LMFDB - Embedded newform 504.2.t.d.193.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(193,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [22,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.10
Character	$\chi$	$=$	504.193
Dual form			504.2.t.d.457.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.51940 + 0.831519i) q^{3} -2.52290 q^{5} +(-1.07705 + 2.41660i) q^{7} +(1.61715 + 2.52682i) q^{9} -5.71296 q^{11} +(-2.45245 + 4.24777i) q^{13} +(-3.83330 - 2.09784i) q^{15} +(2.49483 - 4.32118i) q^{17} +(-0.00383929 - 0.00664984i) q^{19} +(-3.64592 + 2.77620i) q^{21} +0.667754 q^{23} +1.36505 q^{25} +(0.355997 + 5.18394i) q^{27} +(3.85082 + 6.66981i) q^{29} +(3.88302 + 6.72560i) q^{31} +(-8.68028 - 4.75044i) q^{33} +(2.71729 - 6.09686i) q^{35} +(-3.19562 - 5.53498i) q^{37} +(-7.25836 + 4.41480i) q^{39} +(5.21159 - 9.02673i) q^{41} +(4.42935 + 7.67185i) q^{43} +(-4.07992 - 6.37493i) q^{45} +(-1.08052 + 1.87152i) q^{47} +(-4.67994 - 5.20559i) q^{49} +(7.38379 - 4.49109i) q^{51} +(-3.69858 + 6.40613i) q^{53} +14.4133 q^{55} +(-0.000303939 - 0.0132962i) q^{57} +(0.261797 + 0.453446i) q^{59} +(4.49541 - 7.78628i) q^{61} +(-7.84807 + 1.18650i) q^{63} +(6.18730 - 10.7167i) q^{65} +(2.54791 + 4.41311i) q^{67} +(1.01458 + 0.555250i) q^{69} -5.68471 q^{71} +(-1.52062 + 2.63379i) q^{73} +(2.07405 + 1.13506i) q^{75} +(6.15314 - 13.8060i) q^{77} +(-3.08115 + 5.33671i) q^{79} +(-3.76965 + 8.17250i) q^{81} +(-0.258726 - 0.448126i) q^{83} +(-6.29422 + 10.9019i) q^{85} +(0.304852 + 13.3361i) q^{87} +(1.19093 + 2.06274i) q^{89} +(-7.62377 - 10.5017i) q^{91} +(0.307402 + 13.4477i) q^{93} +(0.00968615 + 0.0167769i) q^{95} +(4.32994 + 7.49968i) q^{97} +(-9.23873 - 14.4356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39}+ \cdots - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.51940	+	0.831519i	0.877226	+	0.480078i
$3$	1.51940	+	0.831519i	0.877226	+	0.480078i
$4$		0			0
$5$	−2.52290			−1.12828			−0.564139	−	0.825680i	$-0.690792\pi$
$5$	−2.52290			−1.12828			−0.564139	+	0.825680i	$0.690792\pi$
$6$		0			0
$7$	−1.07705	+	2.41660i	−0.407086	+	0.913390i
$7$	−1.07705	+	2.41660i	−0.407086	+	0.913390i
$8$		0			0
$9$	1.61715	+	2.52682i	0.539050	+	0.842274i
$10$		0			0
$11$	−5.71296			−1.72252			−0.861262	−	0.508161i	$-0.830325\pi$
$11$	−5.71296			−1.72252			−0.861262	+	0.508161i	$0.830325\pi$
$12$		0			0
$13$	−2.45245	+	4.24777i	−0.680188	+	1.17812i	0.294735	+	0.955579i	$0.404769\pi$
$13$	−2.45245	+	4.24777i	−0.680188	+	1.17812i	−0.974923	+	0.222541i	$0.928565\pi$
$14$		0			0
$15$	−3.83330	−	2.09784i	−0.989754	−	0.541661i
$16$		0			0
$17$	2.49483	−	4.32118i	0.605086	−	1.04804i	−0.386952	−	0.922100i	$-0.626472\pi$
$17$	2.49483	−	4.32118i	0.605086	−	1.04804i	0.992038	−	0.125939i	$-0.0401945\pi$
$18$		0			0
$19$	−0.00383929	−	0.00664984i	−0.000880793	−	0.00152558i	0.865585	−	0.500763i	$-0.166947\pi$
$19$	−0.00383929	−	0.00664984i	−0.000880793	−	0.00152558i	−0.866465	+	0.499237i	$0.833614\pi$
$20$		0			0
$21$	−3.64592	+	2.77620i	−0.795605	+	0.605816i
$22$		0			0
$23$	0.667754			0.139236			0.0696181	−	0.997574i	$-0.477822\pi$
$23$	0.667754			0.139236			0.0696181	+	0.997574i	$0.477822\pi$
$24$		0			0
$25$	1.36505			0.273010
$26$		0			0
$27$	0.355997	+	5.18394i	0.0685117	+	0.997650i
$28$		0			0
$29$	3.85082	+	6.66981i	0.715079	+	1.23855i	0.962929	+	0.269754i	$0.0869424\pi$
$29$	3.85082	+	6.66981i	0.715079	+	1.23855i	−0.247851	+	0.968798i	$0.579724\pi$
$30$		0			0
$31$	3.88302	+	6.72560i	0.697412	+	1.20795i	0.969361	+	0.245641i	$0.0789984\pi$
$31$	3.88302	+	6.72560i	0.697412	+	1.20795i	−0.271949	+	0.962312i	$0.587668\pi$
$32$		0			0
$33$	−8.68028	−	4.75044i	−1.51104	−	0.826946i
$34$		0			0
$35$	2.71729	−	6.09686i	0.459306	−	1.03056i
$36$		0			0
$37$	−3.19562	−	5.53498i	−0.525357	−	0.909946i	−0.999564	−	0.0295319i	$-0.990598\pi$
$37$	−3.19562	−	5.53498i	−0.525357	−	0.909946i	0.474207	−	0.880414i	$-0.342735\pi$
$38$		0			0
$39$	−7.25836	+	4.41480i	−1.16227	+	0.706934i
$40$		0			0
$41$	5.21159	−	9.02673i	0.813913	−	1.40974i	−0.0961931	−	0.995363i	$-0.530667\pi$
$41$	5.21159	−	9.02673i	0.813913	−	1.40974i	0.910106	−	0.414376i	$-0.136000\pi$
$42$		0			0
$43$	4.42935	+	7.67185i	0.675469	+	1.16995i	0.976332	+	0.216279i	$0.0693921\pi$
$43$	4.42935	+	7.67185i	0.675469	+	1.16995i	−0.300863	+	0.953668i	$0.597275\pi$
$44$		0			0
$45$	−4.07992	−	6.37493i	−0.608198	−	0.950318i
$46$		0			0
$47$	−1.08052	+	1.87152i	−0.157610	+	0.272989i	−0.934006	−	0.357256i	$-0.883712\pi$
$47$	−1.08052	+	1.87152i	−0.157610	+	0.272989i	0.776396	+	0.630245i	$0.217046\pi$
$48$		0			0
$49$	−4.67994	−	5.20559i	−0.668562	−	0.743656i
$50$		0			0
$51$	7.38379	−	4.49109i	1.03394	−	0.628879i
$52$		0			0
$53$	−3.69858	+	6.40613i	−0.508039	+	0.879950i	0.491917	+	0.870642i	$0.336296\pi$
$53$	−3.69858	+	6.40613i	−0.508039	+	0.879950i	−0.999957	+	0.00930815i	$0.997037\pi$
$54$		0			0
$55$	14.4133			1.94348
$56$		0			0
$57$	−0.000303939	−	0.0132962i	−4.02578e−5	−	0.00176112i
$58$		0			0
$59$	0.261797	+	0.453446i	0.0340831	+	0.0590336i	0.882564	−	0.470193i	$-0.155816\pi$
$59$	0.261797	+	0.453446i	0.0340831	+	0.0590336i	−0.848481	+	0.529226i	$0.822482\pi$
$60$		0			0
$61$	4.49541	−	7.78628i	0.575578	−	0.996931i	−0.420400	−	0.907339i	$-0.638110\pi$
$61$	4.49541	−	7.78628i	0.575578	−	0.996931i	0.995979	−	0.0895919i	$-0.0285563\pi$
$62$		0			0
$63$	−7.84807	+	1.18650i	−0.988764	+	0.149485i
$64$		0			0
$65$	6.18730	−	10.7167i	0.767441	−	1.32925i
$66$		0			0
$67$	2.54791	+	4.41311i	0.311277	+	0.539147i	0.978639	−	0.205586i	$-0.0659101\pi$
$67$	2.54791	+	4.41311i	0.311277	+	0.539147i	−0.667362	+	0.744733i	$0.732577\pi$
$68$		0			0
$69$	1.01458	+	0.555250i	0.122142	+	0.0668443i
$70$		0			0
$71$	−5.68471			−0.674651			−0.337325	−	0.941388i	$-0.609522\pi$
$71$	−5.68471			−0.674651			−0.337325	+	0.941388i	$0.609522\pi$
$72$		0			0
$73$	−1.52062	+	2.63379i	−0.177975	+	0.308262i	−0.941187	−	0.337887i	$-0.890288\pi$
$73$	−1.52062	+	2.63379i	−0.177975	+	0.308262i	0.763212	+	0.646148i	$0.223621\pi$
$74$		0			0
$75$	2.07405	+	1.13506i	0.239491	+	0.131066i
$76$		0			0
$77$	6.15314	−	13.8060i	0.701215	−	1.57334i
$78$		0			0
$79$	−3.08115	+	5.33671i	−0.346657	+	0.600427i	−0.985653	−	0.168783i	$-0.946016\pi$
$79$	−3.08115	+	5.33671i	−0.346657	+	0.600427i	0.638997	+	0.769209i	$0.279350\pi$
$80$		0			0
$81$	−3.76965	+	8.17250i	−0.418850	+	0.908056i
$82$		0			0
$83$	−0.258726	−	0.448126i	−0.0283988	−	0.0491882i	0.851477	−	0.524392i	$-0.175708\pi$
$83$	−0.258726	−	0.448126i	−0.0283988	−	0.0491882i	−0.879876	+	0.475204i	$0.842374\pi$
$84$		0			0
$85$	−6.29422	+	10.9019i	−0.682704	+	1.18248i
$86$		0			0
$87$	0.304852	+	13.3361i	0.0326836	+	1.42978i
$88$		0			0
$89$	1.19093	+	2.06274i	0.126238	+	0.218650i	0.922216	−	0.386675i	$-0.126376\pi$
$89$	1.19093	+	2.06274i	0.126238	+	0.218650i	−0.795978	+	0.605325i	$0.793043\pi$
$90$		0			0
$91$	−7.62377	−	10.5017i	−0.799188	−	1.10087i
$92$		0			0
$93$	0.307402	+	13.4477i	0.0318761	+	1.39446i
$94$		0			0
$95$	0.00968615	+	0.0167769i	0.000993778	+	0.00172127i
$96$		0			0
$97$	4.32994	+	7.49968i	0.439639	+	0.761477i	0.997662	−	0.0683485i	$-0.0217730\pi$
$97$	4.32994	+	7.49968i	0.439639	+	0.761477i	−0.558022	+	0.829826i	$0.688440\pi$
$98$		0			0
$99$	−9.23873	−	14.4356i	−0.928527	−	1.45084i
$100$		0			0
$101$	−9.33566			−0.928933			−0.464466	−	0.885591i	$-0.653754\pi$
$101$	−9.33566			−0.928933			−0.464466	+	0.885591i	$0.653754\pi$
$102$		0			0
$103$	16.2185			1.59806			0.799029	−	0.601293i	$-0.205347\pi$
$103$	16.2185			1.59806			0.799029	+	0.601293i	$0.205347\pi$
$104$		0			0
$105$	9.19830	−	7.00408i	0.897663	−	0.683529i
$106$		0			0
$107$	4.50171	+	7.79718i	0.435196	+	0.753782i	0.997312	−	0.0732767i	$-0.0233456\pi$
$107$	4.50171	+	7.79718i	0.435196	+	0.753782i	−0.562115	+	0.827059i	$0.690012\pi$
$108$		0			0
$109$	3.71563	−	6.43566i	0.355893	−	0.616424i	−0.631378	−	0.775476i	$-0.717510\pi$
$109$	3.71563	−	6.43566i	0.355893	−	0.616424i	0.987270	+	0.159051i	$0.0508435\pi$
$110$		0			0
$111$	−0.252984	−	11.0671i	−0.0240121	−	1.05044i
$112$		0			0
$113$	7.14642	−	12.3780i	0.672278	−	1.16442i	−0.304978	−	0.952359i	$-0.598649\pi$
$113$	7.14642	−	12.3780i	0.672278	−	1.16442i	0.977256	−	0.212061i	$-0.0680175\pi$
$114$		0			0
$115$	−1.68468			−0.157097
$116$		0			0
$117$	−14.6993	+	0.672380i	−1.35895	+	0.0621615i
$118$		0			0
$119$	7.75551	+	10.6831i	0.710947	+	0.979321i
$120$		0			0
$121$	21.6380			1.96709
$122$		0			0
$123$	15.4244	−	9.38168i	1.39077	−	0.845917i
$124$		0			0
$125$	9.17064			0.820247
$126$		0			0
$127$	−1.96011			−0.173932			−0.0869660	−	0.996211i	$-0.527717\pi$
$127$	−1.96011			−0.173932			−0.0869660	+	0.996211i	$0.527717\pi$
$128$		0			0
$129$	0.350652	+	15.3397i	0.0308732	+	1.35059i
$130$		0			0
$131$	−3.98825			−0.348455			−0.174227	−	0.984705i	$-0.555743\pi$
$131$	−3.98825			−0.348455			−0.174227	+	0.984705i	$0.555743\pi$
$132$		0			0
$133$	0.0202051	−	0.00211583i	0.00175201	−	0.000183466i
$134$		0			0
$135$	−0.898147	−	13.0786i	−0.0773002	−	1.12563i
$136$		0			0
$137$	−7.40843			−0.632945			−0.316473	−	0.948602i	$-0.602499\pi$
$137$	−7.40843			−0.632945			−0.316473	+	0.948602i	$0.602499\pi$
$138$		0			0
$139$	6.92660	−	11.9972i	0.587507	−	1.01759i	−0.407051	−	0.913405i	$-0.633443\pi$
$139$	6.92660	−	11.9972i	0.587507	−	1.01759i	0.994558	−	0.104186i	$-0.0332238\pi$
$140$		0			0
$141$	−3.19795	+	1.94511i	−0.269316	+	0.163808i
$142$		0			0
$143$	14.0108	−	24.2674i	1.17164	−	2.02934i
$144$		0			0
$145$	−9.71524	−	16.8273i	−0.806807	−	1.39743i
$146$		0			0
$147$	−2.78214	−	11.8008i	−0.229467	−	0.973316i
$148$		0			0
$149$	−14.1040			−1.15545			−0.577724	−	0.816232i	$-0.696059\pi$
$149$	−14.1040			−1.15545			−0.577724	+	0.816232i	$0.696059\pi$
$150$		0			0
$151$	−10.6005			−0.862660			−0.431330	−	0.902194i	$-0.641956\pi$
$151$	−10.6005			−0.862660			−0.431330	+	0.902194i	$0.641956\pi$
$152$		0			0
$153$	14.9534	−	0.683999i	1.20891	−	0.0552980i
$154$		0			0
$155$	−9.79650	−	16.9680i	−0.786874	−	1.36291i
$156$		0			0
$157$	0.129779	+	0.224784i	0.0103575	+	0.0179397i	0.871158	−	0.491003i	$-0.163370\pi$
$157$	0.129779	+	0.224784i	0.0103575	+	0.0179397i	−0.860800	+	0.508943i	$0.830036\pi$
$158$		0			0
$159$	−10.9465	+	6.65803i	−0.868110	+	0.528016i
$160$		0			0
$161$	−0.719203	+	1.61370i	−0.0566811	+	0.127177i
$162$		0			0
$163$	6.31882	+	10.9445i	0.494928	+	0.857241i	0.999983	−	0.00584647i	$-0.00186100\pi$
$163$	6.31882	+	10.9445i	0.494928	+	0.857241i	−0.505055	+	0.863087i	$0.668528\pi$
$164$		0			0
$165$	21.8995	+	11.9849i	1.70487	+	0.933024i
$166$		0			0
$167$	−5.74959	+	9.95859i	−0.444917	+	0.770619i	−0.998046	−	0.0624765i	$-0.980100\pi$
$167$	−5.74959	+	9.95859i	−0.444917	+	0.770619i	0.553129	+	0.833095i	$0.313433\pi$
$168$		0			0
$169$	−5.52905	−	9.57659i	−0.425311	−	0.736661i
$170$		0			0
$171$	0.0105942	−	0.0204550i	0.000810162	−	0.00156423i
$172$		0			0
$173$	7.90471	−	13.6914i	0.600984	−	1.04094i	−0.391688	−	0.920098i	$-0.628109\pi$
$173$	7.90471	−	13.6914i	0.600984	−	1.04094i	0.992672	−	0.120837i	$-0.0385579\pi$
$174$		0			0
$175$	−1.47022	+	3.29878i	−0.111138	+	0.249364i
$176$		0			0
$177$	0.0207253	+	0.906654i	0.00155781	+	0.0681483i
$178$		0			0
$179$	−8.49849	+	14.7198i	−0.635207	+	1.10021i	0.351265	+	0.936276i	$0.385752\pi$
$179$	−8.49849	+	14.7198i	−0.635207	+	1.10021i	−0.986471	+	0.163934i	$0.947582\pi$
$180$		0			0
$181$	6.35841			0.472617			0.236308	−	0.971678i	$-0.424062\pi$
$181$	6.35841			0.472617			0.236308	+	0.971678i	$0.424062\pi$
$182$		0			0
$183$	13.3048	−	8.09245i	0.983516	−	0.598211i
$184$		0			0
$185$	8.06225	+	13.9642i	0.592749	+	1.02667i
$186$		0			0
$187$	−14.2529	+	24.6867i	−1.04227	+	1.80527i
$188$		0			0
$189$	−12.9110	−	4.72305i	−0.939134	−	0.343551i
$190$		0			0
$191$	2.07047	−	3.58616i	0.149814	−	0.259485i	−0.781345	−	0.624100i	$-0.785466\pi$
$191$	2.07047	−	3.58616i	0.149814	−	0.259485i	0.931159	+	0.364614i	$0.118799\pi$
$192$		0			0
$193$	3.84793	+	6.66481i	0.276980	+	0.479743i	0.970633	−	0.240566i	$-0.0773331\pi$
$193$	3.84793	+	6.66481i	0.276980	+	0.479743i	−0.693653	+	0.720310i	$0.744000\pi$
$194$		0			0
$195$	18.3122	−	11.1381i	1.31136	−	0.797618i
$196$		0			0
$197$	3.29508			0.234765			0.117383	−	0.993087i	$-0.462550\pi$
$197$	3.29508			0.234765			0.117383	+	0.993087i	$0.462550\pi$
$198$		0			0
$199$	8.08840	−	14.0095i	0.573371	−	0.993108i	−0.422845	−	0.906202i	$-0.638969\pi$
$199$	8.08840	−	14.0095i	0.573371	−	0.993108i	0.996216	−	0.0869063i	$-0.0276981\pi$
$200$		0			0
$201$	0.201707	+	8.82391i	0.0142273	+	0.622391i
$202$		0			0
$203$	−20.2658	+	2.12219i	−1.42238	+	0.148948i
$204$		0			0
$205$	−13.1483	+	22.7736i	−0.918319	+	1.59058i
$206$		0			0
$207$	1.07986	+	1.68729i	0.0750553	+	0.117275i
$208$		0			0
$209$	0.0219337	+	0.0379903i	0.00151719	+	0.00262784i
$210$		0			0
$211$	−13.9633	+	24.1851i	−0.961273	+	1.66497i	−0.241961	+	0.970286i	$0.577791\pi$
$211$	−13.9633	+	24.1851i	−0.961273	+	1.66497i	−0.719312	+	0.694687i	$0.755543\pi$
$212$		0			0
$213$	−8.63734	−	4.72694i	−0.591821	−	0.323885i
$214$		0			0
$215$	−11.1748	−	19.3554i	−0.762116	−	1.32002i
$216$		0			0
$217$	−20.4353	+	2.13994i	−1.38724	+	0.145268i
$218$		0			0
$219$	−4.50048	+	2.73736i	−0.304114	+	0.184973i
$220$		0			0
$221$	12.2369	+	21.1950i	0.823144	+	1.42573i
$222$		0			0
$223$	−10.1652	−	17.6066i	−0.680711	−	1.17903i	−0.974764	−	0.223237i	$-0.928338\pi$
$223$	−10.1652	−	17.6066i	−0.680711	−	1.17903i	0.294054	−	0.955789i	$-0.404996\pi$
$224$		0			0
$225$	2.20749	+	3.44923i	0.147166	+	0.229949i
$226$		0			0
$227$	−5.68939			−0.377618			−0.188809	−	0.982014i	$-0.560463\pi$
$227$	−5.68939			−0.377618			−0.188809	+	0.982014i	$0.560463\pi$
$228$		0			0
$229$	14.8542			0.981590			0.490795	−	0.871275i	$-0.336706\pi$
$229$	14.8542			0.981590			0.490795	+	0.871275i	$0.336706\pi$
$230$		0			0
$231$	20.8290	−	15.8603i	1.37045	−	1.04353i
$232$		0			0
$233$	6.70652	+	11.6160i	0.439358	+	0.760991i	0.997640	−	0.0686603i	$-0.0218725\pi$
$233$	6.70652	+	11.6160i	0.439358	+	0.760991i	−0.558282	+	0.829652i	$0.688539\pi$
$234$		0			0
$235$	2.72605	−	4.72166i	0.177828	−	0.308007i
$236$		0			0
$237$	−9.11908	+	5.54656i	−0.592348	+	0.360288i
$238$		0			0
$239$	−9.33123	+	16.1622i	−0.603587	+	1.04544i	0.388686	+	0.921370i	$0.372929\pi$
$239$	−9.33123	+	16.1622i	−0.603587	+	1.04544i	−0.992273	+	0.124073i	$0.960404\pi$
$240$		0			0
$241$	−21.4160			−1.37952			−0.689762	−	0.724036i	$-0.742285\pi$
$241$	−21.4160			−1.37952			−0.689762	+	0.724036i	$0.742285\pi$
$242$		0			0
$243$	−12.5232	+	9.28276i	−0.803363	+	0.595489i
$244$		0			0
$245$	11.8070	+	13.1332i	0.754324	+	0.839050i
$246$		0			0
$247$	0.0376627			0.00239642
$248$		0			0
$249$	−0.0204822	−	0.896018i	−0.00129801	−	0.0567829i
$250$		0			0
$251$	−0.462898			−0.0292179			−0.0146089	−	0.999893i	$-0.504650\pi$
$251$	−0.462898			−0.0292179			−0.0146089	+	0.999893i	$0.504650\pi$
$252$		0			0
$253$	−3.81485			−0.239838
$254$		0			0
$255$	−18.6286	+	11.3306i	−1.16657	+	0.709550i
$256$		0			0
$257$	0.802512			0.0500593			0.0250297	−	0.999687i	$-0.492032\pi$
$257$	0.802512			0.0500593			0.0250297	+	0.999687i	$0.492032\pi$
$258$		0			0
$259$	16.8177	−	1.76111i	1.04500	−	0.109430i
$260$		0			0
$261$	−10.6261	+	20.5164i	−0.657737	+	1.26993i
$262$		0			0
$263$	0.201387			0.0124180			0.00620902	−	0.999981i	$-0.498024\pi$
$263$	0.201387			0.0124180			0.00620902	+	0.999981i	$0.498024\pi$
$264$		0			0
$265$	9.33117	−	16.1621i	0.573209	−	0.992828i
$266$		0			0
$267$	0.0942803	+	4.12441i	0.00576986	+	0.252410i
$268$		0			0
$269$	−11.1773	+	19.3596i	−0.681490	+	1.18038i	0.293036	+	0.956101i	$0.405334\pi$
$269$	−11.1773	+	19.3596i	−0.681490	+	1.18038i	−0.974526	+	0.224274i	$0.927999\pi$
$270$		0			0
$271$	−1.78925	−	3.09907i	−0.108689	−	0.188255i	0.806550	−	0.591166i	$-0.201332\pi$
$271$	−1.78925	−	3.09907i	−0.108689	−	0.188255i	−0.915240	+	0.402910i	$0.867999\pi$
$272$		0			0
$273$	−2.85122	−	22.2955i	−0.172564	−	1.34939i
$274$		0			0
$275$	−7.79847			−0.470266
$276$		0			0
$277$	−10.1067			−0.607254			−0.303627	−	0.952791i	$-0.598198\pi$
$277$	−10.1067			−0.607254			−0.303627	+	0.952791i	$0.598198\pi$
$278$		0			0
$279$	−10.7149	+	20.6880i	−0.641487	+	1.23856i
$280$		0			0
$281$	12.7114	+	22.0167i	0.758296	+	1.31341i	0.943719	+	0.330749i	$0.107301\pi$
$281$	12.7114	+	22.0167i	0.758296	+	1.31341i	−0.185422	+	0.982659i	$0.559365\pi$
$282$		0			0
$283$	−1.93833	−	3.35728i	−0.115222	−	0.199570i	0.802647	−	0.596455i	$-0.203425\pi$
$283$	−1.93833	−	3.35728i	−0.115222	−	0.199570i	−0.917868	+	0.396885i	$0.870091\pi$
$284$		0			0
$285$	0.000766810		0.0335450i	4.54219e−5		0.00198704i
$286$		0			0
$287$	16.2009	+	22.3166i	0.956308	+	1.31730i
$288$		0			0
$289$	−3.94838	−	6.83879i	−0.232257	−	0.402282i
$290$		0			0
$291$	0.342783	+	14.9954i	0.0200943	+	0.879049i
$292$		0			0
$293$	0.428834	−	0.742762i	0.0250527	−	0.0433926i	−0.853227	−	0.521539i	$-0.825358\pi$
$293$	0.428834	−	0.742762i	0.0250527	−	0.0433926i	0.878280	+	0.478147i	$0.158691\pi$
$294$		0			0
$295$	−0.660489	−	1.14400i	−0.0384551	−	0.0666063i
$296$		0			0
$297$	−2.03380	−	29.6157i	−0.118013	−	1.71848i
$298$		0			0
$299$	−1.63763	+	2.83647i	−0.0947068	+	0.164037i
$300$		0			0
$301$	−23.3104	+	2.44102i	−1.34359	+	0.140698i
$302$		0			0
$303$	−14.1846	−	7.76278i	−0.814884	−	0.445960i
$304$		0			0
$305$	−11.3415	+	19.6440i	−0.649412	+	1.12481i
$306$		0			0
$307$	−0.717950			−0.0409756			−0.0204878	−	0.999790i	$-0.506522\pi$
$307$	−0.717950			−0.0409756			−0.0204878	+	0.999790i	$0.506522\pi$
$308$		0			0
$309$	24.6424	+	13.4860i	1.40186	+	0.767192i
$310$		0			0
$311$	4.72606	+	8.18578i	0.267990	+	0.464173i	0.968343	−	0.249624i	$-0.0803071\pi$
$311$	4.72606	+	8.18578i	0.267990	+	0.464173i	−0.700352	+	0.713797i	$0.746974\pi$
$312$		0			0
$313$	11.6317	−	20.1467i	0.657464	−	1.13876i	−0.323806	−	0.946124i	$-0.604962\pi$
$313$	11.6317	−	20.1467i	0.657464	−	1.13876i	0.981270	−	0.192638i	$-0.0617043\pi$
$314$		0			0
$315$	19.7999	−	2.99343i	1.11560	−	0.168661i
$316$		0			0
$317$	−6.61771	+	11.4622i	−0.371687	+	0.643781i	−0.989825	−	0.142288i	$-0.954554\pi$
$317$	−6.61771	+	11.4622i	−0.371687	+	0.643781i	0.618138	+	0.786070i	$0.287887\pi$
$318$		0			0
$319$	−21.9996	−	38.1044i	−1.23174	−	2.13344i
$320$		0			0
$321$	0.356380	+	15.5903i	0.0198912	+	0.870165i
$322$		0			0
$323$	−0.0383135			−0.00213182
$324$		0			0
$325$	−3.34772	+	5.79841i	−0.185698	+	0.321638i
$326$		0			0
$327$	10.9969	−	6.68872i	0.608130	−	0.369887i
$328$		0			0
$329$	−3.35894	−	4.62690i	−0.185184	−	0.255089i
$330$		0			0
$331$	15.2165	−	26.3558i	0.836375	−	1.44864i	−0.0565316	−	0.998401i	$-0.518004\pi$
$331$	15.2165	−	26.3558i	0.836375	−	1.44864i	0.892906	−	0.450243i	$-0.148662\pi$
$332$		0			0
$333$	8.81810	−	17.0257i	0.483229	−	0.933001i
$334$		0			0
$335$	−6.42813	−	11.1339i	−0.351206	−	0.608307i
$336$		0			0
$337$	−0.767420	+	1.32921i	−0.0418041	+	0.0724067i	−0.886170	−	0.463360i	$-0.846644\pi$
$337$	−0.767420	+	1.32921i	−0.0418041	+	0.0724067i	0.844366	+	0.535766i	$0.179977\pi$
$338$		0			0
$339$	21.1508	−	12.8647i	1.14875	−	0.698713i
$340$		0			0
$341$	−22.1836	−	38.4231i	−1.20131	−	2.08073i
$342$		0			0
$343$	17.6204	−	5.70287i	0.951410	−	0.307926i
$344$		0			0
$345$	−2.55970	−	1.40084i	−0.137810	−	0.0754189i
$346$		0			0
$347$	14.3036	+	24.7745i	0.767856	+	1.32997i	0.938723	+	0.344672i	$0.112010\pi$
$347$	14.3036	+	24.7745i	0.767856	+	1.32997i	−0.170867	+	0.985294i	$0.554657\pi$
$348$		0			0
$349$	−9.05123	−	15.6772i	−0.484501	−	0.839181i	0.515340	−	0.856986i	$-0.327666\pi$
$349$	−9.05123	−	15.6772i	−0.484501	−	0.839181i	−0.999841	+	0.0178047i	$0.994332\pi$
$350$		0			0
$351$	−22.8933	−	11.2012i	−1.22195	−	0.597875i
$352$		0			0
$353$	14.5908			0.776591			0.388295	−	0.921535i	$-0.373064\pi$
$353$	14.5908			0.776591			0.388295	+	0.921535i	$0.373064\pi$
$354$		0			0
$355$	14.3420			0.761193
$356$		0			0
$357$	2.90049	+	22.6808i	0.153510	+	1.20040i
$358$		0			0
$359$	−1.05831	−	1.83304i	−0.0558554	−	0.0967443i	0.836746	−	0.547592i	$-0.184455\pi$
$359$	−1.05831	−	1.83304i	−0.0558554	−	0.0967443i	−0.892601	+	0.450847i	$0.851122\pi$
$360$		0			0
$361$	9.49997	−	16.4544i	0.499998	−	0.866023i
$362$		0			0
$363$	32.8767	+	17.9924i	1.72558	+	0.944356i
$364$		0			0
$365$	3.83638	−	6.64480i	0.200805	−	0.347805i
$366$		0			0
$367$	6.66209			0.347758			0.173879	−	0.984767i	$-0.444370\pi$
$367$	6.66209			0.347758			0.173879	+	0.984767i	$0.444370\pi$
$368$		0			0
$369$	31.2368	−	1.42884i	1.62613	−	0.0743825i
$370$		0			0
$371$	−11.4975	−	15.8377i	−0.596922	−	0.822253i
$372$		0			0
$373$	−12.4983			−0.647138			−0.323569	−	0.946205i	$-0.604883\pi$
$373$	−12.4983			−0.647138			−0.323569	+	0.946205i	$0.604883\pi$
$374$		0			0
$375$	13.9339	+	7.62556i	0.719542	+	0.393782i
$376$		0			0
$377$	−37.7758			−1.94555
$378$		0			0
$379$	−19.5504			−1.00423			−0.502117	−	0.864800i	$-0.667445\pi$
$379$	−19.5504			−1.00423			−0.502117	+	0.864800i	$0.667445\pi$
$380$		0			0
$381$	−2.97820	−	1.62987i	−0.152578	−	0.0835009i
$382$		0			0
$383$	−2.67480			−0.136676			−0.0683379	−	0.997662i	$-0.521770\pi$
$383$	−2.67480			−0.136676			−0.0683379	+	0.997662i	$0.521770\pi$
$384$		0			0
$385$	−15.5238	+	34.8311i	−0.791165	+	1.77516i
$386$		0			0
$387$	−12.2225	+	23.5987i	−0.621304	+	1.19959i
$388$		0			0
$389$	−3.96310			−0.200937			−0.100469	−	0.994940i	$-0.532034\pi$
$389$	−3.96310			−0.200937			−0.100469	+	0.994940i	$0.532034\pi$
$390$		0			0
$391$	1.66593	−	2.88548i	0.0842499	−	0.145925i
$392$		0			0
$393$	−6.05974	−	3.31631i	−0.305673	−	0.167285i
$394$		0			0
$395$	7.77345	−	13.4640i	0.391125	−	0.677448i
$396$		0			0
$397$	10.2978	+	17.8362i	0.516829	+	0.895175i	0.999809	+	0.0195431i	$0.00622114\pi$
$397$	10.2978	+	17.8362i	0.516829	+	0.895175i	−0.482980	+	0.875632i	$0.660446\pi$
$398$		0			0
$399$	0.0324590	+	0.0135861i	0.00162498	+	0.000680158i
$400$		0			0
$401$	−3.83957			−0.191739			−0.0958696	−	0.995394i	$-0.530563\pi$
$401$	−3.83957			−0.191739			−0.0958696	+	0.995394i	$0.530563\pi$
$402$		0			0
$403$	−38.0917			−1.89748
$404$		0			0
$405$	9.51046	−	20.6184i	0.472579	−	1.02454i
$406$		0			0
$407$	18.2565	+	31.6212i	0.904940	+	1.56740i
$408$		0			0
$409$	14.7113	+	25.4808i	0.727428	+	1.25994i	0.957967	+	0.286880i	$0.0926180\pi$
$409$	14.7113	+	25.4808i	0.727428	+	1.25994i	−0.230538	+	0.973063i	$0.574049\pi$
$410$		0			0
$411$	−11.2564	−	6.16026i	−0.555236	−	0.303863i
$412$		0			0
$413$	−1.37777	+	0.144276i	−0.0677954	+	0.00709938i
$414$		0			0
$415$	0.652741	+	1.13058i	0.0320418	+	0.0554980i
$416$		0			0
$417$	20.5002	−	12.4690i	1.00390	−	0.610609i
$418$		0			0
$419$	4.40821	−	7.63525i	0.215355	−	0.373006i	−0.738027	−	0.674771i	$-0.764242\pi$
$419$	4.40821	−	7.63525i	0.215355	−	0.373006i	0.953382	+	0.301765i	$0.0975757\pi$
$420$		0			0
$421$	−17.6437	−	30.5597i	−0.859899	−	1.48939i	−0.872024	−	0.489462i	$-0.837193\pi$
$421$	−17.6437	−	30.5597i	−0.859899	−	1.48939i	0.0121255	−	0.999926i	$-0.496140\pi$
$422$		0			0
$423$	−6.47635	+	0.296242i	−0.314891	+	0.0144038i
$424$		0			0
$425$	3.40557	−	5.89861i	0.165194	−	0.286125i
$426$		0			0
$427$	13.9746	+	19.2498i	0.676277	+	0.931564i
$428$		0			0
$429$	41.4668	−	25.2216i	2.00203	−	1.21771i
$430$		0			0
$431$	−12.8099	+	22.1873i	−0.617030	+	1.06873i	0.372995	+	0.927833i	$0.378331\pi$
$431$	−12.8099	+	22.1873i	−0.617030	+	1.06873i	−0.990025	+	0.140893i	$0.955003\pi$
$432$		0			0
$433$	16.8556			0.810030			0.405015	−	0.914310i	$-0.367266\pi$
$433$	16.8556			0.810030			0.405015	+	0.914310i	$0.367266\pi$
$434$		0			0
$435$	−0.769113	−	33.6458i	−0.0368762	−	1.61319i
$436$		0			0
$437$	−0.00256370	−	0.00444045i	−0.000122638	−	0.000212416i
$438$		0			0
$439$	−15.4596	+	26.7768i	−0.737846	+	1.27799i	0.215618	+	0.976478i	$0.430824\pi$
$439$	−15.4596	+	26.7768i	−0.737846	+	1.27799i	−0.953463	+	0.301509i	$0.902510\pi$
$440$		0			0
$441$	5.58544	−	20.2436i	0.265973	−	0.963980i
$442$		0			0
$443$	4.65544	−	8.06345i	0.221186	−	0.383106i	−0.733982	−	0.679169i	$-0.762340\pi$
$443$	4.65544	−	8.06345i	0.221186	−	0.383106i	0.955169	+	0.296063i	$0.0956737\pi$
$444$		0			0
$445$	−3.00459	−	5.20410i	−0.142431	−	0.246698i
$446$		0			0
$447$	−21.4297	−	11.7278i	−1.01359	−	0.554705i
$448$		0			0
$449$	23.8055			1.12345			0.561724	−	0.827324i	$-0.310138\pi$
$449$	23.8055			1.12345			0.561724	+	0.827324i	$0.310138\pi$
$450$		0			0
$451$	−29.7736	+	51.5694i	−1.40198	+	2.42831i
$452$		0			0
$453$	−16.1065	−	8.81456i	−0.756748	−	0.414144i
$454$		0			0
$455$	19.2340	+	26.4947i	0.901706	+	1.24209i
$456$		0			0
$457$	6.90552	−	11.9607i	0.323027	−	0.559498i	−0.658084	−	0.752944i	$-0.728633\pi$
$457$	6.90552	−	11.9607i	0.323027	−	0.559498i	0.981111	+	0.193446i	$0.0619663\pi$
$458$		0			0
$459$	23.2889	+	11.3947i	1.08703	+	0.531861i
$460$		0			0
$461$	−0.00256407	−	0.00444110i	−0.000119421	−	0.000206843i	0.865966	−	0.500103i	$-0.166705\pi$
$461$	−0.00256407	−	0.00444110i	−0.000119421	−	0.000206843i	−0.866085	+	0.499897i	$0.833371\pi$
$462$		0			0
$463$	12.9682	−	22.4616i	0.602685	−	1.04388i	−0.389728	−	0.920930i	$-0.627431\pi$
$463$	12.9682	−	22.4616i	0.602685	−	1.04388i	0.992413	−	0.122951i	$-0.0392358\pi$
$464$		0			0
$465$	−0.775546	−	33.9272i	−0.0359651	−	1.57334i
$466$		0			0
$467$	−12.0484	−	20.8684i	−0.557532	−	0.965673i	−0.997702	−	0.0677588i	$-0.978415\pi$
$467$	−12.0484	−	20.8684i	−0.557532	−	0.965673i	0.440170	−	0.897914i	$-0.354918\pi$
$468$		0			0
$469$	−13.4090	+	1.40416i	−0.619168	+	0.0648379i
$470$		0			0
$471$	0.0102740	+	0.449450i	0.000473402	+	0.0207095i
$472$		0			0
$473$	−25.3047	−	43.8290i	−1.16351	−	2.01526i
$474$		0			0
$475$	−0.00524081	−	0.00907735i	−0.000240465	−	0.000416497i
$476$		0			0
$477$	−22.1683	+	1.01403i	−1.01502	+	0.0464291i
$478$		0			0
$479$	14.7823			0.675420			0.337710	−	0.941250i	$-0.390348\pi$
$479$	14.7823			0.675420			0.337710	+	0.941250i	$0.390348\pi$
$480$		0			0
$481$	31.3485			1.42937
$482$		0			0
$483$	−2.43458	+	1.85382i	−0.110777	+	0.0843516i
$484$		0			0
$485$	−10.9240	−	18.9210i	−0.496035	−	0.859158i
$486$		0			0
$487$	9.38360	−	16.2529i	0.425211	−	0.736488i	−0.571229	−	0.820791i	$-0.693533\pi$
$487$	9.38360	−	16.2529i	0.425211	−	0.736488i	0.996440	+	0.0843033i	$0.0268664\pi$
$488$		0			0
$489$	0.500234	+	21.8833i	0.0226213	+	0.989598i
$490$		0			0
$491$	18.2871	−	31.6741i	0.825284	−	1.42943i	−0.0764182	−	0.997076i	$-0.524348\pi$
$491$	18.2871	−	31.6741i	0.825284	−	1.42943i	0.901702	−	0.432358i	$-0.142318\pi$
$492$		0			0
$493$	38.4286			1.73074
$494$		0			0
$495$	23.3084	+	36.4197i	1.04764	+	1.63695i
$496$		0			0
$497$	6.12270	−	13.7377i	0.274641	−	0.616219i
$498$		0			0
$499$	4.63182			0.207349			0.103674	−	0.994611i	$-0.466940\pi$
$499$	4.63182			0.207349			0.103674	+	0.994611i	$0.466940\pi$
$500$		0			0
$501$	−17.0167	+	10.3502i	−0.760250	+	0.462412i
$502$		0			0
$503$	16.4143			0.731879			0.365940	−	0.930639i	$-0.380748\pi$
$503$	16.4143			0.731879			0.365940	+	0.930639i	$0.380748\pi$
$504$		0			0
$505$	23.5530			1.04809
$506$		0			0
$507$	−0.437711	−	19.1482i	−0.0194394	−	0.850401i
$508$		0			0
$509$	10.4834			0.464668			0.232334	−	0.972636i	$-0.425364\pi$
$509$	10.4834			0.464668			0.232334	+	0.972636i	$0.425364\pi$
$510$		0			0
$511$	−4.72705	−	6.51145i	−0.209112	−	0.288050i
$512$		0			0
$513$	0.0331056	−	0.0222700i	0.00146165	−	0.000983243i
$514$		0			0
$515$	−40.9178			−1.80305
$516$		0			0
$517$	6.17298	−	10.6919i	0.271487	−	0.470230i
$518$		0			0
$519$	23.3951	−	14.2297i	1.02693	−	0.624616i
$520$		0			0
$521$	−11.0087	+	19.0675i	−0.482298	+	0.835364i	−0.999793	−	0.0203215i	$-0.993531\pi$
$521$	−11.0087	+	19.0675i	−0.482298	+	0.835364i	0.517496	+	0.855686i	$0.326864\pi$
$522$		0			0
$523$	−1.18541	−	2.05320i	−0.0518346	−	0.0897801i	0.838944	−	0.544218i	$-0.183174\pi$
$523$	−1.18541	−	2.05320i	−0.0518346	−	0.0897801i	−0.890778	+	0.454438i	$0.849840\pi$
$524$		0			0
$525$	−4.97685	+	3.78964i	−0.217208	+	0.165394i
$526$		0			0
$527$	38.7500			1.68798
$528$		0			0
$529$	−22.5541			−0.980613
$530$		0			0
$531$	−0.722411	+	1.39480i	−0.0313500	+	0.0605293i
$532$		0			0
$533$	25.5623	+	44.2753i	1.10723	+	1.91777i
$534$		0			0
$535$	−11.3574	−	19.6715i	−0.491022	−	0.850475i
$536$		0			0
$537$	−25.1524	+	15.2986i	−1.08541	+	0.660184i
$538$		0			0
$539$	26.7363	+	29.7394i	1.15161	+	1.28097i
$540$		0			0
$541$	6.65209	+	11.5218i	0.285996	+	0.495359i	0.972850	−	0.231436i	$-0.0743423\pi$
$541$	6.65209	+	11.5218i	0.285996	+	0.495359i	−0.686854	+	0.726795i	$0.741009\pi$
$542$		0			0
$543$	9.66096	+	5.28714i	0.414592	+	0.226893i
$544$		0			0
$545$	−9.37418	+	16.2366i	−0.401546	+	0.695498i
$546$		0			0
$547$	−2.43685	−	4.22074i	−0.104192	−	0.180466i	0.809216	−	0.587512i	$-0.199892\pi$
$547$	−2.43685	−	4.22074i	−0.104192	−	0.180466i	−0.913408	+	0.407046i	$0.866559\pi$
$548$		0			0
$549$	26.9443	−	1.23249i	1.14995	−	0.0526014i
$550$		0			0
$551$	0.0295688	−	0.0512146i	0.00125967	−	0.00218182i
$552$		0			0
$553$	−9.57816	−	13.1938i	−0.407305	−	0.561058i
$554$		0			0
$555$	0.638254	+	27.9212i	0.0270924	+	1.18519i
$556$		0			0
$557$	7.09601	−	12.2907i	0.300668	−	0.520772i	−0.675620	−	0.737250i	$-0.736124\pi$
$557$	7.09601	−	12.2907i	0.300668	−	0.520772i	0.976287	+	0.216479i	$0.0694572\pi$
$558$		0			0
$559$	−43.4511			−1.83778
$560$		0			0
$561$	−42.1833	+	25.6575i	−1.78098	+	1.08326i
$562$		0			0
$563$	−3.51985	−	6.09657i	−0.148344	−	0.256940i	0.782271	−	0.622938i	$-0.214061\pi$
$563$	−3.51985	−	6.09657i	−0.148344	−	0.256940i	−0.930616	+	0.365998i	$0.880728\pi$
$564$		0			0
$565$	−18.0297	+	31.2284i	−0.758516	+	1.31379i
$566$		0			0
$567$	−15.6896	−	17.9119i	−0.658901	−	0.752230i
$568$		0			0
$569$	9.15081	−	15.8497i	0.383622	−	0.664453i	−0.607955	−	0.793972i	$-0.708010\pi$
$569$	9.15081	−	15.8497i	0.383622	−	0.664453i	0.991577	+	0.129519i	$0.0413432\pi$
$570$		0			0
$571$	15.2192	+	26.3604i	0.636902	+	1.10315i	0.986109	+	0.166102i	$0.0531180\pi$
$571$	15.2192	+	26.3604i	0.636902	+	1.10315i	−0.349206	+	0.937046i	$0.613549\pi$
$572$		0			0
$573$	6.12783	−	3.72717i	0.255994	−	0.155705i
$574$		0			0
$575$	0.911516			0.0380128
$576$		0			0
$577$	5.65385	−	9.79275i	0.235373	−	0.407678i	−0.724008	−	0.689791i	$-0.757702\pi$
$577$	5.65385	−	9.79275i	0.235373	−	0.407678i	0.959381	+	0.282114i	$0.0910356\pi$
$578$		0			0
$579$	0.304624	+	13.3261i	0.0126597	+	0.553815i
$580$		0			0
$581$	1.36160	−	0.142584i	0.0564888	−	0.00591538i
$582$		0			0
$583$	21.1299	−	36.5980i	0.875110	−	1.51573i
$584$		0			0
$585$	37.0850	−	1.69635i	1.53328	−	0.0701354i
$586$		0			0
$587$	−9.89755	−	17.1431i	−0.408516	−	0.707570i	0.586208	−	0.810161i	$-0.300620\pi$
$587$	−9.89755	−	17.1431i	−0.408516	−	0.707570i	−0.994724	+	0.102591i	$0.967287\pi$
$588$		0			0
$589$	0.0298161	−	0.0516430i	0.00122855	−	0.00212791i
$590$		0			0
$591$	5.00655	+	2.73993i	0.205942	+	0.112706i
$592$		0			0
$593$	2.69067	+	4.66038i	0.110493	+	0.191379i	0.915969	−	0.401249i	$-0.131424\pi$
$593$	2.69067	+	4.66038i	0.110493	+	0.191379i	−0.805476	+	0.592628i	$0.798090\pi$
$594$		0			0
$595$	−19.5664	−	26.9525i	−0.802145	−	1.10495i
$596$		0			0
$597$	23.9387	−	14.5604i	0.979746	−	0.595917i
$598$		0			0
$599$	−1.12979	−	1.95686i	−0.0461622	−	0.0799552i	0.842021	−	0.539445i	$-0.181366\pi$
$599$	−1.12979	−	1.95686i	−0.0461622	−	0.0799552i	−0.888183	+	0.459489i	$0.848032\pi$
$600$		0			0
$601$	18.1873	+	31.5013i	0.741875	+	1.28496i	0.951641	+	0.307213i	$0.0993964\pi$
$601$	18.1873	+	31.5013i	0.741875	+	1.28496i	−0.209766	+	0.977752i	$0.567270\pi$
$602$		0			0
$603$	−7.03078	+	13.5748i	−0.286316	+	0.552808i
$604$		0			0
$605$	−54.5905			−2.21942
$606$		0			0
$607$	16.2161			0.658190			0.329095	−	0.944297i	$-0.393256\pi$
$607$	16.2161			0.658190			0.329095	+	0.944297i	$0.393256\pi$
$608$		0			0
$609$	−32.5565	−	13.6269i	−1.31925	−	0.552192i
$610$		0			0
$611$	−5.29985	−	9.17961i	−0.214409	−	0.371367i
$612$		0			0
$613$	21.6357	−	37.4741i	0.873857	−	1.51357i	0.0158822	−	0.999874i	$-0.494944\pi$
$613$	21.6357	−	37.4741i	0.873857	−	1.51357i	0.857975	−	0.513691i	$-0.171722\pi$
$614$		0			0
$615$	−38.9142	+	23.6691i	−1.56917	+	0.954429i
$616$		0			0
$617$	−5.92248	+	10.2580i	−0.238430	+	0.412973i	−0.960264	−	0.279093i	$-0.909966\pi$
$617$	−5.92248	+	10.2580i	−0.238430	+	0.412973i	0.721834	+	0.692066i	$0.243299\pi$
$618$		0			0
$619$	40.3288			1.62095			0.810475	−	0.585773i	$-0.199209\pi$
$619$	40.3288			1.62095			0.810475	+	0.585773i	$0.199209\pi$
$620$		0			0
$621$	0.237718	+	3.46160i	0.00953931	+	0.138909i
$622$		0			0
$623$	−6.26751	+	0.656320i	−0.251103	+	0.0262949i
$624$		0			0
$625$	−29.9619			−1.19848
$626$		0			0
$627$	0.00173640	+	0.0759607i	6.93450e−5	+	0.00303358i
$628$		0			0
$629$	−31.8902			−1.27154
$630$		0			0
$631$	13.9489			0.555298			0.277649	−	0.960683i	$-0.410445\pi$
$631$	13.9489			0.555298			0.277649	+	0.960683i	$0.410445\pi$
$632$		0			0
$633$	−41.3262	+	25.1361i	−1.64257	+	0.999072i
$634$		0			0
$635$	4.94518			0.196243
$636$		0			0
$637$	33.5895	−	7.11283i	1.33086	−	0.281821i
$638$		0			0
$639$	−9.19303	−	14.3642i	−0.363671	−	0.568240i
$640$		0			0
$641$	17.5395			0.692768			0.346384	−	0.938093i	$-0.387409\pi$
$641$	17.5395			0.692768			0.346384	+	0.938093i	$0.387409\pi$
$642$		0			0
$643$	−13.5329	+	23.4397i	−0.533686	+	0.924371i	0.465540	+	0.885027i	$0.345860\pi$
$643$	−13.5329	+	23.4397i	−0.533686	+	0.924371i	−0.999226	+	0.0393443i	$0.987473\pi$
$644$		0			0
$645$	−0.884662	−	38.7006i	−0.0348335	−	1.52383i
$646$		0			0
$647$	11.3252	−	19.6159i	0.445240	−	0.771179i	−0.552828	−	0.833295i	$-0.686452\pi$
$647$	11.3252	−	19.6159i	0.445240	−	0.771179i	0.998069	+	0.0621160i	$0.0197849\pi$
$648$		0			0
$649$	−1.49564	−	2.59052i	−0.0587089	−	0.101687i
$650$		0			0
$651$	−32.8288	−	13.7409i	−1.28666	−	0.538549i
$652$		0			0
$653$	−0.784108			−0.0306845			−0.0153423	−	0.999882i	$-0.504884\pi$
$653$	−0.784108			−0.0306845			−0.0153423	+	0.999882i	$0.504884\pi$
$654$		0			0
$655$	10.0620			0.393154
$656$		0			0
$657$	−9.11419	+	0.416903i	−0.355578	+	0.0162649i
$658$		0			0
$659$	−16.7219	−	28.9632i	−0.651392	−	1.12824i	−0.982785	−	0.184752i	$-0.940852\pi$
$659$	−16.7219	−	28.9632i	−0.651392	−	1.12824i	0.331393	−	0.943493i	$-0.392481\pi$
$660$		0			0
$661$	−1.53258	−	2.65450i	−0.0596104	−	0.103248i	0.834680	−	0.550735i	$-0.185652\pi$
$661$	−1.53258	−	2.65450i	−0.0596104	−	0.103248i	−0.894291	+	0.447487i	$0.852319\pi$
$662$		0			0
$663$	0.968743	+	42.3788i	0.0376229	+	1.64586i
$664$		0			0
$665$	−0.0509756	+	0.00533805i	−0.00197675	+	0.000207001i
$666$		0			0
$667$	2.57140	+	4.45379i	0.0995649	+	0.172451i
$668$		0			0
$669$	−0.804733	−	35.2040i	−0.0311128	−	1.36107i
$670$		0			0
$671$	−25.6821	+	44.4827i	−0.991447	+	1.71724i
$672$		0			0
$673$	14.4618	+	25.0487i	0.557463	+	0.965555i	0.997707	+	0.0676766i	$0.0215586\pi$
$673$	14.4618	+	25.0487i	0.557463	+	0.965555i	−0.440244	+	0.897878i	$0.645108\pi$
$674$		0			0
$675$	0.485953	+	7.07633i	0.0187044	+	0.272368i
$676$		0			0
$677$	5.85818	−	10.1467i	0.225148	−	0.389968i	−0.731216	−	0.682146i	$-0.761047\pi$
$677$	5.85818	−	10.1467i	0.225148	−	0.389968i	0.956364	+	0.292178i	$0.0943801\pi$
$678$		0			0
$679$	−22.7873	+	2.38624i	−0.874497	+	0.0915753i
$680$		0			0
$681$	−8.64446	−	4.73084i	−0.331256	−	0.181286i
$682$		0			0
$683$	20.7190	−	35.8864i	0.792791	−	1.37315i	−0.131441	−	0.991324i	$-0.541960\pi$
$683$	20.7190	−	35.8864i	0.792791	−	1.37315i	0.924232	−	0.381831i	$-0.124706\pi$
$684$		0			0
$685$	18.6908			0.714138
$686$		0			0
$687$	22.5694	+	12.3515i	0.861076	+	0.471240i
$688$		0			0
$689$	−18.1412	−	31.4215i	−0.691125	−	1.19706i
$690$		0			0
$691$	3.45675	−	5.98727i	0.131501	−	0.227766i	−0.792754	−	0.609541i	$-0.791354\pi$
$691$	3.45675	−	5.98727i	0.131501	−	0.227766i	0.924255	+	0.381775i	$0.124687\pi$
$692$		0			0
$693$	44.8358	−	6.77845i	1.70317	−	0.257492i
$694$		0			0
$695$	−17.4752	+	30.2679i	−0.662871	+	1.14813i
$696$		0			0
$697$	−26.0041	−	45.0404i	−0.984974	−	1.70603i
$698$		0			0
$699$	0.530926	+	23.2260i	0.0200815	+	0.878487i
$700$		0			0
$701$	39.1954			1.48039			0.740195	−	0.672392i	$-0.234733\pi$
$701$	39.1954			1.48039			0.740195	+	0.672392i	$0.234733\pi$
$702$		0			0
$703$	−0.0245378	+	0.0425008i	−0.000925462	+	0.00160295i
$704$		0			0
$705$	8.06811	−	4.90732i	0.303863	−	0.184820i
$706$		0			0
$707$	10.0550	−	22.5606i	0.378155	−	0.848478i
$708$		0			0
$709$	−10.2436	+	17.7424i	−0.384705	+	0.666328i	−0.991728	−	0.128356i	$-0.959030\pi$
$709$	−10.2436	+	17.7424i	−0.384705	+	0.666328i	0.607023	+	0.794684i	$0.292363\pi$
$710$		0			0
$711$	−18.4676	+	0.844748i	−0.692589	+	0.0316805i
$712$		0			0
$713$	2.59290	+	4.49104i	0.0971050	+	0.168191i
$714$		0			0
$715$	−35.3479	+	61.2243i	−1.32193	+	2.28966i
$716$		0			0
$717$	−27.6170	+	16.7977i	−1.03138	+	0.627321i
$718$		0			0
$719$	17.1300	+	29.6700i	0.638840	+	1.10650i	0.985688	+	0.168582i	$0.0539187\pi$
$719$	17.1300	+	29.6700i	0.638840	+	1.10650i	−0.346848	+	0.937921i	$0.612748\pi$
$720$		0			0
$721$	−17.4681	+	39.1937i	−0.650547	+	1.45965i
$722$		0			0
$723$	−32.5394	−	17.8078i	−1.21015	−	0.662279i
$724$		0			0
$725$	5.25655	+	9.10461i	0.195223	+	0.338137i
$726$		0			0
$727$	7.18914	+	12.4520i	0.266631	+	0.461818i	0.967990	−	0.250991i	$-0.0807563\pi$
$727$	7.18914	+	12.4520i	0.266631	+	0.461818i	−0.701359	+	0.712808i	$0.747423\pi$
$728$		0			0
$729$	−26.7465	+	3.69094i	−0.990612	+	0.136701i
$730$		0			0
$731$	44.2019			1.63487
$732$		0			0
$733$	39.5773			1.46182			0.730911	−	0.682473i	$-0.239096\pi$
$733$	39.5773			1.46182			0.730911	+	0.682473i	$0.239096\pi$
$734$		0			0
$735$	7.01907	+	29.7724i	0.258902	+	1.09817i
$736$		0			0
$737$	−14.5561	−	25.2119i	−0.536182	−	0.928694i
$738$		0			0
$739$	10.8407	−	18.7767i	0.398783	−	0.690712i	−0.594793	−	0.803879i	$-0.702766\pi$
$739$	10.8407	−	18.7767i	0.398783	−	0.690712i	0.993576	+	0.113167i	$0.0360995\pi$
$740$		0			0
$741$	0.0572246	+	0.0313172i	0.00210220	+	0.00115047i
$742$		0			0
$743$	16.5692	−	28.6987i	0.607864	−	1.05285i	−0.383727	−	0.923446i	$-0.625360\pi$
$743$	16.5692	−	28.6987i	0.607864	−	1.05285i	0.991592	−	0.129406i	$-0.0413069\pi$
$744$		0			0
$745$	35.5831			1.30366
$746$		0			0
$747$	0.713936	−	1.37844i	0.0261216	−	0.0504345i
$748$		0			0
$749$	−23.6912	+	2.48089i	−0.865659	+	0.0906499i
$750$		0			0
$751$	−25.9324			−0.946288			−0.473144	−	0.880985i	$-0.656881\pi$
$751$	−25.9324			−0.946288			−0.473144	+	0.880985i	$0.656881\pi$
$752$		0			0
$753$	−0.703328	−	0.384909i	−0.0256307	−	0.0140269i
$754$		0			0
$755$	26.7442			0.973320
$756$		0			0
$757$	−30.5846			−1.11162			−0.555808	−	0.831311i	$-0.687591\pi$
$757$	−30.5846			−1.11162			−0.555808	+	0.831311i	$0.687591\pi$
$758$		0			0
$759$	−5.79629	−	3.17212i	−0.210392	−	0.115141i
$760$		0			0
$761$	−36.5295			−1.32419			−0.662097	−	0.749418i	$-0.730333\pi$
$761$	−36.5295			−1.32419			−0.662097	+	0.749418i	$0.730333\pi$
$762$		0			0
$763$	11.5505	+	15.9107i	0.418157	+	0.576007i
$764$		0			0
$765$	−37.7259	+	1.72566i	−1.36398	+	0.0623915i
$766$		0			0
$767$	−2.56818			−0.0927315
$768$		0			0
$769$	−21.3107	+	36.9113i	−0.768485	+	1.33105i	0.169900	+	0.985461i	$0.445656\pi$
$769$	−21.3107	+	36.9113i	−0.768485	+	1.33105i	−0.938384	+	0.345593i	$0.887678\pi$
$770$		0			0
$771$	1.21934	+	0.667305i	0.0439134	+	0.0240324i
$772$		0			0
$773$	16.1309	−	27.9395i	0.580187	−	1.00491i	−0.415270	−	0.909698i	$-0.636313\pi$
$773$	16.1309	−	27.9395i	0.580187	−	1.00491i	0.995457	−	0.0952148i	$-0.0303538\pi$
$774$		0			0
$775$	5.30051	+	9.18076i	0.190400	+	0.329783i
$776$		0			0
$777$	27.0172	+	11.3084i	0.969236	+	0.405687i
$778$		0			0
$779$	−0.0800351			−0.00286755
$780$		0			0
$781$	32.4765			1.16210
$782$		0			0
$783$	−33.2050	+	22.3368i	−1.18665	+	0.798254i
$784$		0			0
$785$	−0.327420	−	0.567107i	−0.0116861	−	0.0202409i
$786$		0			0
$787$	−15.3838	−	26.6455i	−0.548373	−	0.949810i	−0.998386	−	0.0567879i	$-0.981914\pi$
$787$	−15.3838	−	26.6455i	−0.548373	−	0.949810i	0.450013	−	0.893022i	$-0.351419\pi$
$788$		0			0
$789$	0.305987	+	0.167457i	0.0108934	+	0.00596163i
$790$		0			0
$791$	22.2156	+	30.6017i	0.789895	+	1.08807i
$792$		0			0
$793$	22.0496	+	38.1910i	0.783003	+	1.35620i
$794$		0			0
$795$	27.6169	−	16.7976i	0.979469	−	0.595749i
$796$		0			0
$797$	−3.59378	+	6.22460i	−0.127298	+	0.220487i	−0.922629	−	0.385689i	$-0.873964\pi$
$797$	−3.59378	+	6.22460i	−0.127298	+	0.220487i	0.795331	+	0.606176i	$0.207297\pi$
$798$		0			0
$799$	5.39144	+	9.33824i	0.190735	+	0.330363i
$800$		0			0
$801$	−3.28628	+	6.34502i	−0.116115	+	0.224190i
$802$		0			0
$803$	8.68725	−	15.0468i	0.306566	−	0.530989i
$804$		0			0
$805$	1.81448	−	4.07120i	0.0639520	−	0.143491i
$806$		0			0
$807$	−33.0806	+	20.1208i	−1.16449	+	0.708287i
$808$		0			0
$809$	−23.3886	+	40.5103i	−0.822301	+	1.42427i	0.0816637	+	0.996660i	$0.473977\pi$
$809$	−23.3886	+	40.5103i	−0.822301	+	1.42427i	−0.903965	+	0.427607i	$0.859357\pi$
$810$		0			0
$811$	17.6946			0.621341			0.310671	−	0.950518i	$-0.399446\pi$
$811$	17.6946			0.621341			0.310671	+	0.950518i	$0.399446\pi$
$812$		0			0
$813$	−0.141647	−	6.19653i	−0.00496779	−	0.217322i
$814$		0			0
$815$	−15.9418	−	27.6120i	−0.558416	−	0.967205i
$816$		0			0
$817$	0.0340111	−	0.0589089i	0.00118990	−	0.00206096i
$818$		0			0
$819$	14.2070	−	36.2467i	0.496434	−	1.26656i
$820$		0			0
$821$	8.61075	−	14.9143i	0.300517	−	0.520511i	−0.675736	−	0.737144i	$-0.736174\pi$
$821$	8.61075	−	14.9143i	0.300517	−	0.520511i	0.976253	+	0.216633i	$0.0695074\pi$
$822$		0			0
$823$	−5.77170	−	9.99688i	−0.201189	−	0.348469i	0.747723	−	0.664011i	$-0.231147\pi$
$823$	−5.77170	−	9.99688i	−0.201189	−	0.348469i	−0.948912	+	0.315542i	$0.897814\pi$
$824$		0			0
$825$	−11.8490	−	6.48458i	−0.412529	−	0.225764i
$826$		0			0
$827$	−20.1448			−0.700503			−0.350251	−	0.936656i	$-0.613904\pi$
$827$	−20.1448			−0.700503			−0.350251	+	0.936656i	$0.613904\pi$
$828$		0			0
$829$	−4.01358	+	6.95172i	−0.139397	+	0.241443i	−0.927269	−	0.374397i	$-0.877850\pi$
$829$	−4.01358	+	6.95172i	−0.139397	+	0.241443i	0.787871	+	0.615840i	$0.211183\pi$
$830$		0			0
$831$	−15.3561	−	8.40393i	−0.532699	−	0.291529i
$832$		0			0
$833$	−34.1699	+	7.23574i	−1.18392	+	0.250704i
$834$		0			0
$835$	14.5057	−	25.1246i	0.501990	−	0.869472i
$836$		0			0
$837$	−33.4828	+	22.5237i	−1.15733	+	0.778532i
$838$		0			0
$839$	−4.59341	−	7.95603i	−0.158582	−	0.274673i	0.775775	−	0.631009i	$-0.217359\pi$
$839$	−4.59341	−	7.95603i	−0.158582	−	0.274673i	−0.934358	+	0.356337i	$0.884026\pi$
$840$		0			0
$841$	−15.1576	+	26.2537i	−0.522675	+	0.905299i
$842$		0			0
$843$	1.00630	+	44.0220i	0.0346589	+	1.51620i
$844$		0			0
$845$	13.9493	+	24.1608i	0.479869	+	0.831158i
$846$		0			0
$847$	−23.3051	+	52.2904i	−0.800774	+	1.79672i
$848$		0			0
$849$	−0.153449	−	6.71281i	−0.00526636	−	0.230383i
$850$		0			0
$851$	−2.13389	−	3.69600i	−0.0731488	−	0.126697i
$852$		0			0
$853$	−10.7925	−	18.6931i	−0.369527	−	0.640040i	0.619964	−	0.784630i	$-0.287147\pi$
$853$	−10.7925	−	18.6931i	−0.369527	−	0.640040i	−0.989492	+	0.144590i	$0.953814\pi$
$854$		0			0
$855$	−0.0267283	+	0.0516060i	−0.000914088	+	0.00176489i
$856$		0			0
$857$	24.0651			0.822049			0.411024	−	0.911624i	$-0.365171\pi$
$857$	24.0651			0.822049			0.411024	+	0.911624i	$0.365171\pi$
$858$		0			0
$859$	−16.3172			−0.556737			−0.278368	−	0.960474i	$-0.589794\pi$
$859$	−16.3172			−0.556737			−0.278368	+	0.960474i	$0.589794\pi$
$860$		0			0
$861$	6.05898	+	47.3791i	0.206490	+	1.61468i
$862$		0			0
$863$	−9.64675	−	16.7087i	−0.328379	−	0.568770i	0.653811	−	0.756658i	$-0.273169\pi$
$863$	−9.64675	−	16.7087i	−0.328379	−	0.568770i	−0.982190	+	0.187888i	$0.939836\pi$
$864$		0			0
$865$	−19.9428	+	34.5420i	−0.678077	+	1.17446i
$866$		0			0
$867$	−0.312576	−	13.6740i	−0.0106156	−	0.464393i
$868$		0			0
$869$	17.6025	−	30.4884i	0.597124	−	1.03425i
$870$		0			0
$871$	−24.9945			−0.846907
$872$		0			0
$873$	−11.9482	+	23.0691i	−0.404385	+	0.780771i
$874$		0			0
$875$	−9.87722	+	22.1618i	−0.333911	+	0.749205i
$876$		0			0
$877$	30.2928			1.02291			0.511457	−	0.859309i	$-0.329106\pi$
$877$	30.2928			1.02291			0.511457	+	0.859309i	$0.329106\pi$
$878$		0			0
$879$	1.26919	−	0.771968i	0.0428087	−	0.0260378i
$880$		0			0
$881$	19.4943			0.656779			0.328390	−	0.944542i	$-0.393494\pi$
$881$	19.4943			0.656779			0.328390	+	0.944542i	$0.393494\pi$
$882$		0			0
$883$	47.5302			1.59952			0.799759	−	0.600321i	$-0.204960\pi$
$883$	47.5302			1.59952			0.799759	+	0.600321i	$0.204960\pi$
$884$		0			0
$885$	−0.0522880	−	2.28740i	−0.00175764	−	0.0768902i
$886$		0			0
$887$	−4.11892			−0.138300			−0.0691499	−	0.997606i	$-0.522029\pi$
$887$	−4.11892			−0.138300			−0.0691499	+	0.997606i	$0.522029\pi$
$888$		0			0
$889$	2.11114	−	4.73682i	0.0708052	−	0.158868i
$890$		0			0
$891$	21.5359	−	46.6892i	0.721479	−	1.56415i
$892$		0			0
$893$	0.0165937			0.000555287
$894$		0			0
$895$	21.4409	−	37.1367i	0.716689	−	1.24134i
$896$		0			0
$897$	−4.84680	+	2.94800i	−0.161830	+	0.0984309i
$898$		0			0
$899$	−29.9056	+	51.7981i	−0.997408	+	1.72756i
$900$		0			0
$901$	18.4547	+	31.9645i	0.614815	+	1.06489i
$902$		0			0
$903$	−37.4476	−	15.6742i	−1.24618	−	0.521605i
$904$		0			0
$905$	−16.0417			−0.533243
$906$		0			0
$907$	8.14168			0.270340			0.135170	−	0.990822i	$-0.456842\pi$
$907$	8.14168			0.270340			0.135170	+	0.990822i	$0.456842\pi$
$908$		0			0
$909$	−15.0972	−	23.5895i	−0.500741	−	0.782415i
$910$		0			0
$911$	−24.6454	−	42.6871i	−0.816540	−	1.41429i	−0.908217	−	0.418499i	$-0.862556\pi$
$911$	−24.6454	−	42.6871i	−0.816540	−	1.41429i	0.0916774	−	0.995789i	$-0.470777\pi$
$912$		0			0
$913$	1.47809	+	2.56013i	0.0489177	+	0.0847279i
$914$		0			0
$915$	−33.5667	+	20.4165i	−1.10968	+	0.674948i
$916$		0			0
$917$	4.29553	−	9.63801i	0.141851	−	0.318275i
$918$		0			0
$919$	−4.71585	−	8.16809i	−0.155561	−	0.269440i	0.777702	−	0.628633i	$-0.216385\pi$
$919$	−4.71585	−	8.16809i	−0.155561	−	0.269440i	−0.933263	+	0.359193i	$0.883052\pi$
$920$		0			0
$921$	−1.09085	−	0.596989i	−0.0359448	−	0.0196715i
$922$		0			0
$923$	13.9415	−	24.1473i	0.458889	−	0.794819i
$924$		0			0
$925$	−4.36218	−	7.55552i	−0.143428	−	0.248424i
$926$		0			0
$927$	26.2278	+	40.9813i	0.861433	+	1.34600i
$928$		0			0
$929$	−14.7369	+	25.5251i	−0.483503	+	0.837452i	−0.999821	−	0.0189453i	$-0.993969\pi$
$929$	−14.7369	+	25.5251i	−0.483503	+	0.837452i	0.516317	+	0.856397i	$0.327303\pi$
$930$		0			0
$931$	−0.0166487	+	0.0511066i	−0.000545641	+	0.00167495i
$932$		0			0
$933$	0.374142	+	16.3673i	0.0122489	+	0.535841i
$934$		0			0
$935$	35.9587	−	62.2823i	1.17597	−	2.03685i
$936$		0			0
$937$	−54.3451			−1.77538			−0.887688	−	0.460445i	$-0.847690\pi$
$937$	−54.3451			−1.77538			−0.887688	+	0.460445i	$0.847690\pi$
$938$		0			0
$939$	34.4257	−	20.9390i	1.12344	−	0.683317i
$940$		0			0
$941$	1.49087	+	2.58226i	0.0486008	+	0.0841791i	0.889302	−	0.457320i	$-0.151190\pi$
$941$	1.49087	+	2.58226i	0.0486008	+	0.0841791i	−0.840702	+	0.541499i	$0.817857\pi$
$942$		0			0
$943$	3.48005	−	6.02763i	0.113326	−	0.196287i
$944$		0			0
$945$	32.5731	+	11.9158i	1.05960	+	0.387621i
$946$		0			0
$947$	−15.1646	+	26.2659i	−0.492783	+	0.853526i	−0.999965	−	0.00831303i	$-0.997354\pi$
$947$	−15.1646	+	26.2659i	−0.492783	+	0.853526i	0.507182	+	0.861839i	$0.330687\pi$
$948$		0			0
$949$	−7.45850	−	12.9185i	−0.242113	−	0.419352i
$950$		0			0
$951$	−19.5860	+	11.9129i	−0.635119	+	0.386303i
$952$		0			0
$953$	0.380127			0.0123135			0.00615676	−	0.999981i	$-0.498040\pi$
$953$	0.380127			0.0123135			0.00615676	+	0.999981i	$0.498040\pi$
$954$		0			0
$955$	−5.22360	+	9.04754i	−0.169032	+	0.292771i
$956$		0			0
$957$	−1.74161	−	76.1889i	−0.0562983	−	2.46284i
$958$		0			0
$959$	7.97924	−	17.9032i	0.257663	−	0.578126i
$960$		0			0
$961$	−14.6558	+	25.3845i	−0.472766	+	0.818855i
$962$		0			0
$963$	−12.4221	+	23.9842i	−0.400298	+	0.772881i
$964$		0			0
$965$	−9.70796	−	16.8147i	−0.312510	−	0.541284i
$966$		0			0
$967$	−22.6744	+	39.2732i	−0.729160	+	1.26294i	0.228078	+	0.973643i	$0.426756\pi$
$967$	−22.6744	+	39.2732i	−0.729160	+	1.26294i	−0.957239	+	0.289300i	$0.906578\pi$
$968$		0			0
$969$	−0.0582135	−	0.0318584i	−0.00187009	−	0.00102344i
$970$		0			0
$971$	−27.3746	−	47.4141i	−0.878491	−	1.52159i	−0.852996	−	0.521917i	$-0.825217\pi$
$971$	−27.3746	−	47.4141i	−0.878491	−	1.52159i	−0.0254951	−	0.999675i	$-0.508116\pi$
$972$		0			0
$973$	21.5323	+	29.6604i	0.690292	+	0.950870i
$974$		0			0
$975$	−9.90801	+	6.02642i	−0.317310	+	0.193000i
$976$		0			0
$977$	−1.35656	−	2.34962i	−0.0434001	−	0.0751711i	0.843509	−	0.537114i	$-0.180486\pi$
$977$	−1.35656	−	2.34962i	−0.0434001	−	0.0751711i	−0.886909	+	0.461943i	$0.847152\pi$
$978$		0			0
$979$	−6.80371	−	11.7844i	−0.217448	−	0.376630i
$980$		0			0
$981$	22.2705	−	1.01870i	0.711042	−	0.0325246i
$982$		0			0
$983$	42.7656			1.36401			0.682006	−	0.731347i	$-0.261108\pi$
$983$	42.7656			1.36401			0.682006	+	0.731347i	$0.261108\pi$
$984$		0			0
$985$	−8.31318			−0.264880
$986$		0			0
$987$	−1.25621	−	9.82314i	−0.0399857	−	0.312674i
$988$		0			0
$989$	2.95771	+	5.12291i	0.0940498	+	0.162899i
$990$		0			0
$991$	29.6731	−	51.3954i	0.942598	−	1.63263i	0.182107	−	0.983279i	$-0.441708\pi$
$991$	29.6731	−	51.3954i	0.942598	−	1.63263i	0.760491	−	0.649349i	$-0.224958\pi$
$992$		0			0
$993$	45.0353	−	27.3921i	1.42915	−	0.869262i
$994$		0			0
$995$	−20.4063	+	35.3447i	−0.646922	+	1.12050i
$996$		0			0
$997$	44.0641			1.39552			0.697762	−	0.716330i	$-0.254179\pi$
$997$	44.0641			1.39552			0.697762	+	0.716330i	$0.254179\pi$
$998$		0			0
$999$	27.5554	−	18.5364i	0.871814	−	0.586465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.d.193.10	yes	22
3.2	odd	2		1512.2.t.d.361.9		22
4.3	odd	2		1008.2.t.k.193.2		22
7.2	even	3		504.2.q.d.121.3	yes	22
9.2	odd	6		1512.2.q.c.1369.3		22
9.7	even	3		504.2.q.d.25.3	✓	22
12.11	even	2		3024.2.t.l.1873.9		22
21.2	odd	6		1512.2.q.c.793.3		22
28.23	odd	6		1008.2.q.k.625.9		22
36.7	odd	6		1008.2.q.k.529.9		22
36.11	even	6		3024.2.q.k.2881.3		22
63.2	odd	6		1512.2.t.d.289.9		22
63.16	even	3	inner	504.2.t.d.457.10	yes	22
84.23	even	6		3024.2.q.k.2305.3		22
252.79	odd	6		1008.2.t.k.961.2		22
252.191	even	6		3024.2.t.l.289.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.3	✓	22	9.7	even	3
504.2.q.d.121.3	yes	22	7.2	even	3
504.2.t.d.193.10	yes	22	1.1	even	1	trivial
504.2.t.d.457.10	yes	22	63.16	even	3	inner
1008.2.q.k.529.9		22	36.7	odd	6
1008.2.q.k.625.9		22	28.23	odd	6
1008.2.t.k.193.2		22	4.3	odd	2
1008.2.t.k.961.2		22	252.79	odd	6
1512.2.q.c.793.3		22	21.2	odd	6
1512.2.q.c.1369.3		22	9.2	odd	6
1512.2.t.d.289.9		22	63.2	odd	6
1512.2.t.d.361.9		22	3.2	odd	2
3024.2.q.k.2305.3		22	84.23	even	6
3024.2.q.k.2881.3		22	36.11	even	6
3024.2.t.l.289.9		22	252.191	even	6
3024.2.t.l.1873.9		22	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.51940 + 0.831519i) q^{3} -2.52290 q^{5} +(-1.07705 + 2.41660i) q^{7} +(1.61715 + 2.52682i) q^{9} -5.71296 q^{11} +(-2.45245 + 4.24777i) q^{13} +(-3.83330 - 2.09784i) q^{15} +(2.49483 - 4.32118i) q^{17} +(-0.00383929 - 0.00664984i) q^{19} +(-3.64592 + 2.77620i) q^{21} +0.667754 q^{23} +1.36505 q^{25} +(0.355997 + 5.18394i) q^{27} +(3.85082 + 6.66981i) q^{29} +(3.88302 + 6.72560i) q^{31} +(-8.68028 - 4.75044i) q^{33} +(2.71729 - 6.09686i) q^{35} +(-3.19562 - 5.53498i) q^{37} +(-7.25836 + 4.41480i) q^{39} +(5.21159 - 9.02673i) q^{41} +(4.42935 + 7.67185i) q^{43} +(-4.07992 - 6.37493i) q^{45} +(-1.08052 + 1.87152i) q^{47} +(-4.67994 - 5.20559i) q^{49} +(7.38379 - 4.49109i) q^{51} +(-3.69858 + 6.40613i) q^{53} +14.4133 q^{55} +(-0.000303939 - 0.0132962i) q^{57} +(0.261797 + 0.453446i) q^{59} +(4.49541 - 7.78628i) q^{61} +(-7.84807 + 1.18650i) q^{63} +(6.18730 - 10.7167i) q^{65} +(2.54791 + 4.41311i) q^{67} +(1.01458 + 0.555250i) q^{69} -5.68471 q^{71} +(-1.52062 + 2.63379i) q^{73} +(2.07405 + 1.13506i) q^{75} +(6.15314 - 13.8060i) q^{77} +(-3.08115 + 5.33671i) q^{79} +(-3.76965 + 8.17250i) q^{81} +(-0.258726 - 0.448126i) q^{83} +(-6.29422 + 10.9019i) q^{85} +(0.304852 + 13.3361i) q^{87} +(1.19093 + 2.06274i) q^{89} +(-7.62377 - 10.5017i) q^{91} +(0.307402 + 13.4477i) q^{93} +(0.00968615 + 0.0167769i) q^{95} +(4.32994 + 7.49968i) q^{97} +(-9.23873 - 14.4356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39}+ \cdots - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Introduction

L-functions

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