LMFDB - Embedded newform 504.2.cx.a.185.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(185,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("504.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (of order $6$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.8
Character	$\chi$	$=$	504.185
Dual form			504.2.cx.a.425.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03050 + 1.39215i) q^{3} +2.20884 q^{5} +(2.16520 + 1.52049i) q^{7} +(-0.876153 - 2.86921i) q^{9} +O(q^{10})$	\(q+(-1.03050 + 1.39215i) q^{3} +2.20884 q^{5} +(2.16520 + 1.52049i) q^{7} +(-0.876153 - 2.86921i) q^{9} -0.181913i q^{11} +(2.50424 + 1.44582i) q^{13} +(-2.27620 + 3.07503i) q^{15} +(1.98511 - 3.43832i) q^{17} +(0.867067 - 0.500601i) q^{19} +(-4.34798 + 1.44743i) q^{21} +5.61313i q^{23} -0.121025 q^{25} +(4.89724 + 1.73697i) q^{27} +(0.703311 - 0.406057i) q^{29} +(-6.89908 + 3.98319i) q^{31} +(0.253250 + 0.187461i) q^{33} +(4.78259 + 3.35852i) q^{35} +(1.25614 + 2.17569i) q^{37} +(-4.59341 + 1.99636i) q^{39} +(-0.612906 + 1.06158i) q^{41} +(5.47716 + 9.48671i) q^{43} +(-1.93528 - 6.33762i) q^{45} +(3.57551 - 6.19296i) q^{47} +(2.37622 + 6.58434i) q^{49} +(2.74100 + 6.30675i) q^{51} +(-1.75586 - 1.01374i) q^{53} -0.401817i q^{55} +(-0.196598 + 1.72295i) q^{57} +(-3.27911 - 5.67958i) q^{59} +(6.97275 + 4.02572i) q^{61} +(2.46555 - 7.54460i) q^{63} +(5.53147 + 3.19359i) q^{65} +(-3.44505 - 5.96701i) q^{67} +(-7.81431 - 5.78431i) q^{69} -11.4168i q^{71} +(-10.1861 - 5.88094i) q^{73} +(0.124716 - 0.168485i) q^{75} +(0.276597 - 0.393879i) q^{77} +(-6.35501 + 11.0072i) q^{79} +(-7.46471 + 5.02773i) q^{81} +(-7.19085 - 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(-0.159468 + 1.39755i) q^{87} +(-7.11375 - 12.3214i) q^{89} +(3.22383 + 6.93818i) q^{91} +(1.56429 - 13.7092i) q^{93} +(1.91521 - 1.10575i) q^{95} +(-3.01040 + 1.73805i) q^{97} +(-0.521946 + 0.159384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.03050	+	1.39215i	−0.594958	+	0.803757i
$3$	−1.03050	+	1.39215i	−0.594958	+	0.803757i
$4$		0			0
$5$	2.20884			0.987823			0.493912	−	0.869512i	$-0.335567\pi$
$5$	2.20884			0.987823			0.493912	+	0.869512i	$0.335567\pi$
$6$		0			0
$7$	2.16520	+	1.52049i	0.818370	+	0.574691i
$7$	2.16520	+	1.52049i	0.818370	+	0.574691i
$8$		0			0
$9$	−0.876153	−	2.86921i	−0.292051	−	0.956403i
$10$		0			0
$11$		−	0.181913i		−	0.0548488i	−0.999624	−	0.0274244i	$-0.991269\pi$
$11$		−	0.181913i		−	0.0548488i	0.999624	−	0.0274244i	$-0.00873056\pi$
$12$		0			0
$13$	2.50424	+	1.44582i	0.694551	+	0.400999i	0.805315	−	0.592847i	$-0.201996\pi$
$13$	2.50424	+	1.44582i	0.694551	+	0.400999i	−0.110763	+	0.993847i	$0.535330\pi$
$14$		0			0
$15$	−2.27620	+	3.07503i	−0.587713	+	0.793970i
$16$		0			0
$17$	1.98511	−	3.43832i	0.481461	−	0.833915i	−0.518313	−	0.855191i	$-0.673440\pi$
$17$	1.98511	−	3.43832i	0.481461	−	0.833915i	0.999774	+	0.0212765i	$0.00677302\pi$
$18$		0			0
$19$	0.867067	−	0.500601i	0.198919	−	0.114846i	−0.397232	−	0.917718i	$-0.630029\pi$
$19$	0.867067	−	0.500601i	0.198919	−	0.114846i	0.596151	+	0.802872i	$0.296696\pi$
$20$		0			0
$21$	−4.34798	+	1.44743i	−0.948808	+	0.315854i
$22$		0			0
$23$			5.61313i			1.17042i	0.810882	+	0.585210i	$0.198988\pi$
$23$			5.61313i			1.17042i	−0.810882	+	0.585210i	$0.801012\pi$
$24$		0			0
$25$	−0.121025			−0.0242050
$26$		0			0
$27$	4.89724	+	1.73697i	0.942473	+	0.334281i
$28$		0			0
$29$	0.703311	−	0.406057i	0.130602	−	0.0754028i	−0.433276	−	0.901261i	$-0.642642\pi$
$29$	0.703311	−	0.406057i	0.130602	−	0.0754028i	0.563877	+	0.825859i	$0.309309\pi$
$30$		0			0
$31$	−6.89908	+	3.98319i	−1.23911	+	0.715401i	−0.968913	−	0.247403i	$-0.920423\pi$
$31$	−6.89908	+	3.98319i	−1.23911	+	0.715401i	−0.270199	+	0.962805i	$0.587089\pi$
$32$		0			0
$33$	0.253250	+	0.187461i	0.0440851	+	0.0326327i
$34$		0			0
$35$	4.78259	+	3.35852i	0.808405	+	0.567693i
$36$		0			0
$37$	1.25614	+	2.17569i	0.206507	+	0.357681i	0.950612	−	0.310382i	$-0.100457\pi$
$37$	1.25614	+	2.17569i	0.206507	+	0.357681i	−0.744105	+	0.668063i	$0.767124\pi$
$38$		0			0
$39$	−4.59341	+	1.99636i	−0.735535	+	0.319673i
$40$		0			0
$41$	−0.612906	+	1.06158i	−0.0957198	+	0.165792i	−0.909909	−	0.414808i	$-0.863849\pi$
$41$	−0.612906	+	1.06158i	−0.0957198	+	0.165792i	0.814189	+	0.580600i	$0.197182\pi$
$42$		0			0
$43$	5.47716	+	9.48671i	0.835259	+	1.44671i	0.893820	+	0.448426i	$0.148015\pi$
$43$	5.47716	+	9.48671i	0.835259	+	1.44671i	−0.0585613	+	0.998284i	$0.518651\pi$
$44$		0			0
$45$	−1.93528	−	6.33762i	−0.288495	−	0.944757i
$46$		0			0
$47$	3.57551	−	6.19296i	0.521542	−	0.903336i	−0.478145	−	0.878281i	$-0.658691\pi$
$47$	3.57551	−	6.19296i	0.521542	−	0.903336i	0.999686	−	0.0250552i	$-0.00797616\pi$
$48$		0			0
$49$	2.37622	+	6.58434i	0.339460	+	0.940620i
$50$		0			0
$51$	2.74100	+	6.30675i	0.383816	+	0.883121i
$52$		0			0
$53$	−1.75586	−	1.01374i	−0.241186	−	0.139249i	0.374536	−	0.927212i	$-0.377802\pi$
$53$	−1.75586	−	1.01374i	−0.241186	−	0.139249i	−0.615722	+	0.787964i	$0.711135\pi$
$54$		0			0
$55$		−	0.401817i		−	0.0541810i
$56$		0			0
$57$	−0.196598	+	1.72295i	−0.0260401	+	0.228211i
$58$		0			0
$59$	−3.27911	−	5.67958i	−0.426903	−	0.739418i	0.569693	−	0.821858i	$-0.307062\pi$
$59$	−3.27911	−	5.67958i	−0.426903	−	0.739418i	−0.996596	+	0.0824396i	$0.973729\pi$
$60$		0			0
$61$	6.97275	+	4.02572i	0.892769	+	0.515440i	0.874847	−	0.484399i	$-0.160962\pi$
$61$	6.97275	+	4.02572i	0.892769	+	0.515440i	0.0179215	+	0.999839i	$0.494295\pi$
$62$		0			0
$63$	2.46555	−	7.54460i	0.310630	−	0.950531i
$64$		0			0
$65$	5.53147	+	3.19359i	0.686094	+	0.396117i
$66$		0			0
$67$	−3.44505	−	5.96701i	−0.420880	−	0.728986i	0.575145	−	0.818051i	$-0.304945\pi$
$67$	−3.44505	−	5.96701i	−0.420880	−	0.728986i	−0.996026	+	0.0890650i	$0.971612\pi$
$68$		0			0
$69$	−7.81431	−	5.78431i	−0.940733	−	0.696350i
$70$		0			0
$71$		−	11.4168i		−	1.35492i	−0.735560	−	0.677460i	$-0.763081\pi$
$71$		−	11.4168i		−	1.35492i	0.735560	−	0.677460i	$-0.236919\pi$
$72$		0			0
$73$	−10.1861	−	5.88094i	−1.19219	−	0.688312i	−0.233388	−	0.972384i	$-0.574981\pi$
$73$	−10.1861	−	5.88094i	−1.19219	−	0.688312i	−0.958803	+	0.284072i	$0.908315\pi$
$74$		0			0
$75$	0.124716	−	0.168485i	0.0144009	−	0.0194549i
$76$		0			0
$77$	0.276597	−	0.393879i	0.0315211	−	0.0448867i
$78$		0			0
$79$	−6.35501	+	11.0072i	−0.714994	+	1.23841i	0.247968	+	0.968768i	$0.420237\pi$
$79$	−6.35501	+	11.0072i	−0.714994	+	1.23841i	−0.962962	+	0.269638i	$0.913096\pi$
$80$		0			0
$81$	−7.46471	+	5.02773i	−0.829412	+	0.558637i
$82$		0			0
$83$	−7.19085	−	12.4549i	−0.789298	−	1.36710i	−0.926397	−	0.376547i	$-0.877111\pi$
$83$	−7.19085	−	12.4549i	−0.789298	−	1.36710i	0.137099	−	0.990557i	$-0.456222\pi$
$84$		0			0
$85$	4.38480	−	7.59470i	0.475598	−	0.823760i
$86$		0			0
$87$	−0.159468	+	1.39755i	−0.0170968	+	0.149833i
$88$		0			0
$89$	−7.11375	−	12.3214i	−0.754055	−	1.30606i	−0.945843	−	0.324626i	$-0.894762\pi$
$89$	−7.11375	−	12.3214i	−0.754055	−	1.30606i	0.191787	−	0.981437i	$-0.438572\pi$
$90$		0			0
$91$	3.22383	+	6.93818i	0.337949	+	0.727319i
$92$		0			0
$93$	1.56429	−	13.7092i	0.162210	−	1.42158i
$94$		0			0
$95$	1.91521	−	1.10575i	0.196497	−	0.113447i
$96$		0			0
$97$	−3.01040	+	1.73805i	−0.305659	+	0.176473i	−0.644982	−	0.764197i	$-0.723135\pi$
$97$	−3.01040	+	1.73805i	−0.305659	+	0.176473i	0.339323	+	0.940670i	$0.389802\pi$
$98$		0			0
$99$	−0.521946	+	0.159384i	−0.0524576	+	0.0160187i
$100$		0			0
$101$	9.50563			0.945846			0.472923	−	0.881104i	$-0.343199\pi$
$101$	9.50563			0.945846			0.472923	+	0.881104i	$0.343199\pi$
$102$		0			0
$103$		−	8.38505i		−	0.826204i	−0.910685	−	0.413102i	$-0.864445\pi$
$103$		−	8.38505i		−	0.826204i	0.910685	−	0.413102i	$-0.135555\pi$
$104$		0			0
$105$	−9.60400	+	3.19713i	−0.937254	+	0.312008i
$106$		0			0
$107$	12.7310	−	7.35026i	1.23075	−	0.710576i	0.263567	−	0.964641i	$-0.415101\pi$
$107$	12.7310	−	7.35026i	1.23075	−	0.710576i	0.967187	+	0.254065i	$0.0817677\pi$
$108$		0			0
$109$	8.35648	−	14.4738i	0.800405	−	1.38634i	−0.118944	−	0.992901i	$-0.537951\pi$
$109$	8.35648	−	14.4738i	0.800405	−	1.38634i	0.919350	−	0.393442i	$-0.128716\pi$
$110$		0			0
$111$	−4.32333	−	0.493315i	−0.410352	−	0.0468234i
$112$		0			0
$113$	−1.19493	−	0.689894i	−0.112410	−	0.0648998i	0.442741	−	0.896650i	$-0.354006\pi$
$113$	−1.19493	−	0.689894i	−0.112410	−	0.0648998i	−0.555151	+	0.831750i	$0.687339\pi$
$114$		0			0
$115$			12.3985i			1.15617i
$116$		0			0
$117$	1.95427	−	8.45195i	0.180673	−	0.781383i
$118$		0			0
$119$	9.52611	−	4.42632i	0.873257	−	0.405760i
$120$		0			0
$121$	10.9669			0.996992
$122$		0			0
$123$	−0.846285	−	1.94721i	−0.0763069	−	0.175574i
$124$		0			0
$125$	−11.3115			−1.01173
$126$		0			0
$127$	−11.9684			−1.06202			−0.531012	−	0.847364i	$-0.678188\pi$
$127$	−11.9684			−1.06202			−0.531012	+	0.847364i	$0.678188\pi$
$128$		0			0
$129$	−18.8511	−	2.15101i	−1.65975	−	0.189386i
$130$		0			0
$131$	−7.35396			−0.642519			−0.321259	−	0.946991i	$-0.604106\pi$
$131$	−7.35396			−0.642519			−0.321259	+	0.946991i	$0.604106\pi$
$132$		0			0
$133$	2.63854	+	0.234462i	0.228790	+	0.0203305i
$134$		0			0
$135$	10.8172	+	3.83670i	0.930997	+	0.330210i
$136$		0			0
$137$			16.4316i			1.40385i	0.712251	+	0.701925i	$0.247676\pi$
$137$			16.4316i			1.40385i	−0.712251	+	0.701925i	$0.752324\pi$
$138$		0			0
$139$	11.2110	+	6.47266i	0.950903	+	0.549004i	0.893361	−	0.449339i	$-0.148340\pi$
$139$	11.2110	+	6.47266i	0.950903	+	0.549004i	0.0575417	+	0.998343i	$0.481674\pi$
$140$		0			0
$141$	4.93697	+	11.3595i	0.415768	+	0.956639i
$142$		0			0
$143$	0.263014	−	0.455554i	0.0219944	−	0.0380953i
$144$		0			0
$145$	1.55350	−	0.896914i	0.129011	−	0.0744847i
$146$		0			0
$147$	−11.6151	−	3.47709i	−0.957995	−	0.286786i
$148$		0			0
$149$			15.2359i			1.24818i	0.781354	+	0.624088i	$0.214529\pi$
$149$			15.2359i			1.24818i	−0.781354	+	0.624088i	$0.785471\pi$
$150$		0			0
$151$	−13.6625			−1.11184			−0.555919	−	0.831236i	$-0.687634\pi$
$151$	−13.6625			−1.11184			−0.555919	+	0.831236i	$0.687634\pi$
$152$		0			0
$153$	−11.6045	−	2.68321i	−0.938169	−	0.216925i
$154$		0			0
$155$	−15.2390	+	8.79822i	−1.22402	+	0.706690i
$156$		0			0
$157$	10.2322	−	5.90757i	0.816619	−	0.471475i	−0.0326299	−	0.999468i	$-0.510388\pi$
$157$	10.2322	−	5.90757i	0.816619	−	0.471475i	0.849249	+	0.527992i	$0.177055\pi$
$158$		0			0
$159$	3.22069	−	1.39975i	0.255417	−	0.111008i
$160$		0			0
$161$	−8.53471	+	12.1536i	−0.672630	+	0.957836i
$162$		0			0
$163$	−4.35998	−	7.55170i	−0.341500	−	0.591495i	0.643212	−	0.765688i	$-0.277601\pi$
$163$	−4.35998	−	7.55170i	−0.341500	−	0.591495i	−0.984711	+	0.174194i	$0.944268\pi$
$164$		0			0
$165$	0.559389	+	0.414071i	0.0435483	+	0.0322354i
$166$		0			0
$167$	8.89862	−	15.4129i	0.688596	−	1.19268i	−0.283696	−	0.958914i	$-0.591561\pi$
$167$	8.89862	−	15.4129i	0.688596	−	1.19268i	0.972292	−	0.233769i	$-0.0751059\pi$
$168$		0			0
$169$	−2.31918	−	4.01695i	−0.178399	−	0.308996i
$170$		0			0
$171$	−2.19601	−	2.04919i	−0.167933	−	0.156706i
$172$		0			0
$173$	9.56015	−	16.5587i	0.726845	−	1.25893i	−0.231366	−	0.972867i	$-0.574319\pi$
$173$	9.56015	−	16.5587i	0.726845	−	1.25893i	0.958210	−	0.286065i	$-0.0923473\pi$
$174$		0			0
$175$	−0.262044	−	0.184017i	−0.0198086	−	0.0139104i
$176$		0			0
$177$	11.2859	+	1.28779i	0.848302	+	0.0967959i
$178$		0			0
$179$	−5.31891	−	3.07088i	−0.397554	−	0.229528i	0.287874	−	0.957668i	$-0.407052\pi$
$179$	−5.31891	−	3.07088i	−0.397554	−	0.229528i	−0.685428	+	0.728140i	$0.740385\pi$
$180$		0			0
$181$			11.1208i			0.826604i	0.910594	+	0.413302i	$0.135625\pi$
$181$			11.1208i			0.826604i	−0.910594	+	0.413302i	$0.864375\pi$
$182$		0			0
$183$	−12.7898	+	5.55861i	−0.945448	+	0.410904i
$184$		0			0
$185$	2.77460	+	4.80575i	0.203993	+	0.353326i
$186$		0			0
$187$	−0.625475	−	0.361118i	−0.0457393	−	0.0264076i
$188$		0			0
$189$	7.96246	+	11.2071i	0.579184	+	0.815197i
$190$		0			0
$191$	12.9342	+	7.46759i	0.935889	+	0.540336i	0.888669	−	0.458549i	$-0.151631\pi$
$191$	12.9342	+	7.46759i	0.935889	+	0.540336i	0.0472195	+	0.998885i	$0.484964\pi$
$192$		0			0
$193$	6.21387	+	10.7627i	0.447284	+	0.774719i	0.998208	−	0.0598363i	$-0.0190579\pi$
$193$	6.21387	+	10.7627i	0.447284	+	0.774719i	−0.550924	+	0.834556i	$0.685725\pi$
$194$		0			0
$195$	−10.1461	+	4.40963i	−0.726578	+	0.315780i
$196$		0			0
$197$			16.1512i			1.15073i	0.817897	+	0.575364i	$0.195140\pi$
$197$			16.1512i			1.15073i	−0.817897	+	0.575364i	$0.804860\pi$
$198$		0			0
$199$	−21.5762	−	12.4571i	−1.52950	−	0.883057i	−0.999383	−	0.0351325i	$-0.988815\pi$
$199$	−21.5762	−	12.4571i	−1.52950	−	0.883057i	−0.530117	−	0.847925i	$-0.677852\pi$
$200$		0			0
$201$	11.8571	+	1.35296i	0.836334	+	0.0954302i
$202$		0			0
$203$	2.14022	+	0.190181i	0.150214	+	0.0133481i
$204$		0			0
$205$	−1.35381	+	2.34487i	−0.0945542	+	0.163773i
$206$		0			0
$207$	16.1052	−	4.91796i	1.11939	−	0.341822i
$208$		0			0
$209$	−0.0910659	−	0.157731i	−0.00629916	−	0.0109105i
$210$		0			0
$211$	5.78631	−	10.0222i	0.398346	−	0.689955i	−0.595176	−	0.803595i	$-0.702918\pi$
$211$	5.78631	−	10.0222i	0.398346	−	0.689955i	0.993522	+	0.113640i	$0.0362510\pi$
$212$		0			0
$213$	15.8938	+	11.7649i	1.08903	+	0.806120i
$214$		0			0
$215$	12.0982	+	20.9546i	0.825088	+	1.42909i
$216$		0			0
$217$	−20.9943	−	1.86557i	−1.42519	−	0.126643i
$218$		0			0
$219$	18.6839	−	8.12025i	1.26254	−	0.548716i
$220$		0			0
$221$	9.94241	−	5.74025i	0.668799	−	0.386131i
$222$		0			0
$223$	13.9653	−	8.06285i	0.935183	−	0.539928i	0.0467358	−	0.998907i	$-0.485118\pi$
$223$	13.9653	−	8.06285i	0.935183	−	0.539928i	0.888447	+	0.458979i	$0.151785\pi$
$224$		0			0
$225$	0.106036	+	0.347246i	0.00706909	+	0.0231497i
$226$		0			0
$227$	−19.8036			−1.31441			−0.657206	−	0.753711i	$-0.728262\pi$
$227$	−19.8036			−1.31441			−0.657206	+	0.753711i	$0.728262\pi$
$228$		0			0
$229$		−	15.6001i		−	1.03088i	−0.856924	−	0.515442i	$-0.827628\pi$
$229$		−	15.6001i		−	1.03088i	0.856924	−	0.515442i	$-0.172372\pi$
$230$		0			0
$231$	0.263306	+	0.790955i	0.0173242	+	0.0520410i
$232$		0			0
$233$	−10.6450	+	6.14590i	−0.697378	+	0.402631i	−0.806370	−	0.591411i	$-0.798571\pi$
$233$	−10.6450	+	6.14590i	−0.697378	+	0.402631i	0.108992	+	0.994043i	$0.465238\pi$
$234$		0			0
$235$	7.89773	−	13.6793i	0.515191	−	0.892337i
$236$		0			0
$237$	−8.77483	−	20.1900i	−0.569987	−	1.31148i
$238$		0			0
$239$	−13.8058	−	7.97079i	−0.893024	−	0.515588i	−0.0180934	−	0.999836i	$-0.505760\pi$
$239$	−13.8058	−	7.97079i	−0.893024	−	0.515588i	−0.874930	+	0.484249i	$0.839093\pi$
$240$		0			0
$241$			20.6872i			1.33258i	0.745693	+	0.666290i	$0.232119\pi$
$241$			20.6872i			1.33258i	−0.745693	+	0.666290i	$0.767881\pi$
$242$		0			0
$243$	0.693013	−	15.5730i	0.0444568	−	0.999011i
$244$		0			0
$245$	5.24869	+	14.5438i	0.335327	+	0.929167i
$246$		0			0
$247$	2.89513			0.184212
$248$		0			0
$249$	24.7492	+	2.82402i	1.56842	+	0.178965i
$250$		0			0
$251$	7.66566			0.483852			0.241926	−	0.970295i	$-0.422221\pi$
$251$	7.66566			0.483852			0.241926	+	0.970295i	$0.422221\pi$
$252$		0			0
$253$	1.02110			0.0641961
$254$		0			0
$255$	6.05442	+	13.9306i	0.379143	+	0.872368i
$256$		0			0
$257$	−11.9297			−0.744157			−0.372078	−	0.928201i	$-0.621355\pi$
$257$	−11.9297			−0.744157			−0.372078	+	0.928201i	$0.621355\pi$
$258$		0			0
$259$	−0.588325	+	6.62076i	−0.0365568	+	0.411394i
$260$		0			0
$261$	−1.78127	−	1.66218i	−0.110258	−	0.102886i
$262$		0			0
$263$		−	7.72501i		−	0.476345i	−0.971223	−	0.238172i	$-0.923452\pi$
$263$		−	7.72501i		−	0.476345i	0.971223	−	0.238172i	$-0.0765483\pi$
$264$		0			0
$265$	−3.87841	−	2.23920i	−0.238249	−	0.137553i
$266$		0			0
$267$	24.4839	+	2.79374i	1.49839	+	0.170974i
$268$		0			0
$269$	−4.98739	+	8.63841i	−0.304086	+	0.526693i	−0.977058	−	0.212976i	$-0.931685\pi$
$269$	−4.98739	+	8.63841i	−0.304086	+	0.526693i	0.672971	+	0.739669i	$0.265018\pi$
$270$		0			0
$271$	3.61508	−	2.08717i	0.219600	−	0.126786i	−0.386165	−	0.922430i	$-0.626200\pi$
$271$	3.61508	−	2.08717i	0.219600	−	0.126786i	0.605765	+	0.795643i	$0.292867\pi$
$272$		0			0
$273$	−12.9811	−	2.66172i	−0.785653	−	0.161094i
$274$		0			0
$275$			0.0220160i			0.00132761i
$276$		0			0
$277$	4.45007			0.267379			0.133689	−	0.991023i	$-0.457318\pi$
$277$	4.45007			0.267379			0.133689	+	0.991023i	$0.457318\pi$
$278$		0			0
$279$	17.4732	+	16.3050i	1.04610	+	0.976156i
$280$		0			0
$281$	−24.5472	+	14.1723i	−1.46436	+	0.845451i	−0.999209	−	0.0397785i	$-0.987335\pi$
$281$	−24.5472	+	14.1723i	−1.46436	+	0.845451i	−0.465155	+	0.885229i	$0.654001\pi$
$282$		0			0
$283$	−10.0427	+	5.79815i	−0.596976	+	0.344664i	−0.767851	−	0.640628i	$-0.778674\pi$
$283$	−10.0427	+	5.79815i	−0.596976	+	0.344664i	0.170875	+	0.985293i	$0.445341\pi$
$284$		0			0
$285$	−0.434254	+	3.80573i	−0.0257230	+	0.225432i
$286$		0			0
$287$	−2.94119	+	1.36663i	−0.173613	+	0.0806696i
$288$		0			0
$289$	0.618645	+	1.07152i	0.0363909	+	0.0630308i
$290$		0			0
$291$	0.682576	−	5.98198i	0.0400133	−	0.350670i
$292$		0			0
$293$	14.4199	−	24.9760i	0.842418	−	1.45911i	−0.0454266	−	0.998968i	$-0.514465\pi$
$293$	14.4199	−	24.9760i	0.842418	−	1.45911i	0.887845	−	0.460143i	$-0.152202\pi$
$294$		0			0
$295$	−7.24302	−	12.5453i	−0.421705	−	0.730414i
$296$		0			0
$297$	0.315978	−	0.890871i	0.0183349	−	0.0516936i
$298$		0			0
$299$	−8.11560	+	14.0566i	−0.469337	+	0.812916i
$300$		0			0
$301$	−2.56529	+	28.8686i	−0.147861	+	1.66396i
$302$		0			0
$303$	−9.79552	+	13.2332i	−0.562738	+	0.760230i
$304$		0			0
$305$	15.4017	+	8.89216i	0.881898	+	0.509164i
$306$		0			0
$307$			10.8117i			0.617059i	0.951215	+	0.308529i	$0.0998368\pi$
$307$			10.8117i			0.617059i	−0.951215	+	0.308529i	$0.900163\pi$
$308$		0			0
$309$	11.6732	+	8.64077i	0.664067	+	0.491556i
$310$		0			0
$311$	8.59161	+	14.8811i	0.487185	+	0.843830i	0.999891	−	0.0147345i	$-0.00469032\pi$
$311$	8.59161	+	14.8811i	0.487185	+	0.843830i	−0.512706	+	0.858564i	$0.671357\pi$
$312$		0			0
$313$	−7.91893	−	4.57200i	−0.447604	−	0.258425i	0.259214	−	0.965820i	$-0.416537\pi$
$313$	−7.91893	−	4.57200i	−0.447604	−	0.258425i	−0.706818	+	0.707396i	$0.749870\pi$
$314$		0			0
$315$	5.44601	−	16.6648i	0.306848	−	0.938957i
$316$		0			0
$317$	0.984650	+	0.568488i	0.0553034	+	0.0319295i	0.527397	−	0.849619i	$-0.323168\pi$
$317$	0.984650	+	0.568488i	0.0553034	+	0.0319295i	−0.472093	+	0.881549i	$0.656501\pi$
$318$		0			0
$319$	−0.0738670	−	0.127941i	−0.00413576	−	0.00716334i
$320$		0			0
$321$	−2.88663	+	25.2979i	−0.161116	+	1.41199i
$322$		0			0
$323$		−	3.97500i		−	0.221175i
$324$		0			0
$325$	−0.303075	−	0.174981i	−0.0168116	−	0.00970618i
$326$		0			0
$327$	11.5384	+	26.5487i	0.638076	+	1.46815i
$328$		0			0
$329$	17.1580	−	7.97250i	0.945954	−	0.439538i
$330$		0			0
$331$	3.02394	−	5.23761i	0.166211	−	0.287885i	−0.770874	−	0.636988i	$-0.780180\pi$
$331$	3.02394	−	5.23761i	0.166211	−	0.287885i	0.937085	+	0.349102i	$0.113513\pi$
$332$		0			0
$333$	5.14194	−	5.51035i	0.281777	−	0.301965i
$334$		0			0
$335$	−7.60957	−	13.1802i	−0.415755	−	0.720110i
$336$		0			0
$337$	17.6873	−	30.6353i	0.963490	−	1.66881i	0.249871	−	0.968279i	$-0.419612\pi$
$337$	17.6873	−	30.6353i	0.963490	−	1.66881i	0.713619	−	0.700534i	$-0.247055\pi$
$338$		0			0
$339$	2.19181	−	0.952588i	0.119043	−	0.0517375i
$340$		0			0
$341$	0.724593	+	1.25503i	0.0392389	+	0.0679638i
$342$		0			0
$343$	−4.86643	+	17.8695i	−0.262762	+	0.964861i
$344$		0			0
$345$	−17.2606	−	12.7766i	−0.929278	−	0.687870i
$346$		0			0
$347$	−20.1007	+	11.6051i	−1.07906	+	0.622995i	−0.930643	−	0.365929i	$-0.880751\pi$
$347$	−20.1007	+	11.6051i	−1.07906	+	0.622995i	−0.148417	+	0.988925i	$0.547418\pi$
$348$		0			0
$349$	12.7248	−	7.34667i	0.681144	−	0.393258i	−0.119142	−	0.992877i	$-0.538014\pi$
$349$	12.7248	−	7.34667i	0.681144	−	0.393258i	0.800286	+	0.599619i	$0.204681\pi$
$350$		0			0
$351$	9.75250	+	11.4303i	0.520550	+	0.610107i
$352$		0			0
$353$	−13.4624			−0.716533			−0.358267	−	0.933619i	$-0.616632\pi$
$353$	−13.4624			−0.716533			−0.358267	+	0.933619i	$0.616632\pi$
$354$		0			0
$355$		−	25.2178i		−	1.33842i
$356$		0			0
$357$	−3.65453	+	17.8231i	−0.193418	+	0.943296i
$358$		0			0
$359$	13.5004	−	7.79444i	0.712522	−	0.411375i	−0.0994721	−	0.995040i	$-0.531715\pi$
$359$	13.5004	−	7.79444i	0.712522	−	0.411375i	0.811994	+	0.583666i	$0.198382\pi$
$360$		0			0
$361$	−8.99880	+	15.5864i	−0.473621	+	0.820335i
$362$		0			0
$363$	−11.3014	+	15.2676i	−0.593168	+	0.801339i
$364$		0			0
$365$	−22.4994	−	12.9901i	−1.17767	−	0.679930i
$366$		0			0
$367$		−	8.67003i		−	0.452572i	−0.974061	−	0.226286i	$-0.927342\pi$
$367$		−	8.67003i		−	0.452572i	0.974061	−	0.226286i	$-0.0726584\pi$
$368$		0			0
$369$	3.58290	+	0.828444i	0.186519	+	0.0431271i
$370$		0			0
$371$	−2.26040	−	4.86473i	−0.117354	−	0.252564i
$372$		0			0
$373$	−24.0978			−1.24774			−0.623868	−	0.781530i	$-0.714440\pi$
$373$	−24.0978			−1.24774			−0.623868	+	0.781530i	$0.714440\pi$
$374$		0			0
$375$	11.6565	−	15.7473i	0.601939	−	0.813188i
$376$		0			0
$377$	2.34835			0.120946
$378$		0			0
$379$	10.0778			0.517662			0.258831	−	0.965923i	$-0.416663\pi$
$379$	10.0778			0.517662			0.258831	+	0.965923i	$0.416663\pi$
$380$		0			0
$381$	12.3334	−	16.6618i	0.631859	−	0.853609i
$382$		0			0
$383$	4.70476			0.240402			0.120201	−	0.992750i	$-0.461646\pi$
$383$	4.70476			0.240402			0.120201	+	0.992750i	$0.461646\pi$
$384$		0			0
$385$	0.610958	−	0.870015i	0.0311373	−	0.0443401i
$386$		0			0
$387$	22.4205	−	24.0269i	1.13970	−	1.22136i
$388$		0			0
$389$			21.5003i			1.09011i	0.838401	+	0.545055i	$0.183491\pi$
$389$			21.5003i			1.09011i	−0.838401	+	0.545055i	$0.816509\pi$
$390$		0			0
$391$	19.2997	+	11.1427i	0.976030	+	0.563511i
$392$		0			0
$393$	7.57823	−	10.2378i	0.382271	−	0.516429i
$394$		0			0
$395$	−14.0372	+	24.3131i	−0.706288	+	1.22333i
$396$		0			0
$397$	−23.7548	+	13.7148i	−1.19222	+	0.688327i	−0.958809	−	0.284052i	$-0.908321\pi$
$397$	−23.7548	+	13.7148i	−1.19222	+	0.688327i	−0.233408	+	0.972379i	$0.574988\pi$
$398$		0			0
$399$	−3.04541	+	3.43162i	−0.152461	+	0.171796i
$400$		0			0
$401$			29.2299i			1.45967i	0.683622	+	0.729836i	$0.260404\pi$
$401$			29.2299i			1.45967i	−0.683622	+	0.729836i	$0.739596\pi$
$402$		0			0
$403$	−23.0359			−1.14750
$404$		0			0
$405$	−16.4884	+	11.1055i	−0.819313	+	0.551835i
$406$		0			0
$407$	0.395786	−	0.228507i	0.0196184	−	0.0113267i
$408$		0			0
$409$	27.3564	−	15.7942i	1.35269	−	0.780974i	0.364061	−	0.931375i	$-0.381390\pi$
$409$	27.3564	−	15.7942i	1.35269	−	0.780974i	0.988625	+	0.150401i	$0.0480565\pi$
$410$		0			0
$411$	−22.8753	−	16.9328i	−1.12835	−	0.835231i
$412$		0			0
$413$	1.53581	−	17.2833i	0.0755721	−	0.850455i
$414$		0			0
$415$	−15.8834	−	27.5109i	−0.779687	−	1.35046i
$416$		0			0
$417$	−20.5638	+	8.93729i	−1.00701	+	0.437661i
$418$		0			0
$419$	−6.80176	+	11.7810i	−0.332288	+	0.575539i	−0.982960	−	0.183819i	$-0.941154\pi$
$419$	−6.80176	+	11.7810i	−0.332288	+	0.575539i	0.650672	+	0.759359i	$0.274487\pi$
$420$		0			0
$421$	−14.8629	−	25.7432i	−0.724372	−	1.25465i	−0.959232	−	0.282620i	$-0.908797\pi$
$421$	−14.8629	−	25.7432i	−0.724372	−	1.25465i	0.234860	−	0.972029i	$-0.424537\pi$
$422$		0			0
$423$	−20.9016	−	4.83289i	−1.01627	−	0.234983i
$424$		0			0
$425$	−0.240248	+	0.416122i	−0.0116537	+	0.0201849i
$426$		0			0
$427$	8.97636	+	19.3185i	0.434396	+	0.934887i
$428$		0			0
$429$	0.363163	+	0.835602i	0.0175337	+	0.0403432i
$430$		0			0
$431$	−21.6467	−	12.4977i	−1.04268	−	0.601994i	−0.122091	−	0.992519i	$-0.538960\pi$
$431$	−21.6467	−	12.4977i	−1.04268	−	0.601994i	−0.920592	+	0.390525i	$0.872293\pi$
$432$		0			0
$433$		−	18.7778i		−	0.902401i	−0.892423	−	0.451201i	$-0.850996\pi$
$433$		−	18.7778i		−	0.902401i	0.892423	−	0.451201i	$-0.149004\pi$
$434$		0			0
$435$	−0.352240	+	3.08697i	−0.0168886	+	0.148009i
$436$		0			0
$437$	2.80994	+	4.86696i	0.134418	+	0.232818i
$438$		0			0
$439$	−1.82363	−	1.05287i	−0.0870369	−	0.0502508i	0.455850	−	0.890057i	$-0.349335\pi$
$439$	−1.82363	−	1.05287i	−0.0870369	−	0.0502508i	−0.542887	+	0.839806i	$0.682669\pi$
$440$		0			0
$441$	16.8099	−	12.5868i	0.800472	−	0.599370i
$442$		0			0
$443$	−11.6452	−	6.72337i	−0.553281	−	0.319437i	0.197163	−	0.980371i	$-0.436827\pi$
$443$	−11.6452	−	6.72337i	−0.553281	−	0.319437i	−0.750444	+	0.660934i	$0.770160\pi$
$444$		0			0
$445$	−15.7131	−	27.2159i	−0.744874	−	1.29016i
$446$		0			0
$447$	−21.2107	−	15.7006i	−1.00323	−	0.742612i
$448$		0			0
$449$		−	7.42429i		−	0.350374i	−0.984535	−	0.175187i	$-0.943947\pi$
$449$		−	7.42429i		−	0.350374i	0.984535	−	0.175187i	$-0.0560530\pi$
$450$		0			0
$451$	0.193116	+	0.111496i	0.00909347	+	0.00525012i
$452$		0			0
$453$	14.0792	−	19.0202i	0.661496	−	0.893648i
$454$		0			0
$455$	7.12093	+	15.3253i	0.333834	+	0.718462i
$456$		0			0
$457$	0.139009	−	0.240771i	0.00650257	−	0.0112628i	−0.862756	−	0.505621i	$-0.831263\pi$
$457$	0.139009	−	0.240771i	0.00650257	−	0.0112628i	0.869258	+	0.494358i	$0.164597\pi$
$458$		0			0
$459$	15.6938	−	13.3902i	0.732526	−	0.624999i
$460$		0			0
$461$	−3.98573	−	6.90348i	−0.185634	−	0.321527i	0.758156	−	0.652073i	$-0.226100\pi$
$461$	−3.98573	−	6.90348i	−0.185634	−	0.321527i	−0.943790	+	0.330546i	$0.892767\pi$
$462$		0			0
$463$	12.4572	−	21.5765i	0.578936	−	1.00275i	−0.416666	−	0.909060i	$-0.636801\pi$
$463$	12.4572	−	21.5765i	0.578936	−	1.00275i	0.995602	−	0.0936870i	$-0.0298653\pi$
$464$		0			0
$465$	3.45528	−	30.2814i	0.160235	−	1.40427i
$466$		0			0
$467$	18.4485	+	31.9538i	0.853695	+	1.47864i	0.877850	+	0.478935i	$0.158977\pi$
$467$	18.4485	+	31.9538i	0.853695	+	1.47864i	−0.0241548	+	0.999708i	$0.507689\pi$
$468$		0			0
$469$	1.61353	−	18.1580i	0.0745059	−	0.838457i
$470$		0			0
$471$	−2.32005	+	20.3325i	−0.106902	+	0.936872i
$472$		0			0
$473$	1.72576	−	0.996366i	0.0793504	−	0.0458130i
$474$		0			0
$475$	−0.104937	+	0.0605852i	−0.00481483	+	0.00277984i
$476$		0			0
$477$	−1.37024	+	5.92612i	−0.0627392	+	0.271338i
$478$		0			0
$479$	3.41169			0.155884			0.0779420	−	0.996958i	$-0.475165\pi$
$479$	3.41169			0.155884			0.0779420	+	0.996958i	$0.475165\pi$
$480$		0			0
$481$			7.26460i			0.331237i
$482$		0			0
$483$	−8.12459	−	24.4058i	−0.369682	−	1.11050i
$484$		0			0
$485$	−6.64948	+	3.83908i	−0.301938	+	0.174324i
$486$		0			0
$487$	−1.17122	+	2.02861i	−0.0530729	+	0.0919249i	−0.891341	−	0.453333i	$-0.850235\pi$
$487$	−1.17122	+	2.02861i	−0.0530729	+	0.0919249i	0.838268	+	0.545258i	$0.183568\pi$
$488$		0			0
$489$	15.0060	+	1.71227i	0.678596	+	0.0774315i
$490$		0			0
$491$	4.65365	+	2.68678i	0.210016	+	0.121253i	0.601319	−	0.799009i	$-0.294642\pi$
$491$	4.65365	+	2.68678i	0.210016	+	0.121253i	−0.391303	+	0.920262i	$0.627975\pi$
$492$		0			0
$493$		−	3.22428i		−	0.145214i
$494$		0			0
$495$	−1.15290	+	0.352053i	−0.0518188	+	0.0158236i
$496$		0			0
$497$	17.3591	−	24.7196i	0.778660	−	1.10883i
$498$		0			0
$499$	−33.3813			−1.49435			−0.747175	−	0.664627i	$-0.768591\pi$
$499$	−33.3813			−1.49435			−0.747175	+	0.664627i	$0.768591\pi$
$500$		0			0
$501$	12.2870	+	28.2711i	0.548942	+	1.26306i
$502$		0			0
$503$	6.01630			0.268254			0.134127	−	0.990964i	$-0.457177\pi$
$503$	6.01630			0.268254			0.134127	+	0.990964i	$0.457177\pi$
$504$		0			0
$505$	20.9964			0.934328
$506$		0			0
$507$	7.98210	+	0.910801i	0.354497	+	0.0404501i
$508$		0			0
$509$	−10.0398			−0.445007			−0.222503	−	0.974932i	$-0.571423\pi$
$509$	−10.0398			−0.445007			−0.222503	+	0.974932i	$0.571423\pi$
$510$		0			0
$511$	−13.1130	−	28.2213i	−0.580087	−	1.24844i
$512$		0			0
$513$	5.11576	−	0.945490i	0.225867	−	0.0417444i
$514$		0			0
$515$		−	18.5212i		−	0.816143i
$516$		0			0
$517$	−1.12658	−	0.650432i	−0.0495470	−	0.0286059i
$518$		0			0
$519$	13.2004	+	30.3728i	0.579434	+	1.33322i
$520$		0			0
$521$	10.8007	−	18.7074i	0.473188	−	0.819586i	−0.526341	−	0.850274i	$-0.676436\pi$
$521$	10.8007	−	18.7074i	0.473188	−	0.819586i	0.999529	+	0.0306875i	$0.00976968\pi$
$522$		0			0
$523$	11.6105	−	6.70332i	0.507692	−	0.293116i	−0.224193	−	0.974545i	$-0.571974\pi$
$523$	11.6105	−	6.70332i	0.507692	−	0.293116i	0.731884	+	0.681429i	$0.238641\pi$
$524$		0			0
$525$	0.526214	−	0.175174i	0.0229659	−	0.00764524i
$526$		0			0
$527$			31.6283i			1.37775i
$528$		0			0
$529$	−8.50726			−0.369881
$530$		0			0
$531$	−13.4229	+	14.3846i	−0.582504	+	0.624239i
$532$		0			0
$533$	−3.06973	+	1.77231i	−0.132965	+	0.0767672i
$534$		0			0
$535$	28.1208	−	16.2355i	1.21577	−	0.701924i
$536$		0			0
$537$	9.75624	−	4.24019i	0.421013	−	0.182978i
$538$		0			0
$539$	1.19778	−	0.432265i	0.0515919	−	0.0186190i
$540$		0			0
$541$	4.53805	+	7.86013i	0.195106	+	0.337933i	0.946935	−	0.321424i	$-0.104162\pi$
$541$	4.53805	+	7.86013i	0.195106	+	0.337933i	−0.751829	+	0.659358i	$0.770828\pi$
$542$		0			0
$543$	−15.4818	−	11.4600i	−0.664389	−	0.491794i
$544$		0			0
$545$	18.4581	−	31.9704i	0.790659	−	1.36946i
$546$		0			0
$547$	13.5359	+	23.4448i	0.578752	+	1.00243i	0.995623	+	0.0934620i	$0.0297934\pi$
$547$	13.5359	+	23.4448i	0.578752	+	1.00243i	−0.416871	+	0.908966i	$0.636873\pi$
$548$		0			0
$549$	5.44143	−	23.5334i	0.232234	−	1.00438i
$550$		0			0
$551$	0.406545	−	0.704157i	0.0173194	−	0.0299981i
$552$		0			0
$553$	−30.4962	+	14.1701i	−1.29683	+	0.602574i
$554$		0			0
$555$	−9.54954	−	1.08965i	−0.405355	−	0.0462532i
$556$		0			0
$557$	−23.8690	−	13.7808i	−1.01136	−	0.583911i	−0.0997727	−	0.995010i	$-0.531812\pi$
$557$	−23.8690	−	13.7808i	−1.01136	−	0.583911i	−0.911591	+	0.411099i	$0.865145\pi$
$558$		0			0
$559$			31.6760i			1.33975i
$560$		0			0
$561$	1.14728	−	0.498623i	0.0484382	−	0.0210519i
$562$		0			0
$563$	6.92328	+	11.9915i	0.291781	+	0.505380i	0.974231	−	0.225552i	$-0.0724187\pi$
$563$	6.92328	+	11.9915i	0.291781	+	0.505380i	−0.682450	+	0.730933i	$0.739085\pi$
$564$		0			0
$565$	−2.63941	−	1.52387i	−0.111041	−	0.0641095i
$566$		0			0
$567$	−23.8072	−	0.463952i	−0.999810	−	0.0194842i
$568$		0			0
$569$	−10.5219	−	6.07485i	−0.441103	−	0.254671i	0.262962	−	0.964806i	$-0.415300\pi$
$569$	−10.5219	−	6.07485i	−0.441103	−	0.254671i	−0.704065	+	0.710135i	$0.748634\pi$
$570$		0			0
$571$	23.1505	+	40.0979i	0.968819	+	1.67804i	0.698985	+	0.715136i	$0.253635\pi$
$571$	23.1505	+	40.0979i	0.968819	+	1.67804i	0.269833	+	0.962907i	$0.413031\pi$
$572$		0			0
$573$	−23.7247	+	10.3111i	−0.991113	+	0.430750i
$574$		0			0
$575$		−	0.679329i		−	0.0283300i
$576$		0			0
$577$	−10.6284	−	6.13630i	−0.442465	−	0.255457i	0.262178	−	0.965020i	$-0.415559\pi$
$577$	−10.6284	−	6.13630i	−0.442465	−	0.255457i	−0.704643	+	0.709562i	$0.748893\pi$
$578$		0			0
$579$	−21.3867	−	2.44034i	−0.888801	−	0.101417i
$580$		0			0
$581$	3.36792	−	37.9011i	0.139725	−	1.57240i
$582$		0			0
$583$	−0.184413	+	0.319413i	−0.00763762	+	0.0132287i
$584$		0			0
$585$	4.31667	−	18.6690i	0.178473	−	0.771869i
$586$		0			0
$587$	11.9875	+	20.7630i	0.494778	+	0.856980i	0.999982	−	0.00601986i	$-0.00191619\pi$
$587$	11.9875	+	20.7630i	0.494778	+	0.856980i	−0.505204	+	0.863000i	$0.668583\pi$
$588$		0			0
$589$	−3.98798	+	6.90738i	−0.164322	+	0.284614i
$590$		0			0
$591$	−22.4849	−	16.6438i	−0.924906	−	0.684635i
$592$		0			0
$593$	−15.4912	−	26.8315i	−0.636146	−	1.10184i	−0.986271	−	0.165134i	$-0.947194\pi$
$593$	−15.4912	−	26.8315i	−0.636146	−	1.10184i	0.350125	−	0.936703i	$-0.386139\pi$
$594$		0			0
$595$	21.0416	−	9.77702i	0.862623	−	0.400819i
$596$		0			0
$597$	39.5763	−	17.2004i	1.61975	−	0.703965i
$598$		0			0
$599$	−21.4392	+	12.3779i	−0.875981	+	0.505748i	−0.869331	−	0.494230i	$-0.835450\pi$
$599$	−21.4392	+	12.3779i	−0.875981	+	0.505748i	−0.00665010	+	0.999978i	$0.502117\pi$
$600$		0			0
$601$	7.67329	−	4.43017i	0.313000	−	0.180711i	−0.335268	−	0.942123i	$-0.608827\pi$
$601$	7.67329	−	4.43017i	0.313000	−	0.180711i	0.648268	+	0.761412i	$0.275494\pi$
$602$		0			0
$603$	−14.1022	+	15.1126i	−0.574286	+	0.615432i
$604$		0			0
$605$	24.2241			0.984852
$606$		0			0
$607$			13.0415i			0.529339i	0.964339	+	0.264670i	$0.0852629\pi$
$607$			13.0415i			0.529339i	−0.964339	+	0.264670i	$0.914737\pi$
$608$		0			0
$609$	−2.47025	+	2.78352i	−0.100099	+	0.112794i
$610$		0			0
$611$	17.9079	−	10.3391i	0.724475	−	0.418276i
$612$		0			0
$613$	5.90775	−	10.2325i	0.238612	−	0.413288i	−0.721704	−	0.692201i	$-0.756641\pi$
$613$	5.90775	−	10.2325i	0.238612	−	0.413288i	0.960316	+	0.278914i	$0.0899743\pi$
$614$		0			0
$615$	−1.86931	−	4.30108i	−0.0753778	−	0.173436i
$616$		0			0
$617$	−13.7906	−	7.96200i	−0.555188	−	0.320538i	0.196024	−	0.980599i	$-0.437197\pi$
$617$	−13.7906	−	7.96200i	−0.555188	−	0.320538i	−0.751212	+	0.660061i	$0.770530\pi$
$618$		0			0
$619$			30.9231i			1.24291i	0.783452	+	0.621453i	$0.213457\pi$
$619$			30.9231i			1.24291i	−0.783452	+	0.621453i	$0.786543\pi$
$620$		0			0
$621$	−9.74987	+	27.4888i	−0.391249	+	1.10309i
$622$		0			0
$623$	3.33180	−	37.4947i	0.133486	−	1.50219i
$624$		0			0
$625$	−24.3802			−0.975209
$626$		0			0
$627$	0.313428	+	0.0357638i	0.0125171	+	0.00142827i
$628$		0			0
$629$	9.97429			0.397701
$630$		0			0
$631$	0.925450			0.0368416			0.0184208	−	0.999830i	$-0.494136\pi$
$631$	0.925450			0.0368416			0.0184208	+	0.999830i	$0.494136\pi$
$632$		0			0
$633$	7.98959	+	18.3832i	0.317558	+	0.730668i
$634$		0			0
$635$	−26.4363			−1.04909
$636$		0			0
$637$	−3.56917	+	19.9244i	−0.141416	+	0.789433i
$638$		0			0
$639$	−32.7571	+	10.0028i	−1.29585	+	0.395706i
$640$		0			0
$641$			34.3482i			1.35667i	0.734752	+	0.678336i	$0.237298\pi$
$641$			34.3482i			1.35667i	−0.734752	+	0.678336i	$0.762702\pi$
$642$		0			0
$643$	11.8373	+	6.83426i	0.466817	+	0.269517i	0.714906	−	0.699220i	$-0.246469\pi$
$643$	11.8373	+	6.83426i	0.466817	+	0.269517i	−0.248089	+	0.968737i	$0.579803\pi$
$644$		0			0
$645$	−41.6391	−	4.75124i	−1.63954	−	0.187080i
$646$		0			0
$647$	18.1075	−	31.3630i	0.711877	−	1.23301i	−0.252274	−	0.967656i	$-0.581178\pi$
$647$	18.1075	−	31.3630i	0.711877	−	1.23301i	0.964152	−	0.265352i	$-0.0854882\pi$
$648$		0			0
$649$	−1.03319	+	0.596512i	−0.0405562	+	0.0234151i
$650$		0			0
$651$	24.2317	−	27.3047i	0.949716	−	1.07016i
$652$		0			0
$653$		−	36.5270i		−	1.42941i	−0.699426	−	0.714705i	$-0.746561\pi$
$653$		−	36.5270i		−	1.42941i	0.699426	−	0.714705i	$-0.253439\pi$
$654$		0			0
$655$	−16.2437			−0.634695
$656$		0			0
$657$	−7.94907	+	34.3786i	−0.310123	+	1.34124i
$658$		0			0
$659$	−19.5178	+	11.2686i	−0.760305	+	0.438962i	−0.829405	−	0.558648i	$-0.811320\pi$
$659$	−19.5178	+	11.2686i	−0.760305	+	0.438962i	0.0691004	+	0.997610i	$0.477987\pi$
$660$		0			0
$661$	1.29595	−	0.748216i	0.0504065	−	0.0291022i	−0.474585	−	0.880210i	$-0.657402\pi$
$661$	1.29595	−	0.748216i	0.0504065	−	0.0291022i	0.524991	+	0.851107i	$0.324068\pi$
$662$		0			0
$663$	−2.25434	+	19.7566i	−0.0875512	+	0.767283i
$664$		0			0
$665$	5.82811	+	0.517890i	0.226004	+	0.0200829i
$666$		0			0
$667$	2.27925	+	3.94778i	0.0882529	+	0.152859i
$668$		0			0
$669$	−3.16648	+	27.7504i	−0.122423	+	1.07289i
$670$		0			0
$671$	0.732330	−	1.26843i	0.0282713	−	0.0489673i
$672$		0			0
$673$	13.9366	+	24.1389i	0.537215	+	0.930484i	0.999053	+	0.0435197i	$0.0138571\pi$
$673$	13.9366	+	24.1389i	0.537215	+	0.930484i	−0.461837	+	0.886965i	$0.652810\pi$
$674$		0			0
$675$	−0.592687	−	0.210217i	−0.0228125	−	0.00809126i
$676$		0			0
$677$	−15.6344	+	27.0796i	−0.600880	+	1.04075i	0.391809	+	0.920047i	$0.371850\pi$
$677$	−15.6344	+	27.0796i	−0.600880	+	1.04075i	−0.992688	+	0.120707i	$0.961484\pi$
$678$		0			0
$679$	−9.16081	−	0.814037i	−0.351560	−	0.0312399i
$680$		0			0
$681$	20.4075	−	27.5696i	0.782019	−	1.05647i
$682$		0			0
$683$	8.06769	+	4.65788i	0.308701	+	0.178229i	0.646345	−	0.763045i	$-0.276297\pi$
$683$	8.06769	+	4.65788i	0.308701	+	0.178229i	−0.337644	+	0.941274i	$0.609630\pi$
$684$		0			0
$685$			36.2949i			1.38676i
$686$		0			0
$687$	21.7177	+	16.0759i	0.828581	+	0.613333i
$688$		0			0
$689$	−2.93139	−	5.07732i	−0.111677	−	0.193431i
$690$		0			0
$691$	42.0468	+	24.2757i	1.59954	+	0.923493i	0.991576	+	0.129526i	$0.0413456\pi$
$691$	42.0468	+	24.2757i	1.59954	+	0.923493i	0.607961	+	0.793967i	$0.291988\pi$
$692$		0			0
$693$	−1.37246	−	0.448516i	−0.0521355	−	0.0170377i
$694$		0			0
$695$	24.7633	+	14.2971i	0.939324	+	0.542319i
$696$		0			0
$697$	2.43338	+	4.21473i	0.0921707	+	0.159644i
$698$		0			0
$699$	2.41365	−	21.1528i	0.0912925	−	0.800071i
$700$		0			0
$701$			22.9812i			0.867987i	0.900916	+	0.433994i	$0.142896\pi$
$701$			22.9812i			0.867987i	−0.900916	+	0.433994i	$0.857104\pi$
$702$		0			0
$703$	2.17831	+	1.25765i	0.0821564	+	0.0474330i
$704$		0			0
$705$	10.9050	+	25.0912i	0.410705	+	0.944991i
$706$		0			0
$707$	20.5816	+	14.4532i	0.774052	+	0.543569i
$708$		0			0
$709$	−15.3433	+	26.5753i	−0.576228	+	0.998057i	0.419679	+	0.907673i	$0.362143\pi$
$709$	−15.3433	+	26.5753i	−0.576228	+	0.998057i	−0.995907	+	0.0903840i	$0.971191\pi$
$710$		0			0
$711$	37.1499	+	8.58985i	1.39323	+	0.322145i
$712$		0			0
$713$	−22.3582	−	38.7255i	−0.837319	−	1.45028i
$714$		0			0
$715$	0.580956	−	1.00625i	0.0217265	−	0.0376315i
$716$		0			0
$717$	25.3234	−	11.0059i	0.945718	−	0.411022i
$718$		0			0
$719$	2.44166	+	4.22907i	0.0910584	+	0.157718i	0.907957	−	0.419064i	$-0.137642\pi$
$719$	2.44166	+	4.22907i	0.0910584	+	0.157718i	−0.816898	+	0.576782i	$0.804308\pi$
$720$		0			0
$721$	12.7494	−	18.1554i	0.474812	−	0.676141i
$722$		0			0
$723$	−28.7997	−	21.3181i	−1.07107	−	0.792828i
$724$		0			0
$725$	−0.0851181	+	0.0491430i	−0.00316121	+	0.00182512i
$726$		0			0
$727$	32.7779	−	18.9243i	1.21567	−	0.701865i	0.251678	−	0.967811i	$-0.419018\pi$
$727$	32.7779	−	18.9243i	1.21567	−	0.701865i	0.963988	+	0.265946i	$0.0856844\pi$
$728$		0			0
$729$	20.9658	+	17.0127i	0.776513	+	0.630102i
$730$		0			0
$731$	43.4911			1.60858
$732$		0			0
$733$			46.3166i			1.71074i	0.518017	+	0.855370i	$0.326670\pi$
$733$			46.3166i			1.71074i	−0.518017	+	0.855370i	$0.673330\pi$
$734$		0			0
$735$	−25.6558	−	7.68034i	−0.946330	−	0.283294i
$736$		0			0
$737$	−1.08548	+	0.626700i	−0.0399840	+	0.0230848i
$738$		0			0
$739$	5.15606	−	8.93056i	0.189669	−	0.328516i	−0.755471	−	0.655182i	$-0.772592\pi$
$739$	5.15606	−	8.93056i	0.189669	−	0.328516i	0.945140	+	0.326666i	$0.105925\pi$
$740$		0			0
$741$	−2.98342	+	4.03045i	−0.109599	+	0.148062i
$742$		0			0
$743$	21.9984	+	12.7008i	0.807042	+	0.465946i	0.845928	−	0.533298i	$-0.179047\pi$
$743$	21.9984	+	12.7008i	0.807042	+	0.465946i	−0.0388856	+	0.999244i	$0.512381\pi$
$744$		0			0
$745$			33.6537i			1.23298i
$746$		0			0
$747$	−29.4355	+	31.5445i	−1.07699	+	1.15415i
$748$		0			0
$749$	38.7413	+	3.44258i	1.41557	+	0.125789i
$750$		0			0
$751$	−53.7306			−1.96066			−0.980329	−	0.197369i	$-0.936760\pi$
$751$	−53.7306			−1.96066			−0.980329	+	0.197369i	$0.936760\pi$
$752$		0			0
$753$	−7.89944	+	10.6717i	−0.287872	+	0.388900i
$754$		0			0
$755$	−30.1783			−1.09830
$756$		0			0
$757$	28.3821			1.03157			0.515783	−	0.856719i	$-0.327501\pi$
$757$	28.3821			1.03157			0.515783	+	0.856719i	$0.327501\pi$
$758$		0			0
$759$	−1.05224	+	1.42153i	−0.0381940	+	0.0515981i
$760$		0			0
$761$	23.1184			0.838041			0.419021	−	0.907977i	$-0.362374\pi$
$761$	23.1184			0.838041			0.419021	+	0.907977i	$0.362374\pi$
$762$		0			0
$763$	40.1008	−	18.6329i	1.45175	−	0.674556i
$764$		0			0
$765$	−25.6325	−	5.92679i	−0.926746	−	0.214283i
$766$		0			0
$767$		−	18.9640i		−	0.684752i
$768$		0			0
$769$	−23.1698	−	13.3771i	−0.835524	−	0.482390i	0.0202163	−	0.999796i	$-0.493565\pi$
$769$	−23.1698	−	13.3771i	−0.835524	−	0.482390i	−0.855740	+	0.517406i	$0.826898\pi$
$770$		0			0
$771$	12.2936	−	16.6080i	0.442742	−	0.598121i
$772$		0			0
$773$	−3.97203	+	6.87976i	−0.142864	+	0.247448i	−0.928574	−	0.371147i	$-0.878965\pi$
$773$	−3.97203	+	6.87976i	−0.142864	+	0.247448i	0.785710	+	0.618595i	$0.212298\pi$
$774$		0			0
$775$	0.834960	−	0.482065i	0.0299927	−	0.0173163i
$776$		0			0
$777$	−8.61081	−	7.64170i	−0.308911	−	0.274145i
$778$		0			0
$779$			1.22729i			0.0439721i
$780$		0			0
$781$	−2.07686			−0.0743158
$782$		0			0
$783$	4.14959	−	0.766922i	0.148294	−	0.0274076i
$784$		0			0
$785$	22.6013	−	13.0489i	0.806676	−	0.465734i
$786$		0			0
$787$	−10.5602	+	6.09696i	−0.376432	+	0.217333i	−0.676265	−	0.736659i	$-0.736402\pi$
$787$	−10.5602	+	6.09696i	−0.376432	+	0.217333i	0.299833	+	0.953992i	$0.403069\pi$
$788$		0			0
$789$	10.7544	+	7.96060i	0.382866	+	0.283405i
$790$		0			0
$791$	−1.53829	−	3.31064i	−0.0546954	−	0.117713i
$792$		0			0
$793$	11.6410	+	20.1627i	0.413382	+	0.715999i
$794$		0			0
$795$	7.11399	−	3.09183i	0.252307	−	0.109656i
$796$		0			0
$797$	−3.30173	+	5.71876i	−0.116953	+	0.202569i	−0.918559	−	0.395284i	$-0.870646\pi$
$797$	−3.30173	+	5.71876i	−0.116953	+	0.202569i	0.801606	+	0.597853i	$0.203979\pi$
$798$		0			0
$799$	−14.1956	−	24.5875i	−0.502204	−	0.869842i
$800$		0			0
$801$	−29.1198	+	31.2062i	−1.02890	+	1.10262i
$802$		0			0
$803$	−1.06982	+	1.85298i	−0.0377531	+	0.0653903i
$804$		0			0
$805$	−18.8518	+	26.8453i	−0.664439	+	0.946173i
$806$		0			0
$807$	−6.88646	−	15.8450i	−0.242415	−	0.557772i
$808$		0			0
$809$	8.57462	+	4.95056i	0.301468	+	0.174052i	0.643102	−	0.765780i	$-0.277647\pi$
$809$	8.57462	+	4.95056i	0.301468	+	0.174052i	−0.341634	+	0.939833i	$0.610980\pi$
$810$		0			0
$811$			33.1027i			1.16239i	0.813763	+	0.581197i	$0.197416\pi$
$811$			33.1027i			1.16239i	−0.813763	+	0.581197i	$0.802584\pi$
$812$		0			0
$813$	−0.819682	+	7.18355i	−0.0287475	+	0.251938i
$814$		0			0
$815$	−9.63049	−	16.6805i	−0.337341	−	0.584292i
$816$		0			0
$817$	9.49812	+	5.48374i	0.332297	+	0.191852i
$818$		0			0
$819$	17.0825	−	15.3288i	0.596911	−	0.535630i
$820$		0			0
$821$	−9.90100	−	5.71634i	−0.345547	−	0.199502i	0.317175	−	0.948367i	$-0.397266\pi$
$821$	−9.90100	−	5.71634i	−0.345547	−	0.199502i	−0.662722	+	0.748865i	$0.730599\pi$
$822$		0			0
$823$	19.4509	+	33.6900i	0.678017	+	1.17436i	0.975577	+	0.219656i	$0.0704936\pi$
$823$	19.4509	+	33.6900i	0.678017	+	1.17436i	−0.297561	+	0.954703i	$0.596173\pi$
$824$		0			0
$825$	−0.0306495	−	0.0226874i	−0.00106708	−	0.000789874i
$826$		0			0
$827$		−	8.05228i		−	0.280005i	−0.990151	−	0.140003i	$-0.955289\pi$
$827$		−	8.05228i		−	0.280005i	0.990151	−	0.140003i	$-0.0447111\pi$
$828$		0			0
$829$	−11.3389	−	6.54652i	−0.393816	−	0.227370i	0.289996	−	0.957028i	$-0.406346\pi$
$829$	−11.3389	−	6.54652i	−0.393816	−	0.227370i	−0.683812	+	0.729658i	$0.739679\pi$
$830$		0			0
$831$	−4.58578	+	6.19516i	−0.159079	+	0.214908i
$832$		0			0
$833$	27.3561	+	4.90047i	0.947834	+	0.169791i
$834$		0			0
$835$	19.6556	−	34.0445i	0.680211	−	1.17816i
$836$		0			0
$837$	−40.7051	+	7.52307i	−1.40697	+	0.260035i
$838$		0			0
$839$	5.51797	+	9.55740i	0.190501	+	0.329958i	0.945416	−	0.325864i	$-0.105655\pi$
$839$	5.51797	+	9.55740i	0.190501	+	0.329958i	−0.754915	+	0.655822i	$0.772322\pi$
$840$		0			0
$841$	−14.1702	+	24.5436i	−0.488629	+	0.846330i
$842$		0			0
$843$	5.56582	−	48.7779i	0.191697	−	1.68000i
$844$		0			0
$845$	−5.12271	−	8.87279i	−0.176227	−	0.305233i
$846$		0			0
$847$	23.7456	+	16.6751i	0.815908	+	0.572962i
$848$		0			0
$849$	2.27708	−	19.9559i	0.0781491	−	0.684885i
$850$		0			0
$851$	−12.2124	+	7.05085i	−0.418637	+	0.241700i
$852$		0			0
$853$	20.2134	−	11.6702i	0.692092	−	0.399580i	−0.112303	−	0.993674i	$-0.535823\pi$
$853$	20.2134	−	11.6702i	0.692092	−	0.399580i	0.804395	+	0.594094i	$0.202489\pi$
$854$		0			0
$855$	−4.85064	−	4.52634i	−0.165888	−	0.154798i
$856$		0			0
$857$	18.2121			0.622115			0.311057	−	0.950391i	$-0.399317\pi$
$857$	18.2121			0.622115			0.311057	+	0.950391i	$0.399317\pi$
$858$		0			0
$859$		−	39.1597i		−	1.33611i	−0.744111	−	0.668057i	$-0.767126\pi$
$859$		−	39.1597i		−	1.33611i	0.744111	−	0.668057i	$-0.232874\pi$
$860$		0			0
$861$	1.12834	−	5.50288i	0.0384537	−	0.187538i
$862$		0			0
$863$	−22.7847	+	13.1548i	−0.775601	+	0.447793i	−0.834869	−	0.550449i	$-0.814457\pi$
$863$	−22.7847	+	13.1548i	−0.775601	+	0.447793i	0.0592683	+	0.998242i	$0.481123\pi$
$864$		0			0
$865$	21.1168	−	36.5754i	0.717994	−	1.24360i
$866$		0			0
$867$	−2.12923	−	0.242957i	−0.0723125	−	0.00825125i
$868$		0			0
$869$	2.00235	+	1.15606i	0.0679252	+	0.0392166i
$870$		0			0
$871$		−	19.9238i		−	0.675091i
$872$		0			0
$873$	7.62440	+	7.11465i	0.258047	+	0.240795i
$874$		0			0
$875$	−24.4918	−	17.1991i	−0.827973	−	0.581434i
$876$		0			0
$877$	7.19666			0.243014			0.121507	−	0.992591i	$-0.461227\pi$
$877$	7.19666			0.243014			0.121507	+	0.992591i	$0.461227\pi$
$878$		0			0
$879$	19.9106	+	45.8122i	0.671568	+	1.54521i
$880$		0			0
$881$	37.2133			1.25375			0.626874	−	0.779121i	$-0.284334\pi$
$881$	37.2133			1.25375			0.626874	+	0.779121i	$0.284334\pi$
$882$		0			0
$883$	9.72629			0.327316			0.163658	−	0.986517i	$-0.447671\pi$
$883$	9.72629			0.327316			0.163658	+	0.986517i	$0.447671\pi$
$884$		0			0
$885$	24.9288	+	2.84451i	0.837972	+	0.0956172i
$886$		0			0
$887$	20.6986			0.694992			0.347496	−	0.937681i	$-0.387032\pi$
$887$	20.6986			0.694992			0.347496	+	0.937681i	$0.387032\pi$
$888$		0			0
$889$	−25.9140	−	18.1978i	−0.869129	−	0.610336i
$890$		0			0
$891$	0.914610	+	1.35793i	0.0306406	+	0.0454923i
$892$		0			0
$893$		−	7.15962i		−	0.239587i
$894$		0			0
$895$	−11.7486	−	6.78307i	−0.392713	−	0.226733i
$896$		0			0
$897$	−11.2058	−	25.7834i	−0.374151	−	0.860884i
$898$		0			0
$899$	−3.23480	+	5.60284i	−0.107887	+	0.186865i
$900$		0			0
$901$	−6.97115	+	4.02480i	−0.232243	+	0.134085i
$902$		0			0
$903$	−37.5459	−	33.3203i	−1.24945	−	1.10883i
$904$		0			0
$905$			24.5641i			0.816539i
$906$		0			0
$907$	0.990928			0.0329032			0.0164516	−	0.999865i	$-0.494763\pi$
$907$	0.990928			0.0329032			0.0164516	+	0.999865i	$0.494763\pi$
$908$		0			0
$909$	−8.32839	−	27.2736i	−0.276235	−	0.904609i
$910$		0			0
$911$	15.2170	−	8.78552i	0.504161	−	0.291077i	−0.226269	−	0.974065i	$-0.572653\pi$
$911$	15.2170	−	8.78552i	0.504161	−	0.291077i	0.730430	+	0.682987i	$0.239320\pi$
$912$		0			0
$913$	−2.26571	+	1.30811i	−0.0749841	+	0.0432921i
$914$		0			0
$915$	−28.2506	+	12.2781i	−0.933936	+	0.405901i
$916$		0			0
$917$	−15.9228	−	11.1816i	−0.525818	−	0.369250i
$918$		0			0
$919$	−9.22417	−	15.9767i	−0.304277	−	0.527024i	0.672823	−	0.739804i	$-0.265082\pi$
$919$	−9.22417	−	15.9767i	−0.304277	−	0.527024i	−0.977100	+	0.212780i	$0.931748\pi$
$920$		0			0
$921$	−15.0515	−	11.1415i	−0.495965	−	0.367124i
$922$		0			0
$923$	16.5066	−	28.5903i	0.543322	−	0.941061i
$924$		0			0
$925$	−0.152024	−	0.263313i	−0.00499851	−	0.00865767i
$926$		0			0
$927$	−24.0585	+	7.34659i	−0.790184	+	0.241294i
$928$		0			0
$929$	−10.4712	+	18.1367i	−0.343550	+	0.595046i	−0.985089	−	0.172044i	$-0.944963\pi$
$929$	−10.4712	+	18.1367i	−0.343550	+	0.595046i	0.641539	+	0.767090i	$0.278296\pi$
$930$		0			0
$931$	5.35647	+	4.51953i	0.175551	+	0.148122i
$932$		0			0
$933$	−29.5703	−	3.37413i	−0.968089	−	0.110464i
$934$		0			0
$935$	−1.38157	−	0.797652i	−0.0451823	−	0.0260860i
$936$		0			0
$937$			27.1677i			0.887529i	0.896143	+	0.443764i	$0.146357\pi$
$937$			27.1677i			0.887529i	−0.896143	+	0.443764i	$0.853643\pi$
$938$		0			0
$939$	14.5253	−	6.31290i	0.474016	−	0.206014i
$940$		0			0
$941$	−1.42576	−	2.46949i	−0.0464785	−	0.0805031i	0.841850	−	0.539711i	$-0.181467\pi$
$941$	−1.42576	−	2.46949i	−0.0464785	−	0.0805031i	−0.888329	+	0.459208i	$0.848133\pi$
$942$		0			0
$943$	−5.95881	−	3.44032i	−0.194046	−	0.112032i
$944$		0			0
$945$	17.5878	+	24.7547i	0.572132	+	0.805270i
$946$		0			0
$947$	15.2662	+	8.81395i	0.496085	+	0.286415i	0.727095	−	0.686536i	$-0.240870\pi$
$947$	15.2662	+	8.81395i	0.496085	+	0.286415i	−0.231010	+	0.972951i	$0.574203\pi$
$948$		0			0
$949$	−17.0056	−	29.4546i	−0.552025	−	0.956136i
$950$		0			0
$951$	−1.80610	+	0.784953i	−0.0585667	+	0.0254539i
$952$		0			0
$953$		−	47.1766i		−	1.52820i	−0.645097	−	0.764101i	$-0.723183\pi$
$953$		−	47.1766i		−	1.52820i	0.645097	−	0.764101i	$-0.276817\pi$
$954$		0			0
$955$	28.5697	+	16.4947i	0.924493	+	0.533756i
$956$		0			0
$957$	0.254233	+	0.0290094i	0.00821819	+	0.000937740i
$958$		0			0
$959$	−24.9842	+	35.5779i	−0.806780	+	1.14887i
$960$		0			0
$961$	16.2315	−	28.1139i	0.523598	−	0.906899i
$962$		0			0
$963$	−32.2437	−	30.0880i	−1.03904	−	0.969572i
$964$		0			0
$965$	13.7255	+	23.7732i	0.441838	+	0.765286i
$966$		0			0
$967$	−3.62809	+	6.28404i	−0.116672	+	0.202081i	−0.918447	−	0.395545i	$-0.870556\pi$
$967$	−3.62809	+	6.28404i	−0.116672	+	0.202081i	0.801775	+	0.597626i	$0.203889\pi$
$968$		0			0
$969$	5.53379	+	4.09623i	0.177771	+	0.131590i
$970$		0			0
$971$	−10.2653	−	17.7800i	−0.329429	−	0.570588i	0.652970	−	0.757384i	$-0.273523\pi$
$971$	−10.2653	−	17.7800i	−0.329429	−	0.570588i	−0.982399	+	0.186796i	$0.940190\pi$
$972$		0			0
$973$	14.4324	+	31.0608i	0.462683	+	0.995764i
$974$		0			0
$975$	0.555917	−	0.241609i	0.0178036	−	0.00773768i
$976$		0			0
$977$	38.7545	−	22.3749i	1.23987	−	0.715838i	0.270800	−	0.962636i	$-0.412712\pi$
$977$	38.7545	−	22.3749i	1.23987	−	0.715838i	0.969067	+	0.246798i	$0.0793784\pi$
$978$		0			0
$979$	−2.24142	+	1.29408i	−0.0716360	+	0.0413591i
$980$		0			0
$981$	−48.8500	−	11.2952i	−1.55966	−	0.360627i
$982$		0			0
$983$	26.9099			0.858293			0.429146	−	0.903235i	$-0.358814\pi$
$983$	26.9099			0.858293			0.429146	+	0.903235i	$0.358814\pi$
$984$		0			0
$985$			35.6755i			1.13672i
$986$		0			0
$987$	−6.58240	+	32.1022i	−0.209520	+	1.02182i
$988$		0			0
$989$	−53.2502	+	30.7440i	−1.69326	+	0.977602i
$990$		0			0
$991$	13.8668	−	24.0181i	0.440494	−	0.762959i	−0.557232	−	0.830357i	$-0.688136\pi$
$991$	13.8668	−	24.0181i	0.440494	−	0.762959i	0.997726	+	0.0673982i	$0.0214698\pi$
$992$		0			0
$993$	4.17538	+	9.60711i	0.132502	+	0.304873i
$994$		0			0
$995$	−47.6585	−	27.5156i	−1.51088	−	0.872304i
$996$		0			0
$997$			22.4382i			0.710624i	0.934748	+	0.355312i	$0.115625\pi$
$997$			22.4382i			0.710624i	−0.934748	+	0.355312i	$0.884375\pi$
$998$		0			0
$999$	2.37247	+	12.8367i	0.0750617	+	0.406137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.185.8	yes	48
3.2	odd	2		1512.2.cx.a.17.7		48
4.3	odd	2		1008.2.df.e.689.17		48
7.5	odd	6		504.2.bs.a.257.15	✓	48
9.2	odd	6		504.2.bs.a.353.15	yes	48
9.7	even	3		1512.2.bs.a.521.7		48
12.11	even	2		3024.2.df.e.17.7		48
21.5	even	6		1512.2.bs.a.1097.7		48
28.19	even	6		1008.2.ca.e.257.10		48
36.7	odd	6		3024.2.ca.e.2033.7		48
36.11	even	6		1008.2.ca.e.353.10		48
63.47	even	6	inner	504.2.cx.a.425.8	yes	48
63.61	odd	6		1512.2.cx.a.89.7		48
84.47	odd	6		3024.2.ca.e.2609.7		48
252.47	odd	6		1008.2.df.e.929.17		48
252.187	even	6		3024.2.df.e.1601.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.15	✓	48	7.5	odd	6
504.2.bs.a.353.15	yes	48	9.2	odd	6
504.2.cx.a.185.8	yes	48	1.1	even	1	trivial
504.2.cx.a.425.8	yes	48	63.47	even	6	inner
1008.2.ca.e.257.10		48	28.19	even	6
1008.2.ca.e.353.10		48	36.11	even	6
1008.2.df.e.689.17		48	4.3	odd	2
1008.2.df.e.929.17		48	252.47	odd	6
1512.2.bs.a.521.7		48	9.7	even	3
1512.2.bs.a.1097.7		48	21.5	even	6
1512.2.cx.a.17.7		48	3.2	odd	2
1512.2.cx.a.89.7		48	63.61	odd	6
3024.2.ca.e.2033.7		48	36.7	odd	6
3024.2.ca.e.2609.7		48	84.47	odd	6
3024.2.df.e.17.7		48	12.11	even	2
3024.2.df.e.1601.7		48	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03050 + 1.39215i) q^{3} +2.20884 q^{5} +(2.16520 + 1.52049i) q^{7} +(-0.876153 - 2.86921i) q^{9} +O(q^{10})\)	\(q+(-1.03050 + 1.39215i) q^{3} +2.20884 q^{5} +(2.16520 + 1.52049i) q^{7} +(-0.876153 - 2.86921i) q^{9} -0.181913i q^{11} +(2.50424 + 1.44582i) q^{13} +(-2.27620 + 3.07503i) q^{15} +(1.98511 - 3.43832i) q^{17} +(0.867067 - 0.500601i) q^{19} +(-4.34798 + 1.44743i) q^{21} +5.61313i q^{23} -0.121025 q^{25} +(4.89724 + 1.73697i) q^{27} +(0.703311 - 0.406057i) q^{29} +(-6.89908 + 3.98319i) q^{31} +(0.253250 + 0.187461i) q^{33} +(4.78259 + 3.35852i) q^{35} +(1.25614 + 2.17569i) q^{37} +(-4.59341 + 1.99636i) q^{39} +(-0.612906 + 1.06158i) q^{41} +(5.47716 + 9.48671i) q^{43} +(-1.93528 - 6.33762i) q^{45} +(3.57551 - 6.19296i) q^{47} +(2.37622 + 6.58434i) q^{49} +(2.74100 + 6.30675i) q^{51} +(-1.75586 - 1.01374i) q^{53} -0.401817i q^{55} +(-0.196598 + 1.72295i) q^{57} +(-3.27911 - 5.67958i) q^{59} +(6.97275 + 4.02572i) q^{61} +(2.46555 - 7.54460i) q^{63} +(5.53147 + 3.19359i) q^{65} +(-3.44505 - 5.96701i) q^{67} +(-7.81431 - 5.78431i) q^{69} -11.4168i q^{71} +(-10.1861 - 5.88094i) q^{73} +(0.124716 - 0.168485i) q^{75} +(0.276597 - 0.393879i) q^{77} +(-6.35501 + 11.0072i) q^{79} +(-7.46471 + 5.02773i) q^{81} +(-7.19085 - 12.4549i) q^{83} +(4.38480 - 7.59470i) q^{85} +(-0.159468 + 1.39755i) q^{87} +(-7.11375 - 12.3214i) q^{89} +(3.22383 + 6.93818i) q^{91} +(1.56429 - 13.7092i) q^{93} +(1.91521 - 1.10575i) q^{95} +(-3.01040 + 1.73805i) q^{97} +(-0.521946 + 0.159384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

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