LMFDB - Embedded newform 1323.2.h.h.226.7

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			226.7
Character	$\chi$	$=$	1323.226
Dual form			1323.2.h.h.802.7

$q$-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	0.853993	−	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
$10$	−0.0581547	−	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	−0.641248	−	0.767334i	$-0.721583\pi$
$13$	1.23997	−	2.14770i	0.343907	−	0.595664i	0.985155	+	0.171670i	$0.0549162\pi$
$14$		0			0
$15$		0			0
$16$	−1.81805			−0.454512
$17$	−0.806594	−	1.39706i	−0.195628	−	0.338837i	0.751478	−	0.659758i	$-0.229341\pi$
$17$	−0.806594	−	1.39706i	−0.195628	−	0.338837i	−0.947106	+	0.320921i	$0.896008\pi$
$18$		0			0
$19$	−3.84133	+	6.65338i	−0.881262	+	1.52639i	−0.0313221	+	0.999509i	$0.509972\pi$
$19$	−3.84133	+	6.65338i	−0.881262	+	1.52639i	−0.849939	+	0.526880i	$0.823362\pi$
$20$	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	$-0.812642\pi$
$31$	−9.26162			−1.66344			−0.831718	+	0.555199i	$0.812642\pi$
$32$	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	$-0.634621\pi$
$41$	3.74268	−	6.48252i	0.584509	−	1.01240i	0.994936	−	0.100506i	$-0.0320462\pi$
$42$		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	$-0.574875\pi$
$47$	−3.19560			−0.466127			−0.233063	+	0.972462i	$0.574875\pi$
$48$		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	$-0.406241\pi$
$59$	4.45986			0.580625			0.290312	+	0.956932i	$0.406241\pi$
$60$		0			0
$61$	5.67100			0.726097			0.363048	−	0.931770i	$-0.381736\pi$
$61$	5.67100			0.726097			0.363048	+	0.931770i	$0.381736\pi$
$62$	−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	0.694059	−	0.719919i	$-0.255821\pi$
$73$	−2.36189	−	4.09091i	−0.276438	−	0.478805i	−0.970497	+	0.241113i	$0.922488\pi$
$74$	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	0.832167	−	0.554525i	$-0.187100\pi$
$83$	−0.584428	−	1.01226i	−0.0641493	−	0.111110i	−0.896316	+	0.443415i	$0.853767\pi$
$84$		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	−0.980397	−	0.197031i	$-0.936870\pi$
$89$	−3.01477	+	5.22173i	−0.319565	+	0.553503i	0.660832	+	0.750534i	$0.270203\pi$
$90$		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	0.946258	−	0.323413i	$-0.104830\pi$
$97$	1.90127	+	3.29310i	0.193045	+	0.334364i	−0.753213	+	0.657777i	$0.771497\pi$
$98$		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	$0.502017\pi$
$101$	−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
$107$	−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	$0.0599786\pi$
$131$	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
$136$	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	−0.640913	−	0.767614i	$-0.721444\pi$
$139$	4.05943	−	7.03114i	0.344316	−	0.596374i	0.985229	+	0.171240i	$0.0547774\pi$
$140$		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	$-0.338060\pi$
$157$	12.2064			0.974173			0.487087	+	0.873354i	$0.338060\pi$
$158$	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	$-0.597964\pi$
$167$	8.70833	−	15.0833i	0.673871	−	1.16718i	0.976798	−	0.214165i	$-0.0687030\pi$
$168$		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	$-0.534302\pi$
$173$	−2.82933			−0.215110			−0.107555	+	0.994199i	$0.534302\pi$
$174$		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	$-0.719013\pi$
$181$	−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
$185$	−0.209090			−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	0.941307	−	0.337550i	$-0.109598\pi$
$199$	2.51561	+	4.35716i	0.178327	+	0.308871i	−0.762981	+	0.646421i	$0.776265\pi$
$200$	−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	0.990238	−	0.139388i	$-0.0445137\pi$
$223$	5.59106	+	9.68400i	0.374405	+	0.648488i	−0.615833	+	0.787877i	$0.711180\pi$
$224$		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	$-0.544007\pi$
$227$	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
$233$	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	$-0.609654\pi$
$241$	10.0331	−	17.3778i	0.646288	−	1.11940i	0.984003	−	0.178155i	$-0.0570127\pi$
$242$	−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	$-0.431002\pi$
$251$	6.81467			0.430138			0.215069	+	0.976599i	$0.431002\pi$
$252$		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	0.549546	−	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
$262$	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	$-0.871255\pi$
$269$	−13.1285	−	22.7393i	−0.800461	−	1.38644i	0.118852	−	0.992912i	$-0.462079\pi$
$270$		0			0
$271$	−8.96673	+	15.5308i	−0.544690	+	0.943431i	0.453936	+	0.891034i	$0.350019\pi$
$271$	−8.96673	+	15.5308i	−0.544690	+	0.943431i	−0.998626	+	0.0523969i	$0.983314\pi$
$272$	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	$-0.348745\pi$
$283$	15.3927			0.915000			0.457500	+	0.889210i	$0.348745\pi$
$284$	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	$0.438399\pi$
$293$	−12.9013	+	22.3456i	−0.753700	+	1.30545i	−0.946018	+	0.324114i	$0.894934\pi$
$294$		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	$-0.280538\pi$
$307$	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
$311$	−1.30986			−0.0742755			−0.0371377	−	0.999310i	$-0.511824\pi$
$311$	−1.30986			−0.0742755			−0.0371377	+	0.999310i	$0.511824\pi$
$312$		0			0
$313$	−21.5770			−1.21960			−0.609802	−	0.792554i	$-0.708751\pi$
$313$	−21.5770			−1.21960			−0.609802	+	0.792554i	$0.708751\pi$
$314$	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	0.575076	−	0.818100i	$-0.304972\pi$
$349$	−7.86412	−	13.6211i	−0.420957	−	0.729119i	−0.996033	+	0.0889810i	$0.971639\pi$
$350$		0			0
$351$		0			0
$352$	6.90000	−	11.9511i	0.367771	−	0.636998i
$353$	2.07211	−	3.58900i	0.110287	−	0.191023i	−0.805599	−	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
$359$	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	−0.985023	−	0.172423i	$-0.944840\pi$
$367$	−6.57455	+	11.3875i	−0.343189	+	0.594420i	0.641834	+	0.766843i	$0.278174\pi$
$368$	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	0.969930	−	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
$388$	−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	$-0.627029\pi$
$397$	12.0285	−	20.8339i	0.603691	−	1.04562i	0.992257	−	0.124203i	$-0.0396373\pi$
$398$	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	$-0.313689\pi$
$409$	22.3456			1.10492			0.552460	+	0.833539i	$0.313689\pi$
$410$	−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	−0.783809	−	0.621002i	$-0.786726\pi$
$419$	2.98648	−	5.17273i	0.145899	−	0.252704i	0.929708	+	0.368298i	$0.120059\pi$
$420$		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	$-0.510344\pi$
$433$	−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
$437$	14.5754			0.697238
$438$		0			0
$439$	−17.3412			−0.827650			−0.413825	−	0.910356i	$-0.635807\pi$
$439$	−17.3412			−0.827650			−0.413825	+	0.910356i	$0.635807\pi$
$440$	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	0.943964	−	0.330047i	$-0.107065\pi$
$461$	3.99687	+	6.92279i	0.186153	+	0.322426i	−0.757811	+	0.652474i	$0.773731\pi$
$462$		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	$0.335784\pi$
$467$	−10.9489	+	18.9640i	−0.506653	+	0.877549i	−0.999970	+	0.00769944i	$0.997549\pi$
$468$		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	−0.908109	−	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
$485$	0.200520	−	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	$-0.572738\pi$
$503$	−10.1610			−0.453057			−0.226529	+	0.974004i	$0.572738\pi$
$504$		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	$-0.945342\pi$
$509$	−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
$514$	−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	$0.0986883\pi$
$521$	16.8995	+	29.2708i	0.740381	+	1.28238i	−0.211941	+	0.977283i	$0.567978\pi$
$522$		0			0
$523$	7.18895	−	12.4516i	0.314351	−	0.544471i	−0.664949	−	0.746889i	$-0.731547\pi$
$523$	7.18895	−	12.4516i	0.314351	−	0.544471i	0.979299	+	0.202418i	$0.0648799\pi$
$524$	−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	$-0.816691\pi$
$563$	−39.8013			−1.67743			−0.838713	+	0.544574i	$0.816691\pi$
$564$		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	$0.0113773\pi$
$577$	12.7461	+	22.0769i	0.530628	+	0.919075i	−0.468733	+	0.883340i	$0.655289\pi$
$578$	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	$-0.909430\pi$
$587$	−17.5168	−	30.3401i	−0.722998	−	1.25227i	0.236795	−	0.971560i	$-0.423903\pi$
$588$		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	$-0.567294\pi$
$593$	18.0646	−	31.2888i	0.741824	−	1.28488i	0.951664	−	0.307141i	$-0.0993724\pi$
$594$		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	$-0.990974\pi$
$601$	−12.8547	−	22.2650i	−0.524354	−	0.908207i	0.475244	−	0.879854i	$-0.342360\pi$
$602$		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	0.927087	−	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
$611$	−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	−0.941239	−	0.337740i	$-0.890337\pi$
$619$	−4.43178	+	7.67606i	−0.178128	+	0.308527i	0.763111	+	0.646267i	$0.223671\pi$
$620$	−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	$-0.624852\pi$
$643$	15.4460	−	26.7532i	0.609130	−	1.05504i	0.991384	−	0.130987i	$-0.0418147\pi$
$644$		0			0
$645$		0			0
$646$	13.6678			0.537752
$647$	0.649903	+	1.12567i	0.0255503	+	0.0442545i	0.878518	−	0.477710i	$-0.158533\pi$
$647$	0.649903	+	1.12567i	0.0255503	+	0.0442545i	−0.852968	+	0.521964i	$0.825200\pi$
$648$		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	$-0.722009\pi$
$661$	−33.0256			−1.28455			−0.642274	+	0.766475i	$0.722009\pi$
$662$	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	$-0.449002\pi$
$677$	8.30167			0.319059			0.159530	+	0.987193i	$0.449002\pi$
$678$		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	$-0.396026\pi$
$691$	16.8691			0.641731			0.320865	+	0.947125i	$0.396026\pi$
$692$	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	−0.861945	−	0.507002i	$-0.830754\pi$
$719$	0.217311	−	0.376394i	0.00810433	−	0.0140371i	0.870049	+	0.492965i	$0.164087\pi$
$720$		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	$-0.998602\pi$
$727$	−13.5839	−	23.5280i	−0.503799	−	0.872605i	0.496192	−	0.868213i	$-0.334731\pi$
$728$		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	0.808950	−	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
$737$	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	0.760493	−	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
$766$	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	$0.364495\pi$
$769$	−16.1463	+	27.9663i	−0.582252	+	1.00849i	−0.995212	+	0.0977407i	$0.968838\pi$
$770$		0			0
$771$		0			0
$772$	0.201270			0.00724385
$773$	24.2939	+	42.0783i	0.873792	+	1.51345i	0.858044	+	0.513576i	$0.171679\pi$
$773$	24.2939	+	42.0783i	0.873792	+	1.51345i	0.0157473	+	0.999876i	$0.494987\pi$
$774$		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	$-0.837522\pi$
$787$	−48.9551			−1.74506			−0.872531	+	0.488560i	$0.837522\pi$
$788$	−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	−0.839314	−	0.543647i	$-0.817043\pi$
$797$	1.44417	−	2.50137i	0.0511550	−	0.0886030i	0.890469	+	0.455044i	$0.150376\pi$
$798$		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	$-0.402479\pi$
$811$	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
$815$	0.945254			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	0.680928	−	0.732350i	$-0.261577\pi$
$829$	−8.45833	−	14.6503i	−0.293770	−	0.508824i	−0.974698	+	0.223526i	$0.928243\pi$
$830$	−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	0.690029	−	0.723782i	$-0.257598\pi$
$839$	−8.16244	−	14.1378i	−0.281799	−	0.488089i	−0.971828	+	0.235692i	$0.924264\pi$
$840$		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	0.999982	−	0.00594733i	$-0.00189311\pi$
$853$	14.4524	+	25.0323i	0.494841	+	0.857089i	−0.505142	+	0.863036i	$0.668560\pi$
$854$		0			0
$855$		0			0
$856$	27.8547	−	48.2458i	0.952055	−	1.64901i
$857$	14.5284	−	25.1639i	0.496280	−	0.859582i	−0.503711	−	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
$863$	−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	$-0.679425\pi$
$881$	−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	$0.731581\pi$
$884$	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	$-0.850519\pi$
$887$	−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
$892$	−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	$-0.444193\pi$
$929$	10.6329			0.348855			0.174427	+	0.984670i	$0.444193\pi$
$930$		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	$-0.829732\pi$
$937$	−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
$941$	−34.3656			−1.12029			−0.560143	−	0.828396i	$-0.689254\pi$
$941$	−34.3656			−1.12029			−0.560143	+	0.828396i	$0.689254\pi$
$942$		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	$0.427762\pi$
$971$	−22.7886	+	39.4709i	−0.731319	+	1.26668i	−0.956319	+	0.292324i	$0.905572\pi$
$972$		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	$-0.581524\pi$
$983$	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
$989$	−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	−0.939137	−	0.343542i	$-0.888373\pi$
$997$	−5.43262	+	9.40957i	−0.172053	+	0.298004i	0.767085	+	0.641546i	$0.221707\pi$
$998$	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.226.7		24
3.2	odd	2		441.2.h.h.373.6		24
7.2	even	3		1323.2.f.h.442.6		24
7.3	odd	6		1323.2.g.h.361.5		24
7.4	even	3		1323.2.g.h.361.6		24
7.5	odd	6		1323.2.f.h.442.5		24
7.6	odd	2	inner	1323.2.h.h.226.8		24
9.2	odd	6		441.2.g.h.79.8		24
9.7	even	3		1323.2.g.h.667.6		24
21.2	odd	6		441.2.f.h.148.7	✓	24
21.5	even	6		441.2.f.h.148.8	yes	24
21.11	odd	6		441.2.g.h.67.8		24
21.17	even	6		441.2.g.h.67.7		24
21.20	even	2		441.2.h.h.373.5		24
63.2	odd	6		441.2.f.h.295.7	yes	24
63.5	even	6		3969.2.a.bh.1.6		12
63.11	odd	6		441.2.h.h.214.6		24
63.16	even	3		1323.2.f.h.883.6		24
63.20	even	6		441.2.g.h.79.7		24
63.23	odd	6		3969.2.a.bh.1.5		12
63.25	even	3	inner	1323.2.h.h.802.7		24
63.34	odd	6		1323.2.g.h.667.5		24
63.38	even	6		441.2.h.h.214.5		24
63.40	odd	6		3969.2.a.bi.1.7		12
63.47	even	6		441.2.f.h.295.8	yes	24
63.52	odd	6	inner	1323.2.h.h.802.8		24
63.58	even	3		3969.2.a.bi.1.8		12
63.61	odd	6		1323.2.f.h.883.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	21.2	odd	6
441.2.f.h.148.8	yes	24	21.5	even	6
441.2.f.h.295.7	yes	24	63.2	odd	6
441.2.f.h.295.8	yes	24	63.47	even	6
441.2.g.h.67.7		24	21.17	even	6
441.2.g.h.67.8		24	21.11	odd	6
441.2.g.h.79.7		24	63.20	even	6
441.2.g.h.79.8		24	9.2	odd	6
441.2.h.h.214.5		24	63.38	even	6
441.2.h.h.214.6		24	63.11	odd	6
441.2.h.h.373.5		24	21.20	even	2
441.2.h.h.373.6		24	3.2	odd	2
1323.2.f.h.442.5		24	7.5	odd	6
1323.2.f.h.442.6		24	7.2	even	3
1323.2.f.h.883.5		24	63.61	odd	6
1323.2.f.h.883.6		24	63.16	even	3
1323.2.g.h.361.5		24	7.3	odd	6
1323.2.g.h.361.6		24	7.4	even	3
1323.2.g.h.667.5		24	63.34	odd	6
1323.2.g.h.667.6		24	9.7	even	3
1323.2.h.h.226.7		24	1.1	even	1	trivial
1323.2.h.h.226.8		24	7.6	odd	2	inner
1323.2.h.h.802.7		24	63.25	even	3	inner
1323.2.h.h.802.8		24	63.52	odd	6	inner
3969.2.a.bh.1.5		12	63.23	odd	6
3969.2.a.bh.1.6		12	63.5	even	6
3969.2.a.bi.1.7		12	63.40	odd	6
3969.2.a.bi.1.8		12	63.58	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.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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more