LMFDB - Embedded newform 513.2.k.a.8.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(8,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.10
Character	$\chi$	$=$	513.8
Dual form			513.2.k.a.449.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.338203 + 0.585784i) q^{2} +(0.771238 - 1.33582i) q^{4} -0.138609i q^{5} +(0.877021 - 1.51904i) q^{7} +2.39615 q^{8} +(0.0811952 - 0.0468781i) q^{10} +(4.04328 + 2.33439i) q^{11} +(-5.67727 - 3.27778i) q^{13} +1.18644 q^{14} +(-0.732093 - 1.26802i) q^{16} +(-4.06437 - 2.34656i) q^{17} +(4.35516 - 0.180615i) q^{19} +(-0.185158 - 0.106901i) q^{20} +3.15798i q^{22} +(0.942590 + 0.544205i) q^{23} +4.98079 q^{25} -4.43421i q^{26} +(-1.35278 - 2.34309i) q^{28} +0.954272 q^{29} +(5.38094 - 3.10669i) q^{31} +(2.89134 - 5.00795i) q^{32} -3.17445i q^{34} +(-0.210554 - 0.121563i) q^{35} +4.68926i q^{37} +(1.57873 + 2.49010i) q^{38} -0.332129i q^{40} -7.77509 q^{41} +(0.541863 + 0.938533i) q^{43} +(6.23666 - 3.60074i) q^{44} +0.736205i q^{46} +12.5265i q^{47} +(1.96167 + 3.39771i) q^{49} +(1.68451 + 2.91767i) q^{50} +(-8.75706 + 5.05589i) q^{52} +(1.27386 + 2.20639i) q^{53} +(0.323568 - 0.560437i) q^{55} +(2.10147 - 3.63986i) q^{56} +(0.322737 + 0.558997i) q^{58} -11.0310 q^{59} +1.11360 q^{61} +(3.63969 + 2.10138i) q^{62} +0.983063 q^{64} +(-0.454331 + 0.786924i) q^{65} +(-3.83497 - 2.21412i) q^{67} +(-6.26919 + 3.61952i) q^{68} -0.164452i q^{70} +(3.99931 - 6.92701i) q^{71} +(-0.561346 + 0.972280i) q^{73} +(-2.74689 + 1.58592i) q^{74} +(3.11759 - 5.95702i) q^{76} +(7.09208 - 4.09461i) q^{77} +(-2.94960 + 1.70295i) q^{79} +(-0.175760 + 0.101475i) q^{80} +(-2.62956 - 4.55452i) q^{82} +(-3.07334 - 1.77440i) q^{83} +(-0.325256 + 0.563360i) q^{85} +(-0.366519 + 0.634829i) q^{86} +(9.68830 + 5.59354i) q^{88} +(7.79231 + 13.4967i) q^{89} +(-9.95817 + 5.74935i) q^{91} +(1.45392 - 0.839423i) q^{92} +(-7.33782 + 4.23649i) q^{94} +(-0.0250349 - 0.603666i) q^{95} +(-12.6091 + 7.27986i) q^{97} +(-1.32688 + 2.29823i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 15 q^{4} - q^{7} - 12 q^{8} - 6 q^{10} + 9 q^{11} - 6 q^{13} + 6 q^{14} - 9 q^{16} + 27 q^{17} + q^{19} - 9 q^{20} - 9 q^{23} - 22 q^{25} + 2 q^{28} + 24 q^{29} + 12 q^{31} + 15 q^{32}+ \cdots + 84 q^{98}+O(q^{100}) $ 36 * q + 3 * q^2 - 15 * q^4 - q^7 - 12 * q^8 - 6 * q^10 + 9 * q^11 - 6 * q^13 + 6 * q^14 - 9 * q^16 + 27 * q^17 + q^19 - 9 * q^20 - 9 * q^23 - 22 * q^25 + 2 * q^28 + 24 * q^29 + 12 * q^31 + 15 * q^32 - 15 * q^35 + 18 * q^38 - 36 * q^41 + 3 * q^43 - 66 * q^44 - 9 * q^49 - 3 * q^50 + 15 * q^52 + 12 * q^53 - 7 * q^55 - 6 * q^56 - 6 * q^58 + 18 * q^59 - 16 * q^61 + 12 * q^62 + 12 * q^64 + 18 * q^65 + 27 * q^67 - 60 * q^68 - 9 * q^71 - 18 * q^73 - 90 * q^74 - 23 * q^76 + 6 * q^77 - 6 * q^79 + 12 * q^80 - 9 * q^82 + 9 * q^83 + 11 * q^85 - 51 * q^86 + 3 * q^88 + 18 * q^89 + 27 * q^91 + 93 * q^92 + 12 * q^94 + 24 * q^97 + 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.338203	+	0.585784i	0.239145	+	0.414212i	0.960469	−	0.278386i	$-0.0897994\pi$
$2$	0.338203	+	0.585784i	0.239145	+	0.414212i	−0.721324	+	0.692598i	$0.756466\pi$
$3$		0			0
$3$		0			0
$4$	0.771238	−	1.33582i	0.385619	−	0.667912i
$5$		−	0.138609i		−	0.0619880i	−0.999520	−	0.0309940i	$-0.990133\pi$
$5$		−	0.138609i		−	0.0619880i	0.999520	−	0.0309940i	$-0.00986728\pi$
$6$		0			0
$7$	0.877021	−	1.51904i	0.331483	−	0.574145i	−0.651320	−	0.758803i	$-0.725784\pi$
$7$	0.877021	−	1.51904i	0.331483	−	0.574145i	0.982803	+	0.184658i	$0.0591178\pi$
$8$	2.39615			0.847167
$9$		0			0
$10$	0.0811952	−	0.0468781i	0.0256762	−	0.0148241i
$11$	4.04328	+	2.33439i	1.21909	+	0.703845i	0.964724	−	0.263262i	$-0.0847985\pi$
$11$	4.04328	+	2.33439i	1.21909	+	0.703845i	0.254370	+	0.967107i	$0.418132\pi$
$12$		0			0
$13$	−5.67727	−	3.27778i	−1.57459	−	0.909091i	−0.995595	−	0.0937619i	$-0.970111\pi$
$13$	−5.67727	−	3.27778i	−1.57459	−	0.909091i	−0.578998	−	0.815329i	$-0.696556\pi$
$14$	1.18644			0.317090
$15$		0			0
$16$	−0.732093	−	1.26802i	−0.183023	−	0.317005i
$17$	−4.06437	−	2.34656i	−0.985754	−	0.569125i	−0.0817513	−	0.996653i	$-0.526051\pi$
$17$	−4.06437	−	2.34656i	−0.985754	−	0.569125i	−0.904002	+	0.427528i	$0.859385\pi$
$18$		0			0
$19$	4.35516	−	0.180615i	0.999141	−	0.0414359i
$19$	4.35516	−	0.180615i	0.999141	−	0.0414359i
$20$	−0.185158	−	0.106901i	−0.0414025	−	0.0239038i
$21$		0			0
$22$			3.15798i			0.673284i
$23$	0.942590	+	0.544205i	0.196544	+	0.113474i	0.595042	−	0.803694i	$-0.297135\pi$
$23$	0.942590	+	0.544205i	0.196544	+	0.113474i	−0.398499	+	0.917169i	$0.630469\pi$
$24$		0			0
$25$	4.98079			0.996157
$26$		−	4.43421i		−	0.869620i
$27$		0			0
$28$	−1.35278	−	2.34309i	−0.255652	−	0.442802i
$29$	0.954272			0.177204			0.0886019	−	0.996067i	$-0.471760\pi$
$29$	0.954272			0.177204			0.0886019	+	0.996067i	$0.471760\pi$
$30$		0			0
$31$	5.38094	−	3.10669i	0.966445	−	0.557977i	0.0682946	−	0.997665i	$-0.478244\pi$
$31$	5.38094	−	3.10669i	0.966445	−	0.557977i	0.898151	+	0.439688i	$0.144911\pi$
$32$	2.89134	−	5.00795i	0.511122	−	0.885288i
$33$		0			0
$34$		−	3.17445i		−	0.544414i
$35$	−0.210554	−	0.121563i	−0.0355901	−	0.0205480i
$36$		0			0
$37$			4.68926i			0.770909i	0.922727	+	0.385455i	$0.125955\pi$
$37$			4.68926i			0.770909i	−0.922727	+	0.385455i	$0.874045\pi$
$38$	1.57873	+	2.49010i	0.256103	+	0.403947i
$39$		0			0
$40$		−	0.332129i		−	0.0525142i
$41$	−7.77509			−1.21427			−0.607133	−	0.794601i	$-0.707680\pi$
$41$	−7.77509			−1.21427			−0.607133	+	0.794601i	$0.707680\pi$
$42$		0			0
$43$	0.541863	+	0.938533i	0.0826333	+	0.143125i	0.904380	−	0.426728i	$-0.140334\pi$
$43$	0.541863	+	0.938533i	0.0826333	+	0.143125i	−0.821747	+	0.569853i	$0.807000\pi$
$44$	6.23666	−	3.60074i	0.940212	−	0.542832i
$45$		0			0
$46$			0.736205i			0.108548i
$47$			12.5265i			1.82718i	0.406641	+	0.913588i	$0.366700\pi$
$47$			12.5265i			1.82718i	−0.406641	+	0.913588i	$0.633300\pi$
$48$		0			0
$49$	1.96167	+	3.39771i	0.280238	+	0.485387i
$50$	1.68451	+	2.91767i	0.238226	+	0.412620i
$51$		0			0
$52$	−8.75706	+	5.05589i	−1.21439	+	0.701126i
$53$	1.27386	+	2.20639i	0.174978	+	0.303071i	0.940154	−	0.340751i	$-0.110681\pi$
$53$	1.27386	+	2.20639i	0.174978	+	0.303071i	−0.765176	+	0.643822i	$0.777348\pi$
$54$		0			0
$55$	0.323568	−	0.560437i	0.0436299	−	0.0755693i
$56$	2.10147	−	3.63986i	0.280821	−	0.486396i
$57$		0			0
$58$	0.322737	+	0.558997i	0.0423775	+	0.0733999i
$59$	−11.0310			−1.43611			−0.718054	−	0.695987i	$-0.754967\pi$
$59$	−11.0310			−1.43611			−0.718054	+	0.695987i	$0.754967\pi$
$60$		0			0
$61$	1.11360			0.142582			0.0712908	−	0.997456i	$-0.477288\pi$
$61$	1.11360			0.142582			0.0712908	+	0.997456i	$0.477288\pi$
$62$	3.63969	+	2.10138i	0.462242	+	0.266875i
$63$		0			0
$64$	0.983063			0.122883
$65$	−0.454331	+	0.786924i	−0.0563528	+	0.0976059i
$66$		0			0
$67$	−3.83497	−	2.21412i	−0.468517	−	0.270498i	0.247102	−	0.968989i	$-0.420522\pi$
$67$	−3.83497	−	2.21412i	−0.468517	−	0.270498i	−0.715619	+	0.698491i	$0.753855\pi$
$68$	−6.26919	+	3.61952i	−0.760251	+	0.438931i
$69$		0			0
$70$		−	0.164452i		−	0.0196558i
$71$	3.99931	−	6.92701i	0.474631	−	0.822085i	−0.524947	−	0.851135i	$-0.675915\pi$
$71$	3.99931	−	6.92701i	0.474631	−	0.822085i	0.999578	+	0.0290503i	$0.00924829\pi$
$72$		0			0
$73$	−0.561346	+	0.972280i	−0.0657006	+	0.113797i	−0.897005	−	0.442021i	$-0.854262\pi$
$73$	−0.561346	+	0.972280i	−0.0657006	+	0.113797i	0.831304	+	0.555818i	$0.187595\pi$
$74$	−2.74689	+	1.58592i	−0.319320	+	0.184359i
$75$		0			0
$76$	3.11759	−	5.95702i	0.357612	−	0.683317i
$77$	7.09208	−	4.09461i	0.808217	−	0.466625i
$78$		0			0
$79$	−2.94960	+	1.70295i	−0.331856	+	0.191597i	−0.656665	−	0.754182i	$-0.728033\pi$
$79$	−2.94960	+	1.70295i	−0.331856	+	0.191597i	0.324809	+	0.945780i	$0.394700\pi$
$80$	−0.175760	+	0.101475i	−0.0196505	+	0.0113452i
$81$		0			0
$82$	−2.62956	−	4.55452i	−0.290386	−	0.502963i
$83$	−3.07334	−	1.77440i	−0.337343	−	0.194765i	0.321753	−	0.946824i	$-0.395728\pi$
$83$	−3.07334	−	1.77440i	−0.337343	−	0.194765i	−0.659097	+	0.752058i	$0.729061\pi$
$84$		0			0
$85$	−0.325256	+	0.563360i	−0.0352789	+	0.0611049i
$86$	−0.366519	+	0.634829i	−0.0395227	+	0.0684553i
$87$		0			0
$88$	9.68830	+	5.59354i	1.03278	+	0.596273i
$89$	7.79231	+	13.4967i	0.825983	+	1.43065i	0.901165	+	0.433476i	$0.142713\pi$
$89$	7.79231	+	13.4967i	0.825983	+	1.43065i	−0.0751819	+	0.997170i	$0.523954\pi$
$90$		0			0
$91$	−9.95817	+	5.74935i	−1.04390	+	0.602696i
$92$	1.45392	−	0.839423i	0.151582	−	0.0875159i
$93$		0			0
$94$	−7.33782	+	4.23649i	−0.756838	+	0.436961i
$95$	−0.0250349	−	0.603666i	−0.00256853	−	0.0619348i
$96$		0			0
$97$	−12.6091	+	7.27986i	−1.28026	+	0.739158i	−0.976896	−	0.213717i	$-0.931443\pi$
$97$	−12.6091	+	7.27986i	−1.28026	+	0.739158i	−0.303363	+	0.952875i	$0.598110\pi$
$98$	−1.32688	+	2.29823i	−0.134035	+	0.232156i
$99$		0			0
$100$	3.84137	−	6.65345i	0.384137	−	0.665345i
$101$		−	7.52710i		−	0.748975i	−0.927232	−	0.374487i	$-0.877819\pi$
$101$		−	7.52710i		−	0.748975i	0.927232	−	0.374487i	$-0.122181\pi$
$102$		0			0
$103$	0.293683	−	0.169558i	0.0289375	−	0.0167071i	−0.485461	−	0.874258i	$-0.661348\pi$
$103$	0.293683	−	0.169558i	0.0289375	−	0.0167071i	0.514399	+	0.857551i	$0.328015\pi$
$104$	−13.6036	−	7.85404i	−1.33394	−	0.770152i
$105$		0			0
$106$	−0.861646	+	1.49241i	−0.0836904	+	0.144956i
$107$	−11.8620			−1.14674			−0.573369	−	0.819297i	$-0.694364\pi$
$107$	−11.8620			−1.14674			−0.573369	+	0.819297i	$0.694364\pi$
$108$		0			0
$109$	8.94952	+	5.16701i	0.857209	+	0.494910i	0.863077	−	0.505073i	$-0.168534\pi$
$109$	8.94952	+	5.16701i	0.857209	+	0.494910i	−0.00586793	+	0.999983i	$0.501868\pi$
$110$	0.437726			0.0417356
$111$		0			0
$112$	−2.56824			−0.242676
$113$	1.09234	+	1.89199i	0.102759	+	0.177983i	0.912820	−	0.408361i	$-0.133900\pi$
$113$	1.09234	+	1.89199i	0.102759	+	0.177983i	−0.810062	+	0.586345i	$0.800566\pi$
$114$		0			0
$115$	0.0754319	−	0.130652i	0.00703406	−	0.0121834i
$116$	0.735971	−	1.27474i	0.0683332	−	0.118357i
$117$		0			0
$118$	−3.73070	−	6.46176i	−0.343439	−	0.594853i
$119$	−7.12907	+	4.11597i	−0.653521	+	0.377310i
$120$		0			0
$121$	5.39874	+	9.35088i	0.490794	+	0.850080i
$122$	0.376622	+	0.652328i	0.0340977	+	0.0590590i
$123$		0			0
$124$		−	9.58398i		−	0.860667i
$125$		−	1.38343i		−	0.123738i
$126$		0			0
$127$	−4.44199	+	2.56458i	−0.394163	+	0.227570i	−0.683962	−	0.729517i	$-0.739745\pi$
$127$	−4.44199	+	2.56458i	−0.394163	+	0.227570i	0.289799	+	0.957087i	$0.406411\pi$
$128$	−5.45021	−	9.44003i	−0.481735	−	0.834389i
$129$		0			0
$130$	−0.614623			−0.0539060
$131$			15.7328i			1.37458i	0.726383	+	0.687290i	$0.241200\pi$
$131$			15.7328i			1.37458i	−0.726383	+	0.687290i	$0.758800\pi$
$132$		0			0
$133$	3.54520	−	6.77408i	0.307408	−	0.587387i
$134$		−	2.99529i		−	0.258753i
$135$		0			0
$136$	−9.73883	−	5.62271i	−0.835097	−	0.482144i
$137$			3.28444i			0.280609i	0.990108	+	0.140304i	$0.0448081\pi$
$137$			3.28444i			0.280609i	−0.990108	+	0.140304i	$0.955192\pi$
$138$		0			0
$139$	−8.08406	+	14.0020i	−0.685681	+	1.18763i	0.287541	+	0.957768i	$0.407162\pi$
$139$	−8.08406	+	14.0020i	−0.685681	+	1.18763i	−0.973222	+	0.229866i	$0.926171\pi$
$140$	−0.324774	+	0.187509i	−0.0274485	+	0.0158474i
$141$		0			0
$142$	5.41031			0.454023
$143$	−15.3032	−	26.5059i	−1.27972	−	2.21654i
$144$		0			0
$145$		−	0.132271i		−	0.0109845i
$146$	−0.759395			−0.0628480
$147$		0			0
$148$	6.26402	+	3.61653i	0.514899	+	0.297277i
$149$		−	5.99978i		−	0.491522i	−0.969331	−	0.245761i	$-0.920962\pi$
$149$		−	5.99978i		−	0.491522i	0.969331	−	0.245761i	$-0.0790378\pi$
$150$		0			0
$151$	−10.8923	−	6.28866i	−0.886401	−	0.511764i	−0.0136375	−	0.999907i	$-0.504341\pi$
$151$	−10.8923	−	6.28866i	−0.886401	−	0.511764i	−0.872764	+	0.488143i	$0.837674\pi$
$152$	10.4356	−	0.432780i	0.846439	−	0.0351031i
$153$		0			0
$154$	4.79712	+	2.76962i	0.386563	+	0.223182i
$155$	−0.430616	−	0.745849i	−0.0345879	−	0.0599080i
$156$		0			0
$157$	15.7607			1.25784			0.628922	−	0.777469i	$-0.283497\pi$
$157$	15.7607			1.25784			0.628922	+	0.777469i	$0.283497\pi$
$158$	−1.99513	−	1.15189i	−0.158724	−	0.0916392i
$159$		0			0
$160$	−0.694149	−	0.400767i	−0.0548773	−	0.0316834i
$161$	1.65334	−	0.954557i	0.130302	−	0.0752297i
$162$		0			0
$163$	−6.65366			−0.521155			−0.260578	−	0.965453i	$-0.583913\pi$
$163$	−6.65366			−0.521155			−0.260578	+	0.965453i	$0.583913\pi$
$164$	−5.99645	+	10.3861i	−0.468244	+	0.811022i
$165$		0			0
$166$		−	2.40042i		−	0.186309i
$167$	−2.10904	+	3.65296i	−0.163202	+	0.282675i	−0.936015	−	0.351959i	$-0.885516\pi$
$167$	−2.10904	+	3.65296i	−0.163202	+	0.282675i	0.772813	+	0.634634i	$0.218849\pi$
$168$		0			0
$169$	14.9876	+	25.9593i	1.15289	+	1.99687i
$170$	−0.440009			−0.0337472
$171$		0			0
$172$	1.67162			0.127460
$173$	−5.44776	−	9.43580i	−0.414186	−	0.717391i	0.581157	−	0.813792i	$-0.302600\pi$
$173$	−5.44776	−	9.43580i	−0.414186	−	0.717391i	−0.995343	+	0.0964007i	$0.969267\pi$
$174$		0			0
$175$	4.36825	−	7.56604i	0.330209	−	0.571939i
$176$		−	6.83595i		−	0.515279i
$177$		0			0
$178$	−5.27076	+	9.12922i	−0.395060	+	0.684264i
$179$	−5.16954			−0.386390			−0.193195	−	0.981160i	$-0.561885\pi$
$179$	−5.16954			−0.386390			−0.193195	+	0.981160i	$0.561885\pi$
$180$		0			0
$181$	4.70681	−	2.71748i	0.349855	−	0.201989i	−0.314767	−	0.949169i	$-0.601926\pi$
$181$	4.70681	−	2.71748i	0.349855	−	0.201989i	0.664621	+	0.747180i	$0.268593\pi$
$182$	−6.73576	−	3.88889i	−0.499288	−	0.288264i
$183$		0			0
$184$	2.25859	+	1.30400i	0.166505	+	0.0961318i
$185$	0.649975			0.0477871
$186$		0			0
$187$	−10.9556	−	18.9756i	−0.801151	−	1.38763i
$188$	16.7332	+	9.66091i	1.22039	+	0.704594i
$189$		0			0
$190$	0.345151	−	0.218826i	0.0250399	−	0.0158753i
$191$	10.8662	+	6.27361i	0.786251	+	0.453942i	0.838641	−	0.544684i	$-0.183350\pi$
$191$	10.8662	+	6.27361i	0.786251	+	0.453942i	−0.0523898	+	0.998627i	$0.516684\pi$
$192$		0			0
$193$		−	0.119267i		−	0.00858499i	−0.999991	−	0.00429250i	$-0.998634\pi$
$193$		−	0.119267i		−	0.00858499i	0.999991	−	0.00429250i	$-0.00136635\pi$
$194$	−8.52885	−	4.92413i	−0.612336	−	0.353532i
$195$		0			0
$196$	6.05166			0.432261
$197$			14.8993i			1.06153i	0.847519	+	0.530765i	$0.178095\pi$
$197$			14.8993i			1.06153i	−0.847519	+	0.530765i	$0.821905\pi$
$198$		0			0
$199$	3.99752	+	6.92391i	0.283377	+	0.490823i	0.972214	−	0.234093i	$-0.0752120\pi$
$199$	3.99752	+	6.92391i	0.283377	+	0.490823i	−0.688837	+	0.724916i	$0.741879\pi$
$200$	11.9347			0.843911
$201$		0			0
$202$	4.40926	−	2.54568i	0.310234	−	0.179114i
$203$	0.836917	−	1.44958i	0.0587400	−	0.101741i
$204$		0			0
$205$			1.07770i			0.0752699i
$206$	0.198649	+	0.114690i	0.0138405	+	0.00799083i
$207$		0			0
$208$			9.59854i			0.665539i
$209$	18.0307	+	9.43635i	1.24721	+	0.652726i
$210$		0			0
$211$			11.6634i			0.802939i	0.915872	+	0.401470i	$0.131500\pi$
$211$			11.6634i			0.802939i	−0.915872	+	0.401470i	$0.868500\pi$
$212$	3.92980			0.269900
$213$		0			0
$214$	−4.01174	−	6.94854i	−0.274237	−	0.474992i
$215$	0.130090	−	0.0751073i	0.00887204	−	0.00512227i
$216$		0			0
$217$		−	10.8985i		−	0.739840i
$218$			6.98998i			0.473421i
$219$		0			0
$220$	−0.499096	−	0.864460i	−0.0336491	−	0.0582819i
$221$	15.3830	+	26.6442i	1.03477	+	1.79228i
$222$		0			0
$223$	18.0513	−	10.4219i	1.20880	−	0.697903i	0.246306	−	0.969192i	$-0.420783\pi$
$223$	18.0513	−	10.4219i	1.20880	−	0.697903i	0.962498	+	0.271289i	$0.0874498\pi$
$224$	−5.07153	−	8.78415i	−0.338856	−	0.586916i
$225$		0			0
$226$	−0.738865	+	1.27975i	−0.0491486	+	0.0851278i
$227$	11.9369	−	20.6753i	0.792279	−	1.37227i	−0.132274	−	0.991213i	$-0.542228\pi$
$227$	11.9369	−	20.6753i	0.792279	−	1.37227i	0.924553	−	0.381054i	$-0.124439\pi$
$228$		0			0
$229$	−8.94882	−	15.4998i	−0.591355	−	1.02426i	−0.994050	−	0.108923i	$-0.965260\pi$
$229$	−8.94882	−	15.4998i	−0.591355	−	1.02426i	0.402695	−	0.915334i	$-0.368073\pi$
$230$	0.102045			0.00672865
$231$		0			0
$232$	2.28658			0.150121
$233$	−1.17373	−	0.677654i	−0.0768936	−	0.0443946i	0.461060	−	0.887369i	$-0.347469\pi$
$233$	−1.17373	−	0.677654i	−0.0768936	−	0.0443946i	−0.537954	+	0.842974i	$0.680803\pi$
$234$		0			0
$235$	1.73629			0.113263
$236$	−8.50750	+	14.7354i	−0.553791	+	0.959194i
$237$		0			0
$238$	−4.82214	−	2.78406i	−0.312573	−	0.180464i
$239$	6.15584	−	3.55408i	0.398188	−	0.229894i	−0.287514	−	0.957777i	$-0.592829\pi$
$239$	6.15584	−	3.55408i	0.398188	−	0.229894i	0.685702	+	0.727882i	$0.259495\pi$
$240$		0			0
$241$		−	16.5905i		−	1.06869i	−0.845266	−	0.534345i	$-0.820558\pi$
$241$		−	16.5905i		−	1.06869i	0.845266	−	0.534345i	$-0.179442\pi$
$242$	−3.65173	+	6.32499i	−0.234742	+	0.406585i
$243$		0			0
$244$	0.858849	−	1.48757i	0.0549822	−	0.0952319i
$245$	0.470955	−	0.271906i	0.0300882	−	0.0173714i
$246$		0			0
$247$	−25.3174	−	13.2498i	−1.61091	−	0.843066i
$248$	12.8935	−	7.44408i	0.818740	−	0.472700i
$249$		0			0
$250$	0.810392	−	0.467880i	0.0512537	−	0.0295913i
$251$	−4.43373	+	2.55982i	−0.279855	+	0.161574i	−0.633358	−	0.773859i	$-0.718324\pi$
$251$	−4.43373	+	2.55982i	−0.279855	+	0.161574i	0.353503	+	0.935433i	$0.384990\pi$
$252$		0			0
$253$	2.54077	+	4.40074i	0.159737	+	0.276672i
$254$	−3.00458	−	1.73470i	−0.188524	−	0.108845i
$255$		0			0
$256$	4.66961	−	8.08800i	0.291851	−	0.505500i
$257$	1.67885	−	2.90786i	0.104724	−	0.181387i	−0.808901	−	0.587944i	$-0.799937\pi$
$257$	1.67885	−	2.90786i	0.104724	−	0.181387i	0.913625	+	0.406557i	$0.133271\pi$
$258$		0			0
$259$	7.12319	+	4.11258i	0.442614	+	0.255543i
$260$	0.700794	+	1.21381i	0.0434614	+	0.0752774i
$261$		0			0
$262$	−9.21602	+	5.32087i	−0.569367	+	0.328724i
$263$	24.3512	−	14.0592i	1.50156	−	0.866926i	0.501562	−	0.865122i	$-0.332759\pi$
$263$	24.3512	−	14.0592i	1.50156	−	0.866926i	0.999998	−	0.00180407i	$-0.000574255\pi$
$264$		0			0
$265$	0.305827	−	0.176569i	0.0187868	−	0.0108466i
$266$	5.16714	−	0.214289i	0.316818	−	0.0131389i
$267$		0			0
$268$	−5.91535	+	3.41523i	−0.361338	+	0.208618i
$269$	−4.97903	+	8.62394i	−0.303577	+	0.525811i	−0.976944	−	0.213498i	$-0.931514\pi$
$269$	−4.97903	+	8.62394i	−0.303577	+	0.525811i	0.673366	+	0.739309i	$0.264848\pi$
$270$		0			0
$271$	2.04225	−	3.53729i	0.124058	−	0.214875i	−0.797306	−	0.603575i	$-0.793742\pi$
$271$	2.04225	−	3.53729i	0.124058	−	0.214875i	0.921364	+	0.388700i	$0.127076\pi$
$272$			6.87161i			0.416652i
$273$		0			0
$274$	−1.92397	+	1.11081i	−0.116232	+	0.0671063i
$275$	20.1387	+	11.6271i	1.21441	+	0.701140i
$276$		0			0
$277$	−7.84697	+	13.5914i	−0.471479	+	0.816626i	−0.999468	−	0.0326258i	$-0.989613\pi$
$277$	−7.84697	+	13.5914i	−0.471479	+	0.816626i	0.527989	+	0.849251i	$0.322946\pi$
$278$	−10.9362			−0.655909
$279$		0			0
$280$	−0.504519	−	0.291284i	−0.0301508	−	0.0174075i
$281$	−6.85439			−0.408899			−0.204449	−	0.978877i	$-0.565540\pi$
$281$	−6.85439			−0.408899			−0.204449	+	0.978877i	$0.565540\pi$
$282$		0			0
$283$	0.556875			0.0331028			0.0165514	−	0.999863i	$-0.494731\pi$
$283$	0.556875			0.0331028			0.0165514	+	0.999863i	$0.494731\pi$
$284$	−6.16884	−	10.6847i	−0.366053	−	0.634023i
$285$		0			0
$286$	10.3512	−	17.9287i	0.612077	−	1.06015i
$287$	−6.81892	+	11.8107i	−0.402508	+	0.697164i
$288$		0			0
$289$	2.51272	+	4.35215i	0.147807	+	0.256009i
$290$	0.0774823	−	0.0447344i	0.00454992	−	0.00262690i
$291$		0			0
$292$	0.865863	+	1.49972i	0.0506708	+	0.0877644i
$293$	−2.27576	−	3.94172i	−0.132951	−	0.230278i	0.791862	−	0.610700i	$-0.209112\pi$
$293$	−2.27576	−	3.94172i	−0.132951	−	0.230278i	−0.924813	+	0.380422i	$0.875779\pi$
$294$		0			0
$295$			1.52900i			0.0890216i
$296$			11.2362i			0.653088i
$297$		0			0
$298$	3.51458	−	2.02914i	0.203594	−	0.117545i
$299$	−3.56756	−	6.17920i	−0.206317	−	0.357352i
$300$		0			0
$301$	1.90090			0.109566
$302$		−	8.50736i		−	0.489544i
$303$		0			0
$304$	−3.41740	−	5.39021i	−0.196001	−	0.309149i
$305$		−	0.154355i		−	0.00883835i
$306$		0			0
$307$	6.39989	+	3.69498i	0.365261	+	0.210883i	0.671386	−	0.741108i	$-0.265699\pi$
$307$	6.39989	+	3.69498i	0.365261	+	0.210883i	−0.306125	+	0.951991i	$0.599033\pi$
$308$		−	12.6317i		−	0.719757i
$309$		0			0
$310$	0.291271	−	0.504496i	0.0165431	−	0.0286535i
$311$	26.1635	−	15.1055i	1.48360	−	0.856556i	0.483772	−	0.875194i	$-0.339266\pi$
$311$	26.1635	−	15.1055i	1.48360	−	0.856556i	0.999826	+	0.0186380i	$0.00593299\pi$
$312$		0			0
$313$	1.26467			0.0714831			0.0357416	−	0.999361i	$-0.488621\pi$
$313$	1.26467			0.0714831			0.0357416	+	0.999361i	$0.488621\pi$
$314$	5.33032	+	9.23238i	0.300807	+	0.521013i
$315$		0			0
$316$			5.25353i			0.295534i
$317$	−14.1139			−0.792717			−0.396358	−	0.918096i	$-0.629726\pi$
$317$	−14.1139			−0.792717			−0.396358	+	0.918096i	$0.629726\pi$
$318$		0			0
$319$	3.85839	+	2.22764i	0.216028	+	0.124724i
$320$		−	0.136262i		−	0.00761727i
$321$		0			0
$322$	1.11833	+	0.645667i	0.0623220	+	0.0359816i
$323$	−18.1248	−	9.48556i	−1.00849	−	0.527791i
$324$		0			0
$325$	−28.2773	−	16.3259i	−1.56854	−	0.905598i
$326$	−2.25029	−	3.89761i	−0.124632	−	0.215869i
$327$		0			0
$328$	−18.6303			−1.02868
$329$	19.0283	+	10.9860i	1.04906	+	0.605677i
$330$		0			0
$331$	15.7116	+	9.07108i	0.863586	+	0.498592i	0.865212	−	0.501407i	$-0.167184\pi$
$331$	15.7116	+	9.07108i	0.863586	+	0.498592i	−0.00162545	+	0.999999i	$0.500517\pi$
$332$	−4.74056	+	2.73696i	−0.260172	+	0.150210i
$333$		0			0
$334$	−2.85313			−0.156116
$335$	−0.306898	+	0.531563i	−0.0167676	+	0.0290424i
$336$		0			0
$337$			6.16412i			0.335781i	0.985806	+	0.167890i	$0.0536955\pi$
$337$			6.16412i			0.335781i	−0.985806	+	0.167890i	$0.946305\pi$
$338$	−10.1377	+	17.5590i	−0.551418	+	0.955084i
$339$		0			0
$340$	0.501699	+	0.868969i	0.0272085	+	0.0471264i
$341$	29.0089			1.57092
$342$		0			0
$343$	19.1600			1.03454
$344$	1.29838	+	2.24887i	0.0700041	+	0.121251i
$345$		0			0
$346$	3.68490	−	6.38243i	0.198101	−	0.343121i
$347$		−	16.1600i		−	0.867513i	−0.901030	−	0.433756i	$-0.857188\pi$
$347$		−	16.1600i		−	0.867513i	0.901030	−	0.433756i	$-0.142812\pi$
$348$		0			0
$349$	11.5382	−	19.9847i	0.617624	−	1.06976i	−0.372294	−	0.928115i	$-0.621429\pi$
$349$	11.5382	−	19.9847i	0.617624	−	1.06976i	0.989918	−	0.141641i	$-0.0452379\pi$
$350$	5.90942			0.315872
$351$		0			0
$352$	23.3810	−	13.4990i	1.24621	−	0.719500i
$353$	−26.3912	−	15.2370i	−1.40466	−	0.810982i	−0.409795	−	0.912178i	$-0.634400\pi$
$353$	−26.3912	−	15.2370i	−1.40466	−	0.810982i	−0.994867	+	0.101196i	$0.967733\pi$
$354$		0			0
$355$	−0.960149	−	0.554342i	−0.0509594	−	0.0294214i
$356$	24.0389			1.27406
$357$		0			0
$358$	−1.74835	−	3.02823i	−0.0924032	−	0.160047i
$359$	−1.17054	−	0.675809i	−0.0617785	−	0.0356679i	0.468793	−	0.883308i	$-0.344689\pi$
$359$	−1.17054	−	0.675809i	−0.0617785	−	0.0356679i	−0.530571	+	0.847640i	$0.678023\pi$
$360$		0			0
$361$	18.9348	−	1.57321i	0.996566	−	0.0828006i
$362$	3.18371	+	1.83812i	0.167332	+	0.0966093i
$363$		0			0
$364$			17.7365i			0.929644i
$365$	0.134767	+	0.0778079i	0.00705404	+	0.00407265i
$366$		0			0
$367$	1.58741			0.0828622			0.0414311	−	0.999141i	$-0.486808\pi$
$367$	1.58741			0.0828622			0.0414311	+	0.999141i	$0.486808\pi$
$368$		−	1.59363i		−	0.0830739i
$369$		0			0
$370$	0.219823	+	0.380745i	0.0114281	+	0.0197940i
$371$	4.46881			0.232009
$372$		0			0
$373$	26.0140	−	15.0192i	1.34695	−	0.777663i	0.359135	−	0.933285i	$-0.383072\pi$
$373$	26.0140	−	15.0192i	1.34695	−	0.777663i	0.987817	+	0.155622i	$0.0497383\pi$
$374$	7.41041	−	12.8352i	0.383183	−	0.663693i
$375$		0			0
$376$			30.0153i			1.54792i
$377$	−5.41766	−	3.12789i	−0.279024	−	0.161095i
$378$		0			0
$379$		−	20.4900i		−	1.05250i	−0.850330	−	0.526250i	$-0.823598\pi$
$379$		−	20.4900i		−	1.05250i	0.850330	−	0.526250i	$-0.176402\pi$
$380$	−0.825699	−	0.432128i	−0.0423575	−	0.0221677i
$381$		0			0
$382$			8.48700i			0.434233i
$383$	−29.7300			−1.51913			−0.759565	−	0.650431i	$-0.774588\pi$
$383$	−29.7300			−1.51913			−0.759565	+	0.650431i	$0.774588\pi$
$384$		0			0
$385$	−0.567552	−	0.983029i	−0.0289251	−	0.0500998i
$386$	0.0698644	−	0.0403362i	0.00355600	−	0.00205306i
$387$		0			0
$388$			22.4580i			1.14013i
$389$		−	17.1961i		−	0.871875i	−0.899977	−	0.435938i	$-0.856417\pi$
$389$		−	17.1961i		−	0.871875i	0.899977	−	0.435938i	$-0.143583\pi$
$390$		0			0
$391$	−2.55402	−	4.42369i	−0.129162	−	0.223716i
$392$	4.70045	+	8.14142i	0.237409	+	0.411204i
$393$		0			0
$394$	−8.72776	+	5.03897i	−0.439698	+	0.253860i
$395$	0.236046	+	0.408843i	0.0118767	+	0.0205711i
$396$		0			0
$397$	−12.1112	+	20.9772i	−0.607844	+	1.05282i	0.383751	+	0.923437i	$0.374632\pi$
$397$	−12.1112	+	20.9772i	−0.607844	+	1.05282i	−0.991595	+	0.129380i	$0.958701\pi$
$398$	−2.70394	+	4.68337i	−0.135536	+	0.234756i
$399$		0			0
$400$	−3.64640	−	6.31575i	−0.182320	−	0.315787i
$401$	−17.4150			−0.869666			−0.434833	−	0.900511i	$-0.643193\pi$
$401$	−17.4150			−0.869666			−0.434833	+	0.900511i	$0.643193\pi$
$402$		0			0
$403$	−40.7321			−2.02901
$404$	−10.0549	−	5.80519i	−0.500249	−	0.288819i
$405$		0			0
$406$	1.13219			0.0561896
$407$	−10.9465	+	18.9600i	−0.542600	+	0.939811i
$408$		0			0
$409$	20.2058	+	11.6658i	0.999111	+	0.576837i	0.907985	−	0.419002i	$-0.137620\pi$
$409$	20.2058	+	11.6658i	0.999111	+	0.576837i	0.0911258	+	0.995839i	$0.470953\pi$
$410$	−0.631300	+	0.364481i	−0.0311777	+	0.0180004i
$411$		0			0
$412$		−	0.523079i		−	0.0257702i
$413$	−9.67438	+	16.7565i	−0.476045	+	0.824535i
$414$		0			0
$415$	−0.245948	+	0.425994i	−0.0120731	+	0.0209112i
$416$	−32.8299	+	18.9543i	−1.60962	+	0.929312i
$417$		0			0
$418$	0.570379	+	13.7535i	0.0278981	+	0.672706i
$419$	−6.86848	+	3.96552i	−0.335547	+	0.193728i	−0.658301	−	0.752755i	$-0.728725\pi$
$419$	−6.86848	+	3.96552i	−0.335547	+	0.193728i	0.322754	+	0.946483i	$0.395391\pi$
$420$		0			0
$421$	−24.4352	+	14.1077i	−1.19090	+	0.687565i	−0.958510	−	0.285058i	$-0.907987\pi$
$421$	−24.4352	+	14.1077i	−1.19090	+	0.687565i	−0.232387	+	0.972623i	$0.574654\pi$
$422$	−6.83221	+	3.94458i	−0.332587	+	0.192019i
$423$		0			0
$424$	3.05236	+	5.28684i	0.148236	+	0.256752i
$425$	−20.2437	−	11.6877i	−0.981966	−	0.566938i
$426$		0			0
$427$	0.976648	−	1.69160i	0.0472633	−	0.0818625i
$428$	−9.14839	+	15.8455i	−0.442204	+	0.765920i
$429$		0			0
$430$	0.0879933	+	0.0508029i	0.00424341	+	0.00244994i
$431$	−3.39423	−	5.87899i	−0.163494	−	0.283181i	0.772625	−	0.634863i	$-0.218943\pi$
$431$	−3.39423	−	5.87899i	−0.163494	−	0.283181i	−0.936120	+	0.351682i	$0.885610\pi$
$432$		0			0
$433$	29.7286	−	17.1638i	1.42866	−	0.824839i	0.431648	−	0.902042i	$-0.357932\pi$
$433$	29.7286	−	17.1638i	1.42866	−	0.824839i	0.997015	+	0.0772030i	$0.0245990\pi$
$434$	6.38418	−	3.68591i	0.306450	−	0.176929i
$435$		0			0
$436$	13.8044	−	7.96999i	0.661112	−	0.381693i
$437$	4.20342	+	2.19985i	0.201077	+	0.105233i
$438$		0			0
$439$	−11.9531	+	6.90114i	−0.570492	+	0.329373i	−0.757346	−	0.653014i	$-0.773504\pi$
$439$	−11.9531	+	6.90114i	−0.570492	+	0.329373i	0.186854	+	0.982388i	$0.440171\pi$
$440$	0.775318	−	1.34289i	0.0369618	−	0.0640198i
$441$		0			0
$442$	−10.4051	+	18.0222i	−0.494922	+	0.857231i
$443$		−	26.9532i		−	1.28058i	−0.768131	−	0.640292i	$-0.778813\pi$
$443$		−	26.9532i		−	1.28058i	0.768131	−	0.640292i	$-0.221187\pi$
$444$		0			0
$445$	1.87077	−	1.08009i	0.0886829	−	0.0512011i
$446$	12.2100	+	7.04944i	0.578160	+	0.333801i
$447$		0			0
$448$	0.862167	−	1.49332i	0.0407335	−	0.0705526i
$449$	−1.78199			−0.0840972			−0.0420486	−	0.999116i	$-0.513388\pi$
$449$	−1.78199			−0.0840972			−0.0420486	+	0.999116i	$0.513388\pi$
$450$		0			0
$451$	−31.4369	−	18.1501i	−1.48030	−	0.854654i
$452$	3.36982			0.158503
$453$		0			0
$454$	16.1483			0.757879
$455$	0.796915	+	1.38030i	0.0373599	+	0.0647093i
$456$		0			0
$457$	−5.41688	+	9.38231i	−0.253391	+	0.438886i	−0.964457	−	0.264239i	$-0.914879\pi$
$457$	−5.41688	+	9.38231i	−0.253391	+	0.438886i	0.711066	+	0.703125i	$0.248213\pi$
$458$	6.05303	−	10.4842i	0.282839	−	0.489892i
$459$		0			0
$460$	−0.116352	−	0.201527i	−0.00542494	−	0.00939626i
$461$	17.9559	−	10.3669i	0.836290	−	0.482833i	−0.0197111	−	0.999806i	$-0.506275\pi$
$461$	17.9559	−	10.3669i	0.836290	−	0.482833i	0.856002	+	0.516973i	$0.172941\pi$
$462$		0			0
$463$	−13.1769	−	22.8231i	−0.612384	−	1.06068i	−0.990837	−	0.135060i	$-0.956877\pi$
$463$	−13.1769	−	22.8231i	−0.612384	−	1.06068i	0.378453	−	0.925620i	$-0.376456\pi$
$464$	−0.698616	−	1.21004i	−0.0324324	−	0.0561746i
$465$		0			0
$466$		−	0.916736i		−	0.0424670i
$467$			12.0210i			0.556265i	0.960543	+	0.278133i	$0.0897155\pi$
$467$			12.0210i			0.556265i	−0.960543	+	0.278133i	$0.910285\pi$
$468$		0			0
$469$	−6.72670	+	3.88366i	−0.310610	+	0.179331i
$470$	0.587218	+	1.01709i	0.0270863	+	0.0469149i
$471$		0			0
$472$	−26.4318			−1.21662
$473$			5.05967i			0.232644i
$474$		0			0
$475$	21.6921	−	0.899605i	0.995302	−	0.0412767i
$476$			12.6976i			0.581992i
$477$		0			0
$478$	4.16384	+	2.40400i	0.190450	+	0.109956i
$479$		−	35.1118i		−	1.60430i	−0.597124	−	0.802149i	$-0.703690\pi$
$479$		−	35.1118i		−	1.60430i	0.597124	−	0.802149i	$-0.296310\pi$
$480$		0			0
$481$	15.3703	−	26.6222i	0.700827	−	1.21387i
$482$	9.71847	−	5.61096i	0.442664	−	0.255572i
$483$		0			0
$484$	16.6548			0.757038
$485$	1.00906	+	1.74774i	0.0458189	+	0.0793607i
$486$		0			0
$487$			14.1105i			0.639409i	0.947517	+	0.319705i	$0.103584\pi$
$487$			14.1105i			0.639409i	−0.947517	+	0.319705i	$0.896416\pi$
$488$	2.66835			0.120790
$489$		0			0
$490$	0.318556	+	0.183918i	0.0143909	+	0.00830859i
$491$		−	29.5713i		−	1.33453i	−0.744818	−	0.667267i	$-0.767464\pi$
$491$		−	29.5713i		−	1.33453i	0.744818	−	0.667267i	$-0.232536\pi$
$492$		0			0
$493$	−3.87851	−	2.23926i	−0.174679	−	0.100851i
$494$	−0.800884	−	19.3117i	−0.0360335	−	0.868873i
$495$		0			0
$496$	−7.87869	−	4.54877i	−0.353764	−	0.204246i
$497$	−7.01496	−	12.1503i	−0.314664	−	0.545014i
$498$		0			0
$499$	−35.7490			−1.60034			−0.800172	−	0.599770i	$-0.795259\pi$
$499$	−35.7490			−1.60034			−0.800172	+	0.599770i	$0.795259\pi$
$500$	−1.84802	−	1.06696i	−0.0826460	−	0.0477157i
$501$		0			0
$502$	−2.99900	−	1.73147i	−0.133852	−	0.0772794i
$503$	−3.21576	+	1.85662i	−0.143384	+	0.0827826i	−0.569976	−	0.821662i	$-0.693047\pi$
$503$	−3.21576	+	1.85662i	−0.143384	+	0.0827826i	0.426592	+	0.904444i	$0.359714\pi$
$504$		0			0
$505$	−1.04333			−0.0464275
$506$	−1.71859	+	2.97668i	−0.0764006	+	0.132330i
$507$		0			0
$508$			7.91162i			0.351021i
$509$	−17.4709	+	30.2606i	−0.774386	+	1.34128i	0.160753	+	0.986995i	$0.448608\pi$
$509$	−17.4709	+	30.2606i	−0.774386	+	1.34128i	−0.935139	+	0.354281i	$0.884726\pi$
$510$		0			0
$511$	0.984625	+	1.70542i	0.0435572	+	0.0754434i
$512$	−15.4837			−0.684291
$513$		0			0
$514$	2.27117			0.100177
$515$	−0.0235024	−	0.0407073i	−0.00103564	−	0.00179378i
$516$		0			0
$517$	−29.2417	+	50.6481i	−1.28605	+	2.22750i
$518$			5.56353i			0.244448i
$519$		0			0
$520$	−1.08864	+	1.88559i	−0.0477402	+	0.0826884i
$521$	39.1773			1.71639			0.858195	−	0.513324i	$-0.171586\pi$
$521$	39.1773			1.71639			0.858195	+	0.513324i	$0.171586\pi$
$522$		0			0
$523$	−35.3599	+	20.4151i	−1.54618	+	0.892689i	−0.547754	+	0.836639i	$0.684517\pi$
$523$	−35.3599	+	20.4151i	−1.54618	+	0.892689i	−0.998428	+	0.0560491i	$0.982150\pi$
$524$	21.0162	+	12.1337i	0.918099	+	0.530064i
$525$		0			0
$526$	16.4713	+	9.50970i	0.718182	+	0.414643i
$527$	−29.1601			−1.27024
$528$		0			0
$529$	−10.9077	−	18.8927i	−0.474247	−	0.821420i
$530$	0.206863	+	0.119432i	0.00898554	+	0.00518780i
$531$		0			0
$532$	−6.31478	−	9.96019i	−0.273780	−	0.431829i
$533$	44.1413	+	25.4850i	1.91197	+	1.10388i
$534$		0			0
$535$			1.64418i			0.0710840i
$536$	−9.18917	−	5.30537i	−0.396911	−	0.229157i
$537$		0			0
$538$	−6.73569			−0.290396
$539$			18.3172i			0.788977i
$540$		0			0
$541$	−14.5634	−	25.2245i	−0.626129	−	1.08449i	−0.988321	−	0.152384i	$-0.951305\pi$
$541$	−14.5634	−	25.2245i	−0.626129	−	1.08449i	0.362192	−	0.932104i	$-0.382028\pi$
$542$	2.76278			0.118672
$543$		0			0
$544$	−23.5029	+	13.5694i	−1.00768	+	0.581784i
$545$	0.716196	−	1.24049i	0.0306785	−	0.0531367i
$546$		0			0
$547$			18.2325i			0.779566i	0.920907	+	0.389783i	$0.127450\pi$
$547$			18.2325i			0.779566i	−0.920907	+	0.389783i	$0.872550\pi$
$548$	4.38744	+	2.53309i	0.187422	+	0.108208i
$549$		0			0
$550$			15.7292i			0.670697i
$551$	4.15600	−	0.172356i	0.177052	−	0.00734260i
$552$		0			0
$553$			5.97411i			0.254045i
$554$	−10.6155			−0.451008
$555$		0			0
$556$	12.4695	+	21.5978i	0.528823	+	0.915949i
$557$	−30.1772	+	17.4228i	−1.27865	+	0.738230i	−0.976600	−	0.215062i	$-0.931005\pi$
$557$	−30.1772	+	17.4228i	−1.27865	+	0.738230i	−0.302051	+	0.953292i	$0.597671\pi$
$558$		0			0
$559$		−	7.10441i		−	0.300485i
$560$			0.355983i			0.0150430i
$561$		0			0
$562$	−2.31817	−	4.01519i	−0.0977862	−	0.169371i
$563$	13.2981	+	23.0329i	0.560446	+	0.970722i	0.997457	+	0.0712655i	$0.0227038\pi$
$563$	13.2981	+	23.0329i	0.560446	+	0.970722i	−0.437011	+	0.899456i	$0.643963\pi$
$564$		0			0
$565$	0.262248	−	0.151409i	0.0110328	−	0.00636981i
$566$	0.188337	+	0.326209i	0.00791638	+	0.0137116i
$567$		0			0
$568$	9.58294	−	16.5981i	0.402091	−	0.696442i
$569$	−14.6846	+	25.4344i	−0.615610	+	1.06627i	0.374668	+	0.927159i	$0.377757\pi$
$569$	−14.6846	+	25.4344i	−0.615610	+	1.06627i	−0.990277	+	0.139108i	$0.955577\pi$
$570$		0			0
$571$	0.947842	+	1.64171i	0.0396660	+	0.0687035i	0.885177	−	0.465255i	$-0.154037\pi$
$571$	0.947842	+	1.64171i	0.0396660	+	0.0687035i	−0.845511	+	0.533958i	$0.820704\pi$
$572$	−47.2096			−1.97393
$573$		0			0
$574$	−9.22470			−0.385031
$575$	4.69484	+	2.71057i	0.195788	+	0.113038i
$576$		0			0
$577$	15.2421			0.634537			0.317268	−	0.948336i	$-0.397234\pi$
$577$	15.2421			0.634537			0.317268	+	0.948336i	$0.397234\pi$
$578$	−1.69961	+	2.94382i	−0.0706946	+	0.122447i
$579$		0			0
$580$	−0.176691	−	0.102013i	−0.00733669	−	0.00423584i
$581$	−5.39077	+	3.11236i	−0.223647	+	0.129123i
$582$		0			0
$583$			11.8947i			0.492630i
$584$	−1.34507	+	2.32973i	−0.0556594	+	0.0964049i
$585$		0			0
$586$	1.53933	−	2.66620i	0.0635892	−	0.110140i
$587$	−36.2705	+	20.9408i	−1.49705	+	0.864319i	−0.999994	−	0.00340197i	$-0.998917\pi$
$587$	−36.2705	+	20.9408i	−1.49705	+	0.864319i	−0.497051	+	0.867721i	$0.665584\pi$
$588$		0			0
$589$	22.8737	−	14.5020i	0.942495	−	0.597544i
$590$	−0.895661	+	0.517110i	−0.0368738	+	0.0212891i
$591$		0			0
$592$	5.94608	−	3.43297i	0.244382	−	0.141094i
$593$	6.19893	−	3.57896i	0.254560	−	0.146970i	−0.367291	−	0.930106i	$-0.619715\pi$
$593$	6.19893	−	3.57896i	0.254560	−	0.146970i	0.621850	+	0.783136i	$0.286381\pi$
$594$		0			0
$595$	0.570512	+	0.988156i	0.0233887	+	0.0405105i
$596$	−8.01465	−	4.62726i	−0.328293	−	0.189540i
$597$		0			0
$598$	2.41312	−	4.17964i	0.0986796	−	0.170918i
$599$	3.11637	−	5.39771i	0.127331	−	0.220544i	−0.795311	−	0.606202i	$-0.792692\pi$
$599$	3.11637	−	5.39771i	0.127331	−	0.220544i	0.922642	+	0.385658i	$0.126026\pi$
$600$		0			0
$601$	19.8585	+	11.4653i	0.810044	+	0.467679i	0.846971	−	0.531639i	$-0.178424\pi$
$601$	19.8585	+	11.4653i	0.810044	+	0.467679i	−0.0369272	+	0.999318i	$0.511757\pi$
$602$	0.642889	+	1.11352i	0.0262022	+	0.0453835i
$603$		0			0
$604$	−16.8011	+	9.70011i	−0.683626	+	0.394692i
$605$	1.29612	−	0.748316i	0.0526948	−	0.0304234i
$606$		0			0
$607$	1.44140	−	0.832190i	0.0585044	−	0.0337775i	−0.470462	−	0.882420i	$-0.655913\pi$
$607$	1.44140	−	0.832190i	0.0585044	−	0.0337775i	0.528967	+	0.848642i	$0.322580\pi$
$608$	11.6877	−	22.3326i	0.474000	−	0.905707i
$609$		0			0
$610$	0.0904188	−	0.0522033i	0.00366095	−	0.00211365i
$611$	41.0590	−	71.1163i	1.66107	−	2.87706i
$612$		0			0
$613$	18.5832	−	32.1871i	0.750570	−	1.30003i	−0.196977	−	0.980408i	$-0.563112\pi$
$613$	18.5832	−	32.1871i	0.750570	−	1.30003i	0.947547	−	0.319617i	$-0.103554\pi$
$614$			4.99860i			0.201727i
$615$		0			0
$616$	16.9937	−	9.81130i	0.684695	−	0.395309i
$617$	13.5270	+	7.80983i	0.544577	+	0.314412i	0.746932	−	0.664900i	$-0.231526\pi$
$617$	13.5270	+	7.80983i	0.544577	+	0.314412i	−0.202355	+	0.979312i	$0.564859\pi$
$618$		0			0
$619$	−17.0708	+	29.5674i	−0.686132	+	1.18842i	0.286948	+	0.957946i	$0.407359\pi$
$619$	−17.0708	+	29.5674i	−0.686132	+	1.18842i	−0.973080	+	0.230469i	$0.925974\pi$
$620$	−1.32843			−0.0533511
$621$		0			0
$622$	17.6972	+	10.2175i	0.709591	+	0.409683i
$623$	27.3361			1.09520
$624$		0			0
$625$	24.7122			0.988487
$626$	0.427713	+	0.740821i	0.0170948	+	0.0296091i
$627$		0			0
$628$	12.1553	−	21.0536i	0.485048	−	0.840128i
$629$	11.0036	−	19.0589i	0.438744	−	0.759927i
$630$		0			0
$631$	9.09528	+	15.7535i	0.362077	+	0.627136i	0.988303	−	0.152506i	$-0.0487343\pi$
$631$	9.09528	+	15.7535i	0.362077	+	0.627136i	−0.626225	+	0.779642i	$0.715401\pi$
$632$	−7.06769	+	4.08053i	−0.281138	+	0.162315i
$633$		0			0
$634$	−4.77336	−	8.26771i	−0.189574	−	0.328353i
$635$	0.355476	+	0.615702i	0.0141066	+	0.0244334i
$636$		0			0
$637$		−	25.7196i		−	1.01905i
$638$			3.01358i			0.119309i
$639$		0			0
$640$	−1.30848	+	0.755450i	−0.0517221	+	0.0298618i
$641$	6.31100	+	10.9310i	0.249269	+	0.431747i	0.963323	−	0.268344i	$-0.0864762\pi$
$641$	6.31100	+	10.9310i	0.249269	+	0.431747i	−0.714054	+	0.700091i	$0.753143\pi$
$642$		0			0
$643$	26.4006			1.04114			0.520568	−	0.853820i	$-0.325720\pi$
$643$	26.4006			1.04114			0.520568	+	0.853820i	$0.325720\pi$
$644$		−	2.94476i		−	0.116040i
$645$		0			0
$646$	−0.573354	−	13.8252i	−0.0225583	−	0.543947i
$647$		−	17.9111i		−	0.704159i	−0.935970	−	0.352079i	$-0.885475\pi$
$647$		−	17.9111i		−	0.704159i	0.935970	−	0.352079i	$-0.114525\pi$
$648$		0			0
$649$	−44.6013	−	25.7505i	−1.75075	−	1.01080i
$650$		−	22.0858i		−	0.866278i
$651$		0			0
$652$	−5.13156	+	8.88812i	−0.200967	+	0.348086i
$653$	−3.92191	+	2.26431i	−0.153476	+	0.0886094i	−0.574771	−	0.818314i	$-0.694909\pi$
$653$	−3.92191	+	2.26431i	−0.153476	+	0.0886094i	0.421295	+	0.906924i	$0.361576\pi$
$654$		0			0
$655$	2.18071			0.0852075
$656$	5.69209	+	9.85898i	0.222239	+	0.384929i
$657$		0			0
$658$			14.8620i			0.579380i
$659$	−20.9972			−0.817936			−0.408968	−	0.912549i	$-0.634111\pi$
$659$	−20.9972			−0.817936			−0.408968	+	0.912549i	$0.634111\pi$
$660$		0			0
$661$	−16.5587	−	9.56015i	−0.644057	−	0.371847i	0.142118	−	0.989850i	$-0.454609\pi$
$661$	−16.5587	−	9.56015i	−0.644057	−	0.371847i	−0.786176	+	0.618003i	$0.787942\pi$
$662$			12.2714i			0.476943i
$663$		0			0
$664$	−7.36419	−	4.25172i	−0.285786	−	0.164999i
$665$	−0.938951	−	0.491398i	−0.0364110	−	0.0190556i
$666$		0			0
$667$	0.899487	+	0.519319i	0.0348283	+	0.0201081i
$668$	3.25314	+	5.63460i	0.125868	+	0.218009i
$669$		0			0
$670$	−0.415175			−0.0160396
$671$	4.50259	+	2.59957i	0.173820	+	0.100355i
$672$		0			0
$673$	8.12324	+	4.68995i	0.313128	+	0.180784i	0.648325	−	0.761363i	$-0.275470\pi$
$673$	8.12324	+	4.68995i	0.313128	+	0.180784i	−0.335197	+	0.942148i	$0.608803\pi$
$674$	−3.61084	+	2.08472i	−0.139084	+	0.0803004i
$675$		0			0
$676$	46.2361			1.77831
$677$	15.3198	−	26.5347i	0.588787	−	1.01981i	−0.405604	−	0.914049i	$-0.632939\pi$
$677$	15.3198	−	26.5347i	0.588787	−	1.01981i	0.994392	−	0.105761i	$-0.0337278\pi$
$678$		0			0
$679$			25.5384i			0.980072i
$680$	−0.779361	+	1.34989i	−0.0298871	+	0.0517660i
$681$		0			0
$682$	9.81087	+	16.9929i	0.375678	+	0.650693i
$683$	−30.9867			−1.18567			−0.592837	−	0.805323i	$-0.701992\pi$
$683$	−30.9867			−1.18567			−0.592837	+	0.805323i	$0.701992\pi$
$684$		0			0
$685$	0.455255			0.0173944
$686$	6.47996	+	11.2236i	0.247406	+	0.428520i
$687$		0			0
$688$	0.793387	−	1.37419i	0.0302476	−	0.0523904i
$689$		−	16.7017i		−	0.636285i
$690$		0			0
$691$	8.00656	−	13.8678i	0.304584	−	0.527555i	−0.672585	−	0.740020i	$-0.734816\pi$
$691$	8.00656	−	13.8678i	0.304584	−	0.527555i	0.977169	+	0.212465i	$0.0681493\pi$
$692$	−16.8061			−0.638872
$693$		0			0
$694$	9.46625	−	5.46534i	0.359334	−	0.207462i
$695$	1.94081	+	1.12053i	0.0736191	+	0.0425040i
$696$		0			0
$697$	31.6008	+	18.2447i	1.19697	+	0.691069i
$698$	15.6089			0.590807
$699$		0			0
$700$	−6.73793	−	11.6704i	−0.254670	−	0.441101i
$701$	29.7676	+	17.1863i	1.12431	+	0.649119i	0.942497	−	0.334215i	$-0.108471\pi$
$701$	29.7676	+	17.1863i	1.12431	+	0.649119i	0.181810	+	0.983334i	$0.441804\pi$
$702$		0			0
$703$	0.846950	+	20.4224i	0.0319433	+	0.770247i
$704$	3.97480	+	2.29485i	0.149806	+	0.0864904i
$705$		0			0
$706$		−	20.6127i		−	0.775770i
$707$	−11.4340	−	6.60143i	−0.430020	−	0.248272i
$708$		0			0
$709$	−3.35195			−0.125885			−0.0629425	−	0.998017i	$-0.520048\pi$
$709$	−3.35195			−0.125885			−0.0629425	+	0.998017i	$0.520048\pi$
$710$		−	0.749920i		−	0.0281440i
$711$		0			0
$712$	18.6715	+	32.3401i	0.699746	+	1.21199i
$713$	6.76269			0.253265
$714$		0			0
$715$	−3.67397	+	2.12117i	−0.137399	+	0.0793272i
$716$	−3.98695	+	6.90559i	−0.148999	+	0.258074i
$717$		0			0
$718$		−	0.914242i		−	0.0341192i
$719$	−21.7299	−	12.5458i	−0.810389	−	0.467878i	0.0367021	−	0.999326i	$-0.488315\pi$
$719$	−21.7299	−	12.5458i	−0.810389	−	0.467878i	−0.847091	+	0.531448i	$0.821648\pi$
$720$		0			0
$721$		−	0.594824i		−	0.0221524i
$722$	7.32534	+	10.5596i	0.272621	+	0.392988i
$723$		0			0
$724$		−	8.38330i		−	0.311563i
$725$	4.75303			0.176523
$726$		0			0
$727$	−23.4261	−	40.5752i	−0.868825	−	1.50485i	−0.863198	−	0.504866i	$-0.831542\pi$
$727$	−23.4261	−	40.5752i	−0.868825	−	1.50485i	−0.00562747	−	0.999984i	$-0.501791\pi$
$728$	−23.8613	+	13.7763i	−0.884357	+	0.510584i
$729$		0			0
$730$			0.105259i			0.00389582i
$731$		−	5.08606i		−	0.188115i
$732$		0			0
$733$	−11.0279	−	19.1009i	−0.407325	−	0.705508i	0.587264	−	0.809396i	$-0.300205\pi$
$733$	−11.0279	−	19.1009i	−0.407325	−	0.705508i	−0.994589	+	0.103888i	$0.966872\pi$
$734$	0.536867	+	0.929880i	0.0198161	+	0.0343225i
$735$		0			0
$736$	5.45070	−	3.14696i	0.200915	−	0.115999i
$737$	−10.3372	−	17.9046i	−0.380777	−	0.659526i
$738$		0			0
$739$	−6.35102	+	11.0003i	−0.233626	+	0.404652i	−0.958872	−	0.283837i	$-0.908392\pi$
$739$	−6.35102	+	11.0003i	−0.233626	+	0.404652i	0.725247	+	0.688489i	$0.241726\pi$
$740$	0.501286	−	0.868253i	0.0184276	−	0.0319176i
$741$		0			0
$742$	1.51136	+	2.61776i	0.0554839	+	0.0961009i
$743$	27.2706			1.00046			0.500230	−	0.865893i	$-0.333249\pi$
$743$	27.2706			1.00046			0.500230	+	0.865893i	$0.333249\pi$
$744$		0			0
$745$	−0.831627			−0.0304685
$746$	17.5960	+	10.1590i	0.644235	+	0.371949i
$747$		0			0
$748$	−33.7974			−1.23576
$749$	−10.4032	+	18.0188i	−0.380124	+	0.658394i
$750$		0			0
$751$	−35.6693	−	20.5937i	−1.30159	−	0.751475i	−0.320916	−	0.947108i	$-0.603991\pi$
$751$	−35.6693	−	20.5937i	−1.30159	−	0.751475i	−0.980677	+	0.195633i	$0.937324\pi$
$752$	15.8839	−	9.17055i	0.579225	−	0.334416i
$753$		0			0
$754$		−	4.23144i		−	0.154100i
$755$	−0.871668	+	1.50977i	−0.0317232	+	0.0549463i
$756$		0			0
$757$	0.190902	−	0.330651i	0.00693844	−	0.0120177i	−0.862535	−	0.505997i	$-0.831125\pi$
$757$	0.190902	−	0.330651i	0.00693844	−	0.0120177i	0.869474	+	0.493979i	$0.164458\pi$
$758$	12.0027	−	6.92977i	0.435958	−	0.251701i
$759$		0			0
$760$	−0.0599874	−	1.44647i	−0.00217597	−	0.0524691i
$761$	35.7329	−	20.6304i	1.29532	−	0.747852i	0.315726	−	0.948850i	$-0.397752\pi$
$761$	35.7329	−	20.6304i	1.29532	−	0.747852i	0.979592	+	0.200998i	$0.0644185\pi$
$762$		0			0
$763$	15.6978	−	9.06315i	0.568300	−	0.328108i
$764$	16.7609	−	9.67689i	0.606387	−	0.350098i
$765$		0			0
$766$	−10.0547	−	17.4153i	−0.363293	−	0.629242i
$767$	62.6258	+	36.1570i	2.26129	+	1.30555i
$768$		0			0
$769$	−8.54407	+	14.7988i	−0.308107	+	0.533657i	−0.977948	−	0.208847i	$-0.933029\pi$
$769$	−8.54407	+	14.7988i	−0.308107	+	0.533657i	0.669841	+	0.742504i	$0.266362\pi$
$770$	0.383895	−	0.664926i	0.0138346	−	0.0239623i
$771$		0			0
$772$	−0.159319	−	0.0919829i	−0.00573402	−	0.00331054i
$773$	2.79674	+	4.84409i	0.100592	+	0.174230i	0.911929	−	0.410349i	$-0.134593\pi$
$773$	2.79674	+	4.84409i	0.100592	+	0.174230i	−0.811337	+	0.584579i	$0.801260\pi$
$774$		0			0
$775$	26.8013	−	15.4737i	0.962732	−	0.555833i
$776$	−30.2133	+	17.4436i	−1.08459	+	0.626190i
$777$		0			0
$778$	10.0732	−	5.81575i	0.361141	−	0.208505i
$779$	−33.8617	+	1.40430i	−1.21322	+	0.0503142i
$780$		0			0
$781$	32.3406	−	18.6719i	1.15724	−	0.668132i
$782$	1.72755	−	2.99221i	0.0617771	−	0.107001i
$783$		0			0
$784$	2.87225	−	4.97488i	0.102580	−	0.177674i
$785$		−	2.18459i		−	0.0779712i
$786$		0			0
$787$	−5.68500	+	3.28224i	−0.202648	+	0.116999i	−0.597890	−	0.801578i	$-0.703994\pi$
$787$	−5.68500	+	3.28224i	−0.202648	+	0.116999i	0.395242	+	0.918577i	$0.370661\pi$
$788$	19.9028	+	11.4909i	0.709008	+	0.409346i
$789$		0			0
$790$	−0.159662	+	0.276543i	−0.00568053	+	0.00983898i
$791$	3.83202			0.136251
$792$		0			0
$793$	−6.32220	−	3.65012i	−0.224508	−	0.129620i
$794$	−16.3842			−0.581452
$795$		0			0
$796$	12.3322			0.437102
$797$	−14.0122	−	24.2699i	−0.496339	−	0.859684i	0.503652	−	0.863906i	$-0.331989\pi$
$797$	−14.0122	−	24.2699i	−0.496339	−	0.859684i	−0.999991	+	0.00422263i	$0.998656\pi$
$798$		0			0
$799$	29.3942	−	50.9122i	1.03989	−	1.80115i
$800$	14.4011	−	24.9435i	0.509158	−	0.881887i
$801$		0			0
$802$	−5.88981	−	10.2015i	−0.207976	−	0.360226i
$803$	−4.53936	+	2.62080i	−0.160191	+	0.0924860i
$804$		0			0
$805$	−0.132311	−	0.229169i	−0.00466334	−	0.00807714i
$806$	−13.7757	−	23.8602i	−0.485228	−	0.840440i
$807$		0			0
$808$		−	18.0361i		−	0.634506i
$809$		−	32.3776i		−	1.13834i	−0.822221	−	0.569168i	$-0.807266\pi$
$809$		−	32.3776i		−	1.13834i	0.822221	−	0.569168i	$-0.192734\pi$
$810$		0			0
$811$	6.65521	−	3.84239i	0.233696	−	0.134924i	−0.378580	−	0.925569i	$-0.623588\pi$
$811$	6.65521	−	3.84239i	0.233696	−	0.134924i	0.612276	+	0.790644i	$0.290254\pi$
$812$	−1.29092	−	2.23595i	−0.0453025	−	0.0784663i
$813$		0			0
$814$	−14.8086			−0.519041
$815$			0.922261i			0.0323054i
$816$		0			0
$817$	2.52941	+	3.98959i	0.0884928	+	0.139578i
$818$			15.7816i			0.551791i
$819$		0			0
$820$	1.43962	+	0.831164i	0.0502737	+	0.0290255i
$821$			55.2775i			1.92920i	0.263724	+	0.964598i	$0.415049\pi$
$821$			55.2775i			1.92920i	−0.263724	+	0.964598i	$0.584951\pi$
$822$		0			0
$823$	−7.96903	+	13.8028i	−0.277783	+	0.481134i	−0.970833	−	0.239755i	$-0.922933\pi$
$823$	−7.96903	+	13.8028i	−0.277783	+	0.481134i	0.693051	+	0.720889i	$0.256266\pi$
$824$	0.703709	−	0.406287i	0.0245149	−	0.0141537i
$825$		0			0
$826$	−13.0876			−0.455376
$827$	−5.61139	−	9.71922i	−0.195127	−	0.337970i	0.751815	−	0.659374i	$-0.229179\pi$
$827$	−5.61139	−	9.71922i	−0.195127	−	0.337970i	−0.946942	+	0.321404i	$0.895845\pi$
$828$		0			0
$829$			27.7051i			0.962238i	0.876655	+	0.481119i	$0.159769\pi$
$829$			27.7051i			0.962238i	−0.876655	+	0.481119i	$0.840231\pi$
$830$	−0.332721			−0.0115489
$831$		0			0
$832$	−5.58112	−	3.22226i	−0.193490	−	0.111712i
$833$		−	18.4127i		−	0.637963i
$834$		0			0
$835$	0.506335	+	0.292333i	0.0175224	+	0.0101166i
$836$	26.5113	−	16.8082i	0.916912	−	0.581324i
$837$		0			0
$838$	−4.64587	−	2.68229i	−0.160489	−	0.0926583i
$839$	19.5478	+	33.8578i	0.674865	+	1.16890i	0.976508	+	0.215480i	$0.0691317\pi$
$839$	19.5478	+	33.8578i	0.674865	+	1.16890i	−0.301643	+	0.953421i	$0.597535\pi$
$840$		0			0
$841$	−28.0894			−0.968599
$842$	−16.5281	−	9.54249i	−0.569595	−	0.328856i
$843$		0			0
$844$	15.5802	+	8.99523i	0.536293	+	0.309629i
$845$	3.59821	−	2.07743i	0.123782	−	0.0714656i
$846$		0			0
$847$	18.9392			0.650759
$848$	1.86517	−	3.23057i	0.0640501	−	0.110938i
$849$		0			0
$850$		−	15.8113i		−	0.542322i
$851$	−2.55192	+	4.42005i	−0.0874785	+	0.151517i
$852$		0			0
$853$	−2.98578	−	5.17153i	−0.102231	−	0.177070i	0.810372	−	0.585915i	$-0.199265\pi$
$853$	−2.98578	−	5.17153i	−0.102231	−	0.177070i	−0.912604	+	0.408845i	$0.865932\pi$
$854$	1.32122			0.0452112
$855$		0			0
$856$	−28.4230			−0.971478
$857$	−25.2365	−	43.7108i	−0.862061	−	1.49313i	−0.869936	−	0.493165i	$-0.835840\pi$
$857$	−25.2365	−	43.7108i	−0.862061	−	1.49313i	0.00787473	−	0.999969i	$-0.497493\pi$
$858$		0			0
$859$	6.41938	−	11.1187i	0.219026	−	0.379365i	−0.735484	−	0.677542i	$-0.763045\pi$
$859$	6.41938	−	11.1187i	0.219026	−	0.379365i	0.954511	+	0.298177i	$0.0963786\pi$
$860$		−	0.231702i		−	0.00790098i
$861$		0			0
$862$	2.29588	−	3.97658i	0.0781979	−	0.135443i
$863$	23.6047			0.803512			0.401756	−	0.915747i	$-0.368400\pi$
$863$	23.6047			0.803512			0.401756	+	0.915747i	$0.368400\pi$
$864$		0			0
$865$	−1.30789	+	0.755112i	−0.0444697	+	0.0256746i
$866$	20.1085	+	11.6097i	0.683316	+	0.394513i
$867$		0			0
$868$	−14.5585	−	8.40535i	−0.494148	−	0.285296i
$869$	−15.9014			−0.539419
$870$		0			0
$871$	14.5148	+	25.1404i	0.491815	+	0.851848i
$872$	21.4444	+	12.3809i	0.726198	+	0.419271i
$873$		0			0
$874$	0.132970	+	3.20629i	0.00449777	+	0.108454i
$875$	−2.10149	−	1.21330i	−0.0710435	−	0.0410170i
$876$		0			0
$877$			32.1508i			1.08566i	0.839844	+	0.542828i	$0.182647\pi$
$877$			32.1508i			1.08566i	−0.839844	+	0.542828i	$0.817353\pi$
$878$	−8.08515	−	4.66797i	−0.272861	−	0.157536i
$879$		0			0
$880$	−0.947528			−0.0319412
$881$			51.5651i			1.73727i	0.495449	+	0.868637i	$0.335003\pi$
$881$			51.5651i			1.73727i	−0.495449	+	0.868637i	$0.664997\pi$
$882$		0			0
$883$	11.6957	+	20.2576i	0.393592	+	0.681722i	0.992920	−	0.118781i	$-0.0378988\pi$
$883$	11.6957	+	20.2576i	0.393592	+	0.681722i	−0.599328	+	0.800504i	$0.704565\pi$
$884$	47.4559			1.59611
$885$		0			0
$886$	15.7887	−	9.11564i	0.530433	−	0.306246i
$887$	10.7007	−	18.5341i	0.359294	−	0.622315i	−0.628549	−	0.777770i	$-0.716351\pi$
$887$	10.7007	−	18.5341i	0.359294	−	0.622315i	0.987843	+	0.155455i	$0.0496843\pi$
$888$		0			0
$889$			8.99677i			0.301742i
$890$	1.26540	+	0.730577i	0.0424162	+	0.0244890i
$891$		0			0
$892$		−	32.1511i		−	1.07650i
$893$	2.26247	+	54.5548i	0.0757107	+	1.82561i
$894$		0			0
$895$			0.716547i			0.0239515i
$896$	−19.1198			−0.638747
$897$		0			0
$898$	−0.602673	−	1.04386i	−0.0201115	−	0.0348341i
$899$	5.13488	−	2.96463i	0.171258	−	0.0988758i
$900$		0			0
$901$		−	11.9568i		−	0.398338i
$902$		−	24.5536i		−	0.817546i
$903$		0			0
$904$	2.61741	+	4.53349i	0.0870538	+	0.150782i
$905$	−0.376668	−	0.652409i	−0.0125209	−	0.0216868i
$906$		0			0
$907$	30.4962	−	17.6070i	1.01261	−	0.584631i	0.100656	−	0.994921i	$-0.467906\pi$
$907$	30.4962	−	17.6070i	1.01261	−	0.584631i	0.911955	+	0.410290i	$0.134573\pi$
$908$	−18.4124	−	31.8911i	−0.611036	−	1.05834i
$909$		0			0
$910$	−0.539037	+	0.933640i	−0.0178689	+	0.0309499i
$911$	5.48367	−	9.49800i	0.181682	−	0.314683i	−0.760771	−	0.649020i	$-0.775179\pi$
$911$	5.48367	−	9.49800i	0.181682	−	0.314683i	0.942454	+	0.334337i	$0.108512\pi$
$912$		0			0
$913$	−8.28426	−	14.3488i	−0.274169	−	0.474874i
$914$	−7.32801			−0.242389
$915$		0			0
$916$	−27.6067			−0.912151
$917$	23.8988	+	13.7980i	0.789208	+	0.455650i
$918$		0			0
$919$	−34.7810			−1.14732			−0.573659	−	0.819094i	$-0.694477\pi$
$919$	−34.7810			−1.14732			−0.573659	+	0.819094i	$0.694477\pi$
$920$	0.180746	−	0.313061i	0.00595902	−	0.0103213i
$921$		0			0
$922$	12.1455	+	7.01219i	0.399990	+	0.230934i
$923$	−45.4103	+	26.2177i	−1.49470	+	0.862965i
$924$		0			0
$925$			23.3562i			0.767947i
$926$	8.91295	−	15.4377i	0.292898	−	0.507314i
$927$		0			0
$928$	2.75913	−	4.77895i	0.0905727	−	0.156877i
$929$	−31.7219	+	18.3147i	−1.04076	+	0.600885i	−0.920049	−	0.391803i	$-0.871852\pi$
$929$	−31.7219	+	18.3147i	−1.04076	+	0.600885i	−0.120714	+	0.992687i	$0.538518\pi$
$930$		0			0
$931$	9.15705	+	14.4432i	0.300110	+	0.473358i
$932$	−1.81045	+	1.04526i	−0.0593033	+	0.0342388i
$933$		0			0
$934$	−7.04171	+	4.06553i	−0.230412	+	0.133028i
$935$	−2.63020	+	1.51855i	−0.0860167	+	0.0496618i
$936$		0			0
$937$	−7.00421	−	12.1317i	−0.228818	−	0.396324i	0.728640	−	0.684897i	$-0.240153\pi$
$937$	−7.00421	−	12.1317i	−0.228818	−	0.396324i	−0.957458	+	0.288573i	$0.906819\pi$
$938$	−4.54998	−	2.62693i	−0.148562	−	0.0857723i
$939$		0			0
$940$	1.33909	−	2.31938i	0.0436764	−	0.0756497i
$941$	−7.30531	+	12.6532i	−0.238146	+	0.412481i	−0.960182	−	0.279374i	$-0.909873\pi$
$941$	−7.30531	+	12.6532i	−0.238146	+	0.412481i	0.722036	+	0.691855i	$0.243206\pi$
$942$		0			0
$943$	−7.32872	−	4.23124i	−0.238656	−	0.137788i
$944$	8.07569	+	13.9875i	0.262841	+	0.455254i
$945$		0			0
$946$	−2.96387	+	1.71119i	−0.0963638	+	0.0556357i
$947$	17.0322	−	9.83353i	0.553471	−	0.319547i	−0.197050	−	0.980394i	$-0.563136\pi$
$947$	17.0322	−	9.83353i	0.553471	−	0.319547i	0.750521	+	0.660847i	$0.229803\pi$
$948$		0			0
$949$	6.37383	−	3.67993i	0.206903	−	0.119456i
$950$	7.86330	+	12.4026i	0.255119	+	0.402395i
$951$		0			0
$952$	−17.0823	+	9.86247i	−0.553641	+	0.319645i
$953$	−5.16671	+	8.94901i	−0.167366	+	0.289887i	−0.937493	−	0.348004i	$-0.886860\pi$
$953$	−5.16671	+	8.94901i	−0.167366	+	0.289887i	0.770127	+	0.637891i	$0.220193\pi$
$954$		0			0
$955$	0.869582	−	1.50616i	0.0281390	−	0.0487382i
$956$		−	10.9642i		−	0.354606i
$957$		0			0
$958$	20.5679	−	11.8749i	0.664519	−	0.383660i
$959$	4.98921	+	2.88052i	0.161110	+	0.0930170i
$960$		0			0
$961$	3.80301	−	6.58701i	0.122678	−	0.212484i
$962$	20.7931			0.670398
$963$		0			0
$964$	−22.1620	−	12.7953i	−0.713791	−	0.412107i
$965$	−0.0165315			−0.000532167
$966$		0			0
$967$	−19.6447			−0.631732			−0.315866	−	0.948804i	$-0.602295\pi$
$967$	−19.6447			−0.631732			−0.315866	+	0.948804i	$0.602295\pi$
$968$	12.9362	+	22.4061i	0.415784	+	0.720160i
$969$		0			0
$970$	−0.682532	+	1.18218i	−0.0219148	+	0.0379575i
$971$	−11.8669	+	20.5541i	−0.380828	+	0.659614i	−0.991181	−	0.132516i	$-0.957694\pi$
$971$	−11.8669	+	20.5541i	−0.380828	+	0.659614i	0.610353	+	0.792130i	$0.291028\pi$
$972$		0			0
$973$	14.1798	+	24.5601i	0.454583	+	0.787360i
$974$	−8.26572	+	4.77222i	−0.264851	+	0.152912i
$975$		0			0
$976$	−0.815257	−	1.41207i	−0.0260957	−	0.0451991i
$977$	8.38318	+	14.5201i	0.268202	+	0.464539i	0.968397	−	0.249412i	$-0.0802373\pi$
$977$	8.38318	+	14.5201i	0.268202	+	0.464539i	−0.700196	+	0.713951i	$0.746904\pi$
$978$		0			0
$979$			72.7611i			2.32546i
$980$		−	0.838817i		−	0.0267950i
$981$		0			0
$982$	17.3224	−	10.0011i	0.552780	−	0.319148i
$983$	4.29295	+	7.43561i	0.136924	+	0.237159i	0.926331	−	0.376711i	$-0.122945\pi$
$983$	4.29295	+	7.43561i	0.136924	+	0.237159i	−0.789407	+	0.613870i	$0.789612\pi$
$984$		0			0
$985$	2.06518			0.0658021
$986$		−	3.02929i		−	0.0964723i
$987$		0			0
$988$	−37.2252	+	23.6008i	−1.18429	+	0.750843i
$989$			1.17954i			0.0375071i
$990$		0			0
$991$	10.7837	+	6.22600i	0.342557	+	0.197775i	0.661402	−	0.750031i	$-0.269962\pi$
$991$	10.7837	+	6.22600i	0.342557	+	0.197775i	−0.318845	+	0.947807i	$0.603295\pi$
$992$		−	35.9300i		−	1.14078i
$993$		0			0
$994$	4.74495	−	8.21850i	0.150501	−	0.260675i
$995$	0.959719	−	0.554094i	0.0304251	−	0.0175660i
$996$		0			0
$997$	−3.50898			−0.111130			−0.0555652	−	0.998455i	$-0.517696\pi$
$997$	−3.50898			−0.111130			−0.0555652	+	0.998455i	$0.517696\pi$
$998$	−12.0904	−	20.9412i	−0.382715	−	0.662881i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.k.a.8.10		36
3.2	odd	2		171.2.k.a.65.9	yes	36
9.4	even	3		171.2.t.a.122.9	yes	36
9.5	odd	6		513.2.t.a.179.10		36
19.12	odd	6		513.2.t.a.278.10		36
57.50	even	6		171.2.t.a.164.9	yes	36
171.31	odd	6		171.2.k.a.50.9	✓	36
171.50	even	6	inner	513.2.k.a.449.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.9	✓	36	171.31	odd	6
171.2.k.a.65.9	yes	36	3.2	odd	2
171.2.t.a.122.9	yes	36	9.4	even	3
171.2.t.a.164.9	yes	36	57.50	even	6
513.2.k.a.8.10		36	1.1	even	1	trivial
513.2.k.a.449.10		36	171.50	even	6	inner
513.2.t.a.179.10		36	9.5	odd	6
513.2.t.a.278.10		36	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.338203 + 0.585784i) q^{2} +(0.771238 - 1.33582i) q^{4} -0.138609i q^{5} +(0.877021 - 1.51904i) q^{7} +2.39615 q^{8} +(0.0811952 - 0.0468781i) q^{10} +(4.04328 + 2.33439i) q^{11} +(-5.67727 - 3.27778i) q^{13} +1.18644 q^{14} +(-0.732093 - 1.26802i) q^{16} +(-4.06437 - 2.34656i) q^{17} +(4.35516 - 0.180615i) q^{19} +(-0.185158 - 0.106901i) q^{20} +3.15798i q^{22} +(0.942590 + 0.544205i) q^{23} +4.98079 q^{25} -4.43421i q^{26} +(-1.35278 - 2.34309i) q^{28} +0.954272 q^{29} +(5.38094 - 3.10669i) q^{31} +(2.89134 - 5.00795i) q^{32} -3.17445i q^{34} +(-0.210554 - 0.121563i) q^{35} +4.68926i q^{37} +(1.57873 + 2.49010i) q^{38} -0.332129i q^{40} -7.77509 q^{41} +(0.541863 + 0.938533i) q^{43} +(6.23666 - 3.60074i) q^{44} +0.736205i q^{46} +12.5265i q^{47} +(1.96167 + 3.39771i) q^{49} +(1.68451 + 2.91767i) q^{50} +(-8.75706 + 5.05589i) q^{52} +(1.27386 + 2.20639i) q^{53} +(0.323568 - 0.560437i) q^{55} +(2.10147 - 3.63986i) q^{56} +(0.322737 + 0.558997i) q^{58} -11.0310 q^{59} +1.11360 q^{61} +(3.63969 + 2.10138i) q^{62} +0.983063 q^{64} +(-0.454331 + 0.786924i) q^{65} +(-3.83497 - 2.21412i) q^{67} +(-6.26919 + 3.61952i) q^{68} -0.164452i q^{70} +(3.99931 - 6.92701i) q^{71} +(-0.561346 + 0.972280i) q^{73} +(-2.74689 + 1.58592i) q^{74} +(3.11759 - 5.95702i) q^{76} +(7.09208 - 4.09461i) q^{77} +(-2.94960 + 1.70295i) q^{79} +(-0.175760 + 0.101475i) q^{80} +(-2.62956 - 4.55452i) q^{82} +(-3.07334 - 1.77440i) q^{83} +(-0.325256 + 0.563360i) q^{85} +(-0.366519 + 0.634829i) q^{86} +(9.68830 + 5.59354i) q^{88} +(7.79231 + 13.4967i) q^{89} +(-9.95817 + 5.74935i) q^{91} +(1.45392 - 0.839423i) q^{92} +(-7.33782 + 4.23649i) q^{94} +(-0.0250349 - 0.603666i) q^{95} +(-12.6091 + 7.27986i) q^{97} +(-1.32688 + 2.29823i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 15 q^{4} - q^{7} - 12 q^{8} - 6 q^{10} + 9 q^{11} - 6 q^{13} + 6 q^{14} - 9 q^{16} + 27 q^{17} + q^{19} - 9 q^{20} - 9 q^{23} - 22 q^{25} + 2 q^{28} + 24 q^{29} + 12 q^{31} + 15 q^{32}+ \cdots + 84 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 15 * q^4 - q^7 - 12 * q^8 - 6 * q^10 + 9 * q^11 - 6 * q^13 + 6 * q^14 - 9 * q^16 + 27 * q^17 + q^19 - 9 * q^20 - 9 * q^23 - 22 * q^25 + 2 * q^28 + 24 * q^29 + 12 * q^31 + 15 * q^32 - 15 * q^35 + 18 * q^38 - 36 * q^41 + 3 * q^43 - 66 * q^44 - 9 * q^49 - 3 * q^50 + 15 * q^52 + 12 * q^53 - 7 * q^55 - 6 * q^56 - 6 * q^58 + 18 * q^59 - 16 * q^61 + 12 * q^62 + 12 * q^64 + 18 * q^65 + 27 * q^67 - 60 * q^68 - 9 * q^71 - 18 * q^73 - 90 * q^74 - 23 * q^76 + 6 * q^77 - 6 * q^79 + 12 * q^80 - 9 * q^82 + 9 * q^83 + 11 * q^85 - 51 * q^86 + 3 * q^88 + 18 * q^89 + 27 * q^91 + 93 * q^92 + 12 * q^94 + 24 * q^97 + 84 * q^98

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