LMFDB - Embedded newform 285.2.i.e.106.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	285.106
Dual form			285.2.i.e.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 1.40126i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.309017 - 0.535233i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.809017 + 1.40126i) q^{6} +0.763932 q^{7} +2.23607 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.809017 - 1.40126i) q^{10} +2.00000 q^{11} +0.618034 q^{12} +(0.618034 + 1.07047i) q^{13} +(0.618034 - 1.07047i) q^{14} +(0.500000 + 0.866025i) q^{15} +(2.42705 - 4.20378i) q^{16} +(1.73607 - 3.00696i) q^{17} -1.61803 q^{18} +(-4.35410 - 0.204441i) q^{19} -0.618034 q^{20} +(-0.381966 + 0.661585i) q^{21} +(1.61803 - 2.80252i) q^{22} +(1.23607 + 2.14093i) q^{23} +(-1.11803 + 1.93649i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} +1.00000 q^{27} +(-0.236068 - 0.408882i) q^{28} +(0.381966 + 0.661585i) q^{29} +1.61803 q^{30} -8.23607 q^{31} +(-1.69098 - 2.92887i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-2.80902 - 4.86536i) q^{34} +(0.381966 - 0.661585i) q^{35} +(-0.309017 + 0.535233i) q^{36} +2.47214 q^{37} +(-3.80902 + 5.93583i) q^{38} -1.23607 q^{39} +(1.11803 - 1.93649i) q^{40} +(-3.85410 + 6.67550i) q^{41} +(0.618034 + 1.07047i) q^{42} +(-5.85410 + 10.1396i) q^{43} +(-0.618034 - 1.07047i) q^{44} -1.00000 q^{45} +4.00000 q^{46} +(-0.881966 - 1.52761i) q^{47} +(2.42705 + 4.20378i) q^{48} -6.41641 q^{49} -1.61803 q^{50} +(1.73607 + 3.00696i) q^{51} +(0.381966 - 0.661585i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.809017 - 1.40126i) q^{54} +(1.00000 - 1.73205i) q^{55} +1.70820 q^{56} +(2.35410 - 3.66854i) q^{57} +1.23607 q^{58} +(1.00000 - 1.73205i) q^{59} +(0.309017 - 0.535233i) q^{60} +(-6.23607 - 10.8012i) q^{61} +(-6.66312 + 11.5409i) q^{62} +(-0.381966 - 0.661585i) q^{63} +4.23607 q^{64} +1.23607 q^{65} +(1.61803 + 2.80252i) q^{66} +(1.61803 + 2.80252i) q^{67} -2.14590 q^{68} -2.47214 q^{69} +(-0.618034 - 1.07047i) q^{70} +(-4.61803 + 7.99867i) q^{71} +(-1.11803 - 1.93649i) q^{72} +(1.76393 - 3.05522i) q^{73} +(2.00000 - 3.46410i) q^{74} +1.00000 q^{75} +(1.23607 + 2.39364i) q^{76} +1.52786 q^{77} +(-1.00000 + 1.73205i) q^{78} +(-2.42705 - 4.20378i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.23607 + 10.8012i) q^{82} +15.1803 q^{83} +0.472136 q^{84} +(-1.73607 - 3.00696i) q^{85} +(9.47214 + 16.4062i) q^{86} -0.763932 q^{87} +4.47214 q^{88} +(-1.76393 - 3.05522i) q^{89} +(-0.809017 + 1.40126i) q^{90} +(0.472136 + 0.817763i) q^{91} +(0.763932 - 1.32317i) q^{92} +(4.11803 - 7.13264i) q^{93} -2.85410 q^{94} +(-2.35410 + 3.66854i) q^{95} +3.38197 q^{96} +(1.00000 - 1.73205i) q^{97} +(-5.19098 + 8.99105i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + q^{6} + 12 q^{7} - 2 q^{9} - q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} + 3 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + q^6 + 12 * q^7 - 2 * q^9 - q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 + 3 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^19 + 2 * q^20 - 6 * q^21 + 2 * q^22 - 4 * q^23 - 2 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 + 6 * q^29 + 2 * q^30 - 24 * q^31 - 9 * q^32 - 4 * q^33 - 9 * q^34 + 6 * q^35 + q^36 - 8 * q^37 - 13 * q^38 + 4 * q^39 - 2 * q^41 - 2 * q^42 - 10 * q^43 + 2 * q^44 - 4 * q^45 + 16 * q^46 - 8 * q^47 + 3 * q^48 + 28 * q^49 - 2 * q^50 - 2 * q^51 + 6 * q^52 + 2 * q^53 + q^54 + 4 * q^55 - 20 * q^56 - 4 * q^57 - 4 * q^58 + 4 * q^59 - q^60 - 16 * q^61 - 11 * q^62 - 6 * q^63 + 8 * q^64 - 4 * q^65 + 2 * q^66 + 2 * q^67 - 22 * q^68 + 8 * q^69 + 2 * q^70 - 14 * q^71 + 16 * q^73 + 8 * q^74 + 4 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 - 3 * q^80 - 2 * q^81 + 16 * q^82 + 16 * q^83 - 16 * q^84 + 2 * q^85 + 20 * q^86 - 12 * q^87 - 16 * q^89 - q^90 - 16 * q^91 + 12 * q^92 + 12 * q^93 + 2 * q^94 + 4 * q^95 + 18 * q^96 + 4 * q^97 - 23 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	1.40126i	0.572061	−	0.990839i	−0.424293	−	0.905525i	$-0.639477\pi$
$2$	0.809017	−	1.40126i	0.572061	−	0.990839i	0.996354	−	0.0853143i	$-0.0271894\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.309017	−	0.535233i	−0.154508	−	0.267617i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.809017	+	1.40126i	0.330280	+	0.572061i
$7$	0.763932			0.288739			0.144370	−	0.989524i	$-0.453885\pi$
$7$	0.763932			0.288739			0.144370	+	0.989524i	$0.453885\pi$
$8$	2.23607			0.790569
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.809017	−	1.40126i	−0.255834	−	0.443117i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	0.618034			0.178411
$13$	0.618034	+	1.07047i	0.171412	+	0.296894i	0.938914	−	0.344153i	$-0.111834\pi$
$13$	0.618034	+	1.07047i	0.171412	+	0.296894i	−0.767502	+	0.641047i	$0.778500\pi$
$14$	0.618034	−	1.07047i	0.165177	−	0.286094i
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	2.42705	−	4.20378i	0.606763	−	1.05094i
$17$	1.73607	−	3.00696i	0.421058	−	0.729294i	−0.574985	−	0.818164i	$-0.694992\pi$
$17$	1.73607	−	3.00696i	0.421058	−	0.729294i	0.996043	+	0.0888696i	$0.0283254\pi$
$18$	−1.61803			−0.381374
$19$	−4.35410	−	0.204441i	−0.998899	−	0.0469020i
$19$	−4.35410	−	0.204441i	−0.998899	−	0.0469020i
$20$	−0.618034			−0.138197
$21$	−0.381966	+	0.661585i	−0.0833518	+	0.144370i
$22$	1.61803	−	2.80252i	0.344966	−	0.597499i
$23$	1.23607	+	2.14093i	0.257738	+	0.446415i	0.965636	−	0.259900i	$-0.0836895\pi$
$23$	1.23607	+	2.14093i	0.257738	+	0.446415i	−0.707898	+	0.706315i	$0.750356\pi$
$24$	−1.11803	+	1.93649i	−0.228218	+	0.395285i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.00000			0.392232
$27$	1.00000			0.192450
$28$	−0.236068	−	0.408882i	−0.0446127	−	0.0772714i
$29$	0.381966	+	0.661585i	0.0709293	+	0.122853i	0.899309	−	0.437314i	$-0.144070\pi$
$29$	0.381966	+	0.661585i	0.0709293	+	0.122853i	−0.828380	+	0.560167i	$0.810737\pi$
$30$	1.61803			0.295411
$31$	−8.23607			−1.47924			−0.739621	−	0.673024i	$-0.764995\pi$
$31$	−8.23607			−1.47924			−0.739621	+	0.673024i	$0.764995\pi$
$32$	−1.69098	−	2.92887i	−0.298926	−	0.517756i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	−2.80902	−	4.86536i	−0.481742	−	0.834402i
$35$	0.381966	−	0.661585i	0.0645640	−	0.111828i
$36$	−0.309017	+	0.535233i	−0.0515028	+	0.0892055i
$37$	2.47214			0.406417			0.203208	−	0.979136i	$-0.434863\pi$
$37$	2.47214			0.406417			0.203208	+	0.979136i	$0.434863\pi$
$38$	−3.80902	+	5.93583i	−0.617904	+	0.962918i
$39$	−1.23607			−0.197929
$40$	1.11803	−	1.93649i	0.176777	−	0.306186i
$41$	−3.85410	+	6.67550i	−0.601910	+	1.04254i	0.390622	+	0.920551i	$0.372260\pi$
$41$	−3.85410	+	6.67550i	−0.601910	+	1.04254i	−0.992532	+	0.121987i	$0.961073\pi$
$42$	0.618034	+	1.07047i	0.0953647	+	0.165177i
$43$	−5.85410	+	10.1396i	−0.892742	+	1.54627i	−0.0561679	+	0.998421i	$0.517888\pi$
$43$	−5.85410	+	10.1396i	−0.892742	+	1.54627i	−0.836574	+	0.547853i	$0.815445\pi$
$44$	−0.618034	−	1.07047i	−0.0931721	−	0.161379i
$45$	−1.00000			−0.149071
$46$	4.00000			0.589768
$47$	−0.881966	−	1.52761i	−0.128648	−	0.222825i	0.794505	−	0.607258i	$-0.207730\pi$
$47$	−0.881966	−	1.52761i	−0.128648	−	0.222825i	−0.923153	+	0.384433i	$0.874397\pi$
$48$	2.42705	+	4.20378i	0.350315	+	0.606763i
$49$	−6.41641			−0.916630
$50$	−1.61803			−0.228825
$51$	1.73607	+	3.00696i	0.243098	+	0.421058i
$52$	0.381966	−	0.661585i	0.0529692	−	0.0917453i
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	0.898321	−	0.439340i	$-0.144788\pi$
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	−0.829640	+	0.558298i	$0.811454\pi$
$54$	0.809017	−	1.40126i	0.110093	−	0.190687i
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$	1.70820			0.228268
$57$	2.35410	−	3.66854i	0.311808	−	0.485910i
$58$	1.23607			0.162304
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	−0.793560	−	0.608492i	$-0.791775\pi$
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	0.923749	+	0.382998i	$0.125108\pi$
$60$	0.309017	−	0.535233i	0.0398939	−	0.0690983i
$61$	−6.23607	−	10.8012i	−0.798447	−	1.38295i	−0.920627	−	0.390442i	$-0.872322\pi$
$61$	−6.23607	−	10.8012i	−0.798447	−	1.38295i	0.122181	−	0.992508i	$-0.461011\pi$
$62$	−6.66312	+	11.5409i	−0.846217	+	1.46569i
$63$	−0.381966	−	0.661585i	−0.0481232	−	0.0833518i
$64$	4.23607			0.529508
$65$	1.23607			0.153315
$66$	1.61803	+	2.80252i	0.199166	+	0.344966i
$67$	1.61803	+	2.80252i	0.197674	+	0.342382i	0.947774	−	0.318943i	$-0.103328\pi$
$67$	1.61803	+	2.80252i	0.197674	+	0.342382i	−0.750100	+	0.661325i	$0.769994\pi$
$68$	−2.14590			−0.260228
$69$	−2.47214			−0.297610
$70$	−0.618034	−	1.07047i	−0.0738692	−	0.127945i
$71$	−4.61803	+	7.99867i	−0.548060	+	0.949267i	0.450348	+	0.892853i	$0.351300\pi$
$71$	−4.61803	+	7.99867i	−0.548060	+	0.949267i	−0.998407	+	0.0564141i	$0.982033\pi$
$72$	−1.11803	−	1.93649i	−0.131762	−	0.228218i
$73$	1.76393	−	3.05522i	0.206453	−	0.357586i	−0.744142	−	0.668022i	$-0.767141\pi$
$73$	1.76393	−	3.05522i	0.206453	−	0.357586i	0.950595	+	0.310435i	$0.100475\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	1.00000			0.115470
$76$	1.23607	+	2.39364i	0.141787	+	0.274569i
$77$	1.52786			0.174116
$78$	−1.00000	+	1.73205i	−0.113228	+	0.196116i
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−2.42705	−	4.20378i	−0.271353	−	0.469996i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.23607	+	10.8012i	0.688659	+	1.19279i
$83$	15.1803			1.66626			0.833129	−	0.553078i	$-0.186547\pi$
$83$	15.1803			1.66626			0.833129	+	0.553078i	$0.186547\pi$
$84$	0.472136			0.0515143
$85$	−1.73607	−	3.00696i	−0.188303	−	0.326150i
$86$	9.47214	+	16.4062i	1.02141	+	1.76913i
$87$	−0.763932			−0.0819021
$88$	4.47214			0.476731
$89$	−1.76393	−	3.05522i	−0.186976	−	0.323853i	0.757264	−	0.653109i	$-0.226535\pi$
$89$	−1.76393	−	3.05522i	−0.186976	−	0.323853i	−0.944241	+	0.329256i	$0.893202\pi$
$90$	−0.809017	+	1.40126i	−0.0852779	+	0.147706i
$91$	0.472136	+	0.817763i	0.0494933	+	0.0857249i
$92$	0.763932	−	1.32317i	0.0796454	−	0.137950i
$93$	4.11803	−	7.13264i	0.427020	−	0.739621i
$94$	−2.85410			−0.294378
$95$	−2.35410	+	3.66854i	−0.241526	+	0.376385i
$96$	3.38197			0.345170
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	−5.19098	+	8.99105i	−0.524368	+	0.908233i
$99$	−1.00000	−	1.73205i	−0.100504	−	0.174078i
$100$	−0.309017	+	0.535233i	−0.0309017	+	0.0535233i
$101$	−4.09017	−	7.08438i	−0.406987	−	0.704922i	0.587563	−	0.809178i	$-0.300087\pi$
$101$	−4.09017	−	7.08438i	−0.406987	−	0.704922i	−0.994551	+	0.104256i	$0.966754\pi$
$102$	5.61803			0.556268
$103$	0.944272			0.0930419			0.0465209	−	0.998917i	$-0.485187\pi$
$103$	0.944272			0.0930419			0.0465209	+	0.998917i	$0.485187\pi$
$104$	1.38197	+	2.39364i	0.135513	+	0.234715i
$105$	0.381966	+	0.661585i	0.0372761	+	0.0645640i
$106$	1.61803			0.157157
$107$	−13.6525			−1.31983			−0.659917	−	0.751338i	$-0.729409\pi$
$107$	−13.6525			−1.31983			−0.659917	+	0.751338i	$0.729409\pi$
$108$	−0.309017	−	0.535233i	−0.0297352	−	0.0515028i
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$	−1.61803	−	2.80252i	−0.154273	−	0.267210i
$111$	−1.23607	+	2.14093i	−0.117322	+	0.203208i
$112$	1.85410	−	3.21140i	0.175196	−	0.303449i
$113$	6.52786			0.614090			0.307045	−	0.951695i	$-0.400660\pi$
$113$	6.52786			0.614090			0.307045	+	0.951695i	$0.400660\pi$
$114$	−3.23607	−	6.26662i	−0.303086	−	0.586923i
$115$	2.47214			0.230528
$116$	0.236068	−	0.408882i	0.0219184	−	0.0379637i
$117$	0.618034	−	1.07047i	0.0571373	−	0.0989646i
$118$	−1.61803	−	2.80252i	−0.148952	−	0.257993i
$119$	1.32624	−	2.29711i	0.121576	−	0.210576i
$120$	1.11803	+	1.93649i	0.102062	+	0.176777i
$121$	−7.00000			−0.636364
$122$	−20.1803			−1.82704
$123$	−3.85410	−	6.67550i	−0.347513	−	0.601910i
$124$	2.54508	+	4.40822i	0.228555	+	0.395870i
$125$	−1.00000			−0.0894427
$126$	−1.23607			−0.110118
$127$	7.61803	+	13.1948i	0.675991	+	1.17085i	0.976178	+	0.216971i	$0.0696176\pi$
$127$	7.61803	+	13.1948i	0.675991	+	1.17085i	−0.300187	+	0.953880i	$0.597049\pi$
$128$	6.80902	−	11.7936i	0.601838	−	1.04241i
$129$	−5.85410	−	10.1396i	−0.515425	−	0.892742i
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	1.23607	−	2.14093i	0.107996	−	0.187054i	−0.806962	−	0.590603i	$-0.798890\pi$
$131$	1.23607	−	2.14093i	0.107996	−	0.187054i	0.914958	+	0.403549i	$0.132223\pi$
$132$	1.23607			0.107586
$133$	−3.32624	−	0.156179i	−0.288421	−	0.0135424i
$134$	5.23607			0.452327
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	3.88197	−	6.72376i	0.332876	−	0.576558i
$137$	−10.2082	−	17.6811i	−0.872146	−	1.51060i	−0.859772	−	0.510677i	$-0.829395\pi$
$137$	−10.2082	−	17.6811i	−0.872146	−	1.51060i	−0.0123732	−	0.999923i	$-0.503939\pi$
$138$	−2.00000	+	3.46410i	−0.170251	+	0.294884i
$139$	−1.88197	−	3.25966i	−0.159626	−	0.276481i	0.775108	−	0.631829i	$-0.217696\pi$
$139$	−1.88197	−	3.25966i	−0.159626	−	0.276481i	−0.934734	+	0.355348i	$0.884362\pi$
$140$	−0.472136			−0.0399028
$141$	1.76393			0.148550
$142$	7.47214	+	12.9421i	0.627048	+	1.08608i
$143$	1.23607	+	2.14093i	0.103365	+	0.179034i
$144$	−4.85410			−0.404508
$145$	0.763932			0.0634411
$146$	−2.85410	−	4.94345i	−0.236207	−	0.409123i
$147$	3.20820	−	5.55677i	0.264608	−	0.458315i
$148$	−0.763932	−	1.32317i	−0.0627948	−	0.108764i
$149$	4.85410	−	8.40755i	0.397664	−	0.688773i	−0.595774	−	0.803152i	$-0.703154\pi$
$149$	4.85410	−	8.40755i	0.397664	−	0.688773i	0.993437	+	0.114379i	$0.0364878\pi$
$150$	0.809017	−	1.40126i	0.0660560	−	0.114412i
$151$	−16.7082			−1.35969			−0.679847	−	0.733354i	$-0.737954\pi$
$151$	−16.7082			−1.35969			−0.679847	+	0.733354i	$0.737954\pi$
$152$	−9.73607	−	0.457144i	−0.789699	−	0.0370792i
$153$	−3.47214			−0.280706
$154$	1.23607	−	2.14093i	0.0996052	−	0.172521i
$155$	−4.11803	+	7.13264i	−0.330768	+	0.572908i
$156$	0.381966	+	0.661585i	0.0305818	+	0.0529692i
$157$	−10.0000	+	17.3205i	−0.798087	+	1.38233i	0.122774	+	0.992435i	$0.460821\pi$
$157$	−10.0000	+	17.3205i	−0.798087	+	1.38233i	−0.920860	+	0.389892i	$0.872512\pi$
$158$		0			0
$159$	−1.00000			−0.0793052
$160$	−3.38197			−0.267368
$161$	0.944272	+	1.63553i	0.0744191	+	0.128898i
$162$	0.809017	+	1.40126i	0.0635624	+	0.110093i
$163$	8.94427			0.700569			0.350285	−	0.936643i	$-0.386085\pi$
$163$	8.94427			0.700569			0.350285	+	0.936643i	$0.386085\pi$
$164$	4.76393			0.372001
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$	12.2812	−	21.2716i	0.953202	−	1.65099i
$167$	−0.409830	−	0.709846i	−0.0317136	−	0.0549296i	0.849733	−	0.527213i	$-0.176763\pi$
$167$	−0.409830	−	0.709846i	−0.0317136	−	0.0549296i	−0.881447	+	0.472284i	$0.843430\pi$
$168$	−0.854102	+	1.47935i	−0.0658954	+	0.114134i
$169$	5.73607	−	9.93516i	0.441236	−	0.764243i
$170$	−5.61803			−0.430884
$171$	2.00000	+	3.87298i	0.152944	+	0.296174i
$172$	7.23607			0.551745
$173$	5.94427	−	10.2958i	0.451935	−	0.782774i	−0.546572	−	0.837412i	$-0.684067\pi$
$173$	5.94427	−	10.2958i	0.451935	−	0.782774i	0.998506	+	0.0546387i	$0.0174007\pi$
$174$	−0.618034	+	1.07047i	−0.0468530	+	0.0811518i
$175$	−0.381966	−	0.661585i	−0.0288739	−	0.0500111i
$176$	4.85410	−	8.40755i	0.365892	−	0.633743i
$177$	1.00000	+	1.73205i	0.0751646	+	0.130189i
$178$	−5.70820			−0.427848
$179$	17.7082			1.32357			0.661787	−	0.749692i	$-0.269798\pi$
$179$	17.7082			1.32357			0.661787	+	0.749692i	$0.269798\pi$
$180$	0.309017	+	0.535233i	0.0230328	+	0.0398939i
$181$	6.73607	+	11.6672i	0.500688	+	0.867217i	1.00000		0.000794604i	$0.000252930\pi$
$181$	6.73607	+	11.6672i	0.500688	+	0.867217i	−0.499312	+	0.866422i	$0.666414\pi$
$182$	1.52786			0.113253
$183$	12.4721			0.921967
$184$	2.76393	+	4.78727i	0.203760	+	0.352922i
$185$	1.23607	−	2.14093i	0.0908775	−	0.157404i
$186$	−6.66312	−	11.5409i	−0.488564	−	0.846217i
$187$	3.47214	−	6.01392i	0.253908	−	0.439781i
$188$	−0.545085	+	0.944115i	−0.0397544	+	0.0688567i
$189$	0.763932			0.0555679
$190$	3.23607	+	6.26662i	0.234769	+	0.454628i
$191$	21.7082			1.57075			0.785375	−	0.619020i	$-0.212470\pi$
$191$	21.7082			1.57075			0.785375	+	0.619020i	$0.212470\pi$
$192$	−2.11803	+	3.66854i	−0.152856	+	0.264754i
$193$	−2.38197	+	4.12569i	−0.171458	+	0.296973i	−0.938930	−	0.344109i	$-0.888181\pi$
$193$	−2.38197	+	4.12569i	−0.171458	+	0.296973i	0.767472	+	0.641082i	$0.221514\pi$
$194$	−1.61803	−	2.80252i	−0.116168	−	0.201209i
$195$	−0.618034	+	1.07047i	−0.0442583	+	0.0766577i
$196$	1.98278	+	3.43427i	0.141627	+	0.245305i
$197$	11.4721			0.817356			0.408678	−	0.912679i	$-0.365990\pi$
$197$	11.4721			0.817356			0.408678	+	0.912679i	$0.365990\pi$
$198$	−3.23607			−0.229977
$199$	6.94427	+	12.0278i	0.492266	+	0.852630i	0.999960	−	0.00890711i	$-0.00283526\pi$
$199$	6.94427	+	12.0278i	0.492266	+	0.852630i	−0.507694	+	0.861537i	$0.669502\pi$
$200$	−1.11803	−	1.93649i	−0.0790569	−	0.136931i
$201$	−3.23607			−0.228255
$202$	−13.2361			−0.931286
$203$	0.291796	+	0.505406i	0.0204801	+	0.0354725i
$204$	1.07295	−	1.85840i	0.0751215	−	0.130114i
$205$	3.85410	+	6.67550i	0.269182	+	0.466237i
$206$	0.763932	−	1.32317i	0.0532257	−	0.0921896i
$207$	1.23607	−	2.14093i	0.0859127	−	0.148805i
$208$	6.00000			0.416025
$209$	−8.70820	−	0.408882i	−0.602359	−	0.0282829i
$210$	1.23607			0.0852968
$211$	−9.59017	+	16.6107i	−0.660215	+	1.14353i	0.320345	+	0.947301i	$0.396201\pi$
$211$	−9.59017	+	16.6107i	−0.660215	+	1.14353i	−0.980559	+	0.196224i	$0.937132\pi$
$212$	0.309017	−	0.535233i	0.0212234	−	0.0367600i
$213$	−4.61803	−	7.99867i	−0.316422	−	0.548060i
$214$	−11.0451	+	19.1306i	−0.755026	+	1.30774i
$215$	5.85410	+	10.1396i	0.399246	+	0.691515i
$216$	2.23607			0.152145
$217$	−6.29180			−0.427115
$218$	−5.66312	−	9.80881i	−0.383555	−	0.664336i
$219$	1.76393	+	3.05522i	0.119195	+	0.206453i
$220$	−1.23607			−0.0833357
$221$	4.29180			0.288697
$222$	2.00000	+	3.46410i	0.134231	+	0.232495i
$223$	−4.32624	+	7.49326i	−0.289706	+	0.501786i	−0.973740	−	0.227665i	$-0.926891\pi$
$223$	−4.32624	+	7.49326i	−0.289706	+	0.501786i	0.684033	+	0.729451i	$0.260224\pi$
$224$	−1.29180	−	2.23746i	−0.0863118	−	0.149496i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	5.28115	−	9.14723i	0.351297	−	0.608464i
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$	−2.69098	−	0.126351i	−0.178215	−	0.00836783i
$229$	13.4721			0.890264			0.445132	−	0.895465i	$-0.353157\pi$
$229$	13.4721			0.890264			0.445132	+	0.895465i	$0.353157\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$	−0.763932	+	1.32317i	−0.0502630	+	0.0870581i
$232$	0.854102	+	1.47935i	0.0560745	+	0.0971240i
$233$	0.0278640	−	0.0482619i	0.00182543	−	0.00316174i	−0.865111	−	0.501580i	$-0.832752\pi$
$233$	0.0278640	−	0.0482619i	0.00182543	−	0.00316174i	0.866937	+	0.498418i	$0.166086\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$	−1.76393			−0.115066
$236$	−1.23607			−0.0804612
$237$		0			0
$238$	−2.14590	−	3.71680i	−0.139098	−	0.240925i
$239$	21.1246			1.36644			0.683219	−	0.730214i	$-0.260580\pi$
$239$	21.1246			1.36644			0.683219	+	0.730214i	$0.260580\pi$
$240$	4.85410			0.313331
$241$	10.6803	+	18.4989i	0.687981	+	1.19162i	0.972490	+	0.232945i	$0.0748362\pi$
$241$	10.6803	+	18.4989i	0.687981	+	1.19162i	−0.284509	+	0.958673i	$0.591830\pi$
$242$	−5.66312	+	9.80881i	−0.364039	+	0.630534i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.85410	+	6.67550i	−0.246734	+	0.427355i
$245$	−3.20820	+	5.55677i	−0.204965	+	0.355009i
$246$	−12.4721			−0.795194
$247$	−2.47214	−	4.78727i	−0.157298	−	0.304607i
$248$	−18.4164			−1.16944
$249$	−7.59017	+	13.1466i	−0.481007	+	0.833129i
$250$	−0.809017	+	1.40126i	−0.0511667	+	0.0886234i
$251$	−15.7082	−	27.2074i	−0.991493	−	1.71732i	−0.608468	−	0.793578i	$-0.708216\pi$
$251$	−15.7082	−	27.2074i	−0.991493	−	1.71732i	−0.383025	−	0.923738i	$-0.625118\pi$
$252$	−0.236068	+	0.408882i	−0.0148709	+	0.0257571i
$253$	2.47214	+	4.28187i	0.155422	+	0.269199i
$254$	24.6525			1.54683
$255$	3.47214			0.217434
$256$	−6.78115	−	11.7453i	−0.423822	−	0.734081i
$257$	−2.70820	−	4.69075i	−0.168933	−	0.292601i	0.769112	−	0.639114i	$-0.220699\pi$
$257$	−2.70820	−	4.69075i	−0.168933	−	0.292601i	−0.938045	+	0.346513i	$0.887366\pi$
$258$	−18.9443			−1.17942
$259$	1.88854			0.117348
$260$	−0.381966	−	0.661585i	−0.0236885	−	0.0410297i
$261$	0.381966	−	0.661585i	0.0236431	−	0.0409511i
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$	2.35410	−	4.07742i	0.145160	−	0.251425i	−0.784273	−	0.620416i	$-0.786964\pi$
$263$	2.35410	−	4.07742i	0.145160	−	0.251425i	0.929433	+	0.368992i	$0.120297\pi$
$264$	−2.23607	+	3.87298i	−0.137620	+	0.238366i
$265$	1.00000			0.0614295
$266$	−2.90983	+	4.53457i	−0.178413	+	0.278032i
$267$	3.52786			0.215902
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	−12.4721	+	21.6024i	−0.760440	+	1.31712i	0.182185	+	0.983264i	$0.441683\pi$
$269$	−12.4721	+	21.6024i	−0.760440	+	1.31712i	−0.942624	+	0.333856i	$0.891650\pi$
$270$	−0.809017	−	1.40126i	−0.0492352	−	0.0852779i
$271$	−6.11803	+	10.5967i	−0.371644	+	0.643706i	−0.989819	−	0.142334i	$-0.954539\pi$
$271$	−6.11803	+	10.5967i	−0.371644	+	0.643706i	0.618175	+	0.786041i	$0.287872\pi$
$272$	−8.42705	−	14.5961i	−0.510965	−	0.885017i
$273$	−0.944272			−0.0571499
$274$	−33.0344			−1.99568
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$	0.763932	+	1.32317i	0.0459833	+	0.0796454i
$277$	17.7082			1.06398			0.531991	−	0.846750i	$-0.321444\pi$
$277$	17.7082			1.06398			0.531991	+	0.846750i	$0.321444\pi$
$278$	−6.09017			−0.365264
$279$	4.11803	+	7.13264i	0.246540	+	0.427020i
$280$	0.854102	−	1.47935i	0.0510424	−	0.0884080i
$281$	−0.618034	−	1.07047i	−0.0368688	−	0.0638587i	0.847002	−	0.531589i	$-0.178405\pi$
$281$	−0.618034	−	1.07047i	−0.0368688	−	0.0638587i	−0.883871	+	0.467731i	$0.845072\pi$
$282$	1.42705	−	2.47172i	0.0849796	−	0.147189i
$283$	−5.09017	+	8.81643i	−0.302579	+	0.524083i	−0.976719	−	0.214521i	$-0.931181\pi$
$283$	−5.09017	+	8.81643i	−0.302579	+	0.524083i	0.674140	+	0.738603i	$0.264514\pi$
$284$	5.70820			0.338720
$285$	−2.00000	−	3.87298i	−0.118470	−	0.229416i
$286$	4.00000			0.236525
$287$	−2.94427	+	5.09963i	−0.173795	+	0.301022i
$288$	−1.69098	+	2.92887i	−0.0996421	+	0.172585i
$289$	2.47214	+	4.28187i	0.145420	+	0.251874i
$290$	0.618034	−	1.07047i	0.0362922	−	0.0628599i
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	−2.18034			−0.127595
$293$	−3.58359			−0.209356			−0.104678	−	0.994506i	$-0.533381\pi$
$293$	−3.58359			−0.209356			−0.104678	+	0.994506i	$0.533381\pi$
$294$	−5.19098	−	8.99105i	−0.302744	−	0.524368i
$295$	−1.00000	−	1.73205i	−0.0582223	−	0.100844i
$296$	5.52786			0.321301
$297$	2.00000			0.116052
$298$	−7.85410	−	13.6037i	−0.454976	−	0.788041i
$299$	−1.52786	+	2.64634i	−0.0883587	+	0.153042i
$300$	−0.309017	−	0.535233i	−0.0178411	−	0.0309017i
$301$	−4.47214	+	7.74597i	−0.257770	+	0.446470i
$302$	−13.5172	+	23.4125i	−0.777829	+	1.34724i
$303$	8.18034			0.469948
$304$	−11.4271	+	17.8075i	−0.655386	+	1.02133i
$305$	−12.4721			−0.714152
$306$	−2.80902	+	4.86536i	−0.160581	+	0.278134i
$307$	10.0902	−	17.4767i	0.575876	−	0.997447i	−0.420069	−	0.907492i	$-0.637994\pi$
$307$	10.0902	−	17.4767i	0.575876	−	0.997447i	0.995946	−	0.0899552i	$-0.0286724\pi$
$308$	−0.472136	−	0.817763i	−0.0269024	−	0.0465964i
$309$	−0.472136	+	0.817763i	−0.0268589	+	0.0465209i
$310$	6.66312	+	11.5409i	0.378440	+	0.655477i
$311$	−21.4164			−1.21441			−0.607207	−	0.794544i	$-0.707710\pi$
$311$	−21.4164			−1.21441			−0.607207	+	0.794544i	$0.707710\pi$
$312$	−2.76393			−0.156477
$313$	−15.7984	−	27.3636i	−0.892977	−	1.54668i	−0.836289	−	0.548289i	$-0.815279\pi$
$313$	−15.7984	−	27.3636i	−0.892977	−	1.54668i	−0.0566882	−	0.998392i	$-0.518054\pi$
$314$	16.1803	+	28.0252i	0.913109	+	1.58155i
$315$	−0.763932			−0.0430427
$316$		0			0
$317$	−2.44427	−	4.23360i	−0.137284	−	0.237783i	0.789184	−	0.614157i	$-0.210504\pi$
$317$	−2.44427	−	4.23360i	−0.137284	−	0.237783i	−0.926468	+	0.376374i	$0.877171\pi$
$318$	−0.809017	+	1.40126i	−0.0453674	+	0.0785787i
$319$	0.763932	+	1.32317i	0.0427720	+	0.0740832i
$320$	2.11803	−	3.66854i	0.118402	−	0.205078i
$321$	6.82624	−	11.8234i	0.381003	−	0.659917i
$322$	3.05573			0.170289
$323$	−8.17376	+	12.7377i	−0.454800	+	0.708743i
$324$	0.618034			0.0343352
$325$	0.618034	−	1.07047i	0.0342824	−	0.0593788i
$326$	7.23607	−	12.5332i	0.400769	−	0.694152i
$327$	3.50000	+	6.06218i	0.193550	+	0.335239i
$328$	−8.61803	+	14.9269i	−0.475851	+	0.824199i
$329$	−0.673762	−	1.16699i	−0.0371457	−	0.0643382i
$330$	3.23607			0.178140
$331$	−2.47214			−0.135881			−0.0679404	−	0.997689i	$-0.521643\pi$
$331$	−2.47214			−0.135881			−0.0679404	+	0.997689i	$0.521643\pi$
$332$	−4.69098	−	8.12502i	−0.257451	−	0.445918i
$333$	−1.23607	−	2.14093i	−0.0677361	−	0.117322i
$334$	−1.32624			−0.0725685
$335$	3.23607			0.176805
$336$	1.85410	+	3.21140i	0.101150	+	0.175196i
$337$	3.23607	−	5.60503i	0.176280	−	0.305326i	−0.764324	−	0.644833i	$-0.776927\pi$
$337$	3.23607	−	5.60503i	0.176280	−	0.305326i	0.940603	+	0.339507i	$0.110260\pi$
$338$	−9.28115	−	16.0754i	−0.504828	−	0.874388i
$339$	−3.26393	+	5.65330i	−0.177272	+	0.307045i
$340$	−1.07295	+	1.85840i	−0.0581888	+	0.100786i
$341$	−16.4721			−0.892016
$342$	7.04508	+	0.330792i	0.380955	+	0.0178872i
$343$	−10.2492			−0.553406
$344$	−13.0902	+	22.6728i	−0.705775	+	1.22244i
$345$	−1.23607	+	2.14093i	−0.0665477	+	0.115264i
$346$	−9.61803	−	16.6589i	−0.517069	−	0.895589i
$347$	14.0623	−	24.3566i	0.754904	−	1.30753i	−0.190518	−	0.981684i	$-0.561017\pi$
$347$	14.0623	−	24.3566i	0.754904	−	1.30753i	0.945422	−	0.325849i	$-0.105650\pi$
$348$	0.236068	+	0.408882i	0.0126546	+	0.0219184i
$349$	−27.0000			−1.44528			−0.722638	−	0.691226i	$-0.757071\pi$
$349$	−27.0000			−1.44528			−0.722638	+	0.691226i	$0.757071\pi$
$350$	−1.23607			−0.0660706
$351$	0.618034	+	1.07047i	0.0329882	+	0.0571373i
$352$	−3.38197	−	5.85774i	−0.180259	−	0.312218i
$353$	30.9443			1.64700			0.823499	−	0.567318i	$-0.192019\pi$
$353$	30.9443			1.64700			0.823499	+	0.567318i	$0.192019\pi$
$354$	3.23607			0.171995
$355$	4.61803	+	7.99867i	0.245100	+	0.424525i
$356$	−1.09017	+	1.88823i	−0.0577789	+	0.100076i
$357$	1.32624	+	2.29711i	0.0701920	+	0.121576i
$358$	14.3262	−	24.8138i	0.757165	−	1.31145i
$359$	−11.7639	+	20.3757i	−0.620877	+	1.07539i	0.368446	+	0.929649i	$0.379890\pi$
$359$	−11.7639	+	20.3757i	−0.620877	+	1.07539i	−0.989323	+	0.145741i	$0.953443\pi$
$360$	−2.23607			−0.117851
$361$	18.9164	+	1.78031i	0.995600	+	0.0937007i
$362$	21.7984			1.14570
$363$	3.50000	−	6.06218i	0.183702	−	0.318182i
$364$	0.291796	−	0.505406i	0.0152943	−	0.0264905i
$365$	−1.76393	−	3.05522i	−0.0923284	−	0.159918i
$366$	10.0902	−	17.4767i	0.527422	−	0.913521i
$367$	−3.09017	−	5.35233i	−0.161306	−	0.279389i	0.774032	−	0.633147i	$-0.218237\pi$
$367$	−3.09017	−	5.35233i	−0.161306	−	0.279389i	−0.935337	+	0.353758i	$0.884904\pi$
$368$	12.0000			0.625543
$369$	7.70820			0.401273
$370$	−2.00000	−	3.46410i	−0.103975	−	0.180090i
$371$	0.381966	+	0.661585i	0.0198307	+	0.0343478i
$372$	−5.09017			−0.263913
$373$	35.5967			1.84313			0.921565	−	0.388224i	$-0.126911\pi$
$373$	35.5967			1.84313			0.921565	+	0.388224i	$0.126911\pi$
$374$	−5.61803	−	9.73072i	−0.290502	−	0.503164i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−1.97214	−	3.41584i	−0.101705	−	0.176158i
$377$	−0.472136	+	0.817763i	−0.0243162	+	0.0421170i
$378$	0.618034	−	1.07047i	0.0317882	−	0.0550588i
$379$	25.5279			1.31128			0.655639	−	0.755074i	$-0.272399\pi$
$379$	25.5279			1.31128			0.655639	+	0.755074i	$0.272399\pi$
$380$	2.69098	+	0.126351i	0.138045	+	0.00648169i
$381$	−15.2361			−0.780567
$382$	17.5623	−	30.4188i	0.898566	−	1.55636i
$383$	−18.0623	+	31.2848i	−0.922941	+	1.59858i	−0.128101	+	0.991761i	$0.540888\pi$
$383$	−18.0623	+	31.2848i	−0.922941	+	1.59858i	−0.794840	+	0.606819i	$0.792445\pi$
$384$	6.80902	+	11.7936i	0.347471	+	0.601838i
$385$	0.763932	−	1.32317i	0.0389336	−	0.0674349i
$386$	3.85410	+	6.67550i	0.196169	+	0.339774i
$387$	11.7082			0.595161
$388$	−1.23607			−0.0627518
$389$	−3.56231	−	6.17009i	−0.180616	−	0.312836i	0.761474	−	0.648195i	$-0.224476\pi$
$389$	−3.56231	−	6.17009i	−0.180616	−	0.312836i	−0.942091	+	0.335359i	$0.891142\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$	8.58359			0.434091
$392$	−14.3475			−0.724659
$393$	1.23607	+	2.14093i	0.0623514	+	0.107996i
$394$	9.28115	−	16.0754i	0.467578	−	0.809868i
$395$		0			0
$396$	−0.618034	+	1.07047i	−0.0310574	+	0.0537930i
$397$	7.09017	−	12.2805i	0.355845	−	0.616342i	−0.631417	−	0.775444i	$-0.717526\pi$
$397$	7.09017	−	12.2805i	0.355845	−	0.616342i	0.987262	+	0.159101i	$0.0508596\pi$
$398$	22.4721			1.12643
$399$	1.79837	−	2.80252i	0.0900313	−	0.140301i
$400$	−4.85410			−0.242705
$401$	−16.8541	+	29.1922i	−0.841654	+	1.45779i	0.0468422	+	0.998902i	$0.485084\pi$
$401$	−16.8541	+	29.1922i	−0.841654	+	1.45779i	−0.888496	+	0.458885i	$0.848249\pi$
$402$	−2.61803	+	4.53457i	−0.130576	+	0.226164i
$403$	−5.09017	−	8.81643i	−0.253559	−	0.439178i
$404$	−2.52786	+	4.37839i	−0.125766	+	0.217833i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	0.944272			0.0468634
$407$	4.94427			0.245078
$408$	3.88197	+	6.72376i	0.192186	+	0.332876i
$409$	−9.18034	−	15.9008i	−0.453939	−	0.786245i	0.544688	−	0.838639i	$-0.316648\pi$
$409$	−9.18034	−	15.9008i	−0.453939	−	0.786245i	−0.998626	+	0.0523941i	$0.983315\pi$
$410$	12.4721			0.615955
$411$	20.4164			1.00707
$412$	−0.291796	−	0.505406i	−0.0143758	−	0.0248995i
$413$	0.763932	−	1.32317i	0.0375906	−	0.0651089i
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$	7.59017	−	13.1466i	0.372587	−	0.645339i
$416$	2.09017	−	3.62028i	0.102479	−	0.177499i
$417$	3.76393			0.184321
$418$	−7.61803	+	11.8717i	−0.372610	+	0.580662i
$419$	34.9443			1.70714			0.853570	−	0.520979i	$-0.174433\pi$
$419$	34.9443			1.70714			0.853570	+	0.520979i	$0.174433\pi$
$420$	0.236068	−	0.408882i	0.0115189	−	0.0199514i
$421$	9.18034	−	15.9008i	0.447422	−	0.774958i	−0.550795	−	0.834641i	$-0.685675\pi$
$421$	9.18034	−	15.9008i	0.447422	−	0.774958i	0.998217	+	0.0596822i	$0.0190087\pi$
$422$	15.5172	+	26.8766i	0.755366	+	1.30833i
$423$	−0.881966	+	1.52761i	−0.0428827	+	0.0742749i
$424$	1.11803	+	1.93649i	0.0542965	+	0.0940443i
$425$	−3.47214			−0.168423
$426$	−14.9443			−0.724052
$427$	−4.76393	−	8.25137i	−0.230543	−	0.399312i
$428$	4.21885	+	7.30726i	0.203926	+	0.353210i
$429$	−2.47214			−0.119356
$430$	18.9443			0.913574
$431$	0.763932	+	1.32317i	0.0367973	+	0.0637348i	0.883838	−	0.467794i	$-0.154951\pi$
$431$	0.763932	+	1.32317i	0.0367973	+	0.0637348i	−0.847040	+	0.531529i	$0.821618\pi$
$432$	2.42705	−	4.20378i	0.116772	−	0.202254i
$433$	−4.79837	−	8.31103i	−0.230595	−	0.399402i	0.727388	−	0.686226i	$-0.240734\pi$
$433$	−4.79837	−	8.31103i	−0.230595	−	0.399402i	−0.957983	+	0.286824i	$0.907401\pi$
$434$	−5.09017	+	8.81643i	−0.244336	+	0.423202i
$435$	−0.381966	+	0.661585i	−0.0183139	+	0.0317206i
$436$	−4.32624			−0.207189
$437$	−4.94427	−	9.57454i	−0.236517	−	0.458012i
$438$	5.70820			0.272749
$439$	3.11803	−	5.40059i	0.148816	−	0.257756i	−0.781974	−	0.623311i	$-0.785787\pi$
$439$	3.11803	−	5.40059i	0.148816	−	0.257756i	0.930790	+	0.365554i	$0.119121\pi$
$440$	2.23607	−	3.87298i	0.106600	−	0.184637i
$441$	3.20820	+	5.55677i	0.152772	+	0.264608i
$442$	3.47214	−	6.01392i	0.165153	−	0.286053i
$443$	−3.35410	−	5.80948i	−0.159358	−	0.276016i	0.775279	−	0.631619i	$-0.217609\pi$
$443$	−3.35410	−	5.80948i	−0.159358	−	0.276016i	−0.934637	+	0.355602i	$0.884276\pi$
$444$	1.52786			0.0725092
$445$	−3.52786			−0.167237
$446$	7.00000	+	12.1244i	0.331460	+	0.574105i
$447$	4.85410	+	8.40755i	0.229591	+	0.397664i
$448$	3.23607			0.152890
$449$	−26.0689			−1.23027			−0.615133	−	0.788423i	$-0.710898\pi$
$449$	−26.0689			−1.23027			−0.615133	+	0.788423i	$0.710898\pi$
$450$	0.809017	+	1.40126i	0.0381374	+	0.0660560i
$451$	−7.70820	+	13.3510i	−0.362965	+	0.628674i
$452$	−2.01722	−	3.49393i	−0.0948821	−	0.164341i
$453$	8.35410	−	14.4697i	0.392510	−	0.679847i
$454$	3.23607	−	5.60503i	0.151876	−	0.263057i
$455$	0.944272			0.0442681
$456$	5.26393	−	8.20311i	0.246506	−	0.384146i
$457$	24.7639			1.15841			0.579204	−	0.815183i	$-0.303363\pi$
$457$	24.7639			1.15841			0.579204	+	0.815183i	$0.303363\pi$
$458$	10.8992	−	18.8779i	0.509286	−	0.882108i
$459$	1.73607	−	3.00696i	0.0810327	−	0.140353i
$460$	−0.763932	−	1.32317i	−0.0356185	−	0.0616931i
$461$	17.3820	−	30.1064i	0.809559	−	1.40220i	−0.103611	−	0.994618i	$-0.533040\pi$
$461$	17.3820	−	30.1064i	0.809559	−	1.40220i	0.913170	−	0.407579i	$-0.133627\pi$
$462$	1.23607	+	2.14093i	0.0575071	+	0.0996052i
$463$	−37.7082			−1.75245			−0.876224	−	0.481903i	$-0.839946\pi$
$463$	−37.7082			−1.75245			−0.876224	+	0.481903i	$0.839946\pi$
$464$	3.70820			0.172149
$465$	−4.11803	−	7.13264i	−0.190969	−	0.330768i
$466$	−0.0450850	−	0.0780895i	−0.00208852	−	0.00361742i
$467$	−15.7639			−0.729468			−0.364734	−	0.931112i	$-0.618840\pi$
$467$	−15.7639			−0.729468			−0.364734	+	0.931112i	$0.618840\pi$
$468$	−0.763932			−0.0353128
$469$	1.23607	+	2.14093i	0.0570763	+	0.0988591i
$470$	−1.42705	+	2.47172i	−0.0658250	+	0.114012i
$471$	−10.0000	−	17.3205i	−0.460776	−	0.798087i
$472$	2.23607	−	3.87298i	0.102923	−	0.178269i
$473$	−11.7082	+	20.2792i	−0.538344	+	0.932439i
$474$		0			0
$475$	2.00000	+	3.87298i	0.0917663	+	0.177705i
$476$	−1.63932			−0.0751381
$477$	0.500000	−	0.866025i	0.0228934	−	0.0396526i
$478$	17.0902	−	29.6010i	0.781686	−	1.35392i
$479$	17.0344	+	29.5045i	0.778324	+	1.34810i	0.932907	+	0.360116i	$0.117263\pi$
$479$	17.0344	+	29.5045i	0.778324	+	1.34810i	−0.154584	+	0.987980i	$0.549404\pi$
$480$	1.69098	−	2.92887i	0.0771825	−	0.133684i
$481$	1.52786	+	2.64634i	0.0696646	+	0.120663i
$482$	34.5623			1.57427
$483$	−1.88854			−0.0859317
$484$	2.16312	+	3.74663i	0.0983236	+	0.170301i
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$	−1.61803			−0.0733955
$487$	−33.7082			−1.52746			−0.763732	−	0.645533i	$-0.776635\pi$
$487$	−33.7082			−1.52746			−0.763732	+	0.645533i	$0.776635\pi$
$488$	−13.9443	−	24.1522i	−0.631228	−	1.09332i
$489$	−4.47214	+	7.74597i	−0.202237	+	0.350285i
$490$	5.19098	+	8.99105i	0.234505	+	0.406174i
$491$	10.8541	−	18.7999i	0.489839	−	0.848426i	−0.510093	−	0.860119i	$-0.670389\pi$
$491$	10.8541	−	18.7999i	0.489839	−	0.848426i	0.999932	+	0.0116937i	$0.00372231\pi$
$492$	−2.38197	+	4.12569i	−0.107387	+	0.186000i
$493$	2.65248			0.119462
$494$	−8.70820	−	0.408882i	−0.391801	−	0.0183965i
$495$	−2.00000			−0.0898933
$496$	−19.9894	+	34.6226i	−0.897549	+	1.55460i
$497$	−3.52786	+	6.11044i	−0.158246	+	0.274091i
$498$	12.2812	+	21.2716i	0.550332	+	0.953202i
$499$	11.8262	−	20.4836i	0.529415	−	0.916974i	−0.469996	−	0.882668i	$-0.655745\pi$
$499$	11.8262	−	20.4836i	0.529415	−	0.916974i	0.999411	−	0.0343055i	$-0.0109219\pi$
$500$	0.309017	+	0.535233i	0.0138197	+	0.0239364i
$501$	0.819660			0.0366197
$502$	−50.8328			−2.26878
$503$	−11.8820	−	20.5802i	−0.529791	−	0.917624i	−0.999396	−	0.0347480i	$-0.988937\pi$
$503$	−11.8820	−	20.5802i	−0.529791	−	0.917624i	0.469605	−	0.882876i	$-0.344396\pi$
$504$	−0.854102	−	1.47935i	−0.0380447	−	0.0658954i
$505$	−8.18034			−0.364020
$506$	8.00000			0.355643
$507$	5.73607	+	9.93516i	0.254748	+	0.441236i
$508$	4.70820	−	8.15485i	0.208893	−	0.361813i
$509$	−4.14590	−	7.18091i	−0.183764	−	0.318288i	0.759396	−	0.650629i	$-0.225495\pi$
$509$	−4.14590	−	7.18091i	−0.183764	−	0.318288i	−0.943159	+	0.332341i	$0.892161\pi$
$510$	2.80902	−	4.86536i	0.124385	−	0.215442i
$511$	1.34752	−	2.33398i	0.0596110	−	0.103249i
$512$	5.29180			0.233867
$513$	−4.35410	−	0.204441i	−0.192238	−	0.00902628i
$514$	−8.76393			−0.386560
$515$	0.472136	−	0.817763i	0.0208048	−	0.0360350i
$516$	−3.61803	+	6.26662i	−0.159275	+	0.275873i
$517$	−1.76393	−	3.05522i	−0.0775776	−	0.134368i
$518$	1.52786	−	2.64634i	0.0671305	−	0.116273i
$519$	5.94427	+	10.2958i	0.260925	+	0.451935i
$520$	2.76393			0.121206
$521$	−25.4164			−1.11351			−0.556757	−	0.830676i	$-0.687954\pi$
$521$	−25.4164			−1.11351			−0.556757	+	0.830676i	$0.687954\pi$
$522$	−0.618034	−	1.07047i	−0.0270506	−	0.0468530i
$523$	−22.4164	−	38.8264i	−0.980201	−	1.69776i	−0.661578	−	0.749877i	$-0.730113\pi$
$523$	−22.4164	−	38.8264i	−0.980201	−	1.69776i	−0.318623	−	0.947881i	$-0.603221\pi$
$524$	−1.52786			−0.0667451
$525$	0.763932			0.0333407
$526$	−3.80902	−	6.59741i	−0.166081	−	0.287661i
$527$	−14.2984	+	24.7655i	−0.622847	+	1.07880i
$528$	4.85410	+	8.40755i	0.211248	+	0.365892i
$529$	8.44427	−	14.6259i	0.367142	−	0.635909i
$530$	0.809017	−	1.40126i	0.0351415	−	0.0608668i
$531$	−2.00000			−0.0867926
$532$	0.944272	+	1.82857i	0.0409394	+	0.0792788i
$533$	−9.52786			−0.412698
$534$	2.85410	−	4.94345i	0.123509	−	0.213924i
$535$	−6.82624	+	11.8234i	−0.295124	+	0.511170i
$536$	3.61803	+	6.26662i	0.156275	+	0.270677i
$537$	−8.85410	+	15.3358i	−0.382083	+	0.661787i
$538$	20.1803	+	34.9534i	0.870036	+	1.50695i
$539$	−12.8328			−0.552749
$540$	−0.618034			−0.0265959
$541$	21.2082	+	36.7337i	0.911812	+	1.57930i	0.811503	+	0.584348i	$0.198650\pi$
$541$	21.2082	+	36.7337i	0.911812	+	1.57930i	0.100309	+	0.994956i	$0.468017\pi$
$542$	9.89919	+	17.1459i	0.425206	+	0.736479i
$543$	−13.4721			−0.578145
$544$	−11.7426			−0.503462
$545$	−3.50000	−	6.06218i	−0.149924	−	0.259675i
$546$	−0.763932	+	1.32317i	−0.0326933	+	0.0566264i
$547$	−12.4164	−	21.5058i	−0.530887	−	0.919524i	−0.999350	−	0.0360406i	$-0.988525\pi$
$547$	−12.4164	−	21.5058i	−0.530887	−	0.919524i	0.468463	−	0.883483i	$-0.344808\pi$
$548$	−6.30902	+	10.9275i	−0.269508	+	0.466801i
$549$	−6.23607	+	10.8012i	−0.266149	+	0.460983i
$550$	−3.23607			−0.137986
$551$	−1.52786	−	2.95870i	−0.0650892	−	0.126045i
$552$	−5.52786			−0.235282
$553$		0			0
$554$	14.3262	−	24.8138i	0.608664	−	1.05424i
$555$	1.23607	+	2.14093i	0.0524682	+	0.0908775i
$556$	−1.16312	+	2.01458i	−0.0493272	+	0.0854373i
$557$	−7.18034	−	12.4367i	−0.304241	−	0.526960i	0.672851	−	0.739778i	$-0.265069\pi$
$557$	−7.18034	−	12.4367i	−0.304241	−	0.526960i	−0.977092	+	0.212817i	$0.931736\pi$
$558$	13.3262			0.564145
$559$	−14.4721			−0.612106
$560$	−1.85410	−	3.21140i	−0.0783501	−	0.135706i
$561$	3.47214	+	6.01392i	0.146594	+	0.253908i
$562$	−2.00000			−0.0843649
$563$	21.0689			0.887948			0.443974	−	0.896040i	$-0.353568\pi$
$563$	21.0689			0.887948			0.443974	+	0.896040i	$0.353568\pi$
$564$	−0.545085	−	0.944115i	−0.0229522	−	0.0397544i
$565$	3.26393	−	5.65330i	0.137315	−	0.237836i
$566$	8.23607	+	14.2653i	0.346188	+	0.599615i
$567$	−0.381966	+	0.661585i	−0.0160411	+	0.0277839i
$568$	−10.3262	+	17.8856i	−0.433279	+	0.750462i
$569$	−14.9443			−0.626496			−0.313248	−	0.949671i	$-0.601417\pi$
$569$	−14.9443			−0.626496			−0.313248	+	0.949671i	$0.601417\pi$
$570$	−7.04508	−	0.330792i	−0.295086	−	0.0138554i
$571$	15.6525			0.655036			0.327518	−	0.944845i	$-0.393788\pi$
$571$	15.6525			0.655036			0.327518	+	0.944845i	$0.393788\pi$
$572$	0.763932	−	1.32317i	0.0319416	−	0.0553245i
$573$	−10.8541	+	18.7999i	−0.453437	+	0.785375i
$574$	4.76393	+	8.25137i	0.198843	+	0.344406i
$575$	1.23607	−	2.14093i	0.0515476	−	0.0892831i
$576$	−2.11803	−	3.66854i	−0.0882514	−	0.152856i
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	8.00000			0.332756
$579$	−2.38197	−	4.12569i	−0.0989911	−	0.171458i
$580$	−0.236068	−	0.408882i	−0.00980219	−	0.0169779i
$581$	11.5967			0.481114
$582$	3.23607			0.134139
$583$	1.00000	+	1.73205i	0.0414158	+	0.0717342i
$584$	3.94427	−	6.83168i	0.163215	−	0.282697i
$585$	−0.618034	−	1.07047i	−0.0255526	−	0.0442583i
$586$	−2.89919	+	5.02154i	−0.119764	+	0.207438i
$587$	−13.8262	+	23.9477i	−0.570670	+	0.988429i	0.425827	+	0.904804i	$0.359983\pi$
$587$	−13.8262	+	23.9477i	−0.570670	+	0.988429i	−0.996497	+	0.0836249i	$0.973350\pi$
$588$	−3.96556			−0.163537
$589$	35.8607	+	1.68379i	1.47761	+	0.0693793i
$590$	−3.23607			−0.133227
$591$	−5.73607	+	9.93516i	−0.235950	+	0.408678i
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	6.44427	+	11.1618i	0.264635	+	0.458360i	0.967468	−	0.252994i	$-0.0814153\pi$
$593$	6.44427	+	11.1618i	0.264635	+	0.458360i	−0.702833	+	0.711355i	$0.748082\pi$
$594$	1.61803	−	2.80252i	0.0663887	−	0.114989i
$595$	−1.32624	−	2.29711i	−0.0543705	−	0.0941724i
$596$	−6.00000			−0.245770
$597$	−13.8885			−0.568420
$598$	2.47214	+	4.28187i	0.101093	+	0.175098i
$599$	−19.5623	−	33.8829i	−0.799294	−	1.38442i	−0.920076	−	0.391739i	$-0.871874\pi$
$599$	−19.5623	−	33.8829i	−0.799294	−	1.38442i	0.120782	−	0.992679i	$-0.461460\pi$
$600$	2.23607			0.0912871
$601$	−11.8885			−0.484944			−0.242472	−	0.970158i	$-0.577958\pi$
$601$	−11.8885			−0.484944			−0.242472	+	0.970158i	$0.577958\pi$
$602$	7.23607	+	12.5332i	0.294920	+	0.510817i
$603$	1.61803	−	2.80252i	0.0658914	−	0.114127i
$604$	5.16312	+	8.94278i	0.210084	+	0.363877i
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$	6.61803	−	11.4628i	0.268839	−	0.465643i
$607$	12.5836			0.510752			0.255376	−	0.966842i	$-0.417801\pi$
$607$	12.5836			0.510752			0.255376	+	0.966842i	$0.417801\pi$
$608$	6.76393	+	13.0983i	0.274314	+	0.531206i
$609$	−0.583592			−0.0236483
$610$	−10.0902	+	17.4767i	−0.408539	+	0.707610i
$611$	1.09017	−	1.88823i	0.0441036	−	0.0763896i
$612$	1.07295	+	1.85840i	0.0433714	+	0.0751215i
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	−0.998002	−	0.0631797i	$-0.979876\pi$
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	0.553716	+	0.832705i	$0.313209\pi$
$614$	−16.3262	−	28.2779i	−0.658873	−	1.14120i
$615$	−7.70820			−0.310825
$616$	3.41641			0.137651
$617$	10.2082	+	17.6811i	0.410967	+	0.711815i	0.994996	−	0.0999174i	$-0.0318579\pi$
$617$	10.2082	+	17.6811i	0.410967	+	0.711815i	−0.584029	+	0.811733i	$0.698525\pi$
$618$	0.763932	+	1.32317i	0.0307299	+	0.0532257i
$619$	−12.7082			−0.510786			−0.255393	−	0.966837i	$-0.582205\pi$
$619$	−12.7082			−0.510786			−0.255393	+	0.966837i	$0.582205\pi$
$620$	5.09017			0.204426
$621$	1.23607	+	2.14093i	0.0496017	+	0.0859127i
$622$	−17.3262	+	30.0099i	−0.694719	+	1.20329i
$623$	−1.34752	−	2.33398i	−0.0539874	−	0.0935089i
$624$	−3.00000	+	5.19615i	−0.120096	+	0.208013i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−51.1246			−2.04335
$627$	4.70820	−	7.33708i	0.188028	−	0.293015i
$628$	12.3607			0.493245
$629$	4.29180	−	7.43361i	0.171125	−	0.296397i
$630$	−0.618034	+	1.07047i	−0.0246231	+	0.0426484i
$631$	−8.64590	−	14.9751i	−0.344188	−	0.596151i	0.641018	−	0.767526i	$-0.278512\pi$
$631$	−8.64590	−	14.9751i	−0.344188	−	0.596151i	−0.985206	+	0.171375i	$0.945179\pi$
$632$		0			0
$633$	−9.59017	−	16.6107i	−0.381175	−	0.660215i
$634$	−7.90983			−0.314139
$635$	15.2361			0.604625
$636$	0.309017	+	0.535233i	0.0122533	+	0.0212234i
$637$	−3.96556	−	6.86855i	−0.157121	−	0.272142i
$638$	2.47214			0.0978728
$639$	9.23607			0.365373
$640$	−6.80902	−	11.7936i	−0.269150	−	0.466182i
$641$	17.4721	−	30.2626i	0.690108	−	1.19530i	−0.281694	−	0.959504i	$-0.590896\pi$
$641$	17.4721	−	30.2626i	0.690108	−	1.19530i	0.971802	−	0.235798i	$-0.0757703\pi$
$642$	−11.0451	−	19.1306i	−0.435915	−	0.755026i
$643$	−17.1803	+	29.7572i	−0.677526	+	1.17351i	0.298197	+	0.954504i	$0.403615\pi$
$643$	−17.1803	+	29.7572i	−0.677526	+	1.17351i	−0.975724	+	0.219006i	$0.929719\pi$
$644$	0.583592	−	1.01081i	0.0229968	−	0.0398315i
$645$	−11.7082			−0.461010
$646$	11.2361	+	21.7586i	0.442077	+	0.856079i
$647$	26.5967			1.04563			0.522813	−	0.852447i	$-0.324883\pi$
$647$	26.5967			1.04563			0.522813	+	0.852447i	$0.324883\pi$
$648$	−1.11803	+	1.93649i	−0.0439205	+	0.0760726i
$649$	2.00000	−	3.46410i	0.0785069	−	0.135978i
$650$	−1.00000	−	1.73205i	−0.0392232	−	0.0679366i
$651$	3.14590	−	5.44886i	0.123297	−	0.213557i
$652$	−2.76393	−	4.78727i	−0.108244	−	0.187484i
$653$	−3.52786			−0.138056			−0.0690280	−	0.997615i	$-0.521990\pi$
$653$	−3.52786			−0.138056			−0.0690280	+	0.997615i	$0.521990\pi$
$654$	11.3262			0.442891
$655$	−1.23607	−	2.14093i	−0.0482972	−	0.0836532i
$656$	18.7082	+	32.4036i	0.730433	+	1.26515i
$657$	−3.52786			−0.137635
$658$	−2.18034			−0.0849985
$659$	−7.23607	−	12.5332i	−0.281877	−	0.488226i	0.689970	−	0.723838i	$-0.257624\pi$
$659$	−7.23607	−	12.5332i	−0.281877	−	0.488226i	−0.971847	+	0.235612i	$0.924290\pi$
$660$	0.618034	−	1.07047i	0.0240569	−	0.0416678i
$661$	9.79180	+	16.9599i	0.380857	+	0.659663i	0.991185	−	0.132485i	$-0.0422958\pi$
$661$	9.79180	+	16.9599i	0.380857	+	0.659663i	−0.610328	+	0.792149i	$0.708962\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$	−2.14590	+	3.71680i	−0.0833398	+	0.144349i
$664$	33.9443			1.31729
$665$	−1.79837	+	2.80252i	−0.0697379	+	0.108677i
$666$	−4.00000			−0.154997
$667$	−0.944272	+	1.63553i	−0.0365624	+	0.0633279i
$668$	−0.253289	+	0.438709i	−0.00980004	+	0.0169742i
$669$	−4.32624	−	7.49326i	−0.167262	−	0.289706i
$670$	2.61803	−	4.53457i	0.101143	−	0.175186i
$671$	−12.4721	−	21.6024i	−0.481481	−	0.833950i
$672$	2.58359			0.0996642
$673$	15.7082			0.605507			0.302753	−	0.953069i	$-0.402094\pi$
$673$	15.7082			0.605507			0.302753	+	0.953069i	$0.402094\pi$
$674$	−5.23607	−	9.06914i	−0.201686	−	0.349330i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−7.09017			−0.272699
$677$	15.0000			0.576497			0.288248	−	0.957556i	$-0.406927\pi$
$677$	15.0000			0.576497			0.288248	+	0.957556i	$0.406927\pi$
$678$	5.28115	+	9.14723i	0.202821	+	0.351297i
$679$	0.763932	−	1.32317i	0.0293170	−	0.0507786i
$680$	−3.88197	−	6.72376i	−0.148867	−	0.257845i
$681$	−2.00000	+	3.46410i	−0.0766402	+	0.132745i
$682$	−13.3262	+	23.0817i	−0.510288	+	0.883845i
$683$	35.1803			1.34614			0.673069	−	0.739580i	$-0.264976\pi$
$683$	35.1803			1.34614			0.673069	+	0.739580i	$0.264976\pi$
$684$	1.45492	−	2.26728i	0.0556301	−	0.0866918i
$685$	−20.4164			−0.780071
$686$	−8.29180	+	14.3618i	−0.316582	+	0.548337i
$687$	−6.73607	+	11.6672i	−0.256997	+	0.445132i
$688$	28.4164	+	49.2187i	1.08337	+	1.87644i
$689$	−0.618034	+	1.07047i	−0.0235452	+	0.0407815i
$690$	2.00000	+	3.46410i	0.0761387	+	0.131876i
$691$	−4.81966			−0.183349			−0.0916743	−	0.995789i	$-0.529222\pi$
$691$	−4.81966			−0.183349			−0.0916743	+	0.995789i	$0.529222\pi$
$692$	−7.34752			−0.279311
$693$	−0.763932	−	1.32317i	−0.0290194	−	0.0502630i
$694$	−22.7533	−	39.4099i	−0.863703	−	1.49598i
$695$	−3.76393			−0.142774
$696$	−1.70820			−0.0647493
$697$	13.3820	+	23.1782i	0.506878	+	0.877939i
$698$	−21.8435	+	37.8340i	−0.826787	+	1.43204i
$699$	0.0278640	+	0.0482619i	0.00105391	+	0.00182543i
$700$	−0.236068	+	0.408882i	−0.00892253	+	0.0154543i
$701$	−5.18034	+	8.97261i	−0.195659	+	0.338891i	−0.947116	−	0.320891i	$-0.896018\pi$
$701$	−5.18034	+	8.97261i	−0.195659	+	0.338891i	0.751458	+	0.659781i	$0.229351\pi$
$702$	2.00000			0.0754851
$703$	−10.7639	−	0.505406i	−0.405969	−	0.0190617i
$704$	8.47214			0.319306
$705$	0.881966	−	1.52761i	0.0332168	−	0.0575331i
$706$	25.0344	−	43.3609i	0.942184	−	1.63191i
$707$	−3.12461	−	5.41199i	−0.117513	−	0.203539i
$708$	0.618034	−	1.07047i	0.0232271	−	0.0402306i
$709$	−20.9164	−	36.2283i	−0.785532	−	1.36058i	−0.928681	−	0.370880i	$-0.879056\pi$
$709$	−20.9164	−	36.2283i	−0.785532	−	1.36058i	0.143148	−	0.989701i	$-0.454277\pi$
$710$	14.9443			0.560849
$711$		0			0
$712$	−3.94427	−	6.83168i	−0.147818	−	0.256028i
$713$	−10.1803	−	17.6329i	−0.381257	−	0.660356i
$714$	4.29180			0.160616
$715$	2.47214			0.0924526
$716$	−5.47214	−	9.47802i	−0.204503	−	0.354210i
$717$	−10.5623	+	18.2945i	−0.394457	+	0.683219i
$718$	19.0344	+	32.9686i	0.710359	+	1.23038i
$719$	1.52786	−	2.64634i	0.0569797	−	0.0986918i	−0.836129	−	0.548534i	$-0.815186\pi$
$719$	1.52786	−	2.64634i	0.0569797	−	0.0986918i	0.893108	+	0.449842i	$0.148520\pi$
$720$	−2.42705	+	4.20378i	−0.0904508	+	0.156665i
$721$	0.721360			0.0268648
$722$	17.7984	−	25.0665i	0.662387	−	0.932878i
$723$	−21.3607			−0.794412
$724$	4.16312	−	7.21073i	0.154721	−	0.267985i
$725$	0.381966	−	0.661585i	0.0141859	−	0.0245706i
$726$	−5.66312	−	9.80881i	−0.210178	−	0.364039i
$727$	−20.6180	+	35.7115i	−0.764681	+	1.32447i	0.175735	+	0.984438i	$0.443770\pi$
$727$	−20.6180	+	35.7115i	−0.764681	+	1.32447i	−0.940415	+	0.340028i	$0.889563\pi$
$728$	1.05573	+	1.82857i	0.0391279	+	0.0677715i
$729$	1.00000			0.0370370
$730$	−5.70820			−0.211270
$731$	20.3262	+	35.2061i	0.751793	+	1.30214i
$732$	−3.85410	−	6.67550i	−0.142452	−	0.246734i
$733$	49.1246			1.81446			0.907229	−	0.420636i	$-0.138193\pi$
$733$	49.1246			1.81446			0.907229	+	0.420636i	$0.138193\pi$
$734$	−10.0000			−0.369107
$735$	−3.20820	−	5.55677i	−0.118336	−	0.204965i
$736$	4.18034	−	7.24056i	0.154089	−	0.266891i
$737$	3.23607	+	5.60503i	0.119202	+	0.206464i
$738$	6.23607	−	10.8012i	0.229553	−	0.397597i
$739$	9.82624	−	17.0195i	0.361464	−	0.626074i	−0.626738	−	0.779230i	$-0.715610\pi$
$739$	9.82624	−	17.0195i	0.361464	−	0.626074i	0.988202	+	0.153156i	$0.0489437\pi$
$740$	−1.52786			−0.0561654
$741$	5.38197	+	0.252703i	0.197711	+	0.00928327i
$742$	1.23607			0.0453775
$743$	−17.0623	+	29.5528i	−0.625955	+	1.08419i	0.362400	+	0.932023i	$0.381957\pi$
$743$	−17.0623	+	29.5528i	−0.625955	+	1.08419i	−0.988355	+	0.152164i	$0.951376\pi$
$744$	9.20820	−	15.9491i	0.337589	−	0.584722i
$745$	−4.85410	−	8.40755i	−0.177841	−	0.308029i
$746$	28.7984	−	49.8802i	1.05438	−	1.82625i
$747$	−7.59017	−	13.1466i	−0.277710	−	0.481007i
$748$	−4.29180			−0.156924
$749$	−10.4296			−0.381088
$750$	−0.809017	−	1.40126i	−0.0295411	−	0.0511667i
$751$	0.826238	+	1.43109i	0.0301498	+	0.0522211i	0.880707	−	0.473662i	$-0.157068\pi$
$751$	0.826238	+	1.43109i	0.0301498	+	0.0522211i	−0.850557	+	0.525883i	$0.823735\pi$
$752$	−8.56231			−0.312235
$753$	31.4164			1.14488
$754$	0.763932	+	1.32317i	0.0278208	+	0.0481870i
$755$	−8.35410	+	14.4697i	−0.304037	+	0.526607i
$756$	−0.236068	−	0.408882i	−0.00858571	−	0.0148709i
$757$	−10.5623	+	18.2945i	−0.383894	+	0.664923i	−0.991615	−	0.129227i	$-0.958750\pi$
$757$	−10.5623	+	18.2945i	−0.383894	+	0.664923i	0.607721	+	0.794150i	$0.292084\pi$
$758$	20.6525	−	35.7711i	0.750132	−	1.29927i
$759$	−4.94427			−0.179466
$760$	−5.26393	+	8.20311i	−0.190943	+	0.297558i
$761$	10.0000			0.362500			0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000			0.362500			0.181250	+	0.983437i	$0.441986\pi$
$762$	−12.3262	+	21.3497i	−0.446532	+	0.773417i
$763$	2.67376	−	4.63109i	0.0967967	−	0.167657i
$764$	−6.70820	−	11.6190i	−0.242694	−	0.420359i
$765$	−1.73607	+	3.00696i	−0.0627677	+	0.108717i
$766$	29.2254	+	50.6199i	1.05596	+	1.82897i
$767$	2.47214			0.0892637
$768$	13.5623			0.489388
$769$	16.9164	+	29.3001i	0.610021	+	1.05659i	0.991236	+	0.132101i	$0.0421724\pi$
$769$	16.9164	+	29.3001i	0.610021	+	1.05659i	−0.381215	+	0.924486i	$0.624494\pi$
$770$	−1.23607	−	2.14093i	−0.0445448	−	0.0771539i
$771$	5.41641			0.195067
$772$	2.94427			0.105967
$773$	−0.527864	−	0.914287i	−0.0189860	−	0.0328846i	0.856376	−	0.516352i	$-0.172710\pi$
$773$	−0.527864	−	0.914287i	−0.0189860	−	0.0328846i	−0.875362	+	0.483468i	$0.839377\pi$
$774$	9.47214	−	16.4062i	0.340469	−	0.589709i
$775$	4.11803	+	7.13264i	0.147924	+	0.256212i
$776$	2.23607	−	3.87298i	0.0802702	−	0.139032i
$777$	−0.944272	+	1.63553i	−0.0338756	+	0.0586742i
$778$	−11.5279			−0.413294
$779$	18.1459	−	28.2779i	0.650144	−	1.01316i
$780$	0.763932			0.0273532
$781$	−9.23607	+	15.9973i	−0.330492	+	0.572430i
$782$	6.94427	−	12.0278i	0.248327	−	0.430114i
$783$	0.381966	+	0.661585i	0.0136504	+	0.0236431i
$784$	−15.5729	+	26.9731i	−0.556177	+	0.963326i
$785$	10.0000	+	17.3205i	0.356915	+	0.618195i
$786$	4.00000			0.142675
$787$	19.2361			0.685692			0.342846	−	0.939392i	$-0.388609\pi$
$787$	19.2361			0.685692			0.342846	+	0.939392i	$0.388609\pi$
$788$	−3.54508	−	6.14027i	−0.126288	−	0.218738i
$789$	2.35410	+	4.07742i	0.0838082	+	0.145160i
$790$		0			0
$791$	4.98684			0.177312
$792$	−2.23607	−	3.87298i	−0.0794552	−	0.137620i
$793$	7.70820	−	13.3510i	0.273726	−	0.474108i
$794$	−11.4721	−	19.8703i	−0.407131	−	0.705171i
$795$	−0.500000	+	0.866025i	−0.0177332	+	0.0307148i
$796$	4.29180	−	7.43361i	0.152119	−	0.263477i
$797$	10.3050			0.365020			0.182510	−	0.983204i	$-0.441578\pi$
$797$	10.3050			0.365020			0.182510	+	0.983204i	$0.441578\pi$
$798$	−2.47214	−	4.78727i	−0.0875127	−	0.169468i
$799$	−6.12461			−0.216673
$800$	−1.69098	+	2.92887i	−0.0597853	+	0.103551i
$801$	−1.76393	+	3.05522i	−0.0623255	+	0.107951i
$802$	27.2705	+	47.2339i	0.962955	+	1.66789i
$803$	3.52786	−	6.11044i	0.124496	−	0.215633i
$804$	1.00000	+	1.73205i	0.0352673	+	0.0610847i
$805$	1.88854			0.0665624
$806$	−16.4721			−0.580206
$807$	−12.4721	−	21.6024i	−0.439040	−	0.760440i
$808$	−9.14590	−	15.8412i	−0.321752	−	0.557290i
$809$	−10.2918			−0.361840			−0.180920	−	0.983498i	$-0.557908\pi$
$809$	−10.2918			−0.361840			−0.180920	+	0.983498i	$0.557908\pi$
$810$	1.61803			0.0568519
$811$	−18.5344	−	32.1026i	−0.650832	−	1.12727i	−0.982921	−	0.184027i	$-0.941087\pi$
$811$	−18.5344	−	32.1026i	−0.650832	−	1.12727i	0.332089	−	0.943248i	$-0.392247\pi$
$812$	0.180340	−	0.312358i	0.00632869	−	0.0109616i
$813$	−6.11803	−	10.5967i	−0.214569	−	0.371644i
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	4.47214	−	7.74597i	0.156652	−	0.271329i
$816$	16.8541			0.590012
$817$	27.5623	−	42.9520i	0.964283	−	1.50270i
$818$	−29.7082			−1.03872
$819$	0.472136	−	0.817763i	0.0164978	−	0.0285750i
$820$	2.38197	−	4.12569i	0.0831819	−	0.144075i
$821$	2.56231	+	4.43804i	0.0894251	+	0.154889i	0.907268	−	0.420552i	$-0.138164\pi$
$821$	2.56231	+	4.43804i	0.0894251	+	0.154889i	−0.817843	+	0.575441i	$0.804830\pi$
$822$	16.5172	−	28.6087i	0.576104	−	0.997842i
$823$	9.23607	+	15.9973i	0.321949	+	0.557632i	0.980890	−	0.194562i	$-0.0623287\pi$
$823$	9.23607	+	15.9973i	0.321949	+	0.557632i	−0.658941	+	0.752195i	$0.728995\pi$
$824$	2.11146			0.0735561
$825$	2.00000			0.0696311
$826$	−1.23607	−	2.14093i	−0.0430083	−	0.0744926i
$827$	−6.17376	−	10.6933i	−0.214683	−	0.371841i	0.738492	−	0.674263i	$-0.235538\pi$
$827$	−6.17376	−	10.6933i	−0.214683	−	0.371841i	−0.953174	+	0.302421i	$0.902205\pi$
$828$	−1.52786			−0.0530969
$829$	12.4164			0.431240			0.215620	−	0.976477i	$-0.430823\pi$
$829$	12.4164			0.431240			0.215620	+	0.976477i	$0.430823\pi$
$830$	−12.2812	−	21.2716i	−0.426285	−	0.738347i
$831$	−8.85410	+	15.3358i	−0.307145	+	0.531991i
$832$	2.61803	+	4.53457i	0.0907640	+	0.157208i
$833$	−11.1393	+	19.2939i	−0.385955	+	0.668493i
$834$	3.04508	−	5.27424i	0.105443	−	0.182632i
$835$	−0.819660			−0.0283655
$836$	2.47214	+	4.78727i	0.0855006	+	0.165571i
$837$	−8.23607			−0.284680
$838$	28.2705	−	48.9660i	0.976589	−	1.69150i
$839$	1.09017	−	1.88823i	0.0376368	−	0.0651889i	−0.846593	−	0.532240i	$-0.821350\pi$
$839$	1.09017	−	1.88823i	0.0376368	−	0.0651889i	0.884230	+	0.467051i	$0.154684\pi$
$840$	0.854102	+	1.47935i	0.0294693	+	0.0510424i
$841$	14.2082	−	24.6093i	0.489938	−	0.848598i
$842$	−14.8541	−	25.7281i	−0.511906	−	0.886647i
$843$	1.23607			0.0425724
$844$	11.8541			0.408035
$845$	−5.73607	−	9.93516i	−0.197327	−	0.341780i
$846$	1.42705	+	2.47172i	0.0490630	+	0.0849796i
$847$	−5.34752			−0.183743
$848$	4.85410			0.166691
$849$	−5.09017	−	8.81643i	−0.174694	−	0.302579i
$850$	−2.80902	+	4.86536i	−0.0963485	+	0.166880i
$851$	3.05573	+	5.29268i	0.104749	+	0.181431i
$852$	−2.85410	+	4.94345i	−0.0977799	+	0.169360i
$853$	−20.7639	+	35.9642i	−0.710943	+	1.23139i	0.253560	+	0.967320i	$0.418399\pi$
$853$	−20.7639	+	35.9642i	−0.710943	+	1.23139i	−0.964503	+	0.264071i	$0.914935\pi$
$854$	−15.4164			−0.527539
$855$	4.35410	+	0.204441i	0.148907	+	0.00699173i
$856$	−30.5279			−1.04342
$857$	19.4443	−	33.6785i	0.664204	−	1.15043i	−0.315297	−	0.948993i	$-0.602104\pi$
$857$	19.4443	−	33.6785i	0.664204	−	1.15043i	0.979501	−	0.201441i	$-0.0645626\pi$
$858$	−2.00000	+	3.46410i	−0.0682789	+	0.118262i
$859$	−5.06231	−	8.76817i	−0.172724	−	0.299166i	0.766647	−	0.642068i	$-0.221923\pi$
$859$	−5.06231	−	8.76817i	−0.172724	−	0.299166i	−0.939371	+	0.342902i	$0.888590\pi$
$860$	3.61803	−	6.26662i	0.123374	−	0.213690i
$861$	−2.94427	−	5.09963i	−0.100341	−	0.173795i
$862$	2.47214			0.0842013
$863$	−17.3050			−0.589067			−0.294534	−	0.955641i	$-0.595164\pi$
$863$	−17.3050			−0.589067			−0.294534	+	0.955641i	$0.595164\pi$
$864$	−1.69098	−	2.92887i	−0.0575284	−	0.0996421i
$865$	−5.94427	−	10.2958i	−0.202111	−	0.350067i
$866$	−15.5279			−0.527658
$867$	−4.94427			−0.167916
$868$	1.94427	+	3.36758i	0.0659929	+	0.114303i
$869$		0			0
$870$	0.618034	+	1.07047i	0.0209533	+	0.0362922i
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$	7.82624	−	13.5554i	0.265030	−	0.459045i
$873$	−2.00000			−0.0676897
$874$	−17.4164	−	0.817763i	−0.589119	−	0.0276613i
$875$	−0.763932			−0.0258256
$876$	1.09017	−	1.88823i	0.0368334	−	0.0637974i
$877$	−28.3607	+	49.1221i	−0.957672	+	1.65874i	−0.229541	+	0.973299i	$0.573722\pi$
$877$	−28.3607	+	49.1221i	−0.957672	+	1.65874i	−0.728131	+	0.685438i	$0.759611\pi$
$878$	−5.04508	−	8.73834i	−0.170263	−	0.294905i
$879$	1.79180	−	3.10348i	0.0604358	−	0.104678i
$880$	−4.85410	−	8.40755i	−0.163632	−	0.283418i
$881$	22.0689			0.743520			0.371760	−	0.928329i	$-0.378755\pi$
$881$	22.0689			0.743520			0.371760	+	0.928329i	$0.378755\pi$
$882$	10.3820			0.349579
$883$	−17.8885	−	30.9839i	−0.601997	−	1.04269i	−0.992518	−	0.122096i	$-0.961038\pi$
$883$	−17.8885	−	30.9839i	−0.601997	−	1.04269i	0.390521	−	0.920594i	$-0.372295\pi$
$884$	−1.32624	−	2.29711i	−0.0446062	−	0.0772602i
$885$	2.00000			0.0672293
$886$	−10.8541			−0.364651
$887$	26.0623	+	45.1412i	0.875087	+	1.51569i	0.856670	+	0.515864i	$0.172529\pi$
$887$	26.0623	+	45.1412i	0.875087	+	1.51569i	0.0184161	+	0.999830i	$0.494138\pi$
$888$	−2.76393	+	4.78727i	−0.0927515	+	0.160650i
$889$	5.81966	+	10.0799i	0.195185	+	0.338071i
$890$	−2.85410	+	4.94345i	−0.0956697	+	0.165705i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	5.34752			0.179048
$893$	3.52786	+	6.83168i	0.118055	+	0.228613i
$894$	15.7082			0.525361
$895$	8.85410	−	15.3358i	0.295960	−	0.512618i
$896$	5.20163	−	9.00948i	0.173774	−	0.300986i
$897$	−1.52786	−	2.64634i	−0.0510139	−	0.0883587i
$898$	−21.0902	+	36.5292i	−0.703788	+	1.21900i
$899$	−3.14590	−	5.44886i	−0.104922	−	0.181729i
$900$	0.618034			0.0206011
$901$	3.47214			0.115674
$902$	12.4721	+	21.6024i	0.415277	+	0.719280i
$903$	−4.47214	−	7.74597i	−0.148823	−	0.257770i
$904$	14.5967			0.485481
$905$	13.4721			0.447829
$906$	−13.5172	−	23.4125i	−0.449080	−	0.777829i
$907$	13.1803	−	22.8290i	0.437646	−	0.758025i	−0.559861	−	0.828586i	$-0.689146\pi$
$907$	13.1803	−	22.8290i	0.437646	−	0.758025i	0.997507	+	0.0705611i	$0.0224790\pi$
$908$	−1.23607	−	2.14093i	−0.0410204	−	0.0710493i
$909$	−4.09017	+	7.08438i	−0.135662	+	0.234974i
$910$	0.763932	−	1.32317i	0.0253241	−	0.0438626i
$911$	−49.5967			−1.64321			−0.821607	−	0.570055i	$-0.806922\pi$
$911$	−49.5967			−1.64321			−0.821607	+	0.570055i	$0.806922\pi$
$912$	−9.70820	−	18.7999i	−0.321471	−	0.622525i
$913$	30.3607			1.00479
$914$	20.0344	−	34.7007i	0.662680	−	1.14780i
$915$	6.23607	−	10.8012i	0.206158	−	0.357076i
$916$	−4.16312	−	7.21073i	−0.137553	−	0.238249i
$917$	0.944272	−	1.63553i	0.0311826	−	0.0540099i
$918$	−2.80902	−	4.86536i	−0.0927114	−	0.160581i
$919$	−6.70820			−0.221283			−0.110642	−	0.993860i	$-0.535291\pi$
$919$	−6.70820			−0.221283			−0.110642	+	0.993860i	$0.535291\pi$
$920$	5.52786			0.182248
$921$	10.0902	+	17.4767i	0.332482	+	0.575876i
$922$	−28.1246	−	48.7133i	−0.926235	−	1.60429i
$923$	−11.4164			−0.375776
$924$	0.944272			0.0310643
$925$	−1.23607	−	2.14093i	−0.0406417	−	0.0703934i
$926$	−30.5066	+	52.8389i	−1.00251	+	1.73640i
$927$	−0.472136	−	0.817763i	−0.0155070	−	0.0268589i
$928$	1.29180	−	2.23746i	0.0424053	−	0.0734481i
$929$	−27.8885	+	48.3044i	−0.914993	+	1.58482i	−0.108083	+	0.994142i	$0.534471\pi$
$929$	−27.8885	+	48.3044i	−0.914993	+	1.58482i	−0.806911	+	0.590673i	$0.798862\pi$
$930$	−13.3262			−0.436985
$931$	27.9377	+	1.31178i	0.915621	+	0.0429917i
$932$	−0.0344419			−0.00112818
$933$	10.7082	−	18.5472i	0.350571	−	0.607207i
$934$	−12.7533	+	22.0893i	−0.417300	+	0.722785i
$935$	−3.47214	−	6.01392i	−0.113551	−	0.196676i
$936$	1.38197	−	2.39364i	0.0451710	−	0.0782384i
$937$	−1.05573	−	1.82857i	−0.0344891	−	0.0597369i	0.848266	−	0.529571i	$-0.177647\pi$
$937$	−1.05573	−	1.82857i	−0.0344891	−	0.0597369i	−0.882755	+	0.469834i	$0.844314\pi$
$938$	4.00000			0.130605
$939$	31.5967			1.03112
$940$	0.545085	+	0.944115i	0.0177787	+	0.0307936i
$941$	9.52786	+	16.5027i	0.310599	+	0.537974i	0.978492	−	0.206283i	$-0.0661369\pi$
$941$	9.52786	+	16.5027i	0.310599	+	0.537974i	−0.667893	+	0.744257i	$0.732804\pi$
$942$	−32.3607			−1.05437
$943$	−19.0557			−0.620540
$944$	−4.85410	−	8.40755i	−0.157988	−	0.273642i
$945$	0.381966	−	0.661585i	0.0124254	−	0.0215213i
$946$	18.9443	+	32.8124i	0.615931	+	1.06682i
$947$	−3.52786	+	6.11044i	−0.114640	+	0.198563i	−0.917636	−	0.397422i	$-0.869905\pi$
$947$	−3.52786	+	6.11044i	−0.114640	+	0.198563i	0.802996	+	0.595985i	$0.203238\pi$
$948$		0			0
$949$	4.36068			0.141554
$950$	7.04508	+	0.330792i	0.228573	+	0.0107323i
$951$	4.88854			0.158522
$952$	2.96556	−	5.13650i	0.0961143	−	0.166475i
$953$	−27.9164	+	48.3526i	−0.904301	+	1.56630i	−0.0824486	+	0.996595i	$0.526274\pi$
$953$	−27.9164	+	48.3526i	−0.904301	+	1.56630i	−0.821853	+	0.569700i	$0.807059\pi$
$954$	−0.809017	−	1.40126i	−0.0261929	−	0.0453674i
$955$	10.8541	−	18.7999i	0.351230	−	0.608349i
$956$	−6.52786	−	11.3066i	−0.211126	−	0.365681i
$957$	−1.52786			−0.0493888
$958$	55.1246			1.78100
$959$	−7.79837	−	13.5072i	−0.251823	−	0.436170i
$960$	2.11803	+	3.66854i	0.0683593	+	0.118402i
$961$	36.8328			1.18816
$962$	4.94427			0.159410
$963$	6.82624	+	11.8234i	0.219972	+	0.381003i
$964$	6.60081	−	11.4329i	0.212598	−	0.368230i
$965$	2.38197	+	4.12569i	0.0766782	+	0.132811i
$966$	−1.52786	+	2.64634i	−0.0491582	+	0.0851445i
$967$	9.47214	−	16.4062i	0.304603	−	0.527588i	−0.672570	−	0.740034i	$-0.734809\pi$
$967$	9.47214	−	16.4062i	0.304603	−	0.527588i	0.977173	+	0.212445i	$0.0681428\pi$
$968$	−15.6525			−0.503090
$969$	−6.94427	−	13.4475i	−0.223082	−	0.431997i
$970$	−3.23607			−0.103904
$971$	2.90983	−	5.03997i	0.0933809	−	0.161740i	−0.815551	−	0.578685i	$-0.803566\pi$
$971$	2.90983	−	5.03997i	0.0933809	−	0.161740i	0.908932	+	0.416945i	$0.136899\pi$
$972$	−0.309017	+	0.535233i	−0.00991172	+	0.0171676i
$973$	−1.43769	−	2.49016i	−0.0460904	−	0.0798308i
$974$	−27.2705	+	47.2339i	−0.873803	+	1.51347i
$975$	0.618034	+	1.07047i	0.0197929	+	0.0342824i
$976$	−60.5410			−1.93787
$977$	51.7214			1.65471			0.827356	−	0.561677i	$-0.189844\pi$
$977$	51.7214			1.65471			0.827356	+	0.561677i	$0.189844\pi$
$978$	7.23607	+	12.5332i	0.231384	+	0.400769i
$979$	−3.52786	−	6.11044i	−0.112751	−	0.195291i
$980$	3.96556			0.126675
$981$	−7.00000			−0.223493
$982$	−17.5623	−	30.4188i	−0.560436	−	0.970703i
$983$	14.8262	−	25.6798i	0.472884	−	0.819058i	−0.526635	−	0.850092i	$-0.676546\pi$
$983$	14.8262	−	25.6798i	0.472884	−	0.819058i	0.999518	+	0.0310333i	$0.00987979\pi$
$984$	−8.61803	−	14.9269i	−0.274733	−	0.475851i
$985$	5.73607	−	9.93516i	0.182766	−	0.316561i
$986$	2.14590	−	3.71680i	0.0683393	−	0.118367i
$987$	1.34752			0.0428922
$988$	−1.79837	+	2.80252i	−0.0572139	+	0.0891599i
$989$	−28.9443			−0.920374
$990$	−1.61803	+	2.80252i	−0.0514245	+	0.0890698i
$991$	9.82624	−	17.0195i	0.312141	−	0.540644i	−0.666685	−	0.745340i	$-0.732287\pi$
$991$	9.82624	−	17.0195i	0.312141	−	0.540644i	0.978826	+	0.204696i	$0.0656206\pi$
$992$	13.9271	+	24.1224i	0.442184	+	0.765886i
$993$	1.23607	−	2.14093i	0.0392254	−	0.0679404i
$994$	5.70820	+	9.88690i	0.181053	+	0.313593i
$995$	13.8885			0.440296
$996$	9.38197			0.297279
$997$	29.4721	+	51.0472i	0.933392	+	1.61668i	0.777477	+	0.628912i	$0.216499\pi$
$997$	29.4721	+	51.0472i	0.933392	+	1.61668i	0.155915	+	0.987770i	$0.450167\pi$
$998$	−19.1353	−	33.1432i	−0.605716	−	1.04913i
$999$	2.47214			0.0782149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.e.106.2	✓	4
3.2	odd	2		855.2.k.e.676.1		4
19.7	even	3	inner	285.2.i.e.121.2	yes	4
19.8	odd	6		5415.2.a.t.1.2		2
19.11	even	3		5415.2.a.q.1.1		2
57.26	odd	6		855.2.k.e.406.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.e.106.2	✓	4	1.1	even	1	trivial
285.2.i.e.121.2	yes	4	19.7	even	3	inner
855.2.k.e.406.1		4	57.26	odd	6
855.2.k.e.676.1		4	3.2	odd	2
5415.2.a.q.1.1		2	19.11	even	3
5415.2.a.t.1.2		2	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 1.40126i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.309017 - 0.535233i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.809017 + 1.40126i) q^{6} +0.763932 q^{7} +2.23607 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.809017 - 1.40126i) q^{10} +2.00000 q^{11} +0.618034 q^{12} +(0.618034 + 1.07047i) q^{13} +(0.618034 - 1.07047i) q^{14} +(0.500000 + 0.866025i) q^{15} +(2.42705 - 4.20378i) q^{16} +(1.73607 - 3.00696i) q^{17} -1.61803 q^{18} +(-4.35410 - 0.204441i) q^{19} -0.618034 q^{20} +(-0.381966 + 0.661585i) q^{21} +(1.61803 - 2.80252i) q^{22} +(1.23607 + 2.14093i) q^{23} +(-1.11803 + 1.93649i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} +1.00000 q^{27} +(-0.236068 - 0.408882i) q^{28} +(0.381966 + 0.661585i) q^{29} +1.61803 q^{30} -8.23607 q^{31} +(-1.69098 - 2.92887i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-2.80902 - 4.86536i) q^{34} +(0.381966 - 0.661585i) q^{35} +(-0.309017 + 0.535233i) q^{36} +2.47214 q^{37} +(-3.80902 + 5.93583i) q^{38} -1.23607 q^{39} +(1.11803 - 1.93649i) q^{40} +(-3.85410 + 6.67550i) q^{41} +(0.618034 + 1.07047i) q^{42} +(-5.85410 + 10.1396i) q^{43} +(-0.618034 - 1.07047i) q^{44} -1.00000 q^{45} +4.00000 q^{46} +(-0.881966 - 1.52761i) q^{47} +(2.42705 + 4.20378i) q^{48} -6.41641 q^{49} -1.61803 q^{50} +(1.73607 + 3.00696i) q^{51} +(0.381966 - 0.661585i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.809017 - 1.40126i) q^{54} +(1.00000 - 1.73205i) q^{55} +1.70820 q^{56} +(2.35410 - 3.66854i) q^{57} +1.23607 q^{58} +(1.00000 - 1.73205i) q^{59} +(0.309017 - 0.535233i) q^{60} +(-6.23607 - 10.8012i) q^{61} +(-6.66312 + 11.5409i) q^{62} +(-0.381966 - 0.661585i) q^{63} +4.23607 q^{64} +1.23607 q^{65} +(1.61803 + 2.80252i) q^{66} +(1.61803 + 2.80252i) q^{67} -2.14590 q^{68} -2.47214 q^{69} +(-0.618034 - 1.07047i) q^{70} +(-4.61803 + 7.99867i) q^{71} +(-1.11803 - 1.93649i) q^{72} +(1.76393 - 3.05522i) q^{73} +(2.00000 - 3.46410i) q^{74} +1.00000 q^{75} +(1.23607 + 2.39364i) q^{76} +1.52786 q^{77} +(-1.00000 + 1.73205i) q^{78} +(-2.42705 - 4.20378i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.23607 + 10.8012i) q^{82} +15.1803 q^{83} +0.472136 q^{84} +(-1.73607 - 3.00696i) q^{85} +(9.47214 + 16.4062i) q^{86} -0.763932 q^{87} +4.47214 q^{88} +(-1.76393 - 3.05522i) q^{89} +(-0.809017 + 1.40126i) q^{90} +(0.472136 + 0.817763i) q^{91} +(0.763932 - 1.32317i) q^{92} +(4.11803 - 7.13264i) q^{93} -2.85410 q^{94} +(-2.35410 + 3.66854i) q^{95} +3.38197 q^{96} +(1.00000 - 1.73205i) q^{97} +(-5.19098 + 8.99105i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + q^{6} + 12 q^{7} - 2 q^{9} - q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} + 3 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + q^6 + 12 * q^7 - 2 * q^9 - q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 + 3 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^19 + 2 * q^20 - 6 * q^21 + 2 * q^22 - 4 * q^23 - 2 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 + 6 * q^29 + 2 * q^30 - 24 * q^31 - 9 * q^32 - 4 * q^33 - 9 * q^34 + 6 * q^35 + q^36 - 8 * q^37 - 13 * q^38 + 4 * q^39 - 2 * q^41 - 2 * q^42 - 10 * q^43 + 2 * q^44 - 4 * q^45 + 16 * q^46 - 8 * q^47 + 3 * q^48 + 28 * q^49 - 2 * q^50 - 2 * q^51 + 6 * q^52 + 2 * q^53 + q^54 + 4 * q^55 - 20 * q^56 - 4 * q^57 - 4 * q^58 + 4 * q^59 - q^60 - 16 * q^61 - 11 * q^62 - 6 * q^63 + 8 * q^64 - 4 * q^65 + 2 * q^66 + 2 * q^67 - 22 * q^68 + 8 * q^69 + 2 * q^70 - 14 * q^71 + 16 * q^73 + 8 * q^74 + 4 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 - 3 * q^80 - 2 * q^81 + 16 * q^82 + 16 * q^83 - 16 * q^84 + 2 * q^85 + 20 * q^86 - 12 * q^87 - 16 * q^89 - q^90 - 16 * q^91 + 12 * q^92 + 12 * q^93 + 2 * q^94 + 4 * q^95 + 18 * q^96 + 4 * q^97 - 23 * q^98 - 4 * q^99

Introduction

L-functions

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