LMFDB - Embedded newform 441.2.s.b.374.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, 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:	$10$
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			374.1
Root			$1.07065 + 1.85442i$ of defining polynomial
Character	$\chi$	$=$	441.374
Dual form			441.2.s.b.362.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24607 - 1.29677i) q^{2} +(-1.61958 - 0.613974i) q^{3} +(2.36322 + 4.09323i) q^{4} -1.25299 q^{5} +(2.84151 + 3.47925i) q^{6} -7.07116i q^{8} +(2.24607 + 1.98876i) q^{9} +O(q^{10})$	\(q+(-2.24607 - 1.29677i) q^{2} +(-1.61958 - 0.613974i) q^{3} +(2.36322 + 4.09323i) q^{4} -1.25299 q^{5} +(2.84151 + 3.47925i) q^{6} -7.07116i q^{8} +(2.24607 + 1.98876i) q^{9} +(2.81429 + 1.62483i) q^{10} +0.616756i q^{11} +(-1.31429 - 8.08026i) q^{12} +(1.06343 + 0.613974i) q^{13} +(2.02931 + 0.769301i) q^{15} +(-4.44321 + 7.69587i) q^{16} +(2.21501 - 3.83652i) q^{17} +(-2.46587 - 7.37953i) q^{18} +(1.64679 - 0.950775i) q^{19} +(-2.96109 - 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} -4.74890i q^{23} +(-4.34151 + 11.4523i) q^{24} -3.43003 q^{25} +(-1.59237 - 2.75806i) q^{26} +(-2.41664 - 4.59998i) q^{27} +(-5.07629 + 2.93080i) q^{29} +(-3.56037 - 4.35945i) q^{30} +(2.14851 - 1.24044i) q^{31} +(7.71195 - 4.45249i) q^{32} +(0.378672 - 0.998884i) q^{33} +(-9.95016 + 5.74473i) q^{34} +(-2.83247 + 13.8936i) q^{36} +(1.33217 + 2.30738i) q^{37} -4.93175 q^{38} +(-1.34535 - 1.64730i) q^{39} +8.86005i q^{40} +(-2.09966 + 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +(-2.52452 + 1.45753i) q^{44} +(-2.81429 - 2.49189i) q^{45} +(-6.15823 + 10.6664i) q^{46} +(-3.80738 + 6.59458i) q^{47} +(11.9212 - 9.73605i) q^{48} +(7.70409 + 4.44796i) q^{50} +(-5.94291 + 4.85358i) q^{51} +5.80384i q^{52} +(2.67782 + 1.54604i) q^{53} +(-0.537165 + 13.4657i) q^{54} -0.772786i q^{55} +(-3.25086 + 0.528768i) q^{57} +15.2023 q^{58} +(-1.78229 - 3.08702i) q^{59} +(1.64679 + 10.1244i) q^{60} +(-12.5136 - 7.22473i) q^{61} -6.43428 q^{62} -5.32259 q^{64} +(-1.33247 - 0.769301i) q^{65} +(-2.14585 + 1.75252i) q^{66} +(-6.80644 - 11.7891i) q^{67} +20.9383 q^{68} +(-2.91570 + 7.69121i) q^{69} -10.4095i q^{71} +(14.0628 - 15.8823i) q^{72} +(-9.95016 - 5.74473i) q^{73} -6.91006i q^{74} +(5.55520 + 2.10595i) q^{75} +(7.78348 + 4.49379i) q^{76} +(0.885586 + 5.44457i) q^{78} +(2.01592 - 3.49168i) q^{79} +(5.56728 - 9.64281i) q^{80} +(1.08967 + 8.93379i) q^{81} +(9.43196 - 5.44554i) q^{82} +(-4.36775 - 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +11.6521i q^{86} +(10.0209 - 1.62995i) q^{87} +4.36118 q^{88} +(0.811226 + 1.40508i) q^{89} +(3.08970 + 9.24645i) q^{90} +(19.4383 - 11.2227i) q^{92} +(-4.24128 + 0.689866i) q^{93} +(17.1033 - 9.87459i) q^{94} +(-2.06341 + 1.19131i) q^{95} +(-15.2238 + 2.47623i) q^{96} +(8.76527 - 5.06063i) q^{97} +(-1.22658 + 1.38528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 12 q^{6}+O(q^{10}) $ 10 * q + 4 * q^4 + 12 * q^6	$ 10 q + 4 q^{4} + 12 q^{6} + 15 q^{10} - 6 q^{13} - 3 q^{15} - 6 q^{16} + 12 q^{17} - 18 q^{18} - 3 q^{19} + 3 q^{20} + 5 q^{22} - 27 q^{24} - 14 q^{25} - 3 q^{26} - 27 q^{27} - 15 q^{29} + 9 q^{31} + 48 q^{32} + 9 q^{33} - 3 q^{34} - 18 q^{36} + 6 q^{37} - 36 q^{38} + 12 q^{39} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 15 q^{45} - 13 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} - 24 q^{51} - 9 q^{53} - 27 q^{54} - 36 q^{57} - 16 q^{58} + 18 q^{59} - 3 q^{60} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} + 33 q^{66} - 10 q^{67} + 54 q^{68} + 3 q^{69} + 18 q^{72} - 3 q^{73} + 21 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} + 30 q^{80} - 48 q^{81} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 30 q^{87} + 16 q^{88} - 24 q^{89} - 24 q^{90} + 39 q^{92} + 6 q^{93} + 3 q^{94} - 3 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) $ 10 * q + 4 * q^4 + 12 * q^6 + 15 * q^10 - 6 * q^13 - 3 * q^15 - 6 * q^16 + 12 * q^17 - 18 * q^18 - 3 * q^19 + 3 * q^20 + 5 * q^22 - 27 * q^24 - 14 * q^25 - 3 * q^26 - 27 * q^27 - 15 * q^29 + 9 * q^31 + 48 * q^32 + 9 * q^33 - 3 * q^34 - 18 * q^36 + 6 * q^37 - 36 * q^38 + 12 * q^39 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 15 * q^45 - 13 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 - 24 * q^51 - 9 * q^53 - 27 * q^54 - 36 * q^57 - 16 * q^58 + 18 * q^59 - 3 * q^60 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 + 33 * q^66 - 10 * q^67 + 54 * q^68 + 3 * q^69 + 18 * q^72 - 3 * q^73 + 21 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 + 30 * q^80 - 48 * q^81 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 30 * q^87 + 16 * q^88 - 24 * q^89 - 24 * q^90 + 39 * q^92 + 6 * q^93 + 3 * q^94 - 3 * q^96 - 6 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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	$-0.963973\pi$
$2$	−2.24607	−	1.29677i	−1.58821	−	0.916955i	−0.594611	−	0.804014i	$-0.702694\pi$
$3$	−1.61958	−	0.613974i	−0.935064	−	0.354478i
$3$	−1.61958	−	0.613974i	−0.935064	−	0.354478i
$4$	2.36322	+	4.09323i	1.18161	+	2.04661i
$5$	−1.25299			−0.560352			−0.280176	−	0.959949i	$-0.590393\pi$
$5$	−1.25299			−0.560352			−0.280176	+	0.959949i	$0.590393\pi$
$6$	2.84151	+	3.47925i	1.16004	+	1.42040i
$7$		0			0
$7$		0			0
$8$		−	7.07116i		−	2.50003i
$9$	2.24607	+	1.98876i	0.748690	+	0.662920i
$10$	2.81429	+	1.62483i	0.889958	+	0.513817i
$11$			0.616756i			0.185959i	0.995668	+	0.0929794i	$0.0296391\pi$
$11$			0.616756i			0.185959i	−0.995668	+	0.0929794i	$0.970361\pi$
$12$	−1.31429	−	8.08026i	−0.379404	−	2.33257i
$13$	1.06343	+	0.613974i	0.294944	+	0.170286i	0.640169	−	0.768234i	$-0.278864\pi$
$13$	1.06343	+	0.613974i	0.294944	+	0.170286i	−0.345226	+	0.938520i	$0.612198\pi$
$14$		0			0
$15$	2.02931	+	0.769301i	0.523965	+	0.198633i
$16$	−4.44321	+	7.69587i	−1.11080	+	1.92397i
$17$	2.21501	−	3.83652i	0.537220	−	0.930492i	−0.461833	−	0.886967i	$-0.652808\pi$
$17$	2.21501	−	3.83652i	0.537220	−	0.930492i	0.999052	−	0.0435249i	$-0.0138588\pi$
$18$	−2.46587	−	7.37953i	−0.581212	−	1.73937i
$19$	1.64679	−	0.950775i	0.377800	−	0.218123i	−0.299061	−	0.954234i	$-0.596673\pi$
$19$	1.64679	−	0.950775i	0.377800	−	0.218123i	0.676861	+	0.736111i	$0.263340\pi$
$20$	−2.96109	−	5.12875i	−0.662119	−	1.14682i
$21$		0			0
$22$	0.799790	−	1.38528i	0.170516	−	0.295342i
$23$		−	4.74890i		−	0.990213i	−0.868832	−	0.495107i	$-0.835129\pi$
$23$		−	4.74890i		−	0.990213i	0.868832	−	0.495107i	$-0.164871\pi$
$24$	−4.34151	+	11.4523i	−0.886206	+	2.33769i
$25$	−3.43003			−0.686006
$26$	−1.59237	−	2.75806i	−0.312289	−	0.540900i
$27$	−2.41664	−	4.59998i	−0.465083	−	0.885267i
$28$		0			0
$29$	−5.07629	+	2.93080i	−0.942643	+	0.544235i	−0.890788	−	0.454419i	$-0.849847\pi$
$29$	−5.07629	+	2.93080i	−0.942643	+	0.544235i	−0.0518553	+	0.998655i	$0.516513\pi$
$30$	−3.56037	−	4.35945i	−0.650031	−	0.795923i
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	−0.294491	−	0.955654i	$-0.595150\pi$
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	0.680375	+	0.732864i	$0.261817\pi$
$32$	7.71195	−	4.45249i	1.36329	−	0.787097i
$33$	0.378672	−	0.998884i	0.0659183	−	0.173883i
$34$	−9.95016	+	5.74473i	−1.70644	+	0.985213i
$35$		0			0
$36$	−2.83247	+	13.8936i	−0.472078	+	2.31559i
$37$	1.33217	+	2.30738i	0.219007	+	0.379331i	0.954505	−	0.298196i	$-0.0963849\pi$
$37$	1.33217	+	2.30738i	0.219007	+	0.379331i	−0.735498	+	0.677527i	$0.763052\pi$
$38$	−4.93175			−0.800035
$39$	−1.34535	−	1.64730i	−0.215429	−	0.263779i
$40$			8.86005i			1.40090i
$41$	−2.09966	+	3.63671i	−0.327911	+	0.567959i	−0.982097	−	0.188375i	$-0.939678\pi$
$41$	−2.09966	+	3.63671i	−0.327911	+	0.567959i	0.654186	+	0.756334i	$0.273011\pi$
$42$		0			0
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	0.642340	−	0.766419i	$-0.277964\pi$
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	−0.984909	+	0.173073i	$0.944630\pi$
$44$	−2.52452	+	1.45753i	−0.380586	+	0.219731i
$45$	−2.81429	−	2.49189i	−0.419530	−	0.371468i
$46$	−6.15823	+	10.6664i	−0.907981	+	1.57267i
$47$	−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
$51$	−5.94291	+	4.85358i	−0.832174	+	0.679637i
$52$			5.80384i			0.804847i
$53$	2.67782	+	1.54604i	0.367827	+	0.212365i	0.672509	−	0.740089i	$-0.265217\pi$
$53$	2.67782	+	1.54604i	0.367827	+	0.212365i	−0.304682	+	0.952454i	$0.598550\pi$
$54$	−0.537165	+	13.4657i	−0.0730990	+	1.83245i
$55$		−	0.772786i		−	0.104202i
$56$		0			0
$57$	−3.25086	+	0.528768i	−0.430587	+	0.0700371i
$58$	15.2023			1.99616
$59$	−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	$0.907872\pi$
$60$	1.64679	+	10.1244i	0.212600	+	1.30706i
$61$	−12.5136	−	7.22473i	−1.60220	−	0.925032i	−0.991046	−	0.133521i	$-0.957372\pi$
$61$	−12.5136	−	7.22473i	−1.60220	−	0.925032i	−0.611156	−	0.791510i	$-0.709295\pi$
$62$	−6.43428			−0.817154
$63$		0			0
$64$	−5.32259			−0.665324
$65$	−1.33247	−	0.769301i	−0.165272	−	0.0954200i
$66$	−2.14585	+	1.75252i	−0.264136	+	0.215720i
$67$	−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	$-0.479206\pi$
$68$	20.9383			2.53914
$69$	−2.91570	+	7.69121i	−0.351009	+	0.925913i
$70$		0			0
$71$		−	10.4095i		−	1.23538i	−0.786420	−	0.617692i	$-0.788068\pi$
$71$		−	10.4095i		−	1.23538i	0.786420	−	0.617692i	$-0.211932\pi$
$72$	14.0628	−	15.8823i	1.65732	−	1.87175i
$73$	−9.95016	−	5.74473i	−1.16458	−	0.672369i	−0.212181	−	0.977230i	$-0.568057\pi$
$73$	−9.95016	−	5.74473i	−1.16458	−	0.672369i	−0.952397	+	0.304861i	$0.901390\pi$
$74$		−	6.91006i		−	0.803278i
$75$	5.55520	+	2.10595i	0.641459	+	0.243174i
$76$	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	$0.0938373\pi$
$80$	5.56728	−	9.64281i	0.622441	−	1.07810i
$81$	1.08967	+	8.93379i	0.121075	+	0.992643i
$82$	9.43196	−	5.44554i	1.04159	−	0.601360i
$83$	−4.36775	−	7.56516i	−0.479422	−	0.830384i	0.520299	−	0.853984i	$-0.325820\pi$
$83$	−4.36775	−	7.56516i	−0.479422	−	0.830384i	−0.999721	+	0.0236001i	$0.992487\pi$
$84$		0			0
$85$	−2.77538	+	4.80710i	−0.301032	+	0.521403i
$86$			11.6521i			1.25648i
$87$	10.0209	−	1.62995i	1.07435	−	0.174749i
$88$	4.36118			0.464903
$89$	0.811226	+	1.40508i	0.0859897	+	0.148939i	0.905813	−	0.423679i	$-0.139261\pi$
$89$	0.811226	+	1.40508i	0.0859897	+	0.148939i	−0.819823	+	0.572617i	$0.805928\pi$
$90$	3.08970	+	9.24645i	0.325683	+	0.974661i
$91$		0			0
$92$	19.4383	−	11.2227i	2.02658	−	1.17005i
$93$	−4.24128	+	0.689866i	−0.439801	+	0.0715357i
$94$	17.1033	−	9.87459i	1.76407	−	1.01849i
$95$	−2.06341	+	1.19131i	−0.211701	+	0.122226i
$96$	−15.2238	+	2.47623i	−1.55377	+	0.252729i
$97$	8.76527	−	5.06063i	0.889979	−	0.513829i	0.0160431	−	0.999871i	$-0.494893\pi$
$97$	8.76527	−	5.06063i	0.889979	−	0.513829i	0.873936	+	0.486042i	$0.161560\pi$
$98$		0			0
$99$	−1.22658	+	1.38528i	−0.123276	+	0.139226i
$100$	−8.10593	−	14.0399i	−0.810593	−	1.40399i
$101$	1.71322			0.170472			0.0852360	−	0.996361i	$-0.472836\pi$
$101$	1.71322			0.170472			0.0852360	+	0.996361i	$0.472836\pi$
$102$	19.6422	−	3.19490i	1.94487	−	0.316342i
$103$		−	7.40526i		−	0.729662i	−0.931074	−	0.364831i	$-0.881127\pi$
$103$		−	7.40526i		−	0.729662i	0.931074	−	0.364831i	$-0.118873\pi$
$104$	4.34151	−	7.51971i	0.425720	−	0.737368i
$105$		0			0
$106$	−4.00972	−	6.94503i	−0.389458	−	0.674561i
$107$	−0.131657	+	0.0760123i	−0.0127278	+	0.00734839i	−0.506350	−	0.862328i	$-0.669006\pi$
$107$	−0.131657	+	0.0760123i	−0.0127278	+	0.00734839i	0.493623	+	0.869676i	$0.335672\pi$
$108$	13.1177	−	20.7627i	1.26225	−	1.99789i
$109$	2.70051	−	4.67742i	0.258662	−	0.448016i	−0.707222	−	0.706992i	$-0.750052\pi$
$109$	2.70051	−	4.67742i	0.258662	−	0.448016i	0.965884	+	0.258976i	$0.0833851\pi$
$110$	−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	0.212693	−	0.977119i	$-0.431777\pi$
$113$	−5.60391	−	3.23542i	−0.527171	−	0.304362i	−0.739864	+	0.672757i	$0.765110\pi$
$114$	7.98735	+	3.02797i	0.748084	+	0.283595i
$115$			5.95030i			0.554868i
$116$	−23.9928	−	13.8523i	−2.22768	−	1.28615i
$117$	1.16750	+	3.49394i	0.107936	+	0.323015i
$118$			9.24490i			0.851062i
$119$		0			0
$120$	5.43984	−	14.3496i	0.496588	−	1.30993i
$121$	10.6196			0.965419
$122$	18.7376	+	32.4545i	1.69642	+	2.93829i
$123$	5.63341	−	4.60081i	0.507947	−	0.414841i
$124$	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
$129$	1.24931	+	7.68072i	0.109995	+	0.676250i
$130$	1.99521	+	3.45581i	0.174992	+	0.303094i
$131$	−16.2276			−1.41782			−0.708908	−	0.705301i	$-0.750812\pi$
$131$	−16.2276			−1.41782			−0.708908	+	0.705301i	$0.750812\pi$
$132$	4.98355	−	0.810598i	0.433762	−	0.0705535i
$133$		0			0
$134$			35.3055i			3.04993i
$135$	3.02802	+	5.76371i	0.260610	+	0.496061i
$136$	−27.1286	−	15.6627i	−2.32626	−	1.34307i
$137$			17.4026i			1.48680i	0.668845	+	0.743402i	$0.266789\pi$
$137$			17.4026i			1.48680i	−0.668845	+	0.743402i	$0.733211\pi$
$138$	16.5226	−	13.4940i	1.40650	−	1.14869i
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	0.250598	−	0.968091i	$-0.419373\pi$
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	−0.713092	+	0.701070i	$0.752706\pi$
$140$		0			0
$141$	10.2153	−	8.34280i	0.860279	−	0.702591i
$142$	−13.4988	+	23.3805i	−1.13279	+	1.96205i
$143$	−0.378672	+	0.655879i	−0.0316661	+	0.0548474i
$144$	−25.2850	+	8.44899i	−2.10708	+	0.704083i
$145$	6.36052	−	3.67225i	0.528212	−	0.304963i
$146$	14.8992	+	25.8061i	1.23306	+	2.13573i
$147$		0			0
$148$	−6.29642	+	10.9057i	−0.517563	+	0.896445i
$149$		−	10.6269i		−	0.870592i	−0.900287	−	0.435296i	$-0.856644\pi$
$149$		−	10.6269i		−	0.870592i	0.900287	−	0.435296i	$-0.143356\pi$
$150$	−9.74645	−	11.9339i	−0.795794	−	0.974401i
$151$	9.48930			0.772229			0.386114	−	0.922451i	$-0.373817\pi$
$151$	9.48930			0.772229			0.386114	+	0.922451i	$0.373817\pi$
$152$	−6.72308	−	11.6447i	−0.545314	−	0.944511i
$153$	12.6050	−	4.21196i	1.01905	−	0.340517i
$154$		0			0
$155$	−2.69205	+	1.55426i	−0.216231	+	0.124841i
$156$	3.56341	−	9.39977i	0.285301	−	0.752584i
$157$	−20.6214	+	11.9058i	−1.64577	+	0.950185i	−0.667040	+	0.745022i	$0.732439\pi$
$157$	−20.6214	+	11.9058i	−1.64577	+	0.950185i	−0.978728	+	0.205163i	$0.934228\pi$
$158$	−9.05582	+	5.22838i	−0.720442	+	0.415947i
$159$	−3.38771	−	4.14805i	−0.268663	−	0.328961i
$160$	−9.66295	+	5.57891i	−0.763924	+	0.441051i
$161$		0			0
$162$	9.13759	−	21.4790i	0.717916	−	1.68755i
$163$	−4.41101	−	7.64009i	−0.345497	−	0.598418i	0.639947	−	0.768419i	$-0.278956\pi$
$163$	−4.41101	−	7.64009i	−0.345497	−	0.598418i	−0.985444	+	0.170001i	$0.945623\pi$
$164$	−19.8478			−1.54986
$165$	−0.474470	+	1.25159i	−0.0369375	+	0.0974360i
$166$			22.6558i			1.75843i
$167$	11.0335	−	19.1106i	0.853800	−	1.47883i	−0.0239535	−	0.999713i	$-0.507625\pi$
$167$	11.0335	−	19.1106i	0.853800	−	1.47883i	0.877754	−	0.479112i	$-0.159041\pi$
$168$		0			0
$169$	−5.74607	−	9.95249i	−0.442005	−	0.765576i
$170$	12.4674	−	7.19806i	0.956206	−	0.552066i
$171$	5.58967	+	1.13956i	0.427453	+	0.0871445i
$172$	10.6174	−	18.3898i	0.809566	−	1.40221i
$173$	−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
$177$	0.991213	+	6.09396i	0.0745041	+	0.458050i
$178$		−	4.20789i		−	0.315395i
$179$	7.20787	+	4.16146i	0.538741	+	0.311042i	0.744569	−	0.667546i	$-0.232655\pi$
$179$	7.20787	+	4.16146i	0.538741	+	0.311042i	−0.205827	+	0.978588i	$0.565989\pi$
$180$	3.54904	−	17.4084i	0.264530	−	1.29755i
$181$			12.6701i			0.941763i	0.882196	+	0.470881i	$0.156064\pi$
$181$			12.6701i			0.941763i	−0.882196	+	0.470881i	$0.843936\pi$
$182$		0			0
$183$	15.8310	+	19.3840i	1.17026	+	1.43291i
$184$	−33.5802			−2.47556
$185$	−1.66919	−	2.89111i	−0.122721	−	0.212559i
$186$	10.4208	+	3.95048i	0.764092	+	0.289663i
$187$	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	0.376175	−	0.926549i	$-0.377239\pi$
$191$	−3.29133	−	1.90025i	−0.238152	−	0.137497i	−0.614327	+	0.789051i	$0.710573\pi$
$192$	8.62036	+	3.26793i	0.622121	+	0.235843i
$193$	−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	$0.911905\pi$
$194$	−26.2499			−1.88463
$195$	1.68571	+	2.06404i	0.120716	+	0.147809i
$196$		0			0
$197$			6.41453i			0.457017i	0.973542	+	0.228508i	$0.0733848\pi$
$197$			6.41453i			0.457017i	−0.973542	+	0.228508i	$0.926615\pi$
$198$	4.55137	−	1.52084i	0.323452	−	0.108082i
$199$	13.8921	+	8.02063i	0.984788	+	0.568568i	0.903712	−	0.428140i	$-0.140831\pi$
$199$	13.8921	+	8.02063i	0.984788	+	0.568568i	0.0810756	+	0.996708i	$0.474164\pi$
$200$			24.2543i			1.71504i
$201$	3.78536	+	23.2723i	0.266999	+	1.64150i
$202$	−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
$206$	−9.60292	+	16.6327i	−0.669067	+	1.15886i
$207$	9.44441	−	10.6664i	0.656432	−	0.741363i
$208$	−9.45013	+	5.45604i	−0.655249	+	0.378308i
$209$	0.586396	+	1.01567i	0.0405619	+	0.0702552i
$210$		0			0
$211$	−4.06070	+	7.03333i	−0.279550	+	0.484194i	−0.971273	−	0.237968i	$-0.923519\pi$
$211$	−4.06070	+	7.03333i	−0.279550	+	0.484194i	0.691723	+	0.722163i	$0.256852\pi$
$212$			14.6146i			1.00373i
$213$	−6.39118	+	16.8590i	−0.437916	+	1.15516i
$214$	0.394282			0.0269526
$215$	2.81467	+	4.87515i	0.191959	+	0.332483i
$216$	−32.5272	+	17.0885i	−2.21319	+	1.16272i
$217$		0			0
$218$	−12.1311	+	7.00388i	−0.821620	+	0.474363i
$219$	12.5880	+	15.4132i	0.850615	+	1.04153i
$220$	3.16319	−	1.82627i	0.213262	−	0.123127i
$221$	4.71104	−	2.71992i	0.316899	−	0.182962i
$222$	−4.24260	+	11.1914i	−0.284744	+	0.751117i
$223$	6.96205	−	4.01954i	0.466213	−	0.269168i	−0.248440	−	0.968647i	$-0.579918\pi$
$223$	6.96205	−	4.01954i	0.466213	−	0.269168i	0.714653	+	0.699479i	$0.246585\pi$
$224$		0			0
$225$	−7.70409	−	6.82150i	−0.513606	−	0.454767i
$226$	8.39118	+	14.5340i	0.558173	+	0.966784i
$227$	20.8234			1.38210			0.691048	−	0.722809i	$-0.257149\pi$
$227$	20.8234			1.38210			0.691048	+	0.722809i	$0.257149\pi$
$228$	−9.84688	−	12.0569i	−0.652126	−	0.798488i
$229$			6.01918i			0.397759i	0.980024	+	0.198879i	$0.0637302\pi$
$229$			6.01918i			0.397759i	−0.980024	+	0.198879i	$0.936270\pi$
$230$	7.71617	−	13.3648i	0.508789	−	0.881248i
$231$		0			0
$232$	20.7241	+	35.8952i	1.36061	+	2.35664i
$233$	−18.2156	+	10.5168i	−1.19335	+	0.688978i	−0.959064	−	0.283191i	$-0.908607\pi$
$233$	−18.2156	+	10.5168i	−1.19335	+	0.688978i	−0.234282	+	0.972169i	$0.575274\pi$
$234$	1.90855	−	9.36163i	0.124766	−	0.611989i
$235$	4.77059	−	8.26291i	0.311199	−	0.539013i
$236$	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	0.237011	−	0.971507i	$-0.423832\pi$
$239$	−7.51079	−	4.33636i	−0.485832	−	0.280496i	−0.722844	+	0.691011i	$0.757165\pi$
$240$	−14.9371	+	12.1991i	−0.964185	+	0.787450i
$241$		−	8.47315i		−	0.545804i	−0.962042	−	0.272902i	$-0.912017\pi$
$241$		−	8.47315i		−	0.545804i	0.962042	−	0.272902i	$-0.0879834\pi$
$242$	−23.8524	−	13.7712i	−1.53329	−	0.885246i
$243$	3.72030	−	15.1380i	0.238658	−	0.971104i
$244$		−	68.2946i		−	4.37211i
$245$		0			0
$246$	−18.6192	+	3.02851i	−1.18712	+	0.193091i
$247$	2.33501			0.148573
$248$	−8.77137	−	15.1925i	−0.556982	−	0.964722i
$249$	2.42910	+	14.9341i	0.153938	+	0.946407i
$250$	−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
$255$	7.44638	−	6.08146i	0.466310	−	0.380836i
$256$	10.5170	+	18.2159i	0.657310	+	1.13849i
$257$	24.5170			1.52933			0.764665	−	0.644428i	$-0.222904\pi$
$257$	24.5170			1.52933			0.764665	+	0.644428i	$0.222904\pi$
$258$	7.15409	−	18.8715i	0.445394	−	1.17489i
$259$		0			0
$260$		−	7.27212i		−	0.450998i
$261$	−17.2304	−	3.51274i	−1.06653	−	0.217433i
$262$	36.4484	+	21.0435i	2.25179	+	1.30007i
$263$		−	10.5544i		−	0.650811i	−0.945575	−	0.325406i	$-0.894499\pi$
$263$		−	10.5544i		−	0.650811i	0.945575	−	0.325406i	$-0.105501\pi$
$264$	−7.06327	−	2.67765i	−0.434714	−	0.164798i
$265$	−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
$269$	−1.14451	+	1.98235i	−0.0697821	+	0.120866i	−0.898805	−	0.438348i	$-0.855564\pi$
$269$	−1.14451	+	1.98235i	−0.0697821	+	0.120866i	0.829023	+	0.559214i	$0.188897\pi$
$270$	0.673060	−	16.8723i	0.0409611	−	1.02682i
$271$	20.9239	−	12.0804i	1.27103	−	0.733831i	0.295851	−	0.955234i	$-0.404397\pi$
$271$	20.9239	−	12.0804i	1.27103	−	0.733831i	0.975182	+	0.221403i	$0.0710635\pi$
$272$	19.6836	+	34.0929i	1.19349	+	2.06719i
$273$		0			0
$274$	22.5672	−	39.0875i	1.36333	−	2.36136i
$275$		−	2.11549i		−	0.127569i
$276$	−38.3723	+	6.24145i	−2.30974	+	0.375691i
$277$	−11.3710			−0.683219			−0.341609	−	0.939842i	$-0.610972\pi$
$277$	−11.3710			−0.683219			−0.341609	+	0.939842i	$0.610972\pi$
$278$	8.16481	+	14.1419i	0.489693	+	0.848173i
$279$	7.29265	+	1.48675i	0.436600	+	0.0890092i
$280$		0			0
$281$	17.6382	−	10.1834i	1.05221	−	0.607492i	0.128941	−	0.991652i	$-0.458842\pi$
$281$	17.6382	−	10.1834i	1.05221	−	0.607492i	0.923267	+	0.384160i	$0.125509\pi$
$282$	−33.7629	+	5.49170i	−2.01055	+	0.327026i
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	−0.779222	−	0.626749i	$-0.784385\pi$
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	0.153169	+	0.988200i	$0.451052\pi$
$284$	42.6085	−	24.6000i	2.52835	−	1.45974i
$285$	4.07328	−	0.662539i	0.241280	−	0.0392454i
$286$	1.70105	−	0.982101i	0.100585	−	0.0580729i
$287$		0			0
$288$	26.1765	+	5.33658i	1.54247	+	0.314461i
$289$	−1.31257	−	2.27345i	−0.0772103	−	0.133732i
$290$	−19.0482			−1.11855
$291$	−17.3031	+	2.81444i	−1.01433	+	0.164986i
$292$		−	54.3043i		−	3.17792i
$293$	−13.4674	+	23.3262i	−0.786773	+	1.36273i	0.141161	+	0.989987i	$0.454917\pi$
$293$	−13.4674	+	23.3262i	−0.786773	+	1.36273i	−0.927934	+	0.372745i	$0.878417\pi$
$294$		0			0
$295$	2.23319	+	3.86799i	0.130021	+	0.225203i
$296$	16.3159	−	9.41996i	0.948340	−	0.547524i
$297$	2.83707	−	1.49048i	0.164623	−	0.0864863i
$298$	−13.7807	+	23.8688i	−0.798293	+	1.38268i
$299$	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
$303$	−2.77470	−	1.05187i	−0.159402	−	0.0604286i
$304$			16.8980i			0.969166i
$305$	15.6793	+	9.05248i	0.897797	+	0.518343i
$306$	−33.7736	−	6.88540i	−1.93071	−	0.393612i
$307$			21.3700i			1.21965i	0.792536	+	0.609825i	$0.208760\pi$
$307$			21.3700i			1.21965i	−0.792536	+	0.609825i	$0.791240\pi$
$308$		0			0
$309$	−4.54664	+	11.9934i	−0.258649	+	0.682281i
$310$	8.06206			0.457894
$311$	−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	$0.985553\pi$
$312$	−11.6483	+	9.51319i	−0.659456	+	0.538578i
$313$	−12.1941	−	7.04027i	−0.689252	−	0.397940i	0.114080	−	0.993472i	$-0.463608\pi$
$313$	−12.1941	−	7.04027i	−0.689252	−	0.397940i	−0.803332	+	0.595532i	$0.796941\pi$
$314$	61.7562			3.48511
$315$		0			0
$316$	19.0563			1.07200
$317$	17.5776	+	10.1484i	0.987254	+	0.569991i	0.904452	−	0.426575i	$-0.140280\pi$
$317$	17.5776	+	10.1484i	0.987254	+	0.569991i	0.0828017	+	0.996566i	$0.473613\pi$
$318$	2.22998	+	13.7099i	0.125051	+	0.768812i
$319$	−1.80759	−	3.13083i	−0.101205	−	0.175293i
$320$	6.66913			0.372816
$321$	0.259899	−	0.0422738i	0.0145061	−	0.00235950i
$322$		0			0
$323$		−	8.42392i		−	0.468720i
$324$	−33.9929	+	25.5728i	−1.88849	+	1.42071i
$325$	−3.64761	−	2.10595i	−0.202333	−	0.116817i
$326$			22.8802i			1.26722i
$327$	−7.24550	+	5.91741i	−0.400677	+	0.327233i
$328$	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	$0.907390\pi$
$332$	20.6439	−	35.7563i	1.13298	−	1.96238i
$333$	−1.59668	+	7.83190i	−0.0874977	+	0.429186i
$334$	−49.5642	+	28.6159i	−2.71203	+	1.56579i
$335$	8.52836	+	14.7716i	0.465954	+	0.807057i
$336$		0			0
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	−0.909441	−	0.415834i	$-0.863490\pi$
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	0.814843	+	0.579682i	$0.196823\pi$
$338$			29.8053i			1.62120i
$339$	7.08951	+	8.68067i	0.385049	+	0.471469i
$340$	−26.2354			−1.42281
$341$	0.765051	+	1.32511i	0.0414298	+	0.0717585i
$342$	−11.0771	−	9.80806i	−0.598979	−	0.530359i
$343$		0			0
$344$	−27.5127	+	15.8844i	−1.48338	+	0.856432i
$345$	3.65333	−	9.63698i	0.196689	−	0.518837i
$346$	9.13589	−	5.27461i	0.491149	−	0.283565i
$347$	8.14765	−	4.70405i	0.437389	−	0.252527i	−0.265101	−	0.964221i	$-0.585405\pi$
$347$	8.14765	−	4.70405i	0.437389	−	0.252527i	0.702489	+	0.711694i	$0.252072\pi$
$348$	30.3533	+	37.1658i	1.62711	+	1.99230i
$349$	12.3253	−	7.11603i	0.659759	−	0.380912i	−0.132426	−	0.991193i	$-0.542277\pi$
$349$	12.3253	−	7.11603i	0.659759	−	0.380912i	0.792185	+	0.610281i	$0.208943\pi$
$350$		0			0
$351$	0.254329	−	6.37554i	0.0135751	−	0.340301i
$352$	2.74610	+	4.75639i	0.146368	+	0.253516i
$353$	−17.1652			−0.913614			−0.456807	−	0.889566i	$-0.651007\pi$
$353$	−17.1652			−0.913614			−0.456807	+	0.889566i	$0.651007\pi$
$354$	5.67613	−	14.9728i	0.301683	−	0.795798i
$355$			13.0430i			0.692250i
$356$	−3.83422	+	6.64106i	−0.203213	+	0.351975i
$357$		0			0
$358$	−10.7929	−	18.6939i	−0.570424	−	0.988003i
$359$	24.4705	−	14.1281i	1.29150	−	0.745650i	0.312583	−	0.949890i	$-0.398806\pi$
$359$	24.4705	−	14.1281i	1.29150	−	0.745650i	0.978921	+	0.204241i	$0.0654725\pi$
$360$	−17.6205	+	19.9003i	−0.928682	+	1.04884i
$361$	−7.69205	+	13.3230i	−0.404845	+	0.701212i
$362$	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
$366$	−10.4208	−	64.0670i	−0.544705	−	3.34884i
$367$		−	23.0704i		−	1.20427i	−0.798396	−	0.602133i	$-0.794318\pi$
$367$		−	23.0704i		−	1.20427i	0.798396	−	0.602133i	$-0.205682\pi$
$368$	36.5469	+	21.1004i	1.90514	+	1.09993i
$369$	−11.9485	+	3.99260i	−0.622015	+	0.207847i
$370$			8.65820i			0.450118i
$371$		0			0
$372$	−12.8469	−	15.7302i	−0.666080	−	0.815574i
$373$	−13.8727			−0.718301			−0.359150	−	0.933280i	$-0.616933\pi$
$373$	−13.8727			−0.718301			−0.359150	+	0.933280i	$0.616933\pi$
$374$	−3.54309	−	6.13682i	−0.183209	−	0.317327i
$375$	−17.1071	−	6.48523i	−0.883408	−	0.334896i
$376$	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
$381$	4.74820	+	1.80002i	0.243257	+	0.0922177i
$382$	4.92838	+	8.53620i	0.252158	+	0.436750i
$383$	15.2320			0.778317			0.389158	−	0.921171i	$-0.372766\pi$
$383$	15.2320			0.778317			0.389158	+	0.921171i	$0.372766\pi$
$384$	4.38860	+	5.37357i	0.223955	+	0.274219i
$385$		0			0
$386$			17.6075i			0.896196i
$387$	2.69241	−	13.2066i	0.136863	−	0.671328i
$388$	41.4286	+	23.9188i	2.10322	+	1.21429i
$389$		−	14.1479i		−	0.717328i	−0.933467	−	0.358664i	$-0.883232\pi$
$389$		−	14.1479i		−	0.717328i	0.933467	−	0.358664i	$-0.116768\pi$
$390$	−1.10963	−	6.82196i	−0.0561881	−	0.345443i
$391$	−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
$395$	−2.52592	+	4.37503i	−0.127093	+	0.220131i
$396$	−8.56893	−	1.74694i	−0.430605	−	0.0877871i
$397$	−8.40688	+	4.85371i	−0.421929	+	0.243601i	−0.695902	−	0.718136i	$-0.744995\pi$
$397$	−8.40688	+	4.85371i	−0.421929	+	0.243601i	0.273973	+	0.961737i	$0.411662\pi$
$398$	−20.8018	−	36.0298i	−1.04270	−	1.80601i
$399$		0			0
$400$	15.2403	−	26.3970i	0.762017	−	1.31985i
$401$		−	8.73133i		−	0.436022i	−0.975946	−	0.218011i	$-0.930043\pi$
$401$		−	8.73133i		−	0.436022i	0.975946	−	0.218011i	$-0.0699569\pi$
$402$	21.6767	−	57.1801i	1.08113	−	2.85188i
$403$	3.04640			0.151752
$404$	4.04873	+	7.01261i	0.201432	+	0.348890i
$405$	−1.36535	−	11.1939i	−0.0678446	−	0.556230i
$406$		0			0
$407$	−1.42309	+	0.821622i	−0.0705400	+	0.0407263i
$408$	34.3204	+	42.0233i	1.69911	+	2.08046i
$409$	12.8967	−	7.44591i	0.637700	−	0.368176i	−0.146028	−	0.989280i	$-0.546649\pi$
$409$	12.8967	−	7.44591i	0.637700	−	0.368176i	0.783728	+	0.621104i	$0.213316\pi$
$410$	−11.8181	+	6.82318i	−0.583654	+	0.336973i
$411$	10.6847	−	28.1849i	0.527039	−	1.39026i
$412$	30.3114	−	17.5003i	1.49334	−	0.862178i
$413$		0			0
$414$	−35.0446	+	11.7102i	−1.72235	+	0.575524i
$415$	5.47272	+	9.47903i	0.268645	+	0.465307i
$416$	10.9349			0.536126
$417$	6.89825	+	8.44648i	0.337809	+	0.413626i
$418$		−	3.04168i		−	0.148774i
$419$	2.13859	−	3.70414i	0.104477	−	0.180959i	−0.809048	−	0.587743i	$-0.800017\pi$
$419$	2.13859	−	3.70414i	0.104477	−	0.180959i	0.913524	+	0.406784i	$0.133350\pi$
$420$		0			0
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	0.971645	−	0.236443i	$-0.0759816\pi$
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	−0.690588	+	0.723248i	$0.742648\pi$
$422$	18.2412	−	10.5316i	0.887969	−	0.512669i
$423$	−21.6667	+	7.23993i	−1.05347	+	0.352017i
$424$	10.9323	−	18.9353i	0.530919	−	0.919578i
$425$	−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
$429$	1.01598	−	0.829753i	0.0490521	−	0.0400609i
$430$		−	14.5999i		−	0.704071i
$431$	−14.4497	−	8.34254i	−0.696018	−	0.401846i	0.109845	−	0.993949i	$-0.464965\pi$
$431$	−14.4497	−	8.34254i	−0.696018	−	0.401846i	−0.805863	+	0.592103i	$0.798298\pi$
$432$	46.1385	+	1.84053i	2.21984	+	0.0885524i
$433$			12.3503i			0.593516i	0.954953	+	0.296758i	$0.0959055\pi$
$433$			12.3503i			0.593516i	−0.954953	+	0.296758i	$0.904094\pi$
$434$		0			0
$435$	−12.5560	+	2.04230i	−0.602015	+	0.0979207i
$436$	25.5276			1.22255
$437$	−4.51513	−	7.82044i	−0.215988	−	0.374102i
$438$	−8.28610	−	50.9428i	−0.395925	−	2.43414i
$439$	19.1691	+	11.0673i	0.914892	+	0.528213i	0.882002	−	0.471246i	$-0.156195\pi$
$439$	19.1691	+	11.0673i	0.914892	+	0.528213i	0.0328902	+	0.999459i	$0.489529\pi$
$440$	−5.46449			−0.260509
$441$		0			0
$442$	−14.1085			−0.671071
$443$	−4.22906	−	2.44165i	−0.200929	−	0.116006i	0.396160	−	0.918182i	$-0.370343\pi$
$443$	−4.22906	−	2.44165i	−0.200929	−	0.116006i	−0.597089	+	0.802175i	$0.703676\pi$
$444$	16.8934	−	13.7968i	0.801724	−	0.654769i
$445$	−1.01645	−	1.76055i	−0.0481845	−	0.0834580i
$446$	−20.8497			−0.987260
$447$	−6.52466	+	17.2111i	−0.308606	+	0.814059i
$448$		0			0
$449$		−	12.4409i		−	0.587121i	−0.955941	−	0.293560i	$-0.905160\pi$
$449$		−	12.4409i		−	0.587121i	0.955941	−	0.293560i	$-0.0948401\pi$
$450$	8.45802	+	25.3120i	0.398715	+	1.19322i
$451$	−2.24296	−	1.29498i	−0.105617	−	0.0609780i
$452$		−	30.5841i		−	1.43855i
$453$	−15.3687	−	5.82619i	−0.722083	−	0.273738i
$454$	−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	$0.0855691\pi$
$458$	7.80549	−	13.5195i	0.364727	−	0.631725i
$459$	−23.0008	−	0.917533i	−1.07359	−	0.0428268i
$460$	−24.3559	+	14.0619i	−1.13560	+	0.655639i
$461$	0.333303	+	0.577297i	0.0155235	+	0.0268874i	0.873683	−	0.486496i	$-0.161725\pi$
$461$	0.333303	+	0.577297i	0.0155235	+	0.0268874i	−0.858159	+	0.513383i	$0.828392\pi$
$462$		0			0
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.259677	+	0.965696i	$0.583616\pi$
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.706479	+	0.707734i	$0.749717\pi$
$464$		−	52.0886i		−	2.41815i
$465$	5.31426	−	0.864391i	0.246443	−	0.0400852i
$466$	54.5515			2.52705
$467$	−19.6568	−	34.0465i	−0.909606	−	1.57548i	−0.814612	−	0.580006i	$-0.803050\pi$
$467$	−19.6568	−	34.0465i	−0.909606	−	1.57548i	−0.0949943	−	0.995478i	$-0.530283\pi$
$468$	−11.5424	+	13.0358i	−0.533549	+	0.602581i
$469$		0			0
$470$	−21.4302	+	12.3727i	−0.988500	+	0.570711i
$471$	40.7078	−	6.62133i	1.87572	−	0.305095i
$472$	−21.8288	+	12.6029i	−1.00475	+	0.580094i
$473$	2.39969	−	1.38546i	0.110338	−	0.0637036i
$474$	17.8767	−	2.90773i	0.821104	−	0.133557i
$475$	−5.64854	+	3.26119i	−0.259173	+	0.149633i
$476$		0			0
$477$	2.93987	+	8.79805i	0.134608	+	0.402835i
$478$	11.2465	+	19.4795i	0.514403	+	0.890973i
$479$	38.1153			1.74153			0.870767	−	0.491696i	$-0.163623\pi$
$479$	38.1153			1.74153			0.870767	+	0.491696i	$0.163623\pi$
$480$	19.0752	−	3.10268i	0.870661	−	0.141617i
$481$			3.27167i			0.149175i
$482$	−10.9877	+	19.0313i	−0.500477	+	0.866852i
$483$		0			0
$484$	25.0965	+	43.4685i	1.14075	+	1.97584i
$485$	−10.9828	+	6.34090i	−0.498701	+	0.287925i
$486$	−27.9866	+	29.1767i	−1.26950	+	1.32348i
$487$	−3.80277	+	6.58659i	−0.172320	+	0.298467i	−0.939231	−	0.343287i	$-0.888460\pi$
$487$	−3.80277	+	6.58659i	−0.172320	+	0.298467i	0.766911	+	0.641754i	$0.221793\pi$
$488$	−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	0.573318	−	0.819333i	$-0.305656\pi$
$491$	3.33297	+	1.92429i	0.150415	+	0.0868420i	−0.422904	+	0.906175i	$0.638989\pi$
$492$	32.1451	+	12.1861i	1.44921	+	0.549390i
$493$			25.9670i			1.16950i
$494$	−5.24459	−	3.02797i	−0.235965	−	0.136235i
$495$	1.53688	−	1.73573i	0.0690778	−	0.0780154i
$496$			22.0462i			0.989904i
$497$		0			0
$498$	13.9101	−	36.6929i	0.623327	−	1.64425i
$499$	−32.1588			−1.43962			−0.719812	−	0.694169i	$-0.755772\pi$
$499$	−32.1588			−1.43962			−0.719812	+	0.694169i	$0.755772\pi$
$500$	24.9620	+	43.2355i	1.11634	+	1.93355i
$501$	−29.6031	+	24.1769i	−1.32257	+	1.08014i
$502$	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
$507$	3.19565	+	19.6468i	0.141924	+	0.872544i
$508$	−6.92838	−	12.0003i	−0.307397	−	0.532427i
$509$	25.7926			1.14323			0.571617	−	0.820520i	$-0.306316\pi$
$509$	25.7926			1.14323			0.571617	+	0.820520i	$0.306316\pi$
$510$	−24.6114	+	4.00316i	−1.08981	+	0.177263i
$511$		0			0
$512$		−	46.5411i		−	2.05684i
$513$	−8.35326	−	5.27753i	−0.368805	−	0.233008i
$514$	−55.0670	−	31.7929i	−2.42890	−	1.40233i
$515$			9.27868i			0.408868i
$516$	−28.4865	+	23.2650i	−1.25405	+	1.02418i
$517$	−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
$521$	9.07174	−	15.7127i	0.397440	−	0.688386i	−0.595969	−	0.803007i	$-0.703232\pi$
$521$	9.07174	−	15.7127i	0.397440	−	0.688386i	0.993409	+	0.114621i	$0.0365653\pi$
$522$	34.1454	+	30.2337i	1.49450	+	1.32329i
$523$	−12.0723	+	6.96997i	−0.527887	+	0.304776i	−0.740155	−	0.672436i	$-0.765248\pi$
$523$	−12.0723	+	6.96997i	−0.527887	+	0.304776i	0.212269	+	0.977211i	$0.431915\pi$
$524$	−38.3495	−	66.4234i	−1.67531	−	2.90172i
$525$		0			0
$526$	−13.6866	+	23.7059i	−0.596764	+	1.03363i
$527$		−	10.9904i		−	0.478749i
$528$	6.00476	+	7.35247i	0.261324	+	0.319975i
$529$	0.447980			0.0194774
$530$	5.02411	+	8.70202i	0.218234	+	0.377992i
$531$	2.13619	−	10.4782i	0.0927026	−	0.454716i
$532$		0			0
$533$	−4.46569	+	2.57827i	−0.193431	+	0.111677i
$534$	−2.58354	+	6.81501i	−0.111801	+	0.294914i
$535$	0.164965	−	0.0952423i	0.00713204	−	0.00411769i
$536$	−83.3625	+	48.1294i	−3.60071	+	2.07887i
$537$	−9.11868	−	11.1653i	−0.393500	−	0.481817i
$538$	5.14131	−	2.96834i	0.221658	−	0.127974i
$539$		0			0
$540$	−16.4363	+	26.0153i	−0.707305	+	1.11952i
$541$	−14.8576	−	25.7341i	−0.638779	−	1.10640i	−0.985701	−	0.168503i	$-0.946107\pi$
$541$	−14.8576	−	25.7341i	−0.638779	−	1.10640i	0.346922	−	0.937894i	$-0.387227\pi$
$542$	−62.6620			−2.69156
$543$	7.77913	−	20.5203i	0.333834	−	0.880609i
$544$		−	39.4493i		−	1.69138i
$545$	−3.38370	+	5.86074i	−0.144942	+	0.251046i
$546$		0			0
$547$	−9.13516	−	15.8226i	−0.390591	−	0.676524i	0.601937	−	0.798544i	$-0.294396\pi$
$547$	−9.13516	−	15.8226i	−0.390591	−	0.676524i	−0.992528	+	0.122020i	$0.961063\pi$
$548$	−71.2327	+	41.1262i	−3.04291	+	1.75683i
$549$	−13.7382	−	41.1138i	−0.586331	−	1.75469i
$550$	−2.74330	+	4.75154i	−0.116975	+	0.202606i
$551$	−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
$555$	0.928308	+	5.70723i	0.0394045	+	0.242258i
$556$		−	29.7590i		−	1.26206i
$557$	−0.359456	−	0.207532i	−0.0152307	−	0.00879343i	0.492365	−	0.870389i	$-0.336132\pi$
$557$	−0.359456	−	0.207532i	−0.0152307	−	0.00879343i	−0.507596	+	0.861595i	$0.669466\pi$
$558$	−14.4519	−	12.7962i	−0.611796	−	0.541708i
$559$		−	5.51686i		−	0.233338i
$560$		0			0
$561$	−2.99347	−	3.66532i	−0.126385	−	0.154750i
$562$	−52.8222			−2.22817
$563$	−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	$0.857902\pi$
$564$	58.2899	+	22.0974i	2.45445	+	0.930469i
$565$	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	0.976358	−	0.216162i	$-0.0693538\pi$
$569$	30.4692	+	17.5914i	1.27733	+	0.737470i	0.300977	+	0.953631i	$0.402687\pi$
$570$	−10.0080	−	3.79400i	−0.419191	−	0.158913i
$571$	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	$0.765868\pi$
$572$	−3.57955			−0.149668
$573$	4.16387	+	5.09840i	0.173948	+	0.212989i
$574$		0			0
$575$			16.2888i			0.679292i
$576$	−11.9549	−	10.5854i	−0.498122	−	0.441056i
$577$	−0.0597672	−	0.0345066i	−0.00248814	−	0.00143653i	0.498755	−	0.866743i	$-0.333791\pi$
$577$	−0.0597672	−	0.0345066i	−0.00248814	−	0.00143653i	−0.501244	+	0.865306i	$0.667124\pi$
$578$			6.80843i			0.283193i
$579$	1.88782	+	11.6063i	0.0784552	+	0.482342i
$580$	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
$584$	−40.6219	+	70.3591i	−1.68094	+	2.91148i
$585$	−1.46286	−	4.37786i	−0.0604820	−	0.181002i
$586$	60.4974	−	34.9282i	2.49913	−	1.44287i
$587$	11.4799	+	19.8838i	0.473827	+	0.820693i	0.999551	−	0.0299626i	$-0.00953881\pi$
$587$	11.4799	+	19.8838i	0.473827	+	0.820693i	−0.525724	+	0.850655i	$0.676205\pi$
$588$		0			0
$589$	2.35877	−	4.08550i	0.0971913	−	0.168340i
$590$		−	11.5837i		−	0.476894i
$591$	3.93836	−	10.3888i	0.162002	−	0.427340i
$592$	−23.6764			−0.973094
$593$	−14.3970	−	24.9363i	−0.591213	−	1.02401i	−0.994069	−	0.108748i	$-0.965316\pi$
$593$	−14.3970	−	24.9363i	−0.591213	−	1.02401i	0.402856	−	0.915263i	$-0.368018\pi$
$594$	−8.30506	−	0.331300i	−0.340761	−	0.0135934i
$595$		0			0
$596$	43.4984	−	25.1138i	1.78176	−	1.02870i
$597$	−17.5750	−	21.5195i	−0.719295	−	0.880733i
$598$	−13.0977	+	7.56198i	−0.535606	+	0.309233i
$599$	−33.1588	+	19.1442i	−1.35483	+	0.782212i	−0.988922	−	0.148438i	$-0.952575\pi$
$599$	−33.1588	+	19.1442i	−1.35483	+	0.782212i	−0.365910	+	0.930650i	$0.619242\pi$
$600$	14.8915	−	39.2817i	0.607943	−	1.60367i
$601$	−26.7618	+	15.4509i	−1.09164	+	0.630257i	−0.934012	−	0.357242i	$-0.883717\pi$
$601$	−26.7618	+	15.4509i	−1.09164	+	0.630257i	−0.157625	+	0.987499i	$0.550384\pi$
$602$		0			0
$603$	8.15793	−	40.0155i	0.332216	−	1.62956i
$604$	22.4254	+	38.8419i	0.912475	+	1.58045i
$605$	−13.3062			−0.540975
$606$	4.86813	+	5.96073i	0.197754	+	0.242138i
$607$			33.1791i			1.34670i	0.739325	+	0.673349i	$0.235145\pi$
$607$			33.1791i			1.34670i	−0.739325	+	0.673349i	$0.764855\pi$
$608$	8.46664	−	14.6647i	0.343368	−	0.594730i
$609$		0			0
$610$	−23.4780	−	40.6650i	−0.950595	−	1.64648i
$611$	−8.09780	+	4.67527i	−0.327602	+	0.189141i
$612$	47.0289	+	41.6412i	1.90103	+	1.68325i
$613$	−2.01164	+	3.48426i	−0.0812492	+	0.140728i	−0.903787	−	0.427983i	$-0.859224\pi$
$613$	−2.01164	+	3.48426i	−0.0812492	+	0.140728i	0.822538	+	0.568711i	$0.192558\pi$
$614$	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	0.934048	−	0.357147i	$-0.116251\pi$
$617$	27.1191	+	15.6572i	1.09177	+	0.630336i	0.157726	+	0.987483i	$0.449584\pi$
$618$	25.7648	−	21.0421i	1.03641	−	0.846437i
$619$		−	13.9310i		−	0.559934i	−0.960010	−	0.279967i	$-0.909676\pi$
$619$		−	13.9310i		−	0.559934i	0.960010	−	0.279967i	$-0.0903235\pi$
$620$	−12.7238	−	7.34612i	−0.511002	−	0.295027i
$621$	−21.8448	+	11.4764i	−0.876603	+	0.460532i
$622$			42.0962i			1.68790i
$623$		0			0
$624$	18.6551	−	3.03434i	0.746802	−	0.121471i
$625$	3.91523			0.156609
$626$	18.2592	+	31.6259i	0.729786	+	1.26403i
$627$	−0.326121	−	2.00499i	−0.0130240	−	0.0800714i
$628$	−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
$633$	10.8949	−	8.89787i	0.433033	−	0.353659i
$634$	−26.3203	−	45.5881i	−1.04531	−	1.81053i
$635$	3.67344			0.145776
$636$	8.97296	−	23.6694i	0.355801	−	0.938554i
$637$		0			0
$638$			9.37609i			0.371203i
$639$	20.7020	−	23.3805i	0.818960	−	0.924920i
$640$	4.34657	+	2.50949i	0.171813	+	0.0991964i
$641$		−	42.4724i		−	1.67756i	−0.544473	−	0.838779i	$-0.683270\pi$
$641$		−	42.4724i		−	1.67756i	0.544473	−	0.838779i	$-0.316730\pi$
$642$	−0.638571	−	0.242079i	−0.0252024	−	0.00955410i
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	0.560544	−	0.828125i	$-0.310592\pi$
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	−0.436905	+	0.899507i	$0.643926\pi$
$644$		0			0
$645$	−1.56536	−	9.62383i	−0.0616361	−	0.378938i
$646$	−10.9239	+	18.9207i	−0.429795	+	0.744426i
$647$	−6.00617	+	10.4030i	−0.236127	+	0.408984i	−0.959600	−	0.281369i	$-0.909211\pi$
$647$	−6.00617	+	10.4030i	−0.236127	+	0.408984i	0.723473	+	0.690353i	$0.242545\pi$
$648$	63.1722	−	7.70525i	2.48164	−	0.302691i
$649$	1.90394	−	1.09924i	0.0747361	−	0.0431489i
$650$	5.46186	+	9.46022i	0.214232	+	0.371060i
$651$		0			0
$652$	20.8484	−	36.1105i	0.816486	−	1.41420i
$653$			46.1822i			1.80725i	0.428324	+	0.903625i	$0.359104\pi$
$653$			46.1822i			1.80725i	−0.428324	+	0.903625i	$0.640896\pi$
$654$	23.9474	−	3.89517i	0.936419	−	0.152313i
$655$	20.3330			0.794476
$656$	−18.6584	−	32.3174i	−0.728490	−	1.26178i
$657$	−10.9239	−	32.6915i	−0.426182	−	1.27542i
$658$		0			0
$659$	−16.3479	+	9.43847i	−0.636824	+	0.367671i	−0.783390	−	0.621530i	$-0.786511\pi$
$659$	−16.3479	+	9.43847i	−0.636824	+	0.367671i	0.146566	+	0.989201i	$0.453178\pi$
$660$	−6.24431	+	1.01567i	−0.243059	+	0.0395348i
$661$	−2.88202	+	1.66393i	−0.112097	+	0.0647195i	−0.555000	−	0.831850i	$-0.687282\pi$
$661$	−2.88202	+	1.66393i	−0.112097	+	0.0647195i	0.442903	+	0.896570i	$0.353949\pi$
$662$	59.4494	−	34.3231i	2.31057	−	1.33401i
$663$	−9.29987	+	1.51267i	−0.361177	+	0.0587472i
$664$	−53.4944	+	30.8850i	−2.07599	+	1.19857i
$665$		0			0
$666$	13.7424	−	15.5205i	0.532509	−	0.601407i
$667$	13.9181	+	24.1068i	0.538909	+	0.933418i
$668$	104.299			4.03544
$669$	−13.7435	+	2.23544i	−0.531353	+	0.0864273i
$670$		−	44.2373i		−	1.70904i
$671$	4.45589	−	7.71783i	0.172018	−	0.297944i
$672$		0			0
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	−0.987361	−	0.158487i	$-0.949339\pi$
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	0.356427	−	0.934323i	$-0.383995\pi$
$674$	7.80099	−	4.50390i	0.300483	−	0.173484i
$675$	8.28915	+	15.7781i	0.319050	+	0.607298i
$676$	27.1585	−	47.0399i	1.04456	−	1.80923i
$677$	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
$681$	−33.7251	−	12.7850i	−1.29235	−	0.489923i
$682$		−	3.96838i		−	0.151957i
$683$	4.79617	+	2.76907i	0.183520	+	0.105956i	0.588946	−	0.808173i	$-0.299543\pi$
$683$	4.79617	+	2.76907i	0.183520	+	0.105956i	−0.405425	+	0.914128i	$0.632877\pi$
$684$	8.54517	+	25.5728i	0.326733	+	0.977802i
$685$		−	21.8052i		−	0.833133i
$686$		0			0
$687$	3.69562	−	9.74854i	0.140997	−	0.371930i
$688$	39.9244			1.52210
$689$	1.89846	+	3.28822i	0.0723254	+	0.125271i
$690$	−20.7026	+	16.9078i	−0.788134	+	0.643669i
$691$	−12.3417	−	7.12550i	−0.469502	−	0.271067i	0.246530	−	0.969135i	$-0.420710\pi$
$691$	−12.3417	−	7.12550i	−0.469502	−	0.271067i	−0.716031	+	0.698068i	$0.754043\pi$
$692$	−19.2248			−0.730818
$693$		0			0
$694$	−24.4003			−0.926222
$695$	6.83219	+	3.94456i	0.259160	+	0.149626i
$696$	−11.5256	−	70.8592i	−0.436877	−	2.68591i
$697$	9.30154	+	16.1107i	0.352321	+	0.610238i
$698$	−36.9114			−1.39712
$699$	35.9587	−	5.84886i	1.36008	−	0.221224i
$700$		0			0
$701$		−	18.6105i		−	0.702908i	−0.936205	−	0.351454i	$-0.885687\pi$
$701$		−	18.6105i		−	0.702908i	0.936205	−	0.351454i	$-0.114313\pi$
$702$	−8.83884	+	13.9901i	−0.333601	+	0.528022i
$703$	4.38760	+	2.53318i	0.165482	+	0.0955408i
$704$		−	3.28274i		−	0.123723i
$705$	−12.7996	+	10.4534i	−0.482059	+	0.393698i
$706$	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	$0.0851174\pi$
$710$	16.9137	−	29.2955i	0.634762	−	1.09944i
$711$	11.4720	−	3.83338i	0.430234	−	0.143763i
$712$	9.93557	−	5.73630i	0.372351	−	0.214977i
$713$	−5.89074	−	10.2031i	−0.220610	−	0.382107i
$714$		0			0
$715$	0.474470	−	0.821807i	0.0177442	−	0.0307338i
$716$			39.3379i			1.47013i
$717$	9.50190	+	11.6345i	0.354855	+	0.434498i
$718$	−73.2833			−2.73491
$719$	18.8692	+	32.6824i	0.703702	+	1.21885i	0.967158	+	0.254176i	$0.0818042\pi$
$719$	18.8692	+	32.6824i	0.703702	+	1.21885i	−0.263456	+	0.964671i	$0.584863\pi$
$720$	31.6817	−	10.5865i	1.18071	−	0.394534i
$721$		0			0
$722$	34.5538	−	19.9496i	1.28596	−	0.742449i
$723$	−5.20230	+	13.7229i	−0.193476	+	0.510362i
$724$	−51.8617	+	29.9424i	−1.92742	+	1.11280i
$725$	17.4118	−	10.0527i	0.646659	−	0.373348i
$726$	30.1757	+	36.9483i	1.11993	+	1.37128i
$727$	−1.98480	+	1.14592i	−0.0736121	+	0.0424999i	−0.536354	−	0.843993i	$-0.680199\pi$
$727$	−1.98480	+	1.14592i	−0.0736121	+	0.0424999i	0.462742	+	0.886493i	$0.346866\pi$
$728$		0			0
$729$	−15.3197	+	22.2330i	−0.567395	+	0.823446i
$730$	−18.6685	−	32.3347i	−0.690950	−	1.19676i
$731$	−19.9030			−0.736138
$732$	−41.9311	+	110.609i	−1.54982	+	4.08821i
$733$		−	24.7888i		−	0.915596i	−0.889056	−	0.457798i	$-0.848638\pi$
$733$		−	24.7888i		−	0.915596i	0.889056	−	0.457798i	$-0.151362\pi$
$734$	−29.9170	+	51.8178i	−1.10426	+	1.91263i
$735$		0			0
$736$	−21.1444	−	36.6232i	−0.779394	−	1.34995i
$737$	7.27099	−	4.19791i	0.267830	−	0.154632i
$738$	32.0147	+	6.52681i	1.17848	+	0.240255i
$739$	8.10081	−	14.0310i	0.297993	−	0.516139i	−0.677684	−	0.735354i	$-0.737016\pi$
$739$	8.10081	−	14.0310i	0.297993	−	0.516139i	0.975677	+	0.219214i	$0.0703494\pi$
$740$	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	0.113081	−	0.993586i	$-0.463928\pi$
$743$	−18.8312	−	10.8722i	−0.690848	−	0.398862i	−0.803930	+	0.594724i	$0.797261\pi$
$744$	4.87815	+	29.9908i	0.178842	+	1.09952i
$745$			13.3154i			0.487838i
$746$	31.1591	+	17.9897i	1.14081	+	0.658649i
$747$	5.23501	−	25.6783i	0.191539	−	0.939519i
$748$			12.9138i			0.472176i
$749$		0			0
$750$	30.0140	+	36.7503i	1.09596	+	1.34193i
$751$	−7.57995			−0.276596			−0.138298	−	0.990391i	$-0.544163\pi$
$751$	−7.57995			−0.276596			−0.138298	+	0.990391i	$0.544163\pi$
$752$	−33.8340	−	58.6022i	−1.23380	−	2.13700i
$753$	37.9686	+	14.3937i	1.38365	+	0.524536i
$754$	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
$759$	−4.74360	−	1.79827i	−0.172182	−	0.0652732i
$760$	8.42392	+	14.5907i	0.305568	+	0.529259i
$761$	34.4339			1.24823			0.624114	−	0.781333i	$-0.285460\pi$
$761$	34.4339			1.24823			0.624114	+	0.781333i	$0.285460\pi$
$762$	−8.33058	−	10.2003i	−0.301785	−	0.369517i
$763$		0			0
$764$		−	17.9629i		−	0.649874i
$765$	−15.7939	+	5.27753i	−0.571028	+	0.190809i
$766$	−34.2121	−	19.7523i	−1.23613	−	0.713681i
$767$		−	4.37713i		−	0.158049i
$768$	−5.84895	−	35.9593i	−0.211056	−	1.29757i
$769$	12.9344	+	7.46765i	0.466425	+	0.269290i	0.714742	−	0.699388i	$-0.246544\pi$
$769$	12.9344	+	7.46765i	0.466425	+	0.269290i	−0.248317	+	0.968679i	$0.579877\pi$
$770$		0			0
$771$	−39.7073	−	15.0528i	−1.43002	−	0.542114i
$772$	16.0439	−	27.7888i	0.577431	−	1.00014i
$773$	−19.9924	+	34.6278i	−0.719076	+	1.24548i	0.242290	+	0.970204i	$0.422101\pi$
$773$	−19.9924	+	34.6278i	−0.719076	+	1.24548i	−0.961366	+	0.275272i	$0.911232\pi$
$774$	−23.1732	+	26.1715i	−0.832945	+	0.940714i
$775$	−7.36945	+	4.25476i	−0.264719	+	0.152835i
$776$	−35.7845	−	61.9806i	−1.28459	−	2.22497i
$777$		0			0
$778$	−18.3466	+	31.7772i	−0.657758	+	1.13927i
$779$			7.98521i			0.286100i
$780$	−4.46489	+	11.7778i	−0.159869	+	0.421712i
$781$	6.42013			0.229730
$782$	27.2811	+	47.2523i	0.975571	+	1.68974i
$783$	25.7492	+	16.2681i	0.920201	+	0.581376i
$784$		0			0
$785$	25.8383	−	14.9178i	0.922209	−	0.532438i
$786$	−46.1109	−	56.4600i	−1.64472	−	2.01386i
$787$	1.94091	−	1.12059i	0.0691860	−	0.0399446i	−0.465008	−	0.885307i	$-0.653949\pi$
$787$	1.94091	−	1.12059i	0.0691860	−	0.0399446i	0.534194	+	0.845362i	$0.320615\pi$
$788$	−26.2561	+	15.1590i	−0.935336	+	0.540016i
$789$	−6.48012	+	17.0937i	−0.230698	+	0.608550i
$790$	11.3468	−	6.55108i	0.403701	−	0.233077i
$791$		0			0
$792$	9.79551	+	8.67333i	0.348068	+	0.308193i
$793$	−8.87159	−	15.3660i	−0.315039	−	0.545664i
$794$	25.1766			0.893484
$795$	4.24475	+	5.19744i	0.150546	+	0.184334i
$796$			75.8182i			2.68731i
$797$	22.1077	−	38.2916i	0.783094	−	1.35636i	−0.147037	−	0.989131i	$-0.546974\pi$
$797$	22.1077	−	38.2916i	0.783094	−	1.35636i	0.930131	−	0.367227i	$-0.119693\pi$
$798$		0			0
$799$	16.8668	+	29.2142i	0.596705	+	1.03352i
$800$	−26.4522	+	15.2722i	−0.935226	+	0.539953i
$801$	−0.972303	+	4.76925i	−0.0343546	+	0.168513i
$802$	−11.3225	+	19.6112i	−0.399812	+	0.692495i
$803$	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
$807$	3.07074	−	2.50788i	0.108095	−	0.0882814i
$808$		−	12.1145i		−	0.426185i
$809$	4.31478	+	2.49114i	0.151699	+	0.0875837i	0.573928	−	0.818906i	$-0.305419\pi$
$809$	4.31478	+	2.49114i	0.151699	+	0.0875837i	−0.422229	+	0.906489i	$0.638752\pi$
$810$	−11.4493	+	26.9129i	−0.402286	+	0.945621i
$811$		−	36.5749i		−	1.28432i	−0.766571	−	0.642160i	$-0.778039\pi$
$811$		−	36.5749i		−	1.28432i	0.766571	−	0.642160i	$-0.221961\pi$
$812$		0			0
$813$	−41.3049	+	6.71844i	−1.44863	+	0.235626i
$814$	4.26182			0.149377
$815$	5.52693	+	9.57292i	0.193600	+	0.335325i
$816$	−10.9469	−	67.3014i	−0.383218	−	2.35602i
$817$	−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	0.964041	−	0.265753i	$-0.0856205\pi$
$821$	34.8397	+	20.1147i	1.21591	+	0.702008i	0.251872	+	0.967761i	$0.418954\pi$
$822$	−60.5480	+	49.4496i	−2.11185	+	1.72475i
$823$	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	$0.618835\pi$
$824$	−52.3638			−1.82418
$825$	−1.29886	+	3.42620i	−0.0452204	+	0.119285i
$826$		0			0
$827$			32.0733i			1.11530i	0.830077	+	0.557648i	$0.188296\pi$
$827$			32.0733i			1.11530i	−0.830077	+	0.557648i	$0.811704\pi$
$828$	65.9791	+	13.4511i	2.29293	+	0.467458i
$829$	14.0640	+	8.11986i	0.488463	+	0.282014i	0.723937	−	0.689866i	$-0.242331\pi$
$829$	14.0640	+	8.11986i	0.488463	+	0.282014i	−0.235474	+	0.971881i	$0.575664\pi$
$830$		−	28.3874i		−	0.985343i
$831$	18.4163	+	6.98152i	0.638854	+	0.242186i
$832$	−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
$836$	−2.77157	+	4.80050i	−0.0958568	+	0.166029i
$837$	−10.8982	−	6.88540i	−0.376697	−	0.237994i
$838$	−9.60684	+	5.54651i	−0.331863	+	0.191601i
$839$	1.35145	+	2.34077i	0.0466571	+	0.0808125i	0.888411	−	0.459049i	$-0.151810\pi$
$839$	1.35145	+	2.34077i	0.0466571	+	0.0808125i	−0.841754	+	0.539862i	$0.818477\pi$
$840$		0			0
$841$	2.67914	−	4.64041i	0.0923842	−	0.160014i
$842$		−	29.9129i		−	1.03087i
$843$	−34.8188	+	5.66346i	−1.19922	+	0.195060i
$844$	−38.3853			−1.32128
$845$	7.19974	+	12.4703i	0.247679	+	0.428992i
$846$	58.0534	+	11.8353i	1.99592	+	0.406906i
$847$		0			0
$848$	−23.7962	+	13.7388i	−0.817166	+	0.471791i
$849$	20.7904	−	3.38167i	0.713526	−	0.116058i
$850$	34.1293	−	19.7046i	1.17063	−	0.675861i
$851$	10.9575	−	6.32632i	0.375619	−	0.216864i
$852$	−84.1117	+	13.6812i	−2.88162	+	0.468710i
$853$	41.3187	−	23.8554i	1.41473	−	0.816793i	0.418897	−	0.908034i	$-0.362417\pi$
$853$	41.3187	−	23.8554i	1.41473	−	0.816793i	0.995829	+	0.0912411i	$0.0290834\pi$
$854$		0			0
$855$	−7.00378	−	1.42785i	−0.239524	−	0.0488316i
$856$	0.537495	+	0.930969i	0.0183712	+	0.0318199i
$857$	−17.8795			−0.610751			−0.305375	−	0.952232i	$-0.598782\pi$
$857$	−17.8795			−0.610751			−0.305375	+	0.952232i	$0.598782\pi$
$858$	−3.35797	+	0.546190i	−0.114639	+	0.0186466i
$859$			33.7058i			1.15003i	0.818144	+	0.575014i	$0.195003\pi$
$859$			33.7058i			1.15003i	−0.818144	+	0.575014i	$0.804997\pi$
$860$	−13.3034	+	23.0422i	−0.453642	+	0.785731i
$861$		0			0
$862$	21.6367	+	37.4759i	0.736950	+	1.27643i
$863$	−16.4318	+	9.48693i	−0.559347	+	0.322939i	−0.752883	−	0.658154i	$-0.771338\pi$
$863$	−16.4318	+	9.48693i	−0.559347	+	0.322939i	0.193537	+	0.981093i	$0.438004\pi$
$864$	−39.1184	−	24.7147i	−1.33084	−	0.840812i
$865$	2.54826	−	4.41371i	0.0866434	−	0.150071i
$866$	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
$870$	30.8501	+	11.6951i	1.04592	+	0.396502i
$871$		−	16.7159i		−	0.566397i
$872$	−33.0748	−	19.0957i	−1.12005	−	0.646663i
$873$	29.7518	+	6.06547i	1.00695	+	0.205285i
$874$			23.4204i			0.792206i
$875$		0			0
$876$	−33.3415	+	87.9501i	−1.12650	+	2.97156i
$877$	37.2376			1.25742			0.628712	−	0.777638i	$-0.283582\pi$
$877$	37.2376			1.25742			0.628712	+	0.777638i	$0.283582\pi$
$878$	−28.7035	−	49.7159i	−0.968695	−	1.67783i
$879$	36.1332	−	29.5100i	1.21874	−	0.995347i
$880$	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
$885$	−1.24197	−	7.63564i	−0.0417485	−	0.256669i
$886$	6.33251	+	10.9682i	0.212745	+	0.368485i
$887$	−38.4434			−1.29080			−0.645402	−	0.763843i	$-0.723310\pi$
$887$	−38.4434			−1.29080			−0.645402	+	0.763843i	$0.723310\pi$
$888$	−32.2084	+	5.23886i	−1.08084	+	0.175805i
$889$		0			0
$890$			5.27243i			0.176732i
$891$	−5.50997	+	0.672063i	−0.184591	+	0.0225149i
$892$	32.9058	+	18.9981i	1.10177	+	0.636105i
$893$			14.4799i			0.484550i
$894$	36.9737	−	30.1965i	1.23659	−	1.00992i
$895$	−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
$899$	−7.27098	+	12.5937i	−0.242501	+	0.420023i
$900$	9.71544	−	47.6553i	0.323848	−	1.58851i
$901$	11.8628	−	6.84900i	0.395208	−	0.228173i
$902$	3.35857	+	5.81721i	0.111828	+	0.193692i
$903$		0			0
$904$	−22.8781	+	39.6261i	−0.760916	+	1.31794i
$905$		−	15.8755i		−	0.527719i
$906$	26.9639	+	33.0157i	0.895816	+	1.09687i
$907$	43.5902			1.44739			0.723695	−	0.690120i	$-0.242442\pi$
$907$	43.5902			1.44739			0.723695	+	0.690120i	$0.242442\pi$
$908$	49.2103	+	85.2348i	1.63310	+	2.82862i
$909$	3.84802	+	3.40719i	0.127631	+	0.113009i
$910$		0			0
$911$	−1.67736	+	0.968423i	−0.0555734	+	0.0320853i	−0.527529	−	0.849537i	$-0.676881\pi$
$911$	−1.67736	+	0.968423i	−0.0555734	+	0.0320853i	0.471956	+	0.881622i	$0.343548\pi$
$912$	10.3749	−	27.3676i	0.343548	−	0.906233i
$913$	4.66585	−	2.69383i	0.154417	−	0.0891528i
$914$	−24.2025	+	13.9733i	−0.800548	+	0.462197i
$915$	−19.8360	−	24.2879i	−0.655756	−	0.802934i
$916$	−24.6379	+	14.2247i	−0.814058	+	0.469997i
$917$		0			0
$918$	50.4716	+	31.8876i	1.66581	+	1.05245i
$919$	4.61421	+	7.99205i	0.152209	+	0.263634i	0.932039	−	0.362357i	$-0.118028\pi$
$919$	4.61421	+	7.99205i	0.152209	+	0.263634i	−0.779830	+	0.625991i	$0.784695\pi$
$920$	42.0755			1.38719
$921$	13.1206	−	34.6104i	0.432339	−	1.14045i
$922$		−	1.72887i		−	0.0569372i
$923$	6.39118	−	11.0698i	0.210368	−	0.364368i
$924$		0			0
$925$	−4.56937	−	7.91438i	−0.150240	−	0.260223i
$926$	93.3880	−	53.9176i	3.06892	−	1.77184i
$927$	14.7273	−	16.6327i	0.483707	−	0.546291i
$928$	−26.0987	+	45.2043i	−0.856732	+	1.48390i
$929$	−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
$933$	4.51343	+	27.7485i	0.147763	+	0.908446i
$934$			101.961i			3.33627i
$935$	−2.96481	−	1.71173i	−0.0969595	−	0.0559796i
$936$	24.7062	−	8.25560i	0.807548	−	0.269843i
$937$			28.6378i			0.935555i	0.883846	+	0.467778i	$0.154945\pi$
$937$			28.6378i			0.935555i	−0.883846	+	0.467778i	$0.845055\pi$
$938$		0			0
$939$	15.4268	+	18.8891i	0.503434	+	0.616424i
$940$	45.0959			1.47087
$941$	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	$0.826190\pi$
$942$	−100.019	−	37.9167i	−3.25880	−	1.23539i
$943$	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	$-0.989575\pi$
$947$	−47.0080	−	27.1401i	−1.52755	−	0.881933i	−0.528090	−	0.849188i	$-0.677092\pi$
$948$	−30.8632	−	11.7001i	−1.00239	−	0.380001i
$949$	−7.05423	−	12.2183i	−0.228990	−	0.396622i
$950$	16.9160			0.548829
$951$	−22.2374	−	27.2283i	−0.721097	−	0.882939i
$952$		0			0
$953$		−	11.2998i		−	0.366036i	−0.983110	−	0.183018i	$-0.941413\pi$
$953$		−	11.2998i		−	0.366036i	0.983110	−	0.183018i	$-0.0585867\pi$
$954$	4.80589	−	23.5734i	0.155596	−	0.763217i
$955$	4.12399	+	2.38099i	0.133449	+	0.0770469i
$956$		−	40.9911i		−	1.32575i
$957$	1.00528	+	6.18044i	0.0324960	+	0.199785i
$958$	−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
$962$	4.24260	−	7.34839i	0.136787	−	0.236922i
$963$	−0.446882	−	0.0911054i	−0.0144006	−	0.00293583i
$964$	34.6825	−	20.0240i	1.11705	−	0.644928i
$965$	4.25324	+	7.36682i	0.136917	+	0.237146i
$966$		0			0
$967$	5.93412	−	10.2782i	0.190829	−	0.330525i	−0.754696	−	0.656074i	$-0.772216\pi$
$967$	5.93412	−	10.2782i	0.190829	−	0.330525i	0.945525	+	0.325549i	$0.105549\pi$
$968$		−	75.0929i		−	2.41358i
$969$	−5.17207	+	13.6432i	−0.166151	+	0.438283i
$970$	32.8907			1.05606
$971$	−28.0837	−	48.6424i	−0.901249	−	1.56101i	−0.825875	−	0.563853i	$-0.809318\pi$
$971$	−28.0837	−	48.6424i	−0.901249	−	1.56101i	−0.0753736	−	0.997155i	$-0.524015\pi$
$972$	70.7552	−	20.5465i	2.26947	−	0.659029i
$973$		0			0
$974$	17.0826	−	9.86263i	0.547361	−	0.316019i
$975$	4.61459	+	5.65029i	0.147785	+	0.180954i
$976$	111.201	−	64.2020i	3.55946	−	2.05506i
$977$	18.7626	−	10.8326i	0.600268	−	0.346565i	−0.168879	−	0.985637i	$-0.554015\pi$
$977$	18.7626	−	10.8326i	0.600268	−	0.346565i	0.769147	+	0.639072i	$0.220681\pi$
$978$	14.0479	−	37.0564i	0.449202	−	1.18493i
$979$	−0.866594	+	0.500328i	−0.0276964	+	0.0159906i
$980$		0			0
$981$	15.3678	−	5.13516i	0.490656	−	0.163953i
$982$	−4.99072	−	8.64419i	−0.159260	−	0.275847i
$983$	19.4001			0.618768			0.309384	−	0.950937i	$-0.399877\pi$
$983$	19.4001			0.618768			0.309384	+	0.950937i	$0.399877\pi$
$984$	−32.5330	−	39.8347i	−1.03711	−	1.26988i
$985$		−	8.03731i		−	0.256090i
$986$	33.6733	−	58.3238i	1.07238	−	1.85741i
$987$		0			0
$988$	5.51814	+	9.55771i	0.175556	+	0.304071i
$989$	−18.4771	+	10.6678i	−0.587539	+	0.339216i
$990$	−5.70280	+	1.90559i	−0.181247	+	0.0605637i
$991$	−12.6630	+	21.9330i	−0.402254	+	0.696725i	−0.993998	−	0.109402i	$-0.965107\pi$
$991$	−12.6630	+	21.9330i	−0.402254	+	0.696725i	0.591743	+	0.806126i	$0.298440\pi$
$992$	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
$996$	−55.3879	+	45.2354i	−1.75503	+	1.43334i
$997$		−	5.56584i		−	0.176272i	−0.996108	−	0.0881360i	$-0.971909\pi$
$997$		−	5.56584i		−	0.176272i	0.996108	−	0.0881360i	$-0.0280910\pi$
$998$	72.2309	+	41.7025i	2.28643	+	1.32007i
$999$	7.39454	−	11.7041i	0.233953	−	0.370300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.b.374.1		10
3.2	odd	2		1323.2.s.b.962.5		10
7.2	even	3		63.2.i.b.5.5	✓	10
7.3	odd	6		441.2.o.c.293.5		10
7.4	even	3		441.2.o.d.293.5		10
7.5	odd	6		441.2.i.b.68.5		10
7.6	odd	2		63.2.s.b.59.1	yes	10
9.2	odd	6		441.2.i.b.227.1		10
9.7	even	3		1323.2.i.b.521.5		10
21.2	odd	6		189.2.i.b.152.1		10
21.5	even	6		1323.2.i.b.1097.1		10
21.11	odd	6		1323.2.o.c.881.1		10
21.17	even	6		1323.2.o.d.881.1		10
21.20	even	2		189.2.s.b.17.5		10
28.23	odd	6		1008.2.ca.b.257.1		10
28.27	even	2		1008.2.df.b.689.1		10
63.2	odd	6		63.2.s.b.47.1	yes	10
63.11	odd	6		441.2.o.c.146.5		10
63.13	odd	6		567.2.p.c.80.5		10
63.16	even	3		189.2.s.b.89.5		10
63.20	even	6		63.2.i.b.38.1	yes	10
63.23	odd	6		567.2.p.c.404.5		10
63.25	even	3		1323.2.o.d.440.1		10
63.34	odd	6		189.2.i.b.143.5		10
63.38	even	6		441.2.o.d.146.5		10
63.41	even	6		567.2.p.d.80.1		10
63.47	even	6	inner	441.2.s.b.362.1		10
63.52	odd	6		1323.2.o.c.440.1		10
63.58	even	3		567.2.p.d.404.1		10
63.61	odd	6		1323.2.s.b.656.5		10
84.23	even	6		3024.2.ca.b.2609.2		10
84.83	odd	2		3024.2.df.b.17.2		10
252.79	odd	6		3024.2.df.b.1601.2		10
252.83	odd	6		1008.2.ca.b.353.1		10
252.191	even	6		1008.2.df.b.929.1		10
252.223	even	6		3024.2.ca.b.2033.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	7.2	even	3
63.2.i.b.38.1	yes	10	63.20	even	6
63.2.s.b.47.1	yes	10	63.2	odd	6
63.2.s.b.59.1	yes	10	7.6	odd	2
189.2.i.b.143.5		10	63.34	odd	6
189.2.i.b.152.1		10	21.2	odd	6
189.2.s.b.17.5		10	21.20	even	2
189.2.s.b.89.5		10	63.16	even	3
441.2.i.b.68.5		10	7.5	odd	6
441.2.i.b.227.1		10	9.2	odd	6
441.2.o.c.146.5		10	63.11	odd	6
441.2.o.c.293.5		10	7.3	odd	6
441.2.o.d.146.5		10	63.38	even	6
441.2.o.d.293.5		10	7.4	even	3
441.2.s.b.362.1		10	63.47	even	6	inner
441.2.s.b.374.1		10	1.1	even	1	trivial
567.2.p.c.80.5		10	63.13	odd	6
567.2.p.c.404.5		10	63.23	odd	6
567.2.p.d.80.1		10	63.41	even	6
567.2.p.d.404.1		10	63.58	even	3
1008.2.ca.b.257.1		10	28.23	odd	6
1008.2.ca.b.353.1		10	252.83	odd	6
1008.2.df.b.689.1		10	28.27	even	2
1008.2.df.b.929.1		10	252.191	even	6
1323.2.i.b.521.5		10	9.7	even	3
1323.2.i.b.1097.1		10	21.5	even	6
1323.2.o.c.440.1		10	63.52	odd	6
1323.2.o.c.881.1		10	21.11	odd	6
1323.2.o.d.440.1		10	63.25	even	3
1323.2.o.d.881.1		10	21.17	even	6
1323.2.s.b.656.5		10	63.61	odd	6
1323.2.s.b.962.5		10	3.2	odd	2
3024.2.ca.b.2033.2		10	252.223	even	6
3024.2.ca.b.2609.2		10	84.23	even	6
3024.2.df.b.17.2		10	84.83	odd	2
3024.2.df.b.1601.2		10	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.24607 - 1.29677i) q^{2} +(-1.61958 - 0.613974i) q^{3} +(2.36322 + 4.09323i) q^{4} -1.25299 q^{5} +(2.84151 + 3.47925i) q^{6} -7.07116i q^{8} +(2.24607 + 1.98876i) q^{9} +O(q^{10})\)	\(q+(-2.24607 - 1.29677i) q^{2} +(-1.61958 - 0.613974i) q^{3} +(2.36322 + 4.09323i) q^{4} -1.25299 q^{5} +(2.84151 + 3.47925i) q^{6} -7.07116i q^{8} +(2.24607 + 1.98876i) q^{9} +(2.81429 + 1.62483i) q^{10} +0.616756i q^{11} +(-1.31429 - 8.08026i) q^{12} +(1.06343 + 0.613974i) q^{13} +(2.02931 + 0.769301i) q^{15} +(-4.44321 + 7.69587i) q^{16} +(2.21501 - 3.83652i) q^{17} +(-2.46587 - 7.37953i) q^{18} +(1.64679 - 0.950775i) q^{19} +(-2.96109 - 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} -4.74890i q^{23} +(-4.34151 + 11.4523i) q^{24} -3.43003 q^{25} +(-1.59237 - 2.75806i) q^{26} +(-2.41664 - 4.59998i) q^{27} +(-5.07629 + 2.93080i) q^{29} +(-3.56037 - 4.35945i) q^{30} +(2.14851 - 1.24044i) q^{31} +(7.71195 - 4.45249i) q^{32} +(0.378672 - 0.998884i) q^{33} +(-9.95016 + 5.74473i) q^{34} +(-2.83247 + 13.8936i) q^{36} +(1.33217 + 2.30738i) q^{37} -4.93175 q^{38} +(-1.34535 - 1.64730i) q^{39} +8.86005i q^{40} +(-2.09966 + 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +(-2.52452 + 1.45753i) q^{44} +(-2.81429 - 2.49189i) q^{45} +(-6.15823 + 10.6664i) q^{46} +(-3.80738 + 6.59458i) q^{47} +(11.9212 - 9.73605i) q^{48} +(7.70409 + 4.44796i) q^{50} +(-5.94291 + 4.85358i) q^{51} +5.80384i q^{52} +(2.67782 + 1.54604i) q^{53} +(-0.537165 + 13.4657i) q^{54} -0.772786i q^{55} +(-3.25086 + 0.528768i) q^{57} +15.2023 q^{58} +(-1.78229 - 3.08702i) q^{59} +(1.64679 + 10.1244i) q^{60} +(-12.5136 - 7.22473i) q^{61} -6.43428 q^{62} -5.32259 q^{64} +(-1.33247 - 0.769301i) q^{65} +(-2.14585 + 1.75252i) q^{66} +(-6.80644 - 11.7891i) q^{67} +20.9383 q^{68} +(-2.91570 + 7.69121i) q^{69} -10.4095i q^{71} +(14.0628 - 15.8823i) q^{72} +(-9.95016 - 5.74473i) q^{73} -6.91006i q^{74} +(5.55520 + 2.10595i) q^{75} +(7.78348 + 4.49379i) q^{76} +(0.885586 + 5.44457i) q^{78} +(2.01592 - 3.49168i) q^{79} +(5.56728 - 9.64281i) q^{80} +(1.08967 + 8.93379i) q^{81} +(9.43196 - 5.44554i) q^{82} +(-4.36775 - 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +11.6521i q^{86} +(10.0209 - 1.62995i) q^{87} +4.36118 q^{88} +(0.811226 + 1.40508i) q^{89} +(3.08970 + 9.24645i) q^{90} +(19.4383 - 11.2227i) q^{92} +(-4.24128 + 0.689866i) q^{93} +(17.1033 - 9.87459i) q^{94} +(-2.06341 + 1.19131i) q^{95} +(-15.2238 + 2.47623i) q^{96} +(8.76527 - 5.06063i) q^{97} +(-1.22658 + 1.38528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 12 q^{6}+O(q^{10}) \) 10 * q + 4 * q^4 + 12 * q^6	\( 10 q + 4 q^{4} + 12 q^{6} + 15 q^{10} - 6 q^{13} - 3 q^{15} - 6 q^{16} + 12 q^{17} - 18 q^{18} - 3 q^{19} + 3 q^{20} + 5 q^{22} - 27 q^{24} - 14 q^{25} - 3 q^{26} - 27 q^{27} - 15 q^{29} + 9 q^{31} + 48 q^{32} + 9 q^{33} - 3 q^{34} - 18 q^{36} + 6 q^{37} - 36 q^{38} + 12 q^{39} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 15 q^{45} - 13 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} - 24 q^{51} - 9 q^{53} - 27 q^{54} - 36 q^{57} - 16 q^{58} + 18 q^{59} - 3 q^{60} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} + 33 q^{66} - 10 q^{67} + 54 q^{68} + 3 q^{69} + 18 q^{72} - 3 q^{73} + 21 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} + 30 q^{80} - 48 q^{81} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 30 q^{87} + 16 q^{88} - 24 q^{89} - 24 q^{90} + 39 q^{92} + 6 q^{93} + 3 q^{94} - 3 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) \) 10 * q + 4 * q^4 + 12 * q^6 + 15 * q^10 - 6 * q^13 - 3 * q^15 - 6 * q^16 + 12 * q^17 - 18 * q^18 - 3 * q^19 + 3 * q^20 + 5 * q^22 - 27 * q^24 - 14 * q^25 - 3 * q^26 - 27 * q^27 - 15 * q^29 + 9 * q^31 + 48 * q^32 + 9 * q^33 - 3 * q^34 - 18 * q^36 + 6 * q^37 - 36 * q^38 + 12 * q^39 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 15 * q^45 - 13 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 - 24 * q^51 - 9 * q^53 - 27 * q^54 - 36 * q^57 - 16 * q^58 + 18 * q^59 - 3 * q^60 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 + 33 * q^66 - 10 * q^67 + 54 * q^68 + 3 * q^69 + 18 * q^72 - 3 * q^73 + 21 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 + 30 * q^80 - 48 * q^81 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 30 * q^87 + 16 * q^88 - 24 * q^89 - 24 * q^90 + 39 * q^92 + 6 * q^93 + 3 * q^94 - 3 * q^96 - 6 * q^97 + 21 * q^99

Introduction

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