LMFDB - Embedded newform 585.2.bt.b.376.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.14
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23573 - 0.713450i) q^{2} +(-1.00032 + 1.41399i) q^{3} +(0.0180219 + 0.0312149i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.24493 - 1.03364i) q^{6} +(2.69830 + 1.55786i) q^{7} +2.80237i q^{8} +(-0.998738 - 2.82887i) q^{9} +O(q^{10})$	\(q+(-1.23573 - 0.713450i) q^{2} +(-1.00032 + 1.41399i) q^{3} +(0.0180219 + 0.0312149i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.24493 - 1.03364i) q^{6} +(2.69830 + 1.55786i) q^{7} +2.80237i q^{8} +(-0.998738 - 2.82887i) q^{9} +1.42690 q^{10} +(3.29338 + 1.90143i) q^{11} +(-0.0621651 - 0.00574190i) q^{12} +(-1.95544 - 3.02923i) q^{13} +(-2.22292 - 3.85020i) q^{14} +(0.159303 - 1.72471i) q^{15} +(2.03539 - 3.52541i) q^{16} -5.10807 q^{17} +(-0.784087 + 4.20828i) q^{18} -2.45663i q^{19} +(-0.0312149 - 0.0180219i) q^{20} +(-4.90195 + 2.25701i) q^{21} +(-2.71315 - 4.69932i) q^{22} +(3.91395 + 6.77916i) q^{23} +(-3.96252 - 2.80325i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.255200 + 5.13843i) q^{26} +(4.99905 + 1.41756i) q^{27} +0.112303i q^{28} +(-0.937802 + 1.62432i) q^{29} +(-1.42735 + 2.01762i) q^{30} +(-0.553836 + 0.319758i) q^{31} +(-0.176557 + 0.101935i) q^{32} +(-5.98303 + 2.75477i) q^{33} +(6.31221 + 3.64436i) q^{34} -3.11573 q^{35} +(0.0703037 - 0.0821571i) q^{36} +11.3276i q^{37} +(-1.75269 + 3.03574i) q^{38} +(6.23936 + 0.265207i) q^{39} +(-1.40118 - 2.42692i) q^{40} +(-6.13667 + 3.54301i) q^{41} +(7.66777 + 0.708236i) q^{42} +(-3.69930 + 6.40737i) q^{43} +0.137070i q^{44} +(2.27937 + 1.95051i) q^{45} -11.1696i q^{46} +(0.870833 + 0.502776i) q^{47} +(2.94885 + 6.40455i) q^{48} +(1.35388 + 2.34499i) q^{49} +(-1.23573 + 0.713450i) q^{50} +(5.10969 - 7.22277i) q^{51} +(0.0593162 - 0.115631i) q^{52} -2.10815 q^{53} +(-5.16613 - 5.31830i) q^{54} -3.80287 q^{55} +(-4.36571 + 7.56163i) q^{56} +(3.47366 + 2.45741i) q^{57} +(2.31774 - 1.33815i) q^{58} +(-12.5082 + 7.22162i) q^{59} +(0.0567075 - 0.0261099i) q^{60} +(-3.27156 + 5.66651i) q^{61} +0.912524 q^{62} +(1.71210 - 9.18904i) q^{63} -7.85067 q^{64} +(3.20808 + 1.64567i) q^{65} +(9.35881 + 0.864429i) q^{66} +(0.631710 - 0.364718i) q^{67} +(-0.0920572 - 0.159448i) q^{68} +(-13.5009 - 1.24701i) q^{69} +(3.85020 + 2.22292i) q^{70} +10.3248i q^{71} +(7.92755 - 2.79883i) q^{72} -7.51823i q^{73} +(8.08166 - 13.9978i) q^{74} +(0.724394 + 1.57329i) q^{75} +(0.0766835 - 0.0442732i) q^{76} +(5.92435 + 10.2613i) q^{77} +(-7.52097 - 4.77920i) q^{78} +(7.34841 - 12.7278i) q^{79} +4.07079i q^{80} +(-7.00505 + 5.65061i) q^{81} +10.1110 q^{82} +(-1.00753 - 0.581700i) q^{83} +(-0.158795 - 0.112338i) q^{84} +(4.42372 - 2.55404i) q^{85} +(9.14267 - 5.27852i) q^{86} +(-1.35868 - 2.95088i) q^{87} +(-5.32852 + 9.22926i) q^{88} -2.30943i q^{89} +(-1.42510 - 4.03652i) q^{90} +(-0.557245 - 11.2201i) q^{91} +(-0.141074 + 0.244347i) q^{92} +(0.101877 - 1.10298i) q^{93} +(-0.717411 - 1.24259i) q^{94} +(1.22832 + 2.12751i) q^{95} +(0.0324772 - 0.351616i) q^{96} +(13.8897 + 8.01923i) q^{97} -3.86370i q^{98} +(2.08969 - 11.2156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−1.23573	−	0.713450i	−0.873794	−	0.504485i	−0.00518701	−	0.999987i	$-0.501651\pi$
$2$	−1.23573	−	0.713450i	−0.873794	−	0.504485i	−0.868607	+	0.495501i	$0.834984\pi$
$3$	−1.00032	+	1.41399i	−0.577532	+	0.816368i
$3$	−1.00032	+	1.41399i	−0.577532	+	0.816368i
$4$	0.0180219	+	0.0312149i	0.00901095	+	0.0156074i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	2.24493	−	1.03364i	0.916490	−	0.421981i
$7$	2.69830	+	1.55786i	1.01986	+	0.588817i	0.914064	−	0.405571i	$-0.132927\pi$
$7$	2.69830	+	1.55786i	1.01986	+	0.588817i	0.105797	+	0.994388i	$0.466260\pi$
$8$			2.80237i			0.990787i
$9$	−0.998738	−	2.82887i	−0.332913	−	0.942958i
$10$	1.42690			0.451225
$11$	3.29338	+	1.90143i	0.992991	+	0.573304i	0.906167	−	0.422920i	$-0.138995\pi$
$11$	3.29338	+	1.90143i	0.992991	+	0.573304i	0.0868240	+	0.996224i	$0.472328\pi$
$12$	−0.0621651	−	0.00574190i	−0.0179455	−	0.00165754i
$13$	−1.95544	−	3.02923i	−0.542343	−	0.840157i
$13$	−1.95544	−	3.02923i	−0.542343	−	0.840157i
$14$	−2.22292	−	3.85020i	−0.594099	−	1.02901i
$15$	0.159303	−	1.72471i	0.0411320	−	0.445318i
$16$	2.03539	−	3.52541i	0.508849	−	0.881352i
$17$	−5.10807			−1.23889			−0.619445	−	0.785040i	$-0.712642\pi$
$17$	−5.10807			−1.23889			−0.619445	+	0.785040i	$0.712642\pi$
$18$	−0.784087	+	4.20828i	−0.184811	+	0.991901i
$19$		−	2.45663i		−	0.563591i	−0.959475	−	0.281795i	$-0.909070\pi$
$19$		−	2.45663i		−	0.563591i	0.959475	−	0.281795i	$-0.0909299\pi$
$20$	−0.0312149	−	0.0180219i	−0.00697985	−	0.00402982i
$21$	−4.90195	+	2.25701i	−1.06969	+	0.492521i
$22$	−2.71315	−	4.69932i	−0.578447	−	1.00190i
$23$	3.91395	+	6.77916i	0.816115	+	1.41355i	0.908524	+	0.417832i	$0.137210\pi$
$23$	3.91395	+	6.77916i	0.816115	+	1.41355i	−0.0924090	+	0.995721i	$0.529457\pi$
$24$	−3.96252	−	2.80325i	−0.808847	−	0.572212i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.255200	+	5.13843i	0.0500488	+	1.00773i
$27$	4.99905	+	1.41756i	0.962068	+	0.272809i
$28$			0.112303i			0.0212232i
$29$	−0.937802	+	1.62432i	−0.174145	+	0.301629i	−0.939865	−	0.341546i	$-0.889050\pi$
$29$	−0.937802	+	1.62432i	−0.174145	+	0.301629i	0.765720	+	0.643174i	$0.222383\pi$
$30$	−1.42735	+	2.01762i	−0.260597	+	0.368366i
$31$	−0.553836	+	0.319758i	−0.0994719	+	0.0574302i	−0.548911	−	0.835881i	$-0.684957\pi$
$31$	−0.553836	+	0.319758i	−0.0994719	+	0.0574302i	0.449439	+	0.893311i	$0.351624\pi$
$32$	−0.176557	+	0.101935i	−0.0312111	+	0.0180197i
$33$	−5.98303	+	2.75477i	−1.04151	+	0.479544i
$34$	6.31221	+	3.64436i	1.08254	+	0.625002i
$35$	−3.11573			−0.526654
$36$	0.0703037	−	0.0821571i	0.0117173	−	0.0136929i
$37$			11.3276i			1.86224i	0.364711	+	0.931121i	$0.381168\pi$
$37$			11.3276i			1.86224i	−0.364711	+	0.931121i	$0.618832\pi$
$38$	−1.75269	+	3.03574i	−0.284323	+	0.492462i
$39$	6.23936	+	0.265207i	0.999098	+	0.0424671i
$40$	−1.40118	−	2.42692i	−0.221547	−	0.383730i
$41$	−6.13667	+	3.54301i	−0.958386	+	0.553325i	−0.895676	−	0.444707i	$-0.853308\pi$
$41$	−6.13667	+	3.54301i	−0.958386	+	0.553325i	−0.0627104	+	0.998032i	$0.519974\pi$
$42$	7.66777	+	0.708236i	1.18316	+	0.109283i
$43$	−3.69930	+	6.40737i	−0.564137	+	0.977114i	0.432992	+	0.901398i	$0.357458\pi$
$43$	−3.69930	+	6.40737i	−0.564137	+	0.977114i	−0.997129	+	0.0757166i	$0.975876\pi$
$44$			0.137070i			0.0206640i
$45$	2.27937	+	1.95051i	0.339788	+	0.290764i
$46$		−	11.1696i		−	1.64687i
$47$	0.870833	+	0.502776i	0.127024	+	0.0733374i	0.562166	−	0.827025i	$-0.309968\pi$
$47$	0.870833	+	0.502776i	0.127024	+	0.0733374i	−0.435142	+	0.900362i	$0.643302\pi$
$48$	2.94885	+	6.40455i	0.425630	+	0.924417i
$49$	1.35388	+	2.34499i	0.193411	+	0.334998i
$50$	−1.23573	+	0.713450i	−0.174759	+	0.100897i
$51$	5.10969	−	7.22277i	0.715499	−	1.01139i
$52$	0.0593162	−	0.115631i	0.00822567	−	0.0160352i
$53$	−2.10815			−0.289576			−0.144788	−	0.989463i	$-0.546250\pi$
$53$	−2.10815			−0.289576			−0.144788	+	0.989463i	$0.546250\pi$
$54$	−5.16613	−	5.31830i	−0.703021	−	0.723729i
$55$	−3.80287			−0.512778
$56$	−4.36571	+	7.56163i	−0.583392	+	1.01047i
$57$	3.47366	+	2.45741i	0.460097	+	0.325492i
$58$	2.31774	−	1.33815i	0.304335	−	0.175708i
$59$	−12.5082	+	7.22162i	−1.62843	+	0.940175i	−0.643871	+	0.765134i	$0.722672\pi$
$59$	−12.5082	+	7.22162i	−1.62843	+	0.940175i	−0.984561	+	0.175041i	$0.943994\pi$
$60$	0.0567075	−	0.0261099i	0.00732091	−	0.00337078i
$61$	−3.27156	+	5.66651i	−0.418880	+	0.725522i	−0.995827	−	0.0912597i	$-0.970911\pi$
$61$	−3.27156	+	5.66651i	−0.418880	+	0.725522i	0.576947	+	0.816782i	$0.304244\pi$
$62$	0.912524			0.115891
$63$	1.71210	−	9.18904i	0.215705	−	1.15771i
$64$	−7.85067			−0.981334
$65$	3.20808	+	1.64567i	0.397913	+	0.204120i
$66$	9.35881	+	0.864429i	1.15199	+	0.106404i
$67$	0.631710	−	0.364718i	0.0771757	−	0.0445574i	−0.460916	−	0.887444i	$-0.652479\pi$
$67$	0.631710	−	0.364718i	0.0771757	−	0.0445574i	0.538091	+	0.842887i	$0.319146\pi$
$68$	−0.0920572	−	0.159448i	−0.0111636	−	0.0193359i
$69$	−13.5009	−	1.24701i	−1.62531	−	0.150123i
$70$	3.85020	+	2.22292i	0.460187	+	0.265689i
$71$			10.3248i			1.22533i	0.790343	+	0.612665i	$0.209902\pi$
$71$			10.3248i			1.22533i	−0.790343	+	0.612665i	$0.790098\pi$
$72$	7.92755	−	2.79883i	0.934270	−	0.329846i
$73$		−	7.51823i		−	0.879943i	−0.898012	−	0.439971i	$-0.854989\pi$
$73$		−	7.51823i		−	0.879943i	0.898012	−	0.439971i	$-0.145011\pi$
$74$	8.08166	−	13.9978i	0.939474	−	1.62722i
$75$	0.724394	+	1.57329i	0.0836458	+	0.181668i
$76$	0.0766835	−	0.0442732i	0.00879620	−	0.00507849i
$77$	5.92435	+	10.2613i	0.675142	+	1.16938i
$78$	−7.52097	−	4.77920i	−0.851582	−	0.541138i
$79$	7.34841	−	12.7278i	0.826760	−	1.43199i	−0.0738063	−	0.997273i	$-0.523515\pi$
$79$	7.34841	−	12.7278i	0.826760	−	1.43199i	0.900567	−	0.434718i	$-0.143152\pi$
$80$			4.07079i			0.455128i
$81$	−7.00505	+	5.65061i	−0.778338	+	0.627845i
$82$	10.1110			1.11658
$83$	−1.00753	−	0.581700i	−0.110591	−	0.0638498i	0.443684	−	0.896183i	$-0.353671\pi$
$83$	−1.00753	−	0.581700i	−0.110591	−	0.0638498i	−0.554275	+	0.832333i	$0.687005\pi$
$84$	−0.158795	−	0.112338i	−0.0173259	−	0.0122571i
$85$	4.42372	−	2.55404i	0.479820	−	0.277024i
$86$	9.14267	−	5.27852i	0.985880	−	0.569198i
$87$	−1.35868	−	2.95088i	−0.145665	−	0.316367i
$88$	−5.32852	+	9.22926i	−0.568022	+	0.983843i
$89$		−	2.30943i		−	0.244799i	−0.992481	−	0.122400i	$-0.960941\pi$
$89$		−	2.30943i		−	0.244799i	0.992481	−	0.122400i	$-0.0390590\pi$
$90$	−1.42510	−	4.03652i	−0.150219	−	0.425486i
$91$	−0.557245	−	11.2201i	−0.0584151	−	1.17618i
$92$	−0.141074	+	0.244347i	−0.0147080	+	0.0254749i
$93$	0.101877	−	1.10298i	0.0105641	−	0.114373i
$94$	−0.717411	−	1.24259i	−0.0739952	−	0.128164i
$95$	1.22832	+	2.12751i	0.126023	+	0.218278i
$96$	0.0324772	−	0.351616i	0.00331469	−	0.0358867i
$97$	13.8897	+	8.01923i	1.41029	+	0.814230i	0.995415	−	0.0956500i	$-0.0304930\pi$
$97$	13.8897	+	8.01923i	1.41029	+	0.814230i	0.414872	+	0.909880i	$0.363826\pi$
$98$		−	3.86370i		−	0.390292i
$99$	2.08969	−	11.2156i	0.210022	−	1.12721i
$100$	0.0360438			0.00360438
$101$	8.10502	−	14.0383i	0.806479	−	1.39686i	−0.108809	−	0.994063i	$-0.534704\pi$
$101$	8.10502	−	14.0383i	0.806479	−	1.39686i	0.915288	−	0.402800i	$-0.131963\pi$
$102$	−11.4673	+	5.27990i	−1.13543	+	0.522788i
$103$	7.66426	+	13.2749i	0.755182	+	1.30801i	0.945284	+	0.326250i	$0.105785\pi$
$103$	7.66426	+	13.2749i	0.755182	+	1.30801i	−0.190101	+	0.981764i	$0.560882\pi$
$104$	8.48902	−	5.47988i	0.832417	−	0.537346i
$105$	3.11671	−	4.40561i	0.304160	−	0.429943i
$106$	2.60510	+	1.50406i	0.253030	+	0.146087i
$107$	−11.2550			−1.08806			−0.544030	−	0.839066i	$-0.683102\pi$
$107$	−11.2550			−1.08806			−0.544030	+	0.839066i	$0.683102\pi$
$108$	0.0458435	+	0.181592i	0.00441130	+	0.0174737i
$109$			7.04400i			0.674693i	0.941381	+	0.337347i	$0.109529\pi$
$109$			7.04400i			0.674693i	−0.941381	+	0.337347i	$0.890471\pi$
$110$	4.69932	+	2.71315i	0.448063	+	0.258689i
$111$	−16.0171	−	11.3311i	−1.52027	−	1.07550i
$112$	10.9842	−	6.34173i	1.03791	−	0.599237i
$113$	−0.683608	−	1.18404i	−0.0643084	−	0.111385i	0.832079	−	0.554658i	$-0.187151\pi$
$113$	−0.683608	−	1.18404i	−0.0643084	−	0.111385i	−0.896387	+	0.443272i	$0.853817\pi$
$114$	−2.53927	−	5.51498i	−0.237824	−	0.516525i
$115$	−6.77916	−	3.91395i	−0.632160	−	0.364978i
$116$	−0.0676039			−0.00627686
$117$	−6.61633	+	8.55711i	−0.611680	+	0.791105i
$118$	20.6091			1.89722
$119$	−13.7831	−	7.95768i	−1.26350	−	0.729480i
$120$	4.83327	+	0.446427i	0.441215	+	0.0407530i
$121$	1.73089	+	2.99800i	0.157354	+	0.272545i
$122$	8.08554	−	4.66819i	0.732030	−	0.422638i
$123$	1.12883	−	12.2213i	0.101783	−	1.10196i
$124$	−0.0199624	−	0.0115253i	−0.00179267	−	0.00103500i
$125$			1.00000i			0.0894427i
$126$	−8.67162	+	10.1337i	−0.772530	+	0.902781i
$127$	−19.5367			−1.73360			−0.866802	−	0.498653i	$-0.833828\pi$
$127$	−19.5367			−1.73360			−0.866802	+	0.498653i	$0.833828\pi$
$128$	10.0544	+	5.80493i	0.888695	+	0.513089i
$129$	−5.35949	−	11.6402i	−0.471877	−	1.02486i
$130$	−2.79022	−	4.32241i	−0.244719	−	0.379100i
$131$	2.70268	+	4.68119i	0.236135	+	0.408997i	0.959602	−	0.281362i	$-0.0907860\pi$
$131$	2.70268	+	4.68119i	0.236135	+	0.408997i	−0.723467	+	0.690359i	$0.757453\pi$
$132$	−0.193815	−	0.137113i	−0.0168695	−	0.0119342i
$133$	3.82710	−	6.62874i	0.331852	−	0.574784i
$134$	−1.04083			−0.0899142
$135$	−5.03809	+	1.27188i	−0.433609	+	0.109466i
$136$		−	14.3147i		−	1.22748i
$137$	−7.29242	−	4.21028i	−0.623033	−	0.359708i	0.155016	−	0.987912i	$-0.450457\pi$
$137$	−7.29242	−	4.21028i	−0.623033	−	0.359708i	−0.778049	+	0.628204i	$0.783790\pi$
$138$	15.7938	+	11.1732i	1.34445	+	0.951122i
$139$	1.05245	+	1.82289i	0.0892674	+	0.154616i	0.907202	−	0.420696i	$-0.138214\pi$
$139$	1.05245	+	1.82289i	0.0892674	+	0.154616i	−0.817934	+	0.575312i	$0.804881\pi$
$140$	−0.0561513	−	0.0972570i	−0.00474565	−	0.00821971i
$141$	−1.58203	+	0.728415i	−0.133231	+	0.0613436i
$142$	7.36624	−	12.7587i	0.618161	−	1.07069i
$143$	−0.680139	−	13.6945i	−0.0568760	−	1.14520i
$144$	−12.0058	−	2.23691i	−1.00048	−	0.186410i
$145$		−	1.87560i		−	0.155760i
$146$	−5.36388	+	9.29052i	−0.443918	+	0.768889i
$147$	−4.67009	−	0.431355i	−0.385183	−	0.0355775i
$148$	−0.353589	+	0.204144i	−0.0290648	+	0.0167806i
$149$	0.752949	−	0.434715i	0.0616840	−	0.0356133i	−0.468841	−	0.883283i	$-0.655328\pi$
$149$	0.752949	−	0.434715i	0.0616840	−	0.0356133i	0.530525	+	0.847669i	$0.321995\pi$
$150$	0.227310	−	2.46099i	0.0185598	−	0.200939i
$151$	11.6082	+	6.70202i	0.944665	+	0.545402i	0.891419	−	0.453179i	$-0.149710\pi$
$151$	11.6082	+	6.70202i	0.944665	+	0.545402i	0.0532451	+	0.998581i	$0.483044\pi$
$152$	6.88440			0.558398
$153$	5.10163	+	14.4501i	0.412442	+	1.16822i
$154$		−	16.9069i		−	1.36240i
$155$	0.319758	−	0.553836i	0.0256835	−	0.0444852i
$156$	0.104167	+	0.199540i	0.00834002	+	0.0159760i
$157$	−4.13379	−	7.15993i	−0.329912	−	0.571425i	0.652582	−	0.757718i	$-0.273686\pi$
$157$	−4.13379	−	7.15993i	−0.329912	−	0.571425i	−0.982494	+	0.186293i	$0.940353\pi$
$158$	−18.1613	+	10.4854i	−1.44484	+	0.834177i
$159$	2.10881	−	2.98090i	0.167240	−	0.236401i
$160$	0.101935	−	0.176557i	0.00805867	−	0.0139580i
$161$			24.3896i			1.92217i
$162$	12.6878	−	1.98488i	0.996846	−	0.155947i
$163$			3.63387i			0.284626i	0.989822	+	0.142313i	$0.0454540\pi$
$163$			3.63387i			0.284626i	−0.989822	+	0.142313i	$0.954546\pi$
$164$	−0.221189	−	0.127703i	−0.0172719	−	0.00997196i
$165$	3.80407	−	5.37722i	0.296146	−	0.418616i
$166$	0.830027	+	1.43765i	0.0644226	+	0.111583i
$167$	−13.9161	+	8.03445i	−1.07686	+	0.621724i	−0.930047	−	0.367441i	$-0.880234\pi$
$167$	−13.9161	+	8.03445i	−1.07686	+	0.621724i	−0.146811	+	0.989165i	$0.546901\pi$
$168$	−6.32499	−	13.7371i	−0.487983	−	1.05984i
$169$	−5.35248	+	11.8470i	−0.411729	+	0.911306i
$170$	−7.28871			−0.559019
$171$	−6.94951	+	2.45353i	−0.531442	+	0.187626i
$172$	−0.266673			−0.0203337
$173$	8.03065	−	13.9095i	0.610559	−	1.05752i	−0.380587	−	0.924745i	$-0.624278\pi$
$173$	8.03065	−	13.9095i	0.610559	−	1.05752i	0.991146	−	0.132775i	$-0.0423887\pi$
$174$	−0.426343	+	4.61584i	−0.0323210	+	0.349926i
$175$	2.69830	−	1.55786i	0.203972	−	0.117763i
$176$	13.4066	−	7.74033i	1.01056	−	0.583449i
$177$	2.30086	−	24.9104i	0.172943	−	1.87238i
$178$	−1.64766	+	2.85384i	−0.123498	+	0.213904i
$179$	5.73985			0.429016			0.214508	−	0.976722i	$-0.431185\pi$
$179$	5.73985			0.429016			0.214508	+	0.976722i	$0.431185\pi$
$180$	−0.0198062	+	0.106302i	−0.00147627	+	0.00792329i
$181$	3.45555			0.256849			0.128424	−	0.991719i	$-0.459008\pi$
$181$	3.45555			0.256849			0.128424	+	0.991719i	$0.459008\pi$
$182$	−7.31637	+	14.2626i	−0.542325	+	1.05721i
$183$	−4.73980	−	10.2942i	−0.350376	−	0.760973i
$184$	−18.9977	+	10.9683i	−1.40053	+	0.808597i
$185$	−5.66379	−	9.80997i	−0.416410	−	0.721243i
$186$	−0.912812	+	1.29030i	−0.0669306	+	0.0946094i
$187$	−16.8228	−	9.71266i	−1.23021	−	0.710260i
$188$			0.0362439i			0.00264336i
$189$	11.2806	+	11.6128i	0.820541	+	0.844710i
$190$		−	3.50537i		−	0.254306i
$191$	11.1660	−	19.3400i	0.807940	−	1.39939i	−0.106348	−	0.994329i	$-0.533916\pi$
$191$	11.1660	−	19.3400i	0.807940	−	1.39939i	0.914288	−	0.405065i	$-0.132751\pi$
$192$	7.85315	−	11.1008i	0.566752	−	0.801130i
$193$	−2.74053	+	1.58225i	−0.197268	+	0.113892i	−0.595380	−	0.803444i	$-0.702999\pi$
$193$	−2.74053	+	1.58225i	−0.197268	+	0.113892i	0.398113	+	0.917336i	$0.369665\pi$
$194$	−11.4426	−	19.8192i	−0.821534	−	1.42294i
$195$	−5.53605	+	2.89001i	−0.396445	+	0.206958i
$196$	−0.0487989	+	0.0845222i	−0.00348564	+	0.00603730i
$197$			0.561968i			0.0400385i	0.999800	+	0.0200193i	$0.00637276\pi$
$197$			0.561968i			0.0400385i	−0.999800	+	0.0200193i	$0.993627\pi$
$198$	−10.5841	+	12.3686i	−0.752176	+	0.878995i
$199$	1.83634			0.130175			0.0650873	−	0.997880i	$-0.479267\pi$
$199$	1.83634			0.130175			0.0650873	+	0.997880i	$0.479267\pi$
$200$	2.42692	+	1.40118i	0.171609	+	0.0990787i
$201$	−0.116202	+	1.25807i	−0.00819623	+	0.0887371i
$202$	−20.0312	+	11.5650i	−1.40939	+	0.813714i
$203$	−5.06094	+	2.92193i	−0.355208	+	0.205080i
$204$	0.317544	+	0.0293301i	0.0222325	+	0.00205351i
$205$	3.54301	−	6.13667i	0.247454	−	0.428603i
$206$		−	21.8723i		−	1.52391i
$207$	15.2684	−	17.8427i	1.06123	−	1.24015i
$208$	−14.6594	+	0.728056i	−1.01644	+	0.0504816i
$209$	4.67113	−	8.09063i	0.323109	−	0.559640i
$210$	−6.99460	+	3.22053i	−0.482673	+	0.222238i
$211$	8.15159	+	14.1190i	0.561178	+	0.971989i	0.997394	+	0.0721473i	$0.0229852\pi$
$211$	8.15159	+	14.1190i	0.561178	+	0.971989i	−0.436216	+	0.899842i	$0.643682\pi$
$212$	−0.0379928	−	0.0658055i	−0.00260936	−	0.00451954i
$213$	−14.5992	−	10.3281i	−1.00032	−	0.707668i
$214$	13.9081	+	8.02987i	0.950741	+	0.548911i
$215$		−	7.39859i		−	0.504580i
$216$	−3.97253	+	14.0092i	−0.270296	+	0.953205i
$217$	−1.99255			−0.135263
$218$	5.02554	−	8.70450i	0.340373	−	0.589543i
$219$	10.6307	+	7.52061i	0.718357	+	0.508195i
$220$	−0.0685349	−	0.118706i	−0.00462062	−	0.00800315i
$221$	9.98855	+	15.4735i	0.671903	+	1.04086i
$222$	11.7086	+	25.4296i	0.785830	+	1.70673i
$223$	8.18767	+	4.72716i	0.548287	+	0.316554i	0.748431	−	0.663213i	$-0.230808\pi$
$223$	8.18767	+	4.72716i	0.548287	+	0.316554i	−0.200144	+	0.979767i	$0.564141\pi$
$224$	−0.635203			−0.0424413
$225$	−2.94924	−	0.549504i	−0.196616	−	0.0366336i
$226$			1.95088i			0.129771i
$227$	−6.55357	−	3.78370i	−0.434976	−	0.251133i	0.266488	−	0.963838i	$-0.414137\pi$
$227$	−6.55357	−	3.78370i	−0.434976	−	0.251133i	−0.701464	+	0.712705i	$0.747470\pi$
$228$	−0.0141058	+	0.152717i	−0.000934176	+	0.0101139i
$229$	−5.52977	+	3.19261i	−0.365417	+	0.210974i	−0.671455	−	0.741046i	$-0.734330\pi$
$229$	−5.52977	+	3.19261i	−0.365417	+	0.210974i	0.306037	+	0.952020i	$0.400997\pi$
$230$	5.58482	+	9.67319i	0.368252	+	0.637831i
$231$	−20.4356	−	1.88754i	−1.34456	−	0.124191i
$232$	−4.55195	−	2.62807i	−0.298850	−	0.172541i
$233$	27.9712			1.83245			0.916226	−	0.400662i	$-0.131220\pi$
$233$	27.9712			1.83245			0.916226	+	0.400662i	$0.131220\pi$
$234$	14.2811	−	5.85387i	0.933584	−	0.382679i
$235$	−1.00555			−0.0655949
$236$	−0.450844	−	0.260295i	−0.0293474	−	0.0169438i
$237$	10.6463	+	23.1224i	0.691550	+	1.50196i
$238$	11.3548	+	19.6671i	0.736024	+	1.27483i
$239$	14.0126	−	8.09017i	0.906399	−	0.523310i	0.0271283	−	0.999632i	$-0.491364\pi$
$239$	14.0126	−	8.09017i	0.906399	−	0.523310i	0.879271	+	0.476322i	$0.158030\pi$
$240$	−5.75606	−	4.07207i	−0.371552	−	0.262851i
$241$	12.9503	+	7.47688i	0.834204	+	0.481628i	0.855290	−	0.518150i	$-0.173379\pi$
$241$	12.9503	+	7.47688i	0.834204	+	0.481628i	−0.0210859	+	0.999778i	$0.506712\pi$
$242$		−	4.93963i		−	0.317531i
$243$	−0.982647	−	15.5575i	−0.0630369	−	0.998011i
$244$	−0.235839			−0.0150980
$245$	−2.34499	−	1.35388i	−0.149816	−	0.0864961i
$246$	−10.1142	+	14.2969i	−0.644859	+	0.911537i
$247$	−7.44171	+	4.80381i	−0.473505	+	0.305659i
$248$	−0.896079	−	1.55205i	−0.0569011	−	0.0985555i
$249$	1.83037	−	0.842760i	0.115995	−	0.0534077i
$250$	0.713450	−	1.23573i	0.0451225	−	0.0781545i
$251$	−7.03296			−0.443916			−0.221958	−	0.975056i	$-0.571245\pi$
$251$	−7.03296			−0.443916			−0.221958	+	0.975056i	$0.571245\pi$
$252$	0.317690	−	0.112161i	0.0200126	−	0.00706548i
$253$			29.7685i			1.87153i
$254$	24.1421	+	13.9385i	1.51481	+	0.874578i
$255$	−0.813734	+	8.80994i	−0.0509580	+	0.551700i
$256$	−0.432386	−	0.748915i	−0.0270241	−	0.0468072i
$257$	0.216823	+	0.375549i	0.0135251	+	0.0234261i	0.872709	−	0.488241i	$-0.162361\pi$
$257$	0.216823	+	0.375549i	0.0135251	+	0.0234261i	−0.859184	+	0.511667i	$0.829028\pi$
$258$	−1.68177	+	18.2078i	−0.104703	+	1.13357i
$259$	−17.6468	+	30.5652i	−1.09652	+	1.89923i
$260$	0.00644640	+	0.129798i	0.000399789	+	0.00804972i
$261$	5.53161	+	1.03065i	0.342398	+	0.0637957i
$262$		−	7.71292i		−	0.476506i
$263$	−6.57908	+	11.3953i	−0.405684	+	0.702665i	−0.994401	−	0.105674i	$-0.966300\pi$
$263$	−6.57908	+	11.3953i	−0.405684	+	0.702665i	0.588717	+	0.808339i	$0.299633\pi$
$264$	−7.71989	−	16.7666i	−0.475126	−	1.03192i
$265$	1.82571	−	1.05407i	0.112152	−	0.0647512i
$266$	−9.45854	+	5.46089i	−0.579940	+	0.334829i
$267$	3.26551	+	2.31016i	0.199846	+	0.141379i
$268$	0.0227692	+	0.0131458i	0.00139085	+	0.000803009i
$269$	24.0531			1.46654			0.733272	−	0.679935i	$-0.237992\pi$
$269$	24.0531			1.46654			0.733272	+	0.679935i	$0.237992\pi$
$270$	7.13315	+	2.02272i	0.434110	+	0.123099i
$271$		−	18.0317i		−	1.09535i	−0.836692	−	0.547673i	$-0.815514\pi$
$271$		−	18.0317i		−	1.09535i	0.836692	−	0.547673i	$-0.184486\pi$
$272$	−10.3969	+	18.0080i	−0.630407	+	1.09190i
$273$	16.4225	+	10.4357i	0.993936	+	0.631596i
$274$	6.00765	+	10.4055i	0.362935	+	0.628622i
$275$	3.29338	−	1.90143i	0.198598	−	0.114661i
$276$	−0.204386	−	0.443901i	−0.0123026	−	0.0267197i
$277$	−10.4898	+	18.1689i	−0.630271	+	1.09166i	0.357225	+	0.934018i	$0.383723\pi$
$277$	−10.4898	+	18.1689i	−0.630271	+	1.09166i	−0.987496	+	0.157643i	$0.949610\pi$
$278$		−	3.00347i		−	0.180136i
$279$	1.45769	+	1.24738i	0.0872697	+	0.0746786i
$280$		−	8.73142i		−	0.521802i
$281$	20.2396	+	11.6854i	1.20740	+	0.697091i	0.962190	−	0.272380i	$-0.0878109\pi$
$281$	20.2396	+	11.6854i	1.20740	+	0.697091i	0.245207	+	0.969471i	$0.421144\pi$
$282$	2.47465	+	0.228572i	0.147363	+	0.0136113i
$283$	−0.511049	−	0.885163i	−0.0303787	−	0.0526175i	0.850436	−	0.526078i	$-0.176338\pi$
$283$	−0.511049	−	0.885163i	−0.0303787	−	0.0526175i	−0.880815	+	0.473460i	$0.843005\pi$
$284$	−0.322288	+	0.186073i	−0.0191242	+	0.0110414i
$285$	−4.23698	−	0.391350i	−0.250977	−	0.0231816i
$286$	−8.92991	+	17.4080i	−0.528036	+	1.02936i
$287$	−22.0781			−1.30323
$288$	0.464695	+	0.397650i	0.0273824	+	0.0234317i
$289$	9.09242			0.534848
$290$	−1.33815	+	2.31774i	−0.0785788	+	0.136103i
$291$	−25.2332	+	11.6182i	−1.47920	+	0.681069i
$292$	0.234681	−	0.135493i	0.0137336	−	0.00792912i
$293$	−7.17020	+	4.13971i	−0.418887	+	0.241845i	−0.694601	−	0.719395i	$-0.744419\pi$
$293$	−7.17020	+	4.13971i	−0.418887	+	0.241845i	0.275714	+	0.961240i	$0.411086\pi$
$294$	5.46323	+	3.86492i	0.318622	+	0.225406i
$295$	7.22162	−	12.5082i	0.420459	−	0.728257i
$296$	−31.7440			−1.84509
$297$	13.7684	+	14.1739i	0.798922	+	0.822454i
$298$	−1.24059			−0.0718655
$299$	12.8821	−	25.1125i	0.744993	−	1.45230i
$300$	−0.0360552	+	0.0509656i	−0.00208165	+	0.00294250i
$301$	−19.9636	+	11.5260i	−1.15068	+	0.664347i
$302$	−9.56311	−	16.5638i	−0.550295	−	0.953139i
$303$	11.7424	+	25.5031i	0.674586	+	1.46512i
$304$	−8.66064	−	5.00022i	−0.496722	−	0.286782i
$305$		−	6.54312i		−	0.374658i
$306$	4.00518	−	21.4962i	0.228961	−	1.22886i
$307$		−	7.02592i		−	0.400991i	−0.979695	−	0.200495i	$-0.935745\pi$
$307$		−	7.02592i		−	0.400991i	0.979695	−	0.200495i	$-0.0642551\pi$
$308$	−0.213536	+	0.369855i	−0.0121673	+	0.0210745i
$309$	−26.4373	−	2.44189i	−1.50396	−	0.138914i
$310$	−0.790269	+	0.456262i	−0.0448843	+	0.0259139i
$311$	12.0009	+	20.7862i	0.680509	+	1.17868i	0.974826	+	0.222968i	$0.0715744\pi$
$311$	12.0009	+	20.7862i	0.680509	+	1.17868i	−0.294317	+	0.955708i	$0.595092\pi$
$312$	−0.743208	+	17.4850i	−0.0420759	+	0.989893i
$313$	2.55490	−	4.42522i	0.144412	−	0.250128i	−0.784742	−	0.619823i	$-0.787204\pi$
$313$	2.55490	−	4.42522i	0.144412	−	0.250128i	0.929153	+	0.369695i	$0.120538\pi$
$314$			11.7970i			0.665744i
$315$	3.11179	+	8.81400i	0.175330	+	0.496612i
$316$	0.529729			0.0297996
$317$	−24.9621	−	14.4119i	−1.40201	−	0.809452i	−0.407413	−	0.913244i	$-0.633569\pi$
$317$	−24.9621	−	14.4119i	−1.40201	−	0.809452i	−0.994599	+	0.103792i	$0.966903\pi$
$318$	−4.73265	+	2.17906i	−0.265394	+	0.122196i
$319$	−6.17707	+	3.56633i	−0.345850	+	0.199676i
$320$	6.79888	−	3.92534i	0.380069	−	0.219433i
$321$	11.2585	−	15.9144i	0.628390	−	0.888258i
$322$	17.4008	−	30.1390i	0.969707	−	1.67958i
$323$			12.5487i			0.698227i
$324$	−0.302627	−	0.116827i	−0.0168126	−	0.00649038i
$325$	−3.60111	+	0.178849i	−0.199754	+	0.00992076i
$326$	2.59258	−	4.49048i	0.143590	−	0.248705i
$327$	−9.96015	−	7.04623i	−0.550798	−	0.389657i
$328$	−9.92881	−	17.1972i	−0.548227	−	0.949557i
$329$	1.56651	+	2.71328i	0.0863646	+	0.149588i
$330$	−8.53718	+	3.93079i	−0.469956	+	0.216383i
$331$	22.0578	+	12.7350i	1.21240	+	0.699982i	0.963282	−	0.268491i	$-0.0865249\pi$
$331$	22.0578	+	12.7350i	1.21240	+	0.699982i	0.249121	+	0.968472i	$0.419858\pi$
$332$		−	0.0419334i		−	0.00230139i
$333$	32.0443	−	11.3133i	1.75602	−	0.619964i
$334$	22.9287			1.25460
$335$	−0.364718	+	0.631710i	−0.0199267	+	0.0345140i
$336$	−2.02052	+	21.8753i	−0.110228	+	1.19340i
$337$	−12.4843	−	21.6234i	−0.680063	−	1.17790i	−0.974961	−	0.222375i	$-0.928619\pi$
$337$	−12.4843	−	21.6234i	−0.680063	−	1.17790i	0.294898	−	0.955529i	$-0.404714\pi$
$338$	15.0665	−	10.8210i	0.819507	−	0.588583i
$339$	2.35805	+	0.217802i	0.128072	+	0.0118294i
$340$	0.159448	+	0.0920572i	0.00864727	+	0.00499250i
$341$	−2.43199			−0.131700
$342$	10.3382	+	1.92622i	0.559026	+	0.104158i
$343$		−	13.3735i		−	0.722099i
$344$	−17.9558	−	10.3668i	−0.968112	−	0.558940i
$345$	12.3156	−	5.67049i	0.663049	−	0.305289i
$346$	−19.8475	+	11.4589i	−1.06701	+	0.616037i
$347$	−0.109883	−	0.190323i	−0.00589882	−	0.0102170i	0.863061	−	0.505100i	$-0.168544\pi$
$347$	−0.109883	−	0.190323i	−0.00589882	−	0.0102170i	−0.868960	+	0.494883i	$0.835211\pi$
$348$	0.0676252	−	0.0955913i	0.00362509	−	0.00512423i
$349$	−3.19946	−	1.84721i	−0.171263	−	0.0988788i	0.411918	−	0.911221i	$-0.364859\pi$
$349$	−3.19946	−	1.84721i	−0.171263	−	0.0988788i	−0.583181	+	0.812342i	$0.698192\pi$
$350$	−4.44583			−0.237640
$351$	−5.48125	−	17.9152i	−0.292568	−	0.956245i
$352$	−0.775290			−0.0413231
$353$	−0.391714	−	0.226156i	−0.0208488	−	0.0120371i	0.489539	−	0.871981i	$-0.337165\pi$
$353$	−0.391714	−	0.226156i	−0.0208488	−	0.0120371i	−0.510388	+	0.859944i	$0.670498\pi$
$354$	−20.6156	+	29.1410i	−1.09571	+	1.54883i
$355$	−5.16241	−	8.94155i	−0.273992	−	0.474568i
$356$	0.0720886	−	0.0416204i	0.00382069	−	0.00220587i
$357$	25.0395	−	11.5290i	1.32523	−	0.610179i
$358$	−7.09291	−	4.09509i	−0.374872	−	0.216432i
$359$		−	11.8460i		−	0.625207i	−0.949884	−	0.312603i	$-0.898799\pi$
$359$		−	11.8460i		−	0.625207i	0.949884	−	0.312603i	$-0.101201\pi$
$360$	−5.46604	+	6.38763i	−0.288086	+	0.336658i
$361$	12.9649			0.682366
$362$	−4.27013	−	2.46536i	−0.224433	−	0.129576i
$363$	−5.97058	−	0.551475i	−0.313374	−	0.0289449i
$364$	0.340191	−	0.219602i	0.0178308	−	0.0115103i
$365$	3.75912	+	6.51098i	0.196761	+	0.340800i
$366$	−1.48732	+	16.1025i	−0.0777433	+	0.841693i
$367$	9.84909	−	17.0591i	0.514118	−	0.890479i	−0.485748	−	0.874099i	$-0.661453\pi$
$367$	9.84909	−	17.0591i	0.514118	−	0.890479i	0.999866	−	0.0163799i	$-0.00521412\pi$
$368$	31.8657			1.66112
$369$	16.1516	+	13.8213i	0.840821	+	0.719509i
$370$			16.1633i			0.840291i
$371$	−5.68841	−	3.28420i	−0.295327	−	0.170507i
$372$	0.0362653	−	0.0166977i	0.00188027	−	0.000865735i
$373$	4.89975	+	8.48661i	0.253699	+	0.439420i	0.964541	−	0.263932i	$-0.0850193\pi$
$373$	4.89975	+	8.48661i	0.253699	+	0.439420i	−0.710842	+	0.703352i	$0.751686\pi$
$374$	13.8590	+	24.0045i	0.716632	+	1.24124i
$375$	−1.41399	−	1.00032i	−0.0730182	−	0.0516561i
$376$	−1.40896	+	2.44040i	−0.0726617	+	0.125854i
$377$	6.75426	−	0.335450i	0.347862	−	0.0172765i
$378$	−5.65458	−	22.3985i	−0.290840	−	1.15205i
$379$			11.8049i			0.606375i	0.952931	+	0.303187i	$0.0980508\pi$
$379$			11.8049i			0.606375i	−0.952931	+	0.303187i	$0.901949\pi$
$380$	−0.0442732	+	0.0766835i	−0.00227117	+	0.00393378i
$381$	19.5429	−	27.6247i	1.00121	−	1.41526i
$382$	−27.5963	+	15.9327i	−1.41195	+	0.815188i
$383$	21.7194	−	12.5397i	1.10981	−	0.640749i	0.171029	−	0.985266i	$-0.445291\pi$
$383$	21.7194	−	12.5397i	1.10981	−	0.640749i	0.938780	+	0.344517i	$0.111957\pi$
$384$	−18.2657	+	8.41012i	−0.932119	+	0.429177i
$385$	−10.2613	−	5.92435i	−0.522963	−	0.301933i
$386$	4.51541			0.229828
$387$	21.8203	+	4.06556i	1.10919	+	0.206664i
$388$			0.578087i			0.0293479i
$389$	−6.92628	+	11.9967i	−0.351176	+	0.608255i	−0.986456	−	0.164027i	$-0.947551\pi$
$389$	−6.92628	+	11.9967i	−0.351176	+	0.608255i	0.635280	+	0.772282i	$0.280885\pi$
$390$	8.90295	+	0.378424i	0.450818	+	0.0191622i
$391$	−19.9928	−	34.6285i	−1.01108	−	1.75124i
$392$	−6.57151	+	3.79407i	−0.331912	+	0.191629i
$393$	−9.32269	−	0.861094i	−0.470268	−	0.0434364i
$394$	0.400936	−	0.694441i	0.0201989	−	0.0349854i
$395$			14.6968i			0.739477i
$396$	0.387753	−	0.136897i	0.0194853	−	0.00687932i
$397$			36.6002i			1.83691i	0.395525	+	0.918455i	$0.370563\pi$
$397$			36.6002i			1.83691i	−0.395525	+	0.918455i	$0.629437\pi$
$398$	−2.26922	−	1.31014i	−0.113746	−	0.0656712i
$399$	5.54466	+	12.0423i	0.277580	+	0.602870i
$400$	−2.03539	−	3.52541i	−0.101770	−	0.176270i
$401$	16.0606	−	9.27259i	0.802028	−	0.463051i	−0.0421519	−	0.999111i	$-0.513421\pi$
$401$	16.0606	−	9.27259i	0.802028	−	0.463051i	0.844180	+	0.536060i	$0.180088\pi$
$402$	1.04116	−	1.47173i	0.0519284	−	0.0734031i
$403$	2.05162	+	1.05243i	0.102198	+	0.0524253i
$404$	0.584271			0.0290686
$405$	3.24124	−	8.39609i	0.161059	−	0.417205i
$406$	8.33862			0.413839
$407$	−21.5386	+	37.3060i	−1.06763	+	1.84919i
$408$	20.2409	+	14.3192i	1.00207	+	0.708907i
$409$	−4.02574	+	2.32426i	−0.199060	+	0.114927i	−0.596217	−	0.802823i	$-0.703330\pi$
$409$	−4.02574	+	2.32426i	−0.199060	+	0.114927i	0.397157	+	0.917751i	$0.369997\pi$
$410$	−8.75641	+	5.05552i	−0.432448	+	0.249674i
$411$	13.2480	−	6.09980i	0.653476	−	0.300881i
$412$	−0.276249	+	0.478478i	−0.0136098	+	0.0235729i
$413$	−45.0012			−2.21437
$414$	−31.5975	+	11.1555i	−1.55293	+	0.548265i
$415$	1.16340			0.0571090
$416$	0.654031	+	0.335502i	0.0320665	+	0.0164494i
$417$	−3.63033	−	0.335317i	−0.177778	−	0.0164205i
$418$	−11.5445	+	6.66523i	−0.564661	+	0.326007i
$419$	−18.5997	−	32.2156i	−0.908653	−	1.57383i	−0.815937	−	0.578140i	$-0.803779\pi$
$419$	−18.5997	−	32.2156i	−0.908653	−	1.57383i	−0.0927157	−	0.995693i	$-0.529555\pi$
$420$	0.193689	+	0.0178902i	0.00945108	+	0.000872952i
$421$	−9.43320	−	5.44626i	−0.459746	−	0.265435i	0.252191	−	0.967677i	$-0.418849\pi$
$421$	−9.43320	−	5.44626i	−0.459746	−	0.265435i	−0.711938	+	0.702243i	$0.752182\pi$
$422$		−	23.2630i		−	1.13243i
$423$	0.552555	−	2.96562i	0.0268661	−	0.144193i
$424$		−	5.90780i		−	0.286908i
$425$	−2.55404	+	4.42372i	−0.123889	+	0.214582i
$426$	10.6721	+	23.1785i	0.517066	+	1.12300i
$427$	−17.6553	+	10.1933i	−0.854399	+	0.493288i
$428$	−0.202836	−	0.351323i	−0.00980446	−	0.0169818i
$429$	20.0443	+	12.7372i	0.967749	+	0.614956i
$430$	−5.27852	+	9.14267i	−0.254553	+	0.440899i
$431$		−	23.5648i		−	1.13507i	−0.823348	−	0.567537i	$-0.807896\pi$
$431$		−	23.5648i		−	1.13507i	0.823348	−	0.567537i	$-0.192104\pi$
$432$	15.1725	−	14.7384i	0.729988	−	0.709102i
$433$	−14.1222			−0.678670			−0.339335	−	0.940666i	$-0.610202\pi$
$433$	−14.1222			−0.678670			−0.339335	+	0.940666i	$0.610202\pi$
$434$	2.46226	+	1.42159i	0.118192	+	0.0682384i
$435$	2.65209	+	1.87620i	0.127158	+	0.0899567i
$436$	−0.219878	+	0.126946i	−0.0105302	+	0.00607963i
$437$	16.6539	−	9.61515i	0.796665	−	0.459955i
$438$	−7.77113	−	16.8779i	−0.371319	−	0.806459i
$439$	5.21082	−	9.02540i	0.248699	−	0.430759i	−0.714466	−	0.699670i	$-0.753330\pi$
$439$	5.21082	−	9.02540i	0.248699	−	0.430759i	0.963165	+	0.268911i	$0.0866638\pi$
$440$		−	10.6570i		−	0.508054i
$441$	5.28150	−	6.17197i	0.251500	−	0.293904i
$442$	−1.30358	−	26.2475i	−0.0620049	−	1.24846i
$443$	−1.73677	+	3.00818i	−0.0825166	+	0.142923i	−0.904330	−	0.426833i	$-0.859629\pi$
$443$	−1.73677	+	3.00818i	−0.0825166	+	0.142923i	0.821814	+	0.569756i	$0.192962\pi$
$444$	0.0650418	−	0.704180i	0.00308675	−	0.0334189i
$445$	1.15472	+	2.00003i	0.0547388	+	0.0948103i
$446$	−6.74518	−	11.6830i	−0.319393	−	0.553206i
$447$	−0.138503	+	1.49952i	−0.00655098	+	0.0709247i
$448$	−21.1835	−	12.2303i	−1.00082	−	0.577826i
$449$		−	1.71863i		−	0.0811073i	−0.999177	−	0.0405537i	$-0.987088\pi$
$449$		−	1.71863i		−	0.0811073i	0.999177	−	0.0405537i	$-0.0129122\pi$
$450$	3.25243	+	2.78318i	0.153321	+	0.131200i
$451$	−26.9472			−1.26889
$452$	0.0246398	−	0.0426774i	0.00115896	−	0.00200738i
$453$	−21.0885	+	9.70980i	−0.990823	+	0.456206i
$454$	5.39897	+	9.35129i	0.253386	+	0.438878i
$455$	6.09263	+	9.43826i	0.285627	+	0.442472i
$456$	−6.88657	+	9.73447i	−0.322493	+	0.455858i
$457$	16.6057	+	9.58730i	0.776782	+	0.448475i	0.835289	−	0.549812i	$-0.185301\pi$
$457$	16.6057	+	9.58730i	0.776782	+	0.448475i	−0.0585068	+	0.998287i	$0.518634\pi$
$458$	9.11108			0.425733
$459$	−25.5355	−	7.24100i	−1.19190	−	0.337981i
$460$		−	0.282147i		−	0.0131552i
$461$	−9.02588	−	5.21109i	−0.420377	−	0.242705i	0.274862	−	0.961484i	$-0.411368\pi$
$461$	−9.02588	−	5.21109i	−0.420377	−	0.242705i	−0.695239	+	0.718779i	$0.744701\pi$
$462$	23.9062	+	16.9122i	1.11222	+	0.786828i
$463$	11.2122	−	6.47338i	0.521076	−	0.300843i	−0.216299	−	0.976327i	$-0.569399\pi$
$463$	11.2122	−	6.47338i	0.521076	−	0.300843i	0.737375	+	0.675484i	$0.236065\pi$
$464$	3.81759	+	6.61226i	0.177227	+	0.306967i
$465$	0.463261	+	1.00615i	0.0214832	+	0.0466589i
$466$	−34.5648	−	19.9560i	−1.60119	−	0.924445i
$467$	26.2184			1.21324			0.606621	−	0.794991i	$-0.292525\pi$
$467$	26.2184			1.21324			0.606621	+	0.794991i	$0.292525\pi$
$468$	−0.386348	−	0.0523124i	−0.0178589	−	0.00241814i
$469$	2.27272			0.104945
$470$	1.24259	+	0.717411i	0.0573165	+	0.0330917i
$471$	14.2592	+	1.31705i	0.657028	+	0.0606866i
$472$	−20.2377	−	35.0527i	−0.931514	−	1.61343i
$473$	−24.3664	+	14.0679i	−1.12037	+	0.646844i
$474$	3.34073	−	36.1687i	0.153445	−	1.66128i
$475$	−2.12751	−	1.22832i	−0.0976168	−	0.0563591i
$476$		−	0.573650i		−	0.0262932i
$477$	2.10549	+	5.96368i	0.0964035	+	0.273058i
$478$	−23.0877			−1.05601
$479$	16.2297	+	9.37020i	0.741552	+	0.428135i	0.822633	−	0.568572i	$-0.192504\pi$
$479$	16.2297	+	9.37020i	0.741552	+	0.428135i	−0.0810814	+	0.996707i	$0.525837\pi$
$480$	0.147682	+	0.320747i	0.00674074	+	0.0146400i
$481$	34.3138	−	22.1504i	1.56458	−	1.00997i
$482$	−10.6688	−	18.4788i	−0.485948	−	0.841687i
$483$	−34.4867	−	24.3973i	−1.56920	−	1.11012i
$484$	−0.0623880	+	0.108059i	−0.00283582	+	0.00491178i
$485$	−16.0385			−0.728269
$486$	−9.88518	+	19.9259i	−0.448401	+	0.903858i
$487$		−	20.7313i		−	0.939427i	−0.882819	−	0.469713i	$-0.844357\pi$
$487$		−	20.7313i		−	0.939427i	0.882819	−	0.469713i	$-0.155643\pi$
$488$	−15.8796	−	9.16812i	−0.718838	−	0.415021i
$489$	−5.13825	−	3.63501i	−0.232360	−	0.164381i
$490$	1.93185	+	3.34606i	0.0872720	+	0.151160i
$491$	−4.74496	−	8.21851i	−0.214137	−	0.370896i	0.738868	−	0.673850i	$-0.235361\pi$
$491$	−4.74496	−	8.21851i	−0.214137	−	0.370896i	−0.953005	+	0.302954i	$0.902027\pi$
$492$	0.401830	−	0.185015i	0.0181159	−	0.00834113i
$493$	4.79036	−	8.29715i	0.215747	−	0.373685i
$494$	12.6232	−	0.626932i	0.567946	−	0.0282070i
$495$	3.79807	+	10.7578i	0.170710	+	0.483528i
$496$			2.60333i			0.116893i
$497$	−16.0846	+	27.8594i	−0.721495	+	1.24967i
$498$	−2.86311	−	0.264452i	−0.128299	−	0.0118504i
$499$	6.27678	−	3.62390i	0.280987	−	0.162228i	−0.352883	−	0.935667i	$-0.614799\pi$
$499$	6.27678	−	3.62390i	0.280987	−	0.162228i	0.633870	+	0.773439i	$0.281465\pi$
$500$	−0.0312149	+	0.0180219i	−0.00139597	+	0.000805964i
$501$	2.55983	−	27.7142i	0.114365	−	1.23818i
$502$	8.69085	+	5.01766i	0.387892	+	0.223949i
$503$	−27.0218			−1.20484			−0.602420	−	0.798179i	$-0.705797\pi$
$503$	−27.0218			−1.20484			−0.602420	+	0.798179i	$0.705797\pi$
$504$	25.7511	+	4.79795i	1.14704	+	0.213718i
$505$			16.2100i			0.721337i
$506$	21.2383	−	36.7858i	0.944158	−	1.63533i
$507$	−11.3974	−	19.4191i	−0.506174	−	0.862431i
$508$	−0.352089	−	0.609836i	−0.0156214	−	0.0270571i
$509$	−26.9017	+	15.5317i	−1.19240	+	0.688430i	−0.958849	−	0.283915i	$-0.908366\pi$
$509$	−26.9017	+	15.5317i	−1.19240	+	0.688430i	−0.233547	+	0.972346i	$0.575033\pi$
$510$	7.29101	−	10.3062i	0.322851	−	0.456365i
$511$	11.7124	−	20.2864i	0.518125	−	0.897419i
$512$		−	21.9858i		−	0.971644i
$513$	3.48243	−	12.2808i	0.153753	−	0.542213i
$514$		−	0.618770i		−	0.0272928i
$515$	−13.2749	−	7.66426i	−0.584962	−	0.337728i
$516$	0.266758	−	0.377074i	0.0117433	−	0.0165997i
$517$	1.91199	+	3.31166i	0.0840891	+	0.145647i
$518$	43.6135	−	25.1802i	1.91627	−	1.10636i
$519$	11.6347	+	25.2692i	0.510707	+	1.10919i
$520$	−4.61177	+	8.99022i	−0.202240	+	0.394247i
$521$	4.61210			0.202060			0.101030	−	0.994883i	$-0.467786\pi$
$521$	4.61210			0.202060			0.101030	+	0.994883i	$0.467786\pi$
$522$	−6.10027	−	5.22014i	−0.267002	−	0.228479i
$523$	33.5698			1.46790			0.733951	−	0.679202i	$-0.237674\pi$
$523$	33.5698			1.46790			0.733951	+	0.679202i	$0.237674\pi$
$524$	−0.0974151	+	0.168728i	−0.00425560	+	0.00737091i
$525$	−0.496346	+	5.37372i	−0.0216623	+	0.234529i
$526$	16.2600	−	9.38770i	0.708968	−	0.409323i
$527$	2.82904	−	1.63335i	0.123235	−	0.0711496i
$528$	−2.46612	+	26.6996i	−0.107324	+	1.16195i
$529$	−19.1380	+	33.1480i	−0.832088	+	1.44122i
$530$	−3.00811			−0.130664
$531$	32.9215	+	28.1717i	1.42867	+	1.22255i
$532$	0.275887			0.0119612
$533$	22.7325	+	11.6612i	0.984654	+	0.505104i
$534$	−2.38712	−	5.18452i	−0.103301	−	0.224356i
$535$	9.74710	−	5.62749i	0.421404	−	0.243298i
$536$	1.02207	+	1.77028i	0.0441469	+	0.0764647i
$537$	−5.74166	+	8.11609i	−0.247771	+	0.350235i
$538$	−29.7232	−	17.1607i	−1.28146	−	0.739850i
$539$			10.2972i			0.443533i
$540$	−0.130498	−	0.134341i	−0.00561572	−	0.00578113i
$541$			10.2265i			0.439673i	0.975537	+	0.219837i	$0.0705524\pi$
$541$			10.2265i			0.439673i	−0.975537	+	0.219837i	$0.929448\pi$
$542$	−12.8647	+	22.2823i	−0.552586	+	0.957108i
$543$	−3.45664	+	4.88611i	−0.148339	+	0.209683i
$544$	0.901864	−	0.520691i	0.0386671	−	0.0223245i
$545$	−3.52200	−	6.10029i	−0.150866	−	0.261308i
$546$	−12.8485	−	24.6124i	−0.549864	−	1.05331i
$547$	−1.80249	+	3.12200i	−0.0770687	+	0.133487i	−0.901984	−	0.431769i	$-0.857889\pi$
$547$	−1.80249	+	3.12200i	−0.0770687	+	0.133487i	0.824915	+	0.565256i	$0.191223\pi$
$548$		−	0.303509i		−	0.0129653i
$549$	19.2973	+	3.59547i	0.823587	+	0.153451i
$550$	−5.42631			−0.231379
$551$	3.99036	+	2.30384i	0.169995	+	0.0981467i
$552$	3.49459	−	37.8344i	0.148739	−	1.61034i
$553$	39.6564	−	22.8956i	1.68636	−	0.973621i
$554$	25.9252	−	14.9679i	1.10145	−	0.635925i
$555$	19.5368	+	1.80452i	0.829290	+	0.0765976i
$556$	−0.0379342	+	0.0657040i	−0.00160877	+	0.00278647i
$557$			7.30287i			0.309433i	0.987959	+	0.154716i	$0.0494464\pi$
$557$			7.30287i			0.309433i	−0.987959	+	0.154716i	$0.950554\pi$
$558$	−0.911373	−	2.58142i	−0.0385815	−	0.109280i
$559$	26.6432	−	1.32323i	1.12689	−	0.0559667i
$560$	−6.34173	+	10.9842i	−0.267987	+	0.464167i
$561$	30.5617	−	14.0716i	1.29032	−	0.594103i
$562$	−16.6739	−	28.8800i	−0.703344	−	1.21823i
$563$	−9.97539	−	17.2779i	−0.420413	−	0.728176i	0.575567	−	0.817755i	$-0.304781\pi$
$563$	−9.97539	−	17.2779i	−0.420413	−	0.728176i	−0.995980	+	0.0895785i	$0.971448\pi$
$564$	−0.0512485	−	0.0362553i	−0.00215795	−	0.00152662i
$565$	1.18404	+	0.683608i	0.0498131	+	0.0287596i
$566$			1.45843i			0.0613025i
$567$	−27.7046	+	4.33412i	−1.16348	+	0.182016i
$568$	−28.9339			−1.21404
$569$	−8.62999	+	14.9476i	−0.361788	+	0.626635i	−0.988255	−	0.152813i	$-0.951167\pi$
$569$	−8.62999	+	14.9476i	−0.361788	+	0.626635i	0.626467	+	0.779448i	$0.284500\pi$
$570$	4.95656	+	3.50648i	0.207608	+	0.146870i
$571$	12.2674	+	21.2477i	0.513374	+	0.889190i	0.999880	+	0.0155125i	$0.00493799\pi$
$571$	12.2674	+	21.2477i	0.513374	+	0.889190i	−0.486506	+	0.873677i	$0.661729\pi$
$572$	0.415216	−	0.268032i	0.0173611	−	0.0112070i
$573$	16.1771	+	35.1347i	0.675808	+	1.46777i
$574$	27.2826	+	15.7516i	1.13875	+	0.657459i
$575$	7.82790			0.326446
$576$	7.84077	+	22.2086i	0.326699	+	0.925357i
$577$		−	18.7207i		−	0.779353i	−0.920952	−	0.389677i	$-0.872587\pi$
$577$		−	18.7207i		−	0.779353i	0.920952	−	0.389677i	$-0.127413\pi$
$578$	−11.2358	−	6.48699i	−0.467348	−	0.269823i
$579$	0.504114	−	5.45783i	0.0209503	−	0.226819i
$580$	0.0585467	−	0.0338020i	0.00243102	−	0.00140355i
$581$	−1.81242	−	3.13920i	−0.0751918	−	0.130236i
$582$	39.4705	+	3.64570i	1.63610	+	0.151119i
$583$	−6.94292	−	4.00850i	−0.287546	−	0.166015i
$584$	21.0689			0.871836
$585$	1.45136	−	10.7188i	0.0600062	−	0.443170i
$586$	11.8139			0.488028
$587$	5.49088	+	3.17016i	0.226633	+	0.130847i	0.609018	−	0.793157i	$-0.291564\pi$
$587$	5.49088	+	3.17016i	0.226633	+	0.130847i	−0.382385	+	0.924003i	$0.624897\pi$
$588$	−0.0706993	−	0.153550i	−0.00291559	−	0.00633230i
$589$	0.785528	+	1.36057i	0.0323671	+	0.0560615i
$590$	−17.8480	+	10.3045i	−0.734790	+	0.424231i
$591$	−0.794617	−	0.562145i	−0.0326862	−	0.0231235i
$592$	39.9343	+	23.0561i	1.64129	+	0.947599i
$593$		−	46.9160i		−	1.92661i	−0.268411	−	0.963304i	$-0.586499\pi$
$593$		−	46.9160i		−	1.92661i	0.268411	−	0.963304i	$-0.413501\pi$
$594$	−6.90163	−	27.3382i	−0.283177	−	1.12170i
$595$	15.9154			0.652466
$596$	0.0271392	+	0.0156688i	0.00111166	+	0.000641819i
$597$	−1.83692	+	2.59657i	−0.0751800	+	0.106270i
$598$	−33.8354	+	21.8416i	−1.38363	+	0.893169i
$599$	1.84932	+	3.20312i	0.0755613	+	0.130876i	0.901330	−	0.433133i	$-0.142592\pi$
$599$	1.84932	+	3.20312i	0.0755613	+	0.130876i	−0.825769	+	0.564009i	$0.809258\pi$
$600$	−4.40895	+	2.03002i	−0.179995	+	0.0828752i
$601$	13.4947	−	23.3735i	0.550460	−	0.953425i	−0.447781	−	0.894143i	$-0.647786\pi$
$601$	13.4947	−	23.3735i	0.550460	−	0.953425i	0.998241	−	0.0592818i	$-0.0188811\pi$
$602$	32.8929			1.34061
$603$	−1.66265	−	1.42277i	−0.0677085	−	0.0579397i
$604$			0.483132i			0.0196584i
$605$	−2.99800	−	1.73089i	−0.121886	−	0.0703709i
$606$	3.68470	−	39.8927i	0.149681	−	1.62053i
$607$	1.34991	+	2.33811i	0.0547911	+	0.0949010i	0.892120	−	0.451798i	$-0.149217\pi$
$607$	1.34991	+	2.33811i	0.0547911	+	0.0949010i	−0.837329	+	0.546699i	$0.815884\pi$
$608$	0.250417	+	0.433735i	0.0101557	+	0.0175903i
$609$	0.930948	−	10.0790i	0.0377239	−	0.408421i
$610$	−4.66819	+	8.08554i	−0.189009	+	0.327374i
$611$	−0.179842	−	3.62110i	−0.00727562	−	0.146494i
$612$	−0.359117	+	0.419665i	−0.0145164	+	0.0169639i
$613$			27.7909i			1.12246i	0.827659	+	0.561232i	$0.189672\pi$
$613$			27.7909i			1.12246i	−0.827659	+	0.561232i	$0.810328\pi$
$614$	−5.01264	+	8.68215i	−0.202294	+	0.350383i
$615$	5.13306	+	11.1484i	0.206985	+	0.449546i
$616$	−28.7559	+	16.6022i	−1.15861	+	0.668922i
$617$	−21.4742	+	12.3981i	−0.864518	+	0.499130i	−0.865523	−	0.500870i	$-0.833014\pi$
$617$	−21.4742	+	12.3981i	−0.864518	+	0.499130i	0.00100438	+	0.999999i	$0.499680\pi$
$618$	30.9272	+	21.8792i	1.24407	+	0.880110i
$619$	−13.2436	−	7.64617i	−0.532304	−	0.307326i	0.209650	−	0.977776i	$-0.432767\pi$
$619$	−13.2436	−	7.64617i	−0.532304	−	0.307326i	−0.741954	+	0.670451i	$0.766101\pi$
$620$	0.0230506			0.000925733
$621$	9.95618	+	39.4377i	0.399528	+	1.58258i
$622$		−	34.2482i		−	1.37323i
$623$	3.59778	−	6.23154i	0.144142	−	0.249661i
$624$	13.6345	−	21.4565i	0.545818	−	0.858947i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.31434	+	3.64559i	−0.252372	+	0.145707i
$627$	6.76747	+	14.6981i	0.270267	+	0.586986i
$628$	0.148998	−	0.258071i	0.00594565	−	0.0102982i
$629$		−	57.8621i		−	2.30711i
$630$	2.44300	−	13.1118i	0.0973315	−	0.522388i
$631$		−	41.4253i		−	1.64911i	−0.565779	−	0.824557i	$-0.691424\pi$
$631$		−	41.4253i		−	1.64911i	0.565779	−	0.824557i	$-0.308576\pi$
$632$	35.6680	+	20.5929i	1.41880	+	0.819143i
$633$	−28.1182	−	2.59715i	−1.11760	−	0.103227i
$634$	20.5643	+	35.6185i	0.816714	+	1.41459i
$635$	16.9193	−	9.76836i	0.671422	−	0.387646i
$636$	0.131053	+	0.0121048i	0.00519659	+	0.000479985i
$637$	4.45607	−	8.68670i	0.176556	−	0.344179i
$638$	10.1776			0.402935
$639$	29.2076	−	10.3118i	1.15543	−	0.407928i
$640$	−11.6099			−0.458920
$641$	1.51495	−	2.62398i	0.0598370	−	0.103641i	−0.834555	−	0.550924i	$-0.814275\pi$
$641$	1.51495	−	2.62398i	0.0598370	−	0.103641i	0.894392	+	0.447284i	$0.147609\pi$
$642$	−25.2667	+	11.6336i	−0.997197	+	0.459141i
$643$	12.2396	−	7.06653i	0.482682	−	0.278677i	−0.238852	−	0.971056i	$-0.576771\pi$
$643$	12.2396	−	7.06653i	0.482682	−	0.278677i	0.721533	+	0.692380i	$0.243438\pi$
$644$	−0.761318	+	0.439547i	−0.0300001	+	0.0173206i
$645$	10.4615	+	7.40092i	0.411923	+	0.291411i
$646$	8.95285	−	15.5068i	0.352245	−	0.610107i
$647$	2.49987			0.0982801			0.0491400	−	0.998792i	$-0.484352\pi$
$647$	2.49987			0.0982801			0.0491400	+	0.998792i	$0.484352\pi$
$648$	−15.8351	−	19.6307i	−0.622061	−	0.771168i
$649$	−54.9257			−2.15602
$650$	4.57761	+	2.34820i	0.179549	+	0.0921042i
$651$	1.99318	−	2.81745i	0.0781190	−	0.110425i
$652$	−0.113431	+	0.0654892i	−0.00444228	+	0.00256475i
$653$	−21.8454	−	37.8374i	−0.854878	−	1.48069i	−0.876758	−	0.480932i	$-0.840298\pi$
$653$	−21.8454	−	37.8374i	−0.854878	−	1.48069i	0.0218798	−	0.999761i	$-0.493035\pi$
$654$	7.28095	+	15.8133i	0.284708	+	0.618350i
$655$	−4.68119	−	2.70268i	−0.182909	−	0.105603i
$656$			28.8457i			1.12623i
$657$	−21.2681	+	7.50875i	−0.829749	+	0.292944i
$658$		−	4.47051i		−	0.174279i
$659$	−16.6112	+	28.7714i	−0.647079	+	1.12077i	0.336738	+	0.941598i	$0.390676\pi$
$659$	−16.6112	+	28.7714i	−0.647079	+	1.12077i	−0.983817	+	0.179176i	$0.942657\pi$
$660$	0.236406	+	0.0218357i	0.00920207	+	0.000849953i
$661$	−34.3879	+	19.8539i	−1.33753	+	0.772226i	−0.986441	−	0.164114i	$-0.947523\pi$
$661$	−34.3879	+	19.8539i	−1.33753	+	0.772226i	−0.351094	+	0.936340i	$0.614190\pi$
$662$	−18.1716	−	31.4742i	−0.706261	−	1.22328i
$663$	−31.8711	−	1.35470i	−1.23777	−	0.0526121i
$664$	1.63014	−	2.82348i	0.0632616	−	0.109572i
$665$			7.65420i			0.296817i
$666$	−47.6696	−	8.88181i	−1.84716	−	0.344163i
$667$	−14.6820			−0.568491
$668$	−0.501588	−	0.289592i	−0.0194070	−	0.0112047i
$669$	−14.8744	+	6.84865i	−0.575078	+	0.264784i
$670$	0.901387	−	0.520416i	0.0348236	−	0.0201054i
$671$	−21.5490	+	12.4413i	−0.831889	+	0.480291i
$672$	0.635403	−	0.898171i	0.0245112	−	0.0346477i
$673$	10.5676	−	18.3036i	0.407350	−	0.705551i	−0.587242	−	0.809412i	$-0.699786\pi$
$673$	10.5676	−	18.3036i	0.407350	−	0.705551i	0.994592	+	0.103860i	$0.0331195\pi$
$674$			35.6277i			1.37233i
$675$	3.72717	−	3.62053i	0.143459	−	0.139354i
$676$	−0.466264	+	0.0464284i	−0.0179332	+	0.00178571i
$677$	−15.2372	+	26.3915i	−0.585612	+	1.01431i	0.409187	+	0.912450i	$0.365812\pi$
$677$	−15.2372	+	26.3915i	−0.585612	+	1.01431i	−0.994799	+	0.101859i	$0.967521\pi$
$678$	−2.75853	−	1.95150i	−0.105941	−	0.0749467i
$679$	24.9857	+	43.2766i	0.958865	+	1.66080i
$680$	7.15736	+	12.3969i	0.274472	+	0.475400i
$681$	11.9058	−	5.48178i	0.456230	−	0.210062i
$682$	3.00529	+	1.73510i	0.115078	+	0.0664406i
$683$			44.2196i			1.69201i	0.533171	+	0.846007i	$0.321000\pi$
$683$			44.2196i			1.69201i	−0.533171	+	0.846007i	$0.679000\pi$
$684$	−0.201830	−	0.172711i	−0.00771717	−	0.00660375i
$685$	8.42056			0.321733
$686$	−9.54130	+	16.5260i	−0.364288	+	0.630966i
$687$	1.01719	−	11.0127i	0.0388082	−	0.420159i
$688$	15.0590	+	26.0830i	0.574121	+	0.994406i
$689$	4.12236	+	6.38606i	0.157049	+	0.243289i
$690$	−19.2644	−	1.77936i	−0.733382	−	0.0677391i
$691$	−17.1303	−	9.89018i	−0.651667	−	0.376240i	0.137428	−	0.990512i	$-0.456117\pi$
$691$	−17.1303	−	9.89018i	−0.651667	−	0.376240i	−0.789095	+	0.614272i	$0.789450\pi$
$692$	0.578911			0.0220069
$693$	23.1110	−	27.0075i	0.877913	−	1.02593i
$694$			0.313583i			0.0119035i
$695$	−1.82289	−	1.05245i	−0.0691462	−	0.0399216i
$696$	8.26944	−	3.80751i	0.313452	−	0.144323i
$697$	31.3466	−	18.0979i	1.18734	−	0.685508i
$698$	2.63578	+	4.56531i	0.0997658	+	0.172799i
$699$	−27.9800	+	39.5509i	−1.05830	+	1.49595i
$700$	0.0972570	+	0.0561513i	0.00367597	+	0.00212232i
$701$	4.94243			0.186673			0.0933364	−	0.995635i	$-0.470247\pi$
$701$	4.94243			0.186673			0.0933364	+	0.995635i	$0.470247\pi$
$702$	−6.00827	+	26.0490i	−0.226768	+	0.983157i
$703$	27.8277			1.04954
$704$	−25.8552	−	14.9275i	−0.974456	−	0.562603i
$705$	1.00587	−	1.42184i	0.0378832	−	0.0535496i
$706$	0.322702	+	0.558937i	0.0121451	+	0.0210359i
$707$	43.7395	−	25.2530i	1.64499	−	0.949737i
$708$	0.819041	−	0.377112i	0.0307814	−	0.0141727i
$709$	16.6026	+	9.58551i	0.623524	+	0.359992i	0.778240	−	0.627967i	$-0.216113\pi$
$709$	16.6026	+	9.58551i	0.623524	+	0.359992i	−0.154716	+	0.987959i	$0.549446\pi$
$710$			14.7325i			0.552900i
$711$	−43.3445	−	8.07596i	−1.62555	−	0.302872i
$712$	6.47188			0.242544
$713$	−4.33538	−	2.50303i	−0.162361	−	0.0937393i
$714$	−39.1675	−	3.61772i	−1.46581	−	0.135390i
$715$	7.43629	+	11.5198i	0.278102	+	0.430815i
$716$	0.103443	+	0.179168i	0.00386584	+	0.00669584i
$717$	−2.57758	+	27.9064i	−0.0962616	+	1.04218i
$718$	−8.45151	+	14.6385i	−0.315408	+	0.546302i
$719$	38.2210			1.42540			0.712701	−	0.701468i	$-0.247472\pi$
$719$	38.2210			1.42540			0.712701	+	0.701468i	$0.247472\pi$
$720$	11.5157	−	4.06565i	0.429166	−	0.151518i
$721$			47.7595i			1.77866i
$722$	−16.0212	−	9.24984i	−0.596247	−	0.344243i
$723$	−23.5266	+	10.8324i	−0.874965	+	0.402862i
$724$	0.0622756	+	0.107864i	0.00231445	+	0.00400875i
$725$	0.937802	+	1.62432i	0.0348291	+	0.0603257i
$726$	6.98458	+	4.94118i	0.259222	+	0.183385i
$727$	−2.99903	+	5.19447i	−0.111228	+	0.192652i	−0.916266	−	0.400571i	$-0.868812\pi$
$727$	−2.99903	+	5.19447i	−0.111228	+	0.192652i	0.805038	+	0.593224i	$0.202145\pi$
$728$	31.4428	−	1.56160i	1.16535	−	0.0578769i
$729$	22.9810	+	14.1729i	0.851150	+	0.524923i
$730$		−	10.7278i		−	0.397053i
$731$	18.8963	−	32.7293i	0.698904	−	1.21054i
$732$	0.235913	−	0.333474i	0.00871961	−	0.0123256i
$733$	29.8573	−	17.2381i	1.10281	−	0.636705i	0.165850	−	0.986151i	$-0.446963\pi$
$733$	29.8573	−	17.2381i	1.10281	−	0.636705i	0.936957	+	0.349446i	$0.113630\pi$
$734$	−24.3417	+	14.0537i	−0.898467	+	0.518730i
$735$	4.26010	−	1.96148i	0.157136	−	0.0723503i
$736$	−1.38207	−	0.797937i	−0.0509437	−	0.0294123i
$737$	2.77395			0.102180
$738$	−10.0983	−	28.6028i	−0.371723	−	1.05288i
$739$		−	0.921698i		−	0.0339052i	−0.999856	−	0.0169526i	$-0.994604\pi$
$739$		−	0.921698i		−	0.0339052i	0.999856	−	0.0169526i	$-0.00539644\pi$
$740$	0.204144	−	0.353589i	0.00750450	−	0.0129982i
$741$	0.651517	−	15.3278i	0.0239341	−	0.563082i
$742$	4.68623	+	8.11679i	0.172037	+	0.297977i
$743$	−27.8850	+	16.0994i	−1.02300	+	0.590630i	−0.914972	−	0.403518i	$-0.867787\pi$
$743$	−27.8850	+	16.0994i	−1.02300	+	0.590630i	−0.108029	+	0.994148i	$0.534454\pi$
$744$	3.09095	+	0.285497i	0.113320	+	0.0104668i
$745$	−0.434715	+	0.752949i	−0.0159267	+	0.0275859i
$746$		−	13.9829i		−	0.511950i
$747$	−0.639293	+	3.43115i	−0.0233905	+	0.125539i
$748$		−	0.700163i		−	0.0256005i
$749$	−30.3693	−	17.5337i	−1.10967	−	0.640669i
$750$	1.03364	+	2.24493i	0.0377431	+	0.0819734i
$751$	−6.58671	−	11.4085i	−0.240352	−	0.416303i	0.720462	−	0.693494i	$-0.243930\pi$
$751$	−6.58671	−	11.4085i	−0.240352	−	0.416303i	−0.960815	+	0.277192i	$0.910596\pi$
$752$	3.54498	−	2.04669i	0.129272	−	0.0746352i
$753$	7.03518	−	9.94454i	0.256376	−	0.362399i
$754$	−8.58578	−	4.40430i	−0.312676	−	0.160395i
$755$	−13.4040			−0.487823
$756$	−0.159196	+	0.561407i	−0.00578989	+	0.0204182i
$757$	44.5520			1.61927			0.809636	−	0.586932i	$-0.199665\pi$
$757$	44.5520			1.61927			0.809636	+	0.586932i	$0.199665\pi$
$758$	8.42218	−	14.5876i	0.305907	−	0.529847i
$759$	−42.0923	−	29.7779i	−1.52785	−	1.08087i
$760$	−5.96206	+	3.44220i	−0.216267	+	0.124862i
$761$	10.5493	−	6.09063i	0.382411	−	0.220785i	−0.296456	−	0.955047i	$-0.595805\pi$
$761$	10.5493	−	6.09063i	0.382411	−	0.220785i	0.678867	+	0.734261i	$0.262471\pi$
$762$	−43.8586	+	20.1939i	−1.58883	+	0.731548i
$763$	−10.9736	+	19.0068i	−0.397271	+	0.688093i
$764$	0.804927			0.0291213
$765$	−11.6432	−	9.96333i	−0.420960	−	0.360225i
$766$	−35.7858			−1.29299
$767$	46.3351	+	23.7688i	1.67306	+	0.858242i
$768$	1.49148	+	0.137761i	0.0538192	+	0.00497103i
$769$	−10.4500	+	6.03331i	−0.376836	+	0.217567i	−0.676441	−	0.736497i	$-0.736479\pi$
$769$	−10.4500	+	6.03331i	−0.376836	+	0.217567i	0.299605	+	0.954063i	$0.403145\pi$
$770$	8.45345	+	14.6418i	0.304641	+	0.527654i
$771$	−0.747914	−	0.0690814i	−0.0269355	−	0.00248790i
$772$	−0.0987791	−	0.0570301i	−0.00355514	−	0.00205256i
$773$			9.70024i			0.348893i	0.984667	+	0.174447i	$0.0558137\pi$
$773$			9.70024i			0.348893i	−0.984667	+	0.174447i	$0.944186\pi$
$774$	−24.0634	−	20.5916i	−0.864941	−	0.740150i
$775$			0.639515i			0.0229721i
$776$	−22.4729	+	38.9241i	−0.806728	+	1.39729i
$777$	−25.5665	−	55.5273i	−0.917193	−	1.99203i
$778$	17.1180	−	9.88310i	0.613711	−	0.354326i
$779$	8.70387	+	15.0756i	0.311849	+	0.540138i
$780$	−0.189981	−	0.120724i	−0.00680242	−	0.00432260i
$781$	−19.6319	+	34.0035i	−0.702486	+	1.21674i
$782$			57.0553i			2.04029i
$783$	−6.99069	+	6.79067i	−0.249827	+	0.242679i
$784$	11.0227			0.393668
$785$	7.15993	+	4.13379i	0.255549	+	0.147541i
$786$	10.9060	+	7.71535i	0.389004	+	0.275198i
$787$	−21.4458	+	12.3817i	−0.764460	+	0.441361i	−0.830895	−	0.556430i	$-0.812171\pi$
$787$	−21.4458	+	12.3817i	−0.764460	+	0.441361i	0.0664347	+	0.997791i	$0.478838\pi$
$788$	−0.0175417	+	0.0101277i	−0.000624898	+	0.000360785i
$789$	−9.53170	−	20.7017i	−0.339337	−	0.736999i
$790$	10.4854	−	18.1613i	0.373055	−	0.646151i
$791$		−	4.25987i		−	0.151464i
$792$	31.4302	+	5.85608i	1.11682	+	0.208087i
$793$	23.5625	−	1.17023i	0.836729	−	0.0415561i
$794$	26.1124	−	45.2280i	0.926694	−	1.60508i
$795$	−0.335835	+	3.63594i	−0.0119108	+	0.128953i
$796$	0.0330943	+	0.0573210i	0.00117300	+	0.00203169i
$797$	−11.0989	−	19.2238i	−0.393142	−	0.680942i	0.599720	−	0.800210i	$-0.295279\pi$
$797$	−11.0989	−	19.2238i	−0.393142	−	0.680942i	−0.992862	+	0.119268i	$0.961945\pi$
$798$	1.73988	−	18.8369i	0.0615910	−	0.666819i
$799$	−4.44828	−	2.56822i	−0.157369	−	0.0908569i
$800$			0.203870i			0.00720789i
$801$	−6.53309	+	2.30652i	−0.230835	+	0.0814968i
$802$	−26.4621			−0.934410
$803$	14.2954	−	24.7604i	0.504474	−	0.873775i
$804$	−0.0413645	+	0.0190455i	−0.00145881	+	0.000671683i
$805$	−12.1948	−	21.1220i	−0.429810	−	0.744453i
$806$	−1.78439	−	2.76425i	−0.0628525	−	0.0973664i
$807$	−24.0607	+	34.0109i	−0.846977	+	1.19724i
$808$	39.3405	+	22.7132i	1.38399	+	0.799049i
$809$	15.3773			0.540638			0.270319	−	0.962771i	$-0.412871\pi$
$809$	15.3773			0.540638			0.270319	+	0.962771i	$0.412871\pi$
$810$	−9.99550	+	8.06285i	−0.351206	+	0.283300i
$811$			42.8200i			1.50361i	0.659384	+	0.751806i	$0.270817\pi$
$811$			42.8200i			1.50361i	−0.659384	+	0.751806i	$0.729183\pi$
$812$	−0.182416	−	0.105318i	−0.00640153	−	0.00369593i
$813$	25.4966	+	18.0374i	0.894206	+	0.632598i
$814$	53.2319	−	30.7335i	1.86578	−	1.07721i
$815$	−1.81693	−	3.14702i	−0.0636444	−	0.110235i
$816$	−15.0630	−	32.7149i	−0.527309	−	1.14525i
$817$	15.7406	+	9.08782i	0.550693	+	0.317942i
$818$	6.63298			0.231917
$819$	−31.1837	+	12.7823i	−1.08965	+	0.446650i
$820$	0.255407			0.00891920
$821$	−27.4876	−	15.8700i	−0.959325	−	0.553867i	−0.0633598	−	0.997991i	$-0.520182\pi$
$821$	−27.4876	−	15.8700i	−0.959325	−	0.553867i	−0.895965	+	0.444124i	$0.853515\pi$
$822$	−20.7229	−	1.91408i	−0.722794	−	0.0667611i
$823$	−27.5172	−	47.6613i	−0.959191	−	1.66137i	−0.724472	−	0.689304i	$-0.757916\pi$
$823$	−27.5172	−	47.6613i	−0.959191	−	1.66137i	−0.234719	−	0.972063i	$-0.575417\pi$
$824$	−37.2012	+	21.4781i	−1.29596	+	0.748225i
$825$	−0.605809	+	6.55884i	−0.0210916	+	0.228349i
$826$	55.6094	+	32.1061i	1.93490	+	1.11711i
$827$			42.4890i			1.47749i	0.673986	+	0.738744i	$0.264581\pi$
$827$			42.4890i			1.47749i	−0.673986	+	0.738744i	$0.735419\pi$
$828$	0.832122	+	0.155041i	0.0289182	+	0.00538805i
$829$	−1.75047			−0.0607964			−0.0303982	−	0.999538i	$-0.509678\pi$
$829$	−1.75047			−0.0607964			−0.0303982	+	0.999538i	$0.509678\pi$
$830$	−1.43765	−	0.830027i	−0.0499016	−	0.0288107i
$831$	−15.1975	−	33.0071i	−0.527195	−	1.14500i
$832$	15.3516	+	23.7815i	0.532219	+	0.824475i
$833$	−6.91571	−	11.9784i	−0.239615	−	0.415026i
$834$	4.24688	+	3.00442i	0.147058	+	0.104035i
$835$	8.03445	−	13.9161i	0.278043	−	0.481585i
$836$	0.336730			0.0116461
$837$	−3.22193	+	0.813389i	−0.111366	+	0.0281148i
$838$			53.0797i			1.83361i
$839$	5.89152	+	3.40147i	0.203398	+	0.117432i	0.598239	−	0.801317i	$-0.295867\pi$
$839$	5.89152	+	3.40147i	0.203398	+	0.117432i	−0.394841	+	0.918749i	$0.629200\pi$
$840$	12.3461	+	8.73417i	0.425982	+	0.301358i
$841$	12.7411	+	22.0682i	0.439347	+	0.760971i
$842$	7.77127	+	13.4602i	0.267816	+	0.463870i
$843$	−36.7690	+	16.9296i	−1.26639	+	0.583087i
$844$	−0.293814	+	0.508901i	−0.0101135	+	0.0175171i
$845$	−1.28811	−	12.9360i	−0.0443123	−	0.445013i
$846$	−2.79863	+	3.27049i	−0.0962188	+	0.112442i
$847$			10.7860i			0.370611i
$848$	−4.29091	+	7.43207i	−0.147350	+	0.255218i
$849$	1.76282	+	0.162824i	0.0604999	+	0.00558810i
$850$	6.31221	−	3.64436i	0.216507	−	0.125000i
$851$	−76.7915	+	44.3356i	−2.63238	+	1.51980i
$852$	0.0592840	−	0.641843i	0.00203104	−	0.0219892i
$853$	−33.2242	−	19.1820i	−1.13758	−	0.656779i	−0.191746	−	0.981445i	$-0.561415\pi$
$853$	−33.2242	−	19.1820i	−1.13758	−	0.656779i	−0.945829	+	0.324665i	$0.894748\pi$
$854$	29.0896			0.995426
$855$	4.79168	−	5.59958i	0.163872	−	0.191502i
$856$		−	31.5406i		−	1.07804i
$857$	19.0047	−	32.9172i	0.649190	−	1.12443i	−0.334127	−	0.942528i	$-0.608441\pi$
$857$	19.0047	−	32.9172i	0.649190	−	1.12443i	0.983317	−	0.181902i	$-0.0582253\pi$
$858$	−15.6821	−	30.0403i	−0.535377	−	1.02556i
$859$	−4.58973	−	7.94965i	−0.156600	−	0.271238i	0.777041	−	0.629450i	$-0.216720\pi$
$859$	−4.58973	−	7.94965i	−0.156600	−	0.271238i	−0.933640	+	0.358212i	$0.883387\pi$
$860$	0.230946	−	0.133337i	0.00787519	−	0.00454674i
$861$	22.0850	−	31.2182i	0.752656	−	1.06391i
$862$	−16.8123	+	29.1197i	−0.572629	+	0.991822i
$863$			50.4670i			1.71792i	0.512047	+	0.858958i	$0.328887\pi$
$863$			50.4670i			1.71792i	−0.512047	+	0.858958i	$0.671113\pi$
$864$	−1.02711	+	0.259299i	−0.0349431	+	0.00882152i
$865$			16.0613i			0.546101i
$866$	17.4513	+	10.0755i	0.593018	+	0.342379i
$867$	−9.09529	+	12.8566i	−0.308892	+	0.436633i
$868$	−0.0359096	−	0.0621973i	−0.00121885	−	0.00211111i
$869$	48.4022	−	27.9450i	1.64193	−	0.947969i
$870$	−1.93869	−	4.21060i	−0.0657279	−	0.142753i
$871$	−2.34009	−	1.20041i	−0.0792909	−	0.0406743i
$872$	−19.7399			−0.668477
$873$	8.81320	−	47.3014i	0.298282	−	1.60091i
$874$	−27.4397			−0.928162
$875$	−1.55786	+	2.69830i	−0.0526654	+	0.0912192i
$876$	−0.0431690	+	0.467372i	−0.00145854	+	0.0157910i
$877$	49.1440	−	28.3733i	1.65948	−	0.958099i	0.686519	−	0.727111i	$-0.259138\pi$
$877$	49.1440	−	28.3733i	1.65948	−	0.958099i	0.972957	−	0.230988i	$-0.0741957\pi$
$878$	−12.8783	+	7.43531i	−0.434623	+	0.250930i
$879$	1.31894	−	14.2796i	0.0444868	−	0.481639i
$880$	−7.74033	+	13.4066i	−0.260927	+	0.451938i
$881$	−5.18712			−0.174759			−0.0873793	−	0.996175i	$-0.527849\pi$
$881$	−5.18712			−0.174759			−0.0873793	+	0.996175i	$0.527849\pi$
$882$	−10.9299	+	3.85882i	−0.368029	+	0.129933i
$883$	−35.8353			−1.20595			−0.602977	−	0.797758i	$-0.706019\pi$
$883$	−35.8353			−1.20595			−0.602977	+	0.797758i	$0.706019\pi$
$884$	−0.302991	+	0.590654i	−0.0101907	+	0.0198658i
$885$	10.4626	+	22.7235i	0.351697	+	0.763841i
$886$	4.29237	−	2.47820i	0.144205	−	0.0832569i
$887$	−3.54606	−	6.14195i	−0.119065	−	0.206227i	0.800332	−	0.599557i	$-0.204656\pi$
$887$	−3.54606	−	6.14195i	−0.119065	−	0.206227i	−0.919397	+	0.393330i	$0.871323\pi$
$888$	31.7541	−	44.8858i	1.06560	−	1.50627i
$889$	−52.7159	−	30.4355i	−1.76804	−	1.02078i
$890$		−	3.29533i		−	0.110460i
$891$	−33.8145	+	5.28996i	−1.13283	+	0.177220i
$892$			0.340769i			0.0114098i
$893$	1.23514	−	2.13932i	0.0413323	−	0.0715896i
$894$	1.24098	−	1.75418i	0.0415047	−	0.0586687i
$895$	−4.97085	+	2.86992i	−0.166157	+	0.0959309i
$896$	18.0866	+	31.3269i	0.604231	+	1.04656i
$897$	22.6227	+	43.3357i	0.755350	+	1.44694i
$898$	−1.22616	+	2.12377i	−0.0409175	+	0.0708711i
$899$		−	1.19948i		−	0.0400048i
$900$	−0.0359983	−	0.101963i	−0.00119994	−	0.00339878i
$901$	10.7686			0.358753
$902$	33.2995	+	19.2255i	1.10875	+	0.640137i
$903$	3.67226	−	39.7580i	0.122205	−	1.32306i
$904$	3.31813	−	1.91572i	0.110359	−	0.0637159i
$905$	−2.99259	+	1.72777i	−0.0994771	+	0.0574331i
$906$	32.9872	+	3.04687i	1.09593	+	0.101226i
$907$	7.47394	−	12.9453i	0.248168	−	0.429840i	−0.714849	−	0.699278i	$-0.753505\pi$
$907$	7.47394	−	12.9453i	0.248168	−	0.429840i	0.963018	+	0.269438i	$0.0868381\pi$
$908$		−	0.272758i		−	0.00905180i
$909$	−47.8073	−	8.90748i	−1.58567	−	0.295442i
$910$	−0.795132	−	16.0099i	−0.0263584	−	0.530724i
$911$	9.47921	−	16.4185i	0.314060	−	0.543968i	−0.665177	−	0.746686i	$-0.731644\pi$
$911$	9.47921	−	16.4185i	0.314060	−	0.543968i	0.979237	+	0.202717i	$0.0649773\pi$
$912$	15.7336	−	7.24426i	0.520993	−	0.239881i
$913$	−2.21213	−	3.83152i	−0.0732107	−	0.126805i
$914$	−13.6801	−	23.6947i	−0.452498	−	0.783750i
$915$	9.25191	+	6.54518i	0.305859	+	0.216377i
$916$	−0.199314	−	0.115074i	−0.00658552	−	0.00380215i
$917$			16.8417i			0.556160i
$918$	26.3890	+	27.1663i	0.870966	+	0.896620i
$919$	36.3122			1.19783			0.598914	−	0.800813i	$-0.295599\pi$
$919$	36.3122			1.19783			0.598914	+	0.800813i	$0.295599\pi$
$920$	10.9683	−	18.9977i	0.361615	−	0.626336i
$921$	9.93459	+	7.02814i	0.327356	+	0.231585i
$922$	7.43571	+	12.8790i	0.244882	+	0.424148i
$923$	31.2762	−	20.1896i	1.02947	−	0.664548i
$924$	−0.309368	−	0.671910i	−0.0101775	−	0.0221042i
$925$	9.80997	+	5.66379i	0.322550	+	0.186224i
$926$	−18.4737			−0.607084
$927$	29.8984	−	34.9394i	0.981992	−	1.14756i
$928$		−	0.382379i		−	0.0125522i
$929$	29.9694	+	17.3028i	0.983263	+	0.567687i	0.903254	−	0.429107i	$-0.141172\pi$
$929$	29.9694	+	17.3028i	0.983263	+	0.567687i	0.0800095	+	0.996794i	$0.474505\pi$
$930$	0.145368	−	1.57384i	0.00476681	−	0.0516082i
$931$	5.76077	−	3.32598i	0.188802	−	0.109005i
$932$	0.504094	+	0.873116i	0.0165121	+	0.0285999i
$933$	−41.3961	−	3.82357i	−1.35525	−	0.125178i
$934$	−32.3989	−	18.7055i	−1.06012	−	0.612062i
$935$	19.4253			0.635276
$936$	−23.9802	−	18.5414i	−0.783817	−	0.606045i
$937$	−7.88541			−0.257605			−0.128803	−	0.991670i	$-0.541113\pi$
$937$	−7.88541			−0.257605			−0.128803	+	0.991670i	$0.541113\pi$
$938$	−2.80848	−	1.62147i	−0.0917000	−	0.0529430i
$939$	3.70151	+	8.03922i	0.120794	+	0.262350i
$940$	−0.0181219	−	0.0313881i	−0.000591073	−	0.00102377i
$941$	8.47754	−	4.89451i	0.276360	−	0.159557i	−0.355414	−	0.934709i	$-0.615660\pi$
$941$	8.47754	−	4.89451i	0.276360	−	0.159557i	0.631774	+	0.775152i	$0.282327\pi$
$942$	−16.6809	−	11.8007i	−0.543492	−	0.384489i
$943$	−48.0372	−	27.7343i	−1.56431	−	0.903153i
$944$			58.7954i			1.91363i
$945$	−15.5757	−	4.41673i	−0.506677	−	0.143676i
$946$	40.1470			1.30529
$947$	9.98102	+	5.76254i	0.324340	+	0.187258i	0.653325	−	0.757077i	$-0.273373\pi$
$947$	9.98102	+	5.76254i	0.324340	+	0.187258i	−0.328986	+	0.944335i	$0.606707\pi$
$948$	−0.529896	+	0.749032i	−0.0172102	+	0.0243274i
$949$	−22.7745	+	14.7015i	−0.739290	+	0.477230i
$950$	1.75269	+	3.03574i	0.0568647	+	0.0984925i
$951$	45.3483	−	20.8798i	1.47052	−	0.677073i
$952$	22.3004	−	38.6254i	0.722759	−	1.25186i
$953$	−12.5378			−0.406140			−0.203070	−	0.979164i	$-0.565092\pi$
$953$	−12.5378			−0.406140			−0.203070	+	0.979164i	$0.565092\pi$
$954$	1.65297	−	8.87166i	0.0535169	−	0.287231i
$955$			22.3319i			0.722644i
$956$	0.505067	+	0.291601i	0.0163350	+	0.00943104i
$957$	1.13626	−	12.3018i	0.0367300	−	0.397660i
$958$	−13.3703	−	23.1581i	−0.431976	−	0.748204i
$959$	−13.1181	−	22.7212i	−0.423605	−	0.733705i
$960$	−1.25064	+	13.5401i	−0.0403642	+	0.437006i
$961$	−15.2955	+	26.4926i	−0.493404	+	0.854600i
$962$	−58.2059	+	2.89079i	−1.87663	+	0.0932029i
$963$	11.2408	+	31.8389i	0.362229	+	1.02600i
$964$			0.538990i			0.0173597i
$965$	1.58225	−	2.74053i	0.0509343	−	0.0882207i
$966$	25.2100	+	54.7530i	0.811119	+	1.76165i
$967$	50.0039	−	28.8698i	1.60802	−	0.928389i	0.618204	−	0.786018i	$-0.287861\pi$
$967$	50.0039	−	28.8698i	1.60802	−	0.928389i	0.989813	−	0.142372i	$-0.0454728\pi$
$968$	−8.40149	+	4.85061i	−0.270034	+	0.155904i
$969$	−17.7437	−	12.5526i	−0.570010	−	0.403249i
$970$	19.8192	+	11.4426i	0.636357	+	0.367401i
$971$	−28.1560			−0.903569			−0.451785	−	0.892127i	$-0.649212\pi$
$971$	−28.1560			−0.903569			−0.451785	+	0.892127i	$0.649212\pi$
$972$	0.467915	−	0.311048i	0.0150084	−	0.00997688i
$973$			6.55828i			0.210249i
$974$	−14.7908	+	25.6184i	−0.473927	+	0.820866i
$975$	3.34936	−	5.27084i	0.107265	−	0.168802i
$976$	13.3178	+	23.0672i	0.426293	+	0.738362i
$977$	−26.7499	+	15.4441i	−0.855806	+	0.494100i	−0.862605	−	0.505877i	$-0.831169\pi$
$977$	−26.7499	+	15.4441i	−0.855806	+	0.494100i	0.00679992	+	0.999977i	$0.497836\pi$
$978$	3.75610	+	8.15778i	0.120107	+	0.260857i
$979$	4.39123	−	7.60583i	0.140344	−	0.243083i
$980$		−	0.0975978i		−	0.00311765i
$981$	19.9266	−	7.03511i	0.636207	−	0.224614i
$982$			13.5412i			0.432116i
$983$	−21.9648	−	12.6814i	−0.700567	−	0.404472i	0.106992	−	0.994260i	$-0.465878\pi$
$983$	−21.9648	−	12.6814i	−0.700567	−	0.404472i	−0.807558	+	0.589787i	$0.799212\pi$
$984$	34.2486	+	3.16339i	1.09181	+	0.100845i
$985$	−0.280984	−	0.486678i	−0.00895289	−	0.0155069i
$986$	−11.8392	+	6.83537i	−0.377037	+	0.217682i
$987$	−5.40355	−	0.499101i	−0.171997	−	0.0158866i
$988$	−0.284064	−	0.145718i	−0.00903729	−	0.00463591i
$989$	−57.9154			−1.84160
$990$	2.98178	−	16.0035i	0.0947672	−	0.508625i
$991$	−51.1157			−1.62374			−0.811871	−	0.583836i	$-0.801551\pi$
$991$	−51.1157			−1.62374			−0.811871	+	0.583836i	$0.801551\pi$
$992$	0.0651889	−	0.112911i	0.00206975	−	0.00358491i
$993$	−40.0719	+	18.4504i	−1.27164	+	0.585505i
$994$	39.7526	−	22.9512i	1.26088	−	0.727967i
$995$	−1.59032	+	0.918169i	−0.0504164	+	0.0291079i
$996$	0.0592934	+	0.0419466i	0.00187878	+	0.00132913i
$997$	−11.3887	+	19.7258i	−0.360684	+	0.624723i	−0.988074	−	0.153982i	$-0.950790\pi$
$997$	−11.3887	+	19.7258i	−0.360684	+	0.624723i	0.627389	+	0.778706i	$0.284123\pi$
$998$	−10.3419			−0.327367
$999$	−16.0575	+	56.6271i	−0.508037	+	1.79160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.14	✓	108
9.4	even	3	inner	585.2.bt.b.571.41	yes	108
13.12	even	2	inner	585.2.bt.b.376.41	yes	108
117.103	even	6	inner	585.2.bt.b.571.14	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.14	✓	108	1.1	even	1	trivial
585.2.bt.b.376.41	yes	108	13.12	even	2	inner
585.2.bt.b.571.14	yes	108	117.103	even	6	inner
585.2.bt.b.571.41	yes	108	9.4	even	3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23573 - 0.713450i) q^{2} +(-1.00032 + 1.41399i) q^{3} +(0.0180219 + 0.0312149i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.24493 - 1.03364i) q^{6} +(2.69830 + 1.55786i) q^{7} +2.80237i q^{8} +(-0.998738 - 2.82887i) q^{9} +O(q^{10})\)	\(q+(-1.23573 - 0.713450i) q^{2} +(-1.00032 + 1.41399i) q^{3} +(0.0180219 + 0.0312149i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.24493 - 1.03364i) q^{6} +(2.69830 + 1.55786i) q^{7} +2.80237i q^{8} +(-0.998738 - 2.82887i) q^{9} +1.42690 q^{10} +(3.29338 + 1.90143i) q^{11} +(-0.0621651 - 0.00574190i) q^{12} +(-1.95544 - 3.02923i) q^{13} +(-2.22292 - 3.85020i) q^{14} +(0.159303 - 1.72471i) q^{15} +(2.03539 - 3.52541i) q^{16} -5.10807 q^{17} +(-0.784087 + 4.20828i) q^{18} -2.45663i q^{19} +(-0.0312149 - 0.0180219i) q^{20} +(-4.90195 + 2.25701i) q^{21} +(-2.71315 - 4.69932i) q^{22} +(3.91395 + 6.77916i) q^{23} +(-3.96252 - 2.80325i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.255200 + 5.13843i) q^{26} +(4.99905 + 1.41756i) q^{27} +0.112303i q^{28} +(-0.937802 + 1.62432i) q^{29} +(-1.42735 + 2.01762i) q^{30} +(-0.553836 + 0.319758i) q^{31} +(-0.176557 + 0.101935i) q^{32} +(-5.98303 + 2.75477i) q^{33} +(6.31221 + 3.64436i) q^{34} -3.11573 q^{35} +(0.0703037 - 0.0821571i) q^{36} +11.3276i q^{37} +(-1.75269 + 3.03574i) q^{38} +(6.23936 + 0.265207i) q^{39} +(-1.40118 - 2.42692i) q^{40} +(-6.13667 + 3.54301i) q^{41} +(7.66777 + 0.708236i) q^{42} +(-3.69930 + 6.40737i) q^{43} +0.137070i q^{44} +(2.27937 + 1.95051i) q^{45} -11.1696i q^{46} +(0.870833 + 0.502776i) q^{47} +(2.94885 + 6.40455i) q^{48} +(1.35388 + 2.34499i) q^{49} +(-1.23573 + 0.713450i) q^{50} +(5.10969 - 7.22277i) q^{51} +(0.0593162 - 0.115631i) q^{52} -2.10815 q^{53} +(-5.16613 - 5.31830i) q^{54} -3.80287 q^{55} +(-4.36571 + 7.56163i) q^{56} +(3.47366 + 2.45741i) q^{57} +(2.31774 - 1.33815i) q^{58} +(-12.5082 + 7.22162i) q^{59} +(0.0567075 - 0.0261099i) q^{60} +(-3.27156 + 5.66651i) q^{61} +0.912524 q^{62} +(1.71210 - 9.18904i) q^{63} -7.85067 q^{64} +(3.20808 + 1.64567i) q^{65} +(9.35881 + 0.864429i) q^{66} +(0.631710 - 0.364718i) q^{67} +(-0.0920572 - 0.159448i) q^{68} +(-13.5009 - 1.24701i) q^{69} +(3.85020 + 2.22292i) q^{70} +10.3248i q^{71} +(7.92755 - 2.79883i) q^{72} -7.51823i q^{73} +(8.08166 - 13.9978i) q^{74} +(0.724394 + 1.57329i) q^{75} +(0.0766835 - 0.0442732i) q^{76} +(5.92435 + 10.2613i) q^{77} +(-7.52097 - 4.77920i) q^{78} +(7.34841 - 12.7278i) q^{79} +4.07079i q^{80} +(-7.00505 + 5.65061i) q^{81} +10.1110 q^{82} +(-1.00753 - 0.581700i) q^{83} +(-0.158795 - 0.112338i) q^{84} +(4.42372 - 2.55404i) q^{85} +(9.14267 - 5.27852i) q^{86} +(-1.35868 - 2.95088i) q^{87} +(-5.32852 + 9.22926i) q^{88} -2.30943i q^{89} +(-1.42510 - 4.03652i) q^{90} +(-0.557245 - 11.2201i) q^{91} +(-0.141074 + 0.244347i) q^{92} +(0.101877 - 1.10298i) q^{93} +(-0.717411 - 1.24259i) q^{94} +(1.22832 + 2.12751i) q^{95} +(0.0324772 - 0.351616i) q^{96} +(13.8897 + 8.01923i) q^{97} -3.86370i q^{98} +(2.08969 - 11.2156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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