LMFDB - Embedded newform 1323.2.i.b.521.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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([1, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (of order $6$, 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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.4
Root			$0.187540 - 0.324828i$ of defining polynomial
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.b.1097.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.718167i q^{2} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +2.50226i q^{8} +O(q^{10})$	\(q+0.718167i q^{2} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +2.50226i q^{8} +(-0.900304 - 0.519791i) q^{10} +(1.55933 - 0.900281i) q^{11} +(1.88867 - 1.09042i) q^{13} +1.17143 q^{16} +(1.95230 - 3.38149i) q^{17} +(3.47456 - 2.00604i) q^{19} +(-1.07425 + 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} +(4.91522 + 2.83781i) q^{23} +(1.45230 + 2.51546i) q^{25} +(0.783106 + 1.35638i) q^{26} +(-8.49418 - 4.90412i) q^{29} +2.83050i q^{31} +5.84581i q^{32} +(2.42847 + 1.40208i) q^{34} +(-0.411767 - 0.713202i) q^{37} +(1.44067 + 2.49531i) q^{38} +(-3.13687 - 1.81107i) q^{40} +(5.90617 + 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +(2.31442 - 1.33623i) q^{44} +(-2.03802 + 3.52995i) q^{46} +2.33839 q^{47} +(-1.80652 + 1.04299i) q^{50} +(2.80323 - 1.61845i) q^{52} +(-0.996713 - 0.575453i) q^{53} +2.60640i q^{55} +(3.52198 - 6.10024i) q^{58} -9.79110 q^{59} +2.35536i q^{61} -2.03277 q^{62} -1.85540 q^{64} +3.15688i q^{65} -0.312805 q^{67} +(2.89768 - 5.01893i) q^{68} +1.94933i q^{71} +(-2.42847 - 1.40208i) q^{73} +(0.512198 - 0.295717i) q^{74} +(5.15706 - 2.97743i) q^{76} +12.4317 q^{79} +(-0.847852 + 1.46852i) q^{80} +(-7.34669 + 4.24162i) q^{82} +(3.60916 - 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} +(-4.68660 - 2.70581i) q^{86} +(2.25274 + 3.90186i) q^{88} +(-5.28999 - 9.16253i) q^{89} +(7.29536 + 4.21198i) q^{92} +1.67935i q^{94} +5.80767i q^{95} +(13.4322 + 7.75510i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{4}+O(q^{10}) $ 10 * q - 8 * q^4	$ 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} + 30 q^{47} - 3 q^{50} + 12 q^{52} - 9 q^{53} + 8 q^{58} - 36 q^{59} - 12 q^{62} + 6 q^{64} + 20 q^{67} - 27 q^{68} - 3 q^{73} + 30 q^{74} + 9 q^{76} - 40 q^{79} + 30 q^{80} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} - 24 q^{89} - 39 q^{92} + 6 q^{97}+O(q^{100}) $ 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			0.718167i			0.507821i	0.967228	+	0.253910i	$0.0817168\pi$
$2$			0.718167i			0.507821i	−0.967228	+	0.253910i	$0.918283\pi$
$3$		0			0
$3$		0			0
$4$	1.48424			0.742118
$5$	−0.723774	+	1.25361i	−0.323682	+	0.560633i	−0.981245	−	0.192766i	$-0.938254\pi$
$5$	−0.723774	+	1.25361i	−0.323682	+	0.560633i	0.657563	+	0.753400i	$0.271587\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.50226i			0.884683i
$9$		0			0
$10$	−0.900304	−	0.519791i	−0.284701	−	0.164372i
$11$	1.55933	−	0.900281i	0.470156	−	0.271445i	−0.246149	−	0.969232i	$-0.579165\pi$
$11$	1.55933	−	0.900281i	0.470156	−	0.271445i	0.716305	+	0.697787i	$0.245832\pi$
$12$		0			0
$13$	1.88867	−	1.09042i	0.523823	−	0.302429i	−0.214675	−	0.976686i	$-0.568869\pi$
$13$	1.88867	−	1.09042i	0.523823	−	0.302429i	0.738497	+	0.674256i	$0.235536\pi$
$14$		0			0
$15$		0			0
$16$	1.17143			0.292858
$17$	1.95230	−	3.38149i	0.473503	−	0.820131i	−0.526037	−	0.850462i	$-0.676323\pi$
$17$	1.95230	−	3.38149i	0.473503	−	0.820131i	0.999540	+	0.0303308i	$0.00965608\pi$
$18$		0			0
$19$	3.47456	−	2.00604i	0.797118	−	0.460216i	−0.0453446	−	0.998971i	$-0.514439\pi$
$19$	3.47456	−	2.00604i	0.797118	−	0.460216i	0.842462	+	0.538755i	$0.181105\pi$
$20$	−1.07425	+	1.86066i	−0.240210	+	0.416056i
$21$		0			0
$22$	0.646552	+	1.11986i	0.137845	+	0.238755i
$23$	4.91522	+	2.83781i	1.02490	+	0.591723i	0.915518	−	0.402277i	$-0.131781\pi$
$23$	4.91522	+	2.83781i	1.02490	+	0.591723i	0.109377	+	0.994000i	$0.465114\pi$
$24$		0			0
$25$	1.45230	+	2.51546i	0.290460	+	0.503092i
$26$	0.783106	+	1.35638i	0.153580	+	0.266008i
$27$		0			0
$28$		0			0
$29$	−8.49418	−	4.90412i	−1.57733	−	0.910672i	−0.995230	−	0.0975551i	$-0.968898\pi$
$29$	−8.49418	−	4.90412i	−1.57733	−	0.910672i	−0.582100	−	0.813117i	$-0.697769\pi$
$30$		0			0
$31$			2.83050i			0.508374i	0.967155	+	0.254187i	$0.0818078\pi$
$31$			2.83050i			0.508374i	−0.967155	+	0.254187i	$0.918192\pi$
$32$			5.84581i			1.03340i
$33$		0			0
$34$	2.42847	+	1.40208i	0.416479	+	0.240454i
$35$		0			0
$36$		0			0
$37$	−0.411767	−	0.713202i	−0.0676941	−	0.117250i	0.830192	−	0.557478i	$-0.188231\pi$
$37$	−0.411767	−	0.713202i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$38$	1.44067	+	2.49531i	0.233707	+	0.404793i
$39$		0			0
$40$	−3.13687	−	1.81107i	−0.495983	−	0.286356i
$41$	5.90617	+	10.2298i	0.922389	+	1.59762i	0.795708	+	0.605681i	$0.207099\pi$
$41$	5.90617	+	10.2298i	0.922389	+	1.59762i	0.126681	+	0.991943i	$0.459567\pi$
$42$		0			0
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	0.421526	+	0.906816i	$0.361494\pi$
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	−0.996089	+	0.0883555i	$0.971839\pi$
$44$	2.31442	−	1.33623i	0.348912	−	0.201444i
$45$		0			0
$46$	−2.03802	+	3.52995i	−0.300489	+	0.520463i
$47$	2.33839			0.341089			0.170545	−	0.985350i	$-0.445447\pi$
$47$	2.33839			0.341089			0.170545	+	0.985350i	$0.445447\pi$
$48$		0			0
$49$		0			0
$50$	−1.80652	+	1.04299i	−0.255480	+	0.147502i
$51$		0			0
$52$	2.80323	−	1.61845i	0.388738	−	0.224438i
$53$	−0.996713	−	0.575453i	−0.136909	−	0.0790445i	0.429981	−	0.902838i	$-0.358520\pi$
$53$	−0.996713	−	0.575453i	−0.136909	−	0.0790445i	−0.566890	+	0.823793i	$0.691854\pi$
$54$		0			0
$55$			2.60640i			0.351447i
$56$		0			0
$57$		0			0
$58$	3.52198	−	6.10024i	0.462458	−	0.801001i
$59$	−9.79110			−1.27469			−0.637346	−	0.770577i	$-0.719968\pi$
$59$	−9.79110			−1.27469			−0.637346	+	0.770577i	$0.719968\pi$
$60$		0			0
$61$			2.35536i			0.301573i	0.988566	+	0.150786i	$0.0481806\pi$
$61$			2.35536i			0.301573i	−0.988566	+	0.150786i	$0.951819\pi$
$62$	−2.03277			−0.258163
$63$		0			0
$64$	−1.85540			−0.231925
$65$			3.15688i			0.391563i
$66$		0			0
$67$	−0.312805			−0.0382152			−0.0191076	−	0.999817i	$-0.506083\pi$
$67$	−0.312805			−0.0382152			−0.0191076	+	0.999817i	$0.506083\pi$
$68$	2.89768	−	5.01893i	0.351395	−	0.608634i
$69$		0			0
$70$		0			0
$71$			1.94933i			0.231343i	0.993288	+	0.115671i	$0.0369019\pi$
$71$			1.94933i			0.231343i	−0.993288	+	0.115671i	$0.963098\pi$
$72$		0			0
$73$	−2.42847	−	1.40208i	−0.284231	−	0.164101i	0.351106	−	0.936336i	$-0.385806\pi$
$73$	−2.42847	−	1.40208i	−0.284231	−	0.164101i	−0.635337	+	0.772235i	$0.719139\pi$
$74$	0.512198	−	0.295717i	0.0595418	−	0.0343765i
$75$		0			0
$76$	5.15706	−	2.97743i	0.591556	−	0.341535i
$77$		0			0
$78$		0			0
$79$	12.4317			1.39867			0.699336	−	0.714793i	$-0.253479\pi$
$79$	12.4317			1.39867			0.699336	+	0.714793i	$0.253479\pi$
$80$	−0.847852	+	1.46852i	−0.0947927	+	0.164186i
$81$		0			0
$82$	−7.34669	+	4.24162i	−0.811306	+	0.468408i
$83$	3.60916	−	6.25124i	0.396157	−	0.686163i	−0.597092	−	0.802173i	$-0.703677\pi$
$83$	3.60916	−	6.25124i	0.396157	−	0.686163i	0.993248	+	0.116010i	$0.0370104\pi$
$84$		0			0
$85$	2.82605	+	4.89486i	0.306528	+	0.530923i
$86$	−4.68660	−	2.70581i	−0.505369	−	0.291775i
$87$		0			0
$88$	2.25274	+	3.90186i	0.240143	+	0.415939i
$89$	−5.28999	−	9.16253i	−0.560737	−	0.971226i	−0.997432	−	0.0716161i	$-0.977184\pi$
$89$	−5.28999	−	9.16253i	−0.560737	−	0.971226i	0.436695	−	0.899610i	$-0.356149\pi$
$90$		0			0
$91$		0			0
$92$	7.29536	+	4.21198i	0.760593	+	0.439129i
$93$		0			0
$94$			1.67935i			0.173212i
$95$			5.80767i			0.595854i
$96$		0			0
$97$	13.4322	+	7.75510i	1.36384	+	0.787411i	0.990132	−	0.140137i	$-0.0447543\pi$
$97$	13.4322	+	7.75510i	1.36384	+	0.787411i	0.373704	+	0.927548i	$0.378088\pi$
$98$		0			0
$99$		0			0
$100$	2.15556	+	3.73354i	0.215556	+	0.373354i
$101$	−1.97309	−	3.41749i	−0.196330	−	0.340053i	0.751006	−	0.660295i	$-0.229569\pi$
$101$	−1.97309	−	3.41749i	−0.196330	−	0.340053i	−0.947336	+	0.320242i	$0.896236\pi$
$102$		0			0
$103$	−3.59853	−	2.07761i	−0.354573	−	0.204713i	0.312124	−	0.950041i	$-0.398959\pi$
$103$	−3.59853	−	2.07761i	−0.354573	−	0.204713i	−0.666698	+	0.745328i	$0.732293\pi$
$104$	2.72853	+	4.72595i	0.267554	+	0.463417i
$105$		0			0
$106$	0.413271	−	0.715806i	0.0401404	−	0.0695253i
$107$	4.91092	−	2.83532i	0.474757	−	0.274101i	−0.243472	−	0.969908i	$-0.578286\pi$
$107$	4.91092	−	2.83532i	0.474757	−	0.274101i	0.718229	+	0.695807i	$0.244953\pi$
$108$		0			0
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	−0.421468	−	0.906843i	$-0.638485\pi$
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	0.996083	−	0.0884193i	$-0.0281815\pi$
$110$	−1.87183			−0.178472
$111$		0			0
$112$		0			0
$113$	−6.27800	+	3.62461i	−0.590585	+	0.340974i	−0.765329	−	0.643640i	$-0.777424\pi$
$113$	−6.27800	+	3.62461i	−0.590585	+	0.340974i	0.174744	+	0.984614i	$0.444090\pi$
$114$		0			0
$115$	−7.11502	+	4.10786i	−0.663479	+	0.383060i
$116$	−12.6074	−	7.27887i	−1.17057	−	0.675826i
$117$		0			0
$118$		−	7.03164i		−	0.647315i
$119$		0			0
$120$		0			0
$121$	−3.87899	+	6.71861i	−0.352635	+	0.610782i
$122$	−1.69154			−0.153145
$123$		0			0
$124$			4.20114i			0.377273i
$125$	−11.4423			−1.02343
$126$		0			0
$127$	−0.881336			−0.0782059			−0.0391030	−	0.999235i	$-0.512450\pi$
$127$	−0.881336			−0.0782059			−0.0391030	+	0.999235i	$0.512450\pi$
$128$			10.3591i			0.915626i
$129$		0			0
$130$	−2.26717			−0.198844
$131$	−1.48721	+	2.57592i	−0.129938	+	0.225059i	−0.923652	−	0.383232i	$-0.874811\pi$
$131$	−1.48721	+	2.57592i	−0.129938	+	0.225059i	0.793714	+	0.608291i	$0.208144\pi$
$132$		0			0
$133$		0			0
$134$		−	0.224646i		−	0.0194065i
$135$		0			0
$136$	8.46137	+	4.88517i	0.725556	+	0.418900i
$137$	10.3045	−	5.94930i	0.880372	−	0.508283i	0.00959114	−	0.999954i	$-0.496947\pi$
$137$	10.3045	−	5.94930i	0.880372	−	0.508283i	0.870781	+	0.491671i	$0.163614\pi$
$138$		0			0
$139$	−10.4143	+	6.01268i	−0.883327	+	0.509989i	−0.871754	−	0.489944i	$-0.837017\pi$
$139$	−10.4143	+	6.01268i	−0.883327	+	0.509989i	−0.0115731	+	0.999933i	$0.503684\pi$
$140$		0			0
$141$		0			0
$142$	−1.39994			−0.117481
$143$	1.96338	−	3.40067i	0.164186	−	0.284378i
$144$		0			0
$145$	12.2957	−	7.09895i	1.02111	−	0.589536i
$146$	1.00693	−	1.74405i	0.0833338	−	0.144338i
$147$		0			0
$148$	−0.611160	−	1.05856i	−0.0502370	−	0.0870131i
$149$	−6.13061	−	3.53951i	−0.502239	−	0.289968i	0.227399	−	0.973802i	$-0.426978\pi$
$149$	−6.13061	−	3.53951i	−0.502239	−	0.289968i	−0.729638	+	0.683834i	$0.760311\pi$
$150$		0			0
$151$	−7.79093	−	13.4943i	−0.634017	−	1.09815i	−0.986723	−	0.162415i	$-0.948072\pi$
$151$	−7.79093	−	13.4943i	−0.634017	−	1.09815i	0.352706	−	0.935734i	$-0.385262\pi$
$152$	5.01963	+	8.69425i	0.407146	+	0.705197i
$153$		0			0
$154$		0			0
$155$	−3.54836	−	2.04865i	−0.285011	−	0.164551i
$156$		0			0
$157$		−	2.08628i		−	0.166503i	−0.996529	−	0.0832517i	$-0.973469\pi$
$157$		−	2.08628i		−	0.166503i	0.996529	−	0.0832517i	$-0.0265305\pi$
$158$			8.92801i			0.710274i
$159$		0			0
$160$	−7.32839	−	4.23105i	−0.579360	−	0.334494i
$161$		0			0
$162$		0			0
$163$	−5.58983	−	9.68188i	−0.437830	−	0.758343i	0.559692	−	0.828700i	$-0.310919\pi$
$163$	−5.58983	−	9.68188i	−0.437830	−	0.758343i	−0.997522	+	0.0703575i	$0.977586\pi$
$164$	8.76616	+	15.1834i	0.684522	+	1.18563i
$165$		0			0
$166$	4.48944	+	2.59198i	0.348448	+	0.201176i
$167$	−0.960750	−	1.66407i	−0.0743450	−	0.128769i	0.826456	−	0.563001i	$-0.190353\pi$
$167$	−0.960750	−	1.66407i	−0.0743450	−	0.128769i	−0.900801	+	0.434232i	$0.857020\pi$
$168$		0			0
$169$	−4.12195	+	7.13943i	−0.317073	+	0.549187i
$170$	−3.51533	+	2.02958i	−0.269613	+	0.155661i
$171$		0			0
$172$	−5.59210	+	9.68580i	−0.426393	+	0.738535i
$173$	15.2258			1.15760			0.578798	−	0.815471i	$-0.303522\pi$
$173$	15.2258			1.15760			0.578798	+	0.815471i	$0.303522\pi$
$174$		0			0
$175$		0			0
$176$	1.82665	−	1.05462i	0.137689	−	0.0794948i
$177$		0			0
$178$	6.58022	−	3.79909i	0.493208	−	0.284754i
$179$	−0.299401	−	0.172859i	−0.0223783	−	0.0129201i	0.488769	−	0.872413i	$-0.337446\pi$
$179$	−0.299401	−	0.172859i	−0.0223783	−	0.0129201i	−0.511147	+	0.859493i	$0.670779\pi$
$180$		0			0
$181$			3.27661i			0.243548i	0.992558	+	0.121774i	$0.0388583\pi$
$181$			3.27661i			0.243548i	−0.992558	+	0.121774i	$0.961142\pi$
$182$		0			0
$183$		0			0
$184$	−7.10094	+	12.2992i	−0.523488	+	0.906708i
$185$	1.19211			0.0876454
$186$		0			0
$187$		−	7.03048i		−	0.514120i
$188$	3.47073			0.253129
$189$		0			0
$190$	−4.17087			−0.302587
$191$		−	7.39120i		−	0.534808i	−0.963584	−	0.267404i	$-0.913834\pi$
$191$		−	7.39120i		−	0.534808i	0.963584	−	0.267404i	$-0.0861659\pi$
$192$		0			0
$193$	13.0285			0.937812			0.468906	−	0.883248i	$-0.344648\pi$
$193$	13.0285			0.937812			0.468906	+	0.883248i	$0.344648\pi$
$194$	−5.56945	+	9.64658i	−0.399863	+	0.692584i
$195$		0			0
$196$		0			0
$197$		−	4.03035i		−	0.287151i	−0.989639	−	0.143575i	$-0.954140\pi$
$197$		−	4.03035i		−	0.287151i	0.989639	−	0.143575i	$-0.0458599\pi$
$198$		0			0
$199$	−14.2096	−	8.20390i	−1.00729	−	0.581559i	−0.0968925	−	0.995295i	$-0.530890\pi$
$199$	−14.2096	−	8.20390i	−1.00729	−	0.581559i	−0.910397	+	0.413736i	$0.864224\pi$
$200$	−6.29434	+	3.63404i	−0.445077	+	0.256965i
$201$		0			0
$202$	2.45433	−	1.41701i	0.172686	−	0.0997003i
$203$		0			0
$204$		0			0
$205$	−17.0989			−1.19424
$206$	1.49207	−	2.58434i	0.103957	−	0.180060i
$207$		0			0
$208$	2.21245	−	1.27736i	0.153406	−	0.0885688i
$209$	3.61199	−	6.25615i	0.249847	−	0.432747i
$210$		0			0
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	0.581657	−	0.813434i	$-0.302405\pi$
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	−0.995283	+	0.0970121i	$0.969071\pi$
$212$	−1.47936	−	0.854108i	−0.101603	−	0.0586604i
$213$		0			0
$214$	2.03623	+	3.52686i	0.139194	+	0.241091i
$215$	−5.45387	−	9.44638i	−0.371951	−	0.644238i
$216$		0			0
$217$		0			0
$218$	7.46236	+	4.30839i	0.505415	+	0.291801i
$219$		0			0
$220$			3.86851i			0.260815i
$221$		−	8.51535i		−	0.572804i
$222$		0			0
$223$	−22.7932	−	13.1597i	−1.52635	−	0.881237i	−0.999511	−	0.0312693i	$-0.990045\pi$
$223$	−22.7932	−	13.1597i	−1.52635	−	0.881237i	−0.526836	−	0.849967i	$-0.676622\pi$
$224$		0			0
$225$		0			0
$226$	−2.60307	−	4.50865i	−0.173154	−	0.299911i
$227$	5.40410	+	9.36018i	0.358683	+	0.621257i	0.987741	−	0.156101i	$-0.0498926\pi$
$227$	5.40410	+	9.36018i	0.358683	+	0.621257i	−0.629058	+	0.777358i	$0.716559\pi$
$228$		0			0
$229$	8.39777	+	4.84846i	0.554941	+	0.320395i	0.751112	−	0.660174i	$-0.229518\pi$
$229$	8.39777	+	4.84846i	0.554941	+	0.320395i	−0.196172	+	0.980570i	$0.562851\pi$
$230$	−2.95013	−	5.10977i	−0.194526	−	0.336928i
$231$		0			0
$232$	12.2714	−	21.2547i	0.805657	−	1.39544i
$233$	−1.92897	+	1.11369i	−0.126371	+	0.0729605i	−0.561853	−	0.827237i	$-0.689911\pi$
$233$	−1.92897	+	1.11369i	−0.126371	+	0.0729605i	0.435482	+	0.900198i	$0.356578\pi$
$234$		0			0
$235$	−1.69247	+	2.93144i	−0.110404	+	0.191226i
$236$	−14.5323			−0.945973
$237$		0			0
$238$		0			0
$239$	15.9697	−	9.22008i	1.03299	−	0.596398i	0.115151	−	0.993348i	$-0.463265\pi$
$239$	15.9697	−	9.22008i	1.03299	−	0.596398i	0.917840	+	0.396950i	$0.129932\pi$
$240$		0			0
$241$	−5.60475	+	3.23591i	−0.361034	+	0.208443i	−0.669534	−	0.742781i	$-0.733506\pi$
$241$	−5.60475	+	3.23591i	−0.361034	+	0.208443i	0.308500	+	0.951224i	$0.400173\pi$
$242$	−4.82508	−	2.78576i	−0.310168	−	0.179075i
$243$		0			0
$244$			3.49591i			0.223803i
$245$		0			0
$246$		0			0
$247$	4.37486	−	7.57748i	0.278366	−	0.482143i
$248$	−7.08266			−0.449750
$249$		0			0
$250$		−	8.21748i		−	0.519719i
$251$	−0.416679			−0.0263005			−0.0131503	−	0.999914i	$-0.504186\pi$
$251$	−0.416679			−0.0263005			−0.0131503	+	0.999914i	$0.504186\pi$
$252$		0			0
$253$	10.2193			0.642481
$254$		−	0.632946i		−	0.0397146i
$255$		0			0
$256$	−11.1504			−0.696899
$257$	−10.5642	+	18.2977i	−0.658976	+	1.14138i	0.321906	+	0.946772i	$0.395677\pi$
$257$	−10.5642	+	18.2977i	−0.658976	+	1.14138i	−0.980881	+	0.194607i	$0.937657\pi$
$258$		0			0
$259$		0			0
$260$			4.68556i			0.290586i
$261$		0			0
$262$	−1.84994	−	1.06806i	−0.114290	−	0.0659851i
$263$	19.2653	−	11.1228i	1.18795	−	0.685862i	0.230108	−	0.973165i	$-0.426092\pi$
$263$	19.2653	−	11.1228i	1.18795	−	0.685862i	0.957840	+	0.287304i	$0.0927589\pi$
$264$		0			0
$265$	1.44279	−	0.832996i	0.0886299	−	0.0511705i
$266$		0			0
$267$		0			0
$268$	−0.464277			−0.0283602
$269$	14.5164	−	25.1432i	0.885083	−	1.53301i	0.0394642	−	0.999221i	$-0.487435\pi$
$269$	14.5164	−	25.1432i	0.885083	−	1.53301i	0.845619	−	0.533788i	$-0.179232\pi$
$270$		0			0
$271$	−20.8174	+	12.0189i	−1.26456	+	0.730097i	−0.973954	−	0.226745i	$-0.927192\pi$
$271$	−20.8174	+	12.0189i	−1.26456	+	0.730097i	−0.290610	+	0.956842i	$0.593858\pi$
$272$	2.28699	−	3.96118i	0.138669	−	0.240182i
$273$		0			0
$274$	4.27259	+	7.40034i	0.258117	+	0.447071i
$275$	4.52924	+	2.61496i	0.273124	+	0.157688i
$276$		0			0
$277$	−4.03243	−	6.98437i	−0.242285	−	0.419650i	0.719080	−	0.694928i	$-0.244564\pi$
$277$	−4.03243	−	6.98437i	−0.242285	−	0.419650i	−0.961365	+	0.275278i	$0.911230\pi$
$278$	−4.31811	−	7.47918i	−0.258983	−	0.448572i
$279$		0			0
$280$		0			0
$281$	12.0876	+	6.97879i	0.721087	+	0.416320i	0.815153	−	0.579246i	$-0.196653\pi$
$281$	12.0876	+	6.97879i	0.721087	+	0.416320i	−0.0940658	+	0.995566i	$0.529986\pi$
$282$		0			0
$283$		−	15.5375i		−	0.923609i	−0.886982	−	0.461805i	$-0.847202\pi$
$283$		−	15.5375i		−	0.923609i	0.886982	−	0.461805i	$-0.152798\pi$
$284$			2.89326i			0.171684i
$285$		0			0
$286$	2.44225	+	1.41003i	0.144413	+	0.0833769i
$287$		0			0
$288$		0			0
$289$	0.877036	+	1.51907i	0.0515904	+	0.0893571i
$290$	5.09823	+	8.83039i	0.299378	+	0.518539i
$291$		0			0
$292$	−3.60442	−	2.08102i	−0.210933	−	0.121782i
$293$	−6.73712	−	11.6690i	−0.393587	−	0.681712i	0.599333	−	0.800500i	$-0.295433\pi$
$293$	−6.73712	−	11.6690i	−0.393587	−	0.681712i	−0.992920	+	0.118788i	$0.962099\pi$
$294$		0			0
$295$	7.08655	−	12.2743i	0.412595	−	0.714635i
$296$	1.78462	−	1.03035i	0.103729	−	0.0598879i
$297$		0			0
$298$	2.54196	−	4.40280i	0.147252	−	0.255047i
$299$	12.3776			0.715818
$300$		0			0
$301$		0			0
$302$	9.69114	−	5.59518i	0.557663	−	0.321967i
$303$		0			0
$304$	4.07020	−	2.34993i	0.233442	−	0.134778i
$305$	−2.95271	−	1.70475i	−0.169072	−	0.0976136i
$306$		0			0
$307$		−	8.62791i		−	0.492421i	−0.969216	−	0.246210i	$-0.920815\pi$
$307$		−	8.62791i		−	0.492421i	0.969216	−	0.246210i	$-0.0791854\pi$
$308$		0			0
$309$		0			0
$310$	1.47127	−	2.54831i	0.0835625	−	0.144734i
$311$	−16.2440			−0.921113			−0.460556	−	0.887630i	$-0.652350\pi$
$311$	−16.2440			−0.921113			−0.460556	+	0.887630i	$0.652350\pi$
$312$		0			0
$313$			6.77692i			0.383054i	0.981487	+	0.191527i	$0.0613440\pi$
$313$			6.77692i			0.383054i	−0.981487	+	0.191527i	$0.938656\pi$
$314$	1.49830			0.0845538
$315$		0			0
$316$	18.4515			1.03798
$317$		−	21.9676i		−	1.23382i	−0.787033	−	0.616911i	$-0.788384\pi$
$317$		−	21.9676i		−	1.23382i	0.787033	−	0.616911i	$-0.211616\pi$
$318$		0			0
$319$	−17.6603			−0.988789
$320$	1.34289	−	2.32596i	0.0750699	−	0.130025i
$321$		0			0
$322$		0			0
$323$		−	15.6655i		−	0.871654i
$324$		0			0
$325$	5.48584	+	3.16725i	0.304299	+	0.175687i
$326$	6.95320	−	4.01443i	0.385102	−	0.222339i
$327$		0			0
$328$	−25.5976	+	14.7788i	−1.41339	+	0.816022i
$329$		0			0
$330$		0			0
$331$	−14.6036			−0.802685			−0.401342	−	0.915928i	$-0.631456\pi$
$331$	−14.6036			−0.802685			−0.401342	+	0.915928i	$0.631456\pi$
$332$	5.35684	−	9.27833i	0.293995	−	0.509214i
$333$		0			0
$334$	1.19508	−	0.689978i	0.0653917	−	0.0377539i
$335$	0.226400	−	0.392137i	0.0123696	−	0.0214247i
$336$		0			0
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.844685	−	0.535263i	$-0.820212\pi$
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.0412090	−	0.999151i	$-0.513121\pi$
$338$	−5.12730	−	2.96025i	−0.278888	−	0.161016i
$339$		0			0
$340$	4.19453	+	7.26514i	0.227480	+	0.394007i
$341$	2.54825	+	4.41370i	0.137995	+	0.239015i
$342$		0			0
$343$		0			0
$344$	−16.3292	−	9.42767i	−0.880412	−	0.508306i
$345$		0			0
$346$			10.9347i			0.587851i
$347$			3.18703i			0.171089i	0.996334	+	0.0855444i	$0.0272630\pi$
$347$			3.18703i			0.171089i	−0.996334	+	0.0855444i	$0.972737\pi$
$348$		0			0
$349$	−6.48224	−	3.74252i	−0.346986	−	0.200333i	0.316371	−	0.948636i	$-0.397536\pi$
$349$	−6.48224	−	3.74252i	−0.346986	−	0.200333i	−0.663357	+	0.748303i	$0.730869\pi$
$350$		0			0
$351$		0			0
$352$	5.26287	+	9.11556i	0.280512	+	0.485861i
$353$	−5.69040	−	9.85606i	−0.302869	−	0.524585i	0.673915	−	0.738809i	$-0.264611\pi$
$353$	−5.69040	−	9.85606i	−0.302869	−	0.524585i	−0.976785	+	0.214223i	$0.931278\pi$
$354$		0			0
$355$	−2.44370	−	1.41087i	−0.129698	−	0.0748814i
$356$	−7.85159	−	13.5994i	−0.416134	−	0.720764i
$357$		0			0
$358$	0.124142	−	0.215020i	0.00656109	−	0.0113641i
$359$	−4.77569	+	2.75725i	−0.252051	+	0.145522i	−0.620703	−	0.784046i	$-0.713153\pi$
$359$	−4.77569	+	2.75725i	−0.252051	+	0.145522i	0.368652	+	0.929568i	$0.379819\pi$
$360$		0			0
$361$	−1.45164	+	2.51432i	−0.0764022	+	0.132332i
$362$	−2.35315			−0.123679
$363$		0			0
$364$		0			0
$365$	3.51533	−	2.02958i	0.184001	−	0.106233i
$366$		0			0
$367$	18.2753	−	10.5512i	0.953962	−	0.550770i	0.0596526	−	0.998219i	$-0.481001\pi$
$367$	18.2753	−	10.5512i	0.953962	−	0.550770i	0.894309	+	0.447449i	$0.147667\pi$
$368$	5.75785	+	3.32430i	0.300149	+	0.173291i
$369$		0			0
$370$			0.856131i			0.0445081i
$371$		0			0
$372$		0			0
$373$	−7.68498	+	13.3108i	−0.397913	+	0.689206i	−0.993468	−	0.114109i	$-0.963599\pi$
$373$	−7.68498	+	13.3108i	−0.397913	+	0.689206i	0.595555	+	0.803314i	$0.296932\pi$
$374$	5.04906			0.261080
$375$		0			0
$376$			5.85127i			0.301756i
$377$	−21.3903			−1.10166
$378$		0			0
$379$	−32.3630			−1.66238			−0.831188	−	0.555991i	$-0.812339\pi$
$379$	−32.3630			−1.66238			−0.831188	+	0.555991i	$0.812339\pi$
$380$			8.61995i			0.442194i
$381$		0			0
$382$	5.30811			0.271587
$383$	9.91730	−	17.1773i	0.506750	−	0.877718i	−0.493219	−	0.869905i	$-0.664180\pi$
$383$	9.91730	−	17.1773i	0.506750	−	0.877718i	0.999969	−	0.00781236i	$-0.00248678\pi$
$384$		0			0
$385$		0			0
$386$			9.35663i			0.476240i
$387$		0			0
$388$	19.9366	+	11.5104i	1.01213	+	0.584352i
$389$	−4.41918	+	2.55141i	−0.224061	+	0.129362i	−0.607829	−	0.794068i	$-0.707960\pi$
$389$	−4.41918	+	2.55141i	−0.224061	+	0.129362i	0.383768	+	0.923429i	$0.374626\pi$
$390$		0			0
$391$	19.1920	−	11.0805i	0.970581	−	0.560365i
$392$		0			0
$393$		0			0
$394$	2.89446			0.145821
$395$	−8.99772	+	15.5845i	−0.452724	+	0.784141i
$396$		0			0
$397$	11.5288	−	6.65615i	0.578613	−	0.334062i	−0.181969	−	0.983304i	$-0.558247\pi$
$397$	11.5288	−	6.65615i	0.578613	−	0.334062i	0.760582	+	0.649242i	$0.224914\pi$
$398$	5.89177	−	10.2048i	0.295328	−	0.511522i
$399$		0			0
$400$	1.70127	+	2.94669i	0.0850636	+	0.147334i
$401$	−14.1750	−	8.18392i	−0.707864	−	0.408685i	0.102406	−	0.994743i	$-0.467346\pi$
$401$	−14.1750	−	8.18392i	−0.707864	−	0.408685i	−0.810270	+	0.586057i	$0.800679\pi$
$402$		0			0
$403$	3.08645	+	5.34589i	0.153747	+	0.266298i
$404$	−2.92853	−	5.07237i	−0.145700	−	0.252360i
$405$		0			0
$406$		0			0
$407$	−1.28416	−	0.741412i	−0.0636536	−	0.0367504i
$408$		0			0
$409$		−	4.33710i		−	0.214456i	−0.994234	−	0.107228i	$-0.965803\pi$
$409$		−	4.33710i		−	0.214456i	0.994234	−	0.107228i	$-0.0341975\pi$
$410$		−	12.2799i		−	0.606460i
$411$		0			0
$412$	−5.34107	−	3.08367i	−0.263135	−	0.151921i
$413$		0			0
$414$		0			0
$415$	5.22443	+	9.04898i	0.256457	+	0.444197i
$416$	6.37441	+	11.0408i	0.312531	+	0.541320i
$417$		0			0
$418$	4.49296	+	2.59401i	0.219758	+	0.126877i
$419$	9.41294	+	16.3037i	0.459852	+	0.796487i	0.998953	−	0.0457540i	$-0.0145690\pi$
$419$	9.41294	+	16.3037i	0.459852	+	0.796487i	−0.539100	+	0.842241i	$0.681236\pi$
$420$		0			0
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	−0.842907	−	0.538059i	$-0.819158\pi$
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	0.887426	+	0.460950i	$0.152491\pi$
$422$	7.47370	−	4.31494i	0.363814	−	0.210048i
$423$		0			0
$424$	1.43993	−	2.49404i	0.0699294	−	0.121121i
$425$	11.3413			0.550135
$426$		0			0
$427$		0			0
$428$	7.28897	−	4.20829i	0.352326	−	0.203415i
$429$		0			0
$430$	6.78407	−	3.91679i	0.327157	−	0.188884i
$431$	−12.4526	−	7.18954i	−0.599823	−	0.346308i	0.169149	−	0.985590i	$-0.445898\pi$
$431$	−12.4526	−	7.18954i	−0.599823	−	0.346308i	−0.768972	+	0.639283i	$0.779231\pi$
$432$		0			0
$433$			2.22130i			0.106749i	0.998575	+	0.0533745i	$0.0169977\pi$
$433$			2.22130i			0.106749i	−0.998575	+	0.0533745i	$0.983002\pi$
$434$		0			0
$435$		0			0
$436$	8.90417	−	15.4225i	0.426432	−	0.738602i
$437$	22.7710			1.08928
$438$		0			0
$439$			10.0448i			0.479413i	0.970845	+	0.239706i	$0.0770512\pi$
$439$			10.0448i			0.479413i	−0.970845	+	0.239706i	$0.922949\pi$
$440$	−6.52190			−0.310919
$441$		0			0
$442$	6.11544			0.290882
$443$		−	13.8934i		−	0.660097i	−0.943964	−	0.330049i	$-0.892935\pi$
$443$		−	13.8934i		−	0.660097i	0.943964	−	0.330049i	$-0.107065\pi$
$444$		0			0
$445$	15.3150			0.726002
$446$	9.45084	−	16.3693i	0.447510	−	0.775110i
$447$		0			0
$448$		0			0
$449$		−	10.5630i		−	0.498498i	−0.968439	−	0.249249i	$-0.919816\pi$
$449$		−	10.5630i		−	0.498498i	0.968439	−	0.249249i	$-0.0801837\pi$
$450$		0			0
$451$	18.4194	+	10.6344i	0.867334	+	0.500755i
$452$	−9.31804	+	5.37977i	−0.438284	+	0.253043i
$453$		0			0
$454$	−6.72217	+	3.88105i	−0.315487	+	0.182147i
$455$		0			0
$456$		0			0
$457$	5.11307			0.239179			0.119590	−	0.992823i	$-0.461842\pi$
$457$	5.11307			0.239179			0.119590	+	0.992823i	$0.461842\pi$
$458$	−3.48200	+	6.03100i	−0.162703	+	0.281810i
$459$		0			0
$460$	−10.5604	+	6.09704i	−0.492380	+	0.284276i
$461$	4.16691	−	7.21730i	0.194072	−	0.336143i	−0.752524	−	0.658565i	$-0.771164\pi$
$461$	4.16691	−	7.21730i	0.194072	−	0.336143i	0.946596	+	0.322422i	$0.104497\pi$
$462$		0			0
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	0.999220	−	0.0394986i	$-0.0125761\pi$
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	−0.533817	+	0.845600i	$0.679243\pi$
$464$	−9.95036	−	5.74484i	−0.461934	−	0.266698i
$465$		0			0
$466$	−0.799817	−	1.38532i	−0.0370508	−	0.0641739i
$467$	10.3896	+	17.9953i	0.480773	+	0.832723i	0.999757	−	0.0220611i	$-0.00702284\pi$
$467$	10.3896	+	17.9953i	0.480773	+	0.832723i	−0.518984	+	0.854784i	$0.673690\pi$
$468$		0			0
$469$		0			0
$470$	−2.10526	−	1.21547i	−0.0971085	−	0.0560656i
$471$		0			0
$472$		−	24.4999i		−	1.12770i
$473$			13.5678i			0.623848i
$474$		0			0
$475$	10.0922	+	5.82674i	0.463062	+	0.267349i
$476$		0			0
$477$		0			0
$478$	6.62156	+	11.4689i	0.302863	+	0.524574i
$479$	−16.0308	−	27.7662i	−0.732468	−	1.26867i	−0.955825	−	0.293935i	$-0.905035\pi$
$479$	−16.0308	−	27.7662i	−0.732468	−	1.26867i	0.223357	−	0.974737i	$-0.428298\pi$
$480$		0			0
$481$	−1.55538	−	0.898002i	−0.0709194	−	0.0409454i
$482$	−2.32392	−	4.02515i	−0.105852	−	0.183340i
$483$		0			0
$484$	−5.75734	+	9.97200i	−0.261697	+	0.453273i
$485$	−19.4438	+	11.2259i	−0.882897	+	0.509741i
$486$		0			0
$487$	11.8375	−	20.5032i	0.536408	−	0.929087i	−0.462685	−	0.886523i	$-0.653114\pi$
$487$	11.8375	−	20.5032i	0.536408	−	0.929087i	0.999094	−	0.0425641i	$-0.0135527\pi$
$488$	−5.89373			−0.266796
$489$		0			0
$490$		0			0
$491$	−15.4664	+	8.92951i	−0.697987	+	0.402983i	−0.806597	−	0.591101i	$-0.798693\pi$
$491$	−15.4664	+	8.92951i	−0.697987	+	0.402983i	0.108610	+	0.994084i	$0.465360\pi$
$492$		0			0
$493$	−33.1664	+	19.1486i	−1.49374	+	0.862411i
$494$	5.44189	+	3.14188i	0.244842	+	0.141360i
$495$		0			0
$496$			3.31574i			0.148881i
$497$		0			0
$498$		0			0
$499$	11.5602	−	20.0229i	0.517506	−	0.896346i	−0.482288	−	0.876013i	$-0.660194\pi$
$499$	11.5602	−	20.0229i	0.517506	−	0.896346i	0.999793	−	0.0203330i	$-0.00647265\pi$
$500$	−16.9831			−0.759506
$501$		0			0
$502$		−	0.299245i		−	0.0133560i
$503$	13.9995			0.624206			0.312103	−	0.950048i	$-0.398967\pi$
$503$	13.9995			0.624206			0.312103	+	0.950048i	$0.398967\pi$
$504$		0			0
$505$	5.71228			0.254193
$506$			7.33915i			0.326265i
$507$		0			0
$508$	−1.30811			−0.0580381
$509$	−6.79171	+	11.7636i	−0.301037	+	0.521411i	−0.976371	−	0.216100i	$-0.930666\pi$
$509$	−6.79171	+	11.7636i	−0.301037	+	0.521411i	0.675334	+	0.737512i	$0.263999\pi$
$510$		0			0
$511$		0			0
$512$			12.7104i			0.561727i
$513$		0			0
$514$	−13.1408	−	7.58684i	−0.579616	−	0.334641i
$515$	5.20904	−	3.00744i	0.229538	−	0.132524i
$516$		0			0
$517$	3.64633	−	2.10521i	0.160365	−	0.0925870i
$518$		0			0
$519$		0			0
$520$	−7.89935			−0.346409
$521$	−15.9477	+	27.6222i	−0.698682	+	1.21015i	0.270242	+	0.962792i	$0.412896\pi$
$521$	−15.9477	+	27.6222i	−0.698682	+	1.21015i	−0.968924	+	0.247360i	$0.920437\pi$
$522$		0			0
$523$	1.20531	−	0.695886i	0.0527046	−	0.0304290i	−0.473416	−	0.880839i	$-0.656979\pi$
$523$	1.20531	−	0.695886i	0.0527046	−	0.0304290i	0.526121	+	0.850410i	$0.323646\pi$
$524$	−2.20737	+	3.82327i	−0.0964293	+	0.167020i
$525$		0			0
$526$	7.98803	+	13.8357i	0.348295	+	0.603264i
$527$	9.57131	+	5.52600i	0.416933	+	0.240716i
$528$		0			0
$529$	4.60628	+	7.97832i	0.200273	+	0.346883i
$530$	0.598230	+	1.03616i	0.0259854	+	0.0450081i
$531$		0			0
$532$		0			0
$533$	22.3096	+	12.8805i	0.966337	+	0.557915i
$534$		0			0
$535$			8.20854i			0.354886i
$536$		−	0.782720i		−	0.0338084i
$537$		0			0
$538$	18.0570	+	10.4252i	0.778493	+	0.449463i
$539$		0			0
$540$		0			0
$541$	12.9736	+	22.4709i	0.557779	+	0.966101i	0.997682	+	0.0680555i	$0.0216795\pi$
$541$	12.9736	+	22.4709i	0.557779	+	0.966101i	−0.439903	+	0.898045i	$0.644987\pi$
$542$	−8.63158	−	14.9503i	−0.370758	−	0.642172i
$543$		0			0
$544$	19.7675	+	11.4128i	0.847525	+	0.489319i
$545$	8.68407	+	15.0413i	0.371985	+	0.644296i
$546$		0			0
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	−0.993564	−	0.113276i	$-0.963865\pi$
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	0.594882	+	0.803813i	$0.297199\pi$
$548$	15.2943	−	8.83017i	0.653340	−	0.377206i
$549$		0			0
$550$	−1.87798	+	3.25275i	−0.0800772	+	0.138698i
$551$	−39.3514			−1.67642
$552$		0			0
$553$		0			0
$554$	5.01594	−	2.89595i	0.213107	−	0.123037i
$555$		0			0
$556$	−15.4572	+	8.92424i	−0.655533	+	0.378472i
$557$	36.3567	+	20.9905i	1.54048	+	0.889398i	0.998808	+	0.0488092i	$0.0155426\pi$
$557$	36.3567	+	20.9905i	1.54048	+	0.889398i	0.541674	+	0.840589i	$0.317791\pi$
$558$		0			0
$559$			16.4334i			0.695058i
$560$		0			0
$561$		0			0
$562$	−5.01193	+	8.68092i	−0.211416	+	0.366183i
$563$	38.6011			1.62684			0.813422	−	0.581675i	$-0.197602\pi$
$563$	38.6011			1.62684			0.813422	+	0.581675i	$0.197602\pi$
$564$		0			0
$565$		−	10.4936i		−	0.441468i
$566$	11.1585			0.469028
$567$		0			0
$568$	−4.87773			−0.204665
$569$			35.1560i			1.47382i	0.675993	+	0.736908i	$0.263715\pi$
$569$			35.1560i			1.47382i	−0.675993	+	0.736908i	$0.736285\pi$
$570$		0			0
$571$	−35.3532			−1.47948			−0.739742	−	0.672891i	$-0.765052\pi$
$571$	−35.3532			−1.47948			−0.739742	+	0.672891i	$0.765052\pi$
$572$	2.91411	−	5.04739i	0.121845	−	0.211042i
$573$		0			0
$574$		0			0
$575$			16.4854i			0.687489i
$576$		0			0
$577$	−23.2557	−	13.4267i	−0.968147	−	0.558960i	−0.0694761	−	0.997584i	$-0.522133\pi$
$577$	−23.2557	−	13.4267i	−0.968147	−	0.558960i	−0.898671	+	0.438624i	$0.855466\pi$
$578$	−1.09095	+	0.629858i	−0.0453774	+	0.0261986i
$579$		0			0
$580$	18.2498	−	10.5365i	0.757781	−	0.437505i
$581$		0			0
$582$		0			0
$583$	−2.07228			−0.0858249
$584$	3.50837	−	6.07667i	0.145177	−	0.251454i
$585$		0			0
$586$	8.38031	−	4.83837i	0.346187	−	0.199871i
$587$	−15.6788	+	27.1565i	−0.647134	+	1.12087i	0.336671	+	0.941622i	$0.390699\pi$
$587$	−15.6788	+	27.1565i	−0.647134	+	1.12087i	−0.983804	+	0.179246i	$0.942634\pi$
$588$		0			0
$589$	5.67809	+	9.83474i	0.233962	+	0.405234i
$590$	8.81496	+	5.08932i	0.362906	+	0.209524i
$591$		0			0
$592$	−0.482357	−	0.835467i	−0.0198248	−	0.0343375i
$593$	4.56131	+	7.90043i	0.187311	+	0.324432i	0.944353	−	0.328935i	$-0.106690\pi$
$593$	4.56131	+	7.90043i	0.187311	+	0.324432i	−0.757042	+	0.653366i	$0.773356\pi$
$594$		0			0
$595$		0			0
$596$	−9.09927	−	5.25347i	−0.372721	−	0.215190i
$597$		0			0
$598$			8.88921i			0.363507i
$599$			1.28537i			0.0525186i	0.999655	+	0.0262593i	$0.00835956\pi$
$599$			1.28537i			0.0525186i	−0.999655	+	0.0262593i	$0.991640\pi$
$600$		0			0
$601$	−16.7126	−	9.64903i	−0.681721	−	0.393592i	0.118782	−	0.992920i	$-0.462101\pi$
$601$	−16.7126	−	9.64903i	−0.681721	−	0.393592i	−0.800503	+	0.599328i	$0.795434\pi$
$602$		0			0
$603$		0			0
$604$	−11.5636	−	20.0287i	−0.470515	−	0.814956i
$605$	−5.61502	−	9.72551i	−0.228283	−	0.395398i
$606$		0			0
$607$	−33.7319	−	19.4751i	−1.36913	−	0.790470i	−0.378317	−	0.925676i	$-0.623497\pi$
$607$	−33.7319	−	19.4751i	−1.36913	−	0.790470i	−0.990817	+	0.135206i	$0.956830\pi$
$608$	11.7269	+	20.3116i	0.475589	+	0.823744i
$609$		0			0
$610$	1.22429	−	2.12054i	0.0495702	−	0.0858581i
$611$	4.41645	−	2.54984i	0.178670	−	0.103155i
$612$		0			0
$613$	−3.65018	+	6.32229i	−0.147429	+	0.255355i	−0.930277	−	0.366859i	$-0.880433\pi$
$613$	−3.65018	+	6.32229i	−0.147429	+	0.255355i	0.782847	+	0.622214i	$0.213767\pi$
$614$	6.19628			0.250061
$615$		0			0
$616$		0			0
$617$	−38.3641	+	22.1495i	−1.54448	+	0.891706i	−0.545932	+	0.837829i	$0.683824\pi$
$617$	−38.3641	+	22.1495i	−1.54448	+	0.891706i	−0.998548	+	0.0538763i	$0.982842\pi$
$618$		0			0
$619$	0.408449	−	0.235818i	0.0164169	−	0.00947832i	−0.491769	−	0.870726i	$-0.663650\pi$
$619$	0.408449	−	0.235818i	0.0164169	−	0.00947832i	0.508186	+	0.861247i	$0.330316\pi$
$620$	−5.26660	−	3.04068i	−0.211512	−	0.122116i
$621$		0			0
$622$		−	11.6659i		−	0.467760i
$623$		0			0
$624$		0			0
$625$	1.02013	−	1.76692i	0.0408052	−	0.0706768i
$626$	−4.86696			−0.194523
$627$		0			0
$628$		−	3.09653i		−	0.123565i
$629$	−3.21558			−0.128213
$630$		0			0
$631$	10.2247			0.407038			0.203519	−	0.979071i	$-0.434762\pi$
$631$	10.2247			0.407038			0.203519	+	0.979071i	$0.434762\pi$
$632$			31.1073i			1.23738i
$633$		0			0
$634$	15.7764			0.626560
$635$	0.637888	−	1.10485i	0.0253138	−	0.0438448i
$636$		0			0
$637$		0			0
$638$		−	12.6831i		−	0.502127i
$639$		0			0
$640$	−12.9863	−	7.49767i	−0.513330	−	0.296371i
$641$	−43.4584	+	25.0907i	−1.71651	+	0.991025i	−0.791414	+	0.611280i	$0.790655\pi$
$641$	−43.4584	+	25.0907i	−1.71651	+	0.991025i	−0.925091	+	0.379745i	$0.876012\pi$
$642$		0			0
$643$	9.18633	−	5.30373i	0.362274	−	0.209159i	−0.307804	−	0.951450i	$-0.599594\pi$
$643$	9.18633	−	5.30373i	0.362274	−	0.209159i	0.670078	+	0.742291i	$0.266261\pi$
$644$		0			0
$645$		0			0
$646$	11.2505			0.442644
$647$	−14.9203	+	25.8427i	−0.586577	+	1.01598i	0.408100	+	0.912937i	$0.366191\pi$
$647$	−14.9203	+	25.8427i	−0.586577	+	1.01598i	−0.994677	+	0.103044i	$0.967142\pi$
$648$		0			0
$649$	−15.2676	+	8.81474i	−0.599305	+	0.346009i
$650$	−2.27461	+	3.93975i	−0.0892177	+	0.154530i
$651$		0			0
$652$	−8.29664	−	14.3702i	−0.324921	−	0.562780i
$653$	30.5327	+	17.6281i	1.19484	+	0.689839i	0.959400	−	0.282050i	$-0.0910144\pi$
$653$	30.5327	+	17.6281i	1.19484	+	0.689839i	0.235437	+	0.971890i	$0.424348\pi$
$654$		0			0
$655$	−2.15280	−	3.72877i	−0.0841170	−	0.145695i
$656$	6.91868	+	11.9835i	0.270129	+	0.467877i
$657$		0			0
$658$		0			0
$659$	−29.3751	−	16.9597i	−1.14429	−	0.660656i	−0.196801	−	0.980443i	$-0.563055\pi$
$659$	−29.3751	−	16.9597i	−1.14429	−	0.660656i	−0.947489	+	0.319787i	$0.896389\pi$
$660$		0			0
$661$			15.7674i			0.613281i	0.951825	+	0.306641i	$0.0992050\pi$
$661$			15.7674i			0.613281i	−0.951825	+	0.306641i	$0.900795\pi$
$662$		−	10.4878i		−	0.407620i
$663$		0			0
$664$	15.6423	+	9.03106i	0.607037	+	0.350473i
$665$		0			0
$666$		0			0
$667$	−27.8339	−	48.2097i	−1.07773	−	1.86669i
$668$	−1.42598	−	2.46987i	−0.0551728	−	0.0955621i
$669$		0			0
$670$	0.281619	+	0.162593i	0.0108799	+	0.00628152i
$671$	2.12048	+	3.67279i	0.0818604	+	0.141786i
$672$		0			0
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	−0.972260	−	0.233904i	$-0.924850\pi$
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	0.688696	+	0.725050i	$0.258183\pi$
$674$	20.2294	−	11.6794i	0.779207	−	0.449875i
$675$		0			0
$676$	−6.11795	+	10.5966i	−0.235306	+	0.407562i
$677$	3.98434			0.153131			0.0765654	−	0.997065i	$-0.475605\pi$
$677$	3.98434			0.153131			0.0765654	+	0.997065i	$0.475605\pi$
$678$		0			0
$679$		0			0
$680$	−12.2482	+	7.07152i	−0.469698	+	0.271181i
$681$		0			0
$682$	−3.16977	+	1.83007i	−0.121377	+	0.0700769i
$683$	−19.2812	−	11.1320i	−0.737774	−	0.425954i	0.0834856	−	0.996509i	$-0.473395\pi$
$683$	−19.2812	−	11.1320i	−0.737774	−	0.425954i	−0.821259	+	0.570555i	$0.806728\pi$
$684$		0			0
$685$			17.2238i			0.658088i
$686$		0			0
$687$		0			0
$688$	−4.41356	+	7.64450i	−0.168265	+	0.291444i
$689$	−2.50995			−0.0956215
$690$		0			0
$691$		−	48.3823i		−	1.84055i	−0.391271	−	0.920275i	$-0.627965\pi$
$691$		−	48.3823i		−	1.84055i	0.391271	−	0.920275i	$-0.372035\pi$
$692$	22.5987			0.859073
$693$		0			0
$694$	−2.28882			−0.0868824
$695$		−	17.4073i		−	0.660297i
$696$		0			0
$697$	46.1225			1.74701
$698$	2.68775	−	4.65533i	0.101733	−	0.176207i
$699$		0			0
$700$		0			0
$701$			23.3129i			0.880514i	0.897872	+	0.440257i	$0.145113\pi$
$701$			23.3129i			0.880514i	−0.897872	+	0.440257i	$0.854887\pi$
$702$		0			0
$703$	−2.86142	−	1.65204i	−0.107920	−	0.0623079i
$704$	−2.89319	+	1.67038i	−0.109041	+	0.0629549i
$705$		0			0
$706$	7.07830	−	4.08666i	0.266395	−	0.153803i
$707$		0			0
$708$		0			0
$709$	17.6777			0.663899			0.331949	−	0.943297i	$-0.392294\pi$
$709$	17.6777			0.663899			0.331949	+	0.943297i	$0.392294\pi$
$710$	1.01324	−	1.75499i	0.0380263	−	0.0658635i
$711$		0			0
$712$	22.9270	−	13.2369i	0.859227	−	0.496075i
$713$	−8.03242	+	13.9126i	−0.300817	+	0.521030i
$714$		0			0
$715$	2.84208	+	4.92263i	0.106288	+	0.184096i
$716$	−0.444382	−	0.256564i	−0.0166073	−	0.00958824i
$717$		0			0
$718$	−1.98016	−	3.42974i	−0.0738990	−	0.127997i
$719$	−15.2102	−	26.3449i	−0.567246	−	0.982498i	−0.996837	−	0.0794749i	$-0.974676\pi$
$719$	−15.2102	−	26.3449i	−0.567246	−	0.982498i	0.429591	−	0.903024i	$-0.358658\pi$
$720$		0			0
$721$		0			0
$722$	−1.80570	−	1.04252i	−0.0672011	−	0.0387986i
$723$		0			0
$724$			4.86326i			0.180742i
$725$		−	28.4890i		−	1.05806i
$726$		0			0
$727$	38.5219	+	22.2406i	1.42870	+	0.824859i	0.997018	−	0.0771674i	$-0.0245876\pi$
$727$	38.5219	+	22.2406i	1.42870	+	0.824859i	0.431680	+	0.902027i	$0.357921\pi$
$728$		0			0
$729$		0			0
$730$	1.45757	+	2.52459i	0.0539472	+	0.0934393i
$731$	14.7112	+	25.4806i	0.544114	+	0.942433i
$732$		0			0
$733$	39.2270	+	22.6477i	1.44888	+	0.836512i	0.998415	−	0.0562818i	$-0.0179245\pi$
$733$	39.2270	+	22.6477i	1.44888	+	0.836512i	0.450466	+	0.892794i	$0.351258\pi$
$734$	7.57755	+	13.1247i	0.279692	+	0.484442i
$735$		0			0
$736$	−16.5893	+	28.7335i	−0.611489	+	1.05913i
$737$	−0.487767	+	0.281612i	−0.0179671	+	0.0103733i
$738$		0			0
$739$	−10.3086	+	17.8550i	−0.379208	+	0.656808i	−0.990947	−	0.134252i	$-0.957137\pi$
$739$	−10.3086	+	17.8550i	−0.379208	+	0.656808i	0.611739	+	0.791060i	$0.290470\pi$
$740$	1.76937			0.0650432
$741$		0			0
$742$		0			0
$743$	−7.69885	+	4.44493i	−0.282443	+	0.163069i	−0.634529	−	0.772899i	$-0.718806\pi$
$743$	−7.69885	+	4.44493i	−0.282443	+	0.163069i	0.352086	+	0.935968i	$0.385473\pi$
$744$		0			0
$745$	8.87435	−	5.12361i	0.325131	−	0.187714i
$746$	−9.55935	−	5.51909i	−0.349993	−	0.202068i
$747$		0			0
$748$		−	10.4349i		−	0.381538i
$749$		0			0
$750$		0			0
$751$	12.5008	−	21.6521i	0.456162	−	0.790095i	−0.542592	−	0.839996i	$-0.682557\pi$
$751$	12.5008	−	21.6521i	0.456162	−	0.790095i	0.998754	+	0.0499007i	$0.0158905\pi$
$752$	2.73927			0.0998907
$753$		0			0
$754$		−	15.3618i		−	0.559443i
$755$	22.5555			0.820878
$756$		0			0
$757$	−27.1262			−0.985919			−0.492959	−	0.870052i	$-0.664085\pi$
$757$	−27.1262			−0.985919			−0.492959	+	0.870052i	$0.664085\pi$
$758$		−	23.2420i		−	0.844189i
$759$		0			0
$760$	−14.5323			−0.527142
$761$	−1.58366	+	2.74298i	−0.0574075	+	0.0994328i	−0.893301	−	0.449459i	$-0.851617\pi$
$761$	−1.58366	+	2.74298i	−0.0574075	+	0.0994328i	0.835893	+	0.548892i	$0.184950\pi$
$762$		0			0
$763$		0			0
$764$		−	10.9703i		−	0.396891i
$765$		0			0
$766$	12.3361	+	7.12228i	0.445723	+	0.257338i
$767$	−18.4922	+	10.6765i	−0.667713	+	0.385504i
$768$		0			0
$769$	2.48873	−	1.43687i	0.0897460	−	0.0518149i	−0.454455	−	0.890770i	$-0.650166\pi$
$769$	2.48873	−	1.43687i	0.0897460	−	0.0518149i	0.544201	+	0.838955i	$0.316833\pi$
$770$		0			0
$771$		0			0
$772$	19.3374			0.695967
$773$	−6.15679	+	10.6639i	−0.221444	+	0.383553i	−0.955247	−	0.295810i	$-0.904410\pi$
$773$	−6.15679	+	10.6639i	−0.221444	+	0.383553i	0.733802	+	0.679363i	$0.237744\pi$
$774$		0			0
$775$	−7.12002	+	4.11075i	−0.255759	+	0.147662i
$776$	−19.4053	+	33.6110i	−0.696610	+	1.20656i
$777$		0			0
$778$	−1.83234	−	3.17371i	−0.0656926	−	0.113783i
$779$	41.0426	+	23.6960i	1.47051	+	0.848997i
$780$		0			0
$781$	1.75494	+	3.03965i	0.0627968	+	0.108767i
$782$	7.95765	+	13.7831i	0.284565	+	0.492881i
$783$		0			0
$784$		0			0
$785$	2.61539	+	1.51000i	0.0933473	+	0.0538941i
$786$		0			0
$787$			3.81570i			0.136015i	0.997685	+	0.0680076i	$0.0216642\pi$
$787$			3.81570i			0.136015i	−0.997685	+	0.0680076i	$0.978336\pi$
$788$		−	5.98200i		−	0.213100i
$789$		0			0
$790$	−11.1923	−	6.46186i	−0.398203	−	0.229903i
$791$		0			0
$792$		0			0
$793$	2.56834	+	4.44849i	0.0912044	+	0.157971i
$794$	4.78022	+	8.27959i	0.169644	+	0.293832i
$795$		0			0
$796$	−21.0904	−	12.1765i	−0.747528	−	0.431585i
$797$	−24.5682	−	42.5535i	−0.870252	−	1.50732i	−0.861736	−	0.507357i	$-0.830623\pi$
$797$	−24.5682	−	42.5535i	−0.870252	−	1.50732i	−0.00851609	−	0.999964i	$-0.502711\pi$
$798$		0			0
$799$	4.56524	−	7.90724i	0.161507	−	0.279738i
$800$	−14.7049	+	8.48988i	−0.519897	+	0.300162i
$801$		0			0
$802$	5.87742	−	10.1800i	0.207539	−	0.359468i
$803$	−5.04906			−0.178177
$804$		0			0
$805$		0			0
$806$	−3.83924	+	2.21659i	−0.135231	+	0.0780759i
$807$		0			0
$808$	8.55146	−	4.93719i	0.300839	−	0.173690i
$809$	39.4929	+	22.8012i	1.38850	+	0.801648i	0.993146	−	0.116882i	$-0.0372900\pi$
$809$	39.4929	+	22.8012i	1.38850	+	0.801648i	0.395350	+	0.918531i	$0.370623\pi$
$810$		0			0
$811$		−	39.1391i		−	1.37436i	−0.726488	−	0.687180i	$-0.758849\pi$
$811$		−	39.1391i		−	1.37436i	0.726488	−	0.687180i	$-0.241151\pi$
$812$		0			0
$813$		0			0
$814$	0.532458	−	0.922243i	0.0186626	−	0.0323246i
$815$	16.1831			0.566870
$816$		0			0
$817$			30.2322i			1.05769i
$818$	3.11476			0.108905
$819$		0			0
$820$	−25.3789			−0.886269
$821$		−	11.8906i		−	0.414985i	−0.978237	−	0.207492i	$-0.933470\pi$
$821$		−	11.8906i		−	0.414985i	0.978237	−	0.207492i	$-0.0665302\pi$
$822$		0			0
$823$	3.02389			0.105406			0.0527031	−	0.998610i	$-0.483216\pi$
$823$	3.02389			0.105406			0.0527031	+	0.998610i	$0.483216\pi$
$824$	5.19873	−	9.00446i	0.181106	−	0.313685i
$825$		0			0
$826$		0			0
$827$		−	15.2436i		−	0.530071i	−0.964239	−	0.265035i	$-0.914616\pi$
$827$		−	15.2436i		−	0.530071i	0.964239	−	0.265035i	$-0.0853836\pi$
$828$		0			0
$829$	29.7306	+	17.1649i	1.03259	+	0.596163i	0.917724	−	0.397218i	$-0.130024\pi$
$829$	29.7306	+	17.1649i	1.03259	+	0.596163i	0.114861	+	0.993382i	$0.463358\pi$
$830$	−6.49868	+	3.75201i	−0.225572	+	0.130234i
$831$		0			0
$832$	−3.50424	+	2.02317i	−0.121488	+	0.0701409i
$833$		0			0
$834$		0			0
$835$	2.78146			0.0962565
$836$	5.36105	−	9.28561i	0.185416	−	0.321150i
$837$		0			0
$838$	−11.7088	+	6.76006i	−0.404473	+	0.233522i
$839$	6.16024	−	10.6698i	0.212675	−	0.368364i	−0.739876	−	0.672744i	$-0.765116\pi$
$839$	6.16024	−	10.6698i	0.212675	−	0.368364i	0.952551	+	0.304379i	$0.0984491\pi$
$840$		0			0
$841$	33.6008	+	58.1983i	1.15865	+	2.00684i
$842$	1.13625	+	0.656012i	0.0391576	+	0.0226077i
$843$		0			0
$844$	−8.91770	−	15.4459i	−0.306960	−	0.531670i
$845$	−5.96672	−	10.3347i	−0.205262	−	0.355523i
$846$		0			0
$847$		0			0
$848$	−1.16758	−	0.674104i	−0.0400949	−	0.0231488i
$849$		0			0
$850$			8.14496i			0.279370i
$851$		−	4.67406i		−	0.160225i
$852$		0			0
$853$	−3.92537	−	2.26631i	−0.134402	−	0.0775971i	0.431291	−	0.902213i	$-0.358058\pi$
$853$	−3.92537	−	2.26631i	−0.134402	−	0.0775971i	−0.565693	+	0.824616i	$0.691391\pi$
$854$		0			0
$855$		0			0
$856$	7.09472	+	12.2884i	0.242493	+	0.420010i
$857$	−16.1307	−	27.9392i	−0.551014	−	0.954384i	−0.998202	−	0.0599442i	$-0.980908\pi$
$857$	−16.1307	−	27.9392i	−0.551014	−	0.954384i	0.447188	−	0.894440i	$-0.352426\pi$
$858$		0			0
$859$	−15.2711	−	8.81675i	−0.521042	−	0.300824i	0.216319	−	0.976323i	$-0.430595\pi$
$859$	−15.2711	−	8.81675i	−0.521042	−	0.300824i	−0.737361	+	0.675499i	$0.763928\pi$
$860$	−8.09483	−	14.0207i	−0.276032	−	0.478101i
$861$		0			0
$862$	5.16329	−	8.94307i	0.175862	−	0.304602i
$863$	−26.4091	+	15.2473i	−0.898975	+	0.519023i	−0.876867	−	0.480732i	$-0.840371\pi$
$863$	−26.4091	+	15.2473i	−0.898975	+	0.519023i	−0.0221074	+	0.999756i	$0.507038\pi$
$864$		0			0
$865$	−11.0200	+	19.0873i	−0.374693	+	0.648987i
$866$	−1.59526			−0.0542093
$867$		0			0
$868$		0			0
$869$	19.3851	−	11.1920i	0.657594	−	0.379662i
$870$		0			0
$871$	−0.590785	+	0.341090i	−0.0200180	+	0.0115574i
$872$	26.0006	+	15.0115i	0.880492	+	0.508352i
$873$		0			0
$874$			16.3533i			0.553160i
$875$		0			0
$876$		0			0
$877$	−4.40363	+	7.62730i	−0.148700	+	0.257556i	−0.930747	−	0.365663i	$-0.880842\pi$
$877$	−4.40363	+	7.62730i	−0.148700	+	0.257556i	0.782047	+	0.623219i	$0.214176\pi$
$878$	−7.21385			−0.243456
$879$		0			0
$880$			3.05322i			0.102924i
$881$	38.6776			1.30308			0.651540	−	0.758614i	$-0.274123\pi$
$881$	38.6776			1.30308			0.651540	+	0.758614i	$0.274123\pi$
$882$		0			0
$883$	37.4489			1.26026			0.630128	−	0.776491i	$-0.283002\pi$
$883$	37.4489			1.26026			0.630128	+	0.776491i	$0.283002\pi$
$884$		−	12.6388i		−	0.425089i
$885$		0			0
$886$	9.97781			0.335211
$887$	13.7025	−	23.7335i	0.460086	−	0.796892i	−0.538879	−	0.842383i	$-0.681152\pi$
$887$	13.7025	−	23.7335i	0.460086	−	0.796892i	0.998965	+	0.0454915i	$0.0144854\pi$
$888$		0			0
$889$		0			0
$890$			10.9987i			0.368679i
$891$		0			0
$892$	−33.8305	−	19.5321i	−1.13273	−	0.653982i
$893$	8.12487	−	4.69090i	0.271888	−	0.156975i
$894$		0			0
$895$	0.433397	−	0.250222i	0.0144869	−	0.00836400i
$896$		0			0
$897$		0			0
$898$	7.58598			0.253147
$899$	13.8811	−	24.0428i	0.462962	−	0.801873i
$900$		0			0
$901$	−3.89177	+	2.24691i	−0.129654	+	0.0748556i
$902$	−7.63729	+	13.2282i	−0.254294	+	0.440450i
$903$		0			0
$904$	−9.06971	−	15.7092i	−0.301654	−	0.522480i
$905$	−4.10760	−	2.37152i	−0.136541	−	0.0788321i
$906$		0			0
$907$	11.8216	+	20.4757i	0.392531	+	0.679883i	0.992783	−	0.119928i	$-0.0382663\pi$
$907$	11.8216	+	20.4757i	0.392531	+	0.679883i	−0.600252	+	0.799811i	$0.704933\pi$
$908$	8.02097	+	13.8927i	0.266185	+	0.461046i
$909$		0			0
$910$		0			0
$911$	3.92249	+	2.26465i	0.129958	+	0.0750313i	0.563570	−	0.826069i	$-0.309428\pi$
$911$	3.92249	+	2.26465i	0.129958	+	0.0750313i	−0.433612	+	0.901100i	$0.642761\pi$
$912$		0			0
$913$		−	12.9970i		−	0.430139i
$914$			3.67204i			0.121460i
$915$		0			0
$916$	12.4643	+	7.19626i	0.411832	+	0.237771i
$917$		0			0
$918$		0			0
$919$	16.9149	+	29.2975i	0.557971	+	0.966434i	0.997666	+	0.0682866i	$0.0217532\pi$
$919$	16.9149	+	29.2975i	0.557971	+	0.966434i	−0.439695	+	0.898147i	$0.644913\pi$
$920$	−10.2789	−	17.8037i	−0.338887	−	0.586969i
$921$		0			0
$922$	5.18323	+	2.99254i	0.170700	+	0.0985540i
$923$	2.12559	+	3.68164i	0.0699648	+	0.121183i
$924$		0			0
$925$	1.19602	−	2.07157i	0.0393249	−	0.0681127i
$926$	−12.4568	+	7.19192i	−0.409355	+	0.236341i
$927$		0			0
$928$	28.6685	−	49.6554i	0.941091	−	1.63002i
$929$	32.9164			1.07995			0.539976	−	0.841680i	$-0.318433\pi$
$929$	32.9164			1.07995			0.539976	+	0.841680i	$0.318433\pi$
$930$		0			0
$931$		0			0
$932$	−2.86305	+	1.65298i	−0.0937824	+	0.0541453i
$933$		0			0
$934$	−12.9236	+	7.46146i	−0.422874	+	0.244146i
$935$	8.81350	+	5.08848i	0.288232	+	0.166411i
$936$		0			0
$937$			38.1057i			1.24486i	0.782676	+	0.622430i	$0.213854\pi$
$937$			38.1057i			1.24486i	−0.782676	+	0.622430i	$0.786146\pi$
$938$		0			0
$939$		0			0
$940$	−2.51202	+	4.35095i	−0.0819331	+	0.141912i
$941$	−19.8771			−0.647975			−0.323987	−	0.946061i	$-0.605024\pi$
$941$	−19.8771			−0.647975			−0.323987	+	0.946061i	$0.605024\pi$
$942$		0			0
$943$			67.0423i			2.18320i
$944$	−11.4696			−0.373304
$945$		0			0
$946$	−9.74394			−0.316803
$947$		−	20.7495i		−	0.674267i	−0.941457	−	0.337134i	$-0.890543\pi$
$947$		−	20.7495i		−	0.674267i	0.941457	−	0.337134i	$-0.109457\pi$
$948$		0			0
$949$	−6.11544			−0.198516
$950$	−4.18457	+	7.24789i	−0.135765	+	0.235152i
$951$		0			0
$952$		0			0
$953$		−	12.8345i		−	0.415751i	−0.978155	−	0.207876i	$-0.933345\pi$
$953$		−	12.8345i		−	0.415751i	0.978155	−	0.207876i	$-0.0666549\pi$
$954$		0			0
$955$	9.26571	+	5.34956i	0.299831	+	0.173108i
$956$	23.7027	−	13.6848i	0.766602	−	0.442598i
$957$		0			0
$958$	19.9408	−	11.5128i	0.644258	−	0.371962i
$959$		0			0
$960$		0			0
$961$	22.9882			0.741556
$962$	0.644915	−	1.11703i	0.0207929	−	0.0360143i
$963$		0			0
$964$	−8.31878	+	4.80285i	−0.267930	+	0.154689i
$965$	−9.42969	+	16.3327i	−0.303552	+	0.525768i
$966$		0			0
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	−0.995994	−	0.0894195i	$-0.971499\pi$
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	0.420557	−	0.907266i	$-0.361835\pi$
$968$	−16.8117	−	9.70625i	−0.540349	−	0.311971i
$969$		0			0
$970$	−8.06205	−	13.9639i	−0.258857	−	0.448353i
$971$	−14.5129	−	25.1370i	−0.465740	−	0.806686i	0.533494	−	0.845804i	$-0.320879\pi$
$971$	−14.5129	−	25.1370i	−0.465740	−	0.806686i	−0.999235	+	0.0391177i	$0.987545\pi$
$972$		0			0
$973$		0			0
$974$	14.7247	+	8.50130i	0.471809	+	0.272399i
$975$		0			0
$976$			2.75914i			0.0883180i
$977$			8.93090i			0.285725i	0.989743	+	0.142862i	$0.0456306\pi$
$977$			8.93090i			0.285725i	−0.989743	+	0.142862i	$0.954369\pi$
$978$		0			0
$979$	−16.4977	−	9.52495i	−0.527268	−	0.304419i
$980$		0			0
$981$		0			0
$982$	−6.41288	−	11.1074i	−0.204643	−	0.354452i
$983$	−26.1346	−	45.2665i	−0.833566	−	1.44378i	−0.895193	−	0.445679i	$-0.852962\pi$
$983$	−26.1346	−	45.2665i	−0.833566	−	1.44378i	0.0616269	−	0.998099i	$-0.480371\pi$
$984$		0			0
$985$	5.05250	+	2.91707i	0.160986	+	0.0929454i
$986$	−13.7519	−	23.8190i	−0.437950	−	0.758552i
$987$		0			0
$988$	6.49333	−	11.2468i	0.206580	−	0.357807i
$989$	−37.0378	+	21.3838i	−1.17773	+	0.679964i
$990$		0			0
$991$	−21.9151	+	37.9581i	−0.696158	+	1.20578i	0.273631	+	0.961835i	$0.411775\pi$
$991$	−21.9151	+	37.9581i	−0.696158	+	1.20578i	−0.969789	+	0.243946i	$0.921558\pi$
$992$	−16.5466			−0.525355
$993$		0			0
$994$		0			0
$995$	20.5690	−	11.8755i	0.652082	−	0.376480i
$996$		0			0
$997$	38.9689	−	22.4987i	1.23416	−	0.712542i	0.266264	−	0.963900i	$-0.414211\pi$
$997$	38.9689	−	22.4987i	1.23416	−	0.712542i	0.967894	+	0.251358i	$0.0808772\pi$
$998$	14.3797	+	8.30215i	0.455183	+	0.262800i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.b.521.4		10
3.2	odd	2		441.2.i.b.227.2		10
7.2	even	3		189.2.s.b.89.4		10
7.3	odd	6		1323.2.o.c.440.2		10
7.4	even	3		1323.2.o.d.440.2		10
7.5	odd	6		1323.2.s.b.656.4		10
7.6	odd	2		189.2.i.b.143.4		10
9.4	even	3		441.2.s.b.374.2		10
9.5	odd	6		1323.2.s.b.962.4		10
21.2	odd	6		63.2.s.b.47.2	yes	10
21.5	even	6		441.2.s.b.362.2		10
21.11	odd	6		441.2.o.c.146.4		10
21.17	even	6		441.2.o.d.146.4		10
21.20	even	2		63.2.i.b.38.2	yes	10
28.23	odd	6		3024.2.df.b.1601.4		10
28.27	even	2		3024.2.ca.b.2033.4		10
63.2	odd	6		567.2.p.c.404.4		10
63.4	even	3		441.2.o.d.293.4		10
63.5	even	6	inner	1323.2.i.b.1097.2		10
63.13	odd	6		63.2.s.b.59.2	yes	10
63.16	even	3		567.2.p.d.404.2		10
63.20	even	6		567.2.p.d.80.2		10
63.23	odd	6		189.2.i.b.152.2		10
63.31	odd	6		441.2.o.c.293.4		10
63.32	odd	6		1323.2.o.c.881.2		10
63.34	odd	6		567.2.p.c.80.4		10
63.40	odd	6		441.2.i.b.68.4		10
63.41	even	6		189.2.s.b.17.4		10
63.58	even	3		63.2.i.b.5.4	✓	10
63.59	even	6		1323.2.o.d.881.2		10
84.23	even	6		1008.2.df.b.929.2		10
84.83	odd	2		1008.2.ca.b.353.3		10
252.23	even	6		3024.2.ca.b.2609.4		10
252.139	even	6		1008.2.df.b.689.2		10
252.167	odd	6		3024.2.df.b.17.4		10
252.247	odd	6		1008.2.ca.b.257.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	63.58	even	3
63.2.i.b.38.2	yes	10	21.20	even	2
63.2.s.b.47.2	yes	10	21.2	odd	6
63.2.s.b.59.2	yes	10	63.13	odd	6
189.2.i.b.143.4		10	7.6	odd	2
189.2.i.b.152.2		10	63.23	odd	6
189.2.s.b.17.4		10	63.41	even	6
189.2.s.b.89.4		10	7.2	even	3
441.2.i.b.68.4		10	63.40	odd	6
441.2.i.b.227.2		10	3.2	odd	2
441.2.o.c.146.4		10	21.11	odd	6
441.2.o.c.293.4		10	63.31	odd	6
441.2.o.d.146.4		10	21.17	even	6
441.2.o.d.293.4		10	63.4	even	3
441.2.s.b.362.2		10	21.5	even	6
441.2.s.b.374.2		10	9.4	even	3
567.2.p.c.80.4		10	63.34	odd	6
567.2.p.c.404.4		10	63.2	odd	6
567.2.p.d.80.2		10	63.20	even	6
567.2.p.d.404.2		10	63.16	even	3
1008.2.ca.b.257.3		10	252.247	odd	6
1008.2.ca.b.353.3		10	84.83	odd	2
1008.2.df.b.689.2		10	252.139	even	6
1008.2.df.b.929.2		10	84.23	even	6
1323.2.i.b.521.4		10	1.1	even	1	trivial
1323.2.i.b.1097.2		10	63.5	even	6	inner
1323.2.o.c.440.2		10	7.3	odd	6
1323.2.o.c.881.2		10	63.32	odd	6
1323.2.o.d.440.2		10	7.4	even	3
1323.2.o.d.881.2		10	63.59	even	6
1323.2.s.b.656.4		10	7.5	odd	6
1323.2.s.b.962.4		10	9.5	odd	6
3024.2.ca.b.2033.4		10	28.27	even	2
3024.2.ca.b.2609.4		10	252.23	even	6
3024.2.df.b.17.4		10	252.167	odd	6
3024.2.df.b.1601.4		10	28.23	odd	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.718167i q^{2} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +2.50226i q^{8} +O(q^{10})\)	\(q+0.718167i q^{2} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +2.50226i q^{8} +(-0.900304 - 0.519791i) q^{10} +(1.55933 - 0.900281i) q^{11} +(1.88867 - 1.09042i) q^{13} +1.17143 q^{16} +(1.95230 - 3.38149i) q^{17} +(3.47456 - 2.00604i) q^{19} +(-1.07425 + 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} +(4.91522 + 2.83781i) q^{23} +(1.45230 + 2.51546i) q^{25} +(0.783106 + 1.35638i) q^{26} +(-8.49418 - 4.90412i) q^{29} +2.83050i q^{31} +5.84581i q^{32} +(2.42847 + 1.40208i) q^{34} +(-0.411767 - 0.713202i) q^{37} +(1.44067 + 2.49531i) q^{38} +(-3.13687 - 1.81107i) q^{40} +(5.90617 + 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +(2.31442 - 1.33623i) q^{44} +(-2.03802 + 3.52995i) q^{46} +2.33839 q^{47} +(-1.80652 + 1.04299i) q^{50} +(2.80323 - 1.61845i) q^{52} +(-0.996713 - 0.575453i) q^{53} +2.60640i q^{55} +(3.52198 - 6.10024i) q^{58} -9.79110 q^{59} +2.35536i q^{61} -2.03277 q^{62} -1.85540 q^{64} +3.15688i q^{65} -0.312805 q^{67} +(2.89768 - 5.01893i) q^{68} +1.94933i q^{71} +(-2.42847 - 1.40208i) q^{73} +(0.512198 - 0.295717i) q^{74} +(5.15706 - 2.97743i) q^{76} +12.4317 q^{79} +(-0.847852 + 1.46852i) q^{80} +(-7.34669 + 4.24162i) q^{82} +(3.60916 - 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} +(-4.68660 - 2.70581i) q^{86} +(2.25274 + 3.90186i) q^{88} +(-5.28999 - 9.16253i) q^{89} +(7.29536 + 4.21198i) q^{92} +1.67935i q^{94} +5.80767i q^{95} +(13.4322 + 7.75510i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{4}+O(q^{10}) \) 10 * q - 8 * q^4	\( 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} + 30 q^{47} - 3 q^{50} + 12 q^{52} - 9 q^{53} + 8 q^{58} - 36 q^{59} - 12 q^{62} + 6 q^{64} + 20 q^{67} - 27 q^{68} - 3 q^{73} + 30 q^{74} + 9 q^{76} - 40 q^{79} + 30 q^{80} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} - 24 q^{89} - 39 q^{92} + 6 q^{97}+O(q^{100}) \) 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Introduction

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