LMFDB - Embedded newform 1323.2.s.b.656.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (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			656.4
Root			$0.187540 + 0.324828i$ of defining polynomial
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.b.962.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.621951 - 0.359083i) q^{2} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +2.50226i q^{8} +O(q^{10})$	\(q+(0.621951 - 0.359083i) q^{2} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +2.50226i q^{8} +(-0.900304 + 0.519791i) q^{10} +1.80056i q^{11} +(-1.88867 + 1.09042i) q^{13} +(-0.585716 - 1.01449i) q^{16} +(-1.95230 - 3.38149i) q^{17} +(3.47456 + 2.00604i) q^{19} +(1.07425 - 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} -5.67561i q^{23} -2.90460 q^{25} +(-0.783106 + 1.35638i) q^{26} +(-8.49418 - 4.90412i) q^{29} +(2.45129 + 1.41525i) q^{31} +(-5.06262 - 2.92290i) q^{32} +(-2.42847 - 1.40208i) q^{34} +(-0.411767 + 0.713202i) q^{37} +2.88134 q^{38} -3.62215i q^{40} +(-5.90617 - 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +(-2.31442 - 1.33623i) q^{44} +(-2.03802 - 3.52995i) q^{46} +(1.16920 + 2.02511i) q^{47} +(-1.80652 + 1.04299i) q^{50} -3.23689i q^{52} +(0.996713 - 0.575453i) q^{53} -2.60640i q^{55} -7.04395 q^{58} +(-4.89555 + 8.47934i) q^{59} +(-2.03980 + 1.17768i) q^{61} +2.03277 q^{62} -1.85540 q^{64} +(2.73394 - 1.57844i) q^{65} +(0.156402 - 0.270897i) q^{67} +5.79536 q^{68} +1.94933i q^{71} +(-2.42847 + 1.40208i) q^{73} +0.591435i q^{74} +(-5.15706 + 2.97743i) q^{76} +(-6.21583 - 10.7661i) q^{79} +(0.847852 + 1.46852i) q^{80} +(-7.34669 - 4.24162i) q^{82} +(-3.60916 + 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} +5.41161i q^{86} -4.50548 q^{88} +(5.28999 - 9.16253i) q^{89} +(7.29536 + 4.21198i) q^{92} +(1.45436 + 0.839677i) q^{94} +(-5.02959 - 2.90383i) q^{95} +(-13.4322 - 7.75510i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4}+O(q^{10}) $ 10 * q + 4 * q^4	$ 10 q + 4 q^{4} + 15 q^{10} - 6 q^{13} - 6 q^{16} - 12 q^{17} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 14 q^{25} + 3 q^{26} + 15 q^{29} + 9 q^{31} - 48 q^{32} - 3 q^{34} + 6 q^{37} + 36 q^{38} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} + 15 q^{47} - 3 q^{50} + 9 q^{53} - 16 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} - 54 q^{68} - 3 q^{73} - 9 q^{76} + 20 q^{79} - 30 q^{80} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 16 q^{88} + 24 q^{89} - 39 q^{92} + 3 q^{94} - 6 q^{97}+O(q^{100}) $ 10 * q + 4 * q^4 + 15 * q^10 - 6 * q^13 - 6 * q^16 - 12 * q^17 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 14 * q^25 + 3 * q^26 + 15 * q^29 + 9 * q^31 - 48 * q^32 - 3 * q^34 + 6 * q^37 + 36 * q^38 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 + 15 * q^47 - 3 * q^50 + 9 * q^53 - 16 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 - 54 * q^68 - 3 * q^73 - 9 * q^76 + 20 * q^79 - 30 * q^80 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 16 * q^88 + 24 * 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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.621951	−	0.359083i	0.439785	−	0.253910i	−0.263721	−	0.964599i	$-0.584950\pi$
$2$	0.621951	−	0.359083i	0.439785	−	0.253910i	0.703507	+	0.710689i	$0.251617\pi$
$3$		0			0
$3$		0			0
$4$	−0.742118	+	1.28539i	−0.371059	+	0.642693i
$5$	−1.44755			−0.647363			−0.323682	−	0.946166i	$-0.604921\pi$
$5$	−1.44755			−0.647363			−0.323682	+	0.946166i	$0.604921\pi$
$6$		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
$11$			1.80056i			0.542890i	0.962454	+	0.271445i	$0.0875015\pi$
$11$			1.80056i			0.542890i	−0.962454	+	0.271445i	$0.912499\pi$
$12$		0			0
$13$	−1.88867	+	1.09042i	−0.523823	+	0.302429i	−0.738497	−	0.674256i	$-0.764464\pi$
$13$	−1.88867	+	1.09042i	−0.523823	+	0.302429i	0.214675	+	0.976686i	$0.431131\pi$
$14$		0			0
$15$		0			0
$16$	−0.585716	−	1.01449i	−0.146429	−	0.253622i
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	0.526037	−	0.850462i	$-0.323677\pi$
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	−0.999540	+	0.0303308i	$0.990344\pi$
$18$		0			0
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	0.842462	−	0.538755i	$-0.181105\pi$
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	−0.0453446	+	0.998971i	$0.514439\pi$
$20$	1.07425	−	1.86066i	0.240210	−	0.416056i
$21$		0			0
$22$	0.646552	+	1.11986i	0.137845	+	0.238755i
$23$		−	5.67561i		−	1.18345i	−0.806141	−	0.591723i	$-0.798448\pi$
$23$		−	5.67561i		−	1.18345i	0.806141	−	0.591723i	$-0.201552\pi$
$24$		0			0
$25$	−2.90460			−0.580921
$26$	−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
$31$	2.45129	+	1.41525i	0.440264	+	0.254187i	0.703710	−	0.710488i	$-0.251526\pi$
$31$	2.45129	+	1.41525i	0.440264	+	0.254187i	−0.263445	+	0.964674i	$0.584859\pi$
$32$	−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
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$38$	2.88134			0.467414
$39$		0			0
$40$		−	3.62215i		−	0.572712i
$41$	−5.90617	−	10.2298i	−0.922389	−	1.59762i	−0.795708	−	0.605681i	$-0.792901\pi$
$41$	−5.90617	−	10.2298i	−0.922389	−	1.59762i	−0.126681	−	0.991943i	$-0.540433\pi$
$42$		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
$47$	1.16920	+	2.02511i	0.170545	+	0.295392i	0.938610	−	0.344979i	$-0.112114\pi$
$47$	1.16920	+	2.02511i	0.170545	+	0.295392i	−0.768066	+	0.640371i	$0.778781\pi$
$48$		0			0
$49$		0			0
$50$	−1.80652	+	1.04299i	−0.255480	+	0.147502i
$51$		0			0
$52$		−	3.23689i		−	0.448877i
$53$	0.996713	−	0.575453i	0.136909	−	0.0790445i	−0.429981	−	0.902838i	$-0.641480\pi$
$53$	0.996713	−	0.575453i	0.136909	−	0.0790445i	0.566890	+	0.823793i	$0.308146\pi$
$54$		0			0
$55$		−	2.60640i		−	0.351447i
$56$		0			0
$57$		0			0
$58$	−7.04395			−0.924916
$59$	−4.89555	+	8.47934i	−0.637346	+	1.10392i	0.348666	+	0.937247i	$0.386635\pi$
$59$	−4.89555	+	8.47934i	−0.637346	+	1.10392i	−0.986013	+	0.166669i	$0.946699\pi$
$60$		0			0
$61$	−2.03980	+	1.17768i	−0.261170	+	0.150786i	−0.624868	−	0.780730i	$-0.714847\pi$
$61$	−2.03980	+	1.17768i	−0.261170	+	0.150786i	0.363698	+	0.931517i	$0.381514\pi$
$62$	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	−0.856313	−	0.516456i	$-0.827251\pi$
$67$	0.156402	−	0.270897i	0.0191076	−	0.0330953i	0.875421	+	0.483361i	$0.160584\pi$
$68$	5.79536			0.702790
$69$		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	−0.635337	−	0.772235i	$-0.719139\pi$
$73$	−2.42847	+	1.40208i	−0.284231	+	0.164101i	0.351106	+	0.936336i	$0.385806\pi$
$74$			0.591435i			0.0687529i
$75$		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	−0.968697	−	0.248246i	$-0.920146\pi$
$79$	−6.21583	−	10.7661i	−0.699336	−	1.21128i	0.269361	−	0.963039i	$-0.413187\pi$
$80$	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	−0.993248	−	0.116010i	$-0.962990\pi$
$83$	−3.60916	+	6.25124i	−0.396157	+	0.686163i	0.597092	+	0.802173i	$0.296323\pi$
$84$		0			0
$85$	2.82605	+	4.89486i	0.306528	+	0.530923i
$86$			5.41161i			0.583549i
$87$		0			0
$88$	−4.50548			−0.480286
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	−0.436695	−	0.899610i	$-0.643851\pi$
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	0.997432	−	0.0716161i	$-0.0228156\pi$
$90$		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	−0.373704	−	0.927548i	$-0.621912\pi$
$97$	−13.4322	−	7.75510i	−1.36384	−	0.787411i	−0.990132	+	0.140137i	$0.955246\pi$
$98$		0			0
$99$		0			0
$100$	2.15556	−	3.73354i	0.215556	−	0.373354i
$101$	−3.94618			−0.392659			−0.196330	−	0.980538i	$-0.562902\pi$
$101$	−3.94618			−0.392659			−0.196330	+	0.980538i	$0.562902\pi$
$102$		0			0
$103$		−	4.15522i		−	0.409426i	−0.978822	−	0.204713i	$-0.934374\pi$
$103$		−	4.15522i		−	0.409426i	0.978822	−	0.204713i	$-0.0656261\pi$
$104$	−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	$-0.421714\pi$
$107$	−4.91092	−	2.83532i	−0.474757	−	0.274101i	−0.718229	+	0.695807i	$0.755047\pi$
$108$		0			0
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	0.996083	+	0.0884193i	$0.0281815\pi$
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	−0.421468	+	0.906843i	$0.638485\pi$
$110$	−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
$115$			8.21572i			0.766120i
$116$	12.6074	−	7.27887i	1.17057	−	0.675826i
$117$		0			0
$118$			7.03164i			0.647315i
$119$		0			0
$120$		0			0
$121$	7.75798			0.705271
$122$	−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
$131$	−2.97441			−0.259876			−0.129938	−	0.991522i	$-0.541478\pi$
$131$	−2.97441			−0.259876			−0.129938	+	0.991522i	$0.541478\pi$
$132$		0			0
$133$		0			0
$134$		−	0.224646i		−	0.0194065i
$135$		0			0
$136$	8.46137	−	4.88517i	0.725556	−	0.418900i
$137$			11.8986i			1.01657i	0.861190	+	0.508283i	$0.169720\pi$
$137$			11.8986i			1.01657i	−0.861190	+	0.508283i	$0.830280\pi$
$138$		0			0
$139$	10.4143	−	6.01268i	0.883327	−	0.509989i	0.0115731	−	0.999933i	$-0.496316\pi$
$139$	10.4143	−	6.01268i	0.883327	−	0.509989i	0.871754	+	0.489944i	$0.162983\pi$
$140$		0			0
$141$		0			0
$142$	0.699971	+	1.21239i	0.0587403	+	0.101741i
$143$	−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
$149$			7.07901i			0.579935i	0.957036	+	0.289968i	$0.0936446\pi$
$149$			7.07901i			0.579935i	−0.957036	+	0.289968i	$0.906355\pi$
$150$		0			0
$151$	15.5819			1.26803			0.634017	−	0.773319i	$-0.281405\pi$
$151$	15.5819			1.26803			0.634017	+	0.773319i	$0.281405\pi$
$152$	−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
$157$	−1.80677	−	1.04314i	−0.144196	−	0.0832517i	0.426166	−	0.904645i	$-0.359864\pi$
$157$	−1.80677	−	1.04314i	−0.144196	−	0.0832517i	−0.570362	+	0.821393i	$0.693197\pi$
$158$	−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
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	−0.997522	−	0.0703575i	$-0.977586\pi$
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	0.559692	+	0.828700i	$0.310919\pi$
$164$	17.5323			1.36904
$165$		0			0
$166$			5.18395i			0.402353i
$167$	0.960750	+	1.66407i	0.0743450	+	0.128769i	0.900801	−	0.434232i	$-0.142980\pi$
$167$	0.960750	+	1.66407i	0.0743450	+	0.128769i	−0.826456	+	0.563001i	$0.809647\pi$
$168$		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
$173$	7.61290	+	13.1859i	0.578798	+	1.00251i	0.995618	+	0.0935182i	$0.0298113\pi$
$173$	7.61290	+	13.1859i	0.578798	+	1.00251i	−0.416820	+	0.908989i	$0.636855\pi$
$174$		0			0
$175$		0			0
$176$	1.82665	−	1.05462i	0.137689	−	0.0794948i
$177$		0			0
$178$		−	7.59818i		−	0.569508i
$179$	0.299401	−	0.172859i	0.0223783	−	0.0129201i	−0.488769	−	0.872413i	$-0.662554\pi$
$179$	0.299401	−	0.172859i	0.0223783	−	0.0129201i	0.511147	+	0.859493i	$0.329221\pi$
$180$		0			0
$181$		−	3.27661i		−	0.243548i	−0.992558	−	0.121774i	$-0.961142\pi$
$181$		−	3.27661i		−	0.243548i	0.992558	−	0.121774i	$-0.0388583\pi$
$182$		0			0
$183$		0			0
$184$	14.2019			1.04698
$185$	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	$-0.752833\pi$
$191$	−6.40096	+	3.69560i	−0.463158	+	0.267404i	0.250213	+	0.968191i	$0.419499\pi$
$192$		0			0
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	−0.999368	−	0.0355398i	$-0.988685\pi$
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	0.530462	+	0.847708i	$0.322018\pi$
$194$	−11.1389			−0.799727
$195$		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	−0.910397	−	0.413736i	$-0.864224\pi$
$199$	−14.2096	+	8.20390i	−1.00729	+	0.581559i	−0.0968925	+	0.995295i	$0.530890\pi$
$200$		−	7.26808i		−	0.513931i
$201$		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
$206$	−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	$0.969071\pi$
$212$			1.70822i			0.117321i
$213$		0			0
$214$	−4.07247			−0.278388
$215$	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
$220$	3.35023	+	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	$0.00995496\pi$
$223$	22.7932	+	13.1597i	1.52635	+	0.881237i	0.526836	+	0.849967i	$0.323378\pi$
$224$		0			0
$225$		0			0
$226$	−2.60307	+	4.50865i	−0.173154	+	0.299911i
$227$	10.8082			0.717366			0.358683	−	0.933459i	$-0.383226\pi$
$227$	10.8082			0.717366			0.358683	+	0.933459i	$0.383226\pi$
$228$		0			0
$229$			9.69691i			0.640790i	0.947284	+	0.320395i	$0.103816\pi$
$229$			9.69691i			0.640790i	−0.947284	+	0.320395i	$0.896184\pi$
$230$	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	$-0.310089\pi$
$233$	1.92897	+	1.11369i	0.126371	+	0.0729605i	−0.435482	+	0.900198i	$0.643422\pi$
$234$		0			0
$235$	−1.69247	−	2.93144i	−0.110404	−	0.191226i
$236$	−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
$241$			6.47181i			0.416886i	0.978035	+	0.208443i	$0.0668396\pi$
$241$			6.47181i			0.416886i	−0.978035	+	0.208443i	$0.933160\pi$
$242$	4.82508	−	2.78576i	0.310168	−	0.179075i
$243$		0			0
$244$		−	3.49591i		−	0.223803i
$245$		0			0
$246$		0			0
$247$	−8.74972			−0.556731
$248$	−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	$-0.495814\pi$
$251$	0.416679			0.0263005			0.0131503	+	0.999914i	$0.495814\pi$
$252$		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
$257$	−21.1284			−1.31795			−0.658976	−	0.752164i	$-0.729010\pi$
$257$	−21.1284			−1.31795			−0.658976	+	0.752164i	$0.729010\pi$
$258$		0			0
$259$		0			0
$260$			4.68556i			0.290586i
$261$		0			0
$262$	−1.84994	+	1.06806i	−0.114290	+	0.0659851i
$263$			22.2456i			1.37172i	0.727732	+	0.685862i	$0.240574\pi$
$263$			22.2456i			1.37172i	−0.727732	+	0.685862i	$0.759426\pi$
$264$		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
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.845619	−	0.533788i	$-0.820768\pi$
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.0394642	−	0.999221i	$-0.512565\pi$
$270$		0			0
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.290610	−	0.956842i	$-0.593858\pi$
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.973954	+	0.226745i	$0.927192\pi$
$272$	−2.28699	+	3.96118i	−0.138669	+	0.240182i
$273$		0			0
$274$	4.27259	+	7.40034i	0.258117	+	0.447071i
$275$		−	5.22992i		−	0.315376i
$276$		0			0
$277$	8.06485			0.484570			0.242285	−	0.970205i	$-0.422103\pi$
$277$	8.06485			0.484570			0.242285	+	0.970205i	$0.422103\pi$
$278$	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
$283$	−13.4559	−	7.76876i	−0.799869	−	0.461805i	0.0435563	−	0.999051i	$-0.486131\pi$
$283$	−13.4559	−	7.76876i	−0.799869	−	0.461805i	−0.843425	+	0.537246i	$0.819465\pi$
$284$	−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
$289$	0.877036	−	1.51907i	0.0515904	−	0.0893571i
$290$	10.1965			0.598757
$291$		0			0
$292$		−	4.16203i		−	0.243564i
$293$	6.73712	+	11.6690i	0.393587	+	0.681712i	0.992920	−	0.118788i	$-0.0379008\pi$
$293$	6.73712	+	11.6690i	0.393587	+	0.681712i	−0.599333	+	0.800500i	$0.704567\pi$
$294$		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
$299$	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
$304$		−	4.69987i		−	0.269556i
$305$	2.95271	−	1.70475i	0.169072	−	0.0976136i
$306$		0			0
$307$			8.62791i			0.492421i	0.969216	+	0.246210i	$0.0791854\pi$
$307$			8.62791i			0.492421i	−0.969216	+	0.246210i	$0.920815\pi$
$308$		0			0
$309$		0			0
$310$	−2.94254			−0.167125
$311$	−8.12200	+	14.0677i	−0.460556	+	0.797707i	−0.998989	−	0.0449616i	$-0.985683\pi$
$311$	−8.12200	+	14.0677i	−0.460556	+	0.797707i	0.538432	+	0.842669i	$0.319017\pi$
$312$		0			0
$313$	−5.86899	+	3.38846i	−0.331735	+	0.191527i	−0.656611	−	0.754229i	$-0.728011\pi$
$313$	−5.86899	+	3.38846i	−0.331735	+	0.191527i	0.324876	+	0.945757i	$0.394677\pi$
$314$	−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	$-0.878283\pi$
$317$	−19.0245	+	10.9838i	−1.06852	+	0.616911i	−0.140744	+	0.990046i	$0.544949\pi$
$318$		0			0
$319$	8.83017	−	15.2943i	0.494395	−	0.856316i
$320$	2.68578			0.150140
$321$		0			0
$322$		0			0
$323$		−	15.6655i		−	0.871654i
$324$		0			0
$325$	5.48584	−	3.16725i	0.304299	−	0.175687i
$326$			8.02886i			0.444678i
$327$		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	0.993888	−	0.110391i	$-0.0352104\pi$
$331$	7.30179	+	12.6471i	0.401342	+	0.695145i	−0.592546	+	0.805537i	$0.701877\pi$
$332$	−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	$-0.513121\pi$
$338$			5.92049i			0.322032i
$339$		0			0
$340$	−8.38906			−0.454961
$341$	−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
$346$	9.46969	+	5.46733i	0.509094	+	0.293925i
$347$	−2.76005	−	1.59352i	−0.148167	−	0.0855444i	0.424084	−	0.905623i	$-0.360596\pi$
$347$	−2.76005	−	1.59352i	−0.148167	−	0.0855444i	−0.572251	+	0.820079i	$0.693930\pi$
$348$		0			0
$349$	6.48224	+	3.74252i	0.346986	+	0.200333i	0.663357	−	0.748303i	$-0.269131\pi$
$349$	6.48224	+	3.74252i	0.346986	+	0.200333i	−0.316371	+	0.948636i	$0.602464\pi$
$350$		0			0
$351$		0			0
$352$	5.26287	−	9.11556i	0.280512	−	0.485861i
$353$	−11.3808			−0.605739			−0.302869	−	0.953032i	$-0.597945\pi$
$353$	−11.3808			−0.605739			−0.302869	+	0.953032i	$0.597945\pi$
$354$		0			0
$355$		−	2.82175i		−	0.149763i
$356$	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	$-0.286847\pi$
$359$	4.77569	+	2.75725i	0.252051	+	0.145522i	−0.368652	+	0.929568i	$0.620181\pi$
$360$		0			0
$361$	−1.45164	−	2.51432i	−0.0764022	−	0.132332i
$362$	−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
$367$		−	21.1025i		−	1.10154i	−0.834657	−	0.550770i	$-0.814334\pi$
$367$		−	21.1025i		−	1.10154i	0.834657	−	0.550770i	$-0.185666\pi$
$368$	−5.75785	+	3.32430i	−0.300149	+	0.173291i
$369$		0			0
$370$		−	0.856131i		−	0.0445081i
$371$		0			0
$372$		0			0
$373$	15.3700			0.795826			0.397913	−	0.917423i	$-0.369735\pi$
$373$	15.3700			0.795826			0.397913	+	0.917423i	$0.369735\pi$
$374$	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
$383$	19.8346			1.01350			0.506750	−	0.862093i	$-0.330847\pi$
$383$	19.8346			1.01350			0.506750	+	0.862093i	$0.330847\pi$
$384$		0			0
$385$		0			0
$386$			9.35663i			0.476240i
$387$		0			0
$388$	19.9366	−	11.5104i	1.01213	−	0.584352i
$389$		−	5.10283i		−	0.258724i	−0.991597	−	0.129362i	$-0.958707\pi$
$389$		−	5.10283i		−	0.258724i	0.991597	−	0.129362i	$-0.0412928\pi$
$390$		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
$395$	8.99772	+	15.5845i	0.452724	+	0.784141i
$396$		0			0
$397$	11.5288	+	6.65615i	0.578613	+	0.334062i	0.760582	−	0.649242i	$-0.224914\pi$
$397$	11.5288	+	6.65615i	0.578613	+	0.334062i	−0.181969	+	0.983304i	$0.558247\pi$
$398$	−5.89177	+	10.2048i	−0.295328	+	0.511522i
$399$		0			0
$400$	1.70127	+	2.94669i	0.0850636	+	0.147334i
$401$			16.3678i			0.817371i	0.912675	+	0.408685i	$0.134013\pi$
$401$			16.3678i			0.817371i	−0.912675	+	0.408685i	$0.865987\pi$
$402$		0			0
$403$	−6.17290			−0.307494
$404$	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
$409$	−3.75604	−	2.16855i	−0.185724	−	0.107228i	0.404255	−	0.914646i	$-0.367531\pi$
$409$	−3.75604	−	2.16855i	−0.185724	−	0.107228i	−0.589979	+	0.807418i	$0.700864\pi$
$410$	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
$415$	5.22443	−	9.04898i	0.256457	−	0.444197i
$416$	12.7488			0.625062
$417$		0			0
$418$			5.18802i			0.253754i
$419$	−9.41294	−	16.3037i	−0.459852	−	0.796487i	0.539100	−	0.842241i	$-0.318764\pi$
$419$	−9.41294	−	16.3037i	−0.459852	−	0.796487i	−0.998953	+	0.0457540i	$0.985431\pi$
$420$		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
$425$	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
$430$		−	7.83357i		−	0.377768i
$431$	12.4526	−	7.18954i	0.599823	−	0.346308i	−0.169149	−	0.985590i	$-0.554102\pi$
$431$	12.4526	−	7.18954i	0.599823	−	0.346308i	0.768972	+	0.639283i	$0.220769\pi$
$432$		0			0
$433$		−	2.22130i		−	0.106749i	−0.998575	−	0.0533745i	$-0.983002\pi$
$433$		−	2.22130i		−	0.106749i	0.998575	−	0.0533745i	$-0.0169977\pi$
$434$		0			0
$435$		0			0
$436$	−17.8083			−0.852865
$437$	11.3855	−	19.7202i	0.544641	−	0.943347i
$438$		0			0
$439$	−8.69907	+	5.02241i	−0.415184	+	0.239706i	−0.693015	−	0.720924i	$-0.743718\pi$
$439$	−8.69907	+	5.02241i	−0.415184	+	0.239706i	0.277831	+	0.960630i	$0.410385\pi$
$440$	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	$-0.773732\pi$
$443$	−12.0321	+	6.94672i	−0.571661	+	0.330049i	0.186151	+	0.982521i	$0.440398\pi$
$444$		0			0
$445$	−7.65751	+	13.2632i	−0.363001	+	0.628736i
$446$	18.9017			0.895020
$447$		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
$452$		−	10.7595i		−	0.506086i
$453$		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	0.800015	−	0.599979i	$-0.204825\pi$
$457$	−2.55654	−	4.42805i	−0.119590	−	0.207135i	−0.919605	+	0.392844i	$0.871491\pi$
$458$	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	−0.946596	−	0.322422i	$-0.895503\pi$
$461$	−4.16691	+	7.21730i	−0.194072	+	0.336143i	0.752524	+	0.658565i	$0.228836\pi$
$462$		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	$0.679243\pi$
$464$			11.4897i			0.533395i
$465$		0			0
$466$	1.59963			0.0741016
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	−0.999757	−	0.0220611i	$-0.992977\pi$
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	0.518984	+	0.854784i	$0.326310\pi$
$468$		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
$478$	6.62156	−	11.4689i	0.302863	−	0.524574i
$479$	−32.0617			−1.46494			−0.732468	−	0.680802i	$-0.761632\pi$
$479$	−32.0617			−1.46494			−0.732468	+	0.680802i	$0.761632\pi$
$480$		0			0
$481$		−	1.79600i		−	0.0818907i
$482$	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	0.999094	+	0.0425641i	$0.0135527\pi$
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	−0.462685	+	0.886523i	$0.653114\pi$
$488$	−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
$493$			38.2973i			1.72482i
$494$	−5.44189	+	3.14188i	−0.244842	+	0.141360i
$495$		0			0
$496$		−	3.31574i		−	0.148881i
$497$		0			0
$498$		0			0
$499$	−23.1204			−1.03501			−0.517506	−	0.855680i	$-0.673139\pi$
$499$	−23.1204			−1.03501			−0.517506	+	0.855680i	$0.673139\pi$
$500$	−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	$-0.601033\pi$
$503$	−13.9995			−0.624206			−0.312103	+	0.950048i	$0.601033\pi$
$504$		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
$509$	−13.5834			−0.602074			−0.301037	−	0.953612i	$-0.597333\pi$
$509$	−13.5834			−0.602074			−0.301037	+	0.953612i	$0.597333\pi$
$510$		0			0
$511$		0			0
$512$			12.7104i			0.561727i
$513$		0			0
$514$	−13.1408	+	7.58684i	−0.579616	+	0.334641i
$515$			6.01488i			0.265047i
$516$		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
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	0.968924	+	0.247360i	$0.0795630\pi$
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	−0.270242	+	0.962792i	$0.587104\pi$
$522$		0			0
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	0.526121	−	0.850410i	$-0.323646\pi$
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	−0.473416	+	0.880839i	$0.656979\pi$
$524$	2.20737	−	3.82327i	0.0964293	−	0.167020i
$525$		0			0
$526$	7.98803	+	13.8357i	0.348295	+	0.603264i
$527$		−	11.0520i		−	0.481433i
$528$		0			0
$529$	−9.21257			−0.400546
$530$	−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
$535$	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
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	−0.439903	−	0.898045i	$-0.644987\pi$
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	0.997682	−	0.0680555i	$-0.0216795\pi$
$542$	−17.2632			−0.741516
$543$		0			0
$544$			22.8256i			0.978638i
$545$	−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
$551$	−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
$556$			17.8485i			0.756944i
$557$	−36.3567	+	20.9905i	−1.54048	+	0.889398i	−0.541674	+	0.840589i	$0.682209\pi$
$557$	−36.3567	+	20.9905i	−1.54048	+	0.889398i	−0.998808	+	0.0488092i	$0.984457\pi$
$558$		0			0
$559$		−	16.4334i		−	0.695058i
$560$		0			0
$561$		0			0
$562$	10.0239			0.422831
$563$	19.3006	−	33.4295i	0.813422	−	1.40889i	−0.0970343	−	0.995281i	$-0.530936\pi$
$563$	19.3006	−	33.4295i	0.813422	−	1.40889i	0.910456	−	0.413606i	$-0.135731\pi$
$564$		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	$-0.402952\pi$
$569$	30.4460	−	17.5780i	1.27636	−	0.736908i	0.976178	+	0.216973i	$0.0696185\pi$
$570$		0			0
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	−0.212870	−	0.977081i	$-0.568281\pi$
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	0.952611	−	0.304190i	$-0.0983857\pi$
$572$	5.82823			0.243690
$573$		0			0
$574$		0			0
$575$			16.4854i			0.687489i
$576$		0			0
$577$	−23.2557	+	13.4267i	−0.968147	+	0.558960i	−0.898671	−	0.438624i	$-0.855466\pi$
$577$	−23.2557	+	13.4267i	−0.968147	+	0.558960i	−0.0694761	+	0.997584i	$0.522133\pi$
$578$		−	1.25972i		−	0.0523973i
$579$		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
$584$	−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	$-0.609301\pi$
$587$	15.6788	−	27.1565i	0.647134	−	1.12087i	0.983804	−	0.179246i	$-0.0573657\pi$
$588$		0			0
$589$	5.67809	+	9.83474i	0.233962	+	0.405234i
$590$		−	10.1786i		−	0.419048i
$591$		0			0
$592$	0.964714			0.0396495
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	−0.944353	−	0.328935i	$-0.893310\pi$
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	0.757042	+	0.653366i	$0.226644\pi$
$594$		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	$-0.341693\pi$
$599$	−1.11316	−	0.642683i	−0.0454825	−	0.0262593i	−0.522569	+	0.852597i	$0.675026\pi$
$600$		0			0
$601$	16.7126	+	9.64903i	0.681721	+	0.393592i	0.800503	−	0.599328i	$-0.204566\pi$
$601$	16.7126	+	9.64903i	0.681721	+	0.393592i	−0.118782	+	0.992920i	$0.537899\pi$
$602$		0			0
$603$		0			0
$604$	−11.5636	+	20.0287i	−0.470515	+	0.814956i
$605$	−11.2300			−0.456566
$606$		0			0
$607$		−	38.9502i		−	1.58094i	−0.612501	−	0.790470i	$-0.709836\pi$
$607$		−	38.9502i		−	1.58094i	0.612501	−	0.790470i	$-0.290164\pi$
$608$	−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	0.782847	−	0.622214i	$-0.213767\pi$
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	−0.930277	+	0.366859i	$0.880433\pi$
$614$	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
$619$		−	0.471636i		−	0.0189566i	−0.999955	−	0.00947832i	$-0.996983\pi$
$619$		−	0.471636i		−	0.0189566i	0.999955	−	0.00947832i	$-0.00301709\pi$
$620$	5.26660	−	3.04068i	0.211512	−	0.122116i
$621$		0			0
$622$			11.6659i			0.467760i
$623$		0			0
$624$		0			0
$625$	−2.04026			−0.0816105
$626$	−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
$635$	1.27578			0.0506277
$636$		0			0
$637$		0			0
$638$		−	12.6831i		−	0.502127i
$639$		0			0
$640$	−12.9863	+	7.49767i	−0.513330	+	0.296371i
$641$		−	50.1815i		−	1.98205i	−0.133677	−	0.991025i	$-0.542679\pi$
$641$		−	50.1815i		−	1.98205i	0.133677	−	0.991025i	$-0.457321\pi$
$642$		0			0
$643$	−9.18633	+	5.30373i	−0.362274	+	0.209159i	−0.670078	−	0.742291i	$-0.733739\pi$
$643$	−9.18633	+	5.30373i	−0.362274	+	0.209159i	0.307804	+	0.951450i	$0.400406\pi$
$644$		0			0
$645$		0			0
$646$	−5.62524	−	9.74320i	−0.221322	−	0.383341i
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	0.994677	+	0.103044i	$0.0328582\pi$
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	−0.408100	+	0.912937i	$0.633809\pi$
$648$		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
$653$		−	35.2561i		−	1.37968i	−0.723962	−	0.689839i	$-0.757681\pi$
$653$		−	35.2561i		−	1.37968i	0.723962	−	0.689839i	$-0.242319\pi$
$654$		0			0
$655$	4.30561			0.168234
$656$	−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
$661$	13.6550	+	7.88371i	0.531117	+	0.306641i	0.741471	−	0.670985i	$-0.234128\pi$
$661$	13.6550	+	7.88371i	0.531117	+	0.306641i	−0.210354	+	0.977625i	$0.567462\pi$
$662$	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
$667$	−27.8339	+	48.2097i	−1.07773	+	1.86669i
$668$	−2.85196			−0.110346
$669$		0			0
$670$			0.325186i			0.0125630i
$671$	−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
$677$	1.99217	+	3.45054i	0.0765654	+	0.132615i	0.901766	−	0.432225i	$-0.142271\pi$
$677$	1.99217	+	3.45054i	0.0765654	+	0.132615i	−0.825201	+	0.564840i	$0.808938\pi$
$678$		0			0
$679$		0			0
$680$	−12.2482	+	7.07152i	−0.469698	+	0.271181i
$681$		0			0
$682$			3.66013i			0.140154i
$683$	19.2812	−	11.1320i	0.737774	−	0.425954i	−0.0834856	−	0.996509i	$-0.526605\pi$
$683$	19.2812	−	11.1320i	0.737774	−	0.425954i	0.821259	+	0.570555i	$0.193272\pi$
$684$		0			0
$685$		−	17.2238i		−	0.658088i
$686$		0			0
$687$		0			0
$688$	8.82711			0.336530
$689$	−1.25498	+	2.17368i	−0.0478107	+	0.0828106i
$690$		0			0
$691$	41.9003	−	24.1912i	1.59396	−	0.920275i	0.601346	−	0.798989i	$-0.294631\pi$
$691$	41.9003	−	24.1912i	1.59396	−	0.920275i	0.992618	−	0.121287i	$-0.0387020\pi$
$692$	−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
$698$	5.37551			0.203466
$699$		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
$704$		−	3.34076i		−	0.125910i
$705$		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	0.650945	−	0.759125i	$-0.274373\pi$
$709$	−8.83884	−	15.3093i	−0.331949	−	0.574953i	−0.982894	+	0.184172i	$0.941040\pi$
$710$	−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
$716$			0.513128i			0.0191765i
$717$		0			0
$718$	3.96033			0.147798
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	−0.429591	−	0.903024i	$-0.641342\pi$
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	0.996837	−	0.0794749i	$-0.0253244\pi$
$720$		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	−0.431680	−	0.902027i	$-0.642079\pi$
$727$	−38.5219	−	22.2406i	−1.42870	−	0.824859i	−0.997018	+	0.0771674i	$0.975412\pi$
$728$		0			0
$729$		0			0
$730$	1.45757	−	2.52459i	0.0539472	−	0.0934393i
$731$	29.4224			1.08823
$732$		0			0
$733$			45.2954i			1.67302i	0.547949	+	0.836512i	$0.315409\pi$
$733$			45.2954i			1.67302i	−0.547949	+	0.836512i	$0.684591\pi$
$734$	−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	0.611739	−	0.791060i	$-0.290470\pi$
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	−0.990947	+	0.134252i	$0.957137\pi$
$740$	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
$745$		−	10.2472i		−	0.375429i
$746$	9.55935	−	5.51909i	0.349993	−	0.202068i
$747$		0			0
$748$			10.4349i			0.381538i
$749$		0			0
$750$		0			0
$751$	−25.0017			−0.912324			−0.456162	−	0.889897i	$-0.650776\pi$
$751$	−25.0017			−0.912324			−0.456162	+	0.889897i	$0.650776\pi$
$752$	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
$761$	−3.16732			−0.114815			−0.0574075	−	0.998351i	$-0.518283\pi$
$761$	−3.16732			−0.114815			−0.0574075	+	0.998351i	$0.518283\pi$
$762$		0			0
$763$		0			0
$764$		−	10.9703i		−	0.396891i
$765$		0			0
$766$	12.3361	−	7.12228i	0.445723	−	0.257338i
$767$		−	21.3529i		−	0.771009i
$768$		0			0
$769$	−2.48873	+	1.43687i	−0.0897460	+	0.0518149i	−0.544201	−	0.838955i	$-0.683167\pi$
$769$	−2.48873	+	1.43687i	−0.0897460	+	0.0518149i	0.454455	+	0.890770i	$0.349834\pi$
$770$		0			0
$771$		0			0
$772$	−9.66868	−	16.7467i	−0.347984	−	0.602725i
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	0.955247	−	0.295810i	$-0.0955895\pi$
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	−0.733802	+	0.679363i	$0.762256\pi$
$774$		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
$779$		−	47.3920i		−	1.69799i
$780$		0			0
$781$	−3.50988			−0.125594
$782$	−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
$787$	3.30450	+	1.90785i	0.117793	+	0.0680076i	0.557739	−	0.830017i	$-0.311669\pi$
$787$	3.30450	+	1.90785i	0.117793	+	0.0680076i	−0.439946	+	0.898024i	$0.645002\pi$
$788$	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
$793$	2.56834	−	4.44849i	0.0912044	−	0.157971i
$794$	9.56045			0.339288
$795$		0			0
$796$		−	24.3530i		−	0.863171i
$797$	24.5682	+	42.5535i	0.870252	+	1.50732i	0.861736	+	0.507357i	$0.169377\pi$
$797$	24.5682	+	42.5535i	0.870252	+	1.50732i	0.00851609	+	0.999964i	$0.497289\pi$
$798$		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
$803$	−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
$808$		−	9.87437i		−	0.347379i
$809$	−39.4929	+	22.8012i	−1.38850	+	0.801648i	−0.993146	−	0.116882i	$-0.962710\pi$
$809$	−39.4929	+	22.8012i	−1.38850	+	0.801648i	−0.395350	+	0.918531i	$0.629377\pi$
$810$		0			0
$811$			39.1391i			1.37436i	0.726488	+	0.687180i	$0.241151\pi$
$811$			39.1391i			1.37436i	−0.726488	+	0.687180i	$0.758849\pi$
$812$		0			0
$813$		0			0
$814$	−1.06492			−0.0373253
$815$	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	$-0.733197\pi$
$821$	−10.2976	+	5.94530i	−0.359387	+	0.207492i	0.309425	+	0.950924i	$0.399864\pi$
$822$		0			0
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	−0.891173	−	0.453663i	$-0.850117\pi$
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	0.838470	+	0.544947i	$0.183450\pi$
$824$	10.3975			0.362213
$825$		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	0.114861	−	0.993382i	$-0.463358\pi$
$829$	29.7306	−	17.1649i	1.03259	−	0.596163i	0.917724	+	0.397218i	$0.130024\pi$
$830$		−	7.50402i		−	0.260468i
$831$		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
$836$	−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	−0.952551	−	0.304379i	$-0.901551\pi$
$839$	−6.16024	+	10.6698i	−0.212675	+	0.368364i	0.739876	+	0.672744i	$0.234884\pi$
$840$		0			0
$841$	33.6008	+	58.1983i	1.15865	+	2.00684i
$842$		−	1.31202i		−	0.0452153i
$843$		0			0
$844$	17.8354			0.613920
$845$	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
$850$	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	0.565693	−	0.824616i	$-0.308609\pi$
$853$	3.92537	+	2.26631i	0.134402	+	0.0775971i	−0.431291	+	0.902213i	$0.641942\pi$
$854$		0			0
$855$		0			0
$856$	7.09472	−	12.2884i	0.242493	−	0.420010i
$857$	−32.2614			−1.10203			−0.551014	−	0.834496i	$-0.685759\pi$
$857$	−32.2614			−1.10203			−0.551014	+	0.834496i	$0.685759\pi$
$858$		0			0
$859$		−	17.6335i		−	0.601647i	−0.953680	−	0.300824i	$-0.902738\pi$
$859$		−	17.6335i		−	0.601647i	0.953680	−	0.300824i	$-0.0972615\pi$
$860$	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	$-0.159629\pi$
$863$	26.4091	+	15.2473i	0.898975	+	0.519023i	0.0221074	+	0.999756i	$0.492962\pi$
$864$		0			0
$865$	−11.0200	−	19.0873i	−0.374693	−	0.648987i
$866$	−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
$871$			0.682180i			0.0231148i
$872$	−26.0006	+	15.0115i	−0.880492	+	0.508352i
$873$		0			0
$874$		−	16.3533i		−	0.553160i
$875$		0			0
$876$		0			0
$877$	8.80725			0.297400			0.148700	−	0.988882i	$-0.452491\pi$
$877$	8.80725			0.297400			0.148700	+	0.988882i	$0.452491\pi$
$878$	−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	$-0.725877\pi$
$881$	−38.6776			−1.30308			−0.651540	+	0.758614i	$0.725877\pi$
$882$		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
$887$	27.4050			0.920171			0.460086	−	0.887875i	$-0.347819\pi$
$887$	27.4050			0.920171			0.460086	+	0.887875i	$0.347819\pi$
$888$		0			0
$889$		0			0
$890$			10.9987i			0.368679i
$891$		0			0
$892$	−33.8305	+	19.5321i	−1.13273	+	0.653982i
$893$			9.38179i			0.313950i
$894$		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
$899$	−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
$905$			4.74305i			0.157664i
$906$		0			0
$907$	−23.6433			−0.785062			−0.392531	−	0.919739i	$-0.628400\pi$
$907$	−23.6433			−0.785062			−0.392531	+	0.919739i	$0.628400\pi$
$908$	−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
$913$	−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
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	−0.439695	−	0.898147i	$-0.644913\pi$
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	0.997666	−	0.0682866i	$-0.0217532\pi$
$920$	−20.5579			−0.677774
$921$		0			0
$922$			5.98508i			0.197108i
$923$	−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
$929$	16.4582	+	28.5064i	0.539976	+	0.935266i	0.998905	+	0.0467929i	$0.0149001\pi$
$929$	16.4582	+	28.5064i	0.539976	+	0.935266i	−0.458928	+	0.888473i	$0.651767\pi$
$930$		0			0
$931$		0			0
$932$	−2.86305	+	1.65298i	−0.0937824	+	0.0541453i
$933$		0			0
$934$			14.9229i			0.488293i
$935$	−8.81350	+	5.08848i	−0.288232	+	0.166411i
$936$		0			0
$937$		−	38.1057i		−	1.24486i	−0.782676	−	0.622430i	$-0.786146\pi$
$937$		−	38.1057i		−	1.24486i	0.782676	−	0.622430i	$-0.213854\pi$
$938$		0			0
$939$		0			0
$940$	5.02404			0.163866
$941$	−9.93855	+	17.2141i	−0.323987	+	0.561163i	−0.981307	−	0.192449i	$-0.938357\pi$
$941$	−9.93855	+	17.2141i	−0.323987	+	0.561163i	0.657319	+	0.753612i	$0.271690\pi$
$942$		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	$-0.776124\pi$
$947$	−17.9696	+	10.3747i	−0.583933	+	0.337134i	0.178762	+	0.983892i	$0.442791\pi$
$948$		0			0
$949$	3.05772	−	5.29613i	0.0992578	−	0.171919i
$950$	−8.36914			−0.271531
$951$		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
$956$			27.3696i			0.885195i
$957$		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
$962$	−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	$-0.361835\pi$
$968$			19.4125i			0.623941i
$969$		0			0
$970$	16.1241			0.517714
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	−0.533494	−	0.845804i	$-0.679121\pi$
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	0.999235	+	0.0391177i	$0.0124547\pi$
$972$		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	$-0.378964\pi$
$977$	−7.73439	−	4.46545i	−0.247445	−	0.142862i	−0.618594	+	0.785711i	$0.712297\pi$
$978$		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
$983$	−52.2693			−1.66713			−0.833566	−	0.552420i	$-0.813704\pi$
$983$	−52.2693			−1.66713			−0.833566	+	0.552420i	$0.813704\pi$
$984$		0			0
$985$			5.83413i			0.185891i
$986$	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	−0.969789	−	0.243946i	$-0.921558\pi$
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	0.273631	−	0.961835i	$-0.411775\pi$
$992$	−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
$997$		−	44.9975i		−	1.42508i	−0.701630	−	0.712542i	$-0.747544\pi$
$997$		−	44.9975i		−	1.42508i	0.701630	−	0.712542i	$-0.252456\pi$
$998$	−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.s.b.656.4		10
3.2	odd	2		441.2.s.b.362.2		10
7.2	even	3		1323.2.o.c.440.2		10
7.3	odd	6		1323.2.i.b.521.4		10
7.4	even	3		189.2.i.b.143.4		10
7.5	odd	6		1323.2.o.d.440.2		10
7.6	odd	2		189.2.s.b.89.4		10
9.4	even	3		441.2.i.b.68.4		10
9.5	odd	6		1323.2.i.b.1097.2		10
21.2	odd	6		441.2.o.d.146.4		10
21.5	even	6		441.2.o.c.146.4		10
21.11	odd	6		63.2.i.b.38.2	yes	10
21.17	even	6		441.2.i.b.227.2		10
21.20	even	2		63.2.s.b.47.2	yes	10
28.11	odd	6		3024.2.ca.b.2033.4		10
28.27	even	2		3024.2.df.b.1601.4		10
63.4	even	3		63.2.s.b.59.2	yes	10
63.5	even	6		1323.2.o.c.881.2		10
63.11	odd	6		567.2.p.d.80.2		10
63.13	odd	6		63.2.i.b.5.4	✓	10
63.20	even	6		567.2.p.c.404.4		10
63.23	odd	6		1323.2.o.d.881.2		10
63.25	even	3		567.2.p.c.80.4		10
63.31	odd	6		441.2.s.b.374.2		10
63.32	odd	6		189.2.s.b.17.4		10
63.34	odd	6		567.2.p.d.404.2		10
63.40	odd	6		441.2.o.d.293.4		10
63.41	even	6		189.2.i.b.152.2		10
63.58	even	3		441.2.o.c.293.4		10
63.59	even	6	inner	1323.2.s.b.962.4		10
84.11	even	6		1008.2.ca.b.353.3		10
84.83	odd	2		1008.2.df.b.929.2		10
252.67	odd	6		1008.2.df.b.689.2		10
252.95	even	6		3024.2.df.b.17.4		10
252.139	even	6		1008.2.ca.b.257.3		10
252.167	odd	6		3024.2.ca.b.2609.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	63.13	odd	6
63.2.i.b.38.2	yes	10	21.11	odd	6
63.2.s.b.47.2	yes	10	21.20	even	2
63.2.s.b.59.2	yes	10	63.4	even	3
189.2.i.b.143.4		10	7.4	even	3
189.2.i.b.152.2		10	63.41	even	6
189.2.s.b.17.4		10	63.32	odd	6
189.2.s.b.89.4		10	7.6	odd	2
441.2.i.b.68.4		10	9.4	even	3
441.2.i.b.227.2		10	21.17	even	6
441.2.o.c.146.4		10	21.5	even	6
441.2.o.c.293.4		10	63.58	even	3
441.2.o.d.146.4		10	21.2	odd	6
441.2.o.d.293.4		10	63.40	odd	6
441.2.s.b.362.2		10	3.2	odd	2
441.2.s.b.374.2		10	63.31	odd	6
567.2.p.c.80.4		10	63.25	even	3
567.2.p.c.404.4		10	63.20	even	6
567.2.p.d.80.2		10	63.11	odd	6
567.2.p.d.404.2		10	63.34	odd	6
1008.2.ca.b.257.3		10	252.139	even	6
1008.2.ca.b.353.3		10	84.11	even	6
1008.2.df.b.689.2		10	252.67	odd	6
1008.2.df.b.929.2		10	84.83	odd	2
1323.2.i.b.521.4		10	7.3	odd	6
1323.2.i.b.1097.2		10	9.5	odd	6
1323.2.o.c.440.2		10	7.2	even	3
1323.2.o.c.881.2		10	63.5	even	6
1323.2.o.d.440.2		10	7.5	odd	6
1323.2.o.d.881.2		10	63.23	odd	6
1323.2.s.b.656.4		10	1.1	even	1	trivial
1323.2.s.b.962.4		10	63.59	even	6	inner
3024.2.ca.b.2033.4		10	28.11	odd	6
3024.2.ca.b.2609.4		10	252.167	odd	6
3024.2.df.b.17.4		10	252.95	even	6
3024.2.df.b.1601.4		10	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.621951 - 0.359083i) q^{2} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +2.50226i q^{8} +O(q^{10})\)	\(q+(0.621951 - 0.359083i) q^{2} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +2.50226i q^{8} +(-0.900304 + 0.519791i) q^{10} +1.80056i q^{11} +(-1.88867 + 1.09042i) q^{13} +(-0.585716 - 1.01449i) q^{16} +(-1.95230 - 3.38149i) q^{17} +(3.47456 + 2.00604i) q^{19} +(1.07425 - 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} -5.67561i q^{23} -2.90460 q^{25} +(-0.783106 + 1.35638i) q^{26} +(-8.49418 - 4.90412i) q^{29} +(2.45129 + 1.41525i) q^{31} +(-5.06262 - 2.92290i) q^{32} +(-2.42847 - 1.40208i) q^{34} +(-0.411767 + 0.713202i) q^{37} +2.88134 q^{38} -3.62215i q^{40} +(-5.90617 - 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +(-2.31442 - 1.33623i) q^{44} +(-2.03802 - 3.52995i) q^{46} +(1.16920 + 2.02511i) q^{47} +(-1.80652 + 1.04299i) q^{50} -3.23689i q^{52} +(0.996713 - 0.575453i) q^{53} -2.60640i q^{55} -7.04395 q^{58} +(-4.89555 + 8.47934i) q^{59} +(-2.03980 + 1.17768i) q^{61} +2.03277 q^{62} -1.85540 q^{64} +(2.73394 - 1.57844i) q^{65} +(0.156402 - 0.270897i) q^{67} +5.79536 q^{68} +1.94933i q^{71} +(-2.42847 + 1.40208i) q^{73} +0.591435i q^{74} +(-5.15706 + 2.97743i) q^{76} +(-6.21583 - 10.7661i) q^{79} +(0.847852 + 1.46852i) q^{80} +(-7.34669 - 4.24162i) q^{82} +(-3.60916 + 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} +5.41161i q^{86} -4.50548 q^{88} +(5.28999 - 9.16253i) q^{89} +(7.29536 + 4.21198i) q^{92} +(1.45436 + 0.839677i) q^{94} +(-5.02959 - 2.90383i) q^{95} +(-13.4322 - 7.75510i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 10 * q + 4 * q^4	\( 10 q + 4 q^{4} + 15 q^{10} - 6 q^{13} - 6 q^{16} - 12 q^{17} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 14 q^{25} + 3 q^{26} + 15 q^{29} + 9 q^{31} - 48 q^{32} - 3 q^{34} + 6 q^{37} + 36 q^{38} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} + 15 q^{47} - 3 q^{50} + 9 q^{53} - 16 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} - 54 q^{68} - 3 q^{73} - 9 q^{76} + 20 q^{79} - 30 q^{80} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 16 q^{88} + 24 q^{89} - 39 q^{92} + 3 q^{94} - 6 q^{97}+O(q^{100}) \) 10 * q + 4 * q^4 + 15 * q^10 - 6 * q^13 - 6 * q^16 - 12 * q^17 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 14 * q^25 + 3 * q^26 + 15 * q^29 + 9 * q^31 - 48 * q^32 - 3 * q^34 + 6 * q^37 + 36 * q^38 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 + 15 * q^47 - 3 * q^50 + 9 * q^53 - 16 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 - 54 * q^68 - 3 * q^73 - 9 * q^76 + 20 * q^79 - 30 * q^80 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 16 * q^88 + 24 * q^89 - 39 * q^92 + 3 * q^94 - 6 * q^97

Introduction

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