LMFDB - Embedded newform 155.2.q.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(41,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("155.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.q (of order $15$, degree $8$, 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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	155.71
Dual form			155.2.q.a.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.132371 + 0.407396i) q^{2} +(1.24842 + 0.265360i) q^{3} +(1.46958 + 1.06772i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.273361 + 0.473476i) q^{6} +(-2.12201 + 0.944779i) q^{7} +(-1.32262 + 0.960937i) q^{8} +(-1.25250 - 0.557647i) q^{9} +O(q^{10})$	\(q+(-0.132371 + 0.407396i) q^{2} +(1.24842 + 0.265360i) q^{3} +(1.46958 + 1.06772i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.273361 + 0.473476i) q^{6} +(-2.12201 + 0.944779i) q^{7} +(-1.32262 + 0.960937i) q^{8} +(-1.25250 - 0.557647i) q^{9} +(-0.419001 + 0.0890613i) q^{10} +(0.574101 - 5.46220i) q^{11} +(1.55133 + 1.72293i) q^{12} +(1.15773 - 1.28579i) q^{13} +(-0.104007 - 0.989558i) q^{14} +(0.394402 + 1.21384i) q^{15} +(0.906257 + 2.78917i) q^{16} +(0.248318 + 2.36259i) q^{17} +(0.392977 - 0.436445i) q^{18} +(0.0615651 + 0.0683749i) q^{19} +(-0.189877 + 1.80656i) q^{20} +(-2.89987 + 0.616386i) q^{21} +(2.14928 + 0.956923i) q^{22} +(2.64794 - 1.92384i) q^{23} +(-1.90618 + 0.848685i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.370577 + 0.641857i) q^{26} +(-4.51334 - 3.27913i) q^{27} +(-4.12722 - 0.877269i) q^{28} +(2.98015 - 9.17195i) q^{29} -0.546723 q^{30} +(5.50834 + 0.811267i) q^{31} -4.52595 q^{32} +(2.16617 - 6.66679i) q^{33} +(-0.995378 - 0.211574i) q^{34} +(-1.87921 - 1.36532i) q^{35} +(-1.24524 - 2.15682i) q^{36} +(-5.51369 + 9.54999i) q^{37} +(-0.0360051 + 0.0160305i) q^{38} +(1.78654 - 1.29800i) q^{39} +(-1.49350 - 0.664951i) q^{40} +(-5.14120 + 1.09280i) q^{41} +(0.132745 - 1.26298i) q^{42} +(-3.49633 - 3.88307i) q^{43} +(6.67577 - 7.41420i) q^{44} +(-0.143311 - 1.36352i) q^{45} +(0.433254 + 1.33342i) q^{46} +(0.795429 + 2.44808i) q^{47} +(0.391256 + 3.72255i) q^{48} +(-1.07361 + 1.19236i) q^{49} +(-0.286630 - 0.318334i) q^{50} +(-0.316931 + 3.01540i) q^{51} +(3.07425 - 0.653452i) q^{52} +(-3.55264 - 1.58174i) q^{53} +(1.93334 - 1.40465i) q^{54} +(5.01746 - 2.23392i) q^{55} +(1.89873 - 3.28869i) q^{56} +(0.0587152 + 0.101698i) q^{57} +(3.34213 + 2.42820i) q^{58} +(-6.13377 - 1.30377i) q^{59} +(-0.716434 + 2.20496i) q^{60} -0.530885 q^{61} +(-1.05965 + 2.13669i) q^{62} +3.18466 q^{63} +(-1.21341 + 3.73449i) q^{64} +(1.69240 + 0.359730i) q^{65} +(2.42928 + 1.76498i) q^{66} +(4.91249 + 8.50868i) q^{67} +(-2.15765 + 3.73716i) q^{68} +(3.81625 - 1.69911i) q^{69} +(0.804979 - 0.584851i) q^{70} +(0.689090 + 0.306803i) q^{71} +(2.19244 - 0.466016i) q^{72} +(-0.505379 + 4.80836i) q^{73} +(-3.16077 - 3.51039i) q^{74} +(-0.854019 + 0.948485i) q^{75} +(0.0174701 + 0.166217i) q^{76} +(3.94233 + 12.1332i) q^{77} +(0.292312 + 0.899645i) q^{78} +(0.0774835 + 0.737207i) q^{79} +(-1.96237 + 2.17943i) q^{80} +(-2.01221 - 2.23479i) q^{81} +(0.235345 - 2.23916i) q^{82} +(-5.69004 + 1.20946i) q^{83} +(-4.91972 - 2.19040i) q^{84} +(-1.92190 + 1.39634i) q^{85} +(2.04476 - 0.910385i) q^{86} +(6.15435 - 10.6596i) q^{87} +(4.48952 + 7.77607i) q^{88} +(13.8860 + 10.0888i) q^{89} +(0.574461 + 0.122106i) q^{90} +(-1.24193 + 3.82226i) q^{91} +5.94549 q^{92} +(6.66146 + 2.47450i) q^{93} -1.10263 q^{94} +(-0.0284319 + 0.0875044i) q^{95} +(-5.65029 - 1.20101i) q^{96} +(-12.7059 - 9.23136i) q^{97} +(-0.343648 - 0.595216i) q^{98} +(-3.76504 + 6.52124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9} - q^{10} - 28 q^{11} - 13 q^{12} - 6 q^{13} - 6 q^{14} - 2 q^{15} + 8 q^{16} - 10 q^{17} - 27 q^{18} - 13 q^{19} - 5 q^{20} - 8 q^{21} + 2 q^{22} - 12 q^{23} - 82 q^{24} - 20 q^{25} + 32 q^{26} - q^{27} + 22 q^{28} + 42 q^{29} + 8 q^{30} - 10 q^{31} + 4 q^{32} + 13 q^{33} + 32 q^{34} + 8 q^{35} - 13 q^{36} + 12 q^{37} + 30 q^{38} + 37 q^{39} + 44 q^{40} + 36 q^{41} - 64 q^{42} - 78 q^{43} - 56 q^{44} - 2 q^{45} + 18 q^{46} - 4 q^{47} - 41 q^{48} - 31 q^{49} + q^{50} - 2 q^{51} + 49 q^{52} - 11 q^{53} + 22 q^{54} - 17 q^{55} + 9 q^{56} + 38 q^{57} + 11 q^{58} - q^{59} - 11 q^{60} - 100 q^{61} - 35 q^{62} + 110 q^{63} + 17 q^{64} + 6 q^{65} - 40 q^{66} + 30 q^{67} - 34 q^{68} + 8 q^{69} + 18 q^{70} - 2 q^{71} + 151 q^{72} - 23 q^{73} - 2 q^{74} - q^{75} + 2 q^{76} + 36 q^{77} - 2 q^{78} - 67 q^{79} - 41 q^{80} - 83 q^{81} + 2 q^{82} + 26 q^{84} - 5 q^{85} - 5 q^{86} - 46 q^{87} + 70 q^{88} + 20 q^{89} - 33 q^{90} + 19 q^{91} - 10 q^{92} - 67 q^{93} + 130 q^{94} + 4 q^{95} + 46 q^{96} - 18 q^{97} - 65 q^{98} + 53 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9 - q^10 - 28 * q^11 - 13 * q^12 - 6 * q^13 - 6 * q^14 - 2 * q^15 + 8 * q^16 - 10 * q^17 - 27 * q^18 - 13 * q^19 - 5 * q^20 - 8 * q^21 + 2 * q^22 - 12 * q^23 - 82 * q^24 - 20 * q^25 + 32 * q^26 - q^27 + 22 * q^28 + 42 * q^29 + 8 * q^30 - 10 * q^31 + 4 * q^32 + 13 * q^33 + 32 * q^34 + 8 * q^35 - 13 * q^36 + 12 * q^37 + 30 * q^38 + 37 * q^39 + 44 * q^40 + 36 * q^41 - 64 * q^42 - 78 * q^43 - 56 * q^44 - 2 * q^45 + 18 * q^46 - 4 * q^47 - 41 * q^48 - 31 * q^49 + q^50 - 2 * q^51 + 49 * q^52 - 11 * q^53 + 22 * q^54 - 17 * q^55 + 9 * q^56 + 38 * q^57 + 11 * q^58 - q^59 - 11 * q^60 - 100 * q^61 - 35 * q^62 + 110 * q^63 + 17 * q^64 + 6 * q^65 - 40 * q^66 + 30 * q^67 - 34 * q^68 + 8 * q^69 + 18 * q^70 - 2 * q^71 + 151 * q^72 - 23 * q^73 - 2 * q^74 - q^75 + 2 * q^76 + 36 * q^77 - 2 * q^78 - 67 * q^79 - 41 * q^80 - 83 * q^81 + 2 * q^82 + 26 * q^84 - 5 * q^85 - 5 * q^86 - 46 * q^87 + 70 * q^88 + 20 * q^89 - 33 * q^90 + 19 * q^91 - 10 * q^92 - 67 * q^93 + 130 * q^94 + 4 * q^95 + 46 * q^96 - 18 * q^97 - 65 * q^98 + 53 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$1$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−0.132371	+	0.407396i	−0.0936004	+	0.288072i	−0.986886	−	0.161416i	$-0.948394\pi$
$2$	−0.132371	+	0.407396i	−0.0936004	+	0.288072i	0.893286	+	0.449489i	$0.148394\pi$
$3$	1.24842	+	0.265360i	0.720777	+	0.153206i	0.553674	−	0.832734i	$-0.313225\pi$
$3$	1.24842	+	0.265360i	0.720777	+	0.153206i	0.167103	+	0.985939i	$0.446559\pi$
$4$	1.46958	+	1.06772i	0.734792	+	0.533858i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.273361	+	0.473476i	−0.111599	+	0.193296i
$7$	−2.12201	+	0.944779i	−0.802043	+	0.357093i	−0.766475	−	0.642274i	$-0.777991\pi$
$7$	−2.12201	+	0.944779i	−0.802043	+	0.357093i	−0.0355687	+	0.999367i	$0.511324\pi$
$8$	−1.32262	+	0.960937i	−0.467615	+	0.339742i
$9$	−1.25250	−	0.557647i	−0.417499	−	0.185882i
$10$	−0.419001	+	0.0890613i	−0.132500	+	0.0281637i
$11$	0.574101	−	5.46220i	0.173098	−	1.64692i	−0.471116	−	0.882071i	$-0.656149\pi$
$11$	0.574101	−	5.46220i	0.173098	−	1.64692i	0.644214	−	0.764845i	$-0.277185\pi$
$12$	1.55133	+	1.72293i	0.447831	+	0.497367i
$13$	1.15773	−	1.28579i	0.321098	−	0.356615i	−0.560888	−	0.827892i	$-0.689540\pi$
$13$	1.15773	−	1.28579i	0.321098	−	0.356615i	0.881985	+	0.471277i	$0.156207\pi$
$14$	−0.104007	−	0.989558i	−0.0277970	−	0.264470i
$15$	0.394402	+	1.21384i	0.101834	+	0.313413i
$16$	0.906257	+	2.78917i	0.226564	+	0.697293i
$17$	0.248318	+	2.36259i	0.0602260	+	0.573012i	0.982472	+	0.186409i	$0.0596849\pi$
$17$	0.248318	+	2.36259i	0.0602260	+	0.573012i	−0.922246	+	0.386603i	$0.873648\pi$
$18$	0.392977	−	0.436445i	0.0926256	−	0.102871i
$19$	0.0615651	+	0.0683749i	0.0141240	+	0.0156863i	0.750165	−	0.661250i	$-0.229974\pi$
$19$	0.0615651	+	0.0683749i	0.0141240	+	0.0156863i	−0.736041	+	0.676936i	$0.763307\pi$
$20$	−0.189877	+	1.80656i	−0.0424577	+	0.403958i
$21$	−2.89987	+	0.616386i	−0.632803	+	0.134506i
$22$	2.14928	+	0.956923i	0.458229	+	0.204017i
$23$	2.64794	−	1.92384i	0.552133	−	0.401148i	−0.276438	−	0.961032i	$-0.589154\pi$
$23$	2.64794	−	1.92384i	0.552133	−	0.401148i	0.828571	+	0.559883i	$0.189154\pi$
$24$	−1.90618	+	0.848685i	−0.389097	+	0.173237i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.370577	+	0.641857i	0.0726760	+	0.125879i
$27$	−4.51334	−	3.27913i	−0.868593	−	0.631070i
$28$	−4.12722	−	0.877269i	−0.779972	−	0.165788i
$29$	2.98015	−	9.17195i	0.553399	−	1.70319i	−0.146734	−	0.989176i	$-0.546876\pi$
$29$	2.98015	−	9.17195i	0.553399	−	1.70319i	0.700133	−	0.714012i	$-0.253124\pi$
$30$	−0.546723			−0.0998174
$31$	5.50834	+	0.811267i	0.989328	+	0.145708i
$31$	5.50834	+	0.811267i	0.989328	+	0.145708i
$32$	−4.52595			−0.800082
$33$	2.16617	−	6.66679i	0.377082	−	1.16054i
$34$	−0.995378	−	0.211574i	−0.170706	−	0.0362847i
$35$	−1.87921	−	1.36532i	−0.317644	−	0.230782i
$36$	−1.24524	−	2.15682i	−0.207540	−	0.359470i
$37$	−5.51369	+	9.54999i	−0.906445	+	1.57001i	−0.0874786	+	0.996166i	$0.527881\pi$
$37$	−5.51369	+	9.54999i	−0.906445	+	1.57001i	−0.818966	+	0.573842i	$0.805452\pi$
$38$	−0.0360051	+	0.0160305i	−0.00584079	+	0.00260049i
$39$	1.78654	−	1.29800i	0.286075	−	0.207846i
$40$	−1.49350	−	0.664951i	−0.236144	−	0.105138i
$41$	−5.14120	+	1.09280i	−0.802920	+	0.170666i	−0.591053	−	0.806633i	$-0.701288\pi$
$41$	−5.14120	+	1.09280i	−0.802920	+	0.170666i	−0.211867	+	0.977298i	$0.567954\pi$
$42$	0.132745	−	1.26298i	0.0204830	−	0.194883i
$43$	−3.49633	−	3.88307i	−0.533185	−	0.592162i	0.415023	−	0.909811i	$-0.363773\pi$
$43$	−3.49633	−	3.88307i	−0.533185	−	0.592162i	−0.948209	+	0.317648i	$0.897107\pi$
$44$	6.67577	−	7.41420i	1.00641	−	1.11773i
$45$	−0.143311	−	1.36352i	−0.0213636	−	0.203261i
$46$	0.433254	+	1.33342i	0.0638799	+	0.196602i
$47$	0.795429	+	2.44808i	0.116025	+	0.357089i	0.992159	−	0.124978i	$-0.0398861\pi$
$47$	0.795429	+	2.44808i	0.116025	+	0.357089i	−0.876134	+	0.482067i	$0.839886\pi$
$48$	0.391256	+	3.72255i	0.0564729	+	0.537304i
$49$	−1.07361	+	1.19236i	−0.153372	+	0.170337i
$50$	−0.286630	−	0.318334i	−0.0405355	−	0.0450193i
$51$	−0.316931	+	3.01540i	−0.0443793	+	0.422240i
$52$	3.07425	−	0.653452i	0.426322	−	0.0906175i
$53$	−3.55264	−	1.58174i	−0.487992	−	0.217268i	0.147965	−	0.988993i	$-0.452728\pi$
$53$	−3.55264	−	1.58174i	−0.487992	−	0.217268i	−0.635957	+	0.771725i	$0.719394\pi$
$54$	1.93334	−	1.40465i	0.263094	−	0.191149i
$55$	5.01746	−	2.23392i	0.676554	−	0.301221i
$56$	1.89873	−	3.28869i	0.253728	−	0.439470i
$57$	0.0587152	+	0.101698i	0.00777701	+	0.0134702i
$58$	3.34213	+	2.42820i	0.438843	+	0.318838i
$59$	−6.13377	−	1.30377i	−0.798549	−	0.169737i	−0.209473	−	0.977814i	$-0.567175\pi$
$59$	−6.13377	−	1.30377i	−0.798549	−	0.169737i	−0.589076	+	0.808078i	$0.700508\pi$
$60$	−0.716434	+	2.20496i	−0.0924912	+	0.284659i
$61$	−0.530885			−0.0679729			−0.0339864	−	0.999422i	$-0.510820\pi$
$61$	−0.530885			−0.0679729			−0.0339864	+	0.999422i	$0.510820\pi$
$62$	−1.05965	+	2.13669i	−0.134576	+	0.271360i
$63$	3.18466			0.401229
$64$	−1.21341	+	3.73449i	−0.151676	+	0.466812i
$65$	1.69240	+	0.359730i	0.209916	+	0.0446190i
$66$	2.42928	+	1.76498i	0.299024	+	0.217254i
$67$	4.91249	+	8.50868i	0.600156	+	1.03950i	0.992797	+	0.119809i	$0.0382283\pi$
$67$	4.91249	+	8.50868i	0.600156	+	1.03950i	−0.392641	+	0.919692i	$0.628438\pi$
$68$	−2.15765	+	3.73716i	−0.261653	+	0.453197i
$69$	3.81625	−	1.69911i	0.459423	−	0.204548i
$70$	0.804979	−	0.584851i	0.0962134	−	0.0699031i
$71$	0.689090	+	0.306803i	0.0817800	+	0.0364108i	0.447219	−	0.894424i	$-0.352414\pi$
$71$	0.689090	+	0.306803i	0.0817800	+	0.0364108i	−0.365439	+	0.930835i	$0.619081\pi$
$72$	2.19244	−	0.466016i	0.258381	−	0.0549206i
$73$	−0.505379	+	4.80836i	−0.0591501	+	0.562775i	0.924309	+	0.381645i	$0.124642\pi$
$73$	−0.505379	+	4.80836i	−0.0591501	+	0.562775i	−0.983459	+	0.181130i	$0.942024\pi$
$74$	−3.16077	−	3.51039i	−0.367432	−	0.408075i
$75$	−0.854019	+	0.948485i	−0.0986137	+	0.109522i
$76$	0.0174701	+	0.166217i	0.00200396	+	0.0190664i
$77$	3.94233	+	12.1332i	0.449270	+	1.38271i
$78$	0.292312	+	0.899645i	0.0330979	+	0.101865i
$79$	0.0774835	+	0.737207i	0.00871758	+	0.0829422i	0.998016	−	0.0629664i	$-0.0200561\pi$
$79$	0.0774835	+	0.737207i	0.00871758	+	0.0829422i	−0.989298	+	0.145909i	$0.953389\pi$
$80$	−1.96237	+	2.17943i	−0.219399	+	0.243667i
$81$	−2.01221	−	2.23479i	−0.223579	−	0.248310i
$82$	0.235345	−	2.23916i	0.0259895	−	0.247274i
$83$	−5.69004	+	1.20946i	−0.624563	+	0.132755i	−0.509313	−	0.860582i	$-0.670100\pi$
$83$	−5.69004	+	1.20946i	−0.624563	+	0.132755i	−0.115250	+	0.993336i	$0.536767\pi$
$84$	−4.91972	−	2.19040i	−0.536786	−	0.238992i
$85$	−1.92190	+	1.39634i	−0.208460	+	0.151455i
$86$	2.04476	−	0.910385i	0.220492	−	0.0981693i
$87$	6.15435	−	10.6596i	0.659815	−	1.14283i
$88$	4.48952	+	7.77607i	0.478584	+	0.828932i
$89$	13.8860	+	10.0888i	1.47191	+	1.06941i	0.980054	+	0.198732i	$0.0636823\pi$
$89$	13.8860	+	10.0888i	1.47191	+	1.06941i	0.491859	+	0.870675i	$0.336318\pi$
$90$	0.574461	+	0.122106i	0.0605535	+	0.0128711i
$91$	−1.24193	+	3.82226i	−0.130190	+	0.400682i
$92$	5.94549			0.619860
$93$	6.66146	+	2.47450i	0.690761	+	0.256594i
$94$	−1.10263			−0.113727
$95$	−0.0284319	+	0.0875044i	−0.00291705	+	0.00897776i
$96$	−5.65029	−	1.20101i	−0.576680	−	0.122577i
$97$	−12.7059	−	9.23136i	−1.29009	−	0.937303i	−0.290280	−	0.956942i	$-0.593748\pi$
$97$	−12.7059	−	9.23136i	−1.29009	−	0.937303i	−0.999807	+	0.0196387i	$0.993748\pi$
$98$	−0.343648	−	0.595216i	−0.0347137	−	0.0601259i
$99$	−3.76504	+	6.52124i	−0.378401	+	0.655410i
$100$	−1.65946	+	0.738840i	−0.165946	+	0.0738840i
$101$	1.18489	−	0.860874i	0.117901	−	0.0856602i	−0.527272	−	0.849696i	$-0.676785\pi$
$101$	1.18489	−	0.860874i	0.117901	−	0.0856602i	0.645173	+	0.764036i	$0.276785\pi$
$102$	−1.18651	−	0.528268i	−0.117482	−	0.0523063i
$103$	16.4557	−	3.49777i	1.62143	−	0.344646i	0.694388	−	0.719601i	$-0.255675\pi$
$103$	16.4557	−	3.49777i	1.62143	−	0.344646i	0.927043	+	0.374955i	$0.122342\pi$
$104$	−0.295671	+	2.81312i	−0.0289929	+	0.275849i
$105$	−1.98374	−	2.20317i	−0.193593	−	0.215007i
$106$	1.11466	−	1.23795i	0.108265	−	0.120241i
$107$	−1.82093	−	17.3249i	−0.176035	−	1.67487i	−0.624469	−	0.781050i	$-0.714685\pi$
$107$	−1.82093	−	17.3249i	−0.176035	−	1.67487i	0.448434	−	0.893816i	$-0.351982\pi$
$108$	−3.13155	−	9.63793i	−0.301334	−	0.927410i
$109$	1.74808	+	5.38002i	0.167435	+	0.515313i	0.999207	−	0.0398042i	$-0.0126734\pi$
$109$	1.74808	+	5.38002i	0.167435	+	0.515313i	−0.831772	+	0.555117i	$0.812673\pi$
$110$	0.245923	+	2.33980i	0.0234478	+	0.223091i
$111$	−9.41759	+	10.4593i	−0.893878	+	0.992753i
$112$	−4.55824	−	5.06243i	−0.430713	−	0.478355i
$113$	−1.19118	+	11.3334i	−0.112057	+	1.06615i	0.783557	+	0.621320i	$0.213403\pi$
$113$	−1.19118	+	11.3334i	−0.112057	+	1.06615i	−0.895614	+	0.444832i	$0.853263\pi$
$114$	−0.0492034	+	0.0104585i	−0.00460832	+	0.000979528i
$115$	2.99006	+	1.33126i	0.278825	+	0.124141i
$116$	14.1726	−	10.2970i	1.31589	−	0.956053i
$117$	−2.16708	+	0.964844i	−0.200346	+	0.0891999i
$118$	1.34308	−	2.32629i	0.123641	−	0.214152i
$119$	−2.75906	−	4.77882i	−0.252922	−	0.438074i
$120$	−1.68807	−	1.22646i	−0.154099	−	0.111960i
$121$	−18.7465	−	3.98468i	−1.70422	−	0.362244i
$122$	0.0702737	−	0.216280i	0.00636228	−	0.0195811i
$123$	−6.70837			−0.604873
$124$	7.22877	+	7.07357i	0.649163	+	0.635225i
$125$	−1.00000			−0.0894427
$126$	−0.421556	+	1.29742i	−0.0375552	+	0.115583i
$127$	9.96183	+	2.11745i	0.883969	+	0.187893i	0.627460	−	0.778649i	$-0.284094\pi$
$127$	9.96183	+	2.11745i	0.883969	+	0.187893i	0.256509	+	0.966542i	$0.417428\pi$
$128$	−8.68393	−	6.30925i	−0.767558	−	0.557664i
$129$	−3.33448	−	5.77549i	−0.293585	−	0.508504i
$130$	−0.370577	+	0.641857i	−0.0325017	+	0.0562946i
$131$	12.7763	−	5.68837i	1.11627	−	0.496995i	0.236136	−	0.971720i	$-0.424119\pi$
$131$	12.7763	−	5.68837i	1.11627	−	0.496995i	0.880134	+	0.474725i	$0.157452\pi$
$132$	10.3016	−	7.48456i	0.896640	−	0.651447i
$133$	−0.195241	−	0.0869268i	−0.0169295	−	0.00753751i
$134$	−4.11667	+	0.875026i	−0.355626	+	0.0755907i
$135$	0.583143	−	5.54823i	0.0501889	−	0.477516i
$136$	−2.59873	−	2.88618i	−0.222839	−	0.247488i
$137$	−4.16405	+	4.62464i	−0.355758	+	0.395110i	−0.894284	−	0.447499i	$-0.852315\pi$
$137$	−4.16405	+	4.62464i	−0.355758	+	0.395110i	0.538526	+	0.842609i	$0.318981\pi$
$138$	0.187048	+	1.77964i	0.0159225	+	0.151493i
$139$	1.06173	+	3.26767i	0.0900549	+	0.277160i	0.985933	−	0.167139i	$-0.0534528\pi$
$139$	1.06173	+	3.26767i	0.0900549	+	0.277160i	−0.895879	+	0.444299i	$0.853453\pi$
$140$	−1.30388	−	4.01292i	−0.110198	−	0.339153i
$141$	0.343408	+	3.26731i	0.0289202	+	0.275157i
$142$	−0.216206	+	0.240121i	−0.0181436	+	0.0201505i
$143$	−6.35861	−	7.06195i	−0.531734	−	0.590550i
$144$	0.420291	−	3.99880i	0.0350242	−	0.333233i
$145$	9.43321	−	2.00509i	0.783386	−	0.166514i
$146$	−1.89201	−	0.842375i	−0.156584	−	0.0697155i
$147$	−1.65672	+	1.20368i	−0.136644	+	0.0992774i
$148$	−18.2995	+	8.14746i	−1.50421	+	0.669717i
$149$	−11.3013	+	19.5744i	−0.925840	+	1.60360i	−0.135634	+	0.990759i	$0.543307\pi$
$149$	−11.3013	+	19.5744i	−0.925840	+	1.60360i	−0.790205	+	0.612842i	$0.790026\pi$
$150$	−0.273361	−	0.473476i	−0.0223199	−	0.0386591i
$151$	−6.52990	−	4.74425i	−0.531396	−	0.386082i	0.289484	−	0.957183i	$-0.406516\pi$
$151$	−6.52990	−	4.74425i	−0.531396	−	0.386082i	−0.820880	+	0.571101i	$0.806516\pi$
$152$	−0.147131	−	0.0312736i	−0.0119339	−	0.00253663i
$153$	1.00647	−	3.09761i	0.0813685	−	0.250427i
$154$	−5.46488			−0.440372
$155$	2.05159	+	5.17600i	0.164788	+	0.415746i
$156$	4.01136			0.321166
$157$	3.16499	−	9.74083i	0.252593	−	0.777403i	−0.741701	−	0.670731i	$-0.765981\pi$
$157$	3.16499	−	9.74083i	0.252593	−	0.777403i	0.994294	−	0.106672i	$-0.0340194\pi$
$158$	−0.310591	−	0.0660182i	−0.0247093	−	0.00525213i
$159$	−4.01546	−	2.91740i	−0.318447	−	0.231365i
$160$	−2.26297	−	3.91958i	−0.178904	−	0.309870i
$161$	−3.80134	+	6.58412i	−0.299588	+	0.518901i
$162$	1.17680	−	0.523945i	0.0924582	−	0.0411650i
$163$	14.8806	−	10.8114i	1.16554	−	0.846813i	0.175071	−	0.984556i	$-0.443985\pi$
$163$	14.8806	−	10.8114i	1.16554	−	0.846813i	0.990468	+	0.137742i	$0.0439846\pi$
$164$	−8.72222	−	3.88338i	−0.681091	−	0.303241i
$165$	6.85670	−	1.45744i	0.533793	−	0.113461i
$166$	0.260469	−	2.47819i	0.0202163	−	0.192345i
$167$	1.05447	+	1.17111i	0.0815975	+	0.0906232i	0.782561	−	0.622574i	$-0.213913\pi$
$167$	1.05447	+	1.17111i	0.0815975	+	0.0906232i	−0.700963	+	0.713197i	$0.747246\pi$
$168$	3.24310	−	3.60183i	0.250211	−	0.277887i
$169$	1.04595	+	9.95157i	0.0804579	+	0.765506i
$170$	−0.314461	−	0.967810i	−0.0241180	−	0.0742276i
$171$	−0.0389809	−	0.119971i	−0.00298094	−	0.00917440i
$172$	−0.992141	−	9.43959i	−0.0756500	−	0.719762i
$173$	3.57253	−	3.96770i	0.271614	−	0.301658i	−0.591870	−	0.806033i	$-0.701610\pi$
$173$	3.57253	−	3.96770i	0.271614	−	0.301658i	0.863485	+	0.504375i	$0.168277\pi$
$174$	3.52804	+	3.91828i	0.267460	+	0.297044i
$175$	0.242801	−	2.31010i	0.0183541	−	0.174627i
$176$	15.7553	−	3.34890i	1.18760	−	0.252432i
$177$	−7.31156	−	3.25532i	−0.549571	−	0.244685i
$178$	−5.94822	+	4.32164i	−0.445838	+	0.323920i
$179$	−17.3679	+	7.73270i	−1.29814	+	0.577969i	−0.935291	−	0.353879i	$-0.884862\pi$
$179$	−17.3679	+	7.73270i	−1.29814	+	0.577969i	−0.362848	+	0.931848i	$0.618196\pi$
$180$	1.24524	−	2.15682i	0.0928147	−	0.160760i
$181$	8.67074	+	15.0182i	0.644491	+	1.11629i	0.984419	+	0.175840i	$0.0562642\pi$
$181$	8.67074	+	15.0182i	0.644491	+	1.11629i	−0.339927	+	0.940452i	$0.610402\pi$
$182$	−1.39278	−	1.01191i	−0.103240	−	0.0750080i
$183$	−0.662768	−	0.140876i	−0.0489932	−	0.0104138i
$184$	−1.65352	+	5.08900i	−0.121899	+	0.375166i
$185$	−11.0274			−0.810749
$186$	−1.88988	+	2.38630i	−0.138573	+	0.174972i
$187$	13.0475			0.954128
$188$	−1.44490	+	4.44695i	−0.105380	+	0.324327i
$189$	12.6754	+	2.69424i	0.921999	+	0.195977i
$190$	−0.0318854	−	0.0231661i	−0.00231321	−	0.00168064i
$191$	−3.80893	−	6.59727i	−0.275605	−	0.477362i	0.694683	−	0.719316i	$-0.255545\pi$
$191$	−3.80893	−	6.59727i	−0.275605	−	0.477362i	−0.970288	+	0.241955i	$0.922211\pi$
$192$	−2.50583	+	4.34023i	−0.180843	+	0.313229i
$193$	−11.1900	+	4.98213i	−0.805477	+	0.358621i	−0.767817	−	0.640669i	$-0.778657\pi$
$193$	−11.1900	+	4.98213i	−0.805477	+	0.358621i	−0.0376597	+	0.999291i	$0.511990\pi$
$194$	5.44271	−	3.95436i	0.390764	−	0.283906i
$195$	2.01737	+	0.898189i	0.144467	+	0.0643207i
$196$	−2.85085	+	0.605968i	−0.203632	+	0.0432834i
$197$	1.53433	−	14.5982i	0.109316	−	1.04008i	−0.793065	−	0.609137i	$-0.791516\pi$
$197$	1.53433	−	14.5982i	0.109316	−	1.04008i	0.902381	−	0.430938i	$-0.141817\pi$
$198$	−2.15834	−	2.39708i	−0.153387	−	0.170353i
$199$	5.09789	−	5.66178i	0.361380	−	0.401353i	−0.534847	−	0.844949i	$-0.679631\pi$
$199$	5.09789	−	5.66178i	0.361380	−	0.401353i	0.896227	+	0.443596i	$0.146297\pi$
$200$	−0.170888	−	1.62589i	−0.0120836	−	0.114968i
$201$	3.87499	+	11.9260i	0.273321	+	0.841195i
$202$	0.193871	+	0.596674i	0.0136407	+	0.0419819i
$203$	2.34157	+	22.2785i	0.164346	+	1.56365i
$204$	−3.68535	+	4.09299i	−0.258026	+	0.286567i
$205$	−3.51699	−	3.90601i	−0.245637	−	0.272808i
$206$	−0.753282	+	7.16699i	−0.0524836	+	0.499348i
$207$	−4.38936	+	0.932987i	−0.305081	+	0.0648471i
$208$	4.63550	+	2.06386i	0.321414	+	0.143103i
$209$	0.408822	−	0.297027i	0.0282788	−	0.0205458i
$210$	1.16015	−	0.516532i	0.0800579	−	0.0356441i
$211$	4.61719	−	7.99721i	0.317860	−	0.550550i	−0.662181	−	0.749344i	$-0.730369\pi$
$211$	4.61719	−	7.99721i	0.317860	−	0.550550i	0.980041	+	0.198794i	$0.0637023\pi$
$212$	−3.53206	−	6.11770i	−0.242583	−	0.420165i
$213$	0.778862	+	0.565876i	0.0533667	+	0.0387732i
$214$	7.29915	+	1.55148i	0.498959	+	0.106057i
$215$	1.61467	−	4.96945i	0.110120	−	0.338913i
$216$	9.12046			0.620568
$217$	−12.4552	+	3.48265i	−0.845515	+	0.236418i
$218$	−2.42319			−0.164119
$219$	−1.90687	+	5.86875i	−0.128854	+	0.396573i
$220$	9.75877	+	2.07429i	0.657936	+	0.139849i
$221$	3.32529	+	2.41596i	0.223683	+	0.162515i
$222$	−3.01446	−	5.22119i	−0.202317	−	0.350424i
$223$	14.8688	−	25.7535i	0.995689	−	1.72458i	0.417515	−	0.908670i	$-0.362901\pi$
$223$	14.8688	−	25.7535i	0.995689	−	1.72458i	0.578174	−	0.815913i	$-0.303765\pi$
$224$	9.60409	−	4.27602i	0.641700	−	0.285703i
$225$	1.10918	−	0.805870i	0.0739456	−	0.0537247i
$226$	−4.45948	−	1.98549i	−0.296640	−	0.132073i
$227$	10.5426	−	2.24091i	0.699740	−	0.148734i	0.155713	−	0.987802i	$-0.450232\pi$
$227$	10.5426	−	2.24091i	0.699740	−	0.148734i	0.544027	+	0.839068i	$0.316899\pi$
$228$	−0.0222973	+	0.212144i	−0.00147667	+	0.0140496i
$229$	−1.11564	−	1.23905i	−0.0737238	−	0.0818786i	0.705154	−	0.709054i	$-0.250878\pi$
$229$	−1.11564	−	1.23905i	−0.0737238	−	0.0818786i	−0.778878	+	0.627175i	$0.784211\pi$
$230$	−0.938148	+	1.04192i	−0.0618597	+	0.0687021i
$231$	1.70201	+	16.1935i	0.111984	+	1.06546i
$232$	4.87207	+	14.9947i	0.319867	+	0.984450i
$233$	6.43174	+	19.7949i	0.421357	+	1.29680i	0.906439	+	0.422336i	$0.138790\pi$
$233$	6.43174	+	19.7949i	0.421357	+	1.29680i	−0.485082	+	0.874469i	$0.661210\pi$
$234$	−0.106216	−	1.01057i	−0.00694354	−	0.0660633i
$235$	−1.72238	+	1.91290i	−0.112356	+	0.124784i
$236$	−7.62203	−	8.46513i	−0.496152	−	0.551033i
$237$	−0.0988932	+	0.940906i	−0.00642380	+	0.0611184i
$238$	2.31209	−	0.491450i	0.149871	−	0.0318560i
$239$	−3.16870	−	1.41080i	−0.204966	−	0.0912568i	0.301686	−	0.953407i	$-0.402451\pi$
$239$	−3.16870	−	1.41080i	−0.204966	−	0.0912568i	−0.506652	+	0.862151i	$0.669117\pi$
$240$	−3.02819	+	2.20011i	−0.195469	+	0.142017i
$241$	−14.6308	+	6.51407i	−0.942455	+	0.419608i	−0.819677	−	0.572826i	$-0.805847\pi$
$241$	−14.6308	+	6.51407i	−0.942455	+	0.419608i	−0.122778	+	0.992434i	$0.539180\pi$
$242$	4.10483	−	7.10977i	0.263868	−	0.457033i
$243$	6.44913	+	11.1702i	0.413712	+	0.716570i
$244$	−0.780180	−	0.566834i	−0.0499459	−	0.0362878i
$245$	−1.56942	−	0.333590i	−0.100266	−	0.0213123i
$246$	0.887993	−	2.73296i	0.0566163	−	0.174247i
$247$	0.159192			0.0101291
$248$	−8.06500	+	4.22018i	−0.512128	+	0.267981i
$249$	−7.42451			−0.470509
$250$	0.132371	−	0.407396i	0.00837187	−	0.0257660i
$251$	10.9060	+	2.31814i	0.688381	+	0.146320i	0.538805	−	0.842430i	$-0.318876\pi$
$251$	10.9060	+	2.31814i	0.688381	+	0.146320i	0.149576	+	0.988750i	$0.452209\pi$
$252$	4.68013	+	3.40031i	0.294820	+	0.214199i
$253$	−8.98823	−	15.5681i	−0.565085	−	0.978756i
$254$	−2.18130	+	3.77812i	−0.136867	+	0.237060i
$255$	−2.76988	+	1.23323i	−0.173456	+	0.0772278i
$256$	−2.63364	+	1.91345i	−0.164603	+	0.119591i
$257$	11.0665	+	4.92713i	0.690310	+	0.307346i	0.721744	−	0.692160i	$-0.243341\pi$
$257$	11.0665	+	4.92713i	0.690310	+	0.307346i	−0.0314341	+	0.999506i	$0.510007\pi$
$258$	2.79430	−	0.593947i	0.173966	−	0.0369775i
$259$	2.67746	−	25.4744i	0.166369	−	1.58290i
$260$	2.10303	+	2.33565i	0.130424	+	0.144851i
$261$	−8.84733	+	9.82596i	−0.547636	+	0.608212i
$262$	0.626209	+	5.95798i	0.0386873	+	0.368085i
$263$	4.91213	+	15.1180i	0.302895	+	0.932215i	0.980454	+	0.196747i	$0.0630377\pi$
$263$	4.91213	+	15.1180i	0.302895	+	0.932215i	−0.677559	+	0.735468i	$0.736962\pi$
$264$	3.54135	+	10.8992i	0.217955	+	0.670797i
$265$	−0.406495	−	3.86754i	−0.0249708	−	0.237581i
$266$	0.0612578	−	0.0680337i	0.00375596	−	0.00417141i
$267$	14.6584	+	16.2798i	0.897081	+	0.996309i
$268$	−1.86553	+	17.7494i	−0.113956	+	1.08422i
$269$	8.94537	−	1.90140i	0.545409	−	0.115930i	0.0730363	−	0.997329i	$-0.476731\pi$
$269$	8.94537	−	1.90140i	0.545409	−	0.115930i	0.472372	+	0.881399i	$0.343398\pi$
$270$	2.18314	+	0.971995i	0.132861	+	0.0591537i
$271$	2.64009	−	1.91814i	0.160374	−	0.116518i	−0.504704	−	0.863292i	$-0.668398\pi$
$271$	2.64009	−	1.91814i	0.160374	−	0.116518i	0.665078	+	0.746774i	$0.268398\pi$
$272$	−6.36463	+	2.83371i	−0.385912	+	0.171819i
$273$	−2.56473	+	4.44224i	−0.155224	+	0.268857i
$274$	−1.33286	−	2.30858i	−0.0805211	−	0.139467i
$275$	4.44336	+	3.22829i	0.267945	+	0.194673i
$276$	7.42247	+	1.57770i	0.446780	+	0.0949661i
$277$	8.76052	−	26.9621i	0.526369	−	1.62000i	−0.235225	−	0.971941i	$-0.575583\pi$
$277$	8.76052	−	26.9621i	0.526369	−	1.62000i	0.761593	−	0.648055i	$-0.224417\pi$
$278$	−1.47178			−0.0882714
$279$	−6.44678	−	4.08782i	−0.385958	−	0.244731i
$280$	3.79746			0.226941
$281$	1.56040	−	4.80240i	0.0930854	−	0.286487i	−0.893665	−	0.448736i	$-0.851875\pi$
$281$	1.56040	−	4.80240i	0.0930854	−	0.286487i	0.986750	+	0.162248i	$0.0518745\pi$
$282$	−1.37654	−	0.292594i	−0.0819721	−	0.0174237i
$283$	−13.4525	−	9.77381i	−0.799668	−	0.580993i	0.111149	−	0.993804i	$-0.464547\pi$
$283$	−13.4525	−	9.77381i	−0.799668	−	0.580993i	−0.910817	+	0.412811i	$0.864547\pi$
$284$	0.685098	+	1.18662i	0.0406531	+	0.0704132i
$285$	−0.0587152	+	0.101698i	−0.00347799	+	0.00602405i
$286$	3.71870	−	1.65567i	0.219892	−	0.0979020i
$287$	9.87721	−	7.17621i	0.583033	−	0.423599i
$288$	5.66873	+	2.52388i	0.334033	+	0.148721i
$289$	11.1083	−	2.36115i	0.653432	−	0.138891i
$290$	−0.431817	+	4.10847i	−0.0253572	+	0.241257i
$291$	−13.4127	−	14.8963i	−0.786264	−	0.873235i
$292$	−5.87665	+	6.52669i	−0.343905	+	0.381945i
$293$	−0.714986	−	6.80264i	−0.0417699	−	0.397414i	−0.995354	−	0.0962864i	$-0.969304\pi$
$293$	−0.714986	−	6.80264i	−0.0417699	−	0.397414i	0.953584	−	0.301128i	$-0.0973631\pi$
$294$	−0.271071	−	0.834271i	−0.0158092	−	0.0486557i
$295$	−1.93778	−	5.96389i	−0.112822	−	0.347231i
$296$	−1.88444	−	17.9293i	−0.109531	−	1.04212i
$297$	−20.5024	+	22.7702i	−1.18967	+	1.32126i
$298$	−6.47858	−	7.19519i	−0.375294	−	0.416806i
$299$	0.591947	−	5.63200i	0.0342332	−	0.325707i
$300$	−2.26777	+	0.482029i	−0.130930	+	0.0278299i
$301$	11.0879	+	4.93664i	0.639095	+	0.284543i
$302$	2.79716	−	2.03225i	0.160958	−	0.116943i
$303$	1.70769	−	0.760311i	0.0981040	−	0.0436787i
$304$	−0.134916	+	0.233681i	−0.00773795	+	0.0134025i
$305$	−0.265442	−	0.459760i	−0.0151992	−	0.0263258i
$306$	1.12872	+	0.820066i	0.0645248	+	0.0468800i
$307$	−30.5483	−	6.49324i	−1.74348	−	0.370589i	−0.777437	−	0.628961i	$-0.783481\pi$
$307$	−30.5483	−	6.49324i	−1.74348	−	0.370589i	−0.966046	+	0.258372i	$0.916814\pi$
$308$	−7.16126	+	22.0401i	−0.408051	+	1.25585i
$309$	21.4718			1.22149
$310$	−2.38025	+	0.150659i	−0.135189	+	0.00855686i
$311$	−17.3909			−0.986145			−0.493073	−	0.869988i	$-0.664126\pi$
$311$	−17.3909			−0.986145			−0.493073	+	0.869988i	$0.664126\pi$
$312$	−1.11561	+	3.43350i	−0.0631591	+	0.194384i
$313$	8.74600	+	1.85902i	0.494353	+	0.105078i	0.448340	−	0.893863i	$-0.352015\pi$
$313$	8.74600	+	1.85902i	0.494353	+	0.105078i	0.0460126	+	0.998941i	$0.485349\pi$
$314$	3.54942	+	2.57880i	0.200305	+	0.145530i
$315$	1.59233	+	2.75800i	0.0897176	+	0.155395i
$316$	−0.673259	+	1.16612i	−0.0378738	+	0.0655993i
$317$	0.0813240	−	0.0362078i	0.00456761	−	0.00203363i	−0.404452	−	0.914559i	$-0.632538\pi$
$317$	0.0813240	−	0.0362078i	0.00456761	−	0.00203363i	0.409019	+	0.912526i	$0.365871\pi$
$318$	1.72007	−	1.24970i	0.0964565	−	0.0700798i
$319$	−48.3882	−	21.5438i	−2.70922	−	1.20622i
$320$	−3.84087	+	0.816403i	−0.214711	+	0.0456383i
$321$	2.32407	−	22.1120i	0.129717	−	1.23417i
$322$	−2.17916	−	2.42020i	−0.121440	−	0.134872i
$323$	−0.146254	+	0.162432i	−0.00813779	+	0.00903794i
$324$	−0.570997	−	5.43268i	−0.0317221	−	0.301815i
$325$	0.534663	+	1.64552i	0.0296578	+	0.0912772i
$326$	2.43476	+	7.49341i	0.134849	+	0.415021i
$327$	0.754691	+	7.18041i	0.0417345	+	0.397078i
$328$	5.74973	−	6.38572i	0.317475	−	0.352592i
$329$	−4.00080	−	4.44334i	−0.220571	−	0.244969i
$330$	−0.313874	+	2.98631i	−0.0172782	+	0.164391i
$331$	−13.8627	+	2.94660i	−0.761961	+	0.161960i	−0.572473	−	0.819923i	$-0.694016\pi$
$331$	−13.8627	+	2.94660i	−0.761961	+	0.161960i	−0.189488	+	0.981883i	$0.560683\pi$
$332$	−9.65335	−	4.29795i	−0.529796	−	0.235881i
$333$	12.2314	−	8.88663i	0.670276	−	0.486984i
$334$	−0.616687	+	0.274567i	−0.0337436	+	0.0150236i
$335$	−4.91249	+	8.50868i	−0.268398	+	0.464879i
$336$	−4.34723	−	7.52962i	−0.237161	−	0.410775i
$337$	−15.7613	−	11.4512i	−0.858571	−	0.623789i	0.0689246	−	0.997622i	$-0.478043\pi$
$337$	−15.7613	−	11.4512i	−0.858571	−	0.623789i	−0.927496	+	0.373833i	$0.878043\pi$
$338$	−4.19268	−	0.891182i	−0.228052	−	0.0484739i
$339$	−4.49452	+	13.8327i	−0.244109	+	0.751290i
$340$	−4.31530			−0.234030
$341$	7.59365	−	29.6219i	0.411219	−	1.60412i
$342$	0.0540356			0.00292191
$343$	6.17623	−	19.0085i	0.333485	−	1.02636i
$344$	8.35569	+	1.77606i	0.450508	+	0.0957585i
$345$	3.37960	+	2.45542i	0.181951	+	0.132195i
$346$	1.14352	+	1.98064i	0.0614762	+	0.106480i
$347$	−1.44990	+	2.51131i	−0.0778350	+	0.134814i	−0.902316	−	0.431076i	$-0.858134\pi$
$347$	−1.44990	+	2.51131i	−0.0778350	+	0.134814i	0.824481	+	0.565890i	$0.191467\pi$
$348$	20.4258	−	9.09416i	1.09494	−	0.487498i
$349$	25.0794	−	18.2213i	1.34247	−	0.975362i	0.343121	−	0.939291i	$-0.388516\pi$
$349$	25.0794	−	18.2213i	1.34247	−	0.975362i	0.999349	−	0.0360706i	$-0.0114841\pi$
$350$	0.908986	+	0.404707i	0.0485873	+	0.0216325i
$351$	−9.44153	+	2.00686i	−0.503952	+	0.107118i
$352$	−2.59835	+	24.7216i	−0.138492	+	1.31767i
$353$	−12.1174	−	13.4578i	−0.644945	−	0.716284i	0.328679	−	0.944442i	$-0.393396\pi$
$353$	−12.1174	−	13.4578i	−0.644945	−	0.716284i	−0.973624	+	0.228158i	$0.926730\pi$
$354$	2.29404	−	2.54779i	0.121927	−	0.135413i
$355$	0.0788461	+	0.750171i	0.00418472	+	0.0398149i
$356$	9.63471	+	29.6526i	0.510639	+	1.57158i
$357$	−2.17635	−	6.69813i	−0.115185	−	0.354503i
$358$	−0.851260	−	8.09920i	−0.0449905	−	0.428056i
$359$	−2.13487	+	2.37102i	−0.112674	+	0.125138i	−0.796843	−	0.604186i	$-0.793498\pi$
$359$	−2.13487	+	2.37102i	−0.112674	+	0.125138i	0.684169	+	0.729324i	$0.260165\pi$
$360$	1.49980	+	1.66570i	0.0790464	+	0.0877899i
$361$	1.98516	−	18.8875i	0.104482	−	0.994079i
$362$	−7.26609	+	1.54446i	−0.381897	+	0.0811748i
$363$	−22.3461	−	9.94913i	−1.17287	−	0.522194i
$364$	−5.90621	+	4.29111i	−0.309570	+	0.224916i
$365$	−4.41685	+	1.96651i	−0.231188	+	0.102932i
$366$	0.145123	−	0.251361i	0.00758572	−	0.0131389i
$367$	7.09929	+	12.2963i	0.370580	+	0.641863i	0.989655	−	0.143469i	$-0.0458257\pi$
$367$	7.09929	+	12.2963i	0.370580	+	0.641863i	−0.619075	+	0.785332i	$0.712492\pi$
$368$	7.76564	+	5.64207i	0.404812	+	0.294113i
$369$	7.04873	+	1.49825i	0.366942	+	0.0779959i
$370$	1.45970	−	4.49251i	0.0758864	−	0.233554i
$371$	9.03311			0.468976
$372$	7.14751	+	10.7490i	0.370581	+	0.557311i
$373$	−15.3257			−0.793534			−0.396767	−	0.917919i	$-0.629868\pi$
$373$	−15.3257			−0.793534			−0.396767	+	0.917919i	$0.629868\pi$
$374$	−1.72711	+	5.31549i	−0.0893067	+	0.274858i
$375$	−1.24842	−	0.265360i	−0.0644682	−	0.0137031i
$376$	−3.40450	−	2.47351i	−0.175573	−	0.127562i
$377$	−8.34301	−	14.4505i	−0.429687	−	0.744240i
$378$	−2.77547	+	4.80726i	−0.142755	+	0.247259i
$379$	8.33943	−	3.71295i	0.428368	−	0.190722i	−0.181216	−	0.983443i	$-0.558003\pi$
$379$	8.33943	−	3.71295i	0.428368	−	0.190722i	0.609584	+	0.792722i	$0.291337\pi$
$380$	−0.135213	+	0.0982379i	−0.00693627	+	0.00503950i
$381$	11.8747	+	5.28694i	0.608358	+	0.270858i
$382$	3.19189	−	0.678457i	0.163311	−	0.0347129i
$383$	−2.00214	+	19.0491i	−0.102305	+	0.973362i	0.816151	+	0.577838i	$0.196104\pi$
$383$	−2.00214	+	19.0491i	−0.102305	+	0.973362i	−0.918456	+	0.395524i	$0.870563\pi$
$384$	−9.16698	−	10.1810i	−0.467801	−	0.519545i
$385$	−8.53653	+	9.48077i	−0.435062	+	0.483185i
$386$	−0.548461	−	5.21826i	−0.0279160	−	0.265603i
$387$	2.21376	+	6.81325i	0.112532	+	0.346337i
$388$	−8.81590	−	27.1325i	−0.447559	−	1.37745i
$389$	1.03728	+	9.86908i	0.0525923	+	0.500382i	0.988834	+	0.149024i	$0.0476133\pi$
$389$	1.03728	+	9.86908i	0.0525923	+	0.500382i	−0.936241	+	0.351358i	$0.885720\pi$
$390$	−0.632959	+	0.702972i	−0.0320511	+	0.0355964i
$391$	5.20277	+	5.77826i	0.263116	+	0.292219i
$392$	0.274185	−	2.60870i	0.0138485	−	0.131759i
$393$	17.4597	−	3.71117i	0.880724	−	0.187204i
$394$	5.74412	+	2.55745i	0.289385	+	0.128842i
$395$	−0.599698	+	0.435706i	−0.0301741	+	0.0219228i
$396$	−12.4959	+	5.56353i	−0.627942	+	0.279578i
$397$	−3.96326	+	6.86456i	−0.198910	+	0.344523i	−0.948175	−	0.317748i	$-0.897074\pi$
$397$	−3.96326	+	6.86456i	−0.198910	+	0.344523i	0.749265	+	0.662270i	$0.230407\pi$
$398$	1.63177	+	2.82631i	0.0817934	+	0.141670i
$399$	−0.220676	−	0.160330i	−0.0110476	−	0.00802656i
$400$	−2.86862	−	0.609745i	−0.143431	−	0.0304872i
$401$	−0.941046	+	2.89624i	−0.0469936	+	0.144631i	−0.971800	−	0.235807i	$-0.924227\pi$
$401$	−0.941046	+	2.89624i	−0.0469936	+	0.144631i	0.924806	+	0.380438i	$0.124227\pi$
$402$	−5.37154			−0.267908
$403$	7.42032	−	6.14336i	0.369632	−	0.306023i
$404$	2.66047			0.132363
$405$	0.929276	−	2.86002i	0.0461761	−	0.142115i
$406$	−9.38613	−	1.99508i	−0.465826	−	0.0990143i
$407$	48.9986	+	35.5995i	2.42877	+	1.76460i
$408$	−2.47843	−	4.29277i	−0.122701	−	0.212524i
$409$	3.22591	−	5.58744i	0.159511	−	0.276281i	−0.775181	−	0.631739i	$-0.782342\pi$
$409$	3.22591	−	5.58744i	0.159511	−	0.276281i	0.934692	+	0.355457i	$0.115675\pi$
$410$	2.05684	−	0.915764i	0.101580	−	0.0452263i
$411$	−6.42568	+	4.66853i	−0.316955	+	0.230282i
$412$	27.9177	+	12.4298i	1.37541	+	0.612371i
$413$	14.2477	−	3.02844i	0.701083	−	0.149020i
$414$	0.200928	−	1.91171i	0.00987509	−	0.0939552i
$415$	−3.89244	−	4.32299i	−0.191072	−	0.212207i
$416$	−5.23984	+	5.81943i	−0.256904	+	0.285321i
$417$	0.458378	+	4.36118i	0.0224469	+	0.213568i
$418$	0.0668913	+	0.205870i	0.00327176	+	0.0100694i
$419$	2.97598	+	9.15911i	0.145386	+	0.447452i	0.997060	−	0.0766193i	$-0.0244126\pi$
$419$	2.97598	+	9.15911i	0.145386	+	0.447452i	−0.851675	+	0.524071i	$0.824413\pi$
$420$	−0.562918	−	5.35581i	−0.0274676	−	0.261337i
$421$	7.32311	−	8.13314i	0.356906	−	0.396385i	−0.537776	−	0.843088i	$-0.680735\pi$
$421$	7.32311	−	8.13314i	0.356906	−	0.396385i	0.894682	+	0.446703i	$0.147402\pi$
$422$	2.64685	+	2.93962i	0.128846	+	0.143098i
$423$	0.368892	−	3.50978i	0.0179362	−	0.170651i
$424$	6.21872	−	1.32183i	0.302008	−	0.0641937i
$425$	−2.17022	−	0.966244i	−0.105271	−	0.0468697i
$426$	−0.333634	+	0.242399i	−0.0161646	+	0.0117443i
$427$	1.12654	−	0.501569i	0.0545172	−	0.0242726i
$428$	15.8221	−	27.4047i	0.764791	−	1.32466i
$429$	−6.06427	−	10.5036i	−0.292785	−	0.507119i
$430$	1.81080	+	1.31562i	0.0873243	+	0.0634448i
$431$	−10.2955	−	2.18837i	−0.495916	−	0.105410i	−0.0468376	−	0.998903i	$-0.514914\pi$
$431$	−10.2955	−	2.18837i	−0.495916	−	0.105410i	−0.449079	+	0.893492i	$0.648248\pi$
$432$	5.05582	−	15.5602i	0.243248	−	0.748642i
$433$	29.0062			1.39395			0.696974	−	0.717097i	$-0.254529\pi$
$433$	29.0062			1.39395			0.696974	+	0.717097i	$0.254529\pi$
$434$	0.229891	−	5.53520i	0.0110351	−	0.265698i
$435$	12.3087			0.590157
$436$	−3.17539	+	9.77285i	−0.152074	+	0.468035i
$437$	0.294563	+	0.0626113i	0.0140909	+	0.00299510i
$438$	−2.13849	−	1.55370i	−0.102181	−	0.0742388i
$439$	17.4991	+	30.3093i	0.835184	+	1.44658i	0.893880	+	0.448306i	$0.147972\pi$
$439$	17.4991	+	30.3093i	0.835184	+	1.44658i	−0.0586958	+	0.998276i	$0.518694\pi$
$440$	−4.48952	+	7.77607i	−0.214029	+	0.370710i
$441$	2.00960	−	0.894732i	0.0956953	−	0.0426063i
$442$	−1.42442	+	1.03490i	−0.0677529	+	0.0492254i
$443$	−25.3116	−	11.2695i	−1.20259	−	0.535428i	−0.295087	−	0.955471i	$-0.595348\pi$
$443$	−25.3116	−	11.2695i	−1.20259	−	0.535428i	−0.907504	+	0.420043i	$0.862015\pi$
$444$	−25.0075	+	5.31551i	−1.18680	+	0.252263i
$445$	−1.79413	+	17.0700i	−0.0850499	+	0.809196i
$446$	8.52368	+	9.46650i	0.403608	+	0.448252i
$447$	−19.3031	+	21.4382i	−0.913004	+	1.01399i
$448$	−0.953404	−	9.07103i	−0.0450441	−	0.428566i
$449$	−8.87052	−	27.3006i	−0.418626	−	1.28840i	−0.908968	−	0.416867i	$-0.863128\pi$
$449$	−8.87052	−	27.3006i	−0.418626	−	1.28840i	0.490342	−	0.871530i	$-0.336872\pi$
$450$	0.181484	+	0.558551i	0.00855525	+	0.0263303i
$451$	3.01751	+	28.7097i	0.142089	+	1.35188i
$452$	−13.8513	+	15.3835i	−0.651512	+	0.723578i
$453$	−6.89313	−	7.65560i	−0.323868	−	0.359692i
$454$	−0.482603	+	4.59166i	−0.0226497	+	0.215497i
$455$	−3.93114	+	0.835590i	−0.184295	+	0.0391731i
$456$	−0.175383	−	0.0780854i	−0.00821305	−	0.00365668i
$457$	−29.4249	+	21.3785i	−1.37644	+	1.00004i	−0.379237	+	0.925300i	$0.623813\pi$
$457$	−29.4249	+	21.3785i	−1.37644	+	1.00004i	−0.997203	+	0.0747424i	$0.976187\pi$
$458$	0.652461	−	0.290495i	0.0304875	−	0.0135739i
$459$	6.62650	−	11.4774i	0.309298	−	0.535721i
$460$	2.97274	+	5.14894i	0.138605	+	0.240071i
$461$	21.5707	+	15.6720i	1.00465	+	0.729920i	0.963080	−	0.269216i	$-0.0867646\pi$
$461$	21.5707	+	15.6720i	1.00465	+	0.729920i	0.0415684	+	0.999136i	$0.486765\pi$
$462$	−6.82247	−	1.45016i	−0.317410	−	0.0674676i
$463$	−8.02816	+	24.7081i	−0.373100	+	1.14828i	0.571651	+	0.820497i	$0.306303\pi$
$463$	−8.02816	+	24.7081i	−0.373100	+	1.14828i	−0.944751	+	0.327788i	$0.893697\pi$
$464$	28.2829			1.31300
$465$	1.18775	+	7.00624i	0.0550806	+	0.324907i
$466$	−8.91572			−0.413013
$467$	7.06217	−	21.7351i	0.326798	−	1.00578i	−0.643824	−	0.765174i	$-0.722653\pi$
$467$	7.06217	−	21.7351i	0.326798	−	1.00578i	0.970622	−	0.240608i	$-0.0773469\pi$
$468$	−4.21488	−	0.895901i	−0.194833	−	0.0414130i
$469$	−18.4632	−	13.4143i	−0.852550	−	0.619414i
$470$	−0.551314	−	0.954904i	−0.0254302	−	0.0440464i
$471$	6.53607	−	11.3208i	0.301166	−	0.521635i
$472$	9.36547	−	4.16977i	0.431081	−	0.191929i
$473$	−23.2174	+	16.8684i	−1.06754	+	0.775610i
$474$	−0.370230	−	0.164837i	−0.0170052	−	0.00757122i
$475$	−0.0899970	+	0.0191294i	−0.00412934	+	0.000877719i
$476$	1.04776	−	9.96877i	0.0480240	−	0.456918i
$477$	3.56761	+	3.96223i	0.163350	+	0.181418i
$478$	0.994196	−	1.10417i	0.0454734	−	0.0505034i
$479$	2.32302	+	22.1021i	0.106142	+	1.00987i	0.909876	+	0.414881i	$0.136177\pi$
$479$	2.32302	+	22.1021i	0.106142	+	1.00987i	−0.803734	+	0.594988i	$0.797157\pi$
$480$	−1.78504	−	5.49380i	−0.0814757	−	0.250756i
$481$	5.89593	+	18.1458i	0.268831	+	0.827377i
$482$	−0.717107	−	6.82281i	−0.0326633	−	0.310771i
$483$	−6.49284	+	7.21103i	−0.295435	+	0.328113i
$484$	−23.2950	−	25.8717i	−1.05886	−	1.17599i
$485$	1.64165	−	15.6193i	0.0745437	−	0.709236i
$486$	−5.40438	+	1.14874i	−0.245148	+	0.0521077i
$487$	3.72168	+	1.65700i	0.168645	+	0.0750857i	0.489323	−	0.872103i	$-0.337244\pi$
$487$	3.72168	+	1.65700i	0.168645	+	0.0750857i	−0.320678	+	0.947188i	$0.603911\pi$
$488$	0.702157	−	0.510147i	0.0317852	−	0.0230933i
$489$	21.4462	−	9.54845i	0.969830	−	0.431796i
$490$	0.343648	−	0.595216i	0.0155244	−	0.0268891i
$491$	−3.85429	−	6.67583i	−0.173942	−	0.301276i	0.765853	−	0.643016i	$-0.222317\pi$
$491$	−3.85429	−	6.67583i	−0.173942	−	0.301276i	−0.939795	+	0.341740i	$0.888984\pi$
$492$	−9.85852	−	7.16263i	−0.444456	−	0.322916i
$493$	22.4096	+	4.76330i	1.00928	+	0.214528i
$494$	−0.0210724	+	0.0648541i	−0.000948091	+	0.00291793i
$495$	−7.53008			−0.338452
$496$	2.72921	+	16.0989i	0.122545	+	0.722864i
$497$	−1.75211			−0.0785931
$498$	0.982789	−	3.02471i	0.0440398	−	0.135541i
$499$	15.2365	+	3.23861i	0.682077	+	0.144980i	0.535904	−	0.844279i	$-0.319971\pi$
$499$	15.2365	+	3.23861i	0.682077	+	0.144980i	0.146173	+	0.989259i	$0.453304\pi$
$500$	−1.46958	−	1.06772i	−0.0657218	−	0.0477497i
$501$	1.00566	+	1.74185i	0.0449296	+	0.0778203i
$502$	−2.38804	+	4.13621i	−0.106583	+	0.184608i
$503$	−24.7329	+	11.0118i	−1.10279	+	0.490992i	−0.875687	−	0.482880i	$-0.839591\pi$
$503$	−24.7329	+	11.0118i	−1.10279	+	0.490992i	−0.227099	+	0.973872i	$0.572924\pi$
$504$	−4.21208	+	3.06026i	−0.187621	+	0.136315i
$505$	1.33798	+	0.595709i	0.0595395	+	0.0265087i
$506$	7.53214	−	1.60101i	0.334845	−	0.0711734i
$507$	−1.33496	+	12.7013i	−0.0592877	+	0.564085i
$508$	12.3789	+	13.7482i	0.549225	+	0.609977i
$509$	12.2230	−	13.5750i	0.541775	−	0.601702i	−0.408636	−	0.912697i	$-0.633996\pi$
$509$	12.2230	−	13.5750i	0.541775	−	0.601702i	0.950412	+	0.310995i	$0.100662\pi$
$510$	−0.135761	−	1.29168i	−0.00601160	−	0.0571966i
$511$	−3.47041	−	10.6808i	−0.153522	−	0.472492i
$512$	−7.06485	−	21.7434i	−0.312225	−	0.960930i
$513$	−0.0536535	−	0.510479i	−0.00236886	−	0.0225382i
$514$	−3.47218	+	3.85624i	−0.153151	+	0.170092i
$515$	11.2570	+	12.5022i	0.496044	+	0.550912i
$516$	1.26628	−	12.0479i	0.0557449	−	0.530377i
$517$	13.8286	−	2.93935i	0.608179	−	0.129273i
$518$	10.0237	+	4.46285i	0.440417	+	0.196086i
$519$	5.51289	−	4.00535i	0.241989	−	0.175815i
$520$	−2.58407	+	1.15050i	−0.113319	+	0.0504528i
$521$	4.73341	−	8.19851i	0.207374	−	0.359183i	−0.743512	−	0.668722i	$-0.766841\pi$
$521$	4.73341	−	8.19851i	0.207374	−	0.359183i	0.950887	+	0.309539i	$0.100175\pi$
$522$	−2.83192	−	4.90504i	−0.123950	−	0.214688i
$523$	18.9622	+	13.7769i	0.829160	+	0.602420i	0.919322	−	0.393507i	$-0.128738\pi$
$523$	18.9622	+	13.7769i	0.829160	+	0.602420i	−0.0901616	+	0.995927i	$0.528738\pi$
$524$	24.8494	+	5.28191i	1.08555	+	0.230741i
$525$	0.916128	−	2.81955i	0.0399831	−	0.123055i
$526$	−6.80923			−0.296896
$527$	−0.548869	+	13.2154i	−0.0239091	+	0.575672i
$528$	20.5579			0.894669
$529$	−3.79697	+	11.6859i	−0.165086	+	0.508082i
$530$	1.62943	+	0.346346i	0.0707778	+	0.0150443i
$531$	6.95548	+	5.05345i	0.301842	+	0.219301i
$532$	−0.194110	−	0.336208i	−0.00841572	−	0.0145765i
$533$	−4.54703	+	7.87569i	−0.196954	+	0.341134i
$534$	−8.57268	+	3.81680i	−0.370976	+	0.165169i
$535$	14.0934	−	10.2394i	0.609310	−	0.442690i
$536$	−14.6736	−	6.53313i	−0.633805	−	0.282188i
$537$	−23.7344	+	5.04491i	−1.02422	+	0.217704i
$538$	−0.409485	+	3.89599i	−0.0176542	+	0.167968i
$539$	5.89655	+	6.54879i	0.253983	+	0.282076i
$540$	6.78092	−	7.53097i	0.291804	−	0.324081i
$541$	−3.23562	−	30.7849i	−0.139110	−	1.32355i	−0.811937	−	0.583746i	$-0.801587\pi$
$541$	−3.23562	−	30.7849i	−0.139110	−	1.32355i	0.672826	−	0.739801i	$-0.265080\pi$
$542$	0.431970	+	1.32947i	0.0185547	+	0.0571055i
$543$	6.83952	+	21.0499i	0.293512	+	0.903337i
$544$	−1.12387	−	10.6929i	−0.0481857	−	0.458456i
$545$	−3.78520	+	4.20389i	−0.162140	+	0.180075i
$546$	−1.47025	−	1.63288i	−0.0629211	−	0.0698809i
$547$	−1.68009	+	15.9850i	−0.0718353	+	0.683467i	0.898048	+	0.439897i	$0.144985\pi$
$547$	−1.68009	+	15.9850i	−0.0718353	+	0.683467i	−0.969883	+	0.243570i	$0.921681\pi$
$548$	−11.0572	+	2.35028i	−0.472341	+	0.100399i
$549$	0.664931	+	0.296046i	0.0283786	+	0.0126350i
$550$	−1.90336	+	1.38287i	−0.0811596	+	0.0589659i
$551$	0.810604	−	0.360904i	0.0345329	−	0.0153750i
$552$	−3.41471	+	5.91445i	−0.145340	+	0.251736i
$553$	−0.860918	−	1.49115i	−0.0366099	−	0.0634103i
$554$	9.82461	+	7.13800i	0.417408	+	0.303264i
$555$	−13.7668	−	2.92623i	−0.584369	−	0.124211i
$556$	−1.92864	+	5.93575i	−0.0817927	+	0.251732i
$557$	−20.2267			−0.857031			−0.428516	−	0.903534i	$-0.640963\pi$
$557$	−20.2267			−0.857031			−0.428516	+	0.903534i	$0.640963\pi$
$558$	2.51873	−	2.08528i	0.106626	−	0.0882770i
$559$	−9.04064			−0.382378
$560$	2.10508	−	6.47876i	0.0889558	−	0.273778i
$561$	16.2888	+	3.46229i	0.687713	+	0.146178i
$562$	1.74993	+	1.27140i	0.0738162	+	0.0536306i
$563$	−1.36612	−	2.36619i	−0.0575752	−	0.0997232i	0.835801	−	0.549032i	$-0.185004\pi$
$563$	−1.36612	−	2.36619i	−0.0575752	−	0.0997232i	−0.893376	+	0.449309i	$0.851670\pi$
$564$	−2.98389	+	5.16825i	−0.125644	+	0.217623i
$565$	−10.4106	+	4.63508i	−0.437976	+	0.194999i
$566$	5.76253	−	4.18672i	0.242217	−	0.175981i
$567$	6.38130	+	2.84114i	0.267990	+	0.119317i
$568$	−1.20622	+	0.256390i	−0.0506119	+	0.0107579i
$569$	3.74528	−	35.6340i	0.157010	−	1.49385i	−0.578133	−	0.815942i	$-0.696219\pi$
$569$	3.74528	−	35.6340i	0.157010	−	1.49385i	0.735144	−	0.677911i	$-0.237115\pi$
$570$	−0.0336590	−	0.0373821i	−0.00140982	−	0.00156576i
$571$	21.2507	−	23.6013i	0.889315	−	0.987684i	−0.110666	−	0.993858i	$-0.535299\pi$
$571$	21.2507	−	23.6013i	0.889315	−	0.987684i	0.999981	+	0.00617372i	$0.00196517\pi$
$572$	−1.80436	−	17.1673i	−0.0754440	−	0.717802i
$573$	−3.00450	−	9.24691i	−0.125515	−	0.386295i
$574$	1.61610	+	4.97386i	0.0674549	+	0.207605i
$575$	0.342125	+	3.25510i	0.0142676	+	0.135747i
$576$	3.60232	−	4.00078i	0.150097	−	0.166699i
$577$	0.491065	+	0.545382i	0.0204433	+	0.0227046i	0.753280	−	0.657700i	$-0.228471\pi$
$577$	0.491065	+	0.545382i	0.0204433	+	0.0227046i	−0.732836	+	0.680405i	$0.761804\pi$
$578$	−0.508499	+	4.83804i	−0.0211508	+	0.201236i
$579$	−15.2919	+	3.25040i	−0.635511	+	0.135082i
$580$	16.0038	+	7.12534i	0.664521	+	0.295864i
$581$	10.9316	−	7.94230i	0.453521	−	0.329502i
$582$	7.84412	−	3.49243i	0.325149	−	0.144766i
$583$	−10.6793	+	18.4971i	−0.442293	+	0.766074i
$584$	−3.95210	−	6.84525i	−0.163539	−	0.283258i
$585$	−1.91912	−	1.39432i	−0.0793457	−	0.0576481i
$586$	2.86601	+	0.609189i	0.118394	+	0.0251654i
$587$	13.8615	−	42.6613i	0.572125	−	1.76082i	−0.0736408	−	0.997285i	$-0.523462\pi$
$587$	13.8615	−	42.6613i	0.572125	−	1.76082i	0.645766	−	0.763535i	$-0.276538\pi$
$588$	−3.71987			−0.153405
$589$	0.283651	+	0.426578i	0.0116876	+	0.0175769i
$590$	2.68617			0.110588
$591$	5.78926	−	17.8175i	0.238138	−	0.732914i
$592$	−31.6334	−	6.72388i	−1.30012	−	0.276350i
$593$	−14.7186	−	10.6937i	−0.604422	−	0.439138i	0.243024	−	0.970020i	$-0.421861\pi$
$593$	−14.7186	−	10.6937i	−0.604422	−	0.439138i	−0.847446	+	0.530882i	$0.821861\pi$
$594$	−6.56257	−	11.3667i	−0.269266	−	0.466382i
$595$	2.75906	−	4.77882i	0.113110	−	0.195913i
$596$	−37.5082	+	16.6997i	−1.53640	+	0.684047i
$597$	7.86673	−	5.71551i	0.321964	−	0.233920i
$598$	2.21610	+	0.986669i	0.0906229	+	0.0403479i
$599$	−33.4216	+	7.10398i	−1.36557	+	0.290261i	−0.831662	−	0.555282i	$-0.812610\pi$
$599$	−33.4216	+	7.10398i	−1.36557	+	0.290261i	−0.533908	+	0.845543i	$0.679277\pi$
$600$	0.218106	−	2.07514i	0.00890414	−	0.0847172i
$601$	2.70283	+	3.00179i	0.110251	+	0.122446i	0.795744	−	0.605633i	$-0.207080\pi$
$601$	2.70283	+	3.00179i	0.110251	+	0.122446i	−0.685493	+	0.728079i	$0.740413\pi$
$602$	−3.47888	+	3.86369i	−0.141789	+	0.157472i
$603$	−1.40803	−	13.3965i	−0.0573395	−	0.545549i
$604$	−4.53073	−	13.9442i	−0.184353	−	0.567380i
$605$	−5.92239	−	18.2273i	−0.240780	−	0.741043i
$606$	0.0836994	+	0.796347i	0.00340006	+	0.0323494i
$607$	29.3058	−	32.5474i	1.18949	−	1.32106i	0.254207	−	0.967150i	$-0.418186\pi$
$607$	29.3058	−	32.5474i	1.18949	−	1.32106i	0.935280	−	0.353909i	$-0.115148\pi$
$608$	−0.278640	−	0.309461i	−0.0113004	−	0.0125503i
$609$	−2.98857	+	28.4343i	−0.121103	+	1.15222i
$610$	0.222441	−	0.0472813i	0.00900638	−	0.00191436i
$611$	4.06862	+	1.81147i	0.164599	+	0.0732840i
$612$	4.78646	−	3.47757i	0.193481	−	0.140572i
$613$	3.09679	−	1.37878i	0.125078	−	0.0556884i	−0.343243	−	0.939247i	$-0.611526\pi$
$613$	3.09679	−	1.37878i	0.125078	−	0.0556884i	0.468322	+	0.883558i	$0.344859\pi$
$614$	6.68902	−	11.5857i	0.269947	−	0.467562i
$615$	−3.35418	−	5.80962i	−0.135254	−	0.234266i
$616$	−16.8735	−	12.2593i	−0.679851	−	0.493941i
$617$	−7.86461	−	1.67167i	−0.316617	−	0.0672991i	0.0468619	−	0.998901i	$-0.485078\pi$
$617$	−7.86461	−	1.67167i	−0.316617	−	0.0672991i	−0.363479	+	0.931602i	$0.618411\pi$
$618$	−2.84225	+	8.74754i	−0.114332	+	0.351878i
$619$	−39.5519			−1.58973			−0.794863	−	0.606789i	$-0.792457\pi$
$619$	−39.5519			−1.58973			−0.794863	+	0.606789i	$0.792457\pi$
$620$	−2.51150	+	9.79709i	−0.100864	+	0.393461i
$621$	−18.2596			−0.732732
$622$	2.30204	−	7.08496i	0.0923035	−	0.284081i
$623$	−38.9978	−	8.28925i	−1.56242	−	0.332102i
$624$	5.23940	+	3.80664i	0.209744	+	0.152388i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.91507	+	3.31700i	−0.0765417	+	0.132574i
$627$	0.589202	−	0.262330i	0.0235305	−	0.0104764i
$628$	15.0517	−	10.9357i	0.600626	−	0.436381i
$629$	−23.9318	−	10.6551i	−0.954225	−	0.424848i
$630$	−1.33437	+	0.283630i	−0.0531627	+	0.0113001i
$631$	−3.23921	+	30.8190i	−0.128951	+	1.22688i	0.718316	+	0.695717i	$0.244913\pi$
$631$	−3.23921	+	30.8190i	−0.128951	+	1.22688i	−0.847267	+	0.531167i	$0.821753\pi$
$632$	−0.810890	−	0.900585i	−0.0322555	−	0.0358233i
$633$	7.88634	−	8.75867i	0.313454	−	0.348126i
$634$	0.00398596	+	0.0379239i	0.000158303	+	0.00150615i
$635$	3.14715	+	9.68592i	0.124891	+	0.384374i
$636$	−2.78610	−	8.57474i	−0.110476	−	0.340010i
$637$	0.290179	+	2.76087i	0.0114973	+	0.109390i
$638$	15.1820	−	16.8614i	0.601062	−	0.667547i
$639$	−0.691995	−	0.768538i	−0.0273749	−	0.0304029i
$640$	1.12200	−	10.6751i	0.0443510	−	0.421971i
$641$	−7.60937	+	1.61742i	−0.300552	+	0.0638843i	−0.355719	−	0.934593i	$-0.615764\pi$
$641$	−7.60937	+	1.61742i	−0.300552	+	0.0638843i	0.0551673	+	0.998477i	$0.482431\pi$
$642$	8.70071	+	3.87381i	0.343390	+	0.152887i
$643$	−17.4730	+	12.6949i	−0.689067	+	0.500637i	−0.876353	−	0.481669i	$-0.840031\pi$
$643$	−17.4730	+	12.6949i	−0.689067	+	0.500637i	0.187286	+	0.982305i	$0.440031\pi$
$644$	−12.6164	+	5.61717i	−0.497154	+	0.221347i
$645$	3.33448	−	5.77549i	0.131295	−	0.227410i
$646$	−0.0468142	−	0.0810845i	−0.00184188	−	0.00319023i
$647$	−21.0136	−	15.2673i	−0.826131	−	0.600220i	0.0923308	−	0.995728i	$-0.470568\pi$
$647$	−21.0136	−	15.2673i	−0.826131	−	0.600220i	−0.918462	+	0.395509i	$0.870568\pi$
$648$	4.80887	+	1.02216i	0.188910	+	0.0401541i
$649$	−10.6429	+	32.7554i	−0.417769	+	1.28576i
$650$	−0.741153			−0.0290704
$651$	−16.4735	+	1.04270i	−0.645648	+	0.0408666i
$652$	33.4118			1.30851
$653$	−13.9380	+	42.8967i	−0.545436	+	1.67868i	0.174516	+	0.984654i	$0.444164\pi$
$653$	−13.9380	+	42.8967i	−0.545436	+	1.67868i	−0.719952	+	0.694024i	$0.755836\pi$
$654$	−3.02517	−	0.643019i	−0.118293	−	0.0251440i
$655$	11.3144	+	8.22041i	0.442091	+	0.321198i
$656$	−7.70724	−	13.3493i	−0.300917	−	0.521204i
$657$	3.31435	−	5.74062i	0.129305	−	0.223963i
$658$	2.33979	−	1.04174i	0.0912143	−	0.0406112i
$659$	−33.4954	+	24.3359i	−1.30480	+	0.947990i	−0.999990	−	0.00442404i	$-0.998592\pi$
$659$	−33.4954	+	24.3359i	−1.30480	+	0.947990i	−0.304806	+	0.952414i	$0.598592\pi$
$660$	11.6326	+	5.17918i	0.452799	+	0.201599i
$661$	24.3868	−	5.18358i	0.948538	−	0.201618i	0.292432	−	0.956286i	$-0.405536\pi$
$661$	24.3868	−	5.18358i	0.948538	−	0.201618i	0.656106	+	0.754669i	$0.272202\pi$
$662$	0.634581	−	6.03764i	0.0246637	−	0.234659i
$663$	3.51026	+	3.89854i	0.136327	+	0.151407i
$664$	6.36353	−	7.06741i	0.246953	−	0.274269i
$665$	−0.0223396	−	0.212547i	−0.000866291	−	0.00824221i
$666$	2.00129	+	6.15935i	0.0775486	+	0.238670i
$667$	−9.75412	−	30.0201i	−0.377681	−	1.16238i
$668$	0.299224	+	2.84692i	0.0115773	+	0.110151i
$669$	25.3965	−	28.2057i	0.981885	−	1.09049i
$670$	−2.81613	−	3.12763i	−0.108797	−	0.120831i
$671$	−0.304781	+	2.89980i	−0.0117660	+	0.111946i
$672$	13.1246	−	2.78973i	0.506294	−	0.107616i
$673$	3.75635	+	1.67244i	0.144797	+	0.0644676i	0.477856	−	0.878438i	$-0.341414\pi$
$673$	3.75635	+	1.67244i	0.144797	+	0.0644676i	−0.333059	+	0.942906i	$0.608081\pi$
$674$	6.75152	−	4.90527i	0.260059	−	0.188944i
$675$	5.09648	−	2.26910i	0.196164	−	0.0873377i
$676$	−9.08834	+	15.7415i	−0.349551	+	0.605441i
$677$	17.3680	+	30.0823i	0.667508	+	1.15616i	0.978599	+	0.205777i	$0.0659723\pi$
$677$	17.3680	+	30.0823i	0.667508	+	1.15616i	−0.311091	+	0.950380i	$0.600694\pi$
$678$	−5.04044	−	3.66210i	−0.193577	−	0.140642i
$679$	35.6836	+	7.58478i	1.36941	+	0.291077i
$680$	1.20014	−	3.69365i	0.0460233	−	0.141645i
$681$	13.7563			0.527143
$682$	11.0627	+	7.01470i	0.423612	+	0.268607i
$683$	−1.59367			−0.0609800			−0.0304900	−	0.999535i	$-0.509707\pi$
$683$	−1.59367			−0.0609800			−0.0304900	+	0.999535i	$0.509707\pi$
$684$	0.0708091	−	0.217928i	0.00270745	−	0.00833268i
$685$	−6.08708	−	1.29385i	−0.232575	−	0.0494354i
$686$	6.92642	+	5.03234i	0.264452	+	0.192136i
$687$	−1.06400	−	1.84290i	−0.0405941	−	0.0703111i
$688$	7.66197	−	13.2709i	0.292110	−	0.505949i
$689$	−6.14679	+	2.73673i	−0.234174	+	0.104261i
$690$	−1.44769	+	1.05181i	−0.0551125	+	0.0400416i
$691$	6.16088	+	2.74300i	0.234371	+	0.104349i	0.520562	−	0.853824i	$-0.325723\pi$
$691$	6.16088	+	2.74300i	0.234371	+	0.104349i	−0.286191	+	0.958173i	$0.592389\pi$
$692$	9.48651	−	2.01642i	0.360623	−	0.0766528i
$693$	1.82832	−	17.3953i	0.0694520	−	0.660791i
$694$	−0.831171	−	0.923109i	−0.0315508	−	0.0350407i
$695$	−2.29902	+	2.55332i	−0.0872069	+	0.0968531i
$696$	2.10340	+	20.0126i	0.0797294	+	0.758574i
$697$	−3.85848	−	11.8752i	−0.146150	−	0.449804i
$698$	4.10348	+	12.6292i	0.155319	+	0.478023i
$699$	2.77676	+	26.4191i	0.105027	+	0.999261i
$700$	2.82335	−	3.13565i	0.106713	−	0.118516i
$701$	33.8958	+	37.6451i	1.28023	+	1.42184i	0.856584	+	0.516007i	$0.172582\pi$
$701$	33.8958	+	37.6451i	1.28023	+	1.42184i	0.423643	+	0.905829i	$0.360751\pi$
$702$	0.432198	−	4.11209i	0.0163123	−	0.155201i
$703$	−0.992430	+	0.210948i	−0.0374302	+	0.00795604i
$704$	19.7020	+	8.77187i	0.742545	+	0.330602i
$705$	−2.65787	+	1.93105i	−0.100101	+	0.0727277i
$706$	7.08662	−	3.15517i	0.266709	−	0.118746i
$707$	−1.70101	+	2.94624i	−0.0639732	+	0.110805i
$708$	−7.26920	−	12.5906i	−0.273193	−	0.473185i
$709$	32.9286	+	23.9240i	1.23666	+	0.898486i	0.997371	−	0.0724623i	$-0.0230857\pi$
$709$	32.9286	+	23.9240i	1.23666	+	0.898486i	0.239289	+	0.970948i	$0.423086\pi$
$710$	−0.316053	−	0.0671792i	−0.0118613	−	0.00252119i
$711$	0.314053	−	0.966557i	0.0117779	−	0.0362487i
$712$	−28.0605			−1.05161
$713$	16.1465	−	8.44899i	0.604691	−	0.316417i
$714$	3.01688			0.112904
$715$	2.93652	−	9.03769i	0.109820	−	0.337991i
$716$	−33.7800	−	7.18015i	−1.26242	−	0.268335i
$717$	−3.58150	−	2.60211i	−0.133754	−	0.0971777i
$718$	−0.683347	−	1.18359i	−0.0255023	−	0.0441713i
$719$	10.5008	−	18.1880i	0.391614	−	0.678296i	−0.601048	−	0.799213i	$-0.705250\pi$
$719$	10.5008	−	18.1880i	0.391614	−	0.678296i	0.992663	+	0.120917i	$0.0385834\pi$
$720$	3.67321	−	1.63542i	0.136892	−	0.0609484i
$721$	−31.6145	+	22.9693i	−1.17739	+	0.855422i
$722$	7.43191	+	3.30890i	0.276587	+	0.123144i
$723$	−19.9940	+	4.24986i	−0.743586	+	0.158054i
$724$	−3.29274	+	31.3284i	−0.122374	+	1.16431i
$725$	6.45307	+	7.16686i	0.239661	+	0.266170i
$726$	7.01121	−	7.78674i	0.260210	−	0.288993i
$727$	−3.45539	−	32.8758i	−0.128153	−	1.21930i	−0.849826	−	0.527063i	$-0.823293\pi$
$727$	−3.45539	−	32.8758i	−0.128153	−	1.21930i	0.721673	−	0.692234i	$-0.243373\pi$
$728$	−2.03036	−	6.24880i	−0.0752501	−	0.231596i
$729$	7.87493	+	24.2365i	0.291664	+	0.897650i
$730$	−0.216485	−	2.05971i	−0.00801245	−	0.0762334i
$731$	8.30589	−	9.22462i	0.307204	−	0.341185i
$732$	−0.823579	−	0.914677i	−0.0304403	−	0.0338074i
$733$	−3.41206	+	32.4636i	−0.126027	+	1.19907i	0.730480	+	0.682934i	$0.239297\pi$
$733$	−3.41206	+	32.4636i	−0.126027	+	1.19907i	−0.856507	+	0.516135i	$0.827370\pi$
$734$	−5.94921	+	1.26454i	−0.219589	+	0.0466752i
$735$	−1.87077	−	0.832921i	−0.0690044	−	0.0307228i
$736$	−11.9844	+	8.70720i	−0.441752	+	0.320952i
$737$	49.2964	−	21.9482i	1.81586	−	0.808472i
$738$	−1.54343	+	2.67330i	−0.0568144	+	0.0984054i
$739$	8.98184	+	15.5570i	0.330402	+	0.572274i	0.982591	−	0.185783i	$-0.0594822\pi$
$739$	8.98184	+	15.5570i	0.330402	+	0.572274i	−0.652188	+	0.758057i	$0.726149\pi$
$740$	−16.2057	−	11.7741i	−0.595732	−	0.432825i
$741$	0.198739	+	0.0422432i	0.00730085	+	0.00155184i
$742$	−1.19572	+	3.68005i	−0.0438963	+	0.135099i
$743$	5.19321			0.190520			0.0952601	−	0.995452i	$-0.469632\pi$
$743$	5.19321			0.190520			0.0952601	+	0.995452i	$0.469632\pi$
$744$	−11.1884	+	3.12843i	−0.410186	+	0.114694i
$745$	−22.6026			−0.828096
$746$	2.02868	−	6.24362i	0.0742751	−	0.228595i
$747$	7.80120	+	1.65820i	0.285431	+	0.0606702i
$748$	19.1744	+	13.9310i	0.701086	+	0.509369i
$749$	20.2323	+	35.0433i	0.739271	+	1.28045i
$750$	0.273361	−	0.473476i	0.00998174	−	0.0172889i
$751$	−8.37528	+	3.72892i	−0.305618	+	0.136070i	−0.553815	−	0.832640i	$-0.686829\pi$
$751$	−8.37528	+	3.72892i	−0.305618	+	0.136070i	0.248197	+	0.968710i	$0.420162\pi$
$752$	−6.10725	+	4.43718i	−0.222708	+	0.161807i
$753$	13.0002	+	5.78804i	0.473752	+	0.210928i
$754$	6.99145	−	1.48608i	0.254614	−	0.0541198i
$755$	0.843691	−	8.02719i	0.0307051	−	0.292139i
$756$	15.7509	+	17.4931i	0.572854	+	0.636219i
$757$	−15.5560	+	17.2767i	−0.565392	+	0.627932i	−0.956261	−	0.292515i	$-0.905508\pi$
$757$	−15.5560	+	17.2767i	−0.565392	+	0.627932i	0.390869	+	0.920446i	$0.372175\pi$
$758$	0.408744	+	3.88894i	0.0148462	+	0.141253i
$759$	−7.08995	−	21.8206i	−0.257349	−	0.792038i
$760$	−0.0464817	−	0.143056i	−0.00168607	−	0.00518918i
$761$	−2.25529	−	21.4577i	−0.0817542	−	0.777839i	−0.956200	−	0.292715i	$-0.905441\pi$
$761$	−2.25529	−	21.4577i	−0.0817542	−	0.777839i	0.874445	−	0.485124i	$-0.161226\pi$
$762$	−3.72574	+	4.13785i	−0.134969	+	0.149899i
$763$	−8.79236	−	9.76491i	−0.318305	−	0.353513i
$764$	1.44646	−	13.7621i	0.0523309	−	0.497895i
$765$	3.18584	−	0.677172i	0.115184	−	0.0244832i
$766$	−7.49549	−	3.33721i	−0.270823	−	0.120578i
$767$	−8.77765	+	6.37734i	−0.316943	+	0.230272i
$768$	−3.79565	+	1.68993i	−0.136964	+	0.0609802i
$769$	−21.7299	+	37.6373i	−0.783601	+	1.35724i	0.146230	+	0.989251i	$0.453286\pi$
$769$	−21.7299	+	37.6373i	−0.783601	+	1.35724i	−0.929831	+	0.367987i	$0.880047\pi$
$770$	−2.73244	−	4.73272i	−0.0984703	−	0.170556i
$771$	12.5082	+	9.08775i	0.450472	+	0.327287i
$772$	−21.7642	−	4.62612i	−0.783311	−	0.166498i
$773$	16.3675	−	50.3739i	0.588697	−	1.81182i	0.00480839	−	0.999988i	$-0.498469\pi$
$773$	16.3675	−	50.3739i	0.588697	−	1.81182i	0.583888	−	0.811834i	$-0.301531\pi$
$774$	−3.06873			−0.110303
$775$	−3.45675	+	4.36473i	−0.124170	+	0.156786i
$776$	25.6758			0.921706
$777$	10.1025	−	31.0922i	0.362425	−	1.11543i
$778$	−4.15793	−	0.883795i	−0.149069	−	0.0316856i
$779$	−0.391238	−	0.284251i	−0.0140176	−	0.0101844i
$780$	2.00568	+	3.47394i	0.0718149	+	0.124387i
$781$	2.07143	−	3.58782i	0.0741215	−	0.128382i
$782$	−3.04274	+	1.35471i	−0.108808	+	0.0484445i
$783$	−43.5265	+	31.6238i	−1.55551	+	1.13014i
$784$	−4.29866	−	1.91389i	−0.153524	−	0.0683531i
$785$	10.0183	−	2.12945i	0.357568	−	0.0760035i
$786$	−0.799238	+	7.60425i	−0.0285079	+	0.271234i
$787$	17.5935	+	19.5396i	0.627142	+	0.696511i	0.970063	−	0.242853i	$-0.0780832\pi$
$787$	17.5935	+	19.5396i	0.627142	+	0.696511i	−0.342921	+	0.939364i	$0.611416\pi$
$788$	17.8415	−	19.8150i	0.635577	−	0.705880i
$789$	2.12070	+	20.1771i	0.0754989	+	0.718324i
$790$	−0.0981222	−	0.301989i	−0.00349103	−	0.0107443i
$791$	−8.17981	−	25.1749i	−0.290841	−	0.895115i
$792$	−1.28680	−	12.2431i	−0.0457244	−	0.435039i
$793$	−0.614623	+	0.682608i	−0.0218259	+	0.0242401i
$794$	−2.27197	−	2.52328i	−0.0806293	−	0.0895480i
$795$	0.518814	−	4.93619i	0.0184004	−	0.175069i
$796$	13.5370	−	2.87737i	0.479805	−	0.101986i
$797$	20.5837	+	9.16445i	0.729112	+	0.324622i	0.737504	−	0.675343i	$-0.236005\pi$
$797$	20.5837	+	9.16445i	0.729112	+	0.324622i	−0.00839165	+	0.999965i	$0.502671\pi$
$798$	0.0945289	−	0.0686793i	0.00334629	−	0.00243122i
$799$	−5.58628	+	2.48717i	−0.197628	+	0.0879898i
$800$	2.26297	−	3.91958i	0.0800082	−	0.138578i
$801$	−11.7662	−	20.3796i	−0.415738	−	0.720079i
$802$	−1.05535	−	0.766756i	−0.0372657	−	0.0270751i
$803$	25.9741	+	5.52096i	0.916605	+	0.194831i
$804$	−7.03895	+	21.6637i	−0.248245	+	0.764019i
$805$	−7.60269			−0.267959
$806$	1.52054	+	3.83621i	0.0535589	+	0.135125i
$807$	11.6721			0.410879
$808$	−0.739911	+	2.27721i	−0.0260300	+	0.0801120i
$809$	−14.1003	−	2.99710i	−0.495738	−	0.105372i	−0.0467438	−	0.998907i	$-0.514884\pi$
$809$	−14.1003	−	2.99710i	−0.495738	−	0.105372i	−0.448995	+	0.893534i	$0.648218\pi$
$810$	1.04215	+	0.757166i	0.0366174	+	0.0266041i
$811$	25.8602	+	44.7911i	0.908073	+	1.57283i	0.816738	+	0.577008i	$0.195780\pi$
$811$	25.8602	+	44.7911i	0.908073	+	1.57283i	0.0913345	+	0.995820i	$0.470887\pi$
$812$	−20.3460	+	35.2403i	−0.714005	+	1.23669i
$813$	3.80494	−	1.69407i	0.133445	−	0.0594136i
$814$	−20.9891	+	15.2495i	−0.735667	+	0.534493i
$815$	16.8032	+	7.48128i	0.588592	+	0.262058i
$816$	−8.69769	+	1.84875i	−0.304480	+	0.0647192i
$817$	0.0502527	−	0.478123i	0.00175812	−	0.0167274i
$818$	1.84928	+	2.05384i	0.0646587	+	0.0718108i
$819$	3.68699	−	4.09481i	0.128834	−	0.143084i
$820$	−0.998002	−	9.49536i	−0.0348518	−	0.331592i
$821$	−12.0151	−	36.9788i	−0.419331	−	1.29057i	−0.908319	−	0.418278i	$-0.862634\pi$
$821$	−12.0151	−	36.9788i	−0.419331	−	1.29057i	0.488988	−	0.872290i	$-0.337366\pi$
$822$	−1.05137	−	3.23577i	−0.0366706	−	0.112861i
$823$	0.949598	+	9.03483i	0.0331009	+	0.314934i	0.998527	+	0.0542572i	$0.0172791\pi$
$823$	0.949598	+	9.03483i	0.0331009	+	0.314934i	−0.965426	+	0.260677i	$0.916054\pi$
$824$	−18.4035	+	20.4391i	−0.641115	+	0.712031i
$825$	4.69052	+	5.20935i	0.163303	+	0.181366i
$826$	−0.652206	+	6.20532i	−0.0226931	+	0.215911i
$827$	3.67182	−	0.780469i	0.127682	−	0.0271396i	−0.143628	−	0.989632i	$-0.545877\pi$
$827$	3.67182	−	0.780469i	0.127682	−	0.0271396i	0.271309	+	0.962492i	$0.412543\pi$
$828$	−7.44670	−	3.31548i	−0.258791	−	0.115221i
$829$	28.4485	−	20.6691i	0.988059	−	0.717867i	0.0285637	−	0.999592i	$-0.490907\pi$
$829$	28.4485	−	20.6691i	0.988059	−	0.717867i	0.959495	+	0.281725i	$0.0909067\pi$
$830$	2.27641	−	1.01352i	0.0790155	−	0.0351800i
$831$	18.0915	−	31.3354i	0.627587	−	1.08701i
$832$	3.39698	+	5.88374i	0.117769	+	0.203982i
$833$	−3.08365	−	2.24040i	−0.106842	−	0.0776253i
$834$	−1.83740	−	0.390551i	−0.0636240	−	0.0135237i
$835$	−0.486975	+	1.49876i	−0.0168525	+	0.0518666i
$836$	0.917939			0.0317476
$837$	−22.2008	−	21.7241i	−0.767371	−	0.750895i
$838$	−4.12532			−0.142507
$839$	−7.33110	+	22.5628i	−0.253098	+	0.778955i	0.741101	+	0.671394i	$0.234304\pi$
$839$	−7.33110	+	22.5628i	−0.253098	+	0.778955i	−0.994198	+	0.107561i	$0.965696\pi$
$840$	4.74083	+	1.00769i	0.163574	+	0.0347687i
$841$	−51.7819	−	37.6217i	−1.78558	−	1.29730i
$842$	2.34404	+	4.05999i	0.0807809	+	0.139917i
$843$	3.22240	−	5.58136i	0.110985	−	0.192232i
$844$	15.3241	−	6.82273i	0.527477	−	0.234848i
$845$	−8.09534	+	5.88161i	−0.278488	+	0.202333i
$846$	1.38104	+	0.614878i	0.0474810	+	0.0211399i
$847$	43.5448	−	9.25573i	1.49622	−	0.318031i
$848$	1.19213	−	11.3424i	0.0409380	−	0.389499i
$849$	−14.2008	−	15.7716i	−0.487370	−	0.541280i
$850$	0.680918	−	0.756236i	0.0233553	−	0.0259387i
$851$	3.77274	+	35.8952i	0.129328	+	1.23047i
$852$	0.540408	+	1.66321i	0.0185141	+	0.0569805i
$853$	−1.23674	−	3.80630i	−0.0423452	−	0.130325i	0.927649	−	0.373453i	$-0.121826\pi$
$853$	−1.23674	−	3.80630i	−0.0423452	−	0.130325i	−0.969994	+	0.243128i	$0.921826\pi$
$854$	0.0552156	+	0.525341i	0.00188944	+	0.0179768i
$855$	0.0844074	−	0.0937439i	0.00288667	−	0.00320597i
$856$	19.0566	+	21.1645i	0.651340	+	0.723386i
$857$	3.09184	−	29.4169i	0.105615	−	1.00486i	−0.805468	−	0.592640i	$-0.798086\pi$
$857$	3.09184	−	29.4169i	0.105615	−	1.00486i	0.911083	−	0.412223i	$-0.135248\pi$
$858$	5.08186	−	1.08018i	0.173492	−	0.0368768i
$859$	−42.1463	−	18.7648i	−1.43801	−	0.640245i	−0.468097	−	0.883677i	$-0.655060\pi$
$859$	−42.1463	−	18.7648i	−1.43801	−	0.640245i	−0.969918	+	0.243432i	$0.921727\pi$
$860$	7.67885	−	5.57901i	0.261847	−	0.190243i
$861$	14.2352	−	6.33792i	0.485135	−	0.215996i
$862$	2.25436	−	3.90466i	0.0767837	−	0.132993i
$863$	−8.18684	−	14.1800i	−0.278683	−	0.482694i	0.692374	−	0.721538i	$-0.256565\pi$
$863$	−8.18684	−	14.1800i	−0.278683	−	0.482694i	−0.971058	+	0.238845i	$0.923231\pi$
$864$	20.4271	+	14.8412i	0.694945	+	0.504907i
$865$	5.22239	+	1.11005i	0.177567	+	0.0377429i
$866$	−3.83957	+	11.8170i	−0.130474	+	0.401558i
$867$	14.4945			0.492258
$868$	−22.0225	−	8.18058i	−0.747491	−	0.277667i
$869$	4.07126			0.138108
$870$	−1.62931	+	5.01451i	−0.0552389	+	0.170008i
$871$	16.6278	+	3.53434i	0.563410	+	0.119757i
$872$	−7.48190	−	5.43592i	−0.253369	−	0.184083i
$873$	10.7662	+	18.6476i	0.364381	+	0.631127i
$874$	−0.0644991	+	0.111716i	−0.00218172	+	0.00377884i
$875$	2.12201	−	0.944779i	0.0717369	−	0.0319393i
$876$	−9.06846	+	6.58862i	−0.306395	+	0.222609i
$877$	23.0940	+	10.2821i	0.779828	+	0.347202i	0.757742	−	0.652554i	$-0.226303\pi$
$877$	23.0940	+	10.2821i	0.779828	+	0.347202i	0.0220860	+	0.999756i	$0.492969\pi$
$878$	−14.6642	+	3.11698i	−0.494894	+	0.105193i
$879$	0.912546	−	8.68229i	0.0307794	−	0.292846i
$880$	10.7779	+	11.9701i	0.363322	+	0.403510i
$881$	−14.5277	+	16.1347i	−0.489452	+	0.543591i	−0.936384	−	0.350976i	$-0.885850\pi$
$881$	−14.5277	+	16.1347i	−0.489452	+	0.543591i	0.446932	+	0.894568i	$0.352516\pi$
$882$	0.0984974	+	0.937140i	0.00331658	+	0.0315551i
$883$	−4.98562	−	15.3442i	−0.167779	−	0.516372i	0.831451	−	0.555598i	$-0.187511\pi$
$883$	−4.98562	−	15.3442i	−0.167779	−	0.516372i	−0.999230	+	0.0392262i	$0.987511\pi$
$884$	2.30723	+	7.10092i	0.0776005	+	0.238830i
$885$	−0.836593	−	7.95966i	−0.0281218	−	0.267561i
$886$	7.94165	−	8.82009i	0.266805	−	0.296317i
$887$	6.59723	+	7.32697i	0.221513	+	0.246015i	0.843650	−	0.536893i	$-0.180402\pi$
$887$	6.59723	+	7.32697i	0.221513	+	0.246015i	−0.622137	+	0.782908i	$0.713735\pi$
$888$	2.40514	−	22.8833i	0.0807111	−	0.767915i
$889$	−23.1396	+	4.91847i	−0.776077	+	0.164960i
$890$	−6.71676	−	2.99049i	−0.225146	−	0.100242i
$891$	−13.3621	+	9.70811i	−0.447646	+	0.325234i
$892$	49.3484	−	21.9713i	1.65231	−	0.735655i
$893$	−0.118417	+	0.205103i	−0.00396266	+	0.00686353i
$894$	−6.17868	−	10.7018i	−0.206646	−	0.357921i
$895$	−15.3807	−	11.1747i	−0.514119	−	0.373529i
$896$	24.3882	+	5.18387i	0.814753	+	0.173181i
$897$	2.23351	−	6.87403i	0.0745746	−	0.229517i
$898$	12.2964			0.410335
$899$	23.8566	−	48.1045i	0.795661	−	1.60438i
$900$	2.49048			0.0830160
$901$	2.85481	−	8.78619i	0.0951074	−	0.292710i
$902$	−12.0956	−	2.57100i	−0.402740	−	0.0856051i
$903$	12.5324	+	9.10529i	0.417051	+	0.303005i
$904$	−9.31516	−	16.1343i	−0.309818	−	0.536620i
$905$	−8.67074	+	15.0182i	−0.288225	+	0.499221i
$906$	4.03131	−	1.79485i	0.133931	−	0.0596301i
$907$	−2.91520	+	2.11801i	−0.0967975	+	0.0703275i	−0.635131	−	0.772404i	$-0.719054\pi$
$907$	−2.91520	+	2.11801i	−0.0967975	+	0.0703275i	0.538334	+	0.842732i	$0.319054\pi$
$908$	17.8860	+	7.96335i	0.593567	+	0.264273i
$909$	−1.96414	+	0.417490i	−0.0651463	+	0.0138473i
$910$	0.179953	−	1.71214i	0.00596539	−	0.0567568i
$911$	−36.4002	−	40.4265i	−1.20599	−	1.33939i	−0.925134	−	0.379640i	$-0.876048\pi$
$911$	−36.4002	−	40.4265i	−1.20599	−	1.33939i	−0.280857	−	0.959750i	$-0.590619\pi$
$912$	−0.230441	+	0.255931i	−0.00763067	+	0.00847472i
$913$	3.33964	+	31.7745i	0.110526	+	1.05158i
$914$	−4.81449	−	14.8175i	−0.159249	−	0.490118i
$915$	−0.209382	−	0.644412i	−0.00692196	−	0.0213036i
$916$	−0.316582	−	3.01208i	−0.0104602	−	0.0995218i
$917$	−21.7371	+	24.1415i	−0.717824	+	0.797224i
$918$	3.79870	+	4.21888i	0.125376	+	0.139244i
$919$	−1.28593	+	12.2349i	−0.0424191	+	0.403591i	0.952624	+	0.304149i	$0.0983722\pi$
$919$	−1.28593	+	12.2349i	−0.0424191	+	0.403591i	−0.995043	+	0.0994412i	$0.968294\pi$
$920$	−5.23397	+	1.11251i	−0.172559	+	0.0366785i
$921$	−36.4141	−	16.2126i	−1.19989	−	0.534223i
$922$	−9.24006	+	6.71329i	−0.304305	+	0.221091i
$923$	1.19227	−	0.530832i	0.0392440	−	0.0174725i
$924$	−14.7888	+	25.6150i	−0.486517	+	0.842673i
$925$	−5.51369	−	9.54999i	−0.181289	−	0.314002i
$926$	−9.00329	−	6.54128i	−0.295867	−	0.214960i
$927$	−22.5613	−	4.79554i	−0.741009	−	0.157506i
$928$	−13.4880	+	41.5117i	−0.442765	+	1.36269i
$929$	19.0102			0.623706			0.311853	−	0.950130i	$-0.399050\pi$
$929$	19.0102			0.623706			0.311853	+	0.950130i	$0.399050\pi$
$930$	−3.01154	−	0.443538i	−0.0987521	−	0.0145442i
$931$	−0.147624			−0.00483818
$932$	−11.6833	+	35.9575i	−0.382699	+	1.17783i
$933$	−21.7111	−	4.61484i	−0.710790	−	0.151083i
$934$	7.91997	+	5.75420i	0.259149	+	0.188283i
$935$	6.52375	+	11.2995i	0.213349	+	0.369532i
$936$	1.93905	−	3.35854i	0.0633800	−	0.109777i
$937$	−38.3750	+	17.0856i	−1.25366	+	0.558163i	−0.922713	−	0.385488i	$-0.874033\pi$
$937$	−38.3750	+	17.0856i	−1.25366	+	0.558163i	−0.330942	+	0.943651i	$0.607367\pi$
$938$	7.90890	−	5.74616i	0.258235	−	0.187619i
$939$	10.4254	+	4.64168i	0.340219	+	0.151475i
$940$	−4.57362	+	0.972154i	−0.149175	+	0.0317082i
$941$	−3.66124	+	34.8343i	−0.119353	+	1.13557i	0.756838	+	0.653602i	$0.226743\pi$
$941$	−3.66124	+	34.8343i	−0.119353	+	1.13557i	−0.876191	+	0.481964i	$0.839924\pi$
$942$	3.74686	+	4.16131i	0.122079	+	0.135583i
$943$	−11.5112	+	12.7845i	−0.374857	+	0.416321i
$944$	−1.92232	−	18.2897i	−0.0625663	−	0.595279i
$945$	4.00442	+	12.3243i	0.130264	+	0.400911i
$946$	−3.79881	−	11.6915i	−0.123510	−	0.380125i
$947$	−1.85937	−	17.6907i	−0.0604213	−	0.574870i	−0.982290	−	0.187368i	$-0.940004\pi$
$947$	−1.85937	−	17.6907i	−0.0604213	−	0.574870i	0.921869	−	0.387503i	$-0.126662\pi$
$948$	−1.14995	+	1.27715i	−0.0373487	+	0.0414799i
$949$	5.59746	+	6.21661i	0.181701	+	0.201800i
$950$	0.00411972	−	0.0391966i	0.000133662	−	0.00127170i
$951$	0.111135	−	0.0236224i	0.00360379	−	0.000766009i
$952$	8.24132	+	3.66927i	0.267103	+	0.118922i
$953$	10.5043	−	7.63182i	0.340268	−	0.247219i	−0.404507	−	0.914535i	$-0.632557\pi$
$953$	10.5043	−	7.63182i	0.340268	−	0.247219i	0.744775	+	0.667316i	$0.232557\pi$
$954$	−2.08645	+	0.928945i	−0.0675512	+	0.0300757i
$955$	3.80893	−	6.59727i	0.123254	−	0.213483i
$956$	−3.15034	−	5.45655i	−0.101889	−	0.176478i
$957$	−54.6919	−	39.7360i	−1.76794	−	1.28448i
$958$	−9.31179	−	1.97928i	−0.300850	−	0.0639477i
$959$	4.46687	−	13.7476i	0.144243	−	0.443934i
$960$	−5.01167			−0.161751
$961$	29.6837	+	8.93747i	0.957538	+	0.288306i
$962$	−8.17297			−0.263507
$963$	−7.38051	+	22.7149i	−0.237833	+	0.731976i
$964$	−28.4564	−	6.04860i	−0.916520	−	0.194812i
$965$	−9.90967	−	7.19979i	−0.319003	−	0.231770i
$966$	−2.07828	−	3.59969i	−0.0668676	−	0.115818i
$967$	12.9272	−	22.3906i	0.415712	−	0.720034i	−0.579791	−	0.814765i	$-0.696866\pi$
$967$	12.9272	−	22.3906i	0.415712	−	0.720034i	0.995503	+	0.0947314i	$0.0301992\pi$
$968$	28.6234	−	12.7440i	0.919991	−	0.409606i
$969$	−0.225690	+	0.163973i	−0.00725019	+	0.00526757i
$970$	6.14593	+	2.73634i	0.197334	+	0.0878587i
$971$	−24.5784	+	5.22430i	−0.788758	+	0.167656i	−0.584642	−	0.811291i	$-0.698765\pi$
$971$	−24.5784	+	5.22430i	−0.788758	+	0.167656i	−0.204116	+	0.978947i	$0.565432\pi$
$972$	−2.44908	+	23.3014i	−0.0785542	+	0.747393i
$973$	−5.34023	−	5.93093i	−0.171200	−	0.190137i
$974$	−1.16769	+	1.29686i	−0.0374154	+	0.0415540i
$975$	0.230828	+	2.19619i	0.00739242	+	0.0703342i
$976$	−0.481118	−	1.48073i	−0.0154002	−	0.0473970i
$977$	−12.1606	−	37.4265i	−0.389052	−	1.19738i	−0.933498	−	0.358583i	$-0.883260\pi$
$977$	−12.1606	−	37.4265i	−0.389052	−	1.19738i	0.544446	−	0.838796i	$-0.316740\pi$
$978$	1.05115	+	10.0010i	0.0336121	+	0.319797i
$979$	63.0789	−	70.0562i	2.01601	−	2.23900i
$980$	−1.95021	−	2.16593i	−0.0622972	−	0.0691881i
$981$	0.810697	−	7.71327i	0.0258836	−	0.246266i
$982$	3.22990	−	0.686537i	0.103070	−	0.0219083i
$983$	2.48502	+	1.10640i	0.0792597	+	0.0352887i	0.445984	−	0.895041i	$-0.352854\pi$
$983$	2.48502	+	1.10640i	0.0792597	+	0.0352887i	−0.366724	+	0.930330i	$0.619521\pi$
$984$	8.87260	−	6.44632i	0.282848	−	0.205501i
$985$	13.4095	−	5.97031i	0.427263	−	0.190230i
$986$	−4.90692	+	8.49904i	−0.156268	+	0.270664i
$987$	−3.81560	−	6.60881i	−0.121452	−	0.210361i
$988$	0.233946	+	0.169972i	0.00744282	+	0.00540752i
$989$	−16.7285	−	3.55575i	−0.531935	−	0.113066i
$990$	0.996764	−	3.06772i	0.0316792	−	0.0974987i
$991$	−39.1985			−1.24518			−0.622591	−	0.782547i	$-0.713920\pi$
$991$	−39.1985			−1.24518			−0.622591	+	0.782547i	$0.713920\pi$
$992$	−24.9305	−	3.67175i	−0.791543	−	0.116578i
$993$	−18.0884			−0.574017
$994$	0.231929	−	0.713804i	0.00735634	−	0.0226405i
$995$	7.45219	+	1.58401i	0.236250	+	0.0502166i
$996$	−10.9109	−	7.92727i	−0.345727	−	0.251185i
$997$	20.6798	+	35.8184i	0.654935	+	1.13438i	0.981910	+	0.189347i	$0.0606372\pi$
$997$	20.6798	+	35.8184i	0.654935	+	1.13438i	−0.326975	+	0.945033i	$0.606029\pi$
$998$	−3.33626	+	5.77857i	−0.105607	+	0.182917i
$999$	56.2008	−	25.0222i	1.77812	−	0.791668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.q.a.71.3	✓	40
5.2	odd	4		775.2.ck.c.474.5		80
5.3	odd	4		775.2.ck.c.474.6		80
5.4	even	2		775.2.bl.c.226.3		40
31.7	even	15	inner	155.2.q.a.131.3	yes	40
31.10	even	15		4805.2.a.x.1.9		20
31.21	odd	30		4805.2.a.y.1.9		20
155.7	odd	60		775.2.ck.c.224.6		80
155.38	odd	60		775.2.ck.c.224.5		80
155.69	even	30		775.2.bl.c.751.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.71.3	✓	40	1.1	even	1	trivial
155.2.q.a.131.3	yes	40	31.7	even	15	inner
775.2.bl.c.226.3		40	5.4	even	2
775.2.bl.c.751.3		40	155.69	even	30
775.2.ck.c.224.5		80	155.38	odd	60
775.2.ck.c.224.6		80	155.7	odd	60
775.2.ck.c.474.5		80	5.2	odd	4
775.2.ck.c.474.6		80	5.3	odd	4
4805.2.a.x.1.9		20	31.10	even	15
4805.2.a.y.1.9		20	31.21	odd	30

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.132371 + 0.407396i) q^{2} +(1.24842 + 0.265360i) q^{3} +(1.46958 + 1.06772i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.273361 + 0.473476i) q^{6} +(-2.12201 + 0.944779i) q^{7} +(-1.32262 + 0.960937i) q^{8} +(-1.25250 - 0.557647i) q^{9} +O(q^{10})\)	\(q+(-0.132371 + 0.407396i) q^{2} +(1.24842 + 0.265360i) q^{3} +(1.46958 + 1.06772i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.273361 + 0.473476i) q^{6} +(-2.12201 + 0.944779i) q^{7} +(-1.32262 + 0.960937i) q^{8} +(-1.25250 - 0.557647i) q^{9} +(-0.419001 + 0.0890613i) q^{10} +(0.574101 - 5.46220i) q^{11} +(1.55133 + 1.72293i) q^{12} +(1.15773 - 1.28579i) q^{13} +(-0.104007 - 0.989558i) q^{14} +(0.394402 + 1.21384i) q^{15} +(0.906257 + 2.78917i) q^{16} +(0.248318 + 2.36259i) q^{17} +(0.392977 - 0.436445i) q^{18} +(0.0615651 + 0.0683749i) q^{19} +(-0.189877 + 1.80656i) q^{20} +(-2.89987 + 0.616386i) q^{21} +(2.14928 + 0.956923i) q^{22} +(2.64794 - 1.92384i) q^{23} +(-1.90618 + 0.848685i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.370577 + 0.641857i) q^{26} +(-4.51334 - 3.27913i) q^{27} +(-4.12722 - 0.877269i) q^{28} +(2.98015 - 9.17195i) q^{29} -0.546723 q^{30} +(5.50834 + 0.811267i) q^{31} -4.52595 q^{32} +(2.16617 - 6.66679i) q^{33} +(-0.995378 - 0.211574i) q^{34} +(-1.87921 - 1.36532i) q^{35} +(-1.24524 - 2.15682i) q^{36} +(-5.51369 + 9.54999i) q^{37} +(-0.0360051 + 0.0160305i) q^{38} +(1.78654 - 1.29800i) q^{39} +(-1.49350 - 0.664951i) q^{40} +(-5.14120 + 1.09280i) q^{41} +(0.132745 - 1.26298i) q^{42} +(-3.49633 - 3.88307i) q^{43} +(6.67577 - 7.41420i) q^{44} +(-0.143311 - 1.36352i) q^{45} +(0.433254 + 1.33342i) q^{46} +(0.795429 + 2.44808i) q^{47} +(0.391256 + 3.72255i) q^{48} +(-1.07361 + 1.19236i) q^{49} +(-0.286630 - 0.318334i) q^{50} +(-0.316931 + 3.01540i) q^{51} +(3.07425 - 0.653452i) q^{52} +(-3.55264 - 1.58174i) q^{53} +(1.93334 - 1.40465i) q^{54} +(5.01746 - 2.23392i) q^{55} +(1.89873 - 3.28869i) q^{56} +(0.0587152 + 0.101698i) q^{57} +(3.34213 + 2.42820i) q^{58} +(-6.13377 - 1.30377i) q^{59} +(-0.716434 + 2.20496i) q^{60} -0.530885 q^{61} +(-1.05965 + 2.13669i) q^{62} +3.18466 q^{63} +(-1.21341 + 3.73449i) q^{64} +(1.69240 + 0.359730i) q^{65} +(2.42928 + 1.76498i) q^{66} +(4.91249 + 8.50868i) q^{67} +(-2.15765 + 3.73716i) q^{68} +(3.81625 - 1.69911i) q^{69} +(0.804979 - 0.584851i) q^{70} +(0.689090 + 0.306803i) q^{71} +(2.19244 - 0.466016i) q^{72} +(-0.505379 + 4.80836i) q^{73} +(-3.16077 - 3.51039i) q^{74} +(-0.854019 + 0.948485i) q^{75} +(0.0174701 + 0.166217i) q^{76} +(3.94233 + 12.1332i) q^{77} +(0.292312 + 0.899645i) q^{78} +(0.0774835 + 0.737207i) q^{79} +(-1.96237 + 2.17943i) q^{80} +(-2.01221 - 2.23479i) q^{81} +(0.235345 - 2.23916i) q^{82} +(-5.69004 + 1.20946i) q^{83} +(-4.91972 - 2.19040i) q^{84} +(-1.92190 + 1.39634i) q^{85} +(2.04476 - 0.910385i) q^{86} +(6.15435 - 10.6596i) q^{87} +(4.48952 + 7.77607i) q^{88} +(13.8860 + 10.0888i) q^{89} +(0.574461 + 0.122106i) q^{90} +(-1.24193 + 3.82226i) q^{91} +5.94549 q^{92} +(6.66146 + 2.47450i) q^{93} -1.10263 q^{94} +(-0.0284319 + 0.0875044i) q^{95} +(-5.65029 - 1.20101i) q^{96} +(-12.7059 - 9.23136i) q^{97} +(-0.343648 - 0.595216i) q^{98} +(-3.76504 + 6.52124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} - q^{3} - 10 q^{4} + 20 q^{5} + 4 q^{6} + 4 q^{7} + 13 q^{8} + 2 q^{9} - q^{10} - 28 q^{11} - 13 q^{12} - 6 q^{13} - 6 q^{14} - 2 q^{15} + 8 q^{16} - 10 q^{17} - 27 q^{18} - 13 q^{19} - 5 q^{20} - 8 q^{21} + 2 q^{22} - 12 q^{23} - 82 q^{24} - 20 q^{25} + 32 q^{26} - q^{27} + 22 q^{28} + 42 q^{29} + 8 q^{30} - 10 q^{31} + 4 q^{32} + 13 q^{33} + 32 q^{34} + 8 q^{35} - 13 q^{36} + 12 q^{37} + 30 q^{38} + 37 q^{39} + 44 q^{40} + 36 q^{41} - 64 q^{42} - 78 q^{43} - 56 q^{44} - 2 q^{45} + 18 q^{46} - 4 q^{47} - 41 q^{48} - 31 q^{49} + q^{50} - 2 q^{51} + 49 q^{52} - 11 q^{53} + 22 q^{54} - 17 q^{55} + 9 q^{56} + 38 q^{57} + 11 q^{58} - q^{59} - 11 q^{60} - 100 q^{61} - 35 q^{62} + 110 q^{63} + 17 q^{64} + 6 q^{65} - 40 q^{66} + 30 q^{67} - 34 q^{68} + 8 q^{69} + 18 q^{70} - 2 q^{71} + 151 q^{72} - 23 q^{73} - 2 q^{74} - q^{75} + 2 q^{76} + 36 q^{77} - 2 q^{78} - 67 q^{79} - 41 q^{80} - 83 q^{81} + 2 q^{82} + 26 q^{84} - 5 q^{85} - 5 q^{86} - 46 q^{87} + 70 q^{88} + 20 q^{89} - 33 q^{90} + 19 q^{91} - 10 q^{92} - 67 q^{93} + 130 q^{94} + 4 q^{95} + 46 q^{96} - 18 q^{97} - 65 q^{98} + 53 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - q^3 - 10 * q^4 + 20 * q^5 + 4 * q^6 + 4 * q^7 + 13 * q^8 + 2 * q^9 - q^10 - 28 * q^11 - 13 * q^12 - 6 * q^13 - 6 * q^14 - 2 * q^15 + 8 * q^16 - 10 * q^17 - 27 * q^18 - 13 * q^19 - 5 * q^20 - 8 * q^21 + 2 * q^22 - 12 * q^23 - 82 * q^24 - 20 * q^25 + 32 * q^26 - q^27 + 22 * q^28 + 42 * q^29 + 8 * q^30 - 10 * q^31 + 4 * q^32 + 13 * q^33 + 32 * q^34 + 8 * q^35 - 13 * q^36 + 12 * q^37 + 30 * q^38 + 37 * q^39 + 44 * q^40 + 36 * q^41 - 64 * q^42 - 78 * q^43 - 56 * q^44 - 2 * q^45 + 18 * q^46 - 4 * q^47 - 41 * q^48 - 31 * q^49 + q^50 - 2 * q^51 + 49 * q^52 - 11 * q^53 + 22 * q^54 - 17 * q^55 + 9 * q^56 + 38 * q^57 + 11 * q^58 - q^59 - 11 * q^60 - 100 * q^61 - 35 * q^62 + 110 * q^63 + 17 * q^64 + 6 * q^65 - 40 * q^66 + 30 * q^67 - 34 * q^68 + 8 * q^69 + 18 * q^70 - 2 * q^71 + 151 * q^72 - 23 * q^73 - 2 * q^74 - q^75 + 2 * q^76 + 36 * q^77 - 2 * q^78 - 67 * q^79 - 41 * q^80 - 83 * q^81 + 2 * q^82 + 26 * q^84 - 5 * q^85 - 5 * q^86 - 46 * q^87 + 70 * q^88 + 20 * q^89 - 33 * q^90 + 19 * q^91 - 10 * q^92 - 67 * q^93 + 130 * q^94 + 4 * q^95 + 46 * q^96 - 18 * q^97 - 65 * q^98 + 53 * q^99

Introduction

L-functions

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