LMFDB - Embedded newform 441.2.h.d.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	441.373
Dual form			441.2.h.d.214.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34730 q^{2} +(-1.11334 - 1.32683i) q^{3} -0.184793 q^{4} +(-1.26604 - 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+1.34730 q^{2} +(-1.11334 - 1.32683i) q^{3} -0.184793 q^{4} +(-1.26604 - 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-0.520945 + 2.95442i) q^{9} +(-1.70574 - 2.95442i) q^{10} +(-0.233956 + 0.405223i) q^{11} +(0.205737 + 0.245188i) q^{12} +(-2.91147 + 5.04282i) q^{13} +(-1.50000 + 4.12122i) q^{15} -3.59627 q^{16} +(-1.93969 - 3.35965i) q^{17} +(-0.701867 + 3.98048i) q^{18} +(1.09240 - 1.89209i) q^{19} +(0.233956 + 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(0.0530334 + 0.0918566i) q^{23} +(3.27719 + 3.90560i) q^{24} +(-0.705737 + 1.22237i) q^{25} +(-3.92262 + 6.79417i) q^{26} +(4.50000 - 2.59808i) q^{27} +(-4.39053 - 7.60462i) q^{29} +(-2.02094 + 5.55250i) q^{30} -7.68004 q^{31} +1.04189 q^{32} +(0.798133 - 0.140732i) q^{33} +(-2.61334 - 4.52644i) q^{34} +(0.0962667 - 0.545955i) q^{36} +(3.84002 - 6.65111i) q^{37} +(1.47178 - 2.54920i) q^{38} +(9.93242 - 1.75135i) q^{39} +(3.72668 + 6.45480i) q^{40} +(1.11334 - 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(0.0432332 - 0.0748822i) q^{44} +(7.13816 - 2.59808i) q^{45} +(0.0714517 + 0.123758i) q^{46} -5.33275 q^{47} +(4.00387 + 4.77163i) q^{48} +(-0.950837 + 1.64690i) q^{50} +(-2.29813 + 6.31407i) q^{51} +(0.538019 - 0.931876i) q^{52} +(0.358441 + 0.620838i) q^{53} +(6.06283 - 3.50038i) q^{54} +1.18479 q^{55} +(-3.72668 + 0.657115i) q^{57} +(-5.91534 - 10.2457i) q^{58} +0.736482 q^{59} +(0.277189 - 0.761570i) q^{60} +0.958111 q^{61} -10.3473 q^{62} +8.59627 q^{64} +14.7442 q^{65} +(1.07532 - 0.189608i) q^{66} -9.63816 q^{67} +(0.358441 + 0.620838i) q^{68} +(0.0628336 - 0.172634i) q^{69} +13.2344 q^{71} +(1.53343 - 8.69653i) q^{72} +(5.13429 + 8.89284i) q^{73} +(5.17365 - 8.96102i) q^{74} +(2.40760 - 0.424525i) q^{75} +(-0.201867 + 0.349643i) q^{76} +(13.3819 - 2.35959i) q^{78} -12.6382 q^{79} +(4.55303 + 7.88609i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(1.50000 - 2.59808i) q^{82} +(1.36571 + 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(-0.826352 - 1.43128i) q^{86} +(-5.20187 + 14.2920i) q^{87} +(0.688663 - 1.19280i) q^{88} +(4.05690 - 7.02676i) q^{89} +(9.61721 - 3.50038i) q^{90} +(-0.00980018 - 0.0169744i) q^{92} +(8.55051 + 10.1901i) q^{93} -7.18479 q^{94} -5.53209 q^{95} +(-1.15998 - 1.38241i) q^{96} +(6.80200 + 11.7814i) q^{97} +(-1.07532 - 0.902302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 3 q^{5} - 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^5 - 9 * q^6 + 12 * q^8	$ 6 q + 6 q^{2} + 6 q^{4} - 3 q^{5} - 9 q^{6} + 12 q^{8} - 6 q^{11} - 9 q^{12} + 3 q^{13} - 9 q^{15} + 6 q^{16} - 6 q^{17} - 18 q^{18} + 3 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} + 9 q^{24} + 6 q^{25} + 3 q^{26} + 27 q^{27} - 9 q^{29} - 9 q^{30} - 6 q^{31} - 9 q^{33} - 9 q^{34} - 27 q^{36} + 3 q^{37} - 6 q^{38} + 36 q^{39} + 9 q^{40} + 3 q^{43} - 15 q^{44} + 9 q^{45} + 6 q^{47} + 6 q^{50} + 21 q^{52} - 6 q^{53} + 27 q^{54} - 9 q^{57} + 9 q^{58} - 6 q^{59} - 9 q^{60} + 12 q^{61} - 60 q^{62} + 24 q^{64} + 30 q^{65} - 18 q^{66} - 24 q^{67} - 6 q^{68} - 9 q^{69} + 18 q^{71} - 9 q^{72} + 21 q^{73} + 30 q^{74} + 18 q^{75} - 15 q^{76} + 54 q^{78} - 42 q^{79} + 15 q^{80} + 9 q^{82} + 18 q^{83} - 9 q^{85} - 6 q^{86} - 45 q^{87} - 27 q^{88} - 12 q^{89} + 27 q^{90} - 3 q^{92} + 54 q^{93} - 36 q^{94} - 24 q^{95} - 27 q^{96} + 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^5 - 9 * q^6 + 12 * q^8 - 6 * q^11 - 9 * q^12 + 3 * q^13 - 9 * q^15 + 6 * q^16 - 6 * q^17 - 18 * q^18 + 3 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 + 9 * q^24 + 6 * q^25 + 3 * q^26 + 27 * q^27 - 9 * q^29 - 9 * q^30 - 6 * q^31 - 9 * q^33 - 9 * q^34 - 27 * q^36 + 3 * q^37 - 6 * q^38 + 36 * q^39 + 9 * q^40 + 3 * q^43 - 15 * q^44 + 9 * q^45 + 6 * q^47 + 6 * q^50 + 21 * q^52 - 6 * q^53 + 27 * q^54 - 9 * q^57 + 9 * q^58 - 6 * q^59 - 9 * q^60 + 12 * q^61 - 60 * q^62 + 24 * q^64 + 30 * q^65 - 18 * q^66 - 24 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 9 * q^72 + 21 * q^73 + 30 * q^74 + 18 * q^75 - 15 * q^76 + 54 * q^78 - 42 * q^79 + 15 * q^80 + 9 * q^82 + 18 * q^83 - 9 * q^85 - 6 * q^86 - 45 * q^87 - 27 * q^88 - 12 * q^89 + 27 * q^90 - 3 * q^92 + 54 * q^93 - 36 * q^94 - 24 * q^95 - 27 * q^96 + 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.34730			0.952682			0.476341	−	0.879261i	$-0.341963\pi$
$2$	1.34730			0.952682			0.476341	+	0.879261i	$0.341963\pi$
$3$	−1.11334	−	1.32683i	−0.642788	−	0.766044i
$3$	−1.11334	−	1.32683i	−0.642788	−	0.766044i
$4$	−0.184793			−0.0923963
$5$	−1.26604	−	2.19285i	−0.566192	−	0.980674i	−0.996938	−	0.0782003i	$-0.975083\pi$
$5$	−1.26604	−	2.19285i	−0.566192	−	0.980674i	0.430745	−	0.902473i	$-0.358251\pi$
$6$	−1.50000	−	1.78763i	−0.612372	−	0.729797i
$7$		0			0
$7$		0			0
$8$	−2.94356			−1.04071
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$	−1.70574	−	2.95442i	−0.539401	−	0.934271i
$11$	−0.233956	+	0.405223i	−0.0705403	+	0.122179i	−0.899138	−	0.437665i	$-0.855806\pi$
$11$	−0.233956	+	0.405223i	−0.0705403	+	0.122179i	0.828598	+	0.559844i	$0.189139\pi$
$12$	0.205737	+	0.245188i	0.0593912	+	0.0707796i
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	0.107094	+	0.994249i	$0.465845\pi$
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	−0.914592	+	0.404378i	$0.867488\pi$
$14$		0			0
$15$	−1.50000	+	4.12122i	−0.387298	+	1.06409i
$16$	−3.59627			−0.899067
$17$	−1.93969	−	3.35965i	−0.470445	−	0.814834i	0.528984	−	0.848632i	$-0.322573\pi$
$17$	−1.93969	−	3.35965i	−0.470445	−	0.814834i	−0.999429	+	0.0337978i	$0.989240\pi$
$18$	−0.701867	+	3.98048i	−0.165432	+	0.938209i
$19$	1.09240	−	1.89209i	0.250613	−	0.434074i	−0.713082	−	0.701081i	$-0.752701\pi$
$19$	1.09240	−	1.89209i	0.250613	−	0.434074i	0.963695	+	0.267007i	$0.0860345\pi$
$20$	0.233956	+	0.405223i	0.0523141	+	0.0906106i
$21$		0			0
$22$	−0.315207	+	0.545955i	−0.0672025	+	0.116398i
$23$	0.0530334	+	0.0918566i	0.0110582	+	0.0191534i	0.871502	−	0.490393i	$-0.163147\pi$
$23$	0.0530334	+	0.0918566i	0.0110582	+	0.0191534i	−0.860443	+	0.509546i	$0.829813\pi$
$24$	3.27719	+	3.90560i	0.668953	+	0.797228i
$25$	−0.705737	+	1.22237i	−0.141147	+	0.244474i
$26$	−3.92262	+	6.79417i	−0.769289	+	1.33245i
$27$	4.50000	−	2.59808i	0.866025	−	0.500000i
$28$		0			0
$29$	−4.39053	−	7.60462i	−0.815301	−	1.41214i	−0.909112	−	0.416552i	$-0.863238\pi$
$29$	−4.39053	−	7.60462i	−0.815301	−	1.41214i	0.0938108	−	0.995590i	$-0.470095\pi$
$30$	−2.02094	+	5.55250i	−0.368972	+	1.01374i
$31$	−7.68004			−1.37938			−0.689688	−	0.724106i	$-0.742252\pi$
$31$	−7.68004			−1.37938			−0.689688	+	0.724106i	$0.742252\pi$
$32$	1.04189			0.184182
$33$	0.798133	−	0.140732i	0.138937	−	0.0244984i
$34$	−2.61334	−	4.52644i	−0.448184	−	0.776278i
$35$		0			0
$36$	0.0962667	−	0.545955i	0.0160444	−	0.0909926i
$37$	3.84002	−	6.65111i	0.631296	−	1.09344i	−0.355991	−	0.934489i	$-0.615857\pi$
$37$	3.84002	−	6.65111i	0.631296	−	1.09344i	0.987287	−	0.158947i	$-0.0508099\pi$
$38$	1.47178	−	2.54920i	0.238754	−	0.413535i
$39$	9.93242	−	1.75135i	1.59046	−	0.280441i
$40$	3.72668	+	6.45480i	0.589240	+	1.02059i
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	−0.765897	−	0.642964i	$-0.777705\pi$
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	0.939771	+	0.341804i	$0.111038\pi$
$42$		0			0
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	0.815462	−	0.578811i	$-0.196483\pi$
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	−0.908996	+	0.416806i	$0.863150\pi$
$44$	0.0432332	−	0.0748822i	0.00651766	−	0.0112889i
$45$	7.13816	−	2.59808i	1.06409	−	0.387298i
$46$	0.0714517	+	0.123758i	0.0105350	+	0.0182471i
$47$	−5.33275			−0.777861			−0.388931	−	0.921267i	$-0.627155\pi$
$47$	−5.33275			−0.777861			−0.388931	+	0.921267i	$0.627155\pi$
$48$	4.00387	+	4.77163i	0.577909	+	0.688725i
$49$		0			0
$50$	−0.950837	+	1.64690i	−0.134469	+	0.232907i
$51$	−2.29813	+	6.31407i	−0.321803	+	0.884147i
$52$	0.538019	−	0.931876i	0.0746098	−	0.129228i
$53$	0.358441	+	0.620838i	0.0492356	+	0.0852786i	0.889593	−	0.456754i	$-0.150988\pi$
$53$	0.358441	+	0.620838i	0.0492356	+	0.0852786i	−0.840357	+	0.542033i	$0.817655\pi$
$54$	6.06283	−	3.50038i	0.825047	−	0.476341i
$55$	1.18479			0.159757
$56$		0			0
$57$	−3.72668	+	0.657115i	−0.493611	+	0.0870369i
$58$	−5.91534	−	10.2457i	−0.776723	−	1.34532i
$59$	0.736482			0.0958818			0.0479409	−	0.998850i	$-0.484734\pi$
$59$	0.736482			0.0958818			0.0479409	+	0.998850i	$0.484734\pi$
$60$	0.277189	−	0.761570i	0.0357849	−	0.0983183i
$61$	0.958111			0.122674			0.0613368	−	0.998117i	$-0.480464\pi$
$61$	0.958111			0.122674			0.0613368	+	0.998117i	$0.480464\pi$
$62$	−10.3473			−1.31411
$63$		0			0
$64$	8.59627			1.07453
$65$	14.7442			1.82880
$66$	1.07532	−	0.189608i	0.132363	−	0.0233392i
$67$	−9.63816			−1.17749			−0.588744	−	0.808320i	$-0.700377\pi$
$67$	−9.63816			−1.17749			−0.588744	+	0.808320i	$0.700377\pi$
$68$	0.358441	+	0.620838i	0.0434673	+	0.0752876i
$69$	0.0628336	−	0.172634i	0.00756428	−	0.0207827i
$70$		0			0
$71$	13.2344			1.57064			0.785318	−	0.619092i	$-0.212499\pi$
$71$	13.2344			1.57064			0.785318	+	0.619092i	$0.212499\pi$
$72$	1.53343	−	8.69653i	0.180717	−	1.02490i
$73$	5.13429	+	8.89284i	0.600923	+	1.04083i	0.992682	+	0.120761i	$0.0385334\pi$
$73$	5.13429	+	8.89284i	0.600923	+	1.04083i	−0.391759	+	0.920068i	$0.628133\pi$
$74$	5.17365	−	8.96102i	0.601424	−	1.04170i
$75$	2.40760	−	0.424525i	0.278006	−	0.0490200i
$76$	−0.201867	+	0.349643i	−0.0231557	+	0.0401068i
$77$		0			0
$78$	13.3819	−	2.35959i	1.51520	−	0.267171i
$79$	−12.6382			−1.42190			−0.710952	−	0.703241i	$-0.751736\pi$
$79$	−12.6382			−1.42190			−0.710952	+	0.703241i	$0.751736\pi$
$80$	4.55303	+	7.88609i	0.509045	+	0.881691i
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	1.36571	+	2.36549i	0.149907	+	0.259646i	0.931193	−	0.364527i	$-0.118769\pi$
$83$	1.36571	+	2.36549i	0.149907	+	0.259646i	−0.781286	+	0.624173i	$0.785436\pi$
$84$		0			0
$85$	−4.91147	+	8.50692i	−0.532724	+	0.922705i
$86$	−0.826352	−	1.43128i	−0.0891078	−	0.154339i
$87$	−5.20187	+	14.2920i	−0.557699	+	1.53226i
$88$	0.688663	−	1.19280i	0.0734117	−	0.127153i
$89$	4.05690	−	7.02676i	0.430031	−	0.744835i	−0.566845	−	0.823825i	$-0.691836\pi$
$89$	4.05690	−	7.02676i	0.430031	−	0.744835i	0.996875	+	0.0789894i	$0.0251693\pi$
$90$	9.61721	−	3.50038i	1.01374	−	0.368972i
$91$		0			0
$92$	−0.00980018	−	0.0169744i	−0.00102174	−	0.00176970i
$93$	8.55051	+	10.1901i	0.886646	+	1.05666i
$94$	−7.18479			−0.741055
$95$	−5.53209			−0.567580
$96$	−1.15998	−	1.38241i	−0.118390	−	0.141091i
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	0.971629	+	0.236511i	$0.0760039\pi$
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	−0.280990	+	0.959711i	$0.590663\pi$
$98$		0			0
$99$	−1.07532	−	0.902302i	−0.108074	−	0.0906848i
$100$	0.130415	−	0.225885i	0.0130415	−	0.0225885i
$101$	4.78699	−	8.29131i	0.476323	−	0.825016i	−0.523309	−	0.852143i	$-0.675303\pi$
$101$	4.78699	−	8.29131i	0.476323	−	0.825016i	0.999632	+	0.0271271i	$0.00863590\pi$
$102$	−3.09627	+	8.50692i	−0.306576	+	0.842311i
$103$	−1.52094	−	2.63435i	−0.149863	−	0.259571i	0.781314	−	0.624139i	$-0.214550\pi$
$103$	−1.52094	−	2.63435i	−0.149863	−	0.259571i	−0.931177	+	0.364568i	$0.881217\pi$
$104$	8.57011	−	14.8439i	0.840368	−	1.45556i
$105$		0			0
$106$	0.482926	+	0.836452i	0.0469059	+	0.0812434i
$107$	3.25877	−	5.64436i	0.315037	−	0.545660i	−0.664408	−	0.747370i	$-0.731316\pi$
$107$	3.25877	−	5.64436i	0.315037	−	0.545660i	0.979445	+	0.201709i	$0.0646497\pi$
$108$	−0.831566	+	0.480105i	−0.0800175	+	0.0461981i
$109$	−5.31908	−	9.21291i	−0.509475	−	0.882437i	−0.999940	−	0.0109759i	$-0.996506\pi$
$109$	−5.31908	−	9.21291i	−0.509475	−	0.882437i	0.490465	−	0.871461i	$-0.336827\pi$
$110$	1.59627			0.152198
$111$	−13.1001	+	2.30991i	−1.24341	+	0.219247i
$112$		0			0
$113$	−2.58853	+	4.48346i	−0.243508	+	0.421768i	−0.961711	−	0.274065i	$-0.911632\pi$
$113$	−2.58853	+	4.48346i	−0.243508	+	0.421768i	0.718203	+	0.695834i	$0.244965\pi$
$114$	−5.02094	+	0.885328i	−0.470255	+	0.0829186i
$115$	0.134285	−	0.232589i	0.0125222	−	0.0216890i
$116$	0.811337	+	1.40528i	0.0753308	+	0.130477i
$117$	−13.3819	−	11.2288i	−1.23716	−	1.03810i
$118$	0.992259			0.0913449
$119$		0			0
$120$	4.41534	−	12.1311i	0.403064	−	1.10741i
$121$	5.39053	+	9.33667i	0.490048	+	0.848788i
$122$	1.29086			0.116869
$123$	−3.79813	+	0.669713i	−0.342466	+	0.0603860i
$124$	1.41921			0.127449
$125$	−9.08647			−0.812718
$126$		0			0
$127$	−8.88207			−0.788157			−0.394078	−	0.919077i	$-0.628936\pi$
$127$	−8.88207			−0.788157			−0.394078	+	0.919077i	$0.628936\pi$
$128$	9.49794			0.839507
$129$	−0.726682	+	1.99654i	−0.0639807	+	0.175786i
$130$	19.8648			1.74226
$131$	−5.68139	−	9.84045i	−0.496385	−	0.859764i	0.503606	−	0.863933i	$-0.332006\pi$
$131$	−5.68139	−	9.84045i	−0.496385	−	0.859764i	−0.999991	+	0.00416893i	$0.998673\pi$
$132$	−0.147489	+	0.0260063i	−0.0128373	+	0.00226356i
$133$		0			0
$134$	−12.9855			−1.12177
$135$	−11.3944	−	6.57856i	−0.980674	−	0.566192i
$136$	5.70961	+	9.88933i	0.489595	+	0.848003i
$137$	2.86231	−	4.95767i	0.244544	−	0.423562i	−0.717459	−	0.696600i	$-0.754695\pi$
$137$	2.86231	−	4.95767i	0.244544	−	0.423562i	0.962003	+	0.273038i	$0.0880285\pi$
$138$	0.0846555	−	0.232589i	0.00720635	−	0.0197993i
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	−0.845768	−	0.533551i	$-0.820857\pi$
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	0.884953	+	0.465681i	$0.154191\pi$
$140$		0			0
$141$	5.93717	+	7.07564i	0.500000	+	0.595876i
$142$	17.8307			1.49632
$143$	−1.36231	−	2.35959i	−0.113922	−	0.197319i
$144$	1.87346	−	10.6249i	0.156121	−	0.885408i
$145$	−11.1172	+	19.2556i	−0.923234	+	1.59909i
$146$	6.91740	+	11.9813i	0.572488	+	0.991579i
$147$		0			0
$148$	−0.709607	+	1.22908i	−0.0583294	+	0.101029i
$149$	−4.36231	−	7.55574i	−0.357374	−	0.618991i	0.630147	−	0.776476i	$-0.282995\pi$
$149$	−4.36231	−	7.55574i	−0.357374	−	0.618991i	−0.987521	+	0.157485i	$0.949661\pi$
$150$	3.24376	−	0.571962i	0.264852	−	0.0467005i
$151$	−9.21348	+	15.9582i	−0.749782	+	1.29866i	0.198145	+	0.980173i	$0.436508\pi$
$151$	−9.21348	+	15.9582i	−0.749782	+	1.29866i	−0.947927	+	0.318488i	$0.896825\pi$
$152$	−3.21554	+	5.56947i	−0.260815	+	0.451744i
$153$	10.9363	−	3.98048i	0.884147	−	0.321803i
$154$		0			0
$155$	9.72328	+	16.8412i	0.780992	+	1.35272i
$156$	−1.83544	+	0.323637i	−0.146953	+	0.0259117i
$157$	4.92396			0.392975			0.196488	−	0.980506i	$-0.437046\pi$
$157$	4.92396			0.392975			0.196488	+	0.980506i	$0.437046\pi$
$158$	−17.0273			−1.35462
$159$	0.424678	−	1.16679i	0.0336791	−	0.0925327i
$160$	−1.31908	−	2.28471i	−0.104282	−	0.180622i
$161$		0			0
$162$	−11.3944	−	4.14722i	−0.895229	−	0.325837i
$163$	−3.81908	+	6.61484i	−0.299133	+	0.518114i	−0.975938	−	0.218049i	$-0.930031\pi$
$163$	−3.81908	+	6.61484i	−0.299133	+	0.518114i	0.676805	+	0.736163i	$0.263364\pi$
$164$	−0.205737	+	0.356347i	−0.0160654	+	0.0278260i
$165$	−1.31908	−	1.57202i	−0.102690	−	0.122381i
$166$	1.84002	+	3.18701i	0.142813	+	0.247360i
$167$	2.82770	−	4.89771i	0.218814	−	0.378996i	−0.735632	−	0.677382i	$-0.763115\pi$
$167$	2.82770	−	4.89771i	0.218814	−	0.378996i	0.954446	+	0.298385i	$0.0964480\pi$
$168$		0			0
$169$	−10.4534	−	18.1058i	−0.804105	−	1.39275i
$170$	−6.61721	+	11.4613i	−0.507517	+	0.879045i
$171$	5.02094	+	4.21307i	0.383961	+	0.322182i
$172$	0.113341	+	0.196312i	0.00864215	+	0.0149687i
$173$	21.0692			1.60186			0.800932	−	0.598755i	$-0.204338\pi$
$173$	21.0692			1.60186			0.800932	+	0.598755i	$0.204338\pi$
$174$	−7.00846	+	19.2556i	−0.531310	+	1.45976i
$175$		0			0
$176$	0.841367	−	1.45729i	0.0634204	−	0.109847i
$177$	−0.819955	−	0.977185i	−0.0616316	−	0.0734497i
$178$	5.46585	−	9.46713i	0.409683	−	0.709592i
$179$	2.56031	+	4.43458i	0.191366	+	0.331456i	0.945703	−	0.325031i	$-0.105375\pi$
$179$	2.56031	+	4.43458i	0.191366	+	0.331456i	−0.754337	+	0.656487i	$0.772041\pi$
$180$	−1.31908	+	0.480105i	−0.0983183	+	0.0357849i
$181$	−0.319955			−0.0237821			−0.0118910	−	0.999929i	$-0.503785\pi$
$181$	−0.319955			−0.0237821			−0.0118910	+	0.999929i	$0.503785\pi$
$182$		0			0
$183$	−1.06670	−	1.27125i	−0.0788530	−	0.0939734i
$184$	−0.156107	−	0.270386i	−0.0115084	−	0.0199331i
$185$	−19.4466			−1.42974
$186$	11.5201	+	13.7291i	0.844692	+	1.00667i
$187$	1.81521			0.132741
$188$	0.985452			0.0718715
$189$		0			0
$190$	−7.45336			−0.540724
$191$	−15.5672			−1.12640			−0.563200	−	0.826320i	$-0.690430\pi$
$191$	−15.5672			−1.12640			−0.563200	+	0.826320i	$0.690430\pi$
$192$	−9.57057	−	11.4058i	−0.690697	−	0.823140i
$193$	6.04189			0.434905			0.217452	−	0.976071i	$-0.430225\pi$
$193$	6.04189			0.434905			0.217452	+	0.976071i	$0.430225\pi$
$194$	9.16431	+	15.8731i	0.657959	+	1.13962i
$195$	−16.4153	−	19.5630i	−1.17553	−	1.40094i
$196$		0			0
$197$	25.2344			1.79788			0.898939	−	0.438074i	$-0.144339\pi$
$197$	25.2344			1.79788			0.898939	+	0.438074i	$0.144339\pi$
$198$	−1.44878	−	1.21567i	−0.102960	−	0.0863938i
$199$	−1.52094	−	2.63435i	−0.107817	−	0.186744i	0.807069	−	0.590458i	$-0.201053\pi$
$199$	−1.52094	−	2.63435i	−0.107817	−	0.186744i	−0.914886	+	0.403713i	$0.867719\pi$
$200$	2.07738	−	3.59813i	0.146893	−	0.254426i
$201$	10.7306	+	12.7882i	0.756875	+	0.902008i
$202$	6.44949	−	11.1708i	0.453785	−	0.785978i
$203$		0			0
$204$	0.424678	−	1.16679i	0.0297334	−	0.0816918i
$205$	−5.63816			−0.393786
$206$	−2.04916	−	3.54925i	−0.142772	−	0.247288i
$207$	−0.299011	+	0.108831i	−0.0207827	+	0.00756428i
$208$	10.4704	−	18.1353i	0.725994	−	1.25746i
$209$	0.511144	+	0.885328i	0.0353566	+	0.0612394i
$210$		0			0
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	−0.756775	−	0.653676i	$-0.773226\pi$
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	0.944487	+	0.328548i	$0.106559\pi$
$212$	−0.0662372	−	0.114726i	−0.00454919	−	0.00787942i
$213$	−14.7344	−	17.5598i	−1.00959	−	1.20318i
$214$	4.39053	−	7.60462i	0.300130	−	0.519841i
$215$	−1.55303	+	2.68993i	−0.105916	+	0.183452i
$216$	−13.2460	+	7.64760i	−0.901278	+	0.520353i
$217$		0			0
$218$	−7.16637	−	12.4125i	−0.485368	−	0.840682i
$219$	6.08306	−	16.7131i	0.411055	−	1.12937i
$220$	−0.218941			−0.0147610
$221$	22.5895			1.51953
$222$	−17.6498	+	3.11213i	−1.18457	+	0.208872i
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	0.524395	−	0.851475i	$-0.324291\pi$
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	−0.999597	+	0.0284023i	$0.990958\pi$
$224$		0			0
$225$	−3.24376	−	2.72183i	−0.216250	−	0.181456i
$226$	−3.48751	+	6.04055i	−0.231986	+	0.401811i
$227$	1.44697	−	2.50622i	0.0960385	−	0.166344i	−0.814003	−	0.580861i	$-0.802716\pi$
$227$	1.44697	−	2.50622i	0.0960385	−	0.166344i	0.910042	+	0.414517i	$0.136049\pi$
$228$	0.688663	−	0.121430i	0.0456078	−	0.00804189i
$229$	−4.58378	−	7.93934i	−0.302905	−	0.524646i	0.673888	−	0.738834i	$-0.264623\pi$
$229$	−4.58378	−	7.93934i	−0.302905	−	0.524646i	−0.976793	+	0.214187i	$0.931290\pi$
$230$	0.180922	−	0.313366i	0.0119297	−	0.0206628i
$231$		0			0
$232$	12.9238	+	22.3847i	0.848489	+	1.46963i
$233$	−6.63563	+	11.4932i	−0.434715	+	0.752948i	−0.997272	−	0.0738103i	$-0.976484\pi$
$233$	−6.63563	+	11.4932i	−0.434715	+	0.752948i	0.562558	+	0.826758i	$0.309817\pi$
$234$	−18.0294	−	15.1285i	−1.17862	−	0.988979i
$235$	6.75150	+	11.6939i	0.440419	+	0.762828i
$236$	−0.136096			−0.00885912
$237$	14.0706	+	16.7687i	0.913982	+	1.08924i
$238$		0			0
$239$	−4.76857	+	8.25941i	−0.308453	+	0.534257i	−0.978024	−	0.208491i	$-0.933145\pi$
$239$	−4.76857	+	8.25941i	−0.308453	+	0.534257i	0.669571	+	0.742748i	$0.266478\pi$
$240$	5.39440	−	14.8210i	0.348207	−	0.956691i
$241$	4.47906	−	7.75795i	0.288521	−	0.499734i	−0.684936	−	0.728604i	$-0.740170\pi$
$241$	4.47906	−	7.75795i	0.288521	−	0.499734i	0.973457	+	0.228870i	$0.0735031\pi$
$242$	7.26264	+	12.5793i	0.466860	+	0.808626i
$243$	5.33157	+	14.6484i	0.342020	+	0.939693i
$244$	−0.177052			−0.0113346
$245$		0			0
$246$	−5.11721	+	0.902302i	−0.326261	+	0.0575287i
$247$	6.36097	+	11.0175i	0.404739	+	0.701028i
$248$	22.6067			1.43553
$249$	1.61809	−	4.44566i	0.102542	−	0.281732i
$250$	−12.2422			−0.774262
$251$	−24.9982			−1.57788			−0.788938	−	0.614473i	$-0.789369\pi$
$251$	−24.9982			−1.57788			−0.788938	+	0.614473i	$0.789369\pi$
$252$		0			0
$253$	−0.0496299			−0.00312020
$254$	−11.9668			−0.750863
$255$	16.7554	−	2.95442i	1.04926	−	0.185013i
$256$	−4.39599			−0.274750
$257$	−5.42602	−	9.39815i	−0.338466	−	0.586240i	0.645678	−	0.763609i	$-0.276575\pi$
$257$	−5.42602	−	9.39815i	−0.338466	−	0.586240i	−0.984144	+	0.177369i	$0.943241\pi$
$258$	−0.979055	+	2.68993i	−0.0609533	+	0.167468i
$259$		0			0
$260$	−2.72462			−0.168974
$261$	24.7545	−	9.00990i	1.53226	−	0.557699i
$262$	−7.65451	−	13.2580i	−0.472897	−	0.819082i
$263$	−13.0437	+	22.5924i	−0.804309	+	1.39310i	0.112448	+	0.993658i	$0.464131\pi$
$263$	−13.0437	+	22.5924i	−0.804309	+	1.39310i	−0.916757	+	0.399446i	$0.869202\pi$
$264$	−2.34936	+	0.414255i	−0.144593	+	0.0254956i
$265$	0.907604	−	1.57202i	0.0557537	−	0.0965682i
$266$		0			0
$267$	−13.8400	+	2.44037i	−0.846996	+	0.149348i
$268$	1.78106			0.108796
$269$	3.81655	+	6.61046i	0.232699	+	0.403047i	0.958602	−	0.284751i	$-0.0919109\pi$
$269$	3.81655	+	6.61046i	0.232699	+	0.403047i	−0.725902	+	0.687798i	$0.758578\pi$
$270$	−15.3516	−	8.86327i	−0.934271	−	0.539401i
$271$	−1.70187	+	2.94772i	−0.103381	+	0.179061i	−0.913076	−	0.407790i	$-0.866299\pi$
$271$	−1.70187	+	2.94772i	−0.103381	+	0.179061i	0.809695	+	0.586852i	$0.199633\pi$
$272$	6.97565	+	12.0822i	0.422961	+	0.732590i
$273$		0			0
$274$	3.85638	−	6.67945i	0.232973	−	0.403520i
$275$	−0.330222	−	0.571962i	−0.0199131	−	0.0344906i
$276$	−0.0116112	+	0.0319015i	−0.000698911	+	0.00192024i
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	−0.767185	−	0.641426i	$-0.778343\pi$
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	0.939084	+	0.343689i	$0.111676\pi$
$278$	0.622426	−	1.07807i	0.0373306	−	0.0646585i
$279$	4.00088	−	22.6901i	0.239526	−	1.35842i
$280$		0			0
$281$	−14.1887	−	24.5755i	−0.846425	−	1.46605i	−0.884378	−	0.466771i	$-0.845417\pi$
$281$	−14.1887	−	24.5755i	−0.846425	−	1.46605i	0.0379535	−	0.999280i	$-0.487916\pi$
$282$	7.99912	+	9.53298i	0.476341	+	0.567681i
$283$	4.57129			0.271735			0.135867	−	0.990727i	$-0.456618\pi$
$283$	4.57129			0.271735			0.135867	+	0.990727i	$0.456618\pi$
$284$	−2.44562			−0.145121
$285$	6.15910	+	7.34013i	0.364834	+	0.434792i
$286$	−1.83544	−	3.17907i	−0.108532	−	0.187982i
$287$		0			0
$288$	−0.542766	+	3.07818i	−0.0319828	+	0.181384i
$289$	0.975185	−	1.68907i	0.0573638	−	0.0993571i
$290$	−14.9782	+	25.9430i	−0.879549	+	1.52342i
$291$	8.05896	−	22.1418i	0.472425	−	1.29798i
$292$	−0.948778	−	1.64333i	−0.0555230	−	0.0961687i
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	−0.922285	−	0.386512i	$-0.873680\pi$
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	0.795871	+	0.605466i	$0.207013\pi$
$294$		0			0
$295$	−0.932419	−	1.61500i	−0.0542875	−	0.0940287i
$296$	−11.3033	+	19.5780i	−0.656994	+	1.13795i
$297$			2.43134i			0.141081i
$298$	−5.87733	−	10.1798i	−0.340464	−	0.589702i
$299$	−0.617622			−0.0357180
$300$	−0.444907	+	0.0784491i	−0.0256867	+	0.00452926i
$301$		0			0
$302$	−12.4133	+	21.5004i	−0.714304	+	1.23721i
$303$	−16.3307	+	2.87954i	−0.938174	+	0.165425i
$304$	−3.92855	+	6.80445i	−0.225318	+	0.390262i
$305$	−1.21301	−	2.10100i	−0.0694568	−	0.120303i
$306$	14.7344	−	5.36289i	0.842311	−	0.306576i
$307$	12.3773			0.706411			0.353206	−	0.935546i	$-0.385092\pi$
$307$	12.3773			0.706411			0.353206	+	0.935546i	$0.385092\pi$
$308$		0			0
$309$	−1.80200	+	4.95096i	−0.102512	+	0.281651i
$310$	13.1001	+	22.6901i	0.744038	+	1.28871i
$311$	−21.9855			−1.24668			−0.623340	−	0.781951i	$-0.714225\pi$
$311$	−21.9855			−1.24668			−0.623340	+	0.781951i	$0.714225\pi$
$312$	−29.2367	+	5.15522i	−1.65520	+	0.291857i
$313$	−13.8898			−0.785099			−0.392549	−	0.919731i	$-0.628407\pi$
$313$	−13.8898			−0.785099			−0.392549	+	0.919731i	$0.628407\pi$
$314$	6.63404			0.374380
$315$		0			0
$316$	2.33544			0.131379
$317$	−6.18210			−0.347222			−0.173611	−	0.984814i	$-0.555543\pi$
$317$	−6.18210			−0.347222			−0.173611	+	0.984814i	$0.555543\pi$
$318$	0.572167	−	1.57202i	0.0320855	−	0.0881543i
$319$	4.10876			0.230046
$320$	−10.8833	−	18.8504i	−0.608392	−	1.05377i
$321$	−11.1172	+	1.96026i	−0.620502	+	0.109411i
$322$		0			0
$323$	−8.47565			−0.471598
$324$	1.56283	+	0.568825i	0.0868241	+	0.0316014i
$325$	−4.10947	−	7.11781i	−0.227952	−	0.394825i
$326$	−5.14543	+	8.91215i	−0.284979	+	0.493598i
$327$	−6.30200	+	17.3146i	−0.348502	+	0.957500i
$328$	−3.27719	+	5.67626i	−0.180952	+	0.313419i
$329$		0			0
$330$	−1.77719	−	2.11797i	−0.0978310	−	0.116590i
$331$	10.7314			0.589853			0.294926	−	0.955520i	$-0.404705\pi$
$331$	10.7314			0.589853			0.294926	+	0.955520i	$0.404705\pi$
$332$	−0.252374	−	0.437124i	−0.0138508	−	0.0239903i
$333$	17.6498	+	14.8099i	0.967201	+	0.811578i
$334$	3.80974	−	6.59867i	0.208460	−	0.361063i
$335$	12.2023	+	21.1351i	0.666685	+	1.15473i
$336$		0			0
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	−0.493518	−	0.869735i	$-0.664289\pi$
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	0.999972	−	0.00746831i	$-0.00237726\pi$
$338$	−14.0838	−	24.3938i	−0.766057	−	1.32685i
$339$	8.83069	−	1.55709i	0.479617	−	0.0845695i
$340$	0.907604	−	1.57202i	0.0492217	−	0.0852545i
$341$	1.79679	−	3.11213i	0.0973016	−	0.168531i
$342$	6.76470	+	5.67626i	0.365793	+	0.306937i
$343$		0			0
$344$	1.80541	+	3.12706i	0.0973410	+	0.168600i
$345$	−0.458111	+	0.0807773i	−0.0246639	+	0.00434890i
$346$	28.3865			1.52607
$347$	−20.4124			−1.09580			−0.547898	−	0.836545i	$-0.684572\pi$
$347$	−20.4124			−1.09580			−0.547898	+	0.836545i	$0.684572\pi$
$348$	0.961266	−	2.64106i	0.0515293	−	0.141576i
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	0.909750	−	0.415157i	$-0.136274\pi$
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	−0.814412	+	0.580288i	$0.802940\pi$
$350$		0			0
$351$			30.2569i			1.61500i
$352$	−0.243756	+	0.422197i	−0.0129922	+	0.0225032i
$353$	−5.01114	+	8.67956i	−0.266716	+	0.461966i	−0.968012	−	0.250904i	$-0.919272\pi$
$353$	−5.01114	+	8.67956i	−0.266716	+	0.461966i	0.701296	+	0.712871i	$0.252605\pi$
$354$	−1.10472	−	1.31656i	−0.0587153	−	0.0699742i
$355$	−16.7554	−	29.0211i	−0.889283	−	1.54028i
$356$	−0.749686	+	1.29849i	−0.0397333	+	0.0688200i
$357$		0			0
$358$	3.44949	+	5.97470i	0.182311	+	0.315773i
$359$	−4.74035	+	8.21053i	−0.250186	+	0.433335i	−0.963577	−	0.267431i	$-0.913825\pi$
$359$	−4.74035	+	8.21053i	−0.250186	+	0.433335i	0.713391	+	0.700766i	$0.247159\pi$
$360$	−21.0116	+	7.64760i	−1.10741	+	0.403064i
$361$	7.11334	+	12.3207i	0.374386	+	0.648456i
$362$	−0.431074			−0.0226568
$363$	6.38666	−	17.5472i	0.335213	−	0.920989i
$364$		0			0
$365$	13.0005	−	22.5175i	0.680476	−	1.17862i
$366$	−1.43717	−	1.71275i	−0.0751219	−	0.0895268i
$367$	−8.06670	+	13.9719i	−0.421079	+	0.729329i	−0.996045	−	0.0888474i	$-0.971682\pi$
$367$	−8.06670	+	13.9719i	−0.421079	+	0.729329i	0.574967	+	0.818177i	$0.305015\pi$
$368$	−0.190722	−	0.330341i	−0.00994209	−	0.0172202i
$369$	5.11721	+	4.29385i	0.266391	+	0.223529i
$370$	−26.2003			−1.36209
$371$		0			0
$372$	−1.58007	−	1.88305i	−0.0819228	−	0.0976318i
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	0.624841	−	0.780752i	$-0.285164\pi$
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	−0.988572	+	0.150752i	$0.951831\pi$
$374$	2.44562			0.126460
$375$	10.1163	+	12.0562i	0.522405	+	0.622578i
$376$	15.6973			0.809525
$377$	51.1317			2.63341
$378$		0			0
$379$	16.0574			0.824812			0.412406	−	0.911000i	$-0.364689\pi$
$379$	16.0574			0.824812			0.412406	+	0.911000i	$0.364689\pi$
$380$	1.02229			0.0524423
$381$	9.88877	+	11.7850i	0.506617	+	0.603763i
$382$	−20.9736			−1.07310
$383$	16.0103	+	27.7306i	0.818086	+	1.41697i	0.907090	+	0.420936i	$0.138298\pi$
$383$	16.0103	+	27.7306i	0.818086	+	1.41697i	−0.0890039	+	0.996031i	$0.528368\pi$
$384$	−10.5744	−	12.6021i	−0.539625	−	0.643100i
$385$		0			0
$386$	8.14022			0.414326
$387$	3.45811	−	1.25865i	0.175786	−	0.0639807i
$388$	−1.25696	−	2.17712i	−0.0638124	−	0.110526i
$389$	15.0214	−	26.0178i	0.761616	−	1.31916i	−0.180402	−	0.983593i	$-0.557740\pi$
$389$	15.0214	−	26.0178i	0.761616	−	1.31916i	0.942017	−	0.335564i	$-0.108927\pi$
$390$	−22.1163	−	26.3572i	−1.11990	−	1.33465i
$391$	0.205737	−	0.356347i	0.0104046	−	0.0180212i
$392$		0			0
$393$	−6.73127	+	18.4940i	−0.339548	+	0.932899i
$394$	33.9982			1.71281
$395$	16.0005	+	27.7136i	0.805071	+	1.39442i
$396$	0.198711	+	0.166739i	0.00998563	+	0.00837894i
$397$	6.15998	−	10.6694i	0.309160	−	0.535482i	−0.669019	−	0.743246i	$-0.733285\pi$
$397$	6.15998	−	10.6694i	0.309160	−	0.535482i	0.978179	+	0.207764i	$0.0666187\pi$
$398$	−2.04916	−	3.54925i	−0.102715	−	0.177908i
$399$		0			0
$400$	2.53802	−	4.39598i	0.126901	−	0.219799i
$401$	−10.4880	−	18.1657i	−0.523745	−	0.907152i	−0.999618	−	0.0276385i	$-0.991201\pi$
$401$	−10.4880	−	18.1657i	−0.523745	−	0.907152i	0.475873	−	0.879514i	$-0.342132\pi$
$402$	14.4572	+	17.2295i	0.721061	+	0.859327i
$403$	22.3603	−	38.7291i	1.11384	−	1.92923i
$404$	−0.884600	+	1.53217i	−0.0440105	+	0.0762284i
$405$	3.95723	+	22.4426i	0.196637	+	1.11518i
$406$		0			0
$407$	1.79679	+	3.11213i	0.0890635	+	0.154263i
$408$	6.76470	−	18.5859i	0.334903	−	0.920137i
$409$	25.6614			1.26887			0.634437	−	0.772975i	$-0.281232\pi$
$409$	25.6614			1.26887			0.634437	+	0.772975i	$0.281232\pi$
$410$	−7.59627			−0.375153
$411$	−9.76470	+	1.72178i	−0.481657	+	0.0849291i
$412$	0.281059	+	0.486809i	0.0138468	+	0.0239833i
$413$		0			0
$414$	−0.402856	+	0.146628i	−0.0197993	+	0.00720635i
$415$	3.45811	−	5.98962i	0.169752	−	0.294019i
$416$	−3.03343	+	5.25406i	−0.148726	+	0.257601i
$417$	−1.57604	+	0.277898i	−0.0771789	+	0.0136087i
$418$	0.688663	+	1.19280i	0.0336836	+	0.0583417i
$419$	0.739885	−	1.28152i	0.0361458	−	0.0626063i	−0.847387	−	0.530976i	$-0.821825\pi$
$419$	0.739885	−	1.28152i	0.0361458	−	0.0626063i	0.883532	+	0.468370i	$0.155159\pi$
$420$		0			0
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	0.660965	−	0.750417i	$-0.270147\pi$
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	−0.980363	+	0.197203i	$0.936814\pi$
$422$	3.67365	−	6.36295i	0.178830	−	0.309743i
$423$	2.77807	−	15.7552i	0.135074	−	0.766044i
$424$	−1.05509	−	1.82747i	−0.0512398	−	0.0887500i
$425$	5.47565			0.265608
$426$	−19.8516	−	23.6583i	−0.961815	−	1.14625i
$427$		0			0
$428$	−0.602196	+	1.04303i	−0.0291083	+	0.0504170i
$429$	−1.61406	+	4.43458i	−0.0779274	+	0.214104i
$430$	−2.09240	+	3.62414i	−0.100904	+	0.174771i
$431$	−8.86349	−	15.3520i	−0.426939	−	0.739481i	0.569660	−	0.821881i	$-0.307075\pi$
$431$	−8.86349	−	15.3520i	−0.426939	−	0.739481i	−0.996599	+	0.0823997i	$0.973742\pi$
$432$	−16.1832	+	9.34337i	−0.778615	+	0.449533i
$433$	−5.83843			−0.280577			−0.140289	−	0.990111i	$-0.544803\pi$
$433$	−5.83843			−0.280577			−0.140289	+	0.990111i	$0.544803\pi$
$434$		0			0
$435$	37.9261	−	6.68739i	1.81842	−	0.320636i
$436$	0.982926	+	1.70248i	0.0470736	+	0.0815339i
$437$	0.231734			0.0110853
$438$	8.19569	−	22.5175i	0.391605	−	1.07593i
$439$	29.8553			1.42492			0.712459	−	0.701714i	$-0.247582\pi$
$439$	29.8553			1.42492			0.712459	+	0.701714i	$0.247582\pi$
$440$	−3.48751			−0.166261
$441$		0			0
$442$	30.4347			1.44763
$443$	10.6655			0.506733			0.253367	−	0.967370i	$-0.418462\pi$
$443$	10.6655			0.506733			0.253367	+	0.967370i	$0.418462\pi$
$444$	2.42081	−	0.426854i	0.114886	−	0.0202576i
$445$	−20.5449			−0.973921
$446$	−9.56077	−	16.5597i	−0.452716	−	0.784127i
$447$	−5.16843	+	14.2002i	−0.244459	+	0.671644i
$448$		0			0
$449$	3.55438			0.167741			0.0838707	−	0.996477i	$-0.473272\pi$
$449$	3.55438			0.167741			0.0838707	+	0.996477i	$0.473272\pi$
$450$	−4.37030	−	3.66712i	−0.206018	−	0.172870i
$451$	0.520945	+	0.902302i	0.0245303	+	0.0424878i
$452$	0.478340	−	0.828510i	0.0224992	−	0.0389698i
$453$	31.4315	−	5.54223i	1.47678	−	0.260397i
$454$	1.94949	−	3.37662i	0.0914942	−	0.158473i
$455$		0			0
$456$	10.9697	−	1.93426i	0.513704	−	0.0905799i
$457$	5.02322			0.234976			0.117488	−	0.993074i	$-0.462516\pi$
$457$	5.02322			0.234976			0.117488	+	0.993074i	$0.462516\pi$
$458$	−6.17571	−	10.6966i	−0.288572	−	0.499821i
$459$	−17.4572	−	10.0789i	−0.814834	−	0.470445i
$460$	−0.0248149	+	0.0429807i	−0.00115700	+	0.00200399i
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	0.566955	−	0.823749i	$-0.308121\pi$
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	−0.996865	+	0.0791233i	$0.974788\pi$
$462$		0			0
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	−0.651897	−	0.758307i	$-0.726027\pi$
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	0.982662	+	0.185406i	$0.0593600\pi$
$464$	15.7895	+	27.3482i	0.733010	+	1.26961i
$465$	11.5201	−	31.6511i	0.534230	−	1.46779i
$466$	−8.94016	+	15.4848i	−0.414145	+	0.717320i
$467$	1.68433	−	2.91734i	0.0779413	−	0.134998i	−0.824420	−	0.565978i	$-0.808499\pi$
$467$	1.68433	−	2.91734i	0.0779413	−	0.134998i	0.902362	+	0.430980i	$0.141832\pi$
$468$	2.47288	+	2.07499i	0.114309	+	0.0959165i
$469$		0			0
$470$	9.09627	+	15.7552i	0.419579	+	0.726733i
$471$	−5.48205	−	6.53325i	−0.252599	−	0.301036i
$472$	−2.16788			−0.0997848
$473$	0.573978			0.0263915
$474$	18.9572	+	22.5924i	0.870735	+	1.03770i
$475$	1.54189	+	2.67063i	0.0707467	+	0.122537i
$476$		0			0
$477$	−2.02094	+	0.735564i	−0.0925327	+	0.0336791i
$478$	−6.42468	+	11.1279i	−0.293858	+	0.508977i
$479$	18.3833	−	31.8407i	0.839952	−	1.45484i	−0.0499812	−	0.998750i	$-0.515916\pi$
$479$	18.3833	−	31.8407i	0.839952	−	1.45484i	0.889934	−	0.456090i	$-0.150751\pi$
$480$	−1.56283	+	4.29385i	−0.0713333	+	0.195987i
$481$	22.3603	+	38.7291i	1.01954	+	1.76589i
$482$	6.03462	−	10.4523i	0.274869	−	0.476087i
$483$		0			0
$484$	−0.996130	−	1.72535i	−0.0452786	−	0.0784249i
$485$	17.2233	−	29.8316i	0.782069	−	1.35458i
$486$	7.18320	+	19.7357i	0.325837	+	0.895229i
$487$	18.7087	+	32.4045i	0.847773	+	1.46839i	0.883191	+	0.469014i	$0.155391\pi$
$487$	18.7087	+	32.4045i	0.847773	+	1.46839i	−0.0354172	+	0.999373i	$0.511276\pi$
$488$	−2.82026			−0.127667
$489$	13.0287	−	2.29731i	0.589178	−	0.103888i
$490$		0			0
$491$	13.3353	−	23.0974i	0.601813	−	1.04237i	−0.390734	−	0.920504i	$-0.627779\pi$
$491$	13.3353	−	23.0974i	0.601813	−	1.04237i	0.992547	−	0.121866i	$-0.0388879\pi$
$492$	0.701867	−	0.123758i	0.0316426	−	0.00557944i
$493$	−17.0326	+	29.5013i	−0.767108	+	1.32867i
$494$	8.57011	+	14.8439i	0.385587	+	0.667857i
$495$	−0.617211	+	3.50038i	−0.0277416	+	0.157330i
$496$	27.6195			1.24015
$497$		0			0
$498$	2.18004	−	5.98962i	0.0976901	−	0.268401i
$499$	−16.8726	−	29.2242i	−0.755320	−	1.30825i	−0.945215	−	0.326449i	$-0.894148\pi$
$499$	−16.8726	−	29.2242i	−0.755320	−	1.30825i	0.189895	−	0.981804i	$-0.439185\pi$
$500$	1.67911			0.0750921
$501$	−9.64661	+	1.70096i	−0.430979	+	0.0759932i
$502$	−33.6800			−1.50321
$503$	−32.0401			−1.42860			−0.714299	−	0.699840i	$-0.753255\pi$
$503$	−32.0401			−1.42860			−0.714299	+	0.699840i	$0.753255\pi$
$504$		0			0
$505$	−24.2422			−1.07876
$506$	−0.0668661			−0.00297256
$507$	−12.3851	+	34.0277i	−0.550040	+	1.51122i
$508$	1.64134			0.0728227
$509$	3.96926	+	6.87495i	0.175934	+	0.304727i	0.940484	−	0.339838i	$-0.110372\pi$
$509$	3.96926	+	6.87495i	0.175934	+	0.304727i	−0.764550	+	0.644564i	$0.777039\pi$
$510$	22.5744	−	3.98048i	0.999613	−	0.176259i
$511$		0			0
$512$	−24.9186			−1.10126
$513$		−	11.3525i		−	0.501226i
$514$	−7.31046	−	12.6621i	−0.322451	−	0.558501i
$515$	−3.85117	+	6.67042i	−0.169703	+	0.293934i
$516$	0.134285	−	0.368946i	0.00591158	−	0.0162419i
$517$	1.24763	−	2.16095i	0.0548705	−	0.0950386i
$518$		0			0
$519$	−23.4572	−	27.9552i	−1.02966	−	1.22710i
$520$	−43.4005			−1.90324
$521$	7.33750	+	12.7089i	0.321462	+	0.556788i	0.980790	−	0.195067i	$-0.0624926\pi$
$521$	7.33750	+	12.7089i	0.321462	+	0.556788i	−0.659328	+	0.751855i	$0.729159\pi$
$522$	33.3516	−	12.1390i	1.45976	−	0.531310i
$523$	−14.1716	+	24.5459i	−0.619680	+	1.07332i	0.369864	+	0.929086i	$0.379404\pi$
$523$	−14.1716	+	24.5459i	−0.619680	+	1.07332i	−0.989544	+	0.144232i	$0.953929\pi$
$524$	1.04988	+	1.81844i	0.0458641	+	0.0794390i
$525$		0			0
$526$	−17.5737	+	30.4386i	−0.766251	+	1.32719i
$527$	14.8969	+	25.8022i	0.648920	+	1.12396i
$528$	−2.87030	+	0.506111i	−0.124914	+	0.0220257i
$529$	11.4944	−	19.9088i	0.499755	−	0.865602i
$530$	1.22281	−	2.11797i	0.0531155	−	0.0919988i
$531$	−0.383666	+	2.17588i	−0.0166497	+	0.0944251i
$532$		0			0
$533$	6.48293	+	11.2288i	0.280807	+	0.486371i
$534$	−18.6466	+	3.28790i	−0.806918	+	0.142281i
$535$	−16.5030			−0.713487
$536$	28.3705			1.22542
$537$	3.03343	−	8.33429i	0.130902	−	0.359651i
$538$	5.14203	+	8.90625i	0.221688	+	0.383976i
$539$		0			0
$540$	2.10560	+	1.21567i	0.0906106	+	0.0523141i
$541$	−5.64290	+	9.77380i	−0.242607	+	0.420208i	−0.961456	−	0.274958i	$-0.911336\pi$
$541$	−5.64290	+	9.77380i	−0.242607	+	0.420208i	0.718849	+	0.695166i	$0.244669\pi$
$542$	−2.29292	+	3.97145i	−0.0984893	+	0.170588i
$543$	0.356219	+	0.424525i	0.0152868	+	0.0182181i
$544$	−2.02094	−	3.50038i	−0.0866473	−	0.150077i
$545$	−13.4684	+	23.3279i	−0.576922	+	0.999258i
$546$		0			0
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	0.988519	+	0.151099i	$0.0482812\pi$
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	−0.363404	+	0.931632i	$0.618385\pi$
$548$	−0.528934	+	0.916140i	−0.0225949	+	0.0391356i
$549$	−0.499123	+	2.83067i	−0.0213020	+	0.120810i
$550$	−0.444907	−	0.770602i	−0.0189709	−	0.0328586i
$551$	−19.1848			−0.817300
$552$	−0.184955	+	0.508159i	−0.00787219	+	0.0216287i
$553$		0			0
$554$	3.85457	−	6.67631i	0.163765	−	0.283649i
$555$	21.6506	+	25.8022i	0.919019	+	1.09524i
$556$	−0.0853707	+	0.147866i	−0.00362052	+	0.00627093i
$557$	0.387841	+	0.671761i	0.0164334	+	0.0284634i	0.874125	−	0.485701i	$-0.161436\pi$
$557$	0.387841	+	0.671761i	0.0164334	+	0.0284634i	−0.857692	+	0.514164i	$0.828102\pi$
$558$	5.39037	−	30.5703i	0.228192	−	1.29414i
$559$	7.14290			0.302113
$560$		0			0
$561$	−2.02094	−	2.40847i	−0.0853243	−	0.101686i
$562$	−19.1163	−	33.1105i	−0.806374	−	1.39668i
$563$	24.9522			1.05161			0.525806	−	0.850605i	$-0.323764\pi$
$563$	24.9522			1.05161			0.525806	+	0.850605i	$0.323764\pi$
$564$	−1.09714	−	1.30753i	−0.0461981	−	0.0550567i
$565$	13.1088			0.551489
$566$	6.15888			0.258877
$567$		0			0
$568$	−38.9564			−1.63457
$569$	−24.8033			−1.03981			−0.519905	−	0.854224i	$-0.674033\pi$
$569$	−24.8033			−1.03981			−0.519905	+	0.854224i	$0.674033\pi$
$570$	8.29813	+	9.88933i	0.347571	+	0.414218i
$571$	8.79654			0.368124			0.184062	−	0.982915i	$-0.441075\pi$
$571$	8.79654			0.368124			0.184062	+	0.982915i	$0.441075\pi$
$572$	0.251745	+	0.436035i	0.0105260	+	0.0182315i
$573$	17.3316	+	20.6550i	0.724037	+	0.862873i
$574$		0			0
$575$	−0.149711			−0.00624336
$576$	−4.47818	+	25.3970i	−0.186591	+	1.05821i
$577$	6.43717	+	11.1495i	0.267983	+	0.464160i	0.968341	−	0.249632i	$-0.0803096\pi$
$577$	6.43717	+	11.1495i	0.267983	+	0.464160i	−0.700358	+	0.713792i	$0.746976\pi$
$578$	1.31386	−	2.27568i	0.0546495	−	0.0946557i
$579$	−6.72668	−	8.01655i	−0.279551	−	0.333156i
$580$	2.05438	−	3.55829i	0.0853034	−	0.147750i
$581$		0			0
$582$	10.8578	−	29.8316i	0.450071	−	1.23656i
$583$	−0.335437			−0.0138924
$584$	−15.1131	−	26.1766i	−0.625384	−	1.08320i
$585$	−7.68092	+	43.5607i	−0.317567	+	1.80101i
$586$	−2.91534	+	5.04952i	−0.120432	+	0.208594i
$587$	−22.4315	−	38.8526i	−0.925849	−	1.60362i	−0.790190	−	0.612861i	$-0.790018\pi$
$587$	−22.4315	−	38.8526i	−0.925849	−	1.60362i	−0.135658	−	0.990756i	$-0.543315\pi$
$588$		0			0
$589$	−8.38965	+	14.5313i	−0.345690	+	0.598752i
$590$	−1.25624	−	2.17588i	−0.0517188	−	0.0895795i
$591$	−28.0945	−	33.4817i	−1.15565	−	1.37725i
$592$	−13.8097	+	23.9192i	−0.567577	+	0.983072i
$593$	−1.88026	+	3.25671i	−0.0772131	+	0.133737i	−0.902047	−	0.431639i	$-0.857936\pi$
$593$	−1.88026	+	3.25671i	−0.0772131	+	0.133737i	0.824833	+	0.565376i	$0.191269\pi$
$594$			3.27573i			0.134405i
$595$		0			0
$596$	0.806123	+	1.39625i	0.0330201	+	0.0571924i
$597$	−1.80200	+	4.95096i	−0.0737511	+	0.202629i
$598$	−0.832119			−0.0340279
$599$	−3.69047			−0.150789			−0.0753943	−	0.997154i	$-0.524022\pi$
$599$	−3.69047			−0.150789			−0.0753943	+	0.997154i	$0.524022\pi$
$600$	−7.08693	+	1.24962i	−0.289323	+	0.0510154i
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	0.998107	−	0.0615091i	$-0.0195913\pi$
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	−0.552322	+	0.833631i	$0.686258\pi$
$602$		0			0
$603$	5.02094	−	28.4752i	0.204469	−	1.15960i
$604$	1.70258	−	2.94896i	0.0692771	−	0.119991i
$605$	13.6493	−	23.6413i	0.554923	−	0.961155i
$606$	−22.0023	+	3.87960i	−0.893781	+	0.157598i
$607$	−12.1973	−	21.1263i	−0.495072	−	0.857490i	0.504911	−	0.863171i	$-0.331525\pi$
$607$	−12.1973	−	21.1263i	−0.495072	−	0.857490i	−0.999984	+	0.00568063i	$0.998192\pi$
$608$	1.13816	−	1.97134i	0.0461583	−	0.0799485i
$609$		0			0
$610$	−1.63429	−	2.83067i	−0.0661703	−	0.114610i
$611$	15.5262	−	26.8921i	0.628121	−	1.08794i
$612$	−2.02094	+	0.735564i	−0.0816918	+	0.0297334i
$613$	−21.0107	−	36.3917i	−0.848616	−	1.46985i	−0.882444	−	0.470418i	$-0.844103\pi$
$613$	−21.0107	−	36.3917i	−0.848616	−	1.46985i	0.0338284	−	0.999428i	$-0.489230\pi$
$614$	16.6759			0.672986
$615$	6.27719	+	7.48086i	0.253121	+	0.301657i
$616$		0			0
$617$	−23.2049	+	40.1920i	−0.934192	+	1.61807i	−0.158125	+	0.987419i	$0.550545\pi$
$617$	−23.2049	+	40.1920i	−0.934192	+	1.61807i	−0.776068	+	0.630650i	$0.782788\pi$
$618$	−2.42783	+	6.67042i	−0.0976618	+	0.268324i
$619$	13.6047	−	23.5641i	0.546820	−	0.947120i	−0.451670	−	0.892185i	$-0.649172\pi$
$619$	13.6047	−	23.5641i	0.546820	−	0.947120i	0.998490	−	0.0549349i	$-0.0174951\pi$
$620$	−1.79679	−	3.11213i	−0.0721608	−	0.124986i
$621$	0.477301	+	0.275570i	0.0191534	+	0.0110582i
$622$	−29.6209			−1.18769
$623$		0			0
$624$	−35.7196	+	6.29833i	−1.42993	+	0.252135i
$625$	15.0326	+	26.0372i	0.601302	+	1.04149i
$626$	−18.7137			−0.747950
$627$	0.605600	−	1.66387i	0.0241853	−	0.0664487i
$628$	−0.909912			−0.0363094
$629$	−29.7939			−1.18796
$630$		0			0
$631$	−29.6023			−1.17845			−0.589224	−	0.807970i	$-0.700566\pi$
$631$	−29.6023			−1.17845			−0.589224	+	0.807970i	$0.700566\pi$
$632$	37.2012			1.47978
$633$	−9.30200	+	1.64019i	−0.369721	+	0.0651919i
$634$	−8.32913			−0.330792
$635$	11.2451	+	19.4771i	0.446248	+	0.772925i
$636$	−0.0784773	+	0.215615i	−0.00311183	+	0.00854968i
$637$		0			0
$638$	5.53571			0.219161
$639$	−6.89440	+	39.1001i	−0.272738	+	1.54678i
$640$	−12.0248	−	20.8276i	−0.475323	−	0.823283i
$641$	0.139500	−	0.241621i	0.00550991	−	0.00954345i	−0.863257	−	0.504764i	$-0.831579\pi$
$641$	0.139500	−	0.241621i	0.00550991	−	0.00954345i	0.868767	+	0.495221i	$0.164913\pi$
$642$	−14.9782	+	2.64106i	−0.591142	+	0.104234i
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	−0.628181	−	0.778067i	$-0.716200\pi$
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	0.987916	+	0.154988i	$0.0495338\pi$
$644$		0			0
$645$	5.29813	−	0.934204i	0.208614	−	0.0367842i
$646$	−11.4192			−0.449283
$647$	−11.2285	−	19.4483i	−0.441438	−	0.764592i	0.556359	−	0.830942i	$-0.312198\pi$
$647$	−11.2285	−	19.4483i	−0.441438	−	0.764592i	−0.997796	+	0.0663498i	$0.978865\pi$
$648$	24.8944	+	9.06082i	0.977944	+	0.355943i
$649$	−0.172304	+	0.298439i	−0.00676352	+	0.0117148i
$650$	−5.53667	−	9.58980i	−0.217166	−	0.376143i
$651$		0			0
$652$	0.705737	−	1.22237i	0.0276388	−	0.0478718i
$653$	25.2656	+	43.7614i	0.988721	+	1.71251i	0.624066	+	0.781372i	$0.285480\pi$
$653$	25.2656	+	43.7614i	0.988721	+	1.71251i	0.364655	+	0.931143i	$0.381187\pi$
$654$	−8.49067	+	23.3279i	−0.332011	+	0.912194i
$655$	−14.3858	+	24.9169i	−0.562099	+	0.973584i
$656$	−4.00387	+	6.93491i	−0.156325	+	0.270763i
$657$	−28.9479	+	10.5362i	−1.12937	+	0.411055i
$658$		0			0
$659$	1.33631	+	2.31456i	0.0520554	+	0.0901626i	0.890879	−	0.454241i	$-0.150089\pi$
$659$	1.33631	+	2.31456i	0.0520554	+	0.0901626i	−0.838824	+	0.544403i	$0.816756\pi$
$660$	0.243756	+	0.290497i	0.00948818	+	0.0113076i
$661$	−34.6100			−1.34617			−0.673086	−	0.739564i	$-0.735032\pi$
$661$	−34.6100			−1.34617			−0.673086	+	0.739564i	$0.735032\pi$
$662$	14.4584			0.561942
$663$	−25.1498	−	29.9723i	−0.976736	−	1.16403i
$664$	−4.02007	−	6.96296i	−0.156009	−	0.270215i
$665$		0			0
$666$	23.7795	+	19.9533i	0.921436	+	0.773176i
$667$	0.465690	−	0.806598i	0.0180316	−	0.0312316i
$668$	−0.522537	+	0.905061i	−0.0202176	+	0.0350179i
$669$	−8.40760	+	23.0997i	−0.325057	+	0.893086i
$670$	16.4402	+	28.4752i	0.635139	+	1.10009i
$671$	−0.224155	+	0.388249i	−0.00865342	+	0.0149882i
$672$		0			0
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	0.661869	−	0.749619i	$-0.269763\pi$
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	−0.980124	+	0.198386i	$0.936430\pi$
$674$	12.5262	−	21.6959i	0.482490	−	0.835697i
$675$			7.33423i			0.282295i
$676$	1.93170	+	3.34581i	0.0742963	+	0.128685i
$677$	−43.7579			−1.68175			−0.840877	−	0.541226i	$-0.817960\pi$
$677$	−43.7579			−1.68175			−0.840877	+	0.541226i	$0.817960\pi$
$678$	11.8976	−	2.09786i	0.456923	−	0.0805678i
$679$		0			0
$680$	14.4572	−	25.0407i	0.554410	−	0.960266i
$681$	−4.93629	+	0.870401i	−0.189159	+	0.0333538i
$682$	2.42081	−	4.19296i	0.0926975	−	0.160557i
$683$	−14.1206	−	24.4576i	−0.540310	−	0.935845i	−0.998886	−	0.0471895i	$-0.984974\pi$
$683$	−14.1206	−	24.4576i	−0.540310	−	0.935845i	0.458576	−	0.888655i	$-0.348360\pi$
$684$	−0.927833	−	0.778544i	−0.0354766	−	0.0297684i
$685$	−14.4953			−0.553835
$686$		0			0
$687$	−5.43083	+	14.9211i	−0.207199	+	0.569274i
$688$	2.20574	+	3.82045i	0.0840929	+	0.145653i
$689$	−4.17436			−0.159031
$690$	−0.617211	+	0.108831i	−0.0234968	+	0.00414312i
$691$	−29.0651			−1.10569			−0.552844	−	0.833284i	$-0.686458\pi$
$691$	−29.0651			−1.10569			−0.552844	+	0.833284i	$0.686458\pi$
$692$	−3.89344			−0.148006
$693$		0			0
$694$	−27.5016			−1.04395
$695$	−2.33956			−0.0887444
$696$	15.3120	−	42.0694i	0.580401	−	1.59464i
$697$	−8.63816			−0.327193
$698$	2.39961	+	4.15625i	0.0908268	+	0.157317i
$699$	22.6373	−	3.99156i	0.856221	−	0.150975i
$700$		0			0
$701$	−1.10876			−0.0418771			−0.0209386	−	0.999781i	$-0.506665\pi$
$701$	−1.10876			−0.0418771			−0.0209386	+	0.999781i	$0.506665\pi$
$702$			40.7650i			1.53858i
$703$	−8.38965	−	14.5313i	−0.316422	−	0.548059i
$704$	−2.01114	+	3.48340i	−0.0757979	+	0.131286i
$705$	7.99912	−	21.9774i	0.301264	−	0.827717i
$706$	−6.75150	+	11.6939i	−0.254096	+	0.440107i
$707$		0			0
$708$	0.151522	+	0.180576i	0.00569453	+	0.00678648i
$709$	−18.4688			−0.693612			−0.346806	−	0.937937i	$-0.612734\pi$
$709$	−18.4688			−0.693612			−0.346806	+	0.937937i	$0.612734\pi$
$710$	−22.5744	−	39.1001i	−0.847204	−	1.46740i
$711$	6.58378	−	37.3385i	0.246911	−	1.40030i
$712$	−11.9418	+	20.6837i	−0.447536	+	0.775155i
$713$	−0.407299	−	0.705463i	−0.0152535	−	0.0264198i
$714$		0			0
$715$	−3.44949	+	5.97470i	−0.129004	+	0.223441i
$716$	−0.473126	−	0.819478i	−0.0176815	−	0.0306253i
$717$	16.2679	−	2.86846i	0.607534	−	0.107125i
$718$	−6.38666	+	11.0620i	−0.238348	+	0.412831i
$719$	16.8885	−	29.2517i	0.629834	−	1.09090i	−0.357751	−	0.933817i	$-0.616456\pi$
$719$	16.8885	−	29.2517i	0.629834	−	1.09090i	0.987585	−	0.157087i	$-0.0502103\pi$
$720$	−25.6707	+	9.34337i	−0.956691	+	0.348207i
$721$		0			0
$722$	9.58378	+	16.5996i	0.356671	+	0.617773i
$723$	−15.2802	+	2.69431i	−0.568276	+	0.100202i
$724$	0.0591253			0.00219738
$725$	12.3942			0.460310
$726$	8.60472	−	23.6413i	0.319351	−	0.877410i
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	0.667095	−	0.744973i	$-0.267538\pi$
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	−0.978713	+	0.205234i	$0.934204\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	17.5155	−	30.3377i	0.648277	−	1.12285i
$731$	−2.37939	+	4.12122i	−0.0880047	+	0.152429i
$732$	0.197119	+	0.234917i	0.00728573	+	0.00868279i
$733$	6.81820	+	11.8095i	0.251836	+	0.436193i	0.964031	−	0.265789i	$-0.0856323\pi$
$733$	6.81820	+	11.8095i	0.251836	+	0.436193i	−0.712195	+	0.701981i	$0.752299\pi$
$734$	−10.8682	+	18.8243i	−0.401154	+	0.694819i
$735$		0			0
$736$	0.0552549	+	0.0957044i	0.00203672	+	0.00352771i
$737$	2.25490	−	3.90560i	0.0830603	−	0.143865i
$738$	6.89440	+	5.78509i	0.253786	+	0.212952i
$739$	16.0209	+	27.7491i	0.589340	+	1.02077i	0.994319	+	0.106441i	$0.0339455\pi$
$739$	16.0209	+	27.7491i	0.589340	+	1.02077i	−0.404979	+	0.914326i	$0.632721\pi$
$740$	3.59358			0.132103
$741$	7.53643	−	20.7062i	0.276858	−	0.760660i
$742$		0			0
$743$	−16.8764	+	29.2309i	−0.619137	+	1.07238i	0.370507	+	0.928830i	$0.379184\pi$
$743$	−16.8764	+	29.2309i	−0.619137	+	1.07238i	−0.989644	+	0.143547i	$0.954149\pi$
$744$	−25.1690	−	29.9952i	−0.922739	−	1.09968i
$745$	−11.0458	+	19.1318i	−0.404685	+	0.700936i
$746$	−9.46451	−	16.3930i	−0.346520	−	0.600191i
$747$	−7.70011	+	2.80261i	−0.281732	+	0.102542i
$748$	−0.335437			−0.0122648
$749$		0			0
$750$	13.6297	+	16.2432i	0.497686	+	0.593119i
$751$	−13.0582	−	22.6175i	−0.476502	−	0.825326i	0.523135	−	0.852250i	$-0.324762\pi$
$751$	−13.0582	−	22.6175i	−0.476502	−	0.825326i	−0.999637	+	0.0269236i	$0.991429\pi$
$752$	19.1780			0.699349
$753$	27.8316	+	33.1684i	1.01424	+	1.20872i
$754$	68.8895			2.50881
$755$	46.6587			1.69808
$756$		0			0
$757$	35.6536			1.29585			0.647927	−	0.761703i	$-0.275636\pi$
$757$	35.6536			1.29585			0.647927	+	0.761703i	$0.275636\pi$
$758$	21.6340			0.785784
$759$	0.0552549	+	0.0658503i	0.00200563	+	0.00239021i
$760$	16.2841			0.590685
$761$	−20.3824	−	35.3033i	−0.738861	−	1.27974i	−0.953009	−	0.302943i	$-0.902031\pi$
$761$	−20.3824	−	35.3033i	−0.738861	−	1.27974i	0.214148	−	0.976801i	$-0.431302\pi$
$762$	13.3231	+	15.8779i	0.482645	+	0.575194i
$763$		0			0
$764$	2.87670			0.104075
$765$	−22.5744	−	18.9422i	−0.816181	−	0.684857i
$766$	21.5706	+	37.3613i	0.779377	+	1.34992i
$767$	−2.14425	+	3.71395i	−0.0774243	+	0.134103i
$768$	4.89424	+	5.83273i	0.176606	+	0.210470i
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	0.253639	+	0.967299i	$0.418373\pi$
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	−0.964525	+	0.263992i	$0.914961\pi$
$770$		0			0
$771$	−6.42871	+	17.6627i	−0.231524	+	0.636108i
$772$	−1.11650			−0.0401836
$773$	−12.4513	−	21.5663i	−0.447842	−	0.775686i	0.550403	−	0.834899i	$-0.314474\pi$
$773$	−12.4513	−	21.5663i	−0.447842	−	0.775686i	−0.998245	+	0.0592135i	$0.981141\pi$
$774$	4.65910	−	1.69577i	0.167468	−	0.0609533i
$775$	5.42009	−	9.38788i	0.194695	−	0.337222i
$776$	−20.0221	−	34.6793i	−0.718752	−	1.24492i
$777$		0			0
$778$	20.2383	−	35.0538i	0.725578	−	1.25674i
$779$	−2.43242	−	4.21307i	−0.0871504	−	0.150949i
$780$	3.03343	+	3.61510i	0.108614	+	0.129442i
$781$	−3.09627	+	5.36289i	−0.110793	+	0.191899i
$782$	0.277189	−	0.480105i	0.00991225	−	0.0171685i
$783$	−39.5148	−	22.8139i	−1.41214	−	0.815301i
$784$		0			0
$785$	−6.23396	−	10.7975i	−0.222499	−	0.385380i
$786$	−9.06901	+	24.9169i	−0.323481	+	0.888757i
$787$	−30.7050			−1.09452			−0.547258	−	0.836964i	$-0.684328\pi$
$787$	−30.7050			−1.09452			−0.547258	+	0.836964i	$0.684328\pi$
$788$	−4.66313			−0.166117
$789$	44.4982	−	7.84624i	1.58418	−	0.279334i
$790$	21.5574	+	37.3385i	0.766977	+	1.32844i
$791$		0			0
$792$	3.16528	+	2.65598i	0.112473	+	0.0943763i
$793$	−2.78952	+	4.83158i	−0.0990586	+	0.171575i
$794$	8.29932	−	14.3748i	0.294532	−	0.510144i
$795$	−3.09627	+	0.545955i	−0.109813	+	0.0193630i
$796$	0.281059	+	0.486809i	0.00996188	+	0.0172545i
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	−0.751858	−	0.659325i	$-0.770842\pi$
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	0.946921	+	0.321466i	$0.104175\pi$
$798$		0			0
$799$	10.3439	+	17.9161i	0.365941	+	0.633828i
$800$	−0.735300	+	1.27358i	−0.0259968	+	0.0450277i
$801$	18.6466	+	15.6464i	0.658846	+	0.552837i
$802$	−14.1304	−	24.4746i	−0.498962	−	0.864228i
$803$	−4.80478			−0.169557
$804$	−1.98293	−	2.36316i	−0.0699324	−	0.0833422i
$805$		0			0
$806$	30.1259	−	52.1796i	1.06114	−	1.83795i
$807$	4.52182	−	12.4236i	0.159176	−	0.437332i
$808$	−14.0908	+	24.4060i	−0.495713	+	0.858600i
$809$	−8.49407	−	14.7122i	−0.298636	−	0.517252i	0.677188	−	0.735810i	$-0.263198\pi$
$809$	−8.49407	−	14.7122i	−0.298636	−	0.517252i	−0.975824	+	0.218558i	$0.929865\pi$
$810$	5.33157	+	30.2368i	0.187332	+	1.06241i
$811$	37.9796			1.33364			0.666822	−	0.745217i	$-0.267654\pi$
$811$	37.9796			1.33364			0.666822	+	0.745217i	$0.267654\pi$
$812$		0			0
$813$	5.80587	−	1.02373i	0.203621	−	0.0359039i
$814$	2.42081	+	4.19296i	0.0848493	+	0.146963i
$815$	19.3405			0.677468
$816$	8.26470	−	22.7071i	0.289322	−	0.794907i
$817$	−2.68004			−0.0937629
$818$	34.5735			1.20883
$819$		0			0
$820$	1.04189			0.0363843
$821$	8.27868			0.288928			0.144464	−	0.989510i	$-0.453854\pi$
$821$	8.27868			0.288928			0.144464	+	0.989510i	$0.453854\pi$
$822$	−13.1559	+	2.31975i	−0.458866	+	0.0809105i
$823$	54.5526			1.90158			0.950792	−	0.309829i	$-0.100272\pi$
$823$	54.5526			1.90158			0.950792	+	0.309829i	$0.100272\pi$
$824$	4.47700	+	7.75438i	0.155964	+	0.270137i
$825$	−0.391245	+	1.07494i	−0.0136214	+	0.0374245i
$826$		0			0
$827$	−31.8708			−1.10826			−0.554129	−	0.832431i	$-0.686948\pi$
$827$	−31.8708			−1.10826			−0.554129	+	0.832431i	$0.686948\pi$
$828$	0.0552549	−	0.0201112i	0.00192024	−	0.000698911i
$829$	0.176174	+	0.305143i	0.00611879	+	0.0105981i	0.869069	−	0.494692i	$-0.164719\pi$
$829$	0.176174	+	0.305143i	0.00611879	+	0.0105981i	−0.862950	+	0.505290i	$0.831386\pi$
$830$	4.65910	−	8.06980i	0.161720	−	0.280107i
$831$	−9.76011	+	1.72097i	−0.338575	+	0.0596998i
$832$	−25.0278	+	43.3494i	−0.867683	+	1.50287i
$833$		0			0
$834$	−2.12339	+	0.374411i	−0.0735270	+	0.0129648i
$835$	−14.3200			−0.495562
$836$	−0.0944557	−	0.163602i	−0.00326682	−	0.00565829i
$837$	−34.5602	+	19.9533i	−1.19458	+	0.689688i
$838$	0.996845	−	1.72659i	0.0344354	−	0.0596439i
$839$	−12.5077	−	21.6640i	−0.431815	−	0.747926i	0.565215	−	0.824944i	$-0.308793\pi$
$839$	−12.5077	−	21.6640i	−0.431815	−	0.747926i	−0.997030	+	0.0770182i	$0.975460\pi$
$840$		0			0
$841$	−24.0535	+	41.6619i	−0.829431	+	1.43662i
$842$	−8.82951	−	15.2932i	−0.304285	−	0.527037i
$843$	−16.8106	+	46.1868i	−0.578989	+	1.59076i
$844$	−0.503870	+	0.872729i	−0.0173439	+	0.0300406i
$845$	−26.4688	+	45.8454i	−0.910556	+	1.57713i
$846$	3.74288	−	21.2269i	0.128683	−	0.729796i
$847$		0			0
$848$	−1.28905	−	2.23270i	−0.0442661	−	0.0766711i
$849$	−5.08940	−	6.06531i	−0.174668	−	0.208161i
$850$	7.37733			0.253040
$851$	0.814598			0.0279241
$852$	2.72281	+	3.24492i	0.0932820	+	0.111169i
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	−0.977640	−	0.210286i	$-0.932560\pi$
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	0.306706	−	0.951804i	$-0.400773\pi$
$854$		0			0
$855$	2.88191	−	16.3441i	0.0985593	−	0.558958i
$856$	−9.59240	+	16.6145i	−0.327861	+	0.567873i
$857$	−8.20368	+	14.2092i	−0.280232	+	0.485377i	−0.971442	−	0.237278i	$-0.923745\pi$
$857$	−8.20368	+	14.2092i	−0.280232	+	0.485377i	0.691210	+	0.722654i	$0.257078\pi$
$858$	−2.17461	+	5.97470i	−0.0742400	+	0.203973i
$859$	13.4162	+	23.2376i	0.457756	+	0.792856i	0.998842	−	0.0481111i	$-0.0153201\pi$
$859$	13.4162	+	23.2376i	0.457756	+	0.792856i	−0.541086	+	0.840967i	$0.681987\pi$
$860$	0.286989	−	0.497079i	0.00978624	−	0.0169503i
$861$		0			0
$862$	−11.9418	−	20.6837i	−0.406738	−	0.704490i
$863$	−7.25284	+	12.5623i	−0.246890	+	0.427625i	−0.962661	−	0.270709i	$-0.912742\pi$
$863$	−7.25284	+	12.5623i	−0.246890	+	0.427625i	0.715772	+	0.698334i	$0.246075\pi$
$864$	4.68850	−	2.70691i	0.159506	−	0.0920909i
$865$	−26.6746	−	46.2017i	−0.906963	−	1.57091i
$866$	−7.86610			−0.267301
$867$	−3.32682	+	0.586608i	−0.112985	+	0.0199222i
$868$		0			0
$869$	2.95677	−	5.12127i	0.100301	−	0.173727i
$870$	51.0977	−	9.00990i	1.73237	−	0.305464i
$871$	28.0612	−	48.6035i	0.950819	−	1.64687i
$872$	15.6570	+	27.1188i	0.530214	+	0.918358i
$873$	−38.3508	+	13.9585i	−1.29798	+	0.472425i
$874$	0.312214			0.0105608
$875$		0			0
$876$	−1.12410	+	3.08845i	−0.0379800	+	0.104349i
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270131\pi$
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	−0.980352	+	0.197255i	$0.936797\pi$
$878$	40.2240			1.35749
$879$	7.38191	−	1.30163i	0.248986	−	0.0439029i
$880$	−4.26083			−0.143633
$881$	53.8976			1.81585			0.907927	−	0.419128i	$-0.137664\pi$
$881$	53.8976			1.81585			0.907927	+	0.419128i	$0.137664\pi$
$882$		0			0
$883$	43.4252			1.46137			0.730687	−	0.682712i	$-0.239200\pi$
$883$	43.4252			1.46137			0.730687	+	0.682712i	$0.239200\pi$
$884$	−4.17436			−0.140399
$885$	−1.10472	+	3.03520i	−0.0371348	+	0.102027i
$886$	14.3696			0.482756
$887$	19.4800	+	33.7403i	0.654074	+	1.13289i	0.982125	+	0.188229i	$0.0602749\pi$
$887$	19.4800	+	33.7403i	0.654074	+	1.13289i	−0.328051	+	0.944660i	$0.606392\pi$
$888$	38.5611	−	6.79936i	1.29403	−	0.228172i
$889$		0			0
$890$	−27.6800			−0.927837
$891$	3.22597	−	2.70691i	0.108074	−	0.0906848i
$892$	1.31134	+	2.27130i	0.0439068	+	0.0760488i
$893$	−5.82547	+	10.0900i	−0.194942	+	0.337650i
$894$	−6.96341	+	19.1318i	−0.232891	+	0.639864i
$895$	6.48293	−	11.2288i	0.216700	−	0.375336i
$896$		0			0
$897$	0.687623	+	0.819478i	0.0229591	+	0.0273616i
$898$	4.78880			0.159804
$899$	33.7195	+	58.4038i	1.12461	+	1.94788i
$900$	0.599422	+	0.502975i	0.0199807	+	0.0167658i
$901$	1.39053	−	2.40847i	0.0463253	−	0.0802377i
$902$	0.701867	+	1.21567i	0.0233696	+	0.0404773i
$903$		0			0
$904$	7.61949	−	13.1973i	0.253420	−	0.438937i
$905$	0.405078	+	0.701615i	0.0134652	+	0.0233225i
$906$	42.3476	−	7.46702i	1.40690	−	0.248075i
$907$	−17.2638	+	29.9018i	−0.573236	+	0.992874i	0.422995	+	0.906132i	$0.360979\pi$
$907$	−17.2638	+	29.9018i	−0.573236	+	0.992874i	−0.996231	+	0.0867416i	$0.972355\pi$
$908$	−0.267389	+	0.463131i	−0.00887360	+	0.0153695i
$909$	22.0023	+	18.4621i	0.729769	+	0.612349i
$910$		0			0
$911$	−23.2631	−	40.2929i	−0.770741	−	1.33496i	−0.937157	−	0.348907i	$-0.886553\pi$
$911$	−23.2631	−	40.2929i	−0.770741	−	1.33496i	0.166416	−	0.986056i	$-0.446780\pi$
$912$	13.4021	−	2.36316i	0.443789	−	0.0782520i
$913$	−1.27807			−0.0422978
$914$	6.76777			0.223858
$915$	−1.43717	+	3.94858i	−0.0475113	+	0.130536i
$916$	0.847048	+	1.46713i	0.0279873	+	0.0484753i
$917$		0			0
$918$	−23.5201	−	13.5793i	−0.776278	−	0.448184i
$919$	4.97818	−	8.62246i	0.164215	−	0.284429i	−0.772161	−	0.635427i	$-0.780824\pi$
$919$	4.97818	−	8.62246i	0.164215	−	0.284429i	0.936376	+	0.350998i	$0.114158\pi$
$920$	−0.395277	+	0.684640i	−0.0130319	+	0.0225719i
$921$	−13.7802	−	16.4226i	−0.454072	−	0.541142i
$922$	−12.4363	−	21.5403i	−0.409567	−	0.709391i
$923$	−38.5317	+	66.7388i	−1.26829	+	2.19674i
$924$		0			0
$925$	5.42009	+	9.38788i	0.178212	+	0.308671i
$926$	9.58899	−	16.6086i	0.315114	−	0.545793i
$927$	8.57532	−	3.12116i	0.281651	−	0.102512i
$928$	−4.57444	−	7.92317i	−0.150164	−	0.260091i
$929$	9.04601			0.296790			0.148395	−	0.988928i	$-0.452589\pi$
$929$	9.04601			0.296790			0.148395	+	0.988928i	$0.452589\pi$
$930$	15.5209	−	42.6434i	0.508952	−	1.39833i
$931$		0			0
$932$	1.22621	−	2.12387i	0.0401660	−	0.0695696i
$933$	24.4773	+	29.1709i	0.801351	+	0.955013i
$934$	2.26929	−	3.93052i	0.0742533	−	0.128610i
$935$	−2.29813	−	3.98048i	−0.0751570	−	0.130176i
$936$	39.3905	+	33.0526i	1.28752	+	1.08036i
$937$	−24.3928			−0.796878			−0.398439	−	0.917195i	$-0.630448\pi$
$937$	−24.3928			−0.796878			−0.398439	+	0.917195i	$0.630448\pi$
$938$		0			0
$939$	15.4641	+	18.4294i	0.504652	+	0.601421i
$940$	−1.24763	−	2.16095i	−0.0406931	−	0.0704825i
$941$	−59.5381			−1.94089			−0.970443	−	0.241331i	$-0.922416\pi$
$941$	−59.5381			−1.94089			−0.970443	+	0.241331i	$0.922416\pi$
$942$	−7.38594	−	8.80223i	−0.240647	−	0.286792i
$943$	0.236177			0.00769098
$944$	−2.64858			−0.0862041
$945$		0			0
$946$	0.773318			0.0251428
$947$	8.64858			0.281041			0.140521	−	0.990078i	$-0.455122\pi$
$947$	8.64858			0.281041			0.140521	+	0.990078i	$0.455122\pi$
$948$	−2.60014	−	3.09872i	−0.0844485	−	0.100642i
$949$	−59.7934			−1.94097
$950$	2.07738	+	3.59813i	0.0673992	+	0.116739i
$951$	6.88279	+	8.20259i	0.223190	+	0.265987i
$952$		0			0
$953$	3.78249			0.122527			0.0612634	−	0.998122i	$-0.480487\pi$
$953$	3.78249			0.122527			0.0612634	+	0.998122i	$0.480487\pi$
$954$	−2.72281	+	0.991022i	−0.0881543	+	0.0320855i
$955$	19.7087	+	34.1365i	0.637760	+	1.10463i
$956$	0.881196	−	1.52628i	0.0284999	−	0.0493633i
$957$	−4.57444	−	5.45161i	−0.147871	−	0.176226i
$958$	24.7677	−	42.8989i	0.800208	−	1.38600i
$959$		0			0
$960$	−12.8944	+	35.4271i	−0.416165	+	1.14340i
$961$	27.9831			0.902680
$962$	30.1259	+	52.1796i	0.971298	+	1.68234i
$963$	14.9782	+	12.5682i	0.482665	+	0.405004i
$964$	−0.827696	+	1.43361i	−0.0266583	+	0.0461735i
$965$	−7.64930	−	13.2490i	−0.246240	−	0.426500i
$966$		0			0
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	−0.469613	−	0.882872i	$-0.655607\pi$
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	0.999396	−	0.0347392i	$-0.0110601\pi$
$968$	−15.8674	−	27.4831i	−0.509996	−	0.883340i
$969$	9.43629	+	11.2457i	0.303137	+	0.361265i
$970$	23.2049	−	40.1920i	0.745063	−	1.29049i
$971$	27.7285	−	48.0272i	0.889850	−	1.54126i	0.0497974	−	0.998759i	$-0.484142\pi$
$971$	27.7285	−	48.0272i	0.889850	−	1.54126i	0.840052	−	0.542506i	$-0.182524\pi$
$972$	−0.985234	−	2.70691i	−0.0316014	−	0.0868241i
$973$		0			0
$974$	25.2062	+	43.6584i	0.807659	+	1.39891i
$975$	−4.86887	+	13.3771i	−0.155929	+	0.428410i
$976$	−3.44562			−0.110292
$977$	56.5485			1.80915			0.904573	−	0.426318i	$-0.140189\pi$
$977$	56.5485			1.80915			0.904573	+	0.426318i	$0.140189\pi$
$978$	17.5535	−	3.09516i	0.561299	−	0.0989722i
$979$	1.89827	+	3.28790i	0.0606690	+	0.105082i
$980$		0			0
$981$	29.9898	−	10.9154i	0.957500	−	0.348502i
$982$	17.9666	−	31.1190i	0.573336	−	0.993047i
$983$	−14.4987	+	25.1124i	−0.462435	+	0.800961i	−0.999082	−	0.0428458i	$-0.986358\pi$
$983$	−14.4987	+	25.1124i	−0.462435	+	0.800961i	0.536646	+	0.843807i	$0.319691\pi$
$984$	11.1800	−	1.97134i	0.356407	−	0.0628441i
$985$	−31.9479	−	55.3354i	−1.01794	−	1.76313i
$986$	−22.9479	+	39.7469i	−0.730810	+	1.26580i
$987$		0			0
$988$	−1.17546	−	2.03596i	−0.0373963	−	0.0647724i
$989$	0.0650551	−	0.112679i	0.00206863	−	0.00358298i
$990$	−0.831566	+	4.71605i	−0.0264289	+	0.149886i
$991$	−3.40461	−	5.89696i	−0.108151	−	0.187323i	0.806870	−	0.590729i	$-0.201160\pi$
$991$	−3.40461	−	5.89696i	−0.108151	−	0.187323i	−0.915021	+	0.403406i	$0.867826\pi$
$992$	−8.00175			−0.254056
$993$	−11.9477	−	14.2388i	−0.379150	−	0.451853i
$994$		0			0
$995$	−3.85117	+	6.67042i	−0.122090	+	0.211466i
$996$	−0.299011	+	0.821525i	−0.00947452	+	0.0260310i
$997$	19.4688	−	33.7210i	0.616585	−	1.06796i	−0.373520	−	0.927622i	$-0.621849\pi$
$997$	19.4688	−	33.7210i	0.616585	−	1.06796i	0.990104	−	0.140333i	$-0.0448175\pi$
$998$	−22.7324	−	39.3736i	−0.719580	−	1.24635i
$999$		−	39.9067i		−	1.26259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.d.373.2		6
3.2	odd	2		1323.2.h.c.226.2		6
7.2	even	3		63.2.f.a.22.2	✓	6
7.3	odd	6		441.2.g.b.67.2		6
7.4	even	3		441.2.g.c.67.2		6
7.5	odd	6		441.2.f.c.148.2		6
7.6	odd	2		441.2.h.e.373.2		6
9.2	odd	6		1323.2.g.d.667.2		6
9.7	even	3		441.2.g.c.79.2		6
21.2	odd	6		189.2.f.b.64.2		6
21.5	even	6		1323.2.f.d.442.2		6
21.11	odd	6		1323.2.g.d.361.2		6
21.17	even	6		1323.2.g.e.361.2		6
21.20	even	2		1323.2.h.b.226.2		6
28.23	odd	6		1008.2.r.h.337.1		6
63.2	odd	6		189.2.f.b.127.2		6
63.5	even	6		3969.2.a.l.1.2		3
63.11	odd	6		1323.2.h.c.802.2		6
63.16	even	3		63.2.f.a.43.2	yes	6
63.20	even	6		1323.2.g.e.667.2		6
63.23	odd	6		567.2.a.c.1.2		3
63.25	even	3	inner	441.2.h.d.214.2		6
63.34	odd	6		441.2.g.b.79.2		6
63.38	even	6		1323.2.h.b.802.2		6
63.40	odd	6		3969.2.a.q.1.2		3
63.47	even	6		1323.2.f.d.883.2		6
63.52	odd	6		441.2.h.e.214.2		6
63.58	even	3		567.2.a.h.1.2		3
63.61	odd	6		441.2.f.c.295.2		6
84.23	even	6		3024.2.r.k.1009.3		6
252.23	even	6		9072.2.a.bs.1.1		3
252.79	odd	6		1008.2.r.h.673.1		6
252.191	even	6		3024.2.r.k.2017.3		6
252.247	odd	6		9072.2.a.ca.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	7.2	even	3
63.2.f.a.43.2	yes	6	63.16	even	3
189.2.f.b.64.2		6	21.2	odd	6
189.2.f.b.127.2		6	63.2	odd	6
441.2.f.c.148.2		6	7.5	odd	6
441.2.f.c.295.2		6	63.61	odd	6
441.2.g.b.67.2		6	7.3	odd	6
441.2.g.b.79.2		6	63.34	odd	6
441.2.g.c.67.2		6	7.4	even	3
441.2.g.c.79.2		6	9.7	even	3
441.2.h.d.214.2		6	63.25	even	3	inner
441.2.h.d.373.2		6	1.1	even	1	trivial
441.2.h.e.214.2		6	63.52	odd	6
441.2.h.e.373.2		6	7.6	odd	2
567.2.a.c.1.2		3	63.23	odd	6
567.2.a.h.1.2		3	63.58	even	3
1008.2.r.h.337.1		6	28.23	odd	6
1008.2.r.h.673.1		6	252.79	odd	6
1323.2.f.d.442.2		6	21.5	even	6
1323.2.f.d.883.2		6	63.47	even	6
1323.2.g.d.361.2		6	21.11	odd	6
1323.2.g.d.667.2		6	9.2	odd	6
1323.2.g.e.361.2		6	21.17	even	6
1323.2.g.e.667.2		6	63.20	even	6
1323.2.h.b.226.2		6	21.20	even	2
1323.2.h.b.802.2		6	63.38	even	6
1323.2.h.c.226.2		6	3.2	odd	2
1323.2.h.c.802.2		6	63.11	odd	6
3024.2.r.k.1009.3		6	84.23	even	6
3024.2.r.k.2017.3		6	252.191	even	6
3969.2.a.l.1.2		3	63.5	even	6
3969.2.a.q.1.2		3	63.40	odd	6
9072.2.a.bs.1.1		3	252.23	even	6
9072.2.a.ca.1.3		3	252.247	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.34730 q^{2} +(-1.11334 - 1.32683i) q^{3} -0.184793 q^{4} +(-1.26604 - 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+1.34730 q^{2} +(-1.11334 - 1.32683i) q^{3} -0.184793 q^{4} +(-1.26604 - 2.19285i) q^{5} +(-1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-0.520945 + 2.95442i) q^{9} +(-1.70574 - 2.95442i) q^{10} +(-0.233956 + 0.405223i) q^{11} +(0.205737 + 0.245188i) q^{12} +(-2.91147 + 5.04282i) q^{13} +(-1.50000 + 4.12122i) q^{15} -3.59627 q^{16} +(-1.93969 - 3.35965i) q^{17} +(-0.701867 + 3.98048i) q^{18} +(1.09240 - 1.89209i) q^{19} +(0.233956 + 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(0.0530334 + 0.0918566i) q^{23} +(3.27719 + 3.90560i) q^{24} +(-0.705737 + 1.22237i) q^{25} +(-3.92262 + 6.79417i) q^{26} +(4.50000 - 2.59808i) q^{27} +(-4.39053 - 7.60462i) q^{29} +(-2.02094 + 5.55250i) q^{30} -7.68004 q^{31} +1.04189 q^{32} +(0.798133 - 0.140732i) q^{33} +(-2.61334 - 4.52644i) q^{34} +(0.0962667 - 0.545955i) q^{36} +(3.84002 - 6.65111i) q^{37} +(1.47178 - 2.54920i) q^{38} +(9.93242 - 1.75135i) q^{39} +(3.72668 + 6.45480i) q^{40} +(1.11334 - 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(0.0432332 - 0.0748822i) q^{44} +(7.13816 - 2.59808i) q^{45} +(0.0714517 + 0.123758i) q^{46} -5.33275 q^{47} +(4.00387 + 4.77163i) q^{48} +(-0.950837 + 1.64690i) q^{50} +(-2.29813 + 6.31407i) q^{51} +(0.538019 - 0.931876i) q^{52} +(0.358441 + 0.620838i) q^{53} +(6.06283 - 3.50038i) q^{54} +1.18479 q^{55} +(-3.72668 + 0.657115i) q^{57} +(-5.91534 - 10.2457i) q^{58} +0.736482 q^{59} +(0.277189 - 0.761570i) q^{60} +0.958111 q^{61} -10.3473 q^{62} +8.59627 q^{64} +14.7442 q^{65} +(1.07532 - 0.189608i) q^{66} -9.63816 q^{67} +(0.358441 + 0.620838i) q^{68} +(0.0628336 - 0.172634i) q^{69} +13.2344 q^{71} +(1.53343 - 8.69653i) q^{72} +(5.13429 + 8.89284i) q^{73} +(5.17365 - 8.96102i) q^{74} +(2.40760 - 0.424525i) q^{75} +(-0.201867 + 0.349643i) q^{76} +(13.3819 - 2.35959i) q^{78} -12.6382 q^{79} +(4.55303 + 7.88609i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(1.50000 - 2.59808i) q^{82} +(1.36571 + 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(-0.826352 - 1.43128i) q^{86} +(-5.20187 + 14.2920i) q^{87} +(0.688663 - 1.19280i) q^{88} +(4.05690 - 7.02676i) q^{89} +(9.61721 - 3.50038i) q^{90} +(-0.00980018 - 0.0169744i) q^{92} +(8.55051 + 10.1901i) q^{93} -7.18479 q^{94} -5.53209 q^{95} +(-1.15998 - 1.38241i) q^{96} +(6.80200 + 11.7814i) q^{97} +(-1.07532 - 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{5} - 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^5 - 9 * q^6 + 12 * q^8	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{5} - 9 q^{6} + 12 q^{8} - 6 q^{11} - 9 q^{12} + 3 q^{13} - 9 q^{15} + 6 q^{16} - 6 q^{17} - 18 q^{18} + 3 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} + 9 q^{24} + 6 q^{25} + 3 q^{26} + 27 q^{27} - 9 q^{29} - 9 q^{30} - 6 q^{31} - 9 q^{33} - 9 q^{34} - 27 q^{36} + 3 q^{37} - 6 q^{38} + 36 q^{39} + 9 q^{40} + 3 q^{43} - 15 q^{44} + 9 q^{45} + 6 q^{47} + 6 q^{50} + 21 q^{52} - 6 q^{53} + 27 q^{54} - 9 q^{57} + 9 q^{58} - 6 q^{59} - 9 q^{60} + 12 q^{61} - 60 q^{62} + 24 q^{64} + 30 q^{65} - 18 q^{66} - 24 q^{67} - 6 q^{68} - 9 q^{69} + 18 q^{71} - 9 q^{72} + 21 q^{73} + 30 q^{74} + 18 q^{75} - 15 q^{76} + 54 q^{78} - 42 q^{79} + 15 q^{80} + 9 q^{82} + 18 q^{83} - 9 q^{85} - 6 q^{86} - 45 q^{87} - 27 q^{88} - 12 q^{89} + 27 q^{90} - 3 q^{92} + 54 q^{93} - 36 q^{94} - 24 q^{95} - 27 q^{96} + 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^5 - 9 * q^6 + 12 * q^8 - 6 * q^11 - 9 * q^12 + 3 * q^13 - 9 * q^15 + 6 * q^16 - 6 * q^17 - 18 * q^18 + 3 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 + 9 * q^24 + 6 * q^25 + 3 * q^26 + 27 * q^27 - 9 * q^29 - 9 * q^30 - 6 * q^31 - 9 * q^33 - 9 * q^34 - 27 * q^36 + 3 * q^37 - 6 * q^38 + 36 * q^39 + 9 * q^40 + 3 * q^43 - 15 * q^44 + 9 * q^45 + 6 * q^47 + 6 * q^50 + 21 * q^52 - 6 * q^53 + 27 * q^54 - 9 * q^57 + 9 * q^58 - 6 * q^59 - 9 * q^60 + 12 * q^61 - 60 * q^62 + 24 * q^64 + 30 * q^65 - 18 * q^66 - 24 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 9 * q^72 + 21 * q^73 + 30 * q^74 + 18 * q^75 - 15 * q^76 + 54 * q^78 - 42 * q^79 + 15 * q^80 + 9 * q^82 + 18 * q^83 - 9 * q^85 - 6 * q^86 - 45 * q^87 - 27 * q^88 - 12 * q^89 + 27 * q^90 - 3 * q^92 + 54 * q^93 - 36 * q^94 - 24 * q^95 - 27 * q^96 + 3 * q^97 + 18 * q^99

Introduction

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