LMFDB - Embedded newform 441.2.h.g.214.3

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			214.3
Root			$-1.29589 + 0.748185i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.g.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.239123 q^{2} +(-1.70316 + 0.315036i) q^{3} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 + 0.0753324i) q^{6} -0.942820 q^{8} +(2.80150 - 1.07311i) q^{9} +O(q^{10})$	\(q+0.239123 q^{2} +(-1.70316 + 0.315036i) q^{3} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 + 0.0753324i) q^{6} -0.942820 q^{8} +(2.80150 - 1.07311i) q^{9} +(-0.309879 + 0.536725i) q^{10} +(-2.09097 - 3.62167i) q^{11} +(3.30893 - 0.612058i) q^{12} +(1.84155 + 3.18966i) q^{13} +(1.50000 - 4.23109i) q^{15} +3.66019 q^{16} +(0.855536 - 1.48183i) q^{17} +(0.669905 - 0.256606i) q^{18} +(-3.57780 - 6.19694i) q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(2.56238 - 4.43818i) q^{23} +(1.60577 - 0.297022i) q^{24} +(-0.858685 - 1.48729i) q^{25} +(0.440358 + 0.762722i) q^{26} +(-4.43334 + 2.71026i) q^{27} +(1.06238 - 1.84010i) q^{29} +(0.358685 - 1.01175i) q^{30} +6.53585 q^{31} +2.76088 q^{32} +(4.70221 + 5.50955i) q^{33} +(0.204579 - 0.354341i) q^{34} +(-5.44282 + 2.08486i) q^{36} +(-0.830095 - 1.43777i) q^{37} +(-0.855536 - 1.48183i) q^{38} +(-4.14132 - 4.85235i) q^{39} +(1.22180 - 2.11621i) q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(4.06238 + 7.03625i) q^{44} +(-1.22180 + 7.67877i) q^{45} +(0.612725 - 1.06127i) q^{46} -9.33824 q^{47} +(-6.23389 + 1.15309i) q^{48} +(-0.205332 - 0.355645i) q^{50} +(-0.990285 + 2.79332i) q^{51} +(-3.57780 - 6.19694i) q^{52} +(-5.32326 + 9.22015i) q^{53} +(-1.06012 + 0.648085i) q^{54} +10.8387 q^{55} +(8.04583 + 9.42724i) q^{57} +(0.254040 - 0.440011i) q^{58} -6.06429 q^{59} +(-2.91423 + 8.22024i) q^{60} +7.98597 q^{61} +1.56287 q^{62} -6.66019 q^{64} -9.54583 q^{65} +(1.12441 + 1.31746i) q^{66} +8.26320 q^{67} +(-1.66215 + 2.87893i) q^{68} +(-2.96596 + 8.36616i) q^{69} +6.23912 q^{71} +(-2.64132 + 1.01175i) q^{72} +(3.57780 - 6.19694i) q^{73} +(-0.198495 - 0.343803i) q^{74} +(1.93103 + 2.26257i) q^{75} +(6.95103 + 12.0395i) q^{76} +(-0.990285 - 1.16031i) q^{78} -9.82846 q^{79} +(-4.74322 + 8.21550i) q^{80} +(6.69686 - 6.01266i) q^{81} +(-1.22180 - 2.11621i) q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(0.198495 - 0.343803i) q^{86} +(-1.22971 + 3.46867i) q^{87} +(1.97141 + 3.41458i) q^{88} +(-2.51769 - 4.36077i) q^{89} +(-0.292160 + 1.83617i) q^{90} +(-4.97825 + 8.62258i) q^{92} +(-11.1316 + 2.05903i) q^{93} -2.23299 q^{94} +18.5458 q^{95} +(-4.70221 + 0.869775i) q^{96} +(1.53167 - 2.65294i) q^{97} +(-9.74433 - 7.90228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8	$ 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 8 q^{11} + 18 q^{15} + 12 q^{16} + 24 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} + 6 q^{30} + 32 q^{32} - 30 q^{36} + 6 q^{37} - 48 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} + 36 q^{51} - 28 q^{53} - 6 q^{57} - 18 q^{58} + 18 q^{60} - 48 q^{64} - 12 q^{65} + 76 q^{71} - 30 q^{72} - 36 q^{74} + 36 q^{78} - 12 q^{79} + 24 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} - 84 q^{93} + 120 q^{95} - 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 8 * q^11 + 18 * q^15 + 12 * q^16 + 24 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 + 6 * q^30 + 32 * q^32 - 30 * q^36 + 6 * q^37 - 48 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 + 36 * q^51 - 28 * q^53 - 6 * q^57 - 18 * q^58 + 18 * q^60 - 48 * q^64 - 12 * q^65 + 76 * q^71 - 30 * q^72 - 36 * q^74 + 36 * q^78 - 12 * q^79 + 24 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 - 84 * q^93 + 120 * q^95 - 48 * 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 $

$2$	0.239123			0.169086			0.0845428	−	0.996420i	$-0.473057\pi$
$2$	0.239123			0.169086			0.0845428	+	0.996420i	$0.473057\pi$
$3$	−1.70316	+	0.315036i	−0.983320	+	0.181886i
$3$	−1.70316	+	0.315036i	−0.983320	+	0.181886i
$4$	−1.94282			−0.971410
$5$	−1.29589	+	2.24456i	−0.579542	+	1.00380i	0.415990	+	0.909369i	$0.363435\pi$
$5$	−1.29589	+	2.24456i	−0.579542	+	1.00380i	−0.995532	+	0.0944264i	$0.969898\pi$
$6$	−0.407265	+	0.0753324i	−0.166265	+	0.0307543i
$7$		0			0
$7$		0			0
$8$	−0.942820			−0.333337
$9$	2.80150	−	1.07311i	0.933835	−	0.357704i
$10$	−0.309879	+	0.536725i	−0.0979922	+	0.169727i
$11$	−2.09097	−	3.62167i	−0.630452	−	1.09197i	−0.987459	−	0.157873i	$-0.949536\pi$
$11$	−2.09097	−	3.62167i	−0.630452	−	1.09197i	0.357008	−	0.934101i	$-0.383797\pi$
$12$	3.30893	−	0.612058i	0.955207	−	0.176686i
$13$	1.84155	+	3.18966i	0.510755	+	0.884653i	0.999922	+	0.0124633i	$0.00396730\pi$
$13$	1.84155	+	3.18966i	0.510755	+	0.884653i	−0.489168	+	0.872190i	$0.662699\pi$
$14$		0			0
$15$	1.50000	−	4.23109i	0.387298	−	1.09246i
$16$	3.66019			0.915047
$17$	0.855536	−	1.48183i	0.207498	−	0.359397i	−0.743428	−	0.668816i	$-0.766801\pi$
$17$	0.855536	−	1.48183i	0.207498	−	0.359397i	0.950926	+	0.309419i	$0.100135\pi$
$18$	0.669905	−	0.256606i	0.157898	−	0.0604826i
$19$	−3.57780	−	6.19694i	−0.820805	−	1.42168i	−0.905084	−	0.425233i	$-0.860192\pi$
$19$	−3.57780	−	6.19694i	−0.820805	−	1.42168i	0.0842790	−	0.996442i	$-0.473141\pi$
$20$	2.51769	−	4.36077i	0.562973	−	0.975097i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	2.56238	−	4.43818i	0.534294	−	0.925424i	−0.464904	−	0.885361i	$-0.653911\pi$
$23$	2.56238	−	4.43818i	0.534294	−	0.925424i	0.999197	−	0.0400622i	$-0.0127556\pi$
$24$	1.60577	−	0.297022i	0.327777	−	0.0606294i
$25$	−0.858685	−	1.48729i	−0.171737	−	0.297457i
$26$	0.440358	+	0.762722i	0.0863613	+	0.149582i
$27$	−4.43334	+	2.71026i	−0.853197	+	0.521589i
$28$		0			0
$29$	1.06238	−	1.84010i	0.197279	−	0.341698i	−0.750366	−	0.661023i	$-0.770123\pi$
$29$	1.06238	−	1.84010i	0.197279	−	0.341698i	0.947645	+	0.319325i	$0.103456\pi$
$30$	0.358685	−	1.01175i	0.0654866	−	0.184720i
$31$	6.53585			1.17387			0.586937	−	0.809633i	$-0.300334\pi$
$31$	6.53585			1.17387			0.586937	+	0.809633i	$0.300334\pi$
$32$	2.76088			0.488059
$33$	4.70221	+	5.50955i	0.818550	+	0.959089i
$34$	0.204579	−	0.354341i	0.0350850	−	0.0607689i
$35$		0			0
$36$	−5.44282	+	2.08486i	−0.907137	+	0.347477i
$37$	−0.830095	−	1.43777i	−0.136467	−	0.236367i	0.789690	−	0.613506i	$-0.210241\pi$
$37$	−0.830095	−	1.43777i	−0.136467	−	0.236367i	−0.926157	+	0.377139i	$0.876908\pi$
$38$	−0.855536	−	1.48183i	−0.138786	−	0.240385i
$39$	−4.14132	−	4.85235i	−0.663141	−	0.776998i
$40$	1.22180	−	2.11621i	0.193183	−	0.334602i
$41$	−5.10948	−	8.84988i	−0.797967	−	1.38212i	−0.920938	−	0.389708i	$-0.872576\pi$
$41$	−5.10948	−	8.84988i	−0.797967	−	1.38212i	0.122972	−	0.992410i	$-0.460758\pi$
$42$		0			0
$43$	0.830095	−	1.43777i	0.126588	−	0.219257i	−0.795764	−	0.605606i	$-0.792931\pi$
$43$	0.830095	−	1.43777i	0.126588	−	0.219257i	0.922353	+	0.386349i	$0.126264\pi$
$44$	4.06238	+	7.03625i	0.612427	+	1.06075i
$45$	−1.22180	+	7.67877i	−0.182134	+	1.14468i
$46$	0.612725	−	1.06127i	0.0903414	−	0.156476i
$47$	−9.33824			−1.36212			−0.681061	−	0.732226i	$-0.738481\pi$
$47$	−9.33824			−1.36212			−0.681061	+	0.732226i	$0.738481\pi$
$48$	−6.23389	+	1.15309i	−0.899784	+	0.166434i
$49$		0			0
$50$	−0.205332	−	0.355645i	−0.0290383	−	0.0502958i
$51$	−0.990285	+	2.79332i	−0.138668	+	0.391143i
$52$	−3.57780	−	6.19694i	−0.496152	−	0.859361i
$53$	−5.32326	+	9.22015i	−0.731206	+	1.26649i	0.225162	+	0.974321i	$0.427709\pi$
$53$	−5.32326	+	9.22015i	−0.731206	+	1.26649i	−0.956368	+	0.292164i	$0.905625\pi$
$54$	−1.06012	+	0.648085i	−0.144263	+	0.0881932i
$55$	10.8387			1.46149
$56$		0			0
$57$	8.04583	+	9.42724i	1.06570	+	1.24867i
$58$	0.254040	−	0.440011i	0.0333571	−	0.0577762i
$59$	−6.06429			−0.789504			−0.394752	−	0.918788i	$-0.629169\pi$
$59$	−6.06429			−0.789504			−0.394752	+	0.918788i	$0.629169\pi$
$60$	−2.91423	+	8.22024i	−0.376225	+	1.06123i
$61$	7.98597			1.02250			0.511249	−	0.859433i	$-0.329183\pi$
$61$	7.98597			1.02250			0.511249	+	0.859433i	$0.329183\pi$
$62$	1.56287			0.198485
$63$		0			0
$64$	−6.66019			−0.832524
$65$	−9.54583			−1.18401
$66$	1.12441	+	1.31746i	0.138405	+	0.162168i
$67$	8.26320			1.00951			0.504755	−	0.863262i	$-0.331583\pi$
$67$	8.26320			1.00951			0.504755	+	0.863262i	$0.331583\pi$
$68$	−1.66215	+	2.87893i	−0.201566	+	0.349122i
$69$	−2.96596	+	8.36616i	−0.357060	+	1.00717i
$70$		0			0
$71$	6.23912			0.740448			0.370224	−	0.928943i	$-0.379281\pi$
$71$	6.23912			0.740448			0.370224	+	0.928943i	$0.379281\pi$
$72$	−2.64132	+	1.01175i	−0.311282	+	0.119236i
$73$	3.57780	−	6.19694i	0.418750	−	0.725297i	−0.577064	−	0.816699i	$-0.695802\pi$
$73$	3.57780	−	6.19694i	0.418750	−	0.725297i	0.995814	+	0.0914022i	$0.0291349\pi$
$74$	−0.198495	−	0.343803i	−0.0230746	−	0.0399663i
$75$	1.93103	+	2.26257i	0.222976	+	0.261259i
$76$	6.95103	+	12.0395i	0.797338	+	1.38103i
$77$		0			0
$78$	−0.990285	−	1.16031i	−0.112128	−	0.131379i
$79$	−9.82846			−1.10579			−0.552894	−	0.833252i	$-0.686477\pi$
$79$	−9.82846			−1.10579			−0.552894	+	0.833252i	$0.686477\pi$
$80$	−4.74322	+	8.21550i	−0.530308	+	0.918521i
$81$	6.69686	−	6.01266i	0.744096	−	0.668073i
$82$	−1.22180	−	2.11621i	−0.134925	−	0.233696i
$83$	3.44733	−	5.97094i	0.378393	−	0.655396i	−0.612436	−	0.790521i	$-0.709810\pi$
$83$	3.44733	−	5.97094i	0.378393	−	0.655396i	0.990829	+	0.135124i	$0.0431434\pi$
$84$		0			0
$85$	2.21737	+	3.84060i	0.240508	+	0.416571i
$86$	0.198495	−	0.343803i	0.0214043	−	0.0370733i
$87$	−1.22971	+	3.46867i	−0.131839	+	0.371881i
$88$	1.97141	+	3.41458i	0.210153	+	0.363996i
$89$	−2.51769	−	4.36077i	−0.266875	−	0.462240i	0.701178	−	0.712986i	$-0.252658\pi$
$89$	−2.51769	−	4.36077i	−0.266875	−	0.462240i	−0.968053	+	0.250745i	$0.919324\pi$
$90$	−0.292160	+	1.83617i	−0.0307963	+	0.193550i
$91$		0			0
$92$	−4.97825	+	8.62258i	−0.519018	+	0.898966i
$93$	−11.1316	+	2.05903i	−1.15429	+	0.213511i
$94$	−2.23299			−0.230315
$95$	18.5458			1.90276
$96$	−4.70221	+	0.869775i	−0.479918	+	0.0887710i
$97$	1.53167	−	2.65294i	0.155518	−	0.269365i	−0.777730	−	0.628599i	$-0.783629\pi$
$97$	1.53167	−	2.65294i	0.155518	−	0.269365i	0.933247	+	0.359234i	$0.116962\pi$
$98$		0			0
$99$	−9.74433	−	7.90228i	−0.979342	−	0.794209i
$100$	1.66827	+	2.88953i	0.166827	+	0.288953i
$101$	−5.54984	−	9.61260i	−0.552229	−	0.956489i	−0.998113	−	0.0613986i	$-0.980444\pi$
$101$	−5.54984	−	9.61260i	−0.552229	−	0.956489i	0.445884	−	0.895091i	$-0.352889\pi$
$102$	−0.236800	+	0.667948i	−0.0234467	+	0.0661367i
$103$	3.99298	−	6.91605i	0.393440	−	0.681459i	−0.599460	−	0.800404i	$-0.704618\pi$
$103$	3.99298	−	6.91605i	0.393440	−	0.681459i	0.992901	+	0.118946i	$0.0379515\pi$
$104$	−1.73625	−	3.00728i	−0.170254	−	0.294888i
$105$		0			0
$106$	−1.27292	+	2.20475i	−0.123636	+	0.214145i
$107$	−1.97825	−	3.42642i	−0.191244	−	0.331245i	0.754419	−	0.656394i	$-0.227919\pi$
$107$	−1.97825	−	3.42642i	−0.191244	−	0.331245i	−0.945663	+	0.325149i	$0.894586\pi$
$108$	8.61318	−	5.26554i	0.828804	−	0.506677i
$109$	−3.63160	+	6.29012i	−0.347844	+	0.602484i	−0.985866	−	0.167534i	$-0.946420\pi$
$109$	−3.63160	+	6.29012i	−0.347844	+	0.602484i	0.638022	+	0.770018i	$0.279753\pi$
$110$	2.59179			0.247117
$111$	1.86673	+	2.18724i	0.177182	+	0.207603i
$112$		0			0
$113$	−3.46457	−	6.00082i	−0.325920	−	0.564509i	0.655778	−	0.754953i	$-0.272341\pi$
$113$	−3.46457	−	6.00082i	−0.325920	−	0.564509i	−0.981698	+	0.190444i	$0.939007\pi$
$114$	1.92395	+	2.25427i	0.180194	+	0.211132i
$115$	6.64115	+	11.5028i	0.619291	+	1.07264i
$116$	−2.06402	+	3.57498i	−0.191639	+	0.331929i
$117$	8.58198	+	6.95966i	0.793405	+	0.643421i
$118$	−1.45011			−0.133494
$119$		0			0
$120$	−1.41423	+	3.98916i	−0.129101	+	0.364158i
$121$	−3.24433	+	5.61934i	−0.294939	+	0.510849i
$122$	1.90963			0.172890
$123$	11.4903	+	13.4631i	1.03604	+	1.21393i
$124$	−12.6980			−1.14031
$125$	−8.50788			−0.760968
$126$		0			0
$127$	9.11109			0.808479			0.404239	−	0.914653i	$-0.367536\pi$
$127$	9.11109			0.808479			0.404239	+	0.914653i	$0.367536\pi$
$128$	−7.11436			−0.628827
$129$	−0.960836	+	2.71026i	−0.0845969	+	0.238625i
$130$	−2.28263			−0.200200
$131$	−2.15143	+	3.72639i	−0.187971	+	0.325576i	−0.944574	−	0.328299i	$-0.893525\pi$
$131$	−2.15143	+	3.72639i	−0.187971	+	0.325576i	0.756602	+	0.653875i	$0.226858\pi$
$132$	−9.13555	−	10.7041i	−0.795148	−	0.931669i
$133$		0			0
$134$	1.97592			0.170694
$135$	−0.338175	−	13.4631i	−0.0291055	−	1.15872i
$136$	−0.806617	+	1.39710i	−0.0691668	+	0.119800i
$137$	−10.2947	−	17.8309i	−0.879533	−	1.52340i	−0.851854	−	0.523779i	$-0.824522\pi$
$137$	−10.2947	−	17.8309i	−0.879533	−	1.52340i	−0.0276785	−	0.999617i	$-0.508811\pi$
$138$	−0.709230	+	2.00054i	−0.0603737	+	0.170298i
$139$	−7.88067	−	13.6497i	−0.668429	−	1.15775i	−0.978343	−	0.206989i	$-0.933634\pi$
$139$	−7.88067	−	13.6497i	−0.668429	−	1.15775i	0.309914	−	0.950765i	$-0.399700\pi$
$140$		0			0
$141$	15.9045	−	2.94188i	1.33940	−	0.247751i
$142$	1.49192			0.125199
$143$	7.70127	−	13.3390i	0.644012	−	1.11546i
$144$	10.2540	−	3.92779i	0.854503	−	0.327316i
$145$	2.75347	+	4.76915i	0.228663	+	0.396056i
$146$	0.855536	−	1.48183i	0.0708047	−	0.122637i
$147$		0			0
$148$	1.61273	+	2.79332i	0.132565	+	0.229610i
$149$	−3.03379	+	5.25468i	−0.248538	+	0.430480i	−0.963120	−	0.269071i	$-0.913283\pi$
$149$	−3.03379	+	5.25468i	−0.248538	+	0.430480i	0.714582	+	0.699551i	$0.246617\pi$
$150$	0.461753	+	0.541033i	0.0377020	+	0.0441751i
$151$	−2.24433	−	3.88728i	−0.182641	−	0.316343i	0.760138	−	0.649761i	$-0.225131\pi$
$151$	−2.24433	−	3.88728i	−0.182641	−	0.316343i	−0.942779	+	0.333418i	$0.891798\pi$
$152$	3.37323	+	5.84260i	0.273605	+	0.473897i
$153$	0.806617	−	5.06945i	0.0652111	−	0.409841i
$154$		0			0
$155$	−8.46978	+	14.6701i	−0.680309	+	1.17833i
$156$	8.04583	+	9.42724i	0.644182	+	0.754783i
$157$	−1.02891			−0.0821163			−0.0410582	−	0.999157i	$-0.513073\pi$
$157$	−1.02891			−0.0821163			−0.0410582	+	0.999157i	$0.513073\pi$
$158$	−2.35021			−0.186973
$159$	6.16168	−	17.3804i	0.488653	−	1.37836i
$160$	−3.57780	+	6.19694i	−0.282850	+	0.489911i
$161$		0			0
$162$	1.60138	−	1.43777i	0.125816	−	0.112962i
$163$	−3.41423	−	5.91362i	−0.267423	−	0.463190i	0.700772	−	0.713385i	$-0.252839\pi$
$163$	−3.41423	−	5.91362i	−0.267423	−	0.463190i	−0.968196	+	0.250194i	$0.919505\pi$
$164$	9.92680	+	17.1937i	0.775153	+	1.34260i
$165$	−18.4601	+	3.41458i	−1.43711	+	0.265825i
$166$	0.824336	−	1.42779i	0.0639809	−	0.110818i
$167$	8.99716	+	15.5835i	0.696221	+	1.20589i	0.969767	+	0.244032i	$0.0784701\pi$
$167$	8.99716	+	15.5835i	0.696221	+	1.20589i	−0.273546	+	0.961859i	$0.588197\pi$
$168$		0			0
$169$	−0.282630	+	0.489530i	−0.0217408	+	0.0376561i
$170$	0.530225	+	0.918376i	0.0406664	+	0.0704362i
$171$	−16.6733	−	13.5214i	−1.27504	−	1.03401i
$172$	−1.61273	+	2.79332i	−0.122969	+	0.212989i
$173$	0.830357			0.0631309			0.0315654	−	0.999502i	$-0.489951\pi$
$173$	0.830357			0.0631309			0.0315654	+	0.999502i	$0.489951\pi$
$174$	−0.294052	+	0.829440i	−0.0222920	+	0.0628797i
$175$		0			0
$176$	−7.65335	−	13.2560i	−0.576893	−	0.999208i
$177$	10.3285	−	1.91047i	0.776335	−	0.143600i
$178$	−0.602038	−	1.04276i	−0.0451247	−	0.0781582i
$179$	−3.78947	+	6.56355i	−0.283238	+	0.490583i	−0.972180	−	0.234233i	$-0.924742\pi$
$179$	−3.78947	+	6.56355i	−0.283238	+	0.490583i	0.688942	+	0.724816i	$0.258075\pi$
$180$	2.37373	−	14.9185i	0.176927	−	1.11196i
$181$	−0.409157			−0.0304124			−0.0152062	−	0.999884i	$-0.504840\pi$
$181$	−0.409157			−0.0304124			−0.0152062	+	0.999884i	$0.504840\pi$
$182$		0			0
$183$	−13.6014	+	2.51586i	−1.00544	+	0.185978i
$184$	−2.41586	+	4.18440i	−0.178100	+	0.308478i
$185$	4.30286			0.316353
$186$	−2.66182	+	0.492361i	−0.195174	+	0.0361017i
$187$	−7.15561			−0.523270
$188$	18.1425			1.32318
$189$		0			0
$190$	4.43474			0.321730
$191$	16.0241			1.15946			0.579731	−	0.814808i	$-0.303158\pi$
$191$	16.0241			1.15946			0.579731	+	0.814808i	$0.303158\pi$
$192$	11.3434	−	2.09820i	0.818637	−	0.151424i
$193$	−12.3743			−0.890721			−0.445360	−	0.895351i	$-0.646924\pi$
$193$	−12.3743			−0.890721			−0.445360	+	0.895351i	$0.646924\pi$
$194$	0.366259	−	0.634379i	0.0262959	−	0.0455458i
$195$	16.2581	−	3.00728i	1.16426	−	0.215356i
$196$		0			0
$197$	23.1021			1.64595			0.822977	−	0.568075i	$-0.192312\pi$
$197$	23.1021			1.64595			0.822977	+	0.568075i	$0.192312\pi$
$198$	−2.33009	−	1.88962i	−0.165593	−	0.134289i
$199$	−3.37323	+	5.84260i	−0.239122	+	0.414171i	−0.960463	−	0.278409i	$-0.910193\pi$
$199$	−3.37323	+	5.84260i	−0.239122	+	0.414171i	0.721341	+	0.692580i	$0.243526\pi$
$200$	0.809585	+	1.40224i	0.0572463	+	0.0991536i
$201$	−14.0735	+	2.60320i	−0.992672	+	0.183616i
$202$	−1.32710	−	2.29860i	−0.0933741	−	0.161729i
$203$		0			0
$204$	1.92395	−	5.42692i	0.134703	−	0.379961i
$205$	26.4854			1.84982
$206$	0.954815	−	1.65379i	0.0665251	−	0.115225i
$207$	2.41586	−	15.1833i	0.167914	−	1.05531i
$208$	6.74043	+	11.6748i	0.467365	+	0.809500i
$209$	−14.9622	+	25.9153i	−1.03496	+	1.79260i
$210$		0			0
$211$	−8.44282	−	14.6234i	−0.581228	−	1.00672i	−0.995334	−	0.0964875i	$-0.969239\pi$
$211$	−8.44282	−	14.6234i	−0.581228	−	1.00672i	0.414106	−	0.910228i	$-0.364094\pi$
$212$	10.3421	−	17.9131i	0.710301	−	1.23028i
$213$	−10.6262	+	1.96555i	−0.728097	+	0.134677i
$214$	−0.473045	−	0.819338i	−0.0323367	−	0.0560088i
$215$	2.15143	+	3.72639i	0.146726	+	0.254138i
$216$	4.17984	−	2.55528i	0.284402	−	0.173865i
$217$		0			0
$218$	−0.868400	+	1.50411i	−0.0588155	+	0.101871i
$219$	−4.14132	+	11.6815i	−0.279844	+	0.789364i
$220$	−21.0577			−1.41971
$221$	6.30206			0.423922
$222$	0.446379	+	0.523019i	0.0299590	+	0.0351027i
$223$	−2.25071	+	3.89834i	−0.150719	+	0.261052i	−0.931492	−	0.363762i	$-0.881492\pi$
$223$	−2.25071	+	3.89834i	−0.150719	+	0.261052i	0.780773	+	0.624815i	$0.214825\pi$
$224$		0			0
$225$	−4.00163	−	3.24517i	−0.266776	−	0.216345i
$226$	−0.828460	−	1.43494i	−0.0551084	−	0.0954505i
$227$	−3.03215	−	5.25183i	−0.201251	−	0.348576i	0.747681	−	0.664058i	$-0.231167\pi$
$227$	−3.03215	−	5.25183i	−0.201251	−	0.348576i	−0.948932	+	0.315482i	$0.897834\pi$
$228$	−15.6316	−	18.3154i	−1.03523	−	1.21297i
$229$	−5.52466	+	9.56899i	−0.365080	+	0.632336i	−0.988789	−	0.149320i	$-0.952292\pi$
$229$	−5.52466	+	9.56899i	−0.365080	+	0.632336i	0.623709	+	0.781656i	$0.285625\pi$
$230$	1.58805	+	2.75059i	0.104713	+	0.181369i
$231$		0			0
$232$	−1.00163	+	1.73488i	−0.0657605	+	0.113901i
$233$	4.06922	+	7.04809i	0.266583	+	0.461736i	0.967977	−	0.251038i	$-0.0807719\pi$
$233$	4.06922	+	7.04809i	0.266583	+	0.461736i	−0.701394	+	0.712774i	$0.747439\pi$
$234$	2.05215	+	1.66422i	0.134153	+	0.108793i
$235$	12.1014	−	20.9602i	0.789407	−	1.36729i
$236$	11.7818			0.766932
$237$	16.7394	−	3.09632i	1.08734	−	0.201127i
$238$		0			0
$239$	−10.5813	−	18.3273i	−0.684445	−	1.18549i	−0.973611	−	0.228214i	$-0.926711\pi$
$239$	−10.5813	−	18.3273i	−0.684445	−	1.18549i	0.289166	−	0.957279i	$-0.406622\pi$
$240$	5.49028	−	15.4866i	0.354396	−	0.999655i
$241$	6.84573	+	11.8572i	0.440972	+	0.763786i	0.997762	−	0.0668671i	$-0.0213004\pi$
$241$	6.84573	+	11.8572i	0.440972	+	0.763786i	−0.556790	+	0.830654i	$0.687967\pi$
$242$	−0.775794	+	1.34371i	−0.0498699	+	0.0863772i
$243$	−9.51162	+	12.3503i	−0.610171	+	0.792270i
$244$	−15.5153			−0.993265
$245$		0			0
$246$	2.74759	+	3.21934i	0.175180	+	0.205257i
$247$	13.1774	−	22.8240i	0.838460	−	1.45225i
$248$	−6.16213			−0.391296
$249$	−3.99028	+	11.2555i	−0.252874	+	0.713288i
$250$	−2.03443			−0.128669
$251$	−15.2040			−0.959667			−0.479833	−	0.877360i	$-0.659303\pi$
$251$	−15.2040			−0.959667			−0.479833	+	0.877360i	$0.659303\pi$
$252$		0			0
$253$	−21.4315			−1.34738
$254$	2.17867			0.136702
$255$	−4.98646	−	5.84260i	−0.312264	−	0.365878i
$256$	11.6192			0.726198
$257$	12.8107	−	22.1889i	0.799112	−	1.38410i	−0.121082	−	0.992642i	$-0.538637\pi$
$257$	12.8107	−	22.1889i	0.799112	−	1.38410i	0.920195	−	0.391461i	$-0.128030\pi$
$258$	−0.229758	+	0.648085i	−0.0143041	+	0.0403480i
$259$		0			0
$260$	18.5458			1.15016
$261$	1.00163	−	6.29510i	0.0619996	−	0.389657i
$262$	−0.514457	+	0.891066i	−0.0317833	+	0.0550502i
$263$	−3.55034	−	6.14938i	−0.218924	−	0.379187i	0.735556	−	0.677464i	$-0.236921\pi$
$263$	−3.55034	−	6.14938i	−0.218924	−	0.379187i	−0.954479	+	0.298278i	$0.903588\pi$
$264$	−4.43334	−	5.19451i	−0.272853	−	0.319700i
$265$	−13.7968	−	23.8967i	−0.847528	−	1.46796i
$266$		0			0
$267$	5.66182	+	6.63392i	0.346498	+	0.405989i
$268$	−16.0539			−0.980649
$269$	−8.21572	+	14.2301i	−0.500922	+	0.867622i	0.499078	+	0.866557i	$0.333672\pi$
$269$	−8.21572	+	14.2301i	−0.500922	+	0.867622i	−0.999999	+	0.00106448i	$0.999661\pi$
$270$	−0.0808656	−	3.21934i	−0.00492132	−	0.195923i
$271$	6.34899	+	10.9968i	0.385674	+	0.668007i	0.991862	−	0.127314i	$-0.0406357\pi$
$271$	6.34899	+	10.9968i	0.385674	+	0.668007i	−0.606189	+	0.795321i	$0.707302\pi$
$272$	3.13143	−	5.42379i	0.189871	−	0.328865i
$273$		0			0
$274$	−2.46169	−	4.26378i	−0.148716	−	0.257584i
$275$	−3.59097	+	6.21975i	−0.216544	+	0.375065i
$276$	5.76233	−	16.2539i	0.346851	−	0.978373i
$277$	0.414230	+	0.717468i	0.0248887	+	0.0431084i	0.878201	−	0.478291i	$-0.158744\pi$
$277$	0.414230	+	0.717468i	0.0248887	+	0.0431084i	−0.853313	+	0.521399i	$0.825410\pi$
$278$	−1.88445	−	3.26396i	−0.113022	−	0.195760i
$279$	18.3102	−	7.01370i	1.09620	−	0.419899i
$280$		0			0
$281$	−2.60985	+	4.52039i	−0.155690	+	0.269664i	−0.933310	−	0.359071i	$-0.883094\pi$
$281$	−2.60985	+	4.52039i	−0.155690	+	0.269664i	0.777620	+	0.628735i	$0.216427\pi$
$282$	3.80314	−	0.703472i	0.226474	−	0.0418911i
$283$	7.35417			0.437160			0.218580	−	0.975819i	$-0.429858\pi$
$283$	7.35417			0.437160			0.218580	+	0.975819i	$0.429858\pi$
$284$	−12.1215			−0.719278
$285$	−31.5865	+	5.84260i	−1.87102	+	0.346086i
$286$	1.84155	−	3.18966i	0.108893	−	0.188609i
$287$		0			0
$288$	7.73461	−	2.96273i	0.455766	−	0.174581i
$289$	7.03611	+	12.1869i	0.413889	+	0.716877i
$290$	0.658419	+	1.14041i	0.0386637	+	0.0669674i
$291$	−1.77292	+	5.00091i	−0.103930	+	0.293158i
$292$	−6.95103	+	12.0395i	−0.406778	+	0.704561i
$293$	3.91286	+	6.77728i	0.228592	+	0.395933i	0.957391	−	0.288795i	$-0.0932545\pi$
$293$	3.91286	+	6.77728i	0.228592	+	0.395933i	−0.728799	+	0.684728i	$0.759921\pi$
$294$		0			0
$295$	7.85868	−	13.6116i	0.457550	−	0.792500i
$296$	0.782630	+	1.35556i	0.0454895	+	0.0787900i
$297$	19.0856	+	10.3890i	1.10746	+	0.602833i
$298$	−0.725450	+	1.25652i	−0.0420242	+	0.0727881i
$299$	18.8750			1.09157
$300$	−3.75164	−	4.39576i	−0.216601	−	0.253790i
$301$		0			0
$302$	−0.536670	−	0.929540i	−0.0308819	−	0.0534890i
$303$	12.4806	+	14.6234i	0.716990	+	0.840092i
$304$	−13.0954	−	22.6820i	−0.751075	−	1.30090i
$305$	−10.3490	+	17.9249i	−0.592580	+	1.02638i
$306$	0.192881	−	1.21222i	0.0110263	−	0.0692982i
$307$	−22.6709			−1.29390			−0.646948	−	0.762534i	$-0.723955\pi$
$307$	−22.6709			−1.29390			−0.646948	+	0.762534i	$0.723955\pi$
$308$		0			0
$309$	−4.62188	+	13.0371i	−0.262930	+	0.741653i
$310$	−2.02532	+	3.50796i	−0.115030	+	0.199239i
$311$	32.3176			1.83256			0.916281	−	0.400536i	$-0.131176\pi$
$311$	32.3176			1.83256			0.916281	+	0.400536i	$0.131176\pi$
$312$	3.90451	+	4.57489i	0.221050	+	0.259002i
$313$	24.3196			1.37462			0.687312	−	0.726362i	$-0.258791\pi$
$313$	24.3196			1.37462			0.687312	+	0.726362i	$0.258791\pi$
$314$	−0.246037			−0.0138847
$315$		0			0
$316$	19.0949			1.07417
$317$	5.13844			0.288603			0.144302	−	0.989534i	$-0.453906\pi$
$317$	5.13844			0.288603			0.144302	+	0.989534i	$0.453906\pi$
$318$	1.47340	−	4.15606i	0.0826242	−	0.233060i
$319$	−8.88564			−0.497500
$320$	8.63090	−	14.9492i	0.482482	−	0.835684i
$321$	4.44872	+	5.21253i	0.248303	+	0.290935i
$322$		0			0
$323$	−12.2438			−0.681262
$324$	−13.0108	+	11.6815i	−0.722822	+	0.648973i
$325$	3.16263	−	5.47783i	0.175431	−	0.303855i
$326$	−0.816422	−	1.41408i	−0.0452174	−	0.0783189i
$327$	4.20358	−	11.8572i	0.232459	−	0.655702i
$328$	4.81732	+	8.34384i	0.265992	+	0.460712i
$329$		0			0
$330$	−4.41423	+	0.816506i	−0.242995	+	0.0449472i
$331$	−11.6979			−0.642977			−0.321488	−	0.946913i	$-0.604183\pi$
$331$	−11.6979			−0.642977			−0.321488	+	0.946913i	$0.604183\pi$
$332$	−6.69753	+	11.6005i	−0.367575	+	0.636658i
$333$	−3.86840	−	3.13713i	−0.211987	−	0.171913i
$334$	2.15143	+	3.72639i	0.117721	+	0.203899i
$335$	−10.7082	+	18.5472i	−0.585053	+	1.01334i
$336$		0			0
$337$	16.8473	+	29.1804i	0.917733	+	1.58956i	0.802850	+	0.596181i	$0.203316\pi$
$337$	16.8473	+	29.1804i	0.917733	+	1.58956i	0.114883	+	0.993379i	$0.463351\pi$
$338$	−0.0675835	+	0.117058i	−0.00367606	+	0.00636711i
$339$	7.79119	+	9.12888i	0.423160	+	0.495813i
$340$	−4.30795	−	7.46159i	−0.233631	−	0.404661i
$341$	−13.6663	−	23.6707i	−0.740071	−	1.28184i
$342$	−3.98696	−	3.23327i	−0.215590	−	0.174835i
$343$		0			0
$344$	−0.782630	+	1.35556i	−0.0421966	+	0.0730866i
$345$	−14.9347	−	17.4989i	−0.804059	−	0.942111i
$346$	0.198558			0.0106745
$347$	27.3114			1.46615			0.733075	−	0.680148i	$-0.238084\pi$
$347$	27.3114			1.46615			0.733075	+	0.680148i	$0.238084\pi$
$348$	2.38910	−	6.73900i	0.128069	−	0.361248i
$349$	11.4585	−	19.8467i	0.613358	−	1.06237i	−0.377312	−	0.926086i	$-0.623152\pi$
$349$	11.4585	−	19.8467i	0.613358	−	1.06237i	0.990670	−	0.136281i	$-0.0435150\pi$
$350$		0			0
$351$	−16.8090	−	9.14978i	−0.897200	−	0.488379i
$352$	−5.77292	−	9.99898i	−0.307697	−	0.532948i
$353$	5.13466	+	8.89349i	0.273290	+	0.473353i	0.969702	−	0.244289i	$-0.0785547\pi$
$353$	5.13466	+	8.89349i	0.273290	+	0.473353i	−0.696412	+	0.717642i	$0.745221\pi$
$354$	2.46978	−	0.456838i	0.131267	−	0.0242806i
$355$	−8.08525	+	14.0041i	−0.429120	+	0.743258i
$356$	4.89142	+	8.47218i	0.259245	+	0.449025i
$357$		0			0
$358$	−0.906150	+	1.56950i	−0.0478915	+	0.0829505i
$359$	−5.05034	−	8.74745i	−0.266547	−	0.461673i	0.701421	−	0.712747i	$-0.252549\pi$
$359$	−5.05034	−	8.74745i	−0.266547	−	0.461673i	−0.967968	+	0.251075i	$0.919216\pi$
$360$	1.15193	−	7.23970i	0.0607122	−	0.381566i
$361$	−16.1014	+	27.8884i	−0.847441	+	1.46781i
$362$	−0.0978390			−0.00514231
$363$	3.75531	−	10.5927i	0.197103	−	0.555973i
$364$		0			0
$365$	9.27292	+	16.0612i	0.485367	+	0.840680i
$366$	−3.25241	+	0.601602i	−0.170006	+	0.0314462i
$367$	−3.88768	−	6.73367i	−0.202935	−	0.351494i	0.746538	−	0.665343i	$-0.231715\pi$
$367$	−3.88768	−	6.73367i	−0.202935	−	0.351494i	−0.949473	+	0.313849i	$0.898381\pi$
$368$	9.37880	−	16.2446i	0.488904	−	0.846806i
$369$	−23.8111	−	19.3099i	−1.23956	−	1.00523i
$370$	1.02891			0.0534907
$371$		0			0
$372$	21.6267	−	4.00032i	1.12129	−	0.207407i
$373$	−12.0555	+	20.8808i	−0.624212	+	1.08117i	0.364480	+	0.931211i	$0.381247\pi$
$373$	−12.0555	+	20.8808i	−0.624212	+	1.08117i	−0.988693	+	0.149957i	$0.952087\pi$
$374$	−1.71107			−0.0884775
$375$	14.4903	−	2.68029i	0.748275	−	0.138409i
$376$	8.80428			0.454046
$377$	7.82573			0.403045
$378$		0			0
$379$	−13.3581			−0.686161			−0.343081	−	0.939306i	$-0.611470\pi$
$379$	−13.3581			−0.686161			−0.343081	+	0.939306i	$0.611470\pi$
$380$	−36.0312			−1.84836
$381$	−15.5176	+	2.87032i	−0.794993	+	0.147051i
$382$	3.83173			0.196048
$383$	−4.62020	+	8.00242i	−0.236081	+	0.408905i	−0.959586	−	0.281414i	$-0.909196\pi$
$383$	−4.62020	+	8.00242i	−0.236081	+	0.408905i	0.723505	+	0.690319i	$0.242530\pi$
$384$	12.1169	−	2.24128i	0.618337	−	0.114375i
$385$		0			0
$386$	−2.95898			−0.150608
$387$	0.782630	−	4.91870i	0.0397833	−	0.250031i
$388$	−2.97577	+	5.15418i	−0.151072	+	0.261664i
$389$	−5.22421	−	9.04859i	−0.264878	−	0.458782i	0.702654	−	0.711532i	$-0.251998\pi$
$389$	−5.22421	−	9.04859i	−0.264878	−	0.458782i	−0.967532	+	0.252750i	$0.918665\pi$
$390$	3.88768	−	0.719110i	0.196861	−	0.0364136i
$391$	−4.38442	−	7.59404i	−0.221730	−	0.384047i
$392$		0			0
$393$	2.49028	−	7.02441i	0.125618	−	0.354335i
$394$	5.52424			0.278307
$395$	12.7366	−	22.0605i	0.640850	−	1.10999i
$396$	18.9315	+	15.3527i	0.951342	+	0.771502i
$397$	−0.204579	−	0.354341i	−0.0102675	−	0.0177838i	0.860846	−	0.508866i	$-0.169935\pi$
$397$	−0.204579	−	0.354341i	−0.0102675	−	0.0177838i	−0.871114	+	0.491082i	$0.836602\pi$
$398$	−0.806617	+	1.39710i	−0.0404321	+	0.0700304i
$399$		0			0
$400$	−3.14295	−	5.44375i	−0.157147	−	0.272187i
$401$	−7.62640	+	13.2093i	−0.380844	+	0.659641i	−0.991183	−	0.132499i	$-0.957700\pi$
$401$	−7.62640	+	13.2093i	−0.380844	+	0.659641i	0.610339	+	0.792140i	$0.291033\pi$
$402$	−3.36531	+	0.622486i	−0.167847	+	0.0310468i
$403$	12.0361	+	20.8472i	0.599562	+	1.03847i
$404$	10.7823	+	18.6756i	0.536441	+	0.929143i
$405$	4.81732	+	22.8232i	0.239375	+	1.13410i
$406$		0			0
$407$	−3.47141	+	6.01266i	−0.172071	+	0.298036i
$408$	0.933660	−	2.63360i	0.0462231	−	0.130383i
$409$	6.12670			0.302946			0.151473	−	0.988461i	$-0.451598\pi$
$409$	6.12670			0.302946			0.151473	+	0.988461i	$0.451598\pi$
$410$	6.33327			0.312778
$411$	23.1508	+	27.1257i	1.14195	+	1.33801i
$412$	−7.75765	+	13.4366i	−0.382192	+	0.661976i
$413$		0			0
$414$	0.577690	−	3.63068i	0.0283919	−	0.178438i
$415$	8.93474	+	15.4754i	0.438589	+	0.759659i
$416$	5.08430	+	8.80626i	0.249278	+	0.431763i
$417$	17.7222	+	20.7650i	0.867859	+	1.01686i
$418$	−3.57780	+	6.19694i	−0.174996	+	0.303102i
$419$	0.781437	+	1.35349i	0.0381757	+	0.0661223i	0.884482	−	0.466574i	$-0.154512\pi$
$419$	0.781437	+	1.35349i	0.0381757	+	0.0661223i	−0.846306	+	0.532697i	$0.821179\pi$
$420$		0			0
$421$	−11.6316	+	20.1465i	−0.566889	+	0.981881i	0.429982	+	0.902838i	$0.358520\pi$
$421$	−11.6316	+	20.1465i	−0.566889	+	0.981881i	−0.996871	+	0.0790438i	$0.974813\pi$
$422$	−2.01887	−	3.49679i	−0.0982773	−	0.170221i
$423$	−26.1611	+	10.0210i	−1.27200	+	0.487237i
$424$	5.01887	−	8.69295i	0.243738	−	0.422167i
$425$	−2.93854			−0.142540
$426$	−2.54098	+	0.470008i	−0.123111	+	0.0227720i
$427$		0			0
$428$	3.84338	+	6.65692i	0.185777	+	0.321775i
$429$	−8.91423	+	25.1446i	−0.430383	+	1.21399i
$430$	0.514457	+	0.891066i	0.0248093	+	0.0429710i
$431$	−0.502879	+	0.871011i	−0.0242228	+	0.0419551i	−0.877883	−	0.478876i	$-0.841044\pi$
$431$	−0.502879	+	0.871011i	−0.0242228	+	0.0419551i	0.853660	+	0.520831i	$0.174378\pi$
$432$	−16.2269	+	9.92005i	−0.780716	+	0.477279i
$433$	−13.1071			−0.629889			−0.314945	−	0.949110i	$-0.601986\pi$
$433$	−13.1071			−0.629889			−0.314945	+	0.949110i	$0.601986\pi$
$434$		0			0
$435$	−6.19205	−	7.25518i	−0.296886	−	0.347859i
$436$	7.05555	−	12.2206i	0.337899	−	0.585259i
$437$	−36.6708			−1.75420
$438$	−0.990285	+	2.79332i	−0.0473176	+	0.133470i
$439$	−18.6141			−0.888402			−0.444201	−	0.895927i	$-0.646512\pi$
$439$	−18.6141			−0.888402			−0.444201	+	0.895927i	$0.646512\pi$
$440$	−10.2190			−0.487170
$441$		0			0
$442$	1.50697			0.0716792
$443$	−1.11901			−0.0531656			−0.0265828	−	0.999647i	$-0.508463\pi$
$443$	−1.11901			−0.0531656			−0.0265828	+	0.999647i	$0.508463\pi$
$444$	−3.62672	−	4.24941i	−0.172117	−	0.201668i
$445$	13.0506			0.618660
$446$	−0.538197	+	0.932185i	−0.0254844	+	0.0441402i
$447$	3.51162	−	9.90531i	0.166094	−	0.468505i
$448$		0			0
$449$	−39.4419			−1.86138			−0.930689	−	0.365813i	$-0.880791\pi$
$449$	−39.4419			−1.86138			−0.930689	+	0.365813i	$0.880791\pi$
$450$	−0.956884	−	0.775997i	−0.0451079	−	0.0365808i
$451$	−21.3676	+	37.0097i	−1.00616	+	1.74272i
$452$	6.73104	+	11.6585i	0.316602	+	0.548370i
$453$	5.04708	+	5.91362i	0.237132	+	0.277846i
$454$	−0.725057	−	1.25584i	−0.0340286	−	0.0589393i
$455$		0			0
$456$	−7.58577	−	8.88819i	−0.355236	−	0.416228i
$457$	−34.2405			−1.60170			−0.800852	−	0.598863i	$-0.795619\pi$
$457$	−34.2405			−1.60170			−0.800852	+	0.598863i	$0.795619\pi$
$458$	−1.32107	+	2.28817i	−0.0617297	+	0.106919i
$459$	0.223260	+	8.88819i	0.0104209	+	0.414865i
$460$	−12.9026	−	22.3479i	−0.601585	−	1.04198i
$461$	10.1938	−	17.6561i	0.474772	−	0.822328i	−0.524811	−	0.851219i	$-0.675864\pi$
$461$	10.1938	−	17.6561i	0.474772	−	0.822328i	0.999583	+	0.0288903i	$0.00919735\pi$
$462$		0			0
$463$	−3.40451	−	5.89679i	−0.158221	−	0.274047i	0.776006	−	0.630725i	$-0.217243\pi$
$463$	−3.40451	−	5.89679i	−0.158221	−	0.274047i	−0.934227	+	0.356678i	$0.883909\pi$
$464$	3.88852	−	6.73511i	0.180520	−	0.312670i
$465$	9.80378	−	27.6538i	0.454639	−	1.28241i
$466$	0.973045	+	1.68536i	0.0450754	+	0.0780729i
$467$	12.3956	+	21.4698i	0.573598	+	0.993502i	0.996192	+	0.0871825i	$0.0277863\pi$
$467$	12.3956	+	21.4698i	0.573598	+	0.993502i	−0.422594	+	0.906319i	$0.638880\pi$
$468$	−16.6733	−	13.5214i	−0.770721	−	0.625026i
$469$		0			0
$470$	2.89372	−	5.01207i	0.133477	−	0.231190i
$471$	1.75241	−	0.324145i	0.0807466	−	0.0149358i
$472$	5.71754			0.263171
$473$	−6.94282			−0.319231
$474$	4.00279	−	0.740401i	0.183854	−	0.0340078i
$475$	−6.14441	+	10.6424i	−0.281925	+	0.488309i
$476$		0			0
$477$	−5.01887	+	31.5428i	−0.229798	+	1.44424i
$478$	−2.53022	−	4.38248i	−0.115730	−	0.200450i
$479$	−5.54984	−	9.61260i	−0.253579	−	0.439211i	0.710930	−	0.703263i	$-0.248274\pi$
$479$	−5.54984	−	9.61260i	−0.253579	−	0.439211i	−0.964508	+	0.264052i	$0.914941\pi$
$480$	4.14132	−	11.6815i	0.189024	−	0.533186i
$481$	3.05733	−	5.29545i	0.139402	−	0.241452i
$482$	1.63697	+	2.83532i	0.0745621	+	0.129145i
$483$		0			0
$484$	6.30314	−	10.9174i	0.286506	−	0.496244i
$485$	3.96978	+	6.87585i	0.180258	+	0.312216i
$486$	−2.27445	+	2.95324i	−0.103171	+	0.133962i
$487$	5.01887	−	8.69295i	0.227427	−	0.393915i	−0.729618	−	0.683855i	$-0.760302\pi$
$487$	5.01887	−	8.69295i	0.227427	−	0.393915i	0.957045	+	0.289940i	$0.0936354\pi$
$488$	−7.52933			−0.340837
$489$	7.67798	+	8.99623i	0.347210	+	0.406824i
$490$		0			0
$491$	6.19398	+	10.7283i	0.279530	+	0.484161i	0.971268	−	0.237988i	$-0.0764879\pi$
$491$	6.19398	+	10.7283i	0.279530	+	0.484161i	−0.691738	+	0.722149i	$0.743155\pi$
$492$	−22.3236	−	26.1563i	−1.00642	−	1.17922i
$493$	−1.81781	−	3.14854i	−0.0818702	−	0.141803i
$494$	3.15103	−	5.45774i	0.141772	−	0.245556i
$495$	30.3647	−	11.6312i	1.36479	−	0.522782i
$496$	23.9225			1.07415
$497$		0			0
$498$	−0.954170	+	2.69145i	−0.0427574	+	0.120607i
$499$	−5.11109	+	8.85267i	−0.228804	+	0.396300i	−0.957454	−	0.288586i	$-0.906815\pi$
$499$	−5.11109	+	8.85267i	−0.228804	+	0.396300i	0.728650	+	0.684886i	$0.240148\pi$
$500$	16.5293			0.739212
$501$	−20.2330	−	23.7068i	−0.903943	−	1.05914i
$502$	−3.63562			−0.162266
$503$	8.45753			0.377102			0.188551	−	0.982063i	$-0.439621\pi$
$503$	8.45753			0.377102			0.188551	+	0.982063i	$0.439621\pi$
$504$		0			0
$505$	28.7680			1.28016
$506$	−5.12476			−0.227824
$507$	0.327145	−	0.922786i	0.0145290	−	0.0409824i
$508$	−17.7012			−0.785364
$509$	−5.28286	+	9.15018i	−0.234159	+	0.405574i	−0.959028	−	0.283312i	$-0.908567\pi$
$509$	−5.28286	+	9.15018i	−0.234159	+	0.405574i	0.724869	+	0.688886i	$0.241900\pi$
$510$	−1.19238	−	1.39710i	−0.0527994	−	0.0618647i
$511$		0			0
$512$	17.0071			0.751616
$513$	32.6569	+	17.7764i	1.44184	+	0.784847i
$514$	3.06335	−	5.30587i	0.135118	−	0.234032i
$515$	10.3490	+	17.9249i	0.456030	+	0.789867i
$516$	1.86673	−	5.26554i	0.0821783	−	0.231802i
$517$	19.5260	+	33.8200i	0.858752	+	1.48740i
$518$		0			0
$519$	−1.41423	+	0.261592i	−0.0620778	+	0.0114826i
$520$	9.00000			0.394676
$521$	9.87788	−	17.1090i	0.432758	−	0.749558i	−0.564352	−	0.825534i	$-0.690874\pi$
$521$	9.87788	−	17.1090i	0.432758	−	0.749558i	0.997110	+	0.0759760i	$0.0242072\pi$
$522$	0.239514	−	1.50531i	0.0104833	−	0.0658854i
$523$	−16.2641	−	28.1702i	−0.711179	−	1.23180i	−0.964415	−	0.264394i	$-0.914828\pi$
$523$	−16.2641	−	28.1702i	−0.711179	−	1.23180i	0.253236	−	0.967405i	$-0.418505\pi$
$524$	4.17984	−	7.23970i	0.182597	−	0.316268i
$525$		0			0
$526$	−0.848970	−	1.47046i	−0.0370168	−	0.0641150i
$527$	5.59166	−	9.68504i	0.243577	−	0.421887i
$528$	17.2110	+	20.1660i	0.749012	+	0.877612i
$529$	−1.63160	−	2.82601i	−0.0709391	−	0.122870i
$530$	−3.29913	−	5.71426i	−0.143305	−	0.248211i
$531$	−16.9891	+	6.50767i	−0.737266	+	0.282409i
$532$		0			0
$533$	18.8187	−	32.5950i	0.815130	−	1.41185i
$534$	1.35387	+	1.58632i	0.0585879	+	0.0686470i
$535$	10.2544			0.443336
$536$	−7.79071			−0.336507
$537$	4.38631	−	12.3726i	0.189283	−	0.533917i
$538$	−1.96457	+	3.40274i	−0.0846987	+	0.146702i
$539$		0			0
$540$	0.657014	+	26.1563i	0.0282734	+	1.12559i
$541$	−7.61109	−	13.1828i	−0.327226	−	0.566773i	0.654734	−	0.755859i	$-0.272781\pi$
$541$	−7.61109	−	13.1828i	−0.327226	−	0.566773i	−0.981960	+	0.189087i	$0.939447\pi$
$542$	1.51819	+	2.62959i	0.0652119	+	0.112950i
$543$	0.696860	−	0.128899i	0.0299051	−	0.00553159i
$544$	2.36203	−	4.09116i	0.101271	−	0.175407i
$545$	−9.41234	−	16.3027i	−0.403180	−	0.698329i
$546$		0			0
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	−1.00000		0.000339172i	$-0.999892\pi$
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	0.500294	+	0.865856i	$0.333225\pi$
$548$	20.0007	+	34.6422i	0.854387	+	1.47984i
$549$	22.3727	−	8.56984i	0.954845	−	0.365752i
$550$	−0.858685	+	1.48729i	−0.0366144	+	0.0634181i
$551$	−15.2040			−0.647711
$552$	2.79637	−	7.88779i	0.119021	−	0.335726i
$553$		0			0
$554$	0.0990521	+	0.171563i	0.00420832	+	0.00728902i
$555$	−7.32846	+	1.35556i	−0.311076	+	0.0575401i
$556$	15.3107	+	26.5189i	0.649319	+	1.12465i
$557$	−13.8337	+	23.9606i	−0.586151	+	1.01524i	0.408580	+	0.912723i	$0.366024\pi$
$557$	−13.8337	+	23.9606i	−0.586151	+	1.01524i	−0.994731	+	0.102521i	$0.967309\pi$
$558$	4.37840	−	1.67714i	0.185352	−	0.0709990i
$559$	6.11465			0.258622
$560$		0			0
$561$	12.1871	−	2.25427i	0.514542	−	0.0951755i
$562$	−0.624075	+	1.08093i	−0.0263250	+	0.0455963i
$563$	8.55824			0.360687			0.180343	−	0.983604i	$-0.442279\pi$
$563$	8.55824			0.360687			0.180343	+	0.983604i	$0.442279\pi$
$564$	−30.8996	+	5.71554i	−1.30111	+	0.240668i
$565$	17.9589			0.755536
$566$	1.75855			0.0739175
$567$		0			0
$568$	−5.88237			−0.246819
$569$	13.7278			0.575498			0.287749	−	0.957706i	$-0.407093\pi$
$569$	13.7278			0.575498			0.287749	+	0.957706i	$0.407093\pi$
$570$	−7.55307	+	1.39710i	−0.316363	+	0.0585181i
$571$	10.7174			0.448508			0.224254	−	0.974531i	$-0.428005\pi$
$571$	10.7174			0.448508			0.224254	+	0.974531i	$0.428005\pi$
$572$	−14.9622	+	25.9153i	−0.625600	+	1.08357i
$573$	−27.2916	+	5.04816i	−1.14012	+	0.210890i
$574$		0			0
$575$	−8.80111			−0.367032
$576$	−18.6586	+	7.14713i	−0.777440	+	0.297797i
$577$	22.8177	−	39.5214i	0.949912	−	1.64530i	0.204307	−	0.978907i	$-0.434506\pi$
$577$	22.8177	−	39.5214i	0.949912	−	1.64530i	0.745605	−	0.666389i	$-0.232161\pi$
$578$	1.68250	+	2.91417i	0.0699827	+	0.121214i
$579$	21.0754	−	3.89834i	0.875863	−	0.162010i
$580$	−5.34950	−	9.26560i	−0.222126	−	0.384733i
$581$		0			0
$582$	−0.423945	+	1.19583i	−0.0175731	+	0.0495689i
$583$	44.5231			1.84396
$584$	−3.37323	+	5.84260i	−0.139585	+	0.241768i
$585$	−26.7427	+	10.2437i	−1.10567	+	0.423527i
$586$	0.935657	+	1.62060i	0.0386516	+	0.0669466i
$587$	5.10948	−	8.84988i	0.210891	−	0.365274i	−0.741103	−	0.671392i	$-0.765697\pi$
$587$	5.10948	−	8.84988i	0.210891	−	0.365274i	0.951994	+	0.306118i	$0.0990302\pi$
$588$		0			0
$589$	−23.3840	−	40.5023i	−0.963521	−	1.66887i
$590$	1.87919	−	3.25486i	0.0773652	−	0.134000i
$591$	−39.3465	+	7.27798i	−1.61850	+	0.299376i
$592$	−3.03831	−	5.26250i	−0.124874	−	0.216287i
$593$	−5.69804	−	9.86929i	−0.233990	−	0.405283i	0.724988	−	0.688761i	$-0.241845\pi$
$593$	−5.69804	−	9.86929i	−0.233990	−	0.405283i	−0.958979	+	0.283478i	$0.908512\pi$
$594$	4.56382	+	2.48426i	0.187256	+	0.101930i
$595$		0			0
$596$	5.89411	−	10.2089i	0.241432	−	0.418173i
$597$	3.90451	−	11.0136i	0.159801	−	0.450755i
$598$	4.51346			0.184569
$599$	−34.5746			−1.41268			−0.706339	−	0.707874i	$-0.749655\pi$
$599$	−34.5746			−1.41268			−0.706339	+	0.707874i	$0.749655\pi$
$600$	−1.82061	−	2.13320i	−0.0743261	−	0.0870873i
$601$	19.4207	−	33.6376i	0.792187	−	1.37211i	−0.132423	−	0.991193i	$-0.542276\pi$
$601$	19.4207	−	33.6376i	0.792187	−	1.37211i	0.924610	−	0.380915i	$-0.124391\pi$
$602$		0			0
$603$	23.1494	−	8.86734i	0.942716	−	0.361106i
$604$	4.36032	+	7.55230i	0.177419	+	0.307299i
$605$	−8.40861	−	14.5641i	−0.341858	−	0.592116i
$606$	2.98439	+	3.49679i	0.121233	+	0.142048i
$607$	20.6662	−	35.7950i	0.838817	−	1.45287i	−0.0520683	−	0.998644i	$-0.516581\pi$
$607$	20.6662	−	35.7950i	0.838817	−	1.45287i	0.890885	−	0.454229i	$-0.150085\pi$
$608$	−9.87788	−	17.1090i	−0.400601	−	0.693861i
$609$		0			0
$610$	−2.47468	+	4.28627i	−0.100197	+	0.173546i
$611$	−17.1969	−	29.7858i	−0.695710	−	1.20501i
$612$	−1.56711	+	9.84903i	−0.0633467	+	0.398123i
$613$	14.3285	−	24.8176i	0.578721	−	1.00237i	−0.416905	−	0.908950i	$-0.636885\pi$
$613$	14.3285	−	24.8176i	0.578721	−	1.00237i	0.995626	−	0.0934244i	$-0.0297813\pi$
$614$	−5.42114			−0.218779
$615$	−45.1088	+	8.34384i	−1.81896	+	0.336456i
$616$		0			0
$617$	16.8518	+	29.1883i	0.678430	+	1.17508i	0.975454	+	0.220205i	$0.0706726\pi$
$617$	16.8518	+	29.1883i	0.678430	+	1.17508i	−0.297024	+	0.954870i	$0.595994\pi$
$618$	−1.10520	+	3.11747i	−0.0444577	+	0.125403i
$619$	−0.719036	−	1.24541i	−0.0289005	−	0.0500571i	0.851213	−	0.524820i	$-0.175867\pi$
$619$	−0.719036	−	1.24541i	−0.0289005	−	0.0500571i	−0.880114	+	0.474763i	$0.842534\pi$
$620$	16.4552	−	28.5013i	0.660859	−	1.14464i
$621$	0.668677	+	26.6207i	0.0268331	+	1.06825i
$622$	7.72789			0.309860
$623$		0			0
$624$	−15.1580	−	17.7605i	−0.606806	−	0.710990i
$625$	15.3187	−	26.5328i	0.612750	−	1.06131i
$626$	5.81538			0.232429
$627$	17.3187	−	48.8514i	0.691644	−	1.95094i
$628$	1.99900			0.0797686
$629$	−2.84071			−0.113266
$630$		0			0
$631$	−30.7680			−1.22486			−0.612428	−	0.790527i	$-0.709807\pi$
$631$	−30.7680			−1.22486			−0.612428	+	0.790527i	$0.709807\pi$
$632$	9.26647			0.368600
$633$	18.9864	+	22.2462i	0.754640	+	0.884206i
$634$	1.22872			0.0487987
$635$	−11.8070	+	20.4503i	−0.468547	+	0.811547i
$636$	−11.9710	+	33.7670i	−0.474682	+	1.33895i
$637$		0			0
$638$	−2.12476			−0.0841202
$639$	17.4789	−	6.69528i	0.691456	−	0.264861i
$640$	9.21946	−	15.9686i	0.364431	−	0.631213i
$641$	−4.61956	−	8.00132i	−0.182462	−	0.316033i	0.760257	−	0.649623i	$-0.225073\pi$
$641$	−4.61956	−	8.00132i	−0.182462	−	0.316033i	−0.942718	+	0.333590i	$0.891740\pi$
$642$	1.06379	+	1.24644i	0.0419845	+	0.0491929i
$643$	12.7795	+	22.1348i	0.503976	+	0.872912i	0.999989	+	0.00459728i	$0.00146337\pi$
$643$	12.7795	+	22.1348i	0.503976	+	0.872912i	−0.496013	+	0.868315i	$0.665203\pi$
$644$		0			0
$645$	−4.83818	−	5.66886i	−0.190503	−	0.223211i
$646$	−2.92777			−0.115192
$647$	−14.1556	+	24.5181i	−0.556512	+	0.963908i	0.441272	+	0.897374i	$0.354528\pi$
$647$	−14.1556	+	24.5181i	−0.556512	+	0.963908i	−0.997784	+	0.0665343i	$0.978806\pi$
$648$	−6.31393	+	5.66886i	−0.248035	+	0.222694i
$649$	12.6803	+	21.9629i	0.497744	+	0.862118i
$650$	0.756258	−	1.30988i	0.0296629	−	0.0513776i
$651$		0			0
$652$	6.63323	+	11.4891i	0.259778	+	0.449948i
$653$	4.17511	−	7.23150i	0.163385	−	0.282990i	−0.772696	−	0.634776i	$-0.781092\pi$
$653$	4.17511	−	7.23150i	0.163385	−	0.282990i	0.936080	+	0.351786i	$0.114426\pi$
$654$	1.00517	−	2.83532i	0.0393054	−	0.110870i
$655$	−5.57605	−	9.65801i	−0.217874	−	0.377370i
$656$	−18.7017	−	32.3922i	−0.730177	−	1.26470i
$657$	3.37323	−	21.2001i	0.131602	−	0.827096i
$658$		0			0
$659$	16.7862	−	29.0745i	0.653897	−	1.13258i	−0.328272	−	0.944583i	$-0.606466\pi$
$659$	16.7862	−	29.0745i	0.653897	−	1.13258i	0.982169	−	0.188000i	$-0.0602005\pi$
$660$	35.8646	−	6.63392i	1.39603	−	0.258225i
$661$	−16.9534			−0.659410			−0.329705	−	0.944084i	$-0.606949\pi$
$661$	−16.9534			−0.659410			−0.329705	+	0.944084i	$0.606949\pi$
$662$	−2.79725			−0.108718
$663$	−10.7334	+	1.98537i	−0.416851	+	0.0771055i
$664$	−3.25021	+	5.62952i	−0.126133	+	0.218468i
$665$		0			0
$666$	−0.925025	−	0.750160i	−0.0358440	−	0.0290681i
$667$	−5.44445	−	9.43007i	−0.210810	−	0.365134i
$668$	−17.4799	−	30.2760i	−0.676316	−	1.17141i
$669$	2.60520	−	7.34856i	0.100723	−	0.284112i
$670$	−2.56059	+	4.43507i	−0.0989242	+	0.171342i
$671$	−16.6984	−	28.9225i	−0.644636	−	1.11654i
$672$		0			0
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	−0.0190299	−	0.999819i	$-0.506058\pi$
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	0.875384	−	0.483429i	$-0.160609\pi$
$674$	4.02859	+	6.97772i	0.155175	+	0.268772i
$675$	7.83777	+	4.26639i	0.301676	+	0.164213i
$676$	0.549100	−	0.951068i	0.0211192	−	0.0365796i
$677$	−14.3736			−0.552423			−0.276212	−	0.961097i	$-0.589079\pi$
$677$	−14.3736			−0.552423			−0.276212	+	0.961097i	$0.589079\pi$
$678$	1.86306	+	2.18293i	0.0715502	+	0.0838349i
$679$		0			0
$680$	−2.09058	−	3.62099i	−0.0801701	−	0.138859i
$681$	6.81875	+	7.98947i	0.261295	+	0.306157i
$682$	−3.26793	−	5.66021i	−0.125135	−	0.216741i
$683$	16.1546	−	27.9806i	0.618138	−	1.07065i	−0.371687	−	0.928358i	$-0.621220\pi$
$683$	16.1546	−	27.9806i	0.618138	−	1.07065i	0.989825	−	0.142289i	$-0.0454462\pi$
$684$	32.3931	+	26.2696i	1.23858	+	1.00444i
$685$	53.3632			2.03890
$686$		0			0
$687$	6.39480	−	18.0380i	0.243977	−	0.688192i
$688$	3.03831	−	5.26250i	0.115834	−	0.200631i
$689$	−39.2122			−1.49387
$690$	−3.57124	−	4.18440i	−0.135955	−	0.159297i
$691$	−28.9962			−1.10307			−0.551533	−	0.834153i	$-0.685957\pi$
$691$	−28.9962			−1.10307			−0.551533	+	0.834153i	$0.685957\pi$
$692$	−1.61323			−0.0613259
$693$		0			0
$694$	6.53078			0.247905
$695$	40.8500			1.54953
$696$	1.15939	−	3.27033i	0.0439467	−	0.123962i
$697$	−17.4854			−0.662306
$698$	2.73999	−	4.74580i	0.103710	−	0.179631i
$699$	−9.15093	−	10.7221i	−0.346120	−	0.405546i
$700$		0			0
$701$	−26.3912			−0.996783			−0.498392	−	0.866952i	$-0.666076\pi$
$701$	−26.3912			−0.996783			−0.498392	+	0.866952i	$0.666076\pi$
$702$	−4.01943	−	2.18793i	−0.151704	−	0.0825780i
$703$	−5.93984	+	10.2881i	−0.224025	+	0.388023i
$704$	13.9263	+	24.1210i	0.524866	+	0.909095i
$705$	−14.0074	+	39.5109i	−0.527548	+	1.48807i
$706$	1.22782	+	2.12664i	0.0462095	+	0.0800372i
$707$		0			0
$708$	−20.0663	+	3.71170i	−0.754139	+	0.139494i
$709$	−7.88564			−0.296151			−0.148076	−	0.988976i	$-0.547308\pi$
$709$	−7.88564			−0.296151			−0.148076	+	0.988976i	$0.547308\pi$
$710$	−1.93337	+	3.34870i	−0.0725581	+	0.125674i
$711$	−27.5345	+	10.5470i	−1.03262	+	0.395545i
$712$	2.37373	+	4.11142i	0.0889592	+	0.154082i
$713$	16.7473	−	29.0073i	0.627193	−	1.08633i
$714$		0			0
$715$	19.9601	+	34.5718i	0.746464	+	1.29291i
$716$	7.36225	−	12.7518i	0.275140	−	0.476557i
$717$	23.7953	+	27.8808i	0.888652	+	1.04123i
$718$	−1.20765	−	2.09172i	−0.0450693	−	0.0780623i
$719$	16.5754	+	28.7095i	0.618159	+	1.07068i	0.989822	+	0.142314i	$0.0454544\pi$
$719$	16.5754	+	28.7095i	0.618159	+	1.07068i	−0.371663	+	0.928368i	$0.621212\pi$
$720$	−4.47200	+	28.1058i	−0.166662	+	1.04744i
$721$		0			0
$722$	−3.85021	+	6.66877i	−0.143290	+	0.248186i
$723$	−15.3948	−	18.0380i	−0.572539	−	0.670840i
$724$	0.794919			0.0295429
$725$	−3.64900			−0.135521
$726$	0.897982	−	2.53296i	0.0333273	−	0.0940070i
$727$	−16.5502	+	28.6658i	−0.613814	+	1.06316i	0.376777	+	0.926304i	$0.377032\pi$
$727$	−16.5502	+	28.6658i	−0.613814	+	1.06316i	−0.990591	+	0.136853i	$0.956301\pi$
$728$		0			0
$729$	12.3090	−	24.0310i	0.455890	−	0.890036i
$730$	2.21737	+	3.84060i	0.0820685	+	0.142147i
$731$	−1.42035	−	2.46012i	−0.0525337	−	0.0909910i
$732$	26.4250	−	4.88787i	0.976697	−	0.180661i
$733$	22.2795	−	38.5892i	0.822911	−	1.42532i	−0.0805946	−	0.996747i	$-0.525682\pi$
$733$	22.2795	−	38.5892i	0.822911	−	1.42532i	0.903505	−	0.428577i	$-0.140985\pi$
$734$	−0.929636	−	1.61018i	−0.0343135	−	0.0594327i
$735$		0			0
$736$	7.07442	−	12.2533i	0.260767	−	0.451661i
$737$	−17.2781	−	29.9266i	−0.636448	−	1.10236i
$738$	−5.69380	−	4.61745i	−0.209592	−	0.169971i
$739$	−19.9045	+	34.4756i	−0.732199	+	1.26821i	0.223742	+	0.974648i	$0.428173\pi$
$739$	−19.9045	+	34.4756i	−0.732199	+	1.26821i	−0.955941	+	0.293558i	$0.905161\pi$
$740$	−8.35969			−0.307308
$741$	−15.2529	+	43.0242i	−0.560329	+	1.58053i
$742$		0			0
$743$	−5.37072	−	9.30237i	−0.197033	−	0.341271i	0.750532	−	0.660834i	$-0.229797\pi$
$743$	−5.37072	−	9.30237i	−0.197033	−	0.341271i	−0.947565	+	0.319563i	$0.896464\pi$
$744$	10.4951	−	1.94129i	0.384769	−	0.0711712i
$745$	−7.86295	−	13.6190i	−0.288076	−	0.498962i
$746$	−2.88276	+	4.99309i	−0.105545	+	0.182810i
$747$	3.25021	−	20.4270i	0.118919	−	0.747385i
$748$	13.9021			0.508310
$749$		0			0
$750$	3.46496	−	0.640919i	0.126523	−	0.0234031i
$751$	−9.85705	+	17.0729i	−0.359689	+	0.622999i	−0.987909	−	0.155036i	$-0.950450\pi$
$751$	−9.85705	+	17.0729i	−0.359689	+	0.622999i	0.628220	+	0.778036i	$0.283784\pi$
$752$	−34.1797			−1.24641
$753$	25.8948	−	4.78980i	0.943659	−	0.174550i
$754$	1.87131			0.0681492
$755$	11.6336			0.423391
$756$		0			0
$757$	35.3549			1.28499			0.642497	−	0.766288i	$-0.277898\pi$
$757$	35.3549			1.28499			0.642497	+	0.766288i	$0.277898\pi$
$758$	−3.19424			−0.116020
$759$	36.5012	−	6.75168i	1.32491	−	0.245070i
$760$	−17.4854			−0.634261
$761$	19.5572	−	33.8741i	0.708948	−	1.22793i	−0.256300	−	0.966597i	$-0.582503\pi$
$761$	19.5572	−	33.8741i	0.708948	−	1.22793i	0.965248	−	0.261336i	$-0.0841632\pi$
$762$	−3.71063	+	0.686360i	−0.134422	+	0.0248642i
$763$		0			0
$764$	−31.1319			−1.12631
$765$	10.3334	+	8.37997i	0.373604	+	0.302978i
$766$	−1.10480	+	1.91357i	−0.0399180	+	0.0691399i
$767$	−11.1677	−	19.3430i	−0.403243	−	0.698437i
$768$	−19.7893	+	3.66045i	−0.714085	+	0.132085i
$769$	18.9240	+	32.7773i	0.682415	+	1.18198i	0.974242	+	0.225507i	$0.0724038\pi$
$769$	18.9240	+	32.7773i	0.682415	+	1.18198i	−0.291826	+	0.956471i	$0.594263\pi$
$770$		0			0
$771$	−14.8285	+	41.8270i	−0.534034	+	1.50636i
$772$	24.0410			0.865255
$773$	−14.9133	+	25.8305i	−0.536393	+	0.929059i	0.462702	+	0.886514i	$0.346880\pi$
$773$	−14.9133	+	25.8305i	−0.536393	+	0.929059i	−0.999095	+	0.0425453i	$0.986453\pi$
$774$	0.187145	−	1.17617i	0.00672679	−	0.0422767i
$775$	−5.61224	−	9.72068i	−0.201598	−	0.349177i
$776$	−1.44409	+	2.50124i	−0.0518399	+	0.0897894i
$777$		0			0
$778$	−1.24923	−	2.16373i	−0.0447870	−	0.0775734i
$779$	−36.5614	+	63.3263i	−1.30995	+	2.26890i
$780$	−31.5865	+	5.84260i	−1.13098	+	0.209199i
$781$	−13.0458	−	22.5960i	−0.466817	−	0.808550i
$782$	−1.04842	−	1.81591i	−0.0374913	−	0.0649369i
$783$	0.277238	+	11.0371i	0.00990768	+	0.394434i
$784$		0			0
$785$	1.33336	−	2.30946i	0.0475898	−	0.0824280i
$786$	0.595485	−	1.67970i	0.0212402	−	0.0599129i
$787$	17.6206			0.628107			0.314053	−	0.949405i	$-0.398313\pi$
$787$	17.6206			0.628107			0.314053	+	0.949405i	$0.398313\pi$
$788$	−44.8832			−1.59890
$789$	7.98407	+	9.35488i	0.284241	+	0.333043i
$790$	3.04563	−	5.27518i	0.108359	−	0.187683i
$791$		0			0
$792$	9.18715	+	7.45043i	0.326451	+	0.264739i
$793$	14.7066	+	25.4725i	0.522246	+	0.904556i
$794$	−0.0489195	−	0.0847311i	−0.00173609	−	0.00300699i
$795$	31.0264	+	36.3534i	1.10039	+	1.28932i
$796$	6.55357	−	11.3511i	0.232285	−	0.402330i
$797$	−5.06056	−	8.76515i	−0.179254	−	0.310477i	0.762371	−	0.647140i	$-0.224035\pi$
$797$	−5.06056	−	8.76515i	−0.179254	−	0.310477i	−0.941625	+	0.336663i	$0.890702\pi$
$798$		0			0
$799$	−7.98921	+	13.8377i	−0.282638	+	0.489543i
$800$	−2.37072	−	4.10621i	−0.0838177	−	0.145177i
$801$	−11.7329	−	9.51495i	−0.414562	−	0.336194i
$802$	−1.82365	+	3.15865i	−0.0643953	+	0.111536i
$803$	−29.9244			−1.05601
$804$	27.3424	−	5.05756i	0.964291	−	0.178366i
$805$		0			0
$806$	2.87812	+	4.98504i	0.101377	+	0.175591i
$807$	9.50972	−	26.8243i	0.334758	−	0.944260i
$808$	5.23250	+	9.06295i	0.184079	+	0.318834i
$809$	23.5735	−	40.8305i	0.828799	−	1.43552i	−0.0701816	−	0.997534i	$-0.522358\pi$
$809$	23.5735	−	40.8305i	0.828799	−	1.43552i	0.898981	−	0.437988i	$-0.144309\pi$
$810$	1.15193	+	5.45757i	0.0404748	+	0.191759i
$811$	21.0577			0.739435			0.369717	−	0.929144i	$-0.379454\pi$
$811$	21.0577			0.739435			0.369717	+	0.929144i	$0.379454\pi$
$812$		0			0
$813$	−14.2777	−	16.7291i	−0.500742	−	0.586715i
$814$	−0.830095	+	1.43777i	−0.0290948	+	0.0503937i
$815$	17.6979			0.619931
$816$	−3.62463	+	10.2241i	−0.126887	+	0.357915i
$817$	−11.8797			−0.415617
$818$	1.46504			0.0512238
$819$		0			0
$820$	−51.4563			−1.79693
$821$	11.1604			0.389499			0.194750	−	0.980853i	$-0.437611\pi$
$821$	11.1604			0.389499			0.194750	+	0.980853i	$0.437611\pi$
$822$	5.53590	+	6.48638i	0.193087	+	0.226238i
$823$	9.43474			0.328874			0.164437	−	0.986388i	$-0.447419\pi$
$823$	9.43474			0.328874			0.164437	+	0.986388i	$0.447419\pi$
$824$	−3.76466	+	6.52059i	−0.131148	+	0.227156i
$825$	4.15656	−	11.7245i	0.144713	−	0.408195i
$826$		0			0
$827$	17.2646			0.600348			0.300174	−	0.953884i	$-0.402955\pi$
$827$	17.2646			0.600348			0.300174	+	0.953884i	$0.402955\pi$
$828$	−4.69359	+	29.4984i	−0.163114	+	1.02514i
$829$	24.2263	−	41.9612i	0.841415	−	1.45737i	−0.0472838	−	0.998881i	$-0.515057\pi$
$829$	24.2263	−	41.9612i	0.841415	−	1.45737i	0.888699	−	0.458492i	$-0.151610\pi$
$830$	2.13650	+	3.70053i	0.0741591	+	0.128447i
$831$	−0.931528	−	1.09146i	−0.0323143	−	0.0378625i
$832$	−12.2651	−	21.2438i	−0.425215	−	0.736495i
$833$		0			0
$834$	4.23779	+	4.96538i	0.146743	+	0.171937i
$835$	−46.6375			−1.61396
$836$	29.0688	−	50.3487i	1.00537	−	1.74135i
$837$	−28.9757	+	17.7138i	−1.00155	+	0.612280i
$838$	0.186860	+	0.323651i	0.00645497	+	0.0111803i
$839$	7.43429	−	12.8766i	0.256660	−	0.444548i	−0.708685	−	0.705525i	$-0.750711\pi$
$839$	7.43429	−	12.8766i	0.256660	−	0.444548i	0.965345	+	0.260977i	$0.0840446\pi$
$840$		0			0
$841$	12.2427	+	21.2050i	0.422162	+	0.731206i
$842$	−2.78139	+	4.81750i	−0.0958529	+	0.166022i
$843$	3.02090	−	8.52113i	0.104045	−	0.293483i
$844$	16.4029	+	28.4106i	0.564610	+	0.977934i
$845$	−0.732518	−	1.26876i	−0.0251994	−	0.0436466i
$846$	−6.25574	+	2.39625i	−0.215077	+	0.0823848i
$847$		0			0
$848$	−19.4841	+	33.7475i	−0.669088	+	1.15889i
$849$	−12.5253	+	2.31683i	−0.429868	+	0.0795132i
$850$	−0.702674			−0.0241015
$851$	−8.50808			−0.291653
$852$	20.6448	−	3.81870i	0.707281	−	0.130827i
$853$	−3.99900	+	6.92648i	−0.136923	+	0.237158i	−0.926331	−	0.376712i	$-0.877055\pi$
$853$	−3.99900	+	6.92648i	−0.136923	+	0.237158i	0.789407	+	0.613870i	$0.210388\pi$
$854$		0			0
$855$	51.9562	−	19.9018i	1.77687	−	0.680626i
$856$	1.86513	+	3.23050i	0.0637488	+	0.110416i
$857$	21.5661	+	37.3536i	0.736684	+	1.27597i	0.953980	+	0.299869i	$0.0969429\pi$
$857$	21.5661	+	37.3536i	0.736684	+	1.27597i	−0.217296	+	0.976106i	$0.569724\pi$
$858$	−2.13160	+	6.01266i	−0.0727716	+	0.205269i
$859$	1.22180	−	2.11621i	0.0416871	−	0.0722042i	−0.844429	−	0.535667i	$-0.820060\pi$
$859$	1.22180	−	2.11621i	0.0416871	−	0.0722042i	0.886116	+	0.463463i	$0.153393\pi$
$860$	−4.17984	−	7.23970i	−0.142531	−	0.246872i
$861$		0			0
$862$	−0.120250	+	0.208279i	−0.00409573	+	0.00709401i
$863$	−12.8594	−	22.2731i	−0.437738	−	0.758185i	0.559777	−	0.828644i	$-0.310887\pi$
$863$	−12.8594	−	22.2731i	−0.437738	−	0.758185i	−0.997515	+	0.0704589i	$0.977554\pi$
$864$	−12.2399	+	7.48268i	−0.416410	+	0.254566i
$865$	−1.07605	+	1.86378i	−0.0365870	+	0.0633705i
$866$	−3.13422			−0.106505
$867$	−15.8229	−	18.5396i	−0.537375	−	0.629639i
$868$		0			0
$869$	20.5510	+	35.5954i	0.697146	+	1.20749i
$870$	−1.48066	−	1.73488i	−0.0501992	−	0.0588180i
$871$	15.2171	+	26.3568i	0.515612	+	0.893067i
$872$	3.42395	−	5.93045i	0.115949	−	0.200830i
$873$	1.44409	−	9.07587i	0.0488751	−	0.307172i
$874$	−8.76884			−0.296611
$875$		0			0
$876$	8.04583	−	22.6951i	0.271843	−	0.766796i
$877$	10.9795	−	19.0170i	0.370751	−	0.642160i	−0.618930	−	0.785446i	$-0.712434\pi$
$877$	10.9795	−	19.0170i	0.370751	−	0.642160i	0.989681	+	0.143286i	$0.0457670\pi$
$878$	−4.45106			−0.150216
$879$	−8.79931	−	10.3101i	−0.296794	−	0.347751i
$880$	39.6718			1.33733
$881$	−35.0576			−1.18112			−0.590560	−	0.806994i	$-0.701093\pi$
$881$	−35.0576			−1.18112			−0.590560	+	0.806994i	$0.701093\pi$
$882$		0			0
$883$	26.3009			0.885097			0.442549	−	0.896744i	$-0.354074\pi$
$883$	26.3009			0.885097			0.442549	+	0.896744i	$0.354074\pi$
$884$	−12.2438			−0.411803
$885$	−9.09644	+	25.6586i	−0.305774	+	0.862503i
$886$	−0.267580			−0.00898954
$887$	−23.9090	+	41.4116i	−0.802785	+	1.39046i	0.114991	+	0.993366i	$0.463316\pi$
$887$	−23.9090	+	41.4116i	−0.802785	+	1.39046i	−0.917776	+	0.397098i	$0.870017\pi$
$888$	−1.75999	−	2.06217i	−0.0590615	−	0.0692019i
$889$		0			0
$890$	3.12071			0.104607
$891$	−35.7788	−	11.6815i	−1.19864	−	0.391345i
$892$	4.37272	−	7.57378i	0.146410	−	0.253589i
$893$	33.4104	+	57.8685i	1.11804	+	1.93650i
$894$	0.839710	−	2.36859i	0.0280841	−	0.0792175i
$895$	−9.82150	−	17.0113i	−0.328296	−	0.568626i
$896$		0			0
$897$	−32.1472	+	5.94631i	−1.07336	+	0.198542i
$898$	−9.43147			−0.314732
$899$	6.94357	−	12.0266i	0.231581	−	0.401110i
$900$	7.77446	+	6.30479i	0.259149	+	0.210160i
$901$	9.10848	+	15.7764i	0.303448	+	0.525587i
$902$	−5.10948	+	8.84988i	−0.170127	+	0.294669i
$903$		0			0
$904$	3.26647	+	5.65769i	0.108641	+	0.188172i
$905$	0.530225	−	0.918376i	0.0176253	−	0.0305279i
$906$	1.20687	+	1.41409i	0.0400957	+	0.0469798i
$907$	9.55718	+	16.5535i	0.317341	+	0.549651i	0.979932	−	0.199330i	$-0.0638767\pi$
$907$	9.55718	+	16.5535i	0.317341	+	0.549651i	−0.662591	+	0.748981i	$0.730543\pi$
$908$	5.89092	+	10.2034i	0.195497	+	0.338611i
$909$	−25.8633	−	20.9741i	−0.857831	−	0.695669i
$910$		0			0
$911$	9.02928	−	15.6392i	0.299153	−	0.518149i	−0.676789	−	0.736177i	$-0.736629\pi$
$911$	9.02928	−	15.6392i	0.299153	−	0.518149i	0.975942	+	0.218028i	$0.0699625\pi$
$912$	29.4493	+	34.5055i	0.975163	+	1.14259i
$913$	−28.8330			−0.954234
$914$	−8.18770			−0.270825
$915$	11.9789	−	33.7893i	0.396012	−	1.11704i
$916$	10.7334	−	18.5908i	0.354642	−	0.614258i
$917$		0			0
$918$	0.0533866	+	2.12537i	0.00176202	+	0.0701478i
$919$	−8.10464	−	14.0377i	−0.267348	−	0.463060i	0.700828	−	0.713330i	$-0.252814\pi$
$919$	−8.10464	−	14.0377i	−0.267348	−	0.463060i	−0.968176	+	0.250270i	$0.919481\pi$
$920$	−6.26141	−	10.8451i	−0.206433	−	0.357552i
$921$	38.6122	−	7.14215i	1.27231	−	0.235342i
$922$	2.43757	−	4.22199i	0.0802771	−	0.139044i
$923$	11.4897	+	19.9007i	0.378187	+	0.655039i
$924$		0			0
$925$	−1.42558	+	2.46918i	−0.0468728	+	0.0811860i
$926$	−0.814099	−	1.41006i	−0.0267529	−	0.0463375i
$927$	3.76466	−	23.6603i	0.123648	−	0.777105i
$928$	2.93310	−	5.08029i	0.0962839	−	0.166769i
$929$	22.6829			0.744203			0.372102	−	0.928192i	$-0.378637\pi$
$929$	22.6829			0.744203			0.372102	+	0.928192i	$0.378637\pi$
$930$	2.34431	−	6.61266i	0.0768730	−	0.216838i
$931$		0			0
$932$	−7.90576	−	13.6932i	−0.258962	−	0.448535i
$933$	−55.0420	+	10.1812i	−1.80199	+	0.333317i
$934$	2.96407	+	5.13392i	0.0969873	+	0.167987i
$935$	9.27292	−	16.0612i	0.303257	−	0.525256i
$936$	−8.09127	−	6.56171i	−0.264471	−	0.214476i
$937$	−51.2933			−1.67568			−0.837840	−	0.545915i	$-0.816182\pi$
$937$	−51.2933			−1.67568			−0.837840	+	0.545915i	$0.816182\pi$
$938$		0			0
$939$	−41.4201	+	7.66154i	−1.35169	+	0.250025i
$940$	−23.5108	+	40.7219i	−0.766838	+	1.32820i
$941$	31.9318			1.04095			0.520474	−	0.853878i	$-0.325755\pi$
$941$	31.9318			1.04095			0.520474	+	0.853878i	$0.325755\pi$
$942$	0.419041	−	0.0775106i	0.0136531	−	0.00252543i
$943$	−52.3697			−1.70539
$944$	−22.1965			−0.722433
$945$		0			0
$946$	−1.66019			−0.0539774
$947$	−4.49330			−0.146013			−0.0730063	−	0.997331i	$-0.523259\pi$
$947$	−4.49330			−0.146013			−0.0730063	+	0.997331i	$0.523259\pi$
$948$	−32.5217	+	6.01559i	−1.05626	+	0.195377i
$949$	26.3549			0.855515
$950$	−1.46927	+	2.54485i	−0.0476695	+	0.0825660i
$951$	−8.75158	+	1.61879i	−0.283789	+	0.0524929i
$952$		0			0
$953$	1.14635			0.0371340			0.0185670	−	0.999828i	$-0.494090\pi$
$953$	1.14635			0.0371340			0.0185670	+	0.999828i	$0.494090\pi$
$954$	−1.20013	+	7.54261i	−0.0388556	+	0.244201i
$955$	−20.7655	+	35.9669i	−0.671956	+	1.16386i
$956$	20.5575	+	35.6066i	0.664876	+	1.15160i
$957$	15.1337	−	2.79929i	0.489202	−	0.0904883i
$958$	−1.32710	−	2.29860i	−0.0428765	−	0.0742643i
$959$		0			0
$960$	−9.99028	+	28.1799i	−0.322435	+	0.909501i
$961$	11.7174			0.377980
$962$	0.731078	−	1.26626i	0.0235709	−	0.0408260i
$963$	−9.21900	−	7.47626i	−0.297078	−	0.240919i
$964$	−13.3000	−	23.0363i	−0.428365	−	0.741950i
$965$	16.0358	−	27.7748i	0.516210	−	0.894102i
$966$		0			0
$967$	−24.8080	−	42.9686i	−0.797770	−	1.38178i	−0.921065	−	0.389408i	$-0.872680\pi$
$967$	−24.8080	−	42.9686i	−0.797770	−	1.38178i	0.123295	−	0.992370i	$-0.460654\pi$
$968$	3.05881	−	5.29802i	0.0983140	−	0.170285i
$969$	20.8531	−	3.85722i	0.669898	−	0.123912i
$970$	0.949266	+	1.64418i	0.0304791	+	0.0527913i
$971$	−2.56661	−	4.44550i	−0.0823664	−	0.142663i	0.821900	−	0.569632i	$-0.192914\pi$
$971$	−2.56661	−	4.44550i	−0.0823664	−	0.142663i	−0.904266	+	0.426970i	$0.859581\pi$
$972$	18.4794	−	23.9943i	0.592726	−	0.769619i
$973$		0			0
$974$	1.20013	−	2.07869i	0.0384546	−	0.0666054i
$975$	−3.66075	+	10.3260i	−0.117238	+	0.330695i
$976$	29.2302			0.935634
$977$	31.1948			0.998011			0.499006	−	0.866599i	$-0.333699\pi$
$977$	31.1948			0.998011			0.499006	+	0.866599i	$0.333699\pi$
$978$	1.83598	+	2.15121i	0.0587083	+	0.0687881i
$979$	−10.5288	+	18.2365i	−0.336503	+	0.582840i
$980$		0			0
$981$	−3.42395	+	21.5189i	−0.109318	+	0.687046i
$982$	1.48113	+	2.56538i	0.0472646	+	0.0818647i
$983$	10.1700	+	17.6150i	0.324374	+	0.561832i	0.981385	−	0.192049i	$-0.0615131\pi$
$983$	10.1700	+	17.6150i	0.324374	+	0.561832i	−0.657012	+	0.753880i	$0.728180\pi$
$984$	−10.8333	−	12.6933i	−0.345352	−	0.404647i
$985$	−29.9378	+	51.8539i	−0.953899	+	1.65220i
$986$	−0.434681	−	0.752890i	−0.0138431	−	0.0239769i
$987$		0			0
$988$	−25.6014	+	44.3429i	−0.814488	+	1.41074i
$989$	−4.25404	−	7.36821i	−0.135271	−	0.234296i
$990$	7.26091	−	2.78128i	0.230767	−	0.0883949i
$991$	6.48276	−	11.2285i	0.205932	−	0.356684i	−0.744498	−	0.667625i	$-0.767311\pi$
$991$	6.48276	−	11.2285i	0.205932	−	0.356684i	0.950429	+	0.310941i	$0.100644\pi$
$992$	18.0447			0.572919
$993$	19.9235	−	3.68527i	0.632252	−	0.116948i
$994$		0			0
$995$	−8.74269	−	15.1428i	−0.277162	−	0.480059i
$996$	7.75241	−	21.8674i	0.245644	−	0.692895i
$997$	−24.7408	−	42.8523i	−0.783548	−	1.35715i	−0.929863	−	0.367907i	$-0.880074\pi$
$997$	−24.7408	−	42.8523i	−0.783548	−	1.35715i	0.146314	−	0.989238i	$-0.453259\pi$
$998$	−1.22218	+	2.11688i	−0.0386875	+	0.0670086i
$999$	7.57681	+	4.12434i	0.239720	+	0.130488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.g.214.3		12
3.2	odd	2		1323.2.h.g.802.4		12
7.2	even	3		441.2.g.g.79.4		12
7.3	odd	6		441.2.f.g.295.3	yes	12
7.4	even	3		441.2.f.g.295.4	yes	12
7.5	odd	6		441.2.g.g.79.3		12
7.6	odd	2	inner	441.2.h.g.214.4		12
9.4	even	3		441.2.g.g.67.4		12
9.5	odd	6		1323.2.g.g.361.3		12
21.2	odd	6		1323.2.g.g.667.3		12
21.5	even	6		1323.2.g.g.667.4		12
21.11	odd	6		1323.2.f.g.883.4		12
21.17	even	6		1323.2.f.g.883.3		12
21.20	even	2		1323.2.h.g.802.3		12
63.4	even	3		441.2.f.g.148.4	yes	12
63.5	even	6		1323.2.h.g.226.3		12
63.11	odd	6		3969.2.a.bd.1.3		6
63.13	odd	6		441.2.g.g.67.3		12
63.23	odd	6		1323.2.h.g.226.4		12
63.25	even	3		3969.2.a.be.1.4		6
63.31	odd	6		441.2.f.g.148.3	✓	12
63.32	odd	6		1323.2.f.g.442.4		12
63.38	even	6		3969.2.a.bd.1.4		6
63.40	odd	6	inner	441.2.h.g.373.4		12
63.41	even	6		1323.2.g.g.361.4		12
63.52	odd	6		3969.2.a.be.1.3		6
63.58	even	3	inner	441.2.h.g.373.3		12
63.59	even	6		1323.2.f.g.442.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	63.31	odd	6
441.2.f.g.148.4	yes	12	63.4	even	3
441.2.f.g.295.3	yes	12	7.3	odd	6
441.2.f.g.295.4	yes	12	7.4	even	3
441.2.g.g.67.3		12	63.13	odd	6
441.2.g.g.67.4		12	9.4	even	3
441.2.g.g.79.3		12	7.5	odd	6
441.2.g.g.79.4		12	7.2	even	3
441.2.h.g.214.3		12	1.1	even	1	trivial
441.2.h.g.214.4		12	7.6	odd	2	inner
441.2.h.g.373.3		12	63.58	even	3	inner
441.2.h.g.373.4		12	63.40	odd	6	inner
1323.2.f.g.442.3		12	63.59	even	6
1323.2.f.g.442.4		12	63.32	odd	6
1323.2.f.g.883.3		12	21.17	even	6
1323.2.f.g.883.4		12	21.11	odd	6
1323.2.g.g.361.3		12	9.5	odd	6
1323.2.g.g.361.4		12	63.41	even	6
1323.2.g.g.667.3		12	21.2	odd	6
1323.2.g.g.667.4		12	21.5	even	6
1323.2.h.g.226.3		12	63.5	even	6
1323.2.h.g.226.4		12	63.23	odd	6
1323.2.h.g.802.3		12	21.20	even	2
1323.2.h.g.802.4		12	3.2	odd	2
3969.2.a.bd.1.3		6	63.11	odd	6
3969.2.a.bd.1.4		6	63.38	even	6
3969.2.a.be.1.3		6	63.52	odd	6
3969.2.a.be.1.4		6	63.25	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.239123 q^{2} +(-1.70316 + 0.315036i) q^{3} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 + 0.0753324i) q^{6} -0.942820 q^{8} +(2.80150 - 1.07311i) q^{9} +O(q^{10})\)	\(q+0.239123 q^{2} +(-1.70316 + 0.315036i) q^{3} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 + 0.0753324i) q^{6} -0.942820 q^{8} +(2.80150 - 1.07311i) q^{9} +(-0.309879 + 0.536725i) q^{10} +(-2.09097 - 3.62167i) q^{11} +(3.30893 - 0.612058i) q^{12} +(1.84155 + 3.18966i) q^{13} +(1.50000 - 4.23109i) q^{15} +3.66019 q^{16} +(0.855536 - 1.48183i) q^{17} +(0.669905 - 0.256606i) q^{18} +(-3.57780 - 6.19694i) q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(2.56238 - 4.43818i) q^{23} +(1.60577 - 0.297022i) q^{24} +(-0.858685 - 1.48729i) q^{25} +(0.440358 + 0.762722i) q^{26} +(-4.43334 + 2.71026i) q^{27} +(1.06238 - 1.84010i) q^{29} +(0.358685 - 1.01175i) q^{30} +6.53585 q^{31} +2.76088 q^{32} +(4.70221 + 5.50955i) q^{33} +(0.204579 - 0.354341i) q^{34} +(-5.44282 + 2.08486i) q^{36} +(-0.830095 - 1.43777i) q^{37} +(-0.855536 - 1.48183i) q^{38} +(-4.14132 - 4.85235i) q^{39} +(1.22180 - 2.11621i) q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(4.06238 + 7.03625i) q^{44} +(-1.22180 + 7.67877i) q^{45} +(0.612725 - 1.06127i) q^{46} -9.33824 q^{47} +(-6.23389 + 1.15309i) q^{48} +(-0.205332 - 0.355645i) q^{50} +(-0.990285 + 2.79332i) q^{51} +(-3.57780 - 6.19694i) q^{52} +(-5.32326 + 9.22015i) q^{53} +(-1.06012 + 0.648085i) q^{54} +10.8387 q^{55} +(8.04583 + 9.42724i) q^{57} +(0.254040 - 0.440011i) q^{58} -6.06429 q^{59} +(-2.91423 + 8.22024i) q^{60} +7.98597 q^{61} +1.56287 q^{62} -6.66019 q^{64} -9.54583 q^{65} +(1.12441 + 1.31746i) q^{66} +8.26320 q^{67} +(-1.66215 + 2.87893i) q^{68} +(-2.96596 + 8.36616i) q^{69} +6.23912 q^{71} +(-2.64132 + 1.01175i) q^{72} +(3.57780 - 6.19694i) q^{73} +(-0.198495 - 0.343803i) q^{74} +(1.93103 + 2.26257i) q^{75} +(6.95103 + 12.0395i) q^{76} +(-0.990285 - 1.16031i) q^{78} -9.82846 q^{79} +(-4.74322 + 8.21550i) q^{80} +(6.69686 - 6.01266i) q^{81} +(-1.22180 - 2.11621i) q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(0.198495 - 0.343803i) q^{86} +(-1.22971 + 3.46867i) q^{87} +(1.97141 + 3.41458i) q^{88} +(-2.51769 - 4.36077i) q^{89} +(-0.292160 + 1.83617i) q^{90} +(-4.97825 + 8.62258i) q^{92} +(-11.1316 + 2.05903i) q^{93} -2.23299 q^{94} +18.5458 q^{95} +(-4.70221 + 0.869775i) q^{96} +(1.53167 - 2.65294i) q^{97} +(-9.74433 - 7.90228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8	\( 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 8 q^{11} + 18 q^{15} + 12 q^{16} + 24 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} + 6 q^{30} + 32 q^{32} - 30 q^{36} + 6 q^{37} - 48 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} + 36 q^{51} - 28 q^{53} - 6 q^{57} - 18 q^{58} + 18 q^{60} - 48 q^{64} - 12 q^{65} + 76 q^{71} - 30 q^{72} - 36 q^{74} + 36 q^{78} - 12 q^{79} + 24 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} - 84 q^{93} + 120 q^{95} - 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 8 * q^11 + 18 * q^15 + 12 * q^16 + 24 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 + 6 * q^30 + 32 * q^32 - 30 * q^36 + 6 * q^37 - 48 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 + 36 * q^51 - 28 * q^53 - 6 * q^57 - 18 * q^58 + 18 * q^60 - 48 * q^64 - 12 * q^65 + 76 * q^71 - 30 * q^72 - 36 * q^74 + 36 * q^78 - 12 * q^79 + 24 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 - 84 * q^93 + 120 * q^95 - 48 * q^99

Introduction

L-functions

Modular forms

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