LMFDB - Embedded newform 1008.2.ca.e.353.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(257,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, 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("1008.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.24
Character	$\chi$	$=$	1008.353
Dual form			1008.2.ca.e.257.24

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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	−0.243458	−	0.969911i	$-0.578282\pi$
$11$	1.57467	−	0.909136i	0.474781	−	0.274115i	0.718239	+	0.695796i	$0.244948\pi$
$12$		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	−0.240529	−	0.970642i	$-0.577321\pi$
$19$	2.09143	−	1.20749i	0.479807	−	0.277017i	0.720336	+	0.693625i	$0.243988\pi$
$20$		0			0
$21$	−2.97648	+	3.48434i	−0.649520	+	0.760344i
$22$		0			0
$23$	3.33308	+	1.92436i	0.694996	+	0.401256i	0.805481	−	0.592622i	$-0.201907\pi$
$23$	3.33308	+	1.92436i	0.694996	+	0.401256i	−0.110485	+	0.993878i	$0.535240\pi$
$24$		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	$0.144154\pi$
$31$			4.87236i			0.875102i	−0.899193	+	0.437551i	$0.855846\pi$
$32$		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	−0.627751	−	0.778414i	$-0.716024\pi$
$43$	2.36232	−	4.09166i	0.360251	−	0.623973i	0.988002	+	0.154441i	$0.0493577\pi$
$44$		0			0
$45$	8.11107	−	6.82742i	1.20913	−	1.01777i
$46$		0			0
$47$	−7.92151			−1.15547			−0.577736	−	0.816224i	$-0.696064\pi$
$47$	−7.92151			−1.15547			−0.577736	+	0.816224i	$0.696064\pi$
$48$		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	$-0.694460\pi$
$59$	−8.81208			−1.14724			−0.573618	+	0.819123i	$0.694460\pi$
$60$		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	$-0.340864\pi$
$67$	7.84769			0.958748			0.479374	+	0.877611i	$0.340864\pi$
$68$		0			0
$69$	5.10990	+	4.28098i	0.615159	+	0.515369i
$70$		0			0
$71$		−	7.62952i		−	0.905458i	−0.891648	−	0.452729i	$-0.850451\pi$
$71$		−	7.62952i		−	0.905458i	0.891648	−	0.452729i	$-0.149549\pi$
$72$		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	$-0.466948\pi$
$79$	1.84254			0.207301			0.103651	+	0.994614i	$0.466948\pi$
$80$		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	$0.378156\pi$
$83$	−5.61748	+	9.72975i	−0.616598	+	1.06798i	−0.990102	+	0.140351i	$0.955177\pi$
$84$		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	0.474050	−	0.880498i	$-0.342791\pi$
$103$	−0.522237	−	0.301514i	−0.0514576	−	0.0297091i	−0.525508	+	0.850789i	$0.676125\pi$
$104$		0			0
$105$	5.40451	+	15.2665i	0.527426	+	1.48985i
$106$		0			0
$107$	−11.3342	+	6.54381i	−1.09572	+	0.632614i	−0.935094	−	0.354401i	$-0.884685\pi$
$107$	−11.3342	+	6.54381i	−1.09572	+	0.632614i	−0.160627	+	0.987015i	$0.551351\pi$
$108$		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	$-0.792675\pi$
$127$	−17.9246			−1.59055			−0.795277	+	0.606246i	$0.792675\pi$
$128$		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	$0.432489\pi$
$131$	−8.48534	+	14.6970i	−0.741367	+	1.28409i	−0.951873	+	0.306493i	$0.900844\pi$
$132$		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	−0.924328	−	0.381598i	$-0.875374\pi$
$139$	−12.4503	+	7.18817i	−1.05602	+	0.609693i	−0.131690	+	0.991291i	$0.542040\pi$
$140$		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	$0.0588690\pi$
$151$	7.99627	+	13.8499i	0.650727	+	1.12709i	−0.332220	+	0.943202i	$0.607798\pi$
$152$		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	$-0.957615\pi$
$163$	−7.79498	−	13.5013i	−0.610550	−	1.05750i	0.380598	−	0.924740i	$-0.375718\pi$
$164$		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	$-0.996409\pi$
$167$	−6.58728	−	11.4095i	−0.509739	−	0.882893i	0.490198	−	0.871611i	$-0.336925\pi$
$168$		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	0.803507	−	0.595295i	$-0.202965\pi$
$179$	9.22783	+	5.32769i	0.689721	+	0.398210i	−0.113787	+	0.993505i	$0.536298\pi$
$180$		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	$-0.997421\pi$
$191$		−	0.223967i		−	0.0162057i	0.999967	−	0.00810283i	$-0.00257924\pi$
$192$		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	−0.0603949	−	0.998175i	$-0.519236\pi$
$199$	−13.4725	−	7.77832i	−0.955037	−	0.551391i	−0.894642	+	0.446784i	$0.852569\pi$
$200$		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	0.519082	−	0.854724i	$-0.326274\pi$
$211$	−6.98216	−	12.0935i	−0.480672	−	0.832548i	−0.999754	+	0.0221763i	$0.992941\pi$
$212$		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	−0.437198	−	0.899366i	$-0.644029\pi$
$223$	−21.4242	−	12.3693i	−1.43467	−	0.828307i	−0.997472	+	0.0710586i	$0.977362\pi$
$224$		0			0
$225$	−3.93571	−	22.1203i	−0.262381	−	1.47469i
$226$		0			0
$227$	3.12076	+	5.40532i	0.207132	+	0.358764i	0.950810	−	0.309775i	$-0.100254\pi$
$227$	3.12076	+	5.40532i	0.207132	+	0.358764i	−0.743678	+	0.668538i	$0.766920\pi$
$228$		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	0.132744	−	0.991150i	$-0.457621\pi$
$239$	16.3482	−	9.43864i	1.05748	−	0.610535i	0.924733	+	0.380615i	$0.124288\pi$
$240$		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	$-0.337830\pi$
$251$	15.4537			0.975431			0.487716	+	0.873003i	$0.337830\pi$
$252$		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	−0.765923	−	0.642933i	$-0.777718\pi$
$263$	−9.60206	+	5.54375i	−0.592088	+	0.341842i	0.173835	+	0.984775i	$0.444384\pi$
$264$		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	−0.528712	−	0.848802i	$-0.677325\pi$
$271$	−0.954533	+	0.551100i	−0.0579838	+	0.0334769i	0.470728	+	0.882278i	$0.343991\pi$
$272$		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	$0.106804\pi$
$283$			11.0785i			0.658548i	−0.944234	+	0.329274i	$0.893196\pi$
$284$		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	$0.113346\pi$
$307$			12.2163i			0.697219i	−0.937268	+	0.348610i	$0.886654\pi$
$308$		0			0
$309$	−0.800634	−	0.670756i	−0.0455465	−	0.0381580i
$310$		0			0
$311$	9.48967			0.538110			0.269055	−	0.963125i	$-0.413289\pi$
$311$	9.48967			0.538110			0.269055	+	0.963125i	$0.413289\pi$
$312$		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	$-0.597518\pi$
$331$	−10.9739			−0.603183			−0.301591	+	0.953437i	$0.597518\pi$
$332$		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	$-0.958645\pi$
$347$		−	4.82668i		−	0.259110i	0.991572	−	0.129555i	$-0.0413549\pi$
$348$		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	−0.946948	−	0.321386i	$-0.895851\pi$
$359$	−21.6396	+	12.4936i	−1.14209	+	0.659388i	−0.195146	+	0.980774i	$0.562518\pi$
$360$		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	0.172931	−	0.984934i	$-0.444676\pi$
$367$	21.3100	−	12.3034i	1.11237	−	0.642230i	0.939443	+	0.342704i	$0.111343\pi$
$368$		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	$-0.805248\pi$
$379$	−31.8728			−1.63719			−0.818597	+	0.574368i	$0.805248\pi$
$380$		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	$-0.615201\pi$
$383$	12.3860	−	21.4531i	0.632893	−	1.09620i	0.986957	−	0.160982i	$-0.0514660\pi$
$384$		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	0.814596	−	0.580029i	$-0.196959\pi$
$419$	−1.94504	−	3.36891i	−0.0950215	−	0.164582i	−0.909618	+	0.415447i	$0.863625\pi$
$420$		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	0.736048	−	0.676929i	$-0.236690\pi$
$431$	10.7505	+	6.20681i	0.517834	+	0.298971i	−0.218214	+	0.975901i	$0.570023\pi$
$432$		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	$-0.778764\pi$
$439$		−	26.8362i		−	1.28082i	0.768033	−	0.640410i	$-0.221236\pi$
$440$		0			0
$441$	−3.28119	−	20.7421i	−0.156247	−	0.987718i
$442$		0			0
$443$			13.0540i			0.620213i	0.950702	+	0.310107i	$0.100365\pi$
$443$			13.0540i			0.620213i	−0.950702	+	0.310107i	$0.899635\pi$
$444$		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	0.919435	−	0.393242i	$-0.128647\pi$
$463$	2.56402	+	4.44101i	0.119160	+	0.206391i	−0.800275	+	0.599633i	$0.795313\pi$
$464$		0			0
$465$	22.8615	+	19.1529i	1.06017	+	0.888195i
$466$		0			0
$467$	−1.26091	−	2.18396i	−0.0583480	−	0.101062i	0.835376	−	0.549679i	$-0.185250\pi$
$467$	−1.26091	−	2.18396i	−0.0583480	−	0.101062i	−0.893724	+	0.448617i	$0.851917\pi$
$468$		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	0.966919	−	0.255083i	$-0.0821027\pi$
$479$	5.74622	+	9.95275i	0.262552	+	0.454753i	−0.704368	+	0.709835i	$0.748769\pi$
$480$		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	−0.508459	−	0.861086i	$-0.669785\pi$
$487$	10.8463	−	18.7864i	0.491493	−	0.851292i	0.999952	+	0.00979483i	$0.00311784\pi$
$488$		0			0
$489$	−9.25506	−	25.3670i	−0.418528	−	1.14713i
$490$		0			0
$491$	19.3592	−	11.1771i	0.873669	−	0.504413i	0.00510349	−	0.999987i	$-0.498376\pi$
$491$	19.3592	−	11.1771i	0.873669	−	0.504413i	0.868566	+	0.495574i	$0.165042\pi$
$492$		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	−0.600492	−	0.799631i	$-0.705028\pi$
$499$	8.76231	−	15.1768i	0.392255	−	0.679405i	0.992747	+	0.120226i	$0.0383618\pi$
$500$		0			0
$501$	−7.82115	−	21.4368i	−0.349423	−	0.957725i
$502$		0			0
$503$	−7.60926			−0.339280			−0.169640	−	0.985506i	$-0.554261\pi$
$503$	−7.60926			−0.339280			−0.169640	+	0.985506i	$0.554261\pi$
$504$		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	−0.481635	−	0.876372i	$-0.659957\pi$
$523$	0.834923	−	0.482043i	0.0365086	−	0.0210783i	0.518143	+	0.855294i	$0.326623\pi$
$524$		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	−0.847489	−	0.530813i	$-0.821887\pi$
$547$	0.840875	−	1.45644i	0.0359532	−	0.0622728i	0.883442	+	0.468540i	$0.155220\pi$
$548$		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	$-0.272841\pi$
$563$	31.0638			1.30918			0.654591	+	0.755983i	$0.272841\pi$
$564$		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	$-0.447315\pi$
$571$	7.87413			0.329522			0.164761	+	0.986333i	$0.447315\pi$
$572$		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	−0.910903	−	0.412620i	$-0.864614\pi$
$587$	−2.37708	+	4.11722i	−0.0981125	+	0.169936i	0.812791	+	0.582556i	$0.197947\pi$
$588$		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	$-0.810086\pi$
$599$		−	27.5024i		−	1.12372i	0.827233	−	0.561859i	$-0.189914\pi$
$600$		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	0.992037	−	0.125947i	$-0.0401969\pi$
$607$	33.9745	+	19.6152i	1.37898	+	0.796156i	0.386945	+	0.922103i	$0.373530\pi$
$608$		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	0.183504	−	0.983019i	$-0.441256\pi$
$619$	28.0289	−	16.1825i	1.12658	−	0.650429i	0.943072	+	0.332590i	$0.107922\pi$
$620$		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	$-0.248705\pi$
$631$	35.6689			1.41996			0.709978	+	0.704224i	$0.248705\pi$
$632$		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	−0.178287	−	0.983979i	$-0.557056\pi$
$643$	14.8270	−	8.56038i	0.584720	−	0.337588i	0.763007	+	0.646390i	$0.223722\pi$
$644$		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	$-0.605005\pi$
$647$	16.7208	−	28.9613i	0.657363	−	1.13859i	0.981296	−	0.192506i	$-0.0616614\pi$
$648$		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	−0.0976658	−	0.995219i	$-0.531138\pi$
$659$	−25.8862	−	14.9454i	−1.00838	−	0.582191i	−0.910718	+	0.413029i	$0.864471\pi$
$660$		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	0.883222	−	0.468955i	$-0.155369\pi$
$683$	24.0097	+	13.8620i	0.918706	+	0.530415i	0.0354840	+	0.999370i	$0.488703\pi$
$684$		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	$0.296418\pi$
$691$			42.1826i			1.60470i	−0.596853	+	0.802351i	$0.703582\pi$
$692$		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	0.734975	−	0.678094i	$-0.237194\pi$
$719$	−5.89267	−	10.2064i	−0.219760	−	0.380635i	−0.954734	+	0.297460i	$0.903861\pi$
$720$		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	0.298858	−	0.954298i	$-0.403394\pi$
$727$	−10.1963	−	5.88682i	−0.378159	−	0.218330i	−0.677017	+	0.735967i	$0.736728\pi$
$728$		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	$0.338503\pi$
$739$	−13.9728	+	24.2016i	−0.513998	+	0.890270i	−0.999868	+	0.0162393i	$0.994831\pi$
$740$		0			0
$741$	−8.63159	+	10.3029i	−0.317089	+	0.378487i
$742$		0			0
$743$	−31.0951	+	17.9528i	−1.14077	+	0.658623i	−0.946621	−	0.322350i	$-0.895527\pi$
$743$	−31.0951	+	17.9528i	−1.14077	+	0.658623i	−0.194147	+	0.980972i	$0.562194\pi$
$744$		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	−0.886670	−	0.462403i	$-0.846987\pi$
$751$	−1.17516	+	2.03543i	−0.0428821	+	0.0742740i	0.843788	+	0.536677i	$0.180321\pi$
$752$		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	$-0.853906\pi$
$787$		−	24.8566i		−	0.886043i	0.896511	−	0.443022i	$-0.146094\pi$
$788$		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	$-0.786986\pi$
$811$		−	35.3334i		−	1.24072i	0.784316	−	0.620361i	$-0.213014\pi$
$812$		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	$-0.673934\pi$
$823$	−29.8148			−1.03928			−0.519639	+	0.854386i	$0.673934\pi$
$824$		0			0
$825$	−18.0798	−	15.1469i	−0.629456	−	0.527347i
$826$		0			0
$827$		−	0.356137i		−	0.0123841i	−0.999981	−	0.00619205i	$-0.998029\pi$
$827$		−	0.356137i		−	0.0123841i	0.999981	−	0.00619205i	$-0.00197100\pi$
$828$		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	−0.877238	−	0.480056i	$-0.840616\pi$
$839$	−0.662663	+	1.14777i	−0.0228777	+	0.0396253i	0.854360	+	0.519682i	$0.173949\pi$
$840$		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	0.283588	−	0.958946i	$-0.408475\pi$
$859$	−11.8727	−	6.85469i	−0.405090	−	0.233879i	−0.688678	+	0.725067i	$0.741809\pi$
$860$		0			0
$861$	45.3417	+	8.40803i	1.54524	+	0.286545i
$862$		0			0
$863$	28.1125	−	16.2307i	0.956959	−	0.552501i	0.0617233	−	0.998093i	$-0.480340\pi$
$863$	28.1125	−	16.2307i	0.956959	−	0.552501i	0.895236	+	0.445593i	$0.147007\pi$
$864$		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	$-0.365283\pi$
$883$	24.4085			0.821411			0.410705	+	0.911768i	$0.365283\pi$
$884$		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	$-0.641625\pi$
$887$	16.8722	−	29.2235i	0.566513	−	0.981230i	0.996907	−	0.0785887i	$-0.0250414\pi$
$888$		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	0.963518	−	0.267643i	$-0.0862447\pi$
$907$	7.52832	+	13.0394i	0.249974	+	0.432967i	−0.713544	+	0.700610i	$0.752911\pi$
$908$		0			0
$909$	5.84637	+	32.8589i	0.193912	+	1.08986i
$910$		0			0
$911$	21.5047	+	12.4157i	0.712481	+	0.411351i	0.811979	−	0.583686i	$-0.198390\pi$
$911$	21.5047	+	12.4157i	0.712481	+	0.411351i	−0.0994977	+	0.995038i	$0.531724\pi$
$912$		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	0.993493	−	0.113890i	$-0.0363312\pi$
$919$	12.0689	+	20.9039i	0.398115	+	0.689555i	−0.595378	+	0.803445i	$0.702998\pi$
$920$		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	$0.0939344\pi$
$947$			17.9002i			0.581678i	−0.956772	+	0.290839i	$0.906066\pi$
$948$		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	0.506946	−	0.861978i	$-0.330774\pi$
$967$	−15.3313	−	26.5546i	−0.493022	−	0.853939i	−0.999968	+	0.00803913i	$0.997441\pi$
$968$		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	$0.0431010\pi$
$971$	19.0807	+	33.0488i	0.612330	+	1.06059i	−0.378517	+	0.925595i	$0.623566\pi$
$972$		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	0.583522	−	0.812098i	$-0.301674\pi$
$983$	−12.9028	−	22.3484i	−0.411536	−	0.712802i	−0.995058	+	0.0992957i	$0.968341\pi$
$984$		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	−0.625146	−	0.780508i	$-0.714961\pi$
$991$	11.4388	−	19.8126i	0.363366	−	0.629369i	0.988513	+	0.151139i	$0.0482940\pi$
$992$		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	1008.2.ca.e.353.24		48
3.2	odd	2		3024.2.ca.e.2033.3		48
4.3	odd	2		504.2.bs.a.353.1	yes	48
7.5	odd	6		1008.2.df.e.929.18		48
9.4	even	3		3024.2.df.e.17.3		48
9.5	odd	6		1008.2.df.e.689.18		48
12.11	even	2		1512.2.bs.a.521.3		48
21.5	even	6		3024.2.df.e.1601.3		48
28.19	even	6		504.2.cx.a.425.7	yes	48
36.23	even	6		504.2.cx.a.185.7	yes	48
36.31	odd	6		1512.2.cx.a.17.3		48
63.5	even	6	inner	1008.2.ca.e.257.24		48
63.40	odd	6		3024.2.ca.e.2609.3		48
84.47	odd	6		1512.2.cx.a.89.3		48
252.103	even	6		1512.2.bs.a.1097.3		48
252.131	odd	6		504.2.bs.a.257.1	✓	48

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not 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

Varieties

Fields

Representations

Groups

Database

Properties

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