LMFDB - Embedded newform 1338.2.e.h.931.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(931,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.931"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-14,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 21 x^{12} - 26 x^{11} + 217 x^{10} - 335 x^{9} + 1058 x^{8} - 1539 x^{7} + 3657 x^{6} + \cdots + 64 $ x^14 - 3x^13 + 21x^12 - 26x^11 + 217x^10 - 335x^9 + 1058x^8 - 1539x^7 + 3657x^6 - 4850x^5 + 6077x^4 - 4079x^3 + 2145x^2 - 424*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			931.7
Root			$0.802633 + 1.39020i$ of defining polynomial
Character	$\chi$	$=$	1338.931
Dual form			1338.2.e.h.1075.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(2.11078 + 3.65598i) q^{5} +(0.500000 - 0.866025i) q^{6} +2.59085 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.11078 - 3.65598i) q^{10} +(-2.57542 - 4.46076i) q^{11} +(-0.500000 + 0.866025i) q^{12} -4.87229 q^{13} -2.59085 q^{14} -4.22156 q^{15} +1.00000 q^{16} +5.29711 q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.15288 + 5.46095i) q^{19} +(2.11078 + 3.65598i) q^{20} +(-1.29542 + 2.24374i) q^{21} +(2.57542 + 4.46076i) q^{22} +(-2.33881 + 4.05093i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-6.41078 + 11.1038i) q^{25} +4.87229 q^{26} +1.00000 q^{27} +2.59085 q^{28} +(-3.76859 - 6.52739i) q^{29} +4.22156 q^{30} +(-4.69341 + 8.12922i) q^{31} -1.00000 q^{32} +5.15084 q^{33} -5.29711 q^{34} +(5.46871 + 9.47208i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.08733 - 1.88331i) q^{37} +(3.15288 - 5.46095i) q^{38} +(2.43615 - 4.21953i) q^{39} +(-2.11078 - 3.65598i) q^{40} +4.24967 q^{41} +(1.29542 - 2.24374i) q^{42} +(-6.05006 + 10.4790i) q^{43} +(-2.57542 - 4.46076i) q^{44} +(2.11078 - 3.65598i) q^{45} +(2.33881 - 4.05093i) q^{46} +(0.796236 + 1.37912i) q^{47} +(-0.500000 + 0.866025i) q^{48} -0.287512 q^{49} +(6.41078 - 11.1038i) q^{50} +(-2.64855 + 4.58743i) q^{51} -4.87229 q^{52} +(-0.450783 - 0.780778i) q^{53} -1.00000 q^{54} +(10.8723 - 18.8313i) q^{55} -2.59085 q^{56} +(-3.15288 - 5.46095i) q^{57} +(3.76859 + 6.52739i) q^{58} +5.29542 q^{59} -4.22156 q^{60} +(6.65178 - 11.5212i) q^{61} +(4.69341 - 8.12922i) q^{62} +(-1.29542 - 2.24374i) q^{63} +1.00000 q^{64} +(-10.2843 - 17.8130i) q^{65} -5.15084 q^{66} +(-1.27918 + 2.21561i) q^{67} +5.29711 q^{68} +(-2.33881 - 4.05093i) q^{69} +(-5.46871 - 9.47208i) q^{70} +(-7.07517 + 12.2546i) q^{71} +(0.500000 + 0.866025i) q^{72} +(4.53900 + 7.86178i) q^{73} +(1.08733 + 1.88331i) q^{74} +(-6.41078 - 11.1038i) q^{75} +(-3.15288 + 5.46095i) q^{76} +(-6.67251 - 11.5571i) q^{77} +(-2.43615 + 4.21953i) q^{78} +(0.587771 + 1.01805i) q^{79} +(2.11078 + 3.65598i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.24967 q^{82} +(5.17514 + 8.96361i) q^{83} +(-1.29542 + 2.24374i) q^{84} +(11.1810 + 19.3661i) q^{85} +(6.05006 - 10.4790i) q^{86} +7.53718 q^{87} +(2.57542 + 4.46076i) q^{88} +(-1.26932 + 2.19852i) q^{89} +(-2.11078 + 3.65598i) q^{90} -12.6234 q^{91} +(-2.33881 + 4.05093i) q^{92} +(-4.69341 - 8.12922i) q^{93} +(-0.796236 - 1.37912i) q^{94} -26.6202 q^{95} +(0.500000 - 0.866025i) q^{96} +(1.65648 + 2.86911i) q^{97} +0.287512 q^{98} +(-2.57542 + 4.46076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 7 q^{3} + 14 q^{4} - 4 q^{5} + 7 q^{6} + 12 q^{7} - 14 q^{8} - 7 q^{9} + 4 q^{10} - 10 q^{11} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 8 q^{15} + 14 q^{16} + 8 q^{17} + 7 q^{18} - 8 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) $ 14 * q - 14 * q^2 - 7 * q^3 + 14 * q^4 - 4 * q^5 + 7 * q^6 + 12 * q^7 - 14 * q^8 - 7 * q^9 + 4 * q^10 - 10 * q^11 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 8 * q^15 + 14 * q^16 + 8 * q^17 + 7 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 + 10 * q^22 - 8 * q^23 + 7 * q^24 - 13 * q^25 + 4 * q^26 + 14 * q^27 + 12 * q^28 - 6 * q^29 - 8 * q^30 - 10 * q^31 - 14 * q^32 + 20 * q^33 - 8 * q^34 + 18 * q^35 - 7 * q^36 + 15 * q^37 + 8 * q^38 + 2 * q^39 + 4 * q^40 + 24 * q^41 + 6 * q^42 - 14 * q^43 - 10 * q^44 - 4 * q^45 + 8 * q^46 - 10 * q^47 - 7 * q^48 + 54 * q^49 + 13 * q^50 - 4 * q^51 - 4 * q^52 - 9 * q^53 - 14 * q^54 + 13 * q^55 - 12 * q^56 - 8 * q^57 + 6 * q^58 - 20 * q^59 + 8 * q^60 - 20 * q^61 + 10 * q^62 - 6 * q^63 + 14 * q^64 + 7 * q^65 - 20 * q^66 - 13 * q^67 + 8 * q^68 - 8 * q^69 - 18 * q^70 - 26 * q^71 + 7 * q^72 + 7 * q^73 - 15 * q^74 - 13 * q^75 - 8 * q^76 - 13 * q^77 - 2 * q^78 + 36 * q^79 - 4 * q^80 - 7 * q^81 - 24 * q^82 + 27 * q^83 - 6 * q^84 + 27 * q^85 + 14 * q^86 + 12 * q^87 + 10 * q^88 - 33 * q^89 + 4 * q^90 - 14 * q^91 - 8 * q^92 - 10 * q^93 + 10 * q^94 - 40 * q^95 + 7 * q^96 - 19 * q^97 - 54 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	2.11078	+	3.65598i	0.943969	+	1.63500i	0.757801	+	0.652485i	$0.226274\pi$
$5$	2.11078	+	3.65598i	0.943969	+	1.63500i	0.186168	+	0.982518i	$0.440393\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	2.59085			0.979248			0.489624	−	0.871934i	$-0.337134\pi$
$7$	2.59085			0.979248			0.489624	+	0.871934i	$0.337134\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.11078	−	3.65598i	−0.667487	−	1.15612i
$11$	−2.57542	−	4.46076i	−0.776518	−	1.34497i	−0.933937	−	0.357436i	$-0.883651\pi$
$11$	−2.57542	−	4.46076i	−0.776518	−	1.34497i	0.157420	−	0.987532i	$-0.449682\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−4.87229			−1.35133			−0.675666	−	0.737208i	$-0.736144\pi$
$13$	−4.87229			−1.35133			−0.675666	+	0.737208i	$0.736144\pi$
$14$	−2.59085			−0.692433
$15$	−4.22156			−1.09000
$16$	1.00000			0.250000
$17$	5.29711			1.28474			0.642369	−	0.766396i	$-0.277952\pi$
$17$	5.29711			1.28474			0.642369	+	0.766396i	$0.277952\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.15288	+	5.46095i	−0.723321	+	1.25283i	0.236340	+	0.971670i	$0.424052\pi$
$19$	−3.15288	+	5.46095i	−0.723321	+	1.25283i	−0.959661	+	0.281159i	$0.909281\pi$
$20$	2.11078	+	3.65598i	0.471985	+	0.817502i
$21$	−1.29542	+	2.24374i	−0.282685	+	0.489624i
$22$	2.57542	+	4.46076i	0.549081	+	0.951036i
$23$	−2.33881	+	4.05093i	−0.487675	+	0.844678i	−0.999900	−	0.0141737i	$-0.995488\pi$
$23$	−2.33881	+	4.05093i	−0.487675	+	0.844678i	0.512225	+	0.858852i	$0.328822\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−6.41078	+	11.1038i	−1.28216	+	2.22076i
$26$	4.87229			0.955535
$27$	1.00000			0.192450
$28$	2.59085			0.489624
$29$	−3.76859	−	6.52739i	−0.699810	−	1.21211i	−0.968532	−	0.248888i	$-0.919935\pi$
$29$	−3.76859	−	6.52739i	−0.699810	−	1.21211i	0.268723	−	0.963218i	$-0.413399\pi$
$30$	4.22156			0.770748
$31$	−4.69341	+	8.12922i	−0.842961	+	1.46005i	0.0444195	+	0.999013i	$0.485856\pi$
$31$	−4.69341	+	8.12922i	−0.842961	+	1.46005i	−0.887380	+	0.461038i	$0.847477\pi$
$32$	−1.00000			−0.176777
$33$	5.15084			0.896646
$34$	−5.29711			−0.908446
$35$	5.46871	+	9.47208i	0.924380	+	1.60107i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.08733	−	1.88331i	−0.178756	−	0.309614i	0.762699	−	0.646754i	$-0.223874\pi$
$37$	−1.08733	−	1.88331i	−0.178756	−	0.309614i	−0.941455	+	0.337140i	$0.890541\pi$
$38$	3.15288	−	5.46095i	0.511465	−	0.885884i
$39$	2.43615	−	4.21953i	0.390096	−	0.675666i
$40$	−2.11078	−	3.65598i	−0.333744	−	0.578061i
$41$	4.24967			0.663687			0.331843	−	0.943335i	$-0.392329\pi$
$41$	4.24967			0.663687			0.331843	+	0.943335i	$0.392329\pi$
$42$	1.29542	−	2.24374i	0.199888	−	0.346216i
$43$	−6.05006	+	10.4790i	−0.922625	+	1.59803i	−0.127287	+	0.991866i	$0.540627\pi$
$43$	−6.05006	+	10.4790i	−0.922625	+	1.59803i	−0.795337	+	0.606167i	$0.792706\pi$
$44$	−2.57542	−	4.46076i	−0.388259	−	0.672484i
$45$	2.11078	−	3.65598i	0.314656	−	0.545001i
$46$	2.33881	−	4.05093i	0.344838	−	0.597277i
$47$	0.796236	+	1.37912i	0.116143	+	0.201165i	0.918236	−	0.396034i	$-0.129614\pi$
$47$	0.796236	+	1.37912i	0.116143	+	0.201165i	−0.802093	+	0.597199i	$0.796280\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−0.287512			−0.0410732
$50$	6.41078	−	11.1038i	0.906622	−	1.57031i
$51$	−2.64855	+	4.58743i	−0.370872	+	0.642369i
$52$	−4.87229			−0.675666
$53$	−0.450783	−	0.780778i	−0.0619197	−	0.107248i	0.833404	−	0.552665i	$-0.186389\pi$
$53$	−0.450783	−	0.780778i	−0.0619197	−	0.107248i	−0.895323	+	0.445416i	$0.853056\pi$
$54$	−1.00000			−0.136083
$55$	10.8723	−	18.8313i	1.46602	−	2.53922i
$56$	−2.59085			−0.346216
$57$	−3.15288	−	5.46095i	−0.417610	−	0.723321i
$58$	3.76859	+	6.52739i	0.494840	+	0.857088i
$59$	5.29542			0.689404			0.344702	−	0.938712i	$-0.387980\pi$
$59$	5.29542			0.689404			0.344702	+	0.938712i	$0.387980\pi$
$60$	−4.22156			−0.545001
$61$	6.65178	−	11.5212i	0.851673	−	1.47514i	−0.0280250	−	0.999607i	$-0.508922\pi$
$61$	6.65178	−	11.5212i	0.851673	−	1.47514i	0.879698	−	0.475533i	$-0.157745\pi$
$62$	4.69341	−	8.12922i	0.596063	−	1.03241i
$63$	−1.29542	−	2.24374i	−0.163208	−	0.282685i
$64$	1.00000			0.125000
$65$	−10.2843	−	17.8130i	−1.27562	−	2.20943i
$66$	−5.15084			−0.634024
$67$	−1.27918	+	2.21561i	−0.156277	+	0.270680i	−0.933523	−	0.358517i	$-0.883283\pi$
$67$	−1.27918	+	2.21561i	−0.156277	+	0.270680i	0.777246	+	0.629196i	$0.216616\pi$
$68$	5.29711			0.642369
$69$	−2.33881	−	4.05093i	−0.281559	−	0.487675i
$70$	−5.46871	−	9.47208i	−0.653636	−	1.13213i
$71$	−7.07517	+	12.2546i	−0.839669	+	1.45435i	0.0505031	+	0.998724i	$0.483918\pi$
$71$	−7.07517	+	12.2546i	−0.839669	+	1.45435i	−0.890172	+	0.455625i	$0.849416\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	4.53900	+	7.86178i	0.531250	+	0.920152i	0.999335	+	0.0364682i	$0.0116108\pi$
$73$	4.53900	+	7.86178i	0.531250	+	0.920152i	−0.468085	+	0.883683i	$0.655056\pi$
$74$	1.08733	+	1.88331i	0.126399	+	0.218930i
$75$	−6.41078	−	11.1038i	−0.740254	−	1.28216i
$76$	−3.15288	+	5.46095i	−0.361661	+	0.626414i
$77$	−6.67251	−	11.5571i	−0.760404	−	1.31706i
$78$	−2.43615	+	4.21953i	−0.275839	+	0.477768i
$79$	0.587771	+	1.01805i	0.0661295	+	0.114540i	0.897194	−	0.441636i	$-0.145602\pi$
$79$	0.587771	+	1.01805i	0.0661295	+	0.114540i	−0.831065	+	0.556175i	$0.812268\pi$
$80$	2.11078	+	3.65598i	0.235992	+	0.408751i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.24967			−0.469297
$83$	5.17514	+	8.96361i	0.568046	+	0.983884i	0.996759	+	0.0804436i	$0.0256337\pi$
$83$	5.17514	+	8.96361i	0.568046	+	0.983884i	−0.428713	+	0.903441i	$0.641033\pi$
$84$	−1.29542	+	2.24374i	−0.141342	+	0.244812i
$85$	11.1810	+	19.3661i	1.21275	+	2.10055i
$86$	6.05006	−	10.4790i	0.652394	−	1.12998i
$87$	7.53718			0.808071
$88$	2.57542	+	4.46076i	0.274540	+	0.475518i
$89$	−1.26932	+	2.19852i	−0.134547	+	0.233043i	−0.925425	−	0.378932i	$-0.876291\pi$
$89$	−1.26932	+	2.19852i	−0.134547	+	0.233043i	0.790877	+	0.611975i	$0.209625\pi$
$90$	−2.11078	+	3.65598i	−0.222496	+	0.385374i
$91$	−12.6234			−1.32329
$92$	−2.33881	+	4.05093i	−0.243837	+	0.422339i
$93$	−4.69341	−	8.12922i	−0.486684	−	0.842961i
$94$	−0.796236	−	1.37912i	−0.0821255	−	0.142245i
$95$	−26.6202			−2.73117
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	1.65648	+	2.86911i	0.168190	+	0.291314i	0.937784	−	0.347220i	$-0.112874\pi$
$97$	1.65648	+	2.86911i	0.168190	+	0.291314i	−0.769593	+	0.638534i	$0.779541\pi$
$98$	0.287512			0.0290431
$99$	−2.57542	+	4.46076i	−0.258839	+	0.448323i
$100$	−6.41078	+	11.1038i	−0.641078	+	1.11038i
$101$	−1.08941	+	1.88692i	−0.108401	+	0.187755i	−0.915123	−	0.403176i	$-0.867906\pi$
$101$	−1.08941	+	1.88692i	−0.108401	+	0.187755i	0.806722	+	0.590931i	$0.201240\pi$
$102$	2.64855	−	4.58743i	0.262246	−	0.454223i
$103$	−0.308966			−0.0304434			−0.0152217	−	0.999884i	$-0.504845\pi$
$103$	−0.308966			−0.0304434			−0.0152217	+	0.999884i	$0.504845\pi$
$104$	4.87229			0.477768
$105$	−10.9374			−1.06738
$106$	0.450783	+	0.780778i	0.0437839	+	0.0758359i
$107$	−1.46442	−	2.53645i	−0.141571	−	0.245208i	0.786517	−	0.617568i	$-0.211882\pi$
$107$	−1.46442	−	2.53645i	−0.141571	−	0.245208i	−0.928088	+	0.372360i	$0.878549\pi$
$108$	1.00000			0.0962250
$109$	2.15271	+	3.72861i	0.206192	+	0.357136i	0.950512	−	0.310688i	$-0.100559\pi$
$109$	2.15271	+	3.72861i	0.206192	+	0.357136i	−0.744320	+	0.667824i	$0.767226\pi$
$110$	−10.8723	+	18.8313i	−1.03663	+	1.79550i
$111$	2.17466			0.206409
$112$	2.59085			0.244812
$113$	−2.20178	+	3.81359i	−0.207126	+	0.358752i	−0.950808	−	0.309781i	$-0.899744\pi$
$113$	−2.20178	+	3.81359i	−0.207126	+	0.358752i	0.743682	+	0.668533i	$0.233078\pi$
$114$	3.15288	+	5.46095i	0.295295	+	0.511465i
$115$	−19.7468			−1.84140
$116$	−3.76859	−	6.52739i	−0.349905	−	0.606053i
$117$	2.43615	+	4.21953i	0.225222	+	0.390096i
$118$	−5.29542			−0.487482
$119$	13.7240			1.25808
$120$	4.22156			0.385374
$121$	−7.76556	+	13.4503i	−0.705960	+	1.22276i
$122$	−6.65178	+	11.5212i	−0.602224	+	1.04308i
$123$	−2.12483	+	3.68032i	−0.191590	+	0.331843i
$124$	−4.69341	+	8.12922i	−0.421480	+	0.730026i
$125$	−33.0192			−2.95333
$126$	1.29542	+	2.24374i	0.115405	+	0.199888i
$127$	4.98991	−	8.64278i	0.442783	−	0.766923i	−0.555112	−	0.831776i	$-0.687325\pi$
$127$	4.98991	−	8.64278i	0.442783	−	0.766923i	0.997895	+	0.0648530i	$0.0206578\pi$
$128$	−1.00000			−0.0883883
$129$	−6.05006	−	10.4790i	−0.532678	−	0.922625i
$130$	10.2843	+	17.8130i	0.901996	+	1.56230i
$131$	8.41391	−	14.5733i	0.735127	−	1.27328i	−0.219541	−	0.975603i	$-0.570456\pi$
$131$	8.41391	−	14.5733i	0.735127	−	1.27328i	0.954668	−	0.297674i	$-0.0962108\pi$
$132$	5.15084			0.448323
$133$	−8.16864	+	14.1485i	−0.708311	+	1.22683i
$134$	1.27918	−	2.21561i	0.110505	−	0.191399i
$135$	2.11078	+	3.65598i	0.181667	+	0.314656i
$136$	−5.29711			−0.454223
$137$	11.0998	−	19.2255i	0.948323	−	1.64254i	0.199367	−	0.979925i	$-0.436111\pi$
$137$	11.0998	−	19.2255i	0.948323	−	1.64254i	0.748956	−	0.662620i	$-0.230555\pi$
$138$	2.33881	+	4.05093i	0.199092	+	0.344838i
$139$	−2.11269	+	3.65929i	−0.179196	+	0.310377i	−0.941605	−	0.336718i	$-0.890683\pi$
$139$	−2.11269	+	3.65929i	−0.179196	+	0.310377i	0.762409	+	0.647095i	$0.224016\pi$
$140$	5.46871	+	9.47208i	0.462190	+	0.800537i
$141$	−1.59247			−0.134110
$142$	7.07517	−	12.2546i	0.593735	−	1.02838i
$143$	12.5482	+	21.7341i	1.04933	+	1.81750i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	15.9093	−	27.5558i	1.32120	−	2.28838i
$146$	−4.53900	−	7.86178i	−0.375650	−	0.650645i
$147$	0.143756	−	0.248993i	0.0118568	−	0.0205366i
$148$	−1.08733	−	1.88331i	−0.0893779	−	0.154807i
$149$	5.48508	+	9.50043i	0.449355	+	0.778306i	0.998344	−	0.0575237i	$-0.0183205\pi$
$149$	5.48508	+	9.50043i	0.449355	+	0.778306i	−0.548989	+	0.835830i	$0.684987\pi$
$150$	6.41078	+	11.1038i	0.523438	+	0.906622i
$151$	−8.67586	−	15.0270i	−0.706031	−	1.22288i	−0.966318	−	0.257351i	$-0.917150\pi$
$151$	−8.67586	−	15.0270i	−0.706031	−	1.22288i	0.260287	−	0.965531i	$-0.416183\pi$
$152$	3.15288	−	5.46095i	0.255733	−	0.442942i
$153$	−2.64855	−	4.58743i	−0.214123	−	0.370872i
$154$	6.67251	+	11.5571i	0.537687	+	0.931300i
$155$	−39.6270			−3.18292
$156$	2.43615	−	4.21953i	0.195048	−	0.337833i
$157$	17.6832			1.41127			0.705635	−	0.708575i	$-0.250662\pi$
$157$	17.6832			1.41127			0.705635	+	0.708575i	$0.250662\pi$
$158$	−0.587771	−	1.01805i	−0.0467606	−	0.0809917i
$159$	0.901565			0.0714988
$160$	−2.11078	−	3.65598i	−0.166872	−	0.289030i
$161$	−6.05949	+	10.4953i	−0.477555	+	0.827149i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	2.71995			0.213043			0.106521	−	0.994310i	$-0.466029\pi$
$163$	2.71995			0.213043			0.106521	+	0.994310i	$0.466029\pi$
$164$	4.24967			0.331843
$165$	10.8723	+	18.8313i	0.846406	+	1.46602i
$166$	−5.17514	−	8.96361i	−0.401669	−	0.695711i
$167$	5.92085			0.458169			0.229085	−	0.973407i	$-0.426427\pi$
$167$	5.92085			0.458169			0.229085	+	0.973407i	$0.426427\pi$
$168$	1.29542	−	2.24374i	0.0999441	−	0.173108i
$169$	10.7392			0.826095
$170$	−11.1810	−	19.3661i	−0.857546	−	1.48531i
$171$	6.30577			0.482214
$172$	−6.05006	+	10.4790i	−0.461312	+	0.799016i
$173$	7.32250	−	12.6829i	0.556719	−	0.964266i	−0.441048	−	0.897483i	$-0.645393\pi$
$173$	7.32250	−	12.6829i	0.556719	−	0.964266i	0.997768	−	0.0667829i	$-0.0212735\pi$
$174$	−7.53718			−0.571392
$175$	−16.6094	+	28.7683i	−1.25555	+	2.17468i
$176$	−2.57542	−	4.46076i	−0.194129	−	0.336242i
$177$	−2.64771	+	4.58596i	−0.199014	+	0.344702i
$178$	1.26932	−	2.19852i	0.0951394	−	0.164786i
$179$	−1.78315	−	3.08850i	−0.133279	−	0.230845i	0.791660	−	0.610962i	$-0.209217\pi$
$179$	−1.78315	−	3.08850i	−0.133279	−	0.230845i	−0.924939	+	0.380117i	$0.875884\pi$
$180$	2.11078	−	3.65598i	0.157328	−	0.272501i
$181$	−4.44526	+	7.69941i	−0.330413	+	0.572293i	−0.982593	−	0.185772i	$-0.940521\pi$
$181$	−4.44526	+	7.69941i	−0.330413	+	0.572293i	0.652180	+	0.758065i	$0.273855\pi$
$182$	12.6234			0.935706
$183$	6.65178	+	11.5212i	0.491713	+	0.851673i
$184$	2.33881	−	4.05093i	0.172419	−	0.298639i
$185$	4.59023	−	7.95050i	0.337480	−	0.584533i
$186$	4.69341	+	8.12922i	0.344137	+	0.596063i
$187$	−13.6423	−	23.6291i	−0.997621	−	1.72793i
$188$	0.796236	+	1.37912i	0.0580715	+	0.100583i
$189$	2.59085			0.188456
$190$	26.6202			1.93123
$191$	11.5887			0.838531			0.419266	−	0.907864i	$-0.362288\pi$
$191$	11.5887			0.838531			0.419266	+	0.907864i	$0.362288\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−3.59732			−0.258940			−0.129470	−	0.991583i	$-0.541328\pi$
$193$	−3.59732			−0.258940			−0.129470	+	0.991583i	$0.541328\pi$
$194$	−1.65648	−	2.86911i	−0.118928	−	0.205990i
$195$	20.5687			1.47295
$196$	−0.287512			−0.0205366
$197$	5.13007			0.365503			0.182751	−	0.983159i	$-0.441500\pi$
$197$	5.13007			0.365503			0.182751	+	0.983159i	$0.441500\pi$
$198$	2.57542	−	4.46076i	0.183027	−	0.317012i
$199$	−4.18390	+	7.24672i	−0.296589	+	0.513706i	−0.975353	−	0.220649i	$-0.929182\pi$
$199$	−4.18390	+	7.24672i	−0.296589	+	0.513706i	0.678765	+	0.734356i	$0.262516\pi$
$200$	6.41078	−	11.1038i	0.453311	−	0.785157i
$201$	−1.27918	−	2.21561i	−0.0902266	−	0.156277i
$202$	1.08941	−	1.88692i	0.0766509	−	0.132763i
$203$	−9.76384	−	16.9115i	−0.685287	−	1.18695i
$204$	−2.64855	+	4.58743i	−0.185436	+	0.321184i
$205$	8.97011	+	15.5367i	0.626500	+	1.08513i
$206$	0.308966			0.0215267
$207$	4.67761			0.325117
$208$	−4.87229			−0.337833
$209$	32.4800			2.24669
$210$	10.9374			0.754753
$211$	−4.11681	+	7.13052i	−0.283413	+	0.490885i	−0.972223	−	0.234057i	$-0.924800\pi$
$211$	−4.11681	+	7.13052i	−0.283413	+	0.490885i	0.688810	+	0.724942i	$0.258133\pi$
$212$	−0.450783	−	0.780778i	−0.0309599	−	0.0536241i
$213$	−7.07517	−	12.2546i	−0.484783	−	0.839669i
$214$	1.46442	+	2.53645i	0.100106	+	0.173388i
$215$	−51.0813			−3.48372
$216$	−1.00000			−0.0680414
$217$	−12.1599	+	21.0616i	−0.825468	+	1.42975i
$218$	−2.15271	−	3.72861i	−0.145800	−	0.252533i
$219$	−9.07800			−0.613434
$220$	10.8723	−	18.8313i	0.733009	−	1.26961i
$221$	−25.8091			−1.73611
$222$	−2.17466			−0.145954
$223$	10.7116	−	10.4049i	0.717301	−	0.696763i
$223$	10.7116	−	10.4049i	0.717301	−	0.696763i
$224$	−2.59085			−0.173108
$225$	12.8216			0.854771
$226$	2.20178	−	3.81359i	0.146460	−	0.253676i
$227$	−11.4774			−0.761785			−0.380892	−	0.924619i	$-0.624383\pi$
$227$	−11.4774			−0.761785			−0.380892	+	0.924619i	$0.624383\pi$
$228$	−3.15288	−	5.46095i	−0.208805	−	0.361661i
$229$	−4.09598	+	7.09444i	−0.270670	+	0.468814i	−0.969033	−	0.246929i	$-0.920578\pi$
$229$	−4.09598	+	7.09444i	−0.270670	+	0.468814i	0.698364	+	0.715743i	$0.253912\pi$
$230$	19.7468			1.30207
$231$	13.3450			0.878038
$232$	3.76859	+	6.52739i	0.247420	+	0.428544i
$233$	−11.3704	−	19.6941i	−0.744898	−	1.29020i	−0.950242	−	0.311512i	$-0.899165\pi$
$233$	−11.3704	−	19.6941i	−0.744898	−	1.29020i	0.205344	−	0.978690i	$-0.434169\pi$
$234$	−2.43615	−	4.21953i	−0.159256	−	0.275839i
$235$	−3.36136	+	5.82204i	−0.219271	+	0.379788i
$236$	5.29542			0.344702
$237$	−1.17554			−0.0763597
$238$	−13.7240			−0.889594
$239$	13.6010			0.879773			0.439886	−	0.898053i	$-0.355019\pi$
$239$	13.6010			0.879773			0.439886	+	0.898053i	$0.355019\pi$
$240$	−4.22156			−0.272501
$241$	1.96708	+	3.40707i	0.126710	+	0.219469i	0.922400	−	0.386235i	$-0.126225\pi$
$241$	1.96708	+	3.40707i	0.126710	+	0.219469i	−0.795690	+	0.605704i	$0.792891\pi$
$242$	7.76556	−	13.4503i	0.499189	−	0.864621i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	6.65178	−	11.5212i	0.425836	−	0.737570i
$245$	−0.606875	−	1.05114i	−0.0387719	−	0.0671548i
$246$	2.12483	−	3.68032i	0.135474	−	0.234649i
$247$	15.3618	−	26.6074i	0.977446	−	1.69299i
$248$	4.69341	−	8.12922i	0.298032	−	0.516206i
$249$	−10.3503			−0.655923
$250$	33.0192			2.08832
$251$	−0.403689			−0.0254806			−0.0127403	−	0.999919i	$-0.504055\pi$
$251$	−0.403689			−0.0254806			−0.0127403	+	0.999919i	$0.504055\pi$
$252$	−1.29542	−	2.24374i	−0.0816040	−	0.141342i
$253$	24.0936			1.51475
$254$	−4.98991	+	8.64278i	−0.313095	+	0.542296i
$255$	−22.3621			−1.40037
$256$	1.00000			0.0625000
$257$	−7.62435			−0.475594			−0.237797	−	0.971315i	$-0.576425\pi$
$257$	−7.62435			−0.475594			−0.237797	+	0.971315i	$0.576425\pi$
$258$	6.05006	+	10.4790i	0.376660	+	0.652394i
$259$	−2.81710	−	4.87937i	−0.175046	−	0.303189i
$260$	−10.2843	−	17.8130i	−0.637808	−	1.10472i
$261$	−3.76859	+	6.52739i	−0.233270	+	0.404035i
$262$	−8.41391	+	14.5733i	−0.519813	+	0.900343i
$263$	5.53440	+	9.58586i	0.341266	+	0.591089i	0.984668	−	0.174439i	$-0.0558111\pi$
$263$	5.53440	+	9.58586i	0.341266	+	0.591089i	−0.643402	+	0.765528i	$0.722478\pi$
$264$	−5.15084			−0.317012
$265$	1.90301	−	3.29610i	0.116901	−	0.202478i
$266$	8.16864	−	14.1485i	0.500851	−	0.867500i
$267$	−1.26932	−	2.19852i	−0.0776810	−	0.134547i
$268$	−1.27918	+	2.21561i	−0.0781385	+	0.135340i
$269$	−2.72049	+	4.71203i	−0.165871	+	0.287297i	−0.936964	−	0.349425i	$-0.886377\pi$
$269$	−2.72049	+	4.71203i	−0.165871	+	0.287297i	0.771093	+	0.636722i	$0.219710\pi$
$270$	−2.11078	−	3.65598i	−0.128458	−	0.222496i
$271$	−9.23501	+	15.9955i	−0.560987	+	0.971658i	0.436424	+	0.899741i	$0.356245\pi$
$271$	−9.23501	+	15.9955i	−0.560987	+	0.971658i	−0.997411	+	0.0719166i	$0.977088\pi$
$272$	5.29711			0.321184
$273$	6.31168	−	10.9322i	0.382000	−	0.661644i
$274$	−11.0998	+	19.2255i	−0.670566	+	1.16145i
$275$	66.0418			3.98247
$276$	−2.33881	−	4.05093i	−0.140780	−	0.243837i
$277$	18.6872			1.12280			0.561402	−	0.827544i	$-0.310262\pi$
$277$	18.6872			1.12280			0.561402	+	0.827544i	$0.310262\pi$
$278$	2.11269	−	3.65929i	0.126711	−	0.219470i
$279$	9.38682			0.561974
$280$	−5.46871	−	9.47208i	−0.326818	−	0.566065i
$281$	6.86290	+	11.8869i	0.409406	+	0.709112i	0.994823	−	0.101620i	$-0.0324026\pi$
$281$	6.86290	+	11.8869i	0.409406	+	0.709112i	−0.585417	+	0.810732i	$0.699069\pi$
$282$	1.59247			0.0948303
$283$	−9.93309			−0.590461			−0.295230	−	0.955426i	$-0.595396\pi$
$283$	−9.93309			−0.590461			−0.295230	+	0.955426i	$0.595396\pi$
$284$	−7.07517	+	12.2546i	−0.419834	+	0.727174i
$285$	13.3101	−	23.0537i	0.788422	−	1.36559i
$286$	−12.5482	−	21.7341i	−0.741990	−	1.28516i
$287$	11.0102			0.649914
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	11.0593			0.650550
$290$	−15.9093	+	27.5558i	−0.934228	+	1.61813i
$291$	−3.31296			−0.194209
$292$	4.53900	+	7.86178i	0.265625	+	0.460076i
$293$	5.07181	+	8.78464i	0.296298	+	0.513204i	0.975286	−	0.220946i	$-0.0709144\pi$
$293$	5.07181	+	8.78464i	0.296298	+	0.513204i	−0.678988	+	0.734150i	$0.737581\pi$
$294$	−0.143756	+	0.248993i	−0.00838403	+	0.0145216i
$295$	11.1775	+	19.3599i	0.650777	+	1.12718i
$296$	1.08733	+	1.88331i	0.0631997	+	0.109465i
$297$	−2.57542	−	4.46076i	−0.149441	−	0.258839i
$298$	−5.48508	−	9.50043i	−0.317742	−	0.550345i
$299$	11.3954	−	19.7373i	0.659010	−	1.14144i
$300$	−6.41078	−	11.1038i	−0.370127	−	0.641078i
$301$	−15.6748	+	27.1495i	−0.903479	+	1.56487i
$302$	8.67586	+	15.0270i	0.499239	+	0.864708i
$303$	−1.08941	−	1.88692i	−0.0625852	−	0.108401i
$304$	−3.15288	+	5.46095i	−0.180830	+	0.313207i
$305$	56.1617			3.21581
$306$	2.64855	+	4.58743i	0.151408	+	0.262246i
$307$	11.2890	−	19.5532i	0.644299	−	1.11596i	−0.340164	−	0.940366i	$-0.610483\pi$
$307$	11.2890	−	19.5532i	0.644299	−	1.11596i	0.984463	−	0.175592i	$-0.0561840\pi$
$308$	−6.67251	−	11.5571i	−0.380202	−	0.658529i
$309$	0.154483	−	0.267573i	0.00878824	−	0.0152217i
$310$	39.6270			2.25066
$311$	5.64643	+	9.77990i	0.320179	+	0.554567i	0.980525	−	0.196395i	$-0.0629235\pi$
$311$	5.64643	+	9.77990i	0.320179	+	0.554567i	−0.660345	+	0.750962i	$0.729590\pi$
$312$	−2.43615	+	4.21953i	−0.137920	+	0.238884i
$313$	12.7927	−	22.1576i	0.723086	−	1.25242i	−0.236670	−	0.971590i	$-0.576056\pi$
$313$	12.7927	−	22.1576i	0.723086	−	1.25242i	0.959757	−	0.280832i	$-0.0906105\pi$
$314$	−17.6832			−0.997919
$315$	5.46871	−	9.47208i	0.308127	−	0.533691i
$316$	0.587771	+	1.01805i	0.0330647	+	0.0572698i
$317$	−5.50493	−	9.53482i	−0.309188	−	0.535529i	0.668997	−	0.743265i	$-0.266724\pi$
$317$	−5.50493	−	9.53482i	−0.309188	−	0.535529i	−0.978185	+	0.207736i	$0.933391\pi$
$318$	−0.901565			−0.0505573
$319$	−19.4114	+	33.6215i	−1.08683	+	1.88244i
$320$	2.11078	+	3.65598i	0.117996	+	0.204375i
$321$	2.92884			0.163472
$322$	6.05949	−	10.4953i	0.337682	−	0.584883i
$323$	−16.7012	+	28.9273i	−0.929278	+	1.60956i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	31.2352	−	54.1010i	1.73262	−	3.00098i
$326$	−2.71995			−0.150644
$327$	−4.30542			−0.238090
$328$	−4.24967			−0.234649
$329$	2.06293	+	3.57309i	0.113733	+	0.196991i
$330$	−10.8723	−	18.8313i	−0.598499	−	1.03663i
$331$	−10.1688			−0.558930			−0.279465	−	0.960156i	$-0.590157\pi$
$331$	−10.1688			−0.558930			−0.279465	+	0.960156i	$0.590157\pi$
$332$	5.17514	+	8.96361i	0.284023	+	0.491942i
$333$	−1.08733	+	1.88331i	−0.0595853	+	0.103205i
$334$	−5.92085			−0.323974
$335$	−10.8003			−0.590083
$336$	−1.29542	+	2.24374i	−0.0706711	+	0.122406i
$337$	15.4463	+	26.7537i	0.841411	+	1.45737i	0.888702	+	0.458486i	$0.151608\pi$
$337$	15.4463	+	26.7537i	0.841411	+	1.45737i	−0.0472907	+	0.998881i	$0.515059\pi$
$338$	−10.7392			−0.584138
$339$	−2.20178	−	3.81359i	−0.119584	−	0.207126i
$340$	11.1810	+	19.3661i	0.606376	+	1.05027i
$341$	48.3499			2.61830
$342$	−6.30577			−0.340977
$343$	−18.8808			−1.01947
$344$	6.05006	−	10.4790i	0.326197	−	0.564990i
$345$	9.87341	−	17.1013i	0.531567	−	0.920701i
$346$	−7.32250	+	12.6829i	−0.393660	+	0.681839i
$347$	8.30040	−	14.3767i	0.445589	−	0.771783i	−0.552504	−	0.833510i	$-0.686328\pi$
$347$	8.30040	−	14.3767i	0.445589	−	0.771783i	0.998093	+	0.0617276i	$0.0196610\pi$
$348$	7.53718			0.404035
$349$	−1.41114	−	2.44417i	−0.0755368	−	0.130834i	0.825783	−	0.563988i	$-0.190734\pi$
$349$	−1.41114	−	2.44417i	−0.0755368	−	0.130834i	−0.901320	+	0.433155i	$0.857400\pi$
$350$	16.6094	−	28.7683i	0.887808	−	1.53773i
$351$	−4.87229			−0.260064
$352$	2.57542	+	4.46076i	0.137270	+	0.237759i
$353$	−6.39503	−	11.0765i	−0.340373	−	0.589543i	0.644129	−	0.764917i	$-0.277220\pi$
$353$	−6.39503	−	11.0765i	−0.340373	−	0.589543i	−0.984502	+	0.175374i	$0.943887\pi$
$354$	2.64771	−	4.58596i	0.140724	−	0.243741i
$355$	−59.7365			−3.17049
$356$	−1.26932	+	2.19852i	−0.0672737	+	0.116522i
$357$	−6.86200	+	11.8853i	−0.363175	+	0.629038i
$358$	1.78315	+	3.08850i	0.0942423	+	0.163232i
$359$	1.28965			0.0680651			0.0340326	−	0.999421i	$-0.489165\pi$
$359$	1.28965			0.0680651			0.0340326	+	0.999421i	$0.489165\pi$
$360$	−2.11078	+	3.65598i	−0.111248	+	0.192687i
$361$	−10.3814	−	17.9810i	−0.546387	−	0.946370i
$362$	4.44526	−	7.69941i	0.233638	−	0.404672i
$363$	−7.76556	−	13.4503i	−0.407586	−	0.705960i
$364$	−12.6234			−0.661644
$365$	−19.1617	+	33.1890i	−1.00297	+	1.73719i
$366$	−6.65178	−	11.5212i	−0.347694	−	0.602224i
$367$	−0.843112	−	1.46031i	−0.0440101	−	0.0762277i	0.843181	−	0.537629i	$-0.180680\pi$
$367$	−0.843112	−	1.46031i	−0.0440101	−	0.0762277i	−0.887191	+	0.461402i	$0.847347\pi$
$368$	−2.33881	+	4.05093i	−0.121919	+	0.211169i
$369$	−2.12483	−	3.68032i	−0.110614	−	0.191590i
$370$	−4.59023	+	7.95050i	−0.238634	+	0.413327i
$371$	−1.16791	−	2.02288i	−0.0606348	−	0.105023i
$372$	−4.69341	−	8.12922i	−0.243342	−	0.421480i
$373$	−14.0108	−	24.2674i	−0.725451	−	1.25652i	−0.958788	−	0.284123i	$-0.908298\pi$
$373$	−14.0108	−	24.2674i	−0.725451	−	1.25652i	0.233337	−	0.972396i	$-0.425036\pi$
$374$	13.6423	+	23.6291i	0.705425	+	1.22183i
$375$	16.5096	−	28.5955i	0.852552	−	1.47666i
$376$	−0.796236	−	1.37912i	−0.0410627	−	0.0711227i
$377$	18.3617	+	31.8034i	0.945674	+	1.63796i
$378$	−2.59085			−0.133259
$379$	11.1190	−	19.2586i	0.571143	−	0.989248i	−0.425306	−	0.905049i	$-0.639834\pi$
$379$	11.1190	−	19.2586i	0.571143	−	0.989248i	0.996449	−	0.0841987i	$-0.0268331\pi$
$380$	−26.6202			−1.36559
$381$	4.98991	+	8.64278i	0.255641	+	0.442783i
$382$	−11.5887			−0.592931
$383$	11.0899	+	19.2083i	0.566669	+	0.981500i	0.996892	+	0.0787775i	$0.0251017\pi$
$383$	11.0899	+	19.2083i	0.566669	+	0.981500i	−0.430223	+	0.902723i	$0.641565\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	28.1684	−	48.7891i	1.43560	−	2.48652i
$386$	3.59732			0.183099
$387$	12.1001			0.615083
$388$	1.65648	+	2.86911i	0.0840950	+	0.145657i
$389$	−1.25351	−	2.17114i	−0.0635555	−	0.110081i	0.832497	−	0.554030i	$-0.186911\pi$
$389$	−1.25351	−	2.17114i	−0.0635555	−	0.110081i	−0.896052	+	0.443948i	$0.853577\pi$
$390$	−20.5687			−1.04154
$391$	−12.3889	+	21.4582i	−0.626534	+	1.08519i
$392$	0.287512			0.0145216
$393$	8.41391	+	14.5733i	0.424426	+	0.735127i
$394$	−5.13007			−0.258449
$395$	−2.48131	+	4.29776i	−0.124848	+	0.216244i
$396$	−2.57542	+	4.46076i	−0.129420	+	0.224161i
$397$	10.0293			0.503358			0.251679	−	0.967811i	$-0.419017\pi$
$397$	10.0293			0.503358			0.251679	+	0.967811i	$0.419017\pi$
$398$	4.18390	−	7.24672i	0.209720	−	0.363245i
$399$	−8.16864	−	14.1485i	−0.408943	−	0.708311i
$400$	−6.41078	+	11.1038i	−0.320539	+	0.555190i
$401$	11.2259	−	19.4438i	0.560595	−	0.970978i	−0.436850	−	0.899534i	$-0.643906\pi$
$401$	11.2259	−	19.4438i	0.560595	−	0.970978i	0.997445	−	0.0714440i	$-0.0227607\pi$
$402$	1.27918	+	2.21561i	0.0637998	+	0.110505i
$403$	22.8677	−	39.6079i	1.13912	−	1.97301i
$404$	−1.08941	+	1.88692i	−0.0542003	+	0.0938777i
$405$	−4.22156			−0.209771
$406$	9.76384	+	16.9115i	0.484571	+	0.839302i
$407$	−5.60066	+	9.70062i	−0.277614	+	0.480842i
$408$	2.64855	−	4.58743i	0.131123	−	0.227112i
$409$	11.9931	+	20.7726i	0.593020	+	1.02714i	0.993823	+	0.110977i	$0.0353980\pi$
$409$	11.9931	+	20.7726i	0.593020	+	1.02714i	−0.400803	+	0.916164i	$0.631269\pi$
$410$	−8.97011	−	15.5367i	−0.443002	−	0.767303i
$411$	11.0998	+	19.2255i	0.547515	+	0.948323i
$412$	−0.308966			−0.0152217
$413$	13.7196			0.675098
$414$	−4.67761			−0.229892
$415$	−21.8472	+	37.8404i	−1.07244	+	1.85751i
$416$	4.87229			0.238884
$417$	−2.11269	−	3.65929i	−0.103459	−	0.179196i
$418$	−32.4800			−1.58865
$419$	−31.2268			−1.52553			−0.762763	−	0.646678i	$-0.776158\pi$
$419$	−31.2268			−1.52553			−0.762763	+	0.646678i	$0.776158\pi$
$420$	−10.9374			−0.533691
$421$	−14.4217	+	24.9791i	−0.702871	+	1.21741i	0.264583	+	0.964363i	$0.414766\pi$
$421$	−14.4217	+	24.9791i	−0.702871	+	1.21741i	−0.967454	+	0.253046i	$0.918568\pi$
$422$	4.11681	−	7.13052i	0.200403	−	0.347108i
$423$	0.796236	−	1.37912i	0.0387143	−	0.0670552i
$424$	0.450783	+	0.780778i	0.0218919	+	0.0379179i
$425$	−33.9586	+	58.8180i	−1.64723	+	2.85309i
$426$	7.07517	+	12.2546i	0.342793	+	0.593735i
$427$	17.2337	−	29.8497i	0.833999	−	1.44453i
$428$	−1.46442	−	2.53645i	−0.0707855	−	0.122604i
$429$	−25.0964			−1.21166
$430$	51.0813			2.46336
$431$	35.4989			1.70992			0.854961	−	0.518692i	$-0.173581\pi$
$431$	35.4989			1.70992			0.854961	+	0.518692i	$0.173581\pi$
$432$	1.00000			0.0481125
$433$	32.4135			1.55769			0.778846	−	0.627215i	$-0.215805\pi$
$433$	32.4135			1.55769			0.778846	+	0.627215i	$0.215805\pi$
$434$	12.1599	−	21.0616i	0.583694	−	1.01099i
$435$	15.9093	+	27.5558i	0.762794	+	1.32120i
$436$	2.15271	+	3.72861i	0.103096	+	0.178568i
$437$	−14.7480	−	25.5442i	−0.705491	−	1.22195i
$438$	9.07800			0.433764
$439$	21.5280			1.02747			0.513737	−	0.857948i	$-0.328261\pi$
$439$	21.5280			1.02747			0.513737	+	0.857948i	$0.328261\pi$
$440$	−10.8723	+	18.8313i	−0.518316	+	0.897749i
$441$	0.143756	+	0.248993i	0.00684553	+	0.0118568i
$442$	25.8091			1.22761
$443$	−3.75378	+	6.50174i	−0.178347	+	0.308907i	−0.941315	−	0.337530i	$-0.890408\pi$
$443$	−3.75378	+	6.50174i	−0.178347	+	0.308907i	0.762967	+	0.646437i	$0.223742\pi$
$444$	2.17466			0.103205
$445$	−10.7170			−0.508035
$446$	−10.7116	+	10.4049i	−0.507209	+	0.492686i
$447$	−10.9702			−0.518871
$448$	2.59085			0.122406
$449$	−12.6958	+	21.9897i	−0.599150	+	1.03776i	0.393797	+	0.919198i	$0.371161\pi$
$449$	−12.6958	+	21.9897i	−0.599150	+	1.03776i	−0.992947	+	0.118561i	$0.962172\pi$
$450$	−12.8216			−0.604414
$451$	−10.9447	−	18.9567i	−0.515365	−	0.892638i
$452$	−2.20178	+	3.81359i	−0.103563	+	0.179376i
$453$	17.3517			0.815255
$454$	11.4774			0.538663
$455$	−26.6451	−	46.1507i	−1.24914	−	2.16358i
$456$	3.15288	+	5.46095i	0.147647	+	0.255733i
$457$	−11.4188	−	19.7780i	−0.534150	−	0.925174i	−0.999204	−	0.0398923i	$-0.987299\pi$
$457$	−11.4188	−	19.7780i	−0.534150	−	0.925174i	0.465054	−	0.885282i	$-0.346035\pi$
$458$	4.09598	−	7.09444i	0.191392	−	0.331501i
$459$	5.29711			0.247248
$460$	−19.7468			−0.920701
$461$	2.25619			0.105081			0.0525406	−	0.998619i	$-0.483268\pi$
$461$	2.25619			0.105081			0.0525406	+	0.998619i	$0.483268\pi$
$462$	−13.3450			−0.620867
$463$	33.3883			1.55169			0.775843	−	0.630926i	$-0.217325\pi$
$463$	33.3883			1.55169			0.775843	+	0.630926i	$0.217325\pi$
$464$	−3.76859	−	6.52739i	−0.174952	−	0.303026i
$465$	19.8135	−	34.3180i	0.918829	−	1.59146i
$466$	11.3704	+	19.6941i	0.526723	+	0.912310i
$467$	12.6313	−	21.8781i	0.584509	−	1.01240i	−0.410428	−	0.911893i	$-0.634621\pi$
$467$	12.6313	−	21.8781i	0.584509	−	1.01240i	0.994936	−	0.100506i	$-0.0320461\pi$
$468$	2.43615	+	4.21953i	0.112611	+	0.195048i
$469$	−3.31417	+	5.74030i	−0.153034	+	0.265063i
$470$	3.36136	−	5.82204i	0.155048	−	0.268551i
$471$	−8.84158	+	15.3141i	−0.407399	+	0.705635i
$472$	−5.29542			−0.243741
$473$	62.3257			2.86574
$474$	1.17554			0.0539945
$475$	−40.4249	−	70.0180i	−1.85482	−	3.21265i
$476$	13.7240			0.629038
$477$	−0.450783	+	0.780778i	−0.0206399	+	0.0357494i
$478$	−13.6010			−0.622093
$479$	30.1457			1.37739			0.688696	−	0.725050i	$-0.258184\pi$
$479$	30.1457			1.37739			0.688696	+	0.725050i	$0.258184\pi$
$480$	4.22156			0.192687
$481$	5.29779	+	9.17604i	0.241558	+	0.418391i
$482$	−1.96708	−	3.40707i	−0.0895978	−	0.155188i
$483$	−6.05949	−	10.4953i	−0.275716	−	0.477555i
$484$	−7.76556	+	13.4503i	−0.352980	+	0.611379i
$485$	−6.99293	+	12.1121i	−0.317533	+	0.549982i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−28.1640			−1.27623			−0.638116	−	0.769940i	$-0.720286\pi$
$487$	−28.1640			−1.27623			−0.638116	+	0.769940i	$0.720286\pi$
$488$	−6.65178	+	11.5212i	−0.301112	+	0.521541i
$489$	−1.35997	+	2.35555i	−0.0615002	+	0.106521i
$490$	0.606875	+	1.05114i	0.0274158	+	0.0474856i
$491$	−6.70442	+	11.6124i	−0.302566	+	0.524060i	−0.976716	−	0.214534i	$-0.931177\pi$
$491$	−6.70442	+	11.6124i	−0.302566	+	0.524060i	0.674150	+	0.738594i	$0.264510\pi$
$492$	−2.12483	+	3.68032i	−0.0957949	+	0.165922i
$493$	−19.9626	−	34.5763i	−0.899072	−	1.55724i
$494$	−15.3618	+	26.6074i	−0.691159	+	1.19712i
$495$	−21.7446			−0.977345
$496$	−4.69341	+	8.12922i	−0.210740	+	0.365013i
$497$	−18.3307	+	31.7497i	−0.822244	+	1.42417i
$498$	10.3503			0.463807
$499$	7.92225	+	13.7217i	0.354649	+	0.614270i	0.987058	−	0.160365i	$-0.0512671\pi$
$499$	7.92225	+	13.7217i	0.354649	+	0.614270i	−0.632409	+	0.774635i	$0.717934\pi$
$500$	−33.0192			−1.47666
$501$	−2.96042	+	5.12761i	−0.132262	+	0.229085i
$502$	0.403689			0.0180175
$503$	10.2999	+	17.8399i	0.459249	+	0.795443i	0.998921	−	0.0464320i	$-0.0147851\pi$
$503$	10.2999	+	17.8399i	0.459249	+	0.795443i	−0.539672	+	0.841875i	$0.681452\pi$
$504$	1.29542	+	2.24374i	0.0577027	+	0.0999441i
$505$	−9.19805			−0.409308
$506$	−24.0936			−1.07109
$507$	−5.36962	+	9.30046i	−0.238473	+	0.413048i
$508$	4.98991	−	8.64278i	0.221392	−	0.383461i
$509$	−7.28795	−	12.6231i	−0.323033	−	0.559509i	0.658079	−	0.752949i	$-0.271369\pi$
$509$	−7.28795	−	12.6231i	−0.323033	−	0.559509i	−0.981112	+	0.193439i	$0.938036\pi$
$510$	22.3621			0.990208
$511$	11.7599	+	20.3687i	0.520225	+	0.901057i
$512$	−1.00000			−0.0441942
$513$	−3.15288	+	5.46095i	−0.139203	+	0.241107i
$514$	7.62435			0.336296
$515$	−0.652160	−	1.12957i	−0.0287376	−	0.0497750i
$516$	−6.05006	−	10.4790i	−0.266339	−	0.461312i
$517$	4.10128	−	7.10363i	0.180374	−	0.312417i
$518$	2.81710	+	4.87937i	0.123776	+	0.214387i
$519$	7.32250	+	12.6829i	0.321422	+	0.556719i
$520$	10.2843	+	17.8130i	0.450998	+	0.781152i
$521$	22.2064	+	38.4626i	0.972880	+	1.68508i	0.686760	+	0.726884i	$0.259032\pi$
$521$	22.2064	+	38.4626i	0.972880	+	1.68508i	0.286121	+	0.958194i	$0.407634\pi$
$522$	3.76859	−	6.52739i	0.164947	−	0.285696i
$523$	1.54579	+	2.67738i	0.0675926	+	0.117074i	0.897841	−	0.440320i	$-0.145135\pi$
$523$	1.54579	+	2.67738i	0.0675926	+	0.117074i	−0.830249	+	0.557393i	$0.811802\pi$
$524$	8.41391	−	14.5733i	0.367563	−	0.636639i
$525$	−16.6094	−	28.7683i	−0.724892	−	1.25555i
$526$	−5.53440	−	9.58586i	−0.241311	−	0.417963i
$527$	−24.8615	+	43.0614i	−1.08298	+	1.87578i
$528$	5.15084			0.224161
$529$	0.559963	+	0.969884i	0.0243462	+	0.0421689i
$530$	−1.90301	+	3.29610i	−0.0826613	+	0.143174i
$531$	−2.64771	−	4.58596i	−0.114901	−	0.199014i
$532$	−8.16864	+	14.1485i	−0.354155	+	0.613415i
$533$	−20.7056			−0.896860
$534$	1.26932	+	2.19852i	0.0549288	+	0.0951394i
$535$	6.18214	−	10.7078i	0.267277	−	0.462938i
$536$	1.27918	−	2.21561i	0.0552523	−	0.0956997i
$537$	3.56630			0.153897
$538$	2.72049	−	4.71203i	0.117289	−	0.203150i
$539$	0.740465	+	1.28252i	0.0318941	+	0.0552422i
$540$	2.11078	+	3.65598i	0.0908335	+	0.157328i
$541$	13.1630			0.565922			0.282961	−	0.959131i	$-0.408683\pi$
$541$	13.1630			0.565922			0.282961	+	0.959131i	$0.408683\pi$
$542$	9.23501	−	15.9955i	0.396678	−	0.687066i
$543$	−4.44526	−	7.69941i	−0.190764	−	0.330413i
$544$	−5.29711			−0.227112
$545$	−9.08780	+	15.7405i	−0.389279	+	0.674250i
$546$	−6.31168	+	10.9322i	−0.270115	+	0.467853i
$547$	−21.3020	+	36.8961i	−0.910807	+	1.57756i	−0.0978795	+	0.995198i	$0.531206\pi$
$547$	−21.3020	+	36.8961i	−0.910807	+	1.57756i	−0.812927	+	0.582365i	$0.802127\pi$
$548$	11.0998	−	19.2255i	0.474162	−	0.821272i
$549$	−13.3036			−0.567782
$550$	−66.0418			−2.81603
$551$	47.5277			2.02475
$552$	2.33881	+	4.05093i	0.0995462	+	0.172419i
$553$	1.52283	+	2.63761i	0.0647571	+	0.112163i
$554$	−18.6872			−0.793942
$555$	4.59023	+	7.95050i	0.194844	+	0.337480i
$556$	−2.11269	+	3.65929i	−0.0895981	+	0.155188i
$557$	32.0571			1.35831			0.679153	−	0.733997i	$-0.262347\pi$
$557$	32.0571			1.35831			0.679153	+	0.733997i	$0.262347\pi$
$558$	−9.38682			−0.397376
$559$	29.4776	−	51.0568i	1.24677	−	2.15947i
$560$	5.46871	+	9.47208i	0.231095	+	0.400268i
$561$	27.2845			1.15195
$562$	−6.86290	−	11.8869i	−0.289494	−	0.501418i
$563$	−11.5178	−	19.9494i	−0.485418	−	0.840769i	0.514442	−	0.857525i	$-0.327999\pi$
$563$	−11.5178	−	19.9494i	−0.485418	−	0.840769i	−0.999860	+	0.0167567i	$0.994666\pi$
$564$	−1.59247			−0.0670552
$565$	−18.5899			−0.782081
$566$	9.93309			0.417519
$567$	−1.29542	+	2.24374i	−0.0544027	+	0.0942282i
$568$	7.07517	−	12.2546i	0.296868	−	0.514190i
$569$	−1.97889	+	3.42754i	−0.0829593	+	0.143690i	−0.904520	−	0.426432i	$-0.859770\pi$
$569$	−1.97889	+	3.42754i	−0.0829593	+	0.143690i	0.821560	+	0.570121i	$0.193104\pi$
$570$	−13.3101	+	23.0537i	−0.557498	+	0.965615i
$571$	6.04172			0.252838			0.126419	−	0.991977i	$-0.459652\pi$
$571$	6.04172			0.252838			0.126419	+	0.991977i	$0.459652\pi$
$572$	12.5482	+	21.7341i	0.524666	+	0.908749i
$573$	−5.79437	+	10.0361i	−0.242063	+	0.419266i
$574$	−11.0102			−0.459559
$575$	−29.9872	−	51.9393i	−1.25055	−	2.16602i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−5.55669	+	9.62447i	−0.231328	+	0.400672i	−0.958199	−	0.286102i	$-0.907640\pi$
$577$	−5.55669	+	9.62447i	−0.231328	+	0.400672i	0.726871	+	0.686774i	$0.240974\pi$
$578$	−11.0593			−0.460008
$579$	1.79866	−	3.11537i	0.0747497	−	0.129470i
$580$	15.9093	−	27.5558i	0.660599	−	1.14419i
$581$	13.4080	+	23.2233i	0.556258	+	0.963467i
$582$	3.31296			0.137327
$583$	−2.32191	+	4.02166i	−0.0961636	+	0.166560i
$584$	−4.53900	−	7.86178i	−0.187825	−	0.325323i
$585$	−10.2843	+	17.8130i	−0.425205	+	0.736477i
$586$	−5.07181	−	8.78464i	−0.209515	−	0.362890i
$587$	11.0971			0.458028			0.229014	−	0.973423i	$-0.426450\pi$
$587$	11.0971			0.458028			0.229014	+	0.973423i	$0.426450\pi$
$588$	0.143756	−	0.248993i	0.00592841	−	0.0102683i
$589$	−29.5955	−	51.2610i	−1.21946	−	2.11217i
$590$	−11.1775	−	19.3599i	−0.460169	−	0.797035i
$591$	−2.56504	+	4.44277i	−0.105511	+	0.182751i
$592$	−1.08733	−	1.88331i	−0.0446890	−	0.0774035i
$593$	−10.0555	+	17.4167i	−0.412930	+	0.715216i	−0.995209	−	0.0977731i	$-0.968828\pi$
$593$	−10.0555	+	17.4167i	−0.412930	+	0.715216i	0.582278	+	0.812990i	$0.302161\pi$
$594$	2.57542	+	4.46076i	0.105671	+	0.183027i
$595$	28.9683	+	50.1746i	1.18759	+	2.05696i
$596$	5.48508	+	9.50043i	0.224678	+	0.389153i
$597$	−4.18390	−	7.24672i	−0.171235	−	0.296589i
$598$	−11.3954	+	19.7373i	−0.465991	+	0.807120i
$599$	−8.58974	−	14.8779i	−0.350967	−	0.607893i	0.635452	−	0.772140i	$-0.280814\pi$
$599$	−8.58974	−	14.8779i	−0.350967	−	0.607893i	−0.986419	+	0.164247i	$0.947480\pi$
$600$	6.41078	+	11.1038i	0.261719	+	0.453311i
$601$	−32.3849			−1.32101			−0.660505	−	0.750822i	$-0.729658\pi$
$601$	−32.3849			−1.32101			−0.660505	+	0.750822i	$0.729658\pi$
$602$	15.6748	−	27.1495i	0.638856	−	1.10653i
$603$	2.55836			0.104185
$604$	−8.67586	−	15.0270i	−0.353016	−	0.611441i
$605$	−65.5655			−2.66562
$606$	1.08941	+	1.88692i	0.0442544	+	0.0766509i
$607$	−8.21034	+	14.2207i	−0.333247	+	0.577201i	−0.983147	−	0.182819i	$-0.941478\pi$
$607$	−8.21034	+	14.2207i	−0.333247	+	0.577201i	0.649899	+	0.760020i	$0.274811\pi$
$608$	3.15288	−	5.46095i	0.127866	−	0.221471i
$609$	19.5277			0.791302
$610$	−56.1617			−2.27392
$611$	−3.87949	−	6.71948i	−0.156948	−	0.271841i
$612$	−2.64855	−	4.58743i	−0.107061	−	0.185436i
$613$	−8.02686			−0.324202			−0.162101	−	0.986774i	$-0.551827\pi$
$613$	−8.02686			−0.324202			−0.162101	+	0.986774i	$0.551827\pi$
$614$	−11.2890	+	19.5532i	−0.455588	+	0.789102i
$615$	−17.9402			−0.723420
$616$	6.67251	+	11.5571i	0.268843	+	0.465650i
$617$	−31.3545			−1.26228			−0.631142	−	0.775667i	$-0.717414\pi$
$617$	−31.3545			−1.26228			−0.631142	+	0.775667i	$0.717414\pi$
$618$	−0.154483	+	0.267573i	−0.00621423	+	0.0107634i
$619$	0.710174	−	1.23006i	0.0285443	−	0.0494402i	−0.851400	−	0.524516i	$-0.824246\pi$
$619$	0.710174	−	1.23006i	0.0285443	−	0.0494402i	0.879945	+	0.475076i	$0.157579\pi$
$620$	−39.6270			−1.59146
$621$	−2.33881	+	4.05093i	−0.0938531	+	0.162558i
$622$	−5.64643	−	9.77990i	−0.226401	−	0.392138i
$623$	−3.28861	+	5.69604i	−0.131755	+	0.228207i
$624$	2.43615	−	4.21953i	0.0975239	−	0.168916i
$625$	−37.6424	−	65.1985i	−1.50570	−	2.60794i
$626$	−12.7927	+	22.1576i	−0.511299	+	0.885596i
$627$	−16.2400	+	28.1285i	−0.648563	+	1.12334i
$628$	17.6832			0.705635
$629$	−5.75970	−	9.97609i	−0.229654	−	0.397773i
$630$	−5.46871	+	9.47208i	−0.217879	+	0.377377i
$631$	6.13214	−	10.6212i	0.244117	−	0.422823i	−0.717766	−	0.696284i	$-0.754835\pi$
$631$	6.13214	−	10.6212i	0.244117	−	0.422823i	0.961883	+	0.273462i	$0.0881686\pi$
$632$	−0.587771	−	1.01805i	−0.0233803	−	0.0404959i
$633$	−4.11681	−	7.13052i	−0.163628	−	0.283413i
$634$	5.50493	+	9.53482i	0.218629	+	0.378676i
$635$	42.1304			1.67189
$636$	0.901565			0.0357494
$637$	1.40084			0.0555035
$638$	19.4114	−	33.6215i	0.768504	−	1.33109i
$639$	14.1503			0.559779
$640$	−2.11078	−	3.65598i	−0.0834359	−	0.144515i
$641$	43.8623			1.73246			0.866229	−	0.499648i	$-0.166537\pi$
$641$	43.8623			1.73246			0.866229	+	0.499648i	$0.166537\pi$
$642$	−2.92884			−0.115592
$643$	39.2525			1.54797			0.773983	−	0.633206i	$-0.218262\pi$
$643$	39.2525			1.54797			0.773983	+	0.633206i	$0.218262\pi$
$644$	−6.05949	+	10.4953i	−0.238777	+	0.413575i
$645$	25.5407	−	44.2377i	1.00566	−	1.74186i
$646$	16.7012	−	28.9273i	0.657098	−	1.13813i
$647$	1.38754	+	2.40329i	0.0545498	+	0.0944831i	0.892011	−	0.452014i	$-0.149294\pi$
$647$	1.38754	+	2.40329i	0.0545498	+	0.0944831i	−0.837461	+	0.546497i	$0.815961\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−13.6379	−	23.6216i	−0.535335	−	0.927227i
$650$	−31.2352	+	54.1010i	−1.22515	+	2.12202i
$651$	−12.1599	−	21.0616i	−0.476584	−	0.825468i
$652$	2.71995			0.106521
$653$	−27.0817			−1.05979			−0.529895	−	0.848063i	$-0.677769\pi$
$653$	−27.0817			−1.05979			−0.529895	+	0.848063i	$0.677769\pi$
$654$	4.30542			0.168355
$655$	71.0397			2.77575
$656$	4.24967			0.165922
$657$	4.53900	−	7.86178i	0.177083	−	0.306717i
$658$	−2.06293	−	3.57309i	−0.0804212	−	0.139294i
$659$	−12.7753	−	22.1275i	−0.497656	−	0.861966i	0.502340	−	0.864670i	$-0.332473\pi$
$659$	−12.7753	−	22.1275i	−0.497656	−	0.861966i	−0.999996	+	0.00270398i	$0.999139\pi$
$660$	10.8723	+	18.8313i	0.423203	+	0.733009i
$661$	−45.3761			−1.76492			−0.882462	−	0.470383i	$-0.844116\pi$
$661$	−45.3761			−1.76492			−0.882462	+	0.470383i	$0.844116\pi$
$662$	10.1688			0.395224
$663$	12.9045	−	22.3513i	0.501170	−	0.868053i
$664$	−5.17514	−	8.96361i	−0.200835	−	0.347856i
$665$	−68.9688			−2.67450
$666$	1.08733	−	1.88331i	0.0421332	−	0.0729768i
$667$	35.2560			1.36512
$668$	5.92085			0.229085
$669$	3.65510	+	14.4790i	0.141314	+	0.559789i
$670$	10.8003			0.417252
$671$	−68.5244			−2.64536
$672$	1.29542	−	2.24374i	0.0499720	−	0.0865541i
$673$	−29.1342			−1.12304			−0.561520	−	0.827463i	$-0.689783\pi$
$673$	−29.1342			−1.12304			−0.561520	+	0.827463i	$0.689783\pi$
$674$	−15.4463	−	26.7537i	−0.594968	−	1.03051i
$675$	−6.41078	+	11.1038i	−0.246751	+	0.427386i
$676$	10.7392			0.413048
$677$	1.50868			0.0579834			0.0289917	−	0.999580i	$-0.490770\pi$
$677$	1.50868			0.0579834			0.0289917	+	0.999580i	$0.490770\pi$
$678$	2.20178	+	3.81359i	0.0845587	+	0.146460i
$679$	4.29169	+	7.43342i	0.164700	+	0.285268i
$680$	−11.1810	−	19.3661i	−0.428773	−	0.742656i
$681$	5.73872	−	9.93976i	0.219908	−	0.380892i
$682$	−48.3499			−1.85142
$683$	−33.0642			−1.26517			−0.632583	−	0.774493i	$-0.718005\pi$
$683$	−33.0642			−1.26517			−0.632583	+	0.774493i	$0.718005\pi$
$684$	6.30577			0.241107
$685$	93.7173			3.58075
$686$	18.8808			0.720873
$687$	−4.09598	−	7.09444i	−0.156271	−	0.270670i
$688$	−6.05006	+	10.4790i	−0.230656	+	0.399508i
$689$	2.19634	+	3.80418i	0.0836741	+	0.144928i
$690$	−9.87341	+	17.1013i	−0.375874	+	0.651034i
$691$	7.12164	+	12.3350i	0.270920	+	0.469247i	0.969098	−	0.246677i	$-0.0793388\pi$
$691$	7.12164	+	12.3350i	0.270920	+	0.469247i	−0.698178	+	0.715925i	$0.746005\pi$
$692$	7.32250	−	12.6829i	0.278360	−	0.482133i
$693$	−6.67251	+	11.5571i	−0.253468	+	0.439019i
$694$	−8.30040	+	14.3767i	−0.315079	+	0.545733i
$695$	−17.8377			−0.676623
$696$	−7.53718			−0.285696
$697$	22.5109			0.852663
$698$	1.41114	+	2.44417i	0.0534126	+	0.0925133i
$699$	22.7408			0.860134
$700$	−16.6094	+	28.7683i	−0.627775	+	1.08734i
$701$	28.5988			1.08016			0.540080	−	0.841614i	$-0.318394\pi$
$701$	28.5988			1.08016			0.540080	+	0.841614i	$0.318394\pi$
$702$	4.87229			0.183893
$703$	13.7129			0.517191
$704$	−2.57542	−	4.46076i	−0.0970647	−	0.168121i
$705$	−3.36136	−	5.82204i	−0.126596	−	0.219271i
$706$	6.39503	+	11.0765i	0.240680	+	0.416870i
$707$	−2.82250	+	4.88872i	−0.106151	+	0.183859i
$708$	−2.64771	+	4.58596i	−0.0995069	+	0.172351i
$709$	10.8532	+	18.7982i	0.407599	+	0.705982i	0.994620	−	0.103590i	$-0.0330329\pi$
$709$	10.8532	+	18.7982i	0.407599	+	0.705982i	−0.587021	+	0.809571i	$0.699700\pi$
$710$	59.7365			2.24187
$711$	0.587771	−	1.01805i	0.0220432	−	0.0381799i
$712$	1.26932	−	2.19852i	0.0475697	−	0.0823932i
$713$	−21.9539	−	38.0254i	−0.822182	−	1.42406i
$714$	6.86200	−	11.8853i	0.256804	−	0.444797i
$715$	−52.9729	+	91.7518i	−1.98108	+	3.43132i
$716$	−1.78315	−	3.08850i	−0.0666394	−	0.115423i
$717$	−6.80048	+	11.7788i	−0.253969	+	0.439886i
$718$	−1.28965			−0.0481293
$719$	−21.6430	+	37.4867i	−0.807147	+	1.39802i	0.107685	+	0.994185i	$0.465656\pi$
$719$	−21.6430	+	37.4867i	−0.807147	+	1.39802i	−0.914832	+	0.403834i	$0.867677\pi$
$720$	2.11078	−	3.65598i	0.0786641	−	0.136250i
$721$	−0.800485			−0.0298116
$722$	10.3814	+	17.9810i	0.386354	+	0.669185i
$723$	−3.93415			−0.146313
$724$	−4.44526	+	7.69941i	−0.165207	+	0.286146i
$725$	96.6385			3.58906
$726$	7.76556	+	13.4503i	0.288207	+	0.499189i
$727$	14.4099	+	24.9587i	0.534433	+	0.925665i	0.999191	+	0.0402274i	$0.0128082\pi$
$727$	14.4099	+	24.9587i	0.534433	+	0.925665i	−0.464757	+	0.885438i	$0.653858\pi$
$728$	12.6234			0.467853
$729$	1.00000			0.0370370
$730$	19.1617	−	33.1890i	0.709205	−	1.22838i
$731$	−32.0478	+	55.5084i	−1.18533	+	2.05305i
$732$	6.65178	+	11.5212i	0.245857	+	0.425836i
$733$	−1.10859			−0.0409466			−0.0204733	−	0.999790i	$-0.506517\pi$
$733$	−1.10859			−0.0409466			−0.0204733	+	0.999790i	$0.506517\pi$
$734$	0.843112	+	1.46031i	0.0311198	+	0.0539011i
$735$	1.21375			0.0447699
$736$	2.33881	−	4.05093i	0.0862096	−	0.149319i
$737$	13.1777			0.485407
$738$	2.12483	+	3.68032i	0.0782162	+	0.135474i
$739$	6.52367	+	11.2993i	0.239977	+	0.415652i	0.960707	−	0.277563i	$-0.0895268\pi$
$739$	6.52367	+	11.2993i	0.239977	+	0.415652i	−0.720730	+	0.693215i	$0.756193\pi$
$740$	4.59023	−	7.95050i	0.168740	−	0.292266i
$741$	15.3618	+	26.6074i	0.564329	+	0.977446i
$742$	1.16791	+	2.02288i	0.0428753	+	0.0742621i
$743$	−9.71823	−	16.8325i	−0.356527	−	0.617523i	0.630851	−	0.775904i	$-0.282706\pi$
$743$	−9.71823	−	16.8325i	−0.356527	−	0.617523i	−0.987378	+	0.158381i	$0.949373\pi$
$744$	4.69341	+	8.12922i	0.172069	+	0.298032i
$745$	−23.1556	+	40.1067i	−0.848355	+	1.46939i
$746$	14.0108	+	24.2674i	0.512972	+	0.888493i
$747$	5.17514	−	8.96361i	0.189349	−	0.327961i
$748$	−13.6423	−	23.6291i	−0.498811	−	0.863965i
$749$	−3.79409	−	6.57156i	−0.138633	−	0.240120i
$750$	−16.5096	+	28.5955i	−0.602846	+	1.04416i
$751$	13.7586			0.502060			0.251030	−	0.967979i	$-0.419231\pi$
$751$	13.7586			0.502060			0.251030	+	0.967979i	$0.419231\pi$
$752$	0.796236	+	1.37912i	0.0290357	+	0.0502914i
$753$	0.201845	−	0.349605i	0.00735563	−	0.0127403i
$754$	−18.3617	−	31.8034i	−0.668693	−	1.15821i
$755$	36.6256	−	63.4375i	1.33294	−	2.30873i
$756$	2.59085			0.0942282
$757$	16.5995	+	28.7512i	0.603319	+	1.04498i	0.992315	+	0.123739i	$0.0394887\pi$
$757$	16.5995	+	28.7512i	0.603319	+	1.04498i	−0.388996	+	0.921239i	$0.627178\pi$
$758$	−11.1190	+	19.2586i	−0.403859	+	0.699504i
$759$	−12.0468	+	20.8657i	−0.437272	+	0.757377i
$760$	26.6202			0.965615
$761$	−12.3120	+	21.3249i	−0.446308	+	0.773029i	−0.998142	−	0.0609252i	$-0.980595\pi$
$761$	−12.3120	+	21.3249i	−0.446308	+	0.773029i	0.551834	+	0.833954i	$0.313928\pi$
$762$	−4.98991	−	8.64278i	−0.180765	−	0.313095i
$763$	5.57735	+	9.66025i	0.201914	+	0.349724i
$764$	11.5887			0.419266
$765$	11.1810	−	19.3661i	0.404251	−	0.700183i
$766$	−11.0899	−	19.2083i	−0.400696	−	0.694025i
$767$	−25.8008			−0.931613
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	15.0163	−	26.0091i	0.541503	−	0.937910i	−0.457315	−	0.889305i	$-0.651189\pi$
$769$	15.0163	−	26.0091i	0.541503	−	0.937910i	0.998818	−	0.0486057i	$-0.0154778\pi$
$770$	−28.1684	+	48.7891i	−1.01512	+	1.75824i
$771$	3.81218	−	6.60288i	0.137292	−	0.237797i
$772$	−3.59732			−0.129470
$773$	−35.4735			−1.27589			−0.637946	−	0.770081i	$-0.720216\pi$
$773$	−35.4735			−1.27589			−0.637946	+	0.770081i	$0.720216\pi$
$774$	−12.1001			−0.434929
$775$	−60.1768	−	104.229i	−2.16162	−	3.74403i
$776$	−1.65648	−	2.86911i	−0.0594642	−	0.102995i
$777$	5.63421			0.202126
$778$	1.25351	+	2.17114i	0.0449405	+	0.0778393i
$779$	−13.3987	+	23.2072i	−0.480059	+	0.831486i
$780$	20.5687			0.736477
$781$	72.8861			2.60807
$782$	12.3889	−	21.4582i	0.443027	−	0.767345i
$783$	−3.76859	−	6.52739i	−0.134678	−	0.233270i
$784$	−0.287512			−0.0102683
$785$	37.3253	+	64.6493i	1.33220	+	2.30743i
$786$	−8.41391	−	14.5733i	−0.300114	−	0.519813i
$787$	4.00884			0.142900			0.0714499	−	0.997444i	$-0.477237\pi$
$787$	4.00884			0.142900			0.0714499	+	0.997444i	$0.477237\pi$
$788$	5.13007			0.182751
$789$	−11.0688			−0.394059
$790$	2.48131	−	4.29776i	0.0882811	−	0.152907i
$791$	−5.70446	+	9.88042i	−0.202827	+	0.351307i
$792$	2.57542	−	4.46076i	0.0915135	−	0.158506i
$793$	−32.4094	+	56.1347i	−1.15089	+	1.99340i
$794$	−10.0293			−0.355928
$795$	1.90301	+	3.29610i	0.0674926	+	0.116901i
$796$	−4.18390	+	7.24672i	−0.148294	+	0.256853i
$797$	−12.2880			−0.435264			−0.217632	−	0.976031i	$-0.569833\pi$
$797$	−12.2880			−0.435264			−0.217632	+	0.976031i	$0.569833\pi$
$798$	8.16864	+	14.1485i	0.289167	+	0.500851i
$799$	4.21775	+	7.30535i	0.149213	+	0.258445i
$800$	6.41078	−	11.1038i	0.226655	−	0.392579i
$801$	2.53864			0.0896983
$802$	−11.2259	+	19.4438i	−0.396400	+	0.686585i
$803$	23.3796	−	40.4947i	0.825050	−	1.42903i
$804$	−1.27918	−	2.21561i	−0.0451133	−	0.0781385i
$805$	−51.1610			−1.80319
$806$	−22.8677	+	39.6079i	−0.805479	+	1.39513i
$807$	−2.72049	−	4.71203i	−0.0957658	−	0.165871i
$808$	1.08941	−	1.88692i	0.0383254	−	0.0663816i
$809$	8.13262	+	14.0861i	0.285928	+	0.495241i	0.972834	−	0.231505i	$-0.0743650\pi$
$809$	8.13262	+	14.0861i	0.285928	+	0.495241i	−0.686906	+	0.726746i	$0.741032\pi$
$810$	4.22156			0.148330
$811$	−10.1272	+	17.5408i	−0.355613	+	0.615939i	−0.987223	−	0.159347i	$-0.949061\pi$
$811$	−10.1272	+	17.5408i	−0.355613	+	0.615939i	0.631610	+	0.775286i	$0.282394\pi$
$812$	−9.76384	−	16.9115i	−0.342644	−	0.593476i
$813$	−9.23501	−	15.9955i	−0.323886	−	0.560987i
$814$	5.60066	−	9.70062i	0.196303	−	0.340007i
$815$	5.74122	+	9.94408i	0.201106	+	0.348326i
$816$	−2.64855	+	4.58743i	−0.0927179	+	0.160592i
$817$	−38.1502	−	66.0782i	−1.33471	−	2.31178i
$818$	−11.9931	−	20.7726i	−0.419329	−	0.726299i
$819$	6.31168	+	10.9322i	0.220548	+	0.382000i
$820$	8.97011	+	15.5367i	0.313250	+	0.542565i
$821$	4.54961	−	7.88016i	0.158783	−	0.275020i	−0.775647	−	0.631167i	$-0.782576\pi$
$821$	4.54961	−	7.88016i	0.158783	−	0.275020i	0.934430	+	0.356147i	$0.115910\pi$
$822$	−11.0998	−	19.2255i	−0.387151	−	0.670566i
$823$	20.9680	+	36.3177i	0.730900	+	1.26596i	0.956499	+	0.291735i	$0.0942326\pi$
$823$	20.9680	+	36.3177i	0.730900	+	1.26596i	−0.225600	+	0.974220i	$0.572434\pi$
$824$	0.308966			0.0107634
$825$	−33.0209	+	57.1939i	−1.14964	+	1.99124i
$826$	−13.7196			−0.477366
$827$	−17.3218	−	30.0022i	−0.602338	−	1.04328i	−0.992466	−	0.122519i	$-0.960903\pi$
$827$	−17.3218	−	30.0022i	−0.602338	−	1.04328i	0.390129	−	0.920760i	$-0.372431\pi$
$828$	4.67761			0.162558
$829$	3.45142	+	5.97804i	0.119873	+	0.207626i	0.919717	−	0.392582i	$-0.128418\pi$
$829$	3.45142	+	5.97804i	0.119873	+	0.207626i	−0.799844	+	0.600208i	$0.795085\pi$
$830$	21.8472	−	37.8404i	0.758327	−	1.31346i
$831$	−9.34358	+	16.1836i	−0.324125	+	0.561402i
$832$	−4.87229			−0.168916
$833$	−1.52298			−0.0527683
$834$	2.11269	+	3.65929i	0.0731565	+	0.126711i
$835$	12.4976	+	21.6465i	0.432498	+	0.749108i
$836$	32.4800			1.12334
$837$	−4.69341	+	8.12922i	−0.162228	+	0.280987i
$838$	31.2268			1.07871
$839$	−5.97930	−	10.3564i	−0.206428	−	0.357544i	0.744159	−	0.668003i	$-0.232851\pi$
$839$	−5.97930	−	10.3564i	−0.206428	−	0.357544i	−0.950587	+	0.310459i	$0.899517\pi$
$840$	10.9374			0.377377
$841$	−13.9045	+	24.0834i	−0.479467	+	0.830461i
$842$	14.4217	−	24.9791i	0.497005	−	0.860838i
$843$	−13.7258			−0.472741
$844$	−4.11681	+	7.13052i	−0.141706	+	0.245442i
$845$	22.6682	+	39.2624i	0.779809	+	1.35067i
$846$	−0.796236	+	1.37912i	−0.0273752	+	0.0474152i
$847$	−20.1194	+	34.8478i	−0.691310	+	1.19738i
$848$	−0.450783	−	0.780778i	−0.0154799	−	0.0268120i
$849$	4.96654	−	8.60231i	0.170451	−	0.295230i
$850$	33.9586	−	58.8180i	1.16477	−	2.01744i
$851$	10.1722			0.348699
$852$	−7.07517	−	12.2546i	−0.242391	−	0.419834i
$853$	−26.3897	+	45.7083i	−0.903566	+	1.56502i	−0.0807352	+	0.996736i	$0.525727\pi$
$853$	−26.3897	+	45.7083i	−0.903566	+	1.56502i	−0.822831	+	0.568287i	$0.807607\pi$
$854$	−17.2337	+	29.8497i	−0.589726	+	1.02144i
$855$	13.3101	+	23.0537i	0.455195	+	0.788422i
$856$	1.46442	+	2.53645i	0.0500529	+	0.0866941i
$857$	3.50182	+	6.06533i	0.119620	+	0.207188i	0.919617	−	0.392816i	$-0.128499\pi$
$857$	3.50182	+	6.06533i	0.119620	+	0.207188i	−0.799997	+	0.600004i	$0.795166\pi$
$858$	25.0964			0.856776
$859$	−29.3119			−1.00011			−0.500055	−	0.865994i	$-0.666687\pi$
$859$	−29.3119			−1.00011			−0.500055	+	0.865994i	$0.666687\pi$
$860$	−51.0813			−1.74186
$861$	−5.50512	+	9.53515i	−0.187614	+	0.324957i
$862$	−35.4989			−1.20910
$863$	16.3601	+	28.3365i	0.556904	+	0.964587i	0.997753	+	0.0670050i	$0.0213443\pi$
$863$	16.3601	+	28.3365i	0.556904	+	0.964587i	−0.440848	+	0.897582i	$0.645322\pi$
$864$	−1.00000			−0.0340207
$865$	61.8248			2.10210
$866$	−32.4135			−1.10145
$867$	−5.52967	+	9.57767i	−0.187798	+	0.325275i
$868$	−12.1599	+	21.0616i	−0.412734	+	0.714876i
$869$	3.02751	−	5.24381i	0.102701	−	0.177884i
$870$	−15.9093	−	27.5558i	−0.539377	−	0.934228i
$871$	6.23255	−	10.7951i	0.211182	−	0.365778i
$872$	−2.15271	−	3.72861i	−0.0729000	−	0.126267i
$873$	1.65648	−	2.86911i	0.0560633	−	0.0971046i
$874$	14.7480	+	25.5442i	0.498858	+	0.864047i
$875$	−85.5477			−2.89204
$876$	−9.07800			−0.306717
$877$	41.4720			1.40041			0.700205	−	0.713942i	$-0.253092\pi$
$877$	41.4720			1.40041			0.700205	+	0.713942i	$0.253092\pi$
$878$	−21.5280			−0.726533
$879$	−10.1436			−0.342136
$880$	10.8723	−	18.8313i	0.366505	−	0.634804i
$881$	−11.7823	−	20.4075i	−0.396956	−	0.687547i	0.596393	−	0.802693i	$-0.296600\pi$
$881$	−11.7823	−	20.4075i	−0.396956	−	0.687547i	−0.993349	+	0.115145i	$0.963267\pi$
$882$	−0.143756	−	0.248993i	−0.00484052	−	0.00838403i
$883$	−23.9023	−	41.4000i	−0.804376	−	1.39322i	−0.916711	−	0.399550i	$-0.869166\pi$
$883$	−23.9023	−	41.4000i	−0.804376	−	1.39322i	0.112335	−	0.993670i	$-0.464167\pi$
$884$	−25.8091			−0.868053
$885$	−22.3549			−0.751452
$886$	3.75378	−	6.50174i	0.126111	−	0.218430i
$887$	8.34544	+	14.4547i	0.280213	+	0.485342i	0.971437	−	0.237298i	$-0.0762617\pi$
$887$	8.34544	+	14.4547i	0.280213	+	0.485342i	−0.691224	+	0.722640i	$0.742928\pi$
$888$	−2.17466			−0.0729768
$889$	12.9281	−	22.3921i	0.433595	−	0.751008i
$890$	10.7170			0.359235
$891$	5.15084			0.172560
$892$	10.7116	−	10.4049i	0.358651	−	0.348382i
$893$	−10.0418			−0.336035
$894$	10.9702			0.366897
$895$	7.52766	−	13.0383i	0.251622	−	0.435822i
$896$	−2.59085			−0.0865541
$897$	11.3954	+	19.7373i	0.380480	+	0.659010i
$898$	12.6958	−	21.9897i	0.423663	−	0.733806i
$899$	70.7501			2.35965
$900$	12.8216			0.427386
$901$	−2.38784	−	4.13587i	−0.0795506	−	0.137786i
$902$	10.9447	+	18.9567i	0.364418	+	0.631190i
$903$	−15.6748	−	27.1495i	−0.521624	−	0.903479i
$904$	2.20178	−	3.81359i	0.0732300	−	0.126838i
$905$	−37.5318			−1.24760
$906$	−17.3517			−0.576472
$907$	−21.1667			−0.702830			−0.351415	−	0.936220i	$-0.614299\pi$
$907$	−21.1667			−0.702830			−0.351415	+	0.936220i	$0.614299\pi$
$908$	−11.4774			−0.380892
$909$	2.17883			0.0722671
$910$	26.6451	+	46.1507i	0.883278	+	1.52988i
$911$	−16.5585	+	28.6802i	−0.548608	+	0.950216i	0.449763	+	0.893148i	$0.351509\pi$
$911$	−16.5585	+	28.6802i	−0.548608	+	0.950216i	−0.998370	+	0.0570682i	$0.981825\pi$
$912$	−3.15288	−	5.46095i	−0.104402	−	0.180830i
$913$	26.6563	−	46.1701i	0.882195	−	1.52801i
$914$	11.4188	+	19.7780i	0.377701	+	0.654197i
$915$	−28.0809	+	48.6375i	−0.928325	+	1.60791i
$916$	−4.09598	+	7.09444i	−0.135335	+	0.234407i
$917$	21.7992	−	37.7572i	0.719872	−	1.24685i
$918$	−5.29711			−0.174831
$919$	−28.3192			−0.934164			−0.467082	−	0.884214i	$-0.654695\pi$
$919$	−28.3192			−0.934164			−0.467082	+	0.884214i	$0.654695\pi$
$920$	19.7468			0.651034
$921$	11.2890	+	19.5532i	0.371986	+	0.644299i
$922$	−2.25619			−0.0743036
$923$	34.4723	−	59.7078i	1.13467	−	1.96531i
$924$	13.3450			0.439019
$925$	27.8825			0.916772
$926$	−33.3883			−1.09721
$927$	0.154483	+	0.267573i	0.00507389	+	0.00878824i
$928$	3.76859	+	6.52739i	0.123710	+	0.214272i
$929$	−16.9828	−	29.4151i	−0.557187	−	0.965077i	−0.997730	−	0.0673450i	$-0.978547\pi$
$929$	−16.9828	−	29.4151i	−0.557187	−	0.965077i	0.440542	−	0.897732i	$-0.354786\pi$
$930$	−19.8135	+	34.3180i	−0.649710	+	1.12533i
$931$	0.906493	−	1.57009i	0.0297091	−	0.0514577i
$932$	−11.3704	−	19.6941i	−0.372449	−	0.645101i
$933$	−11.2929			−0.369711
$934$	−12.6313	+	21.8781i	−0.413310	+	0.715874i
$935$	57.5916	−	99.7517i	1.88345	−	3.26223i
$936$	−2.43615	−	4.21953i	−0.0796279	−	0.137920i
$937$	16.5063	−	28.5897i	0.539237	−	0.933986i	−0.459708	−	0.888070i	$-0.652046\pi$
$937$	16.5063	−	28.5897i	0.539237	−	0.933986i	0.998945	−	0.0459158i	$-0.0146206\pi$
$938$	3.31417	−	5.74030i	0.108211	−	0.187428i
$939$	12.7927	+	22.1576i	0.417474	+	0.723086i
$940$	−3.36136	+	5.82204i	−0.109635	+	0.189894i
$941$	3.33920			0.108855			0.0544274	−	0.998518i	$-0.482667\pi$
$941$	3.33920			0.108855			0.0544274	+	0.998518i	$0.482667\pi$
$942$	8.84158	−	15.3141i	0.288074	−	0.498959i
$943$	−9.93915	+	17.2151i	−0.323663	+	0.560601i
$944$	5.29542			0.172351
$945$	5.46871	+	9.47208i	0.177897	+	0.308127i
$946$	−62.3257			−2.02638
$947$	−19.8402	+	34.3643i	−0.644720	+	1.11669i	0.339646	+	0.940553i	$0.389693\pi$
$947$	−19.8402	+	34.3643i	−0.644720	+	1.11669i	−0.984366	+	0.176135i	$0.943640\pi$
$948$	−1.17554			−0.0381799
$949$	−22.1153	−	38.3049i	−0.717894	−	1.24343i
$950$	40.4249	+	70.0180i	1.31156	+	2.27168i
$951$	11.0099			0.357019
$952$	−13.7240			−0.444797
$953$	12.6871	−	21.9748i	0.410977	−	0.711832i	−0.584020	−	0.811739i	$-0.698521\pi$
$953$	12.6871	−	21.9748i	0.410977	−	0.711832i	0.994997	+	0.0999067i	$0.0318544\pi$
$954$	0.450783	−	0.780778i	0.0145946	−	0.0252786i
$955$	24.4613	+	42.3682i	0.791548	+	1.37100i
$956$	13.6010			0.439886
$957$	−19.4114	−	33.6215i	−0.627481	−	1.08683i
$958$	−30.1457			−0.973963
$959$	28.7580	−	49.8103i	0.928644	−	1.60846i
$960$	−4.22156			−0.136250
$961$	−28.5561	−	49.4607i	−0.921166	−	1.59551i
$962$	−5.29779	−	9.17604i	−0.170808	−	0.295847i
$963$	−1.46442	+	2.53645i	−0.0471903	+	0.0817360i
$964$	1.96708	+	3.40707i	0.0633552	+	0.109734i
$965$	−7.59314	−	13.1517i	−0.244432	−	0.423368i
$966$	6.05949	+	10.4953i	0.194961	+	0.337682i
$967$	−2.69263	−	4.66378i	−0.0865893	−	0.149977i	0.819478	−	0.573111i	$-0.194263\pi$
$967$	−2.69263	−	4.66378i	−0.0865893	−	0.149977i	−0.906067	+	0.423134i	$0.860930\pi$
$968$	7.76556	−	13.4503i	0.249594	−	0.432310i
$969$	−16.7012	−	28.9273i	−0.536519	−	0.929278i
$970$	6.99293	−	12.1121i	0.224529	−	0.388896i
$971$	−16.6325	−	28.8083i	−0.533762	−	0.924504i	−0.999222	−	0.0394346i	$-0.987444\pi$
$971$	−16.6325	−	28.8083i	−0.533762	−	0.924504i	0.465460	−	0.885069i	$-0.345889\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−5.47366	+	9.48066i	−0.175478	+	0.303936i
$974$	28.1640			0.902433
$975$	31.2352	+	54.1010i	1.00033	+	1.73262i
$976$	6.65178	−	11.5212i	0.212918	−	0.368785i
$977$	−14.7510	−	25.5494i	−0.471925	−	0.817399i	0.527559	−	0.849519i	$-0.323108\pi$
$977$	−14.7510	−	25.5494i	−0.471925	−	0.817399i	−0.999484	+	0.0321198i	$0.989774\pi$
$978$	1.35997	−	2.35555i	0.0434872	−	0.0753220i
$979$	13.0761			0.417914
$980$	−0.606875	−	1.05114i	−0.0193859	−	0.0335774i
$981$	2.15271	−	3.72861i	0.0687308	−	0.119045i
$982$	6.70442	−	11.6124i	0.213947	−	0.370566i
$983$	21.4869			0.685325			0.342663	−	0.939458i	$-0.388671\pi$
$983$	21.4869			0.685325			0.342663	+	0.939458i	$0.388671\pi$
$984$	2.12483	−	3.68032i	0.0677372	−	0.117324i
$985$	10.8285	+	18.7554i	0.345023	+	0.597598i
$986$	19.9626	+	34.5763i	0.635740	+	1.10113i
$987$	−4.12585			−0.131327
$988$	15.3618	−	26.6074i	0.488723	−	0.846493i
$989$	−28.2998	−	49.0167i	−0.899882	−	1.55864i
$990$	21.7446			0.691088
$991$	18.3169	−	31.7258i	0.581855	−	1.00780i	−0.413405	−	0.910547i	$-0.635660\pi$
$991$	18.3169	−	31.7258i	0.581855	−	1.00780i	0.995260	−	0.0972548i	$-0.0310062\pi$
$992$	4.69341	−	8.12922i	0.149016	−	0.258103i
$993$	5.08442	−	8.80648i	0.161349	−	0.279465i
$994$	18.3307	−	31.7497i	0.581414	−	1.00704i
$995$	−35.3251			−1.11988
$996$	−10.3503			−0.327961
$997$	50.8776			1.61131			0.805655	−	0.592385i	$-0.201814\pi$
$997$	50.8776			1.61131			0.805655	+	0.592385i	$0.201814\pi$
$998$	−7.92225	−	13.7217i	−0.250774	−	0.434354i
$999$	−1.08733	−	1.88331i	−0.0344016	−	0.0595853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.h.931.7	✓	14
223.183	even	3	inner	1338.2.e.h.1075.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.h.931.7	✓	14	1.1	even	1	trivial
1338.2.e.h.1075.7	yes	14	223.183	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(2.11078 + 3.65598i) q^{5} +(0.500000 - 0.866025i) q^{6} +2.59085 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.11078 - 3.65598i) q^{10} +(-2.57542 - 4.46076i) q^{11} +(-0.500000 + 0.866025i) q^{12} -4.87229 q^{13} -2.59085 q^{14} -4.22156 q^{15} +1.00000 q^{16} +5.29711 q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.15288 + 5.46095i) q^{19} +(2.11078 + 3.65598i) q^{20} +(-1.29542 + 2.24374i) q^{21} +(2.57542 + 4.46076i) q^{22} +(-2.33881 + 4.05093i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-6.41078 + 11.1038i) q^{25} +4.87229 q^{26} +1.00000 q^{27} +2.59085 q^{28} +(-3.76859 - 6.52739i) q^{29} +4.22156 q^{30} +(-4.69341 + 8.12922i) q^{31} -1.00000 q^{32} +5.15084 q^{33} -5.29711 q^{34} +(5.46871 + 9.47208i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.08733 - 1.88331i) q^{37} +(3.15288 - 5.46095i) q^{38} +(2.43615 - 4.21953i) q^{39} +(-2.11078 - 3.65598i) q^{40} +4.24967 q^{41} +(1.29542 - 2.24374i) q^{42} +(-6.05006 + 10.4790i) q^{43} +(-2.57542 - 4.46076i) q^{44} +(2.11078 - 3.65598i) q^{45} +(2.33881 - 4.05093i) q^{46} +(0.796236 + 1.37912i) q^{47} +(-0.500000 + 0.866025i) q^{48} -0.287512 q^{49} +(6.41078 - 11.1038i) q^{50} +(-2.64855 + 4.58743i) q^{51} -4.87229 q^{52} +(-0.450783 - 0.780778i) q^{53} -1.00000 q^{54} +(10.8723 - 18.8313i) q^{55} -2.59085 q^{56} +(-3.15288 - 5.46095i) q^{57} +(3.76859 + 6.52739i) q^{58} +5.29542 q^{59} -4.22156 q^{60} +(6.65178 - 11.5212i) q^{61} +(4.69341 - 8.12922i) q^{62} +(-1.29542 - 2.24374i) q^{63} +1.00000 q^{64} +(-10.2843 - 17.8130i) q^{65} -5.15084 q^{66} +(-1.27918 + 2.21561i) q^{67} +5.29711 q^{68} +(-2.33881 - 4.05093i) q^{69} +(-5.46871 - 9.47208i) q^{70} +(-7.07517 + 12.2546i) q^{71} +(0.500000 + 0.866025i) q^{72} +(4.53900 + 7.86178i) q^{73} +(1.08733 + 1.88331i) q^{74} +(-6.41078 - 11.1038i) q^{75} +(-3.15288 + 5.46095i) q^{76} +(-6.67251 - 11.5571i) q^{77} +(-2.43615 + 4.21953i) q^{78} +(0.587771 + 1.01805i) q^{79} +(2.11078 + 3.65598i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.24967 q^{82} +(5.17514 + 8.96361i) q^{83} +(-1.29542 + 2.24374i) q^{84} +(11.1810 + 19.3661i) q^{85} +(6.05006 - 10.4790i) q^{86} +7.53718 q^{87} +(2.57542 + 4.46076i) q^{88} +(-1.26932 + 2.19852i) q^{89} +(-2.11078 + 3.65598i) q^{90} -12.6234 q^{91} +(-2.33881 + 4.05093i) q^{92} +(-4.69341 - 8.12922i) q^{93} +(-0.796236 - 1.37912i) q^{94} -26.6202 q^{95} +(0.500000 - 0.866025i) q^{96} +(1.65648 + 2.86911i) q^{97} +0.287512 q^{98} +(-2.57542 + 4.46076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 7 q^{3} + 14 q^{4} - 4 q^{5} + 7 q^{6} + 12 q^{7} - 14 q^{8} - 7 q^{9} + 4 q^{10} - 10 q^{11} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 8 q^{15} + 14 q^{16} + 8 q^{17} + 7 q^{18} - 8 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 7 * q^3 + 14 * q^4 - 4 * q^5 + 7 * q^6 + 12 * q^7 - 14 * q^8 - 7 * q^9 + 4 * q^10 - 10 * q^11 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 8 * q^15 + 14 * q^16 + 8 * q^17 + 7 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 + 10 * q^22 - 8 * q^23 + 7 * q^24 - 13 * q^25 + 4 * q^26 + 14 * q^27 + 12 * q^28 - 6 * q^29 - 8 * q^30 - 10 * q^31 - 14 * q^32 + 20 * q^33 - 8 * q^34 + 18 * q^35 - 7 * q^36 + 15 * q^37 + 8 * q^38 + 2 * q^39 + 4 * q^40 + 24 * q^41 + 6 * q^42 - 14 * q^43 - 10 * q^44 - 4 * q^45 + 8 * q^46 - 10 * q^47 - 7 * q^48 + 54 * q^49 + 13 * q^50 - 4 * q^51 - 4 * q^52 - 9 * q^53 - 14 * q^54 + 13 * q^55 - 12 * q^56 - 8 * q^57 + 6 * q^58 - 20 * q^59 + 8 * q^60 - 20 * q^61 + 10 * q^62 - 6 * q^63 + 14 * q^64 + 7 * q^65 - 20 * q^66 - 13 * q^67 + 8 * q^68 - 8 * q^69 - 18 * q^70 - 26 * q^71 + 7 * q^72 + 7 * q^73 - 15 * q^74 - 13 * q^75 - 8 * q^76 - 13 * q^77 - 2 * q^78 + 36 * q^79 - 4 * q^80 - 7 * q^81 - 24 * q^82 + 27 * q^83 - 6 * q^84 + 27 * q^85 + 14 * q^86 + 12 * q^87 + 10 * q^88 - 33 * q^89 + 4 * q^90 - 14 * q^91 - 8 * q^92 - 10 * q^93 + 10 * q^94 - 40 * q^95 + 7 * q^96 - 19 * q^97 - 54 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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