LMFDB - Embedded newform 690.2.x.a.647.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			647.34
Character	$\chi$	$=$	690.647
Dual form			690.2.x.a.353.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.800541 + 0.599278i) q^{2} +(-0.499902 + 1.65834i) q^{3} +(0.281733 + 0.959493i) q^{4} +(2.04155 + 0.912170i) q^{5} +(-1.39400 + 1.02799i) q^{6} +(-2.52716 - 0.549750i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.50020 - 1.65802i) q^{9} +O(q^{10})$	\(q+(0.800541 + 0.599278i) q^{2} +(-0.499902 + 1.65834i) q^{3} +(0.281733 + 0.959493i) q^{4} +(2.04155 + 0.912170i) q^{5} +(-1.39400 + 1.02799i) q^{6} +(-2.52716 - 0.549750i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.50020 - 1.65802i) q^{9} +(1.08771 + 1.95369i) q^{10} +(-6.20249 - 0.891783i) q^{11} +(-1.73201 - 0.0124434i) q^{12} +(-5.27264 + 1.14699i) q^{13} +(-1.69364 - 1.95457i) q^{14} +(-2.53327 + 2.92960i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(3.90935 - 2.13467i) q^{17} +(-1.00790 - 2.82562i) q^{18} +(2.03960 + 6.94625i) q^{19} +(-0.300048 + 2.21585i) q^{20} +(2.17501 - 3.91607i) q^{21} +(-4.43092 - 4.43092i) q^{22} +(-4.75118 + 0.652932i) q^{23} +(-1.37909 - 1.04791i) q^{24} +(3.33589 + 3.72449i) q^{25} +(-4.90833 - 2.24156i) q^{26} +(3.99941 - 3.31734i) q^{27} +(-0.184502 - 2.57967i) q^{28} +(4.95509 + 1.45495i) q^{29} +(-3.78363 + 0.827136i) q^{30} +(3.82329 + 8.37183i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(4.57952 - 9.84004i) q^{33} +(4.40886 + 0.633898i) q^{34} +(-4.65787 - 3.42754i) q^{35} +(0.886468 - 2.86604i) q^{36} +(-0.158639 + 2.21806i) q^{37} +(-2.52995 + 6.78305i) q^{38} +(0.733696 - 9.31722i) q^{39} +(-1.56811 + 1.59406i) q^{40} +(4.36817 + 3.78504i) q^{41} +(4.08800 - 1.83155i) q^{42} +(0.678875 + 1.82014i) q^{43} +(-0.891783 - 6.20249i) q^{44} +(-3.59190 - 5.66553i) q^{45} +(-4.19480 - 2.32458i) q^{46} +(4.54693 - 4.54693i) q^{47} +(-0.476023 - 1.66535i) q^{48} +(-0.283114 - 0.129294i) q^{49} +(0.438517 + 4.98073i) q^{50} +(1.58572 + 7.55017i) q^{51} +(-2.58600 - 4.73591i) q^{52} +(-4.24020 - 0.922400i) q^{53} +(5.18970 - 0.258906i) q^{54} +(-11.8493 - 7.47835i) q^{55} +(1.39824 - 2.17570i) q^{56} +(-12.5389 - 0.0900838i) q^{57} +(3.09484 + 4.13422i) q^{58} +(4.84016 + 3.11058i) q^{59} +(-3.52464 - 1.60529i) q^{60} +(-0.196690 - 0.430690i) q^{61} +(-1.95635 + 8.99320i) q^{62} +(5.40690 + 5.56455i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(-11.8106 - 2.46789i) q^{65} +(9.56301 - 5.13296i) q^{66} +(-1.84642 + 2.46652i) q^{67} +(3.14959 + 3.14959i) q^{68} +(1.29234 - 8.20548i) q^{69} +(-1.67477 - 5.53525i) q^{70} +(-5.04374 + 0.725180i) q^{71} +(2.42721 - 1.76314i) q^{72} +(1.38692 - 2.53996i) q^{73} +(-1.45623 + 1.68058i) q^{74} +(-7.84410 + 3.67017i) q^{75} +(-6.09026 + 3.91397i) q^{76} +(15.1844 + 5.66350i) q^{77} +(6.17096 - 7.01913i) q^{78} +(2.15836 - 3.35847i) q^{79} +(-2.21062 + 0.336382i) q^{80} +(3.50196 + 8.29073i) q^{81} +(1.22861 + 5.64783i) q^{82} +(-0.134088 + 1.87480i) q^{83} +(4.37021 + 0.983617i) q^{84} +(9.92833 - 0.792049i) q^{85} +(-0.547299 + 1.86393i) q^{86} +(-4.88986 + 7.48990i) q^{87} +(3.00310 - 5.49977i) q^{88} +(5.01417 - 10.9795i) q^{89} +(0.519768 - 6.68804i) q^{90} +13.9554 q^{91} +(-1.96504 - 4.37477i) q^{92} +(-15.7946 + 2.15522i) q^{93} +(6.36487 - 0.915131i) q^{94} +(-2.17220 + 16.0416i) q^{95} +(0.616933 - 1.61845i) q^{96} +(5.04569 - 0.360875i) q^{97} +(-0.149161 - 0.273169i) q^{98} +(14.0288 + 12.5135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$3$	−0.499902	+	1.65834i	−0.288618	+	0.957444i
$3$	−0.499902	+	1.65834i	−0.288618	+	0.957444i
$4$	0.281733	+	0.959493i	0.140866	+	0.479746i
$5$	2.04155	+	0.912170i	0.913011	+	0.407935i
$5$	2.04155	+	0.912170i	0.913011	+	0.407935i
$6$	−1.39400	+	1.02799i	−0.569098	+	0.419676i
$7$	−2.52716	−	0.549750i	−0.955177	−	0.207786i	−0.292142	−	0.956375i	$-0.594368\pi$
$7$	−2.52716	−	0.549750i	−0.955177	−	0.207786i	−0.663034	+	0.748589i	$0.730732\pi$
$8$	−0.349464	+	0.936950i	−0.123554	+	0.331262i
$9$	−2.50020	−	1.65802i	−0.833399	−	0.552672i
$10$	1.08771	+	1.95369i	0.343963	+	0.617810i
$11$	−6.20249	−	0.891783i	−1.87012	−	0.268883i	−0.888380	−	0.459108i	$-0.848169\pi$
$11$	−6.20249	−	0.891783i	−1.87012	−	0.268883i	−0.981740	+	0.190226i	$0.939078\pi$
$12$	−1.73201	−	0.0124434i	−0.499987	−	0.00359209i
$13$	−5.27264	+	1.14699i	−1.46237	+	0.318118i	−0.872195	−	0.489159i	$-0.837304\pi$
$13$	−5.27264	+	1.14699i	−1.46237	+	0.318118i	−0.590172	+	0.807278i	$0.700940\pi$
$14$	−1.69364	−	1.95457i	−0.452645	−	0.522380i
$15$	−2.53327	+	2.92960i	−0.654087	+	0.756420i
$16$	−0.841254	+	0.540641i	−0.210313	+	0.135160i
$17$	3.90935	−	2.13467i	0.948157	−	0.517733i	0.0707576	−	0.997494i	$-0.477458\pi$
$17$	3.90935	−	2.13467i	0.948157	−	0.517733i	0.877399	+	0.479761i	$0.159277\pi$
$18$	−1.00790	−	2.82562i	−0.237564	−	0.666006i
$19$	2.03960	+	6.94625i	0.467917	+	1.59358i	0.768517	+	0.639829i	$0.220995\pi$
$19$	2.03960	+	6.94625i	0.467917	+	1.59358i	−0.300600	+	0.953750i	$0.597187\pi$
$20$	−0.300048	+	2.21585i	−0.0670928	+	0.495478i
$21$	2.17501	−	3.91607i	0.474625	−	0.854557i
$22$	−4.43092	−	4.43092i	−0.944676	−	0.944676i
$23$	−4.75118	+	0.652932i	−0.990689	+	0.136146i
$23$	−4.75118	+	0.652932i	−0.990689	+	0.136146i
$24$	−1.37909	−	1.04791i	−0.281505	−	0.213905i
$25$	3.33589	+	3.72449i	0.667179	+	0.744898i
$26$	−4.90833	−	2.24156i	−0.962603	−	0.439606i
$27$	3.99941	−	3.31734i	0.769687	−	0.638421i
$28$	−0.184502	−	2.57967i	−0.0348676	−	0.487513i
$29$	4.95509	+	1.45495i	0.920137	+	0.270177i	0.707302	−	0.706912i	$-0.249912\pi$
$29$	4.95509	+	1.45495i	0.920137	+	0.270177i	0.212835	+	0.977088i	$0.431730\pi$
$30$	−3.78363	+	0.827136i	−0.690793	+	0.151014i
$31$	3.82329	+	8.37183i	0.686682	+	1.50362i	0.855404	+	0.517961i	$0.173309\pi$
$31$	3.82329	+	8.37183i	0.686682	+	1.50362i	−0.168722	+	0.985664i	$0.553964\pi$
$32$	−0.997452	−	0.0713392i	−0.176326	−	0.0126111i
$33$	4.57952	−	9.84004i	0.797192	−	1.71293i
$34$	4.40886	+	0.633898i	0.756112	+	0.108713i
$35$	−4.65787	−	3.42754i	−0.787324	−	0.579361i
$36$	0.886468	−	2.86604i	0.147745	−	0.477673i
$37$	−0.158639	+	2.21806i	−0.0260800	+	0.364647i	0.967607	+	0.252461i	$0.0812398\pi$
$37$	−0.158639	+	2.21806i	−0.0260800	+	0.364647i	−0.993687	+	0.112186i	$0.964215\pi$
$38$	−2.52995	+	6.78305i	−0.410412	+	1.10036i
$39$	0.733696	−	9.31722i	0.117485	−	1.49195i
$40$	−1.56811	+	1.59406i	−0.247940	+	0.252044i
$41$	4.36817	+	3.78504i	0.682194	+	0.591124i	0.925465	−	0.378834i	$-0.123675\pi$
$41$	4.36817	+	3.78504i	0.682194	+	0.591124i	−0.243271	+	0.969958i	$0.578220\pi$
$42$	4.08800	−	1.83155i	0.630792	−	0.282614i
$43$	0.678875	+	1.82014i	0.103528	+	0.277568i	0.978378	−	0.206825i	$-0.0663131\pi$
$43$	0.678875	+	1.82014i	0.103528	+	0.277568i	−0.874850	+	0.484393i	$0.839040\pi$
$44$	−0.891783	−	6.20249i	−0.134441	−	0.935060i
$45$	−3.59190	−	5.66553i	−0.535448	−	0.844568i
$46$	−4.19480	−	2.32458i	−0.618490	−	0.342740i
$47$	4.54693	−	4.54693i	0.663237	−	0.663237i	−0.292904	−	0.956142i	$-0.594622\pi$
$47$	4.54693	−	4.54693i	0.663237	−	0.663237i	0.956142	+	0.292904i	$0.0946217\pi$
$48$	−0.476023	−	1.66535i	−0.0687080	−	0.240373i
$49$	−0.283114	−	0.129294i	−0.0404448	−	0.0184705i
$50$	0.438517	+	4.98073i	0.0620156	+	0.704382i
$51$	1.58572	+	7.55017i	0.222045	+	1.05723i
$52$	−2.58600	−	4.73591i	−0.358614	−	0.656753i
$53$	−4.24020	−	0.922400i	−0.582437	−	0.126701i	−0.0883127	−	0.996093i	$-0.528147\pi$
$53$	−4.24020	−	0.922400i	−0.582437	−	0.126701i	−0.494124	+	0.869391i	$0.664511\pi$
$54$	5.18970	−	0.258906i	0.706228	−	0.0352326i
$55$	−11.8493	−	7.47835i	−1.59775	−	1.00838i
$56$	1.39824	−	2.17570i	0.186848	−	0.290741i
$57$	−12.5389	−	0.0900838i	−1.66081	−	0.0119319i
$58$	3.09484	+	4.13422i	0.406372	+	0.542850i
$59$	4.84016	+	3.11058i	0.630135	+	0.404963i	0.816360	−	0.577544i	$-0.195989\pi$
$59$	4.84016	+	3.11058i	0.630135	+	0.404963i	−0.186224	+	0.982507i	$0.559625\pi$
$60$	−3.52464	−	1.60529i	−0.455028	−	0.207242i
$61$	−0.196690	−	0.430690i	−0.0251835	−	0.0551442i	0.896622	−	0.442796i	$-0.146013\pi$
$61$	−0.196690	−	0.430690i	−0.0251835	−	0.0551442i	−0.921806	+	0.387652i	$0.873286\pi$
$62$	−1.95635	+	8.99320i	−0.248457	+	1.14214i
$63$	5.40690	+	5.56455i	0.681205	+	0.701068i
$64$	−0.755750	−	0.654861i	−0.0944687	−	0.0818576i
$65$	−11.8106	−	2.46789i	−1.46493	−	0.306104i
$66$	9.56301	−	5.13296i	1.17713	−	0.631823i
$67$	−1.84642	+	2.46652i	−0.225576	+	0.301334i	−0.899023	−	0.437901i	$-0.855722\pi$
$67$	−1.84642	+	2.46652i	−0.225576	+	0.301334i	0.673447	+	0.739235i	$0.264813\pi$
$68$	3.14959	+	3.14959i	0.381944	+	0.381944i
$69$	1.29234	−	8.20548i	0.155579	−	0.987823i
$70$	−1.67477	−	5.53525i	−0.200173	−	0.661589i
$71$	−5.04374	+	0.725180i	−0.598582	+	0.0860631i	−0.434944	−	0.900457i	$-0.643232\pi$
$71$	−5.04374	+	0.725180i	−0.598582	+	0.0860631i	−0.163638	+	0.986521i	$0.552323\pi$
$72$	2.42721	−	1.76314i	0.286049	−	0.207788i
$73$	1.38692	−	2.53996i	0.162327	−	0.297280i	−0.783837	−	0.620966i	$-0.786740\pi$
$73$	1.38692	−	2.53996i	0.162327	−	0.297280i	0.946165	+	0.323686i	$0.104922\pi$
$74$	−1.45623	+	1.68058i	−0.169283	+	0.195363i
$75$	−7.84410	+	3.67017i	−0.905758	+	0.423795i
$76$	−6.09026	+	3.91397i	−0.698600	+	0.448963i
$77$	15.1844	+	5.66350i	1.73043	+	0.645415i
$78$	6.17096	−	7.01913i	0.698723	−	0.794760i
$79$	2.15836	−	3.35847i	0.242834	−	0.377858i	−0.698347	−	0.715759i	$-0.746081\pi$
$79$	2.15836	−	3.35847i	0.242834	−	0.377858i	0.941181	+	0.337902i	$0.109717\pi$
$80$	−2.21062	+	0.336382i	−0.247155	+	0.0376086i
$81$	3.50196	+	8.29073i	0.389107	+	0.921193i
$82$	1.22861	+	5.64783i	0.135677	+	0.623699i
$83$	−0.134088	+	1.87480i	−0.0147181	+	0.205786i	0.984772	+	0.173852i	$0.0556213\pi$
$83$	−0.134088	+	1.87480i	−0.0147181	+	0.205786i	−0.999490	+	0.0319345i	$0.989833\pi$
$84$	4.37021	+	0.983617i	0.476830	+	0.107321i
$85$	9.92833	−	0.792049i	1.07688	−	0.0859097i
$86$	−0.547299	+	1.86393i	−0.0590167	+	0.200993i
$87$	−4.88986	+	7.48990i	−0.524248	+	0.803002i
$88$	3.00310	−	5.49977i	0.320132	−	0.586278i
$89$	5.01417	−	10.9795i	0.531501	−	1.16383i	−0.433398	−	0.901203i	$-0.642685\pi$
$89$	5.01417	−	10.9795i	0.531501	−	1.16383i	0.964899	−	0.262622i	$-0.0845873\pi$
$90$	0.519768	−	6.68804i	0.0547883	−	0.704981i
$91$	13.9554			1.46292
$92$	−1.96504	−	4.37477i	−0.204870	−	0.456101i
$93$	−15.7946	+	2.15522i	−1.63783	+	0.223486i
$94$	6.36487	−	0.915131i	0.656487	−	0.0943885i
$95$	−2.17220	+	16.0416i	−0.222863	+	1.64584i
$96$	0.616933	−	1.61845i	0.0629655	−	0.165183i
$97$	5.04569	−	0.360875i	0.512312	−	0.0366413i	0.187209	−	0.982320i	$-0.440056\pi$
$97$	5.04569	−	0.360875i	0.512312	−	0.0366413i	0.325103	+	0.945679i	$0.394601\pi$
$98$	−0.149161	−	0.273169i	−0.0150676	−	0.0275942i
$99$	14.0288	+	12.5135i	1.40995	+	1.25765i
$100$	−2.63379	+	4.25008i	−0.263379	+	0.425008i
$101$	−1.94958	+	1.68932i	−0.193990	+	0.168093i	−0.746440	−	0.665453i	$-0.768239\pi$
$101$	−1.94958	+	1.68932i	−0.193990	+	0.168093i	0.552450	+	0.833546i	$0.313693\pi$
$102$	−3.25521	+	6.99450i	−0.322314	+	0.692559i
$103$	−1.67662	−	2.23970i	−0.165202	−	0.220684i	0.710299	−	0.703900i	$-0.248560\pi$
$103$	−1.67662	−	2.23970i	−0.165202	−	0.220684i	−0.875501	+	0.483216i	$0.839469\pi$
$104$	0.767924	−	5.34103i	0.0753011	−	0.523731i
$105$	8.01252	−	6.01091i	0.781942	−	0.586604i
$106$	−2.84168	−	3.27948i	−0.276009	−	0.318531i
$107$	−13.0433	−	4.86491i	−1.26095	−	0.470308i	−0.371962	−	0.928248i	$-0.621315\pi$
$107$	−13.0433	−	4.86491i	−1.26095	−	0.470308i	−0.888983	+	0.457940i	$0.848588\pi$
$108$	4.30972	+	2.90281i	0.414703	+	0.279323i
$109$	0.0822916	−	0.280260i	0.00788211	−	0.0268440i	−0.955458	−	0.295127i	$-0.904638\pi$
$109$	0.0822916	−	0.280260i	0.00788211	−	0.0268440i	0.963340	+	0.268283i	$0.0864562\pi$
$110$	−5.00422	−	13.0877i	−0.477133	−	1.24787i
$111$	−3.59900	−	1.37189i	−0.341602	−	0.130214i
$112$	2.42320	−	0.903807i	0.228971	−	0.0854017i
$113$	−7.86383	+	10.5048i	−0.739767	+	0.988213i	0.259978	+	0.965615i	$0.416285\pi$
$113$	−7.86383	+	10.5048i	−0.739767	+	0.988213i	−0.999745	+	0.0225981i	$0.992806\pi$
$114$	−9.98389	−	7.58638i	−0.935077	−	0.710529i
$115$	−10.2954	−	3.00088i	−0.960048	−	0.279834i
$116$			5.16428i			0.479491i
$117$	15.0844	+	5.87441i	1.39455	+	0.543090i
$118$	2.01065	+	5.39075i	0.185095	+	0.496259i
$119$	−11.0531	+	3.24548i	−1.01323	+	0.297513i
$120$	−1.85960	−	3.39733i	−0.169758	−	0.310133i
$121$	27.1212	+	7.96349i	2.46556	+	0.723954i
$122$	0.100645	−	0.462657i	0.00911195	−	0.0418870i
$123$	−8.46055	+	5.35177i	−0.762862	+	0.482553i
$124$	−6.95557	+	6.02703i	−0.624628	+	0.541243i
$125$	3.41304	+	10.6466i	0.305272	+	0.952265i
$126$	0.993734	+	7.69489i	0.0885288	+	0.685515i
$127$	7.16454	−	5.36331i	0.635750	−	0.475916i	−0.232134	−	0.972684i	$-0.574571\pi$
$127$	7.16454	−	5.36331i	0.635750	−	0.475916i	0.867884	+	0.496767i	$0.165480\pi$
$128$	−0.212565	−	0.977147i	−0.0187883	−	0.0863684i
$129$	−3.35778	+	0.215919i	−0.295636	+	0.0190106i
$130$	−7.97594	−	9.05350i	−0.699537	−	0.794044i
$131$	6.92225	+	10.7712i	0.604800	+	0.941087i	0.999749	+	0.0223841i	$0.00712567\pi$
$131$	6.92225	+	10.7712i	0.604800	+	0.941087i	−0.394950	+	0.918703i	$0.629238\pi$
$132$	10.7317	+	1.62175i	0.934070	+	0.141156i
$133$	−1.33570	−	18.6756i	−0.115820	−	1.61938i
$134$	−2.95626	+	0.868037i	−0.255382	+	0.0749870i
$135$	11.1910	−	3.12438i	0.963167	−	0.268904i
$136$	0.633898	+	4.40886i	0.0543563	+	0.378056i
$137$	7.41797	−	7.41797i	0.633760	−	0.633760i	−0.315249	−	0.949009i	$-0.602088\pi$
$137$	7.41797	−	7.41797i	0.633760	−	0.633760i	0.949009	+	0.315249i	$0.102088\pi$
$138$	5.95193	−	5.79435i	0.506662	−	0.493248i
$139$		−	7.19528i		−	0.610296i	−0.952305	−	0.305148i	$-0.901294\pi$
$139$		−	7.19528i		−	0.610296i	0.952305	−	0.305148i	$-0.0987059\pi$
$140$	1.97643	−	5.43484i	0.167039	−	0.459328i
$141$	5.26734	+	9.81338i	0.443590	+	0.826435i
$142$	−4.47231	−	2.44206i	−0.375308	−	0.204933i
$143$	33.7263	−	2.41216i	2.82034	−	0.201715i
$144$	2.99969	+	0.0431040i	0.249974	+	0.00359200i
$145$	8.78893	+	7.49023i	0.729881	+	0.622030i
$146$	2.63243	−	1.20219i	0.217862	−	0.0994941i
$147$	0.355942	−	0.404865i	0.0293576	−	0.0333927i
$148$	−2.17291	+	0.472687i	−0.178612	+	0.0388546i
$149$	−0.448659	+	3.12049i	−0.0367555	+	0.255640i	−0.999912	−	0.0133031i	$-0.995765\pi$
$149$	−0.448659	+	3.12049i	−0.0367555	+	0.255640i	0.963156	+	0.268943i	$0.0866745\pi$
$150$	−8.47897	−	1.76267i	−0.692305	−	0.143921i
$151$	−0.0524966	−	0.0337375i	−0.00427212	−	0.00274552i	0.538503	−	0.842624i	$-0.318990\pi$
$151$	−0.0524966	−	0.0337375i	−0.00427212	−	0.00274552i	−0.542775	+	0.839878i	$0.682626\pi$
$152$	−7.22106	−	0.516460i	−0.585705	−	0.0418905i
$153$	−13.3135	−	1.14468i	−1.07633	−	0.0925420i
$154$	8.76175	+	13.6335i	0.706042	+	1.09862i
$155$	0.168920	+	20.5790i	0.0135680	+	1.65295i
$156$	9.14651	−	1.92099i	0.732307	−	0.153802i
$157$	2.76473	+	1.50966i	0.220650	+	0.120484i	0.585772	−	0.810476i	$-0.300791\pi$
$157$	2.76473	+	1.50966i	0.220650	+	0.120484i	−0.365123	+	0.930959i	$0.618973\pi$
$158$	3.74051	−	1.39514i	0.297579	−	0.110991i
$159$	3.64934	−	6.57060i	0.289411	−	0.521082i
$160$	−1.97128	−	1.05549i	−0.155843	−	0.0834437i
$161$	12.3659	+	0.961896i	0.974572	+	0.0758080i
$162$	−2.16499	+	8.73572i	−0.170097	+	0.686343i
$163$	−12.2319	−	9.15668i	−0.958075	−	0.717206i	0.00110558	−	0.999999i	$-0.499648\pi$
$163$	−12.2319	−	9.15668i	−0.958075	−	0.717206i	−0.959181	+	0.282793i	$0.908739\pi$
$164$	−2.40107	+	5.25760i	−0.187492	+	0.410550i
$165$	18.3251	−	15.9117i	1.42661	−	1.23872i
$166$	−1.23087	+	1.42050i	−0.0955341	+	0.110252i
$167$	−7.55098	+	4.12314i	−0.584312	+	0.319058i	−0.744074	−	0.668097i	$-0.767109\pi$
$167$	−7.55098	+	4.12314i	−0.584312	+	0.319058i	0.159762	+	0.987156i	$0.448927\pi$
$168$	2.90908	+	3.40640i	0.224440	+	0.262809i
$169$	14.6599	−	6.69495i	1.12768	−	0.514996i
$170$	8.42270	+	5.31576i	0.645991	+	0.407700i
$171$	6.41759	−	20.7487i	0.490765	−	1.58669i
$172$	−1.55515	+	1.16417i	−0.118579	+	0.0887669i
$173$	−8.99626	+	6.73452i	−0.683973	+	0.512016i	−0.883829	−	0.467809i	$-0.845043\pi$
$173$	−8.99626	+	6.73452i	−0.683973	+	0.512016i	0.199856	+	0.979825i	$0.435952\pi$
$174$	−8.40306	+	3.06560i	−0.637035	+	0.232402i
$175$	−6.38280	−	11.2463i	−0.482494	−	0.850139i
$176$	5.70000	−	2.60310i	0.429654	−	0.196216i
$177$	−7.57802	+	6.47166i	−0.569599	+	0.486440i
$178$	10.5938	−	5.78466i	0.794041	−	0.433579i
$179$	−8.48277	+	9.78963i	−0.634032	+	0.731712i	−0.978308	−	0.207157i	$-0.933579\pi$
$179$	−8.48277	+	9.78963i	−0.634032	+	0.731712i	0.344276	+	0.938868i	$0.388124\pi$
$180$	4.42409	−	5.04256i	0.329752	−	0.375851i
$181$	−7.87130	+	17.2357i	−0.585069	+	1.28112i	0.353307	+	0.935507i	$0.385057\pi$
$181$	−7.87130	+	17.2357i	−0.585069	+	1.28112i	−0.938376	+	0.345615i	$0.887670\pi$
$182$	11.1718	+	8.36313i	0.828112	+	0.619917i
$183$	0.812557	−	0.110876i	0.0600659	−	0.00819617i
$184$	1.04860	−	4.67979i	0.0773039	−	0.344999i
$185$	−2.34712	+	4.38358i	−0.172563	+	0.322287i
$186$	−13.9358	−	7.74002i	−1.02182	−	0.567526i
$187$	−26.1514	+	9.75396i	−1.91238	+	0.713280i
$188$	5.64376	+	3.08173i	0.411614	+	0.224758i
$189$	−11.9309	+	6.18476i	−0.867842	+	0.449875i
$190$	−11.3523	+	11.5402i	−0.823584	+	0.837216i
$191$	−6.99651	−	10.8868i	−0.506250	−	0.787740i	0.490228	−	0.871594i	$-0.336913\pi$
$191$	−6.99651	−	10.8868i	−0.506250	−	0.787740i	−0.996478	+	0.0838538i	$0.973277\pi$
$192$	1.46378	−	0.925925i	0.105639	−	0.0668229i
$193$	−17.7464	−	1.26925i	−1.27741	−	0.0913624i	−0.583911	−	0.811817i	$-0.698478\pi$
$193$	−17.7464	−	1.26925i	−1.27741	−	0.0913624i	−0.693502	+	0.720455i	$0.743933\pi$
$194$	4.25554	+	2.73487i	0.305530	+	0.196352i
$195$	9.99677	−	18.3524i	0.715883	−	1.31424i
$196$	0.0442940	−	0.308072i	0.00316386	−	0.0220051i
$197$	8.04165	−	1.74935i	0.572944	−	0.124636i	0.0832467	−	0.996529i	$-0.473471\pi$
$197$	8.04165	−	1.74935i	0.572944	−	0.124636i	0.489697	+	0.871893i	$0.337107\pi$
$198$	3.73163	+	18.4247i	0.265196	+	1.30939i
$199$	3.01064	−	1.37491i	0.213418	−	0.0974649i	−0.305838	−	0.952084i	$-0.598936\pi$
$199$	3.01064	−	1.37491i	0.213418	−	0.0974649i	0.519256	+	0.854619i	$0.326209\pi$
$200$	−4.65543	+	1.82399i	−0.329189	+	0.128975i
$201$	−3.16731	−	4.29501i	−0.223405	−	0.302947i
$202$	−2.57309	+	0.184031i	−0.181042	+	0.0129484i
$203$	−11.7224	−	6.40094i	−0.822754	−	0.449258i
$204$	−6.79758	+	3.64861i	−0.475926	+	0.255454i
$205$	5.46526	+	11.7119i	0.381710	+	0.817994i
$206$		−	2.79773i		−	0.194927i
$207$	12.9614	+	6.24507i	0.900883	+	0.434062i
$208$	3.81551	−	3.81551i	0.264558	−	0.264558i
$209$	−6.45607	−	44.9029i	−0.446575	−	3.10600i
$210$	10.0166	−	0.0102561i	0.691208	−	0.000707741i
$211$	3.15697	−	0.926969i	0.217335	−	0.0638152i	−0.171253	−	0.985227i	$-0.554781\pi$
$211$	3.15697	−	0.926969i	0.217335	−	0.0638152i	0.388587	+	0.921412i	$0.372963\pi$
$212$	−0.309567	−	4.32832i	−0.0212612	−	0.297270i
$213$	1.31878	−	8.72677i	0.0903612	−	0.597948i
$214$	−7.52628	−	11.7111i	−0.514486	−	0.800556i
$215$	−0.274311	+	4.33516i	−0.0187079	+	0.295655i
$216$	1.71053	+	4.90654i	0.116387	+	0.333848i
$217$	−5.05964	−	23.2588i	−0.343471	−	1.57891i
$218$	0.233831	−	0.175044i	0.0158370	−	0.0118555i
$219$	3.51880	+	3.56973i	0.237779	+	0.241220i
$220$	3.83710	−	13.4762i	0.258697	−	0.908564i
$221$	−18.1641	+	15.7393i	−1.22185	+	1.05874i
$222$	−2.05900	−	3.25505i	−0.138191	−	0.218465i
$223$	−5.84600	+	26.8736i	−0.391477	+	1.79959i	0.185292	+	0.982684i	$0.440677\pi$
$223$	−5.84600	+	26.8736i	−0.391477	+	1.79959i	−0.576769	+	0.816907i	$0.695687\pi$
$224$	2.48150	+	0.728635i	0.165802	+	0.0486840i
$225$	−2.16512	−	14.8429i	−0.144342	−	0.989528i
$226$	−12.5906	+	3.69694i	−0.837517	+	0.245917i
$227$	−0.695365	−	1.86435i	−0.0461530	−	0.123741i	0.911828	−	0.410572i	$-0.134671\pi$
$227$	−0.695365	−	1.86435i	−0.0461530	−	0.123741i	−0.957981	+	0.286831i	$0.907398\pi$
$228$	−3.44617	−	12.0563i	−0.228228	−	0.798450i
$229$			2.15417i			0.142351i	0.997464	+	0.0711756i	$0.0226751\pi$
$229$			2.15417i			0.142351i	−0.997464	+	0.0711756i	$0.977325\pi$
$230$	−6.44351	−	8.57212i	−0.424872	−	0.565229i
$231$	−16.9827	+	22.3498i	−1.11738	+	1.47051i
$232$	−3.09484	+	4.13422i	−0.203186	+	0.271425i
$233$	9.09367	−	3.39176i	0.595746	−	0.222202i	−0.0334603	−	0.999440i	$-0.510653\pi$
$233$	9.09367	−	3.39176i	0.595746	−	0.222202i	0.629206	+	0.777238i	$0.283380\pi$
$234$	8.55525	+	13.7424i	0.559274	+	0.898371i
$235$	13.4304	−	5.13523i	0.876101	−	0.334986i
$236$	−1.62095	+	5.52045i	−0.105515	+	0.359351i
$237$	4.49053	+	5.25820i	0.291691	+	0.341557i
$238$	−10.7934	−	4.02573i	−0.699632	−	0.260949i
$239$	17.1083	+	19.7441i	1.10665	+	1.27714i	0.957535	+	0.288317i	$0.0930957\pi$
$239$	17.1083	+	19.7441i	1.10665	+	1.27714i	0.149111	+	0.988820i	$0.452359\pi$
$240$	0.547257	−	3.83412i	0.0353253	−	0.247492i
$241$	2.82688	−	19.6614i	0.182095	−	1.26650i	−0.669702	−	0.742630i	$-0.733578\pi$
$241$	2.82688	−	19.6614i	0.182095	−	1.26650i	0.851797	−	0.523871i	$-0.175513\pi$
$242$	16.9393	+	22.6282i	1.08890	+	1.45460i
$243$	−15.4995	+	1.66290i	−0.994294	+	0.106675i
$244$	0.357830	−	0.310062i	0.0229077	−	0.0198497i
$245$	−0.460054	−	0.522208i	−0.0293918	−	0.0333626i
$246$	−9.98022	−	0.785905i	−0.636316	−	0.0501075i
$247$	−18.7214	−	34.2857i	−1.19121	−	2.18154i
$248$	−9.18008	+	0.656573i	−0.582936	+	0.0416924i
$249$	−3.04203	−	1.15958i	−0.192781	−	0.0734855i
$250$	−3.64802	+	10.5684i	−0.230721	+	0.668407i
$251$	0.273494	−	0.0393225i	0.0172628	−	0.00248201i	−0.133678	−	0.991025i	$-0.542679\pi$
$251$	0.273494	−	0.0393225i	0.0172628	−	0.00248201i	0.150941	+	0.988543i	$0.451770\pi$
$252$	−3.81585	+	6.75560i	−0.240376	+	0.425563i
$253$	30.0514	+	0.187217i	1.88931	+	0.0117702i
$254$	8.94962			0.561549
$255$	−3.64970	+	16.8605i	−0.228553	+	1.05585i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−10.0933	+	18.4845i	−0.629603	+	1.15303i	0.346976	+	0.937874i	$0.387209\pi$
$257$	−10.0933	+	18.4845i	−0.629603	+	1.15303i	−0.976579	+	0.215158i	$0.930973\pi$
$258$	−2.81743	−	1.83939i	−0.175406	−	0.114515i
$259$	1.62028	−	5.51818i	0.100679	−	0.342883i
$260$	−0.959513	−	12.0275i	−0.0595065	−	0.745914i
$261$	−9.97637	−	11.8533i	−0.617522	−	0.733699i
$262$	−0.913412	+	12.7712i	−0.0564308	+	0.789005i
$263$	−5.23707	−	24.0744i	−0.322931	−	1.48449i	−0.796987	−	0.603996i	$-0.793574\pi$
$263$	−5.23707	−	24.0744i	−0.322931	−	1.48449i	0.474056	−	0.880495i	$-0.342790\pi$
$264$	7.61925	+	7.72952i	0.468932	+	0.475719i
$265$	−7.81522	−	5.75092i	−0.480085	−	0.353276i
$266$	10.1226	−	15.7510i	0.620654	−	0.965756i
$267$	15.7012	+	13.8039i	0.960897	+	0.844784i
$268$	−2.88681	−	1.07672i	−0.176340	−	0.0657713i
$269$	−6.60017	+	4.24167i	−0.402420	+	0.258619i	−0.726159	−	0.687527i	$-0.758696\pi$
$269$	−6.60017	+	4.24167i	−0.402420	+	0.258619i	0.323739	+	0.946146i	$0.395060\pi$
$270$	10.8312	+	4.20531i	0.659167	+	0.255927i
$271$	15.9937	−	18.4577i	0.971548	−	1.12123i	−0.0210500	−	0.999778i	$-0.506701\pi$
$271$	15.9937	−	18.4577i	0.971548	−	1.12123i	0.992598	−	0.121448i	$-0.0387536\pi$
$272$	−2.13467	+	3.90935i	−0.129433	+	0.237039i
$273$	−6.97631	+	23.1428i	−0.422225	+	1.40066i
$274$	10.3838	−	1.49297i	0.627309	−	0.0901934i
$275$	−17.3694	−	26.0760i	−1.04741	−	1.57244i
$276$	8.23719	−	1.07176i	0.495821	−	0.0645125i
$277$	11.3008	+	11.3008i	0.679000	+	0.679000i	0.959774	−	0.280774i	$-0.0905911\pi$
$277$	11.3008	+	11.3008i	0.679000	+	0.679000i	−0.280774	+	0.959774i	$0.590591\pi$
$278$	4.31197	−	5.76012i	0.258615	−	0.345469i
$279$	4.32166	−	27.2703i	0.258731	−	1.63263i
$280$	4.83919	−	3.16639i	0.289197	−	0.189228i
$281$	−3.29041	−	2.85115i	−0.196289	−	0.170086i	0.551171	−	0.834393i	$-0.314181\pi$
$281$	−3.29041	−	2.85115i	−0.196289	−	0.170086i	−0.747460	+	0.664307i	$0.768727\pi$
$282$	−1.66421	+	11.0126i	−0.0991024	+	0.655792i
$283$	0.553031	−	2.54224i	0.0328743	−	0.151121i	−0.957784	−	0.287489i	$-0.907180\pi$
$283$	0.553031	−	2.54224i	0.0328743	−	0.151121i	0.990658	+	0.136369i	$0.0435431\pi$
$284$	−2.11679	−	4.63513i	−0.125608	−	0.275044i
$285$	−25.5166	−	11.6215i	−1.51147	−	0.688397i
$286$	28.4449	+	18.2804i	1.68198	+	1.08094i
$287$	−8.95824	−	11.9668i	−0.528788	−	0.706378i
$288$	2.37554	+	1.83215i	0.139980	+	0.107961i
$289$	1.53533	−	2.38902i	0.0903135	−	0.140531i
$290$	2.54717	+	11.2633i	0.149575	+	0.661401i
$291$	−1.92389	+	8.54788i	−0.112781	+	0.501085i
$292$	2.82782	+	0.615154i	0.165486	+	0.0359992i
$293$	−3.66184	−	6.70616i	−0.213927	−	0.391778i	0.748576	−	0.663049i	$-0.230738\pi$
$293$	−3.66184	−	6.70616i	−0.213927	−	0.391778i	−0.962503	+	0.271271i	$0.912556\pi$
$294$	0.527573	−	0.110803i	0.0307687	−	0.00646216i
$295$	7.04408	+	10.7655i	0.410122	+	0.626790i
$296$	−2.02277	−	0.923768i	−0.117571	−	0.0536930i
$297$	−27.7646	+	17.0091i	−1.61107	+	0.986970i
$298$	−2.22921	+	2.22921i	−0.129135	+	0.129135i
$299$	24.3023	−	8.89224i	1.40544	−	0.514251i
$300$	−5.73144	−	6.49235i	−0.330905	−	0.374836i
$301$	−0.715007	−	4.97298i	−0.0412123	−	0.286638i
$302$	−0.0218076	−	0.0584684i	−0.00125488	−	0.00336448i
$303$	−1.82687	−	4.07756i	−0.104951	−	0.234250i
$304$	−5.47125	−	4.74087i	−0.313798	−	0.271907i
$305$	−0.00869011	−	1.05869i	−0.000497594	−	0.0606205i
$306$	−9.97199	−	8.89482i	−0.570061	−	0.508483i
$307$	−7.85636	+	21.0637i	−0.448386	+	1.20217i	0.494536	+	0.869157i	$0.335338\pi$
$307$	−7.85636	+	21.0637i	−0.448386	+	1.20217i	−0.942922	+	0.333013i	$0.891935\pi$
$308$	−1.15614	+	16.1649i	−0.0658771	+	0.921083i
$309$	4.55233	−	1.66077i	0.258973	−	0.0944782i
$310$	−12.1973	+	16.5756i	−0.692762	+	0.941430i
$311$	13.8424	+	1.99024i	0.784930	+	0.112856i	0.523115	−	0.852262i	$-0.324770\pi$
$311$	13.8424	+	1.99024i	0.784930	+	0.112856i	0.261815	+	0.965118i	$0.415679\pi$
$312$	8.47337	+	3.94347i	0.479710	+	0.223255i
$313$	32.4829	+	2.32322i	1.83604	+	0.131316i	0.945918	−	0.324405i	$-0.105164\pi$
$313$	32.4829	+	2.32322i	1.83604	+	0.131316i	0.890122	+	0.455722i	$0.150619\pi$
$314$	1.30858	+	2.86538i	0.0738473	+	0.161703i
$315$	5.96267	+	16.2924i	0.335958	+	0.917970i
$316$	3.83051	+	1.12474i	0.215483	+	0.0632715i
$317$	1.03411	+	14.4587i	0.0580813	+	0.812083i	0.940107	+	0.340881i	$0.110725\pi$
$317$	1.03411	+	14.4587i	0.0580813	+	0.812083i	−0.882025	+	0.471202i	$0.843820\pi$
$318$	6.85906	−	3.07307i	0.384637	−	0.172329i
$319$	−29.4364	−	13.4431i	−1.64812	−	0.752672i
$320$	−0.945560	−	2.02631i	−0.0528584	−	0.113274i
$321$	14.5881	−	19.1983i	0.814226	−	1.07154i
$322$	9.32299	+	8.18066i	0.519550	+	0.455891i
$323$	22.8015	+	22.8015i	1.26871	+	1.26871i
$324$	−6.96828	+	5.69588i	−0.387127	+	0.316438i
$325$	−21.8609	−	15.8116i	−1.21263	−	0.877072i
$326$	−4.30474	−	14.6606i	−0.238417	−	0.811975i
$327$	0.423629	+	0.276570i	0.0234267	+	0.0152944i
$328$	−5.07291	+	2.77002i	−0.280105	+	0.152949i
$329$	−13.9905	+	8.99114i	−0.771320	+	0.495697i
$330$	24.2055	−	1.75613i	1.33247	−	0.0966716i
$331$	2.07711	+	2.39712i	0.114169	+	0.131757i	0.809957	−	0.586489i	$-0.199490\pi$
$331$	2.07711	+	2.39712i	0.114169	+	0.131757i	−0.695789	+	0.718247i	$0.744945\pi$
$332$	−1.83664	+	0.399536i	−0.100799	+	0.0219274i
$333$	4.07421	−	5.28256i	0.223265	−	0.289482i
$334$	−8.51578	−	1.22438i	−0.465962	−	0.0669953i
$335$	−6.01945	+	3.35130i	−0.328878	+	0.183101i
$336$	0.287459	+	4.47031i	0.0156822	+	0.243875i
$337$	5.74673	−	15.4076i	0.313044	−	0.839305i	−0.681193	−	0.732104i	$-0.738539\pi$
$337$	5.74673	−	15.4076i	0.313044	−	0.839305i	0.994237	−	0.107201i	$-0.0341888\pi$
$338$	15.7480	+	3.42577i	0.856578	+	0.186337i
$339$	−13.4895	−	18.2923i	−0.732648	−	0.993502i
$340$	3.55710	+	9.30302i	0.192911	+	0.504527i
$341$	−16.2480	−	55.3357i	−0.879880	−	2.99660i
$342$	17.5718	−	12.7643i	0.950173	−	0.690212i
$343$	15.1373	+	11.3316i	0.817336	+	0.611850i
$344$	−1.94262			−0.104739
$345$	10.1232	−	15.5731i	0.545013	−	0.838428i
$346$	−11.2377			−0.604144
$347$	12.2098	+	9.14011i	0.655454	+	0.490667i	0.874486	−	0.485051i	$-0.161199\pi$
$347$	12.2098	+	9.14011i	0.655454	+	0.490667i	−0.219032	+	0.975718i	$0.570290\pi$
$348$	−8.56414	−	2.58163i	−0.459086	−	0.138390i
$349$	6.14552	+	20.9297i	0.328962	+	1.12034i	0.943477	+	0.331437i	$0.107534\pi$
$349$	6.14552	+	20.9297i	0.328962	+	1.12034i	−0.614515	+	0.788905i	$0.710648\pi$
$350$	1.62996	−	12.8282i	0.0871248	−	0.685695i
$351$	−17.2825	+	22.0784i	−0.922471	+	1.17846i
$352$	6.12307	+	1.33199i	0.326361	+	0.0709954i
$353$	6.19875	−	16.6195i	0.329926	−	0.884567i	−0.661027	−	0.750362i	$-0.729879\pi$
$353$	6.19875	−	16.6195i	0.329926	−	0.884567i	0.990954	−	0.134205i	$-0.0428480\pi$
$354$	−9.94483	+	0.639493i	−0.528562	+	0.0339887i
$355$	−10.9586	−	3.12025i	−0.581620	−	0.165606i
$356$	11.9474	+	1.71778i	0.633212	+	0.0910421i
$357$	0.143344	−	19.9522i	0.00758657	−	1.05598i
$358$	−12.6575	+	2.75347i	−0.668970	+	0.145526i
$359$	−0.0339069	−	0.0391307i	−0.00178954	−	0.00206524i	0.754854	−	0.655893i	$-0.227708\pi$
$359$	−0.0339069	−	0.0391307i	−0.00178954	−	0.00206524i	−0.756644	+	0.653828i	$0.773162\pi$
$360$	6.56356	−	1.38552i	0.345930	−	0.0730235i
$361$	−28.1066	+	18.0630i	−1.47930	+	0.950685i
$362$	−16.6303	+	9.08083i	−0.874069	+	0.477278i
$363$	−26.7641	+	40.9952i	−1.40475	+	2.15169i
$364$	3.93168	+	13.3901i	0.206076	+	0.701830i
$365$	5.14836	−	3.92036i	0.269477	−	0.205201i
$366$	0.716931	+	0.398186i	0.0374746	+	0.0208135i
$367$	3.62004	+	3.62004i	0.188964	+	0.188964i	0.795248	−	0.606284i	$-0.207340\pi$
$367$	3.62004	+	3.62004i	0.188964	+	0.188964i	−0.606284	+	0.795248i	$0.707340\pi$
$368$	3.64394	−	3.11796i	0.189954	−	0.162535i
$369$	−4.64563	−	16.7059i	−0.241842	−	0.869672i
$370$	−4.50595	+	2.10267i	−0.234253	+	0.109312i
$371$	10.2086	+	4.66210i	0.530003	+	0.242044i
$372$	−6.51778	−	14.5476i	−0.337931	−	0.754260i
$373$	2.33381	+	32.6309i	0.120840	+	1.68957i	0.590753	+	0.806853i	$0.298831\pi$
$373$	2.33381	+	32.6309i	0.120840	+	1.68957i	−0.469913	+	0.882713i	$0.655715\pi$
$374$	−26.7806	−	7.86349i	−1.38479	−	0.406611i
$375$	−19.3620	+	0.337712i	−0.999848	+	0.0174394i
$376$	2.67125	+	5.84923i	0.137759	+	0.301651i
$377$	−27.7952	−	1.98795i	−1.43153	−	0.102385i
$378$	−13.2575	−	2.19874i	−0.681894	−	0.113091i
$379$	20.9333	+	3.00976i	1.07527	+	0.154601i	0.657128	−	0.753779i	$-0.271771\pi$
$379$	20.9333	+	3.00976i	1.07527	+	0.154601i	0.418146	+	0.908380i	$0.362680\pi$
$380$	−16.0038	+	2.43524i	−0.820978	+	0.124925i
$381$	5.31263	+	14.5624i	0.272174	+	0.746053i
$382$	0.923211	−	12.9082i	0.0472356	−	0.660440i
$383$	−5.80644	+	15.5677i	−0.296695	+	0.795471i	0.699993	+	0.714150i	$0.253187\pi$
$383$	−5.80644	+	15.5677i	−0.296695	+	0.795471i	−0.996688	+	0.0813207i	$0.974086\pi$
$384$	1.72671	+	0.135972i	0.0881156	+	0.00693877i
$385$	25.8338	+	25.4131i	1.31661	+	1.29517i
$386$	−13.4461	−	11.6511i	−0.684388	−	0.593025i
$387$	1.32049	−	5.67628i	0.0671244	−	0.288542i
$388$	1.76779	+	4.73963i	0.0897460	+	0.240618i
$389$	−2.92789	−	20.3639i	−0.148450	−	1.03249i	−0.918759	−	0.394820i	$-0.870807\pi$
$389$	−2.92789	−	20.3639i	−0.148450	−	1.03249i	0.770309	−	0.637671i	$-0.220102\pi$
$390$	19.0010	−	8.70098i	0.962152	−	0.440591i
$391$	−17.1802	+	12.6947i	−0.868841	+	0.642000i
$392$	0.220080	−	0.220080i	0.0111157	−	0.0111157i
$393$	−21.3228	+	6.09490i	−1.07559	+	0.307447i
$394$	7.48602	+	3.41875i	0.377140	+	0.172234i
$395$	7.46990	−	4.88771i	0.375852	−	0.245928i
$396$	−8.05419	+	16.9860i	−0.404738	+	0.853580i
$397$	−13.8266	−	25.3215i	−0.693938	−	1.27085i	−0.952406	−	0.304832i	$-0.901400\pi$
$397$	−13.8266	−	25.3215i	−0.693938	−	1.27085i	0.258469	−	0.966020i	$-0.416782\pi$
$398$	3.23409	+	0.703534i	0.162110	+	0.0352650i
$399$	31.6382	+	7.12089i	1.58389	+	0.356491i
$400$	−4.81994	−	1.32972i	−0.240997	−	0.0664860i
$401$	−0.399693	+	0.621934i	−0.0199597	+	0.0310579i	−0.851090	−	0.525020i	$-0.824058\pi$
$401$	−0.399693	+	0.621934i	−0.0199597	+	0.0310579i	0.831130	+	0.556078i	$0.187694\pi$
$402$	0.0383389	−	5.33643i	0.00191217	−	0.266157i
$403$	−29.7612	−	39.7563i	−1.48251	−	1.98040i
$404$	−2.17015	−	1.39467i	−0.107969	−	0.0693874i
$405$	−0.413105	+	20.1204i	−0.0205274	+	0.999789i
$406$	−5.54836	−	12.1492i	−0.275361	−	0.602956i
$407$	2.96198	−	13.6160i	0.146820	−	0.674921i
$408$	−7.62828	−	1.15278i	−0.377656	−	0.0570709i
$409$	2.48067	+	2.14951i	0.122661	+	0.106287i	0.714031	−	0.700114i	$-0.246867\pi$
$409$	2.48067	+	2.14951i	0.122661	+	0.106287i	−0.591370	+	0.806400i	$0.701413\pi$
$410$	−2.64350	+	12.6511i	−0.130553	+	0.624791i
$411$	8.59327	+	16.0098i	0.423875	+	0.789704i
$412$	1.67662	−	2.23970i	0.0826010	−	0.110342i
$413$	−10.5218	−	10.5218i	−0.517745	−	0.517745i
$414$	6.63364	+	12.7669i	0.326026	+	0.627461i
$415$	−1.98389	+	3.70520i	−0.0973852	+	0.181881i
$416$	5.34103	−	0.767924i	0.261865	−	0.0376506i
$417$	11.9322	+	3.59693i	0.584324	+	0.176143i
$418$	21.7410	−	39.8156i	1.06339	−	1.94745i
$419$	8.74979	−	10.0978i	0.427455	−	0.493310i	−0.500638	−	0.865657i	$-0.666901\pi$
$419$	8.74979	−	10.0978i	0.427455	−	0.493310i	0.928094	+	0.372347i	$0.121447\pi$
$420$	8.02481	+	5.99448i	0.391571	+	0.292501i
$421$	−7.32306	+	4.70625i	−0.356904	+	0.229368i	−0.706789	−	0.707424i	$-0.749857\pi$
$421$	−7.32306	+	4.70625i	−0.356904	+	0.229368i	0.349885	+	0.936793i	$0.386221\pi$
$422$	3.08280	+	1.14982i	0.150068	+	0.0559725i
$423$	−18.9071	+	3.82933i	−0.919294	+	0.186188i
$424$	2.34604	−	3.65051i	0.113934	−	0.177285i
$425$	20.9917	+	7.43932i	1.01825	+	0.360860i
$426$	6.28549	−	6.19582i	0.304533	−	0.300189i
$427$	0.260294	+	1.19655i	0.0125965	+	0.0579052i
$428$	0.993116	−	13.8856i	0.0480041	−	0.671185i
$429$	−12.8597	+	57.1356i	−0.620871	+	2.75854i
$430$	−2.81756	+	3.30608i	−0.135875	+	0.159433i
$431$	7.23601	−	24.6436i	0.348546	−	1.18704i	−0.579624	−	0.814884i	$-0.696801\pi$
$431$	7.23601	−	24.6436i	0.348546	−	1.18704i	0.928170	−	0.372155i	$-0.121381\pi$
$432$	−1.57103	+	4.95296i	−0.0755863	+	0.238300i
$433$	4.18378	−	7.66202i	0.201060	−	0.368213i	−0.757622	−	0.652693i	$-0.773639\pi$
$433$	4.18378	−	7.66202i	0.201060	−	0.368213i	0.958682	+	0.284480i	$0.0918209\pi$
$434$	9.88803	−	21.6518i	0.474640	−	1.03932i
$435$	−16.8150	+	10.8307i	−0.806216	+	0.519291i
$436$	0.292091			0.0139886
$437$	−14.2259	−	31.6711i	−0.680519	−	1.51504i
$438$	0.677687	+	4.96645i	0.0323811	+	0.237306i
$439$	−29.5806	+	4.25305i	−1.41181	+	0.202987i	−0.805665	−	0.592371i	$-0.798192\pi$
$439$	−29.5806	+	4.25305i	−1.41181	+	0.202987i	−0.606140	+	0.795358i	$0.707283\pi$
$440$	11.1477	−	8.48875i	0.531447	−	0.404685i
$441$	0.493469	+	0.792667i	0.0234985	+	0.0377460i
$442$	−23.9734	+	1.71461i	−1.14030	+	0.0815557i
$443$	−13.9859	−	25.6133i	−0.664492	−	1.21693i	−0.964775	−	0.263076i	$-0.915263\pi$
$443$	−13.9859	−	25.6133i	−0.664492	−	1.21693i	0.300283	−	0.953850i	$-0.402919\pi$
$444$	0.302363	−	3.83972i	0.0143495	−	0.182225i
$445$	20.2519	−	17.8415i	0.960031	−	0.845767i
$446$	−20.7847	+	18.0101i	−0.984185	+	0.852801i
$447$	−4.95055	−	2.30397i	−0.234153	−	0.108974i
$448$	1.54989	+	2.07041i	0.0732254	+	0.0978177i
$449$	−3.47587	+	24.1752i	−0.164036	+	1.14090i	0.726891	+	0.686752i	$0.240964\pi$
$449$	−3.47587	+	24.1752i	−0.164036	+	1.14090i	−0.890928	+	0.454145i	$0.849945\pi$
$450$	7.16176	−	13.1799i	0.337609	−	0.621305i
$451$	−23.7181	−	27.3721i	−1.11684	−	1.28890i
$452$	−12.2948	−	4.58573i	−0.578300	−	0.215695i
$453$	0.0821915	−	0.0701919i	0.00386170	−	0.00329790i
$454$	0.560592	−	1.90920i	0.0263099	−	0.0896033i
$455$	28.4906	+	12.7297i	1.33566	+	0.596775i
$456$	4.46629	−	11.7168i	0.209153	−	0.548690i
$457$	11.3629	−	4.23815i	0.531535	−	0.198252i	−0.0693432	−	0.997593i	$-0.522090\pi$
$457$	11.3629	−	4.23815i	0.531535	−	0.198252i	0.600878	+	0.799341i	$0.294818\pi$
$458$	−1.29094	+	1.72450i	−0.0603218	+	0.0805805i
$459$	8.55370	−	21.5060i	0.399252	−	1.00382i
$460$	−0.0212153	−	10.7238i	−0.000989170	−	0.499999i
$461$		−	3.86835i		−	0.180167i	−0.995934	−	0.0900835i	$-0.971287\pi$
$461$		−	3.86835i		−	0.180167i	0.995934	−	0.0900835i	$-0.0287134\pi$
$462$	−26.9891	+	7.71454i	−1.25565	+	0.358913i
$463$	1.15976	+	3.10943i	0.0538986	+	0.144508i	0.961109	−	0.276170i	$-0.0890652\pi$
$463$	1.15976	+	3.10943i	0.0538986	+	0.144508i	−0.907210	+	0.420677i	$0.861792\pi$
$464$	−4.95509	+	1.45495i	−0.230034	+	0.0675442i
$465$	−34.2115	−	10.0074i	−1.58652	−	0.464081i
$466$	9.31247	+	2.73439i	0.431392	+	0.126668i
$467$	−1.65426	+	7.60450i	−0.0765499	+	0.351894i	−0.999451	−	0.0331439i	$-0.989448\pi$
$467$	−1.65426	+	7.60450i	−0.0765499	+	0.351894i	0.922901	+	0.385038i	$0.125812\pi$
$468$	−1.38670	+	16.1284i	−0.0641004	+	0.745533i
$469$	6.02216	−	5.21823i	0.278077	−	0.240955i
$470$	13.8290	+	3.93756i	0.637884	+	0.181626i
$471$	−3.88562	+	3.83019i	−0.179040	+	0.176486i
$472$	−4.60592	+	3.44795i	−0.212005	+	0.158705i
$473$	−2.58755	−	11.8948i	−0.118976	−	0.546922i
$474$	0.443729	+	6.90048i	0.0203811	+	0.316950i
$475$	−19.0673	+	30.7684i	−0.874870	+	1.41175i
$476$	−6.22803	−	9.69100i	−0.285461	−	0.444186i
$477$	9.07199	+	9.33651i	0.415378	+	0.427489i
$478$	1.86375	+	26.0586i	0.0852458	+	1.19189i
$479$	1.27121	−	0.373262i	0.0580832	−	0.0170548i	−0.252562	−	0.967581i	$-0.581273\pi$
$479$	1.27121	−	0.373262i	0.0580832	−	0.0170548i	0.310645	+	0.950526i	$0.399455\pi$
$480$	2.73581	−	2.74142i	0.124872	−	0.125128i
$481$	−1.70765	−	11.8770i	−0.0778622	−	0.541544i
$482$	14.0457	−	14.0457i	0.639763	−	0.639763i
$483$	−7.77690	+	20.0261i	−0.353861	+	0.911219i
$484$			28.2661i			1.28482i
$485$	10.6302	+	3.86578i	0.482694	+	0.175536i
$486$	−13.4045	−	7.95729i	−0.608042	−	0.360950i
$487$	−0.103481	−	0.0565050i	−0.00468918	−	0.00256048i	0.476903	−	0.878956i	$-0.341759\pi$
$487$	−0.103481	−	0.0565050i	−0.00468918	−	0.00256048i	−0.481592	+	0.876396i	$0.659941\pi$
$488$	0.472271	−	0.0337775i	0.0213787	−	0.00152903i
$489$	21.2996	−	15.7072i	0.963203	−	0.710305i
$490$	−0.0553449	−	0.693749i	−0.00250023	−	0.0313404i
$491$	−0.0307082	+	0.0140239i	−0.00138584	+	0.000632892i	−0.416108	−	0.909315i	$-0.636606\pi$
$491$	−0.0307082	+	0.0140239i	−0.00138584	+	0.000632892i	0.414722	+	0.909948i	$0.363879\pi$
$492$	−7.51860	−	6.61007i	−0.338965	−	0.298005i
$493$	22.4770	−	4.88957i	1.01231	−	0.220215i
$494$	5.55939	−	38.6664i	0.250129	−	1.73968i
$495$	17.2263	+	38.3436i	0.774263	+	1.72342i
$496$	−7.74250	−	4.97581i	−0.347649	−	0.223420i
$497$	13.1450	+	0.940149i	0.589634	+	0.0421715i
$498$	−1.74036	−	2.75131i	−0.0779874	−	0.123289i
$499$	22.4471	+	34.9284i	1.00487	+	1.56361i	0.813060	+	0.582180i	$0.197800\pi$
$499$	22.4471	+	34.9284i	1.00487	+	1.56361i	0.191812	+	0.981432i	$0.438564\pi$
$500$	−9.25382	+	6.27430i	−0.413843	+	0.280595i
$501$	−3.06284	−	14.5833i	−0.136837	−	0.651532i
$502$	0.242508	+	0.132420i	0.0108237	+	0.00591017i
$503$	−15.9142	+	5.93567i	−0.709577	+	0.264659i	−0.678230	−	0.734850i	$-0.737253\pi$
$503$	−15.9142	+	5.93567i	−0.709577	+	0.264659i	−0.0313474	+	0.999509i	$0.509980\pi$
$504$	−7.10323	+	3.12138i	−0.316403	+	0.139037i
$505$	−5.52111	+	1.67049i	−0.245686	+	0.0743359i
$506$	23.9452	+	18.1590i	1.06449	+	0.807266i
$507$	3.77401	+	27.6579i	0.167610	+	1.22833i
$508$	7.16454	+	5.36331i	0.317875	+	0.237958i
$509$	1.21331	−	2.65677i	0.0537789	−	0.117759i	−0.880835	−	0.473424i	$-0.843018\pi$
$509$	1.21331	−	2.65677i	0.0537789	−	0.117759i	0.934614	+	0.355664i	$0.115745\pi$
$510$	−13.0259	+	11.3104i	−0.576795	+	0.500831i
$511$	−4.90132	+	5.65643i	−0.216822	+	0.250226i
$512$	0.877679	−	0.479249i	0.0387883	−	0.0211800i
$513$	31.2003	+	21.0149i	1.37752	+	0.927829i
$514$	−19.1575	+	8.74892i	−0.845000	+	0.385898i
$515$	−1.37992	−	6.10182i	−0.0608066	−	0.268878i
$516$	−1.15317	−	3.16093i	−0.0507654	−	0.139152i
$517$	−32.2571	+	24.1474i	−1.41867	+	1.06200i
$518$	4.60402	−	3.44653i	0.202289	−	0.151432i
$519$	−6.67088	−	18.2855i	−0.292819	−	0.802643i
$520$	6.43968	−	10.2035i	0.282399	−	0.447454i
$521$	−35.0860	+	16.0232i	−1.53714	+	0.701990i	−0.990770	−	0.135551i	$-0.956720\pi$
$521$	−35.0860	+	16.0232i	−1.53714	+	0.701990i	−0.546374	+	0.837541i	$0.683992\pi$
$522$	−0.883099	−	15.4676i	−0.0386522	−	0.677001i
$523$	22.9950	−	12.5562i	1.00550	−	0.549045i	0.109919	−	0.993941i	$-0.464941\pi$
$523$	22.9950	−	12.5562i	1.00550	−	0.549045i	0.895583	+	0.444895i	$0.146759\pi$
$524$	−8.38470	+	9.67646i	−0.366287	+	0.422718i
$525$	21.8410	−	4.96282i	0.953218	−	0.216595i
$526$	10.2348	−	22.4110i	0.446257	−	0.977166i
$527$	32.8176	+	24.5670i	1.42956	+	1.07015i
$528$	1.46739	+	10.7538i	0.0638601	+	0.468001i
$529$	22.1474	−	6.20439i	0.962929	−	0.269756i
$530$	−2.81001	−	9.28733i	−0.122059	−	0.403416i
$531$	−6.94396	−	15.8021i	−0.301342	−	0.685754i
$532$	17.5428	−	6.54311i	0.760575	−	0.283680i
$533$	−27.3732	−	14.9469i	−1.18567	−	0.647422i
$534$	4.29708	+	20.4599i	0.185953	+	0.885388i
$535$	−22.1910	−	21.8297i	−0.959402	−	0.943780i
$536$	−1.66575	−	2.59196i	−0.0719495	−	0.111956i
$537$	−11.9940	−	18.9612i	−0.517580	−	0.818235i
$538$	−7.82565	−	0.559701i	−0.337388	−	0.0241304i
$539$	1.64071	+	1.05442i	0.0706703	+	0.0454170i
$540$	6.15069	+	9.85744i	0.264683	+	0.424197i
$541$	−0.780593	+	5.42914i	−0.0335603	+	0.233417i	−0.999697	−	0.0246135i	$-0.992164\pi$
$541$	−0.780593	+	5.42914i	−0.0335603	+	0.233417i	0.966137	+	0.258031i	$0.0830736\pi$
$542$	23.8649	−	5.19149i	1.02509	−	0.222994i
$543$	−24.6479	−	21.6695i	−1.05774	−	0.929926i
$544$	−4.05168	+	1.85034i	−0.173714	+	0.0793326i
$545$	0.423647	−	0.497101i	0.0181471	−	0.0212935i
$546$	−19.4538	+	14.3460i	−0.832544	+	0.613951i
$547$	22.8764	−	1.63615i	0.978123	−	0.0699567i	0.426886	−	0.904305i	$-0.359611\pi$
$547$	22.8764	−	1.63615i	0.978123	−	0.0699567i	0.551237	+	0.834349i	$0.314156\pi$
$548$	9.20737	+	5.02761i	0.393319	+	0.214769i
$549$	−0.222329	+	1.40292i	−0.00948875	+	0.0598753i
$550$	1.72184	−	31.2840i	0.0734195	−	1.33395i
$551$			37.3868i			1.59273i
$552$	7.23649	+	4.07838i	0.308006	+	0.173587i
$553$	−7.30084	+	7.30084i	−0.310463	+	0.310463i
$554$	2.27444	+	15.8191i	0.0966318	+	0.672089i
$555$	−6.09615	−	6.08368i	−0.258767	−	0.258238i
$556$	6.90382	−	2.02715i	0.292787	−	0.0859701i
$557$	−0.759872	−	10.6244i	−0.0321968	−	0.450170i	−0.987822	−	0.155586i	$-0.950273\pi$
$557$	−0.759872	−	10.6244i	−0.0321968	−	0.450170i	0.955626	−	0.294584i	$-0.0951811\pi$
$558$	19.8021	−	19.2411i	0.838291	−	0.814541i
$559$	−5.66714	−	8.81825i	−0.239695	−	0.372972i
$560$	5.77152	+	0.365198i	0.243891	+	0.0154324i
$561$	−3.10228	−	48.2439i	−0.130978	−	2.03686i
$562$	−0.925474	−	4.25433i	−0.0390387	−	0.179458i
$563$	23.6496	−	17.7039i	0.996711	−	0.746129i	0.0293601	−	0.999569i	$-0.490653\pi$
$563$	23.6496	−	17.7039i	0.996711	−	0.746129i	0.967351	+	0.253440i	$0.0815621\pi$
$564$	−7.93188	+	7.81873i	−0.333993	+	0.329228i
$565$	−25.6366	+	14.2731i	−1.07854	+	0.600473i
$566$	1.96623	−	1.70375i	0.0826469	−	0.0716139i
$567$	−4.29219	−	22.8772i	−0.180255	−	0.960752i
$568$	1.08315	−	4.97916i	0.0454479	−	0.208921i
$569$	27.2310	+	7.99575i	1.14158	+	0.335199i	0.797251	−	0.603648i	$-0.206287\pi$
$569$	27.2310	+	7.99575i	1.14158	+	0.335199i	0.344333	+	0.938847i	$0.388105\pi$
$570$	−13.4626	−	24.5950i	−0.563886	−	1.03017i
$571$	43.4627	−	12.7618i	1.81886	−	0.534065i	0.819613	−	0.572918i	$-0.194189\pi$
$571$	43.4627	−	12.7618i	1.81886	−	0.534065i	0.999245	+	0.0388535i	$0.0123706\pi$
$572$	11.8163	+	31.6806i	0.494062	+	1.32463i
$573$	21.5516	−	6.16029i	0.900331	−	0.257350i
$574$		−	14.9484i		−	0.623934i
$575$	−18.2813	−	15.5176i	−0.762381	−	0.647128i
$576$	0.803752	+	2.89033i	0.0334897	+	0.120430i
$577$	26.6206	−	35.5609i	1.10823	−	1.48042i	0.249229	−	0.968445i	$-0.419823\pi$
$577$	26.6206	−	35.5609i	1.10823	−	1.48042i	0.859000	−	0.511976i	$-0.171086\pi$
$578$	2.66078	−	0.992420i	0.110674	−	0.0412792i
$579$	10.9763	−	28.7951i	0.456159	−	1.19668i
$580$	−4.71070	+	10.5432i	−0.195601	+	0.437781i
$581$	1.36954	−	4.66421i	0.0568179	−	0.193504i
$582$	−6.66271	+	5.68998i	−0.276178	+	0.235857i
$583$	25.4772	+	9.50252i	1.05516	+	0.393554i
$584$	1.89514	+	2.18710i	0.0784213	+	0.0905030i
$585$	25.4371	+	25.7524i	1.05169	+	1.06473i
$586$	1.08740	−	7.56302i	0.0449200	−	0.312425i
$587$	−16.9344	−	22.6217i	−0.698956	−	0.933696i	0.300845	−	0.953673i	$-0.402731\pi$
$587$	−16.9344	−	22.6217i	−0.698956	−	0.933696i	−0.999800	+	0.0199776i	$0.993641\pi$
$588$	0.488746	+	0.227460i	0.0201555	+	0.00938031i
$589$	−50.3548	+	43.6327i	−2.07483	+	1.79785i
$590$	−0.812435	+	12.8396i	−0.0334474	+	0.528597i
$591$	−1.11901	+	14.2103i	−0.0460299	+	0.584534i
$592$	−1.06572	−	1.95172i	−0.0438007	−	0.0802150i
$593$	1.61574	−	0.115560i	0.0663506	−	0.00474549i	−0.0381244	−	0.999273i	$-0.512138\pi$
$593$	1.61574	−	0.115560i	0.0663506	−	0.00474549i	0.104475	+	0.994528i	$0.466684\pi$
$594$	−32.4199	−	3.02222i	−1.33021	−	0.124003i
$595$	−25.5259	−	3.45647i	−1.04646	−	0.141701i
$596$	−3.12049	+	0.448659i	−0.127820	+	0.0183778i
$597$	0.775051	+	5.67999i	0.0317207	+	0.232466i
$598$	24.7839	+	7.44524i	1.01349	+	0.304458i
$599$	−0.0646049			−0.00263968			−0.00131984	−	0.999999i	$-0.500420\pi$
$599$	−0.0646049			−0.00263968			−0.00131984	+	0.999999i	$0.500420\pi$
$600$	−0.697536	−	8.63212i	−0.0284768	−	0.352405i
$601$	7.94396	−	17.3948i	0.324041	−	0.709550i	−0.675574	−	0.737292i	$-0.736104\pi$
$601$	7.94396	−	17.3948i	0.324041	−	0.709550i	0.999615	+	0.0277416i	$0.00883155\pi$
$602$	2.40781	−	4.40957i	0.0981348	−	0.179721i
$603$	8.70594	−	3.10540i	0.354533	−	0.126462i
$604$	0.0175809	−	0.0598751i	0.000715358	−	0.00243628i
$605$	48.1053	+	40.9970i	1.95576	+	1.66677i
$606$	0.981105	−	4.35906i	0.0398547	−	0.177075i
$607$	−2.21037	+	30.9050i	−0.0897160	+	1.25439i	0.730729	+	0.682668i	$0.239180\pi$
$607$	−2.21037	+	30.9050i	−0.0897160	+	1.25439i	−0.820445	+	0.571726i	$0.806274\pi$
$608$	−1.53887	−	7.07406i	−0.0624093	−	0.286891i
$609$	16.4750	−	16.2400i	0.667602	−	0.658077i
$610$	0.627493	−	0.852734i	0.0254065	−	0.0345262i
$611$	−18.7590	+	29.1896i	−0.758908	+	1.18088i
$612$	−2.65252	−	13.0967i	−0.107222	−	0.529401i
$613$	−13.0454	−	4.86567i	−0.526898	−	0.196523i	0.0719166	−	0.997411i	$-0.477088\pi$
$613$	−13.0454	−	4.86567i	−0.526898	−	0.196523i	−0.598814	+	0.800888i	$0.704361\pi$
$614$	−18.9124	+	12.1542i	−0.763240	+	0.490505i
$615$	−22.1544	+	3.20848i	−0.893352	+	0.129378i
$616$	−10.6128	+	12.2478i	−0.427603	+	0.493480i
$617$	−15.3323	+	28.0790i	−0.617256	+	1.13042i	0.362832	+	0.931855i	$0.381810\pi$
$617$	−15.3323	+	28.0790i	−0.617256	+	1.13042i	−0.980088	+	0.198565i	$0.936372\pi$
$618$	4.63959	+	1.39859i	0.186632	+	0.0562595i
$619$	1.65480	−	0.237924i	0.0665119	−	0.00956297i	−0.108979	−	0.994044i	$-0.534758\pi$
$619$	1.65480	−	0.237924i	0.0665119	−	0.00956297i	0.175490	+	0.984481i	$0.443849\pi$
$620$	−19.6978	+	5.95986i	−0.791085	+	0.239354i
$621$	−16.8359	+	18.3726i	−0.675602	+	0.737267i
$622$	9.88871	+	9.88871i	0.396501	+	0.396501i
$623$	−18.7076	+	24.9904i	−0.749504	+	1.00122i
$624$	4.42004	+	8.23481i	0.176943	+	0.329656i
$625$	−2.74364	+	24.8490i	−0.109746	+	0.993960i
$626$	24.6116	+	21.3261i	0.983678	+	0.852362i
$627$	77.6918	+	11.7407i	3.10271	+	0.468878i
$628$	−0.669591	+	3.07806i	−0.0267196	+	0.122828i
$629$	4.11464	+	9.00981i	0.164062	+	0.359245i
$630$	−4.99028	+	16.6160i	−0.198818	+	0.661997i
$631$	41.1418	+	26.4402i	1.63783	+	1.05257i	0.942678	+	0.333703i	$0.108298\pi$
$631$	41.1418	+	26.4402i	1.63783	+	1.05257i	0.695149	+	0.718865i	$0.255338\pi$
$632$	2.39245	+	3.19594i	0.0951665	+	0.127128i
$633$	−0.0409417	+	5.69873i	−0.00162729	+	0.226504i
$634$	−7.83694	+	12.1945i	−0.311245	+	0.484306i
$635$	19.5190	−	4.41421i	0.774590	−	0.175173i
$636$	7.33258	+	1.65036i	0.290756	+	0.0654412i
$637$	1.64105	+	0.356990i	0.0650209	+	0.0141444i
$638$	−15.5089	−	28.4024i	−0.614002	−	1.12446i
$639$	13.8127	+	6.54951i	0.546422	+	0.259095i
$640$	0.457360	−	2.18879i	0.0180787	−	0.0865197i
$641$	3.05932	+	1.39714i	0.120836	+	0.0551839i	0.474916	−	0.880031i	$-0.342479\pi$
$641$	3.05932	+	1.39714i	0.120836	+	0.0551839i	−0.354080	+	0.935215i	$0.615206\pi$
$642$	23.1835	−	6.62674i	0.914978	−	0.261537i
$643$	2.37831	−	2.37831i	0.0937914	−	0.0937914i	−0.658654	−	0.752446i	$-0.728874\pi$
$643$	2.37831	−	2.37831i	0.0937914	−	0.0937914i	0.752446	+	0.658654i	$0.228874\pi$
$644$	2.56095	+	12.1360i	0.100916	+	0.478226i
$645$	−7.05204	−	2.62205i	−0.277674	−	0.103243i
$646$	4.58910	+	31.9179i	0.180556	+	1.25579i
$647$	−8.82038	−	23.6483i	−0.346765	−	0.929713i	−0.986883	−	0.161436i	$-0.948387\pi$
$647$	−8.82038	−	23.6483i	−0.346765	−	0.929713i	0.640118	−	0.768276i	$-0.278885\pi$
$648$	−8.99181	+	0.383849i	−0.353232	+	0.0150790i
$649$	−27.2471	−	23.6097i	−1.06954	−	0.926763i
$650$	−8.02500	−	25.7586i	−0.314766	−	1.01034i
$651$	41.1004	+	3.23650i	1.61085	+	0.126848i
$652$	5.33965	−	14.3161i	0.209117	−	0.560663i
$653$	−0.460758	+	6.44223i	−0.0180308	+	0.252104i	0.980440	+	0.196819i	$0.0630612\pi$
$653$	−0.460758	+	6.44223i	−0.0180308	+	0.252104i	−0.998471	+	0.0552848i	$0.982393\pi$
$654$	0.173390	+	0.475277i	0.00678008	+	0.0185848i
$655$	4.30696	+	28.3043i	0.168287	+	1.10594i
$656$	−5.72109	−	0.822568i	−0.223371	−	0.0321159i
$657$	−7.67888	+	4.05086i	−0.299582	+	0.158039i
$658$	−16.5881	−	1.18641i	−0.646673	−	0.0462510i
$659$	6.61758	+	14.4905i	0.257784	+	0.564469i	0.993631	−	0.112679i	$-0.0359431\pi$
$659$	6.61758	+	14.4905i	0.257784	+	0.564469i	−0.735847	+	0.677148i	$0.763216\pi$
$660$	20.4299	+	13.1000i	0.795234	+	0.509916i
$661$	−27.3793	−	8.03928i	−1.06493	−	0.312692i	−0.298095	−	0.954536i	$-0.596351\pi$
$661$	−27.3793	−	8.03928i	−1.06493	−	0.312692i	−0.766835	+	0.641845i	$0.778169\pi$
$662$	0.226277	+	3.16376i	0.00879449	+	0.122963i
$663$	−17.0209	−	37.9905i	−0.661037	−	1.47543i
$664$	−1.70974	−	0.780810i	−0.0663506	−	0.0303013i
$665$	14.3084	−	39.3456i	0.554855	−	1.52576i
$666$	6.42729	−	1.78732i	0.249052	−	0.0692574i
$667$	−24.4925	−	3.67737i	−0.948353	−	0.142388i
$668$	−6.08348	−	6.08348i	−0.235377	−	0.235377i
$669$	−41.6432	−	23.1288i	−1.61002	−	0.894213i
$670$	−6.82717	−	0.924468i	−0.263757	−	0.0357153i
$671$	0.835882	+	2.84675i	0.0322689	+	0.109898i
$672$	−2.44883	+	3.75093i	−0.0944658	+	0.144695i
$673$	−19.8381	+	10.8324i	−0.764701	+	0.417558i	−0.813733	−	0.581239i	$-0.802568\pi$
$673$	−19.8381	+	10.8324i	−0.764701	+	0.417558i	0.0490321	+	0.998797i	$0.484386\pi$
$674$	13.8339	−	8.89052i	0.532863	−	0.342450i
$675$	25.6970	+	3.82949i	0.989077	+	0.147397i
$676$	10.5539	+	12.1799i	0.405920	+	0.468457i
$677$	0.860634	−	0.187219i	0.0330768	−	0.00719543i	−0.195996	−	0.980605i	$-0.562794\pi$
$677$	0.860634	−	0.187219i	0.0330768	−	0.00719543i	0.229073	+	0.973409i	$0.426430\pi$
$678$	0.163284	−	22.7277i	0.00627089	−	0.872852i
$679$	−12.9496	−	1.86188i	−0.496962	−	0.0714523i
$680$	−2.72749	+	9.57914i	−0.104594	+	0.367343i
$681$	3.43934	−	0.221163i	0.131796	−	0.00847499i
$682$	20.1542	−	54.0356i	0.771746	−	2.06913i
$683$	44.6435	+	9.71160i	1.70824	+	0.371604i	0.957373	−	0.288853i	$-0.0932740\pi$
$683$	44.6435	+	9.71160i	1.70824	+	0.371604i	0.750863	+	0.660458i	$0.229638\pi$
$684$	21.7163	+	0.312051i	0.830342	+	0.0119316i
$685$	21.9106	−	8.37774i	0.837162	−	0.320097i
$686$	5.32722	+	18.1429i	0.203394	+	0.692697i
$687$	−3.57234	−	1.07687i	−0.136293	−	0.0410852i
$688$	−1.55515	−	1.16417i	−0.0592894	−	0.0443835i
$689$	23.4150			0.892042
$690$	17.4366	−	6.40032i	0.663801	−	0.243656i
$691$	28.2263			1.07378			0.536889	−	0.843653i	$-0.319599\pi$
$691$	28.2263			1.07378			0.536889	+	0.843653i	$0.319599\pi$
$692$	−8.99626	−	6.73452i	−0.341987	−	0.256008i
$693$	−28.5739	−	39.3359i	−1.08543	−	1.49425i
$694$	4.29695	+	14.6341i	0.163110	+	0.555502i
$695$	6.56332	−	14.6896i	0.248961	−	0.557207i
$696$	−5.30883	−	7.19900i	−0.201231	−	0.272877i
$697$	25.1565	+	5.47247i	0.952871	+	0.207284i
$698$	−7.62297	+	20.4380i	−0.288534	+	0.773589i
$699$	1.07876	+	16.7760i	0.0408025	+	0.634525i
$700$	8.99249	−	9.29269i	0.339884	−	0.351231i
$701$	19.1536	+	2.75387i	0.723422	+	0.104012i	0.494183	−	0.869358i	$-0.335467\pi$
$701$	19.1536	+	2.75387i	0.723422	+	0.104012i	0.229239	+	0.973370i	$0.426376\pi$
$702$	−27.0664	+	7.31766i	−1.02156	+	0.276187i
$703$	−15.7308	+	3.42202i	−0.593297	+	0.129064i
$704$	4.10353	+	4.73573i	0.154658	+	0.178485i
$705$	1.80210	+	24.8393i	0.0678712	+	0.935501i
$706$	14.9221	−	9.58982i	0.561599	−	0.360918i
$707$	5.85559	−	3.19740i	0.220222	−	0.120250i
$708$	−8.34448	−	5.44778i	−0.313605	−	0.204740i
$709$	−5.49656	−	18.7196i	−0.206428	−	0.703028i	−0.995999	−	0.0893688i	$-0.971515\pi$
$709$	−5.49656	−	18.7196i	−0.206428	−	0.703028i	0.789571	−	0.613659i	$-0.210303\pi$
$710$	−6.90288	−	9.06511i	−0.259061	−	0.340208i
$711$	−10.9647	+	4.81824i	−0.411209	+	0.180698i
$712$	8.53497	+	8.53497i	0.319862	+	0.319862i
$713$	−23.6313	−	37.2797i	−0.885001	−	1.39614i
$714$	12.0717	−	15.8867i	0.451771	−	0.594544i
$715$	71.0545	+	25.8396i	2.65729	+	0.966346i
$716$	−11.7830	−	5.38110i	−0.440350	−	0.201101i
$717$	−41.2949	+	18.5014i	−1.54219	+	0.690946i
$718$	−0.00369375	−	0.0516454i	−0.000137849	−	0.00192739i
$719$	−48.2343	−	14.1629i	−1.79883	−	0.528185i	−0.801293	−	0.598272i	$-0.795854\pi$
$719$	−48.2343	−	14.1629i	−1.79883	−	0.528185i	−0.997541	+	0.0700865i	$0.977672\pi$
$720$	6.08471	+	2.82423i	0.226764	+	0.105253i
$721$	3.00580	+	6.58179i	0.111942	+	0.245119i
$722$	−33.3253	−	2.38347i	−1.24024	−	0.0887036i
$723$	31.1921	+	14.5167i	1.16005	+	0.539882i
$724$	−18.7552	−	2.69659i	−0.697030	−	0.100218i
$725$	11.1107	+	23.3087i	0.412642	+	0.865664i
$726$	−45.9933	+	16.7792i	−1.70697	+	0.622735i
$727$	1.50968	−	21.1081i	0.0559910	−	0.782856i	−0.889444	−	0.457045i	$-0.848908\pi$
$727$	1.50968	−	21.1081i	0.0559910	−	0.782856i	0.945435	−	0.325812i	$-0.105638\pi$
$728$	−4.87690	+	13.0755i	−0.180750	+	0.484609i
$729$	4.99058	−	26.5348i	0.184836	−	0.982769i
$730$	6.47086	−	0.0531151i	0.239497	−	0.00196588i
$731$	6.53935	+	5.66638i	0.241866	+	0.209578i
$732$	0.335308	+	0.748405i	0.0123933	+	0.0276618i
$733$	9.30411	+	24.9453i	0.343655	+	0.921376i	0.987696	+	0.156385i	$0.0499839\pi$
$733$	9.30411	+	24.9453i	0.343655	+	0.921376i	−0.644041	+	0.764991i	$0.722743\pi$
$734$	0.728582	+	5.06740i	0.0268924	+	0.187041i
$735$	1.09598	−	0.501875i	0.0404259	−	0.0185119i
$736$	4.78565	−	0.312323i	0.176401	−	0.0115124i
$737$	13.6520	−	13.6520i	0.502877	−	0.502877i
$738$	6.29243	−	16.1577i	0.231628	−	0.594775i
$739$	32.1876	+	14.6996i	1.18404	+	0.540732i	0.907411	−	0.420245i	$-0.138056\pi$
$739$	32.1876	+	14.6996i	1.18404	+	0.540732i	0.276628	+	0.960977i	$0.410783\pi$
$740$	−4.86728	−	1.01704i	−0.178925	−	0.0373872i
$741$	66.2162	−	13.9070i	2.43251	−	0.510886i
$742$	5.37850	+	9.84998i	0.197451	+	0.361604i
$743$	−1.31981	−	0.287108i	−0.0484192	−	0.0105330i	0.188290	−	0.982113i	$-0.439705\pi$
$743$	−1.31981	−	0.287108i	−0.0484192	−	0.0105330i	−0.236710	+	0.971580i	$0.576069\pi$
$744$	3.50032	−	15.5519i	0.128328	−	0.570162i
$745$	−3.76238	+	5.96140i	−0.137843	+	0.218409i
$746$	−17.6867	+	27.5210i	−0.647555	+	1.00762i
$747$	3.44370	−	4.46505i	0.125998	−	0.163368i
$748$	−16.7265	−	22.3440i	−0.611583	−	0.816979i
$749$	30.2881	+	19.4650i	1.10670	+	0.711234i
$750$	−15.7024	−	11.3328i	−0.573372	−	0.413817i
$751$	−10.3249	−	22.6084i	−0.376762	−	0.824993i	−0.999107	−	0.0422503i	$-0.986547\pi$
$751$	−10.3249	−	22.6084i	−0.376762	−	0.824993i	0.622345	−	0.782743i	$-0.286180\pi$
$752$	−1.36686	+	6.28337i	−0.0498444	+	0.229131i
$753$	−0.0715100	+	0.473204i	−0.00260597	+	0.0172445i
$754$	−21.0599	−	18.2485i	−0.766955	−	0.664571i
$755$	−0.0764004	−	0.116763i	−0.00278050	−	0.00424944i
$756$	−9.29554	−	9.70512i	−0.338076	−	0.352972i
$757$	−0.423538	+	0.565780i	−0.0153937	+	0.0205636i	−0.808172	−	0.588946i	$-0.799543\pi$
$757$	−0.423538	+	0.565780i	−0.0153937	+	0.0205636i	0.792778	+	0.609510i	$0.208634\pi$
$758$	14.9543	+	14.9543i	0.543166	+	0.543166i
$759$	−15.3332	+	49.7419i	−0.556560	+	1.80552i
$760$	−14.2711	−	7.64121i	−0.517667	−	0.277176i
$761$	27.9903	−	4.02439i	1.01465	−	0.145884i	0.385123	−	0.922865i	$-0.374159\pi$
$761$	27.9903	−	4.02439i	1.01465	−	0.145884i	0.629524	+	0.776981i	$0.283250\pi$
$762$	−4.47393	+	14.8415i	−0.162073	+	0.537652i
$763$	−0.362037	+	0.663021i	−0.0131066	+	0.0240030i
$764$	8.47465	−	9.78027i	0.306602	−	0.353838i
$765$	−26.1360	−	14.4811i	−0.944950	−	0.523564i
$766$	−13.9777	+	8.98289i	−0.505033	+	0.324565i
$767$	−29.0882	−	10.8494i	−1.05032	−	0.391747i
$768$	1.30081	+	1.14363i	0.0469391	+	0.0412671i
$769$	−11.8689	+	18.4684i	−0.428003	+	0.665986i	−0.986545	−	0.163490i	$-0.947725\pi$
$769$	−11.8689	+	18.4684i	−0.428003	+	0.665986i	0.558542	+	0.829477i	$0.311361\pi$
$770$	5.45148	+	35.8258i	0.196458	+	1.29107i
$771$	−25.6080	−	25.9786i	−0.922249	−	0.935597i
$772$	−3.78190	−	17.3851i	−0.136114	−	0.625704i
$773$	1.12478	−	15.7264i	0.0404554	−	0.565640i	−0.936289	−	0.351231i	$-0.885763\pi$
$773$	1.12478	−	15.7264i	0.0404554	−	0.565640i	0.976744	−	0.214409i	$-0.0687824\pi$
$774$	4.45878	−	3.75276i	0.160267	−	0.134890i
$775$	−18.4267	+	42.1673i	−0.661907	+	1.51469i
$776$	−1.42517	+	4.85367i	−0.0511605	+	0.174237i
$777$	8.34104	+	5.44553i	0.299233	+	0.195357i
$778$	9.85974	−	18.0568i	0.353489	−	0.647366i
$779$	−17.3825	+	38.0624i	−0.622793	+	1.36373i
$780$	20.4254	+	4.42137i	0.731346	+	0.158310i
$781$	31.9304			1.14256
$782$	−21.3611	−	0.133078i	−0.763873	−	0.00475885i
$783$	24.6440	−	10.6188i	0.880704	−	0.379484i
$784$	0.308072	−	0.0442940i	0.0110026	−	0.00158193i
$785$	4.26729	+	5.60395i	0.152306	+	0.200014i
$786$	−20.7223	−	7.89908i	−0.739141	−	0.281751i
$787$	14.3468	−	1.02610i	0.511408	−	0.0365766i	0.186749	−	0.982408i	$-0.440205\pi$
$787$	14.3468	−	1.02610i	0.511408	−	0.0365766i	0.324659	+	0.945831i	$0.394750\pi$
$788$	3.94409	+	7.22305i	0.140502	+	0.257311i
$789$	42.5416	+	3.34999i	1.51452	+	0.119263i
$790$	8.90906	+	0.563729i	0.316970	+	0.0200566i
$791$	25.6482	−	22.2243i	0.911945	−	0.790204i
$792$	−16.6271	+	8.77132i	−0.590817	+	0.311675i
$793$	1.53107	+	2.04527i	0.0543699	+	0.0726297i
$794$	4.10586	−	28.5569i	0.145712	−	1.01345i
$795$	13.4438	−	10.0854i	0.476803	−	0.357693i
$796$	2.16741	+	2.50133i	0.0768219	+	0.0886572i
$797$	29.8813	+	11.1452i	1.05845	+	0.394782i	0.817604	−	0.575781i	$-0.195302\pi$
$797$	29.8813	+	11.1452i	1.05845	+	0.394782i	0.240847	+	0.970563i	$0.422575\pi$
$798$	21.0603	+	24.6606i	0.745526	+	0.872977i
$799$	8.06936	−	27.4817i	0.285473	−	0.972233i
$800$	−3.06169	−	3.95298i	−0.108247	−	0.139759i
$801$	−30.7406	+	19.1373i	−1.08617	+	0.676185i
$802$	−0.692682	+	0.258357i	−0.0244595	+	0.00912291i
$803$	−10.8675	+	14.5173i	−0.383505	+	0.512303i
$804$	3.22870	−	4.24906i	0.113867	−	0.149853i
$805$	24.3683	+	13.2436i	0.858870	+	0.466775i
$806$		−	49.6618i		−	1.74926i
$807$	−3.73471	−	13.0658i	−0.131468	−	0.459937i
$808$	−0.901499	−	2.41701i	−0.0317146	−	0.0850302i
$809$	−25.0308	+	7.34969i	−0.880035	+	0.258401i	−0.690378	−	0.723449i	$-0.742556\pi$
$809$	−25.0308	+	7.34969i	−0.880035	+	0.258401i	−0.189657	+	0.981850i	$0.560738\pi$
$810$	−12.3884	+	15.8596i	−0.435284	+	0.557250i
$811$	22.6302	+	6.64482i	0.794653	+	0.233331i	0.653768	−	0.756695i	$-0.273187\pi$
$811$	22.6302	+	6.64482i	0.794653	+	0.233331i	0.140885	+	0.990026i	$0.455005\pi$
$812$	2.83906	−	13.0510i	0.0996316	−	0.457999i
$813$	22.6139	+	35.7501i	0.793105	+	1.25381i
$814$	10.5310	−	9.12513i	0.369110	−	0.319836i
$815$	−16.6196	−	29.8514i	−0.582160	−	1.04565i
$816$	−5.41592	−	5.49430i	−0.189595	−	0.192339i
$817$	−11.2585	+	8.42799i	−0.393884	+	0.294858i
$818$	0.697724	+	3.20739i	0.0243953	+	0.112144i
$819$	−34.8911	−	23.1382i	−1.21919	−	0.808514i
$820$	−9.69773	+	8.54350i	−0.338659	+	0.298352i
$821$	6.00319	+	9.34114i	0.209513	+	0.326008i	0.930067	−	0.367391i	$-0.119749\pi$
$821$	6.00319	+	9.34114i	0.209513	+	0.326008i	−0.720554	+	0.693399i	$0.756112\pi$
$822$	−2.71504	+	17.9662i	−0.0946978	+	0.626645i
$823$	−2.56566	−	35.8726i	−0.0894333	−	1.25044i	−0.821897	−	0.569636i	$-0.807084\pi$
$823$	−2.56566	−	35.8726i	−0.0894333	−	1.25044i	0.732464	−	0.680806i	$-0.238370\pi$
$824$	2.68440	−	0.788211i	0.0935155	−	0.0274586i
$825$	51.9259	−	15.7690i	1.80783	−	0.549005i
$826$	−2.11766	−	14.7286i	−0.0736828	−	0.512475i
$827$	33.5914	−	33.5914i	1.16809	−	1.16809i	0.185431	−	0.982657i	$-0.440632\pi$
$827$	33.5914	−	33.5914i	1.16809	−	1.16809i	0.982657	−	0.185431i	$-0.0593681\pi$
$828$	−2.34044	+	14.1959i	−0.0813359	+	0.493340i
$829$			18.2502i			0.633855i	0.948450	+	0.316928i	$0.102651\pi$
$829$			18.2502i			0.633855i	−0.948450	+	0.316928i	$0.897349\pi$
$830$	−3.80863	+	1.77727i	−0.132199	+	0.0616898i
$831$	−24.3899	+	13.0913i	−0.846077	+	0.454133i
$832$	4.73591	+	2.58600i	0.164188	+	0.0896536i
$833$	−1.38279	+	0.0988991i	−0.0479108	+	0.00342665i
$834$	7.39669	+	10.0302i	0.256126	+	0.347318i
$835$	−19.1767	+	1.52985i	−0.663638	+	0.0529428i
$836$	41.2652	−	18.8452i	1.42719	−	0.651774i
$837$	43.0630	+	20.7993i	1.48848	+	0.718928i
$838$	13.0560	−	2.84015i	0.451010	−	0.0981113i
$839$	−4.13769	+	28.7783i	−0.142849	+	0.993537i	0.784711	+	0.619862i	$0.212811\pi$
$839$	−4.13769	+	28.7783i	−0.142849	+	0.993537i	−0.927560	+	0.373675i	$0.878098\pi$
$840$	2.83183	+	9.60792i	0.0977074	+	0.331505i
$841$	−1.96030	−	1.25981i	−0.0675967	−	0.0434417i
$842$	−8.68276	−	0.621003i	−0.299228	−	0.0214012i
$843$	6.37307	−	4.03132i	0.219500	−	0.138846i
$844$	1.77884	+	2.76793i	0.0612302	+	0.0952761i
$845$	36.0359	−	0.295795i	1.23967	−	0.0101757i
$846$	−17.4307	−	8.26506i	−0.599281	−	0.284159i
$847$	−64.1616	−	35.0349i	−2.20462	−	1.20381i
$848$	4.06577	−	1.51645i	0.139619	−	0.0520753i
$849$	3.93944	+	2.18798i	0.135201	+	0.0750914i
$850$	12.3465	+	18.5353i	0.423482	+	0.635757i
$851$	−0.694521	−	10.6420i	−0.0238079	−	0.364802i
$852$	8.74481	−	1.19326i	0.299592	−	0.0408803i
$853$	19.9105	+	14.9048i	0.681721	+	0.510330i	0.883101	−	0.469183i	$-0.155452\pi$
$853$	19.9105	+	14.9048i	0.681721	+	0.510330i	−0.201380	+	0.979513i	$0.564543\pi$
$854$	−0.508691	+	1.11388i	−0.0174070	+	0.0381161i
$855$	32.0282	−	36.5057i	1.09534	−	1.24847i
$856$	9.11634	−	10.5208i	0.311590	−	0.359594i
$857$	−20.4227	+	11.1516i	−0.697627	+	0.380933i	−0.788588	−	0.614921i	$-0.789188\pi$
$857$	−20.4227	+	11.1516i	−0.697627	+	0.380933i	0.0909617	+	0.995854i	$0.471006\pi$
$858$	−44.5348	+	38.0329i	−1.52039	+	1.29842i
$859$	−33.3061	+	15.2104i	−1.13639	+	0.518972i	−0.892597	−	0.450855i	$-0.851119\pi$
$859$	−33.3061	+	15.2104i	−1.13639	+	0.518972i	−0.243793	+	0.969827i	$0.578392\pi$
$860$	−4.23683	+	0.958155i	−0.144475	+	0.0326728i
$861$	24.3233	−	8.87360i	0.828936	−	0.302411i
$862$	20.5611	−	15.3918i	0.700313	−	0.524248i
$863$	5.89171	−	4.41048i	0.200556	−	0.150134i	−0.494279	−	0.869303i	$-0.664568\pi$
$863$	5.89171	−	4.41048i	0.200556	−	0.150134i	0.694836	+	0.719169i	$0.255477\pi$
$864$	−4.22588	+	3.02357i	−0.143767	+	0.102864i
$865$	−24.5094	+	5.54277i	−0.833344	+	0.188460i
$866$	7.94097	−	3.62652i	0.269845	−	0.123234i
$867$	3.19430	+	3.74038i	0.108484	+	0.127030i
$868$	20.8912	−	11.4075i	0.709093	−	0.387194i
$869$	−16.3822	+	18.9061i	−0.555729	+	0.641345i
$870$	−19.9517	−	1.40644i	−0.676425	−	0.0476827i
$871$	6.90640	−	15.1229i	0.234014	−	0.512420i
$872$	0.233831	+	0.175044i	0.00791852	+	0.00592773i
$873$	−13.2135	−	7.46357i	−0.447211	−	0.252604i
$874$	7.59135	−	33.8793i	0.256781	−	1.14599i
$875$	−2.77231	−	28.7821i	−0.0937211	−	0.973013i
$876$	−2.43377	+	4.38197i	−0.0822294	+	0.148053i
$877$	25.4552	−	9.49432i	0.859563	−	0.320600i	0.119251	−	0.992864i	$-0.461951\pi$
$877$	25.4552	−	9.49432i	0.859563	−	0.320600i	0.740312	+	0.672264i	$0.234678\pi$
$878$	−26.2293	−	14.3223i	−0.885195	−	0.483353i
$879$	12.9517	−	2.72016i	0.436849	−	0.0917488i
$880$	14.0113	−	0.115010i	0.472322	−	0.00387698i
$881$	−5.35838	−	8.33780i	−0.180528	−	0.280908i	0.739182	−	0.673506i	$-0.235213\pi$
$881$	−5.35838	−	8.33780i	−0.180528	−	0.280908i	−0.919710	+	0.392599i	$0.871576\pi$
$882$	−0.0799854	+	0.930287i	−0.00269325	+	0.0313244i
$883$	−5.35843	−	0.383242i	−0.180325	−	0.0128971i	−0.0191156	−	0.999817i	$-0.506085\pi$
$883$	−5.35843	−	0.383242i	−0.180325	−	0.0128971i	−0.161210	+	0.986920i	$0.551540\pi$
$884$	−20.2192	−	12.9941i	−0.680045	−	0.437039i
$885$	−21.3742	+	6.29981i	−0.718485	+	0.211766i
$886$	4.15318	−	28.8860i	0.139529	−	0.970444i
$887$	−34.1542	+	7.42979i	−1.14679	+	0.249468i	−0.745513	−	0.666491i	$-0.767795\pi$
$887$	−34.1542	+	7.42979i	−1.14679	+	0.249468i	−0.401272	+	0.915959i	$0.631432\pi$
$888$	2.54311	−	2.89265i	0.0853412	−	0.0970711i
$889$	−21.0544	+	9.61523i	−0.706142	+	0.322484i
$890$	26.9045	−	2.14635i	0.901840	−	0.0719457i
$891$	−14.3273	−	54.5462i	−0.479984	−	1.82737i
$892$	−27.4321	+	1.96198i	−0.918493	+	0.0656919i
$893$	40.8580	+	22.3102i	1.36726	+	0.746581i
$894$	−2.58240	−	4.81118i	−0.0863685	−	0.160910i
$895$	−26.2478	+	12.2484i	−0.877368	+	0.409417i
$896$			2.58626i			0.0864010i
$897$	2.59759	+	44.7468i	0.0867310	+	1.49405i
$898$	−17.2702	+	17.2702i	−0.576315	+	0.576315i
$899$	6.76417	+	47.0458i	0.225598	+	1.56907i
$900$	13.6317	−	6.25915i	0.454390	−	0.208638i
$901$	−18.5455	+	5.44544i	−0.617839	+	0.181414i
$902$	−2.58380	−	36.1263i	−0.0860312	−	1.20287i
$903$	8.60434	+	1.30028i	0.286335	+	0.0432705i
$904$	−7.09439	−	11.0391i	−0.235956	−	0.367154i
$905$	−31.7916	+	28.0077i	−1.05679	+	0.931009i
$906$	0.107862	−	0.00693597i	0.00358348	−	0.000230432i
$907$	−9.78120	−	44.9634i	−0.324779	−	1.49299i	−0.792916	−	0.609330i	$-0.791438\pi$
$907$	−9.78120	−	44.9634i	−0.324779	−	1.49299i	0.468137	−	0.883656i	$-0.344925\pi$
$908$	1.59292	−	1.19244i	0.0528629	−	0.0395727i
$909$	7.67524	−	0.991196i	0.254572	−	0.0328759i
$910$	15.1793	+	27.2644i	0.503190	+	0.903806i
$911$	−19.4685	+	16.8696i	−0.645021	+	0.558914i	−0.914749	−	0.404022i	$-0.867612\pi$
$911$	−19.4685	+	16.8696i	−0.645021	+	0.558914i	0.269728	+	0.962937i	$0.413066\pi$
$912$	10.5971	−	6.70324i	0.350904	−	0.221966i
$913$	2.50360	−	11.5089i	0.0828570	−	0.380888i
$914$	11.6363	+	3.41673i	0.384895	+	0.113015i
$915$	1.76002	+	0.514831i	0.0581844	+	0.0170198i
$916$	−2.06691	+	0.606898i	−0.0682925	+	0.0200525i
$917$	−11.5721	−	31.0261i	−0.382146	−	1.02457i
$918$	19.7357	−	12.0904i	0.651374	−	0.399044i
$919$		−	39.2225i		−	1.29383i	−0.762561	−	0.646916i	$-0.776058\pi$
$919$		−	39.2225i		−	1.29383i	0.762561	−	0.646916i	$-0.223942\pi$
$920$	6.40954	−	8.59755i	0.211316	−	0.283453i
$921$	−31.0034	−	23.5583i	−1.02160	−	0.776273i
$922$	2.31822	−	3.09677i	0.0763463	−	0.101987i
$923$	25.7620	−	9.60874i	0.847968	−	0.316276i
$924$	−26.2290	−	9.99815i	−0.862872	−	0.328915i
$925$	−8.79034	+	6.80836i	−0.289024	+	0.223857i
$926$	−0.934979	+	3.18425i	−0.0307253	+	0.104641i
$927$	0.478415	+	8.37954i	0.0157132	+	0.275220i
$928$	−4.83867	−	1.80473i	−0.158837	−	0.0592432i
$929$	17.8836	+	20.6388i	0.586742	+	0.677136i	0.969040	−	0.246903i	$-0.0794128\pi$
$929$	17.8836	+	20.6388i	0.586742	+	0.677136i	−0.382298	+	0.924039i	$0.624867\pi$
$930$	−21.3905	−	28.5135i	−0.701423	−	0.934995i
$931$	0.320667	−	2.23029i	0.0105094	−	0.0730947i
$932$	5.81636	+	7.76974i	0.190521	+	0.254506i
$933$	−10.2203	+	21.9605i	−0.334599	+	0.718955i
$934$	−5.88151	+	5.09636i	−0.192449	+	0.166758i
$935$	−62.2867	−	3.94125i	−2.03699	−	0.128893i
$936$	−10.7755	+	12.0804i	−0.352207	+	0.394860i
$937$	7.56931	+	13.8622i	0.247279	+	0.452857i	0.971608	−	0.236597i	$-0.0760322\pi$
$937$	7.56931	+	13.8622i	0.247279	+	0.452857i	−0.724329	+	0.689454i	$0.757850\pi$
$938$	7.94815	−	0.568463i	0.259516	−	0.0185610i
$939$	−20.0909	+	52.7063i	−0.655643	+	1.72001i
$940$	8.71099	+	11.4396i	0.284121	+	0.373118i
$941$	−13.6293	+	1.95959i	−0.444302	+	0.0638809i	−0.360835	−	0.932630i	$-0.617508\pi$
$941$	−13.6293	+	1.95959i	−0.444302	+	0.0638809i	−0.0834666	+	0.996511i	$0.526599\pi$
$942$	−5.40595	+	0.737658i	−0.176135	+	0.0240342i
$943$	−23.2253	−	15.1313i	−0.756321	−	0.492743i
$944$	−5.75351			−0.187261
$945$	−29.9990	+	1.74356i	−0.975869	+	0.0567181i
$946$	5.05683	−	11.0729i	0.164412	−	0.360012i
$947$	13.4975	−	24.7189i	0.438610	−	0.803255i	−0.561089	−	0.827755i	$-0.689618\pi$
$947$	13.4975	−	24.7189i	0.438610	−	0.803255i	0.999700	+	0.0245001i	$0.00779941\pi$
$948$	−3.78008	+	5.79004i	−0.122771	+	0.188052i
$949$	−4.39943	+	14.9831i	−0.142812	+	0.486372i
$950$	−33.7030	+	13.2048i	−1.09347	+	0.428419i
$951$	−24.4945	−	5.51304i	−0.794287	−	0.178772i
$952$	0.821807	−	11.4904i	0.0266349	−	0.372405i
$953$	9.83224	+	45.1981i	0.318498	+	1.46411i	0.806483	+	0.591258i	$0.201368\pi$
$953$	9.83224	+	45.1981i	0.318498	+	1.46411i	−0.487985	+	0.872852i	$0.662268\pi$
$954$	1.66734	+	12.9109i	0.0539821	+	0.418006i
$955$	−4.35317	−	28.6080i	−0.140865	−	0.925733i
$956$	−14.1243	+	21.9779i	−0.456813	+	0.710815i
$957$	37.0086	−	42.0953i	1.19632	−	1.36075i
$958$	1.24135	+	0.462998i	0.0401061	+	0.0149588i
$959$	−22.8244	+	14.6684i	−0.737039	+	0.473666i
$960$	3.83300	−	0.555108i	0.123709	−	0.0179160i
$961$	−35.1693	+	40.5875i	−1.13449	+	1.30928i
$962$	5.75056	−	10.5314i	0.185406	−	0.339545i
$963$	24.5448	+	33.7893i	0.790944	+	1.08884i
$964$	19.6614	−	2.82688i	0.633251	−	0.0910477i
$965$	−35.0725	−	18.7790i	−1.12902	−	0.604516i
$966$	−18.2269	+	11.3712i	−0.586442	+	0.365862i
$967$	−41.9589	−	41.9589i	−1.34931	−	1.34931i	−0.886414	−	0.462894i	$-0.846811\pi$
$967$	−41.9589	−	41.9589i	−1.34931	−	1.34931i	−0.462894	−	0.886414i	$-0.653189\pi$
$968$	−16.9393	+	22.6282i	−0.544449	+	0.727298i
$969$	−49.2111	+	26.4141i	−1.58089	+	0.848544i
$970$	6.19326	+	9.46517i	0.198854	+	0.303908i
$971$	−31.2414	−	27.0709i	−1.00259	−	0.868745i	−0.0112281	−	0.999937i	$-0.503574\pi$
$971$	−31.2414	−	27.0709i	−1.00259	−	0.868745i	−0.991357	+	0.131192i	$0.958120\pi$
$972$	−5.96226	−	14.4032i	−0.191239	−	0.461982i
$973$	−3.95561	+	18.1836i	−0.126811	+	0.582940i
$974$	−0.0489787	−	0.107248i	−0.00156938	−	0.00343646i
$975$	37.1494	−	28.3486i	1.18973	−	0.907882i
$976$	0.398314	+	0.255981i	0.0127497	+	0.00819375i
$977$	4.81605	+	6.43349i	0.154079	+	0.205826i	0.870938	−	0.491392i	$-0.163512\pi$
$977$	4.81605	+	6.43349i	0.154079	+	0.205826i	−0.716859	+	0.697218i	$0.754421\pi$
$978$	26.4642	+	0.190129i	0.846233	+	0.00607965i
$979$	−40.8917	+	63.6287i	−1.30690	+	2.03358i
$980$	0.371442	−	0.588542i	0.0118653	−	0.0188003i
$981$	−0.670420	+	0.564263i	−0.0214049	+	0.0180155i
$982$	−0.0329874	−	0.00717597i	−0.00105267	−	0.000228994i
$983$	14.5799	+	26.7012i	0.465028	+	0.851635i	0.999977	+	0.00675059i	$0.00214880\pi$
$983$	14.5799	+	26.7012i	0.465028	+	0.851635i	−0.534950	+	0.844884i	$0.679669\pi$
$984$	−2.05768	−	9.79737i	−0.0655965	−	0.312329i
$985$	18.0132	+	3.76395i	0.573947	+	0.119929i
$986$	20.9240	+	9.55567i	0.666356	+	0.304314i
$987$	−7.91651	−	27.6957i	−0.251985	−	0.881564i
$988$	27.6224	−	27.6224i	0.878786	−	0.878786i
$989$	−4.41388	−	8.20453i	−0.140353	−	0.260889i
$990$	−9.18813	+	41.0190i	−0.292018	+	1.30367i
$991$	−0.158259	−	1.10071i	−0.00502726	−	0.0349653i	0.987153	−	0.159775i	$-0.0510770\pi$
$991$	−0.158259	−	1.10071i	−0.00502726	−	0.0349653i	−0.992181	+	0.124810i	$0.960168\pi$
$992$	−3.21630	−	8.62325i	−0.102118	−	0.273788i
$993$	−5.01359	+	2.24624i	−0.159102	+	0.0712823i
$994$	9.95971	+	8.63014i	0.315903	+	0.273731i
$995$	7.40053	−	0.0607461i	0.234613	−	0.00192578i
$996$	0.255571	−	3.24550i	0.00809807	−	0.102838i
$997$	8.33945	−	22.3589i	0.264113	−	0.708115i	−0.735421	−	0.677610i	$-0.763016\pi$
$997$	8.33945	−	22.3589i	0.264113	−	0.708115i	0.999535	−	0.0305048i	$-0.00971149\pi$
$998$	−2.96197	+	41.4137i	−0.0937595	+	1.31093i
$999$	6.72358	+	9.39719i	0.212725	+	0.297314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.647.34	yes	960
3.2	odd	2	inner	690.2.x.a.647.21	yes	960
5.3	odd	4	inner	690.2.x.a.233.28	yes	960
15.8	even	4	inner	690.2.x.a.233.10	yes	960
23.8	even	11	inner	690.2.x.a.77.10	✓	960
69.8	odd	22	inner	690.2.x.a.77.28	yes	960
115.8	odd	44	inner	690.2.x.a.353.21	yes	960
345.8	even	44	inner	690.2.x.a.353.34	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.10	✓	960	23.8	even	11	inner
690.2.x.a.77.28	yes	960	69.8	odd	22	inner
690.2.x.a.233.10	yes	960	15.8	even	4	inner
690.2.x.a.233.28	yes	960	5.3	odd	4	inner
690.2.x.a.353.21	yes	960	115.8	odd	44	inner
690.2.x.a.353.34	yes	960	345.8	even	44	inner
690.2.x.a.647.21	yes	960	3.2	odd	2	inner
690.2.x.a.647.34	yes	960	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.800541 + 0.599278i) q^{2} +(-0.499902 + 1.65834i) q^{3} +(0.281733 + 0.959493i) q^{4} +(2.04155 + 0.912170i) q^{5} +(-1.39400 + 1.02799i) q^{6} +(-2.52716 - 0.549750i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.50020 - 1.65802i) q^{9} +O(q^{10})\)	\(q+(0.800541 + 0.599278i) q^{2} +(-0.499902 + 1.65834i) q^{3} +(0.281733 + 0.959493i) q^{4} +(2.04155 + 0.912170i) q^{5} +(-1.39400 + 1.02799i) q^{6} +(-2.52716 - 0.549750i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-2.50020 - 1.65802i) q^{9} +(1.08771 + 1.95369i) q^{10} +(-6.20249 - 0.891783i) q^{11} +(-1.73201 - 0.0124434i) q^{12} +(-5.27264 + 1.14699i) q^{13} +(-1.69364 - 1.95457i) q^{14} +(-2.53327 + 2.92960i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(3.90935 - 2.13467i) q^{17} +(-1.00790 - 2.82562i) q^{18} +(2.03960 + 6.94625i) q^{19} +(-0.300048 + 2.21585i) q^{20} +(2.17501 - 3.91607i) q^{21} +(-4.43092 - 4.43092i) q^{22} +(-4.75118 + 0.652932i) q^{23} +(-1.37909 - 1.04791i) q^{24} +(3.33589 + 3.72449i) q^{25} +(-4.90833 - 2.24156i) q^{26} +(3.99941 - 3.31734i) q^{27} +(-0.184502 - 2.57967i) q^{28} +(4.95509 + 1.45495i) q^{29} +(-3.78363 + 0.827136i) q^{30} +(3.82329 + 8.37183i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(4.57952 - 9.84004i) q^{33} +(4.40886 + 0.633898i) q^{34} +(-4.65787 - 3.42754i) q^{35} +(0.886468 - 2.86604i) q^{36} +(-0.158639 + 2.21806i) q^{37} +(-2.52995 + 6.78305i) q^{38} +(0.733696 - 9.31722i) q^{39} +(-1.56811 + 1.59406i) q^{40} +(4.36817 + 3.78504i) q^{41} +(4.08800 - 1.83155i) q^{42} +(0.678875 + 1.82014i) q^{43} +(-0.891783 - 6.20249i) q^{44} +(-3.59190 - 5.66553i) q^{45} +(-4.19480 - 2.32458i) q^{46} +(4.54693 - 4.54693i) q^{47} +(-0.476023 - 1.66535i) q^{48} +(-0.283114 - 0.129294i) q^{49} +(0.438517 + 4.98073i) q^{50} +(1.58572 + 7.55017i) q^{51} +(-2.58600 - 4.73591i) q^{52} +(-4.24020 - 0.922400i) q^{53} +(5.18970 - 0.258906i) q^{54} +(-11.8493 - 7.47835i) q^{55} +(1.39824 - 2.17570i) q^{56} +(-12.5389 - 0.0900838i) q^{57} +(3.09484 + 4.13422i) q^{58} +(4.84016 + 3.11058i) q^{59} +(-3.52464 - 1.60529i) q^{60} +(-0.196690 - 0.430690i) q^{61} +(-1.95635 + 8.99320i) q^{62} +(5.40690 + 5.56455i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(-11.8106 - 2.46789i) q^{65} +(9.56301 - 5.13296i) q^{66} +(-1.84642 + 2.46652i) q^{67} +(3.14959 + 3.14959i) q^{68} +(1.29234 - 8.20548i) q^{69} +(-1.67477 - 5.53525i) q^{70} +(-5.04374 + 0.725180i) q^{71} +(2.42721 - 1.76314i) q^{72} +(1.38692 - 2.53996i) q^{73} +(-1.45623 + 1.68058i) q^{74} +(-7.84410 + 3.67017i) q^{75} +(-6.09026 + 3.91397i) q^{76} +(15.1844 + 5.66350i) q^{77} +(6.17096 - 7.01913i) q^{78} +(2.15836 - 3.35847i) q^{79} +(-2.21062 + 0.336382i) q^{80} +(3.50196 + 8.29073i) q^{81} +(1.22861 + 5.64783i) q^{82} +(-0.134088 + 1.87480i) q^{83} +(4.37021 + 0.983617i) q^{84} +(9.92833 - 0.792049i) q^{85} +(-0.547299 + 1.86393i) q^{86} +(-4.88986 + 7.48990i) q^{87} +(3.00310 - 5.49977i) q^{88} +(5.01417 - 10.9795i) q^{89} +(0.519768 - 6.68804i) q^{90} +13.9554 q^{91} +(-1.96504 - 4.37477i) q^{92} +(-15.7946 + 2.15522i) q^{93} +(6.36487 - 0.915131i) q^{94} +(-2.17220 + 16.0416i) q^{95} +(0.616933 - 1.61845i) q^{96} +(5.04569 - 0.360875i) q^{97} +(-0.149161 - 0.273169i) q^{98} +(14.0288 + 12.5135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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