LMFDB - Embedded newform 441.2.g.h.67.8

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			67.8
Character	$\chi$	$=$	441.67
Dual form			441.2.g.h.79.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.551407 - 0.955065i) q^{2} +(0.454745 - 1.67129i) q^{3} +(0.391901 + 0.678793i) q^{4} -0.105466 q^{5} +(-1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-2.58641 - 1.52002i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.551407	−	0.955065i	0.389903	−	0.675333i	−0.602533	−	0.798094i	$-0.705842\pi$
$2$	0.551407	−	0.955065i	0.389903	−	0.675333i	0.992436	+	0.122762i	$0.0391750\pi$
$3$	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	$-0.507507\pi$
$5$	−0.105466			−0.0471659			−0.0235829	+	0.999722i	$0.507507\pi$
$6$	−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	$-0.721583\pi$
$13$	1.23997	−	2.14770i	0.343907	−	0.595664i	0.985155	+	0.171670i	$0.0549162\pi$
$14$		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	$-0.770659\pi$
$17$	0.806594	−	1.39706i	0.195628	−	0.338837i	0.947106	+	0.320921i	$0.103992\pi$
$18$	−2.87788	+	1.63204i	−0.678324	+	0.384676i
$19$	−3.84133	−	6.65338i	−0.881262	−	1.52639i	−0.849939	−	0.526880i	$-0.823362\pi$
$19$	−3.84133	−	6.65338i	−0.881262	−	1.52639i	−0.0313221	−	0.999509i	$-0.509972\pi$
$20$	−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	0.869416	+	0.494080i	$0.164495\pi$
$29$	4.64521	+	8.04574i	0.862594	+	1.49406i	−0.00682200	+	0.999977i	$0.502172\pi$
$30$	0.141898	+	0.142998i	0.0259070	+	0.0261078i
$31$	4.63081	+	8.02080i	0.831718	+	1.44058i	0.896675	+	0.442689i	$0.145976\pi$
$31$	4.63081	+	8.02080i	0.831718	+	1.44058i	−0.0649574	+	0.997888i	$0.520691\pi$
$32$	2.06753	+	3.58107i	0.365491	+	0.633049i
$33$	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	0.935930	−	0.352186i	$-0.114561\pi$
$37$	0.991268	+	1.71693i	0.162963	+	0.282261i	−0.772967	+	0.634447i	$0.781228\pi$
$38$	−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	0.410427	+	0.911893i	$0.365379\pi$
$41$	−3.74268	+	6.48252i	−0.584509	+	1.01240i	−0.994936	+	0.100506i	$0.967954\pi$
$42$		0			0
$43$	−3.77388	−	6.53655i	−0.575512	−	0.996815i	−0.995986	−	0.0895108i	$-0.971470\pi$
$43$	−3.77388	−	6.53655i	−0.575512	−	0.996815i	0.420474	−	0.907304i	$-0.361864\pi$
$44$	1.30790	+	2.26534i	0.197173	+	0.341514i
$45$	0.272779	+	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	$-0.908208\pi$
$47$	−1.59780	+	2.76747i	−0.233063	+	0.403677i	0.725645	+	0.688070i	$0.241542\pi$
$48$	−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	−0.288163	−	0.957581i	$-0.593044\pi$
$53$	4.98839	−	8.64015i	0.685209	−	1.18682i	0.973371	−	0.229234i	$-0.0736223\pi$
$54$	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	$-0.0729075\pi$
$59$	2.22993	+	3.86235i	0.290312	+	0.502836i	−0.683571	+	0.729884i	$0.739574\pi$
$60$	−0.138443	+	0.0365232i	−0.0178729	+	0.00471512i
$61$	−2.83550	+	4.91123i	−0.363048	+	0.628818i	−0.988461	−	0.151476i	$-0.951597\pi$
$61$	−2.83550	+	4.91123i	−0.363048	+	0.628818i	0.625413	+	0.780294i	$0.284931\pi$
$62$	10.2138			1.29716
$63$		0			0
$64$	8.19630			1.02454
$65$	−0.130775	+	0.226509i	−0.0162207	+	0.0280950i
$66$	−4.49016	−	4.52497i	−0.552700	−	0.556985i
$67$	−4.98571	−	8.63550i	−0.609101	−	1.05499i	−0.991389	−	0.130951i	$-0.958197\pi$
$67$	−4.98571	−	8.63550i	−0.609101	−	1.05499i	0.382288	−	0.924043i	$-0.375136\pi$
$68$	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	$-0.922488\pi$
$73$	−2.36189	+	4.09091i	−0.276438	+	0.478805i	0.694059	+	0.719919i	$0.255821\pi$
$74$	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	−0.997115	−	0.0758997i	$-0.975817\pi$
$79$	−3.84705	+	6.66328i	−0.432827	+	0.749678i	0.564289	+	0.825577i	$0.309150\pi$
$80$	−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	$-0.146233\pi$
$83$	0.584428	+	1.01226i	0.0641493	+	0.111110i	−0.832167	+	0.554525i	$0.812900\pi$
$84$		0			0
$85$	−0.0850683	+	0.147343i	−0.00922695	+	0.0159815i
$86$	−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	$-0.0631299\pi$
$89$	3.01477	+	5.22173i	0.319565	+	0.553503i	−0.660832	+	0.750534i	$0.729797\pi$
$90$	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	$-0.104830\pi$
$97$	1.90127	+	3.29310i	0.193045	+	0.334364i	−0.753213	+	0.657777i	$0.771497\pi$
$98$		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	$-0.835351\pi$
$101$	−17.4702			−1.73835			−0.869177	+	0.494501i	$0.835351\pi$
$102$	−2.97946	+	0.786025i	−0.295010	+	0.0778280i
$103$	8.73204			0.860394			0.430197	−	0.902735i	$-0.358444\pi$
$103$	8.73204			0.860394			0.430197	+	0.902735i	$0.358444\pi$
$104$	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	0.854471	+	0.519500i	$0.173882\pi$
$107$	9.07316	+	15.7152i	0.877135	+	1.51924i	0.0226645	+	0.999743i	$0.492785\pi$
$108$	−3.92150	−	1.09961i	−0.377347	−	0.105810i
$109$	2.11124	−	3.65678i	0.202220	−	0.350256i	−0.747023	−	0.664798i	$-0.768518\pi$
$109$	2.11124	−	3.65678i	0.202220	−	0.350256i	0.949243	+	0.314542i	$0.101851\pi$
$110$	−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	−0.813600	−	0.581425i	$-0.802495\pi$
$113$	1.02824	−	1.78096i	0.0967285	−	0.167539i	0.910329	+	0.413886i	$0.135829\pi$
$114$	−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	$-0.273355\pi$
$131$	14.9563			1.30674			0.653370	+	0.757039i	$0.273355\pi$
$132$	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	$-0.721444\pi$
$139$	4.05943	−	7.03114i	0.344316	−	0.596374i	0.985229	+	0.171240i	$0.0547774\pi$
$140$		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	$-0.328607\pi$
$157$	−6.10318	−	10.5710i	−0.487087	−	0.843659i	−0.999890	+	0.0148476i	$0.995274\pi$
$158$	4.24258	+	7.34836i	0.337521	+	0.584604i
$159$	−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	0.635422	−	0.772165i	$-0.280826\pi$
$163$	−4.48132	−	7.76187i	−0.351004	−	0.607957i	−0.986426	+	0.164209i	$0.947493\pi$
$164$	−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	0.302927	+	0.953014i	$0.402036\pi$
$167$	−8.70833	+	15.0833i	−0.673871	+	1.16718i	−0.976798	+	0.214165i	$0.931297\pi$
$168$		0			0
$169$	3.42493	+	5.93216i	0.263456	+	0.456320i
$170$	0.0938145	+	0.162491i	0.00719524	+	0.0124625i
$171$	−0.177999	+	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	$-0.867635\pi$
$173$	−1.41466	+	2.45027i	−0.107555	+	0.186291i	0.807224	+	0.590245i	$0.200969\pi$
$174$	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	−0.611235	−	0.791449i	$-0.709327\pi$
$179$	5.08135	−	8.80115i	0.379798	−	0.657829i	0.991033	+	0.133620i	$0.0426603\pi$
$180$	−0.00191525	+	0.247986i	−0.000142755	+	0.0184838i
$181$	−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
$183$	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	−0.102178	−	0.994766i	$-0.532581\pi$
$191$	11.2000	−	19.3990i	0.810404	−	1.40366i	0.912582	−	0.408894i	$-0.134086\pi$
$192$	3.72723	−	13.6984i	0.268989	−	0.988596i
$193$	0.128393	+	0.222383i	0.00924194	+	0.0160075i	0.870609	−	0.491975i	$-0.163725\pi$
$193$	0.128393	+	0.222383i	0.00924194	+	0.0160075i	−0.861367	+	0.507982i	$0.830391\pi$
$194$	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	$-0.776265\pi$
$199$	2.51561	−	4.35716i	0.178327	−	0.308871i	0.941307	+	0.337550i	$0.109598\pi$
$200$	−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	−0.963027	−	0.269403i	$-0.913174\pi$
$211$	−3.60537	+	6.24468i	−0.248204	+	0.429901i	0.714824	+	0.699305i	$0.246507\pi$
$212$	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	$-0.0445137\pi$
$223$	5.59106	+	9.68400i	0.374405	+	0.648488i	−0.615833	+	0.787877i	$0.711180\pi$
$224$		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	$-0.210673\pi$
$227$	23.7706			1.57771			0.788857	+	0.614577i	$0.210673\pi$
$228$	−7.34649	−	7.40345i	−0.486534	−	0.490306i
$229$	−1.90547			−0.125917			−0.0629586	−	0.998016i	$-0.520054\pi$
$229$	−1.90547			−0.125917			−0.0629586	+	0.998016i	$0.520054\pi$
$230$	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	$-0.235409\pi$
$233$	−3.27092	−	5.66540i	−0.214285	−	0.371153i	−0.953051	+	0.302809i	$0.902075\pi$
$234$	−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	−0.281295	−	0.959621i	$-0.590764\pi$
$239$	10.6735	−	18.4870i	0.690409	−	1.19582i	0.971704	−	0.236202i	$-0.0759028\pi$
$240$	0.233927	+	0.235741i	0.0150999	+	0.0152170i
$241$	−20.0662			−1.29258			−0.646288	−	0.763094i	$-0.723679\pi$
$241$	−20.0662			−1.29258			−0.646288	+	0.763094i	$0.723679\pi$
$242$	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	$-0.568998\pi$
$251$	−6.81467			−0.430138			−0.215069	+	0.976599i	$0.568998\pi$
$252$		0			0
$253$	−6.33151			−0.398059
$254$	0.174884	−	0.302907i	0.0109732	−	0.0190061i
$255$	0.207568	+	0.209177i	0.0129984	+	0.0130992i
$256$	7.77234	+	13.4621i	0.485771	+	0.841380i
$257$	−14.3883			−0.897518			−0.448759	−	0.893653i	$-0.648134\pi$
$257$	−14.3883			−0.897518			−0.448759	+	0.893653i	$0.648134\pi$
$258$	−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	−0.118852	−	0.992912i	$-0.537921\pi$
$269$	13.1285	−	22.7393i	0.800461	−	1.38644i	0.919313	−	0.393527i	$-0.128745\pi$
$270$	−0.149647	−	0.585541i	−0.00910724	−	0.0356349i
$271$	−8.96673	−	15.5308i	−0.544690	−	0.943431i	−0.998626	−	0.0523969i	$-0.983314\pi$
$271$	−8.96673	−	15.5308i	−0.544690	−	0.943431i	0.453936	−	0.891034i	$-0.350019\pi$
$272$	−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	0.781930	−	0.623366i	$-0.214235\pi$
$281$	−2.49578	−	4.32283i	−0.148886	−	0.257878i	−0.930816	+	0.365488i	$0.880902\pi$
$282$	5.90208	−	1.55706i	0.351464	−	0.0927213i
$283$	−7.69634	−	13.3304i	−0.457500	−	0.792413i	0.541328	−	0.840811i	$-0.317922\pi$
$283$	−7.69634	−	13.3304i	−0.457500	−	0.792413i	−0.998828	+	0.0483984i	$0.984588\pi$
$284$	1.28952	+	2.23352i	0.0765190	+	0.132535i
$285$	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	−0.192318	−	0.981333i	$-0.561601\pi$
$293$	12.9013	−	22.3456i	0.753700	−	1.30545i	0.946018	−	0.324114i	$-0.105066\pi$
$294$		0			0
$295$	−0.235182	−	0.407347i	−0.0136928	−	0.0237167i
$296$	3.04321	+	5.27099i	0.176883	+	0.306370i
$297$	−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	$-0.280538\pi$
$307$	22.2914			1.27224			0.636120	+	0.771590i	$0.280538\pi$
$308$		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	$-0.178491\pi$
$311$	−0.654931	−	1.13437i	−0.0371377	−	0.0643245i	−0.883997	+	0.467493i	$0.845157\pi$
$312$	−9.28849	−	9.36050i	−0.525857	−	0.529934i
$313$	10.7885	−	18.6862i	0.609802	−	1.05621i	−0.381471	−	0.924381i	$-0.624582\pi$
$313$	10.7885	−	18.6862i	0.609802	−	1.05621i	0.991273	−	0.131827i	$-0.0420843\pi$
$314$	−13.4613			−0.759667
$315$		0			0
$316$	−6.03065			−0.339250
$317$	12.3910	−	21.4618i	0.695946	−	1.20541i	−0.273915	−	0.961754i	$-0.588319\pi$
$317$	12.3910	−	21.4618i	0.695946	−	1.20541i	0.969861	−	0.243660i	$-0.0783480\pi$
$318$	−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	−0.991133	−	0.132870i	$-0.957581\pi$
$331$	−6.92256	+	11.9902i	−0.380498	+	0.659042i	0.610635	+	0.791912i	$0.290914\pi$
$332$	−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	−0.816178	−	0.577801i	$-0.803911\pi$
$337$	1.69444	−	2.93485i	0.0923018	−	0.159871i	0.908479	+	0.417930i	$0.137244\pi$
$338$	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	0.992395	−	0.123091i	$-0.0392809\pi$
$347$	7.25739	+	12.5702i	0.389597	+	0.674802i	−0.602798	+	0.797894i	$0.705948\pi$
$348$	8.88391	+	8.95279i	0.476228	+	0.479920i
$349$	−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
$351$	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	$-0.464823\pi$
$353$	4.14423			0.220575			0.110287	+	0.993900i	$0.464823\pi$
$354$	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	0.742040	−	0.670356i	$-0.233859\pi$
$359$	−3.96994	−	6.87614i	−0.209525	−	0.362909i	−0.951565	+	0.307447i	$0.900525\pi$
$360$	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	$-0.388493\pi$
$367$	13.1491			0.686377			0.343189	+	0.939266i	$0.388493\pi$
$368$	−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	$-0.411592\pi$
$383$	10.7319			0.548373			0.274186	+	0.961677i	$0.411592\pi$
$384$	−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	0.992257	+	0.124203i	$0.0396373\pi$
$397$	12.0285	+	20.8339i	0.603691	+	1.04562i	−0.388566	+	0.921421i	$0.627029\pi$
$398$	−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	−0.998096	−	0.0616748i	$-0.980356\pi$
$409$	−11.1728	−	19.3519i	−0.552460	−	0.956889i	0.445636	−	0.895214i	$-0.352977\pi$
$410$	−0.435309	−	0.753978i	−0.0214984	−	0.0372363i
$411$	−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	$-0.879941\pi$
$419$	−2.98648	+	5.17273i	−0.145899	+	0.252704i	0.783809	+	0.621002i	$0.213274\pi$
$420$		0			0
$421$	7.31594	+	12.6716i	0.356557	+	0.617575i	0.987383	−	0.158349i	$-0.0506172\pi$
$421$	7.31594	+	12.6716i	0.356557	+	0.617575i	−0.630826	+	0.775924i	$0.717284\pi$
$422$	3.97605	+	6.88672i	0.193551	+	0.335240i
$423$	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	−0.531989	−	0.846751i	$-0.678555\pi$
$431$	9.70169	−	16.8038i	0.467314	−	0.809411i	0.999303	+	0.0373401i	$0.0118885\pi$
$432$	2.33916	+	9.15268i	0.112543	+	0.440359i
$433$	−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
$435$	−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	$-0.697526\pi$
$439$	8.67059	−	15.0179i	0.413825	−	0.716766i	0.995304	+	0.0967954i	$0.0308592\pi$
$440$	−1.08056			−0.0515139
$441$		0			0
$442$	−4.41194			−0.209854
$443$	−9.80499	+	16.9827i	−0.465849	+	0.806874i	−0.999239	−	0.0389949i	$-0.987584\pi$
$443$	−9.80499	+	16.9827i	−0.465849	+	0.806874i	0.533390	+	0.845869i	$0.320918\pi$
$444$	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	−0.871647	−	0.490135i	$-0.836948\pi$
$457$	−0.242725	+	0.420413i	−0.0113542	+	0.0196661i	0.860292	+	0.509801i	$0.170281\pi$
$458$	−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	$-0.226269\pi$
$461$	−3.99687	−	6.92279i	−0.186153	−	0.322426i	−0.943964	+	0.330047i	$0.892935\pi$
$462$		0			0
$463$	5.24280	−	9.08080i	0.243654	−	0.422021i	−0.718098	−	0.695942i	$-0.754987\pi$
$463$	5.24280	−	9.08080i	0.243654	−	0.422021i	0.961752	+	0.273921i	$0.0883206\pi$
$464$	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	0.999970	+	0.00769944i	$0.00245083\pi$
$467$	10.9489	+	18.9640i	0.506653	+	0.877549i	−0.493317	+	0.869849i	$0.664216\pi$
$468$	−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	$-0.529141\pi$
$479$	−4.00169			−0.182842			−0.0914210	+	0.995812i	$0.529141\pi$
$480$	−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	−0.392982	−	0.919546i	$-0.628557\pi$
$487$	13.2377	−	22.9284i	0.599859	−	1.03899i	0.992841	−	0.119440i	$-0.0381100\pi$
$488$	−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	−0.343584	−	0.939122i	$-0.611641\pi$
$491$	14.2149	−	24.6210i	0.641511	−	1.11113i	0.985096	−	0.172008i	$-0.0550255\pi$
$492$	−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	$-0.427262\pi$
$503$	10.1610			0.453057			0.226529	+	0.974004i	$0.427262\pi$
$504$		0			0
$505$	1.84252			0.0819910
$506$	−3.49124	+	6.04700i	−0.155204	+	0.268822i
$507$	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	$-0.721325\pi$
$509$	−28.9063			−1.28125			−0.640625	+	0.767854i	$0.721325\pi$
$510$	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	0.211941	+	0.977283i	$0.432022\pi$
$521$	−16.8995	+	29.2708i	−0.740381	+	1.28238i	−0.952322	+	0.305095i	$0.901312\pi$
$522$	−26.4994	−	15.5735i	−1.15985	−	0.681635i
$523$	7.18895	+	12.4516i	0.314351	+	0.544471i	0.979299	−	0.202418i	$-0.0648799\pi$
$523$	7.18895	+	12.4516i	0.314351	+	0.544471i	−0.664949	+	0.746889i	$0.731547\pi$
$524$	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	0.998835	+	0.0482577i	$0.0153669\pi$
$541$	12.5882	+	21.8034i	0.541210	+	0.937403i	−0.457625	+	0.889145i	$0.651300\pi$
$542$	−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	0.898016	−	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
$549$	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	−0.996391	−	0.0848820i	$-0.972949\pi$
$557$	−10.0229	+	17.3602i	−0.424686	+	0.735577i	0.571705	+	0.820459i	$0.306282\pi$
$558$	−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	−0.890971	−	0.454060i	$-0.849975\pi$
$563$	−19.9007	−	34.4690i	−0.838713	−	1.45269i	0.0522584	−	0.998634i	$-0.483358\pi$
$564$	−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	−0.973714	−	0.227776i	$-0.926855\pi$
$569$	−6.90797	+	11.9649i	−0.289597	+	0.501597i	0.684117	+	0.729373i	$0.260188\pi$
$570$	0.406344	−	1.49341i	0.0170199	−	0.0625519i
$571$	−5.21935	−	9.04019i	−0.218423	−	0.378320i	0.735903	−	0.677087i	$-0.236758\pi$
$571$	−5.21935	−	9.04019i	−0.218423	−	0.378320i	−0.954326	+	0.298767i	$0.903425\pi$
$572$	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	−0.468733	−	0.883340i	$-0.655289\pi$
$577$	12.7461	−	22.0769i	0.530628	−	0.919075i	0.999361	−	0.0357353i	$-0.0113773\pi$
$578$	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	0.959793	+	0.280709i	$0.0905697\pi$
$587$	17.5168	+	30.3401i	0.722998	+	1.25227i	−0.236795	+	0.971560i	$0.576097\pi$
$588$		0			0
$589$	35.5769	−	61.6210i	1.46592	−	2.53905i
$590$	−0.518724			−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	−0.951664	−	0.307141i	$-0.900628\pi$
$593$	−18.0646	−	31.2888i	−0.741824	−	1.28488i	0.209840	−	0.977736i	$-0.432706\pi$
$594$	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	0.892760	+	0.450532i	$0.148766\pi$
$599$	20.4742	+	35.4623i	0.836552	+	1.44895i	−0.0562080	+	0.998419i	$0.517901\pi$
$600$	−6.96484	+	25.5973i	−0.284338	+	1.04501i
$601$	−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
$603$	−0.231028	+	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	$-0.544362\pi$
$607$	−6.84516			−0.277836			−0.138918	+	0.990304i	$0.544362\pi$
$608$	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	−0.406191	−	0.913788i	$-0.633143\pi$
$613$	14.5648	−	25.2271i	0.588269	−	1.01891i	0.994459	−	0.105123i	$-0.0335235\pi$
$614$	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	−0.995559	−	0.0941404i	$-0.969990\pi$
$617$	−10.3395	+	17.9085i	−0.416252	+	0.720969i	0.579307	+	0.815109i	$0.303323\pi$
$618$	−11.7484	−	11.8395i	−0.472591	−	0.476255i
$619$	8.86355			0.356256			0.178128	−	0.984007i	$-0.442996\pi$
$619$	8.86355			0.356256			0.178128	+	0.984007i	$0.442996\pi$
$620$	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	−0.382254	−	0.924057i	$-0.624852\pi$
$643$	15.4460	−	26.7532i	0.609130	−	1.05504i	0.991384	−	0.130987i	$-0.0418147\pi$
$644$		0			0
$645$	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	$-0.841467\pi$
$647$	−0.649903	+	1.12567i	−0.0255503	+	0.0442545i	0.852968	+	0.521964i	$0.174800\pi$
$648$	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	0.986089	−	0.166216i	$-0.0531549\pi$
$659$	8.96167	+	15.5221i	0.349097	+	0.604654i	−0.636992	+	0.770870i	$0.719822\pi$
$660$	−0.462026	+	0.121889i	−0.0179844	+	0.00474454i
$661$	16.5128	+	28.6010i	0.642274	+	1.11245i	0.984924	+	0.172989i	$0.0553424\pi$
$661$	16.5128	+	28.6010i	0.642274	+	1.11245i	−0.342649	+	0.939463i	$0.611324\pi$
$662$	7.63429	+	13.2230i	0.296715	+	0.513925i
$663$	−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	0.583536	−	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
$675$	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	$-0.782336\pi$
$677$	4.15084	−	7.18946i	0.159530	−	0.276313i	0.934699	+	0.355440i	$0.115669\pi$
$678$	−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	−0.888902	−	0.458098i	$-0.848531\pi$
$683$	−1.24728	+	2.16036i	−0.0477259	+	0.0826637i	0.841176	+	0.540762i	$0.181864\pi$
$684$	−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	$-0.937307\pi$
$691$	−8.43455	+	14.6091i	−0.320865	+	0.555755i	0.659801	+	0.751440i	$0.270640\pi$
$692$	−2.21763			−0.0843017
$693$		0			0
$694$	16.0071			0.607621
$695$	−0.428132	+	0.741547i	−0.0162400	+	0.0281285i
$696$	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	−0.444188	−	0.895933i	$-0.646508\pi$
$709$	14.7462	−	25.5412i	0.553807	−	0.959222i	0.997995	−	0.0632882i	$-0.0201587\pi$
$710$	−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	$-0.169246\pi$
$719$	−0.217311	−	0.376394i	−0.00810433	−	0.0140371i	−0.870049	+	0.492965i	$0.835913\pi$
$720$	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	−0.999990	−	0.00439187i	$-0.998602\pi$
$727$	−13.5839	−	23.5280i	−0.503799	−	0.872605i	0.496192	−	0.868213i	$-0.334731\pi$
$728$		0			0
$729$	0.625513	−	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	$-0.466630\pi$
$733$	5.66614			0.209284			0.104642	+	0.994510i	$0.466630\pi$
$734$	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	−0.713279	−	0.700880i	$-0.752791\pi$
$739$	6.80540	−	11.7873i	0.250341	−	0.433603i	0.963620	+	0.267278i	$0.0861241\pi$
$740$	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	−0.958508	−	0.285066i	$-0.907985\pi$
$743$	−6.33421	+	10.9712i	−0.232380	+	0.402493i	0.726128	+	0.687559i	$0.241318\pi$
$744$	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	$-0.558291\pi$
$761$	−10.0472			−0.364209			−0.182104	+	0.983279i	$0.558291\pi$
$762$	−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	0.412960	+	0.910749i	$0.364495\pi$
$769$	−16.1463	+	27.9663i	−0.582252	+	1.00849i	−0.995212	+	0.0977407i	$0.968838\pi$
$770$		0			0
$771$	−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	−0.0157473	+	0.999876i	$0.505013\pi$
$773$	−24.2939	+	42.0783i	−0.873792	+	1.51345i	−0.858044	+	0.513576i	$0.828321\pi$
$774$	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	0.859370	+	0.511354i	$0.170856\pi$
$787$	24.4776	+	42.3964i	0.872531	+	1.51127i	0.0131602	+	0.999913i	$0.495811\pi$
$788$	−0.299165	−	0.518170i	−0.0106573	−	0.0184590i
$789$	−0.699855	+	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	$-0.849624\pi$
$797$	−1.44417	+	2.50137i	−0.0511550	+	0.0886030i	0.839314	+	0.543647i	$0.182957\pi$
$798$		0			0
$799$	2.57755	+	4.46445i	0.0911873	+	0.157941i
$800$	−10.3147	−	17.8655i	−0.364678	−	0.631641i
$801$	0.139698	−	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	−0.950333	−	0.311235i	$-0.899257\pi$
$809$	−5.84869	+	10.1302i	−0.205629	+	0.356160i	0.744704	+	0.667395i	$0.232591\pi$
$810$	−1.04666	−	0.0161682i	−0.0367759	−	0.000568091i
$811$	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
$813$	−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	0.400208	+	0.916424i	$0.368938\pi$
$821$	−17.0068	+	29.4567i	−0.593543	+	1.02805i	−0.993751	+	0.111622i	$0.964396\pi$
$822$	20.5144	+	20.6734i	0.715521	+	0.721068i
$823$	−21.6890	−	37.5664i	−0.756031	−	1.30948i	−0.944860	−	0.327474i	$-0.893803\pi$
$823$	−21.6890	−	37.5664i	−0.756031	−	1.30948i	0.188829	−	0.982010i	$-0.439531\pi$
$824$	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	$-0.928243\pi$
$829$	−8.45833	+	14.6503i	−0.293770	+	0.508824i	0.680928	+	0.732350i	$0.261577\pi$
$830$	−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	$-0.0757357\pi$
$839$	8.16244	+	14.1378i	0.281799	+	0.488089i	−0.690029	+	0.723782i	$0.742402\pi$
$840$		0			0
$841$	−28.6560	+	49.6336i	−0.988138	+	1.71150i
$842$	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	$-0.00189311\pi$
$853$	14.4524	+	25.0323i	0.494841	+	0.857089i	−0.505142	+	0.863036i	$0.668560\pi$
$854$		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	$-0.334699\pi$
$857$	29.0567			0.992559			0.496280	+	0.868163i	$0.334699\pi$
$858$	−15.2859	+	4.03265i	−0.521853	+	0.137673i
$859$	12.5964			0.429783			0.214892	−	0.976638i	$-0.431060\pi$
$859$	12.5964			0.429783			0.214892	+	0.976638i	$0.431060\pi$
$860$	−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	$-0.0863605\pi$
$863$	7.33309	+	12.7013i	0.249621	+	0.432357i	−0.713799	+	0.700350i	$0.753027\pi$
$864$	−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	$-0.320575\pi$
$881$	31.7179			1.06860			0.534301	+	0.845294i	$0.320575\pi$
$882$		0			0
$883$	−39.5231			−1.33006			−0.665029	−	0.746818i	$-0.731581\pi$
$883$	−39.5231			−1.33006			−0.665029	+	0.746818i	$0.731581\pi$
$884$	1.56785	−	2.71559i	0.0527324	−	0.0913352i
$885$	−0.787743	+	0.207818i	−0.0264797	+	0.00698573i
$886$	10.8131	+	18.7288i	0.363272	+	0.629206i
$887$	−49.9026			−1.67556			−0.837782	−	0.546005i	$-0.816148\pi$
$887$	−49.9026			−1.67556			−0.837782	+	0.546005i	$0.816148\pi$
$888$	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	0.907341	−	0.420396i	$-0.138109\pi$
$911$	2.70428	+	4.68394i	0.0895967	+	0.155186i	−0.817744	+	0.575582i	$0.804776\pi$
$912$	−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	−0.997388	−	0.0722280i	$-0.976989\pi$
$919$	−17.0142	−	29.4694i	−0.561245	−	0.972105i	0.436143	−	0.899877i	$-0.356344\pi$
$920$	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	$-0.777526\pi$
$929$	5.31646	−	9.20837i	0.174427	−	0.302117i	0.939963	+	0.341277i	$0.110859\pi$
$930$	−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	$-0.829732\pi$
$937$	−52.6692			−1.72063			−0.860314	+	0.509765i	$0.829732\pi$
$938$		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	−0.997483	−	0.0709006i	$-0.977413\pi$
$941$	−17.1828	−	29.7615i	−0.560143	−	0.970197i	0.437340	−	0.899296i	$-0.355921\pi$
$942$	−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	−0.321370	−	0.946954i	$-0.604143\pi$
$947$	20.2920	−	35.1468i	0.659401	−	1.14212i	0.980771	−	0.195162i	$-0.0625234\pi$
$948$	−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	−0.992497	−	0.122273i	$-0.960982\pi$
$967$	−12.1388	+	21.0250i	−0.390357	+	0.676118i	0.602139	+	0.798391i	$0.294315\pi$
$968$	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	0.956319	+	0.292324i	$0.0944285\pi$
$971$	22.7886	+	39.4709i	0.731319	+	1.26668i	−0.225000	+	0.974359i	$0.572238\pi$
$972$	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	0.959267	−	0.282500i	$-0.0911637\pi$
$977$	7.34481	+	12.7216i	0.234981	+	0.407000i	−0.724286	+	0.689500i	$0.757830\pi$
$978$	−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	$-0.248191\pi$
$983$	44.5909			1.42223			0.711115	+	0.703076i	$0.248191\pi$
$984$	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	−0.991644	−	0.129007i	$-0.958821\pi$
$991$	−12.0915	+	20.9430i	−0.384098	+	0.665277i	0.607546	+	0.794285i	$0.292154\pi$
$992$	−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	$-0.444960\pi$
$997$	10.8652			0.344105			0.172053	+	0.985088i	$0.444960\pi$
$998$	−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.67.8		24
3.2	odd	2		1323.2.g.h.361.6		24
7.2	even	3		441.2.h.h.373.6		24
7.3	odd	6		441.2.f.h.148.8	yes	24
7.4	even	3		441.2.f.h.148.7	✓	24
7.5	odd	6		441.2.h.h.373.5		24
7.6	odd	2	inner	441.2.g.h.67.7		24
9.2	odd	6		1323.2.h.h.802.7		24
9.7	even	3		441.2.h.h.214.6		24
21.2	odd	6		1323.2.h.h.226.7		24
21.5	even	6		1323.2.h.h.226.8		24
21.11	odd	6		1323.2.f.h.442.6		24
21.17	even	6		1323.2.f.h.442.5		24
21.20	even	2		1323.2.g.h.361.5		24
63.2	odd	6		1323.2.g.h.667.6		24
63.4	even	3		3969.2.a.bh.1.5		12
63.11	odd	6		1323.2.f.h.883.6		24
63.16	even	3	inner	441.2.g.h.79.8		24
63.20	even	6		1323.2.h.h.802.8		24
63.25	even	3		441.2.f.h.295.7	yes	24
63.31	odd	6		3969.2.a.bh.1.6		12
63.32	odd	6		3969.2.a.bi.1.8		12
63.34	odd	6		441.2.h.h.214.5		24
63.38	even	6		1323.2.f.h.883.5		24
63.47	even	6		1323.2.g.h.667.5		24
63.52	odd	6		441.2.f.h.295.8	yes	24
63.59	even	6		3969.2.a.bi.1.7		12
63.61	odd	6	inner	441.2.g.h.79.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.7	✓	24	7.4	even	3
441.2.f.h.148.8	yes	24	7.3	odd	6
441.2.f.h.295.7	yes	24	63.25	even	3
441.2.f.h.295.8	yes	24	63.52	odd	6
441.2.g.h.67.7		24	7.6	odd	2	inner
441.2.g.h.67.8		24	1.1	even	1	trivial
441.2.g.h.79.7		24	63.61	odd	6	inner
441.2.g.h.79.8		24	63.16	even	3	inner
441.2.h.h.214.5		24	63.34	odd	6
441.2.h.h.214.6		24	9.7	even	3
441.2.h.h.373.5		24	7.5	odd	6
441.2.h.h.373.6		24	7.2	even	3
1323.2.f.h.442.5		24	21.17	even	6
1323.2.f.h.442.6		24	21.11	odd	6
1323.2.f.h.883.5		24	63.38	even	6
1323.2.f.h.883.6		24	63.11	odd	6
1323.2.g.h.361.5		24	21.20	even	2
1323.2.g.h.361.6		24	3.2	odd	2
1323.2.g.h.667.5		24	63.47	even	6
1323.2.g.h.667.6		24	63.2	odd	6
1323.2.h.h.226.7		24	21.2	odd	6
1323.2.h.h.226.8		24	21.5	even	6
1323.2.h.h.802.7		24	9.2	odd	6
1323.2.h.h.802.8		24	63.20	even	6
3969.2.a.bh.1.5		12	63.4	even	3
3969.2.a.bh.1.6		12	63.31	odd	6
3969.2.a.bi.1.7		12	63.59	even	6
3969.2.a.bi.1.8		12	63.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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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