LMFDB - Embedded newform 567.3.r.c.512.3

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			512.3
Root			$1.03103 + 0.478705i$ of defining polynomial
Character	$\chi$	$=$	567.512
Dual form			567.3.r.c.134.3

$q$-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	0.755546	−	0.655096i	$-0.227372\pi$
$2$	1.13198	+	0.653548i	0.565989	+	0.326774i	−0.189557	+	0.981870i	$0.560705\pi$
$3$		0			0
$3$		0			0
$4$	−1.14575	−	1.98450i	−0.286438	−	0.496125i
$5$	6.39086	−	3.68977i	1.27817	−	0.737953i	0.301660	−	0.953415i	$-0.402459\pi$
$5$	6.39086	−	3.68977i	1.27817	−	0.737953i	0.976512	+	0.215462i	$0.0691258\pi$
$6$		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	0.599365	−	0.800476i	$-0.295420\pi$
$11$	2.26395	+	1.30710i	0.205814	+	0.118827i	−0.393550	+	0.919303i	$0.628753\pi$
$12$		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	$-0.883731\pi$
$17$		−	12.1449i		−	0.714405i	0.934027	−	0.357202i	$-0.116269\pi$
$18$		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	−0.416810	−	0.908993i	$-0.636852\pi$
$23$	3.72591	−	2.15115i	0.161996	−	0.0935284i	0.578806	+	0.815465i	$0.303519\pi$
$24$		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	0.217634	−	0.976031i	$-0.430166\pi$
$29$	−15.0457	−	8.68663i	−0.518817	−	0.299539i	−0.736450	+	0.676492i	$0.763500\pi$
$30$		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	−0.784459	−	0.620181i	$-0.787059\pi$
$41$	−26.2234	+	15.1401i	−0.639595	+	0.369270i	0.144863	+	0.989452i	$0.453726\pi$
$42$		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	0.820825	−	0.571180i	$-0.193514\pi$
$47$	34.6193	+	19.9874i	0.736580	+	0.425265i	−0.0842443	+	0.996445i	$0.526848\pi$
$48$		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	$0.456277\pi$
$53$			105.002i			1.98116i	−0.136928	+	0.990581i	$0.543723\pi$
$54$		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	−0.164695	−	0.986345i	$-0.552664\pi$
$59$	35.8223	−	20.6820i	0.607157	−	0.350542i	0.771852	+	0.635802i	$0.219331\pi$
$60$		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	$-0.841543\pi$
$71$		−	67.8049i		−	0.954999i	0.878632	−	0.477499i	$-0.158457\pi$
$72$		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	−0.0489926	−	0.998799i	$-0.515601\pi$
$83$	−77.8934	−	44.9718i	−0.938474	−	0.541828i	−0.889482	+	0.456971i	$0.848934\pi$
$84$		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	$0.115490\pi$
$89$			63.1745i			0.709826i	−0.934899	+	0.354913i	$0.884510\pi$
$90$		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	0.859437	−	0.511241i	$-0.170814\pi$
$101$	85.4872	+	49.3561i	0.846408	+	0.488674i	−0.0130291	+	0.999915i	$0.504147\pi$
$102$		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	$0.195156\pi$
$107$			123.137i			1.15081i	−0.817868	+	0.575406i	$0.804844\pi$
$108$		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	−0.937267	−	0.348612i	$-0.886653\pi$
$113$	−124.751	+	72.0252i	−1.10399	+	0.637391i	−0.166727	+	0.986003i	$0.553320\pi$
$114$		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	−0.384505	−	0.923123i	$-0.625628\pi$
$131$	29.1725	−	16.8427i	0.222691	−	0.128570i	0.607195	+	0.794552i	$0.292294\pi$
$132$		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	0.368302	−	0.929706i	$-0.379939\pi$
$137$	−34.6193	−	19.9874i	−0.252695	−	0.145894i	−0.620998	+	0.783812i	$0.713272\pi$
$138$		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	−0.956906	−	0.290398i	$-0.906212\pi$
$149$	−176.396	+	101.842i	−1.18387	+	0.683506i	−0.226961	+	0.973904i	$0.572879\pi$
$150$		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	−0.448158	−	0.893954i	$-0.647920\pi$
$167$	17.0255	−	9.82969i	0.101949	−	0.0588604i	0.550108	+	0.835094i	$0.314587\pi$
$168$		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	0.449910	−	0.893074i	$-0.351456\pi$
$173$	−17.0507	−	9.84422i	−0.0985589	−	0.0569030i	−0.548469	+	0.836171i	$0.684789\pi$
$174$		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	$-0.596289\pi$
$179$		−	341.745i		−	1.90919i	0.297910	−	0.954594i	$-0.403711\pi$
$180$		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	0.395199	−	0.918595i	$-0.370676\pi$
$191$	−38.7210	−	22.3556i	−0.202728	−	0.117045i	−0.597927	+	0.801550i	$0.704009\pi$
$192$		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	$0.0712554\pi$
$197$			87.4643i			0.443981i	−0.975049	+	0.221991i	$0.928745\pi$
$198$		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	0.999966	−	0.00829388i	$-0.00264005\pi$
$227$	338.858	+	195.640i	1.49277	+	0.861849i	0.492800	+	0.870143i	$0.335973\pi$
$228$		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	$0.0806963\pi$
$233$			116.877i			0.501616i	−0.968037	+	0.250808i	$0.919304\pi$
$234$		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	−0.604688	−	0.796462i	$-0.706702\pi$
$239$	−51.9289	+	29.9812i	−0.217276	+	0.125444i	0.387412	+	0.921906i	$0.373369\pi$
$240$		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	$0.179447\pi$
$251$			268.248i			1.06872i	−0.845257	+	0.534359i	$0.820553\pi$
$252$		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	−0.0506392	−	0.998717i	$-0.516126\pi$
$257$	202.762	−	117.064i	0.788956	−	0.455504i	0.839595	+	0.543213i	$0.182793\pi$
$258$		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	0.0279999	−	0.999608i	$-0.491086\pi$
$263$	−216.629	−	125.071i	−0.823686	−	0.475555i	−0.851686	+	0.524053i	$0.824420\pi$
$264$		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	$0.218276\pi$
$269$			340.684i			1.26648i	−0.773955	+	0.633241i	$0.781724\pi$
$270$		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	0.816870	−	0.576822i	$-0.195707\pi$
$281$	203.939	+	117.744i	0.725763	+	0.419019i	−0.0911071	+	0.995841i	$0.529041\pi$
$282$		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	$0.695126\pi$
$293$	−460.401	+	265.813i	−1.57133	+	0.907211i	−0.996006	+	0.0892885i	$0.971541\pi$
$294$		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	−0.439291	−	0.898345i	$-0.644770\pi$
$311$	37.0253	−	21.3766i	0.119052	−	0.0687349i	0.558344	+	0.829610i	$0.311437\pi$
$312$		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	0.680014	−	0.733199i	$-0.261974\pi$
$317$	122.061	+	70.4721i	0.385051	+	0.222309i	−0.294963	+	0.955509i	$0.595307\pi$
$318$		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	−0.330815	−	0.943696i	$-0.607324\pi$
$347$	111.401	−	64.3176i	0.321041	−	0.185353i	0.651857	+	0.758342i	$0.273990\pi$
$348$		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	0.764317	−	0.644841i	$-0.223076\pi$
$353$	207.574	+	119.843i	0.588027	+	0.339498i	−0.176290	+	0.984338i	$0.556410\pi$
$354$		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	$0.0807581\pi$
$359$			180.215i			0.501992i	−0.967988	+	0.250996i	$0.919242\pi$
$360$		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	0.358944	−	0.933359i	$-0.383137\pi$
$383$	515.797	−	297.796i	1.34673	−	0.777534i	0.987785	+	0.155825i	$0.0498037\pi$
$384$		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	0.849664	−	0.527325i	$-0.176805\pi$
$389$	318.132	+	183.673i	0.817819	+	0.472168i	−0.0318449	+	0.999493i	$0.510138\pi$
$390$		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	−0.735200	−	0.677850i	$-0.762912\pi$
$401$	−206.822	+	119.409i	−0.515765	+	0.297777i	0.219435	+	0.975627i	$0.429579\pi$
$402$		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	−0.511856	−	0.859071i	$-0.671042\pi$
$419$	−9.97472	+	5.75890i	−0.0238060	+	0.0137444i	0.488050	+	0.872816i	$0.337708\pi$
$420$		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	$0.297893\pi$
$431$			694.004i			1.61022i	−0.593127	+	0.805109i	$0.702107\pi$
$432$		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	0.209695	−	0.977767i	$-0.432753\pi$
$443$	−235.777	−	136.126i	−0.532228	−	0.307282i	−0.741923	+	0.670485i	$0.766086\pi$
$444$		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	$-0.800902\pi$
$449$		−	525.770i		−	1.17098i	0.810680	−	0.585490i	$-0.199098\pi$
$450$		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	−0.313185	−	0.949692i	$-0.601396\pi$
$461$	−595.721	−	343.939i	−1.29224	−	0.746072i	−0.979050	+	0.203620i	$0.934729\pi$
$462$		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	$0.0559589\pi$
$467$			163.353i			0.349792i	−0.984587	+	0.174896i	$0.944041\pi$
$468$		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	−0.291672	−	0.956518i	$-0.594212\pi$
$479$	−606.355	−	350.079i	−1.26588	−	0.730855i	−0.974205	+	0.225664i	$0.927545\pi$
$480$		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	−0.981736	−	0.190247i	$-0.939071\pi$
$491$	−642.152	+	370.747i	−1.30785	+	0.755085i	−0.326110	+	0.945332i	$0.605738\pi$
$492$		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	$-0.846762\pi$
$503$		−	465.808i		−	0.926059i	0.886343	−	0.463029i	$-0.153238\pi$
$504$		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	−0.976282	−	0.216504i	$-0.930535\pi$
$509$	−649.955	+	375.252i	−1.27692	+	0.737233i	−0.300643	+	0.953737i	$0.597201\pi$
$510$		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	$-0.754231\pi$
$521$		−	726.946i		−	1.39529i	0.716443	−	0.697645i	$-0.245769\pi$
$522$		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	$0.149403\pi$
$557$			503.883i			0.904637i	−0.891857	+	0.452318i	$0.850597\pi$
$558$		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	−0.581293	−	0.813694i	$-0.697453\pi$
$563$	−94.1672	+	54.3675i	−0.167260	+	0.0965674i	0.414033	+	0.910262i	$0.364120\pi$
$564$		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	0.131113	−	0.991367i	$-0.458145\pi$
$569$	−376.610	−	217.436i	−0.661880	−	0.382136i	−0.792993	+	0.609231i	$0.791478\pi$
$570$		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	0.932562	−	0.361010i	$-0.117568\pi$
$587$	637.599	+	368.118i	1.08620	+	0.627118i	0.153638	+	0.988127i	$0.450901\pi$
$588$		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	$-0.752173\pi$
$593$		−	832.884i		−	1.40453i	0.711917	−	0.702263i	$-0.247827\pi$
$594$		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	−0.549279	−	0.835639i	$-0.685098\pi$
$599$	−60.0407	+	34.6645i	−0.100235	+	0.0578706i	0.449045	+	0.893509i	$0.351764\pi$
$600$		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	0.378482	−	0.925609i	$-0.376446\pi$
$617$	844.872	−	487.787i	1.36932	−	0.790579i	0.990842	+	0.135030i	$0.0431130\pi$
$618$		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	0.868597	−	0.495520i	$-0.165022\pi$
$641$	560.082	+	323.363i	0.873762	+	0.504467i	0.00516570	+	0.999987i	$0.498356\pi$
$642$		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	$0.186834\pi$
$647$			716.654i			1.10766i	−0.832631	+	0.553828i	$0.813166\pi$
$648$		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	−0.729803	−	0.683658i	$-0.760388\pi$
$653$	−328.223	+	189.500i	−0.502639	+	0.290199i	0.227164	+	0.973857i	$0.427055\pi$
$654$		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	−0.0459222	−	0.998945i	$-0.514623\pi$
$659$	−615.503	−	355.361i	−0.933995	−	0.539242i	−0.888073	+	0.459703i	$0.847956\pi$
$660$		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	0.269768	−	0.962925i	$-0.413053\pi$
$677$	−290.613	−	167.786i	−0.429266	−	0.247837i	−0.699034	+	0.715088i	$0.746386\pi$
$678$		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	$0.0264404\pi$
$683$			113.336i			0.165939i	−0.996552	+	0.0829694i	$0.973560\pi$
$684$		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	$0.213944\pi$
$701$			872.955i			1.24530i	−0.782501	+	0.622650i	$0.786056\pi$
$702$		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	$0.215758\pi$
$719$			901.769i			1.25420i	−0.778939	+	0.627099i	$0.784242\pi$
$720$		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	−0.537138	−	0.843494i	$-0.680495\pi$
$743$	−55.8886	+	32.2673i	−0.0752202	+	0.0434284i	0.461918	+	0.886923i	$0.347161\pi$
$744$		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	−0.295339	−	0.955393i	$-0.595433\pi$
$761$	292.518	−	168.885i	0.384386	−	0.221925i	0.679725	+	0.733467i	$0.262099\pi$
$762$		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	$0.0603682\pi$
$773$			291.448i			0.377035i	−0.982070	+	0.188517i	$0.939632\pi$
$774$		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	−0.776099	−	0.630611i	$-0.782804\pi$
$797$	−492.564	+	284.382i	−0.618023	+	0.356816i	0.158076	+	0.987427i	$0.449471\pi$
$798$		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	$-0.963783\pi$
$809$		−	183.697i		−	0.227067i	0.993534	−	0.113534i	$-0.0362169\pi$
$810$		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	−0.282078	−	0.959391i	$-0.591024\pi$
$821$	−1029.51	−	594.390i	−1.25397	−	0.723983i	−0.971897	+	0.235409i	$0.924357\pi$
$822$		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	$-0.841290\pi$
$827$		−	790.941i		−	0.956398i	0.878252	−	0.478199i	$-0.158710\pi$
$828$		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	0.368855	−	0.929487i	$-0.379750\pi$
$839$	−211.157	−	121.912i	−0.251678	−	0.145306i	−0.620532	+	0.784181i	$0.713083\pi$
$840$		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	0.870878	−	0.491499i	$-0.163551\pi$
$857$	754.732	+	435.744i	0.880667	+	0.508453i	0.00978864	+	0.999952i	$0.496884\pi$
$858$		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	$-0.722638\pi$
$863$		−	1320.74i		−	1.53041i	0.643787	−	0.765205i	$-0.277362\pi$
$864$		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	$0.0951206\pi$
$881$			518.737i			0.588805i	−0.955682	+	0.294403i	$0.904879\pi$
$882$		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	−0.365971	−	0.930626i	$-0.619263\pi$
$887$	227.949	−	131.607i	0.256989	−	0.148373i	0.622960	+	0.782254i	$0.285930\pi$
$888$		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	0.0200514	−	0.999799i	$-0.493617\pi$
$911$	−761.390	−	439.589i	−0.835774	−	0.482534i	−0.855826	+	0.517265i	$0.826950\pi$
$912$		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	$-0.992771\pi$
$929$	−1411.41	−	814.879i	−1.51928	−	0.877157i	−0.519538	−	0.854447i	$-0.673896\pi$
$930$		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	−0.605886	−	0.795552i	$-0.707181\pi$
$941$	−206.888	+	119.447i	−0.219860	+	0.126936i	0.386025	+	0.922488i	$0.373848\pi$
$942$		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	0.773278	−	0.634067i	$-0.218616\pi$
$947$	578.427	+	333.955i	0.610799	+	0.352645i	−0.162479	+	0.986712i	$0.551949\pi$
$948$		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	$-0.998109\pi$
$953$		−	11.3247i		−	0.0118832i	0.999982	−	0.00594162i	$-0.00189129\pi$
$954$		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	$-0.784295\pi$
$971$		−	1217.58i		−	1.25394i	0.779044	−	0.626970i	$-0.215705\pi$
$972$		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	−0.299878	−	0.953978i	$-0.596946\pi$
$977$	367.696	−	212.289i	0.376352	−	0.217287i	0.676230	+	0.736691i	$0.263613\pi$
$978$		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	0.465821	−	0.884879i	$-0.345759\pi$
$983$	−66.4478	−	38.3636i	−0.0675969	−	0.0390271i	−0.533418	+	0.845852i	$0.679093\pi$
$984$		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.512.3		8
3.2	odd	2	inner	567.3.r.c.512.2		8
9.2	odd	6		21.3.b.a.8.3	yes	4
9.4	even	3	inner	567.3.r.c.134.2		8
9.5	odd	6	inner	567.3.r.c.134.3		8
9.7	even	3		21.3.b.a.8.2	✓	4
36.7	odd	6		336.3.d.c.113.4		4
36.11	even	6		336.3.d.c.113.3		4
45.2	even	12		525.3.f.a.449.4		8
45.7	odd	12		525.3.f.a.449.6		8
45.29	odd	6		525.3.c.a.176.2		4
45.34	even	6		525.3.c.a.176.3		4
45.38	even	12		525.3.f.a.449.5		8
45.43	odd	12		525.3.f.a.449.3		8
63.2	odd	6		147.3.h.e.116.3		8
63.11	odd	6		147.3.h.e.128.2		8
63.16	even	3		147.3.h.e.116.2		8
63.20	even	6		147.3.b.f.50.3		4
63.25	even	3		147.3.h.e.128.3		8
63.34	odd	6		147.3.b.f.50.2		4
63.38	even	6		147.3.h.c.128.2		8
63.47	even	6		147.3.h.c.116.3		8
63.52	odd	6		147.3.h.c.128.3		8
63.61	odd	6		147.3.h.c.116.2		8
72.11	even	6		1344.3.d.b.449.2		4
72.29	odd	6		1344.3.d.f.449.3		4
72.43	odd	6		1344.3.d.b.449.1		4
72.61	even	6		1344.3.d.f.449.4		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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