LMFDB - Embedded newform 1323.2.h.h.226.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (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			226.8
Character	$\chi$	$=$	1323.226
Dual form			1323.2.h.h.802.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.10281 q^{2} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} -3.07001 q^{8} +O(q^{10})$	\(q+1.10281 q^{2} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} -3.07001 q^{8} +(0.0581547 + 0.100727i) q^{10} +(1.66866 - 2.89020i) q^{11} +(-1.23997 + 2.14770i) q^{13} -1.81805 q^{16} +(0.806594 + 1.39706i) q^{17} +(3.84133 - 6.65338i) q^{19} +(-0.0413323 - 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +(-0.948593 - 1.64301i) q^{23} +(2.49444 - 4.32049i) q^{25} +(-1.36746 + 2.36851i) q^{26} +(-4.64521 - 8.04574i) q^{29} +9.26162 q^{31} +4.13506 q^{32} +(0.889523 + 1.54070i) q^{34} +(0.991268 - 1.71693i) q^{37} +(4.23627 - 7.33744i) q^{38} +(-0.161891 - 0.280404i) q^{40} +(-3.74268 + 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} +(-1.30790 + 2.26534i) q^{44} +(-1.04612 - 1.81194i) q^{46} +3.19560 q^{47} +(2.75090 - 4.76470i) q^{50} +(0.971894 - 1.68337i) q^{52} +(-4.98839 - 8.64015i) q^{53} +0.351974 q^{55} +(-5.12280 - 8.87296i) q^{58} -4.45986 q^{59} -5.67100 q^{61} +10.2138 q^{62} +8.19630 q^{64} -0.261550 q^{65} +9.97141 q^{67} +(-0.632210 - 1.09502i) q^{68} -3.29042 q^{71} +(2.36189 + 4.09091i) q^{73} +(1.09318 - 1.89345i) q^{74} +(-3.01084 + 5.21493i) q^{76} +7.69409 q^{79} +(-0.0958713 - 0.166054i) q^{80} +(-4.12748 + 7.14901i) q^{82} +(0.584428 + 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +(-4.16189 - 7.20860i) q^{86} +(-5.12280 + 8.87296i) q^{88} +(3.01477 - 5.22173i) q^{89} +(0.743509 + 1.28780i) q^{92} +3.52415 q^{94} +0.810260 q^{95} +(-1.90127 - 3.29310i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.10281			0.779807			0.389903	−	0.920856i	$-0.372508\pi$
$2$	1.10281			0.779807			0.389903	+	0.920856i	$0.372508\pi$
$3$		0			0
$3$		0			0
$4$	−0.783802			−0.391901
$5$	0.0527330	+	0.0913363i	0.0235829	+	0.0408468i	0.877576	−	0.479438i	$-0.159159\pi$
$5$	0.0527330	+	0.0913363i	0.0235829	+	0.0408468i	−0.853993	+	0.520284i	$0.825826\pi$
$6$		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
$11$	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	$-0.945084\pi$
$13$	−1.23997	+	2.14770i	−0.343907	+	0.595664i	0.641248	+	0.767334i	$0.278417\pi$
$14$		0			0
$15$		0			0
$16$	−1.81805			−0.454512
$17$	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
$23$	−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
$26$	−1.36746	+	2.36851i	−0.268181	+	0.464503i
$27$		0			0
$28$		0			0
$29$	−4.64521	−	8.04574i	−0.862594	−	1.49406i	−0.869416	−	0.494080i	$-0.835505\pi$
$29$	−4.64521	−	8.04574i	−0.862594	−	1.49406i	0.00682200	−	0.999977i	$-0.497828\pi$
$30$		0			0
$31$	9.26162			1.66344			0.831718	−	0.555199i	$-0.187358\pi$
$31$	9.26162			1.66344			0.831718	+	0.555199i	$0.187358\pi$
$32$	4.13506			0.730982
$33$		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	$0.114561\pi$
$38$	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	0.410427	+	0.911893i	$0.365379\pi$
$41$	−3.74268	+	6.48252i	−0.584509	+	1.01240i	−0.994936	+	0.100506i	$0.967954\pi$
$42$		0			0
$43$	−3.77388	−	6.53655i	−0.575512	−	0.996815i	−0.995986	−	0.0895108i	$-0.971470\pi$
$43$	−3.77388	−	6.53655i	−0.575512	−	0.996815i	0.420474	−	0.907304i	$-0.361864\pi$
$44$	−1.30790	+	2.26534i	−0.197173	+	0.341514i
$45$		0			0
$46$	−1.04612	−	1.81194i	−0.154242	−	0.267155i
$47$	3.19560			0.466127			0.233063	−	0.972462i	$-0.425125\pi$
$47$	3.19560			0.466127			0.233063	+	0.972462i	$0.425125\pi$
$48$		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
$53$	−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
$58$	−5.12280	−	8.87296i	−0.672657	−	1.16508i
$59$	−4.45986			−0.580625			−0.290312	−	0.956932i	$-0.593759\pi$
$59$	−4.45986			−0.580625			−0.290312	+	0.956932i	$0.593759\pi$
$60$		0			0
$61$	−5.67100			−0.726097			−0.363048	−	0.931770i	$-0.618264\pi$
$61$	−5.67100			−0.726097			−0.363048	+	0.931770i	$0.618264\pi$
$62$	10.2138			1.29716
$63$		0			0
$64$	8.19630			1.02454
$65$	−0.261550			−0.0324413
$66$		0			0
$67$	9.97141			1.21820			0.609101	−	0.793093i	$-0.291530\pi$
$67$	9.97141			1.21820			0.609101	+	0.793093i	$0.291530\pi$
$68$	−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
$73$	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	$0.744179\pi$
$74$	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
$79$	7.69409			0.865653			0.432827	−	0.901477i	$-0.357516\pi$
$79$	7.69409			0.865653			0.432827	+	0.901477i	$0.357516\pi$
$80$	−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	0.896316	−	0.443415i	$-0.146233\pi$
$83$	0.584428	+	1.01226i	0.0641493	+	0.111110i	−0.832167	+	0.554525i	$0.812900\pi$
$84$		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
$89$	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
$94$	3.52415			0.363489
$95$	0.810260			0.0831309
$96$		0			0
$97$	−1.90127	−	3.29310i	−0.193045	−	0.334364i	0.753213	−	0.657777i	$-0.228503\pi$
$97$	−1.90127	−	3.29310i	−0.193045	−	0.334364i	−0.946258	+	0.323413i	$0.895170\pi$
$98$		0			0
$99$		0			0
$100$	−1.95515	+	3.38641i	−0.195515	+	0.338641i
$101$	8.73512	−	15.1297i	0.869177	−	1.50546i	0.00633771	−	0.999980i	$-0.497983\pi$
$101$	8.73512	−	15.1297i	0.869177	−	1.50546i	0.862839	−	0.505479i	$-0.168684\pi$
$102$		0			0
$103$	4.36602	+	7.56217i	0.430197	+	0.745123i	0.996890	−	0.0788062i	$-0.0251108\pi$
$103$	4.36602	+	7.56217i	0.430197	+	0.745123i	−0.566693	+	0.823929i	$0.691777\pi$
$104$	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	$0.768518\pi$
$110$	0.388161			0.0370097
$111$		0			0
$112$		0			0
$113$	−1.02824	+	1.78096i	−0.0967285	+	0.167539i	−0.910329	−	0.413886i	$-0.864171\pi$
$113$	−1.02824	+	1.78096i	−0.0967285	+	0.167539i	0.813600	+	0.581425i	$0.197505\pi$
$114$		0			0
$115$	0.100044	−	0.173282i	0.00932919	−	0.0161586i
$116$	3.64093	+	6.30627i	0.338052	+	0.585523i
$117$		0			0
$118$	−4.91840			−0.452775
$119$		0			0
$120$		0			0
$121$	−0.0688352	−	0.119226i	−0.00625774	−	0.0108387i
$122$	−6.25405			−0.566215
$123$		0			0
$124$	−7.25928			−0.651902
$125$	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	$0.495521\pi$
$128$	0.768871			0.0679592
$129$		0			0
$130$	−0.288441			−0.0252980
$131$	−7.47816	−	12.9525i	−0.653370	−	1.13167i	−0.982300	−	0.187315i	$-0.940021\pi$
$131$	−7.47816	−	12.9525i	−0.653370	−	1.13167i	0.328930	−	0.944354i	$-0.393312\pi$
$132$		0			0
$133$		0			0
$134$	10.9966			0.949962
$135$		0			0
$136$	−2.47625	−	4.28900i	−0.212337	−	0.367779i
$137$	−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	$-0.945223\pi$
$139$	−4.05943	+	7.03114i	−0.344316	+	0.596374i	0.640913	+	0.767614i	$0.278556\pi$
$140$		0			0
$141$		0			0
$142$	−3.62872			−0.304516
$143$	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
$149$	−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	$0.0149774\pi$
$152$	−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
$157$	−12.2064			−0.974173			−0.487087	−	0.873354i	$-0.661940\pi$
$157$	−12.2064			−0.974173			−0.487087	+	0.873354i	$0.661940\pi$
$158$	8.48515			0.675042
$159$		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	$0.280826\pi$
$164$	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	0.302927	+	0.953014i	$0.402036\pi$
$167$	−8.70833	+	15.0833i	−0.673871	+	1.16718i	−0.976798	+	0.214165i	$0.931297\pi$
$168$		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
$173$	2.82933			0.215110			0.107555	−	0.994199i	$-0.465698\pi$
$173$	2.82933			0.215110			0.107555	+	0.994199i	$0.465698\pi$
$174$		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
$179$	−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
$184$	2.91220	+	5.04407i	0.214690	+	0.371854i
$185$	0.209090			0.0153726
$186$		0			0
$187$	5.38371			0.393696
$188$	−2.50472			−0.182676
$189$		0			0
$190$	0.893566			0.0648261
$191$	22.4000			1.62081			0.810404	−	0.585872i	$-0.199248\pi$
$191$	22.4000			1.62081			0.810404	+	0.585872i	$0.199248\pi$
$192$		0			0
$193$	−0.256786			−0.0184839			−0.00924194	−	0.999957i	$-0.502942\pi$
$193$	−0.256786			−0.0184839			−0.00924194	+	0.999957i	$0.502942\pi$
$194$	−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
$199$	−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	$0.890402\pi$
$200$	−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
$205$	−0.789452			−0.0551377
$206$	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	−0.963027	−	0.269403i	$-0.913174\pi$
$211$	−3.60537	+	6.24468i	−0.248204	+	0.429901i	0.714824	+	0.699305i	$0.246507\pi$
$212$	3.90991	+	6.77217i	0.268534	+	0.465114i
$213$		0			0
$214$	−10.0060	+	17.3309i	−0.683996	+	1.18472i
$215$	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
$220$	−0.275878			−0.0185997
$221$	−4.00062			−0.269111
$222$		0			0
$223$	−5.59106	−	9.68400i	−0.374405	−	0.648488i	0.615833	−	0.787877i	$-0.288820\pi$
$223$	−5.59106	−	9.68400i	−0.374405	−	0.648488i	−0.990238	+	0.139388i	$0.955486\pi$
$224$		0			0
$225$		0			0
$226$	−1.13395	+	1.96407i	−0.0754295	+	0.130648i
$227$	−11.8853	+	20.5860i	−0.788857	+	1.36634i	0.137811	+	0.990459i	$0.455993\pi$
$227$	−11.8853	+	20.5860i	−0.788857	+	1.36634i	−0.926668	+	0.375881i	$0.877340\pi$
$228$		0			0
$229$	−0.952737	−	1.65019i	−0.0629586	−	0.109048i	0.832828	−	0.553532i	$-0.186720\pi$
$229$	−0.952737	−	1.65019i	−0.0629586	−	0.109048i	−0.895787	+	0.444484i	$0.853387\pi$
$230$	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
$236$	3.49565			0.227547
$237$		0			0
$238$		0			0
$239$	−10.6735	+	18.4870i	−0.690409	+	1.19582i	0.281295	+	0.959621i	$0.409236\pi$
$239$	−10.6735	+	18.4870i	−0.690409	+	1.19582i	−0.971704	+	0.236202i	$0.924097\pi$
$240$		0			0
$241$	−10.0331	+	17.3778i	−0.646288	+	1.11940i	0.337715	+	0.941248i	$0.390346\pi$
$241$	−10.0331	+	17.3778i	−0.646288	+	1.11940i	−0.984003	+	0.178155i	$0.942987\pi$
$242$	−0.0759124	−	0.131484i	−0.00487983	−	0.00845212i
$243$		0			0
$244$	4.44494			0.284558
$245$		0			0
$246$		0			0
$247$	9.52629	+	16.5000i	0.606144	+	1.04987i
$248$	−28.4333			−1.80552
$249$		0			0
$250$	1.16180			0.0734787
$251$	−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
$254$	0.349767			0.0219464
$255$		0			0
$256$	−15.5447			−0.971542
$257$	7.19415	+	12.4606i	0.448759	+	0.777273i	0.998306	−	0.0581897i	$-0.0185328\pi$
$257$	7.19415	+	12.4606i	0.448759	+	0.777273i	−0.549546	+	0.835463i	$0.685199\pi$
$258$		0			0
$259$		0			0
$260$	0.205004			0.0127138
$261$		0			0
$262$	−8.24701	−	14.2842i	−0.509502	−	0.882484i
$263$	−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
$268$	−7.81562			−0.477415
$269$	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
$275$	−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	$-0.0252032\pi$
$278$	−4.47680	+	7.75404i	−0.268500	+	0.465056i
$279$		0			0
$280$		0			0
$281$	2.49578	+	4.32283i	0.148886	+	0.257878i	0.930816	−	0.365488i	$-0.119098\pi$
$281$	2.49578	+	4.32283i	0.148886	+	0.257878i	−0.781930	+	0.623366i	$0.785765\pi$
$282$		0			0
$283$	−15.3927			−0.915000			−0.457500	−	0.889210i	$-0.651255\pi$
$283$	−15.3927			−0.915000			−0.457500	+	0.889210i	$0.651255\pi$
$284$	2.57904			0.153038
$285$		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
$290$	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	−0.192318	−	0.981333i	$-0.561601\pi$
$293$	12.9013	−	22.3456i	0.753700	−	1.30545i	0.946018	−	0.324114i	$-0.105066\pi$
$294$		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
$299$	4.70492			0.272093
$300$		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
$305$	−0.299049	−	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
$310$	0.538607	+	0.932894i	0.0305908	+	0.0529848i
$311$	1.30986			0.0742755			0.0371377	−	0.999310i	$-0.488176\pi$
$311$	1.30986			0.0742755			0.0371377	+	0.999310i	$0.488176\pi$
$312$		0			0
$313$	21.5770			1.21960			0.609802	−	0.792554i	$-0.291249\pi$
$313$	21.5770			1.21960			0.609802	+	0.792554i	$0.291249\pi$
$314$	−13.4613			−0.759667
$315$		0			0
$316$	−6.03065			−0.339250
$317$	24.7819			1.39189			0.695946	−	0.718094i	$-0.254985\pi$
$317$	24.7819			1.39189			0.695946	+	0.718094i	$0.254985\pi$
$318$		0			0
$319$	−31.0051			−1.73595
$320$	0.432216	+	0.748620i	0.0241616	+	0.0418491i
$321$		0			0
$322$		0			0
$323$	12.3936			0.689597
$324$		0			0
$325$	6.18608	+	10.7146i	0.343142	+	0.594339i
$326$	−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
$331$	13.8451			0.760996			0.380498	−	0.924782i	$-0.375753\pi$
$331$	13.8451			0.760996			0.380498	+	0.924782i	$0.375753\pi$
$332$	−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	−0.816178	−	0.577801i	$-0.803911\pi$
$337$	1.69444	−	2.93485i	0.0923018	−	0.159871i	0.908479	+	0.417930i	$0.137244\pi$
$338$	3.77706	+	6.54206i	0.205445	+	0.355841i
$339$		0			0
$340$	0.0666767	−	0.115487i	0.00361605	−	0.00626319i
$341$	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
$346$	3.12022			0.167744
$347$	14.5148			0.779195			0.389597	−	0.920985i	$-0.372614\pi$
$347$	14.5148			0.779195			0.389597	+	0.920985i	$0.372614\pi$
$348$		0			0
$349$	7.86412	+	13.6211i	0.420957	+	0.729119i	0.996033	−	0.0889810i	$-0.0283610\pi$
$349$	7.86412	+	13.6211i	0.420957	+	0.729119i	−0.575076	+	0.818100i	$0.695028\pi$
$350$		0			0
$351$		0			0
$352$	6.90000	−	11.9511i	0.367771	−	0.636998i
$353$	−2.07211	+	3.58900i	−0.110287	+	0.191023i	−0.915886	−	0.401438i	$-0.868510\pi$
$353$	−2.07211	+	3.58900i	−0.110287	+	0.191023i	0.805599	+	0.592462i	$0.201844\pi$
$354$		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
$359$	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
$362$	18.8437			0.990405
$363$		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	−0.641834	−	0.766843i	$-0.721826\pi$
$367$	6.57455	−	11.3875i	0.343189	−	0.594420i	0.985023	+	0.172423i	$0.0551596\pi$
$368$	1.72459	+	2.98708i	0.0899004	+	0.155712i
$369$		0			0
$370$	0.230588			0.0119877
$371$		0			0
$372$		0			0
$373$	−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	$0.898147\pi$
$374$	5.93723			0.307007
$375$		0			0
$376$	−9.81055			−0.505940
$377$	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	$0.801604\pi$
$380$	−0.635084			−0.0325791
$381$		0			0
$382$	24.7030			1.26392
$383$	−5.36593	−	9.29407i	−0.274186	−	0.474905i	0.695743	−	0.718291i	$-0.255075\pi$
$383$	−5.36593	−	9.29407i	−0.274186	−	0.474905i	−0.969930	+	0.243386i	$0.921742\pi$
$384$		0			0
$385$		0			0
$386$	−0.283187			−0.0144139
$387$		0			0
$388$	1.49022	+	2.58114i	0.0756546	+	0.131038i
$389$	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
$394$	0.841854			0.0424120
$395$	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
$401$	−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
$404$	−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
$409$	−22.3456			−1.10492			−0.552460	−	0.833539i	$-0.686311\pi$
$409$	−22.3456			−1.10492			−0.552460	+	0.833539i	$0.686311\pi$
$410$	−0.870619			−0.0429968
$411$		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
$416$	−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	$-0.879941\pi$
$419$	−2.98648	+	5.17273i	−0.145899	+	0.252704i	0.783809	+	0.621002i	$0.213274\pi$
$420$		0			0
$421$	7.31594	+	12.6716i	0.356557	+	0.617575i	0.987383	−	0.158349i	$-0.0506172\pi$
$421$	7.31594	+	12.6716i	0.356557	+	0.617575i	−0.630826	+	0.775924i	$0.717284\pi$
$422$	−3.97605	+	6.88672i	−0.193551	+	0.335240i
$423$		0			0
$424$	15.3144	+	26.5254i	0.743735	+	1.28819i
$425$	8.04799			0.390385
$426$		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
$431$	−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
$436$	−1.65480	−	2.86619i	−0.0792503	−	0.137266i
$437$	−14.5754			−0.697238
$438$		0			0
$439$	17.3412			0.827650			0.413825	−	0.910356i	$-0.364193\pi$
$439$	17.3412			0.827650			0.413825	+	0.910356i	$0.364193\pi$
$440$	−1.08056			−0.0515139
$441$		0			0
$442$	−4.41194			−0.209854
$443$	−19.6100			−0.931698			−0.465849	−	0.884864i	$-0.654251\pi$
$443$	−19.6100			−0.931698			−0.465849	+	0.884864i	$0.654251\pi$
$444$		0			0
$445$	0.635912			0.0301451
$446$	−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
$451$	12.4905	+	21.6342i	0.588155	+	1.01871i
$452$	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
$457$	0.485451			0.0227084			0.0113542	−	0.999936i	$-0.496386\pi$
$457$	0.485451			0.0227084			0.0113542	+	0.999936i	$0.496386\pi$
$458$	−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	0.757811	−	0.652474i	$-0.226269\pi$
$461$	−3.99687	−	6.92279i	−0.186153	−	0.322426i	−0.943964	+	0.330047i	$0.892935\pi$
$462$		0			0
$463$	5.24280	−	9.08080i	0.243654	−	0.422021i	−0.718098	−	0.695942i	$-0.754987\pi$
$463$	5.24280	−	9.08080i	0.243654	−	0.422021i	0.961752	+	0.273921i	$0.0883206\pi$
$464$	8.44523	+	14.6276i	0.392060	+	0.679068i
$465$		0			0
$466$	3.60721	−	6.24788i	0.167101	−	0.289427i
$467$	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
$472$	13.6918			0.630218
$473$	−25.1893			−1.15820
$474$		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
$479$	2.00085	−	3.46557i	0.0914210	−	0.158346i	−0.816688	−	0.577079i	$-0.804192\pi$
$479$	2.00085	−	3.46557i	0.0914210	−	0.158346i	0.908109	+	0.418733i	$0.137526\pi$
$480$		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
$485$	0.200520	−	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	$0.628557\pi$
$488$	17.4100			0.788116
$489$		0			0
$490$		0			0
$491$	−14.2149	+	24.6210i	−0.641511	+	1.11113i	0.343584	+	0.939122i	$0.388359\pi$
$491$	−14.2149	+	24.6210i	−0.641511	+	1.11113i	−0.985096	+	0.172008i	$0.944975\pi$
$492$		0			0
$493$	7.49360	−	12.9793i	0.337495	−	0.584558i
$494$	10.5057	+	18.1965i	0.472675	+	0.818697i
$495$		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	$0.780141\pi$
$500$	−0.825726			−0.0369276
$501$		0			0
$502$	−7.51531			−0.335425
$503$	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
$506$	−6.98247			−0.310409
$507$		0			0
$508$	−0.248590			−0.0110294
$509$	14.4532	+	25.0336i	0.640625	+	1.10960i	0.985293	+	0.170871i	$0.0546581\pi$
$509$	14.4532	+	25.0336i	0.640625	+	1.10960i	−0.344668	+	0.938725i	$0.612009\pi$
$510$		0			0
$511$		0			0
$512$	−18.6806			−0.825575
$513$		0			0
$514$	7.93381	+	13.7418i	0.349945	+	0.606123i
$515$	−0.460467	+	0.797553i	−0.0202906	+	0.0351444i
$516$		0			0
$517$	5.33237	−	9.23593i	0.234517	−	0.406196i
$518$		0			0
$519$		0			0
$520$	0.802963			0.0352123
$521$	−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
$527$	7.47036	+	12.9390i	0.325414	+	0.563634i
$528$		0			0
$529$	9.70034	−	16.8015i	0.421754	−	0.730499i
$530$	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
$535$	−1.91382			−0.0827417
$536$	−30.6124			−1.32225
$537$		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	$-0.0153669\pi$
$542$	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	0.898016	−	0.439963i	$-0.145009\pi$
$547$	1.59011	+	2.75416i	0.0679883	+	0.117759i	−0.830027	+	0.557723i	$0.811675\pi$
$548$	5.97545	−	10.3498i	0.255258	−	0.442121i
$549$		0			0
$550$	−9.18062	−	15.9013i	−0.391463	−	0.678034i
$551$	−71.3752			−3.04068
$552$		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
$557$	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
$562$	2.75238	+	4.76727i	0.116102	+	0.201095i
$563$	39.8013			1.67743			0.838713	−	0.544574i	$-0.183309\pi$
$563$	39.8013			1.67743			0.838713	+	0.544574i	$0.183309\pi$
$564$		0			0
$565$	−0.216888			−0.00912457
$566$	−16.9753			−0.713523
$567$		0			0
$568$	10.1017			0.423856
$569$	−13.8159			−0.579194			−0.289597	−	0.957149i	$-0.593521\pi$
$569$	−13.8159			−0.579194			−0.289597	+	0.957149i	$0.593521\pi$
$570$		0			0
$571$	10.4387			0.436846			0.218423	−	0.975854i	$-0.429909\pi$
$571$	10.4387			0.436846			0.218423	+	0.975854i	$0.429909\pi$
$572$	−3.24352	−	5.61793i	−0.135618	−	0.234898i
$573$		0			0
$574$		0			0
$575$	−9.46483			−0.394711
$576$		0			0
$577$	−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	$-0.344711\pi$
$578$	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
$583$	−33.2957			−1.37897
$584$	−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	0.959793	+	0.280709i	$0.0905697\pi$
$587$	17.5168	+	30.3401i	0.722998	+	1.25227i	−0.236795	+	0.971560i	$0.576097\pi$
$588$		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
$593$	−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
$598$	5.18865			0.212180
$599$	40.9484			1.67310			0.836552	−	0.547887i	$-0.184568\pi$
$599$	40.9484			1.67310			0.836552	+	0.547887i	$0.184568\pi$
$600$		0			0
$601$	12.8547	+	22.2650i	0.524354	+	0.908207i	0.999598	+	0.0283533i	$0.00902635\pi$
$601$	12.8547	+	22.2650i	0.524354	+	0.908207i	−0.475244	+	0.879854i	$0.657640\pi$
$602$		0			0
$603$		0			0
$604$	−4.41810	+	7.65238i	−0.179770	+	0.311371i
$605$	0.00725978	−	0.0125743i	0.000295152	−	0.000511218i
$606$		0			0
$607$	−3.42258	−	5.92808i	−0.138918	−	0.240613i	0.788169	−	0.615459i	$-0.211029\pi$
$607$	−3.42258	−	5.92808i	−0.138918	−	0.240613i	−0.927087	+	0.374845i	$0.877696\pi$
$608$	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	$0.633143\pi$
$614$	−24.5833			−0.992101
$615$		0			0
$616$		0			0
$617$	10.3395	−	17.9085i	0.416252	−	0.720969i	−0.579307	−	0.815109i	$-0.696677\pi$
$617$	10.3395	−	17.9085i	0.416252	−	0.720969i	0.995559	+	0.0941404i	$0.0300102\pi$
$618$		0			0
$619$	4.43178	−	7.67606i	0.178128	−	0.308527i	−0.763111	−	0.646267i	$-0.776329\pi$
$619$	4.43178	−	7.67606i	0.178128	−	0.308527i	0.941239	+	0.337740i	$0.109663\pi$
$620$	−0.382804	−	0.663035i	−0.0153738	−	0.0266281i
$621$		0			0
$622$	1.44453			0.0579205
$623$		0			0
$624$		0			0
$625$	−12.4166	−	21.5062i	−0.496666	−	0.860250i
$626$	23.7954			0.951055
$627$		0			0
$628$	9.56737			0.381779
$629$	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	$0.323392\pi$
$632$	−23.6210			−0.939592
$633$		0			0
$634$	27.3299			1.08541
$635$	0.0167248	+	0.0289681i	0.000663702	+	0.00114957i
$636$		0			0
$637$		0			0
$638$	−34.1928			−1.35371
$639$		0			0
$640$	0.0405449	+	0.0702258i	0.00160268	+	0.00277592i
$641$	−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	0.382254	+	0.924057i	$0.375148\pi$
$643$	−15.4460	+	26.7532i	−0.609130	+	1.05504i	−0.991384	+	0.130987i	$0.958185\pi$
$644$		0			0
$645$		0			0
$646$	13.6678			0.537752
$647$	−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
$653$	−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
$656$	6.80438	−	11.7855i	0.265667	−	0.460148i
$657$		0			0
$658$		0			0
$659$	−8.96167	−	15.5221i	−0.349097	−	0.604654i	0.636992	−	0.770870i	$-0.280178\pi$
$659$	−8.96167	−	15.5221i	−0.349097	−	0.604654i	−0.986089	+	0.166216i	$0.946845\pi$
$660$		0			0
$661$	33.0256			1.28455			0.642274	−	0.766475i	$-0.277991\pi$
$661$	33.0256			1.28455			0.642274	+	0.766475i	$0.277991\pi$
$662$	15.2686			0.593430
$663$		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
$668$	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	0.583536	−	0.812087i	$-0.301669\pi$
$673$	−10.6758	−	18.4909i	−0.411520	−	0.712774i	−0.995056	+	0.0993135i	$0.968335\pi$
$674$	1.86865	−	3.23659i	0.0719776	−	0.124669i
$675$		0			0
$676$	−2.68447	−	4.64964i	−0.103249	−	0.178832i
$677$	−8.30167			−0.319059			−0.159530	−	0.987193i	$-0.550998\pi$
$677$	−8.30167			−0.319059			−0.159530	+	0.987193i	$0.550998\pi$
$678$		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
$683$	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
$688$	6.86110	+	11.8838i	0.261577	+	0.453065i
$689$	24.7419			0.942591
$690$		0			0
$691$	−16.8691			−0.641731			−0.320865	−	0.947125i	$-0.603974\pi$
$691$	−16.8691			−0.641731			−0.320865	+	0.947125i	$0.603974\pi$
$692$	−2.21763			−0.0843017
$693$		0			0
$694$	16.0071			0.607621
$695$	−0.856265			−0.0324800
$696$		0			0
$697$	−12.0753			−0.457385
$698$	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
$703$	−7.61558	−	13.1906i	−0.287227	−	0.497492i
$704$	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
$709$	−29.4925			−1.10761			−0.553807	−	0.832645i	$-0.686825\pi$
$709$	−29.4925			−1.10761			−0.553807	+	0.832645i	$0.686825\pi$
$710$	−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
$716$	3.98277	+	6.89836i	0.148843	+	0.257804i
$717$		0			0
$718$	4.37810	−	7.58310i	0.163389	−	0.282999i
$719$	−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
$724$	−13.3928			−0.497740
$725$	−46.3488			−1.72135
$726$		0			0
$727$	13.5839	+	23.5280i	0.503799	+	0.872605i	0.999990	+	0.00439187i	$0.00139798\pi$
$727$	13.5839	+	23.5280i	0.503799	+	0.872605i	−0.496192	+	0.868213i	$0.665269\pi$
$728$		0			0
$729$		0			0
$730$	−0.274710	+	0.475812i	−0.0101675	+	0.0176106i
$731$	6.08798	−	10.5447i	0.225172	−	0.390009i
$732$		0			0
$733$	2.83307	+	4.90702i	0.104642	+	0.181245i	0.913592	−	0.406632i	$-0.133297\pi$
$733$	2.83307	+	4.90702i	0.104642	+	0.181245i	−0.808950	+	0.587878i	$0.799964\pi$
$734$	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	$0.752791\pi$
$740$	−0.163885			−0.00602455
$741$		0			0
$742$		0			0
$743$	6.33421	−	10.9712i	0.232380	−	0.402493i	−0.726128	−	0.687559i	$-0.758682\pi$
$743$	6.33421	−	10.9712i	0.232380	−	0.402493i	0.958508	+	0.285066i	$0.0920155\pi$
$744$		0			0
$745$	0.587900	−	1.01827i	0.0215390	−	0.0373066i
$746$	−4.30696	−	7.45988i	−0.157689	−	0.273126i
$747$		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	$0.791717\pi$
$752$	−5.80977			−0.211860
$753$		0			0
$754$	25.4086			0.925325
$755$	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	$0.260192\pi$
$758$	−34.8651			−1.26636
$759$		0			0
$760$	−2.48751			−0.0902315
$761$	5.02358	+	8.70109i	0.182104	+	0.315414i	0.942597	−	0.333933i	$-0.108376\pi$
$761$	5.02358	+	8.70109i	0.182104	+	0.315414i	−0.760493	+	0.649347i	$0.775042\pi$
$762$		0			0
$763$		0			0
$764$	−17.5572			−0.635196
$765$		0			0
$766$	−5.91762	−	10.2496i	−0.213812	−	0.370334i
$767$	5.53011	−	9.57843i	0.199681	−	0.345857i
$768$		0			0
$769$	16.1463	−	27.9663i	0.582252	−	1.00849i	−0.412960	−	0.910749i	$-0.635505\pi$
$769$	16.1463	−	27.9663i	0.582252	−	1.00849i	0.995212	−	0.0977407i	$-0.0311616\pi$
$770$		0			0
$771$		0			0
$772$	0.201270			0.00724385
$773$	−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
$779$	28.7538	+	49.8030i	1.03021	+	1.78438i
$780$		0			0
$781$	−5.49059	+	9.50998i	−0.196469	+	0.340294i
$782$	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
$787$	48.9551			1.74506			0.872531	−	0.488560i	$-0.162478\pi$
$787$	48.9551			1.74506			0.872531	+	0.488560i	$0.162478\pi$
$788$	−0.598331			−0.0213147
$789$		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
$794$	−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	$-0.849624\pi$
$797$	−1.44417	+	2.50137i	−0.0511550	+	0.0886030i	0.839314	+	0.543647i	$0.182957\pi$
$798$		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
$803$	15.7647			0.556326
$804$		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
$809$	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
$814$	−3.64830	−	6.31904i	−0.127873	−	0.221482i
$815$	−0.945254			−0.0331108
$816$		0			0
$817$	−57.9869			−2.02870
$818$	−24.6431			−0.861624
$819$		0			0
$820$	0.618775			0.0216085
$821$	−34.0137			−1.18709			−0.593543	−	0.804803i	$-0.702271\pi$
$821$	−34.0137			−1.18709			−0.593543	+	0.804803i	$0.702271\pi$
$822$		0			0
$823$	43.3780			1.51206			0.756031	−	0.654536i	$-0.227136\pi$
$823$	43.3780			1.51206			0.756031	+	0.654536i	$0.227136\pi$
$824$	−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
$829$	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	$0.738423\pi$
$830$	−0.0679744	+	0.117735i	−0.00235943	+	0.00408665i
$831$		0			0
$832$	−10.1632	+	17.6032i	−0.352345	+	0.610280i
$833$		0			0
$834$		0			0
$835$	−1.83687			−0.0635674
$836$	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	0.971828	−	0.235692i	$-0.0757357\pi$
$839$	8.16244	+	14.1378i	0.281799	+	0.488089i	−0.690029	+	0.723782i	$0.742402\pi$
$840$		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
$845$	−0.361214	+	0.625641i	−0.0124261	+	0.0215227i
$846$		0			0
$847$		0			0
$848$	9.06915	+	15.7082i	0.311436	+	0.539423i
$849$		0			0
$850$	8.87544			0.304425
$851$	−3.76124			−0.128934
$852$		0			0
$853$	−14.4524	−	25.0323i	−0.494841	−	0.857089i	0.505142	−	0.863036i	$-0.331440\pi$
$853$	−14.4524	−	25.0323i	−0.494841	−	0.857089i	−0.999982	+	0.00594733i	$0.998107\pi$
$854$		0			0
$855$		0			0
$856$	27.8547	−	48.2458i	0.952055	−	1.64901i
$857$	−14.5284	+	25.1639i	−0.496280	+	0.859582i	−0.999991	−	0.00429061i	$-0.998634\pi$
$857$	−14.5284	+	25.1639i	−0.496280	+	0.859582i	0.503711	+	0.863872i	$0.331968\pi$
$858$		0			0
$859$	6.29820	+	10.9088i	0.214892	+	0.372203i	0.953239	−	0.302217i	$-0.0977268\pi$
$859$	6.29820	+	10.9088i	0.214892	+	0.372203i	−0.738347	+	0.674421i	$0.764393\pi$
$860$	−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
$866$	1.49119			0.0506726
$867$		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
$872$	−6.48154	−	11.2264i	−0.219493	−	0.380172i
$873$		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	$-0.356010\pi$
$878$	19.1241			0.645407
$879$		0			0
$880$	−0.639905			−0.0215712
$881$	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	$0.731581\pi$
$884$	3.13569			0.105465
$885$		0			0
$886$	−21.6262			−0.726545
$887$	24.9513	+	43.2169i	0.837782	+	1.45108i	0.891745	+	0.452538i	$0.149481\pi$
$887$	24.9513	+	43.2169i	0.837782	+	1.45108i	−0.0539627	+	0.998543i	$0.517185\pi$
$888$		0			0
$889$		0			0
$890$	0.701292			0.0235074
$891$		0			0
$892$	4.38228	+	7.59034i	0.146730	+	0.254143i
$893$	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
$898$	19.5578			0.652653
$899$	−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
$905$	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	$0.0924246\pi$
$908$	9.31574	−	16.1353i	0.309154	−	0.535470i
$909$		0			0
$910$		0			0
$911$	−2.70428	−	4.68394i	−0.0895967	−	0.155186i	0.817744	−	0.575582i	$-0.195224\pi$
$911$	−2.70428	−	4.68394i	−0.0895967	−	0.155186i	−0.907341	+	0.420396i	$0.861891\pi$
$912$		0			0
$913$	3.90084			0.129099
$914$	0.535362			0.0177082
$915$		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	$0.976989\pi$
$920$	−0.307138	+	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
$926$	5.78184	−	10.0144i	0.190003	−	0.329095i
$927$		0			0
$928$	−19.2082	−	33.2696i	−0.630541	−	1.09213i
$929$	−10.6329			−0.348855			−0.174427	−	0.984670i	$-0.555807\pi$
$929$	−10.6329			−0.348855			−0.174427	+	0.984670i	$0.555807\pi$
$930$		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
$935$	0.283900	+	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
$940$	−0.132082	−	0.228772i	−0.00430802	−	0.00746172i
$941$	34.3656			1.12029			0.560143	−	0.828396i	$-0.310746\pi$
$941$	34.3656			1.12029			0.560143	+	0.828396i	$0.310746\pi$
$942$		0			0
$943$	14.2011			0.462453
$944$	8.10825			0.263901
$945$		0			0
$946$	−27.7791			−0.903175
$947$	40.5840			1.31880			0.659401	−	0.751791i	$-0.270810\pi$
$947$	40.5840			1.31880			0.659401	+	0.751791i	$0.270810\pi$
$948$		0			0
$949$	−11.7147			−0.380276
$950$	−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
$955$	1.18122	+	2.04593i	0.0382234	+	0.0662049i
$956$	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
$961$	54.7775			1.76702
$962$	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	−0.992497	−	0.122273i	$-0.960982\pi$
$967$	−12.1388	+	21.0250i	−0.390357	+	0.676118i	0.602139	+	0.798391i	$0.294315\pi$
$968$	0.211325	+	0.366026i	0.00679224	+	0.0117645i
$969$		0			0
$970$	0.221136	−	0.383019i	0.00710025	−	0.0122980i
$971$	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
$976$	10.3102			0.330020
$977$	14.6896			0.469963			0.234981	−	0.972000i	$-0.424497\pi$
$977$	14.6896			0.469963			0.234981	+	0.972000i	$0.424497\pi$
$978$		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
$983$	−22.2955	+	38.6169i	−0.711115	+	1.23169i	0.253324	+	0.967381i	$0.418476\pi$
$983$	−22.2955	+	38.6169i	−0.711115	+	1.23169i	−0.964439	+	0.264305i	$0.914857\pi$
$984$		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
$989$	−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	$0.958821\pi$
$992$	38.2973			1.21594
$993$		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	−0.767085	−	0.641546i	$-0.778293\pi$
$997$	5.43262	−	9.40957i	0.172053	−	0.298004i	0.939137	+	0.343542i	$0.111627\pi$
$998$	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.h.h.226.8		24
3.2	odd	2		441.2.h.h.373.5		24
7.2	even	3		1323.2.f.h.442.5		24
7.3	odd	6		1323.2.g.h.361.6		24
7.4	even	3		1323.2.g.h.361.5		24
7.5	odd	6		1323.2.f.h.442.6		24
7.6	odd	2	inner	1323.2.h.h.226.7		24
9.2	odd	6		441.2.g.h.79.7		24
9.7	even	3		1323.2.g.h.667.5		24
21.2	odd	6		441.2.f.h.148.8	yes	24
21.5	even	6		441.2.f.h.148.7	✓	24
21.11	odd	6		441.2.g.h.67.7		24
21.17	even	6		441.2.g.h.67.8		24
21.20	even	2		441.2.h.h.373.6		24
63.2	odd	6		441.2.f.h.295.8	yes	24
63.5	even	6		3969.2.a.bh.1.5		12
63.11	odd	6		441.2.h.h.214.5		24
63.16	even	3		1323.2.f.h.883.5		24
63.20	even	6		441.2.g.h.79.8		24
63.23	odd	6		3969.2.a.bh.1.6		12
63.25	even	3	inner	1323.2.h.h.802.8		24
63.34	odd	6		1323.2.g.h.667.6		24
63.38	even	6		441.2.h.h.214.6		24
63.40	odd	6		3969.2.a.bi.1.8		12
63.47	even	6		441.2.f.h.295.7	yes	24
63.52	odd	6	inner	1323.2.h.h.802.7		24
63.58	even	3		3969.2.a.bi.1.7		12
63.61	odd	6		1323.2.f.h.883.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	21.5	even	6
441.2.f.h.148.8	yes	24	21.2	odd	6
441.2.f.h.295.7	yes	24	63.47	even	6
441.2.f.h.295.8	yes	24	63.2	odd	6
441.2.g.h.67.7		24	21.11	odd	6
441.2.g.h.67.8		24	21.17	even	6
441.2.g.h.79.7		24	9.2	odd	6
441.2.g.h.79.8		24	63.20	even	6
441.2.h.h.214.5		24	63.11	odd	6
441.2.h.h.214.6		24	63.38	even	6
441.2.h.h.373.5		24	3.2	odd	2
441.2.h.h.373.6		24	21.20	even	2
1323.2.f.h.442.5		24	7.2	even	3
1323.2.f.h.442.6		24	7.5	odd	6
1323.2.f.h.883.5		24	63.16	even	3
1323.2.f.h.883.6		24	63.61	odd	6
1323.2.g.h.361.5		24	7.4	even	3
1323.2.g.h.361.6		24	7.3	odd	6
1323.2.g.h.667.5		24	9.7	even	3
1323.2.g.h.667.6		24	63.34	odd	6
1323.2.h.h.226.7		24	7.6	odd	2	inner
1323.2.h.h.226.8		24	1.1	even	1	trivial
1323.2.h.h.802.7		24	63.52	odd	6	inner
1323.2.h.h.802.8		24	63.25	even	3	inner
3969.2.a.bh.1.5		12	63.5	even	6
3969.2.a.bh.1.6		12	63.23	odd	6
3969.2.a.bi.1.7		12	63.58	even	3
3969.2.a.bi.1.8		12	63.40	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.10281 q^{2} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} -3.07001 q^{8} +O(q^{10})\)	\(q+1.10281 q^{2} -0.783802 q^{4} +(0.0527330 + 0.0913363i) q^{5} -3.07001 q^{8} +(0.0581547 + 0.100727i) q^{10} +(1.66866 - 2.89020i) q^{11} +(-1.23997 + 2.14770i) q^{13} -1.81805 q^{16} +(0.806594 + 1.39706i) q^{17} +(3.84133 - 6.65338i) q^{19} +(-0.0413323 - 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +(-0.948593 - 1.64301i) q^{23} +(2.49444 - 4.32049i) q^{25} +(-1.36746 + 2.36851i) q^{26} +(-4.64521 - 8.04574i) q^{29} +9.26162 q^{31} +4.13506 q^{32} +(0.889523 + 1.54070i) q^{34} +(0.991268 - 1.71693i) q^{37} +(4.23627 - 7.33744i) q^{38} +(-0.161891 - 0.280404i) q^{40} +(-3.74268 + 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} +(-1.30790 + 2.26534i) q^{44} +(-1.04612 - 1.81194i) q^{46} +3.19560 q^{47} +(2.75090 - 4.76470i) q^{50} +(0.971894 - 1.68337i) q^{52} +(-4.98839 - 8.64015i) q^{53} +0.351974 q^{55} +(-5.12280 - 8.87296i) q^{58} -4.45986 q^{59} -5.67100 q^{61} +10.2138 q^{62} +8.19630 q^{64} -0.261550 q^{65} +9.97141 q^{67} +(-0.632210 - 1.09502i) q^{68} -3.29042 q^{71} +(2.36189 + 4.09091i) q^{73} +(1.09318 - 1.89345i) q^{74} +(-3.01084 + 5.21493i) q^{76} +7.69409 q^{79} +(-0.0958713 - 0.166054i) q^{80} +(-4.12748 + 7.14901i) q^{82} +(0.584428 + 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +(-4.16189 - 7.20860i) q^{86} +(-5.12280 + 8.87296i) q^{88} +(3.01477 - 5.22173i) q^{89} +(0.743509 + 1.28780i) q^{92} +3.52415 q^{94} +0.810260 q^{95} +(-1.90127 - 3.29310i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Introduction

L-functions

Modular forms

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Database

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