LMFDB - Embedded newform 930.2.be.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.66175 + 1.49620i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.33377 - 4.97771i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.66175 + 1.49620i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.33377 - 4.97771i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.23300 - 0.117061i) q^{10} +(-3.19757 - 1.84612i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-5.79483 + 1.55272i) q^{13} +(4.46290 - 2.57665i) q^{14} +(1.01512 + 1.99237i) q^{15} -1.00000 q^{16} +(-1.42357 - 0.381444i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-6.55741 + 3.78592i) q^{19} +(-1.49620 - 1.66175i) q^{20} +(-4.46290 - 2.57665i) q^{21} +(-0.955621 - 3.56643i) q^{22} +(4.00981 + 4.00981i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.522793 - 4.97259i) q^{25} +(-5.19550 - 2.99962i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.97771 + 1.33377i) q^{28} +3.10232 q^{29} +(-0.691015 + 2.12662i) q^{30} +(-5.35079 - 1.53917i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.61081 + 2.61081i) q^{33} +(-0.736894 - 1.27634i) q^{34} +(5.23124 + 10.2673i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.73855 - 1.26969i) q^{37} +(-7.31384 - 1.95974i) q^{38} +5.99925i q^{39} +(0.117061 - 2.23300i) q^{40} +(5.81118 - 10.0653i) q^{41} +(-1.33377 - 4.97771i) q^{42} +(-1.29249 + 4.82363i) q^{43} +(1.84612 - 3.19757i) q^{44} +(2.18721 - 0.464871i) q^{45} +5.67073i q^{46} +(-1.03668 - 1.03668i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-16.9365 - 9.77829i) q^{49} +(3.88583 - 3.14648i) q^{50} +(-0.736894 + 1.27634i) q^{51} +(-1.55272 - 5.79483i) q^{52} +(6.85037 - 1.83555i) q^{53} -1.00000 q^{54} +(8.07570 - 1.71642i) q^{55} +(2.57665 + 4.46290i) q^{56} +(1.95974 + 7.31384i) q^{57} +(2.19367 + 2.19367i) q^{58} +(5.40302 - 3.11944i) q^{59} +(-1.99237 + 1.01512i) q^{60} -8.33905i q^{61} +(-2.69522 - 4.87194i) q^{62} +(-3.64394 + 3.64394i) q^{63} -1.00000i q^{64} +(7.30635 - 11.2504i) q^{65} -3.69224 q^{66} +(7.51566 - 2.01382i) q^{67} +(0.381444 - 1.42357i) q^{68} +(4.91099 - 2.83536i) q^{69} +(-3.56101 + 10.9591i) q^{70} +(-2.17115 + 3.76054i) q^{71} +(0.965926 - 0.258819i) q^{72} +(9.85909 - 2.64174i) q^{73} +(-2.45286 - 4.24847i) q^{74} +(-4.66785 - 1.79198i) q^{75} +(-3.78592 - 6.55741i) q^{76} +(-13.4543 + 13.4543i) q^{77} +(-4.24211 + 4.24211i) q^{78} +(1.61367 + 2.79495i) q^{79} +(1.66175 - 1.49620i) q^{80} +(0.500000 + 0.866025i) q^{81} +(11.2263 - 3.00809i) q^{82} +(-8.94413 + 2.39657i) q^{83} +(2.57665 - 4.46290i) q^{84} +(2.93632 - 1.49608i) q^{85} +(-4.32475 + 2.49689i) q^{86} +(0.802941 - 2.99661i) q^{87} +(3.56643 - 0.955621i) q^{88} -11.3115 q^{89} +(1.87531 + 1.21788i) q^{90} +30.9160i q^{91} +(-4.00981 + 4.00981i) q^{92} +(-2.87161 + 4.77010i) q^{93} -1.46609i q^{94} +(5.23226 - 16.1024i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-4.56736 - 4.56736i) q^{97} +(-5.06162 - 18.8902i) q^{98} +(1.84612 + 3.19757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	−1.66175	+	1.49620i	−0.743155	+	0.669119i
$5$	−1.66175	+	1.49620i	−0.743155	+	0.669119i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	1.33377	−	4.97771i	0.504119	−	1.88140i	0.0327484	−	0.999464i	$-0.489574\pi$
$7$	1.33377	−	4.97771i	0.504119	−	1.88140i	0.471371	−	0.881935i	$-0.343759\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−2.23300	−	0.117061i	−0.706137	−	0.0370178i
$11$	−3.19757	−	1.84612i	−0.964104	−	0.556626i	−0.0666703	−	0.997775i	$-0.521238\pi$
$11$	−3.19757	−	1.84612i	−0.964104	−	0.556626i	−0.897434	+	0.441149i	$0.854571\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−5.79483	+	1.55272i	−1.60720	+	0.430647i	−0.947205	−	0.320627i	$-0.896106\pi$
$13$	−5.79483	+	1.55272i	−1.60720	+	0.430647i	−0.659990	+	0.751274i	$0.729440\pi$
$14$	4.46290	−	2.57665i	1.19276	−	0.688640i
$15$	1.01512	+	1.99237i	0.262104	+	0.514427i
$16$	−1.00000			−0.250000
$17$	−1.42357	−	0.381444i	−0.345266	−	0.0925138i	0.0820188	−	0.996631i	$-0.473863\pi$
$17$	−1.42357	−	0.381444i	−0.345266	−	0.0925138i	−0.427285	+	0.904117i	$0.640530\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−6.55741	+	3.78592i	−1.50437	+	0.868551i	−0.504387	+	0.863478i	$0.668281\pi$
$19$	−6.55741	+	3.78592i	−1.50437	+	0.868551i	−0.999987	+	0.00507261i	$0.998385\pi$
$20$	−1.49620	−	1.66175i	−0.334560	−	0.371577i
$21$	−4.46290	−	2.57665i	−0.973884	−	0.562272i
$22$	−0.955621	−	3.56643i	−0.203739	−	0.760365i
$23$	4.00981	+	4.00981i	0.836103	+	0.836103i	0.988343	−	0.152240i	$-0.0486488\pi$
$23$	4.00981	+	4.00981i	0.836103	+	0.836103i	−0.152240	+	0.988343i	$0.548649\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	0.522793	−	4.97259i	0.104559	−	0.994519i
$26$	−5.19550	−	2.99962i	−1.01892	−	0.588274i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.97771	+	1.33377i	0.940699	+	0.252060i
$29$	3.10232			0.576087			0.288044	−	0.957617i	$-0.406995\pi$
$29$	3.10232			0.576087			0.288044	+	0.957617i	$0.406995\pi$
$30$	−0.691015	+	2.12662i	−0.126162	+	0.388265i
$31$	−5.35079	−	1.53917i	−0.961030	−	0.276444i
$31$	−5.35079	−	1.53917i	−0.961030	−	0.276444i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.61081	+	2.61081i	−0.454483	+	0.454483i
$34$	−0.736894	−	1.27634i	−0.126376	−	0.218890i
$35$	5.23124	+	10.2673i	0.884242	+	1.73549i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−4.73855	−	1.26969i	−0.779014	−	0.208736i	−0.152664	−	0.988278i	$-0.548785\pi$
$37$	−4.73855	−	1.26969i	−0.779014	−	0.208736i	−0.626350	+	0.779542i	$0.715452\pi$
$38$	−7.31384	−	1.95974i	−1.18646	−	0.317912i
$39$			5.99925i			0.960648i
$40$	0.117061	−	2.23300i	0.0185089	−	0.353069i
$41$	5.81118	−	10.0653i	0.907554	−	1.57193i	0.0901029	−	0.995932i	$-0.471280\pi$
$41$	5.81118	−	10.0653i	0.907554	−	1.57193i	0.817451	−	0.575998i	$-0.195386\pi$
$42$	−1.33377	−	4.97771i	−0.205806	−	0.768078i
$43$	−1.29249	+	4.82363i	−0.197102	+	0.735596i	0.794610	+	0.607120i	$0.207675\pi$
$43$	−1.29249	+	4.82363i	−0.197102	+	0.735596i	−0.991713	+	0.128476i	$0.958991\pi$
$44$	1.84612	−	3.19757i	0.278313	−	0.482052i
$45$	2.18721	−	0.464871i	0.326050	−	0.0692990i
$46$			5.67073i			0.836103i
$47$	−1.03668	−	1.03668i	−0.151216	−	0.151216i	0.627445	−	0.778661i	$-0.284101\pi$
$47$	−1.03668	−	1.03668i	−0.151216	−	0.151216i	−0.778661	+	0.627445i	$0.784101\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	−16.9365	−	9.77829i	−2.41950	−	1.39690i
$50$	3.88583	−	3.14648i	0.549539	−	0.444980i
$51$	−0.736894	+	1.27634i	−0.103186	+	0.178723i
$52$	−1.55272	−	5.79483i	−0.215323	−	0.803598i
$53$	6.85037	−	1.83555i	0.940971	−	0.252132i	0.244444	−	0.969663i	$-0.421394\pi$
$53$	6.85037	−	1.83555i	0.940971	−	0.252132i	0.696527	+	0.717531i	$0.254728\pi$
$54$	−1.00000			−0.136083
$55$	8.07570	−	1.71642i	1.08893	−	0.231441i
$56$	2.57665	+	4.46290i	0.344320	+	0.596380i
$57$	1.95974	+	7.31384i	0.259574	+	0.968742i
$58$	2.19367	+	2.19367i	0.288044	+	0.288044i
$59$	5.40302	−	3.11944i	0.703414	−	0.406116i	−0.105204	−	0.994451i	$-0.533550\pi$
$59$	5.40302	−	3.11944i	0.703414	−	0.406116i	0.808618	+	0.588335i	$0.200216\pi$
$60$	−1.99237	+	1.01512i	−0.257213	+	0.131052i
$61$		−	8.33905i		−	1.06771i	−0.845577	−	0.533853i	$-0.820744\pi$
$61$		−	8.33905i		−	1.06771i	0.845577	−	0.533853i	$-0.179256\pi$
$62$	−2.69522	−	4.87194i	−0.342293	−	0.618737i
$63$	−3.64394	+	3.64394i	−0.459093	+	0.459093i
$64$		−	1.00000i		−	0.125000i
$65$	7.30635	−	11.2504i	0.906241	−	1.39544i
$66$	−3.69224			−0.454483
$67$	7.51566	−	2.01382i	0.918184	−	0.246027i	0.231375	−	0.972865i	$-0.425678\pi$
$67$	7.51566	−	2.01382i	0.918184	−	0.246027i	0.686809	+	0.726838i	$0.259011\pi$
$68$	0.381444	−	1.42357i	0.0462569	−	0.172633i
$69$	4.91099	−	2.83536i	0.591214	−	0.341338i
$70$	−3.56101	+	10.9591i	−0.425623	+	1.30986i
$71$	−2.17115	+	3.76054i	−0.257668	+	0.446293i	−0.965617	−	0.259970i	$-0.916287\pi$
$71$	−2.17115	+	3.76054i	−0.257668	+	0.446293i	0.707949	+	0.706264i	$0.249621\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	9.85909	−	2.64174i	1.15392	−	0.309192i	0.369385	−	0.929277i	$-0.379568\pi$
$73$	9.85909	−	2.64174i	1.15392	−	0.309192i	0.784535	+	0.620085i	$0.212902\pi$
$74$	−2.45286	−	4.24847i	−0.285139	−	0.493875i
$75$	−4.66785	−	1.79198i	−0.538997	−	0.206920i
$76$	−3.78592	−	6.55741i	−0.434275	−	0.752187i
$77$	−13.4543	+	13.4543i	−1.53326	+	1.53326i
$78$	−4.24211	+	4.24211i	−0.480324	+	0.480324i
$79$	1.61367	+	2.79495i	0.181552	+	0.314457i	0.942409	−	0.334462i	$-0.108555\pi$
$79$	1.61367	+	2.79495i	0.181552	+	0.314457i	−0.760857	+	0.648919i	$0.775221\pi$
$80$	1.66175	−	1.49620i	0.185789	−	0.167280i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	11.2263	−	3.00809i	1.23974	−	0.332188i
$83$	−8.94413	+	2.39657i	−0.981746	+	0.263058i	−0.713780	−	0.700370i	$-0.753018\pi$
$83$	−8.94413	+	2.39657i	−0.981746	+	0.263058i	−0.267966	+	0.963428i	$0.586352\pi$
$84$	2.57665	−	4.46290i	0.281136	−	0.486942i
$85$	2.93632	−	1.49608i	0.318489	−	0.162272i
$86$	−4.32475	+	2.49689i	−0.466349	+	0.269247i
$87$	0.802941	−	2.99661i	0.0860843	−	0.321271i
$88$	3.56643	−	0.955621i	0.380182	−	0.101870i
$89$	−11.3115			−1.19902			−0.599508	−	0.800369i	$-0.704637\pi$
$89$	−11.3115			−1.19902			−0.599508	+	0.800369i	$0.704637\pi$
$90$	1.87531	+	1.21788i	0.197675	+	0.128376i
$91$			30.9160i			3.24087i
$92$	−4.00981	+	4.00981i	−0.418052	+	0.418052i
$93$	−2.87161	+	4.77010i	−0.297772	+	0.494636i
$94$		−	1.46609i		−	0.151216i
$95$	5.23226	−	16.1024i	0.536819	−	1.65207i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−4.56736	−	4.56736i	−0.463745	−	0.463745i	0.436136	−	0.899881i	$-0.356347\pi$
$97$	−4.56736	−	4.56736i	−0.463745	−	0.463745i	−0.899881	+	0.436136i	$0.856347\pi$
$98$	−5.06162	−	18.8902i	−0.511300	−	1.90820i
$99$	1.84612	+	3.19757i	0.185542	+	0.321368i
$100$	4.97259	+	0.522793i	0.497259	+	0.0522793i
$101$	−0.860772			−0.0856500			−0.0428250	−	0.999083i	$-0.513636\pi$
$101$	−0.860772			−0.0856500			−0.0428250	+	0.999083i	$0.513636\pi$
$102$	−1.42357	+	0.381444i	−0.140954	+	0.0377686i
$103$	−1.92409	−	7.18081i	−0.189586	−	0.707546i	−0.993602	−	0.112938i	$-0.963974\pi$
$103$	−1.92409	−	7.18081i	−0.189586	−	0.707546i	0.804016	−	0.594608i	$-0.202693\pi$
$104$	2.99962	−	5.19550i	0.294137	−	0.509461i
$105$	11.2714	−	2.39563i	1.09997	−	0.233789i
$106$	6.14188	+	3.54601i	0.596552	+	0.344419i
$107$	−2.40490	+	8.97521i	−0.232491	+	0.867666i	0.746774	+	0.665078i	$0.231602\pi$
$107$	−2.40490	+	8.97521i	−0.232491	+	0.867666i	−0.979264	+	0.202588i	$0.935065\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	0.693028i		−	0.0663800i	−0.999449	−	0.0331900i	$-0.989433\pi$
$109$		−	0.693028i		−	0.0663800i	0.999449	−	0.0331900i	$-0.0105667\pi$
$110$	6.92407	+	4.49670i	0.660185	+	0.428743i
$111$	−2.45286	+	4.24847i	−0.232815	+	0.403247i
$112$	−1.33377	+	4.97771i	−0.126030	+	0.470350i
$113$	0.853440	+	3.18508i	0.0802849	+	0.299627i	0.994380	−	0.105873i	$-0.0337638\pi$
$113$	0.853440	+	3.18508i	0.0802849	+	0.299627i	−0.914095	+	0.405501i	$0.867097\pi$
$114$	−3.78592	+	6.55741i	−0.354584	+	0.614158i
$115$	−12.6627	−	0.663819i	−1.18081	−	0.0619014i
$116$			3.10232i			0.288044i
$117$	5.79483	+	1.55272i	0.535732	+	0.143549i
$118$	6.02629	+	1.61474i	0.554765	+	0.148649i
$119$	−3.79744	+	6.57736i	−0.348111	+	0.602945i
$120$	−2.12662	−	0.691015i	−0.194133	−	0.0630808i
$121$	1.31631	+	2.27991i	0.119664	+	0.207265i
$122$	5.89660	−	5.89660i	0.533853	−	0.533853i
$123$	−8.21825	−	8.21825i	−0.741015	−	0.741015i
$124$	1.53917	−	5.35079i	0.138222	−	0.480515i
$125$	6.57123	+	9.04538i	0.587748	+	0.809044i
$126$	−5.15331			−0.459093
$127$	−1.96344	−	0.526103i	−0.174227	−	0.0466841i	0.170651	−	0.985332i	$-0.445413\pi$
$127$	−1.96344	−	0.526103i	−0.174227	−	0.0466841i	−0.344878	+	0.938648i	$0.612080\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.32475	+	2.49689i	0.380773	+	0.219839i
$130$	13.1216	−	2.78888i	1.15084	−	0.244601i
$131$	1.47402	+	2.55307i	0.128785	+	0.223063i	0.923206	−	0.384305i	$-0.125559\pi$
$131$	1.47402	+	2.55307i	0.128785	+	0.223063i	−0.794421	+	0.607368i	$0.792226\pi$
$132$	−2.61081	−	2.61081i	−0.227241	−	0.227241i
$133$	10.0991	+	37.6905i	0.875706	+	3.26818i
$134$	6.73836	+	3.89039i	0.582105	+	0.336079i
$135$	0.117061	−	2.23300i	0.0100750	−	0.192186i
$136$	1.27634	−	0.736894i	0.109445	−	0.0631881i
$137$	1.50243	+	5.60714i	0.128361	+	0.479051i	0.999937	−	0.0112099i	$-0.00356828\pi$
$137$	1.50243	+	5.60714i	0.128361	+	0.479051i	−0.871576	+	0.490261i	$0.836902\pi$
$138$	5.47750	+	1.46769i	0.466276	+	0.124938i
$139$	18.8224			1.59650			0.798249	−	0.602327i	$-0.205760\pi$
$139$	18.8224			1.59650			0.798249	+	0.602327i	$0.205760\pi$
$140$	−10.2673	+	5.23124i	−0.867743	+	0.442121i
$141$	−1.26967	+	0.733045i	−0.106926	+	0.0617335i
$142$	−4.19433	+	1.12387i	−0.351981	+	0.0943129i
$143$	21.3959	+	5.73301i	1.78921	+	0.479418i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−5.15527	+	4.64169i	−0.428122	+	0.385471i
$146$	8.83942	+	5.10344i	0.731556	+	0.422364i
$147$	−13.8286	+	13.8286i	−1.14056	+	1.14056i
$148$	1.26969	−	4.73855i	0.104368	−	0.389507i
$149$	−0.444176	+	0.256445i	−0.0363883	+	0.0210088i	−0.518084	−	0.855330i	$-0.673354\pi$
$149$	−0.444176	+	0.256445i	−0.0363883	+	0.0210088i	0.481695	+	0.876339i	$0.340021\pi$
$150$	−2.03354	−	4.56779i	−0.166038	−	0.372958i
$151$		−	6.61373i		−	0.538218i	−0.963110	−	0.269109i	$-0.913271\pi$
$151$		−	6.61373i		−	0.538218i	0.963110	−	0.269109i	$-0.0867292\pi$
$152$	1.95974	−	7.31384i	0.158956	−	0.593231i
$153$	1.04212	+	1.04212i	0.0842508	+	0.0842508i
$154$	−19.0272			−1.53326
$155$	11.1946	−	5.44812i	0.899168	−	0.437603i
$156$	−5.99925			−0.480324
$157$	−5.25938	−	5.25938i	−0.419744	−	0.419744i	0.465372	−	0.885115i	$-0.345921\pi$
$157$	−5.25938	−	5.25938i	−0.419744	−	0.419744i	−0.885115	+	0.465372i	$0.845921\pi$
$158$	−0.835295	+	3.11736i	−0.0664525	+	0.248004i
$159$		−	7.09203i		−	0.562434i
$160$	2.23300	+	0.117061i	0.176534	+	0.00925446i
$161$	25.3079	−	14.6115i	1.99454	−	1.15155i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−11.4002	+	11.4002i	−0.892936	+	0.892936i	−0.994798	−	0.101863i	$-0.967520\pi$
$163$	−11.4002	+	11.4002i	−0.892936	+	0.892936i	0.101863	+	0.994798i	$0.467520\pi$
$164$	10.0653	+	5.81118i	0.785965	+	0.453777i
$165$	0.432216	−	8.24477i	0.0336479	−	0.641855i
$166$	−8.01909	−	4.62982i	−0.622402	−	0.359344i
$167$	−3.37272	−	0.903719i	−0.260989	−	0.0699319i	0.125952	−	0.992036i	$-0.459802\pi$
$167$	−3.37272	−	0.903719i	−0.260989	−	0.0699319i	−0.386941	+	0.922105i	$0.626468\pi$
$168$	4.97771	−	1.33377i	0.384039	−	0.102903i
$169$	19.9107	−	11.4955i	1.53160	−	0.884267i
$170$	3.13418	+	1.01841i	0.240381	+	0.0781084i
$171$	7.57185			0.579034
$172$	−4.82363	−	1.29249i	−0.367798	−	0.0985512i
$173$	−2.31871	−	8.65355i	−0.176288	−	0.657917i	−0.996329	−	0.0856111i	$-0.972716\pi$
$173$	−2.31871	−	8.65355i	−0.176288	−	0.657917i	0.820040	−	0.572306i	$-0.193951\pi$
$174$	2.68669	−	1.55116i	0.203678	−	0.117593i
$175$	−24.0549	−	9.23463i	−1.81838	−	0.698073i
$176$	3.19757	+	1.84612i	0.241026	+	0.139156i
$177$	−1.61474	−	6.02629i	−0.121371	−	0.452964i
$178$	−7.99844	−	7.99844i	−0.599508	−	0.599508i
$179$	0.0616512	+	0.106783i	0.00460803	+	0.00798134i	0.868320	−	0.496004i	$-0.165200\pi$
$179$	0.0616512	+	0.106783i	0.00460803	+	0.00798134i	−0.863712	+	0.503985i	$0.831867\pi$
$180$	0.464871	+	2.18721i	0.0346495	+	0.163025i
$181$	−0.630553	−	0.364050i	−0.0468686	−	0.0270596i	0.476383	−	0.879238i	$-0.341948\pi$
$181$	−0.630553	−	0.364050i	−0.0468686	−	0.0270596i	−0.523251	+	0.852178i	$0.675281\pi$
$182$	−21.8609	+	21.8609i	−1.62044	+	1.62044i
$183$	−8.05491	−	2.15831i	−0.595436	−	0.159547i
$184$	−5.67073			−0.418052
$185$	9.77398	−	4.97990i	0.718597	−	0.366130i
$186$	−5.40351	+	1.34243i	−0.396204	+	0.0984319i
$187$	3.84777	+	3.84777i	0.281377	+	0.281377i
$188$	1.03668	−	1.03668i	0.0756078	−	0.0756078i
$189$	2.57665	+	4.46290i	0.187424	+	0.324628i
$190$	15.0859	−	7.68636i	1.09445	−	0.557627i
$191$	8.22429	−	14.2449i	0.595089	−	1.03072i	−0.398446	−	0.917192i	$-0.630450\pi$
$191$	8.22429	−	14.2449i	0.595089	−	1.03072i	0.993534	−	0.113532i	$-0.0362164\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−12.4183	−	3.32748i	−0.893891	−	0.239517i	−0.217500	−	0.976060i	$-0.569790\pi$
$193$	−12.4183	−	3.32748i	−0.893891	−	0.239517i	−0.676391	+	0.736543i	$0.736457\pi$
$194$		−	6.45922i		−	0.463745i
$195$	−8.97605	−	9.96922i	−0.642788	−	0.713910i
$196$	9.77829	−	16.9365i	0.698449	−	1.20975i
$197$	0.879184	+	3.28116i	0.0626393	+	0.233773i	0.990147	−	0.140031i	$-0.0447201\pi$
$197$	0.879184	+	3.28116i	0.0626393	+	0.233773i	−0.927508	+	0.373804i	$0.878053\pi$
$198$	−0.955621	+	3.56643i	−0.0679131	+	0.253455i
$199$	−1.53922	+	2.66602i	−0.109113	+	0.188989i	−0.915411	−	0.402520i	$-0.868134\pi$
$199$	−1.53922	+	2.66602i	−0.109113	+	0.188989i	0.806298	+	0.591509i	$0.201468\pi$
$200$	3.14648	+	3.88583i	0.222490	+	0.274769i
$201$		−	7.78079i		−	0.548814i
$202$	−0.608658	−	0.608658i	−0.0428250	−	0.0428250i
$203$	4.13780	−	15.4425i	0.290417	−	1.08385i
$204$	−1.27634	−	0.736894i	−0.0893615	−	0.0515929i
$205$	5.40291	+	25.4206i	0.377355	+	1.77545i
$206$	3.71706	−	6.43814i	0.258980	−	0.448566i
$207$	−1.46769	−	5.47750i	−0.102012	−	0.380713i
$208$	5.79483	−	1.55272i	0.401799	−	0.107662i
$209$	27.9571			1.93383
$210$	9.66403	+	6.27610i	0.666881	+	0.433092i
$211$	−3.82823	−	6.63068i	−0.263546	−	0.456475i	0.703636	−	0.710561i	$-0.251559\pi$
$211$	−3.82823	−	6.63068i	−0.263546	−	0.456475i	−0.967182	+	0.254086i	$0.918225\pi$
$212$	1.83555	+	6.85037i	0.126066	+	0.470486i
$213$	3.07046	+	3.07046i	0.210385	+	0.210385i
$214$	−8.04695	+	4.64591i	−0.550079	+	0.317588i
$215$	−5.06931	−	9.94945i	−0.345724	−	0.678547i
$216$		−	1.00000i		−	0.0680414i
$217$	−14.7983	+	24.5818i	−1.00457	+	1.66872i
$218$	0.490045	−	0.490045i	0.0331900	−	0.0331900i
$219$		−	10.2069i		−	0.689717i
$220$	1.71642	+	8.07570i	0.115721	+	0.544464i
$221$	8.84161			0.594751
$222$	−4.73855	+	1.26969i	−0.318031	+	0.0852161i
$223$	4.33389	−	16.1743i	0.290219	−	1.08311i	−0.654722	−	0.755870i	$-0.727214\pi$
$223$	4.33389	−	16.1743i	0.290219	−	1.08311i	0.944941	−	0.327242i	$-0.106119\pi$
$224$	−4.46290	+	2.57665i	−0.298190	+	0.172160i
$225$	−2.93905	+	4.04500i	−0.195937	+	0.269666i
$226$	−1.64872	+	2.85567i	−0.109671	+	0.189956i
$227$	−1.33458	+	0.357599i	−0.0885789	+	0.0237347i	−0.302836	−	0.953043i	$-0.597934\pi$
$227$	−1.33458	+	0.357599i	−0.0885789	+	0.0237347i	0.214257	+	0.976777i	$0.431267\pi$
$228$	−7.31384	+	1.95974i	−0.484371	+	0.129787i
$229$	−1.99964	−	3.46347i	−0.132140	−	0.228873i	0.792361	−	0.610052i	$-0.208851\pi$
$229$	−1.99964	−	3.46347i	−0.132140	−	0.228873i	−0.924501	+	0.381179i	$0.875518\pi$
$230$	−8.48452	−	9.42330i	−0.559453	−	0.621354i
$231$	9.51362	+	16.4781i	0.625950	+	1.08418i
$232$	−2.19367	+	2.19367i	−0.144022	+	0.144022i
$233$	−19.1490	+	19.1490i	−1.25449	+	1.25449i	−0.300806	+	0.953685i	$0.597256\pi$
$233$	−19.1490	+	19.1490i	−1.25449	+	1.25449i	−0.953685	+	0.300806i	$0.902744\pi$
$234$	2.99962	+	5.19550i	0.196091	+	0.339640i
$235$	3.27378	+	0.171621i	0.213558	+	0.0111953i
$236$	3.11944	+	5.40302i	0.203058	+	0.351707i
$237$	3.11736	−	0.835295i	0.202495	−	0.0542583i
$238$	−7.33609	+	1.96570i	−0.475528	+	0.127417i
$239$	−9.75887	+	16.9029i	−0.631249	+	1.09336i	0.356048	+	0.934468i	$0.384124\pi$
$239$	−9.75887	+	16.9029i	−0.631249	+	1.09336i	−0.987297	+	0.158888i	$0.949209\pi$
$240$	−1.01512	−	1.99237i	−0.0655259	−	0.128607i
$241$	−8.90971	+	5.14403i	−0.573925	+	0.331356i	−0.758715	−	0.651422i	$-0.774173\pi$
$241$	−8.90971	+	5.14403i	−0.573925	+	0.331356i	0.184790	+	0.982778i	$0.440839\pi$
$242$	−0.681371	+	2.54291i	−0.0438002	+	0.163465i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	8.33905			0.533853
$245$	42.7744	−	9.09130i	2.73276	−	0.580822i
$246$		−	11.6224i		−	0.741015i
$247$	32.1206	−	32.1206i	2.04378	−	2.04378i
$248$	4.87194	−	2.69522i	0.309368	−	0.171147i
$249$			9.25965i			0.586806i
$250$	−1.74949	+	11.0426i	−0.110648	+	0.698396i
$251$	12.4573	−	7.19220i	0.786296	−	0.453968i	−0.0523613	−	0.998628i	$-0.516675\pi$
$251$	12.4573	−	7.19220i	0.786296	−	0.453968i	0.838657	+	0.544660i	$0.183341\pi$
$252$	−3.64394	−	3.64394i	−0.229547	−	0.229547i
$253$	−5.41907	−	20.2242i	−0.340694	−	1.27149i
$254$	−1.01635	−	1.76037i	−0.0637716	−	0.110456i
$255$	−0.685122	−	3.22348i	−0.0429040	−	0.201862i
$256$	1.00000			0.0625000
$257$	−7.17169	+	1.92165i	−0.447358	+	0.119869i	−0.475463	−	0.879736i	$-0.657719\pi$
$257$	−7.17169	+	1.92165i	−0.447358	+	0.119869i	0.0281050	+	0.999605i	$0.491053\pi$
$258$	1.29249	+	4.82363i	0.0804667	+	0.300306i
$259$	−12.6403	+	21.8937i	−0.785432	+	1.36041i
$260$	11.2504	+	7.30635i	0.697721	+	0.453121i
$261$	−2.68669	−	1.55116i	−0.166302	−	0.0960145i
$262$	−0.763006	+	2.84758i	−0.0471387	+	0.175924i
$263$	19.4862	+	19.4862i	1.20157	+	1.20157i	0.973688	+	0.227885i	$0.0731810\pi$
$263$	19.4862	+	19.4862i	1.20157	+	1.20157i	0.227885	+	0.973688i	$0.426819\pi$
$264$		−	3.69224i		−	0.227241i
$265$	−8.63723	+	13.2997i	−0.530581	+	0.816995i
$266$	−19.5100	+	33.7924i	−1.19624	+	2.07194i
$267$	−2.92763	+	10.9261i	−0.179168	+	0.668665i
$268$	2.01382	+	7.51566i	0.123013	+	0.459092i
$269$	−6.60500	+	11.4402i	−0.402714	+	0.697521i	−0.994052	−	0.108902i	$-0.965266\pi$
$269$	−6.60500	+	11.4402i	−0.402714	+	0.697521i	0.591338	+	0.806424i	$0.298600\pi$
$270$	1.66175	−	1.49620i	0.101131	−	0.0910556i
$271$		−	5.34530i		−	0.324704i	−0.986733	−	0.162352i	$-0.948092\pi$
$271$		−	5.34530i		−	0.324704i	0.986733	−	0.162352i	$-0.0519080\pi$
$272$	1.42357	+	0.381444i	0.0863166	+	0.0231285i
$273$	29.8625	+	8.00164i	1.80736	+	0.484281i
$274$	−2.90247	+	5.02723i	−0.175345	+	0.303706i
$275$	−10.8517	+	14.9351i	−0.654380	+	0.900619i
$276$	2.83536	+	4.91099i	0.170669	+	0.295607i
$277$	3.55245	−	3.55245i	0.213446	−	0.213446i	−0.592283	−	0.805730i	$-0.701773\pi$
$277$	3.55245	−	3.55245i	0.213446	−	0.213446i	0.805730	+	0.592283i	$0.201773\pi$
$278$	13.3095	+	13.3095i	0.798249	+	0.798249i
$279$	3.86433	+	4.00836i	0.231352	+	0.239974i
$280$	−10.9591	−	3.56101i	−0.654932	−	0.212811i
$281$	12.9904			0.774944			0.387472	−	0.921881i	$-0.373348\pi$
$281$	12.9904			0.774944			0.387472	+	0.921881i	$0.373348\pi$
$282$	−1.41613	−	0.379452i	−0.0843295	−	0.0225960i
$283$	−19.4727	+	19.4727i	−1.15753	+	1.15753i	−0.172525	+	0.985005i	$0.555193\pi$
$283$	−19.4727	+	19.4727i	−1.15753	+	1.15753i	−0.985005	+	0.172525i	$0.944807\pi$
$284$	−3.76054	−	2.17115i	−0.223147	−	0.128834i
$285$	−14.1995	−	9.22159i	−0.841108	−	0.546240i
$286$	11.0753	+	19.1830i	0.654897	+	1.13432i
$287$	−42.3512	−	42.3512i	−2.49991	−	2.49991i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−12.8414	−	7.41398i	−0.755375	−	0.436116i
$290$	−6.92749	−	0.363160i	−0.406796	−	0.0213255i
$291$	−5.59385	+	3.22961i	−0.327917	+	0.189323i
$292$	2.64174	+	9.85909i	0.154596	+	0.576960i
$293$	−29.3947	−	7.87629i	−1.71726	−	0.460137i	−0.740072	−	0.672528i	$-0.765208\pi$
$293$	−29.3947	−	7.87629i	−1.71726	−	0.460137i	−0.977185	+	0.212391i	$0.931875\pi$
$294$	−19.5566			−1.14056
$295$	−4.31116	+	13.2677i	−0.251005	+	0.772475i
$296$	4.24847	−	2.45286i	0.246937	−	0.142569i
$297$	3.56643	−	0.955621i	0.206945	−	0.0554508i
$298$	−0.495414	−	0.132746i	−0.0286986	−	0.00768976i
$299$	−29.4623	−	17.0100i	−1.70385	−	0.983716i
$300$	1.79198	−	4.66785i	0.103460	−	0.269498i
$301$	22.2867	+	12.8673i	1.28459	+	0.741656i
$302$	4.67661	−	4.67661i	0.269109	−	0.269109i
$303$	−0.222784	+	0.831442i	−0.0127986	+	0.0477651i
$304$	6.55741	−	3.78592i	0.376093	−	0.217138i
$305$	12.4769	+	13.8574i	0.714423	+	0.793471i
$306$			1.47379i			0.0842508i
$307$	−1.00532	+	3.75189i	−0.0573764	+	0.214132i	−0.988662	−	0.150158i	$-0.952022\pi$
$307$	−1.00532	+	3.75189i	−0.0573764	+	0.214132i	0.931286	+	0.364290i	$0.118688\pi$
$308$	−13.4543	−	13.4543i	−0.766629	−	0.766629i
$309$	−7.43412			−0.422912
$310$	11.7681	+	4.06334i	0.668386	+	0.230782i
$311$	−10.5116			−0.596059			−0.298030	−	0.954557i	$-0.596329\pi$
$311$	−10.5116			−0.596059			−0.298030	+	0.954557i	$0.596329\pi$
$312$	−4.24211	−	4.24211i	−0.240162	−	0.240162i
$313$	−0.726697	+	2.71207i	−0.0410753	+	0.153295i	−0.983418	−	0.181355i	$-0.941952\pi$
$313$	−0.726697	+	2.71207i	−0.0410753	+	0.153295i	0.942342	+	0.334651i	$0.108618\pi$
$314$		−	7.43788i		−	0.419744i
$315$	0.603249	−	11.5073i	0.0339893	−	0.648365i
$316$	−2.79495	+	1.61367i	−0.157228	+	0.0907758i
$317$	6.60370	−	24.6453i	0.370901	−	1.38422i	−0.488342	−	0.872652i	$-0.662398\pi$
$317$	6.60370	−	24.6453i	0.370901	−	1.38422i	0.859243	−	0.511568i	$-0.170935\pi$
$318$	5.01482	−	5.01482i	0.281217	−	0.281217i
$319$	−9.91990	−	5.72726i	−0.555408	−	0.320665i
$320$	1.49620	+	1.66175i	0.0836399	+	0.0928944i
$321$	8.04695	+	4.64591i	0.449137	+	0.259309i
$322$	28.2273	+	7.56347i	1.57304	+	0.421496i
$323$	10.7790	−	2.88824i	0.599762	−	0.160706i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	4.69154	+	29.6271i	0.260240	+	1.64341i
$326$	−16.1224			−0.892936
$327$	−0.669414	−	0.179369i	−0.0370187	−	0.00991912i
$328$	3.00809	+	11.2263i	0.166094	+	0.619871i
$329$	−6.54301	+	3.77761i	−0.360728	+	0.208266i
$330$	6.13556	−	5.52431i	0.337751	−	0.304103i
$331$	−6.43483	−	3.71515i	−0.353690	−	0.204203i	0.312619	−	0.949879i	$-0.398794\pi$
$331$	−6.43483	−	3.71515i	−0.353690	−	0.204203i	−0.666309	+	0.745675i	$0.732127\pi$
$332$	−2.39657	−	8.94413i	−0.131529	−	0.490873i
$333$	3.46886	+	3.46886i	0.190093	+	0.190093i
$334$	−1.74585	−	3.02390i	−0.0955287	−	0.165461i
$335$	−9.47605	+	14.5914i	−0.517732	+	0.797211i
$336$	4.46290	+	2.57665i	0.243471	+	0.140568i
$337$	10.3325	−	10.3325i	0.562848	−	0.562848i	−0.367267	−	0.930115i	$-0.619707\pi$
$337$	10.3325	−	10.3325i	0.562848	−	0.562848i	0.930115	+	0.367267i	$0.119707\pi$
$338$	22.2075	+	5.95049i	1.20793	+	0.323664i
$339$	3.29744			0.179092
$340$	1.49608	+	2.93632i	0.0811361	+	0.159245i
$341$	14.2680	+	14.7998i	0.772657	+	0.801454i
$342$	5.35411	+	5.35411i	0.289517	+	0.289517i
$343$	−45.7554	+	45.7554i	−2.47056	+	2.47056i
$344$	−2.49689	−	4.32475i	−0.134623	−	0.233175i
$345$	−3.91856	+	12.0595i	−0.210968	+	0.649260i
$346$	4.47940	−	7.75856i	0.240814	−	0.417103i
$347$	8.94230	+	2.39608i	0.480048	+	0.128628i	0.490725	−	0.871315i	$-0.336732\pi$
$347$	8.94230	+	2.39608i	0.480048	+	0.128628i	−0.0106770	+	0.999943i	$0.503399\pi$
$348$	2.99661	+	0.802941i	0.160635	+	0.0430421i
$349$		−	32.2950i		−	1.72871i	−0.502882	−	0.864355i	$-0.667727\pi$
$349$		−	32.2950i		−	1.72871i	0.502882	−	0.864355i	$-0.332273\pi$
$350$	−10.4795	−	23.5392i	−0.560152	−	1.25822i
$351$	2.99962	−	5.19550i	0.160108	−	0.277315i
$352$	0.955621	+	3.56643i	0.0509348	+	0.190091i
$353$	−5.16214	+	19.2654i	−0.274753	+	1.02539i	0.681254	+	0.732048i	$0.261435\pi$
$353$	−5.16214	+	19.2654i	−0.274753	+	1.02539i	−0.956007	+	0.293345i	$0.905232\pi$
$354$	3.11944	−	5.40302i	0.165796	−	0.287167i
$355$	−2.01861	−	9.49751i	−0.107137	−	0.504076i
$356$		−	11.3115i		−	0.599508i
$357$	5.37039	+	5.37039i	0.284231	+	0.284231i
$358$	−0.0319130	+	0.119101i	−0.00168666	+	0.00629468i
$359$	12.0432	+	6.95312i	0.635614	+	0.366972i	0.782923	−	0.622119i	$-0.213728\pi$
$359$	12.0432	+	6.95312i	0.635614	+	0.366972i	−0.147309	+	0.989091i	$0.547061\pi$
$360$	−1.21788	+	1.87531i	−0.0641878	+	0.0988373i
$361$	19.1664	−	33.1973i	1.00876	−	1.74722i
$362$	−0.188446	−	0.703291i	−0.00990451	−	0.0369641i
$363$	2.54291	−	0.681371i	0.133468	−	0.0357627i
$364$	−30.9160			−1.62044
$365$	−12.4307	+	19.1410i	−0.650655	+	1.00189i
$366$	−4.16953	−	7.22183i	−0.217945	−	0.377491i
$367$	4.00924	+	14.9627i	0.209281	+	0.781046i	0.988102	+	0.153800i	$0.0491512\pi$
$367$	4.00924	+	14.9627i	0.209281	+	0.781046i	−0.778821	+	0.627246i	$0.784182\pi$
$368$	−4.00981	−	4.00981i	−0.209026	−	0.209026i
$369$	−10.0653	+	5.81118i	−0.523977	+	0.302518i
$370$	10.4326	+	3.38992i	0.542364	+	0.176234i
$371$		−	36.5474i		−	1.89745i
$372$	−4.77010	−	2.87161i	−0.247318	−	0.148886i
$373$	−3.90561	+	3.90561i	−0.202225	+	0.202225i	−0.800953	−	0.598728i	$-0.795673\pi$
$373$	−3.90561	+	3.90561i	−0.202225	+	0.202225i	0.598728	+	0.800953i	$0.295673\pi$
$374$			5.44157i			0.281377i
$375$	10.4379	−	4.00620i	0.539012	−	0.206879i
$376$	1.46609			0.0756078
$377$	−17.9774	+	4.81704i	−0.925885	+	0.248090i
$378$	−1.33377	+	4.97771i	−0.0686019	+	0.256026i
$379$	−32.8443	+	18.9626i	−1.68710	+	0.974046i	−0.730373	+	0.683049i	$0.760654\pi$
$379$	−32.8443	+	18.9626i	−1.68710	+	0.974046i	−0.956724	+	0.290997i	$0.906013\pi$
$380$	16.1024	+	5.23226i	0.826037	+	0.268409i
$381$	−1.01635	+	1.76037i	−0.0520693	+	0.0901867i
$382$	15.8881	−	4.25721i	0.812906	−	0.217818i
$383$	−13.1618	+	3.52670i	−0.672538	+	0.180206i	−0.578898	−	0.815400i	$-0.696517\pi$
$383$	−13.1618	+	3.52670i	−0.672538	+	0.180206i	−0.0936404	+	0.995606i	$0.529850\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	2.22734	−	42.4879i	0.113516	−	2.16538i
$386$	−6.42820	−	11.1340i	−0.327187	−	0.566704i
$387$	3.53114	−	3.53114i	0.179498	−	0.179498i
$388$	4.56736	−	4.56736i	0.231872	−	0.231872i
$389$	−13.1626	−	22.7982i	−0.667368	−	1.15592i	−0.978637	−	0.205594i	$-0.934087\pi$
$389$	−13.1626	−	22.7982i	−0.667368	−	1.15592i	0.311269	−	0.950322i	$-0.399246\pi$
$390$	0.702275	−	13.3963i	0.0355611	−	0.678349i
$391$	−4.17872	−	7.23776i	−0.211327	−	0.366029i
$392$	18.8902	−	5.06162i	0.954100	−	0.255650i
$393$	2.84758	−	0.763006i	0.143641	−	0.0384886i
$394$	−1.69845	+	2.94181i	−0.0855668	+	0.148206i
$395$	−6.86330	−	2.23014i	−0.345330	−	0.112210i
$396$	−3.19757	+	1.84612i	−0.160684	+	0.0927710i
$397$	5.49465	−	20.5063i	0.275769	−	1.02918i	−0.679556	−	0.733624i	$-0.737828\pi$
$397$	5.49465	−	20.5063i	0.275769	−	1.02918i	0.955325	−	0.295559i	$-0.0955058\pi$
$398$	−2.97355	+	0.796761i	−0.149051	+	0.0399380i
$399$	39.0201			1.95345
$400$	−0.522793	+	4.97259i	−0.0261397	+	0.248630i
$401$			14.9539i			0.746764i	0.927678	+	0.373382i	$0.121802\pi$
$401$			14.9539i			0.746764i	−0.927678	+	0.373382i	$0.878198\pi$
$402$	5.50185	−	5.50185i	0.274407	−	0.274407i
$403$	33.3968	+	0.610965i	1.66361	+	0.0304344i
$404$		−	0.860772i		−	0.0428250i
$405$	−2.12662	−	0.691015i	−0.105672	−	0.0343368i
$406$	13.8453	−	7.99362i	0.687133	−	0.396716i
$407$	12.8079	+	12.8079i	0.634862	+	0.634862i
$408$	−0.381444	−	1.42357i	−0.0188843	−	0.0704772i
$409$	−9.24850	−	16.0189i	−0.457309	−	0.792082i	0.541509	−	0.840695i	$-0.317853\pi$
$409$	−9.24850	−	16.0189i	−0.457309	−	0.792082i	−0.998818	+	0.0486130i	$0.984520\pi$
$410$	−14.1546	+	21.7955i	−0.699047	+	1.07640i
$411$	5.80494			0.286337
$412$	7.18081	−	1.92409i	0.353773	−	0.0947932i
$413$	−8.32125	−	31.0553i	−0.409462	−	1.52813i
$414$	2.83536	−	4.91099i	0.139351	−	0.241362i
$415$	11.2771	−	17.3647i	0.553572	−	0.852398i
$416$	5.19550	+	2.99962i	0.254730	+	0.147069i
$417$	4.87161	−	18.1811i	0.238564	−	0.890331i
$418$	19.7686	+	19.7686i	0.966915	+	0.966915i
$419$		−	36.1683i		−	1.76694i	−0.468491	−	0.883468i	$-0.655202\pi$
$419$		−	36.1683i		−	1.76694i	0.468491	−	0.883468i	$-0.344798\pi$
$420$	2.39563	+	11.2714i	0.116895	+	0.549987i
$421$	16.1104	−	27.9041i	0.785175	−	1.35996i	−0.143720	−	0.989618i	$-0.545906\pi$
$421$	16.1104	−	27.9041i	0.785175	−	1.35996i	0.928895	−	0.370344i	$-0.120760\pi$
$422$	1.98164	−	7.39556i	0.0964645	−	0.360010i
$423$	0.379452	+	1.41613i	0.0184496	+	0.0688548i
$424$	−3.54601	+	6.14188i	−0.172210	+	0.298276i
$425$	−2.64100	+	6.87941i	−0.128107	+	0.333701i
$426$			4.34229i			0.210385i
$427$	−41.5094	−	11.1224i	−2.00878	−	0.538251i
$428$	−8.97521	−	2.40490i	−0.433833	−	0.116245i
$429$	11.0753	−	19.1830i	0.534721	−	0.926165i
$430$	3.45078	−	10.6199i	0.166411	−	0.512135i
$431$	−11.4126	−	19.7672i	−0.549726	−	0.952153i	−0.998293	−	0.0584037i	$-0.981399\pi$
$431$	−11.4126	−	19.7672i	−0.549726	−	0.952153i	0.448567	−	0.893749i	$-0.351934\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	11.4750	+	11.4750i	0.551453	+	0.551453i	0.926860	−	0.375407i	$-0.122497\pi$
$433$	11.4750	+	11.4750i	0.551453	+	0.551453i	−0.375407	+	0.926860i	$0.622497\pi$
$434$	−27.8459	+	6.91797i	−1.33665	+	0.332073i
$435$	3.14924	+	6.18097i	0.150995	+	0.296355i
$436$	0.693028			0.0331900
$437$	−41.4748	−	11.1131i	−1.98401	−	0.531614i
$438$	7.21736	−	7.21736i	0.344859	−	0.344859i
$439$	16.4418	+	9.49267i	0.784723	+	0.453060i	0.838102	−	0.545514i	$-0.183666\pi$
$439$	16.4418	+	9.49267i	0.784723	+	0.453060i	−0.0533783	+	0.998574i	$0.516999\pi$
$440$	−4.49670	+	6.92407i	−0.214372	+	0.330092i
$441$	9.77829	+	16.9365i	0.465633	+	0.806500i
$442$	6.25196	+	6.25196i	0.297376	+	0.297376i
$443$	0.703839	+	2.62676i	0.0334404	+	0.124801i	0.980628	−	0.195878i	$-0.0627556\pi$
$443$	0.703839	+	2.62676i	0.0334404	+	0.124801i	−0.947188	+	0.320679i	$0.896089\pi$
$444$	−4.24847	−	2.45286i	−0.201624	−	0.116407i
$445$	18.7968	−	16.9242i	0.891055	−	0.802285i
$446$	14.5015	−	8.37244i	0.686665	−	0.396447i
$447$	0.132746	+	0.495414i	0.00627866	+	0.0234323i
$448$	−4.97771	−	1.33377i	−0.235175	−	0.0630149i
$449$	29.5864			1.39627			0.698134	−	0.715967i	$-0.254014\pi$
$449$	29.5864			1.39627			0.698134	+	0.715967i	$0.254014\pi$
$450$	−4.93847	+	0.782022i	−0.232801	+	0.0368649i
$451$	−37.1633	+	21.4563i	−1.74995	+	1.01034i
$452$	−3.18508	+	0.853440i	−0.149814	+	0.0401424i
$453$	−6.38837	−	1.71176i	−0.300152	−	0.0804255i
$454$	−1.19655	−	0.690827i	−0.0561568	−	0.0324221i
$455$	−46.2563	−	51.3744i	−2.16853	−	2.40847i
$456$	−6.55741	−	3.78592i	−0.307079	−	0.177292i
$457$	−11.9076	+	11.9076i	−0.557015	+	0.557015i	−0.928456	−	0.371442i	$-0.878864\pi$
$457$	−11.9076	+	11.9076i	−0.557015	+	0.557015i	0.371442	+	0.928456i	$0.378864\pi$
$458$	1.03509	−	3.86300i	0.0483665	−	0.180506i
$459$	1.27634	−	0.736894i	0.0595743	−	0.0343952i
$460$	0.663819	−	12.6627i	0.0309507	−	0.590403i
$461$			19.2136i			0.894866i	0.894317	+	0.447433i	$0.147662\pi$
$461$			19.2136i			0.894866i	−0.894317	+	0.447433i	$0.852338\pi$
$462$	−4.92461	+	18.3789i	−0.229114	+	0.855064i
$463$	−5.05722	−	5.05722i	−0.235029	−	0.235029i	0.579759	−	0.814788i	$-0.303147\pi$
$463$	−5.05722	−	5.05722i	−0.235029	−	0.235029i	−0.814788	+	0.579759i	$0.803147\pi$
$464$	−3.10232			−0.144022
$465$	−2.36512	−	12.2232i	−0.109680	−	0.566837i
$466$	−27.0807			−1.25449
$467$	3.95701	+	3.95701i	0.183109	+	0.183109i	0.792709	−	0.609600i	$-0.208670\pi$
$467$	3.95701	+	3.95701i	0.183109	+	0.183109i	−0.609600	+	0.792709i	$0.708670\pi$
$468$	−1.55272	+	5.79483i	−0.0717745	+	0.267866i
$469$		−	40.0968i		−	1.85150i
$470$	2.19356	+	2.43627i	0.101181	+	0.112377i
$471$	−6.44139	+	3.71894i	−0.296804	+	0.171360i
$472$	−1.61474	+	6.02629i	−0.0743244	+	0.277382i
$473$	13.0378	−	13.0378i	0.599479	−	0.599479i
$474$	2.79495	+	1.61367i	0.128376	+	0.0741182i
$475$	15.3977	+	34.5866i	0.706495	+	1.58694i
$476$	−6.57736	−	3.79744i	−0.301473	−	0.174055i
$477$	−6.85037	−	1.83555i	−0.313657	−	0.0840441i
$478$	−18.8527	+	5.05156i	−0.862302	+	0.231053i
$479$	10.6477	−	6.14743i	0.486504	−	0.280883i	−0.236619	−	0.971603i	$-0.576039\pi$
$479$	10.6477	−	6.14743i	0.486504	−	0.280883i	0.723123	+	0.690719i	$0.242706\pi$
$480$	0.691015	−	2.12662i	0.0315404	−	0.0970663i
$481$	29.4306			1.34192
$482$	−9.93749	−	2.66274i	−0.452640	−	0.121285i
$483$	−7.56347	−	28.2273i	−0.344150	−	1.28438i
$484$	−2.27991	+	1.31631i	−0.103632	+	0.0598322i
$485$	14.4234	+	0.756120i	0.654935	+	0.0343336i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−3.75843	−	14.0266i	−0.170311	−	0.635608i	−0.997303	−	0.0733948i	$-0.976617\pi$
$487$	−3.75843	−	14.0266i	−0.170311	−	0.635608i	0.826992	−	0.562213i	$-0.190050\pi$
$488$	5.89660	+	5.89660i	0.266927	+	0.266927i
$489$	8.06119	+	13.9624i	0.364540	+	0.631401i
$490$	36.6746	+	23.8175i	1.65679	+	1.07597i
$491$	−33.2743	−	19.2110i	−1.50165	−	0.866978i	−0.999998	−	0.00190863i	$-0.999392\pi$
$491$	−33.2743	−	19.2110i	−1.50165	−	0.866978i	−0.501652	−	0.865070i	$-0.667274\pi$
$492$	8.21825	−	8.21825i	0.370507	−	0.370507i
$493$	−4.41637	−	1.18336i	−0.198903	−	0.0532960i
$494$	45.4254			2.04378
$495$	−7.85197	−	2.55139i	−0.352920	−	0.114677i
$496$	5.35079	+	1.53917i	0.240258	+	0.0691109i
$497$	15.8230	+	15.8230i	0.709761	+	0.709761i
$498$	−6.54756	+	6.54756i	−0.293403	+	0.293403i
$499$	5.46728	+	9.46961i	0.244749	+	0.423918i	0.962061	−	0.272834i	$-0.0879610\pi$
$499$	5.46728	+	9.46961i	0.244749	+	0.423918i	−0.717312	+	0.696752i	$0.754628\pi$
$500$	−9.04538	+	6.57123i	−0.404522	+	0.293874i
$501$	−1.74585	+	3.02390i	−0.0779989	+	0.135098i
$502$	13.8943	+	3.72296i	0.620132	+	0.166164i
$503$	10.5577	+	2.82893i	0.470745	+	0.126136i	0.486390	−	0.873742i	$-0.338313\pi$
$503$	10.5577	+	2.82893i	0.470745	+	0.126136i	−0.0156447	+	0.999878i	$0.504980\pi$
$504$		−	5.15331i		−	0.229547i
$505$	1.43038	−	1.28788i	0.0636513	−	0.0573101i
$506$	10.4688	−	18.1326i	0.465396	−	0.806090i
$507$	−5.95049	−	22.2075i	−0.264271	−	0.986272i
$508$	0.526103	−	1.96344i	0.0233420	−	0.0871136i
$509$	−0.369403	+	0.639825i	−0.0163735	+	0.0283598i	−0.874096	−	0.485753i	$-0.838545\pi$
$509$	−0.369403	+	0.639825i	−0.0163735	+	0.0283598i	0.857723	+	0.514113i	$0.171879\pi$
$510$	1.79489	−	2.76380i	0.0794792	−	0.122383i
$511$		−	52.5992i		−	2.32685i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.95974	−	7.31384i	0.0865246	−	0.322914i
$514$	−6.42996	−	3.71234i	−0.283614	−	0.163744i
$515$	13.9413	+	9.05386i	0.614325	+	0.398961i
$516$	−2.49689	+	4.32475i	−0.109920	+	0.190386i
$517$	1.40103	+	5.22870i	0.0616171	+	0.229958i
$518$	−24.4192	+	6.54311i	−1.07292	+	0.287488i
$519$	−8.95881			−0.393248
$520$	2.78888	+	13.1216i	0.122300	+	0.575421i
$521$	−3.86445	−	6.69343i	−0.169305	−	0.293245i	0.768871	−	0.639404i	$-0.220819\pi$
$521$	−3.86445	−	6.69343i	−0.169305	−	0.293245i	−0.938176	+	0.346160i	$0.887486\pi$
$522$	−0.802941	−	2.99661i	−0.0351438	−	0.131158i
$523$	25.7662	+	25.7662i	1.12668	+	1.12668i	0.990714	+	0.135961i	$0.0434122\pi$
$523$	25.7662	+	25.7662i	1.12668	+	1.12668i	0.135961	+	0.990714i	$0.456588\pi$
$524$	−2.55307	+	1.47402i	−0.111531	+	0.0643927i
$525$	−15.1458	+	20.8451i	−0.661018	+	0.909755i
$526$			27.5577i			1.20157i
$527$	7.03011	+	4.23215i	0.306236	+	0.184355i
$528$	2.61081	−	2.61081i	0.113621	−	0.113621i
$529$			9.15714i			0.398137i
$530$	−15.5118	+	3.29688i	−0.673788	+	0.143207i
$531$	−6.23887			−0.270744
$532$	−37.6905	+	10.0991i	−1.63409	+	0.437853i
$533$	−18.0463	+	67.3496i	−0.781671	+	2.91723i
$534$	−9.79605	+	5.65575i	−0.423916	+	0.244748i
$535$	−9.43235	−	18.5127i	−0.407796	−	0.800375i
$536$	−3.89039	+	6.73836i	−0.168039	+	0.291053i
$537$	0.119101	−	0.0319130i	0.00513959	−	0.00137715i
$538$	−12.7599	+	3.41900i	−0.550118	+	0.147404i
$539$	36.1038	+	62.5336i	1.55510	+	2.69351i
$540$	2.23300	+	0.117061i	0.0960931	+	0.00503749i
$541$	−21.8653	−	37.8719i	−0.940064	−	1.62824i	−0.765344	−	0.643621i	$-0.777431\pi$
$541$	−21.8653	−	37.8719i	−0.940064	−	1.62824i	−0.174720	−	0.984618i	$-0.555902\pi$
$542$	3.77970	−	3.77970i	0.162352	−	0.162352i
$543$	−0.514844	+	0.514844i	−0.0220941	+	0.0220941i
$544$	0.736894	+	1.27634i	0.0315941	+	0.0547225i
$545$	1.03691	+	1.15164i	0.0444162	+	0.0493307i
$546$	15.4580	+	26.7740i	0.661540	+	1.14582i
$547$	−1.68132	+	0.450509i	−0.0718881	+	0.0192624i	−0.294584	−	0.955626i	$-0.595181\pi$
$547$	−1.68132	+	0.450509i	−0.0718881	+	0.0192624i	0.222696	+	0.974888i	$0.428514\pi$
$548$	−5.60714	+	1.50243i	−0.239525	+	0.0641806i
$549$	−4.16953	+	7.22183i	−0.177951	+	0.308220i
$550$	−18.2340	+	2.88741i	−0.777500	+	0.123120i
$551$	−20.3432	+	11.7452i	−0.866650	+	0.500361i
$552$	−1.46769	+	5.47750i	−0.0624691	+	0.233138i
$553$	16.0647	−	4.30453i	0.683142	−	0.183047i
$554$	5.02393			0.213446
$555$	−2.28053	−	10.7298i	−0.0968029	−	0.455456i
$556$			18.8224i			0.798249i
$557$	15.6032	−	15.6032i	0.661128	−	0.661128i	−0.294518	−	0.955646i	$-0.595159\pi$
$557$	15.6032	−	15.6032i	0.661128	−	0.661128i	0.955646	+	0.294518i	$0.0951590\pi$
$558$	−0.101840	+	5.56683i	−0.00431125	+	0.235663i
$559$		−	29.9589i		−	1.26713i
$560$	−5.23124	−	10.2673i	−0.221060	−	0.433872i
$561$	4.71254	−	2.72079i	0.198964	−	0.114872i
$562$	9.18562	+	9.18562i	0.387472	+	0.387472i
$563$	−5.97785	−	22.3096i	−0.251936	−	0.940239i	−0.969769	−	0.244024i	$-0.921532\pi$
$563$	−5.97785	−	22.3096i	−0.251936	−	0.940239i	0.717833	−	0.696216i	$-0.245134\pi$
$564$	−0.733045	−	1.26967i	−0.0308668	−	0.0534628i
$565$	−6.18371	−	4.01588i	−0.260150	−	0.168949i
$566$	−27.5385			−1.15753
$567$	4.97771	−	1.33377i	0.209044	−	0.0560133i
$568$	−1.12387	−	4.19433i	−0.0471564	−	0.175990i
$569$	0.932490	−	1.61512i	0.0390920	−	0.0677093i	−0.845817	−	0.533472i	$-0.820887\pi$
$569$	0.932490	−	1.61512i	0.0390920	−	0.0677093i	0.884909	+	0.465763i	$0.154220\pi$
$570$	−3.51994	−	16.5612i	−0.147434	−	0.693674i
$571$	27.8907	+	16.1027i	1.16719	+	0.673878i	0.953017	−	0.302918i	$-0.0979608\pi$
$571$	27.8907	+	16.1027i	1.16719	+	0.673878i	0.214174	+	0.976796i	$0.431294\pi$
$572$	−5.73301	+	21.3959i	−0.239709	+	0.894606i
$573$	−11.6309	−	11.6309i	−0.485888	−	0.485888i
$574$		−	59.8936i		−	2.49991i
$575$	22.0355	−	17.8429i	0.918942	−	0.744098i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−4.27289	+	15.9466i	−0.177883	+	0.663867i	0.818160	+	0.574991i	$0.194994\pi$
$577$	−4.27289	+	15.9466i	−0.177883	+	0.663867i	−0.996043	+	0.0888764i	$0.971672\pi$
$578$	−3.83776	−	14.3227i	−0.159630	−	0.595746i
$579$	−6.42820	+	11.1340i	−0.267147	+	0.462712i
$580$	−4.64169	−	5.15527i	−0.192736	−	0.214061i
$581$			47.7178i			1.97967i
$582$	−6.23913	−	1.67177i	−0.258620	−	0.0692970i
$583$	−25.2932	−	6.77729i	−1.04754	−	0.280687i
$584$	−5.10344	+	8.83942i	−0.211182	+	0.365778i
$585$	−11.9527	+	6.08997i	−0.494183	+	0.251789i
$586$	−15.2158	−	26.3546i	−0.628560	−	1.08870i
$587$	−22.8774	+	22.8774i	−0.944253	+	0.944253i	−0.998526	−	0.0542732i	$-0.982716\pi$
$587$	−22.8774	+	22.8774i	−0.944253	+	0.944253i	0.0542732	+	0.998526i	$0.482716\pi$
$588$	−13.8286	−	13.8286i	−0.570282	−	0.570282i
$589$	40.9145	−	10.1647i	1.68585	−	0.418829i
$590$	−12.4301	+	6.33323i	−0.511740	+	0.260735i
$591$	3.39691			0.139730
$592$	4.73855	+	1.26969i	0.194753	+	0.0521840i
$593$	−24.0436	+	24.0436i	−0.987354	+	0.987354i	−0.999921	−	0.0125668i	$-0.996000\pi$
$593$	−24.0436	+	24.0436i	−0.987354	+	0.987354i	0.0125668	+	0.999921i	$0.496000\pi$
$594$	3.19757	+	1.84612i	0.131198	+	0.0757472i
$595$	−3.53064	−	16.6116i	−0.144742	−	0.681010i
$596$	−0.256445	−	0.444176i	−0.0105044	−	0.0181942i
$597$	2.17679	+	2.17679i	0.0890902	+	0.0890902i
$598$	−8.80504	−	32.8609i	−0.360065	−	1.34378i
$599$	15.7834	+	9.11257i	0.644893	+	0.372329i	0.786497	−	0.617594i	$-0.211892\pi$
$599$	15.7834	+	9.11257i	0.644893	+	0.372329i	−0.141604	+	0.989923i	$0.545226\pi$
$600$	4.56779	−	2.03354i	0.186479	−	0.0830191i
$601$	7.47680	−	4.31673i	0.304985	−	0.176083i	−0.339695	−	0.940536i	$-0.610324\pi$
$601$	7.47680	−	4.31673i	0.304985	−	0.176083i	0.644680	+	0.764452i	$0.276991\pi$
$602$	6.66058	+	24.8576i	0.271465	+	1.01312i
$603$	−7.51566	−	2.01382i	−0.306061	−	0.0820089i
$604$	6.61373			0.269109
$605$	−5.59857	−	1.81918i	−0.227614	−	0.0739601i
$606$	−0.745451	+	0.430386i	−0.0302819	+	0.0174832i
$607$	−18.4462	+	4.94265i	−0.748709	+	0.200616i	−0.612945	−	0.790125i	$-0.710015\pi$
$607$	−18.4462	+	4.94265i	−0.748709	+	0.200616i	−0.135764	+	0.990741i	$0.543349\pi$
$608$	7.31384	+	1.95974i	0.296616	+	0.0794779i
$609$	−13.8453	−	7.99362i	−0.561042	−	0.323918i
$610$	−0.976175	+	18.6211i	−0.0395242	+	0.753947i
$611$	7.61707	+	4.39772i	0.308154	+	0.177913i
$612$	−1.04212	+	1.04212i	−0.0421254	+	0.0421254i
$613$	10.0625	−	37.5539i	0.406422	−	1.51679i	−0.394997	−	0.918682i	$-0.629254\pi$
$613$	10.0625	−	37.5539i	0.406422	−	1.51679i	0.801419	−	0.598104i	$-0.204079\pi$
$614$	−3.36385	+	1.94212i	−0.135754	+	0.0783776i
$615$	25.9528	+	1.36052i	1.04652	+	0.0548615i
$616$		−	19.0272i		−	0.766629i
$617$	−2.77043	+	10.3394i	−0.111533	+	0.416248i	−0.999004	−	0.0446159i	$-0.985794\pi$
$617$	−2.77043	+	10.3394i	−0.111533	+	0.416248i	0.887471	+	0.460864i	$0.152460\pi$
$618$	−5.25672	−	5.25672i	−0.211456	−	0.211456i
$619$	−8.86787			−0.356430			−0.178215	−	0.983992i	$-0.557032\pi$
$619$	−8.86787			−0.356430			−0.178215	+	0.983992i	$0.557032\pi$
$620$	5.44812	+	11.1946i	0.218802	+	0.449584i
$621$	−5.67073			−0.227558
$622$	−7.43284	−	7.43284i	−0.298030	−	0.298030i
$623$	−15.0870	+	56.3054i	−0.604447	+	2.25583i
$624$		−	5.99925i		−	0.240162i
$625$	−24.4534	−	5.19928i	−0.978135	−	0.207971i
$626$	−2.43157	+	1.40387i	−0.0971853	+	0.0561099i
$627$	7.23582	−	27.0044i	0.288971	−	1.07845i
$628$	5.25938	−	5.25938i	0.209872	−	0.209872i
$629$	6.26134	+	3.61499i	0.249656	+	0.144139i
$630$	8.56348	−	7.71036i	0.341177	−	0.307188i
$631$	−0.0704252	−	0.0406600i	−0.00280358	−	0.00161865i	0.498598	−	0.866834i	$-0.333849\pi$
$631$	−0.0704252	−	0.0406600i	−0.00280358	−	0.00161865i	−0.501401	+	0.865215i	$0.667182\pi$
$632$	−3.11736	−	0.835295i	−0.124002	−	0.0332263i
$633$	−7.39556	+	1.98164i	−0.293947	+	0.0787629i
$634$	22.0964	−	12.7574i	0.877560	−	0.506660i
$635$	4.04989	−	2.06345i	0.160715	−	0.0818854i
$636$	7.09203			0.281217
$637$	113.327	+	30.3659i	4.49018	+	1.20314i
$638$	−2.96465	−	11.0642i	−0.117371	−	0.438036i
$639$	3.76054	−	2.17115i	0.148764	−	0.0858892i
$640$	−0.117061	+	2.23300i	−0.00462723	+	0.0882671i
$641$	−1.46013	−	0.843007i	−0.0576717	−	0.0332968i	0.470887	−	0.882194i	$-0.343934\pi$
$641$	−1.46013	−	0.843007i	−0.0576717	−	0.0332968i	−0.528559	+	0.848897i	$0.677267\pi$
$642$	2.40490	+	8.97521i	0.0949139	+	0.354223i
$643$	−2.09834	−	2.09834i	−0.0827503	−	0.0827503i	0.664520	−	0.747270i	$-0.268636\pi$
$643$	−2.09834	−	2.09834i	−0.0827503	−	0.0827503i	−0.747270	+	0.664520i	$0.768636\pi$
$644$	14.6115	+	25.3079i	0.575774	+	0.997269i
$645$	−10.9225	+	2.32147i	−0.430072	+	0.0914077i
$646$	9.66423	+	5.57965i	0.380234	+	0.219528i
$647$	32.2688	−	32.2688i	1.26862	−	1.26862i	0.321817	−	0.946802i	$-0.395706\pi$
$647$	32.2688	−	32.2688i	1.26862	−	1.26862i	0.946802	−	0.321817i	$-0.104294\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−23.0354			−0.904218
$650$	−17.6321	+	24.2669i	−0.691587	+	0.951827i
$651$	19.9141	+	20.6563i	0.780495	+	0.809584i
$652$	−11.4002	−	11.4002i	−0.446468	−	0.446468i
$653$	31.6631	−	31.6631i	1.23907	−	1.23907i	0.278695	−	0.960380i	$-0.410098\pi$
$653$	31.6631	−	31.6631i	1.23907	−	1.23907i	0.960380	−	0.278695i	$-0.0899017\pi$
$654$	−0.346514	−	0.600180i	−0.0135498	−	0.0234689i
$655$	−6.26933	−	2.03713i	−0.244963	−	0.0795974i
$656$	−5.81118	+	10.0653i	−0.226889	+	0.392983i
$657$	−9.85909	−	2.64174i	−0.384640	−	0.103064i
$658$	−7.29777	−	1.95543i	−0.284497	−	0.0762307i
$659$		−	9.08769i		−	0.354006i	−0.984210	−	0.177003i	$-0.943360\pi$
$659$		−	9.08769i		−	0.354006i	0.984210	−	0.177003i	$-0.0566403\pi$
$660$	8.24477	+	0.432216i	0.320927	+	0.0168240i
$661$	11.2705	−	19.5211i	0.438373	−	0.759284i	−0.559191	−	0.829039i	$-0.688888\pi$
$661$	11.2705	−	19.5211i	0.438373	−	0.759284i	0.997564	+	0.0697545i	$0.0222216\pi$
$662$	−1.92310	−	7.17712i	−0.0747435	−	0.278947i
$663$	2.28838	−	8.54034i	0.0888732	−	0.331679i
$664$	4.62982	−	8.01909i	0.179672	−	0.311201i
$665$	−73.1746	−	47.5217i	−2.83759	−	1.84281i
$666$			4.90571i			0.190093i
$667$	12.4397	+	12.4397i	0.481668	+	0.481668i
$668$	0.903719	−	3.37272i	0.0349659	−	0.130495i
$669$	−14.5015	−	8.37244i	−0.560660	−	0.323697i
$670$	−17.0182	+	3.61707i	−0.657471	+	0.139739i
$671$	−15.3949	+	26.6647i	−0.594313	+	1.02938i
$672$	1.33377	+	4.97771i	0.0514515	+	0.192019i
$673$	35.7472	−	9.57843i	1.37795	−	0.369221i	0.507576	−	0.861607i	$-0.330542\pi$
$673$	35.7472	−	9.57843i	1.37795	−	0.369221i	0.870377	+	0.492386i	$0.163875\pi$
$674$	14.6124			0.562848
$675$	3.14648	+	3.88583i	0.121108	+	0.149565i
$676$	11.4955	+	19.9107i	0.442134	+	0.765798i
$677$	−8.07146	−	30.1231i	−0.310211	−	1.15772i	−0.928366	−	0.371668i	$-0.878786\pi$
$677$	−8.07146	−	30.1231i	−0.310211	−	1.15772i	0.618154	−	0.786057i	$-0.287881\pi$
$678$	2.33164	+	2.33164i	0.0895461	+	0.0895461i
$679$	−28.8268	+	16.6432i	−1.10627	+	0.638706i
$680$	−1.01841	+	3.13418i	−0.0390542	+	0.120190i
$681$			1.38165i			0.0529451i
$682$	−0.376019	+	20.5541i	−0.0143985	+	0.787056i
$683$	23.1618	−	23.1618i	0.886260	−	0.886260i	−0.107901	−	0.994162i	$-0.534413\pi$
$683$	23.1618	−	23.1618i	0.886260	−	0.886260i	0.994162	+	0.107901i	$0.0344130\pi$
$684$			7.57185i			0.289517i
$685$	−10.8860	−	7.06972i	−0.415934	−	0.270120i
$686$	−64.7079			−2.47056
$687$	−3.86300	+	1.03509i	−0.147383	+	0.0394911i
$688$	1.29249	−	4.82363i	0.0492756	−	0.183899i
$689$	−36.8466	+	21.2734i	−1.40374	+	0.810452i
$690$	−11.2982	+	5.75649i	−0.430114	+	0.219146i
$691$	3.32344	−	5.75636i	0.126429	−	0.218982i	−0.795861	−	0.605479i	$-0.792982\pi$
$691$	3.32344	−	5.75636i	0.126429	−	0.218982i	0.922291	+	0.386497i	$0.126315\pi$
$692$	8.65355	−	2.31871i	0.328958	−	0.0881441i
$693$	18.3789	−	4.92461i	0.698157	−	0.187071i
$694$	4.62888	+	8.01745i	0.175710	+	0.304338i
$695$	−31.2781	+	28.1621i	−1.18645	+	1.06825i
$696$	1.55116	+	2.68669i	0.0587966	+	0.101839i
$697$	−12.1120	+	12.1120i	−0.458773	+	0.458773i
$698$	22.8360	−	22.8360i	0.864355	−	0.864355i
$699$	13.5404	+	23.4526i	0.512144	+	0.887059i
$700$	9.23463	−	24.0549i	0.349036	−	0.909188i
$701$	18.6329	+	32.2732i	0.703756	+	1.21894i	0.967139	+	0.254250i	$0.0818285\pi$
$701$	18.6329	+	32.2732i	0.703756	+	1.21894i	−0.263383	+	0.964691i	$0.584838\pi$
$702$	5.79483	−	1.55272i	0.218712	−	0.0586036i
$703$	35.8796	−	9.61391i	1.35323	−	0.362596i
$704$	−1.84612	+	3.19757i	−0.0695782	+	0.120513i
$705$	1.01309	−	3.11781i	0.0381552	−	0.117424i
$706$	−17.2729	+	9.97249i	−0.650073	+	0.375320i
$707$	−1.14808	+	4.28468i	−0.0431778	+	0.161142i
$708$	6.02629	−	1.61474i	0.226482	−	0.0606856i
$709$	−38.6782			−1.45259			−0.726295	−	0.687383i	$-0.758759\pi$
$709$	−38.6782			−1.45259			−0.726295	+	0.687383i	$0.758759\pi$
$710$	5.28838	−	8.14313i	0.198469	−	0.305606i
$711$		−	3.22733i		−	0.121034i
$712$	7.99844	−	7.99844i	0.299754	−	0.299754i
$713$	−15.2839	−	27.6274i	−0.572385	−	1.03466i
$714$			7.59488i			0.284231i
$715$	−44.1322	+	22.4856i	−1.65045	+	0.840915i
$716$	−0.106783	+	0.0616512i	−0.00399067	+	0.00230401i
$717$	13.8011	+	13.8011i	0.515413	+	0.515413i
$718$	3.59920	+	13.4324i	0.134321	+	0.501293i
$719$	−14.7879	−	25.6133i	−0.551494	−	0.955216i	−0.998167	−	0.0605184i	$-0.980725\pi$
$719$	−14.7879	−	25.6133i	−0.551494	−	0.955216i	0.446673	−	0.894697i	$-0.352609\pi$
$720$	−2.18721	+	0.464871i	−0.0815126	+	0.0173247i
$721$	−38.3103			−1.42675
$722$	37.0267	−	9.92128i	1.37799	−	0.369232i
$723$	2.66274	+	9.93749i	0.0990285	+	0.369579i
$724$	0.364050	−	0.630553i	0.0135298	−	0.0234343i
$725$	1.62187	−	15.4266i	0.0602349	−	0.572929i
$726$	2.27991	+	1.31631i	0.0846155	+	0.0488528i
$727$	5.49648	−	20.5131i	0.203853	−	0.760790i	−0.785943	−	0.618299i	$-0.787822\pi$
$727$	5.49648	−	20.5131i	0.203853	−	0.760790i	0.989796	−	0.142491i	$-0.0455112\pi$
$728$	−21.8609	−	21.8609i	−0.810218	−	0.810218i
$729$		−	1.00000i		−	0.0370370i
$730$	−22.3246	+	4.74489i	−0.826271	+	0.175616i
$731$	3.67989	−	6.37375i	0.136106	−	0.235742i
$732$	2.15831	−	8.05491i	0.0797733	−	0.297718i
$733$	7.97254	+	29.7539i	0.294473	+	1.09899i	0.941635	+	0.336635i	$0.109289\pi$
$733$	7.97254	+	29.7539i	0.294473	+	1.09899i	−0.647163	+	0.762352i	$0.724045\pi$
$734$	−7.74526	+	13.4152i	−0.285883	+	0.495163i
$735$	2.28931	−	43.6699i	0.0844423	−	1.61079i
$736$		−	5.67073i		−	0.209026i
$737$	−27.7496	−	7.43548i	−1.02217	−	0.273890i
$738$	−11.2263	−	3.00809i	−0.413247	−	0.110729i
$739$	−5.96943	+	10.3394i	−0.219589	+	0.380340i	−0.954682	−	0.297626i	$-0.903805\pi$
$739$	−5.96943	+	10.3394i	−0.219589	+	0.380340i	0.735093	+	0.677966i	$0.237138\pi$
$740$	4.97990	+	9.77398i	0.183065	+	0.359299i
$741$	−22.7127	−	39.3395i	−0.834371	−	1.44517i
$742$	25.8429	−	25.8429i	0.948723	−	0.948723i
$743$	20.7127	+	20.7127i	0.759876	+	0.759876i	0.976300	−	0.216423i	$-0.0694391\pi$
$743$	20.7127	+	20.7127i	0.759876	+	0.759876i	−0.216423	+	0.976300i	$0.569439\pi$
$744$	−1.34243	−	5.40351i	−0.0492159	−	0.198102i
$745$	0.354415	−	1.09072i	0.0129848	−	0.0399609i
$746$	−5.52336			−0.202225
$747$	8.94413	+	2.39657i	0.327249	+	0.0876860i
$748$	−3.84777	+	3.84777i	−0.140688	+	0.140688i
$749$	41.4684	+	23.9418i	1.51522	+	0.874815i
$750$	10.2135	+	4.54792i	0.372946	+	0.166067i
$751$	25.1181	+	43.5059i	0.916573	+	1.58755i	0.804581	+	0.593843i	$0.202390\pi$
$751$	25.1181	+	43.5059i	0.916573	+	1.58755i	0.111992	+	0.993709i	$0.464277\pi$
$752$	1.03668	+	1.03668i	0.0378039	+	0.0378039i
$753$	−3.72296	−	13.8943i	−0.135672	−	0.506335i
$754$	−16.1181	−	9.30580i	−0.586987	−	0.338897i
$755$	9.89544	+	10.9903i	0.360132	+	0.399979i
$756$	−4.46290	+	2.57665i	−0.162314	+	0.0937120i
$757$	−3.01090	−	11.2368i	−0.109433	−	0.408410i	0.889377	−	0.457174i	$-0.151138\pi$
$757$	−3.01090	−	11.2368i	−0.109433	−	0.408410i	−0.998810	+	0.0487642i	$0.984472\pi$
$758$	−36.6330	−	9.81579i	−1.33057	−	0.356525i
$759$	−20.9377			−0.759989
$760$	7.68636	+	15.0859i	0.278814	+	0.547223i
$761$	−7.58040	+	4.37655i	−0.274789	+	0.158650i	−0.631062	−	0.775732i	$-0.717381\pi$
$761$	−7.58040	+	4.37655i	−0.274789	+	0.158650i	0.356273	+	0.934382i	$0.384047\pi$
$762$	−1.96344	+	0.526103i	−0.0711280	+	0.0190587i
$763$	−3.44969	−	0.924343i	−0.124887	−	0.0334635i
$764$	14.2449	+	8.22429i	0.515362	+	0.297544i
$765$	−3.29097	−	0.172522i	−0.118985	−	0.00623756i
$766$	−11.8006	−	6.81307i	−0.426372	−	0.246166i
$767$	−26.4660	+	26.4660i	−0.955631	+	0.955631i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−10.7378	+	6.19949i	−0.387216	+	0.223559i	−0.680953	−	0.732327i	$-0.738434\pi$
$769$	−10.7378	+	6.19949i	−0.387216	+	0.223559i	0.293737	+	0.955886i	$0.405101\pi$
$770$	31.6184	−	28.4685i	1.13945	−	1.02593i
$771$			7.42468i			0.267393i
$772$	3.32748	−	12.4183i	0.119759	−	0.446946i
$773$	−28.8341	−	28.8341i	−1.03709	−	1.03709i	−0.999285	−	0.0378045i	$-0.987964\pi$
$773$	−28.8341	−	28.8341i	−1.03709	−	1.03709i	−0.0378045	−	0.999285i	$-0.512036\pi$
$774$	4.99379			0.179498
$775$	−10.4510	+	25.8026i	−0.375412	+	0.926858i
$776$	6.45922			0.231872
$777$	17.8761	+	17.8761i	0.641302	+	0.641302i
$778$	6.81344	−	25.4281i	0.244274	−	0.911642i
$779$			88.0028i			3.15303i
$780$	9.96922	−	8.97605i	0.356955	−	0.321394i
$781$	13.8848	−	8.01639i	0.496837	−	0.286849i
$782$	2.16307	−	8.07267i	0.0773511	−	0.288678i
$783$	−2.19367	+	2.19367i	−0.0783955	+	0.0783955i
$784$	16.9365	+	9.77829i	0.604875	+	0.349225i
$785$	16.6088	+	0.870683i	0.592794	+	0.0310760i
$786$	2.55307	+	1.47402i	0.0910650	+	0.0525764i
$787$	−2.70347	−	0.724394i	−0.0963684	−	0.0258218i	0.210313	−	0.977634i	$-0.432552\pi$
$787$	−2.70347	−	0.724394i	−0.0963684	−	0.0258218i	−0.306681	+	0.951812i	$0.599218\pi$
$788$	−3.28116	+	0.879184i	−0.116886	+	0.0313196i
$789$	23.8657	−	13.7789i	0.849640	−	0.490540i
$790$	−3.27614	−	6.43003i	−0.116560	−	0.228770i
$791$	16.9927			0.604191
$792$	−3.56643	−	0.955621i	−0.126727	−	0.0339565i
$793$	12.9482	+	48.3234i	0.459804	+	1.71601i
$794$	18.3855	−	10.6148i	0.652475	−	0.376707i
$795$	10.6111	+	11.7851i	0.376336	+	0.417976i
$796$	−2.66602	−	1.53922i	−0.0944944	−	0.0545564i
$797$	12.5655	+	46.8951i	0.445093	+	1.66111i	0.715690	+	0.698418i	$0.246112\pi$
$797$	12.5655	+	46.8951i	0.445093	+	1.66111i	−0.270597	+	0.962693i	$0.587221\pi$
$798$	27.5914	+	27.5914i	0.976723	+	0.976723i
$799$	1.08035	+	1.87122i	0.0382201	+	0.0661992i
$800$	−3.88583	+	3.14648i	−0.137385	+	0.111245i
$801$	9.79605	+	5.65575i	0.346126	+	0.199836i
$802$	−10.5740	+	10.5740i	−0.373382	+	0.373382i
$803$	−36.4021	−	9.75392i	−1.28460	−	0.344208i
$804$	7.78079			0.274407
$805$	−20.1935	+	62.1461i	−0.711729	+	2.19036i
$806$	23.1831	+	24.0471i	0.816589	+	0.847024i
$807$	9.34088	+	9.34088i	0.328815	+	0.328815i
$808$	0.608658	−	0.608658i	0.0214125	−	0.0214125i
$809$	−24.5450	−	42.5132i	−0.862956	−	1.49468i	−0.869062	−	0.494703i	$-0.835277\pi$
$809$	−24.5450	−	42.5132i	−0.862956	−	1.49468i	0.00610572	−	0.999981i	$-0.498056\pi$
$810$	−1.01512	−	1.99237i	−0.0356678	−	0.0700046i
$811$	−1.53124	+	2.65219i	−0.0537692	+	0.0931310i	−0.891657	−	0.452711i	$-0.850457\pi$
$811$	−1.53124	+	2.65219i	−0.0537692	+	0.0931310i	0.837888	+	0.545842i	$0.183790\pi$
$812$	15.4425	+	4.13780i	0.541925	+	0.145208i
$813$	−5.16316	−	1.38347i	−0.181080	−	0.0485203i
$814$			18.1131i			0.634862i
$815$	1.88730	−	36.0013i	0.0661091	−	1.26107i
$816$	0.736894	−	1.27634i	0.0257964	−	0.0446807i
$817$	−9.78651	−	36.5238i	−0.342387	−	1.27780i
$818$	4.78737	−	17.8667i	0.167387	−	0.624695i
$819$	15.4580	−	26.7740i	0.540146	−	0.935559i
$820$	−25.4206	+	5.40291i	−0.887725	+	0.188678i
$821$			17.8229i			0.622023i	0.950406	+	0.311012i	$0.100668\pi$
$821$			17.8229i			0.622023i	−0.950406	+	0.311012i	$0.899332\pi$
$822$	4.10471	+	4.10471i	0.143168	+	0.143168i
$823$	−1.04403	+	3.89636i	−0.0363924	+	0.135818i	−0.981732	−	0.190269i	$-0.939064\pi$
$823$	−1.04403	+	3.89636i	−0.0363924	+	0.135818i	0.945339	+	0.326088i	$0.105731\pi$
$824$	6.43814	+	3.71706i	0.224283	+	0.129490i
$825$	11.6176	+	14.3474i	0.404472	+	0.499512i
$826$	16.0754	−	27.8434i	0.559335	−	0.968797i
$827$	12.4144	+	46.3313i	0.431692	+	1.61110i	0.748860	+	0.662728i	$0.230601\pi$
$827$	12.4144	+	46.3313i	0.431692	+	1.61110i	−0.317168	+	0.948369i	$0.602732\pi$
$828$	5.47750	−	1.46769i	0.190356	−	0.0510058i
$829$	30.8205			1.07044			0.535220	−	0.844713i	$-0.320229\pi$
$829$	30.8205			1.07044			0.535220	+	0.844713i	$0.320229\pi$
$830$	20.2528	−	4.30455i	0.702985	−	0.149413i
$831$	−2.51196	−	4.35085i	−0.0871391	−	0.150929i
$832$	1.55272	+	5.79483i	0.0538308	+	0.200899i
$833$	20.3804	+	20.3804i	0.706139	+	0.706139i
$834$	16.3007	−	9.41122i	0.564447	−	0.325884i
$835$	6.95675	−	3.54451i	0.240748	−	0.122663i
$836$			27.9571i			0.966915i
$837$	4.87194	−	2.69522i	0.168399	−	0.0931604i
$838$	25.5748	−	25.5748i	0.883468	−	0.883468i
$839$		−	39.8058i		−	1.37425i	−0.726540	−	0.687124i	$-0.758873\pi$
$839$		−	39.8058i		−	1.37425i	0.726540	−	0.687124i	$-0.241127\pi$
$840$	−6.27610	+	9.66403i	−0.216546	+	0.333441i
$841$	−19.3756			−0.668124
$842$	31.1230	−	8.33938i	1.07257	−	0.287394i
$843$	3.36217	−	12.5478i	0.115799	−	0.432169i
$844$	6.63068	−	3.82823i	0.228237	−	0.131773i
$845$	−15.8871	+	48.8929i	−0.546533	+	1.68197i
$846$	−0.733045	+	1.26967i	−0.0252026	+	0.0436522i
$847$	13.1044	−	3.51132i	0.450273	−	0.120650i
$848$	−6.85037	+	1.83555i	−0.235243	+	0.0630331i
$849$	13.7693	+	23.8491i	0.472560	+	0.818498i
$850$	−6.73195	+	2.99701i	−0.230904	+	0.102797i
$851$	−13.9095	−	24.0919i	−0.476811	−	0.825861i
$852$	−3.07046	+	3.07046i	−0.105192	+	0.105192i
$853$	−7.19160	+	7.19160i	−0.246236	+	0.246236i	−0.819424	−	0.573188i	$-0.805706\pi$
$853$	−7.19160	+	7.19160i	−0.246236	+	0.246236i	0.573188	+	0.819424i	$0.305706\pi$
$854$	−21.4869	−	37.2163i	−0.735265	−	1.27352i
$855$	−12.5825	+	11.3290i	−0.430312	+	0.387443i
$856$	−4.64591	−	8.04695i	−0.158794	−	0.275039i
$857$	−17.4237	+	4.66866i	−0.595182	+	0.159478i	−0.543820	−	0.839202i	$-0.683023\pi$
$857$	−17.4237	+	4.66866i	−0.595182	+	0.159478i	−0.0513614	+	0.998680i	$0.516356\pi$
$858$	21.3959	−	5.73301i	0.730443	−	0.195722i
$859$	−5.86254	+	10.1542i	−0.200027	+	0.346458i	−0.948537	−	0.316666i	$-0.897436\pi$
$859$	−5.86254	+	10.1542i	−0.200027	+	0.346458i	0.748510	+	0.663124i	$0.230770\pi$
$860$	9.94945	−	5.06931i	0.339273	−	0.172862i
$861$	−51.8694	+	29.9468i	−1.76770	+	1.02058i
$862$	5.90760	−	22.0474i	0.201214	−	0.750939i
$863$	−7.98635	+	2.13993i	−0.271858	+	0.0728442i	−0.392173	−	0.919892i	$-0.628276\pi$
$863$	−7.98635	+	2.13993i	−0.271858	+	0.0728442i	0.120314	+	0.992736i	$0.461610\pi$
$864$	1.00000			0.0340207
$865$	16.8005	+	10.9107i	0.571234	+	0.370976i
$866$			16.2281i			0.551453i
$867$	−10.4849	+	10.4849i	−0.356087	+	0.356087i
$868$	−24.5818	−	14.7983i	−0.834360	−	0.502287i
$869$		−	11.9161i		−	0.404225i
$870$	−2.14375	+	6.59745i	−0.0726800	+	0.223675i
$871$	−40.4251	+	23.3394i	−1.36975	+	0.790826i
$872$	0.490045	+	0.490045i	0.0165950	+	0.0165950i
$873$	1.67177	+	6.23913i	0.0565808	+	0.211162i
$874$	−21.4689	−	37.1853i	−0.726198	−	1.25781i
$875$	53.7899	−	20.6452i	1.81843	−	0.697935i
$876$	10.2069			0.344859
$877$	−11.6095	+	3.11076i	−0.392026	+	0.105043i	−0.449447	−	0.893307i	$-0.648379\pi$
$877$	−11.6095	+	3.11076i	−0.392026	+	0.105043i	0.0574212	+	0.998350i	$0.481712\pi$
$878$	4.91377	+	18.3384i	0.165832	+	0.618892i
$879$	−15.2158	+	26.3546i	−0.513217	+	0.888917i
$880$	−8.07570	+	1.71642i	−0.272232	+	0.0578604i
$881$	−29.6226	−	17.1026i	−0.998011	−	0.576202i	−0.0903518	−	0.995910i	$-0.528799\pi$
$881$	−29.6226	−	17.1026i	−0.998011	−	0.576202i	−0.907659	+	0.419708i	$0.862132\pi$
$882$	−5.06162	+	18.8902i	−0.170433	+	0.636066i
$883$	−34.6952	−	34.6952i	−1.16759	−	1.16759i	−0.982774	−	0.184813i	$-0.940832\pi$
$883$	−34.6952	−	34.6952i	−1.16759	−	1.16759i	−0.184813	−	0.982774i	$-0.559168\pi$
$884$			8.84161i			0.297376i
$885$	11.6998	+	7.59819i	0.393284	+	0.255410i
$886$	−1.35971	+	2.35509i	−0.0456804	+	0.0791209i
$887$	−5.88741	+	21.9721i	−0.197680	+	0.737751i	0.793877	+	0.608078i	$0.208059\pi$
$887$	−5.88741	+	21.9721i	−0.197680	+	0.737751i	−0.991557	+	0.129673i	$0.958607\pi$
$888$	−1.26969	−	4.73855i	−0.0426081	−	0.159015i
$889$	−5.23758	+	9.07175i	−0.175663	+	0.304257i
$890$	25.2586	+	1.32413i	0.846670	+	0.0443850i
$891$		−	3.69224i		−	0.123695i
$892$	16.1743	+	4.33389i	0.541556	+	0.145109i
$893$	10.7228	+	2.87315i	0.358823	+	0.0961464i
$894$	−0.256445	+	0.444176i	−0.00857681	+	0.0148555i
$895$	−0.262217	−	0.0852039i	−0.00876495	−	0.00284805i
$896$	−2.57665	−	4.46290i	−0.0860800	−	0.149095i
$897$	−24.0558	+	24.0558i	−0.803201	+	0.803201i
$898$	20.9207	+	20.9207i	0.698134	+	0.698134i
$899$	−16.5999	−	4.77501i	−0.553637	−	0.159256i
$900$	−4.04500	−	2.93905i	−0.134833	−	0.0979683i
$901$	−10.4521			−0.348211
$902$	−41.4503	−	11.1066i	−1.38014	−	0.369809i
$903$	18.1970	−	18.1970i	0.605560	−	0.605560i
$904$	−2.85567	−	1.64872i	−0.0949780	−	0.0548356i
$905$	1.59251	−	0.338473i	0.0529368	−	0.0112512i
$906$	−3.30687	−	5.72766i	−0.109863	−	0.190289i
$907$	38.2934	+	38.2934i	1.27151	+	1.27151i	0.945295	+	0.326217i	$0.105774\pi$
$907$	38.2934	+	38.2934i	1.27151	+	1.27151i	0.326217	+	0.945295i	$0.394226\pi$
$908$	−0.357599	−	1.33458i	−0.0118673	−	0.0442895i
$909$	0.745451	+	0.430386i	0.0247250	+	0.0142750i
$910$	3.61904	−	69.0354i	0.119970	−	2.28850i
$911$	4.04169	−	2.33347i	0.133907	−	0.0773113i	−0.431550	−	0.902089i	$-0.642033\pi$
$911$	4.04169	−	2.33347i	0.133907	−	0.0773113i	0.565457	+	0.824778i	$0.308700\pi$
$912$	−1.95974	−	7.31384i	−0.0648934	−	0.242186i
$913$	33.0239	+	8.84872i	1.09293	+	0.292850i
$914$	−16.8399			−0.557015
$915$	16.6144	−	8.46517i	0.549257	−	0.279850i
$916$	3.46347	−	1.99964i	0.114436	−	0.0660699i
$917$	14.6744	−	3.93201i	0.484593	−	0.129846i
$918$	1.42357	+	0.381444i	0.0469848	+	0.0125895i
$919$	−11.0139	−	6.35886i	−0.363314	−	0.209759i	0.307220	−	0.951639i	$-0.400601\pi$
$919$	−11.0139	−	6.35886i	−0.363314	−	0.209759i	−0.670533	+	0.741879i	$0.733935\pi$
$920$	9.42330	−	8.48452i	0.310677	−	0.279726i
$921$	3.36385	+	1.94212i	0.110843	+	0.0639951i
$922$	−13.5861	+	13.5861i	−0.447433	+	0.447433i
$923$	6.74236	−	25.1628i	0.221927	−	0.828245i
$924$	−16.4781	+	9.51362i	−0.542089	+	0.312975i
$925$	−8.79095	+	22.8991i	−0.289045	+	0.752918i
$926$		−	7.15198i		−	0.235029i
$927$	−1.92409	+	7.18081i	−0.0631955	+	0.235849i
$928$	−2.19367	−	2.19367i	−0.0720109	−	0.0720109i
$929$	26.5995			0.872702			0.436351	−	0.899776i	$-0.356271\pi$
$929$	26.5995			0.872702			0.436351	+	0.899776i	$0.356271\pi$
$930$	6.97071	−	10.3155i	0.228578	−	0.338258i
$931$	148.079			4.85311
$932$	−19.1490	−	19.1490i	−0.627246	−	0.627246i
$933$	−2.72061	+	10.1534i	−0.0890687	+	0.332409i
$934$			5.59606i			0.183109i
$935$	−12.1510	−	0.636994i	−0.397381	−	0.0208319i
$936$	−5.19550	+	2.99962i	−0.169820	+	0.0980457i
$937$	7.68956	−	28.6978i	0.251207	−	0.937517i	−0.718955	−	0.695057i	$-0.755379\pi$
$937$	7.68956	−	28.6978i	0.251207	−	0.937517i	0.970161	−	0.242460i	$-0.0779542\pi$
$938$	28.3527	−	28.3527i	0.925749	−	0.925749i
$939$	2.43157	+	1.40387i	0.0793514	+	0.0458136i
$940$	−0.171621	+	3.27378i	−0.00559767	+	0.106779i
$941$	50.2404	+	29.0063i	1.63779	+	0.945579i	0.981592	+	0.190992i	$0.0611706\pi$
$941$	50.2404	+	29.0063i	1.63779	+	0.945579i	0.656200	+	0.754587i	$0.272163\pi$
$942$	−7.18444	−	1.92507i	−0.234082	−	0.0627220i
$943$	63.6615	−	17.0581i	2.07310	−	0.555487i
$944$	−5.40302	+	3.11944i	−0.175853	+	0.101529i
$945$	−10.9591	−	3.56101i	−0.356500	−	0.115840i
$946$	18.4382			0.599479
$947$	−45.9178	−	12.3036i	−1.49213	−	0.399815i	−0.581673	−	0.813423i	$-0.697602\pi$
$947$	−45.9178	−	12.3036i	−1.49213	−	0.399815i	−0.910455	+	0.413608i	$0.864268\pi$
$948$	0.835295	+	3.11736i	0.0271291	+	0.101247i
$949$	−53.0298	+	30.6168i	−1.72142	+	0.993863i
$950$	−13.5686	+	35.3442i	−0.440224	+	1.14672i
$951$	−22.0964	−	12.7574i	−0.716525	−	0.413686i
$952$	−1.96570	−	7.33609i	−0.0637087	−	0.237764i
$953$	23.2207	+	23.2207i	0.752191	+	0.752191i	0.974888	−	0.222696i	$-0.0714859\pi$
$953$	23.2207	+	23.2207i	0.752191	+	0.752191i	−0.222696	+	0.974888i	$0.571486\pi$
$954$	−3.54601	−	6.14188i	−0.114806	−	0.198851i
$955$	7.64648	+	35.9765i	0.247434	+	1.16417i
$956$	−16.9029	−	9.75887i	−0.546678	−	0.315624i
$957$	−8.09957	+	8.09957i	−0.261822	+	0.261822i
$958$	11.8759	+	3.18214i	0.383694	+	0.102810i
$959$	29.9147			0.965995
$960$	1.99237	−	1.01512i	0.0643034	−	0.0327630i
$961$	26.2619	+	16.4716i	0.847158	+	0.531341i
$962$	20.8106	+	20.8106i	0.670959	+	0.670959i
$963$	6.57031	−	6.57031i	0.211725	−	0.211725i
$964$	−5.14403	−	8.90971i	−0.165678	−	0.286963i
$965$	25.6147	−	13.0508i	0.824565	−	0.420121i
$966$	14.6115	−	25.3079i	0.470117	−	0.814267i
$967$	34.7021	+	9.29840i	1.11594	+	0.299016i	0.769241	−	0.638959i	$-0.220635\pi$
$967$	34.7021	+	9.29840i	1.11594	+	0.299016i	0.346703	+	0.937975i	$0.387301\pi$
$968$	−2.54291	−	0.681371i	−0.0817323	−	0.0219001i
$969$		−	11.1593i		−	0.358488i
$970$	9.66426	+	10.7336i	0.310301	+	0.344634i
$971$	−2.51374	+	4.35393i	−0.0806698	+	0.139724i	−0.903538	−	0.428508i	$-0.859039\pi$
$971$	−2.51374	+	4.35393i	−0.0806698	+	0.139724i	0.822868	+	0.568233i	$0.192373\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	25.1049	−	93.6927i	0.804826	−	3.00365i
$974$	7.26073	−	12.5759i	0.232649	−	0.402959i
$975$	29.8318	+	3.13636i	0.955382	+	0.100444i
$976$			8.33905i			0.266927i
$977$	14.8656	+	14.8656i	0.475594	+	0.475594i	0.903719	−	0.428125i	$-0.140826\pi$
$977$	14.8656	+	14.8656i	0.475594	+	0.475594i	−0.428125	+	0.903719i	$0.640826\pi$
$978$	−4.17278	+	15.5730i	−0.133431	+	0.497970i
$979$	36.1693	+	20.8824i	1.15598	+	0.667403i
$980$	9.09130	+	42.7744i	0.290411	+	1.36638i
$981$	−0.346514	+	0.600180i	−0.0110633	+	0.0191623i
$982$	−9.94432	−	37.1127i	−0.317336	−	1.18431i
$983$	15.5795	−	4.17452i	0.496910	−	0.133147i	−0.00165556	−	0.999999i	$-0.500527\pi$
$983$	15.5795	−	4.17452i	0.496910	−	0.133147i	0.498566	+	0.866852i	$0.333860\pi$
$984$	11.6224			0.370507
$985$	−6.37024	−	4.13702i	−0.202973	−	0.131816i
$986$	−2.28608	−	3.95961i	−0.0728037	−	0.126100i
$987$	1.95543	+	7.29777i	0.0622421	+	0.232291i
$988$	32.1206	+	32.1206i	1.02189	+	1.02189i
$989$	−24.5244	+	14.1592i	−0.779832	+	0.450236i
$990$	−3.74808	−	7.35629i	−0.119122	−	0.233798i
$991$		−	35.6234i		−	1.13161i	−0.824537	−	0.565807i	$-0.808565\pi$
$991$		−	35.6234i		−	1.13161i	0.824537	−	0.565807i	$-0.191435\pi$
$992$	2.69522	+	4.87194i	0.0855733	+	0.154684i
$993$	−5.25401	+	5.25401i	−0.166731	+	0.166731i
$994$			22.3772i			0.709761i
$995$	−1.43108	−	6.73322i	−0.0453684	−	0.213457i
$996$	−9.25965			−0.293403
$997$	42.6512	−	11.4284i	1.35078	−	0.361940i	0.490356	−	0.871522i	$-0.336867\pi$
$997$	42.6512	−	11.4284i	1.35078	−	0.361940i	0.860422	+	0.509582i	$0.170200\pi$
$998$	−2.83007	+	10.5620i	−0.0895844	+	0.334334i
$999$	4.24847	−	2.45286i	0.134416	−	0.0776049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.10	✓	64
5.3	odd	4		930.2.be.b.223.12	yes	64
31.26	odd	6		930.2.be.b.367.12	yes	64
155.88	even	12	inner	930.2.be.a.553.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.10	✓	64	1.1	even	1	trivial
930.2.be.a.553.10	yes	64	155.88	even	12	inner
930.2.be.b.223.12	yes	64	5.3	odd	4
930.2.be.b.367.12	yes	64	31.26	odd	6

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.66175 + 1.49620i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.33377 - 4.97771i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.66175 + 1.49620i) q^{5} +(0.866025 - 0.500000i) q^{6} +(1.33377 - 4.97771i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.23300 - 0.117061i) q^{10} +(-3.19757 - 1.84612i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-5.79483 + 1.55272i) q^{13} +(4.46290 - 2.57665i) q^{14} +(1.01512 + 1.99237i) q^{15} -1.00000 q^{16} +(-1.42357 - 0.381444i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-6.55741 + 3.78592i) q^{19} +(-1.49620 - 1.66175i) q^{20} +(-4.46290 - 2.57665i) q^{21} +(-0.955621 - 3.56643i) q^{22} +(4.00981 + 4.00981i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.522793 - 4.97259i) q^{25} +(-5.19550 - 2.99962i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.97771 + 1.33377i) q^{28} +3.10232 q^{29} +(-0.691015 + 2.12662i) q^{30} +(-5.35079 - 1.53917i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.61081 + 2.61081i) q^{33} +(-0.736894 - 1.27634i) q^{34} +(5.23124 + 10.2673i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.73855 - 1.26969i) q^{37} +(-7.31384 - 1.95974i) q^{38} +5.99925i q^{39} +(0.117061 - 2.23300i) q^{40} +(5.81118 - 10.0653i) q^{41} +(-1.33377 - 4.97771i) q^{42} +(-1.29249 + 4.82363i) q^{43} +(1.84612 - 3.19757i) q^{44} +(2.18721 - 0.464871i) q^{45} +5.67073i q^{46} +(-1.03668 - 1.03668i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-16.9365 - 9.77829i) q^{49} +(3.88583 - 3.14648i) q^{50} +(-0.736894 + 1.27634i) q^{51} +(-1.55272 - 5.79483i) q^{52} +(6.85037 - 1.83555i) q^{53} -1.00000 q^{54} +(8.07570 - 1.71642i) q^{55} +(2.57665 + 4.46290i) q^{56} +(1.95974 + 7.31384i) q^{57} +(2.19367 + 2.19367i) q^{58} +(5.40302 - 3.11944i) q^{59} +(-1.99237 + 1.01512i) q^{60} -8.33905i q^{61} +(-2.69522 - 4.87194i) q^{62} +(-3.64394 + 3.64394i) q^{63} -1.00000i q^{64} +(7.30635 - 11.2504i) q^{65} -3.69224 q^{66} +(7.51566 - 2.01382i) q^{67} +(0.381444 - 1.42357i) q^{68} +(4.91099 - 2.83536i) q^{69} +(-3.56101 + 10.9591i) q^{70} +(-2.17115 + 3.76054i) q^{71} +(0.965926 - 0.258819i) q^{72} +(9.85909 - 2.64174i) q^{73} +(-2.45286 - 4.24847i) q^{74} +(-4.66785 - 1.79198i) q^{75} +(-3.78592 - 6.55741i) q^{76} +(-13.4543 + 13.4543i) q^{77} +(-4.24211 + 4.24211i) q^{78} +(1.61367 + 2.79495i) q^{79} +(1.66175 - 1.49620i) q^{80} +(0.500000 + 0.866025i) q^{81} +(11.2263 - 3.00809i) q^{82} +(-8.94413 + 2.39657i) q^{83} +(2.57665 - 4.46290i) q^{84} +(2.93632 - 1.49608i) q^{85} +(-4.32475 + 2.49689i) q^{86} +(0.802941 - 2.99661i) q^{87} +(3.56643 - 0.955621i) q^{88} -11.3115 q^{89} +(1.87531 + 1.21788i) q^{90} +30.9160i q^{91} +(-4.00981 + 4.00981i) q^{92} +(-2.87161 + 4.77010i) q^{93} -1.46609i q^{94} +(5.23226 - 16.1024i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-4.56736 - 4.56736i) q^{97} +(-5.06162 - 18.8902i) q^{98} +(1.84612 + 3.19757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

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