LMFDB - Embedded newform 690.2.x.a.77.10

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			77.10
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(-0.925925 - 1.46378i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19343 + 1.89096i) q^{5} +(-0.616933 + 1.61845i) q^{6} +(-0.549750 - 2.52716i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.28533 + 2.71071i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.925925 - 1.46378i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19343 + 1.89096i) q^{5} +(-0.616933 + 1.61845i) q^{6} +(-0.549750 - 2.52716i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.28533 + 2.71071i) q^{9} +(2.22899 - 0.177821i) q^{10} +(6.20249 - 0.891783i) q^{11} +(1.66535 - 0.476023i) q^{12} +(-1.14699 + 5.27264i) q^{13} +(-1.69364 + 1.95457i) q^{14} +(3.87298 - 0.00396562i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(2.13467 - 3.90935i) q^{17} +(2.94030 - 0.595511i) q^{18} +(-2.03960 + 6.94625i) q^{19} +(-1.47813 - 1.67783i) q^{20} +(-3.19019 + 3.14468i) q^{21} +(-4.43092 - 4.43092i) q^{22} +(0.652932 - 4.75118i) q^{23} +(-1.37909 - 1.04791i) q^{24} +(-2.15146 - 4.51345i) q^{25} +(4.90833 - 2.24156i) q^{26} +(5.15801 - 0.628475i) q^{27} +(2.57967 + 0.184502i) q^{28} +(4.95509 - 1.45495i) q^{29} +(-2.32417 - 3.09810i) q^{30} +(3.82329 - 8.37183i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-7.04842 - 8.25338i) q^{33} +(-4.40886 + 0.633898i) q^{34} +(5.43484 + 1.97643i) q^{35} +(-2.23879 - 1.99696i) q^{36} +(2.21806 - 0.158639i) q^{37} +(6.78305 - 2.52995i) q^{38} +(8.78003 - 3.20312i) q^{39} +(-0.457360 + 2.18879i) q^{40} +(-4.36817 + 3.78504i) q^{41} +(4.42925 + 0.669343i) q^{42} +(-1.82014 - 0.678875i) 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} +(-0.0124434 + 1.73201i) q^{48} +(0.283114 - 0.129294i) q^{49} +(-2.32388 + 4.42714i) q^{50} +(-7.69899 + 0.495076i) q^{51} +(-4.73591 - 2.58600i) q^{52} +(-0.922400 - 4.24020i) q^{53} +(-3.59420 - 3.75256i) q^{54} +(-5.71590 + 12.7929i) q^{55} +(-1.39824 - 2.17570i) q^{56} +(12.0563 - 3.44617i) q^{57} +(-4.13422 - 3.09484i) q^{58} +(4.84016 - 3.11058i) q^{59} +(-1.08734 + 3.71722i) q^{60} +(-0.196690 + 0.430690i) q^{61} +(-8.99320 + 1.95635i) q^{62} +(7.55700 + 1.75801i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-8.60149 - 8.46143i) q^{65} +(-2.38321 + 10.5886i) q^{66} +(2.46652 - 1.84642i) q^{67} +(3.14959 + 3.14959i) q^{68} +(-7.55926 + 3.44348i) q^{69} +(-1.67477 - 5.53525i) q^{70} +(5.04374 + 0.725180i) q^{71} +(-0.256990 + 2.98897i) q^{72} +(2.53996 - 1.38692i) q^{73} +(-1.45623 - 1.68058i) q^{74} +(-4.61463 + 7.32838i) q^{75} +(-6.09026 - 3.91397i) q^{76} +(-5.66350 - 15.1844i) q^{77} +(-7.82591 - 5.10922i) q^{78} +(-2.15836 - 3.35847i) q^{79} +(2.02631 - 0.945560i) q^{80} +(-5.69588 - 6.96828i) q^{81} +(5.64783 + 1.22861i) q^{82} +(1.87480 - 0.134088i) q^{83} +(-2.11851 - 3.94692i) q^{84} +(4.84485 + 8.70210i) q^{85} +(0.547299 + 1.86393i) q^{86} +(-6.71777 - 5.90601i) q^{87} +(5.49977 - 3.00310i) q^{88} +(5.01417 + 10.9795i) q^{89} +(-2.38295 + 6.27069i) q^{90} +13.9554 q^{91} +(4.37477 + 1.96504i) q^{92} +(-15.7946 + 2.15522i) q^{93} +(-6.36487 - 0.915131i) q^{94} +(-10.7010 - 12.1467i) q^{95} +(1.39400 - 1.02799i) q^{96} +(-0.360875 + 5.04569i) q^{97} +(-0.273169 - 0.149161i) q^{98} +(-5.55485 + 17.9594i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	−0.925925	−	1.46378i	−0.534583	−	0.845116i
$3$	−0.925925	−	1.46378i	−0.534583	−	0.845116i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	−1.19343	+	1.89096i	−0.533718	+	0.845663i
$5$	−1.19343	+	1.89096i	−0.533718	+	0.845663i
$6$	−0.616933	+	1.61845i	−0.251862	+	0.660731i
$7$	−0.549750	−	2.52716i	−0.207786	−	0.955177i	−0.956375	−	0.292142i	$-0.905632\pi$
$7$	−0.549750	−	2.52716i	−0.207786	−	0.955177i	0.748589	−	0.663034i	$-0.230732\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	−1.28533	+	2.71071i	−0.428442	+	0.903569i
$10$	2.22899	−	0.177821i	0.704867	−	0.0562319i
$11$	6.20249	−	0.891783i	1.87012	−	0.268883i	0.888380	−	0.459108i	$-0.151831\pi$
$11$	6.20249	−	0.891783i	1.87012	−	0.268883i	0.981740	+	0.190226i	$0.0609220\pi$
$12$	1.66535	−	0.476023i	0.480746	−	0.137416i
$13$	−1.14699	+	5.27264i	−0.318118	+	1.46237i	0.489159	+	0.872195i	$0.337304\pi$
$13$	−1.14699	+	5.27264i	−0.318118	+	1.46237i	−0.807278	+	0.590172i	$0.799060\pi$
$14$	−1.69364	+	1.95457i	−0.452645	+	0.522380i
$15$	3.87298	−	0.00396562i	0.999999	−	0.00102392i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	2.13467	−	3.90935i	0.517733	−	0.948157i	−0.479761	−	0.877399i	$-0.659277\pi$
$17$	2.13467	−	3.90935i	0.517733	−	0.948157i	0.997494	−	0.0707576i	$-0.0225417\pi$
$18$	2.94030	−	0.595511i	0.693035	−	0.140363i
$19$	−2.03960	+	6.94625i	−0.467917	+	1.59358i	0.300600	+	0.953750i	$0.402813\pi$
$19$	−2.03960	+	6.94625i	−0.467917	+	1.59358i	−0.768517	+	0.639829i	$0.779005\pi$
$20$	−1.47813	−	1.67783i	−0.330521	−	0.375174i
$21$	−3.19019	+	3.14468i	−0.696156	+	0.686224i
$22$	−4.43092	−	4.43092i	−0.944676	−	0.944676i
$23$	0.652932	−	4.75118i	0.136146	−	0.990689i
$23$	0.652932	−	4.75118i	0.136146	−	0.990689i
$24$	−1.37909	−	1.04791i	−0.281505	−	0.213905i
$25$	−2.15146	−	4.51345i	−0.430291	−	0.902690i
$26$	4.90833	−	2.24156i	0.962603	−	0.439606i
$27$	5.15801	−	0.628475i	0.992659	−	0.120950i
$28$	2.57967	+	0.184502i	0.487513	+	0.0348676i
$29$	4.95509	−	1.45495i	0.920137	−	0.270177i	0.212835	−	0.977088i	$-0.431730\pi$
$29$	4.95509	−	1.45495i	0.920137	−	0.270177i	0.707302	+	0.706912i	$0.249912\pi$
$30$	−2.32417	−	3.09810i	−0.424333	−	0.565634i
$31$	3.82329	−	8.37183i	0.686682	−	1.50362i	−0.168722	−	0.985664i	$-0.553964\pi$
$31$	3.82329	−	8.37183i	0.686682	−	1.50362i	0.855404	−	0.517961i	$-0.173309\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	−7.04842	−	8.25338i	−1.22697	−	1.43673i
$34$	−4.40886	+	0.633898i	−0.756112	+	0.108713i
$35$	5.43484	+	1.97643i	0.918656	+	0.334078i
$36$	−2.23879	−	1.99696i	−0.373131	−	0.332826i
$37$	2.21806	−	0.158639i	0.364647	−	0.0260800i	0.112186	−	0.993687i	$-0.464215\pi$
$37$	2.21806	−	0.158639i	0.364647	−	0.0260800i	0.252461	+	0.967607i	$0.418760\pi$
$38$	6.78305	−	2.52995i	1.10036	−	0.410412i
$39$	8.78003	−	3.20312i	1.40593	−	0.512910i
$40$	−0.457360	+	2.18879i	−0.0723150	+	0.346079i
$41$	−4.36817	+	3.78504i	−0.682194	+	0.591124i	−0.925465	−	0.378834i	$-0.876325\pi$
$41$	−4.36817	+	3.78504i	−0.682194	+	0.591124i	0.243271	+	0.969958i	$0.421780\pi$
$42$	4.42925	+	0.669343i	0.683448	+	0.103282i
$43$	−1.82014	−	0.678875i	−0.277568	−	0.103528i	0.206825	−	0.978378i	$-0.433687\pi$
$43$	−1.82014	−	0.678875i	−0.277568	−	0.103528i	−0.484393	+	0.874850i	$0.660960\pi$
$44$	−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	$0.0946217\pi$
$48$	−0.0124434	+	1.73201i	−0.00179605	+	0.249994i
$49$	0.283114	−	0.129294i	0.0404448	−	0.0184705i
$50$	−2.32388	+	4.42714i	−0.328647	+	0.626092i
$51$	−7.69899	+	0.495076i	−1.07807	+	0.0693245i
$52$	−4.73591	−	2.58600i	−0.656753	−	0.358614i
$53$	−0.922400	−	4.24020i	−0.126701	−	0.582437i	−0.996093	−	0.0883127i	$-0.971853\pi$
$53$	−0.922400	−	4.24020i	−0.126701	−	0.582437i	0.869391	−	0.494124i	$-0.164511\pi$
$54$	−3.59420	−	3.75256i	−0.489108	−	0.510659i
$55$	−5.71590	+	12.7929i	−0.770732	+	1.72500i
$56$	−1.39824	−	2.17570i	−0.186848	−	0.290741i
$57$	12.0563	−	3.44617i	1.59690	−	0.456456i
$58$	−4.13422	−	3.09484i	−0.542850	−	0.406372i
$59$	4.84016	−	3.11058i	0.630135	−	0.404963i	−0.186224	−	0.982507i	$-0.559625\pi$
$59$	4.84016	−	3.11058i	0.630135	−	0.404963i	0.816360	+	0.577544i	$0.195989\pi$
$60$	−1.08734	+	3.71722i	−0.140375	+	0.479890i
$61$	−0.196690	+	0.430690i	−0.0251835	+	0.0551442i	−0.921806	−	0.387652i	$-0.873286\pi$
$61$	−0.196690	+	0.430690i	−0.0251835	+	0.0551442i	0.896622	+	0.442796i	$0.146013\pi$
$62$	−8.99320	+	1.95635i	−1.14214	+	0.248457i
$63$	7.55700	+	1.75801i	0.952092	+	0.221488i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	−8.60149	−	8.46143i	−1.06688	−	1.04951i
$66$	−2.38321	+	10.5886i	−0.293353	+	1.30337i
$67$	2.46652	−	1.84642i	0.301334	−	0.225576i	−0.437901	−	0.899023i	$-0.644278\pi$
$67$	2.46652	−	1.84642i	0.301334	−	0.225576i	0.739235	+	0.673447i	$0.235187\pi$
$68$	3.14959	+	3.14959i	0.381944	+	0.381944i
$69$	−7.55926	+	3.44348i	−0.910028	+	0.414547i
$70$	−1.67477	−	5.53525i	−0.200173	−	0.661589i
$71$	5.04374	+	0.725180i	0.598582	+	0.0860631i	0.434944	−	0.900457i	$-0.356768\pi$
$71$	5.04374	+	0.725180i	0.598582	+	0.0860631i	0.163638	+	0.986521i	$0.447677\pi$
$72$	−0.256990	+	2.98897i	−0.0302865	+	0.352254i
$73$	2.53996	−	1.38692i	0.297280	−	0.162327i	−0.323686	−	0.946165i	$-0.604922\pi$
$73$	2.53996	−	1.38692i	0.297280	−	0.162327i	0.620966	+	0.783837i	$0.286740\pi$
$74$	−1.45623	−	1.68058i	−0.169283	−	0.195363i
$75$	−4.61463	+	7.32838i	−0.532851	+	0.846209i
$76$	−6.09026	−	3.91397i	−0.698600	−	0.448963i
$77$	−5.66350	−	15.1844i	−0.645415	−	1.73043i
$78$	−7.82591	−	5.10922i	−0.886109	−	0.578505i
$79$	−2.15836	−	3.35847i	−0.242834	−	0.377858i	0.698347	−	0.715759i	$-0.253919\pi$
$79$	−2.15836	−	3.35847i	−0.242834	−	0.377858i	−0.941181	+	0.337902i	$0.890283\pi$
$80$	2.02631	−	0.945560i	0.226548	−	0.105717i
$81$	−5.69588	−	6.96828i	−0.632875	−	0.774254i
$82$	5.64783	+	1.22861i	0.623699	+	0.135677i
$83$	1.87480	−	0.134088i	0.205786	−	0.0147181i	0.0319345	−	0.999490i	$-0.489833\pi$
$83$	1.87480	−	0.134088i	0.205786	−	0.0147181i	0.173852	+	0.984772i	$0.444379\pi$
$84$	−2.11851	−	3.94692i	−0.231149	−	0.430644i
$85$	4.84485	+	8.70210i	0.525498	+	0.943875i
$86$	0.547299	+	1.86393i	0.0590167	+	0.200993i
$87$	−6.71777	−	5.90601i	−0.720220	−	0.633191i
$88$	5.49977	−	3.00310i	0.586278	−	0.320132i
$89$	5.01417	+	10.9795i	0.531501	+	1.16383i	0.964899	+	0.262622i	$0.0845873\pi$
$89$	5.01417	+	10.9795i	0.531501	+	1.16383i	−0.433398	+	0.901203i	$0.642685\pi$
$90$	−2.38295	+	6.27069i	−0.251185	+	0.660989i
$91$	13.9554			1.46292
$92$	4.37477	+	1.96504i	0.456101	+	0.204870i
$93$	−15.7946	+	2.15522i	−1.63783	+	0.223486i
$94$	−6.36487	−	0.915131i	−0.656487	−	0.0943885i
$95$	−10.7010	−	12.1467i	−1.09790	−	1.24622i
$96$	1.39400	−	1.02799i	0.142274	−	0.104919i
$97$	−0.360875	+	5.04569i	−0.0366413	+	0.512312i	0.945679	+	0.325103i	$0.105399\pi$
$97$	−0.360875	+	5.04569i	−0.0366413	+	0.512312i	−0.982320	+	0.187209i	$0.940056\pi$
$98$	−0.273169	−	0.149161i	−0.0275942	−	0.0150676i
$99$	−5.55485	+	17.9594i	−0.558283	+	1.80498i
$100$	4.93676	−	0.792721i	0.493676	−	0.0792721i
$101$	1.94958	+	1.68932i	0.193990	+	0.168093i	0.746440	−	0.665453i	$-0.231761\pi$
$101$	1.94958	+	1.68932i	0.193990	+	0.168093i	−0.552450	+	0.833546i	$0.686307\pi$
$102$	5.01016	+	5.86667i	0.496080	+	0.580887i
$103$	2.23970	+	1.67662i	0.220684	+	0.165202i	0.703900	−	0.710299i	$-0.251440\pi$
$103$	2.23970	+	1.67662i	0.220684	+	0.165202i	−0.483216	+	0.875501i	$0.660531\pi$
$104$	0.767924	+	5.34103i	0.0753011	+	0.523731i
$105$	−2.13919	−	9.78546i	−0.208764	−	0.954963i
$106$	−2.84168	+	3.27948i	−0.276009	+	0.318531i
$107$	4.86491	+	13.0433i	0.470308	+	1.26095i	0.928248	+	0.371962i	$0.121315\pi$
$107$	4.86491	+	13.0433i	0.470308	+	1.26095i	−0.457940	+	0.888983i	$0.651412\pi$
$108$	−0.850161	+	5.12613i	−0.0818067	+	0.493262i
$109$	−0.0822916	−	0.280260i	−0.00788211	−	0.0268440i	0.955458	−	0.295127i	$-0.0953620\pi$
$109$	−0.0822916	−	0.280260i	−0.00788211	−	0.0268440i	−0.963340	+	0.268283i	$0.913544\pi$
$110$	13.6667	−	3.09070i	1.30307	−	0.294687i
$111$	−2.28597	−	3.09987i	−0.216975	−	0.294227i
$112$	−0.903807	+	2.42320i	−0.0854017	+	0.228971i
$113$	10.5048	−	7.86383i	0.988213	−	0.739767i	0.0225981	−	0.999745i	$-0.492806\pi$
$113$	10.5048	−	7.86383i	0.988213	−	0.739767i	0.965615	+	0.259978i	$0.0837153\pi$
$114$	−9.98389	−	7.58638i	−0.935077	−	0.710529i
$115$	8.20506	+	6.90486i	0.765125	+	0.643881i
$116$			5.16428i			0.479491i
$117$	−12.8183	−	9.88621i	−1.18505	−	0.913981i
$118$	−5.39075	−	2.01065i	−0.496259	−	0.185095i
$119$	−11.0531	−	3.24548i	−1.01323	−	0.297513i
$120$	3.62740	−	1.35718i	0.331135	−	0.123893i
$121$	27.1212	−	7.96349i	2.46556	−	0.723954i
$122$	0.462657	−	0.100645i	0.0418870	−	0.00911195i
$123$	9.58508	+	2.88939i	0.864258	+	0.260528i
$124$	6.95557	+	6.02703i	0.624628	+	0.541243i
$125$	11.1024	+	1.31817i	0.993025	+	0.117900i
$126$	−3.12138	−	7.10323i	−0.278075	−	0.632806i
$127$	−5.36331	+	7.16454i	−0.475916	+	0.635750i	−0.972684	−	0.232134i	$-0.925429\pi$
$127$	−5.36331	+	7.16454i	−0.475916	+	0.635750i	0.496767	+	0.867884i	$0.334520\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	0.691582	+	3.29287i	0.0608904	+	0.289921i
$130$	−1.61904	+	11.9566i	−0.142000	+	1.04866i
$131$	−6.92225	+	10.7712i	−0.604800	+	0.941087i	0.394950	+	0.918703i	$0.370762\pi$
$131$	−6.92225	+	10.7712i	−0.604800	+	0.941087i	−0.999749	+	0.0223841i	$0.992874\pi$
$132$	9.90483	−	4.43766i	0.862104	−	0.386249i
$133$	18.6756	+	1.33570i	1.61938	+	0.115820i
$134$	−2.95626	−	0.868037i	−0.255382	−	0.0749870i
$135$	−4.96729	+	10.5036i	−0.427516	+	0.904008i
$136$	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	$0.102088\pi$
$138$	7.28675	+	3.98790i	0.620289	+	0.339472i
$139$		−	7.19528i		−	0.610296i	−0.952305	−	0.305148i	$-0.901294\pi$
$139$		−	7.19528i		−	0.610296i	0.952305	−	0.305148i	$-0.0987059\pi$
$140$	−3.42754	+	4.65787i	−0.289680	+	0.393662i
$141$	−10.8658	−	2.44560i	−0.915068	−	0.205957i
$142$	−2.44206	−	4.47231i	−0.204933	−	0.375308i
$143$	−2.41216	+	33.7263i	−0.201715	+	2.82034i
$144$	2.54680	−	1.58549i	0.212234	−	0.132124i
$145$	−3.16230	+	11.1062i	−0.262615	+	0.922324i
$146$	−2.63243	−	1.20219i	−0.217862	−	0.0994941i
$147$	−0.451400	−	0.294701i	−0.0372308	−	0.0243065i
$148$	−0.472687	+	2.17291i	−0.0388546	+	0.178612i
$149$	−0.448659	−	3.12049i	−0.0367555	−	0.255640i	0.963156	−	0.268943i	$-0.0866745\pi$
$149$	−0.448659	−	3.12049i	−0.0367555	−	0.255640i	−0.999912	+	0.0133031i	$0.995765\pi$
$150$	8.63212	−	0.697536i	0.704809	−	0.0569536i
$151$	−0.0524966	+	0.0337375i	−0.00427212	+	0.00274552i	−0.542775	−	0.839878i	$-0.682626\pi$
$151$	−0.0524966	+	0.0337375i	−0.00427212	+	0.00274552i	0.538503	+	0.842624i	$0.318990\pi$
$152$	0.516460	+	7.22106i	0.0418905	+	0.585705i
$153$	7.85337	+	10.8112i	0.634907	+	0.874038i
$154$	−8.76175	+	13.6335i	−0.706042	+	1.09862i
$155$	11.2680	+	17.2209i	0.905065	+	1.38321i
$156$	0.599751	+	9.32680i	0.0480185	+	0.746742i
$157$	1.50966	+	2.76473i	0.120484	+	0.220650i	0.930959	−	0.365123i	$-0.118973\pi$
$157$	1.50966	+	2.76473i	0.120484	+	0.220650i	−0.810476	+	0.585772i	$0.800791\pi$
$158$	−1.39514	+	3.74051i	−0.110991	+	0.297579i
$159$	−5.35267	+	5.27630i	−0.424494	+	0.418438i
$160$	−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
$163$	9.15668	+	12.2319i	0.717206	+	0.958075i	0.999999	−	0.00110558i	$-0.000351919\pi$
$163$	9.15668	+	12.2319i	0.717206	+	0.958075i	−0.282793	+	0.959181i	$0.591261\pi$
$164$	−2.40107	−	5.25760i	−0.187492	−	0.410550i
$165$	24.0186	−	3.47846i	1.86984	−	0.270797i
$166$	−1.23087	−	1.42050i	−0.0955341	−	0.110252i
$167$	−4.12314	+	7.55098i	−0.319058	+	0.584312i	−0.987156	−	0.159762i	$-0.948927\pi$
$167$	−4.12314	+	7.55098i	−0.319058	+	0.584312i	0.668097	+	0.744074i	$0.267109\pi$
$168$	−1.89009	+	4.06126i	−0.145824	+	0.313333i
$169$	−14.6599	−	6.69495i	−1.12768	−	0.514996i
$170$	4.06298	−	9.09348i	0.311616	−	0.697438i
$171$	−16.2077	−	14.4570i	−1.23943	−	1.10555i
$172$	1.16417	−	1.55515i	0.0887669	−	0.118579i
$173$	6.73452	−	8.99626i	0.512016	−	0.683973i	−0.467809	−	0.883829i	$-0.654957\pi$
$173$	6.73452	−	8.99626i	0.512016	−	0.683973i	0.979825	+	0.199856i	$0.0640475\pi$
$174$	−0.702195	+	8.91719i	−0.0532333	+	0.676010i
$175$	−10.2234	+	7.91834i	−0.772820	+	0.598570i
$176$	−5.70000	−	2.60310i	−0.429654	−	0.196216i
$177$	−9.03485	−	4.20478i	−0.679101	−	0.316051i
$178$	5.78466	−	10.5938i	0.433579	−	0.794041i
$179$	−8.48277	−	9.78963i	−0.634032	−	0.731712i	0.344276	−	0.938868i	$-0.388124\pi$
$179$	−8.48277	−	9.78963i	−0.634032	−	0.731712i	−0.978308	+	0.207157i	$0.933579\pi$
$180$	6.44799	−	1.85023i	0.480605	−	0.137908i
$181$	−7.87130	−	17.2357i	−0.585069	−	1.28112i	−0.938376	−	0.345615i	$-0.887670\pi$
$181$	−7.87130	−	17.2357i	−0.585069	−	1.28112i	0.353307	−	0.935507i	$-0.385057\pi$
$182$	−8.36313	−	11.1718i	−0.619917	−	0.828112i
$183$	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
$186$	11.1907	+	11.3527i	0.820543	+	0.832418i
$187$	9.75396	−	26.1514i	0.713280	−	1.91238i
$188$	3.08173	+	5.64376i	0.224758	+	0.411614i
$189$	−4.42387	−	12.6896i	−0.321789	−	0.923032i
$190$	−3.31106	+	15.8458i	−0.240209	+	1.14957i
$191$	6.99651	−	10.8868i	0.506250	−	0.787740i	−0.490228	−	0.871594i	$-0.663087\pi$
$191$	6.99651	−	10.8868i	0.506250	−	0.787740i	0.996478	+	0.0838538i	$0.0267229\pi$
$192$	−1.65834	−	0.499902i	−0.119681	−	0.0360773i
$193$	1.26925	+	17.7464i	0.0913624	+	1.27741i	0.811817	+	0.583911i	$0.198478\pi$
$193$	1.26925	+	17.7464i	0.0913624	+	1.27741i	−0.720455	+	0.693502i	$0.756067\pi$
$194$	4.25554	−	2.73487i	0.305530	−	0.196352i
$195$	−4.42137	+	20.4254i	−0.316621	+	1.46269i
$196$	0.0442940	+	0.308072i	0.00316386	+	0.0220051i
$197$	1.74935	−	8.04165i	0.124636	−	0.572944i	−0.871893	−	0.489697i	$-0.837107\pi$
$197$	1.74935	−	8.04165i	0.124636	−	0.572944i	0.996529	−	0.0832467i	$-0.0265290\pi$
$198$	17.7061	−	6.31576i	1.25832	−	0.448842i
$199$	−3.01064	−	1.37491i	−0.213418	−	0.0974649i	0.305838	−	0.952084i	$-0.401064\pi$
$199$	−3.01064	−	1.37491i	−0.213418	−	0.0974649i	−0.519256	+	0.854619i	$0.673791\pi$
$200$	−3.59310	−	3.47702i	−0.254070	−	0.245862i
$201$	−4.98657	−	1.90081i	−0.351725	−	0.134073i
$202$	0.184031	−	2.57309i	0.0129484	−	0.181042i
$203$	−6.40094	−	11.7224i	−0.449258	−	0.822754i
$204$	1.69403	−	7.52660i	0.118606	−	0.526968i
$205$	−1.94426	−	12.7772i	−0.135793	−	0.892399i
$206$		−	2.79773i		−	0.194927i
$207$	12.0398	+	7.87671i	0.836826	+	0.547470i
$208$	3.81551	−	3.81551i	0.264558	−	0.264558i
$209$	−6.45607	+	44.9029i	−0.446575	+	3.10600i
$210$	−6.55170	+	7.57672i	−0.452110	+	0.522843i
$211$	3.15697	+	0.926969i	0.217335	+	0.0638152i	0.388587	−	0.921412i	$-0.372963\pi$
$211$	3.15697	+	0.926969i	0.217335	+	0.0638152i	−0.171253	+	0.985227i	$0.554781\pi$
$212$	4.32832	+	0.309567i	0.297270	+	0.0212612i
$213$	−3.60862	−	8.05441i	−0.247259	−	0.551879i
$214$	7.52628	−	11.7111i	0.514486	−	0.800556i
$215$	3.45593	−	2.63161i	0.235692	−	0.179475i
$216$	4.61316	−	2.39139i	0.313886	−	0.162713i
$217$	−23.2588	−	5.05964i	−1.57891	−	0.343471i
$218$	−0.175044	+	0.233831i	−0.0118555	+	0.0158370i
$219$	−4.38197	−	2.43377i	−0.296106	−	0.164459i
$220$	−10.6644	−	9.08855i	−0.718992	−	0.612750i
$221$	18.1641	+	15.7393i	1.22185	+	1.05874i
$222$	−1.11164	+	3.68770i	−0.0746087	+	0.247502i
$223$	−26.8736	+	5.84600i	−1.79959	+	0.391477i	−0.982684	−	0.185292i	$-0.940677\pi$
$223$	−26.8736	+	5.84600i	−1.79959	+	0.391477i	−0.816907	+	0.576769i	$0.804313\pi$
$224$	2.48150	−	0.728635i	0.165802	−	0.0486840i
$225$	15.0000	−	0.0307175i	0.999998	−	0.00204784i
$226$	−12.5906	−	3.69694i	−0.837517	−	0.245917i
$227$	1.86435	+	0.695365i	0.123741	+	0.0461530i	0.410572	−	0.911828i	$-0.365329\pi$
$227$	1.86435	+	0.695365i	0.123741	+	0.0461530i	−0.286831	+	0.957981i	$0.592602\pi$
$228$	−0.0900838	+	12.5389i	−0.00596594	+	0.830406i
$229$			2.15417i			0.142351i	0.997464	+	0.0711756i	$0.0226751\pi$
$229$			2.15417i			0.142351i	−0.997464	+	0.0711756i	$0.977325\pi$
$230$	0.610518	−	10.7064i	0.0402563	−	0.705960i
$231$	−16.9827	+	22.3498i	−1.11738	+	1.47051i
$232$	4.13422	−	3.09484i	0.271425	−	0.203186i
$233$	−3.39176	+	9.09367i	−0.222202	+	0.595746i	−0.999440	−	0.0334603i	$-0.989347\pi$
$233$	−3.39176	+	9.09367i	−0.222202	+	0.595746i	0.777238	+	0.629206i	$0.216620\pi$
$234$	−0.232587	+	16.1862i	−0.0152047	+	1.05812i
$235$	3.17162	+	14.0245i	0.206894	+	0.914857i
$236$	1.62095	+	5.52045i	0.105515	+	0.359351i
$237$	−2.91760	+	6.26906i	−0.189518	+	0.407219i
$238$	4.02573	+	10.7934i	0.260949	+	0.699632i
$239$	17.1083	−	19.7441i	1.10665	−	1.27714i	0.149111	−	0.988820i	$-0.452359\pi$
$239$	17.1083	−	19.7441i	1.10665	−	1.27714i	0.957535	−	0.288317i	$-0.0930957\pi$
$240$	−3.26030	−	2.09056i	−0.210452	−	0.134945i
$241$	2.82688	+	19.6614i	0.182095	+	1.26650i	0.851797	+	0.523871i	$0.175513\pi$
$241$	2.82688	+	19.6614i	0.182095	+	1.26650i	−0.669702	+	0.742630i	$0.733578\pi$
$242$	−22.6282	−	16.9393i	−1.45460	−	1.08890i
$243$	−4.92610	+	14.7896i	−0.316010	+	0.948756i
$244$	−0.357830	−	0.310062i	−0.0229077	−	0.0198497i
$245$	−0.0933869	+	0.689659i	−0.00596627	+	0.0440607i
$246$	−3.43105	−	9.40480i	−0.218756	−	0.599628i
$247$	−34.2857	−	18.7214i	−2.18154	−	1.19121i
$248$	0.656573	−	9.18008i	0.0416924	−	0.582936i
$249$	−1.93220	−	2.62015i	−0.122448	−	0.166045i
$250$	−5.59815	−	9.67785i	−0.354058	−	0.612081i
$251$	−0.273494	−	0.0393225i	−0.0172628	−	0.00248201i	0.133678	−	0.991025i	$-0.457321\pi$
$251$	−0.273494	−	0.0393225i	−0.0172628	−	0.00248201i	−0.150941	+	0.988543i	$0.548230\pi$
$252$	−3.81585	+	6.75560i	−0.240376	+	0.425563i
$253$	−0.187217	−	30.0514i	−0.0117702	−	1.88931i
$254$	8.94962			0.561549
$255$	8.25202	−	15.1493i	0.516762	−	0.948687i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−18.4845	+	10.0933i	−1.15303	+	0.629603i	−0.937874	−	0.346976i	$-0.887209\pi$
$257$	−18.4845	+	10.0933i	−1.15303	+	0.629603i	−0.215158	+	0.976579i	$0.569027\pi$
$258$	2.22163	−	2.52698i	0.138313	−	0.157323i
$259$	−1.62028	−	5.51818i	−0.100679	−	0.342883i
$260$	10.5420	−	5.86921i	0.653787	−	0.363993i
$261$	−2.42497	+	15.3019i	−0.150102	+	0.947163i
$262$	12.7712	−	0.913412i	0.789005	−	0.0564308i
$263$	−24.0744	−	5.23707i	−1.48449	−	0.322931i	−0.603996	−	0.796987i	$-0.706426\pi$
$263$	−24.0744	−	5.23707i	−1.48449	−	0.322931i	−0.880495	+	0.474056i	$0.842790\pi$
$264$	−9.48827	−	5.26983i	−0.583963	−	0.324336i
$265$	9.11887	+	3.31616i	0.560168	+	0.203710i
$266$	−10.1226	−	15.7510i	−0.620654	−	0.965756i
$267$	11.4289	−	17.5059i	0.699436	−	1.07134i
$268$	1.07672	+	2.88681i	0.0657713	+	0.176340i
$269$	−6.60017	−	4.24167i	−0.402420	−	0.258619i	0.323739	−	0.946146i	$-0.395060\pi$
$269$	−6.60017	−	4.24167i	−0.402420	−	0.258619i	−0.726159	+	0.687527i	$0.758696\pi$
$270$	11.3854	−	2.31806i	0.692891	−	0.141073i
$271$	15.9937	+	18.4577i	0.971548	+	1.12123i	0.992598	+	0.121448i	$0.0387536\pi$
$271$	15.9937	+	18.4577i	0.971548	+	1.12123i	−0.0210500	+	0.999778i	$0.506701\pi$
$272$	−3.90935	+	2.13467i	−0.237039	+	0.129433i
$273$	−12.9216	−	20.4276i	−0.782052	−	1.23634i
$274$	−10.3838	−	1.49297i	−0.627309	−	0.0901934i
$275$	−17.3694	−	26.0760i	−1.04741	−	1.57244i
$276$	−1.17431	−	8.22320i	−0.0706850	−	0.494978i
$277$	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	$0.590591\pi$
$278$	−5.76012	+	4.31197i	−0.345469	+	0.258615i
$279$	17.7794	+	21.1243i	1.06443	+	1.26468i
$280$	5.78287	−	0.0474678i	0.345592	−	0.00283674i
$281$	3.29041	−	2.85115i	0.196289	−	0.170086i	−0.551171	−	0.834393i	$-0.685819\pi$
$281$	3.29041	−	2.85115i	0.196289	−	0.170086i	0.747460	+	0.664307i	$0.231273\pi$
$282$	4.55384	+	10.1641i	0.271177	+	0.605266i
$283$	2.54224	−	0.553031i	0.151121	−	0.0328743i	−0.136369	−	0.990658i	$-0.543543\pi$
$283$	2.54224	−	0.553031i	0.151121	−	0.0328743i	0.287489	+	0.957784i	$0.407180\pi$
$284$	−2.11679	+	4.63513i	−0.125608	+	0.275044i
$285$	−7.87180	+	26.9108i	−0.466285	+	1.59406i
$286$	28.4449	−	18.2804i	1.68198	−	1.08094i
$287$	11.9668	+	8.95824i	0.706378	+	0.528788i
$288$	−2.79550	−	1.08867i	−0.164726	−	0.0641505i
$289$	−1.53533	−	2.38902i	−0.0903135	−	0.140531i
$290$	10.7861	−	4.12417i	0.633382	−	0.242180i
$291$	7.71994	−	4.14369i	0.452551	−	0.242907i
$292$	0.615154	+	2.82782i	0.0359992	+	0.165486i
$293$	−6.70616	−	3.66184i	−0.391778	−	0.213927i	0.271271	−	0.962503i	$-0.412556\pi$
$293$	−6.70616	−	3.66184i	−0.391778	−	0.213927i	−0.663049	+	0.748576i	$0.730738\pi$
$294$	0.0345938	+	0.537972i	0.00201755	+	0.0313752i
$295$	0.105599	+	12.8648i	0.00614820	+	0.749018i
$296$	2.02277	−	0.923768i	0.117571	−	0.0536930i
$297$	31.4320	−	8.49793i	1.82387	−	0.493100i
$298$	−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
$302$	0.0584684	+	0.0218076i	0.00336448	+	0.00125488i
$303$	0.667634	−	4.41794i	0.0383546	−	0.253804i
$304$	5.47125	−	4.74087i	0.313798	−	0.271907i
$305$	−0.579682	−	0.885930i	−0.0331925	−	0.0507282i
$306$	3.94850	−	12.7659i	0.225721	−	0.729777i
$307$	21.0637	−	7.85636i	1.20217	−	0.448386i	0.333013	−	0.942922i	$-0.391935\pi$
$307$	21.0637	−	7.85636i	1.20217	−	0.448386i	0.869157	+	0.494536i	$0.164662\pi$
$308$	16.1649	−	1.15614i	0.921083	−	0.0658771i
$309$	0.380412	−	4.83085i	0.0216409	−	0.274818i
$310$	7.03336	−	19.3405i	0.399468	−	1.09847i
$311$	−13.8424	+	1.99024i	−0.784930	+	0.112856i	−0.523115	−	0.852262i	$-0.675230\pi$
$311$	−13.8424	+	1.99024i	−0.784930	+	0.112856i	−0.261815	+	0.965118i	$0.584321\pi$
$312$	7.10707	−	6.06947i	0.402359	−	0.343616i
$313$	−2.32322	−	32.4829i	−0.131316	−	1.83604i	−0.455722	−	0.890122i	$-0.650619\pi$
$313$	−2.32322	−	32.4829i	−0.131316	−	1.83604i	0.324405	−	0.945918i	$-0.394836\pi$
$314$	1.30858	−	2.86538i	0.0738473	−	0.161703i
$315$	−12.3431	+	12.1919i	−0.695453	+	0.686937i
$316$	3.83051	−	1.12474i	0.215483	−	0.0632715i
$317$	−14.4587	−	1.03411i	−0.812083	−	0.0580813i	−0.340881	−	0.940107i	$-0.610725\pi$
$317$	−14.4587	−	1.03411i	−0.812083	−	0.0580813i	−0.471202	+	0.882025i	$0.656180\pi$
$318$	7.43163	+	1.12306i	0.416745	+	0.0629780i
$319$	29.4364	−	13.4431i	1.64812	−	0.752672i
$320$	0.336382	+	2.21062i	0.0188043	+	0.123577i
$321$	14.5881	−	19.1983i	0.814226	−	1.07154i
$322$	8.18066	+	9.32299i	0.455891	+	0.519550i
$323$	22.8015	+	22.8015i	1.26871	+	1.26871i
$324$	8.29073	−	3.50196i	0.460596	−	0.194554i
$325$	26.2655	−	6.16696i	1.45695	−	0.342081i
$326$	4.30474	−	14.6606i	0.238417	−	0.811975i
$327$	−0.334044	+	0.379957i	−0.0184726	+	0.0210116i
$328$	−2.77002	+	5.07291i	−0.152949	+	0.280105i
$329$	−13.9905	−	8.99114i	−0.771320	−	0.495697i
$330$	−17.1784	−	17.1433i	−0.945643	−	0.943708i
$331$	2.07711	−	2.39712i	0.114169	−	0.131757i	−0.695789	−	0.718247i	$-0.744945\pi$
$331$	2.07711	−	2.39712i	0.114169	−	0.131757i	0.809957	+	0.586489i	$0.199490\pi$
$332$	−0.399536	+	1.83664i	−0.0219274	+	0.100799i
$333$	−2.42090	+	6.21641i	−0.132665	+	0.340657i
$334$	8.51578	−	1.22438i	0.465962	−	0.0669953i
$335$	0.547879	+	6.86766i	0.0299338	+	0.375220i
$336$	4.38390	−	0.920724i	0.239161	−	0.0502296i
$337$	−15.4076	+	5.74673i	−0.839305	+	0.313044i	−0.732104	−	0.681193i	$-0.761461\pi$
$337$	−15.4076	+	5.74673i	−0.839305	+	0.313044i	−0.107201	+	0.994237i	$0.534189\pi$
$338$	3.42577	+	15.7480i	0.186337	+	0.856578i
$339$	−21.2376	−	8.09550i	−1.15347	−	0.439687i
$340$	−9.71456	+	2.19694i	−0.526846	+	0.119146i
$341$	16.2480	−	55.3357i	0.879880	−	2.99660i
$342$	−1.86048	+	21.6387i	−0.100603	+	1.17009i
$343$	−11.3316	−	15.1373i	−0.611850	−	0.817336i
$344$	−1.94262			−0.104739
$345$	2.50995	−	18.4038i	0.135131	−	0.990828i
$346$	−11.2377			−0.604144
$347$	−9.14011	−	12.2098i	−0.490667	−	0.655454i	0.485051	−	0.874486i	$-0.338801\pi$
$347$	−9.14011	−	12.2098i	−0.490667	−	0.655454i	−0.975718	+	0.219032i	$0.929710\pi$
$348$	7.55939	−	4.78174i	0.405226	−	0.256328i
$349$	−6.14552	+	20.9297i	−0.328962	+	1.12034i	0.614515	+	0.788905i	$0.289352\pi$
$349$	−6.14552	+	20.9297i	−0.328962	+	1.12034i	−0.943477	+	0.331437i	$0.892466\pi$
$350$	12.4656	+	3.43901i	0.666317	+	0.183823i
$351$	−2.60247	+	27.9171i	−0.138910	+	1.49011i
$352$	1.33199	+	6.12307i	0.0709954	+	0.326361i
$353$	−16.6195	+	6.19875i	−0.884567	+	0.329926i	−0.750362	−	0.661027i	$-0.770121\pi$
$353$	−16.6195	+	6.19875i	−0.884567	+	0.329926i	−0.134205	+	0.990954i	$0.542848\pi$
$354$	2.04828	+	9.75260i	0.108865	+	0.518345i
$355$	−7.39063	+	8.67206i	−0.392254	+	0.460265i
$356$	−11.9474	+	1.71778i	−0.633212	+	0.0910421i
$357$	5.48365	+	19.1844i	0.290226	+	1.01535i
$358$	−2.75347	+	12.6575i	−0.145526	+	0.668970i
$359$	−0.0339069	+	0.0391307i	−0.00178954	+	0.00206524i	−0.756644	−	0.653828i	$-0.773162\pi$
$359$	−0.0339069	+	0.0391307i	−0.00178954	+	0.00206524i	0.754854	+	0.655893i	$0.227708\pi$
$360$	−5.34533	−	4.05308i	−0.281723	−	0.213616i
$361$	−28.1066	−	18.0630i	−1.47930	−	0.950685i
$362$	−9.08083	+	16.6303i	−0.477278	+	0.874069i
$363$	−36.7690	−	32.3259i	−1.92987	−	1.69667i
$364$	−3.93168	+	13.3901i	−0.206076	+	0.701830i
$365$	−0.408646	+	6.45816i	−0.0213895	+	0.338036i
$366$	−0.575708	−	0.584040i	−0.0300927	−	0.0305282i
$367$	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	$0.707340\pi$
$368$	−3.11796	+	3.64394i	−0.162535	+	0.189954i
$369$	−4.64563	−	16.7059i	−0.241842	−	0.869672i
$370$	4.91581	−	0.748021i	0.255561	−	0.0388877i
$371$	−10.2086	+	4.66210i	−0.530003	+	0.242044i
$372$	2.38194	−	15.7620i	0.123498	−	0.817223i
$373$	−32.6309	−	2.33381i	−1.68957	−	0.120840i	−0.806853	−	0.590753i	$-0.798831\pi$
$373$	−32.6309	−	2.33381i	−1.68957	−	0.120840i	−0.882713	+	0.469913i	$0.844285\pi$
$374$	−26.7806	+	7.86349i	−1.38479	+	0.406611i
$375$	−8.35045	−	17.4720i	−0.431215	−	0.902249i
$376$	2.67125	−	5.84923i	0.137759	−	0.301651i
$377$	1.98795	+	27.7952i	0.102385	+	1.43153i
$378$	−7.50742	+	11.1461i	−0.386140	+	0.573293i
$379$	−20.9333	+	3.00976i	−1.07527	+	0.154601i	−0.657128	−	0.753779i	$-0.728229\pi$
$379$	−20.9333	+	3.00976i	−1.07527	+	0.154601i	−0.418146	+	0.908380i	$0.637320\pi$
$380$	14.6694	−	6.84538i	0.752527	−	0.351161i
$381$	15.4534	+	1.21689i	0.791699	+	0.0623433i
$382$	−12.9082	+	0.923211i	−0.660440	+	0.0472356i
$383$	15.5677	−	5.80644i	0.795471	−	0.296695i	0.0813207	−	0.996688i	$-0.474086\pi$
$383$	15.5677	−	5.80644i	0.795471	−	0.296695i	0.714150	+	0.699993i	$0.246813\pi$
$384$	0.593615	+	1.62715i	0.0302928	+	0.0830352i
$385$	35.4721	+	7.41208i	1.80783	+	0.377755i
$386$	13.4461	−	11.6511i	0.684388	−	0.593025i
$387$	4.17970	−	4.06128i	0.212466	−	0.206446i
$388$	−4.73963	−	1.76779i	−0.240618	−	0.0897460i
$389$	−2.92789	+	20.3639i	−0.148450	+	1.03249i	0.770309	+	0.637671i	$0.220102\pi$
$389$	−2.92789	+	20.3639i	−0.148450	+	1.03249i	−0.918759	+	0.394820i	$0.870807\pi$
$390$	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
$393$	22.1762	+	0.159322i	1.11864	+	0.00803674i
$394$	−7.48602	+	3.41875i	−0.377140	+	0.172234i
$395$	8.92658	−	0.0732725i	0.449145	−	0.00368674i
$396$	−15.6669	−	10.3896i	−0.787292	−	0.522096i
$397$	−25.3215	−	13.8266i	−1.27085	−	0.693938i	−0.304832	−	0.952406i	$-0.598600\pi$
$397$	−25.3215	−	13.8266i	−1.27085	−	0.693938i	−0.966020	+	0.258469i	$0.916782\pi$
$398$	0.703534	+	3.23409i	0.0352650	+	0.162110i
$399$	−15.3370	−	28.5737i	−0.767810	−	1.43048i
$400$	−0.630236	+	4.96012i	−0.0315118	+	0.248006i
$401$	0.399693	+	0.621934i	0.0199597	+	0.0310579i	0.851090	−	0.525020i	$-0.175942\pi$
$401$	0.399693	+	0.621934i	0.0199597	+	0.0310579i	−0.831130	+	0.556078i	$0.812306\pi$
$402$	1.46666	+	5.13107i	0.0731504	+	0.255914i
$403$	39.7563	+	29.7612i	1.98040	+	1.48251i
$404$	−2.17015	+	1.39467i	−0.107969	+	0.0693874i
$405$	19.9744	−	2.45453i	0.992534	−	0.121966i
$406$	−5.54836	+	12.1492i	−0.275361	+	0.602956i
$407$	13.6160	−	2.96198i	0.674921	−	0.146820i
$408$	−7.04055	+	3.15438i	−0.348559	+	0.156165i
$409$	−2.48067	+	2.14951i	−0.122661	+	0.106287i	−0.714031	−	0.700114i	$-0.753133\pi$
$409$	−2.48067	+	2.14951i	−0.122661	+	0.106287i	0.591370	+	0.806400i	$0.298587\pi$
$410$	−9.06354	+	9.21356i	−0.447616	+	0.455025i
$411$	−17.7268	−	3.98982i	−0.874398	−	0.196803i
$412$	−2.23970	+	1.67662i	−0.110342	+	0.0826010i
$413$	−10.5218	−	10.5218i	−0.517745	−	0.517745i
$414$	−0.909563	−	14.3587i	−0.0447026	−	0.705692i
$415$	−1.98389	+	3.70520i	−0.0973852	+	0.181881i
$416$	−5.34103	−	0.767924i	−0.261865	−	0.0376506i
$417$	−10.5323	+	6.66229i	−0.515771	+	0.326254i
$418$	39.8156	−	21.7410i	1.94745	−	1.06339i
$419$	8.74979	+	10.0978i	0.427455	+	0.493310i	0.928094	−	0.372347i	$-0.121447\pi$
$419$	8.74979	+	10.0978i	0.427455	+	0.493310i	−0.500638	+	0.865657i	$0.666901\pi$
$420$	9.99176	+	0.704343i	0.487548	+	0.0343684i
$421$	−7.32306	−	4.70625i	−0.356904	−	0.229368i	0.349885	−	0.936793i	$-0.386221\pi$
$421$	−7.32306	−	4.70625i	−0.356904	−	0.229368i	−0.706789	+	0.707424i	$0.749857\pi$
$422$	−1.14982	−	3.08280i	−0.0559725	−	0.150068i
$423$	6.48111	+	18.1697i	0.315122	+	0.883440i
$424$	−2.34604	−	3.65051i	−0.113934	−	0.177285i
$425$	−22.2373	−	1.22392i	−1.07867	−	0.0593688i
$426$	−4.28532	+	7.71568i	−0.207624	+	0.373826i
$427$	1.19655	+	0.260294i	0.0579052	+	0.0125965i
$428$	−13.8856	+	0.993116i	−0.671185	+	0.0480041i
$429$	51.6015	−	27.6972i	2.49135	−	1.33723i
$430$	−4.17777	−	1.18955i	−0.201470	−	0.0573650i
$431$	−7.23601	−	24.6436i	−0.348546	−	1.18704i	−0.928170	−	0.372155i	$-0.878619\pi$
$431$	−7.23601	−	24.6436i	−0.348546	−	1.18704i	0.579624	−	0.814884i	$-0.303199\pi$
$432$	−4.67897	−	2.25992i	−0.225117	−	0.108731i
$433$	7.66202	−	4.18378i	0.368213	−	0.201060i	−0.284480	−	0.958682i	$-0.591821\pi$
$433$	7.66202	−	4.18378i	0.368213	−	0.201060i	0.652693	+	0.757622i	$0.273639\pi$
$434$	9.88803	+	21.6518i	0.474640	+	1.03932i
$435$	19.1852	−	5.65463i	0.919860	−	0.271119i
$436$	0.292091			0.0139886
$437$	31.6711	+	14.2259i	1.51504	+	0.680519i
$438$	0.677687	+	4.96645i	0.0323811	+	0.237306i
$439$	29.5806	+	4.25305i	1.41181	+	0.202987i	0.805665	−	0.592371i	$-0.201808\pi$
$439$	29.5806	+	4.25305i	1.41181	+	0.202987i	0.606140	+	0.795358i	$0.292717\pi$
$440$	−0.884840	+	13.9838i	−0.0421831	+	0.666653i
$441$	−0.0134157	+	0.933623i	−0.000638842	+	0.0444582i
$442$	1.71461	−	23.9734i	0.0815557	−	1.14030i
$443$	−25.6133	−	13.9859i	−1.21693	−	0.664492i	−0.263076	−	0.964775i	$-0.584737\pi$
$443$	−25.6133	−	13.9859i	−1.21693	−	0.664492i	−0.953850	+	0.300283i	$0.902919\pi$
$444$	3.61834	−	1.32004i	0.171719	−	0.0626462i
$445$	−26.7459	−	3.62166i	−1.26788	−	0.171683i
$446$	20.7847	+	18.0101i	0.984185	+	0.852801i
$447$	−4.15230	+	3.54608i	−0.196397	+	0.167724i
$448$	−2.07041	−	1.54989i	−0.0978177	−	0.0732254i
$449$	−3.47587	−	24.1752i	−0.164036	−	1.14090i	−0.890928	−	0.454145i	$-0.849945\pi$
$449$	−3.47587	−	24.1752i	−0.164036	−	1.14090i	0.726891	−	0.686752i	$-0.240964\pi$
$450$	−9.01374	−	11.9897i	−0.424912	−	0.565199i
$451$	−23.7181	+	27.3721i	−1.11684	+	1.28890i
$452$	4.58573	+	12.2948i	0.215695	+	0.578300i
$453$	0.0979924	+	0.0456053i	0.00460409	+	0.00214272i
$454$	−0.560592	−	1.90920i	−0.0263099	−	0.0896033i
$455$	−16.6547	+	26.3890i	−0.780785	+	1.23714i
$456$	10.0919	−	7.44214i	0.472595	−	0.348510i
$457$	−4.23815	+	11.3629i	−0.198252	+	0.531535i	−0.997593	−	0.0693432i	$-0.977910\pi$
$457$	−4.23815	+	11.3629i	−0.198252	+	0.531535i	0.799341	+	0.600878i	$0.205182\pi$
$458$	1.72450	−	1.29094i	0.0805805	−	0.0603218i
$459$	8.55370	−	21.5060i	0.399252	−	1.00382i
$460$	−8.93679	+	5.92737i	−0.416680	+	0.276365i
$461$		−	3.86835i		−	0.180167i	−0.995934	−	0.0900835i	$-0.971287\pi$
$461$		−	3.86835i		−	0.180167i	0.995934	−	0.0900835i	$-0.0287134\pi$
$462$	28.0693	+	0.201660i	1.30590	+	0.00938207i
$463$	−3.10943	−	1.15976i	−0.144508	−	0.0538986i	0.276170	−	0.961109i	$-0.410935\pi$
$463$	−3.10943	−	1.15976i	−0.144508	−	0.0538986i	−0.420677	+	0.907210i	$0.638208\pi$
$464$	−4.95509	−	1.45495i	−0.230034	−	0.0675442i
$465$	14.7743	−	32.4391i	0.685142	−	1.50433i
$466$	9.31247	−	2.73439i	0.431392	−	0.126668i
$467$	−7.60450	+	1.65426i	−0.351894	+	0.0765499i	−0.385038	−	0.922901i	$-0.625812\pi$
$467$	−7.60450	+	1.65426i	−0.351894	+	0.0765499i	0.0331439	+	0.999451i	$0.489448\pi$
$468$	13.0971	−	9.51382i	0.605413	−	0.439777i
$469$	−6.02216	−	5.21823i	−0.278077	−	0.240955i
$470$	9.32650	−	10.9436i	0.430199	−	0.504790i
$471$	2.64914	−	4.76975i	0.122066	−	0.219778i
$472$	3.44795	−	4.60592i	0.158705	−	0.212005i
$473$	−11.8948	−	2.58755i	−0.546922	−	0.118976i
$474$	6.76709	−	1.42125i	0.310823	−	0.0652803i
$475$	35.7397	−	5.73890i	1.63985	−	0.263319i
$476$	6.22803	−	9.69100i	0.285461	−	0.444186i
$477$	12.6795	+	2.94968i	0.580556	+	0.135057i
$478$	−26.0586	−	1.86375i	−1.19189	−	0.0852458i
$479$	1.27121	+	0.373262i	0.0580832	+	0.0170548i	0.310645	−	0.950526i	$-0.399455\pi$
$479$	1.27121	+	0.373262i	0.0580832	+	0.0170548i	−0.252562	+	0.967581i	$0.581273\pi$
$480$	0.280251	+	3.86283i	0.0127916	+	0.176313i
$481$	−1.70765	+	11.8770i	−0.0778622	+	0.541544i
$482$	14.0457	−	14.0457i	0.639763	−	0.639763i
$483$	12.8579	+	17.2104i	0.585056	+	0.783100i
$484$			28.2661i			1.28482i
$485$	−9.11051	−	6.70407i	−0.413687	−	0.304416i
$486$	14.7918	−	4.91956i	0.670971	−	0.223156i
$487$	−0.0565050	−	0.103481i	−0.00256048	−	0.00468918i	0.876396	−	0.481592i	$-0.159941\pi$
$487$	−0.0565050	−	0.103481i	−0.00256048	−	0.00468918i	−0.878956	+	0.476903i	$0.841759\pi$
$488$	−0.0337775	+	0.472271i	−0.00152903	+	0.0213787i
$489$	9.42644	−	24.7292i	0.426278	−	1.11829i
$490$	0.608065	−	0.338537i	0.0274696	−	0.0152936i
$491$	0.0307082	+	0.0140239i	0.00138584	+	0.000632892i	0.416108	−	0.909315i	$-0.363394\pi$
$491$	0.0307082	+	0.0140239i	0.00138584	+	0.000632892i	−0.414722	+	0.909948i	$0.636121\pi$
$492$	−5.47278	+	8.38279i	−0.246732	+	0.377925i
$493$	4.88957	−	22.4770i	0.220215	−	1.01231i
$494$	5.55939	+	38.6664i	0.250129	+	1.73968i
$495$	−27.3311	−	31.9372i	−1.22844	−	1.43547i
$496$	−7.74250	+	4.97581i	−0.347649	+	0.223420i
$497$	−0.940149	−	13.1450i	−0.0421715	−	0.589634i
$498$	−0.939611	+	3.11700i	−0.0421050	+	0.139676i
$499$	−22.4471	+	34.9284i	−1.00487	+	1.56361i	−0.191812	+	0.981432i	$0.561436\pi$
$499$	−22.4471	+	34.9284i	−1.00487	+	1.56361i	−0.813060	+	0.582180i	$0.802200\pi$
$500$	−4.39267	+	10.2813i	−0.196446	+	0.459792i
$501$	14.8707	−	0.956247i	0.664375	−	0.0427219i
$502$	0.132420	+	0.242508i	0.00591017	+	0.0108237i
$503$	5.93567	−	15.9142i	0.264659	−	0.709577i	−0.734850	−	0.678230i	$-0.762747\pi$
$503$	5.93567	−	15.9142i	0.264659	−	0.709577i	0.999509	−	0.0313474i	$-0.00997982\pi$
$504$	7.69489	−	0.993734i	0.342758	−	0.0442644i
$505$	−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
$508$	−5.36331	−	7.16454i	−0.237958	−	0.317875i
$509$	1.21331	+	2.65677i	0.0537789	+	0.117759i	0.934614	−	0.355664i	$-0.115745\pi$
$509$	1.21331	+	2.65677i	0.0537789	+	0.117759i	−0.880835	+	0.473424i	$0.843018\pi$
$510$	−17.0729	+	2.47256i	−0.756001	+	0.109487i
$511$	−4.90132	−	5.65643i	−0.216822	−	0.250226i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	−6.15474	+	37.1106i	−0.271738	+	1.63847i
$514$	19.1575	+	8.74892i	0.845000	+	0.385898i
$515$	−5.84333	+	2.23425i	−0.257488	+	0.0984530i
$516$	−3.35433	−	0.264141i	−0.147666	−	0.0116282i
$517$	24.1474	−	32.2571i	1.06200	−	1.41867i
$518$	−3.44653	+	4.60402i	−0.151432	+	0.202289i
$519$	−19.4042	−	1.52801i	−0.851752	−	0.0670722i
$520$	−11.0161	−	4.92202i	−0.483089	−	0.215845i
$521$	35.0860	+	16.0232i	1.53714	+	0.701990i	0.990770	−	0.135551i	$-0.0432804\pi$
$521$	35.0860	+	16.0232i	1.53714	+	0.701990i	0.546374	+	0.837541i	$0.316008\pi$
$522$	13.7030	−	7.22879i	0.599765	−	0.316395i
$523$	12.5562	−	22.9950i	0.549045	−	1.00550i	−0.444895	−	0.895583i	$-0.646759\pi$
$523$	12.5562	−	22.9950i	0.549045	−	1.00550i	0.993941	−	0.109919i	$-0.0350591\pi$
$524$	−8.38470	−	9.67646i	−0.366287	−	0.422718i
$525$	21.0569	+	7.63312i	0.918998	+	0.333137i
$526$	10.2348	+	22.4110i	0.446257	+	0.977166i
$527$	−24.5670	−	32.8176i	−1.07015	−	1.42956i
$528$	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
$531$	2.21070	+	17.1184i	0.0959363	+	0.742874i
$532$	−6.54311	+	17.5428i	−0.283680	+	0.760575i
$533$	−14.9469	−	27.3732i	−0.647422	−	1.18567i
$534$	−20.8632	+	1.34159i	−0.902840	+	0.0580562i
$535$	−30.4703	−	6.36693i	−1.31735	−	0.275266i
$536$	1.66575	−	2.59196i	0.0719495	−	0.111956i
$537$	−6.47550	+	21.4814i	−0.279438	+	0.926991i
$538$	0.559701	+	7.82565i	0.0241304	+	0.337388i
$539$	1.64071	−	1.05442i	0.0706703	−	0.0454170i
$540$	−8.67870	−	7.72529i	−0.373472	−	0.332444i
$541$	−0.780593	−	5.42914i	−0.0335603	−	0.233417i	0.966137	−	0.258031i	$-0.0830736\pi$
$541$	−0.780593	−	5.42914i	−0.0335603	−	0.233417i	−0.999697	+	0.0246135i	$0.992164\pi$
$542$	5.19149	−	23.8649i	0.222994	−	1.02509i
$543$	−17.9412	+	27.4809i	−0.769929	+	1.17932i
$544$	4.05168	+	1.85034i	0.173714	+	0.0793326i
$545$	0.628169	+	0.178860i	0.0269078	+	0.00766151i
$546$	−8.60952	+	22.5861i	−0.368453	+	0.966596i
$547$	−1.63615	+	22.8764i	−0.0699567	+	0.978123i	0.834349	+	0.551237i	$0.185844\pi$
$547$	−1.63615	+	22.8764i	−0.0699567	+	0.978123i	−0.904305	+	0.426886i	$0.859611\pi$
$548$	5.02761	+	9.20737i	0.214769	+	0.393319i
$549$	−0.914665	−	1.08674i	−0.0390369	−	0.0463811i
$550$	−10.4658	+	29.5317i	−0.446264	+	1.25924i
$551$			37.3868i			1.59273i
$552$	−5.87927	+	5.86806i	−0.250238	+	0.249761i
$553$	−7.30084	+	7.30084i	−0.310463	+	0.310463i
$554$	2.27444	−	15.8191i	0.0966318	−	0.672089i
$555$	8.58987	−	0.623201i	0.364620	−	0.0264534i
$556$	6.90382	+	2.02715i	0.292787	+	0.0859701i
$557$	10.6244	+	0.759872i	0.450170	+	0.0321968i	0.294584	−	0.955626i	$-0.404819\pi$
$557$	10.6244	+	0.759872i	0.450170	+	0.0321968i	0.155586	+	0.987822i	$0.450273\pi$
$558$	6.25609	−	26.8925i	0.264841	−	1.13845i
$559$	5.66714	−	8.81825i	0.239695	−	0.372972i
$560$	−3.50354	−	4.60098i	−0.148052	−	0.194427i
$561$	−47.3114	+	9.93653i	−1.99749	+	0.419521i
$562$	−4.25433	−	0.925474i	−0.179458	−	0.0390387i
$563$	−17.7039	+	23.6496i	−0.746129	+	0.996711i	0.253440	+	0.967351i	$0.418438\pi$
$563$	−17.7039	+	23.6496i	−0.746129	+	0.996711i	−0.999569	+	0.0293601i	$0.990653\pi$
$564$	5.40780	−	9.73668i	0.227709	−	0.409988i
$565$	2.33340	+	29.2492i	0.0981668	+	1.23052i
$566$	−1.96623	−	1.70375i	−0.0826469	−	0.0716139i
$567$	−14.4787	+	18.2252i	−0.608046	+	0.765387i
$568$	4.97916	−	1.08315i	0.208921	−	0.0454479i
$569$	27.2310	−	7.99575i	1.14158	−	0.335199i	0.344333	−	0.938847i	$-0.388105\pi$
$569$	27.2310	−	7.99575i	1.14158	−	0.335199i	0.797251	+	0.603648i	$0.206287\pi$
$570$	26.2606	−	9.82534i	1.09994	−	0.411538i
$571$	43.4627	+	12.7618i	1.81886	+	0.534065i	0.999245	−	0.0388535i	$-0.0123706\pi$
$571$	43.4627	+	12.7618i	1.81886	+	0.534065i	0.819613	+	0.572918i	$0.194189\pi$
$572$	−31.6806	−	11.8163i	−1.32463	−	0.494062i
$573$	−22.4142	−	0.161032i	−0.936365	−	0.00672719i
$574$		−	14.9484i		−	0.623934i
$575$	−22.8490	+	7.27497i	−0.952867	+	0.303387i
$576$	0.803752	+	2.89033i	0.0334897	+	0.120430i
$577$	−35.5609	+	26.6206i	−1.48042	+	1.10823i	−0.511976	+	0.859000i	$0.671086\pi$
$577$	−35.5609	+	26.6206i	−1.48042	+	1.10823i	−0.968445	+	0.249229i	$0.919823\pi$
$578$	−0.992420	+	2.66078i	−0.0412792	+	0.110674i
$579$	24.8016	−	18.2897i	1.03072	−	0.760095i
$580$	−9.76544	−	6.16320i	−0.405488	−	0.255913i
$581$	−1.36954	−	4.66421i	−0.0568179	−	0.193504i
$582$	−7.94358	−	3.69691i	−0.329272	−	0.153242i
$583$	−9.50252	−	25.4772i	−0.393554	−	1.05516i
$584$	1.89514	−	2.18710i	0.0784213	−	0.0905030i
$585$	33.9922	−	12.4404i	1.40540	−	0.514349i
$586$	1.08740	+	7.56302i	0.0449200	+	0.312425i
$587$	22.6217	+	16.9344i	0.933696	+	0.698956i	0.953673	−	0.300845i	$-0.0972686\pi$
$587$	22.6217	+	16.9344i	0.933696	+	0.698956i	−0.0199776	+	0.999800i	$0.506359\pi$
$588$	0.409938	−	0.350088i	0.0169055	−	0.0144374i
$589$	50.3548	+	43.6327i	2.07483	+	1.79785i
$590$	10.2355	−	7.79413i	0.421390	−	0.320879i
$591$	−13.3910	+	4.88529i	−0.550832	+	0.200954i
$592$	−1.95172	−	1.06572i	−0.0802150	−	0.0438007i
$593$	−0.115560	+	1.61574i	−0.00474549	+	0.0663506i	−0.999273	−	0.0381244i	$-0.987862\pi$
$593$	−0.115560	+	1.61574i	−0.00474549	+	0.0663506i	0.994528	+	0.104475i	$0.0333162\pi$
$594$	−25.6394	−	20.0700i	−1.05200	−	0.823482i
$595$	19.3281	−	17.0277i	0.792377	−	0.698067i
$596$	3.12049	+	0.448659i	0.127820	+	0.0183778i
$597$	0.775051	+	5.67999i	0.0317207	+	0.232466i
$598$	−7.44524	−	24.7839i	−0.304458	−	1.01349i
$599$	−0.0646049			−0.00263968			−0.00131984	−	0.999999i	$-0.500420\pi$
$599$	−0.0646049			−0.00263968			−0.00131984	+	0.999999i	$0.500420\pi$
$600$	−1.76267	+	8.47897i	−0.0719606	+	0.346153i
$601$	7.94396	+	17.3948i	0.324041	+	0.709550i	0.999615	−	0.0277416i	$-0.00883155\pi$
$601$	7.94396	+	17.3948i	0.324041	+	0.709550i	−0.675574	+	0.737292i	$0.736104\pi$
$602$	4.40957	−	2.40781i	0.179721	−	0.0981348i
$603$	1.83481	+	9.05927i	0.0747193	+	0.368922i
$604$	−0.0175809	−	0.0598751i	−0.000715358	−	0.00243628i
$605$	−17.3085	+	60.7889i	−0.703692	+	2.47142i
$606$	−3.93684	+	2.11311i	−0.159923	+	0.0858390i
$607$	30.9050	−	2.21037i	1.25439	−	0.0897160i	0.571726	−	0.820445i	$-0.306274\pi$
$607$	30.9050	−	2.21037i	1.25439	−	0.0897160i	0.682668	+	0.730729i	$0.260820\pi$
$608$	−7.07406	−	1.53887i	−0.286891	−	0.0624093i
$609$	−11.2323	+	20.2237i	−0.455157	+	0.819506i
$610$	−0.361833	+	0.994977i	−0.0146502	+	0.0402855i
$611$	18.7590	+	29.1896i	0.758908	+	1.18088i
$612$	−12.5859	+	4.48937i	−0.508753	+	0.181472i
$613$	4.86567	+	13.0454i	0.196523	+	0.526898i	0.997411	−	0.0719166i	$-0.0229115\pi$
$613$	4.86567	+	13.0454i	0.196523	+	0.526898i	−0.800888	+	0.598814i	$0.795639\pi$
$614$	−18.9124	−	12.1542i	−0.763240	−	0.490505i
$615$	−16.9028	+	14.6767i	−0.681588	+	0.591823i
$616$	−10.6128	−	12.2478i	−0.427603	−	0.493480i
$617$	−28.0790	+	15.3323i	−1.13042	+	0.617256i	−0.931855	−	0.362832i	$-0.881810\pi$
$617$	−28.0790	+	15.3323i	−1.13042	+	0.617256i	−0.198565	+	0.980088i	$0.563628\pi$
$618$	−4.09527	+	2.59049i	−0.164736	+	0.104205i
$619$	−1.65480	−	0.237924i	−0.0665119	−	0.00956297i	0.108979	−	0.994044i	$-0.465242\pi$
$619$	−1.65480	−	0.237924i	−0.0665119	−	0.00956297i	−0.175490	+	0.984481i	$0.556151\pi$
$620$	−19.6978	+	5.95986i	−0.791085	+	0.239354i
$621$	0.381830	−	24.9169i	0.0153223	−	0.999883i
$622$	9.88871	+	9.88871i	0.396501	+	0.396501i
$623$	24.9904	−	18.7076i	1.00122	−	0.749504i
$624$	−9.11797	−	2.05221i	−0.365011	−	0.0821540i
$625$	−15.7425	+	19.4210i	−0.629699	+	0.776839i
$626$	−24.6116	+	21.3261i	−0.983678	+	0.852362i
$627$	71.7060	−	32.1265i	2.86366	−	1.28301i
$628$	−3.07806	+	0.669591i	−0.122828	+	0.0267196i
$629$	4.11464	−	9.00981i	0.164062	−	0.359245i
$630$	17.1571	+	2.57479i	0.683554	+	0.102582i
$631$	41.1418	−	26.4402i	1.63783	−	1.05257i	0.695149	−	0.718865i	$-0.255338\pi$
$631$	41.1418	−	26.4402i	1.63783	−	1.05257i	0.942678	−	0.333703i	$-0.108298\pi$
$632$	−3.19594	−	2.39245i	−0.127128	−	0.0951665i
$633$	−1.56623	−	5.47942i	−0.0622522	−	0.217787i
$634$	7.83694	+	12.1945i	0.311245	+	0.484306i
$635$	−7.14713	−	18.6922i	−0.283625	−	0.741776i
$636$	−3.55456	−	6.62235i	−0.140947	−	0.262593i
$637$	0.356990	+	1.64105i	0.0141444	+	0.0650209i
$638$	−28.4024	−	15.5089i	−1.12446	−	0.614002i
$639$	−8.44860	+	12.7400i	−0.334221	+	0.503987i
$640$	1.56811	−	1.59406i	0.0619849	−	0.0630109i
$641$	−3.05932	+	1.39714i	−0.120836	+	0.0551839i	−0.474916	−	0.880031i	$-0.657521\pi$
$641$	−3.05932	+	1.39714i	−0.120836	+	0.0551839i	0.354080	+	0.935215i	$0.384794\pi$
$642$	−24.1113	−	0.173225i	−0.951598	−	0.00683663i
$643$	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
$647$	23.6483	+	8.82038i	0.929713	+	0.346765i	0.768276	−	0.640118i	$-0.221115\pi$
$647$	23.6483	+	8.82038i	0.929713	+	0.346765i	0.161436	+	0.986883i	$0.448387\pi$
$648$	−7.77192	−	4.53843i	−0.305310	−	0.178286i
$649$	27.2471	−	23.6097i	1.06954	−	0.926763i
$650$	−20.6772	−	17.3309i	−0.811028	−	0.679774i
$651$	14.1297	+	38.7307i	0.553786	+	1.51798i
$652$	−14.3161	+	5.33965i	−0.560663	+	0.209117i
$653$	6.44223	−	0.460758i	0.252104	−	0.0180308i	0.0552848	−	0.998471i	$-0.482393\pi$
$653$	6.44223	−	0.460758i	0.252104	−	0.0180308i	0.196819	+	0.980440i	$0.436939\pi$
$654$	0.504356	+	0.0397161i	0.0197219	+	0.00155302i
$655$	−12.1068	−	25.9444i	−0.473050	−	1.01373i
$656$	5.72109	−	0.822568i	0.223371	−	0.0321159i
$657$	0.494870	+	8.66775i	0.0193067	+	0.338161i
$658$	1.18641	+	16.5881i	0.0462510	+	0.646673i
$659$	6.61758	−	14.4905i	0.257784	−	0.564469i	−0.735847	−	0.677148i	$-0.763216\pi$
$659$	6.61758	−	14.4905i	0.257784	−	0.564469i	0.993631	+	0.112679i	$0.0359431\pi$
$660$	−3.42926	+	24.0257i	−0.133484	+	0.935197i
$661$	−27.3793	+	8.03928i	−1.06493	+	0.312692i	−0.766835	−	0.641845i	$-0.778169\pi$
$661$	−27.3793	+	8.03928i	−1.06493	+	0.312692i	−0.298095	+	0.954536i	$0.596351\pi$
$662$	−3.16376	−	0.226277i	−0.122963	−	0.00879449i
$663$	6.22032	−	41.1618i	0.241577	−	1.59859i
$664$	1.70974	−	0.780810i	0.0663506	−	0.0303013i
$665$	−24.8137	+	33.7207i	−0.962234	+	1.30763i
$666$	6.42729	−	1.78732i	0.249052	−	0.0692574i
$667$	−3.67737	−	24.4925i	−0.142388	−	0.948353i
$668$	−6.08348	−	6.08348i	−0.235377	−	0.235377i
$669$	33.4402	+	33.9242i	1.29287	+	1.31159i
$670$	5.16951	−	4.55424i	0.199716	−	0.175945i
$671$	−0.835882	+	2.84675i	−0.0322689	+	0.109898i
$672$	−3.36425	−	2.95772i	−0.129779	−	0.114097i
$673$	−10.8324	+	19.8381i	−0.417558	+	0.764701i	−0.998797	−	0.0490321i	$-0.984386\pi$
$673$	−10.8324	+	19.8381i	−0.417558	+	0.764701i	0.581239	+	0.813733i	$0.302568\pi$
$674$	13.8339	+	8.89052i	0.532863	+	0.342450i
$675$	−13.9338	−	21.9283i	−0.536313	−	0.844019i
$676$	10.5539	−	12.1799i	0.405920	−	0.468457i
$677$	0.187219	−	0.860634i	0.00719543	−	0.0330768i	−0.973409	−	0.229073i	$-0.926430\pi$
$677$	0.187219	−	0.860634i	0.00719543	−	0.0330768i	0.980605	+	0.195996i	$0.0627941\pi$
$678$	6.24646	+	21.8531i	0.239894	+	0.839262i
$679$	12.9496	−	1.86188i	0.496962	−	0.0714523i
$680$	7.58046	+	6.46033i	0.290697	+	0.247742i
$681$	−0.708381	−	3.37285i	−0.0271452	−	0.129248i
$682$	−54.0356	+	20.1542i	−2.06913	+	0.771746i
$683$	9.71160	+	44.6435i	0.371604	+	1.70824i	0.660458	+	0.750863i	$0.270362\pi$
$683$	9.71160	+	44.6435i	0.371604	+	1.70824i	−0.288853	+	0.957373i	$0.593274\pi$
$684$	18.4376	−	11.4782i	0.704979	−	0.438879i
$685$	5.17426	+	22.8799i	0.197698	+	0.874196i
$686$	−5.32722	+	18.1429i	−0.203394	+	0.692697i
$687$	3.15323	−	1.99460i	0.120303	−	0.0760986i
$688$	1.16417	+	1.55515i	0.0443835	+	0.0592894i
$689$	23.4150			0.892042
$690$	−16.2372	+	9.01967i	−0.618138	+	0.343373i
$691$	28.2263			1.07378			0.536889	−	0.843653i	$-0.319599\pi$
$691$	28.2263			1.07378			0.536889	+	0.843653i	$0.319599\pi$
$692$	6.73452	+	8.99626i	0.256008	+	0.341987i
$693$	48.4400	+	4.16483i	1.84008	+	0.158209i
$694$	−4.29695	+	14.6341i	−0.163110	+	0.555502i
$695$	13.6060	+	8.58706i	0.516105	+	0.325726i
$696$	−8.35815	−	3.18601i	−0.316815	−	0.120766i
$697$	5.47247	+	25.1565i	0.207284	+	0.952871i
$698$	20.4380	−	7.62297i	0.773589	−	0.288534i
$699$	16.4517	−	3.45525i	0.622260	−	0.130690i
$700$	−4.71731	−	12.0402i	−0.178298	−	0.455076i
$701$	−19.1536	+	2.75387i	−0.723422	+	0.104012i	−0.494183	−	0.869358i	$-0.664533\pi$
$701$	−19.1536	+	2.75387i	−0.723422	+	0.104012i	−0.229239	+	0.973370i	$0.573624\pi$
$702$	23.9084	−	14.6467i	0.902366	−	0.552806i
$703$	−3.42202	+	15.7308i	−0.129064	+	0.593297i
$704$	4.10353	−	4.73573i	0.154658	−	0.178485i
$705$	17.5921	−	17.6282i	0.662558	−	0.663916i
$706$	14.9221	+	9.58982i	0.561599	+	0.360918i
$707$	3.19740	−	5.85559i	0.120250	−	0.220222i
$708$	6.57987	−	7.48425i	0.247287	−	0.281275i
$709$	5.49656	−	18.7196i	0.206428	−	0.703028i	−0.789571	−	0.613659i	$-0.789697\pi$
$709$	5.49656	−	18.7196i	0.206428	−	0.703028i	0.995999	−	0.0893688i	$-0.0284850\pi$
$710$	11.3714	+	0.719535i	0.426760	+	0.0270037i
$711$	11.8780	−	1.53395i	0.445461	−	0.0575277i
$712$	8.53497	+	8.53497i	0.319862	+	0.319862i
$713$	−37.2797	−	23.6313i	−1.39614	−	0.885001i
$714$	12.0717	−	15.8867i	0.451771	−	0.594544i
$715$	−60.8964	−	44.8113i	−2.27740	−	1.67585i
$716$	11.7830	−	5.38110i	0.440350	−	0.201101i
$717$	−44.7421	−	6.76137i	−1.67092	−	0.252508i
$718$	0.0516454	+	0.00369375i	0.00192739	+	0.000137849i
$719$	−48.2343	+	14.1629i	−1.79883	+	0.528185i	−0.997541	−	0.0700865i	$-0.977672\pi$
$719$	−48.2343	+	14.1629i	−1.79883	+	0.528185i	−0.801293	+	0.598272i	$0.795854\pi$
$720$	−0.0413245	+	6.70808i	−0.00154007	+	0.249995i
$721$	3.00580	−	6.58179i	0.111942	−	0.245119i
$722$	2.38347	+	33.3253i	0.0887036	+	1.24024i
$723$	26.1625	−	22.3429i	0.972995	−	0.830942i
$724$	18.7552	−	2.69659i	0.697030	−	0.100218i
$725$	−17.2275	−	19.2343i	−0.639813	−	0.714344i
$726$	−3.84339	+	48.8073i	−0.142642	+	1.81141i
$727$	−21.1081	+	1.50968i	−0.782856	+	0.0559910i	−0.457045	−	0.889444i	$-0.651092\pi$
$727$	−21.1081	+	1.50968i	−0.782856	+	0.0559910i	−0.325812	+	0.945435i	$0.605638\pi$
$728$	13.0755	−	4.87690i	0.484609	−	0.180750i
$729$	26.2100	−	6.48336i	0.970742	−	0.240124i
$730$	5.41492	−	3.54309i	0.200415	−	0.131136i
$731$	−6.53935	+	5.66638i	−0.241866	+	0.209578i
$732$	−0.122539	+	0.810880i	−0.00452918	+	0.0299710i
$733$	−24.9453	−	9.30411i	−0.921376	−	0.343655i	−0.156385	−	0.987696i	$-0.549984\pi$
$733$	−24.9453	−	9.30411i	−0.921376	−	0.343655i	−0.764991	+	0.644041i	$0.777257\pi$
$734$	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
$738$	−10.5897	+	13.7305i	−0.389812	+	0.505425i
$739$	−32.1876	+	14.6996i	−1.18404	+	0.540732i	−0.907411	−	0.420245i	$-0.861944\pi$
$739$	−32.1876	+	14.6996i	−1.18404	+	0.540732i	−0.276628	+	0.960977i	$0.589217\pi$
$740$	−3.54476	−	3.48704i	−0.130308	−	0.128186i
$741$	4.34190	+	67.5214i	0.159504	+	2.48046i
$742$	9.84998	+	5.37850i	0.361604	+	0.197451i
$743$	−0.287108	−	1.31981i	−0.0105330	−	0.0484192i	0.971580	−	0.236710i	$-0.0760690\pi$
$743$	−0.287108	−	1.31981i	−0.0105330	−	0.0484192i	−0.982113	+	0.188290i	$0.939705\pi$
$744$	−14.0456	+	7.53899i	−0.514936	+	0.276393i
$745$	6.43616	+	2.87569i	0.235803	+	0.105357i
$746$	17.6867	+	27.5210i	0.647555	+	1.00762i
$747$	−2.04626	+	5.25439i	−0.0748686	+	0.192248i
$748$	22.3440	+	16.7265i	0.816979	+	0.611583i
$749$	30.2881	−	19.4650i	1.10670	−	0.711234i
$750$	−8.98280	+	17.1554i	−0.328006	+	0.626428i
$751$	−10.3249	+	22.6084i	−0.376762	+	0.824993i	0.622345	+	0.782743i	$0.286180\pi$
$751$	−10.3249	+	22.6084i	−0.376762	+	0.824993i	−0.999107	+	0.0422503i	$0.986547\pi$
$752$	−6.28337	+	1.36686i	−0.229131	+	0.0498444i
$753$	0.195675	+	0.436746i	0.00713080	+	0.0159159i
$754$	21.0599	−	18.2485i	0.766955	−	0.664571i
$755$	−0.00114533	−	0.139532i	−4.16828e−5	−	0.00507810i
$756$	13.4219	−	0.669599i	0.488151	−	0.0243531i
$757$	0.565780	−	0.423538i	0.0205636	−	0.0153937i	−0.588946	−	0.808172i	$-0.700457\pi$
$757$	0.565780	−	0.423538i	0.0205636	−	0.0153937i	0.609510	+	0.792778i	$0.291366\pi$
$758$	14.9543	+	14.9543i	0.543166	+	0.543166i
$759$	−43.8154	+	28.0994i	−1.59040	+	1.01994i
$760$	−14.2711	−	7.64121i	−0.517667	−	0.277176i
$761$	−27.9903	−	4.02439i	−1.01465	−	0.145884i	−0.385123	−	0.922865i	$-0.625841\pi$
$761$	−27.9903	−	4.02439i	−1.01465	−	0.145884i	−0.629524	+	0.776981i	$0.716750\pi$
$762$	−8.28668	−	13.1003i	−0.300195	−	0.474574i
$763$	−0.663021	+	0.362037i	−0.0240030	+	0.0131066i
$764$	8.47465	+	9.78027i	0.306602	+	0.353838i
$765$	−29.8161	+	1.94795i	−1.07800	+	0.0704283i
$766$	−13.9777	−	8.98289i	−0.505033	−	0.324565i
$767$	10.8494	+	29.0882i	0.391747	+	1.05032i
$768$	0.946861	−	1.45033i	0.0341669	−	0.0523342i
$769$	11.8689	+	18.4684i	0.428003	+	0.665986i	0.986545	−	0.163490i	$-0.0522752\pi$
$769$	11.8689	+	18.4684i	0.428003	+	0.665986i	−0.558542	+	0.829477i	$0.688639\pi$
$770$	−15.3240	−	32.8388i	−0.552237	−	1.18343i
$771$	31.8897	+	17.7117i	1.14848	+	0.637871i
$772$	−17.3851	−	3.78190i	−0.625704	−	0.136114i
$773$	−15.7264	+	1.12478i	−0.565640	+	0.0404554i	−0.351231	−	0.936289i	$-0.614237\pi$
$773$	−15.7264	+	1.12478i	−0.565640	+	0.0404554i	−0.214409	+	0.976744i	$0.568782\pi$
$774$	−5.75602	−	0.912187i	−0.206896	−	0.0327879i
$775$	−46.0115	+	0.755407i	−1.65278	+	0.0271350i
$776$	1.42517	+	4.85367i	0.0511605	+	0.174237i
$777$	−6.57716	+	7.48116i	−0.235954	+	0.268385i
$778$	18.0568	−	9.85974i	0.647366	−	0.353489i
$779$	−17.3825	−	38.0624i	−0.622793	−	1.36373i
$780$	−18.3524	−	9.99677i	−0.657120	−	0.357942i
$781$	31.9304			1.14256
$782$	0.133078	+	21.3611i	0.00475885	+	0.763873i
$783$	24.6440	−	10.6188i	0.880704	−	0.379484i
$784$	−0.308072	−	0.0442940i	−0.0110026	−	0.00158193i
$785$	−7.02966	−	0.444808i	−0.250899	−	0.0158759i
$786$	−13.1622	−	17.8485i	−0.469479	−	0.636634i
$787$	−1.02610	+	14.3468i	−0.0365766	+	0.511408i	0.945831	+	0.324659i	$0.105250\pi$
$787$	−1.02610	+	14.3468i	−0.0365766	+	0.511408i	−0.982408	+	0.186749i	$0.940205\pi$
$788$	7.22305	+	3.94409i	0.257311	+	0.140502i
$789$	14.6252	+	40.0888i	0.520670	+	1.42720i
$790$	−5.40816	−	7.10219i	−0.192414	−	0.252684i
$791$	−25.6482	−	22.2243i	−0.911945	−	0.790204i
$792$	1.07154	+	18.7682i	0.0380755	+	0.666901i
$793$	−2.04527	−	1.53107i	−0.0726297	−	0.0543699i
$794$	4.10586	+	28.5569i	0.145712	+	1.01345i
$795$	−3.58925	−	16.4186i	−0.127298	−	0.582307i
$796$	2.16741	−	2.50133i	0.0768219	−	0.0886572i
$797$	−11.1452	−	29.8813i	−0.394782	−	1.05845i	−0.970563	−	0.240847i	$-0.922575\pi$
$797$	−11.1452	−	29.8813i	−0.394782	−	1.05845i	0.575781	−	0.817604i	$-0.304698\pi$
$798$	−13.6833	+	29.4015i	−0.484385	+	1.04080i
$799$	−8.06936	−	27.4817i	−0.285473	−	0.972233i
$800$	4.34847	−	2.46796i	0.153742	−	0.0872556i
$801$	−36.2071	−	0.520277i	−1.27931	−	0.0183831i
$802$	0.258357	−	0.692682i	0.00912291	−	0.0244595i
$803$	14.5173	−	10.8675i	0.512303	−	0.383505i
$804$	3.22870	−	4.24906i	0.113867	−	0.149853i
$805$	12.9390	−	24.5314i	0.456038	−	0.864619i
$806$		−	49.6618i		−	1.74926i
$807$	−0.0976262	+	13.5887i	−0.00343660	+	0.478345i
$808$	2.41701	+	0.901499i	0.0850302	+	0.0317146i
$809$	−25.0308	−	7.34969i	−0.880035	−	0.258401i	−0.189657	−	0.981850i	$-0.560738\pi$
$809$	−25.0308	−	7.34969i	−0.880035	−	0.258401i	−0.690378	+	0.723449i	$0.742556\pi$
$810$	−13.9351	−	14.5194i	−0.489631	−	0.510158i
$811$	22.6302	−	6.64482i	0.794653	−	0.233331i	0.140885	−	0.990026i	$-0.455005\pi$
$811$	22.6302	−	6.64482i	0.794653	−	0.233331i	0.653768	+	0.756695i	$0.273187\pi$
$812$	13.0510	−	2.83906i	0.457999	−	0.0996316i
$813$	12.2091	−	40.5018i	0.428193	−	1.42046i
$814$	−10.5310	−	9.12513i	−0.369110	−	0.319836i
$815$	−34.0578	+	2.71702i	−1.19299	+	0.0951730i
$816$	6.74446	+	3.74590i	0.236103	+	0.131133i
$817$	8.42799	−	11.2585i	0.294858	−	0.393884i
$818$	3.20739	+	0.697724i	0.112144	+	0.0243953i
$819$	−17.9372	+	37.8289i	−0.626775	+	1.32185i
$820$	12.8074	+	1.73425i	0.447254	+	0.0605628i
$821$	−6.00319	+	9.34114i	−0.209513	+	0.326008i	−0.930067	−	0.367391i	$-0.880251\pi$
$821$	−6.00319	+	9.34114i	−0.209513	+	0.326008i	0.720554	+	0.693399i	$0.243888\pi$
$822$	7.42925	+	16.5820i	0.259125	+	0.578365i
$823$	35.8726	+	2.56566i	1.25044	+	0.0894333i	0.680806	−	0.732464i	$-0.261630\pi$
$823$	35.8726	+	2.56566i	1.25044	+	0.0894333i	0.569636	+	0.821897i	$0.307084\pi$
$824$	2.68440	+	0.788211i	0.0935155	+	0.0274586i
$825$	−22.0868	+	49.5695i	−0.768965	+	1.72579i
$826$	−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	$-0.0593681\pi$
$828$	−10.9497	+	9.33300i	−0.380527	+	0.324344i
$829$			18.2502i			0.633855i	0.948450	+	0.316928i	$0.102651\pi$
$829$			18.2502i			0.633855i	−0.948450	+	0.316928i	$0.897349\pi$
$830$	4.15506	−	0.632260i	0.144224	−	0.0219461i
$831$	6.07824	−	27.0057i	0.210852	−	0.936816i
$832$	2.58600	+	4.73591i	0.0896536	+	0.164188i
$833$	0.0988991	−	1.38279i	0.00342665	−	0.0479108i
$834$	11.6452	+	4.43901i	0.403242	+	0.153710i
$835$	−9.35791	−	16.8082i	−0.323844	−	0.581673i
$836$	−41.2652	−	18.8452i	−1.42719	−	0.651774i
$837$	14.4590	−	45.5848i	0.499778	−	1.57564i
$838$	2.84015	−	13.0560i	0.0981113	−	0.451010i
$839$	−4.13769	−	28.7783i	−0.142849	−	0.993537i	−0.927560	−	0.373675i	$-0.878098\pi$
$839$	−4.13769	−	28.7783i	−0.142849	−	0.993537i	0.784711	−	0.619862i	$-0.212811\pi$
$840$	−5.42398	−	8.42091i	−0.187145	−	0.290549i
$841$	−1.96030	+	1.25981i	−0.0675967	+	0.0434417i
$842$	0.621003	+	8.68276i	0.0214012	+	0.299228i
$843$	−7.22014	−	2.17649i	−0.248675	−	0.0749623i
$844$	−1.77884	+	2.76793i	−0.0612302	+	0.0952761i
$845$	30.1554	−	19.7313i	1.03738	−	0.678778i
$846$	10.6616	−	16.0771i	0.366553	−	0.552741i
$847$	−35.0349	−	64.1616i	−1.20381	−	2.20462i
$848$	−1.51645	+	4.06577i	−0.0520753	+	0.139619i
$849$	−3.16344	−	3.20923i	−0.108569	−	0.110140i
$850$	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
$853$	−14.9048	−	19.9105i	−0.510330	−	0.681721i	0.469183	−	0.883101i	$-0.344548\pi$
$853$	−14.9048	−	19.9105i	−0.510330	−	0.681721i	−0.979513	+	0.201380i	$0.935457\pi$
$854$	−0.508691	−	1.11388i	−0.0174070	−	0.0381161i
$855$	46.6803	−	13.3948i	1.59643	−	0.458091i
$856$	9.11634	+	10.5208i	0.311590	+	0.359594i
$857$	−11.1516	+	20.4227i	−0.380933	+	0.697627i	−0.995854	−	0.0909617i	$-0.971006\pi$
$857$	−11.1516	+	20.4227i	−0.380933	+	0.697627i	0.614921	+	0.788588i	$0.289188\pi$
$858$	−53.0964	−	24.7109i	−1.81268	−	0.843615i
$859$	33.3061	+	15.2104i	1.13639	+	0.518972i	0.892597	−	0.450855i	$-0.148881\pi$
$859$	33.3061	+	15.2104i	1.13639	+	0.518972i	0.243793	+	0.969827i	$0.421608\pi$
$860$	1.55137	+	4.05735i	0.0529012	+	0.138354i
$861$	2.03256	−	25.8115i	0.0692694	−	0.879653i
$862$	−15.3918	+	20.5611i	−0.524248	+	0.700313i
$863$	−4.41048	+	5.89171i	−0.150134	+	0.200556i	−0.869303	−	0.494279i	$-0.835432\pi$
$863$	−4.41048	+	5.89171i	−0.150134	+	0.200556i	0.719169	+	0.694836i	$0.244523\pi$
$864$	0.994842	+	5.10003i	0.0338452	+	0.173506i
$865$	8.97440	+	23.4711i	0.305139	+	0.798041i
$866$	−7.94097	−	3.62652i	−0.269845	−	0.123234i
$867$	−2.07541	+	4.45944i	−0.0704845	+	0.151451i
$868$	11.4075	−	20.8912i	0.387194	−	0.709093i
$869$	−16.3822	−	18.9061i	−0.555729	−	0.641345i
$870$	−16.0240	−	11.9699i	−0.543265	−	0.405816i
$871$	6.90640	+	15.1229i	0.234014	+	0.512420i
$872$	−0.175044	−	0.233831i	−0.00592773	−	0.00791852i
$873$	−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
$876$	3.56973	−	3.51880i	0.120610	−	0.118889i
$877$	−9.49432	+	25.4552i	−0.320600	+	0.859563i	0.672264	+	0.740312i	$0.265322\pi$
$877$	−9.49432	+	25.4552i	−0.320600	+	0.859563i	−0.992864	+	0.119251i	$0.961951\pi$
$878$	−14.3223	−	26.2293i	−0.483353	−	0.885195i
$879$	0.849260	+	13.2070i	0.0286448	+	0.445460i
$880$	11.7249	−	7.67185i	0.395246	−	0.258618i
$881$	5.35838	−	8.33780i	0.180528	−	0.280908i	−0.739182	−	0.673506i	$-0.764787\pi$
$881$	5.35838	−	8.33780i	0.180528	−	0.280908i	0.919710	+	0.392599i	$0.128424\pi$
$882$	0.755443	−	0.548760i	0.0254371	−	0.0184777i
$883$	0.383242	+	5.35843i	0.0128971	+	0.180325i	0.999817	+	0.0191156i	$0.00608505\pi$
$883$	0.383242	+	5.35843i	0.0128971	+	0.180325i	−0.986920	+	0.161210i	$0.948460\pi$
$884$	−20.2192	+	12.9941i	−0.680045	+	0.437039i
$885$	18.7335	−	12.0664i	0.629720	−	0.405608i
$886$	4.15318	+	28.8860i	0.139529	+	0.970444i
$887$	−7.42979	+	34.1542i	−0.249468	+	1.14679i	0.666491	+	0.745513i	$0.267795\pi$
$887$	−7.42979	+	34.1542i	−0.249468	+	1.14679i	−0.915959	+	0.401272i	$0.868568\pi$
$888$	−3.22513	−	2.10556i	−0.108228	−	0.0706579i
$889$	21.0544	+	9.61523i	0.706142	+	0.322484i
$890$	13.1289	+	23.5815i	0.440082	+	0.790455i
$891$	−41.5428	−	38.1412i	−1.39174	−	1.27778i
$892$	1.96198	−	27.4321i	0.0656919	−	0.918493i
$893$	22.3102	+	40.8580i	0.746581	+	1.36726i
$894$	5.32716	+	1.19900i	0.178167	+	0.0401005i
$895$	28.6354	−	4.35734i	0.957175	−	0.145650i
$896$			2.58626i			0.0864010i
$897$	−9.48583	−	43.8069i	−0.316723	−	1.46267i
$898$	−17.2702	+	17.2702i	−0.576315	+	0.576315i
$899$	6.76417	−	47.0458i	0.225598	−	1.56907i
$900$	−4.19651	+	14.4010i	−0.139884	+	0.480034i
$901$	−18.5455	−	5.44544i	−0.617839	−	0.181414i
$902$	36.1263	+	2.58380i	1.20287	+	0.0860312i
$903$	7.94142	−	3.55800i	0.264274	−	0.118403i
$904$	7.09439	−	11.0391i	0.235956	−	0.367154i
$905$	41.9859	+	5.68532i	1.39566	+	0.188986i
$906$	−0.0222158	−	0.105777i	−0.000738069	−	0.00351421i
$907$	−44.9634	−	9.78120i	−1.49299	−	0.324779i	−0.609330	−	0.792916i	$-0.708562\pi$
$907$	−44.9634	−	9.78120i	−1.49299	−	0.324779i	−0.883656	+	0.468137i	$0.844925\pi$
$908$	−1.19244	+	1.59292i	−0.0395727	+	0.0528629i
$909$	−7.08509	+	3.11341i	−0.234998	+	0.103265i
$910$	31.1063	−	2.48155i	1.03116	−	0.0822627i
$911$	19.4685	+	16.8696i	0.645021	+	0.558914i	0.914749	−	0.404022i	$-0.132388\pi$
$911$	19.4685	+	16.8696i	0.645021	+	0.558914i	−0.269728	+	0.962937i	$0.586934\pi$
$912$	−12.0056	−	3.61904i	−0.397544	−	0.119838i
$913$	11.5089	−	2.50360i	0.380888	−	0.0828570i
$914$	11.6363	−	3.41673i	0.384895	−	0.113015i
$915$	−0.760067	+	1.66883i	−0.0251270	+	0.0551700i
$916$	−2.06691	−	0.606898i	−0.0682925	−	0.0200525i
$917$	31.0261	+	11.5721i	1.02457	+	0.382146i
$918$	−22.3425	+	6.04050i	−0.737413	+	0.199366i
$919$		−	39.2225i		−	1.29383i	−0.762561	−	0.646916i	$-0.776058\pi$
$919$		−	39.2225i		−	1.29383i	0.762561	−	0.646916i	$-0.223942\pi$
$920$	10.1007	+	3.60213i	0.333011	+	0.118759i
$921$	−31.0034	−	23.5583i	−1.02160	−	0.776273i
$922$	−3.09677	+	2.31822i	−0.101987	+	0.0763463i
$923$	−9.60874	+	25.7620i	−0.316276	+	0.847968i
$924$	−16.6599	−	22.5915i	−0.548069	−	0.743205i
$925$	−5.48806	−	9.66979i	−0.180446	−	0.317941i
$926$	0.934979	+	3.18425i	0.0307253	+	0.104641i
$927$	−7.42356	+	3.91617i	−0.243822	+	0.128624i
$928$	1.80473	+	4.83867i	0.0592432	+	0.158837i
$929$	17.8836	−	20.6388i	0.586742	−	0.677136i	−0.382298	−	0.924039i	$-0.624867\pi$
$929$	17.8836	−	20.6388i	0.586742	−	0.677136i	0.969040	+	0.246903i	$0.0794128\pi$
$930$	−34.8227	+	7.61258i	−1.14188	+	0.249626i
$931$	0.320667	+	2.23029i	0.0105094	+	0.0730947i
$932$	−7.76974	−	5.81636i	−0.254506	−	0.190521i
$933$	15.7303	+	18.4195i	0.514987	+	0.603026i
$934$	5.88151	+	5.09636i	0.192449	+	0.166758i
$935$	37.8105	+	49.6541i	1.23654	+	1.62386i
$936$	−15.4650	−	4.78334i	−0.505489	−	0.156348i
$937$	13.8622	+	7.56931i	0.452857	+	0.247279i	0.689454	−	0.724329i	$-0.257850\pi$
$937$	13.8622	+	7.56931i	0.452857	+	0.247279i	−0.236597	+	0.971608i	$0.576032\pi$
$938$	−0.568463	+	7.94815i	−0.0185610	+	0.259516i
$939$	−45.3968	+	33.4774i	−1.48147	+	1.09249i
$940$	−14.3499	−	0.908006i	−0.468044	−	0.0296159i
$941$	13.6293	+	1.95959i	0.444302	+	0.0638809i	0.360835	−	0.932630i	$-0.382492\pi$
$941$	13.6293	+	1.95959i	0.444302	+	0.0638809i	0.0834666	+	0.996511i	$0.473401\pi$
$942$	−5.40595	+	0.737658i	−0.176135	+	0.0240342i
$943$	15.1313	+	23.2253i	0.492743	+	0.756321i
$944$	−5.75351			−0.187261
$945$	29.2751	+	6.77877i	0.952319	+	0.220513i
$946$	5.05683	+	11.0729i	0.164412	+	0.360012i
$947$	24.7189	−	13.4975i	0.803255	−	0.438610i	−0.0245001	−	0.999700i	$-0.507799\pi$
$947$	24.7189	−	13.4975i	0.803255	−	0.438610i	0.827755	+	0.561089i	$0.189618\pi$
$948$	−5.19314	−	4.56561i	−0.168665	−	0.148284i
$949$	4.39943	+	14.9831i	0.142812	+	0.486372i
$950$	−26.0122	−	25.1719i	−0.843948	−	0.816684i
$951$	11.8740	+	22.1220i	0.385040	+	0.717353i
$952$	−11.4904	+	0.821807i	−0.372405	+	0.0266349i
$953$	45.1981	+	9.83224i	1.46411	+	0.318498i	0.872852	−	0.487985i	$-0.162268\pi$
$953$	45.1981	+	9.83224i	1.46411	+	0.318498i	0.591258	+	0.806483i	$0.298632\pi$
$954$	−5.23722	−	11.9182i	−0.169561	−	0.385865i
$955$	12.2366	+	26.2227i	0.395968	+	0.848548i
$956$	14.1243	+	21.9779i	0.456813	+	0.710815i
$957$	−46.9338	−	30.6412i	−1.51715	−	0.990488i
$958$	−0.462998	−	1.24135i	−0.0149588	−	0.0401061i
$959$	−22.8244	−	14.6684i	−0.737039	−	0.473666i
$960$	2.92441	−	2.53926i	0.0943848	−	0.0819543i
$961$	−35.1693	−	40.5875i	−1.13449	−	1.30928i
$962$	10.5314	−	5.75056i	0.339545	−	0.185406i
$963$	−41.6096	−	3.57756i	−1.34085	−	0.115285i
$964$	−19.6614	−	2.82688i	−0.633251	−	0.0910477i
$965$	−35.0725	−	18.7790i	−1.12902	−	0.604516i
$966$	6.07217	−	20.6071i	0.195369	−	0.663023i
$967$	−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	$-0.653189\pi$
$968$	22.6282	−	16.9393i	0.727298	−	0.544449i
$969$	12.2640	−	54.4889i	0.393975	−	1.75043i
$970$	0.0928441	+	11.3109i	0.00298104	+	0.363172i
$971$	31.2414	−	27.0709i	1.00259	−	0.868745i	0.0112281	−	0.999937i	$-0.496426\pi$
$971$	31.2414	−	27.0709i	1.00259	−	0.868745i	0.991357	+	0.131192i	$0.0418804\pi$
$972$	−12.8027	−	8.89328i	−0.410647	−	0.285252i
$973$	−18.1836	+	3.95561i	−0.582940	+	0.126811i
$974$	−0.0489787	+	0.107248i	−0.00156938	+	0.00343646i
$975$	−33.3470	−	32.7369i	−1.06796	−	1.04842i
$976$	0.398314	−	0.255981i	0.0127497	−	0.00819375i
$977$	−6.43349	−	4.81605i	−0.205826	−	0.154079i	0.491392	−	0.870938i	$-0.336488\pi$
$977$	−6.43349	−	4.81605i	−0.205826	−	0.154079i	−0.697218	+	0.716859i	$0.745579\pi$
$978$	−25.4458	+	7.27341i	−0.813667	+	0.232578i
$979$	40.8917	+	63.6287i	1.30690	+	2.03358i
$980$	−0.635413	−	0.283903i	−0.0202975	−	0.00906896i
$981$	0.865474	+	0.137156i	0.0276324	+	0.00437906i
$982$	−0.00717597	−	0.0329874i	−0.000228994	−	0.00105267i
$983$	26.7012	+	14.5799i	0.851635	+	0.465028i	0.844884	−	0.534950i	$-0.179669\pi$
$983$	26.7012	+	14.5799i	0.851635	+	0.465028i	0.00675059	+	0.999977i	$0.497851\pi$
$984$	9.99048	−	0.642428i	0.318485	−	0.0204799i
$985$	13.1187	+	12.9051i	0.417997	+	0.411190i
$986$	−20.9240	+	9.55567i	−0.666356	+	0.304314i
$987$	−0.206940	+	28.8042i	−0.00658696	+	0.916846i
$988$	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	−0.992181	−	0.124810i	$-0.960168\pi$
$991$	−0.158259	+	1.10071i	−0.00502726	+	0.0349653i	0.987153	+	0.159775i	$0.0510770\pi$
$992$	8.62325	+	3.21630i	0.273788	+	0.102118i
$993$	−5.43211	−	0.820894i	−0.172383	−	0.0260503i
$994$	−9.95971	+	8.63014i	−0.315903	+	0.273731i
$995$	6.19288	−	4.05213i	0.196328	−	0.128461i
$996$	3.05838	−	1.11575i	0.0969084	−	0.0353540i
$997$	−22.3589	+	8.33945i	−0.708115	+	0.264113i	−0.677610	−	0.735421i	$-0.736984\pi$
$997$	−22.3589	+	8.33945i	−0.708115	+	0.264113i	−0.0305048	+	0.999535i	$0.509711\pi$
$998$	41.4137	−	2.96197i	1.31093	−	0.0937595i
$999$	11.3411	−	2.21225i	0.358815	−	0.0699926i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.10	✓	960	1.1	even	1	trivial
690.2.x.a.77.28	yes	960	3.2	odd	2	inner
690.2.x.a.233.10	yes	960	345.233	even	44	inner
690.2.x.a.233.28	yes	960	115.3	odd	44	inner
690.2.x.a.353.21	yes	960	5.3	odd	4	inner
690.2.x.a.353.34	yes	960	15.8	even	4	inner
690.2.x.a.647.21	yes	960	69.26	odd	22	inner
690.2.x.a.647.34	yes	960	23.3	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.925925 - 1.46378i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19343 + 1.89096i) q^{5} +(-0.616933 + 1.61845i) q^{6} +(-0.549750 - 2.52716i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.28533 + 2.71071i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.925925 - 1.46378i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.19343 + 1.89096i) q^{5} +(-0.616933 + 1.61845i) q^{6} +(-0.549750 - 2.52716i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-1.28533 + 2.71071i) q^{9} +(2.22899 - 0.177821i) q^{10} +(6.20249 - 0.891783i) q^{11} +(1.66535 - 0.476023i) q^{12} +(-1.14699 + 5.27264i) q^{13} +(-1.69364 + 1.95457i) q^{14} +(3.87298 - 0.00396562i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(2.13467 - 3.90935i) q^{17} +(2.94030 - 0.595511i) q^{18} +(-2.03960 + 6.94625i) q^{19} +(-1.47813 - 1.67783i) q^{20} +(-3.19019 + 3.14468i) q^{21} +(-4.43092 - 4.43092i) q^{22} +(0.652932 - 4.75118i) q^{23} +(-1.37909 - 1.04791i) q^{24} +(-2.15146 - 4.51345i) q^{25} +(4.90833 - 2.24156i) q^{26} +(5.15801 - 0.628475i) q^{27} +(2.57967 + 0.184502i) q^{28} +(4.95509 - 1.45495i) q^{29} +(-2.32417 - 3.09810i) q^{30} +(3.82329 - 8.37183i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-7.04842 - 8.25338i) q^{33} +(-4.40886 + 0.633898i) q^{34} +(5.43484 + 1.97643i) q^{35} +(-2.23879 - 1.99696i) q^{36} +(2.21806 - 0.158639i) q^{37} +(6.78305 - 2.52995i) q^{38} +(8.78003 - 3.20312i) q^{39} +(-0.457360 + 2.18879i) q^{40} +(-4.36817 + 3.78504i) q^{41} +(4.42925 + 0.669343i) q^{42} +(-1.82014 - 0.678875i) 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} +(-0.0124434 + 1.73201i) q^{48} +(0.283114 - 0.129294i) q^{49} +(-2.32388 + 4.42714i) q^{50} +(-7.69899 + 0.495076i) q^{51} +(-4.73591 - 2.58600i) q^{52} +(-0.922400 - 4.24020i) q^{53} +(-3.59420 - 3.75256i) q^{54} +(-5.71590 + 12.7929i) q^{55} +(-1.39824 - 2.17570i) q^{56} +(12.0563 - 3.44617i) q^{57} +(-4.13422 - 3.09484i) q^{58} +(4.84016 - 3.11058i) q^{59} +(-1.08734 + 3.71722i) q^{60} +(-0.196690 + 0.430690i) q^{61} +(-8.99320 + 1.95635i) q^{62} +(7.55700 + 1.75801i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-8.60149 - 8.46143i) q^{65} +(-2.38321 + 10.5886i) q^{66} +(2.46652 - 1.84642i) q^{67} +(3.14959 + 3.14959i) q^{68} +(-7.55926 + 3.44348i) q^{69} +(-1.67477 - 5.53525i) q^{70} +(5.04374 + 0.725180i) q^{71} +(-0.256990 + 2.98897i) q^{72} +(2.53996 - 1.38692i) q^{73} +(-1.45623 - 1.68058i) q^{74} +(-4.61463 + 7.32838i) q^{75} +(-6.09026 - 3.91397i) q^{76} +(-5.66350 - 15.1844i) q^{77} +(-7.82591 - 5.10922i) q^{78} +(-2.15836 - 3.35847i) q^{79} +(2.02631 - 0.945560i) q^{80} +(-5.69588 - 6.96828i) q^{81} +(5.64783 + 1.22861i) q^{82} +(1.87480 - 0.134088i) q^{83} +(-2.11851 - 3.94692i) q^{84} +(4.84485 + 8.70210i) q^{85} +(0.547299 + 1.86393i) q^{86} +(-6.71777 - 5.90601i) q^{87} +(5.49977 - 3.00310i) q^{88} +(5.01417 + 10.9795i) q^{89} +(-2.38295 + 6.27069i) q^{90} +13.9554 q^{91} +(4.37477 + 1.96504i) q^{92} +(-15.7946 + 2.15522i) q^{93} +(-6.36487 - 0.915131i) q^{94} +(-10.7010 - 12.1467i) q^{95} +(1.39400 - 1.02799i) q^{96} +(-0.360875 + 5.04569i) q^{97} +(-0.273169 - 0.149161i) q^{98} +(-5.55485 + 17.9594i) 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

Related objects

Downloads

Learn more