LMFDB - Embedded newform 1080.2.d.i.109.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(109,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1080.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.d (of order $2$, degree $1$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 $ x^20 - 3x^18 + 8x^16 - 24x^14 + 56x^12 - 92x^10 + 224x^8 - 384x^6 + 512x^4 - 768*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.20
Root			$-1.37859 + 0.315404i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.i.109.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37859 + 0.315404i) q^{2} +(1.80104 + 0.869628i) q^{4} +(-2.03021 - 0.937151i) q^{5} +3.36920i q^{7} +(2.20862 + 1.76692i) q^{8} +O(q^{10})$	\(q+(1.37859 + 0.315404i) q^{2} +(1.80104 + 0.869628i) q^{4} +(-2.03021 - 0.937151i) q^{5} +3.36920i q^{7} +(2.20862 + 1.76692i) q^{8} +(-2.50325 - 1.93229i) q^{10} +4.10347i q^{11} -6.13592 q^{13} +(-1.06266 + 4.64476i) q^{14} +(2.48750 + 3.13247i) q^{16} -7.47638i q^{17} +6.20559i q^{19} +(-2.84152 - 3.45337i) q^{20} +(-1.29425 + 5.65702i) q^{22} +3.15814i q^{23} +(3.24349 + 3.80523i) q^{25} +(-8.45894 - 1.93529i) q^{26} +(-2.92995 + 6.06807i) q^{28} +1.34325i q^{29} +0.229172 q^{31} +(2.44125 + 5.10297i) q^{32} +(2.35808 - 10.3069i) q^{34} +(3.15745 - 6.84018i) q^{35} -5.64792 q^{37} +(-1.95727 + 8.55499i) q^{38} +(-2.82809 - 5.65702i) q^{40} +4.52568 q^{41} -2.02966 q^{43} +(-3.56849 + 7.39052i) q^{44} +(-0.996090 + 4.35379i) q^{46} +1.67033i q^{47} -4.35151 q^{49} +(3.27128 + 6.26887i) q^{50} +(-11.0510 - 5.33596i) q^{52} +10.1003 q^{53} +(3.84558 - 8.33091i) q^{55} +(-5.95310 + 7.44128i) q^{56} +(-0.423667 + 1.85180i) q^{58} -3.07651i q^{59} -0.762740i q^{61} +(0.315935 + 0.0722817i) q^{62} +(1.75600 + 7.80490i) q^{64} +(12.4572 + 5.75028i) q^{65} +13.8657 q^{67} +(6.50167 - 13.4653i) q^{68} +(6.51026 - 8.43396i) q^{70} +1.26579 q^{71} +13.9347i q^{73} +(-7.78618 - 1.78137i) q^{74} +(-5.39655 + 11.1765i) q^{76} -13.8254 q^{77} +0.245252 q^{79} +(-2.11454 - 8.69073i) q^{80} +(6.23908 + 1.42742i) q^{82} -13.3602 q^{83} +(-7.00650 + 15.1786i) q^{85} +(-2.79807 - 0.640162i) q^{86} +(-7.25050 + 9.06301i) q^{88} +8.64631 q^{89} -20.6731i q^{91} +(-2.74641 + 5.68794i) q^{92} +(-0.526827 + 2.30270i) q^{94} +(5.81558 - 12.5986i) q^{95} -12.2906i q^{97} +(-5.99897 - 1.37248i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{4}+O(q^{10}) $ 20 * q + 6 * q^4	$ 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64} + 12 q^{70} - 24 q^{76} + 36 q^{79} + 32 q^{82} - 44 q^{85} - 30 q^{88} - 22 q^{94}+O(q^{100}) $ 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.37859	+	0.315404i	0.974813	+	0.223024i
$2$	1.37859	+	0.315404i	0.974813	+	0.223024i
$3$		0			0
$3$		0			0
$4$	1.80104	+	0.869628i	0.900520	+	0.434814i
$5$	−2.03021	−	0.937151i	−0.907937	−	0.419107i
$5$	−2.03021	−	0.937151i	−0.907937	−	0.419107i
$6$		0			0
$7$			3.36920i			1.27344i	0.771096	+	0.636719i	$0.219709\pi$
$7$			3.36920i			1.27344i	−0.771096	+	0.636719i	$0.780291\pi$
$8$	2.20862	+	1.76692i	0.780865	+	0.624700i
$9$		0			0
$10$	−2.50325	−	1.93229i	−0.791598	−	0.611043i
$11$			4.10347i			1.23724i	0.785689	+	0.618622i	$0.212309\pi$
$11$			4.10347i			1.23724i	−0.785689	+	0.618622i	$0.787691\pi$
$12$		0			0
$13$	−6.13592			−1.70180			−0.850899	−	0.525330i	$-0.823942\pi$
$13$	−6.13592			−1.70180			−0.850899	+	0.525330i	$0.823942\pi$
$14$	−1.06266	+	4.64476i	−0.284008	+	1.24136i
$15$		0			0
$16$	2.48750	+	3.13247i	0.621874	+	0.783117i
$17$		−	7.47638i		−	1.81329i	−0.421895	−	0.906645i	$-0.638635\pi$
$17$		−	7.47638i		−	1.81329i	0.421895	−	0.906645i	$-0.361365\pi$
$18$		0			0
$19$			6.20559i			1.42366i	0.702352	+	0.711830i	$0.252133\pi$
$19$			6.20559i			1.42366i	−0.702352	+	0.711830i	$0.747867\pi$
$20$	−2.84152	−	3.45337i	−0.635382	−	0.772198i
$21$		0			0
$22$	−1.29425	+	5.65702i	−0.275935	+	1.20608i
$23$			3.15814i			0.658518i	0.944240	+	0.329259i	$0.106799\pi$
$23$			3.15814i			0.658518i	−0.944240	+	0.329259i	$0.893201\pi$
$24$		0			0
$25$	3.24349	+	3.80523i	0.648699	+	0.761045i
$26$	−8.45894	−	1.93529i	−1.65893	−	0.379542i
$27$		0			0
$28$	−2.92995	+	6.06807i	−0.553708	+	1.14676i
$29$			1.34325i			0.249436i	0.992192	+	0.124718i	$0.0398025\pi$
$29$			1.34325i			0.249436i	−0.992192	+	0.124718i	$0.960197\pi$
$30$		0			0
$31$	0.229172			0.0411605			0.0205802	−	0.999788i	$-0.493449\pi$
$31$	0.229172			0.0411605			0.0205802	+	0.999788i	$0.493449\pi$
$32$	2.44125	+	5.10297i	0.431557	+	0.902086i
$33$		0			0
$34$	2.35808	−	10.3069i	0.404408	−	1.76762i
$35$	3.15745	−	6.84018i	0.533707	−	1.15620i
$36$		0			0
$37$	−5.64792			−0.928512			−0.464256	−	0.885701i	$-0.653678\pi$
$37$	−5.64792			−0.928512			−0.464256	+	0.885701i	$0.653678\pi$
$38$	−1.95727	+	8.55499i	−0.317511	+	1.38780i
$39$		0			0
$40$	−2.82809	−	5.65702i	−0.447160	−	0.894454i
$41$	4.52568			0.706793			0.353397	−	0.935474i	$-0.385027\pi$
$41$	4.52568			0.706793			0.353397	+	0.935474i	$0.385027\pi$
$42$		0			0
$43$	−2.02966			−0.309520			−0.154760	−	0.987952i	$-0.549460\pi$
$43$	−2.02966			−0.309520			−0.154760	+	0.987952i	$0.549460\pi$
$44$	−3.56849	+	7.39052i	−0.537971	+	1.11416i
$45$		0			0
$46$	−0.996090	+	4.35379i	−0.146865	+	0.641932i
$47$			1.67033i			0.243642i	0.992552	+	0.121821i	$0.0388734\pi$
$47$			1.67033i			0.243642i	−0.992552	+	0.121821i	$0.961127\pi$
$48$		0			0
$49$	−4.35151			−0.621645
$50$	3.27128	+	6.26887i	0.462629	+	0.886552i
$51$		0			0
$52$	−11.0510	−	5.33596i	−1.53250	−	0.739965i
$53$	10.1003			1.38738			0.693689	−	0.720274i	$-0.255984\pi$
$53$	10.1003			1.38738			0.693689	+	0.720274i	$0.255984\pi$
$54$		0			0
$55$	3.84558	−	8.33091i	0.518537	−	1.12334i
$56$	−5.95310	+	7.44128i	−0.795517	+	0.994383i
$57$		0			0
$58$	−0.423667	+	1.85180i	−0.0556302	+	0.243153i
$59$		−	3.07651i		−	0.400527i	−0.979742	−	0.200263i	$-0.935820\pi$
$59$		−	3.07651i		−	0.400527i	0.979742	−	0.200263i	$-0.0641798\pi$
$60$		0			0
$61$		−	0.762740i		−	0.0976589i	−0.998807	−	0.0488294i	$-0.984451\pi$
$61$		−	0.762740i		−	0.0976589i	0.998807	−	0.0488294i	$-0.0155491\pi$
$62$	0.315935	+	0.0722817i	0.0401237	+	0.00917978i
$63$		0			0
$64$	1.75600	+	7.80490i	0.219500	+	0.975613i
$65$	12.4572	+	5.75028i	1.54512	+	0.713235i
$66$		0			0
$67$	13.8657			1.69396			0.846980	−	0.531625i	$-0.178418\pi$
$67$	13.8657			1.69396			0.846980	+	0.531625i	$0.178418\pi$
$68$	6.50167	−	13.4653i	0.788443	−	1.63290i
$69$		0			0
$70$	6.51026	−	8.43396i	0.778125	−	1.00805i
$71$	1.26579			0.150222			0.0751110	−	0.997175i	$-0.476069\pi$
$71$	1.26579			0.150222			0.0751110	+	0.997175i	$0.476069\pi$
$72$		0			0
$73$			13.9347i			1.63094i	0.578801	+	0.815469i	$0.303521\pi$
$73$			13.9347i			1.63094i	−0.578801	+	0.815469i	$0.696479\pi$
$74$	−7.78618	−	1.78137i	−0.905125	−	0.207081i
$75$		0			0
$76$	−5.39655	+	11.1765i	−0.619027	+	1.28204i
$77$	−13.8254			−1.57555
$78$		0			0
$79$	0.245252			0.0275930			0.0137965	−	0.999905i	$-0.495608\pi$
$79$	0.245252			0.0275930			0.0137965	+	0.999905i	$0.495608\pi$
$80$	−2.11454	−	8.69073i	−0.236412	−	0.971653i
$81$		0			0
$82$	6.23908	+	1.42742i	0.688991	+	0.157632i
$83$	−13.3602			−1.46647			−0.733234	−	0.679976i	$-0.761990\pi$
$83$	−13.3602			−1.46647			−0.733234	+	0.679976i	$0.761990\pi$
$84$		0			0
$85$	−7.00650	+	15.1786i	−0.759962	+	1.64635i
$86$	−2.79807	−	0.640162i	−0.301724	−	0.0690305i
$87$		0			0
$88$	−7.25050	+	9.06301i	−0.772906	+	0.966120i
$89$	8.64631			0.916507			0.458254	−	0.888821i	$-0.348475\pi$
$89$	8.64631			0.916507			0.458254	+	0.888821i	$0.348475\pi$
$90$		0			0
$91$		−	20.6731i		−	2.16713i
$92$	−2.74641	+	5.68794i	−0.286333	+	0.593009i
$93$		0			0
$94$	−0.526827	+	2.30270i	−0.0543381	+	0.237506i
$95$	5.81558	−	12.5986i	0.596666	−	1.29259i
$96$		0			0
$97$		−	12.2906i		−	1.24792i	−0.781457	−	0.623959i	$-0.785523\pi$
$97$		−	12.2906i		−	1.24792i	0.781457	−	0.623959i	$-0.214477\pi$
$98$	−5.99897	−	1.37248i	−0.605987	−	0.138642i
$99$		0			0
$100$	2.53254	+	9.67400i	0.253254	+	0.967400i
$101$		−	12.9175i		−	1.28534i	−0.766142	−	0.642672i	$-0.777826\pi$
$101$		−	12.9175i		−	1.28534i	0.766142	−	0.642672i	$-0.222174\pi$
$102$		0			0
$103$			11.6484i			1.14776i	0.818941	+	0.573878i	$0.194561\pi$
$103$			11.6484i			1.14776i	−0.818941	+	0.573878i	$0.805439\pi$
$104$	−13.5519	−	10.8417i	−1.32887	−	1.06311i
$105$		0			0
$106$	13.9242	+	3.18566i	1.35243	+	0.309419i
$107$	5.05116			0.488314			0.244157	−	0.969736i	$-0.421489\pi$
$107$	5.05116			0.488314			0.244157	+	0.969736i	$0.421489\pi$
$108$		0			0
$109$			0.118695i			0.0113689i	0.999984	+	0.00568447i	$0.00180943\pi$
$109$			0.118695i			0.0113689i	−0.999984	+	0.00568447i	$0.998191\pi$
$110$	7.92909	−	10.2720i	0.756009	−	0.979400i
$111$		0			0
$112$	−10.5539	+	8.38087i	−0.997251	+	0.791918i
$113$		−	1.90210i		−	0.178934i	−0.995990	−	0.0894671i	$-0.971484\pi$
$113$		−	1.90210i		−	0.178934i	0.995990	−	0.0894671i	$-0.0285164\pi$
$114$		0			0
$115$	2.95966	−	6.41169i	0.275989	−	0.597893i
$116$	−1.16813	+	2.41925i	−0.108458	+	0.224622i
$117$		0			0
$118$	0.970342	−	4.24125i	0.0893272	−	0.390439i
$119$	25.1894			2.30911
$120$		0			0
$121$	−5.83850			−0.530773
$122$	0.240571	−	1.05151i	0.0217803	−	0.0951991i
$123$		0			0
$124$	0.412748	+	0.199294i	0.0370658	+	0.0178971i
$125$	−3.01890	−	10.7650i	−0.270019	−	0.962855i
$126$		0			0
$127$		−	11.2077i		−	0.994519i	−0.867602	−	0.497259i	$-0.834340\pi$
$127$		−	11.2077i		−	0.994519i	0.867602	−	0.497259i	$-0.165660\pi$
$128$	−0.0408867	+	11.3136i	−0.00361391	+	0.999993i
$129$		0			0
$130$	15.3597	+	11.8564i	1.34714	+	1.03987i
$131$		−	5.84987i		−	0.511105i	−0.966795	−	0.255553i	$-0.917743\pi$
$131$		−	5.84987i		−	0.511105i	0.966795	−	0.255553i	$-0.0822574\pi$
$132$		0			0
$133$	−20.9079			−1.81294
$134$	19.1151	+	4.37328i	1.65129	+	0.377794i
$135$		0			0
$136$	13.2102	−	16.5125i	1.13276	−	1.41593i
$137$		−	12.2520i		−	1.04676i	−0.852101	−	0.523378i	$-0.824672\pi$
$137$		−	12.2520i		−	1.04676i	0.852101	−	0.523378i	$-0.175328\pi$
$138$		0			0
$139$		−	6.32429i		−	0.536419i	−0.963361	−	0.268209i	$-0.913568\pi$
$139$		−	6.32429i		−	0.536419i	0.963361	−	0.268209i	$-0.0864319\pi$
$140$	11.6351	−	9.57364i	0.983346	−	0.809120i
$141$		0			0
$142$	1.74501	+	0.399236i	0.146438	+	0.0335032i
$143$		−	25.1786i		−	2.10554i
$144$		0			0
$145$	1.25883	−	2.72708i	0.104540	−	0.226472i
$146$	−4.39507	+	19.2103i	−0.363739	+	1.58986i
$147$		0			0
$148$	−10.1721	−	4.91158i	−0.836144	−	0.403730i
$149$		−	2.50921i		−	0.205563i	−0.994704	−	0.102781i	$-0.967226\pi$
$149$		−	2.50921i		−	0.205563i	0.994704	−	0.102781i	$-0.0327742\pi$
$150$		0			0
$151$	−13.4459			−1.09421			−0.547106	−	0.837063i	$-0.684271\pi$
$151$	−13.4459			−1.09421			−0.547106	+	0.837063i	$0.684271\pi$
$152$	−10.9648	+	13.7058i	−0.889361	+	1.11169i
$153$		0			0
$154$	−19.0596	−	4.36059i	−1.53587	−	0.351387i
$155$	−0.465266	−	0.214769i	−0.0373711	−	0.0172506i
$156$		0			0
$157$	12.2885			0.980728			0.490364	−	0.871518i	$-0.336864\pi$
$157$	12.2885			0.980728			0.490364	+	0.871518i	$0.336864\pi$
$158$	0.338103	+	0.0773534i	0.0268980	+	0.00615391i
$159$		0			0
$160$	−0.173999	−	12.6479i	−0.0137558	−	0.999905i
$161$	−10.6404			−0.838582
$162$		0			0
$163$	8.29583			0.649780			0.324890	−	0.945752i	$-0.394673\pi$
$163$	8.29583			0.649780			0.324890	+	0.945752i	$0.394673\pi$
$164$	8.15094	+	3.93566i	0.636482	+	0.307323i
$165$		0			0
$166$	−18.4182	−	4.21385i	−1.42953	−	0.327058i
$167$			12.4726i			0.965158i	0.875853	+	0.482579i	$0.160300\pi$
$167$			12.4726i			0.965158i	−0.875853	+	0.482579i	$0.839700\pi$
$168$		0			0
$169$	24.6495			1.89611
$170$	−14.4465	+	18.7153i	−1.10800	+	1.43540i
$171$		0			0
$172$	−3.65550	−	1.76505i	−0.278729	−	0.134584i
$173$	−8.83448			−0.671673			−0.335836	−	0.941920i	$-0.609019\pi$
$173$	−8.83448			−0.671673			−0.335836	+	0.941920i	$0.609019\pi$
$174$		0			0
$175$	−12.8206	+	10.9280i	−0.969144	+	0.826078i
$176$	−12.8540	+	10.2074i	−0.968907	+	0.769410i
$177$		0			0
$178$	11.9198	+	2.72708i	0.893423	+	0.204403i
$179$		−	6.64753i		−	0.496860i	−0.968650	−	0.248430i	$-0.920085\pi$
$179$		−	6.64753i		−	0.496860i	0.968650	−	0.248430i	$-0.0799146\pi$
$180$		0			0
$181$			18.7088i			1.39061i	0.718713	+	0.695307i	$0.244732\pi$
$181$			18.7088i			1.39061i	−0.718713	+	0.695307i	$0.755268\pi$
$182$	6.52039	−	28.4999i	0.483323	−	2.11255i
$183$		0			0
$184$	−5.58018	+	6.97513i	−0.411376	+	0.514214i
$185$	11.4664	+	5.29295i	0.843030	+	0.389146i
$186$		0			0
$187$	30.6792			2.24348
$188$	−1.45256	+	3.00833i	−0.105939	+	0.219405i
$189$		0			0
$190$	11.9910	−	15.5342i	0.869917	−	1.12697i
$191$	−16.1381			−1.16771			−0.583855	−	0.811858i	$-0.698456\pi$
$191$	−16.1381			−1.16771			−0.583855	+	0.811858i	$0.698456\pi$
$192$		0			0
$193$			7.19634i			0.518004i	0.965877	+	0.259002i	$0.0833936\pi$
$193$			7.19634i			0.518004i	−0.965877	+	0.259002i	$0.916606\pi$
$194$	3.87649	−	16.9437i	0.278316	−	1.21649i
$195$		0			0
$196$	−7.83725	−	3.78419i	−0.559804	−	0.270300i
$197$	16.3550			1.16524			0.582621	−	0.812744i	$-0.302027\pi$
$197$	16.3550			1.16524			0.582621	+	0.812744i	$0.302027\pi$
$198$		0			0
$199$	6.19894			0.439431			0.219716	−	0.975564i	$-0.429487\pi$
$199$	6.19894			0.439431			0.219716	+	0.975564i	$0.429487\pi$
$200$	0.440123	+	14.1353i	0.0311214	+	0.999516i
$201$		0			0
$202$	4.07424	−	17.8080i	0.286663	−	1.25297i
$203$	−4.52568			−0.317641
$204$		0			0
$205$	−9.18808	−	4.24125i	−0.641724	−	0.296222i
$206$	−3.67396	+	16.0585i	−0.255977	+	1.11885i
$207$		0			0
$208$	−15.2631	−	19.2206i	−1.05830	−	1.33271i
$209$	−25.4645			−1.76142
$210$		0			0
$211$			13.5974i			0.936085i	0.883706	+	0.468043i	$0.155041\pi$
$211$			13.5974i			0.936085i	−0.883706	+	0.468043i	$0.844959\pi$
$212$	18.1910	+	8.78347i	1.24936	+	0.603251i
$213$		0			0
$214$	6.96350	+	1.59316i	0.476015	+	0.108906i
$215$	4.12063	+	1.90210i	0.281025	+	0.129722i
$216$		0			0
$217$			0.772125i			0.0524153i
$218$	−0.0374369	+	0.163632i	−0.00253555	+	0.0110826i
$219$		0			0
$220$	14.1708	−	11.6601i	0.955397	−	0.786123i
$221$			45.8745i			3.08585i
$222$		0			0
$223$		−	13.9367i		−	0.933268i	−0.884451	−	0.466634i	$-0.845467\pi$
$223$		−	13.9367i		−	0.933268i	0.884451	−	0.466634i	$-0.154533\pi$
$224$	−17.1929	+	8.22507i	−1.14875	+	0.549561i
$225$		0			0
$226$	0.599929	−	2.62222i	0.0399067	−	0.174427i
$227$	5.23933			0.347746			0.173873	−	0.984768i	$-0.444372\pi$
$227$	5.23933			0.347746			0.173873	+	0.984768i	$0.444372\pi$
$228$		0			0
$229$			5.41618i			0.357911i	0.983857	+	0.178956i	$0.0572718\pi$
$229$			5.41618i			0.357911i	−0.983857	+	0.178956i	$0.942728\pi$
$230$	6.10243	−	7.90562i	0.402383	−	0.521281i
$231$		0			0
$232$	−2.37342	+	2.96673i	−0.155822	+	0.194775i
$233$			0.0771732i			0.00505578i	0.999997	+	0.00252789i	$0.000804654\pi$
$233$			0.0771732i			0.00505578i	−0.999997	+	0.00252789i	$0.999195\pi$
$234$		0			0
$235$	1.56535	−	3.39111i	0.102112	−	0.221212i
$236$	2.67541	−	5.54091i	0.174155	−	0.360683i
$237$		0			0
$238$	34.7260	+	7.94485i	2.25095	+	0.514988i
$239$	19.5280			1.26316			0.631580	−	0.775311i	$-0.282407\pi$
$239$	19.5280			1.26316			0.631580	+	0.775311i	$0.282407\pi$
$240$		0			0
$241$	15.7282			1.01314			0.506570	−	0.862199i	$-0.330913\pi$
$241$	15.7282			1.01314			0.506570	+	0.862199i	$0.330913\pi$
$242$	−8.04892	−	1.84149i	−0.517404	−	0.118375i
$243$		0			0
$244$	0.663300	−	1.37373i	0.0424634	−	0.0879438i
$245$	8.83448	+	4.07803i	0.564414	+	0.260535i
$246$		0			0
$247$		−	38.0770i		−	2.42278i
$248$	0.506153	+	0.404928i	0.0321408	+	0.0257129i
$249$		0			0
$250$	−0.766498	−	15.7928i	−0.0484776	−	0.998824i
$251$			10.9286i			0.689806i	0.938638	+	0.344903i	$0.112088\pi$
$251$			10.9286i			0.689806i	−0.938638	+	0.344903i	$0.887912\pi$
$252$		0			0
$253$	−12.9594			−0.814747
$254$	3.53494	−	15.4508i	0.221802	−	0.969470i
$255$		0			0
$256$	−3.62473	+	15.5840i	−0.226546	+	0.974001i
$257$			15.8487i			0.988616i	0.869287	+	0.494308i	$0.164579\pi$
$257$			15.8487i			0.988616i	−0.869287	+	0.494308i	$0.835421\pi$
$258$		0			0
$259$		−	19.0290i		−	1.18240i
$260$	17.4353	+	21.1896i	1.08129	+	1.31412i
$261$		0			0
$262$	1.84507	−	8.06459i	0.113989	−	0.498232i
$263$			14.1353i			0.871623i	0.900038	+	0.435811i	$0.143539\pi$
$263$			14.1353i			0.871623i	−0.900038	+	0.435811i	$0.856461\pi$
$264$		0			0
$265$	−20.5057	−	9.46548i	−1.25965	−	0.581460i
$266$	−28.8235	−	6.59443i	−1.76728	−	0.404330i
$267$		0			0
$268$	24.9726	+	12.0580i	1.52545	+	0.736557i
$269$		−	17.9902i		−	1.09688i	−0.836190	−	0.548440i	$-0.815222\pi$
$269$		−	17.9902i		−	1.09688i	0.836190	−	0.548440i	$-0.184778\pi$
$270$		0			0
$271$	13.9198			0.845565			0.422782	−	0.906231i	$-0.361053\pi$
$271$	13.9198			0.845565			0.422782	+	0.906231i	$0.361053\pi$
$272$	23.4195	−	18.5975i	1.42002	−	1.12764i
$273$		0			0
$274$	3.86432	−	16.8905i	0.233452	−	1.02039i
$275$	−15.6146	+	13.3096i	−0.941599	+	0.802599i
$276$		0			0
$277$	−0.765167			−0.0459744			−0.0229872	−	0.999736i	$-0.507318\pi$
$277$	−0.765167			−0.0459744			−0.0229872	+	0.999736i	$0.507318\pi$
$278$	1.99470	−	8.71862i	0.119634	−	0.522908i
$279$		0			0
$280$	19.0596	−	9.52840i	1.13903	−	0.569431i
$281$	0.550096			0.0328160			0.0164080	−	0.999865i	$-0.494777\pi$
$281$	0.550096			0.0328160			0.0164080	+	0.999865i	$0.494777\pi$
$282$		0			0
$283$	11.2958			0.671468			0.335734	−	0.941957i	$-0.391016\pi$
$283$	11.2958			0.671468			0.335734	+	0.941957i	$0.391016\pi$
$284$	2.27975	+	1.10077i	0.135278	+	0.0653186i
$285$		0			0
$286$	7.94142	−	34.7110i	0.469586	−	2.05251i
$287$			15.2479i			0.900057i
$288$		0			0
$289$	−38.8963			−2.28802
$290$	2.59555	−	3.36250i	0.152416	−	0.197453i
$291$		0			0
$292$	−12.1180	+	25.0970i	−0.709154	+	1.46869i
$293$	−15.4265			−0.901225			−0.450612	−	0.892720i	$-0.648794\pi$
$293$	−15.4265			−0.901225			−0.450612	+	0.892720i	$0.648794\pi$
$294$		0			0
$295$	−2.88315	+	6.24595i	−0.167864	+	0.363653i
$296$	−12.4741	−	9.97941i	−0.725042	−	0.580041i
$297$		0			0
$298$	0.791415	−	3.45918i	0.0458455	−	0.200385i
$299$		−	19.3781i		−	1.12066i
$300$		0			0
$301$		−	6.83833i		−	0.394155i
$302$	−18.5364	−	4.24089i	−1.06665	−	0.244036i
$303$		0			0
$304$	−19.4388	+	15.4364i	−1.11489	+	0.885337i
$305$	−0.714803	+	1.54852i	−0.0409295	+	0.0886681i
$306$		0			0
$307$	29.4900			1.68308			0.841542	−	0.540192i	$-0.181648\pi$
$307$	29.4900			1.68308			0.841542	+	0.540192i	$0.181648\pi$
$308$	−24.9002	−	12.0230i	−1.41882	−	0.685072i
$309$		0			0
$310$	−0.573674	−	0.442825i	−0.0325825	−	0.0251508i
$311$	−24.6393			−1.39717			−0.698584	−	0.715528i	$-0.746186\pi$
$311$	−24.6393			−1.39717			−0.698584	+	0.715528i	$0.746186\pi$
$312$		0			0
$313$		−	19.8011i		−	1.11922i	−0.828755	−	0.559612i	$-0.810950\pi$
$313$		−	19.8011i		−	1.11922i	0.828755	−	0.559612i	$-0.189050\pi$
$314$	16.9408	+	3.87584i	0.956026	+	0.218726i
$315$		0			0
$316$	0.441709	+	0.213278i	0.0248481	+	0.0119978i
$317$	8.83448			0.496194			0.248097	−	0.968735i	$-0.420195\pi$
$317$	8.83448			0.496194			0.248097	+	0.968735i	$0.420195\pi$
$318$		0			0
$319$	−5.51200			−0.308613
$320$	3.74933	−	17.4912i	0.209594	−	0.977789i
$321$		0			0
$322$	−14.6688	−	3.35603i	−0.817460	−	0.187024i
$323$	46.3954			2.58151
$324$		0			0
$325$	−19.9018	−	23.3486i	−1.10395	−	1.29514i
$326$	11.4366	+	2.61654i	0.633414	+	0.144917i
$327$		0			0
$328$	9.99551	+	7.99651i	0.551910	+	0.441534i
$329$	−5.62766			−0.310263
$330$		0			0
$331$			8.94044i			0.491411i	0.969345	+	0.245705i	$0.0790196\pi$
$331$			8.94044i			0.491411i	−0.969345	+	0.245705i	$0.920980\pi$
$332$	−24.0622	−	11.6184i	−1.32058	−	0.637641i
$333$		0			0
$334$	−3.93390	+	17.1946i	−0.215254	+	0.940848i
$335$	−28.1502	−	12.9942i	−1.53801	−	0.709950i
$336$		0			0
$337$			26.1273i			1.42324i	0.702562	+	0.711622i	$0.252039\pi$
$337$			26.1273i			1.42324i	−0.702562	+	0.711622i	$0.747961\pi$
$338$	33.9816	+	7.77455i	1.84836	+	0.422880i
$339$		0			0
$340$	−25.8187	+	21.2443i	−1.40022	+	1.15213i
$341$			0.940400i			0.0509255i
$342$		0			0
$343$			8.92329i			0.481812i
$344$	−4.48274	−	3.58624i	−0.241693	−	0.193357i
$345$		0			0
$346$	−12.1792	−	2.78643i	−0.654755	−	0.149799i
$347$	−13.6975			−0.735319			−0.367660	−	0.929960i	$-0.619841\pi$
$347$	−13.6975			−0.735319			−0.367660	+	0.929960i	$0.619841\pi$
$348$		0			0
$349$		−	9.36394i		−	0.501240i	−0.968086	−	0.250620i	$-0.919366\pi$
$349$		−	9.36394i		−	0.501240i	0.968086	−	0.250620i	$-0.0806345\pi$
$350$	−21.1211	+	11.0216i	−1.12897	+	0.589129i
$351$		0			0
$352$	−20.9399	+	10.0176i	−1.11610	+	0.533941i
$353$			27.4608i			1.46159i	0.682595	+	0.730796i	$0.260851\pi$
$353$			27.4608i			1.46159i	−0.682595	+	0.730796i	$0.739149\pi$
$354$		0			0
$355$	−2.56982	−	1.18624i	−0.136392	−	0.0629591i
$356$	15.5724	+	7.51907i	0.825334	+	0.398510i
$357$		0			0
$358$	2.09666	−	9.16425i	0.110812	−	0.484345i
$359$	0.111235			0.00587078			0.00293539	−	0.999996i	$-0.499066\pi$
$359$	0.111235			0.00587078			0.00293539	+	0.999996i	$0.499066\pi$
$360$		0			0
$361$	−19.5094			−1.02681
$362$	−5.90083	+	25.7918i	−0.310141	+	1.35559i
$363$		0			0
$364$	17.9779	−	37.2332i	0.942300	−	1.95155i
$365$	13.0590	−	28.2904i	0.683537	−	1.48079i
$366$		0			0
$367$			11.5485i			0.602828i	0.953493	+	0.301414i	$0.0974586\pi$
$367$			11.5485i			0.602828i	−0.953493	+	0.301414i	$0.902541\pi$
$368$	−9.89278	+	7.85586i	−0.515697	+	0.409515i
$369$		0			0
$370$	14.1382	+	10.9134i	0.735008	+	0.567360i
$371$			34.0298i			1.76674i
$372$		0			0
$373$	−7.87709			−0.407860			−0.203930	−	0.978985i	$-0.565372\pi$
$373$	−7.87709			−0.407860			−0.203930	+	0.978985i	$0.565372\pi$
$374$	42.2941	+	9.67632i	2.18697	+	0.500351i
$375$		0			0
$376$	−2.95133	+	3.68912i	−0.152203	+	0.190252i
$377$		−	8.24208i		−	0.424489i
$378$		0			0
$379$		−	2.27691i		−	0.116957i	−0.998289	−	0.0584785i	$-0.981375\pi$
$379$		−	2.27691i		−	0.116957i	0.998289	−	0.0584785i	$-0.0186249\pi$
$380$	21.4302	−	17.6333i	1.09935	−	0.904569i
$381$		0			0
$382$	−22.2478	−	5.09001i	−1.13830	−	0.260428i
$383$			1.55010i			0.0792066i	0.999215	+	0.0396033i	$0.0126094\pi$
$383$			1.55010i			0.0792066i	−0.999215	+	0.0396033i	$0.987391\pi$
$384$		0			0
$385$	28.0685	+	12.9565i	1.43050	+	0.660325i
$386$	−2.26975	+	9.92082i	−0.115527	+	0.504957i
$387$		0			0
$388$	10.6882	−	22.1358i	0.542612	−	1.12378i
$389$			19.7789i			1.00283i	0.865207	+	0.501415i	$0.167187\pi$
$389$			19.7789i			1.00283i	−0.865207	+	0.501415i	$0.832813\pi$
$390$		0			0
$391$	23.6115			1.19408
$392$	−9.61083	−	7.68877i	−0.485420	−	0.388341i
$393$		0			0
$394$	22.5468	+	5.15842i	1.13589	+	0.259877i
$395$	−0.497913	−	0.229838i	−0.0250527	−	0.0115644i
$396$		0			0
$397$	29.4891			1.48002			0.740009	−	0.672597i	$-0.234821\pi$
$397$	29.4891			1.48002			0.740009	+	0.672597i	$0.234821\pi$
$398$	8.54582	+	1.95517i	0.428363	+	0.0980038i
$399$		0			0
$400$	−3.85157	+	19.6256i	−0.192579	+	0.981282i
$401$	−13.3170			−0.665021			−0.332511	−	0.943100i	$-0.607896\pi$
$401$	−13.3170			−0.665021			−0.332511	+	0.943100i	$0.607896\pi$
$402$		0			0
$403$	−1.40618			−0.0700468
$404$	11.2334	−	23.2650i	0.558885	−	1.15748i
$405$		0			0
$406$	−6.23908	−	1.42742i	−0.309640	−	0.0708416i
$407$		−	23.1761i		−	1.14880i
$408$		0			0
$409$	14.7077			0.727248			0.363624	−	0.931546i	$-0.381539\pi$
$409$	14.7077			0.727248			0.363624	+	0.931546i	$0.381539\pi$
$410$	−11.3289	−	8.74492i	−0.559496	−	0.431881i
$411$		0			0
$412$	−10.1298	+	20.9793i	−0.499060	+	1.03358i
$413$	10.3654			0.510046
$414$		0			0
$415$	27.1239	+	12.5205i	1.33146	+	0.614607i
$416$	−14.9793	−	31.3114i	−0.734422	−	1.53517i
$417$		0			0
$418$	−35.1052	−	8.03160i	−1.71705	−	0.392838i
$419$			21.0125i			1.02653i	0.858231	+	0.513263i	$0.171564\pi$
$419$			21.0125i			1.02653i	−0.858231	+	0.513263i	$0.828436\pi$
$420$		0			0
$421$			6.07559i			0.296106i	0.988979	+	0.148053i	$0.0473006\pi$
$421$			6.07559i			0.296106i	−0.988979	+	0.148053i	$0.952699\pi$
$422$	−4.28868	+	18.7453i	−0.208770	+	0.912508i
$423$		0			0
$424$	22.3077	+	17.8464i	1.08336	+	0.866696i
$425$	28.4493	−	24.2496i	1.38000	−	1.17628i
$426$		0			0
$427$	2.56982			0.124363
$428$	9.09735	+	4.39263i	0.439737	+	0.212326i
$429$		0			0
$430$	5.08075	+	3.92188i	0.245015	+	0.189130i
$431$	−32.9750			−1.58835			−0.794175	−	0.607689i	$-0.792097\pi$
$431$	−32.9750			−1.58835			−0.794175	+	0.607689i	$0.792097\pi$
$432$		0			0
$433$			1.28424i			0.0617166i	0.999524	+	0.0308583i	$0.00982406\pi$
$433$			1.28424i			0.0617166i	−0.999524	+	0.0308583i	$0.990176\pi$
$434$	−0.243531	+	1.06445i	−0.0116899	+	0.0510951i
$435$		0			0
$436$	−0.103221	+	0.213775i	−0.00494337	+	0.0102380i
$437$	−19.5981			−0.937506
$438$		0			0
$439$	−36.8635			−1.75940			−0.879699	−	0.475530i	$-0.842256\pi$
$439$	−36.8635			−1.75940			−0.879699	+	0.475530i	$0.842256\pi$
$440$	23.2135	−	11.6050i	1.10666	−	0.553246i
$441$		0			0
$442$	−14.4690	+	63.2423i	−0.688220	+	3.00813i
$443$	8.33772			0.396137			0.198069	−	0.980188i	$-0.436533\pi$
$443$	8.33772			0.396137			0.198069	+	0.980188i	$0.436533\pi$
$444$		0			0
$445$	−17.5538	−	8.10290i	−0.832131	−	0.384114i
$446$	4.39568	−	19.2130i	0.208141	−	0.909762i
$447$		0			0
$448$	−26.2963	+	5.91631i	−1.24238	+	0.279520i
$449$	−36.5100			−1.72301			−0.861506	−	0.507748i	$-0.830478\pi$
$449$	−36.5100			−1.72301			−0.861506	+	0.507748i	$0.830478\pi$
$450$		0			0
$451$			18.5710i			0.874476i
$452$	1.65412	−	3.42575i	0.0778031	−	0.161134i
$453$		0			0
$454$	7.22290	+	1.65250i	0.338988	+	0.0775559i
$455$	−19.3739	+	41.9708i	−0.908261	+	1.96762i
$456$		0			0
$457$		−	20.7711i		−	0.971633i	−0.874061	−	0.485816i	$-0.838522\pi$
$457$		−	20.7711i		−	0.971633i	0.874061	−	0.485816i	$-0.161478\pi$
$458$	−1.70828	+	7.46671i	−0.0798229	+	0.348896i
$459$		0			0
$460$	10.9062	−	8.97391i	0.508506	−	0.418411i
$461$			2.53355i			0.117999i	0.998258	+	0.0589997i	$0.0187911\pi$
$461$			2.53355i			0.117999i	−0.998258	+	0.0589997i	$0.981209\pi$
$462$		0			0
$463$		−	13.0894i		−	0.608314i	−0.952622	−	0.304157i	$-0.901625\pi$
$463$		−	13.0894i		−	0.608314i	0.952622	−	0.304157i	$-0.0983748\pi$
$464$	−4.20769	+	3.34133i	−0.195337	+	0.155117i
$465$		0			0
$466$	−0.0243407	+	0.106390i	−0.00112756	+	0.00492844i
$467$	−23.2966			−1.07804			−0.539019	−	0.842293i	$-0.681205\pi$
$467$	−23.2966			−1.07804			−0.539019	+	0.842293i	$0.681205\pi$
$468$		0			0
$469$			46.7162i			2.15715i
$470$	3.22755	−	4.18125i	0.148876	−	0.192867i
$471$		0			0
$472$	5.43593	−	6.79483i	0.250209	−	0.312757i
$473$		−	8.32865i		−	0.382952i
$474$		0			0
$475$	−23.6137	+	20.1278i	−1.08347	+	0.923527i
$476$	45.3672	+	21.9054i	2.07940	+	1.00403i
$477$		0			0
$478$	26.9211	+	6.15920i	1.23134	+	0.281715i
$479$	11.0267			0.503823			0.251911	−	0.967750i	$-0.418941\pi$
$479$	11.0267			0.503823			0.251911	+	0.967750i	$0.418941\pi$
$480$		0			0
$481$	34.6552			1.58014
$482$	21.6827	+	4.96072i	0.987622	+	0.225955i
$483$		0			0
$484$	−10.5154	−	5.07732i	−0.477972	−	0.230787i
$485$	−11.5181	+	24.9524i	−0.523011	+	1.13303i
$486$		0			0
$487$		−	6.19428i		−	0.280690i	−0.990103	−	0.140345i	$-0.955179\pi$
$487$		−	6.19428i		−	0.280690i	0.990103	−	0.140345i	$-0.0448211\pi$
$488$	1.34770	−	1.68460i	0.0610075	−	0.0762584i
$489$		0			0
$490$	10.8929	+	8.40837i	0.492092	+	0.379851i
$491$		−	3.80033i		−	0.171506i	−0.996316	−	0.0857532i	$-0.972670\pi$
$491$		−	3.80033i		−	0.171506i	0.996316	−	0.0857532i	$-0.0273297\pi$
$492$		0			0
$493$	10.0427			0.452299
$494$	12.0096	−	52.4927i	0.540339	−	2.36176i
$495$		0			0
$496$	0.570064	+	0.717873i	0.0255966	+	0.0322335i
$497$			4.26471i			0.191298i
$498$		0			0
$499$		−	19.9217i		−	0.891818i	−0.895078	−	0.445909i	$-0.852880\pi$
$499$		−	19.9217i		−	0.891818i	0.895078	−	0.445909i	$-0.147120\pi$
$500$	3.92442	−	22.0136i	0.175505	−	0.984478i
$501$		0			0
$502$	−3.44692	+	15.0661i	−0.153843	+	0.672432i
$503$			24.3013i			1.08354i	0.840526	+	0.541772i	$0.182246\pi$
$503$			24.3013i			1.08354i	−0.840526	+	0.541772i	$0.817754\pi$
$504$		0			0
$505$	−12.1057	+	26.2253i	−0.538696	+	1.16701i
$506$	−17.8657	−	4.08743i	−0.794226	−	0.181708i
$507$		0			0
$508$	9.74649	−	20.1854i	0.432430	−	0.895584i
$509$			3.72468i			0.165093i	0.996587	+	0.0825467i	$0.0263054\pi$
$509$			3.72468i			0.165093i	−0.996587	+	0.0825467i	$0.973695\pi$
$510$		0			0
$511$	−46.9489			−2.07690
$512$	−9.91229	+	20.3408i	−0.438065	+	0.898943i
$513$		0			0
$514$	−4.99875	+	21.8489i	−0.220485	+	0.963716i
$515$	10.9164	−	23.6488i	0.481032	−	1.04209i
$516$		0			0
$517$	−6.85414			−0.301445
$518$	6.00181	−	26.2332i	0.263704	−	1.15262i
$519$		0			0
$520$	17.3529	+	34.7110i	0.760976	+	1.52218i
$521$	11.1905			0.490265			0.245133	−	0.969490i	$-0.421169\pi$
$521$	11.1905			0.490265			0.245133	+	0.969490i	$0.421169\pi$
$522$		0			0
$523$	−18.4017			−0.804648			−0.402324	−	0.915497i	$-0.631797\pi$
$523$	−18.4017			−0.804648			−0.402324	+	0.915497i	$0.631797\pi$
$524$	5.08720	−	10.5358i	0.222236	−	0.460261i
$525$		0			0
$526$	−4.45834	+	19.4869i	−0.194393	+	0.849669i
$527$		−	1.71338i		−	0.0746358i
$528$		0			0
$529$	13.0261			0.566354
$530$	−25.2835	−	19.5166i	−1.09825	−	0.847748i
$531$		0			0
$532$	−37.6559	−	18.1821i	−1.63259	−	0.788293i
$533$	−27.7692			−1.20282
$534$		0			0
$535$	−10.2549	−	4.73370i	−0.443359	−	0.204656i
$536$	30.6240	+	24.4995i	1.32275	+	1.05822i
$537$		0			0
$538$	5.67417	−	24.8011i	0.244631	−	1.06925i
$539$		−	17.8563i		−	0.769126i
$540$		0			0
$541$		−	10.1076i		−	0.434560i	−0.976109	−	0.217280i	$-0.930282\pi$
$541$		−	10.1076i		−	0.434560i	0.976109	−	0.217280i	$-0.0697184\pi$
$542$	19.1897	+	4.39034i	0.824267	+	0.188581i
$543$		0			0
$544$	38.1518	−	18.2517i	1.63574	−	0.782537i
$545$	0.111235	−	0.240976i	0.00476480	−	0.0103223i
$546$		0			0
$547$	−9.83837			−0.420658			−0.210329	−	0.977631i	$-0.567454\pi$
$547$	−9.83837			−0.420658			−0.210329	+	0.977631i	$0.567454\pi$
$548$	10.6546	−	22.0663i	0.455144	−	0.942625i
$549$		0			0
$550$	−25.7241	+	13.4236i	−1.09688	+	0.572385i
$551$	−8.33567			−0.355111
$552$		0			0
$553$			0.826303i			0.0351380i
$554$	−1.05485	−	0.241337i	−0.0448164	−	0.0102534i
$555$		0			0
$556$	5.49977	−	11.3903i	0.233242	−	0.483056i
$557$	24.5189			1.03890			0.519450	−	0.854501i	$-0.326137\pi$
$557$	24.5189			1.03890			0.519450	+	0.854501i	$0.326137\pi$
$558$		0			0
$559$	12.4538			0.526740
$560$	29.2808	−	7.12430i	1.23734	−	0.301057i
$561$		0			0
$562$	0.758359	+	0.173502i	0.0319894	+	0.00731876i
$563$	−22.3948			−0.943829			−0.471914	−	0.881644i	$-0.656437\pi$
$563$	−22.3948			−0.943829			−0.471914	+	0.881644i	$0.656437\pi$
$564$		0			0
$565$	−1.78255	+	3.86165i	−0.0749926	+	0.162461i
$566$	15.5724	+	3.56275i	0.654555	+	0.149754i
$567$		0			0
$568$	2.79566	+	2.23655i	0.117303	+	0.0938437i
$569$	−17.3701			−0.728191			−0.364095	−	0.931362i	$-0.618622\pi$
$569$	−17.3701			−0.728191			−0.364095	+	0.931362i	$0.618622\pi$
$570$		0			0
$571$		−	43.7980i		−	1.83289i	−0.400162	−	0.916444i	$-0.631046\pi$
$571$		−	43.7980i		−	1.83289i	0.400162	−	0.916444i	$-0.368954\pi$
$572$	21.8960	−	45.3477i	0.915517	−	1.89608i
$573$		0			0
$574$	−4.80926	+	21.0207i	−0.200735	+	0.877387i
$575$	−12.0174	+	10.2434i	−0.501162	+	0.427180i
$576$		0			0
$577$		−	27.0993i		−	1.12816i	−0.825721	−	0.564079i	$-0.809231\pi$
$577$		−	27.0993i		−	1.12816i	0.825721	−	0.564079i	$-0.190769\pi$
$578$	−53.6222	−	12.2681i	−2.23039	−	0.510284i
$579$		0			0
$580$	4.63875	−	3.81687i	0.192614	−	0.158487i
$581$		−	45.0131i		−	1.86746i
$582$		0			0
$583$			41.4462i			1.71653i
$584$	−24.6215	+	30.7765i	−1.01885	+	1.27354i
$585$		0			0
$586$	−21.2668	−	4.86557i	−0.878525	−	0.200995i
$587$	20.0250			0.826520			0.413260	−	0.910613i	$-0.364390\pi$
$587$	20.0250			0.826520			0.413260	+	0.910613i	$0.364390\pi$
$588$		0			0
$589$			1.42215i			0.0585985i
$590$	−5.94469	+	7.70127i	−0.244739	+	0.317056i
$591$		0			0
$592$	−14.0492	−	17.6919i	−0.577417	−	0.727134i
$593$		−	32.7272i		−	1.34395i	−0.740576	−	0.671973i	$-0.765447\pi$
$593$		−	32.7272i		−	1.34395i	0.740576	−	0.671973i	$-0.234553\pi$
$594$		0			0
$595$	−51.1398	−	23.6063i	−2.09653	−	0.967765i
$596$	2.18208	−	4.51919i	0.0893815	−	0.185113i
$597$		0			0
$598$	6.11193	−	26.7145i	0.249935	−	1.09244i
$599$	20.0781			0.820367			0.410184	−	0.912003i	$-0.365465\pi$
$599$	20.0781			0.820367			0.410184	+	0.912003i	$0.365465\pi$
$600$		0			0
$601$	−12.6066			−0.514235			−0.257118	−	0.966380i	$-0.582773\pi$
$601$	−12.6066			−0.514235			−0.257118	+	0.966380i	$0.582773\pi$
$602$	2.15683	−	9.42727i	0.0879060	−	0.384227i
$603$		0			0
$604$	−24.2166	−	11.6929i	−0.985360	−	0.475778i
$605$	11.8534	+	5.47156i	0.481908	+	0.222451i
$606$		0			0
$607$			25.6884i			1.04266i	0.853355	+	0.521331i	$0.174564\pi$
$607$			25.6884i			1.04266i	−0.853355	+	0.521331i	$0.825436\pi$
$608$	−31.6669	+	15.1494i	−1.28426	+	0.614390i
$609$		0			0
$610$	−1.47383	+	1.90933i	−0.0596737	+	0.0773065i
$611$		−	10.2490i		−	0.414630i
$612$		0			0
$613$	9.32356			0.376575			0.188288	−	0.982114i	$-0.439706\pi$
$613$	9.32356			0.376575			0.188288	+	0.982114i	$0.439706\pi$
$614$	40.6548	+	9.30127i	1.64069	+	0.375369i
$615$		0			0
$616$	−30.5351	−	24.4284i	−1.23029	−	0.984248i
$617$			6.85132i			0.275824i	0.990445	+	0.137912i	$0.0440391\pi$
$617$			6.85132i			0.275824i	−0.990445	+	0.137912i	$0.955961\pi$
$618$		0			0
$619$			36.6662i			1.47374i	0.676036	+	0.736869i	$0.263696\pi$
$619$			36.6662i			1.47374i	−0.676036	+	0.736869i	$0.736304\pi$
$620$	−0.651195	−	0.791415i	−0.0261526	−	0.0317840i
$621$		0			0
$622$	−33.9676	−	7.77134i	−1.36198	−	0.311603i
$623$			29.1312i			1.16712i
$624$		0			0
$625$	−3.95948	+	24.6845i	−0.158379	+	0.987378i
$626$	6.24534	−	27.2977i	0.249614	−	1.09103i
$627$		0			0
$628$	22.1321	+	10.6864i	0.883166	+	0.426434i
$629$			42.2260i			1.68366i
$630$		0			0
$631$	33.1204			1.31850			0.659251	−	0.751923i	$-0.270873\pi$
$631$	33.1204			1.31850			0.659251	+	0.751923i	$0.270873\pi$
$632$	0.541668	+	0.433340i	0.0215464	+	0.0172374i
$633$		0			0
$634$	12.1792	+	2.78643i	0.483696	+	0.110663i
$635$	−10.5033	+	22.7539i	−0.416810	+	0.902960i
$636$		0			0
$637$	26.7005			1.05791
$638$	−7.59881	−	1.73851i	−0.300840	−	0.0688281i
$639$		0			0
$640$	10.6856	−	22.9307i	0.422385	−	0.906416i
$641$	−12.0700			−0.476737			−0.238369	−	0.971175i	$-0.576613\pi$
$641$	−12.0700			−0.476737			−0.238369	+	0.971175i	$0.576613\pi$
$642$		0			0
$643$	−28.1615			−1.11058			−0.555290	−	0.831657i	$-0.687393\pi$
$643$	−28.1615			−1.11058			−0.555290	+	0.831657i	$0.687393\pi$
$644$	−19.1638	−	9.25320i	−0.755160	−	0.364627i
$645$		0			0
$646$	63.9604	+	14.6333i	2.51649	+	0.575739i
$647$		−	44.7175i		−	1.75803i	−0.476798	−	0.879013i	$-0.658203\pi$
$647$		−	44.7175i		−	1.75803i	0.476798	−	0.879013i	$-0.341797\pi$
$648$		0			0
$649$	12.6244			0.495549
$650$	−20.0723	−	38.4653i	−0.787300	−	1.50873i
$651$		0			0
$652$	14.9411	+	7.21429i	0.585140	+	0.282533i
$653$	32.4930			1.27155			0.635775	−	0.771874i	$-0.280681\pi$
$653$	32.4930			1.27155			0.635775	+	0.771874i	$0.280681\pi$
$654$		0			0
$655$	−5.48221	+	11.8764i	−0.214208	+	0.464051i
$656$	11.2576	+	14.1766i	0.439536	+	0.553502i
$657$		0			0
$658$	−7.75826	−	1.77499i	−0.302449	−	0.0691962i
$659$		−	4.47524i		−	0.174331i	−0.996194	−	0.0871653i	$-0.972219\pi$
$659$		−	4.47524i		−	0.174331i	0.996194	−	0.0871653i	$-0.0277808\pi$
$660$		0			0
$661$		−	0.740119i		−	0.0287873i	−0.999896	−	0.0143936i	$-0.995418\pi$
$661$		−	0.740119i		−	0.0287873i	0.999896	−	0.0143936i	$-0.00458180\pi$
$662$	−2.81985	+	12.3252i	−0.109597	+	0.479034i
$663$		0			0
$664$	−29.5075	−	23.6063i	−1.14511	−	0.916103i
$665$	42.4474	+	19.5938i	1.64604	+	0.759817i
$666$		0			0
$667$	−4.24218			−0.164258
$668$	−10.8465	+	22.4636i	−0.419664	+	0.869144i
$669$		0			0
$670$	−34.7092	−	26.7924i	−1.34093	−	1.03508i
$671$	3.12988			0.120828
$672$		0			0
$673$			19.4450i			0.749550i	0.927116	+	0.374775i	$0.122280\pi$
$673$			19.4450i			0.749550i	−0.927116	+	0.374775i	$0.877720\pi$
$674$	−8.24065	+	36.0189i	−0.317418	+	1.38740i
$675$		0			0
$676$	44.3947	+	21.4359i	1.70749	+	0.824457i
$677$	−16.3550			−0.628572			−0.314286	−	0.949328i	$-0.601765\pi$
$677$	−16.3550			−0.628572			−0.314286	+	0.949328i	$0.601765\pi$
$678$		0			0
$679$	41.4094			1.58915
$680$	−42.2941	+	21.1439i	−1.62190	+	0.810831i
$681$		0			0
$682$	−0.296606	+	1.29643i	−0.0113576	+	0.0496429i
$683$	7.93035			0.303446			0.151723	−	0.988423i	$-0.451518\pi$
$683$	7.93035			0.303446			0.151723	+	0.988423i	$0.451518\pi$
$684$		0			0
$685$	−11.4819	+	24.8740i	−0.438702	+	0.950388i
$686$	−2.81444	+	12.3016i	−0.107456	+	0.469677i
$687$		0			0
$688$	−5.04877	−	6.35784i	−0.192482	−	0.242390i
$689$	−61.9744			−2.36104
$690$		0			0
$691$			36.1856i			1.37657i	0.725443	+	0.688283i	$0.241635\pi$
$691$			36.1856i			1.37657i	−0.725443	+	0.688283i	$0.758365\pi$
$692$	−15.9113	−	7.68271i	−0.604855	−	0.292053i
$693$		0			0
$694$	−18.8833	−	4.32024i	−0.716799	−	0.163994i
$695$	−5.92681	+	12.8396i	−0.224817	+	0.487035i
$696$		0			0
$697$		−	33.8358i		−	1.28162i
$698$	2.95342	−	12.9091i	0.111789	−	0.488615i
$699$		0			0
$700$	−32.5936	+	8.53263i	−1.23192	+	0.322503i
$701$		−	27.8435i		−	1.05163i	−0.850598	−	0.525817i	$-0.823760\pi$
$701$		−	27.8435i		−	1.05163i	0.850598	−	0.525817i	$-0.176240\pi$
$702$		0			0
$703$		−	35.0487i		−	1.32189i
$704$	−32.0272	+	7.20570i	−1.20707	+	0.271575i
$705$		0			0
$706$	−8.66126	+	37.8573i	−0.325971	+	1.42478i
$707$	43.5218			1.63680
$708$		0			0
$709$		−	11.0235i		−	0.413995i	−0.978341	−	0.206998i	$-0.933631\pi$
$709$		−	11.0235i		−	0.413995i	0.978341	−	0.206998i	$-0.0663692\pi$
$710$	−3.16860	−	2.44588i	−0.118915	−	0.0917921i
$711$		0			0
$712$	19.0964	+	15.2773i	0.715668	+	0.572542i
$713$			0.723757i			0.0271049i
$714$		0			0
$715$	−23.5961	+	51.1178i	−0.882446	+	1.91170i
$716$	5.78088	−	11.9725i	0.216042	−	0.447432i
$717$		0			0
$718$	0.153348	+	0.0350841i	0.00572291	+	0.00130933i
$719$	34.3520			1.28111			0.640557	−	0.767910i	$-0.278703\pi$
$719$	34.3520			1.28111			0.640557	+	0.767910i	$0.278703\pi$
$720$		0			0
$721$	−39.2459			−1.46160
$722$	−26.8955	−	6.15333i	−1.00095	−	0.229003i
$723$		0			0
$724$	−16.2697	+	33.6953i	−0.604658	+	1.25228i
$725$	−5.11138	+	4.35683i	−0.189832	+	0.161809i
$726$		0			0
$727$			26.3286i			0.976475i	0.872711	+	0.488237i	$0.162360\pi$
$727$			26.3286i			0.976475i	−0.872711	+	0.488237i	$0.837640\pi$
$728$	36.5277	−	45.6591i	1.35381	−	1.69224i
$729$		0			0
$730$	26.9259	−	34.8822i	0.996573	−	1.29105i
$731$			15.1745i			0.561249i
$732$		0			0
$733$	13.3088			0.491573			0.245787	−	0.969324i	$-0.420954\pi$
$733$	13.3088			0.491573			0.245787	+	0.969324i	$0.420954\pi$
$734$	−3.64245	+	15.9207i	−0.134445	+	0.587644i
$735$		0			0
$736$	−16.1159	+	7.70982i	−0.594040	+	0.284188i
$737$			56.8974i			2.09584i
$738$		0			0
$739$		−	15.8743i		−	0.583947i	−0.956426	−	0.291973i	$-0.905688\pi$
$739$		−	15.8743i		−	0.583947i	0.956426	−	0.291973i	$-0.0943119\pi$
$740$	16.0486	+	19.5044i	0.589960	+	0.716995i
$741$		0			0
$742$	−10.7331	+	46.9133i	−0.394026	+	1.72224i
$743$		−	23.2285i		−	0.852171i	−0.904683	−	0.426086i	$-0.859892\pi$
$743$		−	23.2285i		−	0.852171i	0.904683	−	0.426086i	$-0.140108\pi$
$744$		0			0
$745$	−2.35151	+	5.09423i	−0.0861527	+	0.186638i
$746$	−10.8593	−	2.48446i	−0.397587	−	0.0909627i
$747$		0			0
$748$	55.2544	+	26.6794i	2.02030	+	0.975497i
$749$			17.0184i			0.621838i
$750$		0			0
$751$	34.8181			1.27053			0.635265	−	0.772294i	$-0.280891\pi$
$751$	34.8181			1.27053			0.635265	+	0.772294i	$0.280891\pi$
$752$	−5.23225	+	4.15493i	−0.190800	+	0.151515i
$753$		0			0
$754$	2.59958	−	11.3625i	0.0946713	−	0.413797i
$755$	27.2980	+	12.6008i	0.993475	+	0.458592i
$756$		0			0
$757$	23.4089			0.850811			0.425405	−	0.905003i	$-0.360132\pi$
$757$	23.4089			0.850811			0.425405	+	0.905003i	$0.360132\pi$
$758$	0.718146	−	3.13893i	0.0260842	−	0.114011i
$759$		0			0
$760$	35.1052	−	17.5500i	1.27340	−	0.636604i
$761$	49.2769			1.78629			0.893143	−	0.449773i	$-0.148495\pi$
$761$	49.2769			1.78629			0.893143	+	0.449773i	$0.148495\pi$
$762$		0			0
$763$	−0.399908			−0.0144776
$764$	−29.0653	−	14.0341i	−1.05155	−	0.507736i
$765$		0			0
$766$	−0.488909	+	2.13696i	−0.0176650	+	0.0772116i
$767$			18.8772i			0.681616i
$768$		0			0
$769$	−33.0838			−1.19303			−0.596517	−	0.802601i	$-0.703449\pi$
$769$	−33.0838			−1.19303			−0.596517	+	0.802601i	$0.703449\pi$
$770$	34.6085	+	26.7147i	1.24720	+	0.962731i
$771$		0			0
$772$	−6.25813	+	12.9609i	−0.225235	+	0.466473i
$773$	17.2906			0.621899			0.310949	−	0.950426i	$-0.399353\pi$
$773$	17.2906			0.621899			0.310949	+	0.950426i	$0.399353\pi$
$774$		0			0
$775$	0.743317	+	0.872050i	0.0267007	+	0.0313250i
$776$	21.7164	−	27.1452i	0.779574	−	0.974455i
$777$		0			0
$778$	−6.23834	+	27.2671i	−0.223655	+	0.977571i
$779$			28.0845i			1.00623i
$780$		0			0
$781$			5.19415i			0.185861i
$782$	32.5506	+	7.44715i	1.16401	+	0.266310i
$783$		0			0
$784$	−10.8244	−	13.6310i	−0.386585	−	0.486821i
$785$	−24.9482	−	11.5162i	−0.890439	−	0.411030i
$786$		0			0
$787$	−12.1070			−0.431566			−0.215783	−	0.976441i	$-0.569230\pi$
$787$	−12.1070			−0.431566			−0.215783	+	0.976441i	$0.569230\pi$
$788$	29.4559	+	14.2227i	1.04932	+	0.506664i
$789$		0			0
$790$	−0.613928	−	0.473897i	−0.0218426	−	0.0168605i
$791$	6.40855			0.227862
$792$		0			0
$793$			4.68011i			0.166196i
$794$	40.6535	+	9.30099i	1.44274	+	0.330080i
$795$		0			0
$796$	11.1645	+	5.39077i	0.395717	+	0.191071i
$797$	8.12494			0.287800			0.143900	−	0.989592i	$-0.454036\pi$
$797$	8.12494			0.287800			0.143900	+	0.989592i	$0.454036\pi$
$798$		0			0
$799$	12.4880			0.441794
$800$	−11.4998	+	25.8410i	−0.406578	+	0.913616i
$801$		0			0
$802$	−18.3588	−	4.20025i	−0.648271	−	0.148316i
$803$	−57.1808			−2.01787
$804$		0			0
$805$	21.6023	+	9.97168i	0.761379	+	0.351455i
$806$	−1.93855	−	0.443514i	−0.0682825	−	0.0156221i
$807$		0			0
$808$	22.8242	−	28.5299i	0.802954	−	1.00368i
$809$	−37.7588			−1.32753			−0.663764	−	0.747942i	$-0.731042\pi$
$809$	−37.7588			−1.32753			−0.663764	+	0.747942i	$0.731042\pi$
$810$		0			0
$811$			13.6205i			0.478282i	0.970985	+	0.239141i	$0.0768658\pi$
$811$			13.6205i			0.478282i	−0.970985	+	0.239141i	$0.923134\pi$
$812$	−8.15094	−	3.93566i	−0.286042	−	0.138115i
$813$		0			0
$814$	7.30983	−	31.9504i	0.256209	−	1.11986i
$815$	−16.8423	−	7.77445i	−0.589959	−	0.272327i
$816$		0			0
$817$		−	12.5952i		−	0.440651i
$818$	20.2759	+	4.63886i	0.708930	+	0.162194i
$819$		0			0
$820$	−12.8598	−	15.6289i	−0.449084	−	0.545784i
$821$			3.82718i			0.133569i	0.997767	+	0.0667847i	$0.0212741\pi$
$821$			3.82718i			0.133569i	−0.997767	+	0.0667847i	$0.978726\pi$
$822$		0			0
$823$		−	33.6077i		−	1.17149i	−0.810495	−	0.585746i	$-0.800802\pi$
$823$		−	33.6077i		−	1.17149i	0.810495	−	0.585746i	$-0.199198\pi$
$824$	−20.5818	+	25.7270i	−0.717003	+	0.896242i
$825$		0			0
$826$	14.2896	+	3.26928i	0.497200	+	0.113753i
$827$	−47.5387			−1.65308			−0.826541	−	0.562876i	$-0.809695\pi$
$827$	−47.5387			−1.65308			−0.826541	+	0.562876i	$0.809695\pi$
$828$		0			0
$829$		−	34.9453i		−	1.21370i	−0.794816	−	0.606851i	$-0.792433\pi$
$829$		−	34.9453i		−	1.21370i	0.794816	−	0.606851i	$-0.207567\pi$
$830$	33.4438	+	25.8157i	1.16085	+	0.896075i
$831$		0			0
$832$	−10.7747	−	47.8902i	−0.373544	−	1.66029i
$833$			32.5336i			1.12722i
$834$		0			0
$835$	11.6887	−	25.3220i	0.404504	−	0.876302i
$836$	−45.8626	−	22.1446i	−1.58619	−	0.765888i
$837$		0			0
$838$	−6.62741	+	28.9677i	−0.228940	+	1.00067i
$839$	3.50113			0.120872			0.0604362	−	0.998172i	$-0.480751\pi$
$839$	3.50113			0.120872			0.0604362	+	0.998172i	$0.480751\pi$
$840$		0			0
$841$	27.1957			0.937782
$842$	−1.91626	+	8.37576i	−0.0660388	+	0.288648i
$843$		0			0
$844$	−11.8247	+	24.4895i	−0.407023	+	0.842964i
$845$	−50.0436	−	23.1003i	−1.72155	−	0.794675i
$846$		0			0
$847$		−	19.6711i		−	0.675906i
$848$	25.1244	+	31.6388i	0.862775	+	1.08648i
$849$		0			0
$850$	46.8685	−	24.4573i	1.60758	−	0.838880i
$851$		−	17.8369i		−	0.611442i
$852$		0			0
$853$	29.9745			1.02631			0.513154	−	0.858296i	$-0.328477\pi$
$853$	29.9745			1.02631			0.513154	+	0.858296i	$0.328477\pi$
$854$	3.54274	+	0.810533i	0.121230	+	0.0277359i
$855$		0			0
$856$	11.1561	+	8.92499i	0.381308	+	0.305050i
$857$			48.7191i			1.66421i	0.554615	+	0.832107i	$0.312865\pi$
$857$			48.7191i			1.66421i	−0.554615	+	0.832107i	$0.687135\pi$
$858$		0			0
$859$			33.6152i			1.14694i	0.819228	+	0.573468i	$0.194402\pi$
$859$			33.6152i			1.14694i	−0.819228	+	0.573468i	$0.805598\pi$
$860$	5.76731	+	7.00917i	0.196664	+	0.239011i
$861$		0			0
$862$	−45.4591	−	10.4004i	−1.54834	−	0.354241i
$863$		−	38.1251i		−	1.29779i	−0.760876	−	0.648897i	$-0.775231\pi$
$863$		−	38.1251i		−	1.29779i	0.760876	−	0.648897i	$-0.224769\pi$
$864$		0			0
$865$	17.9358	+	8.27924i	0.609837	+	0.281503i
$866$	−0.405054	+	1.77044i	−0.0137643	+	0.0601621i
$867$		0			0
$868$	−0.671462	+	1.39063i	−0.0227909	+	0.0472010i
$869$			1.00639i			0.0341393i
$870$		0			0
$871$	−85.0785			−2.88278
$872$	−0.209725	+	0.262153i	−0.00710218	+	0.00887761i
$873$		0			0
$874$	−27.0179	−	6.18133i	−0.913893	−	0.209087i
$875$	36.2696	−	10.1713i	1.22614	−	0.343852i
$876$		0			0
$877$	42.9505			1.45034			0.725168	−	0.688572i	$-0.241762\pi$
$877$	42.9505			1.45034			0.725168	+	0.688572i	$0.241762\pi$
$878$	−50.8198	−	11.6269i	−1.71508	−	0.392389i
$879$		0			0
$880$	35.6622	−	8.67695i	1.20217	−	0.292500i
$881$	−1.97970			−0.0666978			−0.0333489	−	0.999444i	$-0.510617\pi$
$881$	−1.97970			−0.0666978			−0.0333489	+	0.999444i	$0.510617\pi$
$882$		0			0
$883$	−31.1386			−1.04790			−0.523949	−	0.851750i	$-0.675542\pi$
$883$	−31.1386			−1.04790			−0.523949	+	0.851750i	$0.675542\pi$
$884$	−39.8937	+	82.6218i	−1.34177	+	2.77887i
$885$		0			0
$886$	11.4943	+	2.62975i	0.386160	+	0.0883482i
$887$		−	58.8602i		−	1.97633i	−0.153385	−	0.988167i	$-0.549017\pi$
$887$		−	58.8602i		−	1.97633i	0.153385	−	0.988167i	$-0.450983\pi$
$888$		0			0
$889$	37.7608			1.26646
$890$	−21.6439	−	16.7072i	−0.725505	−	0.560025i
$891$		0			0
$892$	12.1197	−	25.1005i	0.405798	−	0.840427i
$893$	−10.3654			−0.346864
$894$		0			0
$895$	−6.22974	+	13.4959i	−0.208237	+	0.451117i
$896$	−38.1179	−	0.137755i	−1.27343	−	0.00460209i
$897$		0			0
$898$	−50.3324	−	11.5154i	−1.67961	−	0.384273i
$899$			0.307835i			0.0102669i
$900$		0			0
$901$		−	75.5135i		−	2.51572i
$902$	−5.85737	+	25.6019i	−0.195029	+	0.852450i
$903$		0			0
$904$	3.36085	−	4.20101i	0.111780	−	0.139723i
$905$	17.5330	−	37.9828i	0.582816	−	1.26259i
$906$		0			0
$907$	15.6822			0.520718			0.260359	−	0.965512i	$-0.416159\pi$
$907$	15.6822			0.520718			0.260359	+	0.965512i	$0.416159\pi$
$908$	9.43624	+	4.55626i	0.313153	+	0.151205i
$909$		0			0
$910$	−39.9464	+	51.7501i	−1.32421	+	1.71550i
$911$	38.0864			1.26186			0.630929	−	0.775840i	$-0.282674\pi$
$911$	38.0864			1.26186			0.630929	+	0.775840i	$0.282674\pi$
$912$		0			0
$913$		−	54.8231i		−	1.81438i
$914$	6.55130	−	28.6350i	0.216698	−	0.947160i
$915$		0			0
$916$	−4.71006	+	9.75476i	−0.155625	+	0.322306i
$917$	19.7094			0.650861
$918$		0			0
$919$	9.97964			0.329198			0.164599	−	0.986361i	$-0.447367\pi$
$919$	9.97964			0.329198			0.164599	+	0.986361i	$0.447367\pi$
$920$	17.8657	−	8.93150i	0.589014	−	0.294463i
$921$		0			0
$922$	−0.799093	+	3.49274i	−0.0263167	+	0.115027i
$923$	−7.76680			−0.255647
$924$		0			0
$925$	−18.3190	−	21.4916i	−0.602325	−	0.706639i
$926$	4.12843	−	18.0449i	0.135669	−	0.592992i
$927$		0			0
$928$	−6.85457	+	3.27922i	−0.225012	+	0.107646i
$929$	−9.06397			−0.297379			−0.148690	−	0.988884i	$-0.547506\pi$
$929$	−9.06397			−0.297379			−0.148690	+	0.988884i	$0.547506\pi$
$930$		0			0
$931$		−	27.0037i		−	0.885011i
$932$	−0.0671119	+	0.138992i	−0.00219832	+	0.00455284i
$933$		0			0
$934$	−32.1166	−	7.34784i	−1.05089	−	0.240429i
$935$	−62.2851	−	28.7510i	−2.03694	−	0.940258i
$936$		0			0
$937$			50.7084i			1.65657i	0.560306	+	0.828286i	$0.310684\pi$
$937$			50.7084i			1.65657i	−0.560306	+	0.828286i	$0.689316\pi$
$938$	−14.7345	+	64.4026i	−0.481097	+	2.10282i
$939$		0			0
$940$	5.76826	−	4.74626i	0.188140	−	0.154806i
$941$			47.8274i			1.55913i	0.626323	+	0.779564i	$0.284559\pi$
$941$			47.8274i			1.55913i	−0.626323	+	0.779564i	$0.715441\pi$
$942$		0			0
$943$			14.2927i			0.465436i
$944$	9.63706	−	7.65279i	0.313660	−	0.249077i
$945$		0			0
$946$	2.62689	−	11.4818i	0.0854075	−	0.373306i
$947$	−21.3095			−0.692467			−0.346234	−	0.938148i	$-0.612540\pi$
$947$	−21.3095			−0.692467			−0.346234	+	0.938148i	$0.612540\pi$
$948$		0			0
$949$		−	85.5024i		−	2.77553i
$950$	−38.9020	+	20.3002i	−1.26215	+	0.658626i
$951$		0			0
$952$	55.6339	+	44.5077i	1.80310	+	1.44250i
$953$		−	54.1752i		−	1.75491i	−0.479663	−	0.877453i	$-0.659241\pi$
$953$		−	54.1752i		−	1.75491i	0.479663	−	0.877453i	$-0.340759\pi$
$954$		0			0
$955$	32.7636	+	15.1238i	1.06021	+	0.489395i
$956$	35.1707	+	16.9821i	1.13750	+	0.549239i
$957$		0			0
$958$	15.2013	+	3.47786i	0.491133	+	0.112365i
$959$	41.2793			1.33298
$960$		0			0
$961$	−30.9475			−0.998306
$962$	47.7754	+	10.9304i	1.54034	+	0.352409i
$963$		0			0
$964$	28.3270	+	13.6776i	0.912353	+	0.440527i
$965$	6.74406	−	14.6101i	0.217099	−	0.470315i
$966$		0			0
$967$			16.0178i			0.515097i	0.966265	+	0.257548i	$0.0829147\pi$
$967$			16.0178i			0.515097i	−0.966265	+	0.257548i	$0.917085\pi$
$968$	−12.8950	−	10.3162i	−0.414462	−	0.331574i
$969$		0			0
$970$	−23.7489	+	30.7664i	−0.762531	+	0.987849i
$971$		−	16.1971i		−	0.519789i	−0.965637	−	0.259894i	$-0.916312\pi$
$971$		−	16.1971i		−	0.519789i	0.965637	−	0.259894i	$-0.0836878\pi$
$972$		0			0
$973$	21.3078			0.683096
$974$	1.95370	−	8.53940i	0.0626006	−	0.273620i
$975$		0			0
$976$	2.38926	−	1.89731i	0.0764784	−	0.0607315i
$977$		−	18.8412i		−	0.602784i	−0.953500	−	0.301392i	$-0.902549\pi$
$977$		−	18.8412i		−	0.602784i	0.953500	−	0.301392i	$-0.0974513\pi$
$978$		0			0
$979$			35.4799i			1.13394i
$980$	12.3649	+	15.0274i	0.394982	+	0.480033i
$981$		0			0
$982$	1.19864	−	5.23911i	0.0382501	−	0.167187i
$983$		−	24.3103i		−	0.775377i	−0.921790	−	0.387688i	$-0.873274\pi$
$983$		−	24.3103i		−	0.775377i	0.921790	−	0.387688i	$-0.126726\pi$
$984$		0			0
$985$	−33.2040	−	15.3271i	−1.05797	−	0.488361i
$986$	13.8448	+	3.16750i	0.440907	+	0.100874i
$987$		0			0
$988$	33.1128	−	68.5782i	1.05346	−	2.18176i
$989$		−	6.40995i		−	0.203824i
$990$		0			0
$991$	−18.1831			−0.577606			−0.288803	−	0.957389i	$-0.593257\pi$
$991$	−18.1831			−0.577606			−0.288803	+	0.957389i	$0.593257\pi$
$992$	0.559466	+	1.16946i	0.0177631	+	0.0371303i
$993$		0			0
$994$	−1.34511	+	5.87930i	−0.0426642	+	0.186480i
$995$	−12.5851	−	5.80935i	−0.398976	−	0.184169i
$996$		0			0
$997$	23.1520			0.733231			0.366615	−	0.930373i	$-0.380516\pi$
$997$	23.1520			0.733231			0.366615	+	0.930373i	$0.380516\pi$
$998$	6.28338	−	27.4639i	0.198897	−	0.869356i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.i.109.20	yes	20
3.2	odd	2	inner	1080.2.d.i.109.1	✓	20
4.3	odd	2		4320.2.d.i.3889.3		20
5.4	even	2		1080.2.d.j.109.1	yes	20
8.3	odd	2		4320.2.d.j.3889.18		20
8.5	even	2		1080.2.d.j.109.2	yes	20
12.11	even	2		4320.2.d.i.3889.18		20
15.14	odd	2		1080.2.d.j.109.20	yes	20
20.19	odd	2		4320.2.d.j.3889.17		20
24.5	odd	2		1080.2.d.j.109.19	yes	20
24.11	even	2		4320.2.d.j.3889.3		20
40.19	odd	2		4320.2.d.i.3889.4		20
40.29	even	2	inner	1080.2.d.i.109.19	yes	20
60.59	even	2		4320.2.d.j.3889.4		20
120.29	odd	2	inner	1080.2.d.i.109.2	yes	20
120.59	even	2		4320.2.d.i.3889.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.i.109.1	✓	20	3.2	odd	2	inner
1080.2.d.i.109.2	yes	20	120.29	odd	2	inner
1080.2.d.i.109.19	yes	20	40.29	even	2	inner
1080.2.d.i.109.20	yes	20	1.1	even	1	trivial
1080.2.d.j.109.1	yes	20	5.4	even	2
1080.2.d.j.109.2	yes	20	8.5	even	2
1080.2.d.j.109.19	yes	20	24.5	odd	2
1080.2.d.j.109.20	yes	20	15.14	odd	2
4320.2.d.i.3889.3		20	4.3	odd	2
4320.2.d.i.3889.4		20	40.19	odd	2
4320.2.d.i.3889.17		20	120.59	even	2
4320.2.d.i.3889.18		20	12.11	even	2
4320.2.d.j.3889.3		20	24.11	even	2
4320.2.d.j.3889.4		20	60.59	even	2
4320.2.d.j.3889.17		20	20.19	odd	2
4320.2.d.j.3889.18		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37859 + 0.315404i) q^{2} +(1.80104 + 0.869628i) q^{4} +(-2.03021 - 0.937151i) q^{5} +3.36920i q^{7} +(2.20862 + 1.76692i) q^{8} +O(q^{10})\)	\(q+(1.37859 + 0.315404i) q^{2} +(1.80104 + 0.869628i) q^{4} +(-2.03021 - 0.937151i) q^{5} +3.36920i q^{7} +(2.20862 + 1.76692i) q^{8} +(-2.50325 - 1.93229i) q^{10} +4.10347i q^{11} -6.13592 q^{13} +(-1.06266 + 4.64476i) q^{14} +(2.48750 + 3.13247i) q^{16} -7.47638i q^{17} +6.20559i q^{19} +(-2.84152 - 3.45337i) q^{20} +(-1.29425 + 5.65702i) q^{22} +3.15814i q^{23} +(3.24349 + 3.80523i) q^{25} +(-8.45894 - 1.93529i) q^{26} +(-2.92995 + 6.06807i) q^{28} +1.34325i q^{29} +0.229172 q^{31} +(2.44125 + 5.10297i) q^{32} +(2.35808 - 10.3069i) q^{34} +(3.15745 - 6.84018i) q^{35} -5.64792 q^{37} +(-1.95727 + 8.55499i) q^{38} +(-2.82809 - 5.65702i) q^{40} +4.52568 q^{41} -2.02966 q^{43} +(-3.56849 + 7.39052i) q^{44} +(-0.996090 + 4.35379i) q^{46} +1.67033i q^{47} -4.35151 q^{49} +(3.27128 + 6.26887i) q^{50} +(-11.0510 - 5.33596i) q^{52} +10.1003 q^{53} +(3.84558 - 8.33091i) q^{55} +(-5.95310 + 7.44128i) q^{56} +(-0.423667 + 1.85180i) q^{58} -3.07651i q^{59} -0.762740i q^{61} +(0.315935 + 0.0722817i) q^{62} +(1.75600 + 7.80490i) q^{64} +(12.4572 + 5.75028i) q^{65} +13.8657 q^{67} +(6.50167 - 13.4653i) q^{68} +(6.51026 - 8.43396i) q^{70} +1.26579 q^{71} +13.9347i q^{73} +(-7.78618 - 1.78137i) q^{74} +(-5.39655 + 11.1765i) q^{76} -13.8254 q^{77} +0.245252 q^{79} +(-2.11454 - 8.69073i) q^{80} +(6.23908 + 1.42742i) q^{82} -13.3602 q^{83} +(-7.00650 + 15.1786i) q^{85} +(-2.79807 - 0.640162i) q^{86} +(-7.25050 + 9.06301i) q^{88} +8.64631 q^{89} -20.6731i q^{91} +(-2.74641 + 5.68794i) q^{92} +(-0.526827 + 2.30270i) q^{94} +(5.81558 - 12.5986i) q^{95} -12.2906i q^{97} +(-5.99897 - 1.37248i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4}+O(q^{10}) \) 20 * q + 6 * q^4	\( 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64} + 12 q^{70} - 24 q^{76} + 36 q^{79} + 32 q^{82} - 44 q^{85} - 30 q^{88} - 22 q^{94}+O(q^{100}) \) 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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