LMFDB - Embedded newform 546.2.l.j.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (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:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.2.l.j.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.27492 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.13746 - 3.70219i) q^{10} +(2.00000 + 3.46410i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(-2.13746 - 3.70219i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-3.27492 + 5.67232i) q^{19} +(-2.13746 + 3.70219i) q^{20} +1.00000 q^{21} +(2.00000 - 3.46410i) q^{22} +(2.63746 + 4.56821i) q^{23} +(-0.500000 - 0.866025i) q^{24} +13.2749 q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-4.13746 - 7.16629i) q^{29} +(-2.13746 + 3.70219i) q^{30} -1.27492 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +3.00000 q^{34} +(-2.13746 + 3.70219i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.137459 - 0.238085i) q^{37} +6.54983 q^{38} +(-2.50000 - 2.59808i) q^{39} +4.27492 q^{40} +(-4.13746 - 7.16629i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(5.91238 - 10.2405i) q^{43} -4.00000 q^{44} +(-2.13746 + 3.70219i) q^{45} +(2.63746 - 4.56821i) q^{46} -6.54983 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-6.63746 - 11.4964i) q^{50} +3.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} -3.54983 q^{53} +(-0.500000 - 0.866025i) q^{54} +(8.54983 + 14.8087i) q^{55} +(-0.500000 + 0.866025i) q^{56} +6.54983 q^{57} +(-4.13746 + 7.16629i) q^{58} +(5.91238 - 10.2405i) q^{59} +4.27492 q^{60} +(4.50000 - 7.79423i) q^{61} +(0.637459 + 1.10411i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(14.9622 - 3.70219i) q^{65} -4.00000 q^{66} +(1.36254 + 2.35999i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(2.63746 - 4.56821i) q^{69} +4.27492 q^{70} +(-2.63746 + 4.56821i) q^{71} +(-0.500000 + 0.866025i) q^{72} +5.72508 q^{73} +(-0.137459 + 0.238085i) q^{74} +(-6.63746 - 11.4964i) q^{75} +(-3.27492 - 5.67232i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -8.00000 q^{79} +(-2.13746 - 3.70219i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.13746 + 7.16629i) q^{82} -11.8248 q^{83} +(-0.500000 + 0.866025i) q^{84} +(-6.41238 + 11.1066i) q^{85} -11.8248 q^{86} +(-4.13746 + 7.16629i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-0.362541 - 0.627940i) q^{89} +4.27492 q^{90} +(-1.00000 + 3.46410i) q^{91} -5.27492 q^{92} +(0.637459 + 1.10411i) q^{93} +(3.27492 + 5.67232i) q^{94} +(-14.0000 + 24.2487i) q^{95} +1.00000 q^{96} +(0.274917 - 0.476171i) q^{97} +(-0.500000 + 0.866025i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - q^{10} + 8 q^{11} + 4 q^{12} + 14 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{18} + 2 q^{19} - q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - q^10 + 8 * q^11 + 4 * q^12 + 14 * q^13 + 4 * q^14 - q^15 - 2 * q^16 - 6 * q^17 + 4 * q^18 + 2 * q^19 - q^20 + 4 * q^21 + 8 * q^22 + 3 * q^23 - 2 * q^24 + 38 * q^25 - 10 * q^26 + 4 * q^27 - 2 * q^28 - 9 * q^29 - q^30 + 10 * q^31 - 2 * q^32 + 8 * q^33 + 12 * q^34 - q^35 - 2 * q^36 + 7 * q^37 - 4 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 - 2 * q^42 + q^43 - 16 * q^44 - q^45 + 3 * q^46 + 4 * q^47 - 2 * q^48 - 2 * q^49 - 19 * q^50 + 12 * q^51 - 4 * q^52 + 16 * q^53 - 2 * q^54 + 4 * q^55 - 2 * q^56 - 4 * q^57 - 9 * q^58 + q^59 + 2 * q^60 + 18 * q^61 - 5 * q^62 - 2 * q^63 + 4 * q^64 + 7 * q^65 - 16 * q^66 + 13 * q^67 - 6 * q^68 + 3 * q^69 + 2 * q^70 - 3 * q^71 - 2 * q^72 + 38 * q^73 + 7 * q^74 - 19 * q^75 + 2 * q^76 - 16 * q^77 - 4 * q^78 - 32 * q^79 - q^80 - 2 * q^81 - 9 * q^82 - 2 * q^83 - 2 * q^84 - 3 * q^85 - 2 * q^86 - 9 * q^87 + 8 * q^88 - 9 * q^89 + 2 * q^90 - 4 * q^91 - 6 * q^92 - 5 * q^93 - 2 * q^94 - 56 * q^95 + 4 * q^96 - 14 * q^97 - 2 * q^98 - 16 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	4.27492			1.91180			0.955901	−	0.293691i	$-0.0948835\pi$
$5$	4.27492			1.91180			0.955901	+	0.293691i	$0.0948835\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.13746	−	3.70219i	−0.675924	−	1.17073i
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	1.00000			0.288675
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	1.00000			0.267261
$15$	−2.13746	−	3.70219i	−0.551889	−	0.955901i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	1.00000			0.235702
$19$	−3.27492	+	5.67232i	−0.751318	+	1.30132i	0.195867	+	0.980631i	$0.437248\pi$
$19$	−3.27492	+	5.67232i	−0.751318	+	1.30132i	−0.947184	+	0.320690i	$0.896085\pi$
$20$	−2.13746	+	3.70219i	−0.477950	+	0.827834i
$21$	1.00000			0.218218
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	2.63746	+	4.56821i	0.549948	+	0.952538i	0.998277	+	0.0586697i	$0.0186859\pi$
$23$	2.63746	+	4.56821i	0.549948	+	0.952538i	−0.448329	+	0.893868i	$0.647981\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	13.2749			2.65498
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$	1.00000			0.192450
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	−4.13746	−	7.16629i	−0.768307	−	1.33075i	−0.938480	−	0.345332i	$-0.887766\pi$
$29$	−4.13746	−	7.16629i	−0.768307	−	1.33075i	0.170174	−	0.985414i	$-0.445567\pi$
$30$	−2.13746	+	3.70219i	−0.390245	+	0.675924i
$31$	−1.27492			−0.228982			−0.114491	−	0.993424i	$-0.536524\pi$
$31$	−1.27492			−0.228982			−0.114491	+	0.993424i	$0.536524\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	3.00000			0.514496
$35$	−2.13746	+	3.70219i	−0.361296	+	0.625784i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	0.854505	−	0.519443i	$-0.173860\pi$
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	−0.877103	+	0.480302i	$0.840527\pi$
$38$	6.54983			1.06252
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$	4.27492			0.675924
$41$	−4.13746	−	7.16629i	−0.646162	−	1.11919i	−0.984032	−	0.177993i	$-0.943040\pi$
$41$	−4.13746	−	7.16629i	−0.646162	−	1.11919i	0.337869	−	0.941193i	$-0.390294\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	5.91238	−	10.2405i	0.901629	−	1.56167i	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	5.91238	−	10.2405i	0.901629	−	1.56167i	0.825380	−	0.564578i	$-0.190961\pi$
$44$	−4.00000			−0.603023
$45$	−2.13746	+	3.70219i	−0.318634	+	0.551889i
$46$	2.63746	−	4.56821i	0.388872	−	0.673546i
$47$	−6.54983			−0.955392			−0.477696	−	0.878525i	$-0.658528\pi$
$47$	−6.54983			−0.955392			−0.477696	+	0.878525i	$0.658528\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−6.63746	−	11.4964i	−0.938678	−	1.62584i
$51$	3.00000			0.420084
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	−3.54983			−0.487607			−0.243804	−	0.969825i	$-0.578395\pi$
$53$	−3.54983			−0.487607			−0.243804	+	0.969825i	$0.578395\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	8.54983	+	14.8087i	1.15286	+	1.99681i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	6.54983			0.867547
$58$	−4.13746	+	7.16629i	−0.543275	+	0.940980i
$59$	5.91238	−	10.2405i	0.769726	−	1.33320i	−0.167986	−	0.985789i	$-0.553726\pi$
$59$	5.91238	−	10.2405i	0.769726	−	1.33320i	0.937712	−	0.347415i	$-0.112940\pi$
$60$	4.27492			0.551889
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$	0.637459	+	1.10411i	0.0809573	+	0.140222i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	14.9622	−	3.70219i	1.85583	−	0.459200i
$66$	−4.00000			−0.492366
$67$	1.36254	+	2.35999i	0.166461	+	0.288319i	0.937173	−	0.348865i	$-0.113433\pi$
$67$	1.36254	+	2.35999i	0.166461	+	0.288319i	−0.770712	+	0.637183i	$0.780099\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	2.63746	−	4.56821i	0.317513	−	0.549948i
$70$	4.27492			0.510950
$71$	−2.63746	+	4.56821i	−0.313009	+	0.542147i	−0.979012	−	0.203802i	$-0.934670\pi$
$71$	−2.63746	+	4.56821i	−0.313009	+	0.542147i	0.666003	+	0.745949i	$0.268004\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	5.72508			0.670070			0.335035	−	0.942206i	$-0.391252\pi$
$73$	5.72508			0.670070			0.335035	+	0.942206i	$0.391252\pi$
$74$	−0.137459	+	0.238085i	−0.0159792	+	0.0276769i
$75$	−6.63746	−	11.4964i	−0.766428	−	1.32749i
$76$	−3.27492	−	5.67232i	−0.375659	−	0.650660i
$77$	−4.00000			−0.455842
$78$	−1.00000	+	3.46410i	−0.113228	+	0.392232i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−2.13746	−	3.70219i	−0.238975	−	0.413917i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.13746	+	7.16629i	−0.456906	+	0.791384i
$83$	−11.8248			−1.29794			−0.648968	−	0.760816i	$-0.724799\pi$
$83$	−11.8248			−1.29794			−0.648968	+	0.760816i	$0.724799\pi$
$84$	−0.500000	+	0.866025i	−0.0545545	+	0.0944911i
$85$	−6.41238	+	11.1066i	−0.695520	+	1.20468i
$86$	−11.8248			−1.27510
$87$	−4.13746	+	7.16629i	−0.443582	+	0.768307i
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	−0.362541	−	0.627940i	−0.0384293	−	0.0665615i	0.846171	−	0.532911i	$-0.178902\pi$
$89$	−0.362541	−	0.627940i	−0.0384293	−	0.0665615i	−0.884600	+	0.466350i	$0.845569\pi$
$90$	4.27492			0.450616
$91$	−1.00000	+	3.46410i	−0.104828	+	0.363137i
$92$	−5.27492			−0.549948
$93$	0.637459	+	1.10411i	0.0661014	+	0.114491i
$94$	3.27492	+	5.67232i	0.337782	+	0.585055i
$95$	−14.0000	+	24.2487i	−1.43637	+	2.48787i
$96$	1.00000			0.102062
$97$	0.274917	−	0.476171i	0.0279136	−	0.0483478i	−0.851731	−	0.523979i	$-0.824447\pi$
$97$	0.274917	−	0.476171i	0.0279136	−	0.0483478i	0.879645	+	0.475631i	$0.157780\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	−4.00000			−0.402015
$100$	−6.63746	+	11.4964i	−0.663746	+	1.14964i
$101$	−0.862541	−	1.49397i	−0.0858261	−	0.148655i	0.819917	−	0.572483i	$-0.194020\pi$
$101$	−0.862541	−	1.49397i	−0.0858261	−	0.148655i	−0.905743	+	0.423828i	$0.860686\pi$
$102$	−1.50000	−	2.59808i	−0.148522	−	0.257248i
$103$	5.27492			0.519753			0.259877	−	0.965642i	$-0.416318\pi$
$103$	5.27492			0.519753			0.259877	+	0.965642i	$0.416318\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$	4.27492			0.417189
$106$	1.77492	+	3.07425i	0.172395	+	0.298597i
$107$	−1.27492	−	2.20822i	−0.123251	−	0.213477i	0.797797	−	0.602926i	$-0.205999\pi$
$107$	−1.27492	−	2.20822i	−0.123251	−	0.213477i	−0.921048	+	0.389449i	$0.872665\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−4.54983			−0.435795			−0.217898	−	0.975972i	$-0.569920\pi$
$109$	−4.54983			−0.435795			−0.217898	+	0.975972i	$0.569920\pi$
$110$	8.54983	−	14.8087i	0.815195	−	1.41196i
$111$	−0.137459	+	0.238085i	−0.0130470	+	0.0225981i
$112$	1.00000			0.0944911
$113$	−7.41238	+	12.8386i	−0.697298	+	1.20775i	0.272102	+	0.962268i	$0.412281\pi$
$113$	−7.41238	+	12.8386i	−0.697298	+	1.20775i	−0.969400	+	0.245487i	$0.921052\pi$
$114$	−3.27492	−	5.67232i	−0.306724	−	0.531262i
$115$	11.2749	+	19.5287i	1.05139	+	1.82106i
$116$	8.27492			0.768307
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	−11.8248			−1.08856
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$	−2.13746	−	3.70219i	−0.195122	−	0.337962i
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−9.00000			−0.814822
$123$	−4.13746	+	7.16629i	−0.373062	+	0.646162i
$124$	0.637459	−	1.10411i	0.0572455	−	0.0991521i
$125$	35.3746			3.16400
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−11.8248			−1.04111
$130$	−10.6873	−	11.1066i	−0.937338	−	0.974110i
$131$	−2.72508			−0.238092			−0.119046	−	0.992889i	$-0.537984\pi$
$131$	−2.72508			−0.238092			−0.119046	+	0.992889i	$0.537984\pi$
$132$	2.00000	+	3.46410i	0.174078	+	0.301511i
$133$	−3.27492	−	5.67232i	−0.283971	−	0.491853i
$134$	1.36254	−	2.35999i	0.117706	−	0.203872i
$135$	4.27492			0.367926
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−11.4124	+	19.7668i	−0.975025	+	1.68879i	−0.295173	+	0.955444i	$0.595377\pi$
$137$	−11.4124	+	19.7668i	−0.975025	+	1.68879i	−0.679852	+	0.733349i	$0.737956\pi$
$138$	−5.27492			−0.449031
$139$	4.54983	−	7.88054i	0.385912	−	0.668419i	−0.605983	−	0.795477i	$-0.707220\pi$
$139$	4.54983	−	7.88054i	0.385912	−	0.668419i	0.991895	+	0.127058i	$0.0405535\pi$
$140$	−2.13746	−	3.70219i	−0.180648	−	0.312892i
$141$	3.27492	+	5.67232i	0.275798	+	0.477696i
$142$	5.27492			0.442661
$143$	10.0000	+	10.3923i	0.836242	+	0.869048i
$144$	1.00000			0.0833333
$145$	−17.6873	−	30.6353i	−1.46885	−	2.54412i
$146$	−2.86254	−	4.95807i	−0.236906	−	0.410333i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$	0.274917			0.0225981
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$	−6.63746	+	11.4964i	−0.541946	+	0.938678i
$151$	13.0997			1.06604			0.533018	−	0.846104i	$-0.321058\pi$
$151$	13.0997			1.06604			0.533018	+	0.846104i	$0.321058\pi$
$152$	−3.27492	+	5.67232i	−0.265631	+	0.460086i
$153$	−1.50000	−	2.59808i	−0.121268	−	0.210042i
$154$	2.00000	+	3.46410i	0.161165	+	0.279145i
$155$	−5.45017			−0.437768
$156$	3.50000	−	0.866025i	0.280224	−	0.0693375i
$157$	−3.72508			−0.297294			−0.148647	−	0.988890i	$-0.547492\pi$
$157$	−3.72508			−0.297294			−0.148647	+	0.988890i	$0.547492\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$	1.77492	+	3.07425i	0.140760	+	0.243804i
$160$	−2.13746	+	3.70219i	−0.168981	+	0.292684i
$161$	−5.27492			−0.415722
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	6.63746	−	11.4964i	0.519886	−	0.900469i	−0.479847	−	0.877352i	$-0.659308\pi$
$163$	6.63746	−	11.4964i	0.519886	−	0.900469i	0.999733	−	0.0231165i	$-0.00735887\pi$
$164$	8.27492			0.646162
$165$	8.54983	−	14.8087i	0.665604	−	1.15286i
$166$	5.91238	+	10.2405i	0.458889	+	0.794820i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	1.00000			0.0771517
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	12.8248			0.983614
$171$	−3.27492	−	5.67232i	−0.250439	−	0.433773i
$172$	5.91238	+	10.2405i	0.450814	+	0.780833i
$173$	2.27492	−	3.94027i	0.172959	−	0.299573i	−0.766494	−	0.642251i	$-0.778001\pi$
$173$	2.27492	−	3.94027i	0.172959	−	0.299573i	0.939453	+	0.342678i	$0.111334\pi$
$174$	8.27492			0.627320
$175$	−6.63746	+	11.4964i	−0.501745	+	0.869047i
$176$	2.00000	−	3.46410i	0.150756	−	0.261116i
$177$	−11.8248			−0.888803
$178$	−0.362541	+	0.627940i	−0.0271736	+	0.0470661i
$179$	−0.725083	−	1.25588i	−0.0541952	−	0.0938689i	0.837655	−	0.546200i	$-0.183926\pi$
$179$	−0.725083	−	1.25588i	−0.0541952	−	0.0938689i	−0.891850	+	0.452331i	$0.850593\pi$
$180$	−2.13746	−	3.70219i	−0.159317	−	0.275945i
$181$	−16.8248			−1.25057			−0.625287	−	0.780395i	$-0.715018\pi$
$181$	−16.8248			−1.25057			−0.625287	+	0.780395i	$0.715018\pi$
$182$	3.50000	−	0.866025i	0.259437	−	0.0641941i
$183$	−9.00000			−0.665299
$184$	2.63746	+	4.56821i	0.194436	+	0.336773i
$185$	−0.587624	−	1.01779i	−0.0432030	−	0.0748298i
$186$	0.637459	−	1.10411i	0.0467407	−	0.0809573i
$187$	−12.0000			−0.877527
$188$	3.27492	−	5.67232i	0.238848	−	0.413697i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	28.0000			2.03133
$191$	−3.36254	+	5.82409i	−0.243305	+	0.421417i	−0.961654	−	0.274267i	$-0.911565\pi$
$191$	−3.36254	+	5.82409i	−0.243305	+	0.421417i	0.718349	+	0.695683i	$0.244898\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	12.4124	+	21.4989i	0.893462	+	1.54752i	0.835696	+	0.549192i	$0.185064\pi$
$193$	12.4124	+	21.4989i	0.893462	+	1.54752i	0.0577662	+	0.998330i	$0.481602\pi$
$194$	−0.549834			−0.0394758
$195$	−10.6873	−	11.1066i	−0.765333	−	0.795357i
$196$	1.00000			0.0714286
$197$	10.9124	+	18.9008i	0.777475	+	1.34663i	0.933393	+	0.358856i	$0.116833\pi$
$197$	10.9124	+	18.9008i	0.777475	+	1.34663i	−0.155919	+	0.987770i	$0.549834\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	−5.91238	+	10.2405i	−0.419117	+	0.725932i	−0.995851	−	0.0909999i	$-0.970994\pi$
$199$	−5.91238	+	10.2405i	−0.419117	+	0.725932i	0.576734	+	0.816932i	$0.304327\pi$
$200$	13.2749			0.938678
$201$	1.36254	−	2.35999i	0.0961063	−	0.166461i
$202$	−0.862541	+	1.49397i	−0.0606882	+	0.105115i
$203$	8.27492			0.580785
$204$	−1.50000	+	2.59808i	−0.105021	+	0.181902i
$205$	−17.6873	−	30.6353i	−1.23533	−	2.13966i
$206$	−2.63746	−	4.56821i	−0.183760	−	0.318282i
$207$	−5.27492			−0.366632
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	−26.1993			−1.81225
$210$	−2.13746	−	3.70219i	−0.147499	−	0.255475i
$211$	−10.5498	−	18.2728i	−0.726281	−	1.25795i	−0.958445	−	0.285278i	$-0.907914\pi$
$211$	−10.5498	−	18.2728i	−0.726281	−	1.25795i	0.232164	−	0.972677i	$-0.425419\pi$
$212$	1.77492	−	3.07425i	0.121902	−	0.211140i
$213$	5.27492			0.361431
$214$	−1.27492	+	2.20822i	−0.0871515	+	0.150951i
$215$	25.2749	−	43.7774i	1.72374	−	2.98560i
$216$	1.00000			0.0680414
$217$	0.637459	−	1.10411i	0.0432735	−	0.0749519i
$218$	2.27492	+	3.94027i	0.154077	+	0.266869i
$219$	−2.86254	−	4.95807i	−0.193433	−	0.335035i
$220$	−17.0997			−1.15286
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$	0.274917			0.0184512
$223$	−5.36254	−	9.28819i	−0.359102	−	0.621983i	0.628709	−	0.777641i	$-0.283584\pi$
$223$	−5.36254	−	9.28819i	−0.359102	−	0.621983i	−0.987811	+	0.155657i	$0.950250\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−6.63746	+	11.4964i	−0.442497	+	0.766428i
$226$	14.8248			0.986128
$227$	10.5498	−	18.2728i	0.700217	−	1.21281i	−0.268173	−	0.963371i	$-0.586420\pi$
$227$	10.5498	−	18.2728i	0.700217	−	1.21281i	0.968390	−	0.249441i	$-0.0802468\pi$
$228$	−3.27492	+	5.67232i	−0.216887	+	0.375659i
$229$	12.7251			0.840897			0.420449	−	0.907316i	$-0.361873\pi$
$229$	12.7251			0.840897			0.420449	+	0.907316i	$0.361873\pi$
$230$	11.2749	−	19.5287i	0.743446	−	1.28769i
$231$	2.00000	+	3.46410i	0.131590	+	0.227921i
$232$	−4.13746	−	7.16629i	−0.271637	−	0.470490i
$233$	7.45017			0.488077			0.244038	−	0.969766i	$-0.421528\pi$
$233$	7.45017			0.488077			0.244038	+	0.969766i	$0.421528\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$	−28.0000			−1.82652
$236$	5.91238	+	10.2405i	0.384863	+	0.666602i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	−5.27492			−0.341206			−0.170603	−	0.985340i	$-0.554572\pi$
$239$	−5.27492			−0.341206			−0.170603	+	0.985340i	$0.554572\pi$
$240$	−2.13746	+	3.70219i	−0.137972	+	0.238975i
$241$	7.86254	−	13.6183i	0.506471	−	0.877233i	−0.493501	−	0.869745i	$-0.664283\pi$
$241$	7.86254	−	13.6183i	0.506471	−	0.877233i	0.999972	−	0.00748804i	$-0.00238354\pi$
$242$	5.00000			0.321412
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	4.50000	+	7.79423i	0.288083	+	0.498974i
$245$	−2.13746	−	3.70219i	−0.136557	−	0.236524i
$246$	8.27492			0.527589
$247$	−6.54983	+	22.6893i	−0.416756	+	1.44369i
$248$	−1.27492			−0.0809573
$249$	5.91238	+	10.2405i	0.374682	+	0.648968i
$250$	−17.6873	−	30.6353i	−1.11864	−	1.93755i
$251$	−6.63746	+	11.4964i	−0.418953	+	0.725647i	−0.995834	−	0.0911804i	$-0.970936\pi$
$251$	−6.63746	+	11.4964i	−0.418953	+	0.725647i	0.576882	+	0.816828i	$0.304269\pi$
$252$	1.00000			0.0629941
$253$	−10.5498	+	18.2728i	−0.663262	+	1.14880i
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$	12.8248			0.803117
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$	5.91238	+	10.2405i	0.368088	+	0.637548i
$259$	0.274917			0.0170825
$260$	−4.27492	+	14.8087i	−0.265119	+	0.918400i
$261$	8.27492			0.512205
$262$	1.36254	+	2.35999i	0.0841781	+	0.145801i
$263$	−10.5498	−	18.2728i	−0.650531	−	1.12675i	−0.982994	−	0.183636i	$-0.941213\pi$
$263$	−10.5498	−	18.2728i	−0.650531	−	1.12675i	0.332464	−	0.943116i	$-0.392120\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	−15.1752			−0.932208
$266$	−3.27492	+	5.67232i	−0.200798	+	0.347792i
$267$	−0.362541	+	0.627940i	−0.0221872	+	0.0384293i
$268$	−2.72508			−0.166461
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	−2.13746	−	3.70219i	−0.130082	−	0.225308i
$271$	−12.6375	−	21.8887i	−0.767671	−	1.32965i	−0.938823	−	0.344400i	$-0.888082\pi$
$271$	−12.6375	−	21.8887i	−0.767671	−	1.32965i	0.171152	−	0.985245i	$-0.445251\pi$
$272$	3.00000			0.181902
$273$	3.50000	−	0.866025i	0.211830	−	0.0524142i
$274$	22.8248			1.37889
$275$	26.5498	+	45.9857i	1.60102	+	2.77304i
$276$	2.63746	+	4.56821i	0.158756	+	0.274974i
$277$	−7.41238	+	12.8386i	−0.445366	+	0.771397i	−0.998078	−	0.0619755i	$-0.980260\pi$
$277$	−7.41238	+	12.8386i	−0.445366	+	0.771397i	0.552711	+	0.833373i	$0.313593\pi$
$278$	−9.09967			−0.545762
$279$	0.637459	−	1.10411i	0.0381636	−	0.0661014i
$280$	−2.13746	+	3.70219i	−0.127738	+	0.221248i
$281$	−20.8248			−1.24230			−0.621150	−	0.783691i	$-0.713334\pi$
$281$	−20.8248			−1.24230			−0.621150	+	0.783691i	$0.713334\pi$
$282$	3.27492	−	5.67232i	0.195018	−	0.337782i
$283$	4.72508	+	8.18408i	0.280877	+	0.486493i	0.971601	−	0.236625i	$-0.0760414\pi$
$283$	4.72508	+	8.18408i	0.280877	+	0.486493i	−0.690724	+	0.723119i	$0.742708\pi$
$284$	−2.63746	−	4.56821i	−0.156504	−	0.271074i
$285$	28.0000			1.65858
$286$	4.00000	−	13.8564i	0.236525	−	0.819346i
$287$	8.27492			0.488453
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−17.6873	+	30.6353i	−1.03863	+	1.79897i
$291$	−0.549834			−0.0322319
$292$	−2.86254	+	4.95807i	−0.167518	+	0.290149i
$293$	9.13746	−	15.8265i	0.533816	−	0.924596i	−0.465404	−	0.885099i	$-0.654091\pi$
$293$	9.13746	−	15.8265i	0.533816	−	0.924596i	0.999220	−	0.0394979i	$-0.0125759\pi$
$294$	1.00000			0.0583212
$295$	25.2749	−	43.7774i	1.47156	−	2.54882i
$296$	−0.137459	−	0.238085i	−0.00798962	−	0.0138384i
$297$	2.00000	+	3.46410i	0.116052	+	0.201008i
$298$	−1.00000			−0.0579284
$299$	13.1873	+	13.7046i	0.762641	+	0.792560i
$300$	13.2749			0.766428
$301$	5.91238	+	10.2405i	0.340784	+	0.590255i
$302$	−6.54983	−	11.3446i	−0.376901	−	0.652811i
$303$	−0.862541	+	1.49397i	−0.0495517	+	0.0858261i
$304$	6.54983			0.375659
$305$	19.2371	−	33.3197i	1.10151	−	1.90788i
$306$	−1.50000	+	2.59808i	−0.0857493	+	0.148522i
$307$	−1.45017			−0.0827653			−0.0413827	−	0.999143i	$-0.513176\pi$
$307$	−1.45017			−0.0827653			−0.0413827	+	0.999143i	$0.513176\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$	−2.63746	−	4.56821i	−0.150040	−	0.259877i
$310$	2.72508	+	4.71998i	0.154774	+	0.268077i
$311$	−2.54983			−0.144588			−0.0722939	−	0.997383i	$-0.523032\pi$
$311$	−2.54983			−0.144588			−0.0722939	+	0.997383i	$0.523032\pi$
$312$	−2.50000	−	2.59808i	−0.141535	−	0.147087i
$313$	17.6495			0.997609			0.498804	−	0.866715i	$-0.333773\pi$
$313$	17.6495			0.997609			0.498804	+	0.866715i	$0.333773\pi$
$314$	1.86254	+	3.22602i	0.105109	+	0.182055i
$315$	−2.13746	−	3.70219i	−0.120432	−	0.208595i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	−7.54983			−0.424041			−0.212020	−	0.977265i	$-0.568004\pi$
$317$	−7.54983			−0.424041			−0.212020	+	0.977265i	$0.568004\pi$
$318$	1.77492	−	3.07425i	0.0995324	−	0.172395i
$319$	16.5498	−	28.6652i	0.926613	−	1.60494i
$320$	4.27492			0.238975
$321$	−1.27492	+	2.20822i	−0.0711589	+	0.123251i
$322$	2.63746	+	4.56821i	0.146980	+	0.254577i
$323$	−9.82475	−	17.0170i	−0.546664	−	0.946849i
$324$	1.00000			0.0555556
$325$	46.4622	−	11.4964i	2.57726	−	0.637706i
$326$	−13.2749			−0.735230
$327$	2.27492	+	3.94027i	0.125803	+	0.217898i
$328$	−4.13746	−	7.16629i	−0.228453	−	0.395692i
$329$	3.27492	−	5.67232i	0.180552	−	0.312725i
$330$	−17.0997			−0.941306
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	5.91238	−	10.2405i	0.324484	−	0.562022i
$333$	0.274917			0.0150654
$334$		0			0
$335$	5.82475	+	10.0888i	0.318240	+	0.551208i
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	0.274917			0.0149757			0.00748785	−	0.999972i	$-0.497617\pi$
$337$	0.274917			0.0149757			0.00748785	+	0.999972i	$0.497617\pi$
$338$	−11.0000	−	6.92820i	−0.598321	−	0.376845i
$339$	14.8248			0.805170
$340$	−6.41238	−	11.1066i	−0.347760	−	0.602338i
$341$	−2.54983	−	4.41644i	−0.138081	−	0.239164i
$342$	−3.27492	+	5.67232i	−0.177087	+	0.306724i
$343$	1.00000			0.0539949
$344$	5.91238	−	10.2405i	0.318774	−	0.552133i
$345$	11.2749	−	19.5287i	0.607021	−	1.05139i
$346$	−4.54983			−0.244601
$347$	−15.2749	+	26.4569i	−0.820001	+	1.42028i	0.0856804	+	0.996323i	$0.472694\pi$
$347$	−15.2749	+	26.4569i	−0.820001	+	1.42028i	−0.905681	+	0.423960i	$0.860640\pi$
$348$	−4.13746	−	7.16629i	−0.221791	−	0.384153i
$349$	17.4622	+	30.2454i	0.934731	+	1.61900i	0.775113	+	0.631822i	$0.217693\pi$
$349$	17.4622	+	30.2454i	0.934731	+	1.61900i	0.159617	+	0.987179i	$0.448974\pi$
$350$	13.2749			0.709574
$351$	3.50000	−	0.866025i	0.186816	−	0.0462250i
$352$	−4.00000			−0.213201
$353$	9.77492	+	16.9307i	0.520266	+	0.901128i	0.999722	+	0.0235618i	$0.00750066\pi$
$353$	9.77492	+	16.9307i	0.520266	+	0.901128i	−0.479456	+	0.877566i	$0.659166\pi$
$354$	5.91238	+	10.2405i	0.314239	+	0.544278i
$355$	−11.2749	+	19.5287i	−0.598410	+	1.03648i
$356$	0.725083			0.0384293
$357$	−1.50000	+	2.59808i	−0.0793884	+	0.137505i
$358$	−0.725083	+	1.25588i	−0.0383218	+	0.0663753i
$359$	−1.09967			−0.0580383			−0.0290192	−	0.999579i	$-0.509238\pi$
$359$	−1.09967			−0.0580383			−0.0290192	+	0.999579i	$0.509238\pi$
$360$	−2.13746	+	3.70219i	−0.112654	+	0.195122i
$361$	−11.9502	−	20.6983i	−0.628956	−	1.08938i
$362$	8.41238	+	14.5707i	0.442145	+	0.765817i
$363$	5.00000			0.262432
$364$	−2.50000	−	2.59808i	−0.131036	−	0.136176i
$365$	24.4743			1.28104
$366$	4.50000	+	7.79423i	0.235219	+	0.407411i
$367$	−6.63746	−	11.4964i	−0.346473	−	0.600108i	0.639148	−	0.769084i	$-0.279287\pi$
$367$	−6.63746	−	11.4964i	−0.346473	−	0.600108i	−0.985620	+	0.168976i	$0.945954\pi$
$368$	2.63746	−	4.56821i	0.137487	−	0.238135i
$369$	8.27492			0.430775
$370$	−0.587624	+	1.01779i	−0.0305491	+	0.0529126i
$371$	1.77492	−	3.07425i	0.0921491	−	0.159607i
$372$	−1.27492			−0.0661014
$373$	−13.4124	+	23.2309i	−0.694466	+	1.20285i	0.275894	+	0.961188i	$0.411026\pi$
$373$	−13.4124	+	23.2309i	−0.694466	+	1.20285i	−0.970360	+	0.241663i	$0.922307\pi$
$374$	6.00000	+	10.3923i	0.310253	+	0.537373i
$375$	−17.6873	−	30.6353i	−0.913368	−	1.58200i
$376$	−6.54983			−0.337782
$377$	−20.6873	−	21.4989i	−1.06545	−	1.10725i
$378$	1.00000			0.0514344
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	0.999874	+	0.0158521i	$0.00504609\pi$
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	−0.486209	+	0.873843i	$0.661621\pi$
$380$	−14.0000	−	24.2487i	−0.718185	−	1.24393i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	6.72508			0.344085
$383$	−11.0997	+	19.2252i	−0.567167	+	0.982361i	0.429678	+	0.902982i	$0.358627\pi$
$383$	−11.0997	+	19.2252i	−0.567167	+	0.982361i	−0.996844	+	0.0793791i	$0.974706\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−17.0997			−0.871480
$386$	12.4124	−	21.4989i	0.631773	−	1.09426i
$387$	5.91238	+	10.2405i	0.300543	+	0.520556i
$388$	0.274917	+	0.476171i	0.0139568	+	0.0241739i
$389$	−24.6495			−1.24978			−0.624890	−	0.780713i	$-0.714856\pi$
$389$	−24.6495			−1.24978			−0.624890	+	0.780713i	$0.714856\pi$
$390$	−4.27492	+	14.8087i	−0.216469	+	0.749870i
$391$	−15.8248			−0.800292
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	1.36254	+	2.35999i	0.0687311	+	0.119046i
$394$	10.9124	−	18.9008i	0.549758	−	0.952208i
$395$	−34.1993			−1.72076
$396$	2.00000	−	3.46410i	0.100504	−	0.174078i
$397$	−11.6375	+	20.1567i	−0.584067	+	1.01163i	0.410924	+	0.911670i	$0.365206\pi$
$397$	−11.6375	+	20.1567i	−0.584067	+	1.01163i	−0.994991	+	0.0999645i	$0.968127\pi$
$398$	11.8248			0.592721
$399$	−3.27492	+	5.67232i	−0.163951	+	0.283971i
$400$	−6.63746	−	11.4964i	−0.331873	−	0.574821i
$401$	1.13746	+	1.97014i	0.0568020	+	0.0983839i	0.893028	−	0.450001i	$-0.148576\pi$
$401$	1.13746	+	1.97014i	0.0568020	+	0.0983839i	−0.836226	+	0.548385i	$0.815243\pi$
$402$	−2.72508			−0.135915
$403$	−4.46221	+	1.10411i	−0.222279	+	0.0549997i
$404$	1.72508			0.0858261
$405$	−2.13746	−	3.70219i	−0.106211	−	0.183963i
$406$	−4.13746	−	7.16629i	−0.205339	−	0.355657i
$407$	0.549834	−	0.952341i	0.0272543	−	0.0472058i
$408$	3.00000			0.148522
$409$	14.9622	−	25.9153i	0.739834	−	1.28143i	−0.212736	−	0.977110i	$-0.568238\pi$
$409$	14.9622	−	25.9153i	0.739834	−	1.28143i	0.952570	−	0.304320i	$-0.0984292\pi$
$410$	−17.6873	+	30.6353i	−0.873513	+	1.51297i
$411$	22.8248			1.12586
$412$	−2.63746	+	4.56821i	−0.129938	+	0.225060i
$413$	5.91238	+	10.2405i	0.290929	+	0.503904i
$414$	2.63746	+	4.56821i	0.129624	+	0.224515i
$415$	−50.5498			−2.48139
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	−9.09967			−0.445613
$418$	13.0997	+	22.6893i	0.640726	+	1.10977i
$419$	11.1873	+	19.3770i	0.546535	+	0.946626i	0.998509	+	0.0545951i	$0.0173868\pi$
$419$	11.1873	+	19.3770i	0.546535	+	0.946626i	−0.451974	+	0.892031i	$0.649280\pi$
$420$	−2.13746	+	3.70219i	−0.104297	+	0.180648i
$421$	8.27492			0.403295			0.201647	−	0.979458i	$-0.435370\pi$
$421$	8.27492			0.403295			0.201647	+	0.979458i	$0.435370\pi$
$422$	−10.5498	+	18.2728i	−0.513558	+	0.889508i
$423$	3.27492	−	5.67232i	0.159232	−	0.275798i
$424$	−3.54983			−0.172395
$425$	−19.9124	+	34.4892i	−0.965892	+	1.67297i
$426$	−2.63746	−	4.56821i	−0.127785	−	0.221331i
$427$	4.50000	+	7.79423i	0.217770	+	0.377189i
$428$	2.54983			0.123251
$429$	4.00000	−	13.8564i	0.193122	−	0.668994i
$430$	−50.5498			−2.43773
$431$	6.63746	+	11.4964i	0.319715	+	0.553763i	0.980429	−	0.196875i	$-0.0630795\pi$
$431$	6.63746	+	11.4964i	0.319715	+	0.553763i	−0.660713	+	0.750638i	$0.729746\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	5.13746	−	8.89834i	0.246891	−	0.427627i	−0.715771	−	0.698335i	$-0.753925\pi$
$433$	5.13746	−	8.89834i	0.246891	−	0.427627i	0.962661	+	0.270708i	$0.0872579\pi$
$434$	−1.27492			−0.0611980
$435$	−17.6873	+	30.6353i	−0.848041	+	1.46885i
$436$	2.27492	−	3.94027i	0.108949	−	0.188705i
$437$	−34.5498			−1.65274
$438$	−2.86254	+	4.95807i	−0.136778	+	0.236906i
$439$	−6.54983	−	11.3446i	−0.312607	−	0.541450i	0.666319	−	0.745667i	$-0.267869\pi$
$439$	−6.54983	−	11.3446i	−0.312607	−	0.541450i	−0.978926	+	0.204216i	$0.934535\pi$
$440$	8.54983	+	14.8087i	0.407597	+	0.705979i
$441$	1.00000			0.0476190
$442$	10.5000	−	2.59808i	0.499434	−	0.123578i
$443$	34.5498			1.64151			0.820756	−	0.571279i	$-0.193552\pi$
$443$	34.5498			1.64151			0.820756	+	0.571279i	$0.193552\pi$
$444$	−0.137459	−	0.238085i	−0.00652350	−	0.0112990i
$445$	−1.54983	−	2.68439i	−0.0734692	−	0.127252i
$446$	−5.36254	+	9.28819i	−0.253924	+	0.439809i
$447$	−1.00000			−0.0472984
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	9.54983	−	16.5408i	0.450685	−	0.780609i	−0.547744	−	0.836646i	$-0.684513\pi$
$449$	9.54983	−	16.5408i	0.450685	−	0.780609i	0.998429	+	0.0560374i	$0.0178466\pi$
$450$	13.2749			0.625786
$451$	16.5498	−	28.6652i	0.779301	−	1.34979i
$452$	−7.41238	−	12.8386i	−0.348649	−	0.603877i
$453$	−6.54983	−	11.3446i	−0.307738	−	0.533018i
$454$	−21.0997			−0.990257
$455$	−4.27492	+	14.8087i	−0.200411	+	0.694245i
$456$	6.54983			0.306724
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	−0.595818	+	0.803120i	$0.703172\pi$
$458$	−6.36254	−	11.0202i	−0.297302	−	0.514942i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$	−22.5498			−1.05139
$461$	9.68729	−	16.7789i	0.451182	−	0.781471i	−0.547278	−	0.836951i	$-0.684336\pi$
$461$	9.68729	−	16.7789i	0.451182	−	0.781471i	0.998460	+	0.0554807i	$0.0176691\pi$
$462$	2.00000	−	3.46410i	0.0930484	−	0.161165i
$463$	−10.5498			−0.490292			−0.245146	−	0.969486i	$-0.578836\pi$
$463$	−10.5498			−0.490292			−0.245146	+	0.969486i	$0.578836\pi$
$464$	−4.13746	+	7.16629i	−0.192077	+	0.332687i
$465$	2.72508	+	4.71998i	0.126373	+	0.218884i
$466$	−3.72508	−	6.45203i	−0.172561	−	0.298885i
$467$	−8.17525			−0.378305			−0.189153	−	0.981948i	$-0.560574\pi$
$467$	−8.17525			−0.378305			−0.189153	+	0.981948i	$0.560574\pi$
$468$	−2.50000	−	2.59808i	−0.115563	−	0.120096i
$469$	−2.72508			−0.125833
$470$	14.0000	+	24.2487i	0.645772	+	1.11851i
$471$	1.86254	+	3.22602i	0.0858214	+	0.148647i
$472$	5.91238	−	10.2405i	0.272139	−	0.471359i
$473$	47.2990			2.17481
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	−43.4743	+	75.2996i	−1.99474	+	3.45498i
$476$	3.00000			0.137505
$477$	1.77492	−	3.07425i	0.0812679	−	0.140760i
$478$	2.63746	+	4.56821i	0.120635	+	0.208945i
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	0.541884	−	0.840453i	$-0.317711\pi$
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	−0.998796	+	0.0490589i	$0.984378\pi$
$480$	4.27492			0.195122
$481$	−0.687293	−	0.714256i	−0.0313379	−	0.0325673i
$482$	−15.7251			−0.716258
$483$	2.63746	+	4.56821i	0.120009	+	0.207861i
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	1.17525	−	2.03559i	0.0533653	−	0.0924314i
$486$	1.00000			0.0453609
$487$	0.549834	−	0.952341i	0.0249154	−	0.0431547i	−0.853299	−	0.521422i	$-0.825402\pi$
$487$	0.549834	−	0.952341i	0.0249154	−	0.0431547i	0.878214	+	0.478267i	$0.158735\pi$
$488$	4.50000	−	7.79423i	0.203705	−	0.352828i
$489$	−13.2749			−0.600313
$490$	−2.13746	+	3.70219i	−0.0965605	+	0.167248i
$491$	−12.5498	−	21.7370i	−0.566366	−	0.980975i	−0.996921	−	0.0784105i	$-0.975016\pi$
$491$	−12.5498	−	21.7370i	−0.566366	−	0.980975i	0.430555	−	0.902564i	$-0.358318\pi$
$492$	−4.13746	−	7.16629i	−0.186531	−	0.323081i
$493$	24.8248			1.11805
$494$	22.9244	−	5.67232i	1.03142	−	0.255210i
$495$	−17.0997			−0.768573
$496$	0.637459	+	1.10411i	0.0286227	+	0.0495760i
$497$	−2.63746	−	4.56821i	−0.118306	−	0.204912i
$498$	5.91238	−	10.2405i	0.264940	−	0.458889i
$499$	−31.8248			−1.42467			−0.712336	−	0.701839i	$-0.752363\pi$
$499$	−31.8248			−1.42467			−0.712336	+	0.701839i	$0.752363\pi$
$500$	−17.6873	+	30.6353i	−0.791000	+	1.37005i
$501$		0			0
$502$	13.2749			0.592489
$503$	10.5498	−	18.2728i	0.470394	−	0.814746i	−0.529033	−	0.848601i	$-0.677445\pi$
$503$	10.5498	−	18.2728i	0.470394	−	0.814746i	0.999427	+	0.0338552i	$0.0107785\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$	−3.68729	−	6.38658i	−0.164082	−	0.284199i
$506$	21.0997			0.937995
$507$	−11.0000	−	6.92820i	−0.488527	−	0.307692i
$508$	8.00000			0.354943
$509$	6.58762	+	11.4101i	0.291991	+	0.505744i	0.974281	−	0.225339i	$-0.0723488\pi$
$509$	6.58762	+	11.4101i	0.291991	+	0.505744i	−0.682289	+	0.731082i	$0.739015\pi$
$510$	−6.41238	−	11.1066i	−0.283945	−	0.491807i
$511$	−2.86254	+	4.95807i	−0.126631	+	0.219332i
$512$	1.00000			0.0441942
$513$	−3.27492	+	5.67232i	−0.144591	+	0.250439i
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$	22.5498			0.993664
$516$	5.91238	−	10.2405i	0.260278	−	0.450814i
$517$	−13.0997	−	22.6893i	−0.576123	−	0.997874i
$518$	−0.137459	−	0.238085i	−0.00603958	−	0.0104609i
$519$	−4.54983			−0.199716
$520$	14.9622	−	3.70219i	0.656136	−	0.162352i
$521$	−20.8248			−0.912349			−0.456174	−	0.889890i	$-0.650781\pi$
$521$	−20.8248			−0.912349			−0.456174	+	0.889890i	$0.650781\pi$
$522$	−4.13746	−	7.16629i	−0.181092	−	0.313660i
$523$	13.0997	+	22.6893i	0.572809	+	0.992133i	0.996276	+	0.0862221i	$0.0274795\pi$
$523$	13.0997	+	22.6893i	0.572809	+	0.992133i	−0.423467	+	0.905911i	$0.639187\pi$
$524$	1.36254	−	2.35999i	0.0595229	−	0.103097i
$525$	13.2749			0.579365
$526$	−10.5498	+	18.2728i	−0.459995	+	0.796734i
$527$	1.91238	−	3.31233i	0.0833044	−	0.144287i
$528$	−4.00000			−0.174078
$529$	−2.41238	+	4.17836i	−0.104886	+	0.181668i
$530$	7.58762	+	13.1422i	0.329585	+	0.570859i
$531$	5.91238	+	10.2405i	0.256575	+	0.444401i
$532$	6.54983			0.283971
$533$	−20.6873	−	21.4989i	−0.896066	−	0.931219i
$534$	0.725083			0.0313774
$535$	−5.45017	−	9.43996i	−0.235631	−	0.408125i
$536$	1.36254	+	2.35999i	0.0588528	+	0.101936i
$537$	−0.725083	+	1.25588i	−0.0312896	+	0.0541952i
$538$	−18.0000			−0.776035
$539$	2.00000	−	3.46410i	0.0861461	−	0.149209i
$540$	−2.13746	+	3.70219i	−0.0919816	+	0.159317i
$541$	25.3746			1.09094			0.545469	−	0.838131i	$-0.316351\pi$
$541$	25.3746			1.09094			0.545469	+	0.838131i	$0.316351\pi$
$542$	−12.6375	+	21.8887i	−0.542825	+	0.940201i
$543$	8.41238	+	14.5707i	0.361010	+	0.625287i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	−19.4502			−0.833154
$546$	−2.50000	−	2.59808i	−0.106990	−	0.111187i
$547$	2.90033			0.124009			0.0620046	−	0.998076i	$-0.480251\pi$
$547$	2.90033			0.124009			0.0620046	+	0.998076i	$0.480251\pi$
$548$	−11.4124	−	19.7668i	−0.487513	−	0.844396i
$549$	4.50000	+	7.79423i	0.192055	+	0.332650i
$550$	26.5498	−	45.9857i	1.13209	−	1.96084i
$551$	54.1993			2.30897
$552$	2.63746	−	4.56821i	0.112258	−	0.194436i
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$	14.8248			0.629843
$555$	−0.587624	+	1.01779i	−0.0249433	+	0.0432030i
$556$	4.54983	+	7.88054i	0.192956	+	0.334210i
$557$	17.5997	+	30.4835i	0.745722	+	1.29163i	0.949857	+	0.312685i	$0.101229\pi$
$557$	17.5997	+	30.4835i	0.745722	+	1.29163i	−0.204135	+	0.978943i	$0.565438\pi$
$558$	−1.27492			−0.0539715
$559$	11.8248	−	40.9621i	0.500134	−	1.73251i
$560$	4.27492			0.180648
$561$	6.00000	+	10.3923i	0.253320	+	0.438763i
$562$	10.4124	+	18.0348i	0.439220	+	0.760751i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$	−6.54983			−0.275798
$565$	−31.6873	+	54.8840i	−1.33309	+	2.30899i
$566$	4.72508	−	8.18408i	0.198610	−	0.344003i
$567$	1.00000			0.0419961
$568$	−2.63746	+	4.56821i	−0.110665	+	0.191678i
$569$	−2.45017	−	4.24381i	−0.102716	−	0.177910i	0.810087	−	0.586310i	$-0.199420\pi$
$569$	−2.45017	−	4.24381i	−0.102716	−	0.177910i	−0.912803	+	0.408400i	$0.866087\pi$
$570$	−14.0000	−	24.2487i	−0.586395	−	1.01567i
$571$	−14.7251			−0.616226			−0.308113	−	0.951350i	$-0.599697\pi$
$571$	−14.7251			−0.616226			−0.308113	+	0.951350i	$0.599697\pi$
$572$	−14.0000	+	3.46410i	−0.585369	+	0.144841i
$573$	6.72508			0.280944
$574$	−4.13746	−	7.16629i	−0.172694	−	0.299115i
$575$	35.0120	+	60.6426i	1.46010	+	2.52897i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	9.37459			0.390269			0.195135	−	0.980776i	$-0.437486\pi$
$577$	9.37459			0.390269			0.195135	+	0.980776i	$0.437486\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	12.4124	−	21.4989i	0.515841	−	0.893462i
$580$	35.3746			1.46885
$581$	5.91238	−	10.2405i	0.245287	−	0.424849i
$582$	0.274917	+	0.476171i	0.0113957	+	0.0197379i
$583$	−7.09967	−	12.2970i	−0.294038	−	0.509289i
$584$	5.72508			0.236906
$585$	−4.27492	+	14.8087i	−0.176746	+	0.612266i
$586$	−18.2749			−0.754930
$587$	−4.46221	−	7.72877i	−0.184175	−	0.319001i	0.759123	−	0.650947i	$-0.225628\pi$
$587$	−4.46221	−	7.72877i	−0.184175	−	0.319001i	−0.943298	+	0.331946i	$0.892295\pi$
$588$	−0.500000	−	0.866025i	−0.0206197	−	0.0357143i
$589$	4.17525	−	7.23174i	0.172038	−	0.297979i
$590$	−50.5498			−2.08110
$591$	10.9124	−	18.9008i	0.448875	−	0.777475i
$592$	−0.137459	+	0.238085i	−0.00564951	+	0.00978525i
$593$	4.45017			0.182746			0.0913732	−	0.995817i	$-0.470874\pi$
$593$	4.45017			0.182746			0.0913732	+	0.995817i	$0.470874\pi$
$594$	2.00000	−	3.46410i	0.0820610	−	0.142134i
$595$	−6.41238	−	11.1066i	−0.262882	−	0.455325i
$596$	0.500000	+	0.866025i	0.0204808	+	0.0354738i
$597$	11.8248			0.483955
$598$	5.27492	−	18.2728i	0.215707	−	0.747232i
$599$	−10.7251			−0.438215			−0.219108	−	0.975701i	$-0.570315\pi$
$599$	−10.7251			−0.438215			−0.219108	+	0.975701i	$0.570315\pi$
$600$	−6.63746	−	11.4964i	−0.270973	−	0.469339i
$601$	3.86254	+	6.69012i	0.157556	+	0.272896i	0.933987	−	0.357307i	$-0.116305\pi$
$601$	3.86254	+	6.69012i	0.157556	+	0.272896i	−0.776431	+	0.630203i	$0.782972\pi$
$602$	5.91238	−	10.2405i	0.240970	−	0.417373i
$603$	−2.72508			−0.110974
$604$	−6.54983	+	11.3446i	−0.266509	+	0.461607i
$605$	−10.6873	+	18.5109i	−0.434500	+	0.752577i
$606$	1.72508			0.0700767
$607$	−7.36254	+	12.7523i	−0.298836	+	0.517600i	−0.975870	−	0.218352i	$-0.929932\pi$
$607$	−7.36254	+	12.7523i	−0.298836	+	0.517600i	0.677034	+	0.735952i	$0.263265\pi$
$608$	−3.27492	−	5.67232i	−0.132815	−	0.230043i
$609$	−4.13746	−	7.16629i	−0.167658	−	0.290393i
$610$	−38.4743			−1.55778
$611$	−22.9244	+	5.67232i	−0.927423	+	0.229478i
$612$	3.00000			0.121268
$613$	−14.6873	−	25.4391i	−0.593214	−	1.02748i	−0.993796	−	0.111216i	$-0.964525\pi$
$613$	−14.6873	−	25.4391i	−0.593214	−	1.02748i	0.400582	−	0.916261i	$-0.368808\pi$
$614$	0.725083	+	1.25588i	0.0292620	+	0.0506832i
$615$	−17.6873	+	30.6353i	−0.713220	+	1.23533i
$616$	−4.00000			−0.161165
$617$	−19.9622	+	34.5756i	−0.803648	+	1.39196i	0.113551	+	0.993532i	$0.463777\pi$
$617$	−19.9622	+	34.5756i	−0.803648	+	1.39196i	−0.917200	+	0.398428i	$0.869556\pi$
$618$	−2.63746	+	4.56821i	−0.106094	+	0.183760i
$619$	−15.6495			−0.629007			−0.314503	−	0.949256i	$-0.601838\pi$
$619$	−15.6495			−0.629007			−0.314503	+	0.949256i	$0.601838\pi$
$620$	2.72508	−	4.71998i	0.109442	−	0.189559i
$621$	2.63746	+	4.56821i	0.105838	+	0.183316i
$622$	1.27492	+	2.20822i	0.0511195	+	0.0885416i
$623$	0.725083			0.0290498
$624$	−1.00000	+	3.46410i	−0.0400320	+	0.138675i
$625$	84.8488			3.39395
$626$	−8.82475	−	15.2849i	−0.352708	−	0.610908i
$627$	13.0997	+	22.6893i	0.523150	+	0.906123i
$628$	1.86254	−	3.22602i	0.0743235	−	0.128732i
$629$	0.824752			0.0328850
$630$	−2.13746	+	3.70219i	−0.0851584	+	0.147499i
$631$	14.5498	−	25.2011i	0.579220	−	1.00324i	−0.416349	−	0.909205i	$-0.636691\pi$
$631$	14.5498	−	25.2011i	0.579220	−	1.00324i	0.995569	−	0.0940333i	$-0.0299760\pi$
$632$	−8.00000			−0.318223
$633$	−10.5498	+	18.2728i	−0.419318	+	0.726281i
$634$	3.77492	+	6.53835i	0.149921	+	0.259671i
$635$	−17.0997	−	29.6175i	−0.678580	−	1.17533i
$636$	−3.54983			−0.140760
$637$	−2.50000	−	2.59808i	−0.0990536	−	0.102940i
$638$	−33.0997			−1.31043
$639$	−2.63746	−	4.56821i	−0.104336	−	0.180716i
$640$	−2.13746	−	3.70219i	−0.0844905	−	0.146342i
$641$	−9.41238	+	16.3027i	−0.371766	+	0.643918i	−0.989837	−	0.142204i	$-0.954581\pi$
$641$	−9.41238	+	16.3027i	−0.371766	+	0.643918i	0.618071	+	0.786122i	$0.287914\pi$
$642$	2.54983			0.100634
$643$	16.3746	−	28.3616i	0.645751	−	1.11847i	−0.338377	−	0.941011i	$-0.609878\pi$
$643$	16.3746	−	28.3616i	0.645751	−	1.11847i	0.984128	−	0.177462i	$-0.0567888\pi$
$644$	2.63746	−	4.56821i	0.103930	−	0.180013i
$645$	−50.5498			−1.99040
$646$	−9.82475	+	17.0170i	−0.386550	+	0.669524i
$647$	−4.72508	−	8.18408i	−0.185762	−	0.321750i	0.758071	−	0.652172i	$-0.226142\pi$
$647$	−4.72508	−	8.18408i	−0.185762	−	0.321750i	−0.943833	+	0.330423i	$0.892809\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	47.2990			1.85665
$650$	−33.1873	−	34.4892i	−1.30171	−	1.35278i
$651$	−1.27492			−0.0499679
$652$	6.63746	+	11.4964i	0.259943	+	0.450234i
$653$	−16.7371	−	28.9896i	−0.654974	−	1.13445i	−0.981900	−	0.189399i	$-0.939346\pi$
$653$	−16.7371	−	28.9896i	−0.654974	−	1.13445i	0.326926	−	0.945050i	$-0.393987\pi$
$654$	2.27492	−	3.94027i	0.0889563	−	0.154077i
$655$	−11.6495			−0.455184
$656$	−4.13746	+	7.16629i	−0.161541	+	0.279797i
$657$	−2.86254	+	4.95807i	−0.111678	+	0.193433i
$658$	−6.54983			−0.255339
$659$	6.72508	−	11.6482i	0.261972	−	0.453749i	−0.704794	−	0.709412i	$-0.748961\pi$
$659$	6.72508	−	11.6482i	0.261972	−	0.453749i	0.966766	+	0.255663i	$0.0822938\pi$
$660$	8.54983	+	14.8087i	0.332802	+	0.576430i
$661$	−4.95017	−	8.57394i	−0.192539	−	0.333488i	0.753552	−	0.657388i	$-0.228339\pi$
$661$	−4.95017	−	8.57394i	−0.192539	−	0.333488i	−0.946091	+	0.323901i	$0.895006\pi$
$662$	4.00000			0.155464
$663$	10.5000	−	2.59808i	0.407786	−	0.100901i
$664$	−11.8248			−0.458889
$665$	−14.0000	−	24.2487i	−0.542897	−	0.940325i
$666$	−0.137459	−	0.238085i	−0.00532641	−	0.00922562i
$667$	21.8248	−	37.8016i	0.845058	−	1.46368i
$668$		0			0
$669$	−5.36254	+	9.28819i	−0.207328	+	0.359102i
$670$	5.82475	−	10.0888i	0.225030	−	0.389763i
$671$	36.0000			1.38976
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	9.04983	+	15.6748i	0.348845	+	0.604218i	0.986045	−	0.166481i	$-0.0532405\pi$
$673$	9.04983	+	15.6748i	0.348845	+	0.604218i	−0.637199	+	0.770699i	$0.719907\pi$
$674$	−0.137459	−	0.238085i	−0.00529471	−	0.00917070i
$675$	13.2749			0.510952
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	−33.6495			−1.29326			−0.646628	−	0.762806i	$-0.723821\pi$
$677$	−33.6495			−1.29326			−0.646628	+	0.762806i	$0.723821\pi$
$678$	−7.41238	−	12.8386i	−0.284671	−	0.493064i
$679$	0.274917	+	0.476171i	0.0105504	+	0.0182738i
$680$	−6.41238	+	11.1066i	−0.245903	+	0.425917i
$681$	−21.0997			−0.808541
$682$	−2.54983	+	4.41644i	−0.0976382	+	0.169114i
$683$	2.17525	−	3.76764i	0.0832336	−	0.144165i	−0.821404	−	0.570347i	$-0.806809\pi$
$683$	2.17525	−	3.76764i	0.0832336	−	0.144165i	0.904637	+	0.426183i	$0.140142\pi$
$684$	6.54983			0.250439
$685$	−48.7870	+	84.5015i	−1.86405	+	3.22864i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−6.36254	−	11.0202i	−0.242746	−	0.420449i
$688$	−11.8248			−0.450814
$689$	−12.4244	+	3.07425i	−0.473333	+	0.117119i
$690$	−22.5498			−0.858458
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	2.27492	+	3.94027i	0.0864794	+	0.149787i
$693$	2.00000	−	3.46410i	0.0759737	−	0.131590i
$694$	30.5498			1.15966
$695$	19.4502	−	33.6887i	0.737787	−	1.27788i
$696$	−4.13746	+	7.16629i	−0.156830	+	0.271637i
$697$	24.8248			0.940305
$698$	17.4622	−	30.2454i	0.660954	−	1.14481i
$699$	−3.72508	−	6.45203i	−0.140896	−	0.244038i
$700$	−6.63746	−	11.4964i	−0.250872	−	0.434524i
$701$	14.9244			0.563688			0.281844	−	0.959460i	$-0.409054\pi$
$701$	14.9244			0.563688			0.281844	+	0.959460i	$0.409054\pi$
$702$	−2.50000	−	2.59808i	−0.0943564	−	0.0980581i
$703$	1.80066			0.0679133
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$	14.0000	+	24.2487i	0.527271	+	0.913259i
$706$	9.77492	−	16.9307i	0.367884	−	0.637194i
$707$	1.72508			0.0648784
$708$	5.91238	−	10.2405i	0.222201	−	0.384863i
$709$	23.6873	−	41.0276i	0.889595	−	1.54082i	0.0492402	−	0.998787i	$-0.484320\pi$
$709$	23.6873	−	41.0276i	0.889595	−	1.54082i	0.840355	−	0.542037i	$-0.182347\pi$
$710$	22.5498			0.846280
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$	−0.362541	−	0.627940i	−0.0135868	−	0.0235331i
$713$	−3.36254	−	5.82409i	−0.125928	−	0.218114i
$714$	3.00000			0.112272
$715$	42.7492	+	44.4262i	1.59873	+	1.66145i
$716$	1.45017			0.0541952
$717$	2.63746	+	4.56821i	0.0984977	+	0.170603i
$718$	0.549834	+	0.952341i	0.0205196	+	0.0355411i
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	−0.781748	−	0.623595i	$-0.785672\pi$
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	0.930923	+	0.365216i	$0.119005\pi$
$720$	4.27492			0.159317
$721$	−2.63746	+	4.56821i	−0.0982241	+	0.170129i
$722$	−11.9502	+	20.6983i	−0.444739	+	0.770311i
$723$	−15.7251			−0.584822
$724$	8.41238	−	14.5707i	0.312643	−	0.541514i
$725$	−54.9244	−	95.1319i	−2.03984	−	3.53311i
$726$	−2.50000	−	4.33013i	−0.0927837	−	0.160706i
$727$	19.8248			0.735259			0.367630	−	0.929972i	$-0.380169\pi$
$727$	19.8248			0.735259			0.367630	+	0.929972i	$0.380169\pi$
$728$	−1.00000	+	3.46410i	−0.0370625	+	0.128388i
$729$	1.00000			0.0370370
$730$	−12.2371	−	21.1953i	−0.452916	−	0.784474i
$731$	17.7371	+	30.7216i	0.656031	+	1.13628i
$732$	4.50000	−	7.79423i	0.166325	−	0.288083i
$733$	−32.6495			−1.20594			−0.602968	−	0.797765i	$-0.706016\pi$
$733$	−32.6495			−1.20594			−0.602968	+	0.797765i	$0.706016\pi$
$734$	−6.63746	+	11.4964i	−0.244993	+	0.424340i
$735$	−2.13746	+	3.70219i	−0.0788413	+	0.136557i
$736$	−5.27492			−0.194436
$737$	−5.45017	+	9.43996i	−0.200759	+	0.347726i
$738$	−4.13746	−	7.16629i	−0.152302	−	0.263795i
$739$	24.6375	+	42.6733i	0.906304	+	1.56976i	0.819158	+	0.573568i	$0.194441\pi$
$739$	24.6375	+	42.6733i	0.906304	+	1.56976i	0.0871458	+	0.996196i	$0.472225\pi$
$740$	1.17525			0.0432030
$741$	22.9244	−	5.67232i	0.842150	−	0.208378i
$742$	−3.54983			−0.130319
$743$	2.08762	+	3.61587i	0.0765875	+	0.132653i	0.901776	−	0.432205i	$-0.142264\pi$
$743$	2.08762	+	3.61587i	0.0765875	+	0.132653i	−0.825188	+	0.564858i	$0.808931\pi$
$744$	0.637459	+	1.10411i	0.0233704	+	0.0404787i
$745$	2.13746	−	3.70219i	0.0783104	−	0.135638i
$746$	26.8248			0.982124
$747$	5.91238	−	10.2405i	0.216323	−	0.374682i
$748$	6.00000	−	10.3923i	0.219382	−	0.379980i
$749$	2.54983			0.0931689
$750$	−17.6873	+	30.6353i	−0.645849	+	1.11864i
$751$	9.27492	+	16.0646i	0.338447	+	0.586207i	0.984141	−	0.177390i	$-0.0567652\pi$
$751$	9.27492	+	16.0646i	0.338447	+	0.586207i	−0.645694	+	0.763596i	$0.723432\pi$
$752$	3.27492	+	5.67232i	0.119424	+	0.206848i
$753$	13.2749			0.483765
$754$	−8.27492	+	28.6652i	−0.301355	+	1.04392i
$755$	56.0000			2.03805
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	0.999505	−	0.0314762i	$-0.0100208\pi$
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	−0.527011	+	0.849858i	$0.676688\pi$
$758$	10.0000	−	17.3205i	0.363216	−	0.629109i
$759$	21.0997			0.765869
$760$	−14.0000	+	24.2487i	−0.507833	+	0.879593i
$761$	−10.0997	+	17.4931i	−0.366113	+	0.634126i	−0.988954	−	0.148222i	$-0.952645\pi$
$761$	−10.0997	+	17.4931i	−0.366113	+	0.634126i	0.622841	+	0.782348i	$0.285978\pi$
$762$	8.00000			0.289809
$763$	2.27492	−	3.94027i	0.0823575	−	0.142647i
$764$	−3.36254	−	5.82409i	−0.121652	−	0.210708i
$765$	−6.41238	−	11.1066i	−0.231840	−	0.401559i
$766$	22.1993			0.802095
$767$	11.8248	−	40.9621i	0.426967	−	1.47906i
$768$	1.00000			0.0360844
$769$	−20.8248	−	36.0695i	−0.750960	−	1.30070i	−0.947358	−	0.320176i	$-0.896258\pi$
$769$	−20.8248	−	36.0695i	−0.750960	−	1.30070i	0.196398	−	0.980524i	$-0.437075\pi$
$770$	8.54983	+	14.8087i	0.308115	+	0.533670i
$771$	−7.50000	+	12.9904i	−0.270106	+	0.467837i
$772$	−24.8248			−0.893462
$773$	10.4502	−	18.1002i	0.375866	−	0.651020i	−0.614590	−	0.788847i	$-0.710679\pi$
$773$	10.4502	−	18.1002i	0.375866	−	0.651020i	0.990456	+	0.137827i	$0.0440118\pi$
$774$	5.91238	−	10.2405i	0.212516	−	0.368088i
$775$	−16.9244			−0.607943
$776$	0.274917	−	0.476171i	0.00986895	−	0.0170935i
$777$	−0.137459	−	0.238085i	−0.00493130	−	0.00854126i
$778$	12.3248	+	21.3471i	0.441864	+	0.765330i
$779$	54.1993			1.94189
$780$	14.9622	−	3.70219i	0.535733	−	0.132560i
$781$	−21.0997			−0.755006
$782$	7.91238	+	13.7046i	0.282946	+	0.490077i
$783$	−4.13746	−	7.16629i	−0.147861	−	0.256102i
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−15.9244			−0.568367
$786$	1.36254	−	2.35999i	0.0486002	−	0.0841781i
$787$	−10.5498	+	18.2728i	−0.376061	+	0.651357i	−0.990485	−	0.137619i	$-0.956055\pi$
$787$	−10.5498	+	18.2728i	−0.376061	+	0.651357i	0.614424	+	0.788976i	$0.289388\pi$
$788$	−21.8248			−0.777475
$789$	−10.5498	+	18.2728i	−0.375584	+	0.650531i
$790$	17.0997	+	29.6175i	0.608379	+	1.05374i
$791$	−7.41238	−	12.8386i	−0.263554	−	0.456488i
$792$	−4.00000			−0.142134
$793$	9.00000	−	31.1769i	0.319599	−	1.10712i
$794$	23.2749			0.825996
$795$	7.58762	+	13.1422i	0.269105	+	0.466104i
$796$	−5.91238	−	10.2405i	−0.209559	−	0.362966i
$797$	−8.27492	+	14.3326i	−0.293113	+	0.507686i	−0.974544	−	0.224196i	$-0.928024\pi$
$797$	−8.27492	+	14.3326i	−0.293113	+	0.507686i	0.681431	+	0.731882i	$0.261358\pi$
$798$	6.54983			0.231862
$799$	9.82475	−	17.0170i	0.347575	−	0.602017i
$800$	−6.63746	+	11.4964i	−0.234670	+	0.406460i
$801$	0.725083			0.0256195
$802$	1.13746	−	1.97014i	0.0401651	−	0.0695679i
$803$	11.4502	+	19.8323i	0.404068	+	0.699866i
$804$	1.36254	+	2.35999i	0.0480531	+	0.0832305i
$805$	−22.5498			−0.794777
$806$	3.18729	+	3.31233i	0.112268	+	0.116672i
$807$	−18.0000			−0.633630
$808$	−0.862541	−	1.49397i	−0.0303441	−	0.0525575i
$809$	−4.86254	−	8.42217i	−0.170958	−	0.296108i	0.767797	−	0.640693i	$-0.221353\pi$
$809$	−4.86254	−	8.42217i	−0.170958	−	0.296108i	−0.938755	+	0.344585i	$0.888020\pi$
$810$	−2.13746	+	3.70219i	−0.0751026	+	0.130082i
$811$	5.09967			0.179074			0.0895368	−	0.995984i	$-0.471461\pi$
$811$	5.09967			0.179074			0.0895368	+	0.995984i	$0.471461\pi$
$812$	−4.13746	+	7.16629i	−0.145196	+	0.251487i
$813$	−12.6375	+	21.8887i	−0.443215	+	0.767671i
$814$	−1.09967			−0.0385434
$815$	28.3746	−	49.1462i	0.993918	−	1.72152i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	38.7251	+	67.0738i	1.35482	+	2.34662i
$818$	−29.9244			−1.04628
$819$	−2.50000	−	2.59808i	−0.0873571	−	0.0907841i
$820$	35.3746			1.23533
$821$	−7.63746	−	13.2285i	−0.266549	−	0.461677i	0.701419	−	0.712749i	$-0.252550\pi$
$821$	−7.63746	−	13.2285i	−0.266549	−	0.461677i	−0.967968	+	0.251072i	$0.919217\pi$
$822$	−11.4124	−	19.7668i	−0.398052	−	0.689447i
$823$	3.45017	−	5.97586i	0.120265	−	0.208305i	−0.799607	−	0.600524i	$-0.794959\pi$
$823$	3.45017	−	5.97586i	0.120265	−	0.208305i	0.919872	+	0.392218i	$0.128292\pi$
$824$	5.27492			0.183760
$825$	26.5498	−	45.9857i	0.924347	−	1.60102i
$826$	5.91238	−	10.2405i	0.205718	−	0.356314i
$827$	5.09967			0.177333			0.0886664	−	0.996061i	$-0.471739\pi$
$827$	5.09967			0.177333			0.0886664	+	0.996061i	$0.471739\pi$
$828$	2.63746	−	4.56821i	0.0916580	−	0.158756i
$829$	22.4124	+	38.8194i	0.778414	+	1.34825i	0.932856	+	0.360251i	$0.117309\pi$
$829$	22.4124	+	38.8194i	0.778414	+	1.34825i	−0.154442	+	0.988002i	$0.549358\pi$
$830$	25.2749	+	43.7774i	0.877305	+	1.51954i
$831$	14.8248			0.514265
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	3.00000			0.103944
$834$	4.54983	+	7.88054i	0.157548	+	0.272881i
$835$		0			0
$836$	13.0997	−	22.6893i	0.453062	−	0.784726i
$837$	−1.27492			−0.0440676
$838$	11.1873	−	19.3770i	0.386459	−	0.669366i
$839$	10.3746	−	17.9693i	0.358170	−	0.620369i	−0.629485	−	0.777013i	$-0.716734\pi$
$839$	10.3746	−	17.9693i	0.358170	−	0.620369i	0.987655	+	0.156643i	$0.0500673\pi$
$840$	4.27492			0.147499
$841$	−19.7371	+	34.1857i	−0.680591	+	1.17882i
$842$	−4.13746	−	7.16629i	−0.142586	−	0.246967i
$843$	10.4124	+	18.0348i	0.358621	+	0.621150i
$844$	21.0997			0.726281
$845$	49.1615	−	25.9153i	1.69121	−	0.891514i
$846$	−6.54983			−0.225188
$847$	−2.50000	−	4.33013i	−0.0859010	−	0.148785i
$848$	1.77492	+	3.07425i	0.0609509	+	0.105570i
$849$	4.72508	−	8.18408i	0.162164	−	0.280877i
$850$	39.8248			1.36598
$851$	0.725083	−	1.25588i	0.0248555	−	0.0430510i
$852$	−2.63746	+	4.56821i	−0.0903578	+	0.156504i
$853$	−14.4502			−0.494764			−0.247382	−	0.968918i	$-0.579570\pi$
$853$	−14.4502			−0.494764			−0.247382	+	0.968918i	$0.579570\pi$
$854$	4.50000	−	7.79423i	0.153987	−	0.266713i
$855$	−14.0000	−	24.2487i	−0.478790	−	0.829288i
$856$	−1.27492	−	2.20822i	−0.0435758	−	0.0754755i
$857$	−36.8248			−1.25791			−0.628955	−	0.777442i	$-0.716517\pi$
$857$	−36.8248			−1.25791			−0.628955	+	0.777442i	$0.716517\pi$
$858$	−14.0000	+	3.46410i	−0.477952	+	0.118262i
$859$	−27.6495			−0.943389			−0.471694	−	0.881762i	$-0.656357\pi$
$859$	−27.6495			−0.943389			−0.471694	+	0.881762i	$0.656357\pi$
$860$	25.2749	+	43.7774i	0.861868	+	1.49280i
$861$	−4.13746	−	7.16629i	−0.141004	−	0.244226i
$862$	6.63746	−	11.4964i	0.226073	−	0.391569i
$863$	35.2990			1.20159			0.600796	−	0.799402i	$-0.294850\pi$
$863$	35.2990			1.20159			0.600796	+	0.799402i	$0.294850\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	9.72508	−	16.8443i	0.330663	−	0.572725i
$866$	−10.2749			−0.349156
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	0.637459	+	1.10411i	0.0216368	+	0.0374760i
$869$	−16.0000	−	27.7128i	−0.542763	−	0.940093i
$870$	35.3746			1.19931
$871$	6.81271	+	7.07997i	0.230840	+	0.239896i
$872$	−4.54983			−0.154077
$873$	0.274917	+	0.476171i	0.00930454	+	0.0161159i
$874$	17.2749	+	29.9210i	0.584333	+	1.01209i
$875$	−17.6873	+	30.6353i	−0.597940	+	1.03566i
$876$	5.72508			0.193433
$877$	1.86254	−	3.22602i	0.0628936	−	0.108935i	−0.832864	−	0.553478i	$-0.813300\pi$
$877$	1.86254	−	3.22602i	0.0628936	−	0.108935i	0.895758	+	0.444543i	$0.146634\pi$
$878$	−6.54983	+	11.3446i	−0.221046	+	0.382863i
$879$	−18.2749			−0.616398
$880$	8.54983	−	14.8087i	0.288215	−	0.499203i
$881$	−0.774917	−	1.34220i	−0.0261076	−	0.0452197i	0.852676	−	0.522439i	$-0.174978\pi$
$881$	−0.774917	−	1.34220i	−0.0261076	−	0.0452197i	−0.878784	+	0.477220i	$0.841645\pi$
$882$	−0.500000	−	0.866025i	−0.0168359	−	0.0291606i
$883$	58.0241			1.95267			0.976333	−	0.216273i	$-0.0693900\pi$
$883$	58.0241			1.95267			0.976333	+	0.216273i	$0.0693900\pi$
$884$	−7.50000	−	7.79423i	−0.252252	−	0.262148i
$885$	−50.5498			−1.69921
$886$	−17.2749	−	29.9210i	−0.580362	−	1.00522i
$887$	−23.2749	−	40.3133i	−0.781495	−	1.35359i	−0.931071	−	0.364839i	$-0.881124\pi$
$887$	−23.2749	−	40.3133i	−0.781495	−	1.35359i	0.149575	−	0.988750i	$-0.452209\pi$
$888$	−0.137459	+	0.238085i	−0.00461281	+	0.00798962i
$889$	8.00000			0.268311
$890$	−1.54983	+	2.68439i	−0.0519506	+	0.0899810i
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	10.7251			0.359102
$893$	21.4502	−	37.1528i	0.717802	−	1.24327i
$894$	0.500000	+	0.866025i	0.0167225	+	0.0289642i
$895$	−3.09967	−	5.36878i	−0.103611	−	0.179459i
$896$	1.00000			0.0334077
$897$	5.27492	−	18.2728i	0.176124	−	0.610113i
$898$	−19.0997			−0.637364
$899$	5.27492	+	9.13642i	0.175928	+	0.304717i
$900$	−6.63746	−	11.4964i	−0.221249	−	0.383214i
$901$	5.32475	−	9.22274i	0.177393	−	0.307254i
$902$	−33.0997			−1.10210
$903$	5.91238	−	10.2405i	0.196752	−	0.340784i
$904$	−7.41238	+	12.8386i	−0.246532	+	0.427006i
$905$	−71.9244			−2.39085
$906$	−6.54983	+	11.3446i	−0.217604	+	0.376901i
$907$	19.9124	+	34.4892i	0.661180	+	1.14520i	0.980306	+	0.197484i	$0.0632772\pi$
$907$	19.9124	+	34.4892i	0.661180	+	1.14520i	−0.319126	+	0.947712i	$0.603389\pi$
$908$	10.5498	+	18.2728i	0.350109	+	0.606406i
$909$	1.72508			0.0572174
$910$	14.9622	−	3.70219i	0.495992	−	0.122726i
$911$	−25.0997			−0.831589			−0.415795	−	0.909459i	$-0.636496\pi$
$911$	−25.0997			−0.831589			−0.415795	+	0.909459i	$0.636496\pi$
$912$	−3.27492	−	5.67232i	−0.108443	−	0.187829i
$913$	−23.6495	−	40.9621i	−0.782684	−	1.35565i
$914$	8.50000	−	14.7224i	0.281155	−	0.486975i
$915$	−38.4743			−1.27192
$916$	−6.36254	+	11.0202i	−0.210224	+	0.364119i
$917$	1.36254	−	2.35999i	0.0449951	−	0.0779338i
$918$	3.00000			0.0990148
$919$	−19.8248	+	34.3375i	−0.653958	+	1.13269i	0.328196	+	0.944610i	$0.393559\pi$
$919$	−19.8248	+	34.3375i	−0.653958	+	1.13269i	−0.982154	+	0.188079i	$0.939774\pi$
$920$	11.2749	+	19.5287i	0.371723	+	0.643843i
$921$	0.725083	+	1.25588i	0.0238923	+	0.0413827i
$922$	−19.3746			−0.638068
$923$	−5.27492	+	18.2728i	−0.173626	+	0.601458i
$924$	−4.00000			−0.131590
$925$	−1.82475	−	3.16056i	−0.0599975	−	0.103919i
$926$	5.27492	+	9.13642i	0.173345	+	0.300242i
$927$	−2.63746	+	4.56821i	−0.0866255	+	0.150040i
$928$	8.27492			0.271637
$929$	−26.7749	+	46.3755i	−0.878457	+	1.52153i	−0.0254221	+	0.999677i	$0.508093\pi$
$929$	−26.7749	+	46.3755i	−0.878457	+	1.52153i	−0.853034	+	0.521855i	$0.825240\pi$
$930$	2.72508	−	4.71998i	0.0893590	−	0.154774i
$931$	6.54983			0.214662
$932$	−3.72508	+	6.45203i	−0.122019	+	0.211343i
$933$	1.27492	+	2.20822i	0.0417389	+	0.0722939i
$934$	4.08762	+	7.07997i	0.133751	+	0.231664i
$935$	−51.2990			−1.67766
$936$	−1.00000	+	3.46410i	−0.0326860	+	0.113228i
$937$	19.1752			0.626428			0.313214	−	0.949683i	$-0.398594\pi$
$937$	19.1752			0.626428			0.313214	+	0.949683i	$0.398594\pi$
$938$	1.36254	+	2.35999i	0.0444886	+	0.0770564i
$939$	−8.82475	−	15.2849i	−0.287985	−	0.498804i
$940$	14.0000	−	24.2487i	0.456630	−	0.790906i
$941$	37.6495			1.22734			0.613669	−	0.789563i	$-0.289693\pi$
$941$	37.6495			1.22734			0.613669	+	0.789563i	$0.289693\pi$
$942$	1.86254	−	3.22602i	0.0606849	−	0.105109i
$943$	21.8248	−	37.8016i	0.710712	−	1.23099i
$944$	−11.8248			−0.384863
$945$	−2.13746	+	3.70219i	−0.0695315	+	0.120432i
$946$	−23.6495	−	40.9621i	−0.768912	−	1.33179i
$947$	4.54983	+	7.88054i	0.147850	+	0.256083i	0.930433	−	0.366463i	$-0.119431\pi$
$947$	4.54983	+	7.88054i	0.147850	+	0.256083i	−0.782583	+	0.622547i	$0.786098\pi$
$948$	−8.00000			−0.259828
$949$	20.0378	−	4.95807i	0.650454	−	0.160946i
$950$	86.9485			2.82098
$951$	3.77492	+	6.53835i	0.122410	+	0.212020i
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	5.54983	−	9.61260i	0.179777	−	0.311383i	−0.762027	−	0.647545i	$-0.775796\pi$
$953$	5.54983	−	9.61260i	0.179777	−	0.311383i	0.941804	+	0.336162i	$0.109129\pi$
$954$	−3.54983			−0.114930
$955$	−14.3746	+	24.8975i	−0.465151	+	0.805665i
$956$	2.63746	−	4.56821i	0.0853015	−	0.147747i
$957$	−33.0997			−1.06996
$958$	−10.0000	+	17.3205i	−0.323085	+	0.559600i
$959$	−11.4124	−	19.7668i	−0.368525	−	0.638304i
$960$	−2.13746	−	3.70219i	−0.0689862	−	0.119488i
$961$	−29.3746			−0.947567
$962$	−0.274917	+	0.952341i	−0.00886369	+	0.0307047i
$963$	2.54983			0.0821673
$964$	7.86254	+	13.6183i	0.253235	+	0.438617i
$965$	53.0619	+	91.9059i	1.70812	+	2.95855i
$966$	2.63746	−	4.56821i	0.0848588	−	0.146980i
$967$	−18.5498			−0.596522			−0.298261	−	0.954484i	$-0.596407\pi$
$967$	−18.5498			−0.596522			−0.298261	+	0.954484i	$0.596407\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	−9.82475	+	17.0170i	−0.315616	+	0.546664i
$970$	−2.35050			−0.0754699
$971$	−24.2870	+	42.0663i	−0.779406	+	1.34997i	0.152879	+	0.988245i	$0.451146\pi$
$971$	−24.2870	+	42.0663i	−0.779406	+	1.34997i	−0.932285	+	0.361725i	$0.882188\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	4.54983	+	7.88054i	0.145861	+	0.252639i
$974$	−1.09967			−0.0352357
$975$	−33.1873	−	34.4892i	−1.06284	−	1.10454i
$976$	−9.00000			−0.288083
$977$	−12.3127	−	21.3262i	−0.393918	−	0.682287i	0.599044	−	0.800716i	$-0.295547\pi$
$977$	−12.3127	−	21.3262i	−0.393918	−	0.682287i	−0.992962	+	0.118429i	$0.962214\pi$
$978$	6.63746	+	11.4964i	0.212243	+	0.367615i
$979$	1.45017	−	2.51176i	0.0463475	−	0.0802762i
$980$	4.27492			0.136557
$981$	2.27492	−	3.94027i	0.0726325	−	0.125803i
$982$	−12.5498	+	21.7370i	−0.400481	+	0.693654i
$983$	53.8488			1.71751			0.858756	−	0.512385i	$-0.171238\pi$
$983$	53.8488			1.71751			0.858756	+	0.512385i	$0.171238\pi$
$984$	−4.13746	+	7.16629i	−0.131897	+	0.228453i
$985$	46.6495	+	80.7993i	1.48638	+	2.57448i
$986$	−12.4124	−	21.4989i	−0.395291	−	0.684663i
$987$	−6.54983			−0.208484
$988$	−16.3746	−	17.0170i	−0.520945	−	0.541382i
$989$	62.3746			1.98340
$990$	8.54983	+	14.8087i	0.271732	+	0.470653i
$991$	18.3746	+	31.8257i	0.583688	+	1.01098i	0.995038	+	0.0994996i	$0.0317242\pi$
$991$	18.3746	+	31.8257i	0.583688	+	1.01098i	−0.411350	+	0.911478i	$0.634942\pi$
$992$	0.637459	−	1.10411i	0.0202393	−	0.0350555i
$993$	4.00000			0.126936
$994$	−2.63746	+	4.56821i	−0.0836551	+	0.144895i
$995$	−25.2749	+	43.7774i	−0.801269	+	1.38784i
$996$	−11.8248			−0.374682
$997$	1.95017	−	3.37779i	0.0617624	−	0.106976i	−0.833491	−	0.552533i	$-0.813661\pi$
$997$	1.95017	−	3.37779i	0.0617624	−	0.106976i	0.895253	+	0.445558i	$0.146995\pi$
$998$	15.9124	+	27.5610i	0.503697	+	0.872430i
$999$	−0.137459	−	0.238085i	−0.00434900	−	0.00753269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.j.211.2	✓	4
3.2	odd	2		1638.2.r.x.757.1		4
13.3	even	3		7098.2.a.ca.1.2		2
13.9	even	3	inner	546.2.l.j.295.2	yes	4
13.10	even	6		7098.2.a.bm.1.1		2
39.35	odd	6		1638.2.r.x.1387.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.j.211.2	✓	4	1.1	even	1	trivial
546.2.l.j.295.2	yes	4	13.9	even	3	inner
1638.2.r.x.757.1		4	3.2	odd	2
1638.2.r.x.1387.1		4	39.35	odd	6
7098.2.a.bm.1.1		2	13.10	even	6
7098.2.a.ca.1.2		2	13.3	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (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} +4.27492 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.13746 - 3.70219i) q^{10} +(2.00000 + 3.46410i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(-2.13746 - 3.70219i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-3.27492 + 5.67232i) q^{19} +(-2.13746 + 3.70219i) q^{20} +1.00000 q^{21} +(2.00000 - 3.46410i) q^{22} +(2.63746 + 4.56821i) q^{23} +(-0.500000 - 0.866025i) q^{24} +13.2749 q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-4.13746 - 7.16629i) q^{29} +(-2.13746 + 3.70219i) q^{30} -1.27492 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +3.00000 q^{34} +(-2.13746 + 3.70219i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.137459 - 0.238085i) q^{37} +6.54983 q^{38} +(-2.50000 - 2.59808i) q^{39} +4.27492 q^{40} +(-4.13746 - 7.16629i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(5.91238 - 10.2405i) q^{43} -4.00000 q^{44} +(-2.13746 + 3.70219i) q^{45} +(2.63746 - 4.56821i) q^{46} -6.54983 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-6.63746 - 11.4964i) q^{50} +3.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} -3.54983 q^{53} +(-0.500000 - 0.866025i) q^{54} +(8.54983 + 14.8087i) q^{55} +(-0.500000 + 0.866025i) q^{56} +6.54983 q^{57} +(-4.13746 + 7.16629i) q^{58} +(5.91238 - 10.2405i) q^{59} +4.27492 q^{60} +(4.50000 - 7.79423i) q^{61} +(0.637459 + 1.10411i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(14.9622 - 3.70219i) q^{65} -4.00000 q^{66} +(1.36254 + 2.35999i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(2.63746 - 4.56821i) q^{69} +4.27492 q^{70} +(-2.63746 + 4.56821i) q^{71} +(-0.500000 + 0.866025i) q^{72} +5.72508 q^{73} +(-0.137459 + 0.238085i) q^{74} +(-6.63746 - 11.4964i) q^{75} +(-3.27492 - 5.67232i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -8.00000 q^{79} +(-2.13746 - 3.70219i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.13746 + 7.16629i) q^{82} -11.8248 q^{83} +(-0.500000 + 0.866025i) q^{84} +(-6.41238 + 11.1066i) q^{85} -11.8248 q^{86} +(-4.13746 + 7.16629i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-0.362541 - 0.627940i) q^{89} +4.27492 q^{90} +(-1.00000 + 3.46410i) q^{91} -5.27492 q^{92} +(0.637459 + 1.10411i) q^{93} +(3.27492 + 5.67232i) q^{94} +(-14.0000 + 24.2487i) q^{95} +1.00000 q^{96} +(0.274917 - 0.476171i) q^{97} +(-0.500000 + 0.866025i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - q^{10} + 8 q^{11} + 4 q^{12} + 14 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{18} + 2 q^{19} - q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - q^10 + 8 * q^11 + 4 * q^12 + 14 * q^13 + 4 * q^14 - q^15 - 2 * q^16 - 6 * q^17 + 4 * q^18 + 2 * q^19 - q^20 + 4 * q^21 + 8 * q^22 + 3 * q^23 - 2 * q^24 + 38 * q^25 - 10 * q^26 + 4 * q^27 - 2 * q^28 - 9 * q^29 - q^30 + 10 * q^31 - 2 * q^32 + 8 * q^33 + 12 * q^34 - q^35 - 2 * q^36 + 7 * q^37 - 4 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 - 2 * q^42 + q^43 - 16 * q^44 - q^45 + 3 * q^46 + 4 * q^47 - 2 * q^48 - 2 * q^49 - 19 * q^50 + 12 * q^51 - 4 * q^52 + 16 * q^53 - 2 * q^54 + 4 * q^55 - 2 * q^56 - 4 * q^57 - 9 * q^58 + q^59 + 2 * q^60 + 18 * q^61 - 5 * q^62 - 2 * q^63 + 4 * q^64 + 7 * q^65 - 16 * q^66 + 13 * q^67 - 6 * q^68 + 3 * q^69 + 2 * q^70 - 3 * q^71 - 2 * q^72 + 38 * q^73 + 7 * q^74 - 19 * q^75 + 2 * q^76 - 16 * q^77 - 4 * q^78 - 32 * q^79 - q^80 - 2 * q^81 - 9 * q^82 - 2 * q^83 - 2 * q^84 - 3 * q^85 - 2 * q^86 - 9 * q^87 + 8 * q^88 - 9 * q^89 + 2 * q^90 - 4 * q^91 - 6 * q^92 - 5 * q^93 - 2 * q^94 - 56 * q^95 + 4 * q^96 - 14 * q^97 - 2 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more