LMFDB - Embedded newform 441.2.g.g.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$-1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.g.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23025 + 2.13086i) q^{2} +(0.410052 - 1.68281i) q^{3} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} +(3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(-2.66372 - 1.38008i) q^{9} +O(q^{10})$	\(q+(-1.23025 + 2.13086i) q^{2} +(0.410052 - 1.68281i) q^{3} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} +(3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(-2.66372 - 1.38008i) q^{9} +(-4.50036 + 7.79485i) q^{10} +0.406421 q^{11} +(-6.73945 + 1.97146i) q^{12} +(-0.243398 + 0.421578i) q^{13} +(1.50000 - 6.15585i) q^{15} +(-2.16372 + 3.74766i) q^{16} +(2.42792 - 4.20528i) q^{17} +(6.21780 - 3.97816i) q^{18} +(-0.986757 - 1.70911i) q^{19} +(-7.41507 - 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +4.64766 q^{23} +(2.07244 - 8.50508i) q^{24} +8.38151 q^{25} +(-0.598883 - 1.03729i) q^{26} +(-3.41468 + 3.91663i) q^{27} +(-3.82383 - 6.62307i) q^{29} +(11.2719 + 10.7695i) q^{30} +(3.51360 + 6.08573i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(0.166653 - 0.683930i) q^{33} +(5.97391 + 10.3471i) q^{34} +(0.554084 + 12.1496i) q^{36} +(-1.16372 - 2.01561i) q^{37} +4.85584 q^{38} +(0.609631 + 0.582462i) q^{39} +18.4882 q^{40} +(3.75700 - 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +(-0.823832 - 1.42692i) q^{44} +(-9.74407 - 5.04844i) q^{45} +(-5.71780 + 9.90352i) q^{46} +(-3.15811 + 5.47002i) q^{47} +(5.41938 + 5.17786i) q^{48} +(-10.3114 + 17.8598i) q^{50} +(-6.08113 - 5.81012i) q^{51} +1.97351 q^{52} +(1.78434 - 3.09056i) q^{53} +(-4.14487 - 12.0946i) q^{54} +1.48672 q^{55} +(-3.28074 + 0.959702i) q^{57} +18.8171 q^{58} +(3.05919 + 5.29868i) q^{59} +(-24.6534 + 7.21177i) q^{60} +(-4.01356 + 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(-0.890369 + 1.54216i) q^{65} +(1.25233 + 1.19652i) q^{66} +(-1.80039 - 3.11836i) q^{67} -19.6860 q^{68} +(1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(-13.4626 - 6.97504i) q^{72} +(0.986757 - 1.70911i) q^{73} +5.72665 q^{74} +(3.43685 - 14.1045i) q^{75} +(-4.00040 + 6.92889i) q^{76} +(-1.99115 + 0.582462i) q^{78} +(-4.08113 + 7.06872i) q^{79} +(-7.91503 + 13.7092i) q^{80} +(5.19076 + 7.35228i) q^{81} +(9.24411 + 16.0113i) q^{82} +(6.08600 + 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} -5.72665 q^{86} +(-12.7134 + 3.71899i) q^{87} +2.05408 q^{88} +(7.41507 + 12.8433i) q^{89} +(22.7452 - 14.5524i) q^{90} +(-9.42101 - 16.3177i) q^{92} +(11.6819 - 3.41726i) q^{93} +(-7.77056 - 13.4590i) q^{94} +(-3.60963 - 6.25206i) q^{95} +(-0.896848 + 0.262352i) q^{96} +(-4.74375 - 8.21642i) q^{97} +(-1.08259 - 0.560893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9} + 16 q^{11} + 18 q^{15} - 6 q^{16} + 18 q^{18} - 6 q^{22} + 8 q^{23} + 24 q^{25} - 22 q^{29} + 42 q^{30} - 16 q^{32} - 30 q^{36} + 6 q^{37} + 24 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} - 18 q^{51} - 28 q^{53} - 6 q^{57} + 36 q^{58} - 126 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} - 30 q^{72} + 72 q^{74} + 36 q^{78} + 6 q^{79} + 24 q^{81} + 30 q^{85} - 72 q^{86} - 12 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9 + 16 * q^11 + 18 * q^15 - 6 * q^16 + 18 * q^18 - 6 * q^22 + 8 * q^23 + 24 * q^25 - 22 * q^29 + 42 * q^30 - 16 * q^32 - 30 * q^36 + 6 * q^37 + 24 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 - 18 * q^51 - 28 * q^53 - 6 * q^57 + 36 * q^58 - 126 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 - 30 * q^72 + 72 * q^74 + 36 * q^78 + 6 * q^79 + 24 * q^81 + 30 * q^85 - 72 * q^86 - 12 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.23025	+	2.13086i	−0.869920	+	1.50675i	−0.00784213	+	0.999969i	$0.502496\pi$
$2$	−1.23025	+	2.13086i	−0.869920	+	1.50675i	−0.862078	+	0.506776i	$0.830837\pi$
$3$	0.410052	−	1.68281i	0.236743	−	0.971572i
$3$	0.410052	−	1.68281i	0.236743	−	0.971572i
$4$	−2.02704	−	3.51094i	−1.01352	−	1.75547i
$5$	3.65808			1.63594			0.817970	−	0.575260i	$-0.195099\pi$
$5$	3.65808			1.63594			0.817970	+	0.575260i	$0.195099\pi$
$6$	3.08137	+	2.94405i	1.25796	+	1.20190i
$7$		0			0
$7$		0			0
$8$	5.05408			1.78689
$9$	−2.66372	−	1.38008i	−0.887905	−	0.460027i
$10$	−4.50036	+	7.79485i	−1.42314	+	2.46495i
$11$	0.406421			0.122540			0.0612702	−	0.998121i	$-0.480485\pi$
$11$	0.406421			0.122540			0.0612702	+	0.998121i	$0.480485\pi$
$12$	−6.73945	+	1.97146i	−1.94551	+	0.569113i
$13$	−0.243398	+	0.421578i	−0.0675065	+	0.116925i	−0.897803	−	0.440397i	$-0.854838\pi$
$13$	−0.243398	+	0.421578i	−0.0675065	+	0.116925i	0.830297	+	0.557322i	$0.188171\pi$
$14$		0			0
$15$	1.50000	−	6.15585i	0.387298	−	1.58943i
$16$	−2.16372	+	3.74766i	−0.540929	+	0.936916i
$17$	2.42792	−	4.20528i	0.588857	−	1.01993i	−0.405525	−	0.914084i	$-0.632911\pi$
$17$	2.42792	−	4.20528i	0.588857	−	1.01993i	0.994382	−	0.105847i	$-0.0337553\pi$
$18$	6.21780	−	3.97816i	1.46555	−	0.937660i
$19$	−0.986757	−	1.70911i	−0.226378	−	0.392097i	0.730354	−	0.683069i	$-0.239355\pi$
$19$	−0.986757	−	1.70911i	−0.226378	−	0.392097i	−0.956732	+	0.290971i	$0.906022\pi$
$20$	−7.41507	−	12.8433i	−1.65806	−	2.87185i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	4.64766			0.969105			0.484552	−	0.874762i	$-0.338982\pi$
$23$	4.64766			0.969105			0.484552	+	0.874762i	$0.338982\pi$
$24$	2.07244	−	8.50508i	0.423034	−	1.73609i
$25$	8.38151			1.67630
$26$	−0.598883	−	1.03729i	−0.117451	−	0.203430i
$27$	−3.41468	+	3.91663i	−0.657155	+	0.753756i
$28$		0			0
$29$	−3.82383	−	6.62307i	−0.710068	−	1.22987i	−0.964831	−	0.262870i	$-0.915331\pi$
$29$	−3.82383	−	6.62307i	−0.710068	−	1.22987i	0.254764	−	0.967003i	$-0.418002\pi$
$30$	11.2719	+	10.7695i	2.05795	+	1.96624i
$31$	3.51360	+	6.08573i	0.631061	+	1.09303i	0.987335	+	0.158648i	$0.0507136\pi$
$31$	3.51360	+	6.08573i	0.631061	+	1.09303i	−0.356274	+	0.934381i	$0.615953\pi$
$32$	−0.269748	−	0.467216i	−0.0476851	−	0.0825930i
$33$	0.166653	−	0.683930i	0.0290106	−	0.119057i
$34$	5.97391	+	10.3471i	1.02452	+	1.77452i
$35$		0			0
$36$	0.554084	+	12.1496i	0.0923474	+	2.02494i
$37$	−1.16372	−	2.01561i	−0.191314	−	0.331365i	0.754372	−	0.656447i	$-0.227941\pi$
$37$	−1.16372	−	2.01561i	−0.191314	−	0.331365i	−0.945686	+	0.325082i	$0.894608\pi$
$38$	4.85584			0.787721
$39$	0.609631	+	0.582462i	0.0976191	+	0.0932686i
$40$	18.4882			2.92324
$41$	3.75700	−	6.50731i	0.586744	−	1.01627i	−0.407911	−	0.913022i	$-0.633743\pi$
$41$	3.75700	−	6.50731i	0.586744	−	1.01627i	0.994655	−	0.103249i	$-0.0329240\pi$
$42$		0			0
$43$	1.16372	+	2.01561i	0.177465	+	0.307378i	0.941012	−	0.338374i	$-0.109877\pi$
$43$	1.16372	+	2.01561i	0.177465	+	0.307378i	−0.763547	+	0.645753i	$0.776544\pi$
$44$	−0.823832	−	1.42692i	−0.124197	−	0.215116i
$45$	−9.74407	−	5.04844i	−1.45256	−	0.752577i
$46$	−5.71780	+	9.90352i	−0.843044	+	1.46019i
$47$	−3.15811	+	5.47002i	−0.460658	+	0.797884i	−0.998994	−	0.0448469i	$-0.985720\pi$
$47$	−3.15811	+	5.47002i	−0.460658	+	0.797884i	0.538335	+	0.842731i	$0.319053\pi$
$48$	5.41938	+	5.17786i	0.782220	+	0.747360i
$49$		0			0
$50$	−10.3114	+	17.8598i	−1.45825	+	2.52576i
$51$	−6.08113	−	5.81012i	−0.851528	−	0.813579i
$52$	1.97351			0.273677
$53$	1.78434	−	3.09056i	0.245097	−	0.424521i	−0.717062	−	0.697010i	$-0.754513\pi$
$53$	1.78434	−	3.09056i	0.245097	−	0.424521i	0.962159	+	0.272489i	$0.0878467\pi$
$54$	−4.14487	−	12.0946i	−0.564046	−	1.64587i
$55$	1.48672			0.200469
$56$		0			0
$57$	−3.28074	+	0.959702i	−0.434544	+	0.127116i
$58$	18.8171			2.47081
$59$	3.05919	+	5.29868i	0.398273	+	0.689829i	0.993513	−	0.113719i	$-0.0362763\pi$
$59$	3.05919	+	5.29868i	0.398273	+	0.689829i	−0.595240	+	0.803548i	$0.702943\pi$
$60$	−24.6534	+	7.21177i	−3.18274	+	0.931035i
$61$	−4.01356	+	6.95169i	−0.513884	+	0.890073i	0.485987	+	0.873966i	$0.338460\pi$
$61$	−4.01356	+	6.95169i	−0.513884	+	0.890073i	−0.999870	+	0.0161063i	$0.994873\pi$
$62$	−17.2905			−2.19589
$63$		0			0
$64$	−7.32743			−0.915929
$65$	−0.890369	+	1.54216i	−0.110437	+	0.191282i
$66$	1.25233	+	1.19652i	0.154151	+	0.147282i
$67$	−1.80039	−	3.11836i	−0.219952	−	0.380969i	0.734841	−	0.678240i	$-0.237257\pi$
$67$	−1.80039	−	3.11836i	−0.219952	−	0.380969i	−0.954793	+	0.297271i	$0.903924\pi$
$68$	−19.6860			−2.38728
$69$	1.90578	−	7.82115i	0.229429	−	0.941555i
$70$		0			0
$71$	8.46050			1.00408			0.502039	−	0.864845i	$-0.332584\pi$
$71$	8.46050			1.00408			0.502039	+	0.864845i	$0.332584\pi$
$72$	−13.4626	−	6.97504i	−1.58659	−	0.822017i
$73$	0.986757	−	1.70911i	0.115491	−	0.200037i	−0.802485	−	0.596673i	$-0.796489\pi$
$73$	0.986757	−	1.70911i	0.115491	−	0.200037i	0.917976	+	0.396636i	$0.129822\pi$
$74$	5.72665			0.665710
$75$	3.43685	−	14.1045i	0.396854	−	1.62865i
$76$	−4.00040	+	6.92889i	−0.458877	+	0.794798i
$77$		0			0
$78$	−1.99115	+	0.582462i	−0.225453	+	0.0659509i
$79$	−4.08113	+	7.06872i	−0.459163	+	0.795293i	−0.998917	−	0.0465297i	$-0.985184\pi$
$79$	−4.08113	+	7.06872i	−0.459163	+	0.795293i	0.539754	+	0.841823i	$0.318517\pi$
$80$	−7.91503	+	13.7092i	−0.884928	+	1.53274i
$81$	5.19076	+	7.35228i	0.576751	+	0.816920i
$82$	9.24411	+	16.0113i	1.02084	+	1.76815i
$83$	6.08600	+	10.5413i	0.668025	+	1.15705i	0.978456	+	0.206457i	$0.0661933\pi$
$83$	6.08600	+	10.5413i	0.668025	+	1.15705i	−0.310431	+	0.950596i	$0.600473\pi$
$84$		0			0
$85$	8.88151	−	15.3832i	0.963336	−	1.66855i
$86$	−5.72665			−0.617521
$87$	−12.7134	+	3.71899i	−1.36301	+	0.398718i
$88$	2.05408			0.218966
$89$	7.41507	+	12.8433i	0.785996	+	1.36139i	0.928402	+	0.371577i	$0.121183\pi$
$89$	7.41507	+	12.8433i	0.785996	+	1.36139i	−0.142406	+	0.989808i	$0.545484\pi$
$90$	22.7452	−	14.5524i	2.39755	−	1.53396i
$91$		0			0
$92$	−9.42101	−	16.3177i	−0.982208	−	1.70123i
$93$	11.6819	−	3.41726i	1.21136	−	0.354354i
$94$	−7.77056	−	13.4590i	−0.801472	−	1.38819i
$95$	−3.60963	−	6.25206i	−0.370340	−	0.641448i
$96$	−0.896848	+	0.262352i	−0.0915342	+	0.0267762i
$97$	−4.74375	−	8.21642i	−0.481655	−	0.834251i	0.518123	−	0.855306i	$-0.326631\pi$
$97$	−4.74375	−	8.21642i	−0.481655	−	0.834251i	−0.999778	+	0.0210547i	$0.993298\pi$
$98$		0			0
$99$	−1.08259	−	0.560893i	−0.108804	−	0.0563719i
$100$	−16.9897	−	29.4270i	−1.69897	−	2.94270i
$101$	−8.71176			−0.866852			−0.433426	−	0.901189i	$-0.642696\pi$
$101$	−8.71176			−0.866852			−0.433426	+	0.901189i	$0.642696\pi$
$102$	19.8619	−	5.81012i	1.96662	−	0.575287i
$103$	−8.02712			−0.790936			−0.395468	−	0.918480i	$-0.629418\pi$
$103$	−8.02712			−0.790936			−0.395468	+	0.918480i	$0.629418\pi$
$104$	−1.23016	+	2.13069i	−0.120627	+	0.208931i
$105$		0			0
$106$	4.39037	+	7.60434i	0.426430	+	0.738599i
$107$	−6.42101	−	11.1215i	−0.620742	−	1.07516i	−0.989348	−	0.145571i	$-0.953498\pi$
$107$	−6.42101	−	11.1215i	−0.620742	−	1.07516i	0.368605	−	0.929586i	$-0.379835\pi$
$108$	20.6727	+	4.04955i	1.98924	+	0.389669i
$109$	−1.30039	+	2.25234i	−0.124555	+	0.215735i	−0.921559	−	0.388239i	$-0.873084\pi$
$109$	−1.30039	+	2.25234i	−0.124555	+	0.215735i	0.797004	+	0.603974i	$0.206417\pi$
$110$	−1.82904	+	3.16799i	−0.174392	+	0.302056i
$111$	−3.86908	+	1.13181i	−0.367237	+	0.107427i
$112$		0			0
$113$	6.97509	−	12.0812i	0.656162	−	1.13651i	−0.325440	−	0.945563i	$-0.605512\pi$
$113$	6.97509	−	12.0812i	0.656162	−	1.13651i	0.981601	−	0.190942i	$-0.0611544\pi$
$114$	1.99115	−	8.17147i	0.186488	−	0.765328i
$115$	17.0015			1.58540
$116$	−15.5021	+	26.8505i	−1.43934	+	2.49301i
$117$	1.23016	−	0.787055i	0.113728	−	0.0727633i
$118$	−15.0543			−1.38586
$119$		0			0
$120$	7.58113	−	31.1122i	0.692059	−	2.84014i
$121$	−10.8348			−0.984984
$122$	−9.87538	−	17.1047i	−0.894075	−	1.54858i
$123$	−9.41002	−	8.99066i	−0.848473	−	0.810660i
$124$	14.2444	−	24.6721i	1.27919	−	2.21562i
$125$	12.3698			1.10639
$126$		0			0
$127$	−15.5438			−1.37929			−0.689643	−	0.724149i	$-0.742233\pi$
$127$	−15.5438			−1.37929			−0.689643	+	0.724149i	$0.742233\pi$
$128$	9.55408	−	16.5482i	0.844470	−	1.46266i
$129$	3.86908	−	1.13181i	0.340654	−	0.0996502i
$130$	−2.19076	−	3.79450i	−0.192142	−	0.332800i
$131$	8.51392			0.743864			0.371932	−	0.928260i	$-0.378695\pi$
$131$	8.51392			0.743864			0.371932	+	0.928260i	$0.378695\pi$
$132$	−2.73905	+	0.801244i	−0.238404	+	0.0697393i
$133$		0			0
$134$	8.85973			0.765364
$135$	−12.4911	+	14.3273i	−1.07507	+	1.23310i
$136$	12.2709	−	21.2538i	1.05222	−	1.82250i
$137$	0.377242			0.0322300			0.0161150	−	0.999870i	$-0.494870\pi$
$137$	0.377242			0.0322300			0.0161150	+	0.999870i	$0.494870\pi$
$138$	14.3212	+	13.6829i	1.21910	+	1.16477i
$139$	−9.50067	+	16.4556i	−0.805837	+	1.39575i	0.109888	+	0.993944i	$0.464951\pi$
$139$	−9.50067	+	16.4556i	−0.805837	+	1.39575i	−0.915725	+	0.401806i	$0.868383\pi$
$140$		0			0
$141$	7.91002	+	7.55750i	0.666144	+	0.636457i
$142$	−10.4086	+	18.0281i	−0.873467	+	1.51289i
$143$	−0.0989221	+	0.171338i	−0.00827228	+	0.0143280i
$144$	10.9356	−	6.99661i	0.911300	−	0.583051i
$145$	−13.9879	−	24.2277i	−1.16163	−	2.01200i
$146$	2.42792	+	4.20528i	0.200936	+	0.348032i
$147$		0			0
$148$	−4.71780	+	8.17147i	−0.387801	+	0.671691i
$149$	−9.70175			−0.794798			−0.397399	−	0.917646i	$-0.630087\pi$
$149$	−9.70175			−0.794798			−0.397399	+	0.917646i	$0.630087\pi$
$150$	25.8265	+	24.6756i	2.10873	+	2.01475i
$151$	−12.8348			−1.04448			−0.522242	−	0.852798i	$-0.674904\pi$
$151$	−12.8348			−1.04448			−0.522242	+	0.852798i	$0.674904\pi$
$152$	−4.98715	−	8.63800i	−0.404511	−	0.700634i
$153$	−12.2709	+	7.85095i	−0.992045	+	0.634711i
$154$		0			0
$155$	12.8530	+	22.2621i	1.03238	+	1.78813i
$156$	0.809243	−	3.32105i	0.0647913	−	0.265897i
$157$	10.4743	+	18.1420i	0.835937	+	1.44789i	0.893265	+	0.449531i	$0.148409\pi$
$157$	10.4743	+	18.1420i	0.835937	+	1.44789i	−0.0573276	+	0.998355i	$0.518258\pi$
$158$	−10.0416	−	17.3926i	−0.798869	−	1.38368i
$159$	−4.46917	−	4.26999i	−0.354428	−	0.338633i
$160$	−0.986757	−	1.70911i	−0.0780100	−	0.135117i
$161$		0			0
$162$	−22.0526	+	2.01561i	−1.73262	+	0.158362i
$163$	5.58113	+	9.66679i	0.437148	+	0.757162i	0.997468	−	0.0711140i	$-0.0226554\pi$
$163$	5.58113	+	9.66679i	0.437148	+	0.757162i	−0.560321	+	0.828276i	$0.689322\pi$
$164$	−30.4624			−2.37871
$165$	0.609631	−	2.50187i	0.0474597	−	0.194770i
$166$	−29.9492			−2.32451
$167$	1.73012	−	2.99665i	0.133880	−	0.231888i	−0.791289	−	0.611443i	$-0.790590\pi$
$167$	1.73012	−	2.99665i	0.133880	−	0.231888i	0.925169	+	0.379555i	$0.123923\pi$
$168$		0			0
$169$	6.38151	+	11.0531i	0.490886	+	0.850239i
$170$	21.8530	+	37.8505i	1.67605	+	2.90300i
$171$	0.269726	+	5.91439i	0.0206265	+	0.452285i
$172$	4.71780	−	8.17147i	0.359729	−	0.623069i
$173$	−3.02680	+	5.24258i	−0.230124	+	0.398586i	−0.957844	−	0.287288i	$-0.907246\pi$
$173$	−3.02680	+	5.24258i	−0.230124	+	0.398586i	0.727721	+	0.685874i	$0.240580\pi$
$174$	7.71599	−	31.6657i	0.584948	−	2.40057i
$175$		0			0
$176$	−0.879379	+	1.52313i	−0.0662857	+	0.114810i
$177$	10.1711	−	2.97532i	0.764507	−	0.223638i
$178$	−36.4896			−2.73501
$179$	−4.56654	+	7.90947i	−0.341319	+	0.591182i	−0.984678	−	0.174383i	$-0.944207\pi$
$179$	−4.56654	+	7.90947i	−0.341319	+	0.591182i	0.643359	+	0.765565i	$0.277540\pi$
$180$	2.02688	+	44.4442i	0.151075	+	3.31268i
$181$	−11.9478			−0.888074			−0.444037	−	0.896008i	$-0.646454\pi$
$181$	−11.9478			−0.888074			−0.444037	+	0.896008i	$0.646454\pi$
$182$		0			0
$183$	10.0526	+	9.60462i	0.743111	+	0.709994i
$184$	23.4897			1.73168
$185$	−4.25696	−	7.37327i	−0.312978	−	0.542093i
$186$	−7.08998	+	29.0966i	−0.519863	+	2.13347i
$187$	0.986757	−	1.70911i	0.0721588	−	0.124983i
$188$	25.6065			1.86755
$189$		0			0
$190$	17.7630			1.28867
$191$	−4.57014	+	7.91571i	−0.330683	+	0.572760i	−0.982646	−	0.185491i	$-0.940613\pi$
$191$	−4.57014	+	7.91571i	−0.330683	+	0.572760i	0.651963	+	0.758251i	$0.273946\pi$
$192$	−3.00463	+	12.3307i	−0.216840	+	0.889891i
$193$	−8.47150	−	14.6731i	−0.609792	−	1.05619i	−0.991274	−	0.131814i	$-0.957920\pi$
$193$	−8.47150	−	14.6731i	−0.609792	−	1.05619i	0.381483	−	0.924376i	$-0.375414\pi$
$194$	23.3441			1.67601
$195$	2.23008	+	2.13069i	0.159699	+	0.152582i
$196$		0			0
$197$	−21.3173			−1.51880			−0.759398	−	0.650627i	$-0.774506\pi$
$197$	−21.3173			−1.51880			−0.759398	+	0.650627i	$0.774506\pi$
$198$	2.52704	−	1.61680i	0.179589	−	0.114901i
$199$	4.98715	−	8.63800i	0.353530	−	0.612332i	−0.633335	−	0.773877i	$-0.718315\pi$
$199$	4.98715	−	8.63800i	0.353530	−	0.612332i	0.986865	+	0.161546i	$0.0516479\pi$
$200$	42.3609			2.99537
$201$	−5.98587	+	1.75103i	−0.422211	+	0.123508i
$202$	10.7177	−	18.5635i	0.754092	−	1.30613i
$203$		0			0
$204$	−8.07227	+	33.1278i	−0.565172	+	2.31941i
$205$	13.7434	−	23.8042i	0.959879	−	1.66256i
$206$	9.87538	−	17.1047i	0.688051	−	1.19174i
$207$	−12.3801	−	6.41415i	−0.860473	−	0.445814i
$208$	−1.05329	−	1.82435i	−0.0730324	−	0.126496i
$209$	−0.401038	−	0.694619i	−0.0277404	−	0.0480478i
$210$		0			0
$211$	−2.44592	+	4.23645i	−0.168384	+	0.291649i	−0.937852	−	0.347036i	$-0.887188\pi$
$211$	−2.44592	+	4.23645i	−0.168384	+	0.291649i	0.769468	+	0.638685i	$0.220521\pi$
$212$	−14.4677			−0.993646
$213$	3.46924	−	14.2374i	0.237709	−	0.975533i
$214$	31.5979			2.15998
$215$	4.25696	+	7.37327i	0.290322	+	0.502853i
$216$	−17.2581	+	19.7950i	−1.17426	+	1.34688i
$217$		0			0
$218$	−3.19961	−	5.54189i	−0.216705	−	0.375344i
$219$	−2.47150	−	2.36135i	−0.167008	−	0.159565i
$220$	−3.01364	−	5.21978i	−0.203179	−	0.351917i
$221$	1.18190	+	2.04712i	0.0795034	+	0.137704i
$222$	2.34822	−	9.63688i	0.157602	−	0.646785i
$223$	−11.7044	−	20.2727i	−0.783786	−	1.35756i	−0.929722	−	0.368263i	$-0.879953\pi$
$223$	−11.7044	−	20.2727i	−0.783786	−	1.35756i	0.145936	−	0.989294i	$-0.453381\pi$
$224$		0			0
$225$	−22.3260	−	11.5672i	−1.48840	−	0.771144i
$226$	17.1623	+	29.7259i	1.14162	+	1.97734i
$227$	6.11839			0.406092			0.203046	−	0.979169i	$-0.434916\pi$
$227$	6.11839			0.406092			0.203046	+	0.979169i	$0.434916\pi$
$228$	10.0197	+	9.57312i	0.663568	+	0.633995i
$229$	−1.46039			−0.0965052			−0.0482526	−	0.998835i	$-0.515365\pi$
$229$	−1.46039			−0.0965052			−0.0482526	+	0.998835i	$0.515365\pi$
$230$	−20.9161	+	36.2278i	−1.37917	+	2.38879i
$231$		0			0
$232$	−19.3260	−	33.4736i	−1.26881	−	2.19765i
$233$	6.62422	+	11.4735i	0.433967	+	0.751653i	0.997211	−	0.0746378i	$-0.0237801\pi$
$233$	6.62422	+	11.4735i	0.433967	+	0.751653i	−0.563244	+	0.826291i	$0.690447\pi$
$234$	0.163702	+	3.58956i	0.0107016	+	0.234657i
$235$	−11.5526	+	20.0097i	−0.753610	+	1.30529i
$236$	12.4022	−	21.4813i	0.807316	−	1.39831i
$237$	10.2219	+	9.76631i	0.663981	+	0.634390i
$238$		0			0
$239$	−9.69436	+	16.7911i	−0.627076	+	1.08613i	0.361060	+	0.932543i	$0.382415\pi$
$239$	−9.69436	+	16.7911i	−0.627076	+	1.08613i	−0.988136	+	0.153584i	$0.950918\pi$
$240$	19.8245	+	18.9410i	1.27967	+	1.22264i
$241$	5.05368			0.325536			0.162768	−	0.986664i	$-0.447958\pi$
$241$	5.05368			0.325536			0.162768	+	0.986664i	$0.447958\pi$
$242$	13.3296	−	23.0875i	0.856857	−	1.48412i
$243$	14.5010	−	5.72026i	0.930239	−	0.366955i
$244$	32.5426			2.08333
$245$		0			0
$246$	30.7345	−	8.99066i	1.95956	−	0.573223i
$247$	0.960699			0.0611278
$248$	17.7580	+	30.7578i	1.12764	+	1.95312i
$249$	20.2345	−	5.91913i	1.28231	−	0.375110i
$250$	−15.2180	+	26.3584i	−0.962472	+	1.66705i
$251$	15.0928			0.952647			0.476324	−	0.879270i	$-0.341969\pi$
$251$	15.0928			0.952647			0.476324	+	0.879270i	$0.341969\pi$
$252$		0			0
$253$	1.88891			0.118755
$254$	19.1228	−	33.1216i	1.19987	−	2.07823i
$255$	−22.2452	−	21.2538i	−1.39305	−	1.33097i
$256$	16.1804	+	28.0253i	1.01128	+	1.75158i
$257$	7.71184			0.481051			0.240526	−	0.970643i	$-0.422680\pi$
$257$	7.71184			0.481051			0.240526	+	0.970643i	$0.422680\pi$
$258$	−2.34822	+	9.63688i	−0.146194	+	0.599966i
$259$		0			0
$260$	7.21926			0.447720
$261$	1.04523	+	22.9192i	0.0646981	+	1.41866i
$262$	−10.4743	+	18.1420i	−0.647102	+	1.12081i
$263$	4.21206			0.259727			0.129864	−	0.991532i	$-0.458546\pi$
$263$	4.21206			0.259727			0.129864	+	0.991532i	$0.458546\pi$
$264$	0.842281	−	3.45664i	0.0518388	−	0.212741i
$265$	6.52724	−	11.3055i	0.400965	−	0.694492i
$266$		0			0
$267$	24.6534	−	7.21177i	1.50876	−	0.441353i
$268$	−7.29893	+	12.6421i	−0.445853	+	0.772240i
$269$	−10.3753	+	17.9706i	−0.632596	+	1.09569i	0.354423	+	0.935085i	$0.384677\pi$
$269$	−10.3753	+	17.9706i	−0.632596	+	1.09569i	−0.987019	+	0.160603i	$0.948656\pi$
$270$	−15.1623	−	44.2431i	−0.922745	−	2.69255i
$271$	14.2444	+	24.6721i	0.865287	+	1.49872i	0.866762	+	0.498723i	$0.166197\pi$
$271$	14.2444	+	24.6721i	0.865287	+	1.49872i	−0.00147433	+	0.999999i	$0.500469\pi$
$272$	10.5067	+	18.1981i	0.637060	+	1.10342i
$273$		0			0
$274$	−0.464103	+	0.803851i	−0.0280375	+	0.0485624i
$275$	3.40642			0.205415
$276$	−31.3227	+	9.16270i	−1.88540	+	0.551530i
$277$	17.1623			1.03118			0.515590	−	0.856835i	$-0.327573\pi$
$277$	17.1623			1.03118			0.515590	+	0.856835i	$0.327573\pi$
$278$	−23.3765	−	40.4892i	−1.40203	−	2.42838i
$279$	−0.960429	−	21.0597i	−0.0574994	−	1.26081i
$280$		0			0
$281$	−4.72140	−	8.17770i	−0.281655	−	0.487841i	0.690138	−	0.723678i	$-0.257550\pi$
$281$	−4.72140	−	8.17770i	−0.281655	−	0.487841i	−0.971793	+	0.235837i	$0.924217\pi$
$282$	−25.8353	+	7.55750i	−1.53847	+	0.450043i
$283$	−8.43422	−	14.6085i	−0.501362	−	0.868385i	−0.999999	−	0.00157378i	$-0.999499\pi$
$283$	−8.43422	−	14.6085i	−0.501362	−	0.868385i	0.498636	−	0.866811i	$-0.333834\pi$
$284$	−17.1498	−	29.7043i	−1.01765	−	1.76263i
$285$	−12.0012	+	3.51066i	−0.710889	+	0.207954i
$286$	−0.243398	−	0.421578i	−0.0143924	−	0.0249284i
$287$		0			0
$288$	0.0737345	+	1.61680i	0.00434485	+	0.0952711i
$289$	−3.28959	−	5.69774i	−0.193505	−	0.335161i
$290$	68.8344			4.04210
$291$	−15.7719	+	4.61369i	−0.924564	+	0.270459i
$292$	−8.00079			−0.468211
$293$	1.86143	−	3.22409i	0.108746	−	0.188353i	−0.806517	−	0.591211i	$-0.798650\pi$
$293$	1.86143	−	3.22409i	0.108746	−	0.188353i	0.915262	+	0.402858i	$0.131983\pi$
$294$		0			0
$295$	11.1908	+	19.3830i	0.651551	+	1.12852i
$296$	−5.88151	−	10.1871i	−0.341856	−	0.592112i
$297$	−1.38780	+	1.59180i	−0.0805280	+	0.0923655i
$298$	11.9356	−	20.6731i	0.691411	−	1.19756i
$299$	−1.13123	+	1.95935i	−0.0654209	+	0.113312i
$300$	−56.4868	+	16.5239i	−3.26126	+	0.954006i
$301$		0			0
$302$	15.7901	−	27.3492i	0.908617	−	1.57377i
$303$	−3.57227	+	14.6603i	−0.205222	+	0.842210i
$304$	8.54024			0.489817
$305$	−14.6819	+	25.4298i	−0.840683	+	1.45611i
$306$	−1.63295	−	35.8062i	−0.0933493	−	2.04691i
$307$	30.5691			1.74467			0.872335	−	0.488908i	$-0.162605\pi$
$307$	30.5691			1.74467			0.872335	+	0.488908i	$0.162605\pi$
$308$		0			0
$309$	−3.29153	+	13.5081i	−0.187249	+	0.768451i
$310$	−63.2498			−3.59235
$311$	5.21739	+	9.03678i	0.295851	+	0.512429i	0.975182	−	0.221403i	$-0.0710635\pi$
$311$	5.21739	+	9.03678i	0.295851	+	0.512429i	−0.679332	+	0.733831i	$0.737730\pi$
$312$	3.08113	+	2.94381i	0.174434	+	0.166661i
$313$	0.309930	−	0.536815i	0.0175183	−	0.0303426i	−0.857133	−	0.515095i	$-0.827757\pi$
$313$	0.309930	−	0.536815i	0.0175183	−	0.0303426i	0.874652	+	0.484752i	$0.161090\pi$
$314$	−51.5440			−2.90879
$315$		0			0
$316$	33.0905			1.86148
$317$	−5.12422	+	8.87541i	−0.287805	+	0.498493i	−0.973285	−	0.229598i	$-0.926259\pi$
$317$	−5.12422	+	8.87541i	−0.287805	+	0.498493i	0.685481	+	0.728091i	$0.259592\pi$
$318$	14.5970	−	4.26999i	0.818557	−	0.239449i
$319$	−1.55408	−	2.69175i	−0.0870120	−	0.150709i
$320$	−26.8043			−1.49841
$321$	−21.3484	+	6.24496i	−1.19155	+	0.348560i
$322$		0			0
$323$	−9.58307			−0.533216
$324$	15.2915	−	33.1278i	0.849530	−	1.84043i
$325$	−2.04005	+	3.53346i	−0.113161	+	0.196001i
$326$	−27.4648			−1.52113
$327$	3.25704	+	3.11188i	0.180115	+	0.172088i
$328$	18.9882	−	32.8885i	1.04845	−	1.81596i
$329$		0			0
$330$	4.58113	+	4.37697i	0.252183	+	0.240944i
$331$	10.1819	−	17.6356i	0.559648	−	0.969339i	−0.437878	−	0.899035i	$-0.644270\pi$
$331$	10.1819	−	17.6356i	0.559648	−	0.969339i	0.997526	−	0.0703042i	$-0.0223970\pi$
$332$	24.6731	−	42.7351i	1.35411	−	2.34539i
$333$	0.318097	+	6.97504i	0.0174316	+	0.382230i
$334$	4.25696	+	7.37327i	0.232930	+	0.403447i
$335$	−6.58596	−	11.4072i	−0.359829	−	0.623242i
$336$		0			0
$337$	2.85594	−	4.94662i	0.155573	−	0.269460i	−0.777695	−	0.628642i	$-0.783611\pi$
$337$	2.85594	−	4.94662i	0.155573	−	0.269460i	0.933267	+	0.359182i	$0.116944\pi$
$338$	−31.4035			−1.70812
$339$	−17.4703	−	16.6917i	−0.948855	−	0.906569i
$340$	−72.0128			−3.90544
$341$	1.42800	+	2.47337i	0.0773305	+	0.133940i
$342$	−12.9346	−	6.70145i	−0.699422	−	0.362373i
$343$		0			0
$344$	5.88151	+	10.1871i	0.317110	+	0.549251i
$345$	6.97150	−	28.6103i	0.375333	−	1.54033i
$346$	−7.44746	−	12.8994i	−0.400378	−	0.693475i
$347$	−4.44066	−	7.69145i	−0.238387	−	0.412899i	0.721865	−	0.692034i	$-0.243285\pi$
$347$	−4.44066	−	7.69145i	−0.238387	−	0.412899i	−0.960252	+	0.279136i	$0.909952\pi$
$348$	38.8277	+	37.0973i	2.08138	+	1.98862i
$349$	10.4874	+	18.1648i	0.561379	+	0.972337i	0.997376	+	0.0723893i	$0.0230624\pi$
$349$	10.4874	+	18.1648i	0.561379	+	0.972337i	−0.435997	+	0.899948i	$0.643604\pi$
$350$		0			0
$351$	−0.820039	−	2.39285i	−0.0437704	−	0.127721i
$352$	−0.109631	−	0.189886i	−0.00584335	−	0.0101210i
$353$	14.7654			0.785881			0.392941	−	0.919564i	$-0.371458\pi$
$353$	14.7654			0.785881			0.392941	+	0.919564i	$0.371458\pi$
$354$	−6.17305	+	25.3336i	−0.328094	+	1.34647i
$355$	30.9492			1.64261
$356$	30.0613	−	52.0677i	1.59325	−	2.75959i
$357$		0			0
$358$	−11.2360	−	19.4613i	−0.593840	−	1.02856i
$359$	−3.60603	−	6.24583i	−0.190319	−	0.329642i	0.755037	−	0.655682i	$-0.227619\pi$
$359$	−3.60603	−	6.24583i	−0.190319	−	0.329642i	−0.945356	+	0.326040i	$0.894286\pi$
$360$	−49.2474	−	25.5152i	−2.59556	−	1.34477i
$361$	7.55262	−	13.0815i	0.397506	−	0.688501i
$362$	14.6988	−	25.4591i	0.772554	−	1.33810i
$363$	−4.44284	+	18.2330i	−0.233188	+	0.956983i
$364$		0			0
$365$	3.60963	−	6.25206i	0.188937	−	0.327248i
$366$	−32.8334	+	9.60462i	−1.71623	+	0.502042i
$367$	10.9742			0.572850			0.286425	−	0.958103i	$-0.407533\pi$
$367$	10.9742			0.572850			0.286425	+	0.958103i	$0.407533\pi$
$368$	−10.0562	+	17.4179i	−0.524217	+	0.907970i
$369$	−18.9882	+	12.1487i	−0.988485	+	0.632434i
$370$	20.9485			1.08906
$371$		0			0
$372$	−35.6775	−	34.0875i	−1.84979	−	1.76736i
$373$	−0.543767			−0.0281552			−0.0140776	−	0.999901i	$-0.504481\pi$
$373$	−0.543767			−0.0281552			−0.0140776	+	0.999901i	$0.504481\pi$
$374$	2.42792	+	4.20528i	0.125545	+	0.217450i
$375$	5.07227	−	20.8161i	0.261931	−	1.07494i
$376$	−15.9614	+	27.6459i	−0.823145	+	1.42573i
$377$	3.72286			0.191737
$378$		0			0
$379$	−22.6912			−1.16557			−0.582785	−	0.812626i	$-0.698037\pi$
$379$	−22.6912			−1.16557			−0.582785	+	0.812626i	$0.698037\pi$
$380$	−14.6337	+	25.3464i	−0.750695	+	1.30024i
$381$	−6.37375	+	26.1572i	−0.326537	+	1.34008i
$382$	−11.2448	−	19.4766i	−0.575336	−	0.996511i
$383$	−35.7139			−1.82489			−0.912447	−	0.409194i	$-0.865810\pi$
$383$	−35.7139			−1.82489			−0.912447	+	0.409194i	$0.865810\pi$
$384$	−23.9298	−	22.8633i	−1.22116	−	1.16674i
$385$		0			0
$386$	41.6883			2.12188
$387$	−0.318097	−	6.97504i	−0.0161698	−	0.354561i
$388$	−19.2316	+	33.3101i	−0.976336	+	1.69106i
$389$	38.6591			1.96010			0.980048	−	0.198761i	$-0.0636919\pi$
$389$	38.6591			1.96010			0.980048	+	0.198761i	$0.0636919\pi$
$390$	−7.28376	+	2.13069i	−0.368828	+	0.107892i
$391$	11.2842	−	19.5447i	0.570664	−	0.988420i
$392$		0			0
$393$	3.49115	−	14.3273i	0.176105	−	0.722718i
$394$	26.2257	−	45.4242i	1.32123	−	2.28844i
$395$	−14.9291	+	25.8579i	−0.751163	+	1.30105i
$396$	0.225191	+	4.93786i	0.0113163	+	0.248137i
$397$	−5.97391	−	10.3471i	−0.299822	−	0.519307i	0.676273	−	0.736651i	$-0.263594\pi$
$397$	−5.97391	−	10.3471i	−0.299822	−	0.519307i	−0.976095	+	0.217344i	$0.930261\pi$
$398$	12.2709	+	21.2538i	0.615085	+	1.06536i
$399$		0			0
$400$	−18.1352	+	31.4111i	−0.906761	+	1.57056i
$401$	32.3566			1.61581			0.807906	−	0.589311i	$-0.200601\pi$
$401$	32.3566			1.61581			0.807906	+	0.589311i	$0.200601\pi$
$402$	3.63295	−	14.9093i	0.181195	−	0.743606i
$403$	−3.42082			−0.170403
$404$	17.6591	+	30.5865i	0.878573	+	1.52173i
$405$	18.9882	+	26.8952i	0.943530	+	1.33643i
$406$		0			0
$407$	−0.472958	−	0.819187i	−0.0234437	−	0.0406056i
$408$	−30.7345	−	29.3648i	−1.52159	−	1.45378i
$409$	9.48751	+	16.4328i	0.469127	+	0.812552i	0.999377	−	0.0352893i	$-0.0112353\pi$
$409$	9.48751	+	16.4328i	0.469127	+	0.812552i	−0.530250	+	0.847841i	$0.677902\pi$
$410$	33.8157	+	58.5704i	1.67004	+	2.89259i
$411$	0.154689	−	0.634828i	0.00763024	−	0.0313138i
$412$	16.2713	+	28.1827i	0.801630	+	1.38846i
$413$		0			0
$414$	28.8982	−	18.4891i	1.42027	−	0.908691i
$415$	22.2630	+	38.5607i	1.09285	+	1.89287i
$416$	0.262624			0.0128762
$417$	23.7960	+	22.7355i	1.16530	+	1.11336i
$418$	1.97351			0.0965277
$419$	−8.64523	+	14.9740i	−0.422347	+	0.731526i	−0.996169	−	0.0874539i	$-0.972127\pi$
$419$	−8.64523	+	14.9740i	−0.422347	+	0.731526i	0.573822	+	0.818980i	$0.305460\pi$
$420$		0			0
$421$	−9.30039	−	16.1087i	−0.453273	−	0.785092i	0.545314	−	0.838232i	$-0.316410\pi$
$421$	−9.30039	−	16.1087i	−0.453273	−	0.785092i	−0.998587	+	0.0531397i	$0.983077\pi$
$422$	−6.01819	−	10.4238i	−0.292961	−	0.507423i
$423$	15.9614	−	10.2121i	0.776069	−	0.496530i
$424$	9.01819	−	15.6200i	0.437962	−	0.758572i
$425$	20.3496	−	35.2466i	0.987103	−	1.70971i
$426$	26.0699	+	24.9081i	1.26309	+	1.20680i
$427$		0			0
$428$	−26.0313	+	45.0876i	−1.25827	+	2.17939i
$429$	0.247767	+	0.236725i	0.0119623	+	0.0114292i
$430$	−20.9485			−1.01023
$431$	7.93920	−	13.7511i	0.382418	−	0.662367i	−0.608990	−	0.793178i	$-0.708425\pi$
$431$	7.93920	−	13.7511i	0.382418	−	0.662367i	0.991407	+	0.130811i	$0.0417582\pi$
$432$	−7.28982	−	21.2715i	−0.350732	−	1.02343i
$433$	−40.4367			−1.94326			−0.971631	−	0.236501i	$-0.923999\pi$
$433$	−40.4367			−1.94326			−0.971631	+	0.236501i	$0.923999\pi$
$434$		0			0
$435$	−46.5064	+	13.6043i	−2.22981	+	0.652278i
$436$	10.5438			0.504955
$437$	−4.58611	−	7.94338i	−0.219384	−	0.379984i
$438$	8.07227	−	2.36135i	0.385708	−	0.112830i
$439$	6.23047	−	10.7915i	0.297364	−	0.515050i	−0.678168	−	0.734907i	$-0.737226\pi$
$439$	6.23047	−	10.7915i	0.297364	−	0.515050i	0.975532	+	0.219857i	$0.0705591\pi$
$440$	7.51399			0.358216
$441$		0			0
$442$	−5.81616			−0.276646
$443$	4.11537	−	7.12802i	0.195527	−	0.338663i	−0.751546	−	0.659680i	$-0.770692\pi$
$443$	4.11537	−	7.12802i	0.195527	−	0.338663i	0.947073	+	0.321018i	$0.104025\pi$
$444$	11.8165	+	11.2899i	0.560787	+	0.535795i
$445$	27.1249	+	46.9817i	1.28584	+	2.22715i
$446$	57.5976			2.72732
$447$	−3.97822	+	16.3262i	−0.188163	+	0.772204i
$448$		0			0
$449$	5.64474			0.266392			0.133196	−	0.991090i	$-0.457476\pi$
$449$	5.64474			0.266392			0.133196	+	0.991090i	$0.457476\pi$
$450$	52.1146	−	33.3430i	2.45670	−	1.57180i
$451$	1.52692	−	2.64471i	0.0718999	−	0.124534i
$452$	−56.5552			−2.66013
$453$	−5.26294	+	21.5986i	−0.247275	+	1.01479i
$454$	−7.52716	+	13.0374i	−0.353267	+	0.611876i
$455$		0			0
$456$	−16.5811	+	4.85041i	−0.776482	+	0.227141i
$457$	−2.53443	+	4.38977i	−0.118556	+	0.205345i	−0.919196	−	0.393801i	$-0.871160\pi$
$457$	−2.53443	+	4.38977i	−0.118556	+	0.205345i	0.800640	+	0.599146i	$0.204493\pi$
$458$	1.79665	−	3.11188i	0.0839518	−	0.145409i
$459$	8.17996	+	23.8689i	0.381808	+	1.11411i
$460$	−34.4628	−	59.6913i	−1.60683	−	2.78312i
$461$	−3.88831	−	6.73475i	−0.181097	−	0.313669i	0.761158	−	0.648567i	$-0.224631\pi$
$461$	−3.88831	−	6.73475i	−0.181097	−	0.313669i	−0.942254	+	0.334898i	$0.891298\pi$
$462$		0			0
$463$	4.58998	−	7.95008i	0.213314	−	0.369472i	−0.739435	−	0.673228i	$-0.764907\pi$
$463$	4.58998	−	7.95008i	0.213314	−	0.369472i	0.952750	+	0.303756i	$0.0982408\pi$
$464$	33.0947			1.53638
$465$	42.7333	−	12.5006i	1.98171	−	0.579702i
$466$	−32.5979			−1.51007
$467$	−6.88272	−	11.9212i	−0.318494	−	0.551648i	0.661680	−	0.749787i	$-0.269844\pi$
$467$	−6.88272	−	11.9212i	−0.318494	−	0.551648i	−0.980174	+	0.198138i	$0.936511\pi$
$468$	−5.25688	−	2.72361i	−0.242999	−	0.125899i
$469$		0			0
$470$	−28.4253	−	49.2340i	−1.31116	−	2.27100i
$471$	34.8245	−	10.1871i	1.60463	−	0.469396i
$472$	15.4614	+	26.7800i	0.711669	+	1.23265i
$473$	0.472958	+	0.819187i	0.0217466	+	0.0376663i
$474$	−33.3861	+	9.76631i	−1.53347	+	0.448581i
$475$	−8.27052	−	14.3250i	−0.379477	−	0.657274i
$476$		0			0
$477$	−9.01819	+	5.76985i	−0.412914	+	0.264183i
$478$	−23.8530	−	41.3146i	−1.09101	−	1.88969i
$479$	−8.71176			−0.398050			−0.199025	−	0.979994i	$-0.563778\pi$
$479$	−8.71176			−0.398050			−0.199025	+	0.979994i	$0.563778\pi$
$480$	−3.28074	+	0.959702i	−0.149745	+	0.0438042i
$481$	1.13298			0.0516597
$482$	−6.21731	+	10.7687i	−0.283191	+	0.490501i
$483$		0			0
$484$	21.9626	+	38.0404i	0.998302	+	1.72911i
$485$	−17.3530	−	30.0563i	−0.787960	−	1.36479i
$486$	−5.65082	+	37.9369i	−0.256326	+	1.72085i
$487$	9.01819	−	15.6200i	0.408653	−	0.707808i	−0.586086	−	0.810249i	$-0.699332\pi$
$487$	9.01819	−	15.6200i	0.408653	−	0.707808i	0.994739	+	0.102441i	$0.0326653\pi$
$488$	−20.2849	+	35.1344i	−0.918253	+	1.59046i
$489$	18.5560	−	5.42810i	0.839129	−	0.245467i
$490$		0			0
$491$	−1.02344	+	1.77266i	−0.0461874	+	0.0799989i	−0.888195	−	0.459467i	$-0.848040\pi$
$491$	−1.02344	+	1.77266i	−0.0461874	+	0.0799989i	0.842007	+	0.539466i	$0.181374\pi$
$492$	−12.4911	+	51.2624i	−0.563144	+	2.31109i
$493$	−37.1358			−1.67251
$494$	−1.18190	+	2.04712i	−0.0531763	+	0.0921041i
$495$	−3.96019	−	2.05179i	−0.177997	−	0.0922211i
$496$	−30.4097			−1.36544
$497$		0			0
$498$	−12.2807	+	50.3990i	−0.550313	+	2.25843i
$499$	−39.0875			−1.74980			−0.874899	−	0.484305i	$-0.839072\pi$
$499$	−39.0875			−1.74980			−0.874899	+	0.484305i	$0.839072\pi$
$500$	−25.0742	−	43.4297i	−1.12135	−	1.94224i
$501$	−4.33336	−	4.14024i	−0.193600	−	0.184972i
$502$	−18.5679	+	32.1606i	−0.828727	+	1.43540i
$503$	−5.11846			−0.228221			−0.114111	−	0.993468i	$-0.536402\pi$
$503$	−5.11846			−0.228221			−0.114111	+	0.993468i	$0.536402\pi$
$504$		0			0
$505$	−31.8683			−1.41812
$506$	−2.32383	+	4.02499i	−0.103307	+	0.178933i
$507$	21.2171	−	6.20655i	0.942283	−	0.275642i
$508$	31.5079	+	54.5732i	1.39794	+	2.42130i
$509$	29.5272			1.30877			0.654386	−	0.756161i	$-0.272927\pi$
$509$	29.5272			1.30877			0.654386	+	0.756161i	$0.272927\pi$
$510$	72.6562	−	21.2538i	3.21727	−	0.941136i
$511$		0			0
$512$	−41.4078			−1.82998
$513$	10.0634	+	1.97131i	0.444311	+	0.0870354i
$514$	−9.48751	+	16.4328i	−0.418476	+	0.724822i
$515$	−29.3638			−1.29392
$516$	−11.8165	−	11.2899i	−0.520193	−	0.497010i
$517$	−1.28352	+	2.22313i	−0.0564493	+	0.0977730i
$518$		0			0
$519$	7.58113	+	7.24327i	0.332775	+	0.317944i
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	0.532351	−	0.922058i	0.0233227	−	0.0403961i	−0.854128	−	0.520062i	$-0.825909\pi$
$521$	0.532351	−	0.922058i	0.0233227	−	0.0403961i	0.877451	+	0.479666i	$0.159242\pi$
$522$	−50.1234	−	25.9691i	−2.19384	−	1.13664i
$523$	6.69094	+	11.5890i	0.292574	+	0.506754i	0.974418	−	0.224745i	$-0.0721548\pi$
$523$	6.69094	+	11.5890i	0.292574	+	0.506754i	−0.681843	+	0.731498i	$0.738821\pi$
$524$	−17.2581	−	29.8918i	−0.753922	−	1.30583i
$525$		0			0
$526$	−5.18190	+	8.97532i	−0.225942	+	0.391343i
$527$	34.1230			1.48642
$528$	2.20255	+	2.10439i	0.0958536	+	0.0915818i
$529$	−1.39922			−0.0608358
$530$	16.0603	+	27.8173i	0.697615	+	1.20830i
$531$	−0.836219	−	18.3361i	−0.0362888	−	0.795719i
$532$		0			0
$533$	1.82889	+	3.16774i	0.0792181	+	0.137210i
$534$	−14.9626	+	61.4052i	−0.647497	+	2.65726i
$535$	−23.4885	−	40.6833i	−1.01550	−	1.75889i
$536$	−9.09931	−	15.7605i	−0.393031	−	0.680749i
$537$	11.4376	+	10.9279i	0.493571	+	0.471575i
$538$	−25.5286	−	44.2168i	−1.10062	−	1.90632i
$539$		0			0
$540$	75.6224	+	14.8136i	3.25427	+	0.637475i
$541$	17.0438	+	29.5207i	0.732769	+	1.26919i	0.955695	+	0.294358i	$0.0951056\pi$
$541$	17.0438	+	29.5207i	0.732769	+	1.26919i	−0.222927	+	0.974835i	$0.571561\pi$
$542$	−70.0970			−3.01092
$543$	−4.89922	+	20.1059i	−0.210246	+	0.862828i
$544$	−2.61970			−0.112319
$545$	−4.75692	+	8.23922i	−0.203764	+	0.352930i
$546$		0			0
$547$	2.97150	+	5.14678i	0.127052	+	0.220060i	0.922533	−	0.385918i	$-0.126115\pi$
$547$	2.97150	+	5.14678i	0.127052	+	0.220060i	−0.795481	+	0.605978i	$0.792782\pi$
$548$	−0.764686	−	1.32448i	−0.0326658	−	0.0565788i
$549$	20.2849	−	12.9783i	0.865737	−	0.553900i
$550$	−4.19076	+	7.25860i	−0.178694	+	0.309508i
$551$	−7.54638	+	13.0707i	−0.321487	+	0.556831i
$552$	9.63198	−	39.5287i	0.409964	−	1.68245i
$553$		0			0
$554$	−21.1139	+	36.5704i	−0.897044	+	1.55373i
$555$	−14.1534	+	4.14024i	−0.600778	+	0.175743i
$556$	77.0331			3.26693
$557$	15.0402	−	26.0503i	0.637272	−	1.10379i	−0.348756	−	0.937213i	$-0.613396\pi$
$557$	15.0402	−	26.0503i	0.637272	−	1.10379i	0.986029	−	0.166575i	$-0.0532707\pi$
$558$	46.0568	+	23.8622i	1.94974	+	1.01017i
$559$	−1.13298			−0.0479202
$560$		0			0
$561$	−2.47150	−	2.36135i	−0.104347	−	0.0996963i
$562$	23.2340			0.980069
$563$	9.81060	+	16.9925i	0.413468	+	0.716147i	0.995266	−	0.0971860i	$-0.0309842\pi$
$563$	9.81060	+	16.9925i	0.413468	+	0.716147i	−0.581799	+	0.813333i	$0.697651\pi$
$564$	10.5000	−	43.0910i	0.442130	−	1.81446i
$565$	25.5154	−	44.1940i	1.07344	−	1.85926i
$566$	41.5049			1.74458
$567$		0			0
$568$	42.7601			1.79417
$569$	0.687159	−	1.19019i	0.0288072	−	0.0498955i	−0.851262	−	0.524740i	$-0.824162\pi$
$569$	0.687159	−	1.19019i	0.0288072	−	0.0498955i	0.880070	+	0.474845i	$0.157496\pi$
$570$	7.28376	−	29.8918i	0.305083	−	1.25203i
$571$	−8.69076	−	15.0528i	−0.363697	−	0.629941i	0.624869	−	0.780729i	$-0.285152\pi$
$571$	−8.69076	−	15.0528i	−0.363697	−	0.629941i	−0.988566	+	0.150788i	$0.951819\pi$
$572$	0.802077			0.0335365
$573$	11.4467	+	10.9365i	0.478191	+	0.456880i
$574$		0			0
$575$	38.9545			1.62451
$576$	19.5182	+	10.1124i	0.813258	+	0.421352i
$577$	13.5274	−	23.4301i	0.563153	−	0.975409i	−0.434066	−	0.900881i	$-0.642922\pi$
$577$	13.5274	−	23.4301i	0.563153	−	0.975409i	0.997219	−	0.0745283i	$-0.0237451\pi$
$578$	16.1881			0.673337
$579$	−28.1658	+	8.23922i	−1.17053	+	0.342410i
$580$	−56.7080	+	98.2211i	−2.35467	+	4.07841i
$581$		0			0
$582$	9.57227	−	39.2837i	0.396783	−	1.62836i
$583$	0.725191	−	1.25607i	0.0300344	−	0.0520210i
$584$	4.98715	−	8.63800i	0.206370	−	0.357443i
$585$	4.50000	−	2.87911i	0.186052	−	0.119036i
$586$	4.58005	+	7.93288i	0.189200	+	0.327704i
$587$	−3.75700	−	6.50731i	−0.155068	−	0.268585i	0.778016	−	0.628245i	$-0.216226\pi$
$587$	−3.75700	−	6.50731i	−0.155068	−	0.268585i	−0.933084	+	0.359659i	$0.882893\pi$
$588$		0			0
$589$	6.93414	−	12.0103i	0.285716	−	0.494875i
$590$	−55.0698			−2.26719
$591$	−8.74120	+	35.8730i	−0.359565	+	1.47562i
$592$	10.0718			0.413948
$593$	−17.7904	−	30.8139i	−0.730565	−	1.26538i	−0.956642	−	0.291266i	$-0.905924\pi$
$593$	−17.7904	−	30.8139i	−0.730565	−	1.26538i	0.226077	−	0.974109i	$-0.427410\pi$
$594$	−1.68456	−	4.91551i	−0.0691184	−	0.201686i
$595$		0			0
$596$	19.6659	+	34.0623i	0.805545	+	1.39524i
$597$	−12.4911	−	11.9345i	−0.511229	−	0.488445i
$598$	−2.78340	−	4.82100i	−0.113822	−	0.197145i
$599$	5.74105	+	9.94379i	0.234573	+	0.406292i	0.959148	−	0.282903i	$-0.0912975\pi$
$599$	5.74105	+	9.94379i	0.234573	+	0.406292i	−0.724576	+	0.689195i	$0.757964\pi$
$600$	17.3702	−	71.2854i	0.709133	−	2.91021i
$601$	0.190030	+	0.329142i	0.00775150	+	0.0134260i	0.869875	−	0.493272i	$-0.164199\pi$
$601$	0.190030	+	0.329142i	0.00775150	+	0.0134260i	−0.862124	+	0.506698i	$0.830866\pi$
$602$		0			0
$603$	0.492129	+	10.7911i	0.0200411	+	0.439448i
$604$	26.0167	+	45.0623i	1.05861	+	1.83356i
$605$	−39.6346			−1.61138
$606$	−26.8442	−	25.6478i	−1.09047	−	1.04187i
$607$	−18.5409			−0.752551			−0.376275	−	0.926508i	$-0.622795\pi$
$607$	−18.5409			−0.752551			−0.376275	+	0.926508i	$0.622795\pi$
$608$	−0.532351	+	0.922058i	−0.0215897	+	0.0373944i
$609$		0			0
$610$	−36.1249	−	62.5702i	−1.46265	−	2.53339i
$611$	−1.53736	−	2.66278i	−0.0621949	−	0.107725i
$612$	52.4379	+	27.1682i	2.11967	+	1.09821i
$613$	−3.66225	+	6.34321i	−0.147917	+	0.256200i	−0.930457	−	0.366400i	$-0.880590\pi$
$613$	−3.66225	+	6.34321i	−0.147917	+	0.256200i	0.782540	+	0.622600i	$0.213924\pi$
$614$	−37.6077	+	65.1385i	−1.51772	+	2.62877i
$615$	−34.4226	−	32.8885i	−1.38805	−	1.32619i
$616$		0			0
$617$	12.7427	−	22.0710i	0.513002	−	0.888546i	−0.486884	−	0.873466i	$-0.661867\pi$
$617$	12.7427	−	22.0710i	0.513002	−	0.888546i	0.999886	−	0.0150791i	$-0.00480000\pi$
$618$	−24.7345	−	23.6322i	−0.994968	−	0.950627i
$619$	32.8963			1.32222			0.661108	−	0.750291i	$-0.270087\pi$
$619$	32.8963			1.32222			0.661108	+	0.750291i	$0.270087\pi$
$620$	52.1072	−	90.2523i	2.09267	−	3.62462i
$621$	−15.8703	+	18.2032i	−0.636852	+	0.730468i
$622$	−25.6748			−1.02947
$623$		0			0
$624$	−3.50194	+	1.02441i	−0.140190	+	0.0410092i
$625$	3.34221			0.133689
$626$	0.762585	+	1.32084i	0.0304790	+	0.0527912i
$627$	−1.33336	+	0.390043i	−0.0532493	+	0.0155768i
$628$	42.4636	−	73.5490i	1.69448	−	2.93493i
$629$	−11.3016			−0.450626
$630$		0			0
$631$	29.8683			1.18904			0.594519	−	0.804082i	$-0.297343\pi$
$631$	29.8683			1.18904			0.594519	+	0.804082i	$0.297343\pi$
$632$	−20.6264	+	35.7259i	−0.820472	+	1.42110i
$633$	6.12620	+	5.85318i	0.243495	+	0.232643i
$634$	−12.6082	−	21.8380i	−0.500734	−	0.867297i
$635$	−56.8603			−2.25643
$636$	−5.93251	+	24.3464i	−0.235239	+	0.965399i
$637$		0			0
$638$	7.64766			0.302774
$639$	−22.5364	−	11.6762i	−0.891525	−	0.461902i
$640$	34.9496	−	60.5344i	1.38150	−	2.39283i
$641$	11.4605			0.452663			0.226331	−	0.974050i	$-0.427327\pi$
$641$	11.4605			0.452663			0.226331	+	0.974050i	$0.427327\pi$
$642$	12.9568	−	53.1733i	0.511362	−	2.09858i
$643$	8.69078	−	15.0529i	0.342731	−	0.593627i	−0.642208	−	0.766531i	$-0.721981\pi$
$643$	8.69078	−	15.0529i	0.342731	−	0.593627i	0.984939	+	0.172903i	$0.0553147\pi$
$644$		0			0
$645$	14.1534	−	4.14024i	0.557290	−	0.163022i
$646$	11.7896	−	20.4202i	0.463855	−	0.803421i
$647$	−12.6720	+	21.9485i	−0.498186	+	0.862883i	−0.999998	−	0.00209358i	$-0.999334\pi$
$647$	−12.6720	+	21.9485i	−0.498186	+	0.862883i	0.501812	+	0.864977i	$0.332667\pi$
$648$	26.2345	+	37.1590i	1.03059	+	1.45975i
$649$	1.24332	+	2.15349i	0.0488045	+	0.0845320i
$650$	−5.01954	−	8.69410i	−0.196883	−	0.341011i
$651$		0			0
$652$	22.6264	−	39.1900i	0.886116	−	1.53480i
$653$	14.0833			0.551121			0.275560	−	0.961284i	$-0.411137\pi$
$653$	14.0833			0.551121			0.275560	+	0.961284i	$0.411137\pi$
$654$	−10.6380	+	3.11188i	−0.415977	+	0.121684i
$655$	31.1445			1.21692
$656$	16.2581	+	28.1599i	0.634774	+	1.09946i
$657$	−4.98715	+	3.19079i	−0.194567	+	0.124484i
$658$		0			0
$659$	−19.0854	−	33.0569i	−0.743462	−	1.28771i	−0.950910	−	0.309467i	$-0.899849\pi$
$659$	−19.0854	−	33.0569i	−0.743462	−	1.28771i	0.207449	−	0.978246i	$-0.433484\pi$
$660$	−10.0197	+	2.93101i	−0.390014	+	0.114089i
$661$	0.176866	+	0.306341i	0.00687930	+	0.0119153i	0.869445	−	0.494031i	$-0.164477\pi$
$661$	0.176866	+	0.306341i	0.00687930	+	0.0119153i	−0.862565	+	0.505946i	$0.831144\pi$
$662$	25.0526	+	43.3924i	0.973698	+	1.68649i
$663$	3.92955	−	1.14950i	0.152611	−	0.0446428i
$664$	30.7591	+	53.2764i	1.19369	+	2.06752i
$665$		0			0
$666$	−15.2542	−	7.90324i	−0.591087	−	0.306244i
$667$	−17.7719	−	30.7818i	−0.688130	−	1.19188i
$668$	−14.0281			−0.542762
$669$	−38.9145	+	11.3835i	−1.50452	+	0.440112i
$670$	32.4096			1.25209
$671$	−1.63119	+	2.82531i	−0.0629715	+	0.109070i
$672$		0			0
$673$	10.5555	+	18.2827i	0.406886	+	0.704748i	0.994539	−	0.104365i	$-0.0332811\pi$
$673$	10.5555	+	18.2827i	0.406886	+	0.704748i	−0.587653	+	0.809113i	$0.699948\pi$
$674$	7.02704	+	12.1712i	0.270672	+	0.468817i
$675$	−28.6202	+	32.8273i	−1.10159	+	1.26352i
$676$	25.8712	−	44.8102i	0.995046	−	1.72347i
$677$	−10.5732	+	18.3133i	−0.406361	+	0.703837i	−0.994479	−	0.104938i	$-0.966536\pi$
$677$	−10.5732	+	18.3133i	−0.406361	+	0.703837i	0.588118	+	0.808775i	$0.299869\pi$
$678$	57.0605	−	16.6917i	2.19140	−	0.641041i
$679$		0			0
$680$	44.8879	−	77.7482i	1.72137	−	2.98151i
$681$	2.50885	−	10.2961i	0.0961395	−	0.394547i
$682$	−7.02720			−0.269085
$683$	−17.3858	+	30.1131i	−0.665249	+	1.15224i	0.313969	+	0.949433i	$0.398341\pi$
$683$	−17.3858	+	30.1131i	−0.665249	+	1.15224i	−0.979218	+	0.202811i	$0.934992\pi$
$684$	20.2183	−	12.9357i	0.773067	−	0.494610i
$685$	1.37998			0.0527264
$686$		0			0
$687$	−0.598835	+	2.45756i	−0.0228470	+	0.0937618i
$688$	−10.0718			−0.383984
$689$	0.868609	+	1.50447i	0.0330914	+	0.0573159i
$690$	52.3879	+	50.0532i	1.99437	+	1.90549i
$691$	−17.3246	+	30.0071i	−0.659059	+	1.14152i	0.321801	+	0.946807i	$0.395712\pi$
$691$	−17.3246	+	30.0071i	−0.659059	+	1.14152i	−0.980860	+	0.194716i	$0.937622\pi$
$692$	24.5418			0.932940
$693$		0			0
$694$	21.8525			0.829511
$695$	−34.7542	+	60.1960i	−1.31830	+	2.28336i
$696$	−64.2544	+	18.7961i	−2.43556	+	0.712464i
$697$	−18.2434	−	31.5985i	−0.691017	−	1.19688i
$698$	−51.6087			−1.95342
$699$	22.0240	−	6.44260i	0.833024	−	0.243681i
$700$		0			0
$701$	−48.6050			−1.83579			−0.917894	−	0.396826i	$-0.870111\pi$
$701$	−48.6050			−1.83579			−0.917894	+	0.396826i	$0.870111\pi$
$702$	6.10769	+	1.19643i	0.230520	+	0.0451562i
$703$	−2.29661	+	3.97784i	−0.0866182	+	0.150027i
$704$	−2.97802			−0.112238
$705$	28.9354	+	27.6459i	1.08977	+	1.04121i
$706$	−18.1651	+	31.4629i	−0.683654	+	1.18412i
$707$		0			0
$708$	−31.0634	−	29.6791i	−1.16743	−	1.11541i
$709$	−2.05408	+	3.55778i	−0.0771428	+	0.133615i	−0.902016	−	0.431702i	$-0.857913\pi$
$709$	−2.05408	+	3.55778i	−0.0771428	+	0.133615i	0.824873	+	0.565318i	$0.191246\pi$
$710$	−38.0753	+	65.9483i	−1.42894	+	2.47500i
$711$	20.6264	−	13.1968i	0.773549	−	0.494918i
$712$	37.4764	+	64.9110i	1.40449	+	2.43264i
$713$	16.3300	+	28.2844i	0.611564	+	1.05926i
$714$		0			0
$715$	−0.361864	+	0.626767i	−0.0135330	+	0.0234398i
$716$	37.0263			1.38374
$717$	24.2811	+	23.1990i	0.906795	+	0.866383i
$718$	17.7453			0.662249
$719$	−24.1408	−	41.8131i	−0.900299	−	1.55936i	−0.827106	−	0.562047i	$-0.810014\pi$
$719$	−24.1408	−	41.8131i	−0.900299	−	1.55936i	−0.0731939	−	0.997318i	$-0.523319\pi$
$720$	40.0032	−	25.5941i	1.49083	−	0.953837i
$721$		0			0
$722$	18.5833	+	32.1872i	0.691597	+	1.19788i
$723$	2.07227	−	8.50440i	0.0770686	−	0.316282i
$724$	24.2187	+	41.9481i	0.900082	+	1.55899i
$725$	−32.0495	−	55.5114i	−1.19029	−	2.06164i
$726$	−33.3861	−	31.8982i	−1.23907	−	1.18385i
$727$	20.5151	+	35.5332i	0.760863	+	1.31785i	0.942406	+	0.334470i	$0.108557\pi$
$727$	20.5151	+	35.5332i	0.760863	+	1.31785i	−0.181543	+	0.983383i	$0.558109\pi$
$728$		0			0
$729$	−3.67996	−	26.7480i	−0.136295	−	0.990668i
$730$	8.88151	+	15.3832i	0.328720	+	0.569359i
$731$	11.3016			0.418006
$732$	13.3442	−	54.7631i	0.493214	−	2.02410i
$733$	30.5428			1.12812			0.564062	−	0.825733i	$-0.309238\pi$
$733$	30.5428			1.12812			0.564062	+	0.825733i	$0.309238\pi$
$734$	−13.5011	+	23.3845i	−0.498334	+	0.863139i
$735$		0			0
$736$	−1.25370	−	2.17147i	−0.0462118	−	0.0800413i
$737$	−0.731715	−	1.26737i	−0.0269531	−	0.0466841i
$738$	−2.52684	−	55.4071i	−0.0930143	−	2.03956i
$739$	−11.9100	+	20.6288i	−0.438117	+	0.758841i	−0.997544	−	0.0700384i	$-0.977688\pi$
$739$	−11.9100	+	20.6288i	−0.438117	+	0.758841i	0.559427	+	0.828880i	$0.311021\pi$
$740$	−17.2581	+	29.8918i	−0.634419	+	1.09885i
$741$	0.393936	−	1.61668i	0.0144716	−	0.0593901i
$742$		0			0
$743$	−5.26089	+	9.11213i	−0.193003	+	0.334292i	−0.946244	−	0.323453i	$-0.895156\pi$
$743$	−5.26089	+	9.11213i	−0.193003	+	0.334292i	0.753241	+	0.657745i	$0.228490\pi$
$744$	59.0413	−	17.2711i	2.16456	−	0.633191i
$745$	−35.4897			−1.30024
$746$	0.668971	−	1.15869i	0.0244928	−	0.0424227i
$747$	−1.66358	−	36.4781i	−0.0608673	−	1.33466i
$748$	−8.00079			−0.292538
$749$		0			0
$750$	38.1160	+	36.4174i	1.39180	+	1.32977i
$751$	−10.2704			−0.374773			−0.187386	−	0.982286i	$-0.560002\pi$
$751$	−10.2704			−0.374773			−0.187386	+	0.982286i	$0.560002\pi$
$752$	−13.6665	−	23.6711i	−0.498367	−	0.863197i
$753$	6.18882	−	25.3983i	0.225533	−	0.925565i
$754$	−4.58005	+	7.93288i	−0.166796	+	0.288899i
$755$	−46.9507			−1.70871
$756$		0			0
$757$	8.03930			0.292193			0.146097	−	0.989270i	$-0.453329\pi$
$757$	8.03930			0.292193			0.146097	+	0.989270i	$0.453329\pi$
$758$	27.9159	−	48.3518i	1.01395	−	1.75622i
$759$	0.774549	−	3.17868i	0.0281144	−	0.115379i
$760$	−18.2434	−	31.5985i	−0.661757	−	1.14620i
$761$	27.6604			1.00269			0.501345	−	0.865247i	$-0.332839\pi$
$761$	27.6604			1.00269			0.501345	+	0.865247i	$0.332839\pi$
$762$	−47.8961	−	45.7616i	−1.73509	−	1.65777i
$763$		0			0
$764$	37.0554			1.34062
$765$	−44.8879	+	28.7194i	−1.62293	+	1.03835i
$766$	43.9371	−	76.1013i	1.58751	−	2.74965i
$767$	−2.97841			−0.107544
$768$	53.7962	−	15.7368i	1.94120	−	0.567853i
$769$	16.9613	−	29.3778i	0.611640	−	1.05939i	−0.379324	−	0.925264i	$-0.623843\pi$
$769$	16.9613	−	29.3778i	0.611640	−	1.05939i	0.990964	−	0.134128i	$-0.0428233\pi$
$770$		0			0
$771$	3.16225	−	12.9776i	0.113886	−	0.467376i
$772$	−34.3442	+	59.4858i	−1.23607	+	2.14094i
$773$	14.2978	−	24.7645i	0.514256	−	0.890717i	−0.485607	−	0.874177i	$-0.661401\pi$
$773$	14.2978	−	24.7645i	0.514256	−	0.890717i	0.999863	−	0.0165403i	$-0.00526518\pi$
$774$	15.2542	+	7.90324i	0.548300	+	0.284076i
$775$	29.4493	+	51.0077i	1.05785	+	1.83225i
$776$	−23.9753	−	41.5265i	−0.860664	−	1.49071i
$777$		0			0
$778$	−47.5605	+	82.3772i	−1.70513	+	2.95337i
$779$	−14.8290			−0.531303
$780$	2.96027	−	12.1487i	0.105995	−	0.434992i
$781$	3.43852			0.123040
$782$	27.7647	+	48.0899i	0.992864	+	1.71969i
$783$	38.9973	+	7.63912i	1.39365	+	0.273000i
$784$		0			0
$785$	38.3157	+	66.3647i	1.36754	+	2.36866i
$786$	26.2345	+	25.0654i	0.935755	+	0.894052i
$787$	−23.0017	−	39.8402i	−0.819923	−	1.42015i	−0.905738	−	0.423838i	$-0.860683\pi$
$787$	−23.0017	−	39.8402i	−0.819923	−	1.42015i	0.0858145	−	0.996311i	$-0.472651\pi$
$788$	43.2111	+	74.8438i	1.53933	+	2.66620i
$789$	1.72716	−	7.08811i	0.0614887	−	0.252344i
$790$	−36.7330	−	63.6235i	−1.30690	−	2.26362i
$791$		0			0
$792$	−5.47150	−	2.83480i	−0.194421	−	0.100730i
$793$	−1.95379	−	3.38406i	−0.0693810	−	0.120171i
$794$	29.3977			1.04328
$795$	−16.3485	−	15.6200i	−0.579823	−	0.553983i
$796$	−40.4367			−1.43324
$797$	18.4558	−	31.9664i	0.653739	−	1.13231i	−0.328469	−	0.944515i	$-0.606533\pi$
$797$	18.4558	−	31.9664i	0.653739	−	1.13231i	0.982208	−	0.187795i	$-0.0601339\pi$
$798$		0			0
$799$	15.3353	+	26.5615i	0.542524	+	0.939679i
$800$	−2.26089	−	3.91598i	−0.0799346	−	0.138451i
$801$	−2.02688	−	44.4442i	−0.0716163	−	1.57036i
$802$	−39.8068	+	68.9474i	−1.40563	+	2.43462i
$803$	0.401038	−	0.694619i	0.0141523	−	0.0245126i
$804$	18.2814	+	17.4666i	0.644734	+	0.616001i
$805$		0			0
$806$	4.20847	−	7.28928i	0.148237	−	0.256754i
$807$	25.9868	+	24.8286i	0.914777	+	0.874010i
$808$	−44.0300			−1.54897
$809$	−23.8444	+	41.2996i	−0.838323	+	1.45202i	0.0529735	+	0.998596i	$0.483130\pi$
$809$	−23.8444	+	41.2996i	−0.838323	+	1.45202i	−0.891296	+	0.453422i	$0.850203\pi$
$810$	−80.6701	+	7.37327i	−2.83446	+	0.259070i
$811$	−6.02728			−0.211646			−0.105823	−	0.994385i	$-0.533748\pi$
$811$	−6.02728			−0.211646			−0.105823	+	0.994385i	$0.533748\pi$
$812$		0			0
$813$	47.3594	−	13.8539i	1.66097	−	0.485877i
$814$	2.32743			0.0815764
$815$	20.4162	+	35.3619i	0.715148	+	1.23867i
$816$	34.9322	−	10.2186i	1.22287	−	0.357722i
$817$	2.29661	−	3.97784i	0.0803481	−	0.139167i
$818$	−46.6881			−1.63241
$819$		0			0
$820$	−111.434			−3.89143
$821$	19.6321	−	34.0038i	0.685165	−	1.18674i	−0.288220	−	0.957564i	$-0.593064\pi$
$821$	19.6321	−	34.0038i	0.685165	−	1.18674i	0.973385	−	0.229176i	$-0.0736031\pi$
$822$	1.16242	+	1.11062i	0.0405442	+	0.0387373i
$823$	−11.3815	−	19.7134i	−0.396735	−	0.687165i	0.596586	−	0.802549i	$-0.296523\pi$
$823$	−11.3815	−	19.7134i	−0.396735	−	0.687165i	−0.993321	+	0.115384i	$0.963190\pi$
$824$	−40.5697			−1.41331
$825$	1.39681	−	5.73237i	0.0486306	−	0.199575i
$826$		0			0
$827$	−28.9286			−1.00595			−0.502973	−	0.864302i	$-0.667760\pi$
$827$	−28.9286			−1.00595			−0.502973	+	0.864302i	$0.667760\pi$
$828$	2.57520	+	56.4674i	0.0894943	+	1.96238i
$829$	−16.9883	+	29.4247i	−0.590029	+	1.02196i	0.404198	+	0.914671i	$0.367551\pi$
$829$	−16.9883	+	29.4247i	−0.590029	+	1.02196i	−0.994228	+	0.107290i	$0.965783\pi$
$830$	−109.557			−3.80276
$831$	7.03741	−	28.8809i	0.244125	−	1.00187i
$832$	1.78348	−	3.08908i	0.0618312	−	0.107095i
$833$		0			0
$834$	−77.7213	+	22.7355i	−2.69127	+	0.787267i
$835$	6.32889	−	10.9620i	0.219020	−	0.379354i
$836$	−1.62584	+	2.81604i	−0.0562310	+	0.0973949i
$837$	−35.8334	−	7.01935i	−1.23858	−	0.242624i
$838$	−21.2716	−	36.8435i	−0.734816	−	1.27274i
$839$	19.0206	+	32.9446i	0.656663	+	1.13737i	0.981474	+	0.191595i	$0.0613659\pi$
$839$	19.0206	+	32.9446i	0.656663	+	1.13737i	−0.324811	+	0.945779i	$0.605301\pi$
$840$		0			0
$841$	−14.7434	+	25.5363i	−0.508392	+	0.880561i
$842$	45.7673			1.57725
$843$	−15.6976	+	4.59195i	−0.540652	+	0.158155i
$844$	19.8319			0.682642
$845$	23.3441	+	40.4331i	0.803060	+	1.39094i
$846$	2.12405	+	46.5749i	0.0730264	+	1.60128i
$847$		0			0
$848$	7.72159	+	13.3742i	0.265161	+	0.459272i
$849$	−28.0418	+	8.20297i	−0.962393	+	0.281525i
$850$	50.0704	+	86.7245i	1.71740	+	2.97463i
$851$	−5.40856	−	9.36790i	−0.185403	−	0.321127i
$852$	−57.0191	+	16.6796i	−1.95344	+	0.571433i
$853$	4.90746	+	8.49996i	0.168028	+	0.291033i	0.937726	−	0.347374i	$-0.112927\pi$
$853$	4.90746	+	8.49996i	0.168028	+	0.291033i	−0.769698	+	0.638408i	$0.779593\pi$
$854$		0			0
$855$	0.986679	+	21.6353i	0.0337437	+	0.739912i
$856$	−32.4523	−	56.2091i	−1.10920	−	1.92119i
$857$	−26.7360			−0.913285			−0.456642	−	0.889650i	$-0.650948\pi$
$857$	−26.7360			−0.913285			−0.456642	+	0.889650i	$0.650948\pi$
$858$	−0.809243	+	0.236725i	−0.0276271	+	0.00808165i
$859$	18.4882			0.630810			0.315405	−	0.948957i	$-0.397860\pi$
$859$	18.4882			0.630810			0.315405	+	0.948957i	$0.397860\pi$
$860$	17.2581	−	29.8918i	0.588495	−	1.01930i
$861$		0			0
$862$	19.5344	+	33.8346i	0.665345	+	1.15241i
$863$	4.57393	+	7.92228i	0.155698	+	0.269677i	0.933313	−	0.359064i	$-0.116904\pi$
$863$	4.57393	+	7.92228i	0.155698	+	0.269677i	−0.777615	+	0.628741i	$0.783571\pi$
$864$	2.75101	+	0.538892i	0.0935914	+	0.0183335i
$865$	−11.0723	+	19.1777i	−0.376469	+	0.652063i
$866$	49.7473	−	86.1649i	1.69048	−	2.92800i
$867$	−10.9371	+	3.19940i	−0.371444	+	0.108657i
$868$		0			0
$869$	−1.65865	+	2.87287i	−0.0562660	+	0.0974555i
$870$	28.2257	−	115.835i	0.956940	−	3.92719i
$871$	1.75285			0.0593929
$872$	−6.57227	+	11.3835i	−0.222565	+	0.385494i
$873$	1.29669	+	28.4330i	0.0438862	+	0.962310i
$874$	22.5683			0.763385
$875$		0			0
$876$	−3.28074	+	13.4638i	−0.110846	+	0.454901i
$877$	22.6883			0.766130			0.383065	−	0.923721i	$-0.374869\pi$
$877$	22.6883			0.766130			0.383065	+	0.923721i	$0.374869\pi$
$878$	15.3301	+	26.5525i	0.517366	+	0.896104i
$879$	−4.66225	−	4.45448i	−0.157254	−	0.150246i
$880$	−3.21683	+	5.57172i	−0.108439	+	0.187823i
$881$	−15.3696			−0.517815			−0.258907	−	0.965902i	$-0.583362\pi$
$881$	−15.3696			−0.517815			−0.258907	+	0.965902i	$0.583362\pi$
$882$		0			0
$883$	29.6372			0.997370			0.498685	−	0.866783i	$-0.333817\pi$
$883$	29.6372			0.997370			0.498685	+	0.866783i	$0.333817\pi$
$884$	4.79153	−	8.29918i	0.161157	−	0.279132i
$885$	37.2067	−	10.8839i	1.25069	−	0.365859i
$886$	10.1259	+	17.5385i	0.340185	+	0.589219i
$887$	18.7650			0.630069			0.315034	−	0.949080i	$-0.397984\pi$
$887$	18.7650			0.630069			0.315034	+	0.949080i	$0.397984\pi$
$888$	−19.5547	+	5.72026i	−0.656212	+	0.191959i
$889$		0			0
$890$	−133.482			−4.47432
$891$	2.10963	+	2.98812i	0.0706753	+	0.100106i
$892$	−47.4507	+	82.1870i	−1.58877	+	2.75183i
$893$	12.4652			0.417131
$894$	−29.8947	−	28.5624i	−0.999828	−	0.955270i
$895$	−16.7047	+	28.9335i	−0.558378	+	0.967139i
$896$		0			0
$897$	2.83336	+	2.70709i	0.0946031	+	0.0903871i
$898$	−6.94445	+	12.0281i	−0.231739	+	0.401384i
$899$	26.8708	−	46.5416i	0.896192	−	1.55225i
$900$	4.64406	+	101.832i	0.154802	+	3.39441i
$901$	−8.66445	−	15.0073i	−0.288655	−	0.499965i
$902$	3.75700	+	6.50731i	0.125094	+	0.216670i
$903$		0			0
$904$	35.2527	−	61.0595i	1.17249	−	2.03081i
$905$	−43.7060			−1.45284
$906$	−39.5488	−	37.7863i	−1.31392	−	1.25537i
$907$	−31.1082			−1.03293			−0.516465	−	0.856308i	$-0.672752\pi$
$907$	−31.1082			−1.03293			−0.516465	+	0.856308i	$0.672752\pi$
$908$	−12.4022	−	21.4813i	−0.411582	−	0.712881i
$909$	23.2056	+	12.0229i	0.769683	+	0.398775i
$910$		0			0
$911$	−8.73764	−	15.1340i	−0.289491	−	0.501413i	0.684197	−	0.729297i	$-0.260153\pi$
$911$	−8.73764	−	15.1340i	−0.289491	−	0.501413i	−0.973688	+	0.227884i	$0.926819\pi$
$912$	3.50194	−	14.3716i	0.115961	−	0.475892i
$913$	2.47347	+	4.28418i	0.0818600	+	0.141786i
$914$	−6.23599	−	10.8010i	−0.206268	−	0.357267i
$915$	36.7732	+	35.1344i	1.21569	+	1.16151i
$916$	2.96027	+	5.12734i	0.0978101	+	0.169412i
$917$		0			0
$918$	−60.9248	−	11.9345i	−2.01082	−	0.393896i
$919$	−21.0993	−	36.5451i	−0.696002	−	1.20551i	−0.969842	−	0.243736i	$-0.921627\pi$
$919$	−21.0993	−	36.5451i	−0.696002	−	1.20551i	0.273840	−	0.961775i	$-0.411706\pi$
$920$	85.9270			2.83293
$921$	12.5349	−	51.4421i	0.413039	−	1.69507i
$922$	19.1344			0.630158
$923$	−2.05927	+	3.56676i	−0.0677818	+	0.117401i
$924$		0			0
$925$	−9.75370	−	16.8939i	−0.320700	−	0.555468i
$926$	11.2937	+	19.5612i	0.371133	+	0.642821i
$927$	21.3820	+	11.0781i	0.702276	+	0.363851i
$928$	−2.06294	+	3.57311i	−0.0677193	+	0.117293i
$929$	24.2056	−	41.9253i	0.794159	−	1.37552i	−0.129213	−	0.991617i	$-0.541245\pi$
$929$	24.2056	−	41.9253i	0.794159	−	1.37552i	0.923372	−	0.383907i	$-0.125422\pi$
$930$	−25.9357	+	106.438i	−0.850465	+	3.49022i
$931$		0			0
$932$	26.8551	−	46.5145i	0.879670	−	1.52363i
$933$	17.3466	−	5.07434i	0.567902	−	0.166126i
$934$	33.8699			1.10826
$935$	3.60963	−	6.25206i	0.118048	−	0.204464i
$936$	6.21731	−	3.97784i	0.203219	−	0.130020i
$937$	22.6750			0.740762			0.370381	−	0.928880i	$-0.379227\pi$
$937$	22.6750			0.740762			0.370381	+	0.928880i	$0.379227\pi$
$938$		0			0
$939$	−0.776271	−	0.741676i	−0.0253327	−	0.0242037i
$940$	93.6706			3.05520
$941$	−24.9753	−	43.2584i	−0.814170	−	1.41018i	−0.909922	−	0.414779i	$-0.863859\pi$
$941$	−24.9753	−	43.2584i	−0.814170	−	1.41018i	0.0957523	−	0.995405i	$-0.469474\pi$
$942$	−21.1357	+	86.7388i	−0.688638	+	2.82610i
$943$	17.4613	−	30.2438i	0.568617	−	0.984873i
$944$	−26.4769			−0.861749
$945$		0			0
$946$	−2.32743			−0.0756713
$947$	−8.85613	+	15.3393i	−0.287786	+	0.498459i	−0.973281	−	0.229618i	$-0.926252\pi$
$947$	−8.85613	+	15.3393i	−0.287786	+	0.498459i	0.685495	+	0.728077i	$0.259586\pi$
$948$	13.5688	−	55.6850i	0.440694	−	1.80857i
$949$	0.480350	+	0.831990i	0.0155928	+	0.0270075i
$950$	40.6993			1.32046
$951$	12.8345	+	12.2625i	0.416186	+	0.397638i
$952$		0			0
$953$	38.0229			1.23168			0.615842	−	0.787870i	$-0.288816\pi$
$953$	38.0229			1.23168			0.615842	+	0.787870i	$0.288816\pi$
$954$	−1.20009	−	26.3149i	−0.0388544	−	0.851975i
$955$	−16.7179	+	28.9563i	−0.540979	+	0.937002i
$956$	78.6035			2.54222
$957$	−5.16697	+	1.51147i	−0.167024	+	0.0488590i
$958$	10.7177	−	18.5635i	0.346272	−	0.599761i
$959$		0			0
$960$	−10.9911	+	45.1066i	−0.354738	+	1.45581i
$961$	−9.19076	+	15.9189i	−0.296476	+	0.513512i
$962$	−1.39386	+	2.41423i	−0.0449398	+	0.0778380i
$963$	1.75516	+	38.4861i	0.0565592	+	1.24020i
$964$	−10.2440	−	17.7432i	−0.329938	−	0.571469i
$965$	−30.9894	−	53.6752i	−0.997583	−	1.72786i
$966$		0			0
$967$	15.5064	−	26.8579i	0.498652	−	0.863691i	−0.501346	−	0.865247i	$-0.667162\pi$
$967$	15.5064	−	26.8579i	0.498652	−	0.863691i	0.999999	+	0.00155529i	$0.000495066\pi$
$968$	−54.7601			−1.76006
$969$	−3.92955	+	16.1265i	−0.126235	+	0.518058i
$970$	85.3943			2.74185
$971$	−7.28376	−	12.6158i	−0.233747	−	0.404862i	0.725161	−	0.688580i	$-0.241765\pi$
$971$	−7.28376	−	12.6158i	−0.233747	−	0.404862i	−0.958908	+	0.283718i	$0.908432\pi$
$972$	−49.4776	−	39.3169i	−1.58699	−	1.26109i
$973$		0			0
$974$	22.1893	+	38.4330i	0.710991	+	1.23147i
$975$	5.10963	+	4.88192i	0.163639	+	0.156346i
$976$	−17.3684	−	30.0830i	−0.555949	−	0.962932i
$977$	23.9399	+	41.4651i	0.765904	+	1.32659i	0.939767	+	0.341815i	$0.111042\pi$
$977$	23.9399	+	41.4651i	0.765904	+	1.32659i	−0.173863	+	0.984770i	$0.555625\pi$
$978$	−11.2620	+	46.2181i	−0.360118	+	1.47789i
$979$	3.01364	+	5.21978i	0.0963163	+	0.166825i
$980$		0			0
$981$	6.57227	−	4.20495i	0.209836	−	0.134254i
$982$	−2.51819	−	4.36163i	−0.0803586	−	0.139185i
$983$	44.4257			1.41696			0.708479	−	0.705732i	$-0.249382\pi$
$983$	44.4257			1.41696			0.708479	+	0.705732i	$0.249382\pi$
$984$	−47.5590	−	45.4395i	−1.51613	−	1.44856i
$985$	−77.9803			−2.48466
$986$	45.6864	−	79.1313i	1.45495	−	2.52005i
$987$		0			0
$988$	−1.94738	−	3.37296i	−0.0619544	−	0.107308i
$989$	5.40856	+	9.36790i	0.171982	+	0.297882i
$990$	9.24411	−	5.91439i	0.293797	−	0.187972i
$991$	20.8078	−	36.0401i	0.660981	−	1.14485i	−0.319377	−	0.947628i	$-0.603474\pi$
$991$	20.8078	−	36.0401i	0.660981	−	1.14485i	0.980358	−	0.197225i	$-0.0631929\pi$
$992$	1.89557	−	3.28322i	0.0601844	−	0.104242i
$993$	−25.5023	−	24.3657i	−0.809290	−	0.773223i
$994$		0			0
$995$	18.2434	−	31.5985i	0.578354	−	1.00174i
$996$	−61.7979	−	59.0439i	−1.95814	−	1.87088i
$997$	−13.0281			−0.412606			−0.206303	−	0.978488i	$-0.566143\pi$
$997$	−13.0281			−0.412606			−0.206303	+	0.978488i	$0.566143\pi$
$998$	48.0875	−	83.2901i	1.52218	−	2.63650i
$999$	11.8681	+	2.32483i	0.375491	+	0.0735544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.g.67.2		12
3.2	odd	2		1323.2.g.g.361.5		12
7.2	even	3		441.2.h.g.373.6		12
7.3	odd	6		441.2.f.g.148.2	yes	12
7.4	even	3		441.2.f.g.148.1	✓	12
7.5	odd	6		441.2.h.g.373.5		12
7.6	odd	2	inner	441.2.g.g.67.1		12
9.2	odd	6		1323.2.h.g.802.2		12
9.7	even	3		441.2.h.g.214.6		12
21.2	odd	6		1323.2.h.g.226.2		12
21.5	even	6		1323.2.h.g.226.1		12
21.11	odd	6		1323.2.f.g.442.6		12
21.17	even	6		1323.2.f.g.442.5		12
21.20	even	2		1323.2.g.g.361.6		12
63.2	odd	6		1323.2.g.g.667.5		12
63.4	even	3		3969.2.a.be.1.6		6
63.11	odd	6		1323.2.f.g.883.6		12
63.16	even	3	inner	441.2.g.g.79.2		12
63.20	even	6		1323.2.h.g.802.1		12
63.25	even	3		441.2.f.g.295.1	yes	12
63.31	odd	6		3969.2.a.be.1.5		6
63.32	odd	6		3969.2.a.bd.1.1		6
63.34	odd	6		441.2.h.g.214.5		12
63.38	even	6		1323.2.f.g.883.5		12
63.47	even	6		1323.2.g.g.667.6		12
63.52	odd	6		441.2.f.g.295.2	yes	12
63.59	even	6		3969.2.a.bd.1.2		6
63.61	odd	6	inner	441.2.g.g.79.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.1	✓	12	7.4	even	3
441.2.f.g.148.2	yes	12	7.3	odd	6
441.2.f.g.295.1	yes	12	63.25	even	3
441.2.f.g.295.2	yes	12	63.52	odd	6
441.2.g.g.67.1		12	7.6	odd	2	inner
441.2.g.g.67.2		12	1.1	even	1	trivial
441.2.g.g.79.1		12	63.61	odd	6	inner
441.2.g.g.79.2		12	63.16	even	3	inner
441.2.h.g.214.5		12	63.34	odd	6
441.2.h.g.214.6		12	9.7	even	3
441.2.h.g.373.5		12	7.5	odd	6
441.2.h.g.373.6		12	7.2	even	3
1323.2.f.g.442.5		12	21.17	even	6
1323.2.f.g.442.6		12	21.11	odd	6
1323.2.f.g.883.5		12	63.38	even	6
1323.2.f.g.883.6		12	63.11	odd	6
1323.2.g.g.361.5		12	3.2	odd	2
1323.2.g.g.361.6		12	21.20	even	2
1323.2.g.g.667.5		12	63.2	odd	6
1323.2.g.g.667.6		12	63.47	even	6
1323.2.h.g.226.1		12	21.5	even	6
1323.2.h.g.226.2		12	21.2	odd	6
1323.2.h.g.802.1		12	63.20	even	6
1323.2.h.g.802.2		12	9.2	odd	6
3969.2.a.bd.1.1		6	63.32	odd	6
3969.2.a.bd.1.2		6	63.59	even	6
3969.2.a.be.1.5		6	63.31	odd	6
3969.2.a.be.1.6		6	63.4	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23025 + 2.13086i) q^{2} +(0.410052 - 1.68281i) q^{3} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} +(3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(-2.66372 - 1.38008i) q^{9} +O(q^{10})\)	\(q+(-1.23025 + 2.13086i) q^{2} +(0.410052 - 1.68281i) q^{3} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} +(3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(-2.66372 - 1.38008i) q^{9} +(-4.50036 + 7.79485i) q^{10} +0.406421 q^{11} +(-6.73945 + 1.97146i) q^{12} +(-0.243398 + 0.421578i) q^{13} +(1.50000 - 6.15585i) q^{15} +(-2.16372 + 3.74766i) q^{16} +(2.42792 - 4.20528i) q^{17} +(6.21780 - 3.97816i) q^{18} +(-0.986757 - 1.70911i) q^{19} +(-7.41507 - 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +4.64766 q^{23} +(2.07244 - 8.50508i) q^{24} +8.38151 q^{25} +(-0.598883 - 1.03729i) q^{26} +(-3.41468 + 3.91663i) q^{27} +(-3.82383 - 6.62307i) q^{29} +(11.2719 + 10.7695i) q^{30} +(3.51360 + 6.08573i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(0.166653 - 0.683930i) q^{33} +(5.97391 + 10.3471i) q^{34} +(0.554084 + 12.1496i) q^{36} +(-1.16372 - 2.01561i) q^{37} +4.85584 q^{38} +(0.609631 + 0.582462i) q^{39} +18.4882 q^{40} +(3.75700 - 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +(-0.823832 - 1.42692i) q^{44} +(-9.74407 - 5.04844i) q^{45} +(-5.71780 + 9.90352i) q^{46} +(-3.15811 + 5.47002i) q^{47} +(5.41938 + 5.17786i) q^{48} +(-10.3114 + 17.8598i) q^{50} +(-6.08113 - 5.81012i) q^{51} +1.97351 q^{52} +(1.78434 - 3.09056i) q^{53} +(-4.14487 - 12.0946i) q^{54} +1.48672 q^{55} +(-3.28074 + 0.959702i) q^{57} +18.8171 q^{58} +(3.05919 + 5.29868i) q^{59} +(-24.6534 + 7.21177i) q^{60} +(-4.01356 + 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(-0.890369 + 1.54216i) q^{65} +(1.25233 + 1.19652i) q^{66} +(-1.80039 - 3.11836i) q^{67} -19.6860 q^{68} +(1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(-13.4626 - 6.97504i) q^{72} +(0.986757 - 1.70911i) q^{73} +5.72665 q^{74} +(3.43685 - 14.1045i) q^{75} +(-4.00040 + 6.92889i) q^{76} +(-1.99115 + 0.582462i) q^{78} +(-4.08113 + 7.06872i) q^{79} +(-7.91503 + 13.7092i) q^{80} +(5.19076 + 7.35228i) q^{81} +(9.24411 + 16.0113i) q^{82} +(6.08600 + 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} -5.72665 q^{86} +(-12.7134 + 3.71899i) q^{87} +2.05408 q^{88} +(7.41507 + 12.8433i) q^{89} +(22.7452 - 14.5524i) q^{90} +(-9.42101 - 16.3177i) q^{92} +(11.6819 - 3.41726i) q^{93} +(-7.77056 - 13.4590i) q^{94} +(-3.60963 - 6.25206i) q^{95} +(-0.896848 + 0.262352i) q^{96} +(-4.74375 - 8.21642i) q^{97} +(-1.08259 - 0.560893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9} + 16 q^{11} + 18 q^{15} - 6 q^{16} + 18 q^{18} - 6 q^{22} + 8 q^{23} + 24 q^{25} - 22 q^{29} + 42 q^{30} - 16 q^{32} - 30 q^{36} + 6 q^{37} + 24 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} - 18 q^{51} - 28 q^{53} - 6 q^{57} + 36 q^{58} - 126 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} - 30 q^{72} + 72 q^{74} + 36 q^{78} + 6 q^{79} + 24 q^{81} + 30 q^{85} - 72 q^{86} - 12 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9 + 16 * q^11 + 18 * q^15 - 6 * q^16 + 18 * q^18 - 6 * q^22 + 8 * q^23 + 24 * q^25 - 22 * q^29 + 42 * q^30 - 16 * q^32 - 30 * q^36 + 6 * q^37 + 24 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 - 18 * q^51 - 28 * q^53 - 6 * q^57 + 36 * q^58 - 126 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 - 30 * q^72 + 72 * q^74 + 36 * q^78 + 6 * q^79 + 24 * q^81 + 30 * q^85 - 72 * q^86 - 12 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Introduction

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