LMFDB - Embedded newform 546.2.bb.a.269.10

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			269.10
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.215340 - 1.71861i) q^{3} -1.00000 q^{4} +(-1.07511 - 1.86215i) q^{5} +(-1.71861 + 0.215340i) q^{6} +(-2.48199 - 0.916357i) q^{7} +1.00000i q^{8} +(-2.90726 + 0.740172i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.215340 - 1.71861i) q^{3} -1.00000 q^{4} +(-1.07511 - 1.86215i) q^{5} +(-1.71861 + 0.215340i) q^{6} +(-2.48199 - 0.916357i) q^{7} +1.00000i q^{8} +(-2.90726 + 0.740172i) q^{9} +(-1.86215 + 1.07511i) q^{10} +(0.720909 - 0.416217i) q^{11} +(0.215340 + 1.71861i) q^{12} +(-1.46072 + 3.29641i) q^{13} +(-0.916357 + 2.48199i) q^{14} +(-2.96880 + 2.24870i) q^{15} +1.00000 q^{16} +2.72343 q^{17} +(0.740172 + 2.90726i) q^{18} +(2.22409 + 1.28408i) q^{19} +(1.07511 + 1.86215i) q^{20} +(-1.04039 + 4.46291i) q^{21} +(-0.416217 - 0.720909i) q^{22} -2.48498i q^{23} +(1.71861 - 0.215340i) 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} +(2.24870 + 2.96880i) q^{30} +(-2.06419 - 1.19176i) q^{31} -1.00000i q^{32} +(-0.870557 - 1.14934i) q^{33} -2.72343i q^{34} +(0.962029 + 5.60703i) q^{35} +(2.90726 - 0.740172i) q^{36} -0.179924 q^{37} +(1.28408 - 2.22409i) q^{38} +(5.97980 + 1.80056i) q^{39} +(1.86215 - 1.07511i) q^{40} +(-5.93979 + 10.2880i) q^{41} +(4.46291 + 1.04039i) 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} +(-0.215340 - 1.71861i) q^{48} +(5.32058 + 4.54878i) q^{49} +(-0.326081 - 0.188263i) q^{50} +(-0.586464 - 4.68052i) 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} +(2.96880 - 2.24870i) q^{60} +(3.16538 + 1.82753i) q^{61} +(-1.19176 + 2.06419i) q^{62} +(7.89405 + 0.826982i) q^{63} -1.00000 q^{64} +(7.70885 - 0.823929i) q^{65} +(-1.14934 + 0.870557i) q^{66} +(3.30716 + 5.72816i) q^{67} -2.72343 q^{68} +(-4.27073 + 0.535117i) q^{69} +(5.60703 - 0.962029i) q^{70} +(-7.48494 + 4.32143i) q^{71} +(-0.740172 - 2.90726i) 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} +(1.80056 - 5.97980i) q^{78} +(-3.10814 - 5.38345i) q^{79} +(-1.07511 - 1.86215i) q^{80} +(7.90429 - 4.30374i) q^{81} +(10.2880 + 5.93979i) q^{82} +0.930821 q^{83} +(1.04039 - 4.46291i) 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} +(-1.71861 + 0.215340i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.215340	−	1.71861i	−0.124327	−	0.992241i
$3$	−0.215340	−	1.71861i	−0.124327	−	0.992241i
$4$	−1.00000			−0.500000
$5$	−1.07511	−	1.86215i	−0.480805	−	0.832779i	0.518952	−	0.854803i	$-0.326322\pi$
$5$	−1.07511	−	1.86215i	−0.480805	−	0.832779i	−0.999757	+	0.0220241i	$0.992989\pi$
$6$	−1.71861	+	0.215340i	−0.701621	+	0.0879122i
$7$	−2.48199	−	0.916357i	−0.938105	−	0.346350i
$7$	−2.48199	−	0.916357i	−0.938105	−	0.346350i
$8$			1.00000i			0.353553i
$9$	−2.90726	+	0.740172i	−0.969086	+	0.246724i
$10$	−1.86215	+	1.07511i	−0.588864	+	0.339981i
$11$	0.720909	−	0.416217i	0.217362	−	0.125494i	−0.387366	−	0.921926i	$-0.626615\pi$
$11$	0.720909	−	0.416217i	0.217362	−	0.125494i	0.604728	+	0.796432i	$0.293282\pi$
$12$	0.215340	+	1.71861i	0.0621633	+	0.496121i
$13$	−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
$16$	1.00000			0.250000
$17$	2.72343			0.660529			0.330264	−	0.943889i	$-0.392862\pi$
$17$	2.72343			0.660529			0.330264	+	0.943889i	$0.392862\pi$
$18$	0.740172	+	2.90726i	0.174460	+	0.685247i
$19$	2.22409	+	1.28408i	0.510242	+	0.294589i	0.732933	−	0.680301i	$-0.238151\pi$
$19$	2.22409	+	1.28408i	0.510242	+	0.294589i	−0.222691	+	0.974889i	$0.571484\pi$
$20$	1.07511	+	1.86215i	0.240403	+	0.416390i
$21$	−1.04039	+	4.46291i	−0.227032	+	0.973887i
$22$	−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	$-0.0834185\pi$
$24$	1.71861	−	0.215340i	0.350810	−	0.0439561i
$25$	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	$-0.638151\pi$
$29$	−7.62813	−	4.40410i	−1.41651	−	0.817821i	−0.995990	+	0.0894637i	$0.971485\pi$
$30$	2.24870	+	2.96880i	0.410554	+	0.542026i
$31$	−2.06419	−	1.19176i	−0.370740	−	0.214047i	0.303042	−	0.952977i	$-0.401998\pi$
$31$	−2.06419	−	1.19176i	−0.370740	−	0.214047i	−0.673782	+	0.738931i	$0.735331\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.870557	−	1.14934i	−0.151544	−	0.200074i
$34$		−	2.72343i		−	0.467064i
$35$	0.962029	+	5.60703i	0.162613	+	0.947762i
$36$	2.90726	−	0.740172i	0.484543	−	0.123362i
$37$	−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
$39$	5.97980	+	1.80056i	0.957534	+	0.288321i
$40$	1.86215	−	1.07511i	0.294432	−	0.169990i
$41$	−5.93979	+	10.2880i	−0.927640	+	1.60672i	−0.140381	+	0.990098i	$0.544833\pi$
$41$	−5.93979	+	10.2880i	−0.927640	+	1.60672i	−0.787259	+	0.616622i	$0.788501\pi$
$42$	4.46291	+	1.04039i	0.688642	+	0.160536i
$43$	−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
$45$	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	$-0.186431\pi$
$47$	−0.425408	−	0.736829i	−0.0620522	−	0.107478i	−0.895383	+	0.445298i	$0.853098\pi$
$48$	−0.215340	−	1.71861i	−0.0310817	−	0.248060i
$49$	5.32058	+	4.54878i	0.760083	+	0.649826i
$50$	−0.326081	−	0.188263i	−0.0461148	−	0.0266244i
$51$	−0.586464	−	4.68052i	−0.0821213	−	0.655404i
$52$	1.46072	−	3.29641i	0.202565	−	0.457129i
$53$	−10.3882	−	5.99761i	−1.42692	−	0.823835i	−0.430047	−	0.902807i	$-0.641503\pi$
$53$	−10.3882	−	5.99761i	−1.42692	−	0.823835i	−0.996877	+	0.0789721i	$0.974836\pi$
$54$	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	$-0.447473\pi$
$59$	2.52356			0.328539			0.164270	+	0.986415i	$0.447473\pi$
$60$	2.96880	−	2.24870i	0.383270	−	0.290306i
$61$	3.16538	+	1.82753i	0.405285	+	0.233991i	0.688762	−	0.724988i	$-0.258155\pi$
$61$	3.16538	+	1.82753i	0.405285	+	0.233991i	−0.283477	+	0.958979i	$0.591488\pi$
$62$	−1.19176	+	2.06419i	−0.151354	+	0.262153i
$63$	7.89405	+	0.826982i	0.994557	+	0.104190i
$64$	−1.00000			−0.125000
$65$	7.70885	−	0.823929i	0.956165	−	0.102196i
$66$	−1.14934	+	0.870557i	−0.141473	+	0.107158i
$67$	3.30716	+	5.72816i	0.404033	+	0.699806i	0.994208	−	0.107469i	$-0.0342746\pi$
$67$	3.30716	+	5.72816i	0.404033	+	0.699806i	−0.590175	+	0.807275i	$0.700941\pi$
$68$	−2.72343			−0.330264
$69$	−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	$0.504747\pi$
$72$	−0.740172	−	2.90726i	−0.0872302	−	0.342624i
$73$	−10.9421	−	6.31743i	−1.28068	−	0.739399i	−0.303704	−	0.952766i	$-0.598224\pi$
$73$	−10.9421	−	6.31743i	−1.28068	−	0.739399i	−0.976972	+	0.213367i	$0.931557\pi$
$74$			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
$78$	1.80056	−	5.97980i	0.203874	−	0.677079i
$79$	−3.10814	−	5.38345i	−0.349693	−	0.605686i	0.636502	−	0.771275i	$-0.280381\pi$
$79$	−3.10814	−	5.38345i	−0.349693	−	0.605686i	−0.986195	+	0.165589i	$0.947047\pi$
$80$	−1.07511	−	1.86215i	−0.120201	−	0.208195i
$81$	7.90429	−	4.30374i	0.878254	−	0.478194i
$82$	10.2880	+	5.93979i	1.13612	+	0.655941i
$83$	0.930821			0.102171			0.0510854	−	0.998694i	$-0.483732\pi$
$83$	0.930821			0.102171			0.0510854	+	0.998694i	$0.483732\pi$
$84$	1.04039	−	4.46291i	0.113516	−	0.486944i
$85$	−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	$-0.480656\pi$
$89$	1.14590			0.121465			0.0607324	+	0.998154i	$0.480656\pi$
$90$	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
$96$	−1.71861	+	0.215340i	−0.175405	+	0.0219781i
$97$	−7.08918	+	4.09294i	−0.719797	+	0.415575i	−0.814678	−	0.579914i	$-0.803086\pi$
$97$	−7.08918	+	4.09294i	−0.719797	+	0.415575i	0.0948811	+	0.995489i	$0.469753\pi$
$98$	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	−0.979268	−	0.202569i	$-0.935071\pi$
$101$	−6.68381	−	11.5767i	−0.665064	−	1.15192i	0.314204	−	0.949356i	$-0.398262\pi$
$102$	−4.68052	+	0.586464i	−0.463440	+	0.0580686i
$103$	12.8325	−	7.40885i	1.26442	−	0.730015i	0.290497	−	0.956876i	$-0.406180\pi$
$103$	12.8325	−	7.40885i	1.26442	−	0.730015i	0.973927	+	0.226861i	$0.0728462\pi$
$104$	−3.29641	−	1.46072i	−0.323239	−	0.143235i
$105$	9.42915	−	2.86078i	0.920191	−	0.279183i
$106$	−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	−0.604450	−	0.796643i	$-0.706607\pi$
$109$	4.04758	−	7.01062i	0.387688	−	0.671496i	0.992138	+	0.125147i	$0.0399404\pi$
$110$	−0.894961	+	1.55012i	−0.0853312	+	0.147798i
$111$	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	$0.388111\pi$
$114$	−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
$117$	1.80678	−	10.6647i	0.167037	−	0.985951i
$118$		−	2.52356i		−	0.232312i
$119$	−6.75953	−	2.49563i	−0.619645	−	0.228774i
$120$	−2.24870	−	2.96880i	−0.205277	−	0.271013i
$121$	−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
$126$	0.826982	−	7.89405i	0.0736734	−	0.703258i
$127$	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	$-0.174601\pi$
$128$			1.00000i			0.0883883i
$129$	−10.7460	+	8.13952i	−0.946136	+	0.716645i
$130$	−0.823929	−	7.70885i	−0.0722633	−	0.676110i
$131$	−3.58433	−	6.20825i	−0.313165	−	0.542417i	0.665881	−	0.746058i	$-0.268056\pi$
$131$	−3.58433	−	6.20825i	−0.313165	−	0.542417i	−0.979046	+	0.203641i	$0.934723\pi$
$132$	0.870557	+	1.14934i	0.0757722	+	0.100037i
$133$	−4.34351	−	5.22515i	−0.376630	−	0.453078i
$134$	5.72816	−	3.30716i	0.494838	−	0.285695i
$135$	6.96664	−	8.73497i	0.599593	−	0.751787i
$136$			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	$-0.0860813\pi$
$138$	0.535117	+	4.27073i	0.0455522	+	0.363548i
$139$	1.80427	−	1.04170i	0.153036	−	0.0883555i	−0.421526	−	0.906816i	$-0.638506\pi$
$139$	1.80427	−	1.04170i	0.153036	−	0.0883555i	0.574563	+	0.818461i	$0.305172\pi$
$140$	−0.962029	−	5.60703i	−0.0813063	−	0.473881i
$141$	−1.17472	+	0.889781i	−0.0989289	+	0.0749331i
$142$	4.32143	+	7.48494i	0.362646	+	0.628122i
$143$	0.318974	+	2.98439i	0.0266740	+	0.249567i
$144$	−2.90726	+	0.740172i	−0.242271	+	0.0616810i
$145$			18.9396i			1.57285i
$146$	−6.31743	+	10.9421i	−0.522834	+	0.905575i
$147$	6.67186	−	10.1236i	0.550286	−	0.834976i
$148$	0.179924			0.0147896
$149$	−10.5983	−	6.11893i	−0.868247	−	0.501282i	−0.00148148	−	0.999999i	$-0.500472\pi$
$149$	−10.5983	−	6.11893i	−0.868247	−	0.501282i	−0.866765	+	0.498716i	$0.833805\pi$
$150$	−0.253333	+	0.600948i	−0.0206845	+	0.0490672i
$151$	0.503958	−	0.872882i	0.0410116	−	0.0710341i	−0.844791	−	0.535096i	$-0.820275\pi$
$151$	0.503958	−	0.872882i	0.0410116	−	0.0710341i	0.885803	+	0.464062i	$0.153609\pi$
$152$	−1.28408	+	2.22409i	−0.104153	+	0.180398i
$153$	−7.91771	+	2.01581i	−0.640109	+	0.162968i
$154$	0.372438	+	2.17070i	0.0300119	+	0.174920i
$155$			5.12512i			0.411659i
$156$	−5.97980	−	1.80056i	−0.478767	−	0.144160i
$157$	13.6246	+	7.86616i	1.08736	+	0.627788i	0.932873	−	0.360206i	$-0.117294\pi$
$157$	13.6246	+	7.86616i	1.08736	+	0.627788i	0.154489	+	0.987995i	$0.450627\pi$
$158$	−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
$162$	−4.30374	−	7.90429i	−0.338134	−	0.621020i
$163$	11.9003	−	20.6120i	0.932105	−	1.61445i	0.152388	−	0.988321i	$-0.451304\pi$
$163$	11.9003	−	20.6120i	0.932105	−	1.61445i	0.779717	−	0.626132i	$-0.215363\pi$
$164$	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	$-0.792012\pi$
$167$	1.67287	−	2.89750i	0.129451	−	0.224215i	0.923464	+	0.383685i	$0.125345\pi$
$168$	−4.46291	−	1.04039i	−0.344321	−	0.0802678i
$169$	−8.73259	−	9.63026i	−0.671738	−	0.740789i
$170$	−5.07144	+	2.92799i	−0.388961	+	0.224567i
$171$	−7.41646	−	2.08694i	−0.567151	−	0.159592i
$172$	3.89154	+	6.74035i	0.296727	+	0.513947i
$173$	9.84211	−	17.0470i	0.748282	−	1.29606i	−0.200364	−	0.979721i	$-0.564213\pi$
$173$	9.84211	−	17.0470i	0.748282	−	1.29606i	0.948646	−	0.316340i	$-0.102454\pi$
$174$	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
$177$	−0.543423	−	4.33701i	−0.0408462	−	0.325990i
$178$		−	1.14590i		−	0.0858886i
$179$	−1.15524	+	0.666976i	−0.0863464	+	0.0498521i	−0.542551	−	0.840023i	$-0.682542\pi$
$179$	−1.15524	+	0.666976i	−0.0863464	+	0.0498521i	0.456205	+	0.889875i	$0.349208\pi$
$180$	−4.50394	−	4.61798i	−0.335704	−	0.344204i
$181$			1.13213i			0.0841503i	0.999114	+	0.0420752i	$0.0133969\pi$
$181$			1.13213i			0.0841503i	−0.999114	+	0.0420752i	$0.986603\pi$
$182$	−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
$189$	−0.278646	−	13.7449i	−0.0202685	−	0.999795i
$190$	−5.52213			−0.400618
$191$	18.3935	+	10.6195i	1.33091	+	0.768402i	0.985439	−	0.170028i	$-0.0543858\pi$
$191$	18.3935	+	10.6195i	1.33091	+	0.768402i	0.345471	+	0.938429i	$0.387719\pi$
$192$	0.215340	+	1.71861i	0.0155408	+	0.124030i
$193$	−1.56454	−	2.70986i	−0.112618	−	0.195060i	0.804207	−	0.594349i	$-0.202590\pi$
$193$	−1.56454	−	2.70986i	−0.112618	−	0.195060i	−0.916825	+	0.399289i	$0.869257\pi$
$194$	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	$0.521965\pi$
$198$	1.74365	+	1.78780i	0.123916	+	0.127053i
$199$			27.4125i			1.94322i	0.236587	+	0.971610i	$0.423971\pi$
$199$			27.4125i			1.94322i	−0.236587	+	0.971610i	$0.576029\pi$
$200$	0.326081	+	0.188263i	0.0230574	+	0.0133122i
$201$	9.13233	−	6.91722i	0.644145	−	0.487903i
$202$	−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
$205$	25.5438			1.78406
$206$	−7.40885	−	12.8325i	−0.516199	−	0.894083i
$207$	1.83932	+	7.22449i	0.127841	+	0.502137i
$208$	−1.46072	+	3.29641i	−0.101283	+	0.228565i
$209$	2.13783			0.147877
$210$	−2.86078	−	9.42915i	−0.197412	−	0.650673i
$211$	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	$-0.134075\pi$
$212$	10.3882	+	5.99761i	0.713462	+	0.411917i
$213$	9.03867	+	11.9331i	0.619320	+	0.817644i
$214$	−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
$222$	0.309219	−	0.0387448i	0.0207534	−	0.00260038i
$223$	−25.4264	−	14.6799i	−1.70268	−	0.983041i	−0.943032	−	0.332702i	$-0.892040\pi$
$223$	−25.4264	−	14.6799i	−1.70268	−	0.983041i	−0.759644	−	0.650339i	$-0.774627\pi$
$224$	−0.916357	+	2.48199i	−0.0612267	+	0.165835i
$225$	−0.305973	+	1.08735i	−0.0203982	+	0.0724899i
$226$	1.82030	+	3.15285i	0.121085	+	0.209725i
$227$	28.3861			1.88405			0.942025	−	0.335541i	$-0.108919\pi$
$227$	28.3861			1.88405			0.942025	+	0.335541i	$0.108919\pi$
$228$	−1.72790	+	4.09887i	−0.114433	+	0.271454i
$229$	−12.6122	+	7.28164i	−0.833435	+	0.481184i	−0.855027	−	0.518583i	$-0.826460\pi$
$229$	−12.6122	+	7.28164i	−0.833435	+	0.481184i	0.0215921	+	0.999767i	$0.493126\pi$
$230$	2.67164	+	4.62742i	0.176163	+	0.305123i
$231$	1.10751	+	3.65038i	0.0728691	+	0.240178i
$232$	4.40410	−	7.62813i	0.289143	−	0.500811i
$233$	−12.8119	+	7.39695i	−0.839335	+	0.484590i	−0.857038	−	0.515253i	$-0.827698\pi$
$233$	−12.8119	+	7.39695i	−0.839335	+	0.484590i	0.0177033	+	0.999843i	$0.494365\pi$
$234$	−10.6647	−	1.80678i	−0.697172	−	0.118113i
$235$	−0.914724	+	1.58435i	−0.0596700	+	0.103352i
$236$	−2.52356			−0.164270
$237$	−8.58276	+	6.50096i	−0.557510	+	0.422282i
$238$	−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	$0.775735\pi$
$240$	−2.96880	+	2.24870i	−0.191635	+	0.145153i
$241$		−	10.4032i		−	0.670127i	−0.942196	−	0.335063i	$-0.891242\pi$
$241$		−	10.4032i		−	0.670127i	0.942196	−	0.335063i	$-0.108758\pi$
$242$	8.92617	+	5.15353i	0.573796	+	0.331281i
$243$	−9.09858	−	12.6576i	−0.583674	−	0.811988i
$244$	−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
$249$	−0.200443	−	1.59972i	−0.0127026	−	0.101378i
$250$			11.5607i			0.731166i
$251$	−1.11415	−	1.92977i	−0.0703247	−	0.121806i	0.828719	−	0.559665i	$-0.189070\pi$
$251$	−1.11415	−	1.92977i	−0.0703247	−	0.121806i	−0.899044	+	0.437859i	$0.855737\pi$
$252$	−7.89405	−	0.826982i	−0.497279	−	0.0520949i
$253$	−1.03429	−	1.79145i	−0.0650255	−	0.112627i
$254$	−17.1421	−	9.89702i	−1.07559	−	0.620994i
$255$	−8.08532	+	6.12417i	−0.506322	+	0.383511i
$256$	1.00000			0.0625000
$257$	6.20605			0.387123			0.193561	−	0.981088i	$-0.437996\pi$
$257$	6.20605			0.387123			0.193561	+	0.981088i	$0.437996\pi$
$258$	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
$261$	25.4367	+	7.15772i	1.57449	+	0.443052i
$262$	−6.20825	+	3.58433i	−0.383547	+	0.221441i
$263$	21.2094	−	12.2453i	1.30783	−	0.755075i	0.326095	−	0.945337i	$-0.394267\pi$
$263$	21.2094	−	12.2453i	1.30783	−	0.755075i	0.981733	+	0.190262i	$0.0609337\pi$
$264$	1.14934	−	0.870557i	0.0707367	−	0.0535791i
$265$			25.7924i			1.58442i
$266$	−5.22515	+	4.34351i	−0.320374	+	0.266318i
$267$	−0.246758	−	1.96935i	−0.0151013	−	0.120522i
$268$	−3.30716	−	5.72816i	−0.202017	−	0.349903i
$269$	5.00152			0.304948			0.152474	−	0.988307i	$-0.451276\pi$
$269$	5.00152			0.304948			0.152474	+	0.988307i	$0.451276\pi$
$270$	−8.73497	−	6.96664i	−0.531593	−	0.423976i
$271$			6.59272i			0.400479i	0.979747	+	0.200240i	$0.0641721\pi$
$271$			6.59272i			0.400479i	−0.979747	+	0.200240i	$0.935828\pi$
$272$	2.72343			0.165132
$273$	−13.1919	−	9.94861i	−0.798408	−	0.602117i
$274$	−6.25378			−0.377805
$275$		−	0.313433i		−	0.0189007i
$276$	4.27073	−	0.535117i	0.257067	−	0.0322103i
$277$	−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
$279$	6.88325	+	1.93690i	0.412089	+	0.115959i
$280$	−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	$0.970364\pi$
$282$	0.889781	+	1.17472i	0.0529857	+	0.0699533i
$283$	10.7512	−	6.20719i	0.639091	−	0.368979i	−0.145173	−	0.989406i	$-0.546374\pi$
$283$	10.7512	−	6.20719i	0.639091	−	0.368979i	0.784264	+	0.620427i	$0.213041\pi$
$284$	7.48494	−	4.32143i	0.444149	−	0.256430i
$285$	−9.49041	+	1.18914i	−0.562163	+	0.0704384i
$286$	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
$289$	−9.58293			−0.563702
$290$	18.9396			1.11217
$291$	8.56076	+	11.3022i	0.501841	+	0.662545i
$292$	10.9421	+	6.31743i	0.640338	+	0.369699i
$293$	2.20558	+	3.82017i	0.128851	+	0.223177i	0.923232	−	0.384244i	$-0.125538\pi$
$293$	2.20558	+	3.82017i	0.128851	+	0.223177i	−0.794381	+	0.607420i	$0.792204\pi$
$294$	−10.1236	−	6.67186i	−0.590418	−	0.389111i
$295$	−2.71311	−	4.69924i	−0.157963	−	0.273600i
$296$		−	0.179924i		−	0.0104579i
$297$	3.38164	+	2.69705i	0.196223	+	0.156499i
$298$	−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
$303$	−18.4566	+	13.9798i	−1.06030	+	0.803119i
$304$	2.22409	+	1.28408i	0.127561	+	0.0736471i
$305$		−	7.85921i		−	0.450017i
$306$	2.01581	+	7.91771i	0.115236	+	0.452625i
$307$			16.2434i			0.927062i	0.886081	+	0.463531i	$0.153418\pi$
$307$			16.2434i			0.927062i	−0.886081	+	0.463531i	$0.846582\pi$
$308$	2.17070	−	0.372438i	0.123687	−	0.0212216i
$309$	−15.4963	−	20.4587i	−0.881553	−	1.16385i
$310$	5.12512			0.291087
$311$	−12.4845	+	21.6238i	−0.707930	+	1.22617i	0.257693	+	0.966227i	$0.417038\pi$
$311$	−12.4845	+	21.6238i	−0.707930	+	1.22617i	−0.965624	+	0.259944i	$0.916296\pi$
$312$	−1.80056	+	5.97980i	−0.101937	+	0.338539i
$313$	−23.0661	+	13.3172i	−1.30377	+	0.752733i	−0.981049	−	0.193761i	$-0.937931\pi$
$313$	−23.0661	+	13.3172i	−1.30377	+	0.752733i	−0.322722	+	0.946494i	$0.604598\pi$
$314$	7.86616	−	13.6246i	0.443913	−	0.768880i
$315$	−6.94704	−	15.5890i	−0.391421	−	0.878342i
$316$	3.10814	+	5.38345i	0.174846	+	0.302843i
$317$	7.23589	−	4.17764i	0.406408	−	0.234640i	−0.282837	−	0.959168i	$-0.591276\pi$
$317$	7.23589	−	4.17764i	0.406408	−	0.234640i	0.689245	+	0.724528i	$0.257942\pi$
$318$	19.1447	+	8.07057i	1.07358	+	0.452575i
$319$	−7.33225			−0.410527
$320$	1.07511	+	1.86215i	0.0601007	+	0.104097i
$321$	−2.40785	+	0.301701i	−0.134393	+	0.0168393i
$322$	6.16772	+	2.27713i	0.343713	+	0.126900i
$323$	6.05716	+	3.49711i	0.337030	+	0.194584i
$324$	−7.90429	+	4.30374i	−0.439127	+	0.239097i
$325$	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	−0.997517	−	0.0704239i	$-0.977565\pi$
$331$	−7.96452	+	13.7950i	−0.437770	+	0.758239i	0.559747	+	0.828663i	$0.310898\pi$
$332$	−0.930821			−0.0510854
$333$	0.523085	−	0.133175i	0.0286649	−	0.00729792i
$334$	−2.89750	−	1.67287i	−0.158544	−	0.0915355i
$335$	7.11113	−	12.3168i	0.388523	−	0.672941i
$336$	−1.04039	+	4.46291i	−0.0567579	+	0.243472i
$337$	−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
$339$	3.80733	+	5.02655i	0.206786	+	0.273005i
$340$	2.92799	+	5.07144i	0.158793	+	0.275037i
$341$	−1.98413			−0.107446
$342$	−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
$345$	5.58798	+	7.37742i	0.300847	+	0.397187i
$346$	−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	0.457673	−	0.889121i	$-0.348683\pi$
$349$	−1.55975	−	0.900521i	−0.0834914	−	0.0482038i	−0.541164	+	0.840917i	$0.682016\pi$
$350$	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
$353$	11.9782	+	20.7468i	0.637534	+	1.10424i	0.985972	+	0.166909i	$0.0533787\pi$
$353$	11.9782	+	20.7468i	0.637534	+	1.10424i	−0.348438	+	0.937332i	$0.613288\pi$
$354$	−4.33701	+	0.543423i	−0.230510	+	0.0288826i
$355$	16.0943	+	9.29205i	0.854197	+	0.493171i
$356$	−1.14590			−0.0607324
$357$	−2.83343	+	12.1544i	−0.149961	+	0.643280i
$358$	0.666976	+	1.15524i	0.0352508	+	0.0610561i
$359$	−7.14363	+	4.12438i	−0.377026	+	0.217676i	−0.676524	−	0.736421i	$-0.736514\pi$
$359$	−7.14363	+	4.12438i	−0.377026	+	0.217676i	0.299497	+	0.954097i	$0.403181\pi$
$360$	−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	−0.212466	−	0.977168i	$-0.568149\pi$
$367$	10.1065	−	5.83498i	0.527554	−	0.304583i	0.740020	+	0.672585i	$0.234816\pi$
$368$		−	2.48498i		−	0.129539i
$369$	9.65360	−	34.3064i	0.502546	−	1.78592i
$370$	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	−0.0756809	−	0.997132i	$-0.524113\pi$
$373$	15.9469	−	27.6209i	0.825701	−	1.43016i	0.901382	−	0.433024i	$-0.142554\pi$
$374$	−1.13354	−	1.96335i	−0.0586139	−	0.101522i
$375$	2.48949	+	19.8684i	0.128557	+	1.02600i
$376$	0.736829	−	0.425408i	0.0379990	−	0.0219388i
$377$	25.6603	−	18.7122i	1.32157	−	0.963730i
$378$	−13.7449	+	0.278646i	−0.706962	+	0.0143320i
$379$	−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	$0.996231\pi$
$380$			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	$-0.839297\pi$
$383$	−0.366640	+	0.635039i	−0.0187344	+	0.0324490i	0.856506	+	0.516137i	$0.172630\pi$
$384$	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
$387$	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	$-0.650090\pi$
$389$	−28.6554	−	16.5442i	−1.45289	−	0.838825i	−0.998644	+	0.0520523i	$0.983424\pi$
$390$	−13.0711	+	3.07604i	−0.661881	+	0.155761i
$391$		−	6.76768i		−	0.342256i
$392$	−4.54878	+	5.32058i	−0.229748	+	0.268730i
$393$	−9.89772	+	7.49697i	−0.499274	+	0.378172i
$394$	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	0.735595	−	0.677421i	$-0.236903\pi$
$397$	10.2958	+	5.94426i	0.516729	+	0.298334i	−0.218866	+	0.975755i	$0.570236\pi$
$398$	27.4125			1.37406
$399$	−8.04467	+	8.59000i	−0.402737	+	0.430038i
$400$	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	$-0.200521\pi$
$402$	−6.91722	−	9.13233i	−0.345000	−	0.455479i
$403$	6.94374	−	5.06359i	0.345892	−	0.252235i
$404$	6.68381	+	11.5767i	0.332532	+	0.575962i
$405$	−16.5122	−	10.0920i	−0.820499	−	0.501474i
$406$	17.9210	−	14.8972i	0.889406	−	0.739337i
$407$	−0.129709	+	0.0748874i	−0.00642942	+	0.00371203i
$408$	4.68052	−	0.586464i	0.231720	−	0.0290343i
$409$		−	11.3544i		−	0.561437i	−0.959790	−	0.280718i	$-0.909427\pi$
$409$		−	11.3544i		−	0.561437i	0.959790	−	0.280718i	$-0.0905727\pi$
$410$		−	25.5438i		−	1.26152i
$411$	−10.7478	+	1.34669i	−0.530151	+	0.0664273i
$412$	−12.8325	+	7.40885i	−0.632212	+	0.365008i
$413$	−6.26345	−	2.31248i	−0.308204	−	0.113790i
$414$	7.22449	−	1.83932i	0.355064	−	0.0903975i
$415$	−1.00074	−	1.73333i	−0.0491243	−	0.0850858i
$416$	3.29641	+	1.46072i	0.161620	+	0.0716177i
$417$	−2.17880	−	2.87652i	−0.106696	−	0.140864i
$418$		−	2.13783i		−	0.104565i
$419$	−6.35642	+	11.0096i	−0.310531	+	0.537856i	−0.978477	−	0.206354i	$-0.933840\pi$
$419$	−6.35642	+	11.0096i	−0.310531	+	0.537856i	0.667946	+	0.744210i	$0.267174\pi$
$420$	−9.42915	+	2.86078i	−0.460096	+	0.139592i
$421$	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
$426$	11.9331	−	9.03867i	0.578162	−	0.437925i
$427$	−6.18177	−	7.43653i	−0.299157	−	0.359879i
$428$			1.40104i			0.0677219i
$429$	5.06032	−	1.19085i	0.244314	−	0.0574948i
$430$	14.4933	+	8.36769i	0.698928	+	0.403526i
$431$	−5.17597	+	2.98835i	−0.249318	+	0.143944i	−0.619452	−	0.785035i	$-0.712645\pi$
$431$	−5.17597	+	2.98835i	−0.249318	+	0.143944i	0.370134	+	0.928978i	$0.379312\pi$
$432$	1.89812	+	4.83706i	0.0913233	+	0.232723i
$433$	27.0676	−	15.6275i	1.30079	−	0.751009i	0.320247	−	0.947334i	$-0.396234\pi$
$433$	27.0676	−	15.6275i	1.30079	−	0.751009i	0.980539	+	0.196325i	$0.0629008\pi$
$434$	4.84948	−	4.03123i	0.232783	−	0.193505i
$435$	32.5499	−	4.07846i	1.56065	−	0.195547i
$436$	−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	$-0.748299\pi$
$439$		−	29.7890i		−	1.42175i	0.703319	−	0.710875i	$-0.251701\pi$
$440$	0.894961	−	1.55012i	0.0426656	−	0.0738990i
$441$	−18.8352	−	9.28633i	−0.896913	−	0.442206i
$442$	8.97753	+	3.97817i	0.427018	+	0.189222i
$443$	18.4003	−	10.6234i	0.874224	−	0.504733i	0.00547441	−	0.999985i	$-0.498257\pi$
$443$	18.4003	−	10.6234i	0.874224	−	0.504733i	0.868750	+	0.495252i	$0.164924\pi$
$444$	−0.0387448	−	0.309219i	−0.00183875	−	0.0146749i
$445$	−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	$-0.901128\pi$
$449$	−24.6546	+	14.2344i	−1.16352	+	0.671761i	−0.211377	+	0.977405i	$0.567795\pi$
$450$	1.08735	+	0.305973i	0.0512581	+	0.0144237i
$451$			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	$-0.180162\pi$
$461$	−0.909994	−	1.57616i	−0.0423827	−	0.0734089i	−0.886439	+	0.462846i	$0.846828\pi$
$462$	3.65038	−	1.10751i	0.169831	−	0.0515262i
$463$	−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
$465$	8.80809	−	1.10364i	0.408465	−	0.0511802i
$466$	7.39695	+	12.8119i	0.342657	+	0.593499i
$467$	−3.76001	−	6.51253i	−0.173993	−	0.301364i	0.765820	−	0.643056i	$-0.222334\pi$
$467$	−3.76001	−	6.51253i	−0.173993	−	0.301364i	−0.939812	+	0.341691i	$0.889000\pi$
$468$	−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
$471$	10.5850	−	25.1093i	0.487729	−	1.15698i
$472$			2.52356i			0.116156i
$473$	−5.61090	−	3.23945i	−0.257989	−	0.148950i
$474$	6.50096	+	8.58276i	0.298599	+	0.394219i
$475$	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
$478$	20.0261			0.915974
$479$	−15.4173	−	26.7035i	−0.704433	−	1.22011i	−0.966896	−	0.255172i	$-0.917868\pi$
$479$	−15.4173	−	26.7035i	−0.704433	−	1.22011i	0.262463	−	0.964942i	$-0.415465\pi$
$480$	2.24870	+	2.96880i	0.102639	+	0.135507i
$481$	0.262818	−	0.593102i	0.0119835	−	0.0270431i
$482$	−10.4032			−0.473851
$483$	11.0903	+	2.58535i	0.504625	+	0.117638i
$484$	5.15353	−	8.92617i	0.234251	−	0.405735i
$485$	15.2433	+	8.80074i	0.692164	+	0.399621i
$486$	−12.6576	+	9.09858i	−0.574162	+	0.412720i
$487$	−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	$-0.244776\pi$
$491$	10.5405	+	6.08555i	0.475686	+	0.274637i	−0.242931	+	0.970044i	$0.578109\pi$
$492$	−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
$495$	5.16902	+	1.45453i	0.232330	+	0.0653762i
$496$	−2.06419	−	1.19176i	−0.0926850	−	0.0535117i
$497$	22.5375	−	3.86689i	1.01095	−	0.173454i
$498$	−1.59972	+	0.200443i	−0.0716852	+	0.00898207i
$499$	−16.3741	−	28.3607i	−0.733004	−	1.26960i	−0.955593	−	0.294688i	$-0.904784\pi$
$499$	−16.3741	−	28.3607i	−0.733004	−	1.26960i	0.222589	−	0.974912i	$-0.428549\pi$
$500$	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	−0.982180	−	0.187941i	$-0.939818\pi$
$503$	−14.6644	−	25.3994i	−0.653852	−	1.13251i	0.328328	−	0.944564i	$-0.393515\pi$
$504$	−0.826982	+	7.89405i	−0.0368367	+	0.351629i
$505$	−14.3717	+	24.8925i	−0.639533	+	1.10770i
$506$	−1.79145	+	1.03429i	−0.0796396	+	0.0459799i
$507$	−14.6702	+	17.0817i	−0.651526	+	0.758626i
$508$	−9.89702	+	17.1421i	−0.439109	+	0.760560i
$509$	42.1369			1.86769			0.933843	−	0.357682i	$-0.116433\pi$
$509$	42.1369			1.86769			0.933843	+	0.357682i	$0.116433\pi$
$510$	6.12417	+	8.08532i	0.271183	+	0.358024i
$511$	21.3692	+	25.7067i	0.945318	+	1.13720i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.98958	+	13.1954i	−0.0878423	+	0.582592i
$514$		−	6.20605i		−	0.273737i
$515$	−27.5928	−	15.9307i	−1.21588	−	0.701990i
$516$	10.7460	−	8.13952i	0.473068	−	0.358322i
$517$	−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	$-0.859636\pi$
$521$	−1.88398	+	3.26316i	−0.0825389	+	0.142962i	0.821801	+	0.569775i	$0.192970\pi$
$522$	7.15772	−	25.4367i	0.313285	−	1.11333i
$523$		−	21.1539i		−	0.924995i	−0.886621	−	0.462498i	$-0.846953\pi$
$523$		−	21.1539i		−	0.924995i	0.886621	−	0.462498i	$-0.153047\pi$
$524$	3.58433	+	6.20825i	0.156582	+	0.271209i
$525$	1.25940	+	1.17945i	0.0549649	+	0.0514755i
$526$	−12.2453	−	21.2094i	−0.533919	−	0.924774i
$527$	−5.62168	−	3.24568i	−0.244884	−	0.141384i
$528$	−0.870557	−	1.14934i	−0.0378861	−	0.0500184i
$529$	16.8249			0.731515
$530$	25.7924			1.12035
$531$	−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
$534$	−1.96935	+	0.246758i	−0.0852222	+	0.0106782i
$535$	−2.60895	+	1.50628i	−0.112795	+	0.0651221i
$536$	−5.72816	+	3.30716i	−0.247419	+	0.142847i
$537$	1.39504	+	1.84178i	0.0602005	+	0.0794785i
$538$		−	5.00152i		−	0.215631i
$539$	5.72894	+	1.06474i	0.246763	+	0.0458617i
$540$	−6.96664	+	8.73497i	−0.299797	+	0.375893i
$541$	−9.07775	−	15.7231i	−0.390283	−	0.675990i	0.602204	−	0.798343i	$-0.294290\pi$
$541$	−9.07775	−	15.7231i	−0.390283	−	0.675990i	−0.992487	+	0.122352i	$0.960956\pi$
$542$	6.59272			0.283182
$543$	1.94569	−	0.243792i	0.0834974	−	0.0104621i
$544$		−	2.72343i		−	0.116766i
$545$	−17.4064			−0.745610
$546$	−9.94861	+	13.1919i	−0.425761	+	0.564559i
$547$	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
$549$	−10.5553	−	2.97018i	−0.450487	−	0.126764i
$550$	−0.313433			−0.0133648
$551$	−11.3104	−	19.5903i	−0.481841	−	0.834574i
$552$	−0.535117	−	4.27073i	−0.0227761	−	0.181774i
$553$	2.78121	+	16.2099i	0.118269	+	0.689313i
$554$			16.9907i			0.721866i
$555$	0.534158	−	0.404594i	0.0226737	−	0.0171741i
$556$	−1.80427	+	1.04170i	−0.0765181	+	0.0441777i
$557$	−10.5135	+	6.06999i	−0.445473	+	0.257194i	−0.705916	−	0.708295i	$-0.749465\pi$
$557$	−10.5135	+	6.06999i	−0.445473	+	0.257194i	0.260443	+	0.965489i	$0.416131\pi$
$558$	1.93690	−	6.88325i	0.0819955	−	0.291391i
$559$	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
$562$	3.11696			0.131481
$563$	−2.57546			−0.108543			−0.0542714	−	0.998526i	$-0.517284\pi$
$563$	−2.57546			−0.108543			−0.0542714	+	0.998526i	$0.517284\pi$
$564$	1.17472	−	0.889781i	0.0494644	−	0.0374665i
$565$	6.77935	+	3.91406i	0.285209	+	0.164666i
$566$	−6.20719	−	10.7512i	−0.260908	−	0.451905i
$567$	−23.5622	+	3.43871i	−0.989518	+	0.144412i
$568$	−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	$0.797332\pi$
$570$	1.18914	+	9.49041i	0.0498075	+	0.397509i
$571$	2.33873	−	4.05080i	0.0978729	−	0.169521i	−0.812931	−	0.582360i	$-0.802129\pi$
$571$	2.33873	−	4.05080i	0.0978729	−	0.169521i	0.910804	+	0.412839i	$0.135463\pi$
$572$	−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
$576$	2.90726	−	0.740172i	0.121136	−	0.0308405i
$577$	39.9089	+	23.0414i	1.66143	+	0.959228i	0.972033	+	0.234845i	$0.0754584\pi$
$577$	39.9089	+	23.0414i	1.66143	+	0.959228i	0.689398	+	0.724382i	$0.257875\pi$
$578$			9.58293i			0.398598i
$579$	−4.32029	+	3.27237i	−0.179545	+	0.135995i
$580$		−	18.9396i		−	0.786425i
$581$	−2.31029	−	0.852964i	−0.0958470	−	0.0353869i
$582$	11.3022	−	8.56076i	0.468490	−	0.354855i
$583$	−9.98523			−0.413546
$584$	6.31743	−	10.9421i	0.261417	−	0.452787i
$585$	−21.8017	+	8.10125i	−0.901391	+	0.334945i
$586$	3.82017	−	2.20558i	0.157810	−	0.0911115i
$587$	−4.23462	+	7.33458i	−0.174781	+	0.302730i	−0.940086	−	0.340938i	$-0.889255\pi$
$587$	−4.23462	+	7.33458i	−0.174781	+	0.302730i	0.765304	+	0.643669i	$0.222589\pi$
$588$	−6.67186	+	10.1236i	−0.275143	+	0.417488i
$589$	−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	$-0.101077\pi$
$593$	4.98232	+	8.62964i	0.204599	+	0.354377i	−0.745406	+	0.666611i	$0.767744\pi$
$594$	2.69705	−	3.38164i	0.110661	−	0.138750i
$595$	2.62002	+	15.2704i	0.107410	+	0.626024i
$596$	10.5983	+	6.11893i	0.434123	+	0.250641i
$597$	47.1115	−	5.90301i	1.92814	−	0.241594i
$598$	3.62987	−	8.19152i	0.148436	−	0.334976i
$599$	−29.5283	−	17.0482i	−1.20649	−	0.696569i	−0.244502	−	0.969649i	$-0.578624\pi$
$599$	−29.5283	−	17.0482i	−1.20649	−	0.696569i	−0.961991	+	0.273080i	$0.911958\pi$
$600$	0.253333	−	0.600948i	0.0103423	−	0.0245336i
$601$	10.4907	+	6.05683i	0.427926	+	0.247063i	0.698463	−	0.715646i	$-0.253868\pi$
$601$	10.4907	+	6.05683i	0.427926	+	0.247063i	−0.270537	+	0.962710i	$0.587201\pi$
$602$	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
$606$	13.9798	+	18.4566i	0.567891	+	0.749747i
$607$	−18.3365	−	10.5866i	−0.744255	−	0.429696i	0.0793596	−	0.996846i	$-0.474712\pi$
$607$	−18.3365	−	10.5866i	−0.744255	−	0.429696i	−0.823614	+	0.567150i	$0.808046\pi$
$608$	1.28408	−	2.22409i	0.0520764	−	0.0901990i
$609$	27.5913	−	29.4617i	1.11806	−	1.19385i
$610$	−7.85921			−0.318210
$611$	3.05029	−	0.326018i	0.123402	−	0.0131893i
$612$	7.91771	−	2.01581i	0.320054	−	0.0814842i
$613$	3.06942	+	5.31640i	0.123973	+	0.214727i	0.921331	−	0.388779i	$-0.127103\pi$
$613$	3.06942	+	5.31640i	0.123973	+	0.214727i	−0.797358	+	0.603506i	$0.793770\pi$
$614$	16.2434			0.655532
$615$	−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	$0.423605\pi$
$618$	−20.4587	+	15.4963i	−0.822968	+	0.623352i
$619$	−19.7752	−	11.4172i	−0.794833	−	0.458897i	0.0468282	−	0.998903i	$-0.485089\pi$
$619$	−19.7752	−	11.4172i	−0.794833	−	0.458897i	−0.841661	+	0.540006i	$0.818422\pi$
$620$		−	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
$624$	5.97980	+	1.80056i	0.239383	+	0.0720802i
$625$	11.4878	+	19.8975i	0.459512	+	0.795898i
$626$	13.3172	+	23.0661i	0.532262	+	0.921905i
$627$	−0.460360	−	3.67410i	−0.0183850	−	0.146729i
$628$	−13.6246	−	7.86616i	−0.543681	−	0.313894i
$629$	−0.490010			−0.0195380
$630$	−15.5890	+	6.94704i	−0.621081	+	0.276777i
$631$	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
$633$	−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	$0.872809\pi$
$642$	0.301701	+	2.40785i	0.0119072	+	0.0950302i
$643$	5.10073	−	2.94491i	0.201153	−	0.116136i	−0.396040	−	0.918233i	$-0.629616\pi$
$643$	5.10073	−	2.94491i	0.201153	−	0.116136i	0.597193	+	0.802097i	$0.296283\pi$
$644$	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	−0.988559	−	0.150837i	$-0.951803\pi$
$647$	−15.8953	−	27.5314i	−0.624908	−	1.08237i	0.363651	−	0.931535i	$-0.381530\pi$
$648$	4.30374	+	7.90429i	0.169067	+	0.310510i
$649$	1.81926	−	1.05035i	0.0714120	−	0.0412297i
$650$	1.09690	−	0.799896i	0.0430241	−	0.0313745i
$651$	7.46629	−	7.97241i	0.292627	−	0.312463i
$652$	−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
$657$	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	$-0.0115717\pi$
$660$	1.20429	−	2.85677i	0.0468769	−	0.111200i
$661$	7.16442	−	4.13638i	0.278664	−	0.160887i	−0.354155	−	0.935187i	$-0.615231\pi$
$661$	7.16442	−	4.13638i	0.278664	−	0.160887i	0.632818	+	0.774300i	$0.281898\pi$
$662$	13.7950	+	7.96452i	0.536156	+	0.309550i
$663$	16.2856	+	4.90371i	0.632478	+	0.190444i
$664$			0.930821i			0.0361229i
$665$	−5.06024	+	13.7059i	−0.196228	+	0.531492i
$666$	−0.133175	−	0.523085i	−0.00516041	−	0.0202691i
$667$	−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
$672$	4.46291	+	1.04039i	0.172161	+	0.0401339i
$673$	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	$0.129269\pi$
$674$			1.38803i			0.0534649i
$675$	1.93462	+	0.291699i	0.0744635	+	0.0112275i
$676$	8.73259	+	9.63026i	0.335869	+	0.370394i
$677$	4.15629	+	7.19891i	0.159739	+	0.276677i	0.934775	−	0.355241i	$-0.115601\pi$
$677$	4.15629	+	7.19891i	0.159739	+	0.276677i	−0.775035	+	0.631918i	$0.782268\pi$
$678$	5.02655	−	3.80733i	0.193043	−	0.146220i
$679$	21.3459	−	3.66243i	0.819180	−	0.140551i
$680$	5.07144	−	2.92799i	0.194481	−	0.112283i
$681$	−6.11266	−	48.7847i	−0.234238	−	1.86943i
$682$			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	$0.816756\pi$
$684$	7.41646	+	2.08694i	0.283575	+	0.0797962i
$685$	−11.6455	+	6.72352i	−0.444951	+	0.256893i
$686$	−16.1656	+	9.03734i	−0.617205	+	0.345047i
$687$	15.2302	+	20.1074i	0.581069	+	0.767145i
$688$	−3.89154	−	6.74035i	−0.148364	−	0.256973i
$689$	34.9447	−	25.4828i	1.33129	−	0.970816i
$690$	7.37742	−	5.58798i	0.280854	−	0.212731i
$691$		−	15.1598i		−	0.576706i	−0.957524	−	0.288353i	$-0.906892\pi$
$691$		−	15.1598i		−	0.576706i	0.957524	−	0.288353i	$-0.0931076\pi$
$692$	−9.84211	+	17.0470i	−0.374141	+	0.648031i
$693$	6.03510	−	2.68946i	0.229255	−	0.102164i
$694$	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
$699$	15.4714	+	20.4258i	0.585182	+	0.772575i
$700$	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	$0.836037\pi$
$702$	−0.808620	+	18.7175i	−0.0305194	+	0.706448i
$703$	−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
$708$	0.543423	+	4.33701i	0.0204231	+	0.162995i
$709$	9.56340	−	16.5643i	0.359161	−	0.622085i	−0.628660	−	0.777680i	$-0.716396\pi$
$709$	9.56340	−	16.5643i	0.359161	−	0.622085i	0.987821	+	0.155595i	$0.0497296\pi$
$710$	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
$714$	12.1544	+	2.83343i	0.454868	+	0.106038i
$715$	5.21445	−	3.80253i	0.195009	−	0.142207i
$716$	1.15524	−	0.666976i	0.0431732	−	0.0249261i
$717$	34.4172	−	4.31243i	1.28533	−	0.161051i
$718$	4.12438	+	7.14363i	0.153920	+	0.266598i
$719$	10.9458	−	18.9586i	0.408208	−	0.707037i	−0.586481	−	0.809963i	$-0.699487\pi$
$719$	10.9458	−	18.9586i	0.408208	−	0.707037i	0.994689	+	0.102926i	$0.0328204\pi$
$720$	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
$723$	−17.8790	+	2.24022i	−0.664927	+	0.0833146i
$724$		−	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	$0.217112\pi$
$727$			33.9953i			1.26082i	−0.776264	+	0.630408i	$0.782888\pi$
$728$	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	−0.838052	−	0.545591i	$-0.816305\pi$
$733$	−21.2418	+	12.2639i	−0.784582	+	0.452979i	0.0534695	+	0.998569i	$0.482972\pi$
$734$	−5.83498	−	10.1065i	−0.215373	−	0.373037i
$735$	−26.0246	−	1.54004i	−0.959931	−	0.0568053i
$736$	−2.48498			−0.0915978
$737$	4.76832	+	2.75299i	0.175643	+	0.101408i
$738$	−34.3064	−	9.65360i	−1.26284	−	0.355354i
$739$	−12.5361	−	21.7131i	−0.461146	−	0.798729i	0.537872	−	0.843026i	$-0.319228\pi$
$739$	−12.5361	−	21.7131i	−0.461146	−	0.798729i	−0.999018	+	0.0442977i	$0.985895\pi$
$740$	−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	$0.667802\pi$
$744$	−3.80418	−	1.60367i	−0.139468	−	0.0587935i
$745$			26.3142i			0.964077i
$746$	−27.6209	−	15.9469i	−1.01127	−	0.583859i
$747$	−2.70614	+	0.688968i	−0.0990123	+	0.0252080i
$748$	−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
$751$	−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
$753$	−3.07660	+	2.33035i	−0.112118	+	0.0849227i
$754$	−18.7122	−	25.6603i	−0.681460	−	0.934492i
$755$	−2.16725			−0.0788743
$756$	0.278646	+	13.7449i	0.0101343	+	0.499897i
$757$	−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	$0.814554\pi$
$758$	17.2043	+	9.93293i	0.624890	+	0.360780i
$759$	−2.85608	+	2.16332i	−0.103669	+	0.0785236i
$760$	5.52213			0.200309
$761$	−0.148132	+	0.256572i	−0.00536978	+	0.00930072i	−0.868698	−	0.495342i	$-0.835043\pi$
$761$	−0.148132	+	0.256572i	−0.00536978	+	0.00930072i	0.863328	+	0.504643i	$0.168376\pi$
$762$	−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
$768$	−0.215340	−	1.71861i	−0.00777042	−	0.0620151i
$769$	27.7574	+	16.0257i	1.00096	+	0.577902i	0.908531	−	0.417817i	$-0.137205\pi$
$769$	27.7574	+	16.0257i	1.00096	+	0.577902i	0.0924253	+	0.995720i	$0.470538\pi$
$770$	3.64175	−	3.02728i	0.131240	−	0.109096i
$771$	−1.33641	−	10.6658i	−0.0481297	−	0.384119i
$772$	1.56454	+	2.70986i	0.0563089	+	0.0975299i
$773$	−25.4967			−0.917052			−0.458526	−	0.888681i	$-0.651622\pi$
$773$	−25.4967			−0.917052			−0.458526	+	0.888681i	$0.651622\pi$
$774$	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
$777$	0.187191	−	0.802984i	0.00671543	−	0.0288069i
$778$	−16.5442	+	28.6554i	−0.593139	+	1.02735i
$779$	−26.4213	+	15.2544i	−0.946643	+	0.546544i
$780$	3.07604	+	13.0711i	0.110140	+	0.468020i
$781$	−3.59731	+	6.23072i	−0.128722	+	0.222953i
$782$	−6.76768			−0.242012
$783$	6.82381	−	45.2572i	0.243863	−	1.61736i
$784$	5.32058	+	4.54878i	0.190021	+	0.162457i
$785$		−	33.8281i		−	1.20738i
$786$	7.49697	+	9.89772i	0.267408	+	0.353040i
$787$		−	21.6324i		−	0.771112i	−0.922685	−	0.385556i	$-0.874010\pi$
$787$		−	21.6324i		−	0.771112i	0.922685	−	0.385556i	$-0.125990\pi$
$788$	−10.6747	−	6.16302i	−0.380269	−	0.219548i
$789$	−25.6121	−	33.8139i	−0.911815	−	1.20381i
$790$	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
$795$	44.3272	−	5.55414i	1.57212	−	0.196985i
$796$		−	27.4125i		−	0.971610i
$797$	21.2264	+	36.7652i	0.751878	+	1.30229i	0.946911	+	0.321495i	$0.104185\pi$
$797$	21.2264	+	36.7652i	0.751878	+	1.30229i	−0.195033	+	0.980797i	$0.562481\pi$
$798$	8.59000	+	8.04467i	0.304083	+	0.284778i
$799$	−1.15857	−	2.00670i	−0.0409872	−	0.0709920i
$800$	−0.326081	−	0.188263i	−0.0115287	−	0.00665610i
$801$	−3.33142	+	0.848161i	−0.117710	+	0.0299683i
$802$	−23.5937			−0.833124
$803$	−10.5177			−0.371161
$804$	−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
$807$	−1.07703	−	8.59568i	−0.0379132	−	0.302582i
$808$	11.5767	−	6.68381i	0.407267	−	0.235136i
$809$	26.9231	−	15.5441i	0.946567	−	0.546501i	0.0545541	−	0.998511i	$-0.482626\pi$
$809$	26.9231	−	15.5441i	0.946567	−	0.546501i	0.892013	+	0.452010i	$0.149293\pi$
$810$	−10.0920	+	16.5122i	−0.354596	+	0.580180i
$811$			35.7680i			1.25598i	0.778220	+	0.627992i	$0.216123\pi$
$811$			35.7680i			1.25598i	−0.778220	+	0.627992i	$0.783877\pi$
$812$	−14.8972	−	17.9210i	−0.522790	−	0.628905i
$813$	11.3303	−	1.41968i	0.397372	−	0.0497902i
$814$	0.0748874	+	0.129709i	0.00262480	+	0.00454629i
$815$	−51.1768			−1.79264
$816$	−0.586464	−	4.68052i	−0.0205303	−	0.163851i
$817$		−	19.9882i		−	0.699300i
$818$	−11.3544			−0.396996
$819$	−14.2571	+	24.8140i	−0.498182	+	0.867072i
$820$	−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	$0.957786\pi$
$822$	1.34669	+	10.7478i	0.0469712	+	0.374873i
$823$	−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
$825$	−0.538670	+	0.0674948i	−0.0187541	+	0.00234987i
$826$	−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	$-0.0998243\pi$
$828$	−1.83932	−	7.22449i	−0.0639207	−	0.251068i
$829$	−33.7736	+	19.4992i	−1.17301	+	0.677236i	−0.954386	−	0.298575i	$-0.903489\pi$
$829$	−33.7736	+	19.4992i	−1.17301	+	0.677236i	−0.218620	+	0.975810i	$0.570156\pi$
$830$	−1.73333	+	1.00074i	−0.0601647	+	0.0347361i
$831$	3.65878	+	29.2004i	0.126922	+	1.01295i
$832$	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
$835$	−7.19411			−0.248962
$836$	−2.13783			−0.0739383
$837$	1.84654	−	12.2467i	0.0638258	−	0.423309i
$838$	11.0096	+	6.35642i	0.380321	+	0.219579i
$839$	−16.2641	−	28.1703i	−0.561501	−	0.972548i	−0.997366	−	0.0725356i	$-0.976891\pi$
$839$	−16.2641	−	28.1703i	−0.561501	−	0.972548i	0.435865	−	0.900012i	$-0.356442\pi$
$840$	2.86078	+	9.42915i	0.0987061	+	0.325337i
$841$	24.2922	+	42.0753i	0.837662	+	1.45087i
$842$		−	36.5159i		−	1.25842i
$843$	5.35685	−	0.671207i	0.184500	−	0.0231176i
$844$	−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
$849$	−12.9829	−	17.1404i	−0.445572	−	0.588258i
$850$	−0.888059	−	0.512721i	−0.0304602	−	0.0175862i
$851$			0.447108i			0.0153267i
$852$	−9.03867	−	11.9331i	−0.309660	−	0.408822i
$853$			15.8564i			0.542914i	0.962451	+	0.271457i	$0.0875054\pi$
$853$			15.8564i			0.542914i	−0.962451	+	0.271457i	$0.912495\pi$
$854$	−7.43653	+	6.18177i	−0.254473	+	0.211536i
$855$	4.08733	+	16.0543i	0.139784	+	0.549044i
$856$	1.40104			0.0478866
$857$	24.1157	−	41.7696i	0.823776	−	1.42682i	−0.0790749	−	0.996869i	$-0.525197\pi$
$857$	24.1157	−	41.7696i	0.823776	−	1.42682i	0.902851	−	0.429953i	$-0.141470\pi$
$858$	−1.19085	−	5.06032i	−0.0406550	−	0.172756i
$859$	−31.3554	+	18.1031i	−1.06983	+	0.617669i	−0.928136	−	0.372241i	$-0.878589\pi$
$859$	−31.3554	+	18.1031i	−1.06983	+	0.617669i	−0.141697	+	0.989910i	$0.545256\pi$
$860$	8.36769	−	14.4933i	0.285336	−	0.494216i
$861$	−39.7349	−	37.2123i	−1.35416	−	1.26819i
$862$	2.98835	+	5.17597i	0.101784	+	0.176294i
$863$	−29.7766	+	17.1915i	−1.01361	+	0.585207i	−0.912246	−	0.409643i	$-0.865653\pi$
$863$	−29.7766	+	17.1915i	−1.01361	+	0.585207i	−0.101362	+	0.994850i	$0.532320\pi$
$864$	4.83706	−	1.89812i	0.164560	−	0.0645753i
$865$	−42.3255			−1.43911
$866$	−15.6275	−	27.0676i	−0.531044	−	0.919794i
$867$	2.06359	+	16.4693i	0.0700832	+	0.559328i
$868$	−4.03123	−	4.84948i	−0.136829	−	0.164602i
$869$	−4.48137	−	2.58732i	−0.152020	−	0.0877688i
$870$	−4.07846	−	32.5499i	−0.138273	−	1.10354i
$871$	−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	0.458185	+	0.888857i	$0.348500\pi$
$877$	−16.0118	+	27.7333i	−0.540680	+	0.936486i	−0.998865	+	0.0476290i	$0.984833\pi$
$878$	−29.7890			−1.00533
$879$	6.09044	−	4.61316i	0.205425	−	0.155598i
$880$	−1.55012	−	0.894961i	−0.0522545	−	0.0301691i
$881$	−15.9277	+	27.5876i	−0.536619	+	0.929451i	0.462464	+	0.886638i	$0.346965\pi$
$881$	−15.9277	+	27.5876i	−0.536619	+	0.929451i	−0.999083	+	0.0428131i	$0.986368\pi$
$882$	−9.28633	+	18.8352i	−0.312687	+	0.634214i
$883$	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
$885$	−7.49193	+	5.67472i	−0.251839	+	0.190754i
$886$	−10.6234	−	18.4003i	−0.356900	−	0.618170i
$887$	−27.1455			−0.911458			−0.455729	−	0.890119i	$-0.650621\pi$
$887$	−27.1455			−0.911458			−0.455729	+	0.890119i	$0.650621\pi$
$888$	−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
$891$	3.90698	−	6.39251i	0.130889	−	0.214157i
$892$	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
$897$	4.47437	−	14.8597i	0.149395	−	0.496151i
$898$	14.2344	+	24.6546i	0.475006	+	0.822735i
$899$	10.4973	+	18.1818i	0.350104	+	0.606398i
$900$	0.305973	−	1.08735i	0.0101991	−	0.0362450i
$901$	−28.2914	−	16.3341i	−0.942524	−	0.544166i
$902$	9.88898			0.329267
$903$	34.1303	−	10.3550i	1.13579	−	0.344594i
$904$	−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	0.958150	−	0.286266i	$-0.0924142\pi$
$907$	6.96176	+	12.0581i	0.231161	+	0.400383i	−0.726989	+	0.686649i	$0.759081\pi$
$908$	−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
$915$	−13.5069	+	1.69240i	−0.446526	+	0.0559491i
$916$	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	−0.738666	−	0.674071i	$-0.764544\pi$
$919$	6.50044	−	11.2591i	0.214430	−	0.371403i	0.953096	+	0.302668i	$0.0978774\pi$
$920$	−2.67164	−	4.62742i	−0.0880814	−	0.152561i
$921$	27.9162	−	3.49786i	0.919869	−	0.115259i
$922$	−1.57616	+	0.909994i	−0.0519079	+	0.0299691i
$923$	−3.31179	−	30.9858i	−0.109009	−	1.01991i
$924$	−1.10751	−	3.65038i	−0.0364346	−	0.120089i
$925$	−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	−0.0265955	+	0.999646i	$0.508467\pi$
$929$	−26.7920	+	46.4051i	−0.879017	+	1.52250i	−0.852421	+	0.522855i	$0.824867\pi$
$930$	−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
$933$	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
$936$	10.6647	+	1.80678i	0.348586	+	0.0590565i
$937$		−	19.6964i		−	0.643454i	−0.946833	−	0.321727i	$-0.895737\pi$
$937$		−	19.6964i		−	0.643454i	0.946833	−	0.321727i	$-0.104263\pi$
$938$	−17.2478	+	2.95930i	−0.563160	+	0.0966245i
$939$	27.8542	+	36.7739i	0.908986	+	1.20007i
$940$	0.914724	−	1.58435i	0.0298350	−	0.0516758i
$941$	−7.34272	+	12.7180i	−0.239366	+	0.414594i	−0.960533	−	0.278168i	$-0.910273\pi$
$941$	−7.34272	+	12.7180i	−0.239366	+	0.414594i	0.721167	+	0.692762i	$0.243606\pi$
$942$	−25.1093	−	10.5850i	−0.818105	−	0.344877i
$943$	25.5656	+	14.7603i	0.832530	+	0.480661i
$944$	2.52356			0.0821348
$945$	−25.2955	+	15.2962i	−0.822863	+	0.497586i
$946$	−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	$-0.152725\pi$
$948$	8.58276	−	6.50096i	0.278755	−	0.211141i
$949$	36.8082	−	26.8416i	1.19484	−	0.871316i
$950$	−0.483490	−	0.837430i	−0.0156865	−	0.0271698i
$951$	−8.73792	−	11.5361i	−0.283347	−	0.374083i
$952$	2.49563	−	6.75953i	0.0808839	−	0.219078i
$953$	−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	$0.494679\pi$
$954$	9.74756	−	34.6403i	0.315589	−	1.12152i
$955$		−	45.6687i		−	1.47781i
$956$		−	20.0261i		−	0.647692i
$957$	1.57893	+	12.6013i	0.0510395	+	0.407342i
$958$	−26.7035	+	15.4173i	−0.862751	+	0.498109i
$959$	−5.73069	+	15.5218i	−0.185054	+	0.501226i
$960$	2.96880	−	2.24870i	0.0958176	−	0.0725764i
$961$	−12.6594	−	21.9267i	−0.408368	−	0.707314i
$962$	−0.593102	−	0.262818i	−0.0191224	−	0.00847360i
$963$	1.03701	+	4.07319i	0.0334173	+	0.131257i
$964$			10.4032i			0.335063i
$965$	−3.36411	+	5.82681i	−0.108295	+	0.187572i
$966$	2.58535	−	11.0903i	0.0831823	−	0.356824i
$967$	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	$-0.670694\pi$
$971$	15.2377	−	26.3926i	0.489003	−	0.846977i	0.999920	+	0.0126526i	$0.00402754\pi$
$972$	9.09858	+	12.6576i	0.291837	+	0.405994i
$973$	−5.43275	+	0.932127i	−0.174166	+	0.0298826i
$974$			6.30617i			0.202063i
$975$	1.71290	−	1.61092i	0.0548568	−	0.0515907i
$976$	3.16538	+	1.82753i	0.101321	+	0.0584978i
$977$	32.9481	−	19.0226i	1.05410	−	0.608586i	0.130307	−	0.991474i	$-0.458404\pi$
$977$	32.9481	−	19.0226i	1.05410	−	0.608586i	0.923795	+	0.382887i	$0.125070\pi$
$978$	−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
$981$	−6.57830	+	23.3776i	−0.210029	+	0.746389i
$982$	6.08555	−	10.5405i	0.194198	−	0.336360i
$983$	17.4838	−	30.2829i	0.557648	−	0.965875i	−0.440044	−	0.897976i	$-0.645037\pi$
$983$	17.4838	−	30.2829i	0.557648	−	0.965875i	0.997692	−	0.0678987i	$-0.0216295\pi$
$984$	−7.99278	+	18.9602i	−0.254801	+	0.604429i
$985$		−	26.5038i		−	0.844480i
$986$	−11.9943	+	20.7747i	−0.381975	+	0.661600i
$987$	3.73099	−	1.13197i	0.118759	−	0.0360310i
$988$	7.48164	−	5.45584i	0.238023	−	0.173573i
$989$	−16.7497	+	9.67042i	−0.532608	+	0.307501i
$990$	1.45453	−	5.16902i	0.0462279	−	0.164282i
$991$	−12.6707	−	21.9464i	−0.402500	−	0.697150i	0.591527	−	0.806285i	$-0.298525\pi$
$991$	−12.6707	−	21.9464i	−0.402500	−	0.697150i	−0.994027	+	0.109135i	$0.965192\pi$
$992$	−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
$996$	0.200443	+	1.59972i	0.00635128	+	0.0506891i
$997$		−	13.7527i		−	0.435553i	−0.975999	−	0.217777i	$-0.930120\pi$
$997$		−	13.7527i		−	0.435553i	0.975999	−	0.217777i	$-0.0698804\pi$
$998$	−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.269.10	yes	76
3.2	odd	2	inner	546.2.bb.a.269.35	yes	76
7.5	odd	6		546.2.u.a.425.2	yes	76
13.3	even	3		546.2.u.a.185.37	yes	76
21.5	even	6		546.2.u.a.425.37	yes	76
39.29	odd	6		546.2.u.a.185.2	✓	76
91.68	odd	6	inner	546.2.bb.a.341.16	yes	76
273.68	even	6	inner	546.2.bb.a.341.29	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.2	✓	76	39.29	odd	6
546.2.u.a.185.37	yes	76	13.3	even	3
546.2.u.a.425.2	yes	76	7.5	odd	6
546.2.u.a.425.37	yes	76	21.5	even	6
546.2.bb.a.269.10	yes	76	1.1	even	1	trivial
546.2.bb.a.269.35	yes	76	3.2	odd	2	inner
546.2.bb.a.341.16	yes	76	91.68	odd	6	inner
546.2.bb.a.341.29	yes	76	273.68	even	6	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.215340 - 1.71861i) q^{3} -1.00000 q^{4} +(-1.07511 - 1.86215i) q^{5} +(-1.71861 + 0.215340i) q^{6} +(-2.48199 - 0.916357i) q^{7} +1.00000i q^{8} +(-2.90726 + 0.740172i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.215340 - 1.71861i) q^{3} -1.00000 q^{4} +(-1.07511 - 1.86215i) q^{5} +(-1.71861 + 0.215340i) q^{6} +(-2.48199 - 0.916357i) q^{7} +1.00000i q^{8} +(-2.90726 + 0.740172i) q^{9} +(-1.86215 + 1.07511i) q^{10} +(0.720909 - 0.416217i) q^{11} +(0.215340 + 1.71861i) q^{12} +(-1.46072 + 3.29641i) q^{13} +(-0.916357 + 2.48199i) q^{14} +(-2.96880 + 2.24870i) q^{15} +1.00000 q^{16} +2.72343 q^{17} +(0.740172 + 2.90726i) q^{18} +(2.22409 + 1.28408i) q^{19} +(1.07511 + 1.86215i) q^{20} +(-1.04039 + 4.46291i) q^{21} +(-0.416217 - 0.720909i) q^{22} -2.48498i q^{23} +(1.71861 - 0.215340i) 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} +(2.24870 + 2.96880i) q^{30} +(-2.06419 - 1.19176i) q^{31} -1.00000i q^{32} +(-0.870557 - 1.14934i) q^{33} -2.72343i q^{34} +(0.962029 + 5.60703i) q^{35} +(2.90726 - 0.740172i) q^{36} -0.179924 q^{37} +(1.28408 - 2.22409i) q^{38} +(5.97980 + 1.80056i) q^{39} +(1.86215 - 1.07511i) q^{40} +(-5.93979 + 10.2880i) q^{41} +(4.46291 + 1.04039i) 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} +(-0.215340 - 1.71861i) q^{48} +(5.32058 + 4.54878i) q^{49} +(-0.326081 - 0.188263i) q^{50} +(-0.586464 - 4.68052i) 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} +(2.96880 - 2.24870i) q^{60} +(3.16538 + 1.82753i) q^{61} +(-1.19176 + 2.06419i) q^{62} +(7.89405 + 0.826982i) q^{63} -1.00000 q^{64} +(7.70885 - 0.823929i) q^{65} +(-1.14934 + 0.870557i) q^{66} +(3.30716 + 5.72816i) q^{67} -2.72343 q^{68} +(-4.27073 + 0.535117i) q^{69} +(5.60703 - 0.962029i) q^{70} +(-7.48494 + 4.32143i) q^{71} +(-0.740172 - 2.90726i) 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} +(1.80056 - 5.97980i) q^{78} +(-3.10814 - 5.38345i) q^{79} +(-1.07511 - 1.86215i) q^{80} +(7.90429 - 4.30374i) q^{81} +(10.2880 + 5.93979i) q^{82} +0.930821 q^{83} +(1.04039 - 4.46291i) 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} +(-1.71861 + 0.215340i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more