LMFDB - Embedded newform 441.2.g.h.79.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.7
Character	$\chi$	$=$	441.79
Dual form			441.2.g.h.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.551407 + 0.955065i) q^{2} +(-0.454745 - 1.67129i) q^{3} +(0.391901 - 0.678793i) q^{4} +0.105466 q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-2.58641 + 1.52002i) q^{9} +O(q^{10})$	\(q+(0.551407 + 0.955065i) q^{2} +(-0.454745 - 1.67129i) q^{3} +(0.391901 - 0.678793i) q^{4} +0.105466 q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-2.58641 + 1.52002i) q^{9} +(0.0581547 + 0.100727i) q^{10} +3.33731 q^{11} +(-1.31267 - 0.346303i) q^{12} +(-1.23997 - 2.14770i) q^{13} +(-0.0479602 - 0.176264i) q^{15} +(0.909025 + 1.57448i) q^{16} +(-0.806594 - 1.39706i) q^{17} +(-2.87788 - 1.63204i) q^{18} +(3.84133 - 6.65338i) q^{19} +(0.0413323 - 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} -1.89719 q^{23} +(-1.39607 - 5.13088i) q^{24} -4.98888 q^{25} +(1.36746 - 2.36851i) q^{26} +(3.71655 + 3.63142i) q^{27} +(4.64521 - 8.04574i) q^{29} +(0.141898 - 0.142998i) q^{30} +(-4.63081 + 8.02080i) q^{31} +(2.06753 - 3.58107i) q^{32} +(-1.51763 - 5.57762i) q^{33} +(0.889523 - 1.54070i) q^{34} +(0.0181599 + 2.35134i) q^{36} +(0.991268 - 1.71693i) q^{37} +8.47254 q^{38} +(-3.02555 + 3.04901i) q^{39} +0.323782 q^{40} +(3.74268 + 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +(1.30790 - 2.26534i) q^{44} +(-0.272779 + 0.160311i) q^{45} +(-1.04612 - 1.81194i) q^{46} +(1.59780 + 2.76747i) q^{47} +(2.21803 - 2.23523i) q^{48} +(-2.75090 - 4.76470i) q^{50} +(-1.96810 + 1.98336i) q^{51} -1.94379 q^{52} +(4.98839 + 8.64015i) q^{53} +(-1.41891 + 5.55194i) q^{54} +0.351974 q^{55} +(-12.8665 - 3.39438i) q^{57} +10.2456 q^{58} +(-2.22993 + 3.86235i) q^{59} +(-0.138443 - 0.0365232i) q^{60} +(2.83550 + 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(-0.130775 - 0.226509i) q^{65} +(4.49016 - 4.52497i) q^{66} +(-4.98571 + 8.63550i) q^{67} -1.26442 q^{68} +(0.862736 + 3.17075i) q^{69} +3.29042 q^{71} +(-7.94033 + 4.66648i) q^{72} +(2.36189 + 4.09091i) q^{73} +2.18637 q^{74} +(2.26867 + 8.33786i) q^{75} +(-3.01084 - 5.21493i) q^{76} +(-4.58031 - 1.20835i) q^{78} +(-3.84705 - 6.66328i) q^{79} +(0.0958713 + 0.166054i) q^{80} +(4.37908 - 7.86280i) q^{81} +(-4.12748 + 7.14901i) q^{82} +(-0.584428 + 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} -8.32378 q^{86} +(-15.5591 - 4.10473i) q^{87} +10.2456 q^{88} +(-3.01477 + 5.22173i) q^{89} +(-0.303519 - 0.172125i) q^{90} +(-0.743509 + 1.28780i) q^{92} +(15.5109 + 4.09200i) q^{93} +(-1.76208 + 3.05201i) q^{94} +(0.405130 - 0.701706i) q^{95} +(-6.92520 - 1.82697i) q^{96} +(-1.90127 + 3.29310i) q^{97} +(-8.63168 + 5.07279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.551407	+	0.955065i	0.389903	+	0.675333i	0.992436	−	0.122762i	$-0.0391750\pi$
$2$	0.551407	+	0.955065i	0.389903	+	0.675333i	−0.602533	+	0.798094i	$0.705842\pi$
$3$	−0.454745	−	1.67129i	−0.262547	−	0.964919i
$3$	−0.454745	−	1.67129i	−0.262547	−	0.964919i
$4$	0.391901	−	0.678793i	0.195951	−	0.339396i
$5$	0.105466			0.0471659			0.0235829	−	0.999722i	$-0.492493\pi$
$5$	0.105466			0.0471659			0.0235829	+	0.999722i	$0.492493\pi$
$6$	1.34544	−	1.35587i	0.549273	−	0.553532i
$7$		0			0
$7$		0			0
$8$	3.07001			1.08541
$9$	−2.58641	+	1.52002i	−0.862138	+	0.506673i
$10$	0.0581547	+	0.100727i	0.0183901	+	0.0318527i
$11$	3.33731			1.00624			0.503119	−	0.864217i	$-0.332186\pi$
$11$	3.33731			1.00624			0.503119	+	0.864217i	$0.332186\pi$
$12$	−1.31267	−	0.346303i	−0.378936	−	0.0999689i
$13$	−1.23997	−	2.14770i	−0.343907	−	0.595664i	0.641248	−	0.767334i	$-0.278417\pi$
$13$	−1.23997	−	2.14770i	−0.343907	−	0.595664i	−0.985155	+	0.171670i	$0.945084\pi$
$14$		0			0
$15$	−0.0479602	−	0.176264i	−0.0123833	−	0.0455113i
$16$	0.909025	+	1.57448i	0.227256	+	0.393619i
$17$	−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	$0.896008\pi$
$18$	−2.87788	−	1.63204i	−0.678324	−	0.384676i
$19$	3.84133	−	6.65338i	0.881262	−	1.52639i	0.0313221	−	0.999509i	$-0.490028\pi$
$19$	3.84133	−	6.65338i	0.881262	−	1.52639i	0.849939	−	0.526880i	$-0.176638\pi$
$20$	0.0413323	−	0.0715896i	0.00924218	−	0.0160079i
$21$		0			0
$22$	1.84022	+	3.18735i	0.392336	+	0.679546i
$23$	−1.89719			−0.395591			−0.197795	−	0.980243i	$-0.563378\pi$
$23$	−1.89719			−0.395591			−0.197795	+	0.980243i	$0.563378\pi$
$24$	−1.39607	−	5.13088i	−0.284972	−	1.04734i
$25$	−4.98888			−0.997775
$26$	1.36746	−	2.36851i	0.268181	−	0.464503i
$27$	3.71655	+	3.63142i	0.715251	+	0.698868i
$28$		0			0
$29$	4.64521	−	8.04574i	0.862594	−	1.49406i	−0.00682200	−	0.999977i	$-0.502172\pi$
$29$	4.64521	−	8.04574i	0.862594	−	1.49406i	0.869416	−	0.494080i	$-0.164495\pi$
$30$	0.141898	−	0.142998i	0.0259070	−	0.0261078i
$31$	−4.63081	+	8.02080i	−0.831718	+	1.44058i	0.0649574	+	0.997888i	$0.479309\pi$
$31$	−4.63081	+	8.02080i	−0.831718	+	1.44058i	−0.896675	+	0.442689i	$0.854024\pi$
$32$	2.06753	−	3.58107i	0.365491	−	0.633049i
$33$	−1.51763	−	5.57762i	−0.264185	−	0.970939i
$34$	0.889523	−	1.54070i	0.152552	−	0.264228i
$35$		0			0
$36$	0.0181599	+	2.35134i	0.00302665	+	0.391889i
$37$	0.991268	−	1.71693i	0.162963	−	0.282261i	−0.772967	−	0.634447i	$-0.781228\pi$
$37$	0.991268	−	1.71693i	0.162963	−	0.282261i	0.935930	+	0.352186i	$0.114561\pi$
$38$	8.47254			1.37443
$39$	−3.02555	+	3.04901i	−0.484476	+	0.488232i
$40$	0.323782			0.0511945
$41$	3.74268	+	6.48252i	0.584509	+	1.01240i	0.994936	+	0.100506i	$0.0320462\pi$
$41$	3.74268	+	6.48252i	0.584509	+	1.01240i	−0.410427	+	0.911893i	$0.634621\pi$
$42$		0			0
$43$	−3.77388	+	6.53655i	−0.575512	+	0.996815i	0.420474	+	0.907304i	$0.361864\pi$
$43$	−3.77388	+	6.53655i	−0.575512	+	0.996815i	−0.995986	+	0.0895108i	$0.971470\pi$
$44$	1.30790	−	2.26534i	0.197173	−	0.341514i
$45$	−0.272779	+	0.160311i	−0.0406635	+	0.0238977i
$46$	−1.04612	−	1.81194i	−0.154242	−	0.267155i
$47$	1.59780	+	2.76747i	0.233063	+	0.403677i	0.958708	−	0.284392i	$-0.0917917\pi$
$47$	1.59780	+	2.76747i	0.233063	+	0.403677i	−0.725645	+	0.688070i	$0.758458\pi$
$48$	2.21803	−	2.23523i	0.320145	−	0.322627i
$49$		0			0
$50$	−2.75090	−	4.76470i	−0.389036	−	0.673830i
$51$	−1.96810	+	1.98336i	−0.275589	+	0.277726i
$52$	−1.94379			−0.269555
$53$	4.98839	+	8.64015i	0.685209	+	1.18682i	0.973371	+	0.229234i	$0.0736223\pi$
$53$	4.98839	+	8.64015i	0.685209	+	1.18682i	−0.288163	+	0.957581i	$0.593044\pi$
$54$	−1.41891	+	5.55194i	−0.193090	+	0.755523i
$55$	0.351974			0.0474601
$56$		0			0
$57$	−12.8665	−	3.39438i	−1.70422	−	0.449597i
$58$	10.2456			1.34531
$59$	−2.22993	+	3.86235i	−0.290312	+	0.502836i	−0.973884	−	0.227048i	$-0.927093\pi$
$59$	−2.22993	+	3.86235i	−0.290312	+	0.502836i	0.683571	+	0.729884i	$0.260426\pi$
$60$	−0.138443	−	0.0365232i	−0.0178729	−	0.00471512i
$61$	2.83550	+	4.91123i	0.363048	+	0.628818i	0.988461	−	0.151476i	$-0.0484027\pi$
$61$	2.83550	+	4.91123i	0.363048	+	0.628818i	−0.625413	+	0.780294i	$0.715069\pi$
$62$	−10.2138			−1.29716
$63$		0			0
$64$	8.19630			1.02454
$65$	−0.130775	−	0.226509i	−0.0162207	−	0.0280950i
$66$	4.49016	−	4.52497i	0.552700	−	0.556985i
$67$	−4.98571	+	8.63550i	−0.609101	+	1.05499i	0.382288	+	0.924043i	$0.375136\pi$
$67$	−4.98571	+	8.63550i	−0.609101	+	1.05499i	−0.991389	+	0.130951i	$0.958197\pi$
$68$	−1.26442			−0.153333
$69$	0.862736	+	3.17075i	0.103861	+	0.381713i
$70$		0			0
$71$	3.29042			0.390502			0.195251	−	0.980753i	$-0.437448\pi$
$71$	3.29042			0.390502			0.195251	+	0.980753i	$0.437448\pi$
$72$	−7.94033	+	4.66648i	−0.935777	+	0.549950i
$73$	2.36189	+	4.09091i	0.276438	+	0.478805i	0.970497	−	0.241113i	$-0.0775125\pi$
$73$	2.36189	+	4.09091i	0.276438	+	0.478805i	−0.694059	+	0.719919i	$0.744179\pi$
$74$	2.18637			0.254160
$75$	2.26867	+	8.33786i	0.261963	+	0.962773i
$76$	−3.01084	−	5.21493i	−0.345367	−	0.598194i
$77$		0			0
$78$	−4.58031	−	1.20835i	−0.518618	−	0.136819i
$79$	−3.84705	−	6.66328i	−0.432827	−	0.749678i	0.564289	−	0.825577i	$-0.309150\pi$
$79$	−3.84705	−	6.66328i	−0.432827	−	0.749678i	−0.997115	+	0.0758997i	$0.975817\pi$
$80$	0.0958713	+	0.166054i	0.0107187	+	0.0185654i
$81$	4.37908	−	7.86280i	0.486564	−	0.873645i
$82$	−4.12748	+	7.14901i	−0.455804	+	0.789476i
$83$	−0.584428	+	1.01226i	−0.0641493	+	0.111110i	−0.896316	−	0.443415i	$-0.853767\pi$
$83$	−0.584428	+	1.01226i	−0.0641493	+	0.111110i	0.832167	+	0.554525i	$0.187100\pi$
$84$		0			0
$85$	−0.0850683	−	0.147343i	−0.00922695	−	0.0159815i
$86$	−8.32378			−0.897576
$87$	−15.5591	−	4.10473i	−1.66812	−	0.440073i
$88$	10.2456			1.09219
$89$	−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	$0.270203\pi$
$90$	−0.303519	−	0.172125i	−0.0319937	−	0.0181436i
$91$		0			0
$92$	−0.743509	+	1.28780i	−0.0775162	+	0.134262i
$93$	15.5109	+	4.09200i	1.60841	+	0.424321i
$94$	−1.76208	+	3.05201i	−0.181744	+	0.314791i
$95$	0.405130	−	0.701706i	0.0415655	−	0.0719935i
$96$	−6.92520	−	1.82697i	−0.706800	−	0.186464i
$97$	−1.90127	+	3.29310i	−0.193045	+	0.334364i	−0.946258	−	0.323413i	$-0.895170\pi$
$97$	−1.90127	+	3.29310i	−0.193045	+	0.334364i	0.753213	+	0.657777i	$0.228503\pi$
$98$		0			0
$99$	−8.63168	+	5.07279i	−0.867516	+	0.509834i
$100$	−1.95515	+	3.38641i	−0.195515	+	0.338641i
$101$	17.4702			1.73835			0.869177	−	0.494501i	$-0.164649\pi$
$101$	17.4702			1.73835			0.869177	+	0.494501i	$0.164649\pi$
$102$	−2.97946	−	0.786025i	−0.295010	−	0.0778280i
$103$	−8.73204			−0.860394			−0.430197	−	0.902735i	$-0.641556\pi$
$103$	−8.73204			−0.860394			−0.430197	+	0.902735i	$0.641556\pi$
$104$	−3.80674	−	6.59346i	−0.373281	−	0.646542i
$105$		0			0
$106$	−5.50127	+	9.52848i	−0.534330	+	0.925487i
$107$	9.07316	−	15.7152i	0.877135	−	1.51924i	0.0226645	−	0.999743i	$-0.492785\pi$
$107$	9.07316	−	15.7152i	0.877135	−	1.51924i	0.854471	−	0.519500i	$-0.173882\pi$
$108$	3.92150	−	1.09961i	0.377347	−	0.105810i
$109$	2.11124	+	3.65678i	0.202220	+	0.350256i	0.949243	−	0.314542i	$-0.101851\pi$
$109$	2.11124	+	3.65678i	0.202220	+	0.350256i	−0.747023	+	0.664798i	$0.768518\pi$
$110$	0.194081	+	0.336157i	0.0185049	+	0.0320514i
$111$	−3.32025	−	0.875932i	−0.315145	−	0.0831398i
$112$		0			0
$113$	1.02824	+	1.78096i	0.0967285	+	0.167539i	0.910329	−	0.413886i	$-0.135829\pi$
$113$	1.02824	+	1.78096i	0.0967285	+	0.167539i	−0.813600	+	0.581425i	$0.802495\pi$
$114$	−3.85284	−	14.1601i	−0.360852	−	1.32621i
$115$	−0.200089			−0.0186584
$116$	−3.64093	−	6.30627i	−0.338052	−	0.585523i
$117$	6.47163	+	3.67005i	0.598302	+	0.339296i
$118$	−4.91840			−0.452775
$119$		0			0
$120$	−0.147238	−	0.541134i	−0.0134410	−	0.0493986i
$121$	0.137670			0.0125155
$122$	−3.12703	+	5.41617i	−0.283108	+	0.490357i
$123$	9.13220	−	9.20300i	0.823422	−	0.829806i
$124$	3.62964	+	6.28672i	0.325951	+	0.564564i
$125$	−1.05349			−0.0942268
$126$		0			0
$127$	0.317159			0.0281433			0.0140717	−	0.999901i	$-0.495521\pi$
$127$	0.317159			0.0281433			0.0140717	+	0.999901i	$0.495521\pi$
$128$	0.384435	+	0.665862i	0.0339796	+	0.0588544i
$129$	12.6406	+	3.33478i	1.11294	+	0.293611i
$130$	0.144221	−	0.249797i	0.0126490	−	0.0219087i
$131$	−14.9563			−1.30674			−0.653370	−	0.757039i	$-0.726645\pi$
$131$	−14.9563			−1.30674			−0.653370	+	0.757039i	$0.726645\pi$
$132$	−4.38081	−	1.15572i	−0.381300	−	0.100593i
$133$		0			0
$134$	−10.9966			−0.949962
$135$	0.391970	+	0.382992i	0.0337354	+	0.0329627i
$136$	−2.47625	−	4.28900i	−0.212337	−	0.367779i
$137$	−15.2473			−1.30267			−0.651334	−	0.758791i	$-0.725790\pi$
$137$	−15.2473			−1.30267			−0.651334	+	0.758791i	$0.725790\pi$
$138$	−2.55255	+	2.57234i	−0.217287	+	0.218972i
$139$	−4.05943	−	7.03114i	−0.344316	−	0.596374i	0.640913	−	0.767614i	$-0.278556\pi$
$139$	−4.05943	−	7.03114i	−0.344316	−	0.596374i	−0.985229	+	0.171240i	$0.945223\pi$
$140$		0			0
$141$	3.89866	−	3.92888i	0.328326	−	0.330872i
$142$	1.81436	+	3.14257i	0.152258	+	0.263718i
$143$	−4.13818	−	7.16754i	−0.346052	−	0.599380i
$144$	−4.74435	−	2.69051i	−0.395363	−	0.224210i
$145$	0.489912	−	0.848553i	0.0406850	−	0.0704685i
$146$	−2.60473	+	4.51152i	−0.215569	+	0.373376i
$147$		0			0
$148$	−0.776958	−	1.34573i	−0.0638656	−	0.110618i
$149$	−11.1486			−0.913329			−0.456664	−	0.889639i	$-0.650956\pi$
$149$	−11.1486			−0.913329			−0.456664	+	0.889639i	$0.650956\pi$
$150$	−6.71223	+	6.76427i	−0.548051	+	0.552301i
$151$	−11.2735			−0.917425			−0.458713	−	0.888585i	$-0.651689\pi$
$151$	−11.2735			−0.917425			−0.458713	+	0.888585i	$0.651689\pi$
$152$	11.7929	−	20.4260i	0.956534	−	1.65677i
$153$	4.20975	+	2.38734i	0.340338	+	0.193005i
$154$		0			0
$155$	−0.488393	+	0.845922i	−0.0392287	+	0.0679461i
$156$	0.883928	+	3.24863i	0.0707708	+	0.260099i
$157$	6.10318	−	10.5710i	0.487087	−	0.843659i	−0.512803	−	0.858506i	$-0.671393\pi$
$157$	6.10318	−	10.5710i	0.487087	−	0.843659i	0.999890	+	0.0148476i	$0.00472630\pi$
$158$	4.24258	−	7.34836i	0.337521	−	0.584604i
$159$	12.1717	−	12.2661i	0.965282	−	0.972766i
$160$	0.218054	−	0.377681i	0.0172387	−	0.0298583i
$161$		0			0
$162$	9.92414	−	0.153302i	0.779714	−	0.0120445i
$163$	−4.48132	+	7.76187i	−0.351004	+	0.607957i	−0.986426	−	0.164209i	$-0.947493\pi$
$163$	−4.48132	+	7.76187i	−0.351004	+	0.607957i	0.635422	+	0.772165i	$0.280826\pi$
$164$	5.86705			0.458139
$165$	−0.160058	−	0.588250i	−0.0124605	−	0.0457952i
$166$	−1.28903			−0.100048
$167$	8.70833	+	15.0833i	0.673871	+	1.16718i	0.976798	+	0.214165i	$0.0687030\pi$
$167$	8.70833	+	15.0833i	0.673871	+	1.16718i	−0.302927	+	0.953014i	$0.597964\pi$
$168$		0			0
$169$	3.42493	−	5.93216i	0.263456	−	0.456320i
$170$	0.0938145	−	0.162491i	0.00719524	−	0.0124625i
$171$	0.177999	+	23.0473i	0.0136120	+	1.76247i
$172$	2.95798	+	5.12337i	0.225544	+	0.390653i
$173$	1.41466	+	2.45027i	0.107555	+	0.186291i	0.914779	−	0.403954i	$-0.132365\pi$
$173$	1.41466	+	2.45027i	0.107555	+	0.186291i	−0.807224	+	0.590245i	$0.799031\pi$
$174$	−4.65914	−	17.1234i	−0.353208	−	1.29812i
$175$		0			0
$176$	3.03370	+	5.25453i	0.228674	+	0.396075i
$177$	7.46916	+	1.97047i	0.561416	+	0.148110i
$178$	−6.64946			−0.498398
$179$	5.08135	+	8.80115i	0.379798	+	0.657829i	0.991033	−	0.133620i	$-0.0426603\pi$
$179$	5.08135	+	8.80115i	0.379798	+	0.657829i	−0.611235	+	0.791449i	$0.709327\pi$
$180$	0.00191525	+	0.247986i	0.000142755	+	0.0184838i
$181$	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
$183$	6.91865	−	6.97229i	0.511441	−	0.515407i
$184$	−5.82439			−0.429380
$185$	0.104545	−	0.181078i	0.00768631	−	0.0133131i
$186$	4.64469	+	17.0703i	0.340565	+	1.25165i
$187$	−2.69186	−	4.66243i	−0.196848	−	0.340951i
$188$	2.50472			0.182676
$189$		0			0
$190$	0.893566			0.0648261
$191$	11.2000	+	19.3990i	0.810404	+	1.40366i	0.912582	+	0.408894i	$0.134086\pi$
$191$	11.2000	+	19.3990i	0.810404	+	1.40366i	−0.102178	+	0.994766i	$0.532581\pi$
$192$	−3.72723	−	13.6984i	−0.268989	−	0.988596i
$193$	0.128393	−	0.222383i	0.00924194	−	0.0160075i	−0.861367	−	0.507982i	$-0.830391\pi$
$193$	0.128393	−	0.222383i	0.00924194	−	0.0160075i	0.870609	+	0.491975i	$0.163725\pi$
$194$	−4.19350			−0.301076
$195$	−0.319093	+	0.321567i	−0.0228507	+	0.0230279i
$196$		0			0
$197$	−0.763370			−0.0543878			−0.0271939	−	0.999630i	$-0.508657\pi$
$197$	−0.763370			−0.0543878			−0.0271939	+	0.999630i	$0.508657\pi$
$198$	−9.60440	−	5.44664i	−0.682555	−	0.387076i
$199$	−2.51561	−	4.35716i	−0.178327	−	0.308871i	0.762981	−	0.646421i	$-0.223735\pi$
$199$	−2.51561	−	4.35716i	−0.178327	−	0.308871i	−0.941307	+	0.337550i	$0.890402\pi$
$200$	−15.3159			−1.08300
$201$	16.6996	+	4.40561i	1.17790	+	0.310748i
$202$	9.63321	+	16.6852i	0.677790	+	1.17397i
$203$		0			0
$204$	0.574988	+	2.11321i	0.0402572	+	0.147954i
$205$	0.394726	+	0.683686i	0.0275689	+	0.0477507i
$206$	−4.81491	−	8.33966i	−0.335470	−	0.581052i
$207$	4.90691	−	2.88376i	0.341054	−	0.200435i
$208$	2.25433	−	3.90462i	0.156310	−	0.270737i
$209$	12.8197	−	22.2044i	0.886759	−	1.53591i
$210$		0			0
$211$	−3.60537	−	6.24468i	−0.248204	−	0.429901i	0.714824	−	0.699305i	$-0.246507\pi$
$211$	−3.60537	−	6.24468i	−0.248204	−	0.429901i	−0.963027	+	0.269403i	$0.913174\pi$
$212$	7.81983			0.537068
$213$	−1.49630	−	5.49925i	−0.102525	−	0.376802i
$214$	20.0120			1.36799
$215$	−0.398017	+	0.689385i	−0.0271445	+	0.0470157i
$216$	11.4099	+	11.1485i	0.776343	+	0.758561i
$217$		0			0
$218$	−2.32831	+	4.03274i	−0.157693	+	0.273132i
$219$	5.76304	−	5.80772i	0.389430	−	0.392450i
$220$	0.137939	−	0.238917i	0.00929983	−	0.0161078i
$221$	−2.00031	+	3.46464i	−0.134555	+	0.233057i
$222$	−0.994239	−	3.65405i	−0.0667290	−	0.245244i
$223$	−5.59106	+	9.68400i	−0.374405	+	0.648488i	−0.990238	−	0.139388i	$-0.955486\pi$
$223$	−5.59106	+	9.68400i	−0.374405	+	0.648488i	0.615833	+	0.787877i	$0.288820\pi$
$224$		0			0
$225$	12.9033	−	7.58319i	0.860220	−	0.505546i
$226$	−1.13395	+	1.96407i	−0.0754295	+	0.130648i
$227$	−23.7706			−1.57771			−0.788857	−	0.614577i	$-0.789327\pi$
$227$	−23.7706			−1.57771			−0.788857	+	0.614577i	$0.789327\pi$
$228$	−7.34649	+	7.40345i	−0.486534	+	0.490306i
$229$	1.90547			0.125917			0.0629586	−	0.998016i	$-0.479946\pi$
$229$	1.90547			0.125917			0.0629586	+	0.998016i	$0.479946\pi$
$230$	−0.110330	−	0.191098i	−0.00727497	−	0.0126006i
$231$		0			0
$232$	14.2609	−	24.7006i	0.936272	−	1.62167i
$233$	−3.27092	+	5.66540i	−0.214285	+	0.371153i	−0.953051	−	0.302809i	$-0.902075\pi$
$233$	−3.27092	+	5.66540i	−0.214285	+	0.371153i	0.738766	+	0.673962i	$0.235409\pi$
$234$	0.0633653	+	8.20451i	0.00414232	+	0.536346i
$235$	0.168514	+	0.291875i	0.0109926	+	0.0190398i
$236$	1.74782	+	3.02732i	0.113774	+	0.197062i
$237$	−9.38684	+	9.45962i	−0.609741	+	0.614468i
$238$		0			0
$239$	10.6735	+	18.4870i	0.690409	+	1.19582i	0.971704	+	0.236202i	$0.0759028\pi$
$239$	10.6735	+	18.4870i	0.690409	+	1.19582i	−0.281295	+	0.959621i	$0.590764\pi$
$240$	0.233927	−	0.235741i	0.0150999	−	0.0152170i
$241$	20.0662			1.29258			0.646288	−	0.763094i	$-0.276321\pi$
$241$	20.0662			1.29258			0.646288	+	0.763094i	$0.276321\pi$
$242$	0.0759124	+	0.131484i	0.00487983	+	0.00845212i
$243$	−15.1324	−	3.74313i	−0.970743	−	0.240122i
$244$	4.44494			0.284558
$245$		0			0
$246$	13.8250	+	3.64724i	0.881451	+	0.232540i
$247$	−19.0526			−1.21229
$248$	−14.2167	+	24.6240i	−0.902758	+	1.56362i
$249$	1.95754	+	0.516428i	0.124054	+	0.0327273i
$250$	−0.580900	−	1.00615i	−0.0367394	−	0.0636344i
$251$	6.81467			0.430138			0.215069	−	0.976599i	$-0.431002\pi$
$251$	6.81467			0.430138			0.215069	+	0.976599i	$0.431002\pi$
$252$		0			0
$253$	−6.33151			−0.398059
$254$	0.174884	+	0.302907i	0.0109732	+	0.0190061i
$255$	−0.207568	+	0.209177i	−0.0129984	+	0.0130992i
$256$	7.77234	−	13.4621i	0.485771	−	0.841380i
$257$	14.3883			0.897518			0.448759	−	0.893653i	$-0.351866\pi$
$257$	14.3883			0.897518			0.448759	+	0.893653i	$0.351866\pi$
$258$	3.78519	+	13.9114i	0.235656	+	0.866088i
$259$		0			0
$260$	−0.205004			−0.0127138
$261$	0.215250	+	27.8704i	0.0133236	+	1.72514i
$262$	−8.24701	−	14.2842i	−0.509502	−	0.882484i
$263$	−1.53901			−0.0948992			−0.0474496	−	0.998874i	$-0.515109\pi$
$263$	−1.53901			−0.0948992			−0.0474496	+	0.998874i	$0.515109\pi$
$264$	−4.65914	−	17.1234i	−0.286750	−	1.05387i
$265$	0.526106	+	0.911243i	0.0323185	+	0.0559772i
$266$		0			0
$267$	10.0980	+	2.66399i	0.617986	+	0.163034i
$268$	3.90781	+	6.76852i	0.238707	+	0.413453i
$269$	−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	$-0.462079\pi$
$270$	−0.149647	+	0.585541i	−0.00910724	+	0.0356349i
$271$	8.96673	−	15.5308i	0.544690	−	0.943431i	−0.453936	−	0.891034i	$-0.649981\pi$
$271$	8.96673	−	15.5308i	0.544690	−	0.943431i	0.998626	−	0.0523969i	$-0.0166861\pi$
$272$	1.46643	−	2.53993i	0.0889152	−	0.154006i
$273$		0			0
$274$	−8.40748	−	14.5622i	−0.507915	−	0.879734i
$275$	−16.6495			−1.00400
$276$	2.49039	+	0.657001i	0.149904	+	0.0395468i
$277$	−18.8713			−1.13386			−0.566932	−	0.823764i	$-0.691870\pi$
$277$	−18.8713			−1.13386			−0.566932	+	0.823764i	$0.691870\pi$
$278$	4.47680	−	7.75404i	0.268500	−	0.465056i
$279$	−0.214582	−	27.7840i	−0.0128467	−	1.66339i
$280$		0			0
$281$	−2.49578	+	4.32283i	−0.148886	+	0.257878i	−0.930816	−	0.365488i	$-0.880902\pi$
$281$	−2.49578	+	4.32283i	−0.148886	+	0.257878i	0.781930	+	0.623366i	$0.214235\pi$
$282$	5.90208	+	1.55706i	0.351464	+	0.0927213i
$283$	7.69634	−	13.3304i	0.457500	−	0.792413i	−0.541328	−	0.840811i	$-0.682078\pi$
$283$	7.69634	−	13.3304i	0.457500	−	0.792413i	0.998828	+	0.0483984i	$0.0154117\pi$
$284$	1.28952	−	2.23352i	0.0765190	−	0.132535i
$285$	−1.35698	−	0.357992i	−0.0803808	−	0.0212056i
$286$	4.56364	−	7.90446i	0.269854	−	0.467401i
$287$		0			0
$288$	0.0958052	+	12.4048i	0.00564537	+	0.730960i
$289$	7.19881	−	12.4687i	0.423460	−	0.733454i
$290$	1.08056			0.0634529
$291$	6.36832	+	1.68006i	0.373318	+	0.0984867i
$292$	3.70251			0.216673
$293$	−12.9013	−	22.3456i	−0.753700	−	1.30545i	−0.946018	−	0.324114i	$-0.894934\pi$
$293$	−12.9013	−	22.3456i	−0.753700	−	1.30545i	0.192318	−	0.981333i	$-0.438399\pi$
$294$		0			0
$295$	−0.235182	+	0.407347i	−0.0136928	+	0.0237167i
$296$	3.04321	−	5.27099i	0.176883	−	0.306370i
$297$	12.4033	+	12.1192i	0.719713	+	0.703228i
$298$	−6.14741	−	10.6476i	−0.356110	−	0.616801i
$299$	2.35246	+	4.07458i	0.136046	+	0.235639i
$300$	6.54877	+	1.72766i	0.378093	+	0.0997465i
$301$		0			0
$302$	−6.21629	−	10.7669i	−0.357707	−	0.619567i
$303$	−7.94450	−	29.1978i	−0.456400	−	1.67737i
$304$	13.9675			0.801089
$305$	0.299049	+	0.517968i	0.0171235	+	0.0296588i
$306$	0.0412187	+	5.33698i	0.00235632	+	0.305095i
$307$	−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
$309$	3.97085	+	14.5938i	0.225894	+	0.830210i
$310$	−1.07721			−0.0611816
$311$	0.654931	−	1.13437i	0.0371377	−	0.0643245i	−0.846859	−	0.531817i	$-0.821509\pi$
$311$	0.654931	−	1.13437i	0.0371377	−	0.0643245i	0.883997	+	0.467493i	$0.154843\pi$
$312$	−9.28849	+	9.36050i	−0.525857	+	0.529934i
$313$	−10.7885	−	18.6862i	−0.609802	−	1.05621i	−0.991273	−	0.131827i	$-0.957916\pi$
$313$	−10.7885	−	18.6862i	−0.609802	−	1.05621i	0.381471	−	0.924381i	$-0.375418\pi$
$314$	13.4613			0.759667
$315$		0			0
$316$	−6.03065			−0.339250
$317$	12.3910	+	21.4618i	0.695946	+	1.20541i	0.969861	+	0.243660i	$0.0783480\pi$
$317$	12.3910	+	21.4618i	0.695946	+	1.20541i	−0.273915	+	0.961754i	$0.588319\pi$
$318$	18.4265	+	4.86118i	1.03331	+	0.272602i
$319$	15.5025	−	26.8512i	0.867975	−	1.50338i
$320$	0.864432			0.0483232
$321$	−30.3906	−	8.01748i	−1.69624	−	0.447492i
$322$		0			0
$323$	−12.3936			−0.689597
$324$	−3.62105	−	6.05393i	−0.201169	−	0.336329i
$325$	6.18608	+	10.7146i	0.343142	+	0.594339i
$326$	−9.88412			−0.547431
$327$	5.15145	−	5.19139i	0.284876	−	0.287085i
$328$	11.4901	+	19.9014i	0.634434	+	1.09887i
$329$		0			0
$330$	0.473559	−	0.477231i	0.0260686	−	0.0262707i
$331$	−6.92256	−	11.9902i	−0.380498	−	0.659042i	0.610635	−	0.791912i	$-0.290914\pi$
$331$	−6.92256	−	11.9902i	−0.380498	−	0.659042i	−0.991133	+	0.132870i	$0.957581\pi$
$332$	0.458076	+	0.793410i	0.0251402	+	0.0435440i
$333$	0.0459334	+	5.94743i	0.00251713	+	0.325917i
$334$	−9.60367	+	16.6340i	−0.525489	+	0.910174i
$335$	−0.525823	+	0.910752i	−0.0287288	+	0.0497597i
$336$		0			0
$337$	1.69444	+	2.93485i	0.0923018	+	0.159871i	0.908479	−	0.417930i	$-0.137244\pi$
$337$	1.69444	+	2.93485i	0.0923018	+	0.159871i	−0.816178	+	0.577801i	$0.803911\pi$
$338$	7.55412			0.410890
$339$	2.50891	−	2.52837i	0.136265	−	0.137322i
$340$	−0.133353			−0.00723210
$341$	−15.4545	+	26.7679i	−0.836906	+	1.44956i
$342$	−21.9135	+	12.8784i	−1.18495	+	0.696386i
$343$		0			0
$344$	−11.5859	+	20.0673i	−0.624668	+	1.08196i
$345$	0.0909894	+	0.334406i	0.00489870	+	0.0180038i
$346$	−1.56011	+	2.70219i	−0.0838720	+	0.145271i
$347$	7.25739	−	12.5702i	0.389597	−	0.674802i	−0.602798	−	0.797894i	$-0.705948\pi$
$347$	7.25739	−	12.5702i	0.389597	−	0.674802i	0.992395	+	0.123091i	$0.0392809\pi$
$348$	−8.88391	+	8.95279i	−0.476228	+	0.479920i
$349$	7.86412	−	13.6211i	0.420957	−	0.729119i	−0.575076	−	0.818100i	$-0.695028\pi$
$349$	7.86412	−	13.6211i	0.420957	−	0.729119i	0.996033	+	0.0889810i	$0.0283610\pi$
$350$		0			0
$351$	3.19077	−	12.4849i	0.170311	−	0.666395i
$352$	6.90000	−	11.9511i	0.367771	−	0.636998i
$353$	−4.14423			−0.220575			−0.110287	−	0.993900i	$-0.535177\pi$
$353$	−4.14423			−0.220575			−0.110287	+	0.993900i	$0.535177\pi$
$354$	2.23662	+	8.22006i	0.118875	+	0.436891i
$355$	0.347028			0.0184183
$356$	2.36298	+	4.09281i	0.125238	+	0.216918i
$357$		0			0
$358$	−5.60378	+	9.70603i	−0.296169	+	0.512979i
$359$	−3.96994	+	6.87614i	−0.209525	+	0.362909i	−0.951565	−	0.307447i	$-0.900525\pi$
$359$	−3.96994	+	6.87614i	−0.209525	+	0.362909i	0.742040	+	0.670356i	$0.233859\pi$
$360$	−0.837436	+	0.492156i	−0.0441367	+	0.0259389i
$361$	−20.0116	−	34.6612i	−1.05324	−	1.82427i
$362$	9.42187	+	16.3192i	0.495202	+	0.857716i
$363$	−0.0626049	−	0.230087i	−0.00328590	−	0.0120764i
$364$		0			0
$365$	0.249099	+	0.431453i	0.0130385	+	0.0225833i
$366$	10.4740	+	2.76319i	0.547484	+	0.144434i
$367$	−13.1491			−0.686377			−0.343189	−	0.939266i	$-0.611507\pi$
$367$	−13.1491			−0.686377			−0.343189	+	0.939266i	$0.611507\pi$
$368$	−1.72459	−	2.98708i	−0.0899004	−	0.155712i
$369$	−19.5337	−	11.0775i	−1.01688	−	0.576673i
$370$	0.230588			0.0119877
$371$		0			0
$372$	8.85636	−	8.92503i	0.459181	−	0.462741i
$373$	7.81086			0.404431			0.202216	−	0.979341i	$-0.435186\pi$
$373$	7.81086			0.404431			0.202216	+	0.979341i	$0.435186\pi$
$374$	2.96862	−	5.14180i	0.153504	−	0.265876i
$375$	0.479068	+	1.76068i	0.0247390	+	0.0909213i
$376$	4.90527	+	8.49618i	0.252970	+	0.438157i
$377$	−23.0398			−1.18661
$378$		0			0
$379$	−31.6147			−1.62394			−0.811968	−	0.583702i	$-0.801604\pi$
$379$	−31.6147			−1.62394			−0.811968	+	0.583702i	$0.801604\pi$
$380$	−0.317542	−	0.549999i	−0.0162896	−	0.0282143i
$381$	−0.144226	−	0.530064i	−0.00738894	−	0.0271560i
$382$	−12.3515	+	21.3934i	−0.631958	+	1.09458i
$383$	−10.7319			−0.548373			−0.274186	−	0.961677i	$-0.588408\pi$
$383$	−10.7319			−0.548373			−0.274186	+	0.961677i	$0.588408\pi$
$384$	0.938027	−	0.945300i	0.0478685	−	0.0482396i
$385$		0			0
$386$	0.283187			0.0144139
$387$	−0.174874	−	22.6426i	−0.00888935	−	1.15099i
$388$	1.49022	+	2.58114i	0.0756546	+	0.131038i
$389$	24.1468			1.22429			0.612147	−	0.790744i	$-0.290306\pi$
$389$	24.1468			1.22429			0.612147	+	0.790744i	$0.290306\pi$
$390$	−0.483067	−	0.127440i	−0.0244611	−	0.00645319i
$391$	1.53026	+	2.65049i	0.0773885	+	0.134041i
$392$		0			0
$393$	6.80131	+	24.9963i	0.343081	+	1.26090i
$394$	−0.420927	−	0.729067i	−0.0212060	−	0.0367299i
$395$	−0.405733	−	0.702750i	−0.0204146	−	0.0353592i
$396$	0.0606053	+	7.84715i	0.00304553	+	0.394334i
$397$	−12.0285	+	20.8339i	−0.603691	+	1.04562i	0.388566	+	0.921421i	$0.372971\pi$
$397$	−12.0285	+	20.8339i	−0.603691	+	1.04562i	−0.992257	+	0.124203i	$0.960363\pi$
$398$	2.77424	−	4.80513i	0.139060	−	0.240860i
$399$		0			0
$400$	−4.53501	−	7.85487i	−0.226751	−	0.392744i
$401$	−1.56232			−0.0780183			−0.0390092	−	0.999239i	$-0.512420\pi$
$401$	−1.56232			−0.0780183			−0.0390092	+	0.999239i	$0.512420\pi$
$402$	5.00065	+	18.3785i	0.249410	+	0.916637i
$403$	22.9683			1.14413
$404$	6.84661	−	11.8587i	0.340631	−	0.589991i
$405$	0.461844	−	0.829259i	0.0229492	−	0.0412062i
$406$		0			0
$407$	3.30817	−	5.72992i	0.163980	−	0.284022i
$408$	−6.04209	+	6.08894i	−0.299128	+	0.301447i
$409$	11.1728	−	19.3519i	0.552460	−	0.956889i	−0.445636	−	0.895214i	$-0.647023\pi$
$409$	11.1728	−	19.3519i	0.552460	−	0.956889i	0.998096	−	0.0616748i	$-0.0196442\pi$
$410$	−0.435309	+	0.753978i	−0.0214984	+	0.0372363i
$411$	6.93365	+	25.4827i	0.342012	+	1.25697i
$412$	−3.42210	+	5.92725i	−0.168595	+	0.292014i
$413$		0			0
$414$	5.45988	+	3.09629i	0.268339	+	0.152174i
$415$	−0.0616373	+	0.106759i	−0.00302566	+	0.00524059i
$416$	−10.2547			−0.502779
$417$	−9.90506	+	9.98186i	−0.485053	+	0.488814i
$418$	28.2755			1.38300
$419$	2.98648	+	5.17273i	0.145899	+	0.252704i	0.929708	−	0.368298i	$-0.120059\pi$
$419$	2.98648	+	5.17273i	0.145899	+	0.252704i	−0.783809	+	0.621002i	$0.786726\pi$
$420$		0			0
$421$	7.31594	−	12.6716i	0.356557	−	0.617575i	−0.630826	−	0.775924i	$-0.717284\pi$
$421$	7.31594	−	12.6716i	0.356557	−	0.617575i	0.987383	+	0.158349i	$0.0506172\pi$
$422$	3.97605	−	6.88672i	0.193551	−	0.335240i
$423$	−8.33919	−	4.72914i	−0.405465	−	0.229939i
$424$	15.3144	+	26.5254i	0.743735	+	1.28819i
$425$	4.02400	+	6.96977i	0.195193	+	0.338083i
$426$	4.42707	−	4.46139i	0.214492	−	0.216155i
$427$		0			0
$428$	−7.11156	−	12.3176i	−0.343750	−	0.595393i
$429$	−10.0972	+	10.1755i	−0.487498	+	0.491278i
$430$	−0.877876			−0.0423349
$431$	9.70169	+	16.8038i	0.467314	+	0.809411i	0.999303	−	0.0373401i	$-0.0118885\pi$
$431$	9.70169	+	16.8038i	0.467314	+	0.809411i	−0.531989	+	0.846751i	$0.678555\pi$
$432$	−2.33916	+	9.15268i	−0.112543	+	0.440359i
$433$	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
$435$	−1.64096	−	0.432910i	−0.0786781	−	0.0207564i
$436$	3.30959			0.158501
$437$	−7.28772	+	12.6227i	−0.348619	+	0.603826i
$438$	8.72453	+	2.30166i	0.416874	+	0.109978i
$439$	−8.67059	−	15.0179i	−0.413825	−	0.716766i	0.581479	−	0.813561i	$-0.302474\pi$
$439$	−8.67059	−	15.0179i	−0.413825	−	0.716766i	−0.995304	+	0.0967954i	$0.969141\pi$
$440$	1.08056			0.0515139
$441$		0			0
$442$	−4.41194			−0.209854
$443$	−9.80499	−	16.9827i	−0.465849	−	0.806874i	0.533390	−	0.845869i	$-0.320918\pi$
$443$	−9.80499	−	16.9827i	−0.465849	−	0.806874i	−0.999239	+	0.0389949i	$0.987584\pi$
$444$	−1.89579	+	1.91049i	−0.0899701	+	0.0906676i
$445$	−0.317956	+	0.550716i	−0.0150726	+	0.0261064i
$446$	−12.3318			−0.583927
$447$	5.06977	+	18.6325i	0.239792	+	0.881289i
$448$		0			0
$449$	−17.7345			−0.836942			−0.418471	−	0.908230i	$-0.637434\pi$
$449$	−17.7345			−0.836942			−0.418471	+	0.908230i	$0.637434\pi$
$450$	14.3574	+	8.14206i	0.676815	+	0.383821i
$451$	12.4905	+	21.6342i	0.588155	+	1.01871i
$452$	1.61187			0.0758160
$453$	5.12657	+	18.8413i	0.240867	+	0.885241i
$454$	−13.1073	−	22.7025i	−0.615156	−	1.06548i
$455$		0			0
$456$	−39.5005	−	10.4208i	−1.84978	−	0.487999i
$457$	−0.242725	−	0.420413i	−0.0113542	−	0.0196661i	0.860292	−	0.509801i	$-0.170281\pi$
$457$	−0.242725	−	0.420413i	−0.0113542	−	0.0196661i	−0.871647	+	0.490135i	$0.836948\pi$
$458$	1.05069	+	1.81985i	0.0490956	+	0.0850361i
$459$	2.07558	−	8.12134i	0.0968796	−	0.379071i
$460$	−0.0784150	+	0.135819i	−0.00365612	+	0.00633259i
$461$	3.99687	−	6.92279i	0.186153	−	0.322426i	−0.757811	−	0.652474i	$-0.773731\pi$
$461$	3.99687	−	6.92279i	0.186153	−	0.322426i	0.943964	+	0.330047i	$0.107065\pi$
$462$		0			0
$463$	5.24280	+	9.08080i	0.243654	+	0.422021i	0.961752	−	0.273921i	$-0.0883206\pi$
$463$	5.24280	+	9.08080i	0.243654	+	0.422021i	−0.718098	+	0.695942i	$0.754987\pi$
$464$	16.8905			0.784120
$465$	1.63587	+	0.431568i	0.0758619	+	0.0200135i
$466$	−7.21443			−0.334202
$467$	−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	$0.997549\pi$
$468$	5.02744	−	2.95460i	0.232394	−	0.136576i
$469$		0			0
$470$	−0.185839	+	0.321883i	−0.00857213	+	0.0148474i
$471$	−20.4426	−	5.39306i	−0.941945	−	0.248499i
$472$	−6.84592	+	11.8575i	−0.315109	+	0.545785i
$473$	−12.5946	+	21.8145i	−0.579102	+	1.00303i
$474$	−14.2105	−	3.74894i	−0.652711	−	0.172195i
$475$	−19.1639	+	33.1929i	−0.879301	+	1.52299i
$476$		0			0
$477$	−26.0353	−	14.7645i	−1.19207	−	0.676022i
$478$	−11.7708	+	20.3877i	−0.538386	+	0.932512i
$479$	4.00169			0.182842			0.0914210	−	0.995812i	$-0.470859\pi$
$479$	4.00169			0.182842			0.0914210	+	0.995812i	$0.470859\pi$
$480$	−0.730373	−	0.192683i	−0.0333368	−	0.00879474i
$481$	−4.91658			−0.224177
$482$	11.0646	+	19.1645i	0.503980	+	0.872918i
$483$		0			0
$484$	0.0539532	−	0.0934496i	0.00245242	−	0.00424771i
$485$	−0.200520	+	0.347311i	−0.00910514	+	0.0157706i
$486$	−4.76916	−	16.5164i	−0.216334	−	0.749199i
$487$	13.2377	+	22.9284i	0.599859	+	1.03899i	0.992841	+	0.119440i	$0.0381100\pi$
$487$	13.2377	+	22.9284i	0.599859	+	1.03899i	−0.392982	+	0.919546i	$0.628557\pi$
$488$	8.70502	+	15.0775i	0.394058	+	0.682528i
$489$	15.0102	+	3.95991i	0.678784	+	0.179073i
$490$		0			0
$491$	14.2149	+	24.6210i	0.641511	+	1.11113i	0.985096	+	0.172008i	$0.0550255\pi$
$491$	14.2149	+	24.6210i	0.641511	+	1.11113i	−0.343584	+	0.939122i	$0.611641\pi$
$492$	−2.66801	−	9.80553i	−0.120283	−	0.442068i
$493$	−14.9872			−0.674989
$494$	−10.5057	−	18.1965i	−0.472675	−	0.818697i
$495$	−0.910349	+	0.535007i	−0.0409172	+	0.0240468i
$496$	−16.8381			−0.756052
$497$		0			0
$498$	0.586179	+	2.15434i	0.0262673	+	0.0965383i
$499$	−7.43118			−0.332665			−0.166333	−	0.986070i	$-0.553193\pi$
$499$	−7.43118			−0.332665			−0.166333	+	0.986070i	$0.553193\pi$
$500$	−0.412863	+	0.715100i	−0.0184638	+	0.0319802i
$501$	21.2484	−	21.4132i	0.949310	−	0.956670i
$502$	3.75765	+	6.50845i	0.167712	+	0.290486i
$503$	−10.1610			−0.453057			−0.226529	−	0.974004i	$-0.572738\pi$
$503$	−10.1610			−0.453057			−0.226529	+	0.974004i	$0.572738\pi$
$504$		0			0
$505$	1.84252			0.0819910
$506$	−3.49124	−	6.04700i	−0.155204	−	0.268822i
$507$	−11.4718	−	3.02643i	−0.509481	−	0.134409i
$508$	0.124295	−	0.215285i	0.00551470	−	0.00955174i
$509$	28.9063			1.28125			0.640625	−	0.767854i	$-0.278675\pi$
$509$	28.9063			1.28125			0.640625	+	0.767854i	$0.278675\pi$
$510$	−0.314232	−	0.0828990i	−0.0139144	−	0.00367083i
$511$		0			0
$512$	18.6806			0.825575
$513$	38.4377	−	10.7781i	1.69707	−	0.475866i
$514$	7.93381	+	13.7418i	0.349945	+	0.606123i
$515$	−0.920934			−0.0405812
$516$	7.21750	−	7.27346i	0.317733	−	0.320196i
$517$	5.33237	+	9.23593i	0.234517	+	0.406196i
$518$		0			0
$519$	3.45180	−	3.47856i	0.151517	−	0.152692i
$520$	−0.401482	−	0.695387i	−0.0176061	−	0.0304947i
$521$	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	$0.567978\pi$
$522$	−26.4994	+	15.5735i	−1.15985	+	0.681635i
$523$	−7.18895	+	12.4516i	−0.314351	+	0.544471i	−0.979299	−	0.202418i	$-0.935120\pi$
$523$	−7.18895	+	12.4516i	−0.314351	+	0.544471i	0.664949	+	0.746889i	$0.268453\pi$
$524$	−5.86140	+	10.1522i	−0.256056	+	0.443502i
$525$		0			0
$526$	−0.848618	−	1.46985i	−0.0370015	−	0.0640885i
$527$	14.9407			0.650828
$528$	7.40227	−	7.45966i	0.322143	−	0.324640i
$529$	−19.4007			−0.843508
$530$	−0.580197	+	1.00493i	−0.0252022	+	0.0436514i
$531$	−0.103331	−	13.3792i	−0.00448416	−	0.580607i
$532$		0			0
$533$	9.28166	−	16.0763i	0.402033	−	0.696342i
$534$	3.02381	+	11.1132i	0.130853	+	0.480914i
$535$	0.956910	−	1.65742i	0.0413708	−	0.0716564i
$536$	−15.3062	+	26.5111i	−0.661127	+	1.14511i
$537$	12.3985	−	12.4947i	0.535037	−	0.539185i
$538$	14.4783	−	25.0772i	0.624205	−	1.08116i
$539$		0			0
$540$	0.413586	−	0.115971i	0.0177979	−	0.00499062i
$541$	12.5882	−	21.8034i	0.541210	−	0.937403i	−0.457625	−	0.889145i	$-0.651300\pi$
$541$	12.5882	−	21.8034i	0.541210	−	0.937403i	0.998835	−	0.0482577i	$-0.0153669\pi$
$542$	19.7773			0.849506
$543$	−7.77021	−	28.5573i	−0.333452	−	1.22551i
$544$	−6.67063			−0.286001
$545$	0.222664	+	0.385666i	0.00953789	+	0.0165201i
$546$		0			0
$547$	1.59011	−	2.75416i	0.0679883	−	0.117759i	−0.830027	−	0.557723i	$-0.811675\pi$
$547$	1.59011	−	2.75416i	0.0679883	−	0.117759i	0.898016	+	0.439963i	$0.145009\pi$
$548$	−5.97545	+	10.3498i	−0.255258	+	0.442121i
$549$	−14.7989	−	8.39245i	−0.631603	−	0.358181i
$550$	−9.18062	−	15.9013i	−0.391463	−	0.678034i
$551$	−35.6876	−	61.8127i	−1.52034	−	2.63331i
$552$	2.64861	+	9.73424i	0.112732	+	0.414317i
$553$		0			0
$554$	−10.4057	−	18.0233i	−0.442098	−	0.765736i
$555$	−0.350174	−	0.0923811i	−0.0148641	−	0.00392136i
$556$	−6.36358			−0.269876
$557$	−10.0229	−	17.3602i	−0.424686	−	0.735577i	0.571705	−	0.820459i	$-0.306282\pi$
$557$	−10.0229	−	17.3602i	−0.424686	−	0.735577i	−0.996391	+	0.0848820i	$0.972949\pi$
$558$	26.4172	−	15.5252i	1.11833	−	0.657236i
$559$	18.7181			0.791689
$560$		0			0
$561$	−6.56817	+	6.61909i	−0.277308	+	0.279458i
$562$	−5.50477			−0.232205
$563$	19.9007	−	34.4690i	0.838713	−	1.45269i	−0.0522584	−	0.998634i	$-0.516642\pi$
$563$	19.9007	−	34.4690i	0.838713	−	1.45269i	0.890971	−	0.454060i	$-0.150025\pi$
$564$	−1.13901	−	4.18611i	−0.0479609	−	0.176267i
$565$	0.108444	+	0.187831i	0.00456228	+	0.00790211i
$566$	16.9753			0.713523
$567$		0			0
$568$	10.1017			0.423856
$569$	−6.90797	−	11.9649i	−0.289597	−	0.501597i	0.684117	−	0.729373i	$-0.260188\pi$
$569$	−6.90797	−	11.9649i	−0.289597	−	0.501597i	−0.973714	+	0.227776i	$0.926855\pi$
$570$	−0.406344	−	1.49341i	−0.0170199	−	0.0625519i
$571$	−5.21935	+	9.04019i	−0.218423	+	0.378320i	−0.954326	−	0.298767i	$-0.903425\pi$
$571$	−5.21935	+	9.04019i	−0.218423	+	0.378320i	0.735903	+	0.677087i	$0.236758\pi$
$572$	−6.48703			−0.271236
$573$	27.3281	−	27.5400i	1.14165	−	1.15050i
$574$		0			0
$575$	9.46483			0.394711
$576$	−21.1990	+	12.4585i	−0.883293	+	0.519106i
$577$	−12.7461	−	22.0769i	−0.530628	−	0.919075i	−0.999361	−	0.0357353i	$-0.988623\pi$
$577$	−12.7461	−	22.0769i	−0.530628	−	0.919075i	0.468733	−	0.883340i	$-0.344711\pi$
$578$	15.8779			0.660433
$579$	−0.430053	−	0.113454i	−0.0178724	−	0.00471500i
$580$	−0.383994	−	0.665098i	−0.0159445	−	0.0276167i
$581$		0			0
$582$	1.90697	+	7.00855i	0.0790466	+	0.290514i
$583$	16.6478	+	28.8349i	0.689483	+	1.19422i
$584$	7.25104	+	12.5592i	0.300050	+	0.519702i
$585$	0.682537	+	0.387066i	0.0282194	+	0.0160032i
$586$	14.2277	−	24.6431i	0.587740	−	1.01800i
$587$	−17.5168	+	30.3401i	−0.722998	+	1.25227i	0.236795	+	0.971560i	$0.423903\pi$
$587$	−17.5168	+	30.3401i	−0.722998	+	1.25227i	−0.959793	+	0.280709i	$0.909430\pi$
$588$		0			0
$589$	35.5769	+	61.6210i	1.46592	+	2.53905i
$590$	−0.518724			−0.0213555
$591$	0.347138	+	1.27581i	0.0142794	+	0.0524799i
$592$	3.60435			0.148138
$593$	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	$-0.0993724\pi$
$594$	−4.73536	+	18.5286i	−0.194294	+	0.760236i
$595$		0			0
$596$	−4.36915	+	7.56759i	−0.178967	+	0.309980i
$597$	−6.13811	+	6.18570i	−0.251216	+	0.253164i
$598$	−2.59433	+	4.49350i	−0.106090	+	0.183753i
$599$	20.4742	−	35.4623i	0.836552	−	1.44895i	−0.0562080	−	0.998419i	$-0.517901\pi$
$599$	20.4742	−	35.4623i	0.836552	−	1.44895i	0.892760	−	0.450532i	$-0.148766\pi$
$600$	6.96484	+	25.5973i	0.284338	+	1.04501i
$601$	12.8547	−	22.2650i	0.524354	−	0.908207i	−0.475244	−	0.879854i	$-0.657640\pi$
$601$	12.8547	−	22.2650i	0.524354	−	0.908207i	0.999598	−	0.0283533i	$-0.00902635\pi$
$602$		0			0
$603$	−0.231028	−	29.9133i	−0.00940817	−	1.21817i
$604$	−4.41810	+	7.65238i	−0.179770	+	0.311371i
$605$	0.0145196			0.000590304
$606$	23.5052	−	23.6874i	0.954831	−	0.962234i
$607$	6.84516			0.277836			0.138918	−	0.990304i	$-0.455638\pi$
$607$	6.84516			0.277836			0.138918	+	0.990304i	$0.455638\pi$
$608$	−15.8841	−	27.5121i	−0.644187	−	1.11576i
$609$		0			0
$610$	−0.329795	+	0.571222i	−0.0133530	+	0.0231281i
$611$	3.96246	−	6.86319i	0.160304	−	0.277655i
$612$	3.27031	−	1.92194i	0.132195	−	0.0776900i
$613$	14.5648	+	25.2271i	0.588269	+	1.01891i	0.994459	+	0.105123i	$0.0335235\pi$
$613$	14.5648	+	25.2271i	0.588269	+	1.01891i	−0.406191	+	0.913788i	$0.633143\pi$
$614$	−12.2917	−	21.2898i	−0.496051	−	0.859185i
$615$	0.963137	−	0.970604i	0.0388374	−	0.0391385i
$616$		0			0
$617$	−10.3395	−	17.9085i	−0.416252	−	0.720969i	0.579307	−	0.815109i	$-0.303323\pi$
$617$	−10.3395	−	17.9085i	−0.416252	−	0.720969i	−0.995559	+	0.0941404i	$0.969990\pi$
$618$	−11.7484	+	11.8395i	−0.472591	+	0.476255i
$619$	−8.86355			−0.356256			−0.178128	−	0.984007i	$-0.557004\pi$
$619$	−8.86355			−0.356256			−0.178128	+	0.984007i	$0.557004\pi$
$620$	0.382804	+	0.663035i	0.0153738	+	0.0266281i
$621$	−7.05099	−	6.88949i	−0.282947	−	0.276466i
$622$	1.44453			0.0579205
$623$		0			0
$624$	−7.55090	−	1.99204i	−0.302278	−	0.0797453i
$625$	24.8333			0.993331
$626$	11.8977	−	20.6074i	0.475528	−	0.823638i
$627$	−42.9397	−	11.3281i	−1.71485	−	0.452402i
$628$	−4.78368	−	8.28558i	−0.190890	−	0.330631i
$629$	−3.19820			−0.127521
$630$		0			0
$631$	26.4661			1.05360			0.526799	−	0.849990i	$-0.323392\pi$
$631$	26.4661			1.05360			0.526799	+	0.849990i	$0.323392\pi$
$632$	−11.8105	−	20.4564i	−0.469796	−	0.813711i
$633$	−8.79714	+	8.86535i	−0.349655	+	0.352366i
$634$	−13.6649	+	23.6683i	−0.542704	+	0.939990i
$635$	0.0334495			0.00132740
$636$	−3.55603	−	13.0692i	−0.141006	−	0.518227i
$637$		0			0
$638$	34.1928			1.35371
$639$	−8.51040	+	5.00151i	−0.336666	+	0.197857i
$640$	0.0405449	+	0.0702258i	0.00160268	+	0.00277592i
$641$	−16.5319			−0.652971			−0.326486	−	0.945202i	$-0.605864\pi$
$641$	−16.5319			−0.652971			−0.326486	+	0.945202i	$0.605864\pi$
$642$	−9.10035	−	33.4458i	−0.359162	−	1.32000i
$643$	−15.4460	−	26.7532i	−0.609130	−	1.05504i	−0.991384	−	0.130987i	$-0.958185\pi$
$643$	−15.4460	−	26.7532i	−0.609130	−	1.05504i	0.382254	−	0.924057i	$-0.375148\pi$
$644$		0			0
$645$	1.33316	+	0.351706i	0.0524930	+	0.0138484i
$646$	−6.83390	−	11.8367i	−0.268876	−	0.465707i
$647$	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	$0.825200\pi$
$648$	13.4438	−	24.1389i	0.528124	−	0.948267i
$649$	−7.44198	+	12.8899i	−0.292123	+	0.505972i
$650$	−6.82209	+	11.8162i	−0.267584	+	0.463470i
$651$		0			0
$652$	3.51247	+	6.08377i	0.137559	+	0.238259i
$653$	−44.8870			−1.75656			−0.878281	−	0.478144i	$-0.841310\pi$
$653$	−44.8870			−1.75656			−0.878281	+	0.478144i	$0.841310\pi$
$654$	7.79866	+	2.05740i	0.304952	+	0.0804508i
$655$	−1.57738			−0.0616335
$656$	−6.80438	+	11.7855i	−0.265667	+	0.460148i
$657$	−12.3271	−	6.99068i	−0.480926	−	0.272732i
$658$		0			0
$659$	8.96167	−	15.5221i	0.349097	−	0.604654i	−0.636992	−	0.770870i	$-0.719822\pi$
$659$	8.96167	−	15.5221i	0.349097	−	0.604654i	0.986089	+	0.166216i	$0.0531549\pi$
$660$	−0.462026	−	0.121889i	−0.0179844	−	0.00474454i
$661$	−16.5128	+	28.6010i	−0.642274	+	1.11245i	0.342649	+	0.939463i	$0.388676\pi$
$661$	−16.5128	+	28.6010i	−0.642274	+	1.11245i	−0.984924	+	0.172989i	$0.944658\pi$
$662$	7.63429	−	13.2230i	0.296715	−	0.513925i
$663$	6.70004	+	1.76757i	0.260208	+	0.0686467i
$664$	−1.79420	+	3.10765i	−0.0696285	+	0.120600i
$665$		0			0
$666$	−5.65485	+	3.32332i	−0.219121	+	0.128776i
$667$	−8.81283	+	15.2643i	−0.341234	+	0.591035i
$668$	13.6512			0.528182
$669$	18.7273	+	4.94053i	0.724038	+	0.191012i
$670$	−1.15977			−0.0448058
$671$	9.46295	+	16.3903i	0.365313	+	0.632741i
$672$		0			0
$673$	−10.6758	+	18.4909i	−0.411520	+	0.712774i	−0.995056	−	0.0993135i	$-0.968335\pi$
$673$	−10.6758	+	18.4909i	−0.411520	+	0.712774i	0.583536	+	0.812087i	$0.301669\pi$
$674$	−1.86865	+	3.23659i	−0.0719776	+	0.124669i
$675$	−18.5414	−	18.1167i	−0.713660	−	0.697313i
$676$	−2.68447	−	4.64964i	−0.103249	−	0.178832i
$677$	−4.15084	−	7.18946i	−0.159530	−	0.276313i	0.775170	−	0.631753i	$-0.217664\pi$
$677$	−4.15084	−	7.18946i	−0.159530	−	0.276313i	−0.934699	+	0.355440i	$0.884331\pi$
$678$	3.79818	+	1.00202i	0.145868	+	0.0384822i
$679$		0			0
$680$	−0.261161	−	0.452344i	−0.0100151	−	0.0173466i
$681$	10.8096	+	39.7276i	0.414224	+	1.52237i
$682$	−34.0868			−1.30525
$683$	−1.24728	−	2.16036i	−0.0477259	−	0.0826637i	0.841176	−	0.540762i	$-0.181864\pi$
$683$	−1.24728	−	2.16036i	−0.0477259	−	0.0826637i	−0.888902	+	0.458098i	$0.848531\pi$
$684$	15.7141	+	8.91143i	0.600843	+	0.340737i
$685$	−1.60808			−0.0614414
$686$		0			0
$687$	−0.866505	−	3.18460i	−0.0330592	−	0.121500i
$688$	−13.7222			−0.523154
$689$	12.3710	−	21.4271i	0.471296	−	0.816308i
$690$	−0.269207	+	0.271295i	−0.0102486	+	0.0103280i
$691$	8.43455	+	14.6091i	0.320865	+	0.555755i	0.980667	−	0.195685i	$-0.0626930\pi$
$691$	8.43455	+	14.6091i	0.320865	+	0.555755i	−0.659801	+	0.751440i	$0.729360\pi$
$692$	2.21763			0.0843017
$693$		0			0
$694$	16.0071			0.607621
$695$	−0.428132	−	0.741547i	−0.0162400	−	0.0281285i
$696$	−47.7668	−	12.6016i	−1.81060	−	0.477662i
$697$	6.03765	−	10.4575i	0.228692	−	0.396107i
$698$	17.3453			0.656530
$699$	10.9559	+	2.89034i	0.414392	+	0.109323i
$700$		0			0
$701$	16.4806			0.622465			0.311232	−	0.950334i	$-0.399258\pi$
$701$	16.4806			0.622465			0.311232	+	0.950334i	$0.399258\pi$
$702$	13.6833	−	3.83686i	0.516443	−	0.144813i
$703$	−7.61558	−	13.1906i	−0.287227	−	0.497492i
$704$	27.3536			1.03093
$705$	0.411176	−	0.414364i	0.0154858	−	0.0156058i
$706$	−2.28515	−	3.95800i	−0.0860029	−	0.148961i
$707$		0			0
$708$	4.26472	−	4.29778i	0.160278	−	0.161520i
$709$	14.7462	+	25.5412i	0.553807	+	0.959222i	0.997995	+	0.0632882i	$0.0201587\pi$
$709$	14.7462	+	25.5412i	0.553807	+	0.959222i	−0.444188	+	0.895933i	$0.646508\pi$
$710$	0.191354	+	0.331434i	0.00718138	+	0.0124385i
$711$	20.0784	+	11.3864i	0.752998	+	0.427024i
$712$	−9.25539	+	16.0308i	−0.346860	+	0.600780i
$713$	8.78551	−	15.2169i	0.329020	−	0.569879i
$714$		0			0
$715$	−0.436438	−	0.755933i	−0.0163219	−	0.0282703i
$716$	7.96554			0.297686
$717$	26.0434	−	26.2453i	0.972608	−	0.980149i
$718$	−8.75620			−0.326779
$719$	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	$0.164087\pi$
$720$	−0.500368	−	0.283758i	−0.0186476	−	0.0105750i
$721$		0			0
$722$	22.0691	−	38.2248i	0.821327	−	1.42258i
$723$	−9.12499	−	33.5364i	−0.339362	−	1.24723i
$724$	6.69640	−	11.5985i	0.248870	−	0.431055i
$725$	−23.1744	+	40.1392i	−0.860675	+	1.49073i
$726$	0.185227	−	0.186663i	0.00687443	−	0.00692772i
$727$	13.5839	−	23.5280i	0.503799	−	0.872605i	−0.496192	−	0.868213i	$-0.665269\pi$
$727$	13.5839	−	23.5280i	0.503799	−	0.872605i	0.999990	−	0.00439187i	$-0.00139798\pi$
$728$		0			0
$729$	0.625513	+	26.9928i	0.0231672	+	0.999732i
$730$	−0.274710	+	0.475812i	−0.0101675	+	0.0176106i
$731$	12.1760			0.450344
$732$	−2.02131	−	7.42878i	−0.0747099	−	0.274576i
$733$	−5.66614			−0.209284			−0.104642	−	0.994510i	$-0.533370\pi$
$733$	−5.66614			−0.209284			−0.104642	+	0.994510i	$0.533370\pi$
$734$	−7.25050	−	12.5582i	−0.267621	−	0.463533i
$735$		0			0
$736$	−3.92249	+	6.79395i	−0.144585	+	0.250428i
$737$	−16.6389	+	28.8194i	−0.612901	+	1.06158i
$738$	−0.191259	−	24.7642i	−0.00704035	−	0.911581i
$739$	6.80540	+	11.7873i	0.250341	+	0.433603i	0.963620	−	0.267278i	$-0.0861241\pi$
$739$	6.80540	+	11.7873i	0.250341	+	0.433603i	−0.713279	+	0.700880i	$0.752791\pi$
$740$	−0.0819427	−	0.141929i	−0.00301227	−	0.00521741i
$741$	8.66407	+	31.8424i	0.318282	+	1.16976i
$742$		0			0
$743$	−6.33421	−	10.9712i	−0.232380	−	0.402493i	0.726128	−	0.687559i	$-0.241318\pi$
$743$	−6.33421	−	10.9712i	−0.232380	−	0.402493i	−0.958508	+	0.285066i	$0.907985\pi$
$744$	47.6187	+	12.5625i	1.74579	+	0.460564i
$745$	−1.17580			−0.0430779
$746$	4.30696	+	7.45988i	0.157689	+	0.273126i
$747$	−0.0270812	−	3.50646i	−0.000990849	−	0.128295i
$748$	−4.21977			−0.154290
$749$		0			0
$750$	−1.41740	+	1.42839i	−0.0517563	+	0.0521576i
$751$	−7.14538			−0.260739			−0.130369	−	0.991465i	$-0.541616\pi$
$751$	−7.14538			−0.260739			−0.130369	+	0.991465i	$0.541616\pi$
$752$	−2.90488	+	5.03140i	−0.105930	+	0.183476i
$753$	−3.09894	−	11.3893i	−0.112931	−	0.415048i
$754$	−12.7043	−	22.0045i	−0.462663	−	0.801355i
$755$	−1.18897			−0.0432712
$756$		0			0
$757$	37.6446			1.36822			0.684108	−	0.729381i	$-0.260192\pi$
$757$	37.6446			1.36822			0.684108	+	0.729381i	$0.260192\pi$
$758$	−17.4325	−	30.1940i	−0.633178	−	1.09670i
$759$	2.87922	+	10.5818i	0.104509	+	0.384094i
$760$	1.24376	−	2.15425i	0.0451157	−	0.0781428i
$761$	10.0472			0.364209			0.182104	−	0.983279i	$-0.441709\pi$
$761$	10.0472			0.364209			0.182104	+	0.983279i	$0.441709\pi$
$762$	0.426718	−	0.430027i	0.0154584	−	0.0155782i
$763$		0			0
$764$	17.5572			0.635196
$765$	0.443986	+	0.251783i	0.0160523	+	0.00910325i
$766$	−5.91762	−	10.2496i	−0.213812	−	0.370334i
$767$	11.0602			0.399361
$768$	−26.0335	−	6.86801i	−0.939402	−	0.247828i
$769$	16.1463	+	27.9663i	0.582252	+	1.00849i	0.995212	+	0.0977407i	$0.0311616\pi$
$769$	16.1463	+	27.9663i	0.582252	+	1.00849i	−0.412960	+	0.910749i	$0.635505\pi$
$770$		0			0
$771$	−6.54301	−	24.0470i	−0.235641	−	0.866032i
$772$	−0.100635	−	0.174305i	−0.00362192	−	0.00627336i
$773$	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	$0.494987\pi$
$774$	21.5287	−	12.6523i	0.773834	−	0.454778i
$775$	23.1025	−	40.0148i	0.829867	−	1.43737i
$776$	−5.83694	+	10.1099i	−0.209534	+	0.362923i
$777$		0			0
$778$	13.3147	+	23.0618i	0.477356	+	0.826806i
$779$	57.5075			2.06042
$780$	0.0932244	+	0.342620i	0.00333797	+	0.0122678i
$781$	10.9812			0.392938
$782$	−1.68759	+	2.92299i	−0.0603481	+	0.104526i
$783$	46.4817	−	13.0337i	1.66112	−	0.465786i
$784$		0			0
$785$	0.643678	−	1.11488i	0.0229739	−	0.0397919i
$786$	−20.1228	+	20.2788i	−0.717757	+	0.723322i
$787$	−24.4776	+	42.3964i	−0.872531	+	1.51127i	−0.0131602	+	0.999913i	$0.504189\pi$
$787$	−24.4776	+	42.3964i	−0.872531	+	1.51127i	−0.859370	+	0.511354i	$0.829144\pi$
$788$	−0.299165	+	0.518170i	−0.0106573	+	0.0184590i
$789$	0.699855	+	2.57212i	0.0249155	+	0.0915700i
$790$	0.447448	−	0.775003i	0.0159195	−	0.0275734i
$791$		0			0
$792$	−26.4994	+	15.5735i	−0.941615	+	0.553381i
$793$	7.03188	−	12.1796i	0.249710	−	0.432510i
$794$	−26.5303			−0.941525
$795$	1.28371	−	1.29366i	0.0455284	−	0.0458813i
$796$	−3.94348			−0.139773
$797$	1.44417	+	2.50137i	0.0511550	+	0.0886030i	0.890469	−	0.455044i	$-0.150376\pi$
$797$	1.44417	+	2.50137i	0.0511550	+	0.0886030i	−0.839314	+	0.543647i	$0.817043\pi$
$798$		0			0
$799$	2.57755	−	4.46445i	0.0911873	−	0.157941i
$800$	−10.3147	+	17.8655i	−0.364678	+	0.631641i
$801$	−0.139698	−	18.0881i	−0.00493600	−	0.639111i
$802$	−0.861472	−	1.49211i	−0.0304196	−	0.0526883i
$803$	7.88237	+	13.6527i	0.278163	+	0.481792i
$804$	9.53510	−	9.60903i	0.336277	−	0.338884i
$805$		0			0
$806$	12.6649	+	21.9362i	0.446102	+	0.772671i
$807$	−32.0338	+	32.2822i	−1.12764	+	1.13639i
$808$	53.6339			1.88683
$809$	−5.84869	−	10.1302i	−0.205629	−	0.356160i	0.744704	−	0.667395i	$-0.232591\pi$
$809$	−5.84869	−	10.1302i	−0.205629	−	0.356160i	−0.950333	+	0.311235i	$0.899257\pi$
$810$	1.04666	−	0.0161682i	0.0367759	−	0.000568091i
$811$	−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
$813$	−30.0341	−	7.92343i	−1.05334	−	0.277887i
$814$	7.29660			0.255746
$815$	−0.472627	+	0.818614i	−0.0165554	+	0.0286748i
$816$	−4.91180	−	1.29581i	−0.171947	−	0.0453623i
$817$	28.9934	+	50.2181i	1.01435	+	1.75691i
$818$	24.6431			0.861624
$819$		0			0
$820$	0.618775			0.0216085
$821$	−17.0068	−	29.4567i	−0.593543	−	1.02805i	−0.993751	−	0.111622i	$-0.964396\pi$
$821$	−17.0068	−	29.4567i	−0.593543	−	1.02805i	0.400208	−	0.916424i	$-0.368938\pi$
$822$	−20.5144	+	20.6734i	−0.715521	+	0.721068i
$823$	−21.6890	+	37.5664i	−0.756031	+	1.30948i	0.188829	+	0.982010i	$0.439531\pi$
$823$	−21.6890	+	37.5664i	−0.756031	+	1.30948i	−0.944860	+	0.327474i	$0.893803\pi$
$824$	−26.8075			−0.933883
$825$	7.57125	+	27.8260i	0.263597	+	0.968779i
$826$		0			0
$827$	−34.0909			−1.18546			−0.592728	−	0.805403i	$-0.701949\pi$
$827$	−34.0909			−1.18546			−0.592728	+	0.805403i	$0.701949\pi$
$828$	−0.0344527	−	4.46092i	−0.00119732	−	0.155028i
$829$	8.45833	+	14.6503i	0.293770	+	0.508824i	0.974698	−	0.223526i	$-0.0717567\pi$
$829$	8.45833	+	14.6503i	0.293770	+	0.508824i	−0.680928	+	0.732350i	$0.738423\pi$
$830$	−0.135949			−0.00471885
$831$	8.58161	+	31.5393i	0.297693	+	1.09409i
$832$	−10.1632	−	17.6032i	−0.352345	−	0.610280i
$833$		0			0
$834$	−14.9950	−	3.95591i	−0.519236	−	0.136982i
$835$	0.918434	+	1.59077i	0.0317837	+	0.0550510i
$836$	−10.0481	−	17.4039i	−0.347522	−	0.601926i
$837$	−46.3375	+	12.9933i	−1.60166	+	0.449113i
$838$	−3.29353	+	5.70456i	−0.113773	+	0.197061i
$839$	−8.16244	+	14.1378i	−0.281799	+	0.488089i	−0.971828	−	0.235692i	$-0.924264\pi$
$839$	−8.16244	+	14.1378i	−0.281799	+	0.488089i	0.690029	+	0.723782i	$0.257598\pi$
$840$		0			0
$841$	−28.6560	−	49.6336i	−0.988138	−	1.71150i
$842$	16.1362			0.556092
$843$	8.35964	+	2.20539i	0.287921	+	0.0759578i
$844$	−5.65179			−0.194543
$845$	0.361214	−	0.625641i	0.0124261	−	0.0215227i
$846$	−0.0816511	−	10.5721i	−0.00280722	−	0.363478i
$847$		0			0
$848$	−9.06915	+	15.7082i	−0.311436	+	0.539423i
$849$	−25.7789	−	6.80085i	−0.884730	−	0.233405i
$850$	−4.43772	+	7.68635i	−0.152212	+	0.263640i
$851$	−1.88062	+	3.25733i	−0.0644668	+	0.111660i
$852$	−4.31925	−	1.13948i	−0.147975	−	0.0390380i
$853$	−14.4524	+	25.0323i	−0.494841	+	0.857089i	−0.999982	−	0.00594733i	$-0.998107\pi$
$853$	−14.4524	+	25.0323i	−0.494841	+	0.857089i	0.505142	+	0.863036i	$0.331440\pi$
$854$		0			0
$855$	0.0187729	+	2.43071i	0.000642020	+	0.0831285i
$856$	27.8547	−	48.2458i	0.952055	−	1.64901i
$857$	−29.0567			−0.992559			−0.496280	−	0.868163i	$-0.665301\pi$
$857$	−29.0567			−0.992559			−0.496280	+	0.868163i	$0.665301\pi$
$858$	−15.2859	−	4.03265i	−0.521853	−	0.137673i
$859$	−12.5964			−0.429783			−0.214892	−	0.976638i	$-0.568940\pi$
$859$	−12.5964			−0.429783			−0.214892	+	0.976638i	$0.568940\pi$
$860$	0.311966	+	0.540341i	0.0106380	+	0.0184255i
$861$		0			0
$862$	−10.6992	+	18.5315i	−0.364415	+	0.631185i
$863$	7.33309	−	12.7013i	0.249621	−	0.432357i	−0.713799	−	0.700350i	$-0.753027\pi$
$863$	7.33309	−	12.7013i	0.249621	−	0.432357i	0.963421	+	0.267993i	$0.0863605\pi$
$864$	20.6885	−	5.80114i	0.703836	−	0.197359i
$865$	0.149199	+	0.258420i	0.00507292	+	0.00878655i
$866$	0.745594	+	1.29141i	0.0253363	+	0.0438838i
$867$	−24.1124	−	6.36122i	−0.818901	−	0.216038i
$868$		0			0
$869$	−12.8388	−	22.2375i	−0.435527	−	0.754354i
$870$	−0.491381	−	1.80593i	−0.0166594	−	0.0612269i
$871$	24.7286			0.837896
$872$	6.48154	+	11.2264i	0.219493	+	0.380172i
$873$	−0.0881012	−	11.4073i	−0.00298177	−	0.386079i
$874$	−16.0740			−0.543711
$875$		0			0
$876$	−1.68370	−	6.18797i	−0.0568869	−	0.209072i
$877$	33.1902			1.12075			0.560376	−	0.828238i	$-0.310657\pi$
$877$	33.1902			1.12075			0.560376	+	0.828238i	$0.310657\pi$
$878$	9.56205	−	16.5620i	0.322704	−	0.558939i
$879$	−31.4792	+	31.7233i	−1.06177	+	1.07000i
$880$	0.319953	+	0.554174i	0.0107856	+	0.0186812i
$881$	−31.7179			−1.06860			−0.534301	−	0.845294i	$-0.679425\pi$
$881$	−31.7179			−1.06860			−0.534301	+	0.845294i	$0.679425\pi$
$882$		0			0
$883$	−39.5231			−1.33006			−0.665029	−	0.746818i	$-0.731581\pi$
$883$	−39.5231			−1.33006			−0.665029	+	0.746818i	$0.731581\pi$
$884$	1.56785	+	2.71559i	0.0527324	+	0.0913352i
$885$	0.787743	+	0.207818i	0.0264797	+	0.00698573i
$886$	10.8131	−	18.7288i	0.363272	−	0.629206i
$887$	49.9026			1.67556			0.837782	−	0.546005i	$-0.183852\pi$
$887$	49.9026			1.67556			0.837782	+	0.546005i	$0.183852\pi$
$888$	−10.1932	−	2.68912i	−0.342062	−	0.0902411i
$889$		0			0
$890$	−0.701292			−0.0235074
$891$	14.6144	−	26.2407i	0.489599	−	0.879095i
$892$	4.38228	+	7.59034i	0.146730	+	0.254143i
$893$	24.5507			0.821559
$894$	−14.9998	+	15.1161i	−0.501667	+	0.505557i
$895$	0.535910	+	0.928223i	0.0179135	+	0.0310271i
$896$		0			0
$897$	5.74003	−	5.78454i	0.191654	−	0.193140i
$898$	−9.77891	−	16.9376i	−0.326326	−	0.565214i
$899$	43.0222	+	74.5166i	1.43487	+	2.48527i
$900$	−0.0905975	−	11.7305i	−0.00301992	−	0.391018i
$901$	8.04721	−	13.9382i	0.268092	−	0.464348i
$902$	−13.7747	+	23.8585i	−0.458648	+	0.794401i
$903$		0			0
$904$	3.15671	+	5.46757i	0.104990	+	0.181849i
$905$	1.80210			0.0599037
$906$	−15.1678	+	15.2854i	−0.503917	+	0.507824i
$907$	−13.9216			−0.462259			−0.231129	−	0.972923i	$-0.574242\pi$
$907$	−13.9216			−0.462259			−0.231129	+	0.972923i	$0.574242\pi$
$908$	−9.31574	+	16.1353i	−0.309154	+	0.535470i
$909$	−45.1853	+	26.5551i	−1.49870	+	0.880778i
$910$		0			0
$911$	2.70428	−	4.68394i	0.0895967	−	0.155186i	−0.817744	−	0.575582i	$-0.804776\pi$
$911$	2.70428	−	4.68394i	0.0895967	−	0.155186i	0.907341	+	0.420396i	$0.138109\pi$
$912$	−6.35163	−	23.3437i	−0.210323	−	0.772986i
$913$	−1.95042	+	3.37822i	−0.0645494	+	0.111803i
$914$	0.267681	−	0.463637i	0.00885409	−	0.0153357i
$915$	0.729683	−	0.735340i	0.0241226	−	0.0243096i
$916$	0.746758	−	1.29342i	0.0246736	−	0.0427359i
$917$		0			0
$918$	8.90089	−	2.49585i	0.293773	−	0.0823754i
$919$	−17.0142	+	29.4694i	−0.561245	+	0.972105i	0.436143	+	0.899877i	$0.356344\pi$
$919$	−17.0142	+	29.4694i	−0.561245	+	0.972105i	−0.997388	+	0.0722280i	$0.976989\pi$
$920$	−0.614276			−0.0202521
$921$	10.1369	+	37.2554i	0.334023	+	1.22761i
$922$	8.81561			0.290327
$923$	−4.08004	−	7.06683i	−0.134296	−	0.232608i
$924$		0			0
$925$	−4.94531	+	8.56554i	−0.162601	+	0.281633i
$926$	−5.78184	+	10.0144i	−0.190003	+	0.329095i
$927$	22.5847	−	13.2729i	0.741778	−	0.435939i
$928$	−19.2082	−	33.2696i	−0.630541	−	1.09213i
$929$	−5.31646	−	9.20837i	−0.174427	−	0.302117i	0.765536	−	0.643393i	$-0.222474\pi$
$929$	−5.31646	−	9.20837i	−0.174427	−	0.302117i	−0.939963	+	0.341277i	$0.889141\pi$
$930$	0.489857	+	1.80033i	0.0160631	+	0.0590353i
$931$		0			0
$932$	2.56375	+	4.44055i	0.0839785	+	0.145455i
$933$	−2.19369	−	0.578729i	−0.0718183	−	0.0189467i
$934$	−24.1491			−0.790183
$935$	−0.283900	−	0.491729i	−0.00928451	−	0.0160812i
$936$	19.8680	+	11.2671i	0.649406	+	0.368277i
$937$	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
$939$	−26.3241	+	26.5282i	−0.859053	+	0.865714i
$940$	0.264163			0.00861605
$941$	17.1828	−	29.7615i	0.560143	−	0.970197i	−0.437340	−	0.899296i	$-0.644079\pi$
$941$	17.1828	−	29.7615i	0.560143	−	0.970197i	0.997483	−	0.0709006i	$-0.0225873\pi$
$942$	−6.12147	−	22.4978i	−0.199448	−	0.733017i
$943$	−7.10057	−	12.2985i	−0.231226	−	0.400496i
$944$	−8.10825			−0.263901
$945$		0			0
$946$	−27.7791			−0.903175
$947$	20.2920	+	35.1468i	0.659401	+	1.14212i	0.980771	+	0.195162i	$0.0625234\pi$
$947$	20.2920	+	35.1468i	0.659401	+	1.14212i	−0.321370	+	0.946954i	$0.604143\pi$
$948$	2.74241	+	10.0790i	0.0890692	+	0.327349i
$949$	5.85736	−	10.1453i	0.190138	−	0.329329i
$950$	−42.2685			−1.37137
$951$	30.2341	−	30.4685i	0.980408	−	0.988009i
$952$		0			0
$953$	−22.6904			−0.735013			−0.367507	−	0.930021i	$-0.619789\pi$
$953$	−22.6904			−0.735013			−0.367507	+	0.930021i	$0.619789\pi$
$954$	−0.254918	−	33.0066i	−0.00825326	−	1.06863i
$955$	1.18122	+	2.04593i	0.0382234	+	0.0662049i
$956$	16.7318			0.541144
$957$	−51.9258	−	13.6988i	−1.67852	−	0.442819i
$958$	2.20656	+	3.82187i	0.0712907	+	0.123479i
$959$		0			0
$960$	−0.393096	−	1.44472i	−0.0126871	−	0.0466280i
$961$	−27.3888	−	47.4387i	−0.883509	−	1.53028i
$962$	−2.71104	−	4.69566i	−0.0874074	−	0.151394i
$963$	0.420432	+	54.4373i	0.0135482	+	1.75422i
$964$	7.86395	−	13.6208i	0.253281	−	0.438695i
$965$	0.0135411	−	0.0234539i	0.000435904	−	0.000755008i
$966$		0			0
$967$	−12.1388	−	21.0250i	−0.390357	−	0.676118i	0.602139	−	0.798391i	$-0.294315\pi$
$967$	−12.1388	−	21.0250i	−0.390357	−	0.676118i	−0.992497	+	0.122273i	$0.960982\pi$
$968$	0.422650			0.0135845
$969$	5.63591	+	20.7132i	0.181052	+	0.665405i
$970$	−0.442272			−0.0142005
$971$	−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	$0.905572\pi$
$972$	−8.47121	+	8.80481i	−0.271714	+	0.282414i
$973$		0			0
$974$	−14.5988	+	25.2858i	−0.467774	+	0.810209i
$975$	15.0941	−	15.2111i	0.483398	−	0.487146i
$976$	−5.15508	+	8.92885i	−0.165010	+	0.285806i
$977$	7.34481	−	12.7216i	0.234981	−	0.407000i	−0.724286	−	0.689500i	$-0.757830\pi$
$977$	7.34481	−	12.7216i	0.234981	−	0.407000i	0.959267	+	0.282500i	$0.0911637\pi$
$978$	4.49475	+	16.5192i	0.143726	+	0.528226i
$979$	−10.0612	+	17.4266i	−0.321558	+	0.556956i
$980$		0			0
$981$	−11.0189	−	6.24881i	−0.351807	−	0.199509i
$982$	−15.6764	+	27.1524i	−0.500255	+	0.866467i
$983$	−44.5909			−1.42223			−0.711115	−	0.703076i	$-0.751809\pi$
$983$	−44.5909			−1.42223			−0.711115	+	0.703076i	$0.751809\pi$
$984$	28.0360	−	28.2533i	0.893754	−	0.900684i
$985$	−0.0805096			−0.00256525
$986$	−8.26404	−	14.3137i	−0.263181	−	0.455842i
$987$		0			0
$988$	−7.46673	+	12.9328i	−0.237548	+	0.411446i
$989$	7.15976	−	12.4011i	0.227667	−	0.394331i
$990$	−1.01294	−	0.574436i	−0.0321933	−	0.0182568i
$991$	−12.0915	−	20.9430i	−0.384098	−	0.665277i	0.607546	−	0.794285i	$-0.292154\pi$
$991$	−12.0915	−	20.9430i	−0.384098	−	0.665277i	−0.991644	+	0.129007i	$0.958821\pi$
$992$	19.1487	+	33.1665i	0.607971	+	1.05304i
$993$	−16.8911	+	17.0221i	−0.536024	+	0.540179i
$994$		0			0
$995$	−0.265311	−	0.459532i	−0.00841093	−	0.0145682i
$996$	1.11771	−	1.12638i	0.0354160	−	0.0356906i
$997$	−10.8652			−0.344105			−0.172053	−	0.985088i	$-0.555040\pi$
$997$	−10.8652			−0.344105			−0.172053	+	0.985088i	$0.555040\pi$
$998$	−4.09760	−	7.09726i	−0.129707	−	0.224660i
$999$	9.91899	−	2.78133i	0.313823	−	0.0879974i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	63.40	odd	6
441.2.f.h.148.8	yes	24	63.58	even	3
441.2.f.h.295.7	yes	24	7.5	odd	6
441.2.f.h.295.8	yes	24	7.2	even	3
441.2.g.h.67.7		24	63.4	even	3	inner
441.2.g.h.67.8		24	63.31	odd	6	inner
441.2.g.h.79.7		24	1.1	even	1	trivial
441.2.g.h.79.8		24	7.6	odd	2	inner
441.2.h.h.214.5		24	7.4	even	3
441.2.h.h.214.6		24	7.3	odd	6
441.2.h.h.373.5		24	9.4	even	3
441.2.h.h.373.6		24	63.13	odd	6
1323.2.f.h.442.5		24	63.23	odd	6
1323.2.f.h.442.6		24	63.5	even	6
1323.2.f.h.883.5		24	21.2	odd	6
1323.2.f.h.883.6		24	21.5	even	6
1323.2.g.h.361.5		24	63.32	odd	6
1323.2.g.h.361.6		24	63.59	even	6
1323.2.g.h.667.5		24	3.2	odd	2
1323.2.g.h.667.6		24	21.20	even	2
1323.2.h.h.226.7		24	63.41	even	6
1323.2.h.h.226.8		24	9.5	odd	6
1323.2.h.h.802.7		24	21.17	even	6
1323.2.h.h.802.8		24	21.11	odd	6
3969.2.a.bh.1.5		12	63.61	odd	6
3969.2.a.bh.1.6		12	63.16	even	3
3969.2.a.bi.1.7		12	63.2	odd	6
3969.2.a.bi.1.8		12	63.47	even	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.551407 + 0.955065i) q^{2} +(-0.454745 - 1.67129i) q^{3} +(0.391901 - 0.678793i) q^{4} +0.105466 q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-2.58641 + 1.52002i) q^{9} +O(q^{10})\)	\(q+(0.551407 + 0.955065i) q^{2} +(-0.454745 - 1.67129i) q^{3} +(0.391901 - 0.678793i) q^{4} +0.105466 q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-2.58641 + 1.52002i) q^{9} +(0.0581547 + 0.100727i) q^{10} +3.33731 q^{11} +(-1.31267 - 0.346303i) q^{12} +(-1.23997 - 2.14770i) q^{13} +(-0.0479602 - 0.176264i) q^{15} +(0.909025 + 1.57448i) q^{16} +(-0.806594 - 1.39706i) q^{17} +(-2.87788 - 1.63204i) q^{18} +(3.84133 - 6.65338i) q^{19} +(0.0413323 - 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} -1.89719 q^{23} +(-1.39607 - 5.13088i) q^{24} -4.98888 q^{25} +(1.36746 - 2.36851i) q^{26} +(3.71655 + 3.63142i) q^{27} +(4.64521 - 8.04574i) q^{29} +(0.141898 - 0.142998i) q^{30} +(-4.63081 + 8.02080i) q^{31} +(2.06753 - 3.58107i) q^{32} +(-1.51763 - 5.57762i) q^{33} +(0.889523 - 1.54070i) q^{34} +(0.0181599 + 2.35134i) q^{36} +(0.991268 - 1.71693i) q^{37} +8.47254 q^{38} +(-3.02555 + 3.04901i) q^{39} +0.323782 q^{40} +(3.74268 + 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +(1.30790 - 2.26534i) q^{44} +(-0.272779 + 0.160311i) q^{45} +(-1.04612 - 1.81194i) q^{46} +(1.59780 + 2.76747i) q^{47} +(2.21803 - 2.23523i) q^{48} +(-2.75090 - 4.76470i) q^{50} +(-1.96810 + 1.98336i) q^{51} -1.94379 q^{52} +(4.98839 + 8.64015i) q^{53} +(-1.41891 + 5.55194i) q^{54} +0.351974 q^{55} +(-12.8665 - 3.39438i) q^{57} +10.2456 q^{58} +(-2.22993 + 3.86235i) q^{59} +(-0.138443 - 0.0365232i) q^{60} +(2.83550 + 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(-0.130775 - 0.226509i) q^{65} +(4.49016 - 4.52497i) q^{66} +(-4.98571 + 8.63550i) q^{67} -1.26442 q^{68} +(0.862736 + 3.17075i) q^{69} +3.29042 q^{71} +(-7.94033 + 4.66648i) q^{72} +(2.36189 + 4.09091i) q^{73} +2.18637 q^{74} +(2.26867 + 8.33786i) q^{75} +(-3.01084 - 5.21493i) q^{76} +(-4.58031 - 1.20835i) q^{78} +(-3.84705 - 6.66328i) q^{79} +(0.0958713 + 0.166054i) q^{80} +(4.37908 - 7.86280i) q^{81} +(-4.12748 + 7.14901i) q^{82} +(-0.584428 + 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} -8.32378 q^{86} +(-15.5591 - 4.10473i) q^{87} +10.2456 q^{88} +(-3.01477 + 5.22173i) q^{89} +(-0.303519 - 0.172125i) q^{90} +(-0.743509 + 1.28780i) q^{92} +(15.5109 + 4.09200i) q^{93} +(-1.76208 + 3.05201i) q^{94} +(0.405130 - 0.701706i) q^{95} +(-6.92520 - 1.82697i) q^{96} +(-1.90127 + 3.29310i) q^{97} +(-8.63168 + 5.07279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Introduction

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