LMFDB - Embedded newform 567.3.r.c.512.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,3,Mod(134,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("567.134");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	567.r (of order $6$, degree $2$, not 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:	$15.4496309892$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.39033114624.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 6x^{6} - 30x^{5} + 34x^{4} - 102x^{3} + 486x^{2} - 730x + 373 $ x^8 - 2x^7 + 6x^6 - 30x^5 + 34x^4 - 102x^3 + 486x^2 - 730*x + 373
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			512.2
Root			$-1.85391 - 1.90397i$ of defining polynomial
Character	$\chi$	$=$	567.512
Dual form			567.3.r.c.134.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13198 - 0.653548i) q^{2} +(-1.14575 - 1.98450i) q^{4} +(-6.39086 + 3.68977i) q^{5} +(1.32288 - 2.29129i) q^{7} +8.22359i q^{8} +O(q^{10})$	\(q+(-1.13198 - 0.653548i) q^{2} +(-1.14575 - 1.98450i) q^{4} +(-6.39086 + 3.68977i) q^{5} +(1.32288 - 2.29129i) q^{7} +8.22359i q^{8} +9.64575 q^{10} +(-2.26395 - 1.30710i) q^{11} +(3.17712 + 5.50294i) q^{13} +(-2.99493 + 1.72912i) q^{14} +(0.791503 - 1.37092i) q^{16} +12.1449i q^{17} -10.2288 q^{19} +(14.6447 + 8.45511i) q^{20} +(1.70850 + 2.95920i) q^{22} +(-3.72591 + 2.15115i) q^{23} +(14.7288 - 25.5110i) q^{25} -8.30561i q^{26} -6.06275 q^{28} +(15.0457 + 8.68663i) q^{29} +(-19.6458 - 34.0274i) q^{31} +(26.6954 - 15.4126i) q^{32} +(7.93725 - 13.7477i) q^{34} +19.5244i q^{35} +41.0405 q^{37} +(11.5787 + 6.68498i) q^{38} +(-30.3431 - 52.5559i) q^{40} +(26.2234 - 15.1401i) q^{41} +(27.9373 - 48.3887i) q^{43} +5.99042i q^{44} +5.62352 q^{46} +(-34.6193 - 19.9874i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-33.3452 + 19.2519i) q^{50} +(7.28039 - 12.6100i) q^{52} -105.002i q^{53} +19.2915 q^{55} +(18.8426 + 10.8788i) q^{56} +(-11.3542 - 19.6661i) q^{58} +(-35.8223 + 20.6820i) q^{59} +(10.2399 - 17.7360i) q^{61} +51.3577i q^{62} -46.6235 q^{64} +(-40.6091 - 23.4457i) q^{65} +(13.5830 + 23.5265i) q^{67} +(24.1015 - 13.9150i) q^{68} +(12.7601 - 22.1012i) q^{70} +67.8049i q^{71} +60.7895 q^{73} +(-46.4569 - 26.8219i) q^{74} +(11.7196 + 20.2990i) q^{76} +(-5.98986 + 3.45825i) q^{77} +(31.6235 - 54.7735i) q^{79} +11.6818i q^{80} -39.5791 q^{82} +(77.8934 + 44.9718i) q^{83} +(-44.8118 - 77.6162i) q^{85} +(-63.2487 + 36.5166i) q^{86} +(10.7490 - 18.6178i) q^{88} -63.1745i q^{89} +16.8118 q^{91} +(8.53793 + 4.92937i) q^{92} +(26.1255 + 45.2507i) q^{94} +(65.3706 - 37.7417i) q^{95} +(-9.58301 + 16.5983i) q^{97} +9.14967i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4}+O(q^{10}) $ 8 * q + 12 * q^4	$ 8 q + 12 q^{4} + 56 q^{10} + 36 q^{13} - 36 q^{16} + 24 q^{19} + 56 q^{22} + 12 q^{25} - 112 q^{28} - 136 q^{31} + 32 q^{37} - 84 q^{40} + 160 q^{43} - 336 q^{46} - 28 q^{49} - 164 q^{52} + 112 q^{55} - 112 q^{58} + 156 q^{61} + 8 q^{64} + 24 q^{67} + 28 q^{70} - 64 q^{73} + 316 q^{76} - 128 q^{79} + 784 q^{82} - 168 q^{85} - 168 q^{88} - 56 q^{91} + 336 q^{94} + 8 q^{97}+O(q^{100}) $ 8 * q + 12 * q^4 + 56 * q^10 + 36 * q^13 - 36 * q^16 + 24 * q^19 + 56 * q^22 + 12 * q^25 - 112 * q^28 - 136 * q^31 + 32 * q^37 - 84 * q^40 + 160 * q^43 - 336 * q^46 - 28 * q^49 - 164 * q^52 + 112 * q^55 - 112 * q^58 + 156 * q^61 + 8 * q^64 + 24 * q^67 + 28 * q^70 - 64 * q^73 + 316 * q^76 - 128 * q^79 + 784 * q^82 - 168 * q^85 - 168 * q^88 - 56 * q^91 + 336 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.13198	−	0.653548i	−0.565989	−	0.326774i	0.189557	−	0.981870i	$-0.439295\pi$
$2$	−1.13198	−	0.653548i	−0.565989	−	0.326774i	−0.755546	+	0.655096i	$0.772628\pi$
$3$		0			0
$3$		0			0
$4$	−1.14575	−	1.98450i	−0.286438	−	0.496125i
$5$	−6.39086	+	3.68977i	−1.27817	+	0.737953i	−0.976512	−	0.215462i	$-0.930874\pi$
$5$	−6.39086	+	3.68977i	−1.27817	+	0.737953i	−0.301660	+	0.953415i	$0.597541\pi$
$6$		0			0
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$8$			8.22359i			1.02795i
$9$		0			0
$10$	9.64575			0.964575
$11$	−2.26395	−	1.30710i	−0.205814	−	0.118827i	0.393550	−	0.919303i	$-0.371247\pi$
$11$	−2.26395	−	1.30710i	−0.205814	−	0.118827i	−0.599365	+	0.800476i	$0.704580\pi$
$12$		0			0
$13$	3.17712	+	5.50294i	0.244394	+	0.423303i	0.961961	−	0.273186i	$-0.0880776\pi$
$13$	3.17712	+	5.50294i	0.244394	+	0.423303i	−0.717567	+	0.696490i	$0.754744\pi$
$14$	−2.99493	+	1.72912i	−0.213924	+	0.123509i
$15$		0			0
$16$	0.791503	−	1.37092i	0.0494689	−	0.0856827i
$17$			12.1449i			0.714405i	0.934027	+	0.357202i	$0.116269\pi$
$17$			12.1449i			0.714405i	−0.934027	+	0.357202i	$0.883731\pi$
$18$		0			0
$19$	−10.2288			−0.538356			−0.269178	−	0.963090i	$-0.586752\pi$
$19$	−10.2288			−0.538356			−0.269178	+	0.963090i	$0.586752\pi$
$20$	14.6447	+	8.45511i	0.732234	+	0.422756i
$21$		0			0
$22$	1.70850	+	2.95920i	0.0776590	+	0.134509i
$23$	−3.72591	+	2.15115i	−0.161996	+	0.0935284i	−0.578806	−	0.815465i	$-0.696481\pi$
$23$	−3.72591	+	2.15115i	−0.161996	+	0.0935284i	0.416810	+	0.908993i	$0.363148\pi$
$24$		0			0
$25$	14.7288	−	25.5110i	0.589150	−	1.02044i
$26$		−	8.30561i		−	0.319446i
$27$		0			0
$28$	−6.06275			−0.216527
$29$	15.0457	+	8.68663i	0.518817	+	0.299539i	0.736450	−	0.676492i	$-0.236500\pi$
$29$	15.0457	+	8.68663i	0.518817	+	0.299539i	−0.217634	+	0.976031i	$0.569834\pi$
$30$		0			0
$31$	−19.6458	−	34.0274i	−0.633734	−	1.09766i	−0.986782	−	0.162054i	$-0.948188\pi$
$31$	−19.6458	−	34.0274i	−0.633734	−	1.09766i	0.353048	−	0.935605i	$-0.385145\pi$
$32$	26.6954	−	15.4126i	0.834232	−	0.481644i
$33$		0			0
$34$	7.93725	−	13.7477i	0.233449	−	0.404345i
$35$			19.5244i			0.557840i
$36$		0			0
$37$	41.0405			1.10920			0.554602	−	0.832116i	$-0.312871\pi$
$37$	41.0405			1.10920			0.554602	+	0.832116i	$0.312871\pi$
$38$	11.5787	+	6.68498i	0.304703	+	0.175920i
$39$		0			0
$40$	−30.3431	−	52.5559i	−0.758578	−	1.31390i
$41$	26.2234	−	15.1401i	0.639595	−	0.369270i	−0.144863	−	0.989452i	$-0.546274\pi$
$41$	26.2234	−	15.1401i	0.639595	−	0.369270i	0.784459	+	0.620181i	$0.212941\pi$
$42$		0			0
$43$	27.9373	−	48.3887i	0.649704	−	1.12532i	−0.333490	−	0.942754i	$-0.608226\pi$
$43$	27.9373	−	48.3887i	0.649704	−	1.12532i	0.983194	−	0.182566i	$-0.0584403\pi$
$44$			5.99042i			0.136146i
$45$		0			0
$46$	5.62352			0.122251
$47$	−34.6193	−	19.9874i	−0.736580	−	0.425265i	0.0842443	−	0.996445i	$-0.473152\pi$
$47$	−34.6193	−	19.9874i	−0.736580	−	0.425265i	−0.820825	+	0.571180i	$0.806486\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	−33.3452	+	19.2519i	−0.666905	+	0.385038i
$51$		0			0
$52$	7.28039	−	12.6100i	0.140007	−	0.242500i
$53$		−	105.002i		−	1.98116i	−0.136928	−	0.990581i	$-0.543723\pi$
$53$		−	105.002i		−	1.98116i	0.136928	−	0.990581i	$-0.456277\pi$
$54$		0			0
$55$	19.2915			0.350755
$56$	18.8426	+	10.8788i	0.336475	+	0.194264i
$57$		0			0
$58$	−11.3542	−	19.6661i	−0.195763	−	0.339071i
$59$	−35.8223	+	20.6820i	−0.607157	+	0.350542i	−0.771852	−	0.635802i	$-0.780669\pi$
$59$	−35.8223	+	20.6820i	−0.607157	+	0.350542i	0.164695	+	0.986345i	$0.447336\pi$
$60$		0			0
$61$	10.2399	−	17.7360i	0.167867	−	0.290754i	−0.769803	−	0.638282i	$-0.779646\pi$
$61$	10.2399	−	17.7360i	0.167867	−	0.290754i	0.937670	+	0.347528i	$0.112979\pi$
$62$			51.3577i			0.828350i
$63$		0			0
$64$	−46.6235			−0.728493
$65$	−40.6091	−	23.4457i	−0.624756	−	0.360703i
$66$		0			0
$67$	13.5830	+	23.5265i	0.202731	+	0.351141i	0.949408	−	0.314047i	$-0.101685\pi$
$67$	13.5830	+	23.5265i	0.202731	+	0.351141i	−0.746676	+	0.665188i	$0.768351\pi$
$68$	24.1015	−	13.9150i	0.354434	−	0.204632i
$69$		0			0
$70$	12.7601	−	22.1012i	0.182288	−	0.315731i
$71$			67.8049i			0.954999i	0.878632	+	0.477499i	$0.158457\pi$
$71$			67.8049i			0.954999i	−0.878632	+	0.477499i	$0.841543\pi$
$72$		0			0
$73$	60.7895			0.832733			0.416367	−	0.909197i	$-0.363303\pi$
$73$	60.7895			0.832733			0.416367	+	0.909197i	$0.363303\pi$
$74$	−46.4569	−	26.8219i	−0.627797	−	0.362458i
$75$		0			0
$76$	11.7196	+	20.2990i	0.154205	+	0.267092i
$77$	−5.98986	+	3.45825i	−0.0777904	+	0.0449123i
$78$		0			0
$79$	31.6235	−	54.7735i	0.400298	−	0.693336i	−0.593464	−	0.804861i	$-0.702240\pi$
$79$	31.6235	−	54.7735i	0.400298	−	0.693336i	0.993762	+	0.111525i	$0.0355734\pi$
$80$			11.6818i			0.146023i
$81$		0			0
$82$	−39.5791			−0.482672
$83$	77.8934	+	44.9718i	0.938474	+	0.541828i	0.889482	−	0.456971i	$-0.151066\pi$
$83$	77.8934	+	44.9718i	0.938474	+	0.541828i	0.0489926	+	0.998799i	$0.484399\pi$
$84$		0			0
$85$	−44.8118	−	77.6162i	−0.527197	−	0.913132i
$86$	−63.2487	+	36.5166i	−0.735450	+	0.424612i
$87$		0			0
$88$	10.7490	−	18.6178i	0.122148	−	0.211566i
$89$		−	63.1745i		−	0.709826i	−0.934899	−	0.354913i	$-0.884510\pi$
$89$		−	63.1745i		−	0.709826i	0.934899	−	0.354913i	$-0.115490\pi$
$90$		0			0
$91$	16.8118			0.184745
$92$	8.53793	+	4.92937i	0.0928035	+	0.0535801i
$93$		0			0
$94$	26.1255	+	45.2507i	0.277931	+	0.481390i
$95$	65.3706	−	37.7417i	0.688111	−	0.397281i
$96$		0			0
$97$	−9.58301	+	16.5983i	−0.0987939	+	0.171116i	−0.911186	−	0.411996i	$-0.864832\pi$
$97$	−9.58301	+	16.5983i	−0.0987939	+	0.171116i	0.812392	+	0.583112i	$0.198165\pi$
$98$			9.14967i			0.0933639i
$99$		0			0
$100$	−67.5020			−0.675020
$101$	−85.4872	−	49.3561i	−0.846408	−	0.488674i	0.0130291	−	0.999915i	$-0.495853\pi$
$101$	−85.4872	−	49.3561i	−0.846408	−	0.488674i	−0.859437	+	0.511241i	$0.829186\pi$
$102$		0			0
$103$	28.1255	+	48.7148i	0.273063	+	0.472959i	0.969645	−	0.244519i	$-0.0786299\pi$
$103$	28.1255	+	48.7148i	0.273063	+	0.472959i	−0.696582	+	0.717478i	$0.745297\pi$
$104$	−45.2539	+	26.1274i	−0.435134	+	0.251225i
$105$		0			0
$106$	−68.6235	+	118.859i	−0.647392	+	1.12132i
$107$		−	123.137i		−	1.15081i	−0.817868	−	0.575406i	$-0.804844\pi$
$107$		−	123.137i		−	1.15081i	0.817868	−	0.575406i	$-0.195156\pi$
$108$		0			0
$109$	164.539			1.50953			0.754764	−	0.655996i	$-0.227751\pi$
$109$	164.539			1.50953			0.754764	+	0.655996i	$0.227751\pi$
$110$	−21.8375	−	12.6079i	−0.198523	−	0.114617i
$111$		0			0
$112$	−2.09412	−	3.62712i	−0.0186975	−	0.0323850i
$113$	124.751	−	72.0252i	1.10399	−	0.637391i	0.166727	−	0.986003i	$-0.446680\pi$
$113$	124.751	−	72.0252i	1.10399	−	0.637391i	0.937267	+	0.348612i	$0.113347\pi$
$114$		0			0
$115$	15.8745	−	27.4955i	0.138039	−	0.239091i
$116$		−	39.8109i		−	0.343197i
$117$		0			0
$118$	54.0667			0.458192
$119$	27.8274	+	16.0662i	0.233844	+	0.135010i
$120$		0			0
$121$	−57.0830	−	98.8707i	−0.471760	−	0.817113i
$122$	−23.1826	+	13.3845i	−0.190021	+	0.109709i
$123$		0			0
$124$	−45.0183	+	77.9740i	−0.363051	+	0.628822i
$125$			32.8944i			0.263155i
$126$		0			0
$127$	−36.5830			−0.288055			−0.144028	−	0.989574i	$-0.546005\pi$
$127$	−36.5830			−0.288055			−0.144028	+	0.989574i	$0.546005\pi$
$128$	−54.0049	−	31.1798i	−0.421914	−	0.243592i
$129$		0			0
$130$	30.6458	+	53.0800i	0.235737	+	0.408308i
$131$	−29.1725	+	16.8427i	−0.222691	+	0.128570i	−0.607195	−	0.794552i	$-0.707706\pi$
$131$	−29.1725	+	16.8427i	−0.222691	+	0.128570i	0.384505	+	0.923123i	$0.374372\pi$
$132$		0			0
$133$	−13.5314	+	23.4370i	−0.101740	+	0.176218i
$134$		−	35.5086i		−	0.264989i
$135$		0			0
$136$	−99.8745			−0.734371
$137$	34.6193	+	19.9874i	0.252695	+	0.145894i	0.620998	−	0.783812i	$-0.286728\pi$
$137$	34.6193	+	19.9874i	0.252695	+	0.145894i	−0.368302	+	0.929706i	$0.620061\pi$
$138$		0			0
$139$	97.3209	+	168.565i	0.700150	+	1.21270i	0.968413	+	0.249350i	$0.0802171\pi$
$139$	97.3209	+	168.565i	0.700150	+	1.21270i	−0.268263	+	0.963346i	$0.586450\pi$
$140$	38.7462	−	22.3701i	0.276758	−	0.159787i
$141$		0			0
$142$	44.3137	−	76.7536i	0.312069	−	0.540519i
$143$		−	16.6112i		−	0.116162i
$144$		0			0
$145$	−128.207			−0.884183
$146$	−68.8124	−	39.7288i	−0.471318	−	0.272115i
$147$		0			0
$148$	−47.0222	−	81.4449i	−0.317718	−	0.550303i
$149$	176.396	−	101.842i	1.18387	−	0.683506i	0.226961	−	0.973904i	$-0.427121\pi$
$149$	176.396	−	101.842i	1.18387	−	0.683506i	0.956906	+	0.290398i	$0.0937878\pi$
$150$		0			0
$151$	−82.8745	+	143.543i	−0.548838	+	0.950615i	0.449517	+	0.893272i	$0.351596\pi$
$151$	−82.8745	+	143.543i	−0.548838	+	0.950615i	−0.998355	+	0.0573430i	$0.981737\pi$
$152$		−	84.1171i		−	0.553402i
$153$		0			0
$154$	9.04052			0.0587047
$155$	251.107	+	144.976i	1.62004	+	0.935332i
$156$		0			0
$157$	151.361	+	262.166i	0.964086	+	1.66985i	0.712052	+	0.702127i	$0.247766\pi$
$157$	151.361	+	262.166i	0.964086	+	1.66985i	0.252033	+	0.967719i	$0.418901\pi$
$158$	−71.5942	+	41.3350i	−0.453128	+	0.261614i
$159$		0			0
$160$	−113.738	+	197.000i	−0.710862	+	1.23125i
$161$			11.3828i			0.0707008i
$162$		0			0
$163$	−145.041			−0.889819			−0.444910	−	0.895576i	$-0.646764\pi$
$163$	−145.041			−0.889819			−0.444910	+	0.895576i	$0.646764\pi$
$164$	−60.0910	−	34.6936i	−0.366409	−	0.211546i
$165$		0			0
$166$	−58.7824	−	101.814i	−0.354111	−	0.613338i
$167$	−17.0255	+	9.82969i	−0.101949	+	0.0588604i	−0.550108	−	0.835094i	$-0.685413\pi$
$167$	−17.0255	+	9.82969i	−0.101949	+	0.0588604i	0.448158	+	0.893954i	$0.352080\pi$
$168$		0			0
$169$	64.3118	−	111.391i	0.380543	−	0.659120i
$170$			117.146i			0.689097i
$171$		0			0
$172$	−128.037			−0.744399
$173$	17.0507	+	9.84422i	0.0985589	+	0.0569030i	0.548469	−	0.836171i	$-0.315211\pi$
$173$	17.0507	+	9.84422i	0.0985589	+	0.0569030i	−0.449910	+	0.893074i	$0.648544\pi$
$174$		0			0
$175$	−38.9686	−	67.4956i	−0.222678	−	0.385689i
$176$	−3.58385	+	2.06914i	−0.0203628	+	0.0117565i
$177$		0			0
$178$	−41.2876	+	71.5122i	−0.231953	+	0.401754i
$179$			341.745i			1.90919i	0.297910	+	0.954594i	$0.403711\pi$
$179$			341.745i			1.90919i	−0.297910	+	0.954594i	$0.596289\pi$
$180$		0			0
$181$	215.889			1.19276			0.596378	−	0.802704i	$-0.296606\pi$
$181$	215.889			1.19276			0.596378	+	0.802704i	$0.296606\pi$
$182$	−19.0305	−	10.9873i	−0.104563	−	0.0603697i
$183$		0			0
$184$	−17.6902	−	30.6403i	−0.0961424	−	0.166524i
$185$	−262.284	+	151.430i	−1.41775	+	0.818540i
$186$		0			0
$187$	15.8745	−	27.4955i	0.0848904	−	0.147035i
$188$			91.6026i			0.487248i
$189$		0			0
$190$	−98.6640			−0.519284
$191$	38.7210	+	22.3556i	0.202728	+	0.117045i	0.597927	−	0.801550i	$-0.295991\pi$
$191$	38.7210	+	22.3556i	0.202728	+	0.117045i	−0.395199	+	0.918595i	$0.629324\pi$
$192$		0			0
$193$	72.5608	+	125.679i	0.375963	+	0.651186i	0.990471	−	0.137724i	$-0.0439788\pi$
$193$	72.5608	+	125.679i	0.375963	+	0.651186i	−0.614508	+	0.788911i	$0.710645\pi$
$194$	21.6955	−	12.5259i	0.111832	−	0.0645665i
$195$		0			0
$196$	−8.02026	+	13.8915i	−0.0409197	+	0.0708750i
$197$		−	87.4643i		−	0.443981i	−0.975049	−	0.221991i	$-0.928745\pi$
$197$		−	87.4643i		−	0.443981i	0.975049	−	0.221991i	$-0.0712554\pi$
$198$		0			0
$199$	65.4170			0.328729			0.164364	−	0.986400i	$-0.447443\pi$
$199$	65.4170			0.328729			0.164364	+	0.986400i	$0.447443\pi$
$200$	209.792	+	121.123i	1.04896	+	0.605616i
$201$		0			0
$202$	64.5131	+	111.740i	0.319372	+	0.553168i
$203$	39.8071	−	22.9827i	0.196094	−	0.113215i
$204$		0			0
$205$	−111.727	+	193.516i	−0.545009	+	0.943983i
$206$		−	73.5254i		−	0.356919i
$207$		0			0
$208$	10.0588			0.0483597
$209$	23.1574	+	13.3700i	0.110801	+	0.0639711i
$210$		0			0
$211$	−20.2915	−	35.1459i	−0.0961683	−	0.166568i	0.813927	−	0.580967i	$-0.197325\pi$
$211$	−20.2915	−	35.1459i	−0.0961683	−	0.166568i	−0.910096	+	0.414398i	$0.863992\pi$
$212$	−208.376	+	120.306i	−0.982904	+	0.567480i
$213$		0			0
$214$	−80.4758	+	139.388i	−0.376055	+	0.651347i
$215$			412.328i			1.91780i
$216$		0			0
$217$	−103.956			−0.479058
$218$	−186.254	−	107.534i	−0.854376	−	0.493274i
$219$		0			0
$220$	−22.1033	−	38.2840i	−0.100469	−	0.174018i
$221$	−66.8325	+	38.5858i	−0.302410	+	0.174596i
$222$		0			0
$223$	−50.4797	+	87.4335i	−0.226367	+	0.392078i	−0.956729	−	0.290982i	$-0.906018\pi$
$223$	−50.4797	+	87.4335i	−0.226367	+	0.392078i	0.730362	+	0.683060i	$0.239351\pi$
$224$		−	81.5559i		−	0.364089i
$225$		0			0
$226$	−188.288			−0.833131
$227$	−338.858	−	195.640i	−1.49277	−	0.861849i	−0.492800	−	0.870143i	$-0.664027\pi$
$227$	−338.858	−	195.640i	−1.49277	−	0.861849i	−0.999966	+	0.00829388i	$0.997360\pi$
$228$		0			0
$229$	3.40588	+	5.89916i	0.0148728	+	0.0257605i	0.873366	−	0.487064i	$-0.161932\pi$
$229$	3.40588	+	5.89916i	0.0148728	+	0.0257605i	−0.858493	+	0.512825i	$0.828599\pi$
$230$	−35.9392	+	20.7495i	−0.156257	+	0.0902152i
$231$		0			0
$232$	−71.4353	+	123.730i	−0.307911	+	0.533317i
$233$		−	116.877i		−	0.501616i	−0.968037	−	0.250808i	$-0.919304\pi$
$233$		−	116.877i		−	0.501616i	0.968037	−	0.250808i	$-0.0806963\pi$
$234$		0			0
$235$	294.996			1.25530
$236$	82.0868	+	47.3929i	0.347826	+	0.200817i
$237$		0			0
$238$	−21.0000	−	36.3731i	−0.0882353	−	0.152828i
$239$	51.9289	−	29.9812i	0.217276	−	0.125444i	−0.387412	−	0.921906i	$-0.626631\pi$
$239$	51.9289	−	29.9812i	0.217276	−	0.125444i	0.604688	+	0.796462i	$0.293298\pi$
$240$		0			0
$241$	−67.3765	+	116.699i	−0.279570	+	0.484230i	−0.971278	−	0.237947i	$-0.923525\pi$
$241$	−67.3765	+	116.699i	−0.279570	+	0.484230i	0.691708	+	0.722178i	$0.256859\pi$
$242$			149.226i			0.616636i
$243$		0			0
$244$	−46.9294			−0.192334
$245$	44.7360	+	25.8284i	0.182596	+	0.105422i
$246$		0			0
$247$	−32.4980	−	56.2882i	−0.131571	−	0.227888i
$248$	279.828	−	161.559i	1.12834	−	0.651446i
$249$		0			0
$250$	21.4980	−	37.2357i	0.0859921	−	0.148943i
$251$		−	268.248i		−	1.06872i	−0.845257	−	0.534359i	$-0.820553\pi$
$251$		−	268.248i		−	1.06872i	0.845257	−	0.534359i	$-0.179447\pi$
$252$		0			0
$253$	11.2470			0.0444547
$254$	41.4111	+	23.9087i	0.163036	+	0.0941289i
$255$		0			0
$256$	134.002	+	232.098i	0.523445	+	0.906634i
$257$	−202.762	+	117.064i	−0.788956	+	0.455504i	−0.839595	−	0.543213i	$-0.817207\pi$
$257$	−202.762	+	117.064i	−0.788956	+	0.455504i	0.0506392	+	0.998717i	$0.483874\pi$
$258$		0			0
$259$	54.2915	−	94.0356i	0.209620	−	0.363072i
$260$			107.452i			0.413276i
$261$		0			0
$262$	44.0301			0.168054
$263$	216.629	+	125.071i	0.823686	+	0.475555i	0.851686	−	0.524053i	$-0.175580\pi$
$263$	216.629	+	125.071i	0.823686	+	0.475555i	−0.0279999	+	0.999608i	$0.508914\pi$
$264$		0			0
$265$	387.431	+	671.051i	1.46201	+	2.53227i
$266$	30.6344	−	17.6868i	0.115167	−	0.0664917i
$267$		0			0
$268$	31.1255	−	53.9109i	0.116140	−	0.201160i
$269$		−	340.684i		−	1.26648i	−0.773955	−	0.633241i	$-0.781724\pi$
$269$		−	340.684i		−	1.26648i	0.773955	−	0.633241i	$-0.218276\pi$
$270$		0			0
$271$	−21.2994			−0.0785955			−0.0392977	−	0.999228i	$-0.512512\pi$
$271$	−21.2994			−0.0785955			−0.0392977	+	0.999228i	$0.512512\pi$
$272$	16.6497	+	9.61270i	0.0612121	+	0.0353408i
$273$		0			0
$274$	−26.1255	−	45.2507i	−0.0953485	−	0.165148i
$275$	−66.6905	+	38.5038i	−0.242511	+	0.140014i
$276$		0			0
$277$	113.458	−	196.514i	0.409594	−	0.709437i	−0.585250	−	0.810853i	$-0.699004\pi$
$277$	113.458	−	196.514i	0.409594	−	0.709437i	0.994844	+	0.101415i	$0.0323371\pi$
$278$		−	254.415i		−	0.915163i
$279$		0			0
$280$	−160.561			−0.573431
$281$	−203.939	−	117.744i	−0.725763	−	0.419019i	0.0911071	−	0.995841i	$-0.470959\pi$
$281$	−203.939	−	117.744i	−0.725763	−	0.419019i	−0.816870	+	0.576822i	$0.804293\pi$
$282$		0			0
$283$	−184.317	−	319.246i	−0.651297	−	1.12808i	−0.982808	−	0.184628i	$-0.940892\pi$
$283$	−184.317	−	319.246i	−0.651297	−	1.12808i	0.331512	−	0.943451i	$-0.392441\pi$
$284$	134.559	−	77.6876i	0.473799	−	0.273548i
$285$		0			0
$286$	−10.8562	+	18.8035i	−0.0379588	+	0.0657466i
$287$		−	80.1138i		−	0.279142i
$288$		0			0
$289$	141.502			0.489626
$290$	145.127	+	83.7891i	0.500438	+	0.288928i
$291$		0			0
$292$	−69.6497	−	120.637i	−0.238526	−	0.413140i
$293$	460.401	−	265.813i	1.57133	−	0.907211i	0.575329	−	0.817922i	$-0.304874\pi$
$293$	460.401	−	265.813i	1.57133	−	0.907211i	0.996006	−	0.0892885i	$-0.0284593\pi$
$294$		0			0
$295$	152.624	−	264.352i	0.517368	−	0.896107i
$296$			337.500i			1.14020i
$297$		0			0
$298$	−266.235			−0.893407
$299$	−23.6753	−	13.6690i	−0.0791817	−	0.0457156i
$300$		0			0
$301$	−73.9150	−	128.025i	−0.245565	−	0.425331i
$302$	187.624	−	108.325i	0.621272	−	0.358692i
$303$		0			0
$304$	−8.09609	+	14.0228i	−0.0266319	+	0.0461277i
$305$			151.131i			0.495511i
$306$		0			0
$307$	567.763			1.84939			0.924696	−	0.380706i	$-0.124319\pi$
$307$	567.763			1.84939			0.924696	+	0.380706i	$0.124319\pi$
$308$	13.7258	+	7.92459i	0.0445642	+	0.0257292i
$309$		0			0
$310$	−189.498	−	328.220i	−0.611284	−	1.05877i
$311$	−37.0253	+	21.3766i	−0.119052	+	0.0687349i	−0.558344	−	0.829610i	$-0.688563\pi$
$311$	−37.0253	+	21.3766i	−0.119052	+	0.0687349i	0.439291	+	0.898345i	$0.355230\pi$
$312$		0			0
$313$	79.0588	−	136.934i	0.252584	−	0.437488i	−0.711652	−	0.702532i	$-0.752053\pi$
$313$	79.0588	−	136.934i	0.252584	−	0.437488i	0.964237	+	0.265043i	$0.0853862\pi$
$314$		−	395.688i		−	1.26015i
$315$		0			0
$316$	−144.931			−0.458642
$317$	−122.061	−	70.4721i	−0.385051	−	0.222309i	0.294963	−	0.955509i	$-0.404693\pi$
$317$	−122.061	−	70.4721i	−0.385051	−	0.222309i	−0.680014	+	0.733199i	$0.738026\pi$
$318$		0			0
$319$	−22.7085	−	39.3323i	−0.0711865	−	0.123299i
$320$	297.965	−	172.030i	0.931139	−	0.537594i
$321$		0			0
$322$	7.43922	−	12.8851i	0.0231032	−	0.0400159i
$323$		−	124.227i		−	0.384604i
$324$		0			0
$325$	187.180			0.575940
$326$	164.183	+	94.7909i	0.503628	+	0.290770i
$327$		0			0
$328$	124.506	+	215.651i	0.379591	+	0.657471i
$329$	−91.5940	+	52.8818i	−0.278401	+	0.160735i
$330$		0			0
$331$	129.184	−	223.754i	0.390285	−	0.675993i	−0.602202	−	0.798344i	$-0.705710\pi$
$331$	129.184	−	223.754i	0.390285	−	0.675993i	0.992487	+	0.122350i	$0.0390432\pi$
$332$		−	206.106i		−	0.620801i
$333$		0			0
$334$	25.6967			0.0769362
$335$	−173.614	−	100.236i	−0.518252	−	0.299213i
$336$		0			0
$337$	−164.480	−	284.887i	−0.488070	−	0.845363i	0.511835	−	0.859084i	$-0.328966\pi$
$337$	−164.480	−	284.887i	−0.488070	−	0.845363i	−0.999906	+	0.0137207i	$0.995632\pi$
$338$	−145.599	+	84.0616i	−0.430766	+	0.248703i
$339$		0			0
$340$	−102.686	+	177.858i	−0.302018	+	0.523111i
$341$			102.715i			0.301218i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$	397.929	+	229.745i	1.15677	+	0.667862i
$345$		0			0
$346$	−12.8673	−	22.2869i	−0.0371888	−	0.0644129i
$347$	−111.401	+	64.3176i	−0.321041	+	0.185353i	−0.651857	−	0.758342i	$-0.726010\pi$
$347$	−111.401	+	64.3176i	−0.321041	+	0.185353i	0.330815	+	0.943696i	$0.392676\pi$
$348$		0			0
$349$	36.7418	−	63.6387i	0.105277	−	0.182346i	−0.808574	−	0.588394i	$-0.799760\pi$
$349$	36.7418	−	63.6387i	0.105277	−	0.182346i	0.913852	+	0.406048i	$0.133094\pi$
$350$			101.871i			0.291061i
$351$		0			0
$352$	−80.5830			−0.228929
$353$	−207.574	−	119.843i	−0.588027	−	0.339498i	0.176290	−	0.984338i	$-0.443590\pi$
$353$	−207.574	−	119.843i	−0.588027	−	0.339498i	−0.764317	+	0.644841i	$0.776924\pi$
$354$		0			0
$355$	−250.184	−	433.332i	−0.704745	−	1.22065i
$356$	−125.370	+	72.3823i	−0.352162	+	0.203321i
$357$		0			0
$358$	223.346	−	386.847i	0.623873	−	1.08058i
$359$		−	180.215i		−	0.501992i	−0.967988	−	0.250996i	$-0.919242\pi$
$359$		−	180.215i		−	0.501992i	0.967988	−	0.250996i	$-0.0807581\pi$
$360$		0			0
$361$	−256.373			−0.710173
$362$	−244.381	−	141.094i	−0.675087	−	0.389761i
$363$		0			0
$364$	−19.2621	−	33.3629i	−0.0529179	−	0.0916564i
$365$	−388.498	+	224.299i	−1.06438	+	0.614518i
$366$		0			0
$367$	−114.893	+	199.000i	−0.313059	+	0.542235i	−0.979023	−	0.203749i	$-0.934687\pi$
$367$	−114.893	+	199.000i	−0.313059	+	0.542235i	0.665964	+	0.745984i	$0.268021\pi$
$368$			6.81057i			0.0185070i
$369$		0			0
$370$	395.867			1.06991
$371$	−240.589	−	138.904i	−0.648487	−	0.374404i
$372$		0			0
$373$	−220.875	−	382.566i	−0.592157	−	1.02565i	−0.993941	−	0.109912i	$-0.964943\pi$
$373$	−220.875	−	382.566i	−0.592157	−	1.02565i	0.401785	−	0.915734i	$-0.368390\pi$
$374$	−35.9392	+	20.7495i	−0.0960940	+	0.0554799i
$375$		0			0
$376$	164.369	−	284.695i	0.437151	−	0.757167i
$377$			110.394i			0.292822i
$378$		0			0
$379$	−421.203			−1.11135			−0.555676	−	0.831399i	$-0.687541\pi$
$379$	−421.203			−1.11135			−0.555676	+	0.831399i	$0.687541\pi$
$380$	−149.797	−	86.4853i	−0.394202	−	0.227593i
$381$		0			0
$382$	−29.2209	−	50.6121i	−0.0764945	−	0.132492i
$383$	−515.797	+	297.796i	−1.34673	+	0.777534i	−0.987785	−	0.155825i	$-0.950196\pi$
$383$	−515.797	+	297.796i	−1.34673	+	0.777534i	−0.358944	+	0.933359i	$0.616863\pi$
$384$		0			0
$385$	25.5203	−	44.2024i	0.0662864	−	0.114811i
$386$		−	189.688i		−	0.491419i
$387$		0			0
$388$	43.9190			0.113193
$389$	−318.132	−	183.673i	−0.817819	−	0.472168i	0.0318449	−	0.999493i	$-0.489862\pi$
$389$	−318.132	−	183.673i	−0.817819	−	0.472168i	−0.849664	+	0.527325i	$0.823195\pi$
$390$		0			0
$391$	−26.1255	−	45.2507i	−0.0668171	−	0.115731i
$392$	49.8529	−	28.7826i	0.127176	−	0.0734249i
$393$		0			0
$394$	−57.1621	+	99.0076i	−0.145081	+	0.251288i
$395$			466.734i			1.18160i
$396$		0			0
$397$	408.346			1.02858			0.514290	−	0.857616i	$-0.328055\pi$
$397$	408.346			1.02858			0.514290	+	0.857616i	$0.328055\pi$
$398$	−74.0506	−	42.7531i	−0.186057	−	0.107420i
$399$		0			0
$400$	−23.3157	−	40.3840i	−0.0582892	−	0.100960i
$401$	206.822	−	119.409i	0.515765	−	0.297777i	−0.219435	−	0.975627i	$-0.570421\pi$
$401$	206.822	−	119.409i	0.515765	−	0.297777i	0.735200	+	0.677850i	$0.237088\pi$
$402$		0			0
$403$	124.834	−	216.219i	0.309762	−	0.536523i
$404$			226.199i			0.559899i
$405$		0			0
$406$	−60.0810			−0.147983
$407$	−92.9139	−	53.6439i	−0.228290	−	0.131803i
$408$		0			0
$409$	324.682	+	562.366i	0.793844	+	1.37498i	0.923570	+	0.383429i	$0.125257\pi$
$409$	324.682	+	562.366i	0.793844	+	1.37498i	−0.129726	+	0.991550i	$0.541410\pi$
$410$	252.944	−	146.038i	0.616938	−	0.356189i
$411$		0			0
$412$	64.4496	−	111.630i	0.156431	−	0.270947i
$413$			109.439i			0.264985i
$414$		0			0
$415$	−663.741			−1.59938
$416$	169.629	+	97.9356i	0.407763	+	0.235422i
$417$		0			0
$418$	−17.4758	−	30.2690i	−0.0418081	−	0.0724138i
$419$	9.97472	−	5.75890i	0.0238060	−	0.0137444i	−0.488050	−	0.872816i	$-0.662292\pi$
$419$	9.97472	−	5.75890i	0.0238060	−	0.0137444i	0.511856	+	0.859071i	$0.328958\pi$
$420$		0			0
$421$	41.9961	−	72.7393i	0.0997531	−	0.172777i	−0.811829	−	0.583895i	$-0.801528\pi$
$421$	41.9961	−	72.7393i	0.0997531	−	0.172777i	0.911582	+	0.411117i	$0.134861\pi$
$422$			53.0458i			0.125701i
$423$		0			0
$424$	863.490			2.03653
$425$	309.827	+	178.879i	0.729006	+	0.420892i
$426$		0			0
$427$	−27.0922	−	46.9250i	−0.0634477	−	0.109895i
$428$	−244.365	+	141.084i	−0.570946	+	0.329636i
$429$		0			0
$430$	269.476	−	466.746i	0.626688	−	1.08546i
$431$		−	694.004i		−	1.61022i	−0.593127	−	0.805109i	$-0.702107\pi$
$431$		−	694.004i		−	1.61022i	0.593127	−	0.805109i	$-0.297893\pi$
$432$		0			0
$433$	116.834			0.269824			0.134912	−	0.990858i	$-0.456925\pi$
$433$	116.834			0.269824			0.134912	+	0.990858i	$0.456925\pi$
$434$	117.675	+	67.9399i	0.271141	+	0.156544i
$435$		0			0
$436$	−188.520	−	326.527i	−0.432386	−	0.748914i
$437$	38.1114	−	22.0036i	0.0872114	−	0.0503515i
$438$		0			0
$439$	264.037	−	457.325i	0.601450	−	1.04174i	−0.391152	−	0.920326i	$-0.627923\pi$
$439$	264.037	−	457.325i	0.601450	−	1.04174i	0.992602	−	0.121416i	$-0.0387435\pi$
$440$			158.645i			0.360558i
$441$		0			0
$442$	100.871			0.228214
$443$	235.777	+	136.126i	0.532228	+	0.307282i	0.741923	−	0.670485i	$-0.233914\pi$
$443$	235.777	+	136.126i	0.532228	+	0.307282i	−0.209695	+	0.977767i	$0.567247\pi$
$444$		0			0
$445$	233.099	+	403.740i	0.523819	+	0.907281i
$446$	114.284	−	65.9818i	0.256242	−	0.147941i
$447$		0			0
$448$	−61.6771	+	106.828i	−0.137672	+	0.238455i
$449$			525.770i			1.17098i	0.810680	+	0.585490i	$0.199098\pi$
$449$			525.770i			1.17098i	−0.810680	+	0.585490i	$0.800902\pi$
$450$		0			0
$451$	−79.1581			−0.175517
$452$	−285.868	−	165.046i	−0.632451	−	0.365146i
$453$		0			0
$454$	255.720	+	442.919i	0.563259	+	0.975593i
$455$	−107.442	+	62.0315i	−0.236136	+	0.136333i
$456$		0			0
$457$	256.893	−	444.951i	0.562129	−	0.973635i	−0.435182	−	0.900343i	$-0.643316\pi$
$457$	256.893	−	444.951i	0.562129	−	0.973635i	0.997310	−	0.0732928i	$-0.0233508\pi$
$458$		−	8.90362i		−	0.0194402i
$459$		0			0
$460$	−72.7530			−0.158159
$461$	595.721	+	343.939i	1.29224	+	0.746072i	0.979050	−	0.203620i	$-0.0652706\pi$
$461$	595.721	+	343.939i	1.29224	+	0.746072i	0.313185	+	0.949692i	$0.398604\pi$
$462$		0			0
$463$	−390.531	−	676.419i	−0.843479	−	1.46095i	−0.886936	−	0.461893i	$-0.847170\pi$
$463$	−390.531	−	676.419i	−0.843479	−	1.46095i	0.0434570	−	0.999055i	$-0.486163\pi$
$464$	23.8174	−	13.7510i	0.0513306	−	0.0296357i
$465$		0			0
$466$	−76.3844	+	132.302i	−0.163915	+	0.283909i
$467$		−	163.353i		−	0.349792i	−0.984587	−	0.174896i	$-0.944041\pi$
$467$		−	163.353i		−	0.349792i	0.984587	−	0.174896i	$-0.0559589\pi$
$468$		0			0
$469$	71.8745			0.153251
$470$	−333.929	−	192.794i	−0.710487	−	0.410200i
$471$		0			0
$472$	−170.080	−	294.588i	−0.360340	−	0.624127i
$473$	−126.497	+	73.0333i	−0.267436	+	0.154404i
$474$		0			0
$475$	−150.657	+	260.945i	−0.317172	+	0.549359i
$476$		−	73.6313i		−	0.154688i
$477$		0			0
$478$	−78.3765			−0.163968
$479$	606.355	+	350.079i	1.26588	+	0.730855i	0.974205	−	0.225664i	$-0.0724551\pi$
$479$	606.355	+	350.079i	1.26588	+	0.730855i	0.291672	+	0.956518i	$0.405788\pi$
$480$		0			0
$481$	130.391	+	225.844i	0.271083	+	0.469529i
$482$	152.537	−	88.0675i	0.316467	−	0.182713i
$483$		0			0
$484$	−130.806	+	226.562i	−0.270260	+	0.468104i
$485$		−	141.436i		−	0.291621i
$486$		0			0
$487$	86.5909			0.177805			0.0889023	−	0.996040i	$-0.471664\pi$
$487$	86.5909			0.177805			0.0889023	+	0.996040i	$0.471664\pi$
$488$	145.853	+	84.2085i	0.298880	+	0.172558i
$489$		0			0
$490$	−33.7601	−	58.4743i	−0.0688982	−	0.119335i
$491$	642.152	−	370.747i	1.30785	−	0.755085i	0.326110	−	0.945332i	$-0.394262\pi$
$491$	642.152	−	370.747i	1.30785	−	0.755085i	0.981736	+	0.190247i	$0.0609288\pi$
$492$		0			0
$493$	−105.498	+	182.728i	−0.213992	+	0.370645i
$494$			84.9560i			0.171976i
$495$		0			0
$496$	−62.1987			−0.125401
$497$	155.361	+	89.6975i	0.312597	+	0.180478i
$498$		0			0
$499$	−189.907	−	328.929i	−0.380575	−	0.659176i	0.610569	−	0.791963i	$-0.290941\pi$
$499$	−189.907	−	328.929i	−0.380575	−	0.659176i	−0.991145	+	0.132787i	$0.957607\pi$
$500$	65.2789	−	37.6888i	0.130558	−	0.0753775i
$501$		0			0
$502$	−175.313	+	303.651i	−0.349229	+	0.604883i
$503$			465.808i			0.926059i	0.886343	+	0.463029i	$0.153238\pi$
$503$			465.808i			0.926059i	−0.886343	+	0.463029i	$0.846762\pi$
$504$		0			0
$505$	728.450			1.44247
$506$	−12.7314	−	7.35048i	−0.0251609	−	0.0145266i
$507$		0			0
$508$	41.9150	+	72.5990i	0.0825099	+	0.142911i
$509$	649.955	−	375.252i	1.27692	−	0.737233i	0.300643	−	0.953737i	$-0.402799\pi$
$509$	649.955	−	375.252i	1.27692	−	0.737233i	0.976282	+	0.216504i	$0.0694654\pi$
$510$		0			0
$511$	80.4170	−	139.286i	0.157372	−	0.272576i
$512$		−	100.868i		−	0.197009i
$513$		0			0
$514$	306.029			0.595387
$515$	−359.492	−	207.553i	−0.698043	−	0.403016i
$516$		0			0
$517$	52.2510	+	90.5014i	0.101066	+	0.175051i
$518$	−122.914	+	70.9642i	−0.237285	+	0.136996i
$519$		0			0
$520$	192.808	−	333.953i	0.370784	−	0.642217i
$521$			726.946i			1.39529i	0.716443	+	0.697645i	$0.245769\pi$
$521$			726.946i			1.39529i	−0.716443	+	0.697645i	$0.754231\pi$
$522$		0			0
$523$	−624.707			−1.19447			−0.597234	−	0.802067i	$-0.703734\pi$
$523$	−624.707			−1.19447			−0.597234	+	0.802067i	$0.703734\pi$
$524$	66.8488	+	38.5952i	0.127574	+	0.0736549i
$525$		0			0
$526$	−163.480	−	283.155i	−0.310798	−	0.538318i
$527$	413.259	−	238.595i	0.784173	−	0.452742i
$528$		0			0
$529$	−255.245	+	442.097i	−0.482505	+	0.835723i
$530$		−	1012.82i		−	1.91098i
$531$		0			0
$532$	62.0144			0.116568
$533$	166.630	+	96.2039i	0.312627	+	0.180495i
$534$		0			0
$535$	454.346	+	786.951i	0.849246	+	1.47094i
$536$	−193.472	+	111.701i	−0.360955	+	0.208398i
$537$		0			0
$538$	−222.653	+	385.646i	−0.413853	+	0.716814i
$539$			18.2993i			0.0339505i
$540$		0			0
$541$	−291.757			−0.539292			−0.269646	−	0.962960i	$-0.586907\pi$
$541$	−291.757			−0.539292			−0.269646	+	0.962960i	$0.586907\pi$
$542$	24.1104	+	13.9202i	0.0444842	+	0.0256829i
$543$		0			0
$544$	187.184	+	324.213i	0.344089	+	0.595979i
$545$	−1051.54	+	607.109i	−1.92944	+	1.11396i
$546$		0			0
$547$	−102.476	+	177.493i	−0.187342	+	0.324485i	−0.944363	−	0.328905i	$-0.893320\pi$
$547$	−102.476	+	177.493i	−0.187342	+	0.324485i	0.757022	+	0.653390i	$0.226654\pi$
$548$		−	91.6026i		−	0.167158i
$549$		0			0
$550$	100.656			0.183011
$551$	−153.899	−	88.8534i	−0.279308	−	0.161258i
$552$		0			0
$553$	−83.6680	−	144.917i	−0.151298	−	0.262056i
$554$	−256.863	+	148.300i	−0.463651	+	0.267689i
$555$		0			0
$556$	223.011	−	386.267i	0.401099	−	0.694724i
$557$		−	503.883i		−	0.904637i	−0.891857	−	0.452318i	$-0.850597\pi$
$557$		−	503.883i		−	0.904637i	0.891857	−	0.452318i	$-0.149403\pi$
$558$		0			0
$559$	355.041			0.635135
$560$	26.7665	+	15.4536i	0.0477972	+	0.0275958i
$561$		0			0
$562$	153.903	+	266.568i	0.273849	+	0.474321i
$563$	94.1672	−	54.3675i	0.167260	−	0.0965674i	−0.414033	−	0.910262i	$-0.635880\pi$
$563$	94.1672	−	54.3675i	0.167260	−	0.0965674i	0.581293	+	0.813694i	$0.302547\pi$
$564$		0			0
$565$	−531.512	+	920.606i	−0.940730	+	1.62939i
$566$			481.840i			0.851307i
$567$		0			0
$568$	−557.600			−0.981690
$569$	376.610	+	217.436i	0.661880	+	0.382136i	0.792993	−	0.609231i	$-0.208522\pi$
$569$	376.610	+	217.436i	0.661880	+	0.382136i	−0.131113	+	0.991367i	$0.541855\pi$
$570$		0			0
$571$	−59.5608	−	103.162i	−0.104310	−	0.180670i	0.809146	−	0.587607i	$-0.199930\pi$
$571$	−59.5608	−	103.162i	−0.104310	−	0.180670i	−0.913456	+	0.406938i	$0.866597\pi$
$572$	−32.9649	+	19.0323i	−0.0576310	+	0.0332733i
$573$		0			0
$574$	−52.3582	+	90.6870i	−0.0912164	+	0.157991i
$575$			126.735i			0.220409i
$576$		0			0
$577$	−655.417			−1.13590			−0.567952	−	0.823061i	$-0.692264\pi$
$577$	−655.417			−1.13590			−0.567952	+	0.823061i	$0.692264\pi$
$578$	−160.177	−	92.4783i	−0.277123	−	0.159997i
$579$		0			0
$580$	146.893	+	254.426i	0.253263	+	0.438665i
$581$	206.086	−	118.984i	0.354710	−	0.204792i
$582$		0			0
$583$	−137.247	+	237.719i	−0.235415	+	0.407751i
$584$			499.908i			0.856007i
$585$		0			0
$586$	−694.885			−1.18581
$587$	−637.599	−	368.118i	−1.08620	−	0.627118i	−0.153638	−	0.988127i	$-0.549099\pi$
$587$	−637.599	−	368.118i	−1.08620	−	0.627118i	−0.932562	+	0.361010i	$0.882432\pi$
$588$		0			0
$589$	200.952	+	348.058i	0.341174	+	0.590931i
$590$	−345.533	+	199.493i	−0.585649	+	0.338124i
$591$		0			0
$592$	32.4837	−	56.2634i	0.0548711	−	0.0950395i
$593$			832.884i			1.40453i	0.711917	+	0.702263i	$0.247827\pi$
$593$			832.884i			1.40453i	−0.711917	+	0.702263i	$0.752173\pi$
$594$		0			0
$595$	−237.122			−0.398524
$596$	−404.212	−	233.372i	−0.678208	−	0.391564i
$597$		0			0
$598$	17.8666	+	30.9459i	0.0298773	+	0.0517490i
$599$	60.0407	−	34.6645i	0.100235	−	0.0578706i	−0.449045	−	0.893509i	$-0.648236\pi$
$599$	60.0407	−	34.6645i	0.100235	−	0.0578706i	0.549279	+	0.835639i	$0.314902\pi$
$600$		0			0
$601$	80.8602	−	140.054i	0.134543	−	0.233035i	−0.790880	−	0.611971i	$-0.790377\pi$
$601$	80.8602	−	140.054i	0.134543	−	0.233035i	0.925423	+	0.378937i	$0.123710\pi$
$602$			193.228i			0.320977i
$603$		0			0
$604$	379.814			0.628832
$605$	729.619	+	421.246i	1.20598	+	0.696274i
$606$		0			0
$607$	−464.804	−	805.064i	−0.765740	−	1.32630i	−0.939855	−	0.341574i	$-0.889040\pi$
$607$	−464.804	−	805.064i	−0.765740	−	1.32630i	0.174115	−	0.984725i	$-0.444293\pi$
$608$	−273.061	+	157.652i	−0.449114	+	0.259296i
$609$		0			0
$610$	98.7712	−	171.077i	0.161920	−	0.280454i
$611$		−	254.010i		−	0.415729i
$612$		0			0
$613$	297.940			0.486036			0.243018	−	0.970022i	$-0.421863\pi$
$613$	297.940			0.486036			0.243018	+	0.970022i	$0.421863\pi$
$614$	−642.695	−	371.060i	−1.04674	−	0.604333i
$615$		0			0
$616$	−28.4392	−	49.2582i	−0.0461676	−	0.0799646i
$617$	−844.872	+	487.787i	−1.36932	+	0.790579i	−0.990842	−	0.135030i	$-0.956887\pi$
$617$	−844.872	+	487.787i	−1.36932	+	0.790579i	−0.378482	+	0.925609i	$0.623554\pi$
$618$		0			0
$619$	−178.517	+	309.201i	−0.288396	+	0.499516i	−0.973427	−	0.228998i	$-0.926455\pi$
$619$	−178.517	+	309.201i	−0.288396	+	0.499516i	0.685031	+	0.728514i	$0.259789\pi$
$620$		−	664.428i		−	1.07166i
$621$		0			0
$622$	55.8824			0.0898431
$623$	−144.751	−	83.5721i	−0.232345	−	0.134145i
$624$		0			0
$625$	246.846	+	427.550i	0.394954	+	0.684081i
$626$	−178.986	+	103.337i	−0.285919	+	0.165076i
$627$		0			0
$628$	346.845	−	600.753i	0.552301	−	0.956614i
$629$			498.432i			0.792420i
$630$		0			0
$631$	−813.223			−1.28879			−0.644393	−	0.764695i	$-0.722890\pi$
$631$	−813.223			−1.28879			−0.644393	+	0.764695i	$0.722890\pi$
$632$	450.435	+	260.059i	0.712714	+	0.411486i
$633$		0			0
$634$	92.1137	+	159.546i	0.145290	+	0.251649i
$635$	233.797	−	134.983i	0.368184	−	0.212571i
$636$		0			0
$637$	22.2399	−	38.5206i	0.0349135	−	0.0604719i
$638$			59.3643i			0.0930475i
$639$		0			0
$640$	460.184			0.719038
$641$	−560.082	−	323.363i	−0.873762	−	0.504467i	−0.00516570	−	0.999987i	$-0.501644\pi$
$641$	−560.082	−	323.363i	−0.873762	−	0.504467i	−0.868597	+	0.495520i	$0.834978\pi$
$642$		0			0
$643$	−72.2804	−	125.193i	−0.112411	−	0.194702i	0.804331	−	0.594182i	$-0.202524\pi$
$643$	−72.2804	−	125.193i	−0.112411	−	0.194702i	−0.916742	+	0.399480i	$0.869191\pi$
$644$	22.5892	−	13.0419i	0.0350764	−	0.0202514i
$645$		0			0
$646$	−81.1882	+	140.622i	−0.125678	+	0.217681i
$647$		−	716.654i		−	1.10766i	−0.832631	−	0.553828i	$-0.813166\pi$
$647$		−	716.654i		−	1.10766i	0.832631	−	0.553828i	$-0.186834\pi$
$648$		0			0
$649$	108.133			0.166615
$650$	−211.884	−	122.331i	−0.325975	−	0.188202i
$651$		0			0
$652$	166.180	+	287.833i	0.254878	+	0.441461i
$653$	328.223	−	189.500i	0.502639	−	0.290199i	−0.227164	−	0.973857i	$-0.572945\pi$
$653$	328.223	−	189.500i	0.502639	−	0.290199i	0.729803	+	0.683658i	$0.239612\pi$
$654$		0			0
$655$	124.292	−	215.279i	0.189758	−	0.328671i
$656$		−	47.9337i		−	0.0730696i
$657$		0			0
$658$	138.243			0.210096
$659$	615.503	+	355.361i	0.933995	+	0.539242i	0.888073	−	0.459703i	$-0.152044\pi$
$659$	615.503	+	355.361i	0.933995	+	0.539242i	0.0459222	+	0.998945i	$0.485377\pi$
$660$		0			0
$661$	−45.7523	−	79.2452i	−0.0692167	−	0.119887i	0.829340	−	0.558744i	$-0.188717\pi$
$661$	−45.7523	−	79.2452i	−0.0692167	−	0.119887i	−0.898557	+	0.438857i	$0.855383\pi$
$662$	−292.467	+	168.856i	−0.441794	+	0.255070i
$663$		0			0
$664$	−369.829	+	640.563i	−0.556972	+	0.964704i
$665$		−	199.710i		−	0.300316i
$666$		0			0
$667$	−74.7451			−0.112062
$668$	39.0140	+	22.5248i	0.0584043	+	0.0337197i
$669$		0			0
$670$	131.018	+	226.930i	0.195550	+	0.338702i
$671$	−46.3652	+	26.7690i	−0.0690987	+	0.0398941i
$672$		0			0
$673$	−322.903	+	559.285i	−0.479797	+	0.831032i	−0.999731	−	0.0231737i	$-0.992623\pi$
$673$	−322.903	+	559.285i	−0.479797	+	0.831032i	0.519935	+	0.854206i	$0.325956\pi$
$674$			429.981i			0.637954i
$675$		0			0
$676$	−294.741			−0.436008
$677$	290.613	+	167.786i	0.429266	+	0.247837i	0.699034	−	0.715088i	$-0.253614\pi$
$677$	290.613	+	167.786i	0.429266	+	0.247837i	−0.269768	+	0.962925i	$0.586947\pi$
$678$		0			0
$679$	25.3542	+	43.9148i	0.0373406	+	0.0646758i
$680$	638.284	−	368.514i	0.938653	−	0.541932i
$681$		0			0
$682$	67.1294	−	116.272i	0.0984302	−	0.170486i
$683$		−	113.336i		−	0.165939i	−0.996552	−	0.0829694i	$-0.973560\pi$
$683$		−	113.336i		−	0.165939i	0.996552	−	0.0829694i	$-0.0264404\pi$
$684$		0			0
$685$	−294.996			−0.430651
$686$	20.9645	+	12.1039i	0.0305605	+	0.0176441i
$687$		0			0
$688$	−44.2248	−	76.5996i	−0.0642803	−	0.111337i
$689$	577.818	−	333.603i	0.838632	−	0.484184i
$690$		0			0
$691$	−282.833	+	489.882i	−0.409310	+	0.708946i	−0.994813	−	0.101725i	$-0.967564\pi$
$691$	−282.833	+	489.882i	−0.409310	+	0.708946i	0.585502	+	0.810671i	$0.300897\pi$
$692$		−	45.1161i		−	0.0651967i
$693$		0			0
$694$	168.138			0.242274
$695$	−1243.93	−	718.183i	−1.78983	−	1.03336i
$696$		0			0
$697$	183.875	+	318.480i	0.263808	+	0.456930i
$698$	−83.1819	+	48.0251i	−0.119172	+	0.0688038i
$699$		0			0
$700$	−89.2967	+	154.666i	−0.127567	+	0.220952i
$701$		−	872.955i		−	1.24530i	−0.782501	−	0.622650i	$-0.786056\pi$
$701$		−	872.955i		−	1.24530i	0.782501	−	0.622650i	$-0.213944\pi$
$702$		0			0
$703$	−419.793			−0.597146
$704$	105.554	+	60.9414i	0.149934	+	0.0865645i
$705$		0			0
$706$	156.646	+	271.318i	0.221878	+	0.384304i
$707$	−226.178	+	130.584i	−0.319912	+	0.184701i
$708$		0			0
$709$	−546.018	+	945.731i	−0.770125	+	1.33389i	0.167370	+	0.985894i	$0.446473\pi$
$709$	−546.018	+	945.731i	−0.770125	+	1.33389i	−0.937494	+	0.348001i	$0.886861\pi$
$710$			654.029i			0.921168i
$711$		0			0
$712$	519.522			0.729665
$713$	146.396	+	84.5220i	0.205325	+	0.118544i
$714$		0			0
$715$	61.2915	+	106.160i	0.0857224	+	0.148476i
$716$	678.192	−	391.554i	0.947196	−	0.546864i
$717$		0			0
$718$	−117.779	+	203.999i	−0.164038	+	0.284122i
$719$		−	901.769i		−	1.25420i	−0.778939	−	0.627099i	$-0.784242\pi$
$719$		−	901.769i		−	1.25420i	0.778939	−	0.627099i	$-0.215758\pi$
$720$		0			0
$721$	148.826			0.206416
$722$	290.208	+	167.552i	0.401950	+	0.232066i
$723$		0			0
$724$	−247.355	−	428.431i	−0.341650	−	0.591756i
$725$	443.208	−	255.886i	0.611322	−	0.352947i
$726$		0			0
$727$	−148.753	+	257.648i	−0.204612	+	0.354398i	−0.950009	−	0.312222i	$-0.898927\pi$
$727$	−148.753	+	257.648i	−0.204612	+	0.354398i	0.745397	+	0.666621i	$0.232260\pi$
$728$			138.253i			0.189908i
$729$		0			0
$730$	586.361			0.803234
$731$	587.675	+	339.295i	0.803933	+	0.464151i
$732$		0			0
$733$	−228.483	−	395.744i	−0.311709	−	0.539896i	0.667023	−	0.745037i	$-0.267568\pi$
$733$	−228.483	−	395.744i	−0.311709	−	0.539896i	−0.978733	+	0.205140i	$0.934235\pi$
$734$	260.112	−	150.176i	0.354376	−	0.204599i
$735$		0			0
$736$	−66.3098	+	114.852i	−0.0900948	+	0.156049i
$737$		−	71.0171i		−	0.0963597i
$738$		0			0
$739$	−332.199			−0.449525			−0.224762	−	0.974414i	$-0.572161\pi$
$739$	−332.199			−0.449525			−0.224762	+	0.974414i	$0.572161\pi$
$740$	601.025	+	347.002i	0.812196	+	0.468922i
$741$		0			0
$742$	181.561	+	314.472i	0.244691	+	0.423817i
$743$	55.8886	−	32.2673i	0.0752202	−	0.0434284i	−0.461918	−	0.886923i	$-0.652839\pi$
$743$	55.8886	−	32.2673i	0.0752202	−	0.0434284i	0.537138	+	0.843494i	$0.319505\pi$
$744$		0			0
$745$	−751.549	+	1301.72i	−1.00879	+	1.74728i
$746$			577.408i			0.774005i
$747$		0			0
$748$	−72.7530			−0.0972633
$749$	−282.142	−	162.895i	−0.376692	−	0.217483i
$750$		0			0
$751$	305.834	+	529.720i	0.407236	+	0.705353i	0.994579	−	0.103985i	$-0.0331594\pi$
$751$	305.834	+	529.720i	0.407236	+	0.705353i	−0.587343	+	0.809338i	$0.699826\pi$
$752$	−54.8025	+	31.6402i	−0.0728757	+	0.0420748i
$753$		0			0
$754$	72.1477	−	124.964i	0.0956866	−	0.165734i
$755$		−	1223.15i		−	1.62007i
$756$		0			0
$757$	−207.357			−0.273919			−0.136960	−	0.990577i	$-0.543733\pi$
$757$	−207.357			−0.273919			−0.136960	+	0.990577i	$0.543733\pi$
$758$	476.792	+	275.276i	0.629013	+	0.363161i
$759$		0			0
$760$	310.373	+	537.581i	0.408385	+	0.707343i
$761$	−292.518	+	168.885i	−0.384386	+	0.221925i	−0.679725	−	0.733467i	$-0.737901\pi$
$761$	−292.518	+	168.885i	−0.384386	+	0.221925i	0.295339	+	0.955393i	$0.404567\pi$
$762$		0			0
$763$	217.664	−	377.005i	0.285274	−	0.494109i
$764$		−	102.456i		−	0.134104i
$765$		0			0
$766$	778.494			1.01631
$767$	−227.624	−	131.419i	−0.296771	−	0.171341i
$768$		0			0
$769$	521.110	+	902.589i	0.677646	+	1.17372i	0.975688	+	0.219164i	$0.0703331\pi$
$769$	521.110	+	902.589i	0.677646	+	1.17372i	−0.298042	+	0.954553i	$0.596334\pi$
$770$	−57.7767	+	33.3574i	−0.0750347	+	0.0433213i
$771$		0			0
$772$	166.273	−	287.994i	0.215380	−	0.373049i
$773$		−	291.448i		−	0.377035i	−0.982070	−	0.188517i	$-0.939632\pi$
$773$		−	291.448i		−	0.377035i	0.982070	−	0.188517i	$-0.0603682\pi$
$774$		0			0
$775$	−1157.43			−1.49346
$776$	−136.497	−	78.8067i	−0.175899	−	0.101555i
$777$		0			0
$778$	240.078	+	415.828i	0.308584	+	0.534483i
$779$	−268.233	+	154.864i	−0.344330	+	0.198799i
$780$		0			0
$781$	88.6275	−	153.507i	0.113479	−	0.196552i
$782$			68.2970i			0.0873363i
$783$		0			0
$784$	−11.0810			−0.0141340
$785$	−1934.66	−	1116.98i	−2.46454	−	1.42290i
$786$		0			0
$787$	−146.944	−	254.515i	−0.186715	−	0.323399i	0.757438	−	0.652907i	$-0.226451\pi$
$787$	−146.944	−	254.515i	−0.186715	−	0.323399i	−0.944153	+	0.329507i	$0.893117\pi$
$788$	−173.573	+	100.212i	−0.220270	+	0.127173i
$789$		0			0
$790$	305.033	−	528.332i	0.386117	−	0.668775i
$791$		−	381.122i		−	0.481822i
$792$		0			0
$793$	130.133			0.164103
$794$	−462.239	−	266.874i	−0.582165	−	0.336113i
$795$		0			0
$796$	−74.9516	−	129.820i	−0.0941603	−	0.163090i
$797$	492.564	−	284.382i	0.618023	−	0.356816i	−0.158076	−	0.987427i	$-0.550529\pi$
$797$	492.564	−	284.382i	0.618023	−	0.356816i	0.776099	+	0.630611i	$0.217196\pi$
$798$		0			0
$799$	242.745	−	420.447i	0.303811	−	0.526216i
$800$		−	908.035i		−	1.13504i
$801$		0			0
$802$	−312.157			−0.389223
$803$	−137.625	−	79.4577i	−0.171388	−	0.0989511i
$804$		0			0
$805$	−42.0000	−	72.7461i	−0.0521739	−	0.0903679i
$806$	−282.619	+	163.170i	−0.350643	+	0.202444i
$807$		0			0
$808$	405.884	−	703.012i	0.502332	−	0.870064i
$809$			183.697i			0.227067i	0.993534	+	0.113534i	$0.0362169\pi$
$809$			183.697i			0.227067i	−0.993534	+	0.113534i	$0.963783\pi$
$810$		0			0
$811$	−544.663			−0.671594			−0.335797	−	0.941934i	$-0.609006\pi$
$811$	−544.663			−0.671594			−0.335797	+	0.941934i	$0.609006\pi$
$812$	−91.2181	−	52.6648i	−0.112338	−	0.0648582i
$813$		0			0
$814$	70.1176	+	121.447i	0.0861396	+	0.149198i
$815$	926.934	−	535.166i	1.13734	−	0.656645i
$816$		0			0
$817$	−285.763	+	494.957i	−0.349772	+	0.605822i
$818$		−	848.781i		−	1.03763i
$819$		0			0
$820$	512.044			0.624444
$821$	1029.51	+	594.390i	1.25397	+	0.723983i	0.971897	−	0.235409i	$-0.0756428\pi$
$821$	1029.51	+	594.390i	1.25397	+	0.723983i	0.282078	+	0.959391i	$0.408976\pi$
$822$		0			0
$823$	−632.575	−	1095.65i	−0.768621	−	1.33129i	−0.938311	−	0.345793i	$-0.887610\pi$
$823$	−632.575	−	1095.65i	−0.768621	−	1.33129i	0.169690	−	0.985498i	$-0.445723\pi$
$824$	−400.610	+	231.293i	−0.486178	+	0.280695i
$825$		0			0
$826$	71.5235	−	123.882i	0.0865902	−	0.149979i
$827$			790.941i			0.956398i	0.878252	+	0.478199i	$0.158710\pi$
$827$			790.941i			0.956398i	−0.878252	+	0.478199i	$0.841290\pi$
$828$		0			0
$829$	99.1961			0.119658			0.0598288	−	0.998209i	$-0.480945\pi$
$829$	99.1961			0.119658			0.0598288	+	0.998209i	$0.480945\pi$
$830$	751.340	+	433.786i	0.905229	+	0.522634i
$831$		0			0
$832$	−148.129	−	256.566i	−0.178039	−	0.308373i
$833$	73.6244	−	42.5071i	0.0883846	−	0.0510289i
$834$		0			0
$835$	72.5385	−	125.640i	0.0868725	−	0.150468i
$836$		−	61.2746i		−	0.0732950i
$837$		0			0
$838$	−15.0549			−0.0179652
$839$	211.157	+	121.912i	0.251678	+	0.145306i	0.620532	−	0.784181i	$-0.286917\pi$
$839$	211.157	+	121.912i	0.251678	+	0.145306i	−0.368855	+	0.929487i	$0.620250\pi$
$840$		0			0
$841$	−269.585	−	466.935i	−0.320553	−	0.555214i
$842$	−95.0772	+	54.8928i	−0.112918	+	0.0651934i
$843$		0			0
$844$	−46.4980	+	80.5370i	−0.0550925	+	0.0954229i
$845$			949.182i			1.12329i
$846$		0			0
$847$	−302.055			−0.356617
$848$	−143.949	−	83.1090i	−0.169751	−	0.0980059i
$849$		0			0
$850$	−233.812	−	404.974i	−0.275073	−	0.476440i
$851$	−152.913	+	88.2844i	−0.179686	+	0.103742i
$852$		0			0
$853$	561.029	−	971.731i	0.657713	−	1.13919i	−0.323493	−	0.946231i	$-0.604857\pi$
$853$	561.029	−	971.731i	0.657713	−	1.13919i	0.981206	−	0.192962i	$-0.0618095\pi$
$854$			70.8240i			0.0829321i
$855$		0			0
$856$	1012.63			1.18298
$857$	−754.732	−	435.744i	−0.880667	−	0.508453i	−0.00978864	−	0.999952i	$-0.503116\pi$
$857$	−754.732	−	435.744i	−0.880667	−	0.508453i	−0.870878	+	0.491499i	$0.836449\pi$
$858$		0			0
$859$	837.461	+	1450.52i	0.974925	+	1.68862i	0.680182	+	0.733044i	$0.261901\pi$
$859$	837.461	+	1450.52i	0.974925	+	1.68862i	0.294744	+	0.955576i	$0.404766\pi$
$860$	818.264	−	472.425i	0.951470	−	0.549332i
$861$		0			0
$862$	−453.565	+	785.597i	−0.526177	+	0.911366i
$863$			1320.74i			1.53041i	0.643787	+	0.765205i	$0.277362\pi$
$863$			1320.74i			1.53041i	−0.643787	+	0.765205i	$0.722638\pi$
$864$		0			0
$865$	−145.292			−0.167967
$866$	−132.253	−	76.3566i	−0.152718	−	0.0881716i
$867$		0			0
$868$	119.107	+	206.300i	0.137220	+	0.237672i
$869$	−143.188	+	82.6699i	−0.164774	+	0.0951322i
$870$		0			0
$871$	−86.3098	+	149.493i	−0.0990928	+	0.171634i
$872$			1353.10i			1.55172i
$873$		0			0
$874$	−57.5217			−0.0658142
$875$	75.3705	+	43.5152i	0.0861377	+	0.0497316i
$876$		0			0
$877$	172.395	+	298.596i	0.196573	+	0.340475i	0.947415	−	0.320007i	$-0.103685\pi$
$877$	172.395	+	298.596i	0.196573	+	0.340475i	−0.750842	+	0.660482i	$0.770352\pi$
$878$	−597.767	+	345.121i	−0.680828	+	0.393076i
$879$		0			0
$880$	15.2693	−	26.4472i	0.0173514	−	0.0300536i
$881$		−	518.737i		−	0.588805i	−0.955682	−	0.294403i	$-0.904879\pi$
$881$		−	518.737i		−	0.588805i	0.955682	−	0.294403i	$-0.0951206\pi$
$882$		0			0
$883$	−584.008			−0.661391			−0.330695	−	0.943738i	$-0.607283\pi$
$883$	−584.008			−0.661391			−0.330695	+	0.943738i	$0.607283\pi$
$884$	153.147	+	88.4194i	0.173243	+	0.100022i
$885$		0			0
$886$	−177.929	−	308.183i	−0.200823	−	0.347836i
$887$	−227.949	+	131.607i	−0.256989	+	0.148373i	−0.622960	−	0.782254i	$-0.714070\pi$
$887$	−227.949	+	131.607i	−0.256989	+	0.148373i	0.365971	+	0.930626i	$0.380737\pi$
$888$		0			0
$889$	−48.3948	+	83.8222i	−0.0544373	+	0.0942882i
$890$		−	609.366i		−	0.684681i
$891$		0			0
$892$	231.349			0.259360
$893$	354.112	+	204.447i	0.396542	+	0.228944i
$894$		0			0
$895$	−1260.96	−	2184.04i	−1.40889	−	2.44027i
$896$	−142.884	+	82.4939i	−0.159468	+	0.0920691i
$897$		0			0
$898$	343.616	−	595.160i	0.382645	−	0.662761i
$899$		−	682.621i		−	0.759312i
$900$		0			0
$901$	1275.23			1.41535
$902$	89.6052	+	51.7336i	0.0993406	+	0.0573543i
$903$		0			0
$904$	592.306	+	1025.90i	0.655206	+	1.13485i
$905$	−1379.72	+	796.580i	−1.52455	+	0.880198i
$906$		0			0
$907$	750.859	−	1300.53i	0.827849	−	1.43388i	−0.0718739	−	0.997414i	$-0.522898\pi$
$907$	750.859	−	1300.53i	0.827849	−	1.43388i	0.899723	−	0.436462i	$-0.143769\pi$
$908$			896.618i			0.987464i
$909$		0			0
$910$	162.162			0.178200
$911$	761.390	+	439.589i	0.835774	+	0.482534i	0.855826	−	0.517265i	$-0.173050\pi$
$911$	761.390	+	439.589i	0.835774	+	0.482534i	−0.0200514	+	0.999799i	$0.506383\pi$
$912$		0			0
$913$	−117.565	−	203.628i	−0.128767	−	0.223032i
$914$	−581.594	+	335.783i	−0.636317	+	0.367378i
$915$		0			0
$916$	7.80459	−	13.5179i	0.00852029	−	0.0147576i
$917$			89.1234i			0.0971901i
$918$		0			0
$919$	76.9882			0.0837739			0.0418869	−	0.999122i	$-0.486663\pi$
$919$	76.9882			0.0837739			0.0418869	+	0.999122i	$0.486663\pi$
$920$	226.111	+	130.545i	0.245773	+	0.141897i
$921$		0			0
$922$	−449.561	−	778.663i	−0.487594	−	0.844537i
$923$	−373.126	+	215.425i	−0.404254	+	0.233396i
$924$		0			0
$925$	604.476	−	1046.98i	0.653487	−	1.13187i
$926$			1020.92i			1.10251i
$927$		0			0
$928$	535.535			0.577085
$929$	1411.41	+	814.879i	1.51928	+	0.877157i	0.999742	+	0.0227099i	$0.00722941\pi$
$929$	1411.41	+	814.879i	1.51928	+	0.877157i	0.519538	+	0.854447i	$0.326104\pi$
$930$		0			0
$931$	35.8006	+	62.0085i	0.0384540	+	0.0666042i
$932$	−231.941	+	133.911i	−0.248864	+	0.143682i
$933$		0			0
$934$	−106.759	+	184.912i	−0.114303	+	0.197978i
$935$			234.293i			0.250581i
$936$		0			0
$937$	−497.720			−0.531185			−0.265592	−	0.964085i	$-0.585568\pi$
$937$	−497.720			−0.531185			−0.265592	+	0.964085i	$0.585568\pi$
$938$	−81.3603	−	46.9734i	−0.0867381	−	0.0500783i
$939$		0			0
$940$	−337.992	−	585.420i	−0.359566	−	0.622787i
$941$	206.888	−	119.447i	0.219860	−	0.126936i	−0.386025	−	0.922488i	$-0.626152\pi$
$941$	206.888	−	119.447i	0.219860	−	0.126936i	0.605886	+	0.795552i	$0.292819\pi$
$942$		0			0
$943$	−65.1373	+	112.821i	−0.0690746	+	0.119641i
$944$			65.4794i			0.0693638i
$945$		0			0
$946$	190.923			0.201821
$947$	−578.427	−	333.955i	−0.610799	−	0.352645i	0.162479	−	0.986712i	$-0.448051\pi$
$947$	−578.427	−	333.955i	−0.610799	−	0.352645i	−0.773278	+	0.634067i	$0.781384\pi$
$948$		0			0
$949$	193.136	+	334.521i	0.203515	+	0.352499i
$950$	341.080	−	196.923i	0.359032	−	0.207287i
$951$		0			0
$952$	−132.122	+	228.841i	−0.138783	+	0.240379i
$953$			11.3247i			0.0118832i	0.999982	+	0.00594162i	$0.00189129\pi$
$953$			11.3247i			0.0118832i	−0.999982	+	0.00594162i	$0.998109\pi$
$954$		0			0
$955$	−329.948			−0.345495
$956$	−118.995	−	68.7019i	−0.124472	−	0.0718639i
$957$		0			0
$958$	−457.587	−	792.564i	−0.477648	−	0.827311i
$959$	91.5940	−	52.8818i	0.0955099	−	0.0551427i
$960$		0			0
$961$	−291.411	+	504.739i	−0.303237	+	0.525222i
$962$		−	340.866i		−	0.354331i
$963$		0			0
$964$	308.787			0.320318
$965$	−927.452	−	535.465i	−0.961090	−	0.554886i
$966$		0			0
$967$	−415.162	−	719.082i	−0.429330	−	0.743621i	0.567484	−	0.823385i	$-0.307917\pi$
$967$	−415.162	−	719.082i	−0.429330	−	0.743621i	−0.996814	+	0.0797632i	$0.974584\pi$
$968$	813.072	−	469.427i	0.839950	−	0.484946i
$969$		0			0
$970$	−92.4353	+	160.103i	−0.0952941	+	0.165054i
$971$			1217.58i			1.25394i	0.779044	+	0.626970i	$0.215705\pi$
$971$			1217.58i			1.25394i	−0.779044	+	0.626970i	$0.784295\pi$
$972$		0			0
$973$	514.974			0.529264
$974$	−98.0189	−	56.5913i	−0.100635	−	0.0581019i
$975$		0			0
$976$	−16.2098	−	28.0761i	−0.0166084	−	0.0287665i
$977$	−367.696	+	212.289i	−0.376352	+	0.217287i	−0.676230	−	0.736691i	$-0.736387\pi$
$977$	−367.696	+	212.289i	−0.376352	+	0.217287i	0.299878	+	0.953978i	$0.403054\pi$
$978$		0			0
$979$	−82.5751	+	143.024i	−0.0843464	+	0.146092i
$980$		−	118.372i		−	0.120787i
$981$		0			0
$982$	−969.203			−0.986968
$983$	66.4478	+	38.3636i	0.0675969	+	0.0390271i	0.533418	−	0.845852i	$-0.320907\pi$
$983$	66.4478	+	38.3636i	0.0675969	+	0.0390271i	−0.465821	+	0.884879i	$0.654241\pi$
$984$		0			0
$985$	322.723	+	558.972i	0.327637	+	0.567485i
$986$	238.843	−	137.896i	0.242234	−	0.139854i
$987$		0			0
$988$	−74.4693	+	128.985i	−0.0753738	+	0.130551i
$989$			240.389i			0.243063i
$990$		0			0
$991$	181.271			0.182917			0.0914585	−	0.995809i	$-0.470847\pi$
$991$	181.271			0.182917			0.0914585	+	0.995809i	$0.470847\pi$
$992$	−1048.90	−	605.585i	−1.05736	−	0.610469i
$993$		0			0
$994$	−117.243	−	203.071i	−0.117951	−	0.204297i
$995$	−418.071	+	241.373i	−0.420172	+	0.242586i
$996$		0			0
$997$	592.216	−	1025.75i	0.593998	−	1.02884i	−0.399689	−	0.916651i	$-0.630882\pi$
$997$	592.216	−	1025.75i	0.593998	−	1.02884i	0.993687	−	0.112184i	$-0.0357847\pi$
$998$			496.453i			0.497448i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.3.r.c.512.2		8
3.2	odd	2	inner	567.3.r.c.512.3		8
9.2	odd	6		21.3.b.a.8.2	✓	4
9.4	even	3	inner	567.3.r.c.134.3		8
9.5	odd	6	inner	567.3.r.c.134.2		8
9.7	even	3		21.3.b.a.8.3	yes	4
36.7	odd	6		336.3.d.c.113.3		4
36.11	even	6		336.3.d.c.113.4		4
45.2	even	12		525.3.f.a.449.6		8
45.7	odd	12		525.3.f.a.449.4		8
45.29	odd	6		525.3.c.a.176.3		4
45.34	even	6		525.3.c.a.176.2		4
45.38	even	12		525.3.f.a.449.3		8
45.43	odd	12		525.3.f.a.449.5		8
63.2	odd	6		147.3.h.e.116.2		8
63.11	odd	6		147.3.h.e.128.3		8
63.16	even	3		147.3.h.e.116.3		8
63.20	even	6		147.3.b.f.50.2		4
63.25	even	3		147.3.h.e.128.2		8
63.34	odd	6		147.3.b.f.50.3		4
63.38	even	6		147.3.h.c.128.3		8
63.47	even	6		147.3.h.c.116.2		8
63.52	odd	6		147.3.h.c.128.2		8
63.61	odd	6		147.3.h.c.116.3		8
72.11	even	6		1344.3.d.b.449.1		4
72.29	odd	6		1344.3.d.f.449.4		4
72.43	odd	6		1344.3.d.b.449.2		4
72.61	even	6		1344.3.d.f.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.2	✓	4	9.2	odd	6
21.3.b.a.8.3	yes	4	9.7	even	3
147.3.b.f.50.2		4	63.20	even	6
147.3.b.f.50.3		4	63.34	odd	6
147.3.h.c.116.2		8	63.47	even	6
147.3.h.c.116.3		8	63.61	odd	6
147.3.h.c.128.2		8	63.52	odd	6
147.3.h.c.128.3		8	63.38	even	6
147.3.h.e.116.2		8	63.2	odd	6
147.3.h.e.116.3		8	63.16	even	3
147.3.h.e.128.2		8	63.25	even	3
147.3.h.e.128.3		8	63.11	odd	6
336.3.d.c.113.3		4	36.7	odd	6
336.3.d.c.113.4		4	36.11	even	6
525.3.c.a.176.2		4	45.34	even	6
525.3.c.a.176.3		4	45.29	odd	6
525.3.f.a.449.3		8	45.38	even	12
525.3.f.a.449.4		8	45.7	odd	12
525.3.f.a.449.5		8	45.43	odd	12
525.3.f.a.449.6		8	45.2	even	12
567.3.r.c.134.2		8	9.5	odd	6	inner
567.3.r.c.134.3		8	9.4	even	3	inner
567.3.r.c.512.2		8	1.1	even	1	trivial
567.3.r.c.512.3		8	3.2	odd	2	inner
1344.3.d.b.449.1		4	72.11	even	6
1344.3.d.b.449.2		4	72.43	odd	6
1344.3.d.f.449.3		4	72.61	even	6
1344.3.d.f.449.4		4	72.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	567.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13198 - 0.653548i) q^{2} +(-1.14575 - 1.98450i) q^{4} +(-6.39086 + 3.68977i) q^{5} +(1.32288 - 2.29129i) q^{7} +8.22359i q^{8} +O(q^{10})\)	\(q+(-1.13198 - 0.653548i) q^{2} +(-1.14575 - 1.98450i) q^{4} +(-6.39086 + 3.68977i) q^{5} +(1.32288 - 2.29129i) q^{7} +8.22359i q^{8} +9.64575 q^{10} +(-2.26395 - 1.30710i) q^{11} +(3.17712 + 5.50294i) q^{13} +(-2.99493 + 1.72912i) q^{14} +(0.791503 - 1.37092i) q^{16} +12.1449i q^{17} -10.2288 q^{19} +(14.6447 + 8.45511i) q^{20} +(1.70850 + 2.95920i) q^{22} +(-3.72591 + 2.15115i) q^{23} +(14.7288 - 25.5110i) q^{25} -8.30561i q^{26} -6.06275 q^{28} +(15.0457 + 8.68663i) q^{29} +(-19.6458 - 34.0274i) q^{31} +(26.6954 - 15.4126i) q^{32} +(7.93725 - 13.7477i) q^{34} +19.5244i q^{35} +41.0405 q^{37} +(11.5787 + 6.68498i) q^{38} +(-30.3431 - 52.5559i) q^{40} +(26.2234 - 15.1401i) q^{41} +(27.9373 - 48.3887i) q^{43} +5.99042i q^{44} +5.62352 q^{46} +(-34.6193 - 19.9874i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-33.3452 + 19.2519i) q^{50} +(7.28039 - 12.6100i) q^{52} -105.002i q^{53} +19.2915 q^{55} +(18.8426 + 10.8788i) q^{56} +(-11.3542 - 19.6661i) q^{58} +(-35.8223 + 20.6820i) q^{59} +(10.2399 - 17.7360i) q^{61} +51.3577i q^{62} -46.6235 q^{64} +(-40.6091 - 23.4457i) q^{65} +(13.5830 + 23.5265i) q^{67} +(24.1015 - 13.9150i) q^{68} +(12.7601 - 22.1012i) q^{70} +67.8049i q^{71} +60.7895 q^{73} +(-46.4569 - 26.8219i) q^{74} +(11.7196 + 20.2990i) q^{76} +(-5.98986 + 3.45825i) q^{77} +(31.6235 - 54.7735i) q^{79} +11.6818i q^{80} -39.5791 q^{82} +(77.8934 + 44.9718i) q^{83} +(-44.8118 - 77.6162i) q^{85} +(-63.2487 + 36.5166i) q^{86} +(10.7490 - 18.6178i) q^{88} -63.1745i q^{89} +16.8118 q^{91} +(8.53793 + 4.92937i) q^{92} +(26.1255 + 45.2507i) q^{94} +(65.3706 - 37.7417i) q^{95} +(-9.58301 + 16.5983i) q^{97} +9.14967i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4}+O(q^{10}) \) 8 * q + 12 * q^4	\( 8 q + 12 q^{4} + 56 q^{10} + 36 q^{13} - 36 q^{16} + 24 q^{19} + 56 q^{22} + 12 q^{25} - 112 q^{28} - 136 q^{31} + 32 q^{37} - 84 q^{40} + 160 q^{43} - 336 q^{46} - 28 q^{49} - 164 q^{52} + 112 q^{55} - 112 q^{58} + 156 q^{61} + 8 q^{64} + 24 q^{67} + 28 q^{70} - 64 q^{73} + 316 q^{76} - 128 q^{79} + 784 q^{82} - 168 q^{85} - 168 q^{88} - 56 q^{91} + 336 q^{94} + 8 q^{97}+O(q^{100}) \) 8 * q + 12 * q^4 + 56 * q^10 + 36 * q^13 - 36 * q^16 + 24 * q^19 + 56 * q^22 + 12 * q^25 - 112 * q^28 - 136 * q^31 + 32 * q^37 - 84 * q^40 + 160 * q^43 - 336 * q^46 - 28 * q^49 - 164 * q^52 + 112 * q^55 - 112 * q^58 + 156 * q^61 + 8 * q^64 + 24 * q^67 + 28 * q^70 - 64 * q^73 + 316 * q^76 - 128 * q^79 + 784 * q^82 - 168 * q^85 - 168 * q^88 - 56 * q^91 + 336 * q^94 + 8 * q^97

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