LMFDB - Embedded newform 1080.2.d.j.109.18

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			109.18
Root			$-1.35662 - 0.399488i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.j.109.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35662 + 0.399488i) q^{2} +(1.68082 + 1.08390i) q^{4} +(1.49578 + 1.66212i) q^{5} +1.43534i q^{7} +(1.84722 + 2.14191i) q^{8} +(1.36521 + 2.85240i) q^{10} +0.0984392i q^{11} -1.92218 q^{13} +(-0.573401 + 1.94721i) q^{14} +(1.65030 + 3.64369i) q^{16} +2.03741i q^{17} -0.999558i q^{19} +(0.712569 + 4.41500i) q^{20} +(-0.0393253 + 0.133544i) q^{22} -4.30361i q^{23} +(-0.525254 + 4.97233i) q^{25} +(-2.60767 - 0.767889i) q^{26} +(-1.55577 + 2.41255i) q^{28} -3.56681i q^{29} +1.42267 q^{31} +(0.783216 + 5.60237i) q^{32} +(-0.813920 + 2.76398i) q^{34} +(-2.38570 + 2.14696i) q^{35} -8.27330 q^{37} +(0.399311 - 1.35602i) q^{38} +(-0.797057 + 6.27413i) q^{40} +5.11958 q^{41} +5.50577 q^{43} +(-0.106699 + 0.165458i) q^{44} +(1.71924 - 5.83835i) q^{46} -9.00709i q^{47} +4.93980 q^{49} +(-2.69896 + 6.53572i) q^{50} +(-3.23084 - 2.08346i) q^{52} -4.93699 q^{53} +(-0.163617 + 0.147244i) q^{55} +(-3.07437 + 2.65139i) q^{56} +(1.42490 - 4.83879i) q^{58} -6.27246i q^{59} +12.8449i q^{61} +(1.93002 + 0.568340i) q^{62} +(-1.17556 + 7.91316i) q^{64} +(-2.87517 - 3.19489i) q^{65} -1.89027 q^{67} +(-2.20835 + 3.42451i) q^{68} +(-4.09416 + 1.95954i) q^{70} +12.3259 q^{71} -5.62966i q^{73} +(-11.2237 - 3.30508i) q^{74} +(1.08343 - 1.68008i) q^{76} -0.141294 q^{77} +2.48816 q^{79} +(-3.58774 + 8.19317i) q^{80} +(6.94531 + 2.04521i) q^{82} -2.26930 q^{83} +(-3.38640 + 3.04752i) q^{85} +(7.46923 + 2.19949i) q^{86} +(-0.210848 + 0.181839i) q^{88} +13.3550 q^{89} -2.75898i q^{91} +(4.66470 - 7.23359i) q^{92} +(3.59823 - 12.2192i) q^{94} +(1.66138 - 1.49512i) q^{95} +14.7457i q^{97} +(6.70142 + 1.97339i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 26 q^{40} - 12 q^{43} + 2 q^{46} - 52 q^{49} + 50 q^{52} - 28 q^{55} - 6 q^{58}+ \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 - 26 * q^40 - 12 * q^43 + 2 * q^46 - 52 * q^49 + 50 * q^52 - 28 * q^55 - 6 * q^58 + 54 * q^64 + 64 * 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
$10$	1.36521	+	2.85240i	0.431718	+	0.902009i
$11$			0.0984392i			0.0296805i	0.999890	+	0.0148403i	$0.00472398\pi$
$11$			0.0984392i			0.0296805i	−0.999890	+	0.0148403i	$0.995276\pi$
$12$		0			0
$13$	−1.92218			−0.533118			−0.266559	−	0.963819i	$-0.585887\pi$
$13$	−1.92218			−0.533118			−0.266559	+	0.963819i	$0.585887\pi$
$14$	−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	$-0.963423\pi$
$19$		−	0.999558i		−	0.229314i	0.993405	−	0.114657i	$-0.0365770\pi$
$20$	0.712569	+	4.41500i	0.159335	+	0.987225i
$21$		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	$-0.892557\pi$
$29$		−	3.56681i		−	0.662339i	0.943571	−	0.331170i	$-0.107443\pi$
$30$		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	$-0.738047\pi$
$37$	−8.27330			−1.36012			−0.680061	+	0.733156i	$0.738047\pi$
$38$	0.399311	−	1.35602i	0.0647769	−	0.219975i
$39$		0			0
$40$	−0.797057	+	6.27413i	−0.126026	+	0.992027i
$41$	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	$-0.362096\pi$
$43$	5.50577			0.839623			0.419811	+	0.907611i	$0.362096\pi$
$44$	−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
$50$	−2.69896	+	6.53572i	−0.381690	+	0.924290i
$51$		0			0
$52$	−3.23084	−	2.08346i	−0.448037	−	0.288924i
$53$	−4.93699			−0.678148			−0.339074	−	0.940760i	$-0.610114\pi$
$53$	−4.93699			−0.678148			−0.339074	+	0.940760i	$0.610114\pi$
$54$		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	$-0.866121\pi$
$59$		−	6.27246i		−	0.816605i	0.912847	−	0.408303i	$-0.133879\pi$
$60$		0			0
$61$			12.8449i			1.64463i	0.569035	+	0.822313i	$0.307317\pi$
$61$			12.8449i			1.64463i	−0.569035	+	0.822313i	$0.692683\pi$
$62$	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	$-0.536836\pi$
$67$	−1.89027			−0.230933			−0.115466	+	0.993311i	$0.536836\pi$
$68$	−2.20835	+	3.42451i	−0.267802	+	0.415283i
$69$		0			0
$70$	−4.09416	+	1.95954i	−0.489346	+	0.234210i
$71$	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	$0.455299\pi$
$80$	−3.58774	+	8.19317i	−0.401122	+	0.916025i
$81$		0			0
$82$	6.94531	+	2.04521i	0.766981	+	0.225856i
$83$	−2.26930			−0.249088			−0.124544	−	0.992214i	$-0.539747\pi$
$83$	−2.26930			−0.249088			−0.124544	+	0.992214i	$0.539747\pi$
$84$		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
$100$	−6.27239	+	7.78827i	−0.627239	+	0.778827i
$101$		−	13.6218i		−	1.35542i	−0.735328	−	0.677711i	$-0.762972\pi$
$101$		−	13.6218i		−	1.35542i	0.735328	−	0.677711i	$-0.237028\pi$
$102$		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	$-0.706347\pi$
$107$	−12.4915			−1.20760			−0.603798	+	0.797137i	$0.706347\pi$
$108$		0			0
$109$			16.5739i			1.58749i	0.608250	+	0.793745i	$0.291872\pi$
$109$			16.5739i			1.58749i	−0.608250	+	0.793745i	$0.708128\pi$
$110$	−0.280788	+	0.134390i	−0.0267721	+	0.0128136i
$111$		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
$130$	−2.62419	−	5.48284i	−0.230156	−	0.480877i
$131$		−	22.1895i		−	1.93870i	−0.245678	−	0.969352i	$-0.579011\pi$
$131$		−	22.1895i		−	1.93870i	0.245678	−	0.969352i	$-0.420989\pi$
$132$		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	$-0.770345\pi$
$139$		−	15.5743i		−	1.32100i	0.750827	−	0.660499i	$-0.229655\pi$
$140$	−6.33703	+	1.02278i	−0.535577	+	0.0864406i
$141$		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	$-0.945292\pi$
$149$		−	4.17528i		−	0.342052i	0.985266	−	0.171026i	$-0.0547083\pi$
$150$		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	$-0.803491\pi$
$157$	−20.4342			−1.63083			−0.815414	+	0.578878i	$0.803491\pi$
$158$	3.37547	+	0.993989i	0.268538	+	0.0790775i
$159$		0			0
$160$	−8.14027	+	9.68174i	−0.643545	+	0.765409i
$161$	6.17714			0.486827
$162$		0			0
$163$	19.5466			1.53101			0.765504	−	0.643432i	$-0.222490\pi$
$163$	19.5466			1.53101			0.765504	+	0.643432i	$0.222490\pi$
$164$	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
$170$	−5.81150	+	2.78149i	−0.445722	+	0.213331i
$171$		0			0
$172$	9.25421	+	5.96773i	0.705627	+	0.455035i
$173$	−7.38888			−0.561766			−0.280883	−	0.959742i	$-0.590627\pi$
$173$	−7.38888			−0.561766			−0.280883	+	0.959742i	$0.590627\pi$
$174$		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	$0.241875\pi$
$179$			18.4318i			1.37766i	−0.724924	+	0.688828i	$0.758125\pi$
$180$		0			0
$181$		−	4.75079i		−	0.353123i	−0.984290	−	0.176562i	$-0.943503\pi$
$181$		−	4.75079i		−	0.353123i	0.984290	−	0.176562i	$-0.0564975\pi$
$182$	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
$190$	2.85114	−	1.36461i	0.206844	−	0.0989991i
$191$	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	$-0.550840\pi$
$197$	−4.46451			−0.318083			−0.159042	+	0.987272i	$0.550840\pi$
$198$		0			0
$199$	−19.2962			−1.36787			−0.683936	−	0.729542i	$-0.739733\pi$
$199$	−19.2962			−1.36787			−0.683936	+	0.729542i	$0.739733\pi$
$200$	−11.6206	+	8.05995i	−0.821697	+	0.569924i
$201$		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	$-0.718251\pi$
$211$		−	22.4861i		−	1.54801i	0.633180	−	0.774005i	$-0.281749\pi$
$212$	−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
$220$	−0.434609	+	0.0701447i	−0.0293014	+	0.00472916i
$221$		−	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	$-0.411697\pi$
$227$	8.25244			0.547734			0.273867	+	0.961768i	$0.411697\pi$
$228$		0			0
$229$		−	6.48061i		−	0.428251i	−0.976806	−	0.214125i	$-0.931310\pi$
$229$		−	6.48061i		−	0.428251i	0.976806	−	0.214125i	$-0.0686902\pi$
$230$	12.2756	−	5.87534i	0.809430	−	0.387408i
$231$		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
$250$	−14.9002	+	5.29005i	−0.942370	+	0.334572i
$251$		−	0.277559i		−	0.0175194i	−0.999962	−	0.00875968i	$-0.997212\pi$
$251$		−	0.277559i		−	0.0175194i	0.999962	−	0.00875968i	$-0.00278833\pi$
$252$		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
$260$	−1.36969	−	8.48644i	−0.0849444	−	0.526307i
$261$		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	$0.142957\pi$
$269$			14.2417i			0.868333i	−0.900833	+	0.434167i	$0.857043\pi$
$270$		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	$-0.655594\pi$
$277$	−15.6307			−0.939156			−0.469578	+	0.882891i	$0.655594\pi$
$278$	6.22176	−	21.1284i	0.373156	−	1.26720i
$279$		0			0
$280$	−9.00551	−	1.14405i	−0.538182	−	0.0683699i
$281$	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	$-0.336340\pi$
$283$	16.5466			0.983593			0.491796	+	0.870710i	$0.336340\pi$
$284$	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
$290$	10.1740	−	4.86945i	0.597436	−	0.285944i
$291$		0			0
$292$	6.10202	−	9.46244i	0.357094	−	0.553748i
$293$	20.2544			1.18328			0.591638	−	0.806203i	$-0.298481\pi$
$293$	20.2544			1.18328			0.591638	+	0.806203i	$0.298481\pi$
$294$		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	$-0.550237\pi$
$307$	−5.50772			−0.314342			−0.157171	+	0.987571i	$0.550237\pi$
$308$	−0.237489	−	0.153149i	−0.0135322	−	0.00872646i
$309$		0			0
$310$	1.94225	+	4.05803i	0.110312	+	0.230480i
$311$	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	$-0.433467\pi$
$317$	7.38888			0.415001			0.207500	+	0.978235i	$0.433467\pi$
$318$		0			0
$319$	0.351114			0.0196586
$320$	−14.9110	+	9.88247i	−0.833548	+	0.552447i
$321$		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	$-0.950394\pi$
$331$		−	5.64764i		−	0.310422i	0.987881	−	0.155211i	$-0.0496058\pi$
$332$	−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
$340$	−8.99515	+	1.45179i	−0.487831	+	0.0787345i
$341$			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	$-0.255954\pi$
$347$	25.8465			1.38751			0.693756	+	0.720210i	$0.255954\pi$
$348$		0			0
$349$			13.2897i			0.711382i	0.934604	+	0.355691i	$0.115754\pi$
$349$			13.2897i			0.711382i	−0.934604	+	0.355691i	$0.884246\pi$
$350$	−9.38098	−	3.87392i	−0.501434	−	0.207070i
$351$		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
$370$	−11.2948	−	23.5988i	−0.587189	−	1.22684i
$371$		−	7.08626i		−	0.367900i
$372$		0			0
$373$	−4.85063			−0.251156			−0.125578	−	0.992084i	$-0.540079\pi$
$373$	−4.85063			−0.251156			−0.125578	+	0.992084i	$0.540079\pi$
$374$	−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	$0.134968\pi$
$379$			16.0191i			0.822846i	−0.911445	+	0.411423i	$0.865032\pi$
$380$	4.41305	−	0.712254i	0.226385	−	0.0365379i
$381$		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	$0.125044\pi$
$389$			15.1004i			0.765623i	−0.923827	+	0.382811i	$0.874956\pi$
$390$		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	$-0.717206\pi$
$397$	−25.1307			−1.26127			−0.630636	+	0.776079i	$0.717206\pi$
$398$	−26.1776	−	7.70860i	−1.31216	−	0.386397i
$399$		0			0
$400$	−18.9845	+	6.29199i	−0.949225	+	0.314599i
$401$	−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	$0.516323\pi$
$410$	6.98931	+	14.6031i	0.345177	+	0.721195i
$411$		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	$0.242357\pi$
$419$			28.2449i			1.37985i	−0.723880	+	0.689926i	$0.757643\pi$
$420$		0			0
$421$			4.94229i			0.240873i	0.992721	+	0.120436i	$0.0384294\pi$
$421$			4.94229i			0.240873i	−0.992721	+	0.120436i	$0.961571\pi$
$422$	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
$430$	7.51655	+	15.7047i	0.362480	+	0.757347i
$431$	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	$0.186196\pi$
$440$	−0.617620	−	0.0784617i	−0.0294439	−	0.00374051i
$441$		0			0
$442$	1.56450	−	5.31288i	0.0744158	−	0.252708i
$443$	−23.6112			−1.12180			−0.560900	−	0.827883i	$-0.689545\pi$
$443$	−23.6112			−1.12180			−0.560900	+	0.827883i	$0.689545\pi$
$444$		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
$460$	19.0004	−	3.06662i	0.885900	−	0.142982i
$461$			0.867775i			0.0404163i	0.999796	+	0.0202081i	$0.00643289\pi$
$461$			0.867775i			0.0404163i	−0.999796	+	0.0202081i	$0.993567\pi$
$462$		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	$-0.721497\pi$
$467$	−27.7060			−1.28208			−0.641040	+	0.767507i	$0.721497\pi$
$468$		0			0
$469$		−	2.71317i		−	0.125283i
$470$	25.6919	−	12.2966i	1.18508	−	0.567200i
$471$		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
$490$	6.74388	+	14.0903i	0.304657	+	0.636535i
$491$		−	9.74298i		−	0.439695i	−0.975534	−	0.219847i	$-0.929444\pi$
$491$		−	9.74298i		−	0.439695i	0.975534	−	0.219847i	$-0.0705559\pi$
$492$		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	$0.0494435\pi$
$499$			6.91181i			0.309415i	−0.987960	+	0.154708i	$0.950556\pi$
$500$	−22.3271	+	1.22413i	−0.998500	+	0.0547448i
$501$		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	$-0.779037\pi$
$509$		−	28.8669i		−	1.27950i	0.768582	−	0.639752i	$-0.220963\pi$
$510$		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
$520$	1.53209	−	12.0600i	0.0671866	−	0.528867i
$521$	−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	$-0.578481\pi$
$523$	−11.1631			−0.488127			−0.244064	+	0.969759i	$0.578481\pi$
$524$	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
$530$	−6.74004	−	14.0823i	−0.292769	−	0.611696i
$531$		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	$0.0295066\pi$
$541$			4.30602i			0.185130i	−0.995707	+	0.0925651i	$0.970493\pi$
$542$	−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	$-0.826723\pi$
$547$	−40.0149			−1.71091			−0.855456	+	0.517875i	$0.826723\pi$
$548$	11.6900	−	18.1278i	0.499372	−	0.774380i
$549$		0			0
$550$	−0.643371	−	0.265683i	−0.0274334	−	0.0113288i
$551$	−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	$-0.367659\pi$
$557$	19.0641			0.807771			0.403886	+	0.914809i	$0.367659\pi$
$558$		0			0
$559$	−10.5831			−0.447618
$560$	−11.7600	−	5.14963i	−0.496950	−	0.217611i
$561$		0			0
$562$	7.66753	+	2.25789i	0.323435	+	0.0952432i
$563$	6.40993			0.270147			0.135073	−	0.990836i	$-0.456873\pi$
$563$	6.40993			0.270147			0.135073	+	0.990836i	$0.456873\pi$
$564$		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	$0.205670\pi$
$571$			28.7752i			1.20421i	−0.798418	+	0.602103i	$0.794330\pi$
$572$	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
$580$	15.7475	−	2.54160i	0.653878	−	0.105534i
$581$		−	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	$-0.447778\pi$
$587$	7.91407			0.326649			0.163324	+	0.986572i	$0.447778\pi$
$588$		0			0
$589$		−	1.42204i		−	0.0585942i
$590$	17.8916	−	8.56324i	0.736585	−	0.352543i
$591$		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
$610$	−36.6390	+	17.5361i	−1.48347	+	0.710015i
$611$			17.3133i			0.700420i
$612$		0			0
$613$	−9.54708			−0.385603			−0.192801	−	0.981238i	$-0.561757\pi$
$613$	−9.54708			−0.385603			−0.192801	+	0.981238i	$0.561757\pi$
$614$	−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	$-0.874098\pi$
$619$		−	19.1724i		−	0.770602i	0.922791	−	0.385301i	$-0.125902\pi$
$620$	1.01375	+	6.28109i	0.0407132	+	0.252255i
$621$		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
$640$	−24.1764	+	7.44998i	−0.955656	+	0.294486i
$641$	−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	$-0.573820\pi$
$643$	−11.6563			−0.459681			−0.229840	+	0.973228i	$0.573820\pi$
$644$	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
$650$	5.18789	−	12.5628i	0.203486	−	0.492755i
$651$		0			0
$652$	32.8543	+	21.1866i	1.28667	+	0.829733i
$653$	8.69902			0.340419			0.170209	−	0.985408i	$-0.445556\pi$
$653$	8.69902			0.340419			0.170209	+	0.985408i	$0.445556\pi$
$654$		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	$-0.857610\pi$
$659$		−	22.2085i		−	0.865122i	0.901605	−	0.432561i	$-0.142390\pi$
$660$		0			0
$661$		−	32.1865i		−	1.25191i	−0.779859	−	0.625956i	$-0.784709\pi$
$661$		−	32.1865i		−	1.25191i	0.779859	−	0.625956i	$-0.215291\pi$
$662$	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
$670$	−2.58061	−	5.39180i	−0.0996978	−	0.208303i
$671$	−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	$-0.472658\pi$
$677$	4.46451			0.171585			0.0857925	+	0.996313i	$0.472658\pi$
$678$		0			0
$679$	−21.1650			−0.812240
$680$	−12.7830	−	1.62393i	−0.490204	−	0.0622749i
$681$		0			0
$682$	−0.0559469	+	0.189989i	−0.00214232	+	0.00727507i
$683$	42.7166			1.63450			0.817252	−	0.576281i	$-0.195497\pi$
$683$	42.7166			1.63450			0.817252	+	0.576281i	$0.195497\pi$
$684$		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	$0.0888687\pi$
$691$			14.4881i			0.551153i	−0.961279	+	0.275577i	$0.911131\pi$
$692$	−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
$700$	−11.1788	−	9.00301i	−0.422519	−	0.340282i
$701$			27.2562i			1.02945i	0.857355	+	0.514726i	$0.172106\pi$
$701$			27.2562i			1.02945i	−0.857355	+	0.514726i	$0.827894\pi$
$702$		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	$-0.887475\pi$
$709$		−	18.4360i		−	0.692379i	0.938165	−	0.346190i	$-0.112525\pi$
$710$	16.8274	+	35.1583i	0.631522	+	1.31947i
$711$		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
$730$	16.0581	−	7.68568i	0.594336	−	0.284460i
$731$			11.2175i			0.414894i
$732$		0			0
$733$	35.3194			1.30455			0.652276	−	0.757982i	$-0.273814\pi$
$733$	35.3194			1.30455			0.652276	+	0.757982i	$0.273814\pi$
$734$	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	$0.250501\pi$
$739$			38.5052i			1.41644i	−0.705993	+	0.708219i	$0.749499\pi$
$740$	−5.89530	−	36.5266i	−0.216715	−	1.34275i
$741$		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	$-0.436015\pi$
$757$	10.9870			0.399329			0.199664	+	0.979864i	$0.436015\pi$
$758$	−6.39944	+	21.7318i	−0.232438	+	0.789334i
$759$		0			0
$760$	6.27136	+	0.796705i	0.227486	+	0.0288995i
$761$	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	$0.576743\pi$
$770$	−0.192896	−	0.403026i	−0.00695148	−	0.0145241i
$771$		0			0
$772$	9.21356	−	14.2875i	0.331603	−	0.514220i
$773$	−6.66412			−0.239692			−0.119846	−	0.992793i	$-0.538240\pi$
$773$	−6.66412			−0.239692			−0.119846	+	0.992793i	$0.538240\pi$
$774$		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	$-0.499075\pi$
$787$	0.163075			0.00581301			0.00290650	+	0.999996i	$0.499075\pi$
$788$	−7.50403	−	4.83910i	−0.267320	−	0.172386i
$789$		0			0
$790$	3.39686	+	7.09722i	0.120855	+	0.252508i
$791$	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	$-0.803830\pi$
$797$	−46.0750			−1.63206			−0.816031	+	0.578009i	$0.803830\pi$
$798$		0			0
$799$	18.3511			0.649216
$800$	−28.2683	+	0.951740i	−0.999434	+	0.0336491i
$801$		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	$0.108513\pi$
$811$			19.0427i			0.668680i	−0.942453	+	0.334340i	$0.891487\pi$
$812$	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
$820$	3.64805	+	22.6029i	0.127396	+	0.789329i
$821$			26.1910i			0.914073i	0.889448	+	0.457037i	$0.151089\pi$
$821$			26.1910i			0.914073i	−0.889448	+	0.457037i	$0.848911\pi$
$822$		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	$-0.614492\pi$
$827$	−20.2443			−0.703965			−0.351982	+	0.936007i	$0.614492\pi$
$828$		0			0
$829$		−	32.5375i		−	1.13007i	−0.825066	−	0.565037i	$-0.808862\pi$
$829$		−	32.5375i		−	1.13007i	0.825066	−	0.565037i	$-0.191138\pi$
$830$	−3.09808	−	6.47296i	−0.107536	−	0.224680i
$831$		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
$850$	−13.3159	−	5.49887i	−0.456732	−	0.188610i
$851$			35.6050i			1.22052i
$852$		0			0
$853$	18.5346			0.634611			0.317306	−	0.948323i	$-0.397222\pi$
$853$	18.5346			0.634611			0.317306	+	0.948323i	$0.397222\pi$
$854$	−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	$0.185163\pi$
$859$			32.2074i			1.09890i	−0.835526	+	0.549452i	$0.814837\pi$
$860$	3.92324	+	24.3080i	0.133782	+	0.828896i
$861$		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	$-0.533207\pi$
$877$	−6.16767			−0.208267			−0.104134	+	0.994563i	$0.533207\pi$
$878$	47.3969	+	13.9571i	1.59957	+	0.471030i
$879$		0			0
$880$	−0.806530	−	0.353174i	−0.0271881	−	0.0119055i
$881$	−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	$-0.538521\pi$
$883$	−7.17454			−0.241443			−0.120721	+	0.992686i	$0.538521\pi$
$884$	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
$890$	18.2324	+	38.0939i	0.611153	+	1.27691i
$891$		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	$-0.638597\pi$
$907$	−25.4054			−0.843573			−0.421787	+	0.906695i	$0.638597\pi$
$908$	13.8709	+	8.94486i	0.460321	+	0.296846i
$909$		0			0
$910$	7.86973	−	3.76660i	0.260879	−	0.124862i
$911$	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	$0.446689\pi$
$920$	27.0014	+	3.43022i	0.890210	+	0.113091i
$921$		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
$940$	39.7663	−	6.41818i	1.29704	−	0.209338i
$941$			25.5990i			0.834503i	0.908791	+	0.417252i	$0.137007\pi$
$941$			25.5990i			0.834503i	−0.908791	+	0.417252i	$0.862993\pi$
$942$		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	$-0.361072\pi$
$947$	26.0177			0.845461			0.422730	+	0.906256i	$0.361072\pi$
$948$		0			0
$949$			10.8212i			0.351272i
$950$	6.53283	+	2.69776i	0.211953	+	0.0875270i
$951$		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
$970$	−42.0606	+	20.1310i	−1.35048	+	0.646366i
$971$		−	29.8380i		−	0.957547i	−0.877938	−	0.478774i	$-0.841081\pi$
$971$		−	29.8380i		−	0.957547i	0.877938	−	0.478774i	$-0.158919\pi$
$972$		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
$980$	3.51995	+	21.8092i	0.112441	+	0.696670i
$981$		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	$-0.278364\pi$
$997$	40.5033			1.28275			0.641377	+	0.767226i	$0.278364\pi$
$998$	−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.j.109.18	yes	20
3.2	odd	2	inner	1080.2.d.j.109.3	yes	20
4.3	odd	2		4320.2.d.j.3889.14		20
5.4	even	2		1080.2.d.i.109.3	✓	20
8.3	odd	2		4320.2.d.i.3889.7		20
8.5	even	2		1080.2.d.i.109.4	yes	20
12.11	even	2		4320.2.d.j.3889.7		20
15.14	odd	2		1080.2.d.i.109.18	yes	20
20.19	odd	2		4320.2.d.i.3889.8		20
24.5	odd	2		1080.2.d.i.109.17	yes	20
24.11	even	2		4320.2.d.i.3889.14		20
40.19	odd	2		4320.2.d.j.3889.13		20
40.29	even	2	inner	1080.2.d.j.109.17	yes	20
60.59	even	2		4320.2.d.i.3889.13		20
120.29	odd	2	inner	1080.2.d.j.109.4	yes	20
120.59	even	2		4320.2.d.j.3889.8		20

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

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

\(f(q)\)	\(=\)	\(q+(1.35662 + 0.399488i) q^{2} +(1.68082 + 1.08390i) q^{4} +(1.49578 + 1.66212i) q^{5} +1.43534i q^{7} +(1.84722 + 2.14191i) q^{8} +(1.36521 + 2.85240i) q^{10} +0.0984392i q^{11} -1.92218 q^{13} +(-0.573401 + 1.94721i) q^{14} +(1.65030 + 3.64369i) q^{16} +2.03741i q^{17} -0.999558i q^{19} +(0.712569 + 4.41500i) q^{20} +(-0.0393253 + 0.133544i) q^{22} -4.30361i q^{23} +(-0.525254 + 4.97233i) q^{25} +(-2.60767 - 0.767889i) q^{26} +(-1.55577 + 2.41255i) q^{28} -3.56681i q^{29} +1.42267 q^{31} +(0.783216 + 5.60237i) q^{32} +(-0.813920 + 2.76398i) q^{34} +(-2.38570 + 2.14696i) q^{35} -8.27330 q^{37} +(0.399311 - 1.35602i) q^{38} +(-0.797057 + 6.27413i) q^{40} +5.11958 q^{41} +5.50577 q^{43} +(-0.106699 + 0.165458i) q^{44} +(1.71924 - 5.83835i) q^{46} -9.00709i q^{47} +4.93980 q^{49} +(-2.69896 + 6.53572i) q^{50} +(-3.23084 - 2.08346i) q^{52} -4.93699 q^{53} +(-0.163617 + 0.147244i) q^{55} +(-3.07437 + 2.65139i) q^{56} +(1.42490 - 4.83879i) q^{58} -6.27246i q^{59} +12.8449i q^{61} +(1.93002 + 0.568340i) q^{62} +(-1.17556 + 7.91316i) q^{64} +(-2.87517 - 3.19489i) q^{65} -1.89027 q^{67} +(-2.20835 + 3.42451i) q^{68} +(-4.09416 + 1.95954i) q^{70} +12.3259 q^{71} -5.62966i q^{73} +(-11.2237 - 3.30508i) q^{74} +(1.08343 - 1.68008i) q^{76} -0.141294 q^{77} +2.48816 q^{79} +(-3.58774 + 8.19317i) q^{80} +(6.94531 + 2.04521i) q^{82} -2.26930 q^{83} +(-3.38640 + 3.04752i) q^{85} +(7.46923 + 2.19949i) q^{86} +(-0.210848 + 0.181839i) q^{88} +13.3550 q^{89} -2.75898i q^{91} +(4.66470 - 7.23359i) q^{92} +(3.59823 - 12.2192i) q^{94} +(1.66138 - 1.49512i) q^{95} +14.7457i q^{97} +(6.70142 + 1.97339i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4} - 2 q^{10} + 4 q^{13} - 14 q^{16} + 34 q^{22} + 20 q^{25} - 20 q^{28} + 12 q^{31} + 6 q^{34} + 32 q^{37} - 26 q^{40} - 12 q^{43} + 2 q^{46} - 52 q^{49} + 50 q^{52} - 28 q^{55} - 6 q^{58}+ \cdots - 22 q^{94}+O(q^{100}) \) 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 - 26 * q^40 - 12 * q^43 + 2 * q^46 - 52 * q^49 + 50 * q^52 - 28 * q^55 - 6 * q^58 + 54 * q^64 + 64 * 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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