LMFDB - Embedded newform 585.2.bt.b.571.29

Newspace parameters

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

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			571.29
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.29

$q$-expansion

$f(q)$	$=$	$q+(0.146304 - 0.0844686i) q^{2} +(-0.106608 - 1.72877i) q^{3} +(-0.985730 + 1.70733i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.161624 - 0.243920i) q^{6} +(1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 + 0.368601i) q^{9} +O(q^{10})$	\(q+(0.146304 - 0.0844686i) q^{2} +(-0.106608 - 1.72877i) q^{3} +(-0.985730 + 1.70733i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.161624 - 0.243920i) q^{6} +(1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 + 0.368601i) q^{9} -0.168937 q^{10} +(-3.52392 + 2.03454i) q^{11} +(3.05667 + 1.52208i) q^{12} +(-3.53584 + 0.705562i) q^{13} +(0.161810 - 0.280264i) q^{14} +(-0.772058 + 1.55046i) q^{15} +(-1.91479 - 3.31651i) q^{16} -0.709628 q^{17} +(-0.404451 + 0.305414i) q^{18} -6.45837i q^{19} +(1.70733 - 0.985730i) q^{20} +(-1.83270 - 2.76588i) q^{21} +(-0.343709 + 0.595322i) q^{22} +(-4.18851 + 7.25472i) q^{23} +(1.15988 - 0.0715262i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.457710 + 0.401894i) q^{26} +(0.954626 + 5.10771i) q^{27} +3.77659i q^{28} +(3.53514 + 6.12304i) q^{29} +(0.0180101 + 0.292053i) q^{30} +(-4.30244 - 2.48401i) q^{31} +(-1.72236 - 0.994406i) q^{32} +(3.89292 + 5.87515i) q^{33} +(-0.103821 + 0.0599413i) q^{34} -1.91563 q^{35} +(2.30546 - 5.44654i) q^{36} +5.73681i q^{37} +(-0.545529 - 0.944885i) q^{38} +(1.59670 + 6.03743i) q^{39} +(0.335464 - 0.581040i) q^{40} +(-9.47008 - 5.46755i) q^{41} +(-0.501761 - 0.249854i) q^{42} +(-4.35016 - 7.53470i) q^{43} -8.02202i q^{44} +(2.76269 + 1.16942i) q^{45} +1.41519i q^{46} +(-2.97238 + 1.71611i) q^{47} +(-5.52934 + 3.66379i) q^{48} +(-1.66518 + 2.88418i) q^{49} +(0.146304 + 0.0844686i) q^{50} +(0.0756520 + 1.22678i) q^{51} +(2.28076 - 6.73236i) q^{52} +1.83872 q^{53} +(0.571107 + 0.666642i) q^{54} +4.06908 q^{55} +(0.642624 + 1.11306i) q^{56} +(-11.1650 + 0.688514i) q^{57} +(1.03441 + 0.597217i) q^{58} +(8.61560 + 4.97422i) q^{59} +(-1.88611 - 2.84650i) q^{60} +(1.50640 + 2.60916i) q^{61} -0.839285 q^{62} +(-4.58619 + 3.46317i) q^{63} +7.32317 q^{64} +(3.41491 + 1.15689i) q^{65} +(1.06582 + 0.530727i) q^{66} +(3.37333 + 1.94759i) q^{67} +(0.699502 - 1.21157i) q^{68} +(12.9882 + 6.46755i) q^{69} +(-0.280264 + 0.161810i) q^{70} -5.70024i q^{71} +(-0.247304 - 1.99753i) q^{72} -5.79311i q^{73} +(0.484580 + 0.839317i) q^{74} +(1.44385 - 0.956709i) q^{75} +(11.0266 + 6.36621i) q^{76} +(-3.89742 + 6.75053i) q^{77} +(0.743577 + 0.748428i) q^{78} +(-6.92507 - 11.9946i) q^{79} +3.82958i q^{80} +(8.72827 - 2.19485i) q^{81} -1.84735 q^{82} +(-3.02842 + 1.74846i) q^{83} +(6.52884 - 0.402614i) q^{84} +(0.614556 + 0.354814i) q^{85} +(-1.27289 - 0.734904i) q^{86} +(10.2084 - 6.76420i) q^{87} +(-1.36503 - 2.36430i) q^{88} -10.0932i q^{89} +(0.502972 - 0.0622704i) q^{90} +(-5.19011 + 4.55720i) q^{91} +(-8.25749 - 14.3024i) q^{92} +(-3.83561 + 7.70273i) q^{93} +(-0.289914 + 0.502146i) q^{94} +(-3.22918 + 5.59311i) q^{95} +(-1.53548 + 3.08357i) q^{96} +(14.5254 - 8.38627i) q^{97} +0.562623i q^{98} +(9.74174 - 7.35629i) 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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.146304	−	0.0844686i	0.103452	−	0.0597283i	−0.447381	−	0.894343i	$-0.647643\pi$
$2$	0.146304	−	0.0844686i	0.103452	−	0.0597283i	0.550834	+	0.834615i	$0.314310\pi$
$3$	−0.106608	−	1.72877i	−0.0615502	−	0.998104i
$3$	−0.106608	−	1.72877i	−0.0615502	−	0.998104i
$4$	−0.985730	+	1.70733i	−0.492865	+	0.853667i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.161624	−	0.243920i	−0.0659826	−	0.0995801i
$7$	1.65898	−	0.957814i	0.627037	−	0.362020i	−0.152567	−	0.988293i	$-0.548754\pi$
$7$	1.65898	−	0.957814i	0.627037	−	0.362020i	0.779604	+	0.626273i	$0.215421\pi$
$8$			0.670927i			0.237209i
$9$	−2.97727	+	0.368601i	−0.992423	+	0.122867i
$10$	−0.168937			−0.0534226
$11$	−3.52392	+	2.03454i	−1.06250	+	0.613436i	−0.926124	−	0.377220i	$-0.876880\pi$
$11$	−3.52392	+	2.03454i	−1.06250	+	0.613436i	−0.136380	+	0.990657i	$0.543547\pi$
$12$	3.05667	+	1.52208i	0.882385	+	0.439387i
$13$	−3.53584	+	0.705562i	−0.980666	+	0.195688i
$13$	−3.53584	+	0.705562i	−0.980666	+	0.195688i
$14$	0.161810	−	0.280264i	0.0432457	−	0.0749037i
$15$	−0.772058	+	1.55046i	−0.199345	+	0.400327i
$16$	−1.91479	−	3.31651i	−0.478697	−	0.829127i
$17$	−0.709628			−0.172110			−0.0860550	−	0.996290i	$-0.527426\pi$
$17$	−0.709628			−0.172110			−0.0860550	+	0.996290i	$0.527426\pi$
$18$	−0.404451	+	0.305414i	−0.0953300	+	0.0719867i
$19$		−	6.45837i		−	1.48165i	−0.671697	−	0.740826i	$-0.734435\pi$
$19$		−	6.45837i		−	1.48165i	0.671697	−	0.740826i	$-0.265565\pi$
$20$	1.70733	−	0.985730i	0.381772	−	0.220416i
$21$	−1.83270	−	2.76588i	−0.399928	−	0.603565i
$22$	−0.343709	+	0.595322i	−0.0732791	+	0.126923i
$23$	−4.18851	+	7.25472i	−0.873365	+	1.51271i	−0.0148717	+	0.999889i	$0.504734\pi$
$23$	−4.18851	+	7.25472i	−0.873365	+	1.51271i	−0.858494	+	0.512824i	$0.828599\pi$
$24$	1.15988	−	0.0715262i	0.236759	−	0.0146002i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.457710	+	0.401894i	−0.0897643	+	0.0788179i
$27$	0.954626	+	5.10771i	0.183718	+	0.982979i
$28$			3.77659i			0.713708i
$29$	3.53514	+	6.12304i	0.656459	+	1.13702i	0.981526	+	0.191329i	$0.0612798\pi$
$29$	3.53514	+	6.12304i	0.656459	+	1.13702i	−0.325067	+	0.945691i	$0.605387\pi$
$30$	0.0180101	+	0.292053i	0.00328817	+	0.0533214i
$31$	−4.30244	−	2.48401i	−0.772741	−	0.446142i	0.0611108	−	0.998131i	$-0.480536\pi$
$31$	−4.30244	−	2.48401i	−0.772741	−	0.446142i	−0.833851	+	0.551989i	$0.813869\pi$
$32$	−1.72236	−	0.994406i	−0.304474	−	0.175788i
$33$	3.89292	+	5.87515i	0.677671	+	1.02273i
$34$	−0.103821	+	0.0599413i	−0.0178052	+	0.0102798i
$35$	−1.91563			−0.323800
$36$	2.30546	−	5.44654i	0.384243	−	0.907756i
$37$			5.73681i			0.943125i	0.881833	+	0.471563i	$0.156310\pi$
$37$			5.73681i			0.943125i	−0.881833	+	0.471563i	$0.843690\pi$
$38$	−0.545529	−	0.944885i	−0.0884965	−	0.153281i
$39$	1.59670	+	6.03743i	0.255677	+	0.966762i
$40$	0.335464	−	0.581040i	0.0530415	−	0.0918705i
$41$	−9.47008	−	5.46755i	−1.47898	−	0.853888i	−0.479261	−	0.877673i	$-0.659095\pi$
$41$	−9.47008	−	5.46755i	−1.47898	−	0.853888i	−0.999717	+	0.0237844i	$0.992428\pi$
$42$	−0.501761	−	0.249854i	−0.0774235	−	0.0385533i
$43$	−4.35016	−	7.53470i	−0.663393	−	1.14903i	−0.979718	−	0.200379i	$-0.935782\pi$
$43$	−4.35016	−	7.53470i	−0.663393	−	1.14903i	0.316325	−	0.948651i	$-0.397551\pi$
$44$		−	8.02202i		−	1.20937i
$45$	2.76269	+	1.16942i	0.411838	+	0.174326i
$46$			1.41519i			0.208659i
$47$	−2.97238	+	1.71611i	−0.433567	+	0.250320i	−0.700865	−	0.713294i	$-0.747202\pi$
$47$	−2.97238	+	1.71611i	−0.433567	+	0.250320i	0.267298	+	0.963614i	$0.413869\pi$
$48$	−5.52934	+	3.66379i	−0.798092	+	0.528822i
$49$	−1.66518	+	2.88418i	−0.237883	+	0.412026i
$50$	0.146304	+	0.0844686i	0.0206905	+	0.0119457i
$51$	0.0756520	+	1.22678i	0.0105934	+	0.171784i
$52$	2.28076	−	6.73236i	0.316284	−	0.933610i
$53$	1.83872			0.252567			0.126283	−	0.991994i	$-0.459695\pi$
$53$	1.83872			0.252567			0.126283	+	0.991994i	$0.459695\pi$
$54$	0.571107	+	0.666642i	0.0777178	+	0.0907185i
$55$	4.06908			0.548674
$56$	0.642624	+	1.11306i	0.0858742	+	0.148739i
$57$	−11.1650	+	0.688514i	−1.47884	+	0.0911959i
$58$	1.03441	+	0.597217i	0.135825	+	0.0784184i
$59$	8.61560	+	4.97422i	1.12166	+	0.647588i	0.941823	−	0.336109i	$-0.109111\pi$
$59$	8.61560	+	4.97422i	1.12166	+	0.647588i	0.179832	+	0.983697i	$0.442445\pi$
$60$	−1.88611	−	2.84650i	−0.243496	−	0.367481i
$61$	1.50640	+	2.60916i	0.192874	+	0.334068i	0.946202	−	0.323578i	$-0.104886\pi$
$61$	1.50640	+	2.60916i	0.192874	+	0.334068i	−0.753327	+	0.657646i	$0.771552\pi$
$62$	−0.839285			−0.106589
$63$	−4.58619	+	3.46317i	−0.577805	+	0.436319i
$64$	7.32317			0.915396
$65$	3.41491	+	1.15689i	0.423568	+	0.143494i
$66$	1.06582	+	0.530727i	0.131193	+	0.0653280i
$67$	3.37333	+	1.94759i	0.412118	+	0.237936i	0.691699	−	0.722186i	$-0.256862\pi$
$67$	3.37333	+	1.94759i	0.412118	+	0.237936i	−0.279581	+	0.960122i	$0.590196\pi$
$68$	0.699502	−	1.21157i	0.0848270	−	0.146925i
$69$	12.9882	+	6.46755i	1.56360	+	0.778602i
$70$	−0.280264	+	0.161810i	−0.0334980	+	0.0193401i
$71$		−	5.70024i		−	0.676494i	−0.941057	−	0.338247i	$-0.890166\pi$
$71$		−	5.70024i		−	0.676494i	0.941057	−	0.338247i	$-0.109834\pi$
$72$	−0.247304	−	1.99753i	−0.0291451	−	0.235411i
$73$		−	5.79311i		−	0.678032i	−0.940781	−	0.339016i	$-0.889906\pi$
$73$		−	5.79311i		−	0.678032i	0.940781	−	0.339016i	$-0.110094\pi$
$74$	0.484580	+	0.839317i	0.0563313	+	0.0975687i
$75$	1.44385	−	0.956709i	0.166722	−	0.110471i
$76$	11.0266	+	6.36621i	1.26484	+	0.730254i
$77$	−3.89742	+	6.75053i	−0.444152	+	0.769294i
$78$	0.743577	+	0.748428i	0.0841935	+	0.0847428i
$79$	−6.92507	−	11.9946i	−0.779131	−	1.34949i	−0.932443	−	0.361317i	$-0.882327\pi$
$79$	−6.92507	−	11.9946i	−0.779131	−	1.34949i	0.153312	−	0.988178i	$-0.451006\pi$
$80$			3.82958i			0.428160i
$81$	8.72827	−	2.19485i	0.969807	−	0.243872i
$82$	−1.84735			−0.204005
$83$	−3.02842	+	1.74846i	−0.332412	+	0.191918i	−0.656911	−	0.753968i	$-0.728137\pi$
$83$	−3.02842	+	1.74846i	−0.332412	+	0.191918i	0.324499	+	0.945886i	$0.394804\pi$
$84$	6.52884	−	0.402614i	0.712354	−	0.0439288i
$85$	0.614556	+	0.354814i	0.0666579	+	0.0384850i
$86$	−1.27289	−	0.734904i	−0.137259	−	0.0792467i
$87$	10.2084	−	6.76420i	1.09446	−	0.725198i
$88$	−1.36503	−	2.36430i	−0.145512	−	0.252035i
$89$		−	10.0932i		−	1.06987i	−0.844892	−	0.534937i	$-0.820335\pi$
$89$		−	10.0932i		−	1.06987i	0.844892	−	0.534937i	$-0.179665\pi$
$90$	0.502972	−	0.0622704i	0.0530179	−	0.00656388i
$91$	−5.19011	+	4.55720i	−0.544071	+	0.477724i
$92$	−8.25749	−	14.3024i	−0.860903	−	1.49113i
$93$	−3.83561	+	7.70273i	−0.397734	+	0.798736i
$94$	−0.289914	+	0.502146i	−0.0299024	+	0.0517924i
$95$	−3.22918	+	5.59311i	−0.331307	+	0.573841i
$96$	−1.53548	+	3.08357i	−0.156714	+	0.314716i
$97$	14.5254	−	8.38627i	1.47484	−	0.851497i	0.475238	−	0.879857i	$-0.342362\pi$
$97$	14.5254	−	8.38627i	1.47484	−	0.851497i	0.999598	+	0.0283603i	$0.00902856\pi$
$98$			0.562623i			0.0568335i
$99$	9.74174	−	7.35629i	0.979082	−	0.739335i
$100$	−1.97146			−0.197146
$101$	−3.49270	−	6.04953i	−0.347536	−	0.601951i	0.638275	−	0.769809i	$-0.279648\pi$
$101$	−3.49270	−	6.04953i	−0.347536	−	0.601951i	−0.985811	+	0.167858i	$0.946315\pi$
$102$	0.114693	+	0.173093i	0.0113563	+	0.0171387i
$103$	7.02176	−	12.1620i	0.691875	−	1.19836i	−0.279348	−	0.960190i	$-0.590118\pi$
$103$	7.02176	−	12.1620i	0.691875	−	1.19836i	0.971223	−	0.238172i	$-0.0765483\pi$
$104$	−0.473381	−	2.37229i	−0.0464188	−	0.232623i
$105$	0.204221	+	3.31167i	0.0199300	+	0.323186i
$106$	0.269011	−	0.155314i	0.0261287	−	0.0150854i
$107$	−7.11099			−0.687445			−0.343723	−	0.939071i	$-0.611688\pi$
$107$	−7.11099			−0.687445			−0.343723	+	0.939071i	$0.611688\pi$
$108$	−9.66157	−	3.40496i	−0.929685	−	0.327642i
$109$			14.0348i			1.34429i	0.740420	+	0.672145i	$0.234627\pi$
$109$			14.0348i			1.34429i	−0.740420	+	0.672145i	$0.765373\pi$
$110$	0.595322	−	0.343709i	0.0567617	−	0.0327714i
$111$	9.91760	−	0.611590i	0.941337	−	0.0580495i
$112$	−6.35320	−	3.66802i	−0.600321	−	0.346596i
$113$	−2.53374	+	4.38856i	−0.238354	+	0.412841i	−0.960242	−	0.279169i	$-0.909941\pi$
$113$	−2.53374	+	4.38856i	−0.238354	+	0.412841i	0.721888	+	0.692010i	$0.243274\pi$
$114$	−1.57533	+	1.04383i	−0.147543	+	0.0977632i
$115$	7.25472	−	4.18851i	0.676506	−	0.390581i
$116$	−13.9388			−1.29418
$117$	10.2671	−	3.40396i	0.949192	−	0.314696i
$118$	1.68066			0.154717
$119$	−1.17726	+	0.679692i	−0.107919	+	0.0623072i
$120$	−1.04025	−	0.517995i	−0.0949611	−	0.0472863i
$121$	2.77869	−	4.81284i	0.252609	−	0.437531i
$122$	0.440784	+	0.254487i	0.0399067	+	0.0230401i
$123$	−8.44254	+	16.9544i	−0.761238	+	1.52873i
$124$	8.48208	−	4.89713i	0.761714	−	0.439776i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.378448	+	0.894065i	−0.0337148	+	0.0796496i
$127$	8.64652			0.767255			0.383627	−	0.923488i	$-0.374675\pi$
$127$	8.64652			0.767255			0.383627	+	0.923488i	$0.374675\pi$
$128$	4.51613	−	2.60739i	0.399174	−	0.230463i
$129$	−12.5620	+	8.32367i	−1.10602	+	0.732858i
$130$	0.597335	−	0.119196i	0.0523898	−	0.0104542i
$131$	2.38004	−	4.12236i	0.207945	−	0.360172i	−0.743122	−	0.669156i	$-0.766656\pi$
$131$	2.38004	−	4.12236i	0.207945	−	0.360172i	0.951067	+	0.308984i	$0.0999890\pi$
$132$	−13.8682	+	0.855212i	−1.20707	+	0.0744366i
$133$	−6.18592	−	10.7143i	−0.536387	−	0.929049i
$134$	0.658042			0.0568462
$135$	1.72712	−	4.90072i	0.148647	−	0.421787i
$136$		−	0.476109i		−	0.0408260i
$137$	−8.86562	+	5.11857i	−0.757441	+	0.437309i	−0.828376	−	0.560172i	$-0.810735\pi$
$137$	−8.86562	+	5.11857i	−0.757441	+	0.437309i	0.0709354	+	0.997481i	$0.477402\pi$
$138$	2.44654	−	0.150871i	0.208263	−	0.0128430i
$139$	5.77777	−	10.0074i	0.490064	−	0.848816i	−0.509871	−	0.860251i	$-0.670307\pi$
$139$	5.77777	−	10.0074i	0.490064	−	0.848816i	0.999935	+	0.0114355i	$0.00364012\pi$
$140$	1.88829	−	3.27062i	0.159590	−	0.276418i
$141$	3.28363	+	4.95561i	0.276531	+	0.417337i
$142$	−0.481491	−	0.833967i	−0.0404059	−	0.0699850i
$143$	11.0245	−	9.68015i	0.921919	−	0.809495i
$144$	6.92331	+	9.16835i	0.576942	+	0.764029i
$145$		−	7.07028i		−	0.587155i
$146$	−0.489336	−	0.847555i	−0.0404977	−	0.0701441i
$147$	5.16360	+	2.57124i	0.425887	+	0.212072i
$148$	−9.79465	−	5.65494i	−0.805115	−	0.464833i
$149$	−19.0393	−	10.9923i	−1.55976	−	0.900526i	−0.997279	−	0.0737131i	$-0.976515\pi$
$149$	−19.0393	−	10.9923i	−1.55976	−	0.900526i	−0.562477	−	0.826813i	$-0.690152\pi$
$150$	0.130429	−	0.261930i	0.0106495	−	0.0213865i
$151$	−0.201741	+	0.116475i	−0.0164175	+	0.00947862i	−0.508186	−	0.861247i	$-0.669684\pi$
$151$	−0.201741	+	0.116475i	−0.0164175	+	0.00947862i	0.491769	+	0.870726i	$0.336351\pi$
$152$	4.33310			0.351461
$153$	2.11275	−	0.261569i	0.170806	−	0.0211466i
$154$			1.31684i			0.106114i
$155$	2.48401	+	4.30244i	0.199521	+	0.345580i
$156$	−11.8818	−	3.22517i	−0.951308	−	0.258220i
$157$	−10.2882	+	17.8197i	−0.821087	+	1.42216i	0.0837862	+	0.996484i	$0.473299\pi$
$157$	−10.2882	+	17.8197i	−0.821087	+	1.42216i	−0.904873	+	0.425681i	$0.860035\pi$
$158$	−2.02633	−	1.16990i	−0.161206	−	0.0930724i
$159$	−0.196022	−	3.17871i	−0.0155455	−	0.252088i
$160$	0.994406	+	1.72236i	0.0786147	+	0.136165i
$161$			16.0473i			1.26470i
$162$	1.09158	−	1.05838i	0.0857629	−	0.0831541i
$163$			15.6276i			1.22404i	0.790841	+	0.612022i	$0.209644\pi$
$163$			15.6276i			1.22404i	−0.790841	+	0.612022i	$0.790356\pi$
$164$	18.6699	−	10.7791i	1.45787	−	0.841703i
$165$	−0.433796	−	7.03449i	−0.0337710	−	0.547634i
$166$	−0.295380	+	0.511612i	−0.0229259	+	0.0397088i
$167$	8.64820	+	4.99304i	0.669218	+	0.386373i	0.795780	−	0.605586i	$-0.207061\pi$
$167$	8.64820	+	4.99304i	0.669218	+	0.386373i	−0.126563	+	0.991959i	$0.540394\pi$
$168$	1.85571	−	1.22961i	0.143171	−	0.0948663i
$169$	12.0044	−	4.98951i	0.923413	−	0.383809i
$170$	0.119883			0.00919457
$171$	2.38056	+	19.2283i	0.182046	+	1.47042i
$172$	17.1523			1.30785
$173$	−8.04100	−	13.9274i	−0.611346	−	1.05888i	−0.991014	−	0.133759i	$-0.957295\pi$
$173$	−8.04100	−	13.9274i	−0.611346	−	1.05888i	0.379668	−	0.925123i	$-0.376038\pi$
$174$	0.922172	−	1.85192i	0.0699097	−	0.140394i
$175$	1.65898	+	0.957814i	0.125407	+	0.0724040i
$176$	13.4951	+	7.79142i	1.01723	+	0.587300i
$177$	7.68077	−	15.4246i	0.577322	−	1.15939i
$178$	−0.852557	−	1.47667i	−0.0639018	−	0.110681i
$179$	6.68173			0.499416			0.249708	−	0.968321i	$-0.419665\pi$
$179$	6.68173			0.499416			0.249708	+	0.968321i	$0.419665\pi$
$180$	−4.71985	+	3.56411i	−0.351797	+	0.265653i
$181$	−12.1819			−0.905474			−0.452737	−	0.891644i	$-0.649552\pi$
$181$	−12.1819			−0.905474			−0.452737	+	0.891644i	$0.649552\pi$
$182$	−0.374393	+	1.10514i	−0.0277518	+	0.0819182i
$183$	4.35003	−	2.88237i	0.321563	−	0.213071i
$184$	−4.86739	−	2.81019i	−0.358829	−	0.207170i
$185$	2.86840	−	4.96822i	0.210889	−	0.365271i
$186$	0.0894745	+	1.45093i	0.00656059	+	0.106387i
$187$	2.50068	−	1.44377i	0.182867	−	0.105579i
$188$		−	6.76647i		−	0.493496i
$189$	6.47594	+	7.55925i	0.471056	+	0.549854i
$190$			1.09106i			0.0791537i
$191$	8.26341	+	14.3126i	0.597919	+	1.03563i	0.993128	+	0.117035i	$0.0373390\pi$
$191$	8.26341	+	14.3126i	0.597919	+	1.03563i	−0.395209	+	0.918591i	$0.629328\pi$
$192$	−0.780708	−	12.6600i	−0.0563428	−	0.913660i
$193$	−12.4581	−	7.19271i	−0.896757	−	0.517743i	−0.0206103	−	0.999788i	$-0.506561\pi$
$193$	−12.4581	−	7.19271i	−0.896757	−	0.517743i	−0.876147	+	0.482045i	$0.839894\pi$
$194$	1.41675	−	2.45389i	0.101717	−	0.176179i
$195$	1.63593	−	6.02692i	0.117151	−	0.431597i
$196$	−3.28284	−	5.68605i	−0.234489	−	0.406147i
$197$			24.7703i			1.76481i	0.470489	+	0.882406i	$0.344078\pi$
$197$			24.7703i			1.76481i	−0.470489	+	0.882406i	$0.655922\pi$
$198$	0.803879	−	1.89913i	0.0571292	−	0.134965i
$199$	9.54246			0.676447			0.338224	−	0.941066i	$-0.390174\pi$
$199$	9.54246			0.676447			0.338224	+	0.941066i	$0.390174\pi$
$200$	−0.581040	+	0.335464i	−0.0410857	+	0.0237209i
$201$	3.00731	−	6.03933i	0.212119	−	0.425982i
$202$	−1.02199	−	0.590047i	−0.0719070	−	0.0415155i
$203$	11.7295	+	6.77201i	0.823247	+	0.475302i
$204$	−2.16910	−	1.08011i	−0.151867	−	0.0756230i
$205$	5.46755	+	9.47008i	0.381870	+	0.661419i
$206$		−	2.37247i		−	0.165298i
$207$	9.79624	−	23.1431i	0.680886	−	1.60856i
$208$	9.11039	+	10.3757i	0.631692	+	0.719422i
$209$	13.1398	+	22.7588i	0.908899	+	1.57426i
$210$	0.309611	+	0.467261i	0.0213652	+	0.0322441i
$211$	−4.51728	+	7.82415i	−0.310982	+	0.538637i	−0.978575	−	0.205889i	$-0.933991\pi$
$211$	−4.51728	+	7.82415i	−0.310982	+	0.538637i	0.667593	+	0.744526i	$0.267325\pi$
$212$	−1.81248	+	3.13930i	−0.124481	+	0.215608i
$213$	−9.85438	+	0.607691i	−0.675211	+	0.0416383i
$214$	−1.04037	+	0.600656i	−0.0711180	+	0.0410600i
$215$			8.70032i			0.593357i
$216$	−3.42690	+	0.640485i	−0.233171	+	0.0435795i
$217$	−9.51689			−0.646049
$218$	1.18550	+	2.05335i	0.0802921	+	0.139070i
$219$	−10.0149	+	0.617592i	−0.676747	+	0.0417330i
$220$	−4.01101	+	6.94728i	−0.270422	+	0.468385i
$221$	2.50913	−	0.500686i	0.168783	−	0.0336798i
$222$	1.39932	−	0.927204i	0.0939165	−	0.0622299i
$223$	−12.8944	+	7.44457i	−0.863471	+	0.498525i	−0.865173	−	0.501473i	$-0.832792\pi$
$223$	−12.8944	+	7.44457i	−0.863471	+	0.498525i	0.00170200	+	0.999999i	$0.499458\pi$
$224$	−3.80983			−0.254555
$225$	−1.80785	−	2.39409i	−0.120523	−	0.159606i
$226$			0.856085i			0.0569459i
$227$	−14.1677	+	8.17971i	−0.940341	+	0.542906i	−0.890067	−	0.455829i	$-0.849343\pi$
$227$	−14.1677	+	8.17971i	−0.940341	+	0.542906i	−0.0502738	+	0.998735i	$0.516009\pi$
$228$	9.83016	−	19.7411i	0.651019	−	1.30739i
$229$	−2.01410	−	1.16284i	−0.133096	−	0.0768427i	0.431974	−	0.901886i	$-0.357817\pi$
$229$	−2.01410	−	1.16284i	−0.133096	−	0.0768427i	−0.565069	+	0.825043i	$0.691151\pi$
$230$	0.707596	−	1.22559i	0.0466575	−	0.0808131i
$231$	12.0856	+	6.01807i	0.795173	+	0.395960i
$232$	−4.10812	+	2.37182i	−0.269711	+	0.155718i
$233$	−8.48290			−0.555733			−0.277867	−	0.960620i	$-0.589627\pi$
$233$	−8.48290			−0.555733			−0.277867	+	0.960620i	$0.589627\pi$
$234$	1.21459	−	1.36526i	0.0794000	−	0.0892498i
$235$	3.43221			0.223893
$236$	−16.9853	+	9.80647i	−1.10565	+	0.638347i
$237$	−19.9975	+	13.2505i	−1.29898	+	0.860715i
$238$	−0.114825	+	0.198883i	−0.00744302	+	0.0128917i
$239$	−7.83208	−	4.52185i	−0.506615	−	0.292494i	0.224826	−	0.974399i	$-0.427819\pi$
$239$	−7.83208	−	4.52185i	−0.506615	−	0.292494i	−0.731441	+	0.681905i	$0.761152\pi$
$240$	6.62044	−	0.408263i	0.427348	−	0.0263533i
$241$	−7.31598	+	4.22388i	−0.471264	+	0.272084i	−0.716769	−	0.697311i	$-0.754380\pi$
$241$	−7.31598	+	4.22388i	−0.471264	+	0.272084i	0.245505	+	0.969395i	$0.421046\pi$
$242$		−	0.938850i		−	0.0603516i
$243$	−4.72488	−	14.8551i	−0.303101	−	0.952958i
$244$	−5.93961			−0.380244
$245$	2.88418	−	1.66518i	0.184264	−	0.106385i
$246$	0.196942	+	3.19363i	0.0125566	+	0.203618i
$247$	4.55678	+	22.8358i	0.289941	+	1.45301i
$248$	1.66659	−	2.88662i	0.105829	−	0.183301i
$249$	3.34553	+	5.04903i	0.212014	+	0.319969i
$250$	−0.0844686	−	0.146304i	−0.00534226	−	0.00925307i
$251$	5.17089			0.326384			0.163192	−	0.986594i	$-0.447821\pi$
$251$	5.17089			0.326384			0.163192	+	0.986594i	$0.447821\pi$
$252$	−1.39205	−	11.2439i	−0.0876911	−	0.708300i
$253$		−	34.0868i		−	2.14302i
$254$	1.26502	−	0.730360i	0.0793744	−	0.0458269i
$255$	0.547874	−	1.10025i	0.0343092	−	0.0689003i
$256$	−6.88268	+	11.9212i	−0.430168	+	0.745072i
$257$	4.09728	−	7.09669i	0.255581	−	0.442679i	−0.709472	−	0.704734i	$-0.751067\pi$
$257$	4.09728	−	7.09669i	0.255581	−	0.442679i	0.965053	+	0.262054i	$0.0843999\pi$
$258$	−1.13478	+	2.27888i	−0.0706481	+	0.141877i
$259$	5.49480	+	9.51726i	0.341430	+	0.591374i
$260$	−5.34137	+	4.69002i	−0.331258	+	0.290862i
$261$	−12.7820	−	16.9269i	−0.791187	−	1.04775i
$262$		−	0.804156i		−	0.0496809i
$263$	6.89246	+	11.9381i	0.425008	+	0.736135i	0.996421	−	0.0845276i	$-0.0269381\pi$
$263$	6.89246	+	11.9381i	0.425008	+	0.736135i	−0.571414	+	0.820662i	$0.693605\pi$
$264$	−3.94180	+	2.61187i	−0.242601	+	0.160749i
$265$	−1.59237	−	0.919358i	−0.0978188	−	0.0564757i
$266$	−1.81005	−	1.04503i	−0.110981	−	0.0640750i
$267$	−17.4488	+	1.07601i	−1.06785	+	0.0658510i
$268$	−6.65039	+	3.83960i	−0.406237	+	0.234541i
$269$	16.6922			1.01774			0.508872	−	0.860842i	$-0.330063\pi$
$269$	16.6922			1.01774			0.508872	+	0.860842i	$0.330063\pi$
$270$	−0.161272	−	0.862882i	−0.00981469	−	0.0525133i
$271$		−	1.35107i		−	0.0820715i	−0.999158	−	0.0410358i	$-0.986934\pi$
$271$		−	1.35107i		−	0.0820715i	0.999158	−	0.0410358i	$-0.0130658\pi$
$272$	1.35879	+	2.35349i	0.0823886	+	0.142701i
$273$	8.43163	+	8.48665i	0.510306	+	0.513635i
$274$	−0.864716	+	1.49773i	−0.0522394	+	0.0904813i
$275$	−3.52392	−	2.03454i	−0.212501	−	0.122687i
$276$	−23.8452	+	15.8000i	−1.43531	+	0.951049i
$277$	3.98598	+	6.90392i	0.239494	+	0.414817i	0.960569	−	0.278041i	$-0.0896850\pi$
$277$	3.98598	+	6.90392i	0.239494	+	0.414817i	−0.721075	+	0.692857i	$0.756352\pi$
$278$		−	1.95216i		−	0.117083i
$279$	13.7251	+	5.80970i	0.821702	+	0.347817i
$280$		−	1.28525i		−	0.0768082i
$281$	21.0588	−	12.1583i	1.25626	−	0.725304i	0.283917	−	0.958849i	$-0.408366\pi$
$281$	21.0588	−	12.1583i	1.25626	−	0.725304i	0.972346	+	0.233545i	$0.0750327\pi$
$282$	0.899001	+	0.447661i	0.0535347	+	0.0266578i
$283$	−7.68858	+	13.3170i	−0.457039	+	0.791615i	−0.998803	−	0.0489160i	$-0.984423\pi$
$283$	−7.68858	+	13.3170i	−0.457039	+	0.791615i	0.541764	+	0.840531i	$0.317757\pi$
$284$	9.73222	+	5.61890i	0.577501	+	0.333420i
$285$	10.0134	+	4.98624i	0.593145	+	0.295359i
$286$	0.795265	−	2.34747i	0.0470250	−	0.138809i
$287$	−20.9476			−1.23650
$288$	5.49448	+	2.32575i	0.323765	+	0.137046i
$289$	−16.4964			−0.970378
$290$	−0.597217	−	1.03441i	−0.0350698	−	0.0607426i
$291$	−16.0464	−	24.2171i	−0.940659	−	1.41963i
$292$	9.89078	+	5.71044i	0.578814	+	0.334178i
$293$	−17.2223	−	9.94332i	−1.00614	−	0.580895i	−0.0960804	−	0.995374i	$-0.530631\pi$
$293$	−17.2223	−	9.94332i	−1.00614	−	0.580895i	−0.910059	+	0.414479i	$0.863964\pi$
$294$	0.972644	−	0.0599801i	0.0567258	−	0.00349811i
$295$	−4.97422	−	8.61560i	−0.289610	−	0.501619i
$296$	−3.84898			−0.223718
$297$	−13.7559	−	16.0570i	−0.798196	−	0.931719i
$298$	−3.71402			−0.215148
$299$	9.69127	−	28.6068i	0.560461	−	1.65437i
$300$	0.210173	+	3.40820i	0.0121344	+	0.196772i
$301$	−14.4337	−	8.33329i	−0.831943	−	0.480323i
$302$	−0.0196770	+	0.0340816i	−0.00113228	+	0.00196117i
$303$	−10.0859	+	6.68299i	−0.579418	+	0.383928i
$304$	−21.4192	+	12.3664i	−1.22848	+	0.709262i
$305$		−	3.01280i		−	0.172512i
$306$	0.287010	−	0.216730i	0.0164073	−	0.0123896i
$307$			2.04562i			0.116750i	0.998295	+	0.0583750i	$0.0185919\pi$
$307$			2.04562i			0.116750i	−0.998295	+	0.0583750i	$0.981408\pi$
$308$	−7.68361	−	13.3084i	−0.437814	−	0.758316i
$309$	−21.7739	−	10.8424i	−1.23868	−	0.616804i
$310$	0.726842	+	0.419642i	0.0412818	+	0.0238341i
$311$	11.3301	−	19.6243i	0.642471	−	1.11279i	−0.342408	−	0.939551i	$-0.611243\pi$
$311$	11.3301	−	19.6243i	0.642471	−	1.11279i	0.984879	−	0.173241i	$-0.0554241\pi$
$312$	−4.05068	+	1.07127i	−0.229324	+	0.0606488i
$313$	3.88016	+	6.72064i	0.219320	+	0.379873i	0.954600	−	0.297890i	$-0.0962829\pi$
$313$	3.88016	+	6.72064i	0.219320	+	0.379873i	−0.735280	+	0.677763i	$0.762950\pi$
$314$			3.47612i			0.196169i
$315$	5.70334	−	0.706102i	0.321347	−	0.0397843i
$316$	27.3050			1.53603
$317$	−4.17572	+	2.41085i	−0.234532	+	0.135407i	−0.612661	−	0.790346i	$-0.709901\pi$
$317$	−4.17572	+	2.41085i	−0.234532	+	0.135407i	0.378129	+	0.925753i	$0.376568\pi$
$318$	−0.297180	−	0.448500i	−0.0166650	−	0.0251506i
$319$	−24.9151	−	14.3848i	−1.39498	−	0.805392i
$320$	−6.34205	−	3.66158i	−0.354531	−	0.204689i
$321$	0.758089	+	12.2932i	0.0423124	+	0.686142i
$322$	1.35549	+	2.34778i	0.0755385	+	0.130837i
$323$			4.58304i			0.255007i
$324$	−4.85638	+	17.0656i	−0.269799	+	0.948089i
$325$	−2.37896	−	2.70935i	−0.131961	−	0.150288i
$326$	1.32004	+	2.28637i	0.0731101	+	0.126630i
$327$	24.2629	−	1.49622i	1.34174	−	0.0827412i
$328$	3.66833	−	6.35374i	0.202550	−	0.350826i
$329$	−3.28742	+	5.69398i	−0.181241	+	0.313919i
$330$	−0.657659	−	0.992531i	−0.0362030	−	0.0546370i
$331$	20.1502	−	11.6337i	1.10756	−	0.639448i	0.169361	−	0.985554i	$-0.445830\pi$
$331$	20.1502	−	11.6337i	1.10756	−	0.639448i	0.938195	+	0.346106i	$0.112496\pi$
$332$		−	6.89403i		−	0.378359i
$333$	−2.11459	−	17.0800i	−0.115879	−	0.935979i
$334$	1.68702			0.0923096
$335$	−1.94759	−	3.37333i	−0.106408	−	0.184305i
$336$	−5.66385	+	11.3742i	−0.308989	+	0.620516i
$337$	3.89171	−	6.74063i	0.211995	−	0.367186i	−0.740344	−	0.672228i	$-0.765337\pi$
$337$	3.89171	−	6.74063i	0.211995	−	0.367186i	0.952339	+	0.305043i	$0.0986707\pi$
$338$	1.33483	−	1.74398i	0.0726051	−	0.0948599i
$339$	7.85691	+	3.91238i	0.426729	+	0.212492i
$340$	−1.21157	+	0.699502i	−0.0657067	+	0.0379358i
$341$	20.2153			1.09472
$342$	1.97247	+	2.61209i	0.106659	+	0.141246i
$343$			19.7891i			1.06851i
$344$	5.05523	−	2.91864i	0.272560	−	0.157363i
$345$	−8.01437	−	12.0952i	−0.431479	−	0.651183i
$346$	−2.35286	−	1.35842i	−0.126490	−	0.0730293i
$347$	−8.23126	+	14.2570i	−0.441877	+	0.765354i	−0.997829	−	0.0658610i	$-0.979021\pi$
$347$	−8.23126	+	14.2570i	−0.441877	+	0.765354i	0.555952	+	0.831215i	$0.312354\pi$
$348$	1.48598	+	24.0969i	0.0796571	+	1.29173i
$349$	−31.5526	+	18.2169i	−1.68897	+	0.975127i	−0.733661	+	0.679515i	$0.762190\pi$
$349$	−31.5526	+	18.2169i	−1.68897	+	0.975127i	−0.955308	+	0.295611i	$0.904477\pi$
$350$	0.323621			0.0172983
$351$	−6.97921	−	17.3865i	−0.372523	−	0.928023i
$352$	8.09263			0.431339
$353$	−21.2577	+	12.2732i	−1.13143	+	0.653234i	−0.944295	−	0.329099i	$-0.893255\pi$
$353$	−21.2577	+	12.2732i	−1.13143	+	0.653234i	−0.187139	+	0.982333i	$0.559922\pi$
$354$	−0.179172	−	2.90547i	−0.00952288	−	0.154424i
$355$	−2.85012	+	4.93655i	−0.151269	+	0.262005i
$356$	17.2324	+	9.94915i	0.913317	+	0.527304i
$357$	1.30053	+	1.96275i	0.0688316	+	0.103880i
$358$	0.977563	−	0.564396i	0.0516658	−	0.0298293i
$359$			5.35067i			0.282398i	0.989981	+	0.141199i	$0.0450957\pi$
$359$			5.35067i			0.282398i	−0.989981	+	0.141199i	$0.954904\pi$
$360$	−0.784594	+	1.85357i	−0.0413517	+	0.0976915i
$361$	−22.7105			−1.19529
$362$	−1.78226	+	1.02899i	−0.0936736	+	0.0540825i
$363$	−8.61651	−	4.29063i	−0.452249	−	0.225200i
$364$	−2.66461	−	13.3534i	−0.139664	−	0.699909i
$365$	−2.89656	+	5.01698i	−0.151613	+	0.262601i
$366$	0.392957	−	0.789143i	0.0205402	−	0.0412491i
$367$	10.2844	+	17.8131i	0.536841	+	0.929836i	0.999072	+	0.0430763i	$0.0137158\pi$
$367$	10.2844	+	17.8131i	0.536841	+	0.929836i	−0.462231	+	0.886760i	$0.652951\pi$
$368$	32.0805			1.67231
$369$	30.2103	+	12.7877i	1.57269	+	0.665701i
$370$		−	0.969160i		−	0.0503842i
$371$	3.05040	−	1.76115i	0.158369	−	0.0914342i
$372$	−9.37026	−	14.1415i	−0.485825	−	0.733201i
$373$	−5.65573	+	9.79602i	−0.292843	+	0.507219i	−0.974481	−	0.224471i	$-0.927935\pi$
$373$	−5.65573	+	9.79602i	−0.292843	+	0.507219i	0.681638	+	0.731690i	$0.261268\pi$
$374$	0.243906	−	0.422457i	0.0126121	−	0.0218447i
$375$	−1.72877	+	0.106608i	−0.0892731	+	0.00550521i
$376$	−1.15138	−	1.99425i	−0.0593780	−	0.102846i
$377$	−16.8199	−	19.1558i	−0.866268	−	0.986576i
$378$	1.58598	+	0.558934i	0.0815738	+	0.0287484i
$379$		−	1.06242i		−	0.0545727i	−0.999628	−	0.0272863i	$-0.991313\pi$
$379$		−	1.06242i		−	0.0545727i	0.999628	−	0.0272863i	$-0.00868659\pi$
$380$	−6.36621	−	11.0266i	−0.326580	−	0.565652i
$381$	−0.921789	−	14.9478i	−0.0472247	−	0.765800i
$382$	2.41794	+	1.39600i	0.123712	+	0.0714254i
$383$	0.985655	+	0.569068i	0.0503646	+	0.0290780i	0.524971	−	0.851120i	$-0.324076\pi$
$383$	0.985655	+	0.569068i	0.0503646	+	0.0290780i	−0.474606	+	0.880198i	$0.657410\pi$
$384$	−4.98903	−	7.52937i	−0.254595	−	0.384232i
$385$	6.75053	−	3.89742i	0.344039	−	0.198631i
$386$	−2.43023			−0.123696
$387$	15.7289	+	20.8293i	0.799544	+	1.05882i
$388$			33.0664i			1.67869i
$389$	9.07859	+	15.7246i	0.460303	+	0.797268i	0.998976	−	0.0452472i	$-0.0144075\pi$
$389$	9.07859	+	15.7246i	0.460303	+	0.797268i	−0.538673	+	0.842515i	$0.681074\pi$
$390$	−0.269742	−	1.01995i	−0.0136589	−	0.0516470i
$391$	2.97229	−	5.14815i	0.150315	−	0.260353i
$392$	−1.93508	−	1.11722i	−0.0977362	−	0.0564280i
$393$	−7.38032	−	3.67506i	−0.372288	−	0.185382i
$394$	2.09231	+	3.62399i	0.105409	+	0.182574i
$395$			13.8501i			0.696876i
$396$	2.95692	+	23.8837i	0.148591	+	1.20020i
$397$		−	8.13168i		−	0.408118i	−0.978959	−	0.204059i	$-0.934587\pi$
$397$		−	8.13168i		−	0.408118i	0.978959	−	0.204059i	$-0.0654134\pi$
$398$	1.39610	−	0.806039i	0.0699802	−	0.0404031i
$399$	−17.8631	+	11.8362i	−0.894273	+	0.592553i
$400$	1.91479	−	3.31651i	0.0957394	−	0.165825i
$401$	−25.7963	−	14.8935i	−1.28820	−	0.743745i	−0.309871	−	0.950779i	$-0.600286\pi$
$401$	−25.7963	−	14.8935i	−1.28820	−	0.743745i	−0.978334	+	0.207033i	$0.933619\pi$
$402$	−0.0701526	−	1.13760i	−0.00349889	−	0.0567384i
$403$	16.9654	+	5.74744i	0.845105	+	0.286301i
$404$	13.7714			0.685154
$405$	−8.65632	−	2.46334i	−0.430136	−	0.122404i
$406$	2.28809			0.113556
$407$	−11.6718	−	20.2161i	−0.578547	−	1.00207i
$408$	−0.823081	+	0.0507570i	−0.0407486	+	0.00251285i
$409$	5.57799	+	3.22046i	0.275814	+	0.159241i	0.631527	−	0.775354i	$-0.282429\pi$
$409$	5.57799	+	3.22046i	0.275814	+	0.159241i	−0.355713	+	0.934595i	$0.615762\pi$
$410$	1.59985	+	0.923673i	0.0790109	+	0.0456170i
$411$	9.79395	+	14.7809i	0.483100	+	0.729088i
$412$	13.8431	+	23.9770i	0.682002	+	1.18126i
$413$	19.0575			0.937758
$414$	−0.521641	−	4.21341i	−0.0256372	−	0.207078i
$415$	3.49692			0.171657
$416$	6.79162	+	2.30083i	0.332986	+	0.112808i
$417$	−17.9164	−	8.92155i	−0.877370	−	0.436890i
$418$	3.84481	+	2.21980i	0.188056	+	0.108574i
$419$	0.345757	−	0.598869i	0.0168913	−	0.0292566i	−0.857456	−	0.514557i	$-0.827956\pi$
$419$	0.345757	−	0.598869i	0.0168913	−	0.0292566i	0.874348	+	0.485300i	$0.161290\pi$
$420$	−5.85544	−	2.91574i	−0.285716	−	0.142274i
$421$	−29.7908	+	17.1998i	−1.45192	+	0.838265i	−0.998590	−	0.0530797i	$-0.983096\pi$
$421$	−29.7908	+	17.1998i	−1.45192	+	0.838265i	−0.453327	+	0.891344i	$0.649763\pi$
$422$			1.52627i			0.0742978i
$423$	8.21703	−	6.20493i	0.399526	−	0.301694i
$424$			1.23364i			0.0599111i
$425$	−0.354814	−	0.614556i	−0.0172110	−	0.0298103i
$426$	−1.39040	+	0.921294i	−0.0673653	+	0.0446368i
$427$	4.99818	+	2.88570i	0.241879	+	0.139649i
$428$	7.00952	−	12.1408i	0.338818	−	0.586850i
$429$	−17.9100	−	18.0269i	−0.864705	−	0.870347i
$430$	0.734904	+	1.27289i	0.0354402	+	0.0613842i
$431$		−	5.81003i		−	0.279859i	−0.990161	−	0.139930i	$-0.955312\pi$
$431$		−	5.81003i		−	0.279859i	0.990161	−	0.139930i	$-0.0446877\pi$
$432$	15.1119	−	12.9462i	0.727070	−	0.622875i
$433$	−0.137485			−0.00660711			−0.00330356	−	0.999995i	$-0.501052\pi$
$433$	−0.137485			−0.00660711			−0.00330356	+	0.999995i	$0.501052\pi$
$434$	−1.39236	+	0.803879i	−0.0668354	+	0.0385874i
$435$	−12.2229	+	0.753748i	−0.586041	+	0.0361395i
$436$	−23.9621	−	13.8345i	−1.14758	−	0.662553i
$437$	46.8536	+	27.0510i	2.24131	+	1.29402i
$438$	−1.41306	+	0.936304i	−0.0675185	+	0.0447383i
$439$	−16.8303	−	29.1510i	−0.803267	−	1.39130i	−0.917455	−	0.397840i	$-0.869760\pi$
$439$	−16.8303	−	29.1510i	−0.803267	−	1.39130i	0.114188	−	0.993459i	$-0.463573\pi$
$440$			2.73006i			0.130150i
$441$	3.89459	−	9.20078i	0.185457	−	0.438132i
$442$	0.324804	−	0.285195i	0.0154493	−	0.0135654i
$443$	−3.16074	−	5.47456i	−0.150171	−	0.260104i	0.781119	−	0.624382i	$-0.214649\pi$
$443$	−3.16074	−	5.47456i	−0.150171	−	0.260104i	−0.931290	+	0.364278i	$0.881316\pi$
$444$	−8.73189	+	17.5355i	−0.414397	+	0.832199i
$445$	−5.04659	+	8.74095i	−0.239231	+	0.414361i
$446$	−1.25767	+	2.17834i	−0.0595522	+	0.103147i
$447$	−16.9734	+	34.0863i	−0.802815	+	1.61223i
$448$	12.1490	−	7.01423i	0.573987	−	0.331391i
$449$			2.50392i			0.118167i	0.998253	+	0.0590836i	$0.0188178\pi$
$449$			2.50392i			0.118167i	−0.998253	+	0.0590836i	$0.981182\pi$
$450$	−0.466721	−	0.197558i	−0.0220015	−	0.00931298i
$451$	44.4958			2.09522
$452$	−4.99516	−	8.65187i	−0.234953	−	0.406950i
$453$	0.222866	+	0.336346i	0.0104711	+	0.0158029i
$454$	−1.38186	+	2.39345i	−0.0648537	+	0.112330i
$455$	6.77336	−	1.35159i	0.317540	−	0.0633637i
$456$	−0.461943	−	7.49091i	−0.0216325	−	0.350794i
$457$	14.7320	−	8.50550i	0.689132	−	0.397870i	−0.114155	−	0.993463i	$-0.536416\pi$
$457$	14.7320	−	8.50550i	0.689132	−	0.397870i	0.803287	+	0.595592i	$0.203083\pi$
$458$	−0.392894			−0.0183588
$459$	−0.677429	−	3.62457i	−0.0316197	−	0.169181i
$460$			16.5150i			0.770015i
$461$	−13.4256	+	7.75127i	−0.625292	+	0.361013i	−0.778927	−	0.627115i	$-0.784236\pi$
$461$	−13.4256	+	7.75127i	−0.625292	+	0.361013i	0.153634	+	0.988128i	$0.450902\pi$
$462$	2.27651	−	0.140386i	0.105913	−	0.00653133i
$463$	31.7351	+	18.3223i	1.47486	+	0.851508i	0.999598	−	0.0283393i	$-0.00902188\pi$
$463$	31.7351	+	18.3223i	1.47486	+	0.851508i	0.475257	+	0.879847i	$0.342355\pi$
$464$	13.5381	−	23.4486i	0.628490	−	1.08858i
$465$	7.17310	−	4.75295i	0.332644	−	0.220413i
$466$	−1.24108	+	0.716539i	−0.0574920	+	0.0331930i
$467$	10.1586			0.470084			0.235042	−	0.971985i	$-0.424477\pi$
$467$	10.1586			0.470084			0.235042	+	0.971985i	$0.424477\pi$
$468$	−4.30887	+	20.8847i	−0.199178	+	0.965397i
$469$	7.46173			0.344551
$470$	0.502146	−	0.289914i	0.0231623	−	0.0133727i
$471$	31.9029	+	15.8862i	1.47001	+	0.731996i
$472$	−3.33734	+	5.78044i	−0.153613	+	0.266066i
$473$	30.6593	+	17.7011i	1.40971	+	0.813899i
$474$	−1.80646	+	3.62777i	−0.0829737	+	0.166629i
$475$	5.59311	−	3.22918i	0.256630	−	0.148165i
$476$		−	2.67997i		−	0.122836i
$477$	−5.47435	+	0.677752i	−0.250653	+	0.0310321i
$478$	−1.52782			−0.0698808
$479$	−5.55588	+	3.20769i	−0.253855	+	0.146563i	−0.621528	−	0.783392i	$-0.713488\pi$
$479$	−5.55588	+	3.20769i	−0.253855	+	0.146563i	0.367673	+	0.929955i	$0.380154\pi$
$480$	2.87155	−	1.90271i	0.131068	−	0.0868466i
$481$	−4.04767	−	20.2844i	−0.184558	−	0.924891i
$482$	−0.713571	+	1.23594i	−0.0325023	+	0.0562956i
$483$	27.7420	−	1.71077i	1.26230	−	0.0778426i
$484$	5.47809	+	9.48832i	0.249004	+	0.431287i
$485$	−16.7725			−0.761602
$486$	−1.94606	−	1.77426i	−0.0882752	−	0.0804822i
$487$		−	20.7706i		−	0.941204i	−0.882346	−	0.470602i	$-0.844037\pi$
$487$		−	20.7706i		−	0.941204i	0.882346	−	0.470602i	$-0.155963\pi$
$488$	−1.75056	+	1.01068i	−0.0792439	+	0.0457515i
$489$	27.0164	−	1.66602i	1.22172	−	0.0753401i
$490$	0.281312	−	0.487246i	0.0127084	−	0.0220115i
$491$	1.95213	−	3.38118i	0.0880982	−	0.152591i	−0.818609	−	0.574351i	$-0.805254\pi$
$491$	1.95213	−	3.38118i	0.0880982	−	0.152591i	0.906707	+	0.421761i	$0.138588\pi$
$492$	−20.6248	−	31.1267i	−0.929840	−	1.40330i
$493$	−2.50863	−	4.34508i	−0.112983	−	0.195693i
$494$	2.59558	+	2.95606i	0.116781	+	0.132999i
$495$	−12.1147	+	1.49987i	−0.544517	+	0.0674139i
$496$			19.0254i			0.854267i
$497$	−5.45977	−	9.45660i	−0.244904	−	0.424186i
$498$	0.915948	+	0.456100i	0.0410446	+	0.0204383i
$499$	2.91052	+	1.68039i	0.130293	+	0.0752246i	0.563730	−	0.825959i	$-0.309366\pi$
$499$	2.91052	+	1.68039i	0.130293	+	0.0752246i	−0.433437	+	0.901184i	$0.642699\pi$
$500$	1.70733	+	0.985730i	0.0763543	+	0.0440832i
$501$	7.70983	−	15.4830i	0.344450	−	0.691730i
$502$	0.756521	−	0.436778i	0.0337652	−	0.0194943i
$503$	−18.6413			−0.831173			−0.415586	−	0.909554i	$-0.636424\pi$
$503$	−18.6413			−0.831173			−0.415586	+	0.909554i	$0.636424\pi$
$504$	−2.32354	−	3.07700i	−0.103499	−	0.137060i
$505$			6.98539i			0.310846i
$506$	−2.87926	−	4.98703i	−0.127999	−	0.221700i
$507$	−9.90546	−	20.2208i	−0.439917	−	0.898038i
$508$	−8.52314	+	14.7625i	−0.378153	+	0.654980i
$509$	−0.552125	−	0.318770i	−0.0244725	−	0.0141292i	0.487714	−	0.873004i	$-0.337831\pi$
$509$	−0.552125	−	0.318770i	−0.0244725	−	0.0141292i	−0.512186	+	0.858874i	$0.671164\pi$
$510$	−0.0127804	−	0.207249i	−0.000565928	−	0.00917714i
$511$	−5.54872	−	9.61067i	−0.245461	−	0.425151i
$512$			12.7550i			0.563699i
$513$	32.9875	−	6.16532i	1.45643	−	0.272206i
$514$		−	1.38437i		−	0.0610617i
$515$	−12.1620	+	7.02176i	−0.535924	+	0.309416i
$516$	−1.82858	−	29.6524i	−0.0804985	−	1.30537i
$517$	6.98297	−	12.0949i	0.307111	−	0.531931i
$518$	1.60782	+	0.928275i	0.0706436	+	0.0407861i
$519$	−23.2200	+	15.3858i	−1.01925	+	0.675361i
$520$	−0.776187	+	2.29116i	−0.0340381	+	0.100474i
$521$	−11.6561			−0.510662			−0.255331	−	0.966854i	$-0.582184\pi$
$521$	−11.6561			−0.510662			−0.255331	+	0.966854i	$0.582184\pi$
$522$	−3.29985	−	1.39679i	−0.144431	−	0.0611359i
$523$	−21.6071			−0.944814			−0.472407	−	0.881381i	$-0.656615\pi$
$523$	−21.6071			−0.944814			−0.472407	+	0.881381i	$0.656615\pi$
$524$	4.69216	+	8.12706i	0.204978	+	0.355032i
$525$	1.47898	−	2.97011i	0.0645478	−	0.129626i
$526$	2.01679	+	1.16439i	0.0879362	+	0.0507700i
$527$	3.05313	+	1.76273i	0.132996	+	0.0767855i
$528$	12.0309	−	24.1606i	0.523576	−	1.05145i
$529$	−23.5873	−	40.8544i	−1.02553	−	1.77628i
$530$	−0.310627			−0.0134928
$531$	−27.4845	−	11.6339i	−1.19272	−	0.504867i
$532$	24.3906			1.05747
$533$	37.3424	+	12.6507i	1.61748	+	0.547962i
$534$	−2.46193	+	1.63130i	−0.106538	+	0.0705931i
$535$	6.15830	+	3.55550i	0.266246	+	0.153717i
$536$	−1.30669	+	2.26326i	−0.0564406	+	0.0977580i
$537$	−0.712326	−	11.5512i	−0.0307391	−	0.498469i
$538$	2.44214	−	1.40997i	0.105288	−	0.0607881i
$539$		−	13.5515i		−	0.583705i
$540$	6.66469	+	7.77957i	0.286802	+	0.334779i
$541$		−	32.3894i		−	1.39253i	−0.717785	−	0.696265i	$-0.754844\pi$
$541$		−	32.3894i		−	1.39253i	0.717785	−	0.696265i	$-0.245156\pi$
$542$	−0.114123	−	0.197666i	−0.00490199	−	0.00849050i
$543$	1.29869	+	21.0597i	0.0557321	+	0.903758i
$544$	1.22224	+	0.705659i	0.0524030	+	0.0302549i
$545$	7.01740	−	12.1545i	0.300592	−	0.520641i
$546$	1.95044	+	0.529421i	0.0834710	+	0.0226571i
$547$	−1.61348	−	2.79463i	−0.0689875	−	0.119490i	0.829468	−	0.558554i	$-0.188644\pi$
$547$	−1.61348	−	2.79463i	−0.0689875	−	0.119490i	−0.898456	+	0.439064i	$0.855310\pi$
$548$		−	20.1821i		−	0.862137i
$549$	−5.44669	−	7.21290i	−0.232459	−	0.307839i
$550$	−0.687419			−0.0293116
$551$	39.5448	−	22.8312i	1.68467	−	0.972643i
$552$	−4.33926	+	8.71417i	−0.184691	+	0.370900i
$553$	−22.9771	−	13.2659i	−0.977087	−	0.564122i
$554$	1.16633	+	0.673381i	0.0495526	+	0.0286092i
$555$	−8.89469	−	4.42915i	−0.377559	−	0.188007i
$556$	11.3906	+	19.7292i	0.483071	+	0.836703i
$557$			10.5473i			0.446904i	0.974715	+	0.223452i	$0.0717325\pi$
$557$			10.5473i			0.446904i	−0.974715	+	0.223452i	$0.928267\pi$
$558$	2.49878	−	0.309361i	0.105782	−	0.0130963i
$559$	20.6977	+	23.5722i	0.875418	+	0.996997i
$560$	3.66802	+	6.35320i	0.155002	+	0.268472i
$561$	−2.76253	−	4.16917i	−0.116634	−	0.176022i
$562$	2.05399	−	3.55762i	0.0866424	−	0.150069i
$563$	−5.75539	+	9.96864i	−0.242561	+	0.420128i	−0.961443	−	0.275004i	$-0.911321\pi$
$563$	−5.75539	+	9.96864i	−0.242561	+	0.420128i	0.718882	+	0.695132i	$0.244654\pi$
$564$	−11.6977	+	0.721360i	−0.492560	+	0.0303747i
$565$	4.38856	−	2.53374i	0.184628	−	0.106595i
$566$			2.59778i			0.109193i
$567$	12.3778	−	12.0013i	0.519818	−	0.504006i
$568$	3.82445			0.160470
$569$	−11.4118	−	19.7658i	−0.478406	−	0.828624i	0.521287	−	0.853381i	$-0.325452\pi$
$569$	−11.4118	−	19.7658i	−0.478406	−	0.828624i	−0.999693	+	0.0247571i	$0.992119\pi$
$570$	1.88619	−	0.116316i	0.0790036	−	0.00487192i
$571$	−3.66812	+	6.35337i	−0.153506	+	0.265880i	−0.932514	−	0.361134i	$-0.882390\pi$
$571$	−3.66812	+	6.35337i	−0.153506	+	0.265880i	0.779008	+	0.627014i	$0.215723\pi$
$572$	5.66003	+	28.3646i	0.236658	+	1.18598i
$573$	23.8623	−	15.8113i	0.996861	−	0.660529i
$574$	−3.06472	+	1.76941i	−0.127919	+	0.0738539i
$575$	−8.37703			−0.349346
$576$	−21.8030	+	2.69933i	−0.908460	+	0.112472i
$577$			10.2351i			0.426092i	0.977042	+	0.213046i	$0.0683385\pi$
$577$			10.2351i			0.426092i	−0.977042	+	0.213046i	$0.931662\pi$
$578$	−2.41349	+	1.39343i	−0.100388	+	0.0579591i
$579$	−11.1064	+	22.3040i	−0.461566	+	0.926924i
$580$	12.0713	+	6.96939i	0.501235	+	0.289388i
$581$	−3.34940	+	5.80132i	−0.138956	+	0.240679i
$582$	−4.39324	−	2.18763i	−0.182106	−	0.0906803i
$583$	−6.47949	+	3.74094i	−0.268353	+	0.154934i
$584$	3.88676			0.160835
$585$	−10.5935	−	2.18563i	−0.437989	−	0.0903645i
$586$	−3.35959			−0.138784
$587$	−32.3746	+	18.6915i	−1.33624	+	0.771481i	−0.986248	−	0.165270i	$-0.947150\pi$
$587$	−32.3746	+	18.6915i	−1.33624	+	0.771481i	−0.349996	+	0.936751i	$0.613817\pi$
$588$	−9.47988	+	6.28145i	−0.390944	+	0.259043i
$589$	−16.0427	+	27.7867i	−0.661027	+	1.14493i
$590$	−1.45549	−	0.840330i	−0.0599218	−	0.0345959i
$591$	42.8221	−	2.64071i	1.76147	−	0.108624i
$592$	19.0262	−	10.9848i	0.781971	−	0.451471i
$593$		−	8.06905i		−	0.331356i	−0.986180	−	0.165678i	$-0.947019\pi$
$593$		−	8.06905i		−	0.331356i	0.986180	−	0.165678i	$-0.0529812\pi$
$594$	−3.36884	−	1.18726i	−0.138225	−	0.0487138i
$595$	1.35938			0.0557293
$596$	37.5351	−	21.6709i	1.53750	−	0.887676i
$597$	−1.01730	−	16.4967i	−0.0416354	−	0.675165i
$598$	−0.998505	−	5.00390i	−0.0408319	−	0.204624i
$599$	19.9770	−	34.6011i	0.816237	−	1.41376i	−0.0921994	−	0.995741i	$-0.529390\pi$
$599$	19.9770	−	34.6011i	0.816237	−	1.41376i	0.908436	−	0.418023i	$-0.137277\pi$
$600$	0.641882	+	0.968720i	0.0262047	+	0.0395478i
$601$	−9.30397	−	16.1150i	−0.379517	−	0.657343i	0.611475	−	0.791264i	$-0.290576\pi$
$601$	−9.30397	−	16.1150i	−0.379517	−	0.657343i	−0.990992	+	0.133921i	$0.957243\pi$
$602$	−2.81560			−0.114755
$603$	−10.7612	−	4.55510i	−0.438230	−	0.185498i
$604$		−	0.459253i		−	0.0186867i
$605$	−4.81284	+	2.77869i	−0.195670	+	0.112970i
$606$	−0.911101	+	1.82969i	−0.0370109	+	0.0743260i
$607$	1.43661	−	2.48828i	0.0583102	−	0.100996i	−0.835397	−	0.549647i	$-0.814762\pi$
$607$	1.43661	−	2.48828i	0.0583102	−	0.100996i	0.893707	+	0.448651i	$0.148095\pi$
$608$	−6.42224	+	11.1236i	−0.260456	+	0.451124i
$609$	10.4568	−	20.9995i	0.423730	−	0.850942i
$610$	−0.254487	−	0.440784i	−0.0103039	−	0.0178468i
$611$	9.29906	−	8.16508i	0.376200	−	0.330324i
$612$	−1.63602	+	3.86501i	−0.0661321	+	0.156234i
$613$		−	35.4684i		−	1.43256i	−0.697815	−	0.716278i	$-0.745844\pi$
$613$		−	35.4684i		−	1.43256i	0.697815	−	0.716278i	$-0.254156\pi$
$614$	0.172791	+	0.299283i	0.00697328	+	0.0120781i
$615$	15.7887	−	10.4617i	0.636661	−	0.421857i
$616$	−4.52912	−	2.61489i	−0.182483	−	0.105357i
$617$	−8.29254	−	4.78770i	−0.333845	−	0.192746i	0.323702	−	0.946159i	$-0.395073\pi$
$617$	−8.29254	−	4.78770i	−0.333845	−	0.192746i	−0.657547	+	0.753414i	$0.728406\pi$
$618$	−4.10145	+	0.252925i	−0.164985	+	0.0101741i
$619$	−31.7560	+	18.3343i	−1.27638	+	0.736920i	−0.976181	−	0.216956i	$-0.930387\pi$
$619$	−31.7560	+	18.3343i	−1.27638	+	0.736920i	−0.300201	+	0.953876i	$0.597054\pi$
$620$	−9.79427			−0.393347
$621$	−41.0535	−	14.4682i	−1.64742	−	0.580588i
$622$		−	3.82815i		−	0.153495i
$623$	−9.66739	−	16.7444i	−0.387316	−	0.670851i
$624$	16.9658	−	16.8559i	0.679178	−	0.674775i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.13537	+	0.655504i	0.0453783	+	0.0261992i
$627$	37.9438	−	25.1419i	1.51533	−	1.00407i
$628$	−20.2828	−	35.1308i	−0.809370	−	1.40187i
$629$		−	4.07100i		−	0.162321i
$630$	0.774778	−	0.585059i	0.0308679	−	0.0233093i
$631$		−	3.30174i		−	0.131440i	−0.997838	−	0.0657201i	$-0.979066\pi$
$631$		−	3.30174i		−	0.131440i	0.997838	−	0.0657201i	$-0.0209345\pi$
$632$	8.04749	−	4.64622i	0.320112	−	0.184817i
$633$	14.0077	+	6.97520i	0.556757	+	0.277239i
$634$	−0.407283	+	0.705435i	−0.0161753	+	0.0280164i
$635$	−7.48811	−	4.32326i	−0.297157	−	0.171563i
$636$	5.62035	+	2.79868i	0.222861	+	0.110975i
$637$	3.85286	−	11.3729i	0.152656	−	0.450611i
$638$	−4.86024			−0.192419
$639$	2.10111	+	16.9711i	0.0831187	+	0.671368i
$640$	−5.21478			−0.206132
$641$	23.0575	+	39.9368i	0.910718	+	1.57741i	0.813052	+	0.582191i	$0.197804\pi$
$641$	23.0575	+	39.9368i	0.910718	+	1.57741i	0.0976661	+	0.995219i	$0.468862\pi$
$642$	1.14930	+	1.73452i	0.0453594	+	0.0684559i
$643$	−15.7548	−	9.09606i	−0.621310	−	0.358713i	0.156069	−	0.987746i	$-0.450118\pi$
$643$	−15.7548	−	9.09606i	−0.621310	−	0.358713i	−0.777379	+	0.629033i	$0.783451\pi$
$644$	−27.3981	−	15.8183i	−1.07963	−	0.623328i
$645$	15.0408	−	0.927523i	0.592232	−	0.0365212i
$646$	0.387123	+	0.670517i	0.0152311	+	0.0263811i
$647$	43.5855			1.71352			0.856761	−	0.515714i	$-0.172473\pi$
$647$	43.5855			1.71352			0.856761	+	0.515714i	$0.172473\pi$
$648$	1.47258	+	5.85603i	0.0578485	+	0.230047i
$649$	−40.4809			−1.58902
$650$	−0.576905	−	0.195441i	−0.0226281	−	0.00766584i
$651$	1.01458	+	16.4525i	0.0397644	+	0.644824i
$652$	−26.6815	−	15.4045i	−1.04493	−	0.603289i
$653$	11.5654	−	20.0318i	0.452587	−	0.783904i	−0.545958	−	0.837812i	$-0.683834\pi$
$653$	11.5654	−	20.0318i	0.452587	−	0.783904i	0.998546	+	0.0539078i	$0.0171677\pi$
$654$	3.42337	−	2.26835i	0.133864	−	0.0886997i
$655$	−4.12236	+	2.38004i	−0.161074	+	0.0929960i
$656$			41.8768i			1.63501i
$657$	2.13535	+	17.2477i	0.0833078	+	0.672895i
$658$			1.11074i			0.0433010i
$659$	−7.11951	−	12.3314i	−0.277337	−	0.480361i	0.693385	−	0.720567i	$-0.256118\pi$
$659$	−7.11951	−	12.3314i	−0.277337	−	0.480361i	−0.970722	+	0.240206i	$0.922785\pi$
$660$	12.4378	+	6.19347i	0.484142	+	0.241080i
$661$	35.9030	+	20.7286i	1.39647	+	0.806250i	0.994021	−	0.109194i	$-0.0348268\pi$
$661$	35.9030	+	20.7286i	1.39647	+	0.806250i	0.402446	+	0.915444i	$0.368160\pi$
$662$	1.96537	−	3.40412i	0.0763863	−	0.132305i
$663$	−1.13306	−	4.28433i	−0.0440046	−	0.166390i
$664$	−1.17309	−	2.03185i	−0.0455247	−	0.0788510i
$665$			12.3718i			0.479759i
$666$	−1.75210	−	2.32026i	−0.0678924	−	0.0899082i
$667$	−59.2279			−2.29331
$668$	−17.0496	+	9.84358i	−0.659668	+	0.380859i
$669$	14.2446	+	21.4977i	0.550727	+	0.831150i
$670$	−0.569881	−	0.329021i	−0.0220164	−	0.0127112i
$671$	−10.6169	−	6.12965i	−0.409859	−	0.236632i
$672$	0.406158	+	6.58630i	0.0156679	+	0.254072i
$673$	11.7253	+	20.3088i	0.451976	+	0.782846i	0.998509	−	0.0545919i	$-0.0173858\pi$
$673$	11.7253	+	20.3088i	0.451976	+	0.782846i	−0.546532	+	0.837438i	$0.684052\pi$
$674$		−	1.31491i		−	0.0506484i
$675$	−3.94609	+	3.38058i	−0.151885	+	0.130119i
$676$	−3.31430	+	25.4138i	−0.127473	+	0.977453i
$677$	−0.562558	−	0.974380i	−0.0216209	−	0.0374484i	0.855013	−	0.518607i	$-0.173549\pi$
$677$	−0.562558	−	0.974380i	−0.0216209	−	0.0374484i	−0.876633	+	0.481159i	$0.840216\pi$
$678$	1.47997	−	0.0912655i	0.0568379	−	0.00350503i
$679$	16.0650	−	27.8254i	0.616517	−	1.06784i
$680$	−0.238054	+	0.412322i	−0.00912897	+	0.0158118i
$681$	15.6512	+	23.6206i	0.599755	+	0.905142i
$682$	2.95758	−	1.70756i	0.113251	−	0.0653857i
$683$			12.0170i			0.459819i	0.973212	+	0.229910i	$0.0738430\pi$
$683$			12.0170i			0.459819i	−0.973212	+	0.229910i	$0.926157\pi$
$684$	−35.1757	−	14.8895i	−1.34498	−	0.569314i
$685$	10.2371			0.391141
$686$	1.67156	+	2.89523i	0.0638205	+	0.110540i
$687$	−1.79556	+	3.60588i	−0.0685050	+	0.137573i
$688$	−16.6593	+	28.8547i	−0.635128	+	1.10007i
$689$	−6.50141	+	1.29733i	−0.247684	+	0.0494242i
$690$	−2.19420	−	1.09261i	−0.0835317	−	0.0415950i
$691$	31.5057	−	18.1898i	1.19853	−	0.691973i	0.238304	−	0.971191i	$-0.423409\pi$
$691$	31.5057	−	18.1898i	1.19853	−	0.691973i	0.960228	+	0.279218i	$0.0900752\pi$
$692$	31.7050			1.20524
$693$	9.11542	−	21.5347i	0.346266	−	0.818037i
$694$			2.78113i			0.105570i
$695$	−10.0074	+	5.77777i	−0.379602	+	0.219163i
$696$	4.53829	+	6.84912i	0.172023	+	0.259615i
$697$	6.72023	+	3.87993i	0.254547	+	0.146963i
$698$	−3.07751	+	5.33040i	−0.116485	+	0.201759i
$699$	0.904345	+	14.6650i	0.0342055	+	0.554680i
$700$	−3.27062	+	1.88829i	−0.123618	+	0.0713708i
$701$	14.7142			0.555748			0.277874	−	0.960618i	$-0.410370\pi$
$701$	14.7142			0.555748			0.277874	+	0.960618i	$0.410370\pi$
$702$	−2.48970	−	1.95419i	−0.0939677	−	0.0737562i
$703$	37.0504			1.39738
$704$	−25.8063	+	14.8993i	−0.972611	+	0.561537i
$705$	−0.365901	−	5.93350i	−0.0137806	−	0.223468i
$706$	−2.07339	+	3.59122i	−0.0780332	+	0.135157i
$707$	−11.5887	−	6.69071i	−0.435836	−	0.251630i
$708$	18.7639	+	28.3182i	0.705189	+	1.06426i
$709$	8.92475	−	5.15271i	0.335176	−	0.193514i	−0.322961	−	0.946412i	$-0.604678\pi$
$709$	8.92475	−	5.15271i	0.335176	−	0.193514i	0.658137	+	0.752898i	$0.271345\pi$
$710$			0.962983i			0.0361401i
$711$	25.0390	+	33.1585i	0.939036	+	1.24354i
$712$	6.77179			0.253784
$713$	36.0416	−	20.8086i	1.34977	−	0.779290i
$714$	0.356064	+	0.177304i	0.0133254	+	0.00663542i
$715$	−14.3876	+	2.87099i	−0.538066	+	0.107369i
$716$	−6.58638	+	11.4079i	−0.246145	+	0.426335i
$717$	−6.98227	+	14.0219i	−0.260757	+	0.523657i
$718$	0.451964	+	0.782824i	0.0168671	+	0.0292147i
$719$	14.8608			0.554214			0.277107	−	0.960839i	$-0.410624\pi$
$719$	14.8608			0.554214			0.277107	+	0.960839i	$0.410624\pi$
$720$	−1.41158	−	11.4017i	−0.0526067	−	0.424915i
$721$		−	26.9022i		−	1.00189i
$722$	−3.32264	+	1.91833i	−0.123656	+	0.0713927i
$723$	8.08205	+	12.1973i	0.300575	+	0.453623i
$724$	12.0081	−	20.7986i	0.446277	−	0.772974i
$725$	−3.53514	+	6.12304i	−0.131292	+	0.227404i
$726$	−1.62305	+	0.100089i	−0.0602371	+	0.00371465i
$727$	10.5033	+	18.1923i	0.389547	+	0.674715i	0.992389	−	0.123146i	$-0.0392984\pi$
$727$	10.5033	+	18.1923i	0.389547	+	0.674715i	−0.602842	+	0.797861i	$0.705965\pi$
$728$	−3.05755	−	3.48218i	−0.113320	−	0.129058i
$729$	−25.1774	+	9.75190i	−0.932496	+	0.361181i
$730$			0.978672i			0.0362223i
$731$	3.08699	+	5.34683i	0.114177	+	0.197760i
$732$	0.633210	+	10.2682i	0.0234041	+	0.379523i
$733$	27.4355	+	15.8399i	1.01335	+	0.585059i	0.912171	−	0.409809i	$-0.134405\pi$
$733$	27.4355	+	15.8399i	1.01335	+	0.585059i	0.101180	+	0.994868i	$0.467738\pi$
$734$	3.00929	+	1.73742i	0.111075	+	0.0641292i
$735$	−3.18619	−	4.80856i	−0.117524	−	0.177366i
$736$	14.4283	−	8.33017i	0.531833	−	0.307054i
$737$	−15.8498			−0.583835
$738$	5.50005	−	0.680933i	0.202460	−	0.0250655i
$739$			1.83321i			0.0674357i	0.999431	+	0.0337178i	$0.0107348\pi$
$739$			1.83321i			0.0674357i	−0.999431	+	0.0337178i	$0.989265\pi$
$740$	5.65494	+	9.79465i	0.207880	+	0.360058i
$741$	38.9919	−	10.3121i	1.43240	−	0.378824i
$742$	0.297523	−	0.515326i	0.0109224	−	0.0189182i
$743$	−3.03436	−	1.75189i	−0.111320	−	0.0642705i	0.443306	−	0.896370i	$-0.353805\pi$
$743$	−3.03436	−	1.75189i	−0.111320	−	0.0642705i	−0.554626	+	0.832100i	$0.687139\pi$
$744$	−5.16797	−	2.57341i	−0.189467	−	0.0943459i
$745$	10.9923	+	19.0393i	0.402727	+	0.697544i
$746$			1.91093i			0.0699640i
$747$	8.37193	−	6.32191i	0.306313	−	0.231306i
$748$			5.69265i			0.208144i
$749$	−11.7970	+	6.81101i	−0.431053	+	0.248869i
$750$	−0.243920	+	0.161624i	−0.00890671	+	0.00590166i
$751$	17.3289	−	30.0145i	0.632341	−	1.09525i	−0.354731	−	0.934968i	$-0.615428\pi$
$751$	17.3289	−	30.0145i	0.632341	−	1.09525i	0.987072	−	0.160278i	$-0.0512391\pi$
$752$	11.3830	+	6.57196i	0.415094	+	0.239655i
$753$	−0.551258	−	8.93926i	−0.0200890	−	0.325765i
$754$	−4.07888	−	1.38182i	−0.148544	−	0.0503231i
$755$	0.232951			0.00847794
$756$	−19.2897	+	3.60522i	−0.701560	+	0.131121i
$757$	3.05994			0.111216			0.0556078	−	0.998453i	$-0.482290\pi$
$757$	3.05994			0.111216			0.0556078	+	0.998453i	$0.482290\pi$
$758$	−0.0897409	−	0.155436i	−0.00325954	−	0.00564568i
$759$	−58.9281	+	3.63392i	−2.13895	+	0.131903i
$760$	−3.75257	−	2.16655i	−0.136120	−	0.0785890i
$761$	−24.7251	−	14.2750i	−0.896283	−	0.517469i	−0.0202909	−	0.999794i	$-0.506459\pi$
$761$	−24.7251	−	14.2750i	−0.896283	−	0.517469i	−0.875993	+	0.482325i	$0.839793\pi$
$762$	−1.39748	−	2.10906i	−0.0506255	−	0.0764033i
$763$	13.4427	+	23.2835i	0.486659	+	0.842919i
$764$	−32.5820			−1.17877
$765$	−1.96048	−	0.829851i	−0.0708814	−	0.0300033i
$766$	0.192274			0.00694713
$767$	−33.9730	−	11.5092i	−1.22669	−	0.415574i
$768$	21.3426	+	10.6277i	0.770136	+	0.383493i
$769$	−5.78804	−	3.34173i	−0.208722	−	0.120506i	0.391995	−	0.919967i	$-0.371785\pi$
$769$	−5.78804	−	3.34173i	−0.208722	−	0.120506i	−0.600717	+	0.799461i	$0.705118\pi$
$770$	0.658419	−	1.14042i	0.0237278	−	0.0410977i
$771$	−12.7053	−	6.32667i	−0.457571	−	0.227850i
$772$	24.5607	−	14.1801i	0.883960	−	0.510355i
$773$			7.34991i			0.264358i	0.991226	+	0.132179i	$0.0421973\pi$
$773$			7.34991i			0.264358i	−0.991226	+	0.132179i	$0.957803\pi$
$774$	4.06062

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)

\(f(q)\)	\(=\)	\(q+(0.146304 - 0.0844686i) q^{2} +(-0.106608 - 1.72877i) q^{3} +(-0.985730 + 1.70733i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.161624 - 0.243920i) q^{6} +(1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 + 0.368601i) q^{9} +O(q^{10})\)	\(q+(0.146304 - 0.0844686i) q^{2} +(-0.106608 - 1.72877i) q^{3} +(-0.985730 + 1.70733i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.161624 - 0.243920i) q^{6} +(1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 + 0.368601i) q^{9} -0.168937 q^{10} +(-3.52392 + 2.03454i) q^{11} +(3.05667 + 1.52208i) q^{12} +(-3.53584 + 0.705562i) q^{13} +(0.161810 - 0.280264i) q^{14} +(-0.772058 + 1.55046i) q^{15} +(-1.91479 - 3.31651i) q^{16} -0.709628 q^{17} +(-0.404451 + 0.305414i) q^{18} -6.45837i q^{19} +(1.70733 - 0.985730i) q^{20} +(-1.83270 - 2.76588i) q^{21} +(-0.343709 + 0.595322i) q^{22} +(-4.18851 + 7.25472i) q^{23} +(1.15988 - 0.0715262i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.457710 + 0.401894i) q^{26} +(0.954626 + 5.10771i) q^{27} +3.77659i q^{28} +(3.53514 + 6.12304i) q^{29} +(0.0180101 + 0.292053i) q^{30} +(-4.30244 - 2.48401i) q^{31} +(-1.72236 - 0.994406i) q^{32} +(3.89292 + 5.87515i) q^{33} +(-0.103821 + 0.0599413i) q^{34} -1.91563 q^{35} +(2.30546 - 5.44654i) q^{36} +5.73681i q^{37} +(-0.545529 - 0.944885i) q^{38} +(1.59670 + 6.03743i) q^{39} +(0.335464 - 0.581040i) q^{40} +(-9.47008 - 5.46755i) q^{41} +(-0.501761 - 0.249854i) q^{42} +(-4.35016 - 7.53470i) q^{43} -8.02202i q^{44} +(2.76269 + 1.16942i) q^{45} +1.41519i q^{46} +(-2.97238 + 1.71611i) q^{47} +(-5.52934 + 3.66379i) q^{48} +(-1.66518 + 2.88418i) q^{49} +(0.146304 + 0.0844686i) q^{50} +(0.0756520 + 1.22678i) q^{51} +(2.28076 - 6.73236i) q^{52} +1.83872 q^{53} +(0.571107 + 0.666642i) q^{54} +4.06908 q^{55} +(0.642624 + 1.11306i) q^{56} +(-11.1650 + 0.688514i) q^{57} +(1.03441 + 0.597217i) q^{58} +(8.61560 + 4.97422i) q^{59} +(-1.88611 - 2.84650i) q^{60} +(1.50640 + 2.60916i) q^{61} -0.839285 q^{62} +(-4.58619 + 3.46317i) q^{63} +7.32317 q^{64} +(3.41491 + 1.15689i) q^{65} +(1.06582 + 0.530727i) q^{66} +(3.37333 + 1.94759i) q^{67} +(0.699502 - 1.21157i) q^{68} +(12.9882 + 6.46755i) q^{69} +(-0.280264 + 0.161810i) q^{70} -5.70024i q^{71} +(-0.247304 - 1.99753i) q^{72} -5.79311i q^{73} +(0.484580 + 0.839317i) q^{74} +(1.44385 - 0.956709i) q^{75} +(11.0266 + 6.36621i) q^{76} +(-3.89742 + 6.75053i) q^{77} +(0.743577 + 0.748428i) q^{78} +(-6.92507 - 11.9946i) q^{79} +3.82958i q^{80} +(8.72827 - 2.19485i) q^{81} -1.84735 q^{82} +(-3.02842 + 1.74846i) q^{83} +(6.52884 - 0.402614i) q^{84} +(0.614556 + 0.354814i) q^{85} +(-1.27289 - 0.734904i) q^{86} +(10.2084 - 6.76420i) q^{87} +(-1.36503 - 2.36430i) q^{88} -10.0932i q^{89} +(0.502972 - 0.0622704i) q^{90} +(-5.19011 + 4.55720i) q^{91} +(-8.25749 - 14.3024i) q^{92} +(-3.83561 + 7.70273i) q^{93} +(-0.289914 + 0.502146i) q^{94} +(-3.22918 + 5.59311i) q^{95} +(-1.53548 + 3.08357i) q^{96} +(14.5254 - 8.38627i) q^{97} +0.562623i q^{98} +(9.74174 - 7.35629i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more