LMFDB - Embedded newform 722.2.c.m.429.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.324000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 $ x^8 + 5x^6 + 20x^4 + 25*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.2
Root			$0.587785 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.m.653.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.642040 + 1.11205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84786 + 3.20059i) q^{5} +(-0.642040 - 1.11205i) q^{6} -0.442463 q^{7} +1.00000 q^{8} +(0.675571 + 1.17012i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.642040 + 1.11205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84786 + 3.20059i) q^{5} +(-0.642040 - 1.11205i) q^{6} -0.442463 q^{7} +1.00000 q^{8} +(0.675571 + 1.17012i) q^{9} +(-1.84786 - 3.20059i) q^{10} -4.02967 q^{11} +1.28408 q^{12} +(-2.44575 - 4.23616i) q^{13} +(0.221232 - 0.383185i) q^{14} +(-2.37280 - 4.10980i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.133446 + 0.231136i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(0.284079 - 0.492039i) q^{21} +(2.01484 - 3.48980i) q^{22} +(4.60465 + 7.97549i) q^{23} +(-0.642040 + 1.11205i) q^{24} +(-4.32916 - 7.49833i) q^{25} +4.89149 q^{26} -5.58721 q^{27} +(0.221232 + 0.383185i) q^{28} +(0.111791 + 0.193627i) q^{29} +4.74559 q^{30} +3.47985 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.58721 - 4.48118i) q^{33} +(-0.133446 - 0.231136i) q^{34} +(0.817610 - 1.41614i) q^{35} +(0.675571 - 1.17012i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(-1.84786 + 3.20059i) q^{40} +(3.93236 - 6.81105i) q^{41} +(0.284079 + 0.492039i) q^{42} +(2.81761 - 4.88024i) q^{43} +(2.01484 + 3.48980i) q^{44} -4.99344 q^{45} -9.20930 q^{46} +(-1.09934 - 1.90411i) q^{47} +(-0.642040 - 1.11205i) q^{48} -6.80423 q^{49} +8.65833 q^{50} +(-0.171356 - 0.296797i) q^{51} +(-2.44575 + 4.23616i) q^{52} +(-4.97120 - 8.61038i) q^{53} +(2.79360 - 4.83866i) q^{54} +(7.44627 - 12.8973i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(1.75476 - 3.03934i) q^{59} +(-2.37280 + 4.10980i) q^{60} +(-2.03977 - 3.53299i) q^{61} +(-1.73993 + 3.01364i) q^{62} +(-0.298915 - 0.517736i) q^{63} +1.00000 q^{64} +18.0776 q^{65} +(2.58721 + 4.48118i) q^{66} +(-0.0738814 - 0.127966i) q^{67} +0.266893 q^{68} -11.8255 q^{69} +(0.817610 + 1.41614i) q^{70} +(-5.73456 + 9.93255i) q^{71} +(0.675571 + 1.17012i) q^{72} +(-0.711130 + 1.23171i) q^{73} +(-0.724514 + 1.25490i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(-3.14053 + 5.43956i) q^{78} +(-5.10169 + 8.83638i) q^{79} +(-1.84786 - 3.20059i) q^{80} +(1.56050 - 2.70286i) q^{81} +(3.93236 + 6.81105i) q^{82} -3.28878 q^{83} -0.568158 q^{84} +(-0.493181 - 0.854214i) q^{85} +(2.81761 + 4.88024i) q^{86} -0.287096 q^{87} -4.02967 q^{88} +(2.98037 + 5.16216i) q^{89} +(2.49672 - 4.32444i) q^{90} +(1.08215 + 1.87434i) q^{91} +(4.60465 - 7.97549i) q^{92} +(-2.23420 + 3.86975i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(-2.04238 + 3.53750i) q^{97} +(3.40211 - 5.89263i) q^{98} +(-2.72233 - 4.71521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 18 q^{13} + 2 q^{14} - 4 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{21} - 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} - 8 q^{27} + 2 q^{28} + 2 q^{29} + 8 q^{30} + 52 q^{31} - 4 q^{32} - 16 q^{33} - 6 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} - 20 q^{46} + 12 q^{47} - 2 q^{48} - 24 q^{49} + 12 q^{50} + 2 q^{51} - 18 q^{52} - 8 q^{53} + 4 q^{54} + 26 q^{55} - 4 q^{56} - 4 q^{58} + 8 q^{59} - 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} - 8 q^{65} - 16 q^{66} - 10 q^{67} + 12 q^{68} - 40 q^{69} - 6 q^{70} - 4 q^{72} + 14 q^{73} - 4 q^{74} + 16 q^{75} + 8 q^{77} + 6 q^{78} - 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} + 8 q^{84} + 18 q^{85} + 10 q^{86} - 52 q^{87} + 4 q^{88} + 16 q^{89} + 22 q^{90} + 4 q^{91} + 10 q^{92} - 8 q^{93} - 24 q^{94} + 4 q^{96} - 28 q^{97} + 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 18 * q^13 + 2 * q^14 - 4 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 4 * q^20 - 4 * q^21 - 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 - 8 * q^27 + 2 * q^28 + 2 * q^29 + 8 * q^30 + 52 * q^31 - 4 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 - 20 * q^46 + 12 * q^47 - 2 * q^48 - 24 * q^49 + 12 * q^50 + 2 * q^51 - 18 * q^52 - 8 * q^53 + 4 * q^54 + 26 * q^55 - 4 * q^56 - 4 * q^58 + 8 * q^59 - 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 - 8 * q^65 - 16 * q^66 - 10 * q^67 + 12 * q^68 - 40 * q^69 - 6 * q^70 - 4 * q^72 + 14 * q^73 - 4 * q^74 + 16 * q^75 + 8 * q^77 + 6 * q^78 - 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 + 8 * q^84 + 18 * q^85 + 10 * q^86 - 52 * q^87 + 4 * q^88 + 16 * q^89 + 22 * q^90 + 4 * q^91 + 10 * q^92 - 8 * q^93 - 24 * q^94 + 4 * q^96 - 28 * q^97 + 12 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.642040	+	1.11205i	−0.370682	+	0.642040i	−0.989671	−	0.143360i	$-0.954209\pi$
$3$	−0.642040	+	1.11205i	−0.370682	+	0.642040i	0.618989	+	0.785400i	$0.287543\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.84786	+	3.20059i	−0.826388	+	1.43135i	0.0744667	+	0.997224i	$0.476275\pi$
$5$	−1.84786	+	3.20059i	−0.826388	+	1.43135i	−0.900854	+	0.434122i	$0.857059\pi$
$6$	−0.642040	−	1.11205i	−0.262112	−	0.453990i
$7$	−0.442463			−0.167235			−0.0836177	−	0.996498i	$-0.526647\pi$
$7$	−0.442463			−0.167235			−0.0836177	+	0.996498i	$0.526647\pi$
$8$	1.00000			0.353553
$9$	0.675571	+	1.17012i	0.225190	+	0.390041i
$10$	−1.84786	−	3.20059i	−0.584344	−	1.01211i
$11$	−4.02967			−1.21499			−0.607496	−	0.794323i	$-0.707826\pi$
$11$	−4.02967			−1.21499			−0.607496	+	0.794323i	$0.707826\pi$
$12$	1.28408			0.370682
$13$	−2.44575	−	4.23616i	−0.678328	−	1.17490i	−0.975484	−	0.220069i	$-0.929372\pi$
$13$	−2.44575	−	4.23616i	−0.678328	−	1.17490i	0.297156	−	0.954829i	$-0.403962\pi$
$14$	0.221232	−	0.383185i	0.0591267	−	0.102410i
$15$	−2.37280	−	4.10980i	−0.612653	−	1.06115i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.133446	+	0.231136i	−0.0323655	+	0.0560587i	−0.881754	−	0.471709i	$-0.843637\pi$
$17$	−0.133446	+	0.231136i	−0.0323655	+	0.0560587i	0.849389	+	0.527767i	$0.176971\pi$
$18$	−1.35114			−0.318467
$19$		0			0
$19$		0			0
$20$	3.69572			0.826388
$21$	0.284079	−	0.492039i	0.0619911	−	0.107372i
$22$	2.01484	−	3.48980i	0.429565	−	0.744028i
$23$	4.60465	+	7.97549i	0.960136	+	1.66300i	0.722151	+	0.691735i	$0.243153\pi$
$23$	4.60465	+	7.97549i	0.960136	+	1.66300i	0.237985	+	0.971269i	$0.423513\pi$
$24$	−0.642040	+	1.11205i	−0.131056	+	0.226995i
$25$	−4.32916	−	7.49833i	−0.865833	−	1.49967i
$26$	4.89149			0.959300
$27$	−5.58721			−1.07526
$28$	0.221232	+	0.383185i	0.0418089	+	0.0724151i
$29$	0.111791	+	0.193627i	0.0207590	+	0.0359557i	0.876218	−	0.481914i	$-0.160058\pi$
$29$	0.111791	+	0.193627i	0.0207590	+	0.0359557i	−0.855459	+	0.517870i	$0.826725\pi$
$30$	4.74559			0.866423
$31$	3.47985			0.625000			0.312500	−	0.949918i	$-0.398834\pi$
$31$	3.47985			0.625000			0.312500	+	0.949918i	$0.398834\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.58721	−	4.48118i	0.450375	−	0.780073i
$34$	−0.133446	−	0.231136i	−0.0228859	−	0.0396395i
$35$	0.817610	−	1.41614i	0.138201	−	0.239372i
$36$	0.675571	−	1.17012i	0.112595	−	0.195020i
$37$	1.44903			0.238219			0.119109	−	0.992881i	$-0.461996\pi$
$37$	1.44903			0.238219			0.119109	+	0.992881i	$0.461996\pi$
$38$		0			0
$39$	6.28106			1.00577
$40$	−1.84786	+	3.20059i	−0.292172	+	0.506057i
$41$	3.93236	−	6.81105i	0.614132	−	1.06371i	−0.376404	−	0.926455i	$-0.622840\pi$
$41$	3.93236	−	6.81105i	0.614132	−	1.06371i	0.990536	−	0.137252i	$-0.0438270\pi$
$42$	0.284079	+	0.492039i	0.0438343	+	0.0759233i
$43$	2.81761	−	4.88024i	0.429682	−	0.744230i	−0.567163	−	0.823605i	$-0.691959\pi$
$43$	2.81761	−	4.88024i	0.429682	−	0.744230i	0.996845	+	0.0793752i	$0.0252925\pi$
$44$	2.01484	+	3.48980i	0.303748	+	0.526107i
$45$	−4.99344			−0.744377
$46$	−9.20930			−1.35784
$47$	−1.09934	−	1.90411i	−0.160355	−	0.277743i	0.774641	−	0.632401i	$-0.217931\pi$
$47$	−1.09934	−	1.90411i	−0.160355	−	0.277743i	−0.934996	+	0.354658i	$0.884597\pi$
$48$	−0.642040	−	1.11205i	−0.0926704	−	0.160510i
$49$	−6.80423			−0.972032
$50$	8.65833			1.22447
$51$	−0.171356	−	0.296797i	−0.0239946	−	0.0415599i
$52$	−2.44575	+	4.23616i	−0.339164	+	0.587449i
$53$	−4.97120	−	8.61038i	−0.682847	−	1.18273i	−0.974108	−	0.226083i	$-0.927408\pi$
$53$	−4.97120	−	8.61038i	−0.682847	−	1.18273i	0.291261	−	0.956644i	$-0.405925\pi$
$54$	2.79360	−	4.83866i	0.380161	−	0.658459i
$55$	7.44627	−	12.8973i	1.00405	−	1.73907i
$56$	−0.442463			−0.0591267
$57$		0			0
$58$	−0.223582			−0.0293577
$59$	1.75476	−	3.03934i	0.228451	−	0.395688i	−0.728898	−	0.684622i	$-0.759967\pi$
$59$	1.75476	−	3.03934i	0.228451	−	0.395688i	0.957349	+	0.288934i	$0.0933007\pi$
$60$	−2.37280	+	4.10980i	−0.306327	+	0.530573i
$61$	−2.03977	−	3.53299i	−0.261166	−	0.452353i	0.705386	−	0.708824i	$-0.250774\pi$
$61$	−2.03977	−	3.53299i	−0.261166	−	0.452353i	−0.966552	+	0.256470i	$0.917440\pi$
$62$	−1.73993	+	3.01364i	−0.220971	+	0.382733i
$63$	−0.298915	−	0.517736i	−0.0376598	−	0.0652287i
$64$	1.00000			0.125000
$65$	18.0776			2.24225
$66$	2.58721	+	4.48118i	0.318463	+	0.551595i
$67$	−0.0738814	−	0.127966i	−0.00902605	−	0.0156336i	0.861477	−	0.507796i	$-0.169540\pi$
$67$	−0.0738814	−	0.127966i	−0.00902605	−	0.0156336i	−0.870503	+	0.492163i	$0.836206\pi$
$68$	0.266893			0.0323655
$69$	−11.8255			−1.42362
$70$	0.817610	+	1.41614i	0.0977231	+	0.169261i
$71$	−5.73456	+	9.93255i	−0.680567	+	1.17878i	0.294241	+	0.955731i	$0.404933\pi$
$71$	−5.73456	+	9.93255i	−0.680567	+	1.17878i	−0.974808	+	0.223045i	$0.928400\pi$
$72$	0.675571	+	1.17012i	0.0796167	+	0.137900i
$73$	−0.711130	+	1.23171i	−0.0832315	+	0.144161i	−0.904636	−	0.426185i	$-0.859857\pi$
$73$	−0.711130	+	1.23171i	−0.0832315	+	0.144161i	0.821405	+	0.570346i	$0.193191\pi$
$74$	−0.724514	+	1.25490i	−0.0842230	+	0.145879i
$75$	11.1180			1.28379
$76$		0			0
$77$	1.78298			0.203190
$78$	−3.14053	+	5.43956i	−0.355595	+	0.615909i
$79$	−5.10169	+	8.83638i	−0.573985	+	0.994171i	0.422166	+	0.906518i	$0.361270\pi$
$79$	−5.10169	+	8.83638i	−0.573985	+	0.994171i	−0.996151	+	0.0876525i	$0.972063\pi$
$80$	−1.84786	−	3.20059i	−0.206597	−	0.357836i
$81$	1.56050	−	2.70286i	0.173389	−	0.300318i
$82$	3.93236	+	6.81105i	0.434257	+	0.752155i
$83$	−3.28878			−0.360990			−0.180495	−	0.983576i	$-0.557770\pi$
$83$	−3.28878			−0.360990			−0.180495	+	0.983576i	$0.557770\pi$
$84$	−0.568158			−0.0619911
$85$	−0.493181	−	0.854214i	−0.0534929	−	0.0926525i
$86$	2.81761	+	4.88024i	0.303831	+	0.526250i
$87$	−0.287096			−0.0307800
$88$	−4.02967			−0.429565
$89$	2.98037	+	5.16216i	0.315919	+	0.547188i	0.979632	−	0.200799i	$-0.0643539\pi$
$89$	2.98037	+	5.16216i	0.315919	+	0.547188i	−0.663714	+	0.747987i	$0.731021\pi$
$90$	2.49672	−	4.32444i	0.263177	−	0.455836i
$91$	1.08215	+	1.87434i	0.113440	+	0.196485i
$92$	4.60465	−	7.97549i	0.480068	−	0.831502i
$93$	−2.23420	+	3.86975i	−0.231676	+	0.401275i
$94$	2.19868			0.226776
$95$		0			0
$96$	1.28408			0.131056
$97$	−2.04238	+	3.53750i	−0.207372	+	0.359179i	−0.950886	−	0.309541i	$-0.899824\pi$
$97$	−2.04238	+	3.53750i	−0.207372	+	0.359179i	0.743514	+	0.668721i	$0.233158\pi$
$98$	3.40211	−	5.89263i	0.343665	−	0.595246i
$99$	−2.72233	−	4.71521i	−0.273604	−	0.473896i
$100$	−4.32916	+	7.49833i	−0.432916	+	0.749833i
$101$	−0.212639	−	0.368301i	−0.0211583	−	0.0366473i	0.855252	−	0.518212i	$-0.173402\pi$
$101$	−0.212639	−	0.368301i	−0.0211583	−	0.0366473i	−0.876411	+	0.481564i	$0.840069\pi$
$102$	0.342712			0.0339335
$103$	−4.53618			−0.446963			−0.223482	−	0.974708i	$-0.571742\pi$
$103$	−4.53618			−0.446963			−0.223482	+	0.974708i	$0.571742\pi$
$104$	−2.44575	−	4.23616i	−0.239825	−	0.415389i
$105$	1.04988	+	1.81844i	0.102457	+	0.177461i
$106$	9.94241			0.965692
$107$	−3.17151			−0.306602			−0.153301	−	0.988180i	$-0.548990\pi$
$107$	−3.17151			−0.306602			−0.153301	+	0.988180i	$0.548990\pi$
$108$	2.79360	+	4.83866i	0.268815	+	0.465601i
$109$	3.39056	−	5.87262i	0.324757	−	0.562495i	−0.656706	−	0.754146i	$-0.728051\pi$
$109$	3.39056	−	5.87262i	0.324757	−	0.562495i	0.981463	+	0.191651i	$0.0613843\pi$
$110$	7.44627	+	12.8973i	0.709974	+	1.22971i
$111$	−0.930333	+	1.61138i	−0.0883033	+	0.152946i
$112$	0.221232	−	0.383185i	0.0209044	−	0.0362075i
$113$	−10.0444			−0.944893			−0.472447	−	0.881359i	$-0.656629\pi$
$113$	−10.0444			−0.944893			−0.472447	+	0.881359i	$0.656629\pi$
$114$		0			0
$115$	−34.0350			−3.17378
$116$	0.111791	−	0.193627i	0.0103795	−	0.0179778i
$117$	3.30455	−	5.72364i	0.305506	−	0.529151i
$118$	1.75476	+	3.03934i	0.161539	+	0.279794i
$119$	0.0590452	−	0.102269i	0.00541266	−	0.00937501i
$120$	−2.37280	−	4.10980i	−0.216606	−	0.375172i
$121$	5.23826			0.476205
$122$	4.07955			0.369345
$123$	5.04946	+	8.74593i	0.455295	+	0.788594i
$124$	−1.73993	−	3.01364i	−0.156250	−	0.270633i
$125$	13.5201			1.20928
$126$	0.597831			0.0532590
$127$	−7.04029	−	12.1941i	−0.624725	−	1.08206i	−0.988594	−	0.150605i	$-0.951878\pi$
$127$	−7.04029	−	12.1941i	−0.624725	−	1.08206i	0.363869	−	0.931450i	$-0.381456\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.61803	+	6.26662i	0.318550	+	0.551745i
$130$	−9.03879	+	15.6556i	−0.792754	+	1.37309i
$131$	−7.92075	+	13.7191i	−0.692039	+	1.19865i	0.279129	+	0.960254i	$0.409954\pi$
$131$	−7.92075	+	13.7191i	−0.692039	+	1.19865i	−0.971169	+	0.238394i	$0.923379\pi$
$132$	−5.17442			−0.450375
$133$		0			0
$134$	0.147763			0.0127648
$135$	10.3244	−	17.8823i	0.888581	−	1.53907i
$136$	−0.133446	+	0.231136i	−0.0114429	+	0.0198198i
$137$	−1.10372	−	1.91169i	−0.0942970	−	0.163327i	0.815018	−	0.579436i	$-0.196727\pi$
$137$	−1.10372	−	1.91169i	−0.0942970	−	0.163327i	−0.909315	+	0.416108i	$0.863394\pi$
$138$	5.91273	−	10.2412i	0.503325	−	0.871785i
$139$	8.53222	+	14.7782i	0.723694	+	1.25347i	0.959510	+	0.281676i	$0.0908904\pi$
$139$	8.53222	+	14.7782i	0.723694	+	1.25347i	−0.235816	+	0.971798i	$0.575776\pi$
$140$	−1.63522			−0.138201
$141$	2.82328			0.237763
$142$	−5.73456	−	9.93255i	−0.481234	−	0.833521i
$143$	9.85555	+	17.0703i	0.824163	+	1.42749i
$144$	−1.35114			−0.112595
$145$	−0.826294			−0.0686200
$146$	−0.711130	−	1.23171i	−0.0588535	−	0.101937i
$147$	4.36858	−	7.56661i	0.360315	−	0.624083i
$148$	−0.724514	−	1.25490i	−0.0595547	−	0.103152i
$149$	−6.77288	+	11.7310i	−0.554856	+	0.961039i	0.443059	+	0.896493i	$0.353893\pi$
$149$	−6.77288	+	11.7310i	−0.554856	+	0.961039i	−0.997915	+	0.0645462i	$0.979440\pi$
$150$	−5.55899	+	9.62845i	−0.453890	+	0.786160i
$151$	−9.15317			−0.744875			−0.372437	−	0.928057i	$-0.621478\pi$
$151$	−9.15317			−0.744875			−0.372437	+	0.928057i	$0.621478\pi$
$152$		0			0
$153$	−0.360610			−0.0291536
$154$	−0.891491	+	1.54411i	−0.0718384	+	0.124428i
$155$	−6.43028	+	11.1376i	−0.516492	+	0.894591i
$156$	−3.14053	−	5.43956i	−0.251444	−	0.435513i
$157$	8.19514	−	14.1944i	0.654043	−	1.13284i	−0.328089	−	0.944647i	$-0.606405\pi$
$157$	8.19514	−	14.1944i	0.654043	−	1.13284i	0.982133	−	0.188190i	$-0.0602620\pi$
$158$	−5.10169	−	8.83638i	−0.405869	−	0.702985i
$159$	12.7668			1.01248
$160$	3.69572			0.292172
$161$	−2.03739	−	3.52886i	−0.160569	−	0.278113i
$162$	1.56050	+	2.70286i	0.122604	+	0.212357i
$163$	−13.7722			−1.07873			−0.539363	−	0.842073i	$-0.681335\pi$
$163$	−13.7722			−1.07873			−0.539363	+	0.842073i	$0.681335\pi$
$164$	−7.86472			−0.614132
$165$	9.56159	+	16.5612i	0.744369	+	1.28929i
$166$	1.64439	−	2.84817i	0.127629	−	0.221061i
$167$	5.16640	+	8.94847i	0.399788	+	0.692453i	0.993700	−	0.112077i	$-0.0357504\pi$
$167$	5.16640	+	8.94847i	0.399788	+	0.692453i	−0.593911	+	0.804530i	$0.702417\pi$
$168$	0.284079	−	0.492039i	0.0219172	−	0.0379617i
$169$	−5.46334	+	9.46279i	−0.420257	+	0.727907i
$170$	0.986361			0.0756504
$171$		0			0
$172$	−5.63522			−0.429682
$173$	4.90601	−	8.49745i	0.372997	−	0.646049i	−0.617028	−	0.786941i	$-0.711664\pi$
$173$	4.90601	−	8.49745i	0.372997	−	0.646049i	0.990025	+	0.140892i	$0.0449969\pi$
$174$	0.143548	−	0.248633i	0.0108824	−	0.0188488i
$175$	1.91550	+	3.31774i	0.144798	+	0.250797i
$176$	2.01484	−	3.48980i	0.151874	−	0.263053i
$177$	2.25325	+	3.90275i	0.169365	+	0.293349i
$178$	−5.96075			−0.446777
$179$	−8.79830			−0.657616			−0.328808	−	0.944397i	$-0.606647\pi$
$179$	−8.79830			−0.657616			−0.328808	+	0.944397i	$0.606647\pi$
$180$	2.49672	+	4.32444i	0.186094	+	0.322325i
$181$	−7.26388	−	12.5814i	−0.539920	−	0.935168i	−0.998908	−	0.0467258i	$-0.985121\pi$
$181$	−7.26388	−	12.5814i	−0.539920	−	0.935168i	0.458988	−	0.888442i	$-0.348212\pi$
$182$	−2.16431			−0.160429
$183$	5.23846			0.387238
$184$	4.60465	+	7.97549i	0.339459	+	0.587961i
$185$	−2.67760	+	4.63774i	−0.196861	+	0.340973i
$186$	−2.23420	−	3.86975i	−0.163820	−	0.283744i
$187$	0.537746	−	0.931403i	0.0393239	−	0.0681109i
$188$	−1.09934	+	1.90411i	−0.0801776	+	0.138872i
$189$	2.47214			0.179821
$190$		0			0
$191$	12.7302			0.921122			0.460561	−	0.887628i	$-0.347648\pi$
$191$	12.7302			0.921122			0.460561	+	0.887628i	$0.347648\pi$
$192$	−0.642040	+	1.11205i	−0.0463352	+	0.0802549i
$193$	−8.73903	+	15.1364i	−0.629049	+	1.08954i	0.358694	+	0.933455i	$0.383222\pi$
$193$	−8.73903	+	15.1364i	−0.629049	+	1.08954i	−0.987743	+	0.156090i	$0.950111\pi$
$194$	−2.04238	−	3.53750i	−0.146634	−	0.253978i
$195$	−11.6065	+	20.1031i	−0.831160	+	1.43961i
$196$	3.40211	+	5.89263i	0.243008	+	0.420902i
$197$	−24.5113			−1.74636			−0.873178	−	0.487401i	$-0.837945\pi$
$197$	−24.5113			−1.74636			−0.873178	+	0.487401i	$0.837945\pi$
$198$	5.44466			0.386935
$199$	−8.23305	−	14.2601i	−0.583625	−	1.01087i	−0.995045	−	0.0994230i	$-0.968300\pi$
$199$	−8.23305	−	14.2601i	−0.583625	−	1.01087i	0.411420	−	0.911446i	$-0.365033\pi$
$200$	−4.32916	−	7.49833i	−0.306118	−	0.530212i
$201$	0.189739			0.0133832
$202$	0.425277			0.0299224
$203$	−0.0494633	−	0.0856730i	−0.00347165	−	0.00601307i
$204$	−0.171356	+	0.296797i	−0.0119973	+	0.0207799i
$205$	14.5329	+	25.1717i	1.01502	+	1.75807i
$206$	2.26809	−	3.92845i	0.158025	−	0.273708i
$207$	−6.22153	+	10.7760i	−0.432426	+	0.748984i
$208$	4.89149			0.339164
$209$		0			0
$210$	−2.09975			−0.144897
$211$	−13.7402	+	23.7988i	−0.945916	+	1.63837i	−0.192010	+	0.981393i	$0.561501\pi$
$211$	−13.7402	+	23.7988i	−0.945916	+	1.63837i	−0.753906	+	0.656982i	$0.771833\pi$
$212$	−4.97120	+	8.61038i	−0.341424	+	0.591363i
$213$	−7.36363	−	12.7542i	−0.504547	−	0.873902i
$214$	1.58576	−	2.74661i	0.108400	−	0.187754i
$215$	10.4131	+	18.0360i	0.710167	+	1.23005i
$216$	−5.58721			−0.380161
$217$	−1.53971			−0.104522
$218$	3.39056	+	5.87262i	0.229638	+	0.397744i
$219$	−0.913147	−	1.58162i	−0.0617048	−	0.106876i
$220$	−14.8925			−1.00405
$221$	1.30550			0.0878178
$222$	−0.930333	−	1.61138i	−0.0624399	−	0.108149i
$223$	−10.1853	+	17.6414i	−0.682058	+	1.18136i	0.292294	+	0.956329i	$0.405581\pi$
$223$	−10.1853	+	17.6414i	−0.682058	+	1.18136i	−0.974352	+	0.225030i	$0.927752\pi$
$224$	0.221232	+	0.383185i	0.0147817	+	0.0256026i
$225$	5.84931	−	10.1313i	0.389954	−	0.675420i
$226$	5.02218	−	8.69866i	0.334070	−	0.578626i
$227$	−22.1493			−1.47010			−0.735051	−	0.678011i	$-0.762842\pi$
$227$	−22.1493			−1.47010			−0.735051	+	0.678011i	$0.762842\pi$
$228$		0			0
$229$	12.7148			0.840216			0.420108	−	0.907474i	$-0.361992\pi$
$229$	12.7148			0.840216			0.420108	+	0.907474i	$0.361992\pi$
$230$	17.0175	−	29.4752i	1.12210	−	1.94353i
$231$	−1.14475	+	1.98276i	−0.0753187	+	0.130456i
$232$	0.111791	+	0.193627i	0.00733942	+	0.0127123i
$233$	4.34088	−	7.51863i	0.284381	−	0.492562i	−0.688078	−	0.725637i	$-0.741545\pi$
$233$	4.34088	−	7.51863i	0.284381	−	0.492562i	0.972459	+	0.233075i	$0.0748787\pi$
$234$	3.30455	+	5.72364i	0.216025	+	0.374166i
$235$	8.12569			0.530062
$236$	−3.50953			−0.228451
$237$	−6.55097	−	11.3466i	−0.425531	−	0.737042i
$238$	0.0590452	+	0.102269i	0.00382733	+	0.00662913i
$239$	21.8749			1.41497			0.707485	−	0.706728i	$-0.249830\pi$
$239$	21.8749			1.41497			0.707485	+	0.706728i	$0.249830\pi$
$240$	4.74559			0.306327
$241$	9.48160	+	16.4226i	0.610764	+	1.05787i	0.991112	+	0.133031i	$0.0424709\pi$
$241$	9.48160	+	16.4226i	0.610764	+	1.05787i	−0.380348	+	0.924843i	$0.624196\pi$
$242$	−2.61913	+	4.53647i	−0.168364	+	0.291615i
$243$	−6.37701	−	11.0453i	−0.409085	−	0.708557i
$244$	−2.03977	+	3.53299i	−0.130583	+	0.226177i
$245$	12.5732	−	21.7775i	0.803275	−	1.39131i
$246$	−10.0989			−0.643884
$247$		0			0
$248$	3.47985			0.220971
$249$	2.11153	−	3.65727i	0.133813	−	0.231770i
$250$	−6.76007	+	11.7088i	−0.427545	+	0.740529i
$251$	−1.45138	−	2.51386i	−0.0916102	−	0.158673i	0.816579	−	0.577234i	$-0.195868\pi$
$251$	−1.45138	−	2.51386i	−0.0916102	−	0.158673i	−0.908189	+	0.418561i	$0.862535\pi$
$252$	−0.298915	+	0.517736i	−0.0188299	+	0.0326143i
$253$	−18.5552	−	32.1386i	−1.16656	−	2.02054i
$254$	14.0806			0.883495
$255$	1.26657			0.0793154
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.4525	−	19.8363i	−0.714388	−	1.23736i	−0.963195	−	0.268803i	$-0.913372\pi$
$257$	−11.4525	−	19.8363i	−0.714388	−	1.23736i	0.248807	−	0.968553i	$-0.419961\pi$
$258$	−7.23607			−0.450498
$259$	−0.641142			−0.0398386
$260$	−9.03879	−	15.6556i	−0.560562	−	0.970921i
$261$	−0.151045	+	0.261618i	−0.00934946	+	0.0161937i
$262$	−7.92075	−	13.7191i	−0.489346	−	0.847572i
$263$	2.53118	−	4.38413i	0.156079	−	0.270337i	−0.777372	−	0.629041i	$-0.783448\pi$
$263$	2.53118	−	4.38413i	0.156079	−	0.270337i	0.933452	+	0.358704i	$0.116781\pi$
$264$	2.58721	−	4.48118i	0.159232	−	0.275797i
$265$	36.7443			2.25719
$266$		0			0
$267$	−7.65407			−0.468421
$268$	−0.0738814	+	0.127966i	−0.00451303	+	0.00781679i
$269$	10.3710	−	17.9630i	0.632329	−	1.09523i	−0.354745	−	0.934963i	$-0.615432\pi$
$269$	10.3710	−	17.9630i	0.632329	−	1.09523i	0.987074	−	0.160263i	$-0.0512342\pi$
$270$	10.3244	+	17.8823i	0.628321	+	1.08828i
$271$	−3.14735	+	5.45137i	−0.191188	+	0.331147i	−0.945644	−	0.325203i	$-0.894567\pi$
$271$	−3.14735	+	5.45137i	−0.191188	+	0.331147i	0.754456	+	0.656350i	$0.227901\pi$
$272$	−0.133446	−	0.231136i	−0.00809138	−	0.0140147i
$273$	−2.77914			−0.168201
$274$	2.20744			0.133356
$275$	17.4451	+	30.2158i	1.05198	+	1.82208i
$276$	5.91273	+	10.2412i	0.355905	+	0.616445i
$277$	7.17608			0.431169			0.215584	−	0.976485i	$-0.430834\pi$
$277$	7.17608			0.431169			0.215584	+	0.976485i	$0.430834\pi$
$278$	−17.0644			−1.02346
$279$	2.35089	+	4.07185i	0.140744	+	0.243776i
$280$	0.817610	−	1.41614i	0.0488615	−	0.0846307i
$281$	−1.38696	−	2.40228i	−0.0827388	−	0.143308i	0.821687	−	0.569940i	$-0.193033\pi$
$281$	−1.38696	−	2.40228i	−0.0827388	−	0.143308i	−0.904425	+	0.426632i	$0.859700\pi$
$282$	−1.41164	+	2.44503i	−0.0840618	+	0.145599i
$283$	−3.87431	+	6.71049i	−0.230304	+	0.398897i	−0.957897	−	0.287111i	$-0.907305\pi$
$283$	−3.87431	+	6.71049i	−0.230304	+	0.398897i	0.727594	+	0.686008i	$0.240639\pi$
$284$	11.4691			0.680567
$285$		0			0
$286$	−19.7111			−1.16554
$287$	−1.73993	+	3.01364i	−0.102705	+	0.177890i
$288$	0.675571	−	1.17012i	0.0398084	−	0.0689501i
$289$	8.46438	+	14.6607i	0.497905	+	0.862397i
$290$	0.413147	−	0.715592i	0.0242608	−	0.0420210i
$291$	−2.62258	−	4.54243i	−0.153738	−	0.266282i
$292$	1.42226			0.0832315
$293$	−0.782870			−0.0457358			−0.0228679	−	0.999738i	$-0.507280\pi$
$293$	−0.782870			−0.0457358			−0.0228679	+	0.999738i	$0.507280\pi$
$294$	4.36858	+	7.56661i	0.254781	+	0.441293i
$295$	6.48511	+	11.2325i	0.377578	+	0.653983i
$296$	1.44903			0.0842230
$297$	22.5146			1.30643
$298$	−6.77288	−	11.7310i	−0.392342	−	0.679557i
$299$	22.5236	−	39.0120i	1.30257	−	2.25612i
$300$	−5.55899	−	9.62845i	−0.320948	−	0.555899i
$301$	−1.24669	+	2.15933i	−0.0718580	+	0.124462i
$302$	4.57659	−	7.92688i	0.263353	−	0.456141i
$303$	0.546090			0.0313720
$304$		0			0
$305$	15.0769			0.863298
$306$	0.180305	−	0.312297i	0.0103074	−	0.0178529i
$307$	14.0844	−	24.3949i	0.803839	−	1.39229i	−0.113234	−	0.993568i	$-0.536121\pi$
$307$	14.0844	−	24.3949i	0.803839	−	1.39229i	0.917072	−	0.398721i	$-0.130546\pi$
$308$	−0.891491	−	1.54411i	−0.0507974	−	0.0879837i
$309$	2.91241	−	5.04444i	0.165681	−	0.286968i
$310$	−6.43028	−	11.1376i	−0.365215	−	0.632571i
$311$	3.86827			0.219350			0.109675	−	0.993968i	$-0.465019\pi$
$311$	3.86827			0.219350			0.109675	+	0.993968i	$0.465019\pi$
$312$	6.28106			0.355595
$313$	−15.1939	−	26.3166i	−0.858809	−	1.48750i	−0.873065	−	0.487603i	$-0.837871\pi$
$313$	−15.1939	−	26.3166i	−0.858809	−	1.48750i	0.0142562	−	0.999898i	$-0.495462\pi$
$314$	8.19514	+	14.1944i	0.462479	+	0.801036i
$315$	2.20941			0.124486
$316$	10.2034			0.573985
$317$	−2.66402	−	4.61421i	−0.149626	−	0.259160i	0.781463	−	0.623951i	$-0.214474\pi$
$317$	−2.66402	−	4.61421i	−0.149626	−	0.259160i	−0.931089	+	0.364791i	$0.881140\pi$
$318$	−6.38342	+	11.0564i	−0.357964	+	0.620012i
$319$	−0.450480	−	0.780255i	−0.0252221	−	0.0436859i
$320$	−1.84786	+	3.20059i	−0.103298	+	0.178918i
$321$	2.03624	−	3.52687i	0.113652	−	0.196850i
$322$	4.07478			0.227079
$323$		0			0
$324$	−3.12099			−0.173389
$325$	−21.1761	+	36.6780i	−1.17464	+	2.03453i
$326$	6.88612	−	11.9271i	0.381387	−	0.660582i
$327$	4.35375	+	7.54091i	0.240763	+	0.417013i
$328$	3.93236	−	6.81105i	0.217128	−	0.376077i
$329$	0.486417	+	0.842500i	0.0268171	+	0.0464485i
$330$	−19.1232			−1.05270
$331$	−20.5480			−1.12942			−0.564711	−	0.825289i	$-0.691012\pi$
$331$	−20.5480			−1.12942			−0.564711	+	0.825289i	$0.691012\pi$
$332$	1.64439	+	2.84817i	0.0902476	+	0.156313i
$333$	0.978921	+	1.69554i	0.0536445	+	0.0929150i
$334$	−10.3328			−0.565386
$335$	0.546090			0.0298361
$336$	0.284079	+	0.492039i	0.0154978	+	0.0268429i
$337$	−6.64121	+	11.5029i	−0.361770	+	0.626603i	−0.988252	−	0.152832i	$-0.951161\pi$
$337$	−6.64121	+	11.5029i	−0.361770	+	0.626603i	0.626483	+	0.779435i	$0.284494\pi$
$338$	−5.46334	−	9.46279i	−0.297167	−	0.514708i
$339$	6.44887	−	11.1698i	0.350255	−	0.606659i
$340$	−0.493181	+	0.854214i	−0.0267465	+	0.0463262i
$341$	−14.0227			−0.759370
$342$		0			0
$343$	6.10787			0.329794
$344$	2.81761	−	4.88024i	0.151915	−	0.263125i
$345$	21.8518	−	37.8484i	1.17646	−	2.03769i
$346$	4.90601	+	8.49745i	0.263749	+	0.456826i
$347$	−15.0712	+	26.1040i	−0.809062	+	1.40134i	0.104452	+	0.994530i	$0.466691\pi$
$347$	−15.0712	+	26.1040i	−0.809062	+	1.40134i	−0.913514	+	0.406807i	$0.866642\pi$
$348$	0.143548	+	0.248633i	0.00769499	+	0.0133281i
$349$	35.0653			1.87700			0.938501	−	0.345277i	$-0.112215\pi$
$349$	35.0653			1.87700			0.938501	+	0.345277i	$0.112215\pi$
$350$	−3.83099			−0.204775
$351$	13.6649	+	23.6683i	0.729378	+	1.26332i
$352$	2.01484	+	3.48980i	0.107391	+	0.186007i
$353$	13.5411			0.720718			0.360359	−	0.932814i	$-0.382654\pi$
$353$	13.5411			0.720718			0.360359	+	0.932814i	$0.382654\pi$
$354$	−4.50651			−0.239518
$355$	−21.1933	−	36.7079i	−1.12482	−	1.94825i
$356$	2.98037	−	5.16216i	0.157959	−	0.273594i
$357$	0.0758187	+	0.131322i	0.00401275	+	0.00695029i
$358$	4.39915	−	7.61955i	0.232502	−	0.402706i
$359$	11.7536	−	20.3579i	0.620332	−	1.07445i	−0.369092	−	0.929393i	$-0.620331\pi$
$359$	11.7536	−	20.3579i	0.620332	−	1.07445i	0.989424	−	0.145053i	$-0.0463354\pi$
$360$	−4.99344			−0.263177
$361$		0			0
$362$	14.5278			0.763562
$363$	−3.36317	+	5.82518i	−0.176521	+	0.305743i
$364$	1.08215	−	1.87434i	0.0567202	−	0.0982423i
$365$	−2.62814	−	4.55206i	−0.137563	−	0.238266i
$366$	−2.61923	+	4.53664i	−0.136909	+	0.237134i
$367$	6.34644	+	10.9924i	0.331282	+	0.573796i	0.982763	−	0.184868i	$-0.0591857\pi$
$367$	6.34644	+	10.9924i	0.331282	+	0.573796i	−0.651482	+	0.758664i	$0.725852\pi$
$368$	−9.20930			−0.480068
$369$	10.6264			0.553186
$370$	−2.67760	−	4.63774i	−0.139202	−	0.241104i
$371$	2.19958	+	3.80978i	0.114196	+	0.197794i
$372$	4.46841			0.231676
$373$	2.64950			0.137186			0.0685930	−	0.997645i	$-0.478149\pi$
$373$	2.64950			0.137186			0.0685930	+	0.997645i	$0.478149\pi$
$374$	0.537746	+	0.931403i	0.0278062	+	0.0481617i
$375$	−8.68047	+	15.0350i	−0.448257	+	0.776405i
$376$	−1.09934	−	1.90411i	−0.0566941	−	0.0981970i
$377$	0.546824	−	0.947126i	0.0281629	−	0.0487795i
$378$	−1.23607	+	2.14093i	−0.0635765	+	0.110118i
$379$	18.1672			0.933187			0.466593	−	0.884472i	$-0.345481\pi$
$379$	18.1672			0.933187			0.466593	+	0.884472i	$0.345481\pi$
$380$		0			0
$381$	18.0806			0.926297
$382$	−6.36508	+	11.0246i	−0.325666	+	0.564070i
$383$	−11.5042	+	19.9258i	−0.587835	+	1.01816i	0.406680	+	0.913570i	$0.366686\pi$
$383$	−11.5042	+	19.9258i	−0.587835	+	1.01816i	−0.994515	+	0.104590i	$0.966647\pi$
$384$	−0.642040	−	1.11205i	−0.0327639	−	0.0567488i
$385$	−3.29470	+	5.70659i	−0.167913	+	0.290835i
$386$	−8.73903	−	15.1364i	−0.444805	−	0.770425i
$387$	7.61398			0.387040
$388$	4.08476			0.207372
$389$	8.28531	+	14.3506i	0.420082	+	0.727603i	0.995947	−	0.0899414i	$-0.0286680\pi$
$389$	8.28531	+	14.3506i	0.420082	+	0.727603i	−0.575865	+	0.817545i	$0.695335\pi$
$390$	−11.6065	−	20.1031i	−0.587719	−	1.01796i
$391$	−2.45790			−0.124301
$392$	−6.80423			−0.343665
$393$	−10.1709	−	17.6165i	−0.513053	−	0.888633i
$394$	12.2556	−	21.2274i	0.617430	−	1.06942i
$395$	−18.8544	−	32.6568i	−0.948668	−	1.64314i
$396$	−2.72233	+	4.71521i	−0.136802	+	0.236948i
$397$	8.89741	−	15.4108i	0.446548	−	0.773444i	−0.551610	−	0.834102i	$-0.685986\pi$
$397$	8.89741	−	15.4108i	0.446548	−	0.773444i	0.998159	+	0.0606575i	$0.0193197\pi$
$398$	16.4661			0.825371
$399$		0			0
$400$	8.65833			0.432916
$401$	−15.3107	+	26.5190i	−0.764582	+	1.32429i	0.175886	+	0.984411i	$0.443721\pi$
$401$	−15.3107	+	26.5190i	−0.764582	+	1.32429i	−0.940468	+	0.339884i	$0.889612\pi$
$402$	−0.0948696	+	0.164319i	−0.00473167	+	0.00819549i
$403$	−8.51084	−	14.7412i	−0.423955	−	0.734311i
$404$	−0.212639	+	0.368301i	−0.0105792	+	0.0183237i
$405$	5.76716	+	9.98901i	0.286572	+	0.496358i
$406$	0.0989267			0.00490965
$407$	−5.83911			−0.289434
$408$	−0.171356	−	0.296797i	−0.00848338	−	0.0146936i
$409$	−4.57164	−	7.91831i	−0.226053	−	0.391535i	0.730582	−	0.682825i	$-0.239249\pi$
$409$	−4.57164	−	7.91831i	−0.226053	−	0.391535i	−0.956635	+	0.291290i	$0.905916\pi$
$410$	−29.0658			−1.43546
$411$	2.83452			0.139817
$412$	2.26809	+	3.92845i	0.111741	+	0.193541i
$413$	−0.776418	+	1.34480i	−0.0382051	+	0.0661731i
$414$	−6.22153	−	10.7760i	−0.305772	−	0.529612i
$415$	6.07720	−	10.5260i	0.298318	−	0.516702i
$416$	−2.44575	+	4.23616i	−0.119913	+	0.207695i
$417$	−21.9121			−1.07304
$418$		0			0
$419$	12.6157			0.616315			0.308158	−	0.951335i	$-0.400288\pi$
$419$	12.6157			0.616315			0.308158	+	0.951335i	$0.400288\pi$
$420$	1.04988	−	1.81844i	0.0512287	−	0.0887307i
$421$	−16.6277	+	28.8000i	−0.810383	+	1.40362i	0.102213	+	0.994762i	$0.467408\pi$
$421$	−16.6277	+	28.8000i	−0.810383	+	1.40362i	−0.912596	+	0.408862i	$0.865926\pi$
$422$	−13.7402	−	23.7988i	−0.668864	−	1.15851i
$423$	1.48536	−	2.57272i	0.0722208	−	0.125090i
$424$	−4.97120	−	8.61038i	−0.241423	−	0.418157i
$425$	2.31085			0.112093
$426$	14.7273			0.713538
$427$	0.902526	+	1.56322i	0.0436763	+	0.0756495i
$428$	1.58576	+	2.74661i	0.0766504	+	0.132762i
$429$	−25.3106			−1.22201
$430$	−20.8262			−1.00433
$431$	11.4957	+	19.9112i	0.553730	+	0.959088i	0.998001	+	0.0631958i	$0.0201293\pi$
$431$	11.4957	+	19.9112i	0.553730	+	0.959088i	−0.444271	+	0.895892i	$0.646537\pi$
$432$	2.79360	−	4.83866i	0.134407	−	0.232800i
$433$	−17.3546	−	30.0591i	−0.834010	−	1.44455i	−0.894834	−	0.446399i	$-0.852706\pi$
$433$	−17.3546	−	30.0591i	−0.834010	−	1.44455i	0.0608241	−	0.998148i	$-0.480627\pi$
$434$	0.769854	−	1.33343i	0.0369542	−	0.0640065i
$435$	0.530514	−	0.918877i	0.0254362	−	0.0440568i
$436$	−6.78112			−0.324757
$437$		0			0
$438$	1.82629			0.0872637
$439$	18.2409	−	31.5942i	0.870591	−	1.50791i	0.00920482	−	0.999958i	$-0.497070\pi$
$439$	18.2409	−	31.5942i	0.870591	−	1.50791i	0.861386	−	0.507950i	$-0.169597\pi$
$440$	7.44627	−	12.8973i	0.354987	−	0.614855i
$441$	−4.59673	−	7.96178i	−0.218892	−	0.379132i
$442$	−0.652752	+	1.13060i	−0.0310483	+	0.0537772i
$443$	−5.87915	−	10.1830i	−0.279327	−	0.483808i	0.691891	−	0.722002i	$-0.256778\pi$
$443$	−5.87915	−	10.1830i	−0.279327	−	0.483808i	−0.971218	+	0.238194i	$0.923445\pi$
$444$	1.86067			0.0883033
$445$	−22.0292			−1.04429
$446$	−10.1853	−	17.6414i	−0.482288	−	0.835347i
$447$	−8.69691	−	15.0635i	−0.411350	−	0.712479i
$448$	−0.442463			−0.0209044
$449$	−8.69102			−0.410154			−0.205077	−	0.978746i	$-0.565745\pi$
$449$	−8.69102			−0.410154			−0.205077	+	0.978746i	$0.565745\pi$
$450$	5.84931	+	10.1313i	0.275739	+	0.477594i
$451$	−15.8461	+	27.4463i	−0.746165	+	1.29240i
$452$	5.02218	+	8.69866i	0.236223	+	0.409151i
$453$	5.87670	−	10.1787i	0.276111	−	0.478239i
$454$	11.0747	−	19.1819i	0.519760	−	0.900250i
$455$	−7.99866			−0.374983
$456$		0			0
$457$	−13.0286			−0.609454			−0.304727	−	0.952440i	$-0.598565\pi$
$457$	−13.0286			−0.609454			−0.304727	+	0.952440i	$0.598565\pi$
$458$	−6.35738	+	11.0113i	−0.297061	+	0.514525i
$459$	0.745593	−	1.29141i	0.0348013	−	0.0602777i
$460$	17.0175	+	29.4752i	0.793444	+	1.37429i
$461$	−4.52130	+	7.83112i	−0.210578	+	0.364732i	−0.951896	−	0.306423i	$-0.900868\pi$
$461$	−4.52130	+	7.83112i	−0.210578	+	0.364732i	0.741318	+	0.671154i	$0.234201\pi$
$462$	−1.14475	−	1.98276i	−0.0532584	−	0.0922462i
$463$	−17.7205			−0.823542			−0.411771	−	0.911287i	$-0.635090\pi$
$463$	−17.7205			−0.823542			−0.411771	+	0.911287i	$0.635090\pi$
$464$	−0.223582			−0.0103795
$465$	−8.25698	−	14.3015i	−0.382908	−	0.663217i
$466$	4.34088	+	7.51863i	0.201087	+	0.348294i
$467$	−7.87772			−0.364537			−0.182269	−	0.983249i	$-0.558344\pi$
$467$	−7.87772			−0.364537			−0.182269	+	0.983249i	$0.558344\pi$
$468$	−6.60909			−0.305506
$469$	0.0326898	+	0.0566205i	0.00150948	+	0.00261449i
$470$	−4.06285	+	7.03706i	−0.187405	+	0.324595i
$471$	10.5232	+	18.2267i	0.484884	+	0.839844i
$472$	1.75476	−	3.03934i	0.0807695	−	0.139897i
$473$	−11.3540	+	19.6658i	−0.522060	+	0.904234i
$474$	13.1019			0.601792
$475$		0			0
$476$	−0.118090			−0.00541266
$477$	6.71680	−	11.6338i	0.307541	−	0.532677i
$478$	−10.9375	+	18.9442i	−0.500267	+	0.866489i
$479$	15.0899	+	26.1365i	0.689476	+	1.19421i	0.972008	+	0.234949i	$0.0754924\pi$
$479$	15.0899	+	26.1365i	0.689476	+	1.19421i	−0.282532	+	0.959258i	$0.591174\pi$
$480$	−2.37280	+	4.10980i	−0.108303	+	0.187586i
$481$	−3.54395	−	6.13831i	−0.161590	−	0.279883i
$482$	−18.9632			−0.863751
$483$	5.23234			0.238080
$484$	−2.61913	−	4.53647i	−0.119051	−	0.206203i
$485$	−7.54806	−	13.0736i	−0.342740	−	0.593642i
$486$	12.7540			0.578534
$487$	35.7699			1.62089			0.810445	−	0.585814i	$-0.199225\pi$
$487$	35.7699			1.62089			0.810445	+	0.585814i	$0.199225\pi$
$488$	−2.03977	−	3.53299i	−0.0923362	−	0.159931i
$489$	8.84233	−	15.3154i	0.399864	−	0.692585i
$490$	12.5732	+	21.7775i	0.568001	+	0.983807i
$491$	9.13632	−	15.8246i	0.412316	−	0.714153i	−0.582826	−	0.812597i	$-0.698053\pi$
$491$	9.13632	−	15.8246i	0.412316	−	0.714153i	0.995143	+	0.0984441i	$0.0313866\pi$
$492$	5.04946	−	8.74593i	0.227647	−	0.394297i
$493$	−0.0596724			−0.00268751
$494$		0			0
$495$	20.1219			0.904413
$496$	−1.73993	+	3.01364i	−0.0781250	+	0.135316i
$497$	2.53733	−	4.39479i	0.113815	−	0.197133i
$498$	2.11153	+	3.65727i	0.0946197	+	0.163886i
$499$	−8.84899	+	15.3269i	−0.396135	+	0.686126i	−0.993245	−	0.116033i	$-0.962982\pi$
$499$	−8.84899	+	15.3269i	−0.396135	+	0.686126i	0.597110	+	0.802159i	$0.296316\pi$
$500$	−6.76007	−	11.7088i	−0.302320	−	0.523633i
$501$	−13.2681			−0.592777
$502$	2.90276			0.129556
$503$	5.09512	+	8.82501i	0.227180	+	0.393488i	0.956971	−	0.290182i	$-0.0937160\pi$
$503$	5.09512	+	8.82501i	0.227180	+	0.393488i	−0.729791	+	0.683670i	$0.760383\pi$
$504$	−0.298915	−	0.517736i	−0.0133147	−	0.0230618i
$505$	1.57171			0.0699400
$506$	37.1105			1.64976
$507$	−7.01537	−	12.1510i	−0.311563	−	0.539644i
$508$	−7.04029	+	12.1941i	−0.312363	+	0.541028i
$509$	4.21811	+	7.30598i	0.186964	+	0.323832i	0.944237	−	0.329268i	$-0.106802\pi$
$509$	4.21811	+	7.30598i	0.186964	+	0.323832i	−0.757272	+	0.653099i	$0.773468\pi$
$510$	−0.633283	+	1.09688i	−0.0280422	+	0.0485706i
$511$	0.314649	−	0.544988i	0.0139193	−	0.0241089i
$512$	1.00000			0.0441942
$513$		0			0
$514$	22.9050			1.01030
$515$	8.38222	−	14.5184i	0.369365	−	0.639759i
$516$	3.61803	−	6.26662i	0.159275	−	0.275873i
$517$	4.42998	+	7.67295i	0.194830	+	0.337456i
$518$	0.320571	−	0.555245i	0.0140851	−	0.0243961i
$519$	6.29970	+	10.9114i	0.276526	+	0.478957i
$520$	18.0776			0.792754
$521$	8.96365			0.392705			0.196352	−	0.980533i	$-0.437090\pi$
$521$	8.96365			0.392705			0.196352	+	0.980533i	$0.437090\pi$
$522$	−0.151045	−	0.261618i	−0.00661107	−	0.0114507i
$523$	1.06997	+	1.85324i	0.0467864	+	0.0810364i	0.888470	−	0.458934i	$-0.151769\pi$
$523$	1.06997	+	1.85324i	0.0467864	+	0.0810364i	−0.841684	+	0.539971i	$0.818435\pi$
$524$	15.8415			0.692039
$525$	−4.91930			−0.214696
$526$	2.53118	+	4.38413i	0.110365	+	0.191157i
$527$	−0.464374	+	0.804320i	−0.0202285	+	0.0350367i
$528$	2.58721	+	4.48118i	0.112594	+	0.195018i
$529$	−30.9056	+	53.5301i	−1.34372	+	2.32739i
$530$	−18.3722	+	31.8215i	−0.798036	+	1.38224i
$531$	4.74186			0.205779
$532$		0			0
$533$	−38.4702			−1.66633
$534$	3.82703	−	6.62862i	0.165612	−	0.286848i
$535$	5.86051	−	10.1507i	0.253372	−	0.438853i
$536$	−0.0738814	−	0.127966i	−0.00319119	−	0.00552731i
$537$	5.64886	−	9.78411i	0.243766	−	0.422216i
$538$	10.3710	+	17.9630i	0.447124	+	0.774442i
$539$	27.4188			1.18101
$540$	−20.6487			−0.888581
$541$	5.85577	+	10.1425i	0.251759	+	0.436060i	0.964010	−	0.265865i	$-0.0856575\pi$
$541$	5.85577	+	10.1425i	0.251759	+	0.436060i	−0.712251	+	0.701925i	$0.752324\pi$
$542$	−3.14735	−	5.45137i	−0.135190	−	0.234156i
$543$	18.6548			0.800553
$544$	0.266893			0.0114429
$545$	12.5305	+	21.7035i	0.536750	+	0.929678i
$546$	1.38957	−	2.40681i	0.0594681	−	0.103002i
$547$	12.4948	+	21.6417i	0.534240	+	0.925332i	0.999200	+	0.0399995i	$0.0127356\pi$
$547$	12.4948	+	21.6417i	0.534240	+	0.925332i	−0.464959	+	0.885332i	$0.653931\pi$
$548$	−1.10372	+	1.91169i	−0.0471485	+	0.0816636i
$549$	2.75602	−	4.77357i	0.117624	−	0.203731i
$550$	−34.8902			−1.48772
$551$		0			0
$552$	−11.8255			−0.503325
$553$	2.25731	−	3.90978i	0.0959906	−	0.166261i
$554$	−3.58804	+	6.21467i	−0.152441	+	0.264036i
$555$	−3.43825	−	5.95522i	−0.145946	−	0.252785i
$556$	8.53222	−	14.7782i	0.361847	−	0.626737i
$557$	−4.59783	−	7.96368i	−0.194816	−	0.337432i	0.752024	−	0.659136i	$-0.229078\pi$
$557$	−4.59783	−	7.96368i	−0.194816	−	0.337432i	−0.946840	+	0.321704i	$0.895744\pi$
$558$	−4.70177			−0.199042
$559$	−27.5646			−1.16586
$560$	0.817610	+	1.41614i	0.0345503	+	0.0598429i
$561$	0.690508	+	1.19599i	0.0291533	+	0.0504949i
$562$	2.77391			0.117010
$563$	19.7224			0.831202			0.415601	−	0.909547i	$-0.363571\pi$
$563$	19.7224			0.831202			0.415601	+	0.909547i	$0.363571\pi$
$564$	−1.41164	−	2.44503i	−0.0594407	−	0.102954i
$565$	18.5605	−	32.1478i	0.780848	−	1.35247i
$566$	−3.87431	−	6.71049i	−0.162849	−	0.282063i
$567$	−0.690463	+	1.19592i	−0.0289967	+	0.0502238i
$568$	−5.73456	+	9.93255i	−0.240617	+	0.416760i
$569$	22.1469			0.928446			0.464223	−	0.885718i	$-0.346334\pi$
$569$	22.1469			0.928446			0.464223	+	0.885718i	$0.346334\pi$
$570$		0			0
$571$	−3.02145			−0.126444			−0.0632218	−	0.998000i	$-0.520138\pi$
$571$	−3.02145			−0.126444			−0.0632218	+	0.998000i	$0.520138\pi$
$572$	9.85555	−	17.0703i	0.412081	−	0.713746i
$573$	−8.17327	+	14.1565i	−0.341443	+	0.591397i
$574$	−1.73993	−	3.01364i	−0.0726231	−	0.125787i
$575$	39.8686	−	69.0544i	1.66263	−	2.87977i
$576$	0.675571	+	1.17012i	0.0281488	+	0.0487551i
$577$	2.30938			0.0961407			0.0480704	−	0.998844i	$-0.484693\pi$
$577$	2.30938			0.0961407			0.0480704	+	0.998844i	$0.484693\pi$
$578$	−16.9288			−0.704144
$579$	−11.2216	−	19.4364i	−0.466354	−	0.807749i
$580$	0.413147	+	0.715592i	0.0171550	+	0.0297133i
$581$	1.45516			0.0603704
$582$	5.24515			0.217419
$583$	20.0323	+	34.6970i	0.829654	+	1.43700i
$584$	−0.711130	+	1.23171i	−0.0294268	+	0.0509687i
$585$	12.2127	+	21.1530i	0.504932	+	0.874568i
$586$	0.391435	−	0.677985i	0.0161700	−	0.0280073i
$587$	−14.0445	+	24.3258i	−0.579679	+	1.00403i	0.415837	+	0.909439i	$0.363489\pi$
$587$	−14.0445	+	24.3258i	−0.579679	+	1.00403i	−0.995516	+	0.0945942i	$0.969845\pi$
$588$	−8.73716			−0.360315
$589$		0			0
$590$	−12.9702			−0.533975
$591$	15.7372	−	27.2576i	0.647342	−	1.12123i
$592$	−0.724514	+	1.25490i	−0.0297773	+	0.0515759i
$593$	6.04695	+	10.4736i	0.248318	+	0.430100i	0.963059	−	0.269289i	$-0.0867887\pi$
$593$	6.04695	+	10.4736i	0.248318	+	0.430100i	−0.714741	+	0.699389i	$0.753455\pi$
$594$	−11.2573	+	19.4982i	−0.461893	+	0.800022i
$595$	0.218214	+	0.377958i	0.00894592	+	0.0154948i
$596$	13.5458			0.554856
$597$	21.1438			0.865357
$598$	22.5236	+	39.0120i	0.921059	+	1.59532i
$599$	−9.75126	−	16.8897i	−0.398426	−	0.690094i	0.595106	−	0.803647i	$-0.297110\pi$
$599$	−9.75126	−	16.8897i	−0.398426	−	0.690094i	−0.993532	+	0.113554i	$0.963777\pi$
$600$	11.1180			0.453890
$601$	−38.9632			−1.58934			−0.794671	−	0.607040i	$-0.792357\pi$
$601$	−38.9632			−1.58934			−0.794671	+	0.607040i	$0.792357\pi$
$602$	−1.24669	−	2.15933i	−0.0508113	−	0.0880077i
$603$	0.0998242	−	0.172901i	0.00406516	−	0.00704106i
$604$	4.57659	+	7.92688i	0.186219	+	0.322540i
$605$	−9.67957	+	16.7655i	−0.393530	+	0.681614i
$606$	−0.273045	+	0.472928i	−0.0110917	+	0.0192114i
$607$	8.46029			0.343393			0.171696	−	0.985150i	$-0.445075\pi$
$607$	8.46029			0.343393			0.171696	+	0.985150i	$0.445075\pi$
$608$		0			0
$609$	0.127030			0.00514750
$610$	−7.53843	+	13.0569i	−0.305222	+	0.528660i
$611$	−5.37741	+	9.31394i	−0.217547	+	0.376802i
$612$	0.180305	+	0.312297i	0.00728840	+	0.0126239i
$613$	1.45746	−	2.52440i	0.0588664	−	0.101960i	−0.835090	−	0.550113i	$-0.814585\pi$
$613$	1.45746	−	2.52440i	0.0588664	−	0.101960i	0.893957	+	0.448153i	$0.147918\pi$
$614$	14.0844	+	24.3949i	0.568400	+	0.984497i
$615$	−37.3228			−1.50500
$616$	1.78298			0.0718384
$617$	1.50953	+	2.61457i	0.0607712	+	0.105259i	0.894810	−	0.446446i	$-0.147311\pi$
$617$	1.50953	+	2.61457i	0.0607712	+	0.105259i	−0.834039	+	0.551705i	$0.813977\pi$
$618$	2.91241	+	5.04444i	0.117154	+	0.202917i
$619$	−3.92813			−0.157885			−0.0789423	−	0.996879i	$-0.525154\pi$
$619$	−3.92813			−0.157885			−0.0789423	+	0.996879i	$0.525154\pi$
$620$	12.8606			0.516492
$621$	−25.7271	−	44.5607i	−1.03239	−	1.78816i
$622$	−1.93414	+	3.35002i	−0.0775518	+	0.134324i
$623$	−1.31871	−	2.28407i	−0.0528328	−	0.0915092i
$624$	−3.14053	+	5.43956i	−0.125722	+	0.217757i
$625$	−3.33750	+	5.78072i	−0.133500	+	0.231229i
$626$	30.3878			1.21454
$627$		0			0
$628$	−16.3903			−0.654043
$629$	−0.193368	+	0.334923i	−0.00771007	+	0.0133542i
$630$	−1.10471	+	1.91341i	−0.0440126	+	0.0762320i
$631$	−5.06836	−	8.77865i	−0.201768	−	0.349473i	0.747330	−	0.664453i	$-0.231335\pi$
$631$	−5.06836	−	8.77865i	−0.201768	−	0.349473i	−0.949098	+	0.314980i	$0.898002\pi$
$632$	−5.10169	+	8.83638i	−0.202934	+	0.351493i
$633$	−17.6435	−	30.5595i	−0.701268	−	1.21463i
$634$	5.32803			0.211603
$635$	52.0379			2.06506
$636$	−6.38342	−	11.0564i	−0.253119	−	0.438415i
$637$	16.6414	+	28.8238i	0.659357	+	1.14204i
$638$	0.900961			0.0356694
$639$	−15.4964			−0.613028
$640$	−1.84786	−	3.20059i	−0.0730430	−	0.126514i
$641$	−4.14015	+	7.17096i	−0.163526	+	0.283236i	−0.936131	−	0.351652i	$-0.885620\pi$
$641$	−4.14015	+	7.17096i	−0.163526	+	0.283236i	0.772605	+	0.634887i	$0.218954\pi$
$642$	2.03624	+	3.52687i	0.0803639	+	0.139194i
$643$	−18.4270	+	31.9166i	−0.726691	+	1.25867i	0.231583	+	0.972815i	$0.425610\pi$
$643$	−18.4270	+	31.9166i	−0.726691	+	1.25867i	−0.958274	+	0.285851i	$0.907724\pi$
$644$	−2.03739	+	3.52886i	−0.0802844	+	0.139057i
$645$	−26.7425			−1.05298
$646$		0			0
$647$	−20.1901			−0.793753			−0.396876	−	0.917872i	$-0.629906\pi$
$647$	−20.1901			−0.793753			−0.396876	+	0.917872i	$0.629906\pi$
$648$	1.56050	−	2.70286i	0.0613021	−	0.106178i
$649$	−7.07112	+	12.2475i	−0.277566	+	0.480758i
$650$	−21.1761	−	36.6780i	−0.830594	−	1.43863i
$651$	0.988553	−	1.71222i	0.0387445	−	0.0671074i
$652$	6.88612	+	11.9271i	0.269681	+	0.467102i
$653$	−22.0387			−0.862443			−0.431221	−	0.902246i	$-0.641917\pi$
$653$	−22.0387			−0.862443			−0.431221	+	0.902246i	$0.641917\pi$
$654$	−8.70749			−0.340490
$655$	−29.2729	−	50.7021i	−1.14379	−	1.98109i
$656$	3.93236	+	6.81105i	0.153533	+	0.265927i
$657$	−1.92167			−0.0749716
$658$	−0.972835			−0.0379251
$659$	13.6108	+	23.5746i	0.530202	+	0.918336i	0.999379	+	0.0352322i	$0.0112171\pi$
$659$	13.6108	+	23.5746i	0.530202	+	0.918336i	−0.469178	+	0.883104i	$0.655450\pi$
$660$	9.56159	−	16.5612i	0.372185	−	0.644643i
$661$	4.45412	+	7.71477i	0.173245	+	0.300070i	0.939553	−	0.342404i	$-0.111241\pi$
$661$	4.45412	+	7.71477i	0.173245	+	0.300070i	−0.766307	+	0.642474i	$0.777908\pi$
$662$	10.2740	−	17.7951i	0.399311	−	0.691627i
$663$	−0.838186	+	1.45178i	−0.0325524	+	0.0563825i
$664$	−3.28878			−0.127629
$665$		0			0
$666$	−1.95784			−0.0758648
$667$	−1.02951	+	1.78317i	−0.0398630	+	0.0690447i
$668$	5.16640	−	8.94847i	0.199894	−	0.346227i
$669$	−13.0787	−	22.6530i	−0.505653	−	0.875816i
$670$	−0.273045	+	0.472928i	−0.0105486	+	0.0182708i
$671$	8.21962	+	14.2368i	0.317315	+	0.549606i
$672$	−0.568158			−0.0219172
$673$	35.7010			1.37617			0.688087	−	0.725629i	$-0.258451\pi$
$673$	35.7010			1.37617			0.688087	+	0.725629i	$0.258451\pi$
$674$	−6.64121	−	11.5029i	−0.255810	−	0.443076i
$675$	24.1879	+	41.8947i	0.930994	+	1.61253i
$676$	10.9267			0.420257
$677$	−27.3849			−1.05249			−0.526243	−	0.850334i	$-0.676400\pi$
$677$	−27.3849			−1.05249			−0.526243	+	0.850334i	$0.676400\pi$
$678$	6.44887	+	11.1698i	0.247667	+	0.428972i
$679$	0.903678	−	1.56522i	0.0346800	−	0.0600675i
$680$	−0.493181	−	0.854214i	−0.0189126	−	0.0327576i
$681$	14.2207	−	24.6311i	0.544940	−	0.943864i
$682$	7.01133	−	12.1440i	0.268478	−	0.465017i
$683$	−38.1521			−1.45985			−0.729925	−	0.683528i	$-0.760445\pi$
$683$	−38.1521			−1.45985			−0.729925	+	0.683528i	$0.760445\pi$
$684$		0			0
$685$	8.15806			0.311703
$686$	−3.05393	+	5.28957i	−0.116600	+	0.201957i
$687$	−8.16338	+	14.1394i	−0.311453	+	0.539452i
$688$	2.81761	+	4.88024i	0.107420	+	0.186058i
$689$	−24.3166	+	42.1176i	−0.926389	+	1.60455i
$690$	21.8518	+	37.8484i	0.831884	+	1.44086i
$691$	−28.2058			−1.07300			−0.536499	−	0.843901i	$-0.680254\pi$
$691$	−28.2058			−1.07300			−0.536499	+	0.843901i	$0.680254\pi$
$692$	−9.81201			−0.372997
$693$	1.20453	+	2.08631i	0.0457563	+	0.0792523i
$694$	−15.0712	−	26.1040i	−0.572094	−	0.990895i
$695$	−63.0654			−2.39221
$696$	−0.287096			−0.0108824
$697$	1.04952	+	1.81782i	0.0397534	+	0.0688549i
$698$	−17.5326	+	30.3674i	−0.663620	+	1.14942i
$699$	5.57404	+	9.65451i	0.210829	+	0.365167i
$700$	1.91550	−	3.31774i	0.0723990	−	0.125399i
$701$	−21.3074	+	36.9055i	−0.804769	+	1.39390i	0.111678	+	0.993744i	$0.464378\pi$
$701$	−21.3074	+	36.9055i	−0.804769	+	1.39390i	−0.916447	+	0.400157i	$0.868956\pi$
$702$	−27.3298			−1.03150
$703$		0			0
$704$	−4.02967			−0.151874
$705$	−5.21702	+	9.03614i	−0.196484	+	0.340321i
$706$	−6.77053	+	11.7269i	−0.254812	+	0.441348i
$707$	0.0940849	+	0.162960i	0.00353843	+	0.00612873i
$708$	2.25325	−	3.90275i	0.0846825	−	0.146674i
$709$	11.3446	+	19.6494i	0.426055	+	0.737949i	0.996518	−	0.0833743i	$-0.0265697\pi$
$709$	11.3446	+	19.6494i	0.426055	+	0.737949i	−0.570463	+	0.821323i	$0.693236\pi$
$710$	42.3866			1.59074
$711$	−13.7862			−0.517023
$712$	2.98037	+	5.16216i	0.111694	+	0.193460i
$713$	16.0235	+	27.7535i	0.600085	+	1.03938i
$714$	−0.151637			−0.00567489
$715$	−72.8467			−2.72431
$716$	4.39915	+	7.61955i	0.164404	+	0.284756i
$717$	−14.0446	+	24.3259i	−0.524503	+	0.908467i
$718$	11.7536	+	20.3579i	0.438641	+	0.759748i
$719$	18.9162	−	32.7638i	0.705456	−	1.22188i	−0.261071	−	0.965320i	$-0.584076\pi$
$719$	18.9162	−	32.7638i	0.705456	−	1.22188i	0.966527	−	0.256565i	$-0.0825909\pi$
$720$	2.49672	−	4.32444i	0.0930472	−	0.161162i
$721$	2.00709			0.0747481
$722$		0			0
$723$	−24.3503			−0.905596
$724$	−7.26388	+	12.5814i	−0.269960	+	0.467584i
$725$	0.967921	−	1.67649i	0.0359477	−	0.0622632i
$726$	−3.36317	−	5.82518i	−0.124819	−	0.216193i
$727$	9.77015	−	16.9224i	0.362355	−	0.627617i	−0.625993	−	0.779829i	$-0.715306\pi$
$727$	9.77015	−	16.9224i	0.362355	−	0.627617i	0.988348	+	0.152212i	$0.0486395\pi$
$728$	1.08215	+	1.87434i	0.0401073	+	0.0694678i
$729$	25.7402			0.953339
$730$	5.25627			0.194543
$731$	0.752000	+	1.30250i	0.0278137	+	0.0481748i
$732$	−2.61923	−	4.53664i	−0.0968096	−	0.167679i
$733$	35.1101			1.29682			0.648410	−	0.761291i	$-0.275434\pi$
$733$	35.1101			1.29682			0.648410	+	0.761291i	$0.275434\pi$
$734$	−12.6929			−0.468503
$735$	16.1450	+	27.9640i	0.595519	+	1.03147i
$736$	4.60465	−	7.97549i	0.169730	−	0.293980i
$737$	0.297718	+	0.515663i	0.0109666	+	0.0189947i
$738$	−5.31318	+	9.20269i	−0.195581	+	0.338756i
$739$	8.13874	−	14.0967i	0.299388	−	0.518556i	−0.676608	−	0.736344i	$-0.736551\pi$
$739$	8.13874	−	14.0967i	0.299388	−	0.518556i	0.975996	+	0.217788i	$0.0698841\pi$
$740$	5.35520			0.196861
$741$		0			0
$742$	−4.39915			−0.161498
$743$	−16.6543	+	28.8460i	−0.610986	+	1.05826i	0.380089	+	0.924950i	$0.375893\pi$
$743$	−16.6543	+	28.8460i	−0.610986	+	1.05826i	−0.991075	+	0.133309i	$0.957440\pi$
$744$	−2.23420	+	3.86975i	−0.0819099	+	0.141872i
$745$	−25.0307	−	43.3544i	−0.917052	−	1.58838i
$746$	−1.32475	+	2.29454i	−0.0485026	+	0.0840089i
$747$	−2.22180	−	3.84827i	−0.0812915	−	0.140801i
$748$	−1.07549			−0.0393239
$749$	1.40328			0.0512747
$750$	−8.68047	−	15.0350i	−0.316966	−	0.549001i
$751$	−9.62995	−	16.6796i	−0.351402	−	0.608646i	0.635093	−	0.772435i	$-0.280962\pi$
$751$	−9.62995	−	16.6796i	−0.351402	−	0.608646i	−0.986495	+	0.163789i	$0.947628\pi$
$752$	2.19868			0.0801776
$753$	3.72737			0.135833
$754$	0.546824	+	0.947126i	0.0199141	+	0.0344923i
$755$	16.9138	−	29.2955i	0.615555	−	1.06617i
$756$	−1.23607	−	2.14093i	−0.0449554	−	0.0778650i
$757$	11.9727	−	20.7373i	0.435156	−	0.753712i	−0.562153	−	0.827033i	$-0.690027\pi$
$757$	11.9727	−	20.7373i	0.435156	−	0.753712i	0.997308	+	0.0733218i	$0.0233600\pi$
$758$	−9.08361	+	15.7333i	−0.329931	+	0.571458i
$759$	47.6528			1.72969
$760$		0			0
$761$	−44.7968			−1.62388			−0.811941	−	0.583739i	$-0.801589\pi$
$761$	−44.7968			−1.62388			−0.811941	+	0.583739i	$0.801589\pi$
$762$	−9.04029	+	15.6582i	−0.327495	+	0.567238i
$763$	−1.50020	+	2.59842i	−0.0543108	+	0.0940691i
$764$	−6.36508	−	11.0246i	−0.230281	−	0.398858i
$765$	0.666356	−	1.15416i	0.0240922	−	0.0417289i
$766$	−11.5042	−	19.9258i	−0.415662	−	0.719948i
$767$	−17.1668			−0.619858
$768$	1.28408			0.0463352
$769$	15.8684	+	27.4848i	0.572228	+	0.991128i	0.996337	+	0.0855164i	$0.0272540\pi$
$769$	15.8684	+	27.4848i	0.572228	+	0.991128i	−0.424109	+	0.905611i	$0.639413\pi$
$770$	−3.29470	−	5.70659i	−0.118733	−	0.205651i
$771$	29.4119			1.05924
$772$	17.4781			0.629049
$773$	11.1153	+	19.2523i	0.399791	+	0.692458i	0.993700	−	0.112074i	$-0.0357494\pi$
$773$	11.1153	+	19.2523i	0.399791	+	0.692458i	−0.593909	+	0.804532i	$0.702416\pi$
$774$	−3.80699	+	6.59390i	−0.136839	+	0.237013i
$775$	−15.0649	−	26.0931i	−0.541146	−	0.937292i
$776$	−2.04238	+	3.53750i	−0.0733171	+	0.126989i
$777$	0.411638	−	0.712979i	0.0147674	−	0.0255780i
$778$	−16.5706			−0.594086
$779$		0			0
$780$	23.2130			0.831160
$781$	23.1084	−	40.0249i	0.826883	−	1.43220i
$782$	1.22895	−	2.12860i	0.0439471	−	0.0761186i
$783$	−0.624598	−	1.08184i	−0.0223213	−	0.0386617i
$784$	3.40211	−	5.89263i	0.121504	−	0.210451i
$785$	30.2869	+	52.4585i	1.08099	+	1.87232i
$786$	20.3417			0.725566
$787$	24.4596			0.871891			0.435945	−	0.899973i	$-0.356414\pi$
$787$	24.4596			0.871891			0.435945	+	0.899973i	$0.356414\pi$
$788$	12.2556	+	21.2274i	0.436589	+	0.756194i
$789$	3.25024	+	5.62958i	0.115711	+	0.200418i
$790$	37.7088			1.34162
$791$	4.44426			0.158020
$792$	−2.72233	−	4.71521i	−0.0967337	−	0.167548i
$793$	−9.97754	+	17.2816i	−0.354313	+	0.613688i
$794$	8.89741	+	15.4108i	0.315757	+	0.546908i
$795$	−23.5913	+	40.8613i	−0.836698	+	1.44920i
$796$	−8.23305	+	14.2601i	−0.291813	+	0.505434i
$797$	41.6933			1.47685			0.738426	−	0.674334i	$-0.235569\pi$
$797$	41.6933			1.47685			0.738426	+	0.674334i	$0.235569\pi$
$798$		0			0
$799$	0.586812			0.0207599
$800$	−4.32916	+	7.49833i	−0.153059	+	0.265106i
$801$	−4.02690	+	6.97480i	−0.142284	+	0.246443i
$802$	−15.3107	−	26.5190i	−0.540641	−	0.936417i
$803$	2.86562	−	4.96340i	0.101126	−	0.175155i
$804$	−0.0948696	−	0.164319i	−0.00334579	−	0.00579508i
$805$	15.0592			0.530768
$806$	17.0217			0.599563
$807$	13.3171	+	23.0660i	0.468786	+	0.811960i
$808$	−0.212639	−	0.368301i	−0.00748060	−	0.0129568i
$809$	−49.2488			−1.73150			−0.865748	−	0.500481i	$-0.833157\pi$
$809$	−49.2488			−1.73150			−0.865748	+	0.500481i	$0.833157\pi$
$810$	−11.5343			−0.405275
$811$	−26.0227	−	45.0727i	−0.913782	−	1.58272i	−0.808675	−	0.588256i	$-0.799815\pi$
$811$	−26.0227	−	45.0727i	−0.913782	−	1.58272i	−0.105107	−	0.994461i	$-0.533519\pi$
$812$	−0.0494633	+	0.0856730i	−0.00173582	+	0.00300653i
$813$	−4.04145	−	6.99999i	−0.141740	−	0.245500i
$814$	2.91955	−	5.05682i	0.102330	−	0.177241i
$815$	25.4492	−	44.0793i	0.891446	−	1.54403i
$816$	0.342712			0.0119973
$817$		0			0
$818$	9.14328			0.319687
$819$	−1.46214	+	2.53250i	−0.0510914	+	0.0884928i
$820$	14.5329	−	25.1717i	0.507511	−	0.879035i
$821$	21.1291	+	36.5967i	0.737411	+	1.27723i	0.953657	+	0.300895i	$0.0972854\pi$
$821$	21.1291	+	36.5967i	0.737411	+	1.27723i	−0.216246	+	0.976339i	$0.569381\pi$
$822$	−1.41726	+	2.45477i	−0.0494326	+	0.0856198i
$823$	−16.2386	−	28.1260i	−0.566041	−	0.980411i	−0.996952	−	0.0780169i	$-0.975141\pi$
$823$	−16.2386	−	28.1260i	−0.566041	−	0.980411i	0.430911	−	0.902394i	$-0.358192\pi$
$824$	−4.53618			−0.158025
$825$	−44.8018			−1.55980
$826$	−0.776418	−	1.34480i	−0.0270151	−	0.0467914i
$827$	10.7578	+	18.6331i	0.374086	+	0.647936i	0.990190	−	0.139729i	$-0.0446231\pi$
$827$	10.7578	+	18.6331i	0.374086	+	0.647936i	−0.616104	+	0.787665i	$0.711290\pi$
$828$	12.4431			0.432426
$829$	5.65061			0.196254			0.0981269	−	0.995174i	$-0.468715\pi$
$829$	5.65061			0.196254			0.0981269	+	0.995174i	$0.468715\pi$
$830$	6.07720	+	10.5260i	0.210943	+	0.365363i
$831$	−4.60733	+	7.98012i	−0.159826	+	0.276827i
$832$	−2.44575	−	4.23616i	−0.0847910	−	0.146862i
$833$	0.908000	−	1.57270i	0.0314603	−	0.0544909i
$834$	10.9560	−	18.9764i	0.379377	−	0.657100i
$835$	−38.1871			−1.32152
$836$		0			0
$837$	−19.4427			−0.672037
$838$	−6.30783	+	10.9255i	−0.217900	+	0.377414i
$839$	5.33831	−	9.24623i	0.184299	−	0.319215i	−0.759041	−	0.651043i	$-0.774332\pi$
$839$	5.33831	−	9.24623i	0.184299	−	0.319215i	0.943340	+	0.331828i	$0.107665\pi$
$840$	1.04988	+	1.81844i	0.0362242	+	0.0627421i
$841$	14.4750	−	25.0714i	0.499138	−	0.864533i
$842$	−16.6277	−	28.8000i	−0.573027	−	0.992512i
$843$	3.56192			0.122679
$844$	27.4805			0.945916
$845$	−20.1910	−	34.9718i	−0.694591	−	1.20307i
$846$	1.48536	+	2.57272i	0.0510678	+	0.0884520i
$847$	−2.31774			−0.0796385
$848$	9.94241			0.341424
$849$	−4.97491	−	8.61680i	−0.170739	−	0.295728i
$850$	−1.15542	+	2.00125i	−0.0396307	+	0.0686424i
$851$	6.67227	+	11.5567i	0.228722	+	0.396159i
$852$	−7.36363	+	12.7542i	−0.252274	+	0.436951i
$853$	−5.13329	+	8.89112i	−0.175760	+	0.304426i	−0.940424	−	0.340003i	$-0.889572\pi$
$853$	−5.13329	+	8.89112i	−0.175760	+	0.304426i	0.764664	+	0.644430i	$0.222905\pi$
$854$	−1.80505			−0.0617676
$855$		0			0
$856$	−3.17151			−0.108400
$857$	18.6694	−	32.3363i	0.637734	−	1.10459i	−0.348195	−	0.937422i	$-0.613205\pi$
$857$	18.6694	−	32.3363i	0.637734	−	1.10459i	0.985929	−	0.167165i	$-0.0534613\pi$
$858$	12.6553	−	21.9196i	0.432045	−	0.748324i
$859$	12.1445	+	21.0349i	0.414365	+	0.717701i	0.995362	−	0.0962051i	$-0.0306705\pi$
$859$	12.1445	+	21.0349i	0.414365	+	0.717701i	−0.580997	+	0.813906i	$0.697337\pi$
$860$	10.4131	−	18.0360i	0.355083	−	0.615023i
$861$	−2.23420	−	3.86975i	−0.0761414	−	0.131881i
$862$	−22.9915			−0.783092
$863$	−23.5728			−0.802427			−0.401214	−	0.915985i	$-0.631412\pi$
$863$	−23.5728			−0.802427			−0.401214	+	0.915985i	$0.631412\pi$
$864$	2.79360	+	4.83866i	0.0950404	+	0.164615i
$865$	18.1312	+	31.4042i	0.616480	+	1.06777i
$866$	34.7092			1.17947
$867$	−21.7379			−0.738257
$868$	0.769854	+	1.33343i	0.0261305	+	0.0452594i
$869$	20.5581	−	35.6077i	0.697387	−	1.20791i
$870$	0.530514	+	0.918877i	0.0179861	+	0.0311528i
$871$	−0.361390	+	0.625947i	−0.0122452	+	0.0212094i
$872$	3.39056	−	5.87262i	0.114819	−	0.198872i
$873$	−5.51908			−0.186793
$874$		0			0
$875$	−5.98217			−0.202234
$876$	−0.913147	+	1.58162i	−0.0308524	+	0.0534379i
$877$	15.7191	−	27.2263i	0.530796	−	0.919366i	−0.468558	−	0.883433i	$-0.655226\pi$
$877$	15.7191	−	27.2263i	0.530796	−	0.919366i	0.999354	−	0.0359330i	$-0.0114403\pi$
$878$	18.2409	+	31.5942i	0.615601	+	1.06625i
$879$	0.502634	−	0.870587i	0.0169534	−	0.0293642i
$880$	7.44627	+	12.8973i	0.251014	+	0.434768i
$881$	−41.7600			−1.40693			−0.703466	−	0.710729i	$-0.748365\pi$
$881$	−41.7600			−1.40693			−0.703466	+	0.710729i	$0.748365\pi$
$882$	9.19347			0.309560
$883$	−0.271520	−	0.470287i	−0.00913738	−	0.0158264i	0.861421	−	0.507892i	$-0.169575\pi$
$883$	−0.271520	−	0.470287i	−0.00913738	−	0.0158264i	−0.870558	+	0.492066i	$0.836242\pi$
$884$	−0.652752	−	1.13060i	−0.0219544	−	0.0380262i
$885$	−16.6548			−0.559844
$886$	11.7583			0.395028
$887$	−5.66240	−	9.80757i	−0.190125	−	0.329306i	0.755167	−	0.655533i	$-0.227556\pi$
$887$	−5.66240	−	9.80757i	−0.190125	−	0.329306i	−0.945291	+	0.326227i	$0.894223\pi$
$888$	−0.930333	+	1.61138i	−0.0312199	+	0.0540745i
$889$	3.11507	+	5.39546i	0.104476	+	0.180958i
$890$	11.0146	−	19.0779i	0.369211	−	0.639492i
$891$	−6.28829	+	10.8916i	−0.210666	+	0.364884i
$892$	20.3706			0.682058
$893$		0			0
$894$	17.3938			0.581737
$895$	16.2580	−	28.1597i	0.543446	−	0.941276i
$896$	0.221232	−	0.383185i	0.00739083	−	0.0128013i
$897$	28.9221	+	50.0945i	0.965681	+	1.67261i
$898$	4.34551	−	7.52664i	0.145012	−	0.251167i
$899$	0.389015	+	0.673795i	0.0129744	+	0.0224723i
$900$	−11.6986			−0.389954
$901$	2.65356			0.0884029
$902$	−15.8461	−	27.4463i	−0.527618	−	0.913862i
$903$	−1.60085	−	2.77275i	−0.0532729	−	0.0922713i
$904$	−10.0444			−0.334070
$905$	53.6905			1.78473
$906$	5.87670	+	10.1787i	0.195240	+	0.338166i
$907$	−5.46292	+	9.46206i	−0.181393	+	0.314182i	−0.942355	−	0.334614i	$-0.891394\pi$
$907$	−5.46292	+	9.46206i	−0.181393	+	0.314182i	0.760962	+	0.648797i	$0.224727\pi$
$908$	11.0747	+	19.1819i	0.367526	+	0.636573i
$909$	0.287305	−	0.497627i	0.00952930	−	0.0165052i
$910$	3.99933	−	6.92705i	0.132577	−	0.229629i
$911$	47.4159			1.57096			0.785479	−	0.618888i	$-0.212416\pi$
$911$	47.4159			1.57096			0.785479	+	0.618888i	$0.212416\pi$
$912$		0			0
$913$	13.2527			0.438600
$914$	6.51432	−	11.2831i	0.215474	−	0.373213i
$915$	−9.67994	+	16.7661i	−0.320009	+	0.554272i
$916$	−6.35738	−	11.0113i	−0.210054	−	0.363824i
$917$	3.50464	−	6.07022i	0.115734	−	0.200456i
$918$	0.745593	+	1.29141i	0.0246082	+	0.0426227i
$919$	5.11069			0.168586			0.0842930	−	0.996441i	$-0.473137\pi$
$919$	5.11069			0.168586			0.0842930	+	0.996441i	$0.473137\pi$
$920$	−34.0350			−1.12210
$921$	18.0855	+	31.3250i	0.595937	+	1.03219i
$922$	−4.52130	−	7.83112i	−0.148901	−	0.257904i
$923$	56.1011			1.84659
$924$	2.28949			0.0753187
$925$	−6.27308	−	10.8653i	−0.206258	−	0.357249i
$926$	8.86025	−	15.3464i	0.291166	−	0.504314i
$927$	−3.06451	−	5.30789i	−0.100652	−	0.174334i
$928$	0.111791	−	0.193627i	0.00366971	−	0.00635613i
$929$	21.4221	−	37.1042i	0.702837	−	1.21735i	−0.264630	−	0.964350i	$-0.585250\pi$
$929$	21.4221	−	37.1042i	0.702837	−	1.21735i	0.967467	−	0.252999i	$-0.0814169\pi$
$930$	16.5140			0.541514
$931$		0			0
$932$	−8.68176			−0.284381
$933$	−2.48358	+	4.30169i	−0.0813088	+	0.140831i
$934$	3.93886	−	6.82231i	0.128883	−	0.223233i
$935$	1.98736	+	3.44220i	0.0649935	+	0.112572i
$936$	3.30455	−	5.72364i	0.108013	−	0.187083i
$937$	1.83942	+	3.18597i	0.0600913	+	0.104081i	0.894506	−	0.447056i	$-0.147527\pi$
$937$	1.83942	+	3.18597i	0.0600913	+	0.104081i	−0.834415	+	0.551137i	$0.814194\pi$
$938$	−0.0653797			−0.00213472
$939$	39.0203			1.27338
$940$	−4.06285	−	7.03706i	−0.132515	−	0.229524i
$941$	−9.18974	−	15.9171i	−0.299577	−	0.518882i	0.676462	−	0.736477i	$-0.263512\pi$
$941$	−9.18974	−	15.9171i	−0.299577	−	0.518882i	−0.976039	+	0.217595i	$0.930179\pi$
$942$	−21.0464			−0.685729
$943$	72.4286			2.35860
$944$	1.75476	+	3.03934i	0.0571127	+	0.0989220i
$945$	−4.56816	+	7.91228i	−0.148602	+	0.257387i
$946$	−11.3540	−	19.6658i	−0.369152	−	0.639390i
$947$	−23.3795	+	40.4945i	−0.759732	+	1.31589i	0.183256	+	0.983065i	$0.441336\pi$
$947$	−23.3795	+	40.4945i	−0.759732	+	1.31589i	−0.942987	+	0.332829i	$0.891997\pi$
$948$	−6.55097	+	11.3466i	−0.212766	+	0.368521i
$949$	6.95697			0.225833
$950$		0			0
$951$	6.84162			0.221855
$952$	0.0590452	−	0.102269i	0.00191367	−	0.00331457i
$953$	−12.5275	+	21.6983i	−0.405807	+	0.702878i	−0.994415	−	0.105541i	$-0.966343\pi$
$953$	−12.5275	+	21.6983i	−0.405807	+	0.702878i	0.588608	+	0.808418i	$0.299676\pi$
$954$	6.71680	+	11.6338i	0.217464	+	0.376659i
$955$	−23.5235	+	40.7440i	−0.761204	+	1.31844i
$956$	−10.9375	−	18.9442i	−0.353742	−	0.612700i
$957$	1.15690			0.0373974
$958$	−30.1798			−0.975066
$959$	0.488355	+	0.845855i	0.0157698	+	0.0273141i
$960$	−2.37280	−	4.10980i	−0.0765817	−	0.132643i
$961$	−18.8906			−0.609375
$962$	7.08791			0.228523
$963$	−2.14258	−	3.71106i	−0.0690437	−	0.119587i
$964$	9.48160	−	16.4226i	0.305382	−	0.528937i
$965$	−32.2970	−	55.9400i	−1.03968	−	1.80077i
$966$	−2.61617	+	4.53134i	−0.0841739	+	0.145793i
$967$	−3.55314	+	6.15421i	−0.114261	+	0.197906i	−0.917484	−	0.397772i	$-0.869783\pi$
$967$	−3.55314	+	6.15421i	−0.114261	+	0.197906i	0.803223	+	0.595678i	$0.203117\pi$
$968$	5.23826			0.168364
$969$		0			0
$970$	15.0961			0.484707
$971$	−30.3771	+	52.6147i	−0.974848	+	1.68849i	−0.294414	+	0.955678i	$0.595125\pi$
$971$	−30.3771	+	52.6147i	−0.974848	+	1.68849i	−0.680434	+	0.732809i	$0.738209\pi$
$972$	−6.37701	+	11.0453i	−0.204543	+	0.354278i
$973$	−3.77520	−	6.53883i	−0.121027	−	0.209625i
$974$	−17.8850	+	30.9777i	−0.573071	+	0.992589i
$975$	−27.1917	−	47.0975i	−0.870833	−	1.50833i
$976$	4.07955			0.130583
$977$	−38.5412			−1.23304			−0.616520	−	0.787339i	$-0.711458\pi$
$977$	−38.5412			−1.23304			−0.616520	+	0.787339i	$0.711458\pi$
$978$	8.84233	+	15.3154i	0.282746	+	0.489731i
$979$	−12.0099	−	20.8018i	−0.383839	−	0.664828i
$980$	−25.1465			−0.803275
$981$	9.16225			0.292528
$982$	9.13632	+	15.8246i	0.291552	+	0.504982i
$983$	3.75264	−	6.49977i	0.119691	−	0.207310i	−0.799954	−	0.600061i	$-0.795143\pi$
$983$	3.75264	−	6.49977i	0.119691	−	0.207310i	0.919645	+	0.392750i	$0.128476\pi$
$984$	5.04946	+	8.74593i	0.160971	+	0.278810i
$985$	45.2934	−	78.4504i	1.44317	−	2.49964i
$986$	0.0298362	−	0.0516778i	0.000950177	−	0.00164576i
$987$	−1.24920			−0.0397624
$988$		0			0
$989$	51.8964			1.65021
$990$	−10.0610	+	17.4261i	−0.319758	+	0.553837i
$991$	10.7111	−	18.5521i	0.340248	−	0.589327i	−0.644231	−	0.764831i	$-0.722822\pi$
$991$	10.7111	−	18.5521i	0.340248	−	0.589327i	0.984479	+	0.175504i	$0.0561556\pi$
$992$	−1.73993	−	3.01364i	−0.0552427	−	0.0956832i
$993$	13.1926	−	22.8503i	0.418656	−	0.725133i
$994$	2.53733	+	4.39479i	0.0804793	+	0.139394i
$995$	60.8541			1.92920
$996$	−4.22305			−0.133813
$997$	20.5003	+	35.5075i	0.649250	+	1.12453i	0.983302	+	0.181979i	$0.0582504\pi$
$997$	20.5003	+	35.5075i	0.649250	+	1.12453i	−0.334052	+	0.942554i	$0.608416\pi$
$998$	−8.84899	−	15.3269i	−0.280110	−	0.485165i
$999$	−8.09602			−0.256147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.c.m.429.2		8
19.2	odd	18		722.2.e.s.595.3		24
19.3	odd	18		722.2.e.s.99.2		24
19.4	even	9		722.2.e.r.423.3		24
19.5	even	9		722.2.e.r.389.3		24
19.6	even	9		722.2.e.r.415.2		24
19.7	even	3	inner	722.2.c.m.653.2		8
19.8	odd	6		722.2.a.m.1.2	✓	4
19.9	even	9		722.2.e.r.245.3		24
19.10	odd	18		722.2.e.s.245.2		24
19.11	even	3		722.2.a.n.1.3	yes	4
19.12	odd	6		722.2.c.n.653.3		8
19.13	odd	18		722.2.e.s.415.3		24
19.14	odd	18		722.2.e.s.389.2		24
19.15	odd	18		722.2.e.s.423.2		24
19.16	even	9		722.2.e.r.99.3		24
19.17	even	9		722.2.e.r.595.2		24
19.18	odd	2		722.2.c.n.429.3		8
57.8	even	6		6498.2.a.ca.1.1		4
57.11	odd	6		6498.2.a.bx.1.1		4
76.11	odd	6		5776.2.a.bt.1.2		4
76.27	even	6		5776.2.a.bv.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.2	✓	4	19.8	odd	6
722.2.a.n.1.3	yes	4	19.11	even	3
722.2.c.m.429.2		8	1.1	even	1	trivial
722.2.c.m.653.2		8	19.7	even	3	inner
722.2.c.n.429.3		8	19.18	odd	2
722.2.c.n.653.3		8	19.12	odd	6
722.2.e.r.99.3		24	19.16	even	9
722.2.e.r.245.3		24	19.9	even	9
722.2.e.r.389.3		24	19.5	even	9
722.2.e.r.415.2		24	19.6	even	9
722.2.e.r.423.3		24	19.4	even	9
722.2.e.r.595.2		24	19.17	even	9
722.2.e.s.99.2		24	19.3	odd	18
722.2.e.s.245.2		24	19.10	odd	18
722.2.e.s.389.2		24	19.14	odd	18
722.2.e.s.415.3		24	19.13	odd	18
722.2.e.s.423.2		24	19.15	odd	18
722.2.e.s.595.3		24	19.2	odd	18
5776.2.a.bt.1.2		4	76.11	odd	6
5776.2.a.bv.1.3		4	76.27	even	6
6498.2.a.bx.1.1		4	57.11	odd	6
6498.2.a.ca.1.1		4	57.8	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.642040 + 1.11205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84786 + 3.20059i) q^{5} +(-0.642040 - 1.11205i) q^{6} -0.442463 q^{7} +1.00000 q^{8} +(0.675571 + 1.17012i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.642040 + 1.11205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84786 + 3.20059i) q^{5} +(-0.642040 - 1.11205i) q^{6} -0.442463 q^{7} +1.00000 q^{8} +(0.675571 + 1.17012i) q^{9} +(-1.84786 - 3.20059i) q^{10} -4.02967 q^{11} +1.28408 q^{12} +(-2.44575 - 4.23616i) q^{13} +(0.221232 - 0.383185i) q^{14} +(-2.37280 - 4.10980i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.133446 + 0.231136i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(0.284079 - 0.492039i) q^{21} +(2.01484 - 3.48980i) q^{22} +(4.60465 + 7.97549i) q^{23} +(-0.642040 + 1.11205i) q^{24} +(-4.32916 - 7.49833i) q^{25} +4.89149 q^{26} -5.58721 q^{27} +(0.221232 + 0.383185i) q^{28} +(0.111791 + 0.193627i) q^{29} +4.74559 q^{30} +3.47985 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.58721 - 4.48118i) q^{33} +(-0.133446 - 0.231136i) q^{34} +(0.817610 - 1.41614i) q^{35} +(0.675571 - 1.17012i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(-1.84786 + 3.20059i) q^{40} +(3.93236 - 6.81105i) q^{41} +(0.284079 + 0.492039i) q^{42} +(2.81761 - 4.88024i) q^{43} +(2.01484 + 3.48980i) q^{44} -4.99344 q^{45} -9.20930 q^{46} +(-1.09934 - 1.90411i) q^{47} +(-0.642040 - 1.11205i) q^{48} -6.80423 q^{49} +8.65833 q^{50} +(-0.171356 - 0.296797i) q^{51} +(-2.44575 + 4.23616i) q^{52} +(-4.97120 - 8.61038i) q^{53} +(2.79360 - 4.83866i) q^{54} +(7.44627 - 12.8973i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(1.75476 - 3.03934i) q^{59} +(-2.37280 + 4.10980i) q^{60} +(-2.03977 - 3.53299i) q^{61} +(-1.73993 + 3.01364i) q^{62} +(-0.298915 - 0.517736i) q^{63} +1.00000 q^{64} +18.0776 q^{65} +(2.58721 + 4.48118i) q^{66} +(-0.0738814 - 0.127966i) q^{67} +0.266893 q^{68} -11.8255 q^{69} +(0.817610 + 1.41614i) q^{70} +(-5.73456 + 9.93255i) q^{71} +(0.675571 + 1.17012i) q^{72} +(-0.711130 + 1.23171i) q^{73} +(-0.724514 + 1.25490i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(-3.14053 + 5.43956i) q^{78} +(-5.10169 + 8.83638i) q^{79} +(-1.84786 - 3.20059i) q^{80} +(1.56050 - 2.70286i) q^{81} +(3.93236 + 6.81105i) q^{82} -3.28878 q^{83} -0.568158 q^{84} +(-0.493181 - 0.854214i) q^{85} +(2.81761 + 4.88024i) q^{86} -0.287096 q^{87} -4.02967 q^{88} +(2.98037 + 5.16216i) q^{89} +(2.49672 - 4.32444i) q^{90} +(1.08215 + 1.87434i) q^{91} +(4.60465 - 7.97549i) q^{92} +(-2.23420 + 3.86975i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(-2.04238 + 3.53750i) q^{97} +(3.40211 - 5.89263i) q^{98} +(-2.72233 - 4.71521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 18 q^{13} + 2 q^{14} - 4 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{21} - 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} - 8 q^{27} + 2 q^{28} + 2 q^{29} + 8 q^{30} + 52 q^{31} - 4 q^{32} - 16 q^{33} - 6 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} - 20 q^{46} + 12 q^{47} - 2 q^{48} - 24 q^{49} + 12 q^{50} + 2 q^{51} - 18 q^{52} - 8 q^{53} + 4 q^{54} + 26 q^{55} - 4 q^{56} - 4 q^{58} + 8 q^{59} - 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} - 8 q^{65} - 16 q^{66} - 10 q^{67} + 12 q^{68} - 40 q^{69} - 6 q^{70} - 4 q^{72} + 14 q^{73} - 4 q^{74} + 16 q^{75} + 8 q^{77} + 6 q^{78} - 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} + 8 q^{84} + 18 q^{85} + 10 q^{86} - 52 q^{87} + 4 q^{88} + 16 q^{89} + 22 q^{90} + 4 q^{91} + 10 q^{92} - 8 q^{93} - 24 q^{94} + 4 q^{96} - 28 q^{97} + 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 18 * q^13 + 2 * q^14 - 4 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 4 * q^20 - 4 * q^21 - 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 - 8 * q^27 + 2 * q^28 + 2 * q^29 + 8 * q^30 + 52 * q^31 - 4 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 - 20 * q^46 + 12 * q^47 - 2 * q^48 - 24 * q^49 + 12 * q^50 + 2 * q^51 - 18 * q^52 - 8 * q^53 + 4 * q^54 + 26 * q^55 - 4 * q^56 - 4 * q^58 + 8 * q^59 - 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 - 8 * q^65 - 16 * q^66 - 10 * q^67 + 12 * q^68 - 40 * q^69 - 6 * q^70 - 4 * q^72 + 14 * q^73 - 4 * q^74 + 16 * q^75 + 8 * q^77 + 6 * q^78 - 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 + 8 * q^84 + 18 * q^85 + 10 * q^86 - 52 * q^87 + 4 * q^88 + 16 * q^89 + 22 * q^90 + 4 * q^91 + 10 * q^92 - 8 * q^93 - 24 * q^94 + 4 * q^96 - 28 * q^97 + 12 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more