LMFDB - Embedded newform 324.3.f.o.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.207360000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.4
Root			$-0.437016 + 0.756934i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.o.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +(3.70246 + 6.41285i) q^{5} +(-8.20820 - 4.73901i) q^{7} +(3.16228 + 7.34847i) q^{8} +O(q^{10})$	\(q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +(3.70246 + 6.41285i) q^{5} +(-8.20820 - 4.73901i) q^{7} +(3.16228 + 7.34847i) q^{8} +(2.00000 + 14.6742i) q^{10} +(5.86319 + 3.38511i) q^{11} +(7.20820 + 12.4850i) q^{13} +(-11.6082 - 14.9861i) q^{14} +(0.291796 + 15.9973i) q^{16} -17.8933 q^{17} -5.19615i q^{19} +(-7.40492 + 28.6791i) q^{20} +(8.29180 + 10.7047i) q^{22} +(21.5958 - 12.4683i) q^{23} +(-14.9164 + 25.8360i) q^{25} +(3.89374 + 28.5687i) q^{26} +(-10.1459 - 36.5292i) q^{28} +(14.8098 - 25.6514i) q^{29} +(-14.8328 + 8.56373i) q^{31} +(-11.5687 + 29.8356i) q^{32} +(-33.1246 - 13.5440i) q^{34} -70.1839i q^{35} +6.41641 q^{37} +(3.93314 - 9.61927i) q^{38} +(-35.4164 + 47.4866i) q^{40} +(4.32145 + 7.48497i) q^{41} +(43.4164 + 25.0665i) q^{43} +(7.24730 + 26.0931i) q^{44} +(49.4164 - 6.73516i) q^{46} +(-45.0485 - 26.0088i) q^{47} +(20.4164 + 35.3623i) q^{49} +(-47.1698 + 36.5376i) q^{50} +(-14.4164 + 55.8345i) q^{52} +82.6921 q^{53} +50.1329i q^{55} +(8.86784 - 75.3038i) q^{56} +(46.8328 - 36.2765i) q^{58} +(72.5075 - 41.8622i) q^{59} +(4.20820 - 7.28882i) q^{61} +(-33.9411 + 4.62597i) q^{62} +(-44.0000 + 46.4758i) q^{64} +(-53.3762 + 92.4502i) q^{65} +(25.1656 - 14.5294i) q^{67} +(-51.0693 - 50.1463i) q^{68} +(53.1246 - 129.927i) q^{70} -113.287i q^{71} +2.16718 q^{73} +(11.8782 + 4.85680i) q^{74} +(14.5623 - 14.8303i) q^{76} +(-32.0841 - 55.5714i) q^{77} +(-129.457 - 74.7423i) q^{79} +(-101.508 + 61.1007i) q^{80} +(2.33437 + 17.1275i) q^{82} +(-11.7264 - 6.77022i) q^{83} +(-66.2492 - 114.747i) q^{85} +(61.4001 + 79.2672i) q^{86} +(-6.33437 + 53.7901i) q^{88} -17.8933 q^{89} -136.639i q^{91} +(96.5792 + 24.9366i) q^{92} +(-63.7082 - 82.2469i) q^{94} +(33.3221 - 19.2385i) q^{95} +(69.1656 - 119.798i) q^{97} +(11.0286 + 80.9175i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 12 q^{7}+O(q^{10}) $ 8 * q - 4 * q^4 - 12 * q^7	$ 8 q - 4 q^{4} - 12 q^{7} + 16 q^{10} + 4 q^{13} + 56 q^{16} + 120 q^{22} - 12 q^{25} - 108 q^{28} + 96 q^{31} - 104 q^{34} - 56 q^{37} - 176 q^{40} + 240 q^{43} + 288 q^{46} + 56 q^{49} - 8 q^{52} + 160 q^{58} - 20 q^{61} - 352 q^{64} - 228 q^{67} + 264 q^{70} + 232 q^{73} + 36 q^{76} - 660 q^{79} + 448 q^{82} - 208 q^{85} - 480 q^{88} - 456 q^{94} + 124 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 - 12 * q^7 + 16 * q^10 + 4 * q^13 + 56 * q^16 + 120 * q^22 - 12 * q^25 - 108 * q^28 + 96 * q^31 - 104 * q^34 - 56 * q^37 - 176 * q^40 + 240 * q^43 + 288 * q^46 + 56 * q^49 - 8 * q^52 + 160 * q^58 - 20 * q^61 - 352 * q^64 - 228 * q^67 + 264 * q^70 + 232 * q^73 + 36 * q^76 - 660 * q^79 + 448 * q^82 - 208 * q^85 - 480 * q^88 - 456 * q^94 + 124 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.85123	+	0.756934i	0.925615	+	0.378467i
$2$	1.85123	+	0.756934i	0.925615	+	0.378467i
$3$		0			0
$3$		0			0
$4$	2.85410	+	2.80252i	0.713525	+	0.700629i
$5$	3.70246	+	6.41285i	0.740492	+	1.28257i	0.952272	+	0.305252i	$0.0987407\pi$
$5$	3.70246	+	6.41285i	0.740492	+	1.28257i	−0.211780	+	0.977317i	$0.567926\pi$
$6$		0			0
$7$	−8.20820	−	4.73901i	−1.17260	−	0.677001i	−0.218309	−	0.975880i	$-0.570054\pi$
$7$	−8.20820	−	4.73901i	−1.17260	−	0.677001i	−0.954291	+	0.298878i	$0.903388\pi$
$8$	3.16228	+	7.34847i	0.395285	+	0.918559i
$9$		0			0
$10$	2.00000	+	14.6742i	0.200000	+	1.46742i
$11$	5.86319	+	3.38511i	0.533017	+	0.307737i	0.742244	−	0.670130i	$-0.233762\pi$
$11$	5.86319	+	3.38511i	0.533017	+	0.307737i	−0.209227	+	0.977867i	$0.567095\pi$
$12$		0			0
$13$	7.20820	+	12.4850i	0.554477	+	0.960383i	0.997944	+	0.0640919i	$0.0204151\pi$
$13$	7.20820	+	12.4850i	0.554477	+	0.960383i	−0.443467	+	0.896291i	$0.646252\pi$
$14$	−11.6082	−	14.9861i	−0.829154	−	1.07043i
$15$		0			0
$16$	0.291796	+	15.9973i	0.0182373	+	0.999834i
$17$	−17.8933			−1.05255			−0.526274	−	0.850315i	$-0.676411\pi$
$17$	−17.8933			−1.05255			−0.526274	+	0.850315i	$0.676411\pi$
$18$		0			0
$19$		−	5.19615i		−	0.273482i	−0.990607	−	0.136741i	$-0.956337\pi$
$19$		−	5.19615i		−	0.273482i	0.990607	−	0.136741i	$-0.0436628\pi$
$20$	−7.40492	+	28.6791i	−0.370246	+	1.43396i
$21$		0			0
$22$	8.29180	+	10.7047i	0.376900	+	0.486576i
$23$	21.5958	−	12.4683i	0.938946	−	0.542101i	0.0493164	−	0.998783i	$-0.484296\pi$
$23$	21.5958	−	12.4683i	0.938946	−	0.542101i	0.889630	+	0.456682i	$0.150962\pi$
$24$		0			0
$25$	−14.9164	+	25.8360i	−0.596656	+	1.03344i
$26$	3.89374	+	28.5687i	0.149759	+	1.09880i
$27$		0			0
$28$	−10.1459	−	36.5292i	−0.362354	−	1.30462i
$29$	14.8098	−	25.6514i	0.510684	−	0.884531i	−0.489239	−	0.872150i	$-0.662726\pi$
$29$	14.8098	−	25.6514i	0.510684	−	0.884531i	0.999923	−	0.0123811i	$-0.00394113\pi$
$30$		0			0
$31$	−14.8328	+	8.56373i	−0.478478	+	0.276249i	−0.719782	−	0.694200i	$-0.755758\pi$
$31$	−14.8328	+	8.56373i	−0.478478	+	0.276249i	0.241304	+	0.970450i	$0.422425\pi$
$32$	−11.5687	+	29.8356i	−0.361523	+	0.932363i
$33$		0			0
$34$	−33.1246	−	13.5440i	−0.974253	−	0.398354i
$35$		−	70.1839i		−	2.00526i
$36$		0			0
$37$	6.41641			0.173416			0.0867082	−	0.996234i	$-0.472365\pi$
$37$	6.41641			0.173416			0.0867082	+	0.996234i	$0.472365\pi$
$38$	3.93314	−	9.61927i	0.103504	−	0.253139i
$39$		0			0
$40$	−35.4164	+	47.4866i	−0.885410	+	1.18717i
$41$	4.32145	+	7.48497i	0.105401	+	0.182560i	0.913902	−	0.405935i	$-0.133054\pi$
$41$	4.32145	+	7.48497i	0.105401	+	0.182560i	−0.808501	+	0.588495i	$0.799721\pi$
$42$		0			0
$43$	43.4164	+	25.0665i	1.00968	+	0.582941i	0.911099	−	0.412187i	$-0.135235\pi$
$43$	43.4164	+	25.0665i	1.00968	+	0.582941i	0.0985848	+	0.995129i	$0.468568\pi$
$44$	7.24730	+	26.0931i	0.164711	+	0.593026i
$45$		0			0
$46$	49.4164	−	6.73516i	1.07427	−	0.146416i
$47$	−45.0485	−	26.0088i	−0.958479	−	0.553378i	−0.0627743	−	0.998028i	$-0.519995\pi$
$47$	−45.0485	−	26.0088i	−0.958479	−	0.553378i	−0.895705	+	0.444650i	$0.853328\pi$
$48$		0			0
$49$	20.4164	+	35.3623i	0.416661	+	0.721679i
$50$	−47.1698	+	36.5376i	−0.943396	+	0.730752i
$51$		0			0
$52$	−14.4164	+	55.8345i	−0.277239	+	1.07374i
$53$	82.6921			1.56023			0.780114	−	0.625637i	$-0.215161\pi$
$53$	82.6921			1.56023			0.780114	+	0.625637i	$0.215161\pi$
$54$		0			0
$55$			50.1329i			0.911508i
$56$	8.86784	−	75.3038i	0.158354	−	1.34471i
$57$		0			0
$58$	46.8328	−	36.2765i	0.807462	−	0.625458i
$59$	72.5075	−	41.8622i	1.22894	−	0.709529i	0.262132	−	0.965032i	$-0.415575\pi$
$59$	72.5075	−	41.8622i	1.22894	−	0.709529i	0.966808	+	0.255503i	$0.0822412\pi$
$60$		0			0
$61$	4.20820	−	7.28882i	0.0689869	−	0.119489i	−0.829469	−	0.558553i	$-0.811357\pi$
$61$	4.20820	−	7.28882i	0.0689869	−	0.119489i	0.898456	+	0.439064i	$0.144690\pi$
$62$	−33.9411	+	4.62597i	−0.547438	+	0.0746124i
$63$		0			0
$64$	−44.0000	+	46.4758i	−0.687500	+	0.726184i
$65$	−53.3762	+	92.4502i	−0.821172	+	1.42231i
$66$		0			0
$67$	25.1656	−	14.5294i	0.375606	−	0.216856i	−0.300299	−	0.953845i	$-0.597086\pi$
$67$	25.1656	−	14.5294i	0.375606	−	0.216856i	0.675905	+	0.736989i	$0.263753\pi$
$68$	−51.0693	−	50.1463i	−0.751019	−	0.737445i
$69$		0			0
$70$	53.1246	−	129.927i	0.758923	−	1.85609i
$71$		−	113.287i		−	1.59559i	−0.602928	−	0.797796i	$-0.705999\pi$
$71$		−	113.287i		−	1.59559i	0.602928	−	0.797796i	$-0.294001\pi$
$72$		0			0
$73$	2.16718			0.0296875			0.0148437	−	0.999890i	$-0.495275\pi$
$73$	2.16718			0.0296875			0.0148437	+	0.999890i	$0.495275\pi$
$74$	11.8782	+	4.85680i	0.160517	+	0.0656324i
$75$		0			0
$76$	14.5623	−	14.8303i	0.191609	−	0.195136i
$77$	−32.0841	−	55.5714i	−0.416677	−	0.721706i
$78$		0			0
$79$	−129.457	−	74.7423i	−1.63870	−	0.946105i	−0.981281	−	0.192581i	$-0.938314\pi$
$79$	−129.457	−	74.7423i	−1.63870	−	0.946105i	−0.657421	−	0.753524i	$-0.728352\pi$
$80$	−101.508	+	61.1007i	−1.26885	+	0.763759i
$81$		0			0
$82$	2.33437	+	17.1275i	0.0284679	+	0.208871i
$83$	−11.7264	−	6.77022i	−0.141282	−	0.0815690i	0.427693	−	0.903924i	$-0.359326\pi$
$83$	−11.7264	−	6.77022i	−0.141282	−	0.0815690i	−0.568975	+	0.822355i	$0.692660\pi$
$84$		0			0
$85$	−66.2492	−	114.747i	−0.779403	−	1.34996i
$86$	61.4001	+	79.2672i	0.713954	+	0.921711i
$87$		0			0
$88$	−6.33437	+	53.7901i	−0.0719815	+	0.611251i
$89$	−17.8933			−0.201048			−0.100524	−	0.994935i	$-0.532052\pi$
$89$	−17.8933			−0.201048			−0.100524	+	0.994935i	$0.532052\pi$
$90$		0			0
$91$		−	136.639i		−	1.50153i
$92$	96.5792	+	24.9366i	1.04977	+	0.271050i
$93$		0			0
$94$	−63.7082	−	82.2469i	−0.677747	−	0.874967i
$95$	33.3221	−	19.2385i	0.350759	−	0.202511i
$96$		0			0
$97$	69.1656	−	119.798i	0.713048	−	1.23503i	−0.250660	−	0.968075i	$-0.580648\pi$
$97$	69.1656	−	119.798i	0.713048	−	1.23503i	0.963708	−	0.266960i	$-0.0860191\pi$
$98$	11.0286	+	80.9175i	0.112536	+	0.825689i
$99$		0			0
$100$	−114.979	+	31.9350i	−1.14979	+	0.319350i
$101$	48.7510	−	84.4391i	0.482683	−	0.836031i	−0.517120	−	0.855913i	$-0.672996\pi$
$101$	48.7510	−	84.4391i	0.482683	−	0.836031i	0.999802	+	0.0198821i	$0.00632907\pi$
$102$		0			0
$103$	36.7918	−	21.2418i	0.357202	−	0.206231i	−0.310651	−	0.950524i	$-0.600547\pi$
$103$	36.7918	−	21.2418i	0.357202	−	0.206231i	0.667853	+	0.744294i	$0.267214\pi$
$104$	−68.9511	+	92.4502i	−0.662991	+	0.888944i
$105$		0			0
$106$	153.082	+	62.5924i	1.44417	+	0.590495i
$107$			97.2648i			0.909017i	0.890742	+	0.454509i	$0.150185\pi$
$107$			97.2648i			0.909017i	−0.890742	+	0.454509i	$0.849815\pi$
$108$		0			0
$109$	−96.8328			−0.888374			−0.444187	−	0.895934i	$-0.646507\pi$
$109$	−96.8328			−0.888374			−0.444187	+	0.895934i	$0.646507\pi$
$110$	−37.9473	+	92.8076i	−0.344976	+	0.843705i
$111$		0			0
$112$	73.4164	−	132.692i	0.655504	−	1.18475i
$113$	19.4350	+	33.6625i	0.171991	+	0.297898i	0.939116	−	0.343600i	$-0.111647\pi$
$113$	19.4350	+	33.6625i	0.171991	+	0.297898i	−0.767125	+	0.641498i	$0.778313\pi$
$114$		0			0
$115$	159.915	+	92.3269i	1.39056	+	0.802842i
$116$	114.157	−	31.7069i	0.984114	−	0.273335i
$117$		0			0
$118$	165.915	−	22.6132i	1.40606	−	0.191637i
$119$	146.872	+	84.7965i	1.23422	+	0.712576i
$120$		0			0
$121$	−37.5820	−	65.0940i	−0.310595	−	0.537967i
$122$	13.3075	−	10.3080i	0.109078	−	0.0844914i
$123$		0			0
$124$	−66.3344	−	17.1275i	−0.534955	−	0.138125i
$125$	−35.7866			−0.286293
$126$		0			0
$127$			99.0165i			0.779657i	0.920887	+	0.389829i	$0.127466\pi$
$127$			99.0165i			0.779657i	−0.920887	+	0.389829i	$0.872534\pi$
$128$	−116.633	+	52.7323i	−0.911197	+	0.411971i
$129$		0			0
$130$	−168.790	+	130.744i	−1.29839	+	1.00573i
$131$	−46.9055	+	27.0809i	−0.358057	+	0.206724i	−0.668228	−	0.743956i	$-0.732947\pi$
$131$	−46.9055	+	27.0809i	−0.358057	+	0.206724i	0.310171	+	0.950681i	$0.399614\pi$
$132$		0			0
$133$	−24.6246	+	42.6511i	−0.185147	+	0.320685i
$134$	57.5851	−	7.84850i	0.429740	−	0.0585709i
$135$		0			0
$136$	−56.5836	−	131.488i	−0.416056	−	0.966826i
$137$	−2.77972	+	4.81461i	−0.0202899	+	0.0351432i	−0.875992	−	0.482325i	$-0.839792\pi$
$137$	−2.77972	+	4.81461i	−0.0202899	+	0.0351432i	0.855702	+	0.517469i	$0.173126\pi$
$138$		0			0
$139$	−132.084	+	76.2585i	−0.950242	+	0.548622i	−0.893156	−	0.449747i	$-0.851514\pi$
$139$	−132.084	+	76.2585i	−0.950242	+	0.548622i	−0.0570857	+	0.998369i	$0.518181\pi$
$140$	196.692	−	200.312i	1.40494	−	1.43080i
$141$		0			0
$142$	85.7508	−	209.720i	0.603879	−	1.47690i
$143$			97.6023i			0.682534i
$144$		0			0
$145$	219.331			1.51263
$146$	4.01196	+	1.64042i	0.0274791	+	0.0112357i
$147$		0			0
$148$	18.3131	+	17.9821i	0.123737	+	0.121501i
$149$	68.4897	+	118.628i	0.459663	+	0.796159i	0.998943	−	0.0459672i	$-0.0146370\pi$
$149$	68.4897	+	118.628i	0.459663	+	0.796159i	−0.539280	+	0.842126i	$0.681304\pi$
$150$		0			0
$151$	67.5395	+	38.9939i	0.447281	+	0.258238i	0.706681	−	0.707532i	$-0.250191\pi$
$151$	67.5395	+	38.9939i	0.447281	+	0.258238i	−0.259400	+	0.965770i	$0.583525\pi$
$152$	38.1838	−	16.4317i	0.251209	−	0.108103i
$153$		0			0
$154$	−17.3313	−	127.161i	−0.112541	−	0.825720i
$155$	−109.836	−	63.4137i	−0.708618	−	0.409121i
$156$		0			0
$157$	36.0820	+	62.4959i	0.229822	+	0.398063i	0.957755	−	0.287585i	$-0.0928523\pi$
$157$	36.0820	+	62.4959i	0.229822	+	0.398063i	−0.727933	+	0.685648i	$0.759519\pi$
$158$	−183.080	−	236.356i	−1.15874	−	1.49592i
$159$		0			0
$160$	−234.164	+	36.2765i	−1.46353	+	0.226728i
$161$	−236.350			−1.46801
$162$		0			0
$163$			56.5785i			0.347108i	0.984824	+	0.173554i	$0.0555250\pi$
$163$			56.5785i			0.347108i	−0.984824	+	0.173554i	$0.944475\pi$
$164$	−8.64290	+	33.4738i	−0.0527006	+	0.204109i
$165$		0			0
$166$	−16.5836	−	21.4093i	−0.0999012	−	0.128972i
$167$	−174.623	+	100.819i	−1.04565	+	0.603705i	−0.921428	−	0.388550i	$-0.872976\pi$
$167$	−174.623	+	100.819i	−1.04565	+	0.603705i	−0.124220	+	0.992255i	$0.539643\pi$
$168$		0			0
$169$	−19.4164	+	33.6302i	−0.114890	+	0.198995i
$170$	−35.7866	−	262.569i	−0.210509	−	1.54453i
$171$		0			0
$172$	53.6656	+	193.217i	0.312009	+	1.12336i
$173$	46.2750	−	80.1506i	0.267485	−	0.463298i	−0.700726	−	0.713430i	$-0.747141\pi$
$173$	46.2750	−	80.1506i	0.267485	−	0.463298i	0.968212	+	0.250132i	$0.0804739\pi$
$174$		0			0
$175$	244.874	−	141.378i	1.39928	−	0.807874i
$176$	−52.4419	+	94.7831i	−0.297965	+	0.538540i
$177$		0			0
$178$	−33.1246	−	13.5440i	−0.186093	−	0.0760902i
$179$		−	4.28851i		−	0.0239581i	−0.999928	−	0.0119791i	$-0.996187\pi$
$179$		−	4.28851i		−	0.0239581i	0.999928	−	0.0119791i	$-0.00381315\pi$
$180$		0			0
$181$	−289.748			−1.60082			−0.800408	−	0.599456i	$-0.795384\pi$
$181$	−289.748			−1.60082			−0.800408	+	0.599456i	$0.795384\pi$
$182$	103.427	−	252.950i	0.568278	−	1.38984i
$183$		0			0
$184$	159.915	+	119.268i	0.869102	+	0.648193i
$185$	23.7565	+	41.1474i	0.128413	+	0.222419i
$186$		0			0
$187$	−104.912	−	60.5708i	−0.561025	−	0.323908i
$188$	−55.6830	−	200.481i	−0.296186	−	1.06639i
$189$		0			0
$190$	76.2492	−	10.3923i	0.401312	−	0.0546963i
$191$	−80.2276	−	46.3194i	−0.420040	−	0.242510i	0.275055	−	0.961429i	$-0.411304\pi$
$191$	−80.2276	−	46.3194i	−0.420040	−	0.242510i	−0.695094	+	0.718919i	$0.744637\pi$
$192$		0			0
$193$	121.582	+	210.586i	0.629959	+	1.09112i	0.987559	+	0.157246i	$0.0502616\pi$
$193$	121.582	+	210.586i	0.629959	+	1.09112i	−0.357601	+	0.933875i	$0.616405\pi$
$194$	218.721	−	169.421i	1.12743	−	0.873302i
$195$		0			0
$196$	−40.8328	+	158.145i	−0.208331	+	0.806861i
$197$	139.432			0.707779			0.353890	−	0.935287i	$-0.384859\pi$
$197$	139.432			0.707779			0.353890	+	0.935287i	$0.384859\pi$
$198$		0			0
$199$			110.993i			0.557756i	0.960327	+	0.278878i	$0.0899624\pi$
$199$			110.993i			0.557756i	−0.960327	+	0.278878i	$0.910038\pi$
$200$	−237.025	−	27.9122i	−1.18512	−	0.139561i
$201$		0			0
$202$	154.164	−	119.415i	0.763189	−	0.591163i
$203$	−243.124	+	140.368i	−1.19766	+	0.691467i
$204$		0			0
$205$	−32.0000	+	55.4256i	−0.156098	+	0.270369i
$206$	84.1887	−	11.4744i	0.408683	−	0.0557010i
$207$		0			0
$208$	−197.623	+	118.955i	−0.950111	+	0.571900i
$209$	17.5896	−	30.4660i	0.0841606	−	0.145770i
$210$		0			0
$211$	−229.579	+	132.547i	−1.08805	+	0.628187i	−0.933057	−	0.359728i	$-0.882869\pi$
$211$	−229.579	+	132.547i	−1.08805	+	0.628187i	−0.154995	+	0.987915i	$0.549536\pi$
$212$	236.012	+	231.746i	1.11326	+	1.09314i
$213$		0			0
$214$	−73.6231	+	180.060i	−0.344033	+	0.841400i
$215$			371.230i			1.72665i
$216$		0			0
$217$	162.334			0.748085
$218$	−179.260	−	73.2960i	−0.822293	−	0.336220i
$219$		0			0
$220$	−140.498	+	143.085i	−0.638629	+	0.650384i
$221$	−128.979	−	223.397i	−0.583613	−	1.01085i
$222$		0			0
$223$	−275.331	−	158.963i	−1.23467	−	0.712837i	−0.266670	−	0.963788i	$-0.585923\pi$
$223$	−275.331	−	158.963i	−1.23467	−	0.712837i	−0.968000	+	0.250951i	$0.919257\pi$
$224$	236.350	−	190.072i	1.05513	−	0.848538i
$225$		0			0
$226$	10.4984	+	77.0280i	0.0464533	+	0.340832i
$227$	215.958	+	124.683i	0.951355	+	0.549265i	0.893502	−	0.449060i	$-0.148241\pi$
$227$	215.958	+	124.683i	0.951355	+	0.549265i	0.0578535	+	0.998325i	$0.481574\pi$
$228$		0			0
$229$	−76.1672	−	131.925i	−0.332608	−	0.576094i	0.650415	−	0.759579i	$-0.274595\pi$
$229$	−76.1672	−	131.925i	−0.332608	−	0.576094i	−0.983022	+	0.183486i	$0.941262\pi$
$230$	226.154	+	291.963i	0.983277	+	1.26941i
$231$		0			0
$232$	235.331	+	27.7128i	1.01436	+	0.119452i
$233$	346.793			1.48838			0.744191	−	0.667966i	$-0.232835\pi$
$233$	346.793			1.48838			0.744191	+	0.667966i	$0.232835\pi$
$234$		0			0
$235$		−	385.186i		−	1.63909i
$236$	324.263	+	83.7244i	1.37400	+	0.354764i
$237$		0			0
$238$	207.708	+	268.150i	0.872724	+	1.12668i
$239$	90.0970	−	52.0175i	0.376975	−	0.217647i	−0.299526	−	0.954088i	$-0.596829\pi$
$239$	90.0970	−	52.0175i	0.376975	−	0.217647i	0.676501	+	0.736441i	$0.263495\pi$
$240$		0			0
$241$	−140.913	+	244.069i	−0.584702	+	1.01273i	0.410210	+	0.911991i	$0.365455\pi$
$241$	−140.913	+	244.069i	−0.584702	+	1.01273i	−0.994912	+	0.100743i	$0.967878\pi$
$242$	−20.3011	−	148.951i	−0.0838889	−	0.615500i
$243$		0			0
$244$	32.4377	−	9.00948i	0.132941	−	0.0369241i
$245$	−151.182	+	261.855i	−0.617069	+	1.06879i
$246$		0			0
$247$	64.8738	−	37.4549i	0.262647	−	0.151639i
$248$	−109.836	−	81.9176i	−0.442886	−	0.330313i
$249$		0			0
$250$	−66.2492	−	27.0881i	−0.264997	−	0.108352i
$251$			271.484i			1.08161i	0.841148	+	0.540804i	$0.181880\pi$
$251$			271.484i			1.08161i	−0.841148	+	0.540804i	$0.818120\pi$
$252$		0			0
$253$	168.827			0.667299
$254$	−74.9489	+	183.302i	−0.295075	+	0.721662i
$255$		0			0
$256$	−255.830	+	9.33592i	−0.999335	+	0.0364684i
$257$	−229.552	−	397.597i	−0.893200	−	1.54707i	−0.836016	−	0.548705i	$-0.815121\pi$
$257$	−229.552	−	397.597i	−0.893200	−	1.54707i	−0.0571840	−	0.998364i	$-0.518212\pi$
$258$		0			0
$259$	−52.6672	−	30.4074i	−0.203348	−	0.117403i
$260$	−411.434	+	114.275i	−1.58244	+	0.439518i
$261$		0			0
$262$	−107.331	+	14.6286i	−0.409661	+	0.0558343i
$263$	−176.480	−	101.891i	−0.671027	−	0.387418i	0.125439	−	0.992101i	$-0.459966\pi$
$263$	−176.480	−	101.891i	−0.671027	−	0.387418i	−0.796466	+	0.604684i	$0.793299\pi$
$264$		0			0
$265$	306.164	+	530.292i	1.15534	+	2.00110i
$266$	−77.8699	+	60.3177i	−0.292744	+	0.226758i
$267$		0			0
$268$	112.544	+	29.0588i	0.419941	+	0.108428i
$269$	−323.363			−1.20209			−0.601047	−	0.799213i	$-0.705250\pi$
$269$	−323.363			−1.20209			−0.601047	+	0.799213i	$0.705250\pi$
$270$		0			0
$271$		−	104.928i		−	0.387190i	−0.981082	−	0.193595i	$-0.937985\pi$
$271$		−	104.928i		−	0.387190i	0.981082	−	0.193595i	$-0.0620148\pi$
$272$	−5.22120	−	286.245i	−0.0191956	−	1.05237i
$273$		0			0
$274$	−8.79024	+	6.80889i	−0.0320812	+	0.0248500i
$275$	−174.915	+	100.987i	−0.636056	+	0.367227i
$276$		0			0
$277$	24.4164	−	42.2905i	0.0881459	−	0.152673i	−0.818582	−	0.574390i	$-0.805239\pi$
$277$	24.4164	−	42.2905i	0.0881459	−	0.152673i	0.906727	+	0.421717i	$0.138573\pi$
$278$	−302.240	+	41.1934i	−1.08719	+	0.148178i
$279$		0			0
$280$	515.745	−	221.941i	1.84194	−	0.792647i
$281$	14.8098	−	25.6514i	0.0527040	−	0.0912861i	−0.838470	−	0.544948i	$-0.816549\pi$
$281$	14.8098	−	25.6514i	0.0527040	−	0.0912861i	0.891174	+	0.453662i	$0.149883\pi$
$282$		0			0
$283$	−333.580	+	192.593i	−1.17873	+	0.680540i	−0.955720	−	0.294276i	$-0.904921\pi$
$283$	−333.580	+	192.593i	−1.17873	+	0.680540i	−0.223009	+	0.974816i	$0.571588\pi$
$284$	317.489	−	323.333i	1.11792	−	1.13850i
$285$		0			0
$286$	−73.8785	+	180.684i	−0.258316	+	0.631763i
$287$		−	81.9176i		−	0.285427i
$288$		0			0
$289$	31.1703			0.107856
$290$	406.033	+	166.019i	1.40011	+	0.572480i
$291$		0			0
$292$	6.18536	+	6.07357i	0.0211828	+	0.0207999i
$293$	140.705	+	243.708i	0.480222	+	0.831768i	0.999743	−	0.0226894i	$-0.00722289\pi$
$293$	140.705	+	243.708i	0.480222	+	0.831768i	−0.519521	+	0.854458i	$0.673890\pi$
$294$		0			0
$295$	536.912	+	309.986i	1.82004	+	1.05080i
$296$	20.2905	+	47.1508i	0.0685489	+	0.159293i
$297$		0			0
$298$	36.9969	+	271.449i	0.124151	+	0.910904i
$299$	311.333	+	179.748i	1.04125	+	0.601165i
$300$		0			0
$301$	−237.580	−	411.501i	−0.789304	−	1.36711i
$302$	95.5152	+	123.310i	0.316276	+	0.408310i
$303$		0			0
$304$	83.1246	−	1.51622i	0.273436	−	0.00498756i
$305$	62.3228			0.204337
$306$		0			0
$307$			553.961i			1.80443i	0.431282	+	0.902217i	$0.358061\pi$
$307$			553.961i			1.80443i	−0.431282	+	0.902217i	$0.641939\pi$
$308$	64.1683	−	248.523i	0.208339	−	0.806892i
$309$		0			0
$310$	−155.331	−	200.532i	−0.501069	−	0.646877i
$311$	−13.5833	+	7.84235i	−0.0436764	+	0.0252166i	−0.521679	−	0.853142i	$-0.674694\pi$
$311$	−13.5833	+	7.84235i	−0.0436764	+	0.0252166i	0.478003	+	0.878358i	$0.341361\pi$
$312$		0			0
$313$	154.080	−	266.875i	0.492270	−	0.852637i	−0.507690	−	0.861540i	$-0.669501\pi$
$313$	154.080	−	266.875i	0.492270	−	0.852637i	0.999960	+	0.00890304i	$0.00283396\pi$
$314$	19.4909	+	143.006i	0.0620728	+	0.455433i
$315$		0			0
$316$	−160.018	−	576.129i	−0.506387	−	1.82319i
$317$	−248.053	+	429.641i	−0.782502	+	1.35533i	0.147977	+	0.988991i	$0.452724\pi$
$317$	−248.053	+	429.641i	−0.782502	+	1.35533i	−0.930480	+	0.366343i	$0.880610\pi$
$318$		0			0
$319$	173.666	−	100.266i	0.544406	−	0.314313i
$320$	−460.950	−	110.091i	−1.44047	−	0.344033i
$321$		0			0
$322$	−437.538	−	178.901i	−1.35881	−	0.555594i
$323$			92.9763i			0.287852i
$324$		0			0
$325$	−430.082			−1.32333
$326$	−42.8262	+	104.740i	−0.131369	+	0.321288i
$327$		0			0
$328$	−41.3375	+	55.4256i	−0.126029	+	0.168981i
$329$	246.512	+	426.970i	0.749275	+	1.29778i
$330$		0			0
$331$	74.9164	+	43.2530i	0.226334	+	0.130674i	0.608879	−	0.793263i	$-0.291619\pi$
$331$	74.9164	+	43.2530i	0.226334	+	0.130674i	−0.382546	+	0.923936i	$0.624953\pi$
$332$	−14.4946	−	52.1863i	−0.0436584	−	0.157188i
$333$		0			0
$334$	−399.580	+	54.4604i	−1.19635	+	0.163055i
$335$	186.349	+	107.589i	0.556267	+	0.321161i
$336$		0			0
$337$	−160.330	−	277.699i	−0.475756	−	0.824033i	0.523858	−	0.851805i	$-0.324492\pi$
$337$	−160.330	−	277.699i	−0.475756	−	0.824033i	−0.999614	+	0.0277721i	$0.991159\pi$
$338$	−61.4001	+	47.5603i	−0.181657	+	0.140711i
$339$		0			0
$340$	132.498	−	513.164i	0.389701	−	1.50931i
$341$	−115.957			−0.340049
$342$		0			0
$343$			77.4087i			0.225681i
$344$	−46.9055	+	398.311i	−0.136353	+	1.15788i
$345$		0			0
$346$	146.334	−	113.350i	0.422932	−	0.327601i
$347$	584.358	−	337.379i	1.68403	−	0.972275i	0.725093	−	0.688650i	$-0.241797\pi$
$347$	584.358	−	337.379i	1.68403	−	0.972275i	0.958936	−	0.283624i	$-0.0915368\pi$
$348$		0			0
$349$	−76.9590	+	133.297i	−0.220513	+	0.381939i	−0.954964	−	0.296722i	$-0.904106\pi$
$349$	−76.9590	+	133.297i	−0.220513	+	0.381939i	0.734451	+	0.678662i	$0.237440\pi$
$350$	560.331	−	76.3698i	1.60095	−	0.218199i
$351$		0			0
$352$	−168.827	+	135.770i	−0.479621	+	0.385711i
$353$	311.614	−	539.731i	0.882759	−	1.52898i	0.0344990	−	0.999405i	$-0.489016\pi$
$353$	311.614	−	539.731i	0.882759	−	1.52898i	0.848260	−	0.529579i	$-0.177650\pi$
$354$		0			0
$355$	726.492	−	419.440i	2.04646	−	1.18152i
$356$	−51.0693	−	50.1463i	−0.143453	−	0.140860i
$357$		0			0
$358$	3.24612	−	7.93901i	0.00906737	−	0.0221760i
$359$		−	160.341i		−	0.446633i	−0.974746	−	0.223316i	$-0.928312\pi$
$359$		−	160.341i		−	0.446633i	0.974746	−	0.223316i	$-0.0716883\pi$
$360$		0			0
$361$	334.000			0.925208
$362$	−536.389	−	219.320i	−1.48174	−	0.605856i
$363$		0			0
$364$	382.933	−	389.982i	1.05201	−	1.07138i
$365$	8.02391	+	13.8978i	0.0219833	+	0.0380762i
$366$		0			0
$367$	−246.457	−	142.292i	−0.671546	−	0.387717i	0.125116	−	0.992142i	$-0.460070\pi$
$367$	−246.457	−	142.292i	−0.671546	−	0.387717i	−0.796662	+	0.604425i	$0.793403\pi$
$368$	205.761	+	341.837i	0.559134	+	0.928904i
$369$		0			0
$370$	12.8328	+	94.1555i	0.0346833	+	0.254474i
$371$	−678.754	−	391.879i	−1.82952	−	1.05628i
$372$		0			0
$373$	−150.710	−	261.037i	−0.404048	−	0.699831i	0.590163	−	0.807284i	$-0.299064\pi$
$373$	−150.710	−	261.037i	−0.404048	−	0.699831i	−0.994210	+	0.107453i	$0.965730\pi$
$374$	−148.368	−	191.542i	−0.396705	−	0.512144i
$375$		0			0
$376$	48.6687	−	413.284i	0.129438	−	1.09916i
$377$	427.009			1.13265
$378$		0			0
$379$		−	248.547i		−	0.655796i	−0.944713	−	0.327898i	$-0.893660\pi$
$379$		−	248.547i		−	0.655796i	0.944713	−	0.327898i	$-0.106340\pi$
$380$	149.021	+	38.4771i	0.392161	+	0.101255i
$381$		0			0
$382$	−113.459	−	146.475i	−0.297013	−	0.383442i
$383$	−422.734	+	244.065i	−1.10374	+	0.637247i	−0.937202	−	0.348788i	$-0.886593\pi$
$383$	−422.734	+	244.065i	−1.10374	+	0.637247i	−0.166542	+	0.986034i	$0.553260\pi$
$384$		0			0
$385$	237.580	−	411.501i	0.617092	−	1.06883i
$386$	65.6764	+	481.873i	0.170146	+	1.24838i
$387$		0			0
$388$	533.143	−	148.079i	1.37408	−	0.381647i
$389$	207.934	−	360.152i	0.534534	−	0.925840i	−0.464652	−	0.885493i	$-0.653820\pi$
$389$	207.934	−	360.152i	0.534534	−	0.925840i	0.999186	−	0.0403465i	$-0.0128462\pi$
$390$		0			0
$391$	−386.420	+	223.099i	−0.988285	+	0.570587i
$392$	−195.296	+	261.855i	−0.498204	+	0.667996i
$393$		0			0
$394$	258.122	+	105.541i	0.655131	+	0.267871i
$395$		−	1106.92i		−	2.80233i
$396$		0			0
$397$	−670.827			−1.68974			−0.844870	−	0.534972i	$-0.820322\pi$
$397$	−670.827			−1.68974			−0.844870	+	0.534972i	$0.820322\pi$
$398$	−84.0146	+	205.474i	−0.211092	+	0.516267i
$399$		0			0
$400$	−417.659	−	231.084i	−1.04415	−	0.577710i
$401$	−57.3709	−	99.3693i	−0.143070	−	0.247804i	0.785582	−	0.618758i	$-0.212364\pi$
$401$	−57.3709	−	99.3693i	−0.143070	−	0.247804i	−0.928651	+	0.370955i	$0.879031\pi$
$402$		0			0
$403$	−213.836	−	123.458i	−0.530610	−	0.306348i
$404$	375.782	−	104.373i	0.930154	−	0.258348i
$405$		0			0
$406$	−556.328	+	75.8241i	−1.37027	+	0.186759i
$407$	37.6206	+	21.7203i	0.0924339	+	0.0533667i
$408$		0			0
$409$	73.3359	+	127.022i	0.179305	+	0.310566i	0.941643	−	0.336614i	$-0.109282\pi$
$409$	73.3359	+	127.022i	0.179305	+	0.310566i	−0.762337	+	0.647180i	$0.775948\pi$
$410$	−101.193	+	78.3837i	−0.246812	+	0.191180i
$411$		0			0
$412$	164.538	+	42.4835i	0.399364	+	0.103115i
$413$	−793.541			−1.92141
$414$		0			0
$415$		−	100.266i		−	0.241605i
$416$	−455.887	+	70.6257i	−1.09588	+	0.169773i
$417$		0			0
$418$	55.6231	−	43.0854i	0.133070	−	0.103075i
$419$	464.945	−	268.436i	1.10965	−	0.640659i	0.170914	−	0.985286i	$-0.445328\pi$
$419$	464.945	−	268.436i	1.10965	−	0.640659i	0.938740	+	0.344627i	$0.111995\pi$
$420$		0			0
$421$	183.707	−	318.189i	0.436358	−	0.755794i	−0.561048	−	0.827784i	$-0.689602\pi$
$421$	183.707	−	318.189i	0.436358	−	0.755794i	0.997405	+	0.0719896i	$0.0229349\pi$
$422$	−525.333	+	71.5997i	−1.24486	+	0.169668i
$423$		0			0
$424$	261.495	+	607.660i	0.616734	+	1.43316i
$425$	266.904	−	462.291i	0.628009	−	1.08774i
$426$		0			0
$427$	−69.0836	+	39.8854i	−0.161788	+	0.0934085i
$428$	−272.586	+	277.604i	−0.636884	+	0.648607i
$429$		0			0
$430$	−280.997	+	687.233i	−0.653481	+	1.59822i
$431$		−	735.353i		−	1.70616i	−0.521784	−	0.853078i	$-0.674733\pi$
$431$		−	735.353i		−	1.70616i	0.521784	−	0.853078i	$-0.325267\pi$
$432$		0			0
$433$	765.161			1.76712			0.883558	−	0.468322i	$-0.155141\pi$
$433$	765.161			1.76712			0.883558	+	0.468322i	$0.155141\pi$
$434$	300.518	+	122.876i	0.692438	+	0.283125i
$435$		0			0
$436$	−276.371	−	271.376i	−0.633878	−	0.622421i
$437$	−64.7873	−	112.215i	−0.148255	−	0.256785i
$438$		0			0
$439$	40.1703	+	23.1923i	0.0915041	+	0.0528299i	0.545054	−	0.838401i	$-0.316509\pi$
$439$	40.1703	+	23.1923i	0.0915041	+	0.0528299i	−0.453550	+	0.891231i	$0.649843\pi$
$440$	−368.400	+	158.534i	−0.837274	+	0.360305i
$441$		0			0
$442$	−69.6718	−	511.188i	−0.157629	−	1.15653i
$443$	−120.978	−	69.8465i	−0.273087	−	0.157667i	0.357203	−	0.934027i	$-0.383731\pi$
$443$	−120.978	−	69.8465i	−0.273087	−	0.157667i	−0.630290	+	0.776360i	$0.717064\pi$
$444$		0			0
$445$	−66.2492	−	114.747i	−0.148875	−	0.257858i
$446$	−389.377	−	502.684i	−0.873043	−	1.12709i
$447$		0			0
$448$	581.410	−	172.966i	1.29779	−	0.386086i
$449$	−267.139			−0.594963			−0.297482	−	0.954728i	$-0.596147\pi$
$449$	−267.139			−0.594963			−0.297482	+	0.954728i	$0.596147\pi$
$450$		0			0
$451$			58.5144i			0.129744i
$452$	−38.8701	+	150.543i	−0.0859957	+	0.333060i
$453$		0			0
$454$	305.410	+	394.283i	0.672710	+	0.868464i
$455$	876.245	−	505.900i	1.92581	−	1.11187i
$456$		0			0
$457$	−118.915	+	205.967i	−0.260208	+	0.450693i	−0.966297	−	0.257430i	$-0.917124\pi$
$457$	−118.915	+	205.967i	−0.260208	+	0.450693i	0.706089	+	0.708123i	$0.250458\pi$
$458$	−41.1441	−	301.878i	−0.0898343	−	0.659122i
$459$		0			0
$460$	197.666	+	711.674i	0.429708	+	1.54712i
$461$	−149.325	+	258.638i	−0.323915	+	0.561037i	−0.981292	−	0.192524i	$-0.938333\pi$
$461$	−149.325	+	258.638i	−0.323915	+	0.561037i	0.657377	+	0.753562i	$0.271666\pi$
$462$		0			0
$463$	−423.950	+	244.767i	−0.915658	+	0.528655i	−0.882247	−	0.470786i	$-0.843970\pi$
$463$	−423.950	+	244.767i	−0.915658	+	0.528655i	−0.0334107	+	0.999442i	$0.510637\pi$
$464$	414.675	+	229.433i	0.893697	+	0.494468i
$465$		0			0
$466$	641.994	+	262.500i	1.37767	+	0.563304i
$467$			454.280i			0.972762i	0.873747	+	0.486381i	$0.161683\pi$
$467$			454.280i			0.972762i	−0.873747	+	0.486381i	$0.838317\pi$
$468$		0			0
$469$	−275.420			−0.587248
$470$	291.560	−	713.067i	0.620341	−	1.51716i
$471$		0			0
$472$	536.912	+	400.439i	1.13752	+	0.848387i
$473$	169.706	+	293.939i	0.358786	+	0.621435i
$474$		0			0
$475$	134.248	+	77.5079i	0.282627	+	0.163175i
$476$	181.544	+	653.629i	0.381394	+	1.37317i
$477$		0			0
$478$	206.164	−	28.0989i	0.431306	−	0.0587843i
$479$	3.12946	+	1.80679i	0.00653332	+	0.00377201i	0.503263	−	0.864133i	$-0.332133\pi$
$479$	3.12946	+	1.80679i	0.00653332	+	0.00377201i	−0.496730	+	0.867905i	$0.665466\pi$
$480$		0			0
$481$	46.2508	+	80.1087i	0.0961555	+	0.166546i
$482$	−445.607	+	345.166i	−0.924496	+	0.716111i
$483$		0			0
$484$	75.1641	−	291.109i	0.155298	−	0.601465i
$485$	1024.33			2.11202
$486$		0			0
$487$		−	874.538i		−	1.79577i	−0.440234	−	0.897883i	$-0.645104\pi$
$487$		−	874.538i		−	1.79577i	0.440234	−	0.897883i	$-0.354896\pi$
$488$	66.8692	+	7.87457i	0.137027	+	0.0161364i
$489$		0			0
$490$	−478.079	+	370.318i	−0.975671	+	0.755752i
$491$	−558.756	+	322.598i	−1.13800	+	0.657022i	−0.945934	−	0.324360i	$-0.894851\pi$
$491$	−558.756	+	322.598i	−1.13800	+	0.657022i	−0.192063	+	0.981383i	$0.561518\pi$
$492$		0			0
$493$	−264.997	+	458.988i	−0.537519	+	0.931010i
$494$	148.447	−	20.2325i	0.300501	−	0.0409564i
$495$		0			0
$496$	−141.325	−	234.787i	−0.284930	−	0.473360i
$497$	−536.868	+	929.883i	−1.08022	+	1.87099i
$498$		0			0
$499$	489.167	−	282.421i	0.980295	−	0.565974i	0.0779358	−	0.996958i	$-0.475167\pi$
$499$	489.167	−	282.421i	0.980295	−	0.565974i	0.902359	+	0.430985i	$0.141834\pi$
$500$	−102.139	−	100.293i	−0.204277	−	0.200585i
$501$		0			0
$502$	−205.495	+	502.579i	−0.409353	+	1.00115i
$503$		−	483.048i		−	0.960334i	−0.877177	−	0.480167i	$-0.840576\pi$
$503$		−	483.048i		−	0.960334i	0.877177	−	0.480167i	$-0.159424\pi$
$504$		0			0
$505$	721.994			1.42969
$506$	312.537	+	127.791i	0.617662	+	0.252551i
$507$		0			0
$508$	−277.495	+	282.603i	−0.546251	+	0.556305i
$509$	108.002	+	187.065i	0.212184	+	0.367514i	0.952398	−	0.304858i	$-0.0986090\pi$
$509$	108.002	+	187.065i	0.212184	+	0.367514i	−0.740214	+	0.672372i	$0.765276\pi$
$510$		0			0
$511$	−17.7887	−	10.2703i	−0.0348115	−	0.0200984i
$512$	−480.666	−	176.363i	−0.938801	−	0.344459i
$513$		0			0
$514$	−124.000	−	909.799i	−0.241245	−	1.77004i
$515$	272.440	+	157.293i	0.529010	+	0.305424i
$516$		0			0
$517$	−176.085	−	304.988i	−0.340590	−	0.589920i
$518$	−74.4826	−	96.1567i	−0.143789	−	0.185631i
$519$		0			0
$520$	−848.158	−	99.8798i	−1.63107	−	0.192077i
$521$	454.806			0.872949			0.436475	−	0.899717i	$-0.356227\pi$
$521$	454.806			0.872949			0.436475	+	0.899717i	$0.356227\pi$
$522$		0			0
$523$			325.041i			0.621493i	0.950493	+	0.310747i	$0.100579\pi$
$523$			325.041i			0.621493i	−0.950493	+	0.310747i	$0.899421\pi$
$524$	−209.768	−	54.1618i	−0.400320	−	0.103362i
$525$		0			0
$526$	−249.580	−	322.207i	−0.474488	−	0.612561i
$527$	265.408	−	153.233i	0.503621	−	0.290765i
$528$		0			0
$529$	46.4180	−	80.3983i	0.0877466	−	0.151982i
$530$	165.384	+	1213.44i	0.312046	+	2.28951i
$531$		0			0
$532$	−189.812	+	52.7196i	−0.356789	+	0.0990971i
$533$	−62.2998	+	107.906i	−0.116885	+	0.202451i
$534$		0			0
$535$	−623.745	+	360.119i	−1.16588	+	0.673120i
$536$	186.349	+	138.983i	0.347667	+	0.259296i
$537$		0			0
$538$	−598.620	−	244.765i	−1.11268	−	0.454953i
$539$			276.447i			0.512889i
$540$		0			0
$541$	−962.574			−1.77925			−0.889625	−	0.456692i	$-0.849034\pi$
$541$	−962.574			−1.77925			−0.889625	+	0.456692i	$0.849034\pi$
$542$	79.4239	−	194.247i	0.146539	−	0.358389i
$543$		0			0
$544$	207.003	−	533.858i	0.380520	−	0.981356i
$545$	−358.520	−	620.974i	−0.657834	−	1.13940i
$546$		0			0
$547$	−115.588	−	66.7349i	−0.211313	−	0.122002i	0.390608	−	0.920557i	$-0.372265\pi$
$547$	−115.588	−	66.7349i	−0.211313	−	0.122002i	−0.601921	+	0.798555i	$0.705598\pi$
$548$	−21.4266	+	5.95119i	−0.0390997	+	0.0108598i
$549$		0			0
$550$	−400.249	+	54.5515i	−0.727726	+	0.0991846i
$551$	−133.289	−	76.9542i	−0.241903	−	0.139663i
$552$		0			0
$553$	708.409	+	1227.00i	1.28103	+	2.21881i
$554$	77.2115	−	59.8077i	0.139371	−	0.107956i
$555$		0			0
$556$	−590.696	−	152.517i	−1.06240	−	0.274311i
$557$	413.437			0.742258			0.371129	−	0.928581i	$-0.378971\pi$
$557$	413.437			0.742258			0.371129	+	0.928581i	$0.378971\pi$
$558$		0			0
$559$			722.737i			1.29291i
$560$	1122.76	−	20.4794i	2.00492	−	0.0365704i
$561$		0			0
$562$	46.8328	−	36.2765i	0.0833324	−	0.0645490i
$563$	447.356	−	258.281i	0.794592	−	0.458758i	−0.0469843	−	0.998896i	$-0.514961\pi$
$563$	447.356	−	258.281i	0.794592	−	0.458758i	0.841577	+	0.540137i	$0.181628\pi$
$564$		0			0
$565$	−143.915	+	249.268i	−0.254717	+	0.441182i
$566$	−763.314	+	104.035i	−1.34861	+	0.183808i
$567$		0			0
$568$	832.486	−	358.245i	1.46564	−	0.630713i
$569$	−234.178	+	405.608i	−0.411560	+	0.712843i	−0.995061	−	0.0992699i	$-0.968349\pi$
$569$	−234.178	+	405.608i	−0.411560	+	0.712843i	0.583500	+	0.812113i	$0.301683\pi$
$570$		0			0
$571$	585.409	−	337.986i	1.02523	−	0.591919i	0.109618	−	0.993974i	$-0.465037\pi$
$571$	585.409	−	337.986i	1.02523	−	0.591919i	0.915616	+	0.402055i	$0.131704\pi$
$572$	−273.532	+	278.567i	−0.478203	+	0.487005i
$573$		0			0
$574$	62.0062	−	151.648i	0.108025	−	0.264196i
$575$			743.930i			1.29379i
$576$		0			0
$577$	−354.823			−0.614945			−0.307473	−	0.951557i	$-0.599483\pi$
$577$	−354.823			−0.614945			−0.307473	+	0.951557i	$0.599483\pi$
$578$	57.7034	+	23.5939i	0.0998328	+	0.0408198i
$579$		0			0
$580$	625.994	+	614.680i	1.07930	+	1.05979i
$581$	64.1683	+	111.143i	0.110445	+	0.191296i
$582$		0			0
$583$	484.839	+	279.922i	0.831628	+	0.480141i
$584$	6.85324	+	15.9255i	0.0117350	+	0.0272697i
$585$		0			0
$586$	76.0062	+	557.664i	0.129703	+	0.951645i
$587$	190.940	+	110.239i	0.325281	+	0.187801i	0.653744	−	0.756716i	$-0.273197\pi$
$587$	190.940	+	110.239i	0.325281	+	0.187801i	−0.328463	+	0.944517i	$0.606531\pi$
$588$		0			0
$589$	44.4984	+	77.0736i	0.0755491	+	0.130855i
$590$	759.308	+	980.262i	1.28696	+	1.66146i
$591$		0			0
$592$	1.87228	+	102.645i	0.00316264	+	0.173388i
$593$	−993.520			−1.67541			−0.837707	−	0.546121i	$-0.816104\pi$
$593$	−993.520			−1.67541			−0.837707	+	0.546121i	$0.816104\pi$
$594$		0			0
$595$			1255.82i			2.11063i
$596$	−136.979	+	530.519i	−0.229831	+	0.890133i
$597$		0			0
$598$	440.292	+	568.414i	0.736274	+	0.950526i
$599$	−243.124	+	140.368i	−0.405884	+	0.234337i	−0.689020	−	0.724743i	$-0.741959\pi$
$599$	−243.124	+	140.368i	−0.405884	+	0.234337i	0.283136	+	0.959080i	$0.408625\pi$
$600$		0			0
$601$	−280.915	+	486.559i	−0.467412	+	0.809582i	−0.999307	−	0.0372287i	$-0.988147\pi$
$601$	−280.915	+	486.559i	−0.467412	+	0.809582i	0.531894	+	0.846811i	$0.321480\pi$
$602$	−128.337	−	941.616i	−0.213184	−	1.56415i
$603$		0			0
$604$	83.4834	+	300.573i	0.138218	+	0.497638i
$605$	278.292	−	482.016i	0.459987	−	0.796720i
$606$		0			0
$607$	72.7918	−	42.0264i	0.119921	−	0.0692362i	−0.438840	−	0.898565i	$-0.644610\pi$
$607$	72.7918	−	42.0264i	0.119921	−	0.0692362i	0.558760	+	0.829329i	$0.311277\pi$
$608$	155.030	+	60.1130i	0.254984	+	0.0988700i
$609$		0			0
$610$	115.374	+	47.1743i	0.189137	+	0.0773348i
$611$		−	749.906i		−	1.22734i
$612$		0			0
$613$	730.234			1.19125			0.595623	−	0.803264i	$-0.296905\pi$
$613$	730.234			1.19125			0.595623	+	0.803264i	$0.296905\pi$
$614$	−419.312	+	1025.51i	−0.682919	+	1.67021i
$615$		0			0
$616$	306.906	−	411.501i	0.498223	−	0.668022i
$617$	−274.893	−	476.129i	−0.445532	−	0.771684i	0.552557	−	0.833475i	$-0.313652\pi$
$617$	−274.893	−	476.129i	−0.445532	−	0.771684i	−0.998089	+	0.0617910i	$0.980319\pi$
$618$		0			0
$619$	−63.3297	−	36.5634i	−0.102310	−	0.0590685i	0.447972	−	0.894048i	$-0.352146\pi$
$619$	−63.3297	−	36.5634i	−0.102310	−	0.0590685i	−0.550282	+	0.834979i	$0.685480\pi$
$620$	−135.765	−	488.806i	−0.218975	−	0.788397i
$621$		0			0
$622$	−31.0820	+	4.23629i	−0.0499711	+	0.00681076i
$623$	146.872	+	84.7965i	0.235749	+	0.136110i
$624$		0			0
$625$	240.412	+	416.405i	0.384659	+	0.666249i
$626$	487.245	−	377.419i	0.778347	−	0.602905i
$627$		0			0
$628$	−72.1641	+	279.490i	−0.114911	+	0.445048i
$629$	−114.811			−0.182529
$630$		0			0
$631$		−	779.849i		−	1.23589i	−0.786220	−	0.617947i	$-0.787965\pi$
$631$		−	779.849i		−	1.23589i	0.786220	−	0.617947i	$-0.212035\pi$
$632$	139.861	−	1187.67i	0.221299	−	1.87922i
$633$		0			0
$634$	−784.413	+	607.604i	−1.23724	+	0.958366i
$635$	−634.977	+	366.604i	−0.999965	+	0.577330i
$636$		0			0
$637$	−294.331	+	509.797i	−0.462058	+	0.800309i
$638$	397.390	−	54.1618i	0.622868	−	0.0848931i
$639$		0			0
$640$	−769.994	−	552.712i	−1.20312	−	0.863612i
$641$	222.171	−	384.811i	0.346600	−	0.600329i	−0.639043	−	0.769171i	$-0.720669\pi$
$641$	222.171	−	384.811i	0.346600	−	0.600329i	0.985643	+	0.168842i	$0.0540028\pi$
$642$		0			0
$643$	386.420	−	223.099i	0.600963	−	0.346966i	−0.168457	−	0.985709i	$-0.553878\pi$
$643$	386.420	−	223.099i	0.600963	−	0.346966i	0.769421	+	0.638743i	$0.220545\pi$
$644$	−674.567	−	662.375i	−1.04746	−	1.02853i
$645$		0			0
$646$	−70.3769	+	172.121i	−0.108943	+	0.266440i
$647$			861.386i			1.33135i	0.746240	+	0.665677i	$0.231857\pi$
$647$			861.386i			1.33135i	−0.746240	+	0.665677i	$0.768143\pi$
$648$		0			0
$649$	566.833			0.873394
$650$	−796.181	−	325.544i	−1.22489	−	0.500836i
$651$		0			0
$652$	−158.562	+	161.481i	−0.243194	+	0.247670i
$653$	−438.151	−	758.900i	−0.670982	−	1.16217i	−0.977626	−	0.210350i	$-0.932539\pi$
$653$	−438.151	−	758.900i	−0.670982	−	1.16217i	0.306644	−	0.951824i	$-0.400794\pi$
$654$		0			0
$655$	−347.331	−	200.532i	−0.530277	−	0.306155i
$656$	−118.479	+	71.3158i	−0.180608	+	0.108713i
$657$		0			0
$658$	133.161	+	977.013i	0.202372	+	1.48482i
$659$	489.963	+	282.880i	0.743494	+	0.429257i	0.823338	−	0.567551i	$-0.192109\pi$
$659$	489.963	+	282.880i	0.743494	+	0.429257i	−0.0798443	+	0.996807i	$0.525442\pi$
$660$		0			0
$661$	−316.290	−	547.831i	−0.478503	−	0.828791i	0.521194	−	0.853438i	$-0.325487\pi$
$661$	−316.290	−	547.831i	−0.478503	−	0.828791i	−0.999696	+	0.0246476i	$0.992154\pi$
$662$	105.948	+	136.778i	0.160042	+	0.206613i
$663$		0			0
$664$	12.6687	−	107.580i	0.0190794	−	0.162018i
$665$	−364.686			−0.548401
$666$		0			0
$667$		−	738.615i		−	1.10737i
$668$	−780.938	−	201.637i	−1.16907	−	0.301852i
$669$		0			0
$670$	263.538	+	340.226i	0.393340	+	0.507800i
$671$	49.3470	−	28.4905i	0.0735424	−	0.0424597i
$672$		0			0
$673$	536.330	−	928.950i	0.796924	−	1.38031i	−0.124687	−	0.992196i	$-0.539793\pi$
$673$	536.330	−	928.950i	0.796924	−	1.38031i	0.921610	−	0.388116i	$-0.126874\pi$
$674$	−86.6071	−	635.444i	−0.128497	−	0.942795i
$675$		0			0
$676$	−149.666	+	41.5692i	−0.221399	+	0.0614929i
$677$	239.399	−	414.651i	0.353617	−	0.612483i	−0.633263	−	0.773937i	$-0.718285\pi$
$677$	239.399	−	414.651i	0.353617	−	0.612483i	0.986880	+	0.161454i	$0.0516182\pi$
$678$		0			0
$679$	−1135.45	+	655.553i	−1.67224	+	0.965468i
$680$	633.717	−	849.692i	0.931936	−	1.24955i
$681$		0			0
$682$	−214.663	−	87.7716i	−0.314754	−	0.128697i
$683$			318.418i			0.466206i	0.972452	+	0.233103i	$0.0748879\pi$
$683$			318.418i			0.466206i	−0.972452	+	0.233103i	$0.925112\pi$
$684$		0			0
$685$	−41.1672			−0.0600981
$686$	−58.5933	+	143.301i	−0.0854130	+	0.208894i
$687$		0			0
$688$	−388.328	+	701.861i	−0.564430	+	1.02015i
$689$	596.061	+	1032.41i	0.865111	+	1.49842i
$690$		0			0
$691$	−971.076	−	560.651i	−1.40532	−	0.811362i	−0.410388	−	0.911911i	$-0.634607\pi$
$691$	−971.076	−	560.651i	−1.40532	−	0.811362i	−0.994932	+	0.100550i	$0.967940\pi$
$692$	356.697	−	99.0716i	0.515458	−	0.143167i
$693$		0			0
$694$	1337.15	−	182.246i	1.92674	−	0.262602i
$695$	−978.068	−	564.688i	−1.40729	−	0.812501i
$696$		0			0
$697$	−77.3251	−	133.931i	−0.110940	−	0.192153i
$698$	−243.366	+	188.510i	−0.348661	+	0.270072i
$699$		0			0
$700$	1095.11	+	282.756i	1.56444	+	0.403937i
$701$	413.437			0.589782			0.294891	−	0.955531i	$-0.404717\pi$
$701$	413.437			0.589782			0.294891	+	0.955531i	$0.404717\pi$
$702$		0			0
$703$		−	33.3406i		−	0.0474262i
$704$	−415.306	+	123.551i	−0.589923	+	0.175499i
$705$		0			0
$706$	985.410	−	763.295i	1.39577	−	1.08116i
$707$	−800.316	+	462.062i	−1.13199	+	0.653554i
$708$		0			0
$709$	341.457	−	591.422i	0.481604	−	0.834163i	−0.518173	−	0.855276i	$-0.673388\pi$
$709$	341.457	−	591.422i	0.481604	−	0.834163i	0.999777	+	0.0211129i	$0.00672093\pi$
$710$	1662.39	−	226.574i	2.34140	−	0.319118i
$711$		0			0
$712$	−56.5836	−	131.488i	−0.0794713	−	0.184675i
$713$	−213.551	+	369.881i	−0.299510	+	0.518767i
$714$		0			0
$715$	−625.909	+	361.369i	−0.875397	+	0.505411i
$716$	12.0186	−	12.2398i	0.0167858	−	0.0170948i
$717$		0			0
$718$	121.368	−	296.828i	0.169036	−	0.413410i
$719$			286.374i			0.398295i	0.979970	+	0.199148i	$0.0638173\pi$
$719$			286.374i			0.398295i	−0.979970	+	0.199148i	$0.936183\pi$
$720$		0			0
$721$	−402.659			−0.558474
$722$	618.311	+	252.816i	0.856386	+	0.350161i
$723$		0			0
$724$	−826.969	−	812.023i	−1.14222	−	1.12158i
$725$	441.819	+	765.253i	0.609406	+	1.05552i
$726$		0			0
$727$	279.659	+	161.461i	0.384676	+	0.222093i	0.679851	−	0.733351i	$-0.262045\pi$
$727$	279.659	+	161.461i	0.384676	+	0.222093i	−0.295175	+	0.955443i	$0.595378\pi$
$728$	1004.09	−	432.090i	1.37924	−	0.593531i
$729$		0			0
$730$	4.33437	+	31.8016i	0.00593749	+	0.0435639i
$731$	−776.863	−	448.522i	−1.06274	−	0.613573i
$732$		0			0
$733$	260.915	+	451.918i	0.355955	+	0.616532i	0.987281	−	0.158986i	$-0.0508224\pi$
$733$	260.915	+	451.918i	0.355955	+	0.616532i	−0.631326	+	0.775517i	$0.717489\pi$
$734$	−348.543	−	449.968i	−0.474855	−	0.613035i
$735$		0			0
$736$	122.164	+	788.566i	0.165984	+	1.07142i
$737$	196.734			0.266939
$738$		0			0
$739$		−	965.020i		−	1.30585i	−0.757424	−	0.652923i	$-0.773542\pi$
$739$		−	965.020i		−	1.30585i	0.757424	−	0.652923i	$-0.226458\pi$
$740$	−47.5130	+	184.017i	−0.0642067	+	0.248672i
$741$		0			0
$742$	−959.902	−	1239.23i	−1.29367	−	1.67012i
$743$	−950.317	+	548.666i	−1.27903	+	0.738447i	−0.976669	−	0.214748i	$-0.931107\pi$
$743$	−950.317	+	548.666i	−1.27903	+	0.738447i	−0.302357	+	0.953195i	$0.597774\pi$
$744$		0			0
$745$	−507.161	+	878.429i	−0.680753	+	1.17910i
$746$	−81.4106	−	597.317i	−0.109130	−	0.800693i
$747$		0			0
$748$	−129.678	−	466.892i	−0.173366	−	0.624188i
$749$	460.939	−	798.370i	0.615406	−	1.06591i
$750$		0			0
$751$	1196.02	−	690.524i	1.59257	−	0.919472i	0.599709	−	0.800218i	$-0.295283\pi$
$751$	1196.02	−	690.524i	1.59257	−	0.919472i	0.992864	−	0.119255i	$-0.0380505\pi$
$752$	402.926	−	728.245i	0.535806	−	0.968411i
$753$		0			0
$754$	790.492	+	323.218i	1.04840	+	0.428671i
$755$			577.494i			0.764892i
$756$		0			0
$757$	−516.252			−0.681971			−0.340986	−	0.940068i	$-0.610761\pi$
$757$	−516.252			−0.681971			−0.340986	+	0.940068i	$0.610761\pi$
$758$	188.133	−	460.117i	0.248197	−	0.607014i
$759$		0			0
$760$	246.748	+	184.029i	0.324668	+	0.242143i
$761$	608.092	+	1053.25i	0.799069	+	1.38403i	0.920223	+	0.391394i	$0.128007\pi$
$761$	608.092	+	1053.25i	0.799069	+	1.38403i	−0.121154	+	0.992634i	$0.538659\pi$
$762$		0			0
$763$	794.823	+	458.892i	1.04171	+	0.601431i
$764$	−99.1668	−	357.040i	−0.129799	−	0.467329i
$765$		0			0
$766$	−967.319	+	131.840i	−1.26282	+	0.172114i
$767$	1045.30	+	603.502i	1.36284	+	0.786835i
$768$		0			0
$769$	−502.163	−	869.771i	−0.653007	−	1.13104i	−0.982389	−	0.186845i	$-0.940174\pi$
$769$	−502.163	−	869.771i	−0.653007	−	1.13104i	0.329382	−	0.944197i	$-0.393160\pi$
$770$	751.295	−	581.951i	0.975708	−	0.755780i
$771$		0			0
$772$	−243.164	+	941.770i	−0.314979	+	1.21991i
$773$	−382.580			−0.494929			−0.247464	−	0.968897i	$-0.579597\pi$
$773$	−382.580			−0.494929			−0.247464	+	0.968897i	$0.579597\pi$
$774$		0			0
$775$		−	510.960i		−	0.659304i
$776$	1099.06	+	129.426i	1.41631	+	0.166786i
$777$		0			0
$778$	657.544	−	509.331i	0.845172	−	0.654668i
$779$	38.8931	−	22.4549i	0.0499269	−	0.0288253i
$780$		0			0
$781$	383.489	−	664.223i	0.491023	−	0.850477i
$782$	−884.223	+	120.514i	−1.13072	+	0.154110i
$783$		0			0
$784$	−559.745	+	336.927i	−0.713960	+	0.429754i
$785$	−267.185	+	462.777i	−0.340362	+	0.589525i
$786$		0			0
$787$	−413.327	+	238.634i	−0.525193	+	0.303220i	−0.739057	−	0.673643i	$-0.764728\pi$
$787$	−413.327	+	238.634i	−0.525193	+	0.303220i	0.213864	+	0.976863i	$0.431395\pi$
$788$	397.954	+	390.762i	0.505018	+	0.495891i
$789$		0			0
$790$	837.866	−	2049.16i	1.06059	−	2.59388i
$791$		−	368.411i		−	0.465754i
$792$		0			0
$793$	121.334			0.153007
$794$	−1241.85	−	507.771i	−1.56405	−	0.639511i
$795$		0			0
$796$	−311.061	+	316.786i	−0.390780	+	0.397973i
$797$	−257.304	−	445.663i	−0.322840	−	0.559176i	0.658233	−	0.752815i	$-0.271304\pi$
$797$	−257.304	−	445.663i	−0.322840	−	0.559176i	−0.981073	+	0.193639i	$0.937971\pi$
$798$		0			0
$799$	806.067	+	465.383i	1.00884	+	0.582456i
$800$	−598.268	−	743.930i	−0.747835	−	0.929913i
$801$		0			0
$802$	−30.9907	−	227.381i	−0.0386417	−	0.283518i
$803$	12.7066	+	7.33616i	0.0158239	+	0.00913594i
$804$		0			0
$805$	−875.076	−	1515.68i	−1.08705	−	1.88283i
$806$	−302.410	−	390.409i	−0.375198	−	0.484379i
$807$		0			0
$808$	774.663	+	91.2249i	0.958741	+	0.112902i
$809$	−1463.74			−1.80932			−0.904662	−	0.426129i	$-0.859877\pi$
$809$	−1463.74			−1.80932			−0.904662	+	0.426129i	$0.859877\pi$
$810$		0			0
$811$			1163.05i			1.43410i	0.697023	+	0.717049i	$0.254508\pi$
$811$			1163.05i			1.43410i	−0.697023	+	0.717049i	$0.745492\pi$
$812$	−1087.29	−	280.736i	−1.33902	−	0.345734i
$813$		0			0
$814$	53.2035	+	68.6855i	0.0653606	+	0.0843802i
$815$	−362.830	+	209.480i	−0.445190	+	0.257030i
$816$		0			0
$817$	130.249	−	225.598i	0.159424	−	0.276130i
$818$	39.6147	+	290.656i	0.0484287	+	0.355326i
$819$		0			0
$820$	−246.663	+	68.5098i	−0.300808	+	0.0835486i
$821$	196.276	−	339.961i	0.239070	−	0.414081i	−0.721378	−	0.692542i	$-0.756491\pi$
$821$	196.276	−	339.961i	0.239070	−	0.414081i	0.960448	+	0.278461i	$0.0898242\pi$
$822$		0			0
$823$	1081.53	−	624.422i	1.31413	−	0.758714i	0.331354	−	0.943507i	$-0.392495\pi$
$823$	1081.53	−	624.422i	1.31413	−	0.758714i	0.982778	+	0.184792i	$0.0591613\pi$
$824$	272.440	+	203.191i	0.330631	+	0.246591i
$825$		0			0
$826$	−1469.03	−	600.658i	−1.77848	−	0.727189i
$827$			1369.15i			1.65557i	0.561049	+	0.827783i	$0.310398\pi$
$827$			1369.15i			1.65557i	−0.561049	+	0.827783i	$0.689602\pi$
$828$		0			0
$829$	−73.7477			−0.0889598			−0.0444799	−	0.999010i	$-0.514163\pi$
$829$	−73.7477			−0.0889598			−0.0444799	+	0.999010i	$0.514163\pi$
$830$	75.8947	−	185.615i	0.0914394	−	0.223633i
$831$		0			0
$832$	−897.410	−	214.332i	−1.07862	−	0.257610i
$833$	−365.317	−	632.748i	−0.438556	−	0.759601i
$834$		0			0
$835$	−1293.07	−	746.554i	−1.54859	−	0.894077i
$836$	135.584	−	37.6581i	0.162182	−	0.0450455i
$837$		0			0
$838$	1063.91	−	145.004i	1.26958	−	0.173036i
$839$	1039.73	+	600.286i	1.23924	+	0.715478i	0.968940	−	0.247297i	$-0.0795423\pi$
$839$	1039.73	+	600.286i	1.23924	+	0.715478i	0.270305	+	0.962775i	$0.412876\pi$
$840$		0			0
$841$	−18.1625	−	31.4584i	−0.0215963	−	0.0374060i
$842$	580.931	−	449.988i	0.689942	−	0.534427i
$843$		0			0
$844$	−1026.71	−	265.095i	−1.21648	−	0.314094i
$845$	−287.554			−0.340300
$846$		0			0
$847$			712.406i			0.841094i
$848$	24.1292	+	1322.85i	0.0284543	+	1.55997i
$849$		0			0
$850$	844.024	−	653.778i	0.992969	−	0.769151i
$851$	138.567	−	80.0018i	0.162829	−	0.0940092i
$852$		0			0
$853$	219.539	−	380.254i	0.257373	−	0.445784i	−0.708164	−	0.706048i	$-0.750476\pi$
$853$	219.539	−	380.254i	0.257373	−	0.445784i	0.965537	+	0.260264i	$0.0838097\pi$
$854$	−158.080	+	21.5454i	−0.185106	+	0.0252288i
$855$		0			0
$856$	−714.748	+	307.578i	−0.834986	+	0.359321i
$857$	−255.481	+	442.506i	−0.298111	+	0.516344i	−0.975704	−	0.219094i	$-0.929690\pi$
$857$	−255.481	+	442.506i	−0.298111	+	0.516344i	0.677593	+	0.735437i	$0.263023\pi$
$858$		0			0
$859$	−153.093	+	88.3882i	−0.178222	+	0.102897i	−0.586457	−	0.809980i	$-0.699478\pi$
$859$	−153.093	+	88.3882i	−0.178222	+	0.102897i	0.408235	+	0.912877i	$0.366144\pi$
$860$	−1040.38	+	1059.53i	−1.20974	+	1.23201i
$861$		0			0
$862$	556.614	−	1361.31i	0.645724	−	1.57924i
$863$			1028.28i			1.19152i	0.803163	+	0.595759i	$0.203149\pi$
$863$			1028.28i			1.19152i	−0.803163	+	0.595759i	$0.796851\pi$
$864$		0			0
$865$	685.325			0.792283
$866$	1416.49	+	579.176i	1.63567	+	0.668795i
$867$		0			0
$868$	463.319	+	454.945i	0.533777	+	0.524130i
$869$	−506.022	−	876.456i	−0.582304	−	1.00858i
$870$		0			0
$871$	362.798	+	209.462i	0.416530	+	0.240484i
$872$	−306.212	−	711.573i	−0.351161	−	0.816024i
$873$		0			0
$874$	−34.9969	−	256.775i	−0.0400422	−	0.293793i
$875$	293.744	+	169.593i	0.335707	+	0.193821i
$876$		0			0
$877$	470.457	+	814.856i	0.536439	+	0.929140i	0.999092	+	0.0426008i	$0.0135644\pi$
$877$	470.457	+	814.856i	0.536439	+	0.929140i	−0.462653	+	0.886540i	$0.653102\pi$
$878$	56.8094	+	73.3406i	0.0647032	+	0.0835314i
$879$		0			0
$880$	−801.994	+	14.6286i	−0.911357	+	0.0166234i
$881$	1065.75			1.20970			0.604851	−	0.796339i	$-0.293233\pi$
$881$	1065.75			1.20970			0.604851	+	0.796339i	$0.293233\pi$
$882$		0			0
$883$			1001.97i			1.13474i	0.823464	+	0.567368i	$0.192038\pi$
$883$			1001.97i			1.13474i	−0.823464	+	0.567368i	$0.807962\pi$
$884$	257.957	−	999.064i	0.291807	−	1.13016i
$885$		0			0
$886$	−171.088	−	220.874i	−0.193102	−	0.249293i
$887$	−583.774	+	337.042i	−0.658144	+	0.379980i	−0.791569	−	0.611079i	$-0.790736\pi$
$887$	−583.774	+	337.042i	−0.658144	+	0.379980i	0.133426	+	0.991059i	$0.457402\pi$
$888$		0			0
$889$	469.240	−	812.747i	0.527829	−	0.914227i
$890$	−35.7866	−	262.569i	−0.0402097	−	0.295022i
$891$		0			0
$892$	−340.328	−	1225.32i	−0.381534	−	1.37367i
$893$	−135.146	+	234.079i	−0.151339	+	0.262126i
$894$		0			0
$895$	27.5016	−	15.8780i	0.0307280	−	0.0177408i
$896$	1207.25	+	119.888i	1.34737	+	0.133804i
$897$		0			0
$898$	−494.535	−	202.206i	−0.550707	−	0.225174i
$899$			507.310i			0.564305i
$900$		0			0
$901$	−1479.63			−1.64221
$902$	−44.2915	+	108.324i	−0.0491037	+	0.120093i
$903$		0			0
$904$	−185.909	+	249.268i	−0.205651	+	0.275739i
$905$	−1072.78	−	1858.11i	−1.18539	−	2.05316i
$906$		0			0
$907$	1023.16	+	590.723i	1.12807	+	0.651293i	0.943450	−	0.331516i	$-0.107560\pi$
$907$	1023.16	+	590.723i	1.12807	+	0.651293i	0.184624	+	0.982809i	$0.440893\pi$
$908$	266.938	+	961.083i	0.293985	+	1.05846i
$909$		0			0
$910$	2005.06	−	273.278i	2.20337	−	0.300305i
$911$	−1207.61	−	697.213i	−1.32559	−	0.765328i	−0.340973	−	0.940073i	$-0.610756\pi$
$911$	−1207.61	−	697.213i	−1.32559	−	0.765328i	−0.984614	+	0.174746i	$0.944090\pi$
$912$		0			0
$913$	−45.8359	−	79.3901i	−0.0502036	−	0.0869553i
$914$	−376.042	+	291.281i	−0.411424	+	0.318688i
$915$		0			0
$916$	152.334	−	589.988i	0.166304	−	0.644092i
$917$	513.346			0.559811
$918$		0			0
$919$			210.163i			0.228686i	0.993441	+	0.114343i	$0.0364763\pi$
$919$			210.163i			0.228686i	−0.993441	+	0.114343i	$0.963524\pi$
$920$	−172.766	+	1467.09i	−0.187789	+	1.59467i
$921$		0			0
$922$	−472.207	+	365.770i	−0.512155	+	0.396713i
$923$	1414.39	−	816.596i	1.53238	−	0.884719i
$924$		0			0
$925$	−95.7098	+	165.774i	−0.103470	+	0.179215i
$926$	−970.101	+	132.219i	−1.04763	+	0.142785i
$927$		0			0
$928$	593.994	+	738.615i	0.640080	+	0.795921i
$929$	−83.2996	+	144.279i	−0.0896659	+	0.155306i	−0.907370	−	0.420333i	$-0.861913\pi$
$929$	−83.2996	+	144.279i	−0.0896659	+	0.155306i	0.817704	+	0.575639i	$0.195247\pi$
$930$		0			0
$931$	183.748	−	106.087i	0.197366	−	0.113949i
$932$	989.783	+	971.894i	1.06200	+	1.04280i
$933$		0			0
$934$	−343.860	+	840.976i	−0.368158	+	0.900403i
$935$		−	897.044i		−	0.959405i
$936$		0			0
$937$	251.158			0.268045			0.134022	−	0.990978i	$-0.457211\pi$
$937$	251.158			0.268045			0.134022	+	0.990978i	$0.457211\pi$
$938$	−509.865	−	208.474i	−0.543566	−	0.222254i
$939$		0			0
$940$	1079.49	−	1099.36i	1.14839	−	1.16953i
$941$	407.282	+	705.433i	0.432818	+	0.749663i	0.997115	−	0.0759090i	$-0.0241858\pi$
$941$	407.282	+	705.433i	0.432818	+	0.749663i	−0.564296	+	0.825572i	$0.690853\pi$
$942$		0			0
$943$	186.650	+	107.762i	0.197932	+	0.114276i
$944$	690.841	+	1147.71i	0.731823	+	1.21580i
$945$		0			0
$946$	91.6718	+	672.604i	0.0969047	+	0.710998i
$947$	513.020	+	296.192i	0.541731	+	0.312769i	0.745780	−	0.666192i	$-0.232077\pi$
$947$	513.020	+	296.192i	0.541731	+	0.312769i	−0.204049	+	0.978961i	$0.565410\pi$
$948$		0			0
$949$	15.6215	+	27.0572i	0.0164610	+	0.0285113i
$950$	189.855	+	245.102i	0.199847	+	0.258002i
$951$		0			0
$952$	−158.675	+	1347.43i	−0.166675	+	1.41537i
$953$	844.768			0.886430			0.443215	−	0.896415i	$-0.353838\pi$
$953$	844.768			0.886430			0.443215	+	0.896415i	$0.353838\pi$
$954$		0			0
$955$		−	685.983i		−	0.718307i
$956$	402.926	+	104.035i	0.421471	+	0.108823i
$957$		0			0
$958$	4.42572	+	5.71359i	0.00461975	+	0.00596408i
$959$	45.6330	−	26.3462i	0.0475839	−	0.0274726i
$960$		0			0
$961$	−333.825	+	578.202i	−0.347373	+	0.601667i
$962$	24.9838	+	183.308i	0.0259707	+	0.190549i
$963$		0			0
$964$	−1086.19	+	301.686i	−1.12675	+	0.312952i
$965$	−900.305	+	1559.37i	−0.932959	+	1.61593i
$966$		0			0
$967$	156.035	−	90.0867i	0.161360	−	0.0931611i	−0.417146	−	0.908840i	$-0.636970\pi$
$967$	156.035	−	90.0867i	0.161360	−	0.0931611i	0.578505	+	0.815679i	$0.303636\pi$
$968$	359.496	−	482.016i	0.371381	−	0.497950i
$969$		0			0
$970$	1896.27	+	775.351i	1.95492	+	0.799331i
$971$		−	411.395i		−	0.423682i	−0.977304	−	0.211841i	$-0.932054\pi$
$971$		−	411.395i		−	0.423682i	0.977304	−	0.211841i	$-0.0679458\pi$
$972$		0			0
$973$	1445.56			1.48567
$974$	661.968	−	1618.97i	0.679638	−	1.66219i
$975$		0			0
$976$	117.830	+	65.1932i	0.120727	+	0.0667963i
$977$	878.125	+	1520.96i	0.898797	+	1.55676i	0.829034	+	0.559199i	$0.188891\pi$
$977$	878.125	+	1520.96i	0.898797	+	1.55676i	0.0697635	+	0.997564i	$0.477776\pi$
$978$		0			0
$979$	−104.912	−	60.5708i	−0.107162	−	0.0618701i
$980$	−1165.34	+	323.670i	−1.18912	+	0.330276i
$981$		0			0
$982$	−1278.57	+	174.261i	−1.30201	+	0.177456i
$983$	695.466	+	401.528i	0.707494	+	0.408472i	0.810132	−	0.586247i	$-0.199395\pi$
$983$	695.466	+	401.528i	0.707494	+	0.408472i	−0.102639	+	0.994719i	$0.532729\pi$
$984$		0			0
$985$	516.243	+	894.159i	0.524105	+	0.907776i
$986$	−837.994	+	649.107i	−0.849892	+	0.658324i
$987$		0			0
$988$	290.125	+	74.9099i	0.293648	+	0.0758197i
$989$	1250.15			1.26405
$990$		0			0
$991$			338.466i			0.341540i	0.985311	+	0.170770i	$0.0546254\pi$
$991$			338.466i			0.341540i	−0.985311	+	0.170770i	$0.945375\pi$
$992$	−83.9071	−	541.618i	−0.0845837	−	0.545986i
$993$		0			0
$994$	−1697.73	+	1315.05i	−1.70797	+	1.32299i
$995$	−711.783	+	410.948i	−0.715360	+	0.413013i
$996$		0			0
$997$	−295.906	+	512.523i	−0.296796	+	0.514066i	−0.975401	−	0.220438i	$-0.929251\pi$
$997$	−295.906	+	512.523i	−0.296796	+	0.514066i	0.678605	+	0.734503i	$0.262585\pi$
$998$	1119.33	−	152.558i	1.12158	−	0.152864i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.o.55.4		8
3.2	odd	2	inner	324.3.f.o.55.1		8
4.3	odd	2		324.3.f.p.55.1		8
9.2	odd	6		108.3.d.d.55.6	yes	8
9.4	even	3		324.3.f.p.271.2		8
9.5	odd	6		324.3.f.p.271.3		8
9.7	even	3		108.3.d.d.55.3	✓	8
12.11	even	2		324.3.f.p.55.4		8
36.7	odd	6		108.3.d.d.55.4	yes	8
36.11	even	6		108.3.d.d.55.5	yes	8
36.23	even	6	inner	324.3.f.o.271.1		8
36.31	odd	6	inner	324.3.f.o.271.4		8
72.11	even	6		1728.3.g.l.703.1		8
72.29	odd	6		1728.3.g.l.703.2		8
72.43	odd	6		1728.3.g.l.703.7		8
72.61	even	6		1728.3.g.l.703.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.d.55.3	✓	8	9.7	even	3
108.3.d.d.55.4	yes	8	36.7	odd	6
108.3.d.d.55.5	yes	8	36.11	even	6
108.3.d.d.55.6	yes	8	9.2	odd	6
324.3.f.o.55.1		8	3.2	odd	2	inner
324.3.f.o.55.4		8	1.1	even	1	trivial
324.3.f.o.271.1		8	36.23	even	6	inner
324.3.f.o.271.4		8	36.31	odd	6	inner
324.3.f.p.55.1		8	4.3	odd	2
324.3.f.p.55.4		8	12.11	even	2
324.3.f.p.271.2		8	9.4	even	3
324.3.f.p.271.3		8	9.5	odd	6
1728.3.g.l.703.1		8	72.11	even	6
1728.3.g.l.703.2		8	72.29	odd	6
1728.3.g.l.703.7		8	72.43	odd	6
1728.3.g.l.703.8		8	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +(3.70246 + 6.41285i) q^{5} +(-8.20820 - 4.73901i) q^{7} +(3.16228 + 7.34847i) q^{8} +O(q^{10})\)	\(q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +(3.70246 + 6.41285i) q^{5} +(-8.20820 - 4.73901i) q^{7} +(3.16228 + 7.34847i) q^{8} +(2.00000 + 14.6742i) q^{10} +(5.86319 + 3.38511i) q^{11} +(7.20820 + 12.4850i) q^{13} +(-11.6082 - 14.9861i) q^{14} +(0.291796 + 15.9973i) q^{16} -17.8933 q^{17} -5.19615i q^{19} +(-7.40492 + 28.6791i) q^{20} +(8.29180 + 10.7047i) q^{22} +(21.5958 - 12.4683i) q^{23} +(-14.9164 + 25.8360i) q^{25} +(3.89374 + 28.5687i) q^{26} +(-10.1459 - 36.5292i) q^{28} +(14.8098 - 25.6514i) q^{29} +(-14.8328 + 8.56373i) q^{31} +(-11.5687 + 29.8356i) q^{32} +(-33.1246 - 13.5440i) q^{34} -70.1839i q^{35} +6.41641 q^{37} +(3.93314 - 9.61927i) q^{38} +(-35.4164 + 47.4866i) q^{40} +(4.32145 + 7.48497i) q^{41} +(43.4164 + 25.0665i) q^{43} +(7.24730 + 26.0931i) q^{44} +(49.4164 - 6.73516i) q^{46} +(-45.0485 - 26.0088i) q^{47} +(20.4164 + 35.3623i) q^{49} +(-47.1698 + 36.5376i) q^{50} +(-14.4164 + 55.8345i) q^{52} +82.6921 q^{53} +50.1329i q^{55} +(8.86784 - 75.3038i) q^{56} +(46.8328 - 36.2765i) q^{58} +(72.5075 - 41.8622i) q^{59} +(4.20820 - 7.28882i) q^{61} +(-33.9411 + 4.62597i) q^{62} +(-44.0000 + 46.4758i) q^{64} +(-53.3762 + 92.4502i) q^{65} +(25.1656 - 14.5294i) q^{67} +(-51.0693 - 50.1463i) q^{68} +(53.1246 - 129.927i) q^{70} -113.287i q^{71} +2.16718 q^{73} +(11.8782 + 4.85680i) q^{74} +(14.5623 - 14.8303i) q^{76} +(-32.0841 - 55.5714i) q^{77} +(-129.457 - 74.7423i) q^{79} +(-101.508 + 61.1007i) q^{80} +(2.33437 + 17.1275i) q^{82} +(-11.7264 - 6.77022i) q^{83} +(-66.2492 - 114.747i) q^{85} +(61.4001 + 79.2672i) q^{86} +(-6.33437 + 53.7901i) q^{88} -17.8933 q^{89} -136.639i q^{91} +(96.5792 + 24.9366i) q^{92} +(-63.7082 - 82.2469i) q^{94} +(33.3221 - 19.2385i) q^{95} +(69.1656 - 119.798i) q^{97} +(11.0286 + 80.9175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 12 q^{7}+O(q^{10}) \) 8 * q - 4 * q^4 - 12 * q^7	\( 8 q - 4 q^{4} - 12 q^{7} + 16 q^{10} + 4 q^{13} + 56 q^{16} + 120 q^{22} - 12 q^{25} - 108 q^{28} + 96 q^{31} - 104 q^{34} - 56 q^{37} - 176 q^{40} + 240 q^{43} + 288 q^{46} + 56 q^{49} - 8 q^{52} + 160 q^{58} - 20 q^{61} - 352 q^{64} - 228 q^{67} + 264 q^{70} + 232 q^{73} + 36 q^{76} - 660 q^{79} + 448 q^{82} - 208 q^{85} - 480 q^{88} - 456 q^{94} + 124 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 - 12 * q^7 + 16 * q^10 + 4 * q^13 + 56 * q^16 + 120 * q^22 - 12 * q^25 - 108 * q^28 + 96 * q^31 - 104 * q^34 - 56 * q^37 - 176 * q^40 + 240 * q^43 + 288 * q^46 + 56 * q^49 - 8 * q^52 + 160 * q^58 - 20 * q^61 - 352 * q^64 - 228 * q^67 + 264 * q^70 + 232 * q^73 + 36 * q^76 - 660 * q^79 + 448 * q^82 - 208 * q^85 - 480 * q^88 - 456 * q^94 + 124 * q^97

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