LMFDB - Embedded newform 684.3.be.a.425.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.20
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0979727 - 2.99840i) q^{3} +(5.49889 + 3.17478i) q^{5} +(-3.73312 + 6.46596i) q^{7} +(-8.98080 - 0.587522i) q^{9} +O(q^{10})$	\(q+(0.0979727 - 2.99840i) q^{3} +(5.49889 + 3.17478i) q^{5} +(-3.73312 + 6.46596i) q^{7} +(-8.98080 - 0.587522i) q^{9} +(-4.85076 - 2.80059i) q^{11} +5.19164 q^{13} +(10.0580 - 16.1768i) q^{15} +(10.9238 - 6.30688i) q^{17} +(18.2190 + 5.39160i) q^{19} +(19.0218 + 11.8269i) q^{21} +25.8087i q^{23} +(7.65851 + 13.2649i) q^{25} +(-2.64150 + 26.8705i) q^{27} +(7.93419 - 4.58080i) q^{29} +(23.3648 + 40.4690i) q^{31} +(-8.87253 + 14.2701i) q^{33} +(-41.0560 + 23.7037i) q^{35} +46.3137 q^{37} +(0.508639 - 15.5666i) q^{39} +(22.8225 + 13.1766i) q^{41} -55.8493 q^{43} +(-47.5192 - 31.7428i) q^{45} +(17.7455 - 10.2453i) q^{47} +(-3.37239 - 5.84114i) q^{49} +(-17.8403 - 33.3719i) q^{51} +(45.9725 + 26.5422i) q^{53} +(-17.7825 - 30.8003i) q^{55} +(17.9511 - 54.0995i) q^{57} +(-17.9158 - 10.3437i) q^{59} +(17.7246 + 30.6999i) q^{61} +(37.3253 - 55.8762i) q^{63} +(28.5483 + 16.4823i) q^{65} +107.499 q^{67} +(77.3849 + 2.52855i) q^{69} +(-74.9285 + 43.2600i) q^{71} +(-25.3385 - 43.8876i) q^{73} +(40.5239 - 21.6637i) q^{75} +(36.2170 - 20.9099i) q^{77} -41.7660 q^{79} +(80.3096 + 10.5528i) q^{81} +(90.2997 + 52.1346i) q^{83} +80.0919 q^{85} +(-12.9577 - 24.2387i) q^{87} +(-32.7765 - 18.9235i) q^{89} +(-19.3810 + 33.5689i) q^{91} +(123.631 - 66.0922i) q^{93} +(83.0669 + 87.4891i) q^{95} -162.214 q^{97} +(41.9183 + 28.0015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0979727	−	2.99840i	0.0326576	−	0.999467i
$3$	0.0979727	−	2.99840i	0.0326576	−	0.999467i
$4$		0			0
$5$	5.49889	+	3.17478i	1.09978	+	0.634957i	0.936163	−	0.351567i	$-0.114351\pi$
$5$	5.49889	+	3.17478i	1.09978	+	0.634957i	0.163615	+	0.986524i	$0.447685\pi$
$6$		0			0
$7$	−3.73312	+	6.46596i	−0.533303	+	0.923708i	0.465940	+	0.884816i	$0.345716\pi$
$7$	−3.73312	+	6.46596i	−0.533303	+	0.923708i	−0.999243	+	0.0388918i	$0.987617\pi$
$8$		0			0
$9$	−8.98080	−	0.587522i	−0.997867	−	0.0652803i
$10$		0			0
$11$	−4.85076	−	2.80059i	−0.440978	−	0.254599i	0.263034	−	0.964787i	$-0.415277\pi$
$11$	−4.85076	−	2.80059i	−0.440978	−	0.254599i	−0.704013	+	0.710187i	$0.748610\pi$
$12$		0			0
$13$	5.19164			0.399357			0.199679	−	0.979861i	$-0.436010\pi$
$13$	5.19164			0.399357			0.199679	+	0.979861i	$0.436010\pi$
$14$		0			0
$15$	10.0580	−	16.1768i	0.670534	−	1.07845i
$16$		0			0
$17$	10.9238	−	6.30688i	0.642578	−	0.370993i	−0.143029	−	0.989719i	$-0.545684\pi$
$17$	10.9238	−	6.30688i	0.642578	−	0.370993i	0.785607	+	0.618726i	$0.212351\pi$
$18$		0			0
$19$	18.2190	+	5.39160i	0.958893	+	0.283768i
$19$	18.2190	+	5.39160i	0.958893	+	0.283768i
$20$		0			0
$21$	19.0218	+	11.8269i	0.905799	+	0.563185i
$22$		0			0
$23$			25.8087i			1.12212i	0.827775	+	0.561060i	$0.189606\pi$
$23$			25.8087i			1.12212i	−0.827775	+	0.561060i	$0.810394\pi$
$24$		0			0
$25$	7.65851	+	13.2649i	0.306340	+	0.530597i
$26$		0			0
$27$	−2.64150	+	26.8705i	−0.0978333	+	0.995203i
$28$		0			0
$29$	7.93419	−	4.58080i	0.273593	−	0.157959i	−0.356927	−	0.934132i	$-0.616175\pi$
$29$	7.93419	−	4.58080i	0.273593	−	0.157959i	0.630519	+	0.776174i	$0.282842\pi$
$30$		0			0
$31$	23.3648	+	40.4690i	0.753703	+	1.30545i	0.946016	+	0.324119i	$0.105068\pi$
$31$	23.3648	+	40.4690i	0.753703	+	1.30545i	−0.192313	+	0.981334i	$0.561599\pi$
$32$		0			0
$33$	−8.87253	+	14.2701i	−0.268865	+	0.432429i
$34$		0			0
$35$	−41.0560	+	23.7037i	−1.17303	+	0.677249i
$36$		0			0
$37$	46.3137			1.25172			0.625860	−	0.779935i	$-0.284748\pi$
$37$	46.3137			1.25172			0.625860	+	0.779935i	$0.284748\pi$
$38$		0			0
$39$	0.508639	−	15.5666i	0.0130420	−	0.399144i
$40$		0			0
$41$	22.8225	+	13.1766i	0.556647	+	0.321380i	0.751799	−	0.659393i	$-0.229186\pi$
$41$	22.8225	+	13.1766i	0.556647	+	0.321380i	−0.195151	+	0.980773i	$0.562520\pi$
$42$		0			0
$43$	−55.8493			−1.29882			−0.649411	−	0.760438i	$-0.724984\pi$
$43$	−55.8493			−1.29882			−0.649411	+	0.760438i	$0.724984\pi$
$44$		0			0
$45$	−47.5192	−	31.7428i	−1.05598	−	0.705396i
$46$		0			0
$47$	17.7455	−	10.2453i	0.377563	−	0.217986i	−0.299195	−	0.954192i	$-0.596718\pi$
$47$	17.7455	−	10.2453i	0.377563	−	0.217986i	0.676757	+	0.736206i	$0.263385\pi$
$48$		0			0
$49$	−3.37239	−	5.84114i	−0.0688242	−	0.119207i
$50$		0			0
$51$	−17.8403	−	33.3719i	−0.349810	−	0.654351i
$52$		0			0
$53$	45.9725	+	26.5422i	0.867406	+	0.500797i	0.866485	−	0.499203i	$-0.166374\pi$
$53$	45.9725	+	26.5422i	0.867406	+	0.500797i	0.000920543		1.00000i	$0.499707\pi$
$54$		0			0
$55$	−17.7825	−	30.8003i	−0.323319	−	0.560005i
$56$		0			0
$57$	17.9511	−	54.0995i	0.314932	−	0.949114i
$58$		0			0
$59$	−17.9158	−	10.3437i	−0.303658	−	0.175317i	0.340427	−	0.940271i	$-0.389428\pi$
$59$	−17.9158	−	10.3437i	−0.303658	−	0.175317i	−0.644085	+	0.764954i	$0.722762\pi$
$60$		0			0
$61$	17.7246	+	30.6999i	0.290567	+	0.503277i	0.973944	−	0.226789i	$-0.0728227\pi$
$61$	17.7246	+	30.6999i	0.290567	+	0.503277i	−0.683377	+	0.730066i	$0.739489\pi$
$62$		0			0
$63$	37.3253	−	55.8762i	0.592465	−	0.886923i
$64$		0			0
$65$	28.5483	+	16.4823i	0.439204	+	0.253575i
$66$		0			0
$67$	107.499			1.60446			0.802229	−	0.597017i	$-0.203647\pi$
$67$	107.499			1.60446			0.802229	+	0.597017i	$0.203647\pi$
$68$		0			0
$69$	77.3849	+	2.52855i	1.12152	+	0.0366457i
$70$		0			0
$71$	−74.9285	+	43.2600i	−1.05533	+	0.609296i	−0.924137	−	0.382061i	$-0.875214\pi$
$71$	−74.9285	+	43.2600i	−1.05533	+	0.609296i	−0.131194	+	0.991357i	$0.541881\pi$
$72$		0			0
$73$	−25.3385	−	43.8876i	−0.347103	−	0.601200i	0.638630	−	0.769514i	$-0.279501\pi$
$73$	−25.3385	−	43.8876i	−0.347103	−	0.601200i	−0.985734	+	0.168313i	$0.946168\pi$
$74$		0			0
$75$	40.5239	−	21.6637i	0.540318	−	0.288849i
$76$		0			0
$77$	36.2170	−	20.9099i	0.470350	−	0.271557i
$78$		0			0
$79$	−41.7660			−0.528683			−0.264342	−	0.964429i	$-0.585155\pi$
$79$	−41.7660			−0.528683			−0.264342	+	0.964429i	$0.585155\pi$
$80$		0			0
$81$	80.3096	+	10.5528i	0.991477	+	0.130282i
$82$		0			0
$83$	90.2997	+	52.1346i	1.08795	+	0.628127i	0.933029	−	0.359800i	$-0.117155\pi$
$83$	90.2997	+	52.1346i	1.08795	+	0.628127i	0.154919	+	0.987927i	$0.450488\pi$
$84$		0			0
$85$	80.0919			0.942257
$86$		0			0
$87$	−12.9577	−	24.2387i	−0.148940	−	0.278605i
$88$		0			0
$89$	−32.7765	−	18.9235i	−0.368276	−	0.212624i	0.304429	−	0.952535i	$-0.401534\pi$
$89$	−32.7765	−	18.9235i	−0.368276	−	0.212624i	−0.672705	+	0.739911i	$0.734868\pi$
$90$		0			0
$91$	−19.3810	+	33.5689i	−0.212978	+	0.368889i
$92$		0			0
$93$	123.631	−	66.0922i	1.32937	−	0.710668i
$94$		0			0
$95$	83.0669	+	87.4891i	0.874388	+	0.920938i
$96$		0			0
$97$	−162.214			−1.67231			−0.836157	−	0.548490i	$-0.815203\pi$
$97$	−162.214			−1.67231			−0.836157	+	0.548490i	$0.815203\pi$
$98$		0			0
$99$	41.9183	+	28.0015i	0.423418	+	0.282843i
$100$		0			0
$101$	160.906	−	92.8990i	1.59313	−	0.919792i	0.600360	−	0.799730i	$-0.295024\pi$
$101$	160.906	−	92.8990i	1.59313	−	0.919792i	0.992766	−	0.120062i	$-0.0383093\pi$
$102$		0			0
$103$	−89.3215	−	154.709i	−0.867199	−	1.50203i	−0.864847	−	0.502035i	$-0.832585\pi$
$103$	−89.3215	−	154.709i	−0.867199	−	1.50203i	−0.00235139	−	0.999997i	$-0.500748\pi$
$104$		0			0
$105$	67.0508	+	125.425i	0.638579	+	1.19452i
$106$		0			0
$107$			143.064i			1.33705i	0.743690	+	0.668524i	$0.233074\pi$
$107$			143.064i			1.33705i	−0.743690	+	0.668524i	$0.766926\pi$
$108$		0			0
$109$	−13.3471	−	23.1179i	−0.122451	−	0.212091i	0.798283	−	0.602283i	$-0.205742\pi$
$109$	−13.3471	−	23.1179i	−0.122451	−	0.212091i	−0.920734	+	0.390192i	$0.872409\pi$
$110$		0			0
$111$	4.53747	−	138.867i	0.0408781	−	1.25105i
$112$		0			0
$113$	113.859	−	65.7363i	1.00760	−	0.581737i	0.0971109	−	0.995274i	$-0.469040\pi$
$113$	113.859	−	65.7363i	1.00760	−	0.581737i	0.910488	+	0.413536i	$0.135707\pi$
$114$		0			0
$115$	−81.9372	+	141.919i	−0.712497	+	1.23408i
$116$		0			0
$117$	−46.6251	−	3.05021i	−0.398505	−	0.0260701i
$118$		0			0
$119$			94.1773i			0.791406i
$120$		0			0
$121$	−44.8134	−	77.6191i	−0.370359	−	0.641480i
$122$		0			0
$123$	41.7447	−	67.1402i	0.339388	−	0.545855i
$124$		0			0
$125$		−	61.4828i		−	0.491862i
$126$		0			0
$127$	−45.9185	+	79.5332i	−0.361563	+	0.626245i	−0.988218	−	0.153051i	$-0.951090\pi$
$127$	−45.9185	+	79.5332i	−0.361563	+	0.626245i	0.626655	+	0.779297i	$0.284423\pi$
$128$		0			0
$129$	−5.47171	+	167.459i	−0.0424163	+	1.29813i
$130$		0			0
$131$	−5.86802	−	3.38790i	−0.0447941	−	0.0258619i	0.477436	−	0.878667i	$-0.341566\pi$
$131$	−5.86802	−	3.38790i	−0.0447941	−	0.0258619i	−0.522230	+	0.852805i	$0.674900\pi$
$132$		0			0
$133$	−102.875	+	97.6755i	−0.773500	+	0.734402i
$134$		0			0
$135$	−99.8333	+	139.372i	−0.739506	+	1.03238i
$136$		0			0
$137$	−16.3502	+	9.43981i	−0.119345	+	0.0689037i	−0.558484	−	0.829515i	$-0.688617\pi$
$137$	−16.3502	+	9.43981i	−0.119345	+	0.0689037i	0.439139	+	0.898419i	$0.355283\pi$
$138$		0			0
$139$	−223.615			−1.60874			−0.804369	−	0.594130i	$-0.797497\pi$
$139$	−223.615			−1.60874			−0.804369	+	0.594130i	$0.797497\pi$
$140$		0			0
$141$	−28.9811	−	54.2117i	−0.205539	−	0.384480i
$142$		0			0
$143$	−25.1834	−	14.5397i	−0.176108	−	0.101676i
$144$		0			0
$145$	58.1723			0.401188
$146$		0			0
$147$	−17.8445	+	9.53949i	−0.121391	+	0.0648945i
$148$		0			0
$149$	28.4164	+	16.4062i	0.190714	+	0.110109i	0.592317	−	0.805705i	$-0.298213\pi$
$149$	28.4164	+	16.4062i	0.190714	+	0.110109i	−0.401603	+	0.915814i	$0.631547\pi$
$150$		0			0
$151$	57.6278	−	99.8143i	0.381641	−	0.661022i	−0.609656	−	0.792666i	$-0.708692\pi$
$151$	57.6278	−	99.8143i	0.381641	−	0.661022i	0.991297	+	0.131644i	$0.0420256\pi$
$152$		0			0
$153$	−101.810	+	50.2228i	−0.665426	+	0.328254i
$154$		0			0
$155$			296.713i			1.91428i
$156$		0			0
$157$	8.64555	−	14.9745i	0.0550672	−	0.0953792i	−0.837178	−	0.546931i	$-0.815796\pi$
$157$	8.64555	−	14.9745i	0.0550672	−	0.0953792i	0.892245	+	0.451552i	$0.149129\pi$
$158$		0			0
$159$	84.0883	−	135.244i	0.528857	−	0.850588i
$160$		0			0
$161$	−166.878	−	96.3472i	−1.03651	−	0.598430i
$162$		0			0
$163$	−149.764			−0.918798			−0.459399	−	0.888230i	$-0.651935\pi$
$163$	−149.764			−0.918798			−0.459399	+	0.888230i	$0.651935\pi$
$164$		0			0
$165$	−94.0937	+	50.3016i	−0.570265	+	0.304858i
$166$		0			0
$167$		−	40.0088i		−	0.239574i	−0.992800	−	0.119787i	$-0.961779\pi$
$167$		−	40.0088i		−	0.239574i	0.992800	−	0.119787i	$-0.0382211\pi$
$168$		0			0
$169$	−142.047			−0.840514
$170$		0			0
$171$	−160.453	−	59.1249i	−0.938323	−	0.345760i
$172$		0			0
$173$		−	51.8082i		−	0.299469i	−0.988726	−	0.149735i	$-0.952158\pi$
$173$		−	51.8082i		−	0.299469i	0.988726	−	0.149735i	$-0.0478419\pi$
$174$		0			0
$175$	−114.361			−0.653489
$176$		0			0
$177$	−32.7698	+	52.7054i	−0.185140	+	0.297771i
$178$		0			0
$179$		−	246.793i		−	1.37873i	−0.724413	−	0.689366i	$-0.757889\pi$
$179$		−	246.793i		−	1.37873i	0.724413	−	0.689366i	$-0.242111\pi$
$180$		0			0
$181$	−7.45828	+	12.9181i	−0.0412060	+	0.0713709i	−0.885893	−	0.463890i	$-0.846453\pi$
$181$	−7.45828	+	12.9181i	−0.0412060	+	0.0713709i	0.844687	+	0.535261i	$0.179787\pi$
$182$		0			0
$183$	93.7871	−	50.1377i	0.512498	−	0.273976i
$184$		0			0
$185$	254.674	+	147.036i	1.37661	+	0.794788i
$186$		0			0
$187$	−70.6519			−0.377817
$188$		0			0
$189$	−163.882	−	117.391i	−0.867102	−	0.621114i
$190$		0			0
$191$	221.125	+	127.667i	1.15772	+	0.668412i	0.950758	−	0.309936i	$-0.100307\pi$
$191$	221.125	+	127.667i	1.15772	+	0.668412i	0.206967	+	0.978348i	$0.433641\pi$
$192$		0			0
$193$	−55.0680	+	95.3805i	−0.285326	+	0.494200i	−0.972688	−	0.232115i	$-0.925435\pi$
$193$	−55.0680	+	95.3805i	−0.285326	+	0.494200i	0.687362	+	0.726315i	$0.258769\pi$
$194$		0			0
$195$	52.2176	−	83.9843i	0.267783	−	0.430689i
$196$		0			0
$197$			237.875i			1.20749i	0.797178	+	0.603744i	$0.206325\pi$
$197$			237.875i			1.20749i	−0.797178	+	0.603744i	$0.793675\pi$
$198$		0			0
$199$	41.7395	−	72.2950i	0.209746	−	0.363291i	−0.741888	−	0.670524i	$-0.766070\pi$
$199$	41.7395	−	72.2950i	0.209746	−	0.363291i	0.951635	+	0.307232i	$0.0994029\pi$
$200$		0			0
$201$	10.5319	−	322.324i	0.0523977	−	1.60360i
$202$		0			0
$203$			68.4028i			0.336960i
$204$		0			0
$205$	83.6657	+	144.913i	0.408125	+	0.706894i
$206$		0			0
$207$	15.1632	−	231.783i	0.0732523	−	1.11973i
$208$		0			0
$209$	−73.2762	−	77.1772i	−0.350604	−	0.369269i
$210$		0			0
$211$	−48.1928	+	83.4724i	−0.228402	+	0.395604i	−0.957335	−	0.288982i	$-0.906683\pi$
$211$	−48.1928	+	83.4724i	−0.228402	+	0.395604i	0.728933	+	0.684585i	$0.240017\pi$
$212$		0			0
$213$	122.370	+	228.904i	0.574506	+	1.07467i
$214$		0			0
$215$	−307.109	−	177.310i	−1.42841	−	0.824696i
$216$		0			0
$217$	−348.895			−1.60781
$218$		0			0
$219$	−134.075	+	71.6752i	−0.612215	+	0.327284i
$220$		0			0
$221$	56.7126	−	32.7430i	0.256618	−	0.148159i
$222$		0			0
$223$	41.9524			0.188127			0.0940637	−	0.995566i	$-0.470014\pi$
$223$	41.9524			0.188127			0.0940637	+	0.995566i	$0.470014\pi$
$224$		0			0
$225$	−60.9861	−	123.629i	−0.271049	−	0.549463i
$226$		0			0
$227$	−249.167	−	143.857i	−1.09765	−	0.633731i	−0.162050	−	0.986783i	$-0.551811\pi$
$227$	−249.167	−	143.857i	−1.09765	−	0.633731i	−0.935604	+	0.353052i	$0.885144\pi$
$228$		0			0
$229$	46.6191	+	80.7466i	0.203577	+	0.352605i	0.949678	−	0.313227i	$-0.101410\pi$
$229$	46.6191	+	80.7466i	0.203577	+	0.352605i	−0.746102	+	0.665832i	$0.768077\pi$
$230$		0			0
$231$	−59.1479	−	110.642i	−0.256052	−	0.478968i
$232$		0			0
$233$	55.4506	−	32.0144i	0.237986	−	0.137401i	−0.376265	−	0.926512i	$-0.622792\pi$
$233$	55.4506	−	32.0144i	0.237986	−	0.137401i	0.614251	+	0.789111i	$0.289458\pi$
$234$		0			0
$235$	130.107			0.553647
$236$		0			0
$237$	−4.09193	+	125.231i	−0.0172655	+	0.528401i
$238$		0			0
$239$	−28.1997	+	16.2811i	−0.117990	+	0.0681217i	−0.557834	−	0.829953i	$-0.688367\pi$
$239$	−28.1997	+	16.2811i	−0.117990	+	0.0681217i	0.439843	+	0.898075i	$0.355034\pi$
$240$		0			0
$241$	13.8782	+	24.0377i	0.0575857	+	0.0997413i	0.893381	−	0.449300i	$-0.148326\pi$
$241$	13.8782	+	24.0377i	0.0575857	+	0.0997413i	−0.835795	+	0.549041i	$0.814993\pi$
$242$		0			0
$243$	39.5098	−	239.767i	0.162592	−	0.986693i
$244$		0			0
$245$		−	42.8264i		−	0.174802i
$246$		0			0
$247$	94.5864	+	27.9913i	0.382941	+	0.113325i
$248$		0			0
$249$	165.167	−	265.647i	0.663322	−	1.06685i
$250$		0			0
$251$	234.569	+	135.428i	0.934537	+	0.539555i	0.888244	−	0.459373i	$-0.151926\pi$
$251$	234.569	+	135.428i	0.934537	+	0.539555i	0.0462932	+	0.998928i	$0.485259\pi$
$252$		0			0
$253$	72.2797	−	125.192i	0.285691	−	0.494831i
$254$		0			0
$255$	7.84681	−	240.147i	0.0307718	−	0.941755i
$256$		0			0
$257$			464.897i			1.80894i	0.426539	+	0.904469i	$0.359733\pi$
$257$			464.897i			1.80894i	−0.426539	+	0.904469i	$0.640267\pi$
$258$		0			0
$259$	−172.894	+	299.462i	−0.667546	+	1.15622i
$260$		0			0
$261$	−73.9467	+	36.4778i	−0.283321	+	0.139762i
$262$		0			0
$263$		−	367.854i		−	1.39868i	−0.714787	−	0.699342i	$-0.753476\pi$
$263$		−	367.854i		−	1.39868i	0.714787	−	0.699342i	$-0.246524\pi$
$264$		0			0
$265$	168.532	+	291.906i	0.635969	+	1.10153i
$266$		0			0
$267$	−59.9515	+	96.4232i	−0.224538	+	0.361135i
$268$		0			0
$269$	−154.326	+	89.1001i	−0.573702	+	0.331227i	−0.758627	−	0.651526i	$-0.774129\pi$
$269$	−154.326	+	89.1001i	−0.573702	+	0.331227i	0.184925	+	0.982753i	$0.440796\pi$
$270$		0			0
$271$	−127.792	−	221.342i	−0.471558	−	0.816762i	0.527913	−	0.849299i	$-0.322975\pi$
$271$	−127.792	−	221.342i	−0.471558	−	0.816762i	−0.999471	+	0.0325367i	$0.989641\pi$
$272$		0			0
$273$	98.7543	+	61.4009i	0.361737	+	0.224912i
$274$		0			0
$275$		−	85.7934i		−	0.311976i
$276$		0			0
$277$	148.439	−	257.103i	0.535880	−	0.928171i	−0.463241	−	0.886233i	$-0.653313\pi$
$277$	148.439	−	257.103i	0.535880	−	0.928171i	0.999120	−	0.0419380i	$-0.0133532\pi$
$278$		0			0
$279$	−186.058	−	377.172i	−0.666875	−	1.35187i
$280$		0			0
$281$	−82.6827	+	47.7369i	−0.294244	+	0.169882i	−0.639854	−	0.768496i	$-0.721005\pi$
$281$	−82.6827	+	47.7369i	−0.294244	+	0.169882i	0.345610	+	0.938378i	$0.387672\pi$
$282$		0			0
$283$	84.5784	−	146.494i	0.298864	−	0.517647i	−0.677013	−	0.735971i	$-0.736726\pi$
$283$	84.5784	−	146.494i	0.298864	−	0.517647i	0.975876	+	0.218324i	$0.0700591\pi$
$284$		0			0
$285$	270.466	−	240.496i	0.949002	−	0.843846i
$286$		0			0
$287$	−170.399	+	98.3797i	−0.593723	+	0.342786i
$288$		0			0
$289$	−64.9467	+	112.491i	−0.224729	+	0.389242i
$290$		0			0
$291$	−15.8926	+	486.384i	−0.0546137	+	1.67142i
$292$		0			0
$293$	25.7450	−	14.8639i	0.0878669	−	0.0507300i	−0.455423	−	0.890275i	$-0.650512\pi$
$293$	25.7450	−	14.8639i	0.0878669	−	0.0507300i	0.543290	+	0.839545i	$0.317179\pi$
$294$		0			0
$295$	−65.6781	−	113.758i	−0.222638	−	0.385620i
$296$		0			0
$297$	88.0665	−	122.945i	0.296520	−	0.413955i
$298$		0			0
$299$			133.990i			0.448127i
$300$		0			0
$301$	208.492	−	361.119i	0.692665	−	1.19973i
$302$		0			0
$303$	−262.784	−	491.561i	−0.867274	−	1.62231i
$304$		0			0
$305$			225.087i			0.737990i
$306$		0			0
$307$	−175.632	−	304.203i	−0.572090	−	0.990889i	−0.996351	−	0.0853488i	$-0.972800\pi$
$307$	−175.632	−	304.203i	−0.572090	−	0.990889i	0.424261	−	0.905540i	$-0.360534\pi$
$308$		0			0
$309$	−472.631	+	252.664i	−1.52955	+	0.817683i
$310$		0			0
$311$	62.2618	−	35.9469i	0.200199	−	0.115585i	−0.396549	−	0.918013i	$-0.629792\pi$
$311$	62.2618	−	35.9469i	0.200199	−	0.115585i	0.596748	+	0.802429i	$0.296459\pi$
$312$		0			0
$313$	−197.262	−	341.668i	−0.630231	−	1.09159i	−0.987504	−	0.157592i	$-0.949627\pi$
$313$	−197.262	−	341.668i	−0.630231	−	1.09159i	0.357273	−	0.934000i	$-0.383707\pi$
$314$		0			0
$315$	382.643	−	188.757i	1.21474	−	0.599229i
$316$		0			0
$317$	−347.214	+	200.464i	−1.09531	+	0.632378i	−0.934986	−	0.354686i	$-0.884588\pi$
$317$	−347.214	+	200.464i	−1.09531	+	0.632378i	−0.160326	+	0.987064i	$0.551255\pi$
$318$		0			0
$319$	−51.3158			−0.160865
$320$		0			0
$321$	428.964	+	14.0164i	1.33634	+	0.0436647i
$322$		0			0
$323$	233.025	−	56.0078i	0.721440	−	0.173399i
$324$		0			0
$325$	39.7603	+	68.8668i	0.122339	+	0.211898i
$326$		0			0
$327$	−70.6244	+	37.7551i	−0.215977	+	0.115459i
$328$		0			0
$329$			152.988i			0.465010i
$330$		0			0
$331$	−67.5617	+	117.020i	−0.204114	+	0.353536i	−0.949850	−	0.312706i	$-0.898765\pi$
$331$	−67.5617	+	117.020i	−0.204114	+	0.353536i	0.745736	+	0.666241i	$0.232098\pi$
$332$		0			0
$333$	−415.934	−	27.2103i	−1.24905	−	0.0817126i
$334$		0			0
$335$	591.123	+	341.285i	1.76455	+	1.01876i
$336$		0			0
$337$	−64.1481	+	111.108i	−0.190350	+	0.329697i	−0.945366	−	0.326010i	$-0.894296\pi$
$337$	−64.1481	+	111.108i	−0.190350	+	0.329697i	0.755016	+	0.655706i	$0.227629\pi$
$338$		0			0
$339$	−185.949	−	347.834i	−0.548521	−	1.02606i
$340$		0			0
$341$		−	261.741i		−	0.767569i
$342$		0			0
$343$	−315.488			−0.919789
$344$		0			0
$345$	417.504	+	259.585i	1.21016	+	0.752419i
$346$		0			0
$347$	218.209	+	125.983i	0.628844	+	0.363063i	0.780304	−	0.625400i	$-0.215064\pi$
$347$	218.209	+	125.983i	0.628844	+	0.363063i	−0.151460	+	0.988463i	$0.548398\pi$
$348$		0			0
$349$	−69.2104	+	119.876i	−0.198310	+	0.343484i	−0.947981	−	0.318328i	$-0.896879\pi$
$349$	−69.2104	+	119.876i	−0.198310	+	0.343484i	0.749670	+	0.661812i	$0.230212\pi$
$350$		0			0
$351$	−13.7137	+	139.502i	−0.0390705	+	0.397441i
$352$		0			0
$353$	105.800	+	61.0837i	0.299717	+	0.173042i	0.642316	−	0.766440i	$-0.277974\pi$
$353$	105.800	+	61.0837i	0.299717	+	0.173042i	−0.342599	+	0.939482i	$0.611307\pi$
$354$		0			0
$355$	−549.365			−1.54751
$356$		0			0
$357$	282.381	+	9.22680i	0.790984	+	0.0258454i
$358$		0			0
$359$	−469.734	+	271.201i	−1.30845	+	0.755434i	−0.981838	−	0.189724i	$-0.939241\pi$
$359$	−469.734	+	271.201i	−1.30845	+	0.755434i	−0.326613	+	0.945158i	$0.605907\pi$
$360$		0			0
$361$	302.861	+	196.459i	0.838951	+	0.544207i
$362$		0			0
$363$	−237.124	+	126.764i	−0.653233	+	0.349212i
$364$		0			0
$365$		−	321.777i		−	0.881582i
$366$		0			0
$367$	−12.3943	−	21.4676i	−0.0337720	−	0.0584948i	0.848645	−	0.528962i	$-0.177419\pi$
$367$	−12.3943	−	21.4676i	−0.0337720	−	0.0584948i	−0.882417	+	0.470467i	$0.844085\pi$
$368$		0			0
$369$	−197.223	−	131.745i	−0.534480	−	0.357033i
$370$		0			0
$371$	−343.242	+	198.171i	−0.925180	+	0.534153i
$372$		0			0
$373$	328.888	+	569.650i	0.881736	+	1.52721i	0.849410	+	0.527734i	$0.176958\pi$
$373$	328.888	+	569.650i	0.881736	+	1.52721i	0.0323264	+	0.999477i	$0.489708\pi$
$374$		0			0
$375$	−184.350	−	6.02363i	−0.491600	−	0.0160630i
$376$		0			0
$377$	41.1915	−	23.7819i	0.109261	−	0.0630820i
$378$		0			0
$379$	−352.306			−0.929567			−0.464784	−	0.885424i	$-0.653868\pi$
$379$	−352.306			−0.929567			−0.464784	+	0.885424i	$0.653868\pi$
$380$		0			0
$381$	233.973	+	145.474i	0.614104	+	0.381822i
$382$		0			0
$383$	−576.717	−	332.968i	−1.50579	−	0.869368i	−0.999977	−	0.00672388i	$-0.997860\pi$
$383$	−576.717	−	332.968i	−1.50579	−	0.869368i	−0.505812	−	0.862644i	$-0.668807\pi$
$384$		0			0
$385$	265.537			0.689708
$386$		0			0
$387$	501.572	+	32.8127i	1.29605	+	0.0847874i
$388$		0			0
$389$	302.085	−	174.409i	0.776568	−	0.448352i	−0.0586449	−	0.998279i	$-0.518678\pi$
$389$	302.085	−	174.409i	0.776568	−	0.448352i	0.835212	+	0.549927i	$0.185345\pi$
$390$		0			0
$391$	162.773	+	281.930i	0.416298	+	0.721049i
$392$		0			0
$393$	−10.7332	+	17.2628i	−0.0273109	+	0.0439256i
$394$		0			0
$395$	−229.667	−	132.598i	−0.581434	−	0.335691i
$396$		0			0
$397$	−318.706	−	552.015i	−0.802787	−	1.39047i	−0.917775	−	0.397100i	$-0.870016\pi$
$397$	−318.706	−	552.015i	−0.802787	−	1.39047i	0.114989	−	0.993367i	$-0.463317\pi$
$398$		0			0
$399$	282.791	+	318.031i	0.708750	+	0.797071i
$400$		0			0
$401$	221.843	+	128.081i	0.553223	+	0.319404i	0.750421	−	0.660960i	$-0.229851\pi$
$401$	221.843	+	128.081i	0.553223	+	0.319404i	−0.197198	+	0.980364i	$0.563184\pi$
$402$		0			0
$403$	121.302	+	210.101i	0.300997	+	0.521342i
$404$		0			0
$405$	408.111	+	312.995i	1.00768	+	0.772826i
$406$		0			0
$407$	−224.657	−	129.706i	−0.551982	−	0.318687i
$408$		0			0
$409$	522.852			1.27837			0.639183	−	0.769054i	$-0.279273\pi$
$409$	522.852			1.27837			0.639183	+	0.769054i	$0.279273\pi$
$410$		0			0
$411$	26.7024	+	49.9493i	0.0649694	+	0.121531i
$412$		0			0
$413$	133.764	−	77.2287i	0.323884	−	0.186994i
$414$		0			0
$415$	331.032	+	573.364i	0.797667	+	1.38160i
$416$		0			0
$417$	−21.9081	+	670.486i	−0.0525375	+	1.60788i
$418$		0			0
$419$	69.0044	−	39.8397i	0.164688	−	0.0950828i	−0.415391	−	0.909643i	$-0.636355\pi$
$419$	69.0044	−	39.8397i	0.164688	−	0.0950828i	0.580079	+	0.814560i	$0.303022\pi$
$420$		0			0
$421$	249.760			0.593254			0.296627	−	0.954993i	$-0.404138\pi$
$421$	249.760			0.593254			0.296627	+	0.954993i	$0.404138\pi$
$422$		0			0
$423$	−165.388	+	81.5855i	−0.390988	+	0.192874i
$424$		0			0
$425$	167.320	+	96.6025i	0.393695	+	0.227300i
$426$		0			0
$427$	−264.672			−0.619841
$428$		0			0
$429$	−46.0630	+	74.0855i	−0.107373	+	0.172694i
$430$		0			0
$431$	362.196	+	209.114i	0.840362	+	0.485183i	0.857387	−	0.514672i	$-0.172086\pi$
$431$	362.196	+	209.114i	0.840362	+	0.485183i	−0.0170255	+	0.999855i	$0.505420\pi$
$432$		0			0
$433$	43.8115	−	75.8837i	0.101181	−	0.175251i	−0.810990	−	0.585060i	$-0.801071\pi$
$433$	43.8115	−	75.8837i	0.101181	−	0.175251i	0.912172	+	0.409808i	$0.134404\pi$
$434$		0			0
$435$	5.69929	−	174.424i	0.0131018	−	0.400974i
$436$		0			0
$437$	−139.150	+	470.209i	−0.318422	+	1.07599i
$438$		0			0
$439$	165.311			0.376563			0.188282	−	0.982115i	$-0.439708\pi$
$439$	165.311			0.376563			0.188282	+	0.982115i	$0.439708\pi$
$440$		0			0
$441$	26.8549	+	54.4395i	0.0608955	+	0.123446i
$442$		0			0
$443$	669.156	−	386.337i	1.51051	−	0.872094i	0.510586	−	0.859827i	$-0.329429\pi$
$443$	669.156	−	386.337i	1.51051	−	0.872094i	0.999925	−	0.0122666i	$-0.00390467\pi$
$444$		0			0
$445$	−120.156	−	208.117i	−0.270014	−	0.467678i
$446$		0			0
$447$	51.9764	−	83.5964i	0.116278	−	0.187017i
$448$		0			0
$449$		−	14.1079i		−	0.0314208i	−0.999877	−	0.0157104i	$-0.994999\pi$
$449$		−	14.1079i		−	0.0314208i	0.999877	−	0.0157104i	$-0.00500097\pi$
$450$		0			0
$451$	−73.8045	−	127.833i	−0.163646	−	0.283444i
$452$		0			0
$453$	−293.637	−	182.570i	−0.648206	−	0.403025i
$454$		0			0
$455$	−213.148	+	123.061i	−0.468458	+	0.270464i
$456$		0			0
$457$	337.400	−	584.395i	0.738294	−	1.27876i	−0.214969	−	0.976621i	$-0.568965\pi$
$457$	337.400	−	584.395i	0.738294	−	1.27876i	0.953263	−	0.302142i	$-0.0977016\pi$
$458$		0			0
$459$	140.613	+	310.188i	0.306347	+	0.675791i
$460$		0			0
$461$		−	272.357i		−	0.590795i	−0.955374	−	0.295398i	$-0.904548\pi$
$461$		−	272.357i		−	0.590795i	0.955374	−	0.295398i	$-0.0954522\pi$
$462$		0			0
$463$	−205.309	−	355.606i	−0.443432	−	0.768047i	0.554509	−	0.832178i	$-0.312906\pi$
$463$	−205.309	−	355.606i	−0.443432	−	0.768047i	−0.997942	+	0.0641303i	$0.979573\pi$
$464$		0			0
$465$	889.664	+	29.0697i	1.91326	+	0.0625156i
$466$		0			0
$467$			577.112i			1.23579i	0.786262	+	0.617893i	$0.212014\pi$
$467$			577.112i			1.23579i	−0.786262	+	0.617893i	$0.787986\pi$
$468$		0			0
$469$	−401.306	+	695.082i	−0.855662	+	1.48205i
$470$		0			0
$471$	−44.0526	−	27.3899i	−0.0935300	−	0.0581527i
$472$		0			0
$473$	270.912	+	156.411i	0.572752	+	0.330679i
$474$		0			0
$475$	68.0109	+	282.965i	0.143181	+	0.595715i
$476$		0			0
$477$	−397.276	−	265.381i	−0.832863	−	0.556353i
$478$		0			0
$479$	757.560	−	437.378i	1.58155	−	0.913106i	0.586912	−	0.809651i	$-0.300344\pi$
$479$	757.560	−	437.378i	1.58155	−	0.913106i	0.994634	−	0.103455i	$-0.0329898\pi$
$480$		0			0
$481$	240.444			0.499884
$482$		0			0
$483$	−305.237	+	490.928i	−0.631960	+	1.01641i
$484$		0			0
$485$	−891.999	−	514.996i	−1.83917	−	1.06185i
$486$		0			0
$487$	779.378			1.60037			0.800183	−	0.599756i	$-0.204736\pi$
$487$	779.378			1.60037			0.800183	+	0.599756i	$0.204736\pi$
$488$		0			0
$489$	−14.6728	+	449.053i	−0.0300057	+	0.918308i
$490$		0			0
$491$	768.030	+	443.422i	1.56422	+	0.903100i	0.996823	+	0.0796528i	$0.0253811\pi$
$491$	768.030	+	443.422i	1.56422	+	0.903100i	0.567393	+	0.823447i	$0.307952\pi$
$492$		0			0
$493$	57.7811	−	100.080i	0.117203	−	0.203002i
$494$		0			0
$495$	141.606	+	287.059i	0.286072	+	0.579916i
$496$		0			0
$497$		−	645.979i		−	1.29976i
$498$		0			0
$499$	42.8553	−	74.2276i	0.0858824	−	0.148753i	−0.819884	−	0.572529i	$-0.805962\pi$
$499$	42.8553	−	74.2276i	0.0858824	−	0.148753i	0.905767	+	0.423776i	$0.139296\pi$
$500$		0			0
$501$	−119.962	−	3.91977i	−0.239446	−	0.00782389i
$502$		0			0
$503$	84.7516	+	48.9314i	0.168492	+	0.0972791i	0.581875	−	0.813278i	$-0.302319\pi$
$503$	84.7516	+	48.9314i	0.168492	+	0.0972791i	−0.413382	+	0.910558i	$0.635653\pi$
$504$		0			0
$505$	1179.74			2.33611
$506$		0			0
$507$	−13.9167	+	425.913i	−0.0274491	+	0.840065i
$508$		0			0
$509$		−	368.916i		−	0.724785i	−0.932026	−	0.362392i	$-0.881960\pi$
$509$		−	368.916i		−	0.724785i	0.932026	−	0.362392i	$-0.118040\pi$
$510$		0			0
$511$	378.367			0.740444
$512$		0			0
$513$	−193.000	+	475.310i	−0.376219	+	0.926531i
$514$		0			0
$515$		−	1134.31i		−	2.20253i
$516$		0			0
$517$	−114.772			−0.221996
$518$		0			0
$519$	−155.342	−	5.07578i	−0.299309	−	0.00977993i
$520$		0			0
$521$		−	340.779i		−	0.654087i	−0.945009	−	0.327044i	$-0.893948\pi$
$521$		−	340.779i		−	0.654087i	0.945009	−	0.327044i	$-0.106052\pi$
$522$		0			0
$523$	363.130	−	628.959i	0.694321	−	1.20260i	−0.276088	−	0.961132i	$-0.589038\pi$
$523$	363.130	−	628.959i	0.694321	−	1.20260i	0.970409	−	0.241467i	$-0.0776284\pi$
$524$		0			0
$525$	−11.2042	+	342.899i	−0.0213414	+	0.653140i
$526$		0			0
$527$	510.466	+	294.718i	0.968627	+	0.559237i
$528$		0			0
$529$	−137.091			−0.259152
$530$		0			0
$531$	154.821	+	103.421i	0.291566	+	0.194766i
$532$		0			0
$533$	118.486	+	68.4082i	0.222301	+	0.128346i
$534$		0			0
$535$	−454.198	+	786.694i	−0.848968	+	1.47046i
$536$		0			0
$537$	−739.984	−	24.1790i	−1.37800	−	0.0450260i
$538$		0			0
$539$			37.7787i			0.0700903i
$540$		0			0
$541$	−6.83691	+	11.8419i	−0.0126375	+	0.0218889i	−0.872275	−	0.489016i	$-0.837356\pi$
$541$	−6.83691	+	11.8419i	−0.0126375	+	0.0218889i	0.859637	+	0.510905i	$0.170689\pi$
$542$		0			0
$543$	38.0030	+	23.6285i	0.0699871	+	0.0435148i
$544$		0			0
$545$		−	169.497i		−	0.311004i
$546$		0			0
$547$	−283.409	−	490.879i	−0.518115	−	0.897401i	−0.999779	−	0.0210451i	$-0.993301\pi$
$547$	−283.409	−	490.879i	−0.518115	−	0.897401i	0.481664	−	0.876356i	$-0.340033\pi$
$548$		0			0
$549$	−141.144	−	286.123i	−0.257093	−	0.521172i
$550$		0			0
$551$	169.251	−	40.6796i	0.307170	−	0.0738286i
$552$		0			0
$553$	155.918	−	270.057i	0.281948	−	0.488349i
$554$		0			0
$555$	465.823	−	749.208i	0.839321	−	1.34992i
$556$		0			0
$557$	−550.401	−	317.774i	−0.988153	−	0.570511i	−0.0834316	−	0.996514i	$-0.526588\pi$
$557$	−550.401	−	317.774i	−0.988153	−	0.570511i	−0.904722	+	0.426003i	$0.859921\pi$
$558$		0			0
$559$	−289.950			−0.518694
$560$		0			0
$561$	−6.92195	+	211.843i	−0.0123386	+	0.377616i
$562$		0			0
$563$	230.616	−	133.146i	0.409619	−	0.236494i	−0.281007	−	0.959706i	$-0.590668\pi$
$563$	230.616	−	133.146i	0.409619	−	0.236494i	0.690626	+	0.723212i	$0.257335\pi$
$564$		0			0
$565$	834.794			1.47751
$566$		0			0
$567$	−368.040	+	479.883i	−0.649100	+	0.846355i
$568$		0			0
$569$	−119.581	−	69.0401i	−0.210160	−	0.121336i	0.391226	−	0.920295i	$-0.372051\pi$
$569$	−119.581	−	69.0401i	−0.210160	−	0.121336i	−0.601386	+	0.798959i	$0.705384\pi$
$570$		0			0
$571$	−316.361	−	547.954i	−0.554048	−	0.959639i	−0.997977	−	0.0635774i	$-0.979749\pi$
$571$	−316.361	−	547.954i	−0.554048	−	0.959639i	0.443929	−	0.896062i	$-0.353584\pi$
$572$		0			0
$573$	404.460	−	650.514i	0.705864	−	1.13528i
$574$		0			0
$575$	−342.351	+	197.657i	−0.595393	+	0.343750i
$576$		0			0
$577$	−99.7397			−0.172859			−0.0864296	−	0.996258i	$-0.527546\pi$
$577$	−99.7397			−0.172859			−0.0864296	+	0.996258i	$0.527546\pi$
$578$		0			0
$579$	280.594	+	174.461i	0.484618	+	0.301314i
$580$		0			0
$581$	−674.199	+	389.249i	−1.16041	+	0.669964i
$582$		0			0
$583$	−148.668	−	257.500i	−0.255005	−	0.441681i
$584$		0			0
$585$	−246.703	−	164.797i	−0.421714	−	0.281705i
$586$		0			0
$587$		−	917.290i		−	1.56267i	−0.624109	−	0.781337i	$-0.714538\pi$
$587$		−	917.290i		−	1.56267i	0.624109	−	0.781337i	$-0.285462\pi$
$588$		0			0
$589$	207.490	+	863.277i	0.352275	+	1.46567i
$590$		0			0
$591$	713.245	+	23.3053i	1.20684	+	0.0394336i
$592$		0			0
$593$	−675.475	−	389.986i	−1.13908	−	0.657649i	−0.192878	−	0.981223i	$-0.561782\pi$
$593$	−675.475	−	389.986i	−1.13908	−	0.657649i	−0.946203	+	0.323574i	$0.895116\pi$
$594$		0			0
$595$	−298.993	+	517.870i	−0.502509	+	0.870371i
$596$		0			0
$597$	−212.680	−	132.235i	−0.356248	−	0.221499i
$598$		0			0
$599$			830.980i			1.38728i	0.720322	+	0.693640i	$0.243994\pi$
$599$			830.980i			1.38728i	−0.720322	+	0.693640i	$0.756006\pi$
$600$		0			0
$601$	160.866	−	278.628i	0.267664	−	0.463607i	−0.700594	−	0.713560i	$-0.747082\pi$
$601$	160.866	−	278.628i	0.267664	−	0.463607i	0.968258	+	0.249953i	$0.0804151\pi$
$602$		0			0
$603$	−965.424	−	63.1579i	−1.60104	−	0.104739i
$604$		0			0
$605$		−	569.091i		−	0.940647i
$606$		0			0
$607$	353.985	+	613.121i	0.583172	+	1.01008i	0.995101	+	0.0988672i	$0.0315219\pi$
$607$	353.985	+	613.121i	0.583172	+	1.01008i	−0.411929	+	0.911216i	$0.635145\pi$
$608$		0			0
$609$	205.099	+	6.70160i	0.336780	+	0.0110043i
$610$		0			0
$611$	92.1281	−	53.1902i	0.150782	−	0.0870543i
$612$		0			0
$613$	−239.920	−	415.553i	−0.391386	−	0.677901i	0.601246	−	0.799064i	$-0.294671\pi$
$613$	−239.920	−	415.553i	−0.391386	−	0.677901i	−0.992633	+	0.121163i	$0.961338\pi$
$614$		0			0
$615$	442.705	−	236.666i	0.719845	−	0.384822i
$616$		0			0
$617$		−	712.370i		−	1.15457i	−0.816543	−	0.577285i	$-0.804112\pi$
$617$		−	712.370i		−	1.15457i	0.816543	−	0.577285i	$-0.195888\pi$
$618$		0			0
$619$	−238.695	+	413.431i	−0.385613	+	0.667902i	−0.991854	−	0.127379i	$-0.959343\pi$
$619$	−238.695	+	413.431i	−0.385613	+	0.667902i	0.606241	+	0.795281i	$0.292677\pi$
$620$		0			0
$621$	−693.493	−	68.1738i	−1.11674	−	0.109781i
$622$		0			0
$623$	244.718	−	141.288i	0.392805	−	0.226786i
$624$		0			0
$625$	386.657	−	669.710i	0.618652	−	1.07154i
$626$		0			0
$627$	−238.587	+	212.150i	−0.380522	+	0.338358i
$628$		0			0
$629$	505.922	−	292.094i	0.804328	−	0.464379i
$630$		0			0
$631$	−138.225	+	239.412i	−0.219057	+	0.379417i	−0.954520	−	0.298147i	$-0.903631\pi$
$631$	−138.225	+	239.412i	−0.219057	+	0.379417i	0.735463	+	0.677565i	$0.236965\pi$
$632$		0			0
$633$	245.562	+	152.679i	0.387934	+	0.241200i
$634$		0			0
$635$	−505.001	+	291.563i	−0.795278	+	0.459154i
$636$		0			0
$637$	−17.5082	−	30.3251i	−0.0274854	−	0.0476062i
$638$		0			0
$639$	698.334	−	344.487i	1.09285	−	0.539104i
$640$		0			0
$641$			668.085i			1.04225i	0.853479	+	0.521127i	$0.174488\pi$
$641$			668.085i			1.04225i	−0.853479	+	0.521127i	$0.825512\pi$
$642$		0			0
$643$	77.9765	−	135.059i	0.121270	−	0.210045i	−0.798999	−	0.601333i	$-0.794637\pi$
$643$	77.9765	−	135.059i	0.121270	−	0.210045i	0.920269	+	0.391287i	$0.127970\pi$
$644$		0			0
$645$	−561.733	+	903.465i	−0.870904	+	1.40072i
$646$		0			0
$647$			325.510i			0.503107i	0.967843	+	0.251554i	$0.0809415\pi$
$647$			325.510i			0.503107i	−0.967843	+	0.251554i	$0.919058\pi$
$648$		0			0
$649$	57.9370	+	100.350i	0.0892712	+	0.154622i
$650$		0			0
$651$	−34.1821	+	1046.13i	−0.0525071	+	1.60695i
$652$		0			0
$653$	−970.469	+	560.300i	−1.48617	+	0.858040i	−0.999876	−	0.0157554i	$-0.994985\pi$
$653$	−970.469	+	560.300i	−1.48617	+	0.858040i	−0.486293	+	0.873796i	$0.661651\pi$
$654$		0			0
$655$	−21.5117	−	37.2594i	−0.0328423	−	0.0568846i
$656$		0			0
$657$	201.775	+	409.033i	0.307116	+	0.622577i
$658$		0			0
$659$	1001.48	−	578.202i	1.51969	−	0.877394i	0.519959	−	0.854191i	$-0.325947\pi$
$659$	1001.48	−	578.202i	1.51969	−	0.877394i	0.999731	−	0.0232026i	$-0.00738629\pi$
$660$		0			0
$661$	−819.897			−1.24039			−0.620194	−	0.784448i	$-0.712946\pi$
$661$	−819.897			−1.24039			−0.620194	+	0.784448i	$0.712946\pi$
$662$		0			0
$663$	−92.6205	−	173.255i	−0.139699	−	0.261320i
$664$		0			0
$665$	−875.799	+	210.499i	−1.31699	+	0.316540i
$666$		0			0
$667$	118.225	+	204.771i	0.177249	+	0.307004i
$668$		0			0
$669$	4.11019	−	125.790i	0.00614378	−	0.188027i
$670$		0			0
$671$		−	198.557i		−	0.295912i
$672$		0			0
$673$	307.896	−	533.292i	0.457498	−	0.792410i	−0.541330	−	0.840810i	$-0.682079\pi$
$673$	307.896	−	533.292i	0.457498	−	0.792410i	0.998828	+	0.0484006i	$0.0154124\pi$
$674$		0			0
$675$	−376.665	+	170.748i	−0.558022	+	0.252961i
$676$		0			0
$677$	−721.894	−	416.786i	−1.06631	−	0.615636i	−0.139141	−	0.990273i	$-0.544434\pi$
$677$	−721.894	−	416.786i	−1.06631	−	0.615636i	−0.927172	+	0.374636i	$0.877768\pi$
$678$		0			0
$679$	605.566	−	1048.87i	0.891850	−	1.54473i
$680$		0			0
$681$	−455.752	+	733.009i	−0.669239	+	1.07637i
$682$		0			0
$683$			162.807i			0.238370i	0.992872	+	0.119185i	$0.0380282\pi$
$683$			162.807i			0.238370i	−0.992872	+	0.119185i	$0.961972\pi$
$684$		0			0
$685$	−119.877			−0.175003
$686$		0			0
$687$	246.678	−	131.872i	0.359065	−	0.191953i
$688$		0			0
$689$	238.673	+	137.798i	0.346405	+	0.199997i
$690$		0			0
$691$	−113.291	+	196.226i	−0.163952	+	0.283974i	−0.936283	−	0.351247i	$-0.885758\pi$
$691$	−113.291	+	196.226i	−0.163952	+	0.283974i	0.772330	+	0.635221i	$0.219091\pi$
$692$		0			0
$693$	−337.543	+	166.509i	−0.487074	+	0.240273i
$694$		0			0
$695$	−1229.63	−	709.928i	−1.76925	−	1.02148i
$696$		0			0
$697$	332.413			0.476919
$698$		0			0
$699$	−90.5594	−	169.400i	−0.129556	−	0.242346i
$700$		0			0
$701$	603.483	−	348.421i	0.860888	−	0.497034i	−0.00342124	−	0.999994i	$-0.501089\pi$
$701$	603.483	−	348.421i	0.860888	−	0.497034i	0.864310	+	0.502960i	$0.167756\pi$
$702$		0			0
$703$	843.787	+	249.705i	1.20027	+	0.355199i
$704$		0			0
$705$	12.7469	−	390.113i	0.0180807	−	0.553351i
$706$		0			0
$707$			1387.21i			1.96211i
$708$		0			0
$709$	238.126	+	412.447i	0.335862	+	0.581730i	0.983650	−	0.180091i	$-0.0576391\pi$
$709$	238.126	+	412.447i	0.335862	+	0.581730i	−0.647788	+	0.761821i	$0.724306\pi$
$710$		0			0
$711$	375.092	+	24.5385i	0.527556	+	0.0345126i
$712$		0			0
$713$	−1044.45	+	603.016i	−1.46487	+	0.845745i
$714$		0			0
$715$	−92.3206	−	159.904i	−0.129120	−	0.223642i
$716$		0			0
$717$	46.0544	+	86.1490i	0.0642321	+	0.120152i
$718$		0			0
$719$	−134.505	+	77.6567i	−0.187073	+	0.108007i	−0.590611	−	0.806956i	$-0.701113\pi$
$719$	−134.505	+	77.6567i	−0.187073	+	0.108007i	0.403539	+	0.914963i	$0.367780\pi$
$720$		0			0
$721$	1333.79			1.84992
$722$		0			0
$723$	73.4342	−	39.2572i	0.101569	−	0.0542977i
$724$		0			0
$725$	121.528	+	70.1643i	0.167625	+	0.0967783i
$726$		0			0
$727$	1167.10			1.60537			0.802683	−	0.596406i	$-0.203405\pi$
$727$	1167.10			1.60537			0.802683	+	0.596406i	$0.203405\pi$
$728$		0			0
$729$	−715.045	−	141.957i	−0.980857	−	0.194728i
$730$		0			0
$731$	−610.088	+	352.235i	−0.834594	+	0.481853i
$732$		0			0
$733$	435.020	+	753.476i	0.593478	+	1.02793i	0.993760	+	0.111542i	$0.0355790\pi$
$733$	435.020	+	753.476i	0.593478	+	1.02793i	−0.400281	+	0.916392i	$0.631088\pi$
$734$		0			0
$735$	−128.411	−	4.19582i	−0.174708	−	0.00570859i
$736$		0			0
$737$	−521.451	−	301.060i	−0.707531	−	0.408493i
$738$		0			0
$739$	−264.833	−	458.704i	−0.358367	−	0.620709i	0.629322	−	0.777145i	$-0.283333\pi$
$739$	−264.833	−	458.704i	−0.358367	−	0.620709i	−0.987688	+	0.156436i	$0.950000\pi$
$740$		0			0
$741$	93.1959	−	280.865i	0.125770	−	0.379036i
$742$		0			0
$743$	−414.307	−	239.200i	−0.557613	−	0.321938i	0.194574	−	0.980888i	$-0.437668\pi$
$743$	−414.307	−	239.200i	−0.557613	−	0.321938i	−0.752187	+	0.658950i	$0.771001\pi$
$744$		0			0
$745$	104.172	+	180.432i	0.139829	+	0.242191i
$746$		0			0
$747$	−780.334	−	521.263i	−1.04462	−	0.697809i
$748$		0			0
$749$	−925.047	−	534.076i	−1.23504	−	0.713052i
$750$		0			0
$751$	−760.258			−1.01233			−0.506164	−	0.862437i	$-0.668937\pi$
$751$	−760.258			−1.01233			−0.506164	+	0.862437i	$0.668937\pi$
$752$		0			0
$753$	429.050	−	690.063i	0.569787	−	0.916418i
$754$		0			0
$755$	633.778	−	365.912i	0.839441	−	0.484652i
$756$		0			0
$757$	−189.020	−	327.392i	−0.249696	−	0.432486i	0.713746	−	0.700405i	$-0.246997\pi$
$757$	−189.020	−	327.392i	−0.249696	−	0.432486i	−0.963441	+	0.267919i	$0.913664\pi$
$758$		0			0
$759$	−368.295	−	228.989i	−0.485237	−	0.301698i
$760$		0			0
$761$	362.168	−	209.098i	0.475911	−	0.274767i	−0.242800	−	0.970076i	$-0.578066\pi$
$761$	362.168	−	209.098i	0.475911	−	0.274767i	0.718711	+	0.695309i	$0.244732\pi$
$762$		0			0
$763$	199.306			0.261214
$764$		0			0
$765$	−719.289	−	47.0558i	−0.940247	−	0.0615108i
$766$		0			0
$767$	−93.0126	−	53.7009i	−0.121268	−	0.0700142i
$768$		0			0
$769$	1301.90			1.69297			0.846486	−	0.532411i	$-0.178714\pi$
$769$	1301.90			1.69297			0.846486	+	0.532411i	$0.178714\pi$
$770$		0			0
$771$	1393.95	+	45.5472i	1.80797	+	0.0590755i
$772$		0			0
$773$	−0.961798	−	0.555294i	−0.00124424	−	0.000718362i	0.499378	−	0.866384i	$-0.333562\pi$
$773$	−0.961798	−	0.555294i	−0.00124424	−	0.000718362i	−0.500622	+	0.865666i	$0.666895\pi$
$774$		0			0
$775$	−357.879	+	619.865i	−0.461779	+	0.799826i
$776$		0			0
$777$	880.968	+	547.746i	1.13381	+	0.704950i
$778$		0			0
$779$	344.760	+	363.114i	0.442568	+	0.466128i
$780$		0			0
$781$	484.614			0.620504
$782$		0			0
$783$	102.130	+	225.296i	0.130435	+	0.287734i
$784$		0			0
$785$	95.0818	−	54.8955i	0.121123	−	0.0699306i
$786$		0			0
$787$	−726.228	−	1257.86i	−0.922780	−	1.59830i	−0.795093	−	0.606488i	$-0.792578\pi$
$787$	−726.228	−	1257.86i	−0.922780	−	1.59830i	−0.127687	−	0.991814i	$-0.540755\pi$
$788$		0			0
$789$	−1102.97	−	36.0396i	−1.39794	−	0.0456776i
$790$		0			0
$791$			981.606i			1.24097i
$792$		0			0
$793$	92.0198	+	159.383i	0.116040	+	0.200987i
$794$		0			0
$795$	891.761	−	476.727i	1.12171	−	0.599656i
$796$		0			0
$797$	−565.944	+	326.748i	−0.710093	+	0.409972i	−0.811095	−	0.584914i	$-0.801128\pi$
$797$	−565.944	+	326.748i	−0.710093	+	0.409972i	0.101003	+	0.994886i	$0.467795\pi$
$798$		0			0
$799$	129.232	−	223.837i	0.161742	−	0.280146i
$800$		0			0
$801$	283.242	+	189.206i	0.353610	+	0.236212i
$802$		0			0
$803$			283.851i			0.353488i
$804$		0			0
$805$	−611.763	−	1059.60i	−0.759954	−	1.31628i
$806$		0			0
$807$	252.038	+	471.460i	0.312315	+	0.584213i
$808$		0			0
$809$			307.348i			0.379911i	0.981793	+	0.189956i	$0.0608344\pi$
$809$			307.348i			0.379911i	−0.981793	+	0.189956i	$0.939166\pi$
$810$		0			0
$811$	−483.368	+	837.219i	−0.596015	+	1.03233i	0.397388	+	0.917651i	$0.369917\pi$
$811$	−483.368	+	837.219i	−0.596015	+	1.03233i	−0.993403	+	0.114678i	$0.963416\pi$
$812$		0			0
$813$	−676.193	+	361.486i	−0.831726	+	0.444633i
$814$		0			0
$815$	−823.536	−	475.469i	−1.01047	−	0.583397i
$816$		0			0
$817$	−1017.52	−	301.117i	−1.24543	−	0.368564i
$818$		0			0
$819$	193.780	−	290.089i	0.236605	−	0.354199i
$820$		0			0
$821$	919.053	−	530.615i	1.11943	−	0.646304i	0.178175	−	0.983999i	$-0.442981\pi$
$821$	919.053	−	530.615i	1.11943	−	0.646304i	0.941256	+	0.337695i	$0.109647\pi$
$822$		0			0
$823$	−1137.67			−1.38234			−0.691170	−	0.722692i	$-0.742905\pi$
$823$	−1137.67			−1.38234			−0.691170	+	0.722692i	$0.742905\pi$
$824$		0			0
$825$	−257.243	−	8.40540i	−0.311809	−	0.0101884i
$826$		0			0
$827$	−1240.79	−	716.370i	−1.50035	−	0.866227i	−1.00000		0.000403585i	$-0.999872\pi$
$827$	−1240.79	−	716.370i	−1.50035	−	0.866227i	−0.500349	−	0.865824i	$-0.666795\pi$
$828$		0			0
$829$	476.786			0.575133			0.287567	−	0.957761i	$-0.407154\pi$
$829$	476.786			0.575133			0.287567	+	0.957761i	$0.407154\pi$
$830$		0			0
$831$	−756.355	−	470.267i	−0.910175	−	0.565905i
$832$		0			0
$833$	−73.6787	−	42.5384i	−0.0884499	−	0.0510665i
$834$		0			0
$835$	127.019	−	220.004i	0.152119	−	0.263478i
$836$		0			0
$837$	−1149.14	+	520.924i	−1.37293	+	0.622371i
$838$		0			0
$839$		−	116.111i		−	0.138392i	−0.997603	−	0.0691959i	$-0.977957\pi$
$839$		−	116.111i		−	0.138392i	0.997603	−	0.0691959i	$-0.0220433\pi$
$840$		0			0
$841$	−378.532	+	655.637i	−0.450098	+	0.779593i
$842$		0			0
$843$	135.034	+	252.593i	0.160182	+	0.299635i
$844$		0			0
$845$	−781.100	−	450.968i	−0.924378	−	0.533690i
$846$		0			0
$847$	669.175			0.790054
$848$		0			0
$849$	−430.962	−	267.952i	−0.507611	−	0.315609i
$850$		0			0
$851$			1195.30i			1.40458i
$852$		0			0
$853$	−1320.36			−1.54790			−0.773951	−	0.633246i	$-0.781722\pi$
$853$	−1320.36			−1.54790			−0.773951	+	0.633246i	$0.781722\pi$
$854$		0			0
$855$	−694.605	−	834.526i	−0.812404	−	0.976054i
$856$		0			0
$857$		−	68.7778i		−	0.0802542i	−0.999195	−	0.0401271i	$-0.987224\pi$
$857$		−	68.7778i		−	0.0802542i	0.999195	−	0.0401271i	$-0.0127763\pi$
$858$		0			0
$859$	66.9928			0.0779893			0.0389947	−	0.999239i	$-0.487584\pi$
$859$	66.9928			0.0779893			0.0389947	+	0.999239i	$0.487584\pi$
$860$		0			0
$861$	278.287	+	520.562i	0.323214	+	0.604601i
$862$		0			0
$863$			983.878i			1.14007i	0.821621	+	0.570034i	$0.193070\pi$
$863$			983.878i			1.14007i	−0.821621	+	0.570034i	$0.806930\pi$
$864$		0			0
$865$	164.480	−	284.887i	0.190150	−	0.329349i
$866$		0			0
$867$	330.930	+	205.757i	0.381695	+	0.237321i
$868$		0			0
$869$	202.597	+	116.969i	0.233138	+	0.134602i
$870$		0			0
$871$	558.095			0.640752
$872$		0			0
$873$	1456.82	+	95.3046i	1.66875	+	0.109169i
$874$		0			0
$875$	397.545	+	229.523i	0.454337	+	0.262312i
$876$		0			0
$877$	−397.741	+	688.907i	−0.453524	+	0.785527i	−0.998602	−	0.0528583i	$-0.983167\pi$
$877$	−397.741	+	688.907i	−0.453524	+	0.785527i	0.545078	+	0.838386i	$0.316500\pi$
$878$		0			0
$879$	−42.0455	−	78.6500i	−0.0478334	−	0.0894767i
$880$		0			0
$881$		−	1278.78i		−	1.45151i	−0.687955	−	0.725753i	$-0.741491\pi$
$881$		−	1278.78i		−	1.45151i	0.687955	−	0.725753i	$-0.258509\pi$
$882$		0			0
$883$	−423.514	+	733.548i	−0.479631	+	0.830745i	−0.999727	−	0.0233629i	$-0.992563\pi$
$883$	−423.514	+	733.548i	−0.479631	+	0.830745i	0.520096	+	0.854108i	$0.325896\pi$
$884$		0			0
$885$	−347.526	+	185.784i	−0.392685	+	0.209926i
$886$		0			0
$887$		−	822.198i		−	0.926943i	−0.886112	−	0.463471i	$-0.846604\pi$
$887$		−	822.198i		−	0.926943i	0.886112	−	0.463471i	$-0.153396\pi$
$888$		0			0
$889$	−342.839	−	593.814i	−0.385645	−	0.667957i
$890$		0			0
$891$	−360.009	−	276.104i	−0.404050	−	0.309881i
$892$		0			0
$893$	378.543	−	90.9831i	0.423900	−	0.101885i
$894$		0			0
$895$	783.515	−	1357.09i	0.875435	−	1.51630i
$896$		0			0
$897$	401.755	+	13.1273i	0.447887	+	0.0146347i
$898$		0			0
$899$	370.761	+	214.059i	0.412415	+	0.238108i
$900$		0			0
$901$	669.594			0.743168
$902$		0			0
$903$	−1062.35	−	660.523i	−1.17647	−	0.731476i
$904$		0			0
$905$	−82.0245	+	47.3569i	−0.0906348	+	0.0523280i
$906$		0			0
$907$	−751.679			−0.828753			−0.414376	−	0.910106i	$-0.636000\pi$
$907$	−751.679			−0.828753			−0.414376	+	0.910106i	$0.636000\pi$
$908$		0			0
$909$	−1499.64	+	739.772i	−1.64977	+	0.813830i
$910$		0			0
$911$	−1194.64	−	689.727i	−1.31135	−	0.757110i	−0.329033	−	0.944318i	$-0.606723\pi$
$911$	−1194.64	−	689.727i	−1.31135	−	0.757110i	−0.982320	+	0.187208i	$0.940056\pi$
$912$		0			0
$913$	−292.015	−	505.785i	−0.319841	−	0.553981i
$914$		0			0
$915$	674.901	+	22.0524i	0.737597	+	0.0241010i
$916$		0			0
$917$	43.8121	−	25.2949i	0.0477776	−	0.0275844i
$918$		0			0
$919$	149.957			0.163174			0.0815868	−	0.996666i	$-0.474001\pi$
$919$	149.957			0.163174			0.0815868	+	0.996666i	$0.474001\pi$
$920$		0			0
$921$	−929.329	+	496.810i	−1.00904	+	0.539425i
$922$		0			0
$923$	−389.002	+	224.590i	−0.421454	+	0.243327i
$924$		0			0
$925$	354.694	+	614.347i	0.383452	+	0.664159i
$926$		0			0
$927$	711.283	+	1441.89i	0.767296	+	1.55544i
$928$		0			0
$929$		−	161.959i		−	0.174337i	−0.996194	−	0.0871683i	$-0.972218\pi$
$929$		−	161.959i		−	0.174337i	0.996194	−	0.0871683i	$-0.0277818\pi$
$930$		0			0
$931$	−29.9483	−	124.602i	−0.0321679	−	0.133837i
$932$		0			0
$933$	−101.683	−	190.208i	−0.108985	−	0.203867i
$934$		0			0
$935$	−388.507	−	224.304i	−0.415515	−	0.239898i
$936$		0			0
$937$	−705.449	+	1221.87i	−0.752881	+	1.30403i	0.193540	+	0.981092i	$0.438003\pi$
$937$	−705.449	+	1221.87i	−0.752881	+	1.30403i	−0.946421	+	0.322935i	$0.895330\pi$
$938$		0			0
$939$	−1043.78	+	557.997i	−1.11159	+	0.594246i
$940$		0			0
$941$			342.066i			0.363513i	0.983344	+	0.181757i	$0.0581783\pi$
$941$			342.066i			0.363513i	−0.983344	+	0.181757i	$0.941822\pi$
$942$		0			0
$943$	−340.072	+	589.021i	−0.360627	+	0.624625i
$944$		0			0
$945$	−528.480	−	1165.81i	−0.559239	−	1.23366i
$946$		0			0
$947$			358.584i			0.378652i	0.981914	+	0.189326i	$0.0606303\pi$
$947$			358.584i			0.378652i	−0.981914	+	0.189326i	$0.939370\pi$
$948$		0			0
$949$	−131.549	−	227.849i	−0.138618	−	0.240094i
$950$		0			0
$951$	567.054	+	1060.73i	0.596271	+	1.11538i
$952$		0			0
$953$	228.456	−	131.899i	0.239723	−	0.138404i	−0.375326	−	0.926893i	$-0.622469\pi$
$953$	228.456	−	131.899i	0.239723	−	0.138404i	0.615050	+	0.788488i	$0.289136\pi$
$954$		0			0
$955$	810.629	+	1404.05i	0.848826	+	1.47021i
$956$		0			0
$957$	−5.02755	+	153.865i	−0.00525344	+	0.160779i
$958$		0			0
$959$		−	140.960i		−	0.146986i
$960$		0			0
$961$	−611.328	+	1058.85i	−0.636137	+	1.10182i
$962$		0			0
$963$	84.0534	−	1284.83i	0.0872829	−	1.33420i
$964$		0			0
$965$	−605.625	+	349.658i	−0.627591	+	0.362340i
$966$		0			0
$967$	373.013	−	646.078i	0.385743	−	0.668126i	−0.606129	−	0.795366i	$-0.707279\pi$
$967$	373.013	−	646.078i	0.385743	−	0.668126i	0.991872	+	0.127240i	$0.0406120\pi$
$968$		0			0
$969$	−145.104	−	704.189i	−0.149746	−	0.726718i
$970$		0			0
$971$	1462.99	−	844.659i	1.50669	−	0.869886i	0.506717	−	0.862112i	$-0.330859\pi$
$971$	1462.99	−	844.659i	1.50669	−	0.869886i	0.999970	−	0.00777358i	$-0.00247443\pi$
$972$		0			0
$973$	834.781	−	1445.88i	0.857945	−	1.48600i
$974$		0			0
$975$	210.386	−	112.470i	0.215780	−	0.115354i
$976$		0			0
$977$	1140.33	−	658.373i	1.16718	−	0.673872i	0.214166	−	0.976797i	$-0.431297\pi$
$977$	1140.33	−	658.373i	1.16718	−	0.673872i	0.953014	+	0.302926i	$0.0979634\pi$
$978$		0			0
$979$	105.994	+	183.587i	0.108268	+	0.187525i
$980$		0			0
$981$	106.286	+	215.459i	0.108344	+	0.219632i
$982$		0			0
$983$		−	750.784i		−	0.763768i	−0.924210	−	0.381884i	$-0.875275\pi$
$983$		−	750.784i		−	0.763768i	0.924210	−	0.381884i	$-0.124725\pi$
$984$		0			0
$985$	−755.203	+	1308.05i	−0.766703	+	1.32797i
$986$		0			0
$987$	458.720	+	14.9887i	0.464762	+	0.0151861i
$988$		0			0
$989$		−	1441.40i		−	1.45743i
$990$		0			0
$991$	−140.771	−	243.823i	−0.142050	−	0.246038i	0.786219	−	0.617949i	$-0.212036\pi$
$991$	−140.771	−	243.823i	−0.142050	−	0.246038i	−0.928268	+	0.371911i	$0.878703\pi$
$992$		0			0
$993$	344.254	+	214.042i	0.346681	+	0.215551i
$994$		0			0
$995$	459.042	−	265.028i	0.461349	−	0.266360i
$996$		0			0
$997$	−258.176	−	447.173i	−0.258952	−	0.448519i	0.707009	−	0.707204i	$-0.250044\pi$
$997$	−258.176	−	447.173i	−0.258952	−	0.448519i	−0.965962	+	0.258686i	$0.916711\pi$
$998$		0			0
$999$	−122.338	+	1244.47i	−0.122460	+	1.24572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.20	yes	80
3.2	odd	2		2052.3.be.a.197.6		80
9.4	even	3		2052.3.m.a.881.6		80
9.5	odd	6		684.3.m.a.653.7	yes	80
19.11	even	3		684.3.m.a.353.7	✓	80
57.11	odd	6		2052.3.m.a.1493.35		80
171.49	even	3		2052.3.be.a.125.6		80
171.68	odd	6	inner	684.3.be.a.581.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.7	✓	80	19.11	even	3
684.3.m.a.653.7	yes	80	9.5	odd	6
684.3.be.a.425.20	yes	80	1.1	even	1	trivial
684.3.be.a.581.20	yes	80	171.68	odd	6	inner
2052.3.m.a.881.6		80	9.4	even	3
2052.3.m.a.1493.35		80	57.11	odd	6
2052.3.be.a.125.6		80	171.49	even	3
2052.3.be.a.197.6		80	3.2	odd	2

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0979727 - 2.99840i) q^{3} +(5.49889 + 3.17478i) q^{5} +(-3.73312 + 6.46596i) q^{7} +(-8.98080 - 0.587522i) q^{9} +O(q^{10})\)	\(q+(0.0979727 - 2.99840i) q^{3} +(5.49889 + 3.17478i) q^{5} +(-3.73312 + 6.46596i) q^{7} +(-8.98080 - 0.587522i) q^{9} +(-4.85076 - 2.80059i) q^{11} +5.19164 q^{13} +(10.0580 - 16.1768i) q^{15} +(10.9238 - 6.30688i) q^{17} +(18.2190 + 5.39160i) q^{19} +(19.0218 + 11.8269i) q^{21} +25.8087i q^{23} +(7.65851 + 13.2649i) q^{25} +(-2.64150 + 26.8705i) q^{27} +(7.93419 - 4.58080i) q^{29} +(23.3648 + 40.4690i) q^{31} +(-8.87253 + 14.2701i) q^{33} +(-41.0560 + 23.7037i) q^{35} +46.3137 q^{37} +(0.508639 - 15.5666i) q^{39} +(22.8225 + 13.1766i) q^{41} -55.8493 q^{43} +(-47.5192 - 31.7428i) q^{45} +(17.7455 - 10.2453i) q^{47} +(-3.37239 - 5.84114i) q^{49} +(-17.8403 - 33.3719i) q^{51} +(45.9725 + 26.5422i) q^{53} +(-17.7825 - 30.8003i) q^{55} +(17.9511 - 54.0995i) q^{57} +(-17.9158 - 10.3437i) q^{59} +(17.7246 + 30.6999i) q^{61} +(37.3253 - 55.8762i) q^{63} +(28.5483 + 16.4823i) q^{65} +107.499 q^{67} +(77.3849 + 2.52855i) q^{69} +(-74.9285 + 43.2600i) q^{71} +(-25.3385 - 43.8876i) q^{73} +(40.5239 - 21.6637i) q^{75} +(36.2170 - 20.9099i) q^{77} -41.7660 q^{79} +(80.3096 + 10.5528i) q^{81} +(90.2997 + 52.1346i) q^{83} +80.0919 q^{85} +(-12.9577 - 24.2387i) q^{87} +(-32.7765 - 18.9235i) q^{89} +(-19.3810 + 33.5689i) q^{91} +(123.631 - 66.0922i) q^{93} +(83.0669 + 87.4891i) q^{95} -162.214 q^{97} +(41.9183 + 28.0015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more