LMFDB - Embedded newform 546.2.bb.a.341.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (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			341.16
Character	$\chi$	$=$	546.341
Dual form			546.2.bb.a.269.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.38069 - 1.04580i) q^{3} -1.00000 q^{4} +(1.07511 - 1.86215i) q^{5} +(-1.04580 - 1.38069i) q^{6} +(-2.48199 + 0.916357i) q^{7} +1.00000i q^{8} +(0.812620 - 2.88784i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.38069 - 1.04580i) q^{3} -1.00000 q^{4} +(1.07511 - 1.86215i) q^{5} +(-1.04580 - 1.38069i) q^{6} +(-2.48199 + 0.916357i) q^{7} +1.00000i q^{8} +(0.812620 - 2.88784i) q^{9} +(-1.86215 - 1.07511i) q^{10} +(-0.720909 - 0.416217i) q^{11} +(-1.38069 + 1.04580i) q^{12} +(-1.46072 - 3.29641i) q^{13} +(0.916357 + 2.48199i) q^{14} +(-0.463030 - 3.69541i) q^{15} +1.00000 q^{16} -2.72343 q^{17} +(-2.88784 - 0.812620i) q^{18} +(2.22409 - 1.28408i) q^{19} +(-1.07511 + 1.86215i) q^{20} +(-2.46855 + 3.86087i) q^{21} +(-0.416217 + 0.720909i) q^{22} -2.48498i q^{23} +(1.04580 + 1.38069i) q^{24} +(0.188263 + 0.326081i) q^{25} +(-3.29641 + 1.46072i) q^{26} +(-1.89812 - 4.83706i) q^{27} +(2.48199 - 0.916357i) q^{28} +(7.62813 - 4.40410i) q^{29} +(-3.69541 + 0.463030i) q^{30} +(-2.06419 + 1.19176i) q^{31} -1.00000i q^{32} +(-1.43063 + 0.179257i) q^{33} +2.72343i q^{34} +(-0.962029 + 5.60703i) q^{35} +(-0.812620 + 2.88784i) q^{36} -0.179924 q^{37} +(-1.28408 - 2.22409i) q^{38} +(-5.46417 - 3.02371i) q^{39} +(1.86215 + 1.07511i) q^{40} +(5.93979 + 10.2880i) q^{41} +(3.86087 + 2.46855i) q^{42} +(-3.89154 + 6.74035i) q^{43} +(0.720909 + 0.416217i) q^{44} +(-4.50394 - 4.61798i) q^{45} -2.48498 q^{46} +(0.425408 - 0.736829i) q^{47} +(1.38069 - 1.04580i) q^{48} +(5.32058 - 4.54878i) q^{49} +(0.326081 - 0.188263i) q^{50} +(-3.76022 + 2.84815i) q^{51} +(1.46072 + 3.29641i) q^{52} +(10.3882 - 5.99761i) q^{53} +(-4.83706 + 1.89812i) q^{54} +(-1.55012 + 0.894961i) q^{55} +(-0.916357 - 2.48199i) q^{56} +(1.72790 - 4.09887i) q^{57} +(-4.40410 - 7.62813i) q^{58} -2.52356 q^{59} +(0.463030 + 3.69541i) q^{60} +(3.16538 - 1.82753i) q^{61} +(1.19176 + 2.06419i) q^{62} +(0.629378 + 7.91226i) q^{63} -1.00000 q^{64} +(-7.70885 - 0.823929i) q^{65} +(0.179257 + 1.43063i) q^{66} +(3.30716 - 5.72816i) q^{67} +2.72343 q^{68} +(-2.59879 - 3.43100i) q^{69} +(5.60703 + 0.962029i) q^{70} +(7.48494 + 4.32143i) q^{71} +(2.88784 + 0.812620i) q^{72} +(-10.9421 + 6.31743i) q^{73} +0.179924i q^{74} +(0.600948 + 0.253333i) q^{75} +(-2.22409 + 1.28408i) q^{76} +(2.17070 + 0.372438i) q^{77} +(-3.02371 + 5.46417i) q^{78} +(-3.10814 + 5.38345i) q^{79} +(1.07511 - 1.86215i) q^{80} +(-7.67930 - 4.69344i) q^{81} +(10.2880 - 5.93979i) q^{82} -0.930821 q^{83} +(2.46855 - 3.86087i) q^{84} +(-2.92799 + 5.07144i) q^{85} +(6.74035 + 3.89154i) q^{86} +(5.92630 - 14.0582i) q^{87} +(0.416217 - 0.720909i) q^{88} -1.14590 q^{89} +(-4.61798 + 4.50394i) q^{90} +(6.64618 + 6.84312i) q^{91} +2.48498i q^{92} +(-1.60367 + 3.80418i) q^{93} +(-0.736829 - 0.425408i) q^{94} -5.52213i q^{95} +(-1.04580 - 1.38069i) q^{96} +(-7.08918 - 4.09294i) q^{97} +(-4.54878 - 5.32058i) q^{98} +(-1.78780 + 1.74365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.38069	−	1.04580i	0.797143	−	0.603791i
$3$	1.38069	−	1.04580i	0.797143	−	0.603791i
$4$	−1.00000			−0.500000
$5$	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	$0.00701107\pi$
$6$	−1.04580	−	1.38069i	−0.426945	−	0.563665i
$7$	−2.48199	+	0.916357i	−0.938105	+	0.346350i
$7$	−2.48199	+	0.916357i	−0.938105	+	0.346350i
$8$			1.00000i			0.353553i
$9$	0.812620	−	2.88784i	0.270873	−	0.962615i
$10$	−1.86215	−	1.07511i	−0.588864	−	0.339981i
$11$	−0.720909	−	0.416217i	−0.217362	−	0.125494i	0.387366	−	0.921926i	$-0.373385\pi$
$11$	−0.720909	−	0.416217i	−0.217362	−	0.125494i	−0.604728	+	0.796432i	$0.706718\pi$
$12$	−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
$15$	−0.463030	−	3.69541i	−0.119554	−	0.954150i
$16$	1.00000			0.250000
$17$	−2.72343			−0.660529			−0.330264	−	0.943889i	$-0.607138\pi$
$17$	−2.72343			−0.660529			−0.330264	+	0.943889i	$0.607138\pi$
$18$	−2.88784	−	0.812620i	−0.680672	−	0.191536i
$19$	2.22409	−	1.28408i	0.510242	−	0.294589i	−0.222691	−	0.974889i	$-0.571484\pi$
$19$	2.22409	−	1.28408i	0.510242	−	0.294589i	0.732933	+	0.680301i	$0.238151\pi$
$20$	−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
$23$		−	2.48498i		−	0.518155i	−0.965857	−	0.259078i	$-0.916581\pi$
$23$		−	2.48498i		−	0.518155i	0.965857	−	0.259078i	$-0.0834185\pi$
$24$	1.04580	+	1.38069i	0.213472	+	0.281833i
$25$	0.188263	+	0.326081i	0.0376526	+	0.0652162i
$26$	−3.29641	+	1.46072i	−0.646479	+	0.286471i
$27$	−1.89812	−	4.83706i	−0.365293	−	0.930893i
$28$	2.48199	−	0.916357i	0.469053	−	0.173175i
$29$	7.62813	−	4.40410i	1.41651	−	0.817821i	0.420517	−	0.907285i	$-0.361849\pi$
$29$	7.62813	−	4.40410i	1.41651	−	0.817821i	0.995990	+	0.0894637i	$0.0285153\pi$
$30$	−3.69541	+	0.463030i	−0.674686	+	0.0845373i
$31$	−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	$0.401998\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.43063	+	0.179257i	−0.249041	+	0.0312046i
$34$			2.72343i			0.467064i
$35$	−0.962029	+	5.60703i	−0.162613	+	0.947762i
$36$	−0.812620	+	2.88784i	−0.135437	+	0.481307i
$37$	−0.179924			−0.0295793			−0.0147896	−	0.999891i	$-0.504708\pi$
$37$	−0.179924			−0.0295793			−0.0147896	+	0.999891i	$0.504708\pi$
$38$	−1.28408	−	2.22409i	−0.208306	−	0.360796i
$39$	−5.46417	−	3.02371i	−0.874968	−	0.484180i
$40$	1.86215	+	1.07511i	0.294432	+	0.169990i
$41$	5.93979	+	10.2880i	0.927640	+	1.60672i	0.787259	+	0.616622i	$0.211499\pi$
$41$	5.93979	+	10.2880i	0.927640	+	1.60672i	0.140381	+	0.990098i	$0.455167\pi$
$42$	3.86087	+	2.46855i	0.595744	+	0.380905i
$43$	−3.89154	+	6.74035i	−0.593454	+	1.02789i	0.400309	+	0.916380i	$0.368903\pi$
$43$	−3.89154	+	6.74035i	−0.593454	+	1.02789i	−0.993763	+	0.111513i	$0.964430\pi$
$44$	0.720909	+	0.416217i	0.108681	+	0.0627471i
$45$	−4.50394	−	4.61798i	−0.671408	−	0.688408i
$46$	−2.48498			−0.366391
$47$	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	$0.146902\pi$
$48$	1.38069	−	1.04580i	0.199286	−	0.150948i
$49$	5.32058	−	4.54878i	0.760083	−	0.649826i
$50$	0.326081	−	0.188263i	0.0461148	−	0.0266244i
$51$	−3.76022	+	2.84815i	−0.526536	+	0.398821i
$52$	1.46072	+	3.29641i	0.202565	+	0.457129i
$53$	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	$0.0251638\pi$
$54$	−4.83706	+	1.89812i	−0.658240	+	0.258301i
$55$	−1.55012	+	0.894961i	−0.209018	+	0.120677i
$56$	−0.916357	−	2.48199i	−0.122453	−	0.331670i
$57$	1.72790	−	4.09887i	0.228866	−	0.542909i
$58$	−4.40410	−	7.62813i	−0.578287	−	1.00162i
$59$	−2.52356			−0.328539			−0.164270	−	0.986415i	$-0.552527\pi$
$59$	−2.52356			−0.328539			−0.164270	+	0.986415i	$0.552527\pi$
$60$	0.463030	+	3.69541i	0.0597769	+	0.477075i
$61$	3.16538	−	1.82753i	0.405285	−	0.233991i	−0.283477	−	0.958979i	$-0.591488\pi$
$61$	3.16538	−	1.82753i	0.405285	−	0.233991i	0.688762	+	0.724988i	$0.258155\pi$
$62$	1.19176	+	2.06419i	0.151354	+	0.262153i
$63$	0.629378	+	7.91226i	0.0792941	+	0.996851i
$64$	−1.00000			−0.125000
$65$	−7.70885	−	0.823929i	−0.956165	−	0.102196i
$66$	0.179257	+	1.43063i	0.0220650	+	0.176099i
$67$	3.30716	−	5.72816i	0.404033	−	0.699806i	−0.590175	−	0.807275i	$-0.700941\pi$
$67$	3.30716	−	5.72816i	0.404033	−	0.699806i	0.994208	+	0.107469i	$0.0342746\pi$
$68$	2.72343			0.330264
$69$	−2.59879	−	3.43100i	−0.312857	−	0.413044i
$70$	5.60703	+	0.962029i	0.670169	+	0.114985i
$71$	7.48494	+	4.32143i	0.888299	+	0.512859i	0.873386	−	0.487029i	$-0.161920\pi$
$71$	7.48494	+	4.32143i	0.888299	+	0.512859i	0.0149130	+	0.999889i	$0.495253\pi$
$72$	2.88784	+	0.812620i	0.340336	+	0.0957682i
$73$	−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	$0.598224\pi$
$74$			0.179924i			0.0209157i
$75$	0.600948	+	0.253333i	0.0693915	+	0.0292524i
$76$	−2.22409	+	1.28408i	−0.255121	+	0.147294i
$77$	2.17070	+	0.372438i	0.247374	+	0.0424433i
$78$	−3.02371	+	5.46417i	−0.342367	+	0.618696i
$79$	−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	$0.280381\pi$
$80$	1.07511	−	1.86215i	0.120201	−	0.208195i
$81$	−7.67930	−	4.69344i	−0.853255	−	0.521494i
$82$	10.2880	−	5.93979i	1.13612	−	0.655941i
$83$	−0.930821			−0.102171			−0.0510854	−	0.998694i	$-0.516268\pi$
$83$	−0.930821			−0.102171			−0.0510854	+	0.998694i	$0.516268\pi$
$84$	2.46855	−	3.86087i	0.269340	−	0.421255i
$85$	−2.92799	+	5.07144i	−0.317586	+	0.550074i
$86$	6.74035	+	3.89154i	0.726830	+	0.419636i
$87$	5.92630	−	14.0582i	0.635366	−	1.50719i
$88$	0.416217	−	0.720909i	0.0443689	−	0.0768492i
$89$	−1.14590			−0.121465			−0.0607324	−	0.998154i	$-0.519344\pi$
$89$	−1.14590			−0.121465			−0.0607324	+	0.998154i	$0.519344\pi$
$90$	−4.61798	+	4.50394i	−0.486778	+	0.474757i
$91$	6.64618	+	6.84312i	0.696709	+	0.717354i
$92$			2.48498i			0.259078i
$93$	−1.60367	+	3.80418i	−0.166293	+	0.394475i
$94$	−0.736829	−	0.425408i	−0.0759981	−	0.0438775i
$95$		−	5.52213i		−	0.566559i
$96$	−1.04580	−	1.38069i	−0.106736	−	0.140916i
$97$	−7.08918	−	4.09294i	−0.719797	−	0.415575i	0.0948811	−	0.995489i	$-0.469753\pi$
$97$	−7.08918	−	4.09294i	−0.719797	−	0.415575i	−0.814678	+	0.579914i	$0.803086\pi$
$98$	−4.54878	−	5.32058i	−0.459496	−	0.537460i
$99$	−1.78780	+	1.74365i	−0.179680	+	0.175243i
$100$	−0.188263	−	0.326081i	−0.0188263	−	0.0326081i
$101$	6.68381	−	11.5767i	0.665064	−	1.15192i	−0.314204	−	0.949356i	$-0.601738\pi$
$101$	6.68381	−	11.5767i	0.665064	−	1.15192i	0.979268	−	0.202569i	$-0.0649291\pi$
$102$	2.84815	+	3.76022i	0.282009	+	0.372317i
$103$	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
$107$		−	1.40104i		−	0.135444i	−0.997704	−	0.0677219i	$-0.978427\pi$
$107$		−	1.40104i		−	0.135444i	0.997704	−	0.0677219i	$-0.0215731\pi$
$108$	1.89812	+	4.83706i	0.182647	+	0.465446i
$109$	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	$0.706607\pi$
$110$	0.894961	+	1.55012i	0.0853312	+	0.147798i
$111$	−0.248419	+	0.188164i	−0.0235789	+	0.0178597i
$112$	−2.48199	+	0.916357i	−0.234526	+	0.0865876i
$113$	3.15285	+	1.82030i	0.296595	+	0.171239i	0.640912	−	0.767614i	$-0.278556\pi$
$113$	3.15285	+	1.82030i	0.296595	+	0.171239i	−0.344317	+	0.938853i	$0.611889\pi$
$114$	−4.09887	−	1.72790i	−0.383894	−	0.161833i
$115$	−4.62742	−	2.67164i	−0.431509	−	0.249132i
$116$	−7.62813	+	4.40410i	−0.708254	+	0.408910i
$117$	−10.7065	+	1.53961i	−0.989818	+	0.142337i
$118$			2.52356i			0.232312i
$119$	6.75953	−	2.49563i	0.619645	−	0.228774i
$120$	3.69541	−	0.463030i	0.337343	−	0.0422687i
$121$	−5.15353	−	8.92617i	−0.468502	−	0.811470i
$122$	−1.82753	−	3.16538i	−0.165457	−	0.286580i
$123$	18.9602	+	7.99278i	1.70958	+	0.720685i
$124$	2.06419	−	1.19176i	0.185370	−	0.107023i
$125$	11.5607			1.03402
$126$	7.91226	−	0.629378i	0.704880	−	0.0560694i
$127$	9.89702	+	17.1421i	0.878219	+	1.52112i	0.853294	+	0.521430i	$0.174601\pi$
$127$	9.89702	+	17.1421i	0.878219	+	1.52112i	0.0249248	+	0.999689i	$0.492065\pi$
$128$			1.00000i			0.0883883i
$129$	1.67601	+	13.3761i	0.147564	+	1.17770i
$130$	−0.823929	+	7.70885i	−0.0722633	+	0.676110i
$131$	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	$0.0652774\pi$
$132$	1.43063	−	0.179257i	0.124521	−	0.0156023i
$133$	−4.34351	+	5.22515i	−0.376630	+	0.453078i
$134$	−5.72816	−	3.30716i	−0.494838	−	0.285695i
$135$	−11.0480	−	1.66580i	−0.950863	−	0.143370i
$136$		−	2.72343i		−	0.233532i
$137$		−	6.25378i		−	0.534296i	−0.963655	−	0.267148i	$-0.913919\pi$
$137$		−	6.25378i		−	0.534296i	0.963655	−	0.267148i	$-0.0860813\pi$
$138$	−3.43100	+	2.59879i	−0.292066	+	0.221224i
$139$	1.80427	+	1.04170i	0.153036	+	0.0883555i	0.574563	−	0.818461i	$-0.305172\pi$
$139$	1.80427	+	1.04170i	0.153036	+	0.0883555i	−0.421526	+	0.906816i	$0.638506\pi$
$140$	0.962029	−	5.60703i	0.0813063	−	0.473881i
$141$	−0.183215	−	1.46222i	−0.0154295	−	0.123141i
$142$	4.32143	−	7.48494i	0.362646	−	0.628122i
$143$	−0.318974	+	2.98439i	−0.0266740	+	0.249567i
$144$	0.812620	−	2.88784i	0.0677184	−	0.240654i
$145$		−	18.9396i		−	1.57285i
$146$	6.31743	+	10.9421i	0.522834	+	0.905575i
$147$	2.58898	−	11.8447i	0.213536	−	0.976935i
$148$	0.179924			0.0147896
$149$	10.5983	−	6.11893i	0.868247	−	0.501282i	0.00148148	−	0.999999i	$-0.499528\pi$
$149$	10.5983	−	6.11893i	0.868247	−	0.501282i	0.866765	+	0.498716i	$0.166195\pi$
$150$	0.253333	−	0.600948i	0.0206845	−	0.0490672i
$151$	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	$0.820275\pi$
$152$	1.28408	+	2.22409i	0.104153	+	0.180398i
$153$	−2.21311	+	7.86484i	−0.178920	+	0.635835i
$154$	0.372438	−	2.17070i	0.0300119	−	0.174920i
$155$			5.12512i			0.411659i
$156$	5.46417	+	3.02371i	0.437484	+	0.242090i
$157$	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	$0.117294\pi$
$158$	5.38345	+	3.10814i	0.428284	+	0.247270i
$159$	8.07057	−	19.1447i	0.640038	−	1.51828i
$160$	−1.86215	−	1.07511i	−0.147216	−	0.0849952i
$161$	2.27713	+	6.16772i	0.179463	+	0.486084i
$162$	−4.69344	+	7.67930i	−0.368752	+	0.603342i
$163$	11.9003	+	20.6120i	0.932105	+	1.61445i	0.779717	+	0.626132i	$0.215363\pi$
$163$	11.9003	+	20.6120i	0.932105	+	1.61445i	0.152388	+	0.988321i	$0.451304\pi$
$164$	−5.93979	−	10.2880i	−0.463820	−	0.803360i
$165$	−1.20429	+	2.85677i	−0.0937538	+	0.222400i
$166$			0.930821i			0.0722457i
$167$	−1.67287	−	2.89750i	−0.129451	−	0.224215i	0.794013	−	0.607901i	$-0.207988\pi$
$167$	−1.67287	−	2.89750i	−0.129451	−	0.224215i	−0.923464	+	0.383685i	$0.874655\pi$
$168$	−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
$171$	−1.90088	−	7.46631i	−0.145364	−	0.570963i
$172$	3.89154	−	6.74035i	0.296727	−	0.513947i
$173$	−9.84211	−	17.0470i	−0.748282	−	1.29606i	−0.948646	−	0.316340i	$-0.897546\pi$
$173$	−9.84211	−	17.0470i	−0.748282	−	1.29606i	0.200364	−	0.979721i	$-0.435787\pi$
$174$	−14.0582	−	5.92630i	−1.06575	−	0.449272i
$175$	−0.766074	−	0.636815i	−0.0579098	−	0.0481387i
$176$	−0.720909	−	0.416217i	−0.0543406	−	0.0313736i
$177$	−3.48425	+	2.63913i	−0.261893	+	0.198369i
$178$			1.14590i			0.0858886i
$179$	1.15524	+	0.666976i	0.0863464	+	0.0498521i	0.542551	−	0.840023i	$-0.317458\pi$
$179$	1.15524	+	0.666976i	0.0863464	+	0.0498521i	−0.456205	+	0.889875i	$0.650792\pi$
$180$	4.50394	+	4.61798i	0.335704	+	0.344204i
$181$		−	1.13213i		−	0.0841503i	−0.999114	−	0.0420752i	$-0.986603\pi$
$181$		−	1.13213i		−	0.0841503i	0.999114	−	0.0420752i	$-0.0133969\pi$
$182$	6.84312	−	6.64618i	0.507246	−	0.492648i
$183$	2.45918	−	5.83360i	0.181788	−	0.431232i
$184$	2.48498			0.183196
$185$	−0.193438	+	0.335045i	−0.0142219	+	0.0246330i
$186$	3.80418	+	1.60367i	0.278936	+	0.117587i
$187$	1.96335	+	1.13354i	0.143574	+	0.0828925i
$188$	−0.425408	+	0.736829i	−0.0310261	+	0.0537388i
$189$	9.14359	+	10.2662i	0.665098	+	0.746756i
$190$	−5.52213			−0.400618
$191$	−18.3935	+	10.6195i	−1.33091	+	0.768402i	−0.985439	−	0.170028i	$-0.945614\pi$
$191$	−18.3935	+	10.6195i	−1.33091	+	0.768402i	−0.345471	+	0.938429i	$0.612281\pi$
$192$	−1.38069	+	1.04580i	−0.0996429	+	0.0754738i
$193$	−1.56454	+	2.70986i	−0.112618	+	0.195060i	−0.916825	−	0.399289i	$-0.869257\pi$
$193$	−1.56454	+	2.70986i	−0.112618	+	0.195060i	0.804207	+	0.594349i	$0.202590\pi$
$194$	−4.09294	+	7.08918i	−0.293856	+	0.508973i
$195$	−11.5052	+	6.92429i	−0.823905	+	0.495859i
$196$	−5.32058	+	4.54878i	−0.380041	+	0.324913i
$197$	−10.6747	+	6.16302i	−0.760538	+	0.439097i	−0.829489	−	0.558523i	$-0.811368\pi$
$197$	−10.6747	+	6.16302i	−0.760538	+	0.439097i	0.0689508	+	0.997620i	$0.478035\pi$
$198$	1.74365	+	1.78780i	0.123916	+	0.127053i
$199$		−	27.4125i		−	1.94322i	−0.236587	−	0.971610i	$-0.576029\pi$
$199$		−	27.4125i		−	1.94322i	0.236587	−	0.971610i	$-0.423971\pi$
$200$	−0.326081	+	0.188263i	−0.0230574	+	0.0133122i
$201$	−1.42433	−	11.3674i	−0.100464	−	0.801797i
$202$	−11.5767	−	6.68381i	−0.814534	−	0.470271i
$203$	−14.8972	+	17.9210i	−1.04558	+	1.25781i
$204$	3.76022	−	2.84815i	0.263268	−	0.199411i
$205$	25.5438			1.78406
$206$	7.40885	−	12.8325i	0.516199	−	0.894083i
$207$	−7.17625	−	2.01935i	−0.498784	−	0.140354i
$208$	−1.46072	−	3.29641i	−0.101283	−	0.228565i
$209$	−2.13783			−0.147877
$210$	8.74767	−	4.53555i	0.603647	−	0.312983i
$211$	11.7715	+	20.3889i	0.810384	+	1.40363i	0.912595	+	0.408864i	$0.134075\pi$
$211$	11.7715	+	20.3889i	0.810384	+	1.40363i	−0.102211	+	0.994763i	$0.532592\pi$
$212$	−10.3882	+	5.99761i	−0.713462	+	0.411917i
$213$	14.8537	−	1.86115i	1.01776	−	0.127524i
$214$	−1.40104			−0.0957733
$215$	8.36769	+	14.4933i	0.570672	+	0.988433i
$216$	4.83706	−	1.89812i	0.329120	−	0.129151i
$217$	4.03123	−	4.84948i	0.273658	−	0.329204i
$218$	7.01062	−	4.04758i	0.474819	−	0.274137i
$219$	−8.50093	+	20.1656i	−0.574440	+	1.36267i
$220$	1.55012	−	0.894961i	0.104509	−	0.0603383i
$221$	3.97817	+	8.97753i	0.267601	+	0.603894i
$222$	0.188164	+	0.248419i	0.0126287	+	0.0166728i
$223$	−25.4264	+	14.6799i	−1.70268	+	0.983041i	−0.759644	+	0.650339i	$0.774627\pi$
$223$	−25.4264	+	14.6799i	−1.70268	+	0.983041i	−0.943032	+	0.332702i	$0.892040\pi$
$224$	0.916357	+	2.48199i	0.0612267	+	0.165835i
$225$	1.09466	−	0.278694i	0.0729772	−	0.0185796i
$226$	1.82030	−	3.15285i	0.121085	−	0.209725i
$227$	−28.3861			−1.88405			−0.942025	−	0.335541i	$-0.891081\pi$
$227$	−28.3861			−1.88405			−0.942025	+	0.335541i	$0.891081\pi$
$228$	−1.72790	+	4.09887i	−0.114433	+	0.271454i
$229$	−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
$231$	3.38656	−	1.75588i	0.222819	−	0.115529i
$232$	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	$0.505635\pi$
$234$	1.53961	+	10.7065i	0.100647	+	0.699907i
$235$	−0.914724	−	1.58435i	−0.0596700	−	0.103352i
$236$	2.52356			0.164270
$237$	1.33861	+	10.6834i	0.0869523	+	0.693959i
$238$	−2.49563	−	6.75953i	−0.161768	−	0.438155i
$239$			20.0261i			1.29538i	0.761903	+	0.647692i	$0.224265\pi$
$239$			20.0261i			1.29538i	−0.761903	+	0.647692i	$0.775735\pi$
$240$	−0.463030	−	3.69541i	−0.0298885	−	0.238537i
$241$			10.4032i			0.670127i	0.942196	+	0.335063i	$0.108758\pi$
$241$			10.4032i			0.670127i	−0.942196	+	0.335063i	$0.891242\pi$
$242$	−8.92617	+	5.15353i	−0.573796	+	0.331281i
$243$	−15.5111	+	1.55078i	−0.995039	+	0.0994825i
$244$	−3.16538	+	1.82753i	−0.202642	+	0.116996i
$245$	−2.75029	−	14.7982i	−0.175710	−	0.945421i
$246$	7.99278	−	18.9602i	0.509601	−	1.20886i
$247$	−7.48164	−	5.45584i	−0.476045	−	0.347147i
$248$	−1.19176	−	2.06419i	−0.0756769	−	0.131076i
$249$	−1.28518	+	0.973449i	−0.0814448	+	0.0616898i
$250$		−	11.5607i		−	0.731166i
$251$	1.11415	−	1.92977i	0.0703247	−	0.121806i	−0.828719	−	0.559665i	$-0.810930\pi$
$251$	1.11415	−	1.92977i	0.0703247	−	0.121806i	0.899044	+	0.437859i	$0.144263\pi$
$252$	−0.629378	−	7.91226i	−0.0396471	−	0.498426i
$253$	−1.03429	+	1.79145i	−0.0650255	+	0.112627i
$254$	17.1421	−	9.89702i	1.07559	−	0.620994i
$255$	1.26103	+	10.0642i	0.0789687	+	0.630243i
$256$	1.00000			0.0625000
$257$	−6.20605			−0.387123			−0.193561	−	0.981088i	$-0.562004\pi$
$257$	−6.20605			−0.387123			−0.193561	+	0.981088i	$0.562004\pi$
$258$	13.3761	−	1.67601i	0.832760	−	0.104344i
$259$	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
$262$	−6.20825	−	3.58433i	−0.383547	−	0.221441i
$263$	−21.2094	−	12.2453i	−1.30783	−	0.755075i	−0.326095	−	0.945337i	$-0.605733\pi$
$263$	−21.2094	−	12.2453i	−1.30783	−	0.755075i	−0.981733	+	0.190262i	$0.939066\pi$
$264$	−0.179257	−	1.43063i	−0.0110325	−	0.0880493i
$265$		−	25.7924i		−	1.58442i
$266$	5.22515	+	4.34351i	0.320374	+	0.266318i
$267$	−1.58213	+	1.19837i	−0.0968248	+	0.0733393i
$268$	−3.30716	+	5.72816i	−0.202017	+	0.349903i
$269$	−5.00152			−0.304948			−0.152474	−	0.988307i	$-0.548724\pi$
$269$	−5.00152			−0.304948			−0.152474	+	0.988307i	$0.548724\pi$
$270$	−1.66580	+	11.0480i	−0.101378	+	0.672361i
$271$		−	6.59272i		−	0.400479i	−0.979747	−	0.200240i	$-0.935828\pi$
$271$		−	6.59272i		−	0.400479i	0.979747	−	0.200240i	$-0.0641721\pi$
$272$	−2.72343			−0.165132
$273$	16.3328	+	2.49769i	0.988508	+	0.151167i
$274$	−6.25378			−0.377805
$275$		−	0.313433i		−	0.0189007i
$276$	2.59879	+	3.43100i	0.156429	+	0.206522i
$277$	−16.9907			−1.02087			−0.510436	−	0.859916i	$-0.670516\pi$
$277$	−16.9907			−1.02087			−0.510436	+	0.859916i	$0.670516\pi$
$278$	1.04170	−	1.80427i	0.0624767	−	0.108213i
$279$	1.76422	+	6.92952i	0.105621	+	0.414859i
$280$	−5.60703	−	0.962029i	−0.335084	−	0.0574923i
$281$			3.11696i			0.185942i	0.995669	+	0.0929712i	$0.0296364\pi$
$281$			3.11696i			0.185942i	−0.995669	+	0.0929712i	$0.970364\pi$
$282$	−1.46222	+	0.183215i	−0.0870742	+	0.0109103i
$283$	10.7512	+	6.20719i	0.639091	+	0.368979i	0.784264	−	0.620427i	$-0.213041\pi$
$283$	10.7512	+	6.20719i	0.639091	+	0.368979i	−0.145173	+	0.989406i	$0.546374\pi$
$284$	−7.48494	−	4.32143i	−0.444149	−	0.256430i
$285$	−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
$288$	−2.88784	−	0.812620i	−0.170168	−	0.0478841i
$289$	−9.58293			−0.563702
$290$	−18.9396			−1.11217
$291$	−14.0683	+	1.76275i	−0.824701	+	0.103334i
$292$	10.9421	−	6.31743i	0.640338	−	0.369699i
$293$	−2.20558	+	3.82017i	−0.128851	+	0.223177i	−0.923232	−	0.384244i	$-0.874462\pi$
$293$	−2.20558	+	3.82017i	−0.128851	+	0.223177i	0.794381	+	0.607420i	$0.207796\pi$
$294$	−11.8447	−	2.58898i	−0.690798	−	0.150993i
$295$	−2.71311	+	4.69924i	−0.157963	+	0.273600i
$296$		−	0.179924i		−	0.0104579i
$297$	−0.644896	+	4.27711i	−0.0374206	+	0.248183i
$298$	−6.11893	−	10.5983i	−0.354460	−	0.613943i
$299$	−8.19152	+	3.62987i	−0.473728	+	0.209921i
$300$	−0.600948	−	0.253333i	−0.0346957	−	0.0146262i
$301$	3.48222	−	20.2955i	0.200712	−	1.16982i
$302$	0.872882	−	0.503958i	0.0502287	−	0.0289995i
$303$	−2.87859	−	22.9738i	−0.165370	−	1.31981i
$304$	2.22409	−	1.28408i	0.127561	−	0.0736471i
$305$		−	7.85921i		−	0.450017i
$306$	7.86484	+	2.21311i	0.449603	+	0.126515i
$307$		−	16.2434i		−	0.927062i	−0.886081	−	0.463531i	$-0.846582\pi$
$307$		−	16.2434i		−	0.927062i	0.886081	−	0.463531i	$-0.153418\pi$
$308$	−2.17070	−	0.372438i	−0.123687	−	0.0212216i
$309$	25.4659	−	3.19084i	1.44870	−	0.181521i
$310$	5.12512			0.291087
$311$	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	$0.582962\pi$
$312$	3.02371	−	5.46417i	0.171184	−	0.309348i
$313$	−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
$315$	15.4105	+	7.33458i	0.868282	+	0.413257i
$316$	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	$0.742058\pi$
$318$	−19.1447	−	8.07057i	−1.07358	−	0.452575i
$319$	−7.33225			−0.410527
$320$	−1.07511	+	1.86215i	−0.0601007	+	0.104097i
$321$	−1.46520	−	1.93441i	−0.0817798	−	0.107968i
$322$	6.16772	−	2.27713i	0.343713	−	0.126900i
$323$	−6.05716	+	3.49711i	−0.337030	+	0.194584i
$324$	7.67930	+	4.69344i	0.426628	+	0.260747i
$325$	0.799896	−	1.09690i	0.0443703	−	0.0608453i
$326$	20.6120	−	11.9003i	1.14159	−	0.659098i
$327$	12.9201	+	5.44656i	0.714486	+	0.301195i
$328$	−10.2880	+	5.93979i	−0.568061	+	0.327970i
$329$	−0.380662	+	2.21863i	−0.0209866	+	0.122317i
$330$	2.85677	+	1.20429i	0.157260	+	0.0662939i
$331$	−7.96452	−	13.7950i	−0.437770	−	0.758239i	0.559747	−	0.828663i	$-0.310898\pi$
$331$	−7.96452	−	13.7950i	−0.437770	−	0.758239i	−0.997517	+	0.0704239i	$0.977565\pi$
$332$	0.930821			0.0510854
$333$	−0.146210	+	0.519592i	−0.00801224	+	0.0284735i
$334$	−2.89750	+	1.67287i	−0.158544	+	0.0915355i
$335$	−7.11113	−	12.3168i	−0.388523	−	0.672941i
$336$	−2.46855	+	3.86087i	−0.134670	+	0.210627i
$337$	−1.38803			−0.0756107			−0.0378054	−	0.999285i	$-0.512037\pi$
$337$	−1.38803			−0.0756107			−0.0378054	+	0.999285i	$0.512037\pi$
$338$	9.63026	+	8.73259i	0.523817	+	0.474990i
$339$	6.25678	−	0.783968i	0.339822	−	0.0425793i
$340$	2.92799	−	5.07144i	0.158793	−	0.275037i
$341$	1.98413			0.107446
$342$	−7.46631	+	1.90088i	−0.403732	+	0.102788i
$343$	−9.03734	+	16.1656i	−0.487970	+	0.872860i
$344$	−6.74035	−	3.89154i	−0.363415	−	0.209818i
$345$	−9.18303	+	1.15062i	−0.494398	+	0.0619474i
$346$	−17.0470	+	9.84211i	−0.916454	+	0.529115i
$347$			0.408244i			0.0219157i	0.999940	+	0.0109578i	$0.00348806\pi$
$347$			0.408244i			0.0219157i	−0.999940	+	0.0109578i	$0.996512\pi$
$348$	−5.92630	+	14.0582i	−0.317683	+	0.753597i
$349$	−1.55975	+	0.900521i	−0.0834914	+	0.0482038i	−0.541164	−	0.840917i	$-0.682016\pi$
$349$	−1.55975	+	0.900521i	−0.0834914	+	0.0482038i	0.457673	+	0.889121i	$0.348683\pi$
$350$	−0.636815	+	0.766074i	−0.0340392	+	0.0409484i
$351$	−13.1723	+	13.3226i	−0.703085	+	0.711106i
$352$	−0.416217	+	0.720909i	−0.0221845	+	0.0384246i
$353$	−11.9782	+	20.7468i	−0.637534	+	1.10424i	0.348438	+	0.937332i	$0.386712\pi$
$353$	−11.9782	+	20.7468i	−0.637534	+	1.10424i	−0.985972	+	0.166909i	$0.946621\pi$
$354$	2.63913	+	3.48425i	0.140268	+	0.185186i
$355$	16.0943	−	9.29205i	0.854197	−	0.493171i
$356$	1.14590			0.0607324
$357$	6.72291	−	10.5148i	0.355814	−	0.556502i
$358$	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	$0.596819\pi$
$360$	4.61798	−	4.50394i	0.243389	−	0.237379i
$361$	−6.20227	+	10.7426i	−0.326435	+	0.565402i
$362$	−1.13213			−0.0595033
$363$	−16.4504	−	6.93475i	−0.863421	−	0.363980i
$364$	−6.64618	−	6.84312i	−0.348355	−	0.358677i
$365$			27.1678i			1.42203i
$366$	−5.83360	−	2.45918i	−0.304927	−	0.128544i
$367$	10.1065	+	5.83498i	0.527554	+	0.304583i	0.740020	−	0.672585i	$-0.234816\pi$
$367$	10.1065	+	5.83498i	0.527554	+	0.304583i	−0.212466	+	0.977168i	$0.568149\pi$
$368$		−	2.48498i		−	0.129539i
$369$	34.5370	−	8.79295i	1.79793	−	0.457742i
$370$	0.335045	+	0.193438i	0.0174182	+	0.0100564i
$371$	−20.2874	+	24.4053i	−1.05327	+	1.26706i
$372$	1.60367	−	3.80418i	0.0831466	−	0.197238i
$373$	15.9469	+	27.6209i	0.825701	+	1.43016i	0.901382	+	0.433024i	$0.142554\pi$
$373$	15.9469	+	27.6209i	0.825701	+	1.43016i	−0.0756809	+	0.997132i	$0.524113\pi$
$374$	1.13354	−	1.96335i	0.0586139	−	0.101522i
$375$	15.9618	−	12.0902i	0.824265	−	0.624335i
$376$	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	−0.999930	−	0.0118419i	$-0.996231\pi$
$379$	−9.93293	−	17.2043i	−0.510220	−	0.883727i	0.489710	−	0.871886i	$-0.337103\pi$
$380$			5.52213i			0.283279i
$381$	31.5919	+	13.3178i	1.61850	+	0.682289i
$382$	10.6195	+	18.3935i	0.543342	+	0.941096i
$383$	0.366640	+	0.635039i	0.0187344	+	0.0324490i	0.875241	−	0.483688i	$-0.160703\pi$
$383$	0.366640	+	0.635039i	0.0187344	+	0.0324490i	−0.856506	+	0.516137i	$0.827370\pi$
$384$	1.04580	+	1.38069i	0.0533681	+	0.0704581i
$385$	3.02728	−	3.64175i	0.154284	−	0.185601i
$386$	2.70986	+	1.56454i	0.137928	+	0.0796329i
$387$	16.3027	+	16.7155i	0.828714	+	0.849697i
$388$	7.08918	+	4.09294i	0.359898	+	0.207787i
$389$	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	$0.0165763\pi$
$390$	6.92429	+	11.5052i	0.350625	+	0.582589i
$391$			6.76768i			0.342256i
$392$	4.54878	+	5.32058i	0.229748	+	0.268730i
$393$	−1.54370	−	12.3202i	−0.0778695	−	0.621470i
$394$	6.16302	+	10.6747i	0.310488	+	0.537782i
$395$	6.68320	+	11.5756i	0.336268	+	0.582434i
$396$	1.78780	−	1.74365i	0.0898401	−	0.0876216i
$397$	10.2958	−	5.94426i	0.516729	−	0.298334i	−0.218866	−	0.975755i	$-0.570236\pi$
$397$	10.2958	−	5.94426i	0.516729	−	0.298334i	0.735595	+	0.677421i	$0.236903\pi$
$398$	−27.4125			−1.37406
$399$	−0.532613	+	11.7567i	−0.0266640	+	0.588573i
$400$	0.188263	+	0.326081i	0.00941315	+	0.0163041i
$401$		−	23.5937i		−	1.17821i	−0.808055	−	0.589107i	$-0.799479\pi$
$401$		−	23.5937i		−	1.17821i	0.808055	−	0.589107i	$-0.200521\pi$
$402$	−11.3674	+	1.42433i	−0.566956	+	0.0710390i
$403$	6.94374	+	5.06359i	0.345892	+	0.252235i
$404$	−6.68381	+	11.5767i	−0.332532	+	0.575962i
$405$	−16.9960	+	9.25402i	−0.844539	+	0.459836i
$406$	17.9210	+	14.8972i	0.889406	+	0.739337i
$407$	0.129709	+	0.0748874i	0.00642942	+	0.00371203i
$408$	−2.84815	−	3.76022i	−0.141005	−	0.186158i
$409$			11.3544i			0.561437i	0.959790	+	0.280718i	$0.0905727\pi$
$409$			11.3544i			0.561437i	−0.959790	+	0.280718i	$0.909427\pi$
$410$		−	25.5438i		−	1.26152i
$411$	−6.54018	−	8.63454i	−0.322603	−	0.425911i
$412$	−12.8325	−	7.40885i	−0.632212	−	0.365008i
$413$	6.26345	−	2.31248i	0.308204	−	0.113790i
$414$	−2.01935	+	7.17625i	−0.0992456	+	0.352693i
$415$	−1.00074	+	1.73333i	−0.0491243	+	0.0850858i
$416$	−3.29641	+	1.46072i	−0.161620	+	0.0716177i
$417$	3.58054	−	0.448638i	0.175340	−	0.0219699i
$418$			2.13783i			0.104565i
$419$	6.35642	+	11.0096i	0.310531	+	0.537856i	0.978477	−	0.206354i	$-0.0661597\pi$
$419$	6.35642	+	11.0096i	0.310531	+	0.537856i	−0.667946	+	0.744210i	$0.732826\pi$
$420$	−4.53555	−	8.74767i	−0.221312	−	0.426843i
$421$	36.5159			1.77968			0.889839	−	0.456275i	$-0.150817\pi$
$421$	36.5159			1.77968			0.889839	+	0.456275i	$0.150817\pi$
$422$	20.3889	−	11.7715i	0.992514	−	0.573028i
$423$	−1.78215	−	1.82728i	−0.0866512	−	0.0888452i
$424$	5.99761	+	10.3882i	0.291270	+	0.504494i
$425$	−0.512721	−	0.888059i	−0.0248706	−	0.0430772i
$426$	−1.86115	−	14.8537i	−0.0901733	−	0.719665i
$427$	−6.18177	+	7.43653i	−0.299157	+	0.359879i
$428$			1.40104i			0.0677219i
$429$	2.68066	+	4.45410i	0.129423	+	0.215046i
$430$	14.4933	−	8.36769i	0.698928	−	0.403526i
$431$	5.17597	+	2.98835i	0.249318	+	0.143944i	0.619452	−	0.785035i	$-0.287355\pi$
$431$	5.17597	+	2.98835i	0.249318	+	0.143944i	−0.370134	+	0.928978i	$0.620688\pi$
$432$	−1.89812	−	4.83706i	−0.0913233	−	0.232723i
$433$	27.0676	+	15.6275i	1.30079	+	0.751009i	0.980539	−	0.196325i	$-0.0629008\pi$
$433$	27.0676	+	15.6275i	1.30079	+	0.751009i	0.320247	+	0.947334i	$0.396234\pi$
$434$	−4.84948	−	4.03123i	−0.232783	−	0.193505i
$435$	−19.8070	−	26.1498i	−0.949672	−	1.25379i
$436$	−4.04758	−	7.01062i	−0.193844	−	0.335748i
$437$	−3.19092	−	5.52684i	−0.152643	−	0.264385i
$438$	20.1656	+	8.50093i	0.963551	+	0.406190i
$439$			29.7890i			1.42175i	0.703319	+	0.710875i	$0.251701\pi$
$439$			29.7890i			1.42175i	−0.703319	+	0.710875i	$0.748299\pi$
$440$	−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	$0.835076\pi$
$444$	0.248419	−	0.188164i	0.0117895	−	0.00892985i
$445$	−1.23197	+	2.13383i	−0.0584009	+	0.101153i
$446$	14.6799	+	25.4264i	0.695115	+	1.20397i
$447$	8.23383	−	19.5320i	0.389447	−	0.923833i
$448$	2.48199	−	0.916357i	0.117263	−	0.0432938i
$449$	24.6546	+	14.2344i	1.16352	+	0.671761i	0.952146	−	0.305644i	$-0.0988717\pi$
$449$	24.6546	+	14.2344i	1.16352	+	0.671761i	0.211377	+	0.977405i	$0.432205\pi$
$450$	−0.278694	−	1.09466i	−0.0131378	−	0.0516027i
$451$		−	9.88898i		−	0.465654i
$452$	−3.15285	−	1.82030i	−0.148298	−	0.0856197i
$453$	1.60867	+	0.678143i	0.0755818	+	0.0318619i
$454$			28.3861i			1.33223i
$455$	19.8883	−	5.01907i	0.932379	−	0.235297i
$456$	4.09887	+	1.72790i	0.191947	+	0.0809164i
$457$	−20.4132			−0.954887			−0.477444	−	0.878662i	$-0.658436\pi$
$457$	−20.4132			−0.954887			−0.477444	+	0.878662i	$0.658436\pi$
$458$	−7.28164	+	12.6122i	−0.340249	+	0.589328i
$459$	5.16939	+	13.1734i	0.241287	+	0.614881i
$460$	4.62742	+	2.67164i	0.215754	+	0.124566i
$461$	0.909994	−	1.57616i	0.0423827	−	0.0734089i	−0.844056	−	0.536255i	$-0.819838\pi$
$461$	0.909994	−	1.57616i	0.0423827	−	0.0734089i	0.886439	+	0.462846i	$0.153172\pi$
$462$	−1.75588	−	3.38656i	−0.0816911	−	0.157557i
$463$	−22.0589			−1.02517			−0.512583	−	0.858638i	$-0.671311\pi$
$463$	−22.0589			−1.02517			−0.512583	+	0.858638i	$0.671311\pi$
$464$	7.62813	−	4.40410i	0.354127	−	0.204455i
$465$	5.35983	+	7.07621i	0.248556	+	0.328151i
$466$	7.39695	−	12.8119i	0.342657	−	0.593499i
$467$	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	$0.111000\pi$
$468$	10.7065	−	1.53961i	0.494909	−	0.0711683i
$469$	−2.95930	+	17.2478i	−0.136648	+	0.796429i
$470$	−1.58435	+	0.914724i	−0.0730806	+	0.0421931i
$471$	10.5850	−	25.1093i	0.487729	−	1.15698i
$472$		−	2.52356i		−	0.116156i
$473$	5.61090	−	3.23945i	0.257989	−	0.148950i
$474$	10.6834	−	1.33861i	0.490703	−	0.0614845i
$475$	0.837430	+	0.483490i	0.0384239	+	0.0221841i
$476$	−6.75953	+	2.49563i	−0.309823	+	0.114387i
$477$	−8.87853	−	34.8732i	−0.406520	−	1.59673i
$478$	20.0261			0.915974
$479$	15.4173	−	26.7035i	0.704433	−	1.22011i	−0.262463	−	0.964942i	$-0.584535\pi$
$479$	15.4173	−	26.7035i	0.704433	−	1.22011i	0.966896	−	0.255172i	$-0.0821319\pi$
$480$	−3.69541	+	0.463030i	−0.168671	+	0.0211343i
$481$	0.262818	+	0.593102i	0.0119835	+	0.0270431i
$482$	10.4032			0.473851
$483$	9.59419	+	6.13430i	0.436551	+	0.279120i
$484$	5.15353	+	8.92617i	0.234251	+	0.405735i
$485$	−15.2433	+	8.80074i	−0.692164	+	0.399621i
$486$	1.55078	+	15.5111i	0.0703448	+	0.703599i
$487$	−6.30617			−0.285760			−0.142880	−	0.989740i	$-0.545636\pi$
$487$	−6.30617			−0.285760			−0.142880	+	0.989740i	$0.545636\pi$
$488$	1.82753	+	3.16538i	0.0827284	+	0.143290i
$489$	37.9866	+	16.0135i	1.71781	+	0.724153i
$490$	−14.7982	+	2.75029i	−0.668514	+	0.124245i
$491$	−10.5405	+	6.08555i	−0.475686	+	0.274637i	−0.718617	−	0.695406i	$-0.755224\pi$
$491$	−10.5405	+	6.08555i	−0.475686	+	0.274637i	0.242931	+	0.970044i	$0.421891\pi$
$492$	−18.9602	−	7.99278i	−0.854792	−	0.360342i
$493$	−20.7747	+	11.9943i	−0.935644	+	0.540194i
$494$	−5.45584	+	7.48164i	−0.245470	+	0.336615i
$495$	1.32485	+	5.20376i	0.0595476	+	0.233892i
$496$	−2.06419	+	1.19176i	−0.0926850	+	0.0535117i
$497$	−22.5375	−	3.86689i	−1.01095	−	0.173454i
$498$	0.973449	+	1.28518i	0.0436213	+	0.0575902i
$499$	−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	$0.904784\pi$
$500$	−11.5607			−0.517012
$501$	−5.33991	−	2.25107i	−0.238570	−	0.100570i
$502$	−1.92977	−	1.11415i	−0.0861298	−	0.0497270i
$503$	14.6644	−	25.3994i	0.653852	−	1.13251i	−0.328328	−	0.944564i	$-0.606485\pi$
$503$	14.6644	−	25.3994i	0.653852	−	1.13251i	0.982180	−	0.187941i	$-0.0601815\pi$
$504$	−7.91226	+	0.629378i	−0.352440	+	0.0280347i
$505$	−14.3717	−	24.8925i	−0.639533	−	1.10770i
$506$	1.79145	+	1.03429i	0.0796396	+	0.0459799i
$507$	−1.98573	+	22.4289i	−0.0881895	+	0.996104i
$508$	−9.89702	−	17.1421i	−0.439109	−	0.760560i
$509$	−42.1369			−1.86769			−0.933843	−	0.357682i	$-0.883567\pi$
$509$	−42.1369			−1.86769			−0.933843	+	0.357682i	$0.883567\pi$
$510$	10.0642	−	1.26103i	0.445649	−	0.0558393i
$511$	21.3692	−	25.7067i	0.945318	−	1.13720i
$512$		−	1.00000i		−	0.0441942i
$513$	−10.4328	−	8.32074i	−0.460618	−	0.367370i
$514$			6.20605i			0.273737i
$515$	27.5928	−	15.9307i	1.21588	−	0.701990i
$516$	−1.67601	−	13.3761i	−0.0737822	−	0.588850i
$517$	−0.613362	+	0.354124i	−0.0269756	+	0.0155744i
$518$	−0.164874	−	0.446570i	−0.00724416	−	0.0196211i
$519$	−31.4166	−	13.2439i	−1.37904	−	0.581341i
$520$	0.823929	−	7.70885i	0.0361317	−	0.338055i
$521$	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	$0.807030\pi$
$522$	−25.6077	+	6.51959i	−1.12082	+	0.285355i
$523$			21.1539i			0.924995i	0.886621	+	0.462498i	$0.153047\pi$
$523$			21.1539i			0.924995i	−0.886621	+	0.462498i	$0.846953\pi$
$524$	−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
$527$	5.62168	−	3.24568i	0.244884	−	0.141384i
$528$	−1.43063	+	0.179257i	−0.0622603	+	0.00780114i
$529$	16.8249			0.731515
$530$	−25.7924			−1.12035
$531$	−2.05069	+	7.28764i	−0.0889925	+	0.316257i
$532$	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
$535$	−2.60895	−	1.50628i	−0.112795	−	0.0651221i
$536$	5.72816	+	3.30716i	0.247419	+	0.142847i
$537$	2.29255	−	0.287253i	0.0989307	−	0.0123959i
$538$			5.00152i			0.215631i
$539$	−5.72894	+	1.06474i	−0.246763	+	0.0458617i
$540$	11.0480	+	1.66580i	0.475431	+	0.0716848i
$541$	−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	$0.294290\pi$
$542$	−6.59272			−0.283182
$543$	−1.18397	−	1.56312i	−0.0508092	−	0.0670798i
$544$			2.72343i			0.116766i
$545$	17.4064			0.745610
$546$	2.49769	−	16.3328i	0.106891	−	0.698981i
$547$	26.8382			1.14752			0.573760	−	0.819023i	$-0.305484\pi$
$547$	26.8382			1.14752			0.573760	+	0.819023i	$0.305484\pi$
$548$			6.25378i			0.267148i
$549$	−2.70538	−	10.6262i	−0.115463	−	0.453515i
$550$	−0.313433			−0.0133648
$551$	11.3104	−	19.5903i	0.481841	−	0.834574i
$552$	3.43100	−	2.59879i	0.146033	−	0.110612i
$553$	2.78121	−	16.2099i	0.118269	−	0.689313i
$554$			16.9907i			0.721866i
$555$	0.0833101	+	0.664891i	0.00353632	+	0.0282231i
$556$	−1.80427	−	1.04170i	−0.0765181	−	0.0441777i
$557$	10.5135	+	6.06999i	0.445473	+	0.257194i	0.705916	−	0.708295i	$-0.250535\pi$
$557$	10.5135	+	6.06999i	0.445473	+	0.257194i	−0.260443	+	0.965489i	$0.583869\pi$
$558$	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
$561$	3.89622	−	0.488192i	0.164499	−	0.0206115i
$562$	3.11696			0.131481
$563$	2.57546			0.108543			0.0542714	−	0.998526i	$-0.482716\pi$
$563$	2.57546			0.108543			0.0542714	+	0.998526i	$0.482716\pi$
$564$	0.183215	+	1.46222i	0.00771474	+	0.0615707i
$565$	6.77935	−	3.91406i	0.285209	−	0.164666i
$566$	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
$569$			28.3643i			1.18909i	0.804061	+	0.594547i	$0.202668\pi$
$569$			28.3643i			1.18909i	−0.804061	+	0.594547i	$0.797332\pi$
$570$	−7.62436	+	5.77503i	−0.319350	+	0.241889i
$571$	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	$0.802129\pi$
$572$	0.318974	−	2.98439i	0.0133370	−	0.124783i
$573$	−14.2900	+	33.8982i	−0.596972	+	1.41612i
$574$	−20.0918	+	24.1700i	−0.838617	+	1.00884i
$575$	0.810307	−	0.467831i	0.0337921	−	0.0195099i
$576$	−0.812620	+	2.88784i	−0.0338592	+	0.120327i
$577$	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	$-0.0754584\pi$
$578$			9.58293i			0.398598i
$579$	0.673815	+	5.37767i	0.0280028	+	0.223488i
$580$			18.9396i			0.786425i
$581$	2.31029	−	0.852964i	0.0958470	−	0.0353869i
$582$	1.76275	+	14.0683i	0.0730682	+	0.583152i
$583$	−9.98523			−0.413546
$584$	−6.31743	−	10.9421i	−0.261417	−	0.452787i
$585$	−8.64374	+	21.5924i	−0.357375	+	0.892736i
$586$	3.82017	+	2.20558i	0.157810	+	0.0911115i
$587$	4.23462	+	7.33458i	0.174781	+	0.302730i	0.940086	−	0.340938i	$-0.110745\pi$
$587$	4.23462	+	7.33458i	0.174781	+	0.302730i	−0.765304	+	0.643669i	$0.777411\pi$
$588$	−2.58898	+	11.8447i	−0.106768	+	0.488468i
$589$	−3.06064	+	5.30118i	−0.126111	+	0.218431i
$590$	4.69924	+	2.71311i	0.193465	+	0.111697i
$591$	−8.29316	+	19.6728i	−0.341135	+	0.809229i
$592$	−0.179924			−0.00739482
$593$	−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	$0.232256\pi$
$594$	4.27711	+	0.644896i	0.175492	+	0.0264604i
$595$	2.62002	−	15.2704i	0.107410	−	0.626024i
$596$	−10.5983	+	6.11893i	−0.434123	+	0.250641i
$597$	−28.6679	−	37.8482i	−1.17330	−	1.54902i
$598$	3.62987	+	8.19152i	0.148436	+	0.334976i
$599$	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	$0.0880423\pi$
$600$	−0.253333	+	0.600948i	−0.0103423	+	0.0245336i
$601$	10.4907	−	6.05683i	0.427926	−	0.247063i	−0.270537	−	0.962710i	$-0.587201\pi$
$601$	10.4907	−	6.05683i	0.427926	−	0.247063i	0.698463	+	0.715646i	$0.253868\pi$
$602$	−20.2955	−	3.48222i	−0.827184	−	0.141925i
$603$	−13.8546	−	14.2054i	−0.564202	−	0.578487i
$604$	−0.503958	−	0.872882i	−0.0205058	−	0.0355170i
$605$	−22.1625			−0.901034
$606$	−22.9738	+	2.87859i	−0.933245	+	0.116935i
$607$	−18.3365	+	10.5866i	−0.744255	+	0.429696i	−0.823614	−	0.567150i	$-0.808046\pi$
$607$	−18.3365	+	10.5866i	−0.744255	+	0.429696i	0.0793596	+	0.996846i	$0.474712\pi$
$608$	−1.28408	−	2.22409i	−0.0520764	−	0.0901990i
$609$	−1.82674	+	40.3229i	−0.0740231	+	1.63397i
$610$	−7.85921			−0.318210
$611$	−3.05029	−	0.326018i	−0.123402	−	0.0131893i
$612$	2.21311	−	7.86484i	0.0894598	−	0.317917i
$613$	3.06942	−	5.31640i	0.123973	−	0.214727i	−0.797358	−	0.603506i	$-0.793770\pi$
$613$	3.06942	−	5.31640i	0.123973	−	0.214727i	0.921331	+	0.388779i	$0.127103\pi$
$614$	−16.2434			−0.655532
$615$	35.2681	−	26.7136i	1.42215	−	1.07720i
$616$	−0.372438	+	2.17070i	−0.0150060	+	0.0874598i
$617$	12.0384	+	6.95037i	0.484647	+	0.279811i	0.722351	−	0.691526i	$-0.243061\pi$
$617$	12.0384	+	6.95037i	0.484647	+	0.279811i	−0.237704	+	0.971338i	$0.576395\pi$
$618$	−3.19084	−	25.4659i	−0.128355	−	1.02439i
$619$	−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	$0.485089\pi$
$620$		−	5.12512i		−	0.205830i
$621$	−12.0200	+	4.71680i	−0.482347	+	0.189279i
$622$	21.6238	−	12.4845i	0.867034	−	0.500582i
$623$	2.84411	−	1.05005i	0.113947	−	0.0420694i
$624$	−5.46417	−	3.02371i	−0.218742	−	0.121045i
$625$	11.4878	−	19.8975i	0.459512	−	0.795898i
$626$	−13.3172	+	23.0661i	−0.532262	+	0.921905i
$627$	−2.95168	+	2.23573i	−0.117879	+	0.0892865i
$628$	−13.6246	+	7.86616i	−0.543681	+	0.313894i
$629$	0.490010			0.0195380
$630$	7.33458	−	15.4105i	0.292217	−	0.613968i
$631$	19.2785	−	33.3914i	0.767467	−	1.32929i	−0.171466	−	0.985190i	$-0.554850\pi$
$631$	19.2785	−	33.3914i	0.767467	−	1.32929i	0.938932	−	0.344101i	$-0.111816\pi$
$632$	−5.38345	−	3.10814i	−0.214142	−	0.123635i
$633$	37.5754	+	15.8401i	1.49349	+	0.629589i
$634$	−4.17764	+	7.23589i	−0.165915	+	0.287374i
$635$	42.5617			1.68901
$636$	−8.07057	+	19.1447i	−0.320019	+	0.759139i
$637$	−22.7665	−	10.8943i	−0.902042	−	0.431648i
$638$			7.33225i			0.290287i
$639$	18.5620	−	18.1037i	0.734303	−	0.716170i
$640$	1.86215	+	1.07511i	0.0736080	+	0.0424976i
$641$			19.6991i			0.778068i	0.921223	+	0.389034i	$0.127191\pi$
$641$			19.6991i			0.778068i	−0.921223	+	0.389034i	$0.872809\pi$
$642$	−1.93441	+	1.46520i	−0.0763450	+	0.0578270i
$643$	5.10073	+	2.94491i	0.201153	+	0.116136i	0.597193	−	0.802097i	$-0.296283\pi$
$643$	5.10073	+	2.94491i	0.201153	+	0.116136i	−0.396040	+	0.918233i	$0.629616\pi$
$644$	−2.27713	−	6.16772i	−0.0897316	−	0.243042i
$645$	26.7102	+	11.2598i	1.05171	+	0.443356i
$646$	3.49711	+	6.05716i	0.137592	+	0.238316i
$647$	15.8953	−	27.5314i	0.624908	−	1.08237i	−0.363651	−	0.931535i	$-0.618470\pi$
$647$	15.8953	−	27.5314i	0.624908	−	1.08237i	0.988559	−	0.150837i	$-0.0481968\pi$
$648$	4.69344	−	7.67930i	0.184376	−	0.301671i
$649$	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
$653$		−	18.6752i		−	0.730816i	−0.930847	−	0.365408i	$-0.880929\pi$
$653$		−	18.6752i		−	0.730816i	0.930847	−	0.365408i	$-0.119071\pi$
$654$	5.44656	−	12.9201i	0.212977	−	0.505218i
$655$	−7.70713	−	13.3491i	−0.301143	−	0.521594i
$656$	5.93979	+	10.2880i	0.231910	+	0.401680i
$657$	9.35197	+	36.7328i	0.364855	+	1.43308i
$658$	2.21863	+	0.380662i	0.0864912	+	0.0148398i
$659$	−39.2891	−	22.6836i	−1.53049	−	0.883626i	−0.999339	−	0.0363457i	$-0.988428\pi$
$659$	−39.2891	−	22.6836i	−1.53049	−	0.883626i	−0.531146	−	0.847280i	$-0.678238\pi$
$660$	1.20429	−	2.85677i	0.0468769	−	0.111200i
$661$	7.16442	+	4.13638i	0.278664	+	0.160887i	0.632818	−	0.774300i	$-0.281898\pi$
$661$	7.16442	+	4.13638i	0.278664	+	0.160887i	−0.354155	+	0.935187i	$0.615231\pi$
$662$	−13.7950	+	7.96452i	−0.536156	+	0.309550i
$663$	14.8813	+	8.23485i	0.577941	+	0.319815i
$664$		−	0.930821i		−	0.0361229i
$665$	5.06024	+	13.7059i	0.196228	+	0.531492i
$666$	0.519592	+	0.146210i	0.0201338	+	0.00566551i
$667$	−10.9441	−	18.9558i	−0.423758	−	0.733971i
$668$	1.67287	+	2.89750i	0.0647254	+	0.112108i
$669$	−19.7538	+	46.8593i	−0.763725	+	1.81168i
$670$	−12.3168	+	7.11113i	−0.475841	+	0.274727i
$671$	−3.04260			−0.117458
$672$	3.86087	+	2.46855i	0.148936	+	0.0952262i
$673$	3.04087	+	5.26695i	0.117217	+	0.203026i	0.918664	−	0.395040i	$-0.129269\pi$
$673$	3.04087	+	5.26695i	0.117217	+	0.203026i	−0.801447	+	0.598066i	$0.795936\pi$
$674$			1.38803i			0.0534649i
$675$	1.21993	−	1.52958i	0.0469551	−	0.0588736i
$676$	8.73259	−	9.63026i	0.335869	−	0.370394i
$677$	−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	$0.217732\pi$
$678$	−0.783968	−	6.25678i	−0.0301081	−	0.240290i
$679$	21.3459	+	3.66243i	0.819180	+	0.140551i
$680$	−5.07144	−	2.92799i	−0.194481	−	0.112283i
$681$	−39.1924	+	29.6861i	−1.50186	+	1.13757i
$682$		−	1.98413i		−	0.0759761i
$683$			28.4552i			1.08881i	0.838823	+	0.544404i	$0.183244\pi$
$683$			28.4552i			1.08881i	−0.838823	+	0.544404i	$0.816756\pi$
$684$	1.90088	+	7.46631i	0.0726821	+	0.285482i
$685$	−11.6455	−	6.72352i	−0.444951	−	0.256893i
$686$	16.1656	+	9.03734i	0.617205	+	0.345047i
$687$	−25.0286	+	3.13606i	−0.954902	+	0.119648i
$688$	−3.89154	+	6.74035i	−0.148364	+	0.256973i
$689$	−34.9447	−	25.4828i	−1.33129	−	0.970816i
$690$	1.15062	+	9.18303i	0.0438035	+	0.349592i
$691$			15.1598i			0.576706i	0.957524	+	0.288353i	$0.0931076\pi$
$691$			15.1598i			0.576706i	−0.957524	+	0.288353i	$0.906892\pi$
$692$	9.84211	+	17.0470i	0.374141	+	0.648031i
$693$	2.83950	−	5.96598i	0.107863	−	0.226629i
$694$	0.408244			0.0154967
$695$	3.87959	−	2.23988i	0.147161	−	0.0849635i
$696$	14.0582	+	5.92630i	0.532874	+	0.224636i
$697$	−16.1766	−	28.0187i	−0.612733	−	1.06128i
$698$	0.900521	+	1.55975i	0.0340852	+	0.0590374i
$699$	25.4250	−	3.18572i	0.961661	−	0.120495i
$700$	0.766074	+	0.636815i	0.0289549	+	0.0240693i
$701$			26.0859i			0.985251i	0.870241	+	0.492625i	$0.163963\pi$
$701$			26.0859i			0.985251i	−0.870241	+	0.492625i	$0.836037\pi$
$702$	13.3226	+	13.1723i	0.502828	+	0.497156i
$703$	−0.400167	+	0.231037i	−0.0150926	+	0.00871372i
$704$	0.720909	+	0.416217i	0.0271703	+	0.0156868i
$705$	−2.91986	−	1.23088i	−0.109968	−	0.0463577i
$706$	20.7468	+	11.9782i	0.780816	+	0.450805i
$707$	−5.98079	+	34.8581i	−0.224931	+	1.31097i
$708$	3.48425	−	2.63913i	0.130946	−	0.0991844i
$709$	9.56340	+	16.5643i	0.359161	+	0.622085i	0.987821	−	0.155595i	$-0.0497296\pi$
$709$	9.56340	+	16.5643i	0.359161	+	0.622085i	−0.628660	+	0.777680i	$0.716396\pi$
$710$	−9.29205	−	16.0943i	−0.348725	−	0.604009i
$711$	13.0208	+	13.3505i	0.488320	+	0.500684i
$712$		−	1.14590i		−	0.0429443i
$713$	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
$717$	20.9433	+	27.6499i	0.782140	+	1.03261i
$718$	4.12438	−	7.14363i	0.153920	−	0.266598i
$719$	−10.9458	−	18.9586i	−0.408208	−	0.707037i	0.586481	−	0.809963i	$-0.300513\pi$
$719$	−10.9458	−	18.9586i	−0.408208	−	0.707037i	−0.994689	+	0.102926i	$0.967180\pi$
$720$	−4.50394	−	4.61798i	−0.167852	−	0.172102i
$721$	−38.6393	−	6.62956i	−1.43900	−	0.246898i
$722$	10.7426	+	6.20227i	0.399800	+	0.230825i
$723$	10.8796	+	14.3636i	0.404616	+	0.534187i
$724$			1.13213i			0.0420752i
$725$	2.87219	+	1.65826i	0.106670	+	0.0615862i
$726$	−6.93475	+	16.4504i	−0.257373	+	0.610531i
$727$		−	33.9953i		−	1.26082i	−0.776264	−	0.630408i	$-0.782888\pi$
$727$		−	33.9953i		−	1.26082i	0.776264	−	0.630408i	$-0.217112\pi$
$728$	−6.84312	+	6.64618i	−0.253623	+	0.246324i
$729$	−19.7943	+	18.3626i	−0.733122	+	0.680097i
$730$	27.1678			1.00553
$731$	10.5983	−	18.3569i	0.391994	−	0.678953i
$732$	−2.45918	+	5.83360i	−0.0908941	+	0.215616i
$733$	−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
$735$	−19.2732	−	17.5555i	−0.710902	−	0.647544i
$736$	−2.48498			−0.0915978
$737$	−4.76832	+	2.75299i	−0.175643	+	0.101408i
$738$	−8.79295	−	34.5370i	−0.323673	−	1.27133i
$739$	−12.5361	+	21.7131i	−0.461146	+	0.798729i	−0.999018	−	0.0442977i	$-0.985895\pi$
$739$	−12.5361	+	21.7131i	−0.461146	+	0.798729i	0.537872	+	0.843026i	$0.319228\pi$
$740$	0.193438	−	0.335045i	0.00711094	−	0.0123165i
$741$	−16.0355	+	0.291437i	−0.589080	+	0.0107062i
$742$	24.4053	+	20.2874i	0.895946	+	0.744774i
$743$	0.168411	−	0.0972319i	0.00617839	−	0.00356709i	−0.496908	−	0.867803i	$-0.665531\pi$
$743$	0.168411	−	0.0972319i	0.00617839	−	0.00356709i	0.503086	+	0.864236i	$0.332198\pi$
$744$	−3.80418	−	1.60367i	−0.139468	−	0.0587935i
$745$		−	26.3142i		−	0.964077i
$746$	27.6209	−	15.9469i	1.01127	−	0.583859i
$747$	−0.756404	+	2.68807i	−0.0276754	+	0.0983512i
$748$	−1.96335	−	1.13354i	−0.0717870	−	0.0414463i
$749$	1.28385	+	3.47738i	0.0469110	+	0.127061i
$750$	−12.0902	−	15.9618i	−0.441471	−	0.582844i
$751$	−21.5291			−0.785607			−0.392803	−	0.919622i	$-0.628495\pi$
$751$	−21.5291			−0.785607			−0.392803	+	0.919622i	$0.628495\pi$
$752$	0.425408	−	0.736829i	0.0155130	−	0.0268694i
$753$	−0.479843	−	3.82959i	−0.0174865	−	0.139558i
$754$	−18.7122	+	25.6603i	−0.681460	+	0.934492i
$755$	2.16725			0.0788743
$756$	−9.14359	−	10.2662i	−0.332549	−	0.373378i
$757$	−24.5972	−	42.6036i	−0.894000	−	1.54845i	−0.835038	−	0.550193i	$-0.814554\pi$
$757$	−24.5972	−	42.6036i	−0.894000	−	1.54845i	−0.0589622	−	0.998260i	$-0.518779\pi$
$758$	−17.2043	+	9.93293i	−0.624890	+	0.360780i
$759$	0.445450	+	3.55510i	0.0161688	+	0.129042i
$760$	5.52213			0.200309
$761$	0.148132	+	0.256572i	0.00536978	+	0.00930072i	0.868698	−	0.495342i	$-0.164957\pi$
$761$	0.148132	+	0.256572i	0.00536978	+	0.00930072i	−0.863328	+	0.504643i	$0.831624\pi$
$762$	13.3178	−	31.5919i	0.482451	−	1.14445i
$763$	−16.4703	−	13.6913i	−0.596265	−	0.495658i
$764$	18.3935	−	10.6195i	0.665455	−	0.384201i
$765$	12.2662	+	12.5767i	0.443484	+	0.454713i
$766$	0.635039	−	0.366640i	0.0229449	−	0.0132472i
$767$	3.68621	+	8.31867i	0.133101	+	0.300370i
$768$	1.38069	−	1.04580i	0.0498214	−	0.0377369i
$769$	27.7574	−	16.0257i	1.00096	−	0.577902i	0.0924253	−	0.995720i	$-0.470538\pi$
$769$	27.7574	−	16.0257i	1.00096	−	0.577902i	0.908531	+	0.417817i	$0.137205\pi$
$770$	−3.64175	−	3.02728i	−0.131240	−	0.109096i
$771$	−8.56864	+	6.49026i	−0.308592	+	0.233741i
$772$	1.56454	−	2.70986i	0.0563089	−	0.0975299i
$773$	25.4967			0.917052			0.458526	−	0.888681i	$-0.348378\pi$
$773$	25.4967			0.917052			0.458526	+	0.888681i	$0.348378\pi$
$774$	16.7155	−	16.3027i	0.600827	−	0.585990i
$775$	−0.777222	−	0.448729i	−0.0279186	−	0.0161188i
$776$	4.09294	−	7.08918i	0.146928	−	0.254487i
$777$	0.444150	−	0.694661i	0.0159338	−	0.0249208i
$778$	−16.5442	−	28.6554i	−0.593139	−	1.02735i
$779$	26.4213	+	15.2544i	0.946643	+	0.546544i
$780$	11.5052	−	6.92429i	0.411952	−	0.247929i
$781$	−3.59731	−	6.23072i	−0.128722	−	0.222953i
$782$	6.76768			0.242012
$783$	−35.7820	−	28.5382i	−1.27874	−	1.01987i
$784$	5.32058	−	4.54878i	0.190021	−	0.162457i
$785$		−	33.8281i		−	1.20738i
$786$	−12.3202	+	1.54370i	−0.439446	+	0.0550620i
$787$			21.6324i			0.771112i	0.922685	+	0.385556i	$0.125990\pi$
$787$			21.6324i			0.771112i	−0.922685	+	0.385556i	$0.874010\pi$
$788$	10.6747	−	6.16302i	0.380269	−	0.219548i
$789$	−42.0897	+	5.27379i	−1.49843	+	0.187752i
$790$	11.5756	−	6.68320i	0.411843	−	0.237778i
$791$	−9.49340	−	1.62884i	−0.337547	−	0.0579147i
$792$	−1.74365	−	1.78780i	−0.0619578	−	0.0635266i
$793$	−10.6480	−	7.76486i	−0.378122	−	0.275738i
$794$	−5.94426	−	10.2958i	−0.210954	−	0.365383i
$795$	−26.9736	−	35.6114i	−0.956656	−	1.26301i
$796$			27.4125i			0.971610i
$797$	−21.2264	+	36.7652i	−0.751878	+	1.30229i	0.195033	+	0.980797i	$0.437519\pi$
$797$	−21.2264	+	36.7652i	−0.751878	+	1.30229i	−0.946911	+	0.321495i	$0.895815\pi$
$798$	11.7567	+	0.532613i	0.416184	+	0.0188543i
$799$	−1.15857	+	2.00670i	−0.0409872	+	0.0709920i
$800$	0.326081	−	0.188263i	0.0115287	−	0.00665610i
$801$	−0.931179	+	3.30917i	−0.0329016	+	0.116924i
$802$	−23.5937			−0.833124
$803$	10.5177			0.371161
$804$	1.42433	+	11.3674i	0.0502321	+	0.400899i
$805$	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
$808$	11.5767	+	6.68381i	0.407267	+	0.235136i
$809$	−26.9231	−	15.5441i	−0.946567	−	0.546501i	−0.0545541	−	0.998511i	$-0.517374\pi$
$809$	−26.9231	−	15.5441i	−0.946567	−	0.546501i	−0.892013	+	0.452010i	$0.850707\pi$
$810$	9.25402	+	16.9960i	0.325153	+	0.597179i
$811$		−	35.7680i		−	1.25598i	−0.778220	−	0.627992i	$-0.783877\pi$
$811$		−	35.7680i		−	1.25598i	0.778220	−	0.627992i	$-0.216123\pi$
$812$	14.8972	−	17.9210i	0.522790	−	0.628905i
$813$	−6.89464	−	9.10251i	−0.241806	−	0.319239i
$814$	0.0748874	−	0.129709i	0.00262480	−	0.00454629i
$815$	51.1768			1.79264
$816$	−3.76022	+	2.84815i	−0.131634	+	0.0997053i
$817$			19.9882i			0.699300i
$818$	11.3544			0.396996
$819$	25.1627	−	13.6323i	0.879255	−	0.476351i
$820$	−25.5438			−0.892028
$821$			7.57766i			0.264462i	0.991219	+	0.132231i	$0.0422141\pi$
$821$			7.57766i			0.264462i	−0.991219	+	0.132231i	$0.957786\pi$
$822$	−8.63454	+	6.54018i	−0.301164	+	0.228115i
$823$	−3.01224			−0.105000			−0.0525000	−	0.998621i	$-0.516719\pi$
$823$	−3.01224			−0.105000			−0.0525000	+	0.998621i	$0.516719\pi$
$824$	−7.40885	+	12.8325i	−0.258099	+	0.447041i
$825$	−0.327787	−	0.432755i	−0.0114121	−	0.0150666i
$826$	−2.31248	−	6.26345i	−0.0804614	−	0.217933i
$827$		−	17.7430i		−	0.616984i	−0.951227	−	0.308492i	$-0.900176\pi$
$827$		−	17.7430i		−	0.616984i	0.951227	−	0.308492i	$-0.0998243\pi$
$828$	7.17625	+	2.01935i	0.249392	+	0.0701772i
$829$	−33.7736	−	19.4992i	−1.17301	−	0.677236i	−0.218620	−	0.975810i	$-0.570156\pi$
$829$	−33.7736	−	19.4992i	−1.17301	−	0.677236i	−0.954386	+	0.298575i	$0.903489\pi$
$830$	1.73333	+	1.00074i	0.0601647	+	0.0347361i
$831$	−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
$834$	−0.448638	−	3.58054i	−0.0155351	−	0.123984i
$835$	−7.19411			−0.248962
$836$	2.13783			0.0739383
$837$	9.68270	+	7.72251i	0.334683	+	0.266929i
$838$	11.0096	−	6.35642i	0.380321	−	0.219579i
$839$	16.2641	−	28.1703i	0.561501	−	0.972548i	−0.435865	−	0.900012i	$-0.643558\pi$
$839$	16.2641	−	28.1703i	0.561501	−	0.972548i	0.997366	−	0.0725356i	$-0.0231091\pi$
$840$	−8.74767	+	4.53555i	−0.301823	+	0.156491i
$841$	24.2922	−	42.0753i	0.837662	−	1.45087i
$842$		−	36.5159i		−	1.25842i
$843$	3.25971	+	4.30356i	0.112270	+	0.148223i
$844$	−11.7715	−	20.3889i	−0.405192	−	0.701814i
$845$	8.54446	+	26.6150i	0.293938	+	0.915584i
$846$	−1.82728	+	1.78215i	−0.0628230	+	0.0612716i
$847$	20.9706	+	17.4322i	0.720557	+	0.598978i
$848$	10.3882	−	5.99761i	0.356731	−	0.205959i
$849$	21.3355	−	2.67331i	0.732233	−	0.0917479i
$850$	−0.888059	+	0.512721i	−0.0304602	+	0.0175862i
$851$			0.447108i			0.0153267i
$852$	−14.8537	+	1.86115i	−0.508880	+	0.0637621i
$853$		−	15.8564i		−	0.542914i	−0.962451	−	0.271457i	$-0.912495\pi$
$853$		−	15.8564i		−	0.542914i	0.962451	−	0.271457i	$-0.0875054\pi$
$854$	7.43653	+	6.18177i	0.254473	+	0.211536i
$855$	−15.9471	−	4.48740i	−0.545378	−	0.153466i
$856$	1.40104			0.0478866
$857$	−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	$-0.474803\pi$
$858$	4.45410	−	2.68066i	0.152061	−	0.0915161i
$859$	−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
$861$	−54.3833	−	2.46371i	−1.85338	−	0.0839631i
$862$	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	$0.467680\pi$
$864$	−4.83706	+	1.89812i	−0.164560	+	0.0645753i
$865$	−42.3255			−1.43911
$866$	15.6275	−	27.0676i	0.531044	−	0.919794i
$867$	−13.2311	+	10.0218i	−0.449351	+	0.340358i
$868$	−4.03123	+	4.84948i	−0.136829	+	0.164602i
$869$	4.48137	−	2.58732i	0.152020	−	0.0877688i
$870$	−26.1498	+	19.8070i	−0.886561	+	0.671520i
$871$	−23.7132	−	2.53449i	−0.803490	−	0.0858778i
$872$	−7.01062	+	4.04758i	−0.237410	+	0.137068i
$873$	−17.5806	+	17.1464i	−0.595012	+	0.580319i
$874$	−5.52684	+	3.19092i	−0.186948	+	0.107935i
$875$	−28.6937	+	10.5938i	−0.970024	+	0.358135i
$876$	8.50093	−	20.1656i	0.287220	−	0.681334i
$877$	−16.0118	−	27.7333i	−0.540680	−	0.936486i	−0.998865	−	0.0476290i	$-0.984833\pi$
$877$	−16.0118	−	27.7333i	−0.540680	−	0.936486i	0.458185	−	0.888857i	$-0.348500\pi$
$878$	29.7890			1.00533
$879$	0.949898	+	7.58106i	0.0320393	+	0.255703i
$880$	−1.55012	+	0.894961i	−0.0522545	+	0.0301691i
$881$	15.9277	+	27.5876i	0.536619	+	0.929451i	0.999083	+	0.0428131i	$0.0136320\pi$
$881$	15.9277	+	27.5876i	0.536619	+	0.929451i	−0.462464	+	0.886638i	$0.653035\pi$
$882$	−19.0614	+	8.81256i	−0.641832	+	0.296734i
$883$	33.5180			1.12797			0.563986	−	0.825784i	$-0.309267\pi$
$883$	33.5180			1.12797			0.563986	+	0.825784i	$0.309267\pi$
$884$	−3.97817	−	8.97753i	−0.133800	−	0.301947i
$885$	1.16848	+	9.32556i	0.0392781	+	0.313475i
$886$	−10.6234	+	18.4003i	−0.356900	+	0.618170i
$887$	27.1455			0.911458			0.455729	−	0.890119i	$-0.349379\pi$
$887$	27.1455			0.911458			0.455729	+	0.890119i	$0.349379\pi$
$888$	−0.188164	−	0.248419i	−0.00631436	−	0.00833640i
$889$	−40.2727	−	33.4775i	−1.35070	−	1.12280i
$890$	2.13383	+	1.23197i	0.0715262	+	0.0412957i
$891$	3.58258	+	6.57980i	0.120021	+	0.220432i
$892$	25.4264	−	14.6799i	0.851338	−	0.491520i
$893$		−	2.18504i		−	0.0731194i
$894$	−19.5320	−	8.23383i	−0.653249	−	0.275381i
$895$	2.48402	−	1.43415i	0.0830316	−	0.0479383i
$896$	−0.916357	−	2.48199i	−0.0306133	−	0.0829176i
$897$	−7.51386	+	13.5784i	−0.250881	+	0.453369i
$898$	14.2344	−	24.6546i	0.475006	−	0.822735i
$899$	−10.4973	+	18.1818i	−0.350104	+	0.606398i
$900$	−1.09466	+	0.278694i	−0.0364886	+	0.00928981i
$901$	−28.2914	+	16.3341i	−0.942524	+	0.544166i
$902$	−9.88898			−0.329267
$903$	−16.4171	−	31.6636i	−0.546328	−	1.05370i
$904$	−1.82030	+	3.15285i	−0.0605423	+	0.104862i
$905$	−2.10819	−	1.21716i	−0.0700786	−	0.0404599i
$906$	0.678143	−	1.60867i	0.0225298	−	0.0534444i
$907$	6.96176	−	12.0581i	0.231161	−	0.400383i	−0.726989	−	0.686649i	$-0.759081\pi$
$907$	6.96176	−	12.0581i	0.231161	−	0.400383i	0.958150	+	0.286266i	$0.0924142\pi$
$908$	28.3861			0.942025
$909$	−28.0003	−	28.7093i	−0.928712	−	0.952227i
$910$	−5.01907	−	19.8883i	−0.166380	−	0.659291i
$911$			25.3251i			0.839057i	0.907742	+	0.419528i	$0.137805\pi$
$911$			25.3251i			0.839057i	−0.907742	+	0.419528i	$0.862195\pi$
$912$	1.72790	−	4.09887i	0.0572166	−	0.135727i
$913$	0.671038	+	0.387424i	0.0222081	+	0.0128219i
$914$			20.4132i			0.675207i
$915$	−8.21913	−	10.8511i	−0.271716	−	0.358728i
$916$	12.6122	+	7.28164i	0.416718	+	0.240592i
$917$	−3.20732	+	18.6934i	−0.105915	+	0.617309i
$918$	13.1734	−	5.16939i	0.434787	−	0.170615i
$919$	6.50044	+	11.2591i	0.214430	+	0.371403i	0.953096	−	0.302668i	$-0.0978774\pi$
$919$	6.50044	+	11.2591i	0.214430	+	0.371403i	−0.738666	+	0.674071i	$0.764544\pi$
$920$	2.67164	−	4.62742i	0.0880814	−	0.152561i
$921$	−16.9873	−	22.4272i	−0.559751	−	0.739001i
$922$	−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
$926$			22.0589i			0.724902i
$927$	31.8236	−	31.0377i	1.04522	−	1.01941i
$928$	−4.40410	−	7.62813i	−0.144572	−	0.250405i
$929$	26.7920	+	46.4051i	0.879017	+	1.52250i	0.852421	+	0.522855i	$0.175133\pi$
$929$	26.7920	+	46.4051i	0.879017	+	1.52250i	0.0265955	+	0.999646i	$0.491533\pi$
$930$	7.07621	−	5.35983i	0.232038	−	0.175756i
$931$	5.99247	−	16.9490i	0.196395	−	0.555481i
$932$	−12.8119	−	7.39695i	−0.419667	−	0.242295i
$933$	39.8513	+	16.7995i	1.30467	+	0.549992i
$934$	−6.51253	−	3.76001i	−0.213097	−	0.123031i
$935$	4.22164	−	2.43736i	0.138062	−	0.0797103i
$936$	−1.53961	−	10.7065i	−0.0503236	−	0.349954i
$937$			19.6964i			0.643454i	0.946833	+	0.321727i	$0.104263\pi$
$937$			19.6964i			0.643454i	−0.946833	+	0.321727i	$0.895737\pi$
$938$	17.2478	+	2.95930i	0.563160	+	0.0966245i
$939$	−45.7742	+	5.73546i	−1.49378	+	0.187170i
$940$	0.914724	+	1.58435i	0.0298350	+	0.0516758i
$941$	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	$0.756394\pi$
$942$	−25.1093	−	10.5850i	−0.818105	−	0.344877i
$943$	25.5656	−	14.7603i	0.832530	−	0.480661i
$944$	−2.52356			−0.0821348
$945$	28.9476	−	5.98942i	0.941665	−	0.194836i
$946$	−3.23945	−	5.61090i	−0.105324	−	0.182426i
$947$		−	28.4100i		−	0.923203i	−0.887088	−	0.461601i	$-0.847275\pi$
$947$		−	28.4100i		−	0.923203i	0.887088	−	0.461601i	$-0.152725\pi$
$948$	−1.33861	−	10.6834i	−0.0434761	−	0.346980i
$949$	36.8082	+	26.8416i	1.19484	+	0.871316i
$950$	0.483490	−	0.837430i	0.0156865	−	0.0271698i
$951$	−14.3595	+	1.79923i	−0.465639	+	0.0583440i
$952$	2.49563	+	6.75953i	0.0808839	+	0.219078i
$953$	25.9570	+	14.9863i	0.840829	+	0.485453i	0.857546	−	0.514408i	$-0.171988\pi$
$953$	25.9570	+	14.9863i	0.840829	+	0.485453i	−0.0167172	+	0.999860i	$0.505321\pi$
$954$	−34.8732	+	8.87853i	−1.12906	+	0.287453i
$955$			45.6687i			1.47781i
$956$		−	20.0261i		−	0.647692i
$957$	−10.1236	+	7.66804i	−0.327249	+	0.247872i
$958$	−26.7035	−	15.4173i	−0.862751	−	0.498109i
$959$	5.73069	+	15.5218i	0.185054	+	0.501226i
$960$	0.463030	+	3.69541i	0.0149442	+	0.119269i
$961$	−12.6594	+	21.9267i	−0.408368	+	0.707314i
$962$	0.593102	−	0.262818i	0.0191224	−	0.00847360i
$963$	−4.04599	−	1.13852i	−0.130380	−	0.0366882i
$964$		−	10.4032i		−	0.335063i
$965$	3.36411	+	5.82681i	0.108295	+	0.187572i
$966$	6.13430	−	9.59419i	0.197368	−	0.308688i
$967$	51.3555			1.65148			0.825741	−	0.564050i	$-0.190758\pi$
$967$	51.3555			1.65148			0.825741	+	0.564050i	$0.190758\pi$
$968$	8.92617	−	5.15353i	0.286898	−	0.165641i
$969$	−4.70582	+	11.1630i	−0.151173	+	0.358607i
$970$	8.80074	+	15.2433i	0.282575	+	0.489434i
$971$	−15.2377	−	26.3926i	−0.489003	−	0.846977i	0.510917	−	0.859630i	$-0.329306\pi$
$971$	−15.2377	−	26.3926i	−0.489003	−	0.846977i	−0.999920	+	0.0126526i	$0.995972\pi$
$972$	15.5111	−	1.55078i	0.497520	−	0.0497413i
$973$	−5.43275	−	0.932127i	−0.174166	−	0.0298826i
$974$			6.30617i			0.202063i
$975$	−0.0427285	−	2.35102i	−0.00136841	−	0.0752928i
$976$	3.16538	−	1.82753i	0.101321	−	0.0584978i
$977$	−32.9481	−	19.0226i	−1.05410	−	0.608586i	−0.130307	−	0.991474i	$-0.541596\pi$
$977$	−32.9481	−	19.0226i	−1.05410	−	0.608586i	−0.923795	+	0.382887i	$0.874930\pi$
$978$	16.0135	−	37.9866i	0.512054	−	1.21468i
$979$	0.826087	+	0.476942i	0.0264019	+	0.0152431i
$980$	2.75029	+	14.7982i	0.0878548	+	0.472711i
$981$	23.5347	−	5.99182i	0.751406	−	0.191304i
$982$	6.08555	+	10.5405i	0.194198	+	0.336360i
$983$	−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	$-0.354963\pi$
$984$	−7.99278	+	18.9602i	−0.254801	+	0.604429i
$985$			26.5038i			0.844480i
$986$	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
$990$	5.20376	−	1.32485i	0.165387	−	0.0421065i
$991$	−12.6707	+	21.9464i	−0.402500	+	0.697150i	−0.994027	−	0.109135i	$-0.965192\pi$
$991$	−12.6707	+	21.9464i	−0.402500	+	0.697150i	0.591527	+	0.806285i	$0.298525\pi$
$992$	1.19176	+	2.06419i	0.0378385	+	0.0655382i
$993$	−25.4233	−	10.7173i	−0.806783	−	0.340104i
$994$	−3.86689	+	22.5375i	−0.122650	+	0.714847i
$995$	−51.0462	−	29.4715i	−1.61827	−	0.934311i
$996$	1.28518	−	0.973449i	0.0407224	−	0.0308449i
$997$			13.7527i			0.435553i	0.975999	+	0.217777i	$0.0698804\pi$
$997$			13.7527i			0.435553i	−0.975999	+	0.217777i	$0.930120\pi$
$998$	28.3607	+	16.3741i	0.897743	+	0.518312i
$999$	0.341517	+	0.870302i	0.0108051	+	0.0275351i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.2	✓	76	21.17	even	6
546.2.u.a.185.37	yes	76	7.3	odd	6
546.2.u.a.425.2	yes	76	13.9	even	3
546.2.u.a.425.37	yes	76	39.35	odd	6
546.2.bb.a.269.10	yes	76	91.87	odd	6	inner
546.2.bb.a.269.35	yes	76	273.269	even	6	inner
546.2.bb.a.341.16	yes	76	1.1	even	1	trivial
546.2.bb.a.341.29	yes	76	3.2	odd	2	inner

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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.38069 - 1.04580i) q^{3} -1.00000 q^{4} +(1.07511 - 1.86215i) q^{5} +(-1.04580 - 1.38069i) q^{6} +(-2.48199 + 0.916357i) q^{7} +1.00000i q^{8} +(0.812620 - 2.88784i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.38069 - 1.04580i) q^{3} -1.00000 q^{4} +(1.07511 - 1.86215i) q^{5} +(-1.04580 - 1.38069i) q^{6} +(-2.48199 + 0.916357i) q^{7} +1.00000i q^{8} +(0.812620 - 2.88784i) q^{9} +(-1.86215 - 1.07511i) q^{10} +(-0.720909 - 0.416217i) q^{11} +(-1.38069 + 1.04580i) q^{12} +(-1.46072 - 3.29641i) q^{13} +(0.916357 + 2.48199i) q^{14} +(-0.463030 - 3.69541i) q^{15} +1.00000 q^{16} -2.72343 q^{17} +(-2.88784 - 0.812620i) q^{18} +(2.22409 - 1.28408i) q^{19} +(-1.07511 + 1.86215i) q^{20} +(-2.46855 + 3.86087i) q^{21} +(-0.416217 + 0.720909i) q^{22} -2.48498i q^{23} +(1.04580 + 1.38069i) q^{24} +(0.188263 + 0.326081i) q^{25} +(-3.29641 + 1.46072i) q^{26} +(-1.89812 - 4.83706i) q^{27} +(2.48199 - 0.916357i) q^{28} +(7.62813 - 4.40410i) q^{29} +(-3.69541 + 0.463030i) q^{30} +(-2.06419 + 1.19176i) q^{31} -1.00000i q^{32} +(-1.43063 + 0.179257i) q^{33} +2.72343i q^{34} +(-0.962029 + 5.60703i) q^{35} +(-0.812620 + 2.88784i) q^{36} -0.179924 q^{37} +(-1.28408 - 2.22409i) q^{38} +(-5.46417 - 3.02371i) q^{39} +(1.86215 + 1.07511i) q^{40} +(5.93979 + 10.2880i) q^{41} +(3.86087 + 2.46855i) q^{42} +(-3.89154 + 6.74035i) q^{43} +(0.720909 + 0.416217i) q^{44} +(-4.50394 - 4.61798i) q^{45} -2.48498 q^{46} +(0.425408 - 0.736829i) q^{47} +(1.38069 - 1.04580i) q^{48} +(5.32058 - 4.54878i) q^{49} +(0.326081 - 0.188263i) q^{50} +(-3.76022 + 2.84815i) q^{51} +(1.46072 + 3.29641i) q^{52} +(10.3882 - 5.99761i) q^{53} +(-4.83706 + 1.89812i) q^{54} +(-1.55012 + 0.894961i) q^{55} +(-0.916357 - 2.48199i) q^{56} +(1.72790 - 4.09887i) q^{57} +(-4.40410 - 7.62813i) q^{58} -2.52356 q^{59} +(0.463030 + 3.69541i) q^{60} +(3.16538 - 1.82753i) q^{61} +(1.19176 + 2.06419i) q^{62} +(0.629378 + 7.91226i) q^{63} -1.00000 q^{64} +(-7.70885 - 0.823929i) q^{65} +(0.179257 + 1.43063i) q^{66} +(3.30716 - 5.72816i) q^{67} +2.72343 q^{68} +(-2.59879 - 3.43100i) q^{69} +(5.60703 + 0.962029i) q^{70} +(7.48494 + 4.32143i) q^{71} +(2.88784 + 0.812620i) q^{72} +(-10.9421 + 6.31743i) q^{73} +0.179924i q^{74} +(0.600948 + 0.253333i) q^{75} +(-2.22409 + 1.28408i) q^{76} +(2.17070 + 0.372438i) q^{77} +(-3.02371 + 5.46417i) q^{78} +(-3.10814 + 5.38345i) q^{79} +(1.07511 - 1.86215i) q^{80} +(-7.67930 - 4.69344i) q^{81} +(10.2880 - 5.93979i) q^{82} -0.930821 q^{83} +(2.46855 - 3.86087i) q^{84} +(-2.92799 + 5.07144i) q^{85} +(6.74035 + 3.89154i) q^{86} +(5.92630 - 14.0582i) q^{87} +(0.416217 - 0.720909i) q^{88} -1.14590 q^{89} +(-4.61798 + 4.50394i) q^{90} +(6.64618 + 6.84312i) q^{91} +2.48498i q^{92} +(-1.60367 + 3.80418i) q^{93} +(-0.736829 - 0.425408i) q^{94} -5.52213i q^{95} +(-1.04580 - 1.38069i) q^{96} +(-7.08918 - 4.09294i) q^{97} +(-4.54878 - 5.32058i) q^{98} +(-1.78780 + 1.74365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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