LMFDB - Embedded newform 570.2.s.b.221.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.10
Character	$\chi$	$=$	570.221
Dual form			570.2.s.b.521.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.32792 - 1.11204i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62701 + 0.593994i) q^{6} -0.387589 q^{7} -1.00000 q^{8} +(0.526745 - 2.95339i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.32792 - 1.11204i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62701 + 0.593994i) q^{6} -0.387589 q^{7} -1.00000 q^{8} +(0.526745 - 2.95339i) q^{9} +(0.866025 + 0.500000i) q^{10} -6.28666i q^{11} +(0.299093 + 1.70603i) q^{12} +(5.96278 + 3.44261i) q^{13} +(-0.193795 - 0.335662i) q^{14} +(0.593994 - 1.62701i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.63331 + 2.67504i) q^{17} +(2.82109 - 1.02052i) q^{18} +(0.936449 - 4.25712i) q^{19} +1.00000i q^{20} +(-0.514688 + 0.431014i) q^{21} +(5.44441 - 3.14333i) q^{22} +(5.57852 + 3.22076i) q^{23} +(-1.32792 + 1.11204i) q^{24} +(0.500000 - 0.866025i) q^{25} +6.88523i q^{26} +(-2.58481 - 4.50763i) q^{27} +(0.193795 - 0.335662i) q^{28} +(-2.15245 + 3.72815i) q^{29} +(1.70603 - 0.299093i) q^{30} +5.87016i q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.99100 - 8.34818i) q^{33} +(-4.63331 - 2.67504i) q^{34} +(-0.335662 + 0.193795i) q^{35} +(2.29434 + 1.93287i) q^{36} +2.54580i q^{37} +(4.15500 - 1.31757i) q^{38} +(11.7464 - 2.05932i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.40194 + 2.42823i) q^{41} +(-0.630613 - 0.230226i) q^{42} +(-0.588721 - 1.01969i) q^{43} +(5.44441 + 3.14333i) q^{44} +(-1.02052 - 2.82109i) q^{45} +6.44153i q^{46} +(-6.74336 - 3.89328i) q^{47} +(-1.62701 - 0.593994i) q^{48} -6.84977 q^{49} +1.00000 q^{50} +(-3.17792 + 8.70465i) q^{51} +(-5.96278 + 3.44261i) q^{52} +(1.97481 - 3.42047i) q^{53} +(2.61132 - 4.49233i) q^{54} +(-3.14333 - 5.44441i) q^{55} +0.387589 q^{56} +(-3.49055 - 6.69448i) q^{57} -4.30489 q^{58} +(-0.556791 - 0.964390i) q^{59} +(1.11204 + 1.32792i) q^{60} +(1.28373 - 2.22348i) q^{61} +(-5.08371 + 2.93508i) q^{62} +(-0.204161 + 1.14470i) q^{63} +1.00000 q^{64} +6.88523 q^{65} +(3.73424 - 10.2285i) q^{66} +(6.95760 + 4.01697i) q^{67} -5.35008i q^{68} +(10.9894 - 1.92661i) q^{69} +(-0.335662 - 0.193795i) q^{70} +(4.17799 + 7.23648i) q^{71} +(-0.526745 + 2.95339i) q^{72} +(-0.890700 - 1.54274i) q^{73} +(-2.20473 + 1.27290i) q^{74} +(-0.299093 - 1.70603i) q^{75} +(3.21855 + 2.93955i) q^{76} +2.43664i q^{77} +(7.65663 + 9.14304i) q^{78} +(-12.3862 + 7.15117i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-8.44508 - 3.11137i) q^{81} +(-1.40194 + 2.42823i) q^{82} -3.22583i q^{83} +(-0.115925 - 0.661239i) q^{84} +(-2.67504 + 4.63331i) q^{85} +(0.588721 - 1.01969i) q^{86} +(1.28756 + 7.34428i) q^{87} +6.28666i q^{88} +(-7.49847 + 12.9877i) q^{89} +(1.93287 - 2.29434i) q^{90} +(-2.31111 - 1.33432i) q^{91} +(-5.57852 + 3.22076i) q^{92} +(6.52784 + 7.79511i) q^{93} -7.78656i q^{94} +(-1.31757 - 4.15500i) q^{95} +(-0.299093 - 1.70603i) q^{96} +(-5.33880 + 3.08236i) q^{97} +(-3.42489 - 5.93208i) q^{98} +(-18.5670 - 3.31146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.32792	−	1.11204i	0.766675	−	0.642035i
$3$	1.32792	−	1.11204i	0.766675	−	0.642035i
$4$	−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
$6$	1.62701	+	0.593994i	0.664225	+	0.242497i
$7$	−0.387589			−0.146495			−0.0732475	−	0.997314i	$-0.523336\pi$
$7$	−0.387589			−0.146495			−0.0732475	+	0.997314i	$0.523336\pi$
$8$	−1.00000			−0.353553
$9$	0.526745	−	2.95339i	0.175582	−	0.984465i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	6.28666i		−	1.89550i	−0.319015	−	0.947750i	$-0.603352\pi$
$11$		−	6.28666i		−	1.89550i	0.319015	−	0.947750i	$-0.396648\pi$
$12$	0.299093	+	1.70603i	0.0863406	+	0.492489i
$13$	5.96278	+	3.44261i	1.65378	+	0.954809i	0.975499	+	0.220006i	$0.0706076\pi$
$13$	5.96278	+	3.44261i	1.65378	+	0.954809i	0.678280	+	0.734804i	$0.262726\pi$
$14$	−0.193795	−	0.335662i	−0.0517938	−	0.0897095i
$15$	0.593994	−	1.62701i	0.153369	−	0.420093i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.63331	+	2.67504i	−1.12374	+	0.648793i	−0.942354	−	0.334619i	$-0.891393\pi$
$17$	−4.63331	+	2.67504i	−1.12374	+	0.648793i	−0.181389	+	0.983411i	$0.558059\pi$
$18$	2.82109	−	1.02052i	0.664937	−	0.240540i
$19$	0.936449	−	4.25712i	0.214836	−	0.976650i
$19$	0.936449	−	4.25712i	0.214836	−	0.976650i
$20$			1.00000i			0.223607i
$21$	−0.514688	+	0.431014i	−0.112314	+	0.0940549i
$22$	5.44441	−	3.14333i	1.16075	−	0.670160i
$23$	5.57852	+	3.22076i	1.16320	+	0.671575i	0.952069	−	0.305882i	$-0.0989513\pi$
$23$	5.57852	+	3.22076i	1.16320	+	0.671575i	0.211133	+	0.977457i	$0.432285\pi$
$24$	−1.32792	+	1.11204i	−0.271061	+	0.226994i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			6.88523i			1.35030i
$27$	−2.58481	−	4.50763i	−0.497447	−	0.867494i
$28$	0.193795	−	0.335662i	0.0366237	−	0.0634342i
$29$	−2.15245	+	3.72815i	−0.399699	+	0.692299i	−0.993689	−	0.112173i	$-0.964219\pi$
$29$	−2.15245	+	3.72815i	−0.399699	+	0.692299i	0.593989	+	0.804473i	$0.297552\pi$
$30$	1.70603	−	0.299093i	0.311477	−	0.0546066i
$31$			5.87016i			1.05431i	0.849769	+	0.527156i	$0.176742\pi$
$31$			5.87016i			1.05431i	−0.849769	+	0.527156i	$0.823258\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−6.99100	−	8.34818i	−1.21698	−	1.45323i
$34$	−4.63331	−	2.67504i	−0.794606	−	0.458766i
$35$	−0.335662	+	0.193795i	−0.0567373	+	0.0327573i
$36$	2.29434	+	1.93287i	0.382390	+	0.322145i
$37$			2.54580i			0.418527i	0.977859	+	0.209264i	$0.0671067\pi$
$37$			2.54580i			0.418527i	−0.977859	+	0.209264i	$0.932893\pi$
$38$	4.15500	−	1.31757i	0.674030	−	0.213738i
$39$	11.7464	−	2.05932i	1.88093	−	0.329755i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	1.40194	+	2.42823i	0.218946	+	0.379226i	0.954486	−	0.298256i	$-0.0964048\pi$
$41$	1.40194	+	2.42823i	0.218946	+	0.379226i	−0.735540	+	0.677481i	$0.763071\pi$
$42$	−0.630613	−	0.230226i	−0.0973057	−	0.0355246i
$43$	−0.588721	−	1.01969i	−0.0897791	−	0.155502i	0.817639	−	0.575732i	$-0.195283\pi$
$43$	−0.588721	−	1.01969i	−0.0897791	−	0.155502i	−0.907418	+	0.420230i	$0.861949\pi$
$44$	5.44441	+	3.14333i	0.820775	+	0.473875i
$45$	−1.02052	−	2.82109i	−0.152131	−	0.420543i
$46$			6.44153i			0.949751i
$47$	−6.74336	−	3.89328i	−0.983620	−	0.567893i	−0.0802589	−	0.996774i	$-0.525575\pi$
$47$	−6.74336	−	3.89328i	−0.983620	−	0.567893i	−0.903361	+	0.428881i	$0.858908\pi$
$48$	−1.62701	−	0.593994i	−0.234839	−	0.0857356i
$49$	−6.84977			−0.978539
$50$	1.00000			0.141421
$51$	−3.17792	+	8.70465i	−0.444997	+	1.21890i
$52$	−5.96278	+	3.44261i	−0.826889	+	0.477405i
$53$	1.97481	−	3.42047i	0.271261	−	0.469837i	−0.697924	−	0.716172i	$-0.745893\pi$
$53$	1.97481	−	3.42047i	0.271261	−	0.469837i	0.969185	+	0.246334i	$0.0792261\pi$
$54$	2.61132	−	4.49233i	0.355355	−	0.611328i
$55$	−3.14333	−	5.44441i	−0.423846	−	0.734124i
$56$	0.387589			0.0517938
$57$	−3.49055	−	6.69448i	−0.462334	−	0.886706i
$58$	−4.30489			−0.565260
$59$	−0.556791	−	0.964390i	−0.0724880	−	0.125553i	0.827503	−	0.561461i	$-0.189761\pi$
$59$	−0.556791	−	0.964390i	−0.0724880	−	0.125553i	−0.899991	+	0.435908i	$0.856427\pi$
$60$	1.11204	+	1.32792i	0.143563	+	0.171434i
$61$	1.28373	−	2.22348i	0.164365	−	0.284688i	−0.772065	−	0.635544i	$-0.780776\pi$
$61$	1.28373	−	2.22348i	0.164365	−	0.284688i	0.936429	+	0.350856i	$0.114109\pi$
$62$	−5.08371	+	2.93508i	−0.645632	+	0.372756i
$63$	−0.204161	+	1.14470i	−0.0257218	+	0.144219i
$64$	1.00000			0.125000
$65$	6.88523			0.854008
$66$	3.73424	−	10.2285i	0.459653	−	1.25904i
$67$	6.95760	+	4.01697i	0.850006	+	0.490751i	0.860653	−	0.509192i	$-0.170056\pi$
$67$	6.95760	+	4.01697i	0.850006	+	0.490751i	−0.0106470	+	0.999943i	$0.503389\pi$
$68$		−	5.35008i		−	0.648793i
$69$	10.9894	−	1.92661i	1.32297	−	0.231937i
$70$	−0.335662	−	0.193795i	−0.0401193	−	0.0231629i
$71$	4.17799	+	7.23648i	0.495836	+	0.858813i	0.999988	−	0.00480188i	$-0.00152849\pi$
$71$	4.17799	+	7.23648i	0.495836	+	0.858813i	−0.504153	+	0.863614i	$0.668195\pi$
$72$	−0.526745	+	2.95339i	−0.0620775	+	0.348061i
$73$	−0.890700	−	1.54274i	−0.104249	−	0.180564i	0.809182	−	0.587557i	$-0.199910\pi$
$73$	−0.890700	−	1.54274i	−0.104249	−	0.180564i	−0.913431	+	0.406994i	$0.866577\pi$
$74$	−2.20473	+	1.27290i	−0.256294	+	0.147972i
$75$	−0.299093	−	1.70603i	−0.0345362	−	0.196996i
$76$	3.21855	+	2.93955i	0.369193	+	0.337189i
$77$			2.43664i			0.277681i
$78$	7.65663	+	9.14304i	0.866943	+	1.03524i
$79$	−12.3862	+	7.15117i	−1.39355	+	0.804569i	−0.993707	−	0.112012i	$-0.964270\pi$
$79$	−12.3862	+	7.15117i	−1.39355	+	0.804569i	−0.399848	+	0.916581i	$0.630937\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−8.44508	−	3.11137i	−0.938342	−	0.345708i
$82$	−1.40194	+	2.42823i	−0.154818	+	0.268153i
$83$		−	3.22583i		−	0.354081i	−0.984204	−	0.177040i	$-0.943348\pi$
$83$		−	3.22583i		−	0.354081i	0.984204	−	0.177040i	$-0.0566523\pi$
$84$	−0.115925	−	0.661239i	−0.0126485	−	0.0721471i
$85$	−2.67504	+	4.63331i	−0.290149	+	0.502553i
$86$	0.588721	−	1.01969i	0.0634834	−	0.109956i
$87$	1.28756	+	7.34428i	0.138041	+	0.787390i
$88$			6.28666i			0.670160i
$89$	−7.49847	+	12.9877i	−0.794836	+	1.37670i	0.128107	+	0.991760i	$0.459110\pi$
$89$	−7.49847	+	12.9877i	−0.794836	+	1.37670i	−0.922943	+	0.384936i	$0.874223\pi$
$90$	1.93287	−	2.29434i	0.203743	−	0.241845i
$91$	−2.31111	−	1.33432i	−0.242270	−	0.139875i
$92$	−5.57852	+	3.22076i	−0.581601	+	0.335788i
$93$	6.52784	+	7.79511i	0.676905	+	0.808315i
$94$		−	7.78656i		−	0.803122i
$95$	−1.31757	−	4.15500i	−0.135180	−	0.426294i
$96$	−0.299093	−	1.70603i	−0.0305260	−	0.174121i
$97$	−5.33880	+	3.08236i	−0.542073	+	0.312966i	−0.745919	−	0.666037i	$-0.767989\pi$
$97$	−5.33880	+	3.08236i	−0.542073	+	0.312966i	0.203846	+	0.979003i	$0.434656\pi$
$98$	−3.42489	−	5.93208i	−0.345966	−	0.599230i
$99$	−18.5670	−	3.31146i	−1.86605	−	0.332815i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.63539	−	2.09889i	−0.361734	−	0.208847i	0.308107	−	0.951352i	$-0.400305\pi$
$101$	−3.63539	−	2.09889i	−0.361734	−	0.208847i	−0.669841	+	0.742504i	$0.733638\pi$
$102$	−9.12741	+	1.60017i	−0.903748	+	0.158441i
$103$			14.4685i			1.42562i	0.701356	+	0.712811i	$0.252578\pi$
$103$			14.4685i			1.42562i	−0.701356	+	0.712811i	$0.747422\pi$
$104$	−5.96278	−	3.44261i	−0.584699	−	0.337576i
$105$	−0.230226	+	0.630613i	−0.0224677	+	0.0615415i
$106$	3.94962			0.383621
$107$	2.46390			0.238194			0.119097	−	0.992883i	$-0.462000\pi$
$107$	2.46390			0.238194			0.119097	+	0.992883i	$0.462000\pi$
$108$	5.19613	+	0.0153044i	0.499998	+	0.00147267i
$109$	2.32388	−	1.34169i	0.222587	−	0.128511i	−0.384561	−	0.923100i	$-0.625647\pi$
$109$	2.32388	−	1.34169i	0.222587	−	0.128511i	0.607148	+	0.794589i	$0.292314\pi$
$110$	3.14333	−	5.44441i	0.299705	−	0.519104i
$111$	2.83103	+	3.38062i	0.268709	+	0.320874i
$112$	0.193795	+	0.335662i	0.0183119	+	0.0317171i
$113$	0.146598			0.0137908			0.00689539	−	0.999976i	$-0.497805\pi$
$113$	0.146598			0.0137908			0.00689539	+	0.999976i	$0.497805\pi$
$114$	4.05232	−	6.37014i	0.379534	−	0.596619i
$115$	6.44153			0.600675
$116$	−2.15245	−	3.72815i	−0.199850	−	0.346150i
$117$	13.3083	−	15.7971i	1.23035	−	1.46044i
$118$	0.556791	−	0.964390i	0.0512567	−	0.0887793i
$119$	1.79582	−	1.03682i	0.164623	−	0.0950449i
$120$	−0.593994	+	1.62701i	−0.0542240	+	0.148525i
$121$	−28.5221			−2.59292
$122$	2.56746			0.232447
$123$	4.56195	+	1.66549i	0.411337	+	0.150172i
$124$	−5.08371	−	2.93508i	−0.456530	−	0.263578i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.09342	+	0.395544i	−0.0974099	+	0.0352378i
$127$	−14.1674	−	8.17952i	−1.25715	−	0.725815i	−0.284630	−	0.958638i	$-0.591871\pi$
$127$	−14.1674	−	8.17952i	−1.25715	−	0.725815i	−0.972519	+	0.232822i	$0.925204\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.91571	−	0.699393i	−0.168669	−	0.0615781i
$130$	3.44261	+	5.96278i	0.301937	+	0.522971i
$131$	−2.32705	+	1.34352i	−0.203316	+	0.117384i	−0.598201	−	0.801346i	$-0.704118\pi$
$131$	−2.32705	+	1.34352i	−0.203316	+	0.117384i	0.394886	+	0.918730i	$0.370784\pi$
$132$	10.7252	−	1.88029i	0.933512	−	0.163659i
$133$	−0.362957	+	1.65001i	−0.0314724	+	0.143074i
$134$			8.03394i			0.694027i
$135$	−4.49233	−	2.61132i	−0.386638	−	0.224747i
$136$	4.63331	−	2.67504i	0.397303	−	0.229383i
$137$	11.8037	+	6.81488i	1.00846	+	0.582234i	0.910740	−	0.412980i	$-0.135512\pi$
$137$	11.8037	+	6.81488i	1.00846	+	0.582234i	0.0977189	+	0.995214i	$0.468845\pi$
$138$	7.16322	+	8.55383i	0.609774	+	0.728151i
$139$	11.3319	−	19.6275i	0.961162	−	1.66478i	0.241572	−	0.970383i	$-0.422337\pi$
$139$	11.3319	−	19.6275i	0.961162	−	1.66478i	0.719590	−	0.694399i	$-0.244330\pi$
$140$		−	0.387589i		−	0.0327573i
$141$	−13.2841	+	2.32890i	−1.11872	+	0.196129i
$142$	−4.17799	+	7.23648i	−0.350609	+	0.607272i
$143$	21.6425	−	37.4860i	1.80984	−	3.13474i
$144$	−2.82109	+	1.02052i	−0.235091	+	0.0850436i
$145$			4.30489i			0.357502i
$146$	0.890700	−	1.54274i	0.0737148	−	0.127678i
$147$	−9.09595	+	7.61721i	−0.750222	+	0.628257i
$148$	−2.20473	−	1.27290i	−0.181228	−	0.104632i
$149$	2.36838	−	1.36738i	0.194025	−	0.112020i	−0.399840	−	0.916585i	$-0.630934\pi$
$149$	2.36838	−	1.36738i	0.194025	−	0.112020i	0.593866	+	0.804564i	$0.297601\pi$
$150$	1.32792	−	1.11204i	0.108424	−	0.0907975i
$151$		−	5.03506i		−	0.409747i	−0.978788	−	0.204874i	$-0.934322\pi$
$151$		−	5.03506i		−	0.409747i	0.978788	−	0.204874i	$-0.0656784\pi$
$152$	−0.936449	+	4.25712i	−0.0759560	+	0.345298i
$153$	5.45988	+	15.0931i	0.441405	+	1.22020i
$154$	−2.11019	+	1.21832i	−0.170044	+	0.0981751i
$155$	2.93508	+	5.08371i	0.235751	+	0.408333i
$156$	−4.08978	+	11.2024i	−0.327445	+	0.896906i
$157$	0.931580	+	1.61354i	0.0743482	+	0.128775i	0.900803	−	0.434229i	$-0.142979\pi$
$157$	0.931580	+	1.61354i	0.0743482	+	0.128775i	−0.826454	+	0.563004i	$0.809646\pi$
$158$	−12.3862	−	7.15117i	−0.985392	−	0.568916i
$159$	−1.18130	−	6.73817i	−0.0936833	−	0.534372i
$160$		−	1.00000i		−	0.0790569i
$161$	−2.16218	−	1.24833i	−0.170403	−	0.0983824i
$162$	−1.52801	−	8.86934i	−0.120052	−	0.696841i
$163$	−15.6424			−1.22521			−0.612604	−	0.790390i	$-0.709878\pi$
$163$	−15.6424			−1.22521			−0.612604	+	0.790390i	$0.709878\pi$
$164$	−2.80388			−0.218946
$165$	−10.2285	−	3.73424i	−0.796286	−	0.290710i
$166$	2.79365	−	1.61291i	0.216829	−	0.125186i
$167$	2.58979	−	4.48565i	0.200404	−	0.347110i	−0.748255	−	0.663412i	$-0.769108\pi$
$167$	2.58979	−	4.48565i	0.200404	−	0.347110i	0.948659	+	0.316302i	$0.102441\pi$
$168$	0.514688	−	0.431014i	0.0397090	−	0.0332534i
$169$	17.2032	+	29.7968i	1.32332	+	2.29206i
$170$	−5.35008			−0.410333
$171$	−12.0797	−	5.00812i	−0.923756	−	0.382980i
$172$	1.17744			0.0897791
$173$	−4.91408	−	8.51144i	−0.373611	−	0.647113i	0.616507	−	0.787349i	$-0.288547\pi$
$173$	−4.91408	−	8.51144i	−0.373611	−	0.647113i	−0.990118	+	0.140236i	$0.955214\pi$
$174$	−5.71655	+	4.78720i	−0.433371	+	0.362917i
$175$	−0.193795	+	0.335662i	−0.0146495	+	0.0253737i
$176$	−5.44441	+	3.14333i	−0.410388	+	0.236937i
$177$	−1.81181	−	0.661461i	−0.136184	−	0.0497184i
$178$	−14.9969			−1.12407
$179$	19.6374			1.46777			0.733884	−	0.679275i	$-0.237706\pi$
$179$	19.6374			1.46777			0.733884	+	0.679275i	$0.237706\pi$
$180$	2.95339	+	0.526745i	0.220133	+	0.0392612i
$181$	−19.3105	−	11.1489i	−1.43534	−	0.828691i	−0.437815	−	0.899065i	$-0.644247\pi$
$181$	−19.3105	−	11.1489i	−1.43534	−	0.828691i	−0.997521	+	0.0703737i	$0.977581\pi$
$182$		−	2.66864i		−	0.197813i
$183$	−0.767908	−	4.38017i	−0.0567654	−	0.323791i
$184$	−5.57852	−	3.22076i	−0.411254	−	0.237438i
$185$	1.27290	+	2.20473i	0.0935855	+	0.162095i
$186$	−3.48684	+	9.55083i	−0.255667	+	0.700301i
$187$	16.8171	+	29.1280i	1.22979	+	2.13005i
$188$	6.74336	−	3.89328i	0.491810	−	0.283947i
$189$	1.00184	+	1.74711i	0.0728735	+	0.127084i
$190$	2.93955	−	3.21855i	0.213257	−	0.233498i
$191$			17.2742i			1.24992i	0.780658	+	0.624958i	$0.214884\pi$
$191$			17.2742i			1.24992i	−0.780658	+	0.624958i	$0.785116\pi$
$192$	1.32792	−	1.11204i	0.0958344	−	0.0802544i
$193$	8.44254	−	4.87430i	0.607707	−	0.350860i	−0.164360	−	0.986400i	$-0.552556\pi$
$193$	8.44254	−	4.87430i	0.607707	−	0.350860i	0.772068	+	0.635540i	$0.219223\pi$
$194$	−5.33880	−	3.08236i	−0.383304	−	0.221300i
$195$	9.14304	−	7.65663i	0.654746	−	0.548303i
$196$	3.42489	−	5.93208i	0.244635	−	0.423720i
$197$		−	7.99412i		−	0.569557i	−0.958593	−	0.284779i	$-0.908080\pi$
$197$		−	7.99412i		−	0.569557i	0.958593	−	0.284779i	$-0.0919201\pi$
$198$	−6.41568	−	17.7352i	−0.455943	−	1.26039i
$199$	2.50783	−	4.34368i	0.177775	−	0.307915i	−0.763343	−	0.645993i	$-0.776443\pi$
$199$	2.50783	−	4.34368i	0.177775	−	0.307915i	0.941118	+	0.338078i	$0.109777\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	13.7062	−	2.40289i	0.966758	−	0.169487i
$202$		−	4.19778i		−	0.295355i
$203$	0.834265	−	1.44499i	0.0585539	−	0.101418i
$204$	−5.94949	−	7.10448i	−0.416548	−	0.497413i
$205$	2.42823	+	1.40194i	0.169595	+	0.0979157i
$206$	−12.5301	+	7.23425i	−0.873012	+	0.504034i
$207$	12.4506	−	14.7791i	0.865379	−	1.02722i
$208$		−	6.88523i		−	0.477405i
$209$	−26.7631	−	5.88714i	−1.85124	−	0.407222i
$210$	−0.661239	+	0.115925i	−0.0456299	+	0.00799959i
$211$	−0.901047	+	0.520219i	−0.0620306	+	0.0358134i	−0.530695	−	0.847563i	$-0.678069\pi$
$211$	−0.901047	+	0.520219i	−0.0620306	+	0.0358134i	0.468664	+	0.883377i	$0.344736\pi$
$212$	1.97481	+	3.42047i	0.135630	+	0.234919i
$213$	13.5953	+	4.96340i	0.931533	+	0.340086i
$214$	1.23195	+	2.13380i	0.0842144	+	0.145864i
$215$	−1.01969	−	0.588721i	−0.0695426	−	0.0401504i
$216$	2.58481	+	4.50763i	0.175874	+	0.306706i
$217$		−	2.27521i		−	0.154451i
$218$	2.32388	+	1.34169i	0.157393	+	0.0908708i
$219$	−2.89836	−	1.05814i	−0.195853	−	0.0715025i
$220$	6.28666			0.423846
$221$	−36.8365			−2.47789
$222$	−1.51219	+	4.14205i	−0.101492	+	0.277996i
$223$	−3.44225	+	1.98738i	−0.230510	+	0.133085i	−0.610807	−	0.791779i	$-0.709155\pi$
$223$	−3.44225	+	1.98738i	−0.230510	+	0.133085i	0.380297	+	0.924864i	$0.375822\pi$
$224$	−0.193795	+	0.335662i	−0.0129484	+	0.0224274i
$225$	−2.29434	−	1.93287i	−0.152956	−	0.128858i
$226$	0.0732990	+	0.126958i	0.00487578	+	0.00844509i
$227$	20.9613			1.39125			0.695626	−	0.718404i	$-0.255127\pi$
$227$	20.9613			1.39125			0.695626	+	0.718404i	$0.255127\pi$
$228$	7.54286	+	0.324338i	0.499538	+	0.0214798i
$229$	−8.17578			−0.540271			−0.270135	−	0.962822i	$-0.587068\pi$
$229$	−8.17578			−0.540271			−0.270135	+	0.962822i	$0.587068\pi$
$230$	3.22076	+	5.57852i	0.212371	+	0.367837i
$231$	2.70964	+	3.23567i	0.178281	+	0.212891i
$232$	2.15245	−	3.72815i	0.141315	−	0.244765i
$233$	−3.05627	+	1.76454i	−0.200223	+	0.115599i	−0.596759	−	0.802420i	$-0.703545\pi$
$233$	−3.05627	+	1.76454i	−0.200223	+	0.115599i	0.396537	+	0.918019i	$0.370212\pi$
$234$	20.3348	+	3.62676i	1.32933	+	0.237089i
$235$	−7.78656			−0.507939
$236$	1.11358			0.0724880
$237$	−8.49550	+	23.2701i	−0.551842	+	1.51155i
$238$	1.79582	+	1.03682i	0.116406	+	0.0672069i
$239$			15.8539i			1.02550i	0.858537	+	0.512751i	$0.171374\pi$
$239$			15.8539i			1.02550i	−0.858537	+	0.512751i	$0.828626\pi$
$240$	−1.70603	+	0.299093i	−0.110124	+	0.0193063i
$241$	3.16963	+	1.82999i	0.204174	+	0.117880i	0.598601	−	0.801047i	$-0.295724\pi$
$241$	3.16963	+	1.82999i	0.204174	+	0.117880i	−0.394427	+	0.918927i	$0.629057\pi$
$242$	−14.2610	−	24.7009i	−0.916735	−	1.58783i
$243$	−14.6744	+	5.25960i	−0.941360	+	0.337403i
$244$	1.28373	+	2.22348i	0.0821823	+	0.142344i
$245$	−5.93208	+	3.42489i	−0.378987	+	0.218808i
$246$	0.838620	+	4.78351i	0.0534684	+	0.304985i
$247$	20.2395	−	22.1604i	1.28781	−	1.41004i
$248$		−	5.87016i		−	0.372756i
$249$	−3.58724	−	4.28364i	−0.227332	−	0.271465i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	9.75160	+	5.63009i	0.615516	+	0.355368i	0.775121	−	0.631813i	$-0.217689\pi$
$251$	9.75160	+	5.63009i	0.615516	+	0.355368i	−0.159605	+	0.987181i	$0.551022\pi$
$252$	−0.889262	−	0.749160i	−0.0560183	−	0.0471927i
$253$	20.2478	−	35.0703i	1.27297	−	2.20485i
$254$		−	16.3590i		−	1.02646i
$255$	1.60017	+	9.12741i	0.100207	+	0.571581i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.6499	+	23.6423i	−0.851456	+	1.47477i	0.0284374	+	0.999596i	$0.490947\pi$
$257$	−13.6499	+	23.6423i	−0.851456	+	1.47477i	−0.879894	+	0.475170i	$0.842386\pi$
$258$	−0.352164	−	2.00875i	−0.0219248	−	0.125059i
$259$		−	0.986725i		−	0.0613121i
$260$	−3.44261	+	5.96278i	−0.213502	+	0.369796i
$261$	9.87690	+	8.32080i	0.611365	+	0.515045i
$262$	−2.32705	−	1.34352i	−0.143766	−	0.0830032i
$263$	16.4659	−	9.50659i	1.01533	−	0.586202i	0.102583	−	0.994724i	$-0.467289\pi$
$263$	16.4659	−	9.50659i	1.01533	−	0.586202i	0.912748	+	0.408523i	$0.133956\pi$
$264$	6.99100	+	8.34818i	0.430266	+	0.513795i
$265$		−	3.94962i		−	0.242623i
$266$	−1.61043	+	0.510676i	−0.0987419	+	0.0313116i
$267$	4.48547	+	25.5853i	0.274507	+	1.56579i
$268$	−6.95760	+	4.01697i	−0.425003	+	0.245376i
$269$	9.43473	+	16.3414i	0.575246	+	0.996355i	0.996015	+	0.0891869i	$0.0284268\pi$
$269$	9.43473	+	16.3414i	0.575246	+	0.996355i	−0.420769	+	0.907168i	$0.638240\pi$
$270$	0.0153044	−	5.19613i	0.000931395	−	0.316226i
$271$	9.90543	+	17.1567i	0.601712	+	1.04220i	0.992562	+	0.121741i	$0.0388478\pi$
$271$	9.90543	+	17.1567i	0.601712	+	1.04220i	−0.390850	+	0.920454i	$0.627819\pi$
$272$	4.63331	+	2.67504i	0.280936	+	0.162198i
$273$	−4.55278	+	0.798171i	−0.275547	+	0.0483075i
$274$			13.6298i			0.823403i
$275$	−5.44441	−	3.14333i	−0.328310	−	0.189550i
$276$	−3.82623	+	10.4804i	−0.230312	+	0.630849i
$277$	13.1915			0.792598			0.396299	−	0.918121i	$-0.370294\pi$
$277$	13.1915			0.792598			0.396299	+	0.918121i	$0.370294\pi$
$278$	22.6639			1.35929
$279$	17.3369	+	3.09208i	1.03793	+	0.185118i
$280$	0.335662	−	0.193795i	0.0200596	−	0.0115814i
$281$	8.39558	−	14.5416i	0.500838	−	0.867477i	−0.499161	−	0.866509i	$-0.666359\pi$
$281$	8.39558	−	14.5416i	0.500838	−	0.867477i	1.00000		0.000967983i	$-0.000308119\pi$
$282$	−8.65895	−	10.3399i	−0.515633	−	0.615734i
$283$	3.98624	+	6.90437i	0.236958	+	0.410422i	0.959840	−	0.280549i	$-0.0905164\pi$
$283$	3.98624	+	6.90437i	0.236958	+	0.410422i	−0.722882	+	0.690971i	$0.757183\pi$
$284$	−8.35597			−0.495836
$285$	−6.37014	−	4.05232i	−0.377335	−	0.240039i
$286$	43.2851			2.55950
$287$	−0.543377	−	0.941156i	−0.0320745	−	0.0555547i
$288$	−2.29434	−	1.93287i	−0.135195	−	0.113896i
$289$	5.81170	−	10.0662i	0.341864	−	0.592127i
$290$	−3.72815	+	2.15245i	−0.218924	+	0.126396i
$291$	−3.66180	+	10.0301i	−0.214659	+	0.587973i
$292$	1.78140			0.104249
$293$	4.52893			0.264583			0.132292	−	0.991211i	$-0.457766\pi$
$293$	4.52893			0.264583			0.132292	+	0.991211i	$0.457766\pi$
$294$	−11.1447	−	4.06872i	−0.649970	−	0.237293i
$295$	−0.964390	−	0.556791i	−0.0561489	−	0.0324176i
$296$		−	2.54580i		−	0.147972i
$297$	−28.3380	+	16.2498i	−1.64433	+	0.942911i
$298$	2.36838	+	1.36738i	0.137196	+	0.0792104i
$299$	22.1757	+	38.4094i	1.28245	+	2.22127i
$300$	1.62701	+	0.593994i	0.0939356	+	0.0342943i
$301$	0.228182	+	0.395223i	0.0131522	+	0.0227802i
$302$	4.36049	−	2.51753i	0.250918	−	0.144868i
$303$	−7.16155	+	1.25553i	−0.411420	+	0.0721281i
$304$	−4.15500	+	1.31757i	−0.238305	+	0.0755679i
$305$		−	2.56746i		−	0.147012i
$306$	−10.3410	+	12.2749i	−0.591157	+	0.701711i
$307$	20.5036	−	11.8378i	1.17020	−	0.675618i	0.216476	−	0.976288i	$-0.430544\pi$
$307$	20.5036	−	11.8378i	1.17020	−	0.675618i	0.953728	+	0.300670i	$0.0972104\pi$
$308$	−2.11019	−	1.21832i	−0.120239	−	0.0694203i
$309$	16.0895	+	19.2130i	0.915300	+	1.09299i
$310$	−2.93508	+	5.08371i	−0.166701	+	0.288735i
$311$		−	21.2557i		−	1.20530i	−0.798006	−	0.602650i	$-0.794112\pi$
$311$		−	21.2557i		−	1.20530i	0.798006	−	0.602650i	$-0.205888\pi$
$312$	−11.7464	+	2.05932i	−0.665010	+	0.116586i
$313$	16.1860	−	28.0351i	0.914889	−	1.58463i	0.107826	−	0.994170i	$-0.465611\pi$
$313$	16.1860	−	28.0351i	0.914889	−	1.58463i	0.807063	−	0.590465i	$-0.201056\pi$
$314$	−0.931580	+	1.61354i	−0.0525721	+	0.0910575i
$315$	0.395544	+	1.09342i	0.0222864	+	0.0616074i
$316$		−	14.3023i		−	0.804569i
$317$	−0.273517	+	0.473746i	−0.0153623	+	0.0266082i	−0.873604	−	0.486637i	$-0.838223\pi$
$317$	−0.273517	+	0.473746i	−0.0153623	+	0.0266082i	0.858242	+	0.513245i	$0.171557\pi$
$318$	5.24478	−	4.39212i	0.294112	−	0.246298i
$319$	23.4376	+	13.5317i	1.31225	+	0.757630i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	3.27186	−	2.73995i	0.182618	−	0.152929i
$322$		−	2.49667i		−	0.139134i
$323$	7.04911	+	22.2296i	0.392223	+	1.23689i
$324$	6.91707	−	5.75797i	0.384281	−	0.319887i
$325$	5.96278	−	3.44261i	0.330756	−	0.190962i
$326$	−7.82120	−	13.5467i	−0.433176	−	0.750284i
$327$	1.59391	−	4.36590i	0.0881436	−	0.241435i
$328$	−1.40194	−	2.42823i	−0.0774091	−	0.134077i
$329$	2.61365	+	1.50899i	0.144095	+	0.0831935i
$330$	−1.88029	−	10.7252i	−0.103507	−	0.590405i
$331$		−	12.2880i		−	0.675410i	−0.941252	−	0.337705i	$-0.890349\pi$
$331$		−	12.2880i		−	0.675410i	0.941252	−	0.337705i	$-0.109651\pi$
$332$	2.79365	+	1.61291i	0.153321	+	0.0885202i
$333$	7.51876	+	1.34099i	0.412025	+	0.0734857i
$334$	5.17958			0.283414
$335$	8.03394			0.438941
$336$	0.630613	+	0.230226i	0.0344027	+	0.0125598i
$337$	12.8425	−	7.41464i	0.699577	−	0.403901i	−0.107613	−	0.994193i	$-0.534321\pi$
$337$	12.8425	−	7.41464i	0.699577	−	0.403901i	0.807190	+	0.590292i	$0.200987\pi$
$338$	−17.2032	+	29.7968i	−0.935730	+	1.62073i
$339$	0.194670	−	0.163022i	0.0105730	−	0.00885416i
$340$	−2.67504	−	4.63331i	−0.145074	−	0.251276i
$341$	36.9037			1.99845
$342$	−1.70268	−	12.9654i	−0.0920706	−	0.701087i
$343$	5.36802			0.289846
$344$	0.588721	+	1.01969i	0.0317417	+	0.0549782i
$345$	8.55383	−	7.16322i	0.460523	−	0.385655i
$346$	4.91408	−	8.51144i	0.264183	−	0.457578i
$347$	−8.34699	+	4.81914i	−0.448090	+	0.258705i	−0.707023	−	0.707190i	$-0.749962\pi$
$347$	−8.34699	+	4.81914i	−0.448090	+	0.258705i	0.258933	+	0.965895i	$0.416629\pi$
$348$	−7.00412	−	2.55708i	−0.375460	−	0.137074i
$349$	−25.2299			−1.35053			−0.675263	−	0.737577i	$-0.735970\pi$
$349$	−25.2299			−1.35053			−0.675263	+	0.737577i	$0.735970\pi$
$350$	−0.387589			−0.0207175
$351$	0.105374	−	35.7765i	0.00562446	−	1.90961i
$352$	−5.44441	−	3.14333i	−0.290188	−	0.167540i
$353$			10.0563i			0.535241i	0.963524	+	0.267620i	$0.0862373\pi$
$353$			10.0563i			0.535241i	−0.963524	+	0.267620i	$0.913763\pi$
$354$	−0.333064	−	1.89980i	−0.0177022	−	0.100973i
$355$	7.23648	+	4.17799i	0.384073	+	0.221744i
$356$	−7.49847	−	12.9877i	−0.397418	−	0.688348i
$357$	1.23173	−	3.37383i	0.0651899	−	0.178562i
$358$	9.81870	+	17.0065i	0.518934	+	0.898821i
$359$	9.76791	−	5.63951i	0.515531	−	0.297642i	−0.219573	−	0.975596i	$-0.570467\pi$
$359$	9.76791	−	5.63951i	0.515531	−	0.297642i	0.735104	+	0.677954i	$0.237133\pi$
$360$	1.02052	+	2.82109i	0.0537863	+	0.148684i
$361$	−17.2461	−	7.97315i	−0.907691	−	0.419639i
$362$		−	22.2978i		−	1.17195i
$363$	−37.8751	+	31.7176i	−1.98793	+	1.66474i
$364$	2.31111	−	1.33432i	0.121135	−	0.0699374i
$365$	−1.54274	−	0.890700i	−0.0807505	−	0.0466213i
$366$	3.40938	−	2.85511i	0.178211	−	0.149239i
$367$	−13.2097	+	22.8799i	−0.689540	+	1.19432i	0.282447	+	0.959283i	$0.408854\pi$
$367$	−13.2097	+	22.8799i	−0.689540	+	1.19432i	−0.971987	+	0.235036i	$0.924479\pi$
$368$		−	6.44153i		−	0.335788i
$369$	7.90999	−	2.86142i	0.411777	−	0.148960i
$370$	−1.27290	+	2.20473i	−0.0661750	+	0.114618i
$371$	−0.765414	+	1.32574i	−0.0397383	+	0.0688288i
$372$	−10.0147	+	1.75572i	−0.519237	+	0.0910299i
$373$		−	9.42090i		−	0.487796i	−0.969801	−	0.243898i	$-0.921574\pi$
$373$		−	9.42090i		−	0.487796i	0.969801	−	0.243898i	$-0.0784262\pi$
$374$	−16.8171	+	29.1280i	−0.869590	+	1.50617i
$375$	−1.11204	−	1.32792i	−0.0574254	−	0.0685735i
$376$	6.74336	+	3.89328i	0.347762	+	0.200781i
$377$	−25.6691	+	14.8201i	−1.32203	+	0.763273i
$378$	−1.01212	+	1.74118i	−0.0520578	+	0.0895565i
$379$		−	18.4868i		−	0.949601i	−0.880093	−	0.474801i	$-0.842520\pi$
$379$		−	18.4868i		−	0.949601i	0.880093	−	0.474801i	$-0.157480\pi$
$380$	4.25712	+	0.936449i	0.218386	+	0.0480388i
$381$	−27.9091	+	4.89287i	−1.42982	+	0.250669i
$382$	−14.9599	+	8.63710i	−0.765415	+	0.441912i
$383$	−8.39580	−	14.5419i	−0.429005	−	0.743059i	0.567780	−	0.823180i	$-0.307802\pi$
$383$	−8.39580	−	14.5419i	−0.429005	−	0.743059i	−0.996785	+	0.0801217i	$0.974469\pi$
$384$	1.62701	+	0.593994i	0.0830282	+	0.0303121i
$385$	1.21832	+	2.11019i	0.0620914	+	0.107545i
$386$	8.44254	+	4.87430i	0.429714	+	0.248096i
$387$	−3.32167	+	1.20161i	−0.168850	+	0.0610811i
$388$		−	6.16472i		−	0.312966i
$389$	−3.31963	−	1.91659i	−0.168312	−	0.0971748i	0.413478	−	0.910514i	$-0.364314\pi$
$389$	−3.31963	−	1.91659i	−0.168312	−	0.0971748i	−0.581790	+	0.813339i	$0.697647\pi$
$390$	11.2024	+	4.08978i	0.567253	+	0.207094i
$391$	−34.4627			−1.74285
$392$	6.84977			0.345966
$393$	−1.59609	+	4.37186i	−0.0805121	+	0.220531i
$394$	6.92311	−	3.99706i	0.348781	−	0.201369i
$395$	−7.15117	+	12.3862i	−0.359814	+	0.623217i
$396$	12.1513	−	14.4237i	0.610626	−	0.724821i
$397$	6.16028	+	10.6699i	0.309176	+	0.535508i	0.978182	−	0.207748i	$-0.0666135\pi$
$397$	6.16028	+	10.6699i	0.309176	+	0.535508i	−0.669007	+	0.743257i	$0.733280\pi$
$398$	5.01565			0.251412
$399$	1.35290	+	2.59471i	0.0677296	+	0.129898i
$400$	−1.00000			−0.0500000
$401$	3.20325	+	5.54818i	0.159962	+	0.277063i	0.934855	−	0.355030i	$-0.115529\pi$
$401$	3.20325	+	5.54818i	0.159962	+	0.277063i	−0.774892	+	0.632093i	$0.782196\pi$
$402$	8.93405	+	10.6684i	0.445590	+	0.532093i
$403$	−20.2087	+	35.0025i	−1.00667	+	1.74360i
$404$	3.63539	−	2.09889i	0.180867	−	0.104424i
$405$	−8.86934	+	1.52801i	−0.440721	+	0.0759277i
$406$	1.66853			0.0828078
$407$	16.0046			0.793318
$408$	3.17792	−	8.70465i	0.157330	−	0.430945i
$409$	−28.7986	−	16.6269i	−1.42400	−	0.822147i	−0.427363	−	0.904080i	$-0.640557\pi$
$409$	−28.7986	−	16.6269i	−1.42400	−	0.822147i	−0.996638	+	0.0819327i	$0.973891\pi$
$410$			2.80388i			0.138474i
$411$	23.2528	−	4.07656i	1.14698	−	0.201082i
$412$	−12.5301	−	7.23425i	−0.617313	−	0.356406i
$413$	0.215806	+	0.373787i	0.0106191	+	0.0183929i
$414$	19.0244	+	3.39304i	0.934997	+	0.166759i
$415$	−1.61291	−	2.79365i	−0.0791748	−	0.137135i
$416$	5.96278	−	3.44261i	0.292349	−	0.168788i
$417$	−6.77860	−	38.6653i	−0.331949	−	1.89345i
$418$	−8.28312	−	26.1211i	−0.405141	−	1.27762i
$419$		−	26.2177i		−	1.28082i	−0.768034	−	0.640409i	$-0.778765\pi$
$419$		−	26.2177i		−	1.28082i	0.768034	−	0.640409i	$-0.221235\pi$
$420$	−0.431014	−	0.514688i	−0.0210313	−	0.0251142i
$421$	16.2792	−	9.39883i	0.793402	−	0.458071i	−0.0477568	−	0.998859i	$-0.515207\pi$
$421$	16.2792	−	9.39883i	0.793402	−	0.458071i	0.841159	+	0.540788i	$0.181874\pi$
$422$	−0.901047	−	0.520219i	−0.0438623	−	0.0253239i
$423$	−15.0504	+	17.8650i	−0.731777	+	0.868628i
$424$	−1.97481	+	3.42047i	−0.0959052	+	0.166113i
$425$			5.35008i			0.259517i
$426$	2.49921	+	14.2556i	0.121087	+	0.690684i
$427$	−0.497560	+	0.861799i	−0.0240786	+	0.0417054i
$428$	−1.23195	+	2.13380i	−0.0595485	+	0.103141i
$429$	−12.9463	−	73.8457i	−0.625051	−	3.56531i
$430$		−	1.17744i		−	0.0567813i
$431$	16.8907	−	29.2555i	0.813595	−	1.40919i	−0.0967380	−	0.995310i	$-0.530841\pi$
$431$	16.8907	−	29.2555i	0.813595	−	1.40919i	0.910333	−	0.413877i	$-0.135826\pi$
$432$	−2.61132	+	4.49233i	−0.125637	+	0.216137i
$433$	18.8094	+	10.8596i	0.903920	+	0.521879i	0.878470	−	0.477797i	$-0.158565\pi$
$433$	18.8094	+	10.8596i	0.903920	+	0.521879i	0.0254504	+	0.999676i	$0.491898\pi$
$434$	1.97039	−	1.13761i	0.0945818	−	0.0546068i
$435$	4.78720	+	5.71655i	0.229529	+	0.274088i
$436$			2.68338i			0.128511i
$437$	18.9352	−	20.7324i	0.905792	−	0.991763i
$438$	−0.532803	−	3.03912i	−0.0254583	−	0.145215i
$439$	−4.46634	+	2.57864i	−0.213167	+	0.123072i	−0.602782	−	0.797906i	$-0.705941\pi$
$439$	−4.46634	+	2.57864i	−0.213167	+	0.123072i	0.389616	+	0.920978i	$0.372608\pi$
$440$	3.14333	+	5.44441i	0.149852	+	0.259552i
$441$	−3.60808	+	20.2301i	−0.171813	+	0.963338i
$442$	−18.4183	−	31.9014i	−0.876068	−	1.51739i
$443$	−28.7183	−	16.5805i	−1.36445	−	0.787765i	−0.374237	−	0.927333i	$-0.622095\pi$
$443$	−28.7183	−	16.5805i	−1.36445	−	0.787765i	−0.990212	+	0.139568i	$0.955429\pi$
$444$	−4.34322	+	0.761431i	−0.206120	+	0.0361359i
$445$			14.9969i			0.710923i
$446$	−3.44225	−	1.98738i	−0.162995	−	0.0941053i
$447$	1.62444	−	4.44950i	0.0768332	−	0.210454i
$448$	−0.387589			−0.0183119
$449$	−28.6061			−1.35001			−0.675004	−	0.737815i	$-0.735858\pi$
$449$	−28.6061			−1.35001			−0.675004	+	0.737815i	$0.735858\pi$
$450$	0.526745	−	2.95339i	0.0248310	−	0.139224i
$451$	15.2655	−	8.81352i	0.718822	−	0.415012i
$452$	−0.0732990	+	0.126958i	−0.00344769	+	0.00597158i
$453$	−5.59918	−	6.68616i	−0.263072	−	0.314143i
$454$	10.4807	+	18.1530i	0.491882	+	0.851964i
$455$	−2.66864			−0.125108
$456$	3.49055	+	6.69448i	0.163460	+	0.313498i
$457$	12.0944			0.565752			0.282876	−	0.959156i	$-0.408711\pi$
$457$	12.0944			0.565752			0.282876	+	0.959156i	$0.408711\pi$
$458$	−4.08789	−	7.08043i	−0.191015	−	0.330847i
$459$	24.0343	+	13.9708i	1.12183	+	0.652100i
$460$	−3.22076	+	5.57852i	−0.150169	+	0.260100i
$461$	−23.9736	+	13.8412i	−1.11656	+	0.644647i	−0.940521	−	0.339736i	$-0.889662\pi$
$461$	−23.9736	+	13.8412i	−1.11656	+	0.644647i	−0.176040	+	0.984383i	$0.556329\pi$
$462$	−1.44735	+	3.96445i	−0.0673368	+	0.184443i
$463$	22.5239			1.04678			0.523388	−	0.852094i	$-0.324668\pi$
$463$	22.5239			1.04678			0.523388	+	0.852094i	$0.324668\pi$
$464$	4.30489			0.199850
$465$	9.55083	+	3.48684i	0.442909	+	0.161698i
$466$	−3.05627	−	1.76454i	−0.141579	−	0.0817407i
$467$		−	22.4617i		−	1.03940i	−0.854348	−	0.519701i	$-0.826043\pi$
$467$		−	22.4617i		−	1.03940i	0.854348	−	0.519701i	$-0.173957\pi$
$468$	7.02653	+	19.4238i	0.324802	+	0.897867i
$469$	−2.69669	−	1.55693i	−0.124522	−	0.0718926i
$470$	−3.89328	−	6.74336i	−0.179584	−	0.311048i
$471$	3.03139	+	1.10671i	0.139679	+	0.0509943i
$472$	0.556791	+	0.964390i	0.0256284	+	0.0443896i
$473$	−6.41047	+	3.70109i	−0.294754	+	0.170176i
$474$	−24.4002	+	4.27772i	−1.12074	+	0.196482i
$475$	−3.21855	−	2.93955i	−0.147677	−	0.134876i
$476$			2.07363i			0.0950449i
$477$	−9.06177	−	7.63410i	−0.414910	−	0.349542i
$478$	−13.7299	+	7.92694i	−0.627989	+	0.362570i
$479$	−14.0462	−	8.10959i	−0.641788	−	0.370537i	0.143515	−	0.989648i	$-0.454160\pi$
$479$	−14.0462	−	8.10959i	−0.641788	−	0.370537i	−0.785303	+	0.619111i	$0.787493\pi$
$480$	−1.11204	−	1.32792i	−0.0507573	−	0.0606110i
$481$	−8.76421	+	15.1801i	−0.399614	+	0.692151i
$482$			3.65997i			0.166707i
$483$	−4.25939	+	0.746734i	−0.193809	+	0.0339776i
$484$	14.2610	−	24.7009i	0.648229	−	1.12277i
$485$	−3.08236	+	5.33880i	−0.139963	+	0.242423i
$486$	−11.8921	−	10.0786i	−0.539438	−	0.457173i
$487$		−	26.2560i		−	1.18977i	−0.803809	−	0.594887i	$-0.797197\pi$
$487$		−	26.2560i		−	1.18977i	0.803809	−	0.594887i	$-0.202803\pi$
$488$	−1.28373	+	2.22348i	−0.0581117	+	0.100652i
$489$	−20.7719	+	17.3949i	−0.939337	+	0.786627i
$490$	−5.93208	−	3.42489i	−0.267984	−	0.154721i
$491$	20.1138	−	11.6127i	0.907723	−	0.524074i	0.0280250	−	0.999607i	$-0.491078\pi$
$491$	20.1138	−	11.6127i	0.907723	−	0.524074i	0.879698	+	0.475533i	$0.157745\pi$
$492$	−3.72333	+	3.11802i	−0.167861	+	0.140571i
$493$		−	23.0315i		−	1.03729i
$494$	29.3112	+	6.44766i	1.31878	+	0.290094i
$495$	−17.7352	+	6.41568i	−0.797139	+	0.288363i
$496$	5.08371	−	2.93508i	0.228265	−	0.131789i
$497$	−1.61934	−	2.80478i	−0.0726374	−	0.125812i
$498$	1.91612	−	5.24846i	0.0858635	−	0.235189i
$499$	−5.68385	−	9.84472i	−0.254444	−	0.440710i	0.710300	−	0.703899i	$-0.248559\pi$
$499$	−5.68385	−	9.84472i	−0.254444	−	0.440710i	−0.964744	+	0.263189i	$0.915226\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−1.54917	−	8.83653i	−0.0692120	−	0.394787i
$502$			11.2602i			0.502567i
$503$	−11.7374	−	6.77660i	−0.523346	−	0.302154i	0.214957	−	0.976624i	$-0.431039\pi$
$503$	−11.7374	−	6.77660i	−0.523346	−	0.302154i	−0.738302	+	0.674470i	$0.764372\pi$
$504$	0.204161	−	1.14470i	0.00909403	−	0.0509892i
$505$	−4.19778			−0.186799
$506$	40.4957			1.80025
$507$	55.9796	+	20.4372i	2.48614	+	0.907647i
$508$	14.1674	−	8.17952i	0.628575	−	0.362908i
$509$	−15.5217	+	26.8843i	−0.687986	+	1.19163i	0.284502	+	0.958675i	$0.408172\pi$
$509$	−15.5217	+	26.8843i	−0.687986	+	1.19163i	−0.972488	+	0.232951i	$0.925162\pi$
$510$	−7.10448	+	5.94949i	−0.314592	+	0.263448i
$511$	0.345226	+	0.597948i	0.0152719	+	0.0264517i
$512$	−1.00000			−0.0441942
$513$	−21.6101	+	6.78268i	−0.954108	+	0.299463i
$514$	−27.2998			−1.20414
$515$	7.23425	+	12.5301i	0.318779	+	0.552141i
$516$	1.56355	−	1.30936i	0.0688314	−	0.0576413i
$517$	−24.4757	+	42.3932i	−1.07644	+	1.86445i
$518$	0.854529	−	0.493363i	0.0375459	−	0.0216771i
$519$	−15.9906	−	5.83787i	−0.701908	−	0.256254i
$520$	−6.88523			−0.301937
$521$	7.63094			0.334317			0.167159	−	0.985930i	$-0.446541\pi$
$521$	7.63094			0.334317			0.167159	+	0.985930i	$0.446541\pi$
$522$	−2.26758	+	12.7140i	−0.0992492	+	0.556479i
$523$	−14.6044	−	8.43187i	−0.638607	−	0.368700i	0.145471	−	0.989363i	$-0.453530\pi$
$523$	−14.6044	−	8.43187i	−0.638607	−	0.368700i	−0.784078	+	0.620663i	$0.786864\pi$
$524$		−	2.68705i		−	0.117384i
$525$	0.115925	+	0.661239i	0.00505939	+	0.0288589i
$526$	16.4659	+	9.50659i	0.717948	+	0.414507i
$527$	−15.7029	−	27.1983i	−0.684030	−	1.18477i
$528$	−3.73424	+	10.2285i	−0.162512	+	0.445137i
$529$	9.24662	+	16.0156i	0.402027	+	0.696331i
$530$	3.42047	−	1.97481i	0.148576	−	0.0857802i
$531$	−3.14151	+	1.13644i	−0.136330	+	0.0493171i
$532$	−1.24747	−	1.13934i	−0.0540849	−	0.0493965i
$533$			19.3053i			0.836207i
$534$	−19.9147	+	16.6772i	−0.861795	+	0.721691i
$535$	2.13380	−	1.23195i	0.0922522	−	0.0532618i
$536$	−6.95760	−	4.01697i	−0.300522	−	0.173507i
$537$	26.0769	−	21.8375i	1.12530	−	0.942359i
$538$	−9.43473	+	16.3414i	−0.406760	+	0.704529i
$539$			43.0622i			1.85482i
$540$	4.50763	−	2.58481i	0.193978	−	0.111233i
$541$	−11.3322	+	19.6279i	−0.487208	+	0.843869i	−0.999892	−	0.0147085i	$-0.995318\pi$
$541$	−11.3322	+	19.6279i	−0.487208	+	0.843869i	0.512684	+	0.858577i	$0.328651\pi$
$542$	−9.90543	+	17.1567i	−0.425475	+	0.736944i
$543$	−38.0408	+	6.66911i	−1.63249	+	0.286199i
$544$			5.35008i			0.229383i
$545$	1.34169	−	2.32388i	0.0574717	−	0.0995440i
$546$	−2.96763	−	3.54374i	−0.127003	−	0.151658i
$547$	−1.44092	−	0.831914i	−0.0616091	−	0.0355701i	0.468879	−	0.883262i	$-0.344658\pi$
$547$	−1.44092	−	0.831914i	−0.0616091	−	0.0355701i	−0.530488	+	0.847692i	$0.677991\pi$
$548$	−11.8037	+	6.81488i	−0.504230	+	0.291117i
$549$	−5.89063	−	4.96257i	−0.251406	−	0.211797i
$550$		−	6.28666i		−	0.268064i
$551$	13.8555	+	12.6544i	0.590264	+	0.539097i
$552$	−10.9894	+	1.92661i	−0.467742	+	0.0820021i
$553$	4.80075	−	2.77172i	0.204149	−	0.117865i
$554$	6.59573	+	11.4241i	0.280226	+	0.485365i
$555$	4.14205	+	1.51219i	0.175820	+	0.0641889i
$556$	11.3319	+	19.6275i	0.480581	+	0.832391i
$557$	7.03591	+	4.06218i	0.298121	+	0.172120i	0.641599	−	0.767041i	$-0.278272\pi$
$557$	7.03591	+	4.06218i	0.298121	+	0.172120i	−0.343477	+	0.939161i	$0.611605\pi$
$558$	5.99063	+	16.5602i	0.253604	+	0.701051i
$559$		−	8.10695i		−	0.342888i
$560$	0.335662	+	0.193795i	0.0141843	+	0.00818932i
$561$	54.7232	+	19.9785i	2.31042	+	0.843492i
$562$	16.7912			0.708292
$563$	−6.21069			−0.261749			−0.130875	−	0.991399i	$-0.541779\pi$
$563$	−6.21069			−0.261749			−0.130875	+	0.991399i	$0.541779\pi$
$564$	4.62517	−	12.6688i	0.194755	−	0.533454i
$565$	0.126958	−	0.0732990i	0.00534114	−	0.00308371i
$566$	−3.98624	+	6.90437i	−0.167554	+	0.290213i
$567$	3.27322	+	1.20593i	0.137462	+	0.0506444i
$568$	−4.17799	−	7.23648i	−0.175304	−	0.303636i
$569$	−24.7474			−1.03747			−0.518733	−	0.854936i	$-0.673596\pi$
$569$	−24.7474			−1.03747			−0.518733	+	0.854936i	$0.673596\pi$
$570$	0.324338	−	7.54286i	0.0135850	−	0.315936i
$571$	−2.91055			−0.121803			−0.0609014	−	0.998144i	$-0.519398\pi$
$571$	−2.91055			−0.121803			−0.0609014	+	0.998144i	$0.519398\pi$
$572$	21.6425	+	37.4860i	0.904920	+	1.56737i
$573$	19.2096	+	22.9388i	0.802491	+	0.958280i
$574$	0.543377	−	0.941156i	0.0226801	−	0.0392831i
$575$	5.57852	−	3.22076i	0.232641	−	0.134315i
$576$	0.526745	−	2.95339i	0.0219477	−	0.123058i
$577$	11.1520			0.464264			0.232132	−	0.972684i	$-0.425430\pi$
$577$	11.1520			0.464264			0.232132	+	0.972684i	$0.425430\pi$
$578$	11.6234			0.483469
$579$	5.79061	−	15.8611i	0.240650	−	0.659165i
$580$	−3.72815	−	2.15245i	−0.154803	−	0.0893755i
$581$			1.25030i			0.0518710i
$582$	−10.5172	+	1.84382i	−0.435952	+	0.0764289i
$583$	−21.5033	−	12.4149i	−0.890577	−	0.514175i
$584$	0.890700	+	1.54274i	0.0368574	+	0.0638389i
$585$	3.62676	−	20.3348i	0.149948	−	0.840740i
$586$	2.26447	+	3.92217i	0.0935443	+	0.162023i
$587$	−28.0297	+	16.1829i	−1.15691	+	0.667942i	−0.950561	−	0.310537i	$-0.899491\pi$
$587$	−28.0297	+	16.1829i	−1.15691	+	0.667942i	−0.206348	+	0.978479i	$0.566158\pi$
$588$	−2.04872	−	11.6859i	−0.0844877	−	0.481920i
$589$	24.9900	+	5.49711i	1.02969	+	0.226504i
$590$		−	1.11358i		−	0.0458454i
$591$	−8.88976	−	10.6156i	−0.365676	−	0.436665i
$592$	2.20473	−	1.27290i	0.0906138	−	0.0523159i
$593$	−11.3927	−	6.57758i	−0.467842	−	0.270109i	0.247494	−	0.968889i	$-0.420393\pi$
$593$	−11.3927	−	6.57758i	−0.467842	−	0.270109i	−0.715336	+	0.698781i	$0.753726\pi$
$594$	−28.2417	−	16.4165i	−1.15877	−	0.673576i
$595$	1.03682	−	1.79582i	0.0425054	−	0.0736215i
$596$			2.73477i			0.112020i
$597$	−1.50014	−	8.55686i	−0.0613968	−	0.350209i
$598$	−22.1757	+	38.4094i	−0.906831	+	1.57068i
$599$	19.9168	−	34.4969i	0.813777	−	1.40950i	−0.0964255	−	0.995340i	$-0.530741\pi$
$599$	19.9168	−	34.4969i	0.813777	−	1.40950i	0.910203	−	0.414163i	$-0.135926\pi$
$600$	0.299093	+	1.70603i	0.0122104	+	0.0696484i
$601$		−	2.09040i		−	0.0852692i	−0.999091	−	0.0426346i	$-0.986425\pi$
$601$		−	2.09040i		−	0.0852692i	0.999091	−	0.0426346i	$-0.0135751\pi$
$602$	−0.228182	+	0.395223i	−0.00930000	+	0.0161081i
$603$	15.5286	−	18.4326i	0.632373	−	0.750634i
$604$	4.36049	+	2.51753i	0.177426	+	0.102437i
$605$	−24.7009	+	14.2610i	−1.00423	+	0.579794i
$606$	−4.66809	−	5.57432i	−0.189628	−	0.226441i
$607$			5.53538i			0.224674i	0.993670	+	0.112337i	$0.0358336\pi$
$607$			5.53538i			0.224674i	−0.993670	+	0.112337i	$0.964166\pi$
$608$	−3.21855	−	2.93955i	−0.130529	−	0.119214i
$609$	−0.499045	−	2.84656i	−0.0202223	−	0.115349i
$610$	2.22348	−	1.28373i	0.0900263	−	0.0519767i
$611$	−26.8061	−	46.4296i	−1.08446	−	1.87834i
$612$	−15.8009	−	2.81813i	−0.638714	−	0.113916i
$613$	−10.6274	−	18.4073i	−0.429238	−	0.743462i	0.567568	−	0.823327i	$-0.307885\pi$
$613$	−10.6274	−	18.4073i	−0.429238	−	0.743462i	−0.996806	+	0.0798646i	$0.974551\pi$
$614$	20.5036	+	11.8378i	0.827459	+	0.477734i
$615$	4.78351	−	0.838620i	0.192890	−	0.0338164i
$616$		−	2.43664i		−	0.0981751i
$617$	−3.00091	−	1.73258i	−0.120812	−	0.0697509i	0.438376	−	0.898792i	$-0.355554\pi$
$617$	−3.00091	−	1.73258i	−0.120812	−	0.0697509i	−0.559188	+	0.829041i	$0.688887\pi$
$618$	−8.59420	+	23.5404i	−0.345709	+	0.946935i
$619$	20.0769			0.806960			0.403480	−	0.914989i	$-0.367801\pi$
$619$	20.0769			0.806960			0.403480	+	0.914989i	$0.367801\pi$
$620$	−5.87016			−0.235751
$621$	0.0985836	−	33.4710i	0.00395602	−	1.34315i
$622$	18.4080	−	10.6278i	0.738092	−	0.426138i
$623$	2.90633	−	5.03390i	0.116440	−	0.201679i
$624$	−7.65663	−	9.14304i	−0.306511	−	0.366014i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	32.3721			1.29385
$627$	−42.0859	+	21.9439i	−1.68075	+	0.876354i
$628$	−1.86316			−0.0743482
$629$	−6.81012	−	11.7955i	−0.271537	−	0.470317i
$630$	−0.749160	+	0.889262i	−0.0298473	+	0.0354291i
$631$	−3.03717	+	5.26053i	−0.120908	+	0.209418i	−0.920126	−	0.391623i	$-0.871914\pi$
$631$	−3.03717	+	5.26053i	−0.120908	+	0.209418i	0.799218	+	0.601041i	$0.205247\pi$
$632$	12.3862	−	7.15117i	0.492696	−	0.284458i
$633$	−0.618014	+	1.69281i	−0.0245639	+	0.0672831i
$634$	−0.547035			−0.0217255
$635$	−16.3590			−0.649189
$636$	6.42608	+	2.34605i	0.254811	+	0.0930269i
$637$	−40.8437	−	23.5811i	−1.61829	−	0.934319i
$638$			27.0634i			1.07145i
$639$	23.5729	−	8.52746i	0.932530	−	0.337341i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	2.26142	+	3.91689i	0.0893206	+	0.154708i	0.907224	−	0.420648i	$-0.138197\pi$
$641$	2.26142	+	3.91689i	0.0893206	+	0.154708i	−0.817904	+	0.575355i	$0.804864\pi$
$642$	4.00880	+	1.46354i	0.158215	+	0.0577614i
$643$	5.12601	+	8.87852i	0.202150	+	0.350135i	0.949221	−	0.314610i	$-0.101874\pi$
$643$	5.12601	+	8.87852i	0.202150	+	0.350135i	−0.747071	+	0.664745i	$0.768540\pi$
$644$	2.16218	−	1.24833i	0.0852017	−	0.0491912i
$645$	−2.00875	+	0.352164i	−0.0790945	+	0.0138664i
$646$	−15.7268	+	17.2195i	−0.618764	+	0.677492i
$647$			32.4311i			1.27500i	0.770451	+	0.637500i	$0.220031\pi$
$647$			32.4311i			1.27500i	−0.770451	+	0.637500i	$0.779969\pi$
$648$	8.44508	+	3.11137i	0.331754	+	0.122226i
$649$	−6.06279	+	3.50035i	−0.237985	+	0.137401i
$650$	5.96278	+	3.44261i	0.233880	+	0.135030i
$651$	−2.53012	−	3.02130i	−0.0991632	−	0.118414i
$652$	7.82120	−	13.5467i	0.306302	−	0.530531i
$653$		−	34.6967i		−	1.35778i	−0.734238	−	0.678892i	$-0.762460\pi$
$653$		−	34.6967i		−	1.35778i	0.734238	−	0.678892i	$-0.237540\pi$
$654$	4.57793	−	0.802580i	0.179011	−	0.0313834i
$655$	−1.34352	+	2.32705i	−0.0524958	+	0.0909255i
$656$	1.40194	−	2.42823i	0.0547365	−	0.0948065i
$657$	−5.02548	+	1.81796i	−0.196063	+	0.0709253i
$658$			3.01799i			0.117653i
$659$	−3.29288	+	5.70344i	−0.128272	+	0.222174i	−0.923007	−	0.384782i	$-0.874277\pi$
$659$	−3.29288	+	5.70344i	−0.128272	+	0.222174i	0.794735	+	0.606957i	$0.207610\pi$
$660$	8.34818	−	6.99100i	0.324953	−	0.272124i
$661$	33.4091	+	19.2887i	1.29946	+	0.750245i	0.980311	−	0.197458i	$-0.0632687\pi$
$661$	33.4091	+	19.2887i	1.29946	+	0.750245i	0.319152	+	0.947704i	$0.396602\pi$
$662$	10.6417	−	6.14400i	0.413602	−	0.238793i
$663$	−48.9160	+	40.9636i	−1.89974	+	1.59090i
$664$			3.22583i			0.125186i
$665$	0.510676	+	1.61043i	0.0198032	+	0.0624499i
$666$	2.59805	+	7.18193i	0.100672	+	0.278294i
$667$	−24.0149	+	13.8650i	−0.929862	+	0.536856i
$668$	2.58979	+	4.48565i	0.100202	+	0.173555i
$669$	−2.36099	+	6.46699i	−0.0912810	+	0.250028i
$670$	4.01697	+	6.95760i	0.155189	+	0.268795i
$671$	−13.9783	−	8.07037i	−0.539626	−	0.311553i
$672$	0.115925	+	0.661239i	0.00447191	+	0.0255079i
$673$			27.8104i			1.07201i	0.844214	+	0.536006i	$0.180068\pi$
$673$			27.8104i			1.07201i	−0.844214	+	0.536006i	$0.819932\pi$
$674$	12.8425	+	7.41464i	0.494676	+	0.285601i
$675$	−5.19613	−	0.0153044i	−0.199999	−	0.000589066i
$676$	−34.4064			−1.32332
$677$	20.4612			0.786387			0.393193	−	0.919456i	$-0.371370\pi$
$677$	20.4612			0.786387			0.393193	+	0.919456i	$0.371370\pi$
$678$	0.238517	+	0.0870783i	0.00916018	+	0.00334422i
$679$	2.06926	−	1.19469i	0.0794110	−	0.0458480i
$680$	2.67504	−	4.63331i	0.102583	−	0.177679i
$681$	27.8350	−	23.3098i	1.06664	−	0.893233i
$682$	18.4518	+	31.9595i	0.706558	+	1.22379i
$683$	−6.27342			−0.240046			−0.120023	−	0.992771i	$-0.538297\pi$
$683$	−6.27342			−0.240046			−0.120023	+	0.992771i	$0.538297\pi$
$684$	10.3770	−	7.95725i	0.396774	−	0.304253i
$685$	13.6298			0.520766
$686$	2.68401	+	4.64884i	0.102476	+	0.177494i
$687$	−10.8568	+	9.09177i	−0.414212	+	0.346873i
$688$	−0.588721	+	1.01969i	−0.0224448	+	0.0388755i
$689$	23.5507	−	13.5970i	0.897211	−	0.518005i
$690$	10.4804	+	3.82623i	0.398984	+	0.145662i
$691$	−39.8978			−1.51778			−0.758891	−	0.651217i	$-0.774259\pi$
$691$	−39.8978			−1.51778			−0.758891	+	0.651217i	$0.774259\pi$
$692$	9.82817			0.373611
$693$	7.19636	+	1.28349i	0.273367	+	0.0487557i
$694$	−8.34699	−	4.81914i	−0.316847	−	0.182932i
$695$		−	22.6639i		−	0.859690i
$696$	−1.28756	−	7.34428i	−0.0488049	−	0.278384i
$697$	−12.9912	−	7.50049i	−0.492078	−	0.284101i
$698$	−12.6150	−	21.8497i	−0.477483	−	0.827025i
$699$	−2.09625	+	5.74185i	−0.0792875	+	0.217177i
$700$	−0.193795	−	0.335662i	−0.00732475	−	0.0126868i
$701$	8.46297	−	4.88610i	0.319642	−	0.184545i	−0.331591	−	0.943423i	$-0.607585\pi$
$701$	8.46297	−	4.88610i	0.319642	−	0.184545i	0.651233	+	0.758878i	$0.274252\pi$
$702$	31.0361	−	17.7970i	1.17138	−	0.671705i
$703$	10.8378	+	2.38401i	0.408755	+	0.0899147i
$704$		−	6.28666i		−	0.236937i
$705$	−10.3399	+	8.65895i	−0.389424	+	0.326115i
$706$	−8.70898	+	5.02813i	−0.327767	+	0.189236i
$707$	1.40904	+	0.813507i	0.0529923	+	0.0305951i
$708$	1.47875	−	1.23834i	0.0555747	−	0.0465398i
$709$	−9.26925	+	16.0548i	−0.348114	+	0.602951i	−0.985914	−	0.167251i	$-0.946511\pi$
$709$	−9.26925	+	16.0548i	−0.348114	+	0.602951i	0.637800	+	0.770202i	$0.279844\pi$
$710$			8.35597i			0.313594i
$711$	14.5959	+	40.3481i	0.547388	+	1.51317i
$712$	7.49847	−	12.9877i	0.281017	−	0.486736i
$713$	−18.9064	+	32.7468i	−0.708050	+	1.22638i
$714$	3.53769	−	0.620209i	0.132395	−	0.0232107i
$715$		−	43.2851i		−	1.61877i
$716$	−9.81870	+	17.0065i	−0.366942	+	0.635562i
$717$	17.6301	+	21.0527i	0.658408	+	0.786227i
$718$	9.76791	+	5.63951i	0.364535	+	0.210465i
$719$	−29.2721	+	16.9002i	−1.09166	+	0.630273i	−0.934019	−	0.357223i	$-0.883724\pi$
$719$	−29.2721	+	16.9002i	−1.09166	+	0.630273i	−0.157645	+	0.987496i	$0.550390\pi$
$720$	−1.93287	+	2.29434i	−0.0720339	+	0.0855051i
$721$		−	5.60783i		−	0.208847i
$722$	−1.71811	−	18.9222i	−0.0639416	−	0.704210i
$723$	6.24403	−	1.09467i	0.232218	−	0.0407113i
$724$	19.3105	−	11.1489i	0.717668	−	0.414346i
$725$	2.15245	+	3.72815i	0.0799398	+	0.138460i
$726$	−46.4058	−	16.9419i	−1.72228	−	0.628775i
$727$	−15.8883	−	27.5193i	−0.589264	−	1.02064i	−0.994329	−	0.106347i	$-0.966084\pi$
$727$	−15.8883	−	27.5193i	−0.589264	−	1.02064i	0.405065	−	0.914288i	$-0.367249\pi$
$728$	2.31111	+	1.33432i	0.0856555	+	0.0494532i
$729$	−13.6375	+	23.3028i	−0.505093	+	0.863065i
$730$		−	1.78140i		−	0.0659325i
$731$	5.45545	+	3.14971i	0.201777	+	0.116496i
$732$	4.17729	+	1.52505i	0.154397	+	0.0563676i
$733$	24.0223			0.887283			0.443642	−	0.896204i	$-0.353686\pi$
$733$	24.0223			0.887283			0.443642	+	0.896204i	$0.353686\pi$
$734$	−26.4194			−0.975157
$735$	−4.06872	+	11.1447i	−0.150077	+	0.411077i
$736$	5.57852	−	3.22076i	0.205627	−	0.118719i
$737$	25.2533	−	43.7400i	0.930218	−	1.61119i
$738$	6.43306	+	5.41954i	0.236804	+	0.199496i
$739$	−12.2978	−	21.3005i	−0.452384	−	0.783551i	0.546150	−	0.837687i	$-0.316093\pi$
$739$	−12.2978	−	21.3005i	−0.452384	−	0.783551i	−0.998534	+	0.0541361i	$0.982760\pi$
$740$	−2.54580			−0.0935855
$741$	2.23314	−	51.9343i	0.0820365	−	1.90786i
$742$	−1.53083			−0.0561985
$743$	1.48071	+	2.56467i	0.0543220	+	0.0940885i	0.891908	−	0.452217i	$-0.149367\pi$
$743$	1.48071	+	2.56467i	0.0543220	+	0.0940885i	−0.837586	+	0.546306i	$0.816034\pi$
$744$	−6.52784	−	7.79511i	−0.239322	−	0.285782i
$745$	1.36738	−	2.36838i	0.0500971	−	0.0867707i
$746$	8.15874	−	4.71045i	0.298713	−	0.172462i
$747$	−9.52714	−	1.69919i	−0.348580	−	0.0621700i
$748$	−33.6342			−1.22979
$749$	−0.954981			−0.0348942
$750$	0.593994	−	1.62701i	0.0216896	−	0.0594101i
$751$	8.92680	+	5.15389i	0.325744	+	0.188068i	0.653950	−	0.756538i	$-0.273111\pi$
$751$	8.92680	+	5.15389i	0.325744	+	0.188068i	−0.328206	+	0.944606i	$0.606444\pi$
$752$			7.78656i			0.283947i
$753$	19.2102	−	3.36784i	0.700060	−	0.122731i
$754$	−25.6691	−	14.8201i	−0.934815	−	0.539716i
$755$	−2.51753	−	4.36049i	−0.0916223	−	0.158695i
$756$	−2.01396	−	0.00593182i	−0.0732472	−	0.000215738i
$757$	9.26031	+	16.0393i	0.336572	+	0.582959i	0.983785	−	0.179349i	$-0.0573993\pi$
$757$	9.26031	+	16.0393i	0.336572	+	0.582959i	−0.647214	+	0.762308i	$0.724066\pi$
$758$	16.0100	−	9.24338i	0.581510	−	0.335735i
$759$	−12.1120	−	69.0869i	−0.439636	−	2.50770i
$760$	1.31757	+	4.15500i	0.0477933	+	0.150718i
$761$		−	50.2106i		−	1.82013i	−0.414462	−	0.910067i	$-0.636030\pi$
$761$		−	50.2106i		−	1.82013i	0.414462	−	0.910067i	$-0.363970\pi$
$762$	−18.1919	−	21.7235i	−0.659022	−	0.786960i
$763$	−0.900710	+	0.520025i	−0.0326079	+	0.0188262i
$764$	−14.9599	−	8.63710i	−0.541230	−	0.312479i
$765$	12.2749	+	10.3410i	0.443801	+	0.373881i
$766$	8.39580	−	14.5419i	0.303352	−	0.525422i
$767$		−	7.66726i		−	0.276849i
$768$	0.299093	+	1.70603i	0.0107926	+	0.0615611i
$769$	−17.5253	+	30.3547i	−0.631979	+	1.09462i	0.355168	+	0.934802i	$0.384424\pi$
$769$	−17.5253	+	30.3547i	−0.631979	+	1.09462i	−0.987147	+	0.159817i	$0.948910\pi$
$770$	−1.21832	+	2.11019i	−0.0439052	+	0.0760461i
$771$	8.16516	+	46.5743i	0.294061	+	1.67733i
$772$			9.74861i			0.350860i
$773$	−20.0359	+	34.7031i	−0.720640	+	1.24818i	0.240104	+	0.970747i	$0.422819\pi$
$773$	−20.0359	+	34.7031i	−0.720640	+	1.24818i	−0.960744	+	0.277438i	$0.910515\pi$
$774$	−2.70145	−	2.27584i	−0.0971018	−	0.0818035i
$775$	5.08371	+	2.93508i	0.182612	+	0.105431i
$776$	5.33880	−	3.08236i	0.191652	−	0.110650i
$777$	−1.09728	−	1.31029i	−0.0393645	−	0.0470065i
$778$		−	3.83317i		−	0.137426i
$779$	11.6501	−	3.69431i	0.417408	−	0.132362i
$780$	2.05932	+	11.7464i	0.0737355	+	0.420589i
$781$	45.4933	−	26.2656i	1.62788	−	0.939856i
$782$	−17.2313	−	29.8456i	−0.616192	−	1.06728i
$783$	22.3688	+	0.0658837i	0.799395	+	0.00235449i
$784$	3.42489	+	5.93208i	0.122317	+	0.211860i
$785$	1.61354	+	0.931580i	0.0575898	+	0.0332495i
$786$	−4.58419	+	0.803677i	−0.163513	+	0.0286662i
$787$		−	1.76390i		−	0.0628763i	−0.999506	−	0.0314382i	$-0.989991\pi$
$787$		−	1.76390i		−	0.0628763i	0.999506	−	0.0314382i	$-0.0100087\pi$
$788$	6.92311	+	3.99706i	0.246626	+	0.142389i
$789$	11.2937	−	30.9347i	0.402067	−	1.10130i
$790$	−14.3023			−0.508854
$791$	−0.0568198			−0.00202028
$792$	18.5670	+	3.31146i	0.659749	+	0.117668i
$793$	15.3092	−	8.83877i	0.543646	−	0.313874i
$794$	−6.16028	+	10.6699i	−0.218620	+	0.378661i
$795$	−4.39212	−	5.24478i	−0.155773	−	0.186013i
$796$	2.50783	+	4.34368i	0.0888875	+	0.153958i
$797$	24.2694			0.859666			0.429833	−	0.902908i	$-0.358572\pi$
$797$	24.2694			0.859666			0.429833	+	0.902908i	$0.358572\pi$
$798$	−1.57063	+	2.46900i	−0.0555999	+	0.0874016i
$799$	41.6587			1.47378
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	34.4081	+	28.9872i	1.21575	+	1.02421i
$802$	−3.20325	+	5.54818i	−0.113111	+	0.195913i
$803$	−9.69866	+	5.59953i	−0.342258	+	0.197603i
$804$	−4.77211	+	13.0713i	−0.168299	+	0.460990i
$805$	−2.49667			−0.0879959
$806$	−40.4174			−1.42364
$807$	30.7009	+	11.2083i	1.08072	+	0.394552i
$808$	3.63539	+	2.09889i	0.127892	+	0.0738387i
$809$		−	32.5685i		−	1.14505i	−0.819888	−	0.572525i	$-0.805964\pi$
$809$		−	32.5685i		−	1.14505i	0.819888	−	0.572525i	$-0.194036\pi$
$810$	−5.75797	−	6.91707i	−0.202314	−	0.243041i
$811$	−40.2466	−	23.2364i	−1.41325	−	0.815940i	−0.417556	−	0.908651i	$-0.637113\pi$
$811$	−40.2466	−	23.2364i	−1.41325	−	0.815940i	−0.995693	+	0.0927115i	$0.970447\pi$
$812$	0.834265	+	1.44499i	0.0292770	+	0.0507092i
$813$	32.2325	+	11.7675i	1.13044	+	0.412705i
$814$	8.00229	+	13.8604i	0.280480	+	0.485806i
$815$	−13.5467	+	7.82120i	−0.474521	+	0.273965i
$816$	9.12741	−	1.60017i	0.319523	−	0.0560172i
$817$	−4.89227	+	1.55136i	−0.171159	+	0.0542753i
$818$		−	33.2538i		−	1.16269i
$819$	−5.15814	+	6.12278i	−0.180240	+	0.213947i
$820$	−2.42823	+	1.40194i	−0.0847975	+	0.0489578i
$821$	−15.0238	−	8.67398i	−0.524333	−	0.302724i	0.214373	−	0.976752i	$-0.431229\pi$
$821$	−15.0238	−	8.67398i	−0.524333	−	0.302724i	−0.738706	+	0.674028i	$0.764563\pi$
$822$	15.1568	+	18.0992i	0.528654	+	0.631283i
$823$	−1.52793	+	2.64645i	−0.0532603	+	0.0922496i	−0.891426	−	0.453166i	$-0.850295\pi$
$823$	−1.52793	+	2.64645i	−0.0532603	+	0.0922496i	0.838166	+	0.545415i	$0.183628\pi$
$824$		−	14.4685i		−	0.504034i
$825$	−10.7252	+	1.88029i	−0.373405	+	0.0654634i
$826$	−0.215806	+	0.373787i	−0.00750885	+	0.0130057i
$827$	1.06321	−	1.84154i	0.0369715	−	0.0640366i	−0.846948	−	0.531676i	$-0.821562\pi$
$827$	1.06321	−	1.84154i	0.0369715	−	0.0640366i	0.883919	+	0.467640i	$0.154896\pi$
$828$	6.57372	+	18.1721i	0.228453	+	0.631524i
$829$		−	26.9654i		−	0.936546i	−0.883584	−	0.468273i	$-0.844876\pi$
$829$		−	26.9654i		−	0.936546i	0.883584	−	0.468273i	$-0.155124\pi$
$830$	1.61291	−	2.79365i	0.0559851	−	0.0969690i
$831$	17.5172	−	14.6694i	0.607665	−	0.508876i
$832$	5.96278	+	3.44261i	0.206722	+	0.119351i
$833$	31.7371	−	18.3234i	1.09963	−	0.634869i
$834$	30.0958	−	25.2031i	1.04213	−	0.872711i
$835$		−	5.17958i		−	0.179247i
$836$	18.4799	−	20.2339i	0.639142	−	0.699805i
$837$	26.4605	−	15.1733i	0.914610	−	0.524464i
$838$	22.7052	−	13.1089i	0.784338	−	0.452838i
$839$	−6.48396	−	11.2305i	−0.223851	−	0.387722i	0.732123	−	0.681172i	$-0.238530\pi$
$839$	−6.48396	−	11.2305i	−0.223851	−	0.387722i	−0.955974	+	0.293451i	$0.905196\pi$
$840$	0.230226	−	0.630613i	0.00794354	−	0.0217582i
$841$	5.23395	+	9.06547i	0.180481	+	0.312602i
$842$	16.2792	+	9.39883i	0.561020	+	0.323905i
$843$	−5.02211	−	28.6462i	−0.172971	−	0.986629i
$844$		−	1.04044i		−	0.0358134i
$845$	29.7968	+	17.2032i	1.02504	+	0.591808i
$846$	−22.9968	−	4.10153i	−0.790646	−	0.141013i
$847$	11.0549			0.379849
$848$	−3.94962			−0.135630
$849$	12.9713	+	4.73561i	0.445175	+	0.162526i
$850$	−4.63331	+	2.67504i	−0.158921	+	0.0917532i
$851$	−8.19942	+	14.2018i	−0.281073	+	0.486832i
$852$	−11.0961	+	9.29215i	−0.380145	+	0.318344i
$853$	19.8140	+	34.3188i	0.678418	+	1.17505i	0.975457	+	0.220189i	$0.0706673\pi$
$853$	19.8140	+	34.3188i	0.678418	+	1.17505i	−0.297040	+	0.954865i	$0.595999\pi$
$854$	−0.995119			−0.0340523
$855$	−12.9654	+	1.70268i	−0.443406	+	0.0582306i
$856$	−2.46390			−0.0842144
$857$	−18.7067	−	32.4009i	−0.639008	−	1.10679i	−0.985651	−	0.168798i	$-0.946012\pi$
$857$	−18.7067	−	32.4009i	−0.639008	−	1.10679i	0.346642	−	0.937997i	$-0.387322\pi$
$858$	57.4791	−	48.1346i	1.96231	−	1.64329i
$859$	−22.3252	+	38.6684i	−0.761726	+	1.31935i	0.180234	+	0.983624i	$0.442314\pi$
$859$	−22.3252	+	38.6684i	−0.761726	+	1.31935i	−0.941960	+	0.335724i	$0.891019\pi$
$860$	1.01969	−	0.588721i	0.0347713	−	0.0200752i
$861$	−1.76816	−	0.645525i	−0.0602588	−	0.0219994i
$862$	33.7813			1.15060
$863$	−20.1867			−0.687163			−0.343581	−	0.939123i	$-0.611640\pi$
$863$	−20.1867			−0.687163			−0.343581	+	0.939123i	$0.611640\pi$
$864$	−5.19613	−	0.0153044i	−0.176776	−	0.000520666i
$865$	−8.51144	−	4.91408i	−0.289398	−	0.167084i
$866$			21.7192i			0.738048i
$867$	−3.47647	−	19.8299i	−0.118067	−	0.673458i
$868$	1.97039	+	1.13761i	0.0668794	+	0.0386128i
$869$	44.9570	+	77.8677i	1.52506	+	2.64148i
$870$	−2.55708	+	7.00412i	−0.0866931	+	0.237462i
$871$	27.6578	+	47.9047i	0.937148	+	1.62319i
$872$	−2.32388	+	1.34169i	−0.0786964	+	0.0454354i
$873$	6.29124	+	17.3912i	0.212926	+	0.588603i
$874$	27.4223	+	6.03216i	0.927574	+	0.204041i
$875$			0.387589i			0.0131029i
$876$	2.36556	−	1.98098i	0.0799247	−	0.0669312i
$877$	−46.0744	+	26.6011i	−1.55582	+	0.898254i	−0.558173	+	0.829725i	$0.688497\pi$
$877$	−46.0744	+	26.6011i	−1.55582	+	0.898254i	−0.997649	+	0.0685295i	$0.978169\pi$
$878$	−4.46634	−	2.57864i	−0.150732	−	0.0870249i
$879$	6.01406	−	5.03634i	0.202849	−	0.169872i
$880$	−3.14333	+	5.44441i	−0.105962	+	0.183531i
$881$			29.5768i			0.996466i	0.867043	+	0.498233i	$0.166018\pi$
$881$			29.5768i			0.996466i	−0.867043	+	0.498233i	$0.833982\pi$
$882$	−19.3238	+	6.99035i	−0.650667	+	0.235377i
$883$	−8.68185	+	15.0374i	−0.292168	+	0.506049i	−0.974322	−	0.225159i	$-0.927710\pi$
$883$	−8.68185	+	15.0374i	−0.292168	+	0.506049i	0.682154	+	0.731208i	$0.261043\pi$
$884$	18.4183	−	31.9014i	0.619474	−	1.07296i
$885$	−1.89980	+	0.333064i	−0.0638612	+	0.0111958i
$886$		−	33.1611i		−	1.11407i
$887$	19.2230	−	33.2953i	0.645446	−	1.11795i	−0.338752	−	0.940876i	$-0.610005\pi$
$887$	19.2230	−	33.2953i	0.645446	−	1.11795i	0.984198	−	0.177070i	$-0.0566620\pi$
$888$	−2.83103	−	3.38062i	−0.0950030	−	0.113446i
$889$	5.49111	+	3.17030i	0.184166	+	0.106328i
$890$	−12.9877	+	7.49847i	−0.435350	+	0.251349i
$891$	−19.5601	+	53.0913i	−0.655289	+	1.77863i
$892$		−	3.97476i		−	0.133085i
$893$	−22.8890	+	25.0614i	−0.765950	+	0.838649i
$894$	4.66560	−	0.817949i	0.156041	−	0.0273563i
$895$	17.0065	−	9.81870i	0.568464	−	0.328203i
$896$	−0.193795	−	0.335662i	−0.00647422	−	0.0112137i
$897$	72.1603	+	26.3444i	2.40936	+	0.879615i
$898$	−14.3031	−	24.7736i	−0.477300	−	0.826707i
$899$	−21.8848	−	12.6352i	−0.729899	−	0.421408i
$900$	2.82109	−	1.02052i	0.0940362	−	0.0340174i
$901$			21.1308i			0.703968i
$902$	15.2655	+	8.81352i	0.508284	+	0.293458i
$903$	0.742510	+	0.271077i	0.0247092	+	0.00902089i
$904$	−0.146598			−0.00487578
$905$	−22.2978			−0.741204
$906$	2.99080	−	8.19211i	0.0993625	−	0.272165i
$907$	−5.28915	+	3.05369i	−0.175623	+	0.101396i	−0.585235	−	0.810864i	$-0.698998\pi$
$907$	−5.28915	+	3.05369i	−0.175623	+	0.101396i	0.409611	+	0.912260i	$0.365664\pi$
$908$	−10.4807	+	18.1530i	−0.347813	+	0.602430i
$909$	−8.11377	+	9.63115i	−0.269117	+	0.319445i
$910$	−1.33432	−	2.31111i	−0.0442323	−	0.0766126i
$911$	−30.0434			−0.995381			−0.497690	−	0.867355i	$-0.665818\pi$
$911$	−30.0434			−0.995381			−0.497690	+	0.867355i	$0.665818\pi$
$912$	−4.05232	+	6.37014i	−0.134186	+	0.210937i
$913$	−20.2797			−0.671160
$914$	6.04720	+	10.4741i	0.200024	+	0.346451i
$915$	−2.85511	−	3.40938i	−0.0943870	−	0.112711i
$916$	4.08789	−	7.08043i	0.135068	−	0.233944i
$917$	0.901941	−	0.520736i	0.0297847	−	0.0171962i
$918$	−0.0818798	+	27.7997i	−0.00270243	+	0.917528i
$919$	−5.87159			−0.193686			−0.0968429	−	0.995300i	$-0.530874\pi$
$919$	−5.87159			−0.193686			−0.0968429	+	0.995300i	$0.530874\pi$
$920$	−6.44153			−0.212371
$921$	14.0631	−	38.5204i	0.463396	−	1.26929i
$922$	−23.9736	−	13.8412i	−0.789528	−	0.455834i
$923$			57.5328i			1.89371i
$924$	−4.15699	+	0.728782i	−0.136755	+	0.0239752i
$925$	2.20473	+	1.27290i	0.0724910	+	0.0418527i
$926$	11.2620	+	19.5063i	0.370091	+	0.641017i
$927$	42.7312	+	7.62120i	1.40348	+	0.250313i
$928$	2.15245	+	3.72815i	0.0706575	+	0.122382i
$929$	32.7353	−	18.8998i	1.07401	−	0.620081i	0.144737	−	0.989470i	$-0.453767\pi$
$929$	32.7353	−	18.8998i	1.07401	−	0.620081i	0.929275	+	0.369390i	$0.120433\pi$
$930$	1.75572	+	10.0147i	0.0575724	+	0.328394i
$931$	−6.41446	+	29.1603i	−0.210226	+	0.955690i
$932$		−	3.52908i		−	0.115599i
$933$	−23.6371	−	28.2259i	−0.773845	−	0.924073i
$934$	19.4524	−	11.2308i	0.636501	−	0.367484i
$935$	29.1280	+	16.8171i	0.952588	+	0.549977i
$936$	−13.3083	+	15.7971i	−0.434994	+	0.516343i
$937$	22.4831	−	38.9419i	0.734491	−	1.27218i	−0.220455	−	0.975397i	$-0.570754\pi$
$937$	22.4831	−	38.9419i	0.734491	−	1.27218i	0.954946	−	0.296779i	$-0.0959125\pi$
$938$		−	3.11387i		−	0.101671i
$939$	−9.68226	−	55.2278i	−0.315968	−	1.80229i
$940$	3.89328	−	6.74336i	0.126985	−	0.219944i
$941$	5.62832	−	9.74854i	0.183478	−	0.317793i	−0.759585	−	0.650409i	$-0.774598\pi$
$941$	5.62832	−	9.74854i	0.183478	−	0.317793i	0.943063	+	0.332615i	$0.107931\pi$
$942$	0.557257	+	3.17861i	0.0181564	+	0.103565i
$943$			18.0613i			0.588155i
$944$	−0.556791	+	0.964390i	−0.0181220	+	0.0313882i
$945$	1.74118	+	1.01212i	0.0566405	+	0.0329242i
$946$	−6.41047	−	3.70109i	−0.208422	−	0.120333i
$947$	−35.4047	+	20.4409i	−1.15050	+	0.664240i	−0.949009	−	0.315250i	$-0.897912\pi$
$947$	−35.4047	+	20.4409i	−1.15050	+	0.664240i	−0.201490	+	0.979491i	$0.564578\pi$
$948$	−15.9047	−	18.9924i	−0.516562	−	0.616843i
$949$		−	12.2653i		−	0.398150i
$950$	0.936449	−	4.25712i	0.0303824	−	0.138119i
$951$	0.163614	+	0.933259i	0.00530555	+	0.0302630i
$952$	−1.79582	+	1.03682i	−0.0582029	+	0.0336034i
$953$	−17.8170	−	30.8599i	−0.577148	−	0.999651i	−0.995805	−	0.0915056i	$-0.970832\pi$
$953$	−17.8170	−	30.8599i	−0.577148	−	0.999651i	0.418656	−	0.908145i	$-0.362501\pi$
$954$	2.08044	−	11.6648i	0.0673567	−	0.377661i
$955$	8.63710	+	14.9599i	0.279490	+	0.484091i
$956$	−13.7299	−	7.92694i	−0.444055	−	0.256375i
$957$	46.1710	−	8.09446i	1.49250	−	0.261657i
$958$		−	16.2192i		−	0.524018i
$959$	−4.57499	−	2.64137i	−0.147734	−	0.0852944i
$960$	0.593994	−	1.62701i	0.0191711	−	0.0525116i
$961$	−3.45878			−0.111574
$962$	−17.5284			−0.565139
$963$	1.29785	−	7.27687i	0.0418225	−	0.234494i
$964$	−3.16963	+	1.82999i	−0.102087	+	0.0589399i
$965$	4.87430	−	8.44254i	0.156909	−	0.271775i
$966$	−2.77639	−	3.31537i	−0.0893288	−	0.106670i
$967$	9.57867	+	16.5907i	0.308029	+	0.533522i	0.977931	−	0.208927i	$-0.0669972\pi$
$967$	9.57867	+	16.5907i	0.308029	+	0.533522i	−0.669902	+	0.742450i	$0.733664\pi$
$968$	28.5221			0.916735
$969$	34.0808	+	21.6802i	1.09483	+	0.696469i
$970$	−6.16472			−0.197937
$971$	−8.76880	−	15.1880i	−0.281404	−	0.487406i	0.690327	−	0.723498i	$-0.257467\pi$
$971$	−8.76880	−	15.1880i	−0.281404	−	0.487406i	−0.971731	+	0.236091i	$0.924133\pi$
$972$	2.78223	−	15.3382i	0.0892402	−	0.491972i
$973$	−4.39214	+	7.60740i	−0.140805	+	0.243882i
$974$	22.7384	−	13.1280i	0.728585	−	0.420649i
$975$	4.08978	−	11.2024i	0.130978	−	0.358763i
$976$	−2.56746			−0.0821823
$977$	21.3473			0.682960			0.341480	−	0.939889i	$-0.389072\pi$
$977$	21.3473			0.682960			0.341480	+	0.939889i	$0.389072\pi$
$978$	−25.4504	−	9.29150i	−0.813814	−	0.297109i
$979$	81.6494	+	47.1403i	2.60953	+	1.50661i
$980$		−	6.84977i		−	0.218808i
$981$	−2.73845	−	7.57005i	−0.0874321	−	0.241693i
$982$	20.1138	+	11.6127i	0.641857	+	0.370576i
$983$	21.8784	+	37.8944i	0.697811	+	1.20864i	0.969224	+	0.246181i	$0.0791758\pi$
$983$	21.8784	+	37.8944i	0.697811	+	1.20864i	−0.271413	+	0.962463i	$0.587491\pi$
$984$	−4.56195	−	1.66549i	−0.145430	−	0.0530938i
$985$	−3.99706	−	6.92311i	−0.127357	−	0.220589i
$986$	19.9459	−	11.5158i	0.635207	−	0.366737i
$987$	5.14878	−	0.902658i	0.163888	−	0.0287319i
$988$	9.07178	+	28.6081i	0.288612	+	0.910145i
$989$		−	7.58452i		−	0.241174i
$990$	−14.4237	−	12.1513i	−0.458417	−	0.386194i
$991$	25.4172	−	14.6746i	0.807405	−	0.466155i	−0.0386489	−	0.999253i	$-0.512305\pi$
$991$	25.4172	−	14.6746i	0.807405	−	0.466155i	0.846054	+	0.533097i	$0.178972\pi$
$992$	5.08371	+	2.93508i	0.161408	+	0.0931889i
$993$	−13.6647	−	16.3175i	−0.433637	−	0.517820i
$994$	1.61934	−	2.80478i	0.0513624	−	0.0889623i
$995$		−	5.01565i		−	0.159007i
$996$	5.50336	−	0.964822i	0.174381	−	0.0305715i
$997$	3.34562	−	5.79479i	0.105957	−	0.183523i	−0.808172	−	0.588947i	$-0.799543\pi$
$997$	3.34562	−	5.79479i	0.105957	−	0.183523i	0.914129	+	0.405424i	$0.132876\pi$
$998$	5.68385	−	9.84472i	0.179919	−	0.311629i
$999$	11.4755	−	6.58042i	0.363070	−	0.208195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.b.221.10	yes	24
3.2	odd	2		570.2.s.a.221.11	✓	24
19.8	odd	6		570.2.s.a.521.11	yes	24
57.8	even	6	inner	570.2.s.b.521.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.11	✓	24	3.2	odd	2
570.2.s.a.521.11	yes	24	19.8	odd	6
570.2.s.b.221.10	yes	24	1.1	even	1	trivial
570.2.s.b.521.10	yes	24	57.8	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.32792 - 1.11204i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62701 + 0.593994i) q^{6} -0.387589 q^{7} -1.00000 q^{8} +(0.526745 - 2.95339i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.32792 - 1.11204i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62701 + 0.593994i) q^{6} -0.387589 q^{7} -1.00000 q^{8} +(0.526745 - 2.95339i) q^{9} +(0.866025 + 0.500000i) q^{10} -6.28666i q^{11} +(0.299093 + 1.70603i) q^{12} +(5.96278 + 3.44261i) q^{13} +(-0.193795 - 0.335662i) q^{14} +(0.593994 - 1.62701i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.63331 + 2.67504i) q^{17} +(2.82109 - 1.02052i) q^{18} +(0.936449 - 4.25712i) q^{19} +1.00000i q^{20} +(-0.514688 + 0.431014i) q^{21} +(5.44441 - 3.14333i) q^{22} +(5.57852 + 3.22076i) q^{23} +(-1.32792 + 1.11204i) q^{24} +(0.500000 - 0.866025i) q^{25} +6.88523i q^{26} +(-2.58481 - 4.50763i) q^{27} +(0.193795 - 0.335662i) q^{28} +(-2.15245 + 3.72815i) q^{29} +(1.70603 - 0.299093i) q^{30} +5.87016i q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.99100 - 8.34818i) q^{33} +(-4.63331 - 2.67504i) q^{34} +(-0.335662 + 0.193795i) q^{35} +(2.29434 + 1.93287i) q^{36} +2.54580i q^{37} +(4.15500 - 1.31757i) q^{38} +(11.7464 - 2.05932i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.40194 + 2.42823i) q^{41} +(-0.630613 - 0.230226i) q^{42} +(-0.588721 - 1.01969i) q^{43} +(5.44441 + 3.14333i) q^{44} +(-1.02052 - 2.82109i) q^{45} +6.44153i q^{46} +(-6.74336 - 3.89328i) q^{47} +(-1.62701 - 0.593994i) q^{48} -6.84977 q^{49} +1.00000 q^{50} +(-3.17792 + 8.70465i) q^{51} +(-5.96278 + 3.44261i) q^{52} +(1.97481 - 3.42047i) q^{53} +(2.61132 - 4.49233i) q^{54} +(-3.14333 - 5.44441i) q^{55} +0.387589 q^{56} +(-3.49055 - 6.69448i) q^{57} -4.30489 q^{58} +(-0.556791 - 0.964390i) q^{59} +(1.11204 + 1.32792i) q^{60} +(1.28373 - 2.22348i) q^{61} +(-5.08371 + 2.93508i) q^{62} +(-0.204161 + 1.14470i) q^{63} +1.00000 q^{64} +6.88523 q^{65} +(3.73424 - 10.2285i) q^{66} +(6.95760 + 4.01697i) q^{67} -5.35008i q^{68} +(10.9894 - 1.92661i) q^{69} +(-0.335662 - 0.193795i) q^{70} +(4.17799 + 7.23648i) q^{71} +(-0.526745 + 2.95339i) q^{72} +(-0.890700 - 1.54274i) q^{73} +(-2.20473 + 1.27290i) q^{74} +(-0.299093 - 1.70603i) q^{75} +(3.21855 + 2.93955i) q^{76} +2.43664i q^{77} +(7.65663 + 9.14304i) q^{78} +(-12.3862 + 7.15117i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-8.44508 - 3.11137i) q^{81} +(-1.40194 + 2.42823i) q^{82} -3.22583i q^{83} +(-0.115925 - 0.661239i) q^{84} +(-2.67504 + 4.63331i) q^{85} +(0.588721 - 1.01969i) q^{86} +(1.28756 + 7.34428i) q^{87} +6.28666i q^{88} +(-7.49847 + 12.9877i) q^{89} +(1.93287 - 2.29434i) q^{90} +(-2.31111 - 1.33432i) q^{91} +(-5.57852 + 3.22076i) q^{92} +(6.52784 + 7.79511i) q^{93} -7.78656i q^{94} +(-1.31757 - 4.15500i) q^{95} +(-0.299093 - 1.70603i) q^{96} +(-5.33880 + 3.08236i) q^{97} +(-3.42489 - 5.93208i) q^{98} +(-18.5670 - 3.31146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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