LMFDB - Embedded newform 570.2.s.b.221.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.1
Character	$\chi$	$=$	570.221
Dual form			570.2.s.b.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.71401 - 0.249340i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.641070 - 1.60905i) q^{6} -2.43208 q^{7} -1.00000 q^{8} +(2.87566 + 0.854742i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.71401 - 0.249340i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.641070 - 1.60905i) q^{6} -2.43208 q^{7} -1.00000 q^{8} +(2.87566 + 0.854742i) q^{9} +(0.866025 + 0.500000i) q^{10} +2.32454i q^{11} +(1.07294 - 1.35971i) q^{12} +(-0.190454 - 0.109959i) q^{13} +(-1.21604 - 2.10624i) q^{14} +(-1.60905 + 0.641070i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.43932 + 2.56304i) q^{17} +(0.697602 + 2.91776i) q^{18} +(-3.94445 - 1.85508i) q^{19} +1.00000i q^{20} +(4.16860 + 0.606413i) q^{21} +(-2.01311 + 1.16227i) q^{22} +(-7.51400 - 4.33821i) q^{23} +(1.71401 + 0.249340i) q^{24} +(0.500000 - 0.866025i) q^{25} -0.219917i q^{26} +(-4.71579 - 2.18205i) q^{27} +(1.21604 - 2.10624i) q^{28} +(-3.98772 + 6.90694i) q^{29} +(-1.35971 - 1.07294i) q^{30} -4.02893i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.579599 - 3.98428i) q^{33} +(-4.43932 - 2.56304i) q^{34} +(-2.10624 + 1.21604i) q^{35} +(-2.17806 + 2.06302i) q^{36} +1.28133i q^{37} +(-0.365675 - 4.34353i) q^{38} +(0.299023 + 0.235958i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.19057 + 2.06213i) q^{41} +(1.55913 + 3.91332i) q^{42} +(-0.705429 - 1.22184i) q^{43} +(-2.01311 - 1.16227i) q^{44} +(2.91776 - 0.697602i) q^{45} -8.67642i q^{46} +(4.74957 + 2.74216i) q^{47} +(0.641070 + 1.60905i) q^{48} -1.08501 q^{49} +1.00000 q^{50} +(8.24811 - 3.28618i) q^{51} +(0.190454 - 0.109959i) q^{52} +(-2.04507 + 3.54217i) q^{53} +(-0.468182 - 5.17502i) q^{54} +(1.16227 + 2.01311i) q^{55} +2.43208 q^{56} +(6.29828 + 4.16314i) q^{57} -7.97545 q^{58} +(-0.478076 - 0.828051i) q^{59} +(0.249340 - 1.71401i) q^{60} +(4.12504 - 7.14478i) q^{61} +(3.48915 - 2.01446i) q^{62} +(-6.99382 - 2.07880i) q^{63} +1.00000 q^{64} -0.219917 q^{65} +(3.74029 - 1.49019i) q^{66} +(-6.63960 - 3.83338i) q^{67} -5.12609i q^{68} +(11.7974 + 9.30928i) q^{69} +(-2.10624 - 1.21604i) q^{70} +(5.05616 + 8.75753i) q^{71} +(-2.87566 - 0.854742i) q^{72} +(-1.78502 - 3.09174i) q^{73} +(-1.10967 + 0.640666i) q^{74} +(-1.07294 + 1.35971i) q^{75} +(3.57877 - 2.48845i) q^{76} -5.65345i q^{77} +(-0.0548341 + 0.376940i) q^{78} +(-13.0596 + 7.53998i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(7.53883 + 4.91589i) q^{81} +(-1.19057 + 2.06213i) q^{82} +4.36047i q^{83} +(-2.60947 + 3.30691i) q^{84} +(-2.56304 + 4.43932i) q^{85} +(0.705429 - 1.22184i) q^{86} +(8.55717 - 10.8443i) q^{87} -2.32454i q^{88} +(-2.03041 + 3.51677i) q^{89} +(2.06302 + 2.17806i) q^{90} +(0.463199 + 0.267428i) q^{91} +(7.51400 - 4.33821i) q^{92} +(-1.00457 + 6.90562i) q^{93} +5.48433i q^{94} +(-4.34353 + 0.365675i) q^{95} +(-1.07294 + 1.35971i) q^{96} +(6.10768 - 3.52627i) q^{97} +(-0.542503 - 0.939644i) q^{98} +(-1.98688 + 6.68457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.71401	−	0.249340i	−0.989584	−	0.143956i
$3$	−1.71401	−	0.249340i	−0.989584	−	0.143956i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−0.641070	−	1.60905i	−0.261716	−	0.656890i
$7$	−2.43208			−0.919238			−0.459619	−	0.888116i	$-0.652014\pi$
$7$	−2.43208			−0.919238			−0.459619	+	0.888116i	$0.652014\pi$
$8$	−1.00000			−0.353553
$9$	2.87566	+	0.854742i	0.958553	+	0.284914i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			2.32454i			0.700874i	0.936586	+	0.350437i	$0.113967\pi$
$11$			2.32454i			0.700874i	−0.936586	+	0.350437i	$0.886033\pi$
$12$	1.07294	−	1.35971i	0.309731	−	0.392513i
$13$	−0.190454	−	0.109959i	−0.0528224	−	0.0304970i	0.473356	−	0.880871i	$-0.343042\pi$
$13$	−0.190454	−	0.109959i	−0.0528224	−	0.0304970i	−0.526179	+	0.850374i	$0.676376\pi$
$14$	−1.21604	−	2.10624i	−0.325000	−	0.562916i
$15$	−1.60905	+	0.641070i	−0.415454	+	0.165524i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.43932	+	2.56304i	−1.07669	+	0.621629i	−0.930002	−	0.367553i	$-0.880196\pi$
$17$	−4.43932	+	2.56304i	−1.07669	+	0.621629i	−0.146691	+	0.989182i	$0.546862\pi$
$18$	0.697602	+	2.91776i	0.164426	+	0.687724i
$19$	−3.94445	−	1.85508i	−0.904918	−	0.425585i
$19$	−3.94445	−	1.85508i	−0.904918	−	0.425585i
$20$			1.00000i			0.223607i
$21$	4.16860	+	0.606413i	0.909664	+	0.132330i
$22$	−2.01311	+	1.16227i	−0.429196	+	0.247796i
$23$	−7.51400	−	4.33821i	−1.56678	−	0.904580i	−0.996541	−	0.0830996i	$-0.973518\pi$
$23$	−7.51400	−	4.33821i	−1.56678	−	0.904580i	−0.570237	−	0.821480i	$-0.693149\pi$
$24$	1.71401	+	0.249340i	0.349871	+	0.0508963i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	0.219917i		−	0.0431293i
$27$	−4.71579	−	2.18205i	−0.907554	−	0.419936i
$28$	1.21604	−	2.10624i	0.229810	−	0.398042i
$29$	−3.98772	+	6.90694i	−0.740502	+	1.28259i	0.211765	+	0.977321i	$0.432079\pi$
$29$	−3.98772	+	6.90694i	−0.740502	+	1.28259i	−0.952267	+	0.305266i	$0.901255\pi$
$30$	−1.35971	−	1.07294i	−0.248247	−	0.195891i
$31$		−	4.02893i		−	0.723616i	−0.932253	−	0.361808i	$-0.882160\pi$
$31$		−	4.02893i		−	0.723616i	0.932253	−	0.361808i	$-0.117840\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.579599	−	3.98428i	0.100895	−	0.693574i
$34$	−4.43932	−	2.56304i	−0.761337	−	0.439558i
$35$	−2.10624	+	1.21604i	−0.356019	+	0.205548i
$36$	−2.17806	+	2.06302i	−0.363010	+	0.343837i
$37$			1.28133i			0.210650i	0.994438	+	0.105325i	$0.0335883\pi$
$37$			1.28133i			0.210650i	−0.994438	+	0.105325i	$0.966412\pi$
$38$	−0.365675	−	4.34353i	−0.0593203	−	0.704614i
$39$	0.299023	+	0.235958i	0.0478820	+	0.0377835i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	1.19057	+	2.06213i	0.185936	+	0.322050i	0.943891	−	0.330256i	$-0.107135\pi$
$41$	1.19057	+	2.06213i	0.185936	+	0.322050i	−0.757956	+	0.652306i	$0.773802\pi$
$42$	1.55913	+	3.91332i	0.240579	+	0.603839i
$43$	−0.705429	−	1.22184i	−0.107577	−	0.186329i	0.807211	−	0.590263i	$-0.200976\pi$
$43$	−0.705429	−	1.22184i	−0.107577	−	0.186329i	−0.914788	+	0.403934i	$0.867643\pi$
$44$	−2.01311	−	1.16227i	−0.303487	−	0.175218i
$45$	2.91776	−	0.697602i	0.434955	−	0.103992i
$46$		−	8.67642i		−	1.27927i
$47$	4.74957	+	2.74216i	0.692795	+	0.399986i	0.804658	−	0.593738i	$-0.202348\pi$
$47$	4.74957	+	2.74216i	0.692795	+	0.399986i	−0.111863	+	0.993724i	$0.535682\pi$
$48$	0.641070	+	1.60905i	0.0925305	+	0.232246i
$49$	−1.08501			−0.155001
$50$	1.00000			0.141421
$51$	8.24811	−	3.28618i	1.15497	−	0.460157i
$52$	0.190454	−	0.109959i	0.0264112	−	0.0152485i
$53$	−2.04507	+	3.54217i	−0.280912	+	0.486555i	−0.971610	−	0.236589i	$-0.923970\pi$
$53$	−2.04507	+	3.54217i	−0.280912	+	0.486555i	0.690697	+	0.723144i	$0.257304\pi$
$54$	−0.468182	−	5.17502i	−0.0637114	−	0.704231i
$55$	1.16227	+	2.01311i	0.156720	+	0.271447i
$56$	2.43208			0.325000
$57$	6.29828	+	4.16314i	0.834227	+	0.551421i
$58$	−7.97545			−1.04723
$59$	−0.478076	−	0.828051i	−0.0622402	−	0.107803i	0.833226	−	0.552932i	$-0.186491\pi$
$59$	−0.478076	−	0.828051i	−0.0622402	−	0.107803i	−0.895466	+	0.445129i	$0.853158\pi$
$60$	0.249340	−	1.71401i	0.0321896	−	0.221278i
$61$	4.12504	−	7.14478i	0.528158	−	0.914796i	−0.471304	−	0.881971i	$-0.656216\pi$
$61$	4.12504	−	7.14478i	0.528158	−	0.914796i	0.999461	−	0.0328247i	$-0.0104503\pi$
$62$	3.48915	−	2.01446i	0.443123	−	0.255837i
$63$	−6.99382	−	2.07880i	−0.881139	−	0.261904i
$64$	1.00000			0.125000
$65$	−0.219917			−0.0272774
$66$	3.74029	−	1.49019i	0.460397	−	0.183430i
$67$	−6.63960	−	3.83338i	−0.811157	−	0.468322i	0.0362006	−	0.999345i	$-0.488474\pi$
$67$	−6.63960	−	3.83338i	−0.811157	−	0.468322i	−0.847357	+	0.531023i	$0.821808\pi$
$68$		−	5.12609i		−	0.621629i
$69$	11.7974	+	9.30928i	1.42024	+	1.12071i
$70$	−2.10624	−	1.21604i	−0.251744	−	0.145344i
$71$	5.05616	+	8.75753i	0.600056	+	1.03933i	0.992812	+	0.119685i	$0.0381885\pi$
$71$	5.05616	+	8.75753i	0.600056	+	1.03933i	−0.392756	+	0.919643i	$0.628478\pi$
$72$	−2.87566	−	0.854742i	−0.338900	−	0.100732i
$73$	−1.78502	−	3.09174i	−0.208921	−	0.361861i	0.742454	−	0.669897i	$-0.233662\pi$
$73$	−1.78502	−	3.09174i	−0.208921	−	0.361861i	−0.951375	+	0.308036i	$0.900328\pi$
$74$	−1.10967	+	0.640666i	−0.128996	+	0.0744760i
$75$	−1.07294	+	1.35971i	−0.123892	+	0.157005i
$76$	3.57877	−	2.48845i	0.410513	−	0.285445i
$77$		−	5.65345i		−	0.644270i
$78$	−0.0548341	+	0.376940i	−0.00620874	+	0.0426801i
$79$	−13.0596	+	7.53998i	−1.46932	+	0.848313i	−0.999408	−	0.0343988i	$-0.989048\pi$
$79$	−13.0596	+	7.53998i	−1.46932	+	0.848313i	−0.469914	+	0.882712i	$0.655715\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	7.53883	+	4.91589i	0.837648	+	0.546210i
$82$	−1.19057	+	2.06213i	−0.131476	+	0.227724i
$83$			4.36047i			0.478623i	0.970943	+	0.239312i	$0.0769218\pi$
$83$			4.36047i			0.478623i	−0.970943	+	0.239312i	$0.923078\pi$
$84$	−2.60947	+	3.30691i	−0.284717	+	0.360813i
$85$	−2.56304	+	4.43932i	−0.278001	+	0.481512i
$86$	0.705429	−	1.22184i	0.0760684	−	0.131754i
$87$	8.55717	−	10.8443i	0.917425	−	1.16263i
$88$		−	2.32454i		−	0.247796i
$89$	−2.03041	+	3.51677i	−0.215223	+	0.372776i	−0.953341	−	0.301894i	$-0.902381\pi$
$89$	−2.03041	+	3.51677i	−0.215223	+	0.372776i	0.738119	+	0.674671i	$0.235714\pi$
$90$	2.06302	+	2.17806i	0.217462	+	0.229587i
$91$	0.463199	+	0.267428i	0.0485564	+	0.0280341i
$92$	7.51400	−	4.33821i	0.783389	−	0.452290i
$93$	−1.00457	+	6.90562i	−0.104169	+	0.716079i
$94$			5.48433i			0.565665i
$95$	−4.34353	+	0.365675i	−0.445637	+	0.0375175i
$96$	−1.07294	+	1.35971i	−0.109506	+	0.138774i
$97$	6.10768	−	3.52627i	0.620141	−	0.358038i	−0.156783	−	0.987633i	$-0.550112\pi$
$97$	6.10768	−	3.52627i	0.620141	−	0.358038i	0.776924	+	0.629595i	$0.216779\pi$
$98$	−0.542503	−	0.939644i	−0.0548011	−	0.0949183i
$99$	−1.98688	+	6.68457i	−0.199689	+	0.671825i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	10.2389	+	5.91143i	1.01881	+	0.588209i	0.913759	−	0.406258i	$-0.133166\pi$
$101$	10.2389	+	5.91143i	1.01881	+	0.588209i	0.105050	+	0.994467i	$0.466500\pi$
$102$	6.96997	+	5.49998i	0.690130	+	0.544579i
$103$			17.5769i			1.73190i	0.500130	+	0.865950i	$0.333286\pi$
$103$			17.5769i			1.73190i	−0.500130	+	0.865950i	$0.666714\pi$
$104$	0.190454	+	0.109959i	0.0186756	+	0.0107823i
$105$	3.91332	−	1.55913i	0.381901	−	0.152156i
$106$	−4.09015			−0.397270
$107$	2.80439			0.271111			0.135555	−	0.990770i	$-0.456718\pi$
$107$	2.80439			0.271111			0.135555	+	0.990770i	$0.456718\pi$
$108$	4.24761	−	2.99297i	0.408726	−	0.287998i
$109$	13.8072	−	7.97161i	1.32249	−	0.763542i	0.338368	−	0.941014i	$-0.390125\pi$
$109$	13.8072	−	7.97161i	1.32249	−	0.763542i	0.984126	+	0.177472i	$0.0567919\pi$
$110$	−1.16227	+	2.01311i	−0.110818	+	0.191942i
$111$	0.319487	−	2.19622i	0.0303244	−	0.208456i
$112$	1.21604	+	2.10624i	0.114905	+	0.199021i
$113$	12.1749			1.14532			0.572659	−	0.819794i	$-0.305912\pi$
$113$	12.1749			1.14532			0.572659	+	0.819794i	$0.305912\pi$
$114$	−0.456245	+	7.53604i	−0.0427313	+	0.705814i
$115$	−8.67642			−0.809081
$116$	−3.98772	−	6.90694i	−0.370251	−	0.641293i
$117$	−0.453695	−	0.478993i	−0.0419441	−	0.0442829i
$118$	0.478076	−	0.828051i	0.0440104	−	0.0762283i
$119$	10.7968	−	6.23351i	0.989738	−	0.571425i
$120$	1.60905	−	0.641070i	0.146885	−	0.0585214i
$121$	5.59653			0.508776
$122$	8.25009			0.746928
$123$	−1.52648	−	3.83136i	−0.137638	−	0.345462i
$124$	3.48915	+	2.01446i	0.313335	+	0.180904i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.69662	−	7.09623i	−0.151147	−	0.632182i
$127$	2.43948	+	1.40844i	0.216469	+	0.124979i	0.604314	−	0.796746i	$-0.293447\pi$
$127$	2.43948	+	1.40844i	0.216469	+	0.124979i	−0.387845	+	0.921725i	$0.626780\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.904459	+	2.27014i	0.0796332	+	0.199874i
$130$	−0.109959	−	0.190454i	−0.00964401	−	0.0167039i
$131$	7.22873	−	4.17351i	0.631577	−	0.364641i	−0.149785	−	0.988719i	$-0.547858\pi$
$131$	7.22873	−	4.17351i	0.631577	−	0.364641i	0.781363	+	0.624077i	$0.214525\pi$
$132$	3.16069	+	2.49409i	0.275102	+	0.217082i
$133$	9.59320	+	4.51170i	0.831836	+	0.391214i
$134$		−	7.66675i		−	0.662307i
$135$	−5.17502	+	0.468182i	−0.445395	+	0.0402947i
$136$	4.43932	−	2.56304i	0.380669	−	0.219779i
$137$	−12.6626	−	7.31076i	−1.08184	−	0.624600i	−0.150448	−	0.988618i	$-0.548071\pi$
$137$	−12.6626	−	7.31076i	−1.08184	−	0.624600i	−0.931392	+	0.364018i	$0.881405\pi$
$138$	−2.16338	+	14.8715i	−0.184159	+	1.26594i
$139$	5.51342	−	9.54952i	0.467642	−	0.809979i	−0.531675	−	0.846949i	$-0.678437\pi$
$139$	5.51342	−	9.54952i	0.467642	−	0.809979i	0.999316	+	0.0369693i	$0.0117704\pi$
$140$		−	2.43208i		−	0.205548i
$141$	−7.45707	−	5.88435i	−0.627999	−	0.495552i
$142$	−5.05616	+	8.75753i	−0.424304	+	0.734916i
$143$	0.255603	−	0.442717i	0.0213746	−	0.0370219i
$144$	−0.697602	−	2.91776i	−0.0581335	−	0.243147i
$145$			7.97545i			0.662325i
$146$	1.78502	−	3.09174i	0.147729	−	0.255874i
$147$	1.85971	+	0.270535i	0.153387	+	0.0223134i
$148$	−1.10967	−	0.640666i	−0.0912141	−	0.0526625i
$149$	−18.2772	+	10.5523i	−1.49732	+	0.864480i	−0.999995	−	0.00308349i	$-0.999018\pi$
$149$	−18.2772	+	10.5523i	−1.49732	+	0.864480i	−0.497327	+	0.867563i	$0.665685\pi$
$150$	−1.71401	−	0.249340i	−0.139948	−	0.0203585i
$151$			24.2149i			1.97058i	0.170899	+	0.985289i	$0.445333\pi$
$151$			24.2149i			1.97058i	−0.170899	+	0.985289i	$0.554667\pi$
$152$	3.94445	+	1.85508i	0.319937	+	0.150467i
$153$	−14.9567	+	3.57597i	−1.20918	+	0.289100i
$154$	4.89603	−	2.82672i	0.394533	−	0.227784i
$155$	−2.01446	−	3.48915i	−0.161806	−	0.280255i
$156$	−0.353857	+	0.140982i	−0.0283312	+	0.0112876i
$157$	−6.46343	−	11.1950i	−0.515837	−	0.893457i	−0.999831	−	0.0183851i	$-0.994147\pi$
$157$	−6.46343	−	11.1950i	−0.515837	−	0.893457i	0.483993	−	0.875072i	$-0.339186\pi$
$158$	−13.0596	−	7.53998i	−1.03897	−	0.599848i
$159$	4.38848	−	5.56140i	0.348029	−	0.441048i
$160$		−	1.00000i		−	0.0790569i
$161$	18.2746	+	10.5509i	1.44024	+	0.831524i
$162$	−0.487870	+	8.98677i	−0.0383307	+	0.706067i
$163$	13.6212			1.06690			0.533449	−	0.845832i	$-0.320896\pi$
$163$	13.6212			1.06690			0.533449	+	0.845832i	$0.320896\pi$
$164$	−2.38114			−0.185936
$165$	−1.49019	−	3.74029i	−0.116011	−	0.291181i
$166$	−3.77627	+	2.18023i	−0.293096	+	0.169219i
$167$	−5.43020	+	9.40538i	−0.420202	+	0.727810i	−0.995959	−	0.0898102i	$-0.971374\pi$
$167$	−5.43020	+	9.40538i	−0.420202	+	0.727810i	0.575757	+	0.817621i	$0.304707\pi$
$168$	−4.16860	−	0.606413i	−0.321615	−	0.0467858i
$169$	−6.47582	−	11.2164i	−0.498140	−	0.862804i
$170$	−5.12609			−0.393153
$171$	−9.75727	−	8.70607i	−0.746157	−	0.665770i
$172$	1.41086			0.107577
$173$	−6.04765	−	10.4748i	−0.459794	−	0.796387i	0.539156	−	0.842206i	$-0.318743\pi$
$173$	−6.04765	−	10.4748i	−0.459794	−	0.796387i	−0.998950	+	0.0458193i	$0.985410\pi$
$174$	13.6700	+	1.98860i	1.03632	+	0.150755i
$175$	−1.21604	+	2.10624i	−0.0919238	+	0.159217i
$176$	2.01311	−	1.16227i	0.151744	−	0.0876092i
$177$	0.612960	+	1.53849i	0.0460729	+	0.115640i
$178$	−4.06081			−0.304371
$179$	−9.17378			−0.685681			−0.342840	−	0.939394i	$-0.611389\pi$
$179$	−9.17378			−0.685681			−0.342840	+	0.939394i	$0.611389\pi$
$180$	−0.854742	+	2.87566i	−0.0637087	+	0.214339i
$181$	−8.37372	−	4.83457i	−0.622414	−	0.359351i	0.155395	−	0.987852i	$-0.450335\pi$
$181$	−8.37372	−	4.83457i	−0.622414	−	0.359351i	−0.777808	+	0.628502i	$0.783668\pi$
$182$			0.534856i			0.0396461i
$183$	−8.85184	+	11.2177i	−0.654347	+	0.829236i
$184$	7.51400	+	4.33821i	0.553940	+	0.319817i
$185$	0.640666	+	1.10967i	0.0471027	+	0.0815843i
$186$	−6.48273	+	2.58282i	−0.475337	+	0.189382i
$187$	−5.95789	−	10.3194i	−0.435684	−	0.754626i
$188$	−4.74957	+	2.74216i	−0.346398	+	0.199993i
$189$	11.4692	+	5.30692i	0.834258	+	0.386021i
$190$	−2.48845	−	3.57877i	−0.180531	−	0.259631i
$191$		−	18.7213i		−	1.35463i	−0.735695	−	0.677313i	$-0.763144\pi$
$191$		−	18.7213i		−	1.35463i	0.735695	−	0.677313i	$-0.236856\pi$
$192$	−1.71401	−	0.249340i	−0.123698	−	0.0179945i
$193$	−21.1958	+	12.2374i	−1.52571	+	0.880867i	−0.526171	+	0.850379i	$0.676373\pi$
$193$	−21.1958	+	12.2374i	−1.52571	+	0.880867i	−0.999535	+	0.0304886i	$0.990294\pi$
$194$	6.10768	+	3.52627i	0.438506	+	0.253171i
$195$	0.376940	+	0.0548341i	0.0269933	+	0.00392675i
$196$	0.542503	−	0.939644i	0.0387502	−	0.0671174i
$197$			4.97845i			0.354700i	0.984148	+	0.177350i	$0.0567524\pi$
$197$			4.97845i			0.354700i	−0.984148	+	0.177350i	$0.943248\pi$
$198$	−6.78245	+	1.62160i	−0.482008	+	0.115242i
$199$	9.08451	−	15.7348i	0.643984	−	1.11541i	−0.340551	−	0.940226i	$-0.610614\pi$
$199$	9.08451	−	15.7348i	0.643984	−	1.11541i	0.984535	−	0.175187i	$-0.0560530\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	10.4245	+	8.22596i	0.735290	+	0.580215i
$202$			11.8229i			0.831854i
$203$	9.69845	−	16.7982i	0.680698	−	1.17900i
$204$	−1.27814	+	8.78616i	−0.0894875	+	0.615154i
$205$	2.06213	+	1.19057i	0.144025	+	0.0831529i
$206$	−15.2220	+	8.78844i	−1.06057	+	0.612319i
$207$	−17.8997	−	18.8978i	−1.24411	−	1.31348i
$208$			0.219917i			0.0152485i
$209$	4.31221	−	9.16901i	0.298282	−	0.634234i
$210$	3.30691	+	2.60947i	0.228198	+	0.180071i
$211$	−2.49731	+	1.44183i	−0.171922	+	0.0992593i	−0.583492	−	0.812119i	$-0.698314\pi$
$211$	−2.49731	+	1.44183i	−0.171922	+	0.0992593i	0.411570	+	0.911378i	$0.364981\pi$
$212$	−2.04507	−	3.54217i	−0.140456	−	0.243277i
$213$	−6.48271	−	16.2712i	−0.444188	−	1.11488i
$214$	1.40220	+	2.42868i	0.0958522	+	0.166021i
$215$	−1.22184	−	0.705429i	−0.0833287	−	0.0481099i
$216$	4.71579	+	2.18205i	0.320869	+	0.148470i
$217$			9.79865i			0.665176i
$218$	13.8072	+	7.97161i	0.935144	+	0.539906i
$219$	2.28864	+	5.74435i	0.154652	+	0.388167i
$220$	−2.32454			−0.156720
$221$	1.12732			0.0758314
$222$	2.06172	−	0.821425i	0.138374	−	0.0551304i
$223$	−12.7294	+	7.34931i	−0.852422	+	0.492146i	−0.861467	−	0.507813i	$-0.830454\pi$
$223$	−12.7294	+	7.34931i	−0.852422	+	0.492146i	0.00904511	+	0.999959i	$0.497121\pi$
$224$	−1.21604	+	2.10624i	−0.0812500	+	0.140729i
$225$	2.17806	−	2.06302i	0.145204	−	0.137535i
$226$	6.08745	+	10.5438i	0.404931	+	0.701361i
$227$	11.0675			0.734576			0.367288	−	0.930107i	$-0.380286\pi$
$227$	11.0675			0.734576			0.367288	+	0.930107i	$0.380286\pi$
$228$	−6.75452	+	3.37290i	−0.447329	+	0.223376i
$229$	3.19538			0.211157			0.105578	−	0.994411i	$-0.466331\pi$
$229$	3.19538			0.211157			0.105578	+	0.994411i	$0.466331\pi$
$230$	−4.33821	−	7.51400i	−0.286053	−	0.495459i
$231$	−1.40963	+	9.69007i	−0.0927468	+	0.637559i
$232$	3.98772	−	6.90694i	0.261807	−	0.453463i
$233$	6.96020	−	4.01848i	0.455978	−	0.263259i	−0.254374	−	0.967106i	$-0.581869\pi$
$233$	6.96020	−	4.01848i	0.455978	−	0.263259i	0.710352	+	0.703847i	$0.248536\pi$
$234$	0.187972	−	0.632407i	0.0122881	−	0.0413418i
$235$	5.48433			0.357758
$236$	0.956151			0.0622402
$237$	24.2643	−	9.66731i	1.57614	−	0.627959i
$238$	10.7968	+	6.23351i	0.699850	+	0.404059i
$239$			5.17399i			0.334678i	0.985899	+	0.167339i	$0.0535174\pi$
$239$			5.17399i			0.334678i	−0.985899	+	0.167339i	$0.946483\pi$
$240$	1.35971	+	1.07294i	0.0877687	+	0.0692579i
$241$	−25.4528	−	14.6952i	−1.63956	−	0.946601i	−0.980984	−	0.194086i	$-0.937826\pi$
$241$	−25.4528	−	14.6952i	−1.63956	−	0.946601i	−0.658576	−	0.752514i	$-0.728841\pi$
$242$	2.79827	+	4.84674i	0.179879	+	0.311560i
$243$	−11.6959	−	10.3056i	−0.750293	−	0.661106i
$244$	4.12504	+	7.14478i	0.264079	+	0.457398i
$245$	−0.939644	+	0.542503i	−0.0600316	+	0.0346593i
$246$	2.55482	−	3.23765i	0.162889	−	0.206425i
$247$	0.547253	+	0.787034i	0.0348209	+	0.0500778i
$248$			4.02893i			0.255837i
$249$	1.08724	−	7.47388i	0.0689009	−	0.473638i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	21.7086	+	12.5335i	1.37024	+	0.791107i	0.990958	−	0.134176i	$-0.0428386\pi$
$251$	21.7086	+	12.5335i	1.37024	+	0.791107i	0.379279	+	0.925282i	$0.376172\pi$
$252$	5.29720	−	5.01743i	0.333692	−	0.316068i
$253$	10.0843	−	17.4666i	0.633996	−	1.09811i
$254$			2.81687i			0.176746i
$255$	5.49998	−	6.96997i	0.344422	−	0.436476i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.30955	−	4.00025i	0.144066	−	0.249529i	−0.784958	−	0.619548i	$-0.787316\pi$
$257$	2.30955	−	4.00025i	0.144066	−	0.249529i	0.929024	+	0.370020i	$0.120649\pi$
$258$	−1.51377	+	1.91835i	−0.0942429	+	0.119431i
$259$		−	3.11630i		−	0.193637i
$260$	0.109959	−	0.190454i	0.00681935	−	0.0118115i
$261$	−17.3710	+	16.4535i	−1.07524	+	1.01845i
$262$	7.22873	+	4.17351i	0.446593	+	0.257840i
$263$	−24.7674	+	14.2995i	−1.52723	+	0.881744i	−0.527749	+	0.849401i	$0.676964\pi$
$263$	−24.7674	+	14.2995i	−1.52723	+	0.881744i	−0.999477	+	0.0323436i	$0.989703\pi$
$264$	−0.579599	+	3.98428i	−0.0356719	+	0.245215i
$265$			4.09015i			0.251256i
$266$	0.889349	+	10.5638i	0.0545295	+	0.647708i
$267$	4.35700	−	5.52151i	0.266644	−	0.337911i
$268$	6.63960	−	3.83338i	0.405578	−	0.234161i
$269$	−1.62587	−	2.81609i	−0.0991312	−	0.171700i	0.812194	−	0.583387i	$-0.198273\pi$
$269$	−1.62587	−	2.81609i	−0.0991312	−	0.171700i	−0.911325	+	0.411687i	$0.864940\pi$
$270$	−2.99297	−	4.24761i	−0.182146	−	0.258501i
$271$	−3.17133	−	5.49291i	−0.192645	−	0.333670i	0.753481	−	0.657469i	$-0.228373\pi$
$271$	−3.17133	−	5.49291i	−0.192645	−	0.333670i	−0.946126	+	0.323799i	$0.895040\pi$
$272$	4.43932	+	2.56304i	0.269173	+	0.155407i
$273$	−0.727247	−	0.573868i	−0.0440150	−	0.0347321i
$274$		−	14.6215i		−	0.883318i
$275$	2.01311	+	1.16227i	0.121395	+	0.0700874i
$276$	−13.9608	+	5.56220i	−0.840339	+	0.334805i
$277$	22.1670			1.33189			0.665943	−	0.746002i	$-0.268029\pi$
$277$	22.1670			1.33189			0.665943	+	0.746002i	$0.268029\pi$
$278$	11.0268			0.661345
$279$	3.44369	−	11.5858i	0.206168	−	0.693625i
$280$	2.10624	−	1.21604i	0.125872	−	0.0726722i
$281$	−7.85570	+	13.6065i	−0.468632	+	0.811694i	−0.999357	−	0.0358495i	$-0.988586\pi$
$281$	−7.85570	+	13.6065i	−0.468632	+	0.811694i	0.530725	+	0.847544i	$0.321920\pi$
$282$	1.36746	−	9.40019i	0.0814311	−	0.559773i
$283$	−10.1514	−	17.5827i	−0.603435	−	1.04518i	−0.992297	−	0.123884i	$-0.960465\pi$
$283$	−10.1514	−	17.5827i	−0.603435	−	1.04518i	0.388861	−	0.921296i	$-0.372869\pi$
$284$	−10.1123			−0.600056
$285$	7.53604	+	0.456245i	0.446396	+	0.0270256i
$286$	0.511206			0.0302282
$287$	−2.89555	−	5.01525i	−0.170919	−	0.296041i
$288$	2.17806	−	2.06302i	0.128343	−	0.121565i
$289$	4.63838	−	8.03390i	0.272846	−	0.472583i
$290$	−6.90694	+	3.98772i	−0.405590	+	0.234167i
$291$	−11.3479	+	4.52117i	−0.665223	+	0.265036i
$292$	3.57004			0.208921
$293$	16.1085			0.941067			0.470533	−	0.882382i	$-0.344062\pi$
$293$	16.1085			0.941067			0.470533	+	0.882382i	$0.344062\pi$
$294$	0.695566	+	1.74583i	0.0405662	+	0.101819i
$295$	−0.828051	−	0.478076i	−0.0482110	−	0.0278346i
$296$		−	1.28133i		−	0.0744760i
$297$	5.07226	−	10.9620i	0.294322	−	0.636081i
$298$	−18.2772	−	10.5523i	−1.05877	−	0.611279i
$299$	0.954048	+	1.65246i	0.0551740	+	0.0955642i
$300$	−0.641070	−	1.60905i	−0.0370122	−	0.0928983i
$301$	1.71566	+	2.97160i	0.0988888	+	0.171280i
$302$	−20.9707	+	12.1074i	−1.20673	+	0.696704i
$303$	−16.0756	−	12.6852i	−0.923520	−	0.728747i
$304$	0.365675	+	4.34353i	0.0209729	+	0.249119i
$305$		−	8.25009i		−	0.472399i
$306$	−10.5752	−	11.1649i	−0.604546	−	0.638255i
$307$	6.95957	−	4.01811i	0.397204	−	0.229326i	−0.288073	−	0.957608i	$-0.593015\pi$
$307$	6.95957	−	4.01811i	0.397204	−	0.229326i	0.685277	+	0.728283i	$0.259681\pi$
$308$	4.89603	+	2.82672i	0.278977	+	0.161068i
$309$	4.38261	−	30.1269i	0.249318	−	1.71386i
$310$	2.01446	−	3.48915i	0.114414	−	0.198171i
$311$		−	20.2592i		−	1.14879i	−0.818577	−	0.574396i	$-0.805237\pi$
$311$		−	20.2592i		−	1.14879i	0.818577	−	0.574396i	$-0.194763\pi$
$312$	−0.299023	−	0.235958i	−0.0169288	−	0.0133585i
$313$	−12.0239	+	20.8260i	−0.679631	+	1.17716i	0.295461	+	0.955355i	$0.404527\pi$
$313$	−12.0239	+	20.8260i	−0.679631	+	1.17716i	−0.975092	+	0.221801i	$0.928807\pi$
$314$	6.46343	−	11.1950i	0.364752	−	0.631769i
$315$	−7.09623	+	1.69662i	−0.399827	+	0.0955937i
$316$		−	15.0800i		−	0.848313i
$317$	−6.26988	+	10.8598i	−0.352152	+	0.609944i	−0.986626	−	0.162999i	$-0.947883\pi$
$317$	−6.26988	+	10.8598i	−0.352152	+	0.609944i	0.634475	+	0.772944i	$0.281217\pi$
$318$	7.01055	+	1.01984i	0.393132	+	0.0571896i
$319$	−16.0554	−	9.26961i	−0.898932	−	0.518998i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−4.80676	−	0.699247i	−0.268287	−	0.0390282i
$322$			21.1017i			1.17595i
$323$	22.2653	−	1.87448i	1.23888	−	0.104299i
$324$	−8.02670	+	4.07088i	−0.445928	+	0.226160i
$325$	−0.190454	+	0.109959i	−0.0105645	+	0.00609941i
$326$	6.81062	+	11.7963i	0.377205	+	0.653339i
$327$	−25.6534	+	10.2207i	−1.41864	+	0.565208i
$328$	−1.19057	−	2.06213i	−0.0657382	−	0.113862i
$329$	−11.5513	−	6.66915i	−0.636844	−	0.367682i
$330$	2.49409	−	3.16069i	0.137295	−	0.173990i
$331$		−	5.06995i		−	0.278670i	−0.990245	−	0.139335i	$-0.955504\pi$
$331$		−	5.06995i		−	0.278670i	0.990245	−	0.139335i	$-0.0444965\pi$
$332$	−3.77627	−	2.18023i	−0.207250	−	0.119656i
$333$	−1.09521	+	3.68468i	−0.0600171	+	0.201919i
$334$	−10.8604			−0.594255
$335$	−7.66675			−0.418880
$336$	−1.55913	−	3.91332i	−0.0850576	−	0.213489i
$337$	3.52448	−	2.03486i	0.191991	−	0.110846i	−0.400923	−	0.916112i	$-0.631311\pi$
$337$	3.52448	−	2.03486i	0.191991	−	0.110846i	0.592914	+	0.805266i	$0.297977\pi$
$338$	6.47582	−	11.2164i	0.352238	−	0.610094i
$339$	−20.8679	−	3.03568i	−1.13339	−	0.164876i
$340$	−2.56304	−	4.43932i	−0.139001	−	0.240756i
$341$	9.36538			0.507164
$342$	2.66104	−	12.8031i	0.143893	−	0.692311i
$343$	19.6634			1.06172
$344$	0.705429	+	1.22184i	0.0380342	+	0.0658771i
$345$	14.8715	+	2.16338i	0.800653	+	0.116472i
$346$	6.04765	−	10.4748i	0.325124	−	0.563131i
$347$	−4.31415	+	2.49077i	−0.231596	+	0.133712i	−0.611308	−	0.791393i	$-0.709356\pi$
$347$	−4.31415	+	2.49077i	−0.231596	+	0.133712i	0.379712	+	0.925105i	$0.376023\pi$
$348$	5.11282	+	12.8329i	0.274076	+	0.687914i
$349$	17.2329			0.922458			0.461229	−	0.887281i	$-0.347409\pi$
$349$	17.2329			0.922458			0.461229	+	0.887281i	$0.347409\pi$
$350$	−2.43208			−0.130000
$351$	0.658205	+	0.934122i	0.0351324	+	0.0498598i
$352$	2.01311	+	1.16227i	0.107299	+	0.0619491i
$353$			26.6382i			1.41781i	0.705306	+	0.708903i	$0.250810\pi$
$353$			26.6382i			1.41781i	−0.705306	+	0.708903i	$0.749190\pi$
$354$	−1.02589	+	1.30009i	−0.0545256	+	0.0690987i
$355$	8.75753	+	5.05616i	0.464802	+	0.268353i
$356$	−2.03041	−	3.51677i	−0.107611	−	0.186388i
$357$	−20.0600	+	7.99224i	−1.06169	+	0.422994i
$358$	−4.58689	−	7.94473i	−0.242425	−	0.419892i
$359$	−25.0199	+	14.4453i	−1.32050	+	0.762392i	−0.983809	−	0.179222i	$-0.942642\pi$
$359$	−25.0199	+	14.4453i	−1.32050	+	0.762392i	−0.336694	+	0.941614i	$0.609309\pi$
$360$	−2.91776	+	0.697602i	−0.153780	+	0.0367668i
$361$	12.1173	+	14.6346i	0.637754	+	0.770240i
$362$		−	9.66914i		−	0.508199i
$363$	−9.59251	−	1.39544i	−0.503476	−	0.0732415i
$364$	−0.463199	+	0.267428i	−0.0242782	+	0.0140170i
$365$	−3.09174	−	1.78502i	−0.161829	−	0.0934321i
$366$	−14.1407	−	2.05707i	−0.739148	−	0.107525i
$367$	−10.1670	+	17.6098i	−0.530713	+	0.919222i	0.468644	+	0.883387i	$0.344743\pi$
$367$	−10.1670	+	17.6098i	−0.530713	+	0.919222i	−0.999358	+	0.0358355i	$0.988591\pi$
$368$			8.67642i			0.452290i
$369$	1.66109	+	6.94760i	0.0864727	+	0.361678i
$370$	−0.640666	+	1.10967i	−0.0333067	+	0.0576888i
$371$	4.97377	−	8.61483i	0.258226	−	0.447260i
$372$	−5.47816	−	4.32279i	−0.284029	−	0.224126i
$373$			12.2252i			0.632997i	0.948593	+	0.316499i	$0.102507\pi$
$373$			12.2252i			0.632997i	−0.948593	+	0.316499i	$0.897493\pi$
$374$	5.95789	−	10.3194i	0.308075	−	0.533601i
$375$	−0.249340	+	1.71401i	−0.0128758	+	0.0885111i
$376$	−4.74957	−	2.74216i	−0.244940	−	0.141416i
$377$	1.51896	−	0.876970i	0.0782302	−	0.0451662i
$378$	1.13865	+	12.5860i	0.0585660	+	0.647356i
$379$			37.1799i			1.90980i	0.296925	+	0.954901i	$0.404039\pi$
$379$			37.1799i			1.90980i	−0.296925	+	0.954901i	$0.595961\pi$
$380$	1.85508	−	3.94445i	0.0951637	−	0.202346i
$381$	−3.83012	−	3.02234i	−0.196223	−	0.154839i
$382$	16.2131	−	9.36065i	0.829536	−	0.478933i
$383$	2.24543	+	3.88919i	0.114736	+	0.198728i	0.917674	−	0.397334i	$-0.130064\pi$
$383$	2.24543	+	3.88919i	0.114736	+	0.198728i	−0.802938	+	0.596062i	$0.796731\pi$
$384$	−0.641070	−	1.60905i	−0.0327145	−	0.0821113i
$385$	−2.82672	−	4.89603i	−0.144063	−	0.249525i
$386$	−21.1958	−	12.2374i	−1.07884	−	0.622867i
$387$	−0.984217	−	4.11655i	−0.0500306	−	0.209256i
$388$			7.05254i			0.358038i
$389$	−23.0418	−	13.3032i	−1.16827	−	0.674499i	−0.214996	−	0.976615i	$-0.568974\pi$
$389$	−23.0418	−	13.3032i	−1.16827	−	0.674499i	−0.953271	+	0.302116i	$0.902307\pi$
$390$	0.140982	+	0.353857i	0.00713893	+	0.0179183i
$391$	44.4761			2.24925
$392$	1.08501			0.0548011
$393$	−13.4307	+	5.35103i	−0.677491	+	0.269924i
$394$	−4.31146	+	2.48922i	−0.217208	+	0.125405i
$395$	−7.53998	+	13.0596i	−0.379377	+	0.657101i
$396$	−4.79557	−	5.06297i	−0.240987	−	0.254424i
$397$	−10.5922	−	18.3462i	−0.531606	−	0.920769i	−0.999319	−	0.0368887i	$-0.988255\pi$
$397$	−10.5922	−	18.3462i	−0.531606	−	0.920769i	0.467713	−	0.883880i	$-0.345078\pi$
$398$	18.1690			0.910731
$399$	−15.3179	−	10.1251i	−0.766853	−	0.506887i
$400$	−1.00000			−0.0500000
$401$	−11.5551	−	20.0141i	−0.577036	−	0.999456i	−0.995817	−	0.0913687i	$-0.970876\pi$
$401$	−11.5551	−	20.0141i	−0.577036	−	0.999456i	0.418781	−	0.908087i	$-0.362458\pi$
$402$	−1.91163	+	13.1409i	−0.0953433	+	0.655408i
$403$	−0.443015	+	0.767325i	−0.0220682	+	0.0382232i
$404$	−10.2389	+	5.91143i	−0.509404	+	0.294105i
$405$	8.98677	+	0.487870i	0.446556	+	0.0242424i
$406$	19.3969			0.962652
$407$	−2.97850			−0.147639
$408$	−8.24811	+	3.28618i	−0.408342	+	0.162690i
$409$	8.26190	+	4.77001i	0.408525	+	0.235862i	0.690156	−	0.723661i	$-0.257542\pi$
$409$	8.26190	+	4.77001i	0.408525	+	0.235862i	−0.281631	+	0.959523i	$0.590875\pi$
$410$			2.38114i			0.117596i
$411$	19.8810	+	15.6880i	0.980656	+	0.773832i
$412$	−15.2220	−	8.78844i	−0.749935	−	0.432975i
$413$	1.16272	+	2.01388i	0.0572135	+	0.0990967i
$414$	7.41610	−	24.9504i	0.364481	−	1.22625i
$415$	2.18023	+	3.77627i	0.107023	+	0.185370i
$416$	−0.190454	+	0.109959i	−0.00933778	+	0.00539117i
$417$	−11.8311	+	14.9933i	−0.579373	+	0.734223i
$418$	10.0967	−	0.850025i	0.493846	−	0.0415761i
$419$			0.961723i			0.0469832i	0.999724	+	0.0234916i	$0.00747830\pi$
$419$			0.961723i			0.0469832i	−0.999724	+	0.0234916i	$0.992522\pi$
$420$	−0.606413	+	4.16860i	−0.0295899	+	0.203407i
$421$	−14.4170	+	8.32365i	−0.702641	+	0.405670i	−0.808330	−	0.588729i	$-0.799628\pi$
$421$	−14.4170	+	8.32365i	−0.702641	+	0.405670i	0.105689	+	0.994399i	$0.466295\pi$
$422$	−2.49731	−	1.44183i	−0.121567	−	0.0701870i
$423$	11.3143	+	11.9452i	0.550120	+	0.580794i
$424$	2.04507	−	3.54217i	0.0993176	−	0.172023i
$425$			5.12609i			0.248652i
$426$	10.8499	−	13.7498i	0.525680	−	0.666180i
$427$	−10.0324	+	17.3767i	−0.485503	+	0.840915i
$428$	−1.40220	+	2.42868i	−0.0677777	+	0.117394i
$429$	−0.548493	+	0.695090i	−0.0264815	+	0.0335592i
$430$		−	1.41086i		−	0.0680376i
$431$	−5.03639	+	8.72328i	−0.242594	+	0.420185i	−0.961452	−	0.274971i	$-0.911332\pi$
$431$	−5.03639	+	8.72328i	−0.242594	+	0.420185i	0.718858	+	0.695157i	$0.244665\pi$
$432$	0.468182	+	5.17502i	0.0225254	+	0.248983i
$433$	5.91643	+	3.41585i	0.284326	+	0.164155i	0.635380	−	0.772200i	$-0.280843\pi$
$433$	5.91643	+	3.41585i	0.284326	+	0.164155i	−0.351054	+	0.936355i	$0.614177\pi$
$434$	−8.48588	+	4.89933i	−0.407335	+	0.235175i
$435$	1.98860	−	13.6700i	0.0953459	−	0.655426i
$436$			15.9432i			0.763542i
$437$	21.5909	+	31.0510i	1.03283	+	1.48537i
$438$	−3.83043	+	4.85420i	−0.183025	+	0.231943i
$439$	9.27371	−	5.35418i	0.442610	−	0.255541i	−0.262094	−	0.965042i	$-0.584413\pi$
$439$	9.27371	−	5.35418i	0.442610	−	0.255541i	0.704704	+	0.709501i	$0.251080\pi$
$440$	−1.16227	−	2.01311i	−0.0554090	−	0.0959711i
$441$	−3.12011	−	0.927401i	−0.148577	−	0.0441619i
$442$	0.563658	+	0.976283i	0.0268105	+	0.0464371i
$443$	6.87406	+	3.96874i	0.326596	+	0.188560i	0.654329	−	0.756210i	$-0.272951\pi$
$443$	6.87406	+	3.96874i	0.326596	+	0.188560i	−0.327733	+	0.944771i	$0.606285\pi$
$444$	1.74224	+	1.37479i	0.0826829	+	0.0652448i
$445$			4.06081i			0.192501i
$446$	−12.7294	−	7.34931i	−0.602754	−	0.348000i
$447$	33.9583	−	13.5296i	1.60617	−	0.639926i
$448$	−2.43208			−0.114905
$449$	−16.3905			−0.773515			−0.386757	−	0.922181i	$-0.626405\pi$
$449$	−16.3905			−0.773515			−0.386757	+	0.922181i	$0.626405\pi$
$450$	2.87566	+	0.854742i	0.135560	+	0.0402929i
$451$	−4.79348	+	2.76752i	−0.225716	+	0.130317i
$452$	−6.08745	+	10.5438i	−0.286329	+	0.495937i
$453$	6.03773	−	41.5045i	0.283677	−	1.95005i
$454$	5.53375	+	9.58473i	0.259712	+	0.449834i
$455$	0.534856			0.0250744
$456$	−6.29828	−	4.16314i	−0.294944	−	0.194957i
$457$	−19.8202			−0.927152			−0.463576	−	0.886057i	$-0.653434\pi$
$457$	−19.8202			−0.927152			−0.463576	+	0.886057i	$0.653434\pi$
$458$	1.59769	+	2.76728i	0.0746553	+	0.129307i
$459$	26.5276	−	2.39994i	1.23820	−	0.112020i
$460$	4.33821	−	7.51400i	0.202270	−	0.350342i
$461$	−35.9630	+	20.7632i	−1.67496	+	0.967040i	−0.710170	+	0.704030i	$0.751382\pi$
$461$	−35.9630	+	20.7632i	−1.67496	+	0.967040i	−0.964793	+	0.263010i	$0.915285\pi$
$462$	−9.09666	+	3.62426i	−0.423215	+	0.168616i
$463$	20.2445			0.940843			0.470422	−	0.882442i	$-0.344102\pi$
$463$	20.2445			0.940843			0.470422	+	0.882442i	$0.344102\pi$
$464$	7.97545			0.370251
$465$	2.58282	+	6.48273i	0.119776	+	0.300629i
$466$	6.96020	+	4.01848i	0.322425	+	0.186152i
$467$		−	10.1496i		−	0.469667i	−0.972036	−	0.234833i	$-0.924546\pi$
$467$		−	10.1496i		−	0.469667i	0.972036	−	0.234833i	$-0.0754544\pi$
$468$	0.641667	−	0.153415i	0.0296611	−	0.00709160i
$469$	16.1480	+	9.32306i	0.745646	+	0.430499i
$470$	2.74216	+	4.74957i	0.126487	+	0.219081i
$471$	8.28702	+	20.7999i	0.381846	+	0.958409i
$472$	0.478076	+	0.828051i	0.0220052	+	0.0381142i
$473$	2.84021	−	1.63980i	0.130593	−	0.0753979i
$474$	20.5043	+	16.1799i	0.941794	+	0.743166i
$475$	−3.57877	+	2.48845i	−0.164205	+	0.114178i
$476$			12.4670i			0.571425i
$477$	−8.90858	+	8.43807i	−0.407896	+	0.386353i
$478$	−4.48081	+	2.58700i	−0.204947	+	0.118326i
$479$	−35.2374	−	20.3443i	−1.61004	−	0.929555i	−0.989360	−	0.145488i	$-0.953525\pi$
$479$	−35.2374	−	20.3443i	−1.61004	−	0.929555i	−0.620676	−	0.784067i	$-0.713142\pi$
$480$	−0.249340	+	1.71401i	−0.0113808	+	0.0782335i
$481$	0.140894	−	0.244035i	0.00642420	−	0.0111270i
$482$		−	29.3904i		−	1.33870i
$483$	−28.6921	−	22.6409i	−1.30554	−	1.03020i
$484$	−2.79827	+	4.84674i	−0.127194	+	0.220306i
$485$	3.52627	−	6.10768i	0.160120	−	0.277335i
$486$	3.07697	−	15.2818i	0.139574	−	0.693195i
$487$		−	14.4557i		−	0.655048i	−0.944843	−	0.327524i	$-0.893786\pi$
$487$		−	14.4557i		−	0.655048i	0.944843	−	0.327524i	$-0.106214\pi$
$488$	−4.12504	+	7.14478i	−0.186732	+	0.323429i
$489$	−23.3469	−	3.39632i	−1.05579	−	0.153587i
$490$	−0.939644	−	0.542503i	−0.0424488	−	0.0245078i
$491$	13.6141	−	7.86008i	0.614394	−	0.354721i	−0.160289	−	0.987070i	$-0.551243\pi$
$491$	13.6141	−	7.86008i	0.614394	−	0.354721i	0.774683	+	0.632350i	$0.217909\pi$
$492$	4.08129	+	0.593712i	0.183999	+	0.0267666i
$493$		−	40.8828i		−	1.84127i
$494$	−0.407965	+	0.867452i	−0.0183552	+	0.0390285i
$495$	1.62160	+	6.78245i	0.0728855	+	0.304848i
$496$	−3.48915	+	2.01446i	−0.156668	+	0.0904521i
$497$	−12.2970	−	21.2990i	−0.551595	−	0.955390i
$498$	7.01619	−	2.79537i	0.314403	−	0.125263i
$499$	−16.7701	−	29.0466i	−0.750731	−	1.30030i	−0.947469	−	0.319848i	$-0.896368\pi$
$499$	−16.7701	−	29.0466i	−0.750731	−	1.30030i	0.196738	−	0.980456i	$-0.436965\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	11.6526	−	14.7670i	0.520598	−	0.659739i
$502$			25.0670i			1.11879i
$503$	7.23726	+	4.17843i	0.322694	+	0.186307i	0.652593	−	0.757709i	$-0.273681\pi$
$503$	7.23726	+	4.17843i	0.322694	+	0.186307i	−0.329899	+	0.944016i	$0.607015\pi$
$504$	6.99382	+	2.07880i	0.311530	+	0.0925969i
$505$	11.8229			0.526110
$506$	20.1687			0.896606
$507$	8.30291	+	20.8398i	0.368745	+	0.925527i
$508$	−2.43948	+	1.40844i	−0.108235	+	0.0624893i
$509$	14.3398	−	24.8373i	0.635602	−	1.10090i	−0.350785	−	0.936456i	$-0.614085\pi$
$509$	14.3398	−	24.8373i	0.635602	−	1.10090i	0.986387	−	0.164440i	$-0.0525816\pi$
$510$	8.78616	+	1.27814i	0.389058	+	0.0565969i
$511$	4.34130	+	7.51935i	0.192048	+	0.332636i
$512$	−1.00000			−0.0441942
$513$	14.5533	+	17.3552i	0.642543	+	0.766249i
$514$	4.61909			0.203739
$515$	8.78844	+	15.2220i	0.387265	+	0.670762i
$516$	−2.41822	−	0.351783i	−0.106456	−	0.0154864i
$517$	−6.37426	+	11.0405i	−0.280340	+	0.485562i
$518$	2.69879	−	1.55815i	0.118578	−	0.0684612i
$519$	7.75394	+	19.4619i	0.340360	+	0.854282i
$520$	0.219917			0.00964401
$521$	−22.1970			−0.972468			−0.486234	−	0.873829i	$-0.661630\pi$
$521$	−22.1970			−0.972468			−0.486234	+	0.873829i	$0.661630\pi$
$522$	−22.9347	−	6.81695i	−1.00382	−	0.298370i
$523$	22.4245	+	12.9468i	0.980554	+	0.566123i	0.902437	−	0.430821i	$-0.141776\pi$
$523$	22.4245	+	12.9468i	0.980554	+	0.566123i	0.0781167	+	0.996944i	$0.475109\pi$
$524$			8.34702i			0.364641i
$525$	2.60947	−	3.30691i	0.113887	−	0.144325i
$526$	−24.7674	−	14.2995i	−1.07991	−	0.623487i
$527$	10.3263	+	17.8857i	0.449821	+	0.779113i
$528$	−3.74029	+	1.49019i	−0.162775	+	0.0648522i
$529$	26.1402	+	45.2761i	1.13653	+	1.96853i
$530$	−3.54217	+	2.04507i	−0.153862	+	0.0888323i
$531$	−0.667013	−	2.78983i	−0.0289459	−	0.121068i
$532$	−8.70385	+	6.05210i	−0.377360	+	0.262392i
$533$		−	0.523653i		−	0.0226819i
$534$	6.96027	+	1.01252i	0.301200	+	0.0438161i
$535$	2.42868	−	1.40220i	0.105001	−	0.0606223i
$536$	6.63960	+	3.83338i	0.286787	+	0.165577i
$537$	15.7240	+	2.28739i	0.678539	+	0.0987081i
$538$	1.62587	−	2.81609i	0.0700963	−	0.121410i
$539$		−	2.52214i		−	0.108636i
$540$	2.18205	−	4.71579i	0.0939006	−	0.202935i
$541$	−5.15671	+	8.93169i	−0.221704	+	0.384003i	−0.955326	−	0.295555i	$-0.904495\pi$
$541$	−5.15671	+	8.93169i	−0.221704	+	0.384003i	0.733621	+	0.679559i	$0.237829\pi$
$542$	3.17133	−	5.49291i	0.136220	−	0.235940i
$543$	13.1472	+	10.3744i	0.564200	+	0.445208i
$544$			5.12609i			0.219779i
$545$	7.97161	−	13.8072i	0.341466	−	0.591437i
$546$	0.133361	−	0.916748i	0.00570731	−	0.0392332i
$547$	−6.35260	−	3.66767i	−0.271618	−	0.156818i	0.358005	−	0.933720i	$-0.383457\pi$
$547$	−6.35260	−	3.66767i	−0.271618	−	0.156818i	−0.629622	+	0.776901i	$0.716790\pi$
$548$	12.6626	−	7.31076i	0.540920	−	0.312300i
$549$	17.9692	−	17.0201i	0.766905	−	0.726401i
$550$			2.32454i			0.0991185i
$551$	28.5423	−	19.8465i	1.21594	−	0.845490i
$552$	−11.7974	−	9.30928i	−0.502130	−	0.396229i
$553$	31.7620	−	18.3378i	1.35066	−	0.779802i
$554$	11.0835	+	19.1972i	0.470893	+	0.815611i
$555$	−0.821425	−	2.06172i	−0.0348675	−	0.0875153i
$556$	5.51342	+	9.54952i	0.233821	+	0.404990i
$557$	12.9817	+	7.49498i	0.550051	+	0.317572i	0.749143	−	0.662409i	$-0.230466\pi$
$557$	12.9817	+	7.49498i	0.550051	+	0.317572i	−0.199091	+	0.979981i	$0.563799\pi$
$558$	11.7555	−	2.81059i	0.497648	−	0.118982i
$559$			0.310272i			0.0131231i
$560$	2.10624	+	1.21604i	0.0890049	+	0.0513870i
$561$	7.63885	+	19.1730i	0.322512	+	0.809486i
$562$	−15.7114			−0.662746
$563$	19.5385			0.823450			0.411725	−	0.911308i	$-0.364926\pi$
$563$	19.5385			0.823450			0.411725	+	0.911308i	$0.364926\pi$
$564$	8.82453	−	3.51584i	0.371580	−	0.148044i
$565$	10.5438	−	6.08745i	0.443580	−	0.256101i
$566$	10.1514	−	17.5827i	0.426693	−	0.739054i
$567$	−18.3350	−	11.9558i	−0.769998	−	0.502097i
$568$	−5.05616	−	8.75753i	−0.212152	−	0.367458i
$569$	43.9934			1.84430			0.922149	−	0.386835i	$-0.126432\pi$
$569$	43.9934			1.84430			0.922149	+	0.386835i	$0.126432\pi$
$570$	3.37290	+	6.75452i	0.141275	+	0.282916i
$571$	−17.0307			−0.712711			−0.356356	−	0.934350i	$-0.615981\pi$
$571$	−17.0307			−0.712711			−0.356356	+	0.934350i	$0.615981\pi$
$572$	0.255603	+	0.442717i	0.0106873	+	0.0185109i
$573$	−4.66796	+	32.0885i	−0.195007	+	1.34052i
$574$	2.89555	−	5.01525i	0.120858	−	0.209332i
$575$	−7.51400	+	4.33821i	−0.313356	+	0.180916i
$576$	2.87566	+	0.854742i	0.119819	+	0.0356142i
$577$	−13.3602			−0.556192			−0.278096	−	0.960553i	$-0.589703\pi$
$577$	−13.3602			−0.556192			−0.278096	+	0.960553i	$0.589703\pi$
$578$	9.27675			0.385862
$579$	39.3811	−	15.6901i	1.63662	−	0.652057i
$580$	−6.90694	−	3.98772i	−0.286795	−	0.165581i
$581$		−	10.6050i		−	0.439969i
$582$	−9.58938	−	7.56695i	−0.397493	−	0.313660i
$583$	−8.23391	−	4.75385i	−0.341014	−	0.196884i
$584$	1.78502	+	3.09174i	0.0738646	+	0.127937i
$585$	−0.632407	−	0.187972i	−0.0261468	−	0.00777171i
$586$	8.05424	+	13.9503i	0.332717	+	0.576283i
$587$	23.1836	−	13.3851i	0.956891	−	0.552461i	0.0616763	−	0.998096i	$-0.480355\pi$
$587$	23.1836	−	13.3851i	0.956891	−	0.552461i	0.895215	+	0.445635i	$0.147022\pi$
$588$	−1.16415	+	1.47529i	−0.0480086	+	0.0608400i
$589$	−7.47399	+	15.8919i	−0.307960	+	0.654814i
$590$		−	0.956151i		−	0.0393641i
$591$	1.24132	−	8.53310i	0.0510613	−	0.351005i
$592$	1.10967	−	0.640666i	0.0456070	−	0.0263312i
$593$	8.48127	+	4.89666i	0.348284	+	0.201082i	0.663929	−	0.747795i	$-0.268888\pi$
$593$	8.48127	+	4.89666i	0.348284	+	0.201082i	−0.315645	+	0.948877i	$0.602221\pi$
$594$	12.0295	−	1.08830i	0.493577	−	0.0446537i
$595$	6.23351	−	10.7968i	0.255549	−	0.442624i
$596$		−	21.1046i		−	0.864480i
$597$	−19.4943	+	24.7045i	−0.797847	+	1.01109i
$598$	−0.954048	+	1.65246i	−0.0390139	+	0.0675741i
$599$	−13.4316	+	23.2641i	−0.548799	+	0.950547i	0.449559	+	0.893251i	$0.351581\pi$
$599$	−13.4316	+	23.2641i	−0.548799	+	0.950547i	−0.998357	+	0.0572961i	$0.981752\pi$
$600$	1.07294	−	1.35971i	0.0438026	−	0.0555098i
$601$			26.9483i			1.09925i	0.835413	+	0.549623i	$0.185229\pi$
$601$			26.9483i			1.09925i	−0.835413	+	0.549623i	$0.814771\pi$
$602$	−1.71566	+	2.97160i	−0.0699250	+	0.121114i
$603$	−15.8167	−	16.6986i	−0.644106	−	0.680021i
$604$	−20.9707	−	12.1074i	−0.853285	−	0.492644i
$605$	4.84674	−	2.79827i	0.197048	−	0.113766i
$606$	2.94791	−	20.2645i	0.119751	−	0.823189i
$607$			24.9777i			1.01381i	0.862001	+	0.506906i	$0.169211\pi$
$607$			24.9777i			1.01381i	−0.862001	+	0.506906i	$0.830789\pi$
$608$	−3.57877	+	2.48845i	−0.145138	+	0.100920i
$609$	−20.8117	+	26.3741i	−0.843332	+	1.06873i
$610$	7.14478	−	4.12504i	0.289284	−	0.167018i
$611$	−0.603049	−	1.04451i	−0.0243968	−	0.0422564i
$612$	4.38148	−	14.7409i	0.177111	−	0.595865i
$613$	5.51510	+	9.55243i	0.222753	+	0.385819i	0.955643	−	0.294528i	$-0.0951624\pi$
$613$	5.51510	+	9.55243i	0.222753	+	0.385819i	−0.732890	+	0.680347i	$0.761829\pi$
$614$	6.95957	+	4.01811i	0.280865	+	0.162158i
$615$	−3.23765	−	2.55482i	−0.130555	−	0.103020i
$616$			5.65345i			0.227784i
$617$	−16.4524	−	9.49880i	−0.662349	−	0.382407i	0.130823	−	0.991406i	$-0.458238\pi$
$617$	−16.4524	−	9.49880i	−0.662349	−	0.382407i	−0.793171	+	0.608999i	$0.791571\pi$
$618$	28.2820	−	11.2680i	1.13767	−	0.453266i
$619$	−39.2407			−1.57722			−0.788608	−	0.614896i	$-0.789198\pi$
$619$	−39.2407			−1.57722			−0.788608	+	0.614896i	$0.789198\pi$
$620$	4.02893			0.161806
$621$	25.9682	+	36.8540i	1.04207	+	1.47890i
$622$	17.5450	−	10.1296i	0.703489	−	0.406159i
$623$	4.93810	−	8.55304i	0.197841	−	0.342670i
$624$	0.0548341	−	0.376940i	0.00219512	−	0.0150897i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−24.0478			−0.961144
$627$	−9.67736	+	14.6406i	−0.386477	+	0.584688i
$628$	12.9269			0.515837
$629$	−3.28411	−	5.68825i	−0.130946	−	0.226805i
$630$	−5.01743	−	5.29720i	−0.199899	−	0.211046i
$631$	9.58134	−	16.5954i	0.381427	−	0.660651i	−0.609840	−	0.792525i	$-0.708766\pi$
$631$	9.58134	−	16.5954i	0.381427	−	0.660651i	0.991266	+	0.131874i	$0.0420994\pi$
$632$	13.0596	−	7.53998i	0.519484	−	0.299924i
$633$	4.63993	−	1.84862i	0.184421	−	0.0734762i
$634$	−12.5398			−0.498017
$635$	2.81687			0.111784
$636$	2.62207	+	6.58124i	0.103972	+	0.260963i
$637$	0.206644	+	0.119306i	0.00818753	+	0.00472707i
$638$		−	18.5392i		−	0.733975i
$639$	7.05438	+	29.5054i	0.279067	+	1.16722i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−15.7483	−	27.2768i	−0.622020	−	1.07737i	−0.989109	−	0.147184i	$-0.952979\pi$
$641$	−15.7483	−	27.2768i	−0.622020	−	1.07737i	0.367090	−	0.930186i	$-0.380354\pi$
$642$	−1.79781	−	4.51240i	−0.0709540	−	0.178090i
$643$	4.48834	+	7.77403i	0.177003	+	0.306578i	0.940853	−	0.338816i	$-0.110027\pi$
$643$	4.48834	+	7.77403i	0.177003	+	0.306578i	−0.763850	+	0.645394i	$0.776693\pi$
$644$	−18.2746	+	10.5509i	−0.720121	+	0.415762i
$645$	1.91835	+	1.51377i	0.0755350	+	0.0596044i
$646$	12.7560	+	18.3451i	0.501879	+	0.721778i
$647$			4.22420i			0.166071i	0.996547	+	0.0830353i	$0.0264614\pi$
$647$			4.22420i			0.166071i	−0.996547	+	0.0830353i	$0.973539\pi$
$648$	−7.53883	−	4.91589i	−0.296153	−	0.193114i
$649$	1.92484	−	1.11130i	0.0755564	−	0.0436225i
$650$	−0.190454	−	0.109959i	−0.00747022	−	0.00431293i
$651$	2.44319	−	16.7950i	0.0957563	−	0.658247i
$652$	−6.81062	+	11.7963i	−0.266724	+	0.461980i
$653$		−	20.4175i		−	0.798999i	−0.916733	−	0.399499i	$-0.869184\pi$
$653$		−	20.4175i		−	0.798999i	0.916733	−	0.399499i	$-0.130816\pi$
$654$	−21.6781	−	17.1061i	−0.847681	−	0.668902i
$655$	4.17351	−	7.22873i	0.163073	−	0.282450i
$656$	1.19057	−	2.06213i	0.0464839	−	0.0805125i
$657$	−2.49046	−	10.4165i	−0.0971622	−	0.406387i
$658$		−	13.3383i		−	0.519981i
$659$	−20.4046	+	35.3417i	−0.794849	+	1.37672i	0.128086	+	0.991763i	$0.459117\pi$
$659$	−20.4046	+	35.3417i	−0.794849	+	1.37672i	−0.922935	+	0.384955i	$0.874217\pi$
$660$	3.98428	+	0.579599i	0.155088	+	0.0225609i
$661$	−6.66358	−	3.84722i	−0.259183	−	0.149640i	0.364779	−	0.931094i	$-0.381145\pi$
$661$	−6.66358	−	3.84722i	−0.259183	−	0.149640i	−0.623962	+	0.781455i	$0.714478\pi$
$662$	4.39071	−	2.53498i	0.170650	−	0.0985247i
$663$	−1.93223	−	0.281084i	−0.0750416	−	0.0109164i
$664$		−	4.36047i		−	0.169219i
$665$	10.5638	−	0.889349i	0.409647	−	0.0344875i
$666$	−3.73863	+	0.893860i	−0.144869	+	0.0346364i
$667$	59.9276	−	34.5992i	2.32040	−	1.33969i
$668$	−5.43020	−	9.40538i	−0.210101	−	0.363905i
$669$	23.6508	−	9.42285i	0.914391	−	0.364308i
$670$	−3.83338	−	6.63960i	−0.148096	−	0.256510i
$671$	16.6083	+	9.58881i	0.641157	+	0.370172i
$672$	2.60947	−	3.30691i	0.100662	−	0.127567i
$673$			10.6822i			0.411770i	0.978576	+	0.205885i	$0.0660073\pi$
$673$			10.6822i			0.411770i	−0.978576	+	0.205885i	$0.933993\pi$
$674$	3.52448	+	2.03486i	0.135758	+	0.0783798i
$675$	−4.24761	+	2.99297i	−0.163490	+	0.115199i
$676$	12.9516			0.498140
$677$	−12.9215			−0.496612			−0.248306	−	0.968682i	$-0.579874\pi$
$677$	−12.9215			−0.496612			−0.248306	+	0.968682i	$0.579874\pi$
$678$	−7.80496	−	19.5900i	−0.299748	−	0.752348i
$679$	−14.8543	+	8.57615i	−0.570057	+	0.329123i
$680$	2.56304	−	4.43932i	0.0982882	−	0.170240i
$681$	−18.9698	−	2.75957i	−0.726924	−	0.105747i
$682$	4.68269	+	8.11066i	0.179310	+	0.310573i
$683$	39.7388			1.52056			0.760282	−	0.649593i	$-0.225061\pi$
$683$	39.7388			1.52056			0.760282	+	0.649593i	$0.225061\pi$
$684$	12.4183	−	4.09701i	0.474826	−	0.156653i
$685$	−14.6215			−0.558660
$686$	9.83168	+	17.0290i	0.375375	+	0.650169i
$687$	−5.47692	−	0.796736i	−0.208958	−	0.0303974i
$688$	−0.705429	+	1.22184i	−0.0268942	+	0.0465822i
$689$	0.778985	−	0.449747i	0.0296770	−	0.0171340i
$690$	5.56220	+	13.9608i	0.211749	+	0.531477i
$691$	−9.39689			−0.357474			−0.178737	−	0.983897i	$-0.557201\pi$
$691$	−9.39689			−0.357474			−0.178737	+	0.983897i	$0.557201\pi$
$692$	12.0953			0.459794
$693$	4.83224	−	16.2574i	0.183562	−	0.617567i
$694$	−4.31415	−	2.49077i	−0.163763	−	0.0945485i
$695$		−	11.0268i		−	0.418272i
$696$	−8.55717	+	10.8443i	−0.324359	+	0.411051i
$697$	−10.5706	−	6.10296i	−0.400391	−	0.231166i
$698$	8.61647	+	14.9242i	0.326138	+	0.564888i
$699$	−12.9318	+	5.15225i	−0.489126	+	0.194876i
$700$	−1.21604	−	2.10624i	−0.0459619	−	0.0796084i
$701$	−21.4383	+	12.3774i	−0.809713	+	0.467488i	−0.846856	−	0.531822i	$-0.821508\pi$
$701$	−21.4383	+	12.3774i	−0.809713	+	0.467488i	0.0371431	+	0.999310i	$0.488174\pi$
$702$	−0.479871	+	1.03708i	−0.0181116	+	0.0391422i
$703$	2.37698	−	5.05415i	0.0896494	−	0.190621i
$704$			2.32454i			0.0876092i
$705$	−9.40019	−	1.36746i	−0.354032	−	0.0515015i
$706$	−23.0693	+	13.3191i	−0.868226	+	0.501270i
$707$	−24.9018	−	14.3770i	−0.936528	−	0.540705i
$708$	−1.63885	−	0.238407i	−0.0615919	−	0.00895987i
$709$	6.84044	−	11.8480i	0.256898	−	0.444960i	−0.708511	−	0.705699i	$-0.750633\pi$
$709$	6.84044	−	11.8480i	0.256898	−	0.444960i	0.965409	+	0.260739i	$0.0839662\pi$
$710$			10.1123i			0.379509i
$711$	−43.9997	+	10.5198i	−1.65012	+	0.394523i
$712$	2.03041	−	3.51677i	0.0760927	−	0.131796i
$713$	−17.4783	+	30.2734i	−0.654569	+	1.13375i
$714$	−16.9515	−	13.3764i	−0.634394	−	0.500598i
$715$		−	0.511206i		−	0.0191180i
$716$	4.58689	−	7.94473i	0.171420	−	0.296908i
$717$	1.29008	−	8.86828i	0.0481790	−	0.331192i
$718$	−25.0199	−	14.4453i	−0.933736	−	0.539093i
$719$	−16.2403	+	9.37635i	−0.605661	+	0.349679i	−0.771265	−	0.636514i	$-0.780376\pi$
$719$	−16.2403	+	9.37635i	−0.605661	+	0.349679i	0.165604	+	0.986192i	$0.447043\pi$
$720$	−2.06302	−	2.17806i	−0.0768843	−	0.0811714i
$721$		−	42.7483i		−	1.59203i
$722$	−6.61523	+	17.8112i	−0.246193	+	0.662864i
$723$	39.9623	+	31.5341i	1.48621	+	1.17277i
$724$	8.37372	−	4.83457i	0.311207	−	0.179675i
$725$	3.98772	+	6.90694i	0.148100	+	0.256517i
$726$	−3.58777	−	9.00508i	−0.133155	−	0.334210i
$727$	24.9453	+	43.2065i	0.925170	+	1.60244i	0.791287	+	0.611445i	$0.209411\pi$
$727$	24.9453	+	43.2065i	0.925170	+	1.60244i	0.133883	+	0.990997i	$0.457255\pi$
$728$	−0.463199	−	0.267428i	−0.0171673	−	0.00991153i
$729$	17.4773	+	20.5802i	0.647307	+	0.762229i
$730$		−	3.57004i		−	0.132133i
$731$	6.26325	+	3.61609i	0.231655	+	0.133746i
$732$	−5.28889	−	13.2748i	−0.195483	−	0.490649i
$733$	28.7958			1.06360			0.531799	−	0.846870i	$-0.321516\pi$
$733$	28.7958			1.06360			0.531799	+	0.846870i	$0.321516\pi$
$734$	−20.3340			−0.750542
$735$	1.74583	−	0.695566i	0.0643958	−	0.0256563i
$736$	−7.51400	+	4.33821i	−0.276970	+	0.159909i
$737$	8.91082	−	15.4340i	0.328234	−	0.568519i
$738$	−5.18625	+	4.91234i	−0.190909	+	0.180826i
$739$	−11.8821	−	20.5805i	−0.437092	−	0.757065i	0.560372	−	0.828241i	$-0.310658\pi$
$739$	−11.8821	−	20.5805i	−0.437092	−	0.757065i	−0.997464	+	0.0711761i	$0.977325\pi$
$740$	−1.28133			−0.0471027
$741$	−0.741759	−	1.48544i	−0.0272492	−	0.0545689i
$742$	9.94755			0.365186
$743$	3.44798	+	5.97208i	0.126494	+	0.219094i	0.922316	−	0.386437i	$-0.126294\pi$
$743$	3.44798	+	5.97208i	0.126494	+	0.219094i	−0.795822	+	0.605531i	$0.792961\pi$
$744$	1.00457	−	6.90562i	0.0368294	−	0.253172i
$745$	−10.5523	+	18.2772i	−0.386607	+	0.669623i
$746$	−10.5873	+	6.11260i	−0.387630	+	0.223798i
$747$	−3.72707	+	12.5392i	−0.136366	+	0.458786i
$748$	11.9158			0.435684
$749$	−6.82050			−0.249216
$750$	−1.60905	+	0.641070i	−0.0587541	+	0.0234086i
$751$	−36.8595	−	21.2808i	−1.34502	−	0.776548i	−0.357482	−	0.933920i	$-0.616365\pi$
$751$	−36.8595	−	21.2808i	−1.34502	−	0.776548i	−0.987539	+	0.157372i	$0.949698\pi$
$752$		−	5.48433i		−	0.199993i
$753$	−34.0837	−	26.8953i	−1.24208	−	0.980121i
$754$	1.51896	+	0.876970i	0.0553171	+	0.0319373i
$755$	12.1074	+	20.9707i	0.440634	+	0.763201i
$756$	−10.3305	+	7.27912i	−0.375717	+	0.264739i
$757$	−15.7761	−	27.3249i	−0.573391	−	0.993142i	−0.996214	−	0.0869297i	$-0.972294\pi$
$757$	−15.7761	−	27.3249i	−0.573391	−	0.993142i	0.422824	−	0.906212i	$-0.361039\pi$
$758$	−32.1987	+	18.5899i	−1.16951	+	0.675217i
$759$	−21.6398	+	27.4235i	−0.785473	+	0.995408i
$760$	4.34353	−	0.365675i	0.157557	−	0.0132644i
$761$			22.6385i			0.820646i	0.911940	+	0.410323i	$0.134584\pi$
$761$			22.6385i			0.820646i	−0.911940	+	0.410323i	$0.865416\pi$
$762$	0.702359	−	4.82815i	0.0254438	−	0.174905i
$763$	−33.5803	+	19.3876i	−1.21569	+	0.701877i
$764$	16.2131	+	9.36065i	0.586570	+	0.338656i
$765$	−11.1649	+	10.5752i	−0.403668	+	0.382348i
$766$	−2.24543	+	3.88919i	−0.0811305	+	0.140522i
$767$			0.210274i			0.00759256i
$768$	1.07294	−	1.35971i	0.0387164	−	0.0490642i
$769$	0.580659	−	1.00573i	0.0209391	−	0.0362676i	−0.855366	−	0.518024i	$-0.826668\pi$
$769$	0.580659	−	1.00573i	0.0209391	−	0.0362676i	0.876305	+	0.481757i	$0.160001\pi$
$770$	2.82672	−	4.89603i	0.101868	−	0.176441i
$771$	−4.95601	+	6.28061i	−0.178486	+	0.226191i
$772$		−	24.4748i		−	0.880867i
$773$	7.13678	−	12.3613i	0.256692	−	0.444604i	−0.708661	−	0.705549i	$-0.750701\pi$
$773$	7.13678	−	12.3613i	0.256692	−	0.444604i	0.965354	+	0.260945i	$0.0840340\pi$
$774$	3.07293	−	2.91063i	0.110454	−	0.104621i
$775$	−3.48915	−	2.01446i	−0.125334	−	0.0723616i
$776$	−6.10768	+	3.52627i	−0.219253	+	0.126586i
$777$	−0.777017	+	5.34137i	−0.0278753	+	0.191620i
$778$		−	26.6064i		−	0.953886i
$779$	−0.870722	−	10.3425i	−0.0311969	−	0.370560i
$780$	−0.235958	+	0.299023i	−0.00844865	+	0.0107067i
$781$	−20.3572	+	11.7532i	−0.728438	+	0.420564i
$782$	22.2380	+	38.5174i	0.795231	+	1.37738i
$783$	33.8766	−	23.8702i	1.21065	−	0.853053i
$784$	0.542503	+	0.939644i	0.0193751	+	0.0335587i
$785$	−11.1950	−	6.46343i	−0.399566	−	0.230690i
$786$	−11.3495	−	8.95585i	−0.404823	−	0.319445i
$787$		−	35.6942i		−	1.27236i	−0.771540	−	0.636181i	$-0.780513\pi$
$787$		−	35.6942i		−	1.27236i	0.771540	−	0.636181i	$-0.219487\pi$
$788$	−4.31146	−	2.48922i	−0.153589	−	0.0886749i
$789$	46.0171	−	18.3340i	1.63825	−	0.652706i
$790$	−15.0800			−0.536521
$791$	−29.6103			−1.05282
$792$	1.98688	−	6.68457i	0.0706006	−	0.237526i
$793$	−1.57126	+	0.907168i	−0.0557971	+	0.0322145i
$794$	10.5922	−	18.3462i	0.375902	−	0.651082i
$795$	1.01984	−	7.01055i	0.0361699	−	0.248639i
$796$	9.08451	+	15.7348i	0.321992	+	0.557707i
$797$	−33.7963			−1.19713			−0.598563	−	0.801076i	$-0.704261\pi$
$797$	−33.7963			−1.19713			−0.598563	+	0.801076i	$0.704261\pi$
$798$	1.10962	−	18.3282i	0.0392802	−	0.648812i
$799$	−28.1131			−0.994571
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−8.84468	+	8.37755i	−0.312511	+	0.296006i
$802$	11.5551	−	20.0141i	0.408026	−	0.706722i
$803$	7.18686	−	4.14934i	0.253619	−	0.146427i
$804$	−12.3362	+	4.91493i	−0.435063	+	0.173336i
$805$	21.1017			0.743738
$806$	−0.886031			−0.0312091
$807$	2.08460	+	5.23221i	0.0733813	+	0.184182i
$808$	−10.2389	−	5.91143i	−0.360203	−	0.207963i
$809$		−	9.95048i		−	0.349840i	−0.984583	−	0.174920i	$-0.944033\pi$
$809$		−	9.95048i		−	0.349840i	0.984583	−	0.174920i	$-0.0559667\pi$
$810$	4.07088	+	8.02670i	0.143036	+	0.282030i
$811$	12.1319	+	7.00436i	0.426009	+	0.245956i	0.697645	−	0.716444i	$-0.254231\pi$
$811$	12.1319	+	7.00436i	0.426009	+	0.245956i	−0.271636	+	0.962400i	$0.587565\pi$
$812$	9.69845	+	16.7982i	0.340349	+	0.589501i
$813$	4.06609	+	10.2056i	0.142604	+	0.357927i
$814$	−1.48925	−	2.57946i	−0.0521983	−	0.0904100i
$815$	11.7963	−	6.81062i	0.413208	−	0.238566i
$816$	−6.96997	−	5.49998i	−0.243998	−	0.192538i
$817$	0.515915	+	6.12811i	0.0180496	+	0.214395i
$818$			9.54002i			0.333559i
$819$	1.10342	+	1.16495i	0.0385566	+	0.0407065i
$820$	−2.06213	+	1.19057i	−0.0720125	+	0.0415765i
$821$	−18.2129	−	10.5152i	−0.635634	−	0.366984i	0.147297	−	0.989092i	$-0.452943\pi$
$821$	−18.2129	−	10.5152i	−0.635634	−	0.366984i	−0.782931	+	0.622109i	$0.786276\pi$
$822$	−3.64573	+	25.0614i	−0.127159	+	0.874118i
$823$	−13.6408	+	23.6265i	−0.475488	+	0.823569i	−0.999606	−	0.0280769i	$-0.991062\pi$
$823$	−13.6408	+	23.6265i	−0.475488	+	0.823569i	0.524118	+	0.851646i	$0.324395\pi$
$824$		−	17.5769i		−	0.612319i
$825$	−3.16069	−	2.49409i	−0.110041	−	0.0868329i
$826$	−1.16272	+	2.01388i	−0.0404561	+	0.0700720i
$827$	22.4340	−	38.8568i	0.780105	−	1.35118i	−0.151775	−	0.988415i	$-0.548499\pi$
$827$	22.4340	−	38.8568i	0.780105	−	1.35118i	0.931880	−	0.362767i	$-0.118168\pi$
$828$	25.3158	−	6.05269i	0.879784	−	0.210345i
$829$			9.02419i			0.313423i	0.987644	+	0.156711i	$0.0500893\pi$
$829$			9.02419i			0.313423i	−0.987644	+	0.156711i	$0.949911\pi$
$830$	−2.18023	+	3.77627i	−0.0756770	+	0.131076i
$831$	−37.9945	−	5.52712i	−1.31801	−	0.191734i
$832$	−0.190454	−	0.109959i	−0.00660280	−	0.00381213i
$833$	4.81669	−	2.78092i	0.166889	−	0.0963531i
$834$	−18.9001	−	2.74943i	−0.654457	−	0.0952049i
$835$			10.8604i			0.375840i
$836$	5.78449	+	8.31899i	0.200061	+	0.287718i
$837$	−8.79132	+	18.9996i	−0.303873	+	0.656721i
$838$	−0.832876	+	0.480861i	−0.0287712	+	0.0166111i
$839$	9.31551	+	16.1349i	0.321607	+	0.557040i	0.980820	−	0.194917i	$-0.0624437\pi$
$839$	9.31551	+	16.1349i	0.321607	+	0.557040i	−0.659213	+	0.751957i	$0.729110\pi$
$840$	−3.91332	+	1.55913i	−0.135022	+	0.0537952i
$841$	−17.3039	−	29.9712i	−0.596686	−	1.03349i
$842$	−14.4170	−	8.32365i	−0.496842	−	0.286852i
$843$	16.8574	−	21.3629i	0.580599	−	0.735777i
$844$		−	2.88365i		−	0.0992593i
$845$	−11.2164	−	6.47582i	−0.385857	−	0.222775i
$846$	−4.68768	+	15.7711i	−0.161166	+	0.542220i
$847$	−13.6112			−0.467686
$848$	4.09015			0.140456
$849$	13.0155	+	32.6680i	0.446690	+	1.12116i
$850$	−4.43932	+	2.56304i	−0.152267	+	0.0879116i
$851$	5.55869	−	9.62794i	0.190550	−	0.330042i
$852$	17.3326	+	2.52141i	0.593806	+	0.0863819i
$853$	−7.15637	−	12.3952i	−0.245029	−	0.424403i	0.717111	−	0.696959i	$-0.245464\pi$
$853$	−7.15637	−	12.3952i	−0.245029	−	0.424403i	−0.962140	+	0.272556i	$0.912131\pi$
$854$	−20.0648			−0.686604
$855$	−12.8031	−	2.66104i	−0.437856	−	0.0910057i
$856$	−2.80439			−0.0958522
$857$	−23.2696	−	40.3041i	−0.794873	−	1.37676i	−0.922920	−	0.384993i	$-0.874204\pi$
$857$	−23.2696	−	40.3041i	−0.794873	−	1.37676i	0.128046	−	0.991768i	$-0.459129\pi$
$858$	−0.876212	−	0.127464i	−0.0299134	−	0.00435155i
$859$	−11.8783	+	20.5737i	−0.405281	+	0.701967i	−0.994354	−	0.106113i	$-0.966160\pi$
$859$	−11.8783	+	20.5737i	−0.405281	+	0.701967i	0.589073	+	0.808080i	$0.299493\pi$
$860$	1.22184	−	0.705429i	0.0416644	−	0.0240549i
$861$	3.71251	+	9.31816i	0.126522	+	0.317562i
$862$	−10.0728			−0.343080
$863$	8.13980			0.277082			0.138541	−	0.990357i	$-0.455759\pi$
$863$	8.13980			0.277082			0.138541	+	0.990357i	$0.455759\pi$
$864$	−4.24761	+	2.99297i	−0.144506	+	0.101823i
$865$	−10.4748	−	6.04765i	−0.356155	−	0.205626i
$866$			6.83171i			0.232151i
$867$	−9.95340	+	12.6137i	−0.338035	+	0.428382i
$868$	−8.48588	−	4.89933i	−0.288030	−	0.166294i
$869$	−17.5269	−	30.3576i	−0.594561	−	1.02981i
$870$	12.8329	−	5.11282i	0.435075	−	0.173341i
$871$	0.843026	+	1.46016i	0.0285649	+	0.0494758i
$872$	−13.8072	+	7.97161i	−0.467572	+	0.269953i
$873$	20.5776	−	4.91986i	0.696448	−	0.166512i
$874$	−16.0955	+	34.2237i	−0.544438	+	1.15763i
$875$			2.43208i			0.0822192i
$876$	−6.11908	−	0.890152i	−0.206744	−	0.0300754i
$877$	−31.6447	+	18.2701i	−1.06857	+	0.616937i	−0.927789	−	0.373104i	$-0.878293\pi$
$877$	−31.6447	+	18.2701i	−1.06857	+	0.616937i	−0.140777	+	0.990041i	$0.544960\pi$
$878$	9.27371	+	5.35418i	0.312973	+	0.180695i
$879$	−27.6101	−	4.01648i	−0.931265	−	0.135473i
$880$	1.16227	−	2.01311i	0.0391800	−	0.0678618i
$881$		−	29.6144i		−	0.997735i	−0.866678	−	0.498868i	$-0.833749\pi$
$881$		−	29.6144i		−	0.997735i	0.866678	−	0.498868i	$-0.166251\pi$
$882$	−0.756903	−	3.16580i	−0.0254862	−	0.106598i
$883$	17.6785	−	30.6200i	0.594928	−	1.03045i	−0.398629	−	0.917112i	$-0.630514\pi$
$883$	17.6785	−	30.6200i	0.594928	−	1.03045i	0.993557	−	0.113334i	$-0.0361529\pi$
$884$	−0.563658	+	0.976283i	−0.0189579	+	0.0328360i
$885$	1.30009	+	1.02589i	0.0437019	+	0.0344850i
$886$			7.93748i			0.266665i
$887$	−27.9372	+	48.3886i	−0.938039	+	1.62473i	−0.168916	+	0.985630i	$0.554027\pi$
$887$	−27.9372	+	48.3886i	−0.938039	+	1.62473i	−0.769123	+	0.639101i	$0.779307\pi$
$888$	−0.319487	+	2.19622i	−0.0107213	+	0.0737002i
$889$	−5.93301	−	3.42543i	−0.198987	−	0.114885i
$890$	−3.51677	+	2.03041i	−0.117882	+	0.0680593i
$891$	−11.4272	+	17.5243i	−0.382824	+	0.587086i
$892$		−	14.6986i		−	0.492146i
$893$	−13.6475	−	19.6272i	−0.456695	−	0.656798i
$894$	28.6961	+	22.6440i	0.959741	+	0.757329i
$895$	−7.94473	+	4.58689i	−0.265563	+	0.153323i
$896$	−1.21604	−	2.10624i	−0.0406250	−	0.0703645i
$897$	−1.22322	−	3.07021i	−0.0408423	−	0.102511i
$898$	−8.19524	−	14.1946i	−0.273479	−	0.473679i
$899$	27.8275	+	16.0662i	0.928101	+	0.535839i
$900$	0.697602	+	2.91776i	0.0232534	+	0.0972588i
$901$		−	20.9664i		−	0.698494i
$902$	−4.79348	−	2.76752i	−0.159606	−	0.0921483i
$903$	−2.19971	−	5.52114i	−0.0732019	−	0.183732i
$904$	−12.1749			−0.404931
$905$	−9.66914			−0.321413
$906$	38.9628	−	15.5234i	1.29445	−	0.515731i
$907$	37.7050	−	21.7690i	1.25197	−	0.722828i	0.280473	−	0.959862i	$-0.409509\pi$
$907$	37.7050	−	21.7690i	1.25197	−	0.722828i	0.971501	+	0.237034i	$0.0761754\pi$
$908$	−5.53375	+	9.58473i	−0.183644	+	0.318081i
$909$	24.3908	+	25.7509i	0.808993	+	0.854103i
$910$	0.267428	+	0.463199i	0.00886515	+	0.0153549i
$911$	−34.1334			−1.13089			−0.565444	−	0.824786i	$-0.691295\pi$
$911$	−34.1334			−1.13089			−0.565444	+	0.824786i	$0.691295\pi$
$912$	0.456245	−	7.53604i	0.0151078	−	0.249543i
$913$	−10.1361			−0.335455
$914$	−9.91012	−	17.1648i	−0.327798	−	0.567762i
$915$	−2.05707	+	14.1407i	−0.0680048	+	0.467478i
$916$	−1.59769	+	2.76728i	−0.0527892	+	0.0914336i
$917$	−17.5808	+	10.1503i	−0.580570	+	0.335192i
$918$	15.3422	+	21.7736i	0.506368	+	0.718636i
$919$	−6.05120			−0.199611			−0.0998053	−	0.995007i	$-0.531822\pi$
$919$	−6.05120			−0.199611			−0.0998053	+	0.995007i	$0.531822\pi$
$920$	8.67642			0.286053
$921$	−12.9306	+	5.15178i	−0.426079	+	0.169757i
$922$	−35.9630	−	20.7632i	−1.18438	−	0.683801i
$923$		−	2.22388i		−	0.0731998i
$924$	−7.68703	−	6.06581i	−0.252885	−	0.199550i
$925$	1.10967	+	0.640666i	0.0364856	+	0.0210650i
$926$	10.1223	+	17.5323i	0.332638	+	0.576147i
$927$	−15.0237	+	50.5451i	−0.493443	+	1.66012i
$928$	3.98772	+	6.90694i	0.130903	+	0.226731i
$929$	14.4587	−	8.34775i	0.474376	−	0.273881i	−0.243694	−	0.969852i	$-0.578359\pi$
$929$	14.4587	−	8.34775i	0.474376	−	0.273881i	0.718070	+	0.695971i	$0.245026\pi$
$930$	−4.32279	+	5.47816i	−0.141750	+	0.179636i
$931$	4.27975	+	2.01278i	0.140263	+	0.0659661i
$932$			8.03695i			0.263259i
$933$	−5.05142	+	34.7244i	−0.165376	+	1.13683i
$934$	8.78980	−	5.07479i	0.287611	−	0.166052i
$935$	−10.3194	−	5.95789i	−0.337479	−	0.194844i
$936$	0.453695	+	0.478993i	0.0148295	+	0.0156564i
$937$	18.3641	−	31.8076i	0.599930	−	1.03911i	−0.392901	−	0.919581i	$-0.628528\pi$
$937$	18.3641	−	31.8076i	0.599930	−	1.03911i	0.992831	−	0.119529i	$-0.0381383\pi$
$938$			18.6461i			0.608818i
$939$	25.8018	−	32.6979i	0.842011	−	1.06706i
$940$	−2.74216	+	4.74957i	−0.0894395	+	0.154914i
$941$	19.7858	−	34.2699i	0.644997	−	1.11717i	−0.339305	−	0.940676i	$-0.610192\pi$
$941$	19.7858	−	34.2699i	0.644997	−	1.11717i	0.984302	−	0.176491i	$-0.0564748\pi$
$942$	−13.8697	+	17.5767i	−0.451900	+	0.572680i
$943$		−	20.6598i		−	0.672774i
$944$	−0.478076	+	0.828051i	−0.0155600	+	0.0269508i
$945$	12.5860	−	1.13865i	0.409424	−	0.0370404i
$946$	2.84021	+	1.63980i	0.0923431	+	0.0533143i
$947$	38.8622	−	22.4371i	1.26285	−	0.729108i	0.289227	−	0.957261i	$-0.406602\pi$
$947$	38.8622	−	22.4371i	1.26285	−	0.729108i	0.973625	+	0.228153i	$0.0732686\pi$
$948$	−3.76003	+	25.8472i	−0.122120	+	0.839477i
$949$			0.785113i			0.0254858i
$950$	−3.94445	−	1.85508i	−0.127975	−	0.0601868i
$951$	13.4544	−	17.0504i	0.436289	−	0.552897i
$952$	−10.7968	+	6.23351i	−0.349925	+	0.202029i
$953$	−5.60620	−	9.71022i	−0.181603	−	0.314545i	0.760824	−	0.648958i	$-0.224795\pi$
$953$	−5.60620	−	9.71022i	−0.181603	−	0.314545i	−0.942426	+	0.334414i	$0.891462\pi$
$954$	−11.7619	−	3.49602i	−0.380805	−	0.113188i
$955$	−9.36065	−	16.2131i	−0.302904	−	0.524644i
$956$	−4.48081	−	2.58700i	−0.144920	−	0.0836695i
$957$	25.2079	+	19.8915i	0.814855	+	0.642999i
$958$		−	40.6886i		−	1.31459i
$959$	30.7964	+	17.7803i	0.994468	+	0.574157i
$960$	−1.60905	+	0.641070i	−0.0519317	+	0.0206905i
$961$	14.7678			0.476379
$962$	0.281787			0.00908519
$963$	8.06448	+	2.39703i	0.259874	+	0.0772433i
$964$	25.4528	−	14.6952i	0.819780	−	0.473300i
$965$	−12.2374	+	21.1958i	−0.393936	+	0.682317i
$966$	5.26150	−	36.1686i	0.169286	−	1.16370i
$967$	−10.2650	−	17.7795i	−0.330101	−	0.571751i	0.652431	−	0.757848i	$-0.273749\pi$
$967$	−10.2650	−	17.7795i	−0.330101	−	0.571751i	−0.982531	+	0.186097i	$0.940416\pi$
$968$	−5.59653			−0.179879
$969$	−38.6304	−	2.33875i	−1.24099	−	0.0751315i
$970$	7.05254			0.226443
$971$	18.9504	+	32.8230i	0.608147	+	1.05334i	0.991546	+	0.129759i	$0.0414202\pi$
$971$	18.9504	+	32.8230i	0.608147	+	1.05334i	−0.383399	+	0.923583i	$0.625246\pi$
$972$	14.7729	−	4.97615i	0.473840	−	0.159610i
$973$	−13.4090	+	23.2252i	−0.429874	+	0.744564i
$974$	12.5190	−	7.22783i	0.401134	−	0.231595i
$975$	0.353857	−	0.140982i	0.0113325	−	0.00451505i
$976$	−8.25009			−0.264079
$977$	46.2229			1.47880			0.739400	−	0.673266i	$-0.235109\pi$
$977$	46.2229			1.47880			0.739400	+	0.673266i	$0.235109\pi$
$978$	−8.73217	−	21.9172i	−0.279224	−	0.700835i
$979$	−8.17485	−	4.71975i	−0.261269	−	0.150844i
$980$		−	1.08501i		−	0.0346593i
$981$	46.5186	−	11.1220i	1.48522	−	0.355099i
$982$	13.6141	+	7.86008i	0.434442	+	0.250825i
$983$	1.93851	+	3.35759i	0.0618287	+	0.107091i	0.895283	−	0.445498i	$-0.146973\pi$
$983$	1.93851	+	3.35759i	0.0618287	+	0.107091i	−0.833454	+	0.552589i	$0.813640\pi$
$984$	1.52648	+	3.83136i	0.0486623	+	0.122139i
$985$	2.48922	+	4.31146i	0.0793132	+	0.137375i
$986$	35.4056	−	20.4414i	1.12754	−	0.650987i
$987$	18.1362	+	14.3112i	0.577281	+	0.455530i
$988$	−0.955218	+	0.0804183i	−0.0303895	+	0.00255845i
$989$			12.2412i			0.389248i
$990$	−5.06297	+	4.79557i	−0.160912	+	0.152413i
$991$	−4.36664	+	2.52108i	−0.138711	+	0.0800848i	−0.567750	−	0.823201i	$-0.692186\pi$
$991$	−4.36664	+	2.52108i	−0.138711	+	0.0800848i	0.429039	+	0.903286i	$0.358852\pi$
$992$	−3.48915	−	2.01446i	−0.110781	−	0.0639593i
$993$	−1.26414	+	8.68995i	−0.0401163	+	0.275767i
$994$	12.2970	−	21.2990i	0.390036	−	0.675563i
$995$		−	18.1690i		−	0.575997i
$996$	5.92895	+	4.67852i	0.187866	+	0.148244i
$997$	−20.3710	+	35.2836i	−0.645156	+	1.11744i	0.339110	+	0.940747i	$0.389874\pi$
$997$	−20.3710	+	35.2836i	−0.645156	+	1.11744i	−0.984266	+	0.176696i	$0.943459\pi$
$998$	16.7701	−	29.0466i	0.530847	−	0.919454i
$999$	2.79593	−	6.04249i	0.0884595	−	0.191176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.b.221.1	yes	24
3.2	odd	2		570.2.s.a.221.5	✓	24
19.8	odd	6		570.2.s.a.521.5	yes	24
57.8	even	6	inner	570.2.s.b.521.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.5	✓	24	3.2	odd	2
570.2.s.a.521.5	yes	24	19.8	odd	6
570.2.s.b.221.1	yes	24	1.1	even	1	trivial
570.2.s.b.521.1	yes	24	57.8	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.71401 - 0.249340i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.641070 - 1.60905i) q^{6} -2.43208 q^{7} -1.00000 q^{8} +(2.87566 + 0.854742i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.71401 - 0.249340i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.641070 - 1.60905i) q^{6} -2.43208 q^{7} -1.00000 q^{8} +(2.87566 + 0.854742i) q^{9} +(0.866025 + 0.500000i) q^{10} +2.32454i q^{11} +(1.07294 - 1.35971i) q^{12} +(-0.190454 - 0.109959i) q^{13} +(-1.21604 - 2.10624i) q^{14} +(-1.60905 + 0.641070i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.43932 + 2.56304i) q^{17} +(0.697602 + 2.91776i) q^{18} +(-3.94445 - 1.85508i) q^{19} +1.00000i q^{20} +(4.16860 + 0.606413i) q^{21} +(-2.01311 + 1.16227i) q^{22} +(-7.51400 - 4.33821i) q^{23} +(1.71401 + 0.249340i) q^{24} +(0.500000 - 0.866025i) q^{25} -0.219917i q^{26} +(-4.71579 - 2.18205i) q^{27} +(1.21604 - 2.10624i) q^{28} +(-3.98772 + 6.90694i) q^{29} +(-1.35971 - 1.07294i) q^{30} -4.02893i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.579599 - 3.98428i) q^{33} +(-4.43932 - 2.56304i) q^{34} +(-2.10624 + 1.21604i) q^{35} +(-2.17806 + 2.06302i) q^{36} +1.28133i q^{37} +(-0.365675 - 4.34353i) q^{38} +(0.299023 + 0.235958i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.19057 + 2.06213i) q^{41} +(1.55913 + 3.91332i) q^{42} +(-0.705429 - 1.22184i) q^{43} +(-2.01311 - 1.16227i) q^{44} +(2.91776 - 0.697602i) q^{45} -8.67642i q^{46} +(4.74957 + 2.74216i) q^{47} +(0.641070 + 1.60905i) q^{48} -1.08501 q^{49} +1.00000 q^{50} +(8.24811 - 3.28618i) q^{51} +(0.190454 - 0.109959i) q^{52} +(-2.04507 + 3.54217i) q^{53} +(-0.468182 - 5.17502i) q^{54} +(1.16227 + 2.01311i) q^{55} +2.43208 q^{56} +(6.29828 + 4.16314i) q^{57} -7.97545 q^{58} +(-0.478076 - 0.828051i) q^{59} +(0.249340 - 1.71401i) q^{60} +(4.12504 - 7.14478i) q^{61} +(3.48915 - 2.01446i) q^{62} +(-6.99382 - 2.07880i) q^{63} +1.00000 q^{64} -0.219917 q^{65} +(3.74029 - 1.49019i) q^{66} +(-6.63960 - 3.83338i) q^{67} -5.12609i q^{68} +(11.7974 + 9.30928i) q^{69} +(-2.10624 - 1.21604i) q^{70} +(5.05616 + 8.75753i) q^{71} +(-2.87566 - 0.854742i) q^{72} +(-1.78502 - 3.09174i) q^{73} +(-1.10967 + 0.640666i) q^{74} +(-1.07294 + 1.35971i) q^{75} +(3.57877 - 2.48845i) q^{76} -5.65345i q^{77} +(-0.0548341 + 0.376940i) q^{78} +(-13.0596 + 7.53998i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(7.53883 + 4.91589i) q^{81} +(-1.19057 + 2.06213i) q^{82} +4.36047i q^{83} +(-2.60947 + 3.30691i) q^{84} +(-2.56304 + 4.43932i) q^{85} +(0.705429 - 1.22184i) q^{86} +(8.55717 - 10.8443i) q^{87} -2.32454i q^{88} +(-2.03041 + 3.51677i) q^{89} +(2.06302 + 2.17806i) q^{90} +(0.463199 + 0.267428i) q^{91} +(7.51400 - 4.33821i) q^{92} +(-1.00457 + 6.90562i) q^{93} +5.48433i q^{94} +(-4.34353 + 0.365675i) q^{95} +(-1.07294 + 1.35971i) q^{96} +(6.10768 - 3.52627i) q^{97} +(-0.542503 - 0.939644i) q^{98} +(-1.98688 + 6.68457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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