LMFDB - Embedded newform 136.3.t.b.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	136.41
Dual form			136.3.t.b.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26753 - 1.89699i) q^{3} +(1.74040 + 8.74956i) q^{5} +(-0.705386 + 3.54621i) q^{7} +(1.45221 + 3.50595i) q^{9} +O(q^{10})$	\(q+(1.26753 - 1.89699i) q^{3} +(1.74040 + 8.74956i) q^{5} +(-0.705386 + 3.54621i) q^{7} +(1.45221 + 3.50595i) q^{9} +(4.28632 - 2.86402i) q^{11} +(-1.13715 + 1.13715i) q^{13} +(18.8038 + 7.78880i) q^{15} +(5.25441 - 16.1676i) q^{17} +(7.58919 - 18.3219i) q^{19} +(5.83303 + 5.83303i) q^{21} +(9.73350 + 14.5672i) q^{23} +(-50.4289 + 20.8883i) q^{25} +(28.6303 + 5.69492i) q^{27} +(-12.2375 + 2.43420i) q^{29} +(-16.8775 - 11.2772i) q^{31} -11.7613i q^{33} -32.2555 q^{35} +(-22.8156 + 34.1459i) q^{37} +(0.715793 + 3.59853i) q^{39} +(4.71432 - 23.7005i) q^{41} +(-28.2260 - 68.1437i) q^{43} +(-28.1481 + 18.8079i) q^{45} +(40.4472 - 40.4472i) q^{47} +(33.1920 + 13.7486i) q^{49} +(-24.0096 - 30.4604i) q^{51} +(38.2089 - 92.2445i) q^{53} +(32.5188 + 32.5188i) q^{55} +(-25.1370 - 37.6202i) q^{57} +(-104.199 + 43.1605i) q^{59} +(-18.6460 - 3.70891i) q^{61} +(-13.4572 + 2.67680i) q^{63} +(-11.9287 - 7.97048i) q^{65} +107.703i q^{67} +39.9713 q^{69} +(39.9882 - 59.8466i) q^{71} +(12.8420 + 64.5610i) q^{73} +(-24.2951 + 122.139i) q^{75} +(7.13294 + 17.2204i) q^{77} +(25.3591 - 16.9444i) q^{79} +(22.9429 - 22.9429i) q^{81} +(-68.6449 - 28.4336i) q^{83} +(150.604 + 17.8358i) q^{85} +(-10.8938 + 26.2999i) q^{87} +(22.9153 + 22.9153i) q^{89} +(-3.23045 - 4.83471i) q^{91} +(-42.7854 + 17.7223i) q^{93} +(173.517 + 34.5147i) q^{95} +(157.404 - 31.3096i) q^{97} +(16.2657 + 10.8684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

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
$3$	1.26753	−	1.89699i	0.422509	−	0.632330i	−0.557759	−	0.830003i	$-0.688339\pi$
$3$	1.26753	−	1.89699i	0.422509	−	0.632330i	0.980268	+	0.197673i	$0.0633386\pi$
$4$		0			0
$5$	1.74040	+	8.74956i	0.348079	+	1.74991i	0.617200	+	0.786806i	$0.288267\pi$
$5$	1.74040	+	8.74956i	0.348079	+	1.74991i	−0.269121	+	0.963106i	$0.586733\pi$
$6$		0			0
$7$	−0.705386	+	3.54621i	−0.100769	+	0.506602i	0.897127	+	0.441773i	$0.145650\pi$
$7$	−0.705386	+	3.54621i	−0.100769	+	0.506602i	−0.997896	+	0.0648292i	$0.979350\pi$
$8$		0			0
$9$	1.45221	+	3.50595i	0.161357	+	0.389549i
$10$		0			0
$11$	4.28632	−	2.86402i	0.389665	−	0.260366i	−0.345270	−	0.938503i	$-0.612213\pi$
$11$	4.28632	−	2.86402i	0.389665	−	0.260366i	0.734935	+	0.678138i	$0.237213\pi$
$12$		0			0
$13$	−1.13715	+	1.13715i	−0.0874732	+	0.0874732i	−0.749489	−	0.662016i	$-0.769701\pi$
$13$	−1.13715	+	1.13715i	−0.0874732	+	0.0874732i	0.662016	+	0.749489i	$0.269701\pi$
$14$		0			0
$15$	18.8038	+	7.78880i	1.25359	+	0.519253i
$16$		0			0
$17$	5.25441	−	16.1676i	0.309083	−	0.951035i
$17$	5.25441	−	16.1676i	0.309083	−	0.951035i
$18$		0			0
$19$	7.58919	−	18.3219i	0.399431	−	0.964312i	−0.588370	−	0.808592i	$-0.700230\pi$
$19$	7.58919	−	18.3219i	0.399431	−	0.964312i	0.987801	−	0.155721i	$-0.0497699\pi$
$20$		0			0
$21$	5.83303	+	5.83303i	0.277763	+	0.277763i
$22$		0			0
$23$	9.73350	+	14.5672i	0.423195	+	0.633357i	0.980400	−	0.197019i	$-0.0631260\pi$
$23$	9.73350	+	14.5672i	0.423195	+	0.633357i	−0.557204	+	0.830375i	$0.688126\pi$
$24$		0			0
$25$	−50.4289	+	20.8883i	−2.01715	+	0.835533i
$26$		0			0
$27$	28.6303	+	5.69492i	1.06038	+	0.210923i
$28$		0			0
$29$	−12.2375	+	2.43420i	−0.421984	+	0.0839379i	−0.401515	−	0.915853i	$-0.631516\pi$
$29$	−12.2375	+	2.43420i	−0.421984	+	0.0839379i	−0.0204696	+	0.999790i	$0.506516\pi$
$30$		0			0
$31$	−16.8775	−	11.2772i	−0.544436	−	0.363780i	0.252734	−	0.967536i	$-0.418670\pi$
$31$	−16.8775	−	11.2772i	−0.544436	−	0.363780i	−0.797169	+	0.603756i	$0.793670\pi$
$32$		0			0
$33$		−	11.7613i		−	0.356404i
$34$		0			0
$35$	−32.2555			−0.921585
$36$		0			0
$37$	−22.8156	+	34.1459i	−0.616637	+	0.922863i	−1.00000		0.000735369i	$-0.999766\pi$
$37$	−22.8156	+	34.1459i	−0.616637	+	0.922863i	0.383363	+	0.923598i	$0.374766\pi$
$38$		0			0
$39$	0.715793	+	3.59853i	0.0183537	+	0.0922701i
$40$		0			0
$41$	4.71432	−	23.7005i	0.114983	−	0.578060i	−0.879739	−	0.475457i	$-0.842283\pi$
$41$	4.71432	−	23.7005i	0.114983	−	0.578060i	0.994722	−	0.102603i	$-0.0327172\pi$
$42$		0			0
$43$	−28.2260	−	68.1437i	−0.656419	−	1.58474i	−0.803295	−	0.595582i	$-0.796922\pi$
$43$	−28.2260	−	68.1437i	−0.656419	−	1.58474i	0.146875	−	0.989155i	$-0.453078\pi$
$44$		0			0
$45$	−28.1481	+	18.8079i	−0.625513	+	0.417954i
$46$		0			0
$47$	40.4472	−	40.4472i	0.860579	−	0.860579i	−0.130826	−	0.991405i	$-0.541763\pi$
$47$	40.4472	−	40.4472i	0.860579	−	0.860579i	0.991405	+	0.130826i	$0.0417630\pi$
$48$		0			0
$49$	33.1920	+	13.7486i	0.677388	+	0.280583i
$50$		0			0
$51$	−24.0096	−	30.4604i	−0.470777	−	0.597263i
$52$		0			0
$53$	38.2089	−	92.2445i	0.720923	−	1.74046i	0.0502164	−	0.998738i	$-0.484009\pi$
$53$	38.2089	−	92.2445i	0.720923	−	1.74046i	0.670706	−	0.741723i	$-0.265991\pi$
$54$		0			0
$55$	32.5188	+	32.5188i	0.591252	+	0.591252i
$56$		0			0
$57$	−25.1370	−	37.6202i	−0.441000	−	0.660003i
$58$		0			0
$59$	−104.199	+	43.1605i	−1.76608	+	0.731534i	−0.770518	+	0.637418i	$0.780002\pi$
$59$	−104.199	+	43.1605i	−1.76608	+	0.731534i	−0.995561	+	0.0941155i	$0.969998\pi$
$60$		0			0
$61$	−18.6460	−	3.70891i	−0.305671	−	0.0608018i	0.0398714	−	0.999205i	$-0.487305\pi$
$61$	−18.6460	−	3.70891i	−0.305671	−	0.0608018i	−0.345543	+	0.938403i	$0.612305\pi$
$62$		0			0
$63$	−13.4572	+	2.67680i	−0.213606	+	0.0424889i
$64$		0			0
$65$	−11.9287	−	7.97048i	−0.183518	−	0.122623i
$66$		0			0
$67$			107.703i			1.60751i	0.594958	+	0.803757i	$0.297169\pi$
$67$			107.703i			1.60751i	−0.594958	+	0.803757i	$0.702831\pi$
$68$		0			0
$69$	39.9713			0.579294
$70$		0			0
$71$	39.9882	−	59.8466i	0.563214	−	0.842910i	−0.435134	−	0.900366i	$-0.643299\pi$
$71$	39.9882	−	59.8466i	0.563214	−	0.842910i	0.998348	+	0.0574562i	$0.0182990\pi$
$72$		0			0
$73$	12.8420	+	64.5610i	0.175918	+	0.884398i	0.963402	+	0.268063i	$0.0863834\pi$
$73$	12.8420	+	64.5610i	0.175918	+	0.884398i	−0.787484	+	0.616335i	$0.788617\pi$
$74$		0			0
$75$	−24.2951	+	122.139i	−0.323934	+	1.62853i
$76$		0			0
$77$	7.13294	+	17.2204i	0.0926355	+	0.223642i
$78$		0			0
$79$	25.3591	−	16.9444i	0.321001	−	0.214486i	−0.384621	−	0.923075i	$-0.625668\pi$
$79$	25.3591	−	16.9444i	0.321001	−	0.214486i	0.705622	+	0.708589i	$0.250668\pi$
$80$		0			0
$81$	22.9429	−	22.9429i	0.283246	−	0.283246i
$82$		0			0
$83$	−68.6449	−	28.4336i	−0.827046	−	0.342574i	−0.0713136	−	0.997454i	$-0.522719\pi$
$83$	−68.6449	−	28.4336i	−0.827046	−	0.342574i	−0.755733	+	0.654880i	$0.772719\pi$
$84$		0			0
$85$	150.604	+	17.8358i	1.77181	+	0.209833i
$86$		0			0
$87$	−10.8938	+	26.2999i	−0.125216	+	0.302298i
$88$		0			0
$89$	22.9153	+	22.9153i	0.257475	+	0.257475i	0.824026	−	0.566551i	$-0.191723\pi$
$89$	22.9153	+	22.9153i	0.257475	+	0.257475i	−0.566551	+	0.824026i	$0.691723\pi$
$90$		0			0
$91$	−3.23045	−	4.83471i	−0.0354995	−	0.0531287i
$92$		0			0
$93$	−42.7854	+	17.7223i	−0.460058	+	0.190562i
$94$		0			0
$95$	173.517	+	34.5147i	1.82650	+	0.363313i
$96$		0			0
$97$	157.404	−	31.3096i	1.62272	−	0.322779i	0.701754	−	0.712419i	$-0.252400\pi$
$97$	157.404	−	31.3096i	1.62272	−	0.322779i	0.920967	+	0.389640i	$0.127400\pi$
$98$		0			0
$99$	16.2657	+	10.8684i	0.164300	+	0.109782i
$100$		0			0
$101$		−	13.6406i		−	0.135055i	−0.997717	−	0.0675276i	$-0.978489\pi$
$101$		−	13.6406i		−	0.135055i	0.997717	−	0.0675276i	$-0.0215111\pi$
$102$		0			0
$103$	−66.2973			−0.643663			−0.321831	−	0.946797i	$-0.604298\pi$
$103$	−66.2973			−0.643663			−0.321831	+	0.946797i	$0.604298\pi$
$104$		0			0
$105$	−40.8847	+	61.1883i	−0.389378	+	0.582745i
$106$		0			0
$107$	−41.1050	−	206.649i	−0.384159	−	1.93130i	−0.363723	−	0.931507i	$-0.618494\pi$
$107$	−41.1050	−	206.649i	−0.384159	−	1.93130i	−0.0204366	−	0.999791i	$-0.506506\pi$
$108$		0			0
$109$	−5.69287	+	28.6200i	−0.0522281	+	0.262569i	−0.998073	−	0.0620504i	$-0.980236\pi$
$109$	−5.69287	+	28.6200i	−0.0522281	+	0.262569i	0.945845	+	0.324619i	$0.105236\pi$
$110$		0			0
$111$	35.8551	+	86.5618i	0.323019	+	0.779836i
$112$		0			0
$113$	56.7772	−	37.9373i	0.502453	−	0.335728i	−0.278377	−	0.960472i	$-0.589796\pi$
$113$	56.7772	−	37.9373i	0.502453	−	0.335728i	0.780830	+	0.624744i	$0.214796\pi$
$114$		0			0
$115$	−110.517	+	110.517i	−0.961013	+	0.961013i
$116$		0			0
$117$	−5.63817	−	2.33541i	−0.0481895	−	0.0199608i
$118$		0			0
$119$	53.6274	+	30.0377i	0.450650	+	0.252417i
$120$		0			0
$121$	−36.1348	+	87.2372i	−0.298635	+	0.720969i
$122$		0			0
$123$	−38.9840	−	38.9840i	−0.316943	−	0.316943i
$124$		0			0
$125$	−146.624	−	219.438i	−1.17299	−	1.75551i
$126$		0			0
$127$	35.5091	−	14.7083i	0.279599	−	0.115814i	−0.238477	−	0.971148i	$-0.576648\pi$
$127$	35.5091	−	14.7083i	0.279599	−	0.115814i	0.518076	+	0.855334i	$0.326648\pi$
$128$		0			0
$129$	−165.045	−	32.8295i	−1.27942	−	0.254492i
$130$		0			0
$131$	45.7484	−	9.09992i	0.349224	−	0.0694650i	−0.0173615	−	0.999849i	$-0.505527\pi$
$131$	45.7484	−	9.09992i	0.349224	−	0.0694650i	0.366586	+	0.930384i	$0.380527\pi$
$132$		0			0
$133$	59.6202	+	39.8369i	0.448272	+	0.299526i
$134$		0			0
$135$			260.414i			1.92899i
$136$		0			0
$137$	126.697			0.924795			0.462398	−	0.886673i	$-0.346989\pi$
$137$	126.697			0.924795			0.462398	+	0.886673i	$0.346989\pi$
$138$		0			0
$139$	29.9346	−	44.8003i	0.215357	−	0.322304i	−0.708025	−	0.706187i	$-0.750414\pi$
$139$	29.9346	−	44.8003i	0.215357	−	0.322304i	0.923382	+	0.383883i	$0.125414\pi$
$140$		0			0
$141$	−25.4600	−	127.996i	−0.180567	−	0.907772i
$142$		0			0
$143$	−1.61736	+	8.13102i	−0.0113102	+	0.0568603i
$144$		0			0
$145$	−42.5963	−	102.837i	−0.293768	−	0.709218i
$146$		0			0
$147$	68.1527	−	45.5382i	0.463624	−	0.309784i
$148$		0			0
$149$	−117.059	+	117.059i	−0.785629	+	0.785629i	−0.980774	−	0.195146i	$-0.937482\pi$
$149$	−117.059	+	117.059i	−0.785629	+	0.785629i	0.195146	+	0.980774i	$0.437482\pi$
$150$		0			0
$151$	−176.509	−	73.1124i	−1.16893	−	0.484188i	−0.288093	−	0.957602i	$-0.593021\pi$
$151$	−176.509	−	73.1124i	−1.16893	−	0.484188i	−0.880840	+	0.473414i	$0.843021\pi$
$152$		0			0
$153$	64.3132	−	5.05707i	0.420348	−	0.0330527i
$154$		0			0
$155$	69.2969	−	167.298i	0.447077	−	1.07934i
$156$		0			0
$157$	−30.1867	−	30.1867i	−0.192272	−	0.192272i	0.604405	−	0.796677i	$-0.293411\pi$
$157$	−30.1867	−	30.1867i	−0.192272	−	0.192272i	−0.796677	+	0.604405i	$0.793411\pi$
$158$		0			0
$159$	−126.556	−	189.404i	−0.795949	−	1.19122i
$160$		0			0
$161$	−58.5243	+	24.2416i	−0.363505	+	0.150569i
$162$		0			0
$163$	−187.035	−	37.2036i	−1.14745	−	0.228243i	−0.415497	−	0.909594i	$-0.636392\pi$
$163$	−187.035	−	37.2036i	−1.14745	−	0.228243i	−0.731956	+	0.681352i	$0.761392\pi$
$164$		0			0
$165$	102.906	−	20.4694i	0.623675	−	0.124057i
$166$		0			0
$167$	196.151	+	131.064i	1.17456	+	0.784815i	0.980566	−	0.196188i	$-0.0628562\pi$
$167$	196.151	+	131.064i	1.17456	+	0.784815i	0.193993	+	0.981003i	$0.437856\pi$
$168$		0			0
$169$			166.414i			0.984697i
$170$		0			0
$171$	75.2568			0.440098
$172$		0			0
$173$	−38.3216	+	57.3524i	−0.221512	+	0.331517i	−0.925536	−	0.378660i	$-0.876385\pi$
$173$	−38.3216	+	57.3524i	−0.221512	+	0.331517i	0.704024	+	0.710177i	$0.251385\pi$
$174$		0			0
$175$	−38.5026	−	193.566i	−0.220015	−	1.10609i
$176$		0			0
$177$	−50.1997	+	252.371i	−0.283614	+	1.42582i
$178$		0			0
$179$	−52.8567	−	127.607i	−0.295289	−	0.712891i	−0.999994	−	0.00339050i	$-0.998921\pi$
$179$	−52.8567	−	127.607i	−0.295289	−	0.712891i	0.704705	−	0.709500i	$-0.251079\pi$
$180$		0			0
$181$	−155.667	+	104.013i	−0.860037	+	0.574658i	−0.905518	−	0.424307i	$-0.860518\pi$
$181$	−155.667	+	104.013i	−0.860037	+	0.574658i	0.0454816	+	0.998965i	$0.485518\pi$
$182$		0			0
$183$	−30.6700	+	30.6700i	−0.167596	+	0.167596i
$184$		0			0
$185$	−338.470	−	140.199i	−1.82957	−	0.757831i
$186$		0			0
$187$	−23.7823	−	84.3482i	−0.127178	−	0.451060i
$188$		0			0
$189$	−40.3908	+	97.5121i	−0.213708	+	0.515937i
$190$		0			0
$191$	82.5942	+	82.5942i	0.432430	+	0.432430i	0.889454	−	0.457024i	$-0.151085\pi$
$191$	82.5942	+	82.5942i	0.432430	+	0.432430i	−0.457024	+	0.889454i	$0.651085\pi$
$192$		0			0
$193$	−119.039	−	178.155i	−0.616783	−	0.923081i	0.383217	−	0.923658i	$-0.374816\pi$
$193$	−119.039	−	178.155i	−0.616783	−	0.923081i	−1.00000		0.000577513i	$0.999816\pi$
$194$		0			0
$195$	−30.2398	+	12.5258i	−0.155076	+	0.0642346i
$196$		0			0
$197$	157.761	+	31.3807i	0.800819	+	0.159293i	0.578501	−	0.815681i	$-0.303638\pi$
$197$	157.761	+	31.3807i	0.800819	+	0.159293i	0.222318	+	0.974974i	$0.428638\pi$
$198$		0			0
$199$	−45.2868	+	9.00810i	−0.227572	+	0.0452669i	−0.307559	−	0.951529i	$-0.599512\pi$
$199$	−45.2868	+	9.00810i	−0.227572	+	0.0452669i	0.0799870	+	0.996796i	$0.474512\pi$
$200$		0			0
$201$	204.312	+	136.517i	1.01648	+	0.679189i
$202$		0			0
$203$		−	45.1140i		−	0.222236i
$204$		0			0
$205$	215.573			1.05158
$206$		0			0
$207$	−36.9367	+	55.2797i	−0.178438	+	0.267052i
$208$		0			0
$209$	−19.9448	−	100.269i	−0.0954296	−	0.479757i
$210$		0			0
$211$	9.63067	−	48.4167i	0.0456430	−	0.229463i	−0.951230	−	0.308482i	$-0.900179\pi$
$211$	9.63067	−	48.4167i	0.0456430	−	0.229463i	0.996873	+	0.0790195i	$0.0251789\pi$
$212$		0			0
$213$	−62.8421	−	151.714i	−0.295034	−	0.712274i
$214$		0			0
$215$	547.103	−	365.562i	2.54466	−	1.70029i
$216$		0			0
$217$	51.8965	−	51.8965i	0.239154	−	0.239154i
$218$		0			0
$219$	138.749	+	57.4718i	0.633558	+	0.262428i
$220$		0			0
$221$	12.4099	+	24.3601i	0.0561536	+	0.110227i
$222$		0			0
$223$	−48.6229	+	117.386i	−0.218040	+	0.526395i	−0.994616	−	0.103629i	$-0.966955\pi$
$223$	−48.6229	+	117.386i	−0.218040	+	0.526395i	0.776576	+	0.630023i	$0.216955\pi$
$224$		0			0
$225$	−146.467	−	146.467i	−0.650963	−	0.650963i
$226$		0			0
$227$	224.443	+	335.903i	0.988737	+	1.47975i	0.873745	+	0.486384i	$0.161684\pi$
$227$	224.443	+	335.903i	0.988737	+	1.47975i	0.114992	+	0.993366i	$0.463316\pi$
$228$		0			0
$229$	−180.117	+	74.6069i	−0.786537	+	0.325794i	−0.739550	−	0.673101i	$-0.764962\pi$
$229$	−180.117	+	74.6069i	−0.786537	+	0.325794i	−0.0469867	+	0.998896i	$0.514962\pi$
$230$		0			0
$231$	41.7082	+	8.29627i	0.180555	+	0.0359146i
$232$		0			0
$233$	174.485	−	34.7072i	0.748862	−	0.148958i	0.194117	−	0.980978i	$-0.437816\pi$
$233$	174.485	−	34.7072i	0.748862	−	0.148958i	0.554745	+	0.832020i	$0.312816\pi$
$234$		0			0
$235$	424.290	+	283.501i	1.80549	+	1.20639i
$236$		0			0
$237$		−	69.5834i		−	0.293601i
$238$		0			0
$239$	−175.955			−0.736211			−0.368106	−	0.929784i	$-0.619994\pi$
$239$	−175.955			−0.736211			−0.368106	+	0.929784i	$0.619994\pi$
$240$		0			0
$241$	−29.0872	+	43.5321i	−0.120694	+	0.180631i	−0.886897	−	0.461968i	$-0.847144\pi$
$241$	−29.0872	+	43.5321i	−0.120694	+	0.180631i	0.766203	+	0.642599i	$0.222144\pi$
$242$		0			0
$243$	36.8126	+	185.070i	0.151492	+	0.761603i
$244$		0			0
$245$	−62.5269	+	314.344i	−0.255212	+	1.28304i
$246$		0			0
$247$	12.2048	+	29.4649i	0.0494120	+	0.119291i
$248$		0			0
$249$	−140.948	+	94.1781i	−0.566054	+	0.378225i
$250$		0			0
$251$	−309.942	+	309.942i	−1.23483	+	1.23483i	−0.272744	+	0.962087i	$0.587931\pi$
$251$	−309.942	+	309.942i	−1.23483	+	1.23483i	−0.962087	+	0.272744i	$0.912069\pi$
$252$		0			0
$253$	83.4417	+	34.5627i	0.329809	+	0.136611i
$254$		0			0
$255$	224.729	−	263.087i	0.881291	−	1.03171i
$256$		0			0
$257$	−42.1280	+	101.706i	−0.163922	+	0.395743i	−0.984402	−	0.175932i	$-0.943706\pi$
$257$	−42.1280	+	101.706i	−0.163922	+	0.395743i	0.820480	+	0.571675i	$0.193706\pi$
$258$		0			0
$259$	−104.995	−	104.995i	−0.405386	−	0.405386i
$260$		0			0
$261$	−26.3056	−	39.3692i	−0.100788	−	0.150840i
$262$		0			0
$263$	−454.012	+	188.058i	−1.72628	+	0.715050i	−0.726677	+	0.686979i	$0.758936\pi$
$263$	−454.012	+	188.058i	−1.72628	+	0.715050i	−0.999606	+	0.0280709i	$0.991064\pi$
$264$		0			0
$265$	873.597	+	173.769i	3.29659	+	0.655733i
$266$		0			0
$267$	72.5158	−	14.4243i	0.271595	−	0.0540235i
$268$		0			0
$269$	−258.825	−	172.941i	−0.962173	−	0.642904i	−0.0279564	−	0.999609i	$-0.508900\pi$
$269$	−258.825	−	172.941i	−0.962173	−	0.642904i	−0.934217	+	0.356705i	$0.883900\pi$
$270$		0			0
$271$			171.813i			0.633996i	0.948426	+	0.316998i	$0.102675\pi$
$271$			171.813i			0.633996i	−0.948426	+	0.316998i	$0.897325\pi$
$272$		0			0
$273$	−13.2661			−0.0485937
$274$		0			0
$275$	−156.329	+	233.963i	−0.568470	+	0.850776i
$276$		0			0
$277$	89.4273	+	449.582i	0.322842	+	1.62304i	0.712217	+	0.701959i	$0.247691\pi$
$277$	89.4273	+	449.582i	0.322842	+	1.62304i	−0.389375	+	0.921079i	$0.627309\pi$
$278$		0			0
$279$	15.0275	−	75.5485i	0.0538621	−	0.270783i
$280$		0			0
$281$	−154.330	−	372.587i	−0.549219	−	1.32593i	−0.918061	−	0.396439i	$-0.870246\pi$
$281$	−154.330	−	372.587i	−0.549219	−	1.32593i	0.368842	−	0.929492i	$-0.379754\pi$
$282$		0			0
$283$	−27.8111	+	18.5828i	−0.0982725	+	0.0656636i	−0.603736	−	0.797185i	$-0.706322\pi$
$283$	−27.8111	+	18.5828i	−0.0982725	+	0.0656636i	0.505463	+	0.862848i	$0.331322\pi$
$284$		0			0
$285$	285.412	−	285.412i	1.00144	−	1.00144i
$286$		0			0
$287$	80.7215	+	33.4359i	0.281260	+	0.116502i
$288$		0			0
$289$	−233.782	−	169.902i	−0.808935	−	0.587897i
$290$		0			0
$291$	140.120	−	338.279i	0.481512	−	1.16247i
$292$		0			0
$293$	262.898	+	262.898i	0.897262	+	0.897262i	0.995193	−	0.0979314i	$-0.0312226\pi$
$293$	262.898	+	262.898i	0.897262	+	0.897262i	−0.0979314	+	0.995193i	$0.531223\pi$
$294$		0			0
$295$	−558.982	−	836.576i	−1.89486	−	2.83585i
$296$		0			0
$297$	139.029	−	57.5877i	0.468111	−	0.193898i
$298$		0			0
$299$	−27.6336	−	5.49666i	−0.0924200	−	0.0183835i
$300$		0			0
$301$	261.562	−	52.0280i	0.868978	−	0.172850i
$302$		0			0
$303$	−25.8760	−	17.2898i	−0.0853994	−	0.0570621i
$304$		0			0
$305$		−	169.599i		−	0.556062i
$306$		0			0
$307$	306.941			0.999808			0.499904	−	0.866081i	$-0.333369\pi$
$307$	306.941			0.999808			0.499904	+	0.866081i	$0.333369\pi$
$308$		0			0
$309$	−84.0336	+	125.765i	−0.271953	+	0.407007i
$310$		0			0
$311$	34.9650	+	175.781i	0.112428	+	0.565213i	0.995402	+	0.0957903i	$0.0305378\pi$
$311$	34.9650	+	175.781i	0.112428	+	0.565213i	−0.882974	+	0.469422i	$0.844462\pi$
$312$		0			0
$313$	−7.40968	+	37.2510i	−0.0236731	+	0.119013i	−0.990815	−	0.135225i	$-0.956824\pi$
$313$	−7.40968	+	37.2510i	−0.0236731	+	0.119013i	0.967142	+	0.254237i	$0.0818244\pi$
$314$		0			0
$315$	−46.8417	−	113.086i	−0.148704	−	0.359003i
$316$		0			0
$317$	389.093	−	259.984i	1.22742	−	0.820138i	0.238876	−	0.971050i	$-0.423221\pi$
$317$	389.093	−	259.984i	1.22742	−	0.820138i	0.988547	+	0.150912i	$0.0482211\pi$
$318$		0			0
$319$	−45.4824	+	45.4824i	−0.142578	+	0.142578i
$320$		0			0
$321$	−444.112	−	183.957i	−1.38353	−	0.573076i
$322$		0			0
$323$	−256.345	−	218.970i	−0.793638	−	0.677926i
$324$		0			0
$325$	33.5921	−	81.0984i	0.103360	−	0.249534i
$326$		0			0
$327$	47.0759	+	47.0759i	0.143963	+	0.143963i
$328$		0			0
$329$	114.904	+	171.965i	0.349251	+	0.522691i
$330$		0			0
$331$	−311.036	+	128.835i	−0.939686	+	0.389231i	−0.799345	−	0.600873i	$-0.794820\pi$
$331$	−311.036	+	128.835i	−0.939686	+	0.389231i	−0.140341	+	0.990103i	$0.544820\pi$
$332$		0			0
$333$	−152.847	−	30.4031i	−0.458999	−	0.0913006i
$334$		0			0
$335$	−942.357	+	187.447i	−2.81301	+	0.559542i
$336$		0			0
$337$	−175.720	−	117.412i	−0.521424	−	0.348405i	0.266840	−	0.963741i	$-0.414020\pi$
$337$	−175.720	−	117.412i	−0.521424	−	0.348405i	−0.788265	+	0.615336i	$0.789020\pi$
$338$		0			0
$339$		−	155.792i		−	0.459564i
$340$		0			0
$341$	−104.640			−0.306863
$342$		0			0
$343$	−170.598	+	255.318i	−0.497371	+	0.744369i
$344$		0			0
$345$	69.5659	+	349.731i	0.201640	+	1.01371i
$346$		0			0
$347$	−6.02739	+	30.3017i	−0.0173700	+	0.0873249i	−0.988498	−	0.151234i	$-0.951675\pi$
$347$	−6.02739	+	30.3017i	−0.0173700	+	0.0873249i	0.971128	+	0.238559i	$0.0766752\pi$
$348$		0			0
$349$	−173.433	−	418.703i	−0.496942	−	1.19972i	−0.951123	−	0.308814i	$-0.900068\pi$
$349$	−173.433	−	418.703i	−0.496942	−	1.19972i	0.454181	−	0.890909i	$-0.349932\pi$
$350$		0			0
$351$	−39.0330	+	26.0810i	−0.111205	+	0.0743049i
$352$		0			0
$353$	182.033	−	182.033i	0.515675	−	0.515675i	−0.400585	−	0.916260i	$-0.631193\pi$
$353$	182.033	−	182.033i	0.515675	−	0.515675i	0.916260	+	0.400585i	$0.131193\pi$
$354$		0			0
$355$	593.227	+	245.723i	1.67106	+	0.692176i
$356$		0			0
$357$	124.955	−	63.6570i	0.350015	−	0.178311i
$358$		0			0
$359$	−59.7672	+	144.291i	−0.166483	+	0.401924i	−0.984999	−	0.172558i	$-0.944797\pi$
$359$	−59.7672	+	144.291i	−0.166483	+	0.401924i	0.818517	+	0.574483i	$0.194797\pi$
$360$		0			0
$361$	−22.8319	−	22.8319i	−0.0632463	−	0.0632463i
$362$		0			0
$363$	119.686	+	179.123i	0.329714	+	0.493452i
$364$		0			0
$365$	−542.531	+	224.724i	−1.48639	+	0.615681i
$366$		0			0
$367$	−243.488	−	48.4329i	−0.663456	−	0.131970i	−0.148136	−	0.988967i	$-0.547327\pi$
$367$	−243.488	−	48.4329i	−0.663456	−	0.131970i	−0.515321	+	0.856997i	$0.672327\pi$
$368$		0			0
$369$	89.9387	−	17.8899i	0.243736	−	0.0484822i
$370$		0			0
$371$	300.167	+	200.565i	0.809074	+	0.540606i
$372$		0			0
$373$		−	249.884i		−	0.669931i	−0.942230	−	0.334965i	$-0.891275\pi$
$373$		−	249.884i		−	0.669931i	0.942230	−	0.334965i	$-0.108725\pi$
$374$		0			0
$375$	−602.122			−1.60566
$376$		0			0
$377$	11.1479	−	16.6840i	0.0295700	−	0.0442546i
$378$		0			0
$379$	−97.2322	−	488.819i	−0.256549	−	1.28976i	−0.867240	−	0.497891i	$-0.834108\pi$
$379$	−97.2322	−	488.819i	−0.256549	−	1.28976i	0.610690	−	0.791870i	$-0.290892\pi$
$380$		0			0
$381$	17.1072	−	86.0035i	0.0449007	−	0.225731i
$382$		0			0
$383$	190.333	+	459.506i	0.496954	+	1.19975i	0.951116	+	0.308834i	$0.0999389\pi$
$383$	190.333	+	459.506i	0.496954	+	1.19975i	−0.454162	+	0.890919i	$0.650061\pi$
$384$		0			0
$385$	−138.257	+	92.3804i	−0.359109	+	0.239949i
$386$		0			0
$387$	197.918	−	197.918i	0.511416	−	0.511416i
$388$		0			0
$389$	−440.861	−	182.611i	−1.13332	−	0.469436i	−0.264411	−	0.964410i	$-0.585178\pi$
$389$	−440.861	−	182.611i	−1.13332	−	0.469436i	−0.868908	+	0.494974i	$0.835178\pi$
$390$		0			0
$391$	286.661	−	80.8252i	0.733147	−	0.206714i
$392$		0			0
$393$	40.7249	−	98.3186i	0.103626	−	0.250175i
$394$		0			0
$395$	192.391	+	192.391i	0.487066	+	0.487066i
$396$		0			0
$397$	−1.86118	−	2.78545i	−0.00468810	−	0.00701624i	0.829118	−	0.559073i	$-0.188843\pi$
$397$	−1.86118	−	2.78545i	−0.00468810	−	0.00701624i	−0.833806	+	0.552057i	$0.813843\pi$
$398$		0			0
$399$	151.140	−	62.6044i	0.378798	−	0.156903i
$400$		0			0
$401$	443.648	+	88.2471i	1.10635	+	0.220068i	0.714276	−	0.699864i	$-0.246756\pi$
$401$	443.648	+	88.2471i	1.10635	+	0.220068i	0.392079	+	0.919932i	$0.371756\pi$
$402$		0			0
$403$	32.0162	−	6.36841i	0.0794446	−	0.0158025i
$404$		0			0
$405$	240.670	+	160.811i	0.594247	+	0.397063i
$406$		0			0
$407$			211.704i			0.520158i
$408$		0			0
$409$	−91.2430			−0.223088			−0.111544	−	0.993759i	$-0.535580\pi$
$409$	−91.2430			−0.223088			−0.111544	+	0.993759i	$0.535580\pi$
$410$		0			0
$411$	160.592	−	240.343i	0.390734	−	0.584775i
$412$		0			0
$413$	−79.5561	−	399.956i	−0.192630	−	0.968415i
$414$		0			0
$415$	129.313	−	650.098i	0.311597	−	1.56650i
$416$		0			0
$417$	−47.0427	−	113.571i	−0.112812	−	0.272353i
$418$		0			0
$419$	101.451	−	67.7871i	0.242126	−	0.161783i	−0.428587	−	0.903501i	$-0.640988\pi$
$419$	101.451	−	67.7871i	0.242126	−	0.161783i	0.670713	+	0.741717i	$0.265988\pi$
$420$		0			0
$421$	83.5906	−	83.5906i	0.198552	−	0.198552i	−0.600827	−	0.799379i	$-0.705162\pi$
$421$	83.5906	−	83.5906i	0.198552	−	0.198552i	0.799379	+	0.600827i	$0.205162\pi$
$422$		0			0
$423$	200.544	+	83.0679i	0.474098	+	0.196378i
$424$		0			0
$425$	72.7400	+	925.069i	0.171153	+	2.17663i
$426$		0			0
$427$	26.3052	−	63.5063i	0.0616047	−	0.148727i
$428$		0			0
$429$	13.3744	+	13.3744i	0.0311758	+	0.0311758i
$430$		0			0
$431$	201.545	+	301.633i	0.467621	+	0.699845i	0.988063	−	0.154053i	$-0.0492326\pi$
$431$	201.545	+	301.633i	0.467621	+	0.699845i	−0.520441	+	0.853897i	$0.674233\pi$
$432$		0			0
$433$	−9.92441	+	4.11082i	−0.0229201	+	0.00949382i	−0.394114	−	0.919062i	$-0.628949\pi$
$433$	−9.92441	+	4.11082i	−0.0229201	+	0.00949382i	0.371194	+	0.928555i	$0.378949\pi$
$434$		0			0
$435$	−249.072	−	49.5435i	−0.572579	−	0.113893i
$436$		0			0
$437$	340.769	−	67.7831i	0.779791	−	0.155110i
$438$		0			0
$439$	−307.997	−	205.797i	−0.701588	−	0.468786i	0.152911	−	0.988240i	$-0.451135\pi$
$439$	−307.997	−	205.797i	−0.701588	−	0.468786i	−0.854498	+	0.519454i	$0.826135\pi$
$440$		0			0
$441$			136.335i			0.309150i
$442$		0			0
$443$	487.319			1.10004			0.550022	−	0.835150i	$-0.314619\pi$
$443$	487.319			1.10004			0.550022	+	0.835150i	$0.314619\pi$
$444$		0			0
$445$	−160.617	+	240.380i	−0.360937	+	0.540180i
$446$		0			0
$447$	73.6839	+	370.434i	0.164841	+	0.828712i
$448$		0			0
$449$	−118.148	+	593.972i	−0.263137	+	1.32288i	0.592613	+	0.805487i	$0.298096\pi$
$449$	−118.148	+	593.972i	−0.263137	+	1.32288i	−0.855750	+	0.517390i	$0.826904\pi$
$450$		0			0
$451$	−47.6717	−	115.090i	−0.105702	−	0.255188i
$452$		0			0
$453$	−362.423	+	242.163i	−0.800051	+	0.534577i
$454$		0			0
$455$	36.6794	−	36.6794i	0.0806140	−	0.0806140i
$456$		0			0
$457$	385.048	+	159.492i	0.842556	+	0.348998i	0.761861	−	0.647741i	$-0.224286\pi$
$457$	385.048	+	159.492i	0.842556	+	0.348998i	0.0806952	+	0.996739i	$0.474286\pi$
$458$		0			0
$459$	242.509	−	432.960i	0.528341	−	0.943268i
$460$		0			0
$461$	−18.7757	+	45.3285i	−0.0407282	+	0.0983266i	−0.942935	−	0.332978i	$-0.891947\pi$
$461$	−18.7757	+	45.3285i	−0.0407282	+	0.0983266i	0.902206	+	0.431305i	$0.141947\pi$
$462$		0			0
$463$	−302.357	−	302.357i	−0.653040	−	0.653040i	0.300684	−	0.953724i	$-0.402785\pi$
$463$	−302.357	−	302.357i	−0.653040	−	0.653040i	−0.953724	+	0.300684i	$0.902785\pi$
$464$		0			0
$465$	−229.526	−	343.510i	−0.493604	−	0.738730i
$466$		0			0
$467$	273.749	−	113.390i	0.586186	−	0.242806i	−0.0698230	−	0.997559i	$-0.522243\pi$
$467$	273.749	−	113.390i	0.586186	−	0.242806i	0.656009	+	0.754753i	$0.272243\pi$
$468$		0			0
$469$	−381.939	−	75.9724i	−0.814369	−	0.161988i
$470$		0			0
$471$	−95.5264	+	19.0014i	−0.202816	+	0.0403426i
$472$		0			0
$473$	−316.151	−	211.245i	−0.668395	−	0.446607i
$474$		0			0
$475$			1082.48i			2.27890i
$476$		0			0
$477$	378.891			0.794321
$478$		0			0
$479$	449.304	−	672.431i	0.938005	−	1.40382i	0.0232873	−	0.999729i	$-0.492587\pi$
$479$	449.304	−	672.431i	0.938005	−	1.40382i	0.914717	−	0.404094i	$-0.132413\pi$
$480$		0			0
$481$	−12.8843	−	64.7738i	−0.0267865	−	0.134665i
$482$		0			0
$483$	−28.1952	+	141.747i	−0.0583751	+	0.293472i
$484$		0			0
$485$	547.891	+	1322.73i	1.12967	+	2.72727i
$486$		0			0
$487$	150.102	−	100.295i	0.308217	−	0.205944i	−0.391836	−	0.920035i	$-0.628160\pi$
$487$	150.102	−	100.295i	0.308217	−	0.205944i	0.700053	+	0.714091i	$0.253160\pi$
$488$		0			0
$489$	−307.647	+	307.647i	−0.629134	+	0.629134i
$490$		0			0
$491$	48.8480	+	20.2335i	0.0994868	+	0.0412088i	0.431872	−	0.901935i	$-0.357853\pi$
$491$	48.8480	+	20.2335i	0.0994868	+	0.0412088i	−0.332385	+	0.943144i	$0.607853\pi$
$492$		0			0
$493$	−24.9459	+	210.642i	−0.0506003	+	0.427266i
$494$		0			0
$495$	−66.7851	+	161.233i	−0.134919	+	0.325724i
$496$		0			0
$497$	184.022	+	184.022i	0.370265	+	0.370265i
$498$		0			0
$499$	250.556	+	374.983i	0.502116	+	0.751469i	0.992789	−	0.119874i	$-0.0382492\pi$
$499$	250.556	+	374.983i	0.502116	+	0.751469i	−0.490674	+	0.871344i	$0.663249\pi$
$500$		0			0
$501$	497.254	−	205.970i	0.992524	−	0.411117i
$502$		0			0
$503$	14.2162	+	2.82779i	0.0282629	+	0.00562184i	0.209202	−	0.977873i	$-0.432914\pi$
$503$	14.2162	+	2.82779i	0.0282629	+	0.00562184i	−0.180939	+	0.983494i	$0.557914\pi$
$504$		0			0
$505$	119.349	−	23.7400i	0.236335	−	0.0470099i
$506$		0			0
$507$	315.685	+	210.934i	0.622653	+	0.416043i
$508$		0			0
$509$		−	452.973i		−	0.889927i	−0.895549	−	0.444964i	$-0.853217\pi$
$509$		−	452.973i		−	0.889927i	0.895549	−	0.444964i	$-0.146783\pi$
$510$		0			0
$511$	−238.006			−0.465765
$512$		0			0
$513$	321.623	−	481.343i	0.626945	−	0.938290i
$514$		0			0
$515$	−115.383	−	580.072i	−0.224046	−	1.12635i
$516$		0			0
$517$	57.5277	−	289.211i	0.111272	−	0.559403i
$518$		0			0
$519$	60.2231	+	145.391i	0.116037	+	0.280138i
$520$		0			0
$521$	−142.862	+	95.4571i	−0.274207	+	0.183219i	−0.685069	−	0.728478i	$-0.740228\pi$
$521$	−142.862	+	95.4571i	−0.274207	+	0.183219i	0.410862	+	0.911698i	$0.365228\pi$
$522$		0			0
$523$	−392.475	+	392.475i	−0.750431	+	0.750431i	−0.974560	−	0.224129i	$-0.928046\pi$
$523$	−392.475	+	392.475i	−0.750431	+	0.750431i	0.224129	+	0.974560i	$0.428046\pi$
$524$		0			0
$525$	−415.995	−	172.311i	−0.792372	−	0.328211i
$526$		0			0
$527$	−271.006	+	213.614i	−0.514244	+	0.405339i
$528$		0			0
$529$	84.9770	−	205.153i	0.160637	−	0.387812i
$530$		0			0
$531$	−302.637	−	302.637i	−0.569937	−	0.569937i
$532$		0			0
$533$	21.5901	+	32.3119i	0.0405068	+	0.0606227i
$534$		0			0
$535$	1736.55	−	719.302i	3.24589	−	1.34449i
$536$		0			0
$537$	−309.067	−	61.4773i	−0.575544	−	0.114483i
$538$		0			0
$539$	181.648	−	36.1320i	0.337009	−	0.0670352i
$540$		0			0
$541$	−877.558	−	586.366i	−1.62210	−	1.08386i	−0.933415	−	0.358799i	$-0.883186\pi$
$541$	−877.558	−	586.366i	−1.62210	−	1.08386i	−0.688689	−	0.725057i	$-0.741814\pi$
$542$		0			0
$543$			427.137i			0.786625i
$544$		0			0
$545$	−260.320			−0.477651
$546$		0			0
$547$	106.868	−	159.939i	0.195371	−	0.292394i	−0.720830	−	0.693112i	$-0.756239\pi$
$547$	106.868	−	159.939i	0.195371	−	0.292394i	0.916201	+	0.400718i	$0.131239\pi$
$548$		0			0
$549$	−14.0746	−	70.7578i	−0.0256368	−	0.128885i
$550$		0			0
$551$	−48.2739	+	242.689i	−0.0876114	+	0.440452i
$552$		0			0
$553$	42.2005	+	101.881i	0.0763120	+	0.184233i
$554$		0			0
$555$	−694.975	+	464.368i	−1.25221	+	0.836699i
$556$		0			0
$557$	−613.352	+	613.352i	−1.10117	+	1.10117i	−0.106901	+	0.994270i	$0.534093\pi$
$557$	−613.352	+	613.352i	−1.10117	+	1.10117i	−0.994270	+	0.106901i	$0.965907\pi$
$558$		0			0
$559$	109.587	+	45.3924i	0.196041	+	0.0812029i
$560$		0			0
$561$	−190.152	−	61.7988i	−0.338952	−	0.110158i
$562$		0			0
$563$	117.791	−	284.374i	0.209221	−	0.505104i	−0.784080	−	0.620660i	$-0.786865\pi$
$563$	117.791	−	284.374i	0.209221	−	0.505104i	0.993301	+	0.115556i	$0.0368648\pi$
$564$		0			0
$565$	430.750	+	430.750i	0.762389	+	0.762389i
$566$		0			0
$567$	65.1768	+	97.5440i	0.114950	+	0.172035i
$568$		0			0
$569$	−218.590	+	90.5429i	−0.384165	+	0.159126i	−0.566404	−	0.824128i	$-0.691666\pi$
$569$	−218.590	+	90.5429i	−0.384165	+	0.159126i	0.182239	+	0.983254i	$0.441666\pi$
$570$		0			0
$571$	−530.421	−	105.507i	−0.928933	−	0.184776i	−0.292639	−	0.956223i	$-0.594533\pi$
$571$	−530.421	−	105.507i	−0.928933	−	0.184776i	−0.636294	+	0.771447i	$0.719533\pi$
$572$		0			0
$573$	261.371	−	51.9899i	0.456144	−	0.0907328i
$574$		0			0
$575$	−795.134	−	531.291i	−1.38284	−	0.923985i
$576$		0			0
$577$		−	720.337i		−	1.24842i	−0.781258	−	0.624208i	$-0.785422\pi$
$577$		−	720.337i		−	1.24842i	0.781258	−	0.624208i	$-0.214578\pi$
$578$		0			0
$579$	−488.843			−0.844288
$580$		0			0
$581$	149.253	−	223.373i	0.256890	−	0.384462i
$582$		0			0
$583$	−100.415	−	504.820i	−0.172238	−	0.865901i
$584$		0			0
$585$	10.6211	−	53.3961i	0.0181558	−	0.0912754i
$586$		0			0
$587$	−171.480	−	413.989i	−0.292129	−	0.705262i	0.707870	−	0.706342i	$-0.249656\pi$
$587$	−171.480	−	413.989i	−0.292129	−	0.705262i	−0.999999	+	0.00108058i	$0.999656\pi$
$588$		0			0
$589$	−334.707	+	223.644i	−0.568262	+	0.379701i
$590$		0			0
$591$	259.496	−	259.496i	0.439079	−	0.439079i
$592$		0			0
$593$	−271.056	−	112.275i	−0.457092	−	0.189334i	0.142243	−	0.989832i	$-0.454568\pi$
$593$	−271.056	−	112.275i	−0.457092	−	0.189334i	−0.599336	+	0.800498i	$0.704568\pi$
$594$		0			0
$595$	−169.483	+	521.493i	−0.284846	+	0.876459i
$596$		0			0
$597$	−40.3140	+	97.3266i	−0.0675276	+	0.163026i
$598$		0			0
$599$	−536.423	−	536.423i	−0.895531	−	0.895531i	0.0995057	−	0.995037i	$-0.468274\pi$
$599$	−536.423	−	536.423i	−0.895531	−	0.895531i	−0.995037	+	0.0995057i	$0.968274\pi$
$600$		0			0
$601$	378.123	+	565.901i	0.629156	+	0.941599i	0.999917	+	0.0128703i	$0.00409687\pi$
$601$	378.123	+	565.901i	0.629156	+	0.941599i	−0.370761	+	0.928728i	$0.620903\pi$
$602$		0			0
$603$	−377.602	+	156.408i	−0.626206	+	0.259383i
$604$		0			0
$605$	−826.176	−	164.337i	−1.36558	−	0.271631i
$606$		0			0
$607$	591.881	−	117.732i	0.975093	−	0.193958i	0.318268	−	0.948001i	$-0.396899\pi$
$607$	591.881	−	117.732i	0.975093	−	0.193958i	0.656825	+	0.754043i	$0.271899\pi$
$608$		0			0
$609$	−85.5807	−	57.1832i	−0.140527	−	0.0938969i
$610$		0			0
$611$			91.9892i			0.150555i
$612$		0			0
$613$	239.075			0.390009			0.195004	−	0.980802i	$-0.437528\pi$
$613$	239.075			0.390009			0.195004	+	0.980802i	$0.437528\pi$
$614$		0			0
$615$	273.245	−	408.940i	0.444301	−	0.664944i
$616$		0			0
$617$	−179.641	−	903.115i	−0.291152	−	1.46372i	−0.798508	−	0.601984i	$-0.794377\pi$
$617$	−179.641	−	903.115i	−0.291152	−	1.46372i	0.507356	−	0.861736i	$-0.330623\pi$
$618$		0			0
$619$	30.7903	−	154.793i	0.0497420	−	0.250070i	−0.947912	−	0.318534i	$-0.896810\pi$
$619$	30.7903	−	154.793i	0.0497420	−	0.250070i	0.997654	+	0.0684635i	$0.0218097\pi$
$620$		0			0
$621$	195.714	+	472.495i	0.315159	+	0.760862i
$622$		0			0
$623$	−97.4266	+	65.0984i	−0.156383	+	0.104492i
$624$		0			0
$625$	699.892	−	699.892i	1.11983	−	1.11983i
$626$		0			0
$627$	−215.490	−	89.2590i	−0.343685	−	0.142359i
$628$		0			0
$629$	432.175	+	548.290i	0.687083	+	0.871685i
$630$		0			0
$631$	−202.571	+	489.049i	−0.321031	+	0.775038i	0.678163	+	0.734911i	$0.262776\pi$
$631$	−202.571	+	489.049i	−0.321031	+	0.775038i	−0.999195	+	0.0401266i	$0.987224\pi$
$632$		0			0
$633$	−79.6387	−	79.6387i	−0.125812	−	0.125812i
$634$		0			0
$635$	190.491	+	285.090i	0.299986	+	0.448961i
$636$		0			0
$637$	−53.3786	+	22.1101i	−0.0837969	+	0.0347098i
$638$		0			0
$639$	267.890	+	53.2867i	0.419233	+	0.0833907i
$640$		0			0
$641$	170.145	−	33.8439i	0.265436	−	0.0527985i	−0.0605779	−	0.998163i	$-0.519294\pi$
$641$	170.145	−	33.8439i	0.265436	−	0.0527985i	0.326014	+	0.945365i	$0.394294\pi$
$642$		0			0
$643$	262.970	+	175.711i	0.408973	+	0.273267i	0.742993	−	0.669299i	$-0.233405\pi$
$643$	262.970	+	175.711i	0.408973	+	0.273267i	−0.334020	+	0.942566i	$0.608405\pi$
$644$		0			0
$645$		−	1501.21i		−	2.32745i
$646$		0			0
$647$	−404.590			−0.625332			−0.312666	−	0.949863i	$-0.601222\pi$
$647$	−404.590			−0.625332			−0.312666	+	0.949863i	$0.601222\pi$
$648$		0			0
$649$	−323.016	+	483.427i	−0.497713	+	0.744880i
$650$		0			0
$651$	−32.6668	−	164.227i	−0.0501795	−	0.252269i
$652$		0			0
$653$	219.978	−	1105.90i	0.336873	−	1.69357i	−0.326428	−	0.945222i	$-0.605845\pi$
$653$	219.978	−	1105.90i	0.336873	−	1.69357i	0.663301	−	0.748352i	$-0.269155\pi$
$654$		0			0
$655$	159.241	+	384.441i	0.243115	+	0.586933i
$656$		0			0
$657$	−207.698	+	138.780i	−0.316131	+	0.211232i
$658$		0			0
$659$	459.427	−	459.427i	0.697158	−	0.697158i	−0.266639	−	0.963797i	$-0.585913\pi$
$659$	459.427	−	459.427i	0.697158	−	0.697158i	0.963797	+	0.266639i	$0.0859131\pi$
$660$		0			0
$661$	682.141	+	282.552i	1.03198	+	0.427462i	0.833428	−	0.552628i	$-0.186375\pi$
$661$	682.141	+	282.552i	1.03198	+	0.427462i	0.198555	+	0.980090i	$0.436375\pi$
$662$		0			0
$663$	61.9407	+	7.33553i	0.0934249	+	0.0110641i
$664$		0			0
$665$	−244.793	+	590.983i	−0.368110	+	0.888696i
$666$		0			0
$667$	−154.574	−	154.574i	−0.231744	−	0.231744i
$668$		0			0
$669$	161.049	+	241.027i	0.240731	+	0.360280i
$670$		0			0
$671$	−90.5449	+	37.5049i	−0.134940	+	0.0558941i
$672$		0			0
$673$	−625.391	−	124.398i	−0.929258	−	0.184841i	−0.292819	−	0.956168i	$-0.594593\pi$
$673$	−625.391	−	124.398i	−0.929258	−	0.184841i	−0.636439	+	0.771327i	$0.719593\pi$
$674$		0			0
$675$	−1562.75	+	310.851i	−2.31519	+	0.460519i
$676$		0			0
$677$	522.277	+	348.974i	0.771458	+	0.515472i	0.877898	−	0.478847i	$-0.158945\pi$
$677$	522.277	+	348.974i	0.771458	+	0.515472i	−0.106440	+	0.994319i	$0.533945\pi$
$678$		0			0
$679$			580.274i			0.854600i
$680$		0			0
$681$	921.693			1.35344
$682$		0			0
$683$	36.0870	−	54.0080i	0.0528360	−	0.0790747i	−0.804111	−	0.594479i	$-0.797358\pi$
$683$	36.0870	−	54.0080i	0.0528360	−	0.0790747i	0.856947	+	0.515404i	$0.172358\pi$
$684$		0			0
$685$	220.503	+	1108.54i	0.321902	+	1.61831i
$686$		0			0
$687$	−86.7748	+	436.246i	−0.126310	+	0.635002i
$688$		0			0
$689$	61.4466	+	148.345i	0.0891823	+	0.215305i
$690$		0			0
$691$	−662.177	+	442.452i	−0.958288	+	0.640307i	−0.933192	−	0.359378i	$-0.882989\pi$
$691$	−662.177	+	442.452i	−0.958288	+	0.640307i	−0.0250956	+	0.999685i	$0.507989\pi$
$692$		0			0
$693$	−50.0154	+	50.0154i	−0.0721723	+	0.0721723i
$694$		0			0
$695$	444.081	+	183.944i	0.638965	+	0.264668i
$696$		0			0
$697$	−358.409	−	200.751i	−0.514216	−	0.288022i
$698$		0			0
$699$	155.325	−	374.988i	0.222211	−	0.536464i
$700$		0			0
$701$	−256.359	−	256.359i	−0.365704	−	0.365704i	0.500204	−	0.865908i	$-0.333259\pi$
$701$	−256.359	−	256.359i	−0.365704	−	0.365704i	−0.865908	+	0.500204i	$0.833259\pi$
$702$		0			0
$703$	452.467	+	677.165i	0.643624	+	0.963251i
$704$		0			0
$705$	1075.60	−	445.527i	1.52567	−	0.631953i
$706$		0			0
$707$	48.3724	+	9.62187i	0.0684193	+	0.0136094i
$708$		0			0
$709$	−575.960	+	114.566i	−0.812355	+	0.161588i	−0.583752	−	0.811932i	$-0.698416\pi$
$709$	−575.960	+	114.566i	−0.812355	+	0.161588i	−0.228603	+	0.973520i	$0.573416\pi$
$710$		0			0
$711$	96.2329	+	64.3008i	0.135349	+	0.0904371i
$712$		0			0
$713$		−	355.625i		−	0.498772i
$714$		0			0
$715$	−73.9577			−0.103437
$716$		0			0
$717$	−223.027	+	333.784i	−0.311056	+	0.465528i
$718$		0			0
$719$	274.170	+	1378.35i	0.381322	+	1.91703i	0.398469	+	0.917182i	$0.369542\pi$
$719$	274.170	+	1378.35i	0.381322	+	1.91703i	−0.0171473	+	0.999853i	$0.505458\pi$
$720$		0			0
$721$	46.7651	−	235.104i	0.0648615	−	0.326081i
$722$		0			0
$723$	45.7110	+	110.356i	0.0632241	+	0.152637i
$724$		0			0
$725$	566.279	−	378.376i	0.781074	−	0.521897i
$726$		0			0
$727$	−533.285	+	533.285i	−0.733543	+	0.733543i	−0.971320	−	0.237777i	$-0.923581\pi$
$727$	−533.285	+	533.285i	−0.733543	+	0.733543i	0.237777	+	0.971320i	$0.423581\pi$
$728$		0			0
$729$	667.523	+	276.497i	0.915670	+	0.379283i
$730$		0			0
$731$	−1250.03	+	98.2923i	−1.71003	+	0.134463i
$732$		0			0
$733$	301.313	−	727.435i	0.411069	−	0.992408i	−0.573783	−	0.819008i	$-0.694525\pi$
$733$	301.313	−	727.435i	0.411069	−	0.992408i	0.984851	−	0.173400i	$-0.0554754\pi$
$734$		0			0
$735$	517.052	+	517.052i	0.703472	+	0.703472i
$736$		0			0
$737$	308.465	+	461.651i	0.418542	+	0.626392i
$738$		0			0
$739$	569.262	−	235.796i	0.770314	−	0.319075i	0.0373144	−	0.999304i	$-0.488120\pi$
$739$	569.262	−	235.796i	0.770314	−	0.319075i	0.733000	+	0.680229i	$0.238120\pi$
$740$		0			0
$741$	71.3644	+	14.1953i	0.0963083	+	0.0191569i
$742$		0			0
$743$	−125.334	+	24.9306i	−0.168687	+	0.0335539i	−0.278711	−	0.960375i	$-0.589907\pi$
$743$	−125.334	+	24.9306i	−0.168687	+	0.0335539i	0.110024	+	0.993929i	$0.464907\pi$
$744$		0			0
$745$	−1227.94	−	820.484i	−1.64824	−	1.10132i
$746$		0			0
$747$		−	281.957i		−	0.377452i
$748$		0			0
$749$	761.816			1.01711
$750$		0			0
$751$	50.9367	−	76.2322i	0.0678252	−	0.101508i	−0.796007	−	0.605288i	$-0.793058\pi$
$751$	50.9367	−	76.2322i	0.0678252	−	0.101508i	0.863832	+	0.503780i	$0.168058\pi$
$752$		0			0
$753$	195.097	+	980.818i	0.259093	+	1.30255i
$754$		0			0
$755$	332.506	−	1671.62i	0.440405	−	2.21407i
$756$		0			0
$757$	−222.984	−	538.330i	−0.294562	−	0.711137i	−0.999997	−	0.00236180i	$-0.999248\pi$
$757$	−222.984	−	538.330i	−0.294562	−	0.711137i	0.705435	−	0.708775i	$-0.250752\pi$
$758$		0			0
$759$	171.330	−	114.479i	0.225731	−	0.150828i
$760$		0			0
$761$	444.715	−	444.715i	0.584383	−	0.584383i	−0.351722	−	0.936105i	$-0.614404\pi$
$761$	444.715	−	444.715i	0.584383	−	0.584383i	0.936105	+	0.351722i	$0.114404\pi$
$762$		0			0
$763$	−97.4769	−	40.3762i	−0.127755	−	0.0529177i
$764$		0			0
$765$	156.178	+	553.911i	0.204154	+	0.724067i
$766$		0			0
$767$	69.4096	−	167.570i	0.0904950	−	0.218474i
$768$		0			0
$769$	852.026	+	852.026i	1.10797	+	1.10797i	0.993418	+	0.114548i	$0.0365419\pi$
$769$	852.026	+	852.026i	1.10797	+	1.10797i	0.114548	+	0.993418i	$0.463458\pi$
$770$		0			0
$771$	139.537	+	208.831i	0.180981	+	0.270858i
$772$		0			0
$773$	711.237	−	294.604i	0.920099	−	0.381118i	0.128185	−	0.991750i	$-0.459085\pi$
$773$	711.237	−	294.604i	0.920099	−	0.381118i	0.791914	+	0.610633i	$0.209085\pi$
$774$		0			0
$775$	1086.67	+	216.153i	1.40216	+	0.278907i
$776$		0			0
$777$	−332.258	+	66.0903i	−0.427617	+	0.0850582i
$778$		0			0
$779$	−398.461	−	266.243i	−0.511503	−	0.341775i
$780$		0			0
$781$		−	371.048i		−	0.475094i
$782$		0			0
$783$	−364.227			−0.465169
$784$		0			0
$785$	211.584	−	316.658i	0.269534	−	0.403385i
$786$		0			0
$787$	88.5427	+	445.134i	0.112507	+	0.565609i	0.995381	+	0.0960002i	$0.0306049\pi$
$787$	88.5427	+	445.134i	0.112507	+	0.565609i	−0.882875	+	0.469609i	$0.844395\pi$
$788$		0			0
$789$	−218.729	+	1099.63i	−0.277223	+	1.39370i
$790$		0			0
$791$	94.4840	+	228.104i	0.119449	+	0.288375i
$792$		0			0
$793$	25.4209	−	16.9857i	0.0320566	−	0.0214195i
$794$		0			0
$795$	1436.95	−	1436.95i	1.80748	−	1.80748i
$796$		0			0
$797$	440.728	+	182.556i	0.552984	+	0.229054i	0.641636	−	0.767009i	$-0.278256\pi$
$797$	440.728	+	182.556i	0.552984	+	0.229054i	−0.0886521	+	0.996063i	$0.528256\pi$
$798$		0			0
$799$	−441.408	−	866.460i	−0.552450	−	1.08443i
$800$		0			0
$801$	−47.0619	+	113.617i	−0.0587539	+	0.141845i
$802$		0			0
$803$	239.949	+	239.949i	0.298816	+	0.298816i
$804$		0			0
$805$	−313.958	−	469.872i	−0.390011	−	0.583692i
$806$		0			0
$807$	−656.135	+	271.780i	−0.813054	+	0.336778i
$808$		0			0
$809$	643.075	+	127.915i	0.794901	+	0.158116i	0.575804	−	0.817588i	$-0.304689\pi$
$809$	643.075	+	127.915i	0.794901	+	0.158116i	0.219096	+	0.975703i	$0.429689\pi$
$810$		0			0
$811$	−133.537	+	26.5621i	−0.164657	+	0.0327523i	−0.276730	−	0.960948i	$-0.589251\pi$
$811$	−133.537	+	26.5621i	−0.164657	+	0.0327523i	0.112073	+	0.993700i	$0.464251\pi$
$812$		0			0
$813$	325.927	+	217.778i	0.400895	+	0.267869i
$814$		0			0
$815$		−	1701.22i		−	2.08739i
$816$		0			0
$817$	−1462.74			−1.79038
$818$		0			0
$819$	12.2589	−	18.3468i	0.0149682	−	0.0224015i
$820$		0			0
$821$	78.8427	+	396.369i	0.0960325	+	0.482788i	0.998631	+	0.0523050i	$0.0166568\pi$
$821$	78.8427	+	396.369i	0.0960325	+	0.482788i	−0.902599	+	0.430483i	$0.858343\pi$
$822$		0			0
$823$	103.029	−	517.963i	0.125188	−	0.629360i	−0.866339	−	0.499456i	$-0.833533\pi$
$823$	103.029	−	517.963i	0.125188	−	0.629360i	0.991527	−	0.129904i	$-0.0414669\pi$
$824$		0			0
$825$	245.674	+	593.110i	0.297787	+	0.718921i
$826$		0			0
$827$	40.2691	−	26.9070i	0.0486930	−	0.0325356i	−0.530985	−	0.847381i	$-0.678178\pi$
$827$	40.2691	−	26.9070i	0.0486930	−	0.0325356i	0.579679	+	0.814845i	$0.303178\pi$
$828$		0			0
$829$	−456.033	+	456.033i	−0.550101	+	0.550101i	−0.926470	−	0.376369i	$-0.877172\pi$
$829$	−456.033	+	456.033i	−0.550101	+	0.550101i	0.376369	+	0.926470i	$0.377172\pi$
$830$		0			0
$831$	966.203	+	400.214i	1.16270	+	0.481606i
$832$		0			0
$833$	396.686	−	464.395i	0.476214	−	0.557497i
$834$		0			0
$835$	−805.373	+	1944.34i	−0.964518	+	2.32855i
$836$		0			0
$837$	−418.986	−	418.986i	−0.500580	−	0.500580i
$838$		0			0
$839$	325.656	+	487.379i	0.388148	+	0.580905i	0.973163	−	0.230118i	$-0.0739112\pi$
$839$	325.656	+	487.379i	0.388148	+	0.580905i	−0.585014	+	0.811023i	$0.698911\pi$
$840$		0			0
$841$	−633.151	+	262.260i	−0.752854	+	0.311843i
$842$		0			0
$843$	−902.411	−	179.501i	−1.07048	−	0.212931i
$844$		0			0
$845$	−1456.05	+	289.626i	−1.72313	+	0.342752i
$846$		0			0
$847$	−283.873	−	189.678i	−0.335151	−	0.223941i
$848$		0			0
$849$			76.3116i			0.0898841i
$850$		0			0
$851$	−719.486			−0.845459
$852$		0			0
$853$	−853.360	+	1277.14i	−1.00042	+	1.49724i	−0.138393	+	0.990377i	$0.544194\pi$
$853$	−853.360	+	1277.14i	−1.00042	+	1.49724i	−0.862029	+	0.506859i	$0.830806\pi$
$854$		0			0
$855$	130.977	+	658.464i	0.153189	+	0.770133i
$856$		0			0
$857$	95.3866	−	479.541i	0.111303	−	0.559558i	−0.884382	−	0.466763i	$-0.845420\pi$
$857$	95.3866	−	479.541i	0.111303	−	0.559558i	0.995685	−	0.0927945i	$-0.0295800\pi$
$858$		0			0
$859$	237.536	+	573.462i	0.276526	+	0.667593i	0.999735	−	0.0230367i	$-0.00733347\pi$
$859$	237.536	+	573.462i	0.276526	+	0.667593i	−0.723209	+	0.690630i	$0.757333\pi$
$860$		0			0
$861$	165.744	−	110.747i	0.192502	−	0.128626i
$862$		0			0
$863$	−725.115	+	725.115i	−0.840226	+	0.840226i	−0.988888	−	0.148662i	$-0.952503\pi$
$863$	−725.115	+	725.115i	−0.840226	+	0.840226i	0.148662	+	0.988888i	$0.452503\pi$
$864$		0			0
$865$	−568.503	−	235.482i	−0.657229	−	0.272233i
$866$		0			0
$867$	−618.628	+	228.127i	−0.713528	+	0.263122i
$868$		0			0
$869$	60.1679	−	145.258i	0.0692381	−	0.167155i
$870$		0			0
$871$	−122.475	−	122.475i	−0.140614	−	0.140614i
$872$		0			0
$873$	338.353	+	506.382i	0.387576	+	0.580048i
$874$		0			0
$875$	881.602	−	365.172i	1.00755	−	0.417339i
$876$		0			0
$877$	1419.91	+	282.438i	1.61905	+	0.322050i	0.919668	−	0.392696i	$-0.128458\pi$
$877$	1419.91	+	282.438i	1.61905	+	0.322050i	0.699384	+	0.714746i	$0.253458\pi$
$878$		0			0
$879$	831.944	−	165.484i	0.946466	−	0.188264i
$880$		0			0
$881$	106.659	+	71.2675i	0.121066	+	0.0808939i	0.614629	−	0.788816i	$-0.289306\pi$
$881$	106.659	+	71.2675i	0.121066	+	0.0808939i	−0.493563	+	0.869710i	$0.664306\pi$
$882$		0			0
$883$		−	690.830i		−	0.782366i	−0.920313	−	0.391183i	$-0.872066\pi$
$883$		−	690.830i		−	0.782366i	0.920313	−	0.391183i	$-0.127934\pi$
$884$		0			0
$885$	−2295.50			−2.59379
$886$		0			0
$887$	122.367	−	183.135i	0.137956	−	0.206466i	−0.756058	−	0.654504i	$-0.772877\pi$
$887$	122.367	−	183.135i	0.137956	−	0.206466i	0.894014	+	0.448039i	$0.147877\pi$
$888$		0			0
$889$	27.1113	+	136.298i	0.0304964	+	0.153316i
$890$		0			0
$891$	32.6315	−	164.050i	0.0366234	−	0.184118i
$892$		0			0
$893$	−434.109	−	1048.03i	−0.486125	−	1.17361i
$894$		0			0
$895$	1024.52	−	684.561i	1.14471	−	0.764872i
$896$		0			0
$897$	−45.4534	+	45.4534i	−0.0506727	+	0.0506727i
$898$		0			0
$899$	233.990	+	96.9219i	0.260278	+	0.107811i
$900$		0			0
$901$	−1290.61	−	1102.44i	−1.43241	−	1.22357i
$902$		0			0
$903$	232.841	−	562.128i	0.257853	−	0.622511i
$904$		0			0
$905$	−1180.99	−	1180.99i	−1.30496	−	1.30496i
$906$		0			0
$907$	−15.9891	−	23.9294i	−0.0176286	−	0.0263831i	0.822551	−	0.568692i	$-0.192550\pi$
$907$	−15.9891	−	23.9294i	−0.0176286	−	0.0263831i	−0.840179	+	0.542309i	$0.817550\pi$
$908$		0			0
$909$	47.8231	−	19.8090i	0.0526107	−	0.0217921i
$910$		0			0
$911$	370.087	+	73.6148i	0.406242	+	0.0808066i	0.393982	−	0.919118i	$-0.371097\pi$
$911$	370.087	+	73.6148i	0.406242	+	0.0808066i	0.0122605	+	0.999925i	$0.496097\pi$
$912$		0			0
$913$	−375.668	+	74.7250i	−0.411466	+	0.0818456i
$914$		0			0
$915$	−321.727	−	214.971i	−0.351615	−	0.234941i
$916$		0			0
$917$			168.653i			0.183918i
$918$		0			0
$919$	1009.34			1.09831			0.549153	−	0.835722i	$-0.314951\pi$
$919$	1009.34			1.09831			0.549153	+	0.835722i	$0.314951\pi$
$920$		0			0
$921$	389.056	−	582.263i	0.422428	−	0.632208i
$922$		0			0
$923$	22.5820	+	113.527i	0.0244659	+	0.122998i
$924$		0			0
$925$	437.312	−	2198.52i	0.472770	−	2.37678i
$926$		0			0
$927$	−96.2775	−	232.435i	−0.103859	−	0.250738i
$928$		0			0
$929$	−947.380	+	633.019i	−1.01978	+	0.681398i	−0.948734	−	0.316074i	$-0.897635\pi$
$929$	−947.380	+	633.019i	−1.01978	+	0.681398i	−0.0710503	+	0.997473i	$0.522635\pi$
$930$		0			0
$931$	503.802	−	503.802i	0.541140	−	0.541140i
$932$		0			0
$933$	377.774	+	156.479i	0.404902	+	0.167716i
$934$		0			0
$935$	696.619	−	354.884i	0.745047	−	0.379555i
$936$		0			0
$937$	−323.724	+	781.538i	−0.345489	+	0.834085i	0.651651	+	0.758519i	$0.274077\pi$
$937$	−323.724	+	781.538i	−0.345489	+	0.834085i	−0.997141	+	0.0755666i	$0.975923\pi$
$938$		0			0
$939$	61.2727	+	61.2727i	0.0652531	+	0.0652531i
$940$		0			0
$941$	135.290	+	202.475i	0.143772	+	0.215170i	0.896366	−	0.443315i	$-0.146198\pi$
$941$	135.290	+	202.475i	0.143772	+	0.215170i	−0.752594	+	0.658485i	$0.771198\pi$
$942$		0			0
$943$	391.136	−	162.014i	0.414779	−	0.171807i
$944$		0			0
$945$	−923.484	−	183.692i	−0.977232	−	0.194383i
$946$		0			0
$947$	−1634.71	+	325.164i	−1.72620	+	0.343362i	−0.955758	−	0.294153i	$-0.904962\pi$
$947$	−1634.71	+	325.164i	−1.72620	+	0.343362i	−0.770438	+	0.637515i	$0.779962\pi$
$948$		0			0
$949$	−88.0190	−	58.8124i	−0.0927492	−	0.0619730i
$950$		0			0
$951$		−	1067.64i		−	1.12265i
$952$		0			0
$953$	1067.23			1.11987			0.559933	−	0.828538i	$-0.310827\pi$
$953$	1067.23			1.11987			0.559933	+	0.828538i	$0.310827\pi$
$954$		0			0
$955$	−578.917	+	866.410i	−0.606195	+	0.907236i
$956$		0			0
$957$	28.6294	+	143.930i	0.0299158	+	0.150397i
$958$		0			0
$959$	−89.3702	+	449.294i	−0.0931910	+	0.468503i
$960$		0			0
$961$	−210.084	−	507.187i	−0.218609	−	0.527770i
$962$		0			0
$963$	664.807	−	444.210i	0.690350	−	0.461277i
$964$		0			0
$965$	1351.60	−	1351.60i	1.40062	−	1.40062i
$966$		0			0
$967$	−1119.27	−	463.617i	−1.15747	−	0.479438i	−0.280436	−	0.959873i	$-0.590479\pi$
$967$	−1119.27	−	463.617i	−1.15747	−	0.479438i	−0.877031	+	0.480434i	$0.840479\pi$
$968$		0			0
$969$	−740.308	+	208.733i	−0.763992	+	0.215411i
$970$		0			0
$971$	95.9345	−	231.606i	0.0987997	−	0.238524i	−0.866750	−	0.498743i	$-0.833795\pi$
$971$	95.9345	−	231.606i	0.0987997	−	0.238524i	0.965549	+	0.260220i	$0.0837950\pi$
$972$		0			0
$973$	137.756	+	137.756i	0.141578	+	0.141578i
$974$		0			0
$975$	−111.264	−	166.518i	−0.114117	−	0.170788i
$976$		0			0
$977$	527.129	−	218.344i	0.539538	−	0.223484i	−0.0962367	−	0.995358i	$-0.530681\pi$
$977$	527.129	−	218.344i	0.539538	−	0.223484i	0.635775	+	0.771874i	$0.280681\pi$
$978$		0			0
$979$	163.852	+	32.5922i	0.167367	+	0.0332913i
$980$		0			0
$981$	−108.607	+	21.6033i	−0.110711	+	0.0220217i
$982$		0			0
$983$	300.877	+	201.040i	0.306081	+	0.204517i	0.699119	−	0.715006i	$-0.253576\pi$
$983$	300.877	+	201.040i	0.306081	+	0.204517i	−0.393038	+	0.919522i	$0.628576\pi$
$984$		0			0
$985$			1434.96i			1.45681i
$986$		0			0
$987$	471.860			0.478075
$988$		0			0
$989$	717.925	−	1074.45i	0.725910	−	1.08640i
$990$		0			0
$991$	−170.490	−	857.109i	−0.172038	−	0.864893i	−0.966320	−	0.257344i	$-0.917153\pi$
$991$	−170.490	−	857.109i	−0.172038	−	0.864893i	0.794282	−	0.607549i	$-0.207847\pi$
$992$		0			0
$993$	−149.847	+	753.334i	−0.150904	+	0.758645i
$994$		0			0
$995$	−157.634	−	380.562i	−0.158426	−	0.382474i
$996$		0			0
$997$	−1330.08	+	888.729i	−1.33408	+	0.891404i	−0.998715	−	0.0506846i	$-0.983860\pi$
$997$	−1330.08	+	888.729i	−1.33408	+	0.891404i	−0.335365	+	0.942088i	$0.608860\pi$
$998$		0			0
$999$	−847.675	+	847.675i	−0.848524	+	0.848524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.41.4	✓	40
4.3	odd	2		272.3.bh.g.177.2		40
17.5	odd	16	inner	136.3.t.b.73.4	yes	40
68.39	even	16		272.3.bh.g.209.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.41.4	✓	40	1.1	even	1	trivial
136.3.t.b.73.4	yes	40	17.5	odd	16	inner
272.3.bh.g.177.2		40	4.3	odd	2
272.3.bh.g.209.2		40	68.39	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26753 - 1.89699i) q^{3} +(1.74040 + 8.74956i) q^{5} +(-0.705386 + 3.54621i) q^{7} +(1.45221 + 3.50595i) q^{9} +O(q^{10})\)	\(q+(1.26753 - 1.89699i) q^{3} +(1.74040 + 8.74956i) q^{5} +(-0.705386 + 3.54621i) q^{7} +(1.45221 + 3.50595i) q^{9} +(4.28632 - 2.86402i) q^{11} +(-1.13715 + 1.13715i) q^{13} +(18.8038 + 7.78880i) q^{15} +(5.25441 - 16.1676i) q^{17} +(7.58919 - 18.3219i) q^{19} +(5.83303 + 5.83303i) q^{21} +(9.73350 + 14.5672i) q^{23} +(-50.4289 + 20.8883i) q^{25} +(28.6303 + 5.69492i) q^{27} +(-12.2375 + 2.43420i) q^{29} +(-16.8775 - 11.2772i) q^{31} -11.7613i q^{33} -32.2555 q^{35} +(-22.8156 + 34.1459i) q^{37} +(0.715793 + 3.59853i) q^{39} +(4.71432 - 23.7005i) q^{41} +(-28.2260 - 68.1437i) q^{43} +(-28.1481 + 18.8079i) q^{45} +(40.4472 - 40.4472i) q^{47} +(33.1920 + 13.7486i) q^{49} +(-24.0096 - 30.4604i) q^{51} +(38.2089 - 92.2445i) q^{53} +(32.5188 + 32.5188i) q^{55} +(-25.1370 - 37.6202i) q^{57} +(-104.199 + 43.1605i) q^{59} +(-18.6460 - 3.70891i) q^{61} +(-13.4572 + 2.67680i) q^{63} +(-11.9287 - 7.97048i) q^{65} +107.703i q^{67} +39.9713 q^{69} +(39.9882 - 59.8466i) q^{71} +(12.8420 + 64.5610i) q^{73} +(-24.2951 + 122.139i) q^{75} +(7.13294 + 17.2204i) q^{77} +(25.3591 - 16.9444i) q^{79} +(22.9429 - 22.9429i) q^{81} +(-68.6449 - 28.4336i) q^{83} +(150.604 + 17.8358i) q^{85} +(-10.8938 + 26.2999i) q^{87} +(22.9153 + 22.9153i) q^{89} +(-3.23045 - 4.83471i) q^{91} +(-42.7854 + 17.7223i) q^{93} +(173.517 + 34.5147i) q^{95} +(157.404 - 31.3096i) q^{97} +(16.2657 + 10.8684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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