LMFDB - Embedded newform 324.3.o.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, 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:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87615 - 2.34095i) q^{3} +(-7.80193 + 5.80832i) q^{5} +(5.92166 - 3.89473i) q^{7} +(-1.96012 - 8.78396i) q^{9} +O(q^{10})$	\(q+(1.87615 - 2.34095i) q^{3} +(-7.80193 + 5.80832i) q^{5} +(5.92166 - 3.89473i) q^{7} +(-1.96012 - 8.78396i) q^{9} +(0.0259603 - 0.222104i) q^{11} +(-5.75523 - 19.2238i) q^{13} +(-1.04058 + 29.1612i) q^{15} +(-16.7302 - 2.94999i) q^{17} +(-3.63734 - 20.6284i) q^{19} +(1.99252 - 21.1694i) q^{21} +(12.0237 - 18.2812i) q^{23} +(19.9634 - 66.6825i) q^{25} +(-24.2403 - 11.8915i) q^{27} +(-9.72405 + 9.17417i) q^{29} +(-2.56933 + 44.1136i) q^{31} +(-0.471230 - 0.477473i) q^{33} +(-23.5785 + 64.7813i) q^{35} +(-46.1613 + 16.8013i) q^{37} +(-55.7997 - 22.5940i) q^{39} +(7.10244 - 29.9675i) q^{41} +(2.74269 + 6.35827i) q^{43} +(66.3128 + 57.1468i) q^{45} +(52.8732 - 3.07951i) q^{47} +(0.489143 - 1.13396i) q^{49} +(-38.2942 + 33.6301i) q^{51} +(-21.5125 - 12.4202i) q^{53} +(1.08751 + 1.88363i) q^{55} +(-55.1143 - 30.1871i) q^{57} +(-3.07094 - 26.2736i) q^{59} +(50.8973 + 25.5616i) q^{61} +(-45.8184 - 44.3814i) q^{63} +(156.560 + 116.555i) q^{65} +(47.8640 - 50.7328i) q^{67} +(-20.2370 - 62.4451i) q^{69} +(34.5875 - 41.2198i) q^{71} +(-59.4000 + 49.8425i) q^{73} +(-118.646 - 171.840i) q^{75} +(-0.711310 - 1.41633i) q^{77} +(73.2345 - 17.3569i) q^{79} +(-73.3158 + 34.4353i) q^{81} +(-25.7416 - 108.612i) q^{83} +(147.663 - 74.1590i) q^{85} +(3.23252 + 39.9757i) q^{87} +(69.0322 + 82.2694i) q^{89} +(-108.952 - 91.4217i) q^{91} +(98.4475 + 88.7785i) q^{93} +(148.195 + 139.815i) q^{95} +(38.6405 - 51.9032i) q^{97} +(-2.00184 + 0.207318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{54}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.87615	−	2.34095i	0.625383	−	0.780318i
$3$	1.87615	−	2.34095i	0.625383	−	0.780318i
$4$		0			0
$5$	−7.80193	+	5.80832i	−1.56039	+	1.16166i	−0.641513	+	0.767112i	$0.721693\pi$
$5$	−7.80193	+	5.80832i	−1.56039	+	1.16166i	−0.918874	+	0.394552i	$0.870900\pi$
$6$		0			0
$7$	5.92166	−	3.89473i	0.845951	−	0.556391i	−0.0509101	−	0.998703i	$-0.516212\pi$
$7$	5.92166	−	3.89473i	0.845951	−	0.556391i	0.896861	+	0.442313i	$0.145842\pi$
$8$		0			0
$9$	−1.96012	−	8.78396i	−0.217791	−	0.975995i
$10$		0			0
$11$	0.0259603	−	0.222104i	0.00236003	−	0.0201913i	−0.992007	−	0.126183i	$-0.959727\pi$
$11$	0.0259603	−	0.222104i	0.00236003	−	0.0201913i	0.994367	+	0.105991i	$0.0338016\pi$
$12$		0			0
$13$	−5.75523	−	19.2238i	−0.442710	−	1.47876i	−0.830506	−	0.557010i	$-0.811949\pi$
$13$	−5.75523	−	19.2238i	−0.442710	−	1.47876i	0.387796	−	0.921745i	$-0.373237\pi$
$14$		0			0
$15$	−1.04058	+	29.1612i	−0.0693722	+	1.94408i
$16$		0			0
$17$	−16.7302	−	2.94999i	−0.984131	−	0.173529i	−0.341648	−	0.939828i	$-0.610985\pi$
$17$	−16.7302	−	2.94999i	−0.984131	−	0.173529i	−0.642484	+	0.766299i	$0.722096\pi$
$18$		0			0
$19$	−3.63734	−	20.6284i	−0.191439	−	1.08571i	−0.917399	−	0.397969i	$-0.869715\pi$
$19$	−3.63734	−	20.6284i	−0.191439	−	1.08571i	0.725960	−	0.687737i	$-0.241396\pi$
$20$		0			0
$21$	1.99252	−	21.1694i	0.0948821	−	1.00807i
$22$		0			0
$23$	12.0237	−	18.2812i	0.522770	−	0.794833i	−0.473530	−	0.880778i	$-0.657021\pi$
$23$	12.0237	−	18.2812i	0.522770	−	0.794833i	0.996300	+	0.0859449i	$0.0273909\pi$
$24$		0			0
$25$	19.9634	−	66.6825i	0.798538	−	2.66730i
$26$		0			0
$27$	−24.2403	−	11.8915i	−0.897789	−	0.440425i
$28$		0			0
$29$	−9.72405	+	9.17417i	−0.335312	+	0.316351i	−0.835420	−	0.549613i	$-0.814775\pi$
$29$	−9.72405	+	9.17417i	−0.335312	+	0.316351i	0.500107	+	0.865963i	$0.333294\pi$
$30$		0			0
$31$	−2.56933	+	44.1136i	−0.0828815	+	1.42302i	0.658825	+	0.752296i	$0.271054\pi$
$31$	−2.56933	+	44.1136i	−0.0828815	+	1.42302i	−0.741707	+	0.670725i	$0.765983\pi$
$32$		0			0
$33$	−0.471230	−	0.477473i	−0.0142797	−	0.0144689i
$34$		0			0
$35$	−23.5785	+	64.7813i	−0.673671	+	1.85090i
$36$		0			0
$37$	−46.1613	+	16.8013i	−1.24760	+	0.454090i	−0.879591	−	0.475731i	$-0.842184\pi$
$37$	−46.1613	+	16.8013i	−1.24760	+	0.454090i	−0.368012	+	0.929821i	$0.619961\pi$
$38$		0			0
$39$	−55.7997	−	22.5940i	−1.43076	−	0.579334i
$40$		0			0
$41$	7.10244	−	29.9675i	0.173230	−	0.730916i	−0.815192	−	0.579190i	$-0.803369\pi$
$41$	7.10244	−	29.9675i	0.173230	−	0.730916i	0.988423	−	0.151725i	$-0.0484830\pi$
$42$		0			0
$43$	2.74269	+	6.35827i	0.0637835	+	0.147867i	0.947127	−	0.320860i	$-0.103972\pi$
$43$	2.74269	+	6.35827i	0.0637835	+	0.147867i	−0.883343	+	0.468727i	$0.844713\pi$
$44$		0			0
$45$	66.3128	+	57.1468i	1.47362	+	1.26993i
$46$		0			0
$47$	52.8732	−	3.07951i	1.12496	−	0.0655216i	0.514444	−	0.857524i	$-0.327998\pi$
$47$	52.8732	−	3.07951i	1.12496	−	0.0655216i	0.610518	+	0.792002i	$0.290961\pi$
$48$		0			0
$49$	0.489143	−	1.13396i	0.00998251	−	0.0231421i
$50$		0			0
$51$	−38.2942	+	33.6301i	−0.750867	+	0.659413i
$52$		0			0
$53$	−21.5125	−	12.4202i	−0.405896	−	0.234344i	0.283129	−	0.959082i	$-0.408628\pi$
$53$	−21.5125	−	12.4202i	−0.405896	−	0.234344i	−0.689025	+	0.724738i	$0.741961\pi$
$54$		0			0
$55$	1.08751	+	1.88363i	0.0197730	+	0.0342478i
$56$		0			0
$57$	−55.1143	−	30.1871i	−0.966918	−	0.529599i
$58$		0			0
$59$	−3.07094	−	26.2736i	−0.0520498	−	0.445315i	−0.993985	−	0.109519i	$-0.965069\pi$
$59$	−3.07094	−	26.2736i	−0.0520498	−	0.445315i	0.941935	−	0.335796i	$-0.109005\pi$
$60$		0			0
$61$	50.8973	+	25.5616i	0.834381	+	0.419042i	0.814081	−	0.580752i	$-0.197241\pi$
$61$	50.8973	+	25.5616i	0.834381	+	0.419042i	0.0203007	+	0.999794i	$0.493538\pi$
$62$		0			0
$63$	−45.8184	−	44.3814i	−0.727275	−	0.704467i
$64$		0			0
$65$	156.560	+	116.555i	2.40862	+	1.79315i
$66$		0			0
$67$	47.8640	−	50.7328i	0.714388	−	0.757207i	−0.263879	−	0.964556i	$-0.585002\pi$
$67$	47.8640	−	50.7328i	0.714388	−	0.757207i	0.978267	+	0.207349i	$0.0664836\pi$
$68$		0			0
$69$	−20.2370	−	62.4451i	−0.293291	−	0.905002i
$70$		0			0
$71$	34.5875	−	41.2198i	0.487148	−	0.580560i	−0.465342	−	0.885131i	$-0.654069\pi$
$71$	34.5875	−	41.2198i	0.487148	−	0.580560i	0.952490	+	0.304571i	$0.0985130\pi$
$72$		0			0
$73$	−59.4000	+	49.8425i	−0.813699	+	0.682774i	−0.951488	−	0.307687i	$-0.900445\pi$
$73$	−59.4000	+	49.8425i	−0.813699	+	0.682774i	0.137789	+	0.990462i	$0.456001\pi$
$74$		0			0
$75$	−118.646	−	171.840i	−1.58195	−	2.29120i
$76$		0			0
$77$	−0.711310	−	1.41633i	−0.00923779	−	0.0183939i
$78$		0			0
$79$	73.2345	−	17.3569i	0.927018	−	0.219707i	0.260739	−	0.965409i	$-0.416034\pi$
$79$	73.2345	−	17.3569i	0.927018	−	0.219707i	0.666280	+	0.745702i	$0.267886\pi$
$80$		0			0
$81$	−73.3158	+	34.4353i	−0.905134	+	0.425127i
$82$		0			0
$83$	−25.7416	−	108.612i	−0.310140	−	1.30858i	−0.875291	−	0.483596i	$-0.839330\pi$
$83$	−25.7416	−	108.612i	−0.310140	−	1.30858i	0.565151	−	0.824987i	$-0.308818\pi$
$84$		0			0
$85$	147.663	−	74.1590i	1.73721	−	0.872458i
$86$		0			0
$87$	3.23252	+	39.9757i	0.0371554	+	0.459491i
$88$		0			0
$89$	69.0322	+	82.2694i	0.775643	+	0.924375i	0.998728	−	0.0504239i	$-0.0160572\pi$
$89$	69.0322	+	82.2694i	0.775643	+	0.924375i	−0.223085	+	0.974799i	$0.571613\pi$
$90$		0			0
$91$	−108.952	−	91.4217i	−1.19728	−	1.00463i
$92$		0			0
$93$	98.4475	+	88.7785i	1.05858	+	0.954607i
$94$		0			0
$95$	148.195	+	139.815i	1.55994	+	1.47173i
$96$		0			0
$97$	38.6405	−	51.9032i	0.398356	−	0.535084i	−0.557012	−	0.830505i	$-0.688052\pi$
$97$	38.6405	−	51.9032i	0.398356	−	0.535084i	0.955367	+	0.295420i	$0.0954596\pi$
$98$		0			0
$99$	−2.00184	+	0.207318i	−0.0202206	+	0.00209412i
$100$		0			0
$101$	−64.7388	+	128.906i	−0.640979	+	1.27629i	0.305089	+	0.952324i	$0.401314\pi$
$101$	−64.7388	+	128.906i	−0.640979	+	1.27629i	−0.946068	+	0.323970i	$0.894982\pi$
$102$		0			0
$103$	−72.2711	+	8.44728i	−0.701661	+	0.0820124i	−0.459440	−	0.888209i	$-0.651950\pi$
$103$	−72.2711	+	8.44728i	−0.701661	+	0.0820124i	−0.242221	+	0.970221i	$0.577876\pi$
$104$		0			0
$105$	107.413	+	176.736i	1.02298	+	1.68320i
$106$		0			0
$107$	−117.357	+	67.7563i	−1.09680	+	0.633236i	−0.935378	−	0.353650i	$-0.884940\pi$
$107$	−117.357	+	67.7563i	−1.09680	+	0.633236i	−0.161419	+	0.986886i	$0.551607\pi$
$108$		0			0
$109$	73.2786	−	126.922i	0.672280	−	1.16442i	−0.304975	−	0.952360i	$-0.598648\pi$
$109$	73.2786	−	126.922i	0.672280	−	1.16442i	0.977256	−	0.212064i	$-0.0680184\pi$
$110$		0			0
$111$	−47.2744	+	139.583i	−0.425895	+	1.25751i
$112$		0			0
$113$	15.6022	+	6.73014i	0.138073	+	0.0595588i	0.463995	−	0.885838i	$-0.346416\pi$
$113$	15.6022	+	6.73014i	0.138073	+	0.0595588i	−0.325922	+	0.945397i	$0.605675\pi$
$114$		0			0
$115$	12.3747	+	212.466i	0.107606	+	1.84753i
$116$		0			0
$117$	−157.580	+	88.2348i	−1.34684	+	0.754143i
$118$		0			0
$119$	−110.560	+	47.6910i	−0.929077	+	0.400765i
$120$		0			0
$121$	117.690	+	27.8930i	0.972643	+	0.230521i
$122$		0			0
$123$	−56.8274	−	72.8501i	−0.462011	−	0.592277i
$124$		0			0
$125$	148.393	+	407.706i	1.18714	+	3.26165i
$126$		0			0
$127$	185.745	+	67.6057i	1.46256	+	0.532328i	0.946069	−	0.323965i	$-0.105016\pi$
$127$	185.745	+	67.6057i	1.46256	+	0.532328i	0.516491	+	0.856293i	$0.327238\pi$
$128$		0			0
$129$	20.0301	+	5.50856i	0.155272	+	0.0427020i
$130$		0			0
$131$	−19.7774	−	1.15190i	−0.150972	−	0.00879313i	−0.0175078	−	0.999847i	$-0.505573\pi$
$131$	−19.7774	−	1.15190i	−0.150972	−	0.00879313i	−0.133465	+	0.991054i	$0.542610\pi$
$132$		0			0
$133$	−101.881	−	107.988i	−0.766025	−	0.811939i
$134$		0			0
$135$	258.191	−	48.0191i	1.91252	−	0.355697i
$136$		0			0
$137$	−223.265	−	66.8411i	−1.62967	−	0.487891i	−0.664015	−	0.747720i	$-0.731149\pi$
$137$	−223.265	−	66.8411i	−1.62967	−	0.487891i	−0.965655	+	0.259829i	$0.916334\pi$
$138$		0			0
$139$	4.44861	+	2.92590i	0.0320044	+	0.0210496i	0.565410	−	0.824810i	$-0.308718\pi$
$139$	4.44861	+	2.92590i	0.0320044	+	0.0210496i	−0.533406	+	0.845859i	$0.679088\pi$
$140$		0			0
$141$	91.9891	−	129.551i	0.652405	−	0.918804i
$142$		0			0
$143$	−4.41910	+	0.779207i	−0.0309028	+	0.00544900i
$144$		0			0
$145$	22.5799	−	128.057i	0.155723	−	0.883150i
$146$		0			0
$147$	−1.73684	−	3.27254i	−0.0118153	−	0.0222622i
$148$		0			0
$149$	192.606	−	57.6624i	1.29266	−	0.386996i	0.434633	−	0.900608i	$-0.356878\pi$
$149$	192.606	−	57.6624i	1.29266	−	0.386996i	0.858023	+	0.513612i	$0.171693\pi$
$150$		0			0
$151$	117.886	+	13.7789i	0.780703	+	0.0912511i	0.497103	−	0.867692i	$-0.334397\pi$
$151$	117.886	+	13.7789i	0.780703	+	0.0912511i	0.283600	+	0.958943i	$0.408471\pi$
$152$		0			0
$153$	6.88069	+	152.740i	0.0449719	+	0.998301i
$154$		0			0
$155$	−236.181	−	359.095i	−1.52375	−	2.31674i
$156$		0			0
$157$	−63.5438	−	85.3542i	−0.404738	−	0.543657i	0.552290	−	0.833652i	$-0.313754\pi$
$157$	−63.5438	−	85.3542i	−0.404738	−	0.543657i	−0.957028	+	0.289994i	$0.906347\pi$
$158$		0			0
$159$	−69.4359	+	27.0575i	−0.436704	+	0.170173i
$160$		0			0
$161$		−	155.084i		−	0.963254i
$162$		0			0
$163$	−127.040			−0.779388			−0.389694	−	0.920944i	$-0.627419\pi$
$163$	−127.040			−0.779388			−0.389694	+	0.920944i	$0.627419\pi$
$164$		0			0
$165$	6.44982	+	0.988152i	0.0390898	+	0.00598880i
$166$		0			0
$167$	−100.508	+	74.8255i	−0.601845	+	0.448057i	−0.854465	−	0.519509i	$-0.826115\pi$
$167$	−100.508	+	74.8255i	−0.601845	+	0.448057i	0.252620	+	0.967565i	$0.418708\pi$
$168$		0			0
$169$	−195.235	+	128.408i	−1.15524	+	0.759811i
$170$		0			0
$171$	−174.069	+	72.3845i	−1.01795	+	0.423301i
$172$		0			0
$173$	−12.5925	+	107.736i	−0.0727889	+	0.622749i	0.906775	+	0.421615i	$0.138537\pi$
$173$	−12.5925	+	107.736i	−0.0727889	+	0.622749i	−0.979564	+	0.201134i	$0.935537\pi$
$174$		0			0
$175$	−141.494	−	472.623i	−0.808538	−	2.70070i
$176$		0			0
$177$	−67.2667	−	42.1042i	−0.380038	−	0.237877i
$178$		0			0
$179$	174.081	+	30.6952i	0.972521	+	0.171482i	0.637264	−	0.770645i	$-0.280066\pi$
$179$	174.081	+	30.6952i	0.972521	+	0.171482i	0.335257	+	0.942127i	$0.391177\pi$
$180$		0			0
$181$	15.6742	+	88.8926i	0.0865976	+	0.491120i	0.997000	+	0.0773965i	$0.0246607\pi$
$181$	15.6742	+	88.8926i	0.0865976	+	0.491120i	−0.910403	+	0.413723i	$0.864228\pi$
$182$		0			0
$183$	155.329	−	71.1908i	0.848794	−	0.389021i
$184$		0			0
$185$	262.560	−	399.203i	1.41924	−	2.15785i
$186$		0			0
$187$	−1.08953	+	3.63928i	−0.00582635	+	0.0194614i
$188$		0			0
$189$	−189.857	+	23.9924i	−1.00453	+	0.126944i
$190$		0			0
$191$	−9.65325	+	9.10737i	−0.0505406	+	0.0476826i	−0.711098	−	0.703093i	$-0.751802\pi$
$191$	−9.65325	+	9.10737i	−0.0505406	+	0.0476826i	0.660557	+	0.750776i	$0.270320\pi$
$192$		0			0
$193$	10.8605	−	186.468i	0.0562721	−	0.966155i	−0.845509	−	0.533962i	$-0.820703\pi$
$193$	10.8605	−	186.468i	0.0562721	−	0.966155i	0.901781	−	0.432194i	$-0.142260\pi$
$194$		0			0
$195$	566.579	−	147.826i	2.90553	−	0.758081i
$196$		0			0
$197$	14.6800	−	40.3330i	0.0745179	−	0.204736i	−0.896841	−	0.442353i	$-0.854144\pi$
$197$	14.6800	−	40.3330i	0.0745179	−	0.204736i	0.971359	+	0.237617i	$0.0763662\pi$
$198$		0			0
$199$	−189.630	+	69.0198i	−0.952917	+	0.346833i	−0.771254	−	0.636528i	$-0.780370\pi$
$199$	−189.630	+	69.0198i	−0.952917	+	0.346833i	−0.181663	+	0.983361i	$0.558148\pi$
$200$		0			0
$201$	−28.9632	−	207.230i	−0.144096	−	1.03099i
$202$		0			0
$203$	−21.8515	+	92.1989i	−0.107643	+	0.454182i
$204$		0			0
$205$	118.648	+	275.058i	0.578773	+	1.34175i
$206$		0			0
$207$	−184.149	−	69.7824i	−0.889608	−	0.337113i
$208$		0			0
$209$	−4.67609	+	0.272351i	−0.0223736	+	0.00130311i
$210$		0			0
$211$	−43.5439	+	100.946i	−0.206369	+	0.478417i	−0.989695	−	0.143195i	$-0.954263\pi$
$211$	−43.5439	+	100.946i	−0.206369	+	0.478417i	0.783326	+	0.621612i	$0.213522\pi$
$212$		0			0
$213$	−31.6022	−	158.302i	−0.148367	−	0.743203i
$214$		0			0
$215$	−58.3292	−	33.6764i	−0.271298	−	0.156634i
$216$		0			0
$217$	156.596	+	271.233i	0.721642	+	1.24992i
$218$		0			0
$219$	5.23568	+	232.565i	0.0239072	+	1.06194i
$220$		0			0
$221$	39.5763	+	338.597i	0.179078	+	1.53211i
$222$		0			0
$223$	219.811	+	110.393i	0.985698	+	0.495036i	0.867222	−	0.497921i	$-0.165903\pi$
$223$	219.811	+	110.393i	0.985698	+	0.495036i	0.118475	+	0.992957i	$0.462199\pi$
$224$		0			0
$225$	−624.867	−	44.6521i	−2.77719	−	0.198454i
$226$		0			0
$227$	−306.159	−	227.927i	−1.34872	−	1.00408i	−0.997705	−	0.0677147i	$-0.978429\pi$
$227$	−306.159	−	227.927i	−1.34872	−	1.00408i	−0.351015	−	0.936370i	$-0.614163\pi$
$228$		0			0
$229$	235.591	−	249.712i	1.02878	−	1.09045i	0.0329307	−	0.999458i	$-0.489516\pi$
$229$	235.591	−	249.712i	1.02878	−	1.09045i	0.995852	−	0.0909882i	$-0.0290026\pi$
$230$		0			0
$231$	−4.65009	−	0.992113i	−0.0201303	−	0.00429486i
$232$		0			0
$233$	252.865	−	301.353i	1.08526	−	1.29336i	0.131986	−	0.991252i	$-0.457865\pi$
$233$	252.865	−	301.353i	1.08526	−	1.29336i	0.953273	−	0.302110i	$-0.0976909\pi$
$234$		0			0
$235$	−394.626	+	331.131i	−1.67926	+	1.40907i
$236$		0			0
$237$	96.7672	−	204.003i	0.408300	−	0.860770i
$238$		0			0
$239$	−46.1353	−	91.8629i	−0.193035	−	0.384363i	0.776206	−	0.630480i	$-0.217142\pi$
$239$	−46.1353	−	91.8629i	−0.193035	−	0.384363i	−0.969240	+	0.246116i	$0.920846\pi$
$240$		0			0
$241$	−218.503	+	51.7861i	−0.906650	+	0.214880i	−0.657385	−	0.753555i	$-0.728337\pi$
$241$	−218.503	+	51.7861i	−0.906650	+	0.214880i	−0.249265	+	0.968435i	$0.580189\pi$
$242$		0			0
$243$	−56.9402	+	236.235i	−0.234322	+	0.972159i
$244$		0			0
$245$	2.77015	+	11.6882i	0.0113067	+	0.0477069i
$246$		0			0
$247$	−375.623	+	188.645i	−1.52074	+	0.763745i
$248$		0			0
$249$	−302.552	−	143.513i	−1.21507	−	0.576359i
$250$		0			0
$251$	62.0303	+	73.9248i	0.247133	+	0.294521i	0.875323	−	0.483538i	$-0.160649\pi$
$251$	62.0303	+	73.9248i	0.247133	+	0.294521i	−0.628191	+	0.778059i	$0.716204\pi$
$252$		0			0
$253$	−3.74818	−	3.14510i	−0.0148150	−	0.0124312i
$254$		0			0
$255$	103.435	−	484.805i	0.405626	−	1.90119i
$256$		0			0
$257$	−116.548	−	109.957i	−0.453495	−	0.427850i	0.425298	−	0.905053i	$-0.360169\pi$
$257$	−116.548	−	109.957i	−0.453495	−	0.427850i	−0.878793	+	0.477203i	$0.841651\pi$
$258$		0			0
$259$	−207.915	+	279.278i	−0.802759	+	1.07829i
$260$		0			0
$261$	99.6459	+	67.4332i	0.381785	+	0.258365i
$262$		0			0
$263$	196.054	−	390.375i	0.745452	−	1.48432i	−0.125049	−	0.992151i	$-0.539909\pi$
$263$	196.054	−	390.375i	0.745452	−	1.48432i	0.870501	−	0.492166i	$-0.163795\pi$
$264$		0			0
$265$	239.980	−	28.0496i	0.905584	−	0.105848i
$266$		0			0
$267$	322.104	−	7.25145i	1.20638	−	0.0271590i
$268$		0			0
$269$	−317.324	+	183.207i	−1.17964	+	0.681068i	−0.955932	−	0.293587i	$-0.905151\pi$
$269$	−317.324	+	183.207i	−1.17964	+	0.681068i	−0.223712	+	0.974655i	$0.571817\pi$
$270$		0			0
$271$	240.973	−	417.378i	0.889200	−	1.54014i	0.0483780	−	0.998829i	$-0.484595\pi$
$271$	240.973	−	417.378i	0.889200	−	1.54014i	0.840822	−	0.541311i	$-0.182072\pi$
$272$		0			0
$273$	−418.425	+	83.5310i	−1.53269	+	0.305974i
$274$		0			0
$275$	−14.2922	−	6.16506i	−0.0519717	−	0.0224184i
$276$		0			0
$277$	9.33521	+	160.279i	0.0337011	+	0.578626i	0.972318	+	0.233663i	$0.0750713\pi$
$277$	9.33521	+	160.279i	0.0337011	+	0.578626i	−0.938616	+	0.344962i	$0.887892\pi$
$278$		0			0
$279$	392.529	−	63.8993i	1.40691	−	0.229030i
$280$		0			0
$281$	180.072	−	77.6754i	0.640825	−	0.276425i	−0.0507699	−	0.998710i	$-0.516168\pi$
$281$	180.072	−	77.6754i	0.640825	−	0.276425i	0.691595	+	0.722285i	$0.256908\pi$
$282$		0			0
$283$	−41.1308	−	9.74818i	−0.145339	−	0.0344459i	0.157303	−	0.987550i	$-0.449720\pi$
$283$	−41.1308	−	9.74818i	−0.145339	−	0.0344459i	−0.302641	+	0.953105i	$0.597868\pi$
$284$		0			0
$285$	605.335	−	84.6039i	2.12398	−	0.296856i
$286$		0			0
$287$	−74.6574	−	205.120i	−0.260130	−	0.714702i
$288$		0			0
$289$	−0.372917	−	0.135731i	−0.00129037	−	0.000469656i
$290$		0			0
$291$	−49.0076	−	187.834i	−0.168411	−	0.645477i
$292$		0			0
$293$	144.509	+	8.41666i	0.493203	+	0.0287258i	0.302945	−	0.953008i	$-0.402030\pi$
$293$	144.509	+	8.41666i	0.493203	+	0.0287258i	0.190259	+	0.981734i	$0.439067\pi$
$294$		0			0
$295$	176.565	+	187.148i	0.598524	+	0.634398i
$296$		0			0
$297$	−3.27043	+	5.07517i	−0.0110116	+	0.0170881i
$298$		0			0
$299$	−420.633	−	125.929i	−1.40680	−	0.421168i
$300$		0			0
$301$	41.0050	+	26.9694i	0.136229	+	0.0895995i
$302$		0			0
$303$	180.302	+	393.397i	0.595057	+	1.29834i
$304$		0			0
$305$	−545.567	+	96.1981i	−1.78874	+	0.315404i
$306$		0			0
$307$	19.9945	−	113.395i	0.0651288	−	0.369364i	−0.934772	−	0.355249i	$-0.884396\pi$
$307$	19.9945	−	113.395i	0.0651288	−	0.369364i	0.999900	−	0.0141144i	$-0.00449292\pi$
$308$		0			0
$309$	−115.817	+	185.032i	−0.374811	+	0.598808i
$310$		0			0
$311$	−185.156	+	55.4321i	−0.595357	+	0.178238i	−0.570284	−	0.821447i	$-0.693167\pi$
$311$	−185.156	+	55.4321i	−0.595357	+	0.178238i	−0.0250730	+	0.999686i	$0.507982\pi$
$312$		0			0
$313$	260.741	+	30.4762i	0.833038	+	0.0973681i	0.521911	−	0.853000i	$-0.325219\pi$
$313$	260.741	+	30.4762i	0.833038	+	0.0973681i	0.311127	+	0.950368i	$0.399294\pi$
$314$		0			0
$315$	615.253	+	80.1331i	1.95318	+	0.254391i
$316$		0			0
$317$	−66.9169	−	101.742i	−0.211094	−	0.320953i	0.714384	−	0.699754i	$-0.246707\pi$
$317$	−66.9169	−	101.742i	−0.211094	−	0.320953i	−0.925478	+	0.378801i	$0.876337\pi$
$318$		0			0
$319$	1.78518	+	2.39792i	0.00559619	+	0.00751699i
$320$		0			0
$321$	−61.5657	+	401.849i	−0.191793	+	1.25187i
$322$		0			0
$323$			355.848i			1.10170i
$324$		0			0
$325$	−1396.79			−4.29781
$326$		0			0
$327$	−159.637	−	409.667i	−0.488188	−	1.25280i
$328$		0			0
$329$	301.103	−	224.163i	0.915207	−	0.681346i
$330$		0			0
$331$	245.574	−	161.516i	0.741914	−	0.487965i	−0.121417	−	0.992602i	$-0.538744\pi$
$331$	245.574	−	161.516i	0.741914	−	0.487965i	0.863332	+	0.504637i	$0.168374\pi$
$332$		0			0
$333$	238.064	+	372.546i	0.714907	+	1.11876i
$334$		0			0
$335$	−78.7587	+	673.824i	−0.235101	+	2.01141i
$336$		0			0
$337$	−21.2191	−	70.8766i	−0.0629646	−	0.210316i	0.920718	−	0.390228i	$-0.127604\pi$
$337$	−21.2191	−	70.8766i	−0.0629646	−	0.210316i	−0.983683	+	0.179912i	$0.942419\pi$
$338$		0			0
$339$	45.0270	−	23.8973i	0.132823	−	0.0704935i
$340$		0			0
$341$	9.73113	+	1.71586i	0.0285370	+	0.00503185i
$342$		0			0
$343$	58.7873	+	333.399i	0.171392	+	0.972009i
$344$		0			0
$345$	520.589	+	369.649i	1.50895	+	1.07145i
$346$		0			0
$347$	−4.93395	+	7.50170i	−0.0142189	+	0.0216187i	−0.842527	−	0.538654i	$-0.818933\pi$
$347$	−4.93395	+	7.50170i	−0.0142189	+	0.0216187i	0.828308	+	0.560272i	$0.189304\pi$
$348$		0			0
$349$	71.6586	−	239.356i	0.205326	−	0.685835i	−0.791849	−	0.610717i	$-0.790881\pi$
$349$	71.6586	−	239.356i	0.205326	−	0.685835i	0.997175	−	0.0751184i	$-0.0239335\pi$
$350$		0			0
$351$	−89.0908	+	534.430i	−0.253820	+	1.52259i
$352$		0			0
$353$	433.435	−	408.925i	1.22786	−	1.15843i	0.245911	−	0.969292i	$-0.420913\pi$
$353$	433.435	−	408.925i	1.22786	−	1.15843i	0.981951	−	0.189135i	$-0.0605685\pi$
$354$		0			0
$355$	−30.4315	+	522.489i	−0.0857227	+	1.47180i
$356$		0			0
$357$	−95.7850	+	348.291i	−0.268305	+	0.975606i
$358$		0			0
$359$	67.8611	−	186.447i	0.189028	−	0.519351i	−0.808587	−	0.588377i	$-0.799767\pi$
$359$	67.8611	−	186.447i	0.189028	−	0.519351i	0.997615	+	0.0690264i	$0.0219893\pi$
$360$		0			0
$361$	−73.0719	+	26.5960i	−0.202415	+	0.0736731i
$362$		0			0
$363$	286.100	−	223.175i	0.788154	−	0.614807i
$364$		0			0
$365$	173.933	−	733.882i	0.476530	−	2.01064i
$366$		0			0
$367$	−118.085	−	273.753i	−0.321758	−	0.745920i	−0.999939	−	0.0110248i	$-0.996491\pi$
$367$	−118.085	−	273.753i	−0.321758	−	0.745920i	0.678181	−	0.734895i	$-0.262769\pi$
$368$		0			0
$369$	−277.155	−	3.64748i	−0.751098	−	0.00988477i
$370$		0			0
$371$	−175.763	+	10.2370i	−0.473755	+	0.0275931i
$372$		0			0
$373$	116.880	−	270.958i	0.313351	−	0.726429i	−0.686649	−	0.726989i	$-0.740919\pi$
$373$	116.880	−	270.958i	0.313351	−	0.726429i	1.00000		0.000560420i	$0.000178387\pi$
$374$		0			0
$375$	1232.83	+	417.537i	3.28754	+	1.11343i
$376$		0			0
$377$	232.327	+	134.134i	0.616251	+	0.355793i
$378$		0			0
$379$	33.9982	+	58.8866i	0.0897051	+	0.155374i	0.907386	−	0.420297i	$-0.138074\pi$
$379$	33.9982	+	58.8866i	0.0897051	+	0.155374i	−0.817681	+	0.575671i	$0.804741\pi$
$380$		0			0
$381$	506.747	−	307.982i	1.33005	−	0.808352i
$382$		0			0
$383$	−28.1065	−	240.466i	−0.0733851	−	0.627850i	−0.979016	−	0.203783i	$-0.934676\pi$
$383$	−28.1065	−	240.466i	−0.0733851	−	0.627850i	0.905631	−	0.424067i	$-0.139398\pi$
$384$		0			0
$385$	13.7761	+	6.91862i	0.0357821	+	0.0179705i
$386$		0			0
$387$	50.4748	−	36.5547i	0.130426	−	0.0944565i
$388$		0			0
$389$	−281.915	−	209.878i	−0.724718	−	0.539532i	0.170393	−	0.985376i	$-0.445496\pi$
$389$	−281.915	−	209.878i	−0.724718	−	0.539532i	−0.895111	+	0.445844i	$0.852904\pi$
$390$		0			0
$391$	−255.089	+	270.378i	−0.652400	+	0.691504i
$392$		0			0
$393$	−39.8019	+	44.1368i	−0.101277	+	0.112307i
$394$		0			0
$395$	−470.556	+	560.787i	−1.19128	+	1.41971i
$396$		0			0
$397$	−497.642	+	417.571i	−1.25351	+	1.05182i	−0.257164	+	0.966368i	$0.582788\pi$
$397$	−497.642	+	417.571i	−1.25351	+	1.05182i	−0.996343	+	0.0854486i	$0.972768\pi$
$398$		0			0
$399$	−443.939	+	35.8979i	−1.11263	+	0.0899696i
$400$		0			0
$401$	−1.55912	−	3.10446i	−0.00388808	−	0.00774180i	0.891680	−	0.452666i	$-0.149527\pi$
$401$	−1.55912	−	3.10446i	−0.00388808	−	0.00774180i	−0.895568	+	0.444924i	$0.853231\pi$
$402$		0			0
$403$	862.820	−	204.492i	2.14099	−	0.507424i
$404$		0			0
$405$	371.994	−	694.504i	0.918504	−	1.71482i
$406$		0			0
$407$	2.53329	+	10.6888i	0.00622430	+	0.0262624i
$408$		0			0
$409$	290.223	−	145.755i	0.709591	−	0.356370i	−0.0571155	−	0.998368i	$-0.518190\pi$
$409$	290.223	−	145.755i	0.709591	−	0.356370i	0.766707	+	0.641997i	$0.221894\pi$
$410$		0			0
$411$	−575.350	+	397.248i	−1.39988	+	0.966541i
$412$		0			0
$413$	−120.514	−	143.623i	−0.291800	−	0.347754i
$414$		0			0
$415$	831.690	+	697.871i	2.00407	+	1.68162i
$416$		0			0
$417$	15.1957	−	4.92457i	0.0364404	−	0.0118095i
$418$		0			0
$419$	−469.091	−	442.564i	−1.11955	−	1.05624i	−0.997972	−	0.0636571i	$-0.979724\pi$
$419$	−469.091	−	442.564i	−1.11955	−	1.05624i	−0.121576	−	0.992582i	$-0.538795\pi$
$420$		0			0
$421$	10.0386	−	13.4842i	0.0238446	−	0.0320289i	−0.790041	−	0.613054i	$-0.789941\pi$
$421$	10.0386	−	13.4842i	0.0238446	−	0.0320289i	0.813886	+	0.581025i	$0.197348\pi$
$422$		0			0
$423$	−130.688	−	458.400i	−0.308956	−	1.08369i
$424$		0			0
$425$	−530.706	+	1056.72i	−1.24872	+	2.48641i
$426$		0			0
$427$	400.952	−	46.8645i	0.938997	−	0.109753i
$428$		0			0
$429$	−6.46681	+	11.8068i	−0.0150741	+	0.0275217i
$430$		0			0
$431$	−270.027	+	155.900i	−0.626514	+	0.361718i	−0.779401	−	0.626526i	$-0.784476\pi$
$431$	−270.027	+	155.900i	−0.626514	+	0.361718i	0.152887	+	0.988244i	$0.451143\pi$
$432$		0			0
$433$	67.0785	−	116.183i	0.154916	−	0.268322i	−0.778113	−	0.628125i	$-0.783823\pi$
$433$	67.0785	−	116.183i	0.154916	−	0.268322i	0.933028	+	0.359803i	$0.117156\pi$
$434$		0			0
$435$	−257.412	−	293.112i	−0.591751	−	0.673821i
$436$		0			0
$437$	−420.845	−	181.535i	−0.963033	−	0.415412i
$438$		0			0
$439$	22.8851	+	392.921i	0.0521300	+	0.895037i	0.918447	+	0.395543i	$0.129444\pi$
$439$	22.8851	+	392.921i	0.0521300	+	0.895037i	−0.866317	+	0.499494i	$0.833519\pi$
$440$		0			0
$441$	−10.9194	−	2.07391i	−0.0247607	−	0.00470275i
$442$		0			0
$443$	617.609	−	266.410i	1.39415	−	0.601378i	0.439266	−	0.898357i	$-0.355238\pi$
$443$	617.609	−	266.410i	1.39415	−	0.601378i	0.954884	+	0.296979i	$0.0959791\pi$
$444$		0			0
$445$	−1016.43	−	240.899i	−2.28412	−	0.541345i
$446$		0			0
$447$	226.372	−	559.064i	0.506426	−	1.25070i
$448$		0			0
$449$	204.853	+	562.829i	0.456243	+	1.25352i	0.928262	+	0.371928i	$0.121303\pi$
$449$	204.853	+	562.829i	0.456243	+	1.25352i	−0.472019	+	0.881588i	$0.656475\pi$
$450$		0			0
$451$	−6.47154	−	2.35545i	−0.0143493	−	0.00522272i
$452$		0			0
$453$	253.428	−	250.115i	0.559443	−	0.552129i
$454$		0			0
$455$	1381.04	+	80.4367i	3.03526	+	0.176784i
$456$		0			0
$457$	204.008	+	216.236i	0.446408	+	0.473165i	0.911027	−	0.412346i	$-0.135290\pi$
$457$	204.008	+	216.236i	0.446408	+	0.473165i	−0.464620	+	0.885510i	$0.653809\pi$
$458$		0			0
$459$	370.466	+	270.456i	0.807116	+	0.589228i
$460$		0			0
$461$	516.453	+	154.616i	1.12029	+	0.335392i	0.792811	−	0.609467i	$-0.208617\pi$
$461$	516.453	+	154.616i	1.12029	+	0.335392i	0.327477	+	0.944859i	$0.393802\pi$
$462$		0			0
$463$	434.060	+	285.485i	0.937494	+	0.616599i	0.923622	−	0.383304i	$-0.125214\pi$
$463$	434.060	+	285.485i	0.937494	+	0.616599i	0.0138717	+	0.999904i	$0.495584\pi$
$464$		0			0
$465$	−1283.73	−	120.829i	−2.76072	−	0.259847i
$466$		0			0
$467$	630.053	−	111.095i	1.34915	−	0.237891i	0.548061	−	0.836438i	$-0.315366\pi$
$467$	630.053	−	111.095i	1.34915	−	0.237891i	0.801088	+	0.598547i	$0.204255\pi$
$468$		0			0
$469$	85.8430	−	486.840i	0.183034	−	1.03804i
$470$		0			0
$471$	−319.028	−	11.3841i	−0.677342	−	0.0241701i
$472$		0			0
$473$	1.48340	−	0.444101i	0.00313615	−	0.000938903i
$474$		0			0
$475$	−1448.17	−	169.267i	−3.04878	−	0.356351i
$476$		0			0
$477$	−66.9318	+	213.310i	−0.140318	+	0.447191i
$478$		0			0
$479$	−190.208	−	289.197i	−0.397094	−	0.603752i	0.580498	−	0.814262i	$-0.302858\pi$
$479$	−190.208	−	289.197i	−0.397094	−	0.603752i	−0.977592	+	0.210510i	$0.932488\pi$
$480$		0			0
$481$	588.655	+	790.701i	1.22382	+	1.64387i
$482$		0			0
$483$	−363.044	−	290.961i	−0.751644	−	0.602403i
$484$		0			0
$485$			629.382i			1.29769i
$486$		0			0
$487$	−918.147			−1.88531			−0.942656	−	0.333766i	$-0.891680\pi$
$487$	−918.147			−1.88531			−0.942656	+	0.333766i	$0.891680\pi$
$488$		0			0
$489$	−238.347	+	297.395i	−0.487416	+	0.608170i
$490$		0			0
$491$	173.412	−	129.100i	0.353181	−	0.262934i	−0.405917	−	0.913910i	$-0.633048\pi$
$491$	173.412	−	129.100i	0.353181	−	0.262934i	0.759098	+	0.650976i	$0.225640\pi$
$492$		0			0
$493$	189.749	−	124.800i	0.384887	−	0.253144i
$494$		0			0
$495$	14.4141	−	13.2448i	0.0291193	−	0.0267572i
$496$		0			0
$497$	44.2752	−	378.799i	0.0890849	−	0.762170i
$498$		0			0
$499$	249.130	+	832.151i	0.499258	+	1.66764i	0.721317	+	0.692605i	$0.243537\pi$
$499$	249.130	+	832.151i	0.499258	+	1.66764i	−0.222059	+	0.975033i	$0.571278\pi$
$500$		0			0
$501$	−13.4053	+	375.669i	−0.0267570	+	0.749838i
$502$		0			0
$503$	−175.584	−	30.9602i	−0.349073	−	0.0615510i	−0.00363740	−	0.999993i	$-0.501158\pi$
$503$	−175.584	−	30.9602i	−0.349073	−	0.0615510i	−0.345436	+	0.938442i	$0.612269\pi$
$504$		0			0
$505$	−243.638	−	1381.74i	−0.482451	−	2.73611i
$506$		0			0
$507$	−65.6929	+	697.949i	−0.129572	+	1.37662i
$508$		0			0
$509$	−72.3197	+	109.957i	−0.142082	+	0.216025i	−0.899517	−	0.436885i	$-0.856082\pi$
$509$	−72.3197	+	109.957i	−0.142082	+	0.216025i	0.757435	+	0.652910i	$0.226452\pi$
$510$		0			0
$511$	−157.623	+	526.498i	−0.308460	+	1.03033i
$512$		0			0
$513$	−157.132	+	543.292i	−0.306300	+	1.05905i
$514$		0			0
$515$	514.790	−	485.679i	0.999591	−	0.943066i
$516$		0			0
$517$	0.688630	−	11.8233i	0.00133197	−	0.0228691i
$518$		0			0
$519$	228.578	+	231.606i	0.440421	+	0.446255i
$520$		0			0
$521$	5.11890	−	14.0641i	0.00982514	−	0.0269943i	−0.934683	−	0.355482i	$-0.884317\pi$
$521$	5.11890	−	14.0641i	0.00982514	−	0.0269943i	0.944508	+	0.328488i	$0.106539\pi$
$522$		0			0
$523$	−106.983	+	38.9386i	−0.204556	+	0.0744524i	−0.442266	−	0.896884i	$-0.645825\pi$
$523$	−106.983	+	38.9386i	−0.204556	+	0.0744524i	0.237710	+	0.971336i	$0.423603\pi$
$524$		0			0
$525$	−1371.85	−	555.481i	−2.61305	−	1.05806i
$526$		0			0
$527$	173.120	−	730.452i	0.328502	−	1.38606i
$528$		0			0
$529$	19.8951	+	46.1220i	0.0376089	+	0.0871872i
$530$		0			0
$531$	−224.766	+	78.4744i	−0.423289	+	0.147786i
$532$		0			0
$533$	−616.967	+	35.9342i	−1.15754	+	0.0674188i
$534$		0			0
$535$	522.063	−	1210.28i	0.975819	−	2.26220i
$536$		0			0
$537$	398.459	−	349.927i	0.742009	−	0.651634i
$538$		0			0
$539$	−0.239159	−	0.138079i	−0.000443710	−	0.000256176i
$540$		0			0
$541$	188.006	+	325.636i	0.347516	+	0.601915i	0.985808	−	0.167879i	$-0.0536919\pi$
$541$	188.006	+	325.636i	0.347516	+	0.601915i	−0.638292	+	0.769795i	$0.720359\pi$
$542$		0			0
$543$	237.501	+	130.083i	0.437386	+	0.239564i
$544$		0			0
$545$	165.491	+	1415.86i	0.303653	+	2.59792i
$546$		0			0
$547$	319.183	+	160.300i	0.583515	+	0.293052i	0.715964	−	0.698137i	$-0.245988\pi$
$547$	319.183	+	160.300i	0.583515	+	0.293052i	−0.132448	+	0.991190i	$0.542284\pi$
$548$		0			0
$549$	124.767	−	497.183i	0.227262	−	0.905616i
$550$		0			0
$551$	224.618	+	167.222i	0.407656	+	0.303488i
$552$		0			0
$553$	366.069	−	388.010i	0.661969	−	0.701646i
$554$		0			0
$555$	−441.913	−	1363.60i	−0.796240	−	2.45694i
$556$		0			0
$557$	11.5450	−	13.7588i	0.0207271	−	0.0247016i	−0.755581	−	0.655055i	$-0.772646\pi$
$557$	11.5450	−	13.7588i	0.0207271	−	0.0247016i	0.776308	+	0.630353i	$0.217090\pi$
$558$		0			0
$559$	106.445	−	89.3183i	0.190421	−	0.159782i
$560$		0			0
$561$	6.47525	+	9.37836i	0.0115423	+	0.0167172i
$562$		0			0
$563$	354.677	+	706.219i	0.629976	+	1.25439i	0.951548	+	0.307501i	$0.0994927\pi$
$563$	354.677	+	706.219i	0.629976	+	1.25439i	−0.321571	+	0.946885i	$0.604211\pi$
$564$		0			0
$565$	−160.818	+	38.1146i	−0.284634	+	0.0674595i
$566$		0			0
$567$	−300.035	+	489.459i	−0.529162	+	0.863244i
$568$		0			0
$569$	21.8659	+	92.2596i	0.0384287	+	0.162143i	0.988876	−	0.148742i	$-0.0475225\pi$
$569$	21.8659	+	92.2596i	0.0384287	+	0.162143i	−0.950447	+	0.310886i	$0.899374\pi$
$570$		0			0
$571$	−894.561	+	449.265i	−1.56666	+	0.786804i	−0.999327	−	0.0366865i	$-0.988320\pi$
$571$	−894.561	+	449.265i	−1.56666	+	0.786804i	−0.567330	+	0.823491i	$0.692023\pi$
$572$		0			0
$573$	3.20898	+	39.6846i	0.00560032	+	0.0692576i
$574$		0			0
$575$	−978.999	−	1166.73i	−1.70261	−	2.02909i
$576$		0			0
$577$	278.455	+	233.651i	0.482590	+	0.404941i	0.851362	−	0.524579i	$-0.175777\pi$
$577$	278.455	+	233.651i	0.482590	+	0.404941i	−0.368772	+	0.929520i	$0.620222\pi$
$578$		0			0
$579$	−416.137	−	375.266i	−0.718716	−	0.648127i
$580$		0			0
$581$	−575.450	−	542.909i	−0.990447	−	0.934438i
$582$		0			0
$583$	−3.31706	+	4.45559i	−0.00568964	+	0.00764251i
$584$		0			0
$585$	716.934	−	1603.68i	1.22553	−	2.74133i
$586$		0			0
$587$	−115.552	+	230.083i	−0.196852	+	0.391965i	−0.970303	−	0.241891i	$-0.922232\pi$
$587$	−115.552	+	230.083i	−0.196852	+	0.391965i	0.773451	+	0.633856i	$0.218529\pi$
$588$		0			0
$589$	919.340	−	107.455i	1.56085	−	0.182437i
$590$		0			0
$591$	−66.8758	−	110.036i	−0.113157	−	0.186186i
$592$		0			0
$593$	895.273	−	516.886i	1.50974	−	0.871646i	0.509800	−	0.860293i	$-0.329719\pi$
$593$	895.273	−	516.886i	1.50974	−	0.871646i	0.999936	−	0.0113533i	$-0.00361395\pi$
$594$		0			0
$595$	585.578	−	1014.25i	0.984164	−	1.70462i
$596$		0			0
$597$	−194.203	+	573.407i	−0.325298	+	0.960481i
$598$		0			0
$599$	277.319	+	119.624i	0.462970	+	0.199706i	0.614772	−	0.788705i	$-0.289248\pi$
$599$	277.319	+	119.624i	0.462970	+	0.199706i	−0.151801	+	0.988411i	$0.548507\pi$
$600$		0			0
$601$	−32.1314	−	551.675i	−0.0534632	−	0.917928i	−0.913282	−	0.407328i	$-0.866460\pi$
$601$	−32.1314	−	551.675i	−0.0534632	−	0.917928i	0.859819	−	0.510600i	$-0.170577\pi$
$602$		0			0
$603$	−539.454	−	320.993i	−0.894618	−	0.532326i
$604$		0			0
$605$	−1080.22	+	465.961i	−1.78549	+	0.770183i
$606$		0			0
$607$	323.685	+	76.7148i	0.533254	+	0.126384i	0.488416	−	0.872611i	$-0.337575\pi$
$607$	323.685	+	76.7148i	0.533254	+	0.126384i	0.0448379	+	0.998994i	$0.485723\pi$
$608$		0			0
$609$	174.837	+	224.132i	0.287088	+	0.368034i
$610$		0			0
$611$	−363.498	−	998.702i	−0.594922	−	1.63454i
$612$		0			0
$613$	−13.7463	−	5.00323i	−0.0224246	−	0.00816188i	0.330784	−	0.943707i	$-0.392687\pi$
$613$	−13.7463	−	5.00323i	−0.0224246	−	0.00816188i	−0.353208	+	0.935545i	$0.614909\pi$
$614$		0			0
$615$	866.500	+	238.300i	1.40894	+	0.387479i
$616$		0			0
$617$	−414.972	−	24.1694i	−0.672564	−	0.0391724i	−0.281535	−	0.959551i	$-0.590844\pi$
$617$	−414.972	−	24.1694i	−0.672564	−	0.0391724i	−0.391029	+	0.920378i	$0.627881\pi$
$618$		0			0
$619$	−287.903	−	305.159i	−0.465109	−	0.492987i	0.451780	−	0.892130i	$-0.350789\pi$
$619$	−287.903	−	305.159i	−0.465109	−	0.492987i	−0.916889	+	0.399143i	$0.869308\pi$
$620$		0			0
$621$	−508.848	+	300.161i	−0.819401	+	0.483352i
$622$		0			0
$623$	729.202	+	218.309i	1.17047	+	0.350415i
$624$		0			0
$625$	−2071.95	−	1362.74i	−3.31512	−	2.18039i
$626$		0			0
$627$	−8.13548	+	11.4575i	−0.0129752	+	0.0182735i
$628$		0			0
$629$	821.853	−	144.915i	1.30660	−	0.230389i
$630$		0			0
$631$	27.6743	−	156.949i	0.0438578	−	0.248730i	−0.954995	−	0.296623i	$-0.904140\pi$
$631$	27.6743	−	156.949i	0.0438578	−	0.248730i	0.998852	+	0.0478930i	$0.0152506\pi$
$632$		0			0
$633$	154.615	+	291.324i	0.244258	+	0.460228i
$634$		0			0
$635$	−1841.85	+	551.413i	−2.90055	+	0.868366i
$636$		0			0
$637$	−24.6142	−	2.87699i	−0.0386408	−	0.00451646i
$638$		0			0
$639$	−429.869	−	223.019i	−0.672721	−	0.349013i
$640$		0			0
$641$	−265.484	−	403.649i	−0.414172	−	0.629718i	0.566803	−	0.823853i	$-0.308180\pi$
$641$	−265.484	−	403.649i	−0.414172	−	0.629718i	−0.980975	+	0.194136i	$0.937810\pi$
$642$		0			0
$643$	−259.780	−	348.945i	−0.404012	−	0.542683i	0.552829	−	0.833295i	$-0.313548\pi$
$643$	−259.780	−	348.945i	−0.404012	−	0.542683i	−0.956841	+	0.290612i	$0.906141\pi$
$644$		0			0
$645$	−188.269	+	73.3639i	−0.291890	+	0.113743i
$646$		0			0
$647$			1108.99i			1.71405i	0.515275	+	0.857025i	$0.327690\pi$
$647$			1108.99i			1.71405i	−0.515275	+	0.857025i	$0.672310\pi$
$648$		0			0
$649$	−5.91520			−0.00911432
$650$		0			0
$651$	928.741	+	142.289i	1.42664	+	0.218569i
$652$		0			0
$653$	−376.255	+	280.112i	−0.576195	+	0.428961i	−0.845409	−	0.534119i	$-0.820643\pi$
$653$	−376.255	+	280.112i	−0.576195	+	0.428961i	0.269214	+	0.963080i	$0.413236\pi$
$654$		0			0
$655$	160.992	−	105.886i	0.245790	−	0.161658i
$656$		0			0
$657$	554.246	+	424.070i	0.843601	+	0.645464i
$658$		0			0
$659$	−0.732907	+	6.27042i	−0.00111215	+	0.00951506i	−0.993783	−	0.111334i	$-0.964488\pi$
$659$	−0.732907	+	6.27042i	−0.00111215	+	0.00951506i	0.992671	+	0.120849i	$0.0385617\pi$
$660$		0			0
$661$	−311.588	−	1040.78i	−0.471388	−	1.57455i	−0.781537	−	0.623859i	$-0.785564\pi$
$661$	−311.588	−	1040.78i	−0.471388	−	1.57455i	0.310149	−	0.950688i	$-0.399621\pi$
$662$		0			0
$663$	866.890	+	542.612i	1.30753	+	0.818420i
$664$		0			0
$665$	1422.10	+	250.754i	2.13849	+	0.377074i
$666$		0			0
$667$	50.7953	+	288.074i	0.0761549	+	0.431896i
$668$		0			0
$669$	670.823	−	307.452i	1.00272	−	0.459570i
$670$		0			0
$671$	6.99864	−	10.6409i	0.0104302	−	0.0158583i
$672$		0			0
$673$	305.461	−	1020.31i	0.453879	−	1.51606i	−0.358835	−	0.933401i	$-0.616826\pi$
$673$	305.461	−	1020.31i	0.453879	−	1.51606i	0.812715	−	0.582662i	$-0.197989\pi$
$674$		0			0
$675$	−1276.87	+	1379.01i	−1.89166	+	2.04298i
$676$		0			0
$677$	54.6182	−	51.5296i	0.0806768	−	0.0761146i	−0.644847	−	0.764312i	$-0.723079\pi$
$677$	54.6182	−	51.5296i	0.0806768	−	0.0761146i	0.725524	+	0.688197i	$0.241598\pi$
$678$		0			0
$679$	26.6666	−	457.847i	0.0392733	−	0.674296i
$680$		0			0
$681$	−1107.97	+	289.079i	−1.62697	+	0.424492i
$682$		0			0
$683$	244.956	−	673.012i	0.358648	−	0.985376i	−0.620852	−	0.783928i	$-0.713213\pi$
$683$	244.956	−	673.012i	0.358648	−	0.985376i	0.979499	−	0.201448i	$-0.0645647\pi$
$684$		0			0
$685$	2130.13	−	775.304i	3.10968	−	1.13183i
$686$		0			0
$687$	−142.560	−	1020.01i	−0.207511	−	1.48472i
$688$		0			0
$689$	−114.955	+	485.034i	−0.166843	+	0.703967i
$690$		0			0
$691$	−388.694	−	901.094i	−0.562509	−	1.30404i	−0.927775	−	0.373140i	$-0.878281\pi$
$691$	−388.694	−	901.094i	−0.562509	−	1.30404i	0.365266	−	0.930903i	$-0.380978\pi$
$692$		0			0
$693$	−11.0468	+	9.02430i	−0.0159405	+	0.0130221i
$694$		0			0
$695$	−51.7024	+	3.01132i	−0.0743919	+	0.00433283i
$696$		0			0
$697$	−207.229	+	480.412i	−0.297316	+	0.689257i
$698$		0			0
$699$	−231.040	−	1157.33i	−0.330530	−	1.65569i
$700$		0			0
$701$	−298.741	−	172.478i	−0.426163	−	0.246046i	0.271547	−	0.962425i	$-0.412465\pi$
$701$	−298.741	−	172.478i	−0.426163	−	0.246046i	−0.697711	+	0.716379i	$0.745798\pi$
$702$		0			0
$703$	514.490	+	891.122i	0.731849	+	1.26760i
$704$		0			0
$705$	34.7834	+	1545.05i	0.0493382	+	2.19156i
$706$		0			0
$707$	118.692	+	1015.48i	0.167881	+	1.43632i
$708$		0			0
$709$	1193.71	+	599.502i	1.68365	+	0.845559i	0.992416	+	0.122926i	$0.0392277\pi$
$709$	1193.71	+	599.502i	1.68365	+	0.845559i	0.691231	+	0.722634i	$0.257069\pi$
$710$		0			0
$711$	−296.011	−	609.267i	−0.416330	−	0.856915i
$712$		0			0
$713$	775.555	+	577.380i	1.08774	+	0.809789i
$714$		0			0
$715$	29.9516	−	31.7469i	0.0418904	−	0.0444012i
$716$		0			0
$717$	−301.603	−	64.3480i	−0.420646	−	0.0897462i
$718$		0			0
$719$	−211.094	+	251.572i	−0.293594	+	0.349892i	−0.892597	−	0.450855i	$-0.851119\pi$
$719$	−211.094	+	251.572i	−0.293594	+	0.349892i	0.599003	+	0.800747i	$0.295564\pi$
$720$		0			0
$721$	−395.065	+	331.499i	−0.547940	+	0.459776i
$722$		0			0
$723$	−288.715	+	608.663i	−0.399329	+	0.841857i
$724$		0			0
$725$	417.631	+	831.573i	0.576043	+	1.14700i
$726$		0			0
$727$	−409.726	+	97.1068i	−0.563584	+	0.133572i	−0.502526	−	0.864562i	$-0.667596\pi$
$727$	−409.726	+	97.1068i	−0.563584	+	0.133572i	−0.0610585	+	0.998134i	$0.519448\pi$
$728$		0			0
$729$	446.186	+	576.506i	0.612052	+	0.790818i
$730$		0			0
$731$	−27.1290	−	114.466i	−0.0371122	−	0.156589i
$732$		0			0
$733$	−251.183	+	126.149i	−0.342677	+	0.172099i	−0.611811	−	0.791004i	$-0.709559\pi$
$733$	−251.183	+	126.149i	−0.342677	+	0.172099i	0.269134	+	0.963103i	$0.413263\pi$
$734$		0			0
$735$	32.5587	+	15.4440i	0.0442976	+	0.0210122i
$736$		0			0
$737$	−10.0254	−	11.9478i	−0.0136030	−	0.0162114i
$738$		0			0
$739$	255.809	+	214.649i	0.346155	+	0.290459i	0.799244	−	0.601007i	$-0.205233\pi$
$739$	255.809	+	214.649i	0.346155	+	0.290459i	−0.453089	+	0.891465i	$0.649678\pi$
$740$		0			0
$741$	−263.116	+	1233.24i	−0.355082	+	1.66429i
$742$		0			0
$743$	877.768	+	828.131i	1.18138	+	1.11458i	0.991137	+	0.132841i	$0.0424099\pi$
$743$	877.768	+	828.131i	1.18138	+	1.11458i	0.190246	+	0.981737i	$0.439072\pi$
$744$		0			0
$745$	−1167.78	+	1568.59i	−1.56748	+	2.10550i
$746$		0			0
$747$	−903.590	+	439.007i	−1.20963	+	0.587693i
$748$		0			0
$749$	−431.057	+	858.305i	−0.575510	+	1.14593i
$750$		0			0
$751$	63.6304	−	7.43733i	0.0847275	−	0.00990323i	−0.0736235	−	0.997286i	$-0.523456\pi$
$751$	63.6304	−	7.43733i	0.0847275	−	0.00990323i	0.158351	+	0.987383i	$0.449382\pi$
$752$		0			0
$753$	289.433	−	6.51593i	0.384373	−	0.00865330i
$754$		0			0
$755$	−999.772	+	577.219i	−1.32420	+	0.764528i
$756$		0			0
$757$	−77.6595	+	134.510i	−0.102589	+	0.177689i	−0.912750	−	0.408518i	$-0.866046\pi$
$757$	−77.6595	+	134.510i	−0.102589	+	0.177689i	0.810162	+	0.586206i	$0.199379\pi$
$758$		0			0
$759$	−14.3947	+	2.87364i	−0.0189653	+	0.00378609i
$760$		0			0
$761$	30.1167	+	12.9911i	0.0395751	+	0.0170710i	0.415775	−	0.909467i	$-0.363510\pi$
$761$	30.1167	+	12.9911i	0.0395751	+	0.0170710i	−0.376200	+	0.926538i	$0.622770\pi$
$762$		0			0
$763$	−60.3978	−	1036.99i	−0.0791583	−	1.35910i
$764$		0			0
$765$	−940.846	−	1151.70i	−1.22986	−	1.50549i
$766$		0			0
$767$	−487.404	+	210.246i	−0.635468	+	0.274114i
$768$		0			0
$769$	−44.2413	−	10.4854i	−0.0575309	−	0.0136351i	0.201750	−	0.979437i	$-0.435337\pi$
$769$	−44.2413	−	10.4854i	−0.0575309	−	0.0136351i	−0.259281	+	0.965802i	$0.583485\pi$
$770$		0			0
$771$	−476.067	+	66.5369i	−0.617467	+	0.0862995i
$772$		0			0
$773$	272.957	+	749.942i	0.353113	+	0.970171i	0.981364	+	0.192159i	$0.0615491\pi$
$773$	272.957	+	749.942i	0.353113	+	0.970171i	−0.628251	+	0.778011i	$0.716229\pi$
$774$		0			0
$775$	2890.32	+	1051.99i	3.72944	+	1.35741i
$776$		0			0
$777$	263.697	+	1010.69i	0.339379	+	1.30075i
$778$		0			0
$779$	−644.017	−	37.5097i	−0.826722	−	0.0481511i
$780$		0			0
$781$	−8.25719	−	8.75211i	−0.0105726	−	0.0112063i
$782$		0			0
$783$	344.809	−	106.752i	0.440369	−	0.136337i
$784$		0			0
$785$	991.529	+	296.844i	1.26309	+	0.378146i
$786$		0			0
$787$	853.273	+	561.207i	1.08421	+	0.713096i	0.960236	−	0.279189i	$-0.0900657\pi$
$787$	853.273	+	561.207i	1.08421	+	0.713096i	0.123974	+	0.992285i	$0.460436\pi$
$788$		0			0
$789$	−546.024	−	1191.36i	−0.692045	−	1.50996i
$790$		0			0
$791$	118.603	−	20.9129i	0.149941	−	0.0264386i
$792$		0			0
$793$	198.465	−	1125.55i	0.250271	−	1.41936i
$794$		0			0
$795$	384.575	−	614.407i	0.483742	−	0.772839i
$796$		0			0
$797$	683.504	−	204.628i	0.857596	−	0.256747i	0.172329	−	0.985039i	$-0.444871\pi$
$797$	683.504	−	204.628i	0.857596	−	0.256747i	0.685267	+	0.728292i	$0.259686\pi$
$798$		0			0
$799$	−893.666	−	104.455i	−1.11848	−	0.130732i
$800$		0			0
$801$	587.339	−	767.634i	0.733257	−	0.958345i
$802$		0			0
$803$	9.52820	+	14.4869i	0.0118658	+	0.0180410i
$804$		0			0
$805$	900.777	+	1209.95i	1.11898	+	1.50305i
$806$		0			0
$807$	−166.468	+	1086.57i	−0.206281	+	1.34643i
$808$		0			0
$809$		−	725.872i		−	0.897245i	−0.893721	−	0.448623i	$-0.851915\pi$
$809$		−	725.872i		−	0.897245i	0.893721	−	0.448623i	$-0.148085\pi$
$810$		0			0
$811$	−1619.02			−1.99633			−0.998166	−	0.0605415i	$-0.980717\pi$
$811$	−1619.02			−1.99633			−0.998166	+	0.0605415i	$0.980717\pi$
$812$		0			0
$813$	−524.960	−	1347.17i	−0.645708	−	1.65704i
$814$		0			0
$815$	991.160	−	737.891i	1.21615	−	0.905388i
$816$		0			0
$817$	121.185	−	79.7045i	0.148329	−	0.0975576i
$818$		0			0
$819$	−589.485	+	1136.23i	−0.719762	+	1.38734i
$820$		0			0
$821$	100.775	−	862.183i	0.122746	−	1.05016i	−0.781724	−	0.623625i	$-0.785659\pi$
$821$	100.775	−	862.183i	0.122746	−	1.05016i	0.904470	−	0.426537i	$-0.140267\pi$
$822$		0			0
$823$	−121.780	−	406.773i	−0.147971	−	0.494257i	0.851580	−	0.524225i	$-0.175645\pi$
$823$	−121.780	−	406.773i	−0.147971	−	0.494257i	−0.999551	+	0.0299677i	$0.990460\pi$
$824$		0			0
$825$	−41.2465	+	21.8908i	−0.0499957	+	0.0265344i
$826$		0			0
$827$	1022.26	+	180.252i	1.23610	+	0.217958i	0.753245	−	0.657740i	$-0.228487\pi$
$827$	1022.26	+	180.252i	1.23610	+	0.217958i	0.482859	+	0.875698i	$0.339598\pi$
$828$		0			0
$829$	156.132	+	885.467i	0.188337	+	1.06811i	0.921592	+	0.388160i	$0.126889\pi$
$829$	156.132	+	885.467i	0.188337	+	1.06811i	−0.733255	+	0.679954i	$0.762000\pi$
$830$		0			0
$831$	392.721	+	278.855i	0.472588	+	0.335565i
$832$		0			0
$833$	−11.5287	+	17.5285i	−0.0138399	+	0.0210426i
$834$		0			0
$835$	349.547	−	1167.57i	0.418619	−	1.39828i
$836$		0			0
$837$	586.857	−	1038.78i	0.701144	−	1.24107i
$838$		0			0
$839$	157.714	−	148.796i	0.187979	−	0.177349i	−0.586499	−	0.809950i	$-0.699494\pi$
$839$	157.714	−	148.796i	0.187979	−	0.177349i	0.774478	+	0.632601i	$0.218013\pi$
$840$		0			0
$841$	−38.5080	+	661.157i	−0.0457883	+	0.786156i
$842$		0			0
$843$	156.007	−	567.271i	0.185062	−	0.672919i
$844$		0			0
$845$	777.374	−	2135.82i	0.919970	−	2.52760i
$846$		0			0
$847$	805.554	−	293.198i	0.951067	−	0.346160i
$848$		0			0
$849$	−99.9876	+	77.9963i	−0.117771	+	0.0918684i
$850$		0			0
$851$	−247.882	+	1045.90i	−0.291283	+	1.22902i
$852$		0			0
$853$	135.213	+	313.459i	0.158514	+	0.367478i	0.978902	−	0.204330i	$-0.0655016\pi$
$853$	135.213	+	313.459i	0.158514	+	0.367478i	−0.820388	+	0.571808i	$0.806242\pi$
$854$		0			0
$855$	937.645	−	1575.79i	1.09666	−	1.84303i
$856$		0			0
$857$	−41.5072	+	2.41752i	−0.0484331	+	0.00282091i	−0.0823443	−	0.996604i	$-0.526241\pi$
$857$	−41.5072	+	2.41752i	−0.0484331	+	0.00282091i	0.0339112	+	0.999425i	$0.489204\pi$
$858$		0			0
$859$	−609.251	+	1412.40i	−0.709256	+	1.64424i	0.0543199	+	0.998524i	$0.482701\pi$
$859$	−609.251	+	1412.40i	−0.709256	+	1.64424i	−0.763576	+	0.645718i	$0.776558\pi$
$860$		0			0
$861$	−620.244	−	210.066i	−0.720376	−	0.243979i
$862$		0			0
$863$	−663.192	−	382.894i	−0.768473	−	0.443678i	0.0638568	−	0.997959i	$-0.479660\pi$
$863$	−663.192	−	382.894i	−0.768473	−	0.443678i	−0.832330	+	0.554281i	$0.812993\pi$
$864$		0			0
$865$	−527.517	−	913.686i	−0.609846	−	1.05628i
$866$		0			0
$867$	−1.01739	+	0.618329i	−0.00117346	+	0.000713183i
$868$		0			0
$869$	−1.95385	−	16.7163i	−0.00224839	−	0.0192362i
$870$		0			0
$871$	−1250.75	−	628.149i	−1.43599	−	0.721181i
$872$		0			0
$873$	−531.656	−	237.680i	−0.608998	−	0.272256i
$874$		0			0
$875$	2466.64	+	1836.35i	2.81902	+	2.09868i
$876$		0			0
$877$	−167.210	+	177.233i	−0.190662	+	0.202090i	−0.815652	−	0.578543i	$-0.803622\pi$
$877$	−167.210	+	177.233i	−0.190662	+	0.202090i	0.624990	+	0.780633i	$0.285103\pi$
$878$		0			0
$879$	290.823	−	322.497i	0.330856	−	0.366891i
$880$		0			0
$881$	−374.665	+	446.509i	−0.425273	+	0.506820i	−0.935552	−	0.353188i	$-0.885097\pi$
$881$	−374.665	+	446.509i	−0.425273	+	0.506820i	0.510280	+	0.860009i	$0.329542\pi$
$882$		0			0
$883$	126.862	−	106.450i	0.143671	−	0.120555i	−0.568119	−	0.822946i	$-0.692329\pi$
$883$	126.862	−	106.450i	0.143671	−	0.120555i	0.711791	+	0.702391i	$0.247884\pi$
$884$		0			0
$885$	769.365	−	62.2126i	0.869339	−	0.0702967i
$886$		0			0
$887$	−91.4591	−	182.110i	−0.103111	−	0.205310i	0.836162	−	0.548483i	$-0.184795\pi$
$887$	−91.4591	−	182.110i	−0.103111	−	0.205310i	−0.939272	+	0.343173i	$0.888498\pi$
$888$		0			0
$889$	1363.22	−	323.090i	1.53344	−	0.363431i
$890$		0			0
$891$	5.74492	+	17.1777i	0.00644772	+	0.0192791i
$892$		0			0
$893$	−255.844	−	1079.49i	−0.286499	−	1.20883i
$894$		0			0
$895$	−1536.46	+	771.638i	−1.71671	+	0.862165i
$896$		0			0
$897$	−1083.96	+	748.419i	−1.20843	+	0.834358i
$898$		0			0
$899$	−379.722	−	452.535i	−0.422383	−	0.503376i
$900$		0			0
$901$	323.269	+	271.255i	0.358790	+	0.301060i
$902$		0			0
$903$	140.066	−	45.3922i	0.155112	−	0.0502682i
$904$		0			0
$905$	−638.606	−	602.494i	−0.705642	−	0.665739i
$906$		0			0
$907$	851.074	−	1143.19i	0.938339	−	1.26041i	−0.0270604	−	0.999634i	$-0.508615\pi$
$907$	851.074	−	1143.19i	0.938339	−	1.26041i	0.965400	−	0.260775i	$-0.0839780\pi$
$908$		0			0
$909$	1259.20	+	315.993i	1.38526	+	0.347627i
$910$		0			0
$911$	327.664	−	652.433i	0.359675	−	0.716172i	−0.638914	−	0.769279i	$-0.720616\pi$
$911$	327.664	−	652.433i	0.359675	−	0.716172i	0.998589	+	0.0531061i	$0.0169122\pi$
$912$		0			0
$913$	−24.7916	+	2.89772i	−0.0271540	+	0.00317384i
$914$		0			0
$915$	−798.370	+	1457.63i	−0.872535	+	1.59304i
$916$		0			0
$917$	−121.601	+	70.2064i	−0.132608	+	0.0765610i
$918$		0			0
$919$	−334.695	+	579.708i	−0.364194	+	0.630803i	−0.988647	−	0.150260i	$-0.951989\pi$
$919$	−334.695	+	579.708i	−0.364194	+	0.630803i	0.624452	+	0.781063i	$0.285322\pi$
$920$		0			0
$921$	−227.939	−	259.552i	−0.247491	−	0.281815i
$922$		0			0
$923$	−991.461	−	427.674i	−1.07417	−	0.463353i
$924$		0			0
$925$	198.818	+	3413.57i	0.214938	+	3.69034i
$926$		0			0
$927$	215.861	+	618.269i	0.232859	+	0.666956i
$928$		0			0
$929$	1235.05	−	532.748i	1.32944	−	0.573464i	0.391472	−	0.920190i	$-0.371966\pi$
$929$	1235.05	−	532.748i	1.32944	−	0.573464i	0.937966	+	0.346726i	$0.112707\pi$
$930$		0			0
$931$	−25.1710	−	5.96564i	−0.0270365	−	0.00640777i
$932$		0			0
$933$	−217.617	+	537.441i	−0.233244	+	0.576035i
$934$		0			0
$935$	−12.6377	−	34.7217i	−0.0135162	−	0.0371355i
$936$		0			0
$937$	−528.983	−	192.534i	−0.564549	−	0.205479i	0.0439497	−	0.999034i	$-0.486006\pi$
$937$	−528.983	−	192.534i	−0.564549	−	0.205479i	−0.608499	+	0.793555i	$0.708228\pi$
$938$		0			0
$939$	560.532	−	553.204i	0.596946	−	0.589142i
$940$		0			0
$941$	−1441.45	−	83.9549i	−1.53183	−	0.0892188i	−0.728620	−	0.684918i	$-0.759838\pi$
$941$	−1441.45	−	83.9549i	−1.53183	−	0.0892188i	−0.803207	+	0.595700i	$0.796875\pi$
$942$		0			0
$943$	−462.444	−	490.162i	−0.490396	−	0.519790i
$944$		0			0
$945$	1341.90	−	1289.94i	1.41999	−	1.36501i
$946$		0			0
$947$	−7.61286	−	2.27914i	−0.00803892	−	0.00240670i	0.282781	−	0.959184i	$-0.408743\pi$
$947$	−7.61286	−	2.27914i	−0.00803892	−	0.00240670i	−0.290820	+	0.956778i	$0.593928\pi$
$948$		0			0
$949$	1300.02	+	855.040i	1.36989	+	0.900990i
$950$		0			0
$951$	−363.720	−	34.2343i	−0.382460	−	0.0359982i
$952$		0			0
$953$	442.909	−	78.0969i	0.464753	−	0.0819484i	0.0636316	−	0.997973i	$-0.479732\pi$
$953$	442.909	−	78.0969i	0.464753	−	0.0819484i	0.401121	+	0.916025i	$0.368621\pi$
$954$		0			0
$955$	22.4154	−	127.124i	0.0234717	−	0.133114i
$956$		0			0
$957$	8.96269	+	0.319823i	0.00936540	+	0.000334193i
$958$		0			0
$959$	−1582.42	+	473.747i	−1.65008	+	0.494001i
$960$		0			0
$961$	−984.910	−	115.119i	−1.02488	−	0.119791i
$962$		0			0
$963$	825.203	+	898.051i	0.856909	+	0.932556i
$964$		0			0
$965$	998.333	+	1517.89i	1.03454	+	1.57294i
$966$		0			0
$967$	−530.640	−	712.773i	−0.548748	−	0.737097i	0.438068	−	0.898942i	$-0.355663\pi$
$967$	−530.640	−	712.773i	−0.548748	−	0.737097i	−0.986816	+	0.161845i	$0.948256\pi$
$968$		0			0
$969$	833.024	+	667.625i	0.859674	+	0.688983i
$970$		0			0
$971$		−	815.003i		−	0.839344i	−0.907676	−	0.419672i	$-0.862145\pi$
$971$		−	815.003i		−	0.839344i	0.907676	−	0.419672i	$-0.137855\pi$
$972$		0			0
$973$	37.7388			0.0387860
$974$		0			0
$975$	−2620.58	+	3269.81i	−2.68778	+	3.35365i
$976$		0			0
$977$	−276.459	+	205.816i	−0.282967	+	0.210661i	−0.729279	−	0.684216i	$-0.760145\pi$
$977$	−276.459	+	205.816i	−0.282967	+	0.210661i	0.446312	+	0.894877i	$0.352737\pi$
$978$		0			0
$979$	20.0645	−	13.1966i	0.0204949	−	0.0134797i
$980$		0			0
$981$	−1258.51	−	394.893i	−1.28289	−	0.402541i
$982$		0			0
$983$	−206.389	+	1765.77i	−0.209958	+	1.79631i	0.319100	+	0.947721i	$0.396619\pi$
$983$	−206.389	+	1765.77i	−0.209958	+	1.79631i	−0.529058	+	0.848586i	$0.677455\pi$
$984$		0			0
$985$	119.735	+	399.942i	0.121558	+	0.406032i
$986$		0			0
$987$	40.1597	−	1125.43i	0.0406886	−	1.14025i
$988$		0			0
$989$	149.214	+	26.3104i	0.150873	+	0.0266031i
$990$		0			0
$991$	4.12642	+	23.4021i	0.00416390	+	0.0236146i	0.986819	−	0.161828i	$-0.0517391\pi$
$991$	4.12642	+	23.4021i	0.00416390	+	0.0236146i	−0.982655	+	0.185443i	$0.940628\pi$
$992$		0			0
$993$	82.6309	−	877.905i	0.0832134	−	0.884094i
$994$		0			0
$995$	1078.59	−	1639.92i	1.08401	−	1.64816i
$996$		0			0
$997$	20.2234	−	67.5509i	0.0202843	−	0.0677542i	−0.947248	−	0.320501i	$-0.896149\pi$
$997$	20.2234	−	67.5509i	0.0202843	−	0.0677542i	0.967532	+	0.252747i	$0.0813340\pi$
$998$		0			0
$999$	1318.76	+	141.656i	1.32008	+	0.141798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.15	✓	324
81.65	odd	54	inner	324.3.o.a.65.15	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.15	✓	324	1.1	even	1	trivial
324.3.o.a.65.15	yes	324	81.65	odd	54	inner

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.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.87615 - 2.34095i) q^{3} +(-7.80193 + 5.80832i) q^{5} +(5.92166 - 3.89473i) q^{7} +(-1.96012 - 8.78396i) q^{9} +O(q^{10})\)	\(q+(1.87615 - 2.34095i) q^{3} +(-7.80193 + 5.80832i) q^{5} +(5.92166 - 3.89473i) q^{7} +(-1.96012 - 8.78396i) q^{9} +(0.0259603 - 0.222104i) q^{11} +(-5.75523 - 19.2238i) q^{13} +(-1.04058 + 29.1612i) q^{15} +(-16.7302 - 2.94999i) q^{17} +(-3.63734 - 20.6284i) q^{19} +(1.99252 - 21.1694i) q^{21} +(12.0237 - 18.2812i) q^{23} +(19.9634 - 66.6825i) q^{25} +(-24.2403 - 11.8915i) q^{27} +(-9.72405 + 9.17417i) q^{29} +(-2.56933 + 44.1136i) q^{31} +(-0.471230 - 0.477473i) q^{33} +(-23.5785 + 64.7813i) q^{35} +(-46.1613 + 16.8013i) q^{37} +(-55.7997 - 22.5940i) q^{39} +(7.10244 - 29.9675i) q^{41} +(2.74269 + 6.35827i) q^{43} +(66.3128 + 57.1468i) q^{45} +(52.8732 - 3.07951i) q^{47} +(0.489143 - 1.13396i) q^{49} +(-38.2942 + 33.6301i) q^{51} +(-21.5125 - 12.4202i) q^{53} +(1.08751 + 1.88363i) q^{55} +(-55.1143 - 30.1871i) q^{57} +(-3.07094 - 26.2736i) q^{59} +(50.8973 + 25.5616i) q^{61} +(-45.8184 - 44.3814i) q^{63} +(156.560 + 116.555i) q^{65} +(47.8640 - 50.7328i) q^{67} +(-20.2370 - 62.4451i) q^{69} +(34.5875 - 41.2198i) q^{71} +(-59.4000 + 49.8425i) q^{73} +(-118.646 - 171.840i) q^{75} +(-0.711310 - 1.41633i) q^{77} +(73.2345 - 17.3569i) q^{79} +(-73.3158 + 34.4353i) q^{81} +(-25.7416 - 108.612i) q^{83} +(147.663 - 74.1590i) q^{85} +(3.23252 + 39.9757i) q^{87} +(69.0322 + 82.2694i) q^{89} +(-108.952 - 91.4217i) q^{91} +(98.4475 + 88.7785i) q^{93} +(148.195 + 139.815i) q^{95} +(38.6405 - 51.9032i) q^{97} +(-2.00184 + 0.207318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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