LMFDB - Embedded newform 570.2.s.a.521.5

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			521.5
Character	$\chi$	$=$	570.521
Dual form			570.2.s.a.221.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.641070 - 1.60905i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.71401 + 0.249340i) q^{6} -2.43208 q^{7} +1.00000 q^{8} +(-2.17806 + 2.06302i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.641070 - 1.60905i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.71401 + 0.249340i) q^{6} -2.43208 q^{7} +1.00000 q^{8} +(-2.17806 + 2.06302i) 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} +(-0.249340 + 1.71401i) 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} +(1.55913 + 3.91332i) q^{21} +(-2.01311 - 1.16227i) q^{22} +(7.51400 - 4.33821i) q^{23} +(-0.641070 - 1.60905i) 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} +(3.74029 - 1.49019i) q^{33} +(-4.43932 + 2.56304i) q^{34} +(2.10624 + 1.21604i) q^{35} +(2.87566 + 0.854742i) 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} +(-4.16860 - 0.606413i) 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} +(1.71401 + 0.249340i) q^{48} -1.08501 q^{49} -1.00000 q^{50} +(1.27814 - 8.78616i) q^{51} +(0.190454 + 0.109959i) q^{52} +(2.04507 + 3.54217i) q^{53} +(-4.24761 + 2.99297i) q^{54} +(1.16227 - 2.01311i) q^{55} -2.43208 q^{56} +(5.51358 + 5.15756i) q^{57} -7.97545 q^{58} +(0.478076 - 0.828051i) q^{59} +(1.60905 - 0.641070i) q^{60} +(4.12504 + 7.14478i) q^{61} +(-3.48915 - 2.01446i) q^{62} +(5.29720 - 5.01743i) q^{63} +1.00000 q^{64} +0.219917 q^{65} +(-0.579599 + 3.98428i) 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} +(-2.17806 + 2.06302i) 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} +(-0.353857 + 0.140982i) q^{78} +(-13.0596 - 7.53998i) q^{79} +(0.866025 - 0.500000i) q^{80} +(0.487870 - 8.98677i) 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} +(-0.854742 + 2.87566i) q^{90} +(0.463199 - 0.267428i) q^{91} +(-7.51400 - 4.33821i) q^{92} +(6.48273 - 2.58282i) 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} +(-4.79557 - 5.06297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 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} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 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} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.641070	−	1.60905i	−0.370122	−	0.928983i
$3$	−0.641070	−	1.60905i	−0.370122	−	0.928983i
$4$	−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
$6$	1.71401	+	0.249340i	0.699742	+	0.101793i
$7$	−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
$9$	−2.17806	+	2.06302i	−0.726019	+	0.687674i
$10$	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	−0.526179	−	0.850374i	$-0.676376\pi$
$13$	−0.190454	+	0.109959i	−0.0528224	+	0.0304970i	0.473356	+	0.880871i	$0.343042\pi$
$14$	1.21604	−	2.10624i	0.325000	−	0.562916i
$15$	−0.249340	+	1.71401i	−0.0643792	+	0.442555i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.43932	+	2.56304i	1.07669	+	0.621629i	0.930002	−	0.367553i	$-0.119804\pi$
$17$	4.43932	+	2.56304i	1.07669	+	0.621629i	0.146691	+	0.989182i	$0.453138\pi$
$18$	−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
$21$	1.55913	+	3.91332i	0.340230	+	0.853957i
$22$	−2.01311	−	1.16227i	−0.429196	−	0.247796i
$23$	7.51400	−	4.33821i	1.56678	−	0.904580i	0.570237	−	0.821480i	$-0.306851\pi$
$23$	7.51400	−	4.33821i	1.56678	−	0.904580i	0.996541	−	0.0830996i	$-0.0264820\pi$
$24$	−0.641070	−	1.60905i	−0.130858	−	0.328445i
$25$	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	0.952267	+	0.305266i	$0.0987454\pi$
$29$	3.98772	+	6.90694i	0.740502	+	1.28259i	−0.211765	+	0.977321i	$0.567921\pi$
$30$	−1.35971	−	1.07294i	−0.248247	−	0.195891i
$31$			4.02893i			0.723616i	0.932253	+	0.361808i	$0.117840\pi$
$31$			4.02893i			0.723616i	−0.932253	+	0.361808i	$0.882160\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.74029	−	1.49019i	0.651100	−	0.259409i
$34$	−4.43932	+	2.56304i	−0.761337	+	0.439558i
$35$	2.10624	+	1.21604i	0.356019	+	0.205548i
$36$	2.87566	+	0.854742i	0.479277	+	0.142457i
$37$		−	1.28133i		−	0.210650i	−0.994438	−	0.105325i	$-0.966412\pi$
$37$		−	1.28133i		−	0.210650i	0.994438	−	0.105325i	$-0.0335883\pi$
$38$	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	$-0.892865\pi$
$41$	−1.19057	+	2.06213i	−0.185936	+	0.322050i	0.757956	+	0.652306i	$0.226198\pi$
$42$	−4.16860	−	0.606413i	−0.643229	−	0.0935716i
$43$	−0.705429	+	1.22184i	−0.107577	+	0.186329i	−0.914788	−	0.403934i	$-0.867643\pi$
$43$	−0.705429	+	1.22184i	−0.107577	+	0.186329i	0.807211	+	0.590263i	$0.200976\pi$
$44$	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	$-0.797652\pi$
$47$	−4.74957	+	2.74216i	−0.692795	+	0.399986i	0.111863	+	0.993724i	$0.464318\pi$
$48$	1.71401	+	0.249340i	0.247396	+	0.0359891i
$49$	−1.08501			−0.155001
$50$	−1.00000			−0.141421
$51$	1.27814	−	8.78616i	0.178975	−	1.23031i
$52$	0.190454	+	0.109959i	0.0264112	+	0.0152485i
$53$	2.04507	+	3.54217i	0.280912	+	0.486555i	0.971610	−	0.236589i	$-0.0760296\pi$
$53$	2.04507	+	3.54217i	0.280912	+	0.486555i	−0.690697	+	0.723144i	$0.742696\pi$
$54$	−4.24761	+	2.99297i	−0.578026	+	0.407291i
$55$	1.16227	−	2.01311i	0.156720	−	0.271447i
$56$	−2.43208			−0.325000
$57$	5.51358	+	5.15756i	0.730292	+	0.683135i
$58$	−7.97545			−1.04723
$59$	0.478076	−	0.828051i	0.0622402	−	0.107803i	−0.833226	−	0.552932i	$-0.813509\pi$
$59$	0.478076	−	0.828051i	0.0622402	−	0.107803i	0.895466	+	0.445129i	$0.146842\pi$
$60$	1.60905	−	0.641070i	0.207727	−	0.0827618i
$61$	4.12504	+	7.14478i	0.528158	+	0.914796i	0.999461	+	0.0328247i	$0.0104503\pi$
$61$	4.12504	+	7.14478i	0.528158	+	0.914796i	−0.471304	+	0.881971i	$0.656216\pi$
$62$	−3.48915	−	2.01446i	−0.443123	−	0.255837i
$63$	5.29720	−	5.01743i	0.667385	−	0.632137i
$64$	1.00000			0.125000
$65$	0.219917			0.0272774
$66$	−0.579599	+	3.98428i	−0.0713437	+	0.490431i
$67$	−6.63960	+	3.83338i	−0.811157	+	0.468322i	−0.847357	−	0.531023i	$-0.821808\pi$
$67$	−6.63960	+	3.83338i	−0.811157	+	0.468322i	0.0362006	+	0.999345i	$0.488474\pi$
$68$		−	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	0.392756	+	0.919643i	$0.371522\pi$
$71$	−5.05616	+	8.75753i	−0.600056	+	1.03933i	−0.992812	+	0.119685i	$0.961812\pi$
$72$	−2.17806	+	2.06302i	−0.256687	+	0.243130i
$73$	−1.78502	+	3.09174i	−0.208921	+	0.361861i	−0.951375	−	0.308036i	$-0.900328\pi$
$73$	−1.78502	+	3.09174i	−0.208921	+	0.361861i	0.742454	+	0.669897i	$0.233662\pi$
$74$	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
$78$	−0.353857	+	0.140982i	−0.0400664	+	0.0159631i
$79$	−13.0596	−	7.53998i	−1.46932	−	0.848313i	−0.469914	−	0.882712i	$-0.655715\pi$
$79$	−13.0596	−	7.53998i	−1.46932	−	0.848313i	−0.999408	+	0.0343988i	$0.989048\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	0.487870	−	8.98677i	0.0542078	−	0.998530i
$82$	−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	$-0.0976190\pi$
$89$	2.03041	+	3.51677i	0.215223	+	0.372776i	−0.738119	+	0.674671i	$0.764286\pi$
$90$	−0.854742	+	2.87566i	−0.0900977	+	0.303121i
$91$	0.463199	−	0.267428i	0.0485564	−	0.0280341i
$92$	−7.51400	−	4.33821i	−0.783389	−	0.452290i
$93$	6.48273	−	2.58282i	0.672227	−	0.267826i
$94$		−	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	0.776924	−	0.629595i	$-0.216779\pi$
$97$	6.10768	+	3.52627i	0.620141	+	0.358038i	−0.156783	+	0.987633i	$0.550112\pi$
$98$	0.542503	−	0.939644i	0.0548011	−	0.0949183i
$99$	−4.79557	−	5.06297i	−0.481973	−	0.508848i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−10.2389	+	5.91143i	−1.01881	+	0.588209i	−0.913759	−	0.406258i	$-0.866834\pi$
$101$	−10.2389	+	5.91143i	−1.01881	+	0.588209i	−0.105050	+	0.994467i	$0.533500\pi$
$102$	6.96997	+	5.49998i	0.690130	+	0.544579i
$103$		−	17.5769i		−	1.73190i	−0.500130	−	0.865950i	$-0.666714\pi$
$103$		−	17.5769i		−	1.73190i	0.500130	−	0.865950i	$-0.333286\pi$
$104$	−0.190454	+	0.109959i	−0.0186756	+	0.0107823i
$105$	0.606413	−	4.16860i	0.0591799	−	0.406814i
$106$	−4.09015			−0.397270
$107$	−2.80439			−0.271111			−0.135555	−	0.990770i	$-0.543282\pi$
$107$	−2.80439			−0.271111			−0.135555	+	0.990770i	$0.543282\pi$
$108$	−0.468182	−	5.17502i	−0.0450508	−	0.497966i
$109$	13.8072	+	7.97161i	1.32249	+	0.763542i	0.984126	−	0.177472i	$-0.0567919\pi$
$109$	13.8072	+	7.97161i	1.32249	+	0.763542i	0.338368	+	0.941014i	$0.390125\pi$
$110$	1.16227	+	2.01311i	0.110818	+	0.191942i
$111$	−2.06172	+	0.821425i	−0.195690	+	0.0779662i
$112$	1.21604	−	2.10624i	0.114905	−	0.199021i
$113$	−12.1749			−1.14532			−0.572659	−	0.819794i	$-0.694088\pi$
$113$	−12.1749			−1.14532			−0.572659	+	0.819794i	$0.694088\pi$
$114$	−7.22337	+	2.19612i	−0.676530	+	0.205686i
$115$	−8.67642			−0.809081
$116$	3.98772	−	6.90694i	0.370251	−	0.641293i
$117$	0.187972	−	0.632407i	0.0173781	−	0.0584661i
$118$	0.478076	+	0.828051i	0.0440104	+	0.0762283i
$119$	−10.7968	−	6.23351i	−0.989738	−	0.571425i
$120$	−0.249340	+	1.71401i	−0.0227615	+	0.156467i
$121$	5.59653			0.508776
$122$	−8.25009			−0.746928
$123$	4.08129	+	0.593712i	0.367998	+	0.0535332i
$124$	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	−0.387845	−	0.921725i	$-0.626780\pi$
$127$	2.43948	−	1.40844i	0.216469	−	0.124979i	0.604314	+	0.796746i	$0.293447\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.41822	+	0.351783i	0.212913	+	0.0309728i
$130$	−0.109959	+	0.190454i	−0.00964401	+	0.0167039i
$131$	−7.22873	−	4.17351i	−0.631577	−	0.364641i	0.149785	−	0.988719i	$-0.452142\pi$
$131$	−7.22873	−	4.17351i	−0.631577	−	0.364641i	−0.781363	+	0.624077i	$0.785475\pi$
$132$	−3.16069	−	2.49409i	−0.275102	−	0.217082i
$133$	9.59320	−	4.51170i	0.831836	−	0.391214i
$134$		−	7.66675i		−	0.662307i
$135$	−2.99297	−	4.24761i	−0.257593	−	0.365576i
$136$	4.43932	+	2.56304i	0.380669	+	0.219779i
$137$	12.6626	−	7.31076i	1.08184	−	0.624600i	0.150448	−	0.988618i	$-0.451929\pi$
$137$	12.6626	−	7.31076i	1.08184	−	0.624600i	0.931392	+	0.364018i	$0.118595\pi$
$138$	13.9608	−	5.56220i	1.18842	−	0.473486i
$139$	5.51342	+	9.54952i	0.467642	+	0.809979i	0.999316	−	0.0369693i	$-0.0117704\pi$
$139$	5.51342	+	9.54952i	0.467642	+	0.809979i	−0.531675	+	0.846949i	$0.678437\pi$
$140$		−	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
$147$	0.695566	+	1.74583i	0.0573693	+	0.143993i
$148$	−1.10967	+	0.640666i	−0.0912141	+	0.0526625i
$149$	18.2772	+	10.5523i	1.49732	+	0.864480i	0.999995	−	0.00308349i	$-0.000981508\pi$
$149$	18.2772	+	10.5523i	1.49732	+	0.864480i	0.497327	+	0.867563i	$0.334315\pi$
$150$	0.641070	+	1.60905i	0.0523432	+	0.131378i
$151$		−	24.2149i		−	1.97058i	−0.170899	−	0.985289i	$-0.554667\pi$
$151$		−	24.2149i		−	1.97058i	0.170899	−	0.985289i	$-0.445333\pi$
$152$	−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
$156$	0.0548341	−	0.376940i	0.00439024	−	0.0301794i
$157$	−6.46343	+	11.1950i	−0.515837	+	0.893457i	0.483993	+	0.875072i	$0.339186\pi$
$157$	−6.46343	+	11.1950i	−0.515837	+	0.893457i	−0.999831	+	0.0183851i	$0.994147\pi$
$158$	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
$162$	7.53883	+	4.91589i	0.592307	+	0.386229i
$163$	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
$165$	−3.98428	−	0.579599i	−0.310176	−	0.0451217i
$166$	−3.77627	−	2.18023i	−0.293096	−	0.169219i
$167$	5.43020	+	9.40538i	0.420202	+	0.727810i	0.995959	−	0.0898102i	$-0.0286260\pi$
$167$	5.43020	+	9.40538i	0.420202	+	0.727810i	−0.575757	+	0.817621i	$0.695293\pi$
$168$	1.55913	+	3.91332i	0.120290	+	0.301919i
$169$	−6.47582	+	11.2164i	−0.498140	+	0.862804i
$170$	5.12609			0.393153
$171$	4.76416	−	12.1780i	0.364324	−	0.931272i
$172$	1.41086			0.107577
$173$	6.04765	−	10.4748i	0.459794	−	0.796387i	−0.539156	−	0.842206i	$-0.681257\pi$
$173$	6.04765	−	10.4748i	0.459794	−	0.796387i	0.998950	+	0.0458193i	$0.0145899\pi$
$174$	5.11282	+	12.8329i	0.387602	+	0.972857i
$175$	−1.21604	−	2.10624i	−0.0919238	−	0.159217i
$176$	−2.01311	−	1.16227i	−0.151744	−	0.0876092i
$177$	−1.63885	−	0.238407i	−0.123184	−	0.0179197i
$178$	−4.06081			−0.304371
$179$	9.17378			0.685681			0.342840	−	0.939394i	$-0.388611\pi$
$179$	9.17378			0.685681			0.342840	+	0.939394i	$0.388611\pi$
$180$	−2.06302	−	2.17806i	−0.153769	−	0.162343i
$181$	−8.37372	+	4.83457i	−0.622414	+	0.359351i	−0.777808	−	0.628502i	$-0.783668\pi$
$181$	−8.37372	+	4.83457i	−0.622414	+	0.359351i	0.155395	+	0.987852i	$0.450335\pi$
$182$			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
$186$	−1.00457	+	6.90562i	−0.0736587	+	0.506344i
$187$	−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	$-0.236856\pi$
$192$	−0.641070	−	1.60905i	−0.0462653	−	0.116123i
$193$	−21.1958	−	12.2374i	−1.52571	−	0.880867i	−0.999535	−	0.0304886i	$-0.990294\pi$
$193$	−21.1958	−	12.2374i	−1.52571	−	0.880867i	−0.526171	−	0.850379i	$-0.676373\pi$
$194$	−6.10768	+	3.52627i	−0.438506	+	0.253171i
$195$	−0.140982	−	0.353857i	−0.0100960	−	0.0253402i
$196$	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	0.984535	+	0.175187i	$0.0560530\pi$
$199$	9.08451	+	15.7348i	0.643984	+	1.11541i	−0.340551	+	0.940226i	$0.610614\pi$
$200$	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
$204$	−8.24811	+	3.28618i	−0.577483	+	0.230079i
$205$	2.06213	−	1.19057i	0.144025	−	0.0831529i
$206$	15.2220	+	8.78844i	1.06057	+	0.612319i
$207$	−7.41610	+	24.9504i	−0.515455	+	1.73418i
$208$		−	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	0.411570	−	0.911378i	$-0.364981\pi$
$211$	−2.49731	−	1.44183i	−0.171922	−	0.0992593i	−0.583492	+	0.812119i	$0.698314\pi$
$212$	2.04507	−	3.54217i	0.140456	−	0.243277i
$213$	17.3326	+	2.52141i	1.18761	+	0.172764i
$214$	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
$219$	6.11908	+	0.890152i	0.413489	+	0.0601509i
$220$	−2.32454			−0.156720
$221$	−1.12732			−0.0758314
$222$	0.319487	−	2.19622i	0.0214426	−	0.147400i
$223$	−12.7294	−	7.34931i	−0.852422	−	0.492146i	0.00904511	−	0.999959i	$-0.497121\pi$
$223$	−12.7294	−	7.34931i	−0.852422	−	0.492146i	−0.861467	+	0.507813i	$0.830454\pi$
$224$	1.21604	+	2.10624i	0.0812500	+	0.140729i
$225$	−2.87566	−	0.854742i	−0.191711	−	0.0569828i
$226$	6.08745	−	10.5438i	0.404931	−	0.701361i
$227$	−11.0675			−0.734576			−0.367288	−	0.930107i	$-0.619714\pi$
$227$	−11.0675			−0.734576			−0.367288	+	0.930107i	$0.619714\pi$
$228$	1.70979	−	7.35368i	0.113233	−	0.487009i
$229$	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
$231$	−9.09666	+	3.62426i	−0.598516	+	0.238459i
$232$	3.98772	+	6.90694i	0.261807	+	0.453463i
$233$	−6.96020	−	4.01848i	−0.455978	−	0.263259i	0.254374	−	0.967106i	$-0.418131\pi$
$233$	−6.96020	−	4.01848i	−0.455978	−	0.263259i	−0.710352	+	0.703847i	$0.751464\pi$
$234$	0.453695	+	0.478993i	0.0296589	+	0.0313127i
$235$	5.48433			0.357758
$236$	−0.956151			−0.0622402
$237$	−3.76003	+	25.8472i	−0.244240	+	1.67895i
$238$	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	−0.658576	+	0.752514i	$0.728841\pi$
$241$	−25.4528	+	14.6952i	−1.63956	+	0.946601i	−0.980984	+	0.194086i	$0.937826\pi$
$242$	−2.79827	+	4.84674i	−0.179879	+	0.311560i
$243$	−14.7729	+	4.97615i	−0.947681	+	0.319220i
$244$	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
$249$	7.01619	−	2.79537i	0.444633	−	0.177149i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−21.7086	+	12.5335i	−1.37024	+	0.791107i	−0.990958	−	0.134176i	$-0.957161\pi$
$251$	−21.7086	+	12.5335i	−1.37024	+	0.791107i	−0.379279	+	0.925282i	$0.623828\pi$
$252$	−6.99382	−	2.07880i	−0.440569	−	0.130952i
$253$	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	$-0.212684\pi$
$257$	−2.30955	−	4.00025i	−0.144066	−	0.249529i	−0.929024	+	0.370020i	$0.879351\pi$
$258$	−1.51377	+	1.91835i	−0.0942429	+	0.119431i
$259$			3.11630i			0.193637i
$260$	−0.109959	−	0.190454i	−0.00681935	−	0.0118115i
$261$	−22.9347	−	6.81695i	−1.41962	−	0.421958i
$262$	7.22873	−	4.17351i	0.446593	−	0.257840i
$263$	24.7674	+	14.2995i	1.52723	+	0.881744i	0.999477	+	0.0323436i	$0.0102971\pi$
$263$	24.7674	+	14.2995i	1.52723	+	0.881744i	0.527749	+	0.849401i	$0.323036\pi$
$264$	3.74029	−	1.49019i	0.230199	−	0.0917149i
$265$		−	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	$-0.801727\pi$
$269$	1.62587	−	2.81609i	0.0991312	−	0.171700i	0.911325	+	0.411687i	$0.135060\pi$
$270$	5.17502	−	0.468182i	0.314942	−	0.0284926i
$271$	−3.17133	+	5.49291i	−0.192645	+	0.333670i	−0.946126	−	0.323799i	$-0.895040\pi$
$271$	−3.17133	+	5.49291i	−0.192645	+	0.333670i	0.753481	+	0.657469i	$0.228373\pi$
$272$	−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
$276$	−2.16338	+	14.8715i	−0.130220	+	0.895158i
$277$	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
$279$	−8.31177	−	8.77523i	−0.497613	−	0.525359i
$280$	2.10624	+	1.21604i	0.125872	+	0.0726722i
$281$	7.85570	+	13.6065i	0.468632	+	0.811694i	0.999357	−	0.0358495i	$-0.0114137\pi$
$281$	7.85570	+	13.6065i	0.468632	+	0.811694i	−0.530725	+	0.847544i	$0.678080\pi$
$282$	−8.82453	+	3.51584i	−0.525493	+	0.209365i
$283$	−10.1514	+	17.5827i	−0.603435	+	1.04518i	0.388861	+	0.921296i	$0.372869\pi$
$283$	−10.1514	+	17.5827i	−0.603435	+	1.04518i	−0.992297	+	0.123884i	$0.960465\pi$
$284$	10.1123			0.600056
$285$	−2.19612	−	7.22337i	−0.130087	−	0.427875i
$286$	0.511206			0.0302282
$287$	2.89555	−	5.01525i	0.170919	−	0.296041i
$288$	2.87566	+	0.854742i	0.169450	+	0.0503661i
$289$	4.63838	+	8.03390i	0.272846	+	0.472583i
$290$	6.90694	+	3.98772i	0.405590	+	0.234167i
$291$	1.75848	−	12.0881i	0.103084	−	0.708618i
$292$	3.57004			0.208921
$293$	−16.1085			−0.941067			−0.470533	−	0.882382i	$-0.655938\pi$
$293$	−16.1085			−0.941067			−0.470533	+	0.882382i	$0.655938\pi$
$294$	−1.85971	−	0.270535i	−0.108461	−	0.0157779i
$295$	−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
$300$	−1.71401	−	0.249340i	−0.0989584	−	0.0143956i
$301$	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
$306$	4.38148	−	14.7409i	0.250472	−	0.842680i
$307$	6.95957	+	4.01811i	0.397204	+	0.229326i	0.685277	−	0.728283i	$-0.259681\pi$
$307$	6.95957	+	4.01811i	0.397204	+	0.229326i	−0.288073	+	0.957608i	$0.593015\pi$
$308$	−4.89603	+	2.82672i	−0.278977	+	0.161068i
$309$	−28.2820	+	11.2680i	−1.60891	+	0.641015i
$310$	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	−0.975092	−	0.221801i	$-0.928807\pi$
$313$	−12.0239	−	20.8260i	−0.679631	−	1.17716i	0.295461	−	0.955355i	$-0.404527\pi$
$314$	−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	$-0.0521168\pi$
$317$	6.26988	+	10.8598i	0.352152	+	0.609944i	−0.634475	+	0.772944i	$0.718783\pi$
$318$	2.62207	+	6.58124i	0.147039	+	0.369057i
$319$	−16.0554	+	9.26961i	−0.898932	+	0.518998i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	1.79781	+	4.51240i	0.100344	+	0.251858i
$322$		−	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
$327$	3.97528	−	27.3268i	0.219833	−	1.51118i
$328$	−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	$0.0444965\pi$
$331$			5.06995i			0.278670i	−0.990245	+	0.139335i	$0.955504\pi$
$332$	3.77627	−	2.18023i	0.207250	−	0.119656i
$333$	2.64342	+	2.79082i	0.144858	+	0.152936i
$334$	−10.8604			−0.594255
$335$	7.66675			0.418880
$336$	−4.16860	−	0.606413i	−0.227416	−	0.0330826i
$337$	3.52448	+	2.03486i	0.191991	+	0.110846i	0.592914	−	0.805266i	$-0.297977\pi$
$337$	3.52448	+	2.03486i	0.191991	+	0.110846i	−0.400923	+	0.916112i	$0.631311\pi$
$338$	−6.47582	−	11.2164i	−0.352238	−	0.610094i
$339$	7.80496	+	19.5900i	0.423907	+	1.06398i
$340$	−2.56304	+	4.43932i	−0.139001	+	0.240756i
$341$	−9.36538			−0.507164
$342$	8.16435	+	10.2149i	0.441477	+	0.552356i
$343$	19.6634			1.06172
$344$	−0.705429	+	1.22184i	−0.0380342	+	0.0658771i
$345$	5.56220	+	13.9608i	0.299459	+	0.751622i
$346$	6.04765	+	10.4748i	0.325124	+	0.563131i
$347$	4.31415	+	2.49077i	0.231596	+	0.133712i	0.611308	−	0.791393i	$-0.290644\pi$
$347$	4.31415	+	2.49077i	0.231596	+	0.133712i	−0.379712	+	0.925105i	$0.623977\pi$
$348$	−13.6700	−	1.98860i	−0.732789	−	0.106600i
$349$	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
$351$	−1.13808	+	0.102961i	−0.0607460	+	0.00549566i
$352$	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
$357$	−3.10853	+	21.3686i	−0.164521	+	1.13095i
$358$	−4.58689	+	7.94473i	−0.242425	+	0.419892i
$359$	25.0199	+	14.4453i	1.32050	+	0.762392i	0.983809	−	0.179222i	$-0.0573580\pi$
$359$	25.0199	+	14.4453i	1.32050	+	0.762392i	0.336694	+	0.941614i	$0.390691\pi$
$360$	2.91776	−	0.697602i	0.153780	−	0.0367668i
$361$	12.1173	−	14.6346i	0.637754	−	0.770240i
$362$		−	9.66914i		−	0.508199i
$363$	−3.58777	−	9.00508i	−0.188309	−	0.472644i
$364$	−0.463199	−	0.267428i	−0.0242782	−	0.0140170i
$365$	3.09174	−	1.78502i	0.161829	−	0.0934321i
$366$	5.28889	+	13.2748i	0.276454	+	0.693883i
$367$	−10.1670	−	17.6098i	−0.530713	−	0.919222i	−0.999358	−	0.0358355i	$-0.988591\pi$
$367$	−10.1670	−	17.6098i	−0.530713	−	0.919222i	0.468644	−	0.883387i	$-0.344743\pi$
$368$			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	$-0.897493\pi$
$373$		−	12.2252i		−	0.632997i	0.948593	−	0.316499i	$-0.102507\pi$
$374$	−5.95789	−	10.3194i	−0.308075	−	0.533601i
$375$	−1.60905	+	0.641070i	−0.0830908	+	0.0331047i
$376$	−4.74957	+	2.74216i	−0.244940	+	0.141416i
$377$	−1.51896	−	0.876970i	−0.0782302	−	0.0451662i
$378$	10.3305	−	7.27912i	0.531344	−	0.374398i
$379$		−	37.1799i		−	1.90980i	−0.296925	−	0.954901i	$-0.595961\pi$
$379$		−	37.1799i		−	1.90980i	0.296925	−	0.954901i	$-0.404039\pi$
$380$	−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	$-0.869936\pi$
$383$	−2.24543	+	3.88919i	−0.114736	+	0.198728i	0.802938	+	0.596062i	$0.203269\pi$
$384$	1.71401	+	0.249340i	0.0874677	+	0.0127241i
$385$	−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	$-0.431026\pi$
$389$	23.0418	−	13.3032i	1.16827	−	0.674499i	0.953271	+	0.302116i	$0.0976930\pi$
$390$	0.376940	+	0.0548341i	0.0190871	+	0.00277663i
$391$	44.4761			2.24925
$392$	−1.08501			−0.0548011
$393$	−2.08124	+	14.3069i	−0.104985	+	0.721686i
$394$	−4.31146	−	2.48922i	−0.217208	−	0.125405i
$395$	7.53998	+	13.0596i	0.379377	+	0.657101i
$396$	−1.98688	+	6.68457i	−0.0998444	+	0.335912i
$397$	−10.5922	+	18.3462i	−0.531606	+	0.920769i	0.467713	+	0.883880i	$0.345078\pi$
$397$	−10.5922	+	18.3462i	−0.531606	+	0.920769i	−0.999319	+	0.0368887i	$0.988255\pi$
$398$	−18.1690			−0.910731
$399$	−13.4094	−	12.5436i	−0.671312	−	0.627964i
$400$	−1.00000			−0.0500000
$401$	11.5551	−	20.0141i	0.577036	−	0.999456i	−0.418781	−	0.908087i	$-0.637542\pi$
$401$	11.5551	−	20.0141i	0.577036	−	0.999456i	0.995817	−	0.0913687i	$-0.0291242\pi$
$402$	−12.3362	+	4.91493i	−0.615272	+	0.245134i
$403$	−0.443015	−	0.767325i	−0.0220682	−	0.0382232i
$404$	10.2389	+	5.91143i	0.509404	+	0.294105i
$405$	−4.91589	+	7.53883i	−0.244273	+	0.374608i
$406$	19.3969			0.962652
$407$	2.97850			0.147639
$408$	1.27814	−	8.78616i	0.0632772	−	0.434980i
$409$	8.26190	−	4.77001i	0.408525	−	0.235862i	−0.281631	−	0.959523i	$-0.590875\pi$
$409$	8.26190	−	4.77001i	0.408525	−	0.235862i	0.690156	+	0.723661i	$0.257542\pi$
$410$			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
$414$	−17.8997	−	18.8978i	−0.879721	−	0.928774i
$415$	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	$0.992522\pi$
$420$	−3.91332	+	1.55913i	−0.190951	+	0.0760778i
$421$	−14.4170	−	8.32365i	−0.702641	−	0.405670i	0.105689	−	0.994399i	$-0.466295\pi$
$421$	−14.4170	−	8.32365i	−0.702641	−	0.405670i	−0.808330	+	0.588729i	$0.799628\pi$
$422$	2.49731	−	1.44183i	0.121567	−	0.0701870i
$423$	4.68768	−	15.7711i	0.227923	−	0.766815i
$424$	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	$-0.0886683\pi$
$431$	5.03639	+	8.72328i	0.242594	+	0.420185i	−0.718858	+	0.695157i	$0.755335\pi$
$432$	−4.24761	+	2.99297i	−0.204363	+	0.143999i
$433$	5.91643	−	3.41585i	0.284326	−	0.164155i	−0.351054	−	0.936355i	$-0.614177\pi$
$433$	5.91643	−	3.41585i	0.284326	−	0.164155i	0.635380	+	0.772200i	$0.280843\pi$
$434$	8.48588	+	4.89933i	0.407335	+	0.235175i
$435$	−12.8329	+	5.11282i	−0.615289	+	0.245141i
$436$		−	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	0.704704	−	0.709501i	$-0.251080\pi$
$439$	9.27371	+	5.35418i	0.442610	+	0.255541i	−0.262094	+	0.965042i	$0.584413\pi$
$440$	1.16227	−	2.01311i	0.0554090	−	0.0959711i
$441$	2.36321	−	2.23839i	0.112534	−	0.106590i
$442$	0.563658	−	0.976283i	0.0268105	−	0.0464371i
$443$	−6.87406	+	3.96874i	−0.326596	+	0.188560i	−0.654329	−	0.756210i	$-0.727049\pi$
$443$	−6.87406	+	3.96874i	−0.326596	+	0.188560i	0.327733	+	0.944771i	$0.393715\pi$
$444$	1.74224	+	1.37479i	0.0826829	+	0.0652448i
$445$		−	4.06081i		−	0.192501i
$446$	12.7294	−	7.34931i	0.602754	−	0.348000i
$447$	5.26222	−	36.1736i	0.248895	−	1.71095i
$448$	−2.43208			−0.114905
$449$	16.3905			0.773515			0.386757	−	0.922181i	$-0.373595\pi$
$449$	16.3905			0.773515			0.386757	+	0.922181i	$0.373595\pi$
$450$	2.17806	−	2.06302i	0.102675	−	0.0972519i
$451$	−4.79348	−	2.76752i	−0.225716	−	0.130317i
$452$	6.08745	+	10.5438i	0.286329	+	0.495937i
$453$	−38.9628	+	15.5234i	−1.83063	+	0.729354i
$454$	5.53375	−	9.58473i	0.259712	−	0.449834i
$455$	−0.534856			−0.0250744
$456$	5.51358	+	5.15756i	0.258197	+	0.241525i
$457$	−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
$459$	15.3422	+	21.7736i	0.716113	+	1.01630i
$460$	4.33821	+	7.51400i	0.202270	+	0.350342i
$461$	35.9630	+	20.7632i	1.67496	+	0.967040i	0.964793	+	0.263010i	$0.0847152\pi$
$461$	35.9630	+	20.7632i	1.67496	+	0.967040i	0.710170	+	0.704030i	$0.248618\pi$
$462$	1.40963	−	9.69007i	0.0655819	−	0.450823i
$463$	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
$465$	−6.90562	−	1.00457i	−0.320240	−	0.0465859i
$466$	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
$471$	22.1567	+	3.22318i	1.02093	+	0.148516i
$472$	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
$477$	−11.7619	−	3.49602i	−0.538539	−	0.160072i
$478$	−4.48081	−	2.58700i	−0.204947	−	0.118326i
$479$	35.2374	−	20.3443i	1.61004	−	0.929555i	0.620676	−	0.784067i	$-0.286858\pi$
$479$	35.2374	−	20.3443i	1.61004	−	0.929555i	0.989360	−	0.145488i	$-0.0464751\pi$
$480$	1.60905	−	0.641070i	0.0734426	−	0.0292607i
$481$	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	$0.106214\pi$
$487$			14.4557i			0.655048i	−0.944843	+	0.327524i	$0.893786\pi$
$488$	4.12504	+	7.14478i	0.186732	+	0.323429i
$489$	−8.73217	−	21.9172i	−0.394883	−	0.991130i
$490$	−0.939644	+	0.542503i	−0.0424488	+	0.0245078i
$491$	−13.6141	−	7.86008i	−0.614394	−	0.354721i	0.160289	−	0.987070i	$-0.448757\pi$
$491$	−13.6141	−	7.86008i	−0.614394	−	0.354721i	−0.774683	+	0.632350i	$0.782091\pi$
$492$	−1.52648	−	3.83136i	−0.0688189	−	0.172731i
$493$			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
$498$	−1.08724	+	7.47388i	−0.0487203	+	0.334913i
$499$	−16.7701	+	29.0466i	−0.750731	+	1.30030i	0.196738	+	0.980456i	$0.436965\pi$
$499$	−16.7701	+	29.0466i	−0.750731	+	1.30030i	−0.947469	+	0.319848i	$0.896368\pi$
$500$	−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	$-0.726319\pi$
$503$	−7.23726	+	4.17843i	−0.322694	+	0.186307i	0.329899	+	0.944016i	$0.392985\pi$
$504$	5.29720	−	5.01743i	0.235956	−	0.223494i
$505$	11.8229			0.526110
$506$	−20.1687			−0.896606
$507$	22.1992	+	3.22936i	0.985903	+	0.143421i
$508$	−2.43948	−	1.40844i	−0.108235	−	0.0624893i
$509$	−14.3398	−	24.8373i	−0.635602	−	1.10090i	−0.986387	−	0.164440i	$-0.947418\pi$
$509$	−14.3398	−	24.8373i	−0.635602	−	1.10090i	0.350785	−	0.936456i	$-0.385915\pi$
$510$	−3.28618	−	8.24811i	−0.145515	−	0.365232i
$511$	4.34130	−	7.51935i	0.192048	−	0.332636i
$512$	1.00000			0.0441942
$513$	−22.6491	+	0.141188i	−0.999981	+	0.00623360i
$514$	4.61909			0.203739
$515$	−8.78844	+	15.2220i	−0.387265	+	0.670762i
$516$	−0.904459	−	2.27014i	−0.0398166	−	0.0999371i
$517$	−6.37426	−	11.0405i	−0.280340	−	0.485562i
$518$	−2.69879	−	1.55815i	−0.118578	−	0.0684612i
$519$	−20.7315	−	3.01584i	−0.910010	−	0.132381i
$520$	0.219917			0.00964401
$521$	22.1970			0.972468			0.486234	−	0.873829i	$-0.338370\pi$
$521$	22.1970			0.972468			0.486234	+	0.873829i	$0.338370\pi$
$522$	17.3710	−	16.4535i	0.760307	−	0.720152i
$523$	22.4245	−	12.9468i	0.980554	−	0.566123i	0.0781167	−	0.996944i	$-0.475109\pi$
$523$	22.4245	−	12.9468i	0.980554	−	0.566123i	0.902437	+	0.430821i	$0.141776\pi$
$524$			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
$528$	−0.579599	+	3.98428i	−0.0252238	+	0.173393i
$529$	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
$534$	2.60327	+	6.53403i	0.112654	+	0.282755i
$535$	2.42868	+	1.40220i	0.105001	+	0.0606223i
$536$	−6.63960	+	3.83338i	−0.286787	+	0.165577i
$537$	−5.88104	−	14.7610i	−0.253786	−	0.636986i
$538$	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	0.733621	−	0.679559i	$-0.237829\pi$
$541$	−5.15671	−	8.93169i	−0.221704	−	0.384003i	−0.955326	+	0.295555i	$0.904495\pi$
$542$	−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
$546$	0.860607	−	0.342880i	0.0368306	−	0.0146739i
$547$	−6.35260	+	3.66767i	−0.271618	+	0.156818i	−0.629622	−	0.776901i	$-0.716790\pi$
$547$	−6.35260	+	3.66767i	−0.271618	+	0.156818i	0.358005	+	0.933720i	$0.383457\pi$
$548$	−12.6626	−	7.31076i	−0.540920	−	0.312300i
$549$	−23.7244	−	7.05169i	−1.01253	−	0.300959i
$550$		−	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
$555$	2.19622	+	0.319487i	0.0932242	+	0.0135615i
$556$	5.51342	−	9.54952i	0.233821	−	0.404990i
$557$	−12.9817	+	7.49498i	−0.550051	+	0.317572i	−0.749143	−	0.662409i	$-0.769534\pi$
$557$	−12.9817	+	7.49498i	−0.550051	+	0.317572i	0.199091	+	0.979981i	$0.436201\pi$
$558$	11.7555	−	2.81059i	0.497648	−	0.118982i
$559$		−	0.310272i		−	0.0131231i
$560$	−2.10624	+	1.21604i	−0.0890049	+	0.0513870i
$561$	20.4237	+	2.97108i	0.862291	+	0.125439i
$562$	−15.7114			−0.662746
$563$	−19.5385			−0.823450			−0.411725	−	0.911308i	$-0.635074\pi$
$563$	−19.5385			−0.823450			−0.411725	+	0.911308i	$0.635074\pi$
$564$	1.36746	−	9.40019i	0.0575805	−	0.395819i
$565$	10.5438	+	6.08745i	0.443580	+	0.256101i
$566$	−10.1514	−	17.5827i	−0.426693	−	0.739054i
$567$	−1.18654	+	21.8565i	−0.0498298	+	0.917887i
$568$	−5.05616	+	8.75753i	−0.212152	+	0.367458i
$569$	−43.9934			−1.84430			−0.922149	−	0.386835i	$-0.873568\pi$
$569$	−43.9934			−1.84430			−0.922149	+	0.386835i	$0.873568\pi$
$570$	7.35368	+	1.70979i	0.308012	+	0.0716151i
$571$	−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
$573$	−30.1234	+	12.0017i	−1.25842	+	0.501377i
$574$	2.89555	+	5.01525i	0.120858	+	0.209332i
$575$	7.51400	+	4.33821i	0.313356	+	0.180916i
$576$	−2.17806	+	2.06302i	−0.0907524	+	0.0859593i
$577$	−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
$579$	−6.10254	+	41.9500i	−0.253613	+	1.74338i
$580$	−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
$585$	−0.478993	+	0.453695i	−0.0198039	+	0.0187580i
$586$	8.05424	−	13.9503i	0.332717	−	0.576283i
$587$	−23.1836	−	13.3851i	−0.956891	−	0.552461i	−0.0616763	−	0.998096i	$-0.519645\pi$
$587$	−23.1836	−	13.3851i	−0.956891	−	0.552461i	−0.895215	+	0.445635i	$0.852978\pi$
$588$	1.16415	−	1.47529i	0.0480086	−	0.0608400i
$589$	−7.47399	−	15.8919i	−0.307960	−	0.654814i
$590$		−	0.956151i		−	0.0393641i
$591$	8.01055	−	3.19153i	0.329510	−	0.131282i
$592$	1.10967	+	0.640666i	0.0456070	+	0.0263312i
$593$	−8.48127	+	4.89666i	−0.348284	+	0.201082i	−0.663929	−	0.747795i	$-0.731112\pi$
$593$	−8.48127	+	4.89666i	−0.348284	+	0.201082i	0.315645	+	0.948877i	$0.397779\pi$
$594$	−6.95726	−	9.87371i	−0.285460	−	0.405123i
$595$	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	0.998357	+	0.0572961i	$0.0182479\pi$
$599$	13.4316	+	23.2641i	0.548799	+	0.950547i	−0.449559	+	0.893251i	$0.648419\pi$
$600$	1.07294	−	1.35971i	0.0438026	−	0.0555098i
$601$		−	26.9483i		−	1.09925i	−0.835413	−	0.549623i	$-0.814771\pi$
$601$		−	26.9483i		−	1.09925i	0.835413	−	0.549623i	$-0.185229\pi$
$602$	1.71566	+	2.97160i	0.0699250	+	0.121114i
$603$	6.55309	−	22.0470i	0.266863	−	0.897822i
$604$	−20.9707	+	12.1074i	−0.853285	+	0.492644i
$605$	−4.84674	−	2.79827i	−0.197048	−	0.113766i
$606$	−19.0235	+	7.57929i	−0.772778	+	0.307887i
$607$		−	24.9777i		−	1.01381i	−0.862001	−	0.506906i	$-0.830789\pi$
$607$		−	24.9777i		−	1.01381i	0.862001	−	0.506906i	$-0.169211\pi$
$608$	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
$612$	10.5752	+	11.1649i	0.427479	+	0.451315i
$613$	5.51510	−	9.55243i	0.222753	−	0.385819i	−0.732890	−	0.680347i	$-0.761829\pi$
$613$	5.51510	−	9.55243i	0.222753	−	0.385819i	0.955643	+	0.294528i	$0.0951624\pi$
$614$	−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	$-0.541762\pi$
$617$	16.4524	−	9.49880i	0.662349	−	0.382407i	0.793171	+	0.608999i	$0.208429\pi$
$618$	4.38261	−	30.1269i	0.176295	−	1.21188i
$619$	−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
$621$	44.9007	−	4.06214i	1.80180	−	0.163008i
$622$	17.5450	+	10.1296i	0.703489	+	0.406159i
$623$	−4.93810	−	8.55304i	−0.197841	−	0.342670i
$624$	−0.353857	+	0.140982i	−0.0141656	+	0.00564382i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	24.0478			0.961144
$627$	−11.9889	+	12.8165i	−0.478792	+	0.511843i
$628$	12.9269			0.515837
$629$	3.28411	−	5.68825i	0.130946	−	0.226805i
$630$	2.07880	−	6.99382i	0.0828212	−	0.278641i
$631$	9.58134	+	16.5954i	0.381427	+	0.660651i	0.991266	−	0.131874i	$-0.0420994\pi$
$631$	9.58134	+	16.5954i	0.381427	+	0.660651i	−0.609840	+	0.792525i	$0.708766\pi$
$632$	−13.0596	−	7.53998i	−0.519484	−	0.299924i
$633$	−0.719009	+	4.94261i	−0.0285780	+	0.196451i
$634$	−12.5398			−0.498017
$635$	−2.81687			−0.111784
$636$	−7.01055	−	1.01984i	−0.277987	−	0.0404391i
$637$	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	−0.367090	−	0.930186i	$-0.619646\pi$
$641$	15.7483	−	27.2768i	0.622020	−	1.07737i	0.989109	−	0.147184i	$-0.0470209\pi$
$642$	−4.80676	−	0.699247i	−0.189708	−	0.0275971i
$643$	4.48834	−	7.77403i	0.177003	−	0.306578i	−0.763850	−	0.645394i	$-0.776693\pi$
$643$	4.48834	−	7.77403i	0.177003	−	0.306578i	0.940853	+	0.338816i	$0.110027\pi$
$644$	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	$0.973539\pi$
$648$	0.487870	−	8.98677i	0.0191653	−	0.353034i
$649$	1.92484	+	1.11130i	0.0755564	+	0.0436225i
$650$	0.190454	−	0.109959i	0.00747022	−	0.00431293i
$651$	−15.7665	+	6.28163i	−0.617937	+	0.246196i
$652$	−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	0.922935	+	0.384955i	$0.125783\pi$
$659$	20.4046	+	35.3417i	0.794849	+	1.37672i	−0.128086	+	0.991763i	$0.540883\pi$
$660$	1.49019	+	3.74029i	0.0580056	+	0.145590i
$661$	−6.66358	+	3.84722i	−0.259183	+	0.149640i	−0.623962	−	0.781455i	$-0.714478\pi$
$661$	−6.66358	+	3.84722i	−0.259183	+	0.149640i	0.364779	+	0.931094i	$0.381145\pi$
$662$	−4.39071	−	2.53498i	−0.170650	−	0.0985247i
$663$	0.722688	+	1.81390i	0.0280669	+	0.0704461i
$664$			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
$669$	−3.66495	+	25.1936i	−0.141695	+	0.974040i
$670$	−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	$-0.933993\pi$
$673$		−	10.6822i		−	0.411770i	0.978576	−	0.205885i	$-0.0660073\pi$
$674$	−3.52448	+	2.03486i	−0.135758	+	0.0783798i
$675$	0.468182	+	5.17502i	0.0180203	+	0.199187i
$676$	12.9516			0.498140
$677$	12.9215			0.496612			0.248306	−	0.968682i	$-0.420126\pi$
$677$	12.9215			0.496612			0.248306	+	0.968682i	$0.420126\pi$
$678$	−20.8679	−	3.03568i	−0.801426	−	0.116585i
$679$	−14.8543	−	8.57615i	−0.570057	−	0.329123i
$680$	−2.56304	−	4.43932i	−0.0982882	−	0.170240i
$681$	7.09504	+	17.8081i	0.271883	+	0.682408i
$682$	4.68269	−	8.11066i	0.179310	−	0.310573i
$683$	−39.7388			−1.52056			−0.760282	−	0.649593i	$-0.774939\pi$
$683$	−39.7388			−1.52056			−0.760282	+	0.649593i	$0.774939\pi$
$684$	−12.9285	+	1.96310i	−0.494334	+	0.0750611i
$685$	−14.6215			−0.558660
$686$	−9.83168	+	17.0290i	−0.375375	+	0.650169i
$687$	−2.04847	−	5.14152i	−0.0781539	−	0.196161i
$688$	−0.705429	−	1.22184i	−0.0268942	−	0.0465822i
$689$	−0.778985	−	0.449747i	−0.0296770	−	0.0171340i
$690$	−14.8715	−	2.16338i	−0.566147	−	0.0823584i
$691$	−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
$693$	11.6632	+	12.3135i	0.443048	+	0.467753i
$694$	−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
$699$	−2.00393	+	13.7754i	−0.0757956	+	0.521034i
$700$	−1.21604	+	2.10624i	−0.0459619	+	0.0796084i
$701$	21.4383	+	12.3774i	0.809713	+	0.467488i	0.846856	−	0.531822i	$-0.178492\pi$
$701$	21.4383	+	12.3774i	0.809713	+	0.467488i	−0.0371431	+	0.999310i	$0.511826\pi$
$702$	0.479871	−	1.03708i	0.0181116	−	0.0391422i
$703$	2.37698	+	5.05415i	0.0896494	+	0.190621i
$704$			2.32454i			0.0876092i
$705$	−3.51584	−	8.82453i	−0.132414	−	0.332351i
$706$	−23.0693	−	13.3191i	−0.868226	−	0.501270i
$707$	24.9018	−	14.3770i	0.936528	−	0.540705i
$708$	0.612960	+	1.53849i	0.0230365	+	0.0578201i
$709$	6.84044	+	11.8480i	0.256898	+	0.444960i	0.965409	−	0.260739i	$-0.0839662\pi$
$709$	6.84044	+	11.8480i	0.256898	+	0.444960i	−0.708511	+	0.705699i	$0.750633\pi$
$710$			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
$717$	8.32519	−	3.31689i	0.310910	−	0.123872i
$718$	−25.0199	+	14.4453i	−0.933736	+	0.539093i
$719$	16.2403	+	9.37635i	0.605661	+	0.349679i	0.771265	−	0.636514i	$-0.219624\pi$
$719$	16.2403	+	9.37635i	0.605661	+	0.349679i	−0.165604	+	0.986192i	$0.552957\pi$
$720$	−0.854742	+	2.87566i	−0.0318543	+	0.107169i
$721$			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
$726$	9.59251	+	1.39544i	0.356011	+	0.0517896i
$727$	24.9453	−	43.2065i	0.925170	−	1.60244i	0.133883	−	0.990997i	$-0.457255\pi$
$727$	24.9453	−	43.2065i	0.925170	−	1.60244i	0.791287	−	0.611445i	$-0.209411\pi$
$728$	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
$732$	−14.1407	−	2.05707i	−0.522656	−	0.0760317i
$733$	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
$735$	0.270535	−	1.85971i	0.00997885	−	0.0685965i
$736$	−7.51400	−	4.33821i	−0.276970	−	0.159909i
$737$	−8.91082	−	15.4340i	−0.328234	−	0.568519i
$738$	6.84734	+	2.03526i	0.252054	+	0.0749188i
$739$	−11.8821	+	20.5805i	−0.437092	+	0.757065i	−0.997464	−	0.0711761i	$-0.977325\pi$
$739$	−11.8821	+	20.5805i	−0.437092	+	0.757065i	0.560372	+	0.828241i	$0.310658\pi$
$740$	1.28133			0.0471027
$741$	−1.61720	−	0.376012i	−0.0594094	−	0.0138131i
$742$	9.94755			0.365186
$743$	−3.44798	+	5.97208i	−0.126494	+	0.219094i	−0.922316	−	0.386437i	$-0.873706\pi$
$743$	−3.44798	+	5.97208i	−0.126494	+	0.219094i	0.795822	+	0.605531i	$0.207039\pi$
$744$	6.48273	−	2.58282i	0.237668	−	0.0946910i
$745$	−10.5523	−	18.2772i	−0.386607	−	0.669623i
$746$	10.5873	+	6.11260i	0.387630	+	0.223798i
$747$	−8.99574	−	9.49735i	−0.329137	−	0.347490i
$748$	11.9158			0.435684
$749$	6.82050			0.249216
$750$	0.249340	−	1.71401i	0.00910460	−	0.0625868i
$751$	−36.8595	+	21.2808i	−1.34502	+	0.776548i	−0.987539	−	0.157372i	$-0.949698\pi$
$751$	−36.8595	+	21.2808i	−1.34502	+	0.776548i	−0.357482	+	0.933920i	$0.616365\pi$
$752$		−	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
$756$	1.13865	+	12.5860i	0.0414124	+	0.457750i
$757$	−15.7761	+	27.3249i	−0.573391	+	0.993142i	0.422824	+	0.906212i	$0.361039\pi$
$757$	−15.7761	+	27.3249i	−0.573391	+	0.993142i	−0.996214	+	0.0869297i	$0.972294\pi$
$758$	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	$0.865416\pi$
$762$	4.53248	−	1.80581i	0.164194	−	0.0654177i
$763$	−33.5803	−	19.3876i	−1.21569	−	0.701877i
$764$	−16.2131	+	9.36065i	−0.586570	+	0.338656i
$765$	14.7409	+	4.38148i	0.532958	+	0.158413i
$766$	−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	0.876305	−	0.481757i	$-0.160001\pi$
$769$	0.580659	+	1.00573i	0.0209391	+	0.0362676i	−0.855366	+	0.518024i	$0.826668\pi$
$770$	−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	$-0.249299\pi$
$773$	−7.13678	−	12.3613i	−0.256692	−	0.444604i	−0.965354	+	0.260945i	$0.915966\pi$
$774$	4.05715	+	1.20592i	0.145831	+	0.0433459i
$775$	−3.48915	+	2.01446i	−0.125334	+	0.0723616i
$776$	6.10768	+	3.52627i	0.219253	+	0.126586i
$777$	5.01427	−	1.99777i	0.179886	−	0.0716695i
$778$			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
$783$	3.73396	+	41.2731i	0.133441	+	1.47498i
$784$	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	$0.219487\pi$
$787$			35.6942i			1.27236i	−0.771540	+	0.636181i	$0.780513\pi$
$788$	4.31146	−	2.48922i	0.153589	−	0.0886749i
$789$	7.13086	−	49.0189i	0.253865	−	1.74512i
$790$	−15.0800			−0.536521
$791$	29.6103			1.05282
$792$	−4.79557	−	5.06297i	−0.170403	−	0.179905i
$793$	−1.57126	−	0.907168i	−0.0557971	−	0.0322145i
$794$	−10.5922	−	18.3462i	−0.375902	−	0.651082i
$795$	−6.58124	+	2.62207i	−0.233412	+	0.0929953i
$796$	9.08451	−	15.7348i	0.321992	−	0.557707i
$797$	33.7963			1.19713			0.598563	−	0.801076i	$-0.295739\pi$
$797$	33.7963			1.19713			0.598563	+	0.801076i	$0.295739\pi$
$798$	17.5678	−	5.34114i	0.621893	−	0.189074i
$799$	−28.1131			−0.994571
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−11.6775	−	3.47094i	−0.412605	−	0.122640i
$802$	11.5551	+	20.0141i	0.408026	+	0.706722i
$803$	−7.18686	−	4.14934i	−0.253619	−	0.146427i
$804$	1.91163	−	13.1409i	0.0674179	−	0.463444i
$805$	21.1017			0.743738
$806$	0.886031			0.0312091
$807$	−5.57352	−	0.810789i	−0.196197	−	0.0285411i
$808$	−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	−0.271636	−	0.962400i	$-0.587565\pi$
$811$	12.1319	−	7.00436i	0.426009	−	0.245956i	0.697645	+	0.716444i	$0.254231\pi$
$812$	−9.69845	+	16.7982i	−0.340349	+	0.589501i
$813$	10.8714	+	1.58148i	0.381276	+	0.0554648i
$814$	−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
$819$	−0.457163	+	1.53806i	−0.0159746	+	0.0537443i
$820$	−2.06213	−	1.19057i	−0.0720125	−	0.0415765i
$821$	18.2129	−	10.5152i	0.635634	−	0.366984i	−0.147297	−	0.989092i	$-0.547057\pi$
$821$	18.2129	−	10.5152i	0.635634	−	0.366984i	0.782931	+	0.622109i	$0.213724\pi$
$822$	23.5267	−	9.37342i	0.820588	−	0.326936i
$823$	−13.6408	−	23.6265i	−0.475488	−	0.823569i	0.524118	−	0.851646i	$-0.324395\pi$
$823$	−13.6408	−	23.6265i	−0.475488	−	0.823569i	−0.999606	+	0.0280769i	$0.991062\pi$
$824$		−	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	−0.931880	−	0.362767i	$-0.881832\pi$
$827$	−22.4340	−	38.8568i	−0.780105	−	1.35118i	0.151775	−	0.988415i	$-0.451501\pi$
$828$	25.3158	−	6.05269i	0.879784	−	0.210345i
$829$		−	9.02419i		−	0.313423i	−0.987644	−	0.156711i	$-0.949911\pi$
$829$		−	9.02419i		−	0.313423i	0.987644	−	0.156711i	$-0.0500893\pi$
$830$	2.18023	+	3.77627i	0.0756770	+	0.131076i
$831$	−14.2106	−	35.6677i	−0.492961	−	1.23730i
$832$	−0.190454	+	0.109959i	−0.00660280	+	0.00381213i
$833$	−4.81669	−	2.78092i	−0.166889	−	0.0963531i
$834$	7.06898	+	17.7427i	0.244779	+	0.614379i
$835$		−	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	$-0.937556\pi$
$839$	−9.31551	+	16.1349i	−0.321607	+	0.557040i	0.659213	+	0.751957i	$0.270890\pi$
$840$	0.606413	−	4.16860i	0.0209232	−	0.143830i
$841$	−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
$846$	11.3143	+	11.9452i	0.388993	+	0.410684i
$847$	−13.6112			−0.467686
$848$	−4.09015			−0.140456
$849$	34.7990	+	5.06227i	1.19430	+	0.173737i
$850$	−4.43932	−	2.56304i	−0.152267	−	0.0879116i
$851$	−5.55869	−	9.62794i	−0.190550	−	0.330042i
$852$	−6.48271	−	16.2712i	−0.222094	−	0.557442i
$853$	−7.15637	+	12.3952i	−0.245029	+	0.424403i	−0.962140	−	0.272556i	$-0.912131\pi$
$853$	−7.15637	+	12.3952i	−0.245029	+	0.424403i	0.717111	+	0.696959i	$0.245464\pi$
$854$	20.0648			0.686604
$855$	−10.2149	+	8.16435i	−0.349341	+	0.279215i
$856$	−2.80439			−0.0958522
$857$	23.2696	−	40.3041i	0.794873	−	1.37676i	−0.128046	−	0.991768i	$-0.540871\pi$
$857$	23.2696	−	40.3041i	0.794873	−	1.37676i	0.922920	−	0.384993i	$-0.125796\pi$
$858$	−0.327719	−	0.822554i	−0.0111881	−	0.0280815i
$859$	−11.8783	−	20.5737i	−0.405281	−	0.701967i	0.589073	−	0.808080i	$-0.299493\pi$
$859$	−11.8783	−	20.5737i	−0.405281	−	0.701967i	−0.994354	+	0.106113i	$0.966160\pi$
$860$	−1.22184	−	0.705429i	−0.0416644	−	0.0240549i
$861$	−9.92601	−	1.44395i	−0.338278	−	0.0492098i
$862$	−10.0728			−0.343080
$863$	−8.13980			−0.277082			−0.138541	−	0.990357i	$-0.544241\pi$
$863$	−8.13980			−0.277082			−0.138541	+	0.990357i	$0.544241\pi$
$864$	−0.468182	−	5.17502i	−0.0159279	−	0.176058i
$865$	−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
$870$	1.98860	−	13.6700i	0.0674197	−	0.463456i
$871$	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
$876$	−2.28864	−	5.74435i	−0.0773261	−	0.194084i
$877$	−31.6447	−	18.2701i	−1.06857	−	0.616937i	−0.140777	−	0.990041i	$-0.544960\pi$
$877$	−31.6447	−	18.2701i	−1.06857	−	0.616937i	−0.927789	+	0.373104i	$0.878293\pi$
$878$	−9.27371	+	5.35418i	−0.312973	+	0.180695i
$879$	10.3267	+	25.9193i	0.348310	+	0.874235i
$880$	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	0.993557	+	0.113334i	$0.0361529\pi$
$883$	17.6785	+	30.6200i	0.594928	+	1.03045i	−0.398629	+	0.917112i	$0.630514\pi$
$884$	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	0.769123	+	0.639101i	$0.220693\pi$
$887$	27.9372	+	48.3886i	0.938039	+	1.62473i	0.168916	+	0.985630i	$0.445973\pi$
$888$	−2.06172	+	0.821425i	−0.0691869	+	0.0275652i
$889$	−5.93301	+	3.42543i	−0.198987	+	0.114885i
$890$	3.51677	+	2.03041i	0.117882	+	0.0680593i
$891$	20.8901	+	1.13407i	0.699843	+	0.0379928i
$892$			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
$897$	3.27050	+	0.475764i	0.109199	+	0.0158853i
$898$	−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
$903$	−5.88131	−	0.855563i	−0.195718	−	0.0284713i
$904$	−12.1749			−0.404931
$905$	9.66914			0.321413
$906$	6.03773	−	41.5045i	0.200590	−	1.37889i
$907$	37.7050	+	21.7690i	1.25197	+	0.722828i	0.971501	−	0.237034i	$-0.0761754\pi$
$907$	37.7050	+	21.7690i	1.25197	+	0.722828i	0.280473	+	0.959862i	$0.409509\pi$
$908$	5.53375	+	9.58473i	0.183644	+	0.318081i
$909$	10.1055	−	33.9985i	0.335178	−	1.12766i
$910$	0.267428	−	0.463199i	0.00886515	−	0.0153549i
$911$	34.1334			1.13089			0.565444	−	0.824786i	$-0.308705\pi$
$911$	34.1334			1.13089			0.565444	+	0.824786i	$0.308705\pi$
$912$	−7.22337	+	2.19612i	−0.239190	+	0.0727209i
$913$	−10.1361			−0.335455
$914$	9.91012	−	17.1648i	0.327798	−	0.567762i
$915$	−13.2748	+	5.28889i	−0.438850	+	0.174845i
$916$	−1.59769	−	2.76728i	−0.0527892	−	0.0914336i
$917$	17.5808	+	10.1503i	0.580570	+	0.335192i
$918$	−26.5276	+	2.39994i	−0.875541	+	0.0792098i
$919$	−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
$921$	2.00375	−	13.7742i	0.0660258	−	0.453874i
$922$	−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
$927$	36.2615	+	38.2834i	1.19098	+	1.25739i
$928$	3.98772	−	6.90694i	0.130903	−	0.226731i
$929$	−14.4587	−	8.34775i	−0.474376	−	0.273881i	0.243694	−	0.969852i	$-0.421641\pi$
$929$	−14.4587	−	8.34775i	−0.474376	−	0.273881i	−0.718070	+	0.695971i	$0.754974\pi$
$930$	4.32279	−	5.47816i	0.141750	−	0.179636i
$931$	4.27975	−	2.01278i	0.140263	−	0.0659661i
$932$			8.03695i			0.263259i
$933$	−32.5979	+	12.9876i	−1.06721	+	0.425193i
$934$	8.78980	+	5.07479i	0.287611	+	0.166052i
$935$	10.3194	−	5.95789i	0.337479	−	0.194844i
$936$	0.187972	−	0.632407i	0.00614407	−	0.0206709i
$937$	18.3641	+	31.8076i	0.599930	+	1.03911i	0.992831	+	0.119529i	$0.0381383\pi$
$937$	18.3641	+	31.8076i	0.599930	+	1.03911i	−0.392901	+	0.919581i	$0.628528\pi$
$938$			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	−0.984302	−	0.176491i	$-0.943525\pi$
$941$	−19.7858	−	34.2699i	−0.644997	−	1.11717i	0.339305	−	0.940676i	$-0.389808\pi$
$942$	−13.8697	+	17.5767i	−0.451900	+	0.572680i
$943$			20.6598i			0.672774i
$944$	0.478076	+	0.828051i	0.0155600	+	0.0269508i
$945$	7.27912	+	10.3305i	0.236790	+	0.336051i
$946$	2.84021	−	1.63980i	0.0923431	−	0.0533143i
$947$	−38.8622	−	22.4371i	−1.26285	−	0.729108i	−0.289227	−	0.957261i	$-0.593398\pi$
$947$	−38.8622	−	22.4371i	−1.26285	−	0.729108i	−0.973625	+	0.228153i	$0.926731\pi$
$948$	24.2643	−	9.66731i	0.788069	−	0.313980i
$949$		−	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	$-0.775205\pi$
$953$	5.60620	−	9.71022i	0.181603	−	0.314545i	0.942426	+	0.334414i	$0.108538\pi$
$954$	8.90858	−	8.43807i	0.288426	−	0.273193i
$955$	−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
$960$	−0.249340	+	1.71401i	−0.00804741	+	0.0553194i
$961$	14.7678			0.476379
$962$	−0.281787			−0.00908519
$963$	6.10813	−	5.78553i	0.196832	−	0.186436i
$964$	25.4528	+	14.6952i	0.819780	+	0.473300i
$965$	12.2374	+	21.1958i	0.393936	+	0.682317i
$966$	−33.9536	+	13.5277i	−1.09244	+	0.435246i
$967$	−10.2650	+	17.7795i	−0.330101	+	0.571751i	−0.982531	−	0.186097i	$-0.940416\pi$
$967$	−10.2650	+	17.7795i	−0.330101	+	0.571751i	0.652431	+	0.757848i	$0.273749\pi$
$968$	5.59653			0.179879
$969$	11.2575	+	37.0276i	0.361643	+	1.18950i
$970$	7.05254			0.226443
$971$	−18.9504	+	32.8230i	−0.608147	+	1.05334i	0.383399	+	0.923583i	$0.374754\pi$
$971$	−18.9504	+	32.8230i	−0.608147	+	1.05334i	−0.991546	+	0.129759i	$0.958580\pi$
$972$	11.6959	+	10.3056i	0.375146	+	0.330553i
$973$	−13.4090	−	23.2252i	−0.429874	−	0.744564i
$974$	−12.5190	−	7.22783i	−0.401134	−	0.231595i
$975$	−0.0548341	+	0.376940i	−0.00175610	+	0.0120718i
$976$	−8.25009			−0.264079
$977$	−46.2229			−1.47880			−0.739400	−	0.673266i	$-0.764891\pi$
$977$	−46.2229			−1.47880			−0.739400	+	0.673266i	$0.764891\pi$
$978$	23.3469	+	3.39632i	0.746553	+	0.108602i
$979$	−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	$-0.853027\pi$
$983$	−1.93851	+	3.35759i	−0.0618287	+	0.107091i	0.833454	+	0.552589i	$0.186360\pi$
$984$	4.08129	+	0.593712i	0.130107	+	0.0189269i
$985$	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
$990$	−6.68457	−	1.98688i	−0.212450	−	0.0631471i
$991$	−4.36664	−	2.52108i	−0.138711	−	0.0800848i	0.429039	−	0.903286i	$-0.358852\pi$
$991$	−4.36664	−	2.52108i	−0.138711	−	0.0800848i	−0.567750	+	0.823201i	$0.692186\pi$
$992$	3.48915	−	2.01446i	0.110781	−	0.0639593i
$993$	8.15779	−	3.25020i	0.258880	−	0.103142i
$994$	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	−0.984266	−	0.176696i	$-0.943459\pi$
$997$	−20.3710	−	35.2836i	−0.645156	−	1.11744i	0.339110	−	0.940747i	$-0.389874\pi$
$998$	−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.a.521.5	yes	24
3.2	odd	2		570.2.s.b.521.1	yes	24
19.12	odd	6		570.2.s.b.221.1	yes	24
57.50	even	6	inner	570.2.s.a.221.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.5	✓	24	57.50	even	6	inner
570.2.s.a.521.5	yes	24	1.1	even	1	trivial
570.2.s.b.221.1	yes	24	19.12	odd	6
570.2.s.b.521.1	yes	24	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.641070 - 1.60905i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.71401 + 0.249340i) q^{6} -2.43208 q^{7} +1.00000 q^{8} +(-2.17806 + 2.06302i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.641070 - 1.60905i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.71401 + 0.249340i) q^{6} -2.43208 q^{7} +1.00000 q^{8} +(-2.17806 + 2.06302i) 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} +(-0.249340 + 1.71401i) 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} +(1.55913 + 3.91332i) q^{21} +(-2.01311 - 1.16227i) q^{22} +(7.51400 - 4.33821i) q^{23} +(-0.641070 - 1.60905i) 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} +(3.74029 - 1.49019i) q^{33} +(-4.43932 + 2.56304i) q^{34} +(2.10624 + 1.21604i) q^{35} +(2.87566 + 0.854742i) 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} +(-4.16860 - 0.606413i) 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} +(1.71401 + 0.249340i) q^{48} -1.08501 q^{49} -1.00000 q^{50} +(1.27814 - 8.78616i) q^{51} +(0.190454 + 0.109959i) q^{52} +(2.04507 + 3.54217i) q^{53} +(-4.24761 + 2.99297i) q^{54} +(1.16227 - 2.01311i) q^{55} -2.43208 q^{56} +(5.51358 + 5.15756i) q^{57} -7.97545 q^{58} +(0.478076 - 0.828051i) q^{59} +(1.60905 - 0.641070i) q^{60} +(4.12504 + 7.14478i) q^{61} +(-3.48915 - 2.01446i) q^{62} +(5.29720 - 5.01743i) q^{63} +1.00000 q^{64} +0.219917 q^{65} +(-0.579599 + 3.98428i) 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} +(-2.17806 + 2.06302i) 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} +(-0.353857 + 0.140982i) q^{78} +(-13.0596 - 7.53998i) q^{79} +(0.866025 - 0.500000i) q^{80} +(0.487870 - 8.98677i) 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} +(-0.854742 + 2.87566i) q^{90} +(0.463199 - 0.267428i) q^{91} +(-7.51400 - 4.33821i) q^{92} +(6.48273 - 2.58282i) 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} +(-4.79557 - 5.06297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

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