LMFDB - Embedded newform 1218.2.i.d.1045.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(697,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.697"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,-3,-3,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
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			1045.3
Root			$1.09935 - 1.90412i$ of defining polynomial
Character	$\chi$	$=$	1218.1045
Dual form			1218.2.i.d.697.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.09935 - 1.90412i) q^{5} -1.00000 q^{6} +(2.11581 - 1.58850i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.09935 - 1.90412i) q^{10} +(0.582878 + 1.00958i) q^{11} +(-0.500000 + 0.866025i) q^{12} -2.19869 q^{13} +(-0.317776 - 2.62660i) q^{14} -2.19869 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.88092 - 4.98989i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.23490 - 3.87096i) q^{19} -2.19869 q^{20} +(-2.43359 - 1.03810i) q^{21} +1.16576 q^{22} +(0.234898 - 0.406855i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.0828784 + 0.143550i) q^{25} +(-1.09935 + 1.90412i) q^{26} +1.00000 q^{27} +(-2.43359 - 1.03810i) q^{28} +1.00000 q^{29} +(-1.09935 + 1.90412i) q^{30} +(-1.15202 - 1.99536i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.582878 - 1.00958i) q^{33} -5.76183 q^{34} +(-0.698691 - 5.77508i) q^{35} +1.00000 q^{36} +(-0.265102 + 0.459171i) q^{37} +(-2.23490 - 3.87096i) q^{38} +(1.09935 + 1.90412i) q^{39} +(-1.09935 + 1.90412i) q^{40} +1.23817 q^{41} +(-2.11581 + 1.58850i) q^{42} +2.66849 q^{43} +(0.582878 - 1.00958i) q^{44} +(1.09935 + 1.90412i) q^{45} +(-0.234898 - 0.406855i) q^{46} +(-3.85071 + 6.66963i) q^{47} +1.00000 q^{48} +(1.95333 - 6.72194i) q^{49} +0.165757 q^{50} +(-2.88092 + 4.98989i) q^{51} +(1.09935 + 1.90412i) q^{52} +(0.364448 + 0.631243i) q^{53} +(0.500000 - 0.866025i) q^{54} +2.56314 q^{55} +(-2.11581 + 1.58850i) q^{56} -4.46980 q^{57} +(0.500000 - 0.866025i) q^{58} +(-0.834243 - 1.44495i) q^{59} +(1.09935 + 1.90412i) q^{60} +(-3.26783 + 5.66005i) q^{61} -2.30404 q^{62} +(0.317776 + 2.62660i) q^{63} +1.00000 q^{64} +(-2.41712 + 4.18658i) q^{65} +(-0.582878 - 1.00958i) q^{66} +(-0.629550 - 1.09041i) q^{67} +(-2.88092 + 4.98989i) q^{68} -0.469795 q^{69} +(-5.35071 - 2.28245i) q^{70} -11.3699 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.40065 + 5.89011i) q^{73} +(0.265102 + 0.459171i) q^{74} +(0.0828784 - 0.143550i) q^{75} -4.46980 q^{76} +(2.83697 + 1.21017i) q^{77} +2.19869 q^{78} +(-2.28757 + 3.96219i) q^{79} +(1.09935 + 1.90412i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.619085 - 1.07229i) q^{82} -8.02639 q^{83} +(0.317776 + 2.62660i) q^{84} -12.6685 q^{85} +(1.33424 - 2.31098i) q^{86} +(-0.500000 - 0.866025i) q^{87} +(-0.582878 - 1.00958i) q^{88} +(4.08561 - 7.07648i) q^{89} +2.19869 q^{90} +(-4.65202 + 3.49262i) q^{91} -0.469795 q^{92} +(-1.15202 + 1.99536i) q^{93} +(3.85071 + 6.66963i) q^{94} +(-4.91385 - 8.51104i) q^{95} +(0.500000 - 0.866025i) q^{96} +12.9660 q^{97} +(-4.84471 - 5.05260i) q^{98} -1.16576 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} - 6 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 9 q^{11} - 3 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20}+ \cdots - 18 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 - 6 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 9 * q^11 - 3 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 2 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - q^30 + 4 * q^31 + 3 * q^32 + 9 * q^33 - 12 * q^34 + 7 * q^35 + 6 * q^36 - 7 * q^37 - 8 * q^38 + q^39 - q^40 + 30 * q^41 + 4 * q^42 - 6 * q^43 + 9 * q^44 + q^45 + 4 * q^46 - q^47 + 6 * q^48 + 12 * q^49 + 12 * q^50 - 6 * q^51 + q^52 + 2 * q^53 + 3 * q^54 + 4 * q^55 + 4 * q^56 - 16 * q^57 + 3 * q^58 + 6 * q^59 + q^60 + 8 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 - 9 * q^65 - 9 * q^66 - 9 * q^67 - 6 * q^68 + 8 * q^69 - 10 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 7 * q^74 + 6 * q^75 - 16 * q^76 - 27 * q^77 + 2 * q^78 - 3 * q^79 + q^80 - 3 * q^81 + 15 * q^82 + 30 * q^83 + 2 * q^84 - 54 * q^85 - 3 * q^86 - 3 * q^87 - 9 * q^88 - 3 * q^89 + 2 * q^90 - 17 * q^91 + 8 * q^92 + 4 * q^93 + q^94 + 4 * q^95 + 3 * q^96 - 22 * q^97 - 12 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	1.09935	−	1.90412i	0.491642	−	0.851549i	−0.508311	−	0.861173i	$-0.669730\pi$
$5$	1.09935	−	1.90412i	0.491642	−	0.851549i	0.999954	+	0.00962389i	$0.00306343\pi$
$6$	−1.00000			−0.408248
$7$	2.11581	−	1.58850i	0.799702	−	0.600397i
$7$	2.11581	−	1.58850i	0.799702	−	0.600397i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.09935	−	1.90412i	−0.347644	−	0.602136i
$11$	0.582878	+	1.00958i	0.175744	+	0.304398i	0.940419	−	0.340019i	$-0.110433\pi$
$11$	0.582878	+	1.00958i	0.175744	+	0.304398i	−0.764674	+	0.644417i	$0.777100\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.19869			−0.609807			−0.304904	−	0.952383i	$-0.598624\pi$
$13$	−2.19869			−0.609807			−0.304904	+	0.952383i	$0.598624\pi$
$14$	−0.317776	−	2.62660i	−0.0849292	−	0.701988i
$15$	−2.19869			−0.567700
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.88092	−	4.98989i	−0.698725	−	1.21023i	−0.968909	−	0.247418i	$-0.920418\pi$
$17$	−2.88092	−	4.98989i	−0.698725	−	1.21023i	0.270184	−	0.962809i	$-0.412915\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.23490	−	3.87096i	0.512721	−	0.888058i	−0.487171	−	0.873307i	$-0.661971\pi$
$19$	2.23490	−	3.87096i	0.512721	−	0.888058i	0.999891	−	0.0147514i	$-0.00469568\pi$
$20$	−2.19869			−0.491642
$21$	−2.43359	−	1.03810i	−0.531053	−	0.226531i
$22$	1.16576			0.248540
$23$	0.234898	−	0.406855i	0.0489795	−	0.0848350i	−0.840496	−	0.541817i	$-0.817736\pi$
$23$	0.234898	−	0.406855i	0.0489795	−	0.0848350i	0.889476	+	0.456982i	$0.151070\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	0.0828784	+	0.143550i	0.0165757	+	0.0287099i
$26$	−1.09935	+	1.90412i	−0.215599	+	0.373429i
$27$	1.00000			0.192450
$28$	−2.43359	−	1.03810i	−0.459905	−	0.196182i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	−1.09935	+	1.90412i	−0.200712	+	0.347644i
$31$	−1.15202	−	1.99536i	−0.206909	−	0.358376i	0.743830	−	0.668368i	$-0.233007\pi$
$31$	−1.15202	−	1.99536i	−0.206909	−	0.358376i	−0.950739	+	0.309992i	$0.899674\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.582878	−	1.00958i	0.101466	−	0.175744i
$34$	−5.76183			−0.988146
$35$	−0.698691	−	5.77508i	−0.118100	−	0.976166i
$36$	1.00000			0.166667
$37$	−0.265102	+	0.459171i	−0.0435826	+	0.0754872i	−0.886994	−	0.461781i	$-0.847210\pi$
$37$	−0.265102	+	0.459171i	−0.0435826	+	0.0754872i	0.843411	+	0.537269i	$0.180544\pi$
$38$	−2.23490	−	3.87096i	−0.362548	−	0.627952i
$39$	1.09935	+	1.90412i	0.176036	+	0.304904i
$40$	−1.09935	+	1.90412i	−0.173822	+	0.301068i
$41$	1.23817			0.193370			0.0966848	−	0.995315i	$-0.469176\pi$
$41$	1.23817			0.193370			0.0966848	+	0.995315i	$0.469176\pi$
$42$	−2.11581	+	1.58850i	−0.326477	+	0.245111i
$43$	2.66849			0.406940			0.203470	−	0.979081i	$-0.434778\pi$
$43$	2.66849			0.406940			0.203470	+	0.979081i	$0.434778\pi$
$44$	0.582878	−	1.00958i	0.0878722	−	0.152199i
$45$	1.09935	+	1.90412i	0.163881	+	0.283850i
$46$	−0.234898	−	0.406855i	−0.0346338	−	0.0599874i
$47$	−3.85071	+	6.66963i	−0.561684	+	0.972865i	0.435666	+	0.900108i	$0.356513\pi$
$47$	−3.85071	+	6.66963i	−0.561684	+	0.972865i	−0.997350	+	0.0727565i	$0.976820\pi$
$48$	1.00000			0.144338
$49$	1.95333	−	6.72194i	0.279047	−	0.960277i
$50$	0.165757			0.0234416
$51$	−2.88092	+	4.98989i	−0.403409	+	0.698725i
$52$	1.09935	+	1.90412i	0.152452	+	0.264054i
$53$	0.364448	+	0.631243i	0.0500608	+	0.0867078i	0.889970	−	0.456019i	$-0.150725\pi$
$53$	0.364448	+	0.631243i	0.0500608	+	0.0867078i	−0.839909	+	0.542727i	$0.817392\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.56314			0.345614
$56$	−2.11581	+	1.58850i	−0.282737	+	0.212272i
$57$	−4.46980			−0.592039
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	−0.834243	−	1.44495i	−0.108609	−	0.188117i	0.806598	−	0.591101i	$-0.201306\pi$
$59$	−0.834243	−	1.44495i	−0.108609	−	0.188117i	−0.915207	+	0.402984i	$0.867973\pi$
$60$	1.09935	+	1.90412i	0.141925	+	0.245821i
$61$	−3.26783	+	5.66005i	−0.418403	+	0.724695i	−0.995779	−	0.0917831i	$-0.970743\pi$
$61$	−3.26783	+	5.66005i	−0.418403	+	0.724695i	0.577376	+	0.816478i	$0.304077\pi$
$62$	−2.30404			−0.292613
$63$	0.317776	+	2.62660i	0.0400360	+	0.330920i
$64$	1.00000			0.125000
$65$	−2.41712	+	4.18658i	−0.299807	+	0.519281i
$66$	−0.582878	−	1.00958i	−0.0717474	−	0.124270i
$67$	−0.629550	−	1.09041i	−0.0769118	−	0.133215i	0.825004	−	0.565127i	$-0.191173\pi$
$67$	−0.629550	−	1.09041i	−0.0769118	−	0.133215i	−0.901916	+	0.431911i	$0.857839\pi$
$68$	−2.88092	+	4.98989i	−0.349362	+	0.605113i
$69$	−0.469795			−0.0565567
$70$	−5.35071	−	2.28245i	−0.639532	−	0.272806i
$71$	−11.3699			−1.34936			−0.674680	−	0.738110i	$-0.735718\pi$
$71$	−11.3699			−1.34936			−0.674680	+	0.738110i	$0.735718\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	3.40065	+	5.89011i	0.398016	+	0.689385i	0.993481	−	0.113997i	$-0.0363653\pi$
$73$	3.40065	+	5.89011i	0.398016	+	0.689385i	−0.595465	+	0.803382i	$0.703032\pi$
$74$	0.265102	+	0.459171i	0.0308175	+	0.0533775i
$75$	0.0828784	−	0.143550i	0.00956997	−	0.0165757i
$76$	−4.46980			−0.512721
$77$	2.83697	+	1.21017i	0.323303	+	0.137912i
$78$	2.19869			0.248953
$79$	−2.28757	+	3.96219i	−0.257372	+	0.445781i	−0.965537	−	0.260266i	$-0.916190\pi$
$79$	−2.28757	+	3.96219i	−0.257372	+	0.445781i	0.708165	+	0.706047i	$0.249523\pi$
$80$	1.09935	+	1.90412i	0.122911	+	0.212887i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.619085	−	1.07229i	0.0683665	−	0.118414i
$83$	−8.02639			−0.881011			−0.440505	−	0.897750i	$-0.645201\pi$
$83$	−8.02639			−0.881011			−0.440505	+	0.897750i	$0.645201\pi$
$84$	0.317776	+	2.62660i	0.0346722	+	0.286585i
$85$	−12.6685			−1.37409
$86$	1.33424	−	2.31098i	0.143875	−	0.249199i
$87$	−0.500000	−	0.866025i	−0.0536056	−	0.0928477i
$88$	−0.582878	−	1.00958i	−0.0621350	−	0.107621i
$89$	4.08561	−	7.07648i	0.433074	−	0.750105i	−0.564063	−	0.825732i	$-0.690762\pi$
$89$	4.08561	−	7.07648i	0.433074	−	0.750105i	0.997136	+	0.0756266i	$0.0240957\pi$
$90$	2.19869			0.231762
$91$	−4.65202	+	3.49262i	−0.487664	+	0.366126i
$92$	−0.469795			−0.0489795
$93$	−1.15202	+	1.99536i	−0.119459	+	0.206909i
$94$	3.85071	+	6.66963i	0.397170	+	0.687919i
$95$	−4.91385	−	8.51104i	−0.504150	−	0.873214i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	12.9660			1.31650			0.658248	−	0.752801i	$-0.271298\pi$
$97$	12.9660			1.31650			0.658248	+	0.752801i	$0.271298\pi$
$98$	−4.84471	−	5.05260i	−0.489390	−	0.510390i
$99$	−1.16576			−0.117163
$100$	0.0828784	−	0.143550i	0.00828784	−	0.0143550i
$101$	−6.87764	−	11.9124i	−0.684351	−	1.18533i	−0.973640	−	0.228089i	$-0.926752\pi$
$101$	−6.87764	−	11.9124i	−0.684351	−	1.18533i	0.289289	−	0.957242i	$-0.406581\pi$
$102$	2.88092	+	4.98989i	0.285253	+	0.494073i
$103$	9.13828	−	15.8280i	0.900422	−	1.55958i	0.0734740	−	0.997297i	$-0.476591\pi$
$103$	9.13828	−	15.8280i	0.900422	−	1.55958i	0.826948	−	0.562279i	$-0.190075\pi$
$104$	2.19869			0.215599
$105$	−4.65202	+	3.49262i	−0.453991	+	0.340845i
$106$	0.728896			0.0707966
$107$	0.215158	−	0.372665i	0.0208002	−	0.0360269i	−0.855438	−	0.517905i	$-0.826712\pi$
$107$	0.215158	−	0.372665i	0.0208002	−	0.0360269i	0.876238	+	0.481878i	$0.160045\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	7.08561	+	12.2726i	0.678678	+	1.17551i	0.975379	+	0.220535i	$0.0707802\pi$
$109$	7.08561	+	12.2726i	0.678678	+	1.17551i	−0.296701	+	0.954970i	$0.595886\pi$
$110$	1.28157	−	2.21974i	0.122193	−	0.211644i
$111$	0.530205			0.0503248
$112$	0.317776	+	2.62660i	0.0300270	+	0.248190i
$113$	−0.768374			−0.0722826			−0.0361413	−	0.999347i	$-0.511507\pi$
$113$	−0.768374			−0.0722826			−0.0361413	+	0.999347i	$0.511507\pi$
$114$	−2.23490	+	3.87096i	−0.209317	+	0.362548i
$115$	−0.516467	−	0.894547i	−0.0481608	−	0.0834170i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$	1.09935	−	1.90412i	0.101635	−	0.176036i
$118$	−1.66849			−0.153597
$119$	−14.0219	−	5.98134i	−1.28539	−	0.548308i
$120$	2.19869			0.200712
$121$	4.82051	−	8.34936i	0.438228	−	0.759033i
$122$	3.26783	+	5.66005i	0.295856	+	0.512437i
$123$	−0.619085	−	1.07229i	−0.0558210	−	0.0966848i
$124$	−1.15202	+	1.99536i	−0.103454	+	0.179188i
$125$	11.3579			1.01588
$126$	2.43359	+	1.03810i	0.216801	+	0.0924810i
$127$	1.77383			0.157402			0.0787011	−	0.996898i	$-0.474923\pi$
$127$	1.77383			0.157402			0.0787011	+	0.996898i	$0.474923\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.33424	−	2.31098i	−0.117474	−	0.203470i
$130$	2.41712	+	4.18658i	0.211996	+	0.367187i
$131$	−7.87764	+	13.6445i	−0.688273	+	1.19212i	0.284123	+	0.958788i	$0.408297\pi$
$131$	−7.87764	+	13.6445i	−0.688273	+	1.19212i	−0.972396	+	0.233336i	$0.925036\pi$
$132$	−1.16576			−0.101466
$133$	−1.42039	−	11.7404i	−0.123164	−	1.01802i
$134$	−1.25910			−0.108770
$135$	1.09935	−	1.90412i	0.0946166	−	0.163881i
$136$	2.88092	+	4.98989i	0.247036	+	0.427880i
$137$	6.18222	+	10.7079i	0.528183	+	0.914840i	0.999460	+	0.0328547i	$0.0104598\pi$
$137$	6.18222	+	10.7079i	0.528183	+	0.914840i	−0.471277	+	0.881985i	$0.656207\pi$
$138$	−0.234898	+	0.406855i	−0.0199958	+	0.0346338i
$139$	−0.177760			−0.0150774			−0.00753869	−	0.999972i	$-0.502400\pi$
$139$	−0.177760			−0.0150774			−0.00753869	+	0.999972i	$0.502400\pi$
$140$	−4.65202	+	3.49262i	−0.393167	+	0.295181i
$141$	7.70142			0.648577
$142$	−5.68495	+	9.84663i	−0.477071	+	0.826311i
$143$	−1.28157	−	2.21974i	−0.107170	−	0.185624i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.09935	−	1.90412i	0.0912957	−	0.158129i
$146$	6.80131			0.562880
$147$	−6.79804	+	1.66934i	−0.560693	+	0.137685i
$148$	0.530205			0.0435826
$149$	3.77110	−	6.53174i	0.308941	−	0.535101i	−0.669190	−	0.743091i	$-0.733359\pi$
$149$	3.77110	−	6.53174i	0.308941	−	0.535101i	0.978131	+	0.207990i	$0.0666921\pi$
$150$	−0.0828784	−	0.143550i	−0.00676699	−	0.0117208i
$151$	3.38092	+	5.85592i	0.275135	+	0.476548i	0.970169	−	0.242429i	$-0.0779441\pi$
$151$	3.38092	+	5.85592i	0.275135	+	0.476548i	−0.695034	+	0.718977i	$0.744611\pi$
$152$	−2.23490	+	3.87096i	−0.181274	+	0.313976i
$153$	5.76183			0.465816
$154$	2.46652	−	1.85181i	0.198758	−	0.149223i
$155$	−5.06587			−0.406900
$156$	1.09935	−	1.90412i	0.0880181	−	0.152452i
$157$	4.59935	+	7.96630i	0.367068	+	0.635780i	0.989106	−	0.147207i	$-0.0470284\pi$
$157$	4.59935	+	7.96630i	0.367068	+	0.635780i	−0.622038	+	0.782987i	$0.713695\pi$
$158$	2.28757	+	3.96219i	0.181989	+	0.315215i
$159$	0.364448	−	0.631243i	0.0289026	−	0.0500608i
$160$	2.19869			0.173822
$161$	−0.149290	−	1.23396i	−0.0117657	−	0.0972499i
$162$	−1.00000			−0.0785674
$163$	5.62628	−	9.74500i	0.440684	−	0.763287i	−0.557056	−	0.830475i	$-0.688069\pi$
$163$	5.62628	−	9.74500i	0.440684	−	0.763287i	0.997740	+	0.0671874i	$0.0214026\pi$
$164$	−0.619085	−	1.07229i	−0.0483424	−	0.0837315i
$165$	−1.28157	−	2.21974i	−0.0997701	−	0.172807i
$166$	−4.01320	+	6.95106i	−0.311484	+	0.539507i
$167$	9.03948			0.699496			0.349748	−	0.936844i	$-0.386267\pi$
$167$	9.03948			0.699496			0.349748	+	0.936844i	$0.386267\pi$
$168$	2.43359	+	1.03810i	0.187755	+	0.0800909i
$169$	−8.16576			−0.628135
$170$	−6.33424	+	10.9712i	−0.485814	+	0.841455i
$171$	2.23490	+	3.87096i	0.170907	+	0.296019i
$172$	−1.33424	−	2.31098i	−0.101735	−	0.176210i
$173$	12.6021	−	21.8274i	0.958118	−	1.65951i	0.231052	−	0.972941i	$-0.425783\pi$
$173$	12.6021	−	21.8274i	0.958118	−	1.65951i	0.727066	−	0.686568i	$-0.240883\pi$
$174$	−1.00000			−0.0758098
$175$	0.403384	+	0.172072i	0.0304930	+	0.0130074i
$176$	−1.16576			−0.0878722
$177$	−0.834243	+	1.44495i	−0.0627056	+	0.108609i
$178$	−4.08561	−	7.07648i	−0.306229	−	0.530405i
$179$	−4.80077	−	8.31517i	−0.358826	−	0.621505i	0.628939	−	0.777455i	$-0.283490\pi$
$179$	−4.80077	−	8.31517i	−0.358826	−	0.621505i	−0.987765	+	0.155950i	$0.950156\pi$
$180$	1.09935	−	1.90412i	0.0819404	−	0.141925i
$181$	23.7673			1.76661			0.883304	−	0.468800i	$-0.155313\pi$
$181$	23.7673			1.76661			0.883304	+	0.468800i	$0.155313\pi$
$182$	0.698691	+	5.77508i	0.0517904	+	0.428077i
$183$	6.53566			0.483130
$184$	−0.234898	+	0.406855i	−0.0173169	+	0.0299937i
$185$	0.582878	+	1.00958i	0.0428541	+	0.0742254i
$186$	1.15202	+	1.99536i	0.0844701	+	0.146307i
$187$	3.35845	−	5.81700i	0.245594	−	0.425381i
$188$	7.70142			0.561684
$189$	2.11581	−	1.58850i	0.153903	−	0.115546i
$190$	−9.82770			−0.712976
$191$	−5.52693	+	9.57293i	−0.399915	+	0.692673i	−0.993715	−	0.111940i	$-0.964294\pi$
$191$	−5.52693	+	9.57293i	−0.399915	+	0.692673i	0.593800	+	0.804613i	$0.297627\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	7.46379	+	12.9277i	0.537256	+	0.930554i	0.999050	+	0.0435673i	$0.0138723\pi$
$193$	7.46379	+	12.9277i	0.537256	+	0.930554i	−0.461795	+	0.886987i	$0.652794\pi$
$194$	6.48299	−	11.2289i	0.465452	−	0.806186i
$195$	4.83424			0.346187
$196$	−6.79804	+	1.66934i	−0.485574	+	0.119239i
$197$	17.3030			1.23278			0.616392	−	0.787439i	$-0.288594\pi$
$197$	17.3030			1.23278			0.616392	+	0.787439i	$0.288594\pi$
$198$	−0.582878	+	1.00958i	−0.0414234	+	0.0717474i
$199$	11.7810	+	20.4053i	0.835135	+	1.44650i	0.893921	+	0.448225i	$0.147944\pi$
$199$	11.7810	+	20.4053i	0.835135	+	1.44650i	−0.0587857	+	0.998271i	$0.518723\pi$
$200$	−0.0828784	−	0.143550i	−0.00586039	−	0.0101505i
$201$	−0.629550	+	1.09041i	−0.0444051	+	0.0769118i
$202$	−13.7553			−0.967819
$203$	2.11581	−	1.58850i	0.148501	−	0.111491i
$204$	5.76183			0.403409
$205$	1.36118	−	2.35763i	0.0950687	−	0.164664i
$206$	−9.13828	−	15.8280i	−0.636694	−	1.10279i
$207$	0.234898	+	0.406855i	0.0163265	+	0.0282783i
$208$	1.09935	−	1.90412i	0.0762259	−	0.132027i
$209$	5.21069			0.360431
$210$	0.698691	+	5.77508i	0.0482143	+	0.398518i
$211$	−18.8068			−1.29471			−0.647356	−	0.762188i	$-0.724125\pi$
$211$	−18.8068			−1.29471			−0.647356	+	0.762188i	$0.724125\pi$
$212$	0.364448	−	0.631243i	0.0250304	−	0.0433539i
$213$	5.68495	+	9.84663i	0.389527	+	0.674680i
$214$	−0.215158	−	0.372665i	−0.0147079	−	0.0254749i
$215$	2.93359	−	5.08112i	0.200069	−	0.346530i
$216$	−1.00000			−0.0680414
$217$	−5.60708	−	2.39182i	−0.380634	−	0.162367i
$218$	14.1712			0.959796
$219$	3.40065	−	5.89011i	0.229795	−	0.398016i
$220$	−1.28157	−	2.21974i	−0.0864034	−	0.149655i
$221$	6.33424	+	10.9712i	0.426087	+	0.738005i
$222$	0.265102	−	0.459171i	0.0177925	−	0.0308175i
$223$	−1.33806			−0.0896030			−0.0448015	−	0.998996i	$-0.514266\pi$
$223$	−1.33806			−0.0896030			−0.0448015	+	0.998996i	$0.514266\pi$
$224$	2.43359	+	1.03810i	0.162601	+	0.0693608i
$225$	−0.165757			−0.0110505
$226$	−0.384187	+	0.665432i	−0.0255558	+	0.0442639i
$227$	−6.68495	−	11.5787i	−0.443696	−	0.768504i	0.554264	−	0.832341i	$-0.313000\pi$
$227$	−6.68495	−	11.5787i	−0.443696	−	0.768504i	−0.997960	+	0.0638367i	$0.979666\pi$
$228$	2.23490	+	3.87096i	0.148010	+	0.256360i
$229$	1.81177	−	3.13809i	0.119725	−	0.207371i	−0.799933	−	0.600089i	$-0.795132\pi$
$229$	1.81177	−	3.13809i	0.119725	−	0.207371i	0.919659	+	0.392718i	$0.128465\pi$
$230$	−1.03293			−0.0681097
$231$	−0.370450	−	3.06197i	−0.0243738	−	0.201463i
$232$	−1.00000			−0.0656532
$233$	9.47699	−	16.4146i	0.620858	−	1.07536i	−0.368468	−	0.929640i	$-0.620118\pi$
$233$	9.47699	−	16.4146i	0.620858	−	1.07536i	0.989326	−	0.145718i	$-0.0465491\pi$
$234$	−1.09935	−	1.90412i	−0.0718665	−	0.124476i
$235$	8.46652	+	14.6644i	0.552295	+	0.956603i
$236$	−0.834243	+	1.44495i	−0.0543046	+	0.0940583i
$237$	4.57514			0.297187
$238$	−12.1910	+	9.15267i	−0.790222	+	0.593280i
$239$	15.9935			1.03453			0.517265	−	0.855825i	$-0.326950\pi$
$239$	15.9935			1.03453			0.517265	+	0.855825i	$0.326950\pi$
$240$	1.09935	−	1.90412i	0.0709625	−	0.122911i
$241$	12.0252	+	20.8283i	0.774611	+	1.34167i	0.935013	+	0.354614i	$0.115388\pi$
$241$	12.0252	+	20.8283i	0.774611	+	1.34167i	−0.160402	+	0.987052i	$0.551279\pi$
$242$	−4.82051	−	8.34936i	−0.309874	−	0.536717i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	6.53566			0.418403
$245$	−10.6520	−	11.1091i	−0.680533	−	0.709735i
$246$	−1.23817			−0.0789428
$247$	−4.91385	+	8.51104i	−0.312661	+	0.541544i
$248$	1.15202	+	1.99536i	0.0731533	+	0.126705i
$249$	4.01320	+	6.95106i	0.254326	+	0.440505i
$250$	5.67895	−	9.83623i	0.359168	−	0.622098i
$251$	3.07241			0.193929			0.0969645	−	0.995288i	$-0.469087\pi$
$251$	3.07241			0.193929			0.0969645	+	0.995288i	$0.469087\pi$
$252$	2.11581	−	1.58850i	0.133284	−	0.100066i
$253$	0.547667			0.0344315
$254$	0.886917	−	1.53618i	0.0556501	−	0.0963888i
$255$	6.33424	+	10.9712i	0.396666	+	0.687045i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.91112	−	5.04221i	0.181591	−	0.314524i	−0.760832	−	0.648949i	$-0.775209\pi$
$257$	2.91112	−	5.04221i	0.181591	−	0.314524i	0.942422	+	0.334425i	$0.108542\pi$
$258$	−2.66849			−0.166133
$259$	0.168486	+	1.39264i	0.0104692	+	0.0865341i
$260$	4.83424			0.299807
$261$	−0.500000	+	0.866025i	−0.0309492	+	0.0536056i
$262$	7.87764	+	13.6445i	0.486682	+	0.842959i
$263$	−7.85790	−	13.6103i	−0.484539	−	0.839246i	0.515303	−	0.857008i	$-0.327679\pi$
$263$	−7.85790	−	13.6103i	−0.484539	−	0.839246i	−0.999842	+	0.0177616i	$0.994346\pi$
$264$	−0.582878	+	1.00958i	−0.0358737	+	0.0621350i
$265$	1.60262			0.0984480
$266$	−10.8776	−	4.64008i	−0.666951	−	0.284502i
$267$	−8.17122			−0.500070
$268$	−0.629550	+	1.09041i	−0.0384559	+	0.0666076i
$269$	−13.9830	−	24.2192i	−0.852558	−	1.47667i	−0.878892	−	0.477021i	$-0.841717\pi$
$269$	−13.9830	−	24.2192i	−0.852558	−	1.47667i	0.0263342	−	0.999653i	$-0.491617\pi$
$270$	−1.09935	−	1.90412i	−0.0669040	−	0.115881i
$271$	9.06314	−	15.6978i	0.550547	−	0.953575i	−0.447689	−	0.894190i	$-0.647753\pi$
$271$	9.06314	−	15.6978i	0.550547	−	0.953575i	0.998235	−	0.0593850i	$-0.0189140\pi$
$272$	5.76183			0.349362
$273$	5.35071	+	2.28245i	0.323840	+	0.138140i
$274$	12.3644			0.746964
$275$	−0.0966161	+	0.167344i	−0.00582617	+	0.0100912i
$276$	0.234898	+	0.406855i	0.0141392	+	0.0244898i
$277$	10.1323	+	17.5496i	0.608790	+	1.05445i	0.991440	+	0.130562i	$0.0416780\pi$
$277$	10.1323	+	17.5496i	0.608790	+	1.05445i	−0.382651	+	0.923893i	$0.624989\pi$
$278$	−0.0888799	+	0.153944i	−0.00533066	+	0.00923297i
$279$	2.30404			0.137939
$280$	0.698691	+	5.77508i	0.0417548	+	0.345127i
$281$	−9.59607			−0.572454			−0.286227	−	0.958162i	$-0.592401\pi$
$281$	−9.59607			−0.572454			−0.286227	+	0.958162i	$0.592401\pi$
$282$	3.85071	−	6.66963i	0.229306	−	0.397170i
$283$	−0.986262	−	1.70826i	−0.0586272	−	0.101545i	0.835222	−	0.549913i	$-0.185339\pi$
$283$	−0.986262	−	1.70826i	−0.0586272	−	0.101545i	−0.893849	+	0.448367i	$0.852006\pi$
$284$	5.68495	+	9.84663i	0.337340	+	0.584290i
$285$	−4.91385	+	8.51104i	−0.291071	+	0.504150i
$286$	−2.56314			−0.151562
$287$	2.61973	−	1.96683i	0.154638	−	0.116099i
$288$	−1.00000			−0.0589256
$289$	−8.09935	+	14.0285i	−0.476432	+	0.825205i
$290$	−1.09935	−	1.90412i	−0.0645558	−	0.111814i
$291$	−6.48299	−	11.2289i	−0.380040	−	0.658248i
$292$	3.40065	−	5.89011i	0.199008	−	0.344692i
$293$	−12.3819			−0.723359			−0.361679	−	0.932303i	$-0.617797\pi$
$293$	−12.3819			−0.723359			−0.361679	+	0.932303i	$0.617797\pi$
$294$	−1.95333	+	6.72194i	−0.113920	+	0.392032i
$295$	−3.66849			−0.213588
$296$	0.265102	−	0.459171i	0.0154088	−	0.0266888i
$297$	0.582878	+	1.00958i	0.0338220	+	0.0585815i
$298$	−3.77110	−	6.53174i	−0.218454	−	0.378374i
$299$	−0.516467	+	0.894547i	−0.0298681	+	0.0517330i
$300$	−0.165757			−0.00956997
$301$	5.64602	−	4.23889i	0.325431	−	0.244326i
$302$	6.76183			0.389100
$303$	−6.87764	+	11.9124i	−0.395110	+	0.684351i
$304$	2.23490	+	3.87096i	0.128180	+	0.222015i
$305$	7.18495	+	12.4447i	0.411409	+	0.712582i
$306$	2.88092	−	4.98989i	0.164691	−	0.285253i
$307$	9.76729			0.557449			0.278724	−	0.960371i	$-0.410088\pi$
$307$	9.76729			0.557449			0.278724	+	0.960371i	$0.410088\pi$
$308$	−0.370450	−	3.06197i	−0.0211083	−	0.174472i
$309$	−18.2766			−1.03972
$310$	−2.53293	+	4.38717i	−0.143861	+	0.249175i
$311$	−7.54340	−	13.0656i	−0.427747	−	0.740880i	0.568926	−	0.822389i	$-0.307359\pi$
$311$	−7.54340	−	13.0656i	−0.427747	−	0.740880i	−0.996673	+	0.0815095i	$0.974026\pi$
$312$	−1.09935	−	1.90412i	−0.0622382	−	0.107800i
$313$	13.7843	−	23.8751i	0.779135	−	1.34950i	−0.153306	−	0.988179i	$-0.548992\pi$
$313$	13.7843	−	23.8751i	0.779135	−	1.34950i	0.932441	−	0.361322i	$-0.117675\pi$
$314$	9.19869			0.519112
$315$	5.35071	+	2.28245i	0.301478	+	0.128602i
$316$	4.57514			0.257372
$317$	−0.287571	+	0.498088i	−0.0161516	+	0.0279754i	−0.873988	−	0.485947i	$-0.838475\pi$
$317$	−0.287571	+	0.498088i	−0.0161516	+	0.0279754i	0.857837	+	0.513922i	$0.171808\pi$
$318$	−0.364448	−	0.631243i	−0.0204372	−	0.0353983i
$319$	0.582878	+	1.00958i	0.0326349	+	0.0565253i
$320$	1.09935	−	1.90412i	0.0614553	−	0.106444i
$321$	−0.430317			−0.0240179
$322$	−1.14329	−	0.487693i	−0.0637130	−	0.0271781i
$323$	−25.7542			−1.43300
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−0.182224	−	0.315621i	−0.0101080	−	0.0175075i
$326$	−5.62628	−	9.74500i	−0.311611	−	0.539726i
$327$	7.08561	−	12.2726i	0.391835	−	0.678678i
$328$	−1.23817			−0.0683665
$329$	2.44733	+	20.2285i	0.134925	+	1.11524i
$330$	−2.56314			−0.141096
$331$	3.39019	−	5.87198i	0.186342	−	0.322753i	−0.757686	−	0.652619i	$-0.773670\pi$
$331$	3.39019	−	5.87198i	0.186342	−	0.322753i	0.944028	+	0.329866i	$0.107004\pi$
$332$	4.01320	+	6.95106i	0.220253	+	0.381489i
$333$	−0.265102	−	0.459171i	−0.0145275	−	0.0251624i
$334$	4.51974	−	7.82842i	0.247309	−	0.428352i
$335$	−2.76837			−0.151252
$336$	2.11581	−	1.58850i	0.115427	−	0.0866598i
$337$	6.76075			0.368281			0.184141	−	0.982900i	$-0.441050\pi$
$337$	6.76075			0.368281			0.184141	+	0.982900i	$0.441050\pi$
$338$	−4.08288	+	7.07175i	−0.222079	+	0.384653i
$339$	0.384187	+	0.665432i	0.0208662	+	0.0361413i
$340$	6.33424	+	10.9712i	0.343523	+	0.594999i
$341$	1.34297	−	2.32610i	0.0727261	−	0.125965i
$342$	4.46980			0.241699
$343$	−6.54494	−	17.3252i	−0.353393	−	0.935475i
$344$	−2.66849			−0.143875
$345$	−0.516467	+	0.894547i	−0.0278057	+	0.0481608i
$346$	−12.6021	−	21.8274i	−0.677492	−	1.17345i
$347$	−0.519739	−	0.900215i	−0.0279011	−	0.0483260i	0.851738	−	0.523968i	$-0.175549\pi$
$347$	−0.519739	−	0.900215i	−0.0279011	−	0.0483260i	−0.879639	+	0.475642i	$0.842216\pi$
$348$	−0.500000	+	0.866025i	−0.0268028	+	0.0464238i
$349$	6.20415			0.332101			0.166050	−	0.986117i	$-0.446899\pi$
$349$	6.20415			0.332101			0.166050	+	0.986117i	$0.446899\pi$
$350$	0.350710	−	0.263305i	0.0187463	−	0.0140742i
$351$	−2.19869			−0.117357
$352$	−0.582878	+	1.00958i	−0.0310675	+	0.0538105i
$353$	3.94133	+	6.82658i	0.209776	+	0.363342i	0.951644	−	0.307204i	$-0.0993933\pi$
$353$	3.94133	+	6.82658i	0.209776	+	0.363342i	−0.741868	+	0.670546i	$0.766060\pi$
$354$	0.834243	+	1.44495i	0.0443395	+	0.0767983i
$355$	−12.4995	+	21.6497i	−0.663402	+	1.14905i
$356$	−8.17122			−0.433074
$357$	1.83097	+	15.1340i	0.0969053	+	0.800977i
$358$	−9.60153			−0.507457
$359$	4.34798	−	7.53092i	0.229478	−	0.397467i	−0.728176	−	0.685390i	$-0.759632\pi$
$359$	4.34798	−	7.53092i	0.229478	−	0.397467i	0.957653	+	0.287923i	$0.0929649\pi$
$360$	−1.09935	−	1.90412i	−0.0579406	−	0.100356i
$361$	−0.489534	−	0.847898i	−0.0257650	−	0.0446262i
$362$	11.8836	−	20.5831i	0.624591	−	1.08182i
$363$	−9.64101			−0.506022
$364$	5.35071	+	2.28245i	0.280453	+	0.119633i
$365$	14.9540			0.782727
$366$	3.26783	−	5.66005i	0.170812	−	0.295856i
$367$	4.97972	+	8.62513i	0.259939	+	0.450228i	0.966225	−	0.257699i	$-0.0829641\pi$
$367$	4.97972	+	8.62513i	0.259939	+	0.450228i	−0.706286	+	0.707926i	$0.749631\pi$
$368$	0.234898	+	0.406855i	0.0122449	+	0.0212088i
$369$	−0.619085	+	1.07229i	−0.0322283	+	0.0558210i
$370$	1.16576			0.0606048
$371$	1.77383	+	0.756665i	0.0920928	+	0.0392841i
$372$	2.30404			0.119459
$373$	−7.29476	+	12.6349i	−0.377709	+	0.654211i	−0.990728	−	0.135857i	$-0.956621\pi$
$373$	−7.29476	+	12.6349i	−0.377709	+	0.654211i	0.613020	+	0.790068i	$0.289955\pi$
$374$	−3.35845	−	5.81700i	−0.173661	−	0.300790i
$375$	−5.67895	−	9.83623i	−0.293260	−	0.507941i
$376$	3.85071	−	6.66963i	0.198585	−	0.343960i
$377$	−2.19869			−0.113238
$378$	−0.317776	−	2.62660i	−0.0163446	−	0.135098i
$379$	−19.6829			−1.01104			−0.505521	−	0.862814i	$-0.668700\pi$
$379$	−19.6829			−1.01104			−0.505521	+	0.862814i	$0.668700\pi$
$380$	−4.91385	+	8.51104i	−0.252075	+	0.436607i
$381$	−0.886917	−	1.53618i	−0.0454381	−	0.0787011i
$382$	5.52693	+	9.57293i	0.282782	+	0.489794i
$383$	2.62628	−	4.54885i	0.134197	−	0.232435i	−0.791094	−	0.611695i	$-0.790488\pi$
$383$	2.62628	−	4.54885i	0.134197	−	0.232435i	0.925290	+	0.379260i	$0.123821\pi$
$384$	−1.00000			−0.0510310
$385$	5.42312	−	4.07155i	0.276388	−	0.207505i
$386$	14.9276			0.759794
$387$	−1.33424	+	2.31098i	−0.0678234	+	0.117474i
$388$	−6.48299	−	11.2289i	−0.329124	−	0.570059i
$389$	−0.257366	−	0.445771i	−0.0130490	−	0.0226015i	0.859427	−	0.511258i	$-0.170820\pi$
$389$	−0.257366	−	0.445771i	−0.0130490	−	0.0226015i	−0.872476	+	0.488657i	$0.837487\pi$
$390$	2.41712	−	4.18658i	0.122396	−	0.211996i
$391$	−2.70688			−0.136893
$392$	−1.95333	+	6.72194i	−0.0986580	+	0.339509i
$393$	15.7553			0.794749
$394$	8.65148	−	14.9848i	0.435855	−	0.754923i
$395$	5.02966	+	8.71163i	0.253070	+	0.438330i
$396$	0.582878	+	1.00958i	0.0292907	+	0.0507331i
$397$	15.0823	−	26.1234i	0.756961	−	1.31109i	−0.187433	−	0.982277i	$-0.560017\pi$
$397$	15.0823	−	26.1234i	0.756961	−	1.31109i	0.944394	−	0.328817i	$-0.106650\pi$
$398$	23.5621			1.18106
$399$	−9.45725	+	7.10027i	−0.473455	+	0.355458i
$400$	−0.165757			−0.00828784
$401$	−2.90011	+	5.02314i	−0.144825	+	0.250844i	−0.929308	−	0.369307i	$-0.879595\pi$
$401$	−2.90011	+	5.02314i	−0.144825	+	0.250844i	0.784483	+	0.620151i	$0.212928\pi$
$402$	0.629550	+	1.09041i	0.0313991	+	0.0543849i
$403$	2.53293	+	4.38717i	0.126174	+	0.218541i
$404$	−6.87764	+	11.9124i	−0.342176	+	0.592665i
$405$	−2.19869			−0.109254
$406$	−0.317776	−	2.62660i	−0.0157710	−	0.130356i
$407$	−0.618090			−0.0306376
$408$	2.88092	−	4.98989i	0.142627	−	0.247036i
$409$	6.79749	+	11.7736i	0.336114	+	0.582167i	0.983698	−	0.179827i	$-0.0575538\pi$
$409$	6.79749	+	11.7736i	0.336114	+	0.582167i	−0.647584	+	0.761994i	$0.724220\pi$
$410$	−1.36118	−	2.35763i	−0.0672237	−	0.116435i
$411$	6.18222	−	10.7079i	0.304947	−	0.528183i
$412$	−18.2766			−0.900422
$413$	−4.06041	−	1.73205i	−0.199800	−	0.0852286i
$414$	0.469795			0.0230892
$415$	−8.82378	+	15.2832i	−0.433142	+	0.750224i
$416$	−1.09935	−	1.90412i	−0.0538999	−	0.0933573i
$417$	0.0888799	+	0.153944i	0.00435247	+	0.00753869i
$418$	2.60535	−	4.51259i	0.127432	−	0.220718i
$419$	−16.6105			−0.811474			−0.405737	−	0.913990i	$-0.632985\pi$
$419$	−16.6105			−0.811474			−0.405737	+	0.913990i	$0.632985\pi$
$420$	5.35071	+	2.28245i	0.261088	+	0.111372i
$421$	−27.0713			−1.31938			−0.659688	−	0.751540i	$-0.729312\pi$
$421$	−27.0713			−1.31938			−0.659688	+	0.751540i	$0.729312\pi$
$422$	−9.40338	+	16.2871i	−0.457750	+	0.792846i
$423$	−3.85071	−	6.66963i	−0.187228	−	0.324288i
$424$	−0.364448	−	0.631243i	−0.0176992	−	0.0306558i
$425$	0.477531	−	0.827109i	0.0231637	−	0.0401207i
$426$	11.3699			0.550874
$427$	2.07688	+	17.1666i	0.100507	+	0.830748i
$428$	−0.430317			−0.0208002
$429$	−1.28157	+	2.21974i	−0.0618748	+	0.107170i
$430$	−2.93359	−	5.08112i	−0.141470	−	0.245034i
$431$	19.1395	+	33.1505i	0.921916	+	1.59681i	0.796447	+	0.604708i	$0.206710\pi$
$431$	19.1395	+	33.1505i	0.921916	+	1.59681i	0.125469	+	0.992098i	$0.459957\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	2.25364			0.108303			0.0541516	−	0.998533i	$-0.482755\pi$
$433$	2.25364			0.108303			0.0541516	+	0.998533i	$0.482755\pi$
$434$	−4.87491	+	3.65997i	−0.234003	+	0.175684i
$435$	−2.19869			−0.105419
$436$	7.08561	−	12.2726i	0.339339	−	0.587753i
$437$	−1.04994	−	1.81856i	−0.0502256	−	0.0869933i
$438$	−3.40065	−	5.89011i	−0.162490	−	0.281440i
$439$	0.251907	−	0.436316i	0.0120229	−	0.0208242i	−0.859951	−	0.510376i	$-0.829506\pi$
$439$	0.251907	−	0.436316i	0.0120229	−	0.0208242i	0.871974	+	0.489552i	$0.162840\pi$
$440$	−2.56314			−0.122193
$441$	4.84471	+	5.05260i	0.230700	+	0.240600i
$442$	12.6685			0.602578
$443$	0.830971	−	1.43928i	0.0394806	−	0.0683825i	−0.845610	−	0.533801i	$-0.820763\pi$
$443$	0.830971	−	1.43928i	0.0394806	−	0.0683825i	0.885091	+	0.465419i	$0.154096\pi$
$444$	−0.265102	−	0.459171i	−0.0125812	−	0.0217913i
$445$	−8.98299	−	15.5590i	−0.425835	−	0.737567i
$446$	−0.669029	+	1.15879i	−0.0316794	+	0.0548704i
$447$	−7.54221			−0.356734
$448$	2.11581	−	1.58850i	0.0999628	−	0.0750496i
$449$	−27.2436			−1.28571			−0.642853	−	0.765989i	$-0.722249\pi$
$449$	−27.2436			−1.28571			−0.642853	+	0.765989i	$0.722249\pi$
$450$	−0.0828784	+	0.143550i	−0.00390693	+	0.00676699i
$451$	0.721702	+	1.25002i	0.0339836	+	0.0588614i
$452$	0.384187	+	0.665432i	0.0180706	+	0.0312993i
$453$	3.38092	−	5.85592i	0.158849	−	0.275135i
$454$	−13.3699			−0.627481
$455$	1.53621	+	12.6976i	0.0720185	+	0.595273i
$456$	4.46980			0.209317
$457$	15.1395	−	26.2223i	0.708195	−	1.22663i	−0.257331	−	0.966323i	$-0.582843\pi$
$457$	15.1395	−	26.2223i	0.708195	−	1.22663i	0.965526	−	0.260306i	$-0.0838235\pi$
$458$	−1.81177	−	3.13809i	−0.0846587	−	0.146633i
$459$	−2.88092	−	4.98989i	−0.134470	−	0.232908i
$460$	−0.516467	+	0.894547i	−0.0240804	+	0.0417085i
$461$	26.0988			1.21554			0.607771	−	0.794112i	$-0.292064\pi$
$461$	26.0988			1.21554			0.607771	+	0.794112i	$0.292064\pi$
$462$	−2.83697	−	1.21017i	−0.131988	−	0.0563021i
$463$	−8.03185			−0.373272			−0.186636	−	0.982429i	$-0.559758\pi$
$463$	−8.03185			−0.373272			−0.186636	+	0.982429i	$0.559758\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	2.53293	+	4.38717i	0.117462	+	0.203450i
$466$	−9.47699	−	16.4146i	−0.439013	−	0.760393i
$467$	−6.21516	+	10.7650i	−0.287603	+	0.498143i	−0.973237	−	0.229803i	$-0.926192\pi$
$467$	−6.21516	+	10.7650i	−0.287603	+	0.498143i	0.685634	+	0.727947i	$0.259525\pi$
$468$	−2.19869			−0.101635
$469$	−3.06413	−	1.30707i	−0.141489	−	0.0603548i
$470$	16.9330			0.781063
$471$	4.59935	−	7.96630i	0.211927	−	0.367068i
$472$	0.834243	+	1.44495i	0.0383992	+	0.0665093i
$473$	1.55540	+	2.69404i	0.0715175	+	0.123872i
$474$	2.28757	−	3.96219i	0.105072	−	0.181989i
$475$	0.740899			0.0339948
$476$	1.83097	+	15.1340i	0.0839224	+	0.693666i
$477$	−0.728896			−0.0333739
$478$	7.99673	−	13.8507i	0.365762	−	0.633518i
$479$	7.18168	+	12.4390i	0.328139	+	0.568354i	0.982143	−	0.188138i	$-0.0602451\pi$
$479$	7.18168	+	12.4390i	0.328139	+	0.568354i	−0.654003	+	0.756492i	$0.726912\pi$
$480$	−1.09935	−	1.90412i	−0.0501780	−	0.0869109i
$481$	0.582878	−	1.00958i	0.0265770	−	0.0460327i
$482$	24.0504			1.09547
$483$	−0.993999	+	0.746270i	−0.0452285	+	0.0339565i
$484$	−9.64101			−0.438228
$485$	14.2541	−	24.6888i	0.647245	−	1.12106i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	9.28430	+	16.0809i	0.420712	+	0.728694i	0.996009	−	0.0892501i	$-0.0284470\pi$
$487$	9.28430	+	16.0809i	0.420712	+	0.728694i	−0.575297	+	0.817944i	$0.695114\pi$
$488$	3.26783	−	5.66005i	0.147928	−	0.256218i
$489$	−11.2526			−0.508858
$490$	−14.9468	+	3.67036i	−0.675227	+	0.165810i
$491$	−18.1976			−0.821246			−0.410623	−	0.911805i	$-0.634689\pi$
$491$	−18.1976			−0.821246			−0.410623	+	0.911805i	$0.634689\pi$
$492$	−0.619085	+	1.07229i	−0.0279105	+	0.0483424i
$493$	−2.88092	−	4.98989i	−0.129750	−	0.224733i
$494$	4.91385	+	8.51104i	0.221085	+	0.382930i
$495$	−1.28157	+	2.21974i	−0.0576023	+	0.0997701i
$496$	2.30404			0.103454
$497$	−24.0566	+	18.0611i	−1.07909	+	0.810152i
$498$	8.02639			0.359671
$499$	−18.1455	+	31.4289i	−0.812303	+	1.40695i	0.0989453	+	0.995093i	$0.468453\pi$
$499$	−18.1455	+	31.4289i	−0.812303	+	1.40695i	−0.911248	+	0.411857i	$0.864880\pi$
$500$	−5.67895	−	9.83623i	−0.253970	−	0.439890i
$501$	−4.51974	−	7.82842i	−0.201927	−	0.349748i
$502$	1.53621	−	2.66079i	0.0685642	−	0.118757i
$503$	−16.1317			−0.719279			−0.359639	−	0.933091i	$-0.617100\pi$
$503$	−16.1317			−0.719279			−0.359639	+	0.933091i	$0.617100\pi$
$504$	−0.317776	−	2.62660i	−0.0141549	−	0.116998i
$505$	−30.2436			−1.34582
$506$	0.273833	−	0.474293i	0.0121734	−	0.0210849i
$507$	4.08288	+	7.07175i	0.181327	+	0.314068i
$508$	−0.886917	−	1.53618i	−0.0393506	−	0.0681572i
$509$	−15.6937	+	27.1823i	−0.695610	+	1.20483i	0.274364	+	0.961626i	$0.411533\pi$
$509$	−15.6937	+	27.1823i	−0.695610	+	1.20483i	−0.969975	+	0.243207i	$0.921801\pi$
$510$	12.6685			0.560970
$511$	16.5516	+	7.06042i	0.732199	+	0.312335i
$512$	−1.00000			−0.0441942
$513$	2.23490	−	3.87096i	0.0986731	−	0.170907i
$514$	−2.91112	−	5.04221i	−0.128404	−	0.222402i
$515$	−20.0923	−	34.8008i	−0.885371	−	1.53351i
$516$	−1.33424	+	2.31098i	−0.0587368	+	0.101735i
$517$	−8.97798			−0.394851
$518$	1.29030	+	0.550404i	0.0566926	+	0.0241834i
$519$	−25.2042			−1.10634
$520$	2.41712	−	4.18658i	0.105998	−	0.183594i
$521$	5.14548	+	8.91222i	0.225427	+	0.390452i	0.956448	−	0.291904i	$-0.0942888\pi$
$521$	5.14548	+	8.91222i	0.225427	+	0.390452i	−0.731020	+	0.682356i	$0.760955\pi$
$522$	0.500000	+	0.866025i	0.0218844	+	0.0379049i
$523$	6.32770	−	10.9599i	0.276691	−	0.479243i	−0.693869	−	0.720101i	$-0.744095\pi$
$523$	6.32770	−	10.9599i	0.276691	−	0.479243i	0.970560	+	0.240858i	$0.0774288\pi$
$524$	15.7553			0.688273
$525$	−0.0526735	−	0.435377i	−0.00229886	−	0.0190014i
$526$	−15.7158			−0.685242
$527$	−6.63774	+	11.4969i	−0.289144	+	0.500813i
$528$	0.582878	+	1.00958i	0.0253665	+	0.0439361i
$529$	11.3896	+	19.7274i	0.495202	+	0.857715i
$530$	0.801309	−	1.38791i	0.0348066	−	0.0602868i
$531$	1.66849			0.0724061
$532$	−9.45725	+	7.10027i	−0.410024	+	0.307836i
$533$	−2.72235			−0.117918
$534$	−4.08561	+	7.07648i	−0.176802	+	0.306229i
$535$	−0.473067	−	0.819376i	−0.0204525	−	0.0354247i
$536$	0.629550	+	1.09041i	0.0271924	+	0.0470987i
$537$	−4.80077	+	8.31517i	−0.207168	+	0.358826i
$538$	−27.9660			−1.20570
$539$	7.92486	−	1.94604i	0.341348	−	0.0838221i
$540$	−2.19869			−0.0946166
$541$	−11.2673	+	19.5155i	−0.484419	+	0.839038i	−0.999840	−	0.0178993i	$-0.994302\pi$
$541$	−11.2673	+	19.5155i	−0.484419	+	0.839038i	0.515421	+	0.856937i	$0.327635\pi$
$542$	−9.06314	−	15.6978i	−0.389295	−	0.674279i
$543$	−11.8836	−	20.5831i	−0.509976	−	0.883304i
$544$	2.88092	−	4.98989i	0.123518	−	0.213940i
$545$	31.1581			1.33467
$546$	4.65202	−	3.49262i	0.199088	−	0.149470i
$547$	10.6445			0.455125			0.227563	−	0.973763i	$-0.426924\pi$
$547$	10.6445			0.455125			0.227563	+	0.973763i	$0.426924\pi$
$548$	6.18222	−	10.7079i	0.264092	−	0.457420i
$549$	−3.26783	−	5.66005i	−0.139468	−	0.241565i
$550$	0.0966161	+	0.167344i	0.00411972	+	0.00713557i
$551$	2.23490	−	3.87096i	0.0952098	−	0.164908i
$552$	0.469795			0.0199958
$553$	1.45387	+	12.0171i	0.0618249	+	0.511017i
$554$	20.2646			0.860959
$555$	0.582878	−	1.00958i	0.0247418	−	0.0428541i
$556$	0.0888799	+	0.153944i	0.00376935	+	0.00652870i
$557$	16.6317	+	28.8070i	0.704709	+	1.22059i	0.966796	+	0.255548i	$0.0822559\pi$
$557$	16.6317	+	28.8070i	0.704709	+	1.22059i	−0.262087	+	0.965044i	$0.584411\pi$
$558$	1.15202	−	1.99536i	0.0487689	−	0.0844701i
$559$	−5.86718			−0.248155
$560$	5.35071	+	2.28245i	0.226109	+	0.0964513i
$561$	−6.71689			−0.283587
$562$	−4.79804	+	8.31044i	−0.202393	+	0.350555i
$563$	3.73217	+	6.46430i	0.157292	+	0.272438i	0.933891	−	0.357557i	$-0.116390\pi$
$563$	3.73217	+	6.46430i	0.157292	+	0.272438i	−0.776599	+	0.629995i	$0.783057\pi$
$564$	−3.85071	−	6.66963i	−0.162144	−	0.280842i
$565$	−0.844709	+	1.46308i	−0.0355372	+	0.0615522i
$566$	−1.97252			−0.0829114
$567$	−2.43359	−	1.03810i	−0.102201	−	0.0435960i
$568$	11.3699			0.477071
$569$	3.39792	−	5.88538i	0.142448	−	0.246728i	−0.785970	−	0.618265i	$-0.787836\pi$
$569$	3.39792	−	5.88538i	0.142448	−	0.246728i	0.928418	+	0.371537i	$0.121169\pi$
$570$	4.91385	+	8.51104i	0.205819	+	0.356488i
$571$	−12.1185	−	20.9899i	−0.507145	−	0.878401i	−0.999966	−	0.00827033i	$-0.997367\pi$
$571$	−12.1185	−	20.9899i	−0.507145	−	0.878401i	0.492821	−	0.870131i	$-0.335966\pi$
$572$	−1.28157	+	2.21974i	−0.0535851	+	0.0928121i
$573$	11.0539			0.461782
$574$	−0.393460	−	3.25217i	−0.0164227	−	0.135743i
$575$	0.0778717			0.00324748
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−4.87645	−	8.44626i	−0.203009	−	0.351622i	0.746487	−	0.665400i	$-0.231739\pi$
$577$	−4.87645	−	8.44626i	−0.203009	−	0.351622i	−0.949497	+	0.313777i	$0.898406\pi$
$578$	8.09935	+	14.0285i	0.336888	+	0.583508i
$579$	7.46379	−	12.9277i	0.310185	−	0.537256i
$580$	−2.19869			−0.0912957
$581$	−16.9823	+	12.7499i	−0.704546	+	0.528956i
$582$	−12.9660			−0.537457
$583$	−0.424858	+	0.735875i	−0.0175958	+	0.0304768i
$584$	−3.40065	−	5.89011i	−0.140720	−	0.243734i
$585$	−2.41712	−	4.18658i	−0.0999357	−	0.173094i
$586$	−6.19096	+	10.7230i	−0.255746	+	0.442965i
$587$	11.9935			0.495023			0.247511	−	0.968885i	$-0.420387\pi$
$587$	11.9935			0.495023			0.247511	+	0.968885i	$0.420387\pi$
$588$	4.84471	+	5.05260i	0.199792	+	0.208366i
$589$	−10.2986			−0.424346
$590$	−1.83424	+	3.17700i	−0.0755146	+	0.130795i
$591$	−8.65148	−	14.9848i	−0.355874	−	0.616392i
$592$	−0.265102	−	0.459171i	−0.0108956	−	0.0188718i
$593$	−17.2376	+	29.8564i	−0.707865	+	1.22606i	0.257783	+	0.966203i	$0.417008\pi$
$593$	−17.2376	+	29.8564i	−0.707865	+	1.22606i	−0.965648	+	0.259855i	$0.916325\pi$
$594$	1.16576			0.0478316
$595$	−26.8041	+	20.1239i	−1.09886	+	0.825000i
$596$	−7.54221			−0.308941
$597$	11.7810	−	20.4053i	0.482165	−	0.835135i
$598$	0.516467	+	0.894547i	0.0211199	+	0.0365808i
$599$	16.4046	+	28.4136i	0.670273	+	1.16095i	0.977827	+	0.209416i	$0.0671562\pi$
$599$	16.4046	+	28.4136i	0.670273	+	1.16095i	−0.307554	+	0.951531i	$0.599510\pi$
$600$	−0.0828784	+	0.143550i	−0.00338350	+	0.00586039i
$601$	11.5477			0.471039			0.235520	−	0.971870i	$-0.424321\pi$
$601$	11.5477			0.471039			0.235520	+	0.971870i	$0.424321\pi$
$602$	−0.847981	−	7.00904i	−0.0345611	−	0.285667i
$603$	1.25910			0.0512746
$604$	3.38092	−	5.85592i	0.137567	−	0.238274i
$605$	−10.5988	−	18.3577i	−0.430903	−	0.746345i
$606$	6.87764	+	11.9124i	0.279385	+	0.483909i
$607$	−2.09553	+	3.62957i	−0.0850550	+	0.147320i	−0.905415	−	0.424528i	$-0.860440\pi$
$607$	−2.09553	+	3.62957i	−0.0850550	+	0.147320i	0.820360	+	0.571848i	$0.193773\pi$
$608$	4.46980			0.181274
$609$	−2.43359	−	1.03810i	−0.0986140	−	0.0420658i
$610$	14.3699			0.581821
$611$	8.46652	−	14.6644i	0.342519	−	0.593260i
$612$	−2.88092	−	4.98989i	−0.116454	−	0.201704i
$613$	−6.16194	−	10.6728i	−0.248879	−	0.431070i	0.714336	−	0.699802i	$-0.246729\pi$
$613$	−6.16194	−	10.6728i	−0.248879	−	0.431070i	−0.963215	+	0.268732i	$0.913395\pi$
$614$	4.88364	−	8.45872i	0.197088	−	0.341366i
$615$	−2.72235			−0.109776
$616$	−2.83697	−	1.21017i	−0.114305	−	0.0487591i
$617$	17.7224			0.713475			0.356738	−	0.934205i	$-0.383889\pi$
$617$	17.7224			0.713475			0.356738	+	0.934205i	$0.383889\pi$
$618$	−9.13828	+	15.8280i	−0.367596	+	0.636694i
$619$	3.41385	+	5.91296i	0.137214	+	0.237662i	0.926441	−	0.376440i	$-0.122852\pi$
$619$	3.41385	+	5.91296i	0.137214	+	0.237662i	−0.789227	+	0.614102i	$0.789518\pi$
$620$	2.53293	+	4.38717i	0.101725	+	0.176193i
$621$	0.234898	−	0.406855i	0.00942611	−	0.0163265i
$622$	−15.0868			−0.604926
$623$	−2.59662	−	21.4625i	−0.104031	−	0.859877i
$624$	−2.19869			−0.0880181
$625$	12.0719	−	20.9091i	0.482875	−	0.836364i
$626$	−13.7843	−	23.8751i	−0.550931	−	0.954241i
$627$	−2.60535	−	4.51259i	−0.104048	−	0.180216i
$628$	4.59935	−	7.96630i	0.183534	−	0.317890i
$629$	3.05495			0.121809
$630$	4.65202	−	3.49262i	0.185341	−	0.139149i
$631$	4.69488			0.186900			0.0934501	−	0.995624i	$-0.470210\pi$
$631$	4.69488			0.186900			0.0934501	+	0.995624i	$0.470210\pi$
$632$	2.28757	−	3.96219i	0.0909947	−	0.157607i
$633$	9.40338	+	16.2871i	0.373751	+	0.647356i
$634$	0.287571	+	0.498088i	0.0114209	+	0.0197816i
$635$	1.95006	−	3.37760i	0.0773856	−	0.134036i
$636$	−0.728896			−0.0289026
$637$	−4.29476	+	14.7795i	−0.170165	+	0.585584i
$638$	1.16576			0.0461528
$639$	5.68495	−	9.84663i	0.224893	−	0.389527i
$640$	−1.09935	−	1.90412i	−0.0434555	−	0.0752670i
$641$	3.26183	+	5.64966i	0.128835	+	0.223148i	0.923225	−	0.384259i	$-0.125543\pi$
$641$	3.26183	+	5.64966i	0.128835	+	0.223148i	−0.794391	+	0.607407i	$0.792210\pi$
$642$	−0.215158	+	0.372665i	−0.00849163	+	0.0147079i
$643$	−37.0617			−1.46157			−0.730786	−	0.682607i	$-0.760846\pi$
$643$	−37.0617			−1.46157			−0.730786	+	0.682607i	$0.760846\pi$
$644$	−0.993999	+	0.746270i	−0.0391690	+	0.0294072i
$645$	−5.86718			−0.231020
$646$	−12.8771	+	22.3038i	−0.506643	+	0.877531i
$647$	22.2910	+	38.6091i	0.876348	+	1.51788i	0.855320	+	0.518100i	$0.173360\pi$
$647$	22.2910	+	38.6091i	0.876348	+	1.51788i	0.0210276	+	0.999779i	$0.493306\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	0.972525	−	1.68446i	0.0381749	−	0.0661209i
$650$	−0.364448			−0.0142948
$651$	0.732168	+	6.05178i	0.0286959	+	0.237188i
$652$	−11.2526			−0.440684
$653$	2.91766	−	5.05354i	0.114177	−	0.197760i	−0.803273	−	0.595610i	$-0.796910\pi$
$653$	2.91766	−	5.05354i	0.114177	−	0.197760i	0.917450	+	0.397850i	$0.130244\pi$
$654$	−7.08561	−	12.2726i	−0.277069	−	0.479898i
$655$	17.3205	+	30.0000i	0.676768	+	1.17220i
$656$	−0.619085	+	1.07229i	−0.0241712	+	0.0418657i
$657$	−6.80131			−0.265344
$658$	18.7421	+	7.99482i	0.730643	+	0.311671i
$659$	−17.4018			−0.677876			−0.338938	−	0.940809i	$-0.610068\pi$
$659$	−17.4018			−0.677876			−0.338938	+	0.940809i	$0.610068\pi$
$660$	−1.28157	+	2.21974i	−0.0498850	+	0.0864034i
$661$	−17.0988	−	29.6160i	−0.665066	−	1.15193i	−0.979267	−	0.202572i	$-0.935070\pi$
$661$	−17.0988	−	29.6160i	−0.665066	−	1.15193i	0.314201	−	0.949356i	$-0.398263\pi$
$662$	−3.39019	−	5.87198i	−0.131763	−	0.228221i
$663$	6.33424	−	10.9712i	0.246002	−	0.426087i
$664$	8.02639			0.311484
$665$	−23.9166	−	10.2021i	−0.927445	−	0.395621i
$666$	−0.530205			−0.0205450
$667$	0.234898	−	0.406855i	0.00909527	−	0.0157535i
$668$	−4.51974	−	7.82842i	−0.174874	−	0.302891i
$669$	0.669029	+	1.15879i	0.0258661	+	0.0448015i
$670$	−1.38419	+	2.39748i	−0.0534758	+	0.0926228i
$671$	−7.61899			−0.294128
$672$	−0.317776	−	2.62660i	−0.0122585	−	0.101323i
$673$	37.8111			1.45751			0.728756	−	0.684773i	$-0.240099\pi$
$673$	37.8111			1.45751			0.728756	+	0.684773i	$0.240099\pi$
$674$	3.38037	−	5.85498i	0.130207	−	0.225525i
$675$	0.0828784	+	0.143550i	0.00318999	+	0.00552523i
$676$	4.08288	+	7.07175i	0.157034	+	0.271990i
$677$	−18.3337	+	31.7549i	−0.704621	+	1.22044i	0.262207	+	0.965012i	$0.415550\pi$
$677$	−18.3337	+	31.7549i	−0.704621	+	1.22044i	−0.966828	+	0.255428i	$0.917784\pi$
$678$	0.768374			0.0295092
$679$	27.4336	−	20.5965i	1.05280	−	0.790420i
$680$	12.6685			0.485814
$681$	−6.68495	+	11.5787i	−0.256168	+	0.443696i
$682$	−1.34297	−	2.32610i	−0.0514251	−	0.0890710i
$683$	2.93359	+	5.08112i	0.112251	+	0.194424i	0.916677	−	0.399628i	$-0.130861\pi$
$683$	2.93359	+	5.08112i	0.112251	+	0.194424i	−0.804427	+	0.594052i	$0.797527\pi$
$684$	2.23490	−	3.87096i	0.0854534	−	0.148010i
$685$	27.1856			1.03871
$686$	−18.2766	−	2.99454i	−0.697802	−	0.114332i
$687$	−3.62355			−0.138247
$688$	−1.33424	+	2.31098i	−0.0508675	+	0.0881052i
$689$	−0.801309	−	1.38791i	−0.0305274	−	0.0528751i
$690$	0.516467	+	0.894547i	0.0196616	+	0.0340548i
$691$	−3.96106	+	6.86076i	−0.150686	+	0.260996i	−0.931480	−	0.363793i	$-0.881482\pi$
$691$	−3.96106	+	6.86076i	−0.150686	+	0.260996i	0.780794	+	0.624789i	$0.214815\pi$
$692$	−25.2042			−0.958118
$693$	−2.46652	+	1.85181i	−0.0936955	+	0.0703443i
$694$	−1.03948			−0.0394581
$695$	−0.195419	+	0.338476i	−0.00741268	+	0.0128391i
$696$	0.500000	+	0.866025i	0.0189525	+	0.0328266i
$697$	−3.56706	−	6.17833i	−0.135112	−	0.234021i
$698$	3.10208	−	5.37295i	0.117415	−	0.203369i
$699$	−18.9540			−0.716905
$700$	−0.0526735	−	0.435377i	−0.00199087	−	0.0164557i
$701$	−22.8092			−0.861490			−0.430745	−	0.902474i	$-0.641749\pi$
$701$	−22.8092			−0.861490			−0.430745	+	0.902474i	$0.641749\pi$
$702$	−1.09935	+	1.90412i	−0.0414921	+	0.0718665i
$703$	1.18495	+	2.05240i	0.0446914	+	0.0774077i
$704$	0.582878	+	1.00958i	0.0219681	+	0.0380498i
$705$	8.46652	−	14.6644i	0.318868	−	0.552295i
$706$	7.88265			0.296667
$707$	−33.4747	−	14.2793i	−1.25895	−	0.537029i
$708$	1.66849			0.0627056
$709$	−0.0197391	+	0.0341891i	−0.000741318	+	0.00128400i	−0.866396	−	0.499358i	$-0.833569\pi$
$709$	−0.0197391	+	0.0341891i	−0.000741318	+	0.00128400i	0.865655	+	0.500642i	$0.166903\pi$
$710$	12.4995	+	21.6497i	0.469096	+	0.812499i
$711$	−2.28757	−	3.96219i	−0.0857906	−	0.148594i
$712$	−4.08561	+	7.07648i	−0.153115	+	0.265202i
$713$	−1.08243			−0.0405372
$714$	14.0219	+	5.98134i	0.524757	+	0.223846i
$715$	−5.63555			−0.210758
$716$	−4.80077	+	8.31517i	−0.179413	+	0.310753i
$717$	−7.99673	−	13.8507i	−0.298643	−	0.517265i
$718$	−4.34798	−	7.53092i	−0.162265	−	0.281052i
$719$	−12.6021	+	21.8274i	−0.469978	+	0.814026i	−0.999411	−	0.0343261i	$-0.989072\pi$
$719$	−12.6021	+	21.8274i	−0.469978	+	0.814026i	0.529433	+	0.848352i	$0.322405\pi$
$720$	−2.19869			−0.0819404
$721$	−5.80785	−	48.0052i	−0.216296	−	1.78781i
$722$	−0.979068			−0.0364372
$723$	12.0252	−	20.8283i	0.447222	−	0.774611i
$724$	−11.8836	−	20.5831i	−0.441652	−	0.764964i
$725$	0.0828784	+	0.143550i	0.00307803	+	0.00533130i
$726$	−4.82051	+	8.34936i	−0.178906	+	0.309874i
$727$	6.57207			0.243745			0.121872	−	0.992546i	$-0.461110\pi$
$727$	6.57207			0.243745			0.121872	+	0.992546i	$0.461110\pi$
$728$	4.65202	−	3.49262i	0.172415	−	0.129445i
$729$	1.00000			0.0370370
$730$	7.47699	−	12.9505i	0.276736	−	0.479320i
$731$	−7.68768	−	13.3155i	−0.284339	−	0.492490i
$732$	−3.26783	−	5.66005i	−0.120783	−	0.209202i
$733$	−26.1192	+	45.2398i	−0.964734	+	1.67097i	−0.254407	+	0.967097i	$0.581880\pi$
$733$	−26.1192	+	45.2398i	−0.964734	+	1.67097i	−0.710327	+	0.703872i	$0.751453\pi$
$734$	9.95944			0.367610
$735$	−4.29476	+	14.7795i	−0.158415	+	0.545149i
$736$	0.469795			0.0173169
$737$	0.733903	−	1.27116i	0.0270337	−	0.0468237i
$738$	0.619085	+	1.07229i	0.0227888	+	0.0394714i
$739$	1.44133	+	2.49645i	0.0530200	+	0.0918333i	0.891317	−	0.453380i	$-0.149782\pi$
$739$	1.44133	+	2.49645i	0.0530200	+	0.0918333i	−0.838297	+	0.545213i	$0.816449\pi$
$740$	0.582878	−	1.00958i	0.0214270	−	0.0371127i
$741$	9.82770			0.361030
$742$	1.54221	−	1.15785i	0.0566162	−	0.0425061i
$743$	−0.880265			−0.0322938			−0.0161469	−	0.999870i	$-0.505140\pi$
$743$	−0.880265			−0.0322938			−0.0161469	+	0.999870i	$0.505140\pi$
$744$	1.15202	−	1.99536i	0.0422351	−	0.0731533i
$745$	−8.29149	−	14.3613i	−0.303777	−	0.526157i
$746$	7.29476	+	12.6349i	0.267080	+	0.462597i
$747$	4.01320	−	6.95106i	0.146835	−	0.254326i
$748$	−6.71689			−0.245594
$749$	−0.136744	−	1.13027i	−0.00499653	−	0.0412992i
$750$	−11.3579			−0.414732
$751$	−16.6679	+	28.8697i	−0.608222	+	1.05347i	0.383311	+	0.923619i	$0.374784\pi$
$751$	−16.6679	+	28.8697i	−0.608222	+	1.05347i	−0.991533	+	0.129852i	$0.958550\pi$
$752$	−3.85071	−	6.66963i	−0.140421	−	0.243216i
$753$	−1.53621	−	2.66079i	−0.0559825	−	0.0969645i
$754$	−1.09935	+	1.90412i	−0.0400358	+	0.0693441i
$755$	14.8672			0.541072
$756$	−2.43359	−	1.03810i	−0.0885088	−	0.0377552i
$757$	−25.5477			−0.928546			−0.464273	−	0.885692i	$-0.653684\pi$
$757$	−25.5477			−0.928546			−0.464273	+	0.885692i	$0.653684\pi$
$758$	−9.84144	+	17.0459i	−0.357457	+	0.619134i
$759$	−0.273833	−	0.474293i	−0.00993952	−	0.0172158i
$760$	4.91385	+	8.51104i	0.178244	+	0.308728i
$761$	−16.7256	+	28.9696i	−0.606303	+	1.05015i	0.385541	+	0.922691i	$0.374015\pi$
$761$	−16.7256	+	28.9696i	−0.606303	+	1.05015i	−0.991844	+	0.127457i	$0.959318\pi$
$762$	−1.77383			−0.0642592
$763$	34.4869	+	14.7111i	1.24851	+	0.532577i
$764$	11.0539			0.399915
$765$	6.33424	−	10.9712i	0.229015	−	0.396666i
$766$	−2.62628	−	4.54885i	−0.0948913	−	0.164357i
$767$	1.83424	+	3.17700i	0.0662307	+	0.114715i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−43.2175			−1.55846			−0.779231	−	0.626737i	$-0.784390\pi$
$769$	−43.2175			−1.55846			−0.779231	+	0.626737i	$0.784390\pi$
$770$	−0.814504	−	6.73234i	−0.0293527	−	0.242617i
$771$	−5.82224			−0.209683
$772$	7.46379	−	12.9277i	0.268628	−	0.465277i
$773$	−7.71962	−	13.3708i	−0.277656	−	0.480913i	0.693146	−	0.720797i	$-0.256224\pi$
$773$	−7.71962	−	13.3708i	−0.277656	−	0.480913i	−0.970802	+	0.239884i	$0.922891\pi$
$774$	1.33424	+	2.31098i	0.0479584	+	0.0830664i
$775$	0.190955	−	0.330744i	0.00685931	−	0.0118807i
$776$	−12.9660			−0.465452
$777$	1.12181	−	0.842231i	0.0402449	−	0.0302149i
$778$	−0.514732			−0.0184541
$779$	2.76718	−	4.79290i	0.0991446	−	0.171723i
$780$	−2.41712	−	4.18658i	−0.0865468	−	0.149904i
$781$	−6.62727	−	11.4788i	−0.237142	−	0.410743i
$782$	−1.35344	+	2.34423i	−0.0483989	+	0.0838294i
$783$	1.00000			0.0357371
$784$	4.84471	+	5.05260i	0.173025	+	0.180450i
$785$	20.2251			0.721864
$786$	7.87764	−	13.6445i	0.280986	−	0.486682i
$787$	−11.6317	−	20.1468i	−0.414627	−	0.718154i	0.580763	−	0.814073i	$-0.302754\pi$
$787$	−11.6317	−	20.1468i	−0.414627	−	0.718154i	−0.995389	+	0.0959186i	$0.969421\pi$
$788$	−8.65148	−	14.9848i	−0.308196	−	0.533811i
$789$	−7.85790	+	13.6103i	−0.279749	+	0.484539i
$790$	10.0593			0.357895
$791$	−1.62574	+	1.22056i	−0.0578045	+	0.0433982i
$792$	1.16576			0.0414234
$793$	7.18495	−	12.4447i	0.255145	−	0.441924i
$794$	−15.0823	−	26.1234i	−0.535252	−	0.927084i
$795$	−0.801309	−	1.38791i	−0.0284195	−	0.0492240i
$796$	11.7810	−	20.4053i	0.417567	−	0.723248i
$797$	46.7224			1.65499			0.827495	−	0.561473i	$-0.189765\pi$
$797$	46.7224			1.65499			0.827495	+	0.561473i	$0.189765\pi$
$798$	1.42039	+	11.7404i	0.0502814	+	0.415604i
$799$	44.3743			1.56985
$800$	−0.0828784	+	0.143550i	−0.00293019	+	0.00507525i
$801$	4.08561	+	7.07648i	0.144358	+	0.250035i
$802$	2.90011	+	5.02314i	0.102407	+	0.177373i
$803$	−3.96434	+	6.86643i	−0.139898	+	0.242311i
$804$	1.25910			0.0444051
$805$	−2.51374	−	1.07229i	−0.0885976	−	0.0377931i
$806$	5.06587			0.178438
$807$	−13.9830	+	24.2192i	−0.492225	+	0.852558i
$808$	6.87764	+	11.9124i	0.241955	+	0.419078i
$809$	16.2838	+	28.2043i	0.572506	+	0.991610i	0.996308	+	0.0858550i	$0.0273622\pi$
$809$	16.2838	+	28.2043i	0.572506	+	0.991610i	−0.423801	+	0.905755i	$0.639304\pi$
$810$	−1.09935	+	1.90412i	−0.0386271	+	0.0669040i
$811$	−36.6094			−1.28553			−0.642765	−	0.766064i	$-0.722213\pi$
$811$	−36.6094			−1.28553			−0.642765	+	0.766064i	$0.722213\pi$
$812$	−2.43359	−	1.03810i	−0.0854022	−	0.0364301i
$813$	−18.1263			−0.635716
$814$	−0.309045	+	0.535282i	−0.0108320	+	0.0187616i
$815$	−12.3704	−	21.4262i	−0.433318	−	0.750529i
$816$	−2.88092	−	4.98989i	−0.100852	−	0.174681i
$817$	5.96379	−	10.3296i	0.208647	−	0.361387i
$818$	13.5950			0.475338
$819$	−0.698691	−	5.77508i	−0.0244142	−	0.201798i
$820$	−2.72235			−0.0950687
$821$	13.1185	−	22.7220i	0.457840	−	0.793003i	−0.541006	−	0.841019i	$-0.681956\pi$
$821$	13.1185	−	22.7220i	0.457840	−	0.793003i	0.998847	+	0.0480159i	$0.0152898\pi$
$822$	−6.18222	−	10.7079i	−0.215630	−	0.373482i
$823$	0.613083	+	1.06189i	0.0213707	+	0.0370152i	0.876513	−	0.481378i	$-0.159864\pi$
$823$	0.613083	+	1.06189i	0.0213707	+	0.0370152i	−0.855142	+	0.518393i	$0.826530\pi$
$824$	−9.13828	+	15.8280i	−0.318347	+	0.551393i
$825$	0.193232			0.00672748
$826$	−3.53020	+	2.65039i	−0.122832	+	0.0922190i
$827$	−38.8692			−1.35161			−0.675807	−	0.737079i	$-0.736205\pi$
$827$	−38.8692			−1.35161			−0.675807	+	0.737079i	$0.736205\pi$
$828$	0.234898	−	0.406855i	0.00816325	−	0.0141392i
$829$	−15.4830	−	26.8173i	−0.537746	−	0.931404i	−0.999025	−	0.0441488i	$-0.985942\pi$
$829$	−15.4830	−	26.8173i	−0.537746	−	0.931404i	0.461278	−	0.887255i	$-0.347391\pi$
$830$	8.82378	+	15.2832i	0.306278	+	0.530489i
$831$	10.1323	−	17.5496i	0.351485	−	0.608790i
$832$	−2.19869			−0.0762259
$833$	−39.1691	+	9.61845i	−1.35713	+	0.333260i
$834$	0.177760			0.00615532
$835$	9.93751	−	17.2123i	0.343902	−	0.595655i
$836$	−2.60535	−	4.51259i	−0.0901078	−	0.156071i
$837$	−1.15202	−	1.99536i	−0.0398196	−	0.0689696i
$838$	−8.30523	+	14.3851i	−0.286899	+	0.496924i
$839$	−31.5291			−1.08851			−0.544253	−	0.838921i	$-0.683187\pi$
$839$	−31.5291			−1.08851			−0.544253	+	0.838921i	$0.683187\pi$
$840$	4.65202	−	3.49262i	0.160510	−	0.120507i
$841$	1.00000			0.0344828
$842$	−13.5357	+	23.4445i	−0.466470	+	0.807949i
$843$	4.79804	+	8.31044i	0.165253	+	0.286227i
$844$	9.40338	+	16.2871i	0.323678	+	0.560626i
$845$	−8.97699	+	15.5486i	−0.308818	+	0.534888i
$846$	−7.70142			−0.264780
$847$	−3.06368	−	25.3231i	−0.105269	−	0.870111i
$848$	−0.728896			−0.0250304
$849$	−0.986262	+	1.70826i	−0.0338484	+	0.0586272i
$850$	−0.477531	−	0.827109i	−0.0163792	−	0.0283696i
$851$	0.124544	+	0.215716i	0.00426931	+	0.00739466i
$852$	5.68495	−	9.84663i	0.194763	−	0.337340i
$853$	−34.9858			−1.19789			−0.598946	−	0.800789i	$-0.704414\pi$
$853$	−34.9858			−1.19789			−0.598946	+	0.800789i	$0.704414\pi$
$854$	15.9051	+	6.78465i	0.544262	+	0.232166i
$855$	9.82770			0.336100
$856$	−0.215158	+	0.372665i	−0.00735396	+	0.0127374i
$857$	20.3002	+	35.1610i	0.693442	+	1.20108i	0.970703	+	0.240283i	$0.0772402\pi$
$857$	20.3002	+	35.1610i	0.693442	+	1.20108i	−0.277260	+	0.960795i	$0.589427\pi$
$858$	1.28157	+	2.21974i	0.0437521	+	0.0757808i
$859$	5.10327	−	8.83912i	0.174121	−	0.301587i	−0.765736	−	0.643156i	$-0.777625\pi$
$859$	5.10327	−	8.83912i	0.174121	−	0.301587i	0.939857	+	0.341569i	$0.110958\pi$
$860$	−5.86718			−0.200069
$861$	−3.01320	−	1.28534i	−0.102689	−	0.0438043i
$862$	38.2789			1.30379
$863$	27.1719	−	47.0631i	0.924941	−	1.60204i	0.133285	−	0.991078i	$-0.457447\pi$
$863$	27.1719	−	47.0631i	0.924941	−	1.60204i	0.791656	−	0.610967i	$-0.209219\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−27.7081	−	47.9918i	−0.942103	−	1.63177i
$866$	1.12682	−	1.95171i	0.0382909	−	0.0663218i
$867$	16.1987			0.550136
$868$	0.732168	+	6.05178i	0.0248514	+	0.205411i
$869$	−5.33350			−0.180927
$870$	−1.09935	+	1.90412i	−0.0372713	+	0.0645558i
$871$	1.38419	+	2.39748i	0.0469014	+	0.0812356i
$872$	−7.08561	−	12.2726i	−0.239949	−	0.415604i
$873$	−6.48299	+	11.2289i	−0.219416	+	0.380040i
$874$	−2.09989			−0.0710298
$875$	24.0312	−	18.0420i	0.812403	−	0.609932i
$876$	−6.80131			−0.229795
$877$	−3.13555	+	5.43094i	−0.105880	+	0.183390i	−0.914097	−	0.405495i	$-0.867099\pi$
$877$	−3.13555	+	5.43094i	−0.105880	+	0.183390i	0.808217	+	0.588884i	$0.200433\pi$
$878$	−0.251907	−	0.436316i	−0.00850145	−	0.0147249i
$879$	6.19096	+	10.7230i	0.208816	+	0.361679i
$880$	−1.28157	+	2.21974i	−0.0432017	+	0.0748275i
$881$	0.564224			0.0190092			0.00950459	−	0.999955i	$-0.496975\pi$
$881$	0.564224			0.0190092			0.00950459	+	0.999955i	$0.496975\pi$
$882$	6.79804	−	1.66934i	0.228902	−	0.0562096i
$883$	−1.82116			−0.0612868			−0.0306434	−	0.999530i	$-0.509756\pi$
$883$	−1.82116			−0.0612868			−0.0306434	+	0.999530i	$0.509756\pi$
$884$	6.33424	−	10.9712i	0.213044	−	0.369002i
$885$	1.83424	+	3.17700i	0.0616574	+	0.106794i
$886$	−0.830971	−	1.43928i	−0.0279170	−	0.0483537i
$887$	−16.4138	+	28.4296i	−0.551123	+	0.954573i	0.447071	+	0.894499i	$0.352467\pi$
$887$	−16.4138	+	28.4296i	−0.551123	+	0.954573i	−0.998194	+	0.0600747i	$0.980866\pi$
$888$	−0.530205			−0.0177925
$889$	3.75310	−	2.81774i	0.125875	−	0.0945039i
$890$	−17.9660			−0.602221
$891$	0.582878	−	1.00958i	0.0195272	−	0.0338220i
$892$	0.669029	+	1.15879i	0.0224007	+	0.0387992i
$893$	17.2119	+	29.8119i	0.575974	+	0.997616i
$894$	−3.77110	+	6.53174i	−0.126125	+	0.218454i
$895$	−21.1108			−0.705656
$896$	−0.317776	−	2.62660i	−0.0106162	−	0.0877485i
$897$	1.03293			0.0344887
$898$	−13.6218	+	23.5937i	−0.454566	+	0.787331i
$899$	−1.15202	−	1.99536i	−0.0384220	−	0.0665488i
$900$	0.0828784	+	0.143550i	0.00276261	+	0.00478499i
$901$	2.09989	−	3.63711i	0.0699574	−	0.121170i
$902$	1.44340			0.0480601
$903$	−6.49400	−	2.77015i	−0.216107	−	0.0921847i
$904$	0.768374			0.0255558
$905$	26.1285	−	45.2558i	0.868540	−	1.50435i
$906$	−3.38092	−	5.85592i	−0.112323	−	0.194550i
$907$	−6.97426	−	12.0798i	−0.231576	−	0.401102i	0.726696	−	0.686959i	$-0.241055\pi$
$907$	−6.97426	−	12.0798i	−0.231576	−	0.401102i	−0.958272	+	0.285857i	$0.907722\pi$
$908$	−6.68495	+	11.5787i	−0.221848	+	0.384252i
$909$	13.7553			0.456234
$910$	11.7646	+	5.01841i	0.389991	+	0.166359i
$911$	−42.8881			−1.42095			−0.710473	−	0.703724i	$-0.751519\pi$
$911$	−42.8881			−1.42095			−0.710473	+	0.703724i	$0.751519\pi$
$912$	2.23490	−	3.87096i	0.0740049	−	0.128180i
$913$	−4.67841	−	8.10324i	−0.154833	−	0.268178i
$914$	−15.1395	−	26.2223i	−0.500769	−	0.867358i
$915$	7.18495	−	12.4447i	0.237527	−	0.411409i
$916$	−3.62355			−0.119725
$917$	5.00665	+	41.3828i	0.165334	+	1.36658i
$918$	−5.76183			−0.190169
$919$	15.6904	−	27.1766i	0.517579	−	0.896473i	−0.482213	−	0.876054i	$-0.660167\pi$
$919$	15.6904	−	27.1766i	0.517579	−	0.896473i	0.999792	−	0.0204188i	$-0.00649996\pi$
$920$	0.516467	+	0.894547i	0.0170274	+	0.0294924i
$921$	−4.88364	−	8.45872i	−0.160922	−	0.278724i
$922$	13.0494	−	22.6022i	0.429759	−	0.744365i
$923$	24.9989			0.822849
$924$	−2.46652	+	1.85181i	−0.0811427	+	0.0609199i
$925$	−0.0878851			−0.00288964
$926$	−4.01592	+	6.95579i	−0.131971	+	0.228581i
$927$	9.13828	+	15.8280i	0.300141	+	0.519859i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	5.61973	−	9.73367i	0.184378	−	0.319351i	−0.758989	−	0.651103i	$-0.774306\pi$
$929$	5.61973	−	9.73367i	0.184378	−	0.319351i	0.943367	+	0.331752i	$0.107640\pi$
$930$	5.06587			0.166116
$931$	−21.6549	−	22.5841i	−0.709709	−	0.740164i
$932$	−18.9540			−0.620858
$933$	−7.54340	+	13.0656i	−0.246960	+	0.427747i
$934$	6.21516	+	10.7650i	0.203366	+	0.352241i
$935$	−7.38419	−	12.7898i	−0.241489	−	0.418271i
$936$	−1.09935	+	1.90412i	−0.0359332	+	0.0622382i
$937$	29.9978			0.979986			0.489993	−	0.871726i	$-0.336999\pi$
$937$	29.9978			0.979986			0.489993	+	0.871726i	$0.336999\pi$
$938$	−2.66402	+	2.00008i	−0.0869834	+	0.0653050i
$939$	−27.5686			−0.899667
$940$	8.46652	−	14.6644i	0.276148	−	0.478302i
$941$	4.82051	+	8.34936i	0.157144	+	0.272181i	0.933838	−	0.357697i	$-0.116438\pi$
$941$	4.82051	+	8.34936i	0.157144	+	0.272181i	−0.776694	+	0.629879i	$0.783105\pi$
$942$	−4.59935	−	7.96630i	−0.149855	−	0.259556i
$943$	0.290843	−	0.503755i	0.00947115	−	0.0164045i
$944$	1.66849			0.0543046
$945$	−0.698691	−	5.77508i	−0.0227284	−	0.187863i
$946$	3.11081			0.101141
$947$	9.19815	−	15.9317i	0.298900	−	0.517709i	−0.676985	−	0.735997i	$-0.736714\pi$
$947$	9.19815	−	15.9317i	0.298900	−	0.517709i	0.975884	+	0.218288i	$0.0700471\pi$
$948$	−2.28757	−	3.96219i	−0.0742969	−	0.128686i
$949$	−7.47699	−	12.9505i	−0.242713	−	0.420392i
$950$	0.370450	−	0.641637i	0.0120190	−	0.0208175i
$951$	0.575142			0.0186503
$952$	14.0219	+	5.98134i	0.454453	+	0.193856i
$953$	21.4807			0.695829			0.347914	−	0.937526i	$-0.386890\pi$
$953$	21.4807			0.695829			0.347914	+	0.937526i	$0.386890\pi$
$954$	−0.364448	+	0.631243i	−0.0117994	+	0.0204372i
$955$	12.1520	+	21.0479i	0.393230	+	0.681095i
$956$	−7.99673	−	13.8507i	−0.258633	−	0.447965i
$957$	0.582878	−	1.00958i	0.0188418	−	0.0326349i
$958$	14.3634			0.464059
$959$	30.0900	+	12.8355i	0.971656	+	0.414480i
$960$	−2.19869			−0.0709625
$961$	12.8457	−	22.2494i	0.414378	−	0.717723i
$962$	−0.582878	−	1.00958i	−0.0187928	−	0.0325500i
$963$	0.215158	+	0.372665i	0.00693338	+	0.0120090i
$964$	12.0252	−	20.8283i	0.387306	−	0.670833i
$965$	32.8212			1.05655
$966$	0.149290	+	1.23396i	0.00480331	+	0.0397021i
$967$	−29.0779			−0.935081			−0.467541	−	0.883972i	$-0.654860\pi$
$967$	−29.0779			−0.935081			−0.467541	+	0.883972i	$0.654860\pi$
$968$	−4.82051	+	8.34936i	−0.154937	+	0.268359i
$969$	12.8771	+	22.3038i	0.413672	+	0.716501i
$970$	−14.2541	−	24.6888i	−0.457671	−	0.792710i
$971$	8.71069	−	15.0874i	0.279539	−	0.484177i	−0.691731	−	0.722155i	$-0.743152\pi$
$971$	8.71069	−	15.0874i	0.279539	−	0.484177i	0.971270	+	0.237979i	$0.0764849\pi$
$972$	1.00000			0.0320750
$973$	−0.376106	+	0.282372i	−0.0120574	+	0.00905241i
$974$	18.5686			0.594976
$975$	−0.182224	+	0.315621i	−0.00583584	+	0.0101080i
$976$	−3.26783	−	5.66005i	−0.104601	−	0.181174i
$977$	18.0291	+	31.2274i	0.576803	+	0.999052i	0.995843	+	0.0910840i	$0.0290332\pi$
$977$	18.0291	+	31.2274i	0.576803	+	0.999052i	−0.419041	+	0.907968i	$0.637633\pi$
$978$	−5.62628	+	9.74500i	−0.179909	+	0.311611i
$979$	9.52565			0.304441
$980$	−4.29476	+	14.7795i	−0.137191	+	0.472113i
$981$	−14.1712			−0.452452
$982$	−9.09880	+	15.7596i	−0.290354	+	0.502909i
$983$	12.3644	+	21.4159i	0.394365	+	0.683060i	0.993020	−	0.117947i	$-0.0376314\pi$
$983$	12.3644	+	21.4159i	0.394365	+	0.683060i	−0.598655	+	0.801007i	$0.704298\pi$
$984$	0.619085	+	1.07229i	0.0197357	+	0.0341832i
$985$	19.0219	−	32.9469i	0.606089	−	1.04978i
$986$	−5.76183			−0.183494
$987$	16.2948	−	12.2337i	0.518668	−	0.389403i
$988$	9.82770			0.312661
$989$	0.626821	−	1.08569i	0.0199317	−	0.0345228i
$990$	1.28157	+	2.21974i	0.0407310	+	0.0705481i
$991$	−5.69096	−	9.85702i	−0.180779	−	0.313119i	0.761367	−	0.648321i	$-0.224529\pi$
$991$	−5.69096	−	9.85702i	−0.180779	−	0.313119i	−0.942146	+	0.335203i	$0.891195\pi$
$992$	1.15202	−	1.99536i	0.0365766	−	0.0633526i
$993$	−6.78038			−0.215169
$994$	3.61308	+	29.8642i	0.114600	+	0.947234i
$995$	51.8057			1.64235
$996$	4.01320	−	6.95106i	0.127163	−	0.220253i
$997$	21.2179	+	36.7505i	0.671977	+	1.16390i	0.977343	+	0.211663i	$0.0678881\pi$
$997$	21.2179	+	36.7505i	0.671977	+	1.16390i	−0.305365	+	0.952235i	$0.598779\pi$
$998$	18.1455	+	31.4289i	0.574385	+	0.994864i
$999$	−0.265102	+	0.459171i	−0.00838747	+	0.0145275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.i.d.1045.3	yes	6
7.2	even	3		8526.2.a.bs.1.1		3
7.4	even	3	inner	1218.2.i.d.697.3	✓	6
7.5	odd	6		8526.2.a.bp.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.i.d.697.3	✓	6	7.4	even	3	inner
1218.2.i.d.1045.3	yes	6	1.1	even	1	trivial
8526.2.a.bp.1.3		3	7.5	odd	6
8526.2.a.bs.1.1		3	7.2	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:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.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} +(1.09935 - 1.90412i) q^{5} -1.00000 q^{6} +(2.11581 - 1.58850i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.09935 - 1.90412i) q^{10} +(0.582878 + 1.00958i) q^{11} +(-0.500000 + 0.866025i) q^{12} -2.19869 q^{13} +(-0.317776 - 2.62660i) q^{14} -2.19869 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.88092 - 4.98989i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.23490 - 3.87096i) q^{19} -2.19869 q^{20} +(-2.43359 - 1.03810i) q^{21} +1.16576 q^{22} +(0.234898 - 0.406855i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.0828784 + 0.143550i) q^{25} +(-1.09935 + 1.90412i) q^{26} +1.00000 q^{27} +(-2.43359 - 1.03810i) q^{28} +1.00000 q^{29} +(-1.09935 + 1.90412i) q^{30} +(-1.15202 - 1.99536i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.582878 - 1.00958i) q^{33} -5.76183 q^{34} +(-0.698691 - 5.77508i) q^{35} +1.00000 q^{36} +(-0.265102 + 0.459171i) q^{37} +(-2.23490 - 3.87096i) q^{38} +(1.09935 + 1.90412i) q^{39} +(-1.09935 + 1.90412i) q^{40} +1.23817 q^{41} +(-2.11581 + 1.58850i) q^{42} +2.66849 q^{43} +(0.582878 - 1.00958i) q^{44} +(1.09935 + 1.90412i) q^{45} +(-0.234898 - 0.406855i) q^{46} +(-3.85071 + 6.66963i) q^{47} +1.00000 q^{48} +(1.95333 - 6.72194i) q^{49} +0.165757 q^{50} +(-2.88092 + 4.98989i) q^{51} +(1.09935 + 1.90412i) q^{52} +(0.364448 + 0.631243i) q^{53} +(0.500000 - 0.866025i) q^{54} +2.56314 q^{55} +(-2.11581 + 1.58850i) q^{56} -4.46980 q^{57} +(0.500000 - 0.866025i) q^{58} +(-0.834243 - 1.44495i) q^{59} +(1.09935 + 1.90412i) q^{60} +(-3.26783 + 5.66005i) q^{61} -2.30404 q^{62} +(0.317776 + 2.62660i) q^{63} +1.00000 q^{64} +(-2.41712 + 4.18658i) q^{65} +(-0.582878 - 1.00958i) q^{66} +(-0.629550 - 1.09041i) q^{67} +(-2.88092 + 4.98989i) q^{68} -0.469795 q^{69} +(-5.35071 - 2.28245i) q^{70} -11.3699 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.40065 + 5.89011i) q^{73} +(0.265102 + 0.459171i) q^{74} +(0.0828784 - 0.143550i) q^{75} -4.46980 q^{76} +(2.83697 + 1.21017i) q^{77} +2.19869 q^{78} +(-2.28757 + 3.96219i) q^{79} +(1.09935 + 1.90412i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.619085 - 1.07229i) q^{82} -8.02639 q^{83} +(0.317776 + 2.62660i) q^{84} -12.6685 q^{85} +(1.33424 - 2.31098i) q^{86} +(-0.500000 - 0.866025i) q^{87} +(-0.582878 - 1.00958i) q^{88} +(4.08561 - 7.07648i) q^{89} +2.19869 q^{90} +(-4.65202 + 3.49262i) q^{91} -0.469795 q^{92} +(-1.15202 + 1.99536i) q^{93} +(3.85071 + 6.66963i) q^{94} +(-4.91385 - 8.51104i) q^{95} +(0.500000 - 0.866025i) q^{96} +12.9660 q^{97} +(-4.84471 - 5.05260i) q^{98} -1.16576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} - 6 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 9 q^{11} - 3 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20}+ \cdots - 18 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 - 6 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 9 * q^11 - 3 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 2 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - q^30 + 4 * q^31 + 3 * q^32 + 9 * q^33 - 12 * q^34 + 7 * q^35 + 6 * q^36 - 7 * q^37 - 8 * q^38 + q^39 - q^40 + 30 * q^41 + 4 * q^42 - 6 * q^43 + 9 * q^44 + q^45 + 4 * q^46 - q^47 + 6 * q^48 + 12 * q^49 + 12 * q^50 - 6 * q^51 + q^52 + 2 * q^53 + 3 * q^54 + 4 * q^55 + 4 * q^56 - 16 * q^57 + 3 * q^58 + 6 * q^59 + q^60 + 8 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 - 9 * q^65 - 9 * q^66 - 9 * q^67 - 6 * q^68 + 8 * q^69 - 10 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 7 * q^74 + 6 * q^75 - 16 * q^76 - 27 * q^77 + 2 * q^78 - 3 * q^79 + q^80 - 3 * q^81 + 15 * q^82 + 30 * q^83 + 2 * q^84 - 54 * q^85 - 3 * q^86 - 3 * q^87 - 9 * q^88 - 3 * q^89 + 2 * q^90 - 17 * q^91 + 8 * q^92 + 4 * q^93 + q^94 + 4 * q^95 + 3 * q^96 - 22 * q^97 - 12 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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