LMFDB - Embedded newform 441.2.h.e.214.2

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			214.2
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.e.373.2

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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	−0.430745	−	0.902473i	$-0.641749\pi$
$5$	1.26604	−	2.19285i	0.566192	−	0.980674i	0.996938	−	0.0782003i	$-0.0249174\pi$
$6$	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	0.828598	−	0.559844i	$-0.189139\pi$
$11$	−0.233956	−	0.405223i	−0.0705403	−	0.122179i	−0.899138	+	0.437665i	$0.855806\pi$
$12$	−0.205737	+	0.245188i	−0.0593912	+	0.0707796i
$13$	2.91147	+	5.04282i	0.807498	+	1.39863i	0.914592	+	0.404378i	$0.132512\pi$
$13$	2.91147	+	5.04282i	0.807498	+	1.39863i	−0.107094	+	0.994249i	$0.534155\pi$
$14$		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	$-0.677427\pi$
$17$	1.93969	−	3.35965i	0.470445	−	0.814834i	0.999429	+	0.0337978i	$0.0107602\pi$
$18$	−0.701867	−	3.98048i	−0.165432	−	0.938209i
$19$	−1.09240	−	1.89209i	−0.250613	−	0.434074i	0.713082	−	0.701081i	$-0.247299\pi$
$19$	−1.09240	−	1.89209i	−0.250613	−	0.434074i	−0.963695	+	0.267007i	$0.913965\pi$
$20$	−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	−0.860443	−	0.509546i	$-0.829813\pi$
$23$	0.0530334	−	0.0918566i	0.0110582	−	0.0191534i	0.871502	+	0.490393i	$0.163147\pi$
$24$	−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	0.0938108	+	0.995590i	$0.470095\pi$
$29$	−4.39053	+	7.60462i	−0.815301	+	1.41214i	−0.909112	+	0.416552i	$0.863238\pi$
$30$	−2.02094	−	5.55250i	−0.368972	−	1.01374i
$31$	7.68004			1.37938			0.689688	−	0.724106i	$-0.257748\pi$
$31$	7.68004			1.37938			0.689688	+	0.724106i	$0.257748\pi$
$32$	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	0.987287	+	0.158947i	$0.0508099\pi$
$37$	3.84002	+	6.65111i	0.631296	+	1.09344i	−0.355991	+	0.934489i	$0.615857\pi$
$38$	−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	$-0.222295\pi$
$41$	−1.11334	−	1.92836i	−0.173875	−	0.301160i	−0.939771	+	0.341804i	$0.888962\pi$
$42$		0			0
$43$	−0.613341	+	1.06234i	−0.0935336	+	0.162005i	−0.908996	−	0.416806i	$-0.863150\pi$
$43$	−0.613341	+	1.06234i	−0.0935336	+	0.162005i	0.815462	+	0.578811i	$0.196483\pi$
$44$	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	$-0.372845\pi$
$47$	5.33275			0.777861			0.388931	+	0.921267i	$0.372845\pi$
$48$	−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	−0.840357	−	0.542033i	$-0.817655\pi$
$53$	0.358441	−	0.620838i	0.0492356	−	0.0852786i	0.889593	+	0.456754i	$0.150988\pi$
$54$	−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	$-0.515266\pi$
$59$	−0.736482			−0.0958818			−0.0479409	+	0.998850i	$0.515266\pi$
$60$	0.277189	+	0.761570i	0.0357849	+	0.0983183i
$61$	−0.958111			−0.122674			−0.0613368	−	0.998117i	$-0.519536\pi$
$61$	−0.958111			−0.122674			−0.0613368	+	0.998117i	$0.519536\pi$
$62$	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	0.391759	+	0.920068i	$0.371867\pi$
$73$	−5.13429	+	8.89284i	−0.600923	+	1.04083i	−0.992682	+	0.120761i	$0.961467\pi$
$74$	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	$-0.881231\pi$
$83$	−1.36571	+	2.36549i	−0.149907	+	0.259646i	0.781286	+	0.624173i	$0.214564\pi$
$84$		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	$-0.308164\pi$
$89$	−4.05690	−	7.02676i	−0.430031	−	0.744835i	−0.996875	+	0.0789894i	$0.974831\pi$
$90$	−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	0.280990	+	0.959711i	$0.409337\pi$
$97$	−6.80200	+	11.7814i	−0.690639	+	1.19622i	−0.971629	+	0.236511i	$0.923996\pi$
$98$		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	$-0.324697\pi$
$101$	−4.78699	−	8.29131i	−0.476323	−	0.825016i	−0.999632	+	0.0271271i	$0.991364\pi$
$102$	−3.09627	−	8.50692i	−0.306576	−	0.842311i
$103$	1.52094	−	2.63435i	0.149863	−	0.259571i	−0.781314	−	0.624139i	$-0.785450\pi$
$103$	1.52094	−	2.63435i	0.149863	−	0.259571i	0.931177	+	0.364568i	$0.118783\pi$
$104$	−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	0.979445	−	0.201709i	$-0.0646497\pi$
$107$	3.25877	+	5.64436i	0.315037	+	0.545660i	−0.664408	+	0.747370i	$0.731316\pi$
$108$	0.831566	+	0.480105i	0.0800175	+	0.0461981i
$109$	−5.31908	+	9.21291i	−0.509475	+	0.882437i	0.490465	+	0.871461i	$0.336827\pi$
$109$	−5.31908	+	9.21291i	−0.509475	+	0.882437i	−0.999940	+	0.0109759i	$0.996506\pi$
$110$	−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	0.718203	−	0.695834i	$-0.244965\pi$
$113$	−2.58853	−	4.48346i	−0.243508	−	0.421768i	−0.961711	+	0.274065i	$0.911632\pi$
$114$	−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	$-0.667994\pi$
$131$	5.68139	−	9.84045i	0.496385	−	0.859764i	0.999991	+	0.00416893i	$0.00132701\pi$
$132$	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	0.962003	−	0.273038i	$-0.0880285\pi$
$137$	2.86231	+	4.95767i	0.244544	+	0.423562i	−0.717459	+	0.696600i	$0.754695\pi$
$138$	−0.0846555	−	0.232589i	−0.00720635	−	0.0197993i
$139$	−0.461981	−	0.800175i	−0.0391847	−	0.0678700i	0.845768	−	0.533551i	$-0.179143\pi$
$139$	−0.461981	−	0.800175i	−0.0391847	−	0.0678700i	−0.884953	+	0.465681i	$0.845809\pi$
$140$		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	−0.987521	−	0.157485i	$-0.949661\pi$
$149$	−4.36231	+	7.55574i	−0.357374	+	0.618991i	0.630147	+	0.776476i	$0.282995\pi$
$150$	−3.24376	−	0.571962i	−0.264852	−	0.0467005i
$151$	−9.21348	−	15.9582i	−0.749782	−	1.29866i	−0.947927	−	0.318488i	$-0.896825\pi$
$151$	−9.21348	−	15.9582i	−0.749782	−	1.29866i	0.198145	−	0.980173i	$-0.436508\pi$
$152$	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	$-0.562954\pi$
$157$	−4.92396			−0.392975			−0.196488	+	0.980506i	$0.562954\pi$
$158$	−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	0.676805	−	0.736163i	$-0.263364\pi$
$163$	−3.81908	−	6.61484i	−0.299133	−	0.518114i	−0.975938	+	0.218049i	$0.930031\pi$
$164$	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	$-0.236885\pi$
$167$	−2.82770	−	4.89771i	−0.218814	−	0.378996i	−0.954446	+	0.298385i	$0.903552\pi$
$168$		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	$-0.795662\pi$
$173$	−21.0692			−1.60186			−0.800932	+	0.598755i	$0.795662\pi$
$174$	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	−0.754337	−	0.656487i	$-0.772041\pi$
$179$	2.56031	−	4.43458i	0.191366	−	0.331456i	0.945703	+	0.325031i	$0.105375\pi$
$180$	1.31908	+	0.480105i	0.0983183	+	0.0357849i
$181$	0.319955			0.0237821			0.0118910	−	0.999929i	$-0.496215\pi$
$181$	0.319955			0.0237821			0.0118910	+	0.999929i	$0.496215\pi$
$182$		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	$-0.798947\pi$
$199$	1.52094	−	2.63435i	0.107817	−	0.186744i	0.914886	+	0.403713i	$0.132281\pi$
$200$	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	0.944487	−	0.328548i	$-0.106559\pi$
$211$	2.72668	+	4.72275i	0.187713	+	0.325128i	−0.756775	+	0.653676i	$0.773226\pi$
$212$	−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	$-0.675709\pi$
$223$	7.09627	−	12.2911i	0.475201	−	0.823073i	0.999597	+	0.0284023i	$0.00904195\pi$
$224$		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	$-0.197284\pi$
$227$	−1.44697	−	2.50622i	−0.0960385	−	0.166344i	−0.910042	+	0.414517i	$0.863951\pi$
$228$	0.688663	+	0.121430i	0.0456078	+	0.00804189i
$229$	4.58378	−	7.93934i	0.302905	−	0.524646i	−0.673888	−	0.738834i	$-0.735377\pi$
$229$	4.58378	−	7.93934i	0.302905	−	0.524646i	0.976793	+	0.214187i	$0.0687103\pi$
$230$	−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	0.562558	−	0.826758i	$-0.309817\pi$
$233$	−6.63563	−	11.4932i	−0.434715	−	0.752948i	−0.997272	+	0.0738103i	$0.976484\pi$
$234$	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	0.669571	−	0.742748i	$-0.266478\pi$
$239$	−4.76857	−	8.25941i	−0.308453	−	0.534257i	−0.978024	+	0.208491i	$0.933145\pi$
$240$	5.39440	+	14.8210i	0.348207	+	0.956691i
$241$	−4.47906	−	7.75795i	−0.288521	−	0.499734i	0.684936	−	0.728604i	$-0.259830\pi$
$241$	−4.47906	−	7.75795i	−0.288521	−	0.499734i	−0.973457	+	0.228870i	$0.926497\pi$
$242$	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	$-0.210631\pi$
$251$	24.9982			1.57788			0.788938	+	0.614473i	$0.210631\pi$
$252$		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	$-0.723425\pi$
$257$	5.42602	−	9.39815i	0.338466	−	0.586240i	0.984144	+	0.177369i	$0.0567587\pi$
$258$	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	−0.916757	−	0.399446i	$-0.869202\pi$
$263$	−13.0437	−	22.5924i	−0.804309	−	1.39310i	0.112448	−	0.993658i	$-0.464131\pi$
$264$	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	$-0.908089\pi$
$269$	−3.81655	+	6.61046i	−0.232699	+	0.403047i	0.725902	+	0.687798i	$0.241422\pi$
$270$	−15.3516	+	8.86327i	−0.934271	+	0.539401i
$271$	1.70187	+	2.94772i	0.103381	+	0.179061i	0.913076	−	0.407790i	$-0.133701\pi$
$271$	1.70187	+	2.94772i	0.103381	+	0.179061i	−0.809695	+	0.586852i	$0.800367\pi$
$272$	−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	0.939084	−	0.343689i	$-0.111676\pi$
$277$	2.86097	+	4.95534i	0.171899	+	0.297738i	−0.767185	+	0.641426i	$0.778343\pi$
$278$	−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	0.0379535	+	0.999280i	$0.487916\pi$
$281$	−14.1887	+	24.5755i	−0.846425	+	1.46605i	−0.884378	+	0.466771i	$0.845417\pi$
$282$	7.99912	−	9.53298i	0.476341	−	0.567681i
$283$	−4.57129			−0.271735			−0.135867	−	0.990727i	$-0.543382\pi$
$283$	−4.57129			−0.271735			−0.135867	+	0.990727i	$0.543382\pi$
$284$	−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	$-0.126320\pi$
$293$	2.16385	+	3.74789i	0.126413	+	0.218954i	−0.795871	+	0.605466i	$0.792987\pi$
$294$		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	$-0.614908\pi$
$307$	−12.3773			−0.706411			−0.353206	+	0.935546i	$0.614908\pi$
$308$		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	$-0.285775\pi$
$311$	21.9855			1.24668			0.623340	+	0.781951i	$0.285775\pi$
$312$	−29.2367	−	5.15522i	−1.65520	−	0.291857i
$313$	13.8898			0.785099			0.392549	−	0.919731i	$-0.371593\pi$
$313$	13.8898			0.785099			0.392549	+	0.919731i	$0.371593\pi$
$314$	−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	0.999972	+	0.00746831i	$0.00237726\pi$
$337$	9.29726	+	16.1033i	0.506454	+	0.877204i	−0.493518	+	0.869735i	$0.664289\pi$
$338$	−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	$-0.863726\pi$
$349$	−1.78106	+	3.08489i	−0.0953379	+	0.165130i	0.814412	+	0.580288i	$0.197060\pi$
$350$		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	$-0.0807280\pi$
$353$	5.01114	+	8.67956i	0.266716	+	0.461966i	−0.701296	+	0.712871i	$0.747395\pi$
$354$	−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	0.713391	−	0.700766i	$-0.247159\pi$
$359$	−4.74035	−	8.21053i	−0.250186	−	0.433335i	−0.963577	+	0.267431i	$0.913825\pi$
$360$	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	$-0.0283183\pi$
$367$	8.06670	+	13.9719i	0.421079	+	0.729329i	−0.574967	+	0.818177i	$0.694985\pi$
$368$	−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	−0.988572	−	0.150752i	$-0.951831\pi$
$373$	−7.02481	+	12.1673i	−0.363731	+	0.630001i	0.624841	+	0.780752i	$0.285164\pi$
$374$	−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	0.0890039	+	0.996031i	$0.471632\pi$
$383$	−16.0103	+	27.7306i	−0.818086	+	1.41697i	−0.907090	+	0.420936i	$0.861702\pi$
$384$	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	0.942017	+	0.335564i	$0.108927\pi$
$389$	15.0214	+	26.0178i	0.761616	+	1.31916i	−0.180402	+	0.983593i	$0.557740\pi$
$390$	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	$-0.266715\pi$
$397$	−6.15998	−	10.6694i	−0.309160	−	0.535482i	−0.978179	+	0.207764i	$0.933381\pi$
$398$	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	0.475873	+	0.879514i	$0.342132\pi$
$401$	−10.4880	+	18.1657i	−0.523745	+	0.907152i	−0.999618	+	0.0276385i	$0.991201\pi$
$402$	−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	$-0.718768\pi$
$409$	−25.6614			−1.26887			−0.634437	+	0.772975i	$0.718768\pi$
$410$	−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	$-0.178175\pi$
$419$	−0.739885	−	1.28152i	−0.0361458	−	0.0626063i	−0.883532	+	0.468370i	$0.844841\pi$
$420$		0			0
$421$	−6.55350	+	11.3510i	−0.319398	+	0.553214i	−0.980363	−	0.197203i	$-0.936814\pi$
$421$	−6.55350	+	11.3510i	−0.319398	+	0.553214i	0.660965	+	0.750417i	$0.270147\pi$
$422$	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	−0.996599	−	0.0823997i	$-0.973742\pi$
$431$	−8.86349	+	15.3520i	−0.426939	+	0.739481i	0.569660	+	0.821881i	$0.307075\pi$
$432$	16.1832	+	9.34337i	0.778615	+	0.449533i
$433$	5.83843			0.280577			0.140289	−	0.990111i	$-0.455197\pi$
$433$	5.83843			0.280577			0.140289	+	0.990111i	$0.455197\pi$
$434$		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	$-0.752418\pi$
$439$	−29.8553			−1.42492			−0.712459	+	0.701714i	$0.752418\pi$
$440$	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	$-0.691879\pi$
$461$	9.23055	−	15.9878i	0.429910	−	0.744625i	0.996865	+	0.0791233i	$0.0252121\pi$
$462$		0			0
$463$	7.11721	+	12.3274i	0.330765	+	0.572902i	0.982662	−	0.185406i	$-0.0593600\pi$
$463$	7.11721	+	12.3274i	0.330765	+	0.572902i	−0.651897	+	0.758307i	$0.726027\pi$
$464$	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	$-0.191501\pi$
$467$	−1.68433	−	2.91734i	−0.0779413	−	0.134998i	−0.902362	+	0.430980i	$0.858168\pi$
$468$	−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	−0.889934	−	0.456090i	$-0.849249\pi$
$479$	−18.3833	−	31.8407i	−0.839952	−	1.45484i	0.0499812	−	0.998750i	$-0.484084\pi$
$480$	−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	−0.0354172	−	0.999373i	$-0.511276\pi$
$487$	18.7087	−	32.4045i	0.847773	−	1.46839i	0.883191	−	0.469014i	$-0.155391\pi$
$488$	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	0.992547	+	0.121866i	$0.0388879\pi$
$491$	13.3353	+	23.0974i	0.601813	+	1.04237i	−0.390734	+	0.920504i	$0.627779\pi$
$492$	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	0.189895	+	0.981804i	$0.439185\pi$
$499$	−16.8726	+	29.2242i	−0.755320	+	1.30825i	−0.945215	+	0.326449i	$0.894148\pi$
$500$	−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	$-0.246745\pi$
$503$	32.0401			1.42860			0.714299	+	0.699840i	$0.246745\pi$
$504$		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	$-0.889628\pi$
$509$	−3.96926	+	6.87495i	−0.175934	+	0.304727i	0.764550	+	0.644564i	$0.222961\pi$
$510$	−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	$-0.937507\pi$
$521$	−7.33750	+	12.7089i	−0.321462	+	0.556788i	0.659328	+	0.751855i	$0.270841\pi$
$522$	33.3516	+	12.1390i	1.45976	+	0.531310i
$523$	14.1716	+	24.5459i	0.619680	+	1.07332i	0.989544	+	0.144232i	$0.0460711\pi$
$523$	14.1716	+	24.5459i	0.619680	+	1.07332i	−0.369864	+	0.929086i	$0.620596\pi$
$524$	−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	0.718849	−	0.695166i	$-0.244669\pi$
$541$	−5.64290	−	9.77380i	−0.242607	−	0.420208i	−0.961456	+	0.274958i	$0.911336\pi$
$542$	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	−0.363404	−	0.931632i	$-0.618385\pi$
$547$	14.6202	−	25.3229i	0.625115	−	1.08273i	0.988519	−	0.151099i	$-0.0482812\pi$
$548$	−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	−0.857692	−	0.514164i	$-0.828102\pi$
$557$	0.387841	−	0.671761i	0.0164334	−	0.0284634i	0.874125	+	0.485701i	$0.161436\pi$
$558$	−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	$-0.676236\pi$
$563$	−24.9522			−1.05161			−0.525806	+	0.850605i	$0.676236\pi$
$564$	−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	$-0.919690\pi$
$577$	−6.43717	+	11.1495i	−0.267983	+	0.464160i	0.700358	+	0.713792i	$0.253024\pi$
$578$	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	0.135658	−	0.990756i	$-0.456685\pi$
$587$	22.4315	−	38.8526i	0.925849	−	1.60362i	0.790190	−	0.612861i	$-0.209982\pi$
$588$		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	$-0.142064\pi$
$593$	1.88026	+	3.25671i	0.0772131	+	0.133737i	−0.824833	+	0.565376i	$0.808731\pi$
$594$			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	$-0.980409\pi$
$601$	−10.9285	+	18.9288i	−0.445785	+	0.772122i	0.552322	+	0.833631i	$0.313742\pi$
$602$		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	$-0.668475\pi$
$607$	12.1973	−	21.1263i	0.495072	−	0.857490i	0.999984	+	0.00568063i	$0.00180821\pi$
$608$	−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	0.0338284	+	0.999428i	$0.489230\pi$
$613$	−21.0107	+	36.3917i	−0.848616	+	1.46985i	−0.882444	+	0.470418i	$0.844103\pi$
$614$	−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	−0.776068	−	0.630650i	$-0.782788\pi$
$617$	−23.2049	−	40.1920i	−0.934192	−	1.61807i	−0.158125	−	0.987419i	$-0.550545\pi$
$618$	−2.42783	−	6.67042i	−0.0976618	−	0.268324i
$619$	−13.6047	−	23.5641i	−0.546820	−	0.947120i	−0.998490	−	0.0549349i	$-0.982505\pi$
$619$	−13.6047	−	23.5641i	−0.546820	−	0.947120i	0.451670	−	0.892185i	$-0.350828\pi$
$620$	−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	0.868767	−	0.495221i	$-0.164913\pi$
$641$	0.139500	+	0.241621i	0.00550991	+	0.00954345i	−0.863257	+	0.504764i	$0.831579\pi$
$642$	14.9782	+	2.64106i	0.591142	+	0.104234i
$643$	−9.12196	−	15.7997i	−0.359735	−	0.623079i	0.628181	−	0.778067i	$-0.283800\pi$
$643$	−9.12196	−	15.7997i	−0.359735	−	0.623079i	−0.987916	+	0.154988i	$0.950466\pi$
$644$		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	$-0.687802\pi$
$647$	11.2285	−	19.4483i	0.441438	−	0.764592i	0.997796	+	0.0663498i	$0.0211353\pi$
$648$	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	0.364655	−	0.931143i	$-0.381187\pi$
$653$	25.2656	−	43.7614i	0.988721	−	1.71251i	0.624066	−	0.781372i	$-0.285480\pi$
$654$	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	−0.838824	−	0.544403i	$-0.816756\pi$
$659$	1.33631	−	2.31456i	0.0520554	−	0.0901626i	0.890879	+	0.454241i	$0.150089\pi$
$660$	0.243756	−	0.290497i	0.00948818	−	0.0113076i
$661$	34.6100			1.34617			0.673086	−	0.739564i	$-0.264968\pi$
$661$	34.6100			1.34617			0.673086	+	0.739564i	$0.264968\pi$
$662$	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	−0.980124	−	0.198386i	$-0.936430\pi$
$673$	−8.25624	+	14.3002i	−0.318255	+	0.551234i	0.661869	+	0.749619i	$0.269763\pi$
$674$	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	$-0.182040\pi$
$677$	43.7579			1.68175			0.840877	+	0.541226i	$0.182040\pi$
$678$	−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	0.458576	+	0.888655i	$0.348360\pi$
$683$	−14.1206	+	24.4576i	−0.540310	+	0.935845i	−0.998886	+	0.0471895i	$0.984974\pi$
$684$	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	$-0.313542\pi$
$691$	29.0651			1.10569			0.552844	+	0.833284i	$0.313542\pi$
$692$	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	−0.987585	−	0.157087i	$-0.949790\pi$
$719$	−16.8885	−	29.2517i	−0.629834	−	1.09090i	0.357751	−	0.933817i	$-0.383544\pi$
$720$	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	$-0.732462\pi$
$727$	8.40214	−	14.5529i	0.311618	−	0.539738i	0.978713	+	0.205234i	$0.0657957\pi$
$728$		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	$-0.914368\pi$
$733$	−6.81820	+	11.8095i	−0.251836	+	0.436193i	0.712195	+	0.701981i	$0.247701\pi$
$734$	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	−0.404979	−	0.914326i	$-0.632721\pi$
$739$	16.0209	−	27.7491i	0.589340	−	1.02077i	0.994319	−	0.106441i	$-0.0339455\pi$
$740$	−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	−0.989644	−	0.143547i	$-0.954149\pi$
$743$	−16.8764	−	29.2309i	−0.619137	−	1.07238i	0.370507	−	0.928830i	$-0.379184\pi$
$744$	−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	−0.999637	−	0.0269236i	$-0.991429\pi$
$751$	−13.0582	+	22.6175i	−0.476502	+	0.825326i	0.523135	+	0.852250i	$0.324762\pi$
$752$	−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	−0.214148	−	0.976801i	$-0.568698\pi$
$761$	20.3824	−	35.3033i	0.738861	−	1.27974i	0.953009	−	0.302943i	$-0.0979692\pi$
$762$	−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	0.964525	+	0.263992i	$0.0850392\pi$
$769$	19.7135	+	34.1447i	0.710886	+	1.23129i	−0.253639	+	0.967299i	$0.581627\pi$
$770$		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	$-0.685526\pi$
$773$	12.4513	−	21.5663i	0.447842	−	0.775686i	0.998245	+	0.0592135i	$0.0188593\pi$
$774$	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	$-0.315672\pi$
$787$	30.7050			1.09452			0.547258	+	0.836964i	$0.315672\pi$
$788$	−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	$-0.229158\pi$
$797$	−5.50686	−	9.53817i	−0.195063	−	0.337859i	−0.946921	+	0.321466i	$0.895825\pi$
$798$		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	−0.975824	−	0.218558i	$-0.929865\pi$
$809$	−8.49407	+	14.7122i	−0.298636	+	0.517252i	0.677188	+	0.735810i	$0.263198\pi$
$810$	−5.33157	+	30.2368i	−0.187332	+	1.06241i
$811$	−37.9796			−1.33364			−0.666822	−	0.745217i	$-0.732346\pi$
$811$	−37.9796			−1.33364			−0.666822	+	0.745217i	$0.732346\pi$
$812$		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	$-0.835281\pi$
$829$	−0.176174	+	0.305143i	−0.00611879	+	0.0105981i	0.862950	+	0.505290i	$0.168614\pi$
$830$	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	$-0.691207\pi$
$839$	12.5077	−	21.6640i	0.431815	−	0.747926i	0.997030	+	0.0770182i	$0.0245399\pi$
$840$		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	−0.306706	−	0.951804i	$-0.599227\pi$
$853$	19.5954	−	33.9402i	0.670933	−	1.16209i	0.977640	−	0.210286i	$-0.0674397\pi$
$854$		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	$-0.0762552\pi$
$857$	8.20368	+	14.2092i	0.280232	+	0.485377i	−0.691210	+	0.722654i	$0.742922\pi$
$858$	−2.17461	−	5.97470i	−0.0742400	−	0.203973i
$859$	−13.4162	+	23.2376i	−0.457756	+	0.792856i	−0.998842	−	0.0481111i	$-0.984680\pi$
$859$	−13.4162	+	23.2376i	−0.457756	+	0.792856i	0.541086	+	0.840967i	$0.318013\pi$
$860$	−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	0.715772	−	0.698334i	$-0.246075\pi$
$863$	−7.25284	−	12.5623i	−0.246890	−	0.427625i	−0.962661	+	0.270709i	$0.912742\pi$
$864$	−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	−0.980352	−	0.197255i	$-0.936797\pi$
$877$	−9.45723	+	16.3804i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270131\pi$
$878$	−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	$-0.862336\pi$
$881$	−53.8976			−1.81585			−0.907927	+	0.419128i	$0.862336\pi$
$882$		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	0.328051	+	0.944660i	$0.393608\pi$
$887$	−19.4800	+	33.7403i	−0.654074	+	1.13289i	−0.982125	+	0.188229i	$0.939725\pi$
$888$	−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	−0.996231	−	0.0867416i	$-0.972355\pi$
$907$	−17.2638	−	29.9018i	−0.573236	−	0.992874i	0.422995	−	0.906132i	$-0.360979\pi$
$908$	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	0.166416	+	0.986056i	$0.446780\pi$
$911$	−23.2631	+	40.2929i	−0.770741	+	1.33496i	−0.937157	+	0.348907i	$0.886553\pi$
$912$	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	0.936376	−	0.350998i	$-0.114158\pi$
$919$	4.97818	+	8.62246i	0.164215	+	0.284429i	−0.772161	+	0.635427i	$0.780824\pi$
$920$	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	$-0.547411\pi$
$929$	−9.04601			−0.296790			−0.148395	+	0.988928i	$0.547411\pi$
$930$	−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	$-0.369552\pi$
$937$	24.3928			0.796878			0.398439	+	0.917195i	$0.369552\pi$
$938$		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	$-0.0775839\pi$
$941$	59.5381			1.94089			0.970443	+	0.241331i	$0.0775839\pi$
$942$	−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	0.999396	+	0.0347392i	$0.0110601\pi$
$967$	16.4745	+	28.5346i	0.529783	+	0.917611i	−0.469613	+	0.882872i	$0.655607\pi$
$968$	−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	−0.840052	−	0.542506i	$-0.817476\pi$
$971$	−27.7285	−	48.0272i	−0.889850	−	1.54126i	−0.0497974	−	0.998759i	$-0.515858\pi$
$972$	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	$-0.0136424\pi$
$983$	14.4987	+	25.1124i	0.462435	+	0.800961i	−0.536646	+	0.843807i	$0.680309\pi$
$984$	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	−0.915021	−	0.403406i	$-0.867826\pi$
$991$	−3.40461	+	5.89696i	−0.108151	+	0.187323i	0.806870	+	0.590729i	$0.201160\pi$
$992$	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	−0.990104	−	0.140333i	$-0.955183\pi$
$997$	−19.4688	−	33.7210i	−0.616585	−	1.06796i	0.373520	−	0.927622i	$-0.378151\pi$
$998$	−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.e.214.2		6
3.2	odd	2		1323.2.h.b.802.2		6
7.2	even	3		441.2.g.b.79.2		6
7.3	odd	6		63.2.f.a.43.2	yes	6
7.4	even	3		441.2.f.c.295.2		6
7.5	odd	6		441.2.g.c.79.2		6
7.6	odd	2		441.2.h.d.214.2		6
9.4	even	3		441.2.g.b.67.2		6
9.5	odd	6		1323.2.g.e.361.2		6
21.2	odd	6		1323.2.g.e.667.2		6
21.5	even	6		1323.2.g.d.667.2		6
21.11	odd	6		1323.2.f.d.883.2		6
21.17	even	6		189.2.f.b.127.2		6
21.20	even	2		1323.2.h.c.802.2		6
28.3	even	6		1008.2.r.h.673.1		6
63.4	even	3		441.2.f.c.148.2		6
63.5	even	6		1323.2.h.c.226.2		6
63.11	odd	6		3969.2.a.l.1.2		3
63.13	odd	6		441.2.g.c.67.2		6
63.23	odd	6		1323.2.h.b.226.2		6
63.25	even	3		3969.2.a.q.1.2		3
63.31	odd	6		63.2.f.a.22.2	✓	6
63.32	odd	6		1323.2.f.d.442.2		6
63.38	even	6		567.2.a.c.1.2		3
63.40	odd	6		441.2.h.d.373.2		6
63.41	even	6		1323.2.g.d.361.2		6
63.52	odd	6		567.2.a.h.1.2		3
63.58	even	3	inner	441.2.h.e.373.2		6
63.59	even	6		189.2.f.b.64.2		6
84.59	odd	6		3024.2.r.k.2017.3		6
252.31	even	6		1008.2.r.h.337.1		6
252.59	odd	6		3024.2.r.k.1009.3		6
252.115	even	6		9072.2.a.ca.1.3		3
252.227	odd	6		9072.2.a.bs.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	63.31	odd	6
63.2.f.a.43.2	yes	6	7.3	odd	6
189.2.f.b.64.2		6	63.59	even	6
189.2.f.b.127.2		6	21.17	even	6
441.2.f.c.148.2		6	63.4	even	3
441.2.f.c.295.2		6	7.4	even	3
441.2.g.b.67.2		6	9.4	even	3
441.2.g.b.79.2		6	7.2	even	3
441.2.g.c.67.2		6	63.13	odd	6
441.2.g.c.79.2		6	7.5	odd	6
441.2.h.d.214.2		6	7.6	odd	2
441.2.h.d.373.2		6	63.40	odd	6
441.2.h.e.214.2		6	1.1	even	1	trivial
441.2.h.e.373.2		6	63.58	even	3	inner
567.2.a.c.1.2		3	63.38	even	6
567.2.a.h.1.2		3	63.52	odd	6
1008.2.r.h.337.1		6	252.31	even	6
1008.2.r.h.673.1		6	28.3	even	6
1323.2.f.d.442.2		6	63.32	odd	6
1323.2.f.d.883.2		6	21.11	odd	6
1323.2.g.d.361.2		6	63.41	even	6
1323.2.g.d.667.2		6	21.5	even	6
1323.2.g.e.361.2		6	9.5	odd	6
1323.2.g.e.667.2		6	21.2	odd	6
1323.2.h.b.226.2		6	63.23	odd	6
1323.2.h.b.802.2		6	3.2	odd	2
1323.2.h.c.226.2		6	63.5	even	6
1323.2.h.c.802.2		6	21.20	even	2
3024.2.r.k.1009.3		6	252.59	odd	6
3024.2.r.k.2017.3		6	84.59	odd	6
3969.2.a.l.1.2		3	63.11	odd	6
3969.2.a.q.1.2		3	63.25	even	3
9072.2.a.bs.1.1		3	252.227	odd	6
9072.2.a.ca.1.3		3	252.115	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.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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