LMFDB - Embedded newform 1323.2.o.d.440.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			440.2
Root			$0.187540 + 0.324828i$ of defining polynomial
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.d.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.621951 - 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(-0.723774 - 1.25361i) q^{5} +2.50226i q^{8} +O(q^{10})$	\(q+(-0.621951 - 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(-0.723774 - 1.25361i) q^{5} +2.50226i q^{8} +1.03958i q^{10} +(-1.55933 - 0.900281i) q^{11} +(1.88867 - 1.09042i) q^{13} +(-0.585716 + 1.01449i) q^{16} -3.90460 q^{17} +4.01207i q^{19} +(-1.07425 + 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} +(-4.91522 + 2.83781i) q^{23} +(1.45230 - 2.51546i) q^{25} -1.56621 q^{26} +(-8.49418 - 4.90412i) q^{29} +(2.45129 - 1.41525i) q^{31} +(5.06262 - 2.92290i) q^{32} +(2.42847 + 1.40208i) q^{34} +0.823534 q^{37} +(1.44067 - 2.49531i) q^{38} +(3.13687 - 1.81107i) q^{40} +(5.90617 + 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +2.67246i q^{44} +4.07604 q^{46} +(-1.16920 + 2.02511i) q^{47} +(-1.80652 + 1.04299i) q^{50} +(-2.80323 - 1.61845i) q^{52} +1.15091i q^{53} +2.60640i q^{55} +(3.52198 + 6.10024i) q^{58} +(4.89555 + 8.47934i) q^{59} +(-2.03980 - 1.17768i) q^{61} -2.03277 q^{62} -1.85540 q^{64} +(-2.73394 - 1.57844i) q^{65} +(0.156402 + 0.270897i) q^{67} +(2.89768 + 5.01893i) q^{68} +1.94933i q^{71} +2.80416i q^{73} +(-0.512198 - 0.295717i) q^{74} +(5.15706 - 2.97743i) q^{76} +(-6.21583 + 10.7661i) q^{79} +1.69570 q^{80} -8.48323i q^{82} +(3.60916 - 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} +(4.68660 - 2.70581i) q^{86} +(2.25274 - 3.90186i) q^{88} +10.5800 q^{89} +(7.29536 + 4.21198i) q^{92} +(1.45436 - 0.839677i) q^{94} +(5.02959 - 2.90383i) q^{95} +(13.4322 + 7.75510i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4}+O(q^{10}) $ 10 * q + 4 * q^4	$ 10 q + 4 q^{4} - 12 q^{11} + 6 q^{13} - 6 q^{16} - 24 q^{17} + 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 6 q^{26} + 15 q^{29} + 9 q^{31} + 48 q^{32} + 3 q^{34} - 12 q^{37} + 18 q^{38} + 15 q^{40} + 9 q^{41} + 3 q^{43} + 26 q^{46} - 15 q^{47} - 3 q^{50} - 12 q^{52} + 8 q^{58} + 18 q^{59} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} - 27 q^{68} - 30 q^{74} + 9 q^{76} + 20 q^{79} - 60 q^{80} + 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} + 48 q^{89} - 39 q^{92} + 3 q^{94} + 6 q^{97}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^11 + 6 * q^13 - 6 * q^16 - 24 * q^17 + 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 6 * q^26 + 15 * q^29 + 9 * q^31 + 48 * q^32 + 3 * q^34 - 12 * q^37 + 18 * q^38 + 15 * q^40 + 9 * q^41 + 3 * q^43 + 26 * q^46 - 15 * q^47 - 3 * q^50 - 12 * q^52 + 8 * q^58 + 18 * q^59 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 - 27 * q^68 - 30 * q^74 + 9 * q^76 + 20 * q^79 - 60 * q^80 + 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 + 48 * q^89 - 39 * q^92 + 3 * q^94 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.621951	−	0.359083i	−0.439785	−	0.253910i	0.263721	−	0.964599i	$-0.415050\pi$
$2$	−0.621951	−	0.359083i	−0.439785	−	0.253910i	−0.703507	+	0.710689i	$0.748383\pi$
$3$		0			0
$3$		0			0
$4$	−0.742118	−	1.28539i	−0.371059	−	0.642693i
$5$	−0.723774	−	1.25361i	−0.323682	−	0.560633i	0.657563	−	0.753400i	$-0.271587\pi$
$5$	−0.723774	−	1.25361i	−0.323682	−	0.560633i	−0.981245	+	0.192766i	$0.938254\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.50226i			0.884683i
$9$		0			0
$10$			1.03958i			0.328744i
$11$	−1.55933	−	0.900281i	−0.470156	−	0.271445i	0.246149	−	0.969232i	$-0.420835\pi$
$11$	−1.55933	−	0.900281i	−0.470156	−	0.271445i	−0.716305	+	0.697787i	$0.754168\pi$
$12$		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
$16$	−0.585716	+	1.01449i	−0.146429	+	0.253622i
$17$	−3.90460			−0.947005			−0.473503	−	0.880792i	$-0.657011\pi$
$17$	−3.90460			−0.947005			−0.473503	+	0.880792i	$0.657011\pi$
$18$		0			0
$19$			4.01207i			0.920432i	0.887807	+	0.460216i	$0.152228\pi$
$19$			4.01207i			0.920432i	−0.887807	+	0.460216i	$0.847772\pi$
$20$	−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	$-0.868219\pi$
$23$	−4.91522	+	2.83781i	−1.02490	+	0.591723i	−0.109377	+	0.994000i	$0.534886\pi$
$24$		0			0
$25$	1.45230	−	2.51546i	0.290460	−	0.503092i
$26$	−1.56621			−0.307160
$27$		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
$31$	2.45129	−	1.41525i	0.440264	−	0.254187i	−0.263445	−	0.964674i	$-0.584859\pi$
$31$	2.45129	−	1.41525i	0.440264	−	0.254187i	0.703710	+	0.710488i	$0.251526\pi$
$32$	5.06262	−	2.92290i	0.894953	−	0.516701i
$33$		0			0
$34$	2.42847	+	1.40208i	0.416479	+	0.240454i
$35$		0			0
$36$		0			0
$37$	0.823534			0.135388			0.0676941	−	0.997706i	$-0.478436\pi$
$37$	0.823534			0.135388			0.0676941	+	0.997706i	$0.478436\pi$
$38$	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	$0.971839\pi$
$44$			2.67246i			0.402888i
$45$		0			0
$46$	4.07604			0.600979
$47$	−1.16920	+	2.02511i	−0.170545	+	0.295392i	−0.938610	−	0.344979i	$-0.887886\pi$
$47$	−1.16920	+	2.02511i	−0.170545	+	0.295392i	0.768066	+	0.640371i	$0.221219\pi$
$48$		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
$53$			1.15091i			0.158089i	0.996871	+	0.0790445i	$0.0251869\pi$
$53$			1.15091i			0.158089i	−0.996871	+	0.0790445i	$0.974813\pi$
$54$		0			0
$55$			2.60640i			0.351447i
$56$		0			0
$57$		0			0
$58$	3.52198	+	6.10024i	0.462458	+	0.801001i
$59$	4.89555	+	8.47934i	0.637346	+	1.10392i	0.986013	+	0.166669i	$0.0533013\pi$
$59$	4.89555	+	8.47934i	0.637346	+	1.10392i	−0.348666	+	0.937247i	$0.613365\pi$
$60$		0			0
$61$	−2.03980	−	1.17768i	−0.261170	−	0.150786i	0.363698	−	0.931517i	$-0.381514\pi$
$61$	−2.03980	−	1.17768i	−0.261170	−	0.150786i	−0.624868	+	0.780730i	$0.714847\pi$
$62$	−2.03277			−0.258163
$63$		0			0
$64$	−1.85540			−0.231925
$65$	−2.73394	−	1.57844i	−0.339104	−	0.195782i
$66$		0			0
$67$	0.156402	+	0.270897i	0.0191076	+	0.0330953i	0.875421	−	0.483361i	$-0.160584\pi$
$67$	0.156402	+	0.270897i	0.0191076	+	0.0330953i	−0.856313	+	0.516456i	$0.827251\pi$
$68$	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
$73$			2.80416i			0.328202i	0.986444	+	0.164101i	$0.0524722\pi$
$73$			2.80416i			0.328202i	−0.986444	+	0.164101i	$0.947528\pi$
$74$	−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
$79$	−6.21583	+	10.7661i	−0.699336	+	1.21128i	0.269361	+	0.963039i	$0.413187\pi$
$79$	−6.21583	+	10.7661i	−0.699336	+	1.21128i	−0.968697	+	0.248246i	$0.920146\pi$
$80$	1.69570			0.189585
$81$		0			0
$82$		−	8.48323i		−	0.936816i
$83$	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
$89$	10.5800			1.12147			0.560737	−	0.827994i	$-0.310518\pi$
$89$	10.5800			1.12147			0.560737	+	0.827994i	$0.310518\pi$
$90$		0			0
$91$		0			0
$92$	7.29536	+	4.21198i	0.760593	+	0.439129i
$93$		0			0
$94$	1.45436	−	0.839677i	0.150006	−	0.0866061i
$95$	5.02959	−	2.90383i	0.516025	−	0.297927i
$96$		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
$100$	−4.31112			−0.431112
$101$	−1.97309	+	3.41749i	−0.196330	+	0.340053i	−0.947336	−	0.320242i	$-0.896236\pi$
$101$	−1.97309	+	3.41749i	−0.196330	+	0.340053i	0.751006	+	0.660295i	$0.229569\pi$
$102$		0			0
$103$	3.59853	−	2.07761i	0.354573	−	0.204713i	−0.312124	−	0.950041i	$-0.601041\pi$
$103$	3.59853	−	2.07761i	0.354573	−	0.204713i	0.666698	+	0.745328i	$0.267707\pi$
$104$	2.72853	+	4.72595i	0.267554	+	0.463417i
$105$		0			0
$106$	0.413271	−	0.715806i	0.0401404	−	0.0695253i
$107$			5.67065i			0.548202i	0.961701	+	0.274101i	$0.0883803\pi$
$107$			5.67065i			0.548202i	−0.961701	+	0.274101i	$0.911620\pi$
$108$		0			0
$109$	−11.9983			−1.14923			−0.574615	−	0.818424i	$-0.694848\pi$
$109$	−11.9983			−1.14923			−0.574615	+	0.818424i	$0.694848\pi$
$110$	0.935915	−	1.62105i	0.0892360	−	0.154561i
$111$		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
$116$			14.5577i			1.35165i
$117$		0			0
$118$		−	7.03164i		−	0.647315i
$119$		0			0
$120$		0			0
$121$	−3.87899	−	6.71861i	−0.352635	−	0.610782i
$122$	0.845770	+	1.46492i	0.0765724	+	0.132627i
$123$		0			0
$124$	−3.63829	−	2.10057i	−0.326728	−	0.188637i
$125$	−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	$0.512450\pi$
$128$	−8.97127	−	5.17956i	−0.792956	−	0.457813i
$129$		0			0
$130$	1.13358	+	1.96343i	0.0994219	+	0.172204i
$131$	−1.48721	−	2.57592i	−0.129938	−	0.225059i	0.793714	−	0.608291i	$-0.208144\pi$
$131$	−1.48721	−	2.57592i	−0.129938	−	0.225059i	−0.923652	+	0.383232i	$0.874811\pi$
$132$		0			0
$133$		0			0
$134$		−	0.224646i		−	0.0194065i
$135$		0			0
$136$		−	9.77034i		−	0.837800i
$137$	−10.3045	−	5.94930i	−0.880372	−	0.508283i	−0.00959114	−	0.999954i	$-0.503053\pi$
$137$	−10.3045	−	5.94930i	−0.880372	−	0.508283i	−0.870781	+	0.491671i	$0.836386\pi$
$138$		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
$142$	0.699971	−	1.21239i	0.0587403	−	0.101741i
$143$	−3.92675			−0.328371
$144$		0			0
$145$			14.1979i			1.17907i
$146$	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	$-0.573022\pi$
$149$	6.13061	−	3.53951i	0.502239	−	0.289968i	0.729638	+	0.683834i	$0.239689\pi$
$150$		0			0
$151$	−7.79093	+	13.4943i	−0.634017	+	1.09815i	0.352706	+	0.935734i	$0.385262\pi$
$151$	−7.79093	+	13.4943i	−0.634017	+	1.09815i	−0.986723	+	0.162415i	$0.948072\pi$
$152$	−10.0393			−0.814291
$153$		0			0
$154$		0			0
$155$	−3.54836	−	2.04865i	−0.285011	−	0.164551i
$156$		0			0
$157$	−1.80677	+	1.04314i	−0.144196	+	0.0832517i	−0.570362	−	0.821393i	$-0.693197\pi$
$157$	−1.80677	+	1.04314i	−0.144196	+	0.0832517i	0.426166	+	0.904645i	$0.359864\pi$
$158$	7.73188	−	4.46400i	0.615115	−	0.355137i
$159$		0			0
$160$	−7.32839	−	4.23105i	−0.579360	−	0.334494i
$161$		0			0
$162$		0			0
$163$	11.1797			0.875659			0.437830	−	0.899058i	$-0.355747\pi$
$163$	11.1797			0.875659			0.437830	+	0.899058i	$0.355747\pi$
$164$	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
$170$		−	4.05915i		−	0.311323i
$171$		0			0
$172$	11.1842			0.852787
$173$	−7.61290	+	13.1859i	−0.578798	+	1.00251i	0.416820	+	0.908989i	$0.363145\pi$
$173$	−7.61290	+	13.1859i	−0.578798	+	1.00251i	−0.995618	+	0.0935182i	$0.970189\pi$
$174$		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
$179$			0.345718i			0.0258402i	0.999917	+	0.0129201i	$0.00411271\pi$
$179$			0.345718i			0.0258402i	−0.999917	+	0.0129201i	$0.995887\pi$
$180$		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
$185$	−0.596053	−	1.03239i	−0.0438227	−	0.0759031i
$186$		0			0
$187$	6.08857	+	3.51524i	0.445241	+	0.257060i
$188$	3.47073			0.253129
$189$		0			0
$190$	−4.17087			−0.302587
$191$	6.40096	+	3.69560i	0.463158	+	0.267404i	0.713371	−	0.700787i	$-0.247167\pi$
$191$	6.40096	+	3.69560i	0.463158	+	0.267404i	−0.250213	+	0.968191i	$0.580501\pi$
$192$		0			0
$193$	−6.51425	−	11.2830i	−0.468906	−	0.812169i	0.530462	−	0.847708i	$-0.322018\pi$
$193$	−6.51425	−	11.2830i	−0.468906	−	0.812169i	−0.999368	+	0.0355398i	$0.988685\pi$
$194$	−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
$199$			16.4078i			1.16312i	0.813504	+	0.581559i	$0.197557\pi$
$199$			16.4078i			1.16312i	−0.813504	+	0.581559i	$0.802443\pi$
$200$	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
$205$	8.54947	−	14.8081i	0.597121	−	1.03424i
$206$	−2.98414			−0.207915
$207$		0			0
$208$			2.55471i			0.177138i
$209$	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
$215$	10.9077			0.743902
$216$		0			0
$217$		0			0
$218$	7.46236	+	4.30839i	0.505415	+	0.291801i
$219$		0			0
$220$	3.35023	−	1.93426i	0.225873	−	0.130408i
$221$	−7.37451	+	4.25767i	−0.496063	+	0.286402i
$222$		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
$226$	5.20614			0.346307
$227$	5.40410	−	9.36018i	0.358683	−	0.621257i	−0.629058	−	0.777358i	$-0.716559\pi$
$227$	5.40410	−	9.36018i	0.358683	−	0.621257i	0.987741	+	0.156101i	$0.0498926\pi$
$228$		0			0
$229$	−8.39777	+	4.84846i	−0.554941	+	0.320395i	−0.751112	−	0.660174i	$-0.770482\pi$
$229$	−8.39777	+	4.84846i	−0.554941	+	0.320395i	0.196172	+	0.980570i	$0.437149\pi$
$230$	−2.95013	−	5.10977i	−0.194526	−	0.336928i
$231$		0			0
$232$	12.2714	−	21.2547i	0.805657	−	1.39544i
$233$		−	2.22739i		−	0.145921i	−0.997335	−	0.0729605i	$-0.976755\pi$
$233$		−	2.22739i		−	0.145921i	0.997335	−	0.0729605i	$-0.0232447\pi$
$234$		0			0
$235$	3.38493			0.220809
$236$	7.26616	−	12.5854i	0.472986	−	0.819237i
$237$		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	$-0.266494\pi$
$241$	5.60475	+	3.23591i	0.361034	+	0.208443i	−0.308500	+	0.951224i	$0.599827\pi$
$242$			5.57152i			0.358151i
$243$		0			0
$244$			3.49591i			0.223803i
$245$		0			0
$246$		0			0
$247$	4.37486	+	7.57748i	0.278366	+	0.482143i
$248$	3.54133	+	6.13377i	0.224875	+	0.389495i
$249$		0			0
$250$	7.11654	+	4.10874i	0.450090	+	0.259859i
$251$	−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
$254$	0.548147	+	0.316473i	0.0343938	+	0.0198573i
$255$		0			0
$256$	5.57519	+	9.65652i	0.348449	+	0.603532i
$257$	−10.5642	−	18.2977i	−0.658976	−	1.14138i	−0.980881	−	0.194607i	$-0.937657\pi$
$257$	−10.5642	−	18.2977i	−0.658976	−	1.14138i	0.321906	−	0.946772i	$-0.395677\pi$
$258$		0			0
$259$		0			0
$260$			4.68556i			0.290586i
$261$		0			0
$262$			2.13612i			0.131970i
$263$	−19.2653	−	11.1228i	−1.18795	−	0.685862i	−0.230108	−	0.973165i	$-0.573908\pi$
$263$	−19.2653	−	11.1228i	−1.18795	−	0.685862i	−0.957840	+	0.287304i	$0.907241\pi$
$264$		0			0
$265$	1.44279	−	0.832996i	0.0886299	−	0.0511705i
$266$		0			0
$267$		0			0
$268$	0.232138	−	0.402075i	0.0141801	−	0.0245607i
$269$	−29.0329			−1.77017			−0.885083	−	0.465433i	$-0.845898\pi$
$269$	−29.0329			−1.77017			−0.885083	+	0.465433i	$0.845898\pi$
$270$		0			0
$271$		−	24.0378i		−	1.46019i	−0.683344	−	0.730097i	$-0.739475\pi$
$271$		−	24.0378i		−	1.46019i	0.683344	−	0.730097i	$-0.260525\pi$
$272$	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	−0.961365	−	0.275278i	$-0.911230\pi$
$277$	−4.03243	+	6.98437i	−0.242285	+	0.419650i	0.719080	+	0.694928i	$0.244564\pi$
$278$	8.63622			0.517966
$279$		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
$283$	−13.4559	+	7.76876i	−0.799869	+	0.461805i	−0.843425	−	0.537246i	$-0.819465\pi$
$283$	−13.4559	+	7.76876i	−0.799869	+	0.461805i	0.0435563	+	0.999051i	$0.486131\pi$
$284$	2.50564	−	1.44663i	0.148682	−	0.0858418i
$285$		0			0
$286$	2.44225	+	1.41003i	0.144413	+	0.0833769i
$287$		0			0
$288$		0			0
$289$	−1.75407			−0.103181
$290$	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
$296$			2.06070i			0.119776i
$297$		0			0
$298$	−5.08391			−0.294503
$299$	−6.18882	+	10.7194i	−0.357909	+	0.619916i
$300$		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
$305$			3.40950i			0.195227i
$306$		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
$311$	8.12200	+	14.0677i	0.460556	+	0.797707i	0.998989	−	0.0449616i	$-0.0143165\pi$
$311$	8.12200	+	14.0677i	0.460556	+	0.797707i	−0.538432	+	0.842669i	$0.680983\pi$
$312$		0			0
$313$	−5.86899	−	3.38846i	−0.331735	−	0.191527i	0.324876	−	0.945757i	$-0.394677\pi$
$313$	−5.86899	−	3.38846i	−0.331735	−	0.191527i	−0.656611	+	0.754229i	$0.728011\pi$
$314$	1.49830			0.0845538
$315$		0			0
$316$	18.4515			1.03798
$317$	19.0245	+	10.9838i	1.06852	+	0.616911i	0.927777	−	0.373135i	$-0.121717\pi$
$317$	19.0245	+	10.9838i	1.06852	+	0.616911i	0.140744	+	0.990046i	$0.455051\pi$
$318$		0			0
$319$	8.83017	+	15.2943i	0.494395	+	0.856316i
$320$	1.34289	+	2.32596i	0.0750699	+	0.130025i
$321$		0			0
$322$		0			0
$323$		−	15.6655i		−	0.871654i
$324$		0			0
$325$		−	6.33450i		−	0.351375i
$326$	−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
$331$	7.30179	−	12.6471i	0.401342	−	0.695145i	−0.592546	−	0.805537i	$-0.701877\pi$
$331$	7.30179	−	12.6471i	0.401342	−	0.695145i	0.993888	+	0.110391i	$0.0352104\pi$
$332$	−10.7137			−0.587990
$333$		0			0
$334$			1.37996i			0.0755079i
$335$	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
$341$	−5.09650			−0.275991
$342$		0			0
$343$		0			0
$344$	−16.3292	−	9.42767i	−0.880412	−	0.508306i
$345$		0			0
$346$	9.46969	−	5.46733i	0.509094	−	0.293925i
$347$	2.76005	−	1.59352i	0.148167	−	0.0855444i	−0.424084	−	0.905623i	$-0.639404\pi$
$347$	2.76005	−	1.59352i	0.148167	−	0.0855444i	0.572251	+	0.820079i	$0.306070\pi$
$348$		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
$352$	−10.5257			−0.561024
$353$	−5.69040	+	9.85606i	−0.302869	+	0.524585i	−0.976785	−	0.214223i	$-0.931278\pi$
$353$	−5.69040	+	9.85606i	−0.302869	+	0.524585i	0.673915	+	0.738809i	$0.264611\pi$
$354$		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
$359$		−	5.51449i		−	0.291044i	−0.989355	−	0.145522i	$-0.953514\pi$
$359$		−	5.51449i		−	0.291044i	0.989355	−	0.145522i	$-0.0464861\pi$
$360$		0			0
$361$	2.90328			0.152804
$362$	1.17657	−	2.03789i	0.0618394	−	0.107109i
$363$		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	$-0.518999\pi$
$367$	−18.2753	−	10.5512i	−0.953962	−	0.550770i	−0.894309	+	0.447449i	$0.852333\pi$
$368$		−	6.64859i		−	0.346582i
$369$		0			0
$370$			0.856131i			0.0445081i
$371$		0			0
$372$		0			0
$373$	−7.68498	−	13.3108i	−0.397913	−	0.689206i	0.595555	−	0.803314i	$-0.296932\pi$
$373$	−7.68498	−	13.3108i	−0.397913	−	0.689206i	−0.993468	+	0.114109i	$0.963599\pi$
$374$	−2.52453	−	4.37261i	−0.130540	−	0.226102i
$375$		0			0
$376$	−5.06735	−	2.92563i	−0.261328	−	0.150878i
$377$	−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	$0.812339\pi$
$380$	−7.46510	−	4.30998i	−0.382951	−	0.221097i
$381$		0			0
$382$	−2.65406	−	4.59696i	−0.135793	−	0.235201i
$383$	9.91730	+	17.1773i	0.506750	+	0.877718i	0.999969	+	0.00781236i	$0.00248678\pi$
$383$	9.91730	+	17.1773i	0.506750	+	0.877718i	−0.493219	+	0.869905i	$0.664180\pi$
$384$		0			0
$385$		0			0
$386$			9.35663i			0.476240i
$387$		0			0
$388$		−	23.0208i		−	1.16870i
$389$	4.41918	+	2.55141i	0.224061	+	0.129362i	0.607829	−	0.794068i	$-0.292040\pi$
$389$	4.41918	+	2.55141i	0.224061	+	0.129362i	−0.383768	+	0.923429i	$0.625374\pi$
$390$		0			0
$391$	19.1920	−	11.0805i	0.970581	−	0.560365i
$392$		0			0
$393$		0			0
$394$	−1.44723	+	2.50668i	−0.0729105	+	0.126285i
$395$	17.9954			0.905449
$396$		0			0
$397$			13.3123i			0.668125i	0.942551	+	0.334062i	$0.108420\pi$
$397$			13.3123i			0.668125i	−0.942551	+	0.334062i	$0.891580\pi$
$398$	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	$-0.532654\pi$
$401$	14.1750	−	8.18392i	0.707864	−	0.408685i	0.810270	+	0.586057i	$0.199321\pi$
$402$		0			0
$403$	3.08645	−	5.34589i	0.153747	−	0.266298i
$404$	5.85706			0.291400
$405$		0			0
$406$		0			0
$407$	−1.28416	−	0.741412i	−0.0636536	−	0.0367504i
$408$		0			0
$409$	−3.75604	+	2.16855i	−0.185724	+	0.107228i	−0.589979	−	0.807418i	$-0.700864\pi$
$409$	−3.75604	+	2.16855i	−0.185724	+	0.107228i	0.404255	+	0.914646i	$0.367531\pi$
$410$	−10.6347	+	6.13994i	−0.525210	+	0.303230i
$411$		0			0
$412$	−5.34107	−	3.08367i	−0.263135	−	0.151921i
$413$		0			0
$414$		0			0
$415$	−10.4489			−0.512914
$416$	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	$0.152491\pi$
$422$			8.62988i			0.420096i
$423$		0			0
$424$	−2.87987			−0.139859
$425$	−5.67066	+	9.82187i	−0.275068	+	0.476431i
$426$		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
$431$			14.3791i			0.692616i	0.938121	+	0.346308i	$0.112565\pi$
$431$			14.3791i			0.692616i	−0.938121	+	0.346308i	$0.887435\pi$
$432$		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
$437$	−11.3855	−	19.7202i	−0.544641	−	0.943347i
$438$		0			0
$439$	−8.69907	−	5.02241i	−0.415184	−	0.239706i	0.277831	−	0.960630i	$-0.410385\pi$
$439$	−8.69907	−	5.02241i	−0.415184	−	0.239706i	−0.693015	+	0.720924i	$0.743718\pi$
$440$	−6.52190			−0.310919
$441$		0			0
$442$	6.11544			0.290882
$443$	12.0321	+	6.94672i	0.571661	+	0.330049i	0.757812	−	0.652472i	$-0.226268\pi$
$443$	12.0321	+	6.94672i	0.571661	+	0.330049i	−0.186151	+	0.982521i	$0.559602\pi$
$444$		0			0
$445$	−7.65751	−	13.2632i	−0.363001	−	0.628736i
$446$	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
$451$		−	21.2688i		−	1.00151i
$452$	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
$457$	−2.55654	+	4.42805i	−0.119590	+	0.207135i	−0.919605	−	0.392844i	$-0.871491\pi$
$457$	−2.55654	+	4.42805i	−0.119590	+	0.207135i	0.800015	+	0.599979i	$0.204825\pi$
$458$	6.96400			0.325406
$459$		0			0
$460$		−	12.1941i		−	0.568552i
$461$	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
$467$	−20.7792			−0.961546			−0.480773	−	0.876845i	$-0.659644\pi$
$467$	−20.7792			−0.961546			−0.480773	+	0.876845i	$0.659644\pi$
$468$		0			0
$469$		0			0
$470$	−2.10526	−	1.21547i	−0.0971085	−	0.0560656i
$471$		0			0
$472$	−21.2175	+	12.2500i	−0.976616	+	0.563850i
$473$	11.7501	−	6.78390i	0.540268	−	0.311924i
$474$		0			0
$475$	10.0922	+	5.82674i	0.463062	+	0.267349i
$476$		0			0
$477$		0			0
$478$	−13.2431			−0.605726
$479$	−16.0308	+	27.7662i	−0.732468	+	1.26867i	0.223357	+	0.974737i	$0.428298\pi$
$479$	−16.0308	+	27.7662i	−0.732468	+	1.26867i	−0.955825	+	0.293935i	$0.905035\pi$
$480$		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
$485$		−	22.4518i		−	1.01948i
$486$		0			0
$487$	−23.6750			−1.07282			−0.536408	−	0.843959i	$-0.680219\pi$
$487$	−23.6750			−1.07282			−0.536408	+	0.843959i	$0.680219\pi$
$488$	2.94686	−	5.10412i	0.133398	−	0.231052i
$489$		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
$494$		−	6.28376i		−	0.282720i
$495$		0			0
$496$			3.31574i			0.148881i
$497$		0			0
$498$		0			0
$499$	11.5602	+	20.0229i	0.517506	+	0.896346i	0.999793	+	0.0203330i	$0.00647265\pi$
$499$	11.5602	+	20.0229i	0.517506	+	0.896346i	−0.482288	+	0.876013i	$0.660194\pi$
$500$	8.49154	+	14.7078i	0.379753	+	0.657752i
$501$		0			0
$502$	0.259154	+	0.149622i	0.0115666	+	0.00667798i
$503$	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
$506$	−6.35589	−	3.66958i	−0.282554	−	0.163133i
$507$		0			0
$508$	0.654056	+	1.13286i	0.0290190	+	0.0502624i
$509$	−6.79171	−	11.7636i	−0.301037	−	0.521411i	0.675334	−	0.737512i	$-0.263999\pi$
$509$	−6.79171	−	11.7636i	−0.301037	−	0.521411i	−0.976371	+	0.216100i	$0.930666\pi$
$510$		0			0
$511$		0			0
$512$			12.7104i			0.561727i
$513$		0			0
$514$			15.1737i			0.669283i
$515$	−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
$520$	3.94968	−	6.84104i	0.173205	−	0.299999i
$521$	31.8954			1.39736			0.698682	−	0.715432i	$-0.253770\pi$
$521$	31.8954			1.39736			0.698682	+	0.715432i	$0.253770\pi$
$522$		0			0
$523$			1.39177i			0.0608580i	0.999537	+	0.0304290i	$0.00968734\pi$
$523$			1.39177i			0.0608580i	−0.999537	+	0.0304290i	$0.990313\pi$
$524$	−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
$530$	−1.19646			−0.0519709
$531$		0			0
$532$		0			0
$533$	22.3096	+	12.8805i	0.966337	+	0.557915i
$534$		0			0
$535$	7.10880	−	4.10427i	0.307340	−	0.177443i
$536$	−0.677855	+	0.391360i	−0.0292789	+	0.0169042i
$537$		0			0
$538$	18.0570	+	10.4252i	0.778493	+	0.449463i
$539$		0			0
$540$		0			0
$541$	−25.9472			−1.11556			−0.557779	−	0.829990i	$-0.688346\pi$
$541$	−25.9472			−1.11556			−0.557779	+	0.829990i	$0.688346\pi$
$542$	−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	$0.297199\pi$
$548$			17.6603i			0.754413i
$549$		0			0
$550$	3.75595			0.160154
$551$	19.6757	−	34.0793i	0.838212	−	1.45183i
$552$		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
$557$		−	41.9811i		−	1.77880i	−0.457134	−	0.889398i	$-0.651124\pi$
$557$		−	41.9811i		−	1.77880i	0.457134	−	0.889398i	$-0.348876\pi$
$558$		0			0
$559$			16.4334i			0.695058i
$560$		0			0
$561$		0			0
$562$	−5.01193	−	8.68092i	−0.211416	−	0.366183i
$563$	−19.3006	−	33.4295i	−0.813422	−	1.40889i	−0.910456	−	0.413606i	$-0.864269\pi$
$563$	−19.3006	−	33.4295i	−0.813422	−	1.40889i	0.0970343	−	0.995281i	$-0.469064\pi$
$564$		0			0
$565$	9.08771	+	5.24679i	0.382323	+	0.220734i
$566$	11.1585			0.469028
$567$		0			0
$568$	−4.87773			−0.204665
$569$	−30.4460	−	17.5780i	−1.27636	−	0.736908i	−0.300184	−	0.953881i	$-0.597048\pi$
$569$	−30.4460	−	17.5780i	−1.27636	−	0.736908i	−0.976178	+	0.216973i	$0.930382\pi$
$570$		0			0
$571$	17.6766	+	30.6167i	0.739742	+	1.28127i	0.952611	+	0.304190i	$0.0983857\pi$
$571$	17.6766	+	30.6167i	0.739742	+	1.28127i	−0.212870	+	0.977081i	$0.568281\pi$
$572$	2.91411	+	5.04739i	0.121845	+	0.211042i
$573$		0			0
$574$		0			0
$575$			16.4854i			0.687489i
$576$		0			0
$577$			26.8534i			1.11792i	0.829195	+	0.558960i	$0.188799\pi$
$577$			26.8534i			1.11792i	−0.829195	+	0.558960i	$0.811201\pi$
$578$	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
$583$	1.03614	−	1.79464i	0.0429125	−	0.0743266i
$584$	−7.01673			−0.290355
$585$		0			0
$586$			9.67675i			0.399743i
$587$	−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
$593$	−9.12263			−0.374621			−0.187311	−	0.982301i	$-0.559977\pi$
$593$	−9.12263			−0.374621			−0.187311	+	0.982301i	$0.559977\pi$
$594$		0			0
$595$		0			0
$596$	−9.09927	−	5.25347i	−0.372721	−	0.215190i
$597$		0			0
$598$	7.69828	−	4.44461i	0.314806	−	0.181753i
$599$	1.11316	−	0.642683i	0.0454825	−	0.0262593i	−0.477086	−	0.878856i	$-0.658307\pi$
$599$	1.11316	−	0.642683i	0.0454825	−	0.0262593i	0.522569	+	0.852597i	$0.324974\pi$
$600$		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
$604$	23.1272			0.941031
$605$	−5.61502	+	9.72551i	−0.228283	+	0.395398i
$606$		0			0
$607$	33.7319	−	19.4751i	1.36913	−	0.790470i	0.378317	−	0.925676i	$-0.376503\pi$
$607$	33.7319	−	19.4751i	1.36913	−	0.790470i	0.990817	+	0.135206i	$0.0431697\pi$
$608$	11.7269	+	20.3116i	0.475589	+	0.823744i
$609$		0			0
$610$	1.22429	−	2.12054i	0.0495702	−	0.0858581i
$611$			5.09968i			0.206311i
$612$		0			0
$613$	7.30036			0.294859			0.147429	−	0.989073i	$-0.452900\pi$
$613$	7.30036			0.294859			0.147429	+	0.989073i	$0.452900\pi$
$614$	−3.09814	+	5.36613i	−0.125031	+	0.216560i
$615$		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	$-0.336350\pi$
$619$	−0.408449	−	0.235818i	−0.0164169	−	0.00947832i	−0.508186	+	0.861247i	$0.669684\pi$
$620$			6.08135i			0.244233i
$621$		0			0
$622$		−	11.6659i		−	0.467760i
$623$		0			0
$624$		0			0
$625$	1.02013	+	1.76692i	0.0408052	+	0.0706768i
$626$	2.43348	+	4.21491i	0.0972614	+	0.168462i
$627$		0			0
$628$	2.68168	+	1.54827i	0.107011	+	0.0617826i
$629$	−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	$0.434762\pi$
$632$	−26.9397	−	15.5536i	−1.07160	−	0.618691i
$633$		0			0
$634$	−7.88819	−	13.6627i	−0.313280	−	0.542617i
$635$	0.637888	+	1.10485i	0.0253138	+	0.0438448i
$636$		0			0
$637$		0			0
$638$		−	12.6831i		−	0.502127i
$639$		0			0
$640$			14.9953i			0.592743i
$641$	43.4584	+	25.0907i	1.71651	+	0.991025i	0.925091	+	0.379745i	$0.123988\pi$
$641$	43.4584	+	25.0907i	1.71651	+	0.991025i	0.791414	+	0.611280i	$0.209345\pi$
$642$		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
$646$	−5.62524	+	9.74320i	−0.221322	+	0.383341i
$647$	29.8406			1.17315			0.586577	−	0.809894i	$-0.300475\pi$
$647$	29.8406			1.17315			0.586577	+	0.809894i	$0.300475\pi$
$648$		0			0
$649$		−	17.6295i		−	0.692018i
$650$	−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	$-0.908986\pi$
$653$	−30.5327	+	17.6281i	−1.19484	+	0.689839i	−0.235437	+	0.971890i	$0.575652\pi$
$654$		0			0
$655$	−2.15280	+	3.72877i	−0.0841170	+	0.145695i
$656$	−13.8374			−0.540258
$657$		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
$661$	13.6550	−	7.88371i	0.531117	−	0.306641i	−0.210354	−	0.977625i	$-0.567462\pi$
$661$	13.6550	−	7.88371i	0.531117	−	0.306641i	0.741471	+	0.670985i	$0.234128\pi$
$662$	−9.08270	+	5.24390i	−0.353009	+	0.203810i
$663$		0			0
$664$	15.6423	+	9.03106i	0.607037	+	0.350473i
$665$		0			0
$666$		0			0
$667$	55.6678			2.15546
$668$	−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	$0.258183\pi$
$674$			23.3589i			0.899751i
$675$		0			0
$676$	12.2359			0.470612
$677$	−1.99217	+	3.45054i	−0.0765654	+	0.132615i	−0.901766	−	0.432225i	$-0.857729\pi$
$677$	−1.99217	+	3.45054i	−0.0765654	+	0.132615i	0.825201	+	0.564840i	$0.191062\pi$
$678$		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
$683$			22.2640i			0.851908i	0.904745	+	0.425954i	$0.140061\pi$
$683$			22.2640i			0.851908i	−0.904745	+	0.425954i	$0.859939\pi$
$684$		0			0
$685$			17.2238i			0.658088i
$686$		0			0
$687$		0			0
$688$	−4.41356	−	7.64450i	−0.168265	−	0.291444i
$689$	1.25498	+	2.17368i	0.0478107	+	0.0828106i
$690$		0			0
$691$	41.9003	+	24.1912i	1.59396	+	0.920275i	0.992618	+	0.121287i	$0.0387020\pi$
$691$	41.9003	+	24.1912i	1.59396	+	0.920275i	0.601346	+	0.798989i	$0.294631\pi$
$692$	22.5987			0.859073
$693$		0			0
$694$	−2.28882			−0.0868824
$695$	15.0752	+	8.70365i	0.571834	+	0.330148i
$696$		0			0
$697$	−23.0613	−	39.9433i	−0.873507	−	1.51296i
$698$	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
$703$			3.30408i			0.124616i
$704$	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
$709$	−8.83884	+	15.3093i	−0.331949	+	0.574953i	−0.982894	−	0.184172i	$-0.941040\pi$
$709$	−8.83884	+	15.3093i	−0.331949	+	0.574953i	0.650945	+	0.759125i	$0.274373\pi$
$710$	−2.02648			−0.0760526
$711$		0			0
$712$			26.4739i			0.992150i
$713$	−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
$719$	30.4205			1.13449			0.567246	−	0.823549i	$-0.308009\pi$
$719$	30.4205			1.13449			0.567246	+	0.823549i	$0.308009\pi$
$720$		0			0
$721$		0			0
$722$	−1.80570	−	1.04252i	−0.0672011	−	0.0387986i
$723$		0			0
$724$	4.21171	−	2.43163i	0.156527	−	0.0903708i
$725$	−24.6722	+	14.2445i	−0.916304	+	0.529028i
$726$		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
$730$	−2.91515			−0.107894
$731$	14.7112	−	25.4806i	0.544114	−	0.942433i
$732$		0			0
$733$	−39.2270	+	22.6477i	−1.44888	+	0.836512i	−0.998415	−	0.0562818i	$-0.982075\pi$
$733$	−39.2270	+	22.6477i	−1.44888	+	0.836512i	−0.450466	+	0.892794i	$0.648742\pi$
$734$	7.57755	+	13.1247i	0.279692	+	0.484442i
$735$		0			0
$736$	−16.5893	+	28.7335i	−0.611489	+	1.05913i
$737$		−	0.563225i		−	0.0207466i
$738$		0			0
$739$	20.6172			0.758416			0.379208	−	0.925311i	$-0.376196\pi$
$739$	20.6172			0.758416			0.379208	+	0.925311i	$0.376196\pi$
$740$	−0.884684	+	1.53232i	−0.0325216	+	0.0563291i
$741$		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
$746$			11.0382i			0.404137i
$747$		0			0
$748$		−	10.4349i		−	0.381538i
$749$		0			0
$750$		0			0
$751$	12.5008	+	21.6521i	0.456162	+	0.790095i	0.998754	−	0.0499007i	$-0.0158905\pi$
$751$	12.5008	+	21.6521i	0.456162	+	0.790095i	−0.542592	+	0.839996i	$0.682557\pi$
$752$	−1.36963	−	2.37227i	−0.0499454	−	0.0865079i
$753$		0			0
$754$	13.3037	+	7.68089i	0.484492	+	0.279722i
$755$	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	$0.664085\pi$
$758$	20.1282	+	11.6210i	0.731089	+	0.422094i
$759$		0			0
$760$	7.26616	+	12.5854i	0.263571	+	0.456519i
$761$	−1.58366	−	2.74298i	−0.0574075	−	0.0994328i	0.835893	−	0.548892i	$-0.184950\pi$
$761$	−1.58366	−	2.74298i	−0.0574075	−	0.0994328i	−0.893301	+	0.449459i	$0.851617\pi$
$762$		0			0
$763$		0			0
$764$		−	10.9703i		−	0.396891i
$765$		0			0
$766$		−	14.2446i		−	0.514677i
$767$	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
$772$	−9.66868	+	16.7467i	−0.347984	+	0.602725i
$773$	12.3136			0.442889			0.221444	−	0.975173i	$-0.428923\pi$
$773$	12.3136			0.442889			0.221444	+	0.975173i	$0.428923\pi$
$774$		0			0
$775$		−	8.22149i		−	0.295325i
$776$	−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
$782$	−15.9153			−0.569130
$783$		0			0
$784$		0			0
$785$	2.61539	+	1.51000i	0.0933473	+	0.0538941i
$786$		0			0
$787$	3.30450	−	1.90785i	0.117793	−	0.0680076i	−0.439946	−	0.898024i	$-0.645002\pi$
$787$	3.30450	−	1.90785i	0.117793	−	0.0680076i	0.557739	+	0.830017i	$0.311669\pi$
$788$	−5.18056	+	2.99100i	−0.184550	+	0.106550i
$789$		0			0
$790$	−11.1923	−	6.46186i	−0.398203	−	0.229903i
$791$		0			0
$792$		0			0
$793$	−5.13668			−0.182409
$794$	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
$800$		−	16.9798i		−	0.600325i
$801$		0			0
$802$	−11.7548			−0.415078
$803$	2.52453	−	4.37261i	0.0890886	−	0.154306i
$804$		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
$809$		−	45.6024i		−	1.60330i	−0.597796	−	0.801648i	$-0.703957\pi$
$809$		−	45.6024i		−	1.60330i	0.597796	−	0.801648i	$-0.296043\pi$
$810$		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
$815$	−8.09155	−	14.0150i	−0.283435	−	0.490923i
$816$		0			0
$817$	−26.1819	−	15.1161i	−0.915988	−	0.528846i
$818$	3.11476			0.108905
$819$		0			0
$820$	−25.3789			−0.886269
$821$	10.2976	+	5.94530i	0.359387	+	0.207492i	0.668812	−	0.743432i	$-0.266803\pi$
$821$	10.2976	+	5.94530i	0.359387	+	0.207492i	−0.309425	+	0.950924i	$0.600136\pi$
$822$		0			0
$823$	−1.51195	−	2.61877i	−0.0527031	−	0.0912844i	0.838470	−	0.544947i	$-0.183450\pi$
$823$	−1.51195	−	2.61877i	−0.0527031	−	0.0912844i	−0.891173	+	0.453663i	$0.850117\pi$
$824$	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
$829$		−	34.3299i		−	1.19233i	−0.802863	−	0.596163i	$-0.796691\pi$
$829$		−	34.3299i		−	1.19233i	0.802863	−	0.596163i	$-0.203309\pi$
$830$	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
$835$	−1.39073	+	2.40882i	−0.0481283	+	0.0833606i
$836$	−10.7221			−0.370832
$837$		0			0
$838$		−	13.5201i		−	0.467045i
$839$	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
$845$	11.9334			0.410523
$846$		0			0
$847$		0			0
$848$	−1.16758	−	0.674104i	−0.0400949	−	0.0231488i
$849$		0			0
$850$	7.05374	−	4.07248i	0.241941	−	0.139685i
$851$	−4.04786	+	2.33703i	−0.138759	+	0.0801124i
$852$		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
$856$	−14.1894			−0.484985
$857$	−16.1307	+	27.9392i	−0.551014	+	0.954384i	0.447188	+	0.894440i	$0.352426\pi$
$857$	−16.1307	+	27.9392i	−0.551014	+	0.954384i	−0.998202	+	0.0599442i	$0.980908\pi$
$858$		0			0
$859$	15.2711	−	8.81675i	0.521042	−	0.300824i	−0.216319	−	0.976323i	$-0.569405\pi$
$859$	15.2711	−	8.81675i	0.521042	−	0.300824i	0.737361	+	0.675499i	$0.236072\pi$
$860$	−8.09483	−	14.0207i	−0.276032	−	0.478101i
$861$		0			0
$862$	5.16329	−	8.94307i	0.175862	−	0.304602i
$863$		−	30.4946i		−	1.03805i	−0.854760	−	0.519023i	$-0.826296\pi$
$863$		−	30.4946i		−	1.03805i	0.854760	−	0.519023i	$-0.173704\pi$
$864$		0			0
$865$	22.0401			0.749385
$866$	0.797632	−	1.38154i	0.0271046	−	0.0469466i
$867$		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
$872$		−	30.0229i		−	1.01670i
$873$		0			0
$874$			16.3533i			0.553160i
$875$		0			0
$876$		0			0
$877$	−4.40363	−	7.62730i	−0.148700	−	0.257556i	0.782047	−	0.623219i	$-0.214176\pi$
$877$	−4.40363	−	7.62730i	−0.148700	−	0.257556i	−0.930747	+	0.365663i	$0.880842\pi$
$878$	3.60693	+	6.24738i	0.121728	+	0.210839i
$879$		0			0
$880$	−2.64417	−	1.52661i	−0.0891348	−	0.0514620i
$881$	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	$0.283002\pi$
$884$	10.9455	+	6.31940i	0.368137	+	0.212544i
$885$		0			0
$886$	−4.98890	−	8.64103i	−0.167605	−	0.290301i
$887$	13.7025	+	23.7335i	0.460086	+	0.796892i	0.998965	−	0.0454915i	$-0.0144854\pi$
$887$	13.7025	+	23.7335i	0.460086	+	0.796892i	−0.538879	+	0.842383i	$0.681152\pi$
$888$		0			0
$889$		0			0
$890$			10.9987i			0.368679i
$891$		0			0
$892$			39.0641i			1.30796i
$893$	−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
$898$	−3.79299	+	6.56965i	−0.126574	+	0.219232i
$899$	−27.7623			−0.925923
$900$		0			0
$901$		−	4.49383i		−	0.149711i
$902$	−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	−0.600252	−	0.799811i	$-0.704933\pi$
$907$	11.8216	−	20.4757i	0.392531	−	0.679883i	0.992783	+	0.119928i	$0.0382663\pi$
$908$	−16.0419			−0.532370
$909$		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
$913$	−11.2557	+	6.49851i	−0.372511	+	0.215069i
$914$	3.18008	−	1.83602i	0.105188	−	0.0607301i
$915$		0			0
$916$	12.4643	+	7.19626i	0.411832	+	0.237771i
$917$		0			0
$918$		0			0
$919$	−33.8298			−1.11594			−0.557971	−	0.829861i	$-0.688420\pi$
$919$	−33.8298			−1.11594			−0.557971	+	0.829861i	$0.688420\pi$
$920$	−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
$926$		−	14.3838i		−	0.472682i
$927$		0			0
$928$	−57.3371			−1.88218
$929$	−16.4582	+	28.5064i	−0.539976	+	0.935266i	0.458928	+	0.888473i	$0.348233\pi$
$929$	−16.4582	+	28.5064i	−0.539976	+	0.935266i	−0.998905	+	0.0467929i	$0.985100\pi$
$930$		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
$935$		−	10.1770i		−	0.332822i
$936$		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
$941$	9.93855	+	17.2141i	0.323987	+	0.561163i	0.981307	−	0.192449i	$-0.0616431\pi$
$941$	9.93855	+	17.2141i	0.323987	+	0.561163i	−0.657319	+	0.753612i	$0.728310\pi$
$942$		0			0
$943$	−58.0603	−	33.5211i	−1.89070	−	1.09160i
$944$	−11.4696			−0.373304
$945$		0			0
$946$	−9.74394			−0.316803
$947$	17.9696	+	10.3747i	0.583933	+	0.337134i	0.762695	−	0.646759i	$-0.223876\pi$
$947$	17.9696	+	10.3747i	0.583933	+	0.337134i	−0.178762	+	0.983892i	$0.557209\pi$
$948$		0			0
$949$	3.05772	+	5.29613i	0.0992578	+	0.171919i
$950$	−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
$955$		−	10.6991i		−	0.346215i
$956$	−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
$961$	−11.4941	+	19.9084i	−0.370778	+	0.642207i
$962$	−1.28983			−0.0415858
$963$		0			0
$964$		−	9.60570i		−	0.309379i
$965$	−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
$971$	29.0258			0.931481			0.465740	−	0.884921i	$-0.345788\pi$
$971$	29.0258			0.931481			0.465740	+	0.884921i	$0.345788\pi$
$972$		0			0
$973$		0			0
$974$	14.7247	+	8.50130i	0.471809	+	0.272399i
$975$		0			0
$976$	2.38949	−	1.37957i	0.0764856	−	0.0441590i
$977$	7.73439	−	4.46545i	0.247445	−	0.142862i	−0.371149	−	0.928573i	$-0.621036\pi$
$977$	7.73439	−	4.46545i	0.247445	−	0.142862i	0.618594	+	0.785711i	$0.287703\pi$
$978$		0			0
$979$	−16.4977	−	9.52495i	−0.527268	−	0.304419i
$980$		0			0
$981$		0			0
$982$	12.8258			0.409286
$983$	−26.1346	+	45.2665i	−0.833566	+	1.44378i	0.0616269	+	0.998099i	$0.480371\pi$
$983$	−26.1346	+	45.2665i	−0.833566	+	1.44378i	−0.895193	+	0.445679i	$0.852962\pi$
$984$		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
$989$		−	42.7675i		−	1.35993i
$990$		0			0
$991$	43.8303			1.39232			0.696158	−	0.717889i	$-0.254892\pi$
$991$	43.8303			1.39232			0.696158	+	0.717889i	$0.254892\pi$
$992$	8.27329	−	14.3298i	0.262677	−	0.454970i
$993$		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	$-0.585789\pi$
$997$	−38.9689	−	22.4987i	−1.23416	−	0.712542i	−0.967894	+	0.251358i	$0.919123\pi$
$998$		−	16.6043i		−	0.525600i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	63.4	even	3
63.2.i.b.38.2	yes	10	21.5	even	6
63.2.s.b.47.2	yes	10	21.11	odd	6
63.2.s.b.59.2	yes	10	63.40	odd	6
189.2.i.b.143.4		10	7.5	odd	6
189.2.i.b.152.2		10	63.32	odd	6
189.2.s.b.17.4		10	63.5	even	6
189.2.s.b.89.4		10	7.4	even	3
441.2.i.b.68.4		10	63.31	odd	6
441.2.i.b.227.2		10	21.2	odd	6
441.2.o.c.146.4		10	3.2	odd	2
441.2.o.c.293.4		10	63.13	odd	6
441.2.o.d.146.4		10	21.20	even	2
441.2.o.d.293.4		10	9.4	even	3
441.2.s.b.362.2		10	21.17	even	6
441.2.s.b.374.2		10	63.58	even	3
567.2.p.c.80.4		10	63.61	odd	6
567.2.p.c.404.4		10	63.11	odd	6
567.2.p.d.80.2		10	63.47	even	6
567.2.p.d.404.2		10	63.25	even	3
1008.2.ca.b.257.3		10	252.67	odd	6
1008.2.ca.b.353.3		10	84.47	odd	6
1008.2.df.b.689.2		10	252.103	even	6
1008.2.df.b.929.2		10	84.11	even	6
1323.2.i.b.521.4		10	7.2	even	3
1323.2.i.b.1097.2		10	63.59	even	6
1323.2.o.c.440.2		10	7.6	odd	2
1323.2.o.c.881.2		10	9.5	odd	6
1323.2.o.d.440.2		10	1.1	even	1	trivial
1323.2.o.d.881.2		10	63.41	even	6	inner
1323.2.s.b.656.4		10	7.3	odd	6
1323.2.s.b.962.4		10	63.23	odd	6
3024.2.ca.b.2033.4		10	28.19	even	6
3024.2.ca.b.2609.4		10	252.95	even	6
3024.2.df.b.17.4		10	252.131	odd	6
3024.2.df.b.1601.4		10	28.11	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.621951 - 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(-0.723774 - 1.25361i) q^{5} +2.50226i q^{8} +O(q^{10})\)	\(q+(-0.621951 - 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +(-0.723774 - 1.25361i) q^{5} +2.50226i q^{8} +1.03958i q^{10} +(-1.55933 - 0.900281i) q^{11} +(1.88867 - 1.09042i) q^{13} +(-0.585716 + 1.01449i) q^{16} -3.90460 q^{17} +4.01207i q^{19} +(-1.07425 + 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} +(-4.91522 + 2.83781i) q^{23} +(1.45230 - 2.51546i) q^{25} -1.56621 q^{26} +(-8.49418 - 4.90412i) q^{29} +(2.45129 - 1.41525i) q^{31} +(5.06262 - 2.92290i) q^{32} +(2.42847 + 1.40208i) q^{34} +0.823534 q^{37} +(1.44067 - 2.49531i) q^{38} +(3.13687 - 1.81107i) q^{40} +(5.90617 + 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +2.67246i q^{44} +4.07604 q^{46} +(-1.16920 + 2.02511i) q^{47} +(-1.80652 + 1.04299i) q^{50} +(-2.80323 - 1.61845i) q^{52} +1.15091i q^{53} +2.60640i q^{55} +(3.52198 + 6.10024i) q^{58} +(4.89555 + 8.47934i) q^{59} +(-2.03980 - 1.17768i) q^{61} -2.03277 q^{62} -1.85540 q^{64} +(-2.73394 - 1.57844i) q^{65} +(0.156402 + 0.270897i) q^{67} +(2.89768 + 5.01893i) q^{68} +1.94933i q^{71} +2.80416i q^{73} +(-0.512198 - 0.295717i) q^{74} +(5.15706 - 2.97743i) q^{76} +(-6.21583 + 10.7661i) q^{79} +1.69570 q^{80} -8.48323i q^{82} +(3.60916 - 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} +(4.68660 - 2.70581i) q^{86} +(2.25274 - 3.90186i) q^{88} +10.5800 q^{89} +(7.29536 + 4.21198i) q^{92} +(1.45436 - 0.839677i) q^{94} +(5.02959 - 2.90383i) q^{95} +(13.4322 + 7.75510i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 10 * q + 4 * q^4	\( 10 q + 4 q^{4} - 12 q^{11} + 6 q^{13} - 6 q^{16} - 24 q^{17} + 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 6 q^{26} + 15 q^{29} + 9 q^{31} + 48 q^{32} + 3 q^{34} - 12 q^{37} + 18 q^{38} + 15 q^{40} + 9 q^{41} + 3 q^{43} + 26 q^{46} - 15 q^{47} - 3 q^{50} - 12 q^{52} + 8 q^{58} + 18 q^{59} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} - 27 q^{68} - 30 q^{74} + 9 q^{76} + 20 q^{79} - 60 q^{80} + 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} + 48 q^{89} - 39 q^{92} + 3 q^{94} + 6 q^{97}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^11 + 6 * q^13 - 6 * q^16 - 24 * q^17 + 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 6 * q^26 + 15 * q^29 + 9 * q^31 + 48 * q^32 + 3 * q^34 - 12 * q^37 + 18 * q^38 + 15 * q^40 + 9 * q^41 + 3 * q^43 + 26 * q^46 - 15 * q^47 - 3 * q^50 - 12 * q^52 + 8 * q^58 + 18 * q^59 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 - 27 * q^68 - 30 * q^74 + 9 * q^76 + 20 * q^79 - 60 * q^80 + 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 + 48 * q^89 - 39 * q^92 + 3 * q^94 + 6 * q^97

Introduction

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