LMFDB - Embedded newform 722.2.c.n.429.3

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			429.3
Root			$0.587785 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.n.653.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.642040 - 1.11205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84786 + 3.20059i) q^{5} +(-0.642040 - 1.11205i) q^{6} -0.442463 q^{7} -1.00000 q^{8} +(0.675571 + 1.17012i) q^{9} +O(q^{10})$	\(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	−0.618989	−	0.785400i	$-0.712457\pi$
$3$	0.642040	−	1.11205i	0.370682	−	0.642040i	0.989671	+	0.143360i	$0.0457907\pi$
$4$	−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	$0.0706284\pi$
$13$	2.44575	+	4.23616i	0.678328	+	1.17490i	−0.297156	+	0.954829i	$0.596038\pi$
$14$	−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	0.855459	−	0.517870i	$-0.173275\pi$
$29$	−0.111791	−	0.193627i	−0.0207590	−	0.0359557i	−0.876218	+	0.481914i	$0.839942\pi$
$30$	4.74559			0.866423
$31$	−3.47985			−0.625000			−0.312500	−	0.949918i	$-0.601166\pi$
$31$	−3.47985			−0.625000			−0.312500	+	0.949918i	$0.601166\pi$
$32$	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	$-0.538004\pi$
$37$	−1.44903			−0.238219			−0.119109	+	0.992881i	$0.538004\pi$
$38$		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	$0.377160\pi$
$41$	−3.93236	+	6.81105i	−0.614132	+	1.06371i	−0.990536	+	0.137252i	$0.956173\pi$
$42$	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	$0.0725919\pi$
$53$	4.97120	+	8.61038i	0.682847	+	1.18273i	−0.291261	+	0.956644i	$0.594075\pi$
$54$	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	−0.957349	−	0.288934i	$-0.906699\pi$
$59$	−1.75476	+	3.03934i	−0.228451	+	0.395688i	0.728898	+	0.684622i	$0.240033\pi$
$60$	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	0.870503	−	0.492163i	$-0.163794\pi$
$67$	0.0738814	+	0.127966i	0.00902605	+	0.0156336i	−0.861477	+	0.507796i	$0.830460\pi$
$68$	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	$-0.595067\pi$
$71$	5.73456	−	9.93255i	0.680567	−	1.17878i	0.974808	−	0.223045i	$-0.0715998\pi$
$72$	−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	$-0.638730\pi$
$79$	5.10169	−	8.83638i	0.573985	−	0.994171i	0.996151	−	0.0876525i	$-0.0279365\pi$
$80$	−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	0.663714	−	0.747987i	$-0.268979\pi$
$89$	−2.98037	−	5.16216i	−0.315919	−	0.547188i	−0.979632	+	0.200799i	$0.935646\pi$
$90$	−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	−0.743514	−	0.668721i	$-0.766842\pi$
$97$	2.04238	−	3.53750i	0.207372	−	0.359179i	0.950886	+	0.309541i	$0.100176\pi$
$98$	−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	$-0.428258\pi$
$103$	4.53618			0.446963			0.223482	+	0.974708i	$0.428258\pi$
$104$	−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	$-0.451010\pi$
$107$	3.17151			0.306602			0.153301	+	0.988180i	$0.451010\pi$
$108$	−2.79360	−	4.83866i	−0.268815	−	0.465601i
$109$	−3.39056	+	5.87262i	−0.324757	+	0.562495i	−0.981463	−	0.191651i	$-0.938616\pi$
$109$	−3.39056	+	5.87262i	−0.324757	+	0.562495i	0.656706	+	0.754146i	$0.271949\pi$
$110$	−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	$-0.343371\pi$
$113$	10.0444			0.944893			0.472447	+	0.881359i	$0.343371\pi$
$114$		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	$0.0481223\pi$
$127$	7.04029	+	12.1941i	0.624725	+	1.08206i	−0.363869	+	0.931450i	$0.618544\pi$
$128$	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	$-0.378522\pi$
$151$	9.15317			0.744875			0.372437	+	0.928057i	$0.378522\pi$
$152$		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	0.593911	−	0.804530i	$-0.297583\pi$
$167$	−5.16640	−	8.94847i	−0.399788	−	0.692453i	−0.993700	+	0.112077i	$0.964250\pi$
$168$	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	−0.990025	−	0.140892i	$-0.955003\pi$
$173$	−4.90601	+	8.49745i	−0.372997	+	0.646049i	0.617028	+	0.786941i	$0.288336\pi$
$174$	−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	$-0.393353\pi$
$179$	8.79830			0.657616			0.328808	+	0.944397i	$0.393353\pi$
$180$	2.49672	+	4.32444i	0.186094	+	0.322325i
$181$	7.26388	+	12.5814i	0.539920	+	0.935168i	0.998908	+	0.0467258i	$0.0148787\pi$
$181$	7.26388	+	12.5814i	0.539920	+	0.935168i	−0.458988	+	0.888442i	$0.651788\pi$
$182$	−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	$-0.616778\pi$
$193$	8.73903	−	15.1364i	0.629049	−	1.08954i	0.987743	−	0.156090i	$-0.0498889\pi$
$194$	−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	$-0.438499\pi$
$211$	13.7402	−	23.7988i	0.945916	−	1.63837i	0.753906	−	0.656982i	$-0.228167\pi$
$212$	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	$-0.594419\pi$
$223$	10.1853	−	17.6414i	0.682058	−	1.18136i	0.974352	−	0.225030i	$-0.0722481\pi$
$224$	−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	$-0.237158\pi$
$227$	22.1493			1.47010			0.735051	+	0.678011i	$0.237158\pi$
$228$		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	$-0.957529\pi$
$241$	−9.48160	−	16.4226i	−0.610764	−	1.05787i	0.380348	−	0.924843i	$-0.375804\pi$
$242$	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	$0.0866281\pi$
$257$	11.4525	+	19.8363i	0.714388	+	1.23736i	−0.248807	+	0.968553i	$0.580039\pi$
$258$	−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	$0.384568\pi$
$269$	−10.3710	+	17.9630i	−0.632329	+	1.09523i	−0.987074	+	0.160263i	$0.948766\pi$
$270$	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	0.904425	−	0.426632i	$-0.140300\pi$
$281$	1.38696	+	2.40228i	0.0827388	+	0.143308i	−0.821687	+	0.569940i	$0.806967\pi$
$282$	−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	$-0.492720\pi$
$293$	0.782870			0.0457358			0.0228679	+	0.999738i	$0.492720\pi$
$294$	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	$0.463879\pi$
$307$	−14.0844	+	24.3949i	−0.803839	+	1.39229i	−0.917072	+	0.398721i	$0.869454\pi$
$308$	−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	0.931089	−	0.364791i	$-0.118860\pi$
$317$	2.66402	+	4.61421i	0.149626	+	0.259160i	−0.781463	+	0.623951i	$0.785526\pi$
$318$	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	$-0.308988\pi$
$331$	20.5480			1.12942			0.564711	+	0.825289i	$0.308988\pi$
$332$	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	−0.626483	−	0.779435i	$-0.715506\pi$
$337$	6.64121	−	11.5029i	0.361770	−	0.626603i	0.988252	+	0.152832i	$0.0488393\pi$
$338$	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	$-0.521851\pi$
$373$	−2.64950			−0.137186			−0.0685930	+	0.997645i	$0.521851\pi$
$374$	−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	$-0.654519\pi$
$379$	−18.1672			−0.933187			−0.466593	+	0.884472i	$0.654519\pi$
$380$		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	$-0.633314\pi$
$383$	11.5042	−	19.9258i	0.587835	−	1.01816i	0.994515	−	0.104590i	$-0.0333529\pi$
$384$	−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	$-0.556279\pi$
$401$	15.3107	−	26.5190i	0.764582	−	1.32429i	0.940468	−	0.339884i	$-0.110388\pi$
$402$	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	0.956635	−	0.291290i	$-0.0940844\pi$
$409$	4.57164	+	7.91831i	0.226053	+	0.391535i	−0.730582	+	0.682825i	$0.760751\pi$
$410$	−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	$-0.532592\pi$
$421$	16.6277	−	28.8000i	0.810383	−	1.40362i	0.912596	−	0.408862i	$-0.134074\pi$
$422$	−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	$-0.979871\pi$
$431$	−11.4957	−	19.9112i	−0.553730	−	0.959088i	0.444271	−	0.895892i	$-0.353463\pi$
$432$	−2.79360	+	4.83866i	−0.134407	+	0.232800i
$433$	17.3546	+	30.0591i	0.834010	+	1.44455i	0.894834	+	0.446399i	$0.147294\pi$
$433$	17.3546	+	30.0591i	0.834010	+	1.44455i	−0.0608241	+	0.998148i	$0.519373\pi$
$434$	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	$0.502930\pi$
$439$	−18.2409	+	31.5942i	−0.870591	+	1.50791i	−0.861386	+	0.507950i	$0.830403\pi$
$440$	−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	$-0.434255\pi$
$449$	8.69102			0.410154			0.205077	+	0.978746i	$0.434255\pi$
$450$	−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	$-0.800775\pi$
$487$	−35.7699			−1.62089			−0.810445	+	0.585814i	$0.800775\pi$
$488$	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	0.757272	−	0.653099i	$-0.226532\pi$
$509$	−4.21811	−	7.30598i	−0.186964	−	0.323832i	−0.944237	+	0.329268i	$0.893198\pi$
$510$	−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	$-0.562910\pi$
$521$	−8.96365			−0.392705			−0.196352	+	0.980533i	$0.562910\pi$
$522$	−0.151045	−	0.261618i	−0.00661107	−	0.0114507i
$523$	−1.06997	−	1.85324i	−0.0467864	−	0.0810364i	0.841684	−	0.539971i	$-0.181565\pi$
$523$	−1.06997	−	1.85324i	−0.0467864	−	0.0810364i	−0.888470	+	0.458934i	$0.848231\pi$
$524$	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	$-0.987264\pi$
$547$	−12.4948	−	21.6417i	−0.534240	−	0.925332i	0.464959	−	0.885332i	$-0.346069\pi$
$548$	−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	$-0.636429\pi$
$563$	−19.7224			−0.831202			−0.415601	+	0.909547i	$0.636429\pi$
$564$	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	$-0.653666\pi$
$569$	−22.1469			−0.928446			−0.464223	+	0.885718i	$0.653666\pi$
$570$		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	0.993532	−	0.113554i	$-0.0362233\pi$
$599$	9.75126	+	16.8897i	0.398426	+	0.690094i	−0.595106	+	0.803647i	$0.702890\pi$
$600$	11.1180			0.453890
$601$	38.9632			1.58934			0.794671	−	0.607040i	$-0.207643\pi$
$601$	38.9632			1.58934			0.794671	+	0.607040i	$0.207643\pi$
$602$	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	$-0.554925\pi$
$607$	−8.46029			−0.343393			−0.171696	+	0.985150i	$0.554925\pi$
$608$		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	−0.772605	−	0.634887i	$-0.781046\pi$
$641$	4.14015	−	7.17096i	0.163526	−	0.283236i	0.936131	+	0.351652i	$0.114380\pi$
$642$	−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	$-0.988783\pi$
$659$	−13.6108	−	23.5746i	−0.530202	−	0.918336i	0.469178	−	0.883104i	$-0.344550\pi$
$660$	−9.56159	+	16.5612i	−0.372185	+	0.644643i
$661$	−4.45412	−	7.71477i	−0.173245	−	0.300070i	0.766307	−	0.642474i	$-0.222092\pi$
$661$	−4.45412	−	7.71477i	−0.173245	−	0.300070i	−0.939553	+	0.342404i	$0.888759\pi$
$662$	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	$-0.741549\pi$
$673$	−35.7010			−1.37617			−0.688087	+	0.725629i	$0.741549\pi$
$674$	−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	$-0.323600\pi$
$677$	27.3849			1.05249			0.526243	+	0.850334i	$0.323600\pi$
$678$	−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	$-0.239555\pi$
$683$	38.1521			1.45985			0.729925	+	0.683528i	$0.239555\pi$
$684$		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	$-0.624107\pi$
$743$	16.6543	−	28.8460i	0.610986	−	1.05826i	0.991075	−	0.133309i	$-0.0425602\pi$
$744$	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	0.986495	−	0.163789i	$-0.0523718\pi$
$751$	9.62995	+	16.6796i	0.351402	+	0.608646i	−0.635093	+	0.772435i	$0.719038\pi$
$752$	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	0.593909	−	0.804532i	$-0.297584\pi$
$773$	−11.1153	−	19.2523i	−0.399791	−	0.692458i	−0.993700	+	0.112074i	$0.964251\pi$
$774$	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	$-0.643586\pi$
$787$	−24.4596			−0.871891			−0.435945	+	0.899973i	$0.643586\pi$
$788$	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	$-0.764431\pi$
$797$	−41.6933			−1.47685			−0.738426	+	0.674334i	$0.764431\pi$
$798$		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	$0.200185\pi$
$811$	26.0227	+	45.0727i	0.913782	+	1.58272i	0.105107	+	0.994461i	$0.466481\pi$
$812$	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	0.616104	−	0.787665i	$-0.288710\pi$
$827$	−10.7578	−	18.6331i	−0.374086	−	0.647936i	−0.990190	+	0.139729i	$0.955377\pi$
$828$	12.4431			0.432426
$829$	−5.65061			−0.196254			−0.0981269	−	0.995174i	$-0.531285\pi$
$829$	−5.65061			−0.196254			−0.0981269	+	0.995174i	$0.531285\pi$
$830$	−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	−0.943340	−	0.331828i	$-0.892335\pi$
$839$	−5.33831	+	9.24623i	−0.184299	+	0.319215i	0.759041	+	0.651043i	$0.225668\pi$
$840$	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	$0.386795\pi$
$857$	−18.6694	+	32.3363i	−0.637734	+	1.10459i	−0.985929	+	0.167165i	$0.946539\pi$
$858$	−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	$-0.368588\pi$
$863$	23.5728			0.802427			0.401214	+	0.915985i	$0.368588\pi$
$864$	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	$0.344774\pi$
$877$	−15.7191	+	27.2263i	−0.530796	+	0.919366i	−0.999354	+	0.0359330i	$0.988560\pi$
$878$	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	0.945291	−	0.326227i	$-0.105777\pi$
$887$	5.66240	+	9.80757i	0.190125	+	0.329306i	−0.755167	+	0.655533i	$0.772444\pi$
$888$	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	−0.760962	−	0.648797i	$-0.775273\pi$
$907$	5.46292	−	9.46206i	0.181393	−	0.314182i	0.942355	+	0.334614i	$0.108606\pi$
$908$	−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	$-0.787584\pi$
$911$	−47.4159			−1.57096			−0.785479	+	0.618888i	$0.787584\pi$
$912$		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	0.976039	−	0.217595i	$-0.0698211\pi$
$941$	9.18974	+	15.9171i	0.299577	+	0.518882i	−0.676462	+	0.736477i	$0.736488\pi$
$942$	−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	−0.588608	−	0.808418i	$-0.700324\pi$
$953$	12.5275	−	21.6983i	0.405807	−	0.702878i	0.994415	+	0.105541i	$0.0336573\pi$
$954$	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	$-0.404875\pi$
$971$	30.3771	−	52.6147i	0.974848	−	1.68849i	0.680434	−	0.732809i	$-0.261791\pi$
$972$	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	$-0.288542\pi$
$977$	38.5412			1.23304			0.616520	+	0.787339i	$0.288542\pi$
$978$	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	−0.919645	−	0.392750i	$-0.871524\pi$
$983$	−3.75264	+	6.49977i	−0.119691	+	0.207310i	0.799954	+	0.600061i	$0.204857\pi$
$984$	−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	−0.984479	−	0.175504i	$-0.943844\pi$
$991$	−10.7111	+	18.5521i	−0.340248	+	0.589327i	0.644231	+	0.764831i	$0.277178\pi$
$992$	−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.n.429.3		8
19.2	odd	18		722.2.e.r.595.2		24
19.3	odd	18		722.2.e.r.99.3		24
19.4	even	9		722.2.e.s.423.2		24
19.5	even	9		722.2.e.s.389.2		24
19.6	even	9		722.2.e.s.415.3		24
19.7	even	3	inner	722.2.c.n.653.3		8
19.8	odd	6		722.2.a.n.1.3	yes	4
19.9	even	9		722.2.e.s.245.2		24
19.10	odd	18		722.2.e.r.245.3		24
19.11	even	3		722.2.a.m.1.2	✓	4
19.12	odd	6		722.2.c.m.653.2		8
19.13	odd	18		722.2.e.r.415.2		24
19.14	odd	18		722.2.e.r.389.3		24
19.15	odd	18		722.2.e.r.423.3		24
19.16	even	9		722.2.e.s.99.2		24
19.17	even	9		722.2.e.s.595.3		24
19.18	odd	2		722.2.c.m.429.2		8
57.8	even	6		6498.2.a.bx.1.1		4
57.11	odd	6		6498.2.a.ca.1.1		4
76.11	odd	6		5776.2.a.bv.1.3		4
76.27	even	6		5776.2.a.bt.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.2	✓	4	19.11	even	3
722.2.a.n.1.3	yes	4	19.8	odd	6
722.2.c.m.429.2		8	19.18	odd	2
722.2.c.m.653.2		8	19.12	odd	6
722.2.c.n.429.3		8	1.1	even	1	trivial
722.2.c.n.653.3		8	19.7	even	3	inner
722.2.e.r.99.3		24	19.3	odd	18
722.2.e.r.245.3		24	19.10	odd	18
722.2.e.r.389.3		24	19.14	odd	18
722.2.e.r.415.2		24	19.13	odd	18
722.2.e.r.423.3		24	19.15	odd	18
722.2.e.r.595.2		24	19.2	odd	18
722.2.e.s.99.2		24	19.16	even	9
722.2.e.s.245.2		24	19.9	even	9
722.2.e.s.389.2		24	19.5	even	9
722.2.e.s.415.3		24	19.6	even	9
722.2.e.s.423.2		24	19.4	even	9
722.2.e.s.595.3		24	19.17	even	9
5776.2.a.bt.1.2		4	76.27	even	6
5776.2.a.bv.1.3		4	76.11	odd	6
6498.2.a.bx.1.1		4	57.8	even	6
6498.2.a.ca.1.1		4	57.11	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
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

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