LMFDB - Embedded newform 570.2.u.a.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.271
Dual form			570.2.u.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.64543 + 2.84997i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.64543 + 2.84997i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-0.939693 - 0.342020i) q^{10} +(-0.939693 + 1.62760i) q^{11} +(0.500000 + 0.866025i) q^{12} +(1.23783 + 7.02006i) q^{13} +(2.52094 + 2.11532i) q^{14} +(0.766044 - 0.642788i) q^{15} +(0.173648 - 0.984808i) q^{16} +(4.41147 - 1.60565i) q^{17} -1.00000 q^{18} +(-3.93969 - 1.86516i) q^{19} -1.00000 q^{20} +(-3.09240 + 1.12554i) q^{21} +(-0.326352 + 1.85083i) q^{22} +(5.20961 - 4.37138i) q^{23} +(0.766044 + 0.642788i) q^{24} +(0.173648 + 0.984808i) q^{25} +(3.56418 + 6.17334i) q^{26} +(0.500000 - 0.866025i) q^{27} +(3.09240 + 1.12554i) q^{28} +(2.53209 + 0.921605i) q^{29} +(0.500000 - 0.866025i) q^{30} +(2.22668 + 3.85673i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.43969 - 1.20805i) q^{33} +(3.59627 - 3.01763i) q^{34} +(0.571452 - 3.24086i) q^{35} +(-0.939693 + 0.342020i) q^{36} +1.73648 q^{37} +(-4.34002 - 0.405223i) q^{38} -7.12836 q^{39} +(-0.939693 + 0.342020i) q^{40} +(-1.12701 + 6.39160i) q^{41} +(-2.52094 + 2.11532i) q^{42} +(-6.57398 - 5.51622i) q^{43} +(0.326352 + 1.85083i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.40033 - 5.88954i) q^{46} +(-3.16637 - 1.15247i) q^{47} +(0.939693 + 0.342020i) q^{48} +(-1.91488 + 3.31667i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.815207 + 4.62327i) q^{51} +(5.46064 + 4.58202i) q^{52} +(-3.33615 + 2.79936i) q^{53} +(0.173648 - 0.984808i) q^{54} +(1.76604 - 0.642788i) q^{55} +3.29086 q^{56} +(2.52094 - 3.55596i) q^{57} +2.69459 q^{58} +(6.92514 - 2.52055i) q^{59} +(0.173648 - 0.984808i) q^{60} +(-1.63041 + 1.36808i) q^{61} +(3.41147 + 2.86257i) q^{62} +(-0.571452 - 3.24086i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.56418 - 6.17334i) q^{65} +(-1.76604 - 0.642788i) q^{66} +(-8.94356 - 3.25519i) q^{67} +(2.34730 - 4.06564i) q^{68} +(3.40033 + 5.88954i) q^{69} +(-0.571452 - 3.24086i) q^{70} +(-3.78106 - 3.17269i) q^{71} +(-0.766044 + 0.642788i) q^{72} +(0.837496 - 4.74968i) q^{73} +(1.63176 - 0.593912i) q^{74} -1.00000 q^{75} +(-4.21688 + 1.10359i) q^{76} -6.18479 q^{77} +(-6.69846 + 2.43804i) q^{78} +(2.24123 - 12.7106i) q^{79} +(-0.766044 + 0.642788i) q^{80} +(0.766044 + 0.642788i) q^{81} +(1.12701 + 6.39160i) q^{82} +(-4.10607 - 7.11192i) q^{83} +(-1.64543 + 2.84997i) q^{84} +(-4.41147 - 1.60565i) q^{85} +(-8.06418 - 2.93512i) q^{86} +(-1.34730 + 2.33359i) q^{87} +(0.939693 + 1.62760i) q^{88} +(-2.44949 - 13.8918i) q^{89} +(0.766044 + 0.642788i) q^{90} +(-17.9702 + 15.0788i) q^{91} +(1.18092 - 6.69734i) q^{92} +(-4.18479 + 1.52314i) q^{93} -3.36959 q^{94} +(1.81908 + 3.96118i) q^{95} +1.00000 q^{96} +(1.22668 - 0.446476i) q^{97} +(-0.665030 + 3.77157i) q^{98} +(1.43969 - 1.20805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 6 * q^7 + 3 * q^8	$ 6 q - 6 q^{7} + 3 q^{8} + 3 q^{12} - 12 q^{13} + 12 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 15 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 3 q^{27} + 15 q^{28} + 6 q^{29} + 3 q^{30} - 3 q^{33} - 6 q^{34} + 3 q^{35} - 6 q^{38} - 6 q^{39} + 21 q^{41} - 12 q^{42} - 24 q^{43} + 3 q^{44} + 3 q^{45} + 6 q^{46} - 33 q^{49} + 3 q^{50} + 12 q^{51} + 24 q^{52} - 24 q^{53} + 6 q^{55} - 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{61} - 3 q^{63} - 3 q^{64} + 3 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 12 q^{71} + 15 q^{74} - 6 q^{75} - 9 q^{76} - 30 q^{77} - 12 q^{78} + 36 q^{79} - 21 q^{82} + 6 q^{84} - 6 q^{85} - 30 q^{86} - 6 q^{87} - 12 q^{89} + 24 q^{91} + 24 q^{92} - 18 q^{93} - 6 q^{94} - 6 q^{95} + 6 q^{96} - 6 q^{97} + 6 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^7 + 3 * q^8 + 3 * q^12 - 12 * q^13 + 12 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 15 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 3 * q^27 + 15 * q^28 + 6 * q^29 + 3 * q^30 - 3 * q^33 - 6 * q^34 + 3 * q^35 - 6 * q^38 - 6 * q^39 + 21 * q^41 - 12 * q^42 - 24 * q^43 + 3 * q^44 + 3 * q^45 + 6 * q^46 - 33 * q^49 + 3 * q^50 + 12 * q^51 + 24 * q^52 - 24 * q^53 + 6 * q^55 - 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^61 - 3 * q^63 - 3 * q^64 + 3 * q^65 - 6 * q^66 - 24 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 12 * q^71 + 15 * q^74 - 6 * q^75 - 9 * q^76 - 30 * q^77 - 12 * q^78 + 36 * q^79 - 21 * q^82 + 6 * q^84 - 6 * q^85 - 30 * q^86 - 6 * q^87 - 12 * q^89 + 24 * q^91 + 24 * q^92 - 18 * q^93 - 6 * q^94 - 6 * q^95 + 6 * q^96 - 6 * q^97 + 6 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$6$	0.173648	+	0.984808i	0.0708916	+	0.402046i
$7$	1.64543	+	2.84997i	0.621914	+	1.07719i	0.989129	+	0.147051i	$0.0469780\pi$
$7$	1.64543	+	2.84997i	0.621914	+	1.07719i	−0.367215	+	0.930136i	$0.619689\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−0.939693	−	0.342020i	−0.297157	−	0.108156i
$11$	−0.939693	+	1.62760i	−0.283328	+	0.490738i	−0.972202	−	0.234142i	$-0.924772\pi$
$11$	−0.939693	+	1.62760i	−0.283328	+	0.490738i	0.688874	+	0.724881i	$0.258105\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.23783	+	7.02006i	0.343311	+	1.94701i	0.320418	+	0.947276i	$0.396177\pi$
$13$	1.23783	+	7.02006i	0.343311	+	1.94701i	0.0228935	+	0.999738i	$0.492712\pi$
$14$	2.52094	+	2.11532i	0.673751	+	0.565344i
$15$	0.766044	−	0.642788i	0.197792	−	0.165967i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	4.41147	−	1.60565i	1.06994	−	0.389426i	0.253786	−	0.967261i	$-0.418324\pi$
$17$	4.41147	−	1.60565i	1.06994	−	0.389426i	0.816154	+	0.577834i	$0.196102\pi$
$18$	−1.00000			−0.235702
$19$	−3.93969	−	1.86516i	−0.903827	−	0.427897i
$19$	−3.93969	−	1.86516i	−0.903827	−	0.427897i
$20$	−1.00000			−0.223607
$21$	−3.09240	+	1.12554i	−0.674816	+	0.245613i
$22$	−0.326352	+	1.85083i	−0.0695784	+	0.394599i
$23$	5.20961	−	4.37138i	1.08628	−	0.911496i	0.0898513	−	0.995955i	$-0.471361\pi$
$23$	5.20961	−	4.37138i	1.08628	−	0.911496i	0.996427	+	0.0844595i	$0.0269164\pi$
$24$	0.766044	+	0.642788i	0.156368	+	0.131208i
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	3.56418	+	6.17334i	0.698993	+	1.21069i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	3.09240	+	1.12554i	0.584408	+	0.212707i
$29$	2.53209	+	0.921605i	0.470197	+	0.171138i	0.566242	−	0.824239i	$-0.308397\pi$
$29$	2.53209	+	0.921605i	0.470197	+	0.171138i	−0.0960445	+	0.995377i	$0.530619\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	2.22668	+	3.85673i	0.399924	+	0.692688i	0.993716	−	0.111930i	$-0.0357032\pi$
$31$	2.22668	+	3.85673i	0.399924	+	0.692688i	−0.593792	+	0.804618i	$0.702370\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−1.43969	−	1.20805i	−0.250618	−	0.210294i
$34$	3.59627	−	3.01763i	0.616755	−	0.517519i
$35$	0.571452	−	3.24086i	0.0965930	−	0.547806i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	1.73648			0.285476			0.142738	−	0.989761i	$-0.454409\pi$
$37$	1.73648			0.285476			0.142738	+	0.989761i	$0.454409\pi$
$38$	−4.34002	−	0.405223i	−0.704045	−	0.0657358i
$39$	−7.12836			−1.14145
$40$	−0.939693	+	0.342020i	−0.148578	+	0.0540781i
$41$	−1.12701	+	6.39160i	−0.176010	+	0.998200i	0.760962	+	0.648796i	$0.224727\pi$
$41$	−1.12701	+	6.39160i	−0.176010	+	0.998200i	−0.936972	+	0.349404i	$0.886384\pi$
$42$	−2.52094	+	2.11532i	−0.388990	+	0.326402i
$43$	−6.57398	−	5.51622i	−1.00252	−	0.841216i	−0.0151903	−	0.999885i	$-0.504835\pi$
$43$	−6.57398	−	5.51622i	−1.00252	−	0.841216i	−0.987332	+	0.158669i	$0.949280\pi$
$44$	0.326352	+	1.85083i	0.0491994	+	0.279024i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	3.40033	−	5.88954i	0.501351	−	0.868366i
$47$	−3.16637	−	1.15247i	−0.461863	−	0.168104i	0.100600	−	0.994927i	$-0.467924\pi$
$47$	−3.16637	−	1.15247i	−0.461863	−	0.168104i	−0.562463	+	0.826823i	$0.690146\pi$
$48$	0.939693	+	0.342020i	0.135633	+	0.0493664i
$49$	−1.91488	+	3.31667i	−0.273554	+	0.473809i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	0.815207	+	4.62327i	0.114152	+	0.647387i
$52$	5.46064	+	4.58202i	0.757254	+	0.635412i
$53$	−3.33615	+	2.79936i	−0.458256	+	0.384522i	−0.842489	−	0.538714i	$-0.818910\pi$
$53$	−3.33615	+	2.79936i	−0.458256	+	0.384522i	0.384233	+	0.923236i	$0.374466\pi$
$54$	0.173648	−	0.984808i	0.0236305	−	0.134015i
$55$	1.76604	−	0.642788i	0.238133	−	0.0866735i
$56$	3.29086			0.439760
$57$	2.52094	−	3.55596i	0.333907	−	0.470998i
$58$	2.69459			0.353817
$59$	6.92514	−	2.52055i	0.901577	−	0.328147i	0.150692	−	0.988581i	$-0.451850\pi$
$59$	6.92514	−	2.52055i	0.901577	−	0.328147i	0.750885	+	0.660433i	$0.229627\pi$
$60$	0.173648	−	0.984808i	0.0224179	−	0.127138i
$61$	−1.63041	+	1.36808i	−0.208753	+	0.175165i	−0.741170	−	0.671318i	$-0.765729\pi$
$61$	−1.63041	+	1.36808i	−0.208753	+	0.175165i	0.532416	+	0.846483i	$0.321284\pi$
$62$	3.41147	+	2.86257i	0.433258	+	0.363546i
$63$	−0.571452	−	3.24086i	−0.0719962	−	0.408310i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.56418	−	6.17334i	0.442082	−	0.765708i
$66$	−1.76604	−	0.642788i	−0.217385	−	0.0791217i
$67$	−8.94356	−	3.25519i	−1.09263	−	0.397685i	−0.268036	−	0.963409i	$-0.586374\pi$
$67$	−8.94356	−	3.25519i	−1.09263	−	0.397685i	−0.824595	+	0.565724i	$0.808597\pi$
$68$	2.34730	−	4.06564i	0.284651	−	0.493031i
$69$	3.40033	+	5.88954i	0.409352	+	0.709018i
$70$	−0.571452	−	3.24086i	−0.0683015	−	0.387357i
$71$	−3.78106	−	3.17269i	−0.448729	−	0.376528i	0.390235	−	0.920715i	$-0.372394\pi$
$71$	−3.78106	−	3.17269i	−0.448729	−	0.376528i	−0.838964	+	0.544187i	$0.816838\pi$
$72$	−0.766044	+	0.642788i	−0.0902792	+	0.0757532i
$73$	0.837496	−	4.74968i	0.0980215	−	0.555908i	−0.895758	−	0.444542i	$-0.853366\pi$
$73$	0.837496	−	4.74968i	0.0980215	−	0.555908i	0.993780	−	0.111366i	$-0.0355225\pi$
$74$	1.63176	−	0.593912i	0.189688	−	0.0690408i
$75$	−1.00000			−0.115470
$76$	−4.21688	+	1.10359i	−0.483709	+	0.126590i
$77$	−6.18479			−0.704823
$78$	−6.69846	+	2.43804i	−0.758452	+	0.276054i
$79$	2.24123	−	12.7106i	0.252158	−	1.43006i	−0.551106	−	0.834436i	$-0.685794\pi$
$79$	2.24123	−	12.7106i	0.252158	−	1.43006i	0.803264	−	0.595624i	$-0.203095\pi$
$80$	−0.766044	+	0.642788i	−0.0856464	+	0.0718658i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	1.12701	+	6.39160i	0.124458	+	0.705834i
$83$	−4.10607	−	7.11192i	−0.450699	−	0.780634i	0.547730	−	0.836655i	$-0.315492\pi$
$83$	−4.10607	−	7.11192i	−0.450699	−	0.780634i	−0.998430	+	0.0560208i	$0.982159\pi$
$84$	−1.64543	+	2.84997i	−0.179531	+	0.310957i
$85$	−4.41147	−	1.60565i	−0.478492	−	0.174157i
$86$	−8.06418	−	2.93512i	−0.869583	−	0.316502i
$87$	−1.34730	+	2.33359i	−0.144445	+	0.250187i
$88$	0.939693	+	1.62760i	0.100172	+	0.173502i
$89$	−2.44949	−	13.8918i	−0.259646	−	1.47252i	−0.783860	−	0.620938i	$-0.786752\pi$
$89$	−2.44949	−	13.8918i	−0.259646	−	1.47252i	0.524214	−	0.851586i	$-0.324359\pi$
$90$	0.766044	+	0.642788i	0.0807482	+	0.0677558i
$91$	−17.9702	+	15.0788i	−1.88379	+	1.58069i
$92$	1.18092	−	6.69734i	0.123120	−	0.698246i
$93$	−4.18479	+	1.52314i	−0.433943	+	0.157942i
$94$	−3.36959			−0.347546
$95$	1.81908	+	3.96118i	0.186633	+	0.406409i
$96$	1.00000			0.102062
$97$	1.22668	−	0.446476i	0.124551	−	0.0453327i	−0.278993	−	0.960293i	$-0.590001\pi$
$97$	1.22668	−	0.446476i	0.124551	−	0.0453327i	0.403544	+	0.914960i	$0.367778\pi$
$98$	−0.665030	+	3.77157i	−0.0671782	+	0.380986i
$99$	1.43969	−	1.20805i	0.144695	−	0.121413i
$100$	0.766044	+	0.642788i	0.0766044	+	0.0642788i
$101$	0.204393	+	1.15917i	0.0203379	+	0.115342i	0.993287	−	0.115679i	$-0.0369045\pi$
$101$	0.204393	+	1.15917i	0.0203379	+	0.115342i	−0.972949	+	0.231021i	$0.925793\pi$
$102$	2.34730	+	4.06564i	0.232417	+	0.402558i
$103$	6.95084	−	12.0392i	0.684886	−	1.18626i	−0.288586	−	0.957454i	$-0.593185\pi$
$103$	6.95084	−	12.0392i	0.684886	−	1.18626i	0.973473	−	0.228804i	$-0.0734815\pi$
$104$	6.69846	+	2.43804i	0.656838	+	0.239070i
$105$	3.09240	+	1.12554i	0.301787	+	0.109841i
$106$	−2.17752	+	3.77157i	−0.211499	+	0.366328i
$107$	−3.38919	−	5.87024i	−0.327645	−	0.567498i	0.654399	−	0.756149i	$-0.272922\pi$
$107$	−3.38919	−	5.87024i	−0.327645	−	0.567498i	−0.982044	+	0.188652i	$0.939588\pi$
$108$	−0.173648	−	0.984808i	−0.0167093	−	0.0947632i
$109$	0.347296	+	0.291416i	0.0332650	+	0.0279126i	0.659269	−	0.751908i	$-0.270866\pi$
$109$	0.347296	+	0.291416i	0.0332650	+	0.0279126i	−0.626004	+	0.779820i	$0.715310\pi$
$110$	1.43969	−	1.20805i	0.137269	−	0.115183i
$111$	−0.301537	+	1.71010i	−0.0286206	+	0.162316i
$112$	3.09240	−	1.12554i	0.292204	−	0.106354i
$113$	7.30541			0.687235			0.343617	−	0.939110i	$-0.388348\pi$
$113$	7.30541			0.687235			0.343617	+	0.939110i	$0.388348\pi$
$114$	1.15270	−	4.20372i	0.107961	−	0.393715i
$115$	−6.80066			−0.634165
$116$	2.53209	−	0.921605i	0.235099	−	0.0855689i
$117$	1.23783	−	7.02006i	0.114437	−	0.649005i
$118$	5.64543	−	4.73708i	0.519704	−	0.436083i
$119$	11.8348	+	9.93058i	1.08490	+	0.910335i
$120$	−0.173648	−	0.984808i	−0.0158518	−	0.0899002i
$121$	3.73396	+	6.46740i	0.339451	+	0.587946i
$122$	−1.06418	+	1.84321i	−0.0963461	+	0.166876i
$123$	−6.09879	−	2.21978i	−0.549910	−	0.200151i
$124$	4.18479	+	1.52314i	0.375805	+	0.136782i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−1.64543	−	2.84997i	−0.146587	−	0.253895i
$127$	2.09714	+	11.8935i	0.186091	+	1.05538i	0.924545	+	0.381073i	$0.124445\pi$
$127$	2.09714	+	11.8935i	0.186091	+	1.05538i	−0.738454	+	0.674304i	$0.764444\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	6.57398	−	5.51622i	0.578806	−	0.485676i
$130$	1.23783	−	7.02006i	0.108565	−	0.615700i
$131$	2.63176	−	0.957882i	0.229938	−	0.0836905i	−0.224482	−	0.974478i	$-0.572069\pi$
$131$	2.63176	−	0.957882i	0.229938	−	0.0836905i	0.454420	+	0.890788i	$0.349847\pi$
$132$	−1.87939			−0.163579
$133$	−1.16684	−	14.2970i	−0.101178	−	1.23971i
$134$	−9.51754			−0.822190
$135$	−0.939693	+	0.342020i	−0.0808759	+	0.0294364i
$136$	0.815207	−	4.62327i	0.0699035	−	0.396442i
$137$	11.1702	−	9.37295i	0.954338	−	0.800785i	−0.0256844	−	0.999670i	$-0.508177\pi$
$137$	11.1702	−	9.37295i	0.954338	−	0.800785i	0.980023	+	0.198885i	$0.0637321\pi$
$138$	5.20961	+	4.37138i	0.443471	+	0.372117i
$139$	1.94016	+	11.0032i	0.164562	+	0.933278i	0.949515	+	0.313723i	$0.101576\pi$
$139$	1.94016	+	11.0032i	0.164562	+	0.933278i	−0.784953	+	0.619556i	$0.787313\pi$
$140$	−1.64543	−	2.84997i	−0.139064	−	0.240866i
$141$	1.68479	−	2.91815i	0.141885	−	0.245752i
$142$	−4.63816	−	1.68815i	−0.389225	−	0.141666i
$143$	−12.5890	−	4.58202i	−1.05274	−	0.383168i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.34730	−	2.33359i	−0.111887	−	0.193794i
$146$	−0.837496	−	4.74968i	−0.0693117	−	0.393086i
$147$	−2.93376	−	2.46172i	−0.241973	−	0.203039i
$148$	1.33022	−	1.11619i	0.109344	−	0.0917502i
$149$	3.32770	−	18.8723i	0.272615	−	1.54608i	−0.473820	−	0.880622i	$-0.657125\pi$
$149$	3.32770	−	18.8723i	0.272615	−	1.54608i	0.746436	−	0.665458i	$-0.231764\pi$
$150$	−0.939693	+	0.342020i	−0.0767256	+	0.0279258i
$151$	−4.69459			−0.382041			−0.191020	−	0.981586i	$-0.561180\pi$
$151$	−4.69459			−0.382041			−0.191020	+	0.981586i	$0.561180\pi$
$152$	−3.58512	+	2.47929i	−0.290792	+	0.201097i
$153$	−4.69459			−0.379535
$154$	−5.81180	+	2.11532i	−0.468329	+	0.170458i
$155$	0.773318	−	4.38571i	0.0621144	−	0.352268i
$156$	−5.46064	+	4.58202i	−0.437201	+	0.366855i
$157$	8.55690	+	7.18009i	0.682915	+	0.573034i	0.916857	−	0.399217i	$-0.130718\pi$
$157$	8.55690	+	7.18009i	0.682915	+	0.573034i	−0.233941	+	0.972251i	$0.575162\pi$
$158$	−2.24123	−	12.7106i	−0.178303	−	1.01120i
$159$	−2.17752	−	3.77157i	−0.172688	−	0.299105i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	21.0303	+	7.65442i	1.65742	+	0.603252i
$162$	0.939693	+	0.342020i	0.0738292	+	0.0268716i
$163$	−8.45336	+	14.6417i	−0.662119	+	1.14682i	0.317939	+	0.948111i	$0.397009\pi$
$163$	−8.45336	+	14.6417i	−0.662119	+	1.14682i	−0.980058	+	0.198712i	$0.936324\pi$
$164$	3.24510	+	5.62068i	0.253400	+	0.438901i
$165$	0.326352	+	1.85083i	0.0254065	+	0.144087i
$166$	−6.29086	−	5.27866i	−0.488265	−	0.409703i
$167$	−18.9008	+	15.8597i	−1.46259	+	1.22726i	−0.539888	+	0.841737i	$0.681533\pi$
$167$	−18.9008	+	15.8597i	−1.46259	+	1.22726i	−0.922700	+	0.385520i	$0.874022\pi$
$168$	−0.571452	+	3.24086i	−0.0440885	+	0.250038i
$169$	−35.5330	+	12.9330i	−2.73331	+	0.994843i
$170$	−4.69459			−0.360059
$171$	3.06418	+	3.10013i	0.234324	+	0.237073i
$172$	−8.58172			−0.654350
$173$	14.9217	−	5.43107i	1.13448	−	0.412917i	0.294562	−	0.955632i	$-0.404826\pi$
$173$	14.9217	−	5.43107i	1.13448	−	0.412917i	0.839916	+	0.542716i	$0.182604\pi$
$174$	−0.467911	+	2.65366i	−0.0354722	+	0.201173i
$175$	−2.52094	+	2.11532i	−0.190565	+	0.159903i
$176$	1.43969	+	1.20805i	0.108521	+	0.0910599i
$177$	1.27972	+	7.25762i	0.0961893	+	0.545516i
$178$	−7.05303	−	12.2162i	−0.528647	−	0.915644i
$179$	−8.13950	+	14.0980i	−0.608375	+	1.05374i	0.383134	+	0.923693i	$0.374845\pi$
$179$	−8.13950	+	14.0980i	−0.608375	+	1.05374i	−0.991508	+	0.130043i	$0.958488\pi$
$180$	0.939693	+	0.342020i	0.0700406	+	0.0254927i
$181$	21.7665	+	7.92236i	1.61789	+	0.588865i	0.982979	−	0.183719i	$-0.0588136\pi$
$181$	21.7665	+	7.92236i	1.61789	+	0.588865i	0.634913	+	0.772583i	$0.281036\pi$
$182$	−11.7292	+	20.3156i	−0.869427	+	1.50589i
$183$	−1.06418	−	1.84321i	−0.0786663	−	0.136254i
$184$	−1.18092	−	6.69734i	−0.0870587	−	0.493735i
$185$	−1.33022	−	1.11619i	−0.0977999	−	0.0820638i
$186$	−3.41147	+	2.86257i	−0.250141	+	0.209894i
$187$	−1.53209	+	8.68891i	−0.112037	+	0.635396i
$188$	−3.16637	+	1.15247i	−0.230932	+	0.0840522i
$189$	3.29086			0.239375
$190$	3.06418	+	3.10013i	0.222299	+	0.224907i
$191$	0.980400			0.0709392			0.0354696	−	0.999371i	$-0.488707\pi$
$191$	0.980400			0.0709392			0.0354696	+	0.999371i	$0.488707\pi$
$192$	0.939693	−	0.342020i	0.0678165	−	0.0246832i
$193$	1.67499	−	9.49935i	0.120569	−	0.683778i	−0.863273	−	0.504737i	$-0.831589\pi$
$193$	1.67499	−	9.49935i	0.120569	−	0.683778i	0.983842	−	0.179041i	$-0.0572995\pi$
$194$	1.00000	−	0.839100i	0.0717958	−	0.0602438i
$195$	5.46064	+	4.58202i	0.391044	+	0.328125i
$196$	0.665030	+	3.77157i	0.0475021	+	0.269398i
$197$	−11.3735	−	19.6994i	−0.810325	−	1.40352i	−0.912637	−	0.408772i	$-0.865957\pi$
$197$	−11.3735	−	19.6994i	−0.810325	−	1.40352i	0.102311	−	0.994752i	$-0.467376\pi$
$198$	0.939693	−	1.62760i	0.0667810	−	0.115668i
$199$	−17.7023	−	6.44312i	−1.25489	−	0.456741i	−0.372836	−	0.927897i	$-0.621614\pi$
$199$	−17.7023	−	6.44312i	−1.25489	−	0.456741i	−0.882050	+	0.471157i	$0.843837\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	4.75877	−	8.24243i	0.335658	−	0.581376i
$202$	0.588526	+	1.01936i	0.0414085	+	0.0717217i
$203$	1.53983	+	8.73281i	0.108075	+	0.612923i
$204$	3.59627	+	3.01763i	0.251789	+	0.211276i
$205$	4.97178	−	4.17182i	0.347244	−	0.291373i
$206$	2.41400	−	13.6905i	0.168191	−	0.953861i
$207$	−6.39053	+	2.32596i	−0.444173	+	0.161666i
$208$	7.12836			0.494263
$209$	6.73783	−	4.65955i	0.466065	−	0.322308i
$210$	3.29086			0.227091
$211$	15.5471	−	5.65868i	1.07031	−	0.389560i	0.254015	−	0.967200i	$-0.418249\pi$
$211$	15.5471	−	5.65868i	1.07031	−	0.389560i	0.816291	+	0.577640i	$0.196026\pi$
$212$	−0.756244	+	4.28887i	−0.0519391	+	0.294561i
$213$	3.78106	−	3.17269i	0.259074	−	0.217389i
$214$	−5.19253	−	4.35705i	−0.354954	−	0.297842i
$215$	1.49020	+	8.45134i	0.101631	+	0.576377i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−7.32770	+	12.6919i	−0.497436	+	0.861585i
$218$	0.426022	+	0.155059i	0.0288539	+	0.0105019i
$219$	4.53209	+	1.64955i	0.306250	+	0.111466i
$220$	0.939693	−	1.62760i	0.0633541	−	0.109732i
$221$	16.7324	+	28.9813i	1.12554	+	1.94949i
$222$	0.301537	+	1.71010i	0.0202378	+	0.114774i
$223$	1.59446	+	1.33791i	0.106773	+	0.0895929i	0.694611	−	0.719385i	$-0.255576\pi$
$223$	1.59446	+	1.33791i	0.106773	+	0.0895929i	−0.587838	+	0.808978i	$0.700021\pi$
$224$	2.52094	−	2.11532i	0.168438	−	0.141336i
$225$	0.173648	−	0.984808i	0.0115765	−	0.0656539i
$226$	6.86484	−	2.49860i	0.456642	−	0.166204i
$227$	11.0196			0.731397			0.365698	−	0.930733i	$-0.380830\pi$
$227$	11.0196			0.731397			0.365698	+	0.930733i	$0.380830\pi$
$228$	−0.354570	−	4.34445i	−0.0234820	−	0.287718i
$229$	−25.5621			−1.68919			−0.844596	−	0.535404i	$-0.820159\pi$
$229$	−25.5621			−1.68919			−0.844596	+	0.535404i	$0.820159\pi$
$230$	−6.39053	+	2.32596i	−0.421379	+	0.153369i
$231$	1.07398	−	6.09083i	0.0706626	−	0.400747i
$232$	2.06418	−	1.73205i	0.135520	−	0.113715i
$233$	−1.43376	−	1.20307i	−0.0939289	−	0.0788157i	0.594614	−	0.804011i	$-0.297305\pi$
$233$	−1.43376	−	1.20307i	−0.0939289	−	0.0788157i	−0.688543	+	0.725196i	$0.741749\pi$
$234$	−1.23783	−	7.02006i	−0.0809192	−	0.458916i
$235$	1.68479	+	2.91815i	0.109904	+	0.190359i
$236$	3.68479	−	6.38225i	0.239860	−	0.415449i
$237$	12.1284	+	4.41436i	0.787821	+	0.286744i
$238$	14.5175	+	5.28395i	0.941032	+	0.342508i
$239$	9.24897	−	16.0197i	0.598266	−	1.03623i	−0.394811	−	0.918762i	$-0.629190\pi$
$239$	9.24897	−	16.0197i	0.598266	−	1.03623i	0.993077	−	0.117465i	$-0.0374768\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	2.76217	+	15.6651i	0.177927	+	1.00908i	0.934711	+	0.355410i	$0.115659\pi$
$241$	2.76217	+	15.6651i	0.177927	+	1.00908i	−0.756783	+	0.653666i	$0.773230\pi$
$242$	5.72075	+	4.80028i	0.367744	+	0.308574i
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$	−0.369585	+	2.09602i	−0.0236603	+	0.134184i
$245$	3.59879	−	1.30985i	0.229918	−	0.0836835i
$246$	−6.49020			−0.413800
$247$	8.21688	−	29.9656i	0.522828	−	1.90667i
$248$	4.45336			0.282789
$249$	7.71688	−	2.80872i	0.489037	−	0.177995i
$250$	0.173648	−	0.984808i	0.0109825	−	0.0622847i
$251$	−13.7738	+	11.5576i	−0.869394	+	0.729508i	−0.963970	−	0.266010i	$-0.914295\pi$
$251$	−13.7738	+	11.5576i	−0.869394	+	0.729508i	0.0945767	+	0.995518i	$0.469850\pi$
$252$	−2.52094	−	2.11532i	−0.158805	−	0.133253i
$253$	2.21941	+	12.5869i	0.139533	+	0.791331i
$254$	6.03849	+	10.4590i	0.378888	+	0.656254i
$255$	2.34730	−	4.06564i	0.146993	−	0.254600i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	4.49020	+	1.63430i	0.280091	+	0.101945i	0.478246	−	0.878226i	$-0.341273\pi$
$257$	4.49020	+	1.63430i	0.280091	+	0.101945i	−0.198155	+	0.980171i	$0.563495\pi$
$258$	4.29086	−	7.43199i	0.267137	−	0.462695i
$259$	2.85726	+	4.94892i	0.177541	+	0.307511i
$260$	−1.23783	−	7.02006i	−0.0767667	−	0.435366i
$261$	−2.06418	−	1.73205i	−0.127769	−	0.107211i
$262$	2.14543	−	1.80023i	0.132545	−	0.111219i
$263$	−1.30406	+	7.39571i	−0.0804120	+	0.456039i	0.917841	+	0.396949i	$0.129931\pi$
$263$	−1.30406	+	7.39571i	−0.0804120	+	0.456039i	−0.998253	+	0.0590900i	$0.981180\pi$
$264$	−1.76604	+	0.642788i	−0.108693	+	0.0395608i
$265$	4.35504			0.267528
$266$	−5.98633	−	13.0357i	−0.367045	−	0.799269i
$267$	14.1061			0.863277
$268$	−8.94356	+	3.25519i	−0.546315	+	0.198842i
$269$	−5.25402	+	29.7970i	−0.320343	+	1.81676i	0.220215	+	0.975451i	$0.429324\pi$
$269$	−5.25402	+	29.7970i	−0.320343	+	1.81676i	−0.540558	+	0.841306i	$0.681787\pi$
$270$	−0.766044	+	0.642788i	−0.0466200	+	0.0391188i
$271$	16.0378	+	13.4573i	0.974225	+	0.817472i	0.983208	−	0.182488i	$-0.0584150\pi$
$271$	16.0378	+	13.4573i	0.974225	+	0.817472i	−0.00898298	+	0.999960i	$0.502859\pi$
$272$	−0.815207	−	4.62327i	−0.0494292	−	0.280327i
$273$	−11.7292	−	20.3156i	−0.709884	−	1.22956i
$274$	7.29086	−	12.6281i	0.440457	−	0.762894i
$275$	−1.76604	−	0.642788i	−0.106496	−	0.0387616i
$276$	6.39053	+	2.32596i	0.384665	+	0.140006i
$277$	0.953363	−	1.65127i	0.0572820	−	0.0992154i	−0.835962	−	0.548787i	$-0.815090\pi$
$277$	0.953363	−	1.65127i	0.0572820	−	0.0992154i	0.893244	+	0.449571i	$0.148423\pi$
$278$	5.58647	+	9.67604i	0.335054	+	0.580331i
$279$	−0.773318	−	4.38571i	−0.0462974	−	0.262565i
$280$	−2.52094	−	2.11532i	−0.150655	−	0.126415i
$281$	−18.0685	+	15.1613i	−1.07788	+	0.904446i	−0.995743	−	0.0921749i	$-0.970618\pi$
$281$	−18.0685	+	15.1613i	−1.07788	+	0.904446i	−0.0821344	+	0.996621i	$0.526174\pi$
$282$	0.585122	−	3.31839i	0.0348435	−	0.197607i
$283$	14.5030	−	5.27866i	0.862113	−	0.313784i	0.127144	−	0.991884i	$-0.459419\pi$
$283$	14.5030	−	5.27866i	0.862113	−	0.313784i	0.734969	+	0.678101i	$0.237197\pi$
$284$	−4.93582			−0.292887
$285$	−4.21688	+	1.10359i	−0.249786	+	0.0653710i
$286$	−13.3969			−0.792177
$287$	−20.0703	+	7.30498i	−1.18471	+	0.431199i
$288$	−0.173648	+	0.984808i	−0.0102323	+	0.0580304i
$289$	3.86025	−	3.23914i	0.227074	−	0.190537i
$290$	−2.06418	−	1.73205i	−0.121213	−	0.101710i
$291$	0.226682	+	1.28558i	0.0132883	+	0.0753618i
$292$	−2.41147	−	4.17680i	−0.141121	−	0.244428i
$293$	12.9859	−	22.4923i	0.758645	−	1.31401i	−0.184896	−	0.982758i	$-0.559195\pi$
$293$	12.9859	−	22.4923i	0.758645	−	1.31401i	0.943541	−	0.331254i	$-0.107472\pi$
$294$	−3.59879	−	1.30985i	−0.209886	−	0.0763922i
$295$	−6.92514	−	2.52055i	−0.403198	−	0.146752i
$296$	0.868241	−	1.50384i	0.0504655	−	0.0874088i
$297$	0.939693	+	1.62760i	0.0545265	+	0.0944427i
$298$	−3.32770	−	18.8723i	−0.192768	−	1.09324i
$299$	37.1359	+	31.1607i	2.14763	+	1.80207i
$300$	−0.766044	+	0.642788i	−0.0442276	+	0.0371114i
$301$	4.90404	−	27.8122i	0.282664	−	1.60307i
$302$	−4.41147	+	1.60565i	−0.253852	+	0.0923945i
$303$	−1.17705			−0.0676199
$304$	−2.52094	+	3.55596i	−0.144586	+	0.203948i
$305$	2.12836			0.121869
$306$	−4.41147	+	1.60565i	−0.252187	+	0.0917886i
$307$	3.90941	−	22.1714i	0.223122	−	1.26539i	−0.643121	−	0.765765i	$-0.722361\pi$
$307$	3.90941	−	22.1714i	0.223122	−	1.26539i	0.866243	−	0.499623i	$-0.166528\pi$
$308$	−4.73783	+	3.97551i	−0.269963	+	0.226526i
$309$	10.6493	+	8.93582i	0.605818	+	0.508341i
$310$	−0.773318	−	4.38571i	−0.0439215	−	0.249091i
$311$	−6.80840	−	11.7925i	−0.386069	−	0.668691i	0.605848	−	0.795580i	$-0.292834\pi$
$311$	−6.80840	−	11.7925i	−0.386069	−	0.668691i	−0.991917	+	0.126889i	$0.959501\pi$
$312$	−3.56418	+	6.17334i	−0.201782	+	0.349496i
$313$	16.7716	+	6.10435i	0.947985	+	0.345038i	0.769314	−	0.638871i	$-0.220598\pi$
$313$	16.7716	+	6.10435i	0.947985	+	0.345038i	0.178671	+	0.983909i	$0.442820\pi$
$314$	10.4966	+	3.82045i	0.592357	+	0.215600i
$315$	−1.64543	+	2.84997i	−0.0927095	+	0.160577i
$316$	−6.45336	−	11.1776i	−0.363030	−	0.628786i
$317$	−3.76692	−	21.3633i	−0.211571	−	1.19988i	−0.886758	−	0.462234i	$-0.847048\pi$
$317$	−3.76692	−	21.3633i	−0.211571	−	1.19988i	0.675187	−	0.737647i	$-0.264063\pi$
$318$	−3.33615	−	2.79936i	−0.187082	−	0.156981i
$319$	−3.87939	+	3.25519i	−0.217204	+	0.182256i
$320$	−0.173648	+	0.984808i	−0.00970723	+	0.0550524i
$321$	6.36959	−	2.31834i	0.355516	−	0.129397i
$322$	22.3800			1.24719
$323$	−20.3746	−	1.90236i	−1.13368	−	0.105850i
$324$	1.00000			0.0555556
$325$	−6.69846	+	2.43804i	−0.371564	+	0.135238i
$326$	−2.93582	+	16.6499i	−0.162600	+	0.922151i
$327$	−0.347296	+	0.291416i	−0.0192055	+	0.0161154i
$328$	4.97178	+	4.17182i	0.274521	+	0.230350i
$329$	−1.92556	−	10.9204i	−0.106159	−	0.602059i
$330$	0.939693	+	1.62760i	0.0517284	+	0.0895962i
$331$	2.70961	−	4.69318i	0.148933	−	0.257960i	−0.781900	−	0.623404i	$-0.785749\pi$
$331$	2.70961	−	4.69318i	0.148933	−	0.257960i	0.930834	+	0.365443i	$0.119083\pi$
$332$	−7.71688	−	2.80872i	−0.423519	−	0.154148i
$333$	−1.63176	−	0.593912i	−0.0894198	−	0.0325462i
$334$	−12.3366	+	21.3677i	−0.675030	+	1.16919i
$335$	4.75877	+	8.24243i	0.259999	+	0.450332i
$336$	0.571452	+	3.24086i	0.0311752	+	0.176804i
$337$	25.5553	+	21.4435i	1.39209	+	1.16810i	0.964487	+	0.264131i	$0.0850852\pi$
$337$	25.5553	+	21.4435i	1.39209	+	1.16810i	0.427600	+	0.903968i	$0.359359\pi$
$338$	−28.9668	+	24.3060i	−1.57559	+	1.32207i
$339$	−1.26857	+	7.19442i	−0.0688993	+	0.390747i
$340$	−4.41147	+	1.60565i	−0.239246	+	0.0870783i
$341$	−8.36959			−0.453238
$342$	3.93969	+	1.86516i	0.213034	+	0.100856i
$343$	10.4328			0.563320
$344$	−8.06418	+	2.93512i	−0.434791	+	0.158251i
$345$	1.18092	−	6.69734i	0.0635787	−	0.360573i
$346$	12.1643	−	10.2071i	0.653958	−	0.548736i
$347$	−10.4192	−	8.74276i	−0.559333	−	0.469336i	0.318754	−	0.947838i	$-0.396736\pi$
$347$	−10.4192	−	8.74276i	−0.559333	−	0.469336i	−0.878087	+	0.478502i	$0.841180\pi$
$348$	0.467911	+	2.65366i	0.0250827	+	0.142251i
$349$	6.65776	+	11.5316i	0.356382	+	0.617271i	0.987353	−	0.158535i	$-0.0506770\pi$
$349$	6.65776	+	11.5316i	0.356382	+	0.617271i	−0.630972	+	0.775806i	$0.717344\pi$
$350$	−1.64543	+	2.84997i	−0.0879519	+	0.152337i
$351$	6.69846	+	2.43804i	0.357538	+	0.130133i
$352$	1.76604	+	0.642788i	0.0941305	+	0.0342607i
$353$	10.4534	−	18.1058i	0.556376	−	0.963672i	−0.441419	−	0.897301i	$-0.645525\pi$
$353$	10.4534	−	18.1058i	0.556376	−	0.963672i	0.997795	−	0.0663709i	$-0.0211421\pi$
$354$	3.68479	+	6.38225i	0.195845	+	0.339213i
$355$	0.857097	+	4.86084i	0.0454900	+	0.257986i
$356$	−10.8059	−	9.06720i	−0.572710	−	0.480561i
$357$	−11.8348	+	9.93058i	−0.626364	+	0.525582i
$358$	−2.82682	+	16.0317i	−0.149402	+	0.847301i
$359$	12.4243	−	4.52206i	0.655728	−	0.238665i	0.00733699	−	0.999973i	$-0.497665\pi$
$359$	12.4243	−	4.52206i	0.655728	−	0.238665i	0.648391	+	0.761308i	$0.275442\pi$
$360$	1.00000			0.0527046
$361$	12.0424	+	14.6963i	0.633808	+	0.773490i
$362$	23.1634			1.21744
$363$	−7.01754	+	2.55418i	−0.368325	+	0.134059i
$364$	−4.07351	+	23.1020i	−0.213510	+	1.21088i
$365$	−3.69459	+	3.10013i	−0.193384	+	0.162268i
$366$	−1.63041	−	1.36808i	−0.0852232	−	0.0715107i
$367$	−3.54829	−	20.1233i	−0.185219	−	1.05043i	−0.925674	−	0.378323i	$-0.876501\pi$
$367$	−3.54829	−	20.1233i	−0.185219	−	1.05043i	0.740455	−	0.672106i	$-0.234610\pi$
$368$	−3.40033	−	5.88954i	−0.177254	−	0.307014i
$369$	3.24510	−	5.62068i	0.168933	−	0.292601i
$370$	−1.63176	−	0.593912i	−0.0848311	−	0.0308760i
$371$	−13.4675	−	4.90177i	−0.699198	−	0.254487i
$372$	−2.22668	+	3.85673i	−0.115448	+	0.199962i
$373$	14.8944	+	25.7979i	0.771203	+	1.33576i	0.936904	+	0.349586i	$0.113678\pi$
$373$	14.8944	+	25.7979i	0.771203	+	1.33576i	−0.165701	+	0.986176i	$0.552989\pi$
$374$	1.53209	+	8.68891i	0.0792224	+	0.449293i
$375$	0.766044	+	0.642788i	0.0395584	+	0.0331934i
$376$	−2.58125	+	2.16593i	−0.133118	+	0.111699i
$377$	−3.33544	+	18.9162i	−0.171784	+	0.974234i
$378$	3.09240	−	1.12554i	0.159056	−	0.0578915i
$379$	−4.95542			−0.254543			−0.127271	−	0.991868i	$-0.540622\pi$
$379$	−4.95542			−0.254543			−0.127271	+	0.991868i	$0.540622\pi$
$380$	3.93969	+	1.86516i	0.202102	+	0.0956807i
$381$	−12.0770			−0.618722
$382$	0.921274	−	0.335316i	0.0471365	−	0.0171563i
$383$	2.75268	−	15.6112i	0.140655	−	0.797696i	−0.830098	−	0.557617i	$-0.811716\pi$
$383$	2.75268	−	15.6112i	0.140655	−	0.797696i	0.970753	−	0.240079i	$-0.0771732\pi$
$384$	0.766044	−	0.642788i	0.0390920	−	0.0328021i
$385$	4.73783	+	3.97551i	0.241462	+	0.202611i
$386$	−1.67499	−	9.49935i	−0.0852549	−	0.483504i
$387$	4.29086	+	7.43199i	0.218117	+	0.377789i
$388$	0.652704	−	1.13052i	0.0331360	−	0.0573932i
$389$	−27.0574	−	9.84808i	−1.37186	−	0.499317i	−0.452162	−	0.891936i	$-0.649347\pi$
$389$	−27.0574	−	9.84808i	−1.37186	−	0.499317i	−0.919701	+	0.392619i	$0.871569\pi$
$390$	6.69846	+	2.43804i	0.339190	+	0.123455i
$391$	15.9632	−	27.6490i	0.807292	−	1.39827i
$392$	1.91488	+	3.31667i	0.0967159	+	0.167517i
$393$	0.486329	+	2.75811i	0.0245321	+	0.139128i
$394$	−17.4251	−	14.6214i	−0.877866	−	0.736617i
$395$	−9.88713	+	8.29628i	−0.497475	+	0.417431i
$396$	0.326352	−	1.85083i	0.0163998	−	0.0930079i
$397$	27.1707	−	9.88933i	1.36366	−	0.496331i	0.446475	−	0.894796i	$-0.352679\pi$
$397$	27.1707	−	9.88933i	1.36366	−	0.496331i	0.917184	+	0.398465i	$0.130457\pi$
$398$	−18.8384			−0.944285
$399$	14.2824	+	1.33353i	0.715014	+	0.0667601i
$400$	1.00000			0.0500000
$401$	−27.0428	+	9.84278i	−1.35045	+	0.491525i	−0.913090	−	0.407759i	$-0.866310\pi$
$401$	−27.0428	+	9.84278i	−1.35045	+	0.491525i	−0.437365	+	0.899284i	$0.644088\pi$
$402$	1.65270	−	9.37295i	0.0824294	−	0.467480i
$403$	−24.3182	+	20.4054i	−1.21138	+	1.01647i
$404$	0.901674	+	0.756594i	0.0448600	+	0.0376420i
$405$	−0.173648	−	0.984808i	−0.00862865	−	0.0489355i
$406$	4.43376	+	7.67950i	0.220044	+	0.381127i
$407$	−1.63176	+	2.82629i	−0.0808833	+	0.140094i
$408$	4.41147	+	1.60565i	0.218401	+	0.0794913i
$409$	14.7160	+	5.35619i	0.727660	+	0.264846i	0.679174	−	0.733977i	$-0.262338\pi$
$409$	14.7160	+	5.35619i	0.727660	+	0.264846i	0.0484857	+	0.998824i	$0.484560\pi$
$410$	3.24510	−	5.62068i	0.160264	−	0.277585i
$411$	7.29086	+	12.6281i	0.359632	+	0.622900i
$412$	−2.41400	−	13.6905i	−0.118929	−	0.674481i
$413$	18.5783	+	15.5891i	0.914179	+	0.767087i
$414$	−5.20961	+	4.37138i	−0.256038	+	0.214842i
$415$	−1.42602	+	8.08737i	−0.0700007	+	0.396994i
$416$	6.69846	−	2.43804i	0.328419	−	0.119535i
$417$	−11.1729			−0.547141
$418$	4.73783	−	6.68302i	0.231735	−	0.326877i
$419$	0.753718			0.0368215			0.0184108	−	0.999831i	$-0.494139\pi$
$419$	0.753718			0.0368215			0.0184108	+	0.999831i	$0.494139\pi$
$420$	3.09240	−	1.12554i	0.150893	−	0.0549207i
$421$	−0.522593	+	2.96377i	−0.0254696	+	0.144446i	−0.994891	−	0.100958i	$-0.967809\pi$
$421$	−0.522593	+	2.96377i	−0.0254696	+	0.144446i	0.969421	+	0.245403i	$0.0789204\pi$
$422$	12.6741	−	10.6348i	0.616966	−	0.517696i
$423$	2.58125	+	2.16593i	0.125505	+	0.105311i
$424$	0.756244	+	4.28887i	0.0367265	+	0.208286i
$425$	2.34730	+	4.06564i	0.113861	+	0.197212i
$426$	2.46791	−	4.27455i	0.119571	−	0.207103i
$427$	−6.58172	−	2.39555i	−0.318512	−	0.115929i
$428$	−6.36959	−	2.31834i	−0.307886	−	0.112061i
$429$	6.69846	−	11.6021i	0.323405	−	0.560154i
$430$	4.29086	+	7.43199i	0.206924	+	0.358402i
$431$	−4.68004	−	26.5419i	−0.225430	−	1.27848i	−0.861862	−	0.507143i	$-0.830702\pi$
$431$	−4.68004	−	26.5419i	−0.225430	−	1.27848i	0.636432	−	0.771333i	$-0.280410\pi$
$432$	−0.766044	−	0.642788i	−0.0368563	−	0.0309261i
$433$	7.04189	−	5.90885i	0.338412	−	0.283961i	−0.457705	−	0.889104i	$-0.651328\pi$
$433$	7.04189	−	5.90885i	0.338412	−	0.283961i	0.796117	+	0.605143i	$0.206884\pi$
$434$	−2.54488	+	14.4327i	−0.122158	+	0.692794i
$435$	2.53209	−	0.921605i	0.121404	−	0.0441876i
$436$	0.453363			0.0217122
$437$	−28.6776	+	7.50514i	−1.37183	+	0.359020i
$438$	4.82295			0.230449
$439$	−0.453363	+	0.165011i	−0.0216378	+	0.00787553i	−0.352816	−	0.935693i	$-0.614776\pi$
$439$	−0.453363	+	0.165011i	−0.0216378	+	0.00787553i	0.331179	+	0.943568i	$0.392554\pi$
$440$	0.326352	−	1.85083i	0.0155582	−	0.0882350i
$441$	2.93376	−	2.46172i	0.139703	−	0.117225i
$442$	25.6355	+	21.5107i	1.21935	+	1.02316i
$443$	5.74422	+	32.5771i	0.272916	+	1.54778i	0.745504	+	0.666501i	$0.232209\pi$
$443$	5.74422	+	32.5771i	0.272916	+	1.54778i	−0.472588	+	0.881284i	$0.656680\pi$
$444$	0.868241	+	1.50384i	0.0412049	+	0.0713690i
$445$	−7.05303	+	12.2162i	−0.334346	+	0.579104i
$446$	1.95589	+	0.711886i	0.0926140	+	0.0337088i
$447$	18.0077	+	6.55428i	0.851737	+	0.310007i
$448$	1.64543	−	2.84997i	0.0777392	−	0.134648i
$449$	3.44949	+	5.97470i	0.162792	+	0.281963i	0.935869	−	0.352349i	$-0.114617\pi$
$449$	3.44949	+	5.97470i	0.162792	+	0.281963i	−0.773077	+	0.634312i	$0.781284\pi$
$450$	−0.173648	−	0.984808i	−0.00818585	−	0.0464243i
$451$	−9.34389	−	7.84046i	−0.439987	−	0.369193i
$452$	5.59627	−	4.69583i	0.263226	−	0.220873i
$453$	0.815207	−	4.62327i	0.0383018	−	0.217220i
$454$	10.3550	−	3.76893i	0.485986	−	0.176884i
$455$	23.4584			1.09975
$456$	−1.81908	−	3.96118i	−0.0851861	−	0.185499i
$457$	−28.8830			−1.35109			−0.675545	−	0.737319i	$-0.736092\pi$
$457$	−28.8830			−1.35109			−0.675545	+	0.737319i	$0.736092\pi$
$458$	−24.0205	+	8.74276i	−1.12241	+	0.408522i
$459$	0.815207	−	4.62327i	0.0380506	−	0.215796i
$460$	−5.20961	+	4.37138i	−0.242899	+	0.203817i
$461$	−10.5294	−	8.83522i	−0.490403	−	0.411497i	0.363768	−	0.931490i	$-0.381490\pi$
$461$	−10.5294	−	8.83522i	−0.490403	−	0.411497i	−0.854171	+	0.519993i	$0.825935\pi$
$462$	−1.07398	−	6.09083i	−0.0499660	−	0.283371i
$463$	0.180922	+	0.313366i	0.00840816	+	0.0145634i	0.870199	−	0.492701i	$-0.163990\pi$
$463$	0.180922	+	0.313366i	0.00840816	+	0.0145634i	−0.861791	+	0.507264i	$0.830657\pi$
$464$	1.34730	−	2.33359i	0.0625467	−	0.108334i
$465$	4.18479	+	1.52314i	0.194065	+	0.0706339i
$466$	−1.75877	−	0.640140i	−0.0814735	−	0.0296539i
$467$	−8.81521	+	15.2684i	−0.407919	+	0.706537i	−0.994656	−	0.103241i	$-0.967079\pi$
$467$	−8.81521	+	15.2684i	−0.407919	+	0.706537i	0.586737	+	0.809777i	$0.300412\pi$
$468$	−3.56418	−	6.17334i	−0.164754	−	0.285363i
$469$	−5.43882	−	30.8451i	−0.251141	−	1.42429i
$470$	2.58125	+	2.16593i	0.119064	+	0.0999068i
$471$	−8.55690	+	7.18009i	−0.394281	+	0.330841i
$472$	1.27972	−	7.25762i	0.0589037	−	0.334059i
$473$	15.1557	−	5.51622i	0.696860	−	0.253636i
$474$	12.9067			0.592826
$475$	1.15270	−	4.20372i	0.0528897	−	0.192880i
$476$	15.4492			0.708115
$477$	4.09240	−	1.48951i	0.187378	−	0.0682000i
$478$	3.21213	−	18.2169i	0.146920	−	0.833222i
$479$	−13.7888	+	11.5702i	−0.630026	+	0.528655i	−0.900937	−	0.433950i	$-0.857120\pi$
$479$	−13.7888	+	11.5702i	−0.630026	+	0.528655i	0.270911	+	0.962604i	$0.412675\pi$
$480$	−0.766044	−	0.642788i	−0.0349650	−	0.0293391i
$481$	2.14946	+	12.1902i	0.0980070	+	0.555826i
$482$	7.95336	+	13.7756i	0.362266	+	0.627463i
$483$	−11.1900	+	19.3817i	−0.509163	+	0.881896i
$484$	7.01754	+	2.55418i	0.318979	+	0.116099i
$485$	−1.22668	−	0.446476i	−0.0557007	−	0.0202734i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−19.0646	−	33.0209i	−0.863902	−	1.49632i	−0.868134	−	0.496330i	$-0.834681\pi$
$487$	−19.0646	−	33.0209i	−0.863902	−	1.49632i	0.00423228	−	0.999991i	$-0.498653\pi$
$488$	0.369585	+	2.09602i	0.0167303	+	0.0948824i
$489$	−12.9513	−	10.8674i	−0.585678	−	0.491442i
$490$	2.93376	−	2.46172i	0.132534	−	0.111209i
$491$	−3.68123	+	20.8773i	−0.166131	+	0.942178i	0.781759	+	0.623581i	$0.214323\pi$
$491$	−3.68123	+	20.8773i	−0.166131	+	0.942178i	−0.947890	+	0.318597i	$0.896788\pi$
$492$	−6.09879	+	2.21978i	−0.274955	+	0.100075i
$493$	12.6500			0.569728
$494$	−2.52750	−	30.9688i	−0.113718	−	1.39335i
$495$	−1.87939			−0.0844721
$496$	4.18479	−	1.52314i	0.187903	−	0.0683910i
$497$	2.82058	−	15.9963i	0.126520	−	0.717533i
$498$	6.29086	−	5.27866i	0.281900	−	0.236542i
$499$	−30.7108	−	25.7694i	−1.37480	−	1.15360i	−0.971090	−	0.238712i	$-0.923275\pi$
$499$	−30.7108	−	25.7694i	−1.37480	−	1.15360i	−0.403713	−	0.914886i	$-0.632281\pi$
$500$	−0.173648	−	0.984808i	−0.00776578	−	0.0440419i
$501$	−12.3366	−	21.3677i	−0.551159	−	0.954636i
$502$	−8.99020	+	15.5715i	−0.401252	+	0.694989i
$503$	−28.5599	−	10.3950i	−1.27342	−	0.463488i	−0.385171	−	0.922845i	$-0.625858\pi$
$503$	−28.5599	−	10.3950i	−1.27342	−	0.463488i	−0.888252	+	0.459357i	$0.848080\pi$
$504$	−3.09240	−	1.12554i	−0.137746	−	0.0501355i
$505$	0.588526	−	1.01936i	0.0261891	−	0.0453608i
$506$	6.39053	+	11.0687i	0.284094	+	0.492065i
$507$	−6.56624	−	37.2390i	−0.291617	−	1.65384i
$508$	9.25150	+	7.76293i	0.410469	+	0.344424i
$509$	−27.7178	+	23.2580i	−1.22857	+	1.03089i	−0.230240	+	0.973134i	$0.573951\pi$
$509$	−27.7178	+	23.2580i	−1.22857	+	1.03089i	−0.998331	+	0.0577592i	$0.981604\pi$
$510$	0.815207	−	4.62327i	0.0360980	−	0.204722i
$511$	14.9145	−	5.42842i	0.659777	−	0.240139i
$512$	−1.00000			−0.0441942
$513$	−3.58512	+	2.47929i	−0.158287	+	0.109463i
$514$	4.77837			0.210765
$515$	−13.0633	+	4.75465i	−0.575638	+	0.209515i
$516$	1.49020	−	8.45134i	0.0656024	−	0.372050i
$517$	4.85117	−	4.07061i	0.213354	−	0.179025i
$518$	4.37757	+	3.67322i	0.192340	+	0.161392i
$519$	2.75743	+	15.6381i	0.121038	+	0.686438i
$520$	−3.56418	−	6.17334i	−0.156300	−	0.270719i
$521$	−0.433763	+	0.751299i	−0.0190035	+	0.0329150i	−0.875371	−	0.483452i	$-0.839383\pi$
$521$	−0.433763	+	0.751299i	−0.0190035	+	0.0329150i	0.856367	+	0.516367i	$0.172716\pi$
$522$	−2.53209	−	0.921605i	−0.110827	−	0.0403376i
$523$	−9.19759	−	3.34765i	−0.402182	−	0.146382i	0.133006	−	0.991115i	$-0.457537\pi$
$523$	−9.19759	−	3.34765i	−0.402182	−	0.146382i	−0.535188	+	0.844733i	$0.679759\pi$
$524$	1.40033	−	2.42544i	0.0611737	−	0.105956i
$525$	−1.64543	−	2.84997i	−0.0718124	−	0.124383i
$526$	1.30406	+	7.39571i	0.0568599	+	0.322468i
$527$	16.0155	+	13.4386i	0.697645	+	0.585394i
$528$	−1.43969	+	1.20805i	−0.0626546	+	0.0525734i
$529$	4.03714	−	22.8958i	0.175528	−	0.995468i
$530$	4.09240	−	1.48951i	0.177762	−	0.0647002i
$531$	−7.36959			−0.319813
$532$	−10.0838	−	10.2021i	−0.437187	−	0.442317i
$533$	−46.2645			−2.00394
$534$	13.2554	−	4.82456i	0.573616	−	0.208779i
$535$	−1.17705	+	6.67539i	−0.0508884	+	0.288602i
$536$	−7.29086	+	6.11776i	−0.314917	+	0.264247i
$537$	−12.4704	−	10.4639i	−0.538139	−	0.451552i
$538$	5.25402	+	29.7970i	0.226517	+	1.28464i
$539$	−3.59879	−	6.23329i	−0.155011	−	0.268487i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−38.1908	−	13.9003i	−1.64195	−	0.597621i	−0.654571	−	0.756000i	$-0.727151\pi$
$541$	−38.1908	−	13.9003i	−1.64195	−	0.597621i	−0.987378	+	0.158379i	$0.949373\pi$
$542$	19.6732	+	7.16047i	0.845038	+	0.307569i
$543$	−11.5817	+	20.0601i	−0.497019	+	0.860862i
$544$	−2.34730	−	4.06564i	−0.100640	−	0.174313i
$545$	−0.0787257	−	0.446476i	−0.00337224	−	0.0191249i
$546$	−17.9702	−	15.0788i	−0.769053	−	0.645312i
$547$	−28.4911	+	23.9069i	−1.21819	+	1.02219i	−0.219276	+	0.975663i	$0.570369\pi$
$547$	−28.4911	+	23.9069i	−1.21819	+	1.02219i	−0.998917	+	0.0465223i	$0.985186\pi$
$548$	2.53209	−	14.3602i	0.108165	−	0.613437i
$549$	2.00000	−	0.727940i	0.0853579	−	0.0310677i
$550$	−1.87939			−0.0801373
$551$	−8.25671	−	8.35359i	−0.351748	−	0.355875i
$552$	6.80066			0.289455
$553$	39.9127	−	14.5270i	1.69726	−	0.617753i
$554$	0.331100	−	1.87776i	0.0140671	−	0.0797783i
$555$	1.33022	−	1.11619i	0.0564648	−	0.0473796i
$556$	8.55896	+	7.18182i	0.362981	+	0.304577i
$557$	−3.58424	−	20.3273i	−0.151869	−	0.861294i	−0.961592	−	0.274482i	$-0.911494\pi$
$557$	−3.58424	−	20.3273i	−0.151869	−	0.861294i	0.809723	−	0.586812i	$-0.199617\pi$
$558$	−2.22668	−	3.85673i	−0.0942629	−	0.163268i
$559$	30.5868	−	52.9778i	1.29368	−	2.24072i
$560$	−3.09240	−	1.12554i	−0.130678	−	0.0475628i
$561$	−8.29086	−	3.01763i	−0.350040	−	0.127404i
$562$	−11.7934	+	20.4267i	−0.497474	+	0.861650i
$563$	14.6578	+	25.3880i	0.617751	+	1.06998i	0.989895	+	0.141801i	$0.0452893\pi$
$563$	14.6578	+	25.3880i	0.617751	+	1.06998i	−0.372144	+	0.928175i	$0.621377\pi$
$564$	−0.585122	−	3.31839i	−0.0246381	−	0.139730i
$565$	−5.59627	−	4.69583i	−0.235437	−	0.197555i
$566$	11.8229	−	9.92063i	0.496956	−	0.416995i
$567$	−0.571452	+	3.24086i	−0.0239987	+	0.136103i
$568$	−4.63816	+	1.68815i	−0.194613	+	0.0708332i
$569$	11.7050			0.490700			0.245350	−	0.969435i	$-0.421097\pi$
$569$	11.7050			0.490700			0.245350	+	0.969435i	$0.421097\pi$
$570$	−3.58512	+	2.47929i	−0.150164	+	0.103846i
$571$	−0.216252			−0.00904988			−0.00452494	−	0.999990i	$-0.501440\pi$
$571$	−0.216252			−0.00904988			−0.00452494	+	0.999990i	$0.501440\pi$
$572$	−12.5890	+	4.58202i	−0.526372	+	0.191584i
$573$	−0.170245	+	0.965505i	−0.00711207	+	0.0403346i
$574$	−16.3614	+	13.7289i	−0.682913	+	0.573032i
$575$	5.20961	+	4.37138i	0.217256	+	0.182299i
$576$	0.173648	+	0.984808i	0.00723534	+	0.0410337i
$577$	−9.73917	−	16.8687i	−0.405447	−	0.702255i	0.588926	−	0.808187i	$-0.299551\pi$
$577$	−9.73917	−	16.8687i	−0.405447	−	0.702255i	−0.994373	+	0.105932i	$0.966217\pi$
$578$	2.51960	−	4.36408i	0.104802	−	0.181522i
$579$	9.06418	+	3.29909i	0.376694	+	0.137106i
$580$	−2.53209	−	0.921605i	−0.105139	−	0.0382676i
$581$	13.5125	−	23.4043i	0.560592	−	0.970975i
$582$	0.652704	+	1.13052i	0.0270554	+	0.0468614i
$583$	−1.42127	−	8.06045i	−0.0588632	−	0.333830i
$584$	−3.69459	−	3.10013i	−0.152883	−	0.128284i
$585$	−5.46064	+	4.58202i	−0.225770	+	0.189443i
$586$	4.50996	−	25.5773i	0.186305	−	1.05659i
$587$	27.8307	−	10.1295i	1.14870	−	0.418091i	0.303649	−	0.952784i	$-0.401795\pi$
$587$	27.8307	−	10.1295i	1.14870	−	0.418091i	0.845046	+	0.534693i	$0.179573\pi$
$588$	−3.82976			−0.157936
$589$	−1.57903	−	19.3474i	−0.0650628	−	0.797197i
$590$	−7.36959			−0.303401
$591$	21.3751	−	7.77990i	0.879254	−	0.320022i
$592$	0.301537	−	1.71010i	0.0123931	−	0.0702847i
$593$	−14.4875	+	12.1565i	−0.594931	+	0.499206i	−0.889812	−	0.456328i	$-0.849164\pi$
$593$	−14.4875	+	12.1565i	−0.594931	+	0.499206i	0.294881	+	0.955534i	$0.404720\pi$
$594$	1.43969	+	1.20805i	0.0590713	+	0.0495667i
$595$	−2.68273	−	15.2145i	−0.109981	−	0.623735i
$596$	−9.58172	−	16.5960i	−0.392482	−	0.679800i
$597$	9.41921	−	16.3146i	0.385503	−	0.667710i
$598$	45.5540	+	16.5803i	1.86284	+	0.678018i
$599$	−6.73143	−	2.45004i	−0.275039	−	0.100106i	0.200818	−	0.979628i	$-0.435640\pi$
$599$	−6.73143	−	2.45004i	−0.275039	−	0.100106i	−0.475857	+	0.879523i	$0.657862\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	6.23736	+	10.8034i	0.254427	+	0.440681i	0.964740	−	0.263206i	$-0.0847797\pi$
$601$	6.23736	+	10.8034i	0.254427	+	0.440681i	−0.710313	+	0.703886i	$0.751446\pi$
$602$	−4.90404	−	27.8122i	−0.199874	−	1.13354i
$603$	7.29086	+	6.11776i	0.296907	+	0.249134i
$604$	−3.59627	+	3.01763i	−0.146330	+	0.122785i
$605$	1.29679	−	7.35446i	0.0527220	−	0.299001i
$606$	−1.10607	+	0.402575i	−0.0449309	+	0.0163535i
$607$	30.9469			1.25609			0.628047	−	0.778175i	$-0.283854\pi$
$607$	30.9469			1.25609			0.628047	+	0.778175i	$0.283854\pi$
$608$	−1.15270	+	4.20372i	−0.0467483	+	0.170483i
$609$	−8.86753			−0.359330
$610$	2.00000	−	0.727940i	0.0809776	−	0.0294734i
$611$	4.17096	−	23.6547i	0.168739	−	0.956966i
$612$	−3.59627	+	3.01763i	−0.145370	+	0.121980i
$613$	−4.30722	−	3.61419i	−0.173967	−	0.145976i	0.551647	−	0.834078i	$-0.314000\pi$
$613$	−4.30722	−	3.61419i	−0.173967	−	0.145976i	−0.725614	+	0.688102i	$0.758444\pi$
$614$	−3.90941	−	22.1714i	−0.157771	−	0.894765i
$615$	3.24510	+	5.62068i	0.130855	+	0.226648i
$616$	−3.09240	+	5.35619i	−0.124596	+	0.215807i
$617$	−12.7297	−	4.63322i	−0.512477	−	0.186527i	0.0728202	−	0.997345i	$-0.476800\pi$
$617$	−12.7297	−	4.63322i	−0.512477	−	0.186527i	−0.585298	+	0.810819i	$0.699022\pi$
$618$	13.0633	+	4.75465i	0.525483	+	0.191260i
$619$	−23.8876	+	41.3745i	−0.960123	+	1.66298i	−0.237941	+	0.971280i	$0.576473\pi$
$619$	−23.8876	+	41.3745i	−0.960123	+	1.66298i	−0.722182	+	0.691703i	$0.756861\pi$
$620$	−2.22668	−	3.85673i	−0.0894257	−	0.154890i
$621$	−1.18092	−	6.69734i	−0.0473888	−	0.268755i
$622$	−10.4311	−	8.75271i	−0.418248	−	0.350952i
$623$	35.5606	−	29.8389i	1.42471	−	1.19547i
$624$	−1.23783	+	7.02006i	−0.0495527	+	0.281027i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	17.8479			0.713347
$627$	3.41875	+	7.44459i	0.136532	+	0.297308i
$628$	11.1702			0.445741
$629$	7.66044	−	2.78817i	0.305442	−	0.111172i
$630$	−0.571452	+	3.24086i	−0.0227672	+	0.129119i
$631$	−12.3131	+	10.3320i	−0.490179	+	0.411309i	−0.854090	−	0.520125i	$-0.825885\pi$
$631$	−12.3131	+	10.3320i	−0.490179	+	0.411309i	0.363912	+	0.931433i	$0.381441\pi$
$632$	−9.88713	−	8.29628i	−0.393289	−	0.330008i
$633$	2.87299	+	16.2935i	0.114191	+	0.647610i
$634$	−10.8464	−	18.7865i	−0.430766	−	0.746109i
$635$	6.03849	−	10.4590i	0.239630	−	0.415051i
$636$	−4.09240	−	1.48951i	−0.162274	−	0.0590629i
$637$	−25.6535	−	9.33710i	−1.01643	−	0.369949i
$638$	−2.53209	+	4.38571i	−0.100246	+	0.173632i
$639$	2.46791	+	4.27455i	0.0976291	+	0.169098i
$640$	0.173648	+	0.984808i	0.00686405	+	0.0389279i
$641$	−24.0501	−	20.1804i	−0.949922	−	0.797079i	0.0293627	−	0.999569i	$-0.490652\pi$
$641$	−24.0501	−	20.1804i	−0.949922	−	0.797079i	−0.979284	+	0.202490i	$0.935097\pi$
$642$	5.19253	−	4.35705i	0.204933	−	0.171959i
$643$	3.50805	−	19.8951i	0.138344	−	0.784587i	−0.834129	−	0.551570i	$-0.814029\pi$
$643$	3.50805	−	19.8951i	0.138344	−	0.784587i	0.972473	−	0.233017i	$-0.0748598\pi$
$644$	21.0303	−	7.65442i	0.828711	−	0.301626i
$645$	−8.58172			−0.337905
$646$	−19.7965	+	5.18091i	−0.778884	+	0.203840i
$647$	−2.16426			−0.0850858			−0.0425429	−	0.999095i	$-0.513546\pi$
$647$	−2.16426			−0.0850858			−0.0425429	+	0.999095i	$0.513546\pi$
$648$	0.939693	−	0.342020i	0.0369146	−	0.0134358i
$649$	−2.40508	+	13.6399i	−0.0944076	+	0.535412i
$650$	−5.46064	+	4.58202i	−0.214184	+	0.179722i
$651$	−11.2267	−	9.42030i	−0.440008	−	0.369211i
$652$	2.93582	+	16.6499i	0.114976	+	0.652059i
$653$	18.0346	+	31.2369i	0.705749	+	1.22239i	0.966421	+	0.256966i	$0.0827227\pi$
$653$	18.0346	+	31.2369i	0.705749	+	1.22239i	−0.260672	+	0.965428i	$0.583944\pi$
$654$	−0.226682	+	0.392624i	−0.00886395	+	0.0153528i
$655$	−2.63176	−	0.957882i	−0.102831	−	0.0374275i
$656$	6.09879	+	2.21978i	0.238118	+	0.0866678i
$657$	−2.41147	+	4.17680i	−0.0940806	+	0.162952i
$658$	−5.54442	−	9.60321i	−0.216144	−	0.374372i
$659$	0.937166	+	5.31493i	0.0365068	+	0.207040i	0.997605	−	0.0691659i	$-0.0220338\pi$
$659$	0.937166	+	5.31493i	0.0365068	+	0.207040i	−0.961098	+	0.276206i	$0.910923\pi$
$660$	1.43969	+	1.20805i	0.0560400	+	0.0470231i
$661$	4.73648	−	3.97438i	0.184228	−	0.154585i	−0.546010	−	0.837779i	$-0.683854\pi$
$661$	4.73648	−	3.97438i	0.184228	−	0.154585i	0.730238	+	0.683193i	$0.239409\pi$
$662$	0.941037	−	5.33688i	0.0365744	−	0.207424i
$663$	−31.4466	+	11.4456i	−1.22128	+	0.444511i
$664$	−8.21213			−0.318693
$665$	−8.29607	+	11.7022i	−0.321708	+	0.453790i
$666$	−1.73648			−0.0672873
$667$	17.2199	−	6.26752i	0.666756	−	0.242679i
$668$	−4.28446	+	24.2984i	−0.165771	+	0.940133i
$669$	−1.59446	+	1.33791i	−0.0616452	+	0.0517265i
$670$	7.29086	+	6.11776i	0.281670	+	0.236350i
$671$	−0.694593	−	3.93923i	−0.0268145	−	0.152072i
$672$	1.64543	+	2.84997i	0.0634738	+	0.109940i
$673$	−14.1780	+	24.5570i	−0.546521	+	0.946602i	0.451988	+	0.892024i	$0.350715\pi$
$673$	−14.1780	+	24.5570i	−0.546521	+	0.946602i	−0.998509	+	0.0545786i	$0.982618\pi$
$674$	31.3482	+	11.4098i	1.20749	+	0.439490i
$675$	0.939693	+	0.342020i	0.0361688	+	0.0131644i
$676$	−18.9067	+	32.7474i	−0.727182	+	1.25952i
$677$	6.35844	+	11.0131i	0.244375	+	0.423269i	0.961956	−	0.273206i	$-0.0880840\pi$
$677$	6.35844	+	11.0131i	0.244375	+	0.423269i	−0.717581	+	0.696475i	$0.754751\pi$
$678$	1.26857	+	7.19442i	0.0487192	+	0.276300i
$679$	3.29086	+	2.76136i	0.126292	+	0.105971i
$680$	−3.59627	+	3.01763i	−0.137911	+	0.115721i
$681$	−1.91353	+	10.8522i	−0.0733268	+	0.415857i
$682$	−7.86484	+	2.86257i	−0.301160	+	0.109613i
$683$	−51.2918			−1.96263			−0.981313	−	0.192418i	$-0.938367\pi$
$683$	−51.2918			−1.96263			−0.981313	+	0.192418i	$0.938367\pi$
$684$	4.34002	+	0.405223i	0.165945	+	0.0154941i
$685$	−14.5817			−0.557139
$686$	9.80365	−	3.56824i	0.374305	−	0.136236i
$687$	4.43882	−	25.1738i	0.169351	−	0.960439i
$688$	−6.57398	+	5.51622i	−0.250631	+	0.210304i
$689$	−23.7813	−	19.9549i	−0.905995	−	0.760220i
$690$	−1.18092	−	6.69734i	−0.0449569	−	0.254963i
$691$	−17.5337	−	30.3693i	−0.667015	−	1.15530i	−0.978735	−	0.205130i	$-0.934238\pi$
$691$	−17.5337	−	30.3693i	−0.667015	−	1.15530i	0.311720	−	0.950174i	$-0.399095\pi$
$692$	7.93969	−	13.7520i	0.301822	−	0.522771i
$693$	5.81180	+	2.11532i	0.220772	+	0.0803545i
$694$	−12.7811	−	4.65193i	−0.485162	−	0.176585i
$695$	5.58647	−	9.67604i	0.211907	−	0.367033i
$696$	1.34730	+	2.33359i	0.0510691	+	0.0884543i
$697$	5.29086	+	30.0060i	0.200406	+	1.13656i
$698$	10.2003	+	8.55905i	0.386086	+	0.323965i
$699$	1.43376	−	1.20307i	0.0542299	−	0.0455043i
$700$	−0.571452	+	3.24086i	−0.0215988	+	0.122493i
$701$	22.6604	−	8.24773i	0.855873	−	0.311512i	0.123441	−	0.992352i	$-0.460607\pi$
$701$	22.6604	−	8.24773i	0.855873	−	0.311512i	0.732433	+	0.680840i	$0.238385\pi$
$702$	7.12836			0.269042
$703$	−6.84120	−	3.23882i	−0.258021	−	0.122154i
$704$	1.87939			0.0708320
$705$	−3.16637	+	1.15247i	−0.119253	+	0.0434044i
$706$	3.63041	−	20.5891i	0.136632	−	0.774881i
$707$	−2.96728	+	2.48985i	−0.111596	+	0.0936403i
$708$	5.64543	+	4.73708i	0.212168	+	0.178030i
$709$	−1.60039	−	9.07624i	−0.0601037	−	0.340865i	0.939896	−	0.341461i	$-0.110922\pi$
$709$	−1.60039	−	9.07624i	−0.0601037	−	0.340865i	−1.00000		0.000595379i	$0.999810\pi$
$710$	2.46791	+	4.27455i	0.0926191	+	0.160421i
$711$	−6.45336	+	11.1776i	−0.242020	+	0.419191i
$712$	−13.2554	−	4.82456i	−0.496766	−	0.180808i
$713$	28.4593	+	10.3584i	1.06581	+	0.387923i
$714$	−7.72462	+	13.3794i	−0.289087	+	0.500713i
$715$	6.69846	+	11.6021i	0.250508	+	0.433893i
$716$	2.82682	+	16.0317i	0.105643	+	0.599132i
$717$	14.1702	+	11.8902i	0.529197	+	0.444049i
$718$	10.1284	−	8.49870i	0.377987	−	0.317169i
$719$	3.63816	−	20.6330i	0.135680	−	0.769481i	−0.838703	−	0.544589i	$-0.816686\pi$
$719$	3.63816	−	20.6330i	0.135680	−	0.769481i	0.974384	−	0.224893i	$-0.0722031\pi$
$720$	0.939693	−	0.342020i	0.0350203	−	0.0127463i
$721$	45.7485			1.70376
$722$	16.3425	+	9.69129i	0.608207	+	0.360672i
$723$	−15.9067			−0.591578
$724$	21.7665	−	7.92236i	0.808946	−	0.294432i
$725$	−0.467911	+	2.65366i	−0.0173778	+	0.0985543i
$726$	−5.72075	+	4.80028i	−0.212317	+	0.178155i
$727$	6.56624	+	5.50973i	0.243528	+	0.204344i	0.756380	−	0.654133i	$-0.226966\pi$
$727$	6.56624	+	5.50973i	0.243528	+	0.204344i	−0.512851	+	0.858477i	$0.671411\pi$
$728$	4.07351	+	23.1020i	0.150974	+	0.856218i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−2.41147	+	4.17680i	−0.0892527	+	0.154590i
$731$	−37.8580	−	13.7792i	−1.40023	−	0.509642i
$732$	−2.00000	−	0.727940i	−0.0739221	−	0.0269055i
$733$	−25.3478	+	43.9036i	−0.936241	+	1.62162i	−0.163835	+	0.986488i	$0.552387\pi$
$733$	−25.3478	+	43.9036i	−0.936241	+	1.62162i	−0.772406	+	0.635129i	$0.780947\pi$
$734$	−10.2169	−	17.6962i	−0.377112	−	0.653177i
$735$	0.665030	+	3.77157i	0.0245300	+	0.139117i
$736$	−5.20961	−	4.37138i	−0.192029	−	0.161131i
$737$	13.7023	−	11.4976i	0.504732	−	0.423520i
$738$	1.12701	−	6.39160i	0.0414859	−	0.235278i
$739$	15.3195	−	5.57586i	0.563539	−	0.205111i	−0.0445130	−	0.999009i	$-0.514174\pi$
$739$	15.3195	−	5.57586i	0.563539	−	0.205111i	0.608052	+	0.793898i	$0.291951\pi$
$740$	−1.73648			−0.0638343
$741$	28.0835	+	13.2955i	1.03167	+	0.488423i
$742$	−14.3318			−0.526137
$743$	16.2258	−	5.90571i	0.595267	−	0.216659i	−0.0267774	−	0.999641i	$-0.508525\pi$
$743$	16.2258	−	5.90571i	0.595267	−	0.216659i	0.622044	+	0.782982i	$0.286302\pi$
$744$	−0.773318	+	4.38571i	−0.0283512	+	0.160788i
$745$	−14.6800	+	12.3180i	−0.537835	+	0.451297i
$746$	22.8195	+	19.1479i	0.835483	+	0.701053i
$747$	1.42602	+	8.08737i	0.0521754	+	0.295902i
$748$	4.41147	+	7.64090i	0.161299	+	0.279379i
$749$	11.1533	−	19.3181i	0.407534	−	0.705869i
$750$	0.939693	+	0.342020i	0.0343127	+	0.0124888i
$751$	26.0351	+	9.47599i	0.950034	+	0.345784i	0.770120	−	0.637899i	$-0.220196\pi$
$751$	26.0351	+	9.47599i	0.950034	+	0.345784i	0.179913	+	0.983682i	$0.442418\pi$
$752$	−1.68479	+	2.91815i	−0.0614381	+	0.106414i
$753$	−8.99020	−	15.5715i	−0.327621	−	0.567456i
$754$	3.33544	+	18.9162i	0.121469	+	0.688887i
$755$	3.59627	+	3.01763i	0.130882	+	0.109823i
$756$	2.52094	−	2.11532i	0.0916859	−	0.0769336i
$757$	−7.47431	+	42.3889i	−0.271658	+	1.54065i	0.477722	+	0.878511i	$0.341463\pi$
$757$	−7.47431	+	42.3889i	−0.271658	+	1.54065i	−0.749380	+	0.662140i	$0.769648\pi$
$758$	−4.65657	+	1.69485i	−0.169134	+	0.0615599i
$759$	−12.7811			−0.463923
$760$	4.34002	+	0.405223i	0.157429	+	0.0146990i
$761$	−17.5098			−0.634730			−0.317365	−	0.948304i	$-0.602798\pi$
$761$	−17.5098			−0.634730			−0.317365	+	0.948304i	$0.602798\pi$
$762$	−11.3486	+	4.13057i	−0.411118	+	0.149635i
$763$	−0.259075	+	1.46929i	−0.00937915	+	0.0531918i
$764$	0.751030	−	0.630189i	0.0271713	−	0.0227994i
$765$	3.59627	+	3.01763i	0.130023	+	0.109102i
$766$	−2.75268	−	15.6112i	−0.0994583	−	0.564056i
$767$	26.2665	+	45.4949i	0.948429	+	1.64273i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	14.6694	+	5.33921i	0.528991	+	0.192537i	0.592688	−	0.805432i	$-0.298067\pi$
$769$	14.6694	+	5.33921i	0.528991	+	0.192537i	−0.0636968	+	0.997969i	$0.520289\pi$
$770$	5.81180	+	2.11532i	0.209443	+	0.0762310i
$771$	−2.38919	+	4.13819i	−0.0860444	+	0.149033i
$772$	−4.82295	−	8.35359i	−0.173582	−	0.300652i
$773$	5.26234	+	29.8442i	0.189273	+	1.07342i	0.920341	+	0.391116i	$0.127911\pi$
$773$	5.26234	+	29.8442i	0.189273	+	1.07342i	−0.731068	+	0.682304i	$0.760978\pi$
$774$	6.57398	+	5.51622i	0.236297	+	0.198277i
$775$	−3.41147	+	2.86257i	−0.122544	+	0.102826i
$776$	0.226682	−	1.28558i	0.00813740	−	0.0461495i
$777$	−5.36989	+	1.95448i	−0.192644	+	0.0701166i
$778$	−28.7939			−1.03231
$779$	16.3614	−	23.0789i	0.586209	−	0.826887i
$780$	7.12836			0.255236
$781$	8.71688	−	3.17269i	0.311915	−	0.113528i
$782$	5.54395	−	31.4413i	0.198251	−	1.12434i
$783$	2.06418	−	1.73205i	0.0737677	−	0.0618984i
$784$	2.93376	+	2.46172i	0.104777	+	0.0879185i
$785$	−1.93969	−	11.0005i	−0.0692306	−	0.392626i
$786$	1.40033	+	2.42544i	0.0499481	+	0.0865127i
$787$	10.5672	−	18.3029i	0.376679	−	0.652427i	−0.613898	−	0.789385i	$-0.710399\pi$
$787$	10.5672	−	18.3029i	0.376679	−	0.652427i	0.990577	+	0.136958i	$0.0437327\pi$
$788$	−21.3751	−	7.77990i	−0.761457	−	0.277148i
$789$	−7.05690	−	2.56850i	−0.251232	−	0.0914411i
$790$	−6.45336	+	11.1776i	−0.229600	+	0.397679i
$791$	12.0205	+	20.8202i	0.427401	+	0.740280i
$792$	−0.326352	−	1.85083i	−0.0115964	−	0.0657665i
$793$	−11.6222	−	9.75216i	−0.412716	−	0.346310i
$794$	22.1498	−	18.5859i	0.786066	−	0.659588i
$795$	−0.756244	+	4.28887i	−0.0268212	+	0.152111i
$796$	−17.7023	+	6.44312i	−0.627443	+	0.228370i
$797$	10.5057			0.372130			0.186065	−	0.982537i	$-0.440426\pi$
$797$	10.5057			0.372130			0.186065	+	0.982537i	$0.440426\pi$
$798$	13.8772	−	3.63176i	0.491246	−	0.128563i
$799$	−15.8188			−0.559630
$800$	0.939693	−	0.342020i	0.0332232	−	0.0120922i
$801$	−2.44949	+	13.8918i	−0.0865486	+	0.490841i
$802$	−22.0455	+	18.4984i	−0.778454	+	0.653201i
$803$	6.94356	+	5.82634i	0.245033	+	0.205607i
$804$	−1.65270	−	9.37295i	−0.0582864	−	0.330558i
$805$	−11.1900	−	19.3817i	−0.394396	−	0.683114i
$806$	−15.8726	+	27.4921i	−0.559088	+	0.968368i
$807$	−28.4320	−	10.3484i	−1.00085	−	0.364281i
$808$	1.10607	+	0.402575i	0.0389113	+	0.0141626i
$809$	−0.726682	+	1.25865i	−0.0255488	+	0.0442518i	−0.878517	−	0.477711i	$-0.841467\pi$
$809$	−0.726682	+	1.25865i	−0.0255488	+	0.0442518i	0.852968	+	0.521963i	$0.174800\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	7.36025	+	41.7421i	0.258453	+	1.46576i	0.787050	+	0.616889i	$0.211607\pi$
$811$	7.36025	+	41.7421i	0.258453	+	1.46576i	−0.528597	+	0.848873i	$0.677282\pi$
$812$	6.79292	+	5.69994i	0.238385	+	0.200029i
$813$	−16.0378	+	13.4573i	−0.562469	+	0.471968i
$814$	−0.566704	+	3.21394i	−0.0198630	+	0.112648i
$815$	15.8871	−	5.78244i	0.556502	−	0.202550i
$816$	4.69459			0.164344
$817$	15.6108	+	33.9937i	0.546153	+	1.18929i
$818$	15.6604			0.547555
$819$	22.0437	−	8.02325i	0.770269	−	0.280355i
$820$	1.12701	−	6.39160i	0.0393569	−	0.223204i
$821$	22.0455	−	18.4984i	0.769394	−	0.645598i	−0.171160	−	0.985243i	$-0.554751\pi$
$821$	22.0455	−	18.4984i	0.769394	−	0.645598i	0.940554	+	0.339645i	$0.110307\pi$
$822$	11.1702	+	9.37295i	0.389607	+	0.326919i
$823$	3.63253	+	20.6011i	0.126622	+	0.718109i	0.980331	+	0.197359i	$0.0632366\pi$
$823$	3.63253	+	20.6011i	0.126622	+	0.718109i	−0.853709	+	0.520750i	$0.825652\pi$
$824$	−6.95084	−	12.0392i	−0.242144	−	0.419406i
$825$	0.939693	−	1.62760i	0.0327159	−	0.0566656i
$826$	22.7897	+	8.29476i	0.792954	+	0.288612i
$827$	−3.48070	−	1.26687i	−0.121036	−	0.0440535i	0.280792	−	0.959769i	$-0.409403\pi$
$827$	−3.48070	−	1.26687i	−0.121036	−	0.0440535i	−0.401828	+	0.915715i	$0.631625\pi$
$828$	−3.40033	+	5.88954i	−0.118170	+	0.204676i
$829$	−2.59627	−	4.49687i	−0.0901721	−	0.156183i	0.817411	−	0.576054i	$-0.195408\pi$
$829$	−2.59627	−	4.49687i	−0.0901721	−	0.156183i	−0.907583	+	0.419872i	$0.862075\pi$
$830$	1.42602	+	8.08737i	0.0494979	+	0.280717i
$831$	1.46064	+	1.22562i	0.0506689	+	0.0425163i
$832$	5.46064	−	4.58202i	0.189314	−	0.158853i
$833$	−3.12205	+	17.7060i	−0.108172	+	0.613476i
$834$	−10.4991	+	3.82137i	−0.363555	+	0.132323i
$835$	24.6732			0.853853
$836$	2.16637	−	7.90041i	0.0749256	−	0.273241i
$837$	4.45336			0.153931
$838$	0.708263	−	0.257787i	0.0244665	−	0.00890510i
$839$	−4.23679	+	24.0280i	−0.146270	+	0.829539i	0.820068	+	0.572265i	$0.193935\pi$
$839$	−4.23679	+	24.0280i	−0.146270	+	0.829539i	−0.966339	+	0.257274i	$0.917176\pi$
$840$	2.52094	−	2.11532i	0.0869808	−	0.0729856i
$841$	−16.6532	−	13.9737i	−0.574247	−	0.481851i
$842$	0.522593	+	2.96377i	0.0180098	+	0.102138i
$843$	−11.7934	−	20.4267i	−0.406186	−	0.703534i
$844$	8.27244	−	14.3283i	0.284749	−	0.493200i
$845$	35.5330	+	12.9330i	1.22237	+	0.444907i
$846$	3.16637	+	1.15247i	0.108862	+	0.0396226i
$847$	−12.2879	+	21.2833i	−0.422218	+	0.731303i
$848$	2.17752	+	3.77157i	0.0747763	+	0.129516i
$849$	2.68004	+	15.1993i	0.0919789	+	0.521638i
$850$	3.59627	+	3.01763i	0.123351	+	0.103504i
$851$	9.04639	−	7.59082i	0.310106	−	0.260210i
$852$	0.857097	−	4.86084i	0.0293636	−	0.166529i
$853$	−22.6771	+	8.25379i	−0.776449	+	0.282604i	−0.699691	−	0.714445i	$-0.746679\pi$
$853$	−22.6771	+	8.25379i	−0.776449	+	0.282604i	−0.0767581	+	0.997050i	$0.524457\pi$
$854$	−7.00412			−0.239676
$855$	−0.354570	−	4.34445i	−0.0121260	−	0.148577i
$856$	−6.77837			−0.231680
$857$	5.15745	−	1.87716i	0.176175	−	0.0641225i	−0.252427	−	0.967616i	$-0.581229\pi$
$857$	5.15745	−	1.87716i	0.176175	−	0.0641225i	0.428602	+	0.903494i	$0.359006\pi$
$858$	2.32635	−	13.1934i	0.0794203	−	0.450415i
$859$	22.0763	−	18.5242i	0.753232	−	0.632037i	−0.183123	−	0.983090i	$-0.558621\pi$
$859$	22.0763	−	18.5242i	0.753232	−	0.632037i	0.936356	+	0.351053i	$0.114176\pi$
$860$	6.57398	+	5.51622i	0.224171	+	0.188102i
$861$	−3.70884	−	21.0339i	−0.126397	−	0.716832i
$862$	−13.4757	−	23.3405i	−0.458983	−	0.794981i
$863$	−7.42989	+	12.8690i	−0.252916	+	0.438064i	−0.964328	−	0.264712i	$-0.914723\pi$
$863$	−7.42989	+	12.8690i	−0.252916	+	0.438064i	0.711411	+	0.702776i	$0.248056\pi$
$864$	−0.939693	−	0.342020i	−0.0319690	−	0.0116358i
$865$	−14.9217	−	5.43107i	−0.507354	−	0.184662i
$866$	4.59627	−	7.96097i	0.156187	−	0.270525i
$867$	2.51960	+	4.36408i	0.0855701	+	0.148212i
$868$	2.54488	+	14.4327i	0.0863789	+	0.489879i
$869$	18.5817	+	15.5919i	0.630342	+	0.528919i
$870$	2.06418	−	1.73205i	0.0699822	−	0.0587220i
$871$	11.7811	−	66.8137i	0.399186	−	2.26390i
$872$	0.426022	−	0.155059i	0.0144269	−	0.00525097i
$873$	−1.30541			−0.0441813
$874$	−24.3812	+	16.8608i	−0.824706	+	0.570326i
$875$	3.29086			0.111251
$876$	4.53209	−	1.64955i	0.153125	−	0.0557330i
$877$	3.77316	−	21.3986i	0.127410	−	0.722580i	−0.852437	−	0.522831i	$-0.824876\pi$
$877$	3.77316	−	21.3986i	0.127410	−	0.722580i	0.979847	−	0.199750i	$-0.0640129\pi$
$878$	−0.369585	+	0.310119i	−0.0124729	+	0.0104660i
$879$	19.8956	+	16.6944i	0.671061	+	0.563087i
$880$	−0.326352	−	1.85083i	−0.0110013	−	0.0623916i
$881$	21.9508	+	38.0200i	0.739542	+	1.28093i	0.952701	+	0.303908i	$0.0982914\pi$
$881$	21.9508	+	38.0200i	0.739542	+	1.28093i	−0.213159	+	0.977018i	$0.568375\pi$
$882$	1.91488	−	3.31667i	0.0644773	−	0.111678i
$883$	−23.8307	−	8.67366i	−0.801967	−	0.291892i	−0.0916654	−	0.995790i	$-0.529219\pi$
$883$	−23.8307	−	8.67366i	−0.801967	−	0.291892i	−0.710301	+	0.703898i	$0.751441\pi$
$884$	31.4466	+	11.4456i	1.05766	+	0.384958i
$885$	3.68479	−	6.38225i	0.123863	−	0.214537i
$886$	16.5398	+	28.6478i	0.555666	+	0.962443i
$887$	−5.59792	−	31.7474i	−0.187960	−	1.06597i	−0.922093	−	0.386967i	$-0.873523\pi$
$887$	−5.59792	−	31.7474i	−0.187960	−	1.06597i	0.734134	−	0.679005i	$-0.237588\pi$
$888$	1.33022	+	1.11619i	0.0446393	+	0.0374568i
$889$	−30.4454	+	25.5467i	−1.02111	+	0.856809i
$890$	−2.44949	+	13.8918i	−0.0821072	+	0.465653i
$891$	−1.76604	+	0.642788i	−0.0591647	+	0.0215342i
$892$	2.08141			0.0696909
$893$	10.3250	+	10.4462i	0.345513	+	0.349567i
$894$	19.1634			0.640921
$895$	15.2973	−	5.56775i	0.511331	−	0.186109i
$896$	0.571452	−	3.24086i	0.0190909	−	0.108270i
$897$	−37.1359	+	31.1607i	−1.23993	+	1.04043i
$898$	5.28493	+	4.43458i	0.176360	+	0.147984i
$899$	2.08378	+	11.8177i	0.0694979	+	0.394142i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−10.2226	+	17.7060i	−0.340563	+	0.589872i
$902$	−11.4620	−	4.17182i	−0.381642	−	0.138906i
$903$	26.5381	+	9.65907i	0.883132	+	0.321434i
$904$	3.65270	−	6.32667i	0.121487	−	0.210422i
$905$	−11.5817	−	20.0601i	−0.384989	−	0.666821i
$906$	−0.815207	−	4.62327i	−0.0270835	−	0.153598i
$907$	−45.3233	−	38.0307i	−1.50493	−	1.26279i	−0.872952	−	0.487807i	$-0.837797\pi$
$907$	−45.3233	−	38.0307i	−1.50493	−	1.26279i	−0.631982	−	0.774983i	$-0.717758\pi$
$908$	8.44150	−	7.08326i	0.280141	−	0.235066i
$909$	0.204393	−	1.15917i	0.00677928	−	0.0384472i
$910$	22.0437	−	8.02325i	0.730742	−	0.265968i
$911$	24.5972			0.814942			0.407471	−	0.913218i	$-0.366411\pi$
$911$	24.5972			0.814942			0.407471	+	0.913218i	$0.366411\pi$
$912$	−3.06418	−	3.10013i	−0.101465	−	0.102656i
$913$	15.4338			0.510783
$914$	−27.1411	+	9.87857i	−0.897749	+	0.326754i
$915$	−0.369585	+	2.09602i	−0.0122181	+	0.0692923i
$916$	−19.5817	+	16.4310i	−0.646998	+	0.542896i
$917$	7.06031	+	5.92430i	0.233152	+	0.195638i
$918$	−0.815207	−	4.62327i	−0.0269059	−	0.152591i
$919$	6.81790	+	11.8089i	0.224902	+	0.389541i	0.956290	−	0.292420i	$-0.0944606\pi$
$919$	6.81790	+	11.8089i	0.224902	+	0.389541i	−0.731388	+	0.681961i	$0.761127\pi$
$920$	−3.40033	+	5.88954i	−0.112106	+	0.194173i
$921$	21.1557	+	7.70004i	0.697104	+	0.253725i
$922$	−12.9162	−	4.70112i	−0.425373	−	0.154823i
$923$	17.5921	−	30.4705i	0.579053	−	1.00295i
$924$	−3.09240	−	5.35619i	−0.101732	−	0.176206i
$925$	0.301537	+	1.71010i	0.00991447	+	0.0562278i
$926$	0.277189	+	0.232589i	0.00910899	+	0.00764335i
$927$	−10.6493	+	8.93582i	−0.349769	+	0.293491i
$928$	0.467911	−	2.65366i	0.0153599	−	0.0871105i
$929$	−9.63903	+	3.50832i	−0.316246	+	0.115104i	−0.495266	−	0.868741i	$-0.664930\pi$
$929$	−9.63903	+	3.50832i	−0.316246	+	0.115104i	0.179020	+	0.983845i	$0.442707\pi$
$930$	4.45336			0.146032
$931$	13.7301	−	9.49509i	0.449987	−	0.311189i
$932$	−1.87164			−0.0613078
$933$	12.7956	−	4.65722i	0.418909	−	0.152471i
$934$	−3.06149	+	17.3626i	−0.100175	+	0.568121i
$935$	6.75877	−	5.67128i	0.221035	−	0.185471i
$936$	−5.46064	−	4.58202i	−0.178487	−	0.149768i
$937$	−1.71925	−	9.75033i	−0.0561653	−	0.318529i	0.943762	−	0.330627i	$-0.107260\pi$
$937$	−1.71925	−	9.75033i	−0.0561653	−	0.318529i	−0.999927	+	0.0120977i	$0.996149\pi$
$938$	−15.6604	−	27.1247i	−0.511332	−	0.885652i
$939$	−8.92396	+	15.4568i	−0.291223	+	0.504412i
$940$	3.16637	+	1.15247i	0.103276	+	0.0375893i
$941$	11.1284	+	4.05039i	0.362774	+	0.132039i	0.516975	−	0.856001i	$-0.327058\pi$
$941$	11.1284	+	4.05039i	0.362774	+	0.132039i	−0.154201	+	0.988040i	$0.549280\pi$
$942$	−5.58512	+	9.67372i	−0.181973	+	0.315187i
$943$	22.0688	+	38.2243i	0.718660	+	1.24476i
$944$	−1.27972	−	7.25762i	−0.0416512	−	0.236216i
$945$	−2.52094	−	2.11532i	−0.0820063	−	0.0688115i
$946$	12.3550	−	10.3671i	0.401697	−	0.337064i
$947$	−9.02910	+	51.2065i	−0.293406	+	1.66399i	0.380204	+	0.924903i	$0.375854\pi$
$947$	−9.02910	+	51.2065i	−0.293406	+	1.66399i	−0.673610	+	0.739087i	$0.735257\pi$
$948$	12.1284	−	4.41436i	0.393911	−	0.143372i
$949$	34.3797			1.11601
$950$	−0.354570	−	4.34445i	−0.0115038	−	0.140953i
$951$	21.6928			0.703438
$952$	14.5175	−	5.28395i	0.470516	−	0.171254i
$953$	4.22844	−	23.9807i	0.136972	−	0.776810i	−0.836493	−	0.547977i	$-0.815398\pi$
$953$	4.22844	−	23.9807i	0.136972	−	0.776810i	0.973466	−	0.228832i	$-0.0734908\pi$
$954$	3.33615	−	2.79936i	0.108012	−	0.0906328i
$955$	−0.751030	−	0.630189i	−0.0243028	−	0.0203924i
$956$	−3.21213	−	18.2169i	−0.103888	−	0.589177i
$957$	−2.53209	−	4.38571i	−0.0818508	−	0.141770i
$958$	−9.00000	+	15.5885i	−0.290777	+	0.503640i
$959$	45.0925	+	16.4123i	1.45611	+	0.529981i
$960$	−0.939693	−	0.342020i	−0.0303284	−	0.0110387i
$961$	5.58378	−	9.67139i	0.180122	−	0.311980i
$962$	6.18913	+	10.7199i	0.199546	+	0.345623i
$963$	1.17705	+	6.67539i	0.0379300	+	0.215112i
$964$	12.1853	+	10.2246i	0.392461	+	0.329314i
$965$	−7.38919	+	6.20026i	−0.237866	+	0.199594i
$966$	−3.88625	+	22.0400i	−0.125038	+	0.709126i
$967$	33.0797	−	12.0400i	1.06377	−	0.387181i	0.249927	−	0.968265i	$-0.419593\pi$
$967$	33.0797	−	12.0400i	1.06377	−	0.387181i	0.813844	+	0.581084i	$0.197371\pi$
$968$	7.46791			0.240028
$969$	5.41147	−	19.7348i	0.173842	−	0.633972i
$970$	−1.30541			−0.0419141
$971$	−25.0903	+	9.13214i	−0.805187	+	0.293064i	−0.711634	−	0.702550i	$-0.752045\pi$
$971$	−25.0903	+	9.13214i	−0.805187	+	0.293064i	−0.0935530	+	0.995614i	$0.529822\pi$
$972$	−0.173648	+	0.984808i	−0.00556977	+	0.0315877i
$973$	−28.1663	+	23.6344i	−0.902972	+	0.757683i
$974$	−29.2087	−	24.5090i	−0.935908	−	0.785320i
$975$	−1.23783	−	7.02006i	−0.0396422	−	0.224822i
$976$	1.06418	+	1.84321i	0.0340635	+	0.0589997i
$977$	7.98814	−	13.8359i	0.255563	−	0.442649i	−0.709485	−	0.704720i	$-0.751072\pi$
$977$	7.98814	−	13.8359i	0.255563	−	0.442649i	0.965048	+	0.262072i	$0.0844058\pi$
$978$	−15.8871	−	5.78244i	−0.508014	−	0.184902i
$979$	24.9119	+	9.06720i	0.796189	+	0.289789i
$980$	1.91488	−	3.31667i	0.0611685	−	0.105947i
$981$	−0.226682	−	0.392624i	−0.00723739	−	0.0125355i
$982$	3.68123	+	20.8773i	0.117473	+	0.666221i
$983$	9.46632	+	7.94318i	0.301929	+	0.253348i	0.781147	−	0.624348i	$-0.214635\pi$
$983$	9.46632	+	7.94318i	0.301929	+	0.253348i	−0.479218	+	0.877696i	$0.659080\pi$
$984$	−4.97178	+	4.17182i	−0.158495	+	0.132993i
$985$	−3.94996	+	22.4013i	−0.125856	+	0.713766i
$986$	11.8871	−	4.32656i	0.378563	−	0.137786i
$987$	11.0888			0.352961
$988$	−12.9670	−	28.2367i	−0.412536	−	0.898329i
$989$	−58.3613			−1.85578
$990$	−1.76604	+	0.642788i	−0.0561286	+	0.0204291i
$991$	2.26682	−	12.8558i	0.0720078	−	0.408376i	−0.927403	−	0.374063i	$-0.877964\pi$
$991$	2.26682	−	12.8558i	0.0720078	−	0.408376i	0.999411	−	0.0343135i	$-0.0109245\pi$
$992$	3.41147	−	2.86257i	0.108314	−	0.0908866i
$993$	4.15136	+	3.48340i	0.131739	+	0.110542i
$994$	−2.82058	−	15.9963i	−0.0894635	−	0.507373i
$995$	9.41921	+	16.3146i	0.298609	+	0.517206i
$996$	4.10607	−	7.11192i	0.130106	−	0.225350i
$997$	−40.9654	−	14.9102i	−1.29739	−	0.472211i	−0.401243	−	0.915972i	$-0.631422\pi$
$997$	−40.9654	−	14.9102i	−1.29739	−	0.472211i	−0.896145	+	0.443761i	$0.853644\pi$
$998$	−37.6724	−	13.7116i	−1.19250	−	0.434034i
$999$	0.868241	−	1.50384i	0.0274699	−	0.0475793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.a.271.1	yes	6
19.4	even	9	inner	570.2.u.a.61.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.a.61.1	✓	6	19.4	even	9	inner
570.2.u.a.271.1	yes	6	1.1	even	1	trivial

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.64543 + 2.84997i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.64543 + 2.84997i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-0.939693 - 0.342020i) q^{10} +(-0.939693 + 1.62760i) q^{11} +(0.500000 + 0.866025i) q^{12} +(1.23783 + 7.02006i) q^{13} +(2.52094 + 2.11532i) q^{14} +(0.766044 - 0.642788i) q^{15} +(0.173648 - 0.984808i) q^{16} +(4.41147 - 1.60565i) q^{17} -1.00000 q^{18} +(-3.93969 - 1.86516i) q^{19} -1.00000 q^{20} +(-3.09240 + 1.12554i) q^{21} +(-0.326352 + 1.85083i) q^{22} +(5.20961 - 4.37138i) q^{23} +(0.766044 + 0.642788i) q^{24} +(0.173648 + 0.984808i) q^{25} +(3.56418 + 6.17334i) q^{26} +(0.500000 - 0.866025i) q^{27} +(3.09240 + 1.12554i) q^{28} +(2.53209 + 0.921605i) q^{29} +(0.500000 - 0.866025i) q^{30} +(2.22668 + 3.85673i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.43969 - 1.20805i) q^{33} +(3.59627 - 3.01763i) q^{34} +(0.571452 - 3.24086i) q^{35} +(-0.939693 + 0.342020i) q^{36} +1.73648 q^{37} +(-4.34002 - 0.405223i) q^{38} -7.12836 q^{39} +(-0.939693 + 0.342020i) q^{40} +(-1.12701 + 6.39160i) q^{41} +(-2.52094 + 2.11532i) q^{42} +(-6.57398 - 5.51622i) q^{43} +(0.326352 + 1.85083i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.40033 - 5.88954i) q^{46} +(-3.16637 - 1.15247i) q^{47} +(0.939693 + 0.342020i) q^{48} +(-1.91488 + 3.31667i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.815207 + 4.62327i) q^{51} +(5.46064 + 4.58202i) q^{52} +(-3.33615 + 2.79936i) q^{53} +(0.173648 - 0.984808i) q^{54} +(1.76604 - 0.642788i) q^{55} +3.29086 q^{56} +(2.52094 - 3.55596i) q^{57} +2.69459 q^{58} +(6.92514 - 2.52055i) q^{59} +(0.173648 - 0.984808i) q^{60} +(-1.63041 + 1.36808i) q^{61} +(3.41147 + 2.86257i) q^{62} +(-0.571452 - 3.24086i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.56418 - 6.17334i) q^{65} +(-1.76604 - 0.642788i) q^{66} +(-8.94356 - 3.25519i) q^{67} +(2.34730 - 4.06564i) q^{68} +(3.40033 + 5.88954i) q^{69} +(-0.571452 - 3.24086i) q^{70} +(-3.78106 - 3.17269i) q^{71} +(-0.766044 + 0.642788i) q^{72} +(0.837496 - 4.74968i) q^{73} +(1.63176 - 0.593912i) q^{74} -1.00000 q^{75} +(-4.21688 + 1.10359i) q^{76} -6.18479 q^{77} +(-6.69846 + 2.43804i) q^{78} +(2.24123 - 12.7106i) q^{79} +(-0.766044 + 0.642788i) q^{80} +(0.766044 + 0.642788i) q^{81} +(1.12701 + 6.39160i) q^{82} +(-4.10607 - 7.11192i) q^{83} +(-1.64543 + 2.84997i) q^{84} +(-4.41147 - 1.60565i) q^{85} +(-8.06418 - 2.93512i) q^{86} +(-1.34730 + 2.33359i) q^{87} +(0.939693 + 1.62760i) q^{88} +(-2.44949 - 13.8918i) q^{89} +(0.766044 + 0.642788i) q^{90} +(-17.9702 + 15.0788i) q^{91} +(1.18092 - 6.69734i) q^{92} +(-4.18479 + 1.52314i) q^{93} -3.36959 q^{94} +(1.81908 + 3.96118i) q^{95} +1.00000 q^{96} +(1.22668 - 0.446476i) q^{97} +(-0.665030 + 3.77157i) q^{98} +(1.43969 - 1.20805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 6 * q^7 + 3 * q^8	\( 6 q - 6 q^{7} + 3 q^{8} + 3 q^{12} - 12 q^{13} + 12 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 15 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 3 q^{27} + 15 q^{28} + 6 q^{29} + 3 q^{30} - 3 q^{33} - 6 q^{34} + 3 q^{35} - 6 q^{38} - 6 q^{39} + 21 q^{41} - 12 q^{42} - 24 q^{43} + 3 q^{44} + 3 q^{45} + 6 q^{46} - 33 q^{49} + 3 q^{50} + 12 q^{51} + 24 q^{52} - 24 q^{53} + 6 q^{55} - 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{61} - 3 q^{63} - 3 q^{64} + 3 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 12 q^{71} + 15 q^{74} - 6 q^{75} - 9 q^{76} - 30 q^{77} - 12 q^{78} + 36 q^{79} - 21 q^{82} + 6 q^{84} - 6 q^{85} - 30 q^{86} - 6 q^{87} - 12 q^{89} + 24 q^{91} + 24 q^{92} - 18 q^{93} - 6 q^{94} - 6 q^{95} + 6 q^{96} - 6 q^{97} + 6 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^7 + 3 * q^8 + 3 * q^12 - 12 * q^13 + 12 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 15 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 3 * q^27 + 15 * q^28 + 6 * q^29 + 3 * q^30 - 3 * q^33 - 6 * q^34 + 3 * q^35 - 6 * q^38 - 6 * q^39 + 21 * q^41 - 12 * q^42 - 24 * q^43 + 3 * q^44 + 3 * q^45 + 6 * q^46 - 33 * q^49 + 3 * q^50 + 12 * q^51 + 24 * q^52 - 24 * q^53 + 6 * q^55 - 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^61 - 3 * q^63 - 3 * q^64 + 3 * q^65 - 6 * q^66 - 24 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 12 * q^71 + 15 * q^74 - 6 * q^75 - 9 * q^76 - 30 * q^77 - 12 * q^78 + 36 * q^79 - 21 * q^82 + 6 * q^84 - 6 * q^85 - 30 * q^86 - 6 * q^87 - 12 * q^89 + 24 * q^91 + 24 * q^92 - 18 * q^93 - 6 * q^94 - 6 * q^95 + 6 * q^96 - 6 * q^97 + 6 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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