LMFDB - Embedded newform 546.2.i.i.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.i (of order $3$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
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			79.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.i.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.292893 - 0.507306i) q^{5} -1.00000 q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.292893 + 0.507306i) q^{10} +(0.207107 + 0.358719i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-2.62132 + 0.358719i) q^{14} +0.585786 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.20711 + 2.09077i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.08579 - 1.88064i) q^{19} -0.585786 q^{20} +(-1.00000 + 2.44949i) q^{21} -0.414214 q^{22} +(-0.707107 + 1.22474i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.32843 + 4.03295i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 - 2.44949i) q^{28} -1.82843 q^{29} +(-0.292893 + 0.507306i) q^{30} +(4.24264 + 7.34847i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.207107 + 0.358719i) q^{33} -2.41421 q^{34} +(1.53553 - 0.210133i) q^{35} +1.00000 q^{36} +(-0.707107 + 1.22474i) q^{37} +(1.08579 + 1.88064i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.292893 - 0.507306i) q^{40} -9.89949 q^{41} +(-1.62132 - 2.09077i) q^{42} +6.48528 q^{43} +(0.207107 - 0.358719i) q^{44} +(0.292893 + 0.507306i) q^{45} +(-0.707107 - 1.22474i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000 q^{48} +(-1.74264 + 6.77962i) q^{49} -4.65685 q^{50} +(-1.20711 + 2.09077i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-4.74264 - 8.21449i) q^{53} +(0.500000 - 0.866025i) q^{54} +0.242641 q^{55} +(1.62132 + 2.09077i) q^{56} +2.17157 q^{57} +(0.914214 - 1.58346i) q^{58} +(-1.03553 - 1.79360i) q^{59} +(-0.292893 - 0.507306i) q^{60} +(2.20711 - 3.82282i) q^{61} -8.48528 q^{62} +(-2.62132 + 0.358719i) q^{63} +1.00000 q^{64} +(0.292893 - 0.507306i) q^{65} +(-0.207107 - 0.358719i) q^{66} +(-0.914214 - 1.58346i) q^{67} +(1.20711 - 2.09077i) q^{68} -1.41421 q^{69} +(-0.585786 + 1.43488i) q^{70} -5.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(-0.707107 - 1.22474i) q^{74} +(-2.32843 + 4.03295i) q^{75} -2.17157 q^{76} +(-0.414214 + 1.01461i) q^{77} -1.00000 q^{78} +(5.82843 - 10.0951i) q^{79} +(0.292893 + 0.507306i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.94975 - 8.57321i) q^{82} +7.65685 q^{83} +(2.62132 - 0.358719i) q^{84} +1.41421 q^{85} +(-3.24264 + 5.61642i) q^{86} +(-0.914214 - 1.58346i) q^{87} +(0.207107 + 0.358719i) q^{88} +(-1.29289 + 2.23936i) q^{89} -0.585786 q^{90} +(1.62132 + 2.09077i) q^{91} +1.41421 q^{92} +(-4.24264 + 7.34847i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-0.636039 - 1.10165i) q^{95} +(0.500000 - 0.866025i) q^{96} -0.928932 q^{97} +(-5.00000 - 4.89898i) q^{98} -0.414214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{17} - 2 q^{18} + 10 q^{19} - 8 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 8 * q^15 - 2 * q^16 + 2 * q^17 - 2 * q^18 + 10 * q^19 - 8 * q^20 - 4 * q^21 + 4 * q^22 + 2 * q^24 - 2 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^32 + 2 * q^33 - 4 * q^34 - 8 * q^35 + 4 * q^36 + 10 * q^38 + 2 * q^39 + 4 * q^40 + 2 * q^42 - 8 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^47 - 4 * q^48 + 10 * q^49 + 4 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 + 2 * q^54 - 16 * q^55 - 2 * q^56 + 20 * q^57 - 2 * q^58 + 10 * q^59 - 4 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + 4 * q^65 + 2 * q^66 + 2 * q^67 + 2 * q^68 - 8 * q^70 - 20 * q^71 - 2 * q^72 + 2 * q^75 - 20 * q^76 + 4 * q^77 - 4 * q^78 + 12 * q^79 + 4 * q^80 - 2 * q^81 + 8 * q^83 + 2 * q^84 + 4 * q^86 + 2 * q^87 - 2 * q^88 - 8 * q^89 - 8 * q^90 - 2 * q^91 - 2 * q^94 - 28 * q^95 + 2 * q^96 - 32 * q^97 - 20 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	−0.793071	−	0.609129i	$-0.791519\pi$
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	0.924057	+	0.382255i	$0.124852\pi$
$6$	−1.00000			−0.408248
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.292893	+	0.507306i	0.0926210	+	0.160424i
$11$	0.207107	+	0.358719i	0.0624450	+	0.108158i	0.895558	−	0.444945i	$-0.146777\pi$
$11$	0.207107	+	0.358719i	0.0624450	+	0.108158i	−0.833113	+	0.553103i	$0.813444\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−2.62132	+	0.358719i	−0.700577	+	0.0958718i
$15$	0.585786			0.151249
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.20711	+	2.09077i	0.292766	+	0.507086i	0.974463	−	0.224549i	$-0.0720908\pi$
$17$	1.20711	+	2.09077i	0.292766	+	0.507086i	−0.681696	+	0.731635i	$0.738758\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.08579	−	1.88064i	0.249096	−	0.431448i	−0.714179	−	0.699963i	$-0.753200\pi$
$19$	1.08579	−	1.88064i	0.249096	−	0.431448i	0.963275	+	0.268515i	$0.0865330\pi$
$20$	−0.585786			−0.130986
$21$	−1.00000	+	2.44949i	−0.218218	+	0.534522i
$22$	−0.414214			−0.0883106
$23$	−0.707107	+	1.22474i	−0.147442	+	0.255377i	−0.930281	−	0.366847i	$-0.880437\pi$
$23$	−0.707107	+	1.22474i	−0.147442	+	0.255377i	0.782839	+	0.622224i	$0.213771\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.32843	+	4.03295i	0.465685	+	0.806591i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	−1.00000			−0.192450
$28$	1.00000	−	2.44949i	0.188982	−	0.462910i
$29$	−1.82843			−0.339530			−0.169765	−	0.985485i	$-0.554301\pi$
$29$	−1.82843			−0.339530			−0.169765	+	0.985485i	$0.554301\pi$
$30$	−0.292893	+	0.507306i	−0.0534747	+	0.0926210i
$31$	4.24264	+	7.34847i	0.762001	+	1.31982i	0.941818	+	0.336124i	$0.109116\pi$
$31$	4.24264	+	7.34847i	0.762001	+	1.31982i	−0.179817	+	0.983700i	$0.557551\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.207107	+	0.358719i	−0.0360527	+	0.0624450i
$34$	−2.41421			−0.414034
$35$	1.53553	−	0.210133i	0.259553	−	0.0355190i
$36$	1.00000			0.166667
$37$	−0.707107	+	1.22474i	−0.116248	+	0.201347i	−0.918278	−	0.395937i	$-0.870420\pi$
$37$	−0.707107	+	1.22474i	−0.116248	+	0.201347i	0.802030	+	0.597284i	$0.203753\pi$
$38$	1.08579	+	1.88064i	0.176138	+	0.305080i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	0.292893	−	0.507306i	0.0463105	−	0.0802121i
$41$	−9.89949			−1.54604			−0.773021	−	0.634381i	$-0.781255\pi$
$41$	−9.89949			−1.54604			−0.773021	+	0.634381i	$0.781255\pi$
$42$	−1.62132	−	2.09077i	−0.250175	−	0.322613i
$43$	6.48528			0.988996			0.494498	−	0.869179i	$-0.335352\pi$
$43$	6.48528			0.988996			0.494498	+	0.869179i	$0.335352\pi$
$44$	0.207107	−	0.358719i	0.0312225	−	0.0540790i
$45$	0.292893	+	0.507306i	0.0436619	+	0.0756247i
$46$	−0.707107	−	1.22474i	−0.104257	−	0.180579i
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	−0.900185	−	0.435507i	$-0.856569\pi$
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	0.827253	+	0.561830i	$0.189902\pi$
$48$	−1.00000			−0.144338
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	−4.65685			−0.658579
$51$	−1.20711	+	2.09077i	−0.169029	+	0.292766i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−4.74264	−	8.21449i	−0.651452	−	1.12835i	−0.982771	−	0.184829i	$-0.940827\pi$
$53$	−4.74264	−	8.21449i	−0.651452	−	1.12835i	0.331319	−	0.943519i	$-0.392506\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	0.242641			0.0327177
$56$	1.62132	+	2.09077i	0.216658	+	0.279391i
$57$	2.17157			0.287632
$58$	0.914214	−	1.58346i	0.120042	−	0.207919i
$59$	−1.03553	−	1.79360i	−0.134815	−	0.233506i	0.790712	−	0.612189i	$-0.209711\pi$
$59$	−1.03553	−	1.79360i	−0.134815	−	0.233506i	−0.925527	+	0.378682i	$0.876377\pi$
$60$	−0.292893	−	0.507306i	−0.0378124	−	0.0654929i
$61$	2.20711	−	3.82282i	0.282591	−	0.489462i	−0.689431	−	0.724351i	$-0.742139\pi$
$61$	2.20711	−	3.82282i	0.282591	−	0.489462i	0.972022	+	0.234889i	$0.0754727\pi$
$62$	−8.48528			−1.07763
$63$	−2.62132	+	0.358719i	−0.330255	+	0.0451944i
$64$	1.00000			0.125000
$65$	0.292893	−	0.507306i	0.0363289	−	0.0629236i
$66$	−0.207107	−	0.358719i	−0.0254931	−	0.0441553i
$67$	−0.914214	−	1.58346i	−0.111689	−	0.193451i	0.804762	−	0.593597i	$-0.202293\pi$
$67$	−0.914214	−	1.58346i	−0.111689	−	0.193451i	−0.916451	+	0.400146i	$0.868959\pi$
$68$	1.20711	−	2.09077i	0.146383	−	0.253543i
$69$	−1.41421			−0.170251
$70$	−0.585786	+	1.43488i	−0.0700149	+	0.171501i
$71$	−5.00000			−0.593391			−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000			−0.593391			−0.296695	+	0.954972i	$0.595885\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	0.821674	−	0.569958i	$-0.193040\pi$
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	−0.904435	+	0.426612i	$0.859707\pi$
$74$	−0.707107	−	1.22474i	−0.0821995	−	0.142374i
$75$	−2.32843	+	4.03295i	−0.268864	+	0.465685i
$76$	−2.17157			−0.249096
$77$	−0.414214	+	1.01461i	−0.0472040	+	0.115626i
$78$	−1.00000			−0.113228
$79$	5.82843	−	10.0951i	0.655749	−	1.13579i	−0.325956	−	0.945385i	$-0.605686\pi$
$79$	5.82843	−	10.0951i	0.655749	−	1.13579i	0.981705	−	0.190406i	$-0.0609805\pi$
$80$	0.292893	+	0.507306i	0.0327465	+	0.0567185i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.94975	−	8.57321i	0.546608	−	0.946753i
$83$	7.65685			0.840449			0.420224	−	0.907420i	$-0.361951\pi$
$83$	7.65685			0.840449			0.420224	+	0.907420i	$0.361951\pi$
$84$	2.62132	−	0.358719i	0.286009	−	0.0391395i
$85$	1.41421			0.153393
$86$	−3.24264	+	5.61642i	−0.349663	+	0.605634i
$87$	−0.914214	−	1.58346i	−0.0980140	−	0.169765i
$88$	0.207107	+	0.358719i	0.0220777	+	0.0382396i
$89$	−1.29289	+	2.23936i	−0.137046	+	0.237371i	−0.926377	−	0.376597i	$-0.877094\pi$
$89$	−1.29289	+	2.23936i	−0.137046	+	0.237371i	0.789331	+	0.613968i	$0.210428\pi$
$90$	−0.585786			−0.0617473
$91$	1.62132	+	2.09077i	0.169961	+	0.219172i
$92$	1.41421			0.147442
$93$	−4.24264	+	7.34847i	−0.439941	+	0.762001i
$94$	−0.500000	−	0.866025i	−0.0515711	−	0.0893237i
$95$	−0.636039	−	1.10165i	−0.0652562	−	0.113027i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−0.928932			−0.0943188			−0.0471594	−	0.998887i	$-0.515017\pi$
$97$	−0.928932			−0.0943188			−0.0471594	+	0.998887i	$0.515017\pi$
$98$	−5.00000	−	4.89898i	−0.505076	−	0.494872i
$99$	−0.414214			−0.0416300
$100$	2.32843	−	4.03295i	0.232843	−	0.403295i
$101$	7.41421	+	12.8418i	0.737742	+	1.27781i	0.953510	+	0.301362i	$0.0974412\pi$
$101$	7.41421	+	12.8418i	0.737742	+	1.27781i	−0.215768	+	0.976445i	$0.569226\pi$
$102$	−1.20711	−	2.09077i	−0.119521	−	0.207017i
$103$	8.41421	−	14.5738i	0.829077	−	1.43600i	−0.0696860	−	0.997569i	$-0.522200\pi$
$103$	8.41421	−	14.5738i	0.829077	−	1.43600i	0.898763	−	0.438435i	$-0.144467\pi$
$104$	1.00000			0.0980581
$105$	0.949747	+	1.22474i	0.0926859	+	0.119523i
$106$	9.48528			0.921292
$107$	9.65685	−	16.7262i	0.933563	−	1.61698i	0.156387	−	0.987696i	$-0.450015\pi$
$107$	9.65685	−	16.7262i	0.933563	−	1.61698i	0.777176	−	0.629283i	$-0.216651\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	4.82843	+	8.36308i	0.462479	+	0.801038i	0.999084	−	0.0427961i	$-0.0136266\pi$
$109$	4.82843	+	8.36308i	0.462479	+	0.801038i	−0.536604	+	0.843834i	$0.680293\pi$
$110$	−0.121320	+	0.210133i	−0.0115674	+	0.0200354i
$111$	−1.41421			−0.134231
$112$	−2.62132	+	0.358719i	−0.247691	+	0.0338958i
$113$	4.89949			0.460906			0.230453	−	0.973083i	$-0.425979\pi$
$113$	4.89949			0.460906			0.230453	+	0.973083i	$0.425979\pi$
$114$	−1.08579	+	1.88064i	−0.101693	+	0.176138i
$115$	0.414214	+	0.717439i	0.0386256	+	0.0669015i
$116$	0.914214	+	1.58346i	0.0848826	+	0.147021i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	2.07107			0.190657
$119$	−2.41421	+	5.91359i	−0.221311	+	0.542098i
$120$	0.585786			0.0534747
$121$	5.41421	−	9.37769i	0.492201	−	0.852518i
$122$	2.20711	+	3.82282i	0.199822	+	0.346102i
$123$	−4.94975	−	8.57321i	−0.446304	−	0.773021i
$124$	4.24264	−	7.34847i	0.381000	−	0.659912i
$125$	5.65685			0.505964
$126$	1.00000	−	2.44949i	0.0890871	−	0.218218i
$127$	−7.89949			−0.700967			−0.350483	−	0.936569i	$-0.613983\pi$
$127$	−7.89949			−0.700967			−0.350483	+	0.936569i	$0.613983\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.24264	+	5.61642i	0.285499	+	0.494498i
$130$	0.292893	+	0.507306i	0.0256884	+	0.0444937i
$131$	4.77817	−	8.27604i	0.417471	−	0.723081i	−0.578213	−	0.815886i	$-0.696250\pi$
$131$	4.77817	−	8.27604i	0.417471	−	0.723081i	0.995684	+	0.0928046i	$0.0295832\pi$
$132$	0.414214			0.0360527
$133$	5.69239	−	0.778985i	0.493593	−	0.0675466i
$134$	1.82843			0.157952
$135$	−0.292893	+	0.507306i	−0.0252082	+	0.0436619i
$136$	1.20711	+	2.09077i	0.103509	+	0.179282i
$137$	−5.53553	−	9.58783i	−0.472933	−	0.819143i	0.526587	−	0.850121i	$-0.323471\pi$
$137$	−5.53553	−	9.58783i	−0.472933	−	0.819143i	−0.999520	+	0.0309777i	$0.990138\pi$
$138$	0.707107	−	1.22474i	0.0601929	−	0.104257i
$139$	−13.0711			−1.10867			−0.554337	−	0.832292i	$-0.687028\pi$
$139$	−13.0711			−1.10867			−0.554337	+	0.832292i	$0.687028\pi$
$140$	−0.949747	−	1.22474i	−0.0802683	−	0.103510i
$141$	−1.00000			−0.0842152
$142$	2.50000	−	4.33013i	0.209795	−	0.363376i
$143$	0.207107	+	0.358719i	0.0173191	+	0.0299976i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.535534	+	0.927572i	−0.0444737	+	0.0770307i
$146$	1.41421			0.117041
$147$	−6.74264	+	1.88064i	−0.556124	+	0.155112i
$148$	1.41421			0.116248
$149$	2.46447	−	4.26858i	0.201897	−	0.349696i	−0.747243	−	0.664551i	$-0.768623\pi$
$149$	2.46447	−	4.26858i	0.201897	−	0.349696i	0.949140	+	0.314856i	$0.101956\pi$
$150$	−2.32843	−	4.03295i	−0.190115	−	0.329289i
$151$	−2.03553	−	3.52565i	−0.165649	−	0.286913i	0.771236	−	0.636549i	$-0.219639\pi$
$151$	−2.03553	−	3.52565i	−0.165649	−	0.286913i	−0.936886	+	0.349636i	$0.886305\pi$
$152$	1.08579	−	1.88064i	0.0880689	−	0.152540i
$153$	−2.41421			−0.195178
$154$	−0.671573	−	0.866025i	−0.0541169	−	0.0697863i
$155$	4.97056			0.399245
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	−4.86396	−	8.42463i	−0.388186	−	0.672358i	0.604019	−	0.796970i	$-0.293565\pi$
$157$	−4.86396	−	8.42463i	−0.388186	−	0.672358i	−0.992206	+	0.124611i	$0.960232\pi$
$158$	5.82843	+	10.0951i	0.463685	+	0.803126i
$159$	4.74264	−	8.21449i	0.376116	−	0.651452i
$160$	−0.585786			−0.0463105
$161$	−3.70711	+	0.507306i	−0.292161	+	0.0399813i
$162$	1.00000			0.0785674
$163$	9.32843	−	16.1573i	0.730659	−	1.26554i	−0.225943	−	0.974140i	$-0.572546\pi$
$163$	9.32843	−	16.1573i	0.730659	−	1.26554i	0.956602	−	0.291398i	$-0.0941203\pi$
$164$	4.94975	+	8.57321i	0.386510	+	0.669456i
$165$	0.121320	+	0.210133i	0.00944478	+	0.0163588i
$166$	−3.82843	+	6.63103i	−0.297144	+	0.514668i
$167$	−0.656854			−0.0508289			−0.0254145	−	0.999677i	$-0.508091\pi$
$167$	−0.656854			−0.0508289			−0.0254145	+	0.999677i	$0.508091\pi$
$168$	−1.00000	+	2.44949i	−0.0771517	+	0.188982i
$169$	1.00000			0.0769231
$170$	−0.707107	+	1.22474i	−0.0542326	+	0.0939336i
$171$	1.08579	+	1.88064i	0.0830322	+	0.143816i
$172$	−3.24264	−	5.61642i	−0.247249	−	0.428248i
$173$	−2.74264	+	4.75039i	−0.208519	+	0.361166i	−0.951248	−	0.308426i	$-0.900198\pi$
$173$	−2.74264	+	4.75039i	−0.208519	+	0.361166i	0.742729	+	0.669592i	$0.233531\pi$
$174$	1.82843			0.138613
$175$	−4.65685	+	11.4069i	−0.352025	+	0.862282i
$176$	−0.414214			−0.0312225
$177$	1.03553	−	1.79360i	0.0778355	−	0.134815i
$178$	−1.29289	−	2.23936i	−0.0969064	−	0.167847i
$179$	−9.82843	−	17.0233i	−0.734611	−	1.27238i	−0.954894	−	0.296948i	$-0.904031\pi$
$179$	−9.82843	−	17.0233i	−0.734611	−	1.27238i	0.220283	−	0.975436i	$-0.429302\pi$
$180$	0.292893	−	0.507306i	0.0218310	−	0.0378124i
$181$	2.89949			0.215518			0.107759	−	0.994177i	$-0.465633\pi$
$181$	2.89949			0.215518			0.107759	+	0.994177i	$0.465633\pi$
$182$	−2.62132	+	0.358719i	−0.194305	+	0.0265901i
$183$	4.41421			0.326308
$184$	−0.707107	+	1.22474i	−0.0521286	+	0.0902894i
$185$	0.414214	+	0.717439i	0.0304536	+	0.0527472i
$186$	−4.24264	−	7.34847i	−0.311086	−	0.538816i
$187$	−0.500000	+	0.866025i	−0.0365636	+	0.0633300i
$188$	1.00000			0.0729325
$189$	−1.62132	−	2.09077i	−0.117934	−	0.152081i
$190$	1.27208			0.0922862
$191$	5.17157	−	8.95743i	0.374202	−	0.648137i	−0.616005	−	0.787742i	$-0.711250\pi$
$191$	5.17157	−	8.95743i	0.374202	−	0.648137i	0.990207	+	0.139605i	$0.0445834\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	1.46447	+	2.53653i	0.105415	+	0.182583i	0.913908	−	0.405922i	$-0.133050\pi$
$193$	1.46447	+	2.53653i	0.105415	+	0.182583i	−0.808493	+	0.588506i	$0.799716\pi$
$194$	0.464466	−	0.804479i	0.0333467	−	0.0577582i
$195$	0.585786			0.0419490
$196$	6.74264	−	1.88064i	0.481617	−	0.134331i
$197$	−15.5563			−1.10834			−0.554172	−	0.832402i	$-0.686965\pi$
$197$	−15.5563			−1.10834			−0.554172	+	0.832402i	$0.686965\pi$
$198$	0.207107	−	0.358719i	0.0147184	−	0.0254931i
$199$	−1.36396	−	2.36245i	−0.0966886	−	0.167470i	0.813623	−	0.581392i	$-0.197492\pi$
$199$	−1.36396	−	2.36245i	−0.0966886	−	0.167470i	−0.910312	+	0.413923i	$0.864158\pi$
$200$	2.32843	+	4.03295i	0.164645	+	0.285173i
$201$	0.914214	−	1.58346i	0.0644837	−	0.111689i
$202$	−14.8284			−1.04332
$203$	−2.96447	−	3.82282i	−0.208065	−	0.268309i
$204$	2.41421			0.169029
$205$	−2.89949	+	5.02207i	−0.202510	+	0.350757i
$206$	8.41421	+	14.5738i	0.586246	+	1.01541i
$207$	−0.707107	−	1.22474i	−0.0491473	−	0.0851257i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	0.899495			0.0622194
$210$	−1.53553	+	0.210133i	−0.105962	+	0.0145006i
$211$	−12.9289			−0.890064			−0.445032	−	0.895515i	$-0.646808\pi$
$211$	−12.9289			−0.890064			−0.445032	+	0.895515i	$0.646808\pi$
$212$	−4.74264	+	8.21449i	−0.325726	+	0.564174i
$213$	−2.50000	−	4.33013i	−0.171297	−	0.296695i
$214$	9.65685	+	16.7262i	0.660129	+	1.14338i
$215$	1.89949	−	3.29002i	0.129544	−	0.224378i
$216$	−1.00000			−0.0680414
$217$	−8.48528	+	20.7846i	−0.576018	+	1.41095i
$218$	−9.65685			−0.654045
$219$	0.707107	−	1.22474i	0.0477818	−	0.0827606i
$220$	−0.121320	−	0.210133i	−0.00817942	−	0.0141672i
$221$	1.20711	+	2.09077i	0.0811988	+	0.140640i
$222$	0.707107	−	1.22474i	0.0474579	−	0.0821995i
$223$	−7.92893			−0.530961			−0.265480	−	0.964116i	$-0.585531\pi$
$223$	−7.92893			−0.530961			−0.265480	+	0.964116i	$0.585531\pi$
$224$	1.00000	−	2.44949i	0.0668153	−	0.163663i
$225$	−4.65685			−0.310457
$226$	−2.44975	+	4.24309i	−0.162955	+	0.282246i
$227$	10.5858	+	18.3351i	0.702603	+	1.21694i	0.967550	+	0.252681i	$0.0813125\pi$
$227$	10.5858	+	18.3351i	0.702603	+	1.21694i	−0.264946	+	0.964263i	$0.585354\pi$
$228$	−1.08579	−	1.88064i	−0.0719080	−	0.124548i
$229$	−13.2426	+	22.9369i	−0.875098	+	1.51571i	−0.0184404	+	0.999830i	$0.505870\pi$
$229$	−13.2426	+	22.9369i	−0.875098	+	1.51571i	−0.856658	+	0.515885i	$0.827463\pi$
$230$	−0.828427			−0.0546249
$231$	−1.08579	+	0.148586i	−0.0714395	+	0.00977627i
$232$	−1.82843			−0.120042
$233$	8.86396	−	15.3528i	0.580697	−	1.00580i	−0.414699	−	0.909958i	$-0.636113\pi$
$233$	8.86396	−	15.3528i	0.580697	−	1.00580i	0.995397	−	0.0958390i	$-0.0305534\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	0.292893	+	0.507306i	0.0191062	+	0.0330930i
$236$	−1.03553	+	1.79360i	−0.0674075	+	0.116753i
$237$	11.6569			0.757194
$238$	−3.91421	−	5.04757i	−0.253721	−	0.327185i
$239$	4.51472			0.292033			0.146016	−	0.989282i	$-0.453355\pi$
$239$	4.51472			0.292033			0.146016	+	0.989282i	$0.453355\pi$
$240$	−0.292893	+	0.507306i	−0.0189062	+	0.0327465i
$241$	1.07107	+	1.85514i	0.0689935	+	0.119500i	0.898459	−	0.439058i	$-0.144688\pi$
$241$	1.07107	+	1.85514i	0.0689935	+	0.119500i	−0.829465	+	0.558559i	$0.811355\pi$
$242$	5.41421	+	9.37769i	0.348039	+	0.602821i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.41421			−0.282591
$245$	2.92893	+	2.86976i	0.187123	+	0.183342i
$246$	9.89949			0.631169
$247$	1.08579	−	1.88064i	0.0690869	−	0.119662i
$248$	4.24264	+	7.34847i	0.269408	+	0.466628i
$249$	3.82843	+	6.63103i	0.242617	+	0.420224i
$250$	−2.82843	+	4.89898i	−0.178885	+	0.309839i
$251$	24.8284			1.56716			0.783578	−	0.621293i	$-0.213392\pi$
$251$	24.8284			1.56716			0.783578	+	0.621293i	$0.213392\pi$
$252$	1.62132	+	2.09077i	0.102134	+	0.131706i
$253$	−0.585786			−0.0368281
$254$	3.94975	−	6.84116i	0.247829	−	0.429253i
$255$	0.707107	+	1.22474i	0.0442807	+	0.0766965i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.2426	+	22.9369i	−0.826053	+	1.43077i	0.0750585	+	0.997179i	$0.476086\pi$
$257$	−13.2426	+	22.9369i	−0.826053	+	1.43077i	−0.901112	+	0.433587i	$0.857248\pi$
$258$	−6.48528			−0.403756
$259$	−3.70711	+	0.507306i	−0.230348	+	0.0315225i
$260$	−0.585786			−0.0363289
$261$	0.914214	−	1.58346i	0.0565884	−	0.0980140i
$262$	4.77817	+	8.27604i	0.295197	+	0.511296i
$263$	−10.2929	−	17.8278i	−0.634687	−	1.09931i	−0.986581	−	0.163270i	$-0.947796\pi$
$263$	−10.2929	−	17.8278i	−0.634687	−	1.09931i	0.351894	−	0.936040i	$-0.385538\pi$
$264$	−0.207107	+	0.358719i	−0.0127465	+	0.0220777i
$265$	−5.55635			−0.341324
$266$	−2.17157	+	5.31925i	−0.133148	+	0.326144i
$267$	−2.58579			−0.158248
$268$	−0.914214	+	1.58346i	−0.0558445	+	0.0967255i
$269$	4.57107	+	7.91732i	0.278703	+	0.482728i	0.971063	−	0.238825i	$-0.0767622\pi$
$269$	4.57107	+	7.91732i	0.278703	+	0.482728i	−0.692360	+	0.721552i	$0.743429\pi$
$270$	−0.292893	−	0.507306i	−0.0178249	−	0.0308737i
$271$	−13.1066	+	22.7013i	−0.796169	+	1.37901i	0.125925	+	0.992040i	$0.459810\pi$
$271$	−13.1066	+	22.7013i	−0.796169	+	1.37901i	−0.922094	+	0.386966i	$0.873523\pi$
$272$	−2.41421			−0.146383
$273$	−1.00000	+	2.44949i	−0.0605228	+	0.148250i
$274$	11.0711			0.668828
$275$	−0.964466	+	1.67050i	−0.0581595	+	0.100735i
$276$	0.707107	+	1.22474i	0.0425628	+	0.0737210i
$277$	−9.03553	−	15.6500i	−0.542893	−	0.940318i	−0.998736	−	0.0502577i	$-0.983996\pi$
$277$	−9.03553	−	15.6500i	−0.542893	−	0.940318i	0.455844	−	0.890060i	$-0.349338\pi$
$278$	6.53553	−	11.3199i	0.391975	−	0.678921i
$279$	−8.48528			−0.508001
$280$	1.53553	−	0.210133i	0.0917657	−	0.0125578i
$281$	0.686292			0.0409407			0.0204704	−	0.999790i	$-0.493484\pi$
$281$	0.686292			0.0409407			0.0204704	+	0.999790i	$0.493484\pi$
$282$	0.500000	−	0.866025i	0.0297746	−	0.0515711i
$283$	7.87868	+	13.6463i	0.468339	+	0.811187i	0.999345	−	0.0361811i	$-0.0115193\pi$
$283$	7.87868	+	13.6463i	0.468339	+	0.811187i	−0.531006	+	0.847368i	$0.678186\pi$
$284$	2.50000	+	4.33013i	0.148348	+	0.256946i
$285$	0.636039	−	1.10165i	0.0376757	−	0.0652562i
$286$	−0.414214			−0.0244930
$287$	−16.0503	−	20.6976i	−0.947416	−	1.22174i
$288$	1.00000			0.0589256
$289$	5.58579	−	9.67487i	0.328576	−	0.569110i
$290$	−0.535534	−	0.927572i	−0.0314476	−	0.0544689i
$291$	−0.464466	−	0.804479i	−0.0272275	−	0.0471594i
$292$	−0.707107	+	1.22474i	−0.0413803	+	0.0716728i
$293$	−9.89949			−0.578335			−0.289167	−	0.957279i	$-0.593378\pi$
$293$	−9.89949			−0.578335			−0.289167	+	0.957279i	$0.593378\pi$
$294$	1.74264	−	6.77962i	0.101633	−	0.395395i
$295$	−1.21320			−0.0706354
$296$	−0.707107	+	1.22474i	−0.0410997	+	0.0711868i
$297$	−0.207107	−	0.358719i	−0.0120176	−	0.0208150i
$298$	2.46447	+	4.26858i	0.142763	+	0.247272i
$299$	−0.707107	+	1.22474i	−0.0408930	+	0.0708288i
$300$	4.65685			0.268864
$301$	10.5147	+	13.5592i	0.606058	+	0.781541i
$302$	4.07107			0.234264
$303$	−7.41421	+	12.8418i	−0.425935	+	0.737742i
$304$	1.08579	+	1.88064i	0.0622741	+	0.107862i
$305$	−1.29289	−	2.23936i	−0.0740309	−	0.128225i
$306$	1.20711	−	2.09077i	0.0690057	−	0.119521i
$307$	−28.1127			−1.60448			−0.802238	−	0.597004i	$-0.796358\pi$
$307$	−28.1127			−1.60448			−0.802238	+	0.597004i	$0.796358\pi$
$308$	1.08579	−	0.148586i	0.0618684	−	0.00846650i
$309$	16.8284			0.957336
$310$	−2.48528	+	4.30463i	−0.141154	+	0.244487i
$311$	4.05025	+	7.01524i	0.229669	+	0.397798i	0.957710	−	0.287735i	$-0.0929024\pi$
$311$	4.05025	+	7.01524i	0.229669	+	0.397798i	−0.728041	+	0.685533i	$0.759569\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	−1.75736	+	3.04384i	−0.0993318	+	0.172048i	−0.911408	−	0.411503i	$-0.865004\pi$
$313$	−1.75736	+	3.04384i	−0.0993318	+	0.172048i	0.812076	+	0.583551i	$0.198337\pi$
$314$	9.72792			0.548978
$315$	−0.585786	+	1.43488i	−0.0330053	+	0.0808462i
$316$	−11.6569			−0.655749
$317$	−14.8995	+	25.8067i	−0.836839	+	1.44945i	0.0556853	+	0.998448i	$0.482266\pi$
$317$	−14.8995	+	25.8067i	−0.836839	+	1.44945i	−0.892524	+	0.450999i	$0.851068\pi$
$318$	4.74264	+	8.21449i	0.265954	+	0.460646i
$319$	−0.378680	−	0.655892i	−0.0212020	−	0.0367229i
$320$	0.292893	−	0.507306i	0.0163732	−	0.0283593i
$321$	19.3137			1.07799
$322$	1.41421	−	3.46410i	0.0788110	−	0.193047i
$323$	5.24264			0.291708
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	2.32843	+	4.03295i	0.129158	+	0.223708i
$326$	9.32843	+	16.1573i	0.516654	+	0.894871i
$327$	−4.82843	+	8.36308i	−0.267013	+	0.462479i
$328$	−9.89949			−0.546608
$329$	−2.62132	+	0.358719i	−0.144518	+	0.0197768i
$330$	−0.242641			−0.0133569
$331$	11.2426	−	19.4728i	0.617951	−	1.07032i	−0.371908	−	0.928270i	$-0.621296\pi$
$331$	11.2426	−	19.4728i	0.617951	−	1.07032i	0.989859	−	0.142053i	$-0.0453705\pi$
$332$	−3.82843	−	6.63103i	−0.210112	−	0.363925i
$333$	−0.707107	−	1.22474i	−0.0387492	−	0.0671156i
$334$	0.328427	−	0.568852i	0.0179707	−	0.0311262i
$335$	−1.07107			−0.0585187
$336$	−1.62132	−	2.09077i	−0.0884503	−	0.114061i
$337$	−20.3137			−1.10656			−0.553279	−	0.832996i	$-0.686624\pi$
$337$	−20.3137			−1.10656			−0.553279	+	0.832996i	$0.686624\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	2.44975	+	4.24309i	0.133052	+	0.230453i
$340$	−0.707107	−	1.22474i	−0.0383482	−	0.0664211i
$341$	−1.75736	+	3.04384i	−0.0951663	+	0.164833i
$342$	−2.17157			−0.117425
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	6.48528			0.349663
$345$	−0.414214	+	0.717439i	−0.0223005	+	0.0386256i
$346$	−2.74264	−	4.75039i	−0.147445	−	0.255383i
$347$	4.36396	+	7.55860i	0.234270	+	0.405767i	0.959060	−	0.283202i	$-0.0913968\pi$
$347$	4.36396	+	7.55860i	0.234270	+	0.405767i	−0.724790	+	0.688969i	$0.758063\pi$
$348$	−0.914214	+	1.58346i	−0.0490070	+	0.0848826i
$349$	−6.72792			−0.360137			−0.180069	−	0.983654i	$-0.557632\pi$
$349$	−6.72792			−0.360137			−0.180069	+	0.983654i	$0.557632\pi$
$350$	−7.55025	−	9.73641i	−0.403578	−	0.520433i
$351$	−1.00000			−0.0533761
$352$	0.207107	−	0.358719i	0.0110388	−	0.0191198i
$353$	−6.31371	−	10.9357i	−0.336045	−	0.582047i	0.647640	−	0.761946i	$-0.275756\pi$
$353$	−6.31371	−	10.9357i	−0.336045	−	0.582047i	−0.983685	+	0.179900i	$0.942423\pi$
$354$	1.03553	+	1.79360i	0.0550380	+	0.0953286i
$355$	−1.46447	+	2.53653i	−0.0777258	+	0.134625i
$356$	2.58579			0.137046
$357$	−6.32843	+	0.866025i	−0.334936	+	0.0458349i
$358$	19.6569			1.03890
$359$	0.414214	−	0.717439i	0.0218614	−	0.0378650i	−0.854888	−	0.518813i	$-0.826374\pi$
$359$	0.414214	−	0.717439i	0.0218614	−	0.0378650i	0.876749	+	0.480948i	$0.159707\pi$
$360$	0.292893	+	0.507306i	0.0154368	+	0.0267374i
$361$	7.14214	+	12.3705i	0.375902	+	0.651081i
$362$	−1.44975	+	2.51104i	−0.0761970	+	0.131977i
$363$	10.8284			0.568345
$364$	1.00000	−	2.44949i	0.0524142	−	0.128388i
$365$	−0.828427			−0.0433619
$366$	−2.20711	+	3.82282i	−0.115367	+	0.199822i
$367$	−6.31371	−	10.9357i	−0.329573	−	0.570837i	0.652854	−	0.757484i	$-0.273571\pi$
$367$	−6.31371	−	10.9357i	−0.329573	−	0.570837i	−0.982427	+	0.186647i	$0.940238\pi$
$368$	−0.707107	−	1.22474i	−0.0368605	−	0.0638442i
$369$	4.94975	−	8.57321i	0.257674	−	0.446304i
$370$	−0.828427			−0.0430679
$371$	9.48528	−	23.2341i	0.492451	−	1.20625i
$372$	8.48528			0.439941
$373$	2.79289	−	4.83743i	0.144611	−	0.250473i	−0.784617	−	0.619981i	$-0.787140\pi$
$373$	2.79289	−	4.83743i	0.144611	−	0.250473i	0.929228	+	0.369508i	$0.120474\pi$
$374$	−0.500000	−	0.866025i	−0.0258544	−	0.0447811i
$375$	2.82843	+	4.89898i	0.146059	+	0.252982i
$376$	−0.500000	+	0.866025i	−0.0257855	+	0.0446619i
$377$	−1.82843			−0.0941688
$378$	2.62132	−	0.358719i	0.134826	−	0.0184505i
$379$	18.6274			0.956826			0.478413	−	0.878135i	$-0.341212\pi$
$379$	18.6274			0.956826			0.478413	+	0.878135i	$0.341212\pi$
$380$	−0.636039	+	1.10165i	−0.0326281	+	0.0565135i
$381$	−3.94975	−	6.84116i	−0.202352	−	0.350483i
$382$	5.17157	+	8.95743i	0.264601	+	0.458302i
$383$	−5.58579	+	9.67487i	−0.285420	+	0.494363i	−0.972711	−	0.232020i	$-0.925467\pi$
$383$	−5.58579	+	9.67487i	−0.285420	+	0.494363i	0.687291	+	0.726382i	$0.258800\pi$
$384$	−1.00000			−0.0510310
$385$	0.393398	+	0.507306i	0.0200494	+	0.0258547i
$386$	−2.92893			−0.149079
$387$	−3.24264	+	5.61642i	−0.164833	+	0.285499i
$388$	0.464466	+	0.804479i	0.0235797	+	0.0408412i
$389$	2.25736	+	3.90986i	0.114453	+	0.198238i	0.917561	−	0.397595i	$-0.130155\pi$
$389$	2.25736	+	3.90986i	0.114453	+	0.198238i	−0.803108	+	0.595833i	$0.796822\pi$
$390$	−0.292893	+	0.507306i	−0.0148312	+	0.0256884i
$391$	−3.41421			−0.172664
$392$	−1.74264	+	6.77962i	−0.0880166	+	0.342422i
$393$	9.55635			0.482054
$394$	7.77817	−	13.4722i	0.391859	−	0.678719i
$395$	−3.41421	−	5.91359i	−0.171788	−	0.297545i
$396$	0.207107	+	0.358719i	0.0104075	+	0.0180263i
$397$	4.77817	−	8.27604i	0.239810	−	0.415363i	−0.720850	−	0.693091i	$-0.756248\pi$
$397$	4.77817	−	8.27604i	0.239810	−	0.415363i	0.960660	+	0.277729i	$0.0895816\pi$
$398$	2.72792			0.136738
$399$	3.52082	+	4.54026i	0.176261	+	0.227297i
$400$	−4.65685			−0.232843
$401$	−9.94975	+	17.2335i	−0.496867	+	0.860598i	−0.999993	−	0.00361428i	$-0.998850\pi$
$401$	−9.94975	+	17.2335i	−0.496867	+	0.860598i	0.503127	+	0.864213i	$0.332183\pi$
$402$	0.914214	+	1.58346i	0.0455968	+	0.0789760i
$403$	4.24264	+	7.34847i	0.211341	+	0.366053i
$404$	7.41421	−	12.8418i	0.368871	−	0.638903i
$405$	−0.585786			−0.0291080
$406$	4.79289	−	0.655892i	0.237867	−	0.0325514i
$407$	−0.585786			−0.0290364
$408$	−1.20711	+	2.09077i	−0.0597607	+	0.103509i
$409$	−16.2929	−	28.2201i	−0.805632	−	1.39540i	−0.915864	−	0.401489i	$-0.868493\pi$
$409$	−16.2929	−	28.2201i	−0.805632	−	1.39540i	0.110232	−	0.993906i	$-0.464841\pi$
$410$	−2.89949	−	5.02207i	−0.143196	−	0.248022i
$411$	5.53553	−	9.58783i	0.273048	−	0.472933i
$412$	−16.8284			−0.829077
$413$	2.07107	−	5.07306i	0.101911	−	0.249629i
$414$	1.41421			0.0695048
$415$	2.24264	−	3.88437i	0.110087	−	0.190676i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−6.53553	−	11.3199i	−0.320046	−	0.554337i
$418$	−0.449747	+	0.778985i	−0.0219979	+	0.0381014i
$419$	27.4558			1.34131			0.670653	−	0.741771i	$-0.266014\pi$
$419$	27.4558			1.34131			0.670653	+	0.741771i	$0.266014\pi$
$420$	0.585786	−	1.43488i	0.0285835	−	0.0700149i
$421$	1.07107			0.0522007			0.0261003	−	0.999659i	$-0.491691\pi$
$421$	1.07107			0.0522007			0.0261003	+	0.999659i	$0.491691\pi$
$422$	6.46447	−	11.1968i	0.314685	−	0.545051i
$423$	−0.500000	−	0.866025i	−0.0243108	−	0.0421076i
$424$	−4.74264	−	8.21449i	−0.230323	−	0.398931i
$425$	−5.62132	+	9.73641i	−0.272674	+	0.472285i
$426$	5.00000			0.242251
$427$	11.5711	−	1.58346i	0.559963	−	0.0766292i
$428$	−19.3137			−0.933563
$429$	−0.207107	+	0.358719i	−0.00999921	+	0.0173191i
$430$	1.89949	+	3.29002i	0.0916018	+	0.158659i
$431$	−15.2426	−	26.4010i	−0.734212	−	1.27169i	−0.955068	−	0.296386i	$-0.904218\pi$
$431$	−15.2426	−	26.4010i	−0.734212	−	1.27169i	0.220856	−	0.975306i	$-0.429115\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	29.9706			1.44029			0.720147	−	0.693822i	$-0.244074\pi$
$433$	29.9706			1.44029			0.720147	+	0.693822i	$0.244074\pi$
$434$	−13.7574	−	17.7408i	−0.660374	−	0.851584i
$435$	−1.07107			−0.0513538
$436$	4.82843	−	8.36308i	0.231240	−	0.400519i
$437$	1.53553	+	2.65962i	0.0734545	+	0.127227i
$438$	0.707107	+	1.22474i	0.0337869	+	0.0585206i
$439$	−8.29289	+	14.3637i	−0.395798	+	0.685543i	−0.993203	−	0.116397i	$-0.962865\pi$
$439$	−8.29289	+	14.3637i	−0.395798	+	0.685543i	0.597405	+	0.801940i	$0.296199\pi$
$440$	0.242641			0.0115674
$441$	−5.00000	−	4.89898i	−0.238095	−	0.233285i
$442$	−2.41421			−0.114832
$443$	16.8492	−	29.1837i	0.800532	−	1.38656i	−0.118735	−	0.992926i	$-0.537884\pi$
$443$	16.8492	−	29.1837i	0.800532	−	1.38656i	0.919267	−	0.393636i	$-0.128783\pi$
$444$	0.707107	+	1.22474i	0.0335578	+	0.0581238i
$445$	0.757359	+	1.31178i	0.0359023	+	0.0621846i
$446$	3.96447	−	6.86666i	0.187723	−	0.325146i
$447$	4.92893			0.233130
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$	24.9706			1.17843			0.589217	−	0.807975i	$-0.299436\pi$
$449$	24.9706			1.17843			0.589217	+	0.807975i	$0.299436\pi$
$450$	2.32843	−	4.03295i	0.109763	−	0.190115i
$451$	−2.05025	−	3.55114i	−0.0965426	−	0.167217i
$452$	−2.44975	−	4.24309i	−0.115226	−	0.199578i
$453$	2.03553	−	3.52565i	0.0956377	−	0.165649i
$454$	−21.1716			−0.993631
$455$	1.53553	−	0.210133i	0.0719869	−	0.00985119i
$456$	2.17157			0.101693
$457$	1.53553	−	2.65962i	0.0718292	−	0.124412i	−0.827874	−	0.560914i	$-0.810450\pi$
$457$	1.53553	−	2.65962i	0.0718292	−	0.124412i	0.899703	+	0.436503i	$0.143783\pi$
$458$	−13.2426	−	22.9369i	−0.618788	−	1.07177i
$459$	−1.20711	−	2.09077i	−0.0563429	−	0.0975888i
$460$	0.414214	−	0.717439i	0.0193128	−	0.0334508i
$461$	−4.48528			−0.208900			−0.104450	−	0.994530i	$-0.533308\pi$
$461$	−4.48528			−0.208900			−0.104450	+	0.994530i	$0.533308\pi$
$462$	0.414214	−	1.01461i	0.0192710	−	0.0472040i
$463$	−20.9706			−0.974585			−0.487292	−	0.873239i	$-0.662015\pi$
$463$	−20.9706			−0.974585			−0.487292	+	0.873239i	$0.662015\pi$
$464$	0.914214	−	1.58346i	0.0424413	−	0.0735105i
$465$	2.48528	+	4.30463i	0.115252	+	0.199623i
$466$	8.86396	+	15.3528i	0.410615	+	0.711206i
$467$	5.70711	−	9.88500i	0.264093	−	0.457423i	−0.703232	−	0.710960i	$-0.748261\pi$
$467$	5.70711	−	9.88500i	0.264093	−	0.457423i	0.967326	+	0.253537i	$0.0815939\pi$
$468$	1.00000			0.0462250
$469$	1.82843	−	4.47871i	0.0844289	−	0.206808i
$470$	−0.585786			−0.0270203
$471$	4.86396	−	8.42463i	0.224119	−	0.388186i
$472$	−1.03553	−	1.79360i	−0.0476643	−	0.0825570i
$473$	1.34315	+	2.32640i	0.0617579	+	0.106968i
$474$	−5.82843	+	10.0951i	−0.267709	+	0.463685i
$475$	10.1127			0.464002
$476$	6.32843	−	0.866025i	0.290063	−	0.0396942i
$477$	9.48528			0.434301
$478$	−2.25736	+	3.90986i	−0.103249	+	0.178833i
$479$	16.0563	+	27.8104i	0.733633	+	1.27069i	0.955320	+	0.295572i	$0.0955103\pi$
$479$	16.0563	+	27.8104i	0.733633	+	1.27069i	−0.221687	+	0.975118i	$0.571156\pi$
$480$	−0.292893	−	0.507306i	−0.0133687	−	0.0231552i
$481$	−0.707107	+	1.22474i	−0.0322413	+	0.0558436i
$482$	−2.14214			−0.0975716
$483$	−2.29289	−	2.95680i	−0.104330	−	0.134539i
$484$	−10.8284			−0.492201
$485$	−0.272078	+	0.471253i	−0.0123544	+	0.0213985i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−8.10660	−	14.0410i	−0.367345	−	0.636261i	0.621804	−	0.783173i	$-0.286400\pi$
$487$	−8.10660	−	14.0410i	−0.367345	−	0.636261i	−0.989150	+	0.146912i	$0.953067\pi$
$488$	2.20711	−	3.82282i	0.0999110	−	0.173051i
$489$	18.6569			0.843692
$490$	−3.94975	+	1.10165i	−0.178431	+	0.0497676i
$491$	23.6569			1.06762			0.533809	−	0.845605i	$-0.320760\pi$
$491$	23.6569			1.06762			0.533809	+	0.845605i	$0.320760\pi$
$492$	−4.94975	+	8.57321i	−0.223152	+	0.386510i
$493$	−2.20711	−	3.82282i	−0.0994031	−	0.172171i
$494$	1.08579	+	1.88064i	0.0488518	+	0.0846139i
$495$	−0.121320	+	0.210133i	−0.00545294	+	0.00944478i
$496$	−8.48528			−0.381000
$497$	−8.10660	−	10.4539i	−0.363631	−	0.468919i
$498$	−7.65685			−0.343112
$499$	−1.82843	+	3.16693i	−0.0818516	+	0.141771i	−0.904045	−	0.427437i	$-0.859417\pi$
$499$	−1.82843	+	3.16693i	−0.0818516	+	0.141771i	0.822194	+	0.569208i	$0.192750\pi$
$500$	−2.82843	−	4.89898i	−0.126491	−	0.219089i
$501$	−0.328427	−	0.568852i	−0.0146730	−	0.0254145i
$502$	−12.4142	+	21.5020i	−0.554073	+	0.959683i
$503$	26.1421			1.16562			0.582810	−	0.812608i	$-0.301953\pi$
$503$	26.1421			1.16562			0.582810	+	0.812608i	$0.301953\pi$
$504$	−2.62132	+	0.358719i	−0.116763	+	0.0159786i
$505$	8.68629			0.386535
$506$	0.292893	−	0.507306i	0.0130207	−	0.0225525i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	3.94975	+	6.84116i	0.175242	+	0.303528i
$509$	−5.31371	+	9.20361i	−0.235526	+	0.407943i	−0.959425	−	0.281963i	$-0.909015\pi$
$509$	−5.31371	+	9.20361i	−0.235526	+	0.407943i	0.723899	+	0.689906i	$0.242348\pi$
$510$	−1.41421			−0.0626224
$511$	1.41421	−	3.46410i	0.0625611	−	0.153243i
$512$	1.00000			0.0441942
$513$	−1.08579	+	1.88064i	−0.0479386	+	0.0830322i
$514$	−13.2426	−	22.9369i	−0.584108	−	1.01170i
$515$	−4.92893	−	8.53716i	−0.217195	−	0.376192i
$516$	3.24264	−	5.61642i	0.142749	−	0.247249i
$517$	−0.414214			−0.0182171
$518$	1.41421	−	3.46410i	0.0621370	−	0.152204i
$519$	−5.48528			−0.240777
$520$	0.292893	−	0.507306i	0.0128442	−	0.0222468i
$521$	−20.3137	−	35.1844i	−0.889960	−	1.54146i	−0.839921	−	0.542708i	$-0.817399\pi$
$521$	−20.3137	−	35.1844i	−0.889960	−	1.54146i	−0.0500384	−	0.998747i	$-0.515934\pi$
$522$	0.914214	+	1.58346i	0.0400140	+	0.0693064i
$523$	8.41421	−	14.5738i	0.367928	−	0.637270i	−0.621314	−	0.783562i	$-0.713401\pi$
$523$	8.41421	−	14.5738i	0.367928	−	0.637270i	0.989241	+	0.146292i	$0.0467340\pi$
$524$	−9.55635			−0.417471
$525$	−12.2071	+	1.67050i	−0.532762	+	0.0729068i
$526$	20.5858			0.897583
$527$	−10.2426	+	17.7408i	−0.446176	+	0.772800i
$528$	−0.207107	−	0.358719i	−0.00901317	−	0.0156113i
$529$	10.5000	+	18.1865i	0.456522	+	0.790719i
$530$	2.77817	−	4.81194i	0.120676	−	0.209017i
$531$	2.07107			0.0898767
$532$	−3.52082	−	4.54026i	−0.152647	−	0.196845i
$533$	−9.89949			−0.428795
$534$	1.29289	−	2.23936i	0.0559490	−	0.0969064i
$535$	−5.65685	−	9.79796i	−0.244567	−	0.423603i
$536$	−0.914214	−	1.58346i	−0.0394880	−	0.0683952i
$537$	9.82843	−	17.0233i	0.424128	−	0.734611i
$538$	−9.14214			−0.394145
$539$	−2.79289	+	0.778985i	−0.120298	+	0.0335533i
$540$	0.585786			0.0252082
$541$	−11.5355	+	19.9801i	−0.495951	+	0.859013i	−0.999989	−	0.00466870i	$-0.998514\pi$
$541$	−11.5355	+	19.9801i	−0.495951	+	0.859013i	0.504038	+	0.863682i	$0.331847\pi$
$542$	−13.1066	−	22.7013i	−0.562977	−	0.975104i
$543$	1.44975	+	2.51104i	0.0622146	+	0.107759i
$544$	1.20711	−	2.09077i	0.0517543	−	0.0896410i
$545$	5.65685			0.242313
$546$	−1.62132	−	2.09077i	−0.0693861	−	0.0894767i
$547$	−30.8701			−1.31991			−0.659954	−	0.751306i	$-0.729424\pi$
$547$	−30.8701			−1.31991			−0.659954	+	0.751306i	$0.729424\pi$
$548$	−5.53553	+	9.58783i	−0.236466	+	0.409572i
$549$	2.20711	+	3.82282i	0.0941970	+	0.163154i
$550$	−0.964466	−	1.67050i	−0.0411250	−	0.0712305i
$551$	−1.98528	+	3.43861i	−0.0845758	+	0.146490i
$552$	−1.41421			−0.0601929
$553$	30.5563	−	4.18154i	1.29939	−	0.177817i
$554$	18.0711			0.767766
$555$	−0.414214	+	0.717439i	−0.0175824	+	0.0304536i
$556$	6.53553	+	11.3199i	0.277168	+	0.480070i
$557$	16.3137	+	28.2562i	0.691234	+	1.19725i	0.971434	+	0.237311i	$0.0762660\pi$
$557$	16.3137	+	28.2562i	0.691234	+	1.19725i	−0.280200	+	0.959942i	$0.590401\pi$
$558$	4.24264	−	7.34847i	0.179605	−	0.311086i
$559$	6.48528			0.274298
$560$	−0.585786	+	1.43488i	−0.0247540	+	0.0606347i
$561$	−1.00000			−0.0422200
$562$	−0.343146	+	0.594346i	−0.0144747	+	0.0250710i
$563$	16.3848	+	28.3793i	0.690536	+	1.19604i	0.971662	+	0.236373i	$0.0759586\pi$
$563$	16.3848	+	28.3793i	0.690536	+	1.19604i	−0.281126	+	0.959671i	$0.590708\pi$
$564$	0.500000	+	0.866025i	0.0210538	+	0.0364662i
$565$	1.43503	−	2.48554i	0.0603721	−	0.104568i
$566$	−15.7574			−0.662331
$567$	1.00000	−	2.44949i	0.0419961	−	0.102869i
$568$	−5.00000			−0.209795
$569$	−11.8640	+	20.5490i	−0.497363	+	0.861458i	−0.999995	−	0.00304214i	$-0.999032\pi$
$569$	−11.8640	+	20.5490i	−0.497363	+	0.861458i	0.502632	+	0.864500i	$0.332365\pi$
$570$	0.636039	+	1.10165i	0.0266407	+	0.0461431i
$571$	15.6569	+	27.1185i	0.655219	+	1.13487i	0.981839	+	0.189717i	$0.0607570\pi$
$571$	15.6569	+	27.1185i	0.655219	+	1.13487i	−0.326620	+	0.945156i	$0.605910\pi$
$572$	0.207107	−	0.358719i	0.00865957	−	0.0149988i
$573$	10.3431			0.432091
$574$	25.9497	−	3.55114i	1.08312	−	0.148222i
$575$	−6.58579			−0.274646
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.17157	−	14.1536i	−0.340187	−	0.589221i	0.644280	−	0.764790i	$-0.277157\pi$
$577$	−8.17157	−	14.1536i	−0.340187	−	0.589221i	−0.984467	+	0.175568i	$0.943824\pi$
$578$	5.58579	+	9.67487i	0.232338	+	0.402421i
$579$	−1.46447	+	2.53653i	−0.0608611	+	0.105415i
$580$	1.07107			0.0444737
$581$	12.4142	+	16.0087i	0.515028	+	0.664154i
$582$	0.928932			0.0385055
$583$	1.96447	−	3.40256i	0.0813599	−	0.140919i
$584$	−0.707107	−	1.22474i	−0.0292603	−	0.0506803i
$585$	0.292893	+	0.507306i	0.0121096	+	0.0209745i
$586$	4.94975	−	8.57321i	0.204472	−	0.354156i
$587$	−1.58579			−0.0654524			−0.0327262	−	0.999464i	$-0.510419\pi$
$587$	−1.58579			−0.0654524			−0.0327262	+	0.999464i	$0.510419\pi$
$588$	5.00000	+	4.89898i	0.206197	+	0.202031i
$589$	18.4264			0.759247
$590$	0.606602	−	1.05066i	0.0249734	−	0.0432552i
$591$	−7.77817	−	13.4722i	−0.319951	−	0.554172i
$592$	−0.707107	−	1.22474i	−0.0290619	−	0.0503367i
$593$	17.1924	−	29.7781i	0.706007	−	1.22284i	−0.260320	−	0.965522i	$-0.583828\pi$
$593$	17.1924	−	29.7781i	0.706007	−	1.22284i	0.966327	−	0.257317i	$-0.0828385\pi$
$594$	0.414214			0.0169954
$595$	2.29289	+	2.95680i	0.0939995	+	0.121217i
$596$	−4.92893			−0.201897
$597$	1.36396	−	2.36245i	0.0558232	−	0.0966886i
$598$	−0.707107	−	1.22474i	−0.0289157	−	0.0500835i
$599$	−0.778175	−	1.34784i	−0.0317954	−	0.0550712i	0.849690	−	0.527283i	$-0.176789\pi$
$599$	−0.778175	−	1.34784i	−0.0317954	−	0.0550712i	−0.881485	+	0.472212i	$0.843456\pi$
$600$	−2.32843	+	4.03295i	−0.0950576	+	0.164645i
$601$	1.20101			0.0489902			0.0244951	−	0.999700i	$-0.492202\pi$
$601$	1.20101			0.0489902			0.0244951	+	0.999700i	$0.492202\pi$
$602$	−17.0000	+	2.32640i	−0.692868	+	0.0948169i
$603$	1.82843			0.0744593
$604$	−2.03553	+	3.52565i	−0.0828247	+	0.143457i
$605$	−3.17157	−	5.49333i	−0.128943	−	0.223335i
$606$	−7.41421	−	12.8418i	−0.301182	−	0.521662i
$607$	−17.2635	+	29.9012i	−0.700702	+	1.21365i	0.267518	+	0.963553i	$0.413796\pi$
$607$	−17.2635	+	29.9012i	−0.700702	+	1.21365i	−0.968220	+	0.250099i	$0.919537\pi$
$608$	−2.17157			−0.0880689
$609$	1.82843	−	4.47871i	0.0740916	−	0.181487i
$610$	2.58579			0.104695
$611$	−0.500000	+	0.866025i	−0.0202278	+	0.0350356i
$612$	1.20711	+	2.09077i	0.0487944	+	0.0845144i
$613$	3.89949	+	6.75412i	0.157499	+	0.272796i	0.933966	−	0.357361i	$-0.116324\pi$
$613$	3.89949	+	6.75412i	0.157499	+	0.272796i	−0.776467	+	0.630158i	$0.782990\pi$
$614$	14.0563	−	24.3463i	0.567268	−	0.982537i
$615$	−5.79899			−0.233838
$616$	−0.414214	+	1.01461i	−0.0166891	+	0.0408799i
$617$	−24.1421			−0.971926			−0.485963	−	0.873979i	$-0.661531\pi$
$617$	−24.1421			−0.971926			−0.485963	+	0.873979i	$0.661531\pi$
$618$	−8.41421	+	14.5738i	−0.338469	+	0.586246i
$619$	−10.4142	−	18.0379i	−0.418583	−	0.725006i	0.577215	−	0.816593i	$-0.304140\pi$
$619$	−10.4142	−	18.0379i	−0.418583	−	0.725006i	−0.995797	+	0.0915862i	$0.970806\pi$
$620$	−2.48528	−	4.30463i	−0.0998113	−	0.172878i
$621$	0.707107	−	1.22474i	0.0283752	−	0.0491473i
$622$	−8.10051			−0.324801
$623$	−6.77817	+	0.927572i	−0.271562	+	0.0371624i
$624$	−1.00000			−0.0400320
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$	−1.75736	−	3.04384i	−0.0702382	−	0.121656i
$627$	0.449747	+	0.778985i	0.0179612	+	0.0311097i
$628$	−4.86396	+	8.42463i	−0.194093	+	0.336179i
$629$	−3.41421			−0.136134
$630$	−0.949747	−	1.22474i	−0.0378388	−	0.0487950i
$631$	32.6274			1.29888			0.649438	−	0.760414i	$-0.275004\pi$
$631$	32.6274			1.29888			0.649438	+	0.760414i	$0.275004\pi$
$632$	5.82843	−	10.0951i	0.231842	−	0.401563i
$633$	−6.46447	−	11.1968i	−0.256939	−	0.445032i
$634$	−14.8995	−	25.8067i	−0.591735	−	1.02491i
$635$	−2.31371	+	4.00746i	−0.0918167	+	0.159031i
$636$	−9.48528			−0.376116
$637$	−1.74264	+	6.77962i	−0.0690459	+	0.268618i
$638$	0.757359			0.0299841
$639$	2.50000	−	4.33013i	0.0988985	−	0.171297i
$640$	0.292893	+	0.507306i	0.0115776	+	0.0200530i
$641$	−15.8995	−	27.5387i	−0.627992	−	1.08771i	−0.987954	−	0.154748i	$-0.950544\pi$
$641$	−15.8995	−	27.5387i	−0.627992	−	1.08771i	0.359962	−	0.932967i	$-0.382790\pi$
$642$	−9.65685	+	16.7262i	−0.381126	+	0.660129i
$643$	−2.51472			−0.0991708			−0.0495854	−	0.998770i	$-0.515790\pi$
$643$	−2.51472			−0.0991708			−0.0495854	+	0.998770i	$0.515790\pi$
$644$	2.29289	+	2.95680i	0.0903527	+	0.116514i
$645$	3.79899			0.149585
$646$	−2.62132	+	4.54026i	−0.103134	+	0.178634i
$647$	4.51472	+	7.81972i	0.177492	+	0.307425i	0.941021	−	0.338349i	$-0.109868\pi$
$647$	4.51472	+	7.81972i	0.177492	+	0.307425i	−0.763529	+	0.645774i	$0.776535\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	0.428932	−	0.742932i	0.0168371	−	0.0291626i
$650$	−4.65685			−0.182657
$651$	−22.2426	+	3.04384i	−0.871758	+	0.119297i
$652$	−18.6569			−0.730659
$653$	−11.0711	+	19.1757i	−0.433244	+	0.750401i	−0.997151	−	0.0754376i	$-0.975965\pi$
$653$	−11.0711	+	19.1757i	−0.433244	+	0.750401i	0.563906	+	0.825839i	$0.309298\pi$
$654$	−4.82843	−	8.36308i	−0.188806	−	0.327022i
$655$	−2.79899	−	4.84799i	−0.109366	−	0.189427i
$656$	4.94975	−	8.57321i	0.193255	−	0.334728i
$657$	1.41421			0.0551737
$658$	1.00000	−	2.44949i	0.0389841	−	0.0954911i
$659$	10.5858			0.412364			0.206182	−	0.978514i	$-0.433896\pi$
$659$	10.5858			0.412364			0.206182	+	0.978514i	$0.433896\pi$
$660$	0.121320	−	0.210133i	0.00472239	−	0.00817942i
$661$	−20.1213	−	34.8511i	−0.782629	−	1.35555i	−0.930405	−	0.366532i	$-0.880545\pi$
$661$	−20.1213	−	34.8511i	−0.782629	−	1.35555i	0.147777	−	0.989021i	$-0.452788\pi$
$662$	11.2426	+	19.4728i	0.436958	+	0.756833i
$663$	−1.20711	+	2.09077i	−0.0468801	+	0.0811988i
$664$	7.65685			0.297144
$665$	1.27208	−	3.11594i	0.0493291	−	0.120831i
$666$	1.41421			0.0547997
$667$	1.29289	−	2.23936i	0.0500610	−	0.0867082i
$668$	0.328427	+	0.568852i	0.0127072	+	0.0220096i
$669$	−3.96447	−	6.86666i	−0.153275	−	0.265480i
$670$	0.535534	−	0.927572i	0.0206895	−	0.0358352i
$671$	1.82843			0.0705856
$672$	2.62132	−	0.358719i	0.101120	−	0.0138379i
$673$	42.1421			1.62446			0.812230	−	0.583337i	$-0.198253\pi$
$673$	42.1421			1.62446			0.812230	+	0.583337i	$0.198253\pi$
$674$	10.1569	−	17.5922i	0.391227	−	0.677626i
$675$	−2.32843	−	4.03295i	−0.0896212	−	0.155228i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	−0.973392	−	0.229147i	$-0.926406\pi$
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	0.685143	+	0.728408i	$0.259740\pi$
$678$	−4.89949			−0.188164
$679$	−1.50610	−	1.94218i	−0.0577987	−	0.0745342i
$680$	1.41421			0.0542326
$681$	−10.5858	+	18.3351i	−0.405648	+	0.702603i
$682$	−1.75736	−	3.04384i	−0.0672928	−	0.116554i
$683$	7.07107	+	12.2474i	0.270567	+	0.468636i	0.969007	−	0.247033i	$-0.0794555\pi$
$683$	7.07107	+	12.2474i	0.270567	+	0.468636i	−0.698440	+	0.715668i	$0.746122\pi$
$684$	1.08579	−	1.88064i	0.0415161	−	0.0719080i
$685$	−6.48528			−0.247790
$686$	2.13604	−	18.3967i	0.0815543	−	0.702388i
$687$	−26.4853			−1.01048
$688$	−3.24264	+	5.61642i	−0.123625	+	0.214124i
$689$	−4.74264	−	8.21449i	−0.180680	−	0.312947i
$690$	−0.414214	−	0.717439i	−0.0157688	−	0.0273124i
$691$	10.3284	−	17.8894i	0.392912	−	0.680543i	−0.599920	−	0.800060i	$-0.704801\pi$
$691$	10.3284	−	17.8894i	0.392912	−	0.680543i	0.992832	+	0.119516i	$0.0381344\pi$
$692$	5.48528			0.208519
$693$	−0.671573	−	0.866025i	−0.0255109	−	0.0328976i
$694$	−8.72792			−0.331307
$695$	−3.82843	+	6.63103i	−0.145221	+	0.251529i
$696$	−0.914214	−	1.58346i	−0.0346532	−	0.0600211i
$697$	−11.9497	−	20.6976i	−0.452629	−	0.783976i
$698$	3.36396	−	5.82655i	0.127328	−	0.220538i
$699$	17.7279			0.670532
$700$	12.2071	−	1.67050i	0.461385	−	0.0631391i
$701$	−29.1716			−1.10180			−0.550898	−	0.834573i	$-0.685715\pi$
$701$	−29.1716			−1.10180			−0.550898	+	0.834573i	$0.685715\pi$
$702$	0.500000	−	0.866025i	0.0188713	−	0.0326860i
$703$	1.53553	+	2.65962i	0.0579138	+	0.100310i
$704$	0.207107	+	0.358719i	0.00780563	+	0.0135197i
$705$	−0.292893	+	0.507306i	−0.0110310	+	0.0191062i
$706$	12.6274			0.475239
$707$	−14.8284	+	36.3221i	−0.557680	+	1.36603i
$708$	−2.07107			−0.0778355
$709$	18.4350	−	31.9304i	0.692342	−	1.19917i	−0.278726	−	0.960371i	$-0.589912\pi$
$709$	18.4350	−	31.9304i	0.692342	−	1.19917i	0.971069	−	0.238801i	$-0.0767544\pi$
$710$	−1.46447	−	2.53653i	−0.0549604	−	0.0951943i
$711$	5.82843	+	10.0951i	0.218583	+	0.378597i
$712$	−1.29289	+	2.23936i	−0.0484532	+	0.0839234i
$713$	−12.0000			−0.449404
$714$	2.41421	−	5.91359i	0.0903497	−	0.221311i
$715$	0.242641			0.00907425
$716$	−9.82843	+	17.0233i	−0.367306	+	0.636192i
$717$	2.25736	+	3.90986i	0.0843026	+	0.146016i
$718$	0.414214	+	0.717439i	0.0154583	+	0.0267746i
$719$	−4.65685	+	8.06591i	−0.173671	+	0.300808i	−0.939701	−	0.341998i	$-0.888896\pi$
$719$	−4.65685	+	8.06591i	−0.173671	+	0.300808i	0.766029	+	0.642806i	$0.222230\pi$
$720$	−0.585786			−0.0218310
$721$	44.1127	−	6.03668i	1.64284	−	0.224818i
$722$	−14.2843			−0.531606
$723$	−1.07107	+	1.85514i	−0.0398334	+	0.0689935i
$724$	−1.44975	−	2.51104i	−0.0538794	−	0.0933219i
$725$	−4.25736	−	7.37396i	−0.158114	−	0.273862i
$726$	−5.41421	+	9.37769i	−0.200940	+	0.348039i
$727$	−50.4264			−1.87021			−0.935106	−	0.354368i	$-0.884696\pi$
$727$	−50.4264			−1.87021			−0.935106	+	0.354368i	$0.884696\pi$
$728$	1.62132	+	2.09077i	0.0600901	+	0.0774891i
$729$	1.00000			0.0370370
$730$	0.414214	−	0.717439i	0.0153307	−	0.0265536i
$731$	7.82843	+	13.5592i	0.289545	+	0.501506i
$732$	−2.20711	−	3.82282i	−0.0815770	−	0.141296i
$733$	14.2929	−	24.7560i	0.527920	−	0.914384i	−0.471550	−	0.881839i	$-0.656305\pi$
$733$	14.2929	−	24.7560i	0.527920	−	0.914384i	0.999470	−	0.0325451i	$-0.0103613\pi$
$734$	12.6274			0.466086
$735$	−1.02082	+	3.97141i	−0.0376533	+	0.146488i
$736$	1.41421			0.0521286
$737$	0.378680	−	0.655892i	0.0139488	−	0.0241601i
$738$	4.94975	+	8.57321i	0.182203	+	0.315584i
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	0.998146	+	0.0608653i	$0.0193860\pi$
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	−0.446362	+	0.894852i	$0.647281\pi$
$740$	0.414214	−	0.717439i	0.0152268	−	0.0263736i
$741$	2.17157			0.0797747
$742$	15.3787	+	19.8315i	0.564569	+	0.728039i
$743$	12.1716			0.446532			0.223266	−	0.974758i	$-0.428328\pi$
$743$	12.1716			0.446532			0.223266	+	0.974758i	$0.428328\pi$
$744$	−4.24264	+	7.34847i	−0.155543	+	0.269408i
$745$	−1.44365	−	2.50048i	−0.0528913	−	0.0916104i
$746$	2.79289	+	4.83743i	0.102255	+	0.177111i
$747$	−3.82843	+	6.63103i	−0.140075	+	0.242617i
$748$	1.00000			0.0365636
$749$	50.6274	−	6.92820i	1.84989	−	0.253151i
$750$	−5.65685			−0.206559
$751$	9.65685	−	16.7262i	0.352384	−	0.610346i	−0.634283	−	0.773101i	$-0.718705\pi$
$751$	9.65685	−	16.7262i	0.352384	−	0.610346i	0.986667	+	0.162755i	$0.0520379\pi$
$752$	−0.500000	−	0.866025i	−0.0182331	−	0.0315807i
$753$	12.4142	+	21.5020i	0.452399	+	0.783578i
$754$	0.914214	−	1.58346i	0.0332937	−	0.0576664i
$755$	−2.38478			−0.0867909
$756$	−1.00000	+	2.44949i	−0.0363696	+	0.0890871i
$757$	−30.7574			−1.11790			−0.558948	−	0.829203i	$-0.688795\pi$
$757$	−30.7574			−1.11790			−0.558948	+	0.829203i	$0.688795\pi$
$758$	−9.31371	+	16.1318i	−0.338289	+	0.585934i
$759$	−0.292893	−	0.507306i	−0.0106314	−	0.0184140i
$760$	−0.636039	−	1.10165i	−0.0230716	−	0.0399611i
$761$	−21.5563	+	37.3367i	−0.781417	+	1.35345i	0.149699	+	0.988732i	$0.452169\pi$
$761$	−21.5563	+	37.3367i	−0.781417	+	1.35345i	−0.931116	+	0.364722i	$0.881164\pi$
$762$	7.89949			0.286169
$763$	−9.65685	+	23.6544i	−0.349602	+	0.856346i
$764$	−10.3431			−0.374202
$765$	−0.707107	+	1.22474i	−0.0255655	+	0.0442807i
$766$	−5.58579	−	9.67487i	−0.201823	−	0.349567i
$767$	−1.03553	−	1.79360i	−0.0373910	−	0.0647630i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	9.89949			0.356985			0.178492	−	0.983941i	$-0.442878\pi$
$769$	9.89949			0.356985			0.178492	+	0.983941i	$0.442878\pi$
$770$	−0.636039	+	0.0870399i	−0.0229213	+	0.00313670i
$771$	−26.4853			−0.953844
$772$	1.46447	−	2.53653i	0.0527073	−	0.0912917i
$773$	−9.48528	−	16.4290i	−0.341162	−	0.590910i	0.643487	−	0.765457i	$-0.277487\pi$
$773$	−9.48528	−	16.4290i	−0.341162	−	0.590910i	−0.984649	+	0.174547i	$0.944154\pi$
$774$	−3.24264	−	5.61642i	−0.116554	−	0.201878i
$775$	−19.7574	+	34.2208i	−0.709705	+	1.22925i
$776$	−0.928932			−0.0333467
$777$	−2.29289	−	2.95680i	−0.0822571	−	0.106074i
$778$	−4.51472			−0.161861
$779$	−10.7487	+	18.6174i	−0.385113	+	0.667036i
$780$	−0.292893	−	0.507306i	−0.0104873	−	0.0181645i
$781$	−1.03553	−	1.79360i	−0.0370543	−	0.0641800i
$782$	1.70711	−	2.95680i	0.0610460	−	0.105735i
$783$	1.82843			0.0653427
$784$	−5.00000	−	4.89898i	−0.178571	−	0.174964i
$785$	−5.69848			−0.203388
$786$	−4.77817	+	8.27604i	−0.170432	+	0.295197i
$787$	13.1569	+	22.7883i	0.468991	+	0.812317i	0.999372	−	0.0354431i	$-0.0112843\pi$
$787$	13.1569	+	22.7883i	0.468991	+	0.812317i	−0.530380	+	0.847760i	$0.677951\pi$
$788$	7.77817	+	13.4722i	0.277086	+	0.479927i
$789$	10.2929	−	17.8278i	0.366437	−	0.634687i
$790$	6.82843			0.242945
$791$	7.94365	+	10.2437i	0.282444	+	0.364225i
$792$	−0.414214			−0.0147184
$793$	2.20711	−	3.82282i	0.0783767	−	0.135752i
$794$	4.77817	+	8.27604i	0.169571	+	0.293706i
$795$	−2.77817	−	4.81194i	−0.0985317	−	0.170662i
$796$	−1.36396	+	2.36245i	−0.0483443	+	0.0837348i
$797$	34.3431			1.21650			0.608248	−	0.793747i	$-0.291872\pi$
$797$	34.3431			1.21650			0.608248	+	0.793747i	$0.291872\pi$
$798$	−5.69239	+	0.778985i	−0.201508	+	0.0275758i
$799$	−2.41421			−0.0854087
$800$	2.32843	−	4.03295i	0.0823223	−	0.142586i
$801$	−1.29289	−	2.23936i	−0.0456821	−	0.0791238i
$802$	−9.94975	−	17.2335i	−0.351338	−	0.608535i
$803$	0.292893	−	0.507306i	0.0103360	−	0.0179024i
$804$	−1.82843			−0.0644837
$805$	−0.828427	+	2.02922i	−0.0291982	+	0.0715207i
$806$	−8.48528			−0.298881
$807$	−4.57107	+	7.91732i	−0.160909	+	0.278703i
$808$	7.41421	+	12.8418i	0.260831	+	0.451773i
$809$	8.79289	+	15.2297i	0.309142	+	0.535449i	0.978175	−	0.207783i	$-0.0666249\pi$
$809$	8.79289	+	15.2297i	0.309142	+	0.535449i	−0.669033	+	0.743233i	$0.733292\pi$
$810$	0.292893	−	0.507306i	0.0102912	−	0.0178249i
$811$	55.4558			1.94732			0.973659	−	0.228009i	$-0.0732216\pi$
$811$	55.4558			1.94732			0.973659	+	0.228009i	$0.0732216\pi$
$812$	−1.82843	+	4.47871i	−0.0641652	+	0.157172i
$813$	−26.2132			−0.919337
$814$	0.292893	−	0.507306i	0.0102659	−	0.0177811i
$815$	−5.46447	−	9.46473i	−0.191412	−	0.331535i
$816$	−1.20711	−	2.09077i	−0.0422572	−	0.0731916i
$817$	7.04163	−	12.1965i	0.246355	−	0.426700i
$818$	32.5858			1.13934
$819$	−2.62132	+	0.358719i	−0.0915963	+	0.0125347i
$820$	5.79899			0.202510
$821$	−23.9497	+	41.4822i	−0.835852	+	1.44774i	0.0574829	+	0.998346i	$0.481693\pi$
$821$	−23.9497	+	41.4822i	−0.835852	+	1.44774i	−0.893335	+	0.449392i	$0.851641\pi$
$822$	5.53553	+	9.58783i	0.193074	+	0.334414i
$823$	21.9203	+	37.9671i	0.764094	+	1.32345i	0.940724	+	0.339172i	$0.110147\pi$
$823$	21.9203	+	37.9671i	0.764094	+	1.32345i	−0.176630	+	0.984277i	$0.556520\pi$
$824$	8.41421	−	14.5738i	0.293123	−	0.507704i
$825$	−1.92893			−0.0671568
$826$	3.35786	+	4.33013i	0.116835	+	0.150664i
$827$	46.3553			1.61193			0.805967	−	0.591961i	$-0.201646\pi$
$827$	46.3553			1.61193			0.805967	+	0.591961i	$0.201646\pi$
$828$	−0.707107	+	1.22474i	−0.0245737	+	0.0425628i
$829$	13.3492	+	23.1216i	0.463638	+	0.803045i	0.999139	−	0.0414897i	$-0.0132104\pi$
$829$	13.3492	+	23.1216i	0.463638	+	0.803045i	−0.535501	+	0.844535i	$0.679877\pi$
$830$	2.24264	+	3.88437i	0.0778432	+	0.134828i
$831$	9.03553	−	15.6500i	0.313439	−	0.542893i
$832$	1.00000			0.0346688
$833$	−16.2782	+	4.54026i	−0.564005	+	0.157311i
$834$	13.0711			0.452614
$835$	−0.192388	+	0.333226i	−0.00665787	+	0.0115318i
$836$	−0.449747	−	0.778985i	−0.0155548	−	0.0269418i
$837$	−4.24264	−	7.34847i	−0.146647	−	0.254000i
$838$	−13.7279	+	23.7775i	−0.474223	+	0.821379i
$839$	−31.8284			−1.09884			−0.549420	−	0.835547i	$-0.685151\pi$
$839$	−31.8284			−1.09884			−0.549420	+	0.835547i	$0.685151\pi$
$840$	0.949747	+	1.22474i	0.0327694	+	0.0422577i
$841$	−25.6569			−0.884719
$842$	−0.535534	+	0.927572i	−0.0184557	+	0.0319662i
$843$	0.343146	+	0.594346i	0.0118186	+	0.0204704i
$844$	6.46447	+	11.1968i	0.222516	+	0.385409i
$845$	0.292893	−	0.507306i	0.0100758	−	0.0174519i
$846$	1.00000			0.0343807
$847$	28.3848	−	3.88437i	0.975312	−	0.133468i
$848$	9.48528			0.325726
$849$	−7.87868	+	13.6463i	−0.270396	+	0.468339i
$850$	−5.62132	−	9.73641i	−0.192810	−	0.333956i
$851$	−1.00000	−	1.73205i	−0.0342796	−	0.0593739i
$852$	−2.50000	+	4.33013i	−0.0856486	+	0.148348i
$853$	6.72792			0.230360			0.115180	−	0.993345i	$-0.463256\pi$
$853$	6.72792			0.230360			0.115180	+	0.993345i	$0.463256\pi$
$854$	−4.41421	+	10.8126i	−0.151051	+	0.369999i
$855$	1.27208			0.0435041
$856$	9.65685	−	16.7262i	0.330064	−	0.571688i
$857$	−10.2782	−	17.8023i	−0.351096	−	0.608116i	0.635346	−	0.772228i	$-0.280858\pi$
$857$	−10.2782	−	17.8023i	−0.351096	−	0.608116i	−0.986442	+	0.164112i	$0.947524\pi$
$858$	−0.207107	−	0.358719i	−0.00707051	−	0.0122465i
$859$	5.89949	−	10.2182i	0.201288	−	0.348641i	−0.747656	−	0.664087i	$-0.768821\pi$
$859$	5.89949	−	10.2182i	0.201288	−	0.348641i	0.948944	+	0.315445i	$0.102154\pi$
$860$	−3.79899			−0.129544
$861$	9.89949	−	24.2487i	0.337374	−	0.826394i
$862$	30.4853			1.03833
$863$	−19.6569	+	34.0467i	−0.669127	+	1.15896i	0.309021	+	0.951055i	$0.399998\pi$
$863$	−19.6569	+	34.0467i	−0.669127	+	1.15896i	−0.978149	+	0.207907i	$0.933335\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	1.60660	+	2.78272i	0.0546261	+	0.0946152i
$866$	−14.9853	+	25.9553i	−0.509221	+	0.881996i
$867$	11.1716			0.379407
$868$	22.2426	−	3.04384i	0.754964	−	0.103315i
$869$	4.82843			0.163793
$870$	0.535534	−	0.927572i	0.0181563	−	0.0314476i
$871$	−0.914214	−	1.58346i	−0.0309769	−	0.0536536i
$872$	4.82843	+	8.36308i	0.163511	+	0.283210i
$873$	0.464466	−	0.804479i	0.0157198	−	0.0272275i
$874$	−3.07107			−0.103880
$875$	9.17157	+	11.8272i	0.310056	+	0.399832i
$876$	−1.41421			−0.0477818
$877$	20.0208	−	34.6771i	0.676055	−	1.17096i	−0.300104	−	0.953906i	$-0.597022\pi$
$877$	20.0208	−	34.6771i	0.676055	−	1.17096i	0.976159	−	0.217055i	$-0.0696451\pi$
$878$	−8.29289	−	14.3637i	−0.279872	−	0.484752i
$879$	−4.94975	−	8.57321i	−0.166951	−	0.289167i
$880$	−0.121320	+	0.210133i	−0.00408971	+	0.00708358i
$881$	18.4853			0.622785			0.311392	−	0.950281i	$-0.399205\pi$
$881$	18.4853			0.622785			0.311392	+	0.950281i	$0.399205\pi$
$882$	6.74264	−	1.88064i	0.227037	−	0.0633244i
$883$	−9.75736			−0.328361			−0.164181	−	0.986430i	$-0.552498\pi$
$883$	−9.75736			−0.328361			−0.164181	+	0.986430i	$0.552498\pi$
$884$	1.20711	−	2.09077i	0.0405994	−	0.0703202i
$885$	−0.606602	−	1.05066i	−0.0203907	−	0.0353177i
$886$	16.8492	+	29.1837i	0.566061	+	0.980447i
$887$	−24.4558	+	42.3588i	−0.821147	+	1.42227i	0.0836819	+	0.996493i	$0.473332\pi$
$887$	−24.4558	+	42.3588i	−0.821147	+	1.42227i	−0.904829	+	0.425776i	$0.860001\pi$
$888$	−1.41421			−0.0474579
$889$	−12.8076	−	16.5160i	−0.429554	−	0.553930i
$890$	−1.51472			−0.0507735
$891$	0.207107	−	0.358719i	0.00693834	−	0.0120176i
$892$	3.96447	+	6.86666i	0.132740	+	0.229913i
$893$	1.08579	+	1.88064i	0.0363345	+	0.0629331i
$894$	−2.46447	+	4.26858i	−0.0824241	+	0.142763i
$895$	−11.5147			−0.384895
$896$	−2.62132	+	0.358719i	−0.0875722	+	0.0119840i
$897$	−1.41421			−0.0472192
$898$	−12.4853	+	21.6251i	−0.416639	+	0.721640i
$899$	−7.75736	−	13.4361i	−0.258722	−	0.448120i
$900$	2.32843	+	4.03295i	0.0776142	+	0.134432i
$901$	11.4497	−	19.8315i	0.381446	−	0.660685i
$902$	4.10051			0.136532
$903$	−6.48528	+	15.8856i	−0.215817	+	0.528641i
$904$	4.89949			0.162955
$905$	0.849242	−	1.47093i	0.0282298	−	0.0488954i
$906$	2.03553	+	3.52565i	0.0676261	+	0.117132i
$907$	−27.1924	−	47.0986i	−0.902908	−	1.56388i	−0.823700	−	0.567025i	$-0.808094\pi$
$907$	−27.1924	−	47.0986i	−0.902908	−	1.56388i	−0.0792080	−	0.996858i	$-0.525239\pi$
$908$	10.5858	−	18.3351i	0.351302	−	0.608472i
$909$	−14.8284			−0.491828
$910$	−0.585786	+	1.43488i	−0.0194186	+	0.0475657i
$911$	−4.34315			−0.143895			−0.0719474	−	0.997408i	$-0.522921\pi$
$911$	−4.34315			−0.143895			−0.0719474	+	0.997408i	$0.522921\pi$
$912$	−1.08579	+	1.88064i	−0.0359540	+	0.0622741i
$913$	1.58579	+	2.74666i	0.0524819	+	0.0909013i
$914$	1.53553	+	2.65962i	0.0507909	+	0.0879725i
$915$	1.29289	−	2.23936i	0.0427417	−	0.0740309i
$916$	26.4853			0.875098
$917$	25.0503	−	3.42805i	0.827232	−	0.113204i
$918$	2.41421			0.0796809
$919$	−0.899495	+	1.55797i	−0.0296716	+	0.0513927i	−0.880480	−	0.474083i	$-0.842779\pi$
$919$	−0.899495	+	1.55797i	−0.0296716	+	0.0513927i	0.850808	+	0.525476i	$0.176113\pi$
$920$	0.414214	+	0.717439i	0.0136562	+	0.0236533i
$921$	−14.0563	−	24.3463i	−0.463172	−	0.802238i
$922$	2.24264	−	3.88437i	0.0738574	−	0.127925i
$923$	−5.00000			−0.164577
$924$	0.671573	+	0.866025i	0.0220931	+	0.0284901i
$925$	−6.58579			−0.216539
$926$	10.4853	−	18.1610i	0.344568	−	0.596809i
$927$	8.41421	+	14.5738i	0.276359	+	0.478668i
$928$	0.914214	+	1.58346i	0.0300105	+	0.0519798i
$929$	−17.3431	+	30.0392i	−0.569010	+	0.985554i	0.427654	+	0.903942i	$0.359340\pi$
$929$	−17.3431	+	30.0392i	−0.569010	+	0.985554i	−0.996664	+	0.0816120i	$0.973993\pi$
$930$	−4.97056			−0.162991
$931$	10.8579	+	10.6385i	0.355852	+	0.348662i
$932$	−17.7279			−0.580697
$933$	−4.05025	+	7.01524i	−0.132599	+	0.229669i
$934$	5.70711	+	9.88500i	0.186742	+	0.323447i
$935$	0.292893	+	0.507306i	0.00957863	+	0.0165907i
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	42.6569			1.39354			0.696769	−	0.717295i	$-0.254620\pi$
$937$	42.6569			1.39354			0.696769	+	0.717295i	$0.254620\pi$
$938$	2.96447	+	3.82282i	0.0967932	+	0.124820i
$939$	−3.51472			−0.114699
$940$	0.292893	−	0.507306i	0.00955312	−	0.0165465i
$941$	6.48528	+	11.2328i	0.211414	+	0.366180i	0.952157	−	0.305608i	$-0.0988598\pi$
$941$	6.48528	+	11.2328i	0.211414	+	0.366180i	−0.740743	+	0.671788i	$0.765526\pi$
$942$	4.86396	+	8.42463i	0.158476	+	0.274489i
$943$	7.00000	−	12.1244i	0.227951	−	0.394823i
$944$	2.07107			0.0674075
$945$	−1.53553	+	0.210133i	−0.0499509	+	0.00683563i
$946$	−2.68629			−0.0873389
$947$	−4.20711	+	7.28692i	−0.136713	+	0.236793i	−0.926250	−	0.376909i	$-0.876987\pi$
$947$	−4.20711	+	7.28692i	−0.136713	+	0.236793i	0.789538	+	0.613702i	$0.210320\pi$
$948$	−5.82843	−	10.0951i	−0.189299	−	0.327875i
$949$	−0.707107	−	1.22474i	−0.0229537	−	0.0397569i
$950$	−5.05635	+	8.75785i	−0.164050	+	0.284142i
$951$	−29.7990			−0.966298
$952$	−2.41421	+	5.91359i	−0.0782451	+	0.191661i
$953$	−41.5858			−1.34710			−0.673548	−	0.739144i	$-0.735230\pi$
$953$	−41.5858			−1.34710			−0.673548	+	0.739144i	$0.735230\pi$
$954$	−4.74264	+	8.21449i	−0.153549	+	0.265954i
$955$	−3.02944	−	5.24714i	−0.0980303	−	0.169793i
$956$	−2.25736	−	3.90986i	−0.0730082	−	0.126454i
$957$	0.378680	−	0.655892i	0.0122410	−	0.0212020i
$958$	−32.1127			−1.03751
$959$	11.0711	−	27.1185i	0.357503	−	0.875701i
$960$	0.585786			0.0189062
$961$	−20.5000	+	35.5070i	−0.661290	+	1.14539i
$962$	−0.707107	−	1.22474i	−0.0227980	−	0.0394874i
$963$	9.65685	+	16.7262i	0.311188	+	0.538993i
$964$	1.07107	−	1.85514i	0.0344968	−	0.0597502i
$965$	1.71573			0.0552313
$966$	3.70711	−	0.507306i	0.119274	−	0.0163223i
$967$	−13.5858			−0.436889			−0.218445	−	0.975849i	$-0.570098\pi$
$967$	−13.5858			−0.436889			−0.218445	+	0.975849i	$0.570098\pi$
$968$	5.41421	−	9.37769i	0.174019	−	0.301410i
$969$	2.62132	+	4.54026i	0.0842089	+	0.145854i
$970$	−0.272078	−	0.471253i	−0.00873590	−	0.0151310i
$971$	16.2635	−	28.1691i	0.521919	−	0.903990i	−0.477756	−	0.878493i	$-0.658550\pi$
$971$	16.2635	−	28.1691i	0.521919	−	0.903990i	0.999675	−	0.0254978i	$-0.00811707\pi$
$972$	−1.00000			−0.0320750
$973$	−21.1924	−	27.3286i	−0.679397	−	0.876115i
$974$	16.2132			0.519505
$975$	−2.32843	+	4.03295i	−0.0745693	+	0.129158i
$976$	2.20711	+	3.82282i	0.0706478	+	0.122366i
$977$	−21.5858	−	37.3877i	−0.690590	−	1.19614i	−0.971645	−	0.236446i	$-0.924017\pi$
$977$	−21.5858	−	37.3877i	−0.690590	−	1.19614i	0.281054	−	0.959692i	$-0.409316\pi$
$978$	−9.32843	+	16.1573i	−0.298290	+	0.516654i
$979$	−1.07107			−0.0342315
$980$	1.02082	−	3.97141i	0.0326087	−	0.126862i
$981$	−9.65685			−0.308320
$982$	−11.8284	+	20.4874i	−0.377460	+	0.653780i
$983$	14.7426	+	25.5350i	0.470217	+	0.814440i	0.999420	−	0.0340553i	$-0.0108422\pi$
$983$	14.7426	+	25.5350i	0.470217	+	0.814440i	−0.529203	+	0.848495i	$0.677509\pi$
$984$	−4.94975	−	8.57321i	−0.157792	−	0.273304i
$985$	−4.55635	+	7.89183i	−0.145177	+	0.251455i
$986$	4.41421			0.140577
$987$	−1.62132	−	2.09077i	−0.0516072	−	0.0665500i
$988$	−2.17157			−0.0690869
$989$	−4.58579	+	7.94282i	−0.145820	+	0.252567i
$990$	−0.121320	−	0.210133i	−0.00385581	−	0.00667847i
$991$	0.343146	+	0.594346i	0.0109004	+	0.0188800i	0.871424	−	0.490530i	$-0.163197\pi$
$991$	0.343146	+	0.594346i	0.0109004	+	0.0188800i	−0.860524	+	0.509410i	$0.829864\pi$
$992$	4.24264	−	7.34847i	0.134704	−	0.233314i
$993$	22.4853			0.713549
$994$	13.1066	−	1.79360i	0.415716	−	0.0568895i
$995$	−1.59798			−0.0506594
$996$	3.82843	−	6.63103i	0.121308	−	0.210112i
$997$	−26.2487	−	45.4641i	−0.831306	−	1.43986i	−0.897003	−	0.442024i	$-0.854260\pi$
$997$	−26.2487	−	45.4641i	−0.831306	−	1.43986i	0.0656972	−	0.997840i	$-0.479073\pi$
$998$	−1.82843	−	3.16693i	−0.0578778	−	0.100247i
$999$	0.707107	−	1.22474i	0.0223719	−	0.0387492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.i.79.1	✓	4
3.2	odd	2		1638.2.j.m.1171.2		4
7.2	even	3		3822.2.a.bn.1.2		2
7.4	even	3	inner	546.2.i.i.235.1	yes	4
7.5	odd	6		3822.2.a.bu.1.1		2
21.11	odd	6		1638.2.j.m.235.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.i.79.1	✓	4	1.1	even	1	trivial
546.2.i.i.235.1	yes	4	7.4	even	3	inner
1638.2.j.m.235.2		4	21.11	odd	6
1638.2.j.m.1171.2		4	3.2	odd	2
3822.2.a.bn.1.2		2	7.2	even	3
3822.2.a.bu.1.1		2	7.5	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.292893 - 0.507306i) q^{5} -1.00000 q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.292893 + 0.507306i) q^{10} +(0.207107 + 0.358719i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-2.62132 + 0.358719i) q^{14} +0.585786 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.20711 + 2.09077i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.08579 - 1.88064i) q^{19} -0.585786 q^{20} +(-1.00000 + 2.44949i) q^{21} -0.414214 q^{22} +(-0.707107 + 1.22474i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.32843 + 4.03295i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 - 2.44949i) q^{28} -1.82843 q^{29} +(-0.292893 + 0.507306i) q^{30} +(4.24264 + 7.34847i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.207107 + 0.358719i) q^{33} -2.41421 q^{34} +(1.53553 - 0.210133i) q^{35} +1.00000 q^{36} +(-0.707107 + 1.22474i) q^{37} +(1.08579 + 1.88064i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.292893 - 0.507306i) q^{40} -9.89949 q^{41} +(-1.62132 - 2.09077i) q^{42} +6.48528 q^{43} +(0.207107 - 0.358719i) q^{44} +(0.292893 + 0.507306i) q^{45} +(-0.707107 - 1.22474i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000 q^{48} +(-1.74264 + 6.77962i) q^{49} -4.65685 q^{50} +(-1.20711 + 2.09077i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-4.74264 - 8.21449i) q^{53} +(0.500000 - 0.866025i) q^{54} +0.242641 q^{55} +(1.62132 + 2.09077i) q^{56} +2.17157 q^{57} +(0.914214 - 1.58346i) q^{58} +(-1.03553 - 1.79360i) q^{59} +(-0.292893 - 0.507306i) q^{60} +(2.20711 - 3.82282i) q^{61} -8.48528 q^{62} +(-2.62132 + 0.358719i) q^{63} +1.00000 q^{64} +(0.292893 - 0.507306i) q^{65} +(-0.207107 - 0.358719i) q^{66} +(-0.914214 - 1.58346i) q^{67} +(1.20711 - 2.09077i) q^{68} -1.41421 q^{69} +(-0.585786 + 1.43488i) q^{70} -5.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(-0.707107 - 1.22474i) q^{74} +(-2.32843 + 4.03295i) q^{75} -2.17157 q^{76} +(-0.414214 + 1.01461i) q^{77} -1.00000 q^{78} +(5.82843 - 10.0951i) q^{79} +(0.292893 + 0.507306i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.94975 - 8.57321i) q^{82} +7.65685 q^{83} +(2.62132 - 0.358719i) q^{84} +1.41421 q^{85} +(-3.24264 + 5.61642i) q^{86} +(-0.914214 - 1.58346i) q^{87} +(0.207107 + 0.358719i) q^{88} +(-1.29289 + 2.23936i) q^{89} -0.585786 q^{90} +(1.62132 + 2.09077i) q^{91} +1.41421 q^{92} +(-4.24264 + 7.34847i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-0.636039 - 1.10165i) q^{95} +(0.500000 - 0.866025i) q^{96} -0.928932 q^{97} +(-5.00000 - 4.89898i) q^{98} -0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{17} - 2 q^{18} + 10 q^{19} - 8 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 8 * q^15 - 2 * q^16 + 2 * q^17 - 2 * q^18 + 10 * q^19 - 8 * q^20 - 4 * q^21 + 4 * q^22 + 2 * q^24 - 2 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^32 + 2 * q^33 - 4 * q^34 - 8 * q^35 + 4 * q^36 + 10 * q^38 + 2 * q^39 + 4 * q^40 + 2 * q^42 - 8 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^47 - 4 * q^48 + 10 * q^49 + 4 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 + 2 * q^54 - 16 * q^55 - 2 * q^56 + 20 * q^57 - 2 * q^58 + 10 * q^59 - 4 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + 4 * q^65 + 2 * q^66 + 2 * q^67 + 2 * q^68 - 8 * q^70 - 20 * q^71 - 2 * q^72 + 2 * q^75 - 20 * q^76 + 4 * q^77 - 4 * q^78 + 12 * q^79 + 4 * q^80 - 2 * q^81 + 8 * q^83 + 2 * q^84 + 4 * q^86 + 2 * q^87 - 2 * q^88 - 8 * q^89 - 8 * q^90 - 2 * q^91 - 2 * q^94 - 28 * q^95 + 2 * q^96 - 32 * q^97 - 20 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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