LMFDB - Embedded newform 432.2.l.a.107.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.16
Character	$\chi$	$=$	432.107
Dual form			432.2.l.a.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39769 - 0.215558i) q^{2} +(1.90707 - 0.602567i) q^{4} +(1.33778 - 1.33778i) q^{5} +0.400629 q^{7} +(2.53560 - 1.25329i) q^{8} +O(q^{10})$	\(q+(1.39769 - 0.215558i) q^{2} +(1.90707 - 0.602567i) q^{4} +(1.33778 - 1.33778i) q^{5} +0.400629 q^{7} +(2.53560 - 1.25329i) q^{8} +(1.58143 - 2.15816i) q^{10} +(-0.0888310 - 0.0888310i) q^{11} +(-3.59973 + 3.59973i) q^{13} +(0.559955 - 0.0863589i) q^{14} +(3.27383 - 2.29827i) q^{16} +0.898464i q^{17} +(-3.16604 - 3.16604i) q^{19} +(1.74513 - 3.35733i) q^{20} +(-0.143306 - 0.105010i) q^{22} -7.09331i q^{23} +1.42071i q^{25} +(-4.25536 + 5.80726i) q^{26} +(0.764027 - 0.241406i) q^{28} +(5.95366 + 5.95366i) q^{29} +5.25833i q^{31} +(4.08038 - 3.91797i) q^{32} +(0.193671 + 1.25577i) q^{34} +(0.535952 - 0.535952i) q^{35} +(0.934713 + 0.934713i) q^{37} +(-5.10760 - 3.74267i) q^{38} +(1.71545 - 5.06868i) q^{40} +5.47587 q^{41} +(-6.81132 + 6.81132i) q^{43} +(-0.222933 - 0.115880i) q^{44} +(-1.52902 - 9.91425i) q^{46} -6.60040 q^{47} -6.83950 q^{49} +(0.306246 + 1.98571i) q^{50} +(-4.69586 + 9.03402i) q^{52} +(3.33939 - 3.33939i) q^{53} -0.237672 q^{55} +(1.01584 - 0.502103i) q^{56} +(9.60473 + 7.03801i) q^{58} +(-4.12522 - 4.12522i) q^{59} +(-7.11449 + 7.11449i) q^{61} +(1.13348 + 7.34951i) q^{62} +(4.85855 - 6.35567i) q^{64} +9.63127i q^{65} +(-1.42735 - 1.42735i) q^{67} +(0.541384 + 1.71343i) q^{68} +(0.633565 - 0.864623i) q^{70} +0.567075i q^{71} -12.1338i q^{73} +(1.50792 + 1.10495i) q^{74} +(-7.94560 - 4.13010i) q^{76} +(-0.0355883 - 0.0355883i) q^{77} +4.45380i q^{79} +(1.30507 - 7.45422i) q^{80} +(7.65357 - 1.18037i) q^{82} +(-6.47534 + 6.47534i) q^{83} +(1.20194 + 1.20194i) q^{85} +(-8.05187 + 10.9883i) q^{86} +(-0.336570 - 0.113909i) q^{88} -6.04927 q^{89} +(-1.44216 + 1.44216i) q^{91} +(-4.27420 - 13.5274i) q^{92} +(-9.22531 + 1.42277i) q^{94} -8.47090 q^{95} +15.8673 q^{97} +(-9.55949 + 1.47431i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) $ 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.39769	−	0.215558i	0.988315	−	0.152423i
$2$	1.39769	−	0.215558i	0.988315	−	0.152423i
$3$		0			0
$3$		0			0
$4$	1.90707	−	0.602567i	0.953535	−	0.301284i
$5$	1.33778	−	1.33778i	0.598272	−	0.598272i	−0.341581	−	0.939852i	$-0.610962\pi$
$5$	1.33778	−	1.33778i	0.598272	−	0.598272i	0.939852	+	0.341581i	$0.110962\pi$
$6$		0			0
$7$	0.400629			0.151424			0.0757118	−	0.997130i	$-0.475877\pi$
$7$	0.400629			0.151424			0.0757118	+	0.997130i	$0.475877\pi$
$8$	2.53560	−	1.25329i	0.896470	−	0.443103i
$9$		0			0
$10$	1.58143	−	2.15816i	0.500091	−	0.682471i
$11$	−0.0888310	−	0.0888310i	−0.0267835	−	0.0267835i	0.693588	−	0.720372i	$-0.256029\pi$
$11$	−0.0888310	−	0.0888310i	−0.0267835	−	0.0267835i	−0.720372	+	0.693588i	$0.756029\pi$
$12$		0			0
$13$	−3.59973	+	3.59973i	−0.998386	+	0.998386i	−0.999999	−	0.00161228i	$-0.999487\pi$
$13$	−3.59973	+	3.59973i	−0.998386	+	0.998386i	0.00161228	+	0.999999i	$0.499487\pi$
$14$	0.559955	−	0.0863589i	0.149654	−	0.0230804i
$15$		0			0
$16$	3.27383	−	2.29827i	0.818457	−	0.574568i
$17$			0.898464i			0.217909i	0.994047	+	0.108955i	$0.0347503\pi$
$17$			0.898464i			0.217909i	−0.994047	+	0.108955i	$0.965250\pi$
$18$		0			0
$19$	−3.16604	−	3.16604i	−0.726339	−	0.726339i	0.243550	−	0.969888i	$-0.421688\pi$
$19$	−3.16604	−	3.16604i	−0.726339	−	0.726339i	−0.969888	+	0.243550i	$0.921688\pi$
$20$	1.74513	−	3.35733i	0.390223	−	0.750722i
$21$		0			0
$22$	−0.143306	−	0.105010i	−0.0305530	−	0.0223882i
$23$		−	7.09331i		−	1.47906i	−0.673125	−	0.739529i	$-0.735048\pi$
$23$		−	7.09331i		−	1.47906i	0.673125	−	0.739529i	$-0.264952\pi$
$24$		0			0
$25$			1.42071i			0.284142i
$26$	−4.25536	+	5.80726i	−0.834544	+	1.13890i
$27$		0			0
$28$	0.764027	−	0.241406i	0.144388	−	0.0456214i
$29$	5.95366	+	5.95366i	1.10557	+	1.10557i	0.993726	+	0.111841i	$0.0356748\pi$
$29$	5.95366	+	5.95366i	1.10557	+	1.10557i	0.111841	+	0.993726i	$0.464325\pi$
$30$		0			0
$31$			5.25833i			0.944423i	0.881485	+	0.472212i	$0.156544\pi$
$31$			5.25833i			0.944423i	−0.881485	+	0.472212i	$0.843456\pi$
$32$	4.08038	−	3.91797i	0.721316	−	0.692606i
$33$		0			0
$34$	0.193671	+	1.25577i	0.0332144	+	0.215363i
$35$	0.535952	−	0.535952i	0.0905924	−	0.0905924i
$36$		0			0
$37$	0.934713	+	0.934713i	0.153666	+	0.153666i	0.779753	−	0.626087i	$-0.215345\pi$
$37$	0.934713	+	0.934713i	0.153666	+	0.153666i	−0.626087	+	0.779753i	$0.715345\pi$
$38$	−5.10760	−	3.74267i	−0.828562	−	0.607141i
$39$		0			0
$40$	1.71545	−	5.06868i	0.271237	−	0.801429i
$41$	5.47587			0.855188			0.427594	−	0.903971i	$-0.359361\pi$
$41$	5.47587			0.855188			0.427594	+	0.903971i	$0.359361\pi$
$42$		0			0
$43$	−6.81132	+	6.81132i	−1.03872	+	1.03872i	−0.0394961	+	0.999220i	$0.512575\pi$
$43$	−6.81132	+	6.81132i	−1.03872	+	1.03872i	−0.999220	+	0.0394961i	$0.987425\pi$
$44$	−0.222933	−	0.115880i	−0.0336085	−	0.0174696i
$45$		0			0
$46$	−1.52902	−	9.91425i	−0.225442	−	1.46178i
$47$	−6.60040			−0.962767			−0.481384	−	0.876510i	$-0.659866\pi$
$47$	−6.60040			−0.962767			−0.481384	+	0.876510i	$0.659866\pi$
$48$		0			0
$49$	−6.83950			−0.977071
$50$	0.306246	+	1.98571i	0.0433097	+	0.280822i
$51$		0			0
$52$	−4.69586	+	9.03402i	−0.651199	+	1.25279i
$53$	3.33939	−	3.33939i	0.458701	−	0.458701i	−0.439528	−	0.898229i	$-0.644854\pi$
$53$	3.33939	−	3.33939i	0.458701	−	0.458701i	0.898229	+	0.439528i	$0.144854\pi$
$54$		0			0
$55$	−0.237672			−0.0320477
$56$	1.01584	−	0.502103i	0.135747	−	0.0670963i
$57$		0			0
$58$	9.60473	+	7.03801i	1.26116	+	0.924136i
$59$	−4.12522	−	4.12522i	−0.537058	−	0.537058i	0.385606	−	0.922664i	$-0.373992\pi$
$59$	−4.12522	−	4.12522i	−0.537058	−	0.537058i	−0.922664	+	0.385606i	$0.873992\pi$
$60$		0			0
$61$	−7.11449	+	7.11449i	−0.910916	+	0.910916i	−0.996344	−	0.0854279i	$-0.972774\pi$
$61$	−7.11449	+	7.11449i	−0.910916	+	0.910916i	0.0854279	+	0.996344i	$0.472774\pi$
$62$	1.13348	+	7.34951i	0.143952	+	0.933388i
$63$		0			0
$64$	4.85855	−	6.35567i	0.607319	−	0.794458i
$65$			9.63127i			1.19461i
$66$		0			0
$67$	−1.42735	−	1.42735i	−0.174378	−	0.174378i	0.614522	−	0.788900i	$-0.289349\pi$
$67$	−1.42735	−	1.42735i	−0.174378	−	0.174378i	−0.788900	+	0.614522i	$0.789349\pi$
$68$	0.541384	+	1.71343i	0.0656525	+	0.207784i
$69$		0			0
$70$	0.633565	−	0.864623i	0.0757255	−	0.103342i
$71$			0.567075i			0.0672994i	0.999434	+	0.0336497i	$0.0107131\pi$
$71$			0.567075i			0.0672994i	−0.999434	+	0.0336497i	$0.989287\pi$
$72$		0			0
$73$		−	12.1338i		−	1.42015i	−0.704127	−	0.710074i	$-0.748661\pi$
$73$		−	12.1338i		−	1.42015i	0.704127	−	0.710074i	$-0.251339\pi$
$74$	1.50792	+	1.10495i	0.175293	+	0.128448i
$75$		0			0
$76$	−7.94560	−	4.13010i	−0.911423	−	0.473755i
$77$	−0.0355883	−	0.0355883i	−0.00405566	−	0.00405566i
$78$		0			0
$79$			4.45380i			0.501092i	0.968105	+	0.250546i	$0.0806101\pi$
$79$			4.45380i			0.501092i	−0.968105	+	0.250546i	$0.919390\pi$
$80$	1.30507	−	7.45422i	0.145911	−	0.833407i
$81$		0			0
$82$	7.65357	−	1.18037i	0.845195	−	0.130350i
$83$	−6.47534	+	6.47534i	−0.710761	+	0.710761i	−0.966694	−	0.255934i	$-0.917617\pi$
$83$	−6.47534	+	6.47534i	−0.710761	+	0.710761i	0.255934	+	0.966694i	$0.417617\pi$
$84$		0			0
$85$	1.20194	+	1.20194i	0.130369	+	0.130369i
$86$	−8.05187	+	10.9883i	−0.868255	+	1.18490i
$87$		0			0
$88$	−0.336570	−	0.113909i	−0.0358785	−	0.0121428i
$89$	−6.04927			−0.641221			−0.320610	−	0.947211i	$-0.603888\pi$
$89$	−6.04927			−0.641221			−0.320610	+	0.947211i	$0.603888\pi$
$90$		0			0
$91$	−1.44216	+	1.44216i	−0.151179	+	0.151179i
$92$	−4.27420	−	13.5274i	−0.445616	−	1.41033i
$93$		0			0
$94$	−9.22531	+	1.42277i	−0.951518	+	0.146748i
$95$	−8.47090			−0.869096
$96$		0			0
$97$	15.8673			1.61108			0.805539	−	0.592543i	$-0.201876\pi$
$97$	15.8673			1.61108			0.805539	+	0.592543i	$0.201876\pi$
$98$	−9.55949	+	1.47431i	−0.965654	+	0.148928i
$99$		0			0
$100$	0.856073	+	2.70939i	0.0856073	+	0.270939i
$101$	−9.74391	+	9.74391i	−0.969555	+	0.969555i	−0.999550	−	0.0299946i	$-0.990451\pi$
$101$	−9.74391	+	9.74391i	−0.969555	+	0.969555i	0.0299946	+	0.999550i	$0.490451\pi$
$102$		0			0
$103$	18.0741			1.78089			0.890446	−	0.455088i	$-0.150392\pi$
$103$	18.0741			1.78089			0.890446	+	0.455088i	$0.150392\pi$
$104$	−4.61599	+	13.6390i	−0.452635	+	1.33741i
$105$		0			0
$106$	3.94760	−	5.38726i	0.383424	−	0.523257i
$107$	−13.0466	−	13.0466i	−1.26126	−	1.26126i	−0.950482	−	0.310778i	$-0.899410\pi$
$107$	−13.0466	−	13.0466i	−1.26126	−	1.26126i	−0.310778	−	0.950482i	$-0.600590\pi$
$108$		0			0
$109$	−0.427292	+	0.427292i	−0.0409272	+	0.0409272i	−0.727274	−	0.686347i	$-0.759213\pi$
$109$	−0.427292	+	0.427292i	−0.0409272	+	0.0409272i	0.686347	+	0.727274i	$0.259213\pi$
$110$	−0.332191	+	0.0512321i	−0.0316732	+	0.00488479i
$111$		0			0
$112$	1.31159	−	0.920755i	0.123934	−	0.0870032i
$113$		−	0.221571i		−	0.0208436i	−0.999946	−	0.0104218i	$-0.996683\pi$
$113$		−	0.221571i		−	0.0208436i	0.999946	−	0.0104218i	$-0.00331743\pi$
$114$		0			0
$115$	−9.48926	−	9.48926i	−0.884879	−	0.884879i
$116$	14.9415	+	7.76657i	1.38729	+	0.721107i
$117$		0			0
$118$	−6.65500	−	4.87655i	−0.612642	−	0.448922i
$119$			0.359951i			0.0329966i
$120$		0			0
$121$		−	10.9842i		−	0.998565i
$122$	−8.41025	+	11.4774i	−0.761428	+	1.03912i
$123$		0			0
$124$	3.16849	+	10.0280i	0.284539	+	0.900540i
$125$	8.58947	+	8.58947i	0.768266	+	0.768266i
$126$		0			0
$127$			7.09237i			0.629346i	0.949200	+	0.314673i	$0.101895\pi$
$127$			7.09237i			0.629346i	−0.949200	+	0.314673i	$0.898105\pi$
$128$	5.42072	−	9.93055i	0.479129	−	0.877745i
$129$		0			0
$130$	2.07610	+	13.4615i	0.182086	+	1.18065i
$131$	2.90047	−	2.90047i	0.253415	−	0.253415i	−0.568954	−	0.822369i	$-0.692652\pi$
$131$	2.90047	−	2.90047i	0.253415	−	0.253415i	0.822369	+	0.568954i	$0.192652\pi$
$132$		0			0
$133$	−1.26841	−	1.26841i	−0.109985	−	0.109985i
$134$	−2.30267	−	1.68731i	−0.198920	−	0.145762i
$135$		0			0
$136$	1.12603	+	2.27815i	0.0965564	+	0.195349i
$137$	21.6135			1.84656			0.923282	−	0.384123i	$-0.125496\pi$
$137$	21.6135			1.84656			0.923282	+	0.384123i	$0.125496\pi$
$138$		0			0
$139$	12.7140	−	12.7140i	1.07839	−	1.07839i	0.0817338	−	0.996654i	$-0.473954\pi$
$139$	12.7140	−	12.7140i	1.07839	−	1.07839i	0.996654	−	0.0817338i	$-0.0260457\pi$
$140$	0.699150	−	1.34504i	0.0590890	−	0.113677i
$141$		0			0
$142$	0.122238	+	0.792595i	0.0102580	+	0.0665131i
$143$	0.639535			0.0534806
$144$		0			0
$145$	15.9293			1.32286
$146$	−2.61553	−	16.9592i	−0.216463	−	1.40355i
$147$		0			0
$148$	2.34579	+	1.21934i	0.192823	+	0.100229i
$149$	−3.66096	+	3.66096i	−0.299918	+	0.299918i	−0.840981	−	0.541064i	$-0.818022\pi$
$149$	−3.66096	+	3.66096i	−0.299918	+	0.299918i	0.541064	+	0.840981i	$0.318022\pi$
$150$		0			0
$151$	13.8388			1.12618			0.563091	−	0.826395i	$-0.309612\pi$
$151$	13.8388			1.12618			0.563091	+	0.826395i	$0.309612\pi$
$152$	−11.9958	−	4.05986i	−0.972985	−	0.329298i
$153$		0			0
$154$	−0.0574127	−	0.0420700i	−0.00462644	−	0.00339009i
$155$	7.03446	+	7.03446i	0.565022	+	0.565022i
$156$		0			0
$157$	−14.3513	+	14.3513i	−1.14536	+	1.14536i	−0.157908	+	0.987454i	$0.550475\pi$
$157$	−14.3513	+	14.3513i	−1.14536	+	1.14536i	−0.987454	+	0.157908i	$0.949525\pi$
$158$	0.960054	+	6.22503i	0.0763778	+	0.495237i
$159$		0			0
$160$	0.217263	−	10.7000i	0.0171761	−	0.845910i
$161$		−	2.84179i		−	0.223964i
$162$		0			0
$163$	−15.9588	−	15.9588i	−1.24999	−	1.24999i	−0.955723	−	0.294267i	$-0.904924\pi$
$163$	−15.9588	−	15.9588i	−1.24999	−	1.24999i	−0.294267	−	0.955723i	$-0.595076\pi$
$164$	10.4429	−	3.29958i	0.815451	−	0.257654i
$165$		0			0
$166$	−7.65470	+	10.4463i	−0.594120	+	0.810792i
$167$		−	0.346611i		−	0.0268215i	−0.999910	−	0.0134108i	$-0.995731\pi$
$167$		−	0.346611i		−	0.0268215i	0.999910	−	0.0134108i	$-0.00426891\pi$
$168$		0			0
$169$		−	12.9162i		−	0.993551i
$170$	1.93903	+	1.42085i	0.148717	+	0.108975i
$171$		0			0
$172$	−8.88538	+	17.0939i	−0.677504	+	1.30340i
$173$	−10.4179	−	10.4179i	−0.792060	−	0.792060i	0.189769	−	0.981829i	$-0.439226\pi$
$173$	−10.4179	−	10.4179i	−0.792060	−	0.792060i	−0.981829	+	0.189769i	$0.939226\pi$
$174$		0			0
$175$			0.569178i			0.0430258i
$176$	−0.494975	−	0.0866592i	−0.0373101	−	0.00653218i
$177$		0			0
$178$	−8.45499	+	1.30397i	−0.633728	+	0.0977366i
$179$	12.9741	−	12.9741i	0.969731	−	0.969731i	−0.0298239	−	0.999555i	$-0.509495\pi$
$179$	12.9741	−	12.9741i	0.969731	−	0.969731i	0.999555	+	0.0298239i	$0.00949464\pi$
$180$		0			0
$181$	13.1716	+	13.1716i	0.979035	+	0.979035i	0.999785	−	0.0207495i	$-0.00660523\pi$
$181$	13.1716	+	13.1716i	0.979035	+	0.979035i	−0.0207495	+	0.999785i	$0.506605\pi$
$182$	−1.70482	+	2.32656i	−0.126370	+	0.172456i
$183$		0			0
$184$	−8.88995	−	17.9858i	−0.655376	−	1.32593i
$185$	2.50087			0.183868
$186$		0			0
$187$	0.0798114	−	0.0798114i	0.00583639	−	0.00583639i
$188$	−12.5874	+	3.97718i	−0.918032	+	0.290066i
$189$		0			0
$190$	−11.8397	+	1.82597i	−0.858941	+	0.132470i
$191$	8.78032			0.635322			0.317661	−	0.948204i	$-0.397103\pi$
$191$	8.78032			0.635322			0.317661	+	0.948204i	$0.397103\pi$
$192$		0			0
$193$	−4.59474			−0.330737			−0.165368	−	0.986232i	$-0.552881\pi$
$193$	−4.59474			−0.330737			−0.165368	+	0.986232i	$0.552881\pi$
$194$	22.1775	−	3.42032i	1.59225	−	0.245565i
$195$		0			0
$196$	−13.0434	+	4.12125i	−0.931671	+	0.294375i
$197$	16.0449	−	16.0449i	1.14315	−	1.14315i	0.155282	−	0.987870i	$-0.450371\pi$
$197$	16.0449	−	16.0449i	1.14315	−	1.14315i	0.987870	−	0.155282i	$-0.0496286\pi$
$198$		0			0
$199$	−0.106373			−0.00754061			−0.00377030	−	0.999993i	$-0.501200\pi$
$199$	−0.106373			−0.00754061			−0.00377030	+	0.999993i	$0.501200\pi$
$200$	1.78056	+	3.60236i	0.125904	+	0.254725i
$201$		0			0
$202$	−11.5186	+	15.7193i	−0.810444	+	1.10601i
$203$	2.38521	+	2.38521i	0.167409	+	0.167409i
$204$		0			0
$205$	7.32549	−	7.32549i	0.511635	−	0.511635i
$206$	25.2620	−	3.89602i	1.76008	−	0.271449i
$207$		0			0
$208$	−3.51173	+	20.0581i	−0.243494	+	1.39078i
$209$			0.562484i			0.0389079i
$210$		0			0
$211$	1.19501	+	1.19501i	0.0822678	+	0.0822678i	0.747043	−	0.664775i	$-0.231473\pi$
$211$	1.19501	+	1.19501i	0.0822678	+	0.0822678i	−0.664775	+	0.747043i	$0.731473\pi$
$212$	4.35624	−	8.38066i	0.299188	−	0.575586i
$213$		0			0
$214$	−21.0474	−	15.4228i	−1.43877	−	1.05428i
$215$			18.2240i			1.24287i
$216$		0			0
$217$			2.10664i			0.143008i
$218$	−0.505116	+	0.689328i	−0.0342107	+	0.0466872i
$219$		0			0
$220$	−0.453257	+	0.143213i	−0.0305586	+	0.00965543i
$221$	−3.23423	−	3.23423i	−0.217558	−	0.217558i
$222$		0			0
$223$		−	14.5834i		−	0.976579i	−0.872682	−	0.488289i	$-0.837621\pi$
$223$		−	14.5834i		−	0.976579i	0.872682	−	0.488289i	$-0.162379\pi$
$224$	1.63472	−	1.56965i	0.109224	−	0.104877i
$225$		0			0
$226$	−0.0477615	−	0.309687i	−0.00317705	−	0.0206001i
$227$	−8.19520	+	8.19520i	−0.543934	+	0.543934i	−0.924680	−	0.380745i	$-0.875667\pi$
$227$	−8.19520	+	8.19520i	−0.543934	+	0.543934i	0.380745	+	0.924680i	$0.375667\pi$
$228$		0			0
$229$	−9.72607	−	9.72607i	−0.642717	−	0.642717i	0.308506	−	0.951222i	$-0.400171\pi$
$229$	−9.72607	−	9.72607i	−0.642717	−	0.642717i	−0.951222	+	0.308506i	$0.900171\pi$
$230$	−15.3085	−	11.2176i	−1.00941	−	0.739663i
$231$		0			0
$232$	22.5578	+	7.63447i	1.48099	+	0.501228i
$233$	−11.4450			−0.749789			−0.374894	−	0.927067i	$-0.622321\pi$
$233$	−11.4450			−0.749789			−0.374894	+	0.927067i	$0.622321\pi$
$234$		0			0
$235$	−8.82986	+	8.82986i	−0.575996	+	0.575996i
$236$	−10.3528	−	5.38136i	−0.673910	−	0.350296i
$237$		0			0
$238$	0.0775903	+	0.503099i	0.00502943	+	0.0326111i
$239$	13.2746			0.858665			0.429333	−	0.903146i	$-0.358749\pi$
$239$	13.2746			0.858665			0.429333	+	0.903146i	$0.358749\pi$
$240$		0			0
$241$	1.84447			0.118813			0.0594064	−	0.998234i	$-0.481079\pi$
$241$	1.84447			0.118813			0.0594064	+	0.998234i	$0.481079\pi$
$242$	−2.36774	−	15.3525i	−0.152204	−	0.986897i
$243$		0			0
$244$	−9.28086	+	17.8548i	−0.594146	+	1.14303i
$245$	−9.14971	+	9.14971i	−0.584554	+	0.584554i
$246$		0			0
$247$	22.7938			1.45033
$248$	6.59019	+	13.3330i	0.418477	+	0.846648i
$249$		0			0
$250$	13.8569	+	10.1539i	0.876390	+	0.642188i
$251$	−10.4562	−	10.4562i	−0.659991	−	0.659991i	0.295387	−	0.955378i	$-0.404551\pi$
$251$	−10.4562	−	10.4562i	−0.659991	−	0.659991i	−0.955378	+	0.295387i	$0.904551\pi$
$252$		0			0
$253$	−0.630106	+	0.630106i	−0.0396144	+	0.0396144i
$254$	1.52882	+	9.91293i	0.0959266	+	0.621992i
$255$		0			0
$256$	5.43587	−	15.0483i	0.339742	−	0.940519i
$257$		−	21.7170i		−	1.35467i	−0.735676	−	0.677334i	$-0.763135\pi$
$257$		−	21.7170i		−	1.35467i	0.735676	−	0.677334i	$-0.236865\pi$
$258$		0			0
$259$	0.374473	+	0.374473i	0.0232686	+	0.0232686i
$260$	5.80349	+	18.3675i	0.359917	+	1.13910i
$261$		0			0
$262$	3.42874	−	4.67918i	0.211828	−	0.289081i
$263$		−	16.5149i		−	1.01835i	−0.860663	−	0.509175i	$-0.829950\pi$
$263$		−	16.5149i		−	1.01835i	0.860663	−	0.509175i	$-0.170050\pi$
$264$		0			0
$265$		−	8.93471i		−	0.548855i
$266$	−2.04625	−	1.49942i	−0.125464	−	0.0919355i
$267$		0			0
$268$	−3.58213	−	1.86198i	−0.218813	−	0.113738i
$269$	2.47977	+	2.47977i	0.151194	+	0.151194i	0.778651	−	0.627457i	$-0.215904\pi$
$269$	2.47977	+	2.47977i	0.151194	+	0.151194i	−0.627457	+	0.778651i	$0.715904\pi$
$270$		0			0
$271$			3.40817i			0.207031i	0.994628	+	0.103516i	$0.0330092\pi$
$271$			3.40817i			0.207031i	−0.994628	+	0.103516i	$0.966991\pi$
$272$	2.06492	+	2.94141i	0.125204	+	0.178349i
$273$		0			0
$274$	30.2089	−	4.65897i	1.82499	−	0.281458i
$275$	0.126203	−	0.126203i	0.00761033	−	0.00761033i
$276$		0			0
$277$	7.62191	+	7.62191i	0.457956	+	0.457956i	0.897984	−	0.440028i	$-0.145032\pi$
$277$	7.62191	+	7.62191i	0.457956	+	0.457956i	−0.440028	+	0.897984i	$0.645032\pi$
$278$	15.0296	−	20.5108i	0.901417	−	1.23016i
$279$		0			0
$280$	0.687259	−	2.03066i	0.0410716	−	0.121355i
$281$	−11.8744			−0.708365			−0.354182	−	0.935176i	$-0.615241\pi$
$281$	−11.8744			−0.708365			−0.354182	+	0.935176i	$0.615241\pi$
$282$		0			0
$283$	0.383322	−	0.383322i	0.0227861	−	0.0227861i	−0.695622	−	0.718408i	$-0.744871\pi$
$283$	0.383322	−	0.383322i	0.0227861	−	0.0227861i	0.718408	+	0.695622i	$0.244871\pi$
$284$	0.341701	+	1.08145i	0.0202762	+	0.0641723i
$285$		0			0
$286$	0.893872	−	0.137857i	0.0528557	−	0.00815167i
$287$	2.19379			0.129496
$288$		0			0
$289$	16.1928			0.952515
$290$	22.2643	−	3.43370i	1.30740	−	0.201634i
$291$		0			0
$292$	−7.31140	−	23.1399i	−0.427867	−	1.35416i
$293$	3.99171	−	3.99171i	0.233198	−	0.233198i	−0.580828	−	0.814026i	$-0.697271\pi$
$293$	3.99171	−	3.99171i	0.233198	−	0.233198i	0.814026	+	0.580828i	$0.197271\pi$
$294$		0			0
$295$	−11.0372			−0.642613
$296$	3.54152	+	1.19860i	0.205847	+	0.0696670i
$297$		0			0
$298$	−4.32773	+	5.90603i	−0.250699	+	0.342127i
$299$	25.5340	+	25.5340i	1.47667	+	1.47667i
$300$		0			0
$301$	−2.72881	+	2.72881i	−0.157286	+	0.157286i
$302$	19.3423	−	2.98306i	1.11302	−	0.171656i
$303$		0			0
$304$	−17.6415	−	3.08863i	−1.01181	−	0.177145i
$305$			19.0352i			1.08995i
$306$		0			0
$307$	9.45335	+	9.45335i	0.539531	+	0.539531i	0.923391	−	0.383860i	$-0.125406\pi$
$307$	9.45335	+	9.45335i	0.539531	+	0.539531i	−0.383860	+	0.923391i	$0.625406\pi$
$308$	−0.0893136	−	0.0464250i	−0.00508911	−	0.00264531i
$309$		0			0
$310$	11.3483	+	8.31566i	0.644542	+	0.472297i
$311$		−	13.0887i		−	0.742193i	−0.928594	−	0.371097i	$-0.878982\pi$
$311$		−	13.0887i		−	0.742193i	0.928594	−	0.371097i	$-0.121018\pi$
$312$		0			0
$313$		−	12.6165i		−	0.713128i	−0.934271	−	0.356564i	$-0.883948\pi$
$313$		−	12.6165i		−	0.713128i	0.934271	−	0.356564i	$-0.116052\pi$
$314$	−16.9652	+	23.1523i	−0.957400	+	1.30656i
$315$		0			0
$316$	2.68371	+	8.49371i	0.150971	+	0.477808i
$317$	−4.29010	−	4.29010i	−0.240956	−	0.240956i	0.576290	−	0.817245i	$-0.304500\pi$
$317$	−4.29010	−	4.29010i	−0.240956	−	0.240956i	−0.817245	+	0.576290i	$0.804500\pi$
$318$		0			0
$319$		−	1.05774i		−	0.0592220i
$320$	−2.00281	−	15.0021i	−0.111960	−	0.838643i
$321$		0			0
$322$	−0.612571	−	3.97193i	−0.0341372	−	0.221347i
$323$	2.84457	−	2.84457i	0.158276	−	0.158276i
$324$		0			0
$325$	−5.11418	−	5.11418i	−0.283684	−	0.283684i
$326$	−25.7455	−	18.8654i	−1.42591	−	1.04486i
$327$		0			0
$328$	13.8846	−	6.86284i	0.766651	−	0.378937i
$329$	−2.64431			−0.145786
$330$		0			0
$331$	4.94758	−	4.94758i	0.271943	−	0.271943i	−0.557939	−	0.829882i	$-0.688408\pi$
$331$	4.94758	−	4.94758i	0.271943	−	0.271943i	0.829882	+	0.557939i	$0.188408\pi$
$332$	−8.44709	+	16.2507i	−0.463595	+	0.891876i
$333$		0			0
$334$	−0.0747148	−	0.484454i	−0.00408821	−	0.0265082i
$335$	−3.81895			−0.208651
$336$		0			0
$337$	−11.7846			−0.641949			−0.320974	−	0.947088i	$-0.604010\pi$
$337$	−11.7846			−0.641949			−0.320974	+	0.947088i	$0.604010\pi$
$338$	−2.78419	−	18.0528i	−0.151440	−	0.981942i
$339$		0			0
$340$	3.01644	+	1.56794i	0.163589	+	0.0850333i
$341$	0.467102	−	0.467102i	0.0252950	−	0.0252950i
$342$		0			0
$343$	−5.54450			−0.299375
$344$	−8.73426	+	25.8073i	−0.470919	+	1.39144i
$345$		0			0
$346$	−16.8067	−	12.3153i	−0.903533	−	0.662077i
$347$	23.1112	+	23.1112i	1.24067	+	1.24067i	0.959722	+	0.280951i	$0.0906500\pi$
$347$	23.1112	+	23.1112i	1.24067	+	1.24067i	0.280951	+	0.959722i	$0.409350\pi$
$348$		0			0
$349$	0.296412	−	0.296412i	0.0158666	−	0.0158666i	−0.699129	−	0.714996i	$-0.746429\pi$
$349$	0.296412	−	0.296412i	0.0158666	−	0.0158666i	0.714996	+	0.699129i	$0.246429\pi$
$350$	0.122691	+	0.795534i	0.00655811	+	0.0425231i
$351$		0			0
$352$	−0.710501	−	0.0144267i	−0.0378698	−	0.000768944i
$353$		−	30.2800i		−	1.61164i	−0.592159	−	0.805821i	$-0.701724\pi$
$353$		−	30.2800i		−	1.61164i	0.592159	−	0.805821i	$-0.298276\pi$
$354$		0			0
$355$	0.758619	+	0.758619i	0.0402633	+	0.0402633i
$356$	−11.5364	+	3.64509i	−0.611426	+	0.193189i
$357$		0			0
$358$	15.3371	−	20.9305i	0.810591	−	1.10621i
$359$			33.7158i			1.77945i	0.456496	+	0.889725i	$0.349104\pi$
$359$			33.7158i			1.77945i	−0.456496	+	0.889725i	$0.650896\pi$
$360$		0			0
$361$			1.04759i			0.0551364i
$362$	21.2490	+	15.5705i	1.11682	+	0.818368i
$363$		0			0
$364$	−1.88130	+	3.61929i	−0.0986068	+	0.189702i
$365$	−16.2322	−	16.2322i	−0.849634	−	0.849634i
$366$		0			0
$367$			31.1671i			1.62691i	0.581627	+	0.813456i	$0.302416\pi$
$367$			31.1671i			1.62691i	−0.581627	+	0.813456i	$0.697584\pi$
$368$	−16.3024	−	23.2223i	−0.849820	−	1.21054i
$369$		0			0
$370$	3.49544	−	0.539084i	0.181719	−	0.0280257i
$371$	1.33786	−	1.33786i	0.0694581	−	0.0694581i
$372$		0			0
$373$	−9.61943	−	9.61943i	−0.498075	−	0.498075i	0.412763	−	0.910838i	$-0.364564\pi$
$373$	−9.61943	−	9.61943i	−0.498075	−	0.498075i	−0.910838	+	0.412763i	$0.864564\pi$
$374$	0.0943475	−	0.128755i	0.00487859	−	0.00665779i
$375$		0			0
$376$	−16.7360	+	8.27219i	−0.863092	+	0.426606i
$377$	−42.8632			−2.20757
$378$		0			0
$379$	−12.6109	+	12.6109i	−0.647779	+	0.647779i	−0.952456	−	0.304677i	$-0.901451\pi$
$379$	−12.6109	+	12.6109i	−0.647779	+	0.647779i	0.304677	+	0.952456i	$0.401451\pi$
$380$	−16.1546	+	5.10428i	−0.828713	+	0.261844i
$381$		0			0
$382$	12.2722	−	1.89267i	0.627898	−	0.0968375i
$383$	1.18861			0.0607352			0.0303676	−	0.999539i	$-0.490332\pi$
$383$	1.18861			0.0607352			0.0303676	+	0.999539i	$0.490332\pi$
$384$		0			0
$385$	−0.0952182			−0.00485277
$386$	−6.42202	+	0.990435i	−0.326872	+	0.0504118i
$387$		0			0
$388$	30.2600	−	9.56109i	1.53622	−	0.485391i
$389$	8.71146	−	8.71146i	0.441689	−	0.441689i	−0.450891	−	0.892579i	$-0.648894\pi$
$389$	8.71146	−	8.71146i	0.441689	−	0.441689i	0.892579	+	0.450891i	$0.148894\pi$
$390$		0			0
$391$	6.37308			0.322301
$392$	−17.3422	+	8.57184i	−0.875915	+	0.432944i
$393$		0			0
$394$	18.9672	−	25.8844i	0.955552	−	1.30404i
$395$	5.95819	+	5.95819i	0.299789	+	0.299789i
$396$		0			0
$397$	−6.02248	+	6.02248i	−0.302260	+	0.302260i	−0.841897	−	0.539638i	$-0.818561\pi$
$397$	−6.02248	+	6.02248i	−0.302260	+	0.302260i	0.539638	+	0.841897i	$0.318561\pi$
$398$	−0.148677	+	0.0229297i	−0.00745250	+	0.00114936i
$399$		0			0
$400$	3.26518	+	4.65116i	0.163259	+	0.232558i
$401$			19.2694i			0.962268i	0.876647	+	0.481134i	$0.159775\pi$
$401$			19.2694i			0.962268i	−0.876647	+	0.481134i	$0.840225\pi$
$402$		0			0
$403$	−18.9286	−	18.9286i	−0.942899	−	0.942899i
$404$	−12.7110	+	24.4537i	−0.632394	+	1.21662i
$405$		0			0
$406$	3.84793	+	2.81963i	0.190970	+	0.139936i
$407$		−	0.166063i		−	0.00823143i
$408$		0			0
$409$			28.6427i			1.41629i	0.706066	+	0.708146i	$0.250468\pi$
$409$			28.6427i			1.41629i	−0.706066	+	0.708146i	$0.749532\pi$
$410$	8.65969	−	11.8178i	0.427672	−	0.583641i
$411$		0			0
$412$	34.4685	−	10.8908i	1.69814	−	0.536554i
$413$	−1.65268	−	1.65268i	−0.0813232	−	0.0813232i
$414$		0			0
$415$			17.3251i			0.850456i
$416$	−0.584618	+	28.7919i	−0.0286632	+	1.41164i
$417$		0			0
$418$	0.121248	+	0.786178i	0.00593044	+	0.0384532i
$419$	−23.0226	+	23.0226i	−1.12473	+	1.12473i	−0.133708	+	0.991021i	$0.542688\pi$
$419$	−23.0226	+	23.0226i	−1.12473	+	1.12473i	−0.991021	+	0.133708i	$0.957312\pi$
$420$		0			0
$421$	6.40655	+	6.40655i	0.312236	+	0.312236i	0.845775	−	0.533539i	$-0.179138\pi$
$421$	6.40655	+	6.40655i	0.312236	+	0.312236i	−0.533539	+	0.845775i	$0.679138\pi$
$422$	1.92785	+	1.41266i	0.0938461	+	0.0687671i
$423$		0			0
$424$	4.28215	−	12.6526i	0.207960	−	0.614463i
$425$	−1.27646			−0.0619172
$426$		0			0
$427$	−2.85027	+	2.85027i	−0.137934	+	0.137934i
$428$	−32.7422	−	17.0193i	−1.58265	−	0.822659i
$429$		0			0
$430$	3.92834	+	25.4715i	0.189441	+	1.22835i
$431$	22.2371			1.07112			0.535561	−	0.844497i	$-0.320100\pi$
$431$	22.2371			1.07112			0.535561	+	0.844497i	$0.320100\pi$
$432$		0			0
$433$	−22.5346			−1.08294			−0.541472	−	0.840719i	$-0.682133\pi$
$433$	−22.5346			−1.08294			−0.541472	+	0.840719i	$0.682133\pi$
$434$	0.454103	+	2.94443i	0.0217977	+	0.141337i
$435$		0			0
$436$	−0.557404	+	1.07235i	−0.0266948	+	0.0513562i
$437$	−22.4577	+	22.4577i	−1.07430	+	1.07430i
$438$		0			0
$439$	−24.5770			−1.17300			−0.586498	−	0.809951i	$-0.699494\pi$
$439$	−24.5770			−1.17300			−0.586498	+	0.809951i	$0.699494\pi$
$440$	−0.602641	+	0.297871i	−0.0287298	+	0.0142004i
$441$		0			0
$442$	−5.21761	−	3.82328i	−0.248176	−	0.181855i
$443$	−12.3160	−	12.3160i	−0.585151	−	0.585151i	0.351163	−	0.936314i	$-0.385786\pi$
$443$	−12.3160	−	12.3160i	−0.585151	−	0.585151i	−0.936314	+	0.351163i	$0.885786\pi$
$444$		0			0
$445$	−8.09256	+	8.09256i	−0.383624	+	0.383624i
$446$	−3.14358	−	20.3831i	−0.148853	−	0.965168i
$447$		0			0
$448$	1.94648	−	2.54626i	0.0919623	−	0.120300i
$449$		−	10.3537i		−	0.488622i	−0.969697	−	0.244311i	$-0.921438\pi$
$449$		−	10.3537i		−	0.488622i	0.969697	−	0.244311i	$-0.0785618\pi$
$450$		0			0
$451$	−0.486427	−	0.486427i	−0.0229050	−	0.0229050i
$452$	−0.133511	−	0.422551i	−0.00627985	−	0.0198751i
$453$		0			0
$454$	−9.68780	+	13.2209i	−0.454671	+	0.620487i
$455$			3.85857i			0.180892i
$456$		0			0
$457$			13.0734i			0.611550i	0.952104	+	0.305775i	$0.0989155\pi$
$457$			13.0734i			0.611550i	−0.952104	+	0.305775i	$0.901085\pi$
$458$	−15.6906	−	11.4975i	−0.733171	−	0.537242i
$459$		0			0
$460$	−23.8146	−	12.3788i	−1.11036	−	0.577163i
$461$	−11.5609	−	11.5609i	−0.538445	−	0.538445i	0.384627	−	0.923072i	$-0.374330\pi$
$461$	−11.5609	−	11.5609i	−0.538445	−	0.538445i	−0.923072	+	0.384627i	$0.874330\pi$
$462$		0			0
$463$		−	19.2687i		−	0.895493i	−0.894160	−	0.447747i	$-0.852227\pi$
$463$		−	19.2687i		−	0.895493i	0.894160	−	0.447747i	$-0.147773\pi$
$464$	33.1744	+	5.80811i	1.54008	+	0.269635i
$465$		0			0
$466$	−15.9966	+	2.46707i	−0.741028	+	0.114285i
$467$	−9.38675	+	9.38675i	−0.434367	+	0.434367i	−0.890111	−	0.455744i	$-0.849373\pi$
$467$	−9.38675	+	9.38675i	−0.434367	+	0.434367i	0.455744	+	0.890111i	$0.349373\pi$
$468$		0			0
$469$	−0.571837	−	0.571837i	−0.0264050	−	0.0264050i
$470$	−10.4380	+	14.2447i	−0.481471	+	0.657061i
$471$		0			0
$472$	−15.6300	−	5.28983i	−0.719428	−	0.243484i
$473$	1.21011			0.0556410
$474$		0			0
$475$	4.49802	−	4.49802i	0.206383	−	0.206383i
$476$	0.216894	+	0.686451i	0.00994134	+	0.0314634i
$477$		0			0
$478$	18.5538	−	2.86146i	0.848632	−	0.130880i
$479$	−9.84751			−0.449944			−0.224972	−	0.974365i	$-0.572229\pi$
$479$	−9.84751			−0.449944			−0.224972	+	0.974365i	$0.572229\pi$
$480$		0			0
$481$	−6.72944			−0.306836
$482$	2.57800	−	0.397591i	0.117425	−	0.0181098i
$483$		0			0
$484$	−6.61873	−	20.9477i	−0.300851	−	0.952167i
$485$	21.2269	−	21.2269i	0.963862	−	0.963862i
$486$		0			0
$487$	−23.1365			−1.04841			−0.524207	−	0.851591i	$-0.675638\pi$
$487$	−23.1365			−1.04841			−0.524207	+	0.851591i	$0.675638\pi$
$488$	−9.12301	+	26.9560i	−0.412979	+	1.22024i
$489$		0			0
$490$	−10.8162	+	14.7608i	−0.488624	+	0.666823i
$491$	0.406284	+	0.406284i	0.0183353	+	0.0183353i	0.716215	−	0.697880i	$-0.245873\pi$
$491$	0.406284	+	0.406284i	0.0183353	+	0.0183353i	−0.697880	+	0.716215i	$0.745873\pi$
$492$		0			0
$493$	−5.34915	+	5.34915i	−0.240914	+	0.240914i
$494$	31.8586	−	4.91339i	1.43339	−	0.221064i
$495$		0			0
$496$	12.0851	+	17.2148i	0.542636	+	0.772969i
$497$			0.227187i			0.0101907i
$498$		0			0
$499$	20.4984	+	20.4984i	0.917634	+	0.917634i	0.996857	−	0.0792231i	$-0.0252439\pi$
$499$	20.4984	+	20.4984i	0.917634	+	0.917634i	−0.0792231	+	0.996857i	$0.525244\pi$
$500$	21.5565	+	11.2050i	0.964034	+	0.501102i
$501$		0			0
$502$	−16.8685	−	12.3606i	−0.752877	−	0.551681i
$503$			15.1375i			0.674948i	0.941335	+	0.337474i	$0.109572\pi$
$503$			15.1375i			0.674948i	−0.941335	+	0.337474i	$0.890428\pi$
$504$		0			0
$505$			26.0703i			1.16012i
$506$	−0.744867	+	1.01652i	−0.0331134	+	0.0451897i
$507$		0			0
$508$	4.27363	+	13.5256i	0.189612	+	0.600103i
$509$	9.83348	+	9.83348i	0.435861	+	0.435861i	0.890616	−	0.454755i	$-0.150273\pi$
$509$	9.83348	+	9.83348i	0.435861	+	0.435861i	−0.454755	+	0.890616i	$0.650273\pi$
$510$		0			0
$511$		−	4.86113i		−	0.215044i
$512$	4.35387	−	22.2046i	0.192416	−	0.981313i
$513$		0			0
$514$	−4.68128	−	30.3536i	−0.206482	−	1.33884i
$515$	24.1791	−	24.1791i	1.06546	−	1.06546i
$516$		0			0
$517$	0.586320	+	0.586320i	0.0257863	+	0.0257863i
$518$	0.604118	+	0.442676i	0.0265434	+	0.0194501i
$519$		0			0
$520$	12.0707	+	24.4211i	0.529337	+	1.07093i
$521$	−24.0077			−1.05180			−0.525898	−	0.850548i	$-0.676270\pi$
$521$	−24.0077			−1.05180			−0.525898	+	0.850548i	$0.676270\pi$
$522$		0			0
$523$	−5.16641	+	5.16641i	−0.225911	+	0.225911i	−0.810982	−	0.585071i	$-0.801067\pi$
$523$	−5.16641	+	5.16641i	−0.225911	+	0.225911i	0.585071	+	0.810982i	$0.301067\pi$
$524$	3.78367	−	7.27913i	0.165291	−	0.317990i
$525$		0			0
$526$	−3.55992	−	23.0827i	−0.155220	−	1.00645i
$527$	−4.72441			−0.205799
$528$		0			0
$529$	−27.3151			−1.18761
$530$	−1.92595	−	12.4880i	−0.0836580	−	0.542442i
$531$		0			0
$532$	−3.18324	−	1.65464i	−0.138011	−	0.0717377i
$533$	−19.7117	+	19.7117i	−0.853808	+	0.853808i
$534$		0			0
$535$	−34.9068			−1.50915
$536$	−5.40806	−	1.83031i	−0.233593	−	0.0790574i
$537$		0			0
$538$	4.00048	+	2.93141i	0.172473	+	0.126382i
$539$	0.607559	+	0.607559i	0.0261694	+	0.0261694i
$540$		0			0
$541$	12.3668	−	12.3668i	0.531690	−	0.531690i	−0.389385	−	0.921075i	$-0.627312\pi$
$541$	12.3668	−	12.3668i	0.531690	−	0.531690i	0.921075	+	0.389385i	$0.127312\pi$
$542$	0.734659	+	4.76356i	0.0315563	+	0.204612i
$543$		0			0
$544$	3.52016	+	3.66607i	0.150925	+	0.157182i
$545$			1.14324i			0.0489712i
$546$		0			0
$547$	27.0945	+	27.0945i	1.15848	+	1.15848i	0.984803	+	0.173673i	$0.0555637\pi$
$547$	27.0945	+	27.0945i	1.15848	+	1.15848i	0.173673	+	0.984803i	$0.444436\pi$
$548$	41.2184	−	13.0236i	1.76076	−	0.556339i
$549$		0			0
$550$	0.149189	−	0.203597i	0.00636142	−	0.00868139i
$551$		−	37.6990i		−	1.60603i
$552$		0			0
$553$			1.78432i			0.0758771i
$554$	12.2960	+	9.01009i	0.522408	+	0.382802i
$555$		0			0
$556$	16.5855	−	31.9075i	0.703380	−	1.35318i
$557$	2.13075	+	2.13075i	0.0902829	+	0.0902829i	0.750806	−	0.660523i	$-0.229665\pi$
$557$	2.13075	+	2.13075i	0.0902829	+	0.0902829i	−0.660523	+	0.750806i	$0.729665\pi$
$558$		0			0
$559$		−	49.0378i		−	2.07408i
$560$	0.522849	−	2.98638i	0.0220944	−	0.126197i
$561$		0			0
$562$	−16.5967	+	2.55962i	−0.700088	+	0.107971i
$563$	5.84040	−	5.84040i	0.246144	−	0.246144i	−0.573242	−	0.819386i	$-0.694315\pi$
$563$	5.84040	−	5.84040i	0.246144	−	0.246144i	0.819386	+	0.573242i	$0.194315\pi$
$564$		0			0
$565$	−0.296412	−	0.296412i	−0.0124702	−	0.0124702i
$566$	0.453136	−	0.618393i	0.0190467	−	0.0259930i
$567$		0			0
$568$	0.710707	+	1.43788i	0.0298206	+	0.0603319i
$569$	41.0580			1.72124			0.860620	−	0.509248i	$-0.170076\pi$
$569$	41.0580			1.72124			0.860620	+	0.509248i	$0.170076\pi$
$570$		0			0
$571$	−7.21253	+	7.21253i	−0.301835	+	0.301835i	−0.841731	−	0.539896i	$-0.818463\pi$
$571$	−7.21253	+	7.21253i	−0.301835	+	0.301835i	0.539896	+	0.841731i	$0.318463\pi$
$572$	1.21964	−	0.385363i	0.0509956	−	0.0161128i
$573$		0			0
$574$	3.06624	−	0.472891i	0.127982	−	0.0197381i
$575$	10.0775			0.420263
$576$		0			0
$577$	1.89438			0.0788641			0.0394321	−	0.999222i	$-0.487445\pi$
$577$	1.89438			0.0788641			0.0394321	+	0.999222i	$0.487445\pi$
$578$	22.6324	−	3.49048i	0.941386	−	0.145185i
$579$		0			0
$580$	30.3783	−	9.59849i	1.26139	−	0.398556i
$581$	−2.59421	+	2.59421i	−0.107626	+	0.107626i
$582$		0			0
$583$	−0.593283			−0.0245713
$584$	−15.2071	−	30.7664i	−0.629273	−	1.27312i
$585$		0			0
$586$	4.71872	−	6.43961i	0.194928	−	0.266018i
$587$	0.311972	+	0.311972i	0.0128765	+	0.0128765i	0.713516	−	0.700639i	$-0.247102\pi$
$587$	0.311972	+	0.311972i	0.0128765	+	0.0128765i	−0.700639	+	0.713516i	$0.747102\pi$
$588$		0			0
$589$	16.6481	−	16.6481i	0.685971	−	0.685971i
$590$	−15.4266	+	2.37917i	−0.635104	+	0.0979488i
$591$		0			0
$592$	5.20832	+	0.911861i	0.214060	+	0.0374773i
$593$			2.80521i			0.115196i	0.998340	+	0.0575981i	$0.0183442\pi$
$593$			2.80521i			0.115196i	−0.998340	+	0.0575981i	$0.981656\pi$
$594$		0			0
$595$	0.481533	+	0.481533i	0.0197409	+	0.0197409i
$596$	−4.77573	+	9.18768i	−0.195622	+	0.376342i
$597$		0			0
$598$	41.1927	+	30.1846i	1.68450	+	1.23434i
$599$			18.3317i			0.749015i	0.927224	+	0.374507i	$0.122188\pi$
$599$			18.3317i			0.749015i	−0.927224	+	0.374507i	$0.877812\pi$
$600$		0			0
$601$			24.1264i			0.984138i	0.870556	+	0.492069i	$0.163759\pi$
$601$			24.1264i			0.984138i	−0.870556	+	0.492069i	$0.836241\pi$
$602$	−3.22581	+	4.40225i	−0.131474	+	0.179422i
$603$		0			0
$604$	26.3915	−	8.33878i	1.07385	−	0.339300i
$605$	−14.6944	−	14.6944i	−0.597413	−	0.597413i
$606$		0			0
$607$		−	0.442565i		−	0.0179631i	−0.999960	−	0.00898157i	$-0.997141\pi$
$607$		−	0.442565i		−	0.0179631i	0.999960	−	0.00898157i	$-0.00285896\pi$
$608$	−25.3231	−	0.514183i	−1.02699	−	0.0208529i
$609$		0			0
$610$	4.10319	+	26.6053i	0.166133	+	1.07722i
$611$	23.7597	−	23.7597i	0.961214	−	0.961214i
$612$		0			0
$613$	−1.17275	−	1.17275i	−0.0473668	−	0.0473668i	0.683027	−	0.730393i	$-0.260663\pi$
$613$	−1.17275	−	1.17275i	−0.0473668	−	0.0473668i	−0.730393	+	0.683027i	$0.760663\pi$
$614$	15.2506	+	11.1751i	0.615464	+	0.450990i
$615$		0			0
$616$	−0.134840	−	0.0456354i	−0.00543285	−	0.00183870i
$617$	38.5977			1.55388			0.776942	−	0.629573i	$-0.216770\pi$
$617$	38.5977			1.55388			0.776942	+	0.629573i	$0.216770\pi$
$618$		0			0
$619$	−2.69799	+	2.69799i	−0.108441	+	0.108441i	−0.759246	−	0.650804i	$-0.774432\pi$
$619$	−2.69799	+	2.69799i	−0.108441	+	0.108441i	0.650804	+	0.759246i	$0.274432\pi$
$620$	17.6539	+	9.17647i	0.708999	+	0.368536i
$621$		0			0
$622$	−2.82138	−	18.2940i	−0.113127	−	0.733521i
$623$	−2.42351			−0.0970959
$624$		0			0
$625$	15.8780			0.635121
$626$	−2.71960	−	17.6340i	−0.108697	−	0.704795i
$627$		0			0
$628$	−18.7214	+	36.0166i	−0.747064	+	1.43722i
$629$	−0.839806	+	0.839806i	−0.0334852	+	0.0334852i
$630$		0			0
$631$	9.96430			0.396673			0.198336	−	0.980134i	$-0.436446\pi$
$631$	9.96430			0.396673			0.198336	+	0.980134i	$0.436446\pi$
$632$	5.58189	+	11.2931i	0.222035	+	0.449214i
$633$		0			0
$634$	−6.92099	−	5.07145i	−0.274867	−	0.201413i
$635$	9.48800	+	9.48800i	0.376520	+	0.376520i
$636$		0			0
$637$	24.6204	−	24.6204i	0.975494	−	0.975494i
$638$	−0.228004	−	1.47839i	−0.00902678	−	0.0585300i
$639$		0			0
$640$	−6.03313	−	20.5366i	−0.238481	−	0.811779i
$641$		−	39.6666i		−	1.56674i	−0.621557	−	0.783369i	$-0.713500\pi$
$641$		−	39.6666i		−	1.56674i	0.621557	−	0.783369i	$-0.286500\pi$
$642$		0			0
$643$	5.45283	+	5.45283i	0.215039	+	0.215039i	0.806404	−	0.591365i	$-0.201411\pi$
$643$	5.45283	+	5.45283i	0.215039	+	0.215039i	−0.591365	+	0.806404i	$0.701411\pi$
$644$	−1.71237	−	5.41949i	−0.0674767	−	0.213558i
$645$		0			0
$646$	3.36265	−	4.58899i	0.132302	−	0.180552i
$647$			31.5177i			1.23909i	0.784962	+	0.619545i	$0.212683\pi$
$647$			31.5177i			1.23909i	−0.784962	+	0.619545i	$0.787317\pi$
$648$		0			0
$649$			0.732894i			0.0287686i
$650$	−8.25044	−	6.04563i	−0.323609	−	0.237129i
$651$		0			0
$652$	−40.0508	−	20.8183i	−1.56851	−	0.815308i
$653$	0.413396	+	0.413396i	0.0161774	+	0.0161774i	0.715149	−	0.698972i	$-0.246359\pi$
$653$	0.413396	+	0.413396i	0.0161774	+	0.0161774i	−0.698972	+	0.715149i	$0.746359\pi$
$654$		0			0
$655$		−	7.76037i		−	0.303223i
$656$	17.9271	−	12.5851i	0.699934	−	0.491364i
$657$		0			0
$658$	−3.69593	+	0.570003i	−0.144082	+	0.0222210i
$659$	−20.8956	+	20.8956i	−0.813979	+	0.813979i	−0.985228	−	0.171249i	$-0.945220\pi$
$659$	−20.8956	+	20.8956i	−0.813979	+	0.813979i	0.171249	+	0.985228i	$0.445220\pi$
$660$		0			0
$661$	1.58152	+	1.58152i	0.0615141	+	0.0615141i	0.737195	−	0.675681i	$-0.236150\pi$
$661$	1.58152	+	1.58152i	0.0615141	+	0.0615141i	−0.675681	+	0.737195i	$0.736150\pi$
$662$	5.84868	−	7.98167i	0.227316	−	0.310216i
$663$		0			0
$664$	−8.30343	+	24.5343i	−0.322235	+	0.952117i
$665$	−3.39369			−0.131602
$666$		0			0
$667$	42.2312	−	42.2312i	1.63520	−	1.63520i
$668$	−0.208856	−	0.661011i	−0.00808089	−	0.0255753i
$669$		0			0
$670$	−5.33770	+	0.823205i	−0.206213	+	0.0318032i
$671$	1.26397			0.0487951
$672$		0			0
$673$	−34.7821			−1.34075			−0.670376	−	0.742021i	$-0.733867\pi$
$673$	−34.7821			−1.34075			−0.670376	+	0.742021i	$0.733867\pi$
$674$	−16.4712	+	2.54027i	−0.634448	+	0.0978476i
$675$		0			0
$676$	−7.78285	−	24.6320i	−0.299340	−	0.947385i
$677$	26.1786	−	26.1786i	1.00613	−	1.00613i	0.00614604	−	0.999981i	$-0.498044\pi$
$677$	26.1786	−	26.1786i	1.00613	−	1.00613i	0.999981	−	0.00614604i	$-0.00195636\pi$
$678$		0			0
$679$	6.35689			0.243955
$680$	4.55403	+	1.54127i	0.174639	+	0.0591050i
$681$		0			0
$682$	0.552176	−	0.753551i	0.0211439	−	0.0288550i
$683$	−34.1451	−	34.1451i	−1.30653	−	1.30653i	−0.923905	−	0.382622i	$-0.875021\pi$
$683$	−34.1451	−	34.1451i	−1.30653	−	1.30653i	−0.382622	−	0.923905i	$-0.624979\pi$
$684$		0			0
$685$	28.9140	−	28.9140i	1.10475	−	1.10475i
$686$	−7.74949	+	1.19516i	−0.295877	+	0.0456316i
$687$		0			0
$688$	−6.64479	+	37.9533i	−0.253330	+	1.44696i
$689$			24.0418i			0.915921i
$690$		0			0
$691$	26.0328	+	26.0328i	0.990336	+	0.990336i	0.999954	−	0.00961752i	$-0.00306140\pi$
$691$	26.0328	+	26.0328i	0.990336	+	0.990336i	−0.00961752	+	0.999954i	$0.503061\pi$
$692$	−26.1452	−	13.5902i	−0.993891	−	0.516622i
$693$		0			0
$694$	37.2841	+	27.3204i	1.41528	+	1.03707i
$695$		−	34.0170i		−	1.29034i
$696$		0			0
$697$			4.91987i			0.186353i
$698$	0.350398	−	0.478186i	0.0132628	−	0.0180996i
$699$		0			0
$700$	0.342968	+	1.08546i	0.0129630	+	0.0410266i
$701$	30.8467	+	30.8467i	1.16506	+	1.16506i	0.983352	+	0.181712i	$0.0581639\pi$
$701$	30.8467	+	30.8467i	1.16506	+	1.16506i	0.181712	+	0.983352i	$0.441836\pi$
$702$		0			0
$703$		−	5.91867i		−	0.223227i
$704$	−0.996169	+	0.132990i	−0.0375445	+	0.00501227i
$705$		0			0
$706$	−6.52711	−	42.3220i	−0.245651	−	1.59281i
$707$	−3.90369	+	3.90369i	−0.146814	+	0.146814i
$708$		0			0
$709$	3.04194	+	3.04194i	0.114242	+	0.114242i	0.761917	−	0.647675i	$-0.224258\pi$
$709$	3.04194	+	3.04194i	0.114242	+	0.114242i	−0.647675	+	0.761917i	$0.724258\pi$
$710$	1.22384	+	0.896787i	0.0459299	+	0.0336558i
$711$		0			0
$712$	−15.3385	+	7.58146i	−0.574836	+	0.284127i
$713$	37.2990			1.39686
$714$		0			0
$715$	0.855555	−	0.855555i	0.0319960	−	0.0319960i
$716$	16.9248	−	32.5603i	0.632508	−	1.21684i
$717$		0			0
$718$	7.26772	+	47.1242i	0.271229	+	1.75866i
$719$	5.30074			0.197684			0.0988422	−	0.995103i	$-0.468486\pi$
$719$	5.30074			0.197684			0.0988422	+	0.995103i	$0.468486\pi$
$720$		0			0
$721$	7.24100			0.269669
$722$	0.225817	+	1.46421i	0.00840404	+	0.0544921i
$723$		0			0
$724$	33.0559	+	17.1823i	1.22851	+	0.638577i
$725$	−8.45843	+	8.45843i	−0.314138	+	0.314138i
$726$		0			0
$727$	−8.86455			−0.328768			−0.164384	−	0.986396i	$-0.552564\pi$
$727$	−8.86455			−0.328768			−0.164384	+	0.986396i	$0.552564\pi$
$728$	−1.84930	+	5.46417i	−0.0685397	+	0.202516i
$729$		0			0
$730$	−26.1866	−	19.1886i	−0.969210	−	0.710203i
$731$	−6.11972	−	6.11972i	−0.226346	−	0.226346i
$732$		0			0
$733$	23.1329	−	23.1329i	0.854432	−	0.854432i	−0.136244	−	0.990675i	$-0.543503\pi$
$733$	23.1329	−	23.1329i	0.854432	−	0.854432i	0.990675	+	0.136244i	$0.0435030\pi$
$734$	6.71834	+	43.5620i	0.247978	+	1.60790i
$735$		0			0
$736$	−27.7914	−	28.9434i	−1.02440	−	1.06687i
$737$			0.253585i			0.00934094i
$738$		0			0
$739$	16.5956	+	16.5956i	0.610479	+	0.610479i	0.943071	−	0.332592i	$-0.107923\pi$
$739$	16.5956	+	16.5956i	0.610479	+	0.610479i	−0.332592	+	0.943071i	$0.607923\pi$
$740$	4.76934	−	1.50694i	0.175324	−	0.0553964i
$741$		0			0
$742$	1.58152	−	2.15829i	0.0580595	−	0.0792335i
$743$			9.09962i			0.333833i	0.985971	+	0.166916i	$0.0533810\pi$
$743$			9.09962i			0.333833i	−0.985971	+	0.166916i	$0.946619\pi$
$744$		0			0
$745$			9.79509i			0.358864i
$746$	−15.5185	−	11.3714i	−0.568173	−	0.416337i
$747$		0			0
$748$	0.104114	−	0.200298i	0.00380679	−	0.00732360i
$749$	−5.22684	−	5.22684i	−0.190985	−	0.190985i
$750$		0			0
$751$			20.9026i			0.762746i	0.924421	+	0.381373i	$0.124549\pi$
$751$			20.9026i			0.762746i	−0.924421	+	0.381373i	$0.875451\pi$
$752$	−21.6086	+	15.1695i	−0.787983	+	0.553176i
$753$		0			0
$754$	−59.9094	+	9.23952i	−2.18177	+	0.336483i
$755$	18.5132	−	18.5132i	0.673763	−	0.673763i
$756$		0			0
$757$	−28.3380	−	28.3380i	−1.02996	−	1.02996i	−0.999537	−	0.0304265i	$-0.990313\pi$
$757$	−28.3380	−	28.3380i	−1.02996	−	1.02996i	−0.0304265	−	0.999537i	$-0.509687\pi$
$758$	−14.9077	+	20.3445i	−0.541473	+	0.738946i
$759$		0			0
$760$	−21.4788	+	10.6165i	−0.779119	+	0.385099i
$761$	−34.6170			−1.25487			−0.627433	−	0.778670i	$-0.715894\pi$
$761$	−34.6170			−1.25487			−0.627433	+	0.778670i	$0.715894\pi$
$762$		0			0
$763$	−0.171186	+	0.171186i	−0.00619734	+	0.00619734i
$764$	16.7447	−	5.29073i	0.605801	−	0.191412i
$765$		0			0
$766$	1.66131	−	0.256215i	0.0600255	−	0.00925742i
$767$	29.6994			1.07238
$768$		0			0
$769$	8.08510			0.291556			0.145778	−	0.989317i	$-0.453431\pi$
$769$	8.08510			0.291556			0.145778	+	0.989317i	$0.453431\pi$
$770$	−0.133085	+	0.0205251i	−0.00479607	+	0.000739673i
$771$		0			0
$772$	−8.76250	+	2.76864i	−0.315369	+	0.0996456i
$773$	7.19198	−	7.19198i	0.258678	−	0.258678i	−0.565839	−	0.824516i	$-0.691447\pi$
$773$	7.19198	−	7.19198i	0.258678	−	0.258678i	0.824516	+	0.565839i	$0.191447\pi$
$774$		0			0
$775$	−7.47056			−0.268350
$776$	40.2331	−	19.8862i	1.44428	−	0.713874i
$777$		0			0
$778$	10.2981	−	14.0537i	0.369204	−	0.503851i
$779$	−17.3368	−	17.3368i	−0.621156	−	0.621156i
$780$		0			0
$781$	0.0503738	−	0.0503738i	0.00180252	−	0.00180252i
$782$	8.90759	−	1.37377i	0.318535	−	0.0491260i
$783$		0			0
$784$	−22.3913	+	15.7190i	−0.799690	+	0.561394i
$785$			38.3978i			1.37048i
$786$		0			0
$787$	−22.3422	−	22.3422i	−0.796415	−	0.796415i	0.186113	−	0.982528i	$-0.440411\pi$
$787$	−22.3422	−	22.3422i	−0.796415	−	0.796415i	−0.982528	+	0.186113i	$0.940411\pi$
$788$	20.9306	−	40.2669i	0.745622	−	1.43445i
$789$		0			0
$790$	9.61203	+	7.04336i	0.341981	+	0.250591i
$791$		−	0.0887678i		−	0.00315622i
$792$		0			0
$793$		−	51.2205i		−	1.81889i
$794$	−7.11936	+	9.71575i	−0.252657	+	0.344799i
$795$		0			0
$796$	−0.202861	+	0.0640971i	−0.00719023	+	0.00227186i
$797$	25.2255	+	25.2255i	0.893533	+	0.893533i	0.994854	−	0.101321i	$-0.0323069\pi$
$797$	25.2255	+	25.2255i	0.893533	+	0.893533i	−0.101321	+	0.994854i	$0.532307\pi$
$798$		0			0
$799$		−	5.93022i		−	0.209796i
$800$	5.56630	+	5.79704i	0.196799	+	0.204956i
$801$		0			0
$802$	4.15368	+	26.9326i	0.146672	+	0.951025i
$803$	−1.07785	+	1.07785i	−0.0380366	+	0.0380366i
$804$		0			0
$805$	−3.80167	−	3.80167i	−0.133991	−	0.133991i
$806$	−30.5365	−	22.3760i	−1.07560	−	0.788163i
$807$		0			0
$808$	−12.4948	+	36.9186i	−0.439564	+	1.29879i
$809$	36.1976			1.27264			0.636320	−	0.771425i	$-0.280456\pi$
$809$	36.1976			1.27264			0.636320	+	0.771425i	$0.280456\pi$
$810$		0			0
$811$	3.61005	−	3.61005i	0.126766	−	0.126766i	−0.640877	−	0.767643i	$-0.721429\pi$
$811$	3.61005	−	3.61005i	0.126766	−	0.126766i	0.767643	+	0.640877i	$0.221429\pi$
$812$	5.98601	+	3.11151i	0.210068	+	0.109193i
$813$		0			0
$814$	−0.0357962	−	0.232104i	−0.00125466	−	0.00813525i
$815$	−42.6986			−1.49567
$816$		0			0
$817$	43.1298			1.50892
$818$	6.17418	+	40.0337i	0.215875	+	1.39974i
$819$		0			0
$820$	9.55612	−	18.3843i	0.333714	−	0.642008i
$821$	−26.2109	+	26.2109i	−0.914767	+	0.914767i	−0.996643	−	0.0818758i	$-0.973909\pi$
$821$	−26.2109	+	26.2109i	−0.914767	+	0.914767i	0.0818758	+	0.996643i	$0.473909\pi$
$822$		0			0
$823$	−41.6489			−1.45179			−0.725895	−	0.687806i	$-0.758574\pi$
$823$	−41.6489			−1.45179			−0.725895	+	0.687806i	$0.758574\pi$
$824$	45.8287	−	22.6520i	1.59652	−	0.789120i
$825$		0			0
$826$	−2.66618	−	1.95369i	−0.0927684	−	0.0679774i
$827$	−15.3260	−	15.3260i	−0.532937	−	0.532937i	0.388509	−	0.921445i	$-0.372990\pi$
$827$	−15.3260	−	15.3260i	−0.532937	−	0.532937i	−0.921445	+	0.388509i	$0.872990\pi$
$828$		0			0
$829$	−4.87849	+	4.87849i	−0.169437	+	0.169437i	−0.786732	−	0.617295i	$-0.788229\pi$
$829$	−4.87849	+	4.87849i	−0.169437	+	0.169437i	0.617295	+	0.786732i	$0.288229\pi$
$830$	3.73457	+	24.2151i	0.129629	+	0.840519i
$831$		0			0
$832$	5.38923	+	40.3682i	0.186838	+	1.39952i
$833$		−	6.14504i		−	0.212913i
$834$		0			0
$835$	−0.463688	−	0.463688i	−0.0160466	−	0.0160466i
$836$	0.338934	+	1.07270i	0.0117223	+	0.0371000i
$837$		0			0
$838$	−27.2158	+	37.1412i	−0.940153	+	1.28302i
$839$		−	29.0936i		−	1.00442i	−0.864745	−	0.502212i	$-0.832520\pi$
$839$		−	29.0936i		−	1.00442i	0.864745	−	0.502212i	$-0.167480\pi$
$840$		0			0
$841$			41.8922i			1.44456i
$842$	10.3353	+	7.57338i	0.356179	+	0.260996i
$843$		0			0
$844$	2.99904	+	1.55889i	0.103231	+	0.0536593i
$845$	−17.2789	−	17.2789i	−0.594413	−	0.594413i
$846$		0			0
$847$		−	4.40060i		−	0.151206i
$848$	3.25775	−	18.6074i	0.111872	−	0.638981i
$849$		0			0
$850$	−1.78409	+	0.275151i	−0.0611938	+	0.00943759i
$851$	6.63021	−	6.63021i	0.227281	−	0.227281i
$852$		0			0
$853$	−20.0191	−	20.0191i	−0.685440	−	0.685440i	0.275781	−	0.961221i	$-0.411064\pi$
$853$	−20.0191	−	20.0191i	−0.685440	−	0.685440i	−0.961221	+	0.275781i	$0.911064\pi$
$854$	−3.36939	+	4.59819i	−0.115298	+	0.157347i
$855$		0			0
$856$	−49.4320	−	16.7298i	−1.68955	−	0.571814i
$857$	−21.8661			−0.746930			−0.373465	−	0.927644i	$-0.621830\pi$
$857$	−21.8661			−0.746930			−0.373465	+	0.927644i	$0.621830\pi$
$858$		0			0
$859$	−6.37648	+	6.37648i	−0.217563	+	0.217563i	−0.807471	−	0.589908i	$-0.799164\pi$
$859$	−6.37648	+	6.37648i	−0.217563	+	0.217563i	0.589908	+	0.807471i	$0.299164\pi$
$860$	10.9812	+	34.7545i	0.374456	+	1.18512i
$861$		0			0
$862$	31.0805	−	4.79339i	1.05861	−	0.163263i
$863$	−49.2993			−1.67817			−0.839084	−	0.544002i	$-0.816908\pi$
$863$	−49.2993			−1.67817			−0.839084	+	0.544002i	$0.816908\pi$
$864$		0			0
$865$	−27.8737			−0.947734
$866$	−31.4964	+	4.85752i	−1.07029	+	0.165065i
$867$		0			0
$868$	1.26939	+	4.01751i	0.0430859	+	0.136363i
$869$	0.395635	−	0.395635i	0.0134210	−	0.0134210i
$870$		0			0
$871$	10.2761			0.348194
$872$	−0.547924	+	1.61896i	−0.0185550	+	0.0548250i
$873$		0			0
$874$	−26.5479	+	36.2298i	−0.897997	+	1.22549i
$875$	3.44119	+	3.44119i	0.116334	+	0.116334i
$876$		0			0
$877$	14.1317	−	14.1317i	0.477194	−	0.477194i	−0.427039	−	0.904233i	$-0.640443\pi$
$877$	14.1317	−	14.1317i	0.477194	−	0.477194i	0.904233	+	0.427039i	$0.140443\pi$
$878$	−34.3510	+	5.29778i	−1.15929	+	0.178791i
$879$		0			0
$880$	−0.778096	+	0.546235i	−0.0262296	+	0.0184136i
$881$			41.7497i			1.40658i	0.710901	+	0.703292i	$0.248287\pi$
$881$			41.7497i			1.40658i	−0.710901	+	0.703292i	$0.751713\pi$
$882$		0			0
$883$	34.0583	+	34.0583i	1.14615	+	1.14615i	0.987303	+	0.158849i	$0.0507783\pi$
$883$	34.0583	+	34.0583i	1.14615	+	1.14615i	0.158849	+	0.987303i	$0.449222\pi$
$884$	−8.11674	−	4.21906i	−0.272995	−	0.141902i
$885$		0			0
$886$	−19.8688	−	14.5591i	−0.667505	−	0.489124i
$887$		−	29.9835i		−	1.00675i	−0.864069	−	0.503373i	$-0.832092\pi$
$887$		−	29.9835i		−	1.00675i	0.864069	−	0.503373i	$-0.167908\pi$
$888$		0			0
$889$			2.84141i			0.0952978i
$890$	−9.56647	+	13.0553i	−0.320669	+	0.437615i
$891$		0			0
$892$	−8.78750	−	27.8116i	−0.294227	−	0.931202i
$893$	20.8971	+	20.8971i	0.699295	+	0.699295i
$894$		0			0
$895$		−	34.7129i		−	1.16033i
$896$	2.17170	−	3.97847i	0.0725514	−	0.132911i
$897$		0			0
$898$	−2.23183	−	14.4713i	−0.0744771	−	0.482913i
$899$	−31.3063	+	31.3063i	−1.04412	+	1.04412i
$900$		0			0
$901$	3.00032	+	3.00032i	0.0999552	+	0.0999552i
$902$	−0.784727	−	0.575020i	−0.0261286	−	0.0191461i
$903$		0			0
$904$	−0.277692	−	0.561816i	−0.00923589	−	0.0186857i
$905$	35.2412			1.17146
$906$		0			0
$907$	23.3538	−	23.3538i	0.775449	−	0.775449i	−0.203604	−	0.979053i	$-0.565266\pi$
$907$	23.3538	−	23.3538i	0.775449	−	0.775449i	0.979053	+	0.203604i	$0.0652656\pi$
$908$	−10.6907	+	20.5670i	−0.354782	+	0.682539i
$909$		0			0
$910$	0.831746	+	5.39308i	0.0275721	+	0.178779i
$911$	−48.5847			−1.60968			−0.804842	−	0.593490i	$-0.797750\pi$
$911$	−48.5847			−1.60968			−0.804842	+	0.593490i	$0.797750\pi$
$912$		0			0
$913$	1.15042			0.0380734
$914$	2.81809	+	18.2726i	0.0932141	+	0.604404i
$915$		0			0
$916$	−24.4089	−	12.6877i	−0.806492	−	0.419213i
$917$	1.16201	−	1.16201i	0.0383731	−	0.0383731i
$918$		0			0
$919$	43.2259			1.42589			0.712945	−	0.701220i	$-0.247361\pi$
$919$	43.2259			1.42589			0.712945	+	0.701220i	$0.247361\pi$
$920$	−35.9538	−	12.1682i	−1.18536	−	0.401175i
$921$		0			0
$922$	−18.6506	−	13.6665i	−0.614225	−	0.450082i
$923$	−2.04132	−	2.04132i	−0.0671908	−	0.0671908i
$924$		0			0
$925$	−1.32796	+	1.32796i	−0.0436629	+	0.0436629i
$926$	−4.15353	−	26.9317i	−0.136494	−	0.885030i
$927$		0			0
$928$	47.6195	+	0.966910i	1.56319	+	0.0317404i
$929$			7.28105i			0.238884i	0.992841	+	0.119442i	$0.0381105\pi$
$929$			7.28105i			0.238884i	−0.992841	+	0.119442i	$0.961890\pi$
$930$		0			0
$931$	21.6541	+	21.6541i	0.709685	+	0.709685i
$932$	−21.8265	+	6.89640i	−0.714950	+	0.225899i
$933$		0			0
$934$	−11.0964	+	15.1431i	−0.363084	+	0.495499i
$935$		−	0.213539i		−	0.00698349i
$936$		0			0
$937$			51.3576i			1.67778i	0.544301	+	0.838890i	$0.316795\pi$
$937$			51.3576i			1.67778i	−0.544301	+	0.838890i	$0.683205\pi$
$938$	−0.922515	−	0.675986i	−0.0301212	−	0.0220717i
$939$		0			0
$940$	−11.5186	+	22.1597i	−0.375694	+	0.722771i
$941$	−9.58389	−	9.58389i	−0.312426	−	0.312426i	0.533423	−	0.845849i	$-0.320905\pi$
$941$	−9.58389	−	9.58389i	−0.312426	−	0.312426i	−0.845849	+	0.533423i	$0.820905\pi$
$942$		0			0
$943$		−	38.8421i		−	1.26487i
$944$	−22.9861	−	4.02436i	−0.748135	−	0.130982i
$945$		0			0
$946$	1.69136	−	0.260850i	0.0549908	−	0.00848095i
$947$	−26.5428	+	26.5428i	−0.862525	+	0.862525i	−0.991631	−	0.129106i	$-0.958789\pi$
$947$	−26.5428	+	26.5428i	−0.862525	+	0.862525i	0.129106	+	0.991631i	$0.458789\pi$
$948$		0			0
$949$	43.6783	+	43.6783i	1.41786	+	1.41786i
$950$	5.31725	−	7.25642i	0.172514	−	0.235429i
$951$		0			0
$952$	0.451121	+	0.912691i	0.0146209	+	0.0295805i
$953$	−44.9098			−1.45477			−0.727386	−	0.686228i	$-0.759265\pi$
$953$	−44.9098			−1.45477			−0.727386	+	0.686228i	$0.759265\pi$
$954$		0			0
$955$	11.7461	−	11.7461i	0.380095	−	0.380095i
$956$	25.3157	−	7.99886i	0.818767	−	0.258702i
$957$		0			0
$958$	−13.7638	+	2.12271i	−0.444687	+	0.0685817i
$959$	8.65899			0.279613
$960$		0			0
$961$	3.35000			0.108065
$962$	−9.40566	+	1.45059i	−0.303251	+	0.0467688i
$963$		0			0
$964$	3.51753	−	1.11142i	0.113292	−	0.0357963i
$965$	−6.14674	+	6.14674i	−0.197871	+	0.197871i
$966$		0			0
$967$	−53.3311			−1.71501			−0.857506	−	0.514475i	$-0.827987\pi$
$967$	−53.3311			−1.71501			−0.857506	+	0.514475i	$0.827987\pi$
$968$	−13.7664	−	27.8516i	−0.442468	−	0.895184i
$969$		0			0
$970$	25.0929	−	34.2442i	0.805685	−	1.09951i
$971$	6.32571	+	6.32571i	0.203002	+	0.203002i	0.801285	−	0.598283i	$-0.204150\pi$
$971$	6.32571	+	6.32571i	0.203002	+	0.203002i	−0.598283	+	0.801285i	$0.704150\pi$
$972$		0			0
$973$	5.09360	−	5.09360i	0.163293	−	0.163293i
$974$	−32.3376	+	4.98726i	−1.03616	+	0.159802i
$975$		0			0
$976$	−6.94055	+	39.6426i	−0.222162	+	1.26893i
$977$		−	28.9918i		−	0.927528i	−0.885959	−	0.463764i	$-0.846499\pi$
$977$		−	28.9918i		−	0.927528i	0.885959	−	0.463764i	$-0.153501\pi$
$978$		0			0
$979$	0.537362	+	0.537362i	0.0171742	+	0.0171742i
$980$	−11.9358	+	22.9625i	−0.381276	+	0.733509i
$981$		0			0
$982$	0.655436	+	0.480280i	0.0209158	+	0.0153264i
$983$			35.0011i			1.11636i	0.829719	+	0.558182i	$0.188501\pi$
$983$			35.0011i			1.11636i	−0.829719	+	0.558182i	$0.811499\pi$
$984$		0			0
$985$		−	42.9290i		−	1.36783i
$986$	−6.32339	+	8.62950i	−0.201378	+	0.274819i
$987$		0			0
$988$	43.4693	−	13.7348i	1.38294	−	0.436962i
$989$	48.3148	+	48.3148i	1.53632	+	1.53632i
$990$		0			0
$991$		−	7.17980i		−	0.228074i	−0.993477	−	0.114037i	$-0.963622\pi$
$991$		−	7.17980i		−	0.228074i	0.993477	−	0.114037i	$-0.0363782\pi$
$992$	20.6020	+	21.4560i	0.654114	+	0.681228i
$993$		0			0
$994$	0.0489720	+	0.317536i	0.00155330	+	0.0100716i
$995$	−0.142304	+	0.142304i	−0.00451133	+	0.00451133i
$996$		0			0
$997$	−15.4953	−	15.4953i	−0.490742	−	0.490742i	0.417798	−	0.908540i	$-0.362802\pi$
$997$	−15.4953	−	15.4953i	−0.490742	−	0.490742i	−0.908540	+	0.417798i	$0.862802\pi$
$998$	33.0690	+	24.2318i	1.04678	+	0.767043i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.a.107.16	yes	32
3.2	odd	2	inner	432.2.l.a.107.1	✓	32
4.3	odd	2		1728.2.l.a.1295.12		32
12.11	even	2		1728.2.l.a.1295.5		32
16.3	odd	4	inner	432.2.l.a.323.1	yes	32
16.13	even	4		1728.2.l.a.431.5		32
48.29	odd	4		1728.2.l.a.431.12		32
48.35	even	4	inner	432.2.l.a.323.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.a.107.1	✓	32	3.2	odd	2	inner
432.2.l.a.107.16	yes	32	1.1	even	1	trivial
432.2.l.a.323.1	yes	32	16.3	odd	4	inner
432.2.l.a.323.16	yes	32	48.35	even	4	inner
1728.2.l.a.431.5		32	16.13	even	4
1728.2.l.a.431.12		32	48.29	odd	4
1728.2.l.a.1295.5		32	12.11	even	2
1728.2.l.a.1295.12		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39769 - 0.215558i) q^{2} +(1.90707 - 0.602567i) q^{4} +(1.33778 - 1.33778i) q^{5} +0.400629 q^{7} +(2.53560 - 1.25329i) q^{8} +O(q^{10})\)	\(q+(1.39769 - 0.215558i) q^{2} +(1.90707 - 0.602567i) q^{4} +(1.33778 - 1.33778i) q^{5} +0.400629 q^{7} +(2.53560 - 1.25329i) q^{8} +(1.58143 - 2.15816i) q^{10} +(-0.0888310 - 0.0888310i) q^{11} +(-3.59973 + 3.59973i) q^{13} +(0.559955 - 0.0863589i) q^{14} +(3.27383 - 2.29827i) q^{16} +0.898464i q^{17} +(-3.16604 - 3.16604i) q^{19} +(1.74513 - 3.35733i) q^{20} +(-0.143306 - 0.105010i) q^{22} -7.09331i q^{23} +1.42071i q^{25} +(-4.25536 + 5.80726i) q^{26} +(0.764027 - 0.241406i) q^{28} +(5.95366 + 5.95366i) q^{29} +5.25833i q^{31} +(4.08038 - 3.91797i) q^{32} +(0.193671 + 1.25577i) q^{34} +(0.535952 - 0.535952i) q^{35} +(0.934713 + 0.934713i) q^{37} +(-5.10760 - 3.74267i) q^{38} +(1.71545 - 5.06868i) q^{40} +5.47587 q^{41} +(-6.81132 + 6.81132i) q^{43} +(-0.222933 - 0.115880i) q^{44} +(-1.52902 - 9.91425i) q^{46} -6.60040 q^{47} -6.83950 q^{49} +(0.306246 + 1.98571i) q^{50} +(-4.69586 + 9.03402i) q^{52} +(3.33939 - 3.33939i) q^{53} -0.237672 q^{55} +(1.01584 - 0.502103i) q^{56} +(9.60473 + 7.03801i) q^{58} +(-4.12522 - 4.12522i) q^{59} +(-7.11449 + 7.11449i) q^{61} +(1.13348 + 7.34951i) q^{62} +(4.85855 - 6.35567i) q^{64} +9.63127i q^{65} +(-1.42735 - 1.42735i) q^{67} +(0.541384 + 1.71343i) q^{68} +(0.633565 - 0.864623i) q^{70} +0.567075i q^{71} -12.1338i q^{73} +(1.50792 + 1.10495i) q^{74} +(-7.94560 - 4.13010i) q^{76} +(-0.0355883 - 0.0355883i) q^{77} +4.45380i q^{79} +(1.30507 - 7.45422i) q^{80} +(7.65357 - 1.18037i) q^{82} +(-6.47534 + 6.47534i) q^{83} +(1.20194 + 1.20194i) q^{85} +(-8.05187 + 10.9883i) q^{86} +(-0.336570 - 0.113909i) q^{88} -6.04927 q^{89} +(-1.44216 + 1.44216i) q^{91} +(-4.27420 - 13.5274i) q^{92} +(-9.22531 + 1.42277i) q^{94} -8.47090 q^{95} +15.8673 q^{97} +(-9.55949 + 1.47431i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) \) 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Introduction

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