LMFDB - Embedded newform 504.2.bs.a.353.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(257,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.257"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.1
Character	$\chi$	$=$	504.353
Dual form			504.2.bs.a.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70597 - 0.299447i) q^{3} +(1.76701 - 3.06054i) q^{5} +(1.34480 - 2.27849i) q^{7} +(2.82066 + 1.02170i) q^{9} +(-1.57467 + 0.909136i) q^{11} +(-2.78280 + 1.60665i) q^{13} +(-3.93093 + 4.69207i) q^{15} +(2.93434 - 5.08242i) q^{17} +(-2.09143 + 1.20749i) q^{19} +(-2.97648 + 3.48434i) q^{21} +(-3.33308 - 1.92436i) q^{23} +(-3.74462 - 6.48586i) q^{25} +(-4.50602 - 2.58762i) q^{27} +(5.79110 + 3.34349i) q^{29} -4.87236i q^{31} +(2.95858 - 1.07943i) q^{33} +(-4.59714 - 8.14192i) q^{35} +(-0.905385 - 1.56817i) q^{37} +(5.22847 - 1.90759i) q^{39} +(-5.03152 - 8.71485i) q^{41} +(-2.36232 + 4.09166i) q^{43} +(8.11107 - 6.82742i) q^{45} +7.92151 q^{47} +(-3.38302 - 6.12823i) q^{49} +(-6.52781 + 7.79178i) q^{51} +(-2.26517 - 1.30780i) q^{53} +6.42580i q^{55} +(3.92950 - 1.43366i) q^{57} +8.81208 q^{59} +10.3744i q^{61} +(6.12115 - 5.05287i) q^{63} +11.3558i q^{65} -7.84769 q^{67} +(5.10990 + 4.28098i) q^{69} +7.62952i q^{71} +(-11.7672 - 6.79382i) q^{73} +(4.44602 + 12.1860i) q^{75} +(-0.0461599 + 4.81048i) q^{77} -1.84254 q^{79} +(6.91227 + 5.76372i) q^{81} +(5.61748 - 9.72975i) q^{83} +(-10.3700 - 17.9613i) q^{85} +(-8.87824 - 7.43803i) q^{87} +(6.89792 + 11.9475i) q^{89} +(-0.0815748 + 8.50119i) q^{91} +(-1.45902 + 8.31210i) q^{93} +8.53455i q^{95} +(13.7982 + 7.96638i) q^{97} +(-5.37048 + 0.955533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70597	−	0.299447i	−0.984942	−	0.172886i
$3$	−1.70597	−	0.299447i	−0.984942	−	0.172886i
$4$		0			0
$5$	1.76701	−	3.06054i	0.790229	−	1.36872i	−0.135596	−	0.990764i	$-0.543295\pi$
$5$	1.76701	−	3.06054i	0.790229	−	1.36872i	0.925825	−	0.377952i	$-0.123372\pi$
$6$		0			0
$7$	1.34480	−	2.27849i	0.508287	−	0.861188i
$7$	1.34480	−	2.27849i	0.508287	−	0.861188i
$8$		0			0
$9$	2.82066	+	1.02170i	0.940221	+	0.340565i
$10$		0			0
$11$	−1.57467	+	0.909136i	−0.474781	+	0.274115i	−0.718239	−	0.695796i	$-0.755052\pi$
$11$	−1.57467	+	0.909136i	−0.474781	+	0.274115i	0.243458	+	0.969911i	$0.421718\pi$
$12$		0			0
$13$	−2.78280	+	1.60665i	−0.771809	+	0.445604i	−0.833519	−	0.552490i	$-0.813678\pi$
$13$	−2.78280	+	1.60665i	−0.771809	+	0.445604i	0.0617107	+	0.998094i	$0.480344\pi$
$14$		0			0
$15$	−3.93093	+	4.69207i	−1.01496	+	1.21149i
$16$		0			0
$17$	2.93434	−	5.08242i	0.711682	−	1.23267i	−0.252544	−	0.967585i	$-0.581267\pi$
$17$	2.93434	−	5.08242i	0.711682	−	1.23267i	0.964225	−	0.265083i	$-0.0853995\pi$
$18$		0			0
$19$	−2.09143	+	1.20749i	−0.479807	+	0.277017i	−0.720336	−	0.693625i	$-0.756012\pi$
$19$	−2.09143	+	1.20749i	−0.479807	+	0.277017i	0.240529	+	0.970642i	$0.422679\pi$
$20$		0			0
$21$	−2.97648	+	3.48434i	−0.649520	+	0.760344i
$22$		0			0
$23$	−3.33308	−	1.92436i	−0.694996	−	0.401256i	0.110485	−	0.993878i	$-0.464760\pi$
$23$	−3.33308	−	1.92436i	−0.694996	−	0.401256i	−0.805481	+	0.592622i	$0.798093\pi$
$24$		0			0
$25$	−3.74462	−	6.48586i	−0.748923	−	1.29717i
$26$		0			0
$27$	−4.50602	−	2.58762i	−0.867184	−	0.497988i
$28$		0			0
$29$	5.79110	+	3.34349i	1.07538	+	0.620871i	0.929647	−	0.368452i	$-0.120112\pi$
$29$	5.79110	+	3.34349i	1.07538	+	0.620871i	0.145734	+	0.989324i	$0.453446\pi$
$30$		0			0
$31$		−	4.87236i		−	0.875102i	−0.899193	−	0.437551i	$-0.855846\pi$
$31$		−	4.87236i		−	0.875102i	0.899193	−	0.437551i	$-0.144154\pi$
$32$		0			0
$33$	2.95858	−	1.07943i	0.515022	−	0.187904i
$34$		0			0
$35$	−4.59714	−	8.14192i	−0.777059	−	1.37624i
$36$		0			0
$37$	−0.905385	−	1.56817i	−0.148844	−	0.257806i	0.781956	−	0.623333i	$-0.214222\pi$
$37$	−0.905385	−	1.56817i	−0.148844	−	0.257806i	−0.930801	+	0.365527i	$0.880889\pi$
$38$		0			0
$39$	5.22847	−	1.90759i	0.837225	−	0.305459i
$40$		0			0
$41$	−5.03152	−	8.71485i	−0.785792	−	1.36103i	−0.928525	−	0.371270i	$-0.878922\pi$
$41$	−5.03152	−	8.71485i	−0.785792	−	1.36103i	0.142733	−	0.989761i	$-0.454411\pi$
$42$		0			0
$43$	−2.36232	+	4.09166i	−0.360251	+	0.623973i	−0.988002	−	0.154441i	$-0.950642\pi$
$43$	−2.36232	+	4.09166i	−0.360251	+	0.623973i	0.627751	+	0.778414i	$0.283976\pi$
$44$		0			0
$45$	8.11107	−	6.82742i	1.20913	−	1.01777i
$46$		0			0
$47$	7.92151			1.15547			0.577736	−	0.816224i	$-0.303936\pi$
$47$	7.92151			1.15547			0.577736	+	0.816224i	$0.303936\pi$
$48$		0			0
$49$	−3.38302	−	6.12823i	−0.483289	−	0.875461i
$50$		0			0
$51$	−6.52781	+	7.79178i	−0.914076	+	1.09107i
$52$		0			0
$53$	−2.26517	−	1.30780i	−0.311146	−	0.179640i	0.336293	−	0.941757i	$-0.390827\pi$
$53$	−2.26517	−	1.30780i	−0.311146	−	0.179640i	−0.647439	+	0.762117i	$0.724160\pi$
$54$		0			0
$55$			6.42580i			0.866454i
$56$		0			0
$57$	3.92950	−	1.43366i	0.520474	−	0.189893i
$58$		0			0
$59$	8.81208			1.14724			0.573618	−	0.819123i	$-0.305540\pi$
$59$	8.81208			1.14724			0.573618	+	0.819123i	$0.305540\pi$
$60$		0			0
$61$			10.3744i			1.32830i	0.747599	+	0.664151i	$0.231207\pi$
$61$			10.3744i			1.32830i	−0.747599	+	0.664151i	$0.768793\pi$
$62$		0			0
$63$	6.12115	−	5.05287i	0.771193	−	0.636602i
$64$		0			0
$65$			11.3558i			1.40852i
$66$		0			0
$67$	−7.84769			−0.958748			−0.479374	−	0.877611i	$-0.659136\pi$
$67$	−7.84769			−0.958748			−0.479374	+	0.877611i	$0.659136\pi$
$68$		0			0
$69$	5.10990	+	4.28098i	0.615159	+	0.515369i
$70$		0			0
$71$			7.62952i			0.905458i	0.891648	+	0.452729i	$0.149549\pi$
$71$			7.62952i			0.905458i	−0.891648	+	0.452729i	$0.850451\pi$
$72$		0			0
$73$	−11.7672	−	6.79382i	−1.37725	−	0.795156i	−0.385423	−	0.922740i	$-0.625945\pi$
$73$	−11.7672	−	6.79382i	−1.37725	−	0.795156i	−0.991828	+	0.127584i	$0.959278\pi$
$74$		0			0
$75$	4.44602	+	12.1860i	0.513383	+	1.40712i
$76$		0			0
$77$	−0.0461599	+	4.81048i	−0.00526041	+	0.548205i
$78$		0			0
$79$	−1.84254			−0.207301			−0.103651	−	0.994614i	$-0.533052\pi$
$79$	−1.84254			−0.207301			−0.103651	+	0.994614i	$0.533052\pi$
$80$		0			0
$81$	6.91227	+	5.76372i	0.768031	+	0.640413i
$82$		0			0
$83$	5.61748	−	9.72975i	0.616598	−	1.06798i	−0.373504	−	0.927629i	$-0.621844\pi$
$83$	5.61748	−	9.72975i	0.616598	−	1.06798i	0.990102	−	0.140351i	$-0.0448230\pi$
$84$		0			0
$85$	−10.3700	−	17.9613i	−1.12478	−	1.94818i
$86$		0			0
$87$	−8.87824	−	7.43803i	−0.951848	−	0.797440i
$88$		0			0
$89$	6.89792	+	11.9475i	0.731178	+	1.26644i	0.956380	+	0.292125i	$0.0943624\pi$
$89$	6.89792	+	11.9475i	0.731178	+	1.26644i	−0.225202	+	0.974312i	$0.572304\pi$
$90$		0			0
$91$	−0.0815748	+	8.50119i	−0.00855137	+	0.891167i
$92$		0			0
$93$	−1.45902	+	8.31210i	−0.151293	+	0.861925i
$94$		0			0
$95$			8.53455i			0.875627i
$96$		0			0
$97$	13.7982	+	7.96638i	1.40099	+	0.808863i	0.994494	−	0.104789i	$-0.0334168\pi$
$97$	13.7982	+	7.96638i	1.40099	+	0.808863i	0.406497	+	0.913652i	$0.366750\pi$
$98$		0			0
$99$	−5.37048	+	0.955533i	−0.539753	+	0.0960346i
$100$		0			0
$101$	5.56250	+	9.63453i	0.553489	+	0.958671i	0.998019	+	0.0629076i	$0.0200373\pi$
$101$	5.56250	+	9.63453i	0.553489	+	0.958671i	−0.444530	+	0.895764i	$0.646629\pi$
$102$		0			0
$103$	0.522237	+	0.301514i	0.0514576	+	0.0297091i	0.525508	−	0.850789i	$-0.323875\pi$
$103$	0.522237	+	0.301514i	0.0514576	+	0.0297091i	−0.474050	+	0.880498i	$0.657209\pi$
$104$		0			0
$105$	5.40451	+	15.2665i	0.527426	+	1.48985i
$106$		0			0
$107$	11.3342	−	6.54381i	1.09572	−	0.632614i	0.160627	−	0.987015i	$-0.448649\pi$
$107$	11.3342	−	6.54381i	1.09572	−	0.632614i	0.935094	+	0.354401i	$0.115315\pi$
$108$		0			0
$109$	−1.37061	+	2.37396i	−0.131280	+	0.227384i	−0.924170	−	0.381981i	$-0.875242\pi$
$109$	−1.37061	+	2.37396i	−0.131280	+	0.227384i	0.792890	+	0.609365i	$0.208575\pi$
$110$		0			0
$111$	1.07497	+	2.94637i	0.102032	+	0.279657i
$112$		0			0
$113$	6.65125	−	3.84010i	0.625697	−	0.361246i	−0.153387	−	0.988166i	$-0.549018\pi$
$113$	6.65125	−	3.84010i	0.625697	−	0.361246i	0.779084	+	0.626920i	$0.215685\pi$
$114$		0			0
$115$	−11.7792	+	6.80070i	−1.09841	+	0.634168i
$116$		0			0
$117$	−9.49083	+	1.68864i	−0.877428	+	0.156115i
$118$		0			0
$119$	−7.63415	−	13.5207i	−0.699821	−	1.23944i
$120$		0			0
$121$	−3.84694	+	6.66310i	−0.349722	+	0.605736i
$122$		0			0
$123$	5.97398	+	16.3739i	0.538656	+	1.47639i
$124$		0			0
$125$	−8.79697			−0.786825
$126$		0			0
$127$	17.9246			1.59055			0.795277	−	0.606246i	$-0.207325\pi$
$127$	17.9246			1.59055			0.795277	+	0.606246i	$0.207325\pi$
$128$		0			0
$129$	5.25529	−	6.27286i	0.462702	−	0.552295i
$130$		0			0
$131$	8.48534	−	14.6970i	0.741367	−	1.28409i	−0.210506	−	0.977593i	$-0.567511\pi$
$131$	8.48534	−	14.6970i	0.741367	−	1.28409i	0.951873	−	0.306493i	$-0.0991556\pi$
$132$		0			0
$133$	−0.0613082	+	6.38913i	−0.00531609	+	0.554008i
$134$		0			0
$135$	−15.8817	+	9.21852i	−1.36688	+	0.793404i
$136$		0			0
$137$	4.81631	−	2.78070i	0.411485	−	0.237571i	−0.279943	−	0.960017i	$-0.590315\pi$
$137$	4.81631	−	2.78070i	0.411485	−	0.237571i	0.691428	+	0.722446i	$0.256982\pi$
$138$		0			0
$139$	12.4503	−	7.18817i	1.05602	−	0.609693i	0.131690	−	0.991291i	$-0.457960\pi$
$139$	12.4503	−	7.18817i	1.05602	−	0.609693i	0.924328	+	0.381598i	$0.124626\pi$
$140$		0			0
$141$	−13.5139	−	2.37208i	−1.13807	−	0.199765i
$142$		0			0
$143$	2.92132	−	5.05988i	0.244293	−	0.423129i
$144$		0			0
$145$	20.4658	−	11.8159i	1.69959	−	0.981261i
$146$		0			0
$147$	3.93626	+	11.4676i	0.324657	+	0.945832i
$148$		0			0
$149$	−5.56086	−	3.21056i	−0.455563	−	0.263019i	0.254614	−	0.967043i	$-0.418052\pi$
$149$	−5.56086	−	3.21056i	−0.455563	−	0.263019i	−0.710177	+	0.704023i	$0.751385\pi$
$150$		0			0
$151$	−7.99627	−	13.8499i	−0.650727	−	1.12709i	−0.982947	−	0.183890i	$-0.941131\pi$
$151$	−7.99627	−	13.8499i	−0.650727	−	1.12709i	0.332220	−	0.943202i	$-0.392202\pi$
$152$		0			0
$153$	13.4695	−	11.3378i	1.08894	−	0.916607i
$154$		0			0
$155$	−14.9121	−	8.60949i	−1.19777	−	0.691531i
$156$		0			0
$157$		−	13.9271i		−	1.11151i	−0.831348	−	0.555753i	$-0.812430\pi$
$157$		−	13.9271i		−	1.11151i	0.831348	−	0.555753i	$-0.187570\pi$
$158$		0			0
$159$	3.47270	+	2.90937i	0.275403	+	0.230728i
$160$		0			0
$161$	−8.86696	+	5.00652i	−0.698814	+	0.394569i
$162$		0			0
$163$	7.79498	+	13.5013i	0.610550	+	1.05750i	0.991148	+	0.132762i	$0.0423847\pi$
$163$	7.79498	+	13.5013i	0.610550	+	1.05750i	−0.380598	+	0.924740i	$0.624282\pi$
$164$		0			0
$165$	1.92419	−	10.9622i	0.149798	−	0.853407i
$166$		0			0
$167$	6.58728	+	11.4095i	0.509739	+	0.882893i	0.999936	+	0.0112821i	$0.00359127\pi$
$167$	6.58728	+	11.4095i	0.509739	+	0.882893i	−0.490198	+	0.871611i	$0.663075\pi$
$168$		0			0
$169$	−1.33736	+	2.31638i	−0.102874	+	0.178183i
$170$		0			0
$171$	−7.13291	+	1.26911i	−0.545467	+	0.0970513i
$172$		0			0
$173$	−11.2080			−0.852132			−0.426066	−	0.904692i	$-0.640101\pi$
$173$	−11.2080			−0.852132			−0.426066	+	0.904692i	$0.640101\pi$
$174$		0			0
$175$	−19.8137	−	0.190127i	−1.49778	−	0.0143722i
$176$		0			0
$177$	−15.0331	−	2.63875i	−1.12996	−	0.198341i
$178$		0			0
$179$	−9.22783	−	5.32769i	−0.689721	−	0.398210i	0.113787	−	0.993505i	$-0.463702\pi$
$179$	−9.22783	−	5.32769i	−0.689721	−	0.398210i	−0.803507	+	0.595295i	$0.797035\pi$
$180$		0			0
$181$			11.8897i			0.883754i	0.897076	+	0.441877i	$0.145687\pi$
$181$			11.8897i			0.883754i	−0.897076	+	0.441877i	$0.854313\pi$
$182$		0			0
$183$	3.10658	−	17.6984i	0.229645	−	1.30830i
$184$		0			0
$185$	−6.39928			−0.470484
$186$		0			0
$187$			10.6709i			0.780330i
$188$		0			0
$189$	−11.9556	+	6.78708i	−0.869639	+	0.493688i
$190$		0			0
$191$			0.223967i			0.0162057i	0.999967	+	0.00810283i	$0.00257924\pi$
$191$			0.223967i			0.0162057i	−0.999967	+	0.00810283i	$0.997421\pi$
$192$		0			0
$193$	26.0745			1.87688			0.938442	−	0.345437i	$-0.112269\pi$
$193$	26.0745			1.87688			0.938442	+	0.345437i	$0.112269\pi$
$194$		0			0
$195$	3.40047	−	19.3727i	0.243513	−	1.38731i
$196$		0			0
$197$		−	1.56289i		−	0.111352i	−0.998449	−	0.0556758i	$-0.982269\pi$
$197$		−	1.56289i		−	0.111352i	0.998449	−	0.0556758i	$-0.0177313\pi$
$198$		0			0
$199$	13.4725	+	7.77832i	0.955037	+	0.551391i	0.894642	−	0.446784i	$-0.147431\pi$
$199$	13.4725	+	7.77832i	0.955037	+	0.551391i	0.0603949	+	0.998175i	$0.480764\pi$
$200$		0			0
$201$	13.3879	+	2.34997i	0.944311	+	0.165754i
$202$		0			0
$203$	15.4060	−	8.69863i	1.08129	−	0.610524i
$204$		0			0
$205$	−35.5629			−2.48382
$206$		0			0
$207$	−7.43540	−	8.83336i	−0.516796	−	0.613961i
$208$		0			0
$209$	2.19554	−	3.80279i	0.151869	−	0.263045i
$210$		0			0
$211$	6.98216	+	12.0935i	0.480672	+	0.832548i	0.999754	−	0.0221763i	$-0.00705950\pi$
$211$	6.98216	+	12.0935i	0.480672	+	0.832548i	−0.519082	+	0.854724i	$0.673726\pi$
$212$		0			0
$213$	2.28464	−	13.0157i	0.156541	−	0.891823i
$214$		0			0
$215$	8.34848	+	14.4600i	0.569361	+	0.986163i
$216$		0			0
$217$	−11.1016	−	6.55236i	−0.753628	−	0.444803i
$218$		0			0
$219$	18.0402	+	15.1137i	1.21904	+	1.02129i
$220$		0			0
$221$			18.8578i			1.26851i
$222$		0			0
$223$	21.4242	+	12.3693i	1.43467	+	0.828307i	0.997472	−	0.0710586i	$-0.0226377\pi$
$223$	21.4242	+	12.3693i	1.43467	+	0.828307i	0.437198	+	0.899366i	$0.355971\pi$
$224$		0			0
$225$	−3.93571	−	22.1203i	−0.262381	−	1.47469i
$226$		0			0
$227$	−3.12076	−	5.40532i	−0.207132	−	0.358764i	0.743678	−	0.668538i	$-0.233080\pi$
$227$	−3.12076	−	5.40532i	−0.207132	−	0.358764i	−0.950810	+	0.309775i	$0.899746\pi$
$228$		0			0
$229$	−13.7329	−	7.92870i	−0.907496	−	0.523943i	−0.0278714	−	0.999612i	$-0.508873\pi$
$229$	−13.7329	−	7.92870i	−0.907496	−	0.523943i	−0.879625	+	0.475668i	$0.842206\pi$
$230$		0			0
$231$	1.51923	−	8.19270i	0.0999581	−	0.539040i
$232$		0			0
$233$	−2.94574	+	1.70072i	−0.192982	+	0.111418i	−0.593378	−	0.804924i	$-0.702206\pi$
$233$	−2.94574	+	1.70072i	−0.192982	+	0.111418i	0.400396	+	0.916342i	$0.368873\pi$
$234$		0			0
$235$	13.9974	−	24.2441i	0.913087	−	1.58151i
$236$		0			0
$237$	3.14331	+	0.551742i	0.204180	+	0.0358395i
$238$		0			0
$239$	−16.3482	+	9.43864i	−1.05748	+	0.610535i	−0.924733	−	0.380615i	$-0.875712\pi$
$239$	−16.3482	+	9.43864i	−1.05748	+	0.610535i	−0.132744	+	0.991150i	$0.542379\pi$
$240$		0			0
$241$	−9.68610	+	5.59227i	−0.623937	+	0.360230i	−0.778400	−	0.627768i	$-0.783968\pi$
$241$	−9.68610	+	5.59227i	−0.623937	+	0.360230i	0.154463	+	0.987999i	$0.450635\pi$
$242$		0			0
$243$	−10.0662	−	11.9026i	−0.645747	−	0.763552i
$244$		0			0
$245$	−24.7335	−	0.474714i	−1.58017	−	0.0303284i
$246$		0			0
$247$	3.88002	−	6.72039i	0.246880	−	0.427608i
$248$		0			0
$249$	−12.4968	+	14.9165i	−0.791952	+	0.945296i
$250$		0			0
$251$	−15.4537			−0.975431			−0.487716	−	0.873003i	$-0.662170\pi$
$251$	−15.4537			−0.975431			−0.487716	+	0.873003i	$0.662170\pi$
$252$		0			0
$253$	6.99801			0.439961
$254$		0			0
$255$	12.3124	+	33.7468i	0.771032	+	2.11330i
$256$		0			0
$257$	−5.32238	+	9.21864i	−0.332001	+	0.575043i	−0.982904	−	0.184118i	$-0.941057\pi$
$257$	−5.32238	+	9.21864i	−0.332001	+	0.575043i	0.650903	+	0.759161i	$0.274390\pi$
$258$		0			0
$259$	−4.79063	−	0.0459694i	−0.297675	−	0.00285640i
$260$		0			0
$261$	12.9187	+	15.3476i	0.799648	+	0.949994i
$262$		0			0
$263$	9.60206	−	5.54375i	0.592088	−	0.341842i	−0.173835	−	0.984775i	$-0.555616\pi$
$263$	9.60206	−	5.54375i	0.592088	−	0.341842i	0.765923	+	0.642933i	$0.222282\pi$
$264$		0			0
$265$	−8.00515	+	4.62178i	−0.491753	+	0.283913i
$266$		0			0
$267$	−8.18998	−	22.4477i	−0.501218	−	1.37378i
$268$		0			0
$269$	3.14147	−	5.44119i	0.191539	−	0.331755i	−0.754221	−	0.656620i	$-0.771986\pi$
$269$	3.14147	−	5.44119i	0.191539	−	0.331755i	0.945760	+	0.324865i	$0.105319\pi$
$270$		0			0
$271$	0.954533	−	0.551100i	0.0579838	−	0.0334769i	−0.470728	−	0.882278i	$-0.656009\pi$
$271$	0.954533	−	0.551100i	0.0579838	−	0.0334769i	0.528712	+	0.848802i	$0.322675\pi$
$272$		0			0
$273$	2.68482	−	14.4783i	0.162493	−	0.876269i
$274$		0			0
$275$	11.7931	+	6.80873i	0.711149	+	0.410582i
$276$		0			0
$277$	7.68081	+	13.3036i	0.461495	+	0.799333i	0.999036	−	0.0439049i	$-0.0139798\pi$
$277$	7.68081	+	13.3036i	0.461495	+	0.799333i	−0.537541	+	0.843238i	$0.680647\pi$
$278$		0			0
$279$	4.97807	−	13.7433i	0.298030	−	0.822790i
$280$		0			0
$281$	18.9133	+	10.9196i	1.12827	+	0.651407i	0.943499	−	0.331374i	$-0.107512\pi$
$281$	18.9133	+	10.9196i	1.12827	+	0.651407i	0.184771	+	0.982782i	$0.440846\pi$
$282$		0			0
$283$		−	11.0785i		−	0.658548i	−0.944234	−	0.329274i	$-0.893196\pi$
$283$		−	11.0785i		−	0.658548i	0.944234	−	0.329274i	$-0.106804\pi$
$284$		0			0
$285$	2.55565	−	14.5597i	0.151384	−	0.862441i
$286$		0			0
$287$	−26.6231	−	0.255467i	−1.57151	−	0.0150797i
$288$		0			0
$289$	−8.72069	−	15.1047i	−0.512982	−	0.888511i
$290$		0			0
$291$	−21.1537	−	17.7222i	−1.24005	−	1.03889i
$292$		0			0
$293$	−12.6330	−	21.8810i	−0.738027	−	1.27830i	−0.953382	−	0.301765i	$-0.902424\pi$
$293$	−12.6330	−	21.8810i	−0.738027	−	1.27830i	0.215355	−	0.976536i	$-0.430909\pi$
$294$		0			0
$295$	15.5710	−	26.9698i	0.906578	−	1.57024i
$296$		0			0
$297$	9.44800	−	0.0219345i	0.548228	−	0.00127277i
$298$		0			0
$299$	12.3671			0.715206
$300$		0			0
$301$	6.14596	+	10.8850i	0.354247	+	0.627401i
$302$		0			0
$303$	−6.60442	−	18.1019i	−0.379414	−	1.03993i
$304$		0			0
$305$	31.7512	+	18.3316i	1.81807	+	1.04966i
$306$		0			0
$307$		−	12.2163i		−	0.697219i	−0.937268	−	0.348610i	$-0.886654\pi$
$307$		−	12.2163i		−	0.697219i	0.937268	−	0.348610i	$-0.113346\pi$
$308$		0			0
$309$	−0.800634	−	0.670756i	−0.0455465	−	0.0381580i
$310$		0			0
$311$	−9.48967			−0.538110			−0.269055	−	0.963125i	$-0.586711\pi$
$311$	−9.48967			−0.538110			−0.269055	+	0.963125i	$0.586711\pi$
$312$		0			0
$313$		−	13.5513i		−	0.765964i	−0.923756	−	0.382982i	$-0.874897\pi$
$313$		−	13.5513i		−	0.765964i	0.923756	−	0.382982i	$-0.125103\pi$
$314$		0			0
$315$	−4.64842	−	27.6625i	−0.261909	−	1.55861i
$316$		0			0
$317$			15.8839i			0.892131i	0.895000	+	0.446065i	$0.147175\pi$
$317$			15.8839i			0.892131i	−0.895000	+	0.446065i	$0.852825\pi$
$318$		0			0
$319$	−12.1588			−0.680761
$320$		0			0
$321$	−21.2954	+	7.76954i	−1.18859	+	0.433654i
$322$		0			0
$323$			14.1727i			0.788591i
$324$		0			0
$325$	20.8410	+	12.0326i	1.15605	+	0.667446i
$326$		0			0
$327$	3.04909	−	3.63948i	0.168615	−	0.201264i
$328$		0			0
$329$	10.6529	−	18.0491i	0.587311	−	0.995078i
$330$		0			0
$331$	10.9739			0.603183			0.301591	−	0.953437i	$-0.402482\pi$
$331$	10.9739			0.603183			0.301591	+	0.953437i	$0.402482\pi$
$332$		0			0
$333$	−0.951590	−	5.34831i	−0.0521468	−	0.293086i
$334$		0			0
$335$	−13.8669	+	24.0182i	−0.757630	+	1.31225i
$336$		0			0
$337$	2.80751	+	4.86275i	0.152935	+	0.264891i	0.932305	−	0.361673i	$-0.117794\pi$
$337$	2.80751	+	4.86275i	0.152935	+	0.264891i	−0.779370	+	0.626564i	$0.784461\pi$
$338$		0			0
$339$	−12.4967	+	4.55940i	−0.678730	+	0.247632i
$340$		0			0
$341$	4.42964	+	7.67237i	0.239879	+	0.415482i
$342$		0			0
$343$	−18.5126	−	0.533054i	−0.999586	−	0.0287822i
$344$		0			0
$345$	22.1313	−	8.07455i	1.19151	−	0.434719i
$346$		0			0
$347$			4.82668i			0.259110i	0.991572	+	0.129555i	$0.0413549\pi$
$347$			4.82668i			0.259110i	−0.991572	+	0.129555i	$0.958645\pi$
$348$		0			0
$349$	−22.7167	−	13.1155i	−1.21600	−	0.702056i	−0.251937	−	0.967744i	$-0.581068\pi$
$349$	−22.7167	−	13.1155i	−1.21600	−	0.702056i	−0.964059	+	0.265688i	$0.914401\pi$
$350$		0			0
$351$	16.6967	−	0.0387633i	0.891206	−	0.00206903i
$352$		0			0
$353$	−17.4957	−	30.3034i	−0.931201	−	1.61289i	−0.781271	−	0.624192i	$-0.785428\pi$
$353$	−17.4957	−	30.3034i	−0.931201	−	1.61289i	−0.149930	−	0.988697i	$-0.547905\pi$
$354$		0			0
$355$	23.3505	+	13.4814i	1.23931	+	0.715519i
$356$		0			0
$357$	8.97488	+	25.3519i	0.475001	+	1.34177i
$358$		0			0
$359$	21.6396	−	12.4936i	1.14209	−	0.659388i	0.195146	−	0.980774i	$-0.437482\pi$
$359$	21.6396	−	12.4936i	1.14209	−	0.659388i	0.946948	+	0.321386i	$0.104149\pi$
$360$		0			0
$361$	−6.58394	+	11.4037i	−0.346523	+	0.600196i
$362$		0			0
$363$	8.55801	−	10.2151i	0.449179	−	0.536153i
$364$		0			0
$365$	−41.5855	+	24.0094i	−2.17669	+	1.25671i
$366$		0			0
$367$	−21.3100	+	12.3034i	−1.11237	+	0.642230i	−0.939443	−	0.342704i	$-0.888657\pi$
$367$	−21.3100	+	12.3034i	−1.11237	+	0.642230i	−0.172931	+	0.984934i	$0.555324\pi$
$368$		0			0
$369$	−5.28830	−	29.7223i	−0.275298	−	1.54728i
$370$		0			0
$371$	−6.02601	+	3.40245i	−0.312855	+	0.176646i
$372$		0			0
$373$	5.21870	−	9.03905i	0.270214	−	0.468024i	−0.698703	−	0.715412i	$-0.746239\pi$
$373$	5.21870	−	9.03905i	0.270214	−	0.468024i	0.968916	+	0.247388i	$0.0795723\pi$
$374$		0			0
$375$	15.0074	+	2.63423i	0.774977	+	0.136031i
$376$		0			0
$377$	−21.4873			−1.10665
$378$		0			0
$379$	31.8728			1.63719			0.818597	−	0.574368i	$-0.194752\pi$
$379$	31.8728			1.63719			0.818597	+	0.574368i	$0.194752\pi$
$380$		0			0
$381$	−30.5789	−	5.36749i	−1.56660	−	0.274985i
$382$		0			0
$383$	−12.3860	+	21.4531i	−0.632893	+	1.09620i	0.354065	+	0.935221i	$0.384799\pi$
$383$	−12.3860	+	21.4531i	−0.632893	+	1.09620i	−0.986957	+	0.160982i	$0.948534\pi$
$384$		0			0
$385$	14.6411	+	8.64141i	0.746180	+	0.440407i
$386$		0			0
$387$	−10.8438	+	9.12763i	−0.551219	+	0.463983i
$388$		0			0
$389$	19.9382	−	11.5113i	1.01091	−	0.583647i	0.0994499	−	0.995043i	$-0.468292\pi$
$389$	19.9382	−	11.5113i	1.01091	−	0.583647i	0.911457	+	0.411395i	$0.134958\pi$
$390$		0			0
$391$	−19.5608	+	11.2934i	−0.989232	+	0.571133i
$392$		0			0
$393$	−18.8767	+	22.5318i	−0.952204	+	1.13658i
$394$		0			0
$395$	−3.25577	+	5.63916i	−0.163816	+	0.283737i
$396$		0			0
$397$	23.9247	−	13.8129i	1.20075	−	0.693251i	0.240025	−	0.970767i	$-0.422844\pi$
$397$	23.9247	−	13.8129i	1.20075	−	0.693251i	0.960721	+	0.277515i	$0.0895109\pi$
$398$		0			0
$399$	2.01780	−	10.8813i	0.101016	−	0.544747i
$400$		0			0
$401$	4.61058	+	2.66192i	0.230241	+	0.132930i	0.610683	−	0.791875i	$-0.290895\pi$
$401$	4.61058	+	2.66192i	0.230241	+	0.132930i	−0.380442	+	0.924805i	$0.624228\pi$
$402$		0			0
$403$	7.82817	+	13.5588i	0.389949	+	0.675412i
$404$		0			0
$405$	29.8541	−	10.9708i	1.48346	−	0.545143i
$406$		0			0
$407$	2.85137	+	1.64624i	0.141337	+	0.0816009i
$408$		0			0
$409$			7.06575i			0.349379i	0.984624	+	0.174690i	$0.0558922\pi$
$409$			7.06575i			0.349379i	−0.984624	+	0.174690i	$0.944108\pi$
$410$		0			0
$411$	−9.04915	+	3.30155i	−0.446362	+	0.162854i
$412$		0			0
$413$	11.8505	−	20.0782i	0.583124	−	0.987985i
$414$		0			0
$415$	−19.8522	−	34.3851i	−0.974507	−	1.68790i
$416$		0			0
$417$	−23.3923	+	8.53459i	−1.14552	+	0.417941i
$418$		0			0
$419$	1.94504	+	3.36891i	0.0950215	+	0.164582i	0.909618	−	0.415447i	$-0.136375\pi$
$419$	1.94504	+	3.36891i	0.0950215	+	0.164582i	−0.814596	+	0.580029i	$0.803041\pi$
$420$		0			0
$421$	−2.18533	+	3.78510i	−0.106506	+	0.184475i	−0.914353	−	0.404919i	$-0.867300\pi$
$421$	−2.18533	+	3.78510i	−0.106506	+	0.184475i	0.807846	+	0.589393i	$0.200633\pi$
$422$		0			0
$423$	22.3439	+	8.09338i	1.08640	+	0.393514i
$424$		0			0
$425$	−43.9519			−2.13198
$426$		0			0
$427$	23.6379	+	13.9515i	1.14392	+	0.675158i
$428$		0			0
$429$	−6.49886	+	7.75722i	−0.313768	+	0.374522i
$430$		0			0
$431$	−10.7505	−	6.20681i	−0.517834	−	0.298971i	0.218214	−	0.975901i	$-0.429977\pi$
$431$	−10.7505	−	6.20681i	−0.517834	−	0.298971i	−0.736048	+	0.676929i	$0.763310\pi$
$432$		0			0
$433$			25.2979i			1.21574i	0.794036	+	0.607870i	$0.207976\pi$
$433$			25.2979i			1.21574i	−0.794036	+	0.607870i	$0.792024\pi$
$434$		0			0
$435$	−38.4523	+	14.0292i	−1.84365	+	0.672649i
$436$		0			0
$437$	9.29455			0.444619
$438$		0			0
$439$			26.8362i			1.28082i	0.768033	+	0.640410i	$0.221236\pi$
$439$			26.8362i			1.28082i	−0.768033	+	0.640410i	$0.778764\pi$
$440$		0			0
$441$	−3.28119	−	20.7421i	−0.156247	−	0.987718i
$442$		0			0
$443$		−	13.0540i		−	0.620213i	−0.950702	−	0.310107i	$-0.899635\pi$
$443$		−	13.0540i		−	0.620213i	0.950702	−	0.310107i	$-0.100365\pi$
$444$		0			0
$445$	48.7546			2.31119
$446$		0			0
$447$	8.52526	+	7.14230i	0.403231	+	0.337819i
$448$		0			0
$449$			0.468645i			0.0221167i	0.999939	+	0.0110584i	$0.00352006\pi$
$449$			0.468645i			0.0221167i	−0.999939	+	0.0110584i	$0.996480\pi$
$450$		0			0
$451$	15.8460	+	9.14868i	0.746158	+	0.430795i
$452$		0			0
$453$	9.49406	+	26.0220i	0.446070	+	1.22262i
$454$		0			0
$455$	25.8741	+	15.2713i	1.21300	+	0.715930i
$456$		0			0
$457$	−4.12972			−0.193180			−0.0965901	−	0.995324i	$-0.530794\pi$
$457$	−4.12972			−0.193180			−0.0965901	+	0.995324i	$0.530794\pi$
$458$		0			0
$459$	−26.3736	+	15.3085i	−1.23101	+	0.714542i
$460$		0			0
$461$	−12.9115	+	22.3633i	−0.601347	+	1.04156i	0.391271	+	0.920276i	$0.372036\pi$
$461$	−12.9115	+	22.3633i	−0.601347	+	1.04156i	−0.992617	+	0.121288i	$0.961298\pi$
$462$		0			0
$463$	−2.56402	−	4.44101i	−0.119160	−	0.206391i	0.800275	−	0.599633i	$-0.204687\pi$
$463$	−2.56402	−	4.44101i	−0.119160	−	0.206391i	−0.919435	+	0.393242i	$0.871353\pi$
$464$		0			0
$465$	22.8615	+	19.1529i	1.06017	+	0.888195i
$466$		0			0
$467$	1.26091	+	2.18396i	0.0583480	+	0.101062i	0.893724	−	0.448617i	$-0.148083\pi$
$467$	1.26091	+	2.18396i	0.0583480	+	0.101062i	−0.835376	+	0.549679i	$0.814750\pi$
$468$		0			0
$469$	−10.5536	+	17.8809i	−0.487319	+	0.825662i
$470$		0			0
$471$	−4.17044	+	23.7592i	−0.192164	+	1.09477i
$472$		0			0
$473$		−	8.59070i		−	0.395001i
$474$		0			0
$475$	15.6632	+	9.04316i	0.718677	+	0.414929i
$476$		0			0
$477$	−5.05312	−	6.00318i	−0.231366	−	0.274867i
$478$		0			0
$479$	−5.74622	−	9.95275i	−0.262552	−	0.454753i	0.704368	−	0.709835i	$-0.251231\pi$
$479$	−5.74622	−	9.95275i	−0.262552	−	0.454753i	−0.966919	+	0.255083i	$0.917897\pi$
$480$		0			0
$481$	5.03900	+	2.90927i	0.229759	+	0.132651i
$482$		0			0
$483$	16.6260	−	5.88578i	0.756507	−	0.267812i
$484$		0			0
$485$	48.7629	−	28.1533i	2.21421	−	1.27837i
$486$		0			0
$487$	−10.8463	+	18.7864i	−0.491493	+	0.851292i	−0.999952	−	0.00979483i	$-0.996882\pi$
$487$	−10.8463	+	18.7864i	−0.491493	+	0.851292i	0.508459	+	0.861086i	$0.330215\pi$
$488$		0			0
$489$	−9.25506	−	25.3670i	−0.418528	−	1.14713i
$490$		0			0
$491$	−19.3592	+	11.1771i	−0.873669	+	0.504413i	−0.868566	−	0.495574i	$-0.834958\pi$
$491$	−19.3592	+	11.1771i	−0.873669	+	0.504413i	−0.00510349	+	0.999987i	$0.501624\pi$
$492$		0			0
$493$	33.9861	−	19.6219i	1.53066	−	0.883726i
$494$		0			0
$495$	−6.56521	+	18.1250i	−0.295084	+	0.814658i
$496$		0			0
$497$	17.3838	+	10.2602i	0.779769	+	0.460232i
$498$		0			0
$499$	−8.76231	+	15.1768i	−0.392255	+	0.679405i	−0.992747	−	0.120226i	$-0.961638\pi$
$499$	−8.76231	+	15.1768i	−0.392255	+	0.679405i	0.600492	+	0.799631i	$0.294972\pi$
$500$		0			0
$501$	−7.82115	−	21.4368i	−0.349423	−	0.957725i
$502$		0			0
$503$	7.60926			0.339280			0.169640	−	0.985506i	$-0.445739\pi$
$503$	7.60926			0.339280			0.169640	+	0.985506i	$0.445739\pi$
$504$		0			0
$505$	39.3159			1.74953
$506$		0			0
$507$	2.97514	−	3.55121i	0.132130	−	0.157715i
$508$		0			0
$509$	−3.39373	+	5.87811i	−0.150424	+	0.260543i	−0.931384	−	0.364039i	$-0.881397\pi$
$509$	−3.39373	+	5.87811i	−0.150424	+	0.260543i	0.780959	+	0.624582i	$0.214731\pi$
$510$		0			0
$511$	−31.3042	+	17.6752i	−1.38482	+	0.781905i
$512$		0			0
$513$	12.5486	−	0.0291328i	0.554032	−	0.00128624i
$514$		0			0
$515$	1.84559	−	1.06555i	0.0813265	−	0.0469539i
$516$		0			0
$517$	−12.4738	+	7.20174i	−0.548596	+	0.316732i
$518$		0			0
$519$	19.1206	+	3.35622i	0.839300	+	0.147322i
$520$		0			0
$521$	13.8435	−	23.9777i	0.606497	−	1.05048i	−0.385316	−	0.922785i	$-0.625908\pi$
$521$	13.8435	−	23.9777i	0.606497	−	1.05048i	0.991813	−	0.127698i	$-0.0407590\pi$
$522$		0			0
$523$	−0.834923	+	0.482043i	−0.0365086	+	0.0210783i	−0.518143	−	0.855294i	$-0.673377\pi$
$523$	−0.834923	+	0.482043i	−0.0365086	+	0.0210783i	0.481635	+	0.876372i	$0.340043\pi$
$524$		0			0
$525$	33.7447	+	6.25752i	1.47274	+	0.273101i
$526$		0			0
$527$	−24.7634	−	14.2972i	−1.07871	−	0.622794i
$528$		0			0
$529$	−4.09370	−	7.09049i	−0.177987	−	0.308282i
$530$		0			0
$531$	24.8559	+	9.00327i	1.07865	+	0.390709i
$532$		0			0
$533$	28.0034	+	16.1678i	1.21296	+	0.700304i
$534$		0			0
$535$		−	46.2518i		−	1.99964i
$536$		0			0
$537$	14.1470	+	11.8521i	0.610490	+	0.511457i
$538$		0			0
$539$	10.8985	+	6.57430i	0.469433	+	0.283175i
$540$		0			0
$541$	2.36867	+	4.10266i	0.101837	+	0.176387i	0.912442	−	0.409207i	$-0.134195\pi$
$541$	2.36867	+	4.10266i	0.101837	+	0.176387i	−0.810604	+	0.585594i	$0.800861\pi$
$542$		0			0
$543$	3.56034	−	20.2835i	0.152789	−	0.870447i
$544$		0			0
$545$	4.84374	+	8.38960i	0.207483	+	0.359371i
$546$		0			0
$547$	−0.840875	+	1.45644i	−0.0359532	+	0.0622728i	−0.883442	−	0.468540i	$-0.844780\pi$
$547$	−0.840875	+	1.45644i	−0.0359532	+	0.0622728i	0.847489	+	0.530813i	$0.178113\pi$
$548$		0			0
$549$	−10.5994	+	29.2626i	−0.452373	+	1.24890i
$550$		0			0
$551$	−16.1489			−0.687967
$552$		0			0
$553$	−2.47784	+	4.19820i	−0.105369	+	0.178525i
$554$		0			0
$555$	10.9170	+	1.91625i	0.463400	+	0.0813402i
$556$		0			0
$557$	−8.14983	−	4.70530i	−0.345319	−	0.199370i	0.317303	−	0.948324i	$-0.397223\pi$
$557$	−8.14983	−	4.70530i	−0.345319	−	0.199370i	−0.662622	+	0.748954i	$0.730556\pi$
$558$		0			0
$559$		−	15.1817i		−	0.642117i
$560$		0			0
$561$	3.19536	−	18.2042i	0.134908	−	0.768580i
$562$		0			0
$563$	−31.0638			−1.30918			−0.654591	−	0.755983i	$-0.727159\pi$
$563$	−31.0638			−1.30918			−0.654591	+	0.755983i	$0.727159\pi$
$564$		0			0
$565$		−	27.1419i		−	1.14187i
$566$		0			0
$567$	22.4282	−	7.99849i	0.941896	−	0.335905i
$568$		0			0
$569$			20.1032i			0.842769i	0.906882	+	0.421384i	$0.138456\pi$
$569$			20.1032i			0.842769i	−0.906882	+	0.421384i	$0.861544\pi$
$570$		0			0
$571$	−7.87413			−0.329522			−0.164761	−	0.986333i	$-0.552685\pi$
$571$	−7.87413			−0.329522			−0.164761	+	0.986333i	$0.552685\pi$
$572$		0			0
$573$	0.0670662	−	0.382080i	0.00280173	−	0.0159616i
$574$		0			0
$575$			28.8239i			1.20204i
$576$		0			0
$577$	−2.77842	−	1.60412i	−0.115667	−	0.0667805i	0.441050	−	0.897482i	$-0.354606\pi$
$577$	−2.77842	−	1.60412i	−0.115667	−	0.0667805i	−0.556717	+	0.830702i	$0.687939\pi$
$578$		0			0
$579$	−44.4823	−	7.80794i	−1.84862	−	0.324487i
$580$		0			0
$581$	−14.6148	−	25.8839i	−0.606322	−	1.07385i
$582$		0			0
$583$	4.75587			0.196968
$584$		0			0
$585$	−11.6022	+	32.0309i	−0.479692	+	1.32432i
$586$		0			0
$587$	2.37708	−	4.11722i	0.0981125	−	0.169936i	−0.812791	−	0.582556i	$-0.802053\pi$
$587$	2.37708	−	4.11722i	0.0981125	−	0.169936i	0.910903	+	0.412620i	$0.135386\pi$
$588$		0			0
$589$	5.88332	+	10.1902i	0.242418	+	0.419880i
$590$		0			0
$591$	−0.468004	+	2.66625i	−0.0192511	+	0.109675i
$592$		0			0
$593$	−13.0354	−	22.5780i	−0.535300	−	0.927166i	−0.999149	−	0.0412519i	$-0.986865\pi$
$593$	−13.0354	−	22.5780i	−0.535300	−	0.927166i	0.463849	−	0.885914i	$-0.346468\pi$
$594$		0			0
$595$	−54.8703	−	0.526519i	−2.24946	−	0.0215852i
$596$		0			0
$597$	−20.6544	−	17.3039i	−0.845328	−	0.708200i
$598$		0			0
$599$			27.5024i			1.12372i	0.827233	+	0.561859i	$0.189914\pi$
$599$			27.5024i			1.12372i	−0.827233	+	0.561859i	$0.810086\pi$
$600$		0			0
$601$	26.8647	+	15.5104i	1.09584	+	0.632681i	0.935124	−	0.354320i	$-0.115288\pi$
$601$	26.8647	+	15.5104i	1.09584	+	0.632681i	0.160712	+	0.987001i	$0.448621\pi$
$602$		0			0
$603$	−22.1357	−	8.01795i	−0.901435	−	0.326516i
$604$		0			0
$605$	13.5951	+	23.5475i	0.552721	+	0.957340i
$606$		0			0
$607$	−33.9745	−	19.6152i	−1.37898	−	0.796156i	−0.386945	−	0.922103i	$-0.626470\pi$
$607$	−33.9745	−	19.6152i	−1.37898	−	0.796156i	−0.992037	+	0.125947i	$0.959803\pi$
$608$		0			0
$609$	−28.8869	+	10.2263i	−1.17056	+	0.414391i
$610$		0			0
$611$	−22.0440	+	12.7271i	−0.891803	+	0.514883i
$612$		0			0
$613$	−11.5364	+	19.9817i	−0.465951	+	0.807051i	−0.999244	−	0.0388795i	$-0.987621\pi$
$613$	−11.5364	+	19.9817i	−0.465951	+	0.807051i	0.533293	+	0.845931i	$0.320954\pi$
$614$		0			0
$615$	60.6692	+	10.6492i	2.44642	+	0.429418i
$616$		0			0
$617$	5.15715	−	2.97748i	0.207619	−	0.119869i	−0.392585	−	0.919716i	$-0.628419\pi$
$617$	5.15715	−	2.97748i	0.207619	−	0.119869i	0.600204	+	0.799847i	$0.295086\pi$
$618$		0			0
$619$	−28.0289	+	16.1825i	−1.12658	+	0.650429i	−0.943072	−	0.332590i	$-0.892078\pi$
$619$	−28.0289	+	16.1825i	−1.12658	+	0.650429i	−0.183504	+	0.983019i	$0.558744\pi$
$620$		0			0
$621$	10.0394	+	17.2960i	0.402869	+	0.694063i
$622$		0			0
$623$	36.4987	+	0.350230i	1.46229	+	0.0140317i
$624$		0			0
$625$	3.17879	−	5.50582i	0.127152	−	0.220233i
$626$		0			0
$627$	−4.88426	+	5.83000i	−0.195059	+	0.232828i
$628$		0			0
$629$	−10.6268			−0.423719
$630$		0			0
$631$	−35.6689			−1.41996			−0.709978	−	0.704224i	$-0.751295\pi$
$631$	−35.6689			−1.41996			−0.709978	+	0.704224i	$0.751295\pi$
$632$		0			0
$633$	−8.29000	−	22.7219i	−0.329498	−	0.903113i
$634$		0			0
$635$	31.6729	−	54.8591i	1.25690	−	2.17702i
$636$		0			0
$637$	19.2602	+	11.6183i	0.763116	+	0.460333i
$638$		0			0
$639$	−7.79505	+	21.5203i	−0.308367	+	0.851330i
$640$		0			0
$641$	21.5239	−	12.4268i	0.850141	−	0.490829i	−0.0105572	−	0.999944i	$-0.503361\pi$
$641$	21.5239	−	12.4268i	0.850141	−	0.490829i	0.860699	+	0.509115i	$0.170027\pi$
$642$		0			0
$643$	−14.8270	+	8.56038i	−0.584720	+	0.337588i	−0.763007	−	0.646390i	$-0.776278\pi$
$643$	−14.8270	+	8.56038i	−0.584720	+	0.337588i	0.178287	+	0.983979i	$0.442944\pi$
$644$		0			0
$645$	−9.91224	−	27.1682i	−0.390294	−	1.06975i
$646$		0			0
$647$	−16.7208	+	28.9613i	−0.657363	+	1.13859i	0.323933	+	0.946080i	$0.394995\pi$
$647$	−16.7208	+	28.9613i	−0.657363	+	1.13859i	−0.981296	+	0.192506i	$0.938339\pi$
$648$		0			0
$649$	−13.8761	+	8.01138i	−0.544686	+	0.314474i
$650$		0			0
$651$	16.9770	+	14.5025i	0.665379	+	0.568397i
$652$		0			0
$653$	22.8837	+	13.2119i	0.895508	+	0.517022i	0.875740	−	0.482783i	$-0.160374\pi$
$653$	22.8837	+	13.2119i	0.895508	+	0.517022i	0.0197678	+	0.999805i	$0.493707\pi$
$654$		0			0
$655$	−29.9873	−	51.9395i	−1.17170	−	2.02944i
$656$		0			0
$657$	−26.2502	−	31.1856i	−1.02412	−	1.21667i
$658$		0			0
$659$	25.8862	+	14.9454i	1.00838	+	0.582191i	0.910718	−	0.413029i	$-0.135529\pi$
$659$	25.8862	+	14.9454i	1.00838	+	0.582191i	0.0976658	+	0.995219i	$0.468862\pi$
$660$		0			0
$661$		−	4.53368i		−	0.176340i	−0.996105	−	0.0881699i	$-0.971898\pi$
$661$		−	4.53368i		−	0.176340i	0.996105	−	0.0881699i	$-0.0281018\pi$
$662$		0			0
$663$	5.64692	−	32.1708i	0.219308	−	1.24941i
$664$		0			0
$665$	19.4459	+	11.4773i	0.754079	+	0.445069i
$666$		0			0
$667$	−12.8682	−	22.2883i	−0.498257	−	0.863006i
$668$		0			0
$669$	−32.8451	−	27.5170i	−1.26986	−	1.06387i
$670$		0			0
$671$	−9.43172	−	16.3362i	−0.364107	−	0.630652i
$672$		0			0
$673$	4.12239	−	7.14019i	0.158907	−	0.275234i	−0.775568	−	0.631264i	$-0.782536\pi$
$673$	4.12239	−	7.14019i	0.158907	−	0.275234i	0.934475	+	0.356030i	$0.115870\pi$
$674$		0			0
$675$	0.0903455	+	38.9151i	0.00347740	+	1.49784i
$676$		0			0
$677$	5.51263			0.211867			0.105934	−	0.994373i	$-0.466217\pi$
$677$	5.51263			0.211867			0.105934	+	0.994373i	$0.466217\pi$
$678$		0			0
$679$	36.7071	−	20.7258i	1.40869	−	0.795383i
$680$		0			0
$681$	3.70532	+	10.1558i	0.141988	+	0.389172i
$682$		0			0
$683$	−24.0097	−	13.8620i	−0.918706	−	0.530415i	−0.0354840	−	0.999370i	$-0.511297\pi$
$683$	−24.0097	−	13.8620i	−0.918706	−	0.530415i	−0.883222	+	0.468955i	$0.844631\pi$
$684$		0			0
$685$		−	19.6540i		−	0.750942i
$686$		0			0
$687$	21.0537	+	17.6384i	0.803248	+	0.672947i
$688$		0			0
$689$	8.40469			0.320193
$690$		0			0
$691$		−	42.1826i		−	1.60470i	−0.596853	−	0.802351i	$-0.703582\pi$
$691$		−	42.1826i		−	1.60470i	0.596853	−	0.802351i	$-0.296418\pi$
$692$		0			0
$693$	−5.04505	+	13.5216i	−0.191645	+	0.513642i
$694$		0			0
$695$		−	50.8061i		−	1.92719i
$696$		0			0
$697$	−59.0568			−2.23693
$698$		0			0
$699$	5.53461	−	2.01929i	0.209338	−	0.0763764i
$700$		0			0
$701$		−	1.07738i		−	0.0406922i	−0.999793	−	0.0203461i	$-0.993523\pi$
$701$		−	1.07738i		−	0.0406922i	0.999793	−	0.0203461i	$-0.00647681\pi$
$702$		0			0
$703$	3.78710	+	2.18648i	0.142833	+	0.0824648i
$704$		0			0
$705$	−31.1389	+	37.1683i	−1.17276	+	1.39984i
$706$		0			0
$707$	29.4326	+	0.282426i	1.10693	+	0.0106217i
$708$		0			0
$709$	−21.9612			−0.824769			−0.412385	−	0.911010i	$-0.635304\pi$
$709$	−21.9612			−0.824769			−0.412385	+	0.911010i	$0.635304\pi$
$710$		0			0
$711$	−5.19717	−	1.88251i	−0.194909	−	0.0705997i
$712$		0			0
$713$	−9.37617	+	16.2400i	−0.351140	+	0.608193i
$714$		0			0
$715$	−10.3240	−	17.8817i	−0.386095	−	0.668737i
$716$		0			0
$717$	30.7159	−	11.2066i	1.14711	−	0.418518i
$718$		0			0
$719$	5.89267	+	10.2064i	0.219760	+	0.380635i	0.954734	−	0.297460i	$-0.0961394\pi$
$719$	5.89267	+	10.2064i	0.219760	+	0.380635i	−0.734975	+	0.678094i	$0.762806\pi$
$720$		0			0
$721$	1.38930	−	0.784436i	0.0517403	−	0.0292139i
$722$		0			0
$723$	18.1988	−	6.63977i	0.676820	−	0.246936i
$724$		0			0
$725$		−	50.0804i		−	1.85994i
$726$		0			0
$727$	10.1963	+	5.88682i	0.378159	+	0.218330i	0.677017	−	0.735967i	$-0.263272\pi$
$727$	10.1963	+	5.88682i	0.378159	+	0.218330i	−0.298858	+	0.954298i	$0.596606\pi$
$728$		0			0
$729$	13.6084	+	23.3198i	0.504016	+	0.863694i
$730$		0			0
$731$	13.8637	+	24.0127i	0.512768	+	0.888140i
$732$		0			0
$733$	−37.9020	−	21.8828i	−1.39994	−	0.808258i	−0.405558	−	0.914069i	$-0.632923\pi$
$733$	−37.9020	−	21.8828i	−1.39994	−	0.808258i	−0.994386	+	0.105812i	$0.966256\pi$
$734$		0			0
$735$	42.0525	+	8.21624i	1.55113	+	0.303060i
$736$		0			0
$737$	12.3575	−	7.13462i	0.455195	−	0.262807i
$738$		0			0
$739$	13.9728	−	24.2016i	0.513998	−	0.890270i	−0.485870	−	0.874031i	$-0.661497\pi$
$739$	13.9728	−	24.2016i	0.513998	−	0.890270i	0.999868	−	0.0162393i	$-0.00516935\pi$
$740$		0			0
$741$	−8.63159	+	10.3029i	−0.317089	+	0.378487i
$742$		0			0
$743$	31.0951	−	17.9528i	1.14077	−	0.658623i	0.194147	−	0.980972i	$-0.437806\pi$
$743$	31.0951	−	17.9528i	1.14077	−	0.658623i	0.946621	+	0.322350i	$0.104473\pi$
$744$		0			0
$745$	−19.6521	+	11.3462i	−0.719998	+	0.415691i
$746$		0			0
$747$	25.7859	−	21.7050i	0.943455	−	0.794144i
$748$		0			0
$749$	0.332251	−	34.6250i	0.0121402	−	1.26517i
$750$		0			0
$751$	1.17516	−	2.03543i	0.0428821	−	0.0742740i	−0.843788	−	0.536677i	$-0.819679\pi$
$751$	1.17516	−	2.03543i	0.0428821	−	0.0742740i	0.886670	+	0.462403i	$0.153013\pi$
$752$		0			0
$753$	26.3636	+	4.62758i	0.960743	+	0.168638i
$754$		0			0
$755$	−56.5178			−2.05689
$756$		0			0
$757$	8.88061			0.322771			0.161386	−	0.986891i	$-0.448404\pi$
$757$	8.88061			0.322771			0.161386	+	0.986891i	$0.448404\pi$
$758$		0			0
$759$	−11.9384	−	2.09554i	−0.433336	−	0.0760632i
$760$		0			0
$761$	13.4883	−	23.3624i	0.488951	−	0.846888i	−0.510968	−	0.859600i	$-0.670713\pi$
$761$	13.4883	−	23.3624i	0.488951	−	0.846888i	0.999919	+	0.0127118i	$0.00404640\pi$
$762$		0			0
$763$	3.56585	+	6.31541i	0.129092	+	0.228633i
$764$		0			0
$765$	−10.8992	−	61.2579i	−0.394061	−	2.21478i
$766$		0			0
$767$	−24.5222	+	14.1579i	−0.885446	+	0.511213i
$768$		0			0
$769$	−7.88232	+	4.55086i	−0.284244	+	0.164108i	−0.635343	−	0.772230i	$-0.719141\pi$
$769$	−7.88232	+	4.55086i	−0.284244	+	0.164108i	0.351099	+	0.936338i	$0.385808\pi$
$770$		0			0
$771$	11.8403	−	14.1329i	0.426419	−	0.508985i
$772$		0			0
$773$	6.46864	−	11.2040i	0.232661	−	0.402980i	−0.725929	−	0.687769i	$-0.758590\pi$
$773$	6.46864	−	11.2040i	0.232661	−	0.402980i	0.958590	+	0.284789i	$0.0919235\pi$
$774$		0			0
$775$	−31.6015	+	18.2451i	−1.13516	+	0.655384i
$776$		0			0
$777$	8.15890	+	1.51296i	0.292699	+	0.0542772i
$778$		0			0
$779$	21.0462	+	12.1510i	0.754057	+	0.435355i
$780$		0			0
$781$	−6.93628	−	12.0140i	−0.248199	−	0.429894i
$782$		0			0
$783$	−17.4431	−	30.0510i	−0.623366	−	1.07394i
$784$		0			0
$785$	−42.6245	−	24.6093i	−1.52134	−	0.878343i
$786$		0			0
$787$			24.8566i			0.886043i	0.896511	+	0.443022i	$0.146094\pi$
$787$			24.8566i			0.886043i	−0.896511	+	0.443022i	$0.853906\pi$
$788$		0			0
$789$	−18.0409	+	6.58216i	−0.642272	+	0.234331i
$790$		0			0
$791$	0.194975	−	20.3190i	0.00693250	−	0.722460i
$792$		0			0
$793$	−16.6680	−	28.8697i	−0.591896	−	1.02519i
$794$		0			0
$795$	15.0405	−	5.48749i	0.533432	−	0.194621i
$796$		0			0
$797$	−6.71671	−	11.6337i	−0.237918	−	0.412086i	0.722199	−	0.691686i	$-0.243132\pi$
$797$	−6.71671	−	11.6337i	−0.237918	−	0.412086i	−0.960117	+	0.279600i	$0.909798\pi$
$798$		0			0
$799$	23.2444	−	40.2605i	0.822328	−	1.42431i
$800$		0			0
$801$	7.24994	+	40.7476i	0.256164	+	1.43974i
$802$		0			0
$803$	24.7060			0.871857
$804$		0			0
$805$	−0.345294	+	35.9843i	−0.0121700	+	1.26828i
$806$		0			0
$807$	−6.98860	+	8.34180i	−0.246011	+	0.293645i
$808$		0			0
$809$	9.38524	+	5.41857i	0.329967	+	0.190507i	0.655827	−	0.754912i	$-0.272320\pi$
$809$	9.38524	+	5.41857i	0.329967	+	0.190507i	−0.325859	+	0.945418i	$0.605654\pi$
$810$		0			0
$811$			35.3334i			1.24072i	0.784316	+	0.620361i	$0.213014\pi$
$811$			35.3334i			1.24072i	−0.784316	+	0.620361i	$0.786986\pi$
$812$		0			0
$813$	−1.79343	+	0.654327i	−0.0628983	+	0.0229483i
$814$		0			0
$815$	55.0951			1.92990
$816$		0			0
$817$		−	11.4099i		−	0.399182i
$818$		0			0
$819$	−8.91573	+	23.8956i	−0.311541	+	0.834981i
$820$		0			0
$821$		−	19.2156i		−	0.670631i	−0.942106	−	0.335315i	$-0.891157\pi$
$821$		−	19.2156i		−	0.670631i	0.942106	−	0.335315i	$-0.108843\pi$
$822$		0			0
$823$	29.8148			1.03928			0.519639	−	0.854386i	$-0.326066\pi$
$823$	29.8148			1.03928			0.519639	+	0.854386i	$0.326066\pi$
$824$		0			0
$825$	−18.0798	−	15.1469i	−0.629456	−	0.527347i
$826$		0			0
$827$			0.356137i			0.0123841i	0.999981	+	0.00619205i	$0.00197100\pi$
$827$			0.356137i			0.0123841i	−0.999981	+	0.00619205i	$0.998029\pi$
$828$		0			0
$829$	−17.5571	−	10.1366i	−0.609783	−	0.352058i	0.163098	−	0.986610i	$-0.447851\pi$
$829$	−17.5571	−	10.1366i	−0.609783	−	0.352058i	−0.772880	+	0.634552i	$0.781185\pi$
$830$		0			0
$831$	−9.11951	−	24.9955i	−0.316352	−	0.867083i
$832$		0			0
$833$	−41.0732	−	0.788324i	−1.42310	−	0.0273138i
$834$		0			0
$835$	46.5590			1.61124
$836$		0			0
$837$	−12.6078	+	21.9550i	−0.435791	+	0.758875i
$838$		0			0
$839$	0.662663	−	1.14777i	0.0228777	−	0.0396253i	−0.854360	−	0.519682i	$-0.826051\pi$
$839$	0.662663	−	1.14777i	0.0228777	−	0.0396253i	0.877238	+	0.480056i	$0.159384\pi$
$840$		0			0
$841$	7.85791	+	13.6103i	0.270962	+	0.469321i
$842$		0			0
$843$	−28.9956	−	24.2920i	−0.998662	−	0.836661i
$844$		0			0
$845$	4.72626	+	8.18612i	0.162588	+	0.281611i
$846$		0			0
$847$	10.0084	+	17.7258i	0.343894	+	0.609064i
$848$		0			0
$849$	−3.31743	+	18.8996i	−0.113854	+	0.648632i
$850$		0			0
$851$			6.96914i			0.238899i
$852$		0			0
$853$	41.7558	+	24.1077i	1.42969	+	0.825432i	0.997096	−	0.0761571i	$-0.0242650\pi$
$853$	41.7558	+	24.1077i	1.42969	+	0.825432i	0.432594	+	0.901589i	$0.357598\pi$
$854$		0			0
$855$	−8.71972	+	24.0731i	−0.298208	+	0.823282i
$856$		0			0
$857$	−10.4387	−	18.0803i	−0.356578	−	0.617611i	0.630809	−	0.775938i	$-0.282723\pi$
$857$	−10.4387	−	18.0803i	−0.356578	−	0.617611i	−0.987387	+	0.158328i	$0.949390\pi$
$858$		0			0
$859$	11.8727	+	6.85469i	0.405090	+	0.233879i	0.688678	−	0.725067i	$-0.258191\pi$
$859$	11.8727	+	6.85469i	0.405090	+	0.233879i	−0.283588	+	0.958946i	$0.591525\pi$
$860$		0			0
$861$	45.3417	+	8.40803i	1.54524	+	0.286545i
$862$		0			0
$863$	−28.1125	+	16.2307i	−0.956959	+	0.552501i	−0.895236	−	0.445593i	$-0.852993\pi$
$863$	−28.1125	+	16.2307i	−0.956959	+	0.552501i	−0.0617233	+	0.998093i	$0.519660\pi$
$864$		0			0
$865$	−19.8047	+	34.3027i	−0.673379	+	1.16633i
$866$		0			0
$867$	10.3542	+	28.3795i	0.351646	+	0.963819i
$868$		0			0
$869$	2.90139	−	1.67512i	0.0984228	−	0.0568244i
$870$		0			0
$871$	21.8385	−	12.6085i	0.739970	−	0.427222i
$872$		0			0
$873$	30.7808	+	36.5680i	1.04177	+	1.23764i
$874$		0			0
$875$	−11.8302	+	20.0438i	−0.399933	+	0.677604i
$876$		0			0
$877$	−10.9669	+	18.9953i	−0.370326	+	0.641424i	−0.989616	−	0.143739i	$-0.954087\pi$
$877$	−10.9669	+	18.9953i	−0.370326	+	0.641424i	0.619289	+	0.785163i	$0.287421\pi$
$878$		0			0
$879$	14.9993	+	41.1112i	0.505913	+	1.38665i
$880$		0			0
$881$	−21.8019			−0.734526			−0.367263	−	0.930117i	$-0.619705\pi$
$881$	−21.8019			−0.734526			−0.367263	+	0.930117i	$0.619705\pi$
$882$		0			0
$883$	−24.4085			−0.821411			−0.410705	−	0.911768i	$-0.634717\pi$
$883$	−24.4085			−0.821411			−0.410705	+	0.911768i	$0.634717\pi$
$884$		0			0
$885$	−34.6397	+	41.3469i	−1.16440	+	1.38986i
$886$		0			0
$887$	−16.8722	+	29.2235i	−0.566513	+	0.981230i	0.430394	+	0.902641i	$0.358375\pi$
$887$	−16.8722	+	29.2235i	−0.566513	+	0.981230i	−0.996907	+	0.0785887i	$0.974959\pi$
$888$		0			0
$889$	24.1051	−	40.8411i	0.808458	−	1.36977i
$890$		0			0
$891$	−16.1246	−	2.79176i	−0.540193	−	0.0935274i
$892$		0			0
$893$	−16.5673	+	9.56513i	−0.554403	+	0.320085i
$894$		0			0
$895$	−32.6113	+	18.8281i	−1.09007	+	0.629355i
$896$		0			0
$897$	−21.0978	−	3.70328i	−0.704436	−	0.123649i
$898$		0			0
$899$	16.2907	−	28.2164i	0.543326	−	0.941068i
$900$		0			0
$901$	−13.2936	+	7.67505i	−0.442873	+	0.255693i
$902$		0			0
$903$	−7.22533	−	20.4099i	−0.240444	−	0.679198i
$904$		0			0
$905$	36.3889	+	21.0092i	1.20961	+	0.698368i
$906$		0			0
$907$	−7.52832	−	13.0394i	−0.249974	−	0.432967i	0.713544	−	0.700610i	$-0.247089\pi$
$907$	−7.52832	−	13.0394i	−0.249974	−	0.432967i	−0.963518	+	0.267643i	$0.913755\pi$
$908$		0			0
$909$	5.84637	+	32.8589i	0.193912	+	1.08986i
$910$		0			0
$911$	−21.5047	−	12.4157i	−0.712481	−	0.411351i	0.0994977	−	0.995038i	$-0.468276\pi$
$911$	−21.5047	−	12.4157i	−0.712481	−	0.411351i	−0.811979	+	0.583686i	$0.801610\pi$
$912$		0			0
$913$			20.4282i			0.676075i
$914$		0			0
$915$	−48.6772	−	40.7809i	−1.60922	−	1.34817i
$916$		0			0
$917$	−22.0759	−	39.0983i	−0.729012	−	1.29114i
$918$		0			0
$919$	−12.0689	−	20.9039i	−0.398115	−	0.689555i	0.595378	−	0.803445i	$-0.297002\pi$
$919$	−12.0689	−	20.9039i	−0.398115	−	0.689555i	−0.993493	+	0.113890i	$0.963669\pi$
$920$		0			0
$921$	−3.65813	+	20.8406i	−0.120539	+	0.686720i
$922$		0			0
$923$	−12.2580	−	21.2314i	−0.403476	−	0.698840i
$924$		0			0
$925$	−6.78064	+	11.7444i	−0.222946	+	0.386154i
$926$		0			0
$927$	1.16500	+	1.38404i	0.0382636	+	0.0454577i
$928$		0			0
$929$	−26.6620			−0.874752			−0.437376	−	0.899279i	$-0.644092\pi$
$929$	−26.6620			−0.874752			−0.437376	+	0.899279i	$0.644092\pi$
$930$		0			0
$931$	14.4751	+	8.73180i	0.474403	+	0.286173i
$932$		0			0
$933$	16.1891	+	2.84166i	0.530007	+	0.0930317i
$934$		0			0
$935$	32.6586	+	18.8555i	1.06805	+	0.616640i
$936$		0			0
$937$			8.17165i			0.266956i	0.991052	+	0.133478i	$0.0426146\pi$
$937$			8.17165i			0.266956i	−0.991052	+	0.133478i	$0.957385\pi$
$938$		0			0
$939$	−4.05790	+	23.1181i	−0.132424	+	0.754430i
$940$		0			0
$941$	32.0272			1.04406			0.522028	−	0.852928i	$-0.325176\pi$
$941$	32.0272			1.04406			0.522028	+	0.852928i	$0.325176\pi$
$942$		0			0
$943$			38.7298i			1.26122i
$944$		0			0
$945$	−0.353392	+	48.5833i	−0.0114958	+	1.58042i
$946$		0			0
$947$		−	17.9002i		−	0.581678i	−0.956772	−	0.290839i	$-0.906066\pi$
$947$		−	17.9002i		−	0.581678i	0.956772	−	0.290839i	$-0.0939344\pi$
$948$		0			0
$949$	43.6611			1.41730
$950$		0			0
$951$	4.75640	−	27.0975i	0.154237	−	0.878697i
$952$		0			0
$953$			11.2737i			0.365191i	0.983188	+	0.182596i	$0.0584499\pi$
$953$			11.2737i			0.365191i	−0.983188	+	0.182596i	$0.941550\pi$
$954$		0			0
$955$	0.685459	+	0.395750i	0.0221809	+	0.0128062i
$956$		0			0
$957$	20.7425	+	3.64091i	0.670510	+	0.117694i
$958$		0			0
$959$	0.141185	−	14.7134i	0.00455911	−	0.475120i
$960$		0			0
$961$	7.26007			0.234196
$962$		0			0
$963$	38.6558	−	6.87776i	1.24567	−	0.221633i
$964$		0			0
$965$	46.0738	−	79.8022i	1.48317	−	2.56892i
$966$		0			0
$967$	15.3313	+	26.5546i	0.493022	+	0.853939i	0.999968	−	0.00803913i	$-0.00255896\pi$
$967$	15.3313	+	26.5546i	0.493022	+	0.853939i	−0.506946	+	0.861978i	$0.669226\pi$
$968$		0			0
$969$	4.24398	−	24.1782i	0.136336	−	0.776716i
$970$		0			0
$971$	−19.0807	−	33.0488i	−0.612330	−	1.06059i	−0.990847	−	0.134992i	$-0.956899\pi$
$971$	−19.0807	−	33.0488i	−0.612330	−	1.06059i	0.378517	−	0.925595i	$-0.376434\pi$
$972$		0			0
$973$	0.364967	−	38.0345i	0.0117003	−	1.21933i
$974$		0			0
$975$	−31.9510	−	26.7680i	−1.02325	−	0.857261i
$976$		0			0
$977$		−	30.6991i		−	0.982151i	−0.871117	−	0.491076i	$-0.836604\pi$
$977$		−	30.6991i		−	0.982151i	0.871117	−	0.491076i	$-0.163396\pi$
$978$		0			0
$979$	−21.7239	−	12.5423i	−0.694299	−	0.400854i
$980$		0			0
$981$	−6.29148	+	5.29580i	−0.200872	+	0.169082i
$982$		0			0
$983$	12.9028	+	22.3484i	0.411536	+	0.712802i	0.995058	−	0.0992957i	$-0.0316590\pi$
$983$	12.9028	+	22.3484i	0.411536	+	0.712802i	−0.583522	+	0.812098i	$0.698326\pi$
$984$		0			0
$985$	−4.78330	−	2.76164i	−0.152409	−	0.0879932i
$986$		0			0
$987$	−23.5782	+	27.6012i	−0.750502	+	0.878556i
$988$		0			0
$989$	15.7476	−	9.09191i	0.500746	−	0.289106i
$990$		0			0
$991$	−11.4388	+	19.8126i	−0.363366	+	0.629369i	−0.988513	−	0.151139i	$-0.951706\pi$
$991$	−11.4388	+	19.8126i	−0.363366	+	0.629369i	0.625146	+	0.780508i	$0.285039\pi$
$992$		0			0
$993$	−18.7212	−	3.28612i	−0.594100	−	0.104282i
$994$		0			0
$995$	47.6118	−	27.4887i	1.50940	−	0.871450i
$996$		0			0
$997$	−35.9753	+	20.7704i	−1.13935	+	0.657804i	−0.946269	−	0.323379i	$-0.895181\pi$
$997$	−35.9753	+	20.7704i	−1.13935	+	0.657804i	−0.193080	+	0.981183i	$0.561848\pi$
$998$		0			0
$999$	0.0218440	+	9.40901i	0.000691115	+	0.297688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.353.1	yes	48
3.2	odd	2		1512.2.bs.a.521.3		48
4.3	odd	2		1008.2.ca.e.353.24		48
7.5	odd	6		504.2.cx.a.425.7	yes	48
9.4	even	3		1512.2.cx.a.17.3		48
9.5	odd	6		504.2.cx.a.185.7	yes	48
12.11	even	2		3024.2.ca.e.2033.3		48
21.5	even	6		1512.2.cx.a.89.3		48
28.19	even	6		1008.2.df.e.929.18		48
36.23	even	6		1008.2.df.e.689.18		48
36.31	odd	6		3024.2.df.e.17.3		48
63.5	even	6	inner	504.2.bs.a.257.1	✓	48
63.40	odd	6		1512.2.bs.a.1097.3		48
84.47	odd	6		3024.2.df.e.1601.3		48
252.103	even	6		3024.2.ca.e.2609.3		48
252.131	odd	6		1008.2.ca.e.257.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.1	✓	48	63.5	even	6	inner
504.2.bs.a.353.1	yes	48	1.1	even	1	trivial
504.2.cx.a.185.7	yes	48	9.5	odd	6
504.2.cx.a.425.7	yes	48	7.5	odd	6
1008.2.ca.e.257.24		48	252.131	odd	6
1008.2.ca.e.353.24		48	4.3	odd	2
1008.2.df.e.689.18		48	36.23	even	6
1008.2.df.e.929.18		48	28.19	even	6
1512.2.bs.a.521.3		48	3.2	odd	2
1512.2.bs.a.1097.3		48	63.40	odd	6
1512.2.cx.a.17.3		48	9.4	even	3
1512.2.cx.a.89.3		48	21.5	even	6
3024.2.ca.e.2033.3		48	12.11	even	2
3024.2.ca.e.2609.3		48	252.103	even	6
3024.2.df.e.17.3		48	36.31	odd	6
3024.2.df.e.1601.3		48	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.70597 - 0.299447i) q^{3} +(1.76701 - 3.06054i) q^{5} +(1.34480 - 2.27849i) q^{7} +(2.82066 + 1.02170i) q^{9} +(-1.57467 + 0.909136i) q^{11} +(-2.78280 + 1.60665i) q^{13} +(-3.93093 + 4.69207i) q^{15} +(2.93434 - 5.08242i) q^{17} +(-2.09143 + 1.20749i) q^{19} +(-2.97648 + 3.48434i) q^{21} +(-3.33308 - 1.92436i) q^{23} +(-3.74462 - 6.48586i) q^{25} +(-4.50602 - 2.58762i) q^{27} +(5.79110 + 3.34349i) q^{29} -4.87236i q^{31} +(2.95858 - 1.07943i) q^{33} +(-4.59714 - 8.14192i) q^{35} +(-0.905385 - 1.56817i) q^{37} +(5.22847 - 1.90759i) q^{39} +(-5.03152 - 8.71485i) q^{41} +(-2.36232 + 4.09166i) q^{43} +(8.11107 - 6.82742i) q^{45} +7.92151 q^{47} +(-3.38302 - 6.12823i) q^{49} +(-6.52781 + 7.79178i) q^{51} +(-2.26517 - 1.30780i) q^{53} +6.42580i q^{55} +(3.92950 - 1.43366i) q^{57} +8.81208 q^{59} +10.3744i q^{61} +(6.12115 - 5.05287i) q^{63} +11.3558i q^{65} -7.84769 q^{67} +(5.10990 + 4.28098i) q^{69} +7.62952i q^{71} +(-11.7672 - 6.79382i) q^{73} +(4.44602 + 12.1860i) q^{75} +(-0.0461599 + 4.81048i) q^{77} -1.84254 q^{79} +(6.91227 + 5.76372i) q^{81} +(5.61748 - 9.72975i) q^{83} +(-10.3700 - 17.9613i) q^{85} +(-8.87824 - 7.43803i) q^{87} +(6.89792 + 11.9475i) q^{89} +(-0.0815748 + 8.50119i) q^{91} +(-1.45902 + 8.31210i) q^{93} +8.53455i q^{95} +(13.7982 + 7.96638i) q^{97} +(-5.37048 + 0.955533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

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Database

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