LMFDB - Embedded newform 731.2.m.c.689.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.19
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.639626 - 0.639626i) q^{2} +(-0.916759 - 0.379734i) q^{3} +1.18176i q^{4} +(0.199818 - 0.482403i) q^{5} +(-0.829270 + 0.343495i) q^{6} +(0.462611 + 1.11684i) q^{7} +(2.03513 + 2.03513i) q^{8} +(-1.42507 - 1.42507i) q^{9} +O(q^{10})$	\(q+(0.639626 - 0.639626i) q^{2} +(-0.916759 - 0.379734i) q^{3} +1.18176i q^{4} +(0.199818 - 0.482403i) q^{5} +(-0.829270 + 0.343495i) q^{6} +(0.462611 + 1.11684i) q^{7} +(2.03513 + 2.03513i) q^{8} +(-1.42507 - 1.42507i) q^{9} +(-0.180749 - 0.436366i) q^{10} +(1.30474 - 0.540439i) q^{11} +(0.448753 - 1.08339i) q^{12} +6.44237i q^{13} +(1.01026 + 0.418463i) q^{14} +(-0.366369 + 0.366369i) q^{15} +0.239934 q^{16} +(-2.99591 + 2.83276i) q^{17} -1.82303 q^{18} +(3.13514 - 3.13514i) q^{19} +(0.570083 + 0.236136i) q^{20} -1.19954i q^{21} +(0.488864 - 1.18022i) q^{22} +(-5.39622 + 2.23519i) q^{23} +(-1.09292 - 2.63854i) q^{24} +(3.34275 + 3.34275i) q^{25} +(4.12071 + 4.12071i) q^{26} +(1.90450 + 4.59787i) q^{27} +(-1.31984 + 0.546694i) q^{28} +(1.18499 - 2.86083i) q^{29} +0.468679i q^{30} +(5.43572 + 2.25155i) q^{31} +(-3.91680 + 3.91680i) q^{32} -1.40135 q^{33} +(-0.104355 + 3.72817i) q^{34} +0.631205 q^{35} +(1.68409 - 1.68409i) q^{36} +(6.99643 + 2.89802i) q^{37} -4.01064i q^{38} +(2.44639 - 5.90610i) q^{39} +(1.38841 - 0.575098i) q^{40} +(1.27061 + 3.06752i) q^{41} +(-0.767259 - 0.767259i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.638668 + 1.54188i) q^{44} +(-0.972213 + 0.402704i) q^{45} +(-2.02188 + 4.88125i) q^{46} +5.93360i q^{47} +(-0.219962 - 0.0911111i) q^{48} +(3.91642 - 3.91642i) q^{49} +4.27622 q^{50} +(3.82222 - 1.45931i) q^{51} -7.61332 q^{52} +(-7.37026 + 7.37026i) q^{53} +(4.15909 + 1.72275i) q^{54} -0.737397i q^{55} +(-1.33145 + 3.21440i) q^{56} +(-4.06469 + 1.68365i) q^{57} +(-1.07191 - 2.58781i) q^{58} +(3.01122 + 3.01122i) q^{59} +(-0.432960 - 0.432960i) q^{60} +(-5.47181 - 13.2101i) q^{61} +(4.91698 - 2.03668i) q^{62} +(0.932326 - 2.25083i) q^{63} +5.49044i q^{64} +(3.10782 + 1.28730i) q^{65} +(-0.896340 + 0.896340i) q^{66} +8.65354 q^{67} +(-3.34764 - 3.54044i) q^{68} +5.79581 q^{69} +(0.403735 - 0.403735i) q^{70} +(-7.66813 - 3.17625i) q^{71} -5.80042i q^{72} +(3.55138 - 8.57380i) q^{73} +(6.32874 - 2.62145i) q^{74} +(-1.79514 - 4.33385i) q^{75} +(3.70498 + 3.70498i) q^{76} +(1.20717 + 1.20717i) q^{77} +(-2.21292 - 5.34247i) q^{78} +(2.04936 - 0.848873i) q^{79} +(0.0479431 - 0.115745i) q^{80} +1.10772i q^{81} +(2.77478 + 1.14935i) q^{82} +(-1.34503 + 1.34503i) q^{83} +1.41757 q^{84} +(0.767895 + 2.01127i) q^{85} -0.904568 q^{86} +(-2.17271 + 2.17271i) q^{87} +(3.75518 + 1.55545i) q^{88} -5.67384i q^{89} +(-0.364273 + 0.879432i) q^{90} +(-7.19511 + 2.98031i) q^{91} +(-2.64145 - 6.37703i) q^{92} +(-4.12826 - 4.12826i) q^{93} +(3.79528 + 3.79528i) q^{94} +(-0.885945 - 2.13886i) q^{95} +(5.07810 - 2.10342i) q^{96} +(-0.981607 + 2.36981i) q^{97} -5.01009i q^{98} +(-2.62950 - 1.08918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	0.639626	−	0.639626i	0.452284	−	0.452284i	−0.443828	−	0.896112i	$-0.646380\pi$
$2$	0.639626	−	0.639626i	0.452284	−	0.452284i	0.896112	+	0.443828i	$0.146380\pi$
$3$	−0.916759	−	0.379734i	−0.529291	−	0.219239i	0.102002	−	0.994784i	$-0.467475\pi$
$3$	−0.916759	−	0.379734i	−0.529291	−	0.219239i	−0.631293	+	0.775545i	$0.717475\pi$
$4$			1.18176i			0.590879i
$5$	0.199818	−	0.482403i	0.0893612	−	0.215737i	−0.872880	−	0.487935i	$-0.837750\pi$
$5$	0.199818	−	0.482403i	0.0893612	−	0.215737i	0.962241	+	0.272198i	$0.0877504\pi$
$6$	−0.829270	+	0.343495i	−0.338548	+	0.140231i
$7$	0.462611	+	1.11684i	0.174851	+	0.422127i	0.986873	−	0.161500i	$-0.0516332\pi$
$7$	0.462611	+	1.11684i	0.174851	+	0.422127i	−0.812022	+	0.583627i	$0.801633\pi$
$8$	2.03513	+	2.03513i	0.719529	+	0.719529i
$9$	−1.42507	−	1.42507i	−0.475024	−	0.475024i
$10$	−0.180749	−	0.436366i	−0.0571577	−	0.137991i
$11$	1.30474	−	0.540439i	0.393392	−	0.162948i	−0.177214	−	0.984172i	$-0.556708\pi$
$11$	1.30474	−	0.540439i	0.393392	−	0.162948i	0.570606	+	0.821224i	$0.306708\pi$
$12$	0.448753	−	1.08339i	0.129544	−	0.312747i
$13$			6.44237i			1.78679i	0.449270	+	0.893396i	$0.351684\pi$
$13$			6.44237i			1.78679i	−0.449270	+	0.893396i	$0.648316\pi$
$14$	1.01026	+	0.418463i	0.270003	+	0.111839i
$15$	−0.366369	+	0.366369i	−0.0945962	+	0.0945962i
$16$	0.239934			0.0599835
$17$	−2.99591	+	2.83276i	−0.726615	+	0.687045i
$17$	−2.99591	+	2.83276i	−0.726615	+	0.687045i
$18$	−1.82303			−0.429691
$19$	3.13514	−	3.13514i	0.719251	−	0.719251i	−0.249201	−	0.968452i	$-0.580168\pi$
$19$	3.13514	−	3.13514i	0.719251	−	0.719251i	0.968452	+	0.249201i	$0.0801678\pi$
$20$	0.570083	+	0.236136i	0.127474	+	0.0528016i
$21$		−	1.19954i		−	0.261762i
$22$	0.488864	−	1.18022i	0.104226	−	0.251624i
$23$	−5.39622	+	2.23519i	−1.12519	+	0.466069i	−0.866143	−	0.499796i	$-0.833408\pi$
$23$	−5.39622	+	2.23519i	−1.12519	+	0.466069i	−0.259047	+	0.965865i	$0.583408\pi$
$24$	−1.09292	−	2.63854i	−0.223091	−	0.538589i
$25$	3.34275	+	3.34275i	0.668550	+	0.668550i
$26$	4.12071	+	4.12071i	0.808137	+	0.808137i
$27$	1.90450	+	4.59787i	0.366521	+	0.884861i
$28$	−1.31984	+	0.546694i	−0.249426	+	0.103315i
$29$	1.18499	−	2.86083i	0.220048	−	0.531242i	−0.774848	−	0.632147i	$-0.782174\pi$
$29$	1.18499	−	2.86083i	0.220048	−	0.531242i	0.994896	+	0.100905i	$0.0321738\pi$
$30$			0.468679i			0.0855686i
$31$	5.43572	+	2.25155i	0.976285	+	0.404390i	0.813048	−	0.582197i	$-0.197807\pi$
$31$	5.43572	+	2.25155i	0.976285	+	0.404390i	0.163237	+	0.986587i	$0.447807\pi$
$32$	−3.91680	+	3.91680i	−0.692399	+	0.692399i
$33$	−1.40135			−0.243944
$34$	−0.104355	+	3.72817i	−0.0178967	+	0.639375i
$35$	0.631205			0.106693
$36$	1.68409	−	1.68409i	0.280681	−	0.280681i
$37$	6.99643	+	2.89802i	1.15021	+	0.476431i	0.874603	−	0.484840i	$-0.161122\pi$
$37$	6.99643	+	2.89802i	1.15021	+	0.476431i	0.275603	+	0.961271i	$0.411122\pi$
$38$		−	4.01064i		−	0.650611i
$39$	2.44639	−	5.90610i	0.391735	−	0.945733i
$40$	1.38841	−	0.575098i	0.219527	−	0.0909310i
$41$	1.27061	+	3.06752i	0.198436	+	0.479066i	0.991506	−	0.130064i	$-0.0415184\pi$
$41$	1.27061	+	3.06752i	0.198436	+	0.479066i	−0.793070	+	0.609131i	$0.791518\pi$
$42$	−0.767259	−	0.767259i	−0.118391	−	0.118391i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	0.638668	+	1.54188i	0.0962828	+	0.232447i
$45$	−0.972213	+	0.402704i	−0.144929	+	0.0600315i
$46$	−2.02188	+	4.88125i	−0.298110	+	0.719701i
$47$			5.93360i			0.865504i	0.901513	+	0.432752i	$0.142457\pi$
$47$			5.93360i			0.865504i	−0.901513	+	0.432752i	$0.857543\pi$
$48$	−0.219962	−	0.0911111i	−0.0317487	−	0.0131508i
$49$	3.91642	−	3.91642i	0.559489	−	0.559489i
$50$	4.27622			0.604748
$51$	3.82222	−	1.45931i	0.535218	−	0.204344i
$52$	−7.61332			−1.05578
$53$	−7.37026	+	7.37026i	−1.01238	+	1.01238i	−0.0124602	+	0.999922i	$0.503966\pi$
$53$	−7.37026	+	7.37026i	−1.01238	+	1.01238i	−0.999922	+	0.0124602i	$0.996034\pi$
$54$	4.15909	+	1.72275i	0.565980	+	0.234437i
$55$		−	0.737397i		−	0.0994306i
$56$	−1.33145	+	3.21440i	−0.177922	+	0.429542i
$57$	−4.06469	+	1.68365i	−0.538382	+	0.223005i
$58$	−1.07191	−	2.58781i	−0.140748	−	0.339796i
$59$	3.01122	+	3.01122i	0.392028	+	0.392028i	0.875410	−	0.483382i	$-0.160592\pi$
$59$	3.01122	+	3.01122i	0.392028	+	0.392028i	−0.483382	+	0.875410i	$0.660592\pi$
$60$	−0.432960	−	0.432960i	−0.0558949	−	0.0558949i
$61$	−5.47181	−	13.2101i	−0.700593	−	1.69138i	−0.722265	−	0.691616i	$-0.756899\pi$
$61$	−5.47181	−	13.2101i	−0.700593	−	1.69138i	0.0216720	−	0.999765i	$-0.493101\pi$
$62$	4.91698	−	2.03668i	0.624457	−	0.258659i
$63$	0.932326	−	2.25083i	0.117462	−	0.283578i
$64$			5.49044i			0.686305i
$65$	3.10782	+	1.28730i	0.385477	+	0.159670i
$66$	−0.896340	+	0.896340i	−0.110332	+	0.110332i
$67$	8.65354			1.05720			0.528599	−	0.848872i	$-0.322718\pi$
$67$	8.65354			1.05720			0.528599	+	0.848872i	$0.322718\pi$
$68$	−3.34764	−	3.54044i	−0.405960	−	0.429341i
$69$	5.79581			0.697734
$70$	0.403735	−	0.403735i	0.0482556	−	0.0482556i
$71$	−7.66813	−	3.17625i	−0.910040	−	0.376951i	−0.121968	−	0.992534i	$-0.538921\pi$
$71$	−7.66813	−	3.17625i	−0.910040	−	0.376951i	−0.788072	+	0.615583i	$0.788921\pi$
$72$		−	5.80042i		−	0.683587i
$73$	3.55138	−	8.57380i	0.415658	−	1.00349i	−0.567933	−	0.823075i	$-0.692257\pi$
$73$	3.55138	−	8.57380i	0.415658	−	1.00349i	0.983591	−	0.180412i	$-0.0577432\pi$
$74$	6.32874	−	2.62145i	0.735702	−	0.304738i
$75$	−1.79514	−	4.33385i	−0.207285	−	0.500430i
$76$	3.70498	+	3.70498i	0.424990	+	0.424990i
$77$	1.20717	+	1.20717i	0.137570	+	0.137570i
$78$	−2.21292	−	5.34247i	−0.250564	−	0.604915i
$79$	2.04936	−	0.848873i	0.230571	−	0.0955057i	−0.264407	−	0.964411i	$-0.585176\pi$
$79$	2.04936	−	0.848873i	0.230571	−	0.0955057i	0.494978	+	0.868906i	$0.335176\pi$
$80$	0.0479431	−	0.115745i	0.00536020	−	0.0129407i
$81$			1.10772i			0.123080i
$82$	2.77478	+	1.14935i	0.306423	+	0.126925i
$83$	−1.34503	+	1.34503i	−0.147636	+	0.147636i	−0.777061	−	0.629425i	$-0.783290\pi$
$83$	−1.34503	+	1.34503i	−0.147636	+	0.147636i	0.629425	+	0.777061i	$0.283290\pi$
$84$	1.41757			0.154670
$85$	0.767895	+	2.01127i	0.0832899	+	0.218153i
$86$	−0.904568			−0.0975420
$87$	−2.17271	+	2.17271i	−0.232939	+	0.232939i
$88$	3.75518	+	1.55545i	0.400303	+	0.165811i
$89$		−	5.67384i		−	0.601426i	−0.953715	−	0.300713i	$-0.902775\pi$
$89$		−	5.67384i		−	0.601426i	0.953715	−	0.300713i	$-0.0972247\pi$
$90$	−0.364273	+	0.879432i	−0.0383977	+	0.0927003i
$91$	−7.19511	+	2.98031i	−0.754252	+	0.312421i
$92$	−2.64145	−	6.37703i	−0.275390	−	0.664851i
$93$	−4.12826	−	4.12826i	−0.428080	−	0.428080i
$94$	3.79528	+	3.79528i	0.391454	+	0.391454i
$95$	−0.885945	−	2.13886i	−0.0908960	−	0.219442i
$96$	5.07810	−	2.10342i	0.518282	−	0.214679i
$97$	−0.981607	+	2.36981i	−0.0996671	+	0.240618i	−0.965846	−	0.259116i	$-0.916569\pi$
$97$	−0.981607	+	2.36981i	−0.0996671	+	0.240618i	0.866179	+	0.499734i	$0.166569\pi$
$98$		−	5.01009i		−	0.506095i
$99$	−2.62950	−	1.08918i	−0.264275	−	0.109466i
$100$	−3.95032	+	3.95032i	−0.395032	+	0.395032i
$101$	−14.6890			−1.46161			−0.730805	−	0.682587i	$-0.760855\pi$
$101$	−14.6890			−1.46161			−0.730805	+	0.682587i	$0.760855\pi$
$102$	1.51138	−	3.37820i	0.149649	−	0.334492i
$103$	3.13315			0.308718			0.154359	−	0.988015i	$-0.450669\pi$
$103$	3.13315			0.308718			0.154359	+	0.988015i	$0.450669\pi$
$104$	−13.1111	+	13.1111i	−1.28565	+	1.28565i
$105$	−0.578663	−	0.239690i	−0.0564717	−	0.0233914i
$106$			9.42841i			0.915768i
$107$	1.88230	−	4.54428i	0.181969	−	0.439312i	−0.806403	−	0.591366i	$-0.798589\pi$
$107$	1.88230	−	4.54428i	0.181969	−	0.439312i	0.988372	+	0.152054i	$0.0485888\pi$
$108$	−5.43357	+	2.25066i	−0.522845	+	0.216570i
$109$	−4.86895	−	11.7547i	−0.466361	−	1.12589i	−0.965740	−	0.259511i	$-0.916439\pi$
$109$	−4.86895	−	11.7547i	−0.466361	−	1.12589i	0.499379	−	0.866383i	$-0.333561\pi$
$110$	−0.471658	−	0.471658i	−0.0449708	−	0.0449708i
$111$	−5.31356	−	5.31356i	−0.504341	−	0.504341i
$112$	0.110996	+	0.267968i	0.0104881	+	0.0253206i
$113$	5.99660	−	2.48387i	0.564113	−	0.233663i	−0.0823567	−	0.996603i	$-0.526245\pi$
$113$	5.99660	−	2.48387i	0.564113	−	0.233663i	0.646470	+	0.762940i	$0.276245\pi$
$114$	−1.52298	+	3.67679i	−0.142640	+	0.344363i
$115$			3.04978i			0.284394i
$116$	3.38080	+	1.40038i	0.313900	+	0.130022i
$117$	9.18084	−	9.18084i	0.848769	−	0.848769i
$118$	3.85211			0.354616
$119$	−4.54969	−	2.03549i	−0.417069	−	0.186593i
$120$	−1.49122			−0.136129
$121$	−6.36792	+	6.36792i	−0.578901	+	0.578901i
$122$	−11.9494	−	4.94962i	−1.08185	−	0.448117i
$123$		−	3.29467i		−	0.297070i
$124$	−2.66079	+	6.42371i	−0.238946	+	0.576866i
$125$	4.69251	−	1.94370i	0.419710	−	0.173850i
$126$	−0.843352	−	2.03603i	−0.0751317	−	0.181384i
$127$	−6.44963	−	6.44963i	−0.572312	−	0.572312i	0.360462	−	0.932774i	$-0.382619\pi$
$127$	−6.44963	−	6.44963i	−0.572312	−	0.572312i	−0.932774	+	0.360462i	$0.882619\pi$
$128$	−4.32177	−	4.32177i	−0.381994	−	0.381994i
$129$	0.379734	+	0.916759i	0.0334337	+	0.0807161i
$130$	2.81123	−	1.16445i	0.246561	−	0.102129i
$131$	−0.335160	+	0.809148i	−0.0292831	+	0.0706956i	−0.937845	−	0.347055i	$-0.887182\pi$
$131$	−0.335160	+	0.809148i	−0.0292831	+	0.0706956i	0.908562	+	0.417751i	$0.137182\pi$
$132$		−	1.65606i		−	0.144141i
$133$	4.95181	+	2.05111i	0.429377	+	0.177854i
$134$	5.53503	−	5.53503i	0.478153	−	0.478153i
$135$	2.59858			0.223650
$136$	−11.8621	−	0.332031i	−1.01717	−	0.0284714i
$137$	−12.9262			−1.10436			−0.552181	−	0.833724i	$-0.686204\pi$
$137$	−12.9262			−1.10436			−0.552181	+	0.833724i	$0.686204\pi$
$138$	3.70715	−	3.70715i	0.315574	−	0.315574i
$139$	18.2574	+	7.56245i	1.54857	+	0.641439i	0.983057	−	0.183300i	$-0.0586779\pi$
$139$	18.2574	+	7.56245i	1.54857	+	0.641439i	0.565514	+	0.824739i	$0.308678\pi$
$140$			0.745932i			0.0630427i
$141$	2.25319	−	5.43968i	0.189753	−	0.458104i
$142$	−6.93635	+	2.87313i	−0.582085	+	0.241108i
$143$	3.48171	+	8.40558i	0.291155	+	0.702910i
$144$	−0.341923	−	0.341923i	−0.0284936	−	0.0284936i
$145$	−1.14329	−	1.14329i	−0.0949449	−	0.0949449i
$146$	−3.21247	−	7.75558i	−0.265866	−	0.641856i
$147$	−5.07761	+	2.10322i	−0.418794	+	0.173470i
$148$	−3.42475	+	8.26808i	−0.281513	+	0.679632i
$149$		−	21.9825i		−	1.80088i	−0.434984	−	0.900438i	$-0.643246\pi$
$149$		−	21.9825i		−	1.80088i	0.434984	−	0.900438i	$-0.356754\pi$
$150$	−3.92026	−	1.62382i	−0.320088	−	0.132585i
$151$	−4.42564	+	4.42564i	−0.360153	+	0.360153i	−0.863869	−	0.503716i	$-0.831966\pi$
$151$	−4.42564	+	4.42564i	−0.360153	+	0.360153i	0.503716	+	0.863869i	$0.331966\pi$
$152$	12.7609			1.03504
$153$	8.30627	+	0.232500i	0.671522	+	0.0187965i
$154$	1.54427			0.124441
$155$	2.17231	−	2.17231i	0.174484	−	0.174484i
$156$	6.97958	+	2.89104i	0.558813	+	0.231468i
$157$		−	6.68135i		−	0.533230i	−0.963803	−	0.266615i	$-0.914095\pi$
$157$		−	6.68135i		−	0.533230i	0.963803	−	0.266615i	$-0.0859051\pi$
$158$	0.767863	−	1.85379i	0.0610879	−	0.147479i
$159$	9.55548	−	3.95801i	0.757799	−	0.313891i
$160$	1.10683	+	2.67212i	0.0875025	+	0.211250i
$161$	−4.99270	−	4.99270i	−0.393480	−	0.393480i
$162$	0.708529	+	0.708529i	0.0556673	+	0.0556673i
$163$	−4.17338	−	10.0754i	−0.326885	−	0.789169i	−0.998820	−	0.0485597i	$-0.984537\pi$
$163$	−4.17338	−	10.0754i	−0.326885	−	0.789169i	0.671936	−	0.740609i	$-0.265463\pi$
$164$	−3.62507	+	1.50155i	−0.283070	+	0.117251i
$165$	−0.280015	+	0.676015i	−0.0217991	+	0.0526277i
$166$			1.72063i			0.133547i
$167$	−4.19006	−	1.73558i	−0.324237	−	0.134303i	0.214627	−	0.976696i	$-0.431146\pi$
$167$	−4.19006	−	1.73558i	−0.324237	−	0.134303i	−0.538864	+	0.842393i	$0.681146\pi$
$168$	2.44123	−	2.44123i	0.188345	−	0.188345i
$169$	−28.5041			−2.19262
$170$	1.77763	+	0.795295i	0.136338	+	0.0609963i
$171$	−8.93561			−0.683323
$172$	0.835629	−	0.835629i	0.0637161	−	0.0637161i
$173$	6.44678	+	2.67035i	0.490140	+	0.203023i	0.614044	−	0.789272i	$-0.289542\pi$
$173$	6.44678	+	2.67035i	0.490140	+	0.203023i	−0.123904	+	0.992294i	$0.539542\pi$
$174$			2.77944i			0.210709i
$175$	−2.18693	+	5.27971i	−0.165316	+	0.399109i
$176$	0.313050	−	0.129670i	0.0235971	−	0.00977422i
$177$	−1.61710	−	3.90403i	−0.121549	−	0.293445i
$178$	−3.62914	−	3.62914i	−0.272015	−	0.272015i
$179$	17.0397	+	17.0397i	1.27360	+	1.27360i	0.944183	+	0.329422i	$0.106854\pi$
$179$	17.0397	+	17.0397i	1.27360	+	1.27360i	0.329422	+	0.944183i	$0.393146\pi$
$180$	−0.475898	−	1.14892i	−0.0354714	−	0.0856354i
$181$	4.07779	−	1.68908i	0.303100	−	0.125548i	−0.225950	−	0.974139i	$-0.572549\pi$
$181$	4.07779	−	1.68908i	0.303100	−	0.125548i	0.529050	+	0.848591i	$0.322549\pi$
$182$	−2.69589	+	6.50846i	−0.199833	+	0.482439i
$183$			14.1883i			1.04883i
$184$	−15.5309	−	6.43313i	−1.14496	−	0.474257i
$185$	2.79602	−	2.79602i	0.205568	−	0.205568i
$186$	−5.28108			−0.387228
$187$	−2.37793	+	5.31511i	−0.173892	+	0.388679i
$188$	−7.01207			−0.511408
$189$	−4.25405	+	4.25405i	−0.309437	+	0.309437i
$190$	−1.93474	−	0.801397i	−0.140361	−	0.0581394i
$191$		−	9.30167i		−	0.673045i	−0.941675	−	0.336523i	$-0.890749\pi$
$191$		−	9.30167i		−	0.673045i	0.941675	−	0.336523i	$-0.109251\pi$
$192$	2.08491	−	5.03341i	0.150465	−	0.363255i
$193$	7.03237	−	2.91290i	0.506201	−	0.209675i	−0.114942	−	0.993372i	$-0.536668\pi$
$193$	7.03237	−	2.91290i	0.506201	−	0.209675i	0.621144	+	0.783697i	$0.286668\pi$
$194$	0.887930	+	2.14365i	0.0637496	+	0.153905i
$195$	−2.36029	−	2.36029i	−0.169024	−	0.169024i
$196$	4.62826	+	4.62826i	0.330590	+	0.330590i
$197$	2.13815	+	5.16195i	0.152337	+	0.367773i	0.981563	−	0.191140i	$-0.0612184\pi$
$197$	2.13815	+	5.16195i	0.152337	+	0.367773i	−0.829226	+	0.558913i	$0.811218\pi$
$198$	−2.37856	+	0.985234i	−0.169037	+	0.0700175i
$199$	−0.0345027	+	0.0832969i	−0.00244583	+	0.00590476i	−0.925098	−	0.379729i	$-0.876017\pi$
$199$	−0.0345027	+	0.0832969i	−0.00244583	+	0.00590476i	0.922652	+	0.385634i	$0.126017\pi$
$200$			13.6059i			0.962081i
$201$	−7.93321	−	3.28604i	−0.559565	−	0.231779i
$202$	−9.39546	+	9.39546i	−0.661062	+	0.661062i
$203$	3.74328			0.262727
$204$	1.72455	+	4.51694i	0.120743	+	0.316249i
$205$	1.73367			0.121085
$206$	2.00404	−	2.00404i	0.139628	−	0.139628i
$207$	10.8753	+	4.50470i	0.755886	+	0.313098i
$208$			1.54574i			0.107178i
$209$	2.39618	−	5.78489i	0.165747	−	0.400149i
$210$	−0.523440	+	0.216816i	−0.0361208	+	0.0149617i
$211$	10.5831	+	25.5499i	0.728572	+	1.75893i	0.647297	+	0.762238i	$0.275899\pi$
$211$	10.5831	+	25.5499i	0.728572	+	1.75893i	0.0812751	+	0.996692i	$0.474101\pi$
$212$	−8.70986	−	8.70986i	−0.598195	−	0.598195i
$213$	5.82370	+	5.82370i	0.399033	+	0.399033i
$214$	−1.70267	−	4.11061i	−0.116392	−	0.280995i
$215$	−0.482403	+	0.199818i	−0.0328996	+	0.0136275i
$216$	−5.48137	+	13.2332i	−0.372960	+	0.900405i
$217$			7.11243i			0.482824i
$218$	−10.6329	−	4.40429i	−0.720151	−	0.298296i
$219$	−6.51152	+	6.51152i	−0.440008	+	0.440008i
$220$	0.871425			0.0587514
$221$	−18.2497	−	19.3008i	−1.22761	−	1.29831i
$222$	−6.79739			−0.456211
$223$	4.91058	−	4.91058i	0.328837	−	0.328837i	−0.523307	−	0.852144i	$-0.675302\pi$
$223$	4.91058	−	4.91058i	0.328837	−	0.328837i	0.852144	+	0.523307i	$0.175302\pi$
$224$	−6.18640	−	2.56249i	−0.413346	−	0.171214i
$225$		−	9.52731i		−	0.635154i
$226$	2.24683	−	5.42433i	0.149457	−	0.360821i
$227$	5.63411	−	2.33372i	0.373949	−	0.154895i	−0.187790	−	0.982209i	$-0.560133\pi$
$227$	5.63411	−	2.33372i	0.373949	−	0.154895i	0.561739	+	0.827314i	$0.310133\pi$
$228$	−1.98967	−	4.80348i	−0.131769	−	0.318118i
$229$	−10.5862	−	10.5862i	−0.699556	−	0.699556i	0.264759	−	0.964315i	$-0.414708\pi$
$229$	−10.5862	−	10.5862i	−0.699556	−	0.699556i	−0.964315	+	0.264759i	$0.914708\pi$
$230$	1.95072	+	1.95072i	0.128627	+	0.128627i
$231$	−0.648280	−	1.56509i	−0.0426537	−	0.102975i
$232$	8.23379	−	3.41055i	0.540575	−	0.223913i
$233$	6.28407	−	15.1711i	0.411683	−	0.993892i	−0.573002	−	0.819554i	$-0.694221\pi$
$233$	6.28407	−	15.1711i	0.411683	−	0.993892i	0.984686	−	0.174338i	$-0.0557786\pi$
$234$		−	11.7446i		−	0.767769i
$235$	2.86238	+	1.18564i	0.186721	+	0.0773425i
$236$	−3.55854	+	3.55854i	−0.231641	+	0.231641i
$237$	−2.20112			−0.142978
$238$	−4.21205	+	1.60814i	−0.273027	+	0.104240i
$239$	−20.4604			−1.32348			−0.661738	−	0.749735i	$-0.730181\pi$
$239$	−20.4604			−1.32348			−0.661738	+	0.749735i	$0.730181\pi$
$240$	−0.0879045	+	0.0879045i	−0.00567421	+	0.00567421i
$241$	11.4902	+	4.75940i	0.740149	+	0.306580i	0.720715	−	0.693231i	$-0.243814\pi$
$241$	11.4902	+	4.75940i	0.740149	+	0.306580i	0.0194338	+	0.999811i	$0.493814\pi$
$242$			8.14617i			0.523655i
$243$	6.13414	−	14.8091i	0.393505	−	0.950006i
$244$	15.6111	−	6.46635i	0.999401	−	0.413966i
$245$	−1.10672	−	2.67186i	−0.0707059	−	0.170699i
$246$	−2.10736	−	2.10736i	−0.134360	−	0.134360i
$247$	20.1978	+	20.1978i	1.28515	+	1.28515i
$248$	6.48022	+	15.6446i	0.411494	+	0.993435i
$249$	1.74382	−	0.722313i	0.110510	−	0.0457747i
$250$	1.75821	−	4.24469i	0.111199	−	0.268458i
$251$			20.9555i			1.32270i	0.750078	+	0.661349i	$0.230016\pi$
$251$			20.9555i			1.32270i	−0.750078	+	0.661349i	$0.769984\pi$
$252$	2.65994	+	1.10178i	0.167560	+	0.0694058i
$253$	−5.83266	+	5.83266i	−0.366696	+	0.366696i
$254$	−8.25070			−0.517695
$255$	0.0597730	−	2.13545i	0.00374313	−	0.133727i
$256$	−16.5095			−1.03184
$257$	12.9891	−	12.9891i	0.810238	−	0.810238i	−0.174431	−	0.984669i	$-0.555809\pi$
$257$	12.9891	−	12.9891i	0.810238	−	0.810238i	0.984669	+	0.174431i	$0.0558086\pi$
$258$	0.829270	+	0.343495i	0.0516281	+	0.0213851i
$259$			9.15456i			0.568837i
$260$	−1.52128	+	3.67269i	−0.0943455	+	0.227770i
$261$	−5.76558	+	2.38818i	−0.356881	+	0.147825i
$262$	0.303175	+	0.731929i	0.0187302	+	0.0452187i
$263$	−2.96775	−	2.96775i	−0.182999	−	0.182999i	0.609662	−	0.792661i	$-0.291305\pi$
$263$	−2.96775	−	2.96775i	−0.182999	−	0.182999i	−0.792661	+	0.609662i	$0.791305\pi$
$264$	−2.85194	−	2.85194i	−0.175525	−	0.175525i
$265$	2.08272	+	5.02814i	0.127941	+	0.308876i
$266$	4.47925	−	1.85537i	0.274640	−	0.113760i
$267$	−2.15455	+	5.20155i	−0.131856	+	0.318330i
$268$			10.2264i			0.624676i
$269$	12.4325	+	5.14970i	0.758022	+	0.313983i	0.728010	−	0.685567i	$-0.240446\pi$
$269$	12.4325	+	5.14970i	0.758022	+	0.313983i	0.0300118	+	0.999550i	$0.490446\pi$
$270$	1.66212	−	1.66212i	0.101153	−	0.101153i
$271$	22.2794			1.35338			0.676688	−	0.736270i	$-0.263415\pi$
$271$	22.2794			1.35338			0.676688	+	0.736270i	$0.263415\pi$
$272$	−0.718821	+	0.679675i	−0.0435849	+	0.0412114i
$273$	7.72790			0.467714
$274$	−8.26794	+	8.26794i	−0.499485	+	0.499485i
$275$	6.16795	+	2.55485i	0.371942	+	0.154063i
$276$			6.84924i			0.412276i
$277$	−0.323712	+	0.781511i	−0.0194500	+	0.0469564i	−0.933306	−	0.359082i	$-0.883090\pi$
$277$	−0.323712	+	0.781511i	−0.0194500	+	0.0469564i	0.913856	+	0.406038i	$0.133090\pi$
$278$	16.5150	−	6.84075i	0.990506	−	0.410281i
$279$	−4.53767	−	10.9549i	−0.271663	−	0.655854i
$280$	1.28459	+	1.28459i	0.0767688	+	0.0767688i
$281$	14.0553	+	14.0553i	0.838466	+	0.838466i	0.988657	−	0.150191i	$-0.0479888\pi$
$281$	14.0553	+	14.0553i	0.838466	+	0.838466i	−0.150191	+	0.988657i	$0.547989\pi$
$282$	−2.03816	−	4.92056i	−0.121371	−	0.293015i
$283$	26.6533	−	11.0402i	1.58437	−	0.656270i	0.595276	−	0.803521i	$-0.297043\pi$
$283$	26.6533	−	11.0402i	1.58437	−	0.656270i	0.989099	+	0.147252i	$0.0470428\pi$
$284$	3.75355	−	9.06188i	0.222732	−	0.537723i
$285$			2.29724i			0.136077i
$286$	7.60342	+	3.14944i	0.449600	+	0.186230i
$287$	−2.83814	+	2.83814i	−0.167530	+	0.167530i
$288$	11.1634			0.657812
$289$	0.950945	−	16.9734i	0.0559379	−	0.998434i
$290$	−1.46255			−0.0858841
$291$	1.79979	−	1.79979i	0.105506	−	0.105506i
$292$	10.1321	+	4.19687i	0.592939	+	0.245603i
$293$		−	19.4741i		−	1.13769i	−0.822444	−	0.568845i	$-0.807390\pi$
$293$		−	19.4741i		−	1.13769i	0.822444	−	0.568845i	$-0.192610\pi$
$294$	−1.90250	+	4.59304i	−0.110956	+	0.267872i
$295$	2.05432	−	0.850927i	0.119607	−	0.0495429i
$296$	8.34082	+	20.1365i	0.484801	+	1.17041i
$297$	4.96974	+	4.96974i	0.288373	+	0.288373i
$298$	−14.0606	−	14.0606i	−0.814507	−	0.814507i
$299$	−14.3999	−	34.7645i	−0.832768	−	2.01048i
$300$	5.12156	−	2.12142i	0.295693	−	0.122480i
$301$	0.462611	−	1.11684i	0.0266645	−	0.0643737i
$302$			5.66151i			0.325783i
$303$	13.4663	+	5.57791i	0.773617	+	0.320443i
$304$	0.752228	−	0.752228i	0.0431432	−	0.0431432i
$305$	−7.46596			−0.427500
$306$	5.46162	−	5.16419i	0.312220	−	0.295217i
$307$	13.6342			0.778145			0.389073	−	0.921207i	$-0.372796\pi$
$307$	13.6342			0.778145			0.389073	+	0.921207i	$0.372796\pi$
$308$	−1.42658	+	1.42658i	−0.0812870	+	0.0812870i
$309$	−2.87234	−	1.18976i	−0.163402	−	0.0676832i
$310$		−	2.77893i		−	0.157833i
$311$	6.91817	−	16.7019i	0.392293	−	0.947080i	−0.597146	−	0.802133i	$-0.703699\pi$
$311$	6.91817	−	16.7019i	0.392293	−	0.947080i	0.989439	−	0.144947i	$-0.0463013\pi$
$312$	16.9984	−	7.04098i	0.962347	−	0.398617i
$313$	−2.54624	−	6.14718i	−0.143922	−	0.347459i	0.835437	−	0.549586i	$-0.185215\pi$
$313$	−2.54624	−	6.14718i	−0.143922	−	0.347459i	−0.979359	+	0.202127i	$0.935215\pi$
$314$	−4.27356	−	4.27356i	−0.241171	−	0.241171i
$315$	−0.899513	−	0.899513i	−0.0506818	−	0.0506818i
$316$	1.00316	+	2.42185i	0.0564323	+	0.136240i
$317$	−14.5390	+	6.02226i	−0.816593	+	0.338244i	−0.751581	−	0.659641i	$-0.770709\pi$
$317$	−14.5390	+	6.02226i	−0.816593	+	0.338244i	−0.0650118	+	0.997884i	$0.520709\pi$
$318$	3.58029	−	8.64358i	0.200773	−	0.484708i
$319$		−	4.37304i		−	0.244843i
$320$	2.64860	+	1.09709i	0.148061	+	0.0613291i
$321$	−3.45123	+	3.45123i	−0.192629	+	0.192629i
$322$	−6.38693			−0.355929
$323$	−0.511497	+	18.2737i	−0.0284605	+	1.01678i
$324$	−1.30906			−0.0727256
$325$	−21.5352	+	21.5352i	−1.19456	+	1.19456i
$326$	−9.11391	−	3.77511i	−0.504773	−	0.209084i
$327$			12.6251i			0.698170i
$328$	−3.65696	+	8.82868i	−0.201922	+	0.487482i
$329$	−6.62689	+	2.74495i	−0.365352	+	0.151334i
$330$	0.253292	+	0.611501i	0.0139433	+	0.0336620i
$331$	−1.07157	−	1.07157i	−0.0588989	−	0.0588989i	0.677044	−	0.735943i	$-0.263261\pi$
$331$	−1.07157	−	1.07157i	−0.0588989	−	0.0588989i	−0.735943	+	0.677044i	$0.763261\pi$
$332$	−1.58950	−	1.58950i	−0.0872349	−	0.0872349i
$333$	−5.84053	−	14.1003i	−0.320059	−	0.772691i
$334$	−3.79020	+	1.56995i	−0.207390	+	0.0859039i
$335$	1.72913	−	4.17449i	0.0944725	−	0.228077i
$336$		−	0.287811i		−	0.0157014i
$337$	1.33511	+	0.553022i	0.0727283	+	0.0301250i	0.418751	−	0.908101i	$-0.362468\pi$
$337$	1.33511	+	0.553022i	0.0727283	+	0.0301250i	−0.346023	+	0.938226i	$0.612468\pi$
$338$	−18.2320	+	18.2320i	−0.991689	+	0.991689i
$339$	−6.44065			−0.349808
$340$	−2.37683	+	0.907466i	−0.128902	+	0.0492143i
$341$	8.30900			0.449958
$342$	−5.71545	+	5.71545i	−0.309056	+	0.309056i
$343$	14.0037	+	5.80052i	0.756128	+	0.313199i
$344$		−	2.87811i		−	0.155178i
$345$	1.15811	−	2.79592i	0.0623503	−	0.150527i
$346$	5.83155	−	2.41551i	0.313506	−	0.129859i
$347$	−1.58723	−	3.83192i	−0.0852071	−	0.205708i	0.875533	−	0.483159i	$-0.160511\pi$
$347$	−1.58723	−	3.83192i	−0.0852071	−	0.205708i	−0.960740	+	0.277451i	$0.910511\pi$
$348$	−2.56761	−	2.56761i	−0.137638	−	0.137638i
$349$	−14.4784	−	14.4784i	−0.775011	−	0.775011i	0.203967	−	0.978978i	$-0.434617\pi$
$349$	−14.4784	−	14.4784i	−0.775011	−	0.775011i	−0.978978	+	0.203967i	$0.934617\pi$
$350$	1.97823	+	4.77586i	0.105741	+	0.255280i
$351$	−29.6212	+	12.2695i	−1.58106	+	0.654897i
$352$	−2.99360	+	7.22718i	−0.159559	+	0.385210i
$353$			26.2626i			1.39782i	0.715210	+	0.698909i	$0.246331\pi$
$353$			26.2626i			1.39782i	−0.715210	+	0.698909i	$0.753669\pi$
$354$	−3.53146	−	1.46278i	−0.187695	−	0.0777458i
$355$	−3.06446	+	3.06446i	−0.162645	+	0.162645i
$356$	6.70511			0.355370
$357$	3.39802	+	3.59372i	0.179842	+	0.190200i
$358$	21.7980			1.15206
$359$	19.5669	−	19.5669i	1.03270	−	1.03270i	0.0332557	−	0.999447i	$-0.489412\pi$
$359$	19.5669	−	19.5669i	1.03270	−	1.03270i	0.999447	−	0.0332557i	$-0.0105876\pi$
$360$	−2.79814	−	1.15903i	−0.147475	−	0.0610861i
$361$		−	0.658257i		−	0.0346451i
$362$	1.52788	−	3.68864i	0.0803038	−	0.193871i
$363$	8.25596	−	3.41973i	0.433325	−	0.179489i
$364$	−3.52201	−	8.50287i	−0.184603	−	0.445672i
$365$	−3.42639	−	3.42639i	−0.179346	−	0.179346i
$366$	9.07521	+	9.07521i	0.474369	+	0.474369i
$367$	−6.48867	−	15.6650i	−0.338706	−	0.817708i	−0.997841	−	0.0656835i	$-0.979077\pi$
$367$	−6.48867	−	15.6650i	−0.338706	−	0.817708i	0.659135	−	0.752025i	$-0.270923\pi$
$368$	−1.29474	+	0.536298i	−0.0674929	+	0.0279565i
$369$	2.56073	−	6.18215i	0.133306	−	0.321830i
$370$		−	3.57682i		−	0.185950i
$371$	−11.6410	−	4.82185i	−0.604369	−	0.250338i
$372$	4.87860	−	4.87860i	0.252944	−	0.252944i
$373$	−15.0546			−0.779499			−0.389750	−	0.920921i	$-0.627438\pi$
$373$	−15.0546			−0.779499			−0.389750	+	0.920921i	$0.627438\pi$
$374$	1.87869	+	4.92067i	0.0971448	+	0.254442i
$375$	−5.03998			−0.260264
$376$	−12.0757	+	12.0757i	−0.622755	+	0.622755i
$377$	18.4305	+	7.63417i	0.949219	+	0.393180i
$378$			5.44200i			0.279906i
$379$	−4.85909	+	11.7309i	−0.249595	+	0.602575i	−0.998170	−	0.0604753i	$-0.980738\pi$
$379$	−4.85909	+	11.7309i	−0.249595	+	0.602575i	0.748575	+	0.663050i	$0.230738\pi$
$380$	2.52761	−	1.04697i	0.129664	−	0.0537085i
$381$	3.46361	+	8.36190i	0.177446	+	0.428393i
$382$	−5.94959	−	5.94959i	−0.304408	−	0.304408i
$383$	9.58132	+	9.58132i	0.489583	+	0.489583i	0.908174	−	0.418592i	$-0.137476\pi$
$383$	9.58132	+	9.58132i	0.489583	+	0.489583i	−0.418592	+	0.908174i	$0.637476\pi$
$384$	2.32090	+	5.60315i	0.118438	+	0.285934i
$385$	0.823556	−	0.341128i	0.0419723	−	0.0173855i
$386$	2.63492	−	6.36125i	0.134114	−	0.323779i
$387$			2.01536i			0.102446i
$388$	−2.80054	−	1.16002i	−0.142176	−	0.0588912i
$389$	−10.3817	+	10.3817i	−0.526371	+	0.526371i	−0.919488	−	0.393117i	$-0.871397\pi$
$389$	−10.3817	+	10.3817i	−0.526371	+	0.526371i	0.393117	+	0.919488i	$0.371397\pi$
$390$	−3.01940			−0.152893
$391$	9.83484	−	21.9826i	0.497369	−	1.11171i
$392$	15.9409			0.805136
$393$	0.614522	−	0.614522i	0.0309985	−	0.0309985i
$394$	4.66933	+	1.93410i	0.235237	+	0.0974385i
$395$		−	1.15824i		−	0.0582772i
$396$	1.28714	−	3.10744i	0.0646814	−	0.156155i
$397$	−23.6051	+	9.77757i	−1.18471	+	0.490722i	−0.886028	−	0.463631i	$-0.846546\pi$
$397$	−23.6051	+	9.77757i	−1.18471	+	0.490722i	−0.298680	+	0.954353i	$0.596546\pi$
$398$	0.0312100	+	0.0753477i	0.00156442	+	0.00377684i
$399$	−3.76074	−	3.76074i	−0.188273	−	0.188273i
$400$	0.802039	+	0.802039i	0.0401020	+	0.0401020i
$401$	11.9956	+	28.9600i	0.599033	+	1.44619i	0.874568	+	0.484903i	$0.161145\pi$
$401$	11.9956	+	28.9600i	0.599033	+	1.44619i	−0.275534	+	0.961291i	$0.588855\pi$
$402$	−7.17612	+	2.97245i	−0.357912	+	0.148252i
$403$	−14.5053	+	35.0189i	−0.722561	+	1.74442i
$404$		−	17.3588i		−	0.863634i
$405$	0.534369	+	0.221343i	0.0265530	+	0.0109986i
$406$	2.39430	−	2.39430i	0.118827	−	0.118827i
$407$	10.6947			0.530116
$408$	10.7486	+	4.80884i	0.532136	+	0.238073i
$409$	−5.10090			−0.252223			−0.126112	−	0.992016i	$-0.540250\pi$
$409$	−5.10090			−0.252223			−0.126112	+	0.992016i	$0.540250\pi$
$410$	1.10890	−	1.10890i	0.0547647	−	0.0547647i
$411$	11.8502	+	4.90852i	0.584528	+	0.242120i
$412$			3.70262i			0.182415i
$413$	−1.97004	+	4.75609i	−0.0969391	+	0.234032i
$414$	9.83745	−	4.07480i	0.483484	−	0.200266i
$415$	0.380084	+	0.917605i	0.0186576	+	0.0450434i
$416$	−25.2335	−	25.2335i	−1.23717	−	1.23717i
$417$	−13.8659	−	13.8659i	−0.679016	−	0.679016i
$418$	−2.16751	−	5.23282i	−0.106016	−	0.255946i
$419$	28.3031	−	11.7235i	1.38270	−	0.572732i	0.437496	−	0.899220i	$-0.355865\pi$
$419$	28.3031	−	11.7235i	1.38270	−	0.572732i	0.945201	+	0.326488i	$0.105865\pi$
$420$	0.283256	−	0.683840i	0.0138215	−	0.0333680i
$421$			0.721867i			0.0351817i	0.999845	+	0.0175908i	$0.00559962\pi$
$421$			0.721867i			0.0351817i	−0.999845	+	0.0175908i	$0.994400\pi$
$422$	23.1116	+	9.57315i	1.12506	+	0.466014i
$423$	8.45580	−	8.45580i	0.411135	−	0.411135i
$424$	−29.9989			−1.45688
$425$	−19.4838	−	0.545368i	−0.945102	−	0.0264542i
$426$	7.44998			0.360953
$427$	12.2223	−	12.2223i	0.591478	−	0.591478i
$428$	5.37023	+	2.22442i	0.259580	+	0.107522i
$429$		−	9.02802i		−	0.435877i
$430$	−0.180749	+	0.436366i	−0.00871647	+	0.0210434i
$431$	−5.79080	+	2.39863i	−0.278933	+	0.115538i	−0.517765	−	0.855523i	$-0.673236\pi$
$431$	−5.79080	+	2.39863i	−0.278933	+	0.115538i	0.238831	+	0.971061i	$0.423236\pi$
$432$	0.456955	+	1.10319i	0.0219852	+	0.0530770i
$433$	16.4151	+	16.4151i	0.788859	+	0.788859i	0.981307	−	0.192448i	$-0.0616428\pi$
$433$	16.4151	+	16.4151i	0.788859	+	0.788859i	−0.192448	+	0.981307i	$0.561643\pi$
$434$	4.54930	+	4.54930i	0.218373	+	0.218373i
$435$	0.613974	+	1.48227i	0.0294378	+	0.0710692i
$436$	13.8912	−	5.75392i	0.665267	−	0.275563i
$437$	−9.91030	+	23.9256i	−0.474074	+	1.14452i
$438$			8.32988i			0.398017i
$439$	34.9630	+	14.4822i	1.66869	+	0.691196i	0.998690	−	0.0511616i	$-0.0162924\pi$
$439$	34.9630	+	14.4822i	1.66869	+	0.691196i	0.670004	+	0.742357i	$0.266292\pi$
$440$	1.50070	−	1.50070i	0.0715432	−	0.0715432i
$441$	−11.1624			−0.531541
$442$	−24.0182	−	0.672291i	−1.14243	−	0.0319776i
$443$	24.5839			1.16802			0.584008	−	0.811748i	$-0.301484\pi$
$443$	24.5839			1.16802			0.584008	+	0.811748i	$0.301484\pi$
$444$	6.27934	−	6.27934i	0.298005	−	0.298005i
$445$	−2.73708	−	1.13373i	−0.129750	−	0.0537442i
$446$		−	6.28187i		−	0.297455i
$447$	−8.34750	+	20.1526i	−0.394823	+	0.953188i
$448$	−6.13196	+	2.53994i	−0.289708	+	0.120001i
$449$	−13.8243	−	33.3748i	−0.652408	−	1.57505i	−0.809273	−	0.587432i	$-0.800139\pi$
$449$	−13.8243	−	33.3748i	−0.652408	−	1.57505i	0.156865	−	0.987620i	$-0.449861\pi$
$450$	−6.09391	−	6.09391i	−0.287270	−	0.287270i
$451$	3.31562	+	3.31562i	0.156126	+	0.156126i
$452$	2.93534	+	7.08653i	0.138067	+	0.333322i
$453$	5.73781	−	2.37668i	0.269586	−	0.111666i
$454$	2.11101	−	5.09643i	0.0990746	−	0.239187i
$455$			4.06646i			0.190639i
$456$	−11.6986	−	4.84574i	−0.547839	−	0.226923i
$457$	−10.9019	+	10.9019i	−0.509970	+	0.509970i	−0.914517	−	0.404547i	$-0.867429\pi$
$457$	−10.9019	+	10.9019i	−0.509970	+	0.509970i	0.404547	+	0.914517i	$0.367429\pi$
$458$	−13.5424			−0.632795
$459$	−18.7304	−	8.37981i	−0.874259	−	0.391136i
$460$	−3.60410			−0.168042
$461$	7.08350	−	7.08350i	0.329911	−	0.329911i	−0.522641	−	0.852553i	$-0.675053\pi$
$461$	7.08350	−	7.08350i	0.329911	−	0.329911i	0.852553	+	0.522641i	$0.175053\pi$
$462$	−1.41573	−	0.586413i	−0.0658656	−	0.0272824i
$463$		−	1.65429i		−	0.0768813i	−0.999261	−	0.0384406i	$-0.987761\pi$
$463$		−	1.65429i		−	0.0768813i	0.999261	−	0.0384406i	$-0.0122391\pi$
$464$	0.284320	−	0.686410i	0.0131992	−	0.0318658i
$465$	−2.81638	+	1.16658i	−0.130607	+	0.0540990i
$466$	−5.68437	−	13.7233i	−0.263323	−	0.635719i
$467$	10.5504	+	10.5504i	0.488214	+	0.488214i	0.907742	−	0.419528i	$-0.137804\pi$
$467$	10.5504	+	10.5504i	0.488214	+	0.488214i	−0.419528	+	0.907742i	$0.637804\pi$
$468$	10.8495	+	10.8495i	0.501519	+	0.501519i
$469$	4.00322	+	9.66463i	0.184852	+	0.446271i
$470$	2.58922	−	1.07249i	0.119432	−	0.0494703i
$471$	−2.53713	+	6.12518i	−0.116905	+	0.282234i
$472$			12.2565i			0.564151i
$473$	−1.30474	−	0.540439i	−0.0599918	−	0.0248494i
$474$	−1.40789	+	1.40789i	−0.0646665	+	0.0646665i
$475$	20.9600			0.961711
$476$	2.40546	−	5.37662i	0.110254	−	0.246437i
$477$	21.0063			0.961812
$478$	−13.0870	+	13.0870i	−0.598587	+	0.598587i
$479$	37.9080	+	15.7020i	1.73206	+	0.717443i	0.999318	+	0.0369366i	$0.0117600\pi$
$479$	37.9080	+	15.7020i	1.73206	+	0.717443i	0.732742	+	0.680506i	$0.238240\pi$
$480$		−	2.86999i		−	0.130997i
$481$	−18.6701	+	45.0736i	−0.851283	+	2.05518i
$482$	10.3937	−	4.30520i	0.473418	−	0.196096i
$483$	2.68121	+	6.47300i	0.121999	+	0.294532i
$484$	−7.52533	−	7.52533i	−0.342061	−	0.342061i
$485$	0.947060	+	0.947060i	0.0430038	+	0.0430038i
$486$	−5.54875	−	13.3959i	−0.251696	−	0.607648i
$487$	7.86097	−	3.25612i	0.356214	−	0.147549i	−0.197398	−	0.980323i	$-0.563249\pi$
$487$	7.86097	−	3.25612i	0.356214	−	0.147549i	0.553612	+	0.832775i	$0.313249\pi$
$488$	15.7485	−	38.0202i	0.712901	−	1.72109i
$489$			10.8215i			0.489366i
$490$	−2.41688	−	1.00110i	−0.109184	−	0.0452253i
$491$	−19.5906	+	19.5906i	−0.884110	+	0.884110i	−0.993949	−	0.109839i	$-0.964966\pi$
$491$	−19.5906	+	19.5906i	−0.884110	+	0.884110i	0.109839	+	0.993949i	$0.464966\pi$
$492$	3.89350			0.175533
$493$	4.55390	+	11.9276i	0.205098	+	0.537191i
$494$	25.8380			1.16251
$495$	−1.05084	+	1.05084i	−0.0472319	+	0.0472319i
$496$	1.30421	+	0.540223i	0.0585610	+	0.0242568i
$497$		−	10.0335i		−	0.450062i
$498$	0.653381	−	1.57740i	0.0292787	−	0.0706850i
$499$	−17.2890	+	7.16136i	−0.773964	+	0.320586i	−0.734477	−	0.678634i	$-0.762572\pi$
$499$	−17.2890	+	7.16136i	−0.773964	+	0.320586i	−0.0394870	+	0.999220i	$0.512572\pi$
$500$	2.29698	+	5.54540i	0.102724	+	0.247998i
$501$	3.18222	+	3.18222i	0.142171	+	0.142171i
$502$	13.4037	+	13.4037i	0.598235	+	0.598235i
$503$	−10.1322	−	24.4613i	−0.451773	−	1.09068i	−0.971648	−	0.236434i	$-0.924021\pi$
$503$	−10.1322	−	24.4613i	−0.451773	−	1.09068i	0.519875	−	0.854243i	$-0.325979\pi$
$504$	6.47816	−	2.68334i	0.288560	−	0.119525i
$505$	−2.93512	+	7.08601i	−0.130611	+	0.315323i
$506$			7.46144i			0.331701i
$507$	26.1314	+	10.8240i	1.16054	+	0.480710i
$508$	7.62190	−	7.62190i	0.338167	−	0.338167i
$509$	11.7714			0.521759			0.260880	−	0.965371i	$-0.415987\pi$
$509$	11.7714			0.521759			0.260880	+	0.965371i	$0.415987\pi$
$510$	−1.32765	−	1.40412i	−0.0587895	−	0.0621754i
$511$	11.2185			0.496276
$512$	−1.91637	+	1.91637i	−0.0846924	+	0.0846924i
$513$	20.3859	+	8.44411i	0.900058	+	0.372816i
$514$		−	16.6163i		−	0.732915i
$515$	0.626059	−	1.51144i	0.0275874	−	0.0666020i
$516$	−1.08339	+	0.448753i	−0.0476934	+	0.0197553i
$517$	3.20675	+	7.74177i	0.141033	+	0.340483i
$518$	5.85549	+	5.85549i	0.257276	+	0.257276i
$519$	−4.89613	−	4.89613i	−0.214916	−	0.214916i
$520$	3.70500	+	8.94465i	0.162475	+	0.392249i
$521$	−7.41863	+	3.07290i	−0.325016	+	0.134626i	−0.539225	−	0.842162i	$-0.681283\pi$
$521$	−7.41863	+	3.07290i	−0.325016	+	0.134626i	0.214209	+	0.976788i	$0.431283\pi$
$522$	−2.16027	+	5.21536i	−0.0945526	+	0.228270i
$523$			43.9153i			1.92028i	0.279513	+	0.960142i	$0.409827\pi$
$523$			43.9153i			1.92028i	−0.279513	+	0.960142i	$0.590173\pi$
$524$	−0.956217	−	0.396078i	−0.0417725	−	0.0173028i
$525$	4.00977	−	4.00977i	0.175001	−	0.175001i
$526$	−3.79650			−0.165535
$527$	−22.6630	+	8.65266i	−0.987217	+	0.376916i
$528$	−0.336232			−0.0146326
$529$	7.85969	−	7.85969i	0.341726	−	0.341726i
$530$	4.54829	+	1.88396i	0.197565	+	0.0818342i
$531$		−	8.58242i		−	0.372445i
$532$	−2.42391	+	5.85184i	−0.105090	+	0.253710i
$533$	−19.7621	+	8.18573i	−0.855992	+	0.354563i
$534$	1.94894	+	4.70515i	0.0843388	+	0.203612i
$535$	−1.81605	−	1.81605i	−0.0785149	−	0.0785149i
$536$	17.6111	+	17.6111i	0.760684	+	0.760684i
$537$	−9.15073	−	22.0918i	−0.394883	−	0.953332i
$538$	11.2460	−	4.65825i	0.484850	−	0.200832i
$539$	2.99331	−	7.22648i	0.128931	−	0.311266i
$540$			3.07089i			0.132150i
$541$	−27.4936	−	11.3882i	−1.18204	−	0.489619i	−0.296887	−	0.954912i	$-0.595949\pi$
$541$	−27.4936	−	11.3882i	−1.18204	−	0.489619i	−0.885156	+	0.465294i	$0.845949\pi$
$542$	14.2505	−	14.2505i	0.612110	−	0.612110i
$543$	−4.37975			−0.187953
$544$	0.639024	−	22.8297i	0.0273979	−	0.978817i
$545$	−6.64339			−0.284572
$546$	4.94297	−	4.94297i	0.211539	−	0.211539i
$547$	−41.5771	−	17.2218i	−1.77771	−	0.736350i	−0.993226	−	0.116196i	$-0.962930\pi$
$547$	−41.5771	−	17.2218i	−1.77771	−	0.736350i	−0.784480	−	0.620154i	$-0.787070\pi$
$548$		−	15.2757i		−	0.652544i
$549$	−11.0276	+	26.6231i	−0.470648	+	1.13624i
$550$	5.57933	−	2.31103i	0.237903	−	0.0985428i
$551$	−5.25398	−	12.6842i	−0.223827	−	0.540367i
$552$	11.7953	+	11.7953i	0.502039	+	0.502039i
$553$	1.89611	+	1.89611i	0.0806310	+	0.0806310i
$554$	0.292820	+	0.706929i	0.0124407	+	0.0300345i
$555$	−3.62502	+	1.50153i	−0.153874	+	0.0637365i
$556$	−8.93699	+	21.5758i	−0.379013	+	0.915018i
$557$			13.9798i			0.592342i	0.955135	+	0.296171i	$0.0957098\pi$
$557$			13.9798i			0.592342i	−0.955135	+	0.296171i	$0.904290\pi$
$558$	−9.90946	−	4.10463i	−0.419501	−	0.173763i
$559$	4.55544	−	4.55544i	0.192675	−	0.192675i
$560$	0.151448			0.00639983
$561$	4.19832	−	3.96969i	0.177253	−	0.167600i
$562$	17.9802			0.758449
$563$	−24.2319	+	24.2319i	−1.02125	+	1.02125i	−0.0214825	+	0.999769i	$0.506839\pi$
$563$	−24.2319	+	24.2319i	−1.02125	+	1.02125i	−0.999769	+	0.0214825i	$0.993161\pi$
$564$	6.42838	+	2.66272i	0.270684	+	0.112121i
$565$		−	3.38910i		−	0.142580i
$566$	9.98657	−	24.1097i	0.419767	−	1.01341i
$567$	−1.23715	+	0.512445i	−0.0519555	+	0.0215207i
$568$	−9.14160	−	22.0698i	−0.383573	−	0.926027i
$569$	−18.9485	−	18.9485i	−0.794362	−	0.794362i	0.187838	−	0.982200i	$-0.439852\pi$
$569$	−18.9485	−	18.9485i	−0.794362	−	0.794362i	−0.982200	+	0.187838i	$0.939852\pi$
$570$	1.46938	+	1.46938i	0.0615454	+	0.0615454i
$571$	−0.240236	−	0.579981i	−0.0100536	−	0.0242715i	0.918773	−	0.394786i	$-0.129181\pi$
$571$	−0.240236	−	0.579981i	−0.0100536	−	0.0242715i	−0.928827	+	0.370515i	$0.879181\pi$
$572$	−9.93336	+	4.11453i	−0.415335	+	0.172037i
$573$	−3.53216	+	8.52739i	−0.147558	+	0.356237i
$574$			3.63069i			0.151542i
$575$	−25.5099	−	10.5665i	−1.06384	−	0.440655i
$576$	7.82427	−	7.82427i	0.326011	−	0.326011i
$577$	5.83950			0.243101			0.121551	−	0.992585i	$-0.461213\pi$
$577$	5.83950			0.243101			0.121551	+	0.992585i	$0.461213\pi$
$578$	−10.2484	−	11.4649i	−0.426276	−	0.476875i
$579$	−7.55312			−0.313897
$580$	1.35109	−	1.35109i	0.0561009	−	0.0561009i
$581$	−2.12441	−	0.879958i	−0.0881352	−	0.0365068i
$582$		−	2.30239i		−	0.0954371i
$583$	−5.63306	+	13.5994i	−0.233297	+	0.563230i
$584$	24.6764	−	10.2213i	1.02112	−	0.422960i
$585$	−2.59437	−	6.26335i	−0.107264	−	0.258958i
$586$	−12.4562	−	12.4562i	−0.514559	−	0.514559i
$587$	−10.5807	−	10.5807i	−0.436710	−	0.436710i	0.454193	−	0.890903i	$-0.349928\pi$
$587$	−10.5807	−	10.5807i	−0.436710	−	0.436710i	−0.890903	+	0.454193i	$0.849928\pi$
$588$	−2.48549	−	6.00051i	−0.102500	−	0.247457i
$589$	24.1007	−	9.98284i	0.993052	−	0.411336i
$590$	0.769721	−	1.85827i	0.0316889	−	0.0765038i
$591$		−	5.54419i		−	0.228057i
$592$	1.67868	+	0.695333i	0.0689934	+	0.0285780i
$593$	23.4782	−	23.4782i	0.964132	−	0.964132i	−0.0352463	−	0.999379i	$-0.511222\pi$
$593$	23.4782	−	23.4782i	0.964132	−	0.964132i	0.999379	+	0.0352463i	$0.0112216\pi$
$594$	6.35755			0.260853
$595$	−1.89103	+	1.78805i	−0.0775248	+	0.0733030i
$596$	25.9780			1.06410
$597$	0.0632613	−	0.0632613i	0.00258911	−	0.00258911i
$598$	−31.4468	−	13.0257i	−1.28596	−	0.532660i
$599$		−	14.8261i		−	0.605777i	−0.953026	−	0.302888i	$-0.902049\pi$
$599$		−	14.8261i		−	0.605777i	0.953026	−	0.302888i	$-0.0979509\pi$
$600$	5.16662	−	12.4733i	0.210926	−	0.509221i
$601$	36.2753	−	15.0257i	1.47970	−	0.612912i	0.510653	−	0.859787i	$-0.329404\pi$
$601$	36.2753	−	15.0257i	1.47970	−	0.612912i	0.969047	+	0.246875i	$0.0794036\pi$
$602$	−0.418463	−	1.01026i	−0.0170553	−	0.0411751i
$603$	−12.3319	−	12.3319i	−0.502194	−	0.502194i
$604$	−5.23003	−	5.23003i	−0.212807	−	0.212807i
$605$	1.79948	+	4.34432i	0.0731592	+	0.176622i
$606$	12.1811	−	5.04560i	0.494825	−	0.204963i
$607$	−12.0379	+	29.0621i	−0.488605	+	1.17960i	0.466818	+	0.884353i	$0.345400\pi$
$607$	−12.0379	+	29.0621i	−0.488605	+	1.17960i	−0.955422	+	0.295242i	$0.904600\pi$
$608$			24.5595i			0.996018i
$609$	−3.43169	−	1.42145i	−0.139059	−	0.0576001i
$610$	−4.77542	+	4.77542i	−0.193351	+	0.193351i
$611$	−38.2264			−1.54648
$612$	−0.274758	+	9.81600i	−0.0111064	+	0.396788i
$613$	−36.1297			−1.45927			−0.729633	−	0.683839i	$-0.760309\pi$
$613$	−36.1297			−1.45927			−0.729633	+	0.683839i	$0.760309\pi$
$614$	8.72079	−	8.72079i	0.351942	−	0.351942i
$615$	−1.58936	−	0.658334i	−0.0640891	−	0.0265466i
$616$			4.91351i			0.197971i
$617$	10.8485	−	26.1907i	0.436746	−	1.05440i	−0.540320	−	0.841460i	$-0.681697\pi$
$617$	10.8485	−	26.1907i	0.436746	−	1.05440i	0.977066	−	0.212938i	$-0.0683033\pi$
$618$	−2.59823	+	1.07622i	−0.104516	+	0.0432920i
$619$	−15.7017	−	37.9072i	−0.631104	−	1.52362i	−0.838236	−	0.545308i	$-0.816413\pi$
$619$	−15.7017	−	37.9072i	−0.631104	−	1.52362i	0.207131	−	0.978313i	$-0.433587\pi$
$620$	2.56714	+	2.56714i	0.103099	+	0.103099i
$621$	−20.5542	−	20.5542i	−0.824812	−	0.824812i
$622$	−6.25795	−	15.1080i	−0.250921	−	0.605777i
$623$	6.33679	−	2.62478i	0.253878	−	0.105160i
$624$	0.586971	−	1.41707i	0.0234977	−	0.0567284i
$625$			20.9847i			0.839390i
$626$	−5.56054	−	2.30325i	−0.222244	−	0.0920564i
$627$	−4.39344	+	4.39344i	−0.175457	+	0.175457i
$628$	7.89573			0.315074
$629$	−29.1701	+	11.1370i	−1.16309	+	0.444062i
$630$	−1.15070			−0.0458451
$631$	0.683703	−	0.683703i	0.0272178	−	0.0272178i	−0.693367	−	0.720585i	$-0.743873\pi$
$631$	0.683703	−	0.683703i	0.0272178	−	0.0272178i	0.720585	+	0.693367i	$0.243873\pi$
$632$	5.89829	+	2.44315i	0.234622	+	0.0971834i
$633$		−	27.4419i		−	1.09072i
$634$	−5.44754	+	13.1515i	−0.216350	+	0.522314i
$635$	−4.40007	+	1.82257i	−0.174611	+	0.0723264i
$636$	4.67741	+	11.2923i	0.185471	+	0.447767i
$637$	25.2310	+	25.2310i	0.999690	+	0.999690i
$638$	−2.79711	−	2.79711i	−0.110739	−	0.110739i
$639$	6.40126	+	15.4540i	0.253230	+	0.611351i
$640$	−2.94840	+	1.22127i	−0.116546	+	0.0482749i
$641$	9.27939	−	22.4024i	0.366514	−	0.884843i	−0.627802	−	0.778373i	$-0.716045\pi$
$641$	9.27939	−	22.4024i	0.366514	−	0.884843i	0.994316	−	0.106470i	$-0.0339547\pi$
$642$			4.41499i			0.174246i
$643$	−9.12200	−	3.77846i	−0.359737	−	0.149008i	0.195492	−	0.980705i	$-0.437369\pi$
$643$	−9.12200	−	3.77846i	−0.359737	−	0.149008i	−0.555229	+	0.831697i	$0.687369\pi$
$644$	5.90017	−	5.90017i	0.232499	−	0.232499i
$645$	0.518125			0.0204011
$646$	11.3612	+	12.0155i	0.446999	+	0.472744i
$647$	0.0624048			0.00245338			0.00122669	−	0.999999i	$-0.499610\pi$
$647$	0.0624048			0.00245338			0.00122669	+	0.999999i	$0.499610\pi$
$648$	−2.25437	+	2.25437i	−0.0885599	+	0.0885599i
$649$	5.55623	+	2.30147i	0.218101	+	0.0903405i
$650$			27.5490i			1.08056i
$651$	2.70083	−	6.52039i	0.105854	−	0.255554i
$652$	11.9067	−	4.93193i	0.466303	−	0.193149i
$653$	10.1017	+	24.3876i	0.395309	+	0.954360i	0.988763	+	0.149492i	$0.0477639\pi$
$653$	10.1017	+	24.3876i	0.395309	+	0.954360i	−0.593454	+	0.804868i	$0.702236\pi$
$654$	8.07535	+	8.07535i	0.315771	+	0.315771i
$655$	0.323364	+	0.323364i	0.0126349	+	0.0126349i
$656$	0.304862	+	0.736003i	0.0119029	+	0.0287361i
$657$	−17.2792	+	7.15730i	−0.674128	+	0.279233i
$658$	−2.48299	+	5.99447i	−0.0967971	+	0.233689i
$659$			33.6076i			1.30917i	0.755990	+	0.654583i	$0.227156\pi$
$659$			33.6076i			1.30917i	−0.755990	+	0.654583i	$0.772844\pi$
$660$	−0.798886	−	0.330909i	−0.0310966	−	0.0128806i
$661$	8.46905	−	8.46905i	0.329408	−	0.329408i	−0.522953	−	0.852361i	$-0.675170\pi$
$661$	8.46905	−	8.46905i	0.329408	−	0.329408i	0.852361	+	0.522953i	$0.175170\pi$
$662$	−1.37081			−0.0532781
$663$	9.40141	+	24.6242i	0.365120	+	0.956323i
$664$	−5.47462			−0.212456
$665$	1.97892	−	1.97892i	0.0767392	−	0.0767392i
$666$	−12.7547	−	5.28316i	−0.494233	−	0.204718i
$667$			18.0863i			0.700306i
$668$	2.05104	−	4.95164i	0.0793570	−	0.191585i
$669$	−6.36653	+	2.63710i	−0.246144	+	0.101956i
$670$	−1.56411	−	3.77611i	−0.0604270	−	0.145884i
$671$	−14.2785	−	14.2785i	−0.551216	−	0.551216i
$672$	4.69837	+	4.69837i	0.181244	+	0.181244i
$673$	8.37785	+	20.2259i	0.322943	+	0.779652i	0.999080	+	0.0428771i	$0.0136524\pi$
$673$	8.37785	+	20.2259i	0.322943	+	0.779652i	−0.676138	+	0.736775i	$0.736348\pi$
$674$	1.20770	−	0.500246i	0.0465189	−	0.0192688i
$675$	−9.00326	+	21.7358i	−0.346536	+	0.836611i
$676$		−	33.6850i		−	1.29558i
$677$	−13.8298	−	5.72847i	−0.531521	−	0.220163i	0.100748	−	0.994912i	$-0.467876\pi$
$677$	−13.8298	−	5.72847i	−0.531521	−	0.220163i	−0.632269	+	0.774749i	$0.717876\pi$
$678$	−4.11961	+	4.11961i	−0.158213	+	0.158213i
$679$	−3.10080			−0.118998
$680$	−2.53044	+	5.65598i	−0.0970378	+	0.216897i
$681$	−6.05131			−0.231887
$682$	5.31465	−	5.31465i	0.203509	−	0.203509i
$683$	−18.6315	−	7.71743i	−0.712915	−	0.295299i	−0.00340503	−	0.999994i	$-0.501084\pi$
$683$	−18.6315	−	7.71743i	−0.712915	−	0.295299i	−0.709510	+	0.704695i	$0.751084\pi$
$684$		−	10.5597i		−	0.403761i
$685$	−2.58289	+	6.23564i	−0.0986871	+	0.238252i
$686$	12.6673	−	5.24696i	0.483639	−	0.200330i
$687$	5.68505	+	13.7249i	0.216898	+	0.523639i
$688$	−0.169659	−	0.169659i	−0.00646819	−	0.00646819i
$689$	−47.4819	−	47.4819i	−1.80892	−	1.80892i
$690$	−1.04759	−	2.52909i	−0.0398809	−	0.0962810i
$691$	−47.4912	+	19.6715i	−1.80665	+	0.748339i	−0.823052	+	0.567966i	$0.807730\pi$
$691$	−47.4912	+	19.6715i	−1.80665	+	0.748339i	−0.983598	+	0.180373i	$0.942270\pi$
$692$	−3.15570	+	7.61854i	−0.119962	+	0.289613i
$693$		−	3.44061i		−	0.130698i
$694$	−3.46623	−	1.43576i	−0.131576	−	0.0545006i
$695$	7.29630	−	7.29630i	0.276764	−	0.276764i
$696$	−8.84350			−0.335212
$697$	−12.4962	−	5.59069i	−0.473327	−	0.211762i
$698$	−18.5215			−0.701050
$699$	−11.5220	+	11.5220i	−0.435801	+	0.435801i
$700$	−6.23934	−	2.58442i	−0.235825	−	0.0976819i
$701$		−	3.32047i		−	0.125412i	−0.998032	−	0.0627062i	$-0.980027\pi$
$701$		−	3.32047i		−	0.125412i	0.998032	−	0.0627062i	$-0.0199731\pi$
$702$	−11.0986	+	26.7944i	−0.418889	+	1.01129i
$703$	31.0205	−	12.8491i	1.16996	−	0.484614i
$704$	2.96725	+	7.16357i	0.111832	+	0.269987i
$705$	−2.17389	−	2.17389i	−0.0818734	−	0.0818734i
$706$	16.7983	+	16.7983i	0.632211	+	0.632211i
$707$	−6.79529	−	16.4053i	−0.255563	−	0.616984i
$708$	4.61362	−	1.91102i	0.173390	−	0.0718207i
$709$	16.6060	−	40.0904i	0.623651	−	1.50563i	−0.223736	−	0.974650i	$-0.571825\pi$
$709$	16.6060	−	40.0904i	0.623651	−	1.50563i	0.847387	−	0.530976i	$-0.178175\pi$
$710$			3.92021i			0.147123i
$711$	−4.13019	−	1.71078i	−0.154894	−	0.0641593i
$712$	11.5470	−	11.5470i	0.432743	−	0.432743i
$713$	−34.3650			−1.28698
$714$	4.47210	+	0.125178i	0.167364	+	0.00468467i
$715$	4.75058			0.177662
$716$	−20.1368	+	20.1368i	−0.752546	+	0.752546i
$717$	18.7573	+	7.76953i	0.700504	+	0.290158i
$718$		−	25.0310i		−	0.934149i
$719$	1.99490	−	4.81611i	0.0743972	−	0.179611i	−0.882306	−	0.470677i	$-0.844010\pi$
$719$	1.99490	−	4.81611i	0.0743972	−	0.179611i	0.956703	+	0.291066i	$0.0940099\pi$
$720$	−0.233267	+	0.0966223i	−0.00869335	+	0.00360090i
$721$	1.44943	+	3.49923i	0.0539796	+	0.130318i
$722$	−0.421038	−	0.421038i	−0.0156694	−	0.0156694i
$723$	−8.72644	−	8.72644i	−0.324540	−	0.324540i
$724$	1.99608	+	4.81896i	0.0741837	+	0.179095i
$725$	13.5242	−	5.60189i	0.502275	−	0.208049i
$726$	3.09338	−	7.46807i	0.114806	−	0.277166i
$727$		−	20.9921i		−	0.778552i	−0.921121	−	0.389276i	$-0.872725\pi$
$727$		−	20.9921i		−	0.778552i	0.921121	−	0.389276i	$-0.127275\pi$
$728$	−20.7083	−	8.57768i	−0.767502	−	0.317910i
$729$	−8.89722	+	8.89722i	−0.329527	+	0.329527i
$730$	−4.38322			−0.162230
$731$	4.12149	+	0.115364i	0.152439	+	0.00426690i
$732$	−16.7672			−0.619732
$733$	5.33284	−	5.33284i	0.196973	−	0.196973i	−0.601728	−	0.798701i	$-0.705521\pi$
$733$	5.33284	−	5.33284i	0.196973	−	0.196973i	0.798701	+	0.601728i	$0.205521\pi$
$734$	−14.1701	−	5.86944i	−0.523027	−	0.216645i
$735$			2.86971i			0.105851i
$736$	12.3811	−	29.8907i	0.456375	−	1.10179i
$737$	11.2906	−	4.67671i	0.415894	−	0.172269i
$738$	−2.31635	−	5.59217i	−0.0852661	−	0.205851i
$739$	36.9764	+	36.9764i	1.36020	+	1.36020i	0.873657	+	0.486543i	$0.161742\pi$
$739$	36.9764	+	36.9764i	1.36020	+	1.36020i	0.486543	+	0.873657i	$0.338258\pi$
$740$	3.30422	+	3.30422i	0.121466	+	0.121466i
$741$	−10.8467	−	26.1862i	−0.398463	−	0.961976i
$742$	−10.5300	+	4.36169i	−0.386570	+	0.160123i
$743$	16.8760	−	40.7424i	0.619122	−	1.49469i	−0.233603	−	0.972332i	$-0.575052\pi$
$743$	16.8760	−	40.7424i	0.619122	−	1.49469i	0.852725	−	0.522360i	$-0.174948\pi$
$744$		−	16.8031i		−	0.616032i
$745$	−10.6044	−	4.39249i	−0.388516	−	0.160929i
$746$	−9.62933	+	9.62933i	−0.352555	+	0.352555i
$747$	3.83352			0.140261
$748$	−6.28117	−	2.81014i	−0.229662	−	0.102749i
$749$	5.94601			0.217263
$750$	−3.22370	+	3.22370i	−0.117713	+	0.117713i
$751$	−5.61679	−	2.32655i	−0.204960	−	0.0848970i	0.277842	−	0.960627i	$-0.410381\pi$
$751$	−5.61679	−	2.32655i	−0.204960	−	0.0848970i	−0.482802	+	0.875730i	$0.660381\pi$
$752$			1.42367i			0.0519160i
$753$	7.95751	−	19.2111i	0.289988	−	0.700092i
$754$	16.6716	−	6.90562i	0.607145	−	0.251488i
$755$	1.25062	+	3.01926i	0.0455147	+	0.109882i
$756$	−5.02726	−	5.02726i	−0.182840	−	0.182840i
$757$	−23.6814	−	23.6814i	−0.860716	−	0.860716i	0.130706	−	0.991421i	$-0.458276\pi$
$757$	−23.6814	−	23.6814i	−0.860716	−	0.860716i	−0.991421	+	0.130706i	$0.958276\pi$
$758$	4.39537	+	10.6114i	0.159647	+	0.385422i
$759$	7.56200	−	3.13228i	0.274483	−	0.113695i
$760$	2.54985	−	6.15588i	0.0924928	−	0.223297i
$761$			15.2033i			0.551119i	0.961284	+	0.275560i	$0.0888631\pi$
$761$			15.2033i			0.551119i	−0.961284	+	0.275560i	$0.911137\pi$
$762$	7.56390	+	3.13307i	0.274011	+	0.113499i
$763$	10.8757	−	10.8757i	0.393726	−	0.393726i
$764$	10.9923			0.397688
$765$	1.77190	−	3.96051i	0.0640631	−	0.143193i
$766$	12.2569			0.442861
$767$	−19.3994	+	19.3994i	−0.700473	+	0.700473i
$768$	15.1352	+	6.26922i	0.546146	+	0.226221i
$769$		−	21.0273i		−	0.758264i	−0.925343	−	0.379132i	$-0.876223\pi$
$769$		−	21.0273i		−	0.758264i	0.925343	−	0.379132i	$-0.123777\pi$
$770$	0.308573	−	0.744962i	0.0111202	−	0.0268466i
$771$	−16.8403	+	6.97547i	−0.606488	+	0.251216i
$772$	3.44235	+	8.31056i	0.123893	+	0.299104i
$773$	−8.96396	−	8.96396i	−0.322411	−	0.322411i	0.527280	−	0.849691i	$-0.323212\pi$
$773$	−8.96396	−	8.96396i	−0.322411	−	0.322411i	−0.849691	+	0.527280i	$0.823212\pi$
$774$	1.28907	+	1.28907i	0.0463348	+	0.0463348i
$775$	10.6439	+	25.6966i	0.382340	+	0.923050i
$776$	−6.82058	+	2.82518i	−0.244845	+	0.101418i
$777$	3.47630	−	8.39252i	0.124711	−	0.301080i
$778$			13.2807i			0.476138i
$779$	13.6007	+	5.63358i	0.487294	+	0.201844i
$780$	2.78929	−	2.78929i	0.0998725	−	0.0998725i
$781$	−11.7215			−0.419426
$782$	−7.77004	−	20.3513i	−0.277856	−	0.727760i
$783$	15.4105			0.550728
$784$	0.939683	−	0.939683i	0.0335601	−	0.0335601i
$785$	−3.22310	−	1.33505i	−0.115037	−	0.0476500i
$786$		−	0.786128i		−	0.0280403i
$787$	−2.64948	+	6.39640i	−0.0944437	+	0.228007i	−0.964041	−	0.265755i	$-0.914379\pi$
$787$	−2.64948	+	6.39640i	−0.0944437	+	0.228007i	0.869597	+	0.493762i	$0.164379\pi$
$788$	−6.10017	+	2.52677i	−0.217310	+	0.0900126i
$789$	1.59375	+	3.84766i	0.0567392	+	0.136980i
$790$	−0.740838	−	0.740838i	−0.0263578	−	0.0263578i
$791$	5.54819	+	5.54819i	0.197271	+	0.197271i
$792$	−3.13478	−	7.56802i	−0.111389	−	0.268918i
$793$	85.1044	−	35.2514i	3.02215	−	1.25181i
$794$	−8.84447	+	21.3524i	−0.313878	+	0.757770i
$795$		−	5.40047i		−	0.191535i
$796$	−0.0984368	−	0.0407738i	−0.00348900	−	0.00144519i
$797$	4.13731	−	4.13731i	0.146551	−	0.146551i	−0.630024	−	0.776575i	$-0.716955\pi$
$797$	4.13731	−	4.13731i	0.146551	−	0.146551i	0.776575	+	0.630024i	$0.216955\pi$
$798$	−4.81094			−0.170305
$799$	−16.8085	−	17.7765i	−0.594641	−	0.628888i
$800$	−26.1858			−0.925806
$801$	−8.08563	+	8.08563i	−0.285692	+	0.285692i
$802$	26.1963	+	10.8509i	0.925023	+	0.383157i
$803$		−	13.1058i		−	0.462495i
$804$	3.88330	−	9.37512i	0.136954	−	0.330635i
$805$	−3.40613	+	1.41086i	−0.120050	+	0.0497264i
$806$	13.1210	+	31.6770i	0.462169	+	1.11577i
$807$	−9.44207	−	9.44207i	−0.332377	−	0.332377i
$808$	−29.8941	−	29.8941i	−1.05167	−	1.05167i
$809$	−17.2231	−	41.5803i	−0.605533	−	1.46189i	−0.867811	−	0.496894i	$-0.834474\pi$
$809$	−17.2231	−	41.5803i	−0.605533	−	1.46189i	0.262278	−	0.964992i	$-0.415526\pi$
$810$	0.483373	−	0.200220i	0.0169840	−	0.00703500i
$811$	−11.6605	+	28.1509i	−0.409456	+	0.988513i	0.575826	+	0.817572i	$0.304681\pi$
$811$	−11.6605	+	28.1509i	−0.409456	+	0.988513i	−0.985281	+	0.170941i	$0.945319\pi$
$812$			4.42365i			0.155240i
$813$	−20.4248	−	8.46024i	−0.716330	−	0.296713i
$814$	6.84060	−	6.84060i	0.239763	−	0.239763i
$815$	−5.69433			−0.199464
$816$	0.917081	−	0.350138i	0.0321043	−	0.0122573i
$817$	−4.43376			−0.155118
$818$	−3.26267	+	3.26267i	−0.114076	+	0.114076i
$819$	14.5007	+	6.00639i	0.506695	+	0.209880i
$820$			2.04878i			0.0715465i
$821$	−13.6322	+	32.9109i	−0.475765	+	1.14860i	0.485811	+	0.874064i	$0.338524\pi$
$821$	−13.6322	+	32.9109i	−0.475765	+	1.14860i	−0.961577	+	0.274536i	$0.911476\pi$
$822$	10.7193	−	4.44009i	0.373880	−	0.154866i
$823$	−18.9470	−	45.7421i	−0.660451	−	1.59447i	−0.797097	−	0.603851i	$-0.793632\pi$
$823$	−18.9470	−	45.7421i	−0.660451	−	1.59447i	0.136646	−	0.990620i	$-0.456368\pi$
$824$	6.37638	+	6.37638i	0.222132	+	0.222132i
$825$	−4.68436	−	4.68436i	−0.163089	−	0.163089i
$826$	1.78203	+	4.30220i	0.0620048	+	0.149693i
$827$	32.8985	−	13.6270i	1.14399	−	0.473858i	0.271479	−	0.962444i	$-0.412487\pi$
$827$	32.8985	−	13.6270i	1.14399	−	0.473858i	0.872516	+	0.488586i	$0.162487\pi$
$828$	−5.32346	+	12.8520i	−0.185003	+	0.446637i
$829$		−	43.4546i		−	1.50924i	−0.656162	−	0.754620i	$-0.727821\pi$
$829$		−	43.4546i		−	1.50924i	0.656162	−	0.754620i	$-0.272179\pi$
$830$	0.830035	+	0.343812i	0.0288110	+	0.0119339i
$831$	0.593532	−	0.593532i	0.0205894	−	0.0205894i
$832$	−35.3715			−1.22628
$833$	−0.638962	+	22.8275i	−0.0221387	+	0.790927i
$834$	−17.7380			−0.614216
$835$	−1.67450	+	1.67450i	−0.0579484	+	0.0579484i
$836$	6.83633	+	2.83170i	0.236440	+	0.0979365i
$837$			29.2808i			1.01209i
$838$	10.6047	−	25.6021i	0.366334	−	0.884409i
$839$	−0.589198	+	0.244054i	−0.0203414	+	0.00842568i	−0.392831	−	0.919611i	$-0.628504\pi$
$839$	−0.589198	+	0.244054i	−0.0203414	+	0.00842568i	0.372490	+	0.928036i	$0.378504\pi$
$840$	−0.689856	−	1.66546i	−0.0238023	−	0.0574638i
$841$	13.7260	+	13.7260i	0.473309	+	0.473309i
$842$	0.461725	+	0.461725i	0.0159121	+	0.0159121i
$843$	−7.54802	−	18.2225i	−0.259968	−	0.627617i
$844$	−30.1938	+	12.5067i	−1.03931	+	0.430498i
$845$	−5.69563	+	13.7505i	−0.195936	+	0.473030i
$846$		−	10.8171i		−	0.371900i
$847$	−10.0578	−	4.16609i	−0.345591	−	0.143148i
$848$	−1.76838	+	1.76838i	−0.0607263	+	0.0607263i
$849$	−28.6270			−0.982475
$850$	−12.8112	+	12.1135i	−0.439419	+	0.415489i
$851$	−44.2319			−1.51625
$852$	−6.88220	+	6.88220i	−0.235780	+	0.235780i
$853$	6.96863	+	2.88650i	0.238601	+	0.0988319i	0.498780	−	0.866729i	$-0.333782\pi$
$853$	6.96863	+	2.88650i	0.238601	+	0.0988319i	−0.260179	+	0.965560i	$0.583782\pi$
$854$		−	15.6354i		−	0.535032i
$855$	−1.78549	+	4.31056i	−0.0610626	+	0.147418i
$856$	13.0789	−	5.41748i	0.447029	−	0.185166i
$857$	−10.7346	−	25.9156i	−0.366687	−	0.885260i	−0.994289	−	0.106725i	$-0.965963\pi$
$857$	−10.7346	−	25.9156i	−0.366687	−	0.885260i	0.627602	−	0.778534i	$-0.284037\pi$
$858$	−5.77455	−	5.77455i	−0.197140	−	0.197140i
$859$	24.6325	+	24.6325i	0.840449	+	0.840449i	0.988917	−	0.148468i	$-0.0474341\pi$
$859$	24.6325	+	24.6325i	0.840449	+	0.840449i	−0.148468	+	0.988917i	$0.547434\pi$
$860$	−0.236136	−	0.570083i	−0.00805218	−	0.0194397i
$861$	3.67963	−	1.52415i	0.125401	−	0.0519429i
$862$	−2.16972	+	5.23817i	−0.0739010	+	0.178413i
$863$			0.574219i			0.0195466i	0.999952	+	0.00977332i	$0.00311099\pi$
$863$			0.574219i			0.0195466i	−0.999952	+	0.00977332i	$0.996889\pi$
$864$	−25.4685	−	10.5494i	−0.866456	−	0.358898i
$865$	2.57636	−	2.57636i	0.0875990	−	0.0875990i
$866$	20.9990			0.713576
$867$	−7.31716	+	15.1994i	−0.248504	+	0.516198i
$868$	−8.40517			−0.285290
$869$	2.21511	−	2.21511i	0.0751424	−	0.0751424i
$870$	1.34081	+	0.555381i	0.0454577	+	0.0188292i
$871$			55.7493i			1.88899i
$872$	14.0134	−	33.8313i	0.474553	−	1.14567i
$873$	4.77601	−	1.97829i	0.161643	−	0.0669549i
$874$	8.96453	+	21.6423i	0.303230	+	0.732062i
$875$	4.34161	+	4.34161i	0.146773	+	0.146773i
$876$	−7.69504	−	7.69504i	−0.259991	−	0.259991i
$877$	14.1886	+	34.2544i	0.479116	+	1.15669i	0.960024	+	0.279918i	$0.0903073\pi$
$877$	14.1886	+	34.2544i	0.479116	+	1.15669i	−0.480908	+	0.876771i	$0.659693\pi$
$878$	31.6264	−	13.1001i	1.06734	−	0.442107i
$879$	−7.39499	+	17.8531i	−0.249427	+	0.602170i
$880$		−	0.176927i		−	0.00596420i
$881$	−6.32032	−	2.61796i	−0.212937	−	0.0882014i	0.273665	−	0.961825i	$-0.411764\pi$
$881$	−6.32032	−	2.61796i	−0.212937	−	0.0882014i	−0.486602	+	0.873624i	$0.661764\pi$
$882$	−7.13973	+	7.13973i	−0.240407	+	0.240407i
$883$	−42.4752			−1.42940			−0.714702	−	0.699430i	$-0.753437\pi$
$883$	−42.4752			−1.42940			−0.714702	+	0.699430i	$0.753437\pi$
$884$	22.8088	−	21.5667i	0.767143	−	0.725367i
$885$	−2.20644			−0.0741687
$886$	15.7245	−	15.7245i	0.528275	−	0.528275i
$887$	18.1556	+	7.52028i	0.609604	+	0.252506i	0.666059	−	0.745899i	$-0.267980\pi$
$887$	18.1556	+	7.52028i	0.609604	+	0.252506i	−0.0564552	+	0.998405i	$0.517980\pi$
$888$		−	21.6276i		−	0.725776i
$889$	4.21954	−	10.1869i	0.141519	−	0.341657i
$890$	−2.47587	+	1.02554i	−0.0829914	+	0.0343762i
$891$	0.598657	+	1.44529i	0.0200558	+	0.0484189i
$892$	5.80312	+	5.80312i	0.194303	+	0.194303i
$893$	18.6027	+	18.6027i	0.622515	+	0.622515i
$894$	7.55088	+	18.2294i	0.252539	+	0.609683i
$895$	11.6248	−	4.81515i	0.388575	−	0.160953i
$896$	2.82744	−	6.82604i	0.0944580	−	0.228042i
$897$			37.3388i			1.24670i
$898$	−30.1897	−	12.5050i	−1.00744	−	0.417297i
$899$	12.8826	−	12.8826i	0.429659	−	0.429659i
$900$	11.2590			0.375299
$901$	1.20245	−	42.9588i	0.0400595	−	1.43116i
$902$	4.24151			0.141227
$903$	−0.848205	+	0.848205i	−0.0282265	+	0.0282265i
$904$	17.2589	+	7.14887i	0.574023	+	0.237768i
$905$		−	2.30465i		−	0.0766090i
$906$	2.14987	−	5.19024i	0.0714245	−	0.172434i
$907$	−15.7553	+	6.52605i	−0.523146	+	0.216694i	−0.628598	−	0.777730i	$-0.716371\pi$
$907$	−15.7553	+	6.52605i	−0.523146	+	0.216694i	0.105453	+	0.994424i	$0.466371\pi$
$908$	2.75790	+	6.65815i	0.0915240	+	0.220958i
$909$	20.9329	+	20.9329i	0.694299	+	0.694299i
$910$	2.60101	+	2.60101i	0.0862227	+	0.0862227i
$911$	4.00855	+	9.67751i	0.132809	+	0.320630i	0.976269	−	0.216563i	$-0.0694847\pi$
$911$	4.00855	+	9.67751i	0.132809	+	0.320630i	−0.843459	+	0.537193i	$0.819485\pi$
$912$	−0.975258	+	0.403965i	−0.0322940	+	0.0133766i
$913$	−1.02800	+	2.48181i	−0.0340218	+	0.0821359i
$914$			13.9463i			0.461302i
$915$	6.84448	+	2.83508i	0.226272	+	0.0937248i
$916$	12.5103	−	12.5103i	0.413353	−	0.413353i
$917$	−1.05874			−0.0349627
$918$	−17.3404	+	6.62049i	−0.572318	+	0.218509i
$919$	28.8314			0.951061			0.475531	−	0.879699i	$-0.342256\pi$
$919$	28.8314			0.951061			0.475531	+	0.879699i	$0.342256\pi$
$920$	−6.20672	+	6.20672i	−0.204629	+	0.204629i
$921$	−12.4993	−	5.17737i	−0.411865	−	0.170600i
$922$		−	9.06158i		−	0.298427i
$923$	20.4625	−	49.4010i	0.673533	−	1.62605i
$924$	1.84955	−	0.766110i	0.0608458	−	0.0252032i
$925$	13.7000	+	33.0746i	0.450452	+	1.08749i
$926$	−1.05813	−	1.05813i	−0.0347722	−	0.0347722i
$927$	−4.46496	−	4.46496i	−0.146649	−	0.146649i
$928$	6.56391	+	15.8467i	0.215471	+	0.520193i
$929$	16.2581	−	6.73431i	0.533410	−	0.220946i	−0.0996859	−	0.995019i	$-0.531784\pi$
$929$	16.2581	−	6.73431i	0.533410	−	0.220946i	0.633096	+	0.774073i	$0.281784\pi$
$930$	−1.05525	+	2.54761i	−0.0346031	+	0.0835393i
$931$		−	24.5571i		−	0.804826i
$932$	17.9286	+	7.42625i	0.587270	+	0.243255i
$933$	−12.6846	+	12.6846i	−0.415275	+	0.415275i
$934$	13.4966			0.441623
$935$	2.08887	+	2.20917i	0.0683133	+	0.0722477i
$936$	37.3685			1.22143
$937$	4.32581	−	4.32581i	0.141318	−	0.141318i	−0.632909	−	0.774227i	$-0.718139\pi$
$937$	4.32581	−	4.32581i	0.141318	−	0.141318i	0.774227	+	0.632909i	$0.218139\pi$
$938$	8.74231	+	3.62118i	0.285447	+	0.118236i
$939$			6.60238i			0.215460i
$940$	−1.40114	+	3.38264i	−0.0457001	+	0.110330i
$941$	−17.7542	+	7.35404i	−0.578771	+	0.239735i	−0.652812	−	0.757520i	$-0.726411\pi$
$941$	−17.7542	+	7.35404i	−0.578771	+	0.239735i	0.0740403	+	0.997255i	$0.476411\pi$
$942$	2.29501	+	5.54064i	0.0747755	+	0.180524i
$943$	−13.7130	−	13.7130i	−0.446556	−	0.446556i
$944$	0.722495	+	0.722495i	0.0235152	+	0.0235152i
$945$	1.20213	+	2.90220i	0.0391053	+	0.0944086i
$946$	−1.18022	+	0.488864i	−0.0383723	+	0.0158943i
$947$	−15.2897	+	36.9126i	−0.496848	+	1.19950i	0.454324	+	0.890837i	$0.349881\pi$
$947$	−15.2897	+	36.9126i	−0.496848	+	1.19950i	−0.951172	+	0.308661i	$0.900119\pi$
$948$		−	2.60118i		−	0.0844826i
$949$	55.2356	+	22.8793i	1.79302	+	0.742694i
$950$	13.4066	−	13.4066i	0.434966	−	0.434966i
$951$	15.6156			0.506372
$952$	−5.11672	−	13.4017i	−0.165834	−	0.434352i
$953$	14.4242			0.467245			0.233622	−	0.972327i	$-0.424942\pi$
$953$	14.4242			0.467245			0.233622	+	0.972327i	$0.424942\pi$
$954$	13.4362	−	13.4362i	0.435012	−	0.435012i
$955$	−4.48715	−	1.85864i	−0.145201	−	0.0601442i
$956$		−	24.1793i		−	0.782014i
$957$	−1.66059	+	4.00902i	−0.0536793	+	0.129593i
$958$	34.2903	−	14.2035i	1.10787	−	0.458895i
$959$	−5.97981	−	14.4365i	−0.193098	−	0.466180i
$960$	−2.01153	−	2.01153i	−0.0649218	−	0.0649218i
$961$	2.55730	+	2.55730i	0.0824934	+	0.0824934i
$962$	16.8884	+	40.7721i	0.544503	+	1.31455i
$963$	−9.15833	+	3.79351i	−0.295123	+	0.122244i
$964$	−5.62445	+	13.5786i	−0.181151	+	0.437338i
$965$		−	3.97448i		−	0.127943i
$966$	5.85527	+	2.42533i	0.188390	+	0.0780338i
$967$	12.5538	−	12.5538i	0.403703	−	0.403703i	−0.475833	−	0.879536i	$-0.657853\pi$
$967$	12.5538	−	12.5538i	0.403703	−	0.403703i	0.879536	+	0.475833i	$0.157853\pi$
$968$	−25.9191			−0.833072
$969$	7.40807	−	16.5584i	0.237982	−	0.531931i
$970$	1.21153			0.0388998
$971$	31.1335	−	31.1335i	0.999121	−	0.999121i	−0.000878135	−	1.00000i	$-0.500280\pi$
$971$	31.1335	−	31.1335i	0.999121	−	0.999121i	1.00000		0.000878135i	$0.000279519\pi$
$972$	17.5008	+	7.24907i	0.561338	+	0.232514i
$973$			23.8891i			0.765849i
$974$	2.94538	−	7.11077i	0.0943760	−	0.227844i
$975$	27.9203	−	11.5649i	0.894164	−	0.370375i
$976$	−1.31287	−	3.16956i	−0.0420240	−	0.101455i
$977$	−22.3761	−	22.3761i	−0.715873	−	0.715873i	0.251884	−	0.967757i	$-0.418950\pi$
$977$	−22.3761	−	22.3761i	−0.715873	−	0.715873i	−0.967757	+	0.251884i	$0.918950\pi$
$978$	6.92172	+	6.92172i	0.221332	+	0.221332i
$979$	−3.06637	−	7.40286i	−0.0980015	−	0.236597i
$980$	3.15749	−	1.30788i	0.100862	−	0.0417786i
$981$	−9.81266	+	23.6899i	−0.313294	+	0.756359i
$982$			25.0613i			0.799737i
$983$	−27.6950	−	11.4716i	−0.883333	−	0.365889i	−0.105545	−	0.994415i	$-0.533659\pi$
$983$	−27.6950	−	11.4716i	−0.883333	−	0.365889i	−0.777789	+	0.628526i	$0.783659\pi$
$984$	6.70510	−	6.70510i	0.213751	−	0.213751i
$985$	2.91738			0.0929554
$986$	10.5420	+	4.71640i	0.335725	+	0.150201i
$987$	7.11761			0.226556
$988$	−23.8688	+	23.8688i	−0.759369	+	0.759369i
$989$	5.39622	+	2.23519i	0.171590	+	0.0710749i
$990$			1.34429i			0.0427244i
$991$	−3.51438	+	8.48447i	−0.111638	+	0.269518i	−0.969818	−	0.243832i	$-0.921596\pi$
$991$	−3.51438	+	8.48447i	−0.111638	+	0.269518i	0.858180	+	0.513350i	$0.171596\pi$
$992$	−30.1095	+	12.4718i	−0.955978	+	0.395979i
$993$	0.575461	+	1.38929i	0.0182617	+	0.0440876i
$994$	−6.41766	−	6.41766i	−0.203556	−	0.203556i
$995$	0.0332884	+	0.0332884i	0.00105531	+	0.00105531i
$996$	0.853599	+	2.06077i	0.0270473	+	0.0652980i
$997$	−5.78837	+	2.39762i	−0.183320	+	0.0759335i	−0.472455	−	0.881355i	$-0.656632\pi$
$997$	−5.78837	+	2.39762i	−0.183320	+	0.0759335i	0.289136	+	0.957288i	$0.406632\pi$
$998$	−6.47793	+	15.6391i	−0.205055	+	0.495047i
$999$			37.6880i			1.19239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.19	yes	128
17.2	even	8	inner	731.2.m.c.87.19	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.19	✓	128	17.2	even	8	inner
731.2.m.c.689.19	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.639626 - 0.639626i) q^{2} +(-0.916759 - 0.379734i) q^{3} +1.18176i q^{4} +(0.199818 - 0.482403i) q^{5} +(-0.829270 + 0.343495i) q^{6} +(0.462611 + 1.11684i) q^{7} +(2.03513 + 2.03513i) q^{8} +(-1.42507 - 1.42507i) q^{9} +O(q^{10})\)	\(q+(0.639626 - 0.639626i) q^{2} +(-0.916759 - 0.379734i) q^{3} +1.18176i q^{4} +(0.199818 - 0.482403i) q^{5} +(-0.829270 + 0.343495i) q^{6} +(0.462611 + 1.11684i) q^{7} +(2.03513 + 2.03513i) q^{8} +(-1.42507 - 1.42507i) q^{9} +(-0.180749 - 0.436366i) q^{10} +(1.30474 - 0.540439i) q^{11} +(0.448753 - 1.08339i) q^{12} +6.44237i q^{13} +(1.01026 + 0.418463i) q^{14} +(-0.366369 + 0.366369i) q^{15} +0.239934 q^{16} +(-2.99591 + 2.83276i) q^{17} -1.82303 q^{18} +(3.13514 - 3.13514i) q^{19} +(0.570083 + 0.236136i) q^{20} -1.19954i q^{21} +(0.488864 - 1.18022i) q^{22} +(-5.39622 + 2.23519i) q^{23} +(-1.09292 - 2.63854i) q^{24} +(3.34275 + 3.34275i) q^{25} +(4.12071 + 4.12071i) q^{26} +(1.90450 + 4.59787i) q^{27} +(-1.31984 + 0.546694i) q^{28} +(1.18499 - 2.86083i) q^{29} +0.468679i q^{30} +(5.43572 + 2.25155i) q^{31} +(-3.91680 + 3.91680i) q^{32} -1.40135 q^{33} +(-0.104355 + 3.72817i) q^{34} +0.631205 q^{35} +(1.68409 - 1.68409i) q^{36} +(6.99643 + 2.89802i) q^{37} -4.01064i q^{38} +(2.44639 - 5.90610i) q^{39} +(1.38841 - 0.575098i) q^{40} +(1.27061 + 3.06752i) q^{41} +(-0.767259 - 0.767259i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.638668 + 1.54188i) q^{44} +(-0.972213 + 0.402704i) q^{45} +(-2.02188 + 4.88125i) q^{46} +5.93360i q^{47} +(-0.219962 - 0.0911111i) q^{48} +(3.91642 - 3.91642i) q^{49} +4.27622 q^{50} +(3.82222 - 1.45931i) q^{51} -7.61332 q^{52} +(-7.37026 + 7.37026i) q^{53} +(4.15909 + 1.72275i) q^{54} -0.737397i q^{55} +(-1.33145 + 3.21440i) q^{56} +(-4.06469 + 1.68365i) q^{57} +(-1.07191 - 2.58781i) q^{58} +(3.01122 + 3.01122i) q^{59} +(-0.432960 - 0.432960i) q^{60} +(-5.47181 - 13.2101i) q^{61} +(4.91698 - 2.03668i) q^{62} +(0.932326 - 2.25083i) q^{63} +5.49044i q^{64} +(3.10782 + 1.28730i) q^{65} +(-0.896340 + 0.896340i) q^{66} +8.65354 q^{67} +(-3.34764 - 3.54044i) q^{68} +5.79581 q^{69} +(0.403735 - 0.403735i) q^{70} +(-7.66813 - 3.17625i) q^{71} -5.80042i q^{72} +(3.55138 - 8.57380i) q^{73} +(6.32874 - 2.62145i) q^{74} +(-1.79514 - 4.33385i) q^{75} +(3.70498 + 3.70498i) q^{76} +(1.20717 + 1.20717i) q^{77} +(-2.21292 - 5.34247i) q^{78} +(2.04936 - 0.848873i) q^{79} +(0.0479431 - 0.115745i) q^{80} +1.10772i q^{81} +(2.77478 + 1.14935i) q^{82} +(-1.34503 + 1.34503i) q^{83} +1.41757 q^{84} +(0.767895 + 2.01127i) q^{85} -0.904568 q^{86} +(-2.17271 + 2.17271i) q^{87} +(3.75518 + 1.55545i) q^{88} -5.67384i q^{89} +(-0.364273 + 0.879432i) q^{90} +(-7.19511 + 2.98031i) q^{91} +(-2.64145 - 6.37703i) q^{92} +(-4.12826 - 4.12826i) q^{93} +(3.79528 + 3.79528i) q^{94} +(-0.885945 - 2.13886i) q^{95} +(5.07810 - 2.10342i) q^{96} +(-0.981607 + 2.36981i) q^{97} -5.01009i q^{98} +(-2.62950 - 1.08918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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