−7.62813	+	4.40410i	−0.708254	+	0.408910i
$117$	10.1393	−	3.76763i	0.937377	−	0.348317i
$118$			2.52356i			0.232312i
$119$	−5.54105	−	4.60611i	−0.507947	−	0.422241i
$120$	−2.24870	−	2.96880i	−0.205277	−	0.271013i
$121$	10.3071			0.937005
$122$	−1.82753	−	3.16538i	−0.165457	−	0.286580i
$123$	−16.4021	+	12.4236i	−1.47892	+	1.12020i
$124$			2.38352i			0.214047i
$125$	11.5607			1.03402
$126$	−3.41107	+	7.16691i	−0.303883	+	0.638479i
$127$	9.89702	−	17.1421i	0.878219	−	1.52112i	0.0249248	−	0.999689i	$-0.492065\pi$
$127$	9.89702	−	17.1421i	0.878219	−	1.52112i	0.853294	−	0.521430i	$-0.174601\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.67601	+	13.3761i	0.147564	+	1.17770i
$130$	7.08802	+	3.14088i	0.621661	+	0.275473i
$131$	3.58433	−	6.20825i	0.313165	−	0.542417i	−0.665881	−	0.746058i	$-0.731944\pi$
$131$	3.58433	−	6.20825i	0.313165	−	0.542417i	0.979046	+	0.203641i	$0.0652774\pi$
$132$	−0.870557	−	1.14934i	−0.0757722	−	0.100037i
$133$	6.69687	+	1.14902i	0.580692	+	0.0996325i
$134$	5.72816	−	3.30716i	0.494838	−	0.285695i
$135$	−11.0480	−	1.66580i	−0.950863	−	0.143370i
$136$	2.35856	+	1.36171i	0.202245	+	0.116766i
$137$	5.41593	+	3.12689i	0.462714	+	0.267148i	0.713185	−	0.700976i	$-0.247252\pi$
$137$	5.41593	+	3.12689i	0.462714	+	0.267148i	−0.250471	+	0.968124i	$0.580585\pi$
$138$	−3.43100	+	2.59879i	−0.292066	+	0.221224i
$139$	−1.80427	+	1.04170i	−0.153036	+	0.0883555i	−0.574563	−	0.818461i	$-0.694828\pi$
$139$	−1.80427	+	1.04170i	−0.153036	+	0.0883555i	0.421526	+	0.906816i	$0.361494\pi$
$140$	−5.33685	+	1.97037i	−0.451046	+	0.166527i
$141$	−1.17472	+	0.889781i	−0.0989289	+	0.0749331i
$142$	4.32143	−	7.48494i	0.362646	−	0.628122i
$143$	2.74404	+	1.21595i	0.229468	+	0.101683i
$144$	0.812620	−	2.88784i	0.0677184	−	0.240654i
$145$	−16.4022	+	9.46981i	−1.36213	+	0.786425i
$146$	6.31743	−	10.9421i	0.522834	−	0.905575i
$147$	8.96333	+	8.16448i	0.739283	+	0.673395i
$148$	0.179924			0.0147896
$149$			12.2379i			1.00256i	0.865284	+	0.501282i	$0.167138\pi$
$149$			12.2379i			1.00256i	−0.865284	+	0.501282i	$0.832862\pi$
$150$	0.393770	+	0.519866i	0.0321511	+	0.0424469i
$151$	0.503958	+	0.872882i	0.0410116	+	0.0710341i	0.885803	−	0.464062i	$-0.153609\pi$
$151$	0.503958	+	0.872882i	0.0410116	+	0.0710341i	−0.844791	+	0.535096i	$0.820275\pi$
$152$	−2.56816			−0.208306
$153$	7.91771	−	2.01581i	0.640109	−	0.162968i
$154$	−2.06610	+	0.762807i	−0.166491	+	0.0614687i
$155$			5.12512i			0.411659i
$156$	1.43056	+	6.07894i	0.114537	+	0.486705i
$157$	13.6246	−	7.86616i	1.08736	−	0.627788i	0.154489	−	0.987995i	$-0.450627\pi$
$157$	13.6246	−	7.86616i	1.08736	−	0.627788i	0.932873	+	0.360206i	$0.117294\pi$
$158$		−	6.21627i		−	0.494540i
$159$	−20.6151	+	2.58305i	−1.63489	+	0.204849i
$160$	1.86215	−	1.07511i	0.147216	−	0.0849952i
$161$	2.27713	+	6.16772i	0.179463	+	0.486084i
$162$	−4.30374	−	7.90429i	−0.338134	−	0.621020i
$163$	−23.8006			−1.86421			−0.932105	−	0.362188i	$-0.882030\pi$
$163$	−23.8006			−1.86421			−0.932105	+	0.362188i	$0.882030\pi$
$164$	−5.93979	−	10.2880i	−0.463820	−	0.803360i
$165$	−1.87189	−	2.47133i	−0.145727	−	0.192393i
$166$	0.806115	−	0.465411i	0.0625666	−	0.0361229i
$167$	−1.67287	+	2.89750i	−0.129451	+	0.224215i	−0.923464	−	0.383685i	$-0.874655\pi$
$167$	−1.67287	+	2.89750i	−0.129451	+	0.224215i	0.794013	+	0.607901i	$0.207988\pi$
$168$	−3.86087	−	2.46855i	−0.297872	−	0.190452i
$169$	−8.73259	−	9.63026i	−0.671738	−	0.740789i
$170$	5.07144	+	2.92799i	0.388961	+	0.224567i
$171$	−5.51557	+	5.37937i	−0.421786	+	0.411371i
$172$	−7.78308			−0.593454
$173$	19.6842			1.49656			0.748282	−	0.663381i	$-0.230879\pi$
$173$	19.6842			1.49656			0.748282	+	0.663381i	$0.230879\pi$
$174$	−14.0582	−	5.92630i	−1.06575	−	0.449272i
$175$	0.934535	−	0.345032i	0.0706442	−	0.0260820i
$176$	0.720909	−	0.416217i	0.0543406	−	0.0313736i
$177$	−3.48425	+	2.63913i	−0.261893	+	0.198369i
$178$	−0.992375	−	0.572948i	−0.0743817	−	0.0429443i
$179$		−	1.33395i		−	0.0997042i	−0.998757	−	0.0498521i	$-0.984125\pi$
$179$		−	1.33395i		−	0.0997042i	0.998757	−	0.0498521i	$-0.0158750\pi$
$180$	1.74732	−	6.20952i	0.130237	−	0.462830i
$181$		−	1.13213i		−	0.0841503i	−0.999114	−	0.0420752i	$-0.986603\pi$
$181$		−	1.13213i		−	0.0841503i	0.999114	−	0.0420752i	$-0.0133969\pi$
$182$	9.52020	+	0.604814i	0.705684	+	0.0448318i
$183$	2.45918	−	5.83360i	0.181788	−	0.431232i
$184$	−1.24249	−	2.15206i	−0.0915978	−	0.158652i
$185$	0.386877			0.0284437
$186$	−3.29091	+	2.49268i	−0.241301	+	0.182772i
$187$	1.96335	+	1.13354i	0.143574	+	0.0828925i
$188$	−0.425408	−	0.736829i	−0.0310261	−	0.0537388i
$189$	−13.4626	+	2.78548i	−0.979259	+	0.202614i
$190$	−5.52213			−0.400618
$191$		−	21.2390i		−	1.53680i	−0.639968	−	0.768402i	$-0.721052\pi$
$191$		−	21.2390i		−	1.53680i	0.639968	−	0.768402i	$-0.278948\pi$
$192$	1.59603	+	0.672816i	0.115184	+	0.0485563i
$193$	3.12907			0.225236			0.112618	−	0.993638i	$-0.464076\pi$
$193$	3.12907			0.225236			0.112618	+	0.993638i	$0.464076\pi$
$194$	−4.09294	+	7.08918i	−0.293856	+	0.508973i
$195$	3.07604	+	13.0711i	0.220280	+	0.936040i
$196$	−5.32058	+	4.54878i	−0.380041	+	0.324913i
$197$	10.6747	+	6.16302i	0.760538	+	0.439097i	0.829489	−	0.558523i	$-0.188632\pi$
$197$	10.6747	+	6.16302i	0.760538	+	0.439097i	−0.0689508	+	0.997620i	$0.521965\pi$
$198$	0.676453	−	2.40394i	0.0480734	−	0.170841i
$199$	23.7399	+	13.7062i	1.68288	+	0.971610i	0.959733	+	0.280915i	$0.0906378\pi$
$199$	23.7399	+	13.7062i	1.68288	+	0.971610i	0.723146	+	0.690696i	$0.242696\pi$
$200$	−0.326081	+	0.188263i	−0.0230574	+	0.0133122i
$201$	10.5567	+	4.45022i	0.744609	+	0.313894i
$202$	11.5767	−	6.68381i	0.814534	−	0.470271i
$203$	−14.8972	+	17.9210i	−1.04558	+	1.25781i
$204$	0.586464	+	4.68052i	0.0410607	+	0.327702i
$205$	−12.7719	−	22.1216i	−0.892028	−	1.54504i
$206$	−14.8177			−1.03240
$207$	−7.17625	−	2.01935i	−0.498784	−	0.140354i
$208$	−3.58513	+	0.383182i	−0.248584	+	0.0265689i
$209$	−2.13783			−0.147877
$210$	−8.30174	−	5.30793i	−0.572874	−	0.366282i
$211$	11.7715	−	20.3889i	0.810384	−	1.40363i	−0.102211	−	0.994763i	$-0.532592\pi$
$211$	11.7715	−	20.3889i	0.810384	−	1.40363i	0.912595	−	0.408864i	$-0.134075\pi$
$212$		−	11.9952i		−	0.823835i
$213$	14.8537	−	1.86115i	1.01776	−	0.127524i
$214$	0.700521	−	1.21334i	0.0478866	−	0.0829421i
$215$	−16.7354			−1.14134
$216$	4.83706	−	1.89812i	0.329120	−	0.129151i
$217$	2.18416	+	5.91589i	0.148270	+	0.401597i
$218$	−7.01062	−	4.04758i	−0.474819	−	0.274137i
$219$	21.7144	−	2.72079i	1.46732	−	0.183854i
$220$	1.55012	−	0.894961i	0.104509	−	0.0603383i
$221$	−5.78568	−	7.93396i	−0.389187	−	0.533696i
$222$	0.188164	+	0.248419i	0.0126287	+	0.0166728i
$223$	25.4264	+	14.6799i	1.70268	+	0.983041i	0.943032	+	0.332702i	$0.107960\pi$
$223$	25.4264	+	14.6799i	1.70268	+	0.983041i	0.759644	+	0.650339i	$0.225373\pi$
$224$	1.69129	−	2.03458i	0.113004	−	0.135941i
$225$	−0.305973	+	1.08735i	−0.0203982	+	0.0724899i
$226$	1.82030	−	3.15285i	0.121085	−	0.209725i
$227$	14.1930	−	24.5831i	0.942025	−	1.63164i	0.180425	−	0.983589i	$-0.442253\pi$
$227$	14.1930	−	24.5831i	0.942025	−	1.63164i	0.761600	−	0.648047i	$-0.224414\pi$
$228$	−2.68578	−	3.54584i	−0.177870	−	0.234829i
$229$	−12.6122	−	7.28164i	−0.833435	−	0.481184i	0.0215921	−	0.999767i	$-0.493126\pi$
$229$	−12.6122	−	7.28164i	−0.833435	−	0.481184i	−0.855027	+	0.518583i	$0.826460\pi$
$230$	−2.67164	−	4.62742i	−0.176163	−	0.305123i
$231$	−3.21392	−	2.05490i	−0.211460	−	0.135203i
$232$	4.40410	−	7.62813i	0.289143	−	0.500811i
$233$	12.8119	+	7.39695i	0.839335	+	0.484590i	0.857038	−	0.515253i	$-0.172302\pi$
$233$	12.8119	+	7.39695i	0.839335	+	0.484590i	−0.0177033	+	0.999843i	$0.505635\pi$
$234$	−6.89706	+	8.33250i	−0.450875	+	0.544713i
$235$	−0.914724	−	1.58435i	−0.0596700	−	0.103352i
$236$	−1.26178	−	2.18546i	−0.0821348	−	0.142262i
$237$	8.58276	−	6.50096i	0.557510	−	0.422282i
$238$	7.10174	+	1.21849i	0.460338	+	0.0789827i
$239$			20.0261i			1.29538i	0.761903	+	0.647692i	$0.224265\pi$
$239$			20.0261i			1.29538i	−0.761903	+	0.647692i	$0.775735\pi$
$240$	3.43183	+	1.44671i	0.221524	+	0.0933845i
$241$	−9.00940	−	5.20158i	−0.580347	−	0.335063i	0.180924	−	0.983497i	$-0.442091\pi$
$241$	−9.00940	−	5.20158i	−0.580347	−	0.335063i	−0.761271	+	0.648434i	$0.775424\pi$
$242$	−8.92617	+	5.15353i	−0.573796	+	0.331281i
$243$	6.41255	−	14.2084i	0.411365	−	0.911471i
$244$	3.16538	+	1.82753i	0.202642	+	0.116996i
$245$	−11.4405	+	9.78091i	−0.730904	+	0.624880i
$246$	7.99278	−	18.9602i	0.509601	−	1.20886i
$247$	8.46571	+	3.75137i	0.538660	+	0.238694i
$248$	−1.19176	−	2.06419i	−0.0756769	−	0.131076i
$249$	1.48562	+	0.626271i	0.0941474	+	0.0396883i
$250$	−10.0119	+	5.78037i	−0.633208	+	0.365583i
$251$	1.11415	+	1.92977i	0.0703247	+	0.121806i	0.899044	−	0.437859i	$-0.144263\pi$
$251$	1.11415	+	1.92977i	0.0703247	+	0.121806i	−0.828719	+	0.559665i	$0.810930\pi$
$252$	−0.629378	−	7.91226i	−0.0396471	−	0.498426i
$253$	−1.03429	−	1.79145i	−0.0650255	−	0.112627i
$254$			19.7940i			1.24199i
$255$	1.26103	+	10.0642i	0.0789687	+	0.630243i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.10302	+	5.37459i	0.193561	+	0.335258i	0.946428	−	0.322915i	$-0.104663\pi$
$257$	3.10302	+	5.37459i	0.193561	+	0.335258i	−0.752867	+	0.658173i	$0.771329\pi$
$258$	−8.13952	−	10.7460i	−0.506744	−	0.669019i
$259$	0.446570	−	0.164874i	0.0277485	−	0.0102448i
$260$	−7.70885	+	0.823929i	−0.478082	+	0.0510979i
$261$	−6.51959	−	25.6077i	−0.403552	−	1.58508i
$262$			7.16867i			0.442882i
$263$			24.4905i			1.51015i	0.655638	+	0.755075i	$0.272400\pi$
$263$			24.4905i			1.51015i	−0.655638	+	0.755075i	$0.727600\pi$
$264$	1.32859	+	0.560075i	0.0817692	+	0.0344703i
$265$		−	25.7924i		−	1.58442i
$266$	−6.37416	+	2.35335i	−0.390825	+	0.144293i
$267$	−0.246758	−	1.96935i	−0.0151013	−	0.120522i
$268$	−3.30716	+	5.72816i	−0.202017	+	0.349903i
$269$	2.50076	−	4.33145i	0.152474	−	0.264093i	−0.779662	−	0.626200i	$-0.784609\pi$
$269$	2.50076	−	4.33145i	0.152474	−	0.264093i	0.932136	+	0.362107i	$0.117943\pi$
$270$	10.4008	−	4.08139i	0.632971	−	0.248385i
$271$	−5.70946	+	3.29636i	−0.346825	+	0.200240i	−0.663286	−	0.748366i	$-0.730839\pi$
$271$	−5.70946	+	3.29636i	−0.346825	+	0.200240i	0.316461	+	0.948606i	$0.397505\pi$
$272$	−2.72343			−0.165132
$273$	9.12113	+	13.7770i	0.552036	+	0.833820i
$274$	−6.25378			−0.377805
$275$	−0.271441	+	0.156717i	−0.0163685	+	0.00945037i
$276$	1.67194	−	3.96612i	0.100639	−	0.238732i
$277$	8.49535	−	14.7144i	0.510436	−	0.884101i	−0.489491	−	0.872009i	$-0.662817\pi$
$277$	8.49535	−	14.7144i	0.510436	−	0.884101i	0.999927	−	0.0120929i	$-0.00384937\pi$
$278$	1.04170	−	1.80427i	0.0624767	−	0.108213i
$279$	−6.88325	−	1.93690i	−0.412089	−	0.115959i
$280$	3.63666	−	4.37482i	0.217332	−	0.261445i
$281$			3.11696i			0.185942i	0.995669	+	0.0929712i	$0.0296364\pi$
$281$			3.11696i			0.185942i	−0.995669	+	0.0929712i	$0.970364\pi$
$282$	0.572443	−	1.35793i	0.0340885	−	0.0808636i
$283$		−	12.4144i		−	0.737958i	−0.929438	−	0.368979i	$-0.879707\pi$
$283$		−	12.4144i		−	0.737958i	0.929438	−	0.368979i	$-0.120293\pi$
$284$			8.64286i			0.512859i
$285$	−5.77503	−	7.62436i	−0.342083	−	0.451628i
$286$	−2.98439	+	0.318974i	−0.176471	+	0.0188613i
$287$	−24.1700	−	20.0918i	−1.42671	−	1.18598i
$288$	0.740172	+	2.90726i	0.0436151	+	0.171312i
$289$	4.79147	+	8.29906i	0.281851	+	0.488180i
$290$	9.46981	−	16.4022i	0.556087	−	0.963170i
$291$	−14.0683	+	1.76275i	−0.824701	+	0.103334i
$292$			12.6349i			0.739399i
$293$	−2.20558	−	3.82017i	−0.128851	−	0.223177i	0.794381	−	0.607420i	$-0.207796\pi$
$293$	−2.20558	−	3.82017i	−0.128851	−	0.223177i	−0.923232	+	0.384244i	$0.874462\pi$
$294$	−11.8447	−	2.58898i	−0.690798	−	0.150993i
$295$	−2.71311	−	4.69924i	−0.157963	−	0.273600i
$296$	−0.155819	+	0.0899619i	−0.00905677	+	0.00522893i
$297$	4.02653	−	1.58006i	0.233643	−	0.0916843i
$298$	−6.11893	−	10.5983i	−0.354460	−	0.613943i
$299$	0.952202	+	8.90900i	0.0550673	+	0.515221i
$300$	−0.600948	−	0.253333i	−0.0346957	−	0.0146262i
$301$	−19.3176	+	7.13208i	−1.11345	+	0.411086i
$302$	−0.872882	−	0.503958i	−0.0502287	−	0.0289995i
$303$	21.3352	+	8.99395i	1.22567	+	0.516689i
$304$	2.22409	−	1.28408i	0.127561	−	0.0736471i
$305$	6.80628	+	3.92961i	0.389726	+	0.225009i
$306$	−5.84903	+	5.70459i	−0.334367	+	0.326110i
$307$		−	16.2434i		−	0.927062i	−0.886081	−	0.463531i	$-0.846582\pi$
$307$		−	16.2434i		−	0.927062i	0.886081	−	0.463531i	$-0.153418\pi$
$308$	1.40789	−	1.69366i	0.0802219	−	0.0965051i
$309$	−15.4963	−	20.4587i	−0.881553	−	1.16385i
$310$	−2.56256	−	4.43848i	−0.145543	−	0.252089i
$311$	12.4845	+	21.6238i	0.707930	+	1.22617i	0.965624	+	0.259944i	$0.0837042\pi$
$311$	12.4845	+	21.6238i	0.707930	+	1.22617i	−0.257693	+	0.966227i	$0.582962\pi$
$312$	−4.27837	−	4.54923i	−0.242215	−	0.257550i
$313$	−23.0661	−	13.3172i	−1.30377	−	0.752733i	−0.322722	−	0.946494i	$-0.604598\pi$
$313$	−23.0661	−	13.3172i	−1.30377	−	0.752733i	−0.981049	+	0.193761i	$0.937931\pi$
$314$	−7.86616	+	13.6246i	−0.443913	+	0.768880i
$315$	−1.35330	−	17.0132i	−0.0762501	−	0.958583i
$316$	3.10814	+	5.38345i	0.174846	+	0.302843i
$317$	−7.23589	−	4.17764i	−0.406408	−	0.234640i	0.282837	−	0.959168i	$-0.408724\pi$
$317$	−7.23589	−	4.17764i	−0.406408	−	0.234640i	−0.689245	+	0.724528i	$0.742058\pi$
$318$	16.5617	−	12.5445i	0.928734	−	0.703463i
$319$	3.66612	−	6.34991i	0.205264	−	0.355527i
$320$	−1.07511	+	1.86215i	−0.0601007	+	0.104097i
$321$	2.40785	−	0.301701i	0.134393	−	0.0168393i
$322$	−5.05591	−	4.20283i	−0.281755	−	0.234215i
$323$	6.05716	+	3.49711i	0.337030	+	0.194584i
$324$	7.67930	+	4.69344i	0.426628	+	0.260747i
$325$	1.34990	−	0.144278i	0.0748787	−	0.00800311i
$326$	20.6120	−	11.9003i	1.14159	−	0.659098i
$327$	−1.74321	−	13.9125i	−0.0964000	−	0.769361i
$328$	10.2880	+	5.93979i	0.568061	+	0.327970i
$329$	−1.73106	−	1.43898i	−0.0954363	−	0.0793334i
$330$	2.85677	+	1.20429i	0.157260	+	0.0662939i
$331$	15.9290			0.875539			0.437770	−	0.899087i	$-0.355769\pi$
$331$	15.9290			0.875539			0.437770	+	0.899087i	$0.355769\pi$
$332$	−0.465411	+	0.806115i	−0.0255427	+	0.0442413i
$333$	−0.146210	+	0.519592i	−0.00801224	+	0.0284735i
$334$		−	3.34574i		−	0.183071i
$335$	−7.11113	+	12.3168i	−0.388523	+	0.672941i
$336$	4.57788	+	0.207390i	0.249744	+	0.0113141i
$337$	−1.38803			−0.0756107			−0.0378054	−	0.999285i	$-0.512037\pi$
$337$	−1.38803			−0.0756107			−0.0378054	+	0.999285i	$0.512037\pi$
$338$	12.3778	+	3.97375i	0.673262	+	0.216144i
$339$	6.25678	−	0.783968i	0.339822	−	0.0425793i
$340$	−5.85599			−0.317586
$341$	−0.992063	−	1.71830i	−0.0537232	−	0.0930514i
$342$	2.08694	−	7.41646i	0.112849	−	0.401036i
$343$	−9.03734	+	16.1656i	−0.487970	+	0.872860i
$344$	6.74035	−	3.89154i	0.363415	−	0.209818i
$345$	3.59505	−	8.52805i	0.193551	−	0.459135i
$346$	−17.0470	+	9.84211i	−0.916454	+	0.529115i
$347$	−0.353549	−	0.204122i	−0.0189795	−	0.0109578i	0.490480	−	0.871452i	$-0.336821\pi$
$347$	−0.353549	−	0.204122i	−0.0189795	−	0.0109578i	−0.509460	+	0.860494i	$0.670155\pi$
$348$	15.1379	−	1.89676i	0.811476	−	0.101677i
$349$	1.55975	+	0.900521i	0.0834914	+	0.0482038i	0.541164	−	0.840917i	$-0.317984\pi$
$349$	1.55975	+	0.900521i	0.0834914	+	0.0482038i	−0.457673	+	0.889121i	$0.651317\pi$
$350$	−0.636815	+	0.766074i	−0.0340392	+	0.0409484i
$351$	−18.7175	−	0.808620i	−0.999068	−	0.0431609i
$352$	−0.416217	+	0.720909i	−0.0221845	+	0.0384246i
$353$	23.9563			1.27507			0.637534	−	0.770422i	$-0.279955\pi$
$353$	23.9563			1.27507			0.637534	+	0.770422i	$0.279955\pi$
$354$	1.69789	−	4.02768i	0.0902418	−	0.214069i
$355$			18.5841i			0.986342i
$356$	1.14590			0.0607324
$357$	5.74462	+	11.0796i	0.304038	+	0.586395i
$358$	0.666976	+	1.15524i	0.0352508	+	0.0610561i
$359$	7.14363	+	4.12438i	0.377026	+	0.217676i	0.676524	−	0.736421i	$-0.263486\pi$
$359$	7.14363	+	4.12438i	0.377026	+	0.217676i	−0.299497	+	0.954097i	$0.596819\pi$
$360$	1.59154	+	6.25126i	0.0838814	+	0.329470i
$361$	12.4045			0.652870
$362$	0.566063	+	0.980451i	0.0297516	+	0.0515313i
$363$	−16.4504	−	6.93475i	−0.863421	−	0.363980i
$364$	−8.54714	+	4.23632i	−0.447992	+	0.222043i
$365$			27.1678i			1.42203i
$366$	0.787082	+	6.28164i	0.0411414	+	0.328346i
$367$		−	11.6700i		−	0.609167i	−0.952486	−	0.304583i	$-0.901483\pi$
$367$		−	11.6700i		−	0.609167i	0.952486	−	0.304583i	$-0.0985172\pi$
$368$	2.15206	+	1.24249i	0.112184	+	0.0647694i
$369$	34.5370	−	8.79295i	1.79793	−	0.457742i
$370$	−0.335045	+	0.193438i	−0.0174182	+	0.0100564i
$371$	−10.9919	−	29.7720i	−0.570671	−	1.54569i
$372$	1.60367	−	3.80418i	0.0831466	−	0.197238i
$373$	−31.8939			−1.65140			−0.825701	−	0.564108i	$-0.809220\pi$
$373$	−31.8939			−1.65140			−0.825701	+	0.564108i	$0.809220\pi$
$374$	−2.26708			−0.117228
$375$	−18.4513	−	7.77826i	−0.952822	−	0.401668i
$376$	0.736829	+	0.425408i	0.0379990	+	0.0219388i
$377$	−25.6603	+	18.7122i	−1.32157	+	0.963730i
$378$	10.2662	−	9.14359i	0.528036	−	0.470296i
$379$	−9.93293	+	17.2043i	−0.510220	+	0.883727i	0.489710	+	0.871886i	$0.337103\pi$
$379$	−9.93293	+	17.2043i	−0.510220	+	0.883727i	−0.999930	+	0.0118419i	$0.996231\pi$
$380$	4.78231	−	2.76107i	0.245327	−	0.141640i
$381$	−27.3295	+	20.7005i	−1.40013	+	1.06052i
$382$	10.6195	+	18.3935i	0.543342	+	0.941096i
$383$	−0.733280			−0.0374689			−0.0187344	−	0.999824i	$-0.505964\pi$
$383$	−0.733280			−0.0374689			−0.0187344	+	0.999824i	$0.505964\pi$
$384$	−1.71861	+	0.215340i	−0.0877026	+	0.0109890i
$385$	3.02728	−	3.64175i	0.154284	−	0.185601i
$386$	−2.70986	+	1.56454i	−0.137928	+	0.0796329i
$387$	6.32469	−	22.4763i	0.321502	−	1.14254i
$388$		−	8.18588i		−	0.415575i
$389$	28.6554	−	16.5442i	1.45289	−	0.838825i	0.454244	−	0.890878i	$-0.349910\pi$
$389$	28.6554	−	16.5442i	1.45289	−	0.838825i	0.998644	+	0.0520523i	$0.0165763\pi$
$390$	−9.19947	−	9.78188i	−0.465833	−	0.495325i
$391$			6.76768i			0.342256i
$392$	2.33337	−	6.59965i	0.117853	−	0.333333i
$393$	−9.89772	+	7.49697i	−0.499274	+	0.378172i
$394$	−12.3260			−0.620977
$395$	6.68320	+	11.5756i	0.336268	+	0.582434i
$396$	0.616145	+	2.42010i	0.0309625	+	0.121615i
$397$			11.8885i			0.596667i	0.954462	+	0.298334i	$0.0964308\pi$
$397$			11.8885i			0.596667i	−0.954462	+	0.298334i	$0.903569\pi$
$398$	−27.4125			−1.37406
$399$	−9.91533	−	6.33963i	−0.496388	−	0.317378i
$400$	0.188263	−	0.326081i	0.00941315	−	0.0163041i
$401$	−20.4328	+	11.7969i	−1.02036	+	0.589107i	−0.914209	−	0.405242i	$-0.867187\pi$
$401$	−20.4328	+	11.7969i	−1.02036	+	0.589107i	−0.106155	+	0.994350i	$0.533854\pi$
$402$	−11.3674	+	1.42433i	−0.566956	+	0.0710390i
$403$	0.913324	+	8.54525i	0.0454959	+	0.425669i
$404$	−6.68381	+	11.5767i	−0.332532	+	0.575962i
$405$	16.5122	+	10.0920i	0.820499	+	0.501474i
$406$	3.94086	−	22.9687i	0.195582	−	1.13992i
$407$	−0.129709	+	0.0748874i	−0.00642942	+	0.00371203i
$408$	−2.84815	−	3.76022i	−0.141005	−	0.186158i
$409$	−9.83316	−	5.67718i	−0.486218	−	0.280718i	0.236786	−	0.971562i	$-0.423906\pi$
$409$	−9.83316	−	5.67718i	−0.486218	−	0.280718i	−0.723004	+	0.690844i	$0.757239\pi$
$410$	22.1216	+	12.7719i	1.09251	+	0.630759i
$411$	−6.54018	−	8.63454i	−0.322603	−	0.425911i
$412$	12.8325	−	7.40885i	0.632212	−	0.365008i
$413$	−5.13439	−	4.26807i	−0.252647	−	0.210018i
$414$	7.22449	−	1.83932i	0.355064	−	0.0903975i
$415$	−1.00074	+	1.73333i	−0.0491243	+	0.0850858i
$416$	2.91322	−	2.12441i	0.142833	−	0.104158i
$417$	3.58054	−	0.448638i	0.175340	−	0.0219699i
$418$	1.85141	−	1.06891i	0.0905556	−	0.0522823i
$419$	6.35642	−	11.0096i	0.310531	−	0.537856i	−0.667946	−	0.744210i	$-0.732826\pi$
$419$	6.35642	−	11.0096i	0.310531	−	0.537856i	0.978477	+	0.206354i	$0.0661597\pi$
$420$	9.84348	+	0.445937i	0.480313	+	0.0217595i
$421$	36.5159			1.77968			0.889839	−	0.456275i	$-0.150817\pi$
$421$	36.5159			1.77968			0.889839	+	0.456275i	$0.150817\pi$
$422$			23.5430i			1.14606i
$423$	2.47354	−	0.629751i	0.120268	−	0.0306195i
$424$	5.99761	+	10.3882i	0.291270	+	0.504494i
$425$	1.02544			0.0497412
$426$	−11.9331	+	9.03867i	−0.578162	+	0.437925i
$427$	9.53111	+	1.63531i	0.461243	+	0.0791380i
$428$			1.40104i			0.0677219i
$429$	−3.56147	−	3.78694i	−0.171949	−	0.182835i
$430$	14.4933	−	8.36769i	0.698928	−	0.403526i
$431$		−	5.97670i		−	0.287887i	−0.989586	−	0.143944i	$-0.954022\pi$
$431$		−	5.97670i		−	0.287887i	0.989586	−	0.143944i	$-0.0459784\pi$
$432$	−3.23996	+	4.06235i	−0.155883	+	0.195450i
$433$	−27.0676	+	15.6275i	−1.30079	+	0.751009i	−0.980539	−	0.196325i	$-0.937099\pi$
$433$	−27.0676	+	15.6275i	−1.30079	+	0.751009i	−0.320247	+	0.947334i	$0.603766\pi$
$434$	−4.84948	−	4.03123i	−0.232783	−	0.193505i
$435$	32.5499	−	4.07846i	1.56065	−	0.195547i
$436$	8.09517			0.387688
$437$	−3.19092	−	5.52684i	−0.152643	−	0.264385i
$438$	−17.4448	+	13.2135i	−0.833547	+	0.631365i
$439$	25.7980	−	14.8945i	1.23127	−	0.710875i	0.263976	−	0.964529i	$-0.414966\pi$
$439$	25.7980	−	14.8945i	1.23127	−	0.710875i	0.967295	+	0.253654i	$0.0816326\pi$
$440$	−0.894961	+	1.55012i	−0.0426656	+	0.0738990i
$441$	−8.81256	−	19.0614i	−0.419646	−	0.907688i
$442$	8.97753	+	3.97817i	0.427018	+	0.189222i
$443$	−18.4003	−	10.6234i	−0.874224	−	0.504733i	−0.00547441	−	0.999985i	$-0.501743\pi$
$443$	−18.4003	−	10.6234i	−0.874224	−	0.504733i	−0.868750	+	0.495252i	$0.835076\pi$
$444$	−0.287164	−	0.121056i	−0.0136282	−	0.00574504i
$445$	2.46394			0.116802
$446$	−29.3599			−1.39023
$447$	8.23383	−	19.5320i	0.389447	−	0.923833i
$448$	−0.447408	+	2.60765i	−0.0211381	+	0.123200i
$449$	−24.6546	+	14.2344i	−1.16352	+	0.671761i	−0.952146	−	0.305644i	$-0.901128\pi$
$449$	−24.6546	+	14.2344i	−1.16352	+	0.671761i	−0.211377	+	0.977405i	$0.567795\pi$
$450$	−0.278694	−	1.09466i	−0.0131378	−	0.0516027i
$451$	8.56411	+	4.94449i	0.403268	+	0.232827i
$452$			3.64060i			0.171239i
$453$	−0.217045	−	1.73222i	−0.0101977	−	0.0813867i
$454$			28.3861i			1.33223i
$455$	−18.3783	+	9.10904i	−0.861588	+	0.427038i
$456$	4.09887	+	1.72790i	0.191947	+	0.0809164i
$457$	10.2066	+	17.6783i	0.477444	+	0.826956i	0.999666	−	0.0258530i	$-0.00823019\pi$
$457$	10.2066	+	17.6783i	0.477444	+	0.826956i	−0.522222	+	0.852809i	$0.674897\pi$
$458$	14.5633			0.680497
$459$	−13.9932	−	2.10987i	−0.653146	−	0.0984803i
$460$	4.62742	+	2.67164i	0.215754	+	0.124566i
$461$	0.909994	+	1.57616i	0.0423827	+	0.0734089i	0.886439	−	0.462846i	$-0.153172\pi$
$461$	0.909994	+	1.57616i	0.0423827	+	0.0734089i	−0.844056	+	0.536255i	$0.819838\pi$
$462$	3.81078	+	0.172639i	0.177294	+	0.00803189i
$463$	−22.0589			−1.02517			−0.512583	−	0.858638i	$-0.671311\pi$
$463$	−22.0589			−1.02517			−0.512583	+	0.858638i	$0.671311\pi$
$464$			8.80820i			0.408910i
$465$	3.44826	−	8.17985i	0.159909	−	0.379331i
$466$	−14.7939			−0.685314
$467$	3.76001	−	6.51253i	0.173993	−	0.301364i	−0.765820	−	0.643056i	$-0.777666\pi$
$467$	3.76001	−	6.51253i	0.173993	−	0.301364i	0.939812	+	0.341691i	$0.111000\pi$
$468$	1.80678	−	10.6647i	0.0835184	−	0.492975i
$469$	−2.95930	+	17.2478i	−0.136648	+	0.796429i
$470$	1.58435	+	0.914724i	0.0730806	+	0.0421931i
$471$	−27.0378	+	3.38780i	−1.24584	+	0.156102i
$472$	2.18546	+	1.26178i	0.100594	+	0.0580780i
$473$	5.61090	−	3.23945i	0.257989	−	0.148950i
$474$	−4.18241	+	9.92137i	−0.192104	+	0.455704i
$475$	−0.837430	+	0.483490i	−0.0384239	+	0.0221841i
$476$	−6.75953	+	2.49563i	−0.309823	+	0.114387i
$477$	34.6403	+	9.74756i	1.58607	+	0.446310i
$478$	−10.0131	−	17.3431i	−0.457987	−	0.793257i
$479$	−30.8345			−1.40887			−0.704433	−	0.709771i	$-0.748799\pi$
$479$	−30.8345			−1.40887			−0.704433	+	0.709771i	$0.748799\pi$
$480$	−3.69541	+	0.463030i	−0.168671	+	0.0211343i
$481$	0.645050	−	0.0689436i	0.0294118	−	0.00314356i
$482$	10.4032			0.473851
$483$	0.515362	−	11.3760i	0.0234498	−	0.517624i
$484$	5.15353	−	8.92617i	0.234251	−	0.405735i
$485$		−	17.6015i		−	0.799242i
$486$	1.55078	+	15.5111i	0.0703448	+	0.703599i
$487$	3.15309	−	5.46131i	0.142880	−	0.247475i	−0.785700	−	0.618608i	$-0.787697\pi$
$487$	3.15309	−	5.46131i	0.142880	−	0.247475i	0.928580	+	0.371132i	$0.121030\pi$
$488$	−3.65506			−0.165457
$489$	37.9866	+	16.0135i	1.71781	+	0.724153i
$490$	5.01727	−	14.1907i	0.226657	−	0.641073i
$491$	10.5405	+	6.08555i	0.475686	+	0.274637i	0.718617	−	0.695406i	$-0.244776\pi$
$491$	10.5405	+	6.08555i	0.475686	+	0.274637i	−0.242931	+	0.970044i	$0.578109\pi$
$492$	2.55815	+	20.4164i	0.115330	+	0.920443i
$493$	−20.7747	+	11.9943i	−0.935644	+	0.540194i
$494$	−9.20721	+	0.984075i	−0.414252	+	0.0442756i
$495$	1.32485	+	5.20376i	0.0595476	+	0.233892i
$496$	2.06419	+	1.19176i	0.0926850	+	0.0535117i
$497$	7.91994	+	21.4515i	0.355258	+	0.962232i
$498$	−1.59972	+	0.200443i	−0.0716852	+	0.00898207i
$499$	−16.3741	+	28.3607i	−0.733004	+	1.26960i	0.222589	+	0.974912i	$0.428549\pi$
$499$	−16.3741	+	28.3607i	−0.733004	+	1.26960i	−0.955593	+	0.294688i	$0.904784\pi$
$500$	5.78037	−	10.0119i	0.258506	−	0.447746i
$501$	4.61944	−	3.49897i	0.206381	−	0.156322i
$502$	−1.92977	−	1.11415i	−0.0861298	−	0.0497270i
$503$	14.6644	+	25.3994i	0.653852	+	1.13251i	0.982180	+	0.187941i	$0.0601815\pi$
$503$	14.6644	+	25.3994i	0.653852	+	1.13251i	−0.328328	+	0.944564i	$0.606485\pi$
$504$	4.50119	+	6.53753i	0.200499	+	0.291205i
$505$	−14.3717	+	24.8925i	−0.639533	+	1.10770i
$506$	1.79145	+	1.03429i	0.0796396	+	0.0459799i
$507$	7.45811	+	21.2456i	0.331226	+	0.943551i
$508$	−9.89702	−	17.1421i	−0.439109	−	0.760560i
$509$	21.0685	+	36.4917i	0.933843	+	1.61746i	0.776683	+	0.629891i	$0.216901\pi$
$509$	21.0685	+	36.4917i	0.933843	+	1.61746i	0.157160	+	0.987573i	$0.449766\pi$
$510$	−6.12417	−	8.08532i	−0.271183	−	0.358024i
$511$	11.5780	+	31.3596i	0.512182	+	1.38727i
$512$		−	1.00000i		−	0.0441942i
$513$	12.4224	−	4.87468i	0.548461	−	0.215222i
$514$	−5.37459	−	3.10302i	−0.237063	−	0.136868i
$515$	27.5928	−	15.9307i	1.21588	−	0.701990i
$516$	12.4220	+	5.23658i	0.546850	+	0.230528i
$517$	0.613362	+	0.354124i	0.0269756	+	0.0155744i
$518$	−0.304303	+	0.366070i	−0.0133703	+	0.0160842i
$519$	−31.4166	−	13.2439i	−1.37904	−	0.581341i
$520$	6.26409	−	4.56797i	0.274699	−	0.200319i
$521$	1.88398	+	3.26316i	0.0825389	+	0.142962i	0.904340	−	0.426813i	$-0.140364\pi$
$521$	1.88398	+	3.26316i	0.0825389	+	0.142962i	−0.821801	+	0.569775i	$0.807030\pi$
$522$	18.4500	+	18.9171i	0.807534	+	0.827980i
$523$	18.3198	−	10.5769i	0.801069	−	0.462498i	−0.0427757	−	0.999085i	$-0.513620\pi$
$523$	18.3198	−	10.5769i	0.801069	−	0.462498i	0.843845	+	0.536587i	$0.180287\pi$
$524$	−3.58433	−	6.20825i	−0.156582	−	0.271209i
$525$	−1.72369	−	0.0780879i	−0.0752281	−	0.00340804i
$526$	−12.2453	−	21.2094i	−0.533919	−	0.924774i
$527$			6.49136i			0.282768i
$528$	−1.43063	+	0.179257i	−0.0622603	+	0.00780114i
$529$	−8.41243	+	14.5707i	−0.365758	+	0.633511i
$530$	12.8962	+	22.3369i	0.560176	+	0.970253i
$531$	7.33663	−	1.86787i	0.318382	−	0.0810585i
$532$	4.34351	−	5.22515i	0.188315	−	0.226539i
$533$	−25.2371	−	34.6079i	−1.09314	−	1.49903i
$534$	1.19837	+	1.58213i	0.0518587	+	0.0684655i
$535$			3.01256i			0.130244i
$536$		−	6.61431i		−	0.285695i
$537$	−0.897504	+	2.12903i	−0.0387302	+	0.0918744i
$538$			5.00152i			0.215631i
$539$	1.94237	−	5.49378i	0.0836640	−	0.236634i
$540$	−6.96664	+	8.73497i	−0.299797	+	0.375893i
$541$	−9.07775	+	15.7231i	−0.390283	+	0.675990i	−0.992487	−	0.122352i	$-0.960956\pi$
$541$	−9.07775	+	15.7231i	−0.390283	+	0.675990i	0.602204	+	0.798343i	$0.294290\pi$
$542$	3.29636	−	5.70946i	0.141591	−	0.245242i
$543$	−0.761713	+	1.80691i	−0.0326882	+	0.0775420i
$544$	2.35856	−	1.36171i	0.101122	−	0.0583830i
$545$	17.4064			0.745610
$546$	−14.7876	−	7.37065i	−0.632852	−	0.315435i
$547$	26.8382			1.14752			0.573760	−	0.819023i	$-0.305484\pi$
$547$	26.8382			1.14752			0.573760	+	0.819023i	$0.305484\pi$
$548$	5.41593	−	3.12689i	0.231357	−	0.133574i
$549$	−7.84988	+	7.65603i	−0.335025	+	0.326751i
$550$	0.156717	−	0.271441i	0.00668242	−	0.0115743i
$551$	11.3104	−	19.5903i	0.481841	−	0.834574i
$552$	0.535117	+	4.27073i	0.0227761	+	0.181774i
$553$	12.6475	+	10.5135i	0.537828	+	0.447081i
$554$			16.9907i			0.721866i
$555$	−0.617468	−	0.260297i	−0.0262100	−	0.0110490i
$556$			2.08339i			0.0883555i
$557$		−	12.1400i		−	0.514388i	−0.966360	−	0.257194i	$-0.917202\pi$
$557$		−	12.1400i		−	0.514388i	0.966360	−	0.257194i	$-0.0827979\pi$
$558$	6.92952	−	1.76422i	0.293350	−	0.0746853i
$559$	−27.9034	+	2.98234i	−1.18019	+	0.126140i
$560$	−0.962029	+	5.60703i	−0.0406532	+	0.236940i
$561$	−2.37090	−	3.13013i	−0.100099	−	0.132154i
$562$	−1.55848	−	2.69937i	−0.0657405	−	0.113866i
$563$	−1.28773	+	2.23042i	−0.0542714	+	0.0940008i	−0.891885	−	0.452263i	$-0.850617\pi$
$563$	−1.28773	+	2.23042i	−0.0542714	+	0.0940008i	0.837613	+	0.546264i	$0.183950\pi$
$564$	0.183215	+	1.46222i	0.00771474	+	0.0615707i
$565$			7.82812i			0.329331i
$566$	6.20719	+	10.7512i	0.260908	+	0.451905i
$567$	23.3608	+	4.61212i	0.981063	+	0.193691i
$568$	−4.32143	−	7.48494i	−0.181323	−	0.314061i
$569$	24.5642	−	14.1822i	1.02979	−	0.594547i	0.112862	−	0.993611i	$-0.463998\pi$
$569$	24.5642	−	14.1822i	1.02979	−	0.594547i	0.916923	+	0.399064i	$0.130665\pi$
$570$	8.81350	+	3.71538i	0.369157	+	0.155620i
$571$	2.33873	+	4.05080i	0.0978729	+	0.169521i	0.910804	−	0.412839i	$-0.135463\pi$
$571$	2.33873	+	4.05080i	0.0978729	+	0.169521i	−0.812931	+	0.582360i	$0.802129\pi$
$572$	2.42507	−	1.76843i	0.101397	−	0.0739419i
$573$	−14.2900	+	33.8982i	−0.596972	+	1.41612i
$574$	30.9778	+	5.31503i	1.29299	+	0.221845i
$575$	−0.810307	−	0.467831i	−0.0337921	−	0.0195099i
$576$	−2.09464	−	2.14767i	−0.0872765	−	0.0894863i
$577$	39.9089	−	23.0414i	1.66143	−	0.959228i	0.689398	−	0.724382i	$-0.257875\pi$
$577$	39.9089	−	23.0414i	1.66143	−	0.959228i	0.972033	−	0.234845i	$-0.0754584\pi$
$578$	−8.29906	−	4.79147i	−0.345196	−	0.199299i
$579$	−4.99410	−	2.10529i	−0.207548	−	0.0874930i
$580$			18.9396i			0.786425i
$581$	−0.416457	+	2.42725i	−0.0172776	+	0.100699i
$582$	11.3022	−	8.56076i	0.468490	−	0.354855i
$583$	4.99261	+	8.64746i	0.206773	+	0.358141i
$584$	−6.31743	−	10.9421i	−0.261417	−	0.452787i
$585$	3.88499	−	22.9315i	0.160624	−	0.948101i
$586$	3.82017	+	2.20558i	0.157810	+	0.0911115i
$587$	4.23462	−	7.33458i	0.174781	−	0.302730i	−0.765304	−	0.643669i	$-0.777411\pi$
$587$	4.23462	−	7.33458i	0.174781	−	0.302730i	0.940086	+	0.340938i	$0.110745\pi$
$588$	11.5523	−	3.68023i	0.476409	−	0.151770i
$589$	−3.06064	−	5.30118i	−0.126111	−	0.218431i
$590$	4.69924	+	2.71311i	0.193465	+	0.111697i
$591$	−12.8905	−	17.0185i	−0.530245	−	0.700046i
$592$	0.0899619	−	0.155819i	0.00369741	−	0.00640410i
$593$	−4.98232	+	8.62964i	−0.204599	+	0.354377i	−0.950005	−	0.312235i	$-0.898923\pi$
$593$	−4.98232	+	8.62964i	−0.204599	+	0.354377i	0.745406	+	0.666611i	$0.232256\pi$
$594$	−2.69705	+	3.38164i	−0.110661	+	0.138750i
$595$	−14.5345	+	5.36617i	−0.595857	+	0.219992i
$596$	10.5983	+	6.11893i	0.434123	+	0.250641i
$597$	−28.6679	−	37.8482i	−1.17330	−	1.54902i
$598$	−5.27913	−	7.23932i	−0.215880	−	0.296038i
$599$	29.5283	−	17.0482i	1.20649	−	0.696569i	0.244502	−	0.969649i	$-0.421376\pi$
$599$	29.5283	−	17.0482i	1.20649	−	0.696569i	0.961991	+	0.273080i	$0.0880423\pi$
$600$	0.647102	−	0.0810812i	0.0264178	−	0.00331013i
$601$	−10.4907	−	6.05683i	−0.427926	−	0.247063i	0.270537	−	0.962710i	$-0.412799\pi$
$601$	−10.4907	−	6.05683i	−0.427926	−	0.247063i	−0.698463	+	0.715646i	$0.746132\pi$
$602$	13.1635	−	15.8353i	0.536502	−	0.645400i
$603$	−13.8546	−	14.2054i	−0.564202	−	0.578487i
$604$	1.00792			0.0410116
$605$	11.0812	−	19.1933i	0.450517	−	0.780318i
$606$	−22.9738	+	2.87859i	−0.933245	+	0.116935i
$607$		−	21.1731i		−	0.859391i	−0.902974	−	0.429696i	$-0.858621\pi$
$607$		−	21.1731i		−	0.859391i	0.902974	−	0.429696i	$-0.141379\pi$
$608$	−1.28408	+	2.22409i	−0.0520764	+	0.0901990i
$609$	35.8340	−	18.5794i	1.45207	−	0.752877i
$610$	−7.85921			−0.318210
$611$	−1.80748	−	2.47862i	−0.0731230	−	0.100274i
$612$	2.21311	−	7.86484i	0.0894598	−	0.317917i
$613$	−6.13885			−0.247946			−0.123973	−	0.992286i	$-0.539564\pi$
$613$	−6.13885			−0.247946			−0.123973	+	0.992286i	$0.539564\pi$
$614$	8.12172	+	14.0672i	0.327766	+	0.567707i
$615$	5.50061	+	43.8999i	0.221806	+	1.77022i
$616$	−0.372438	+	2.17070i	−0.0150060	+	0.0874598i
$617$	−12.0384	+	6.95037i	−0.484647	+	0.279811i	−0.722351	−	0.691526i	$-0.756939\pi$
$617$	−12.0384	+	6.95037i	−0.484647	+	0.279811i	0.237704	+	0.971338i	$0.423605\pi$
$618$	23.6495	+	9.96958i	0.951323	+	0.401036i
$619$	−19.7752	+	11.4172i	−0.794833	+	0.458897i	−0.841661	−	0.540006i	$-0.818422\pi$
$619$	−19.7752	+	11.4172i	−0.794833	+	0.458897i	0.0468282	+	0.998903i	$0.485089\pi$
$620$	4.43848	+	2.56256i	0.178254	+	0.102915i
$621$	10.0949	+	8.05124i	0.405093	+	0.323085i
$622$	−21.6238	−	12.4845i	−0.867034	−	0.500582i
$623$	2.84411	−	1.05005i	0.113947	−	0.0420694i
$624$	5.97980	+	1.80056i	0.239383	+	0.0720802i
$625$	11.4878	−	19.8975i	0.459512	−	0.795898i
$626$	26.6344			1.06452
$627$	3.41204	+	1.43836i	0.136264	+	0.0574428i
$628$		−	15.7323i		−	0.627788i
$629$	0.490010			0.0195380
$630$	9.67857	+	14.0572i	0.385604	+	0.560051i
$631$	19.2785	+	33.3914i	0.767467	+	1.32929i	0.938932	+	0.344101i	$0.111816\pi$
$631$	19.2785	+	33.3914i	0.767467	+	1.32929i	−0.171466	+	0.985190i	$0.554850\pi$
$632$	−5.38345	−	3.10814i	−0.214142	−	0.123635i
$633$	−32.5057	+	24.6212i	−1.29198	+	0.978605i
$634$	8.35528			0.331831
$635$	−21.2808	−	36.8595i	−0.844504	−	1.46272i
$636$	−8.07057	+	19.1447i	−0.320019	+	0.759139i
$637$	−17.3320	+	18.3467i	−0.686718	+	0.726924i
$638$			7.33225i			0.290287i
$639$	−24.9592	−	7.02337i	−0.987372	−	0.277840i
$640$		−	2.15023i		−	0.0849952i
$641$	−17.0599	−	9.84956i	−0.673827	−	0.389034i	0.123698	−	0.992320i	$-0.460525\pi$
$641$	−17.0599	−	9.84956i	−0.673827	−	0.389034i	−0.797525	+	0.603286i	$0.793858\pi$
$642$	−1.93441	+	1.46520i	−0.0763450	+	0.0578270i
$643$	−5.10073	+	2.94491i	−0.201153	+	0.116136i	−0.597193	−	0.802097i	$-0.703717\pi$
$643$	−5.10073	+	2.94491i	−0.201153	+	0.116136i	0.396040	+	0.918233i	$0.370384\pi$
$644$	6.47996	+	1.11180i	0.255346	+	0.0438112i
$645$	26.7102	+	11.2598i	1.05171	+	0.443356i
$646$	−6.99421			−0.275184
$647$	−31.7906			−1.24982			−0.624908	−	0.780698i	$-0.714864\pi$
$647$	−31.7906			−1.24982			−0.624908	+	0.780698i	$0.714864\pi$
$648$	−8.99719	−	0.224993i	−0.353443	−	0.00883857i
$649$	1.81926	+	1.05035i	0.0714120	+	0.0412297i
$650$	−1.09690	+	0.799896i	−0.0430241	+	0.0313745i
$651$	0.494320	−	10.9115i	0.0193739	−	0.427655i
$652$	−11.9003	+	20.6120i	−0.466052	+	0.807227i
$653$	−16.1732	+	9.33759i	−0.632905	+	0.365408i	−0.781876	−	0.623433i	$-0.785737\pi$
$653$	−16.1732	+	9.33759i	−0.632905	+	0.365408i	0.148971	+	0.988842i	$0.452404\pi$
$654$	8.46590	+	11.1769i	0.331043	+	0.437053i
$655$	−7.70713	−	13.3491i	−0.301143	−	0.521594i
$656$	−11.8796			−0.463820
$657$	−36.4875	−	10.2673i	−1.42351	−	0.400567i
$658$	2.21863	+	0.380662i	0.0864912	+	0.0148398i
$659$	39.2891	−	22.6836i	1.53049	−	0.883626i	0.531146	−	0.847280i	$-0.321762\pi$
$659$	39.2891	−	22.6836i	1.53049	−	0.883626i	0.999339	−	0.0363457i	$-0.0115717\pi$
$660$	−3.07618	+	0.385442i	−0.119740	+	0.0150033i
$661$		−	8.27276i		−	0.321773i	−0.986973	−	0.160887i	$-0.948565\pi$
$661$		−	8.27276i		−	0.321773i	0.986973	−	0.160887i	$-0.0514353\pi$
$662$	−13.7950	+	7.96452i	−0.536156	+	0.309550i
$663$	3.89604	+	16.5556i	0.151310	+	0.642965i
$664$		−	0.930821i		−	0.0361229i
$665$	9.33953	−	11.2352i	0.362172	−	0.435684i
$666$	−0.133175	−	0.523085i	−0.00516041	−	0.0202691i
$667$	21.8882			0.847516
$668$	1.67287	+	2.89750i	0.0647254	+	0.112108i
$669$	−30.7044	−	40.5369i	−1.18710	−	1.56725i
$670$		−	14.2223i		−	0.549454i
$671$	−3.04260			−0.117458
$672$	−4.06826	+	2.10933i	−0.156936	+	0.0813694i
$673$	3.04087	−	5.26695i	0.117217	−	0.203026i	−0.801447	−	0.598066i	$-0.795936\pi$
$673$	3.04087	−	5.26695i	0.117217	−	0.203026i	0.918664	+	0.395040i	$0.129269\pi$
$674$	1.20207	−	0.694014i	0.0463019	−	0.0267324i
$675$	1.21993	−	1.52958i	0.0469551	−	0.0588736i
$676$	−12.7063	+	2.74752i	−0.488705	+	0.105674i
$677$	−4.15629	+	7.19891i	−0.159739	+	0.276677i	−0.934775	−	0.355241i	$-0.884399\pi$
$677$	−4.15629	+	7.19891i	−0.159739	+	0.276677i	0.775035	+	0.631918i	$0.217732\pi$
$678$	−5.02655	+	3.80733i	−0.193043	+	0.146220i
$679$	−7.50118	−	20.3173i	−0.287869	−	0.779706i
$680$	5.07144	−	2.92799i	0.194481	−	0.112283i
$681$	−39.1924	+	29.6861i	−1.50186	+	1.13757i
$682$	1.71830	+	0.992063i	0.0657973	+	0.0379881i
$683$	−24.6429	−	14.2276i	−0.942935	−	0.544404i	−0.0520558	−	0.998644i	$-0.516577\pi$
$683$	−24.6429	−	14.2276i	−0.942935	−	0.544404i	−0.890879	+	0.454240i	$0.849911\pi$
$684$	1.90088	+	7.46631i	0.0726821	+	0.285482i
$685$	11.6455	−	6.72352i	0.444951	−	0.256893i
$686$	−0.256233	−	18.5185i	−0.00978304	−	0.707039i
$687$	15.2302	+	20.1074i	0.581069	+	0.767145i
$688$	−3.89154	+	6.74035i	−0.148364	+	0.256973i
$689$	−4.59635	−	43.0044i	−0.175107	−	1.63834i
$690$	1.15062	+	9.18303i	0.0438035	+	0.349592i
$691$	13.1288	−	7.57990i	0.499442	−	0.288353i	−0.229041	−	0.973417i	$-0.573559\pi$
$691$	13.1288	−	7.57990i	0.499442	−	0.288353i	0.728483	+	0.685064i	$0.240226\pi$
$692$	9.84211	−	17.0470i	0.374141	−	0.648031i
$693$	3.74694	+	5.44207i	0.142335	+	0.206727i
$694$	0.408244			0.0154967
$695$			4.47976i			0.169927i
$696$	−12.1614	+	9.21158i	−0.460977	+	0.349164i
$697$	−16.1766	−	28.0187i	−0.612733	−	1.06128i
$698$	−1.80104			−0.0681705
$699$	−15.4714	−	20.4258i	−0.585182	−	0.772575i
$700$	0.168461	−	0.981847i	0.00636722	−	0.0371103i
$701$			26.0859i			0.985251i	0.870241	+	0.492625i	$0.163963\pi$
$701$			26.0859i			0.985251i	−0.870241	+	0.492625i	$0.836037\pi$
$702$	16.6142	−	8.65848i	0.627061	−	0.326793i
$703$	−0.400167	+	0.231037i	−0.0150926	+	0.00871372i
$704$		−	0.832434i		−	0.0313736i
$705$	0.393954	+	3.14411i	0.0148372	+	0.118414i
$706$	−20.7468	+	11.9782i	−0.780816	+	0.450805i
$707$	−5.98079	+	34.8581i	−0.224931	+	1.31097i
$708$	0.543423	+	4.33701i	0.0204231	+	0.162995i
$709$	−19.1268			−0.718322			−0.359161	−	0.933276i	$-0.616937\pi$
$709$	−19.1268			−0.718322			−0.359161	+	0.933276i	$0.616937\pi$
$710$	−9.29205	−	16.0943i	−0.348725	−	0.604009i
$711$	−18.0723	+	4.60112i	−0.677765	+	0.172555i
$712$	−0.992375	+	0.572948i	−0.0371908	+	0.0214721i
$713$	2.96151	−	5.12949i	0.110909	−	0.192101i
$714$	−10.5148	−	6.72291i	−0.393506	−	0.251599i
$715$	5.21445	−	3.80253i	0.195009	−	0.142207i
$716$	−1.15524	−	0.666976i	−0.0431732	−	0.0249261i
$717$	13.4739	−	31.9624i	0.503192	−	1.19366i
$718$	−8.24875			−0.307841
$719$	21.8915			0.816416			0.408208	−	0.912889i	$-0.366154\pi$
$719$	21.8915			0.816416			0.408208	+	0.912889i	$0.366154\pi$
$720$	−4.50394	−	4.61798i	−0.167852	−	0.172102i
$721$	25.0610	−	30.1479i	0.933322	−	1.12276i
$722$	−10.7426	+	6.20227i	−0.399800	+	0.230825i
$723$	10.8796	+	14.3636i	0.404616	+	0.534187i
$724$	−0.980451	−	0.566063i	−0.0364382	−	0.0210376i
$725$		−	3.31652i		−	0.123172i
$726$	17.7138	−	2.21952i	0.657422	−	0.0823742i
$727$		−	33.9953i		−	1.26082i	−0.776264	−	0.630408i	$-0.782888\pi$
$727$		−	33.9953i		−	1.26082i	0.776264	−	0.630408i	$-0.217112\pi$
$728$	5.28388	−	7.94233i	0.195834	−	0.294362i
$729$	−19.7943	+	18.3626i	−0.733122	+	0.680097i
$730$	−13.5839	−	23.5280i	−0.502763	−	0.870810i
$731$	−21.1967			−0.783987
$732$	−3.82245	−	5.04651i	−0.141282	−	0.186525i
$733$	−21.2418	−	12.2639i	−0.784582	−	0.452979i	0.0534695	−	0.998569i	$-0.482972\pi$
$733$	−21.2418	−	12.2639i	−0.784582	−	0.452979i	−0.838052	+	0.545591i	$0.816305\pi$
$734$	5.83498	+	10.1065i	0.215373	+	0.373037i
$735$	24.8401	−	7.91333i	0.916240	−	0.291887i
$736$	−2.48498			−0.0915978
$737$		−	5.50598i		−	0.202815i
$738$	−25.5135	+	24.8834i	−0.939164	+	0.915972i
$739$	25.0721			0.922293			0.461146	−	0.887324i	$-0.347438\pi$
$739$	25.0721			0.922293			0.461146	+	0.887324i	$0.347438\pi$
$740$	0.193438	−	0.335045i	0.00711094	−	0.0123165i
$741$	−10.9876	−	11.6832i	−0.403638	−	0.429192i
$742$	24.4053	+	20.2874i	0.895946	+	0.744774i
$743$	−0.168411	−	0.0972319i	−0.00617839	−	0.00356709i	0.496908	−	0.867803i	$-0.334469\pi$
$743$	−0.168411	−	0.0972319i	−0.00617839	−	0.00356709i	−0.503086	+	0.864236i	$0.667802\pi$
$744$	0.513268	+	4.09635i	0.0188173	+	0.150180i
$745$	22.7887	+	13.1571i	0.834915	+	0.482038i
$746$	27.6209	−	15.9469i	1.01127	−	0.583859i
$747$	−1.94973	−	1.99910i	−0.0713370	−	0.0731432i
$748$	1.96335	−	1.13354i	0.0717870	−	0.0414463i
$749$	1.28385	+	3.47738i	0.0469110	+	0.127061i
$750$	19.8684	−	2.48949i	0.725493	−	0.0909034i
$751$	10.7645	+	18.6447i	0.392803	+	0.680356i	0.992818	−	0.119633i	$-0.0381719\pi$
$751$	10.7645	+	18.6447i	0.392803	+	0.680356i	−0.600015	+	0.799989i	$0.704839\pi$
$752$	−0.850817			−0.0310261
$753$	−0.479843	−	3.82959i	−0.0174865	−	0.139558i
$754$	12.8663	−	29.0354i	0.468564	−	1.05741i
$755$	2.16725			0.0788743
$756$	−4.31899	+	13.0517i	−0.157080	+	0.474685i
$757$	−24.5972	+	42.6036i	−0.894000	+	1.54845i	−0.0589622	+	0.998260i	$0.518779\pi$
$757$	−24.5972	+	42.6036i	−0.894000	+	1.54845i	−0.835038	+	0.550193i	$0.814554\pi$
$758$		−	19.8659i		−	0.721560i
$759$	0.445450	+	3.55510i	0.0161688	+	0.129042i
$760$	−2.76107	+	4.78231i	−0.100154	+	0.173473i
$761$	−0.296264			−0.0107396			−0.00536978	−	0.999986i	$-0.501709\pi$
$761$	−0.296264			−0.0107396			−0.00536978	+	0.999986i	$0.501709\pi$
$762$	13.3178	−	31.5919i	0.482451	−	1.14445i
$763$	20.0922	−	7.41806i	0.727385	−	0.268552i
$764$	−18.3935	−	10.6195i	−0.665455	−	0.384201i
$765$	4.75870	−	16.9112i	0.172051	−	0.611425i
$766$	0.635039	−	0.366640i	0.0229449	−	0.0132472i
$767$	−5.36107	−	7.35168i	−0.193577	−	0.265454i
$768$	1.38069	−	1.04580i	0.0498214	−	0.0377369i
$769$	−27.7574	−	16.0257i	−1.00096	−	0.577902i	−0.0924253	−	0.995720i	$-0.529462\pi$
$769$	−27.7574	−	16.0257i	−1.00096	−	0.577902i	−0.908531	+	0.417817i	$0.862795\pi$
$770$	−0.800826	+	4.66749i	−0.0288598	+	0.168205i
$771$	−1.33641	−	10.6658i	−0.0481297	−	0.384119i
$772$	1.56454	−	2.70986i	0.0563089	−	0.0975299i
$773$	−12.7483	+	22.0808i	−0.458526	+	0.794190i	−0.998883	−	0.0472456i	$-0.984956\pi$
$773$	−12.7483	+	22.0808i	−0.458526	+	0.794190i	0.540358	+	0.841436i	$0.318289\pi$
$774$	5.76082	+	22.6274i	0.207069	+	0.813326i
$775$	−0.777222	−	0.448729i	−0.0279186	−	0.0161188i
$776$	4.09294	+	7.08918i	0.146928	+	0.254487i
$777$	−0.823669	−	0.0373145i	−0.0295490	−	0.00133865i
$778$	−16.5442	+	28.6554i	−0.593139	+	1.02735i
$779$	26.4213	+	15.2544i	0.946643	+	0.546544i
$780$	12.8579	+	3.87162i	0.460387	+	0.138626i
$781$	−3.59731	−	6.23072i	−0.128722	−	0.222953i
$782$	−3.38384	−	5.86098i	−0.121006	−	0.209588i
$783$	−6.82381	+	45.2572i	−0.243863	+	1.61736i
$784$	1.27907	+	6.88215i	0.0456811	+	0.245791i
$785$		−	33.8281i		−	1.20738i
$786$	4.82320	−	11.4414i	0.172038	−	0.408102i
$787$	−18.7342	−	10.8162i	−0.667802	−	0.385556i	0.127441	−	0.991846i	$-0.459324\pi$
$787$	−18.7342	−	10.8162i	−0.667802	−	0.385556i	−0.795243	+	0.606290i	$0.792657\pi$
$788$	10.6747	−	6.16302i	0.380269	−	0.219548i
$789$	16.4776	−	39.0877i	0.586619	−	1.39156i
$790$	−11.5756	−	6.68320i	−0.411843	−	0.237778i
$791$	3.33609	+	9.03595i	0.118618	+	0.321281i
$792$	−1.74365	−	1.78780i	−0.0619578	−	0.0635266i
$793$	12.0486	+	5.33902i	0.427857	+	0.189594i
$794$	−5.94426	−	10.2958i	−0.210954	−	0.365383i
$795$	−17.3536	+	41.1655i	−0.615467	+	1.45999i
$796$	23.7399	−	13.7062i	0.841439	−	0.485805i
$797$	−21.2264	−	36.7652i	−0.751878	−	1.30229i	−0.946911	−	0.321495i	$-0.895815\pi$
$797$	−21.2264	−	36.7652i	−0.751878	−	1.30229i	0.195033	−	0.980797i	$-0.437519\pi$
$798$	11.7567	+	0.532613i	0.416184	+	0.0188543i
$799$	−1.15857	−	2.00670i	−0.0409872	−	0.0709920i
$800$			0.376526i			0.0133122i
$801$	−0.931179	+	3.30917i	−0.0329016	+	0.116924i
$802$	11.7969	−	20.4328i	0.416562	−	0.721506i
$803$	−5.25884	−	9.10858i	−0.185581	−	0.321435i
$804$	9.13233	−	6.91722i	0.322072	−	0.243952i
$805$	13.9334	+	2.39063i	0.491088	+	0.0842586i
$806$	−5.06359	−	6.94374i	−0.178357	−	0.244583i
$807$	−6.90556	+	5.23057i	−0.243087	+	0.184125i
$808$		−	13.3676i		−	0.470271i
$809$			31.0882i			1.09300i	0.837459	+	0.546501i	$0.184040\pi$
$809$			31.0882i			1.09300i	−0.837459	+	0.546501i	$0.815960\pi$
$810$	−19.3460	−	0.483787i	−0.679749	−	0.0169985i
$811$		−	35.7680i		−	1.25598i	−0.778220	−	0.627992i	$-0.783877\pi$
$811$		−	35.7680i		−	1.25598i	0.778220	−	0.627992i	$-0.216123\pi$
$812$	8.07145	+	21.8619i	0.283252	+	0.767202i
$813$	11.3303	−	1.41968i	0.397372	−	0.0497902i
$814$	0.0748874	−	0.129709i	0.00262480	−	0.00454629i
$815$	−25.5884	+	44.3204i	−0.896322	+	1.55248i
$816$	4.34668	+	1.83237i	0.152164	+	0.0641457i
$817$	17.3103	−	9.99411i	0.605611	−	0.349650i
$818$	11.3544			0.396996
$819$	−5.28824	−	28.1253i	−0.184786	−	0.982779i
$820$	−25.5438			−0.892028
$821$	6.56245	−	3.78883i	0.229031	−	0.132231i	−0.381094	−	0.924536i	$-0.624453\pi$
$821$	6.56245	−	3.78883i	0.229031	−	0.132231i	0.610125	+	0.792305i	$0.291119\pi$
$822$	9.98123	+	4.20764i	0.348135	+	0.146758i
$823$	1.50612	−	2.60868i	0.0525000	−	0.0909327i	−0.838581	−	0.544777i	$-0.816614\pi$
$823$	1.50612	−	2.60868i	0.0525000	−	0.0909327i	0.891081	+	0.453844i	$0.149948\pi$
$824$	−7.40885	+	12.8325i	−0.258099	+	0.447041i
$825$	0.538670	−	0.0674948i	0.0187541	−	0.00234987i
$826$	6.58054	+	1.12906i	0.228966	+	0.0392850i
$827$		−	17.7430i		−	0.616984i	−0.951227	−	0.308492i	$-0.900176\pi$
$827$		−	17.7430i		−	0.616984i	0.951227	−	0.308492i	$-0.0998243\pi$
$828$	−5.33693	+	5.20514i	−0.185471	+	0.180891i
$829$			38.9984i			1.35447i	0.735766	+	0.677236i	$0.236822\pi$
$829$			38.9984i			1.35447i	−0.735766	+	0.677236i	$0.763178\pi$
$830$		−	2.00148i		−	0.0694723i
$831$	−23.4589	+	17.7688i	−0.813781	+	0.616393i
$832$	−1.46072	+	3.29641i	−0.0506414	+	0.114282i
$833$	−14.4902	+	12.3883i	−0.502057	+	0.429229i
$834$	−2.87652	+	2.17880i	−0.0996058	+	0.0754458i
$835$	3.59705	+	6.23028i	0.124481	+	0.215608i
$836$	−1.06891	+	1.85141i	−0.0369692	+	0.0640325i
$837$	9.68270	+	7.72251i	0.334683	+	0.266929i
$838$			12.7128i			0.439157i
$839$	16.2641	+	28.1703i	0.561501	+	0.972548i	0.997366	+	0.0725356i	$0.0231091\pi$
$839$	16.2641	+	28.1703i	0.561501	+	0.972548i	−0.435865	+	0.900012i	$0.643558\pi$
$840$	−8.74767	+	4.53555i	−0.301823	+	0.156491i
$841$	24.2922	+	42.0753i	0.837662	+	1.45087i
$842$	−31.6237	+	18.2580i	−1.08983	+	0.629211i
$843$	2.09714	−	4.97477i	0.0722294	−	0.171340i
$844$	−11.7715	−	20.3889i	−0.405192	−	0.701814i
$845$	−27.3215	+	5.90779i	−0.939889	+	0.203234i
$846$	−1.82728	+	1.78215i	−0.0628230	+	0.0612716i
$847$	4.61146	−	26.8772i	0.158452	−	0.923510i
$848$	−10.3882	−	5.99761i	−0.356731	−	0.205959i
$849$	−8.35260	+	19.8138i	−0.286660	+	0.680006i
$850$	−0.888059	+	0.512721i	−0.0304602	+	0.0175862i
$851$	−0.387207	−	0.223554i	−0.0132733	−	0.00766333i
$852$	5.81506	−	13.7943i	0.199221	−	0.472584i
$853$		−	15.8564i		−	0.542914i	−0.962451	−	0.271457i	$-0.912495\pi$
$853$		−	15.8564i		−	0.542914i	0.962451	−	0.271457i	$-0.0875054\pi$
$854$	−9.07184	+	3.34934i	−0.310432	+	0.114612i
$855$	4.08733	+	16.0543i	0.139784	+	0.549044i
$856$	−0.700521	−	1.21334i	−0.0239433	−	0.0414711i
$857$	−24.1157	−	41.7696i	−0.823776	−	1.42682i	−0.902851	−	0.429953i	$-0.858530\pi$
$857$	−24.1157	−	41.7696i	−0.823776	−	1.42682i	0.0790749	−	0.996869i	$-0.474803\pi$
$858$	4.97779	+	1.49885i	0.169939	+	0.0511699i
$859$	−31.3554	−	18.1031i	−1.06983	−	0.617669i	−0.141697	−	0.989910i	$-0.545256\pi$
$859$	−31.3554	−	18.1031i	−1.06983	−	0.617669i	−0.928136	+	0.372241i	$0.878589\pi$
$860$	−8.36769	+	14.4933i	−0.285336	+	0.494216i
$861$	25.0580	+	48.3292i	0.853975	+	1.64706i
$862$	2.98835	+	5.17597i	0.101784	+	0.176294i
$863$	29.7766	+	17.1915i	1.01361	+	0.585207i	0.912246	−	0.409643i	$-0.134347\pi$
$863$	29.7766	+	17.1915i	1.01361	+	0.585207i	0.101362	+	0.994850i	$0.467680\pi$
$864$	0.774711	−	5.13808i	0.0263562	−	0.174801i
$865$	21.1628	−	36.6550i	0.719555	−	1.24631i
$866$	15.6275	−	27.0676i	0.531044	−	0.919794i
$867$	−2.06359	−	16.4693i	−0.0700832	−	0.559328i
$868$	6.21539	+	1.06641i	0.210964	+	0.0361963i
$869$	−4.48137	−	2.58732i	−0.152020	−	0.0877688i
$870$	−26.1498	+	19.8070i	−0.886561	+	0.671520i
$871$	−9.66166	+	21.8035i	−0.327373	+	0.738782i
$872$	−7.01062	+	4.04758i	−0.237410	+	0.137068i
$873$	23.6395	+	6.65201i	0.800077	+	0.225136i
$874$	5.52684	+	3.19092i	0.186948	+	0.107935i
$875$	5.17238	−	30.1464i	0.174858	−	1.01913i
$876$	8.50093	−	20.1656i	0.287220	−	0.681334i
$877$	32.0236			1.08136			0.540680	−	0.841228i	$-0.318167\pi$
$877$	32.0236			1.08136			0.540680	+	0.841228i	$0.318167\pi$
$878$	−14.8945	+	25.7980i	−0.502664	+	0.870640i
$879$	0.949898	+	7.58106i	0.0320393	+	0.255703i
$880$		−	1.78992i		−	0.0603383i
$881$	15.9277	−	27.5876i	0.536619	−	0.929451i	−0.462464	−	0.886638i	$-0.653035\pi$
$881$	15.9277	−	27.5876i	0.536619	−	0.929451i	0.999083	−	0.0428131i	$-0.0136320\pi$
$882$	17.1626	+	12.1014i	0.577896	+	0.407476i
$883$	33.5180			1.12797			0.563986	−	0.825784i	$-0.309267\pi$
$883$	33.5180			1.12797			0.563986	+	0.825784i	$0.309267\pi$
$884$	−9.76385	+	1.04357i	−0.328394	+	0.0350991i
$885$	1.16848	+	9.32556i	0.0392781	+	0.313475i
$886$	21.2468			0.713801
$887$	−13.5728	−	23.5087i	−0.455729	−	0.789346i	0.543001	−	0.839732i	$-0.317288\pi$
$887$	−13.5728	−	23.5087i	−0.455729	−	0.789346i	−0.998730	+	0.0503866i	$0.983955\pi$
$888$	0.309219	−	0.0387448i	0.0103767	−	0.00130019i
$889$	−40.2727	−	33.4775i	−1.35070	−	1.12280i
$890$	−2.13383	+	1.23197i	−0.0715262	+	0.0412957i
$891$	−7.48957	−	0.187292i	−0.250910	−	0.00627452i
$892$	25.4264	−	14.6799i	0.851338	−	0.491520i
$893$	1.89230	+	1.09252i	0.0633233	+	0.0365597i
$894$	2.63530	+	21.0321i	0.0881377	+	0.703420i
$895$	−2.48402	−	1.43415i	−0.0830316	−	0.0479383i
$896$	−0.916357	−	2.48199i	−0.0306133	−	0.0829176i
$897$	4.47437	−	14.8597i	0.149395	−	0.496151i
$898$	14.2344	−	24.6546i	0.475006	−	0.822735i
$899$	20.9946			0.700208
$900$	0.788685	+	0.808655i	0.0262895	+	0.0269552i
$901$		−	32.6681i		−	1.08833i
$902$	−9.88898			−0.329267
$903$	35.6300	+	1.61414i	1.18569	+	0.0537151i
$904$	−1.82030	−	3.15285i	−0.0605423	−	0.104862i
$905$	−2.10819	−	1.21716i	−0.0700786	−	0.0404599i
$906$	1.05408	+	1.39162i	0.0350193	+	0.0462336i
$907$	−13.9235			−0.462323			−0.231161	−	0.972915i	$-0.574253\pi$
$907$	−13.9235			−0.462323			−0.231161	+	0.972915i	$0.574253\pi$
$908$	−14.1930	−	24.5831i	−0.471013	−	0.815818i
$909$	−28.0003	−	28.7093i	−0.928712	−	0.952227i
$910$	11.3615	−	17.0778i	0.376632	−	0.566124i
$911$			25.3251i			0.839057i	0.907742	+	0.419528i	$0.137805\pi$
$911$			25.3251i			0.839057i	−0.907742	+	0.419528i	$0.862195\pi$
$912$	−4.41368	+	0.553029i	−0.146151	+	0.0183126i
$913$		−	0.774847i		−	0.0256437i
$914$	−17.6783	−	10.2066i	−0.584746	−	0.337604i
$915$	−8.21913	−	10.8511i	−0.271716	−	0.358728i
$916$	−12.6122	+	7.28164i	−0.416718	+	0.240592i
$917$	−14.5853	−	12.1243i	−0.481648	−	0.400380i
$918$	13.1734	−	5.16939i	0.434787	−	0.170615i
$919$	−13.0009			−0.428859			−0.214430	−	0.976739i	$-0.568789\pi$
$919$	−13.0009			−0.428859			−0.214430	+	0.976739i	$0.568789\pi$
$920$	−5.34328			−0.176163
$921$	−10.9288	+	25.9250i	−0.360118	+	0.854259i
$922$	−1.57616	−	0.909994i	−0.0519079	−	0.0299691i
$923$	3.31179	+	30.9858i	0.109009	+	1.01991i
$924$	−3.38656	+	1.75588i	−0.111410	+	0.0577643i
$925$	−0.0338730	+	0.0586697i	−0.00111374	+	0.00192905i
$926$	19.1036	−	11.0295i	0.627783	−	0.362451i
$927$	10.9676	+	43.0788i	0.360225	+	1.41490i
$928$	−4.40410	−	7.62813i	−0.144572	−	0.250405i
$929$	−53.5840			−1.75803			−0.879017	−	0.476791i	$-0.841800\pi$
$929$	−53.5840			−1.75803			−0.879017	+	0.476791i	$0.841800\pi$
$930$	1.10364	+	8.80809i	0.0361899	+	0.288829i
$931$	5.99247	−	16.9490i	0.196395	−	0.555481i
$932$	12.8119	−	7.39695i	0.419667	−	0.242295i
$933$	−5.37682	−	42.9120i	−0.176029	−	1.40488i
$934$			7.52003i			0.246063i
$935$	4.22164	−	2.43736i	0.138062	−	0.0797103i
$936$	3.76763	+	10.1393i	0.123149	+	0.331413i
$937$			19.6964i			0.643454i	0.946833	+	0.321727i	$0.104263\pi$
$937$			19.6964i			0.643454i	−0.946833	+	0.321727i	$0.895737\pi$
$938$	−6.06107	−	16.4167i	−0.197901	−	0.536023i
$939$	27.8542	+	36.7739i	0.908986	+	1.20007i
$940$	−1.82945			−0.0596700
$941$	7.34272	+	12.7180i	0.239366	+	0.414594i	0.960533	−	0.278168i	$-0.0897271\pi$
$941$	7.34272	+	12.7180i	0.239366	+	0.414594i	−0.721167	+	0.692762i	$0.756394\pi$
$942$	21.7215	−	16.4528i	0.707725	−	0.536062i
$943$			29.5206i			0.961323i
$944$	−2.52356			−0.0821348
$945$	−9.28681	+	28.0641i	−0.302100	+	0.912924i
$946$	−3.23945	+	5.61090i	−0.105324	+	0.182426i
$947$	−24.6038	+	14.2050i	−0.799517	+	0.461601i	−0.843302	−	0.537440i	$-0.819392\pi$
$947$	−24.6038	+	14.2050i	−0.799517	+	0.461601i	0.0437853	+	0.999041i	$0.486058\pi$
$948$	−1.33861	−	10.6834i	−0.0434761	−	0.346980i
$949$	4.84145	+	45.2976i	0.157160	+	1.47042i
$950$	0.483490	−	0.837430i	0.0156865	−	0.0271698i
$951$	8.73792	+	11.5361i	0.283347	+	0.374083i
$952$	4.60611	−	5.54105i	0.149285	−	0.179586i
$953$	−25.9570	+	14.9863i	−0.840829	+	0.485453i	−0.857546	−	0.514408i	$-0.828012\pi$
$953$	−25.9570	+	14.9863i	−0.840829	+	0.485453i	0.0167172	+	0.999860i	$0.494679\pi$
$954$	−34.8732	+	8.87853i	−1.12906	+	0.287453i
$955$	−39.5503	−	22.8344i	−1.27982	−	0.738903i
$956$	17.3431	+	10.0131i	0.560917	+	0.323846i
$957$	−10.1236	+	7.66804i	−0.327249	+	0.247872i
$958$	26.7035	−	15.4173i	0.862751	−	0.498109i
$959$	10.5770	−	12.7238i	0.341548	−	0.410874i
$960$	2.96880	−	2.24870i	0.0958176	−	0.0725764i
$961$	−12.6594	+	21.9267i	−0.408368	+	0.707314i
$962$	−0.524158	+	0.382232i	−0.0168995	+	0.0123237i
$963$	−4.04599	−	1.13852i	−0.130380	−	0.0366882i
$964$	−9.00940	+	5.20158i	−0.290173	+	0.167532i
$965$	3.36411	−	5.82681i	0.108295	−	0.187572i
$966$	5.24166	+	10.1096i	0.168648	+	0.325270i
$967$	51.3555			1.65148			0.825741	−	0.564050i	$-0.190758\pi$
$967$	51.3555			1.65148			0.825741	+	0.564050i	$0.190758\pi$
$968$			10.3071i			0.331281i
$969$	−7.31452	−	9.65685i	−0.234976	−	0.310223i
$970$	8.80074	+	15.2433i	0.282575	+	0.489434i
$971$	30.4755			0.978005			0.489003	−	0.872282i	$-0.337361\pi$
$971$	30.4755			0.978005			0.489003	+	0.872282i	$0.337361\pi$
$972$	−9.09858	−	12.6576i	−0.291837	−	0.405994i
$973$	1.90913	+	5.17096i	0.0612039	+	0.165773i
$974$			6.30617i			0.202063i
$975$	−2.25155	−	0.677959i	−0.0721073	−	0.0217121i
$976$	3.16538	−	1.82753i	0.101321	−	0.0584978i
$977$			38.0452i			1.21717i	0.793488	+	0.608586i	$0.208263\pi$
$977$			38.0452i			1.21717i	−0.793488	+	0.608586i	$0.791737\pi$
$978$	−40.9041	+	5.12523i	−1.30797	+	0.163887i
$979$	−0.826087	+	0.476942i	−0.0264019	+	0.0152431i
$980$	2.75029	+	14.7982i	0.0878548	+	0.472711i
$981$	−6.57830	+	23.3776i	−0.210029	+	0.746389i
$982$	−12.1711			−0.388396
$983$	−17.4838	−	30.2829i	−0.557648	−	0.965875i	−0.997692	−	0.0678987i	$-0.978371\pi$
$983$	−17.4838	−	30.2829i	−0.557648	−	0.965875i	0.440044	−	0.897976i	$-0.354963\pi$
$984$	−12.4236	−	16.4021i	−0.396051	−	0.522878i
$985$	22.9529	−	13.2519i	0.731341	−	0.422240i
$986$	11.9943	−	20.7747i	0.381975	−	0.661600i
$987$	1.79466	+	3.46134i	0.0571246	+	0.110176i
$988$	7.48164	−	5.45584i	0.238023	−	0.173573i
$989$	16.7497	+	9.67042i	0.532608	+	0.307501i
$990$	−3.74924	−	3.84417i	−0.119159	−	0.122176i
$991$	25.3415			0.804999			0.402500	−	0.915420i	$-0.368141\pi$
$991$	25.3415			0.804999			0.402500	+	0.915420i	$0.368141\pi$
$992$	−2.38352			−0.0756769
$993$	−25.4233	−	10.7173i	−0.806783	−	0.340104i
$994$	−17.5846	−	14.6176i	−0.557751	−	0.463642i
$995$	51.0462	−	29.4715i	1.61827	−	0.934311i
$996$	1.28518	−	0.973449i	0.0407224	−	0.0308449i
$997$	−11.9102	−	6.87636i	−0.377200	−	0.217777i	0.299399	−	0.954128i	$-0.403214\pi$
$997$	−11.9102	−	6.87636i	−0.377200	−	0.217777i	−0.676599	+	0.736351i	$0.736547\pi$
$998$		−	32.7481i		−	1.03662i
$999$	0.582945	−	0.730913i	0.0184436	−	0.0231251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.2	yes	76
3.2	odd	2	inner	546.2.u.a.425.37	yes	76
7.3	odd	6		546.2.bb.a.269.10	yes	76
13.3	even	3		546.2.bb.a.341.16	yes	76
21.17	even	6		546.2.bb.a.269.35	yes	76
39.29	odd	6		546.2.bb.a.341.29	yes	76
91.3	odd	6	inner	546.2.u.a.185.37	yes	76
273.185	even	6	inner	546.2.u.a.185.2	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.2	✓	76	273.185	even	6	inner
546.2.u.a.185.37	yes	76	91.3	odd	6	inner
546.2.u.a.425.2	yes	76	1.1	even	1	trivial
546.2.u.a.425.37	yes	76	3.2	odd	2	inner
546.2.bb.a.269.10	yes	76	7.3	odd	6
546.2.bb.a.269.35	yes	76	21.17	even	6
546.2.bb.a.341.16	yes	76	13.3	even	3
546.2.bb.a.341.29	yes	76	39.29	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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.59603 - 0.672816i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.07511 - 1.86215i) q^{5} +(1.71861 - 0.215340i) q^{6} +(0.447408 - 2.60765i) q^{7} +1.00000i q^{8} +(2.09464 + 2.14767i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.59603 - 0.672816i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.07511 - 1.86215i) q^{5} +(1.71861 - 0.215340i) q^{6} +(0.447408 - 2.60765i) q^{7} +1.00000i q^{8} +(2.09464 + 2.14767i) q^{9} +2.15023i q^{10} +0.832434i q^{11} +(-1.38069 + 1.04580i) q^{12} +(1.46072 - 3.29641i) q^{13} +(0.916357 + 2.48199i) q^{14} +(-2.96880 + 2.24870i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.36171 - 2.35856i) q^{17} +(-2.88784 - 0.812620i) q^{18} +2.56816i q^{19} +(-1.07511 - 1.86215i) q^{20} +(-2.46855 + 3.86087i) q^{21} +(-0.416217 - 0.720909i) q^{22} +(-2.15206 + 1.24249i) q^{23} +(0.672816 - 1.59603i) q^{24} +(0.188263 + 0.326081i) q^{25} +(0.383182 + 3.58513i) q^{26} +(-1.89812 - 4.83706i) q^{27} +(-2.03458 - 1.69129i) q^{28} +(-7.62813 - 4.40410i) q^{29} +(1.44671 - 3.43183i) q^{30} +(-2.06419 + 1.19176i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.560075 - 1.32859i) q^{33} +2.72343i q^{34} +(-4.37482 - 3.63666i) q^{35} +(2.90726 - 0.740172i) q^{36} +(0.0899619 + 0.155819i) q^{37} +(-1.28408 - 2.22409i) q^{38} +(-4.54923 + 4.27837i) q^{39} +(1.86215 + 1.07511i) q^{40} +(5.93979 - 10.2880i) q^{41} +(0.207390 - 4.57788i) q^{42} +(-3.89154 - 6.74035i) q^{43} +(0.720909 + 0.416217i) q^{44} +(6.25126 - 1.59154i) q^{45} +(1.24249 - 2.15206i) q^{46} +(0.425408 - 0.736829i) q^{47} +(0.215340 + 1.71861i) q^{48} +(-6.59965 - 2.33337i) q^{49} +(-0.326081 - 0.188263i) q^{50} +(-3.76022 + 2.84815i) q^{51} +(-2.12441 - 2.91322i) q^{52} +(10.3882 - 5.99761i) q^{53} +(4.06235 + 3.23996i) q^{54} +(1.55012 + 0.894961i) q^{55} +(2.60765 + 0.447408i) q^{56} +(1.72790 - 4.09887i) q^{57} +8.80820 q^{58} +(1.26178 - 2.18546i) q^{59} +(0.463030 + 3.69541i) q^{60} +3.65506i q^{61} +(1.19176 - 2.06419i) q^{62} +(6.53753 - 4.50119i) q^{63} -1.00000 q^{64} +(-4.56797 - 6.26409i) q^{65} +(0.179257 + 1.43063i) q^{66} -6.61431 q^{67} +(-1.36171 - 2.35856i) q^{68} +(4.27073 - 0.535117i) q^{69} +(5.60703 + 0.962029i) q^{70} +(-7.48494 + 4.32143i) q^{71} +(-2.14767 + 2.09464i) q^{72} +(-10.9421 + 6.31743i) q^{73} +(-0.155819 - 0.0899619i) q^{74} +(-0.0810812 - 0.647102i) q^{75} +(2.22409 + 1.28408i) q^{76} +(2.17070 + 0.372438i) q^{77} +(1.80056 - 5.97980i) q^{78} +(-3.10814 + 5.38345i) q^{79} -2.15023 q^{80} +(-0.224993 + 8.99719i) q^{81} +11.8796i q^{82} -0.930821 q^{83} +(2.10933 + 4.06826i) q^{84} +(-2.92799 - 5.07144i) q^{85} +(6.74035 + 3.89154i) q^{86} +(9.21158 + 12.1614i) q^{87} -0.832434 q^{88} +(0.572948 + 0.992375i) q^{89} +(-4.61798 + 4.50394i) q^{90} +(-7.94233 - 5.28388i) q^{91} +2.48498i q^{92} +(4.09635 - 0.513268i) q^{93} +0.850817i q^{94} +(4.78231 + 2.76107i) q^{95} +(-1.04580 - 1.38069i) q^{96} +(7.08918 - 4.09294i) q^{97} +(6.88215 - 1.27907i) q^{98} +(-1.78780 + 1.74365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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