LMFDB - Embedded newform 1080.2.k.d.541.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(541,1080)]

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, 0]))

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

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

chi := DirichletCharacter("1080.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.k (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} - x^{18} + 5x^{16} + 28x^{12} - 28x^{10} + 112x^{8} + 320x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + 5x^16 + 28x^12 - 28x^10 + 112x^8 + 320x^4 - 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			541.19
Root			$1.34522 + 0.436333i$ of defining polynomial
Character	$\chi$	$=$	1080.541
Dual form			1080.2.k.d.541.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34522 - 0.436333i) q^{2} +(1.61923 - 1.17393i) q^{4} -1.00000i q^{5} -3.61492 q^{7} +(1.66599 - 2.28571i) q^{8} +O(q^{10})$	\(q+(1.34522 - 0.436333i) q^{2} +(1.61923 - 1.17393i) q^{4} -1.00000i q^{5} -3.61492 q^{7} +(1.66599 - 2.28571i) q^{8} +(-0.436333 - 1.34522i) q^{10} -0.460301i q^{11} -3.67457i q^{13} +(-4.86285 + 1.57731i) q^{14} +(1.24379 - 3.80171i) q^{16} -6.59150 q^{17} -3.13421i q^{19} +(-1.17393 - 1.61923i) q^{20} +(-0.200845 - 0.619206i) q^{22} +3.60210 q^{23} -1.00000 q^{25} +(-1.60333 - 4.94310i) q^{26} +(-5.85337 + 4.24365i) q^{28} -9.83716i q^{29} +9.34649 q^{31} +(0.0143608 - 5.65684i) q^{32} +(-8.86701 + 2.87609i) q^{34} +3.61492i q^{35} +6.66397i q^{37} +(-1.36756 - 4.21619i) q^{38} +(-2.28571 - 1.66599i) q^{40} -10.2939 q^{41} +6.05114i q^{43} +(-0.540360 - 0.745332i) q^{44} +(4.84562 - 1.57172i) q^{46} +6.61929 q^{47} +6.06762 q^{49} +(-1.34522 + 0.436333i) q^{50} +(-4.31367 - 5.94996i) q^{52} +3.27127i q^{53} -0.460301 q^{55} +(-6.02242 + 8.26265i) q^{56} +(-4.29228 - 13.2331i) q^{58} -5.19188i q^{59} -6.80877i q^{61} +(12.5731 - 4.07818i) q^{62} +(-2.44895 - 7.61595i) q^{64} -3.67457 q^{65} +10.0766i q^{67} +(-10.6731 + 7.73794i) q^{68} +(1.57731 + 4.86285i) q^{70} -2.98940 q^{71} +2.27127 q^{73} +(2.90771 + 8.96449i) q^{74} +(-3.67933 - 5.07499i) q^{76} +1.66395i q^{77} +14.9124 q^{79} +(-3.80171 - 1.24379i) q^{80} +(-13.8475 + 4.49155i) q^{82} -6.88619i q^{83} +6.59150i q^{85} +(2.64031 + 8.14011i) q^{86} +(-1.05212 - 0.766858i) q^{88} +6.05114 q^{89} +13.2833i q^{91} +(5.83262 - 4.22861i) q^{92} +(8.90439 - 2.88821i) q^{94} -3.13421 q^{95} +13.0408 q^{97} +(8.16228 - 2.64751i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4}+O(q^{10}) $ 20 * q + 2 * q^4	$ 20 q + 2 q^{4} - 2 q^{10} - 18 q^{16} + 16 q^{22} - 20 q^{25} + 16 q^{28} + 20 q^{31} - 6 q^{34} - 4 q^{40} + 54 q^{46} + 36 q^{49} + 56 q^{52} - 72 q^{58} - 28 q^{64} - 40 q^{73} + 58 q^{76} - 4 q^{79} - 92 q^{82} - 116 q^{88} + 72 q^{94} + 40 q^{97}+O(q^{100}) $ 20 * q + 2 * q^4 - 2 * q^10 - 18 * q^16 + 16 * q^22 - 20 * q^25 + 16 * q^28 + 20 * q^31 - 6 * q^34 - 4 * q^40 + 54 * q^46 + 36 * q^49 + 56 * q^52 - 72 * q^58 - 28 * q^64 - 40 * q^73 + 58 * q^76 - 4 * q^79 - 92 * q^82 - 116 * q^88 + 72 * q^94 + 40 * q^97

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 $

$2$	1.34522	−	0.436333i	0.951213	−	0.308534i
$2$	1.34522	−	0.436333i	0.951213	−	0.308534i
$3$		0			0
$3$		0			0
$4$	1.61923	−	1.17393i	0.809613	−	0.586963i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−3.61492			−1.36631			−0.683155	−	0.730273i	$-0.739393\pi$
$7$	−3.61492			−1.36631			−0.683155	+	0.730273i	$0.739393\pi$
$8$	1.66599	−	2.28571i	0.589017	−	0.808121i
$9$		0			0
$10$	−0.436333	−	1.34522i	−0.137981	−	0.425396i
$11$		−	0.460301i		−	0.138786i	−0.997589	−	0.0693930i	$-0.977894\pi$
$11$		−	0.460301i		−	0.138786i	0.997589	−	0.0693930i	$-0.0221063\pi$
$12$		0			0
$13$		−	3.67457i		−	1.01914i	−0.860429	−	0.509571i	$-0.829804\pi$
$13$		−	3.67457i		−	1.01914i	0.860429	−	0.509571i	$-0.170196\pi$
$14$	−4.86285	+	1.57731i	−1.29965	+	0.421553i
$15$		0			0
$16$	1.24379	−	3.80171i	0.310948	−	0.950427i
$17$	−6.59150			−1.59867			−0.799337	−	0.600883i	$-0.794816\pi$
$17$	−6.59150			−1.59867			−0.799337	+	0.600883i	$0.794816\pi$
$18$		0			0
$19$		−	3.13421i		−	0.719036i	−0.933138	−	0.359518i	$-0.882941\pi$
$19$		−	3.13421i		−	0.719036i	0.933138	−	0.359518i	$-0.117059\pi$
$20$	−1.17393	−	1.61923i	−0.262498	−	0.362070i
$21$		0			0
$22$	−0.200845	−	0.619206i	−0.0428202	−	0.132015i
$23$	3.60210			0.751090			0.375545	−	0.926804i	$-0.377455\pi$
$23$	3.60210			0.751090			0.375545	+	0.926804i	$0.377455\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.60333	−	4.94310i	−0.314440	−	0.969421i
$27$		0			0
$28$	−5.85337	+	4.24365i	−1.10618	+	0.801974i
$29$		−	9.83716i		−	1.82671i	−0.407159	−	0.913357i	$-0.633481\pi$
$29$		−	9.83716i		−	1.82671i	0.407159	−	0.913357i	$-0.366519\pi$
$30$		0			0
$31$	9.34649			1.67868			0.839340	−	0.543607i	$-0.182942\pi$
$31$	9.34649			1.67868			0.839340	+	0.543607i	$0.182942\pi$
$32$	0.0143608	−	5.65684i	0.00253866	−	0.999997i
$33$		0			0
$34$	−8.86701	+	2.87609i	−1.52068	+	0.493245i
$35$			3.61492i			0.611032i
$36$		0			0
$37$			6.66397i			1.09555i	0.836626	+	0.547775i	$0.184525\pi$
$37$			6.66397i			1.09555i	−0.836626	+	0.547775i	$0.815475\pi$
$38$	−1.36756	−	4.21619i	−0.221847	−	0.683957i
$39$		0			0
$40$	−2.28571	−	1.66599i	−0.361403	−	0.263416i
$41$	−10.2939			−1.60763			−0.803815	−	0.594880i	$-0.797200\pi$
$41$	−10.2939			−1.60763			−0.803815	+	0.594880i	$0.797200\pi$
$42$		0			0
$43$			6.05114i			0.922790i	0.887195	+	0.461395i	$0.152651\pi$
$43$			6.05114i			0.922790i	−0.887195	+	0.461395i	$0.847349\pi$
$44$	−0.540360	−	0.745332i	−0.0814623	−	0.112363i
$45$		0			0
$46$	4.84562	−	1.57172i	0.714447	−	0.231737i
$47$	6.61929			0.965522			0.482761	−	0.875752i	$-0.339634\pi$
$47$	6.61929			0.965522			0.482761	+	0.875752i	$0.339634\pi$
$48$		0			0
$49$	6.06762			0.866803
$50$	−1.34522	+	0.436333i	−0.190243	+	0.0617068i
$51$		0			0
$52$	−4.31367	−	5.94996i	−0.598199	−	0.825111i
$53$			3.27127i			0.449344i	0.974434	+	0.224672i	$0.0721311\pi$
$53$			3.27127i			0.449344i	−0.974434	+	0.224672i	$0.927869\pi$
$54$		0			0
$55$	−0.460301			−0.0620670
$56$	−6.02242	+	8.26265i	−0.804780	+	1.10414i
$57$		0			0
$58$	−4.29228	−	13.2331i	−0.563604	−	1.73759i
$59$		−	5.19188i		−	0.675925i	−0.941160	−	0.337962i	$-0.890262\pi$
$59$		−	5.19188i		−	0.675925i	0.941160	−	0.337962i	$-0.109738\pi$
$60$		0			0
$61$		−	6.80877i		−	0.871774i	−0.900001	−	0.435887i	$-0.856435\pi$
$61$		−	6.80877i		−	0.871774i	0.900001	−	0.435887i	$-0.143565\pi$
$62$	12.5731	−	4.07818i	1.59678	−	0.517930i
$63$		0			0
$64$	−2.44895	−	7.61595i	−0.306118	−	0.951993i
$65$	−3.67457			−0.455774
$66$		0			0
$67$			10.0766i			1.23105i	0.788117	+	0.615525i	$0.211056\pi$
$67$			10.0766i			1.23105i	−0.788117	+	0.615525i	$0.788944\pi$
$68$	−10.6731	+	7.73794i	−1.29431	+	0.938363i
$69$		0			0
$70$	1.57731	+	4.86285i	0.188524	+	0.581222i
$71$	−2.98940			−0.354776			−0.177388	−	0.984141i	$-0.556765\pi$
$71$	−2.98940			−0.354776			−0.177388	+	0.984141i	$0.556765\pi$
$72$		0			0
$73$	2.27127			0.265833			0.132916	−	0.991127i	$-0.457566\pi$
$73$	2.27127			0.265833			0.132916	+	0.991127i	$0.457566\pi$
$74$	2.90771	+	8.96449i	0.338014	+	1.04210i
$75$		0			0
$76$	−3.67933	−	5.07499i	−0.422048	−	0.582141i
$77$			1.66395i			0.189625i
$78$		0			0
$79$	14.9124			1.67777			0.838887	−	0.544306i	$-0.183207\pi$
$79$	14.9124			1.67777			0.838887	+	0.544306i	$0.183207\pi$
$80$	−3.80171	−	1.24379i	−0.425044	−	0.139060i
$81$		0			0
$82$	−13.8475	+	4.49155i	−1.52920	+	0.496009i
$83$		−	6.88619i		−	0.755858i	−0.925835	−	0.377929i	$-0.876636\pi$
$83$		−	6.88619i		−	0.755858i	0.925835	−	0.377929i	$-0.123364\pi$
$84$		0			0
$85$			6.59150i			0.714949i
$86$	2.64031	+	8.14011i	0.284712	+	0.877771i
$87$		0			0
$88$	−1.05212	−	0.766858i	−0.112156	−	0.0817473i
$89$	6.05114			0.641420			0.320710	−	0.947177i	$-0.396079\pi$
$89$	6.05114			0.641420			0.320710	+	0.947177i	$0.396079\pi$
$90$		0			0
$91$			13.2833i			1.39246i
$92$	5.83262	−	4.22861i	0.608093	−	0.440863i
$93$		0			0
$94$	8.90439	−	2.88821i	0.918418	−	0.297897i
$95$	−3.13421			−0.321563
$96$		0			0
$97$	13.0408			1.32409			0.662047	−	0.749463i	$-0.269688\pi$
$97$	13.0408			1.32409			0.662047	+	0.749463i	$0.269688\pi$
$98$	8.16228	−	2.64751i	0.824515	−	0.267438i
$99$		0			0
$100$	−1.61923	+	1.17393i	−0.161923	+	0.117393i
$101$		−	2.99241i		−	0.297756i	−0.988856	−	0.148878i	$-0.952434\pi$
$101$		−	2.99241i		−	0.297756i	0.988856	−	0.148878i	$-0.0475661\pi$
$102$		0			0
$103$	−0.0869913			−0.00857151			−0.00428575	−	0.999991i	$-0.501364\pi$
$103$	−0.0869913			−0.00857151			−0.00428575	+	0.999991i	$0.501364\pi$
$104$	−8.39900	−	6.12180i	−0.823589	−	0.600291i
$105$		0			0
$106$	1.42737	+	4.40058i	0.138638	+	0.427422i
$107$			4.14702i			0.400908i	0.979703	+	0.200454i	$0.0642417\pi$
$107$			4.14702i			0.400908i	−0.979703	+	0.200454i	$0.935758\pi$
$108$		0			0
$109$			19.2619i			1.84496i	0.386047	+	0.922479i	$0.373840\pi$
$109$			19.2619i			1.84496i	−0.386047	+	0.922479i	$0.626160\pi$
$110$	−0.619206	+	0.200845i	−0.0590390	+	0.0191498i
$111$		0			0
$112$	−4.49620	+	13.7429i	−0.424851	+	1.29858i
$113$	−14.2190			−1.33762			−0.668808	−	0.743436i	$-0.733195\pi$
$113$	−14.2190			−1.33762			−0.668808	+	0.743436i	$0.733195\pi$
$114$		0			0
$115$		−	3.60210i		−	0.335898i
$116$	−11.5481	−	15.9286i	−1.07221	−	1.47893i
$117$		0			0
$118$	−2.26539	−	6.98421i	−0.208546	−	0.642949i
$119$	23.8277			2.18428
$120$		0			0
$121$	10.7881			0.980738
$122$	−2.97089	−	9.15929i	−0.268972	−	0.829243i
$123$		0			0
$124$	15.1341	−	10.9721i	1.35908	−	0.985324i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−1.91301			−0.169752			−0.0848760	−	0.996392i	$-0.527049\pi$
$127$	−1.91301			−0.169752			−0.0848760	+	0.996392i	$0.527049\pi$
$128$	−6.61746	−	9.17656i	−0.584906	−	0.811101i
$129$		0			0
$130$	−4.94310	+	1.60333i	−0.433538	+	0.140622i
$131$			8.63351i			0.754313i	0.926150	+	0.377157i	$0.123098\pi$
$131$			8.63351i			0.754313i	−0.926150	+	0.377157i	$0.876902\pi$
$132$		0			0
$133$			11.3299i			0.982427i
$134$	4.39675	+	13.5552i	0.379821	+	1.17099i
$135$		0			0
$136$	−10.9814	+	15.0663i	−0.941646	+	1.29192i
$137$	9.11300			0.778576			0.389288	−	0.921116i	$-0.372721\pi$
$137$	9.11300			0.778576			0.389288	+	0.921116i	$0.372721\pi$
$138$		0			0
$139$		−	9.77039i		−	0.828713i	−0.910115	−	0.414357i	$-0.864007\pi$
$139$		−	9.77039i		−	0.828713i	0.910115	−	0.414357i	$-0.135993\pi$
$140$	4.24365	+	5.85337i	0.358654	+	0.494700i
$141$		0			0
$142$	−4.02140	+	1.30437i	−0.337468	+	0.109461i
$143$	−1.69141			−0.141443
$144$		0			0
$145$	−9.83716			−0.816931
$146$	3.05536	−	0.991032i	0.252863	−	0.0820184i
$147$		0			0
$148$	7.82301	+	10.7905i	0.643047	+	0.886971i
$149$		−	15.8372i		−	1.29743i	−0.761031	−	0.648715i	$-0.775307\pi$
$149$		−	15.8372i		−	1.29743i	0.761031	−	0.648715i	$-0.224693\pi$
$150$		0			0
$151$	−8.38445			−0.682317			−0.341158	−	0.940006i	$-0.610819\pi$
$151$	−8.38445			−0.682317			−0.341158	+	0.940006i	$0.610819\pi$
$152$	−7.16389	−	5.22156i	−0.581068	−	0.423524i
$153$		0			0
$154$	0.726037	+	2.23838i	0.0585057	+	0.180374i
$155$		−	9.34649i		−	0.750728i
$156$		0			0
$157$		−	10.8788i		−	0.868221i	−0.900860	−	0.434110i	$-0.857063\pi$
$157$		−	10.8788i		−	0.868221i	0.900860	−	0.434110i	$-0.142937\pi$
$158$	20.0604	−	6.50676i	1.59592	−	0.517650i
$159$		0			0
$160$	−5.65684	−	0.0143608i	−0.447212	−	0.00113532i
$161$	−13.0213			−1.02622
$162$		0			0
$163$		−	11.4469i		−	0.896592i	−0.893885	−	0.448296i	$-0.852031\pi$
$163$		−	11.4469i		−	0.896592i	0.893885	−	0.448296i	$-0.147969\pi$
$164$	−16.6681	+	12.0842i	−1.30156	+	0.943620i
$165$		0			0
$166$	−3.00467	−	9.26343i	−0.233208	−	0.718982i
$167$	−1.88089			−0.145548			−0.0727740	−	0.997348i	$-0.523185\pi$
$167$	−1.88089			−0.145548			−0.0727740	+	0.997348i	$0.523185\pi$
$168$		0			0
$169$	−0.502438			−0.0386490
$170$	2.87609	+	8.86701i	0.220586	+	0.680069i
$171$		0			0
$172$	7.10360	+	9.79817i	0.541644	+	0.747104i
$173$			2.11666i			0.160927i	0.996758	+	0.0804633i	$0.0256400\pi$
$173$			2.11666i			0.160927i	−0.996758	+	0.0804633i	$0.974360\pi$
$174$		0			0
$175$	3.61492			0.273262
$176$	−1.74993	−	0.572519i	−0.131906	−	0.0431552i
$177$		0			0
$178$	8.14011	−	2.64031i	0.610127	−	0.197900i
$179$		−	2.30923i		−	0.172600i	−0.996269	−	0.0863000i	$-0.972496\pi$
$179$		−	2.30923i		−	0.172600i	0.996269	−	0.0863000i	$-0.0275044\pi$
$180$		0			0
$181$		−	3.60210i		−	0.267742i	−0.990999	−	0.133871i	$-0.957259\pi$
$181$		−	3.60210i		−	0.267742i	0.990999	−	0.133871i	$-0.0427408\pi$
$182$	5.79592	+	17.8689i	0.429622	+	1.32453i
$183$		0			0
$184$	6.00107	−	8.23337i	0.442405	−	0.606972i
$185$	6.66397			0.489944
$186$		0			0
$187$			3.03408i			0.221874i
$188$	10.7181	−	7.77056i	0.781700	−	0.566726i
$189$		0			0
$190$	−4.21619	+	1.36756i	−0.305875	+	0.0992131i
$191$	0.250626			0.0181346			0.00906732	−	0.999959i	$-0.497114\pi$
$191$	0.250626			0.0181346			0.00906732	+	0.999959i	$0.497114\pi$
$192$		0			0
$193$	13.6901			0.985437			0.492719	−	0.870189i	$-0.336003\pi$
$193$	13.6901			0.985437			0.492719	+	0.870189i	$0.336003\pi$
$194$	17.5427	−	5.69014i	1.25950	−	0.408528i
$195$		0			0
$196$	9.82486	−	7.12295i	0.701776	−	0.508782i
$197$		−	2.11735i		−	0.150855i	−0.997151	−	0.0754276i	$-0.975968\pi$
$197$		−	2.11735i		−	0.150855i	0.997151	−	0.0754276i	$-0.0240322\pi$
$198$		0			0
$199$	4.80338			0.340502			0.170251	−	0.985401i	$-0.445542\pi$
$199$	4.80338			0.340502			0.170251	+	0.985401i	$0.445542\pi$
$200$	−1.66599	+	2.28571i	−0.117803	+	0.161624i
$201$		0			0
$202$	−1.30569	−	4.02544i	−0.0918677	−	0.283229i
$203$			35.5605i			2.49586i
$204$		0			0
$205$			10.2939i			0.718954i
$206$	−0.117022	+	0.0379572i	−0.00815333	+	0.00264460i
$207$		0			0
$208$	−13.9696	−	4.57039i	−0.968619	−	0.316900i
$209$	−1.44268			−0.0997922
$210$		0			0
$211$			24.5575i			1.69061i	0.534288	+	0.845303i	$0.320580\pi$
$211$			24.5575i			1.69061i	−0.534288	+	0.845303i	$0.679420\pi$
$212$	3.84024	+	5.29693i	0.263749	+	0.363795i
$213$		0			0
$214$	1.80948	+	5.57865i	0.123694	+	0.381349i
$215$	6.05114			0.412684
$216$		0			0
$217$	−33.7868			−2.29360
$218$	8.40462	+	25.9115i	0.569232	+	1.75495i
$219$		0			0
$220$	−0.745332	+	0.540360i	−0.0502503	+	0.0364311i
$221$			24.2209i			1.62927i
$222$		0			0
$223$	22.4334			1.50225			0.751126	−	0.660159i	$-0.229511\pi$
$223$	22.4334			1.50225			0.751126	+	0.660159i	$0.229511\pi$
$224$	−0.0519131	+	20.4490i	−0.00346859	+	1.36631i
$225$		0			0
$226$	−19.1277	+	6.20424i	−1.27236	+	0.412700i
$227$			12.6411i			0.839019i	0.907751	+	0.419510i	$0.137798\pi$
$227$			12.6411i			0.839019i	−0.907751	+	0.419510i	$0.862202\pi$
$228$		0			0
$229$		−	23.9002i		−	1.57937i	−0.613513	−	0.789685i	$-0.710244\pi$
$229$		−	23.9002i		−	1.57937i	0.613513	−	0.789685i	$-0.289756\pi$
$230$	−1.57172	−	4.84562i	−0.103636	−	0.319510i
$231$		0			0
$232$	−22.4849	−	16.3886i	−1.47621	−	1.07597i
$233$	−12.8040			−0.838820			−0.419410	−	0.907797i	$-0.637763\pi$
$233$	−12.8040			−0.838820			−0.419410	+	0.907797i	$0.637763\pi$
$234$		0			0
$235$		−	6.61929i		−	0.431795i
$236$	−6.09488	−	8.40683i	−0.396743	−	0.547238i
$237$		0			0
$238$	32.0535	−	10.3968i	2.07772	−	0.673926i
$239$	26.4216			1.70907			0.854535	−	0.519394i	$-0.173842\pi$
$239$	26.4216			1.70907			0.854535	+	0.519394i	$0.173842\pi$
$240$		0			0
$241$	−10.5273			−0.678122			−0.339061	−	0.940764i	$-0.610109\pi$
$241$	−10.5273			−0.678122			−0.339061	+	0.940764i	$0.610109\pi$
$242$	14.5124	−	4.70721i	0.932891	−	0.302591i
$243$		0			0
$244$	−7.99300	−	11.0249i	−0.511699	−	0.705800i
$245$		−	6.06762i		−	0.387646i
$246$		0			0
$247$	−11.5168			−0.732800
$248$	15.5712	−	21.3634i	0.988771	−	1.35658i
$249$		0			0
$250$	0.436333	+	1.34522i	0.0275961	+	0.0850791i
$251$			19.6743i			1.24183i	0.783877	+	0.620916i	$0.213239\pi$
$251$			19.6743i			1.24183i	−0.783877	+	0.620916i	$0.786761\pi$
$252$		0			0
$253$		−	1.65805i		−	0.104241i
$254$	−2.57342	+	0.834709i	−0.161470	+	0.0523743i
$255$		0			0
$256$	−12.9060	−	9.45706i	−0.806623	−	0.591067i
$257$	−0.423338			−0.0264071			−0.0132035	−	0.999913i	$-0.504203\pi$
$257$	−0.423338			−0.0264071			−0.0132035	+	0.999913i	$0.504203\pi$
$258$		0			0
$259$		−	24.0897i		−	1.49686i
$260$	−5.94996	+	4.31367i	−0.369001	+	0.267523i
$261$		0			0
$262$	3.76708	+	11.6140i	0.232731	+	0.717513i
$263$	3.20667			0.197732			0.0988659	−	0.995101i	$-0.468479\pi$
$263$	3.20667			0.197732			0.0988659	+	0.995101i	$0.468479\pi$
$264$		0			0
$265$	3.27127			0.200953
$266$	4.94361	+	15.2412i	0.303112	+	0.934497i
$267$		0			0
$268$	11.8292	+	16.3163i	0.722582	+	0.996675i
$269$			20.4597i			1.24745i	0.781645	+	0.623724i	$0.214381\pi$
$269$			20.4597i			1.24745i	−0.781645	+	0.623724i	$0.785619\pi$
$270$		0			0
$271$	−9.60732			−0.583603			−0.291802	−	0.956479i	$-0.594255\pi$
$271$	−9.60732			−0.583603			−0.291802	+	0.956479i	$0.594255\pi$
$272$	−8.19845	+	25.0590i	−0.497104	+	1.51942i
$273$		0			0
$274$	12.2590	−	3.97630i	0.740592	−	0.240217i
$275$			0.460301i			0.0277572i
$276$		0			0
$277$			23.3766i			1.40456i	0.711899	+	0.702282i	$0.247835\pi$
$277$			23.3766i			1.40456i	−0.711899	+	0.702282i	$0.752165\pi$
$278$	−4.26314	−	13.1433i	−0.255686	−	0.788283i
$279$		0			0
$280$	8.26265	+	6.02242i	0.493788	+	0.359908i
$281$	−14.4810			−0.863864			−0.431932	−	0.901906i	$-0.642168\pi$
$281$	−14.4810			−0.863864			−0.431932	+	0.901906i	$0.642168\pi$
$282$		0			0
$283$		−	8.92352i		−	0.530448i	−0.964187	−	0.265224i	$-0.914554\pi$
$283$		−	8.92352i		−	0.530448i	0.964187	−	0.265224i	$-0.0854459\pi$
$284$	−4.84051	+	3.50934i	−0.287232	+	0.208241i
$285$		0			0
$286$	−2.27531	+	0.738017i	−0.134542	+	0.0436399i
$287$	37.2114			2.19652
$288$		0			0
$289$	26.4479			1.55576
$290$	−13.2331	+	4.29228i	−0.777076	+	0.252051i
$291$		0			0
$292$	3.67771	−	2.66631i	0.215222	−	0.156034i
$293$		−	0.117355i		−	0.00685593i	−0.999994	−	0.00342796i	$-0.998909\pi$
$293$		−	0.117355i		−	0.00685593i	0.999994	−	0.00342796i	$-0.00109116\pi$
$294$		0			0
$295$	−5.19188			−0.302283
$296$	15.2319	+	11.1021i	0.885336	+	0.645297i
$297$		0			0
$298$	−6.91028	−	21.3044i	−0.400301	−	1.23413i
$299$		−	13.2362i		−	0.765467i
$300$		0			0
$301$		−	21.8744i		−	1.26082i
$302$	−11.2789	+	3.65841i	−0.649029	+	0.210518i
$303$		0			0
$304$	−11.9153	−	3.89830i	−0.683391	−	0.223583i
$305$	−6.80877			−0.389869
$306$		0			0
$307$			20.9667i			1.19663i	0.801260	+	0.598316i	$0.204163\pi$
$307$			20.9667i			1.19663i	−0.801260	+	0.598316i	$0.795837\pi$
$308$	1.95336	+	2.69431i	0.111303	+	0.153523i
$309$		0			0
$310$	−4.07818	−	12.5731i	−0.231625	−	0.714103i
$311$	23.9561			1.35842			0.679212	−	0.733942i	$-0.262322\pi$
$311$	23.9561			1.35842			0.679212	+	0.733942i	$0.262322\pi$
$312$		0			0
$313$	−6.83089			−0.386105			−0.193052	−	0.981188i	$-0.561839\pi$
$313$	−6.83089			−0.386105			−0.193052	+	0.981188i	$0.561839\pi$
$314$	−4.74677	−	14.6343i	−0.267876	−	0.825863i
$315$		0			0
$316$	24.1465	−	17.5060i	1.35835	−	0.984792i
$317$		−	13.6557i		−	0.766982i	−0.923545	−	0.383491i	$-0.874722\pi$
$317$		−	13.6557i		−	0.766982i	0.923545	−	0.383491i	$-0.125278\pi$
$318$		0			0
$319$	−4.52806			−0.253522
$320$	−7.61595	+	2.44895i	−0.425744	+	0.136900i
$321$		0			0
$322$	−17.5165	+	5.68163i	−0.976156	+	0.316625i
$323$			20.6591i			1.14950i
$324$		0			0
$325$			3.67457i			0.203828i
$326$	−4.99467	−	15.3986i	−0.276629	−	0.852850i
$327$		0			0
$328$	−17.1495	+	23.5288i	−0.946921	+	1.29916i
$329$	−23.9282			−1.31920
$330$		0			0
$331$		−	30.3581i		−	1.66863i	−0.551287	−	0.834316i	$-0.685863\pi$
$331$		−	30.3581i		−	1.66863i	0.551287	−	0.834316i	$-0.314137\pi$
$332$	−8.08388	−	11.1503i	−0.443661	−	0.611953i
$333$		0			0
$334$	−2.53021	+	0.820696i	−0.138447	+	0.0449065i
$335$	10.0766			0.550543
$336$		0			0
$337$	−8.67022			−0.472297			−0.236148	−	0.971717i	$-0.575885\pi$
$337$	−8.67022			−0.472297			−0.236148	+	0.971717i	$0.575885\pi$
$338$	−0.675889	+	0.219230i	−0.0367635	+	0.0119245i
$339$		0			0
$340$	7.73794	+	10.6731i	0.419649	+	0.578832i
$341$		−	4.30220i		−	0.232977i
$342$		0			0
$343$	3.37046			0.181988
$344$	13.8312	+	10.0811i	0.745726	+	0.543539i
$345$		0			0
$346$	0.923568	+	2.84737i	0.0496513	+	0.153075i
$347$		−	30.6433i		−	1.64502i	−0.568751	−	0.822510i	$-0.692573\pi$
$347$		−	30.6433i		−	1.64502i	0.568751	−	0.822510i	$-0.307427\pi$
$348$		0			0
$349$			7.74457i			0.414557i	0.978282	+	0.207279i	$0.0664606\pi$
$349$			7.74457i			0.414557i	−0.978282	+	0.207279i	$0.933539\pi$
$350$	4.86285	−	1.57731i	0.259930	−	0.0843106i
$351$		0			0
$352$	−2.60385	−	0.00661030i	−0.138786	−	0.000352330i
$353$	−6.41334			−0.341348			−0.170674	−	0.985328i	$-0.554594\pi$
$353$	−6.41334			−0.341348			−0.170674	+	0.985328i	$0.554594\pi$
$354$		0			0
$355$			2.98940i			0.158661i
$356$	9.79817	−	7.10360i	0.519302	−	0.376490i
$357$		0			0
$358$	−1.00759	−	3.10642i	−0.0532530	−	0.164179i
$359$	−27.4857			−1.45064			−0.725320	−	0.688412i	$-0.758308\pi$
$359$	−27.4857			−1.45064			−0.725320	+	0.688412i	$0.758308\pi$
$360$		0			0
$361$	9.17675			0.482987
$362$	−1.57172	−	4.84562i	−0.0826076	−	0.254680i
$363$		0			0
$364$	15.5936	+	21.5086i	0.817325	+	1.12736i
$365$		−	2.27127i		−	0.118884i
$366$		0			0
$367$	−7.52793			−0.392955			−0.196477	−	0.980508i	$-0.562950\pi$
$367$	−7.52793			−0.392955			−0.196477	+	0.980508i	$0.562950\pi$
$368$	4.48027	−	13.6941i	0.233550	−	0.713857i
$369$		0			0
$370$	8.96449	−	2.90771i	0.466042	−	0.151165i
$371$		−	11.8254i		−	0.613943i
$372$		0			0
$373$		−	12.4978i		−	0.647113i	−0.946209	−	0.323557i	$-0.895121\pi$
$373$		−	12.4978i		−	0.647113i	0.946209	−	0.323557i	$-0.104879\pi$
$374$	1.32387	+	4.08150i	0.0684556	+	0.211049i
$375$		0			0
$376$	11.0277	−	15.1298i	0.568709	−	0.780259i
$377$	−36.1473			−1.86168
$378$		0			0
$379$			6.59150i			0.338583i	0.985566	+	0.169291i	$0.0541479\pi$
$379$			6.59150i			0.338583i	−0.985566	+	0.169291i	$0.945852\pi$
$380$	−5.07499	+	3.67933i	−0.260342	+	0.188746i
$381$		0			0
$382$	0.337147	−	0.109356i	0.0172499	−	0.00559516i
$383$	−6.51916			−0.333113			−0.166557	−	0.986032i	$-0.553265\pi$
$383$	−6.51916			−0.333113			−0.166557	+	0.986032i	$0.553265\pi$
$384$		0			0
$385$	1.66395			0.0848028
$386$	18.4162	−	5.97346i	0.937361	−	0.304041i
$387$		0			0
$388$	21.1160	−	15.3090i	1.07200	−	0.777194i
$389$		−	14.6791i		−	0.744261i	−0.928180	−	0.372131i	$-0.878627\pi$
$389$		−	14.6791i		−	0.744261i	0.928180	−	0.372131i	$-0.121373\pi$
$390$		0			0
$391$	−23.7433			−1.20075
$392$	10.1086	−	13.8688i	0.510562	−	0.700482i
$393$		0			0
$394$	−0.923872	−	2.84830i	−0.0465440	−	0.143496i
$395$		−	14.9124i		−	0.750323i
$396$		0			0
$397$		−	28.9764i		−	1.45429i	−0.686486	−	0.727143i	$-0.740848\pi$
$397$		−	28.9764i		−	1.45429i	0.686486	−	0.727143i	$-0.259152\pi$
$398$	6.46160	−	2.09587i	0.323890	−	0.105057i
$399$		0			0
$400$	−1.24379	+	3.80171i	−0.0621896	+	0.190085i
$401$	23.8391			1.19047			0.595233	−	0.803553i	$-0.297060\pi$
$401$	23.8391			1.19047			0.595233	+	0.803553i	$0.297060\pi$
$402$		0			0
$403$		−	34.3443i		−	1.71081i
$404$	−3.51287	−	4.84538i	−0.174772	−	0.241067i
$405$		0			0
$406$	15.5162	+	47.8367i	0.770057	+	2.37409i
$407$	3.06743			0.152047
$408$		0			0
$409$	−25.7793			−1.27470			−0.637352	−	0.770573i	$-0.719970\pi$
$409$	−25.7793			−1.27470			−0.637352	+	0.770573i	$0.719970\pi$
$410$	4.49155	+	13.8475i	0.221822	+	0.683878i
$411$		0			0
$412$	−0.140859	+	0.102121i	−0.00693961	+	0.00503116i
$413$			18.7682i			0.923523i
$414$		0			0
$415$	−6.88619			−0.338030
$416$	−20.7864	−	0.0527697i	−1.01914	−	0.00258725i
$417$		0			0
$418$	−1.94072	+	0.629489i	−0.0949237	+	0.0307893i
$419$		−	25.8254i		−	1.26165i	−0.775924	−	0.630826i	$-0.782716\pi$
$419$		−	25.8254i		−	1.26165i	0.775924	−	0.630826i	$-0.217284\pi$
$420$		0			0
$421$		−	20.6935i		−	1.00854i	−0.863546	−	0.504270i	$-0.831762\pi$
$421$		−	20.6935i		−	1.00854i	0.863546	−	0.504270i	$-0.168238\pi$
$422$	10.7152	+	33.0352i	0.521609	+	1.60813i
$423$		0			0
$424$	7.47719	+	5.44991i	0.363124	+	0.264671i
$425$	6.59150			0.319735
$426$		0			0
$427$			24.6131i			1.19111i
$428$	4.86830	+	6.71497i	0.235318	+	0.324580i
$429$		0			0
$430$	8.14011	−	2.64031i	0.392551	−	0.127327i
$431$	−14.4065			−0.693937			−0.346969	−	0.937877i	$-0.612789\pi$
$431$	−14.4065			−0.693937			−0.346969	+	0.937877i	$0.612789\pi$
$432$		0			0
$433$	−4.24912			−0.204200			−0.102100	−	0.994774i	$-0.532556\pi$
$433$	−4.24912			−0.204200			−0.102100	+	0.994774i	$0.532556\pi$
$434$	−45.4506	+	14.7423i	−2.18170	+	0.707653i
$435$		0			0
$436$	22.6121	+	31.1894i	1.08292	+	1.49370i
$437$		−	11.2897i		−	0.540061i
$438$		0			0
$439$	−4.77643			−0.227967			−0.113983	−	0.993483i	$-0.536361\pi$
$439$	−4.77643			−0.227967			−0.113983	+	0.993483i	$0.536361\pi$
$440$	−0.766858	+	1.05212i	−0.0365585	+	0.0501576i
$441$		0			0
$442$	10.5684	+	32.5824i	0.502687	+	1.54979i
$443$			15.5792i			0.740189i	0.928994	+	0.370094i	$0.120675\pi$
$443$			15.5792i			0.740189i	−0.928994	+	0.370094i	$0.879325\pi$
$444$		0			0
$445$		−	6.05114i		−	0.286852i
$446$	30.1778	−	9.78844i	1.42896	−	0.463496i
$447$		0			0
$448$	8.85274	+	27.5310i	0.418253	+	1.30072i
$449$	39.8219			1.87931			0.939655	−	0.342124i	$-0.111146\pi$
$449$	39.8219			1.87931			0.939655	+	0.342124i	$0.111146\pi$
$450$		0			0
$451$			4.73827i			0.223117i
$452$	−23.0239	+	16.6921i	−1.08295	+	0.785131i
$453$		0			0
$454$	5.51573	+	17.0050i	0.258866	+	0.798086i
$455$	13.2833			0.622728
$456$		0			0
$457$	−37.4853			−1.75349			−0.876744	−	0.480958i	$-0.840289\pi$
$457$	−37.4853			−1.75349			−0.876744	+	0.480958i	$0.840289\pi$
$458$	−10.4284	−	32.1510i	−0.487289	−	1.50232i
$459$		0			0
$460$	−4.22861	−	5.83262i	−0.197160	−	0.271947i
$461$		−	41.2161i		−	1.91963i	−0.280642	−	0.959813i	$-0.590547\pi$
$461$		−	41.2161i		−	1.91963i	0.280642	−	0.959813i	$-0.409453\pi$
$462$		0			0
$463$	−9.97645			−0.463645			−0.231823	−	0.972758i	$-0.574469\pi$
$463$	−9.97645			−0.463645			−0.231823	+	0.972758i	$0.574469\pi$
$464$	−37.3980	−	12.2354i	−1.73616	−	0.568013i
$465$		0			0
$466$	−17.2242	+	5.58682i	−0.797897	+	0.258805i
$467$			30.9987i			1.43445i	0.696842	+	0.717225i	$0.254588\pi$
$467$			30.9987i			1.43445i	−0.696842	+	0.717225i	$0.745412\pi$
$468$		0			0
$469$		−	36.4260i		−	1.68200i
$470$	−2.88821	−	8.90439i	−0.133223	−	0.410729i
$471$		0			0
$472$	−11.8671	−	8.64962i	−0.546229	−	0.398131i
$473$	2.78535			0.128070
$474$		0			0
$475$			3.13421i			0.143807i
$476$	38.5825	−	27.9720i	1.76843	−	1.28210i
$477$		0			0
$478$	35.5428	−	11.5286i	1.62569	−	0.527306i
$479$	15.7934			0.721620			0.360810	−	0.932639i	$-0.382500\pi$
$479$	15.7934			0.721620			0.360810	+	0.932639i	$0.382500\pi$
$480$		0			0
$481$	24.4872			1.11652
$482$	−14.1615	+	4.59341i	−0.645039	+	0.209224i
$483$		0			0
$484$	17.4684	−	12.6645i	0.794019	−	0.575658i
$485$		−	13.0408i		−	0.592153i
$486$		0			0
$487$	−31.5225			−1.42842			−0.714211	−	0.699930i	$-0.753215\pi$
$487$	−31.5225			−1.42842			−0.714211	+	0.699930i	$0.753215\pi$
$488$	−15.5629	−	11.3434i	−0.704499	−	0.513490i
$489$		0			0
$490$	−2.64751	−	8.16228i	−0.119602	−	0.368734i
$491$			22.5728i			1.01870i	0.860561	+	0.509348i	$0.170113\pi$
$491$			22.5728i			1.01870i	−0.860561	+	0.509348i	$0.829887\pi$
$492$		0			0
$493$			64.8416i			2.92032i
$494$	−15.4927	+	5.02518i	−0.697049	+	0.226094i
$495$		0			0
$496$	11.6251	−	35.5326i	0.521982	−	1.59546i
$497$	10.8064			0.484735
$498$		0			0
$499$			39.6903i			1.77678i	0.459089	+	0.888390i	$0.348176\pi$
$499$			39.6903i			1.77678i	−0.459089	+	0.888390i	$0.651824\pi$
$500$	1.17393	+	1.61923i	0.0524996	+	0.0724140i
$501$		0			0
$502$	8.58455	+	26.4663i	0.383147	+	1.18125i
$503$	−15.5597			−0.693773			−0.346886	−	0.937907i	$-0.612761\pi$
$503$	−15.5597			−0.693773			−0.346886	+	0.937907i	$0.612761\pi$
$504$		0			0
$505$	−2.99241			−0.133160
$506$	−0.723463	−	2.23044i	−0.0321619	−	0.0991553i
$507$		0			0
$508$	−3.09760	+	2.24573i	−0.137434	+	0.0996383i
$509$		−	22.0581i		−	0.977707i	−0.872366	−	0.488853i	$-0.837415\pi$
$509$		−	22.0581i		−	0.977707i	0.872366	−	0.488853i	$-0.162585\pi$
$510$		0			0
$511$	−8.21047			−0.363210
$512$	−21.4878	−	7.09052i	−0.949635	−	0.313360i
$513$		0			0
$514$	−0.569482	+	0.184716i	−0.0251188	+	0.00814749i
$515$			0.0869913i			0.00383329i
$516$		0			0
$517$		−	3.04687i		−	0.134001i
$518$	−10.5111	−	32.4059i	−0.461832	−	1.42383i
$519$		0			0
$520$	−6.12180	+	8.39900i	−0.268458	+	0.368320i
$521$	−11.3190			−0.495895			−0.247947	−	0.968774i	$-0.579756\pi$
$521$	−11.3190			−0.495895			−0.247947	+	0.968774i	$0.579756\pi$
$522$		0			0
$523$		−	31.9623i		−	1.39761i	−0.715311	−	0.698806i	$-0.753715\pi$
$523$		−	31.9623i		−	1.39761i	0.715311	−	0.698806i	$-0.246285\pi$
$524$	10.1351	+	13.9796i	0.442754	+	0.610702i
$525$		0			0
$526$	4.31367	−	1.39918i	0.188085	−	0.0610070i
$527$	−61.6074			−2.68366
$528$		0			0
$529$	−10.0249			−0.435863
$530$	4.40058	−	1.42737i	0.191149	−	0.0620008i
$531$		0			0
$532$	13.3005	+	18.3457i	0.576648	+	0.795386i
$533$			37.8254i			1.63840i
$534$		0			0
$535$	4.14702			0.179291
$536$	23.0322	+	16.7875i	0.994837	+	0.725109i
$537$		0			0
$538$	8.92723	+	27.5227i	0.384880	+	1.18659i
$539$		−	2.79294i		−	0.120300i
$540$		0			0
$541$			9.47508i			0.407366i	0.979037	+	0.203683i	$0.0652911\pi$
$541$			9.47508i			0.407366i	−0.979037	+	0.203683i	$0.934709\pi$
$542$	−12.9240	+	4.19199i	−0.555131	+	0.180062i
$543$		0			0
$544$	−0.0946593	+	37.2870i	−0.00405848	+	1.59867i
$545$	19.2619			0.825090
$546$		0			0
$547$		−	23.6218i		−	1.00999i	−0.863121	−	0.504997i	$-0.831493\pi$
$547$		−	23.6218i		−	1.00999i	0.863121	−	0.504997i	$-0.168507\pi$
$548$	14.7560	−	10.6980i	0.630346	−	0.456996i
$549$		0			0
$550$	0.200845	+	0.619206i	0.00856405	+	0.0264030i
$551$	−30.8317			−1.31347
$552$		0			0
$553$	−53.9070			−2.29236
$554$	10.2000	+	31.4467i	0.433356	+	1.33604i
$555$		0			0
$556$	−11.4697	−	15.8205i	−0.486424	−	0.670937i
$557$			21.2630i			0.900944i	0.892791	+	0.450472i	$0.148744\pi$
$557$			21.2630i			0.900944i	−0.892791	+	0.450472i	$0.851256\pi$
$558$		0			0
$559$	22.2353			0.940454
$560$	13.7429	+	4.49620i	0.580742	+	0.189999i
$561$		0			0
$562$	−19.4801	+	6.31854i	−0.821719	+	0.266531i
$563$		−	35.1684i		−	1.48217i	−0.671411	−	0.741086i	$-0.734311\pi$
$563$		−	35.1684i		−	1.48217i	0.671411	−	0.741086i	$-0.265689\pi$
$564$		0			0
$565$			14.2190i			0.598200i
$566$	−3.89363	−	12.0041i	−0.163661	−	0.504569i
$567$		0			0
$568$	−4.98031	+	6.83290i	−0.208969	+	0.286702i
$569$	4.53588			0.190154			0.0950770	−	0.995470i	$-0.469690\pi$
$569$	4.53588			0.190154			0.0950770	+	0.995470i	$0.469690\pi$
$570$		0			0
$571$			43.9496i			1.83923i	0.392819	+	0.919616i	$0.371500\pi$
$571$			43.9496i			1.83923i	−0.392819	+	0.919616i	$0.628500\pi$
$572$	−2.73877	+	1.98559i	−0.114514	+	0.0830216i
$573$		0			0
$574$	50.0575	−	16.2366i	2.08936	−	0.677702i
$575$	−3.60210			−0.150218
$576$		0			0
$577$	32.8371			1.36703			0.683513	−	0.729938i	$-0.260451\pi$
$577$	32.8371			1.36703			0.683513	+	0.729938i	$0.260451\pi$
$578$	35.5782	−	11.5401i	1.47986	−	0.480005i
$579$		0			0
$580$	−15.9286	+	11.5481i	−0.661399	+	0.479509i
$581$			24.8930i			1.03274i
$582$		0			0
$583$	1.50577			0.0623627
$584$	3.78392	−	5.19148i	0.156580	−	0.214825i
$585$		0			0
$586$	−0.0512057	−	0.157868i	−0.00211529	−	0.00652145i
$587$		−	26.1919i		−	1.08106i	−0.841326	−	0.540529i	$-0.818224\pi$
$587$		−	26.1919i		−	1.08106i	0.841326	−	0.540529i	$-0.181776\pi$
$588$		0			0
$589$		−	29.2938i		−	1.20703i
$590$	−6.98421	+	2.26539i	−0.287535	+	0.0932645i
$591$		0			0
$592$	25.3344	+	8.28858i	1.04124	+	0.340659i
$593$	−35.2748			−1.44856			−0.724281	−	0.689505i	$-0.757828\pi$
$593$	−35.2748			−1.44856			−0.724281	+	0.689505i	$0.757828\pi$
$594$		0			0
$595$		−	23.8277i		−	0.976842i
$596$	−18.5917	−	25.6440i	−0.761544	−	1.05042i
$597$		0			0
$598$	−5.77538	−	17.8055i	−0.236173	−	0.728123i
$599$	−4.41530			−0.180404			−0.0902022	−	0.995923i	$-0.528751\pi$
$599$	−4.41530			−0.180404			−0.0902022	+	0.995923i	$0.528751\pi$
$600$		0			0
$601$	−8.09117			−0.330046			−0.165023	−	0.986290i	$-0.552770\pi$
$601$	−8.09117			−0.330046			−0.165023	+	0.986290i	$0.552770\pi$
$602$	−9.54451	−	29.4258i	−0.389005	−	1.19931i
$603$		0			0
$604$	−13.5763	+	9.84273i	−0.552413	+	0.400495i
$605$		−	10.7881i		−	0.438600i
$606$		0			0
$607$	15.0891			0.612449			0.306225	−	0.951959i	$-0.400934\pi$
$607$	15.0891			0.612449			0.306225	+	0.951959i	$0.400934\pi$
$608$	−17.7297	−	0.0450097i	−0.719034	−	0.00182539i
$609$		0			0
$610$	−9.15929	+	2.97089i	−0.370849	+	0.120288i
$611$		−	24.3230i		−	0.984004i
$612$		0			0
$613$			39.7493i			1.60546i	0.596344	+	0.802729i	$0.296619\pi$
$613$			39.7493i			1.60546i	−0.596344	+	0.802729i	$0.703381\pi$
$614$	9.14845	+	28.2048i	0.369202	+	1.13825i
$615$		0			0
$616$	3.80331	+	2.77213i	0.153240	+	0.111692i
$617$	5.32118			0.214223			0.107111	−	0.994247i	$-0.465840\pi$
$617$	5.32118			0.214223			0.107111	+	0.994247i	$0.465840\pi$
$618$		0			0
$619$			13.7069i			0.550927i	0.961312	+	0.275463i	$0.0888313\pi$
$619$			13.7069i			0.550927i	−0.961312	+	0.275463i	$0.911169\pi$
$620$	−10.9721	−	15.1341i	−0.440650	−	0.607800i
$621$		0			0
$622$	32.2262	−	10.4528i	1.29215	−	0.419120i
$623$	−21.8744			−0.876378
$624$		0			0
$625$	1.00000			0.0400000
$626$	−9.18904	+	2.98054i	−0.367268	+	0.119127i
$627$		0			0
$628$	−12.7709	−	17.6152i	−0.509614	−	0.702923i
$629$		−	43.9255i		−	1.75143i
$630$		0			0
$631$	22.8516			0.909710			0.454855	−	0.890566i	$-0.349691\pi$
$631$	22.8516			0.909710			0.454855	+	0.890566i	$0.349691\pi$
$632$	24.8439	−	34.0854i	0.988237	−	1.35584i
$633$		0			0
$634$	−5.95844	−	18.3699i	−0.236640	−	0.729563i
$635$			1.91301i			0.0759154i
$636$		0			0
$637$		−	22.2959i		−	0.883395i
$638$	−6.09123	+	1.97574i	−0.241154	+	0.0782203i
$639$		0			0
$640$	−9.17656	+	6.61746i	−0.362735	+	0.261578i
$641$	22.8938			0.904252			0.452126	−	0.891954i	$-0.350666\pi$
$641$	22.8938			0.904252			0.452126	+	0.891954i	$0.350666\pi$
$642$		0			0
$643$		−	29.0899i		−	1.14719i	−0.819138	−	0.573597i	$-0.805548\pi$
$643$		−	29.0899i		−	1.14719i	0.819138	−	0.573597i	$-0.194452\pi$
$644$	−21.0844	+	15.2861i	−0.830843	+	0.602355i
$645$		0			0
$646$	9.01426	+	27.7910i	0.354661	+	1.09342i
$647$	−23.5493			−0.925819			−0.462910	−	0.886405i	$-0.653195\pi$
$647$	−23.5493			−0.925819			−0.462910	+	0.886405i	$0.653195\pi$
$648$		0			0
$649$	−2.38983			−0.0938089
$650$	1.60333	+	4.94310i	0.0628880	+	0.193884i
$651$		0			0
$652$	−13.4378	−	18.5352i	−0.526267	−	0.725893i
$653$			0.995952i			0.0389746i	0.999810	+	0.0194873i	$0.00620339\pi$
$653$			0.995952i			0.0389746i	−0.999810	+	0.0194873i	$0.993797\pi$
$654$		0			0
$655$	8.63351			0.337339
$656$	−12.8034	+	39.1342i	−0.499889	+	1.52793i
$657$		0			0
$658$	−32.1886	+	10.4407i	−1.25484	+	0.407019i
$659$		−	5.16847i		−	0.201335i	−0.994920	−	0.100668i	$-0.967902\pi$
$659$		−	5.16847i		−	0.201335i	0.994920	−	0.100668i	$-0.0320979\pi$
$660$		0			0
$661$		−	42.6961i		−	1.66069i	−0.557252	−	0.830343i	$-0.688144\pi$
$661$		−	42.6961i		−	1.66069i	0.557252	−	0.830343i	$-0.311856\pi$
$662$	−13.2462	−	40.8383i	−0.514830	−	1.58722i
$663$		0			0
$664$	−15.7398	−	11.4723i	−0.610824	−	0.445213i
$665$	11.3299			0.439354
$666$		0			0
$667$		−	35.4345i		−	1.37203i
$668$	−3.04559	+	2.20803i	−0.117838	+	0.0854313i
$669$		0			0
$670$	13.5552	−	4.39675i	0.523683	−	0.169861i
$671$	−3.13409			−0.120990
$672$		0			0
$673$	−0.845304			−0.0325841			−0.0162920	−	0.999867i	$-0.505186\pi$
$673$	−0.845304			−0.0325841			−0.0162920	+	0.999867i	$0.505186\pi$
$674$	−11.6633	+	3.78310i	−0.449255	+	0.145720i
$675$		0			0
$676$	−0.813561	+	0.589825i	−0.0312908	+	0.0226856i
$677$			46.3596i			1.78175i	0.454253	+	0.890873i	$0.349906\pi$
$677$			46.3596i			1.78175i	−0.454253	+	0.890873i	$0.650094\pi$
$678$		0			0
$679$	−47.1414			−1.80912
$680$	15.0663	+	10.9814i	0.577765	+	0.421117i
$681$		0			0
$682$	−1.87719	−	5.78740i	−0.0718814	−	0.221611i
$683$		−	9.34244i		−	0.357479i	−0.983896	−	0.178739i	$-0.942798\pi$
$683$		−	9.34244i		−	0.357479i	0.983896	−	0.178739i	$-0.0572019\pi$
$684$		0			0
$685$		−	9.11300i		−	0.348190i
$686$	4.53401	−	1.47064i	0.173109	−	0.0561494i
$687$		0			0
$688$	23.0047	+	7.52636i	0.877045	+	0.286940i
$689$	12.0205			0.457945
$690$		0			0
$691$			24.7917i			0.943122i	0.881833	+	0.471561i	$0.156309\pi$
$691$			24.7917i			0.943122i	−0.881833	+	0.471561i	$0.843691\pi$
$692$	2.48480	+	3.42735i	0.0944580	+	0.130288i
$693$		0			0
$694$	−13.3707	−	41.2220i	−0.507545	−	1.56476i
$695$	−9.77039			−0.370612
$696$		0			0
$697$	67.8520			2.57008
$698$	3.37921	+	10.4181i	0.127905	+	0.394332i
$699$		0			0
$700$	5.85337	−	4.24365i	0.221237	−	0.160395i
$701$			30.1602i			1.13914i	0.821944	+	0.569568i	$0.192890\pi$
$701$			30.1602i			1.13914i	−0.821944	+	0.569568i	$0.807110\pi$
$702$		0			0
$703$	20.8862			0.787739
$704$	−3.50563	+	1.12725i	−0.132123	+	0.0424850i
$705$		0			0
$706$	−8.62734	+	2.79835i	−0.324694	+	0.105317i
$707$			10.8173i			0.406826i
$708$		0			0
$709$		−	1.78076i		−	0.0668780i	−0.999441	−	0.0334390i	$-0.989354\pi$
$709$		−	1.78076i		−	0.0668780i	0.999441	−	0.0334390i	$-0.0106459\pi$
$710$	1.30437	+	4.02140i	0.0489523	+	0.150920i
$711$		0			0
$712$	10.0811	−	13.8312i	0.377807	−	0.518345i
$713$	33.6670			1.26084
$714$		0			0
$715$			1.69141i			0.0632551i
$716$	−2.71087	−	3.73917i	−0.101310	−	0.139739i
$717$		0			0
$718$	−36.9743	+	11.9929i	−1.37987	+	0.447572i
$719$	−14.4640			−0.539416			−0.269708	−	0.962942i	$-0.586927\pi$
$719$	−14.4640			−0.539416			−0.269708	+	0.962942i	$0.586927\pi$
$720$		0			0
$721$	0.314466			0.0117113
$722$	12.3447	−	4.00412i	0.459424	−	0.149018i
$723$		0			0
$724$	−4.22861	−	5.83262i	−0.157155	−	0.216768i
$725$			9.83716i			0.365343i
$726$		0			0
$727$	35.6743			1.32309			0.661544	−	0.749907i	$-0.269902\pi$
$727$	35.6743			1.32309			0.661544	+	0.749907i	$0.269902\pi$
$728$	30.3617	+	22.1298i	1.12528	+	0.820184i
$729$		0			0
$730$	−0.991032	−	3.05536i	−0.0366797	−	0.113084i
$731$		−	39.8861i		−	1.47524i
$732$		0			0
$733$			40.6687i			1.50213i	0.660226	+	0.751067i	$0.270460\pi$
$733$			40.6687i			1.50213i	−0.660226	+	0.751067i	$0.729540\pi$
$734$	−10.1267	+	3.28468i	−0.373784	+	0.121240i
$735$		0			0
$736$	0.0517291	−	20.3765i	0.00190676	−	0.751088i
$737$	4.63826			0.170853
$738$		0			0
$739$			24.2936i			0.893655i	0.894620	+	0.446827i	$0.147446\pi$
$739$			24.2936i			0.893655i	−0.894620	+	0.446827i	$0.852554\pi$
$740$	10.7905	−	7.82301i	0.396666	−	0.287579i
$741$		0			0
$742$	−5.15981	−	15.9077i	−0.189422	−	0.583991i
$743$	−22.4851			−0.824897			−0.412448	−	0.910981i	$-0.635326\pi$
$743$	−22.4851			−0.824897			−0.412448	+	0.910981i	$0.635326\pi$
$744$		0			0
$745$	−15.8372			−0.580229
$746$	−5.45322	−	16.8123i	−0.199657	−	0.615543i
$747$		0			0
$748$	3.56178	+	4.91286i	0.130232	+	0.179632i
$749$		−	14.9911i		−	0.547764i
$750$		0			0
$751$	−26.0441			−0.950364			−0.475182	−	0.879887i	$-0.657618\pi$
$751$	−26.0441			−0.950364			−0.475182	+	0.879887i	$0.657618\pi$
$752$	8.23301	−	25.1646i	0.300227	−	0.917658i
$753$		0			0
$754$	−48.6260	+	15.7723i	−1.77085	+	0.574392i
$755$			8.38445i			0.305141i
$756$		0			0
$757$		−	12.4087i		−	0.451003i	−0.974243	−	0.225501i	$-0.927598\pi$
$757$		−	12.4087i		−	0.451003i	0.974243	−	0.225501i	$-0.0724020\pi$
$758$	2.87609	+	8.86701i	0.104464	+	0.322064i
$759$		0			0
$760$	−5.22156	+	7.16389i	−0.189406	+	0.259862i
$761$	14.4810			0.524936			0.262468	−	0.964941i	$-0.415464\pi$
$761$	14.4810			0.524936			0.262468	+	0.964941i	$0.415464\pi$
$762$		0			0
$763$		−	69.6303i		−	2.52079i
$764$	0.405820	−	0.294216i	0.0146821	−	0.0106444i
$765$		0			0
$766$	−8.76969	+	2.84452i	−0.316862	+	0.102777i
$767$	−19.0779			−0.688863
$768$		0			0
$769$	31.4714			1.13489			0.567445	−	0.823412i	$-0.307932\pi$
$769$	31.4714			1.13489			0.567445	+	0.823412i	$0.307932\pi$
$770$	2.23838	−	0.726037i	0.0806655	−	0.0261646i
$771$		0			0
$772$	22.1674	−	16.0712i	0.797823	−	0.578416i
$773$		−	6.49345i		−	0.233553i	−0.993158	−	0.116777i	$-0.962744\pi$
$773$		−	6.49345i		−	0.233553i	0.993158	−	0.116777i	$-0.0372561\pi$
$774$		0			0
$775$	−9.34649			−0.335736
$776$	21.7259	−	29.8075i	0.779913	−	1.07003i
$777$		0			0
$778$	−6.40499	−	19.7466i	−0.229630	−	0.707951i
$779$			32.2631i			1.15594i
$780$		0			0
$781$			1.37602i			0.0492380i
$782$	−31.9399	+	10.3600i	−1.14217	+	0.370472i
$783$		0			0
$784$	7.54686	−	23.0673i	0.269531	−	0.823833i
$785$	−10.8788			−0.388280
$786$		0			0
$787$			38.2974i			1.36515i	0.730813	+	0.682577i	$0.239141\pi$
$787$			38.2974i			1.36515i	−0.730813	+	0.682577i	$0.760859\pi$
$788$	−2.48562	−	3.42848i	−0.0885465	−	0.122134i
$789$		0			0
$790$	−6.50676	−	20.0604i	−0.231500	−	0.713717i
$791$	51.4007			1.82760
$792$		0			0
$793$	−25.0193			−0.888461
$794$	−12.6434	−	38.9796i	−0.448697	−	1.38334i
$795$		0			0
$796$	7.77776	−	5.63882i	0.275675	−	0.199863i
$797$			3.86049i			0.136746i	0.997660	+	0.0683728i	$0.0217807\pi$
$797$			3.86049i			0.136746i	−0.997660	+	0.0683728i	$0.978219\pi$
$798$		0			0
$799$	−43.6310			−1.54356
$800$	−0.0143608	+	5.65684i	−0.000507731	+	0.199999i
$801$		0			0
$802$	32.0687	−	10.4018i	1.13239	−	0.367299i
$803$		−	1.04547i		−	0.0368939i
$804$		0			0
$805$			13.0213i			0.458941i
$806$	−14.9856	−	46.2006i	−0.527844	−	1.62735i
$807$		0			0
$808$	−6.83977	−	4.98532i	−0.240622	−	0.175383i
$809$	52.9957			1.86323			0.931614	−	0.363449i	$-0.118401\pi$
$809$	52.9957			1.86323			0.931614	+	0.363449i	$0.118401\pi$
$810$		0			0
$811$			14.3640i			0.504387i	0.967677	+	0.252194i	$0.0811520\pi$
$811$			14.3640i			0.504387i	−0.967677	+	0.252194i	$0.918848\pi$
$812$	41.7454	+	57.5805i	1.46498	+	2.02068i
$813$		0			0
$814$	4.12637	−	1.33842i	0.144629	−	0.0469117i
$815$	−11.4469			−0.400968
$816$		0			0
$817$	18.9655			0.663520
$818$	−34.6788	+	11.2484i	−1.21251	+	0.393289i
$819$		0			0
$820$	12.0842	+	16.6681i	0.422000	+	0.582075i
$821$			28.6033i			0.998261i	0.866527	+	0.499131i	$0.166347\pi$
$821$			28.6033i			0.998261i	−0.866527	+	0.499131i	$0.833653\pi$
$822$		0			0
$823$	8.30220			0.289397			0.144698	−	0.989476i	$-0.453779\pi$
$823$	8.30220			0.289397			0.144698	+	0.989476i	$0.453779\pi$
$824$	−0.144927	+	0.198837i	−0.00504876	+	0.00692681i
$825$		0			0
$826$	8.18919	+	25.2473i	0.284938	+	0.878467i
$827$		−	2.35542i		−	0.0819058i	−0.999161	−	0.0409529i	$-0.986961\pi$
$827$		−	2.35542i		−	0.0819058i	0.999161	−	0.0409529i	$-0.0130394\pi$
$828$		0			0
$829$			14.5848i			0.506551i	0.967394	+	0.253275i	$0.0815079\pi$
$829$			14.5848i			0.506551i	−0.967394	+	0.253275i	$0.918492\pi$
$830$	−9.26343	+	3.00467i	−0.321538	+	0.104294i
$831$		0			0
$832$	−27.9853	+	8.99882i	−0.970216	+	0.311978i
$833$	−39.9948			−1.38574
$834$		0			0
$835$			1.88089i			0.0650910i
$836$	−2.33603	+	1.69360i	−0.0807931	+	0.0585744i
$837$		0			0
$838$	−11.2685	−	34.7408i	−0.389263	−	1.20010i
$839$	46.9537			1.62102			0.810511	−	0.585723i	$-0.199189\pi$
$839$	46.9537			1.62102			0.810511	+	0.585723i	$0.199189\pi$
$840$		0			0
$841$	−67.7697			−2.33688
$842$	−9.02927	−	27.8373i	−0.311169	−	0.959337i
$843$		0			0
$844$	28.8287	+	39.7641i	0.992323	+	1.36874i
$845$			0.502438i			0.0172844i
$846$		0			0
$847$	−38.9982			−1.33999
$848$	12.4364	+	4.06878i	0.427069	+	0.139723i
$849$		0			0
$850$	8.86701	−	2.87609i	0.304136	−	0.0986491i
$851$			24.0043i			0.822856i
$852$		0			0
$853$			15.9013i			0.544449i	0.962234	+	0.272224i	$0.0877593\pi$
$853$			15.9013i			0.544449i	−0.962234	+	0.272224i	$0.912241\pi$
$854$	10.7395	+	33.1101i	0.367499	+	1.13300i
$855$		0			0
$856$	9.47889	+	6.90890i	0.323982	+	0.236141i
$857$	1.31445			0.0449009			0.0224504	−	0.999748i	$-0.492853\pi$
$857$	1.31445			0.0449009			0.0224504	+	0.999748i	$0.492853\pi$
$858$		0			0
$859$		−	7.87272i		−	0.268614i	−0.990940	−	0.134307i	$-0.957119\pi$
$859$		−	7.87272i		−	0.268614i	0.990940	−	0.134307i	$-0.0428808\pi$
$860$	9.79817	−	7.10360i	0.334115	−	0.242231i
$861$		0			0
$862$	−19.3799	+	6.28604i	−0.660082	+	0.214103i
$863$	15.7044			0.534584			0.267292	−	0.963616i	$-0.413871\pi$
$863$	15.7044			0.534584			0.267292	+	0.963616i	$0.413871\pi$
$864$		0			0
$865$	2.11666			0.0719685
$866$	−5.71600	+	1.85403i	−0.194237	+	0.0630026i
$867$		0			0
$868$	−54.7085	+	39.6632i	−1.85693	+	1.34626i
$869$		−	6.86419i		−	0.232852i
$870$		0			0
$871$	37.0271			1.25461
$872$	44.0272	+	32.0902i	1.49095	+	1.08671i
$873$		0			0
$874$	−4.92608	−	15.1872i	−0.166627	−	0.513713i
$875$		−	3.61492i		−	0.122206i
$876$		0			0
$877$			7.74255i			0.261447i	0.991419	+	0.130724i	$0.0417301\pi$
$877$			7.74255i			0.261447i	−0.991419	+	0.130724i	$0.958270\pi$
$878$	−6.42534	+	2.08411i	−0.216845	+	0.0703355i
$879$		0			0
$880$	−0.572519	+	1.74993i	−0.0192996	+	0.0589902i
$881$	24.8472			0.837123			0.418562	−	0.908188i	$-0.362534\pi$
$881$	24.8472			0.837123			0.418562	+	0.908188i	$0.362534\pi$
$882$		0			0
$883$		−	36.9495i		−	1.24345i	−0.783236	−	0.621724i	$-0.786432\pi$
$883$		−	36.9495i		−	1.24345i	0.783236	−	0.621724i	$-0.213568\pi$
$884$	28.4336	+	39.2191i	0.956325	+	1.31908i
$885$		0			0
$886$	6.79771	+	20.9574i	0.228374	+	0.704078i
$887$	−14.4532			−0.485291			−0.242646	−	0.970115i	$-0.578015\pi$
$887$	−14.4532			−0.485291			−0.242646	+	0.970115i	$0.578015\pi$
$888$		0			0
$889$	6.91537			0.231934
$890$	−2.64031	−	8.14011i	−0.0885035	−	0.272857i
$891$		0			0
$892$	36.3248	−	26.3352i	1.21624	−	0.881767i
$893$		−	20.7462i		−	0.694245i
$894$		0			0
$895$	−2.30923			−0.0771891
$896$	23.9216	+	33.1725i	0.799163	+	1.10822i
$897$		0			0
$898$	53.5691	−	17.3756i	1.78762	−	0.579831i
$899$		−	91.9429i		−	3.06647i
$900$		0			0
$901$		−	21.5626i		−	0.718355i
$902$	2.06747	+	6.37402i	0.0688391	+	0.212231i
$903$		0			0
$904$	−23.6888	+	32.5006i	−0.787878	+	1.08095i
$905$	−3.60210			−0.119738
$906$		0			0
$907$			22.2344i			0.738282i	0.929373	+	0.369141i	$0.120348\pi$
$907$			22.2344i			0.738282i	−0.929373	+	0.369141i	$0.879652\pi$
$908$	14.8397	+	20.4688i	0.492474	+	0.679281i
$909$		0			0
$910$	17.8689	−	5.79592i	0.592348	−	0.192133i
$911$	−5.74665			−0.190395			−0.0951975	−	0.995458i	$-0.530348\pi$
$911$	−5.74665			−0.190395			−0.0951975	+	0.995458i	$0.530348\pi$
$912$		0			0
$913$	−3.16972			−0.104903
$914$	−50.4259	+	16.3561i	−1.66794	+	0.541011i
$915$		0			0
$916$	−28.0571	−	38.6998i	−0.927032	−	1.27868i
$917$		−	31.2094i		−	1.03063i
$918$		0			0
$919$	56.8021			1.87373			0.936864	−	0.349693i	$-0.113714\pi$
$919$	56.8021			1.87373			0.936864	+	0.349693i	$0.113714\pi$
$920$	−8.23337	−	6.00107i	−0.271446	−	0.197849i
$921$		0			0
$922$	−17.9839	−	55.4447i	−0.592270	−	1.82597i
$923$			10.9847i			0.361567i
$924$		0			0
$925$		−	6.66397i		−	0.219110i
$926$	−13.4205	+	4.35306i	−0.441025	+	0.143050i
$927$		0			0
$928$	−55.6472	−	0.141270i	−1.82671	−	0.00463740i
$929$	−35.4250			−1.16226			−0.581129	−	0.813812i	$-0.697389\pi$
$929$	−35.4250			−1.16226			−0.581129	+	0.813812i	$0.697389\pi$
$930$		0			0
$931$		−	19.0172i		−	0.623263i
$932$	−20.7326	+	15.0310i	−0.679120	+	0.492357i
$933$		0			0
$934$	13.5258	+	41.7001i	0.442577	+	1.36447i
$935$	3.03408			0.0992249
$936$		0			0
$937$	−29.4633			−0.962524			−0.481262	−	0.876577i	$-0.659821\pi$
$937$	−29.4633			−0.962524			−0.481262	+	0.876577i	$0.659821\pi$
$938$	−15.8939	−	49.0009i	−0.518953	−	1.59994i
$939$		0			0
$940$	−7.77056	−	10.7181i	−0.253448	−	0.349587i
$941$		−	21.8705i		−	0.712956i	−0.934304	−	0.356478i	$-0.883977\pi$
$941$		−	21.8705i		−	0.712956i	0.934304	−	0.356478i	$-0.116023\pi$
$942$		0			0
$943$	−37.0795			−1.20748
$944$	−19.7380	−	6.45761i	−0.642417	−	0.210177i
$945$		0			0
$946$	3.74690	−	1.21534i	0.121822	−	0.0395141i
$947$			60.9594i			1.98092i	0.137816	+	0.990458i	$0.455992\pi$
$947$			60.9594i			1.98092i	−0.137816	+	0.990458i	$0.544008\pi$
$948$		0			0
$949$		−	8.34595i		−	0.270921i
$950$	1.36756	+	4.21619i	0.0443694	+	0.136791i
$951$		0			0
$952$	39.6968	−	54.4633i	1.28658	−	1.76517i
$953$	42.1708			1.36604			0.683022	−	0.730397i	$-0.260665\pi$
$953$	42.1708			1.36604			0.683022	+	0.730397i	$0.260665\pi$
$954$		0			0
$955$		−	0.250626i		−	0.00811006i
$956$	42.7825	−	31.0170i	1.38369	−	1.00316i
$957$		0			0
$958$	21.2456	−	6.89120i	0.686415	−	0.222644i
$959$	−32.9428			−1.06378
$960$		0			0
$961$	56.3569			1.81797
$962$	32.9406	−	10.6846i	1.06205	−	0.344484i
$963$		0			0
$964$	−17.0461	+	12.3583i	−0.549017	+	0.398033i
$965$		−	13.6901i		−	0.440701i
$966$		0			0
$967$	34.5812			1.11206			0.556028	−	0.831164i	$-0.312325\pi$
$967$	34.5812			1.11206			0.556028	+	0.831164i	$0.312325\pi$
$968$	17.9729	−	24.6585i	0.577671	−	0.792555i
$969$		0			0
$970$	−5.69014	−	17.5427i	−0.182699	−	0.563263i
$971$			11.7129i			0.375885i	0.982180	+	0.187942i	$0.0601819\pi$
$971$			11.7129i			0.375885i	−0.982180	+	0.187942i	$0.939818\pi$
$972$		0			0
$973$			35.3191i			1.13228i
$974$	−42.4047	+	13.7543i	−1.35873	+	0.440717i
$975$		0			0
$976$	−25.8850	−	8.46869i	−0.828558	−	0.271076i
$977$	−4.75315			−0.152067			−0.0760334	−	0.997105i	$-0.524226\pi$
$977$	−4.75315			−0.152067			−0.0760334	+	0.997105i	$0.524226\pi$
$978$		0			0
$979$		−	2.78535i		−	0.0890201i
$980$	−7.12295	−	9.82486i	−0.227534	−	0.313844i
$981$		0			0
$982$	9.84925	+	30.3653i	0.314302	+	0.968997i
$983$	−54.1689			−1.72772			−0.863860	−	0.503731i	$-0.831960\pi$
$983$	−54.1689			−1.72772			−0.863860	+	0.503731i	$0.831960\pi$
$984$		0			0
$985$	−2.11735			−0.0674645
$986$	28.2926	+	87.2262i	0.901018	+	2.77785i
$987$		0			0
$988$	−18.6484	+	13.5199i	−0.593284	+	0.430127i
$989$			21.7968i			0.693099i
$990$		0			0
$991$	15.8470			0.503398			0.251699	−	0.967806i	$-0.419011\pi$
$991$	15.8470			0.503398			0.251699	+	0.967806i	$0.419011\pi$
$992$	0.134223	−	52.8716i	0.00426159	−	1.67867i
$993$		0			0
$994$	14.5370	−	4.71520i	0.461086	−	0.149557i
$995$		−	4.80338i		−	0.152277i
$996$		0			0
$997$		−	18.0274i		−	0.570934i	−0.958389	−	0.285467i	$-0.907851\pi$
$997$		−	18.0274i		−	0.570934i	0.958389	−	0.285467i	$-0.0921487\pi$
$998$	17.3182	+	53.3921i	0.548197	+	1.69010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.k.d.541.19	yes	20
3.2	odd	2	inner	1080.2.k.d.541.2	yes	20
4.3	odd	2		4320.2.k.d.2161.9		20
8.3	odd	2		4320.2.k.d.2161.20		20
8.5	even	2	inner	1080.2.k.d.541.20	yes	20
12.11	even	2		4320.2.k.d.2161.19		20
24.5	odd	2	inner	1080.2.k.d.541.1	✓	20
24.11	even	2		4320.2.k.d.2161.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.k.d.541.1	✓	20	24.5	odd	2	inner
1080.2.k.d.541.2	yes	20	3.2	odd	2	inner
1080.2.k.d.541.19	yes	20	1.1	even	1	trivial
1080.2.k.d.541.20	yes	20	8.5	even	2	inner
4320.2.k.d.2161.9		20	4.3	odd	2
4320.2.k.d.2161.10		20	24.11	even	2
4320.2.k.d.2161.19		20	12.11	even	2
4320.2.k.d.2161.20		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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34522 - 0.436333i) q^{2} +(1.61923 - 1.17393i) q^{4} -1.00000i q^{5} -3.61492 q^{7} +(1.66599 - 2.28571i) q^{8} +O(q^{10})\)	\(q+(1.34522 - 0.436333i) q^{2} +(1.61923 - 1.17393i) q^{4} -1.00000i q^{5} -3.61492 q^{7} +(1.66599 - 2.28571i) q^{8} +(-0.436333 - 1.34522i) q^{10} -0.460301i q^{11} -3.67457i q^{13} +(-4.86285 + 1.57731i) q^{14} +(1.24379 - 3.80171i) q^{16} -6.59150 q^{17} -3.13421i q^{19} +(-1.17393 - 1.61923i) q^{20} +(-0.200845 - 0.619206i) q^{22} +3.60210 q^{23} -1.00000 q^{25} +(-1.60333 - 4.94310i) q^{26} +(-5.85337 + 4.24365i) q^{28} -9.83716i q^{29} +9.34649 q^{31} +(0.0143608 - 5.65684i) q^{32} +(-8.86701 + 2.87609i) q^{34} +3.61492i q^{35} +6.66397i q^{37} +(-1.36756 - 4.21619i) q^{38} +(-2.28571 - 1.66599i) q^{40} -10.2939 q^{41} +6.05114i q^{43} +(-0.540360 - 0.745332i) q^{44} +(4.84562 - 1.57172i) q^{46} +6.61929 q^{47} +6.06762 q^{49} +(-1.34522 + 0.436333i) q^{50} +(-4.31367 - 5.94996i) q^{52} +3.27127i q^{53} -0.460301 q^{55} +(-6.02242 + 8.26265i) q^{56} +(-4.29228 - 13.2331i) q^{58} -5.19188i q^{59} -6.80877i q^{61} +(12.5731 - 4.07818i) q^{62} +(-2.44895 - 7.61595i) q^{64} -3.67457 q^{65} +10.0766i q^{67} +(-10.6731 + 7.73794i) q^{68} +(1.57731 + 4.86285i) q^{70} -2.98940 q^{71} +2.27127 q^{73} +(2.90771 + 8.96449i) q^{74} +(-3.67933 - 5.07499i) q^{76} +1.66395i q^{77} +14.9124 q^{79} +(-3.80171 - 1.24379i) q^{80} +(-13.8475 + 4.49155i) q^{82} -6.88619i q^{83} +6.59150i q^{85} +(2.64031 + 8.14011i) q^{86} +(-1.05212 - 0.766858i) q^{88} +6.05114 q^{89} +13.2833i q^{91} +(5.83262 - 4.22861i) q^{92} +(8.90439 - 2.88821i) q^{94} -3.13421 q^{95} +13.0408 q^{97} +(8.16228 - 2.64751i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4}+O(q^{10}) \) 20 * q + 2 * q^4	\( 20 q + 2 q^{4} - 2 q^{10} - 18 q^{16} + 16 q^{22} - 20 q^{25} + 16 q^{28} + 20 q^{31} - 6 q^{34} - 4 q^{40} + 54 q^{46} + 36 q^{49} + 56 q^{52} - 72 q^{58} - 28 q^{64} - 40 q^{73} + 58 q^{76} - 4 q^{79} - 92 q^{82} - 116 q^{88} + 72 q^{94} + 40 q^{97}+O(q^{100}) \) 20 * q + 2 * q^4 - 2 * q^10 - 18 * q^16 + 16 * q^22 - 20 * q^25 + 16 * q^28 + 20 * q^31 - 6 * q^34 - 4 * q^40 + 54 * q^46 + 36 * q^49 + 56 * q^52 - 72 * q^58 - 28 * q^64 - 40 * q^73 + 58 * q^76 - 4 * q^79 - 92 * q^82 - 116 * q^88 + 72 * q^94 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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