LMFDB - Embedded newform 784.2.bb.b.111.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.9
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.b.671.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0556550 - 0.0697892i) q^{3} +(-3.27604 + 2.61256i) q^{5} +(1.51276 - 2.17061i) q^{7} +(0.665790 - 2.91702i) q^{9} +O(q^{10})$	\(q+(-0.0556550 - 0.0697892i) q^{3} +(-3.27604 + 2.61256i) q^{5} +(1.51276 - 2.17061i) q^{7} +(0.665790 - 2.91702i) q^{9} +(-1.29768 + 0.296186i) q^{11} +(1.55477 - 0.354867i) q^{13} +(0.364657 + 0.0832305i) q^{15} +(-0.356067 + 0.739382i) q^{17} +5.85496 q^{19} +(-0.235678 + 0.0152307i) q^{21} +(1.52265 + 3.16182i) q^{23} +(2.79440 - 12.2431i) q^{25} +(-0.481902 + 0.232072i) q^{27} +(0.642325 + 0.309328i) q^{29} +9.57067 q^{31} +(0.0928928 + 0.0740795i) q^{33} +(0.714960 + 11.0632i) q^{35} +(-4.49018 - 2.16236i) q^{37} +(-0.111297 - 0.0887562i) q^{39} +(8.02209 - 6.39740i) q^{41} +(4.98247 + 3.97338i) q^{43} +(5.43972 + 11.2957i) q^{45} +(2.26804 + 9.93692i) q^{47} +(-2.42309 - 6.56724i) q^{49} +(0.0714178 - 0.0163006i) q^{51} +(5.11790 - 2.46465i) q^{53} +(3.47744 - 4.36057i) q^{55} +(-0.325858 - 0.408613i) q^{57} +(2.50280 - 3.13841i) q^{59} +(-4.17258 + 8.66445i) q^{61} +(-5.32452 - 5.85793i) q^{63} +(-4.16639 + 5.22449i) q^{65} -12.7266i q^{67} +(0.135918 - 0.282236i) q^{69} +(-3.72479 - 7.73461i) q^{71} +(4.61647 + 1.05368i) q^{73} +(-1.00996 + 0.486369i) q^{75} +(-1.32017 + 3.26481i) q^{77} +3.67446i q^{79} +(-8.04417 - 3.87387i) q^{81} +(2.48373 - 10.8819i) q^{83} +(-0.765185 - 3.35249i) q^{85} +(-0.0141609 - 0.0620430i) q^{87} +(-13.2955 - 3.03460i) q^{89} +(1.58173 - 3.91163i) q^{91} +(-0.532656 - 0.667929i) q^{93} +(-19.1811 + 15.2964i) q^{95} +9.96407i q^{97} +3.98254i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 24 q^{9}+O(q^{10}) $ 120 * q - 24 * q^9	$ 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) $ 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

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
$3$	−0.0556550	−	0.0697892i	−0.0321324	−	0.0402928i	0.765506	−	0.643429i	$-0.222489\pi$
$3$	−0.0556550	−	0.0697892i	−0.0321324	−	0.0402928i	−0.797638	+	0.603136i	$0.793917\pi$
$4$		0			0
$5$	−3.27604	+	2.61256i	−1.46509	+	1.16837i	−0.514678	+	0.857384i	$0.672088\pi$
$5$	−3.27604	+	2.61256i	−1.46509	+	1.16837i	−0.950414	+	0.310988i	$0.899340\pi$
$6$		0			0
$7$	1.51276	−	2.17061i	0.571771	−	0.820413i
$7$	1.51276	−	2.17061i	0.571771	−	0.820413i
$8$		0			0
$9$	0.665790	−	2.91702i	0.221930	−	0.972338i
$10$		0			0
$11$	−1.29768	+	0.296186i	−0.391264	+	0.0893035i	−0.413627	−	0.910446i	$-0.635738\pi$
$11$	−1.29768	+	0.296186i	−0.391264	+	0.0893035i	0.0223629	+	0.999750i	$0.492881\pi$
$12$		0			0
$13$	1.55477	−	0.354867i	0.431216	−	0.0984223i	−0.00140297	−	0.999999i	$-0.500447\pi$
$13$	1.55477	−	0.354867i	0.431216	−	0.0984223i	0.432619	+	0.901577i	$0.357589\pi$
$14$		0			0
$15$	0.364657	+	0.0832305i	0.0941539	+	0.0214900i
$16$		0			0
$17$	−0.356067	+	0.739382i	−0.0863590	+	0.179326i	−0.939676	−	0.342067i	$-0.888873\pi$
$17$	−0.356067	+	0.739382i	−0.0863590	+	0.179326i	0.853317	+	0.521393i	$0.174587\pi$
$18$		0			0
$19$	5.85496			1.34322			0.671609	−	0.740905i	$-0.265603\pi$
$19$	5.85496			1.34322			0.671609	+	0.740905i	$0.265603\pi$
$20$		0			0
$21$	−0.235678	+	0.0152307i	−0.0514292	+	0.00332361i
$22$		0			0
$23$	1.52265	+	3.16182i	0.317495	+	0.659285i	0.997247	−	0.0741573i	$-0.0236267\pi$
$23$	1.52265	+	3.16182i	0.317495	+	0.659285i	−0.679752	+	0.733442i	$0.737912\pi$
$24$		0			0
$25$	2.79440	−	12.2431i	0.558880	−	2.44861i
$26$		0			0
$27$	−0.481902	+	0.232072i	−0.0927421	+	0.0446623i
$28$		0			0
$29$	0.642325	+	0.309328i	0.119277	+	0.0574407i	0.492571	−	0.870273i	$-0.336057\pi$
$29$	0.642325	+	0.309328i	0.119277	+	0.0574407i	−0.373294	+	0.927713i	$0.621772\pi$
$30$		0			0
$31$	9.57067			1.71894			0.859472	−	0.511184i	$-0.170793\pi$
$31$	9.57067			1.71894			0.859472	+	0.511184i	$0.170793\pi$
$32$		0			0
$33$	0.0928928	+	0.0740795i	0.0161706	+	0.0128956i
$34$		0			0
$35$	0.714960	+	11.0632i	0.120850	+	1.87002i
$36$		0			0
$37$	−4.49018	−	2.16236i	−0.738181	−	0.355489i	0.0267149	−	0.999643i	$-0.491495\pi$
$37$	−4.49018	−	2.16236i	−0.738181	−	0.355489i	−0.764896	+	0.644154i	$0.777210\pi$
$38$		0			0
$39$	−0.111297	−	0.0887562i	−0.0178217	−	0.0142124i
$40$		0			0
$41$	8.02209	−	6.39740i	1.25284	−	0.999107i	0.253344	−	0.967376i	$-0.418470\pi$
$41$	8.02209	−	6.39740i	1.25284	−	0.999107i	0.999496	−	0.0317305i	$-0.0101018\pi$
$42$		0			0
$43$	4.98247	+	3.97338i	0.759819	+	0.605935i	0.924841	−	0.380354i	$-0.124198\pi$
$43$	4.98247	+	3.97338i	0.759819	+	0.605935i	−0.165022	+	0.986290i	$0.552769\pi$
$44$		0			0
$45$	5.43972	+	11.2957i	0.810905	+	1.68386i
$46$		0			0
$47$	2.26804	+	9.93692i	0.330827	+	1.44945i	0.817532	+	0.575882i	$0.195341\pi$
$47$	2.26804	+	9.93692i	0.330827	+	1.44945i	−0.486705	+	0.873566i	$0.661801\pi$
$48$		0			0
$49$	−2.42309	−	6.56724i	−0.346155	−	0.938177i
$50$		0			0
$51$	0.0714178	−	0.0163006i	0.0100005	−	0.00228255i
$52$		0			0
$53$	5.11790	−	2.46465i	0.702998	−	0.338546i	−0.0480027	−	0.998847i	$-0.515286\pi$
$53$	5.11790	−	2.46465i	0.702998	−	0.338546i	0.751001	+	0.660301i	$0.229571\pi$
$54$		0			0
$55$	3.47744	−	4.36057i	0.468898	−	0.587980i
$56$		0			0
$57$	−0.325858	−	0.408613i	−0.0431609	−	0.0541221i
$58$		0			0
$59$	2.50280	−	3.13841i	0.325836	−	0.408586i	−0.591751	−	0.806121i	$-0.701563\pi$
$59$	2.50280	−	3.13841i	0.325836	−	0.408586i	0.917587	+	0.397535i	$0.130134\pi$
$60$		0			0
$61$	−4.17258	+	8.66445i	−0.534244	+	1.10937i	0.442857	+	0.896592i	$0.353965\pi$
$61$	−4.17258	+	8.66445i	−0.534244	+	1.10937i	−0.977101	+	0.212776i	$0.931749\pi$
$62$		0			0
$63$	−5.32452	−	5.85793i	−0.670826	−	0.738029i
$64$		0			0
$65$	−4.16639	+	5.22449i	−0.516778	+	0.648019i
$66$		0			0
$67$		−	12.7266i		−	1.55480i	−0.629004	−	0.777402i	$-0.716537\pi$
$67$		−	12.7266i		−	1.55480i	0.629004	−	0.777402i	$-0.283463\pi$
$68$		0			0
$69$	0.135918	−	0.282236i	0.0163626	−	0.0339772i
$70$		0			0
$71$	−3.72479	−	7.73461i	−0.442052	−	0.917930i	−0.996330	−	0.0855983i	$-0.972720\pi$
$71$	−3.72479	−	7.73461i	−0.442052	−	0.917930i	0.554278	−	0.832332i	$-0.312994\pi$
$72$		0			0
$73$	4.61647	+	1.05368i	0.540317	+	0.123324i	0.483966	−	0.875087i	$-0.339196\pi$
$73$	4.61647	+	1.05368i	0.540317	+	0.123324i	0.0563519	+	0.998411i	$0.482053\pi$
$74$		0			0
$75$	−1.00996	+	0.486369i	−0.116620	+	0.0561611i
$76$		0			0
$77$	−1.32017	+	3.26481i	−0.150448	+	0.372059i
$78$		0			0
$79$			3.67446i			0.413409i	0.978403	+	0.206704i	$0.0662738\pi$
$79$			3.67446i			0.413409i	−0.978403	+	0.206704i	$0.933726\pi$
$80$		0			0
$81$	−8.04417	−	3.87387i	−0.893796	−	0.430430i
$82$		0			0
$83$	2.48373	−	10.8819i	0.272625	−	1.19445i	−0.634277	−	0.773106i	$-0.718702\pi$
$83$	2.48373	−	10.8819i	0.272625	−	1.19445i	0.906902	−	0.421342i	$-0.138441\pi$
$84$		0			0
$85$	−0.765185	−	3.35249i	−0.0829959	−	0.363629i
$86$		0			0
$87$	−0.0141609	−	0.0620430i	−0.00151821	−	0.00665171i
$88$		0			0
$89$	−13.2955	−	3.03460i	−1.40932	−	0.321667i	−0.550878	−	0.834586i	$-0.685707\pi$
$89$	−13.2955	−	3.03460i	−1.40932	−	0.321667i	−0.858437	+	0.512918i	$0.828564\pi$
$90$		0			0
$91$	1.58173	−	3.91163i	0.165810	−	0.410051i
$92$		0			0
$93$	−0.532656	−	0.667929i	−0.0552338	−	0.0692610i
$94$		0			0
$95$	−19.1811	+	15.2964i	−1.96794	+	1.56938i
$96$		0			0
$97$			9.96407i			1.01170i	0.862622	+	0.505849i	$0.168821\pi$
$97$			9.96407i			1.01170i	−0.862622	+	0.505849i	$0.831179\pi$
$98$		0			0
$99$			3.98254i			0.400260i
$100$		0			0
$101$	5.24723	−	4.18453i	0.522119	−	0.416376i	−0.326646	−	0.945147i	$-0.605918\pi$
$101$	5.24723	−	4.18453i	0.522119	−	0.416376i	0.848765	+	0.528771i	$0.177347\pi$
$102$		0			0
$103$	−1.01325	−	1.27057i	−0.0998382	−	0.125193i	0.729402	−	0.684085i	$-0.239798\pi$
$103$	−1.01325	−	1.27057i	−0.0998382	−	0.125193i	−0.829241	+	0.558892i	$0.811227\pi$
$104$		0			0
$105$	0.732300	−	0.665619i	0.0714652	−	0.0649578i
$106$		0			0
$107$	−3.82923	−	0.873996i	−0.370185	−	0.0844923i	0.0333813	−	0.999443i	$-0.489372\pi$
$107$	−3.82923	−	0.873996i	−0.370185	−	0.0844923i	−0.403566	+	0.914950i	$0.632230\pi$
$108$		0			0
$109$	−1.54200	−	6.75594i	−0.147697	−	0.647102i	−0.993522	−	0.113641i	$-0.963749\pi$
$109$	−1.54200	−	6.75594i	−0.147697	−	0.647102i	0.845825	−	0.533460i	$-0.179109\pi$
$110$		0			0
$111$	0.0989919	+	0.433712i	0.00939590	+	0.0411661i
$112$		0			0
$113$	1.50661	−	6.60089i	0.141730	−	0.620960i	−0.853303	−	0.521415i	$-0.825404\pi$
$113$	1.50661	−	6.60089i	0.141730	−	0.620960i	0.995033	−	0.0995444i	$-0.0317385\pi$
$114$		0			0
$115$	−13.2487	−	6.38024i	−1.23545	−	0.594961i
$116$		0			0
$117$		−	4.77156i		−	0.441131i
$118$		0			0
$119$	1.06626	+	1.89139i	0.0977441	+	0.173384i
$120$		0			0
$121$	−8.31442	+	4.00401i	−0.755856	+	0.364001i
$122$		0			0
$123$	−0.892939	−	0.203808i	−0.0805136	−	0.0183767i
$124$		0			0
$125$	13.7408	+	28.5331i	1.22902	+	2.55208i
$126$		0			0
$127$	5.60457	−	11.6380i	0.497325	−	1.03271i	−0.489663	−	0.871912i	$-0.662880\pi$
$127$	5.60457	−	11.6380i	0.497325	−	1.03271i	0.986988	−	0.160794i	$-0.0514055\pi$
$128$		0			0
$129$		−	0.568861i		−	0.0500854i
$130$		0			0
$131$	−2.89463	+	3.62975i	−0.252905	+	0.317133i	−0.892035	−	0.451965i	$-0.850723\pi$
$131$	−2.89463	+	3.62975i	−0.252905	+	0.317133i	0.639130	+	0.769099i	$0.279294\pi$
$132$		0			0
$133$	8.85717	−	12.7088i	0.768014	−	1.10199i
$134$		0			0
$135$	0.972432	−	2.01928i	0.0836936	−	0.173792i
$136$		0			0
$137$	−2.72069	+	3.41164i	−0.232444	+	0.291476i	−0.884350	−	0.466824i	$-0.845398\pi$
$137$	−2.72069	+	3.41164i	−0.232444	+	0.291476i	0.651906	+	0.758300i	$0.273970\pi$
$138$		0			0
$139$	13.0776	+	16.3988i	1.10923	+	1.39093i	0.911810	+	0.410612i	$0.134685\pi$
$139$	13.0776	+	16.3988i	1.10923	+	1.39093i	0.197420	+	0.980319i	$0.436744\pi$
$140$		0			0
$141$	0.567262	−	0.711324i	0.0477721	−	0.0599043i
$142$		0			0
$143$	−1.91248	+	0.921004i	−0.159930	+	0.0770182i
$144$		0			0
$145$	−2.91242	+	0.664742i	−0.241864	+	0.0552038i
$146$		0			0
$147$	−0.323465	+	0.534605i	−0.0266790	+	0.0440935i
$148$		0			0
$149$	2.77038	+	12.1378i	0.226958	+	0.994369i	0.952104	+	0.305774i	$0.0989152\pi$
$149$	2.77038	+	12.1378i	0.226958	+	0.994369i	−0.725146	+	0.688595i	$0.758228\pi$
$150$		0			0
$151$	7.09252	+	14.7278i	0.577181	+	1.19853i	0.961366	+	0.275272i	$0.0887680\pi$
$151$	7.09252	+	14.7278i	0.577181	+	1.19853i	−0.384185	+	0.923256i	$0.625518\pi$
$152$		0			0
$153$	1.91972	+	1.53093i	0.155200	+	0.123768i
$154$		0			0
$155$	−31.3539	+	25.0039i	−2.51841	+	2.00836i
$156$		0			0
$157$	3.19837	+	2.55061i	0.255257	+	0.203561i	0.742755	−	0.669563i	$-0.233519\pi$
$157$	3.19837	+	2.55061i	0.255257	+	0.203561i	−0.487498	+	0.873124i	$0.662090\pi$
$158$		0			0
$159$	−0.456843	−	0.220004i	−0.0362300	−	0.0174475i
$160$		0			0
$161$	9.16649	+	1.47801i	0.722421	+	0.116483i
$162$		0			0
$163$	9.55540	+	7.62018i	0.748437	+	0.596859i	0.921648	−	0.388026i	$-0.126843\pi$
$163$	9.55540	+	7.62018i	0.748437	+	0.596859i	−0.173211	+	0.984885i	$0.555414\pi$
$164$		0			0
$165$	−0.497858			−0.0387582
$166$		0			0
$167$	−3.51842	−	1.69438i	−0.272264	−	0.131115i	0.292771	−	0.956183i	$-0.405423\pi$
$167$	−3.51842	−	1.69438i	−0.272264	−	0.131115i	−0.565034	+	0.825067i	$0.691137\pi$
$168$		0			0
$169$	−9.42121	+	4.53701i	−0.724708	+	0.349001i
$170$		0			0
$171$	3.89817	−	17.0790i	0.298100	−	1.30606i
$172$		0			0
$173$	−1.16029	−	2.40937i	−0.0882153	−	0.183181i	0.852194	−	0.523226i	$-0.175272\pi$
$173$	−1.16029	−	2.40937i	−0.0882153	−	0.183181i	−0.940409	+	0.340045i	$0.889558\pi$
$174$		0			0
$175$	−22.3477	−	24.5864i	−1.68932	−	1.85856i
$176$		0			0
$177$	−0.358320			−0.0269330
$178$		0			0
$179$	7.87798	−	16.3588i	0.588828	−	1.22271i	−0.367392	−	0.930066i	$-0.619749\pi$
$179$	7.87798	−	16.3588i	0.588828	−	1.22271i	0.956220	−	0.292648i	$-0.0945364\pi$
$180$		0			0
$181$	−18.4302	−	4.20658i	−1.36991	−	0.312673i	−0.526605	−	0.850110i	$-0.676535\pi$
$181$	−18.4302	−	4.20658i	−1.36991	−	0.312673i	−0.843304	+	0.537437i	$0.819393\pi$
$182$		0			0
$183$	0.836909	−	0.191019i	0.0618661	−	0.0141205i
$184$		0			0
$185$	20.3593	−	4.64688i	1.49685	−	0.341645i
$186$		0			0
$187$	0.243066	−	1.06494i	0.0177747	−	0.0778761i
$188$		0			0
$189$	−0.225267	+	1.39709i	−0.0163858	+	0.101623i
$190$		0			0
$191$	9.80154	−	7.81647i	0.709215	−	0.565580i	−0.201063	−	0.979578i	$-0.564440\pi$
$191$	9.80154	−	7.81647i	0.709215	−	0.565580i	0.910278	+	0.413998i	$0.135868\pi$
$192$		0			0
$193$	9.38078	+	11.7631i	0.675243	+	0.846728i	0.994906	−	0.100803i	$-0.0321412\pi$
$193$	9.38078	+	11.7631i	0.675243	+	0.846728i	−0.319663	+	0.947531i	$0.603570\pi$
$194$		0			0
$195$	0.596494			0.0427158
$196$		0			0
$197$	−17.4994			−1.24678			−0.623389	−	0.781912i	$-0.714245\pi$
$197$	−17.4994			−1.24678			−0.623389	+	0.781912i	$0.714245\pi$
$198$		0			0
$199$	−4.17071	−	5.22991i	−0.295654	−	0.370738i	0.611712	−	0.791081i	$-0.290481\pi$
$199$	−4.17071	−	5.22991i	−0.295654	−	0.370738i	−0.907365	+	0.420343i	$0.861910\pi$
$200$		0			0
$201$	−0.888180	+	0.708300i	−0.0626474	+	0.0499597i
$202$		0			0
$203$	1.64312	−	0.926298i	0.115324	−	0.0650134i
$204$		0			0
$205$	−9.56714	+	41.9164i	−0.668198	+	2.92757i
$206$		0			0
$207$	10.2368	−	2.33649i	0.711510	−	0.162397i
$208$		0			0
$209$	−7.59784	+	1.73416i	−0.525553	+	0.119954i
$210$		0			0
$211$	−13.1756	−	3.00724i	−0.907043	−	0.207027i	−0.256543	−	0.966533i	$-0.582584\pi$
$211$	−13.1756	−	3.00724i	−0.907043	−	0.207027i	−0.650500	+	0.759506i	$0.725441\pi$
$212$		0			0
$213$	−0.332489	+	0.690420i	−0.0227818	+	0.0473068i
$214$		0			0
$215$	−26.7035			−1.82116
$216$		0			0
$217$	14.4782	−	20.7742i	0.982842	−	1.41024i
$218$		0			0
$219$	−0.183395	−	0.380823i	−0.0123927	−	0.0257336i
$220$		0			0
$221$	−0.291222	+	1.27593i	−0.0195897	+	0.0858281i
$222$		0			0
$223$	−18.9538	+	9.12765i	−1.26924	+	0.611233i	−0.942602	−	0.333918i	$-0.891629\pi$
$223$	−18.9538	+	9.12765i	−1.26924	+	0.611233i	−0.326635	+	0.945150i	$0.605915\pi$
$224$		0			0
$225$	−33.8527	−	16.3026i	−2.25685	−	1.08684i
$226$		0			0
$227$	−16.2427			−1.07807			−0.539034	−	0.842284i	$-0.681211\pi$
$227$	−16.2427			−1.07807			−0.539034	+	0.842284i	$0.681211\pi$
$228$		0			0
$229$	−6.98874	−	5.57333i	−0.461829	−	0.368296i	0.364761	−	0.931101i	$-0.381151\pi$
$229$	−6.98874	−	5.57333i	−0.461829	−	0.368296i	−0.826590	+	0.562805i	$0.809722\pi$
$230$		0			0
$231$	0.301323	−	0.0895691i	0.0198256	−	0.00589321i
$232$		0			0
$233$	6.01234	+	2.89539i	0.393882	+	0.189683i	0.620332	−	0.784339i	$-0.286998\pi$
$233$	6.01234	+	2.89539i	0.393882	+	0.189683i	−0.226450	+	0.974023i	$0.572712\pi$
$234$		0			0
$235$	−33.3910	−	26.6284i	−2.17819	−	1.73705i
$236$		0			0
$237$	0.256437	−	0.204502i	0.0166574	−	0.0132838i
$238$		0			0
$239$	15.4166	+	12.2943i	0.997216	+	0.795254i	0.978850	−	0.204578i	$-0.0655821\pi$
$239$	15.4166	+	12.2943i	0.997216	+	0.795254i	0.0183661	+	0.999831i	$0.494154\pi$
$240$		0			0
$241$	−6.69437	−	13.9010i	−0.431223	−	0.895443i	−0.997462	−	0.0712021i	$-0.977316\pi$
$241$	−6.69437	−	13.9010i	−0.431223	−	0.895443i	0.566239	−	0.824241i	$-0.308398\pi$
$242$		0			0
$243$	0.534404	+	2.34138i	0.0342821	+	0.150199i
$244$		0			0
$245$	25.0954	+	15.1841i	1.60329	+	0.970077i
$246$		0			0
$247$	9.10312	−	2.07773i	0.579218	−	0.132203i
$248$		0			0
$249$	−0.897674	+	0.432297i	−0.0568878	+	0.0273957i
$250$		0			0
$251$	14.5845	−	18.2883i	0.920563	−	1.15435i	−0.0670988	−	0.997746i	$-0.521374\pi$
$251$	14.5845	−	18.2883i	0.920563	−	1.15435i	0.987662	−	0.156603i	$-0.0500543\pi$
$252$		0			0
$253$	−2.91240	−	3.65203i	−0.183101	−	0.229601i
$254$		0			0
$255$	−0.191381	+	0.239985i	−0.0119848	+	0.0150284i
$256$		0			0
$257$	3.92857	−	8.15776i	0.245058	−	0.508867i	−0.741768	−	0.670657i	$-0.766012\pi$
$257$	3.92857	−	8.15776i	0.245058	−	0.508867i	0.986825	+	0.161790i	$0.0517266\pi$
$258$		0			0
$259$	−11.4862	+	6.47529i	−0.713719	+	0.402355i
$260$		0			0
$261$	1.32997	−	1.66773i	0.0823229	−	0.103230i
$262$		0			0
$263$			20.8986i			1.28866i	0.764747	+	0.644330i	$0.222864\pi$
$263$			20.8986i			1.28866i	−0.764747	+	0.644330i	$0.777136\pi$
$264$		0			0
$265$	−10.3274	+	21.4451i	−0.634409	+	1.31736i
$266$		0			0
$267$	0.528177	+	1.09677i	0.0323239	+	0.0671212i
$268$		0			0
$269$	6.32829	+	1.44439i	0.385842	+	0.0880660i	0.411042	−	0.911616i	$-0.365165\pi$
$269$	6.32829	+	1.44439i	0.385842	+	0.0880660i	−0.0251996	+	0.999682i	$0.508022\pi$
$270$		0			0
$271$	9.23226	−	4.44602i	0.560820	−	0.270077i	−0.131924	−	0.991260i	$-0.542116\pi$
$271$	9.23226	−	4.44602i	0.560820	−	0.270077i	0.692745	+	0.721183i	$0.256401\pi$
$272$		0			0
$273$	−0.361021	+	0.107315i	−0.0218500	+	0.00649497i
$274$		0			0
$275$			16.7152i			1.00796i
$276$		0			0
$277$	−6.15247	−	2.96287i	−0.369666	−	0.178022i	0.239822	−	0.970817i	$-0.422911\pi$
$277$	−6.15247	−	2.96287i	−0.369666	−	0.178022i	−0.609488	+	0.792795i	$0.708625\pi$
$278$		0			0
$279$	6.37205	−	27.9178i	0.381485	−	1.67139i
$280$		0			0
$281$	−4.15102	−	18.1868i	−0.247629	−	1.08493i	−0.933885	−	0.357574i	$-0.883604\pi$
$281$	−4.15102	−	18.1868i	−0.247629	−	1.08493i	0.686256	−	0.727360i	$-0.259253\pi$
$282$		0			0
$283$	3.53217	+	15.4754i	0.209966	+	0.919920i	0.964588	+	0.263761i	$0.0849629\pi$
$283$	3.53217	+	15.4754i	0.209966	+	0.919920i	−0.754622	+	0.656159i	$0.772180\pi$
$284$		0			0
$285$	2.13505	+	0.487311i	0.126469	+	0.0288658i
$286$		0			0
$287$	−1.75073	−	27.0906i	−0.103342	−	1.59911i
$288$		0			0
$289$	10.1794	+	12.7646i	0.598790	+	0.750859i
$290$		0			0
$291$	0.695385	−	0.554551i	0.0407642	−	0.0325083i
$292$		0			0
$293$			13.3055i			0.777318i	0.921382	+	0.388659i	$0.127062\pi$
$293$			13.3055i			0.777318i	−0.921382	+	0.388659i	$0.872938\pi$
$294$		0			0
$295$			16.8203i			0.979313i
$296$		0			0
$297$	0.556617	−	0.443887i	0.0322982	−	0.0257569i
$298$		0			0
$299$	3.48940	+	4.37557i	0.201797	+	0.253046i
$300$		0			0
$301$	16.1620	−	4.80419i	0.931560	−	0.276909i
$302$		0			0
$303$	−0.584069	−	0.133310i	−0.0335539	−	0.00765846i
$304$		0			0
$305$	−8.96682	−	39.2862i	−0.513439	−	2.24952i
$306$		0			0
$307$	2.39121	+	10.4766i	0.136473	+	0.597929i	0.996194	+	0.0871641i	$0.0277804\pi$
$307$	2.39121	+	10.4766i	0.136473	+	0.597929i	−0.859721	+	0.510764i	$0.829362\pi$
$308$		0			0
$309$	−0.0322799	+	0.141427i	−0.00183634	+	0.00804552i
$310$		0			0
$311$	21.2094	+	10.2139i	1.20267	+	0.579177i	0.924437	−	0.381336i	$-0.124536\pi$
$311$	21.2094	+	10.2139i	1.20267	+	0.579177i	0.278236	+	0.960513i	$0.410250\pi$
$312$		0			0
$313$			24.8263i			1.40326i	0.712540	+	0.701632i	$0.247545\pi$
$313$			24.8263i			1.40326i	−0.712540	+	0.701632i	$0.752455\pi$
$314$		0			0
$315$	32.7475	+	5.28021i	1.84511	+	0.297506i
$316$		0			0
$317$	15.3238	−	7.37957i	0.860673	−	0.414478i	0.0491447	−	0.998792i	$-0.484350\pi$
$317$	15.3238	−	7.37957i	0.860673	−	0.414478i	0.811528	+	0.584314i	$0.198636\pi$
$318$		0			0
$319$	−0.925149	−	0.211159i	−0.0517984	−	0.0118226i
$320$		0			0
$321$	0.152120	+	0.315881i	0.00849052	+	0.0176307i
$322$		0			0
$323$	−2.08476	+	4.32905i	−0.115999	+	0.240875i
$324$		0			0
$325$		−	20.0268i		−	1.11089i
$326$		0			0
$327$	−0.385672	+	0.483617i	−0.0213277	+	0.0267441i
$328$		0			0
$329$	25.0002	+	10.1092i	1.37830	+	0.557338i
$330$		0			0
$331$	10.9830	−	22.8065i	0.603681	−	1.25356i	−0.345379	−	0.938463i	$-0.612250\pi$
$331$	10.9830	−	22.8065i	0.603681	−	1.25356i	0.949061	−	0.315094i	$-0.102036\pi$
$332$		0			0
$333$	−9.29714	+	11.6583i	−0.509480	+	0.638868i
$334$		0			0
$335$	33.2490	+	41.6930i	1.81659	+	2.27793i
$336$		0			0
$337$	17.2179	−	21.5906i	0.937920	−	1.17611i	−0.0462580	−	0.998930i	$-0.514730\pi$
$337$	17.2179	−	21.5906i	0.937920	−	1.17611i	0.984178	−	0.177185i	$-0.0566989\pi$
$338$		0			0
$339$	−0.544521	+	0.262228i	−0.0295743	+	0.0142422i
$340$		0			0
$341$	−12.4196	+	2.83470i	−0.672561	+	0.153508i
$342$		0			0
$343$	−17.9205	−	4.67511i	−0.967615	−	0.252432i
$344$		0			0
$345$	0.292085	+	1.27971i	0.0157253	+	0.0688973i
$346$		0			0
$347$	13.2493	+	27.5124i	0.711258	+	1.47694i	0.871774	+	0.489909i	$0.162970\pi$
$347$	13.2493	+	27.5124i	0.711258	+	1.47694i	−0.160516	+	0.987033i	$0.551316\pi$
$348$		0			0
$349$	−3.66464	−	2.92245i	−0.196164	−	0.156435i	0.520482	−	0.853872i	$-0.325752\pi$
$349$	−3.66464	−	2.92245i	−0.196164	−	0.156435i	−0.716646	+	0.697437i	$0.754324\pi$
$350$		0			0
$351$	−0.666894	+	0.531830i	−0.0355962	+	0.0283870i
$352$		0			0
$353$	12.0153	+	9.58184i	0.639507	+	0.509990i	0.888715	−	0.458460i	$-0.151599\pi$
$353$	12.0153	+	9.58184i	0.639507	+	0.509990i	−0.249208	+	0.968450i	$0.580170\pi$
$354$		0			0
$355$	32.4097	+	15.6077i	1.72013	+	0.828371i
$356$		0			0
$357$	0.0726559	−	0.179679i	0.00384536	−	0.00950963i
$358$		0			0
$359$	−8.10713	−	6.46522i	−0.427878	−	0.341221i	0.385754	−	0.922602i	$-0.373941\pi$
$359$	−8.10713	−	6.46522i	−0.427878	−	0.341221i	−0.813632	+	0.581380i	$0.802513\pi$
$360$		0			0
$361$	15.2805			0.804237
$362$		0			0
$363$	0.742176	+	0.357413i	0.0389541	+	0.0187593i
$364$		0			0
$365$	−17.8766	+	8.60890i	−0.935703	+	0.450611i
$366$		0			0
$367$	4.15917	−	18.2225i	0.217107	−	0.951207i	−0.742496	−	0.669850i	$-0.766358\pi$
$367$	4.15917	−	18.2225i	0.217107	−	0.951207i	0.959603	−	0.281357i	$-0.0907845\pi$
$368$		0			0
$369$	−13.3203	−	27.6599i	−0.693427	−	1.43992i
$370$		0			0
$371$	2.39239	−	14.8374i	0.124206	−	0.770320i
$372$		0			0
$373$	−10.9832			−0.568687			−0.284343	−	0.958723i	$-0.591776\pi$
$373$	−10.9832			−0.568687			−0.284343	+	0.958723i	$0.591776\pi$
$374$		0			0
$375$	1.22656	−	2.54697i	0.0633391	−	0.131525i
$376$		0			0
$377$	1.10844	+	0.252994i	0.0570876	+	0.0130299i
$378$		0			0
$379$	−4.37177	+	0.997828i	−0.224563	+	0.0512550i	−0.333322	−	0.942813i	$-0.608170\pi$
$379$	−4.37177	+	0.997828i	−0.224563	+	0.0512550i	0.108759	+	0.994068i	$0.465312\pi$
$380$		0			0
$381$	−1.12413	+	0.256575i	−0.0575909	+	0.0131447i
$382$		0			0
$383$	−4.25886	+	18.6593i	−0.217618	+	0.953445i	0.741615	+	0.670826i	$0.234060\pi$
$383$	−4.25886	+	18.6593i	−0.217618	+	0.953445i	−0.959232	+	0.282619i	$0.908797\pi$
$384$		0			0
$385$	−4.20455	−	14.1447i	−0.214284	−	0.720880i
$386$		0			0
$387$	14.9077	−	11.8885i	0.757801	−	0.604326i
$388$		0			0
$389$	−10.5715	−	13.2562i	−0.535995	−	0.672116i	0.437924	−	0.899012i	$-0.355714\pi$
$389$	−10.5715	−	13.2562i	−0.535995	−	0.672116i	−0.973919	+	0.226896i	$0.927142\pi$
$390$		0			0
$391$	−2.87996			−0.145646
$392$		0			0
$393$	0.414418			0.0209046
$394$		0			0
$395$	−9.59973	−	12.0377i	−0.483015	−	0.605682i
$396$		0			0
$397$	−10.4752	+	8.35372i	−0.525737	+	0.419261i	−0.850060	−	0.526685i	$-0.823435\pi$
$397$	−10.4752	+	8.35372i	−0.525737	+	0.419261i	0.324324	+	0.945946i	$0.394863\pi$
$398$		0			0
$399$	−1.37988	+	0.0891751i	−0.0690806	+	0.00446434i
$400$		0			0
$401$	3.92245	−	17.1854i	0.195878	−	0.858196i	−0.777481	−	0.628907i	$-0.783503\pi$
$401$	3.92245	−	17.1854i	0.195878	−	0.858196i	0.973358	−	0.229289i	$-0.0736402\pi$
$402$		0			0
$403$	14.8802	−	3.39631i	0.741236	−	0.169182i
$404$		0			0
$405$	36.4737	−	8.32489i	1.81240	−	0.413667i
$406$		0			0
$407$	6.46726	+	1.47611i	0.320570	+	0.0731681i
$408$		0			0
$409$	−4.14500	+	8.60718i	−0.204957	+	0.425597i	−0.977956	−	0.208809i	$-0.933041\pi$
$409$	−4.14500	+	8.60718i	−0.204957	+	0.425597i	0.772999	+	0.634407i	$0.218756\pi$
$410$		0			0
$411$	0.389516			0.0192134
$412$		0			0
$413$	−3.02611	−	10.1803i	−0.148905	−	0.500938i
$414$		0			0
$415$	20.2929	+	42.1386i	0.996139	+	2.06850i
$416$		0			0
$417$	0.416625	−	1.82535i	0.0204022	−	0.0893880i
$418$		0			0
$419$	−27.0650	+	13.0338i	−1.32221	+	0.636743i	−0.955884	−	0.293744i	$-0.905099\pi$
$419$	−27.0650	+	13.0338i	−1.32221	+	0.636743i	−0.366326	+	0.930487i	$0.619385\pi$
$420$		0			0
$421$	−8.09208	−	3.89694i	−0.394384	−	0.189925i	0.226172	−	0.974087i	$-0.427379\pi$
$421$	−8.09208	−	3.89694i	−0.394384	−	0.189925i	−0.620556	+	0.784162i	$0.713093\pi$
$422$		0			0
$423$	30.4962			1.48278
$424$		0			0
$425$	8.05731	+	6.42549i	0.390837	+	0.311682i
$426$		0			0
$427$	12.4950	+	22.1643i	0.604675	+	1.07261i
$428$		0			0
$429$	0.170716	+	0.0822123i	0.00824222	+	0.00396925i
$430$		0			0
$431$	−23.9689	−	19.1145i	−1.15454	−	0.920715i	−0.156781	−	0.987633i	$-0.550112\pi$
$431$	−23.9689	−	19.1145i	−1.15454	−	0.920715i	−0.997758	+	0.0669186i	$0.978683\pi$
$432$		0			0
$433$	12.9560	−	10.3321i	0.622628	−	0.496529i	−0.260616	−	0.965442i	$-0.583926\pi$
$433$	12.9560	−	10.3321i	0.622628	−	0.496529i	0.883244	+	0.468913i	$0.155354\pi$
$434$		0			0
$435$	0.208483	+	0.166259i	0.00999598	+	0.00797153i
$436$		0			0
$437$	8.91506	+	18.5123i	0.426465	+	0.885564i
$438$		0			0
$439$	−3.23513	−	14.1740i	−0.154404	−	0.676490i	−0.991573	−	0.129546i	$-0.958648\pi$
$439$	−3.23513	−	14.1740i	−0.154404	−	0.676490i	0.837169	−	0.546944i	$-0.184209\pi$
$440$		0			0
$441$	−20.7700	+	2.69579i	−0.989048	+	0.128371i
$442$		0			0
$443$	−12.2818	+	2.80324i	−0.583526	+	0.133186i	−0.504086	−	0.863654i	$-0.668170\pi$
$443$	−12.2818	+	2.80324i	−0.583526	+	0.133186i	−0.0794401	+	0.996840i	$0.525313\pi$
$444$		0			0
$445$	51.4846	−	24.7937i	2.44060	−	1.17533i
$446$		0			0
$447$	0.692903	−	0.868873i	0.0327732	−	0.0410963i
$448$		0			0
$449$	14.2791	+	17.9054i	0.673871	+	0.845008i	0.994774	−	0.102104i	$-0.0325575\pi$
$449$	14.2791	+	17.9054i	0.673871	+	0.845008i	−0.320902	+	0.947112i	$0.603986\pi$
$450$		0			0
$451$	−8.51526	+	10.6778i	−0.400968	+	0.502798i
$452$		0			0
$453$	0.633104	−	1.31465i	0.0297458	−	0.0617679i
$454$		0			0
$455$	5.03756	+	16.9470i	0.236164	+	0.794489i
$456$		0			0
$457$	−24.6134	+	30.8643i	−1.15137	+	1.44377i	−0.275445	+	0.961317i	$0.588825\pi$
$457$	−24.6134	+	30.8643i	−1.15137	+	1.44377i	−0.875922	+	0.482452i	$0.839746\pi$
$458$		0			0
$459$		−	0.438943i		−	0.0204881i
$460$		0			0
$461$	−1.98370	+	4.11919i	−0.0923900	+	0.191850i	−0.942043	−	0.335493i	$-0.891097\pi$
$461$	−1.98370	+	4.11919i	−0.0923900	+	0.191850i	0.849653	+	0.527342i	$0.176812\pi$
$462$		0			0
$463$	−8.40671	−	17.4567i	−0.390693	−	0.811282i	−0.999834	−	0.0182203i	$-0.994200\pi$
$463$	−8.40671	−	17.4567i	−0.390693	−	0.811282i	0.609141	−	0.793062i	$-0.291514\pi$
$464$		0			0
$465$	3.49001	+	0.796572i	0.161845	+	0.0369401i
$466$		0			0
$467$	18.3849	−	8.85370i	0.850752	−	0.409700i	0.0428950	−	0.999080i	$-0.486342\pi$
$467$	18.3849	−	8.85370i	0.850752	−	0.409700i	0.807856	+	0.589379i	$0.200628\pi$
$468$		0			0
$469$	−27.6245	−	19.2524i	−1.27558	−	0.888992i
$470$		0			0
$471$		−	0.365166i		−	0.0168259i
$472$		0			0
$473$	−7.64249	−	3.68043i	−0.351402	−	0.169226i
$474$		0			0
$475$	16.3611	−	71.6826i	0.750699	−	3.28903i
$476$		0			0
$477$	−3.78198	−	16.5699i	−0.173165	−	0.758686i
$478$		0			0
$479$	−5.74876	−	25.1870i	−0.262668	−	1.15082i	−0.918345	−	0.395781i	$-0.870474\pi$
$479$	−5.74876	−	25.1870i	−0.262668	−	1.15082i	0.655677	−	0.755041i	$-0.272383\pi$
$480$		0			0
$481$	−7.74856	−	1.76856i	−0.353304	−	0.0806393i
$482$		0			0
$483$	−0.407012	−	0.721980i	−0.0185197	−	0.0328512i
$484$		0			0
$485$	−26.0317	−	32.6427i	−1.18204	−	1.48223i
$486$		0			0
$487$	−22.3637	+	17.8345i	−1.01340	+	0.808156i	−0.981525	−	0.191336i	$-0.938718\pi$
$487$	−22.3637	+	17.8345i	−1.01340	+	0.808156i	−0.0318713	+	0.999492i	$0.510147\pi$
$488$		0			0
$489$		−	1.09097i		−	0.0493351i
$490$		0			0
$491$			2.41607i			0.109036i	0.998513	+	0.0545179i	$0.0173622\pi$
$491$			2.41607i			0.109036i	−0.998513	+	0.0545179i	$0.982638\pi$
$492$		0			0
$493$	−0.457422	+	0.364782i	−0.0206013	+	0.0164290i
$494$		0			0
$495$	−10.4046	−	13.0470i	−0.467653	−	0.586418i
$496$		0			0
$497$	−22.4236	−	3.61558i	−1.00583	−	0.162181i
$498$		0			0
$499$	−1.40569	−	0.320839i	−0.0629272	−	0.0143627i	0.190941	−	0.981601i	$-0.438846\pi$
$499$	−1.40569	−	0.320839i	−0.0629272	−	0.0143627i	−0.253869	+	0.967239i	$0.581703\pi$
$500$		0			0
$501$	0.0775683	+	0.339849i	0.00346549	+	0.0151833i
$502$		0			0
$503$	3.07606	+	13.4771i	0.137155	+	0.600913i	0.996052	+	0.0887664i	$0.0282925\pi$
$503$	3.07606	+	13.4771i	0.137155	+	0.600913i	−0.858898	+	0.512147i	$0.828850\pi$
$504$		0			0
$505$	−6.25784	+	27.4174i	−0.278470	+	1.22006i
$506$		0			0
$507$	0.840972	+	0.404991i	0.0373489	+	0.0179863i
$508$		0			0
$509$		−	4.25026i		−	0.188389i	−0.995554	−	0.0941947i	$-0.969972\pi$
$509$		−	4.25026i		−	0.188389i	0.995554	−	0.0941947i	$-0.0300276\pi$
$510$		0			0
$511$	9.27077	−	8.42659i	0.410115	−	0.372770i
$512$		0			0
$513$	−2.82152	+	1.35877i	−0.124573	+	0.0599912i
$514$		0			0
$515$	6.63888	+	1.51528i	0.292544	+	0.0667713i
$516$		0			0
$517$	−5.88636	−	12.2231i	−0.258882	−	0.537573i
$518$		0			0
$519$	−0.103572	+	0.215069i	−0.00454630	+	0.00944049i
$520$		0			0
$521$			41.1357i			1.80219i	0.433626	+	0.901093i	$0.357234\pi$
$521$			41.1357i			1.80219i	−0.433626	+	0.901093i	$0.642766\pi$
$522$		0			0
$523$	−19.8003	+	24.8288i	−0.865807	+	1.08569i	0.129752	+	0.991546i	$0.458582\pi$
$523$	−19.8003	+	24.8288i	−0.865807	+	1.08569i	−0.995559	+	0.0941407i	$0.969990\pi$
$524$		0			0
$525$	−0.472108	+	2.92798i	−0.0206045	+	0.127788i
$526$		0			0
$527$	−3.40780	+	7.07638i	−0.148446	+	0.308252i
$528$		0			0
$529$	6.66163	−	8.35342i	0.289636	−	0.363192i
$530$		0			0
$531$	−7.48844	−	9.39021i	−0.324971	−	0.407501i
$532$		0			0
$533$	10.2023	−	12.7933i	0.441911	−	0.554139i
$534$		0			0
$535$	14.8281	−	7.14082i	0.641074	−	0.308725i
$536$		0			0
$537$	−1.58012	+	0.360651i	−0.0681871	+	0.0155633i
$538$		0			0
$539$	5.08951	+	7.80447i	0.219221	+	0.336162i
$540$		0			0
$541$	−1.37088	−	6.00621i	−0.0589387	−	0.258227i	0.936871	−	0.349675i	$-0.113708\pi$
$541$	−1.37088	−	6.00621i	−0.0589387	−	0.258227i	−0.995810	+	0.0914473i	$0.970851\pi$
$542$		0			0
$543$	0.732162	+	1.52035i	0.0314201	+	0.0652444i
$544$		0			0
$545$	22.7019	+	18.1042i	0.972444	+	0.775499i
$546$		0			0
$547$	23.6635	−	18.8710i	1.01178	−	0.806865i	0.0305127	−	0.999534i	$-0.490286\pi$
$547$	23.6635	−	18.8710i	1.01178	−	0.806865i	0.981264	+	0.192670i	$0.0617146\pi$
$548$		0			0
$549$	22.4963	+	17.9402i	0.960117	+	0.765668i
$550$		0			0
$551$	3.76079	+	1.81110i	0.160215	+	0.0771554i
$552$		0			0
$553$	7.97581	+	5.55859i	0.339166	+	0.236375i
$554$		0			0
$555$	−1.45740	−	1.16224i	−0.0618632	−	0.0493342i
$556$		0			0
$557$	−39.6120			−1.67842			−0.839208	−	0.543811i	$-0.816981\pi$
$557$	−39.6120			−1.67842			−0.839208	+	0.543811i	$0.816981\pi$
$558$		0			0
$559$	9.15662	+	4.40960i	0.387284	+	0.186506i
$560$		0			0
$561$	−0.0878491	+	0.0423059i	−0.00370899	+	0.00178616i
$562$		0			0
$563$	−8.68269	+	38.0414i	−0.365932	+	1.60325i	0.371903	+	0.928271i	$0.378705\pi$
$563$	−8.68269	+	38.0414i	−0.365932	+	1.60325i	−0.737835	+	0.674981i	$0.764152\pi$
$564$		0			0
$565$	12.3095	+	25.5609i	0.517864	+	1.07536i
$566$		0			0
$567$	−20.5776	+	11.6005i	−0.864177	+	0.487175i
$568$		0			0
$569$	26.7518			1.12149			0.560747	−	0.827987i	$-0.310514\pi$
$569$	26.7518			1.12149			0.560747	+	0.827987i	$0.310514\pi$
$570$		0			0
$571$	8.88230	−	18.4443i	0.371713	−	0.771870i	−0.628268	−	0.777997i	$-0.716236\pi$
$571$	8.88230	−	18.4443i	0.371713	−	0.771870i	0.999981	+	0.00612706i	$0.00195032\pi$
$572$		0			0
$573$	−1.09101	−	0.249016i	−0.0455776	−	0.0104028i
$574$		0			0
$575$	42.9653	−	9.80655i	1.79178	−	0.408961i
$576$		0			0
$577$	7.84383	−	1.79030i	0.326543	−	0.0745313i	−0.0561069	−	0.998425i	$-0.517869\pi$
$577$	7.84383	−	1.79030i	0.326543	−	0.0745313i	0.382650	+	0.923894i	$0.375012\pi$
$578$		0			0
$579$	0.298851	−	1.30935i	0.0124198	−	0.0544149i
$580$		0			0
$581$	−19.8631	−	21.8530i	−0.824062	−	0.906616i
$582$		0			0
$583$	−5.91139	+	4.71417i	−0.244825	+	0.195241i
$584$		0			0
$585$	12.4660	+	15.6318i	0.515405	+	0.646297i
$586$		0			0
$587$	4.31024			0.177902			0.0889512	−	0.996036i	$-0.471648\pi$
$587$	4.31024			0.177902			0.0889512	+	0.996036i	$0.471648\pi$
$588$		0			0
$589$	56.0359			2.30892
$590$		0			0
$591$	0.973927	+	1.22127i	0.0400620	+	0.0502362i
$592$		0			0
$593$	−23.8170	+	18.9934i	−0.978047	+	0.779967i	−0.975493	−	0.220030i	$-0.929384\pi$
$593$	−23.8170	+	18.9934i	−0.978047	+	0.779967i	−0.00255407	+	0.999997i	$0.500813\pi$
$594$		0			0
$595$	−8.43450	−	3.41062i	−0.345781	−	0.139822i
$596$		0			0
$597$	−0.132870	+	0.582141i	−0.00543800	+	0.0238254i
$598$		0			0
$599$	−7.23546	+	1.65145i	−0.295633	+	0.0674762i	−0.367765	−	0.929919i	$-0.619877\pi$
$599$	−7.23546	+	1.65145i	−0.295633	+	0.0674762i	0.0721321	+	0.997395i	$0.477020\pi$
$600$		0			0
$601$	6.60432	−	1.50739i	0.269396	−	0.0614879i	−0.0856889	−	0.996322i	$-0.527309\pi$
$601$	6.60432	−	1.50739i	0.269396	−	0.0614879i	0.355085	+	0.934834i	$0.384452\pi$
$602$		0			0
$603$	−37.1237	−	8.47325i	−1.51180	−	0.345058i
$604$		0			0
$605$	16.7777	−	34.8392i	0.682110	−	1.41642i
$606$		0			0
$607$	10.5994			0.430218			0.215109	−	0.976590i	$-0.430989\pi$
$607$	10.5994			0.430218			0.215109	+	0.976590i	$0.430989\pi$
$608$		0			0
$609$	−0.156093	−	0.0631186i	−0.00632522	−	0.00255770i
$610$		0			0
$611$	7.05256	+	14.6448i	0.285316	+	0.592465i
$612$		0			0
$613$	3.28448	−	14.3903i	0.132659	−	0.581217i	−0.864278	−	0.503014i	$-0.832224\pi$
$613$	3.28448	−	14.3903i	0.132659	−	0.581217i	0.996937	−	0.0782036i	$-0.0249184\pi$
$614$		0			0
$615$	3.45777	−	1.66517i	0.139431	−	0.0671463i
$616$		0			0
$617$	36.9865	+	17.8118i	1.48902	+	0.717074i	0.988859	−	0.148858i	$-0.0475598\pi$
$617$	36.9865	+	17.8118i	1.48902	+	0.717074i	0.500161	+	0.865932i	$0.333274\pi$
$618$		0			0
$619$	3.53198			0.141962			0.0709811	−	0.997478i	$-0.477387\pi$
$619$	3.53198			0.141962			0.0709811	+	0.997478i	$0.477387\pi$
$620$		0			0
$621$	−1.46754	−	1.17032i	−0.0588903	−	0.0469635i
$622$		0			0
$623$	−26.6998	+	24.2686i	−1.06971	+	0.972301i
$624$		0			0
$625$	−62.9884	−	30.3336i	−2.51954	−	1.21334i
$626$		0			0
$627$	0.543883	+	0.433732i	0.0217206	+	0.0173216i
$628$		0			0
$629$	3.19761	−	2.55001i	0.127497	−	0.101676i
$630$		0			0
$631$	13.6273	+	10.8674i	0.542493	+	0.432623i	0.856010	−	0.516959i	$-0.172936\pi$
$631$	13.6273	+	10.8674i	0.542493	+	0.432623i	−0.313518	+	0.949582i	$0.601507\pi$
$632$		0			0
$633$	0.523414	+	1.08688i	0.0208038	+	0.0431996i
$634$		0			0
$635$	12.0442	+	52.7689i	0.477958	+	2.09407i
$636$		0			0
$637$	−6.09785	−	9.35069i	−0.241605	−	0.370488i
$638$		0			0
$639$	−25.0419	+	5.71565i	−0.990643	+	0.226108i
$640$		0			0
$641$	−20.0483	+	9.65477i	−0.791862	+	0.381341i	−0.785674	−	0.618640i	$-0.787684\pi$
$641$	−20.0483	+	9.65477i	−0.791862	+	0.381341i	−0.00618750	+	0.999981i	$0.501970\pi$
$642$		0			0
$643$	−17.7520	+	22.2603i	−0.700071	+	0.877861i	−0.997029	−	0.0770293i	$-0.975456\pi$
$643$	−17.7520	+	22.2603i	−0.700071	+	0.877861i	0.296958	+	0.954891i	$0.404028\pi$
$644$		0			0
$645$	1.48618	+	1.86361i	0.0585184	+	0.0733797i
$646$		0			0
$647$	19.4743	−	24.4200i	0.765615	−	0.960051i	−0.234312	−	0.972162i	$-0.575284\pi$
$647$	19.4743	−	24.4200i	0.765615	−	0.960051i	0.999927	+	0.0121108i	$0.00385507\pi$
$648$		0			0
$649$	−2.31827	+	4.81393i	−0.0909999	+	0.188963i
$650$		0			0
$651$	−2.25560	+	0.145768i	−0.0884038	+	0.00571310i
$652$		0			0
$653$	18.7441	−	23.5044i	0.733514	−	0.919797i	−0.265504	−	0.964110i	$-0.585538\pi$
$653$	18.7441	−	23.5044i	0.733514	−	0.919797i	0.999018	+	0.0443125i	$0.0141097\pi$
$654$		0			0
$655$		−	19.4536i		−	0.760116i
$656$		0			0
$657$	6.14720	−	12.7648i	0.239825	−	0.498002i
$658$		0			0
$659$	−14.0682	−	29.2130i	−0.548020	−	1.13798i	−0.972578	−	0.232575i	$-0.925285\pi$
$659$	−14.0682	−	29.2130i	−0.548020	−	1.13798i	0.424558	−	0.905401i	$-0.360429\pi$
$660$		0			0
$661$	−29.1469	−	6.65260i	−1.13368	−	0.258756i	−0.385799	−	0.922583i	$-0.626074\pi$
$661$	−29.1469	−	6.65260i	−1.13368	−	0.258756i	−0.747886	+	0.663827i	$0.768931\pi$
$662$		0			0
$663$	0.105254	−	0.0506876i	0.00408772	−	0.00196854i
$664$		0			0
$665$	4.18606	+	64.7745i	0.162328	+	2.51185i
$666$		0			0
$667$			2.50192i			0.0968746i
$668$		0			0
$669$	1.69188	+	0.814768i	0.0654120	+	0.0315007i
$670$		0			0
$671$	2.84837	−	12.4795i	0.109960	−	0.481766i
$672$		0			0
$673$	6.00174	+	26.2954i	0.231350	+	1.01361i	0.948521	+	0.316714i	$0.102580\pi$
$673$	6.00174	+	26.2954i	0.231350	+	1.01361i	−0.717171	+	0.696897i	$0.754563\pi$
$674$		0			0
$675$	1.49464	+	6.54846i	0.0575289	+	0.252051i
$676$		0			0
$677$	−29.7326	−	6.78628i	−1.14272	−	0.260818i	−0.391056	−	0.920367i	$-0.627890\pi$
$677$	−29.7326	−	6.78628i	−1.14272	−	0.260818i	−0.751661	+	0.659549i	$0.770747\pi$
$678$		0			0
$679$	21.6281	+	15.0733i	0.830011	+	0.578460i
$680$		0			0
$681$	0.903989	+	1.13357i	0.0346410	+	0.0434384i
$682$		0			0
$683$	−31.0604	+	24.7698i	−1.18849	+	0.947790i	−0.999416	−	0.0341722i	$-0.989121\pi$
$683$	−31.0604	+	24.7698i	−1.18849	+	0.947790i	−0.189076	+	0.981963i	$0.560549\pi$
$684$		0			0
$685$		−	18.2846i		−	0.698620i
$686$		0			0
$687$			0.797922i			0.0304426i
$688$		0			0
$689$	7.08255	−	5.64815i	0.269824	−	0.215177i
$690$		0			0
$691$	2.63286	+	3.30151i	0.100159	+	0.125595i	0.829385	−	0.558678i	$-0.188691\pi$
$691$	2.63286	+	3.30151i	0.100159	+	0.125595i	−0.729226	+	0.684273i	$0.760120\pi$
$692$		0			0
$693$	8.64454	+	6.02464i	0.328379	+	0.228857i
$694$		0			0
$695$	−85.6858	−	19.5572i	−3.25025	−	0.741848i
$696$		0			0
$697$	1.87372	+	8.20929i	0.0709721	+	0.310949i
$698$		0			0
$699$	−0.132550	−	0.580740i	−0.00501350	−	0.0219656i
$700$		0			0
$701$	−0.506981	+	2.22123i	−0.0191484	+	0.0838947i	−0.983599	−	0.180368i	$-0.942271\pi$
$701$	−0.506981	+	2.22123i	−0.0191484	+	0.0838947i	0.964451	+	0.264262i	$0.0851284\pi$
$702$		0			0
$703$	−26.2898	−	12.6605i	−0.991539	−	0.477500i
$704$		0			0
$705$			3.81233i			0.143581i
$706$		0			0
$707$	−1.14515	−	17.7199i	−0.0430678	−	0.666425i
$708$		0			0
$709$	3.54940	−	1.70930i	0.133301	−	0.0641942i	−0.366045	−	0.930597i	$-0.619288\pi$
$709$	3.54940	−	1.70930i	0.133301	−	0.0641942i	0.499345	+	0.866403i	$0.333574\pi$
$710$		0			0
$711$	10.7184	+	2.44642i	0.401973	+	0.0917478i
$712$		0			0
$713$	14.5728	+	30.2607i	0.545756	+	1.13327i
$714$		0			0
$715$	3.85921	−	8.01373i	0.144326	−	0.299696i
$716$		0			0
$717$		−	1.76015i		−	0.0657341i
$718$		0			0
$719$	−5.52467	+	6.92771i	−0.206035	+	0.258360i	−0.874103	−	0.485740i	$-0.838550\pi$
$719$	−5.52467	+	6.92771i	−0.206035	+	0.258360i	0.668068	+	0.744100i	$0.267122\pi$
$720$		0			0
$721$	−4.29072	+	0.277288i	−0.159795	+	0.0103267i
$722$		0			0
$723$	−0.597565	+	1.24086i	−0.0222237	+	0.0461479i
$724$		0			0
$725$	5.58204	−	6.99965i	0.207312	−	0.259961i
$726$		0			0
$727$	−4.22044	−	5.29226i	−0.156527	−	0.196279i	0.697384	−	0.716698i	$-0.254347\pi$
$727$	−4.22044	−	5.29226i	−0.156527	−	0.196279i	−0.853911	+	0.520419i	$0.825776\pi$
$728$		0			0
$729$	−16.5665	+	20.7738i	−0.613576	+	0.769400i
$730$		0			0
$731$	−4.71194	+	2.26915i	−0.174277	+	0.0839276i
$732$		0			0
$733$	28.2958	−	6.45833i	1.04513	−	0.238544i	0.334709	−	0.942322i	$-0.391362\pi$
$733$	28.2958	−	6.45833i	1.04513	−	0.238544i	0.710420	+	0.703778i	$0.248505\pi$
$734$		0			0
$735$	−0.337001	−	2.59646i	−0.0124305	−	0.0957720i
$736$		0			0
$737$	3.76945	+	16.5150i	0.138849	+	0.608339i
$738$		0			0
$739$	−13.7031	−	28.4547i	−0.504075	−	1.04672i	−0.985412	−	0.170187i	$-0.945563\pi$
$739$	−13.7031	−	28.4547i	−0.504075	−	1.04672i	0.481337	−	0.876536i	$-0.340152\pi$
$740$		0			0
$741$	−0.651638	−	0.519664i	−0.0239385	−	0.0190903i
$742$		0			0
$743$	−13.7093	+	10.9328i	−0.502946	+	0.401086i	−0.841831	−	0.539742i	$-0.818522\pi$
$743$	−13.7093	+	10.9328i	−0.502946	+	0.401086i	0.338885	+	0.940828i	$0.389950\pi$
$744$		0			0
$745$	−40.7867	−	32.5263i	−1.49431	−	1.19167i
$746$		0			0
$747$	−30.0891	−	14.4902i	−1.10090	−	0.530168i
$748$		0			0
$749$	−7.68982	+	6.98960i	−0.280980	+	0.255394i
$750$		0			0
$751$	−2.55543	−	2.03789i	−0.0932490	−	0.0743636i	0.575756	−	0.817622i	$-0.304708\pi$
$751$	−2.55543	−	2.03789i	−0.0932490	−	0.0743636i	−0.669005	+	0.743258i	$0.733279\pi$
$752$		0			0
$753$	−2.08803			−0.0760919
$754$		0			0
$755$	−61.7125	−	29.7192i	−2.24595	−	1.08159i
$756$		0			0
$757$	5.14216	−	2.47633i	0.186895	−	0.0900039i	−0.338096	−	0.941112i	$-0.609783\pi$
$757$	5.14216	−	2.47633i	0.186895	−	0.0900039i	0.524991	+	0.851108i	$0.324069\pi$
$758$		0			0
$759$	−0.0927827	+	0.406508i	−0.00336780	+	0.0147553i
$760$		0			0
$761$	−0.0881927	−	0.183134i	−0.00319698	−	0.00663860i	0.899364	−	0.437200i	$-0.144030\pi$
$761$	−0.0881927	−	0.183134i	−0.00319698	−	0.00663860i	−0.902561	+	0.430561i	$0.858316\pi$
$762$		0			0
$763$	−16.9972	−	6.87307i	−0.615340	−	0.248822i
$764$		0			0
$765$	−10.2887			−0.371990
$766$		0			0
$767$	2.77756	−	5.76767i	0.100292	−	0.208258i
$768$		0			0
$769$	−41.4807	−	9.46770i	−1.49583	−	0.341414i	−0.605176	−	0.796092i	$-0.706897\pi$
$769$	−41.4807	−	9.46770i	−1.49583	−	0.341414i	−0.890656	+	0.454678i	$0.849754\pi$
$770$		0			0
$771$	−0.787968	+	0.179849i	−0.0283780	+	0.00647709i
$772$		0			0
$773$	−46.7547	+	10.6715i	−1.68165	+	0.383826i	−0.953453	−	0.301542i	$-0.902499\pi$
$773$	−46.7547	+	10.6715i	−1.68165	+	0.383826i	−0.728197	+	0.685368i	$0.759641\pi$
$774$		0			0
$775$	26.7443	−	117.174i	0.960683	−	4.20903i
$776$		0			0
$777$	1.09117	+	0.441231i	0.0391455	+	0.0158291i
$778$		0			0
$779$	46.9690	−	37.4565i	1.68284	−	1.34202i
$780$		0			0
$781$	7.12446	+	8.93379i	0.254933	+	0.319676i
$782$		0			0
$783$	−0.381324			−0.0136274
$784$		0			0
$785$	−17.1416			−0.611810
$786$		0			0
$787$	23.6943	+	29.7117i	0.844611	+	1.05911i	0.997486	+	0.0708631i	$0.0225754\pi$
$787$	23.6943	+	29.7117i	0.844611	+	1.05911i	−0.152875	+	0.988246i	$0.548853\pi$
$788$		0			0
$789$	1.45849	−	1.16311i	0.0519238	−	0.0414078i
$790$		0			0
$791$	−12.0488	−	13.2559i	−0.428406	−	0.471324i
$792$		0			0
$793$	−3.41269	+	14.9520i	−0.121188	+	0.530959i
$794$		0			0
$795$	2.07141	−	0.472786i	0.0734654	−	0.0167680i
$796$		0			0
$797$	−8.95126	+	2.04307i	−0.317070	+	0.0723691i	−0.378094	−	0.925767i	$-0.623420\pi$
$797$	−8.95126	+	2.04307i	−0.317070	+	0.0723691i	0.0610243	+	0.998136i	$0.480563\pi$
$798$		0			0
$799$	−8.15475	−	1.86127i	−0.288494	−	0.0658469i
$800$		0			0
$801$	−17.7040	+	36.7627i	−0.625539	+	1.29894i
$802$		0			0
$803$	−6.30277			−0.222420
$804$		0			0
$805$	−33.8912	+	19.1060i	−1.19451	+	0.673397i
$806$		0			0
$807$	−0.251398	−	0.522033i	−0.00884963	−	0.0183764i
$808$		0			0
$809$	−5.40968	+	23.7013i	−0.190194	+	0.833295i	0.786316	+	0.617824i	$0.211986\pi$
$809$	−5.40968	+	23.7013i	−0.190194	+	0.833295i	−0.976510	+	0.215471i	$0.930871\pi$
$810$		0			0
$811$	−8.18843	+	3.94334i	−0.287535	+	0.138469i	−0.572092	−	0.820190i	$-0.693868\pi$
$811$	−8.18843	+	3.94334i	−0.287535	+	0.138469i	0.284557	+	0.958659i	$0.408154\pi$
$812$		0			0
$813$	−0.824106	−	0.396869i	−0.0289027	−	0.0139188i
$814$		0			0
$815$	−51.2121			−1.79388
$816$		0			0
$817$	29.1721	+	23.2640i	1.02060	+	0.813904i
$818$		0			0
$819$	−10.3572	−	7.21825i	−0.361910	−	0.252226i
$820$		0			0
$821$	42.5519	+	20.4919i	1.48507	+	0.715173i	0.988274	−	0.152692i	$-0.0487943\pi$
$821$	42.5519	+	20.4919i	1.48507	+	0.715173i	0.496799	+	0.867866i	$0.334509\pi$
$822$		0			0
$823$	34.3864	+	27.4222i	1.19863	+	0.955879i	0.999709	−	0.0241356i	$-0.00768336\pi$
$823$	34.3864	+	27.4222i	1.19863	+	0.955879i	0.198926	+	0.980015i	$0.436255\pi$
$824$		0			0
$825$	1.16654	−	0.930285i	0.0406137	−	0.0323884i
$826$		0			0
$827$	−35.1835	−	28.0579i	−1.22345	−	0.975669i	−1.00000		0.000953963i	$-0.999696\pi$
$827$	−35.1835	−	28.0579i	−1.22345	−	0.975669i	−0.223451	−	0.974715i	$-0.571732\pi$
$828$		0			0
$829$	16.8184	+	34.9238i	0.584128	+	1.21295i	0.958345	+	0.285613i	$0.0921970\pi$
$829$	16.8184	+	34.9238i	0.584128	+	1.21295i	−0.374218	+	0.927341i	$0.622089\pi$
$830$		0			0
$831$	0.135639	+	0.594275i	0.00470528	+	0.0206152i
$832$		0			0
$833$	5.71848	+	0.546793i	0.198134	+	0.0189453i
$834$		0			0
$835$	15.9532	−	3.64121i	0.552083	−	0.126009i
$836$		0			0
$837$	−4.61213	+	2.22108i	−0.159418	+	0.0767719i
$838$		0			0
$839$	−15.1606	+	19.0108i	−0.523403	+	0.656326i	−0.971328	−	0.237745i	$-0.923592\pi$
$839$	−15.1606	+	19.0108i	−0.523403	+	0.656326i	0.447925	+	0.894071i	$0.352163\pi$
$840$		0			0
$841$	−17.7643	−	22.2757i	−0.612562	−	0.768129i
$842$		0			0
$843$	−1.03822	+	1.30188i	−0.0357581	+	0.0448392i
$844$		0			0
$845$	19.0111	−	39.4769i	0.654001	−	1.35805i
$846$		0			0
$847$	−3.88661	+	24.1045i	−0.133545	+	0.828240i
$848$		0			0
$849$	0.883436	−	1.10779i	0.0303194	−	0.0380194i
$850$		0			0
$851$		−	17.4897i		−	0.599538i
$852$		0			0
$853$	−2.70532	+	5.61765i	−0.0926283	+	0.192345i	−0.942135	−	0.335232i	$-0.891185\pi$
$853$	−2.70532	+	5.61765i	−0.0926283	+	0.192345i	0.849507	+	0.527577i	$0.176899\pi$
$854$		0			0
$855$	31.8493	+	66.1357i	1.08922	+	2.26179i
$856$		0			0
$857$	26.7107	+	6.09654i	0.912420	+	0.208254i	0.652865	−	0.757474i	$-0.273567\pi$
$857$	26.7107	+	6.09654i	0.912420	+	0.208254i	0.259555	+	0.965728i	$0.416424\pi$
$858$		0			0
$859$	−42.7069	+	20.5665i	−1.45714	+	0.701721i	−0.983818	−	0.179169i	$-0.942659\pi$
$859$	−42.7069	+	20.5665i	−1.45714	+	0.701721i	−0.473321	+	0.880890i	$0.656945\pi$
$860$		0			0
$861$	−1.79319	+	1.62991i	−0.0611119	+	0.0555472i
$862$		0			0
$863$			12.5493i			0.427182i	0.976923	+	0.213591i	$0.0685160\pi$
$863$			12.5493i			0.427182i	−0.976923	+	0.213591i	$0.931484\pi$
$864$		0			0
$865$	10.0958	+	4.86187i	0.343267	+	0.165309i
$866$		0			0
$867$	0.324295	−	1.42083i	0.0110136	−	0.0482538i
$868$		0			0
$869$	−1.08832	−	4.76826i	−0.0369188	−	0.161752i
$870$		0			0
$871$	−4.51625	−	19.7870i	−0.153027	−	0.670457i
$872$		0			0
$873$	29.0654	+	6.63398i	0.983713	+	0.224526i
$874$		0			0
$875$	82.7208	+	13.3379i	2.79647	+	0.450904i
$876$		0			0
$877$	−13.8617	−	17.3820i	−0.468075	−	0.586948i	0.490623	−	0.871372i	$-0.336769\pi$
$877$	−13.8617	−	17.3820i	−0.468075	−	0.586948i	−0.958699	+	0.284424i	$0.908198\pi$
$878$		0			0
$879$	0.928583	−	0.740520i	0.0313203	−	0.0249771i
$880$		0			0
$881$		−	42.1539i		−	1.42020i	−0.704100	−	0.710101i	$-0.748649\pi$
$881$		−	42.1539i		−	1.42020i	0.704100	−	0.710101i	$-0.251351\pi$
$882$		0			0
$883$			15.6328i			0.526087i	0.964784	+	0.263043i	$0.0847262\pi$
$883$			15.6328i			0.526087i	−0.964784	+	0.263043i	$0.915274\pi$
$884$		0			0
$885$	1.17387	−	0.936132i	0.0394593	−	0.0314677i
$886$		0			0
$887$	−32.7452	−	41.0612i	−1.09948	−	1.37870i	−0.918597	−	0.395195i	$-0.870677\pi$
$887$	−32.7452	−	41.0612i	−1.09948	−	1.37870i	−0.180880	−	0.983505i	$-0.557894\pi$
$888$		0			0
$889$	−16.7832	−	29.7709i	−0.562889	−	0.998483i
$890$		0			0
$891$	11.5861	+	2.64445i	0.388149	+	0.0885925i
$892$		0			0
$893$	13.2793	+	58.1802i	0.444373	+	1.94693i
$894$		0			0
$895$	16.9297	+	74.1738i	0.565897	+	2.47936i
$896$		0			0
$897$	0.111165	−	0.487045i	0.00371169	−	0.0162620i
$898$		0			0
$899$	6.14749	+	2.96047i	0.205030	+	0.0987373i
$900$		0			0
$901$			4.66167i			0.155303i
$902$		0			0
$903$	−1.23478	−	0.860553i	−0.0410907	−	0.0286374i
$904$		0			0
$905$	71.3682	−	34.3691i	2.37236	−	1.14247i
$906$		0			0
$907$	17.5697	+	4.01017i	0.583392	+	0.133155i	0.504023	−	0.863690i	$-0.331853\pi$
$907$	17.5697	+	4.01017i	0.583392	+	0.133155i	0.0793684	+	0.996845i	$0.474710\pi$
$908$		0			0
$909$	−8.71278	−	18.0923i	−0.288985	−	0.600083i
$910$		0			0
$911$	7.10130	−	14.7460i	0.235276	−	0.488557i	−0.749583	−	0.661910i	$-0.769746\pi$
$911$	7.10130	−	14.7460i	0.235276	−	0.488557i	0.984860	+	0.173354i	$0.0554603\pi$
$912$		0			0
$913$			14.8569i			0.491691i
$914$		0			0
$915$	−2.24270	+	2.81226i	−0.0741415	+	0.0929705i
$916$		0			0
$917$	3.49988	+	11.7741i	0.115576	+	0.388814i
$918$		0			0
$919$	9.32697	−	19.3677i	0.307668	−	0.638880i	−0.688604	−	0.725137i	$-0.741776\pi$
$919$	9.32697	−	19.3677i	0.307668	−	0.638880i	0.996273	+	0.0862570i	$0.0274906\pi$
$920$		0			0
$921$	0.598068	−	0.749953i	0.0197070	−	0.0247118i
$922$		0			0
$923$	−8.53596	−	10.7038i	−0.280965	−	0.352319i
$924$		0			0
$925$	−39.0213	+	48.9311i	−1.28301	+	1.60884i
$926$		0			0
$927$	−4.38089	+	2.10972i	−0.143887	+	0.0692924i
$928$		0			0
$929$	7.08044	−	1.61606i	0.232302	−	0.0530214i	−0.104785	−	0.994495i	$-0.533415\pi$
$929$	7.08044	−	1.61606i	0.232302	−	0.0530214i	0.337087	+	0.941474i	$0.390558\pi$
$930$		0			0
$931$	−14.1871	−	38.4509i	−0.464963	−	1.26018i
$932$		0			0
$933$	−0.467588	−	2.04864i	−0.0153082	−	0.0670694i
$934$		0			0
$935$	1.98592	+	4.12381i	0.0649467	+	0.134863i
$936$		0			0
$937$	−24.7109	−	19.7063i	−0.807269	−	0.643776i	0.130339	−	0.991469i	$-0.458393\pi$
$937$	−24.7109	−	19.7063i	−0.807269	−	0.643776i	−0.937608	+	0.347694i	$0.886965\pi$
$938$		0			0
$939$	1.73261	−	1.38171i	0.0565414	−	0.0450903i
$940$		0			0
$941$	−41.3951	−	33.0115i	−1.34944	−	1.07614i	−0.989710	−	0.143087i	$-0.954297\pi$
$941$	−41.3951	−	33.0115i	−1.34944	−	1.07614i	−0.359731	−	0.933056i	$-0.617132\pi$
$942$		0			0
$943$	32.4423	+	15.6234i	1.05647	+	0.508768i
$944$		0			0
$945$	−2.91200	−	5.16546i	−0.0947273	−	0.168032i
$946$		0			0
$947$	3.28463	+	2.61941i	0.106736	+	0.0851192i	0.675404	−	0.737448i	$-0.263969\pi$
$947$	3.28463	+	2.61941i	0.106736	+	0.0851192i	−0.568667	+	0.822568i	$0.692541\pi$
$948$		0			0
$949$	7.55148			0.245132
$950$		0			0
$951$	−1.36786	−	0.658728i	−0.0443560	−	0.0213607i
$952$		0			0
$953$	44.6586	−	21.5064i	1.44663	−	0.696662i	0.464627	−	0.885507i	$-0.346188\pi$
$953$	44.6586	−	21.5064i	1.44663	−	0.696662i	0.982007	+	0.188844i	$0.0604742\pi$
$954$		0			0
$955$	−11.6893	+	51.2142i	−0.378257	+	1.65725i
$956$		0			0
$957$	0.0367526	+	0.0763175i	0.00118804	+	0.00246699i
$958$		0			0
$959$	3.28957	+	11.0666i	0.106226	+	0.357358i
$960$		0			0
$961$	60.5977			1.95477
$962$		0			0
$963$	−5.09892	+	10.5880i	−0.164310	+	0.341194i
$964$		0			0
$965$	−61.4637	−	14.0287i	−1.97859	−	0.451599i
$966$		0			0
$967$	−30.4158	+	6.94221i	−0.978106	+	0.223246i	−0.681552	−	0.731770i	$-0.738695\pi$
$967$	−30.4158	+	6.94221i	−0.978106	+	0.223246i	−0.296554	+	0.955016i	$0.595838\pi$
$968$		0			0
$969$	0.418148	−	0.0954395i	0.0134328	−	0.00306596i
$970$		0			0
$971$	−2.64310	+	11.5802i	−0.0848210	+	0.371625i	−0.999468	−	0.0326294i	$-0.989612\pi$
$971$	−2.64310	+	11.5802i	−0.0848210	+	0.371625i	0.914646	+	0.404255i	$0.132469\pi$
$972$		0			0
$973$	55.3788	−	3.57886i	1.77536	−	0.114733i
$974$		0			0
$975$	−1.39766	+	1.11459i	−0.0447608	+	0.0356956i
$976$		0			0
$977$	13.8450	+	17.3611i	0.442942	+	0.555431i	0.952316	−	0.305114i	$-0.0986945\pi$
$977$	13.8450	+	17.3611i	0.442942	+	0.555431i	−0.509374	+	0.860545i	$0.670123\pi$
$978$		0			0
$979$	18.1520			0.580141
$980$		0			0
$981$	−20.7338			−0.661980
$982$		0			0
$983$	11.5949	+	14.5395i	0.369819	+	0.463738i	0.931567	−	0.363570i	$-0.118442\pi$
$983$	11.5949	+	14.5395i	0.369819	+	0.463738i	−0.561748	+	0.827308i	$0.689871\pi$
$984$		0			0
$985$	57.3287	−	45.7181i	1.82664	−	1.45670i
$986$		0			0
$987$	−0.685873	−	2.30737i	−0.0218316	−	0.0734444i
$988$		0			0
$989$	−4.97656	+	21.8037i	−0.158245	+	0.693319i
$990$		0			0
$991$	3.33425	−	0.761021i	0.105916	−	0.0241746i	−0.169234	−	0.985576i	$-0.554129\pi$
$991$	3.33425	−	0.761021i	0.105916	−	0.0241746i	0.275150	+	0.961401i	$0.411272\pi$
$992$		0			0
$993$	−2.20290	+	0.502799i	−0.0699071	+	0.0159558i
$994$		0			0
$995$	27.3269	+	6.23718i	0.866320	+	0.197732i
$996$		0			0
$997$	10.2476	−	21.2793i	0.324543	−	0.673921i	−0.673313	−	0.739357i	$-0.735130\pi$
$997$	10.2476	−	21.2793i	0.324543	−	0.673921i	0.997857	+	0.0654361i	$0.0208438\pi$
$998$		0			0
$999$	2.66565			0.0843374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.b.111.9	✓	120
4.3	odd	2	inner	784.2.bb.b.111.12	yes	120
49.34	odd	14	inner	784.2.bb.b.671.12	yes	120
196.83	even	14	inner	784.2.bb.b.671.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.b.111.9	✓	120	1.1	even	1	trivial
784.2.bb.b.111.12	yes	120	4.3	odd	2	inner
784.2.bb.b.671.9	yes	120	196.83	even	14	inner
784.2.bb.b.671.12	yes	120	49.34	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0556550 - 0.0697892i) q^{3} +(-3.27604 + 2.61256i) q^{5} +(1.51276 - 2.17061i) q^{7} +(0.665790 - 2.91702i) q^{9} +O(q^{10})\)	\(q+(-0.0556550 - 0.0697892i) q^{3} +(-3.27604 + 2.61256i) q^{5} +(1.51276 - 2.17061i) q^{7} +(0.665790 - 2.91702i) q^{9} +(-1.29768 + 0.296186i) q^{11} +(1.55477 - 0.354867i) q^{13} +(0.364657 + 0.0832305i) q^{15} +(-0.356067 + 0.739382i) q^{17} +5.85496 q^{19} +(-0.235678 + 0.0152307i) q^{21} +(1.52265 + 3.16182i) q^{23} +(2.79440 - 12.2431i) q^{25} +(-0.481902 + 0.232072i) q^{27} +(0.642325 + 0.309328i) q^{29} +9.57067 q^{31} +(0.0928928 + 0.0740795i) q^{33} +(0.714960 + 11.0632i) q^{35} +(-4.49018 - 2.16236i) q^{37} +(-0.111297 - 0.0887562i) q^{39} +(8.02209 - 6.39740i) q^{41} +(4.98247 + 3.97338i) q^{43} +(5.43972 + 11.2957i) q^{45} +(2.26804 + 9.93692i) q^{47} +(-2.42309 - 6.56724i) q^{49} +(0.0714178 - 0.0163006i) q^{51} +(5.11790 - 2.46465i) q^{53} +(3.47744 - 4.36057i) q^{55} +(-0.325858 - 0.408613i) q^{57} +(2.50280 - 3.13841i) q^{59} +(-4.17258 + 8.66445i) q^{61} +(-5.32452 - 5.85793i) q^{63} +(-4.16639 + 5.22449i) q^{65} -12.7266i q^{67} +(0.135918 - 0.282236i) q^{69} +(-3.72479 - 7.73461i) q^{71} +(4.61647 + 1.05368i) q^{73} +(-1.00996 + 0.486369i) q^{75} +(-1.32017 + 3.26481i) q^{77} +3.67446i q^{79} +(-8.04417 - 3.87387i) q^{81} +(2.48373 - 10.8819i) q^{83} +(-0.765185 - 3.35249i) q^{85} +(-0.0141609 - 0.0620430i) q^{87} +(-13.2955 - 3.03460i) q^{89} +(1.58173 - 3.91163i) q^{91} +(-0.532656 - 0.667929i) q^{93} +(-19.1811 + 15.2964i) q^{95} +9.96407i q^{97} +3.98254i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 24 q^{9}+O(q^{10}) \) 120 * q - 24 * q^9	\( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) \) 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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