LMFDB - Embedded newform 324.3.f.r.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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.119023932416481.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 3 x^{10} + 11 x^{9} - 5 x^{8} - 14 x^{7} + 29 x^{6} - 28 x^{5} - 20 x^{4} + \cdots + 64 $ x^12 - 2x^11 - 3x^10 + 11x^9 - 5x^8 - 14x^7 + 29x^6 - 28x^5 - 20x^4 + 88x^3 - 48x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.4
Root			$1.25131 - 0.658947i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.r.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.461217 + 1.94609i) q^{2} +(-3.57456 + 1.79514i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(-1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +O(q^{10})$	\(q+(0.461217 + 1.94609i) q^{2} +(-3.57456 + 1.79514i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(-1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +(6.36427 - 6.00429i) q^{10} +(10.9277 + 6.30914i) q^{11} +(-4.63163 - 8.02222i) q^{13} +(1.22482 - 4.09108i) q^{14} +(9.55494 - 12.8337i) q^{16} +14.6381 q^{17} -34.5778i q^{19} +(14.6202 + 9.61619i) q^{20} +(-7.23811 + 24.1763i) q^{22} +(35.3255 - 20.3952i) q^{23} +(2.93057 - 5.07589i) q^{25} +(13.4758 - 12.7136i) q^{26} +(8.52653 + 0.496747i) q^{28} +(-9.52010 + 16.4893i) q^{29} +(0.860391 - 0.496747i) q^{31} +(29.3824 + 12.6757i) q^{32} +(6.75132 + 28.4870i) q^{34} +9.34128i q^{35} -66.4263 q^{37} +(67.2917 - 15.9479i) q^{38} +(-11.9709 + 32.8875i) q^{40} +(-12.9434 - 22.4187i) q^{41} +(36.4816 + 21.0627i) q^{43} +(-50.3877 - 2.93554i) q^{44} +(55.9836 + 59.3401i) q^{46} +(-30.1126 - 17.3855i) q^{47} +(-22.2204 - 38.4868i) q^{49} +(11.2298 + 3.36207i) q^{50} +(30.9571 + 20.3615i) q^{52} -12.2231 q^{53} -55.2024i q^{55} +(2.96586 + 16.8225i) q^{56} +(-36.4805 - 10.9219i) q^{58} +(49.1301 - 28.3653i) q^{59} +(-36.8804 + 63.8788i) q^{61} +(1.36354 + 1.44529i) q^{62} +(-11.1164 + 63.0272i) q^{64} +(-20.2625 + 35.0956i) q^{65} +(82.4391 - 47.5962i) q^{67} +(-52.3246 + 26.2774i) q^{68} +(-18.1790 + 4.30835i) q^{70} +75.5614i q^{71} -56.7185 q^{73} +(-30.6369 - 129.272i) q^{74} +(62.0721 + 123.600i) q^{76} +(-13.4716 - 23.3334i) q^{77} +(-64.5777 - 37.2839i) q^{79} +(-69.5232 - 8.12830i) q^{80} +(37.6591 - 35.5290i) q^{82} +(-56.7179 - 32.7461i) q^{83} +(-32.0193 - 55.4590i) q^{85} +(-24.1640 + 80.7110i) q^{86} +(-17.5268 - 99.4130i) q^{88} +150.050 q^{89} +19.7794i q^{91} +(-89.6608 + 136.318i) q^{92} +(19.9454 - 66.6204i) q^{94} +(-131.005 + 75.6355i) q^{95} +(56.4426 - 97.7615i) q^{97} +(64.6505 - 60.9936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

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 $

$2$	0.461217	+	1.94609i	0.230608	+	0.973047i
$2$	0.461217	+	1.94609i	0.230608	+	0.973047i
$3$		0			0
$3$		0			0
$4$	−3.57456	+	1.79514i	−0.893640	+	0.448785i
$5$	−2.18740	−	3.78869i	−0.437480	−	0.757737i	0.560014	−	0.828483i	$-0.310796\pi$
$5$	−2.18740	−	3.78869i	−0.437480	−	0.757737i	−0.997494	+	0.0707454i	$0.977462\pi$
$6$		0			0
$7$	−1.84918	−	1.06762i	−0.264168	−	0.152518i	0.362066	−	0.932152i	$-0.382071\pi$
$7$	−1.84918	−	1.06762i	−0.264168	−	0.152518i	−0.626235	+	0.779635i	$0.715405\pi$
$8$	−5.14216	−	6.12848i	−0.642770	−	0.766059i
$9$		0			0
$10$	6.36427	−	6.00429i	0.636427	−	0.600429i
$11$	10.9277	+	6.30914i	0.993432	+	0.573558i	0.906298	−	0.422639i	$-0.138896\pi$
$11$	10.9277	+	6.30914i	0.993432	+	0.573558i	0.0871333	+	0.996197i	$0.472229\pi$
$12$		0			0
$13$	−4.63163	−	8.02222i	−0.356279	−	0.617094i	0.631057	−	0.775737i	$-0.282622\pi$
$13$	−4.63163	−	8.02222i	−0.356279	−	0.617094i	−0.987336	+	0.158643i	$0.949288\pi$
$14$	1.22482	−	4.09108i	0.0874874	−	0.292220i
$15$		0			0
$16$	9.55494	−	12.8337i	0.597184	−	0.802105i
$17$	14.6381			0.861063			0.430531	−	0.902576i	$-0.358326\pi$
$17$	14.6381			0.861063			0.430531	+	0.902576i	$0.358326\pi$
$18$		0			0
$19$		−	34.5778i		−	1.81989i	−0.414734	−	0.909943i	$-0.636125\pi$
$19$		−	34.5778i		−	1.81989i	0.414734	−	0.909943i	$-0.363875\pi$
$20$	14.6202	+	9.61619i	0.731011	+	0.480810i
$21$		0			0
$22$	−7.23811	+	24.1763i	−0.329005	+	1.09892i
$23$	35.3255	−	20.3952i	1.53589	−	0.886747i	0.536818	−	0.843698i	$-0.319626\pi$
$23$	35.3255	−	20.3952i	1.53589	−	0.886747i	0.999073	−	0.0430488i	$-0.0137071\pi$
$24$		0			0
$25$	2.93057	−	5.07589i	0.117223	−	0.203036i
$26$	13.4758	−	12.7136i	0.518300	−	0.488983i
$27$		0			0
$28$	8.52653	+	0.496747i	0.304519	+	0.0177410i
$29$	−9.52010	+	16.4893i	−0.328279	+	0.568596i	−0.982171	−	0.187992i	$-0.939802\pi$
$29$	−9.52010	+	16.4893i	−0.328279	+	0.568596i	0.653891	+	0.756589i	$0.273135\pi$
$30$		0			0
$31$	0.860391	−	0.496747i	0.0277546	−	0.0160241i	−0.486059	−	0.873926i	$-0.661566\pi$
$31$	0.860391	−	0.496747i	0.0277546	−	0.0160241i	0.513813	+	0.857902i	$0.328232\pi$
$32$	29.3824	+	12.6757i	0.918201	+	0.396116i
$33$		0			0
$34$	6.75132	+	28.4870i	0.198568	+	0.837854i
$35$			9.34128i			0.266894i
$36$		0			0
$37$	−66.4263			−1.79530			−0.897652	−	0.440705i	$-0.854729\pi$
$37$	−66.4263			−1.79530			−0.897652	+	0.440705i	$0.854729\pi$
$38$	67.2917	−	15.9479i	1.77083	−	0.419681i
$39$		0			0
$40$	−11.9709	+	32.8875i	−0.299273	+	0.822186i
$41$	−12.9434	−	22.4187i	−0.315693	−	0.546797i	0.663891	−	0.747829i	$-0.268904\pi$
$41$	−12.9434	−	22.4187i	−0.315693	−	0.546797i	−0.979585	+	0.201032i	$0.935570\pi$
$42$		0			0
$43$	36.4816	+	21.0627i	0.848409	+	0.489829i	0.860114	−	0.510102i	$-0.170392\pi$
$43$	36.4816	+	21.0627i	0.848409	+	0.489829i	−0.0117046	+	0.999931i	$0.503726\pi$
$44$	−50.3877	−	2.93554i	−1.14517	−	0.0667167i
$45$		0			0
$46$	55.9836	+	59.3401i	1.21704	+	1.29000i
$47$	−30.1126	−	17.3855i	−0.640694	−	0.369905i	0.144188	−	0.989550i	$-0.453943\pi$
$47$	−30.1126	−	17.3855i	−0.640694	−	0.369905i	−0.784882	+	0.619646i	$0.787276\pi$
$48$		0			0
$49$	−22.2204	−	38.4868i	−0.453477	−	0.785445i
$50$	11.2298	+	3.36207i	0.224596	+	0.0672414i
$51$		0			0
$52$	30.9571	+	20.3615i	0.595328	+	0.391567i
$53$	−12.2231			−0.230624			−0.115312	−	0.993329i	$-0.536787\pi$
$53$	−12.2231			−0.230624			−0.115312	+	0.993329i	$0.536787\pi$
$54$		0			0
$55$		−	55.2024i		−	1.00368i
$56$	2.96586	+	16.8225i	0.0529618	+	0.300402i
$57$		0			0
$58$	−36.4805	−	10.9219i	−0.628975	−	0.188308i
$59$	49.1301	−	28.3653i	0.832714	−	0.480768i	−0.0220670	−	0.999756i	$-0.507025\pi$
$59$	49.1301	−	28.3653i	0.832714	−	0.480768i	0.854781	+	0.518989i	$0.173691\pi$
$60$		0			0
$61$	−36.8804	+	63.8788i	−0.604597	+	1.04719i	0.387518	+	0.921862i	$0.373333\pi$
$61$	−36.8804	+	63.8788i	−0.604597	+	1.04719i	−0.992115	+	0.125331i	$0.960001\pi$
$62$	1.36354	+	1.44529i	0.0219926	+	0.0233112i
$63$		0			0
$64$	−11.1164	+	63.0272i	−0.173694	+	0.984800i
$65$	−20.2625	+	35.0956i	−0.311730	+	0.539932i
$66$		0			0
$67$	82.4391	−	47.5962i	1.23043	−	0.710392i	0.263314	−	0.964710i	$-0.415184\pi$
$67$	82.4391	−	47.5962i	1.23043	−	0.710392i	0.967121	+	0.254318i	$0.0818511\pi$
$68$	−52.3246	+	26.2774i	−0.769480	+	0.386432i
$69$		0			0
$70$	−18.1790	+	4.30835i	−0.259700	+	0.0615479i
$71$			75.5614i			1.06424i	0.846667	+	0.532122i	$0.178605\pi$
$71$			75.5614i			1.06424i	−0.846667	+	0.532122i	$0.821395\pi$
$72$		0			0
$73$	−56.7185			−0.776965			−0.388483	−	0.921456i	$-0.627001\pi$
$73$	−56.7185			−0.776965			−0.388483	+	0.921456i	$0.627001\pi$
$74$	−30.6369	−	129.272i	−0.414012	−	1.74691i
$75$		0			0
$76$	62.0721	+	123.600i	0.816738	+	1.62632i
$77$	−13.4716	−	23.3334i	−0.174955	−	0.303032i
$78$		0			0
$79$	−64.5777	−	37.2839i	−0.817439	−	0.471949i	0.0320934	−	0.999485i	$-0.489783\pi$
$79$	−64.5777	−	37.2839i	−0.817439	−	0.471949i	−0.849533	+	0.527536i	$0.823116\pi$
$80$	−69.5232	−	8.12830i	−0.869040	−	0.101604i
$81$		0			0
$82$	37.6591	−	35.5290i	0.459257	−	0.433280i
$83$	−56.7179	−	32.7461i	−0.683349	−	0.394532i	0.117767	−	0.993041i	$-0.462426\pi$
$83$	−56.7179	−	32.7461i	−0.683349	−	0.394532i	−0.801116	+	0.598510i	$0.795760\pi$
$84$		0			0
$85$	−32.0193	−	55.4590i	−0.376698	−	0.652459i
$86$	−24.1640	+	80.7110i	−0.280977	+	0.938500i
$87$		0			0
$88$	−17.5268	−	99.4130i	−0.199168	−	1.12969i
$89$	150.050			1.68595			0.842977	−	0.537950i	$-0.180801\pi$
$89$	150.050			1.68595			0.842977	+	0.537950i	$0.180801\pi$
$90$		0			0
$91$			19.7794i			0.217356i
$92$	−89.6608	+	136.318i	−0.974574	+	1.48172i
$93$		0			0
$94$	19.9454	−	66.6204i	0.212185	−	0.708728i
$95$	−131.005	+	75.6355i	−1.37900	+	0.796163i
$96$		0			0
$97$	56.4426	−	97.7615i	0.581883	−	1.00785i	−0.413373	−	0.910562i	$-0.635650\pi$
$97$	56.4426	−	97.7615i	0.581883	−	1.00785i	0.995256	−	0.0972889i	$-0.0310171\pi$
$98$	64.6505	−	60.9936i	0.659699	−	0.622384i
$99$		0			0
$100$	−1.36354	+	23.4048i	−0.0136354	+	0.234048i
$101$	21.9708	−	38.0545i	0.217532	−	0.376777i	−0.736521	−	0.676415i	$-0.763533\pi$
$101$	21.9708	−	38.0545i	0.217532	−	0.376777i	0.954053	+	0.299638i	$0.0968659\pi$
$102$		0			0
$103$	66.4269	−	38.3516i	0.644921	−	0.372345i	−0.141587	−	0.989926i	$-0.545220\pi$
$103$	66.4269	−	38.3516i	0.644921	−	0.372345i	0.786508	+	0.617581i	$0.211887\pi$
$104$	−25.3474	+	69.6364i	−0.243725	+	0.669581i
$105$		0			0
$106$	−5.63748	−	23.7872i	−0.0531838	−	0.224408i
$107$		−	9.53448i		−	0.0891073i	−0.999007	−	0.0445537i	$-0.985813\pi$
$107$		−	9.53448i		−	0.0891073i	0.999007	−	0.0445537i	$-0.0141866\pi$
$108$		0			0
$109$	51.4021			0.471579			0.235790	−	0.971804i	$-0.424232\pi$
$109$	51.4021			0.471579			0.235790	+	0.971804i	$0.424232\pi$
$110$	107.429	−	25.4603i	0.976628	−	0.231457i
$111$		0			0
$112$	−31.3703	+	13.5307i	−0.280092	+	0.120810i
$113$	−0.914995	−	1.58482i	−0.00809730	−	0.0140249i	0.861948	−	0.506996i	$-0.169244\pi$
$113$	−0.914995	−	1.58482i	−0.00809730	−	0.0140249i	−0.870046	+	0.492971i	$0.835911\pi$
$114$		0			0
$115$	−154.542	−	89.2248i	−1.34384	−	0.775868i
$116$	4.42954	−	76.0319i	0.0381857	−	0.655447i
$117$		0			0
$118$	77.8611	+	82.5293i	0.659840	+	0.699401i
$119$	−27.0684	−	15.6279i	−0.227465	−	0.131327i
$120$		0			0
$121$	19.1104	+	33.1002i	0.157937	+	0.273556i
$122$	−141.324	−	42.3108i	−1.15839	−	0.346810i
$123$		0			0
$124$	−2.18379	+	3.32018i	−0.0176112	+	0.0267756i
$125$	−135.011			−1.08009
$126$		0			0
$127$			46.6614i			0.367413i	0.982981	+	0.183706i	$0.0588096\pi$
$127$			46.6614i			0.367413i	−0.982981	+	0.183706i	$0.941190\pi$
$128$	−127.784	+	7.43556i	−0.998311	+	0.0580903i
$129$		0			0
$130$	−77.6447	−	23.2460i	−0.597267	−	0.178815i
$131$	−100.596	+	58.0793i	−0.767910	+	0.443353i	−0.832129	−	0.554583i	$-0.812878\pi$
$131$	−100.596	+	58.0793i	−0.767910	+	0.443353i	0.0642183	+	0.997936i	$0.479545\pi$
$132$		0			0
$133$	−36.9161	+	63.9406i	−0.277565	+	0.480756i
$134$	130.649	+	138.482i	0.974993	+	1.03345i
$135$		0			0
$136$	−75.2712	−	89.7090i	−0.553465	−	0.659625i
$137$	−53.9555	+	93.4536i	−0.393836	+	0.682143i	−0.992952	−	0.118519i	$-0.962185\pi$
$137$	−53.9555	+	93.4536i	−0.393836	+	0.682143i	0.599116	+	0.800662i	$0.295519\pi$
$138$		0			0
$139$	−130.016	+	75.0646i	−0.935365	+	0.540033i	−0.888504	−	0.458868i	$-0.848255\pi$
$139$	−130.016	+	75.0646i	−0.935365	+	0.540033i	−0.0468609	+	0.998901i	$0.514922\pi$
$140$	−16.7689	−	33.3909i	−0.119778	−	0.238507i
$141$		0			0
$142$	−147.050	+	34.8502i	−1.03556	+	0.245424i
$143$		−	116.886i		−	0.817388i
$144$		0			0
$145$	83.2970			0.574462
$146$	−26.1595	−	110.379i	−0.179175	−	0.756023i
$147$		0			0
$148$	237.445	−	119.244i	1.60435	−	0.805706i
$149$	−3.81611	−	6.60970i	−0.0256115	−	0.0443604i	0.852936	−	0.522016i	$-0.174820\pi$
$149$	−3.81611	−	6.60970i	−0.0256115	−	0.0443604i	−0.878547	+	0.477656i	$0.841487\pi$
$150$		0			0
$151$	183.627	+	106.017i	1.21607	+	0.702099i	0.964075	−	0.265629i	$-0.0855796\pi$
$151$	183.627	+	106.017i	1.21607	+	0.702099i	0.251996	+	0.967728i	$0.418913\pi$
$152$	−211.909	+	177.805i	−1.39414	+	1.16977i
$153$		0			0
$154$	39.1957	−	36.9787i	0.254518	−	0.240121i
$155$	−3.76404	−	2.17317i	−0.0242841	−	0.0140204i
$156$		0			0
$157$	30.6558	+	53.0973i	0.195260	+	0.338199i	0.946986	−	0.321276i	$-0.104112\pi$
$157$	30.6558	+	53.0973i	0.195260	+	0.338199i	−0.751726	+	0.659476i	$0.770778\pi$
$158$	42.7737	−	142.870i	0.270720	−	0.904242i
$159$		0			0
$160$	−16.2468	−	139.048i	−0.101543	−	0.869048i
$161$	−87.0975			−0.540978
$162$		0			0
$163$			25.3264i			0.155377i	0.996978	+	0.0776885i	$0.0247540\pi$
$163$			25.3264i			0.155377i	−0.996978	+	0.0776885i	$0.975246\pi$
$164$	86.5117	+	56.9016i	0.527511	+	0.346961i
$165$		0			0
$166$	37.5678	−	125.481i	0.226312	−	0.755912i
$167$	120.244	−	69.4230i	0.720025	−	0.415707i	−0.0947370	−	0.995502i	$-0.530201\pi$
$167$	120.244	−	69.4230i	0.720025	−	0.415707i	0.814762	+	0.579796i	$0.196868\pi$
$168$		0			0
$169$	41.5960	−	72.0463i	0.246130	−	0.426310i
$170$	93.1606	−	87.8912i	0.548004	−	0.517007i
$171$		0			0
$172$	−168.216	−	9.80010i	−0.978000	−	0.0569773i
$173$	45.1000	−	78.1155i	0.260694	−	0.451534i	−0.705733	−	0.708478i	$-0.749382\pi$
$173$	45.1000	−	78.1155i	0.260694	−	0.451534i	0.966426	+	0.256944i	$0.0827155\pi$
$174$		0			0
$175$	−10.8383	+	6.25748i	−0.0619330	+	0.0357570i
$176$	185.383	−	79.9597i	1.05331	−	0.454317i
$177$		0			0
$178$	69.2055	+	292.011i	0.388795	+	1.64051i
$179$			41.7114i			0.233025i	0.993189	+	0.116512i	$0.0371715\pi$
$179$			41.7114i			0.233025i	−0.993189	+	0.116512i	$0.962829\pi$
$180$		0			0
$181$	84.6616			0.467744			0.233872	−	0.972267i	$-0.424860\pi$
$181$	84.6616			0.467744			0.233872	+	0.972267i	$0.424860\pi$
$182$	−38.4925	+	9.12257i	−0.211497	+	0.0501240i
$183$		0			0
$184$	−306.641	−	111.616i	−1.66652	−	0.606610i
$185$	145.301	+	251.668i	0.785409	+	1.36037i
$186$		0			0
$187$	159.961	+	92.3536i	0.855407	+	0.493869i
$188$	138.849	+	8.08919i	0.738557	+	0.0430276i
$189$		0			0
$190$	−207.615	−	220.063i	−1.09271	−	1.15823i
$191$	152.525	+	88.0606i	0.798562	+	0.461050i	0.842968	−	0.537963i	$-0.180806\pi$
$191$	152.525	+	88.0606i	0.798562	+	0.461050i	−0.0444058	+	0.999014i	$0.514139\pi$
$192$		0			0
$193$	166.424	+	288.255i	0.862300	+	1.49355i	0.869704	+	0.493574i	$0.164310\pi$
$193$	166.424	+	288.255i	0.862300	+	1.49355i	−0.00740395	+	0.999973i	$0.502357\pi$
$194$	216.285	+	64.7534i	1.11487	+	0.333780i
$195$		0			0
$196$	148.517	+	97.6846i	0.757741	+	0.498391i
$197$	−137.238			−0.696637			−0.348319	−	0.937376i	$-0.613247\pi$
$197$	−137.238			−0.696637			−0.348319	+	0.937376i	$0.613247\pi$
$198$		0			0
$199$			286.157i			1.43798i	0.695023	+	0.718988i	$0.255394\pi$
$199$			286.157i			1.43798i	−0.695023	+	0.718988i	$0.744606\pi$
$200$	−46.1769	+	8.14112i	−0.230885	+	0.0407056i
$201$		0			0
$202$	84.1908	+	25.2058i	0.416786	+	0.124781i
$203$	35.2087	−	20.3278i	0.173442	−	0.100137i
$204$		0			0
$205$	−56.6249	+	98.0772i	−0.276219	+	0.478425i
$206$	105.273	+	111.585i	0.511034	+	0.541672i
$207$		0			0
$208$	−147.210	−	17.2110i	−0.707738	−	0.0827451i
$209$	218.156	−	377.858i	1.04381	−	1.80793i
$210$		0			0
$211$	−273.062	+	157.653i	−1.29413	+	0.747169i	−0.979384	−	0.202006i	$-0.935254\pi$
$211$	−273.062	+	157.653i	−1.29413	+	0.747169i	−0.314750	+	0.949175i	$0.601921\pi$
$212$	43.6921	−	21.9421i	0.206095	−	0.103501i
$213$		0			0
$214$	18.5550	−	4.39746i	0.0867056	−	0.0205489i
$215$		−	184.290i		−	0.857162i
$216$		0			0
$217$	−2.12136			−0.00977583
$218$	23.7075	+	100.033i	0.108750	+	0.458869i
$219$		0			0
$220$	99.0961	+	197.324i	0.450437	+	0.896929i
$221$	−67.7981	−	117.430i	−0.306779	−	0.531357i
$222$		0			0
$223$	−25.8734	−	14.9380i	−0.116024	−	0.0669865i	0.440865	−	0.897573i	$-0.354672\pi$
$223$	−25.8734	−	14.9380i	−0.116024	−	0.0669865i	−0.556889	+	0.830587i	$0.688005\pi$
$224$	−40.8005	−	54.8090i	−0.182145	−	0.244683i
$225$		0			0
$226$	2.66219	−	2.51161i	0.0117796	−	0.0111133i
$227$	307.799	+	177.708i	1.35594	+	0.782855i	0.989074	−	0.147418i	$-0.0470961\pi$
$227$	307.799	+	177.708i	1.35594	+	0.782855i	0.366870	+	0.930272i	$0.380429\pi$
$228$		0			0
$229$	−44.0925	−	76.3705i	−0.192544	−	0.333496i	0.753549	−	0.657392i	$-0.228340\pi$
$229$	−44.0925	−	76.3705i	−0.192544	−	0.333496i	−0.946093	+	0.323896i	$0.895007\pi$
$230$	102.363	−	341.905i	0.445054	−	1.48654i
$231$		0			0
$232$	150.008	−	26.4469i	0.646587	−	0.113995i
$233$	251.720			1.08034			0.540172	−	0.841555i	$-0.318359\pi$
$233$	251.720			1.08034			0.540172	+	0.841555i	$0.318359\pi$
$234$		0			0
$235$			152.116i			0.647303i
$236$	−124.699	+	189.589i	−0.528385	+	0.803343i
$237$		0			0
$238$	17.9290	−	59.8855i	0.0753321	−	0.251620i
$239$	123.211	−	71.1356i	0.515525	−	0.297639i	−0.219577	−	0.975595i	$-0.570468\pi$
$239$	123.211	−	71.1356i	0.515525	−	0.297639i	0.735102	+	0.677957i	$0.237134\pi$
$240$		0			0
$241$	28.5164	−	49.3918i	0.118325	−	0.204945i	−0.800779	−	0.598960i	$-0.795581\pi$
$241$	28.5164	−	49.3918i	0.118325	−	0.204945i	0.919104	+	0.394015i	$0.128914\pi$
$242$	−55.6021	+	52.4571i	−0.229761	+	0.216765i
$243$		0			0
$244$	17.1598	−	294.544i	0.0703272	−	1.20715i
$245$	−97.2096	+	168.372i	−0.396774	+	0.687233i
$246$		0			0
$247$	−277.391	+	160.152i	−1.12304	+	0.648388i
$248$	−7.46857	−	2.71854i	−0.0301152	−	0.0109618i
$249$		0			0
$250$	−62.2694	−	262.745i	−0.249078	−	1.05098i
$251$		−	0.579617i		−	0.00230923i	−0.999999	−	0.00115462i	$-0.999632\pi$
$251$		−	0.579617i		−	0.00230923i	0.999999	−	0.00115462i	$-0.000367526\pi$
$252$		0			0
$253$	514.704			2.03440
$254$	−90.8075	+	21.5210i	−0.357510	+	0.0847284i
$255$		0			0
$256$	−73.4063	−	245.250i	−0.286743	−	0.958007i
$257$	159.160	+	275.674i	0.619301	+	1.07266i	0.989614	+	0.143753i	$0.0459171\pi$
$257$	159.160	+	275.674i	0.619301	+	1.07266i	−0.370313	+	0.928907i	$0.620750\pi$
$258$		0			0
$259$	122.834	+	70.9182i	0.474262	+	0.273816i
$260$	9.42778	−	161.825i	0.0362607	−	0.622405i
$261$		0			0
$262$	−159.424	−	168.983i	−0.608490	−	0.644972i
$263$	270.344	+	156.083i	1.02792	+	0.593472i	0.916389	−	0.400288i	$-0.131090\pi$
$263$	270.344	+	156.083i	1.02792	+	0.593472i	0.111535	+	0.993761i	$0.464423\pi$
$264$		0			0
$265$	26.7367	+	46.3094i	0.100893	+	0.174752i
$266$	−141.461	−	42.3517i	−0.531807	−	0.159217i
$267$		0			0
$268$	−209.241	+	318.125i	−0.780752	+	1.18704i
$269$	−480.302			−1.78551			−0.892755	−	0.450542i	$-0.851231\pi$
$269$	−480.302			−1.78551			−0.892755	+	0.450542i	$0.851231\pi$
$270$		0			0
$271$		−	457.090i		−	1.68668i	−0.537381	−	0.843340i	$-0.680586\pi$
$271$		−	457.090i		−	1.68668i	0.537381	−	0.843340i	$-0.319414\pi$
$272$	139.866	−	187.860i	0.514212	−	0.690662i
$273$		0			0
$274$	−206.755	−	61.9000i	−0.754579	−	0.225913i
$275$	64.0490	−	36.9787i	0.232905	−	0.134468i
$276$		0			0
$277$	85.6037	−	148.270i	0.309039	−	0.535271i	−0.669114	−	0.743160i	$-0.733326\pi$
$277$	85.6037	−	148.270i	0.309039	−	0.535271i	0.978152	+	0.207889i	$0.0666594\pi$
$278$	−206.048	−	218.402i	−0.741181	−	0.785618i
$279$		0			0
$280$	57.2478	−	48.0343i	0.204456	−	0.171551i
$281$	19.9973	−	34.6363i	0.0711647	−	0.123261i	−0.828247	−	0.560363i	$-0.810662\pi$
$281$	19.9973	−	34.6363i	0.0711647	−	0.123261i	0.899412	+	0.437102i	$0.143995\pi$
$282$		0			0
$283$	338.527	−	195.449i	1.19621	−	0.690632i	0.236501	−	0.971631i	$-0.423999\pi$
$283$	338.527	−	195.449i	1.19621	−	0.690632i	0.959708	+	0.281000i	$0.0906660\pi$
$284$	−135.643	−	270.099i	−0.477617	−	0.951051i
$285$		0			0
$286$	227.472	−	53.9100i	0.795356	−	0.188496i
$287$			55.2748i			0.192595i
$288$		0			0
$289$	−74.7271			−0.258571
$290$	38.4180	+	162.104i	0.132476	+	0.558979i
$291$		0			0
$292$	202.743	−	101.818i	0.694327	−	0.348690i
$293$	−251.725	−	436.001i	−0.859131	−	1.48806i	−0.872759	−	0.488152i	$-0.837671\pi$
$293$	−251.725	−	436.001i	−0.859131	−	1.48806i	0.0136273	−	0.999907i	$-0.495662\pi$
$294$		0			0
$295$	−214.934	−	124.092i	−0.728591	−	0.420652i
$296$	341.574	+	407.092i	1.15397	+	1.37531i
$297$		0			0
$298$	11.1030	−	10.4750i	0.0372585	−	0.0351511i
$299$	−327.229	−	188.926i	−1.09441	−	0.631859i
$300$		0			0
$301$	−44.9740	−	77.8972i	−0.149415	−	0.258795i
$302$	−121.627	+	406.252i	−0.402739	+	1.34520i
$303$		0			0
$304$	−443.761	−	330.389i	−1.45974	−	1.08681i
$305$	322.689			1.05800
$306$		0			0
$307$			103.154i			0.336006i	0.985786	+	0.168003i	$0.0537318\pi$
$307$			103.154i			0.336006i	−0.985786	+	0.168003i	$0.946268\pi$
$308$	90.0417	+	59.2234i	0.292343	+	0.192284i
$309$		0			0
$310$	2.49315	−	8.32747i	0.00804243	−	0.0268628i
$311$	−396.709	+	229.040i	−1.27559	+	0.736463i	−0.976035	−	0.217615i	$-0.930172\pi$
$311$	−396.709	+	229.040i	−1.27559	+	0.736463i	−0.299557	+	0.954078i	$0.596839\pi$
$312$		0			0
$313$	−9.31582	+	16.1355i	−0.0297630	+	0.0515510i	−0.880523	−	0.474003i	$-0.842809\pi$
$313$	−9.31582	+	16.1355i	−0.0297630	+	0.0515510i	0.850760	+	0.525554i	$0.176142\pi$
$314$	−89.1934	+	84.1483i	−0.284055	+	0.267988i
$315$		0			0
$316$	297.767	+	17.3476i	0.942300	+	0.0548974i
$317$	−107.895	+	186.880i	−0.340363	+	0.589527i	−0.984500	−	0.175384i	$-0.943883\pi$
$317$	−107.895	+	186.880i	−0.340363	+	0.589527i	0.644137	+	0.764910i	$0.277217\pi$
$318$		0			0
$319$	−208.066	+	120.127i	−0.652246	+	0.376574i
$320$	263.106	−	95.7489i	0.822207	−	0.299215i
$321$		0			0
$322$	−40.1708	−	169.500i	−0.124754	−	0.526397i
$323$		−	506.152i		−	1.56704i
$324$		0			0
$325$	−54.2932			−0.167056
$326$	−49.2876	+	11.6810i	−0.151189	+	0.0358312i
$327$		0			0
$328$	−70.8352	+	194.604i	−0.215961	+	0.593304i
$329$	37.1224	+	64.2978i	0.112834	+	0.195434i
$330$		0			0
$331$	−215.753	−	124.565i	−0.651822	−	0.376329i	0.137332	−	0.990525i	$-0.456147\pi$
$331$	−215.753	−	124.565i	−0.651822	−	0.376329i	−0.789154	+	0.614196i	$0.789481\pi$
$332$	261.526	+	15.2362i	0.787727	+	0.0458922i
$333$		0			0
$334$	190.562	+	201.987i	0.570546	+	0.604752i
$335$	−360.655	−	208.224i	−1.07658	−	0.621564i
$336$		0			0
$337$	135.945	+	235.464i	0.403398	+	0.698705i	0.994134	−	0.108160i	$-0.0344958\pi$
$337$	135.945	+	235.464i	0.403398	+	0.698705i	−0.590736	+	0.806865i	$0.701162\pi$
$338$	159.394	+	47.7207i	0.471579	+	0.141185i
$339$		0			0
$340$	214.012	+	140.762i	0.629446	+	0.414007i
$341$	12.5362			0.0367630
$342$		0			0
$343$			199.519i			0.581688i
$344$	−58.5121	−	331.884i	−0.170093	−	0.964779i
$345$		0			0
$346$	172.821	+	51.7406i	0.499482	+	0.149539i
$347$	−280.781	+	162.109i	−0.809169	+	0.467174i	−0.846667	−	0.532123i	$-0.821394\pi$
$347$	−280.781	+	162.109i	−0.809169	+	0.467174i	0.0374985	+	0.999297i	$0.488061\pi$
$348$		0			0
$349$	50.5198	−	87.5029i	0.144756	−	0.250725i	−0.784526	−	0.620096i	$-0.787094\pi$
$349$	50.5198	−	87.5029i	0.144756	−	0.250725i	0.929282	+	0.369371i	$0.120427\pi$
$350$	−17.1764	−	18.2062i	−0.0490755	−	0.0520178i
$351$		0			0
$352$	241.111	+	323.895i	0.684974	+	0.920155i
$353$	−75.9329	+	131.520i	−0.215107	+	0.372577i	−0.953306	−	0.302007i	$-0.902343\pi$
$353$	−75.9329	+	131.520i	−0.215107	+	0.372577i	0.738198	+	0.674584i	$0.235677\pi$
$354$		0			0
$355$	286.278	−	165.283i	0.806418	−	0.465586i
$356$	−536.362	+	269.361i	−1.50663	+	0.756631i
$357$		0			0
$358$	−81.1744	+	19.2380i	−0.226744	+	0.0537375i
$359$			594.808i			1.65685i	0.560102	+	0.828424i	$0.310762\pi$
$359$			594.808i			1.65685i	−0.560102	+	0.828424i	$0.689238\pi$
$360$		0			0
$361$	−834.626			−2.31198
$362$	39.0473	+	164.759i	0.107866	+	0.455136i
$363$		0			0
$364$	−35.5067	−	70.7025i	−0.0975460	−	0.194238i
$365$	124.066	+	214.888i	0.339907	+	0.588736i
$366$		0			0
$367$	151.089	+	87.2311i	0.411686	+	0.237687i	0.691514	−	0.722363i	$-0.256944\pi$
$367$	151.089	+	87.2311i	0.411686	+	0.237687i	−0.279828	+	0.960050i	$0.590277\pi$
$368$	75.7878	−	648.230i	0.205945	−	1.76150i
$369$		0			0
$370$	−422.755	+	398.842i	−1.14258	+	1.07795i
$371$	22.6026	+	13.0496i	0.0609235	+	0.0351742i
$372$		0			0
$373$	−144.383	−	250.078i	−0.387085	−	0.670452i	0.604971	−	0.796248i	$-0.293185\pi$
$373$	−144.383	−	250.078i	−0.387085	−	0.670452i	−0.992056	+	0.125796i	$0.959851\pi$
$374$	−105.952	+	353.894i	−0.283294	+	0.946241i
$375$		0			0
$376$	48.2970	+	273.943i	0.128449	+	0.728573i
$377$	176.374			0.467837
$378$		0			0
$379$		−	260.534i		−	0.687425i	−0.939075	−	0.343713i	$-0.888315\pi$
$379$		−	260.534i		−	0.687425i	0.939075	−	0.343713i	$-0.111685\pi$
$380$	332.507	−	505.535i	0.875019	−	1.33036i
$381$		0			0
$382$	−101.027	+	337.444i	−0.264468	+	0.883360i
$383$	303.817	−	175.409i	0.793257	−	0.457987i	−0.0478509	−	0.998854i	$-0.515237\pi$
$383$	303.817	−	175.409i	0.793257	−	0.457987i	0.841108	+	0.540867i	$0.181904\pi$
$384$		0			0
$385$	−58.9354	+	102.079i	−0.153079	+	0.265141i
$386$	−484.213	+	456.824i	−1.25444	+	1.18348i
$387$		0			0
$388$	−26.2618	+	450.777i	−0.0676851	+	1.16180i
$389$	16.5571	−	28.6777i	0.0425632	−	0.0737216i	−0.843959	−	0.536408i	$-0.819781\pi$
$389$	16.5571	−	28.6777i	0.0425632	−	0.0737216i	0.886522	+	0.462686i	$0.153114\pi$
$390$		0			0
$391$	517.097	−	298.546i	1.32250	−	0.763545i
$392$	−121.605	+	334.082i	−0.310216	+	0.852250i
$393$		0			0
$394$	−63.2962	−	267.077i	−0.160650	−	0.677861i
$395$			326.220i			0.825872i
$396$		0			0
$397$	357.151			0.899625			0.449813	−	0.893123i	$-0.351491\pi$
$397$	357.151			0.899625			0.449813	+	0.893123i	$0.351491\pi$
$398$	−556.888	+	131.980i	−1.39922	+	0.331609i
$399$		0			0
$400$	−37.1409	−	86.1097i	−0.0928523	−	0.215274i
$401$	159.123	+	275.608i	0.396814	+	0.687303i	0.993331	−	0.115298i	$-0.0367823\pi$
$401$	159.123	+	275.608i	0.396814	+	0.687303i	−0.596517	+	0.802601i	$0.703449\pi$
$402$		0			0
$403$	−7.97003	−	4.60150i	−0.0197768	−	0.0114181i
$404$	−10.2226	+	175.469i	−0.0253035	+	0.434328i
$405$		0			0
$406$	55.7986	+	59.1439i	0.137435	+	0.145675i
$407$	−725.889	−	419.092i	−1.78351	−	1.02971i
$408$		0			0
$409$	−256.803	−	444.796i	−0.627880	−	1.08752i	−0.987976	−	0.154605i	$-0.950590\pi$
$409$	−256.803	−	444.796i	−0.627880	−	1.08752i	0.360097	−	0.932915i	$-0.382744\pi$
$410$	−216.984	−	64.9625i	−0.529229	−	0.158445i
$411$		0			0
$412$	−168.600	+	256.336i	−0.409224	+	0.622174i
$413$	−121.134			−0.293302
$414$		0			0
$415$			286.515i			0.690399i
$416$	−34.4013	−	294.421i	−0.0826954	−	0.707744i
$417$		0			0
$418$	835.964	+	250.278i	1.99991	+	0.598752i
$419$	62.7466	−	36.2268i	0.149753	−	0.0864601i	−0.423251	−	0.906012i	$-0.639111\pi$
$419$	62.7466	−	36.2268i	0.149753	−	0.0864601i	0.573004	+	0.819552i	$0.305778\pi$
$420$		0			0
$421$	−315.617	+	546.665i	−0.749685	+	1.29849i	0.198289	+	0.980144i	$0.436462\pi$
$421$	−315.617	+	546.665i	−0.749685	+	1.29849i	−0.947974	+	0.318349i	$0.896872\pi$
$422$	−432.748	−	458.693i	−1.02547	−	1.08695i
$423$		0			0
$424$	62.8529	+	74.9088i	0.148238	+	0.176672i
$425$	42.8978	−	74.3012i	0.100936	−	0.174826i
$426$		0			0
$427$	136.397	−	78.7488i	0.319431	−	0.184423i
$428$	17.1157	+	34.0816i	0.0399900	+	0.0796298i
$429$		0			0
$430$	358.645	−	84.9975i	0.834059	−	0.197669i
$431$			73.3222i			0.170121i	0.996376	+	0.0850606i	$0.0271084\pi$
$431$			73.3222i			0.170121i	−0.996376	+	0.0850606i	$0.972892\pi$
$432$		0			0
$433$	−575.286			−1.32860			−0.664302	−	0.747464i	$-0.731271\pi$
$433$	−575.286			−1.32860			−0.664302	+	0.747464i	$0.731271\pi$
$434$	−0.978404	−	4.12836i	−0.00225439	−	0.00951234i
$435$		0			0
$436$	−183.740	+	92.2741i	−0.421422	+	0.211638i
$437$	−705.221	−	1221.48i	−1.61378	−	2.79515i
$438$		0			0
$439$	−206.677	−	119.325i	−0.470791	−	0.271811i	0.245780	−	0.969326i	$-0.420956\pi$
$439$	−206.677	−	119.325i	−0.470791	−	0.271811i	−0.716571	+	0.697514i	$0.754289\pi$
$440$	−338.307	+	283.860i	−0.768879	+	0.645135i
$441$		0			0
$442$	197.260	−	186.102i	0.446289	−	0.421045i
$443$	−45.3661	−	26.1921i	−0.102407	−	0.0591244i	0.447922	−	0.894073i	$-0.352164\pi$
$443$	−45.3661	−	26.1921i	−0.102407	−	0.0591244i	−0.550329	+	0.834948i	$0.685498\pi$
$444$		0			0
$445$	−328.219	−	568.492i	−0.737571	−	1.27751i
$446$	17.1375	−	57.2416i	0.0384249	−	0.128344i
$447$		0			0
$448$	87.8455	−	104.680i	0.196084	−	0.233661i
$449$	566.091			1.26078			0.630391	−	0.776277i	$-0.282894\pi$
$449$	566.091			1.26078			0.630391	+	0.776277i	$0.282894\pi$
$450$		0			0
$451$		−	326.648i		−	0.724274i
$452$	6.11568	+	4.02248i	0.0135303	+	0.00889929i
$453$		0			0
$454$	−203.874	+	680.968i	−0.449062	+	1.49993i
$455$	74.9378	−	43.2654i	0.164698	−	0.0950887i
$456$		0			0
$457$	17.1799	−	29.7564i	0.0375927	−	0.0651125i	−0.846617	−	0.532203i	$-0.821364\pi$
$457$	17.1799	−	29.7564i	0.0375927	−	0.0651125i	0.884210	+	0.467090i	$0.154698\pi$
$458$	128.288	−	121.032i	0.280105	−	0.264261i
$459$		0			0
$460$	712.590	+	41.5148i	1.54911	+	0.0902496i
$461$	−136.272	+	236.031i	−0.295602	+	0.511997i	−0.975125	−	0.221657i	$-0.928853\pi$
$461$	−136.272	+	236.031i	−0.295602	+	0.511997i	0.679523	+	0.733654i	$0.262187\pi$
$462$		0			0
$463$	489.759	−	282.763i	1.05780	−	0.610719i	0.132974	−	0.991120i	$-0.457547\pi$
$463$	489.759	−	282.763i	1.05780	−	0.610719i	0.924822	+	0.380401i	$0.124214\pi$
$464$	120.654	+	279.732i	0.260031	+	0.602871i
$465$		0			0
$466$	116.097	+	489.871i	0.249136	+	1.05122i
$467$			893.925i			1.91419i	0.289780	+	0.957093i	$0.406418\pi$
$467$			893.925i			1.91419i	−0.289780	+	0.957093i	$0.593582\pi$
$468$		0			0
$469$	−203.259			−0.433389
$470$	−296.032	+	70.1585i	−0.629856	+	0.149274i
$471$		0			0
$472$	−426.471	−	155.234i	−0.903540	−	0.328886i
$473$	265.774	+	460.335i	0.561891	+	0.973224i
$474$		0			0
$475$	−175.513	−	101.333i	−0.369502	−	0.213332i
$476$	124.812	+	7.27142i	0.262210	+	0.0152761i
$477$		0			0
$478$	195.263	+	206.970i	0.408501	+	0.432992i
$479$	467.745	+	270.053i	0.976504	+	0.563785i	0.901213	−	0.433377i	$-0.142678\pi$
$479$	467.745	+	270.053i	0.976504	+	0.563785i	0.0752909	+	0.997162i	$0.476011\pi$
$480$		0			0
$481$	307.662	+	532.886i	0.639630	+	1.10787i
$482$	109.273	+	32.7152i	0.226708	+	0.0678739i
$483$		0			0
$484$	−127.731	−	84.0128i	−0.263907	−	0.173580i
$485$	−493.850			−1.01825
$486$		0			0
$487$		−	518.681i		−	1.06505i	−0.846413	−	0.532526i	$-0.821243\pi$
$487$		−	518.681i		−	1.06505i	0.846413	−	0.532526i	$-0.178757\pi$
$488$	581.124	−	102.454i	1.19083	−	0.209947i
$489$		0			0
$490$	−372.502	−	111.523i	−0.760209	−	0.227598i
$491$	130.195	−	75.1683i	0.265163	−	0.153092i	−0.361524	−	0.932363i	$-0.617744\pi$
$491$	130.195	−	75.1683i	0.265163	−	0.153092i	0.626688	+	0.779271i	$0.284410\pi$
$492$		0			0
$493$	−139.356	+	241.371i	−0.282669	+	0.489597i
$494$	−439.608	−	465.964i	−0.889894	−	0.943247i
$495$		0			0
$496$	1.84589	−	15.7884i	0.00372156	−	0.0318314i
$497$	80.6711	−	139.726i	0.162316	−	0.281140i
$498$		0			0
$499$	−265.749	+	153.430i	−0.532564	+	0.307476i	−0.742060	−	0.670334i	$-0.766151\pi$
$499$	−265.749	+	153.430i	−0.532564	+	0.307476i	0.209496	+	0.977810i	$0.432818\pi$
$500$	482.606	−	242.364i	0.965211	−	0.484728i
$501$		0			0
$502$	1.12799	−	0.267329i	0.00224699	−	0.000532528i
$503$		−	731.474i		−	1.45422i	−0.686520	−	0.727111i	$-0.740863\pi$
$503$		−	731.474i		−	1.45422i	0.686520	−	0.727111i	$-0.259137\pi$
$504$		0			0
$505$	−192.235			−0.380664
$506$	237.390	+	1001.66i	0.469150	+	1.97957i
$507$		0			0
$508$	−83.7638	−	166.794i	−0.164889	−	0.328335i
$509$	−29.6107	−	51.2873i	−0.0581743	−	0.100761i	0.835472	−	0.549534i	$-0.185195\pi$
$509$	−29.6107	−	51.2873i	−0.0581743	−	0.100761i	−0.893646	+	0.448773i	$0.851861\pi$
$510$		0			0
$511$	104.883	+	60.5540i	0.205250	+	0.118501i
$512$	443.423	−	255.969i	0.866060	−	0.499939i
$513$		0			0
$514$	−463.079	+	436.886i	−0.900933	+	0.849973i
$515$	−290.604	−	167.780i	−0.564280	−	0.325787i
$516$		0			0
$517$	−219.375	−	379.969i	−0.424323	−	0.734950i
$518$	−81.3604	+	271.755i	−0.157066	+	0.524624i
$519$		0			0
$520$	319.275	−	56.2892i	0.613991	−	0.108248i
$521$	689.100			1.32265			0.661324	−	0.750100i	$-0.269995\pi$
$521$	689.100			1.32265			0.661324	+	0.750100i	$0.269995\pi$
$522$		0			0
$523$		−	431.237i		−	0.824544i	−0.911061	−	0.412272i	$-0.864735\pi$
$523$		−	431.237i		−	0.824544i	0.911061	−	0.412272i	$-0.135265\pi$
$524$	255.327	−	388.192i	0.487265	−	0.740825i
$525$		0			0
$526$	−179.065	+	598.103i	−0.340428	+	1.13708i
$527$	12.5945	−	7.27142i	0.0238984	−	0.0137978i
$528$		0			0
$529$	567.427	−	982.812i	1.07264	−	1.85787i
$530$	−77.7910	+	73.3908i	−0.146775	+	0.138473i
$531$		0			0
$532$	17.1764	−	294.829i	0.0322865	−	0.554190i
$533$	−119.898	+	207.670i	−0.224950	+	0.389625i
$534$		0			0
$535$	−36.1232	+	20.8557i	−0.0675199	+	0.0389827i
$536$	−715.607	−	260.479i	−1.33509	−	0.485968i
$537$		0			0
$538$	−221.523	−	934.713i	−0.411753	−	1.73738i
$539$		−	560.765i		−	1.04038i
$540$		0			0
$541$	99.8398			0.184547			0.0922734	−	0.995734i	$-0.470587\pi$
$541$	99.8398			0.184547			0.0922734	+	0.995734i	$0.470587\pi$
$542$	889.540	−	210.818i	1.64122	−	0.388962i
$543$		0			0
$544$	430.102	+	185.548i	0.790628	+	0.341080i
$545$	−112.437	−	194.747i	−0.206306	−	0.357333i
$546$		0			0
$547$	413.671	+	238.833i	0.756254	+	0.436624i	0.827949	−	0.560803i	$-0.189507\pi$
$547$	413.671	+	238.833i	0.756254	+	0.436624i	−0.0716949	+	0.997427i	$0.522841\pi$
$548$	25.1046	−	430.913i	0.0458113	−	0.786338i
$549$		0			0
$550$	101.504	+	107.590i	0.184554	+	0.195618i
$551$	570.164	+	329.184i	1.03478	+	0.597431i
$552$		0			0
$553$	79.6104	+	137.889i	0.143961	+	0.249348i
$554$	328.029	+	98.2082i	0.592110	+	0.177271i
$555$		0			0
$556$	329.997	−	501.720i	0.593520	−	0.902373i
$557$	227.316			0.408108			0.204054	−	0.978960i	$-0.434588\pi$
$557$	227.316			0.408108			0.204054	+	0.978960i	$0.434588\pi$
$558$		0			0
$559$		−	390.218i		−	0.698064i
$560$	119.883	+	89.2553i	0.214077	+	0.159384i
$561$		0			0
$562$	76.6286	+	22.9417i	0.136350	+	0.0408216i
$563$	671.826	−	387.879i	1.19330	−	0.688950i	0.234244	−	0.972178i	$-0.424738\pi$
$563$	671.826	−	387.879i	1.19330	−	0.688950i	0.959053	+	0.283227i	$0.0914051\pi$
$564$		0			0
$565$	−4.00292	+	6.93326i	−0.00708481	+	0.0122713i
$566$	536.496	+	568.661i	0.947872	+	1.00470i
$567$		0			0
$568$	463.076	−	388.549i	0.815275	−	0.684064i
$569$	−477.933	+	827.803i	−0.839952	+	1.45484i	0.0499825	+	0.998750i	$0.484083\pi$
$569$	−477.933	+	827.803i	−0.839952	+	1.45484i	−0.889934	+	0.456089i	$0.849250\pi$
$570$		0			0
$571$	−754.720	+	435.738i	−1.32175	+	0.763113i	−0.984008	−	0.178125i	$-0.942997\pi$
$571$	−754.720	+	435.738i	−1.32175	+	0.763113i	−0.337743	+	0.941238i	$0.609663\pi$
$572$	209.828	+	417.817i	0.366831	+	0.730450i
$573$		0			0
$574$	−107.570	+	25.4937i	−0.187404	+	0.0444141i
$575$		−	239.078i		−	0.415787i
$576$		0			0
$577$	241.573			0.418671			0.209335	−	0.977844i	$-0.432870\pi$
$577$	241.573			0.418671			0.209335	+	0.977844i	$0.432870\pi$
$578$	−34.4654	−	145.426i	−0.0596287	−	0.251602i
$579$		0			0
$580$	−297.750	+	149.530i	−0.513362	+	0.257810i
$581$	69.9210	+	121.107i	0.120346	+	0.208445i
$582$		0			0
$583$	−133.571	−	77.1170i	−0.229109	−	0.132276i
$584$	291.655	+	347.598i	0.499410	+	0.595202i
$585$		0			0
$586$	732.399	−	690.972i	1.24983	−	1.17913i
$587$	577.552	+	333.450i	0.983905	+	0.568058i	0.903447	−	0.428700i	$-0.141028\pi$
$587$	577.552	+	333.450i	0.983905	+	0.568058i	0.0804579	+	0.996758i	$0.474362\pi$
$588$		0			0
$589$	−17.1764	−	29.7505i	−0.0291620	−	0.0505101i
$590$	142.364	−	475.516i	0.241295	−	0.805959i
$591$		0			0
$592$	−634.699	+	852.493i	−1.07213	+	1.44002i
$593$	−207.914			−0.350613			−0.175307	−	0.984514i	$-0.556092\pi$
$593$	−207.914			−0.350613			−0.175307	+	0.984514i	$0.556092\pi$
$594$		0			0
$595$			136.738i			0.229812i
$596$	25.5063	+	16.7763i	0.0427957	+	0.0281482i
$597$		0			0
$598$	216.744	−	723.955i	0.362448	−	1.21063i
$599$	283.333	−	163.582i	0.473010	−	0.273092i	−0.244489	−	0.969652i	$-0.578620\pi$
$599$	283.333	−	163.582i	0.473010	−	0.273092i	0.717499	+	0.696560i	$0.245287\pi$
$600$		0			0
$601$	−25.0218	+	43.3391i	−0.0416337	+	0.0721116i	−0.886091	−	0.463511i	$-0.846590\pi$
$601$	−25.0218	+	43.3391i	−0.0416337	+	0.0721116i	0.844458	+	0.535622i	$0.179923\pi$
$602$	130.853	−	123.451i	0.217363	−	0.205068i
$603$		0			0
$604$	−846.700	−	49.3279i	−1.40182	−	0.0816687i
$605$	83.6043	−	144.807i	0.138189	−	0.239350i
$606$		0			0
$607$	−359.185	+	207.375i	−0.591737	+	0.341640i	−0.765784	−	0.643098i	$-0.777649\pi$
$607$	−359.185	+	207.375i	−0.591737	+	0.341640i	0.174047	+	0.984737i	$0.444316\pi$
$608$	438.298	−	1015.98i	0.720885	−	1.67102i
$609$		0			0
$610$	148.829	+	627.983i	0.243983	+	1.02948i
$611$			322.093i			0.527158i
$612$		0			0
$613$	−287.998			−0.469817			−0.234909	−	0.972017i	$-0.575479\pi$
$613$	−287.998			−0.469817			−0.234909	+	0.972017i	$0.575479\pi$
$614$	−200.747	+	47.5763i	−0.326950	+	0.0774858i
$615$		0			0
$616$	−73.7255	+	202.544i	−0.119684	+	0.328806i
$617$	127.843	+	221.430i	0.207201	+	0.358882i	0.950832	−	0.309708i	$-0.100231\pi$
$617$	127.843	+	221.430i	0.207201	+	0.358882i	−0.743631	+	0.668590i	$0.766898\pi$
$618$		0			0
$619$	8.60391	+	4.96747i	0.0138997	+	0.00802499i	0.506934	−	0.861985i	$-0.330779\pi$
$619$	8.60391	+	4.96747i	0.0138997	+	0.00802499i	−0.493034	+	0.870010i	$0.664112\pi$
$620$	17.3559	+	1.01114i	0.0279934	+	0.00163087i
$621$		0			0
$622$	−628.702	−	666.396i	−1.01078	−	1.07138i
$623$	−277.469	−	160.197i	−0.445375	−	0.257138i
$624$		0			0
$625$	222.059	+	384.618i	0.355295	+	0.615389i
$626$	−35.6977	−	10.6875i	−0.0570251	−	0.0170727i
$627$		0			0
$628$	−204.898	−	134.768i	−0.326271	−	0.214599i
$629$	−972.352			−1.54587
$630$		0			0
$631$		−	784.610i		−	1.24344i	−0.783240	−	0.621719i	$-0.786434\pi$
$631$		−	784.610i		−	1.24344i	0.783240	−	0.621719i	$-0.213566\pi$
$632$	103.575	+	587.483i	0.163884	+	0.929561i
$633$		0			0
$634$	−413.449	−	123.782i	−0.652128	−	0.195240i
$635$	176.786	−	102.067i	0.278402	−	0.160736i
$636$		0			0
$637$	−205.833	+	356.513i	−0.323129	+	0.559676i
$638$	−329.742	−	349.512i	−0.516838	−	0.547825i
$639$		0			0
$640$	307.685	+	467.868i	0.480758	+	0.731045i
$641$	585.512	−	1014.14i	0.913436	−	1.58212i	0.104261	−	0.994550i	$-0.466752\pi$
$641$	585.512	−	1014.14i	0.913436	−	1.58212i	0.809175	−	0.587567i	$-0.199914\pi$
$642$		0			0
$643$	466.249	−	269.189i	0.725115	−	0.418645i	−0.0915175	−	0.995803i	$-0.529172\pi$
$643$	466.249	−	269.189i	0.725115	−	0.418645i	0.816632	+	0.577158i	$0.195838\pi$
$644$	311.335	−	156.352i	0.483440	−	0.242783i
$645$		0			0
$646$	985.020	−	233.446i	1.52480	−	0.361371i
$647$			170.070i			0.262860i	0.991325	+	0.131430i	$0.0419568\pi$
$647$			170.070i			0.262860i	−0.991325	+	0.131430i	$0.958043\pi$
$648$		0			0
$649$	715.842			1.10299
$650$	−25.0409	−	105.660i	−0.0385245	−	0.162553i
$651$		0			0
$652$	−45.4645	−	90.5309i	−0.0697309	−	0.138851i
$653$	−79.1035	−	137.011i	−0.121139	−	0.209818i	0.799078	−	0.601227i	$-0.205321\pi$
$653$	−79.1035	−	137.011i	−0.121139	−	0.209818i	−0.920217	+	0.391409i	$0.871988\pi$
$654$		0			0
$655$	440.088	+	254.085i	0.671891	+	0.387916i
$656$	−411.388	−	48.0973i	−0.627115	−	0.0733191i
$657$		0			0
$658$	−108.008	+	101.899i	−0.164146	+	0.154861i
$659$	−227.314	−	131.240i	−0.344938	−	0.199150i	0.317516	−	0.948253i	$-0.397151\pi$
$659$	−227.314	−	131.240i	−0.344938	−	0.199150i	−0.662453	+	0.749103i	$0.730485\pi$
$660$		0			0
$661$	133.649	+	231.487i	0.202192	+	0.350207i	0.949234	−	0.314569i	$-0.101860\pi$
$661$	133.649	+	231.487i	0.202192	+	0.350207i	−0.747042	+	0.664776i	$0.768527\pi$
$662$	142.906	−	477.327i	0.215871	−	0.721037i
$663$		0			0
$664$	90.9688	+	515.980i	0.137001	+	0.777079i
$665$	323.001			0.485716
$666$		0			0
$667$			776.656i			1.16440i
$668$	−305.196	+	464.012i	−0.456880	+	0.694628i
$669$		0			0
$670$	238.884	−	797.904i	0.356543	−	1.19090i
$671$	−806.040	+	465.367i	−1.20125	+	0.693543i
$672$		0			0
$673$	47.8491	−	82.8770i	0.0710982	−	0.123146i	−0.828285	−	0.560307i	$-0.810683\pi$
$673$	47.8491	−	82.8770i	0.0710982	−	0.123146i	0.899383	+	0.437162i	$0.144016\pi$
$674$	−395.534	+	373.161i	−0.586846	+	0.553652i
$675$		0			0
$676$	−19.3539	+	332.204i	−0.0286300	+	0.491427i
$677$	266.057	−	460.825i	0.392995	−	0.680687i	−0.599848	−	0.800114i	$-0.704772\pi$
$677$	266.057	−	460.825i	0.392995	−	0.680687i	0.992843	+	0.119427i	$0.0381057\pi$
$678$		0			0
$679$	−208.745	+	120.519i	−0.307430	+	0.177495i
$680$	−175.231	+	481.409i	−0.257693	+	0.707954i
$681$		0			0
$682$	5.78190	+	24.3966i	0.00847785	+	0.0357721i
$683$		−	622.200i		−	0.910981i	−0.890241	−	0.455491i	$-0.849464\pi$
$683$		−	622.200i		−	0.910981i	0.890241	−	0.455491i	$-0.150536\pi$
$684$		0			0
$685$	472.089			0.689181
$686$	−388.283	+	92.0215i	−0.566010	+	0.134142i
$687$		0			0
$688$	618.891	−	266.940i	0.899550	−	0.387995i
$689$	56.6128	+	98.0562i	0.0821666	+	0.142317i
$690$		0			0
$691$	−225.074	−	129.946i	−0.325722	−	0.188056i	0.328218	−	0.944602i	$-0.393552\pi$
$691$	−225.074	−	129.946i	−0.325722	−	0.188056i	−0.653940	+	0.756546i	$0.726885\pi$
$692$	−20.9843	+	360.189i	−0.0303241	+	0.520505i
$693$		0			0
$694$	−444.981	−	471.660i	−0.641183	−	0.679625i
$695$	568.793	+	328.393i	0.818407	+	0.472508i
$696$		0			0
$697$	−189.467	−	328.166i	−0.271832	−	0.470826i
$698$	193.589	+	57.9585i	0.277349	+	0.0830351i
$699$		0			0
$700$	27.5090	−	41.8240i	0.0392986	−	0.0597485i
$701$	−1233.75			−1.75998			−0.879992	−	0.474988i	$-0.842452\pi$
$701$	−1233.75			−1.75998			−0.879992	+	0.474988i	$0.842452\pi$
$702$		0			0
$703$			2296.88i			3.26725i
$704$	−519.125	+	618.610i	−0.737393	+	0.878707i
$705$		0			0
$706$	−290.971	−	87.1135i	−0.412140	−	0.123390i
$707$	−81.2557	+	46.9130i	−0.114930	+	0.0663550i
$708$		0			0
$709$	−124.002	+	214.778i	−0.174897	+	0.302930i	−0.940126	−	0.340828i	$-0.889293\pi$
$709$	−124.002	+	214.778i	−0.174897	+	0.302930i	0.765229	+	0.643759i	$0.222626\pi$
$710$	453.692	+	480.893i	0.639003	+	0.677315i
$711$		0			0
$712$	−771.580	−	919.577i	−1.08368	−	1.29154i
$713$	20.2625	−	35.0957i	0.0284186	−	0.0492225i
$714$		0			0
$715$	−442.846	+	255.677i	−0.619365	+	0.357591i
$716$	−74.8779	−	149.100i	−0.104578	−	0.208240i
$717$		0			0
$718$	−1157.55	+	274.335i	−1.61219	+	0.382083i
$719$			925.022i			1.28654i	0.765639	+	0.643270i	$0.222423\pi$
$719$			925.022i			1.28654i	−0.765639	+	0.643270i	$0.777577\pi$
$720$		0			0
$721$	−163.780			−0.227157
$722$	−384.943	−	1624.26i	−0.533163	−	2.24967i
$723$		0			0
$724$	−302.628	+	151.979i	−0.417994	+	0.209916i
$725$	55.7986	+	96.6459i	0.0769635	+	0.133305i
$726$		0			0
$727$	611.539	+	353.072i	0.841182	+	0.485657i	0.857666	−	0.514207i	$-0.171914\pi$
$727$	611.539	+	353.072i	0.841182	+	0.485657i	−0.0164837	+	0.999864i	$0.505247\pi$
$728$	121.217	−	101.709i	0.166507	−	0.139710i
$729$		0			0
$730$	−360.972	+	340.554i	−0.494482	+	0.466512i
$731$	534.020	+	308.317i	0.730533	+	0.421774i
$732$		0			0
$733$	392.416	+	679.684i	0.535356	+	0.927264i	0.999146	+	0.0413185i	$0.0131558\pi$
$733$	392.416	+	679.684i	0.535356	+	0.927264i	−0.463790	+	0.885945i	$0.653511\pi$
$734$	−100.075	+	334.265i	−0.136342	+	0.455402i
$735$		0			0
$736$	1296.47	−	151.485i	1.76151	−	0.205821i
$737$	1201.17			1.62980
$738$		0			0
$739$			758.298i			1.02611i	0.858355	+	0.513057i	$0.171487\pi$
$739$			758.298i			1.02611i	−0.858355	+	0.513057i	$0.828513\pi$
$740$	−971.166	−	638.768i	−1.31239	−	0.863200i
$741$		0			0
$742$	−14.9711	+	50.0055i	−0.0201767	+	0.0673929i
$743$	−103.996	+	60.0421i	−0.139968	+	0.0808103i	−0.568349	−	0.822788i	$-0.692417\pi$
$743$	−103.996	+	60.0421i	−0.139968	+	0.0808103i	0.428381	+	0.903598i	$0.359084\pi$
$744$		0			0
$745$	−16.6947	+	28.9161i	−0.0224090	+	0.0388136i
$746$	420.084	−	396.323i	0.563116	−	0.531264i
$747$		0			0
$748$	−737.578	−	42.9706i	−0.986067	−	0.0574473i
$749$	−10.1792	+	17.6310i	−0.0135904	+	0.0235393i
$750$		0			0
$751$	−175.822	+	101.511i	−0.234117	+	0.135167i	−0.612470	−	0.790494i	$-0.709824\pi$
$751$	−175.822	+	101.511i	−0.234117	+	0.135167i	0.378353	+	0.925661i	$0.376491\pi$
$752$	−510.844	+	220.338i	−0.679314	+	0.293002i
$753$		0			0
$754$	81.3468	+	343.241i	0.107887	+	0.455227i
$755$		−	927.606i		−	1.22862i
$756$		0			0
$757$	690.610			0.912298			0.456149	−	0.889903i	$-0.349228\pi$
$757$	690.610			0.912298			0.456149	+	0.889903i	$0.349228\pi$
$758$	507.024	−	120.163i	0.668897	−	0.158526i
$759$		0			0
$760$	1137.18	+	413.929i	1.49628	+	0.544643i
$761$	574.862	+	995.691i	0.755404	+	1.30840i	0.945173	+	0.326569i	$0.105893\pi$
$761$	574.862	+	995.691i	0.755404	+	1.30840i	−0.189770	+	0.981829i	$0.560774\pi$
$762$		0			0
$763$	−95.0517	−	54.8781i	−0.124576	−	0.0719241i
$764$	−703.292	−	40.9731i	−0.920540	−	0.0536297i
$765$		0			0
$766$	481.488	+	510.355i	0.628574	+	0.666260i
$767$	−455.105	−	262.755i	−0.593358	−	0.342575i
$768$		0			0
$769$	317.346	+	549.659i	0.412673	+	0.714771i	0.995181	−	0.0980542i	$-0.0312618\pi$
$769$	317.346	+	549.659i	0.412673	+	0.714771i	−0.582508	+	0.812825i	$0.697929\pi$
$770$	−225.837	−	67.6132i	−0.293295	−	0.0878094i
$771$		0			0
$772$	−1112.35	−	731.629i	−1.44087	−	0.947705i
$773$	−267.560			−0.346132			−0.173066	−	0.984910i	$-0.555367\pi$
$773$	−267.560			−0.346132			−0.173066	+	0.984910i	$0.555367\pi$
$774$		0			0
$775$		−	5.82300i		−	0.00751355i
$776$	−889.366	+	156.798i	−1.14609	+	0.202059i
$777$		0			0
$778$	63.4459	+	18.9950i	0.0815500	+	0.0244152i
$779$	−775.189	+	447.556i	−0.995108	+	0.574526i
$780$		0			0
$781$	−476.727	+	825.716i	−0.610406	+	1.05725i
$782$	819.492	+	868.624i	1.04794	+	1.11077i
$783$		0			0
$784$	−706.241	−	82.5701i	−0.900818	−	0.105319i
$785$	134.113	−	232.290i	0.170844	−	0.295911i
$786$		0			0
$787$	563.164	−	325.143i	0.715583	−	0.413142i	−0.0975416	−	0.995231i	$-0.531098\pi$
$787$	563.164	−	325.143i	0.715583	−	0.413142i	0.813125	+	0.582089i	$0.197765\pi$
$788$	490.564	−	246.361i	0.622543	−	0.312641i
$789$		0			0
$790$	−634.854	+	150.458i	−0.803612	+	0.190453i
$791$			3.90748i			0.00493993i
$792$		0			0
$793$	683.266			0.861622
$794$	164.724	+	695.050i	0.207461	+	0.875378i
$795$		0			0
$796$	−513.692	−	1022.89i	−0.645342	−	1.28503i
$797$	503.422	+	871.953i	0.631646	+	1.09404i	0.987215	+	0.159393i	$0.0509538\pi$
$797$	503.422	+	871.953i	0.631646	+	1.09404i	−0.355569	+	0.934650i	$0.615713\pi$
$798$		0			0
$799$	−440.790	−	254.490i	−0.551677	−	0.318511i
$800$	150.448	−	111.995i	0.188059	−	0.139994i
$801$		0			0
$802$	−462.970	+	436.783i	−0.577269	+	0.544617i
$803$	−619.805	−	357.845i	−0.771862	−	0.445635i
$804$		0			0
$805$	190.517	+	329.985i	0.236667	+	0.409919i
$806$	5.27904	−	17.6327i	0.00654968	−	0.0218768i
$807$		0			0
$808$	−346.193	+	61.0348i	−0.428457	+	0.0755382i
$809$	135.483			0.167469			0.0837347	−	0.996488i	$-0.473315\pi$
$809$	135.483			0.167469			0.0837347	+	0.996488i	$0.473315\pi$
$810$		0			0
$811$		−	86.4723i		−	0.106624i	−0.998578	−	0.0533122i	$-0.983022\pi$
$811$		−	86.4723i		−	0.106624i	0.998578	−	0.0533122i	$-0.0169778\pi$
$812$	−89.3644	+	135.867i	−0.110055	+	0.167324i
$813$		0			0
$814$	480.801	−	1605.94i	0.590664	−	1.97290i
$815$	95.9540	−	55.3991i	0.117735	−	0.0679743i
$816$		0			0
$817$	728.301	−	1261.45i	0.891433	−	1.54401i
$818$	747.172	−	704.909i	0.913413	−	0.861748i
$819$		0			0
$820$	26.3466	−	452.232i	0.0321300	−	0.551503i
$821$	334.340	−	579.094i	0.407235	−	0.705352i	−0.587344	−	0.809338i	$-0.699826\pi$
$821$	334.340	−	579.094i	0.407235	−	0.705352i	0.994579	+	0.103986i	$0.0331596\pi$
$822$		0			0
$823$	−710.023	+	409.932i	−0.862725	+	0.498095i	−0.864924	−	0.501903i	$-0.832633\pi$
$823$	−710.023	+	409.932i	−0.862725	+	0.498095i	0.00219864	+	0.999998i	$0.499300\pi$
$824$	−576.614	−	209.886i	−0.699774	−	0.254716i
$825$		0			0
$826$	−55.8689	−	235.738i	−0.0676379	−	0.285397i
$827$			357.121i			0.431827i	0.976413	+	0.215913i	$0.0692729\pi$
$827$			357.121i			0.431827i	−0.976413	+	0.215913i	$0.930727\pi$
$828$		0			0
$829$	257.314			0.310390			0.155195	−	0.987884i	$-0.450399\pi$
$829$	257.314			0.310390			0.155195	+	0.987884i	$0.450399\pi$
$830$	−557.586	+	132.146i	−0.671790	+	0.159212i
$831$		0			0
$832$	557.105	−	202.740i	0.669598	−	0.243678i
$833$	−325.263	−	563.372i	−0.390472	−	0.676317i
$834$		0			0
$835$	−526.044	−	303.712i	−0.629993	−	0.363726i
$836$	−101.504	+	1742.30i	−0.121417	+	2.08409i
$837$		0			0
$838$	99.4405	+	105.402i	0.118664	+	0.125779i
$839$	−580.117	−	334.931i	−0.691439	−	0.399203i	0.112712	−	0.993628i	$-0.464046\pi$
$839$	−580.117	−	334.931i	−0.691439	−	0.399203i	−0.804151	+	0.594425i	$0.797380\pi$
$840$		0			0
$841$	239.235	+	414.368i	0.284465	+	0.492709i
$842$	−1209.43	−	362.090i	−1.43638	−	0.430035i
$843$		0			0
$844$	693.069	−	1053.72i	0.821171	−	1.24849i
$845$	−363.948			−0.430708
$846$		0			0
$847$		−	81.6110i		−	0.0963530i
$848$	−116.791	+	156.867i	−0.137725	+	0.184985i
$849$		0			0
$850$	164.382	+	49.2142i	0.193391	+	0.0578991i
$851$	−2346.54	+	1354.78i	−2.75739	+	1.59198i
$852$		0			0
$853$	444.254	−	769.470i	0.520813	−	0.902075i	−0.478894	−	0.877873i	$-0.658962\pi$
$853$	444.254	−	769.470i	0.520813	−	0.902075i	0.999707	−	0.0242024i	$-0.00770462\pi$
$854$	216.161	+	229.121i	0.253116	+	0.268291i
$855$		0			0
$856$	−58.4318	+	49.0278i	−0.0682615	+	0.0572755i
$857$	−238.204	+	412.582i	−0.277951	+	0.481426i	−0.970876	−	0.239585i	$-0.922989\pi$
$857$	−238.204	+	412.582i	−0.277951	+	0.481426i	0.692924	+	0.721011i	$0.256322\pi$
$858$		0			0
$859$	719.684	−	415.510i	0.837816	−	0.483714i	−0.0187050	−	0.999825i	$-0.505954\pi$
$859$	719.684	−	415.510i	0.837816	−	0.483714i	0.856521	+	0.516112i	$0.172621\pi$
$860$	330.826	+	658.755i	0.384682	+	0.765994i
$861$		0			0
$862$	−142.692	+	33.8174i	−0.165536	+	0.0392313i
$863$		−	985.009i		−	1.14138i	−0.821166	−	0.570689i	$-0.806676\pi$
$863$		−	985.009i		−	1.14138i	0.821166	−	0.570689i	$-0.193324\pi$
$864$		0			0
$865$	−394.607			−0.456193
$866$	−265.331	−	1119.56i	−0.306387	−	1.29279i
$867$		0			0
$868$	7.58291	−	3.80813i	0.00873607	−	0.00438725i
$869$	−470.459	−	814.859i	−0.541380	−	0.937697i
$870$		0			0
$871$	−763.655	−	440.897i	−0.876757	−	0.506196i
$872$	−264.318	−	315.017i	−0.303117	−	0.361258i
$873$		0			0
$874$	2051.85	−	1935.79i	2.34766	−	2.21487i
$875$	249.660	+	144.141i	0.285326	+	0.164733i
$876$		0			0
$877$	−266.136	−	460.961i	−0.303462	−	0.525611i	0.673456	−	0.739227i	$-0.264809\pi$
$877$	−266.136	−	460.961i	−0.303462	−	0.525611i	−0.976918	+	0.213616i	$0.931476\pi$
$878$	136.895	−	457.248i	0.155917	−	0.520784i
$879$		0			0
$880$	−708.450	−	527.456i	−0.805057	−	0.599381i
$881$	−1579.81			−1.79320			−0.896599	−	0.442844i	$-0.853970\pi$
$881$	−1579.81			−1.79320			−0.896599	+	0.442844i	$0.853970\pi$
$882$		0			0
$883$		−	89.6114i		−	0.101485i	−0.998712	−	0.0507426i	$-0.983841\pi$
$883$		−	89.6114i		−	0.101485i	0.998712	−	0.0507426i	$-0.0161588\pi$
$884$	453.151	+	298.053i	0.512615	+	0.337163i
$885$		0			0
$886$	30.0487	−	100.367i	0.0339150	−	0.113281i
$887$	79.9393	−	46.1530i	0.0901232	−	0.0520327i	−0.454261	−	0.890869i	$-0.650097\pi$
$887$	79.9393	−	46.1530i	0.0901232	−	0.0520327i	0.544384	+	0.838836i	$0.316763\pi$
$888$		0			0
$889$	49.8168	−	86.2853i	0.0560369	−	0.0970588i
$890$	954.958	−	900.943i	1.07299	−	1.01230i
$891$		0			0
$892$	119.302	+	6.95039i	0.133746	+	0.00779192i
$893$	−601.153	+	1041.23i	−0.673184	+	1.16599i
$894$		0			0
$895$	158.032	−	91.2396i	0.176572	−	0.101944i
$896$	244.233	+	122.675i	0.272582	+	0.136914i
$897$		0			0
$898$	261.091	+	1101.67i	0.290747	+	1.22680i
$899$			18.9163i			0.0210415i
$900$		0			0
$901$	−178.922			−0.198582
$902$	635.687	−	150.655i	0.704752	−	0.167024i
$903$		0			0
$904$	−5.00747	+	13.7569i	−0.00553924	+	0.0152178i
$905$	−185.189	−	320.756i	−0.204628	−	0.354427i
$906$		0			0
$907$	457.854	+	264.342i	0.504801	+	0.291447i	0.730694	−	0.682705i	$-0.239197\pi$
$907$	457.854	+	264.342i	0.504801	+	0.291447i	−0.225893	+	0.974152i	$0.572530\pi$
$908$	−1419.26	−	82.6846i	−1.56306	−	0.0910623i
$909$		0			0
$910$	118.761	+	125.881i	0.130507	+	0.138331i
$911$	−291.269	−	168.164i	−0.319725	−	0.184593i	0.331545	−	0.943439i	$-0.392430\pi$
$911$	−291.269	−	168.164i	−0.319725	−	0.184593i	−0.651270	+	0.758846i	$0.725763\pi$
$912$		0			0
$913$	−413.200	−	715.683i	−0.452573	−	0.783880i
$914$	65.8324	+	19.7095i	0.0720267	+	0.0215640i
$915$		0			0
$916$	294.707	+	193.839i	0.321733	+	0.211614i
$917$	248.027			0.270477
$918$		0			0
$919$			1037.58i			1.12903i	0.825423	+	0.564515i	$0.190937\pi$
$919$			1037.58i			1.12903i	−0.825423	+	0.564515i	$0.809063\pi$
$920$	247.867	+	1405.91i	0.269420	+	1.52817i
$921$		0			0
$922$	−522.189	−	156.337i	−0.566365	−	0.169563i
$923$	606.170	−	349.973i	0.656739	−	0.379169i
$924$		0			0
$925$	−194.667	+	337.172i	−0.210450	+	0.364511i
$926$	776.168	+	822.703i	0.838194	+	0.888448i
$927$		0			0
$928$	−488.737	+	363.821i	−0.526656	+	0.392049i
$929$	−248.930	+	431.159i	−0.267954	+	0.464111i	−0.968333	−	0.249661i	$-0.919681\pi$
$929$	−248.930	+	431.159i	−0.267954	+	0.464111i	0.700379	+	0.713771i	$0.253014\pi$
$930$		0			0
$931$	−1330.79	+	768.332i	−1.42942	+	0.825276i
$932$	−899.788	+	451.873i	−0.965438	+	0.484842i
$933$		0			0
$934$	−1739.66	+	412.293i	−1.86259	+	0.441427i
$935$		−	808.057i		−	0.864232i
$936$		0			0
$937$	1236.91			1.32008			0.660039	−	0.751231i	$-0.270540\pi$
$937$	1236.91			1.32008			0.660039	+	0.751231i	$0.270540\pi$
$938$	−93.7466	−	395.562i	−0.0999431	−	0.421708i
$939$		0			0
$940$	−273.070	−	543.749i	−0.290500	−	0.578456i
$941$	337.684	+	584.887i	0.358857	+	0.621558i	0.987770	−	0.155917i	$-0.0498333\pi$
$941$	337.684	+	584.887i	0.358857	+	0.621558i	−0.628913	+	0.777476i	$0.716500\pi$
$942$		0			0
$943$	−914.466	−	527.967i	−0.969741	−	0.559880i
$944$	105.404	−	901.549i	0.111657	−	0.955030i
$945$		0			0
$946$	−773.275	+	729.536i	−0.817415	+	0.771180i
$947$	160.432	+	92.6256i	0.169411	+	0.0978095i	0.582308	−	0.812968i	$-0.302150\pi$
$947$	160.432	+	92.6256i	0.169411	+	0.0978095i	−0.412897	+	0.910778i	$0.635483\pi$
$948$		0			0
$949$	262.699	+	455.008i	0.276817	+	0.479461i
$950$	116.253	−	388.301i	0.122372	−	0.408738i
$951$		0			0
$952$	43.4145	+	246.249i	0.0456034	+	0.258665i
$953$	399.942			0.419667			0.209833	−	0.977737i	$-0.432708\pi$
$953$	399.942			0.419667			0.209833	+	0.977737i	$0.432708\pi$
$954$		0			0
$955$		−	770.495i		−	0.806801i
$956$	−312.725	+	475.459i	−0.327118	+	0.497342i
$957$		0			0
$958$	−309.816	+	1034.83i	−0.323399	+	1.08020i
$959$	199.547	−	115.208i	0.208078	−	0.120134i
$960$		0			0
$961$	−480.006	+	831.396i	−0.499486	+	0.865136i
$962$	−895.147	+	844.515i	−0.930507	+	0.877874i
$963$		0			0
$964$	−13.2682	+	227.745i	−0.0137637	+	0.236250i
$965$	728.071	−	1261.06i	0.754478	−	1.30679i
$966$		0			0
$967$	−62.7437	+	36.2251i	−0.0648849	+	0.0374613i	−0.532091	−	0.846687i	$-0.678594\pi$
$967$	−62.7437	+	36.2251i	−0.0648849	+	0.0374613i	0.467207	+	0.884148i	$0.345260\pi$
$968$	104.585	−	287.324i	0.108043	−	0.296823i
$969$		0			0
$970$	−227.772	−	961.079i	−0.234816	−	0.990803i
$971$			1165.69i			1.20051i	0.799810	+	0.600253i	$0.204933\pi$
$971$			1165.69i			1.20051i	−0.799810	+	0.600253i	$0.795067\pi$
$972$		0			0
$973$	320.563			0.329458
$974$	1009.40	−	239.224i	1.03635	−	0.245610i
$975$		0			0
$976$	467.409	+	1083.67i	0.478903	+	1.11032i
$977$	−182.949	−	316.877i	−0.187256	−	0.324337i	0.757078	−	0.653324i	$-0.226626\pi$
$977$	−182.949	−	316.877i	−0.187256	−	0.324337i	−0.944334	+	0.328987i	$0.893293\pi$
$978$		0			0
$979$	1639.71	+	946.685i	1.67488	+	0.966992i
$980$	45.2300	−	776.360i	0.0461531	−	0.792205i
$981$		0			0
$982$	206.333	+	218.703i	0.210115	+	0.222712i
$983$	892.550	+	515.314i	0.907986	+	0.524226i	0.879782	−	0.475376i	$-0.157688\pi$
$983$	892.550	+	515.314i	0.907986	+	0.524226i	0.0282031	+	0.999602i	$0.491021\pi$
$984$		0			0
$985$	300.193	+	519.950i	0.304765	+	0.527868i
$986$	−534.004	−	159.875i	−0.541587	−	0.162145i
$987$		0			0
$988$	704.055	−	1070.43i	0.712607	−	1.08343i
$989$	1718.31			1.73742
$990$		0			0
$991$		−	1893.70i		−	1.91090i	−0.295148	−	0.955451i	$-0.595369\pi$
$991$		−	1893.70i		−	1.91090i	0.295148	−	0.955451i	$-0.404631\pi$
$992$	31.5770	−	3.68957i	0.0318317	−	0.00371933i
$993$		0			0
$994$	309.128	+	92.5494i	0.310994	+	0.0931080i
$995$	1084.16	−	625.940i	1.08961	−	0.629085i
$996$		0			0
$997$	644.593	−	1116.47i	0.646533	−	1.11983i	−0.337412	−	0.941357i	$-0.609552\pi$
$997$	644.593	−	1116.47i	0.646533	−	1.11983i	0.983945	−	0.178471i	$-0.0571150\pi$
$998$	−421.158	−	446.408i	−0.422002	−	0.447303i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.r.55.4		12
3.2	odd	2		324.3.f.q.55.3		12
4.3	odd	2	inner	324.3.f.r.55.1		12
9.2	odd	6		324.3.d.f.163.2	yes	6
9.4	even	3	inner	324.3.f.r.271.1		12
9.5	odd	6		324.3.f.q.271.6		12
9.7	even	3		324.3.d.e.163.5	✓	6
12.11	even	2		324.3.f.q.55.6		12
36.7	odd	6		324.3.d.e.163.6	yes	6
36.11	even	6		324.3.d.f.163.1	yes	6
36.23	even	6		324.3.f.q.271.3		12
36.31	odd	6	inner	324.3.f.r.271.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.e.163.5	✓	6	9.7	even	3
324.3.d.e.163.6	yes	6	36.7	odd	6
324.3.d.f.163.1	yes	6	36.11	even	6
324.3.d.f.163.2	yes	6	9.2	odd	6
324.3.f.q.55.3		12	3.2	odd	2
324.3.f.q.55.6		12	12.11	even	2
324.3.f.q.271.3		12	36.23	even	6
324.3.f.q.271.6		12	9.5	odd	6
324.3.f.r.55.1		12	4.3	odd	2	inner
324.3.f.r.55.4		12	1.1	even	1	trivial
324.3.f.r.271.1		12	9.4	even	3	inner
324.3.f.r.271.4		12	36.31	odd	6	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.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.461217 + 1.94609i) q^{2} +(-3.57456 + 1.79514i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(-1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +O(q^{10})\)	\(q+(0.461217 + 1.94609i) q^{2} +(-3.57456 + 1.79514i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(-1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +(6.36427 - 6.00429i) q^{10} +(10.9277 + 6.30914i) q^{11} +(-4.63163 - 8.02222i) q^{13} +(1.22482 - 4.09108i) q^{14} +(9.55494 - 12.8337i) q^{16} +14.6381 q^{17} -34.5778i q^{19} +(14.6202 + 9.61619i) q^{20} +(-7.23811 + 24.1763i) q^{22} +(35.3255 - 20.3952i) q^{23} +(2.93057 - 5.07589i) q^{25} +(13.4758 - 12.7136i) q^{26} +(8.52653 + 0.496747i) q^{28} +(-9.52010 + 16.4893i) q^{29} +(0.860391 - 0.496747i) q^{31} +(29.3824 + 12.6757i) q^{32} +(6.75132 + 28.4870i) q^{34} +9.34128i q^{35} -66.4263 q^{37} +(67.2917 - 15.9479i) q^{38} +(-11.9709 + 32.8875i) q^{40} +(-12.9434 - 22.4187i) q^{41} +(36.4816 + 21.0627i) q^{43} +(-50.3877 - 2.93554i) q^{44} +(55.9836 + 59.3401i) q^{46} +(-30.1126 - 17.3855i) q^{47} +(-22.2204 - 38.4868i) q^{49} +(11.2298 + 3.36207i) q^{50} +(30.9571 + 20.3615i) q^{52} -12.2231 q^{53} -55.2024i q^{55} +(2.96586 + 16.8225i) q^{56} +(-36.4805 - 10.9219i) q^{58} +(49.1301 - 28.3653i) q^{59} +(-36.8804 + 63.8788i) q^{61} +(1.36354 + 1.44529i) q^{62} +(-11.1164 + 63.0272i) q^{64} +(-20.2625 + 35.0956i) q^{65} +(82.4391 - 47.5962i) q^{67} +(-52.3246 + 26.2774i) q^{68} +(-18.1790 + 4.30835i) q^{70} +75.5614i q^{71} -56.7185 q^{73} +(-30.6369 - 129.272i) q^{74} +(62.0721 + 123.600i) q^{76} +(-13.4716 - 23.3334i) q^{77} +(-64.5777 - 37.2839i) q^{79} +(-69.5232 - 8.12830i) q^{80} +(37.6591 - 35.5290i) q^{82} +(-56.7179 - 32.7461i) q^{83} +(-32.0193 - 55.4590i) q^{85} +(-24.1640 + 80.7110i) q^{86} +(-17.5268 - 99.4130i) q^{88} +150.050 q^{89} +19.7794i q^{91} +(-89.6608 + 136.318i) q^{92} +(19.9454 - 66.6204i) q^{94} +(-131.005 + 75.6355i) q^{95} +(56.4426 - 97.7615i) q^{97} +(64.6505 - 60.9936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

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