LMFDB - Embedded newform 1080.2.k.d.541.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1080,2,Mod(541,1080)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [20,0,0,2,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	20.0.1780383353079852270621853183383699456.1
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			541.4
Root			$-1.19357 - 0.758543i$ of defining polynomial
Character	$\chi$	$=$	1080.541
Dual form			1080.2.k.d.541.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19357 + 0.758543i) q^{2} +(0.849224 - 1.81075i) q^{4} +1.00000i q^{5} +4.63236 q^{7} +(0.359923 + 2.80543i) q^{8} +(-0.758543 - 1.19357i) q^{10} +2.39533i q^{11} +1.95421i q^{13} +(-5.52905 + 3.51385i) q^{14} +(-2.55764 - 3.07547i) q^{16} -4.76655 q^{17} +6.29155i q^{19} +(1.81075 + 0.849224i) q^{20} +(-1.81696 - 2.85900i) q^{22} +5.28106 q^{23} -1.00000 q^{25} +(-1.48235 - 2.33248i) q^{26} +(3.93391 - 8.38805i) q^{28} -0.201291i q^{29} -3.26964 q^{31} +(5.38560 + 1.73071i) q^{32} +(5.68921 - 3.61563i) q^{34} +4.63236i q^{35} -1.43969i q^{37} +(-4.77242 - 7.50942i) q^{38} +(-2.80543 + 0.359923i) q^{40} +8.53808 q^{41} -9.10390i q^{43} +(4.33735 + 2.03417i) q^{44} +(-6.30332 + 4.00591i) q^{46} -10.4923 q^{47} +14.4588 q^{49} +(1.19357 - 0.758543i) q^{50} +(3.53858 + 1.65956i) q^{52} +3.03261i q^{53} -2.39533 q^{55} +(1.66730 + 12.9958i) q^{56} +(0.152688 + 0.240255i) q^{58} +2.75805i q^{59} +8.24576i q^{61} +(3.90254 - 2.48016i) q^{62} +(-7.74091 + 2.01948i) q^{64} -1.95421 q^{65} +12.0173i q^{67} +(-4.04787 + 8.63103i) q^{68} +(-3.51385 - 5.52905i) q^{70} +0.514512 q^{71} -4.03261 q^{73} +(1.09207 + 1.71838i) q^{74} +(11.3924 + 5.34294i) q^{76} +11.0960i q^{77} -1.43832 q^{79} +(3.07547 - 2.55764i) q^{80} +(-10.1908 + 6.47650i) q^{82} -7.66497i q^{83} -4.76655i q^{85} +(6.90570 + 10.8661i) q^{86} +(-6.71994 + 0.862136i) q^{88} +9.10390 q^{89} +9.05259i q^{91} +(4.48480 - 9.56268i) q^{92} +(12.5233 - 7.95885i) q^{94} -6.29155 q^{95} -11.6927 q^{97} +(-17.2576 + 10.9676i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	−1.19357	+	0.758543i	−0.843982	+	0.536371i
$2$	−1.19357	+	0.758543i	−0.843982	+	0.536371i
$3$		0			0
$3$		0			0
$4$	0.849224	−	1.81075i	0.424612	−	0.905375i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	4.63236			1.75087			0.875434	−	0.483338i	$-0.160576\pi$
$7$	4.63236			1.75087			0.875434	+	0.483338i	$0.160576\pi$
$8$	0.359923	+	2.80543i	0.127252	+	0.991870i
$9$		0			0
$10$	−0.758543	−	1.19357i	−0.239872	−	0.377440i
$11$			2.39533i			0.722220i	0.932523	+	0.361110i	$0.117602\pi$
$11$			2.39533i			0.722220i	−0.932523	+	0.361110i	$0.882398\pi$
$12$		0			0
$13$			1.95421i			0.541999i	0.962579	+	0.271000i	$0.0873542\pi$
$13$			1.95421i			0.541999i	−0.962579	+	0.271000i	$0.912646\pi$
$14$	−5.52905	+	3.51385i	−1.47770	+	0.939115i
$15$		0			0
$16$	−2.55764	−	3.07547i	−0.639409	−	0.768867i
$17$	−4.76655			−1.15606			−0.578029	−	0.816016i	$-0.696178\pi$
$17$	−4.76655			−1.15606			−0.578029	+	0.816016i	$0.696178\pi$
$18$		0			0
$19$			6.29155i			1.44338i	0.692216	+	0.721691i	$0.256635\pi$
$19$			6.29155i			1.44338i	−0.692216	+	0.721691i	$0.743365\pi$
$20$	1.81075	+	0.849224i	0.404896	+	0.189892i
$21$		0			0
$22$	−1.81696	−	2.85900i	−0.387378	−	0.609541i
$23$	5.28106			1.10118			0.550589	−	0.834777i	$-0.314403\pi$
$23$	5.28106			1.10118			0.550589	+	0.834777i	$0.314403\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.48235	−	2.33248i	−0.290713	−	0.457438i
$27$		0			0
$28$	3.93391	−	8.38805i	0.743439	−	1.58519i
$29$		−	0.201291i		−	0.0373787i	−0.999825	−	0.0186894i	$-0.994051\pi$
$29$		−	0.201291i		−	0.0373787i	0.999825	−	0.0186894i	$-0.00594935\pi$
$30$		0			0
$31$	−3.26964			−0.587244			−0.293622	−	0.955922i	$-0.594861\pi$
$31$	−3.26964			−0.587244			−0.293622	+	0.955922i	$0.594861\pi$
$32$	5.38560	+	1.73071i	0.952048	+	0.305949i
$33$		0			0
$34$	5.68921	−	3.61563i	0.975692	−	0.620076i
$35$			4.63236i			0.783012i
$36$		0			0
$37$		−	1.43969i		−	0.236684i	−0.992973	−	0.118342i	$-0.962242\pi$
$37$		−	1.43969i		−	0.236684i	0.992973	−	0.118342i	$-0.0377580\pi$
$38$	−4.77242	−	7.50942i	−0.774188	−	1.21819i
$39$		0			0
$40$	−2.80543	+	0.359923i	−0.443578	+	0.0569089i
$41$	8.53808			1.33342			0.666712	−	0.745316i	$-0.267701\pi$
$41$	8.53808			1.33342			0.666712	+	0.745316i	$0.267701\pi$
$42$		0			0
$43$		−	9.10390i		−	1.38833i	−0.719815	−	0.694166i	$-0.755774\pi$
$43$		−	9.10390i		−	1.38833i	0.719815	−	0.694166i	$-0.244226\pi$
$44$	4.33735	+	2.03417i	0.653880	+	0.306663i
$45$		0			0
$46$	−6.30332	+	4.00591i	−0.929374	+	0.590640i
$47$	−10.4923			−1.53046			−0.765228	−	0.643759i	$-0.777374\pi$
$47$	−10.4923			−1.53046			−0.765228	+	0.643759i	$0.777374\pi$
$48$		0			0
$49$	14.4588			2.06554
$50$	1.19357	−	0.758543i	0.168796	−	0.107274i
$51$		0			0
$52$	3.53858	+	1.65956i	0.490713	+	0.230139i
$53$			3.03261i			0.416561i	0.978069	+	0.208280i	$0.0667867\pi$
$53$			3.03261i			0.416561i	−0.978069	+	0.208280i	$0.933213\pi$
$54$		0			0
$55$	−2.39533			−0.322986
$56$	1.66730	+	12.9958i	0.222802	+	1.73663i
$57$		0			0
$58$	0.152688	+	0.240255i	0.0200489	+	0.0315470i
$59$			2.75805i			0.359068i	0.983752	+	0.179534i	$0.0574590\pi$
$59$			2.75805i			0.359068i	−0.983752	+	0.179534i	$0.942541\pi$
$60$		0			0
$61$			8.24576i			1.05576i	0.849319	+	0.527881i	$0.177013\pi$
$61$			8.24576i			1.05576i	−0.849319	+	0.527881i	$0.822987\pi$
$62$	3.90254	−	2.48016i	0.495624	−	0.314981i
$63$		0			0
$64$	−7.74091	+	2.01948i	−0.967614	+	0.252435i
$65$	−1.95421			−0.242389
$66$		0			0
$67$			12.0173i			1.46815i	0.679071	+	0.734073i	$0.262383\pi$
$67$			12.0173i			1.46815i	−0.679071	+	0.734073i	$0.737617\pi$
$68$	−4.04787	+	8.63103i	−0.490876	+	1.04667i
$69$		0			0
$70$	−3.51385	−	5.52905i	−0.419985	−	0.660848i
$71$	0.514512			0.0610614			0.0305307	−	0.999534i	$-0.490280\pi$
$71$	0.514512			0.0610614			0.0305307	+	0.999534i	$0.490280\pi$
$72$		0			0
$73$	−4.03261			−0.471981			−0.235991	−	0.971755i	$-0.575833\pi$
$73$	−4.03261			−0.471981			−0.235991	+	0.971755i	$0.575833\pi$
$74$	1.09207	+	1.71838i	0.126951	+	0.199757i
$75$		0			0
$76$	11.3924	+	5.34294i	1.30680	+	0.612877i
$77$			11.0960i			1.26451i
$78$		0			0
$79$	−1.43832			−0.161824			−0.0809118	−	0.996721i	$-0.525783\pi$
$79$	−1.43832			−0.161824			−0.0809118	+	0.996721i	$0.525783\pi$
$80$	3.07547	−	2.55764i	0.343848	−	0.285952i
$81$		0			0
$82$	−10.1908	+	6.47650i	−1.12539	+	0.715210i
$83$		−	7.66497i		−	0.841340i	−0.907214	−	0.420670i	$-0.861795\pi$
$83$		−	7.66497i		−	0.841340i	0.907214	−	0.420670i	$-0.138205\pi$
$84$		0			0
$85$		−	4.76655i		−	0.517005i
$86$	6.90570	+	10.8661i	0.744661	+	1.17173i
$87$		0			0
$88$	−6.71994	+	0.862136i	−0.716348	+	0.0919040i
$89$	9.10390			0.965011			0.482506	−	0.875893i	$-0.339727\pi$
$89$	9.10390			0.965011			0.482506	+	0.875893i	$0.339727\pi$
$90$		0			0
$91$			9.05259i			0.948969i
$92$	4.48480	−	9.56268i	0.467573	−	0.996979i
$93$		0			0
$94$	12.5233	−	7.95885i	1.29168	−	0.820893i
$95$	−6.29155			−0.645500
$96$		0			0
$97$	−11.6927			−1.18721			−0.593605	−	0.804757i	$-0.702296\pi$
$97$	−11.6927			−1.18721			−0.593605	+	0.804757i	$0.702296\pi$
$98$	−17.2576	+	10.9676i	−1.74328	+	1.10789i
$99$		0			0
$100$	−0.849224	+	1.81075i	−0.0849224	+	0.181075i
$101$			17.6958i			1.76080i	0.474235	+	0.880398i	$0.342725\pi$
$101$			17.6958i			1.76080i	−0.474235	+	0.880398i	$0.657275\pi$
$102$		0			0
$103$	18.4865			1.82152			0.910762	−	0.412931i	$-0.135495\pi$
$103$	18.4865			1.82152			0.910762	+	0.412931i	$0.135495\pi$
$104$	−5.48240	+	0.703365i	−0.537593	+	0.0689706i
$105$		0			0
$106$	−2.30036	−	3.61963i	−0.223431	−	0.351570i
$107$		−	8.66810i		−	0.837977i	−0.907992	−	0.418988i	$-0.862385\pi$
$107$		−	8.66810i		−	0.837977i	0.907992	−	0.418988i	$-0.137615\pi$
$108$		0			0
$109$		−	3.37816i		−	0.323569i	−0.986826	−	0.161785i	$-0.948275\pi$
$109$		−	3.37816i		−	0.323569i	0.986826	−	0.161785i	$-0.0517250\pi$
$110$	2.85900	−	1.81696i	0.272595	−	0.173241i
$111$		0			0
$112$	−11.8479	−	14.2467i	−1.11952	−	1.34618i
$113$	11.0736			1.04171			0.520857	−	0.853644i	$-0.325612\pi$
$113$	11.0736			1.04171			0.520857	+	0.853644i	$0.325612\pi$
$114$		0			0
$115$			5.28106i			0.492461i
$116$	−0.364487	−	0.170941i	−0.0338418	−	0.0158715i
$117$		0			0
$118$	−2.09210	−	3.29193i	−0.192594	−	0.303047i
$119$	−22.0804			−2.02410
$120$		0			0
$121$	5.26239			0.478399
$122$	−6.25477	−	9.84190i	−0.566280	−	0.891044i
$123$		0			0
$124$	−2.77665	+	5.92050i	−0.249351	+	0.531676i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−20.4865			−1.81788			−0.908939	−	0.416928i	$-0.863107\pi$
$127$	−20.4865			−1.81788			−0.908939	+	0.416928i	$0.863107\pi$
$128$	7.70746	−	8.28221i	0.681250	−	0.732051i
$129$		0			0
$130$	2.33248	−	1.48235i	0.204572	−	0.130011i
$131$		−	13.2901i		−	1.16116i	−0.814203	−	0.580580i	$-0.802826\pi$
$131$		−	13.2901i		−	1.16116i	0.814203	−	0.580580i	$-0.197174\pi$
$132$		0			0
$133$			29.1447i			2.52717i
$134$	−9.11563	−	14.3435i	−0.787471	−	1.23909i
$135$		0			0
$136$	−1.71559	−	13.3722i	−0.147111	−	1.14666i
$137$	5.26253			0.449608			0.224804	−	0.974404i	$-0.427826\pi$
$137$	5.26253			0.449608			0.224804	+	0.974404i	$0.427826\pi$
$138$		0			0
$139$			22.9901i			1.94999i	0.222220	+	0.974996i	$0.428670\pi$
$139$			22.9901i			1.94999i	−0.222220	+	0.974996i	$0.571330\pi$
$140$	8.38805	+	3.93391i	0.708920	+	0.332476i
$141$		0			0
$142$	−0.614107	+	0.390280i	−0.0515347	+	0.0327516i
$143$	−4.68097			−0.391443
$144$		0			0
$145$	0.201291			0.0167163
$146$	4.81320	−	3.05891i	0.398344	−	0.253157i
$147$		0			0
$148$	−2.60693	−	1.22262i	−0.214288	−	0.100499i
$149$			5.79871i			0.475049i	0.971382	+	0.237524i	$0.0763360\pi$
$149$			5.79871i			0.475049i	−0.971382	+	0.237524i	$0.923664\pi$
$150$		0			0
$151$	18.2924			1.48862			0.744308	−	0.667837i	$-0.232780\pi$
$151$	18.2924			1.48862			0.744308	+	0.667837i	$0.232780\pi$
$152$	−17.6505	+	2.26448i	−1.43165	+	0.183673i
$153$		0			0
$154$	−8.41683	−	13.2439i	−0.678247	−	1.06722i
$155$		−	3.26964i		−	0.262624i
$156$		0			0
$157$			12.5163i			0.998912i	0.866339	+	0.499456i	$0.166467\pi$
$157$			12.5163i			0.998912i	−0.866339	+	0.499456i	$0.833533\pi$
$158$	1.71674	−	1.09103i	0.136576	−	0.0867975i
$159$		0			0
$160$	−1.73071	+	5.38560i	−0.136825	+	0.425769i
$161$	24.4638			1.92802
$162$		0			0
$163$		−	7.07985i		−	0.554537i	−0.960793	−	0.277268i	$-0.910571\pi$
$163$		−	7.07985i		−	0.554537i	0.960793	−	0.277268i	$-0.0894291\pi$
$164$	7.25074	−	15.4603i	0.566188	−	1.20725i
$165$		0			0
$166$	5.81421	+	9.14869i	0.451270	+	0.710076i
$167$	−23.4190			−1.81222			−0.906109	−	0.423045i	$-0.860961\pi$
$167$	−23.4190			−1.81222			−0.906109	+	0.423045i	$0.860961\pi$
$168$		0			0
$169$	9.18108			0.706237
$170$	3.61563	+	5.68921i	0.277306	+	0.436343i
$171$		0			0
$172$	−16.4849	−	7.73125i	−1.25696	−	0.589502i
$173$		−	5.99508i		−	0.455798i	−0.973685	−	0.227899i	$-0.926814\pi$
$173$		−	5.99508i		−	0.455798i	0.973685	−	0.227899i	$-0.0731856\pi$
$174$		0			0
$175$	−4.63236			−0.350174
$176$	7.36676	−	6.12639i	0.555291	−	0.461794i
$177$		0			0
$178$	−10.8661	+	6.90570i	−0.814452	+	0.517604i
$179$		−	18.0554i		−	1.34952i	−0.738036	−	0.674761i	$-0.764247\pi$
$179$		−	18.0554i		−	1.34952i	0.738036	−	0.674761i	$-0.235753\pi$
$180$		0			0
$181$			5.28106i			0.392538i	0.980550	+	0.196269i	$0.0628826\pi$
$181$			5.28106i			0.392538i	−0.980550	+	0.196269i	$0.937117\pi$
$182$	−6.86678	−	10.8049i	−0.509000	−	0.800913i
$183$		0			0
$184$	1.90078	+	14.8157i	0.140127	+	1.09223i
$185$	1.43969			0.105848
$186$		0			0
$187$		−	11.4175i		−	0.834928i
$188$	−8.91030	+	18.9989i	−0.649850	+	1.38564i
$189$		0			0
$190$	7.50942	−	4.77242i	0.544790	−	0.346227i
$191$	−4.48971			−0.324864			−0.162432	−	0.986720i	$-0.551934\pi$
$191$	−4.48971			−0.324864			−0.162432	+	0.986720i	$0.551934\pi$
$192$		0			0
$193$	−0.869389			−0.0625800			−0.0312900	−	0.999510i	$-0.509962\pi$
$193$	−0.869389			−0.0625800			−0.0312900	+	0.999510i	$0.509962\pi$
$194$	13.9560	−	8.86939i	1.00198	−	0.636785i
$195$		0			0
$196$	12.2787	−	26.1812i	0.877052	−	1.87009i
$197$		−	15.8134i		−	1.12666i	−0.826232	−	0.563330i	$-0.809520\pi$
$197$		−	15.8134i		−	1.12666i	0.826232	−	0.563330i	$-0.190480\pi$
$198$		0			0
$199$	11.2679			0.798757			0.399378	−	0.916786i	$-0.369226\pi$
$199$	11.2679			0.798757			0.399378	+	0.916786i	$0.369226\pi$
$200$	−0.359923	−	2.80543i	−0.0254504	−	0.198374i
$201$		0			0
$202$	−13.4230	−	21.1212i	−0.944441	−	1.48608i
$203$		−	0.932450i		−	0.0654452i
$204$		0			0
$205$			8.53808i			0.596325i
$206$	−22.0649	+	14.0228i	−1.53733	+	0.977013i
$207$		0			0
$208$	6.01010	−	4.99815i	0.416725	−	0.346559i
$209$	−15.0704			−1.04244
$210$		0			0
$211$		−	5.78010i		−	0.397919i	−0.980008	−	0.198959i	$-0.936244\pi$
$211$		−	5.78010i		−	0.397919i	0.980008	−	0.198959i	$-0.0637561\pi$
$212$	5.49130	+	2.57536i	0.377144	+	0.176877i
$213$		0			0
$214$	6.57513	+	10.3460i	0.449466	+	0.707237i
$215$	9.10390			0.620881
$216$		0			0
$217$	−15.1461			−1.02819
$218$	2.56248	+	4.03208i	0.173553	+	0.273087i
$219$		0			0
$220$	−2.03417	+	4.33735i	−0.137144	+	0.292424i
$221$		−	9.31482i		−	0.626583i
$222$		0			0
$223$	9.30304			0.622978			0.311489	−	0.950250i	$-0.399172\pi$
$223$	9.30304			0.622978			0.311489	+	0.950250i	$0.399172\pi$
$224$	24.9480	+	8.01727i	1.66691	+	0.535676i
$225$		0			0
$226$	−13.2171	+	8.39979i	−0.879188	+	0.558745i
$227$		−	2.59429i		−	0.172189i	−0.996287	−	0.0860945i	$-0.972561\pi$
$227$		−	2.59429i		−	0.172189i	0.996287	−	0.0860945i	$-0.0274387\pi$
$228$		0			0
$229$		−	25.4072i		−	1.67896i	−0.543393	−	0.839478i	$-0.682861\pi$
$229$		−	25.4072i		−	1.67896i	0.543393	−	0.839478i	$-0.317139\pi$
$230$	−4.00591	−	6.30332i	−0.264142	−	0.415629i
$231$		0			0
$232$	0.564707	−	0.0724492i	0.0370748	−	0.00475652i
$233$	27.9430			1.83061			0.915303	−	0.402766i	$-0.131951\pi$
$233$	27.9430			1.83061			0.915303	+	0.402766i	$0.131951\pi$
$234$		0			0
$235$		−	10.4923i		−	0.684441i
$236$	4.99415	+	2.34221i	0.325091	+	0.152465i
$237$		0			0
$238$	26.3545	−	16.7489i	1.70831	−	1.08567i
$239$	−11.4515			−0.740734			−0.370367	−	0.928886i	$-0.620768\pi$
$239$	−11.4515			−0.740734			−0.370367	+	0.928886i	$0.620768\pi$
$240$		0			0
$241$	14.0707			0.906372			0.453186	−	0.891416i	$-0.350287\pi$
$241$	14.0707			0.906372			0.453186	+	0.891416i	$0.350287\pi$
$242$	−6.28103	+	3.99175i	−0.403760	+	0.256599i
$243$		0			0
$244$	14.9310	+	7.00250i	0.955860	+	0.448289i
$245$			14.4588i			0.923736i
$246$		0			0
$247$	−12.2950			−0.782312
$248$	−1.17682	−	9.17275i	−0.0747281	−	0.582470i
$249$		0			0
$250$	0.758543	+	1.19357i	0.0479745	+	0.0754881i
$251$			0.402581i			0.0254107i	0.999919	+	0.0127053i	$0.00404435\pi$
$251$			0.402581i			0.0254107i	−0.999919	+	0.0127053i	$0.995956\pi$
$252$		0			0
$253$			12.6499i			0.795292i
$254$	24.4520	−	15.5399i	1.53426	−	0.975058i
$255$		0			0
$256$	−2.91699	+	15.7319i	−0.182312	+	0.983241i
$257$	26.4022			1.64693			0.823463	−	0.567369i	$-0.192039\pi$
$257$	26.4022			1.64693			0.823463	+	0.567369i	$0.192039\pi$
$258$		0			0
$259$		−	6.66918i		−	0.414403i
$260$	−1.65956	+	3.53858i	−0.102921	+	0.219453i
$261$		0			0
$262$	10.0811	+	15.8627i	0.622812	+	0.979998i
$263$	2.96470			0.182811			0.0914056	−	0.995814i	$-0.470864\pi$
$263$	2.96470			0.182811			0.0914056	+	0.995814i	$0.470864\pi$
$264$		0			0
$265$	−3.03261			−0.186292
$266$	−22.1076	−	34.7863i	−1.35550	−	2.13289i
$267$		0			0
$268$	21.7603	+	10.2054i	1.32922	+	0.623392i
$269$			12.5294i			0.763933i	0.924176	+	0.381967i	$0.124753\pi$
$269$			12.5294i			0.763933i	−0.924176	+	0.381967i	$0.875247\pi$
$270$		0			0
$271$	−16.0634			−0.975784			−0.487892	−	0.872904i	$-0.662234\pi$
$271$	−16.0634			−0.975784			−0.487892	+	0.872904i	$0.662234\pi$
$272$	12.1911	+	14.6594i	0.739194	+	0.888854i
$273$		0			0
$274$	−6.28120	+	3.99186i	−0.379461	+	0.241157i
$275$		−	2.39533i		−	0.144444i
$276$		0			0
$277$		−	19.5807i		−	1.17649i	−0.808683	−	0.588245i	$-0.799819\pi$
$277$		−	19.5807i		−	1.17649i	0.808683	−	0.588245i	$-0.200181\pi$
$278$	−17.4390	−	27.4403i	−1.04592	−	1.64576i
$279$		0			0
$280$	−12.9958	+	1.66730i	−0.776646	+	0.0996400i
$281$	−4.33761			−0.258760			−0.129380	−	0.991595i	$-0.541299\pi$
$281$	−4.33761			−0.258760			−0.129380	+	0.991595i	$0.541299\pi$
$282$		0			0
$283$		−	13.4755i		−	0.801036i	−0.916289	−	0.400518i	$-0.868830\pi$
$283$		−	13.4755i		−	0.801036i	0.916289	−	0.400518i	$-0.131170\pi$
$284$	0.436936	−	0.931654i	0.0259274	−	0.0552835i
$285$		0			0
$286$	5.58707	−	3.55072i	0.330371	−	0.209958i
$287$	39.5514			2.33465
$288$		0			0
$289$	5.71998			0.336470
$290$	−0.240255	+	0.152688i	−0.0141082	+	0.00896613i
$291$		0			0
$292$	−3.42459	+	7.30205i	−0.200409	+	0.427320i
$293$		−	17.8134i		−	1.04067i	−0.853962	−	0.520336i	$-0.825807\pi$
$293$		−	17.8134i		−	1.04067i	0.853962	−	0.520336i	$-0.174193\pi$
$294$		0			0
$295$	−2.75805			−0.160580
$296$	4.03897	−	0.518180i	0.234760	−	0.0301186i
$297$		0			0
$298$	−4.39857	−	6.92117i	−0.254802	−	0.400933i
$299$			10.3203i			0.596837i
$300$		0			0
$301$		−	42.1725i		−	2.43078i
$302$	−21.8333	+	13.8756i	−1.25636	+	0.798450i
$303$		0			0
$304$	19.3495	−	16.0915i	1.10977	−	0.922911i
$305$	−8.24576			−0.472151
$306$		0			0
$307$		−	20.3999i		−	1.16429i	−0.813087	−	0.582143i	$-0.802214\pi$
$307$		−	20.3999i		−	1.16429i	0.813087	−	0.582143i	$-0.197786\pi$
$308$	20.0922	+	9.42302i	1.14486	+	0.536927i
$309$		0			0
$310$	2.48016	+	3.90254i	0.140864	+	0.221650i
$311$	19.8854			1.12760			0.563799	−	0.825912i	$-0.309339\pi$
$311$	19.8854			1.12760			0.563799	+	0.825912i	$0.309339\pi$
$312$		0			0
$313$	−24.6108			−1.39108			−0.695541	−	0.718486i	$-0.744835\pi$
$313$	−24.6108			−1.39108			−0.695541	+	0.718486i	$0.744835\pi$
$314$	−9.49418	−	14.9391i	−0.535787	−	0.843064i
$315$		0			0
$316$	−1.22146	+	2.60444i	−0.0687122	+	0.146511i
$317$		−	19.3250i		−	1.08540i	−0.839926	−	0.542701i	$-0.817402\pi$
$317$		−	19.3250i		−	1.08540i	0.839926	−	0.542701i	$-0.182598\pi$
$318$		0			0
$319$	0.482158			0.0269956
$320$	−2.01948	−	7.74091i	−0.112893	−	0.432730i
$321$		0			0
$322$	−29.1993	+	18.5568i	−1.62721	+	1.03413i
$323$		−	29.9890i		−	1.66863i
$324$		0			0
$325$		−	1.95421i		−	0.108400i
$326$	5.37037	+	8.45031i	0.297437	+	0.468019i
$327$		0			0
$328$	3.07305	+	23.9530i	0.169681	+	1.32258i
$329$	−48.6040			−2.67963
$330$		0			0
$331$			5.91393i			0.325059i	0.986704	+	0.162529i	$0.0519652\pi$
$331$			5.91393i			0.325059i	−0.986704	+	0.162529i	$0.948035\pi$
$332$	−13.8793	−	6.50928i	−0.761728	−	0.357243i
$333$		0			0
$334$	27.9523	−	17.7643i	1.52948	−	0.972021i
$335$	−12.0173			−0.656575
$336$		0			0
$337$	31.9081			1.73814			0.869072	−	0.494686i	$-0.164717\pi$
$337$	31.9081			1.73814			0.869072	+	0.494686i	$0.164717\pi$
$338$	−10.9583	+	6.96425i	−0.596051	+	0.378805i
$339$		0			0
$340$	−8.63103	−	4.04787i	−0.468083	−	0.219526i
$341$		−	7.83186i		−	0.424119i
$342$		0			0
$343$	34.5517			1.86561
$344$	25.5404	−	3.27671i	1.37704	−	0.176668i
$345$		0			0
$346$	4.54753	+	7.15556i	0.244477	+	0.384685i
$347$		−	25.0004i		−	1.34209i	−0.741417	−	0.671045i	$-0.765846\pi$
$347$		−	25.0004i		−	1.34209i	0.741417	−	0.671045i	$-0.234154\pi$
$348$		0			0
$349$		−	6.22477i		−	0.333204i	−0.986024	−	0.166602i	$-0.946720\pi$
$349$		−	6.22477i		−	0.333204i	0.986024	−	0.166602i	$-0.0532796\pi$
$350$	5.52905	−	3.51385i	0.295540	−	0.187823i
$351$		0			0
$352$	−4.14562	+	12.9003i	−0.220962	+	0.687588i
$353$	−5.92940			−0.315590			−0.157795	−	0.987472i	$-0.550439\pi$
$353$	−5.92940			−0.315590			−0.157795	+	0.987472i	$0.550439\pi$
$354$		0			0
$355$			0.514512i			0.0273075i
$356$	7.73125	−	16.4849i	0.409755	−	0.873697i
$357$		0			0
$358$	13.6958	+	21.5504i	0.723845	+	1.13897i
$359$	−28.4933			−1.50382			−0.751910	−	0.659265i	$-0.770867\pi$
$359$	−28.4933			−1.50382			−0.751910	+	0.659265i	$0.770867\pi$
$360$		0			0
$361$	−20.5837			−1.08335
$362$	−4.00591	−	6.30332i	−0.210546	−	0.331295i
$363$		0			0
$364$	16.3920	+	7.68768i	0.859173	+	0.402944i
$365$		−	4.03261i		−	0.211076i
$366$		0			0
$367$	−17.8541			−0.931976			−0.465988	−	0.884791i	$-0.654301\pi$
$367$	−17.8541			−0.931976			−0.465988	+	0.884791i	$0.654301\pi$
$368$	−13.5070	−	16.2417i	−0.704103	−	0.846658i
$369$		0			0
$370$	−1.71838	+	1.09207i	−0.0893342	+	0.0567740i
$371$			14.0481i			0.729343i
$372$		0			0
$373$			7.06438i			0.365780i	0.983133	+	0.182890i	$0.0585452\pi$
$373$			7.06438i			0.365780i	−0.983133	+	0.182890i	$0.941455\pi$
$374$	8.66064	+	13.6276i	0.447831	+	0.704664i
$375$		0			0
$376$	−3.77642	−	29.4354i	−0.194754	−	1.51801i
$377$	0.393363			0.0202592
$378$		0			0
$379$		−	4.76655i		−	0.244841i	−0.992478	−	0.122421i	$-0.960934\pi$
$379$		−	4.76655i		−	0.244841i	0.992478	−	0.122421i	$-0.0390657\pi$
$380$	−5.34294	+	11.3924i	−0.274087	+	0.584420i
$381$		0			0
$382$	5.35878	−	3.40564i	0.274179	−	0.174248i
$383$	5.36637			0.274209			0.137104	−	0.990557i	$-0.456220\pi$
$383$	5.36637			0.274209			0.137104	+	0.990557i	$0.456220\pi$
$384$		0			0
$385$	−11.0960			−0.565506
$386$	1.03768	−	0.659469i	0.0528164	−	0.0335661i
$387$		0			0
$388$	−9.92969	+	21.1725i	−0.504104	+	1.07487i
$389$			31.9686i			1.62087i	0.585828	+	0.810435i	$0.300769\pi$
$389$			31.9686i			1.62087i	−0.585828	+	0.810435i	$0.699231\pi$
$390$		0			0
$391$	−25.1724			−1.27302
$392$	5.20405	+	40.5631i	0.262844	+	2.04875i
$393$		0			0
$394$	11.9952	+	18.8745i	0.604308	+	0.950882i
$395$		−	1.43832i		−	0.0723697i
$396$		0			0
$397$		−	18.9244i		−	0.949789i	−0.880043	−	0.474894i	$-0.842486\pi$
$397$		−	18.9244i		−	0.949789i	0.880043	−	0.474894i	$-0.157514\pi$
$398$	−13.4490	+	8.54715i	−0.674137	+	0.428430i
$399$		0			0
$400$	2.55764	+	3.07547i	0.127882	+	0.153773i
$401$	−2.17947			−0.108838			−0.0544189	−	0.998518i	$-0.517331\pi$
$401$	−2.17947			−0.108838			−0.0544189	+	0.998518i	$0.517331\pi$
$402$		0			0
$403$		−	6.38955i		−	0.318286i
$404$	32.0427	+	15.0277i	1.59418	+	0.747656i
$405$		0			0
$406$	0.707304	+	1.11295i	0.0351029	+	0.0552346i
$407$	3.44854			0.170938
$408$		0			0
$409$	−3.78279			−0.187047			−0.0935236	−	0.995617i	$-0.529813\pi$
$409$	−3.78279			−0.187047			−0.0935236	+	0.995617i	$0.529813\pi$
$410$	−6.47650	−	10.1908i	−0.319852	−	0.503288i
$411$		0			0
$412$	15.6991	−	33.4744i	0.773441	−	1.64916i
$413$			12.7763i			0.628681i
$414$		0			0
$415$	7.66497			0.376259
$416$	−3.38216	+	10.5246i	−0.165824	+	0.516009i
$417$		0			0
$418$	17.9875	−	11.4315i	0.879800	−	0.559134i
$419$			28.0481i			1.37024i	0.728430	+	0.685120i	$0.240250\pi$
$419$			28.0481i			1.37024i	−0.728430	+	0.685120i	$0.759750\pi$
$420$		0			0
$421$		−	28.3719i		−	1.38276i	−0.722490	−	0.691381i	$-0.757002\pi$
$421$		−	28.3719i		−	1.38276i	0.722490	−	0.691381i	$-0.242998\pi$
$422$	4.38446	+	6.89896i	0.213432	+	0.335836i
$423$		0			0
$424$	−8.50778	+	1.09151i	−0.413174	+	0.0530083i
$425$	4.76655			0.231212
$426$		0			0
$427$			38.1973i			1.84850i
$428$	−15.6958	−	7.36116i	−0.758683	−	0.355815i
$429$		0			0
$430$	−10.8661	+	6.90570i	−0.524012	+	0.333022i
$431$	−15.2246			−0.733341			−0.366671	−	0.930351i	$-0.619502\pi$
$431$	−15.2246			−0.733341			−0.366671	+	0.930351i	$0.619502\pi$
$432$		0			0
$433$	21.1508			1.01644			0.508221	−	0.861226i	$-0.330303\pi$
$433$	21.1508			1.01644			0.508221	+	0.861226i	$0.330303\pi$
$434$	18.0780	−	11.4890i	0.867771	−	0.551490i
$435$		0			0
$436$	−6.11701	−	2.86882i	−0.292952	−	0.137391i
$437$			33.2261i			1.58942i
$438$		0			0
$439$	6.54732			0.312487			0.156243	−	0.987719i	$-0.450062\pi$
$439$	6.54732			0.312487			0.156243	+	0.987719i	$0.450062\pi$
$440$	−0.862136	−	6.71994i	−0.0411007	−	0.320361i
$441$		0			0
$442$	7.06569	+	11.1179i	0.336081	+	0.528825i
$443$			24.2042i			1.14998i	0.818161	+	0.574989i	$0.194994\pi$
$443$			24.2042i			1.14998i	−0.818161	+	0.574989i	$0.805006\pi$
$444$		0			0
$445$			9.10390i			0.431566i
$446$	−11.1038	+	7.05676i	−0.525782	+	0.334147i
$447$		0			0
$448$	−35.8587	+	9.35497i	−1.69416	+	0.441981i
$449$	1.56084			0.0736607			0.0368304	−	0.999322i	$-0.488274\pi$
$449$	1.56084			0.0736607			0.0368304	+	0.999322i	$0.488274\pi$
$450$		0			0
$451$			20.4515i			0.963024i
$452$	9.40395	−	20.0515i	0.442324	−	0.943143i
$453$		0			0
$454$	1.96788	+	3.09647i	0.0923572	+	0.145324i
$455$	−9.05259			−0.424392
$456$		0			0
$457$	−9.16948			−0.428930			−0.214465	−	0.976732i	$-0.568801\pi$
$457$	−9.16948			−0.428930			−0.214465	+	0.976732i	$0.568801\pi$
$458$	19.2725	+	30.3253i	0.900544	+	1.41701i
$459$		0			0
$460$	9.56268	+	4.48480i	0.445862	+	0.209105i
$461$		−	11.0563i		−	0.514944i	−0.966286	−	0.257472i	$-0.917110\pi$
$461$		−	11.0563i		−	0.514944i	0.966286	−	0.257472i	$-0.0828895\pi$
$462$		0			0
$463$	−34.4988			−1.60330			−0.801649	−	0.597795i	$-0.796044\pi$
$463$	−34.4988			−1.60330			−0.801649	+	0.597795i	$0.796044\pi$
$464$	−0.619062	+	0.514828i	−0.0287393	+	0.0239003i
$465$		0			0
$466$	−33.3519	+	21.1960i	−1.54500	+	0.981884i
$467$			38.8495i			1.79774i	0.438213	+	0.898871i	$0.355612\pi$
$467$			38.8495i			1.79774i	−0.438213	+	0.898871i	$0.644388\pi$
$468$		0			0
$469$			55.6684i			2.57053i
$470$	7.95885	+	12.5233i	0.367114	+	0.577656i
$471$		0			0
$472$	−7.73754	+	0.992689i	−0.356149	+	0.0456922i
$473$	21.8068			1.00268
$474$		0			0
$475$		−	6.29155i		−	0.288676i
$476$	−18.7512	+	39.9820i	−0.859459	+	1.83257i
$477$		0			0
$478$	13.6681	−	8.68643i	0.625166	−	0.397308i
$479$	−28.4575			−1.30026			−0.650128	−	0.759825i	$-0.725285\pi$
$479$	−28.4575			−1.30026			−0.650128	+	0.759825i	$0.725285\pi$
$480$		0			0
$481$	2.81346			0.128283
$482$	−16.7944	+	10.6732i	−0.764962	+	0.486152i
$483$		0			0
$484$	4.46895	−	9.52887i	0.203134	−	0.433131i
$485$		−	11.6927i		−	0.530936i
$486$		0			0
$487$	−10.9552			−0.496429			−0.248214	−	0.968705i	$-0.579844\pi$
$487$	−10.9552			−0.496429			−0.248214	+	0.968705i	$0.579844\pi$
$488$	−23.1329	+	2.96784i	−1.04718	+	0.134348i
$489$		0			0
$490$	−10.9676	−	17.2576i	−0.495466	−	0.779617i
$491$		−	25.9440i		−	1.17084i	−0.810731	−	0.585419i	$-0.800930\pi$
$491$		−	25.9440i		−	1.17084i	0.810731	−	0.585419i	$-0.199070\pi$
$492$		0			0
$493$			0.959461i			0.0432120i
$494$	14.6750	−	9.32629i	0.660257	−	0.419609i
$495$		0			0
$496$	8.36254	+	10.0557i	0.375489	+	0.451512i
$497$	2.38341			0.106910
$498$		0			0
$499$		−	20.5554i		−	0.920184i	−0.887871	−	0.460092i	$-0.847816\pi$
$499$		−	20.5554i		−	0.920184i	0.887871	−	0.460092i	$-0.152184\pi$
$500$	−1.81075	−	0.849224i	−0.0809792	−	0.0379785i
$501$		0			0
$502$	−0.305375	−	0.480509i	−0.0136296	−	0.0214462i
$503$	−3.22301			−0.143707			−0.0718535	−	0.997415i	$-0.522891\pi$
$503$	−3.22301			−0.143707			−0.0718535	+	0.997415i	$0.522891\pi$
$504$		0			0
$505$	−17.6958			−0.787452
$506$	−9.59549	−	15.0985i	−0.426572	−	0.671212i
$507$		0			0
$508$	−17.3976	+	37.0959i	−0.771893	+	1.64586i
$509$		−	2.88647i		−	0.127941i	−0.997952	−	0.0639703i	$-0.979624\pi$
$509$		−	2.88647i		−	0.127941i	0.997952	−	0.0639703i	$-0.0203763\pi$
$510$		0			0
$511$	−18.6805			−0.826376
$512$	−8.45166	−	20.9897i	−0.373514	−	0.927625i
$513$		0			0
$514$	−31.5130	+	20.0272i	−1.38998	+	0.883364i
$515$			18.4865i			0.814610i
$516$		0			0
$517$		−	25.1325i		−	1.10533i
$518$	5.05886	+	7.96014i	0.222274	+	0.349749i
$519$		0			0
$520$	−0.703365	−	5.48240i	−0.0308446	−	0.240419i
$521$	−13.3049			−0.582898			−0.291449	−	0.956586i	$-0.594137\pi$
$521$	−13.3049			−0.582898			−0.291449	+	0.956586i	$0.594137\pi$
$522$		0			0
$523$		−	34.2889i		−	1.49935i	−0.661806	−	0.749675i	$-0.730210\pi$
$523$		−	34.2889i		−	1.49935i	0.661806	−	0.749675i	$-0.269790\pi$
$524$	−24.0650	−	11.2863i	−1.05129	−	0.493042i
$525$		0			0
$526$	−3.53858	+	2.24885i	−0.154289	+	0.0980547i
$527$	15.5849			0.678888
$528$		0			0
$529$	4.88960			0.212591
$530$	3.61963	−	2.30036i	0.157227	−	0.0999215i
$531$		0			0
$532$	52.7739	+	24.7504i	2.28804	+	1.07307i
$533$			16.6852i			0.722715i
$534$		0			0
$535$	8.66810			0.374755
$536$	−33.7137	+	4.32530i	−1.45621	+	0.186825i
$537$		0			0
$538$	−9.50412	−	14.9548i	−0.409752	−	0.644746i
$539$			34.6335i			1.49177i
$540$		0			0
$541$		−	15.5478i		−	0.668453i	−0.942493	−	0.334226i	$-0.891525\pi$
$541$		−	15.5478i		−	0.668453i	0.942493	−	0.334226i	$-0.108475\pi$
$542$	19.1728	−	12.1848i	0.823544	−	0.523382i
$543$		0			0
$544$	−25.6707	−	8.24951i	−1.10062	−	0.353695i
$545$	3.37816			0.144705
$546$		0			0
$547$		−	5.65869i		−	0.241948i	−0.992656	−	0.120974i	$-0.961398\pi$
$547$		−	5.65869i		−	0.241948i	0.992656	−	0.120974i	$-0.0386018\pi$
$548$	4.46907	−	9.52913i	0.190909	−	0.407064i
$549$		0			0
$550$	1.81696	+	2.85900i	0.0774755	+	0.121908i
$551$	1.26643			0.0539518
$552$		0			0
$553$	−6.66281			−0.283332
$554$	14.8528	+	23.3710i	0.631036	+	0.992937i
$555$		0			0
$556$	41.6293	+	19.5237i	1.76548	+	0.827991i
$557$			5.26159i			0.222941i	0.993768	+	0.111470i	$0.0355560\pi$
$557$			5.26159i			0.222941i	−0.993768	+	0.111470i	$0.964444\pi$
$558$		0			0
$559$	17.7909			0.752475
$560$	14.2467	−	11.8479i	0.602032	−	0.500665i
$561$		0			0
$562$	5.17725	−	3.29027i	0.218389	−	0.138792i
$563$			0.523609i			0.0220675i	0.999939	+	0.0110337i	$0.00351222\pi$
$563$			0.523609i			0.0220675i	−0.999939	+	0.0110337i	$0.996488\pi$
$564$		0			0
$565$			11.0736i			0.465869i
$566$	10.2218	+	16.0840i	0.429653	+	0.676060i
$567$		0			0
$568$	0.185185	+	1.44343i	0.00777019	+	0.0605650i
$569$	10.8202			0.453605			0.226803	−	0.973941i	$-0.427173\pi$
$569$	10.8202			0.453605			0.226803	+	0.973941i	$0.427173\pi$
$570$		0			0
$571$			45.7061i			1.91274i	0.292156	+	0.956371i	$0.405628\pi$
$571$			45.7061i			1.91274i	−0.292156	+	0.956371i	$0.594372\pi$
$572$	−3.97519	+	8.47607i	−0.166211	+	0.354402i
$573$		0			0
$574$	−47.2075	+	30.0015i	−1.97040	+	1.25224i
$575$	−5.28106			−0.220235
$576$		0			0
$577$	−18.5983			−0.774259			−0.387129	−	0.922025i	$-0.626533\pi$
$577$	−18.5983			−0.774259			−0.387129	+	0.922025i	$0.626533\pi$
$578$	−6.82721	+	4.33886i	−0.283974	+	0.180473i
$579$		0			0
$580$	0.170941	−	0.364487i	0.00709793	−	0.0151345i
$581$		−	35.5069i		−	1.47307i
$582$		0			0
$583$	−7.26410			−0.300848
$584$	−1.45143	−	11.3132i	−0.0600606	−	0.468144i
$585$		0			0
$586$	13.5123	+	21.2616i	0.558186	+	0.878309i
$587$		−	32.9752i		−	1.36103i	−0.732732	−	0.680517i	$-0.761755\pi$
$587$		−	32.9752i		−	1.36103i	0.732732	−	0.680517i	$-0.238245\pi$
$588$		0			0
$589$		−	20.5711i		−	0.847617i
$590$	3.29193	−	2.09210i	0.135527	−	0.0861306i
$591$		0			0
$592$	−4.42773	+	3.68221i	−0.181979	+	0.151338i
$593$	42.6200			1.75019			0.875097	−	0.483948i	$-0.160798\pi$
$593$	42.6200			1.75019			0.875097	+	0.483948i	$0.160798\pi$
$594$		0			0
$595$		−	22.0804i		−	0.905207i
$596$	10.5000	+	4.92440i	0.430097	+	0.201711i
$597$		0			0
$598$	−7.82838	−	12.3180i	−0.320126	−	0.503720i
$599$	26.0947			1.06620			0.533101	−	0.846052i	$-0.321027\pi$
$599$	26.0947			1.06620			0.533101	+	0.846052i	$0.321027\pi$
$600$		0			0
$601$	8.04009			0.327962			0.163981	−	0.986463i	$-0.447566\pi$
$601$	8.04009			0.327962			0.163981	+	0.986463i	$0.447566\pi$
$602$	31.9897	+	50.3359i	1.30380	+	2.05154i
$603$		0			0
$604$	15.5344	−	33.1230i	0.632084	−	1.34776i
$605$			5.26239i			0.213946i
$606$		0			0
$607$	7.65218			0.310593			0.155296	−	0.987868i	$-0.450367\pi$
$607$	7.65218			0.310593			0.155296	+	0.987868i	$0.450367\pi$
$608$	−10.8889	+	33.8838i	−0.441601	+	1.37417i
$609$		0			0
$610$	9.84190	−	6.25477i	0.398487	−	0.253248i
$611$		−	20.5041i		−	0.829506i
$612$		0			0
$613$		−	18.3475i		−	0.741047i	−0.928823	−	0.370524i	$-0.879178\pi$
$613$		−	18.3475i		−	0.741047i	0.928823	−	0.370524i	$-0.120822\pi$
$614$	15.4742	+	24.3488i	0.624489	+	0.982636i
$615$		0			0
$616$	−31.1292	+	3.99372i	−1.25423	+	0.160912i
$617$	8.16298			0.328629			0.164315	−	0.986408i	$-0.447459\pi$
$617$	8.16298			0.328629			0.164315	+	0.986408i	$0.447459\pi$
$618$		0			0
$619$		−	40.3555i		−	1.62202i	−0.585030	−	0.811012i	$-0.698917\pi$
$619$		−	40.3555i		−	1.62202i	0.585030	−	0.811012i	$-0.301083\pi$
$620$	−5.92050	−	2.77665i	−0.237773	−	0.111513i
$621$		0			0
$622$	−23.7347	+	15.0840i	−0.951673	+	0.604811i
$623$	42.1725			1.68961
$624$		0			0
$625$	1.00000			0.0400000
$626$	29.3747	−	18.6683i	1.17405	−	0.746136i
$627$		0			0
$628$	22.6640	+	10.6292i	0.904390	+	0.424150i
$629$			6.86237i			0.273621i
$630$		0			0
$631$	5.21565			0.207632			0.103816	−	0.994597i	$-0.466895\pi$
$631$	5.21565			0.207632			0.103816	+	0.994597i	$0.466895\pi$
$632$	−0.517685	−	4.03511i	−0.0205924	−	0.160508i
$633$		0			0
$634$	14.6589	+	23.0658i	0.582178	+	0.916059i
$635$		−	20.4865i		−	0.812980i
$636$		0			0
$637$			28.2554i			1.11952i
$638$	−0.575489	+	0.365737i	−0.0227838	+	0.0144797i
$639$		0			0
$640$	8.28221	+	7.70746i	0.327383	+	0.304664i
$641$	−14.1597			−0.559275			−0.279637	−	0.960106i	$-0.590214\pi$
$641$	−14.1597			−0.559275			−0.279637	+	0.960106i	$0.590214\pi$
$642$		0			0
$643$		−	11.7095i		−	0.461778i	−0.972980	−	0.230889i	$-0.925837\pi$
$643$		−	11.7095i		−	0.461778i	0.972980	−	0.230889i	$-0.0741634\pi$
$644$	20.7752	−	44.2978i	0.818659	−	1.74558i
$645$		0			0
$646$	22.7480	+	35.7940i	0.895006	+	1.40830i
$647$	2.33183			0.0916738			0.0458369	−	0.998949i	$-0.485405\pi$
$647$	2.33183			0.0916738			0.0458369	+	0.998949i	$0.485405\pi$
$648$		0			0
$649$	−6.60646			−0.259326
$650$	1.48235	+	2.33248i	0.0581426	+	0.0914876i
$651$		0			0
$652$	−12.8198	−	6.01238i	−0.502064	−	0.235463i
$653$			16.7826i			0.656755i	0.944547	+	0.328377i	$0.106502\pi$
$653$			16.7826i			0.656755i	−0.944547	+	0.328377i	$0.893498\pi$
$654$		0			0
$655$	13.2901			0.519286
$656$	−21.8373	−	26.2586i	−0.852603	−	1.02522i
$657$		0			0
$658$	58.0124	−	36.8683i	2.26156	−	1.43727i
$659$		−	47.5355i		−	1.85172i	−0.377865	−	0.925861i	$-0.623342\pi$
$659$		−	47.5355i		−	1.85172i	0.377865	−	0.925861i	$-0.376658\pi$
$660$		0			0
$661$		−	15.1189i		−	0.588057i	−0.955797	−	0.294028i	$-0.905004\pi$
$661$		−	15.1189i		−	0.588057i	0.955797	−	0.294028i	$-0.0949960\pi$
$662$	−4.48597	−	7.05869i	−0.174352	−	0.274344i
$663$		0			0
$664$	21.5036	−	2.75880i	0.834500	−	0.107062i
$665$	−29.1447			−1.13018
$666$		0			0
$667$		−	1.06303i		−	0.0411606i
$668$	−19.8880	+	42.4060i	−0.769489	+	1.64074i
$669$		0			0
$670$	14.3435	−	9.11563i	0.554137	−	0.352168i
$671$	−19.7513			−0.762492
$672$		0			0
$673$	−29.0868			−1.12121			−0.560607	−	0.828082i	$-0.689432\pi$
$673$	−29.0868			−1.12121			−0.560607	+	0.828082i	$0.689432\pi$
$674$	−38.0846	+	24.2037i	−1.46696	+	0.932290i
$675$		0			0
$676$	7.79679	−	16.6246i	0.299877	−	0.639409i
$677$			25.6431i			0.985545i	0.870158	+	0.492772i	$0.164016\pi$
$677$			25.6431i			0.985545i	−0.870158	+	0.492772i	$0.835984\pi$
$678$		0			0
$679$	−54.1646			−2.07865
$680$	13.3722	−	1.71559i	0.512802	−	0.0657900i
$681$		0			0
$682$	5.94081	+	9.34789i	0.227485	+	0.357949i
$683$		−	21.0523i		−	0.805542i	−0.915301	−	0.402771i	$-0.868047\pi$
$683$		−	21.0523i		−	0.805542i	0.915301	−	0.402771i	$-0.131953\pi$
$684$		0			0
$685$			5.26253i			0.201071i
$686$	−41.2399	+	26.2089i	−1.57455	+	1.00066i
$687$		0			0
$688$	−27.9987	+	23.2845i	−1.06744	+	0.887712i
$689$	−5.92634			−0.225776
$690$		0			0
$691$		−	22.9903i		−	0.874594i	−0.899317	−	0.437297i	$-0.855936\pi$
$691$		−	22.9903i		−	0.874594i	0.899317	−	0.437297i	$-0.144064\pi$
$692$	−10.8556	−	5.09117i	−0.412668	−	0.193537i
$693$		0			0
$694$	18.9639	+	29.8397i	0.719858	+	1.13270i
$695$	−22.9901			−0.872063
$696$		0			0
$697$	−40.6971			−1.54151
$698$	4.72176	+	7.42971i	0.178721	+	0.281219i
$699$		0			0
$700$	−3.93391	+	8.38805i	−0.148688	+	0.317038i
$701$			42.7645i			1.61519i	0.589735	+	0.807597i	$0.299232\pi$
$701$			42.7645i			1.61519i	−0.589735	+	0.807597i	$0.700768\pi$
$702$		0			0
$703$	9.05791			0.341626
$704$	−4.83733	−	18.5420i	−0.182314	−	0.698830i
$705$		0			0
$706$	7.07716	−	4.49771i	0.266352	−	0.169273i
$707$			81.9733i			3.08292i
$708$		0			0
$709$			28.5449i			1.07203i	0.844209	+	0.536014i	$0.180070\pi$
$709$			28.5449i			1.07203i	−0.844209	+	0.536014i	$0.819930\pi$
$710$	−0.390280	−	0.614107i	−0.0146469	−	0.0230470i
$711$		0			0
$712$	3.27671	+	25.5404i	0.122800	+	0.957166i
$713$	−17.2672			−0.646660
$714$		0			0
$715$		−	4.68097i		−	0.175058i
$716$	−32.6938	−	15.3331i	−1.22182	−	0.573024i
$717$		0			0
$718$	34.0088	−	21.6134i	1.26920	−	0.806606i
$719$	9.39342			0.350315			0.175158	−	0.984540i	$-0.443956\pi$
$719$	9.39342			0.350315			0.175158	+	0.984540i	$0.443956\pi$
$720$		0			0
$721$	85.6359			3.18925
$722$	24.5681	−	15.6136i	0.914329	−	0.581078i
$723$		0			0
$724$	9.56268	+	4.48480i	0.355394	+	0.166676i
$725$			0.201291i			0.00747574i
$726$		0			0
$727$	15.5974			0.578476			0.289238	−	0.957257i	$-0.406598\pi$
$727$	15.5974			0.578476			0.289238	+	0.957257i	$0.406598\pi$
$728$	−25.3964	+	3.25824i	−0.941254	+	0.120758i
$729$		0			0
$730$	3.05891	+	4.81320i	0.113215	+	0.178145i
$731$			43.3942i			1.60499i
$732$		0			0
$733$		−	38.0264i		−	1.40454i	−0.711912	−	0.702269i	$-0.752170\pi$
$733$		−	38.0264i		−	1.40454i	0.711912	−	0.702269i	$-0.247830\pi$
$734$	21.3101	−	13.5431i	0.786571	−	0.499885i
$735$		0			0
$736$	28.4417	+	9.13998i	1.04837	+	0.336904i
$737$	−28.7854			−1.06032
$738$		0			0
$739$			15.5308i			0.571309i	0.958333	+	0.285654i	$0.0922109\pi$
$739$			15.5308i			0.571309i	−0.958333	+	0.285654i	$0.907789\pi$
$740$	1.22262	−	2.60693i	0.0449445	−	0.0958325i
$741$		0			0
$742$	−10.6561	−	16.7674i	−0.391198	−	0.615552i
$743$	28.8169			1.05719			0.528594	−	0.848875i	$-0.322719\pi$
$743$	28.8169			1.05719			0.528594	+	0.848875i	$0.322719\pi$
$744$		0			0
$745$	−5.79871			−0.212448
$746$	−5.35864	−	8.43184i	−0.196194	−	0.308712i
$747$		0			0
$748$	−20.6742	−	9.69599i	−0.755923	−	0.354520i
$749$		−	40.1538i		−	1.46719i
$750$		0			0
$751$	−2.22432			−0.0811664			−0.0405832	−	0.999176i	$-0.512922\pi$
$751$	−2.22432			−0.0811664			−0.0405832	+	0.999176i	$0.512922\pi$
$752$	26.8354	+	32.2687i	0.978588	+	1.17672i
$753$		0			0
$754$	−0.469507	+	0.298383i	−0.0170984	+	0.0108665i
$755$			18.2924i			0.665729i
$756$		0			0
$757$		−	43.7191i		−	1.58900i	−0.607265	−	0.794499i	$-0.707733\pi$
$757$		−	43.7191i		−	1.58900i	0.607265	−	0.794499i	$-0.292267\pi$
$758$	3.61563	+	5.68921i	0.131326	+	0.206642i
$759$		0			0
$760$	−2.26448	−	17.6505i	−0.0821413	−	0.640252i
$761$	4.33761			0.157238			0.0786192	−	0.996905i	$-0.474949\pi$
$761$	4.33761			0.157238			0.0786192	+	0.996905i	$0.474949\pi$
$762$		0			0
$763$		−	15.6489i		−	0.566527i
$764$	−3.81277	+	8.12974i	−0.137941	+	0.294124i
$765$		0			0
$766$	−6.40515	+	4.07063i	−0.231427	+	0.147078i
$767$	−5.38981			−0.194615
$768$		0			0
$769$	−13.7789			−0.496879			−0.248439	−	0.968647i	$-0.579918\pi$
$769$	−13.7789			−0.496879			−0.248439	+	0.968647i	$0.579918\pi$
$770$	13.2439	−	8.41683i	0.477277	−	0.303321i
$771$		0			0
$772$	−0.738306	+	1.57425i	−0.0265722	+	0.0566584i
$773$		−	42.9986i		−	1.54655i	−0.634070	−	0.773276i	$-0.718617\pi$
$773$		−	42.9986i		−	1.54655i	0.634070	−	0.773276i	$-0.281383\pi$
$774$		0			0
$775$	3.26964			0.117449
$776$	−4.20846	−	32.8030i	−0.151075	−	1.17756i
$777$		0			0
$778$	−24.2495	−	38.1567i	−0.869388	−	1.36799i
$779$			53.7178i			1.92464i
$780$		0			0
$781$			1.23243i			0.0440997i
$782$	30.0451	−	19.0944i	1.07441	−	0.682814i
$783$		0			0
$784$	−36.9803	−	44.4674i	−1.32072	−	1.58812i
$785$	−12.5163			−0.446727
$786$		0			0
$787$			37.6437i			1.34185i	0.741525	+	0.670926i	$0.234103\pi$
$787$			37.6437i			1.34185i	−0.741525	+	0.670926i	$0.765897\pi$
$788$	−28.6342	−	13.4292i	−1.02005	−	0.478394i
$789$		0			0
$790$	1.09103	+	1.71674i	0.0388170	+	0.0610787i
$791$	51.2968			1.82390
$792$		0			0
$793$	−16.1139			−0.572222
$794$	14.3550	+	22.5876i	0.509439	+	0.801605i
$795$		0			0
$796$	9.56893	−	20.4033i	0.339162	−	0.723175i
$797$		−	2.69524i		−	0.0954704i	−0.998860	−	0.0477352i	$-0.984800\pi$
$797$		−	2.69524i		−	0.0954704i	0.998860	−	0.0477352i	$-0.0152004\pi$
$798$		0			0
$799$	50.0120			1.76930
$800$	−5.38560	−	1.73071i	−0.190410	−	0.0611898i
$801$		0			0
$802$	2.60136	−	1.65323i	0.0918571	−	0.0583774i
$803$		−	9.65943i		−	0.340874i
$804$		0			0
$805$			24.4638i			0.862235i
$806$	4.84675	+	7.62638i	0.170719	+	0.268628i
$807$		0			0
$808$	−49.6444	+	6.36913i	−1.74648	+	0.224065i
$809$	−29.8268			−1.04866			−0.524328	−	0.851517i	$-0.675683\pi$
$809$	−29.8268			−1.04866			−0.524328	+	0.851517i	$0.675683\pi$
$810$		0			0
$811$			17.7273i			0.622489i	0.950330	+	0.311245i	$0.100746\pi$
$811$			17.7273i			0.622489i	−0.950330	+	0.311245i	$0.899254\pi$
$812$	−1.68844	−	0.791859i	−0.0592525	−	0.0277888i
$813$		0			0
$814$	−4.11608	+	2.61587i	−0.144269	+	0.0916862i
$815$	7.07985			0.247996
$816$		0			0
$817$	57.2777			2.00389
$818$	4.51503	−	2.86941i	0.157864	−	0.100327i
$819$		0			0
$820$	15.4603	+	7.25074i	0.539898	+	0.253207i
$821$		−	17.2808i		−	0.603105i	−0.953450	−	0.301552i	$-0.902495\pi$
$821$		−	17.2808i		−	0.603105i	0.953450	−	0.301552i	$-0.0975048\pi$
$822$		0			0
$823$	−3.83186			−0.133570			−0.0667852	−	0.997767i	$-0.521274\pi$
$823$	−3.83186			−0.133570			−0.0667852	+	0.997767i	$0.521274\pi$
$824$	6.65371	+	51.8625i	0.231793	+	1.80672i
$825$		0			0
$826$	−9.69138	−	15.2494i	−0.337206	−	0.530595i
$827$		−	11.8492i		−	0.412036i	−0.978548	−	0.206018i	$-0.933949\pi$
$827$		−	11.8492i		−	0.412036i	0.978548	−	0.206018i	$-0.0660506\pi$
$828$		0			0
$829$		−	0.601935i		−	0.0209061i	−0.999945	−	0.0104530i	$-0.996673\pi$
$829$		−	0.601935i		−	0.0209061i	0.999945	−	0.0104530i	$-0.00332736\pi$
$830$	−9.14869	+	5.81421i	−0.317555	+	0.201814i
$831$		0			0
$832$	−3.94649	−	15.1273i	−0.136820	−	0.524446i
$833$	−68.9184			−2.38788
$834$		0			0
$835$		−	23.4190i		−	0.810448i
$836$	−12.7981	+	27.2887i	−0.442632	+	0.943798i
$837$		0			0
$838$	−21.2757	−	33.4774i	−0.734958	−	1.15646i
$839$	1.99004			0.0687039			0.0343520	−	0.999410i	$-0.489063\pi$
$839$	1.99004			0.0687039			0.0343520	+	0.999410i	$0.489063\pi$
$840$		0			0
$841$	28.9595			0.998603
$842$	21.5213	+	33.8639i	0.741674	+	1.16703i
$843$		0			0
$844$	−10.4663	−	4.90860i	−0.360266	−	0.168961i
$845$			9.18108i			0.315839i
$846$		0			0
$847$	24.3773			0.837613
$848$	9.32668	−	7.75631i	0.320280	−	0.266353i
$849$		0			0
$850$	−5.68921	+	3.61563i	−0.195138	+	0.124015i
$851$		−	7.60311i		−	0.260631i
$852$		0			0
$853$			47.3134i			1.61998i	0.586444	+	0.809989i	$0.300527\pi$
$853$			47.3134i			1.61998i	−0.586444	+	0.809989i	$0.699473\pi$
$854$	−28.9743	−	45.5912i	−0.991481	−	1.56010i
$855$		0			0
$856$	24.3178	−	3.11985i	0.831164	−	0.106634i
$857$	−40.3552			−1.37851			−0.689254	−	0.724520i	$-0.742062\pi$
$857$	−40.3552			−1.37851			−0.689254	+	0.724520i	$0.742062\pi$
$858$		0			0
$859$		−	41.0795i		−	1.40162i	−0.713350	−	0.700808i	$-0.752823\pi$
$859$		−	41.0795i		−	1.40162i	0.713350	−	0.700808i	$-0.247177\pi$
$860$	7.73125	−	16.4849i	0.263633	−	0.562130i
$861$		0			0
$862$	18.1716	−	11.5485i	0.618927	−	0.393343i
$863$	23.4889			0.799570			0.399785	−	0.916609i	$-0.369085\pi$
$863$	23.4889			0.799570			0.399785	+	0.916609i	$0.369085\pi$
$864$		0			0
$865$	5.99508			0.203839
$866$	−25.2450	+	16.0438i	−0.857860	+	0.545191i
$867$		0			0
$868$	−12.8625	+	27.4259i	−0.436580	+	0.930895i
$869$		−	3.44525i		−	0.116872i
$870$		0			0
$871$	−23.4843			−0.795734
$872$	9.47721	−	1.21588i	0.320939	−	0.0411749i
$873$		0			0
$874$	−25.2034	−	39.6577i	−0.852518	−	1.34144i
$875$		−	4.63236i		−	0.156602i
$876$		0			0
$877$		−	13.7849i		−	0.465482i	−0.972539	−	0.232741i	$-0.925231\pi$
$877$		−	13.7849i		−	0.465482i	0.972539	−	0.232741i	$-0.0747694\pi$
$878$	−7.81469	+	4.96643i	−0.263733	+	0.167609i
$879$		0			0
$880$	6.12639	+	7.36676i	0.206520	+	0.248333i
$881$	5.93246			0.199870			0.0999348	−	0.994994i	$-0.468137\pi$
$881$	5.93246			0.199870			0.0999348	+	0.994994i	$0.468137\pi$
$882$		0			0
$883$			24.1403i			0.812384i	0.913788	+	0.406192i	$0.133144\pi$
$883$			24.1403i			0.812384i	−0.913788	+	0.406192i	$0.866856\pi$
$884$	−16.8668	−	7.91037i	−0.567292	−	0.266054i
$885$		0			0
$886$	−18.3600	−	28.8895i	−0.616815	−	0.970561i
$887$	−19.5964			−0.657984			−0.328992	−	0.944333i	$-0.606709\pi$
$887$	−19.5964			−0.657984			−0.328992	+	0.944333i	$0.606709\pi$
$888$		0			0
$889$	−94.9006			−3.18286
$890$	−6.90570	−	10.8661i	−0.231480	−	0.364234i
$891$		0			0
$892$	7.90037	−	16.8455i	0.264524	−	0.564029i
$893$		−	66.0128i		−	2.20903i
$894$		0			0
$895$	18.0554			0.603525
$896$	35.7037	−	38.3662i	1.19278	−	1.28172i
$897$		0			0
$898$	−1.86298	+	1.18397i	−0.0621684	+	0.0395095i
$899$			0.658147i			0.0219504i
$900$		0			0
$901$		−	14.4551i		−	0.481568i
$902$	−15.5134	−	24.4103i	−0.516539	−	0.812776i
$903$		0			0
$904$	3.98564	+	31.0662i	0.132560	+	1.03325i
$905$	−5.28106			−0.175548
$906$		0			0
$907$			24.3272i			0.807770i	0.914810	+	0.403885i	$0.132340\pi$
$907$			24.3272i			0.807770i	−0.914810	+	0.403885i	$0.867660\pi$
$908$	−4.69761	−	2.20313i	−0.155896	−	0.0731135i
$909$		0			0
$910$	10.8049	−	6.86678i	0.358179	−	0.227632i
$911$	39.2591			1.30071			0.650357	−	0.759629i	$-0.274619\pi$
$911$	39.2591			1.30071			0.650357	+	0.759629i	$0.274619\pi$
$912$		0			0
$913$	18.3601			0.607632
$914$	10.9444	−	6.95545i	0.362009	−	0.230066i
$915$		0			0
$916$	−46.0061	−	21.5764i	−1.52009	−	0.712905i
$917$		−	61.5644i		−	2.03304i
$918$		0			0
$919$	−6.58169			−0.217110			−0.108555	−	0.994090i	$-0.534622\pi$
$919$	−6.58169			−0.217110			−0.108555	+	0.994090i	$0.534622\pi$
$920$	−14.8157	+	1.90078i	−0.488458	+	0.0626668i
$921$		0			0
$922$	8.38670	+	13.1965i	0.276201	+	0.434604i
$923$			1.00546i			0.0330952i
$924$		0			0
$925$			1.43969i			0.0473368i
$926$	41.1768	−	26.1689i	1.35315	−	0.859962i
$927$		0			0
$928$	0.348376	−	1.08407i	0.0114360	−	0.0355863i
$929$	15.0642			0.494242			0.247121	−	0.968985i	$-0.420516\pi$
$929$	15.0642			0.494242			0.247121	+	0.968985i	$0.420516\pi$
$930$		0			0
$931$			90.9681i			2.98136i
$932$	23.7299	−	50.5978i	0.777297	−	1.65739i
$933$		0			0
$934$	−29.4691	−	46.3697i	−0.964257	−	1.51726i
$935$	11.4175			0.373391
$936$		0			0
$937$	54.0670			1.76629			0.883146	−	0.469099i	$-0.155421\pi$
$937$	54.0670			1.76629			0.883146	+	0.469099i	$0.155421\pi$
$938$	−42.2269	−	66.4442i	−1.37876	−	2.16948i
$939$		0			0
$940$	−18.9989	−	8.91030i	−0.619676	−	0.290622i
$941$		−	16.2573i		−	0.529973i	−0.964252	−	0.264986i	$-0.914633\pi$
$941$		−	16.2573i		−	0.529973i	0.964252	−	0.264986i	$-0.0853674\pi$
$942$		0			0
$943$	45.0901			1.46834
$944$	8.48230	−	7.05410i	0.276076	−	0.229591i
$945$		0			0
$946$	−26.0280	+	16.5414i	−0.846244	+	0.537809i
$947$			7.94302i			0.258113i	0.991637	+	0.129057i	$0.0411949\pi$
$947$			7.94302i			0.258113i	−0.991637	+	0.129057i	$0.958805\pi$
$948$		0			0
$949$		−	7.88055i		−	0.255813i
$950$	4.77242	+	7.50942i	0.154838	+	0.243638i
$951$		0			0
$952$	−7.94724	−	61.9450i	−0.257572	−	2.00765i
$953$	10.5096			0.340439			0.170219	−	0.985406i	$-0.445552\pi$
$953$	10.5096			0.340439			0.170219	+	0.985406i	$0.445552\pi$
$954$		0			0
$955$		−	4.48971i		−	0.145283i
$956$	−9.72486	+	20.7358i	−0.314524	+	0.670642i
$957$		0			0
$958$	33.9661	−	21.5862i	1.09739	−	0.697420i
$959$	24.3779			0.787205
$960$		0			0
$961$	−20.3095			−0.655144
$962$	−3.35806	+	2.13413i	−0.108268	+	0.0688071i
$963$		0			0
$964$	11.9492	−	25.4785i	0.384857	−	0.820607i
$965$		−	0.869389i		−	0.0279866i
$966$		0			0
$967$	−17.4035			−0.559659			−0.279830	−	0.960050i	$-0.590278\pi$
$967$	−17.4035			−0.559659			−0.279830	+	0.960050i	$0.590278\pi$
$968$	1.89406	+	14.7633i	0.0608773	+	0.474510i
$969$		0			0
$970$	8.86939	+	13.9560i	0.284779	+	0.448101i
$971$		−	12.4994i		−	0.401125i	−0.979681	−	0.200563i	$-0.935723\pi$
$971$		−	12.4994i		−	0.401125i	0.979681	−	0.200563i	$-0.0642770\pi$
$972$		0			0
$973$			106.498i			3.41418i
$974$	13.0758	−	8.31001i	0.418977	−	0.266270i
$975$		0			0
$976$	25.3596	−	21.0897i	0.811740	−	0.675064i
$977$	−14.2994			−0.457478			−0.228739	−	0.973488i	$-0.573460\pi$
$977$	−14.2994			−0.457478			−0.228739	+	0.973488i	$0.573460\pi$
$978$		0			0
$979$			21.8068i			0.696950i
$980$	26.1812	+	12.2787i	0.836328	+	0.392230i
$981$		0			0
$982$	19.6797	+	30.9661i	0.628004	+	0.988167i
$983$	43.3572			1.38288			0.691441	−	0.722433i	$-0.256976\pi$
$983$	43.3572			1.38288			0.691441	+	0.722433i	$0.256976\pi$
$984$		0			0
$985$	15.8134			0.503858
$986$	−0.727793	−	1.14519i	−0.0231776	−	0.0364701i
$987$		0			0
$988$	−10.4412	+	22.2632i	−0.332179	+	0.708286i
$989$		−	48.0782i		−	1.52880i
$990$		0			0
$991$	−13.0947			−0.415967			−0.207983	−	0.978132i	$-0.566690\pi$
$991$	−13.0947			−0.415967			−0.207983	+	0.978132i	$0.566690\pi$
$992$	−17.6089	−	5.65879i	−0.559085	−	0.179667i
$993$		0			0
$994$	−2.84477	+	1.80792i	−0.0902305	+	0.0573436i
$995$			11.2679i			0.357215i
$996$		0			0
$997$			53.5961i			1.69741i	0.528870	+	0.848703i	$0.322616\pi$
$997$			53.5961i			1.69741i	−0.528870	+	0.848703i	$0.677384\pi$
$998$	15.5921	+	24.5343i	0.493560	+	0.776619i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.k.d.541.4	yes	20
3.2	odd	2	inner	1080.2.k.d.541.17	yes	20
4.3	odd	2		4320.2.k.d.2161.12		20
8.3	odd	2		4320.2.k.d.2161.1		20
8.5	even	2	inner	1080.2.k.d.541.3	✓	20
12.11	even	2		4320.2.k.d.2161.2		20
24.5	odd	2	inner	1080.2.k.d.541.18	yes	20
24.11	even	2		4320.2.k.d.2161.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.k.d.541.3	✓	20	8.5	even	2	inner
1080.2.k.d.541.4	yes	20	1.1	even	1	trivial
1080.2.k.d.541.17	yes	20	3.2	odd	2	inner
1080.2.k.d.541.18	yes	20	24.5	odd	2	inner
4320.2.k.d.2161.1		20	8.3	odd	2
4320.2.k.d.2161.2		20	12.11	even	2
4320.2.k.d.2161.11		20	24.11	even	2
4320.2.k.d.2161.12		20	4.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.19357 + 0.758543i) q^{2} +(0.849224 - 1.81075i) q^{4} +1.00000i q^{5} +4.63236 q^{7} +(0.359923 + 2.80543i) q^{8} +(-0.758543 - 1.19357i) q^{10} +2.39533i q^{11} +1.95421i q^{13} +(-5.52905 + 3.51385i) q^{14} +(-2.55764 - 3.07547i) q^{16} -4.76655 q^{17} +6.29155i q^{19} +(1.81075 + 0.849224i) q^{20} +(-1.81696 - 2.85900i) q^{22} +5.28106 q^{23} -1.00000 q^{25} +(-1.48235 - 2.33248i) q^{26} +(3.93391 - 8.38805i) q^{28} -0.201291i q^{29} -3.26964 q^{31} +(5.38560 + 1.73071i) q^{32} +(5.68921 - 3.61563i) q^{34} +4.63236i q^{35} -1.43969i q^{37} +(-4.77242 - 7.50942i) q^{38} +(-2.80543 + 0.359923i) q^{40} +8.53808 q^{41} -9.10390i q^{43} +(4.33735 + 2.03417i) q^{44} +(-6.30332 + 4.00591i) q^{46} -10.4923 q^{47} +14.4588 q^{49} +(1.19357 - 0.758543i) q^{50} +(3.53858 + 1.65956i) q^{52} +3.03261i q^{53} -2.39533 q^{55} +(1.66730 + 12.9958i) q^{56} +(0.152688 + 0.240255i) q^{58} +2.75805i q^{59} +8.24576i q^{61} +(3.90254 - 2.48016i) q^{62} +(-7.74091 + 2.01948i) q^{64} -1.95421 q^{65} +12.0173i q^{67} +(-4.04787 + 8.63103i) q^{68} +(-3.51385 - 5.52905i) q^{70} +0.514512 q^{71} -4.03261 q^{73} +(1.09207 + 1.71838i) q^{74} +(11.3924 + 5.34294i) q^{76} +11.0960i q^{77} -1.43832 q^{79} +(3.07547 - 2.55764i) q^{80} +(-10.1908 + 6.47650i) q^{82} -7.66497i q^{83} -4.76655i q^{85} +(6.90570 + 10.8661i) q^{86} +(-6.71994 + 0.862136i) q^{88} +9.10390 q^{89} +9.05259i q^{91} +(4.48480 - 9.56268i) q^{92} +(12.5233 - 7.95885i) q^{94} -6.29155 q^{95} -11.6927 q^{97} +(-17.2576 + 10.9676i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - 2 q^{10} - 18 q^{16} + 16 q^{22} - 20 q^{25} + 16 q^{28} + 20 q^{31} - 6 q^{34} - 4 q^{40} + 54 q^{46} + 36 q^{49} + 56 q^{52} - 72 q^{58} - 28 q^{64} - 40 q^{73} + 58 q^{76} - 4 q^{79}+ \cdots + 40 q^{97}+O(q^{100}) \) 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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