LMFDB - Embedded newform 1323.2.f.h.883.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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			883.6
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.h.442.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.551407 + 0.955065i) q^{2} +(0.391901 + 0.678793i) q^{4} +(-0.0527330 - 0.0913363i) q^{5} -3.07001 q^{8} +O(q^{10})$	\(q+(-0.551407 + 0.955065i) q^{2} +(0.391901 + 0.678793i) q^{4} +(-0.0527330 - 0.0913363i) q^{5} -3.07001 q^{8} +0.116309 q^{10} +(1.66866 - 2.89020i) q^{11} +(1.23997 + 2.14770i) q^{13} +(0.909025 - 1.57448i) q^{16} +1.61319 q^{17} +7.68266 q^{19} +(0.0413323 - 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} +(-0.948593 - 1.64301i) q^{23} +(2.49444 - 4.32049i) q^{25} -2.73492 q^{26} +(-4.64521 + 8.04574i) q^{29} +(4.63081 + 8.02080i) q^{31} +(-2.06753 - 3.58107i) q^{32} +(-0.889523 + 1.54070i) q^{34} -1.98254 q^{37} +(-4.23627 + 7.33744i) q^{38} +(0.161891 + 0.280404i) q^{40} +(3.74268 + 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +2.61579 q^{44} +2.09224 q^{46} +(1.59780 - 2.76747i) q^{47} +(2.75090 + 4.76470i) q^{50} +(-0.971894 + 1.68337i) q^{52} +9.97679 q^{53} -0.351974 q^{55} +(-5.12280 - 8.87296i) q^{58} +(-2.22993 - 3.86235i) q^{59} +(-2.83550 + 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(0.130775 - 0.226509i) q^{65} +(-4.98571 - 8.63550i) q^{67} +(0.632210 + 1.09502i) q^{68} -3.29042 q^{71} +4.72378 q^{73} +(1.09318 - 1.89345i) q^{74} +(3.01084 + 5.21493i) q^{76} +(-3.84705 + 6.66328i) q^{79} -0.191743 q^{80} -8.25496 q^{82} +(-0.584428 + 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} +(-4.16189 - 7.20860i) q^{86} +(-5.12280 + 8.87296i) q^{88} +6.02954 q^{89} +(0.743509 - 1.28780i) q^{92} +(1.76208 + 3.05201i) q^{94} +(-0.405130 - 0.701706i) q^{95} +(1.90127 - 3.29310i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.551407	+	0.955065i	−0.389903	+	0.675333i	−0.992436	−	0.122762i	$-0.960825\pi$
$2$	−0.551407	+	0.955065i	−0.389903	+	0.675333i	0.602533	+	0.798094i	$0.294158\pi$
$3$		0			0
$3$		0			0
$4$	0.391901	+	0.678793i	0.195951	+	0.339396i
$5$	−0.0527330	−	0.0913363i	−0.0235829	−	0.0408468i	0.853993	−	0.520284i	$-0.174174\pi$
$5$	−0.0527330	−	0.0913363i	−0.0235829	−	0.0408468i	−0.877576	+	0.479438i	$0.840841\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−3.07001			−1.08541
$9$		0			0
$10$	0.116309			0.0367803
$11$	1.66866	−	2.89020i	0.503119	−	0.871428i	−0.496874	−	0.867822i	$-0.665519\pi$
$11$	1.66866	−	2.89020i	0.503119	−	0.871428i	0.999994	−	0.00360543i	$-0.00114765\pi$
$12$		0			0
$13$	1.23997	+	2.14770i	0.343907	+	0.595664i	0.985155	−	0.171670i	$-0.0549162\pi$
$13$	1.23997	+	2.14770i	0.343907	+	0.595664i	−0.641248	+	0.767334i	$0.721583\pi$
$14$		0			0
$15$		0			0
$16$	0.909025	−	1.57448i	0.227256	−	0.393619i
$17$	1.61319			0.391255			0.195628	−	0.980678i	$-0.437326\pi$
$17$	1.61319			0.391255			0.195628	+	0.980678i	$0.437326\pi$
$18$		0			0
$19$	7.68266			1.76252			0.881262	−	0.472629i	$-0.156695\pi$
$19$	7.68266			1.76252			0.881262	+	0.472629i	$0.156695\pi$
$20$	0.0413323	−	0.0715896i	0.00924218	−	0.0160079i
$21$		0			0
$22$	1.84022	+	3.18735i	0.392336	+	0.679546i
$23$	−0.948593	−	1.64301i	−0.197795	−	0.342592i	0.750018	−	0.661417i	$-0.230045\pi$
$23$	−0.948593	−	1.64301i	−0.197795	−	0.342592i	−0.947813	+	0.318826i	$0.896711\pi$
$24$		0			0
$25$	2.49444	−	4.32049i	0.498888	−	0.864099i
$26$	−2.73492			−0.536362
$27$		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	0.896675	+	0.442689i	$0.145976\pi$
$31$	4.63081	+	8.02080i	0.831718	+	1.44058i	−0.0649574	+	0.997888i	$0.520691\pi$
$32$	−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
$37$	−1.98254			−0.325927			−0.162963	−	0.986632i	$-0.552105\pi$
$37$	−1.98254			−0.325927			−0.162963	+	0.986632i	$0.552105\pi$
$38$	−4.23627	+	7.33744i	−0.687214	+	1.19029i
$39$		0			0
$40$	0.161891	+	0.280404i	0.0255973	+	0.0443357i
$41$	3.74268	+	6.48252i	0.584509	+	1.01240i	0.994936	+	0.100506i	$0.0320462\pi$
$41$	3.74268	+	6.48252i	0.584509	+	1.01240i	−0.410427	+	0.911893i	$0.634621\pi$
$42$		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	$0.971470\pi$
$44$	2.61579			0.394346
$45$		0			0
$46$	2.09224			0.308484
$47$	1.59780	−	2.76747i	0.233063	−	0.403677i	−0.725645	−	0.688070i	$-0.758458\pi$
$47$	1.59780	−	2.76747i	0.233063	−	0.403677i	0.958708	+	0.284392i	$0.0917917\pi$
$48$		0			0
$49$		0			0
$50$	2.75090	+	4.76470i	0.389036	+	0.673830i
$51$		0			0
$52$	−0.971894	+	1.68337i	−0.134777	+	0.233441i
$53$	9.97679			1.37042			0.685209	−	0.728347i	$-0.259711\pi$
$53$	9.97679			1.37042			0.685209	+	0.728347i	$0.259711\pi$
$54$		0			0
$55$	−0.351974			−0.0474601
$56$		0			0
$57$		0			0
$58$	−5.12280	−	8.87296i	−0.672657	−	1.16508i
$59$	−2.22993	−	3.86235i	−0.290312	−	0.502836i	0.683571	−	0.729884i	$-0.260426\pi$
$59$	−2.22993	−	3.86235i	−0.290312	−	0.502836i	−0.973884	+	0.227048i	$0.927093\pi$
$60$		0			0
$61$	−2.83550	+	4.91123i	−0.363048	+	0.628818i	−0.988461	−	0.151476i	$-0.951597\pi$
$61$	−2.83550	+	4.91123i	−0.363048	+	0.628818i	0.625413	+	0.780294i	$0.284931\pi$
$62$	−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	−0.991389	−	0.130951i	$-0.958197\pi$
$67$	−4.98571	−	8.63550i	−0.609101	−	1.05499i	0.382288	−	0.924043i	$-0.375136\pi$
$68$	0.632210	+	1.09502i	0.0766667	+	0.132791i
$69$		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
$73$	4.72378			0.552877			0.276438	−	0.961032i	$-0.410846\pi$
$73$	4.72378			0.552877			0.276438	+	0.961032i	$0.410846\pi$
$74$	1.09318	−	1.89345i	0.127080	−	0.220109i
$75$		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	−0.997115	−	0.0758997i	$-0.975817\pi$
$79$	−3.84705	+	6.66328i	−0.432827	+	0.749678i	0.564289	+	0.825577i	$0.309150\pi$
$80$	−0.191743			−0.0214375
$81$		0			0
$82$	−8.25496			−0.911608
$83$	−0.584428	+	1.01226i	−0.0641493	+	0.111110i	−0.896316	−	0.443415i	$-0.853767\pi$
$83$	−0.584428	+	1.01226i	−0.0641493	+	0.111110i	0.832167	+	0.554525i	$0.187100\pi$
$84$		0			0
$85$	−0.0850683	−	0.147343i	−0.00922695	−	0.0159815i
$86$	−4.16189	−	7.20860i	−0.448788	−	0.777323i
$87$		0			0
$88$	−5.12280	+	8.87296i	−0.546093	+	0.945860i
$89$	6.02954			0.639130			0.319565	−	0.947564i	$-0.396463\pi$
$89$	6.02954			0.639130			0.319565	+	0.947564i	$0.396463\pi$
$90$		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	−0.753213	−	0.657777i	$-0.771497\pi$
$97$	1.90127	−	3.29310i	0.193045	−	0.334364i	0.946258	+	0.323413i	$0.104830\pi$
$98$		0			0
$99$		0			0
$100$	3.91029			0.391029
$101$	−8.73512	+	15.1297i	−0.869177	+	1.50546i	−0.00633771	+	0.999980i	$0.502017\pi$
$101$	−8.73512	+	15.1297i	−0.869177	+	1.50546i	−0.862839	+	0.505479i	$0.831316\pi$
$102$		0			0
$103$	−4.36602	−	7.56217i	−0.430197	−	0.745123i	0.566693	−	0.823929i	$-0.308223\pi$
$103$	−4.36602	−	7.56217i	−0.430197	−	0.745123i	−0.996890	+	0.0788062i	$0.974889\pi$
$104$	−3.80674	−	6.59346i	−0.373281	−	0.646542i
$105$		0			0
$106$	−5.50127	+	9.52848i	−0.534330	+	0.925487i
$107$	18.1463			1.75427			0.877135	−	0.480244i	$-0.159452\pi$
$107$	18.1463			1.75427			0.877135	+	0.480244i	$0.159452\pi$
$108$		0			0
$109$	−4.22248			−0.404440			−0.202220	−	0.979340i	$-0.564816\pi$
$109$	−4.22248			−0.404440			−0.202220	+	0.979340i	$0.564816\pi$
$110$	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
$115$	−0.100044	+	0.173282i	−0.00932919	+	0.0161586i
$116$	−7.28186			−0.676103
$117$		0			0
$118$	4.91840			0.452775
$119$		0			0
$120$		0			0
$121$	−0.0688352	−	0.119226i	−0.00625774	−	0.0108387i
$122$	−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
$131$	7.47816	+	12.9525i	0.653370	+	1.13167i	0.982300	+	0.187315i	$0.0599786\pi$
$131$	7.47816	+	12.9525i	0.653370	+	1.13167i	−0.328930	+	0.944354i	$0.606688\pi$
$132$		0			0
$133$		0			0
$134$	10.9966			0.949962
$135$		0			0
$136$	−4.95251			−0.424674
$137$	−7.62367	+	13.2046i	−0.651334	+	1.12814i	0.331466	+	0.943467i	$0.392457\pi$
$137$	−7.62367	+	13.2046i	−0.651334	+	1.12814i	−0.982799	+	0.184676i	$0.940876\pi$
$138$		0			0
$139$	4.05943	+	7.03114i	0.344316	+	0.596374i	0.985229	−	0.171240i	$-0.0547774\pi$
$139$	4.05943	+	7.03114i	0.344316	+	0.596374i	−0.640913	+	0.767614i	$0.721444\pi$
$140$		0			0
$141$		0			0
$142$	1.81436	−	3.14257i	0.152258	−	0.263718i
$143$	8.27636			0.692104
$144$		0			0
$145$	0.979825			0.0813700
$146$	−2.60473	+	4.51152i	−0.215569	+	0.373376i
$147$		0			0
$148$	−0.776958	−	1.34573i	−0.0638656	−	0.110618i
$149$	−5.57430	−	9.65497i	−0.456664	−	0.790966i	0.542118	−	0.840303i	$-0.317623\pi$
$149$	−5.57430	−	9.65497i	−0.456664	−	0.790966i	−0.998782	+	0.0493365i	$0.984289\pi$
$150$		0			0
$151$	5.63676	−	9.76315i	0.458713	−	0.794514i	−0.540180	−	0.841549i	$-0.681644\pi$
$151$	5.63676	−	9.76315i	0.458713	−	0.794514i	0.998893	+	0.0470354i	$0.0149774\pi$
$152$	−23.5859			−1.91307
$153$		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	$-0.328607\pi$
$157$	−6.10318	−	10.5710i	−0.487087	−	0.843659i	−0.999890	+	0.0148476i	$0.995274\pi$
$158$	−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
$163$	8.96264			0.702008			0.351004	−	0.936374i	$-0.385840\pi$
$163$	8.96264			0.702008			0.351004	+	0.936374i	$0.385840\pi$
$164$	−2.93352	+	5.08101i	−0.229070	+	0.396760i
$165$		0			0
$166$	−0.644515	−	1.11633i	−0.0500240	−	0.0866442i
$167$	8.70833	+	15.0833i	0.673871	+	1.16718i	0.976798	+	0.214165i	$0.0687030\pi$
$167$	8.70833	+	15.0833i	0.673871	+	1.16718i	−0.302927	+	0.953014i	$0.597964\pi$
$168$		0			0
$169$	3.42493	−	5.93216i	0.263456	−	0.456320i
$170$	0.187629			0.0143905
$171$		0			0
$172$	−5.91595			−0.451087
$173$	1.41466	−	2.45027i	0.107555	−	0.186291i	−0.807224	−	0.590245i	$-0.799031\pi$
$173$	1.41466	−	2.45027i	0.107555	−	0.186291i	0.914779	+	0.403954i	$0.132365\pi$
$174$		0			0
$175$		0			0
$176$	−3.03370	−	5.25453i	−0.228674	−	0.396075i
$177$		0			0
$178$	−3.32473	+	5.75860i	−0.249199	+	0.431625i
$179$	10.1627			0.759595			0.379798	−	0.925070i	$-0.375994\pi$
$179$	10.1627			0.759595			0.379798	+	0.925070i	$0.375994\pi$
$180$		0			0
$181$	−17.0870			−1.27006			−0.635032	−	0.772486i	$-0.719013\pi$
$181$	−17.0870			−1.27006			−0.635032	+	0.772486i	$0.719013\pi$
$182$		0			0
$183$		0			0
$184$	2.91220	+	5.04407i	0.214690	+	0.371854i
$185$	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	0.102178	+	0.994766i	$0.467419\pi$
$191$	−11.2000	+	19.3990i	−0.810404	+	1.40366i	−0.912582	+	0.408894i	$0.865914\pi$
$192$		0			0
$193$	0.128393	+	0.222383i	0.00924194	+	0.0160075i	0.870609	−	0.491975i	$-0.163725\pi$
$193$	0.128393	+	0.222383i	0.00924194	+	0.0160075i	−0.861367	+	0.507982i	$0.830391\pi$
$194$	2.09675	+	3.63168i	0.150538	+	0.260739i
$195$		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
$199$	−5.03121			−0.356653			−0.178327	−	0.983971i	$-0.557068\pi$
$199$	−5.03121			−0.356653			−0.178327	+	0.983971i	$0.557068\pi$
$200$	−7.65796	+	13.2640i	−0.541500	+	0.937905i
$201$		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
$206$	9.62981			0.670941
$207$		0			0
$208$	4.50867			0.312620
$209$	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	$0.913174\pi$
$212$	3.90991	+	6.77217i	0.268534	+	0.465114i
$213$		0			0
$214$	−10.0060	+	17.3309i	−0.683996	+	1.18472i
$215$	0.796033			0.0542890
$216$		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	−0.615833	−	0.787877i	$-0.711180\pi$
$223$	5.59106	−	9.68400i	0.374405	−	0.648488i	0.990238	+	0.139388i	$0.0445137\pi$
$224$		0			0
$225$		0			0
$226$	2.26791			0.150859
$227$	11.8853	−	20.5860i	0.788857	−	1.36634i	−0.137811	−	0.990459i	$-0.544007\pi$
$227$	11.8853	−	20.5860i	0.788857	−	1.36634i	0.926668	−	0.375881i	$-0.122660\pi$
$228$		0			0
$229$	0.952737	+	1.65019i	0.0629586	+	0.109048i	0.895787	−	0.444484i	$-0.146613\pi$
$229$	0.952737	+	1.65019i	0.0629586	+	0.109048i	−0.832828	+	0.553532i	$0.813280\pi$
$230$	−0.110330	−	0.191098i	−0.00727497	−	0.0126006i
$231$		0			0
$232$	14.2609	−	24.7006i	0.936272	−	1.62167i
$233$	−6.54184			−0.428570			−0.214285	−	0.976771i	$-0.568742\pi$
$233$	−6.54184			−0.428570			−0.214285	+	0.976771i	$0.568742\pi$
$234$		0			0
$235$	−0.337028			−0.0219853
$236$	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
$241$	10.0331	−	17.3778i	0.646288	−	1.11940i	−0.337715	−	0.941248i	$-0.609654\pi$
$241$	10.0331	−	17.3778i	0.646288	−	1.11940i	0.984003	−	0.178155i	$-0.0570127\pi$
$242$	0.151825			0.00975967
$243$		0			0
$244$	−4.44494			−0.284558
$245$		0			0
$246$		0			0
$247$	9.52629	+	16.5000i	0.606144	+	1.04987i
$248$	−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	$-0.431002\pi$
$251$	6.81467			0.430138			0.215069	+	0.976599i	$0.431002\pi$
$252$		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
$257$	−7.19415	−	12.4606i	−0.448759	−	0.777273i	0.549546	−	0.835463i	$-0.314801\pi$
$257$	−7.19415	−	12.4606i	−0.448759	−	0.777273i	−0.998306	+	0.0581897i	$0.981467\pi$
$258$		0			0
$259$		0			0
$260$	0.205004			0.0127138
$261$		0			0
$262$	−16.4940			−1.01900
$263$	−0.769503	+	1.33282i	−0.0474496	+	0.0821851i	−0.888775	−	0.458344i	$-0.848443\pi$
$263$	−0.769503	+	1.33282i	−0.0474496	+	0.0821851i	0.841325	+	0.540529i	$0.181776\pi$
$264$		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
$269$	26.2571			1.60092			0.800461	−	0.599385i	$-0.204588\pi$
$269$	26.2571			1.60092			0.800461	+	0.599385i	$0.204588\pi$
$270$		0			0
$271$	17.9335			1.08938			0.544690	−	0.838637i	$-0.316647\pi$
$271$	17.9335			1.08938			0.544690	+	0.838637i	$0.316647\pi$
$272$	1.46643	−	2.53993i	0.0889152	−	0.154006i
$273$		0			0
$274$	−8.40748	−	14.5622i	−0.507915	−	0.879734i
$275$	−8.32473	−	14.4188i	−0.502000	−	0.869489i
$276$		0			0
$277$	9.43563	−	16.3430i	0.566932	−	0.981955i	−0.429935	−	0.902860i	$-0.641463\pi$
$277$	9.43563	−	16.3430i	0.566932	−	0.981955i	0.996867	−	0.0790954i	$-0.0252032\pi$
$278$	−8.95359			−0.537001
$279$		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	$-0.317922\pi$
$283$	−7.69634	−	13.3304i	−0.457500	−	0.792413i	−0.998828	+	0.0483984i	$0.984588\pi$
$284$	−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
$289$	−14.3976			−0.846919
$290$	−0.540282	+	0.935796i	−0.0317265	+	0.0549518i
$291$		0			0
$292$	1.85126	+	3.20647i	0.108337	+	0.187644i
$293$	−12.9013	−	22.3456i	−0.753700	−	1.30545i	−0.946018	−	0.324114i	$-0.894934\pi$
$293$	−12.9013	−	22.3456i	−0.753700	−	1.30545i	0.192318	−	0.981333i	$-0.438399\pi$
$294$		0			0
$295$	−0.235182	+	0.407347i	−0.0136928	+	0.0237167i
$296$	6.08642			0.353766
$297$		0			0
$298$	12.2948			0.712220
$299$	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
$304$	6.98373	−	12.0962i	0.400544	−	0.693763i
$305$	0.598098			0.0342470
$306$		0			0
$307$	22.2914			1.27224			0.636120	−	0.771590i	$-0.280538\pi$
$307$	22.2914			1.27224			0.636120	+	0.771590i	$0.280538\pi$
$308$		0			0
$309$		0			0
$310$	0.538607	+	0.932894i	0.0305908	+	0.0529848i
$311$	0.654931	+	1.13437i	0.0371377	+	0.0643245i	0.883997	−	0.467493i	$-0.154843\pi$
$311$	0.654931	+	1.13437i	0.0371377	+	0.0643245i	−0.846859	+	0.531817i	$0.821509\pi$
$312$		0			0
$313$	10.7885	−	18.6862i	0.609802	−	1.05621i	−0.381471	−	0.924381i	$-0.624582\pi$
$313$	10.7885	−	18.6862i	0.609802	−	1.05621i	0.991273	−	0.131827i	$-0.0420843\pi$
$314$	13.4613			0.759667
$315$		0			0
$316$	−6.03065			−0.339250
$317$	−12.3910	+	21.4618i	−0.695946	+	1.20541i	0.273915	+	0.961754i	$0.411681\pi$
$317$	−12.3910	+	21.4618i	−0.695946	+	1.20541i	−0.969861	+	0.243660i	$0.921652\pi$
$318$		0			0
$319$	15.5025	+	26.8512i	0.867975	+	1.50338i
$320$	−0.432216	−	0.748620i	−0.0241616	−	0.0418491i
$321$		0			0
$322$		0			0
$323$	12.3936			0.689597
$324$		0			0
$325$	12.3722			0.686283
$326$	−4.94206	+	8.55990i	−0.273715	+	0.474089i
$327$		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	−0.991133	−	0.132870i	$-0.957581\pi$
$331$	−6.92256	+	11.9902i	−0.380498	+	0.659042i	0.610635	+	0.791912i	$0.290914\pi$
$332$	−0.916151			−0.0502803
$333$		0			0
$334$	−19.2073			−1.05098
$335$	−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	$0.803911\pi$
$338$	3.77706	+	6.54206i	0.205445	+	0.355841i
$339$		0			0
$340$	0.0666767	−	0.115487i	0.00361605	−	0.00626319i
$341$	30.9089			1.67381
$342$		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	0.602798	−	0.797894i	$-0.294052\pi$
$347$	−7.25739	−	12.5702i	−0.389597	−	0.674802i	−0.992395	+	0.123091i	$0.960719\pi$
$348$		0			0
$349$	−7.86412	+	13.6211i	−0.420957	+	0.729119i	−0.996033	−	0.0889810i	$-0.971639\pi$
$349$	−7.86412	+	13.6211i	−0.420957	+	0.729119i	0.575076	+	0.818100i	$0.304972\pi$
$350$		0			0
$351$		0			0
$352$	−13.8000			−0.735542
$353$	2.07211	−	3.58900i	0.110287	−	0.191023i	−0.805599	−	0.592462i	$-0.798156\pi$
$353$	2.07211	−	3.58900i	0.110287	−	0.191023i	0.915886	+	0.401438i	$0.131490\pi$
$354$		0			0
$355$	0.173514	+	0.300535i	0.00920917	+	0.0159508i
$356$	2.36298	+	4.09281i	0.125238	+	0.216918i
$357$		0			0
$358$	−5.60378	+	9.70603i	−0.296169	+	0.512979i
$359$	−7.93988			−0.419051			−0.209525	−	0.977803i	$-0.567192\pi$
$359$	−7.93988			−0.419051			−0.209525	+	0.977803i	$0.567192\pi$
$360$		0			0
$361$	40.0233			2.10649
$362$	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
$367$	−6.57455	+	11.3875i	−0.343189	+	0.594420i	−0.985023	−	0.172423i	$-0.944840\pi$
$367$	−6.57455	+	11.3875i	−0.343189	+	0.594420i	0.641834	+	0.766843i	$0.278174\pi$
$368$	−3.44918			−0.179801
$369$		0			0
$370$	−0.230588			−0.0119877
$371$		0			0
$372$		0			0
$373$	−3.90543	−	6.76441i	−0.202216	−	0.350248i	0.747026	−	0.664794i	$-0.231481\pi$
$373$	−3.90543	−	6.76441i	−0.202216	−	0.350248i	−0.949242	+	0.314547i	$0.898147\pi$
$374$	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
$383$	5.36593	+	9.29407i	0.274186	+	0.474905i	0.969930	−	0.243386i	$-0.0782582\pi$
$383$	5.36593	+	9.29407i	0.274186	+	0.474905i	−0.695743	+	0.718291i	$0.744925\pi$
$384$		0			0
$385$		0			0
$386$	−0.283187			−0.0144139
$387$		0			0
$388$	2.98045			0.151309
$389$	12.0734	−	20.9118i	0.612147	−	1.06027i	−0.378731	−	0.925507i	$-0.623639\pi$
$389$	12.0734	−	20.9118i	0.612147	−	1.06027i	0.990878	−	0.134763i	$-0.0430272\pi$
$390$		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
$395$	0.811466			0.0408293
$396$		0			0
$397$	−24.0569			−1.20738			−0.603691	−	0.797218i	$-0.706304\pi$
$397$	−24.0569			−1.20738			−0.603691	+	0.797218i	$0.706304\pi$
$398$	2.77424	−	4.80513i	0.139060	−	0.240860i
$399$		0			0
$400$	−4.53501	−	7.85487i	−0.226751	−	0.392744i
$401$	−0.781158	−	1.35301i	−0.0390092	−	0.0675659i	0.845862	−	0.533402i	$-0.179087\pi$
$401$	−0.781158	−	1.35301i	−0.0390092	−	0.0675659i	−0.884871	+	0.465836i	$0.845753\pi$
$402$		0			0
$403$	−11.4842	+	19.8911i	−0.572067	+	0.990849i
$404$	−13.6932			−0.681263
$405$		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	−0.998096	−	0.0616748i	$-0.980356\pi$
$409$	−11.1728	−	19.3519i	−0.552460	−	0.956889i	0.445636	−	0.895214i	$-0.352977\pi$
$410$	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
$415$	0.123275			0.00605131
$416$	5.12736	−	8.88086i	0.251390	−	0.435420i
$417$		0			0
$418$	14.1378	+	24.4873i	0.691501	+	1.19771i
$419$	2.98648	+	5.17273i	0.145899	+	0.252704i	0.929708	−	0.368298i	$-0.120059\pi$
$419$	2.98648	+	5.17273i	0.145899	+	0.252704i	−0.783809	+	0.621002i	$0.786726\pi$
$420$		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	$0.0506172\pi$
$422$	7.95210			0.387102
$423$		0			0
$424$	−30.6289			−1.48747
$425$	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
$430$	−0.438938	+	0.760263i	−0.0211675	+	0.0366631i
$431$	19.4034			0.934628			0.467314	−	0.884091i	$-0.345222\pi$
$431$	19.4034			0.934628			0.467314	+	0.884091i	$0.345222\pi$
$432$		0			0
$433$	−1.35217			−0.0649810			−0.0324905	−	0.999472i	$-0.510344\pi$
$433$	−1.35217			−0.0649810			−0.0324905	+	0.999472i	$0.510344\pi$
$434$		0			0
$435$		0			0
$436$	−1.65480	−	2.86619i	−0.0792503	−	0.137266i
$437$	−7.28772	−	12.6227i	−0.348619	−	0.603826i
$438$		0			0
$439$	8.67059	−	15.0179i	0.413825	−	0.716766i	−0.581479	−	0.813561i	$-0.697526\pi$
$439$	8.67059	−	15.0179i	0.413825	−	0.716766i	0.995304	+	0.0967954i	$0.0308592\pi$
$440$	1.08056			0.0515139
$441$		0			0
$442$	−4.41194			−0.209854
$443$	9.80499	−	16.9827i	0.465849	−	0.806874i	−0.533390	−	0.845869i	$-0.679082\pi$
$443$	9.80499	−	16.9827i	0.465849	−	0.806874i	0.999239	+	0.0389949i	$0.0124156\pi$
$444$		0			0
$445$	−0.317956	−	0.550716i	−0.0150726	−	0.0261064i
$446$	6.16590	+	10.6796i	0.291964	+	0.505696i
$447$		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
$451$	24.9810			1.17631
$452$	0.805935	−	1.39592i	0.0379080	−	0.0656586i
$453$		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	−0.871647	−	0.490135i	$-0.836948\pi$
$457$	−0.242725	+	0.420413i	−0.0113542	+	0.0196661i	0.860292	+	0.509801i	$0.170281\pi$
$458$	−2.10138			−0.0981912
$459$		0			0
$460$	−0.156830			−0.00731224
$461$	3.99687	−	6.92279i	0.186153	−	0.322426i	−0.757811	−	0.652474i	$-0.773731\pi$
$461$	3.99687	−	6.92279i	0.186153	−	0.322426i	0.943964	+	0.330047i	$0.107065\pi$
$462$		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	$0.754987\pi$
$464$	8.44523	+	14.6276i	0.392060	+	0.679068i
$465$		0			0
$466$	3.60721	−	6.24788i	0.167101	−	0.289427i
$467$	21.8977			1.01331			0.506653	−	0.862150i	$-0.330883\pi$
$467$	21.8977			1.01331			0.506653	+	0.862150i	$0.330883\pi$
$468$		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
$478$	23.5417			1.07677
$479$	−2.00085	+	3.46557i	−0.0914210	+	0.158346i	−0.908109	−	0.418733i	$-0.862474\pi$
$479$	−2.00085	+	3.46557i	−0.0914210	+	0.158346i	0.816688	+	0.577079i	$0.195808\pi$
$480$		0			0
$481$	−2.45829	−	4.25789i	−0.112088	−	0.194143i
$482$	11.0646	+	19.1645i	0.503980	+	0.872918i
$483$		0			0
$484$	0.0539532	−	0.0934496i	0.00245242	−	0.00424771i
$485$	−0.401040			−0.0182103
$486$		0			0
$487$	−26.4755			−1.19972			−0.599859	−	0.800106i	$-0.704777\pi$
$487$	−26.4755			−1.19972			−0.599859	+	0.800106i	$0.704777\pi$
$488$	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
$493$	−7.49360	+	12.9793i	−0.337495	+	0.584558i
$494$	−21.0115			−0.945350
$495$		0			0
$496$	16.8381			0.756052
$497$		0			0
$498$		0			0
$499$	3.71559	+	6.43559i	0.166333	+	0.288097i	0.937128	−	0.348986i	$-0.113474\pi$
$499$	3.71559	+	6.43559i	0.166333	+	0.288097i	−0.770795	+	0.637083i	$0.780141\pi$
$500$	−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	$-0.572738\pi$
$503$	−10.1610			−0.453057			−0.226529	+	0.974004i	$0.572738\pi$
$504$		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
$509$	−14.4532	−	25.0336i	−0.640625	−	1.10960i	−0.985293	−	0.170871i	$-0.945342\pi$
$509$	−14.4532	−	25.0336i	−0.640625	−	1.10960i	0.344668	−	0.938725i	$-0.387991\pi$
$510$		0			0
$511$		0			0
$512$	−18.6806			−0.825575
$513$		0			0
$514$	15.8676			0.699891
$515$	−0.460467	+	0.797553i	−0.0202906	+	0.0351444i
$516$		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
$521$	−33.7990			−1.48076			−0.740381	−	0.672187i	$-0.765355\pi$
$521$	−33.7990			−1.48076			−0.740381	+	0.672187i	$0.765355\pi$
$522$		0			0
$523$	−14.3779			−0.628701			−0.314351	−	0.949307i	$-0.601787\pi$
$523$	−14.3779			−0.628701			−0.314351	+	0.949307i	$0.601787\pi$
$524$	−5.86140	+	10.1522i	−0.256056	+	0.443502i
$525$		0			0
$526$	−0.848618	−	1.46985i	−0.0370015	−	0.0640885i
$527$	7.47036	+	12.9390i	0.325414	+	0.563634i
$528$		0			0
$529$	9.70034	−	16.8015i	0.421754	−	0.730499i
$530$	1.16039			0.0504043
$531$		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
$541$	−25.1764			−1.08242			−0.541210	−	0.840888i	$-0.682034\pi$
$541$	−25.1764			−1.08242			−0.541210	+	0.840888i	$0.682034\pi$
$542$	−9.88863	+	17.1276i	−0.424753	+	0.735694i
$543$		0			0
$544$	−3.33531	−	5.77693i	−0.143000	−	0.247684i
$545$	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	$0.145009\pi$
$548$	−11.9509			−0.510517
$549$		0			0
$550$	18.3612			0.782926
$551$	−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
$556$	−3.18179	+	5.51102i	−0.134938	+	0.233719i
$557$	−20.0459			−0.849371			−0.424686	−	0.905341i	$-0.639615\pi$
$557$	−20.0459			−0.849371			−0.424686	+	0.905341i	$0.639615\pi$
$558$		0			0
$559$	−18.7181			−0.791689
$560$		0			0
$561$		0			0
$562$	2.75238	+	4.76727i	0.116102	+	0.201095i
$563$	19.9007	+	34.4690i	0.838713	+	1.45269i	0.890971	+	0.454060i	$0.150025\pi$
$563$	19.9007	+	34.4690i	0.838713	+	1.45269i	−0.0522584	+	0.998634i	$0.516642\pi$
$564$		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	−0.684117	−	0.729373i	$-0.739812\pi$
$569$	6.90797	−	11.9649i	0.289597	−	0.501597i	0.973714	+	0.227776i	$0.0731454\pi$
$570$		0			0
$571$	−5.21935	−	9.04019i	−0.218423	−	0.378320i	0.735903	−	0.677087i	$-0.236758\pi$
$571$	−5.21935	−	9.04019i	−0.218423	−	0.378320i	−0.954326	+	0.298767i	$0.903425\pi$
$572$	3.24352	+	5.61793i	0.135618	+	0.234898i
$573$		0			0
$574$		0			0
$575$	−9.46483			−0.394711
$576$		0			0
$577$	−25.4923			−1.06126			−0.530628	−	0.847605i	$-0.678044\pi$
$577$	−25.4923			−1.06126			−0.530628	+	0.847605i	$0.678044\pi$
$578$	7.93895	−	13.7507i	0.330217	−	0.571952i
$579$		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
$584$	−14.5021			−0.600100
$585$		0			0
$586$	28.4554			1.17548
$587$	−17.5168	+	30.3401i	−0.722998	+	1.25227i	0.236795	+	0.971560i	$0.423903\pi$
$587$	−17.5168	+	30.3401i	−0.722998	+	1.25227i	−0.959793	+	0.280709i	$0.909430\pi$
$588$		0			0
$589$	35.5769	+	61.6210i	1.46592	+	2.53905i
$590$	−0.259362	−	0.449228i	−0.0106778	−	0.0184944i
$591$		0			0
$592$	−1.80217	+	3.12146i	−0.0740689	+	0.128291i
$593$	−36.1292			−1.48365			−0.741824	−	0.670594i	$-0.766039\pi$
$593$	−36.1292			−1.48365			−0.741824	+	0.670594i	$0.766039\pi$
$594$		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	−0.892760	−	0.450532i	$-0.851234\pi$
$599$	−20.4742	−	35.4623i	−0.836552	−	1.44895i	0.0562080	−	0.998419i	$-0.482099\pi$
$600$		0			0
$601$	−12.8547	+	22.2650i	−0.524354	+	0.908207i	0.475244	+	0.879854i	$0.342360\pi$
$601$	−12.8547	+	22.2650i	−0.524354	+	0.908207i	−0.999598	+	0.0283533i	$0.990974\pi$
$602$		0			0
$603$		0			0
$604$	8.83620			0.359540
$605$	−0.00725978	+	0.0125743i	−0.000295152	+	0.000511218i
$606$		0			0
$607$	3.42258	+	5.92808i	0.138918	+	0.240613i	0.927087	−	0.374845i	$-0.122304\pi$
$607$	3.42258	+	5.92808i	0.138918	+	0.240613i	−0.788169	+	0.615459i	$0.788971\pi$
$608$	−15.8841	−	27.5121i	−0.644187	−	1.11576i
$609$		0			0
$610$	−0.329795	+	0.571222i	−0.0133530	+	0.0231281i
$611$	7.92493			0.320608
$612$		0			0
$613$	−29.1297			−1.17654			−0.588269	−	0.808666i	$-0.700190\pi$
$613$	−29.1297			−1.17654			−0.588269	+	0.808666i	$0.700190\pi$
$614$	−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
$619$	−4.43178	+	7.67606i	−0.178128	+	0.308527i	−0.941239	−	0.337740i	$-0.890337\pi$
$619$	−4.43178	+	7.67606i	−0.178128	+	0.308527i	0.763111	+	0.646267i	$0.223671\pi$
$620$	0.765607			0.0307475
$621$		0			0
$622$	−1.44453			−0.0579205
$623$		0			0
$624$		0			0
$625$	−12.4166	−	21.5062i	−0.496666	−	0.860250i
$626$	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
$635$	−0.0167248	−	0.0289681i	−0.000663702	−	0.00114957i
$636$		0			0
$637$		0			0
$638$	−34.1928			−1.35371
$639$		0			0
$640$	0.0810898			0.00320536
$641$	−8.26595	+	14.3171i	−0.326486	+	0.565489i	−0.981812	−	0.189856i	$-0.939198\pi$
$641$	−8.26595	+	14.3171i	−0.326486	+	0.565489i	0.655326	+	0.755346i	$0.272531\pi$
$642$		0			0
$643$	15.4460	+	26.7532i	0.609130	+	1.05504i	0.991384	+	0.130987i	$0.0418147\pi$
$643$	15.4460	+	26.7532i	0.609130	+	1.05504i	−0.382254	+	0.924057i	$0.624852\pi$
$644$		0			0
$645$		0			0
$646$	−6.83390	+	11.8367i	−0.268876	+	0.465707i
$647$	−1.29981			−0.0511007			−0.0255503	−	0.999674i	$-0.508134\pi$
$647$	−1.29981			−0.0511007			−0.0255503	+	0.999674i	$0.508134\pi$
$648$		0			0
$649$	−14.8840			−0.584247
$650$	−6.82209	+	11.8162i	−0.267584	+	0.463470i
$651$		0			0
$652$	3.51247	+	6.08377i	0.137559	+	0.238259i
$653$	−22.4435	−	38.8733i	−0.878281	−	1.52123i	−0.853226	−	0.521542i	$-0.825357\pi$
$653$	−22.4435	−	38.8733i	−0.878281	−	1.52123i	−0.0250558	−	0.999686i	$-0.507976\pi$
$654$		0			0
$655$	0.788692	−	1.36605i	0.0308167	−	0.0533762i
$656$	13.6088			0.531333
$657$		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	0.984924	+	0.172989i	$0.0553424\pi$
$661$	16.5128	+	28.6010i	0.642274	+	1.11245i	−0.342649	+	0.939463i	$0.611324\pi$
$662$	−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
$667$	17.6257			0.682469
$668$	−6.82561	+	11.8223i	−0.264091	+	0.457419i
$669$		0			0
$670$	−0.579885	−	1.00439i	−0.0224029	−	0.0388030i
$671$	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	$0.301669\pi$
$674$	−3.73729			−0.143955
$675$		0			0
$676$	5.36894			0.206498
$677$	−4.15084	+	7.18946i	−0.159530	+	0.276313i	−0.934699	−	0.355440i	$-0.884331\pi$
$677$	−4.15084	+	7.18946i	−0.159530	+	0.276313i	0.775170	+	0.631753i	$0.217664\pi$
$678$		0			0
$679$		0			0
$680$	0.261161	+	0.452344i	0.0100151	+	0.0173466i
$681$		0			0
$682$	−17.0434	+	29.5200i	−0.652625	+	1.13038i
$683$	−2.49456			−0.0954518			−0.0477259	−	0.998860i	$-0.515197\pi$
$683$	−2.49456			−0.0954518			−0.0477259	+	0.998860i	$0.515197\pi$
$684$		0			0
$685$	1.60808			0.0614414
$686$		0			0
$687$		0			0
$688$	6.86110	+	11.8838i	0.261577	+	0.453065i
$689$	12.3710	+	21.4271i	0.471296	+	0.816308i
$690$		0			0
$691$	−8.43455	+	14.6091i	−0.320865	+	0.555755i	−0.980667	−	0.195685i	$-0.937307\pi$
$691$	−8.43455	+	14.6091i	−0.320865	+	0.555755i	0.659801	+	0.751440i	$0.270640\pi$
$692$	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
$698$	−8.67266	−	15.0215i	−0.328265	−	0.568572i
$699$		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
$703$	−15.2312			−0.574454
$704$	13.6768	−	23.6889i	0.515464	−	0.892811i
$705$		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	−0.444188	−	0.895933i	$-0.646508\pi$
$709$	14.7462	−	25.5412i	0.553807	−	0.959222i	0.997995	−	0.0632882i	$-0.0201587\pi$
$710$	−0.382707			−0.0143628
$711$		0			0
$712$	−18.5108			−0.693721
$713$	8.78551	−	15.2169i	0.329020	−	0.569879i
$714$		0			0
$715$	−0.436438	−	0.755933i	−0.0163219	−	0.0282703i
$716$	3.98277	+	6.89836i	0.148843	+	0.257804i
$717$		0			0
$718$	4.37810	−	7.58310i	0.163389	−	0.282999i
$719$	−0.434622			−0.0162087			−0.00810433	−	0.999967i	$-0.502580\pi$
$719$	−0.434622			−0.0162087			−0.00810433	+	0.999967i	$0.502580\pi$
$720$		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	$0.334731\pi$
$727$	−13.5839	+	23.5280i	−0.503799	+	0.872605i	−0.999990	+	0.00439187i	$0.998602\pi$
$728$		0			0
$729$		0			0
$730$	0.549420			0.0203350
$731$	−6.08798	+	10.5447i	−0.225172	+	0.390009i
$732$		0			0
$733$	−2.83307	−	4.90702i	−0.104642	−	0.181245i	0.808950	−	0.587878i	$-0.200036\pi$
$733$	−2.83307	−	4.90702i	−0.104642	−	0.181245i	−0.913592	+	0.406632i	$0.866703\pi$
$734$	−7.25050	−	12.5582i	−0.267621	−	0.463533i
$735$		0			0
$736$	−3.92249	+	6.79395i	−0.144585	+	0.250428i
$737$	−33.2777			−1.22580
$738$		0			0
$739$	−13.6108			−0.500681			−0.250341	−	0.968158i	$-0.580543\pi$
$739$	−13.6108			−0.500681			−0.250341	+	0.968158i	$0.580543\pi$
$740$	−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
$745$	−0.587900	+	1.01827i	−0.0215390	+	0.0373066i
$746$	8.61393			0.315378
$747$		0			0
$748$	4.21977			0.154290
$749$		0			0
$750$		0			0
$751$	3.57269	+	6.18808i	0.130369	+	0.225806i	0.923819	−	0.382830i	$-0.125050\pi$
$751$	3.57269	+	6.18808i	0.130369	+	0.225806i	−0.793450	+	0.608636i	$0.791717\pi$
$752$	−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
$761$	−5.02358	−	8.70109i	−0.182104	−	0.315414i	0.760493	−	0.649347i	$-0.224958\pi$
$761$	−5.02358	−	8.70109i	−0.182104	−	0.315414i	−0.942597	+	0.333933i	$0.891624\pi$
$762$		0			0
$763$		0			0
$764$	−17.5572			−0.635196
$765$		0			0
$766$	−11.8352			−0.427625
$767$	5.53011	−	9.57843i	0.199681	−	0.345857i
$768$		0			0
$769$	−16.1463	−	27.9663i	−0.582252	−	1.00849i	−0.995212	−	0.0977407i	$-0.968838\pi$
$769$	−16.1463	−	27.9663i	−0.582252	−	1.00849i	0.412960	−	0.910749i	$-0.364495\pi$
$770$		0			0
$771$		0			0
$772$	−0.100635	+	0.174305i	−0.00362192	+	0.00627336i
$773$	−48.5878			−1.74758			−0.873792	−	0.486300i	$-0.838346\pi$
$773$	−48.5878			−1.74758			−0.873792	+	0.486300i	$0.838346\pi$
$774$		0			0
$775$	46.2051			1.65973
$776$	−5.83694	+	10.1099i	−0.209534	+	0.362923i
$777$		0			0
$778$	13.3147	+	23.0618i	0.477356	+	0.826806i
$779$	28.7538	+	49.8030i	1.03021	+	1.78438i
$780$		0			0
$781$	−5.49059	+	9.50998i	−0.196469	+	0.340294i
$782$	3.37518			0.120696
$783$		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	0.859370	+	0.511354i	$0.170856\pi$
$787$	24.4776	+	42.3964i	0.872531	+	1.51127i	0.0131602	+	0.999913i	$0.495811\pi$
$788$	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
$793$	−14.0638			−0.499419
$794$	13.2652	−	22.9759i	0.470763	−	0.815385i
$795$		0			0
$796$	−1.97174	−	3.41515i	−0.0698864	−	0.121047i
$797$	1.44417	+	2.50137i	0.0511550	+	0.0886030i	0.890469	−	0.455044i	$-0.150376\pi$
$797$	1.44417	+	2.50137i	0.0511550	+	0.0886030i	−0.839314	+	0.543647i	$0.817043\pi$
$798$		0			0
$799$	2.57755	−	4.46445i	0.0911873	−	0.157941i
$800$	−20.6293			−0.729356
$801$		0			0
$802$	1.72294			0.0608393
$803$	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
$808$	26.8169	−	46.4483i	0.943417	−	1.63405i
$809$	−11.6974			−0.411258			−0.205629	−	0.978630i	$-0.565924\pi$
$809$	−11.6974			−0.411258			−0.205629	+	0.978630i	$0.565924\pi$
$810$		0			0
$811$	17.1780			0.603199			0.301600	−	0.953435i	$-0.402479\pi$
$811$	17.1780			0.603199			0.301600	+	0.953435i	$0.402479\pi$
$812$		0			0
$813$		0			0
$814$	−3.64830	−	6.31904i	−0.127873	−	0.221482i
$815$	−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	−0.400208	−	0.916424i	$-0.631062\pi$
$821$	17.0068	−	29.4567i	0.593543	−	1.02805i	0.993751	−	0.111622i	$-0.0356045\pi$
$822$		0			0
$823$	−21.6890	−	37.5664i	−0.756031	−	1.30948i	−0.944860	−	0.327474i	$-0.893803\pi$
$823$	−21.6890	−	37.5664i	−0.756031	−	1.30948i	0.188829	−	0.982010i	$-0.439531\pi$
$824$	13.4037	+	23.2160i	0.466942	+	0.808767i
$825$		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
$829$	16.9167			0.587540			0.293770	−	0.955876i	$-0.405090\pi$
$829$	16.9167			0.587540			0.293770	+	0.955876i	$0.405090\pi$
$830$	−0.0679744	+	0.117735i	−0.00235943	+	0.00408665i
$831$		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
$836$	20.0963			0.695044
$837$		0			0
$838$	−6.58705			−0.227546
$839$	−8.16244	+	14.1378i	−0.281799	+	0.488089i	−0.971828	−	0.235692i	$-0.924264\pi$
$839$	−8.16244	+	14.1378i	−0.281799	+	0.488089i	0.690029	+	0.723782i	$0.257598\pi$
$840$		0			0
$841$	−28.6560	−	49.6336i	−0.988138	−	1.71150i
$842$	8.06812	+	13.9744i	0.278046	+	0.481589i
$843$		0			0
$844$	2.82590	−	4.89459i	0.0972713	−	0.168479i
$845$	−0.722428			−0.0248523
$846$		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	−0.505142	−	0.863036i	$-0.668560\pi$
$853$	14.4524	−	25.0323i	0.494841	−	0.857089i	0.999982	+	0.00594733i	$0.00189311\pi$
$854$		0			0
$855$		0			0
$856$	−55.7095			−1.90411
$857$	14.5284	−	25.1639i	0.496280	−	0.859582i	−0.503711	−	0.863872i	$-0.668032\pi$
$857$	14.5284	−	25.1639i	0.496280	−	0.859582i	0.999991	+	0.00429061i	$0.00136575\pi$
$858$		0			0
$859$	−6.29820	−	10.9088i	−0.214892	−	0.372203i	0.738347	−	0.674421i	$-0.235607\pi$
$859$	−6.29820	−	10.9088i	−0.214892	−	0.372203i	−0.953239	+	0.302217i	$0.902273\pi$
$860$	0.311966	+	0.540341i	0.0106380	+	0.0184255i
$861$		0			0
$862$	−10.6992	+	18.5315i	−0.364415	+	0.631185i
$863$	14.6662			0.499243			0.249621	−	0.968344i	$-0.419694\pi$
$863$	14.6662			0.499243			0.249621	+	0.968344i	$0.419694\pi$
$864$		0			0
$865$	−0.298398			−0.0101458
$866$	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
$871$	12.3643	−	21.4156i	0.418948	−	0.725639i
$872$	12.9631			0.438985
$873$		0			0
$874$	16.0740			0.543711
$875$		0			0
$876$		0			0
$877$	−16.5951	−	28.7435i	−0.560376	−	0.970600i	−0.997463	−	0.0711811i	$-0.977323\pi$
$877$	−16.5951	−	28.7435i	−0.560376	−	0.970600i	0.437087	−	0.899419i	$-0.356010\pi$
$878$	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	$-0.679425\pi$
$881$	−31.7179			−1.06860			−0.534301	+	0.845294i	$0.679425\pi$
$882$		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
$887$	−24.9513	−	43.2169i	−0.837782	−	1.45108i	−0.891745	−	0.452538i	$-0.850519\pi$
$887$	−24.9513	−	43.2169i	−0.837782	−	1.45108i	0.0539627	−	0.998543i	$-0.482815\pi$
$888$		0			0
$889$		0			0
$890$	0.701292			0.0235074
$891$		0			0
$892$	8.76457			0.293459
$893$	12.2754	−	21.2616i	0.410779	−	0.711491i
$894$		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
$899$	−86.0443			−2.86974
$900$		0			0
$901$	16.0944			0.536183
$902$	−13.7747	+	23.8585i	−0.458648	+	0.794401i
$903$		0			0
$904$	3.15671	+	5.46757i	0.104990	+	0.181849i
$905$	0.901048	+	1.56066i	0.0299518	+	0.0518781i
$906$		0			0
$907$	6.96080	−	12.0565i	0.231129	−	0.400328i	−0.727011	−	0.686625i	$-0.759091\pi$
$907$	6.96080	−	12.0565i	0.231129	−	0.400328i	0.958141	+	0.286298i	$0.0924246\pi$
$908$	18.6315			0.618308
$909$		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
$919$	34.0283			1.12249			0.561245	−	0.827649i	$-0.310322\pi$
$919$	34.0283			1.12249			0.561245	+	0.827649i	$0.310322\pi$
$920$	0.307138	−	0.531978i	0.0101260	−	0.0175388i
$921$		0			0
$922$	4.40781	+	7.63455i	0.145163	+	0.251430i
$923$	−4.08004	−	7.06683i	−0.134296	−	0.232608i
$924$		0			0
$925$	−4.94531	+	8.56554i	−0.162601	+	0.281633i
$926$	−11.5637			−0.380006
$927$		0			0
$928$	38.4165			1.26108
$929$	−5.31646	+	9.20837i	−0.174427	+	0.302117i	−0.939963	−	0.341277i	$-0.889141\pi$
$929$	−5.31646	+	9.20837i	−0.174427	+	0.302117i	0.765536	+	0.643393i	$0.222474\pi$
$930$		0			0
$931$		0			0
$932$	−2.56375	−	4.44055i	−0.0839785	−	0.145455i
$933$		0			0
$934$	−12.0746	+	20.9137i	−0.395092	+	0.684319i
$935$	−0.567799			−0.0185690
$936$		0			0
$937$	−52.6692			−1.72063			−0.860314	−	0.509765i	$-0.829732\pi$
$937$	−52.6692			−1.72063			−0.860314	+	0.509765i	$0.829732\pi$
$938$		0			0
$939$		0			0
$940$	−0.132082	−	0.228772i	−0.00430802	−	0.00746172i
$941$	17.1828	+	29.7615i	0.560143	+	0.970197i	0.997483	+	0.0709006i	$0.0225873\pi$
$941$	17.1828	+	29.7615i	0.560143	+	0.970197i	−0.437340	+	0.899296i	$0.644079\pi$
$942$		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	0.321370	+	0.946954i	$0.395857\pi$
$947$	−20.2920	+	35.1468i	−0.659401	+	1.14212i	−0.980771	+	0.195162i	$0.937477\pi$
$948$		0			0
$949$	5.85736	+	10.1453i	0.190138	+	0.329329i
$950$	21.1342	+	36.6056i	0.685685	+	1.18764i
$951$		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
$955$	2.36244			0.0764468
$956$	8.36589	−	14.4901i	0.270572	−	0.468645i
$957$		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
$962$	5.42208			0.174815
$963$		0			0
$964$	15.7279			0.506562
$965$	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	$0.960982\pi$
$968$	0.211325	+	0.366026i	0.00679224	+	0.0117645i
$969$		0			0
$970$	0.221136	−	0.383019i	0.00710025	−	0.0122980i
$971$	45.5771			1.46264			0.731319	−	0.682035i	$-0.238905\pi$
$971$	45.5771			1.46264			0.731319	+	0.682035i	$0.238905\pi$
$972$		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	0.724286	−	0.689500i	$-0.242170\pi$
$977$	−7.34481	−	12.7216i	−0.234981	−	0.407000i	−0.959267	+	0.282500i	$0.908836\pi$
$978$		0			0
$979$	10.0612	−	17.4266i	0.321558	−	0.556956i
$980$		0			0
$981$		0			0
$982$	31.3528			1.00051
$983$	22.2955	−	38.6169i	0.711115	−	1.23169i	−0.253324	−	0.967381i	$-0.581524\pi$
$983$	22.2955	−	38.6169i	0.711115	−	1.23169i	0.964439	−	0.264305i	$-0.0851427\pi$
$984$		0			0
$985$	−0.0402548	−	0.0697234i	−0.00128262	−	0.00222157i
$986$	−8.26404	−	14.3137i	−0.263181	−	0.455842i
$987$		0			0
$988$	−7.46673	+	12.9328i	−0.237548	+	0.411446i
$989$	14.3195			0.455334
$990$		0			0
$991$	24.1829			0.768196			0.384098	−	0.923292i	$-0.374512\pi$
$991$	24.1829			0.768196			0.384098	+	0.923292i	$0.374512\pi$
$992$	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
$997$	−5.43262	+	9.40957i	−0.172053	+	0.298004i	−0.939137	−	0.343542i	$-0.888373\pi$
$997$	−5.43262	+	9.40957i	−0.172053	+	0.298004i	0.767085	+	0.641546i	$0.221707\pi$
$998$	−8.19521			−0.259415
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	9.5	odd	6
441.2.f.h.148.8	yes	24	63.41	even	6
441.2.f.h.295.7	yes	24	3.2	odd	2
441.2.f.h.295.8	yes	24	21.20	even	2
441.2.g.h.67.7		24	63.5	even	6
441.2.g.h.67.8		24	63.23	odd	6
441.2.g.h.79.7		24	21.17	even	6
441.2.g.h.79.8		24	21.11	odd	6
441.2.h.h.214.5		24	21.5	even	6
441.2.h.h.214.6		24	21.2	odd	6
441.2.h.h.373.5		24	63.59	even	6
441.2.h.h.373.6		24	63.32	odd	6
1323.2.f.h.442.5		24	63.13	odd	6	inner
1323.2.f.h.442.6		24	9.4	even	3	inner
1323.2.f.h.883.5		24	7.6	odd	2	inner
1323.2.f.h.883.6		24	1.1	even	1	trivial
1323.2.g.h.361.5		24	63.40	odd	6
1323.2.g.h.361.6		24	63.58	even	3
1323.2.g.h.667.5		24	7.3	odd	6
1323.2.g.h.667.6		24	7.4	even	3
1323.2.h.h.226.7		24	63.4	even	3
1323.2.h.h.226.8		24	63.31	odd	6
1323.2.h.h.802.7		24	7.2	even	3
1323.2.h.h.802.8		24	7.5	odd	6
3969.2.a.bh.1.5		12	9.2	odd	6
3969.2.a.bh.1.6		12	63.20	even	6
3969.2.a.bi.1.7		12	63.34	odd	6
3969.2.a.bi.1.8		12	9.7	even	3

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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.551407 + 0.955065i) q^{2} +(0.391901 + 0.678793i) q^{4} +(-0.0527330 - 0.0913363i) q^{5} -3.07001 q^{8} +O(q^{10})\)	\(q+(-0.551407 + 0.955065i) q^{2} +(0.391901 + 0.678793i) q^{4} +(-0.0527330 - 0.0913363i) q^{5} -3.07001 q^{8} +0.116309 q^{10} +(1.66866 - 2.89020i) q^{11} +(1.23997 + 2.14770i) q^{13} +(0.909025 - 1.57448i) q^{16} +1.61319 q^{17} +7.68266 q^{19} +(0.0413323 - 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} +(-0.948593 - 1.64301i) q^{23} +(2.49444 - 4.32049i) q^{25} -2.73492 q^{26} +(-4.64521 + 8.04574i) q^{29} +(4.63081 + 8.02080i) q^{31} +(-2.06753 - 3.58107i) q^{32} +(-0.889523 + 1.54070i) q^{34} -1.98254 q^{37} +(-4.23627 + 7.33744i) q^{38} +(0.161891 + 0.280404i) q^{40} +(3.74268 + 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +2.61579 q^{44} +2.09224 q^{46} +(1.59780 - 2.76747i) q^{47} +(2.75090 + 4.76470i) q^{50} +(-0.971894 + 1.68337i) q^{52} +9.97679 q^{53} -0.351974 q^{55} +(-5.12280 - 8.87296i) q^{58} +(-2.22993 - 3.86235i) q^{59} +(-2.83550 + 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(0.130775 - 0.226509i) q^{65} +(-4.98571 - 8.63550i) q^{67} +(0.632210 + 1.09502i) q^{68} -3.29042 q^{71} +4.72378 q^{73} +(1.09318 - 1.89345i) q^{74} +(3.01084 + 5.21493i) q^{76} +(-3.84705 + 6.66328i) q^{79} -0.191743 q^{80} -8.25496 q^{82} +(-0.584428 + 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} +(-4.16189 - 7.20860i) q^{86} +(-5.12280 + 8.87296i) q^{88} +6.02954 q^{89} +(0.743509 - 1.28780i) q^{92} +(1.76208 + 3.05201i) q^{94} +(-0.405130 - 0.701706i) q^{95} +(1.90127 - 3.29310i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more