LMFDB - Embedded newform 1080.2.d.i.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1080.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	20.0.71899280742356107798058983489536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 $ x^20 - 3x^18 + 8x^16 - 24x^14 + 56x^12 - 92x^10 + 224x^8 - 384x^6 + 512x^4 - 768*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.4
Root			$1.35662 + 0.399488i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.i.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35662 + 0.399488i) q^{2} +(1.68082 - 1.08390i) q^{4} +(-1.49578 - 1.66212i) q^{5} +1.43534i q^{7} +(-1.84722 + 2.14191i) q^{8} +(2.69320 + 1.65731i) q^{10} -0.0984392i q^{11} +1.92218 q^{13} +(-0.573401 - 1.94721i) q^{14} +(1.65030 - 3.64369i) q^{16} +2.03741i q^{17} +0.999558i q^{19} +(-4.31572 - 1.17243i) q^{20} +(0.0393253 + 0.133544i) q^{22} -4.30361i q^{23} +(-0.525254 + 4.97233i) q^{25} +(-2.60767 + 0.767889i) q^{26} +(1.55577 + 2.41255i) q^{28} +3.56681i q^{29} +1.42267 q^{31} +(-0.783216 + 5.60237i) q^{32} +(-0.813920 - 2.76398i) q^{34} +(2.38570 - 2.14696i) q^{35} +8.27330 q^{37} +(-0.399311 - 1.35602i) q^{38} +(6.32315 - 0.133544i) q^{40} +5.11958 q^{41} -5.50577 q^{43} +(-0.106699 - 0.165458i) q^{44} +(1.71924 + 5.83835i) q^{46} -9.00709i q^{47} +4.93980 q^{49} +(-1.27382 - 6.95539i) q^{50} +(3.23084 - 2.08346i) q^{52} +4.93699 q^{53} +(-0.163617 + 0.147244i) q^{55} +(-3.07437 - 2.65139i) q^{56} +(-1.42490 - 4.83879i) q^{58} +6.27246i q^{59} -12.8449i q^{61} +(-1.93002 + 0.568340i) q^{62} +(-1.17556 - 7.91316i) q^{64} +(-2.87517 - 3.19489i) q^{65} +1.89027 q^{67} +(2.20835 + 3.42451i) q^{68} +(-2.37880 + 3.86566i) q^{70} +12.3259 q^{71} -5.62966i q^{73} +(-11.2237 + 3.30508i) q^{74} +(1.08343 + 1.68008i) q^{76} +0.141294 q^{77} +2.48816 q^{79} +(-8.52474 + 2.70719i) q^{80} +(-6.94531 + 2.04521i) q^{82} +2.26930 q^{83} +(3.38640 - 3.04752i) q^{85} +(7.46923 - 2.19949i) q^{86} +(0.210848 + 0.181839i) q^{88} +13.3550 q^{89} +2.75898i q^{91} +(-4.66470 - 7.23359i) q^{92} +(3.59823 + 12.2192i) q^{94} +(1.66138 - 1.49512i) q^{95} +14.7457i q^{97} +(-6.70142 + 1.97339i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64}+ \cdots - 22 q^{94}+O(q^{100}) $ 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

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 $

$2$	−1.35662	+	0.399488i	−0.959273	+	0.282481i
$2$	−1.35662	+	0.399488i	−0.959273	+	0.282481i
$3$		0			0
$3$		0			0
$4$	1.68082	−	1.08390i	0.840409	−	0.541952i
$5$	−1.49578	−	1.66212i	−0.668935	−	0.743321i
$5$	−1.49578	−	1.66212i	−0.668935	−	0.743321i
$6$		0			0
$7$			1.43534i			0.542507i	0.962508	+	0.271254i	$0.0874382\pi$
$7$			1.43534i			0.542507i	−0.962508	+	0.271254i	$0.912562\pi$
$8$	−1.84722	+	2.14191i	−0.653091	+	0.757280i
$9$		0			0
$10$	2.69320	+	1.65731i	0.851665	+	0.524086i
$11$		−	0.0984392i		−	0.0296805i	−0.999890	−	0.0148403i	$-0.995276\pi$
$11$		−	0.0984392i		−	0.0296805i	0.999890	−	0.0148403i	$-0.00472398\pi$
$12$		0			0
$13$	1.92218			0.533118			0.266559	−	0.963819i	$-0.414113\pi$
$13$	1.92218			0.533118			0.266559	+	0.963819i	$0.414113\pi$
$14$	−0.573401	−	1.94721i	−0.153248	−	0.520413i
$15$		0			0
$16$	1.65030	−	3.64369i	0.412576	−	0.910923i
$17$			2.03741i			0.494144i	0.968997	+	0.247072i	$0.0794684\pi$
$17$			2.03741i			0.494144i	−0.968997	+	0.247072i	$0.920532\pi$
$18$		0			0
$19$			0.999558i			0.229314i	0.993405	+	0.114657i	$0.0365770\pi$
$19$			0.999558i			0.229314i	−0.993405	+	0.114657i	$0.963423\pi$
$20$	−4.31572	−	1.17243i	−0.965024	−	0.262162i
$21$		0			0
$22$	0.0393253	+	0.133544i	0.00838418	+	0.0284717i
$23$		−	4.30361i		−	0.897364i	−0.893691	−	0.448682i	$-0.851894\pi$
$23$		−	4.30361i		−	0.897364i	0.893691	−	0.448682i	$-0.148106\pi$
$24$		0			0
$25$	−0.525254	+	4.97233i	−0.105051	+	0.994467i
$26$	−2.60767	+	0.767889i	−0.511405	+	0.150595i
$27$		0			0
$28$	1.55577	+	2.41255i	0.294013	+	0.455928i
$29$			3.56681i			0.662339i	0.943571	+	0.331170i	$0.107443\pi$
$29$			3.56681i			0.662339i	−0.943571	+	0.331170i	$0.892557\pi$
$30$		0			0
$31$	1.42267			0.255519			0.127760	−	0.991805i	$-0.459221\pi$
$31$	1.42267			0.255519			0.127760	+	0.991805i	$0.459221\pi$
$32$	−0.783216	+	5.60237i	−0.138454	+	0.990369i
$33$		0			0
$34$	−0.813920	−	2.76398i	−0.139586	−	0.474019i
$35$	2.38570	−	2.14696i	0.403257	−	0.362902i
$36$		0			0
$37$	8.27330			1.36012			0.680061	−	0.733156i	$-0.261953\pi$
$37$	8.27330			1.36012			0.680061	+	0.733156i	$0.261953\pi$
$38$	−0.399311	−	1.35602i	−0.0647769	−	0.219975i
$39$		0			0
$40$	6.32315	−	0.133544i	0.999777	−	0.0211152i
$41$	5.11958			0.799544			0.399772	−	0.916615i	$-0.369089\pi$
$41$	5.11958			0.799544			0.399772	+	0.916615i	$0.369089\pi$
$42$		0			0
$43$	−5.50577			−0.839623			−0.419811	−	0.907611i	$-0.637904\pi$
$43$	−5.50577			−0.839623			−0.419811	+	0.907611i	$0.637904\pi$
$44$	−0.106699	−	0.165458i	−0.0160854	−	0.0249438i
$45$		0			0
$46$	1.71924	+	5.83835i	0.253488	+	0.860817i
$47$		−	9.00709i		−	1.31382i	−0.753969	−	0.656910i	$-0.771863\pi$
$47$		−	9.00709i		−	1.31382i	0.753969	−	0.656910i	$-0.228137\pi$
$48$		0			0
$49$	4.93980			0.705686
$50$	−1.27382	−	6.95539i	−0.180145	−	0.983640i
$51$		0			0
$52$	3.23084	−	2.08346i	0.448037	−	0.288924i
$53$	4.93699			0.678148			0.339074	−	0.940760i	$-0.389886\pi$
$53$	4.93699			0.678148			0.339074	+	0.940760i	$0.389886\pi$
$54$		0			0
$55$	−0.163617	+	0.147244i	−0.0220622	+	0.0198544i
$56$	−3.07437	−	2.65139i	−0.410830	−	0.354307i
$57$		0			0
$58$	−1.42490	−	4.83879i	−0.187098	−	0.635364i
$59$			6.27246i			0.816605i	0.912847	+	0.408303i	$0.133879\pi$
$59$			6.27246i			0.816605i	−0.912847	+	0.408303i	$0.866121\pi$
$60$		0			0
$61$		−	12.8449i		−	1.64463i	−0.569035	−	0.822313i	$-0.692683\pi$
$61$		−	12.8449i		−	1.64463i	0.569035	−	0.822313i	$-0.307317\pi$
$62$	−1.93002	+	0.568340i	−0.245113	+	0.0721792i
$63$		0			0
$64$	−1.17556	−	7.91316i	−0.146945	−	0.989145i
$65$	−2.87517	−	3.19489i	−0.356621	−	0.396277i
$66$		0			0
$67$	1.89027			0.230933			0.115466	−	0.993311i	$-0.463164\pi$
$67$	1.89027			0.230933			0.115466	+	0.993311i	$0.463164\pi$
$68$	2.20835	+	3.42451i	0.267802	+	0.415283i
$69$		0			0
$70$	−2.37880	+	3.86566i	−0.284320	+	0.462035i
$71$	12.3259			1.46281			0.731406	−	0.681942i	$-0.238864\pi$
$71$	12.3259			1.46281			0.731406	+	0.681942i	$0.238864\pi$
$72$		0			0
$73$		−	5.62966i		−	0.658902i	−0.944173	−	0.329451i	$-0.893136\pi$
$73$		−	5.62966i		−	0.658902i	0.944173	−	0.329451i	$-0.106864\pi$
$74$	−11.2237	+	3.30508i	−1.30473	+	0.384208i
$75$		0			0
$76$	1.08343	+	1.68008i	0.124277	+	0.192718i
$77$	0.141294			0.0161019
$78$		0			0
$79$	2.48816			0.279939			0.139970	−	0.990156i	$-0.455299\pi$
$79$	2.48816			0.279939			0.139970	+	0.990156i	$0.455299\pi$
$80$	−8.52474	+	2.70719i	−0.953094	+	0.302673i
$81$		0			0
$82$	−6.94531	+	2.04521i	−0.766981	+	0.225856i
$83$	2.26930			0.249088			0.124544	−	0.992214i	$-0.460253\pi$
$83$	2.26930			0.249088			0.124544	+	0.992214i	$0.460253\pi$
$84$		0			0
$85$	3.38640	−	3.04752i	0.367307	−	0.330550i
$86$	7.46923	−	2.19949i	0.805427	−	0.237177i
$87$		0			0
$88$	0.210848	+	0.181839i	0.0224765	+	0.0193841i
$89$	13.3550			1.41563			0.707815	−	0.706398i	$-0.249681\pi$
$89$	13.3550			1.41563			0.707815	+	0.706398i	$0.249681\pi$
$90$		0			0
$91$			2.75898i			0.289220i
$92$	−4.66470	−	7.23359i	−0.486329	−	0.754153i
$93$		0			0
$94$	3.59823	+	12.2192i	0.371129	+	1.26031i
$95$	1.66138	−	1.49512i	0.170454	−	0.153396i
$96$		0			0
$97$			14.7457i			1.49720i	0.663024	+	0.748598i	$0.269273\pi$
$97$			14.7457i			1.49720i	−0.663024	+	0.748598i	$0.730727\pi$
$98$	−6.70142	+	1.97339i	−0.676945	+	0.199343i
$99$		0			0
$100$	4.50668	+	8.92692i	0.450668	+	0.892692i
$101$			13.6218i			1.35542i	0.735328	+	0.677711i	$0.237028\pi$
$101$			13.6218i			1.35542i	−0.735328	+	0.677711i	$0.762972\pi$
$102$		0			0
$103$		−	10.8458i		−	1.06867i	−0.845272	−	0.534336i	$-0.820562\pi$
$103$		−	10.8458i		−	1.06867i	0.845272	−	0.534336i	$-0.179438\pi$
$104$	−3.55069	+	4.11714i	−0.348174	+	0.403719i
$105$		0			0
$106$	−6.69761	+	1.97227i	−0.650529	+	0.191564i
$107$	12.4915			1.20760			0.603798	−	0.797137i	$-0.293653\pi$
$107$	12.4915			1.20760			0.603798	+	0.797137i	$0.293653\pi$
$108$		0			0
$109$		−	16.5739i		−	1.58749i	−0.608250	−	0.793745i	$-0.708128\pi$
$109$		−	16.5739i		−	1.58749i	0.608250	−	0.793745i	$-0.291872\pi$
$110$	0.163144	−	0.265117i	0.0155552	−	0.0252779i
$111$		0			0
$112$	5.22994	+	2.36874i	0.494183	+	0.223825i
$113$		−	9.15123i		−	0.860875i	−0.902620	−	0.430438i	$-0.858359\pi$
$113$		−	9.15123i		−	0.860875i	0.902620	−	0.430438i	$-0.141641\pi$
$114$		0			0
$115$	−7.15309	+	6.43727i	−0.667029	+	0.600279i
$116$	3.86608	+	5.99515i	0.358956	+	0.556636i
$117$		0			0
$118$	−2.50577	−	8.50933i	−0.230675	−	0.783347i
$119$	−2.92437			−0.268077
$120$		0			0
$121$	10.9903			0.999119
$122$	5.13140	+	17.4257i	0.464575	+	1.57765i
$123$		0			0
$124$	2.39125	−	1.54204i	0.214741	−	0.138479i
$125$	9.05026	−	6.56451i	0.809480	−	0.587148i
$126$		0			0
$127$			10.9648i			0.972972i	0.873688	+	0.486486i	$0.161722\pi$
$127$			10.9648i			0.972972i	−0.873688	+	0.486486i	$0.838278\pi$
$128$	4.75599	+	10.2655i	0.420374	+	0.907351i
$129$		0			0
$130$	5.17683	+	3.18564i	0.454038	+	0.279399i
$131$			22.1895i			1.93870i	0.245678	+	0.969352i	$0.420989\pi$
$131$			22.1895i			1.93870i	−0.245678	+	0.969352i	$0.579011\pi$
$132$		0			0
$133$	−1.43471			−0.124405
$134$	−2.56437	+	0.755139i	−0.221528	+	0.0652340i
$135$		0			0
$136$	−4.36394	−	3.76354i	−0.374205	−	0.322721i
$137$		−	10.7851i		−	0.921431i	−0.887548	−	0.460716i	$-0.847593\pi$
$137$		−	10.7851i		−	0.921431i	0.887548	−	0.460716i	$-0.152407\pi$
$138$		0			0
$139$			15.5743i			1.32100i	0.750827	+	0.660499i	$0.229655\pi$
$139$			15.5743i			1.32100i	−0.750827	+	0.660499i	$0.770345\pi$
$140$	1.68283	−	6.19452i	0.142225	−	0.523532i
$141$		0			0
$142$	−16.7215	+	4.92404i	−1.40324	+	0.413216i
$143$		−	0.189218i		−	0.0158232i
$144$		0			0
$145$	5.92844	−	5.33518i	0.492330	−	0.443062i
$146$	2.24898	+	7.63730i	0.186127	+	0.632067i
$147$		0			0
$148$	13.9059	−	8.96746i	1.14306	−	0.737121i
$149$			4.17528i			0.342052i	0.985266	+	0.171026i	$0.0547083\pi$
$149$			4.17528i			0.342052i	−0.985266	+	0.171026i	$0.945292\pi$
$150$		0			0
$151$	−3.18461			−0.259160			−0.129580	−	0.991569i	$-0.541363\pi$
$151$	−3.18461			−0.259160			−0.129580	+	0.991569i	$0.541363\pi$
$152$	−2.14096	−	1.84640i	−0.173655	−	0.149763i
$153$		0			0
$154$	−0.191681	+	0.0564451i	−0.0154461	+	0.00454848i
$155$	−2.12801	−	2.36464i	−0.170926	−	0.189933i
$156$		0			0
$157$	20.4342			1.63083			0.815414	−	0.578878i	$-0.196509\pi$
$157$	20.4342			1.63083			0.815414	+	0.578878i	$0.196509\pi$
$158$	−3.37547	+	0.993989i	−0.268538	+	0.0790775i
$159$		0			0
$160$	10.4833	−	7.07815i	0.828778	−	0.559577i
$161$	6.17714			0.486827
$162$		0			0
$163$	−19.5466			−1.53101			−0.765504	−	0.643432i	$-0.777510\pi$
$163$	−19.5466			−1.53101			−0.765504	+	0.643432i	$0.777510\pi$
$164$	8.60508	−	5.54913i	0.671944	−	0.433315i
$165$		0			0
$166$	−3.07857	+	0.906559i	−0.238944	+	0.0703626i
$167$		−	1.16218i		−	0.0899322i	−0.998989	−	0.0449661i	$-0.985682\pi$
$167$		−	1.16218i		−	0.0899322i	0.998989	−	0.0449661i	$-0.0143180\pi$
$168$		0			0
$169$	−9.30521			−0.715786
$170$	−3.37660	+	5.48715i	−0.258974	+	0.420845i
$171$		0			0
$172$	−9.25421	+	5.96773i	−0.705627	+	0.455035i
$173$	7.38888			0.561766			0.280883	−	0.959742i	$-0.409373\pi$
$173$	7.38888			0.561766			0.280883	+	0.959742i	$0.409373\pi$
$174$		0			0
$175$	−7.13699	−	0.753918i	−0.539506	−	0.0569909i
$176$	−0.358682	−	0.162454i	−0.0270367	−	0.0122455i
$177$		0			0
$178$	−18.1177	+	5.33518i	−1.35798	+	0.399888i
$179$		−	18.4318i		−	1.37766i	−0.724924	−	0.688828i	$-0.758125\pi$
$179$		−	18.4318i		−	1.37766i	0.724924	−	0.688828i	$-0.241875\pi$
$180$		0			0
$181$			4.75079i			0.353123i	0.984290	+	0.176562i	$0.0564975\pi$
$181$			4.75079i			0.353123i	−0.984290	+	0.176562i	$0.943503\pi$
$182$	−1.10218	−	3.74289i	−0.0816991	−	0.277441i
$183$		0			0
$184$	9.21794	+	7.94971i	0.679556	+	0.586061i
$185$	−12.3751	−	13.7512i	−0.909833	−	1.01101i
$186$		0			0
$187$	0.200561			0.0146664
$188$	−9.76283	−	15.1393i	−0.712028	−	1.10415i
$189$		0			0
$190$	−1.65657	+	2.69201i	−0.120180	+	0.195299i
$191$	13.1635			0.952479			0.476240	−	0.879316i	$-0.341999\pi$
$191$	13.1635			0.952479			0.476240	+	0.879316i	$0.341999\pi$
$192$		0			0
$193$		−	8.50034i		−	0.611868i	−0.952053	−	0.305934i	$-0.901031\pi$
$193$		−	8.50034i		−	0.611868i	0.952053	−	0.305934i	$-0.0989687\pi$
$194$	−5.89072	−	20.0042i	−0.422929	−	1.43622i
$195$		0			0
$196$	8.30291	−	5.35427i	0.593065	−	0.382448i
$197$	4.46451			0.318083			0.159042	−	0.987272i	$-0.449160\pi$
$197$	4.46451			0.318083			0.159042	+	0.987272i	$0.449160\pi$
$198$		0			0
$199$	−19.2962			−1.36787			−0.683936	−	0.729542i	$-0.739733\pi$
$199$	−19.2962			−1.36787			−0.683936	+	0.729542i	$0.739733\pi$
$200$	−9.68003	−	10.3100i	−0.684482	−	0.729030i
$201$		0			0
$202$	−5.44176	−	18.4796i	−0.382881	−	1.30022i
$203$	−5.11958			−0.359324
$204$		0			0
$205$	−7.65779	−	8.50933i	−0.534843	−	0.594317i
$206$	4.33278	+	14.7136i	0.301879	+	1.02515i
$207$		0			0
$208$	3.17218	−	7.00384i	0.219951	−	0.485629i
$209$	0.0983957			0.00680617
$210$		0			0
$211$			22.4861i			1.54801i	0.633180	+	0.774005i	$0.281749\pi$
$211$			22.4861i			1.54801i	−0.633180	+	0.774005i	$0.718251\pi$
$212$	8.29819	−	5.35123i	0.569922	−	0.367524i
$213$		0			0
$214$	−16.9461	+	4.99019i	−1.15841	+	0.341123i
$215$	8.23545	+	9.15123i	0.561653	+	0.624109i
$216$		0			0
$217$			2.04201i			0.138621i
$218$	6.62107	+	22.4844i	0.448436	+	1.52284i
$219$		0			0
$220$	−0.115413	+	0.424836i	−0.00778112	+	0.0286424i
$221$			3.91627i			0.263437i
$222$		0			0
$223$		−	27.6890i		−	1.85419i	−0.374822	−	0.927097i	$-0.622296\pi$
$223$		−	27.6890i		−	1.85419i	0.374822	−	0.927097i	$-0.377704\pi$
$224$	−8.04131	−	1.12418i	−0.537282	−	0.0751125i
$225$		0			0
$226$	3.65581	+	12.4147i	0.243181	+	0.825815i
$227$	−8.25244			−0.547734			−0.273867	−	0.961768i	$-0.588303\pi$
$227$	−8.25244			−0.547734			−0.273867	+	0.961768i	$0.588303\pi$
$228$		0			0
$229$			6.48061i			0.428251i	0.976806	+	0.214125i	$0.0686902\pi$
$229$			6.48061i			0.428251i	−0.976806	+	0.214125i	$0.931310\pi$
$230$	7.13239	−	11.5905i	0.470296	−	0.764254i
$231$		0			0
$232$	−7.63978	−	6.58868i	−0.501576	−	0.432568i
$233$		−	8.27937i		−	0.542399i	−0.962523	−	0.271200i	$-0.912580\pi$
$233$		−	8.27937i		−	0.542399i	0.962523	−	0.271200i	$-0.0874204\pi$
$234$		0			0
$235$	−14.9708	+	13.4727i	−0.976589	+	0.878861i
$236$	6.79875	+	10.5429i	0.442561	+	0.686283i
$237$		0			0
$238$	3.96725	−	1.16825i	0.257159	−	0.0757265i
$239$	−26.3117			−1.70196			−0.850980	−	0.525198i	$-0.823991\pi$
$239$	−26.3117			−1.70196			−0.850980	+	0.525198i	$0.823991\pi$
$240$		0			0
$241$	−24.8023			−1.59765			−0.798827	−	0.601560i	$-0.794546\pi$
$241$	−24.8023			−1.59765			−0.798827	+	0.601560i	$0.794546\pi$
$242$	−14.9096	+	4.39050i	−0.958428	+	0.282232i
$243$		0			0
$244$	−13.9227	−	21.5900i	−0.891309	−	1.38216i
$245$	−7.38888	−	8.21052i	−0.472058	−	0.524551i
$246$		0			0
$247$			1.92133i			0.122252i
$248$	−2.62798	+	3.04723i	−0.166877	+	0.193499i
$249$		0			0
$250$	−9.65529	+	12.5210i	−0.610654	+	0.791897i
$251$			0.277559i			0.0175194i	0.999962	+	0.00875968i	$0.00278833\pi$
$251$			0.277559i			0.0175194i	−0.999962	+	0.00875968i	$0.997212\pi$
$252$		0			0
$253$	−0.423644			−0.0266343
$254$	−4.38032	−	14.8751i	−0.274846	−	0.933346i
$255$		0			0
$256$	−10.5530	−	12.0264i	−0.659563	−	0.751649i
$257$			14.2367i			0.888062i	0.896011	+	0.444031i	$0.146452\pi$
$257$			14.2367i			0.888062i	−0.896011	+	0.444031i	$0.853548\pi$
$258$		0			0
$259$			11.8750i			0.737876i
$260$	−8.29560	−	2.25362i	−0.514471	−	0.139763i
$261$		0			0
$262$	−8.86443	−	30.1026i	−0.547646	−	1.85975i
$263$			17.1353i			1.05661i	0.849056	+	0.528303i	$0.177172\pi$
$263$			17.1353i			1.05661i	−0.849056	+	0.528303i	$0.822828\pi$
$264$		0			0
$265$	−7.38468	−	8.20585i	−0.453637	−	0.504082i
$266$	1.94635	−	0.573148i	0.119338	−	0.0351419i
$267$		0			0
$268$	3.17719	−	2.04887i	0.194078	−	0.125155i
$269$		−	14.2417i		−	0.868333i	−0.900833	−	0.434167i	$-0.857043\pi$
$269$		−	14.2417i		−	0.868333i	0.900833	−	0.434167i	$-0.142957\pi$
$270$		0			0
$271$	−16.1177			−0.979078			−0.489539	−	0.871981i	$-0.662835\pi$
$271$	−16.1177			−0.979078			−0.489539	+	0.871981i	$0.662835\pi$
$272$	7.42369	+	3.36234i	0.450127	+	0.203872i
$273$		0			0
$274$	4.30851	+	14.6312i	0.260287	+	0.883904i
$275$	0.489473	+	0.0517056i	0.0295163	+	0.00311797i
$276$		0			0
$277$	15.6307			0.939156			0.469578	−	0.882891i	$-0.344406\pi$
$277$	15.6307			0.939156			0.469578	+	0.882891i	$0.344406\pi$
$278$	−6.22176	−	21.1284i	−0.373156	−	1.26720i
$279$		0			0
$280$	0.191681	+	9.07586i	0.0114552	+	0.542386i
$281$	5.65195			0.337167			0.168583	−	0.985687i	$-0.446081\pi$
$281$	5.65195			0.337167			0.168583	+	0.985687i	$0.446081\pi$
$282$		0			0
$283$	−16.5466			−0.983593			−0.491796	−	0.870710i	$-0.663660\pi$
$283$	−16.5466			−0.983593			−0.491796	+	0.870710i	$0.663660\pi$
$284$	20.7176	−	13.3601i	1.22936	−	0.792774i
$285$		0			0
$286$	0.0755904	+	0.256696i	0.00446975	+	0.0151788i
$287$			7.34833i			0.433758i
$288$		0			0
$289$	12.8490			0.755822
$290$	−5.91129	+	9.60613i	−0.347123	+	0.564091i
$291$		0			0
$292$	−6.10202	−	9.46244i	−0.357094	−	0.553748i
$293$	−20.2544			−1.18328			−0.591638	−	0.806203i	$-0.701519\pi$
$293$	−20.2544			−1.18328			−0.591638	+	0.806203i	$0.701519\pi$
$294$		0			0
$295$	10.4256	−	9.38226i	0.606999	−	0.546256i
$296$	−15.2826	+	17.7207i	−0.888283	+	1.02999i
$297$		0			0
$298$	−1.66798	−	5.66426i	−0.0966232	−	0.328122i
$299$		−	8.27232i		−	0.478401i
$300$		0			0
$301$		−	7.90265i		−	0.455501i
$302$	4.32029	−	1.27221i	0.248605	−	0.0732077i
$303$		0			0
$304$	3.64208	+	1.64957i	0.208888	+	0.0946095i
$305$	−21.3498	+	19.2133i	−1.22248	+	1.10015i
$306$		0			0
$307$	5.50772			0.314342			0.157171	−	0.987571i	$-0.449763\pi$
$307$	5.50772			0.314342			0.157171	+	0.987571i	$0.449763\pi$
$308$	0.237489	−	0.153149i	0.0135322	−	0.00872646i
$309$		0			0
$310$	3.83154	+	2.35780i	0.217617	+	0.133914i
$311$	8.57632			0.486318			0.243159	−	0.969986i	$-0.421816\pi$
$311$	8.57632			0.486318			0.243159	+	0.969986i	$0.421816\pi$
$312$		0			0
$313$			9.83297i			0.555793i	0.960611	+	0.277896i	$0.0896372\pi$
$313$			9.83297i			0.555793i	−0.960611	+	0.277896i	$0.910363\pi$
$314$	−27.7214	+	8.16323i	−1.56441	+	0.460677i
$315$		0			0
$316$	4.18214	−	2.69692i	0.235264	−	0.151714i
$317$	−7.38888			−0.415001			−0.207500	−	0.978235i	$-0.566533\pi$
$317$	−7.38888			−0.415001			−0.207500	+	0.978235i	$0.566533\pi$
$318$		0			0
$319$	0.351114			0.0196586
$320$	−11.3942	+	13.7903i	−0.636955	+	0.770901i
$321$		0			0
$322$	−8.38001	+	2.46769i	−0.467000	+	0.137519i
$323$	−2.03651			−0.113314
$324$		0			0
$325$	−1.00964	+	9.55774i	−0.0560045	+	0.530168i
$326$	26.5172	−	7.80863i	1.46865	−	0.432480i
$327$		0			0
$328$	−9.45699	+	10.9657i	−0.522175	+	0.605478i
$329$	12.9282			0.712757
$330$		0			0
$331$			5.64764i			0.310422i	0.987881	+	0.155211i	$0.0496058\pi$
$331$			5.64764i			0.310422i	−0.987881	+	0.155211i	$0.950394\pi$
$332$	3.81428	−	2.45971i	0.209336	−	0.134994i
$333$		0			0
$334$	0.464277	+	1.57663i	0.0254041	+	0.0862695i
$335$	−2.82743	−	3.14184i	−0.154479	−	0.171657i
$336$		0			0
$337$			7.91137i			0.430960i	0.976508	+	0.215480i	$0.0691315\pi$
$337$			7.91137i			0.430960i	−0.976508	+	0.215480i	$0.930868\pi$
$338$	12.6236	−	3.71732i	0.686634	−	0.202196i
$339$		0			0
$340$	2.38871	−	8.79287i	0.129546	−	0.476860i
$341$		−	0.140046i		−	0.00758394i
$342$		0			0
$343$			17.1377i			0.925347i
$344$	10.1704	−	11.7929i	0.548350	−	0.635829i
$345$		0			0
$346$	−10.0239	+	2.95177i	−0.538887	+	0.158688i
$347$	−25.8465			−1.38751			−0.693756	−	0.720210i	$-0.744046\pi$
$347$	−25.8465			−1.38751			−0.693756	+	0.720210i	$0.744046\pi$
$348$		0			0
$349$		−	13.2897i		−	0.711382i	−0.934604	−	0.355691i	$-0.884246\pi$
$349$		−	13.2897i		−	0.711382i	0.934604	−	0.355691i	$-0.115754\pi$
$350$	9.98334	−	1.82836i	0.533632	−	0.0977301i
$351$		0			0
$352$	0.551493	+	0.0770991i	0.0293947	+	0.00410940i
$353$			28.1761i			1.49966i	0.661629	+	0.749831i	$0.269865\pi$
$353$			28.1761i			1.49966i	−0.661629	+	0.749831i	$0.730135\pi$
$354$		0			0
$355$	−18.4369	−	20.4870i	−0.978527	−	1.08734i
$356$	22.4474	−	14.4756i	1.18971	−	0.767204i
$357$		0			0
$358$	7.36328	+	25.0049i	0.389162	+	1.32155i
$359$	−27.5477			−1.45391			−0.726956	−	0.686684i	$-0.759066\pi$
$359$	−27.5477			−1.45391			−0.726956	+	0.686684i	$0.759066\pi$
$360$		0			0
$361$	18.0009			0.947415
$362$	−1.89788	−	6.44500i	−0.0997505	−	0.338742i
$363$		0			0
$364$	2.99048	+	4.63735i	0.156744	+	0.243063i
$365$	−9.35715	+	8.42077i	−0.489776	+	0.440763i
$366$		0			0
$367$		−	15.8778i		−	0.828815i	−0.910091	−	0.414407i	$-0.863989\pi$
$367$		−	15.8778i		−	0.828815i	0.910091	−	0.414407i	$-0.136011\pi$
$368$	−15.6810	−	7.10226i	−0.817430	−	0.370231i
$369$		0			0
$370$	22.2817	+	13.7114i	1.15837	+	0.712821i
$371$			7.08626i			0.367900i
$372$		0			0
$373$	4.85063			0.251156			0.125578	−	0.992084i	$-0.459921\pi$
$373$	4.85063			0.251156			0.125578	+	0.992084i	$0.459921\pi$
$374$	−0.272084	+	0.0801216i	−0.0140691	+	0.00414299i
$375$		0			0
$376$	19.2924	+	16.6381i	0.994929	+	0.858044i
$377$			6.85605i			0.353105i
$378$		0			0
$379$		−	16.0191i		−	0.822846i	−0.911445	−	0.411423i	$-0.865032\pi$
$379$		−	16.0191i		−	0.822846i	0.911445	−	0.411423i	$-0.134968\pi$
$380$	1.17191	−	4.31381i	0.0601176	−	0.221294i
$381$		0			0
$382$	−17.8579	+	5.25867i	−0.913688	+	0.269057i
$383$		−	6.83627i		−	0.349317i	−0.984629	−	0.174658i	$-0.944118\pi$
$383$		−	6.83627i		−	0.349317i	0.984629	−	0.174658i	$-0.0558821\pi$
$384$		0			0
$385$	−0.211345	−	0.234846i	−0.0107711	−	0.0119689i
$386$	3.39579	+	11.5317i	0.172841	+	0.586948i
$387$		0			0
$388$	15.9829	+	24.7848i	0.811409	+	1.25826i
$389$		−	15.1004i		−	0.765623i	−0.923827	−	0.382811i	$-0.874956\pi$
$389$		−	15.1004i		−	0.765623i	0.923827	−	0.382811i	$-0.125044\pi$
$390$		0			0
$391$	8.76820			0.443427
$392$	−9.12490	+	10.5806i	−0.460877	+	0.534401i
$393$		0			0
$394$	−6.05663	+	1.78352i	−0.305129	+	0.0898524i
$395$	−3.72175	−	4.13560i	−0.187261	−	0.208085i
$396$		0			0
$397$	25.1307			1.26127			0.630636	−	0.776079i	$-0.282794\pi$
$397$	25.1307			1.26127			0.630636	+	0.776079i	$0.282794\pi$
$398$	26.1776	−	7.70860i	1.31216	−	0.386397i
$399$		0			0
$400$	17.2508	+	10.1197i	0.862542	+	0.505986i
$401$	−27.2424			−1.36042			−0.680211	−	0.733016i	$-0.738112\pi$
$401$	−27.2424			−1.36042			−0.680211	+	0.733016i	$0.738112\pi$
$402$		0			0
$403$	2.73463			0.136222
$404$	14.7648	+	22.8958i	0.734574	+	1.13911i
$405$		0			0
$406$	6.94531	−	2.04521i	0.344690	−	0.101502i
$407$		−	0.814417i		−	0.0403691i
$408$		0			0
$409$	−2.07322			−0.102514			−0.0512571	−	0.998685i	$-0.516323\pi$
$409$	−2.07322			−0.102514			−0.0512571	+	0.998685i	$0.516323\pi$
$410$	13.7881	+	8.48470i	0.680944	+	0.419030i
$411$		0			0
$412$	−11.7558	−	18.2299i	−0.579169	−	0.898121i
$413$	−9.00311			−0.443014
$414$		0			0
$415$	−3.39439	−	3.77184i	−0.166624	−	0.185152i
$416$	−1.50548	+	10.7688i	−0.0738124	+	0.527983i
$417$		0			0
$418$	−0.133485	+	0.0393079i	−0.00652898	+	0.00192261i
$419$		−	28.2449i		−	1.37985i	−0.723880	−	0.689926i	$-0.757643\pi$
$419$		−	28.2449i		−	1.37985i	0.723880	−	0.689926i	$-0.242357\pi$
$420$		0			0
$421$		−	4.94229i		−	0.240873i	−0.992721	−	0.120436i	$-0.961571\pi$
$421$		−	4.94229i		−	0.240873i	0.992721	−	0.120436i	$-0.0384294\pi$
$422$	−8.98294	−	30.5051i	−0.437283	−	1.48496i
$423$		0			0
$424$	−9.11972	+	10.5746i	−0.442893	+	0.513548i
$425$	−10.1307	−	1.07016i	−0.491410	−	0.0519102i
$426$		0			0
$427$	18.4369			0.892222
$428$	20.9959	−	13.5396i	1.01487	−	0.654459i
$429$		0			0
$430$	−14.8282	−	9.12475i	−0.715078	−	0.440034i
$431$	5.01109			0.241376			0.120688	−	0.992691i	$-0.461490\pi$
$431$	5.01109			0.241376			0.120688	+	0.992691i	$0.461490\pi$
$432$		0			0
$433$		−	7.79967i		−	0.374828i	−0.982281	−	0.187414i	$-0.939989\pi$
$433$		−	7.79967i		−	0.374828i	0.982281	−	0.187414i	$-0.0600106\pi$
$434$	−0.815760	−	2.77023i	−0.0391577	−	0.132975i
$435$		0			0
$436$	−17.9645	−	27.8577i	−0.860344	−	1.33414i
$437$	4.30171			0.205779
$438$		0			0
$439$	34.9376			1.66748			0.833739	−	0.552158i	$-0.186196\pi$
$439$	34.9376			1.66748			0.833739	+	0.552158i	$0.186196\pi$
$440$	−0.0131460	−	0.622445i	−0.000626711	−	0.0296739i
$441$		0			0
$442$	−1.56450	−	5.31288i	−0.0744158	−	0.252708i
$443$	23.6112			1.12180			0.560900	−	0.827883i	$-0.310455\pi$
$443$	23.6112			1.12180			0.560900	+	0.827883i	$0.310455\pi$
$444$		0			0
$445$	−19.9763	−	22.1976i	−0.946965	−	1.05227i
$446$	11.0614	+	37.5634i	0.523774	+	1.77868i
$447$		0			0
$448$	11.3581	−	1.68732i	0.536618	−	0.0797185i
$449$	9.39141			0.443208			0.221604	−	0.975137i	$-0.428871\pi$
$449$	9.39141			0.443208			0.221604	+	0.975137i	$0.428871\pi$
$450$		0			0
$451$		−	0.503967i		−	0.0237309i
$452$	−9.91906	−	15.3816i	−0.466553	−	0.723488i
$453$		0			0
$454$	11.1954	−	3.29675i	0.525426	−	0.154724i
$455$	4.58575	−	4.12685i	0.214983	−	0.193470i
$456$		0			0
$457$			31.0457i			1.45226i	0.687560	+	0.726128i	$0.258682\pi$
$457$			31.0457i			1.45226i	−0.687560	+	0.726128i	$0.741318\pi$
$458$	−2.58893	−	8.79171i	−0.120973	−	0.410810i
$459$		0			0
$460$	−5.04566	+	18.5732i	−0.235255	+	0.865978i
$461$		−	0.867775i		−	0.0404163i	−0.999796	−	0.0202081i	$-0.993567\pi$
$461$		−	0.867775i		−	0.0404163i	0.999796	−	0.0202081i	$-0.00643289\pi$
$462$		0			0
$463$			31.0297i			1.44207i	0.692898	+	0.721035i	$0.256333\pi$
$463$			31.0297i			1.44207i	−0.692898	+	0.721035i	$0.743667\pi$
$464$	12.9964	+	5.88631i	0.603340	+	0.273265i
$465$		0			0
$466$	3.30751	+	11.2319i	0.153217	+	0.520309i
$467$	27.7060			1.28208			0.641040	−	0.767507i	$-0.278503\pi$
$467$	27.7060			1.28208			0.641040	+	0.767507i	$0.278503\pi$
$468$		0			0
$469$			2.71317i			0.125283i
$470$	14.9275	−	24.2579i	0.688555	−	1.11893i
$471$		0			0
$472$	−13.4351	−	11.5866i	−0.618398	−	0.533317i
$473$			0.541984i			0.0249204i
$474$		0			0
$475$	−4.97014	−	0.525022i	−0.228046	−	0.0240897i
$476$	−4.91534	+	3.16974i	−0.225294	+	0.145285i
$477$		0			0
$478$	35.6949	−	10.5112i	1.63264	−	0.480771i
$479$	−30.8989			−1.41181			−0.705903	−	0.708309i	$-0.749459\pi$
$479$	−30.8989			−1.41181			−0.705903	+	0.708309i	$0.749459\pi$
$480$		0			0
$481$	15.9028			0.725105
$482$	33.6472	−	9.90821i	1.53259	−	0.451307i
$483$		0			0
$484$	18.4727	−	11.9124i	0.839669	−	0.541475i
$485$	24.5090	−	22.0563i	1.11290	−	1.00153i
$486$		0			0
$487$			21.5162i			0.974991i	0.873125	+	0.487496i	$0.162090\pi$
$487$			21.5162i			0.974991i	−0.873125	+	0.487496i	$0.837910\pi$
$488$	27.5127	+	23.7274i	1.24544	+	1.07409i
$489$		0			0
$490$	13.3039	+	8.18676i	0.601008	+	0.369840i
$491$			9.74298i			0.439695i	0.975534	+	0.219847i	$0.0705559\pi$
$491$			9.74298i			0.439695i	−0.975534	+	0.219847i	$0.929444\pi$
$492$		0			0
$493$	−7.26704			−0.327291
$494$	−0.767550	−	2.60651i	−0.0345337	−	0.117273i
$495$		0			0
$496$	2.34784	−	5.18377i	0.105421	−	0.232758i
$497$			17.6918i			0.793586i
$498$		0			0
$499$		−	6.91181i		−	0.309415i	−0.987960	−	0.154708i	$-0.950556\pi$
$499$		−	6.91181i		−	0.309415i	0.987960	−	0.154708i	$-0.0494435\pi$
$500$	8.09655	−	20.8434i	0.362089	−	0.932144i
$501$		0			0
$502$	−0.110881	−	0.376541i	−0.00494888	−	0.0168059i
$503$		−	15.3213i		−	0.683142i	−0.939856	−	0.341571i	$-0.889041\pi$
$503$		−	15.3213i		−	0.683142i	0.939856	−	0.341571i	$-0.110959\pi$
$504$		0			0
$505$	22.6411	−	20.3753i	1.00751	−	0.906690i
$506$	0.574722	−	0.169241i	0.0255495	−	0.00752366i
$507$		0			0
$508$	11.8848	+	18.4299i	0.527304	+	0.817695i
$509$			28.8669i			1.27950i	0.768582	+	0.639752i	$0.220963\pi$
$509$			28.8669i			1.27950i	−0.768582	+	0.639752i	$0.779037\pi$
$510$		0			0
$511$	8.08048			0.357459
$512$	19.1208	+	12.0994i	0.845027	+	0.534723i
$513$		0			0
$514$	−5.68740	−	19.3138i	−0.250860	−	0.851894i
$515$	−18.0270	+	16.2230i	−0.794365	+	0.714872i
$516$		0			0
$517$	−0.886651			−0.0389949
$518$	−4.74392	−	16.1098i	−0.208436	−	0.707824i
$519$		0			0
$520$	12.1542	−	0.256696i	0.532999	−	0.0112569i
$521$	−0.525190			−0.0230090			−0.0115045	−	0.999934i	$-0.503662\pi$
$521$	−0.525190			−0.0230090			−0.0115045	+	0.999934i	$0.503662\pi$
$522$		0			0
$523$	11.1631			0.488127			0.244064	−	0.969759i	$-0.421519\pi$
$523$	11.1631			0.488127			0.244064	+	0.969759i	$0.421519\pi$
$524$	24.0513	+	37.2965i	1.05068	+	1.62930i
$525$		0			0
$526$	−6.84534	−	23.2460i	−0.298471	−	1.01357i
$527$			2.89856i			0.126263i
$528$		0			0
$529$	4.47895			0.194737
$530$	13.2963	+	8.18211i	0.577555	+	0.355408i
$531$		0			0
$532$	−2.41148	+	1.55508i	−0.104551	+	0.0674214i
$533$	9.84076			0.426251
$534$		0			0
$535$	−18.6846	−	20.7623i	−0.807804	−	0.897631i
$536$	−3.49174	+	4.04878i	−0.150820	+	0.174881i
$537$		0			0
$538$	5.68940	+	19.3206i	0.245287	+	0.832969i
$539$		−	0.486270i		−	0.0209451i
$540$		0			0
$541$		−	4.30602i		−	0.185130i	−0.995707	−	0.0925651i	$-0.970493\pi$
$541$		−	4.30602i		−	0.185130i	0.995707	−	0.0925651i	$-0.0295066\pi$
$542$	21.8655	−	6.43881i	0.939203	−	0.276571i
$543$		0			0
$544$	−11.4143	−	1.59573i	−0.489384	−	0.0684163i
$545$	−27.5477	+	24.7910i	−1.18001	+	1.06193i
$546$		0			0
$547$	40.0149			1.71091			0.855456	−	0.517875i	$-0.173277\pi$
$547$	40.0149			1.71091			0.855456	+	0.517875i	$0.173277\pi$
$548$	−11.6900	−	18.1278i	−0.499372	−	0.774380i
$549$		0			0
$550$	−0.684683	+	0.125394i	−0.0291950	+	0.00534681i
$551$	−3.56523			−0.151884
$552$		0			0
$553$			3.57135i			0.151869i
$554$	−21.2048	+	6.24427i	−0.900907	+	0.265293i
$555$		0			0
$556$	16.8811	+	26.1776i	0.715918	+	1.11018i
$557$	−19.0641			−0.807771			−0.403886	−	0.914809i	$-0.632341\pi$
$557$	−19.0641			−0.807771			−0.403886	+	0.914809i	$0.632341\pi$
$558$		0			0
$559$	−10.5831			−0.447618
$560$	−3.88574	−	12.2359i	−0.164202	−	0.517061i
$561$		0			0
$562$	−7.66753	+	2.25789i	−0.323435	+	0.0952432i
$563$	−6.40993			−0.270147			−0.135073	−	0.990836i	$-0.543127\pi$
$563$	−6.40993			−0.270147			−0.135073	+	0.990836i	$0.543127\pi$
$564$		0			0
$565$	−15.2104	+	13.6883i	−0.639906	+	0.575870i
$566$	22.4474	−	6.61017i	0.943534	−	0.277846i
$567$		0			0
$568$	−22.7686	+	26.4009i	−0.955349	+	1.10776i
$569$	37.1532			1.55754			0.778771	−	0.627308i	$-0.215843\pi$
$569$	37.1532			1.55754			0.778771	+	0.627308i	$0.215843\pi$
$570$		0			0
$571$		−	28.7752i		−	1.20421i	−0.798418	−	0.602103i	$-0.794330\pi$
$571$		−	28.7752i		−	1.20421i	0.798418	−	0.602103i	$-0.205670\pi$
$572$	−0.205094	−	0.318041i	−0.00857543	−	0.0132980i
$573$		0			0
$574$	−2.93557	−	9.96887i	−0.122528	−	0.416093i
$575$	21.3990	+	2.26049i	0.892399	+	0.0942689i
$576$		0			0
$577$		−	20.0173i		−	0.833332i	−0.909060	−	0.416666i	$-0.863198\pi$
$577$		−	20.0173i		−	0.833332i	0.909060	−	0.416666i	$-0.136802\pi$
$578$	−17.4311	+	5.13301i	−0.725040	+	0.213505i
$579$		0			0
$580$	4.18182	−	15.3933i	0.173641	−	0.639173i
$581$			3.25722i			0.135132i
$582$		0			0
$583$		−	0.485994i		−	0.0201278i
$584$	12.0582	+	10.3992i	0.498973	+	0.430323i
$585$		0			0
$586$	27.4775	−	8.09141i	1.13509	−	0.334253i
$587$	−7.91407			−0.326649			−0.163324	−	0.986572i	$-0.552222\pi$
$587$	−7.91407			−0.326649			−0.163324	+	0.986572i	$0.552222\pi$
$588$		0			0
$589$			1.42204i			0.0585942i
$590$	−10.3954	+	16.8930i	−0.427971	+	0.695474i
$591$		0			0
$592$	13.6534	−	30.1454i	0.561153	−	1.23897i
$593$			14.4728i			0.594325i	0.954827	+	0.297163i	$0.0960404\pi$
$593$			14.4728i			0.594325i	−0.954827	+	0.297163i	$0.903960\pi$
$594$		0			0
$595$	4.37423	+	4.86064i	0.179326	+	0.199267i
$596$	4.52561	+	7.01789i	0.185376	+	0.287464i
$597$		0			0
$598$	3.30469	+	11.2224i	0.135139	+	0.458917i
$599$	−20.6597			−0.844133			−0.422067	−	0.906565i	$-0.638695\pi$
$599$	−20.6597			−0.844133			−0.422067	+	0.906565i	$0.638695\pi$
$600$		0			0
$601$	−32.3742			−1.32057			−0.660286	−	0.751014i	$-0.729565\pi$
$601$	−32.3742			−1.32057			−0.660286	+	0.751014i	$0.729565\pi$
$602$	3.15702	+	10.7209i	0.128670	+	0.436950i
$603$		0			0
$604$	−5.35275	+	3.45181i	−0.217800	+	0.140452i
$605$	−16.4391	−	18.2672i	−0.668346	−	0.742666i
$606$		0			0
$607$			41.1110i			1.66865i	0.551276	+	0.834323i	$0.314141\pi$
$607$			41.1110i			1.66865i	−0.551276	+	0.834323i	$0.685859\pi$
$608$	−5.59990	−	0.782870i	−0.227106	−	0.0317496i
$609$		0			0
$610$	21.2880	−	34.5940i	0.861926	−	1.40067i
$611$		−	17.3133i		−	0.700420i
$612$		0			0
$613$	9.54708			0.385603			0.192801	−	0.981238i	$-0.438243\pi$
$613$	9.54708			0.385603			0.192801	+	0.981238i	$0.438243\pi$
$614$	−7.47187	+	2.20027i	−0.301540	+	0.0887956i
$615$		0			0
$616$	−0.261000	+	0.302638i	−0.0105160	+	0.0121936i
$617$		−	26.7796i		−	1.07811i	−0.842272	−	0.539053i	$-0.818782\pi$
$617$		−	26.7796i		−	1.07811i	0.842272	−	0.539053i	$-0.181218\pi$
$618$		0			0
$619$			19.1724i			0.770602i	0.922791	+	0.385301i	$0.125902\pi$
$619$			19.1724i			0.770602i	−0.922791	+	0.385301i	$0.874098\pi$
$620$	−6.13984	−	1.66798i	−0.246582	−	0.0669875i
$621$		0			0
$622$	−11.6348	+	3.42614i	−0.466512	+	0.137376i
$623$			19.1690i			0.767990i
$624$		0			0
$625$	−24.4482	−	5.22348i	−0.977929	−	0.208939i
$626$	−3.92816	−	13.3396i	−0.157001	−	0.533157i
$627$		0			0
$628$	34.3462	−	22.1487i	1.37056	−	0.883831i
$629$			16.8561i			0.672095i
$630$		0			0
$631$	−9.42121			−0.375052			−0.187526	−	0.982260i	$-0.560047\pi$
$631$	−9.42121			−0.375052			−0.187526	+	0.982260i	$0.560047\pi$
$632$	−4.59617	+	5.32941i	−0.182826	+	0.211992i
$633$		0			0
$634$	10.0239	−	2.95177i	0.398099	−	0.117230i
$635$	18.2248	−	16.4010i	0.723230	−	0.650856i
$636$		0			0
$637$	9.49520			0.376214
$638$	−0.476327	+	0.140266i	−0.0188580	+	0.00555317i
$639$		0			0
$640$	9.94851	−	23.2600i	0.393249	−	0.919432i
$641$	−36.5224			−1.44255			−0.721275	−	0.692649i	$-0.756443\pi$
$641$	−36.5224			−1.44255			−0.721275	+	0.692649i	$0.756443\pi$
$642$		0			0
$643$	11.6563			0.459681			0.229840	−	0.973228i	$-0.426180\pi$
$643$	11.6563			0.459681			0.229840	+	0.973228i	$0.426180\pi$
$644$	10.3827	−	6.69543i	0.409134	−	0.263837i
$645$		0			0
$646$	2.76276	−	0.813560i	0.108699	−	0.0320091i
$647$			40.2063i			1.58067i	0.612673	+	0.790337i	$0.290094\pi$
$647$			40.2063i			1.58067i	−0.612673	+	0.790337i	$0.709906\pi$
$648$		0			0
$649$	0.617456			0.0242373
$650$	−2.44851	−	13.3695i	−0.0960386	−	0.524396i
$651$		0			0
$652$	−32.8543	+	21.1866i	−1.28667	+	0.829733i
$653$	−8.69902			−0.340419			−0.170209	−	0.985408i	$-0.554444\pi$
$653$	−8.69902			−0.340419			−0.170209	+	0.985408i	$0.554444\pi$
$654$		0			0
$655$	36.8815	−	33.1907i	1.44108	−	1.29687i
$656$	8.44885	−	18.6542i	0.329872	−	0.728323i
$657$		0			0
$658$	−17.5387	+	5.16468i	−0.683728	+	0.201340i
$659$			22.2085i			0.865122i	0.901605	+	0.432561i	$0.142390\pi$
$659$			22.2085i			0.865122i	−0.901605	+	0.432561i	$0.857610\pi$
$660$		0			0
$661$			32.1865i			1.25191i	0.779859	+	0.625956i	$0.215291\pi$
$661$			32.1865i			1.25191i	−0.779859	+	0.625956i	$0.784709\pi$
$662$	−2.25616	−	7.66168i	−0.0876883	−	0.297780i
$663$		0			0
$664$	−4.19190	+	4.86064i	−0.162677	+	0.188629i
$665$	2.14601	+	2.38465i	0.0832187	+	0.0924726i
$666$		0			0
$667$	15.3501			0.594360
$668$	−1.25969	−	1.95341i	−0.0487390	−	0.0755799i
$669$		0			0
$670$	5.09087	+	3.13275i	0.196677	+	0.121029i
$671$	−1.26445			−0.0488134
$672$		0			0
$673$			39.8887i			1.53760i	0.639492	+	0.768798i	$0.279145\pi$
$673$			39.8887i			1.53760i	−0.639492	+	0.768798i	$0.720855\pi$
$674$	−3.16050	−	10.7327i	−0.121738	−	0.413408i
$675$		0			0
$676$	−15.6404	+	10.0860i	−0.601553	+	0.387922i
$677$	−4.46451			−0.171585			−0.0857925	−	0.996313i	$-0.527342\pi$
$677$	−4.46451			−0.171585			−0.0857925	+	0.996313i	$0.527342\pi$
$678$		0			0
$679$	−21.1650			−0.812240
$680$	0.272084	+	12.8828i	0.0104339	+	0.494034i
$681$		0			0
$682$	0.0559469	+	0.189989i	0.00214232	+	0.00727507i
$683$	−42.7166			−1.63450			−0.817252	−	0.576281i	$-0.804503\pi$
$683$	−42.7166			−1.63450			−0.817252	+	0.576281i	$0.804503\pi$
$684$		0			0
$685$	−17.9260	+	16.1322i	−0.684919	+	0.616378i
$686$	−6.84629	−	23.2492i	−0.261393	−	0.887660i
$687$		0			0
$688$	−9.08619	+	20.0614i	−0.346408	+	0.764832i
$689$	9.48981			0.361533
$690$		0			0
$691$		−	14.4881i		−	0.551153i	−0.961279	−	0.275577i	$-0.911131\pi$
$691$		−	14.4881i		−	0.551153i	0.961279	−	0.275577i	$-0.0888687\pi$
$692$	12.4194	−	8.00884i	0.472113	−	0.304450i
$693$		0			0
$694$	35.0638	−	10.3254i	1.33100	−	0.391946i
$695$	25.8863	−	23.2959i	0.981925	−	0.883662i
$696$		0			0
$697$			10.4307i			0.395090i
$698$	5.30908	+	18.0291i	0.200952	+	0.682410i
$699$		0			0
$700$	−12.8132	+	6.46861i	−0.484292	+	0.244491i
$701$		−	27.2562i		−	1.02945i	−0.857355	−	0.514726i	$-0.827894\pi$
$701$		−	27.2562i		−	1.02945i	0.857355	−	0.514726i	$-0.172106\pi$
$702$		0			0
$703$			8.26964i			0.311895i
$704$	−0.778965	+	0.115721i	−0.0293583	+	0.00436139i
$705$		0			0
$706$	−11.2560	−	38.2242i	−0.423626	−	1.43859i
$707$	−19.5520			−0.735327
$708$		0			0
$709$			18.4360i			0.692379i	0.938165	+	0.346190i	$0.112525\pi$
$709$			18.4360i			0.692379i	−0.938165	+	0.346190i	$0.887475\pi$
$710$	33.1961	+	20.4277i	1.24583	+	0.766639i
$711$		0			0
$712$	−24.6697	+	28.6053i	−0.924535	+	1.07203i
$713$		−	6.12261i		−	0.229294i
$714$		0			0
$715$	−0.314502	+	0.283030i	−0.0117617	+	0.0105847i
$716$	−19.9783	−	30.9805i	−0.746624	−	1.15780i
$717$		0			0
$718$	37.3717	−	11.0050i	1.39470	−	0.410702i
$719$	−20.2329			−0.754561			−0.377280	−	0.926099i	$-0.623141\pi$
$719$	−20.2329			−0.754561			−0.377280	+	0.926099i	$0.623141\pi$
$720$		0			0
$721$	15.5674			0.579762
$722$	−24.4203	+	7.19114i	−0.908830	+	0.267626i
$723$		0			0
$724$	5.14940	+	7.98521i	0.191376	+	0.296768i
$725$	−17.7354	−	1.87348i	−0.658675	−	0.0695793i
$726$		0			0
$727$			3.89252i			0.144366i	0.997391	+	0.0721828i	$0.0229965\pi$
$727$			3.89252i			0.144366i	−0.997391	+	0.0721828i	$0.977003\pi$
$728$	−5.90950	−	5.09645i	−0.219021	−	0.188887i
$729$		0			0
$730$	9.33007	−	15.1618i	0.345321	−	0.561164i
$731$		−	11.2175i		−	0.414894i
$732$		0			0
$733$	−35.3194			−1.30455			−0.652276	−	0.757982i	$-0.726186\pi$
$733$	−35.3194			−1.30455			−0.652276	+	0.757982i	$0.726186\pi$
$734$	6.34299	+	21.5401i	0.234124	+	0.795060i
$735$		0			0
$736$	24.1104	+	3.37065i	0.888722	+	0.124244i
$737$		−	0.186076i		−	0.00685421i
$738$		0			0
$739$		−	38.5052i		−	1.41644i	−0.705993	−	0.708219i	$-0.749499\pi$
$739$		−	38.5052i		−	1.41644i	0.705993	−	0.708219i	$-0.250501\pi$
$740$	−35.7052	−	9.69983i	−1.31255	−	0.356573i
$741$		0			0
$742$	−2.83088	−	9.61334i	−0.103925	−	0.352917i
$743$			19.4158i			0.712295i	0.934430	+	0.356148i	$0.115910\pi$
$743$			19.4158i			0.712295i	−0.934430	+	0.356148i	$0.884090\pi$
$744$		0			0
$745$	6.93980	−	6.24532i	0.254255	−	0.228811i
$746$	−6.58044	+	1.93777i	−0.240927	+	0.0709467i
$747$		0			0
$748$	0.337106	−	0.217389i	0.0123258	−	0.00794851i
$749$			17.9295i			0.655130i
$750$		0			0
$751$	36.4832			1.33129			0.665646	−	0.746267i	$-0.268156\pi$
$751$	36.4832			1.33129			0.665646	+	0.746267i	$0.268156\pi$
$752$	−32.8191	−	14.8644i	−1.19679	−	0.542050i
$753$		0			0
$754$	−2.73891	−	9.30104i	−0.0997453	−	0.338724i
$755$	4.76349	+	5.29319i	0.173361	+	0.192639i
$756$		0			0
$757$	−10.9870			−0.399329			−0.199664	−	0.979864i	$-0.563985\pi$
$757$	−10.9870			−0.399329			−0.199664	+	0.979864i	$0.563985\pi$
$758$	6.39944	+	21.7318i	0.232438	+	0.789334i
$759$		0			0
$760$	0.133485	+	6.32035i	0.00484202	+	0.229263i
$761$	12.1991			0.442216			0.221108	−	0.975249i	$-0.429033\pi$
$761$	12.1991			0.442216			0.221108	+	0.975249i	$0.429033\pi$
$762$		0			0
$763$	23.7892			0.861225
$764$	22.1255	−	14.2680i	0.800472	−	0.516198i
$765$		0			0
$766$	2.73101	+	9.27419i	0.0986753	+	0.335090i
$767$			12.0568i			0.435347i
$768$		0			0
$769$	−13.2424			−0.477531			−0.238766	−	0.971077i	$-0.576743\pi$
$769$	−13.2424			−0.477531			−0.238766	+	0.971077i	$0.576743\pi$
$770$	0.380532	+	0.234167i	0.0137134	+	0.00843878i
$771$		0			0
$772$	−9.21356	−	14.2875i	−0.331603	−	0.514220i
$773$	6.66412			0.239692			0.119846	−	0.992793i	$-0.461760\pi$
$773$	6.66412			0.239692			0.119846	+	0.992793i	$0.461760\pi$
$774$		0			0
$775$	−0.747264	+	7.07399i	−0.0268425	+	0.254105i
$776$	−31.5839	−	27.2385i	−1.13380	−	0.977805i
$777$		0			0
$778$	6.03244	+	20.4855i	0.216274	+	0.734441i
$779$			5.11732i			0.183347i
$780$		0			0
$781$		−	1.21335i		−	0.0434170i
$782$	−11.8951	+	3.50279i	−0.425368	+	0.125260i
$783$		0			0
$784$	8.15216	−	17.9991i	0.291149	−	0.642826i
$785$	−30.5652	−	33.9640i	−1.09092	−	1.21223i
$786$		0			0
$787$	−0.163075			−0.00581301			−0.00290650	−	0.999996i	$-0.500925\pi$
$787$	−0.163075			−0.00581301			−0.00290650	+	0.999996i	$0.500925\pi$
$788$	7.50403	−	4.83910i	0.267320	−	0.172386i
$789$		0			0
$790$	6.70111	+	4.12363i	0.238415	+	0.146712i
$791$	13.1351			0.467031
$792$		0			0
$793$		−	24.6903i		−	0.876780i
$794$	−34.0927	+	10.0394i	−1.20990	+	0.356285i
$795$		0			0
$796$	−32.4334	+	20.9152i	−1.14957	+	0.741321i
$797$	46.0750			1.63206			0.816031	−	0.578009i	$-0.196170\pi$
$797$	46.0750			1.63206			0.816031	+	0.578009i	$0.196170\pi$
$798$		0			0
$799$	18.3511			0.649216
$800$	−27.4455	−	6.83708i	−0.970344	−	0.241727i
$801$		0			0
$802$	36.9575	−	10.8830i	1.30502	−	0.384293i
$803$	−0.554180			−0.0195566
$804$		0			0
$805$	−9.23967	−	10.2671i	−0.325656	−	0.361868i
$806$	−3.70985	+	1.09245i	−0.130674	+	0.0384800i
$807$		0			0
$808$	−29.1767	−	25.1625i	−1.02643	−	0.885214i
$809$	48.0231			1.68840			0.844201	−	0.536026i	$-0.180075\pi$
$809$	48.0231			1.68840			0.844201	+	0.536026i	$0.180075\pi$
$810$		0			0
$811$		−	19.0427i		−	0.668680i	−0.942453	−	0.334340i	$-0.891487\pi$
$811$		−	19.0427i		−	0.668680i	0.942453	−	0.334340i	$-0.108513\pi$
$812$	−8.60508	+	5.54913i	−0.301979	+	0.194736i
$813$		0			0
$814$	0.325350	+	1.10485i	0.0114035	+	0.0387250i
$815$	29.2375	+	32.4887i	1.02414	+	1.13803i
$816$		0			0
$817$		−	5.50334i		−	0.192538i
$818$	2.81257	−	0.828228i	0.0983392	−	0.0289583i
$819$		0			0
$820$	−22.0947	−	6.00233i	−0.771579	−	0.209610i
$821$		−	26.1910i		−	0.914073i	−0.889448	−	0.457037i	$-0.848911\pi$
$821$		−	26.1910i		−	0.914073i	0.889448	−	0.457037i	$-0.151089\pi$
$822$		0			0
$823$		−	11.9142i		−	0.415302i	−0.978203	−	0.207651i	$-0.933418\pi$
$823$		−	11.9142i		−	0.415302i	0.978203	−	0.207651i	$-0.0665819\pi$
$824$	23.2308	+	20.0346i	0.809283	+	0.697940i
$825$		0			0
$826$	12.2138	−	3.59664i	0.424972	−	0.125143i
$827$	20.2443			0.703965			0.351982	−	0.936007i	$-0.385508\pi$
$827$	20.2443			0.703965			0.351982	+	0.936007i	$0.385508\pi$
$828$		0			0
$829$			32.5375i			1.13007i	0.825066	+	0.565037i	$0.191138\pi$
$829$			32.5375i			1.13007i	−0.825066	+	0.565037i	$0.808862\pi$
$830$	6.11169	+	3.76093i	0.212140	+	0.130544i
$831$		0			0
$832$	−2.25964	−	15.2105i	−0.0783387	−	0.527330i
$833$			10.0644i			0.348710i
$834$		0			0
$835$	−1.93168	+	1.73837i	−0.0668484	+	0.0601588i
$836$	0.165385	−	0.106652i	0.00571997	−	0.00368862i
$837$		0			0
$838$	11.2835	+	38.3175i	0.389781	+	1.32365i
$839$	−40.6959			−1.40498			−0.702489	−	0.711695i	$-0.747928\pi$
$839$	−40.6959			−1.40498			−0.702489	+	0.711695i	$0.747928\pi$
$840$		0			0
$841$	16.2779			0.561307
$842$	1.97439	+	6.70480i	0.0680419	+	0.231063i
$843$		0			0
$844$	24.3728	+	37.7951i	0.838947	+	1.30096i
$845$	13.9186	+	15.4663i	0.478814	+	0.532058i
$846$		0			0
$847$			15.7748i			0.542029i
$848$	8.14753	−	17.9889i	0.279787	−	0.617741i
$849$		0			0
$850$	14.1709	−	2.59529i	0.486060	−	0.0890176i
$851$		−	35.6050i		−	1.22052i
$852$		0			0
$853$	−18.5346			−0.634611			−0.317306	−	0.948323i	$-0.602778\pi$
$853$	−18.5346			−0.634611			−0.317306	+	0.948323i	$0.602778\pi$
$854$	−25.0118	+	7.36530i	−0.855885	+	0.252036i
$855$		0			0
$856$	−23.0745	+	26.7556i	−0.788670	+	0.914488i
$857$		−	46.9004i		−	1.60209i	−0.598607	−	0.801043i	$-0.704279\pi$
$857$		−	46.9004i		−	1.60209i	0.598607	−	0.801043i	$-0.295721\pi$
$858$		0			0
$859$		−	32.2074i		−	1.09890i	−0.835526	−	0.549452i	$-0.814837\pi$
$859$		−	32.2074i		−	1.09890i	0.835526	−	0.549452i	$-0.185163\pi$
$860$	23.7614	+	6.45511i	0.810256	+	0.220118i
$861$		0			0
$862$	−6.79813	+	2.00187i	−0.231545	+	0.0681840i
$863$		−	23.5848i		−	0.802836i	−0.915895	−	0.401418i	$-0.868517\pi$
$863$		−	23.5848i		−	0.802836i	0.915895	−	0.401418i	$-0.131483\pi$
$864$		0			0
$865$	−11.0522	−	12.2812i	−0.375785	−	0.417572i
$866$	3.11588	+	10.5812i	0.105882	+	0.359563i
$867$		0			0
$868$	2.21335	+	3.43226i	0.0751259	+	0.116498i
$869$		−	0.244932i		−	0.00830875i
$870$		0			0
$871$	3.63344			0.123114
$872$	35.4998	+	30.6156i	1.20217	+	1.03678i
$873$		0			0
$874$	−5.83577	+	1.71848i	−0.197398	+	0.0581285i
$875$	9.42230	+	12.9902i	0.318532	+	0.439149i
$876$		0			0
$877$	6.16767			0.208267			0.104134	−	0.994563i	$-0.466793\pi$
$877$	6.16767			0.208267			0.104134	+	0.994563i	$0.466793\pi$
$878$	−47.3969	+	13.9571i	−1.59957	+	0.471030i
$879$		0			0
$880$	0.266494	+	0.839168i	0.00898350	+	0.0282884i
$881$	−48.3515			−1.62900			−0.814502	−	0.580161i	$-0.802990\pi$
$881$	−48.3515			−1.62900			−0.814502	+	0.580161i	$0.802990\pi$
$882$		0			0
$883$	7.17454			0.241443			0.120721	−	0.992686i	$-0.461479\pi$
$883$	7.17454			0.241443			0.120721	+	0.992686i	$0.461479\pi$
$884$	4.24486	+	6.58254i	0.142770	+	0.221395i
$885$		0			0
$886$	−32.0313	+	9.43238i	−1.07611	+	0.316887i
$887$		−	33.8797i		−	1.13757i	−0.822486	−	0.568785i	$-0.807414\pi$
$887$		−	33.8797i		−	1.13757i	0.822486	−	0.568785i	$-0.192586\pi$
$888$		0			0
$889$	−15.7383			−0.527845
$890$	35.9678	+	22.1334i	1.20564	+	0.741912i
$891$		0			0
$892$	−30.0122	−	46.5402i	−1.00488	−	1.55828i
$893$	9.00311			0.301278
$894$		0			0
$895$	−30.6358	+	27.5700i	−1.02404	+	0.921564i
$896$	−14.7345	+	6.82646i	−0.492244	+	0.228056i
$897$		0			0
$898$	−12.7405	+	3.75176i	−0.425158	+	0.125198i
$899$			5.07439i			0.169240i
$900$		0			0
$901$			10.0587i			0.335103i
$902$	0.201329	+	0.683690i	0.00670352	+	0.0227644i
$903$		0			0
$904$	19.6011	+	16.9043i	0.651923	+	0.562230i
$905$	7.89635	−	7.10615i	0.262484	−	0.236217i
$906$		0			0
$907$	25.4054			0.843573			0.421787	−	0.906695i	$-0.361403\pi$
$907$	25.4054			0.843573			0.421787	+	0.906695i	$0.361403\pi$
$908$	−13.8709	+	8.94486i	−0.460321	+	0.296846i
$909$		0			0
$910$	−4.57248	+	7.43050i	−0.151576	+	0.246319i
$911$	12.7243			0.421574			0.210787	−	0.977532i	$-0.432397\pi$
$911$	12.7243			0.421574			0.210787	+	0.977532i	$0.432397\pi$
$912$		0			0
$913$		−	0.223388i		−	0.00739307i
$914$	−12.4024	−	42.1171i	−0.410234	−	1.39311i
$915$		0			0
$916$	7.02437	+	10.8927i	0.232092	+	0.359906i
$917$	−31.8494			−1.05176
$918$		0			0
$919$	10.1070			0.333399			0.166699	−	0.986008i	$-0.446689\pi$
$919$	10.1070			0.333399			0.166699	+	0.986008i	$0.446689\pi$
$920$	−0.574722	−	27.2123i	−0.0189480	−	0.897164i
$921$		0			0
$922$	0.346666	+	1.17724i	0.0114168	+	0.0387703i
$923$	23.6926			0.779851
$924$		0			0
$925$	−4.34559	+	41.1376i	−0.142882	+	1.35260i
$926$	−12.3960	−	42.0954i	−0.407357	−	1.38334i
$927$		0			0
$928$	−19.9826	−	2.79358i	−0.655960	−	0.0917037i
$929$	28.2928			0.928257			0.464129	−	0.885768i	$-0.346368\pi$
$929$	28.2928			0.928257			0.464129	+	0.885768i	$0.346368\pi$
$930$		0			0
$931$			4.93762i			0.161824i
$932$	−8.97404	−	13.9161i	−0.293955	−	0.455837i
$933$		0			0
$934$	−37.5864	+	11.0682i	−1.22987	+	0.362163i
$935$	−0.299996	−	0.333355i	−0.00981091	−	0.0109019i
$936$		0			0
$937$		−	21.5800i		−	0.704987i	−0.935814	−	0.352493i	$-0.885334\pi$
$937$		−	21.5800i		−	0.704987i	0.935814	−	0.352493i	$-0.114666\pi$
$938$	−1.08388	−	3.68074i	−0.0353899	−	0.120180i
$939$		0			0
$940$	−10.5602	+	38.8721i	−0.344434	+	1.26787i
$941$		−	25.5990i		−	0.834503i	−0.908791	−	0.417252i	$-0.862993\pi$
$941$		−	25.5990i		−	0.834503i	0.908791	−	0.417252i	$-0.137007\pi$
$942$		0			0
$943$		−	22.0327i		−	0.717482i
$944$	22.8549	+	10.3515i	0.743865	+	0.336911i
$945$		0			0
$946$	−0.216516	−	0.735265i	−0.00703955	−	0.0239055i
$947$	−26.0177			−0.845461			−0.422730	−	0.906256i	$-0.638928\pi$
$947$	−26.0177			−0.845461			−0.422730	+	0.906256i	$0.638928\pi$
$948$		0			0
$949$		−	10.8212i		−	0.351272i
$950$	6.95231	−	1.27326i	0.225563	−	0.0413099i
$951$		0			0
$952$	5.40195	−	6.26374i	0.175078	−	0.203009i
$953$		−	58.0689i		−	1.88104i	−0.339745	−	0.940518i	$-0.610341\pi$
$953$		−	58.0689i		−	1.88104i	0.339745	−	0.940518i	$-0.389659\pi$
$954$		0			0
$955$	−19.6898	−	21.8793i	−0.637147	−	0.707997i
$956$	−44.2251	+	28.5193i	−1.43034	+	0.922381i
$957$		0			0
$958$	41.9179	−	12.3437i	1.35431	−	0.398808i
$959$	15.4802			0.499883
$960$		0			0
$961$	−28.9760			−0.934710
$962$	−21.5740	+	6.35297i	−0.695573	+	0.204828i
$963$		0			0
$964$	−41.6881	+	26.8833i	−1.34268	+	0.865853i
$965$	−14.1285	+	12.7147i	−0.454814	+	0.409300i
$966$		0			0
$967$		−	29.7133i		−	0.955516i	−0.878491	−	0.477758i	$-0.841450\pi$
$967$		−	29.7133i		−	0.955516i	0.878491	−	0.477758i	$-0.158550\pi$
$968$	−20.3015	+	23.5403i	−0.652516	+	0.756612i
$969$		0			0
$970$	−24.4381	+	39.7131i	−0.784659	+	1.27511i
$971$			29.8380i			0.957547i	0.877938	+	0.478774i	$0.158919\pi$
$971$			29.8380i			0.957547i	−0.877938	+	0.478774i	$0.841081\pi$
$972$		0			0
$973$	−22.3545			−0.716651
$974$	−8.59546	−	29.1892i	−0.275416	−	0.935283i
$975$		0			0
$976$	−46.8030	−	21.1980i	−1.49813	−	0.678533i
$977$			15.4533i			0.494394i	0.968965	+	0.247197i	$0.0795094\pi$
$977$			15.4533i			0.494394i	−0.968965	+	0.247197i	$0.920491\pi$
$978$		0			0
$979$		−	1.31466i		−	0.0420167i
$980$	−21.3188	−	5.79155i	−0.681004	−	0.185004i
$981$		0			0
$982$	−3.89221	−	13.2175i	−0.124205	−	0.421787i
$983$		−	5.17515i		−	0.165062i	−0.996589	−	0.0825309i	$-0.973700\pi$
$983$		−	5.17515i		−	0.165062i	0.996589	−	0.0825309i	$-0.0263003\pi$
$984$		0			0
$985$	−6.67795	−	7.42053i	−0.212777	−	0.236438i
$986$	9.85858	−	2.90309i	0.313961	−	0.0924533i
$987$		0			0
$988$	2.08254	+	3.22941i	0.0662545	+	0.102741i
$989$			23.6947i			0.753448i
$990$		0			0
$991$	−18.2392			−0.579388			−0.289694	−	0.957119i	$-0.593554\pi$
$991$	−18.2392			−0.579388			−0.289694	+	0.957119i	$0.593554\pi$
$992$	−1.11426	+	7.97033i	−0.0353777	+	0.253058i
$993$		0			0
$994$	−7.06767	−	24.0010i	−0.224173	−	0.761266i
$995$	28.8630	+	32.0725i	0.915018	+	1.01677i
$996$		0			0
$997$	−40.5033			−1.28275			−0.641377	−	0.767226i	$-0.721636\pi$
$997$	−40.5033			−1.28275			−0.641377	+	0.767226i	$0.721636\pi$
$998$	2.76119	+	9.37668i	0.0874038	+	0.296814i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.i.109.4	yes	20
3.2	odd	2	inner	1080.2.d.i.109.17	yes	20
4.3	odd	2		4320.2.d.i.3889.7		20
5.4	even	2		1080.2.d.j.109.17	yes	20
8.3	odd	2		4320.2.d.j.3889.14		20
8.5	even	2		1080.2.d.j.109.18	yes	20
12.11	even	2		4320.2.d.i.3889.14		20
15.14	odd	2		1080.2.d.j.109.4	yes	20
20.19	odd	2		4320.2.d.j.3889.13		20
24.5	odd	2		1080.2.d.j.109.3	yes	20
24.11	even	2		4320.2.d.j.3889.7		20
40.19	odd	2		4320.2.d.i.3889.8		20
40.29	even	2	inner	1080.2.d.i.109.3	✓	20
60.59	even	2		4320.2.d.j.3889.8		20
120.29	odd	2	inner	1080.2.d.i.109.18	yes	20
120.59	even	2		4320.2.d.i.3889.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.i.109.3	✓	20	40.29	even	2	inner
1080.2.d.i.109.4	yes	20	1.1	even	1	trivial
1080.2.d.i.109.17	yes	20	3.2	odd	2	inner
1080.2.d.i.109.18	yes	20	120.29	odd	2	inner
1080.2.d.j.109.3	yes	20	24.5	odd	2
1080.2.d.j.109.4	yes	20	15.14	odd	2
1080.2.d.j.109.17	yes	20	5.4	even	2
1080.2.d.j.109.18	yes	20	8.5	even	2
4320.2.d.i.3889.7		20	4.3	odd	2
4320.2.d.i.3889.8		20	40.19	odd	2
4320.2.d.i.3889.13		20	120.59	even	2
4320.2.d.i.3889.14		20	12.11	even	2
4320.2.d.j.3889.7		20	24.11	even	2
4320.2.d.j.3889.8		20	60.59	even	2
4320.2.d.j.3889.13		20	20.19	odd	2
4320.2.d.j.3889.14		20	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.35662 + 0.399488i) q^{2} +(1.68082 - 1.08390i) q^{4} +(-1.49578 - 1.66212i) q^{5} +1.43534i q^{7} +(-1.84722 + 2.14191i) q^{8} +(2.69320 + 1.65731i) q^{10} -0.0984392i q^{11} +1.92218 q^{13} +(-0.573401 - 1.94721i) q^{14} +(1.65030 - 3.64369i) q^{16} +2.03741i q^{17} +0.999558i q^{19} +(-4.31572 - 1.17243i) q^{20} +(0.0393253 + 0.133544i) q^{22} -4.30361i q^{23} +(-0.525254 + 4.97233i) q^{25} +(-2.60767 + 0.767889i) q^{26} +(1.55577 + 2.41255i) q^{28} +3.56681i q^{29} +1.42267 q^{31} +(-0.783216 + 5.60237i) q^{32} +(-0.813920 - 2.76398i) q^{34} +(2.38570 - 2.14696i) q^{35} +8.27330 q^{37} +(-0.399311 - 1.35602i) q^{38} +(6.32315 - 0.133544i) q^{40} +5.11958 q^{41} -5.50577 q^{43} +(-0.106699 - 0.165458i) q^{44} +(1.71924 + 5.83835i) q^{46} -9.00709i q^{47} +4.93980 q^{49} +(-1.27382 - 6.95539i) q^{50} +(3.23084 - 2.08346i) q^{52} +4.93699 q^{53} +(-0.163617 + 0.147244i) q^{55} +(-3.07437 - 2.65139i) q^{56} +(-1.42490 - 4.83879i) q^{58} +6.27246i q^{59} -12.8449i q^{61} +(-1.93002 + 0.568340i) q^{62} +(-1.17556 - 7.91316i) q^{64} +(-2.87517 - 3.19489i) q^{65} +1.89027 q^{67} +(2.20835 + 3.42451i) q^{68} +(-2.37880 + 3.86566i) q^{70} +12.3259 q^{71} -5.62966i q^{73} +(-11.2237 + 3.30508i) q^{74} +(1.08343 + 1.68008i) q^{76} +0.141294 q^{77} +2.48816 q^{79} +(-8.52474 + 2.70719i) q^{80} +(-6.94531 + 2.04521i) q^{82} +2.26930 q^{83} +(3.38640 - 3.04752i) q^{85} +(7.46923 - 2.19949i) q^{86} +(0.210848 + 0.181839i) q^{88} +13.3550 q^{89} +2.75898i q^{91} +(-4.66470 - 7.23359i) q^{92} +(3.59823 + 12.2192i) q^{94} +(1.66138 - 1.49512i) q^{95} +14.7457i q^{97} +(-6.70142 + 1.97339i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64}+ \cdots - 22 q^{94}+O(q^{100}) \) 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

Introduction

L-functions

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