LMFDB - Embedded newform 441.2.o.d.146.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(146,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.146"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.5
Root			$1.07065 - 1.85442i$ of defining polynomial
Character	$\chi$	$=$	441.146
Dual form			441.2.o.d.293.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.24607 + 1.29677i) q^{2} +(0.278072 - 1.70958i) q^{3} +(2.36322 + 4.09323i) q^{4} +(0.626493 + 1.08512i) q^{5} +(2.84151 - 3.47925i) q^{6} +7.07116i q^{8} +(-2.84535 - 0.950775i) q^{9} +3.24967i q^{10} +(0.534126 + 0.308378i) q^{11} +(7.65486 - 2.90192i) q^{12} +(1.06343 - 0.613974i) q^{13} +(2.02931 - 0.769301i) q^{15} +(-4.44321 + 7.69587i) q^{16} -4.43003 q^{17} +(-5.15793 - 5.82528i) q^{18} -1.90155i q^{19} +(-2.96109 + 5.12875i) q^{20} +(0.799790 + 1.38528i) q^{22} +(4.11267 - 2.37445i) q^{23} +(12.0887 + 1.96629i) q^{24} +(1.71501 - 2.97049i) q^{25} +3.18473 q^{26} +(-2.41664 + 4.59998i) q^{27} +(-5.07629 - 2.93080i) q^{29} +(5.55558 + 0.903642i) q^{30} +(-2.14851 + 1.24044i) q^{31} +(-7.71195 + 4.45249i) q^{32} +(0.675723 - 0.827382i) q^{33} +(-9.95016 - 5.74473i) q^{34} +(-2.83247 - 13.8936i) q^{36} -2.66433 q^{37} +(2.46587 - 4.27102i) q^{38} +(-0.753929 - 1.98876i) q^{39} +(-7.67303 + 4.43003i) q^{40} +(-2.09966 - 3.63671i) q^{41} +(-2.24637 + 3.89083i) q^{43} +2.91506i q^{44} +(-0.750889 - 3.68319i) q^{45} +12.3165 q^{46} +(-3.80738 + 6.59458i) q^{47} +(11.9212 + 9.73605i) q^{48} +(7.70409 - 4.44796i) q^{50} +(-1.23187 + 7.57350i) q^{51} +(5.02627 + 2.90192i) q^{52} +3.09208i q^{53} +(-11.3931 + 7.19806i) q^{54} +0.772786i q^{55} +(-3.25086 - 0.528768i) q^{57} +(-7.60114 - 13.1656i) q^{58} +(-1.78229 - 3.08702i) q^{59} +(7.94463 + 6.48839i) q^{60} +(12.5136 + 7.22473i) q^{61} -6.43428 q^{62} -5.32259 q^{64} +(1.33247 + 0.769301i) q^{65} +(2.59065 - 0.982101i) q^{66} +(-6.80644 - 11.7891i) q^{67} +(-10.4692 - 18.1331i) q^{68} +(-2.91570 - 7.69121i) q^{69} +10.4095i q^{71} +(6.72308 - 20.1199i) q^{72} -11.4895i q^{73} +(-5.98429 - 3.45503i) q^{74} +(-4.60141 - 3.75797i) q^{75} +(7.78348 - 4.49379i) q^{76} +(0.885586 - 5.44457i) q^{78} +(2.01592 - 3.49168i) q^{79} -11.1346 q^{80} +(7.19205 + 5.41058i) q^{81} -10.8911i q^{82} +(-4.36775 + 7.56516i) q^{83} +(-2.77538 - 4.80710i) q^{85} +(-10.0910 + 5.82605i) q^{86} +(-6.42202 + 7.86337i) q^{87} +(-2.18059 + 3.77689i) q^{88} -1.62245 q^{89} +(3.08970 - 9.24645i) q^{90} +(19.4383 + 11.2227i) q^{92} +(1.52320 + 4.01799i) q^{93} +(-17.1033 + 9.87459i) q^{94} +(2.06341 - 1.19131i) q^{95} +(5.46743 + 14.4223i) q^{96} +(8.76527 + 5.06063i) q^{97} +(-1.22658 - 1.38528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} + 4 q^{4} + 12 q^{6} - 3 q^{9} + 12 q^{11} + 12 q^{12} - 6 q^{13} - 3 q^{15} - 6 q^{16} - 24 q^{17} - 6 q^{18} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 27 q^{24} + 7 q^{25} + 6 q^{26} - 27 q^{27}+ \cdots + 21 q^{99}+O(q^{100}) $ 10 * q + 3 * q^3 + 4 * q^4 + 12 * q^6 - 3 * q^9 + 12 * q^11 + 12 * q^12 - 6 * q^13 - 3 * q^15 - 6 * q^16 - 24 * q^17 - 6 * q^18 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 27 * q^24 + 7 * q^25 + 6 * q^26 - 27 * q^27 - 15 * q^29 - 6 * q^30 - 9 * q^31 - 48 * q^32 - 9 * q^33 - 3 * q^34 - 18 * q^36 - 12 * q^37 + 18 * q^38 - 30 * q^39 - 15 * q^40 + 9 * q^41 + 3 * q^43 - 15 * q^45 + 26 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 + 3 * q^51 + 12 * q^52 + 18 * q^54 - 36 * q^57 + 8 * q^58 + 18 * q^59 + 51 * q^60 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 + 6 * q^66 - 10 * q^67 - 27 * q^68 + 3 * q^69 + 12 * q^72 + 30 * q^74 - 27 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 - 60 * q^80 + 33 * q^81 + 15 * q^83 + 18 * q^85 - 54 * q^86 + 24 * q^87 - 8 * q^88 + 48 * q^89 - 24 * q^90 + 39 * q^92 - 42 * q^93 - 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.24607	+	1.29677i	1.58821	+	0.916955i	0.993602	+	0.112941i	$0.0360271\pi$
$2$	2.24607	+	1.29677i	1.58821	+	0.916955i	0.594611	+	0.804014i	$0.297306\pi$
$3$	0.278072	−	1.70958i	0.160545	−	0.987029i
$3$	0.278072	−	1.70958i	0.160545	−	0.987029i
$4$	2.36322	+	4.09323i	1.18161	+	2.04661i
$5$	0.626493	+	1.08512i	0.280176	+	0.485279i	0.971428	−	0.237335i	$-0.0762738\pi$
$5$	0.626493	+	1.08512i	0.280176	+	0.485279i	−0.691252	+	0.722614i	$0.742941\pi$
$6$	2.84151	−	3.47925i	1.16004	−	1.42040i
$7$		0			0
$7$		0			0
$8$			7.07116i			2.50003i
$9$	−2.84535	−	0.950775i	−0.948451	−	0.316925i
$10$			3.24967i			1.02763i
$11$	0.534126	+	0.308378i	0.161045	+	0.0929794i	0.578357	−	0.815784i	$-0.303694\pi$
$11$	0.534126	+	0.308378i	0.161045	+	0.0929794i	−0.417311	+	0.908764i	$0.637028\pi$
$12$	7.65486	−	2.90192i	2.20977	−	0.837712i
$13$	1.06343	−	0.613974i	0.294944	−	0.170286i	−0.345226	−	0.938520i	$-0.612198\pi$
$13$	1.06343	−	0.613974i	0.294944	−	0.170286i	0.640169	+	0.768234i	$0.278864\pi$
$14$		0			0
$15$	2.02931	−	0.769301i	0.523965	−	0.198633i
$16$	−4.44321	+	7.69587i	−1.11080	+	1.92397i
$17$	−4.43003			−1.07444			−0.537220	−	0.843442i	$-0.680525\pi$
$17$	−4.43003			−1.07444			−0.537220	+	0.843442i	$0.680525\pi$
$18$	−5.15793	−	5.82528i	−1.21573	−	1.37303i
$19$		−	1.90155i		−	0.436246i	−0.975921	−	0.218123i	$-0.930007\pi$
$19$		−	1.90155i		−	0.436246i	0.975921	−	0.218123i	$-0.0699933\pi$
$20$	−2.96109	+	5.12875i	−0.662119	+	1.14682i
$21$		0			0
$22$	0.799790	+	1.38528i	0.170516	+	0.295342i
$23$	4.11267	−	2.37445i	0.857550	−	0.495107i	−0.00564111	−	0.999984i	$-0.501796\pi$
$23$	4.11267	−	2.37445i	0.857550	−	0.495107i	0.863191	+	0.504877i	$0.168462\pi$
$24$	12.0887	+	1.96629i	2.46760	+	0.401368i
$25$	1.71501	−	2.97049i	0.343003	−	0.594098i
$26$	3.18473			0.624578
$27$	−2.41664	+	4.59998i	−0.465083	+	0.885267i
$28$		0			0
$29$	−5.07629	−	2.93080i	−0.942643	−	0.544235i	−0.0518553	−	0.998655i	$-0.516513\pi$
$29$	−5.07629	−	2.93080i	−0.942643	−	0.544235i	−0.890788	+	0.454419i	$0.849847\pi$
$30$	5.55558	+	0.903642i	1.01431	+	0.164982i
$31$	−2.14851	+	1.24044i	−0.385884	+	0.222790i	−0.680375	−	0.732864i	$-0.738183\pi$
$31$	−2.14851	+	1.24044i	−0.385884	+	0.222790i	0.294491	+	0.955654i	$0.404850\pi$
$32$	−7.71195	+	4.45249i	−1.36329	+	0.787097i
$33$	0.675723	−	0.827382i	0.117628	−	0.144029i
$34$	−9.95016	−	5.74473i	−1.70644	−	0.985213i
$35$		0			0
$36$	−2.83247	−	13.8936i	−0.472078	−	2.31559i
$37$	−2.66433			−0.438014			−0.219007	−	0.975723i	$-0.570282\pi$
$37$	−2.66433			−0.438014			−0.219007	+	0.975723i	$0.570282\pi$
$38$	2.46587	−	4.27102i	0.400018	−	0.692851i
$39$	−0.753929	−	1.98876i	−0.120725	−	0.318456i
$40$	−7.67303	+	4.43003i	−1.21321	+	0.700449i
$41$	−2.09966	−	3.63671i	−0.327911	−	0.567959i	0.654186	−	0.756334i	$-0.273011\pi$
$41$	−2.09966	−	3.63671i	−0.327911	−	0.567959i	−0.982097	+	0.188375i	$0.939678\pi$
$42$		0			0
$43$	−2.24637	+	3.89083i	−0.342568	+	0.593346i	−0.984909	−	0.173073i	$-0.944630\pi$
$43$	−2.24637	+	3.89083i	−0.342568	+	0.593346i	0.642340	+	0.766419i	$0.277964\pi$
$44$			2.91506i			0.439463i
$45$	−0.750889	−	3.68319i	−0.111936	−	0.549058i
$46$	12.3165			1.81596
$47$	−3.80738	+	6.59458i	−0.555364	+	0.961918i	0.442512	+	0.896763i	$0.354088\pi$
$47$	−3.80738	+	6.59458i	−0.555364	+	0.961918i	−0.997875	+	0.0651551i	$0.979246\pi$
$48$	11.9212	+	9.73605i	1.72068	+	1.40528i
$49$		0			0
$50$	7.70409	−	4.44796i	1.08952	−	0.629036i
$51$	−1.23187	+	7.57350i	−0.172496	+	1.06050i
$52$	5.02627	+	2.90192i	0.697018	+	0.402424i
$53$			3.09208i			0.424730i	0.977190	+	0.212365i	$0.0681165\pi$
$53$			3.09208i			0.424730i	−0.977190	+	0.212365i	$0.931883\pi$
$54$	−11.3931	+	7.19806i	−1.55040	+	0.979532i
$55$			0.772786i			0.104202i
$56$		0			0
$57$	−3.25086	−	0.528768i	−0.430587	−	0.0700371i
$58$	−7.60114	−	13.1656i	−0.998078	−	1.72872i
$59$	−1.78229	−	3.08702i	−0.232035	−	0.401896i	0.726372	−	0.687302i	$-0.241205\pi$
$59$	−1.78229	−	3.08702i	−0.232035	−	0.401896i	−0.958407	+	0.285406i	$0.907872\pi$
$60$	7.94463	+	6.48839i	1.02565	+	0.837647i
$61$	12.5136	+	7.22473i	1.60220	+	0.925032i	0.991046	+	0.133521i	$0.0426284\pi$
$61$	12.5136	+	7.22473i	1.60220	+	0.925032i	0.611156	+	0.791510i	$0.290705\pi$
$62$	−6.43428			−0.817154
$63$		0			0
$64$	−5.32259			−0.665324
$65$	1.33247	+	0.769301i	0.165272	+	0.0954200i
$66$	2.59065	−	0.982101i	0.318887	−	0.120888i
$67$	−6.80644	−	11.7891i	−0.831539	−	1.44027i	−0.896818	−	0.442400i	$-0.854127\pi$
$67$	−6.80644	−	11.7891i	−0.831539	−	1.44027i	0.0652791	−	0.997867i	$-0.479206\pi$
$68$	−10.4692	−	18.1331i	−1.26957	−	2.19896i
$69$	−2.91570	−	7.69121i	−0.351009	−	0.925913i
$70$		0			0
$71$			10.4095i			1.23538i	0.786420	+	0.617692i	$0.211932\pi$
$71$			10.4095i			1.23538i	−0.786420	+	0.617692i	$0.788068\pi$
$72$	6.72308	−	20.1199i	0.792323	−	2.37116i
$73$		−	11.4895i		−	1.34474i	−0.740216	−	0.672369i	$-0.765277\pi$
$73$		−	11.4895i		−	1.34474i	0.740216	−	0.672369i	$-0.234723\pi$
$74$	−5.98429	−	3.45503i	−0.695659	−	0.401639i
$75$	−4.60141	−	3.75797i	−0.531325	−	0.433933i
$76$	7.78348	−	4.49379i	0.892826	−	0.515473i
$77$		0			0
$78$	0.885586	−	5.44457i	0.100273	−	0.616476i
$79$	2.01592	−	3.49168i	0.226809	−	0.392845i	−0.730052	−	0.683392i	$-0.760504\pi$
$79$	2.01592	−	3.49168i	0.226809	−	0.392845i	0.956861	+	0.290547i	$0.0938373\pi$
$80$	−11.1346			−1.24488
$81$	7.19205	+	5.41058i	0.799117	+	0.601176i
$82$		−	10.8911i		−	1.20272i
$83$	−4.36775	+	7.56516i	−0.479422	+	0.830384i	−0.999721	−	0.0236001i	$-0.992487\pi$
$83$	−4.36775	+	7.56516i	−0.479422	+	0.830384i	0.520299	+	0.853984i	$0.325820\pi$
$84$		0			0
$85$	−2.77538	−	4.80710i	−0.301032	−	0.521403i
$86$	−10.0910	+	5.82605i	−1.08814	+	0.628240i
$87$	−6.42202	+	7.86337i	−0.688513	+	0.843041i
$88$	−2.18059	+	3.77689i	−0.232451	+	0.402618i
$89$	−1.62245			−0.171979			−0.0859897	−	0.996296i	$-0.527405\pi$
$89$	−1.62245			−0.171979			−0.0859897	+	0.996296i	$0.527405\pi$
$90$	3.08970	−	9.24645i	0.325683	−	0.974661i
$91$		0			0
$92$	19.4383	+	11.2227i	2.02658	+	1.17005i
$93$	1.52320	+	4.01799i	0.157949	+	0.416646i
$94$	−17.1033	+	9.87459i	−1.76407	+	1.01849i
$95$	2.06341	−	1.19131i	0.211701	−	0.122226i
$96$	5.46743	+	14.4223i	0.558017	+	1.47197i
$97$	8.76527	+	5.06063i	0.889979	+	0.513829i	0.873936	−	0.486042i	$-0.161560\pi$
$97$	8.76527	+	5.06063i	0.889979	+	0.513829i	0.0160431	+	0.999871i	$0.494893\pi$
$98$		0			0
$99$	−1.22658	−	1.38528i	−0.123276	−	0.139226i
$100$	16.2119			1.62119
$101$	−0.856611	+	1.48369i	−0.0852360	+	0.147633i	−0.905492	−	0.424364i	$-0.860498\pi$
$101$	−0.856611	+	1.48369i	−0.0852360	+	0.147633i	0.820256	+	0.571997i	$0.193831\pi$
$102$	−12.5880	+	15.4132i	−1.24639	+	1.52613i
$103$	6.41315	−	3.70263i	0.631906	−	0.364831i	−0.149584	−	0.988749i	$-0.547793\pi$
$103$	6.41315	−	3.70263i	0.631906	−	0.364831i	0.781490	+	0.623918i	$0.214460\pi$
$104$	4.34151	+	7.51971i	0.425720	+	0.737368i
$105$		0			0
$106$	−4.00972	+	6.94503i	−0.389458	+	0.674561i
$107$			0.152025i			0.0146968i	0.999973	+	0.00734839i	$0.00233909\pi$
$107$			0.152025i			0.0146968i	−0.999973	+	0.00734839i	$0.997661\pi$
$108$	−24.5398	+	0.978927i	−2.36135	+	0.0941973i
$109$	−5.40102			−0.517324			−0.258662	−	0.965968i	$-0.583282\pi$
$109$	−5.40102			−0.517324			−0.258662	+	0.965968i	$0.583282\pi$
$110$	−1.00213	+	1.73573i	−0.0955489	+	0.165496i
$111$	−0.740877	+	4.55490i	−0.0703210	+	0.432332i
$112$		0			0
$113$	−5.60391	+	3.23542i	−0.527171	+	0.304362i	−0.739864	−	0.672757i	$-0.765110\pi$
$113$	−5.60391	+	3.23542i	−0.527171	+	0.304362i	0.212693	+	0.977119i	$0.431777\pi$
$114$	−6.61597	−	5.40327i	−0.619643	−	0.506063i
$115$	5.15311	+	2.97515i	0.480530	+	0.277434i
$116$		−	27.7045i		−	2.57230i
$117$	−3.60960	+	0.735885i	−0.333707	+	0.0680326i
$118$		−	9.24490i		−	0.851062i
$119$		0			0
$120$	5.43984	+	14.3496i	0.496588	+	1.30993i
$121$	−5.30981	−	9.19685i	−0.482710	−	0.836078i
$122$	18.7376	+	32.4545i	1.69642	+	2.93829i
$123$	−6.80112	+	2.57827i	−0.613236	+	0.232475i
$124$	−10.1548	−	5.86289i	−0.911930	−	0.526503i
$125$	10.5627			0.944757
$126$		0			0
$127$	−2.93175			−0.260151			−0.130075	−	0.991504i	$-0.541522\pi$
$127$	−2.93175			−0.260151			−0.130075	+	0.991504i	$0.541522\pi$
$128$	3.46897	+	2.00281i	0.306617	+	0.177025i
$129$	6.02705	+	4.92229i	0.530652	+	0.433384i
$130$	1.99521	+	3.45581i	0.174992	+	0.303094i
$131$	8.11382	+	14.0535i	0.708908	+	1.22786i	0.965263	+	0.261281i	$0.0841450\pi$
$131$	8.11382	+	14.0535i	0.708908	+	1.22786i	−0.256355	+	0.966583i	$0.582522\pi$
$132$	4.98355	+	0.810598i	0.433762	+	0.0705535i
$133$		0			0
$134$		−	35.3055i		−	3.04993i
$135$	−6.50553	+	0.259514i	−0.559907	+	0.0223354i
$136$		−	31.3254i		−	2.68613i
$137$	15.0711	+	8.70129i	1.28761	+	0.743402i	0.978227	−	0.207536i	$-0.0665445\pi$
$137$	15.0711	+	8.70129i	1.28761	+	0.743402i	0.309382	+	0.950938i	$0.399878\pi$
$138$	3.42486	−	21.0560i	0.291544	−	1.79241i
$139$	−5.45273	+	3.14813i	−0.462494	+	0.267021i	−0.713092	−	0.701070i	$-0.752706\pi$
$139$	−5.45273	+	3.14813i	−0.462494	+	0.267021i	0.250598	+	0.968091i	$0.419373\pi$
$140$		0			0
$141$	10.2153	+	8.34280i	0.860279	+	0.702591i
$142$	−13.4988	+	23.3805i	−1.13279	+	1.96205i
$143$	0.757344			0.0633323
$144$	19.9595	−	17.6730i	1.66330	−	1.47275i
$145$		−	7.34449i		−	0.609927i
$146$	14.8992	−	25.8061i	1.23306	−	2.13573i
$147$		0			0
$148$	−6.29642	−	10.9057i	−0.517563	−	0.896445i
$149$	9.20319	−	5.31346i	0.753954	−	0.435296i	−0.0731665	−	0.997320i	$-0.523310\pi$
$149$	9.20319	−	5.31346i	0.753954	−	0.435296i	0.827121	+	0.562024i	$0.189977\pi$
$150$	−5.46186	−	14.4076i	−0.445959	−	1.17638i
$151$	−4.74465	+	8.21798i	−0.386114	+	0.668770i	−0.991923	−	0.126841i	$-0.959516\pi$
$151$	−4.74465	+	8.21798i	−0.386114	+	0.668770i	0.605809	+	0.795610i	$0.292850\pi$
$152$	13.4462			1.09063
$153$	12.6050	+	4.21196i	1.01905	+	0.340517i
$154$		0			0
$155$	−2.69205	−	1.55426i	−0.216231	−	0.124841i
$156$	6.35874	−	7.78588i	0.509106	−	0.623370i
$157$	20.6214	−	11.9058i	1.64577	−	0.950185i	0.667040	−	0.745022i	$-0.267561\pi$
$157$	20.6214	−	11.9058i	1.64577	−	0.950185i	0.978728	−	0.205163i	$-0.0657723\pi$
$158$	9.05582	−	5.22838i	0.720442	−	0.415947i
$159$	5.28617	+	0.859821i	0.419220	+	0.0681883i
$160$	−9.66295	−	5.57891i	−0.763924	−	0.441051i
$161$		0			0
$162$	9.13759	+	21.4790i	0.717916	+	1.68755i
$163$	8.82201			0.690993			0.345497	−	0.938420i	$-0.387710\pi$
$163$	8.82201			0.690993			0.345497	+	0.938420i	$0.387710\pi$
$164$	9.92392	−	17.1887i	0.774928	−	1.34221i
$165$	1.32114	+	0.214890i	0.102851	+	0.0167292i
$166$	−19.6205	+	11.3279i	−1.52285	+	0.879217i
$167$	11.0335	+	19.1106i	0.853800	+	1.47883i	0.877754	+	0.479112i	$0.159041\pi$
$167$	11.0335	+	19.1106i	0.853800	+	1.47883i	−0.0239535	+	0.999713i	$0.507625\pi$
$168$		0			0
$169$	−5.74607	+	9.95249i	−0.442005	+	0.765576i
$170$		−	14.3961i		−	1.10413i
$171$	−1.80795	+	5.41058i	−0.138257	+	0.413757i
$172$	−21.2347			−1.61913
$173$	−2.03375	+	3.52256i	−0.154623	+	0.267815i	−0.932922	−	0.360079i	$-0.882750\pi$
$173$	−2.03375	+	3.52256i	−0.154623	+	0.267815i	0.778299	+	0.627894i	$0.216083\pi$
$174$	−24.6213	+	9.33381i	−1.86653	+	0.707594i
$175$		0			0
$176$	−4.74647	+	2.74038i	−0.357779	+	0.206564i
$177$	−5.77313	+	2.18856i	−0.433935	+	0.164503i
$178$	−3.64414	−	2.10395i	−0.273140	−	0.157697i
$179$			8.32293i			0.622085i	0.950396	+	0.311042i	$0.100678\pi$
$179$			8.32293i			0.622085i	−0.950396	+	0.311042i	$0.899322\pi$
$180$	13.3016	−	11.7778i	0.991444	−	0.877863i
$181$		−	12.6701i		−	0.941763i	−0.882196	−	0.470881i	$-0.843936\pi$
$181$		−	12.6701i		−	0.941763i	0.882196	−	0.470881i	$-0.156064\pi$
$182$		0			0
$183$	15.8310	−	19.3840i	1.17026	−	1.43291i
$184$	16.7901	+	29.0813i	1.23778	+	2.14390i
$185$	−1.66919	−	2.89111i	−0.122721	−	0.212559i
$186$	−1.78919	+	10.9999i	−0.131190	+	0.806555i
$187$	−2.36619	−	1.36612i	−0.173033	−	0.0999008i
$188$	−35.9908			−2.62490
$189$		0			0
$190$	6.17941			0.448301
$191$	3.29133	+	1.90025i	0.238152	+	0.137497i	0.614327	−	0.789051i	$-0.289427\pi$
$191$	3.29133	+	1.90025i	0.238152	+	0.137497i	−0.376175	+	0.926549i	$0.622761\pi$
$192$	−1.48006	+	9.09941i	−0.106814	+	0.656694i
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	0.717606	−	0.696450i	$-0.245238\pi$
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	−0.961946	+	0.273240i	$0.911905\pi$
$194$	13.1250	+	22.7331i	0.942317	+	1.63214i
$195$	1.68571	−	2.06404i	0.120716	−	0.147809i
$196$		0			0
$197$		−	6.41453i		−	0.457017i	−0.973542	−	0.228508i	$-0.926615\pi$
$197$		−	6.41453i		−	0.457017i	0.973542	−	0.228508i	$-0.0733848\pi$
$198$	−0.958597	−	4.70202i	−0.0681245	−	0.334158i
$199$			16.0413i			1.13714i	0.822637	+	0.568568i	$0.192502\pi$
$199$			16.0413i			1.13714i	−0.822637	+	0.568568i	$0.807498\pi$
$200$	21.0048	+	12.1271i	1.48526	+	0.857518i
$201$	−22.0471	+	8.35795i	−1.55508	+	0.589525i
$202$	−3.84802	+	2.22166i	−0.270746	+	0.156315i
$203$		0			0
$204$	−33.9112	+	12.8556i	−2.37426	+	0.900070i
$205$	2.63084	−	4.55675i	0.183746	−	0.318257i
$206$	19.2058			1.33813
$207$	−13.9595	+	2.84592i	−0.970255	+	0.197805i
$208$			10.9121i			0.756616i
$209$	0.586396	−	1.01567i	0.0405619	−	0.0702552i
$210$		0			0
$211$	−4.06070	−	7.03333i	−0.279550	−	0.484194i	0.691723	−	0.722163i	$-0.256852\pi$
$211$	−4.06070	−	7.03333i	−0.279550	−	0.484194i	−0.971273	+	0.237968i	$0.923519\pi$
$212$	−12.6566	+	7.30728i	−0.869257	+	0.501866i
$213$	17.7960	+	2.89460i	1.21936	+	0.198335i
$214$	−0.197141	+	0.341458i	−0.0134763	+	0.0233416i
$215$	−5.62934			−0.383918
$216$	−32.5272	−	17.0885i	−2.21319	−	1.16272i
$217$		0			0
$218$	−12.1311	−	7.00388i	−0.821620	−	0.474363i
$219$	−19.6422	−	3.19490i	−1.32730	−	0.215891i
$220$	−3.16319	+	1.82627i	−0.213262	+	0.123127i
$221$	−4.71104	+	2.71992i	−0.316899	+	0.182962i
$222$	−7.57072	+	9.26989i	−0.508114	+	0.622154i
$223$	6.96205	+	4.01954i	0.466213	+	0.269168i	0.714653	−	0.699479i	$-0.246585\pi$
$223$	6.96205	+	4.01954i	0.466213	+	0.269168i	−0.248440	+	0.968647i	$0.579918\pi$
$224$		0			0
$225$	−7.70409	+	6.82150i	−0.513606	+	0.454767i
$226$	−16.7824			−1.11635
$227$	−10.4117	+	18.0336i	−0.691048	+	1.19693i	0.280447	+	0.959870i	$0.409517\pi$
$227$	−10.4117	+	18.0336i	−0.691048	+	1.19693i	−0.971495	+	0.237061i	$0.923816\pi$
$228$	−5.51814	−	14.5561i	−0.365448	−	0.964001i
$229$	−5.21276	+	3.00959i	−0.344469	+	0.198879i	−0.662247	−	0.749286i	$-0.730397\pi$
$229$	−5.21276	+	3.00959i	−0.344469	+	0.198879i	0.317777	+	0.948165i	$0.397064\pi$
$230$	7.71617	+	13.3648i	0.508789	+	0.881248i
$231$		0			0
$232$	20.7241	−	35.8952i	1.36061	−	2.35664i
$233$			21.0336i			1.37796i	0.724782	+	0.688978i	$0.241940\pi$
$233$			21.0336i			1.37796i	−0.724782	+	0.688978i	$0.758060\pi$
$234$	−9.06169	−	3.02797i	−0.592381	−	0.197944i
$235$	−9.54118			−0.622398
$236$	8.42392	−	14.5907i	0.548350	−	0.949771i
$237$	−5.40875	−	4.41733i	−0.351336	−	0.286936i
$238$		0			0
$239$	−7.51079	+	4.33636i	−0.485832	+	0.280496i	−0.722844	−	0.691011i	$-0.757165\pi$
$239$	−7.51079	+	4.33636i	−0.485832	+	0.280496i	0.237011	+	0.971507i	$0.423832\pi$
$240$	−3.09621	+	19.0355i	−0.199860	+	1.22873i
$241$	−7.33797	−	4.23658i	−0.472680	−	0.272902i	0.244681	−	0.969604i	$-0.421317\pi$
$241$	−7.33797	−	4.23658i	−0.472680	−	0.272902i	−0.717361	+	0.696702i	$0.754650\pi$
$242$		−	27.5424i		−	1.77049i
$243$	11.2497	−	10.7909i	0.721672	−	0.692235i
$244$			68.2946i			4.37211i
$245$		0			0
$246$	−18.6192	−	3.02851i	−1.18712	−	0.193091i
$247$	−1.16750	−	2.02217i	−0.0742864	−	0.128668i
$248$	−8.77137	−	15.1925i	−0.556982	−	0.964722i
$249$	11.7187	+	9.57069i	0.742644	+	0.606518i
$250$	23.7246	+	13.6974i	1.50047	+	0.866299i
$251$	−23.4435			−1.47974			−0.739871	−	0.672749i	$-0.765113\pi$
$251$	−23.4435			−1.47974			−0.739871	+	0.672749i	$0.765113\pi$
$252$		0			0
$253$	2.92891			0.184139
$254$	−6.58492	−	3.80180i	−0.413174	−	0.238546i
$255$	−8.98989	+	3.40802i	−0.562969	+	0.213419i
$256$	10.5170	+	18.2159i	0.657310	+	1.13849i
$257$	−12.2585	−	21.2324i	−0.764665	−	1.32444i	−0.940423	−	0.340005i	$-0.889571\pi$
$257$	−12.2585	−	21.2324i	−0.764665	−	1.32444i	0.175758	−	0.984433i	$-0.443762\pi$
$258$	7.15409	+	18.8715i	0.445394	+	1.17489i
$259$		0			0
$260$			7.27212i			0.450998i
$261$	11.6573	+	13.1656i	0.721569	+	0.814928i
$262$			42.0870i			2.60014i
$263$	−9.14036	−	5.27719i	−0.563619	−	0.325406i	0.190978	−	0.981594i	$-0.438834\pi$
$263$	−9.14036	−	5.27719i	−0.563619	−	0.325406i	−0.754597	+	0.656189i	$0.772167\pi$
$264$	5.85055	+	4.77814i	0.360076	+	0.294074i
$265$	−3.35527	+	1.93716i	−0.206112	+	0.118999i
$266$		0			0
$267$	−0.451159	+	2.77372i	−0.0276105	+	0.169749i
$268$	32.1703	−	55.7206i	1.96511	−	3.40367i
$269$	2.28902			0.139564			0.0697821	−	0.997562i	$-0.477770\pi$
$269$	2.28902			0.139564			0.0697821	+	0.997562i	$0.477770\pi$
$270$	−14.9484	−	7.85329i	−0.909731	−	0.477936i
$271$		−	24.1608i		−	1.46766i	−0.679332	−	0.733831i	$-0.737730\pi$
$271$		−	24.1608i		−	1.46766i	0.679332	−	0.733831i	$-0.262270\pi$
$272$	19.6836	−	34.0929i	1.19349	−	2.06719i
$273$		0			0
$274$	22.5672	+	39.0875i	1.36333	+	2.36136i
$275$	1.83207	−	1.05774i	0.110478	−	0.0637844i
$276$	24.5914	−	30.1107i	1.48023	−	1.81245i
$277$	5.68551	−	9.84760i	0.341609	−	0.591685i	−0.643122	−	0.765763i	$-0.722361\pi$
$277$	5.68551	−	9.84760i	0.341609	−	0.591685i	0.984732	+	0.174079i	$0.0556947\pi$
$278$	−16.3296			−0.979386
$279$	7.29265	−	1.48675i	0.436600	−	0.0890092i
$280$		0			0
$281$	17.6382	+	10.1834i	1.05221	+	0.607492i	0.923267	−	0.384160i	$-0.125509\pi$
$281$	17.6382	+	10.1834i	1.05221	+	0.607492i	0.128941	+	0.991652i	$0.458842\pi$
$282$	12.1255	+	31.9854i	0.722062	+	1.90470i
$283$	10.5318	−	6.08055i	0.626052	−	0.361451i	−0.153169	−	0.988200i	$-0.548948\pi$
$283$	10.5318	−	6.08055i	0.626052	−	0.361451i	0.779222	+	0.626749i	$0.215615\pi$
$284$	−42.6085	+	24.6000i	−2.52835	+	1.45974i
$285$	−1.46286	−	3.85883i	−0.0866526	−	0.228578i
$286$	1.70105	+	0.982101i	0.100585	+	0.0580729i
$287$		0			0
$288$	26.1765	−	5.33658i	1.54247	−	0.314461i
$289$	2.62515			0.154421
$290$	9.52411	−	16.4962i	0.559275	−	0.968693i
$291$	11.0890	−	13.5777i	0.650046	−	0.795941i
$292$	47.0289	−	27.1522i	2.75216	−	1.58896i
$293$	−13.4674	−	23.3262i	−0.786773	−	1.36273i	−0.927934	−	0.372745i	$-0.878417\pi$
$293$	−13.4674	−	23.3262i	−0.786773	−	1.36273i	0.141161	−	0.989987i	$-0.454917\pi$
$294$		0			0
$295$	2.23319	−	3.86799i	0.130021	−	0.225203i
$296$		−	18.8399i		−	1.09505i
$297$	−2.70932	+	1.71173i	−0.157211	+	0.0993247i
$298$	27.5614			1.59659
$299$	2.91570	−	5.05014i	0.168619	−	0.292057i
$300$	4.50807	−	27.7155i	0.260273	−	1.60016i
$301$		0			0
$302$	−21.3137	+	12.3054i	−1.22646	+	0.708099i
$303$	2.29830	+	1.87702i	0.132034	+	0.107832i
$304$	14.6341	+	8.44899i	0.839322	+	0.484583i
$305$			18.1050i			1.03669i
$306$	22.8498	+	25.8061i	1.30623	+	1.47524i
$307$		−	21.3700i		−	1.21965i	−0.792536	−	0.609825i	$-0.791240\pi$
$307$		−	21.3700i		−	1.21965i	0.792536	−	0.609825i	$-0.208760\pi$
$308$		0			0
$309$	−4.54664	−	11.9934i	−0.258649	−	0.682281i
$310$	−4.03103	−	6.98195i	−0.228947	−	0.396548i
$311$	−8.11558	−	14.0566i	−0.460192	−	0.797076i	0.538778	−	0.842448i	$-0.318886\pi$
$311$	−8.11558	−	14.0566i	−0.460192	−	0.797076i	−0.998970	+	0.0453714i	$0.985553\pi$
$312$	14.0628	−	5.33115i	0.796151	−	0.301817i
$313$	12.1941	+	7.04027i	0.689252	+	0.397940i	0.803332	−	0.595532i	$-0.203059\pi$
$313$	12.1941	+	7.04027i	0.689252	+	0.397940i	−0.114080	+	0.993472i	$0.536392\pi$
$314$	61.7562			3.48511
$315$		0			0
$316$	19.0563			1.07200
$317$	−17.5776	−	10.1484i	−0.987254	−	0.569991i	−0.0828017	−	0.996566i	$-0.526387\pi$
$317$	−17.5776	−	10.1484i	−0.987254	−	0.569991i	−0.904452	+	0.426575i	$0.859720\pi$
$318$	10.7581	+	8.78616i	0.603285	+	0.492704i
$319$	−1.80759	−	3.13083i	−0.101205	−	0.175293i
$320$	−3.33456	−	5.77563i	−0.186408	−	0.322868i
$321$	0.259899	+	0.0422738i	0.0145061	+	0.00235950i
$322$		0			0
$323$			8.42392i			0.468720i
$324$	−5.15029	+	42.2251i	−0.286127	+	2.34584i
$325$		−	4.21190i		−	0.233634i
$326$	19.8149	+	11.4401i	1.09744	+	0.633610i
$327$	−1.50187	+	9.23349i	−0.0830538	+	0.510613i
$328$	25.7158	−	14.8470i	1.41991	−	0.819788i
$329$		0			0
$330$	2.68872	+	2.19588i	0.148009	+	0.120879i
$331$	−13.2341	+	22.9221i	−0.727411	+	1.25991i	0.230563	+	0.973057i	$0.425943\pi$
$331$	−13.2341	+	22.9221i	−0.727411	+	1.25991i	−0.957974	+	0.286856i	$0.907390\pi$
$332$	−41.2879			−2.26597
$333$	7.58097	+	2.53318i	0.415435	+	0.138818i
$334$			57.2318i			3.13158i
$335$	8.52836	−	14.7716i	0.465954	−	0.807057i
$336$		0			0
$337$	−1.73659	−	3.00785i	−0.0945979	−	0.163848i	0.814843	−	0.579682i	$-0.196823\pi$
$337$	−1.73659	−	3.00785i	−0.0945979	−	0.163848i	−0.909441	+	0.415834i	$0.863490\pi$
$338$	−25.8122	+	14.9027i	−1.40400	+	0.810598i
$339$	3.97293	+	10.4800i	0.215780	+	0.569197i
$340$	13.1177	−	22.7205i	0.711407	−	1.23219i
$341$	−1.53010			−0.0828596
$342$	−11.0771	+	9.80806i	−0.598979	+	0.530359i
$343$		0			0
$344$	−27.5127	−	15.8844i	−1.48338	−	0.856432i
$345$	6.51920	−	7.98236i	0.350982	−	0.429756i
$346$	−9.13589	+	5.27461i	−0.491149	+	0.283565i
$347$	−8.14765	+	4.70405i	−0.437389	+	0.252527i	−0.702489	−	0.711694i	$-0.747928\pi$
$347$	−8.14765	+	4.70405i	−0.437389	+	0.252527i	0.265101	+	0.964221i	$0.414595\pi$
$348$	−47.3632	−	7.70386i	−2.53893	−	0.412970i
$349$	12.3253	+	7.11603i	0.659759	+	0.380912i	0.792185	−	0.610281i	$-0.208943\pi$
$349$	12.3253	+	7.11603i	0.659759	+	0.380912i	−0.132426	+	0.991193i	$0.542277\pi$
$350$		0			0
$351$	0.254329	+	6.37554i	0.0135751	+	0.340301i
$352$	−5.49220			−0.292735
$353$	8.58262	−	14.8655i	0.456807	−	0.791213i	−0.541983	−	0.840389i	$-0.682326\pi$
$353$	8.58262	−	14.8655i	0.456807	−	0.791213i	0.998790	+	0.0491765i	$0.0156597\pi$
$354$	−15.8049	−	2.57075i	−0.840022	−	0.136634i
$355$	−11.2956	+	6.52149i	−0.599506	+	0.346125i
$356$	−3.83422	−	6.64106i	−0.203213	−	0.351975i
$357$		0			0
$358$	−10.7929	+	18.6939i	−0.570424	+	0.988003i
$359$		−	28.2561i		−	1.49130i	−0.666338	−	0.745650i	$-0.732139\pi$
$359$		−	28.2561i		−	1.49130i	0.666338	−	0.745650i	$-0.267861\pi$
$360$	26.0444	−	5.30965i	1.37266	−	0.279843i
$361$	15.3841			0.809690
$362$	16.4302	−	28.4580i	0.863554	−	1.49572i
$363$	−17.1993	+	6.52017i	−0.902729	+	0.342220i
$364$		0			0
$365$	12.4674	−	7.19806i	0.652574	−	0.376764i
$366$	60.6941	−	23.0088i	3.17253	−	1.20269i
$367$	−19.9796	−	11.5352i	−1.04293	−	0.602133i	−0.122265	−	0.992498i	$-0.539016\pi$
$367$	−19.9796	−	11.5352i	−1.04293	−	0.602133i	−0.920661	+	0.390364i	$0.872349\pi$
$368$			42.2007i			2.19986i
$369$	2.51657	+	12.3440i	0.131007	+	0.642604i
$370$		−	8.65820i		−	0.450118i
$371$		0			0
$372$	−12.8469	+	15.7302i	−0.666080	+	0.815574i
$373$	6.93635	+	12.0141i	0.359150	+	0.622067i	0.987819	−	0.155607i	$-0.0497332\pi$
$373$	6.93635	+	12.0141i	0.359150	+	0.622067i	−0.628669	+	0.777673i	$0.716400\pi$
$374$	−3.54309	−	6.13682i	−0.183209	−	0.317327i
$375$	2.93719	−	18.0578i	0.151676	−	0.932502i
$376$	−46.6313	−	26.9226i	−2.40482	−	1.38843i
$377$	−7.19773			−0.370702
$378$		0			0
$379$	22.7814			1.17020			0.585101	−	0.810961i	$-0.301055\pi$
$379$	22.7814			1.17020			0.585101	+	0.810961i	$0.301055\pi$
$380$	9.75258	+	5.63065i	0.500297	+	0.288846i
$381$	−0.815238	+	5.01207i	−0.0417659	+	0.256776i
$382$	4.92838	+	8.53620i	0.252158	+	0.436750i
$383$	−7.61598	−	13.1913i	−0.389158	−	0.674042i	0.603178	−	0.797606i	$-0.293901\pi$
$383$	−7.61598	−	13.1913i	−0.389158	−	0.674042i	−0.992337	+	0.123564i	$0.960567\pi$
$384$	4.38860	−	5.37357i	0.223955	−	0.274219i
$385$		0			0
$386$		−	17.6075i		−	0.896196i
$387$	10.0910	−	8.93498i	0.512956	−	0.454191i
$388$			47.8376i			2.42859i
$389$	−12.2525	−	7.07396i	−0.621224	−	0.358664i	0.156121	−	0.987738i	$-0.450101\pi$
$389$	−12.2525	−	7.07396i	−0.621224	−	0.358664i	−0.777346	+	0.629074i	$0.783434\pi$
$390$	6.46281	−	2.45002i	0.327257	−	0.124061i
$391$	−18.2192	+	10.5189i	−0.921386	+	0.531962i
$392$		0			0
$393$	26.2819	−	9.96335i	1.32575	−	0.502584i
$394$	8.31817	−	14.4075i	0.419063	−	0.725839i
$395$	5.05184			0.254186
$396$	2.77157	−	8.29438i	0.139277	−	0.416808i
$397$			9.70742i			0.487202i	0.969876	+	0.243601i	$0.0783287\pi$
$397$			9.70742i			0.487202i	−0.969876	+	0.243601i	$0.921671\pi$
$398$	−20.8018	+	36.0298i	−1.04270	+	1.80601i
$399$		0			0
$400$	15.2403	+	26.3970i	0.762017	+	1.31985i
$401$	7.56156	−	4.36567i	0.377606	−	0.218011i	−0.299170	−	0.954200i	$-0.596710\pi$
$401$	7.56156	−	4.36567i	0.377606	−	0.218011i	0.676776	+	0.736189i	$0.263376\pi$
$402$	−60.3578	−	9.81749i	−3.01037	−	0.489652i
$403$	−1.52320	+	2.63826i	−0.0758760	+	0.131421i
$404$	−8.09746			−0.402864
$405$	−1.36535	+	11.1939i	−0.0678446	+	0.556230i
$406$		0			0
$407$	−1.42309	−	0.821622i	−0.0705400	−	0.0407263i
$408$	−53.5534	−	8.71073i	−2.65129	−	0.431245i
$409$	−12.8967	+	7.44591i	−0.637700	+	0.368176i	−0.783728	−	0.621104i	$-0.786684\pi$
$409$	−12.8967	+	7.44591i	−0.637700	+	0.368176i	0.146028	+	0.989280i	$0.453351\pi$
$410$	11.8181	−	6.82318i	0.583654	−	0.336973i
$411$	19.0664	−	23.3457i	0.940478	−	1.15156i
$412$	30.3114	+	17.5003i	1.49334	+	0.862178i
$413$		0			0
$414$	−35.0446	−	11.7102i	−1.72235	−	0.575524i
$415$	−10.9454			−0.537291
$416$	−5.46743	+	9.46987i	−0.268063	+	0.464299i
$417$	3.86575	+	10.1973i	0.189306	+	0.499364i
$418$	2.63418	−	1.52084i	0.128842	−	0.0743868i
$419$	2.13859	+	3.70414i	0.104477	+	0.180959i	0.913524	−	0.406784i	$-0.133350\pi$
$419$	2.13859	+	3.70414i	0.104477	+	0.180959i	−0.809048	+	0.587743i	$0.800017\pi$
$420$		0			0
$421$	5.76681	−	9.98841i	0.281057	−	0.486805i	−0.690588	−	0.723248i	$-0.742648\pi$
$421$	5.76681	−	9.98841i	0.281057	−	0.486805i	0.971645	+	0.236443i	$0.0759816\pi$
$422$		−	21.0632i		−	1.02534i
$423$	17.1033	−	15.1439i	0.831591	−	0.736323i
$424$	−21.8646			−1.06184
$425$	−7.59756	+	13.1594i	−0.368536	+	0.638323i
$426$	36.2174	+	29.5787i	1.75474	+	1.43309i
$427$		0			0
$428$	−0.622271	+	0.359268i	−0.0300786	+	0.0173659i
$429$	0.210596	−	1.29474i	0.0101677	−	0.0625108i
$430$	−12.6439	−	7.29996i	−0.609743	−	0.352035i
$431$		−	16.6851i		−	0.803692i	−0.915707	−	0.401846i	$-0.868369\pi$
$431$		−	16.6851i		−	0.803692i	0.915707	−	0.401846i	$-0.131631\pi$
$432$	−24.6632	−	39.0369i	−1.18661	−	1.87816i
$433$		−	12.3503i		−	0.593516i	−0.954953	−	0.296758i	$-0.904094\pi$
$433$		−	12.3503i		−	0.593516i	0.954953	−	0.296758i	$-0.0959055\pi$
$434$		0			0
$435$	−12.5560	−	2.04230i	−0.602015	−	0.0979207i
$436$	−12.7638	−	22.1076i	−0.611276	−	1.05876i
$437$	−4.51513	−	7.82044i	−0.215988	−	0.374102i
$438$	−39.9747	−	32.6474i	−1.91006	−	1.55995i
$439$	−19.1691	−	11.0673i	−0.914892	−	0.528213i	−0.0328902	−	0.999459i	$-0.510471\pi$
$439$	−19.1691	−	11.0673i	−0.914892	−	0.528213i	−0.882002	+	0.471246i	$0.843805\pi$
$440$	−5.46449			−0.260509
$441$		0			0
$442$	−14.1085			−0.671071
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	0.597089	−	0.802175i	$-0.296324\pi$
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	−0.396160	+	0.918182i	$0.629657\pi$
$444$	−20.3951	+	7.73168i	−0.967909	+	0.366929i
$445$	−1.01645	−	1.76055i	−0.0481845	−	0.0834580i
$446$	10.4248	+	18.0563i	0.493630	+	0.854993i
$447$	−6.52466	−	17.2111i	−0.308606	−	0.814059i
$448$		0			0
$449$			12.4409i			0.587121i	0.955941	+	0.293560i	$0.0948401\pi$
$449$			12.4409i			0.587121i	−0.955941	+	0.293560i	$0.905160\pi$
$450$	−26.1498	+	5.33115i	−1.23272	+	0.251313i
$451$		−	2.58995i		−	0.121956i
$452$	−26.4866	−	15.2920i	−1.24582	−	0.719277i
$453$	12.7300	+	10.3966i	0.598106	+	0.488473i
$454$	−46.7708	+	27.0031i	−2.19506	+	1.26732i
$455$		0			0
$456$	3.73900	−	22.9873i	0.175095	−	1.07648i
$457$	5.38774	−	9.33185i	0.252028	−	0.436525i	−0.712056	−	0.702123i	$-0.752236\pi$
$457$	5.38774	−	9.33185i	0.252028	−	0.436525i	0.964084	+	0.265597i	$0.0855691\pi$
$458$	−15.6110			−0.729454
$459$	10.7058	−	20.3781i	0.499704	−	0.951166i
$460$			28.1238i			1.31128i
$461$	0.333303	−	0.577297i	0.0155235	−	0.0268874i	−0.858159	−	0.513383i	$-0.828392\pi$
$461$	0.333303	−	0.577297i	0.0155235	−	0.0268874i	0.873683	+	0.486496i	$0.161725\pi$
$462$		0			0
$463$	−20.7892	−	36.0079i	−0.966155	−	1.67343i	−0.706479	−	0.707734i	$-0.749717\pi$
$463$	−20.7892	−	36.0079i	−0.966155	−	1.67343i	−0.259677	−	0.965696i	$-0.583616\pi$
$464$	45.1101	−	26.0443i	2.09418	−	1.20908i
$465$	−3.40572	+	4.17009i	−0.157936	+	0.193383i
$466$	−27.2757	+	47.2429i	−1.26352	+	2.18849i
$467$	39.3135			1.81921			0.909606	−	0.415471i	$-0.136383\pi$
$467$	39.3135			1.81921			0.909606	+	0.415471i	$0.136383\pi$
$468$	−11.5424	−	13.0358i	−0.533549	−	0.602581i
$469$		0			0
$470$	−21.4302	−	12.3727i	−0.988500	−	0.570711i
$471$	−14.6197	−	38.5647i	−0.673639	−	1.77697i
$472$	21.8288	−	12.6029i	1.00475	−	0.580094i
$473$	−2.39969	+	1.38546i	−0.110338	+	0.0637036i
$474$	−6.42018	−	16.9355i	−0.294889	−	0.777875i
$475$	−5.64854	−	3.26119i	−0.259173	−	0.149633i
$476$		0			0
$477$	2.93987	−	8.79805i	0.134608	−	0.402835i
$478$	−22.4930			−1.02881
$479$	−19.0577	+	33.0088i	−0.870767	+	1.50821i	−0.00956182	+	0.999954i	$0.503044\pi$
$479$	−19.0577	+	33.0088i	−0.870767	+	1.50821i	−0.861205	+	0.508258i	$0.830290\pi$
$480$	−12.2246	+	14.9683i	−0.557975	+	0.683206i
$481$	−2.83335	+	1.63583i	−0.129189	+	0.0745875i
$482$	−10.9877	−	19.0313i	−0.500477	−	0.866852i
$483$		0			0
$484$	25.0965	−	43.4685i	1.14075	−	1.97584i
$485$			12.6818i			0.575851i
$486$	39.2610	−	9.64876i	1.78092	−	0.437676i
$487$	7.60554			0.344640			0.172320	−	0.985041i	$-0.444874\pi$
$487$	7.60554			0.344640			0.172320	+	0.985041i	$0.444874\pi$
$488$	−51.0872	+	88.4856i	−2.31261	+	4.00555i
$489$	2.45316	−	15.0820i	0.110936	−	0.682030i
$490$		0			0
$491$	3.33297	−	1.92429i	0.150415	−	0.0868420i	−0.422904	−	0.906175i	$-0.638989\pi$
$491$	3.33297	−	1.92429i	0.150415	−	0.0868420i	0.573318	+	0.819333i	$0.305656\pi$
$492$	−26.6260	−	21.7455i	−1.20039	−	0.980362i
$493$	22.4881	+	12.9835i	1.01281	+	0.584748i
$494$		−	6.05593i		−	0.272469i
$495$	0.734746	−	2.19885i	0.0330244	−	0.0988308i
$496$		−	22.0462i		−	0.989904i
$497$		0			0
$498$	13.9101	+	36.6929i	0.623327	+	1.64425i
$499$	16.0794	+	27.8503i	0.719812	+	1.24675i	0.961074	+	0.276291i	$0.0891053\pi$
$499$	16.0794	+	27.8503i	0.719812	+	1.24675i	−0.241262	+	0.970460i	$0.577561\pi$
$500$	24.9620	+	43.2355i	1.11634	+	1.93355i
$501$	35.7393	−	13.5486i	1.59672	−	0.605307i
$502$	−52.6558	−	30.4009i	−2.35014	−	1.35686i
$503$	0.425693			0.0189807			0.00949035	−	0.999955i	$-0.496979\pi$
$503$	0.425693			0.0189807			0.00949035	+	0.999955i	$0.496979\pi$
$504$		0			0
$505$	−2.14664			−0.0955243
$506$	6.57854	+	3.79812i	0.292452	+	0.168847i
$507$	15.4168	+	12.5909i	0.684684	+	0.559181i
$508$	−6.92838	−	12.0003i	−0.307397	−	0.532427i
$509$	−12.8963	−	22.3370i	−0.571617	−	0.990071i	−0.996400	−	0.0847751i	$-0.972983\pi$
$509$	−12.8963	−	22.3370i	−0.571617	−	0.990071i	0.424783	−	0.905295i	$-0.360351\pi$
$510$	−24.6114	−	4.00316i	−1.08981	−	0.177263i
$511$		0			0
$512$			46.5411i			2.05684i
$513$	8.74710	+	4.59537i	0.386194	+	0.202891i
$514$		−	63.5859i		−	2.80465i
$515$	8.03558	+	4.63934i	0.354090	+	0.204434i
$516$	−5.90479	+	36.3025i	−0.259944	+	1.59813i
$517$	−4.06724	+	2.34822i	−0.178877	+	0.103275i
$518$		0			0
$519$	5.45658	+	4.45639i	0.239517	+	0.195614i
$520$	−5.43984	+	9.42209i	−0.238553	+	0.413186i
$521$	−18.1435			−0.794880			−0.397440	−	0.917628i	$-0.630101\pi$
$521$	−18.1435			−0.794880			−0.397440	+	0.917628i	$0.630101\pi$
$522$	9.11042	+	44.6876i	0.398752	+	1.95592i
$523$			13.9399i			0.609551i	0.952424	+	0.304776i	$0.0985814\pi$
$523$			13.9399i			0.609551i	−0.952424	+	0.304776i	$0.901419\pi$
$524$	−38.3495	+	66.4234i	−1.67531	+	2.90172i
$525$		0			0
$526$	−13.6866	−	23.7059i	−0.596764	−	1.03363i
$527$	9.51796	−	5.49520i	0.414609	−	0.239375i
$528$	3.36504	+	8.87651i	0.146445	+	0.386301i
$529$	−0.223990	+	0.387962i	−0.00973870	+	0.0168679i
$530$	−10.0482			−0.436467
$531$	2.13619	+	10.4782i	0.0927026	+	0.454716i
$532$		0			0
$533$	−4.46569	−	2.57827i	−0.193431	−	0.111677i
$534$	−4.61021	+	5.64491i	−0.199503	+	0.244279i
$535$	−0.164965	+	0.0952423i	−0.00713204	+	0.00411769i
$536$	83.3625	−	48.1294i	3.60071	−	2.07887i
$537$	14.2287	+	2.31438i	0.614015	+	0.0998727i
$538$	5.14131	+	2.96834i	0.221658	+	0.127974i
$539$		0			0
$540$	−16.4363	−	26.0153i	−0.707305	−	1.11952i
$541$	29.7152			1.27756			0.638779	−	0.769390i	$-0.279440\pi$
$541$	29.7152			1.27756			0.638779	+	0.769390i	$0.279440\pi$
$542$	31.3310	−	54.2668i	1.34578	−	2.33096i
$543$	−21.6606	−	3.52321i	−0.929547	−	0.151195i
$544$	34.1641	−	19.7247i	1.46478	−	0.845688i
$545$	−3.38370	−	5.86074i	−0.144942	−	0.251046i
$546$		0			0
$547$	−9.13516	+	15.8226i	−0.390591	+	0.676524i	−0.992528	−	0.122020i	$-0.961063\pi$
$547$	−9.13516	+	15.8226i	−0.390591	+	0.676524i	0.601937	+	0.798544i	$0.294396\pi$
$548$			82.2524i			3.51365i
$549$	−28.7365	−	32.4545i	−1.22644	−	1.38512i
$550$	5.48661			0.233950
$551$	−5.57306	+	9.65282i	−0.237420	+	0.411224i
$552$	54.3858	−	20.6174i	2.31481	−	0.877533i
$553$		0			0
$554$	25.5401	−	14.7456i	1.08510	−	0.626481i
$555$	−5.40676	+	2.04967i	−0.229504	+	0.0870038i
$556$	−25.7720	−	14.8795i	−1.09298	−	0.631031i
$557$		−	0.415065i		−	0.0175869i	−0.999961	−	0.00879343i	$-0.997201\pi$
$557$		−	0.415065i		−	0.0175869i	0.999961	−	0.00879343i	$-0.00279907\pi$
$558$	18.3078	+	6.11755i	0.775030	+	0.258977i
$559$			5.51686i			0.233338i
$560$		0			0
$561$	−2.99347	+	3.66532i	−0.126385	+	0.154750i
$562$	26.4111	+	45.7454i	1.11409	+	1.92965i
$563$	−1.82962	−	3.16900i	−0.0771095	−	0.133558i	0.824892	−	0.565290i	$-0.191236\pi$
$563$	−1.82962	−	3.16900i	−0.0771095	−	0.133558i	−0.902002	+	0.431733i	$0.857902\pi$
$564$	−10.0080	+	61.5292i	−0.421414	+	2.59085i
$565$	−7.02161	−	4.05393i	−0.295401	−	0.170550i
$566$	31.5403			1.32574
$567$		0			0
$568$	−73.6074			−3.08850
$569$	−30.4692	−	17.5914i	−1.27733	−	0.737470i	−0.300977	−	0.953631i	$-0.597313\pi$
$569$	−30.4692	−	17.5914i	−1.27733	−	0.737470i	−0.976358	+	0.216162i	$0.930646\pi$
$570$	1.71832	−	10.5642i	0.0719726	−	0.442486i
$571$	5.02680	+	8.70667i	0.210365	+	0.364363i	0.951829	−	0.306630i	$-0.0992014\pi$
$571$	5.02680	+	8.70667i	0.210365	+	0.364363i	−0.741464	+	0.670993i	$0.765868\pi$
$572$	1.78977	+	3.09998i	0.0748342	+	0.129617i
$573$	4.16387	−	5.09840i	0.173948	−	0.212989i
$574$		0			0
$575$		−	16.2888i		−	0.679292i
$576$	15.1446	+	5.06059i	0.631027	+	0.210858i
$577$		−	0.0690132i		−	0.00287306i	−0.999999	−	0.00143653i	$-0.999543\pi$
$577$		−	0.0690132i		−	0.00287306i	0.999999	−	0.00143653i	$-0.000457261\pi$
$578$	5.89627	+	3.40421i	0.245253	+	0.141597i
$579$	−10.9953	+	4.16825i	−0.456948	+	0.173227i
$580$	30.0627	−	17.3567i	1.24828	−	0.720697i
$581$		0			0
$582$	42.5138	−	16.1168i	1.76225	−	0.668061i
$583$	−0.953529	+	1.65156i	−0.0394911	+	0.0684006i
$584$	81.2437			3.36189
$585$	−3.05991	−	3.45581i	−0.126512	−	0.142880i
$586$		−	69.8564i		−	2.88574i
$587$	11.4799	−	19.8838i	0.473827	−	0.820693i	−0.525724	−	0.850655i	$-0.676205\pi$
$587$	11.4799	−	19.8838i	0.473827	−	0.820693i	0.999551	+	0.0299626i	$0.00953881\pi$
$588$		0			0
$589$	2.35877	+	4.08550i	0.0971913	+	0.168340i
$590$	10.0318	−	5.79186i	0.413003	−	0.238447i
$591$	−10.9662	−	1.78370i	−0.451088	−	0.0733717i
$592$	11.8382	−	20.5044i	0.486547	−	0.842725i
$593$	28.7940			1.18243			0.591213	−	0.806515i	$-0.298649\pi$
$593$	28.7940			1.18243			0.591213	+	0.806515i	$0.298649\pi$
$594$	−8.30506	+	0.331300i	−0.340761	+	0.0135934i
$595$		0			0
$596$	43.4984	+	25.1138i	1.78176	+	1.02870i
$597$	27.4239	+	4.46063i	1.12238	+	0.182561i
$598$	13.0977	−	7.56198i	0.535606	−	0.309233i
$599$	33.1588	−	19.1442i	1.35483	−	0.782212i	0.365910	−	0.930650i	$-0.380758\pi$
$599$	33.1588	−	19.1442i	1.35483	−	0.782212i	0.988922	+	0.148438i	$0.0474246\pi$
$600$	26.5732	−	32.5373i	1.08485	−	1.32833i
$601$	−26.7618	−	15.4509i	−1.09164	−	0.630257i	−0.157625	−	0.987499i	$-0.550384\pi$
$601$	−26.7618	−	15.4509i	−1.09164	−	0.630257i	−0.934012	+	0.357242i	$0.883717\pi$
$602$		0			0
$603$	8.15793	+	40.0155i	0.332216	+	1.62956i
$604$	−44.8507			−1.82495
$605$	6.65311	−	11.5235i	0.270487	−	0.468498i
$606$	2.72808	+	7.19629i	0.110821	+	0.292329i
$607$	−28.7339	+	16.5895i	−1.16627	+	0.673349i	−0.952800	−	0.303600i	$-0.901811\pi$
$607$	−28.7339	+	16.5895i	−1.16627	+	0.673349i	−0.213475	+	0.976949i	$0.568478\pi$
$608$	8.46664	+	14.6647i	0.343368	+	0.594730i
$609$		0			0
$610$	−23.4780	+	40.6650i	−0.950595	+	1.64648i
$611$			9.35053i			0.378282i
$612$	12.5479	+	61.5489i	0.507219	+	2.48797i
$613$	4.02327			0.162498			0.0812492	−	0.996694i	$-0.474109\pi$
$613$	4.02327			0.162498			0.0812492	+	0.996694i	$0.474109\pi$
$614$	27.7120	−	47.9985i	1.11836	−	1.93706i
$615$	−7.05857	−	5.76474i	−0.284629	−	0.232457i
$616$		0			0
$617$	27.1191	−	15.6572i	1.09177	−	0.630336i	0.157726	−	0.987483i	$-0.449584\pi$
$617$	27.1191	−	15.6572i	1.09177	−	0.630336i	0.934048	+	0.357147i	$0.116251\pi$
$618$	5.34061	−	32.8340i	0.214831	−	1.32078i
$619$	−12.0646	−	6.96550i	−0.484917	−	0.279967i	0.237546	−	0.971376i	$-0.423657\pi$
$619$	−12.0646	−	6.96550i	−0.484917	−	0.279967i	−0.722463	+	0.691409i	$0.756990\pi$
$620$		−	14.6922i		−	0.590054i
$621$	0.983576	+	24.6564i	0.0394695	+	0.989426i
$622$		−	42.0962i		−	1.68790i
$623$		0			0
$624$	18.6551	+	3.03434i	0.746802	+	0.121471i
$625$	−1.95762	−	3.39069i	−0.0783047	−	0.135628i
$626$	18.2592	+	31.6259i	0.729786	+	1.26403i
$627$	−1.57331	−	1.28492i	−0.0628319	−	0.0513148i
$628$	97.4661	+	56.2721i	3.88932	+	2.24550i
$629$	11.8031			0.470620
$630$		0			0
$631$	−4.61815			−0.183846			−0.0919229	−	0.995766i	$-0.529301\pi$
$631$	−4.61815			−0.183846			−0.0919229	+	0.995766i	$0.529301\pi$
$632$	24.6902	+	14.2549i	0.982124	+	0.567030i
$633$	−13.1532	+	4.98632i	−0.522794	+	0.198189i
$634$	−26.3203	−	45.5881i	−1.04531	−	1.81053i
$635$	−1.83672	−	3.18129i	−0.0728879	−	0.126246i
$636$	8.97296	+	23.6694i	0.355801	+	0.938554i
$637$		0			0
$638$		−	9.37609i		−	0.371203i
$639$	9.89712	−	29.6188i	0.391524	−	1.17170i
$640$			5.01899i			0.198393i
$641$	−36.7821	−	21.2362i	−1.45281	−	0.838779i	−0.454167	−	0.890917i	$-0.650063\pi$
$641$	−36.7821	−	21.2362i	−1.45281	−	0.838779i	−0.998640	+	0.0521380i	$0.983396\pi$
$642$	0.528932	+	0.431979i	0.0208753	+	0.0170489i
$643$	3.13514	−	1.81008i	0.123638	−	0.0713825i	−0.436905	−	0.899507i	$-0.643926\pi$
$643$	3.13514	−	1.81008i	0.123638	−	0.0713825i	0.560544	+	0.828125i	$0.310592\pi$
$644$		0			0
$645$	−1.56536	+	9.62383i	−0.0616361	+	0.378938i
$646$	−10.9239	+	18.9207i	−0.429795	+	0.744426i
$647$	12.0123			0.472254			0.236127	−	0.971722i	$-0.424122\pi$
$647$	12.0123			0.472254			0.236127	+	0.971722i	$0.424122\pi$
$648$	−38.2591	+	50.8561i	−1.50296	+	1.99782i
$649$		−	2.19848i		−	0.0862979i
$650$	5.46186	−	9.46022i	0.214232	−	0.371060i
$651$		0			0
$652$	20.8484	+	36.1105i	0.816486	+	1.41420i
$653$	−39.9950	+	23.0911i	−1.56512	+	0.903625i	−0.568400	+	0.822752i	$0.692437\pi$
$653$	−39.9950	+	23.0911i	−1.56512	+	0.903625i	−0.996724	+	0.0808728i	$0.974229\pi$
$654$	−15.3470	+	18.7915i	−0.600117	+	0.734806i
$655$	−10.1665	+	17.6089i	−0.397238	+	0.688036i
$656$	37.3169			1.45698
$657$	−10.9239	+	32.6915i	−0.426182	+	1.27542i
$658$		0			0
$659$	−16.3479	−	9.43847i	−0.636824	−	0.367671i	0.146566	−	0.989201i	$-0.453178\pi$
$659$	−16.3479	−	9.43847i	−0.636824	−	0.367671i	−0.783390	+	0.621530i	$0.786511\pi$
$660$	2.24256	+	5.91556i	0.0872916	+	0.230263i
$661$	2.88202	−	1.66393i	0.112097	−	0.0647195i	−0.442903	−	0.896570i	$-0.646051\pi$
$661$	2.88202	−	1.66393i	0.112097	−	0.0647195i	0.555000	+	0.831850i	$0.312718\pi$
$662$	−59.4494	+	34.3231i	−2.31057	+	1.33401i
$663$	3.33992	+	8.81026i	0.129712	+	0.342162i
$664$	−53.4944	−	30.8850i	−2.07599	−	1.19857i
$665$		0			0
$666$	13.7424	+	15.5205i	0.532509	+	0.601407i
$667$	−27.8361			−1.07782
$668$	−52.1494	+	90.3254i	−2.01772	+	3.49480i
$669$	8.80769	−	10.7845i	0.340525	−	0.416952i
$670$	38.3106	−	22.1187i	1.48007	−	0.854518i
$671$	4.45589	+	7.71783i	0.172018	+	0.297944i
$672$		0			0
$673$	−16.3678	+	28.3499i	−0.630934	+	1.09281i	0.356427	+	0.934323i	$0.383995\pi$
$673$	−16.3678	+	28.3499i	−0.630934	+	1.09281i	−0.987361	+	0.158487i	$0.949339\pi$
$674$		−	9.00781i		−	0.346968i
$675$	9.51963	+	15.0677i	0.366411	+	0.579954i
$676$	−54.3170			−2.08912
$677$	16.9228	−	29.3111i	0.650396	−	1.12652i	−0.332631	−	0.943057i	$-0.607937\pi$
$677$	16.9228	−	29.3111i	0.650396	−	1.12652i	0.983027	−	0.183461i	$-0.0587302\pi$
$678$	−4.66671	+	28.6909i	−0.179224	+	1.10187i
$679$		0			0
$680$	33.9917	−	19.6251i	1.30352	−	0.752590i
$681$	27.9347	+	22.8143i	1.07046	+	0.874245i
$682$	−3.43672	−	1.98419i	−0.131599	−	0.0759785i
$683$			5.53814i			0.211911i	0.994371	+	0.105956i	$0.0337901\pi$
$683$			5.53814i			0.211911i	−0.994371	+	0.105956i	$0.966210\pi$
$684$	−26.4193	+	5.38608i	−1.01017	+	0.205942i
$685$			21.8052i			0.833133i
$686$		0			0
$687$	3.69562	+	9.74854i	0.140997	+	0.371930i
$688$	−19.9622	−	34.5756i	−0.761052	−	1.31818i
$689$	1.89846	+	3.28822i	0.0723254	+	0.125271i
$690$	24.9939	−	9.47505i	0.951501	−	0.360709i
$691$	12.3417	+	7.12550i	0.469502	+	0.271067i	0.716031	−	0.698068i	$-0.245957\pi$
$691$	12.3417	+	7.12550i	0.469502	+	0.271067i	−0.246530	+	0.969135i	$0.579290\pi$
$692$	−19.2248			−0.730818
$693$		0			0
$694$	−24.4003			−0.926222
$695$	−6.83219	−	3.94456i	−0.259160	−	0.149626i
$696$	−55.6031	−	45.4111i	−2.10763	−	1.72130i
$697$	9.30154	+	16.1107i	0.352321	+	0.610238i
$698$	18.4557	+	31.9662i	0.698559	+	1.20994i
$699$	35.9587	+	5.84886i	1.36008	+	0.221224i
$700$		0			0
$701$			18.6105i			0.702908i	0.936205	+	0.351454i	$0.114313\pi$
$701$			18.6105i			0.702908i	−0.936205	+	0.351454i	$0.885687\pi$
$702$	−7.69636	+	14.6497i	−0.290481	+	0.552918i
$703$			5.06637i			0.191082i
$704$	−2.84293	−	1.64137i	−0.107147	−	0.0618614i
$705$	−2.65314	+	16.3114i	−0.0999230	+	0.614325i
$706$	38.5544	−	22.2594i	1.45101	−	0.837743i
$707$		0			0
$708$	−22.6015	−	18.4587i	−0.849416	−	0.693719i
$709$	6.74733	−	11.6867i	0.253401	−	0.438904i	−0.711059	−	0.703133i	$-0.751784\pi$
$709$	6.74733	−	11.6867i	0.253401	−	0.438904i	0.964460	+	0.264229i	$0.0851174\pi$
$710$	−33.8275			−1.26952
$711$	−9.05582	+	8.01837i	−0.339620	+	0.300712i
$712$		−	11.4726i		−	0.429954i
$713$	−5.89074	+	10.2031i	−0.220610	+	0.382107i
$714$		0			0
$715$	0.474470	+	0.821807i	0.0177442	+	0.0307338i
$716$	−34.0676	+	19.6689i	−1.27317	+	0.735063i
$717$	5.32482	+	14.0461i	0.198859	+	0.524563i
$718$	36.6417	−	63.4652i	1.36745	−	2.36850i
$719$	−37.7384			−1.40740			−0.703702	−	0.710496i	$-0.748471\pi$
$719$	−37.7384			−1.40740			−0.703702	+	0.710496i	$0.748471\pi$
$720$	31.6817	+	10.5865i	1.18071	+	0.394534i
$721$		0			0
$722$	34.5538	+	19.9496i	1.28596	+	0.742449i
$723$	−9.28327	+	11.3668i	−0.345248	+	0.422736i
$724$	51.8617	−	29.9424i	1.92742	−	1.11280i
$725$	−17.4118	+	10.0527i	−0.646659	+	0.373348i
$726$	−47.0860	−	7.65877i	−1.74753	−	0.284244i
$727$	−1.98480	−	1.14592i	−0.0736121	−	0.0424999i	0.462742	−	0.886493i	$-0.346866\pi$
$727$	−1.98480	−	1.14592i	−0.0736121	−	0.0424999i	−0.536354	+	0.843993i	$0.680199\pi$
$728$		0			0
$729$	−15.3197	−	22.2330i	−0.567395	−	0.823446i
$730$	37.3369			1.38190
$731$	9.95149	−	17.2365i	0.368069	−	0.637514i
$732$	116.755	+	18.9908i	4.31540	+	0.701921i
$733$	21.4678	−	12.3944i	0.792930	−	0.457798i	−0.0480633	−	0.998844i	$-0.515305\pi$
$733$	21.4678	−	12.3944i	0.792930	−	0.457798i	0.840993	+	0.541046i	$0.181972\pi$
$734$	−29.9170	−	51.8178i	−1.10426	−	1.91263i
$735$		0			0
$736$	−21.1444	+	36.6232i	−0.779394	+	1.34995i
$737$		−	8.39582i		−	0.309264i
$738$	−10.3550	+	30.9890i	−0.381172	+	1.14072i
$739$	−16.2016			−0.595986			−0.297993	−	0.954568i	$-0.596317\pi$
$739$	−16.2016			−0.595986			−0.297993	+	0.954568i	$0.596317\pi$
$740$	7.88932	−	13.6647i	0.290017	−	0.502325i
$741$	−3.78173	+	1.43363i	−0.138925	+	0.0526658i
$742$		0			0
$743$	−18.8312	+	10.8722i	−0.690848	+	0.398862i	−0.803930	−	0.594724i	$-0.797261\pi$
$743$	−18.8312	+	10.8722i	−0.690848	+	0.398862i	0.113081	+	0.993586i	$0.463928\pi$
$744$	−28.4118	+	10.7708i	−1.04163	+	0.394876i
$745$	11.5315	+	6.65769i	0.422480	+	0.243919i
$746$			35.9794i			1.31730i
$747$	19.6205	−	17.3728i	0.717878	−	0.635637i
$748$		−	12.9138i		−	0.472176i
$749$		0			0
$750$	30.0140	−	36.7503i	1.09596	−	1.34193i
$751$	3.78997	+	6.56443i	0.138298	+	0.239539i	0.926853	−	0.375426i	$-0.122503\pi$
$751$	3.78997	+	6.56443i	0.138298	+	0.239539i	−0.788554	+	0.614965i	$0.789170\pi$
$752$	−33.8340	−	58.6022i	−1.23380	−	2.13700i
$753$	−6.51899	+	40.0787i	−0.237565	+	1.46055i
$754$	−16.1666	−	9.33381i	−0.588754	−	0.339917i
$755$	−11.8900			−0.432720
$756$		0			0
$757$	10.3436			0.375944			0.187972	−	0.982174i	$-0.439809\pi$
$757$	10.3436			0.375944			0.187972	+	0.982174i	$0.439809\pi$
$758$	51.1686	+	29.5422i	1.85853	+	1.07302i
$759$	0.814448	−	5.00721i	0.0295626	−	0.181750i
$760$	8.42392	+	14.5907i	0.305568	+	0.529259i
$761$	−17.2169	−	29.8206i	−0.624114	−	1.08100i	−0.988711	−	0.149832i	$-0.952127\pi$
$761$	−17.2169	−	29.8206i	−0.624114	−	1.08100i	0.364598	−	0.931165i	$-0.381207\pi$
$762$	−8.33058	+	10.2003i	−0.301785	+	0.369517i
$763$		0			0
$764$			17.9629i			0.649874i
$765$	3.32646	+	16.3166i	0.120268	+	0.589930i
$766$		−	39.5047i		−	1.42736i
$767$	−3.79070	−	2.18856i	−0.136874	−	0.0790245i
$768$	34.0661	−	12.9143i	1.22925	−	0.466004i
$769$	12.9344	−	7.46765i	0.466425	−	0.269290i	−0.248317	−	0.968679i	$-0.579877\pi$
$769$	12.9344	−	7.46765i	0.466425	−	0.269290i	0.714742	+	0.699388i	$0.246544\pi$
$770$		0			0
$771$	−39.7073	+	15.0528i	−1.43002	+	0.542114i
$772$	16.0439	−	27.7888i	0.577431	−	1.00014i
$773$	39.9848			1.43815			0.719076	−	0.694931i	$-0.244565\pi$
$773$	39.9848			1.43815			0.719076	+	0.694931i	$0.244565\pi$
$774$	34.2518	−	6.98288i	1.23115	−	0.250994i
$775$			8.50951i			0.305671i
$776$	−35.7845	+	61.9806i	−1.28459	+	2.22497i
$777$		0			0
$778$	−18.3466	−	31.7772i	−0.657758	−	1.13927i
$779$	−6.91539	+	3.99260i	−0.247770	+	0.143050i
$780$	12.4323	+	2.02217i	0.445148	+	0.0724055i
$781$	−3.21007	+	5.56000i	−0.114865	+	0.198952i
$782$	−54.5622			−1.95114
$783$	25.7492	−	16.2681i	0.920201	−	0.581376i
$784$		0			0
$785$	25.8383	+	14.9178i	0.922209	+	0.532438i
$786$	71.9513	+	11.7032i	2.56642	+	0.417440i
$787$	−1.94091	+	1.12059i	−0.0691860	+	0.0399446i	−0.534194	−	0.845362i	$-0.679385\pi$
$787$	−1.94091	+	1.12059i	−0.0691860	+	0.0399446i	0.465008	+	0.885307i	$0.346051\pi$
$788$	26.2561	−	15.1590i	0.935336	−	0.540016i
$789$	−11.5635	+	14.1588i	−0.411671	+	0.504066i
$790$	11.3468	+	6.55108i	0.403701	+	0.233077i
$791$		0			0
$792$	9.79551	−	8.67333i	0.348068	−	0.308193i
$793$	17.7432			0.630079
$794$	−12.5883	+	21.8036i	−0.446742	+	0.773780i
$795$	2.37874	+	6.27478i	0.0843652	+	0.222544i
$796$	−65.6605	+	37.9091i	−2.32727	+	1.34365i
$797$	22.1077	+	38.2916i	0.783094	+	1.35636i	0.930131	+	0.367227i	$0.119693\pi$
$797$	22.1077	+	38.2916i	0.783094	+	1.35636i	−0.147037	+	0.989131i	$0.546974\pi$
$798$		0			0
$799$	16.8668	−	29.2142i	0.596705	−	1.03352i
$800$			30.5444i			1.07991i
$801$	4.61644	+	1.54259i	0.163114	+	0.0545046i
$802$	22.6451			0.799625
$803$	3.54309	−	6.13682i	0.125033	−	0.216564i
$804$	−86.3133	−	70.4921i	−3.04404	−	2.48607i
$805$		0			0
$806$	−6.84243	+	3.95048i	−0.241014	+	0.139150i
$807$	0.636514	−	3.91328i	0.0224064	−	0.137754i
$808$	−10.4914	−	6.05723i	−0.369087	−	0.213093i
$809$			4.98227i			0.175167i	0.996157	+	0.0875837i	$0.0279145\pi$
$809$			4.98227i			0.175167i	−0.996157	+	0.0875837i	$0.972085\pi$
$810$	−17.5826	+	23.3718i	−0.617789	+	0.821201i
$811$			36.5749i			1.28432i	0.766571	+	0.642160i	$0.221961\pi$
$811$			36.5749i			1.28432i	−0.766571	+	0.642160i	$0.778039\pi$
$812$		0			0
$813$	−41.3049	−	6.71844i	−1.44863	−	0.235626i
$814$	−2.13091	−	3.69084i	−0.0746883	−	0.129364i
$815$	5.52693	+	9.57292i	0.193600	+	0.335325i
$816$	−52.8112	−	43.1310i	−1.84876	−	1.50989i
$817$	7.39861	+	4.27159i	0.258845	+	0.149444i
$818$	−38.6225			−1.35040
$819$		0			0
$820$	24.8690			0.868465
$821$	−34.8397	−	20.1147i	−1.21591	−	0.702008i	−0.251872	−	0.967761i	$-0.581046\pi$
$821$	−34.8397	−	20.1147i	−1.21591	−	0.702008i	−0.964041	+	0.265753i	$0.914379\pi$
$822$	73.0986	−	27.7113i	2.54961	−	0.966542i
$823$	17.9016	+	31.0065i	0.624011	+	1.08082i	0.988731	+	0.149701i	$0.0478313\pi$
$823$	17.9016	+	31.0065i	0.624011	+	1.08082i	−0.364720	+	0.931117i	$0.618835\pi$
$824$	26.1819	+	45.3483i	0.912089	+	1.57978i
$825$	−1.29886	−	3.42620i	−0.0452204	−	0.119285i
$826$		0			0
$827$		−	32.0733i		−	1.11530i	−0.830077	−	0.557648i	$-0.811704\pi$
$827$		−	32.0733i		−	1.11530i	0.830077	−	0.557648i	$-0.188296\pi$
$828$	−44.6385	−	50.4140i	−1.55130	−	1.75201i
$829$			16.2397i			0.564029i	0.959410	+	0.282014i	$0.0910026\pi$
$829$			16.2397i			0.564029i	−0.959410	+	0.282014i	$0.908997\pi$
$830$	−24.5842	−	14.1937i	−0.853332	−	0.492671i
$831$	−15.2543	−	12.4582i	−0.529166	−	0.432170i
$832$	−5.66023	+	3.26793i	−0.196233	+	0.113295i
$833$		0			0
$834$	−4.54081	+	27.9169i	−0.157236	+	0.966682i
$835$	−13.8248	+	23.9453i	−0.478429	+	0.828663i
$836$	5.54314			0.191714
$837$	−0.513833	−	12.8808i	−0.0177607	−	0.445226i
$838$			11.0930i			0.383202i
$839$	1.35145	−	2.34077i	0.0466571	−	0.0808125i	−0.841754	−	0.539862i	$-0.818477\pi$
$839$	1.35145	−	2.34077i	0.0466571	−	0.0808125i	0.888411	+	0.459049i	$0.151810\pi$
$840$		0			0
$841$	2.67914	+	4.64041i	0.0923842	+	0.160014i
$842$	25.9053	−	14.9565i	0.892757	−	0.515434i
$843$	22.3141	−	27.3223i	0.768539	−	0.941029i
$844$	19.1927	−	33.2427i	0.660639	−	1.14426i
$845$	−14.3995			−0.495357
$846$	58.0534	−	11.8353i	1.99592	−	0.406906i
$847$		0			0
$848$	−23.7962	−	13.7388i	−0.817166	−	0.471791i
$849$	−7.46660	−	19.6959i	−0.256253	−	0.675960i
$850$	−34.1293	+	19.7046i	−1.17063	+	0.675861i
$851$	−10.9575	+	6.32632i	−0.375619	+	0.216864i
$852$	30.2076	+	79.6834i	1.03489	+	2.72991i
$853$	41.3187	+	23.8554i	1.41473	+	0.816793i	0.995829	−	0.0912411i	$-0.0290834\pi$
$853$	41.3187	+	23.8554i	1.41473	+	0.816793i	0.418897	+	0.908034i	$0.362417\pi$
$854$		0			0
$855$	−7.00378	+	1.42785i	−0.239524	+	0.0488316i
$856$	−1.07499			−0.0367424
$857$	8.93973	−	15.4841i	0.305375	−	0.528926i	−0.671969	−	0.740579i	$-0.734551\pi$
$857$	8.93973	−	15.4841i	0.305375	−	0.528926i	0.977345	+	0.211653i	$0.0678847\pi$
$858$	2.15200	−	2.63499i	0.0734680	−	0.0899571i
$859$	−29.1901	+	16.8529i	−0.995953	+	0.575014i	−0.907048	−	0.421026i	$-0.861670\pi$
$859$	−29.1901	+	16.8529i	−0.995953	+	0.575014i	−0.0889047	+	0.996040i	$0.528337\pi$
$860$	−13.3034	−	23.0422i	−0.453642	−	0.785731i
$861$		0			0
$862$	21.6367	−	37.4759i	0.736950	−	1.27643i
$863$			18.9739i			0.645878i	0.946420	+	0.322939i	$0.104671\pi$
$863$			18.9739i			0.645878i	−0.946420	+	0.322939i	$0.895329\pi$
$864$	−1.84437	−	46.2349i	−0.0627468	−	1.57294i
$865$	−5.09652			−0.173287
$866$	16.0155	−	27.7396i	0.544228	−	0.942630i
$867$	0.729981	−	4.48791i	0.0247915	−	0.152417i
$868$		0			0
$869$	2.15351	−	1.24333i	0.0730530	−	0.0421772i
$870$	−25.5533	−	20.8694i	−0.866339	−	0.707540i
$871$	−14.4764	−	8.35795i	−0.490514	−	0.283198i
$872$		−	38.1915i		−	1.29333i
$873$	−20.1288	−	22.7331i	−0.681255	−	0.769398i
$874$		−	23.4204i		−	0.792206i
$875$		0			0
$876$	−33.3415	−	87.9501i	−1.12650	−	2.97156i
$877$	−18.6188	−	32.2487i	−0.628712	−	1.08896i	−0.987810	−	0.155662i	$-0.950249\pi$
$877$	−18.6188	−	32.2487i	−0.628712	−	1.08896i	0.359098	−	0.933300i	$-0.383084\pi$
$878$	−28.7035	−	49.7159i	−0.968695	−	1.67783i
$879$	−43.6230	+	16.5373i	−1.47137	+	0.557788i
$880$	−5.94726	−	3.43365i	−0.200482	−	0.115748i
$881$	4.71527			0.158862			0.0794308	−	0.996840i	$-0.474690\pi$
$881$	4.71527			0.158862			0.0794308	+	0.996840i	$0.474690\pi$
$882$		0			0
$883$	30.1766			1.01552			0.507762	−	0.861497i	$-0.330473\pi$
$883$	30.1766			1.01552			0.507762	+	0.861497i	$0.330473\pi$
$884$	−22.2665	−	12.8556i	−0.748904	−	0.432380i
$885$	−5.99167	−	4.89340i	−0.201408	−	0.164490i
$886$	6.33251	+	10.9682i	0.212745	+	0.368485i
$887$	19.2217	+	33.2930i	0.645402	+	1.11787i	0.984208	+	0.177013i	$0.0566436\pi$
$887$	19.2217	+	33.2930i	0.645402	+	1.11787i	−0.338806	+	0.940856i	$0.610023\pi$
$888$	−32.2084	−	5.23886i	−1.08084	−	0.175805i
$889$		0			0
$890$		−	5.27243i		−	0.176732i
$891$	2.17296	+	5.10780i	0.0727969	+	0.171118i
$892$			37.9963i			1.27221i
$893$	12.5399	+	7.23993i	0.419632	+	0.242275i
$894$	7.66405	−	47.1184i	0.256324	−	1.57588i
$895$	−9.03135	+	5.21425i	−0.301885	+	0.174293i
$896$		0			0
$897$	−7.82286	−	6.38894i	−0.261198	−	0.213320i
$898$	−16.1329	+	27.9431i	−0.538363	+	0.932472i
$899$	14.5420			0.485001
$900$	−46.1284	−	15.4138i	−1.53761	−	0.513794i
$901$		−	13.6980i		−	0.456346i
$902$	3.35857	−	5.81721i	0.111828	−	0.193692i
$903$		0			0
$904$	−22.8781	−	39.6261i	−0.760916	−	1.31794i
$905$	13.7486	−	7.93774i	0.457018	−	0.263859i
$906$	15.1105	+	39.8593i	0.502011	+	1.32424i
$907$	−21.7951	+	37.7503i	−0.723695	+	1.25348i	0.235814	+	0.971798i	$0.424224\pi$
$907$	−21.7951	+	37.7503i	−0.723695	+	1.25348i	−0.959509	+	0.281678i	$0.909109\pi$
$908$	−98.4206			−3.26620
$909$	3.84802	−	3.40719i	0.127631	−	0.113009i
$910$		0			0
$911$	−1.67736	−	0.968423i	−0.0555734	−	0.0320853i	0.471956	−	0.881622i	$-0.343548\pi$
$911$	−1.67736	−	0.968423i	−0.0555734	−	0.0320853i	−0.527529	+	0.849537i	$0.676881\pi$
$912$	18.5136	−	22.6688i	0.613046	−	0.750638i
$913$	−4.66585	+	2.69383i	−0.154417	+	0.0891528i
$914$	24.2025	−	13.9733i	0.800548	−	0.462197i
$915$	30.9519	+	5.03448i	1.02324	+	0.166435i
$916$	−24.6379	−	14.2247i	−0.814058	−	0.469997i
$917$		0			0
$918$	50.4716	−	31.8876i	1.66581	−	1.05245i
$919$	−9.22843			−0.304418			−0.152209	−	0.988348i	$-0.548639\pi$
$919$	−9.22843			−0.304418			−0.152209	+	0.988348i	$0.548639\pi$
$920$	−21.0377	+	36.4384i	−0.693594	+	1.20134i
$921$	−36.5338	−	5.94240i	−1.20383	−	0.195809i
$922$	1.49724	−	0.864434i	0.0493091	−	0.0284686i
$923$	6.39118	+	11.0698i	0.210368	+	0.364368i
$924$		0			0
$925$	−4.56937	+	7.91438i	−0.150240	+	0.260223i
$926$		−	107.835i		−	3.54368i
$927$	−21.7680	+	4.43783i	−0.714956	+	0.145757i
$928$	52.1974			1.71346
$929$	−26.6849	+	46.2197i	−0.875504	+	1.51642i	−0.0192794	+	0.999814i	$0.506137\pi$
$929$	−26.6849	+	46.2197i	−0.875504	+	1.51642i	−0.856225	+	0.516603i	$0.827196\pi$
$930$	−13.0571	+	4.94989i	−0.428160	+	0.162313i
$931$		0			0
$932$	−86.0952	+	49.7071i	−2.82014	+	1.62821i
$933$	−26.2876	+	9.96551i	−0.860619	+	0.326256i
$934$	88.3010	+	50.9806i	2.88930	+	1.66814i
$935$		−	3.42346i		−	0.111959i
$936$	−5.20356	−	25.5240i	−0.170084	−	0.834279i
$937$		−	28.6378i		−	0.935555i	−0.883846	−	0.467778i	$-0.845055\pi$
$937$		−	28.6378i		−	0.935555i	0.883846	−	0.467778i	$-0.154945\pi$
$938$		0			0
$939$	15.4268	−	18.8891i	0.503434	−	0.616424i
$940$	−22.5480	−	39.0542i	−0.735433	−	1.27381i
$941$	0.688308	+	1.19218i	0.0224382	+	0.0388641i	0.877026	−	0.480442i	$-0.159524\pi$
$941$	0.688308	+	1.19218i	0.0224382	+	0.0388641i	−0.854588	+	0.519306i	$0.826190\pi$
$942$	17.1727	−	105.577i	0.559516	−	3.43990i
$943$	−17.2704	−	9.97105i	−0.562401	−	0.324702i
$944$	31.6764			1.03098
$945$		0			0
$946$	−7.18651			−0.233653
$947$	47.0080	+	27.1401i	1.52755	+	0.881933i	0.999464	+	0.0327450i	$0.0104249\pi$
$947$	47.0080	+	27.1401i	1.52755	+	0.881933i	0.528090	+	0.849188i	$0.322908\pi$
$948$	5.29903	−	32.5784i	0.172105	−	1.05810i
$949$	−7.05423	−	12.2183i	−0.228990	−	0.396622i
$950$	−8.45802	−	14.6497i	−0.274414	−	0.475300i
$951$	−22.2374	+	27.2283i	−0.721097	+	0.882939i
$952$		0			0
$953$			11.2998i			0.366036i	0.983110	+	0.183018i	$0.0585867\pi$
$953$			11.2998i			0.366036i	−0.983110	+	0.183018i	$0.941413\pi$
$954$	18.0122	−	15.9487i	0.583167	−	0.516359i
$955$			4.76197i			0.154094i
$956$	−35.4994	−	20.4956i	−1.14813	−	0.662874i
$957$	−5.85506	+	2.21962i	−0.189267	+	0.0717502i
$958$	−85.6097	+	49.4268i	−2.76592	+	1.59691i
$959$		0			0
$960$	−10.8012	+	4.09467i	−0.348607	+	0.132155i
$961$	−12.4226	+	21.5166i	−0.400729	+	0.694083i
$962$	−8.48519			−0.273574
$963$	0.144541	−	0.432564i	0.00465778	−	0.0139392i
$964$		−	40.0479i		−	1.28986i
$965$	4.25324	−	7.36682i	0.136917	−	0.237146i
$966$		0			0
$967$	5.93412	+	10.2782i	0.190829	+	0.330525i	0.945525	−	0.325549i	$-0.105549\pi$
$967$	5.93412	+	10.2782i	0.190829	+	0.330525i	−0.754696	+	0.656074i	$0.772216\pi$
$968$	65.0324	−	37.5465i	2.09022	−	1.20679i
$969$	14.4014	+	2.34246i	0.462640	+	0.0752506i
$970$	−16.4454	+	28.4842i	−0.528029	+	0.914573i
$971$	56.1674			1.80250			0.901249	−	0.433302i	$-0.142652\pi$
$971$	56.1674			1.80250			0.901249	+	0.433302i	$0.142652\pi$
$972$	70.7552	+	20.5465i	2.26947	+	0.659029i
$973$		0			0
$974$	17.0826	+	9.86263i	0.547361	+	0.316019i
$975$	−7.20059	−	1.17121i	−0.230603	−	0.0375088i
$976$	−111.201	+	64.2020i	−3.55946	+	2.05506i
$977$	−18.7626	+	10.8326i	−0.600268	+	0.346565i	−0.769147	−	0.639072i	$-0.779319\pi$
$977$	−18.7626	+	10.8326i	−0.600268	+	0.346565i	0.168879	+	0.985637i	$0.445985\pi$
$978$	25.0678	−	30.6940i	0.801580	−	0.981486i
$979$	−0.866594	−	0.500328i	−0.0276964	−	0.0159906i
$980$		0			0
$981$	15.3678	+	5.13516i	0.490656	+	0.163953i
$982$	9.98145			0.318521
$983$	−9.70006	+	16.8010i	−0.309384	+	0.535869i	−0.978228	−	0.207534i	$-0.933456\pi$
$983$	−9.70006	+	16.8010i	−0.309384	+	0.535869i	0.668844	+	0.743403i	$0.266789\pi$
$984$	−18.2313	−	48.0918i	−0.581194	−	1.53311i
$985$	6.96052	−	4.01866i	0.221781	−	0.128045i
$986$	33.6733	+	58.3238i	1.07238	+	1.85741i
$987$		0			0
$988$	5.51814	−	9.55771i	0.175556	−	0.304071i
$989$			21.3356i			0.678432i
$990$	4.50169	−	3.98597i	0.143073	−	0.126683i
$991$	25.3261			0.804509			0.402254	−	0.915528i	$-0.368227\pi$
$991$	25.3261			0.804509			0.402254	+	0.915528i	$0.368227\pi$
$992$	11.0461	−	19.1325i	0.350715	−	0.607456i
$993$	35.5072	+	28.9988i	1.12679	+	0.920248i
$994$		0			0
$995$	−17.4066	+	10.0497i	−0.551828	+	0.318598i
$996$	−11.4810	+	70.5851i	−0.363790	+	2.23657i
$997$	−4.82016	−	2.78292i	−0.152656	−	0.0881360i	0.421726	−	0.906723i	$-0.361424\pi$
$997$	−4.82016	−	2.78292i	−0.152656	−	0.0881360i	−0.574382	+	0.818587i	$0.694758\pi$
$998$			83.4050i			2.64014i
$999$	6.43875	−	12.2559i	0.203713	−	0.387759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.d.146.5		10
3.2	odd	2		1323.2.o.c.440.1		10
7.2	even	3		63.2.i.b.38.1	yes	10
7.3	odd	6		63.2.s.b.47.1	yes	10
7.4	even	3		441.2.s.b.362.1		10
7.5	odd	6		441.2.i.b.227.1		10
7.6	odd	2		441.2.o.c.146.5		10
9.4	even	3		1323.2.o.d.881.1		10
9.5	odd	6		441.2.o.c.293.5		10
21.2	odd	6		189.2.i.b.143.5		10
21.5	even	6		1323.2.i.b.521.5		10
21.11	odd	6		1323.2.s.b.656.5		10
21.17	even	6		189.2.s.b.89.5		10
21.20	even	2		1323.2.o.d.440.1		10
28.3	even	6		1008.2.df.b.929.1		10
28.23	odd	6		1008.2.ca.b.353.1		10
63.2	odd	6		567.2.p.c.80.5		10
63.4	even	3		1323.2.i.b.1097.1		10
63.5	even	6		441.2.s.b.374.1		10
63.13	odd	6		1323.2.o.c.881.1		10
63.16	even	3		567.2.p.d.80.1		10
63.23	odd	6		63.2.s.b.59.1	yes	10
63.31	odd	6		189.2.i.b.152.1		10
63.32	odd	6		441.2.i.b.68.5		10
63.38	even	6		567.2.p.d.404.1		10
63.40	odd	6		1323.2.s.b.962.5		10
63.41	even	6	inner	441.2.o.d.293.5		10
63.52	odd	6		567.2.p.c.404.5		10
63.58	even	3		189.2.s.b.17.5		10
63.59	even	6		63.2.i.b.5.5	✓	10
84.23	even	6		3024.2.ca.b.2033.2		10
84.59	odd	6		3024.2.df.b.1601.2		10
252.23	even	6		1008.2.df.b.689.1		10
252.31	even	6		3024.2.ca.b.2609.2		10
252.59	odd	6		1008.2.ca.b.257.1		10
252.247	odd	6		3024.2.df.b.17.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	63.59	even	6
63.2.i.b.38.1	yes	10	7.2	even	3
63.2.s.b.47.1	yes	10	7.3	odd	6
63.2.s.b.59.1	yes	10	63.23	odd	6
189.2.i.b.143.5		10	21.2	odd	6
189.2.i.b.152.1		10	63.31	odd	6
189.2.s.b.17.5		10	63.58	even	3
189.2.s.b.89.5		10	21.17	even	6
441.2.i.b.68.5		10	63.32	odd	6
441.2.i.b.227.1		10	7.5	odd	6
441.2.o.c.146.5		10	7.6	odd	2
441.2.o.c.293.5		10	9.5	odd	6
441.2.o.d.146.5		10	1.1	even	1	trivial
441.2.o.d.293.5		10	63.41	even	6	inner
441.2.s.b.362.1		10	7.4	even	3
441.2.s.b.374.1		10	63.5	even	6
567.2.p.c.80.5		10	63.2	odd	6
567.2.p.c.404.5		10	63.52	odd	6
567.2.p.d.80.1		10	63.16	even	3
567.2.p.d.404.1		10	63.38	even	6
1008.2.ca.b.257.1		10	252.59	odd	6
1008.2.ca.b.353.1		10	28.23	odd	6
1008.2.df.b.689.1		10	252.23	even	6
1008.2.df.b.929.1		10	28.3	even	6
1323.2.i.b.521.5		10	21.5	even	6
1323.2.i.b.1097.1		10	63.4	even	3
1323.2.o.c.440.1		10	3.2	odd	2
1323.2.o.c.881.1		10	63.13	odd	6
1323.2.o.d.440.1		10	21.20	even	2
1323.2.o.d.881.1		10	9.4	even	3
1323.2.s.b.656.5		10	21.11	odd	6
1323.2.s.b.962.5		10	63.40	odd	6
3024.2.ca.b.2033.2		10	84.23	even	6
3024.2.ca.b.2609.2		10	252.31	even	6
3024.2.df.b.17.2		10	252.247	odd	6
3024.2.df.b.1601.2		10	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24607 + 1.29677i) q^{2} +(0.278072 - 1.70958i) q^{3} +(2.36322 + 4.09323i) q^{4} +(0.626493 + 1.08512i) q^{5} +(2.84151 - 3.47925i) q^{6} +7.07116i q^{8} +(-2.84535 - 0.950775i) q^{9} +3.24967i q^{10} +(0.534126 + 0.308378i) q^{11} +(7.65486 - 2.90192i) q^{12} +(1.06343 - 0.613974i) q^{13} +(2.02931 - 0.769301i) q^{15} +(-4.44321 + 7.69587i) q^{16} -4.43003 q^{17} +(-5.15793 - 5.82528i) q^{18} -1.90155i q^{19} +(-2.96109 + 5.12875i) q^{20} +(0.799790 + 1.38528i) q^{22} +(4.11267 - 2.37445i) q^{23} +(12.0887 + 1.96629i) q^{24} +(1.71501 - 2.97049i) q^{25} +3.18473 q^{26} +(-2.41664 + 4.59998i) q^{27} +(-5.07629 - 2.93080i) q^{29} +(5.55558 + 0.903642i) q^{30} +(-2.14851 + 1.24044i) q^{31} +(-7.71195 + 4.45249i) q^{32} +(0.675723 - 0.827382i) q^{33} +(-9.95016 - 5.74473i) q^{34} +(-2.83247 - 13.8936i) q^{36} -2.66433 q^{37} +(2.46587 - 4.27102i) q^{38} +(-0.753929 - 1.98876i) q^{39} +(-7.67303 + 4.43003i) q^{40} +(-2.09966 - 3.63671i) q^{41} +(-2.24637 + 3.89083i) q^{43} +2.91506i q^{44} +(-0.750889 - 3.68319i) q^{45} +12.3165 q^{46} +(-3.80738 + 6.59458i) q^{47} +(11.9212 + 9.73605i) q^{48} +(7.70409 - 4.44796i) q^{50} +(-1.23187 + 7.57350i) q^{51} +(5.02627 + 2.90192i) q^{52} +3.09208i q^{53} +(-11.3931 + 7.19806i) q^{54} +0.772786i q^{55} +(-3.25086 - 0.528768i) q^{57} +(-7.60114 - 13.1656i) q^{58} +(-1.78229 - 3.08702i) q^{59} +(7.94463 + 6.48839i) q^{60} +(12.5136 + 7.22473i) q^{61} -6.43428 q^{62} -5.32259 q^{64} +(1.33247 + 0.769301i) q^{65} +(2.59065 - 0.982101i) q^{66} +(-6.80644 - 11.7891i) q^{67} +(-10.4692 - 18.1331i) q^{68} +(-2.91570 - 7.69121i) q^{69} +10.4095i q^{71} +(6.72308 - 20.1199i) q^{72} -11.4895i q^{73} +(-5.98429 - 3.45503i) q^{74} +(-4.60141 - 3.75797i) q^{75} +(7.78348 - 4.49379i) q^{76} +(0.885586 - 5.44457i) q^{78} +(2.01592 - 3.49168i) q^{79} -11.1346 q^{80} +(7.19205 + 5.41058i) q^{81} -10.8911i q^{82} +(-4.36775 + 7.56516i) q^{83} +(-2.77538 - 4.80710i) q^{85} +(-10.0910 + 5.82605i) q^{86} +(-6.42202 + 7.86337i) q^{87} +(-2.18059 + 3.77689i) q^{88} -1.62245 q^{89} +(3.08970 - 9.24645i) q^{90} +(19.4383 + 11.2227i) q^{92} +(1.52320 + 4.01799i) q^{93} +(-17.1033 + 9.87459i) q^{94} +(2.06341 - 1.19131i) q^{95} +(5.46743 + 14.4223i) q^{96} +(8.76527 + 5.06063i) q^{97} +(-1.22658 - 1.38528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} + 4 q^{4} + 12 q^{6} - 3 q^{9} + 12 q^{11} + 12 q^{12} - 6 q^{13} - 3 q^{15} - 6 q^{16} - 24 q^{17} - 6 q^{18} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 27 q^{24} + 7 q^{25} + 6 q^{26} - 27 q^{27}+ \cdots + 21 q^{99}+O(q^{100}) \) 10 * q + 3 * q^3 + 4 * q^4 + 12 * q^6 - 3 * q^9 + 12 * q^11 + 12 * q^12 - 6 * q^13 - 3 * q^15 - 6 * q^16 - 24 * q^17 - 6 * q^18 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 27 * q^24 + 7 * q^25 + 6 * q^26 - 27 * q^27 - 15 * q^29 - 6 * q^30 - 9 * q^31 - 48 * q^32 - 9 * q^33 - 3 * q^34 - 18 * q^36 - 12 * q^37 + 18 * q^38 - 30 * q^39 - 15 * q^40 + 9 * q^41 + 3 * q^43 - 15 * q^45 + 26 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 + 3 * q^51 + 12 * q^52 + 18 * q^54 - 36 * q^57 + 8 * q^58 + 18 * q^59 + 51 * q^60 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 + 6 * q^66 - 10 * q^67 - 27 * q^68 + 3 * q^69 + 12 * q^72 + 30 * q^74 - 27 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 - 60 * q^80 + 33 * q^81 + 15 * q^83 + 18 * q^85 - 54 * q^86 + 24 * q^87 - 8 * q^88 + 48 * q^89 - 24 * q^90 + 39 * q^92 - 42 * q^93 - 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^99

Introduction

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