LMFDB - Embedded newform 1323.2.g.h.667.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.5
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.h.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.551407 - 0.955065i) q^{2} +(0.391901 - 0.678793i) q^{4} -0.105466 q^{5} -3.07001 q^{8} +O(q^{10})$	\(q+(-0.551407 - 0.955065i) q^{2} +(0.391901 - 0.678793i) q^{4} -0.105466 q^{5} -3.07001 q^{8} +(0.0581547 + 0.100727i) q^{10} -3.33731 q^{11} +(-1.23997 - 2.14770i) q^{13} +(0.909025 + 1.57448i) q^{16} +(0.806594 + 1.39706i) q^{17} +(3.84133 - 6.65338i) q^{19} +(-0.0413323 + 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} +1.89719 q^{23} -4.98888 q^{25} +(-1.36746 + 2.36851i) q^{26} +(-4.64521 + 8.04574i) q^{29} +(-4.63081 + 8.02080i) q^{31} +(-2.06753 + 3.58107i) q^{32} +(0.889523 - 1.54070i) q^{34} +(0.991268 - 1.71693i) q^{37} -8.47254 q^{38} +0.323782 q^{40} +(-3.74268 - 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +(-1.30790 + 2.26534i) q^{44} +(-1.04612 - 1.81194i) q^{46} +(-1.59780 - 2.76747i) q^{47} +(2.75090 + 4.76470i) q^{50} -1.94379 q^{52} +(-4.98839 - 8.64015i) q^{53} +0.351974 q^{55} +10.2456 q^{58} +(2.22993 - 3.86235i) q^{59} +(2.83550 + 4.91123i) q^{61} +10.2138 q^{62} +8.19630 q^{64} +(0.130775 + 0.226509i) q^{65} +(-4.98571 + 8.63550i) q^{67} +1.26442 q^{68} -3.29042 q^{71} +(2.36189 + 4.09091i) q^{73} -2.18637 q^{74} +(-3.01084 - 5.21493i) q^{76} +(-3.84705 - 6.66328i) q^{79} +(-0.0958713 - 0.166054i) q^{80} +(-4.12748 + 7.14901i) q^{82} +(0.584428 - 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} +8.32378 q^{86} +10.2456 q^{88} +(3.01477 - 5.22173i) q^{89} +(0.743509 - 1.28780i) q^{92} +(-1.76208 + 3.05201i) q^{94} +(-0.405130 + 0.701706i) q^{95} +(-1.90127 + 3.29310i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} + 40 q^{11} - 12 q^{16} + 64 q^{23} + 24 q^{25} - 16 q^{29} - 48 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} + 136 q^{74} + 12 q^{79} + 12 q^{85} + 152 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 + 40 * q^11 - 12 * q^16 + 64 * q^23 + 24 * q^25 - 16 * q^29 - 48 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 + 136 * q^74 + 12 * q^79 + 12 * q^85 + 152 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.551407	−	0.955065i	−0.389903	−	0.675333i	0.602533	−	0.798094i	$-0.294158\pi$
$2$	−0.551407	−	0.955065i	−0.389903	−	0.675333i	−0.992436	+	0.122762i	$0.960825\pi$
$3$		0			0
$3$		0			0
$4$	0.391901	−	0.678793i	0.195951	−	0.339396i
$5$	−0.105466			−0.0471659			−0.0235829	−	0.999722i	$-0.507507\pi$
$5$	−0.105466			−0.0471659			−0.0235829	+	0.999722i	$0.507507\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−3.07001			−1.08541
$9$		0			0
$10$	0.0581547	+	0.100727i	0.0183901	+	0.0318527i
$11$	−3.33731			−1.00624			−0.503119	−	0.864217i	$-0.667814\pi$
$11$	−3.33731			−1.00624			−0.503119	+	0.864217i	$0.667814\pi$
$12$		0			0
$13$	−1.23997	−	2.14770i	−0.343907	−	0.595664i	0.641248	−	0.767334i	$-0.278417\pi$
$13$	−1.23997	−	2.14770i	−0.343907	−	0.595664i	−0.985155	+	0.171670i	$0.945084\pi$
$14$		0			0
$15$		0			0
$16$	0.909025	+	1.57448i	0.227256	+	0.393619i
$17$	0.806594	+	1.39706i	0.195628	+	0.338837i	0.947106	−	0.320921i	$-0.103992\pi$
$17$	0.806594	+	1.39706i	0.195628	+	0.338837i	−0.751478	+	0.659758i	$0.770659\pi$
$18$		0			0
$19$	3.84133	−	6.65338i	0.881262	−	1.52639i	0.0313221	−	0.999509i	$-0.490028\pi$
$19$	3.84133	−	6.65338i	0.881262	−	1.52639i	0.849939	−	0.526880i	$-0.176638\pi$
$20$	−0.0413323	+	0.0715896i	−0.00924218	+	0.0160079i
$21$		0			0
$22$	1.84022	+	3.18735i	0.392336	+	0.679546i
$23$	1.89719			0.395591			0.197795	−	0.980243i	$-0.436622\pi$
$23$	1.89719			0.395591			0.197795	+	0.980243i	$0.436622\pi$
$24$		0			0
$25$	−4.98888			−0.997775
$26$	−1.36746	+	2.36851i	−0.268181	+	0.464503i
$27$		0			0
$28$		0			0
$29$	−4.64521	+	8.04574i	−0.862594	+	1.49406i	0.00682200	+	0.999977i	$0.497828\pi$
$29$	−4.64521	+	8.04574i	−0.862594	+	1.49406i	−0.869416	+	0.494080i	$0.835505\pi$
$30$		0			0
$31$	−4.63081	+	8.02080i	−0.831718	+	1.44058i	0.0649574	+	0.997888i	$0.479309\pi$
$31$	−4.63081	+	8.02080i	−0.831718	+	1.44058i	−0.896675	+	0.442689i	$0.854024\pi$
$32$	−2.06753	+	3.58107i	−0.365491	+	0.633049i
$33$		0			0
$34$	0.889523	−	1.54070i	0.152552	−	0.264228i
$35$		0			0
$36$		0			0
$37$	0.991268	−	1.71693i	0.162963	−	0.282261i	−0.772967	−	0.634447i	$-0.781228\pi$
$37$	0.991268	−	1.71693i	0.162963	−	0.282261i	0.935930	+	0.352186i	$0.114561\pi$
$38$	−8.47254			−1.37443
$39$		0			0
$40$	0.323782			0.0511945
$41$	−3.74268	−	6.48252i	−0.584509	−	1.01240i	−0.994936	−	0.100506i	$-0.967954\pi$
$41$	−3.74268	−	6.48252i	−0.584509	−	1.01240i	0.410427	−	0.911893i	$-0.365379\pi$
$42$		0			0
$43$	−3.77388	+	6.53655i	−0.575512	+	0.996815i	0.420474	+	0.907304i	$0.361864\pi$
$43$	−3.77388	+	6.53655i	−0.575512	+	0.996815i	−0.995986	+	0.0895108i	$0.971470\pi$
$44$	−1.30790	+	2.26534i	−0.197173	+	0.341514i
$45$		0			0
$46$	−1.04612	−	1.81194i	−0.154242	−	0.267155i
$47$	−1.59780	−	2.76747i	−0.233063	−	0.403677i	0.725645	−	0.688070i	$-0.241542\pi$
$47$	−1.59780	−	2.76747i	−0.233063	−	0.403677i	−0.958708	+	0.284392i	$0.908208\pi$
$48$		0			0
$49$		0			0
$50$	2.75090	+	4.76470i	0.389036	+	0.673830i
$51$		0			0
$52$	−1.94379			−0.269555
$53$	−4.98839	−	8.64015i	−0.685209	−	1.18682i	−0.973371	−	0.229234i	$-0.926378\pi$
$53$	−4.98839	−	8.64015i	−0.685209	−	1.18682i	0.288163	−	0.957581i	$-0.406956\pi$
$54$		0			0
$55$	0.351974			0.0474601
$56$		0			0
$57$		0			0
$58$	10.2456			1.34531
$59$	2.22993	−	3.86235i	0.290312	−	0.502836i	−0.683571	−	0.729884i	$-0.739574\pi$
$59$	2.22993	−	3.86235i	0.290312	−	0.502836i	0.973884	+	0.227048i	$0.0729075\pi$
$60$		0			0
$61$	2.83550	+	4.91123i	0.363048	+	0.628818i	0.988461	−	0.151476i	$-0.0484027\pi$
$61$	2.83550	+	4.91123i	0.363048	+	0.628818i	−0.625413	+	0.780294i	$0.715069\pi$
$62$	10.2138			1.29716
$63$		0			0
$64$	8.19630			1.02454
$65$	0.130775	+	0.226509i	0.0162207	+	0.0280950i
$66$		0			0
$67$	−4.98571	+	8.63550i	−0.609101	+	1.05499i	0.382288	+	0.924043i	$0.375136\pi$
$67$	−4.98571	+	8.63550i	−0.609101	+	1.05499i	−0.991389	+	0.130951i	$0.958197\pi$
$68$	1.26442			0.153333
$69$		0			0
$70$		0			0
$71$	−3.29042			−0.390502			−0.195251	−	0.980753i	$-0.562552\pi$
$71$	−3.29042			−0.390502			−0.195251	+	0.980753i	$0.562552\pi$
$72$		0			0
$73$	2.36189	+	4.09091i	0.276438	+	0.478805i	0.970497	−	0.241113i	$-0.0775125\pi$
$73$	2.36189	+	4.09091i	0.276438	+	0.478805i	−0.694059	+	0.719919i	$0.744179\pi$
$74$	−2.18637			−0.254160
$75$		0			0
$76$	−3.01084	−	5.21493i	−0.345367	−	0.598194i
$77$		0			0
$78$		0			0
$79$	−3.84705	−	6.66328i	−0.432827	−	0.749678i	0.564289	−	0.825577i	$-0.309150\pi$
$79$	−3.84705	−	6.66328i	−0.432827	−	0.749678i	−0.997115	+	0.0758997i	$0.975817\pi$
$80$	−0.0958713	−	0.166054i	−0.0107187	−	0.0185654i
$81$		0			0
$82$	−4.12748	+	7.14901i	−0.455804	+	0.789476i
$83$	0.584428	−	1.01226i	0.0641493	−	0.111110i	−0.832167	−	0.554525i	$-0.812900\pi$
$83$	0.584428	−	1.01226i	0.0641493	−	0.111110i	0.896316	+	0.443415i	$0.146233\pi$
$84$		0			0
$85$	−0.0850683	−	0.147343i	−0.00922695	−	0.0159815i
$86$	8.32378			0.897576
$87$		0			0
$88$	10.2456			1.09219
$89$	3.01477	−	5.22173i	0.319565	−	0.553503i	−0.660832	−	0.750534i	$-0.729797\pi$
$89$	3.01477	−	5.22173i	0.319565	−	0.553503i	0.980397	+	0.197031i	$0.0631299\pi$
$90$		0			0
$91$		0			0
$92$	0.743509	−	1.28780i	0.0775162	−	0.134262i
$93$		0			0
$94$	−1.76208	+	3.05201i	−0.181744	+	0.314791i
$95$	−0.405130	+	0.701706i	−0.0415655	+	0.0719935i
$96$		0			0
$97$	−1.90127	+	3.29310i	−0.193045	+	0.334364i	−0.946258	−	0.323413i	$-0.895170\pi$
$97$	−1.90127	+	3.29310i	−0.193045	+	0.334364i	0.753213	+	0.657777i	$0.228503\pi$
$98$		0			0
$99$		0			0
$100$	−1.95515	+	3.38641i	−0.195515	+	0.338641i
$101$	−17.4702			−1.73835			−0.869177	−	0.494501i	$-0.835351\pi$
$101$	−17.4702			−1.73835			−0.869177	+	0.494501i	$0.835351\pi$
$102$		0			0
$103$	−8.73204			−0.860394			−0.430197	−	0.902735i	$-0.641556\pi$
$103$	−8.73204			−0.860394			−0.430197	+	0.902735i	$0.641556\pi$
$104$	3.80674	+	6.59346i	0.373281	+	0.646542i
$105$		0			0
$106$	−5.50127	+	9.52848i	−0.534330	+	0.925487i
$107$	−9.07316	+	15.7152i	−0.877135	+	1.51924i	−0.0226645	+	0.999743i	$0.507215\pi$
$107$	−9.07316	+	15.7152i	−0.877135	+	1.51924i	−0.854471	+	0.519500i	$0.826118\pi$
$108$		0			0
$109$	2.11124	+	3.65678i	0.202220	+	0.350256i	0.949243	−	0.314542i	$-0.101851\pi$
$109$	2.11124	+	3.65678i	0.202220	+	0.350256i	−0.747023	+	0.664798i	$0.768518\pi$
$110$	−0.194081	−	0.336157i	−0.0185049	−	0.0320514i
$111$		0			0
$112$		0			0
$113$	−1.02824	−	1.78096i	−0.0967285	−	0.167539i	0.813600	−	0.581425i	$-0.197505\pi$
$113$	−1.02824	−	1.78096i	−0.0967285	−	0.167539i	−0.910329	+	0.413886i	$0.864171\pi$
$114$		0			0
$115$	−0.200089			−0.0186584
$116$	3.64093	+	6.30627i	0.338052	+	0.585523i
$117$		0			0
$118$	−4.91840			−0.452775
$119$		0			0
$120$		0			0
$121$	0.137670			0.0125155
$122$	3.12703	−	5.41617i	0.283108	−	0.490357i
$123$		0			0
$124$	3.62964	+	6.28672i	0.325951	+	0.564564i
$125$	1.05349			0.0942268
$126$		0			0
$127$	0.317159			0.0281433			0.0140717	−	0.999901i	$-0.495521\pi$
$127$	0.317159			0.0281433			0.0140717	+	0.999901i	$0.495521\pi$
$128$	−0.384435	−	0.665862i	−0.0339796	−	0.0588544i
$129$		0			0
$130$	0.144221	−	0.249797i	0.0126490	−	0.0219087i
$131$	14.9563			1.30674			0.653370	−	0.757039i	$-0.273355\pi$
$131$	14.9563			1.30674			0.653370	+	0.757039i	$0.273355\pi$
$132$		0			0
$133$		0			0
$134$	10.9966			0.949962
$135$		0			0
$136$	−2.47625	−	4.28900i	−0.212337	−	0.367779i
$137$	15.2473			1.30267			0.651334	−	0.758791i	$-0.274210\pi$
$137$	15.2473			1.30267			0.651334	+	0.758791i	$0.274210\pi$
$138$		0			0
$139$	−4.05943	−	7.03114i	−0.344316	−	0.596374i	0.640913	−	0.767614i	$-0.278556\pi$
$139$	−4.05943	−	7.03114i	−0.344316	−	0.596374i	−0.985229	+	0.171240i	$0.945223\pi$
$140$		0			0
$141$		0			0
$142$	1.81436	+	3.14257i	0.152258	+	0.263718i
$143$	4.13818	+	7.16754i	0.346052	+	0.599380i
$144$		0			0
$145$	0.489912	−	0.848553i	0.0406850	−	0.0704685i
$146$	2.60473	−	4.51152i	0.215569	−	0.373376i
$147$		0			0
$148$	−0.776958	−	1.34573i	−0.0638656	−	0.110618i
$149$	11.1486			0.913329			0.456664	−	0.889639i	$-0.349044\pi$
$149$	11.1486			0.913329			0.456664	+	0.889639i	$0.349044\pi$
$150$		0			0
$151$	−11.2735			−0.917425			−0.458713	−	0.888585i	$-0.651689\pi$
$151$	−11.2735			−0.917425			−0.458713	+	0.888585i	$0.651689\pi$
$152$	−11.7929	+	20.4260i	−0.956534	+	1.65677i
$153$		0			0
$154$		0			0
$155$	0.488393	−	0.845922i	0.0392287	−	0.0679461i
$156$		0			0
$157$	6.10318	−	10.5710i	0.487087	−	0.843659i	−0.512803	−	0.858506i	$-0.671393\pi$
$157$	6.10318	−	10.5710i	0.487087	−	0.843659i	0.999890	+	0.0148476i	$0.00472630\pi$
$158$	−4.24258	+	7.34836i	−0.337521	+	0.584604i
$159$		0			0
$160$	0.218054	−	0.377681i	0.0172387	−	0.0298583i
$161$		0			0
$162$		0			0
$163$	−4.48132	+	7.76187i	−0.351004	+	0.607957i	−0.986426	−	0.164209i	$-0.947493\pi$
$163$	−4.48132	+	7.76187i	−0.351004	+	0.607957i	0.635422	+	0.772165i	$0.280826\pi$
$164$	−5.86705			−0.458139
$165$		0			0
$166$	−1.28903			−0.100048
$167$	−8.70833	−	15.0833i	−0.673871	−	1.16718i	−0.976798	−	0.214165i	$-0.931297\pi$
$167$	−8.70833	−	15.0833i	−0.673871	−	1.16718i	0.302927	−	0.953014i	$-0.402036\pi$
$168$		0			0
$169$	3.42493	−	5.93216i	0.263456	−	0.456320i
$170$	−0.0938145	+	0.162491i	−0.00719524	+	0.0124625i
$171$		0			0
$172$	2.95798	+	5.12337i	0.225544	+	0.390653i
$173$	−1.41466	−	2.45027i	−0.107555	−	0.186291i	0.807224	−	0.590245i	$-0.200969\pi$
$173$	−1.41466	−	2.45027i	−0.107555	−	0.186291i	−0.914779	+	0.403954i	$0.867635\pi$
$174$		0			0
$175$		0			0
$176$	−3.03370	−	5.25453i	−0.228674	−	0.396075i
$177$		0			0
$178$	−6.64946			−0.498398
$179$	−5.08135	−	8.80115i	−0.379798	−	0.657829i	0.611235	−	0.791449i	$-0.290673\pi$
$179$	−5.08135	−	8.80115i	−0.379798	−	0.657829i	−0.991033	+	0.133620i	$0.957340\pi$
$180$		0			0
$181$	17.0870			1.27006			0.635032	−	0.772486i	$-0.280987\pi$
$181$	17.0870			1.27006			0.635032	+	0.772486i	$0.280987\pi$
$182$		0			0
$183$		0			0
$184$	−5.82439			−0.429380
$185$	−0.104545	+	0.181078i	−0.00768631	+	0.0133131i
$186$		0			0
$187$	−2.69186	−	4.66243i	−0.196848	−	0.340951i
$188$	−2.50472			−0.182676
$189$		0			0
$190$	0.893566			0.0648261
$191$	−11.2000	−	19.3990i	−0.810404	−	1.40366i	−0.912582	−	0.408894i	$-0.865914\pi$
$191$	−11.2000	−	19.3990i	−0.810404	−	1.40366i	0.102178	−	0.994766i	$-0.467419\pi$
$192$		0			0
$193$	0.128393	−	0.222383i	0.00924194	−	0.0160075i	−0.861367	−	0.507982i	$-0.830391\pi$
$193$	0.128393	−	0.222383i	0.00924194	−	0.0160075i	0.870609	+	0.491975i	$0.163725\pi$
$194$	4.19350			0.301076
$195$		0			0
$196$		0			0
$197$	0.763370			0.0543878			0.0271939	−	0.999630i	$-0.491343\pi$
$197$	0.763370			0.0543878			0.0271939	+	0.999630i	$0.491343\pi$
$198$		0			0
$199$	−2.51561	−	4.35716i	−0.178327	−	0.308871i	0.762981	−	0.646421i	$-0.223735\pi$
$199$	−2.51561	−	4.35716i	−0.178327	−	0.308871i	−0.941307	+	0.337550i	$0.890402\pi$
$200$	15.3159			1.08300
$201$		0			0
$202$	9.63321	+	16.6852i	0.677790	+	1.17397i
$203$		0			0
$204$		0			0
$205$	0.394726	+	0.683686i	0.0275689	+	0.0477507i
$206$	4.81491	+	8.33966i	0.335470	+	0.581052i
$207$		0			0
$208$	2.25433	−	3.90462i	0.156310	−	0.270737i
$209$	−12.8197	+	22.2044i	−0.886759	+	1.53591i
$210$		0			0
$211$	−3.60537	−	6.24468i	−0.248204	−	0.429901i	0.714824	−	0.699305i	$-0.246507\pi$
$211$	−3.60537	−	6.24468i	−0.248204	−	0.429901i	−0.963027	+	0.269403i	$0.913174\pi$
$212$	−7.81983			−0.537068
$213$		0			0
$214$	20.0120			1.36799
$215$	0.398017	−	0.689385i	0.0271445	−	0.0470157i
$216$		0			0
$217$		0			0
$218$	2.32831	−	4.03274i	0.157693	−	0.273132i
$219$		0			0
$220$	0.137939	−	0.238917i	0.00929983	−	0.0161078i
$221$	2.00031	−	3.46464i	0.134555	−	0.233057i
$222$		0			0
$223$	−5.59106	+	9.68400i	−0.374405	+	0.648488i	−0.990238	−	0.139388i	$-0.955486\pi$
$223$	−5.59106	+	9.68400i	−0.374405	+	0.648488i	0.615833	+	0.787877i	$0.288820\pi$
$224$		0			0
$225$		0			0
$226$	−1.13395	+	1.96407i	−0.0754295	+	0.130648i
$227$	23.7706			1.57771			0.788857	−	0.614577i	$-0.210673\pi$
$227$	23.7706			1.57771			0.788857	+	0.614577i	$0.210673\pi$
$228$		0			0
$229$	1.90547			0.125917			0.0629586	−	0.998016i	$-0.479946\pi$
$229$	1.90547			0.125917			0.0629586	+	0.998016i	$0.479946\pi$
$230$	0.110330	+	0.191098i	0.00727497	+	0.0126006i
$231$		0			0
$232$	14.2609	−	24.7006i	0.936272	−	1.62167i
$233$	3.27092	−	5.66540i	0.214285	−	0.371153i	−0.738766	−	0.673962i	$-0.764591\pi$
$233$	3.27092	−	5.66540i	0.214285	−	0.371153i	0.953051	+	0.302809i	$0.0979245\pi$
$234$		0			0
$235$	0.168514	+	0.291875i	0.0109926	+	0.0190398i
$236$	−1.74782	−	3.02732i	−0.113774	−	0.197062i
$237$		0			0
$238$		0			0
$239$	−10.6735	−	18.4870i	−0.690409	−	1.19582i	−0.971704	−	0.236202i	$-0.924097\pi$
$239$	−10.6735	−	18.4870i	−0.690409	−	1.19582i	0.281295	−	0.959621i	$-0.409236\pi$
$240$		0			0
$241$	20.0662			1.29258			0.646288	−	0.763094i	$-0.276321\pi$
$241$	20.0662			1.29258			0.646288	+	0.763094i	$0.276321\pi$
$242$	−0.0759124	−	0.131484i	−0.00487983	−	0.00845212i
$243$		0			0
$244$	4.44494			0.284558
$245$		0			0
$246$		0			0
$247$	−19.0526			−1.21229
$248$	14.2167	−	24.6240i	0.902758	−	1.56362i
$249$		0			0
$250$	−0.580900	−	1.00615i	−0.0367394	−	0.0636344i
$251$	−6.81467			−0.430138			−0.215069	−	0.976599i	$-0.568998\pi$
$251$	−6.81467			−0.430138			−0.215069	+	0.976599i	$0.568998\pi$
$252$		0			0
$253$	−6.33151			−0.398059
$254$	−0.174884	−	0.302907i	−0.0109732	−	0.0190061i
$255$		0			0
$256$	7.77234	−	13.4621i	0.485771	−	0.841380i
$257$	−14.3883			−0.897518			−0.448759	−	0.893653i	$-0.648134\pi$
$257$	−14.3883			−0.897518			−0.448759	+	0.893653i	$0.648134\pi$
$258$		0			0
$259$		0			0
$260$	0.205004			0.0127138
$261$		0			0
$262$	−8.24701	−	14.2842i	−0.509502	−	0.882484i
$263$	1.53901			0.0948992			0.0474496	−	0.998874i	$-0.484891\pi$
$263$	1.53901			0.0948992			0.0474496	+	0.998874i	$0.484891\pi$
$264$		0			0
$265$	0.526106	+	0.911243i	0.0323185	+	0.0559772i
$266$		0			0
$267$		0			0
$268$	3.90781	+	6.76852i	0.238707	+	0.413453i
$269$	13.1285	+	22.7393i	0.800461	+	1.38644i	0.919313	+	0.393527i	$0.128745\pi$
$269$	13.1285	+	22.7393i	0.800461	+	1.38644i	−0.118852	+	0.992912i	$0.537921\pi$
$270$		0			0
$271$	8.96673	−	15.5308i	0.544690	−	0.943431i	−0.453936	−	0.891034i	$-0.649981\pi$
$271$	8.96673	−	15.5308i	0.544690	−	0.943431i	0.998626	−	0.0523969i	$-0.0166861\pi$
$272$	−1.46643	+	2.53993i	−0.0889152	+	0.154006i
$273$		0			0
$274$	−8.40748	−	14.5622i	−0.507915	−	0.879734i
$275$	16.6495			1.00400
$276$		0			0
$277$	−18.8713			−1.13386			−0.566932	−	0.823764i	$-0.691870\pi$
$277$	−18.8713			−1.13386			−0.566932	+	0.823764i	$0.691870\pi$
$278$	−4.47680	+	7.75404i	−0.268500	+	0.465056i
$279$		0			0
$280$		0			0
$281$	2.49578	−	4.32283i	0.148886	−	0.257878i	−0.781930	−	0.623366i	$-0.785765\pi$
$281$	2.49578	−	4.32283i	0.148886	−	0.257878i	0.930816	+	0.365488i	$0.119098\pi$
$282$		0			0
$283$	7.69634	−	13.3304i	0.457500	−	0.792413i	−0.541328	−	0.840811i	$-0.682078\pi$
$283$	7.69634	−	13.3304i	0.457500	−	0.792413i	0.998828	+	0.0483984i	$0.0154117\pi$
$284$	−1.28952	+	2.23352i	−0.0765190	+	0.132535i
$285$		0			0
$286$	4.56364	−	7.90446i	0.269854	−	0.467401i
$287$		0			0
$288$		0			0
$289$	7.19881	−	12.4687i	0.423460	−	0.733454i
$290$	−1.08056			−0.0634529
$291$		0			0
$292$	3.70251			0.216673
$293$	12.9013	+	22.3456i	0.753700	+	1.30545i	0.946018	+	0.324114i	$0.105066\pi$
$293$	12.9013	+	22.3456i	0.753700	+	1.30545i	−0.192318	+	0.981333i	$0.561601\pi$
$294$		0			0
$295$	−0.235182	+	0.407347i	−0.0136928	+	0.0237167i
$296$	−3.04321	+	5.27099i	−0.176883	+	0.306370i
$297$		0			0
$298$	−6.14741	−	10.6476i	−0.356110	−	0.616801i
$299$	−2.35246	−	4.07458i	−0.136046	−	0.235639i
$300$		0			0
$301$		0			0
$302$	6.21629	+	10.7669i	0.357707	+	0.619567i
$303$		0			0
$304$	13.9675			0.801089
$305$	−0.299049	−	0.517968i	−0.0171235	−	0.0296588i
$306$		0			0
$307$	−22.2914			−1.27224			−0.636120	−	0.771590i	$-0.719462\pi$
$307$	−22.2914			−1.27224			−0.636120	+	0.771590i	$0.719462\pi$
$308$		0			0
$309$		0			0
$310$	−1.07721			−0.0611816
$311$	−0.654931	+	1.13437i	−0.0371377	+	0.0643245i	−0.883997	−	0.467493i	$-0.845157\pi$
$311$	−0.654931	+	1.13437i	−0.0371377	+	0.0643245i	0.846859	+	0.531817i	$0.178491\pi$
$312$		0			0
$313$	−10.7885	−	18.6862i	−0.609802	−	1.05621i	−0.991273	−	0.131827i	$-0.957916\pi$
$313$	−10.7885	−	18.6862i	−0.609802	−	1.05621i	0.381471	−	0.924381i	$-0.375418\pi$
$314$	−13.4613			−0.759667
$315$		0			0
$316$	−6.03065			−0.339250
$317$	−12.3910	−	21.4618i	−0.695946	−	1.20541i	−0.969861	−	0.243660i	$-0.921652\pi$
$317$	−12.3910	−	21.4618i	−0.695946	−	1.20541i	0.273915	−	0.961754i	$-0.411681\pi$
$318$		0			0
$319$	15.5025	−	26.8512i	0.867975	−	1.50338i
$320$	−0.864432			−0.0483232
$321$		0			0
$322$		0			0
$323$	12.3936			0.689597
$324$		0			0
$325$	6.18608	+	10.7146i	0.343142	+	0.594339i
$326$	9.88412			0.547431
$327$		0			0
$328$	11.4901	+	19.9014i	0.634434	+	1.09887i
$329$		0			0
$330$		0			0
$331$	−6.92256	−	11.9902i	−0.380498	−	0.659042i	0.610635	−	0.791912i	$-0.290914\pi$
$331$	−6.92256	−	11.9902i	−0.380498	−	0.659042i	−0.991133	+	0.132870i	$0.957581\pi$
$332$	−0.458076	−	0.793410i	−0.0251402	−	0.0435440i
$333$		0			0
$334$	−9.60367	+	16.6340i	−0.525489	+	0.910174i
$335$	0.525823	−	0.910752i	0.0287288	−	0.0497597i
$336$		0			0
$337$	1.69444	+	2.93485i	0.0923018	+	0.159871i	0.908479	−	0.417930i	$-0.137244\pi$
$337$	1.69444	+	2.93485i	0.0923018	+	0.159871i	−0.816178	+	0.577801i	$0.803911\pi$
$338$	−7.55412			−0.410890
$339$		0			0
$340$	−0.133353			−0.00723210
$341$	15.4545	−	26.7679i	0.836906	−	1.44956i
$342$		0			0
$343$		0			0
$344$	11.5859	−	20.0673i	0.624668	−	1.08196i
$345$		0			0
$346$	−1.56011	+	2.70219i	−0.0838720	+	0.145271i
$347$	−7.25739	+	12.5702i	−0.389597	+	0.674802i	−0.992395	−	0.123091i	$-0.960719\pi$
$347$	−7.25739	+	12.5702i	−0.389597	+	0.674802i	0.602798	+	0.797894i	$0.294052\pi$
$348$		0			0
$349$	7.86412	−	13.6211i	0.420957	−	0.729119i	−0.575076	−	0.818100i	$-0.695028\pi$
$349$	7.86412	−	13.6211i	0.420957	−	0.729119i	0.996033	+	0.0889810i	$0.0283610\pi$
$350$		0			0
$351$		0			0
$352$	6.90000	−	11.9511i	0.367771	−	0.636998i
$353$	4.14423			0.220575			0.110287	−	0.993900i	$-0.464823\pi$
$353$	4.14423			0.220575			0.110287	+	0.993900i	$0.464823\pi$
$354$		0			0
$355$	0.347028			0.0184183
$356$	−2.36298	−	4.09281i	−0.125238	−	0.216918i
$357$		0			0
$358$	−5.60378	+	9.70603i	−0.296169	+	0.512979i
$359$	3.96994	−	6.87614i	0.209525	−	0.362909i	−0.742040	−	0.670356i	$-0.766141\pi$
$359$	3.96994	−	6.87614i	0.209525	−	0.362909i	0.951565	+	0.307447i	$0.0994748\pi$
$360$		0			0
$361$	−20.0116	−	34.6612i	−1.05324	−	1.82427i
$362$	−9.42187	−	16.3192i	−0.495202	−	0.857716i
$363$		0			0
$364$		0			0
$365$	−0.249099	−	0.431453i	−0.0130385	−	0.0225833i
$366$		0			0
$367$	−13.1491			−0.686377			−0.343189	−	0.939266i	$-0.611507\pi$
$367$	−13.1491			−0.686377			−0.343189	+	0.939266i	$0.611507\pi$
$368$	1.72459	+	2.98708i	0.0899004	+	0.155712i
$369$		0			0
$370$	0.230588			0.0119877
$371$		0			0
$372$		0			0
$373$	7.81086			0.404431			0.202216	−	0.979341i	$-0.435186\pi$
$373$	7.81086			0.404431			0.202216	+	0.979341i	$0.435186\pi$
$374$	−2.96862	+	5.14180i	−0.153504	+	0.265876i
$375$		0			0
$376$	4.90527	+	8.49618i	0.252970	+	0.438157i
$377$	23.0398			1.18661
$378$		0			0
$379$	−31.6147			−1.62394			−0.811968	−	0.583702i	$-0.801604\pi$
$379$	−31.6147			−1.62394			−0.811968	+	0.583702i	$0.801604\pi$
$380$	0.317542	+	0.549999i	0.0162896	+	0.0282143i
$381$		0			0
$382$	−12.3515	+	21.3934i	−0.631958	+	1.09458i
$383$	10.7319			0.548373			0.274186	−	0.961677i	$-0.411592\pi$
$383$	10.7319			0.548373			0.274186	+	0.961677i	$0.411592\pi$
$384$		0			0
$385$		0			0
$386$	−0.283187			−0.0144139
$387$		0			0
$388$	1.49022	+	2.58114i	0.0756546	+	0.131038i
$389$	−24.1468			−1.22429			−0.612147	−	0.790744i	$-0.709694\pi$
$389$	−24.1468			−1.22429			−0.612147	+	0.790744i	$0.709694\pi$
$390$		0			0
$391$	1.53026	+	2.65049i	0.0773885	+	0.134041i
$392$		0			0
$393$		0			0
$394$	−0.420927	−	0.729067i	−0.0212060	−	0.0367299i
$395$	0.405733	+	0.702750i	0.0204146	+	0.0353592i
$396$		0			0
$397$	−12.0285	+	20.8339i	−0.603691	+	1.04562i	0.388566	+	0.921421i	$0.372971\pi$
$397$	−12.0285	+	20.8339i	−0.603691	+	1.04562i	−0.992257	+	0.124203i	$0.960363\pi$
$398$	−2.77424	+	4.80513i	−0.139060	+	0.240860i
$399$		0			0
$400$	−4.53501	−	7.85487i	−0.226751	−	0.392744i
$401$	1.56232			0.0780183			0.0390092	−	0.999239i	$-0.487580\pi$
$401$	1.56232			0.0780183			0.0390092	+	0.999239i	$0.487580\pi$
$402$		0			0
$403$	22.9683			1.14413
$404$	−6.84661	+	11.8587i	−0.340631	+	0.589991i
$405$		0			0
$406$		0			0
$407$	−3.30817	+	5.72992i	−0.163980	+	0.284022i
$408$		0			0
$409$	11.1728	−	19.3519i	0.552460	−	0.956889i	−0.445636	−	0.895214i	$-0.647023\pi$
$409$	11.1728	−	19.3519i	0.552460	−	0.956889i	0.998096	−	0.0616748i	$-0.0196442\pi$
$410$	0.435309	−	0.753978i	0.0214984	−	0.0372363i
$411$		0			0
$412$	−3.42210	+	5.92725i	−0.168595	+	0.292014i
$413$		0			0
$414$		0			0
$415$	−0.0616373	+	0.106759i	−0.00302566	+	0.00524059i
$416$	10.2547			0.502779
$417$		0			0
$418$	28.2755			1.38300
$419$	−2.98648	−	5.17273i	−0.145899	−	0.252704i	0.783809	−	0.621002i	$-0.213274\pi$
$419$	−2.98648	−	5.17273i	−0.145899	−	0.252704i	−0.929708	+	0.368298i	$0.879941\pi$
$420$		0			0
$421$	7.31594	−	12.6716i	0.356557	−	0.617575i	−0.630826	−	0.775924i	$-0.717284\pi$
$421$	7.31594	−	12.6716i	0.356557	−	0.617575i	0.987383	+	0.158349i	$0.0506172\pi$
$422$	−3.97605	+	6.88672i	−0.193551	+	0.335240i
$423$		0			0
$424$	15.3144	+	26.5254i	0.743735	+	1.28819i
$425$	−4.02400	−	6.96977i	−0.195193	−	0.338083i
$426$		0			0
$427$		0			0
$428$	7.11156	+	12.3176i	0.343750	+	0.595393i
$429$		0			0
$430$	−0.877876			−0.0423349
$431$	−9.70169	−	16.8038i	−0.467314	−	0.809411i	0.531989	−	0.846751i	$-0.321445\pi$
$431$	−9.70169	−	16.8038i	−0.467314	−	0.809411i	−0.999303	+	0.0373401i	$0.988112\pi$
$432$		0			0
$433$	1.35217			0.0649810			0.0324905	−	0.999472i	$-0.489656\pi$
$433$	1.35217			0.0649810			0.0324905	+	0.999472i	$0.489656\pi$
$434$		0			0
$435$		0			0
$436$	3.30959			0.158501
$437$	7.28772	−	12.6227i	0.348619	−	0.603826i
$438$		0			0
$439$	−8.67059	−	15.0179i	−0.413825	−	0.716766i	0.581479	−	0.813561i	$-0.302474\pi$
$439$	−8.67059	−	15.0179i	−0.413825	−	0.716766i	−0.995304	+	0.0967954i	$0.969141\pi$
$440$	−1.08056			−0.0515139
$441$		0			0
$442$	−4.41194			−0.209854
$443$	9.80499	+	16.9827i	0.465849	+	0.806874i	0.999239	−	0.0389949i	$-0.0124156\pi$
$443$	9.80499	+	16.9827i	0.465849	+	0.806874i	−0.533390	+	0.845869i	$0.679082\pi$
$444$		0			0
$445$	−0.317956	+	0.550716i	−0.0150726	+	0.0261064i
$446$	12.3318			0.583927
$447$		0			0
$448$		0			0
$449$	17.7345			0.836942			0.418471	−	0.908230i	$-0.362566\pi$
$449$	17.7345			0.836942			0.418471	+	0.908230i	$0.362566\pi$
$450$		0			0
$451$	12.4905	+	21.6342i	0.588155	+	1.01871i
$452$	−1.61187			−0.0758160
$453$		0			0
$454$	−13.1073	−	22.7025i	−0.615156	−	1.06548i
$455$		0			0
$456$		0			0
$457$	−0.242725	−	0.420413i	−0.0113542	−	0.0196661i	0.860292	−	0.509801i	$-0.170281\pi$
$457$	−0.242725	−	0.420413i	−0.0113542	−	0.0196661i	−0.871647	+	0.490135i	$0.836948\pi$
$458$	−1.05069	−	1.81985i	−0.0490956	−	0.0850361i
$459$		0			0
$460$	−0.0784150	+	0.135819i	−0.00365612	+	0.00633259i
$461$	−3.99687	+	6.92279i	−0.186153	+	0.322426i	−0.943964	−	0.330047i	$-0.892935\pi$
$461$	−3.99687	+	6.92279i	−0.186153	+	0.322426i	0.757811	+	0.652474i	$0.226269\pi$
$462$		0			0
$463$	5.24280	+	9.08080i	0.243654	+	0.422021i	0.961752	−	0.273921i	$-0.0883206\pi$
$463$	5.24280	+	9.08080i	0.243654	+	0.422021i	−0.718098	+	0.695942i	$0.754987\pi$
$464$	−16.8905			−0.784120
$465$		0			0
$466$	−7.21443			−0.334202
$467$	10.9489	−	18.9640i	0.506653	−	0.877549i	−0.493317	−	0.869849i	$-0.664216\pi$
$467$	10.9489	−	18.9640i	0.506653	−	0.877549i	0.999970	−	0.00769944i	$-0.00245083\pi$
$468$		0			0
$469$		0			0
$470$	0.185839	−	0.321883i	0.00857213	−	0.0148474i
$471$		0			0
$472$	−6.84592	+	11.8575i	−0.315109	+	0.545785i
$473$	12.5946	−	21.8145i	0.579102	−	1.00303i
$474$		0			0
$475$	−19.1639	+	33.1929i	−0.879301	+	1.52299i
$476$		0			0
$477$		0			0
$478$	−11.7708	+	20.3877i	−0.538386	+	0.932512i
$479$	−4.00169			−0.182842			−0.0914210	−	0.995812i	$-0.529141\pi$
$479$	−4.00169			−0.182842			−0.0914210	+	0.995812i	$0.529141\pi$
$480$		0			0
$481$	−4.91658			−0.224177
$482$	−11.0646	−	19.1645i	−0.503980	−	0.872918i
$483$		0			0
$484$	0.0539532	−	0.0934496i	0.00245242	−	0.00424771i
$485$	0.200520	−	0.347311i	0.00910514	−	0.0157706i
$486$		0			0
$487$	13.2377	+	22.9284i	0.599859	+	1.03899i	0.992841	+	0.119440i	$0.0381100\pi$
$487$	13.2377	+	22.9284i	0.599859	+	1.03899i	−0.392982	+	0.919546i	$0.628557\pi$
$488$	−8.70502	−	15.0775i	−0.394058	−	0.682528i
$489$		0			0
$490$		0			0
$491$	−14.2149	−	24.6210i	−0.641511	−	1.11113i	−0.985096	−	0.172008i	$-0.944975\pi$
$491$	−14.2149	−	24.6210i	−0.641511	−	1.11113i	0.343584	−	0.939122i	$-0.388359\pi$
$492$		0			0
$493$	−14.9872			−0.674989
$494$	10.5057	+	18.1965i	0.472675	+	0.818697i
$495$		0			0
$496$	−16.8381			−0.756052
$497$		0			0
$498$		0			0
$499$	−7.43118			−0.332665			−0.166333	−	0.986070i	$-0.553193\pi$
$499$	−7.43118			−0.332665			−0.166333	+	0.986070i	$0.553193\pi$
$500$	0.412863	−	0.715100i	0.0184638	−	0.0319802i
$501$		0			0
$502$	3.75765	+	6.50845i	0.167712	+	0.290486i
$503$	10.1610			0.453057			0.226529	−	0.974004i	$-0.427262\pi$
$503$	10.1610			0.453057			0.226529	+	0.974004i	$0.427262\pi$
$504$		0			0
$505$	1.84252			0.0819910
$506$	3.49124	+	6.04700i	0.155204	+	0.268822i
$507$		0			0
$508$	0.124295	−	0.215285i	0.00551470	−	0.00955174i
$509$	−28.9063			−1.28125			−0.640625	−	0.767854i	$-0.721325\pi$
$509$	−28.9063			−1.28125			−0.640625	+	0.767854i	$0.721325\pi$
$510$		0			0
$511$		0			0
$512$	−18.6806			−0.825575
$513$		0			0
$514$	7.93381	+	13.7418i	0.349945	+	0.606123i
$515$	0.920934			0.0405812
$516$		0			0
$517$	5.33237	+	9.23593i	0.234517	+	0.406196i
$518$		0			0
$519$		0			0
$520$	−0.401482	−	0.695387i	−0.0176061	−	0.0304947i
$521$	−16.8995	−	29.2708i	−0.740381	−	1.28238i	−0.952322	−	0.305095i	$-0.901312\pi$
$521$	−16.8995	−	29.2708i	−0.740381	−	1.28238i	0.211941	−	0.977283i	$-0.432022\pi$
$522$		0			0
$523$	−7.18895	+	12.4516i	−0.314351	+	0.544471i	−0.979299	−	0.202418i	$-0.935120\pi$
$523$	−7.18895	+	12.4516i	−0.314351	+	0.544471i	0.664949	+	0.746889i	$0.268453\pi$
$524$	5.86140	−	10.1522i	0.256056	−	0.443502i
$525$		0			0
$526$	−0.848618	−	1.46985i	−0.0370015	−	0.0640885i
$527$	−14.9407			−0.650828
$528$		0			0
$529$	−19.4007			−0.843508
$530$	0.580197	−	1.00493i	0.0252022	−	0.0436514i
$531$		0			0
$532$		0			0
$533$	−9.28166	+	16.0763i	−0.402033	+	0.696342i
$534$		0			0
$535$	0.956910	−	1.65742i	0.0413708	−	0.0716564i
$536$	15.3062	−	26.5111i	0.661127	−	1.14511i
$537$		0			0
$538$	14.4783	−	25.0772i	0.624205	−	1.08116i
$539$		0			0
$540$		0			0
$541$	12.5882	−	21.8034i	0.541210	−	0.937403i	−0.457625	−	0.889145i	$-0.651300\pi$
$541$	12.5882	−	21.8034i	0.541210	−	0.937403i	0.998835	−	0.0482577i	$-0.0153669\pi$
$542$	−19.7773			−0.849506
$543$		0			0
$544$	−6.67063			−0.286001
$545$	−0.222664	−	0.385666i	−0.00953789	−	0.0165201i
$546$		0			0
$547$	1.59011	−	2.75416i	0.0679883	−	0.117759i	−0.830027	−	0.557723i	$-0.811675\pi$
$547$	1.59011	−	2.75416i	0.0679883	−	0.117759i	0.898016	+	0.439963i	$0.145009\pi$
$548$	5.97545	−	10.3498i	0.255258	−	0.442121i
$549$		0			0
$550$	−9.18062	−	15.9013i	−0.391463	−	0.678034i
$551$	35.6876	+	61.8127i	1.52034	+	2.63331i
$552$		0			0
$553$		0			0
$554$	10.4057	+	18.0233i	0.442098	+	0.765736i
$555$		0			0
$556$	−6.36358			−0.269876
$557$	10.0229	+	17.3602i	0.424686	+	0.735577i	0.996391	−	0.0848820i	$-0.0270513\pi$
$557$	10.0229	+	17.3602i	0.424686	+	0.735577i	−0.571705	+	0.820459i	$0.693718\pi$
$558$		0			0
$559$	18.7181			0.791689
$560$		0			0
$561$		0			0
$562$	−5.50477			−0.232205
$563$	−19.9007	+	34.4690i	−0.838713	+	1.45269i	0.0522584	+	0.998634i	$0.483358\pi$
$563$	−19.9007	+	34.4690i	−0.838713	+	1.45269i	−0.890971	+	0.454060i	$0.849975\pi$
$564$		0			0
$565$	0.108444	+	0.187831i	0.00456228	+	0.00790211i
$566$	−16.9753			−0.713523
$567$		0			0
$568$	10.1017			0.423856
$569$	6.90797	+	11.9649i	0.289597	+	0.501597i	0.973714	−	0.227776i	$-0.0731454\pi$
$569$	6.90797	+	11.9649i	0.289597	+	0.501597i	−0.684117	+	0.729373i	$0.739812\pi$
$570$		0			0
$571$	−5.21935	+	9.04019i	−0.218423	+	0.378320i	−0.954326	−	0.298767i	$-0.903425\pi$
$571$	−5.21935	+	9.04019i	−0.218423	+	0.378320i	0.735903	+	0.677087i	$0.236758\pi$
$572$	6.48703			0.271236
$573$		0			0
$574$		0			0
$575$	−9.46483			−0.394711
$576$		0			0
$577$	−12.7461	−	22.0769i	−0.530628	−	0.919075i	−0.999361	−	0.0357353i	$-0.988623\pi$
$577$	−12.7461	−	22.0769i	−0.530628	−	0.919075i	0.468733	−	0.883340i	$-0.344711\pi$
$578$	−15.8779			−0.660433
$579$		0			0
$580$	−0.383994	−	0.665098i	−0.0159445	−	0.0276167i
$581$		0			0
$582$		0			0
$583$	16.6478	+	28.8349i	0.689483	+	1.19422i
$584$	−7.25104	−	12.5592i	−0.300050	−	0.519702i
$585$		0			0
$586$	14.2277	−	24.6431i	0.587740	−	1.01800i
$587$	17.5168	−	30.3401i	0.722998	−	1.25227i	−0.236795	−	0.971560i	$-0.576097\pi$
$587$	17.5168	−	30.3401i	0.722998	−	1.25227i	0.959793	−	0.280709i	$-0.0905697\pi$
$588$		0			0
$589$	35.5769	+	61.6210i	1.46592	+	2.53905i
$590$	0.518724			0.0213555
$591$		0			0
$592$	3.60435			0.148138
$593$	−18.0646	+	31.2888i	−0.741824	+	1.28488i	0.209840	+	0.977736i	$0.432706\pi$
$593$	−18.0646	+	31.2888i	−0.741824	+	1.28488i	−0.951664	+	0.307141i	$0.900628\pi$
$594$		0			0
$595$		0			0
$596$	4.36915	−	7.56759i	0.178967	−	0.309980i
$597$		0			0
$598$	−2.59433	+	4.49350i	−0.106090	+	0.183753i
$599$	−20.4742	+	35.4623i	−0.836552	+	1.44895i	0.0562080	+	0.998419i	$0.482099\pi$
$599$	−20.4742	+	35.4623i	−0.836552	+	1.44895i	−0.892760	+	0.450532i	$0.851234\pi$
$600$		0			0
$601$	12.8547	−	22.2650i	0.524354	−	0.908207i	−0.475244	−	0.879854i	$-0.657640\pi$
$601$	12.8547	−	22.2650i	0.524354	−	0.908207i	0.999598	−	0.0283533i	$-0.00902635\pi$
$602$		0			0
$603$		0			0
$604$	−4.41810	+	7.65238i	−0.179770	+	0.311371i
$605$	−0.0145196			−0.000590304
$606$		0			0
$607$	6.84516			0.277836			0.138918	−	0.990304i	$-0.455638\pi$
$607$	6.84516			0.277836			0.138918	+	0.990304i	$0.455638\pi$
$608$	15.8841	+	27.5121i	0.644187	+	1.11576i
$609$		0			0
$610$	−0.329795	+	0.571222i	−0.0133530	+	0.0231281i
$611$	−3.96246	+	6.86319i	−0.160304	+	0.277655i
$612$		0			0
$613$	14.5648	+	25.2271i	0.588269	+	1.01891i	0.994459	+	0.105123i	$0.0335235\pi$
$613$	14.5648	+	25.2271i	0.588269	+	1.01891i	−0.406191	+	0.913788i	$0.633143\pi$
$614$	12.2917	+	21.2898i	0.496051	+	0.859185i
$615$		0			0
$616$		0			0
$617$	10.3395	+	17.9085i	0.416252	+	0.720969i	0.995559	−	0.0941404i	$-0.0300102\pi$
$617$	10.3395	+	17.9085i	0.416252	+	0.720969i	−0.579307	+	0.815109i	$0.696677\pi$
$618$		0			0
$619$	−8.86355			−0.356256			−0.178128	−	0.984007i	$-0.557004\pi$
$619$	−8.86355			−0.356256			−0.178128	+	0.984007i	$0.557004\pi$
$620$	−0.382804	−	0.663035i	−0.0153738	−	0.0266281i
$621$		0			0
$622$	1.44453			0.0579205
$623$		0			0
$624$		0			0
$625$	24.8333			0.993331
$626$	−11.8977	+	20.6074i	−0.475528	+	0.823638i
$627$		0			0
$628$	−4.78368	−	8.28558i	−0.190890	−	0.330631i
$629$	3.19820			0.127521
$630$		0			0
$631$	26.4661			1.05360			0.526799	−	0.849990i	$-0.323392\pi$
$631$	26.4661			1.05360			0.526799	+	0.849990i	$0.323392\pi$
$632$	11.8105	+	20.4564i	0.469796	+	0.813711i
$633$		0			0
$634$	−13.6649	+	23.6683i	−0.542704	+	0.939990i
$635$	−0.0334495			−0.00132740
$636$		0			0
$637$		0			0
$638$	−34.1928			−1.35371
$639$		0			0
$640$	0.0405449	+	0.0702258i	0.00160268	+	0.00277592i
$641$	16.5319			0.652971			0.326486	−	0.945202i	$-0.394136\pi$
$641$	16.5319			0.652971			0.326486	+	0.945202i	$0.394136\pi$
$642$		0			0
$643$	−15.4460	−	26.7532i	−0.609130	−	1.05504i	−0.991384	−	0.130987i	$-0.958185\pi$
$643$	−15.4460	−	26.7532i	−0.609130	−	1.05504i	0.382254	−	0.924057i	$-0.375148\pi$
$644$		0			0
$645$		0			0
$646$	−6.83390	−	11.8367i	−0.268876	−	0.465707i
$647$	−0.649903	−	1.12567i	−0.0255503	−	0.0442545i	0.852968	−	0.521964i	$-0.174800\pi$
$647$	−0.649903	−	1.12567i	−0.0255503	−	0.0442545i	−0.878518	+	0.477710i	$0.841467\pi$
$648$		0			0
$649$	−7.44198	+	12.8899i	−0.292123	+	0.505972i
$650$	6.82209	−	11.8162i	0.267584	−	0.463470i
$651$		0			0
$652$	3.51247	+	6.08377i	0.137559	+	0.238259i
$653$	44.8870			1.75656			0.878281	−	0.478144i	$-0.158690\pi$
$653$	44.8870			1.75656			0.878281	+	0.478144i	$0.158690\pi$
$654$		0			0
$655$	−1.57738			−0.0616335
$656$	6.80438	−	11.7855i	0.265667	−	0.460148i
$657$		0			0
$658$		0			0
$659$	−8.96167	+	15.5221i	−0.349097	+	0.604654i	−0.986089	−	0.166216i	$-0.946845\pi$
$659$	−8.96167	+	15.5221i	−0.349097	+	0.604654i	0.636992	+	0.770870i	$0.280178\pi$
$660$		0			0
$661$	−16.5128	+	28.6010i	−0.642274	+	1.11245i	0.342649	+	0.939463i	$0.388676\pi$
$661$	−16.5128	+	28.6010i	−0.642274	+	1.11245i	−0.984924	+	0.172989i	$0.944658\pi$
$662$	−7.63429	+	13.2230i	−0.296715	+	0.513925i
$663$		0			0
$664$	−1.79420	+	3.10765i	−0.0696285	+	0.120600i
$665$		0			0
$666$		0			0
$667$	−8.81283	+	15.2643i	−0.341234	+	0.591035i
$668$	−13.6512			−0.528182
$669$		0			0
$670$	−1.15977			−0.0448058
$671$	−9.46295	−	16.3903i	−0.365313	−	0.632741i
$672$		0			0
$673$	−10.6758	+	18.4909i	−0.411520	+	0.712774i	−0.995056	−	0.0993135i	$-0.968335\pi$
$673$	−10.6758	+	18.4909i	−0.411520	+	0.712774i	0.583536	+	0.812087i	$0.301669\pi$
$674$	1.86865	−	3.23659i	0.0719776	−	0.124669i
$675$		0			0
$676$	−2.68447	−	4.64964i	−0.103249	−	0.178832i
$677$	4.15084	+	7.18946i	0.159530	+	0.276313i	0.934699	−	0.355440i	$-0.115669\pi$
$677$	4.15084	+	7.18946i	0.159530	+	0.276313i	−0.775170	+	0.631753i	$0.782336\pi$
$678$		0			0
$679$		0			0
$680$	0.261161	+	0.452344i	0.0100151	+	0.0173466i
$681$		0			0
$682$	−34.0868			−1.30525
$683$	1.24728	+	2.16036i	0.0477259	+	0.0826637i	0.888902	−	0.458098i	$-0.151469\pi$
$683$	1.24728	+	2.16036i	0.0477259	+	0.0826637i	−0.841176	+	0.540762i	$0.818136\pi$
$684$		0			0
$685$	−1.60808			−0.0614414
$686$		0			0
$687$		0			0
$688$	−13.7222			−0.523154
$689$	−12.3710	+	21.4271i	−0.471296	+	0.816308i
$690$		0			0
$691$	8.43455	+	14.6091i	0.320865	+	0.555755i	0.980667	−	0.195685i	$-0.0626930\pi$
$691$	8.43455	+	14.6091i	0.320865	+	0.555755i	−0.659801	+	0.751440i	$0.729360\pi$
$692$	−2.21763			−0.0843017
$693$		0			0
$694$	16.0071			0.607621
$695$	0.428132	+	0.741547i	0.0162400	+	0.0281285i
$696$		0			0
$697$	6.03765	−	10.4575i	0.228692	−	0.396107i
$698$	−17.3453			−0.656530
$699$		0			0
$700$		0			0
$701$	−16.4806			−0.622465			−0.311232	−	0.950334i	$-0.600742\pi$
$701$	−16.4806			−0.622465			−0.311232	+	0.950334i	$0.600742\pi$
$702$		0			0
$703$	−7.61558	−	13.1906i	−0.287227	−	0.497492i
$704$	−27.3536			−1.03093
$705$		0			0
$706$	−2.28515	−	3.95800i	−0.0860029	−	0.148961i
$707$		0			0
$708$		0			0
$709$	14.7462	+	25.5412i	0.553807	+	0.959222i	0.997995	+	0.0632882i	$0.0201587\pi$
$709$	14.7462	+	25.5412i	0.553807	+	0.959222i	−0.444188	+	0.895933i	$0.646508\pi$
$710$	−0.191354	−	0.331434i	−0.00718138	−	0.0124385i
$711$		0			0
$712$	−9.25539	+	16.0308i	−0.346860	+	0.600780i
$713$	−8.78551	+	15.2169i	−0.329020	+	0.569879i
$714$		0			0
$715$	−0.436438	−	0.755933i	−0.0163219	−	0.0282703i
$716$	−7.96554			−0.297686
$717$		0			0
$718$	−8.75620			−0.326779
$719$	−0.217311	+	0.376394i	−0.00810433	+	0.0140371i	−0.870049	−	0.492965i	$-0.835913\pi$
$719$	−0.217311	+	0.376394i	−0.00810433	+	0.0140371i	0.861945	+	0.507002i	$0.169246\pi$
$720$		0			0
$721$		0			0
$722$	−22.0691	+	38.2248i	−0.821327	+	1.42258i
$723$		0			0
$724$	6.69640	−	11.5985i	0.248870	−	0.431055i
$725$	23.1744	−	40.1392i	0.860675	−	1.49073i
$726$		0			0
$727$	13.5839	−	23.5280i	0.503799	−	0.872605i	−0.496192	−	0.868213i	$-0.665269\pi$
$727$	13.5839	−	23.5280i	0.503799	−	0.872605i	0.999990	−	0.00439187i	$-0.00139798\pi$
$728$		0			0
$729$		0			0
$730$	−0.274710	+	0.475812i	−0.0101675	+	0.0176106i
$731$	−12.1760			−0.450344
$732$		0			0
$733$	−5.66614			−0.209284			−0.104642	−	0.994510i	$-0.533370\pi$
$733$	−5.66614			−0.209284			−0.104642	+	0.994510i	$0.533370\pi$
$734$	7.25050	+	12.5582i	0.267621	+	0.463533i
$735$		0			0
$736$	−3.92249	+	6.79395i	−0.144585	+	0.250428i
$737$	16.6389	−	28.8194i	0.612901	−	1.06158i
$738$		0			0
$739$	6.80540	+	11.7873i	0.250341	+	0.433603i	0.963620	−	0.267278i	$-0.0861241\pi$
$739$	6.80540	+	11.7873i	0.250341	+	0.433603i	−0.713279	+	0.700880i	$0.752791\pi$
$740$	0.0819427	+	0.141929i	0.00301227	+	0.00521741i
$741$		0			0
$742$		0			0
$743$	6.33421	+	10.9712i	0.232380	+	0.402493i	0.958508	−	0.285066i	$-0.0920155\pi$
$743$	6.33421	+	10.9712i	0.232380	+	0.402493i	−0.726128	+	0.687559i	$0.758682\pi$
$744$		0			0
$745$	−1.17580			−0.0430779
$746$	−4.30696	−	7.45988i	−0.157689	−	0.273126i
$747$		0			0
$748$	−4.21977			−0.154290
$749$		0			0
$750$		0			0
$751$	−7.14538			−0.260739			−0.130369	−	0.991465i	$-0.541616\pi$
$751$	−7.14538			−0.260739			−0.130369	+	0.991465i	$0.541616\pi$
$752$	2.90488	−	5.03140i	0.105930	−	0.183476i
$753$		0			0
$754$	−12.7043	−	22.0045i	−0.462663	−	0.801355i
$755$	1.18897			0.0432712
$756$		0			0
$757$	37.6446			1.36822			0.684108	−	0.729381i	$-0.260192\pi$
$757$	37.6446			1.36822			0.684108	+	0.729381i	$0.260192\pi$
$758$	17.4325	+	30.1940i	0.633178	+	1.09670i
$759$		0			0
$760$	1.24376	−	2.15425i	0.0451157	−	0.0781428i
$761$	−10.0472			−0.364209			−0.182104	−	0.983279i	$-0.558291\pi$
$761$	−10.0472			−0.364209			−0.182104	+	0.983279i	$0.558291\pi$
$762$		0			0
$763$		0			0
$764$	−17.5572			−0.635196
$765$		0			0
$766$	−5.91762	−	10.2496i	−0.213812	−	0.370334i
$767$	−11.0602			−0.399361
$768$		0			0
$769$	16.1463	+	27.9663i	0.582252	+	1.00849i	0.995212	+	0.0977407i	$0.0311616\pi$
$769$	16.1463	+	27.9663i	0.582252	+	1.00849i	−0.412960	+	0.910749i	$0.635505\pi$
$770$		0			0
$771$		0			0
$772$	−0.100635	−	0.174305i	−0.00362192	−	0.00627336i
$773$	−24.2939	−	42.0783i	−0.873792	−	1.51345i	−0.858044	−	0.513576i	$-0.828321\pi$
$773$	−24.2939	−	42.0783i	−0.873792	−	1.51345i	−0.0157473	−	0.999876i	$-0.505013\pi$
$774$		0			0
$775$	23.1025	−	40.0148i	0.829867	−	1.43737i
$776$	5.83694	−	10.1099i	0.209534	−	0.362923i
$777$		0			0
$778$	13.3147	+	23.0618i	0.477356	+	0.826806i
$779$	−57.5075			−2.06042
$780$		0			0
$781$	10.9812			0.392938
$782$	1.68759	−	2.92299i	0.0603481	−	0.104526i
$783$		0			0
$784$		0			0
$785$	−0.643678	+	1.11488i	−0.0229739	+	0.0397919i
$786$		0			0
$787$	−24.4776	+	42.3964i	−0.872531	+	1.51127i	−0.0131602	+	0.999913i	$0.504189\pi$
$787$	−24.4776	+	42.3964i	−0.872531	+	1.51127i	−0.859370	+	0.511354i	$0.829144\pi$
$788$	0.299165	−	0.518170i	0.0106573	−	0.0184590i
$789$		0			0
$790$	0.447448	−	0.775003i	0.0159195	−	0.0275734i
$791$		0			0
$792$		0			0
$793$	7.03188	−	12.1796i	0.249710	−	0.432510i
$794$	26.5303			0.941525
$795$		0			0
$796$	−3.94348			−0.139773
$797$	−1.44417	−	2.50137i	−0.0511550	−	0.0886030i	0.839314	−	0.543647i	$-0.182957\pi$
$797$	−1.44417	−	2.50137i	−0.0511550	−	0.0886030i	−0.890469	+	0.455044i	$0.849624\pi$
$798$		0			0
$799$	2.57755	−	4.46445i	0.0911873	−	0.157941i
$800$	10.3147	−	17.8655i	0.364678	−	0.631641i
$801$		0			0
$802$	−0.861472	−	1.49211i	−0.0304196	−	0.0526883i
$803$	−7.88237	−	13.6527i	−0.278163	−	0.481792i
$804$		0			0
$805$		0			0
$806$	−12.6649	−	21.9362i	−0.446102	−	0.772671i
$807$		0			0
$808$	53.6339			1.88683
$809$	5.84869	+	10.1302i	0.205629	+	0.356160i	0.950333	−	0.311235i	$-0.100743\pi$
$809$	5.84869	+	10.1302i	0.205629	+	0.356160i	−0.744704	+	0.667395i	$0.767409\pi$
$810$		0			0
$811$	−17.1780			−0.603199			−0.301600	−	0.953435i	$-0.597521\pi$
$811$	−17.1780			−0.603199			−0.301600	+	0.953435i	$0.597521\pi$
$812$		0			0
$813$		0			0
$814$	7.29660			0.255746
$815$	0.472627	−	0.818614i	0.0165554	−	0.0286748i
$816$		0			0
$817$	28.9934	+	50.2181i	1.01435	+	1.75691i
$818$	−24.6431			−0.861624
$819$		0			0
$820$	0.618775			0.0216085
$821$	17.0068	+	29.4567i	0.593543	+	1.02805i	0.993751	+	0.111622i	$0.0356045\pi$
$821$	17.0068	+	29.4567i	0.593543	+	1.02805i	−0.400208	+	0.916424i	$0.631062\pi$
$822$		0			0
$823$	−21.6890	+	37.5664i	−0.756031	+	1.30948i	0.188829	+	0.982010i	$0.439531\pi$
$823$	−21.6890	+	37.5664i	−0.756031	+	1.30948i	−0.944860	+	0.327474i	$0.893803\pi$
$824$	26.8075			0.933883
$825$		0			0
$826$		0			0
$827$	34.0909			1.18546			0.592728	−	0.805403i	$-0.298051\pi$
$827$	34.0909			1.18546			0.592728	+	0.805403i	$0.298051\pi$
$828$		0			0
$829$	8.45833	+	14.6503i	0.293770	+	0.508824i	0.974698	−	0.223526i	$-0.0717567\pi$
$829$	8.45833	+	14.6503i	0.293770	+	0.508824i	−0.680928	+	0.732350i	$0.738423\pi$
$830$	0.135949			0.00471885
$831$		0			0
$832$	−10.1632	−	17.6032i	−0.352345	−	0.610280i
$833$		0			0
$834$		0			0
$835$	0.918434	+	1.59077i	0.0317837	+	0.0550510i
$836$	10.0481	+	17.4039i	0.347522	+	0.601926i
$837$		0			0
$838$	−3.29353	+	5.70456i	−0.113773	+	0.197061i
$839$	8.16244	−	14.1378i	0.281799	−	0.488089i	−0.690029	−	0.723782i	$-0.742402\pi$
$839$	8.16244	−	14.1378i	0.281799	−	0.488089i	0.971828	+	0.235692i	$0.0757357\pi$
$840$		0			0
$841$	−28.6560	−	49.6336i	−0.988138	−	1.71150i
$842$	−16.1362			−0.556092
$843$		0			0
$844$	−5.65179			−0.194543
$845$	−0.361214	+	0.625641i	−0.0124261	+	0.0215227i
$846$		0			0
$847$		0			0
$848$	9.06915	−	15.7082i	0.311436	−	0.539423i
$849$		0			0
$850$	−4.43772	+	7.68635i	−0.152212	+	0.263640i
$851$	1.88062	−	3.25733i	0.0644668	−	0.111660i
$852$		0			0
$853$	−14.4524	+	25.0323i	−0.494841	+	0.857089i	−0.999982	−	0.00594733i	$-0.998107\pi$
$853$	−14.4524	+	25.0323i	−0.494841	+	0.857089i	0.505142	+	0.863036i	$0.331440\pi$
$854$		0			0
$855$		0			0
$856$	27.8547	−	48.2458i	0.952055	−	1.64901i
$857$	29.0567			0.992559			0.496280	−	0.868163i	$-0.334699\pi$
$857$	29.0567			0.992559			0.496280	+	0.868163i	$0.334699\pi$
$858$		0			0
$859$	−12.5964			−0.429783			−0.214892	−	0.976638i	$-0.568940\pi$
$859$	−12.5964			−0.429783			−0.214892	+	0.976638i	$0.568940\pi$
$860$	−0.311966	−	0.540341i	−0.0106380	−	0.0184255i
$861$		0			0
$862$	−10.6992	+	18.5315i	−0.364415	+	0.631185i
$863$	−7.33309	+	12.7013i	−0.249621	+	0.432357i	−0.963421	−	0.267993i	$-0.913640\pi$
$863$	−7.33309	+	12.7013i	−0.249621	+	0.432357i	0.713799	+	0.700350i	$0.246973\pi$
$864$		0			0
$865$	0.149199	+	0.258420i	0.00507292	+	0.00878655i
$866$	−0.745594	−	1.29141i	−0.0253363	−	0.0438838i
$867$		0			0
$868$		0			0
$869$	12.8388	+	22.2375i	0.435527	+	0.754354i
$870$		0			0
$871$	24.7286			0.837896
$872$	−6.48154	−	11.2264i	−0.219493	−	0.380172i
$873$		0			0
$874$	−16.0740			−0.543711
$875$		0			0
$876$		0			0
$877$	33.1902			1.12075			0.560376	−	0.828238i	$-0.310657\pi$
$877$	33.1902			1.12075			0.560376	+	0.828238i	$0.310657\pi$
$878$	−9.56205	+	16.5620i	−0.322704	+	0.558939i
$879$		0			0
$880$	0.319953	+	0.554174i	0.0107856	+	0.0186812i
$881$	31.7179			1.06860			0.534301	−	0.845294i	$-0.320575\pi$
$881$	31.7179			1.06860			0.534301	+	0.845294i	$0.320575\pi$
$882$		0			0
$883$	−39.5231			−1.33006			−0.665029	−	0.746818i	$-0.731581\pi$
$883$	−39.5231			−1.33006			−0.665029	+	0.746818i	$0.731581\pi$
$884$	−1.56785	−	2.71559i	−0.0527324	−	0.0913352i
$885$		0			0
$886$	10.8131	−	18.7288i	0.363272	−	0.629206i
$887$	−49.9026			−1.67556			−0.837782	−	0.546005i	$-0.816148\pi$
$887$	−49.9026			−1.67556			−0.837782	+	0.546005i	$0.816148\pi$
$888$		0			0
$889$		0			0
$890$	0.701292			0.0235074
$891$		0			0
$892$	4.38228	+	7.59034i	0.146730	+	0.254143i
$893$	−24.5507			−0.821559
$894$		0			0
$895$	0.535910	+	0.928223i	0.0179135	+	0.0310271i
$896$		0			0
$897$		0			0
$898$	−9.77891	−	16.9376i	−0.326326	−	0.565214i
$899$	−43.0222	−	74.5166i	−1.43487	−	2.48527i
$900$		0			0
$901$	8.04721	−	13.9382i	0.268092	−	0.464348i
$902$	13.7747	−	23.8585i	0.458648	−	0.794401i
$903$		0			0
$904$	3.15671	+	5.46757i	0.104990	+	0.181849i
$905$	−1.80210			−0.0599037
$906$		0			0
$907$	−13.9216			−0.462259			−0.231129	−	0.972923i	$-0.574242\pi$
$907$	−13.9216			−0.462259			−0.231129	+	0.972923i	$0.574242\pi$
$908$	9.31574	−	16.1353i	0.309154	−	0.535470i
$909$		0			0
$910$		0			0
$911$	−2.70428	+	4.68394i	−0.0895967	+	0.155186i	−0.907341	−	0.420396i	$-0.861891\pi$
$911$	−2.70428	+	4.68394i	−0.0895967	+	0.155186i	0.817744	+	0.575582i	$0.195224\pi$
$912$		0			0
$913$	−1.95042	+	3.37822i	−0.0645494	+	0.111803i
$914$	−0.267681	+	0.463637i	−0.00885409	+	0.0153357i
$915$		0			0
$916$	0.746758	−	1.29342i	0.0246736	−	0.0427359i
$917$		0			0
$918$		0			0
$919$	−17.0142	+	29.4694i	−0.561245	+	0.972105i	0.436143	+	0.899877i	$0.356344\pi$
$919$	−17.0142	+	29.4694i	−0.561245	+	0.972105i	−0.997388	+	0.0722280i	$0.976989\pi$
$920$	0.614276			0.0202521
$921$		0			0
$922$	8.81561			0.290327
$923$	4.08004	+	7.06683i	0.134296	+	0.232608i
$924$		0			0
$925$	−4.94531	+	8.56554i	−0.162601	+	0.281633i
$926$	5.78184	−	10.0144i	0.190003	−	0.329095i
$927$		0			0
$928$	−19.2082	−	33.2696i	−0.630541	−	1.09213i
$929$	5.31646	+	9.20837i	0.174427	+	0.302117i	0.939963	−	0.341277i	$-0.110859\pi$
$929$	5.31646	+	9.20837i	0.174427	+	0.302117i	−0.765536	+	0.643393i	$0.777526\pi$
$930$		0			0
$931$		0			0
$932$	−2.56375	−	4.44055i	−0.0839785	−	0.145455i
$933$		0			0
$934$	−24.1491			−0.790183
$935$	0.283900	+	0.491729i	0.00928451	+	0.0160812i
$936$		0			0
$937$	52.6692			1.72063			0.860314	−	0.509765i	$-0.170268\pi$
$937$	52.6692			1.72063			0.860314	+	0.509765i	$0.170268\pi$
$938$		0			0
$939$		0			0
$940$	0.264163			0.00861605
$941$	−17.1828	+	29.7615i	−0.560143	+	0.970197i	0.437340	+	0.899296i	$0.355921\pi$
$941$	−17.1828	+	29.7615i	−0.560143	+	0.970197i	−0.997483	+	0.0709006i	$0.977413\pi$
$942$		0			0
$943$	−7.10057	−	12.2985i	−0.231226	−	0.400496i
$944$	8.10825			0.263901
$945$		0			0
$946$	−27.7791			−0.903175
$947$	−20.2920	−	35.1468i	−0.659401	−	1.14212i	−0.980771	−	0.195162i	$-0.937477\pi$
$947$	−20.2920	−	35.1468i	−0.659401	−	1.14212i	0.321370	−	0.946954i	$-0.395857\pi$
$948$		0			0
$949$	5.85736	−	10.1453i	0.190138	−	0.329329i
$950$	42.2685			1.37137
$951$		0			0
$952$		0			0
$953$	22.6904			0.735013			0.367507	−	0.930021i	$-0.380211\pi$
$953$	22.6904			0.735013			0.367507	+	0.930021i	$0.380211\pi$
$954$		0			0
$955$	1.18122	+	2.04593i	0.0382234	+	0.0662049i
$956$	−16.7318			−0.541144
$957$		0			0
$958$	2.20656	+	3.82187i	0.0712907	+	0.123479i
$959$		0			0
$960$		0			0
$961$	−27.3888	−	47.4387i	−0.883509	−	1.53028i
$962$	2.71104	+	4.69566i	0.0874074	+	0.151394i
$963$		0			0
$964$	7.86395	−	13.6208i	0.253281	−	0.438695i
$965$	−0.0135411	+	0.0234539i	−0.000435904	+	0.000755008i
$966$		0			0
$967$	−12.1388	−	21.0250i	−0.390357	−	0.676118i	0.602139	−	0.798391i	$-0.294315\pi$
$967$	−12.1388	−	21.0250i	−0.390357	−	0.676118i	−0.992497	+	0.122273i	$0.960982\pi$
$968$	−0.422650			−0.0135845
$969$		0			0
$970$	−0.442272			−0.0142005
$971$	22.7886	−	39.4709i	0.731319	−	1.26668i	−0.225000	−	0.974359i	$-0.572238\pi$
$971$	22.7886	−	39.4709i	0.731319	−	1.26668i	0.956319	−	0.292324i	$-0.0944285\pi$
$972$		0			0
$973$		0			0
$974$	14.5988	−	25.2858i	0.467774	−	0.810209i
$975$		0			0
$976$	−5.15508	+	8.92885i	−0.165010	+	0.285806i
$977$	−7.34481	+	12.7216i	−0.234981	+	0.407000i	−0.959267	−	0.282500i	$-0.908836\pi$
$977$	−7.34481	+	12.7216i	−0.234981	+	0.407000i	0.724286	+	0.689500i	$0.242170\pi$
$978$		0			0
$979$	−10.0612	+	17.4266i	−0.321558	+	0.556956i
$980$		0			0
$981$		0			0
$982$	−15.6764	+	27.1524i	−0.500255	+	0.866467i
$983$	44.5909			1.42223			0.711115	−	0.703076i	$-0.248191\pi$
$983$	44.5909			1.42223			0.711115	+	0.703076i	$0.248191\pi$
$984$		0			0
$985$	−0.0805096			−0.00256525
$986$	8.26404	+	14.3137i	0.263181	+	0.455842i
$987$		0			0
$988$	−7.46673	+	12.9328i	−0.237548	+	0.411446i
$989$	−7.15976	+	12.4011i	−0.227667	+	0.394331i
$990$		0			0
$991$	−12.0915	−	20.9430i	−0.384098	−	0.665277i	0.607546	−	0.794285i	$-0.292154\pi$
$991$	−12.0915	−	20.9430i	−0.384098	−	0.665277i	−0.991644	+	0.129007i	$0.958821\pi$
$992$	−19.1487	−	33.1665i	−0.607971	−	1.05304i
$993$		0			0
$994$		0			0
$995$	0.265311	+	0.459532i	0.00841093	+	0.0145682i
$996$		0			0
$997$	−10.8652			−0.344105			−0.172053	−	0.985088i	$-0.555040\pi$
$997$	−10.8652			−0.344105			−0.172053	+	0.985088i	$0.555040\pi$
$998$	4.09760	+	7.09726i	0.129707	+	0.224660i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.g.h.667.5		24
3.2	odd	2		441.2.g.h.79.7		24
7.2	even	3		1323.2.f.h.883.5		24
7.3	odd	6		1323.2.h.h.802.7		24
7.4	even	3		1323.2.h.h.802.8		24
7.5	odd	6		1323.2.f.h.883.6		24
7.6	odd	2	inner	1323.2.g.h.667.6		24
9.4	even	3		1323.2.h.h.226.8		24
9.5	odd	6		441.2.h.h.373.5		24
21.2	odd	6		441.2.f.h.295.8	yes	24
21.5	even	6		441.2.f.h.295.7	yes	24
21.11	odd	6		441.2.h.h.214.5		24
21.17	even	6		441.2.h.h.214.6		24
21.20	even	2		441.2.g.h.79.8		24
63.2	odd	6		3969.2.a.bh.1.6		12
63.4	even	3	inner	1323.2.g.h.361.5		24
63.5	even	6		441.2.f.h.148.7	✓	24
63.13	odd	6		1323.2.h.h.226.7		24
63.16	even	3		3969.2.a.bi.1.7		12
63.23	odd	6		441.2.f.h.148.8	yes	24
63.31	odd	6	inner	1323.2.g.h.361.6		24
63.32	odd	6		441.2.g.h.67.7		24
63.40	odd	6		1323.2.f.h.442.6		24
63.41	even	6		441.2.h.h.373.6		24
63.47	even	6		3969.2.a.bh.1.5		12
63.58	even	3		1323.2.f.h.442.5		24
63.59	even	6		441.2.g.h.67.8		24
63.61	odd	6		3969.2.a.bi.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	63.5	even	6
441.2.f.h.148.8	yes	24	63.23	odd	6
441.2.f.h.295.7	yes	24	21.5	even	6
441.2.f.h.295.8	yes	24	21.2	odd	6
441.2.g.h.67.7		24	63.32	odd	6
441.2.g.h.67.8		24	63.59	even	6
441.2.g.h.79.7		24	3.2	odd	2
441.2.g.h.79.8		24	21.20	even	2
441.2.h.h.214.5		24	21.11	odd	6
441.2.h.h.214.6		24	21.17	even	6
441.2.h.h.373.5		24	9.5	odd	6
441.2.h.h.373.6		24	63.41	even	6
1323.2.f.h.442.5		24	63.58	even	3
1323.2.f.h.442.6		24	63.40	odd	6
1323.2.f.h.883.5		24	7.2	even	3
1323.2.f.h.883.6		24	7.5	odd	6
1323.2.g.h.361.5		24	63.4	even	3	inner
1323.2.g.h.361.6		24	63.31	odd	6	inner
1323.2.g.h.667.5		24	1.1	even	1	trivial
1323.2.g.h.667.6		24	7.6	odd	2	inner
1323.2.h.h.226.7		24	63.13	odd	6
1323.2.h.h.226.8		24	9.4	even	3
1323.2.h.h.802.7		24	7.3	odd	6
1323.2.h.h.802.8		24	7.4	even	3
3969.2.a.bh.1.5		12	63.47	even	6
3969.2.a.bh.1.6		12	63.2	odd	6
3969.2.a.bi.1.7		12	63.16	even	3
3969.2.a.bi.1.8		12	63.61	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.551407 - 0.955065i) q^{2} +(0.391901 - 0.678793i) q^{4} -0.105466 q^{5} -3.07001 q^{8} +O(q^{10})\)	\(q+(-0.551407 - 0.955065i) q^{2} +(0.391901 - 0.678793i) q^{4} -0.105466 q^{5} -3.07001 q^{8} +(0.0581547 + 0.100727i) q^{10} -3.33731 q^{11} +(-1.23997 - 2.14770i) q^{13} +(0.909025 + 1.57448i) q^{16} +(0.806594 + 1.39706i) q^{17} +(3.84133 - 6.65338i) q^{19} +(-0.0413323 + 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} +1.89719 q^{23} -4.98888 q^{25} +(-1.36746 + 2.36851i) q^{26} +(-4.64521 + 8.04574i) q^{29} +(-4.63081 + 8.02080i) q^{31} +(-2.06753 + 3.58107i) q^{32} +(0.889523 - 1.54070i) q^{34} +(0.991268 - 1.71693i) q^{37} -8.47254 q^{38} +0.323782 q^{40} +(-3.74268 - 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +(-1.30790 + 2.26534i) q^{44} +(-1.04612 - 1.81194i) q^{46} +(-1.59780 - 2.76747i) q^{47} +(2.75090 + 4.76470i) q^{50} -1.94379 q^{52} +(-4.98839 - 8.64015i) q^{53} +0.351974 q^{55} +10.2456 q^{58} +(2.22993 - 3.86235i) q^{59} +(2.83550 + 4.91123i) q^{61} +10.2138 q^{62} +8.19630 q^{64} +(0.130775 + 0.226509i) q^{65} +(-4.98571 + 8.63550i) q^{67} +1.26442 q^{68} -3.29042 q^{71} +(2.36189 + 4.09091i) q^{73} -2.18637 q^{74} +(-3.01084 - 5.21493i) q^{76} +(-3.84705 - 6.66328i) q^{79} +(-0.0958713 - 0.166054i) q^{80} +(-4.12748 + 7.14901i) q^{82} +(0.584428 - 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} +8.32378 q^{86} +10.2456 q^{88} +(3.01477 - 5.22173i) q^{89} +(0.743509 - 1.28780i) q^{92} +(-1.76208 + 3.05201i) q^{94} +(-0.405130 + 0.701706i) q^{95} +(-1.90127 + 3.29310i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} + 40 q^{11} - 12 q^{16} + 64 q^{23} + 24 q^{25} - 16 q^{29} - 48 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} + 136 q^{74} + 12 q^{79} + 12 q^{85} + 152 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 + 40 * q^11 - 12 * q^16 + 64 * q^23 + 24 * q^25 - 16 * q^29 - 48 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 + 136 * q^74 + 12 * q^79 + 12 * q^85 + 152 * q^86 - 16 * q^92 - 64 * q^95

Introduction

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