LMFDB - Embedded newform 324.3.f.q.55.3

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			55.3
Root			$1.25131 - 0.658947i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.q.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.461217 - 1.94609i) q^{2} +(-3.57456 + 1.79514i) q^{4} +(2.18740 + 3.78869i) q^{5} +(-1.84918 - 1.06762i) q^{7} +(5.14216 + 6.12848i) q^{8} +O(q^{10})$	\(q+(-0.461217 - 1.94609i) q^{2} +(-3.57456 + 1.79514i) q^{4} +(2.18740 + 3.78869i) q^{5} +(-1.84918 - 1.06762i) q^{7} +(5.14216 + 6.12848i) q^{8} +(6.36427 - 6.00429i) q^{10} +(-10.9277 - 6.30914i) q^{11} +(-4.63163 - 8.02222i) q^{13} +(-1.22482 + 4.09108i) q^{14} +(9.55494 - 12.8337i) q^{16} -14.6381 q^{17} -34.5778i q^{19} +(-14.6202 - 9.61619i) q^{20} +(-7.23811 + 24.1763i) q^{22} +(-35.3255 + 20.3952i) q^{23} +(2.93057 - 5.07589i) q^{25} +(-13.4758 + 12.7136i) q^{26} +(8.52653 + 0.496747i) q^{28} +(9.52010 - 16.4893i) q^{29} +(0.860391 - 0.496747i) q^{31} +(-29.3824 - 12.6757i) q^{32} +(6.75132 + 28.4870i) q^{34} -9.34128i q^{35} -66.4263 q^{37} +(-67.2917 + 15.9479i) q^{38} +(-11.9709 + 32.8875i) q^{40} +(12.9434 + 22.4187i) q^{41} +(36.4816 + 21.0627i) q^{43} +(50.3877 + 2.93554i) q^{44} +(55.9836 + 59.3401i) q^{46} +(30.1126 + 17.3855i) q^{47} +(-22.2204 - 38.4868i) q^{49} +(-11.2298 - 3.36207i) q^{50} +(30.9571 + 20.3615i) q^{52} +12.2231 q^{53} -55.2024i q^{55} +(-2.96586 - 16.8225i) q^{56} +(-36.4805 - 10.9219i) q^{58} +(-49.1301 + 28.3653i) q^{59} +(-36.8804 + 63.8788i) q^{61} +(-1.36354 - 1.44529i) q^{62} +(-11.1164 + 63.0272i) q^{64} +(20.2625 - 35.0956i) q^{65} +(82.4391 - 47.5962i) q^{67} +(52.3246 - 26.2774i) q^{68} +(-18.1790 + 4.30835i) q^{70} -75.5614i q^{71} -56.7185 q^{73} +(30.6369 + 129.272i) q^{74} +(62.0721 + 123.600i) q^{76} +(13.4716 + 23.3334i) q^{77} +(-64.5777 - 37.2839i) q^{79} +(69.5232 + 8.12830i) q^{80} +(37.6591 - 35.5290i) q^{82} +(56.7179 + 32.7461i) q^{83} +(-32.0193 - 55.4590i) q^{85} +(24.1640 - 80.7110i) q^{86} +(-17.5268 - 99.4130i) q^{88} -150.050 q^{89} +19.7794i q^{91} +(89.6608 - 136.318i) q^{92} +(19.9454 - 66.6204i) q^{94} +(131.005 - 75.6355i) q^{95} +(56.4426 - 97.7615i) q^{97} +(-64.6505 + 60.9936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.997494	−	0.0707454i	$-0.0225378\pi$
$5$	2.18740	+	3.78869i	0.437480	+	0.757737i	−0.560014	+	0.828483i	$0.689204\pi$
$6$		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	−0.0871333	−	0.996197i	$-0.527771\pi$
$11$	−10.9277	−	6.30914i	−0.993432	−	0.573558i	−0.906298	+	0.422639i	$0.861104\pi$
$12$		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	$-0.641674\pi$
$17$	−14.6381			−0.861063			−0.430531	+	0.902576i	$0.641674\pi$
$18$		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	$0.680374\pi$
$23$	−35.3255	+	20.3952i	−1.53589	+	0.886747i	−0.999073	+	0.0430488i	$0.986293\pi$
$24$		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	−0.653891	−	0.756589i	$-0.726865\pi$
$29$	9.52010	−	16.4893i	0.328279	−	0.568596i	0.982171	+	0.187992i	$0.0601980\pi$
$30$		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	0.979585	−	0.201032i	$-0.0644296\pi$
$41$	12.9434	+	22.4187i	0.315693	+	0.546797i	−0.663891	+	0.747829i	$0.731096\pi$
$42$		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	0.784882	−	0.619646i	$-0.212724\pi$
$47$	30.1126	+	17.3855i	0.640694	+	0.369905i	−0.144188	+	0.989550i	$0.546057\pi$
$48$		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	$-0.463213\pi$
$53$	12.2231			0.230624			0.115312	+	0.993329i	$0.463213\pi$
$54$		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	−0.854781	−	0.518989i	$-0.826309\pi$
$59$	−49.1301	+	28.3653i	−0.832714	+	0.480768i	0.0220670	+	0.999756i	$0.492975\pi$
$60$		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	$-0.821395\pi$
$71$		−	75.5614i		−	1.06424i	0.846667	−	0.532122i	$-0.178605\pi$
$72$		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	0.801116	−	0.598510i	$-0.204240\pi$
$83$	56.7179	+	32.7461i	0.683349	+	0.394532i	−0.117767	+	0.993041i	$0.537574\pi$
$84$		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	$-0.819199\pi$
$89$	−150.050			−1.68595			−0.842977	+	0.537950i	$0.819199\pi$
$90$		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	−0.954053	−	0.299638i	$-0.903134\pi$
$101$	−21.9708	+	38.0545i	−0.217532	+	0.376777i	0.736521	+	0.676415i	$0.236467\pi$
$102$		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	$0.0141866\pi$
$107$			9.53448i			0.0891073i	−0.999007	+	0.0445537i	$0.985813\pi$
$108$		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	0.870046	−	0.492971i	$-0.164089\pi$
$113$	0.914995	+	1.58482i	0.00809730	+	0.0140249i	−0.861948	+	0.506996i	$0.830756\pi$
$114$		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	−0.0642183	−	0.997936i	$-0.520455\pi$
$131$	100.596	−	58.0793i	0.767910	−	0.443353i	0.832129	+	0.554583i	$0.187122\pi$
$132$		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	−0.599116	−	0.800662i	$-0.704481\pi$
$137$	53.9555	−	93.4536i	0.393836	−	0.682143i	0.992952	+	0.118519i	$0.0378146\pi$
$138$		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	0.878547	−	0.477656i	$-0.158513\pi$
$149$	3.81611	+	6.60970i	0.0256115	+	0.0443604i	−0.852936	+	0.522016i	$0.825180\pi$
$150$		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	−0.814762	−	0.579796i	$-0.803132\pi$
$167$	−120.244	+	69.4230i	−0.720025	+	0.415707i	0.0947370	+	0.995502i	$0.469799\pi$
$168$		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	−0.966426	−	0.256944i	$-0.917285\pi$
$173$	−45.1000	+	78.1155i	−0.260694	+	0.451534i	0.705733	+	0.708478i	$0.250618\pi$
$174$		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	$-0.962829\pi$
$179$		−	41.7114i		−	0.233025i	0.993189	−	0.116512i	$-0.0371715\pi$
$180$		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	0.0444058	−	0.999014i	$-0.485861\pi$
$191$	−152.525	−	88.0606i	−0.798562	−	0.461050i	−0.842968	+	0.537963i	$0.819194\pi$
$192$		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	$-0.386753\pi$
$197$	137.238			0.696637			0.348319	+	0.937376i	$0.386753\pi$
$198$		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	−0.366870	−	0.930272i	$-0.619571\pi$
$227$	−307.799	−	177.708i	−1.35594	−	0.782855i	−0.989074	+	0.147418i	$0.952904\pi$
$228$		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	$-0.681641\pi$
$233$	−251.720			−1.08034			−0.540172	+	0.841555i	$0.681641\pi$
$234$		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	−0.735102	−	0.677957i	$-0.762866\pi$
$239$	−123.211	+	71.1356i	−0.515525	+	0.297639i	0.219577	+	0.975595i	$0.429532\pi$
$240$		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	$0.000367526\pi$
$251$			0.579617i			0.00230923i	−0.999999	+	0.00115462i	$0.999632\pi$
$252$		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	$-0.954083\pi$
$257$	−159.160	−	275.674i	−0.619301	−	1.07266i	0.370313	−	0.928907i	$-0.379250\pi$
$258$		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	−0.111535	−	0.993761i	$-0.535577\pi$
$263$	−270.344	−	156.083i	−1.02792	−	0.593472i	−0.916389	+	0.400288i	$0.868910\pi$
$264$		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	$-0.148769\pi$
$269$	480.302			1.78551			0.892755	+	0.450542i	$0.148769\pi$
$270$		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	−0.899412	−	0.437102i	$-0.856005\pi$
$281$	−19.9973	+	34.6363i	−0.0711647	+	0.123261i	0.828247	+	0.560363i	$0.189338\pi$
$282$		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	$0.162329\pi$
$293$	251.725	+	436.001i	0.859131	+	1.48806i	−0.0136273	+	0.999907i	$0.504338\pi$
$294$		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	0.299557	−	0.954078i	$-0.403161\pi$
$311$	396.709	−	229.040i	1.27559	−	0.736463i	0.976035	+	0.217615i	$0.0698277\pi$
$312$		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	−0.644137	−	0.764910i	$-0.722783\pi$
$317$	107.895	−	186.880i	0.340363	−	0.589527i	0.984500	+	0.175384i	$0.0561166\pi$
$318$		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	−0.0374985	−	0.999297i	$-0.511939\pi$
$347$	280.781	−	162.109i	0.809169	−	0.467174i	0.846667	+	0.532123i	$0.178606\pi$
$348$		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	−0.738198	−	0.674584i	$-0.764323\pi$
$353$	75.9329	−	131.520i	0.215107	−	0.372577i	0.953306	+	0.302007i	$0.0976565\pi$
$354$		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	$-0.689238\pi$
$359$		−	594.808i		−	1.65685i	0.560102	−	0.828424i	$-0.310762\pi$
$360$		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	−0.841108	−	0.540867i	$-0.818096\pi$
$383$	−303.817	+	175.409i	−0.793257	+	0.457987i	0.0478509	+	0.998854i	$0.484763\pi$
$384$		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	−0.886522	−	0.462686i	$-0.846886\pi$
$389$	−16.5571	+	28.6777i	−0.0425632	+	0.0737216i	0.843959	+	0.536408i	$0.180219\pi$
$390$		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	0.596517	−	0.802601i	$-0.296551\pi$
$401$	−159.123	−	275.608i	−0.396814	−	0.687303i	−0.993331	+	0.115298i	$0.963218\pi$
$402$		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	−0.573004	−	0.819552i	$-0.694222\pi$
$419$	−62.7466	+	36.2268i	−0.149753	+	0.0864601i	0.423251	+	0.906012i	$0.360889\pi$
$420$		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	$-0.972892\pi$
$431$		−	73.3222i		−	0.170121i	0.996376	−	0.0850606i	$-0.0271084\pi$
$432$		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	0.550329	−	0.834948i	$-0.314502\pi$
$443$	45.3661	+	26.1921i	0.102407	+	0.0591244i	−0.447922	+	0.894073i	$0.647836\pi$
$444$		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	$-0.717106\pi$
$449$	−566.091			−1.26078			−0.630391	+	0.776277i	$0.717106\pi$
$450$		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	−0.679523	−	0.733654i	$-0.737813\pi$
$461$	136.272	−	236.031i	0.295602	−	0.511997i	0.975125	+	0.221657i	$0.0711466\pi$
$462$		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	$-0.593582\pi$
$467$		−	893.925i		−	1.91419i	0.289780	−	0.957093i	$-0.406418\pi$
$468$		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	−0.0752909	−	0.997162i	$-0.523989\pi$
$479$	−467.745	−	270.053i	−0.976504	−	0.563785i	−0.901213	+	0.433377i	$0.857322\pi$
$480$		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	−0.626688	−	0.779271i	$-0.715590\pi$
$491$	−130.195	+	75.1683i	−0.265163	+	0.153092i	0.361524	+	0.932363i	$0.382256\pi$
$492$		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	$0.259137\pi$
$503$			731.474i			1.45422i	−0.686520	+	0.727111i	$0.740863\pi$
$504$		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	0.893646	−	0.448773i	$-0.148139\pi$
$509$	29.6107	+	51.2873i	0.0581743	+	0.100761i	−0.835472	+	0.549534i	$0.814805\pi$
$510$		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	$-0.730005\pi$
$521$	−689.100			−1.32265			−0.661324	+	0.750100i	$0.730005\pi$
$522$		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	$-0.565412\pi$
$557$	−227.316			−0.408108			−0.204054	+	0.978960i	$0.565412\pi$
$558$		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	−0.959053	−	0.283227i	$-0.908595\pi$
$563$	−671.826	+	387.879i	−1.19330	+	0.688950i	−0.234244	+	0.972178i	$0.575262\pi$
$564$		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	$-0.515917\pi$
$569$	477.933	−	827.803i	0.839952	−	1.45484i	0.889934	−	0.456089i	$-0.150750\pi$
$570$		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	−0.0804579	−	0.996758i	$-0.525638\pi$
$587$	−577.552	−	333.450i	−0.983905	−	0.568058i	−0.903447	+	0.428700i	$0.858972\pi$
$588$		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	$-0.443908\pi$
$593$	207.914			0.350613			0.175307	+	0.984514i	$0.443908\pi$
$594$		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	−0.717499	−	0.696560i	$-0.754713\pi$
$599$	−283.333	+	163.582i	−0.473010	+	0.273092i	0.244489	+	0.969652i	$0.421380\pi$
$600$		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	0.743631	−	0.668590i	$-0.233102\pi$
$617$	−127.843	−	221.430i	−0.207201	−	0.358882i	−0.950832	+	0.309708i	$0.899769\pi$
$618$		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	$0.533248\pi$
$641$	−585.512	+	1014.14i	−0.913436	+	1.58212i	−0.809175	+	0.587567i	$0.800086\pi$
$642$		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	$-0.958043\pi$
$647$		−	170.070i		−	0.262860i	0.991325	−	0.131430i	$-0.0419568\pi$
$648$		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	0.920217	−	0.391409i	$-0.128012\pi$
$653$	79.1035	+	137.011i	0.121139	+	0.209818i	−0.799078	+	0.601227i	$0.794679\pi$
$654$		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	0.662453	−	0.749103i	$-0.269515\pi$
$659$	227.314	+	131.240i	0.344938	+	0.199150i	−0.317516	+	0.948253i	$0.602849\pi$
$660$		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	−0.992843	−	0.119427i	$-0.961894\pi$
$677$	−266.057	+	460.825i	−0.392995	+	0.680687i	0.599848	+	0.800114i	$0.295228\pi$
$678$		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	$0.150536\pi$
$683$			622.200i			0.910981i	−0.890241	+	0.455491i	$0.849464\pi$
$684$		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	$-0.157548\pi$
$701$	1233.75			1.75998			0.879992	+	0.474988i	$0.157548\pi$
$702$		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	$-0.777577\pi$
$719$		−	925.022i		−	1.28654i	0.765639	−	0.643270i	$-0.222423\pi$
$720$		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	−0.428381	−	0.903598i	$-0.640916\pi$
$743$	103.996	−	60.0421i	0.139968	−	0.0808103i	0.568349	+	0.822788i	$0.307583\pi$
$744$		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	$-0.894107\pi$
$761$	−574.862	−	995.691i	−0.755404	−	1.30840i	0.189770	−	0.981829i	$-0.439226\pi$
$762$		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	$-0.444633\pi$
$773$	267.560			0.346132			0.173066	+	0.984910i	$0.444633\pi$
$774$		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	$-0.949046\pi$
$797$	−503.422	−	871.953i	−0.631646	−	1.09404i	0.355569	−	0.934650i	$-0.384287\pi$
$798$		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	$-0.526685\pi$
$809$	−135.483			−0.167469			−0.0837347	+	0.996488i	$0.526685\pi$
$810$		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	−0.994579	−	0.103986i	$-0.966840\pi$
$821$	−334.340	+	579.094i	−0.407235	+	0.705352i	0.587344	+	0.809338i	$0.300174\pi$
$822$		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	$-0.930727\pi$
$827$		−	357.121i		−	0.431827i	0.976413	−	0.215913i	$-0.0692729\pi$
$828$		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	0.804151	−	0.594425i	$-0.202620\pi$
$839$	580.117	+	334.931i	0.691439	+	0.399203i	−0.112712	+	0.993628i	$0.535954\pi$
$840$		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	−0.692924	−	0.721011i	$-0.743678\pi$
$857$	238.204	−	412.582i	0.277951	−	0.481426i	0.970876	+	0.239585i	$0.0770112\pi$
$858$		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	$0.193324\pi$
$863$			985.009i			1.14138i	−0.821166	+	0.570689i	$0.806676\pi$
$864$		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	$-0.146030\pi$
$881$	1579.81			1.79320			0.896599	+	0.442844i	$0.146030\pi$
$882$		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	−0.544384	−	0.838836i	$-0.683237\pi$
$887$	−79.9393	+	46.1530i	−0.0901232	+	0.0520327i	0.454261	+	0.890869i	$0.349903\pi$
$888$		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	0.651270	−	0.758846i	$-0.274237\pi$
$911$	291.269	+	168.164i	0.319725	+	0.184593i	−0.331545	+	0.943439i	$0.607570\pi$
$912$		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	−0.700379	−	0.713771i	$-0.746986\pi$
$929$	248.930	−	431.159i	0.267954	−	0.464111i	0.968333	+	0.249661i	$0.0803190\pi$
$930$		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	0.628913	−	0.777476i	$-0.283500\pi$
$941$	−337.684	−	584.887i	−0.358857	−	0.621558i	−0.987770	+	0.155917i	$0.950167\pi$
$942$		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	0.412897	−	0.910778i	$-0.364517\pi$
$947$	−160.432	−	92.6256i	−0.169411	−	0.0978095i	−0.582308	+	0.812968i	$0.697850\pi$
$948$		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	$-0.567292\pi$
$953$	−399.942			−0.419667			−0.209833	+	0.977737i	$0.567292\pi$
$954$		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	$-0.795067\pi$
$971$		−	1165.69i		−	1.20051i	0.799810	−	0.600253i	$-0.204933\pi$
$972$		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	0.944334	−	0.328987i	$-0.106707\pi$
$977$	182.949	+	316.877i	0.187256	+	0.324337i	−0.757078	+	0.653324i	$0.773374\pi$
$978$		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	−0.0282031	−	0.999602i	$-0.508979\pi$
$983$	−892.550	−	515.314i	−0.907986	−	0.524226i	−0.879782	+	0.475376i	$0.842312\pi$
$984$		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.q.55.3		12
3.2	odd	2		324.3.f.r.55.4		12
4.3	odd	2	inner	324.3.f.q.55.6		12
9.2	odd	6		324.3.d.e.163.5	✓	6
9.4	even	3	inner	324.3.f.q.271.6		12
9.5	odd	6		324.3.f.r.271.1		12
9.7	even	3		324.3.d.f.163.2	yes	6
12.11	even	2		324.3.f.r.55.1		12
36.7	odd	6		324.3.d.f.163.1	yes	6
36.11	even	6		324.3.d.e.163.6	yes	6
36.23	even	6		324.3.f.r.271.4		12
36.31	odd	6	inner	324.3.f.q.271.3		12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

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