LMFDB - Embedded newform 1323.2.h.c.802.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, not 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.c.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.53209 q^{2} +4.41147 q^{4} +(-0.439693 + 0.761570i) q^{5} -6.10607 q^{8} +(1.11334 - 1.92836i) q^{10} +(1.93969 + 3.35965i) q^{11} +(2.72668 + 4.72275i) q^{13} +6.63816 q^{16} +(0.826352 - 1.43128i) q^{17} +(-1.20574 - 2.08840i) q^{19} +(-1.93969 + 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +(1.58125 - 2.73881i) q^{23} +(2.11334 + 3.66041i) q^{25} +(-6.90420 - 11.9584i) q^{26} +(-3.02481 + 5.23913i) q^{29} -4.55438 q^{31} -4.59627 q^{32} +(-2.09240 + 3.62414i) q^{34} +(2.27719 + 3.94421i) q^{37} +(3.05303 + 5.28801i) q^{38} +(2.68479 - 4.65020i) q^{40} +(-0.592396 - 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(8.55690 + 14.8210i) q^{44} +(-4.00387 + 6.93491i) q^{46} +1.02229 q^{47} +(-5.35117 - 9.26849i) q^{50} +(12.0287 + 20.8343i) q^{52} +(3.64543 - 6.31407i) q^{53} -3.41147 q^{55} +(7.65910 - 13.2660i) q^{58} -6.66044 q^{59} -2.59627 q^{61} +11.5321 q^{62} -1.63816 q^{64} -4.79561 q^{65} -2.95811 q^{67} +(3.64543 - 6.31407i) q^{68} +3.68004 q^{71} +(6.39053 - 11.0687i) q^{73} +(-5.76604 - 9.98708i) q^{74} +(-5.31908 - 9.21291i) q^{76} -5.95811 q^{79} +(-2.91875 + 5.05542i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +(0.233956 - 0.405223i) q^{86} +(-11.8439 - 20.5142i) q^{88} +(5.51367 + 9.54996i) q^{89} +(6.97565 - 12.0822i) q^{92} -2.58853 q^{94} +2.12061 q^{95} +(-6.25150 + 10.8279i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38}+ \cdots + 3 q^{97}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 6 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 3 * q^26 + 9 * q^29 - 6 * q^31 - 9 * q^34 + 3 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 + 15 * q^44 - 6 * q^47 - 6 * q^50 + 21 * q^52 + 6 * q^53 + 9 * q^58 + 6 * q^59 + 12 * q^61 + 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 + 6 * q^68 - 18 * q^71 + 21 * q^73 - 30 * q^74 - 15 * q^76 - 42 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 12 * q^89 + 3 * q^92 - 36 * q^94 + 24 * q^95 + 3 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.53209			−1.79046			−0.895229	−	0.445607i	$-0.852988\pi$
$2$	−2.53209			−1.79046			−0.895229	+	0.445607i	$0.852988\pi$
$3$		0			0
$3$		0			0
$4$	4.41147			2.20574
$5$	−0.439693	+	0.761570i	−0.196637	+	0.340584i	−0.947436	−	0.319946i	$-0.896335\pi$
$5$	−0.439693	+	0.761570i	−0.196637	+	0.340584i	0.750799	+	0.660530i	$0.229669\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−6.10607			−2.15882
$9$		0			0
$10$	1.11334	−	1.92836i	0.352069	−	0.609802i
$11$	1.93969	+	3.35965i	0.584839	+	1.01297i	0.994895	+	0.100911i	$0.0321758\pi$
$11$	1.93969	+	3.35965i	0.584839	+	1.01297i	−0.410056	+	0.912060i	$0.634491\pi$
$12$		0			0
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	0.944753	+	0.327784i	$0.106302\pi$
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	−0.188507	+	0.982072i	$0.560365\pi$
$14$		0			0
$15$		0			0
$16$	6.63816			1.65954
$17$	0.826352	−	1.43128i	0.200420	−	0.347137i	−0.748244	−	0.663424i	$-0.769103\pi$
$17$	0.826352	−	1.43128i	0.200420	−	0.347137i	0.948664	+	0.316286i	$0.102436\pi$
$18$		0			0
$19$	−1.20574	−	2.08840i	−0.276615	−	0.479111i	0.693926	−	0.720046i	$-0.255879\pi$
$19$	−1.20574	−	2.08840i	−0.276615	−	0.479111i	−0.970541	+	0.240935i	$0.922546\pi$
$20$	−1.93969	+	3.35965i	−0.433728	+	0.751240i
$21$		0			0
$22$	−4.91147	−	8.50692i	−1.04713	−	1.81368i
$23$	1.58125	−	2.73881i	0.329714	−	0.571081i	−0.652741	−	0.757581i	$-0.726381\pi$
$23$	1.58125	−	2.73881i	0.329714	−	0.571081i	0.982455	+	0.186500i	$0.0597144\pi$
$24$		0			0
$25$	2.11334	+	3.66041i	0.422668	+	0.732083i
$26$	−6.90420	−	11.9584i	−1.35403	−	2.34524i
$27$		0			0
$28$		0			0
$29$	−3.02481	+	5.23913i	−0.561694	+	0.972883i	0.435655	+	0.900114i	$0.356517\pi$
$29$	−3.02481	+	5.23913i	−0.561694	+	0.972883i	−0.997349	+	0.0727688i	$0.976816\pi$
$30$		0			0
$31$	−4.55438			−0.817990			−0.408995	−	0.912537i	$-0.634121\pi$
$31$	−4.55438			−0.817990			−0.408995	+	0.912537i	$0.634121\pi$
$32$	−4.59627			−0.812513
$33$		0			0
$34$	−2.09240	+	3.62414i	−0.358843	+	0.621534i
$35$		0			0
$36$		0			0
$37$	2.27719	+	3.94421i	0.374368	+	0.648424i	0.990232	−	0.139428i	$-0.0445265\pi$
$37$	2.27719	+	3.94421i	0.374368	+	0.648424i	−0.615865	+	0.787852i	$0.711193\pi$
$38$	3.05303	+	5.28801i	0.495267	+	0.857828i
$39$		0			0
$40$	2.68479	−	4.65020i	0.424503	−	0.735261i
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	0.816053	−	0.577977i	$-0.196158\pi$
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	−0.908570	+	0.417734i	$0.862825\pi$
$42$		0			0
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	−0.872985	−	0.487748i	$-0.837819\pi$
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	0.858894	+	0.512153i	$0.171152\pi$
$44$	8.55690	+	14.8210i	1.29000	+	2.23435i
$45$		0			0
$46$	−4.00387	+	6.93491i	−0.590338	+	1.02250i
$47$	1.02229			0.149116			0.0745581	−	0.997217i	$-0.476245\pi$
$47$	1.02229			0.149116			0.0745581	+	0.997217i	$0.476245\pi$
$48$		0			0
$49$		0			0
$50$	−5.35117	−	9.26849i	−0.756769	−	1.31076i
$51$		0			0
$52$	12.0287	+	20.8343i	1.66808	+	2.88920i
$53$	3.64543	−	6.31407i	0.500738	−	0.867304i	−0.499261	−	0.866451i	$-0.666395\pi$
$53$	3.64543	−	6.31407i	0.500738	−	0.867304i	1.00000		0.000852699i	$-0.000271423\pi$
$54$		0			0
$55$	−3.41147			−0.460003
$56$		0			0
$57$		0			0
$58$	7.65910	−	13.2660i	1.00569	−	1.74190i
$59$	−6.66044			−0.867116			−0.433558	−	0.901126i	$-0.642742\pi$
$59$	−6.66044			−0.867116			−0.433558	+	0.901126i	$0.642742\pi$
$60$		0			0
$61$	−2.59627			−0.332418			−0.166209	−	0.986091i	$-0.553153\pi$
$61$	−2.59627			−0.332418			−0.166209	+	0.986091i	$0.553153\pi$
$62$	11.5321			1.46458
$63$		0			0
$64$	−1.63816			−0.204769
$65$	−4.79561			−0.594822
$66$		0			0
$67$	−2.95811			−0.361391			−0.180695	−	0.983539i	$-0.557835\pi$
$67$	−2.95811			−0.361391			−0.180695	+	0.983539i	$0.557835\pi$
$68$	3.64543	−	6.31407i	0.442073	−	0.765693i
$69$		0			0
$70$		0			0
$71$	3.68004			0.436741			0.218370	−	0.975866i	$-0.429926\pi$
$71$	3.68004			0.436741			0.218370	+	0.975866i	$0.429926\pi$
$72$		0			0
$73$	6.39053	−	11.0687i	0.747955	−	1.29550i	−0.200847	−	0.979623i	$-0.564369\pi$
$73$	6.39053	−	11.0687i	0.747955	−	1.29550i	0.948801	−	0.315873i	$-0.102297\pi$
$74$	−5.76604	−	9.98708i	−0.670289	−	1.16097i
$75$		0			0
$76$	−5.31908	−	9.21291i	−0.610140	−	1.05679i
$77$		0			0
$78$		0			0
$79$	−5.95811			−0.670340			−0.335170	−	0.942158i	$-0.608794\pi$
$79$	−5.95811			−0.670340			−0.335170	+	0.942158i	$0.608794\pi$
$80$	−2.91875	+	5.05542i	−0.326326	+	0.565213i
$81$		0			0
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	−0.109470	+	0.189608i	−0.0120159	+	0.0208122i	−0.871971	−	0.489558i	$-0.837158\pi$
$83$	−0.109470	+	0.189608i	−0.0120159	+	0.0208122i	0.859955	+	0.510370i	$0.170492\pi$
$84$		0			0
$85$	0.726682	+	1.25865i	0.0788197	+	0.136520i
$86$	0.233956	−	0.405223i	0.0252281	−	0.0436963i
$87$		0			0
$88$	−11.8439	−	20.5142i	−1.26256	−	2.18682i
$89$	5.51367	+	9.54996i	0.584448	+	1.01229i	0.994944	+	0.100431i	$0.0320222\pi$
$89$	5.51367	+	9.54996i	0.584448	+	1.01229i	−0.410496	+	0.911862i	$0.634644\pi$
$90$		0			0
$91$		0			0
$92$	6.97565	−	12.0822i	0.727262	−	1.25965i
$93$		0			0
$94$	−2.58853			−0.266986
$95$	2.12061			0.217570
$96$		0			0
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	0.351826	+	0.936065i	$0.385561\pi$
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	−0.986569	+	0.163342i	$0.947773\pi$
$98$		0			0
$99$		0			0
$100$	9.32295	+	16.1478i	0.932295	+	1.61478i
$101$	−4.85844	−	8.41507i	−0.483433	−	0.837330i	0.516386	−	0.856356i	$-0.327277\pi$
$101$	−4.85844	−	8.41507i	−0.483433	−	0.837330i	−0.999819	+	0.0190255i	$0.993944\pi$
$102$		0			0
$103$	−3.29813	+	5.71253i	−0.324975	+	0.562873i	−0.981507	−	0.191425i	$-0.938689\pi$
$103$	−3.29813	+	5.71253i	−0.324975	+	0.562873i	0.656533	+	0.754298i	$0.272022\pi$
$104$	−16.6493	−	28.8374i	−1.63260	−	2.82774i
$105$		0			0
$106$	−9.23055	+	15.9878i	−0.896550	+	1.55287i
$107$	1.19459	+	2.06910i	0.115486	+	0.200027i	0.917974	−	0.396641i	$-0.129824\pi$
$107$	1.19459	+	2.06910i	0.115486	+	0.200027i	−0.802488	+	0.596668i	$0.796491\pi$
$108$		0			0
$109$	−1.97906	+	3.42782i	−0.189559	+	0.328326i	−0.945103	−	0.326772i	$-0.894039\pi$
$109$	−1.97906	+	3.42782i	−0.189559	+	0.328326i	0.755544	+	0.655098i	$0.227373\pi$
$110$	8.63816			0.823616
$111$		0			0
$112$		0			0
$113$	8.22668	+	14.2490i	0.773901	+	1.34044i	0.935410	+	0.353565i	$0.115031\pi$
$113$	8.22668	+	14.2490i	0.773901	+	1.34044i	−0.161509	+	0.986871i	$0.551636\pi$
$114$		0			0
$115$	1.39053	+	2.40847i	0.129668	+	0.224591i
$116$	−13.3439	+	23.1123i	−1.23895	+	2.14592i
$117$		0			0
$118$	16.8648			1.55253
$119$		0			0
$120$		0			0
$121$	−2.02481	+	3.50708i	−0.184074	+	0.318826i
$122$	6.57398			0.595180
$123$		0			0
$124$	−20.0915			−1.80427
$125$	−8.11381			−0.725721
$126$		0			0
$127$	17.6536			1.56651			0.783253	−	0.621702i	$-0.213559\pi$
$127$	17.6536			1.56651			0.783253	+	0.621702i	$0.213559\pi$
$128$	13.3405			1.17914
$129$		0			0
$130$	12.1429			1.06500
$131$	−9.59879	+	16.6256i	−0.838650	+	1.45259i	0.0523729	+	0.998628i	$0.483322\pi$
$131$	−9.59879	+	16.6256i	−0.838650	+	1.45259i	−0.891023	+	0.453958i	$0.850012\pi$
$132$		0			0
$133$		0			0
$134$	7.49020			0.647055
$135$		0			0
$136$	−5.04576	+	8.73951i	−0.432670	+	0.749407i
$137$	9.07785	+	15.7233i	0.775573	+	1.34333i	0.934472	+	0.356037i	$0.115872\pi$
$137$	9.07785	+	15.7233i	0.775573	+	1.34333i	−0.158899	+	0.987295i	$0.550794\pi$
$138$		0			0
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.773846	−	0.633374i	$-0.781670\pi$
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.161595	−	0.986857i	$-0.551664\pi$
$140$		0			0
$141$		0			0
$142$	−9.31820			−0.781966
$143$	−10.5778	+	18.3214i	−0.884564	+	1.53211i
$144$		0			0
$145$	−2.65998	−	4.60722i	−0.220899	−	0.382608i
$146$	−16.1814	+	28.0270i	−1.33918	+	2.31953i
$147$		0			0
$148$	10.0458	+	17.3998i	0.825756	+	1.43025i
$149$	−7.57785	+	13.1252i	−0.620802	+	1.07526i	0.368535	+	0.929614i	$0.379859\pi$
$149$	−7.57785	+	13.1252i	−0.620802	+	1.07526i	−0.989337	+	0.145646i	$0.953474\pi$
$150$		0			0
$151$	9.47818	+	16.4167i	0.771323	+	1.33597i	0.936838	+	0.349764i	$0.113738\pi$
$151$	9.47818	+	16.4167i	0.771323	+	1.33597i	−0.165515	+	0.986207i	$0.552929\pi$
$152$	7.36231	+	12.7519i	0.597162	+	1.03432i
$153$		0			0
$154$		0			0
$155$	2.00253	−	3.46848i	0.160847	−	0.278595i
$156$		0			0
$157$	−18.0574			−1.44114			−0.720568	−	0.693385i	$-0.756119\pi$
$157$	−18.0574			−1.44114			−0.720568	+	0.693385i	$0.756119\pi$
$158$	15.0865			1.20021
$159$		0			0
$160$	2.02094	−	3.50038i	0.159770	−	0.276729i
$161$		0			0
$162$		0			0
$163$	−0.479055	−	0.829748i	−0.0375225	−	0.0649909i	0.846654	−	0.532143i	$-0.178613\pi$
$163$	−0.479055	−	0.829748i	−0.0375225	−	0.0649909i	−0.884177	+	0.467152i	$0.845280\pi$
$164$	−2.61334	−	4.52644i	−0.204068	−	0.353456i
$165$		0			0
$166$	0.277189	−	0.480105i	0.0215140	−	0.0372634i
$167$	9.91921	+	17.1806i	0.767572	+	1.32947i	0.938876	+	0.344255i	$0.111869\pi$
$167$	9.91921	+	17.1806i	0.767572	+	1.32947i	−0.171304	+	0.985218i	$0.554798\pi$
$168$		0			0
$169$	−8.36959	+	14.4965i	−0.643814	+	1.11512i
$170$	−1.84002	−	3.18701i	−0.141123	−	0.244433i
$171$		0			0
$172$	−0.407604	+	0.705990i	−0.0310795	+	0.0538313i
$173$	−22.6827			−1.72454			−0.862268	−	0.506452i	$-0.830957\pi$
$173$	−22.6827			−1.72454			−0.862268	+	0.506452i	$0.830957\pi$
$174$		0			0
$175$		0			0
$176$	12.8760	+	22.3019i	0.970564	+	1.68107i
$177$		0			0
$178$	−13.9611	−	24.1813i	−1.04643	−	1.81247i
$179$	−3.67365	+	6.36295i	−0.274581	+	0.475589i	−0.970029	−	0.242988i	$-0.921873\pi$
$179$	−3.67365	+	6.36295i	−0.274581	+	0.475589i	0.695448	+	0.718576i	$0.255206\pi$
$180$		0			0
$181$	−3.44562			−0.256111			−0.128056	−	0.991767i	$-0.540874\pi$
$181$	−3.44562			−0.256111			−0.128056	+	0.991767i	$0.540874\pi$
$182$		0			0
$183$		0			0
$184$	−9.65523	+	16.7233i	−0.711793	+	1.23286i
$185$	−4.00505			−0.294457
$186$		0			0
$187$	6.41147			0.468853
$188$	4.50980			0.328911
$189$		0			0
$190$	−5.36959			−0.389551
$191$	−5.65776			−0.409381			−0.204690	−	0.978827i	$-0.565619\pi$
$191$	−5.65776			−0.409381			−0.204690	+	0.978827i	$0.565619\pi$
$192$		0			0
$193$	9.59627			0.690754			0.345377	−	0.938464i	$-0.387751\pi$
$193$	9.59627			0.690754			0.345377	+	0.938464i	$0.387751\pi$
$194$	15.8293	−	27.4172i	1.13648	−	1.96844i
$195$		0			0
$196$		0			0
$197$	−8.31996			−0.592772			−0.296386	−	0.955068i	$-0.595782\pi$
$197$	−8.31996			−0.592772			−0.296386	+	0.955068i	$0.595782\pi$
$198$		0			0
$199$	−3.29813	+	5.71253i	−0.233798	+	0.404951i	−0.958923	−	0.283667i	$-0.908449\pi$
$199$	−3.29813	+	5.71253i	−0.233798	+	0.404951i	0.725124	+	0.688618i	$0.241782\pi$
$200$	−12.9042	−	22.3507i	−0.912465	−	1.58044i
$201$		0			0
$202$	12.3020	+	21.3077i	0.865566	+	1.49920i
$203$		0			0
$204$		0			0
$205$	1.04189			0.0727687
$206$	8.35117	−	14.4646i	0.581853	−	1.00780i
$207$		0			0
$208$	18.1001	+	31.3504i	1.25502	+	2.17376i
$209$	4.67752	−	8.10170i	0.323551	−	0.560406i
$210$		0			0
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	0.918173	−	0.396179i	$-0.129664\pi$
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	−0.802188	+	0.597072i	$0.796331\pi$
$212$	16.0817	−	27.8544i	1.10450	−	1.91304i
$213$		0			0
$214$	−3.02481	−	5.23913i	−0.206772	−	0.358140i
$215$	−0.0812519	−	0.140732i	−0.00554133	−	0.00959787i
$216$		0			0
$217$		0			0
$218$	5.01114	−	8.67956i	0.339398	−	0.587854i
$219$		0			0
$220$	−15.0496			−1.01465
$221$	9.01279			0.606266
$222$		0			0
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	−0.741614	−	0.670827i	$-0.765939\pi$
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	0.951760	+	0.306843i	$0.0992726\pi$
$224$		0			0
$225$		0			0
$226$	−20.8307	−	36.0798i	−1.38564	−	2.39999i
$227$	−3.08125	−	5.33688i	−0.204510	−	0.354221i	0.745467	−	0.666543i	$-0.232227\pi$
$227$	−3.08125	−	5.33688i	−0.204510	−	0.354221i	−0.949976	+	0.312322i	$0.898893\pi$
$228$		0			0
$229$	−11.6925	+	20.2521i	−0.772664	+	1.33829i	0.163434	+	0.986554i	$0.447743\pi$
$229$	−11.6925	+	20.2521i	−0.772664	+	1.33829i	−0.936098	+	0.351740i	$0.885590\pi$
$230$	−3.52094	−	6.09845i	−0.232164	−	0.402120i
$231$		0			0
$232$	18.4697	−	31.9905i	1.21260	−	2.10028i
$233$	−4.26264	−	7.38311i	−0.279255	−	0.483684i	0.691945	−	0.721950i	$-0.256754\pi$
$233$	−4.26264	−	7.38311i	−0.279255	−	0.483684i	−0.971200	+	0.238267i	$0.923421\pi$
$234$		0			0
$235$	−0.449493	+	0.778544i	−0.0293217	+	0.0507866i
$236$	−29.3824			−1.91263
$237$		0			0
$238$		0			0
$239$	7.28106	+	12.6112i	0.470973	+	0.815748i	0.999449	−	0.0331997i	$-0.0105697\pi$
$239$	7.28106	+	12.6112i	0.470973	+	0.815748i	−0.528476	+	0.848948i	$0.677236\pi$
$240$		0			0
$241$	2.70187	+	4.67977i	0.174043	+	0.301451i	0.939830	−	0.341644i	$-0.110984\pi$
$241$	2.70187	+	4.67977i	0.174043	+	0.301451i	−0.765787	+	0.643094i	$0.777650\pi$
$242$	5.12701	−	8.88024i	0.329577	−	0.570844i
$243$		0			0
$244$	−11.4534			−0.733226
$245$		0			0
$246$		0			0
$247$	6.57532	−	11.3888i	0.418378	−	0.724651i
$248$	27.8093			1.76589
$249$		0			0
$250$	20.5449			1.29937
$251$	12.0669			0.761654			0.380827	−	0.924646i	$-0.375639\pi$
$251$	12.0669			0.761654			0.380827	+	0.924646i	$0.375639\pi$
$252$		0			0
$253$	12.2686			0.771318
$254$	−44.7006			−2.80476
$255$		0			0
$256$	−30.5030			−1.90644
$257$	5.28312	−	9.15063i	0.329552	−	0.570801i	−0.652871	−	0.757469i	$-0.726436\pi$
$257$	5.28312	−	9.15063i	0.329552	−	0.570801i	0.982423	+	0.186668i	$0.0597690\pi$
$258$		0			0
$259$		0			0
$260$	−21.1557			−1.31202
$261$		0			0
$262$	24.3050	−	42.0975i	1.50157	−	2.60079i
$263$	−14.1766	−	24.5547i	−0.874169	−	1.51411i	−0.857645	−	0.514242i	$-0.828073\pi$
$263$	−14.1766	−	24.5547i	−0.874169	−	1.51411i	−0.0165240	−	0.999863i	$-0.505260\pi$
$264$		0			0
$265$	3.20574	+	5.55250i	0.196927	+	0.341087i
$266$		0			0
$267$		0			0
$268$	−13.0496			−0.797133
$269$	3.74170	−	6.48081i	0.228135	−	0.395142i	−0.729120	−	0.684386i	$-0.760070\pi$
$269$	3.74170	−	6.48081i	0.228135	−	0.395142i	0.957255	+	0.289244i	$0.0934038\pi$
$270$		0			0
$271$	−6.81908	−	11.8110i	−0.414229	−	0.717467i	0.581118	−	0.813819i	$-0.302616\pi$
$271$	−6.81908	−	11.8110i	−0.414229	−	0.717467i	−0.995347	+	0.0963530i	$0.969282\pi$
$272$	5.48545	−	9.50108i	0.332604	−	0.576088i
$273$		0			0
$274$	−22.9859	−	39.8128i	−1.38863	−	2.40518i
$275$	−8.19846	+	14.2002i	−0.494386	+	0.856302i
$276$		0			0
$277$	3.07532	+	5.32661i	0.184778	+	0.320045i	0.943502	−	0.331368i	$-0.107510\pi$
$277$	3.07532	+	5.32661i	0.184778	+	0.320045i	−0.758724	+	0.651413i	$0.774177\pi$
$278$	27.9256	+	48.3686i	1.67487	+	2.90095i
$279$		0			0
$280$		0			0
$281$	1.65611	−	2.86846i	0.0987951	−	0.171118i	−0.812391	−	0.583113i	$-0.801835\pi$
$281$	1.65611	−	2.86846i	0.0987951	−	0.171118i	0.911186	+	0.411995i	$0.135168\pi$
$282$		0			0
$283$	29.0232			1.72525			0.862626	−	0.505843i	$-0.168818\pi$
$283$	29.0232			1.72525			0.862626	+	0.505843i	$0.168818\pi$
$284$	16.2344			0.963336
$285$		0			0
$286$	26.7841	−	46.3913i	1.58377	−	2.74318i
$287$		0			0
$288$		0			0
$289$	7.13429	+	12.3569i	0.419664	+	0.726879i
$290$	6.73530	+	11.6659i	0.395510	+	0.685044i
$291$		0			0
$292$	28.1917	−	48.8294i	1.64979	−	2.85752i
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	0.716464	−	0.697624i	$-0.245759\pi$
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	−0.962392	+	0.271664i	$0.912426\pi$
$294$		0			0
$295$	2.92855	−	5.07239i	0.170507	−	0.295326i
$296$	−13.9047	−	24.0836i	−0.808192	−	1.39983i
$297$		0			0
$298$	19.1878	−	33.2342i	1.11152	−	1.92521i
$299$	17.2463			0.997378
$300$		0			0
$301$		0			0
$302$	−23.9996	−	41.5685i	−1.38102	−	2.39200i
$303$		0			0
$304$	−8.00387	−	13.8631i	−0.459053	−	0.795104i
$305$	1.14156	−	1.97724i	0.0653655	−	0.113216i
$306$		0			0
$307$	−12.6878			−0.724130			−0.362065	−	0.932153i	$-0.617928\pi$
$307$	−12.6878			−0.724130			−0.362065	+	0.932153i	$0.617928\pi$
$308$		0			0
$309$		0			0
$310$	−5.07057	+	8.78249i	−0.287989	+	0.498812i
$311$	16.4902			0.935073			0.467537	−	0.883974i	$-0.345142\pi$
$311$	16.4902			0.935073			0.467537	+	0.883974i	$0.345142\pi$
$312$		0			0
$313$	28.5185			1.61196			0.805980	−	0.591943i	$-0.201639\pi$
$313$	28.5185			1.61196			0.805980	+	0.591943i	$0.201639\pi$
$314$	45.7229			2.58029
$315$		0			0
$316$	−26.2841			−1.47859
$317$	25.8949			1.45440			0.727200	−	0.686425i	$-0.240821\pi$
$317$	25.8949			1.45440			0.727200	+	0.686425i	$0.240821\pi$
$318$		0			0
$319$	−23.4688			−1.31400
$320$	0.720285	−	1.24757i	0.0402652	−	0.0697413i
$321$		0			0
$322$		0			0
$323$	−3.98545			−0.221756
$324$		0			0
$325$	−11.5248	+	19.9616i	−0.639282	+	1.10727i
$326$	1.21301	+	2.10100i	0.0671825	+	0.116363i
$327$		0			0
$328$	3.61721	+	6.26519i	0.199727	+	0.345937i
$329$		0			0
$330$		0			0
$331$	8.21894			0.451754			0.225877	−	0.974156i	$-0.427475\pi$
$331$	8.21894			0.451754			0.225877	+	0.974156i	$0.427475\pi$
$332$	−0.482926	+	0.836452i	−0.0265040	+	0.0459063i
$333$		0			0
$334$	−25.1163	−	43.5028i	−1.37430	−	2.38037i
$335$	1.30066	−	2.25281i	0.0710626	−	0.123084i
$336$		0			0
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	0.797033	−	0.603936i	$-0.206402\pi$
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	−0.921540	+	0.388283i	$0.873068\pi$
$338$	21.1925	−	36.7065i	1.15272	−	1.99657i
$339$		0			0
$340$	3.20574	+	5.55250i	0.173856	+	0.301127i
$341$	−8.83409	−	15.3011i	−0.478393	−	0.828601i
$342$		0			0
$343$		0			0
$344$	0.564178	−	0.977185i	0.0304184	−	0.0526863i
$345$		0			0
$346$	57.4347			3.08771
$347$	−22.4662			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$347$	−22.4662			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$348$		0			0
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	0.270445	+	0.962735i	$0.412829\pi$
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	−0.968976	+	0.247155i	$0.920504\pi$
$350$		0			0
$351$		0			0
$352$	−8.91534	−	15.4418i	−0.475189	−	0.823052i
$353$	−0.177519	−	0.307471i	−0.00944836	−	0.0163650i	0.861263	−	0.508160i	$-0.169674\pi$
$353$	−0.177519	−	0.307471i	−0.00944836	−	0.0163650i	−0.870711	+	0.491795i	$0.836341\pi$
$354$		0			0
$355$	−1.61809	+	2.80261i	−0.0858792	+	0.148747i
$356$	24.3234	+	42.1294i	1.28914	+	2.23285i
$357$		0			0
$358$	9.30200	−	16.1115i	0.491626	−	0.851522i
$359$	2.72803	+	4.72508i	0.143980	+	0.249380i	0.928992	−	0.370100i	$-0.120677\pi$
$359$	2.72803	+	4.72508i	0.143980	+	0.249380i	−0.785012	+	0.619480i	$0.787343\pi$
$360$		0			0
$361$	6.59240	−	11.4184i	0.346968	−	0.600967i
$362$	8.72462			0.458556
$363$		0			0
$364$		0			0
$365$	5.61974	+	9.73367i	0.294150	+	0.509484i
$366$		0			0
$367$	−5.46198	−	9.46043i	−0.285113	−	0.493830i	0.687523	−	0.726162i	$-0.258698\pi$
$367$	−5.46198	−	9.46043i	−0.285113	−	0.493830i	−0.972637	+	0.232332i	$0.925364\pi$
$368$	10.4966	−	18.1806i	0.547173	−	0.947731i
$369$		0			0
$370$	10.1411			0.527213
$371$		0			0
$372$		0			0
$373$	−0.865715	+	1.49946i	−0.0448250	+	0.0776392i	−0.887567	−	0.460678i	$-0.847606\pi$
$373$	−0.865715	+	1.49946i	−0.0448250	+	0.0776392i	0.842742	+	0.538317i	$0.180940\pi$
$374$	−16.2344			−0.839462
$375$		0			0
$376$	−6.24216			−0.321915
$377$	−32.9908			−1.69911
$378$		0			0
$379$	−12.1334			−0.623251			−0.311626	−	0.950205i	$-0.600873\pi$
$379$	−12.1334			−0.623251			−0.311626	+	0.950205i	$0.600873\pi$
$380$	9.35504			0.479903
$381$		0			0
$382$	14.3259			0.732979
$383$	−4.35591	+	7.54467i	−0.222577	+	0.385514i	−0.955590	−	0.294700i	$-0.904780\pi$
$383$	−4.35591	+	7.54467i	−0.222577	+	0.385514i	0.733013	+	0.680215i	$0.238113\pi$
$384$		0			0
$385$		0			0
$386$	−24.2986			−1.23677
$387$		0			0
$388$	−27.5783	+	47.7670i	−1.40008	+	2.42500i
$389$	1.82160	+	3.15511i	0.0923590	+	0.159970i	0.908503	−	0.417878i	$-0.137226\pi$
$389$	1.82160	+	3.15511i	0.0923590	+	0.159970i	−0.816144	+	0.577848i	$0.803893\pi$
$390$		0			0
$391$	−2.61334	−	4.52644i	−0.132162	−	0.228912i
$392$		0			0
$393$		0			0
$394$	21.0669			1.06133
$395$	2.61974	−	4.53752i	0.131813	−	0.228307i
$396$		0			0
$397$	7.72281	+	13.3763i	0.387597	+	0.671337i	0.992126	−	0.125246i	$-0.0399720\pi$
$397$	7.72281	+	13.3763i	0.387597	+	0.671337i	−0.604529	+	0.796583i	$0.706639\pi$
$398$	8.35117	−	14.4646i	0.418606	−	0.725047i
$399$		0			0
$400$	14.0287	+	24.2984i	0.701434	+	1.21492i
$401$	9.21095	−	15.9538i	0.459973	−	0.796697i	−0.538986	−	0.842315i	$-0.681192\pi$
$401$	9.21095	−	15.9538i	0.459973	−	0.796697i	0.998959	+	0.0456182i	$0.0145258\pi$
$402$		0			0
$403$	−12.4183	−	21.5092i	−0.618601	−	1.07145i
$404$	−21.4329	−	37.1228i	−1.06633	−	1.84693i
$405$		0			0
$406$		0			0
$407$	−8.83409	+	15.3011i	−0.437890	+	0.758447i
$408$		0			0
$409$	−28.6364			−1.41598			−0.707989	−	0.706223i	$-0.750398\pi$
$409$	−28.6364			−1.41598			−0.707989	+	0.706223i	$0.750398\pi$
$410$	−2.63816			−0.130289
$411$		0			0
$412$	−14.5496	+	25.2007i	−0.716809	+	1.24155i
$413$		0			0
$414$		0			0
$415$	−0.0962667	−	0.166739i	−0.00472554	−	0.00818488i
$416$	−12.5326	−	21.7070i	−0.614459	−	1.06427i
$417$		0			0
$418$	−11.8439	+	20.5142i	−0.579304	+	1.00338i
$419$	−17.3478	−	30.0472i	−0.847494	−	1.46790i	−0.883438	−	0.468548i	$-0.844777\pi$
$419$	−17.3478	−	30.0472i	−0.847494	−	1.46790i	0.0359442	−	0.999354i	$-0.488556\pi$
$420$		0			0
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	−0.310788	−	0.950479i	$-0.600593\pi$
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	0.978533	−	0.206090i	$-0.0660738\pi$
$422$	−4.26604	−	7.38901i	−0.207668	−	0.359691i
$423$		0			0
$424$	−22.2592	+	38.5541i	−1.08100	+	1.87235i
$425$	6.98545			0.338844
$426$		0			0
$427$		0			0
$428$	5.26991	+	9.12776i	0.254731	+	0.441207i
$429$		0			0
$430$	0.205737	+	0.356347i	0.00992152	+	0.0171846i
$431$	13.2961	−	23.0295i	0.640449	−	1.10929i	−0.344883	−	0.938646i	$-0.612081\pi$
$431$	13.2961	−	23.0295i	0.640449	−	1.10929i	0.985333	−	0.170645i	$-0.0545852\pi$
$432$		0			0
$433$	37.1830			1.78690			0.893451	−	0.449160i	$-0.148277\pi$
$433$	37.1830			1.78690			0.893451	+	0.449160i	$0.148277\pi$
$434$		0			0
$435$		0			0
$436$	−8.73055	+	15.1218i	−0.418118	+	0.724201i
$437$	−7.62630			−0.364815
$438$		0			0
$439$	25.0746			1.19675			0.598373	−	0.801218i	$-0.295814\pi$
$439$	25.0746			1.19675			0.598373	+	0.801218i	$0.295814\pi$
$440$	20.8307			0.993064
$441$		0			0
$442$	−22.8212			−1.08549
$443$	−2.04458			−0.0971408			−0.0485704	−	0.998820i	$-0.515467\pi$
$443$	−2.04458			−0.0971408			−0.0485704	+	0.998820i	$0.515467\pi$
$444$		0			0
$445$	−9.69728			−0.459695
$446$	−7.94609	+	13.7630i	−0.376258	+	0.651698i
$447$		0			0
$448$		0			0
$449$	10.2344			0.482992			0.241496	−	0.970402i	$-0.422362\pi$
$449$	10.2344			0.482992			0.241496	+	0.970402i	$0.422362\pi$
$450$		0			0
$451$	2.29813	−	3.98048i	0.108215	−	0.187434i
$452$	36.2918	+	62.8592i	1.70702	+	2.95665i
$453$		0			0
$454$	7.80200	+	13.5135i	0.366166	+	0.634218i
$455$		0			0
$456$		0			0
$457$	−42.5945			−1.99249			−0.996244	−	0.0865948i	$-0.972401\pi$
$457$	−42.5945			−1.99249			−0.996244	+	0.0865948i	$0.972401\pi$
$458$	29.6065	−	51.2800i	1.38342	−	2.39616i
$459$		0			0
$460$	6.13429	+	10.6249i	0.286013	+	0.495388i
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	−0.860088	−	0.510145i	$-0.829592\pi$
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	0.871843	+	0.489786i	$0.162925\pi$
$462$		0			0
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	0.833206	−	0.552962i	$-0.186503\pi$
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	−0.895482	+	0.445097i	$0.853169\pi$
$464$	−20.0792	+	34.7782i	−0.932153	+	1.61454i
$465$		0			0
$466$	10.7934	+	18.6947i	0.499994	+	0.866015i
$467$	−15.7083	−	27.2075i	−0.726892	−	1.25901i	−0.958191	−	0.286131i	$-0.907631\pi$
$467$	−15.7083	−	27.2075i	−0.726892	−	1.25901i	0.231299	−	0.972883i	$-0.425702\pi$
$468$		0			0
$469$		0			0
$470$	1.13816	−	1.97134i	0.0524992	−	0.0909313i
$471$		0			0
$472$	40.6691			1.87195
$473$	−0.716881			−0.0329622
$474$		0			0
$475$	5.09627	−	8.82699i	0.233833	−	0.405010i
$476$		0			0
$477$		0			0
$478$	−18.4363	−	31.9326i	−0.843256	−	1.46056i
$479$	−8.22028	−	14.2380i	−0.375594	−	0.650549i	0.614821	−	0.788666i	$-0.289228\pi$
$479$	−8.22028	−	14.2380i	−0.375594	−	0.650549i	−0.990416	+	0.138118i	$0.955895\pi$
$480$		0			0
$481$	−12.4183	+	21.5092i	−0.566227	+	0.980735i
$482$	−6.84137	−	11.8496i	−0.311616	−	0.539734i
$483$		0			0
$484$	−8.93242	+	15.4714i	−0.406019	+	0.703246i
$485$	−5.49747	−	9.52190i	−0.249627	−	0.432367i
$486$		0			0
$487$	1.48767	−	2.57673i	0.0674129	−	0.116763i	−0.830349	−	0.557244i	$-0.811859\pi$
$487$	1.48767	−	2.57673i	0.0674129	−	0.116763i	0.897762	+	0.440481i	$0.145192\pi$
$488$	15.8530			0.717631
$489$		0			0
$490$		0			0
$491$	−13.2430	−	22.9376i	−0.597650	−	1.03516i	−0.993167	−	0.116702i	$-0.962768\pi$
$491$	−13.2430	−	22.9376i	−0.597650	−	1.03516i	0.395517	−	0.918459i	$-0.370565\pi$
$492$		0			0
$493$	4.99912	+	8.65873i	0.225149	+	0.389970i
$494$	−16.6493	+	28.8374i	−0.749087	+	1.29746i
$495$		0			0
$496$	−30.2327			−1.35749
$497$		0			0
$498$		0			0
$499$	6.72193	−	11.6427i	0.300915	−	0.521200i	−0.675428	−	0.737426i	$-0.736041\pi$
$499$	6.72193	−	11.6427i	0.300915	−	0.521200i	0.976343	+	0.216225i	$0.0693746\pi$
$500$	−35.7939			−1.60075
$501$		0			0
$502$	−30.5544			−1.36371
$503$	22.6631			1.01050			0.505250	−	0.862973i	$-0.331400\pi$
$503$	22.6631			1.01050			0.505250	+	0.862973i	$0.331400\pi$
$504$		0			0
$505$	8.54488			0.380242
$506$	−31.0651			−1.38101
$507$		0			0
$508$	77.8786			3.45530
$509$	4.77379	−	8.26844i	0.211594	−	0.366492i	−0.740619	−	0.671925i	$-0.765468\pi$
$509$	4.77379	−	8.26844i	0.211594	−	0.366492i	0.952214	+	0.305433i	$0.0988011\pi$
$510$		0			0
$511$		0			0
$512$	50.5553			2.23425
$513$		0			0
$514$	−13.3773	+	23.1702i	−0.590049	+	1.02199i
$515$	−2.90033	−	5.02352i	−0.127804	−	0.221363i
$516$		0			0
$517$	1.98293	+	3.43453i	0.0872090	+	0.151050i
$518$		0			0
$519$		0			0
$520$	29.2823			1.28411
$521$	−1.55644	+	2.69583i	−0.0681887	+	0.118106i	−0.898104	−	0.439783i	$-0.855055\pi$
$521$	−1.55644	+	2.69583i	−0.0681887	+	0.118106i	0.829915	+	0.557889i	$0.188389\pi$
$522$		0			0
$523$	8.07444	+	13.9853i	0.353071	+	0.611537i	0.986786	−	0.162030i	$-0.0518041\pi$
$523$	8.07444	+	13.9853i	0.353071	+	0.611537i	−0.633715	+	0.773567i	$0.718471\pi$
$524$	−42.3448	+	73.3434i	−1.84984	+	3.20402i
$525$		0			0
$526$	35.8965	+	62.1746i	1.56516	+	2.71094i
$527$	−3.76352	+	6.51860i	−0.163941	+	0.283955i
$528$		0			0
$529$	6.49928	+	11.2571i	0.282578	+	0.489439i
$530$	−8.11721	−	14.0594i	−0.352589	−	0.610702i
$531$		0			0
$532$		0			0
$533$	3.23055	−	5.59548i	0.139931	−	0.242367i
$534$		0			0
$535$	−2.10101			−0.0908348
$536$	18.0624			0.780178
$537$		0			0
$538$	−9.47431	+	16.4100i	−0.408466	+	0.707485i
$539$		0			0
$540$		0			0
$541$	2.50774	+	4.34353i	0.107816	+	0.186743i	0.914885	−	0.403714i	$-0.132281\pi$
$541$	2.50774	+	4.34353i	0.107816	+	0.186743i	−0.807069	+	0.590457i	$0.798948\pi$
$542$	17.2665	+	29.9065i	0.741660	+	1.28459i
$543$		0			0
$544$	−3.79813	+	6.57856i	−0.162844	+	0.282053i
$545$	−1.74035	−	3.01438i	−0.0745485	−	0.129122i
$546$		0			0
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	−0.986648	−	0.162870i	$-0.947925\pi$
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	0.634373	+	0.773027i	$0.281258\pi$
$548$	40.0467	+	69.3629i	1.71071	+	2.96304i
$549$		0			0
$550$	20.7592	−	35.9561i	0.885177	−	1.53317i
$551$	14.5885			0.621492
$552$		0			0
$553$		0			0
$554$	−7.78699	−	13.4875i	−0.330837	−	0.573027i
$555$		0			0
$556$	−48.6528	−	84.2691i	−2.06334	−	3.57380i
$557$	−17.2815	+	29.9325i	−0.732242	+	1.26828i	0.223681	+	0.974662i	$0.428193\pi$
$557$	−17.2815	+	29.9325i	−0.732242	+	1.26828i	−0.955923	+	0.293618i	$0.905141\pi$
$558$		0			0
$559$	−1.00774			−0.0426229
$560$		0			0
$561$		0			0
$562$	−4.19341	+	7.26320i	−0.176888	+	0.306380i
$563$	37.2104			1.56823			0.784115	−	0.620615i	$-0.213117\pi$
$563$	37.2104			1.56823			0.784115	+	0.620615i	$0.213117\pi$
$564$		0			0
$565$	−14.4688			−0.608709
$566$	−73.4894			−3.08899
$567$		0			0
$568$	−22.4706			−0.942845
$569$	−0.404667			−0.0169645			−0.00848226	−	0.999964i	$-0.502700\pi$
$569$	−0.404667			−0.0169645			−0.00848226	+	0.999964i	$0.502700\pi$
$570$		0			0
$571$	−37.7793			−1.58101			−0.790507	−	0.612453i	$-0.790183\pi$
$571$	−37.7793			−1.58101			−0.790507	+	0.612453i	$0.790183\pi$
$572$	−46.6639	+	80.8243i	−1.95112	+	3.37943i
$573$		0			0
$574$		0			0
$575$	13.3669			0.557438
$576$		0			0
$577$	1.10560	−	1.91496i	0.0460267	−	0.0797206i	−0.842094	−	0.539330i	$-0.818677\pi$
$577$	1.10560	−	1.91496i	0.0460267	−	0.0797206i	0.888121	+	0.459610i	$0.152011\pi$
$578$	−18.0646	−	31.2889i	−0.751390	−	1.30145i
$579$		0			0
$580$	−11.7344	−	20.3246i	−0.487245	−	0.843934i
$581$		0			0
$582$		0			0
$583$	28.2841			1.17141
$584$	−39.0210	+	67.5864i	−1.61470	+	2.79674i
$585$		0			0
$586$	10.6591	+	18.4621i	0.440323	+	0.762662i
$587$	12.1049	−	20.9663i	0.499622	−	0.865371i	−0.500378	−	0.865807i	$-0.666806\pi$
$587$	12.1049	−	20.9663i	0.499622	−	0.865371i	1.00000		0.000436347i	$0.000138894\pi$
$588$		0			0
$589$	5.49138	+	9.51135i	0.226268	+	0.391908i
$590$	−7.41534	+	12.8438i	−0.305285	+	0.528769i
$591$		0			0
$592$	15.1163	+	26.1823i	0.621277	+	1.07608i
$593$	6.11927	+	10.5989i	0.251288	+	0.435244i	0.963881	−	0.266334i	$-0.0858124\pi$
$593$	6.11927	+	10.5989i	0.251288	+	0.435244i	−0.712592	+	0.701578i	$0.752479\pi$
$594$		0			0
$595$		0			0
$596$	−33.4295	+	57.9016i	−1.36932	+	2.37174i
$597$		0			0
$598$	−43.6691			−1.78576
$599$	−39.6168			−1.61870			−0.809349	−	0.587328i	$-0.800180\pi$
$599$	−39.6168			−1.61870			−0.809349	+	0.587328i	$0.800180\pi$
$600$		0			0
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	−0.378879	−	0.925446i	$-0.623690\pi$
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	0.990899	−	0.134605i	$-0.0429764\pi$
$602$		0			0
$603$		0			0
$604$	41.8127	+	72.4218i	1.70134	+	2.94680i
$605$	−1.78059	−	3.08408i	−0.0723914	−	0.125386i
$606$		0			0
$607$	9.74216	−	16.8739i	0.395422	−	0.684891i	−0.597733	−	0.801695i	$-0.703932\pi$
$607$	9.74216	−	16.8739i	0.395422	−	0.684891i	0.993155	+	0.116804i	$0.0372650\pi$
$608$	5.54189	+	9.59883i	0.224753	+	0.389284i
$609$		0			0
$610$	−2.89053	+	5.00654i	−0.117034	+	0.202709i
$611$	2.78746	+	4.82802i	0.112768	+	0.195321i
$612$		0			0
$613$	9.26382	−	16.0454i	0.374162	−	0.648068i	−0.616039	−	0.787716i	$-0.711264\pi$
$613$	9.26382	−	16.0454i	0.374162	−	0.648068i	0.990201	+	0.139648i	$0.0445970\pi$
$614$	32.1266			1.29652
$615$		0			0
$616$		0			0
$617$	13.9201	+	24.1103i	0.560402	+	0.970644i	0.997461	+	0.0712118i	$0.0226866\pi$
$617$	13.9201	+	24.1103i	0.560402	+	0.970644i	−0.437059	+	0.899433i	$0.643980\pi$
$618$		0			0
$619$	22.4907	+	38.9550i	0.903976	+	1.56573i	0.822286	+	0.569075i	$0.192699\pi$
$619$	22.4907	+	38.9550i	0.903976	+	1.56573i	0.0816906	+	0.996658i	$0.473968\pi$
$620$	8.83409	−	15.3011i	0.354786	−	0.614507i
$621$		0			0
$622$	−41.7547			−1.67421
$623$		0			0
$624$		0			0
$625$	−6.99912	+	12.1228i	−0.279965	+	0.484913i
$626$	−72.2113			−2.88614
$627$		0			0
$628$	−79.6596			−3.17877
$629$	7.52704			0.300123
$630$		0			0
$631$	9.43613			0.375646			0.187823	−	0.982203i	$-0.439857\pi$
$631$	9.43613			0.375646			0.187823	+	0.982203i	$0.439857\pi$
$632$	36.3806			1.44714
$633$		0			0
$634$	−65.5681			−2.60404
$635$	−7.76217	+	13.4445i	−0.308032	+	0.533528i
$636$		0			0
$637$		0			0
$638$	59.4252			2.35267
$639$		0			0
$640$	−5.86571	+	10.1597i	−0.231863	+	0.401598i
$641$	18.6951	+	32.3808i	0.738410	+	1.27896i	0.953211	+	0.302306i	$0.0977566\pi$
$641$	18.6951	+	32.3808i	0.738410	+	1.27896i	−0.214800	+	0.976658i	$0.568910\pi$
$642$		0			0
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	0.849698	−	0.527270i	$-0.176784\pi$
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	−0.881478	+	0.472225i	$0.843451\pi$
$644$		0			0
$645$		0			0
$646$	10.0915			0.397046
$647$	−20.5881	+	35.6597i	−0.809402	+	1.40193i	0.103876	+	0.994590i	$0.466875\pi$
$647$	−20.5881	+	35.6597i	−0.809402	+	1.40193i	−0.913278	+	0.407336i	$0.866458\pi$
$648$		0			0
$649$	−12.9192	−	22.3767i	−0.507124	−	0.878364i
$650$	29.1819	−	50.5445i	1.14461	−	1.98252i
$651$		0			0
$652$	−2.11334	−	3.66041i	−0.0827648	−	0.143353i
$653$	1.52600	−	2.64310i	0.0597169	−	0.103433i	−0.834621	−	0.550824i	$-0.814314\pi$
$653$	1.52600	−	2.64310i	0.0597169	−	0.103433i	0.894338	+	0.447391i	$0.147647\pi$
$654$		0			0
$655$	−8.44104	−	14.6203i	−0.329819	−	0.571263i
$656$	−3.93242	−	6.81115i	−0.153535	−	0.265931i
$657$		0			0
$658$		0			0
$659$	20.8175	−	36.0569i	0.810934	−	1.40458i	−0.101277	−	0.994858i	$-0.532293\pi$
$659$	20.8175	−	36.0569i	0.810934	−	1.40458i	0.912211	−	0.409721i	$-0.134374\pi$
$660$		0			0
$661$	20.3010			0.789616			0.394808	−	0.918764i	$-0.370811\pi$
$661$	20.3010			0.789616			0.394808	+	0.918764i	$0.370811\pi$
$662$	−20.8111			−0.808846
$663$		0			0
$664$	0.668434	−	1.15776i	0.0259403	−	0.0449298i
$665$		0			0
$666$		0			0
$667$	9.56599	+	16.5688i	0.370397	+	0.641546i
$668$	43.7584	+	75.7917i	1.69306	+	2.93247i
$669$		0			0
$670$	−3.29339	+	5.70431i	−0.127235	+	0.220377i
$671$	−5.03596	−	8.72254i	−0.194411	−	0.336730i
$672$		0			0
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	−0.857909	−	0.513801i	$-0.828237\pi$
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	0.873920	+	0.486071i	$0.161570\pi$
$674$	5.78746	+	10.0242i	0.222924	+	0.386117i
$675$		0			0
$676$	−36.9222	+	63.9511i	−1.42008	+	2.45966i
$677$	−10.8672			−0.417660			−0.208830	−	0.977952i	$-0.566966\pi$
$677$	−10.8672			−0.417660			−0.208830	+	0.977952i	$0.566966\pi$
$678$		0			0
$679$		0			0
$680$	−4.43717	−	7.68540i	−0.170158	−	0.294722i
$681$		0			0
$682$	22.3687	+	38.7437i	0.856542	+	1.48357i
$683$	16.3473	−	28.3143i	0.625512	−	1.08342i	−0.362930	−	0.931817i	$-0.618223\pi$
$683$	16.3473	−	28.3143i	0.625512	−	1.08342i	0.988442	−	0.151602i	$-0.0484432\pi$
$684$		0			0
$685$	−15.9659			−0.610024
$686$		0			0
$687$		0			0
$688$	−0.613341	+	1.06234i	−0.0233834	+	0.0405012i
$689$	39.7597			1.51472
$690$		0			0
$691$	14.9982			0.570560			0.285280	−	0.958444i	$-0.407913\pi$
$691$	14.9982			0.570560			0.285280	+	0.958444i	$0.407913\pi$
$692$	−100.064			−3.80387
$693$		0			0
$694$	56.8863			2.15937
$695$	19.3969			0.735767
$696$		0			0
$697$	−1.95811			−0.0741687
$698$	33.0428	−	57.2318i	1.25069	−	2.16626i
$699$		0			0
$700$		0			0
$701$	−26.4688			−0.999714			−0.499857	−	0.866108i	$-0.666614\pi$
$701$	−26.4688			−0.999714			−0.499857	+	0.866108i	$0.666614\pi$
$702$		0			0
$703$	5.49138	−	9.51135i	0.207111	−	0.358727i
$704$	−3.17752	−	5.50362i	−0.119757	−	0.207426i
$705$		0			0
$706$	0.449493	+	0.778544i	0.0169169	+	0.0293009i
$707$		0			0
$708$		0			0
$709$	15.3601			0.576860			0.288430	−	0.957501i	$-0.406867\pi$
$709$	15.3601			0.576860			0.288430	+	0.957501i	$0.406867\pi$
$710$	4.09714	−	7.09646i	0.153763	−	0.266325i
$711$		0			0
$712$	−33.6668	−	58.3127i	−1.26172	−	2.18536i
$713$	−7.20162	+	12.4736i	−0.269703	+	0.467139i
$714$		0			0
$715$	−9.30200	−	16.1115i	−0.347875	−	0.602538i
$716$	−16.2062	+	28.0700i	−0.605654	+	1.04902i
$717$		0			0
$718$	−6.90760	−	11.9643i	−0.257789	−	0.446504i
$719$	13.3653	+	23.1494i	0.498442	+	0.863326i	0.999998	−	0.00179839i	$-0.000572447\pi$
$719$	13.3653	+	23.1494i	0.498442	+	0.863326i	−0.501557	+	0.865125i	$0.667239\pi$
$720$		0			0
$721$		0			0
$722$	−16.6925	+	28.9123i	−0.621232	+	1.07600i
$723$		0			0
$724$	−15.2003			−0.564914
$725$	−25.5699			−0.949641
$726$		0			0
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	−0.0379552	−	0.999279i	$-0.512084\pi$
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	0.884379	−	0.466770i	$-0.154582\pi$
$728$		0			0
$729$		0			0
$730$	−14.2297	−	24.6465i	−0.526664	−	0.912209i
$731$	0.152704	+	0.264490i	0.00564795	+	0.00978253i
$732$		0			0
$733$	−2.98751	+	5.17452i	−0.110346	+	0.191125i	−0.915910	−	0.401384i	$-0.868529\pi$
$733$	−2.98751	+	5.17452i	−0.110346	+	0.191125i	0.805564	+	0.592509i	$0.201863\pi$
$734$	13.8302	+	23.9546i	0.510483	+	0.884182i
$735$		0			0
$736$	−7.26786	+	12.5883i	−0.267897	+	0.464011i
$737$	−5.73783	−	9.93821i	−0.211356	−	0.366079i
$738$		0			0
$739$	17.7981	−	30.8273i	0.654715	−	1.13400i	−0.327250	−	0.944938i	$-0.606122\pi$
$739$	17.7981	−	30.8273i	0.654715	−	1.13400i	0.981965	−	0.189062i	$-0.0605447\pi$
$740$	−17.6682			−0.649495
$741$		0			0
$742$		0			0
$743$	−14.6544	−	25.3821i	−0.537616	−	0.931178i	−0.999032	−	0.0439943i	$-0.985992\pi$
$743$	−14.6544	−	25.3821i	−0.537616	−	0.931178i	0.461416	−	0.887184i	$-0.347342\pi$
$744$		0			0
$745$	−6.66385	−	11.5421i	−0.244145	−	0.422871i
$746$	2.19207	−	3.79677i	0.0802573	−	0.139010i
$747$		0			0
$748$	28.2841			1.03417
$749$		0			0
$750$		0			0
$751$	8.66684	−	15.0114i	0.316258	−	0.547774i	−0.663446	−	0.748224i	$-0.730907\pi$
$751$	8.66684	−	15.0114i	0.316258	−	0.547774i	0.979704	+	0.200450i	$0.0642403\pi$
$752$	6.78611			0.247464
$753$		0			0
$754$	83.5357			3.04219
$755$	−16.6699			−0.606681
$756$		0			0
$757$	−2.77156			−0.100734			−0.0503671	−	0.998731i	$-0.516039\pi$
$757$	−2.77156			−0.100734			−0.0503671	+	0.998731i	$0.516039\pi$
$758$	30.7229			1.11590
$759$		0			0
$760$	−12.9486			−0.469696
$761$	3.75372	−	6.50163i	0.136072	−	0.235684i	−0.789934	−	0.613191i	$-0.789885\pi$
$761$	3.75372	−	6.50163i	0.136072	−	0.235684i	0.926007	+	0.377508i	$0.123219\pi$
$762$		0			0
$763$		0			0
$764$	−24.9590			−0.902987
$765$		0			0
$766$	11.0296	−	19.1038i	0.398514	−	0.690247i
$767$	−18.1609	−	31.4556i	−0.655752	−	1.13580i
$768$		0			0
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	0.847013	−	0.531572i	$-0.178398\pi$
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	−0.883861	+	0.467749i	$0.845065\pi$
$770$		0			0
$771$		0			0
$772$	42.3337			1.52362
$773$	−12.4709	+	21.6002i	−0.448547	+	0.776907i	−0.998292	−	0.0584263i	$-0.981392\pi$
$773$	−12.4709	+	21.6002i	−0.448547	+	0.776907i	0.549744	+	0.835333i	$0.314725\pi$
$774$		0			0
$775$	−9.62495	−	16.6709i	−0.345738	−	0.598837i
$776$	38.1721	−	66.1159i	1.37030	−	2.37342i
$777$		0			0
$778$	−4.61246	−	7.98902i	−0.165365	−	0.286420i
$779$	−1.42855	+	2.47432i	−0.0511831	+	0.0886516i
$780$		0			0
$781$	7.13816	+	12.3636i	0.255423	+	0.442406i
$782$	6.61721	+	11.4613i	0.236631	+	0.409857i
$783$		0			0
$784$		0			0
$785$	7.93969	−	13.7520i	0.283380	−	0.490828i
$786$		0			0
$787$	7.10700			0.253337			0.126669	−	0.991945i	$-0.459572\pi$
$787$	7.10700			0.253337			0.126669	+	0.991945i	$0.459572\pi$
$788$	−36.7033			−1.30750
$789$		0			0
$790$	−6.63341	+	11.4894i	−0.236006	+	0.408774i
$791$		0			0
$792$		0			0
$793$	−7.07919	−	12.2615i	−0.251389	−	0.435419i
$794$	−19.5548	−	33.8700i	−0.693975	−	1.20200i
$795$		0			0
$796$	−14.5496	+	25.2007i	−0.515698	+	0.893215i
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	0.993376	+	0.114905i	$0.0366564\pi$
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	−0.397178	+	0.917742i	$0.630010\pi$
$798$		0			0
$799$	0.844770	−	1.46318i	0.0298858	−	0.0517638i
$800$	−9.71348	−	16.8242i	−0.343423	−	0.594827i
$801$		0			0
$802$	−23.3229	+	40.3965i	−0.823562	+	1.42645i
$803$	49.5827			1.74973
$804$		0			0
$805$		0			0
$806$	31.4443	+	54.4632i	1.10758	+	1.91838i
$807$		0			0
$808$	29.6660	+	51.3830i	1.04364	+	1.80765i
$809$	−6.40807	+	11.0991i	−0.225296	+	0.390224i	−0.956408	−	0.292033i	$-0.905668\pi$
$809$	−6.40807	+	11.0991i	−0.225296	+	0.390224i	0.731112	+	0.682257i	$0.239002\pi$
$810$		0			0
$811$	−26.1239			−0.917335			−0.458667	−	0.888608i	$-0.651673\pi$
$811$	−26.1239			−0.917335			−0.458667	+	0.888608i	$0.651673\pi$
$812$		0			0
$813$		0			0
$814$	22.3687	−	38.7437i	0.784023	−	1.35797i
$815$	0.842549			0.0295132
$816$		0			0
$817$	0.445622			0.0155904
$818$	72.5099			2.53525
$819$		0			0
$820$	4.59627			0.160509
$821$	−27.6641			−0.965483			−0.482741	−	0.875763i	$-0.660359\pi$
$821$	−27.6641			−0.965483			−0.482741	+	0.875763i	$0.660359\pi$
$822$		0			0
$823$	27.8324			0.970178			0.485089	−	0.874465i	$-0.338787\pi$
$823$	27.8324			0.970178			0.485089	+	0.874465i	$0.338787\pi$
$824$	20.1386	−	34.8811i	0.701562	−	1.21514i
$825$		0			0
$826$		0			0
$827$	−4.65507			−0.161873			−0.0809363	−	0.996719i	$-0.525791\pi$
$827$	−4.65507			−0.161873			−0.0809363	+	0.996719i	$0.525791\pi$
$828$		0			0
$829$	4.98680	−	8.63738i	0.173199	−	0.299989i	−0.766338	−	0.642438i	$-0.777923\pi$
$829$	4.98680	−	8.63738i	0.173199	−	0.299989i	0.939536	+	0.342449i	$0.111256\pi$
$830$	0.243756	+	0.422197i	0.00846089	+	0.0146547i
$831$		0			0
$832$	−4.46673	−	7.73660i	−0.154856	−	0.268218i
$833$		0			0
$834$		0			0
$835$	−17.4456			−0.603731
$836$	20.6348	−	35.7404i	0.713668	−	1.23611i
$837$		0			0
$838$	43.9261	+	76.0822i	1.51740	+	2.62822i
$839$	−3.36484	+	5.82807i	−0.116167	+	0.201207i	−0.918246	−	0.396011i	$-0.870394\pi$
$839$	−3.36484	+	5.82807i	−0.116167	+	0.201207i	0.802079	+	0.597218i	$0.203727\pi$
$840$		0			0
$841$	−3.79901	−	6.58008i	−0.131000	−	0.226899i
$842$	−34.6921	+	60.0885i	−1.19557	+	2.07079i
$843$		0			0
$844$	7.43242	+	12.8733i	0.255834	+	0.443118i
$845$	−7.36009	−	12.7480i	−0.253195	−	0.438546i
$846$		0			0
$847$		0			0
$848$	24.1989	−	41.9138i	0.830995	−	1.43932i
$849$		0			0
$850$	−17.6878			−0.606686
$851$	14.4032			0.493737
$852$		0			0
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	−0.911326	−	0.411686i	$-0.864940\pi$
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	0.812193	+	0.583388i	$0.198273\pi$
$854$		0			0
$855$		0			0
$856$	−7.29426	−	12.6340i	−0.249313	−	0.431822i
$857$	−17.4538	−	30.2309i	−0.596211	−	1.03267i	−0.993375	−	0.114921i	$-0.963339\pi$
$857$	−17.4538	−	30.2309i	−0.596211	−	1.03267i	0.397163	−	0.917748i	$-0.369995\pi$
$858$		0			0
$859$	6.30747	−	10.9249i	0.215208	−	0.372751i	−0.738129	−	0.674660i	$-0.764290\pi$
$859$	6.30747	−	10.9249i	0.215208	−	0.372751i	0.953337	+	0.301909i	$0.0976237\pi$
$860$	−0.358441	−	0.620838i	−0.0122227	−	0.0211704i
$861$		0			0
$862$	−33.6668	+	58.3127i	−1.14670	+	1.98614i
$863$	−12.1027	−	20.9624i	−0.411979	−	0.713569i	0.583127	−	0.812381i	$-0.301829\pi$
$863$	−12.1027	−	20.9624i	−0.411979	−	0.713569i	−0.995106	+	0.0988119i	$0.968496\pi$
$864$		0			0
$865$	9.97343	−	17.2745i	0.339107	−	0.587350i
$866$	−94.1508			−3.19937
$867$		0			0
$868$		0			0
$869$	−11.5569	−	20.0171i	−0.392041	−	0.679035i
$870$		0			0
$871$	−8.06583	−	13.9704i	−0.273300	−	0.473370i
$872$	12.0842	−	20.9305i	0.409224	−	0.708797i
$873$		0			0
$874$	19.3105			0.653186
$875$		0			0
$876$		0			0
$877$	0.562834	−	0.974856i	0.0190055	−	0.0329186i	−0.856366	−	0.516369i	$-0.827283\pi$
$877$	0.562834	−	0.974856i	0.0190055	−	0.0329186i	0.875372	+	0.483450i	$0.160617\pi$
$878$	−63.4911			−2.14272
$879$		0			0
$880$	−22.6459			−0.763393
$881$	4.38331			0.147678			0.0738388	−	0.997270i	$-0.476475\pi$
$881$	4.38331			0.147678			0.0738388	+	0.997270i	$0.476475\pi$
$882$		0			0
$883$	−6.88949			−0.231850			−0.115925	−	0.993258i	$-0.536983\pi$
$883$	−6.88949			−0.231850			−0.115925	+	0.993258i	$0.536983\pi$
$884$	39.7597			1.33726
$885$		0			0
$886$	5.17705			0.173926
$887$	19.5376	−	33.8401i	0.656009	−	1.13624i	−0.325631	−	0.945497i	$-0.605577\pi$
$887$	19.5376	−	33.8401i	0.656009	−	1.13624i	0.981640	−	0.190744i	$-0.0610899\pi$
$888$		0			0
$889$		0			0
$890$	24.5544			0.823065
$891$		0			0
$892$	13.8439	−	23.9783i	0.463528	−	0.802854i
$893$	−1.23261	−	2.13495i	−0.0412478	−	0.0714432i
$894$		0			0
$895$	−3.23055	−	5.59548i	−0.107985	−	0.187036i
$896$		0			0
$897$		0			0
$898$	−25.9145			−0.864777
$899$	13.7761	−	23.8610i	0.459460	−	0.795809i
$900$		0			0
$901$	−6.02481	−	10.4353i	−0.200716	−	0.347650i
$902$	−5.81908	+	10.0789i	−0.193754	+	0.335592i
$903$		0			0
$904$	−50.2327	−	87.0055i	−1.67071	−	2.89376i
$905$	1.51501	−	2.62408i	0.0503608	−	0.0872275i
$906$		0			0
$907$	−21.2469	−	36.8007i	−0.705492	−	1.22195i	−0.966514	−	0.256615i	$-0.917393\pi$
$907$	−21.2469	−	36.8007i	−0.705492	−	1.22195i	0.261022	−	0.965333i	$-0.415941\pi$
$908$	−13.5929	−	23.5435i	−0.451095	−	0.781319i
$909$		0			0
$910$		0			0
$911$	−7.74675	+	13.4178i	−0.256661	+	0.444550i	−0.965345	−	0.260976i	$-0.915956\pi$
$911$	−7.74675	+	13.4178i	−0.256661	+	0.444550i	0.708684	+	0.705526i	$0.249289\pi$
$912$		0			0
$913$	−0.849356			−0.0281096
$914$	107.853			3.56746
$915$		0			0
$916$	−51.5813	+	89.3414i	−1.70429	+	2.95192i
$917$		0			0
$918$		0			0
$919$	−3.26470	−	5.65463i	−0.107693	−	0.186529i	0.807143	−	0.590357i	$-0.201013\pi$
$919$	−3.26470	−	5.65463i	−0.107693	−	0.186529i	−0.914835	+	0.403828i	$0.867680\pi$
$920$	−8.49067	−	14.7063i	−0.279929	−	0.484851i
$921$		0			0
$922$	−0.639033	+	1.10684i	−0.0210454	+	0.0364518i
$923$	10.0343	+	17.3799i	0.330283	+	0.572068i
$924$		0			0
$925$	−9.62495	+	16.6709i	−0.316466	+	0.548136i
$926$	3.39306	+	5.87695i	0.111503	+	0.193128i
$927$		0			0
$928$	13.9029	−	24.0805i	0.456384	−	0.790480i
$929$	−58.2772			−1.91201			−0.956007	−	0.293343i	$-0.905232\pi$
$929$	−58.2772			−1.91201			−0.956007	+	0.293343i	$0.905232\pi$
$930$		0			0
$931$		0			0
$932$	−18.8045	−	32.5704i	−0.615963	−	1.06688i
$933$		0			0
$934$	39.7747	+	68.8918i	1.30147	+	2.25421i
$935$	−2.81908	+	4.88279i	−0.0921937	+	0.159684i
$936$		0			0
$937$	32.4175			1.05903			0.529516	−	0.848300i	$-0.322374\pi$
$937$	32.4175			1.05903			0.529516	+	0.848300i	$0.322374\pi$
$938$		0			0
$939$		0			0
$940$	−1.98293	+	3.43453i	−0.0646759	+	0.112022i
$941$	27.3226			0.890693			0.445346	−	0.895358i	$-0.353081\pi$
$941$	27.3226			0.890693			0.445346	+	0.895358i	$0.353081\pi$
$942$		0			0
$943$	−3.74691			−0.122016
$944$	−44.2131			−1.43901
$945$		0			0
$946$	1.81521			0.0590175
$947$	38.2131			1.24176			0.620879	−	0.783906i	$-0.286776\pi$
$947$	38.2131			1.24176			0.620879	+	0.783906i	$0.286776\pi$
$948$		0			0
$949$	69.6998			2.26255
$950$	−12.9042	+	22.3507i	−0.418668	+	0.725153i
$951$		0			0
$952$		0			0
$953$	−58.9377			−1.90918			−0.954590	−	0.297924i	$-0.903706\pi$
$953$	−58.9377			−1.90918			−0.954590	+	0.297924i	$0.903706\pi$
$954$		0			0
$955$	2.48767	−	4.30878i	0.0804992	−	0.139429i
$956$	32.1202	+	55.6338i	1.03884	+	1.79933i
$957$		0			0
$958$	20.8145	+	36.0518i	0.672486	+	1.16478i
$959$		0			0
$960$		0			0
$961$	−10.2576			−0.330892
$962$	31.4443	−	54.4632i	1.01381	−	1.75596i
$963$		0			0
$964$	11.9192	+	20.6447i	0.383892	+	0.664921i
$965$	−4.21941	+	7.30823i	−0.135828	+	0.235260i
$966$		0			0
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	0.595960	−	0.803014i	$-0.296772\pi$
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	−0.993411	+	0.114609i	$0.963438\pi$
$968$	12.3637	−	21.4145i	0.397383	−	0.688287i
$969$		0			0
$970$	13.9201	+	24.1103i	0.446947	+	0.774135i
$971$	4.08812	+	7.08082i	0.131194	+	0.227234i	0.924137	−	0.382061i	$-0.124786\pi$
$971$	4.08812	+	7.08082i	0.131194	+	0.227234i	−0.792943	+	0.609296i	$0.791452\pi$
$972$		0			0
$973$		0			0
$974$	−3.76692	+	6.52450i	−0.120700	+	0.209058i
$975$		0			0
$976$	−17.2344			−0.551660
$977$	15.8485			0.507040			0.253520	−	0.967330i	$-0.418412\pi$
$977$	15.8485			0.507040			0.253520	+	0.967330i	$0.418412\pi$
$978$		0			0
$979$	−21.3897	+	37.0480i	−0.683616	+	1.18406i
$980$		0			0
$981$		0			0
$982$	33.5326	+	58.0801i	1.07007	+	1.85341i
$983$	26.6532	+	46.1646i	0.850104	+	1.47242i	0.881114	+	0.472904i	$0.156794\pi$
$983$	26.6532	+	46.1646i	0.850104	+	1.47242i	−0.0310096	+	0.999519i	$0.509872\pi$
$984$		0			0
$985$	3.65822	−	6.33623i	0.116561	−	0.201889i
$986$	−12.6582	−	21.9247i	−0.403120	−	0.698224i
$987$		0			0
$988$	29.0069	−	50.2414i	0.922831	−	1.59839i
$989$	0.292204	+	0.506111i	0.00929153	+	0.0160934i
$990$		0			0
$991$	−20.1047	+	34.8224i	−0.638648	+	1.10617i	0.347082	+	0.937835i	$0.387172\pi$
$991$	−20.1047	+	34.8224i	−0.638648	+	1.10617i	−0.985730	+	0.168335i	$0.946161\pi$
$992$	20.9331			0.664628
$993$		0			0
$994$		0			0
$995$	−2.90033	−	5.02352i	−0.0919466	−	0.159256i
$996$		0			0
$997$	−14.3601	−	24.8724i	−0.454789	−	0.787717i	0.543887	−	0.839158i	$-0.316952\pi$
$997$	−14.3601	−	24.8724i	−0.454789	−	0.787717i	−0.998676	+	0.0514412i	$0.983619\pi$
$998$	−17.0205	+	29.4804i	−0.538776	+	0.933187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.c.802.1		6
3.2	odd	2		441.2.h.d.214.3		6
7.2	even	3		1323.2.g.d.667.3		6
7.3	odd	6		1323.2.f.d.883.3		6
7.4	even	3		189.2.f.b.127.3		6
7.5	odd	6		1323.2.g.e.667.3		6
7.6	odd	2		1323.2.h.b.802.1		6
9.4	even	3		1323.2.g.d.361.3		6
9.5	odd	6		441.2.g.c.67.1		6
21.2	odd	6		441.2.g.c.79.1		6
21.5	even	6		441.2.g.b.79.1		6
21.11	odd	6		63.2.f.a.43.1	yes	6
21.17	even	6		441.2.f.c.295.1		6
21.20	even	2		441.2.h.e.214.3		6
28.11	odd	6		3024.2.r.k.2017.1		6
63.4	even	3		189.2.f.b.64.3		6
63.5	even	6		441.2.h.e.373.3		6
63.11	odd	6		567.2.a.h.1.3		3
63.13	odd	6		1323.2.g.e.361.3		6
63.23	odd	6		441.2.h.d.373.3		6
63.25	even	3		567.2.a.c.1.1		3
63.31	odd	6		1323.2.f.d.442.3		6
63.32	odd	6		63.2.f.a.22.1	✓	6
63.38	even	6		3969.2.a.q.1.3		3
63.40	odd	6		1323.2.h.b.226.1		6
63.41	even	6		441.2.g.b.67.1		6
63.52	odd	6		3969.2.a.l.1.1		3
63.58	even	3	inner	1323.2.h.c.226.1		6
63.59	even	6		441.2.f.c.148.1		6
84.11	even	6		1008.2.r.h.673.3		6
252.11	even	6		9072.2.a.ca.1.1		3
252.67	odd	6		3024.2.r.k.1009.1		6
252.95	even	6		1008.2.r.h.337.3		6
252.151	odd	6		9072.2.a.bs.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	63.32	odd	6
63.2.f.a.43.1	yes	6	21.11	odd	6
189.2.f.b.64.3		6	63.4	even	3
189.2.f.b.127.3		6	7.4	even	3
441.2.f.c.148.1		6	63.59	even	6
441.2.f.c.295.1		6	21.17	even	6
441.2.g.b.67.1		6	63.41	even	6
441.2.g.b.79.1		6	21.5	even	6
441.2.g.c.67.1		6	9.5	odd	6
441.2.g.c.79.1		6	21.2	odd	6
441.2.h.d.214.3		6	3.2	odd	2
441.2.h.d.373.3		6	63.23	odd	6
441.2.h.e.214.3		6	21.20	even	2
441.2.h.e.373.3		6	63.5	even	6
567.2.a.c.1.1		3	63.25	even	3
567.2.a.h.1.3		3	63.11	odd	6
1008.2.r.h.337.3		6	252.95	even	6
1008.2.r.h.673.3		6	84.11	even	6
1323.2.f.d.442.3		6	63.31	odd	6
1323.2.f.d.883.3		6	7.3	odd	6
1323.2.g.d.361.3		6	9.4	even	3
1323.2.g.d.667.3		6	7.2	even	3
1323.2.g.e.361.3		6	63.13	odd	6
1323.2.g.e.667.3		6	7.5	odd	6
1323.2.h.b.226.1		6	63.40	odd	6
1323.2.h.b.802.1		6	7.6	odd	2
1323.2.h.c.226.1		6	63.58	even	3	inner
1323.2.h.c.802.1		6	1.1	even	1	trivial
3024.2.r.k.1009.1		6	252.67	odd	6
3024.2.r.k.2017.1		6	28.11	odd	6
3969.2.a.l.1.1		3	63.52	odd	6
3969.2.a.q.1.3		3	63.38	even	6
9072.2.a.bs.1.3		3	252.151	odd	6
9072.2.a.ca.1.1		3	252.11	even	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.53209 q^{2} +4.41147 q^{4} +(-0.439693 + 0.761570i) q^{5} -6.10607 q^{8} +(1.11334 - 1.92836i) q^{10} +(1.93969 + 3.35965i) q^{11} +(2.72668 + 4.72275i) q^{13} +6.63816 q^{16} +(0.826352 - 1.43128i) q^{17} +(-1.20574 - 2.08840i) q^{19} +(-1.93969 + 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +(1.58125 - 2.73881i) q^{23} +(2.11334 + 3.66041i) q^{25} +(-6.90420 - 11.9584i) q^{26} +(-3.02481 + 5.23913i) q^{29} -4.55438 q^{31} -4.59627 q^{32} +(-2.09240 + 3.62414i) q^{34} +(2.27719 + 3.94421i) q^{37} +(3.05303 + 5.28801i) q^{38} +(2.68479 - 4.65020i) q^{40} +(-0.592396 - 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(8.55690 + 14.8210i) q^{44} +(-4.00387 + 6.93491i) q^{46} +1.02229 q^{47} +(-5.35117 - 9.26849i) q^{50} +(12.0287 + 20.8343i) q^{52} +(3.64543 - 6.31407i) q^{53} -3.41147 q^{55} +(7.65910 - 13.2660i) q^{58} -6.66044 q^{59} -2.59627 q^{61} +11.5321 q^{62} -1.63816 q^{64} -4.79561 q^{65} -2.95811 q^{67} +(3.64543 - 6.31407i) q^{68} +3.68004 q^{71} +(6.39053 - 11.0687i) q^{73} +(-5.76604 - 9.98708i) q^{74} +(-5.31908 - 9.21291i) q^{76} -5.95811 q^{79} +(-2.91875 + 5.05542i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +(0.233956 - 0.405223i) q^{86} +(-11.8439 - 20.5142i) q^{88} +(5.51367 + 9.54996i) q^{89} +(6.97565 - 12.0822i) q^{92} -2.58853 q^{94} +2.12061 q^{95} +(-6.25150 + 10.8279i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38}+ \cdots + 3 q^{97}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 6 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 3 * q^26 + 9 * q^29 - 6 * q^31 - 9 * q^34 + 3 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 + 15 * q^44 - 6 * q^47 - 6 * q^50 + 21 * q^52 + 6 * q^53 + 9 * q^58 + 6 * q^59 + 12 * q^61 + 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 + 6 * q^68 - 18 * q^71 + 21 * q^73 - 30 * q^74 - 15 * q^76 - 42 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 12 * q^89 + 3 * q^92 - 36 * q^94 + 24 * q^95 + 3 * q^97

Introduction

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