LMFDB - Embedded newform 504.2.q.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, 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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	504.121
Dual form			504.2.q.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71769 - 0.222607i) q^{3} +(0.234085 + 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +(2.90089 + 0.764737i) q^{9} +O(q^{10})$	\(q+(-1.71769 - 0.222607i) q^{3} +(0.234085 + 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +(2.90089 + 0.764737i) q^{9} +(0.674293 - 1.16791i) q^{11} +(-3.16486 + 5.48171i) q^{13} +(-0.311829 - 0.748538i) q^{15} +(-2.47120 - 4.28024i) q^{17} +(2.38910 - 4.13804i) q^{19} +(-0.951805 + 4.48264i) q^{21} +(-3.81399 - 6.60603i) q^{23} +(2.39041 - 4.14031i) q^{25} +(-4.81259 - 1.95934i) q^{27} +(-1.80565 - 3.12747i) q^{29} +6.49878 q^{31} +(-1.41821 + 1.85600i) q^{33} +(1.11896 - 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(6.65651 - 8.71133i) q^{39} +(-0.0251630 + 0.0435837i) q^{41} +(-0.431869 - 0.748019i) q^{43} +(0.368994 + 1.35517i) q^{45} -10.9883 q^{47} +(-6.90982 - 1.12000i) q^{49} +(3.29193 + 7.90221i) q^{51} +(5.84976 + 10.1321i) q^{53} +0.631366 q^{55} +(-5.02488 + 6.57603i) q^{57} -3.87784 q^{59} +3.74462 q^{61} +(2.63277 - 7.48789i) q^{63} -2.96338 q^{65} -2.64871 q^{67} +(5.08070 + 12.1961i) q^{69} -7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(-5.02763 + 6.57963i) q^{75} +(-2.93685 - 2.02626i) q^{77} +3.17902 q^{79} +(7.83036 + 4.43684i) q^{81} +(4.90272 + 8.49176i) q^{83} +(1.15694 - 2.00388i) q^{85} +(2.40534 + 5.77396i) q^{87} +(5.30709 - 9.19214i) q^{89} +(13.7844 + 9.51045i) q^{91} +(-11.1629 - 1.44667i) q^{93} +2.23701 q^{95} +(6.97792 + 12.0861i) q^{97} +(2.84919 - 2.87232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.71769	−	0.222607i	−0.991707	−	0.128522i
$3$	−1.71769	−	0.222607i	−0.991707	−	0.128522i
$4$		0			0
$5$	0.234085	+	0.405446i	0.104686	+	0.181321i	0.913610	−	0.406592i	$-0.133283\pi$
$5$	0.234085	+	0.405446i	0.104686	+	0.181321i	−0.808924	+	0.587913i	$0.799950\pi$
$6$		0			0
$7$	0.212345	−	2.63722i	0.0802590	−	0.996774i
$7$	0.212345	−	2.63722i	0.0802590	−	0.996774i
$8$		0			0
$9$	2.90089	+	0.764737i	0.966964	+	0.254912i
$10$		0			0
$11$	0.674293	−	1.16791i	0.203307	−	0.352138i	−0.746285	−	0.665626i	$-0.768164\pi$
$11$	0.674293	−	1.16791i	0.203307	−	0.352138i	0.949592	+	0.313489i	$0.101498\pi$
$12$		0			0
$13$	−3.16486	+	5.48171i	−0.877775	+	1.52035i	−0.0239988	+	0.999712i	$0.507640\pi$
$13$	−3.16486	+	5.48171i	−0.877775	+	1.52035i	−0.853777	+	0.520640i	$0.825694\pi$
$14$		0			0
$15$	−0.311829	−	0.748538i	−0.0805139	−	0.193272i
$16$		0			0
$17$	−2.47120	−	4.28024i	−0.599353	−	1.03811i	−0.992917	−	0.118813i	$-0.962091\pi$
$17$	−2.47120	−	4.28024i	−0.599353	−	1.03811i	0.393563	−	0.919298i	$-0.371242\pi$
$18$		0			0
$19$	2.38910	−	4.13804i	0.548097	−	0.949332i	−0.450308	−	0.892873i	$-0.648686\pi$
$19$	2.38910	−	4.13804i	0.548097	−	0.949332i	0.998405	−	0.0564585i	$-0.0179809\pi$
$20$		0			0
$21$	−0.951805	+	4.48264i	−0.207701	+	0.978192i
$22$		0			0
$23$	−3.81399	−	6.60603i	−0.795273	−	1.37745i	−0.922666	−	0.385600i	$-0.873994\pi$
$23$	−3.81399	−	6.60603i	−0.795273	−	1.37745i	0.127393	−	0.991852i	$-0.459339\pi$
$24$		0			0
$25$	2.39041	−	4.14031i	0.478082	−	0.828062i
$26$		0			0
$27$	−4.81259	−	1.95934i	−0.926183	−	0.377074i
$28$		0			0
$29$	−1.80565	−	3.12747i	−0.335300	−	0.580757i	0.648242	−	0.761434i	$-0.275504\pi$
$29$	−1.80565	−	3.12747i	−0.335300	−	0.580757i	−0.983542	+	0.180677i	$0.942171\pi$
$30$		0			0
$31$	6.49878			1.16721			0.583607	−	0.812036i	$-0.301641\pi$
$31$	6.49878			1.16721			0.583607	+	0.812036i	$0.301641\pi$
$32$		0			0
$33$	−1.41821	+	1.85600i	−0.246878	+	0.323088i
$34$		0			0
$35$	1.11896	−	0.531237i	0.189138	−	0.0897954i
$36$		0			0
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	−0.00838383	−	0.999965i	$-0.502669\pi$
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	0.870187	−	0.492722i	$-0.163998\pi$
$38$		0			0
$39$	6.65651	−	8.71133i	1.06589	−	1.39493i
$40$		0			0
$41$	−0.0251630	+	0.0435837i	−0.00392981	+	0.00680662i	−0.867984	−	0.496593i	$-0.834584\pi$
$41$	−0.0251630	+	0.0435837i	−0.00392981	+	0.00680662i	0.864054	+	0.503399i	$0.167918\pi$
$42$		0			0
$43$	−0.431869	−	0.748019i	−0.0658594	−	0.114072i	0.831215	−	0.555950i	$-0.187646\pi$
$43$	−0.431869	−	0.748019i	−0.0658594	−	0.114072i	−0.897075	+	0.441879i	$0.854312\pi$
$44$		0			0
$45$	0.368994	+	1.35517i	0.0550064	+	0.202017i
$46$		0			0
$47$	−10.9883			−1.60282			−0.801408	−	0.598118i	$-0.795915\pi$
$47$	−10.9883			−1.60282			−0.801408	+	0.598118i	$0.795915\pi$
$48$		0			0
$49$	−6.90982	−	1.12000i	−0.987117	−	0.160000i
$50$		0			0
$51$	3.29193	+	7.90221i	0.460963	+	1.10653i
$52$		0			0
$53$	5.84976	+	10.1321i	0.803526	+	1.39175i	0.917282	+	0.398239i	$0.130378\pi$
$53$	5.84976	+	10.1321i	0.803526	+	1.39175i	−0.113756	+	0.993509i	$0.536288\pi$
$54$		0			0
$55$	0.631366			0.0851334
$56$		0			0
$57$	−5.02488	+	6.57603i	−0.665561	+	0.871016i
$58$		0			0
$59$	−3.87784			−0.504852			−0.252426	−	0.967616i	$-0.581228\pi$
$59$	−3.87784			−0.504852			−0.252426	+	0.967616i	$0.581228\pi$
$60$		0			0
$61$	3.74462			0.479450			0.239725	−	0.970841i	$-0.422943\pi$
$61$	3.74462			0.479450			0.239725	+	0.970841i	$0.422943\pi$
$62$		0			0
$63$	2.63277	−	7.48789i	0.331698	−	0.943386i
$64$		0			0
$65$	−2.96338			−0.367562
$66$		0			0
$67$	−2.64871			−0.323592			−0.161796	−	0.986824i	$-0.551729\pi$
$67$	−2.64871			−0.323592			−0.161796	+	0.986824i	$0.551729\pi$
$68$		0			0
$69$	5.08070	+	12.1961i	0.611644	+	1.46824i
$70$		0			0
$71$	−7.04562			−0.836161			−0.418081	−	0.908410i	$-0.637297\pi$
$71$	−7.04562			−0.836161			−0.418081	+	0.908410i	$0.637297\pi$
$72$		0			0
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	0.605586	−	0.795780i	$-0.292939\pi$
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	−0.991959	+	0.126563i	$0.959605\pi$
$74$		0			0
$75$	−5.02763	+	6.57963i	−0.580541	+	0.759750i
$76$		0			0
$77$	−2.93685	−	2.02626i	−0.334685	−	0.230913i
$78$		0			0
$79$	3.17902			0.357667			0.178834	−	0.983879i	$-0.442768\pi$
$79$	3.17902			0.357667			0.178834	+	0.983879i	$0.442768\pi$
$80$		0			0
$81$	7.83036	+	4.43684i	0.870040	+	0.492982i
$82$		0			0
$83$	4.90272	+	8.49176i	0.538143	+	0.932092i	0.999004	+	0.0446192i	$0.0142074\pi$
$83$	4.90272	+	8.49176i	0.538143	+	0.932092i	−0.460861	+	0.887472i	$0.652459\pi$
$84$		0			0
$85$	1.15694	−	2.00388i	0.125488	−	0.217351i
$86$		0			0
$87$	2.40534	+	5.77396i	0.257879	+	0.619034i
$88$		0			0
$89$	5.30709	−	9.19214i	0.562550	−	0.974365i	−0.434723	−	0.900564i	$-0.643154\pi$
$89$	5.30709	−	9.19214i	0.562550	−	0.974365i	0.997273	−	0.0738011i	$-0.0235130\pi$
$90$		0			0
$91$	13.7844	+	9.51045i	1.44500	+	0.996966i
$92$		0			0
$93$	−11.1629	−	1.44667i	−1.15753	−	0.150013i
$94$		0			0
$95$	2.23701			0.229512
$96$		0			0
$97$	6.97792	+	12.0861i	0.708500	+	1.22716i	0.965413	+	0.260724i	$0.0839611\pi$
$97$	6.97792	+	12.0861i	0.708500	+	1.22716i	−0.256913	+	0.966434i	$0.582706\pi$
$98$		0			0
$99$	2.84919	−	2.87232i	0.286355	−	0.288679i
$100$		0			0
$101$	−2.12472	+	3.68013i	−0.211418	+	0.366187i	−0.952159	−	0.305604i	$-0.901141\pi$
$101$	−2.12472	+	3.68013i	−0.211418	+	0.366187i	0.740741	+	0.671791i	$0.234475\pi$
$102$		0			0
$103$	4.47820	+	7.75647i	0.441250	+	0.764268i	0.997783	−	0.0665580i	$-0.0212017\pi$
$103$	4.47820	+	7.75647i	0.441250	+	0.764268i	−0.556532	+	0.830826i	$0.687868\pi$
$104$		0			0
$105$	−2.04027	+	0.663411i	−0.199110	+	0.0647423i
$106$		0			0
$107$	−0.810731	+	1.40423i	−0.0783763	+	0.135752i	−0.902550	−	0.430586i	$-0.858307\pi$
$107$	−0.810731	+	1.40423i	−0.0783763	+	0.135752i	0.824173	+	0.566338i	$0.191640\pi$
$108$		0			0
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	0.972631	−	0.232354i	$-0.0746428\pi$
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	−0.687540	+	0.726146i	$0.741309\pi$
$110$		0			0
$111$	−11.0255	+	14.4291i	−1.04650	+	1.36955i
$112$		0			0
$113$	4.14346	−	7.17669i	0.389784	−	0.675126i	−0.602636	−	0.798016i	$-0.705883\pi$
$113$	4.14346	−	7.17669i	0.389784	−	0.675126i	0.992420	+	0.122890i	$0.0392162\pi$
$114$		0			0
$115$	1.78559	−	3.09274i	0.166508	−	0.288399i
$116$		0			0
$117$	−13.3730	+	13.4816i	−1.23633	+	1.24637i
$118$		0			0
$119$	−11.8127	+	5.60819i	−1.08287	+	0.514102i
$120$		0			0
$121$	4.59066	+	7.95125i	0.417333	+	0.722841i
$122$		0			0
$123$	0.0529242	−	0.0692616i	0.00477202	−	0.00624511i
$124$		0			0
$125$	4.57908			0.409565
$126$		0			0
$127$	8.12368			0.720860			0.360430	−	0.932786i	$-0.382630\pi$
$127$	8.12368			0.720860			0.360430	+	0.932786i	$0.382630\pi$
$128$		0			0
$129$	0.575302	+	1.38100i	0.0506525	+	0.121590i
$130$		0			0
$131$	−9.74823	−	16.8844i	−0.851707	−	1.47520i	−0.879667	−	0.475591i	$-0.842234\pi$
$131$	−9.74823	−	16.8844i	−0.851707	−	1.47520i	0.0279597	−	0.999609i	$-0.491099\pi$
$132$		0			0
$133$	−10.4056	−	7.17927i	−0.902280	−	0.622521i
$134$		0			0
$135$	−0.332147	−	2.40990i	−0.0285867	−	0.207411i
$136$		0			0
$137$	7.55175	−	13.0800i	0.645189	−	1.11750i	−0.339069	−	0.940762i	$-0.610112\pi$
$137$	7.55175	−	13.0800i	0.645189	−	1.11750i	0.984258	−	0.176739i	$-0.0565548\pi$
$138$		0			0
$139$	−2.18826	+	3.79017i	−0.185605	+	0.321478i	−0.943780	−	0.330573i	$-0.892758\pi$
$139$	−2.18826	+	3.79017i	−0.185605	+	0.321478i	0.758175	+	0.652051i	$0.226091\pi$
$140$		0			0
$141$	18.8745	+	2.44608i	1.58952	+	0.205997i
$142$		0			0
$143$	4.26809	+	7.39255i	0.356916	+	0.618196i
$144$		0			0
$145$	0.845348	−	1.46419i	0.0702023	−	0.121594i
$146$		0			0
$147$	11.6196	+	3.46198i	0.958367	+	0.285540i
$148$		0			0
$149$	5.87820	+	10.1813i	0.481561	+	0.834087i	0.999776	−	0.0211627i	$-0.00673679\pi$
$149$	5.87820	+	10.1813i	0.481561	+	0.834087i	−0.518215	+	0.855250i	$0.673403\pi$
$150$		0			0
$151$	2.57153	−	4.45401i	0.209268	−	0.362462i	−0.742216	−	0.670160i	$-0.766225\pi$
$151$	2.57153	−	4.45401i	0.209268	−	0.362462i	0.951484	+	0.307698i	$0.0995586\pi$
$152$		0			0
$153$	−3.89542	−	14.3063i	−0.314926	−	1.15660i
$154$		0			0
$155$	1.52126	+	2.63490i	0.122191	+	0.211641i
$156$		0			0
$157$	−12.0889			−0.964803			−0.482401	−	0.875950i	$-0.660235\pi$
$157$	−12.0889			−0.964803			−0.482401	+	0.875950i	$0.660235\pi$
$158$		0			0
$159$	−7.79258	−	18.7059i	−0.617992	−	1.48348i
$160$		0			0
$161$	−18.2314	+	8.65557i	−1.43684	+	0.682154i
$162$		0			0
$163$	−2.74663	+	4.75730i	−0.215133	+	0.372621i	−0.953314	−	0.301982i	$-0.902352\pi$
$163$	−2.74663	+	4.75730i	−0.215133	+	0.372621i	0.738181	+	0.674603i	$0.235685\pi$
$164$		0			0
$165$	−1.08449	−	0.140546i	−0.0844273	−	0.0109415i
$166$		0			0
$167$	−3.59378	+	6.22461i	−0.278095	+	0.481675i	−0.970911	−	0.239440i	$-0.923036\pi$
$167$	−3.59378	+	6.22461i	−0.278095	+	0.481675i	0.692816	+	0.721114i	$0.256370\pi$
$168$		0			0
$169$	−13.5327	−	23.4394i	−1.04098	−	1.80303i
$170$		0			0
$171$	10.0950	−	10.1770i	0.771986	−	0.778253i
$172$		0			0
$173$	−7.95902			−0.605113			−0.302557	−	0.953131i	$-0.597840\pi$
$173$	−7.95902			−0.605113			−0.302557	+	0.953131i	$0.597840\pi$
$174$		0			0
$175$	−10.4113	−	7.18320i	−0.787020	−	0.542999i
$176$		0			0
$177$	6.66092	+	0.863234i	0.500665	+	0.0648846i
$178$		0			0
$179$	0.168821	+	0.292406i	0.0126182	+	0.0218554i	0.872266	−	0.489032i	$-0.162650\pi$
$179$	0.168821	+	0.292406i	0.0126182	+	0.0218554i	−0.859647	+	0.510888i	$0.829317\pi$
$180$		0			0
$181$	7.05801			0.524618			0.262309	−	0.964984i	$-0.415516\pi$
$181$	7.05801			0.524618			0.262309	+	0.964984i	$0.415516\pi$
$182$		0			0
$183$	−6.43209	−	0.833578i	−0.475474	−	0.0616198i
$184$		0			0
$185$	4.90842			0.360874
$186$		0			0
$187$	−6.66524			−0.487411
$188$		0			0
$189$	−6.18912	+	12.2758i	−0.450192	+	0.892932i
$190$		0			0
$191$	17.7187			1.28208			0.641039	−	0.767508i	$-0.278504\pi$
$191$	17.7187			1.28208			0.641039	+	0.767508i	$0.278504\pi$
$192$		0			0
$193$	−16.8024			−1.20946			−0.604732	−	0.796429i	$-0.706720\pi$
$193$	−16.8024			−1.20946			−0.604732	+	0.796429i	$0.706720\pi$
$194$		0			0
$195$	5.09016	+	0.659669i	0.364514	+	0.0472399i
$196$		0			0
$197$	5.97545			0.425733			0.212867	−	0.977081i	$-0.431720\pi$
$197$	5.97545			0.425733			0.212867	+	0.977081i	$0.431720\pi$
$198$		0			0
$199$	6.26093	+	10.8443i	0.443826	+	0.768729i	0.997970	−	0.0636923i	$-0.0202876\pi$
$199$	6.26093	+	10.8443i	0.443826	+	0.768729i	−0.554144	+	0.832421i	$0.686954\pi$
$200$		0			0
$201$	4.54966	+	0.589621i	0.320908	+	0.0415887i
$202$		0			0
$203$	−8.63124	+	4.09778i	−0.605794	+	0.287607i
$204$		0			0
$205$	−0.0235611			−0.00164558
$206$		0			0
$207$	−6.01211	−	22.0801i	−0.417871	−	1.53467i
$208$		0			0
$209$	−3.22190	−	5.58050i	−0.222864	−	0.386011i
$210$		0			0
$211$	1.17688	−	2.03842i	0.0810198	−	0.140330i	−0.822668	−	0.568521i	$-0.807516\pi$
$211$	1.17688	−	2.03842i	0.0810198	−	0.140330i	0.903688	+	0.428191i	$0.140849\pi$
$212$		0			0
$213$	12.1022	+	1.56840i	0.829227	+	0.107465i
$214$		0			0
$215$	0.202188	−	0.350199i	0.0137891	−	0.0238834i
$216$		0			0
$217$	1.37999	−	17.1387i	0.0936795	−	1.16345i
$218$		0			0
$219$	4.39755	+	10.5562i	0.297159	+	0.713324i
$220$		0			0
$221$	31.2840			2.10439
$222$		0			0
$223$	5.30709	+	9.19215i	0.355389	+	0.615552i	0.987184	−	0.159583i	$-0.0510150\pi$
$223$	5.30709	+	9.19215i	0.355389	+	0.615552i	−0.631795	+	0.775135i	$0.717682\pi$
$224$		0			0
$225$	10.1006	−	10.1826i	0.673371	−	0.678837i
$226$		0			0
$227$	−0.637749	+	1.10461i	−0.0423289	+	0.0733158i	−0.886414	−	0.462894i	$-0.846811\pi$
$227$	−0.637749	+	1.10461i	−0.0423289	+	0.0733158i	0.844085	+	0.536210i	$0.180144\pi$
$228$		0			0
$229$	6.73313	+	11.6621i	0.444938	+	0.770655i	0.998048	−	0.0624532i	$-0.0198924\pi$
$229$	6.73313	+	11.6621i	0.444938	+	0.770655i	−0.553110	+	0.833108i	$0.686559\pi$
$230$		0			0
$231$	4.59352	+	4.13423i	0.302232	+	0.272013i
$232$		0			0
$233$	9.98509	−	17.2947i	0.654145	−	1.13301i	−0.327963	−	0.944691i	$-0.606362\pi$
$233$	9.98509	−	17.2947i	0.654145	−	1.13301i	0.982107	−	0.188321i	$-0.0603047\pi$
$234$		0			0
$235$	−2.57220	−	4.45519i	−0.167792	−	0.290624i
$236$		0			0
$237$	−5.46055	−	0.707670i	−0.354701	−	0.0459681i
$238$		0			0
$239$	−14.1092	+	24.4379i	−0.912650	+	1.58076i	−0.102345	+	0.994749i	$0.532635\pi$
$239$	−14.1092	+	24.4379i	−0.912650	+	1.58076i	−0.810305	+	0.586008i	$0.800699\pi$
$240$		0			0
$241$	8.67622	−	15.0277i	0.558884	−	0.968016i	−0.438706	−	0.898631i	$-0.644563\pi$
$241$	8.67622	−	15.0277i	0.558884	−	0.968016i	0.997590	−	0.0693852i	$-0.0221038\pi$
$242$		0			0
$243$	−12.4624	−	9.36418i	−0.799465	−	0.600713i
$244$		0			0
$245$	−1.16338	−	3.06374i	−0.0743257	−	0.195735i
$246$		0			0
$247$	15.1223	+	26.1927i	0.962212	+	1.66660i
$248$		0			0
$249$	−6.53101	−	15.6776i	−0.413886	−	0.993525i
$250$		0			0
$251$	6.29051			0.397054			0.198527	−	0.980095i	$-0.436384\pi$
$251$	6.29051			0.397054			0.198527	+	0.980095i	$0.436384\pi$
$252$		0			0
$253$	−10.2870			−0.646738
$254$		0			0
$255$	−2.43333	+	3.18449i	−0.152381	+	0.199420i
$256$		0			0
$257$	3.06819	+	5.31426i	0.191388	+	0.331494i	0.945711	−	0.325010i	$-0.105368\pi$
$257$	3.06819	+	5.31426i	0.191388	+	0.331494i	−0.754322	+	0.656504i	$0.772034\pi$
$258$		0			0
$259$	−22.8319	−	15.7527i	−1.41870	−	0.978825i
$260$		0			0
$261$	−2.84629	−	10.4533i	−0.176181	−	0.647043i
$262$		0			0
$263$	−2.93957	+	5.09148i	−0.181262	+	0.313954i	−0.942310	−	0.334740i	$-0.891351\pi$
$263$	−2.93957	+	5.09148i	−0.181262	+	0.313954i	0.761049	+	0.648695i	$0.224685\pi$
$264$		0			0
$265$	−2.73868	+	4.74352i	−0.168235	+	0.291392i
$266$		0			0
$267$	−11.1621	+	14.6078i	−0.683112	+	0.893985i
$268$		0			0
$269$	−15.4633	−	26.7832i	−0.942812	−	1.63300i	−0.760074	−	0.649837i	$-0.774837\pi$
$269$	−15.4633	−	26.7832i	−0.942812	−	1.63300i	−0.182738	−	0.983162i	$-0.558496\pi$
$270$		0			0
$271$	5.44528	−	9.43150i	0.330777	−	0.572923i	−0.651887	−	0.758316i	$-0.726022\pi$
$271$	5.44528	−	9.43150i	0.330777	−	0.572923i	0.982664	+	0.185393i	$0.0593558\pi$
$272$		0			0
$273$	−21.5602	−	19.4045i	−1.30488	−	1.17441i
$274$		0			0
$275$	−3.22367	−	5.58356i	−0.194395	−	0.336701i
$276$		0			0
$277$	−9.79498	+	16.9654i	−0.588524	+	1.01935i	0.405903	+	0.913916i	$0.366957\pi$
$277$	−9.79498	+	16.9654i	−0.588524	+	1.01935i	−0.994426	+	0.105436i	$0.966376\pi$
$278$		0			0
$279$	18.8522	+	4.96985i	1.12865	+	0.297537i
$280$		0			0
$281$	−0.142477	−	0.246777i	−0.00849944	−	0.0147215i	0.861744	−	0.507343i	$-0.169372\pi$
$281$	−0.142477	−	0.246777i	−0.00849944	−	0.0147215i	−0.870244	+	0.492621i	$0.836039\pi$
$282$		0			0
$283$	2.84269			0.168981			0.0844903	−	0.996424i	$-0.473074\pi$
$283$	2.84269			0.168981			0.0844903	+	0.996424i	$0.473074\pi$
$284$		0			0
$285$	−3.84247	−	0.497972i	−0.227608	−	0.0294973i
$286$		0			0
$287$	0.109596	+	0.0756152i	0.00646926	+	0.00446342i
$288$		0			0
$289$	−3.71364	+	6.43221i	−0.218449	+	0.378365i
$290$		0			0
$291$	−9.29542	−	22.3135i	−0.544907	−	1.30804i
$292$		0			0
$293$	−1.45979	+	2.52842i	−0.0852816	+	0.147712i	−0.905511	−	0.424322i	$-0.860512\pi$
$293$	−1.45979	+	2.52842i	−0.0852816	+	0.147712i	0.820230	+	0.572034i	$0.193846\pi$
$294$		0			0
$295$	−0.907743	−	1.57226i	−0.0528509	−	0.0915404i
$296$		0			0
$297$	−5.53342	+	4.29950i	−0.321082	+	0.249482i
$298$		0			0
$299$	48.2831			2.79228
$300$		0			0
$301$	−2.06439	+	0.980094i	−0.118990	+	0.0564917i
$302$		0			0
$303$	4.46883	−	5.84833i	0.256728	−	0.335978i
$304$		0			0
$305$	0.876558	+	1.51824i	0.0501916	+	0.0869344i
$306$		0			0
$307$	−4.12553			−0.235457			−0.117728	−	0.993046i	$-0.537561\pi$
$307$	−4.12553			−0.235457			−0.117728	+	0.993046i	$0.537561\pi$
$308$		0			0
$309$	−5.96550	−	14.3201i	−0.339366	−	0.814640i
$310$		0			0
$311$	15.3917			0.872781			0.436390	−	0.899757i	$-0.356257\pi$
$311$	15.3917			0.872781			0.436390	+	0.899757i	$0.356257\pi$
$312$		0			0
$313$	−20.7240			−1.17139			−0.585694	−	0.810533i	$-0.699178\pi$
$313$	−20.7240			−1.17139			−0.585694	+	0.810533i	$0.699178\pi$
$314$		0			0
$315$	3.65223	−	0.685354i	0.205780	−	0.0386153i
$316$		0			0
$317$	−0.488292			−0.0274252			−0.0137126	−	0.999906i	$-0.504365\pi$
$317$	−0.488292			−0.0274252			−0.0137126	+	0.999906i	$0.504365\pi$
$318$		0			0
$319$	−4.87014			−0.272675
$320$		0			0
$321$	1.70517	−	2.23155i	0.0951734	−	0.124553i
$322$		0			0
$323$	−23.6157			−1.31402
$324$		0			0
$325$	15.1306	+	26.2070i	0.839297	+	1.45370i
$326$		0			0
$327$	−3.96497	−	9.51784i	−0.219264	−	0.526338i
$328$		0			0
$329$	−2.33333	+	28.9787i	−0.128640	+	1.59764i
$330$		0			0
$331$	−18.9573			−1.04199			−0.520993	−	0.853561i	$-0.674438\pi$
$331$	−18.9573			−1.04199			−0.520993	+	0.853561i	$0.674438\pi$
$332$		0			0
$333$	22.1504	−	22.3303i	1.21384	−	1.22369i
$334$		0			0
$335$	−0.620023	−	1.07391i	−0.0338755	−	0.0586740i
$336$		0			0
$337$	11.6202	−	20.1268i	0.632993	−	1.09638i	−0.353944	−	0.935267i	$-0.615160\pi$
$337$	11.6202	−	20.1268i	0.632993	−	1.09638i	0.986937	−	0.161109i	$-0.0515071\pi$
$338$		0			0
$339$	−8.71475	+	11.4049i	−0.473320	+	0.619431i
$340$		0			0
$341$	4.38208	−	7.58998i	0.237303	−	0.411020i
$342$		0			0
$343$	−4.42096	+	17.9849i	−0.238709	+	0.971091i
$344$		0			0
$345$	−3.75556	+	4.91487i	−0.202192	+	0.264608i
$346$		0			0
$347$	18.1888			0.976425			0.488212	−	0.872725i	$-0.337649\pi$
$347$	18.1888			0.976425			0.488212	+	0.872725i	$0.337649\pi$
$348$		0			0
$349$	−9.40155	−	16.2840i	−0.503253	−	0.871661i	−0.999993	−	0.00376081i	$-0.998803\pi$
$349$	−9.40155	−	16.2840i	−0.503253	−	0.871661i	0.496740	−	0.867900i	$-0.334530\pi$
$350$		0			0
$351$	25.9717	−	20.1802i	1.38627	−	1.07714i
$352$		0			0
$353$	5.95997	−	10.3230i	0.317217	−	0.549436i	−0.662689	−	0.748895i	$-0.730585\pi$
$353$	5.95997	−	10.3230i	0.317217	−	0.549436i	0.979906	+	0.199458i	$0.0639182\pi$
$354$		0			0
$355$	−1.64927	−	2.85662i	−0.0875342	−	0.151614i
$356$		0			0
$357$	21.5389	−	7.00354i	1.13996	−	0.370667i
$358$		0			0
$359$	−17.3849	+	30.1115i	−0.917540	+	1.58923i	−0.114400	+	0.993435i	$0.536495\pi$
$359$	−17.3849	+	30.1115i	−0.917540	+	1.58923i	−0.803140	+	0.595791i	$0.796839\pi$
$360$		0			0
$361$	−1.91559	−	3.31790i	−0.100821	−	0.174626i
$362$		0			0
$363$	−6.11531	−	14.6797i	−0.320971	−	0.770483i
$364$		0			0
$365$	1.54551	−	2.67689i	0.0808954	−	0.140115i
$366$		0			0
$367$	14.4431	−	25.0161i	0.753922	−	1.30583i	−0.191987	−	0.981398i	$-0.561493\pi$
$367$	14.4431	−	25.0161i	0.753922	−	1.30583i	0.945909	−	0.324433i	$-0.105174\pi$
$368$		0			0
$369$	−0.106325	+	0.107188i	−0.00553507	+	0.00558001i
$370$		0			0
$371$	27.9626	−	13.2756i	1.45175	−	0.689233i
$372$		0			0
$373$	−7.15472	−	12.3923i	−0.370457	−	0.641651i	0.619179	−	0.785250i	$-0.287466\pi$
$373$	−7.15472	−	12.3923i	−0.370457	−	0.641651i	−0.989636	+	0.143599i	$0.954132\pi$
$374$		0			0
$375$	−7.86542	−	1.01933i	−0.406168	−	0.0526381i
$376$		0			0
$377$	22.8585			1.17727
$378$		0			0
$379$	1.15511			0.0593340			0.0296670	−	0.999560i	$-0.490555\pi$
$379$	1.15511			0.0593340			0.0296670	+	0.999560i	$0.490555\pi$
$380$		0			0
$381$	−13.9539	−	1.80839i	−0.714882	−	0.0926464i
$382$		0			0
$383$	−16.9131	−	29.2944i	−0.864219	−	1.49687i	−0.867820	−	0.496878i	$-0.834479\pi$
$383$	−16.9131	−	29.2944i	−0.864219	−	1.49687i	0.00360069	−	0.999994i	$-0.498854\pi$
$384$		0			0
$385$	0.134068	−	1.66505i	0.00683272	−	0.0848587i
$386$		0			0
$387$	−0.680768	−	2.50019i	−0.0346054	−	0.127092i
$388$		0			0
$389$	−9.66080	+	16.7330i	−0.489822	+	0.848397i	−0.999931	−	0.0117128i	$-0.996272\pi$
$389$	−9.66080	+	16.7330i	−0.489822	+	0.848397i	0.510109	+	0.860110i	$0.329605\pi$
$390$		0			0
$391$	−18.8503	+	32.6496i	−0.953299	+	1.65116i
$392$		0			0
$393$	12.9858	+	31.1722i	0.655048	+	1.57243i
$394$		0			0
$395$	0.744159	+	1.28892i	0.0374427	+	0.0648526i
$396$		0			0
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	−0.978419	−	0.206632i	$-0.933750\pi$
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	0.668158	+	0.744019i	$0.267083\pi$
$398$		0			0
$399$	16.2754	+	14.6481i	0.814789	+	0.733321i
$400$		0			0
$401$	15.2568	+	26.4256i	0.761889	+	1.31963i	0.941876	+	0.335961i	$0.109061\pi$
$401$	15.2568	+	26.4256i	0.761889	+	1.31963i	−0.179987	+	0.983669i	$0.557606\pi$
$402$		0			0
$403$	−20.5677	+	35.6244i	−1.02455	+	1.77458i
$404$		0			0
$405$	0.0340656	+	4.21338i	0.00169273	+	0.209365i
$406$		0			0
$407$	−7.06948	−	12.2447i	−0.350421	−	0.606947i
$408$		0			0
$409$	−5.25446			−0.259816			−0.129908	−	0.991526i	$-0.541468\pi$
$409$	−5.25446			−0.259816			−0.129908	+	0.991526i	$0.541468\pi$
$410$		0			0
$411$	−15.8832	+	20.7863i	−0.783462	+	1.02531i
$412$		0			0
$413$	−0.823443	+	10.2267i	−0.0405190	+	0.503224i
$414$		0			0
$415$	−2.29530	+	3.97558i	−0.112672	+	0.195154i
$416$		0			0
$417$	4.60245	−	6.02320i	0.225383	−	0.294958i
$418$		0			0
$419$	15.2824	−	26.4699i	0.746594	−	1.29314i	−0.202852	−	0.979209i	$-0.565021\pi$
$419$	15.2824	−	26.4699i	0.746594	−	1.29314i	0.949446	−	0.313930i	$-0.101646\pi$
$420$		0			0
$421$	3.11608	+	5.39721i	0.151869	+	0.263044i	0.931914	−	0.362678i	$-0.118138\pi$
$421$	3.11608	+	5.39721i	0.151869	+	0.263044i	−0.780046	+	0.625722i	$0.784804\pi$
$422$		0			0
$423$	−31.8760	−	8.40319i	−1.54987	−	0.408577i
$424$		0			0
$425$	−23.6287			−1.14616
$426$		0			0
$427$	0.795154	−	9.87538i	0.0384802	−	0.477903i
$428$		0			0
$429$	−5.68561	−	13.6482i	−0.274504	−	0.658940i
$430$		0			0
$431$	14.8142	+	25.6590i	0.713576	+	1.23595i	0.963506	+	0.267686i	$0.0862590\pi$
$431$	14.8142	+	25.6590i	0.713576	+	1.23595i	−0.249930	+	0.968264i	$0.580408\pi$
$432$		0			0
$433$	7.36815			0.354091			0.177045	−	0.984203i	$-0.443346\pi$
$433$	7.36815			0.354091			0.177045	+	0.984203i	$0.443346\pi$
$434$		0			0
$435$	−1.77798	+	2.32683i	−0.0852476	+	0.111563i
$436$		0			0
$437$	−36.4480			−1.74355
$438$		0			0
$439$	10.4427			0.498403			0.249201	−	0.968452i	$-0.419832\pi$
$439$	10.4427			0.498403			0.249201	+	0.968452i	$0.419832\pi$
$440$		0			0
$441$	−19.1881	−	8.53320i	−0.913721	−	0.406343i
$442$		0			0
$443$	5.66664			0.269230			0.134615	−	0.990898i	$-0.457020\pi$
$443$	5.66664			0.269230			0.134615	+	0.990898i	$0.457020\pi$
$444$		0			0
$445$	4.96923			0.235564
$446$		0			0
$447$	−7.83046	−	18.7969i	−0.370368	−	0.889061i
$448$		0			0
$449$	11.4794			0.541748			0.270874	−	0.962615i	$-0.412687\pi$
$449$	11.4794			0.541748			0.270874	+	0.962615i	$0.412687\pi$
$450$		0			0
$451$	0.0339345	+	0.0587763i	0.00159791	+	0.00276767i
$452$		0			0
$453$	−5.40857	+	7.07816i	−0.254117	+	0.332561i
$454$		0			0
$455$	−0.629261	+	7.81508i	−0.0295002	+	0.366377i
$456$		0			0
$457$	19.5872			0.916251			0.458126	−	0.888887i	$-0.348521\pi$
$457$	19.5872			0.916251			0.458126	+	0.888887i	$0.348521\pi$
$458$		0			0
$459$	3.50643	+	25.4409i	0.163666	+	1.18748i
$460$		0			0
$461$	17.3028	+	29.9693i	0.805871	+	1.39581i	0.915701	+	0.401859i	$0.131636\pi$
$461$	17.3028	+	29.9693i	0.805871	+	1.39581i	−0.109830	+	0.993950i	$0.535031\pi$
$462$		0			0
$463$	6.91882	−	11.9837i	0.321545	−	0.556932i	−0.659262	−	0.751913i	$-0.729131\pi$
$463$	6.91882	−	11.9837i	0.321545	−	0.556932i	0.980807	+	0.194981i	$0.0624646\pi$
$464$		0			0
$465$	−2.02651	−	4.86458i	−0.0939769	−	0.225590i
$466$		0			0
$467$	3.71088	−	6.42743i	0.171719	−	0.297426i	−0.767302	−	0.641286i	$-0.778401\pi$
$467$	3.71088	−	6.42743i	0.171719	−	0.297426i	0.939021	+	0.343860i	$0.111735\pi$
$468$		0			0
$469$	−0.562442	+	6.98523i	−0.0259712	+	0.322548i
$470$		0			0
$471$	20.7650	+	2.69108i	0.956801	+	0.123998i
$472$		0			0
$473$	−1.16482			−0.0535587
$474$		0			0
$475$	−11.4218	−	19.7832i	−0.524070	−	0.907716i
$476$		0			0
$477$	9.22114	+	33.8656i	0.422207	+	1.55060i
$478$		0			0
$479$	3.89577	−	6.74767i	0.178002	−	0.308309i	−0.763194	−	0.646170i	$-0.776370\pi$
$479$	3.89577	−	6.74767i	0.178002	−	0.308309i	0.941196	+	0.337860i	$0.109703\pi$
$480$		0			0
$481$	33.1813	+	57.4718i	1.51294	+	2.62049i
$482$		0			0
$483$	33.2426	−	10.8091i	1.51259	−	0.491832i
$484$		0			0
$485$	−3.26684	+	5.65834i	−0.148340	+	0.256932i
$486$		0			0
$487$	−1.04434	−	1.80886i	−0.0473238	−	0.0819672i	0.841393	−	0.540423i	$-0.181736\pi$
$487$	−1.04434	−	1.80886i	−0.0473238	−	0.0819672i	−0.888717	+	0.458456i	$0.848403\pi$
$488$		0			0
$489$	5.77686	−	7.56014i	0.261239	−	0.341881i
$490$		0			0
$491$	−16.8767	+	29.2312i	−0.761633	+	1.31919i	0.180375	+	0.983598i	$0.442269\pi$
$491$	−16.8767	+	29.2312i	−0.761633	+	1.31919i	−0.942008	+	0.335590i	$0.891064\pi$
$492$		0			0
$493$	−8.92422	+	15.4572i	−0.401927	+	0.696157i
$494$		0			0
$495$	1.83153	+	0.482829i	0.0823209	+	0.0217015i
$496$		0			0
$497$	−1.49611	+	18.5808i	−0.0671095	+	0.833464i
$498$		0			0
$499$	−20.9098	−	36.2169i	−0.936052	−	1.62129i	−0.772747	−	0.634714i	$-0.781118\pi$
$499$	−20.9098	−	36.2169i	−0.936052	−	1.62129i	−0.163304	−	0.986576i	$-0.552215\pi$
$500$		0			0
$501$	7.55862	−	9.89192i	0.337694	−	0.441939i
$502$		0			0
$503$	6.54978			0.292040			0.146020	−	0.989282i	$-0.453354\pi$
$503$	6.54978			0.292040			0.146020	+	0.989282i	$0.453354\pi$
$504$		0			0
$505$	−1.98946			−0.0885299
$506$		0			0
$507$	18.0272	+	43.2740i	0.800617	+	1.92186i
$508$		0			0
$509$	6.30653	+	10.9232i	0.279532	+	0.484164i	0.971269	−	0.237986i	$-0.0764873\pi$
$509$	6.30653	+	10.9232i	0.279532	+	0.484164i	−0.691736	+	0.722150i	$0.743154\pi$
$510$		0			0
$511$	−15.7800	+	7.49175i	−0.698068	+	0.331415i
$512$		0			0
$513$	−19.6056	+	15.2336i	−0.865607	+	0.672582i
$514$		0			0
$515$	−2.09656	+	3.63134i	−0.0923853	+	0.160016i
$516$		0			0
$517$	−7.40936	+	12.8334i	−0.325863	+	0.564412i
$518$		0			0
$519$	13.6711	+	1.77173i	0.600095	+	0.0777703i
$520$		0			0
$521$	10.2688	+	17.7861i	0.449883	+	0.779221i	0.998378	−	0.0569331i	$-0.0181322\pi$
$521$	10.2688	+	17.7861i	0.449883	+	0.779221i	−0.548495	+	0.836154i	$0.684799\pi$
$522$		0			0
$523$	14.4579	−	25.0419i	0.632202	−	1.09501i	−0.354899	−	0.934905i	$-0.615485\pi$
$523$	14.4579	−	25.0419i	0.632202	−	1.09501i	0.987101	−	0.160101i	$-0.0511820\pi$
$524$		0			0
$525$	16.2843	+	14.6561i	0.710706	+	0.639645i
$526$		0			0
$527$	−16.0598	−	27.8163i	−0.699574	−	1.21170i
$528$		0			0
$529$	−17.5931	+	30.4721i	−0.764917	+	1.32488i
$530$		0			0
$531$	−11.2492	−	2.96553i	−0.488174	−	0.128693i
$532$		0			0
$533$	−0.159275	−	0.275873i	−0.00689897	−	0.0119494i
$534$		0			0
$535$	−0.759119			−0.0328196
$536$		0			0
$537$	−0.224889	−	0.539842i	−0.00970469	−	0.0232959i
$538$		0			0
$539$	−5.96730	+	7.31483i	−0.257030	+	0.315072i
$540$		0			0
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	−0.786524	−	0.617560i	$-0.788121\pi$
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	0.928085	+	0.372369i	$0.121455\pi$
$542$		0			0
$543$	−12.1234	−	1.57116i	−0.520267	−	0.0674249i
$544$		0			0
$545$	−1.39348	+	2.41357i	−0.0596900	+	0.103386i
$546$		0			0
$547$	4.46777	+	7.73840i	0.191028	+	0.330870i	0.945591	−	0.325357i	$-0.105485\pi$
$547$	4.46777	+	7.73840i	0.191028	+	0.330870i	−0.754563	+	0.656227i	$0.772151\pi$
$548$		0			0
$549$	10.8627	+	2.86365i	0.463611	+	0.122218i
$550$		0			0
$551$	−17.2555			−0.735108
$552$		0			0
$553$	0.675050	−	8.38376i	0.0287060	−	0.356514i
$554$		0			0
$555$	−8.43113	−	1.09265i	−0.357881	−	0.0463803i
$556$		0			0
$557$	−2.93523	−	5.08396i	−0.124370	−	0.215414i	0.797117	−	0.603825i	$-0.206358\pi$
$557$	−2.93523	−	5.08396i	−0.124370	−	0.215414i	−0.921486	+	0.388411i	$0.873024\pi$
$558$		0			0
$559$	5.46723			0.231239
$560$		0			0
$561$	11.4488	+	1.48373i	0.483368	+	0.0626430i
$562$		0			0
$563$	27.5972			1.16308			0.581541	−	0.813517i	$-0.302450\pi$
$563$	27.5972			1.16308			0.581541	+	0.813517i	$0.302450\pi$
$564$		0			0
$565$	3.87968			0.163220
$566$		0			0
$567$	13.3636	−	19.7082i	0.561220	−	0.827667i
$568$		0			0
$569$	−27.9202			−1.17048			−0.585238	−	0.810862i	$-0.698999\pi$
$569$	−27.9202			−1.17048			−0.585238	+	0.810862i	$0.698999\pi$
$570$		0			0
$571$	−31.7974			−1.33068			−0.665339	−	0.746541i	$-0.731713\pi$
$571$	−31.7974			−1.33068			−0.665339	+	0.746541i	$0.731713\pi$
$572$		0			0
$573$	−30.4351	−	3.94430i	−1.27145	−	0.164775i
$574$		0			0
$575$	−36.4680			−1.52082
$576$		0			0
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	0.996327	+	0.0856281i	$0.0272897\pi$
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	−0.424007	+	0.905659i	$0.639377\pi$
$578$		0			0
$579$	28.8613	+	3.74033i	1.19943	+	0.155443i
$580$		0			0
$581$	23.4357	−	11.1263i	0.972276	−	0.461599i
$582$		0			0
$583$	15.7778			0.653449
$584$		0			0
$585$	−8.59646	−	2.26621i	−0.355420	−	0.0936962i
$586$		0			0
$587$	−7.12422	−	12.3395i	−0.294048	−	0.509306i	0.680715	−	0.732548i	$-0.261669\pi$
$587$	−7.12422	−	12.3395i	−0.294048	−	0.509306i	−0.974763	+	0.223242i	$0.928336\pi$
$588$		0			0
$589$	15.5262	−	26.8922i	0.639747	−	1.10807i
$590$		0			0
$591$	−10.2639	−	1.33017i	−0.422202	−	0.0547161i
$592$		0			0
$593$	15.4636	−	26.7838i	0.635015	−	1.09988i	−0.351498	−	0.936189i	$-0.614327\pi$
$593$	15.4636	−	26.7838i	0.635015	−	1.09988i	0.986512	−	0.163689i	$-0.0523392\pi$
$594$		0			0
$595$	−5.03898	−	3.47661i	−0.206578	−	0.142527i
$596$		0			0
$597$	−8.34031	−	20.0207i	−0.341346	−	0.819395i
$598$		0			0
$599$	36.5315			1.49264			0.746318	−	0.665589i	$-0.231820\pi$
$599$	36.5315			1.49264			0.746318	+	0.665589i	$0.231820\pi$
$600$		0			0
$601$	7.11575	+	12.3248i	0.290257	+	0.502741i	0.973871	−	0.227104i	$-0.0729257\pi$
$601$	7.11575	+	12.3248i	0.290257	+	0.502741i	−0.683613	+	0.729845i	$0.739592\pi$
$602$		0			0
$603$	−7.68363	−	2.02557i	−0.312902	−	0.0824875i
$604$		0			0
$605$	−2.14920	+	3.72253i	−0.0873776	+	0.151342i
$606$		0			0
$607$	14.6729	+	25.4141i	0.595553	+	1.03153i	0.993469	+	0.114106i	$0.0364003\pi$
$607$	14.6729	+	25.4141i	0.595553	+	1.03153i	−0.397916	+	0.917422i	$0.630266\pi$
$608$		0			0
$609$	15.7380	−	5.11732i	0.637734	−	0.207364i
$610$		0			0
$611$	34.7766	−	60.2349i	1.40691	−	2.43684i
$612$		0			0
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	0.779213	−	0.626760i	$-0.215619\pi$
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	−0.932396	+	0.361438i	$0.882286\pi$
$614$		0			0
$615$	0.0404706	+	0.00524486i	0.00163193	+	0.000211493i
$616$		0			0
$617$	−10.4367	+	18.0769i	−0.420165	+	0.727748i	−0.995955	−	0.0898500i	$-0.971361\pi$
$617$	−10.4367	+	18.0769i	−0.420165	+	0.727748i	0.575790	+	0.817598i	$0.304695\pi$
$618$		0			0
$619$	12.6300	−	21.8758i	0.507642	−	0.879262i	−0.492319	−	0.870415i	$-0.663851\pi$
$619$	12.6300	−	21.8758i	0.507642	−	0.879262i	0.999961	−	0.00884679i	$-0.00281606\pi$
$620$		0			0
$621$	5.41175	+	39.2650i	0.217166	+	1.57565i
$622$		0			0
$623$	−23.1147	−	15.9478i	−0.926072	−	0.638937i
$624$		0			0
$625$	−10.8802	−	18.8450i	−0.435206	−	0.753799i
$626$		0			0
$627$	4.29196	+	10.3028i	0.171405	+	0.411453i
$628$		0			0
$629$	−51.8175			−2.06610
$630$		0			0
$631$	−34.0114			−1.35397			−0.676986	−	0.735996i	$-0.736714\pi$
$631$	−34.0114			−1.35397			−0.676986	+	0.735996i	$0.736714\pi$
$632$		0			0
$633$	−2.47528	+	3.23938i	−0.0983835	+	0.128754i
$634$		0			0
$635$	1.90163	+	3.29372i	0.0754638	+	0.130707i
$636$		0			0
$637$	28.0082	−	34.3329i	1.10972	−	1.36032i
$638$		0			0
$639$	−20.4386	−	5.38804i	−0.808538	−	0.213148i
$640$		0			0
$641$	−2.64947	+	4.58902i	−0.104648	+	0.181255i	−0.913594	−	0.406627i	$-0.866705\pi$
$641$	−2.64947	+	4.58902i	−0.104648	+	0.181255i	0.808946	+	0.587882i	$0.200038\pi$
$642$		0			0
$643$	19.4304	−	33.6544i	0.766260	−	1.32720i	−0.173318	−	0.984866i	$-0.555449\pi$
$643$	19.4304	−	33.6544i	0.766260	−	1.32720i	0.939578	−	0.342335i	$-0.111218\pi$
$644$		0			0
$645$	−0.425252	+	0.556525i	−0.0167443	+	0.0219131i
$646$		0			0
$647$	4.11420	+	7.12601i	0.161746	+	0.280152i	0.935495	−	0.353340i	$-0.114954\pi$
$647$	4.11420	+	7.12601i	0.161746	+	0.280152i	−0.773749	+	0.633492i	$0.781621\pi$
$648$		0			0
$649$	−2.61480	+	4.52897i	−0.102640	+	0.177778i
$650$		0			0
$651$	−6.18557	+	29.1317i	−0.242431	+	1.14176i
$652$		0			0
$653$	−21.0164	−	36.4015i	−0.822436	−	1.42450i	−0.903863	−	0.427821i	$-0.859281\pi$
$653$	−21.0164	−	36.4015i	−0.822436	−	1.42450i	0.0814277	−	0.996679i	$-0.474052\pi$
$654$		0			0
$655$	4.56382	−	7.90477i	0.178323	−	0.308865i
$656$		0			0
$657$	−5.20373	−	19.1112i	−0.203017	−	0.745600i
$658$		0			0
$659$	7.33484	+	12.7043i	0.285725	+	0.494890i	0.972785	−	0.231711i	$-0.0744323\pi$
$659$	7.33484	+	12.7043i	0.285725	+	0.494890i	−0.687060	+	0.726601i	$0.741099\pi$
$660$		0			0
$661$	5.86605			0.228163			0.114081	−	0.993471i	$-0.463608\pi$
$661$	5.86605			0.228163			0.114081	+	0.993471i	$0.463608\pi$
$662$		0			0
$663$	−53.7361	−	6.96403i	−2.08694	−	0.270461i
$664$		0			0
$665$	0.475018	−	5.89947i	0.0184204	−	0.228771i
$666$		0			0
$667$	−13.7734	+	23.8563i	−0.533310	+	0.923720i
$668$		0			0
$669$	−7.06969	−	16.9706i	−0.273330	−	0.656123i
$670$		0			0
$671$	2.52497	−	4.37338i	0.0974754	−	0.168832i
$672$		0			0
$673$	9.42591	+	16.3261i	0.363342	+	0.629327i	0.988509	−	0.151165i	$-0.0483023\pi$
$673$	9.42591	+	16.3261i	0.363342	+	0.629327i	−0.625167	+	0.780491i	$0.714969\pi$
$674$		0			0
$675$	−19.6163	+	15.2420i	−0.755032	+	0.586665i
$676$		0			0
$677$	29.9144			1.14970			0.574852	−	0.818257i	$-0.305059\pi$
$677$	29.9144			1.14970			0.574852	+	0.818257i	$0.305059\pi$
$678$		0			0
$679$	33.3554	−	15.8358i	1.28006	−	0.607724i
$680$		0			0
$681$	1.34135	−	1.75541i	0.0514005	−	0.0672676i
$682$		0			0
$683$	12.8525	+	22.2612i	0.491788	+	0.851802i	0.999955	−	0.00945677i	$-0.00301023\pi$
$683$	12.8525	+	22.2612i	0.491788	+	0.851802i	−0.508167	+	0.861258i	$0.669677\pi$
$684$		0			0
$685$	7.07099			0.270169
$686$		0			0
$687$	−8.96934	−	21.5307i	−0.342202	−	0.821448i
$688$		0			0
$689$	−74.0547			−2.82126
$690$		0			0
$691$	38.4020			1.46088			0.730440	−	0.682976i	$-0.239315\pi$
$691$	38.4020			1.46088			0.730440	+	0.682976i	$0.239315\pi$
$692$		0			0
$693$	−6.96992	−	8.12386i	−0.264765	−	0.308600i
$694$		0			0
$695$	−2.04895			−0.0777210
$696$		0			0
$697$	0.248731			0.00942137
$698$		0			0
$699$	−21.0012	+	27.4841i	−0.794337	+	1.03954i
$700$		0			0
$701$	11.5694			0.436972			0.218486	−	0.975840i	$-0.429888\pi$
$701$	11.5694			0.436972			0.218486	+	0.975840i	$0.429888\pi$
$702$		0			0
$703$	−25.0480	−	43.3844i	−0.944703	−	1.63627i
$704$		0			0
$705$	3.42648	+	8.22520i	0.129049	+	0.309779i
$706$		0			0
$707$	9.25413	+	6.38482i	0.348037	+	0.240126i
$708$		0			0
$709$	52.0550			1.95497			0.977483	−	0.211013i	$-0.0676763\pi$
$709$	52.0550			1.95497			0.977483	+	0.211013i	$0.0676763\pi$
$710$		0			0
$711$	9.22199	+	2.43111i	0.345852	+	0.0911738i
$712$		0			0
$713$	−24.7863	−	42.9311i	−0.928254	−	1.60778i
$714$		0			0
$715$	−1.99819	+	3.46096i	−0.0747280	+	0.129433i
$716$		0			0
$717$	29.6753	−	38.8359i	1.10824	−	1.45035i
$718$		0			0
$719$	0.416175	−	0.720836i	0.0155207	−	0.0268827i	−0.858161	−	0.513381i	$-0.828393\pi$
$719$	0.416175	−	0.720836i	0.0155207	−	0.0268827i	0.873681	+	0.486498i	$0.161726\pi$
$720$		0			0
$721$	21.4064	−	10.1629i	0.797217	−	0.378488i
$722$		0			0
$723$	−18.2483	+	23.8814i	−0.678661	+	0.888159i
$724$		0			0
$725$	−17.2649			−0.641203
$726$		0			0
$727$	10.7029	+	18.5379i	0.396948	+	0.687534i	0.993348	−	0.115154i	$-0.0367361\pi$
$727$	10.7029	+	18.5379i	0.396948	+	0.687534i	−0.596400	+	0.802687i	$0.703403\pi$
$728$		0			0
$729$	19.3220	+	18.8590i	0.715630	+	0.698480i
$730$		0			0
$731$	−2.13447	+	3.69701i	−0.0789461	+	0.136739i
$732$		0			0
$733$	3.72620	+	6.45396i	0.137630	+	0.238383i	0.926599	−	0.376051i	$-0.122718\pi$
$733$	3.72620	+	6.45396i	0.137630	+	0.238383i	−0.788969	+	0.614433i	$0.789385\pi$
$734$		0			0
$735$	1.31632	+	5.52151i	0.0485531	+	0.203664i
$736$		0			0
$737$	−1.78601	+	3.09346i	−0.0657885	+	0.113949i
$738$		0			0
$739$	−17.9473	−	31.0857i	−0.660203	−	1.14351i	−0.980562	−	0.196210i	$-0.937137\pi$
$739$	−17.9473	−	31.0857i	−0.660203	−	1.14351i	0.320358	−	0.947296i	$-0.396197\pi$
$740$		0			0
$741$	−20.1448	−	48.3571i	−0.740037	−	1.77644i
$742$		0			0
$743$	16.8379	−	29.1641i	0.617723	−	1.06993i	−0.372177	−	0.928162i	$-0.621389\pi$
$743$	16.8379	−	29.1641i	0.617723	−	1.06993i	0.989900	−	0.141766i	$-0.0452781\pi$
$744$		0			0
$745$	−2.75199	+	4.76659i	−0.100825	+	0.174634i
$746$		0			0
$747$	7.72830	+	28.3830i	0.282764	+	1.03848i
$748$		0			0
$749$	3.53110	+	2.43625i	0.129023	+	0.0890188i
$750$		0			0
$751$	−7.51689	−	13.0196i	−0.274295	−	0.475093i	0.695662	−	0.718369i	$-0.255111\pi$
$751$	−7.51689	−	13.0196i	−0.274295	−	0.475093i	−0.969957	+	0.243276i	$0.921778\pi$
$752$		0			0
$753$	−10.8051	−	1.40031i	−0.393761	−	0.0510301i
$754$		0			0
$755$	2.40782			0.0876295
$756$		0			0
$757$	−34.2548			−1.24501			−0.622507	−	0.782615i	$-0.713886\pi$
$757$	−34.2548			−1.24501			−0.622507	+	0.782615i	$0.713886\pi$
$758$		0			0
$759$	17.6698	+	2.28995i	0.641374	+	0.0831200i
$760$		0			0
$761$	−21.1043	−	36.5538i	−0.765031	−	1.32507i	−0.940230	−	0.340540i	$-0.889390\pi$
$761$	−21.1043	−	36.5538i	−0.765031	−	1.32507i	0.175199	−	0.984533i	$-0.443943\pi$
$762$		0			0
$763$	14.2278	−	6.75480i	0.515081	−	0.244540i
$764$		0			0
$765$	4.88859	−	4.92828i	0.176747	−	0.178182i
$766$		0			0
$767$	12.2728	−	21.2572i	0.443147	−	0.767553i
$768$		0			0
$769$	22.2741	−	38.5799i	0.803226	−	1.39123i	−0.114256	−	0.993451i	$-0.536448\pi$
$769$	22.2741	−	38.5799i	0.803226	−	1.39123i	0.917482	−	0.397777i	$-0.130218\pi$
$770$		0			0
$771$	−4.08719	−	9.81122i	−0.147197	−	0.353343i
$772$		0			0
$773$	−9.61003	−	16.6451i	−0.345649	−	0.598681i	0.639823	−	0.768523i	$-0.279008\pi$
$773$	−9.61003	−	16.6451i	−0.345649	−	0.598681i	−0.985471	+	0.169841i	$0.945674\pi$
$774$		0			0
$775$	15.5347	−	26.9069i	0.558024	−	0.966526i
$776$		0			0
$777$	35.7114	+	32.1407i	1.28114	+	1.15304i
$778$		0			0
$779$	0.120234	+	0.208251i	0.00430783	+	0.00746138i
$780$		0			0
$781$	−4.75081	+	8.22864i	−0.169997	+	0.294444i
$782$		0			0
$783$	2.56207	+	18.5891i	0.0915608	+	0.664320i
$784$		0			0
$785$	−2.82984	−	4.90142i	−0.101001	−	0.174939i
$786$		0			0
$787$	−40.3502			−1.43833			−0.719165	−	0.694839i	$-0.755476\pi$
$787$	−40.3502			−1.43833			−0.719165	+	0.694839i	$0.755476\pi$
$788$		0			0
$789$	6.18266	−	8.09121i	0.220108	−	0.288055i
$790$		0			0
$791$	−18.0466	−	12.4512i	−0.641665	−	0.442712i
$792$		0			0
$793$	−11.8512	+	20.5269i	−0.420849	+	0.728932i
$794$		0			0
$795$	5.76012	−	7.53824i	0.204291	−	0.267354i
$796$		0			0
$797$	22.4965	−	38.9651i	0.796867	−	1.38021i	−0.124780	−	0.992184i	$-0.539823\pi$
$797$	22.4965	−	38.9651i	0.796867	−	1.38021i	0.921647	−	0.388029i	$-0.126844\pi$
$798$		0			0
$799$	27.1544	+	47.0328i	0.960653	+	1.66390i
$800$		0			0
$801$	22.4249	−	22.6069i	0.792343	−	0.798776i
$802$		0			0
$803$	−8.90381			−0.314209
$804$		0			0
$805$	−7.77706	−	5.36573i	−0.274105	−	0.189117i
$806$		0			0
$807$	20.5989	+	49.4473i	0.725117	+	1.74063i
$808$		0			0
$809$	16.8858	+	29.2470i	0.593672	+	1.02827i	0.993733	+	0.111782i	$0.0356558\pi$
$809$	16.8858	+	29.2470i	0.593672	+	1.02827i	−0.400061	+	0.916489i	$0.631011\pi$
$810$		0			0
$811$	−31.7254			−1.11403			−0.557014	−	0.830503i	$-0.688053\pi$
$811$	−31.7254			−1.11403			−0.557014	+	0.830503i	$0.688053\pi$
$812$		0			0
$813$	−11.4528	+	14.9882i	−0.401667	+	0.525659i
$814$		0			0
$815$	−2.57178			−0.0900854
$816$		0			0
$817$	−4.12711			−0.144389
$818$		0			0
$819$	32.7141	+	38.1302i	1.14312	+	1.33238i
$820$		0			0
$821$	−11.7504			−0.410093			−0.205046	−	0.978752i	$-0.565735\pi$
$821$	−11.7504			−0.410093			−0.205046	+	0.978752i	$0.565735\pi$
$822$		0			0
$823$	−8.50742			−0.296550			−0.148275	−	0.988946i	$-0.547372\pi$
$823$	−8.50742			−0.296550			−0.148275	+	0.988946i	$0.547372\pi$
$824$		0			0
$825$	4.29432	+	10.3084i	0.149509	+	0.358893i
$826$		0			0
$827$	−13.9662			−0.485651			−0.242825	−	0.970070i	$-0.578074\pi$
$827$	−13.9662			−0.485651			−0.242825	+	0.970070i	$0.578074\pi$
$828$		0			0
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	−0.984483	−	0.175480i	$-0.943852\pi$
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	0.340271	−	0.940327i	$-0.389481\pi$
$830$		0			0
$831$	20.6013	−	26.9608i	0.714652	−	0.935261i
$832$		0			0
$833$	12.2817	+	32.3434i	0.425534	+	1.12063i
$834$		0			0
$835$	−3.36499			−0.116450
$836$		0			0
$837$	−31.2759	−	12.7333i	−1.08105	−	0.440127i
$838$		0			0
$839$	−1.32105	−	2.28813i	−0.0456077	−	0.0789949i	0.842320	−	0.538977i	$-0.181189\pi$
$839$	−1.32105	−	2.28813i	−0.0456077	−	0.0789949i	−0.887928	+	0.459982i	$0.847856\pi$
$840$		0			0
$841$	7.97928	−	13.8205i	0.275148	−	0.476570i
$842$		0			0
$843$	0.189796	+	0.455601i	0.00653692	+	0.0156917i
$844$		0			0
$845$	6.33561	−	10.9736i	0.217952	−	0.377503i
$846$		0			0
$847$	21.9440	−	10.4181i	0.754004	−	0.357972i
$848$		0			0
$849$	−4.88286	−	0.632803i	−0.167579	−	0.0217177i
$850$		0			0
$851$	−79.9740			−2.74147
$852$		0			0
$853$	17.3405	+	30.0346i	0.593726	+	1.02836i	0.993725	+	0.111848i	$0.0356771\pi$
$853$	17.3405	+	30.0346i	0.593726	+	1.02836i	−0.399999	+	0.916516i	$0.630990\pi$
$854$		0			0
$855$	6.48931	+	1.71072i	0.221930	+	0.0585054i
$856$		0			0
$857$	−11.8611	+	20.5441i	−0.405169	+	0.701773i	−0.994341	−	0.106234i	$-0.966121\pi$
$857$	−11.8611	+	20.5441i	−0.405169	+	0.701773i	0.589172	+	0.808008i	$0.299454\pi$
$858$		0			0
$859$	10.9075	+	18.8923i	0.372158	+	0.644597i	0.989897	−	0.141786i	$-0.0452845\pi$
$859$	10.9075	+	18.8923i	0.372158	+	0.644597i	−0.617739	+	0.786383i	$0.711951\pi$
$860$		0			0
$861$	−0.171420	−	0.154280i	−0.00584196	−	0.00525785i
$862$		0			0
$863$	−14.6899	+	25.4436i	−0.500049	+	0.866111i	0.499951	+	0.866054i	$0.333351\pi$
$863$	−14.6899	+	25.4436i	−0.500049	+	0.866111i	−1.00000		5.68129e-5i	$0.999982\pi$
$864$		0			0
$865$	−1.86308	−	3.22696i	−0.0633467	−	0.109720i
$866$		0			0
$867$	7.81071	−	10.2218i	0.265266	−	0.347152i
$868$		0			0
$869$	2.14359	−	3.71280i	0.0727162	−	0.125948i
$870$		0			0
$871$	8.38282	−	14.5195i	0.284041	−	0.491973i
$872$		0			0
$873$	10.9995	+	40.3968i	0.372277	+	1.36722i
$874$		0			0
$875$	0.972346	−	12.0760i	0.0328713	−	0.408244i
$876$		0			0
$877$	2.81065	+	4.86818i	0.0949087	+	0.164387i	0.909571	−	0.415550i	$-0.136411\pi$
$877$	2.81065	+	4.86818i	0.0949087	+	0.164387i	−0.814662	+	0.579936i	$0.803077\pi$
$878$		0			0
$879$	3.07030	−	4.01808i	0.103559	−	0.135526i
$880$		0			0
$881$	2.75442			0.0927987			0.0463994	−	0.998923i	$-0.485225\pi$
$881$	2.75442			0.0927987			0.0463994	+	0.998923i	$0.485225\pi$
$882$		0			0
$883$	33.8917			1.14055			0.570274	−	0.821455i	$-0.306837\pi$
$883$	33.8917			1.14055			0.570274	+	0.821455i	$0.306837\pi$
$884$		0			0
$885$	1.20922	+	2.90272i	0.0406476	+	0.0975737i
$886$		0			0
$887$	27.8447	+	48.2284i	0.934932	+	1.61935i	0.774755	+	0.632261i	$0.217873\pi$
$887$	27.8447	+	48.2284i	0.934932	+	1.61935i	0.160177	+	0.987088i	$0.448794\pi$
$888$		0			0
$889$	1.72503	−	21.4239i	0.0578555	−	0.718535i
$890$		0			0
$891$	10.4618	−	6.15342i	0.350483	−	0.206147i
$892$		0			0
$893$	−26.2523	+	45.4702i	−0.878498	+	1.52160i
$894$		0			0
$895$	−0.0790366	+	0.136895i	−0.00264190	+	0.00457591i
$896$		0			0
$897$	−82.9352	−	10.7481i	−2.76913	−	0.358870i
$898$		0			0
$899$	−11.7345	−	20.3247i	−0.391367	−	0.677868i
$900$		0			0
$901$	28.9118	−	50.0767i	0.963192	−	1.66830i
$902$		0			0
$903$	3.76416	−	1.22395i	0.125263	−	0.0407304i
$904$		0			0
$905$	1.65217	+	2.86164i	0.0549200	+	0.0951243i
$906$		0			0
$907$	−26.7313	+	46.2999i	−0.887597	+	1.53736i	−0.0448901	+	0.998992i	$0.514294\pi$
$907$	−26.7313	+	46.2999i	−0.887597	+	1.53736i	−0.842707	+	0.538372i	$0.819040\pi$
$908$		0			0
$909$	−8.97793	+	9.05081i	−0.297779	+	0.300196i
$910$		0			0
$911$	9.77060	+	16.9232i	0.323714	+	0.560690i	0.981251	−	0.192732i	$-0.0617350\pi$
$911$	9.77060	+	16.9232i	0.323714	+	0.560690i	−0.657537	+	0.753422i	$0.728402\pi$
$912$		0			0
$913$	13.2235			0.437633
$914$		0			0
$915$	−1.16768	−	2.80299i	−0.0386024	−	0.0926641i
$916$		0			0
$917$	−46.5979	+	22.1229i	−1.53880	+	0.730561i
$918$		0			0
$919$	0.0878895	−	0.152229i	0.00289921	−	0.00502157i	−0.864572	−	0.502509i	$-0.832410\pi$
$919$	0.0878895	−	0.152229i	0.00289921	−	0.00502157i	0.867471	+	0.497487i	$0.165744\pi$
$920$		0			0
$921$	7.08637	+	0.918371i	0.233504	+	0.0302613i
$922$		0			0
$923$	22.2984	−	38.6220i	0.733962	−	1.27126i
$924$		0			0
$925$	−25.0617	−	43.4082i	−0.824025	−	1.42725i
$926$		0			0
$927$	7.05912	+	25.9253i	0.231852	+	0.851500i
$928$		0			0
$929$	−24.6016			−0.807152			−0.403576	−	0.914946i	$-0.632233\pi$
$929$	−24.6016			−0.807152			−0.403576	+	0.914946i	$0.632233\pi$
$930$		0			0
$931$	−21.1429	+	25.9173i	−0.692929	+	0.849406i
$932$		0			0
$933$	−26.4380	−	3.42629i	−0.865543	−	0.112172i
$934$		0			0
$935$	−1.56023	−	2.70240i	−0.0510250	−	0.0883779i
$936$		0			0
$937$	−28.5655			−0.933195			−0.466598	−	0.884470i	$-0.654520\pi$
$937$	−28.5655			−0.933195			−0.466598	+	0.884470i	$0.654520\pi$
$938$		0			0
$939$	35.5973	+	4.61329i	1.16167	+	0.150549i
$940$		0			0
$941$	37.5604			1.22443			0.612217	−	0.790689i	$-0.290278\pi$
$941$	37.5604			1.22443			0.612217	+	0.790689i	$0.290278\pi$
$942$		0			0
$943$	0.383887			0.0125011
$944$		0			0
$945$	−6.42595	+	0.364213i	−0.209036	+	0.0118479i
$946$		0			0
$947$	9.66763			0.314156			0.157078	−	0.987586i	$-0.449793\pi$
$947$	9.66763			0.314156			0.157078	+	0.987586i	$0.449793\pi$
$948$		0			0
$949$	41.7910			1.35659
$950$		0			0
$951$	0.838732	+	0.108697i	0.0271977	+	0.00352474i
$952$		0			0
$953$	58.1964			1.88517			0.942583	−	0.333971i	$-0.108389\pi$
$953$	58.1964			1.88517			0.942583	+	0.333971i	$0.108389\pi$
$954$		0			0
$955$	4.14767	+	7.18397i	0.134215	+	0.232468i
$956$		0			0
$957$	8.36537	+	1.08412i	0.270414	+	0.0350448i
$958$		0			0
$959$	−32.8912	−	22.6931i	−1.06211	−	0.732797i
$960$		0			0
$961$	11.2341			0.362390
$962$		0			0
$963$	−3.42571	+	3.45352i	−0.110392	+	0.111288i
$964$		0			0
$965$	−3.93319	−	6.81248i	−0.126614	−	0.219301i
$966$		0			0
$967$	7.97991	−	13.8216i	0.256617	−	0.444473i	−0.708717	−	0.705493i	$-0.750726\pi$
$967$	7.97991	−	13.8216i	0.256617	−	0.444473i	0.965333	+	0.261020i	$0.0840589\pi$
$968$		0			0
$969$	40.5644	+	5.25702i	1.30312	+	0.168880i
$970$		0			0
$971$	−1.67394	+	2.89935i	−0.0537193	+	0.0930445i	−0.891635	−	0.452756i	$-0.850441\pi$
$971$	−1.67394	+	2.89935i	−0.0537193	+	0.0930445i	0.837915	+	0.545800i	$0.183774\pi$
$972$		0			0
$973$	9.53083	+	6.57573i	0.305544	+	0.210808i
$974$		0			0
$975$	−20.1558	−	48.3836i	−0.645503	−	1.54952i
$976$		0			0
$977$	23.8803			0.763999			0.382000	−	0.924162i	$-0.375236\pi$
$977$	23.8803			0.763999			0.382000	+	0.924162i	$0.375236\pi$
$978$		0			0
$979$	−7.15706	−	12.3964i	−0.228741	−	0.396190i
$980$		0			0
$981$	4.69185	+	17.2313i	0.149799	+	0.550153i
$982$		0			0
$983$	−18.8786	+	32.6988i	−0.602135	+	1.04293i	0.390362	+	0.920661i	$0.372350\pi$
$983$	−18.8786	+	32.6988i	−0.602135	+	1.04293i	−0.992497	+	0.122267i	$0.960983\pi$
$984$		0			0
$985$	1.39876	+	2.42272i	0.0445682	+	0.0771944i
$986$		0			0
$987$	10.4588	−	49.2568i	0.332906	−	1.56786i
$988$		0			0
$989$	−3.29429	+	5.70588i	−0.104752	+	0.181436i
$990$		0			0
$991$	−1.08487	−	1.87904i	−0.0344619	−	0.0596898i	0.848280	−	0.529548i	$-0.177638\pi$
$991$	−1.08487	−	1.87904i	−0.0344619	−	0.0596898i	−0.882742	+	0.469858i	$0.844305\pi$
$992$		0			0
$993$	32.5627	+	4.22002i	1.03335	+	0.133918i
$994$		0			0
$995$	−2.93117	+	5.07694i	−0.0929245	+	0.160950i
$996$		0			0
$997$	4.34727	−	7.52969i	0.137679	−	0.238468i	−0.788938	−	0.614472i	$-0.789369\pi$
$997$	4.34727	−	7.52969i	0.137679	−	0.238468i	0.926618	+	0.376005i	$0.122702\pi$
$998$		0			0
$999$	−43.0184	+	33.4255i	−1.36104	+	1.05754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.121.1	yes	22
3.2	odd	2		1512.2.q.d.793.5		22
4.3	odd	2		1008.2.q.l.625.11		22
7.4	even	3		504.2.t.c.193.7	yes	22
9.2	odd	6		1512.2.t.c.289.7		22
9.7	even	3		504.2.t.c.457.7	yes	22
12.11	even	2		3024.2.q.l.2305.5		22
21.11	odd	6		1512.2.t.c.361.7		22
28.11	odd	6		1008.2.t.l.193.5		22
36.7	odd	6		1008.2.t.l.961.5		22
36.11	even	6		3024.2.t.k.289.7		22
63.11	odd	6		1512.2.q.d.1369.5		22
63.25	even	3	inner	504.2.q.c.25.1	✓	22
84.11	even	6		3024.2.t.k.1873.7		22
252.11	even	6		3024.2.q.l.2881.5		22
252.151	odd	6		1008.2.q.l.529.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.1	✓	22	63.25	even	3	inner
504.2.q.c.121.1	yes	22	1.1	even	1	trivial
504.2.t.c.193.7	yes	22	7.4	even	3
504.2.t.c.457.7	yes	22	9.7	even	3
1008.2.q.l.529.11		22	252.151	odd	6
1008.2.q.l.625.11		22	4.3	odd	2
1008.2.t.l.193.5		22	28.11	odd	6
1008.2.t.l.961.5		22	36.7	odd	6
1512.2.q.d.793.5		22	3.2	odd	2
1512.2.q.d.1369.5		22	63.11	odd	6
1512.2.t.c.289.7		22	9.2	odd	6
1512.2.t.c.361.7		22	21.11	odd	6
3024.2.q.l.2305.5		22	12.11	even	2
3024.2.q.l.2881.5		22	252.11	even	6
3024.2.t.k.289.7		22	36.11	even	6
3024.2.t.k.1873.7		22	84.11	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.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71769 - 0.222607i) q^{3} +(0.234085 + 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +(2.90089 + 0.764737i) q^{9} +O(q^{10})\)	\(q+(-1.71769 - 0.222607i) q^{3} +(0.234085 + 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +(2.90089 + 0.764737i) q^{9} +(0.674293 - 1.16791i) q^{11} +(-3.16486 + 5.48171i) q^{13} +(-0.311829 - 0.748538i) q^{15} +(-2.47120 - 4.28024i) q^{17} +(2.38910 - 4.13804i) q^{19} +(-0.951805 + 4.48264i) q^{21} +(-3.81399 - 6.60603i) q^{23} +(2.39041 - 4.14031i) q^{25} +(-4.81259 - 1.95934i) q^{27} +(-1.80565 - 3.12747i) q^{29} +6.49878 q^{31} +(-1.41821 + 1.85600i) q^{33} +(1.11896 - 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(6.65651 - 8.71133i) q^{39} +(-0.0251630 + 0.0435837i) q^{41} +(-0.431869 - 0.748019i) q^{43} +(0.368994 + 1.35517i) q^{45} -10.9883 q^{47} +(-6.90982 - 1.12000i) q^{49} +(3.29193 + 7.90221i) q^{51} +(5.84976 + 10.1321i) q^{53} +0.631366 q^{55} +(-5.02488 + 6.57603i) q^{57} -3.87784 q^{59} +3.74462 q^{61} +(2.63277 - 7.48789i) q^{63} -2.96338 q^{65} -2.64871 q^{67} +(5.08070 + 12.1961i) q^{69} -7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(-5.02763 + 6.57963i) q^{75} +(-2.93685 - 2.02626i) q^{77} +3.17902 q^{79} +(7.83036 + 4.43684i) q^{81} +(4.90272 + 8.49176i) q^{83} +(1.15694 - 2.00388i) q^{85} +(2.40534 + 5.77396i) q^{87} +(5.30709 - 9.19214i) q^{89} +(13.7844 + 9.51045i) q^{91} +(-11.1629 - 1.44667i) q^{93} +2.23701 q^{95} +(6.97792 + 12.0861i) q^{97} +(2.84919 - 2.87232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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