LMFDB - Embedded newform 690.2.i.c.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	690.47
Dual form			690.2.i.c.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(0.224745 - 2.22474i) q^{10} -5.65685i q^{11} +(1.70711 + 0.292893i) q^{12} +(-3.44949 + 3.44949i) q^{13} -3.46410 q^{14} +(-1.90691 - 3.37101i) q^{15} -1.00000 q^{16} +(-5.19615 + 5.19615i) q^{17} +(2.70711 - 1.29289i) q^{18} +2.44949i q^{19} +(1.41421 + 1.73205i) q^{20} +(-4.89898 + 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(1.00000 - 4.89898i) q^{25} -4.87832i q^{26} +(2.53553 - 4.53553i) q^{27} +(2.44949 - 2.44949i) q^{28} -2.19275 q^{29} +(3.73205 + 1.03528i) q^{30} +4.89898 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.65685 + 1.65685i) q^{33} -7.34847i q^{34} +(-7.70674 - 0.778539i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(-1.73205 - 1.73205i) q^{38} +(-4.87832 - 6.89898i) q^{39} +(-2.22474 - 0.224745i) q^{40} -8.48528i q^{41} +(1.01461 - 5.91359i) q^{42} +(2.89898 - 2.89898i) q^{43} -5.65685 q^{44} +(6.31319 - 2.26795i) q^{45} +1.00000 q^{46} +(-4.87832 + 4.87832i) q^{47} +(0.292893 - 1.70711i) q^{48} +5.00000i q^{49} +(2.75699 + 4.17121i) q^{50} +(-7.34847 - 10.3923i) q^{51} +(3.44949 + 3.44949i) q^{52} +(-0.953512 - 0.953512i) q^{53} +(1.41421 + 5.00000i) q^{54} +(8.00000 + 9.79796i) q^{55} +3.46410i q^{56} +(-4.18154 - 0.717439i) q^{57} +(1.55051 - 1.55051i) q^{58} -5.51399 q^{59} +(-3.37101 + 1.90691i) q^{60} +0.898979 q^{61} +(-3.46410 + 3.46410i) q^{62} +(-4.47871 - 9.37769i) q^{63} +1.00000i q^{64} +(1.09638 - 10.8530i) q^{65} +(-8.00000 + 5.65685i) q^{66} +(-10.8990 - 10.8990i) q^{67} +(5.19615 + 5.19615i) q^{68} +(1.41421 - 1.00000i) q^{69} +(6.00000 - 4.89898i) q^{70} +14.6349i q^{71} +(-1.29289 - 2.70711i) q^{72} +(-1.89898 + 1.89898i) q^{73} +3.46410 q^{74} +(8.07019 + 3.14198i) q^{75} +2.44949 q^{76} +(13.8564 - 13.8564i) q^{77} +(8.32780 + 1.42883i) q^{78} +4.44949i q^{79} +(1.73205 - 1.41421i) q^{80} +(7.00000 + 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(1.41421 + 1.41421i) q^{83} +(3.46410 + 4.89898i) q^{84} +(1.65153 - 16.3485i) q^{85} +4.09978i q^{86} +(0.642242 - 3.74326i) q^{87} +(4.00000 - 4.00000i) q^{88} +9.12096 q^{89} +(-2.86042 + 6.06778i) q^{90} -16.8990 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-1.43488 + 8.36308i) q^{93} -6.89898i q^{94} +(-3.46410 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +(-0.449490 - 0.449490i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-5.65685 + 16.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 8 * q - 8 * q^3 - 8 * q^6	$ 8 q - 8 q^{3} - 8 q^{6} - 8 q^{10} + 8 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 16 q^{18} + 32 q^{22} + 8 q^{25} - 8 q^{27} + 16 q^{30} + 32 q^{33} - 8 q^{36} - 8 q^{40} - 16 q^{43} + 8 q^{46} + 8 q^{48} + 8 q^{52} + 64 q^{55} + 32 q^{58} + 8 q^{60} - 32 q^{61} - 64 q^{66} - 48 q^{67} + 48 q^{70} - 16 q^{72} + 24 q^{73} - 8 q^{75} + 8 q^{78} + 56 q^{81} + 48 q^{82} + 72 q^{85} - 32 q^{87} + 32 q^{88} - 8 q^{90} - 96 q^{91} + 8 q^{96} + 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^3 - 8 * q^6 - 8 * q^10 + 8 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 16 * q^18 + 32 * q^22 + 8 * q^25 - 8 * q^27 + 16 * q^30 + 32 * q^33 - 8 * q^36 - 8 * q^40 - 16 * q^43 + 8 * q^46 + 8 * q^48 + 8 * q^52 + 64 * q^55 + 32 * q^58 + 8 * q^60 - 32 * q^61 - 64 * q^66 - 48 * q^67 + 48 * q^70 - 16 * q^72 + 24 * q^73 - 8 * q^75 + 8 * q^78 + 56 * q^81 + 48 * q^82 + 72 * q^85 - 32 * q^87 + 32 * q^88 - 8 * q^90 - 96 * q^91 + 8 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$4$		−	1.00000i		−	0.500000i
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	2.44949	+	2.44949i	0.925820	+	0.925820i	0.997433	−	0.0716124i	$-0.0228145\pi$
$7$	2.44949	+	2.44949i	0.925820	+	0.925820i	−0.0716124	+	0.997433i	$0.522814\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$10$	0.224745	−	2.22474i	0.0710706	−	0.703526i
$11$		−	5.65685i		−	1.70561i	−0.522233	−	0.852803i	$-0.674901\pi$
$11$		−	5.65685i		−	1.70561i	0.522233	−	0.852803i	$-0.325099\pi$
$12$	1.70711	+	0.292893i	0.492799	+	0.0845510i
$13$	−3.44949	+	3.44949i	−0.956716	+	0.956716i	−0.999101	−	0.0423850i	$-0.986504\pi$
$13$	−3.44949	+	3.44949i	−0.956716	+	0.956716i	0.0423850	+	0.999101i	$0.486504\pi$
$14$	−3.46410			−0.925820
$15$	−1.90691	−	3.37101i	−0.492361	−	0.870391i
$16$	−1.00000			−0.250000
$17$	−5.19615	+	5.19615i	−1.26025	+	1.26025i	−0.309282	+	0.950971i	$0.600089\pi$
$17$	−5.19615	+	5.19615i	−1.26025	+	1.26025i	−0.950971	+	0.309282i	$0.899911\pi$
$18$	2.70711	−	1.29289i	0.638071	−	0.304738i
$19$			2.44949i			0.561951i	0.959715	+	0.280976i	$0.0906580\pi$
$19$			2.44949i			0.561951i	−0.959715	+	0.280976i	$0.909342\pi$
$20$	1.41421	+	1.73205i	0.316228	+	0.387298i
$21$	−4.89898	+	3.46410i	−1.06904	+	0.755929i
$22$	4.00000	+	4.00000i	0.852803	+	0.852803i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	−1.41421	+	1.00000i	−0.288675	+	0.204124i
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$		−	4.87832i		−	0.956716i
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$	2.44949	−	2.44949i	0.462910	−	0.462910i
$29$	−2.19275			−0.407184			−0.203592	−	0.979056i	$-0.565262\pi$
$29$	−2.19275			−0.407184			−0.203592	+	0.979056i	$0.565262\pi$
$30$	3.73205	+	1.03528i	0.681376	+	0.189015i
$31$	4.89898			0.879883			0.439941	−	0.898027i	$-0.354999\pi$
$31$	4.89898			0.879883			0.439941	+	0.898027i	$0.354999\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	9.65685	+	1.65685i	1.68104	+	0.288421i
$34$		−	7.34847i		−	1.26025i
$35$	−7.70674	−	0.778539i	−1.30268	−	0.131597i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	−2.44949	−	2.44949i	−0.402694	−	0.402694i	0.476488	−	0.879181i	$-0.341910\pi$
$37$	−2.44949	−	2.44949i	−0.402694	−	0.402694i	−0.879181	+	0.476488i	$0.841910\pi$
$38$	−1.73205	−	1.73205i	−0.280976	−	0.280976i
$39$	−4.87832	−	6.89898i	−0.781156	−	1.10472i
$40$	−2.22474	−	0.224745i	−0.351763	−	0.0355353i
$41$		−	8.48528i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$	1.01461	−	5.91359i	0.156558	−	0.912487i
$43$	2.89898	−	2.89898i	0.442090	−	0.442090i	−0.450624	−	0.892714i	$-0.648798\pi$
$43$	2.89898	−	2.89898i	0.442090	−	0.442090i	0.892714	+	0.450624i	$0.148798\pi$
$44$	−5.65685			−0.852803
$45$	6.31319	−	2.26795i	0.941115	−	0.338086i
$46$	1.00000			0.147442
$47$	−4.87832	+	4.87832i	−0.711575	+	0.711575i	−0.966865	−	0.255289i	$-0.917829\pi$
$47$	−4.87832	+	4.87832i	−0.711575	+	0.711575i	0.255289	+	0.966865i	$0.417829\pi$
$48$	0.292893	−	1.70711i	0.0422755	−	0.246400i
$49$			5.00000i			0.714286i
$50$	2.75699	+	4.17121i	0.389898	+	0.589898i
$51$	−7.34847	−	10.3923i	−1.02899	−	1.45521i
$52$	3.44949	+	3.44949i	0.478358	+	0.478358i
$53$	−0.953512	−	0.953512i	−0.130975	−	0.130975i	0.638580	−	0.769555i	$-0.279522\pi$
$53$	−0.953512	−	0.953512i	−0.130975	−	0.130975i	−0.769555	+	0.638580i	$0.779522\pi$
$54$	1.41421	+	5.00000i	0.192450	+	0.680414i
$55$	8.00000	+	9.79796i	1.07872	+	1.32116i
$56$			3.46410i			0.462910i
$57$	−4.18154	−	0.717439i	−0.553859	−	0.0950271i
$58$	1.55051	−	1.55051i	0.203592	−	0.203592i
$59$	−5.51399			−0.717860			−0.358930	−	0.933364i	$-0.616858\pi$
$59$	−5.51399			−0.717860			−0.358930	+	0.933364i	$0.616858\pi$
$60$	−3.37101	+	1.90691i	−0.435195	+	0.246181i
$61$	0.898979			0.115103			0.0575513	−	0.998343i	$-0.481671\pi$
$61$	0.898979			0.115103			0.0575513	+	0.998343i	$0.481671\pi$
$62$	−3.46410	+	3.46410i	−0.439941	+	0.439941i
$63$	−4.47871	−	9.37769i	−0.564265	−	1.18148i
$64$			1.00000i			0.125000i
$65$	1.09638	−	10.8530i	0.135989	−	1.34615i
$66$	−8.00000	+	5.65685i	−0.984732	+	0.696311i
$67$	−10.8990	−	10.8990i	−1.33152	−	1.33152i	−0.904009	−	0.427513i	$-0.859390\pi$
$67$	−10.8990	−	10.8990i	−1.33152	−	1.33152i	−0.427513	−	0.904009i	$-0.640610\pi$
$68$	5.19615	+	5.19615i	0.630126	+	0.630126i
$69$	1.41421	−	1.00000i	0.170251	−	0.120386i
$70$	6.00000	−	4.89898i	0.717137	−	0.585540i
$71$			14.6349i			1.73685i	0.495822	+	0.868424i	$0.334867\pi$
$71$			14.6349i			1.73685i	−0.495822	+	0.868424i	$0.665133\pi$
$72$	−1.29289	−	2.70711i	−0.152369	−	0.319036i
$73$	−1.89898	+	1.89898i	−0.222259	+	0.222259i	−0.809449	−	0.587190i	$-0.800234\pi$
$73$	−1.89898	+	1.89898i	−0.222259	+	0.222259i	0.587190	+	0.809449i	$0.300234\pi$
$74$	3.46410			0.402694
$75$	8.07019	+	3.14198i	0.931865	+	0.362805i
$76$	2.44949			0.280976
$77$	13.8564	−	13.8564i	1.57908	−	1.57908i
$78$	8.32780	+	1.42883i	0.942938	+	0.161783i
$79$			4.44949i			0.500607i	0.968167	+	0.250303i	$0.0805304\pi$
$79$			4.44949i			0.500607i	−0.968167	+	0.250303i	$0.919470\pi$
$80$	1.73205	−	1.41421i	0.193649	−	0.158114i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	6.00000	+	6.00000i	0.662589	+	0.662589i
$83$	1.41421	+	1.41421i	0.155230	+	0.155230i	0.780449	−	0.625219i	$-0.214990\pi$
$83$	1.41421	+	1.41421i	0.155230	+	0.155230i	−0.625219	+	0.780449i	$0.714990\pi$
$84$	3.46410	+	4.89898i	0.377964	+	0.534522i
$85$	1.65153	−	16.3485i	0.179134	−	1.77324i
$86$			4.09978i			0.442090i
$87$	0.642242	−	3.74326i	0.0688556	−	0.401320i
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$	9.12096			0.966819			0.483410	−	0.875394i	$-0.339398\pi$
$89$	9.12096			0.966819			0.483410	+	0.875394i	$0.339398\pi$
$90$	−2.86042	+	6.06778i	−0.301515	+	0.639601i
$91$	−16.8990			−1.77149
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	−1.43488	+	8.36308i	−0.148790	+	0.867211i
$94$		−	6.89898i		−	0.711575i
$95$	−3.46410	−	4.24264i	−0.355409	−	0.435286i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$	−0.449490	−	0.449490i	−0.0456388	−	0.0456388i	0.683919	−	0.729558i	$-0.260274\pi$
$97$	−0.449490	−	0.449490i	−0.0456388	−	0.0456388i	−0.729558	+	0.683919i	$0.760274\pi$
$98$	−3.53553	−	3.53553i	−0.357143	−	0.357143i
$99$	−5.65685	+	16.0000i	−0.568535	+	1.60806i
$100$	−4.89898	−	1.00000i	−0.489898	−	0.100000i
$101$		−	0.635674i		−	0.0632520i	−0.999500	−	0.0316260i	$-0.989931\pi$
$101$		−	0.635674i		−	0.0632520i	0.999500	−	0.0316260i	$-0.0100685\pi$
$102$	12.5446	+	2.15232i	1.24210	+	0.213111i
$103$	−10.8990	+	10.8990i	−1.07391	+	1.07391i	−0.0768670	+	0.997041i	$0.524492\pi$
$103$	−10.8990	+	10.8990i	−1.07391	+	1.07391i	−0.997041	+	0.0768670i	$0.975508\pi$
$104$	−4.87832			−0.478358
$105$	3.58630	−	12.9282i	0.349987	−	1.26166i
$106$	1.34847			0.130975
$107$	7.70674	−	7.70674i	0.745039	−	0.745039i	−0.228504	−	0.973543i	$-0.573383\pi$
$107$	7.70674	−	7.70674i	0.745039	−	0.745039i	0.973543	+	0.228504i	$0.0733834\pi$
$108$	−4.53553	−	2.53553i	−0.436432	−	0.243982i
$109$			13.7980i			1.32160i	0.750560	+	0.660802i	$0.229784\pi$
$109$			13.7980i			1.32160i	−0.750560	+	0.660802i	$0.770216\pi$
$110$	−12.5851	−	1.27135i	−1.19994	−	0.121218i
$111$	4.89898	−	3.46410i	0.464991	−	0.328798i
$112$	−2.44949	−	2.44949i	−0.231455	−	0.231455i
$113$	8.02458	+	8.02458i	0.754889	+	0.754889i	0.975387	−	0.220498i	$-0.0707684\pi$
$113$	8.02458	+	8.02458i	0.754889	+	0.754889i	−0.220498	+	0.975387i	$0.570768\pi$
$114$	3.46410	−	2.44949i	0.324443	−	0.229416i
$115$	2.22474	+	0.224745i	0.207459	+	0.0209576i
$116$			2.19275i			0.203592i
$117$	13.2061	−	6.30714i	1.22091	−	0.583095i
$118$	3.89898	−	3.89898i	0.358930	−	0.358930i
$119$	−25.4558			−2.33353
$120$	1.03528	−	3.73205i	0.0945074	−	0.340688i
$121$	−21.0000			−1.90909
$122$	−0.635674	+	0.635674i	−0.0575513	+	0.0575513i
$123$	14.4853	+	2.48528i	1.30609	+	0.224090i
$124$		−	4.89898i		−	0.439941i
$125$	5.19615	+	9.89949i	0.464758	+	0.885438i
$126$	9.79796	+	3.46410i	0.872872	+	0.308607i
$127$	−3.55051	−	3.55051i	−0.315057	−	0.315057i	0.531808	−	0.846865i	$-0.321513\pi$
$127$	−3.55051	−	3.55051i	−0.315057	−	0.315057i	−0.846865	+	0.531808i	$0.821513\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	4.09978	+	5.79796i	0.360965	+	0.510482i
$130$	6.89898	+	8.44949i	0.605081	+	0.741069i
$131$		−	0.142865i		−	0.0124821i	−0.999981	−	0.00624107i	$-0.998013\pi$
$131$		−	0.142865i		−	0.0124821i	0.999981	−	0.00624107i	$-0.00198661\pi$
$132$	1.65685	−	9.65685i	0.144211	−	0.840521i
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	15.4135			1.33152
$135$	2.02254	+	11.4416i	0.174073	+	0.984733i
$136$	−7.34847			−0.630126
$137$	−13.6814	+	13.6814i	−1.16888	+	1.16888i	−0.186412	+	0.982472i	$0.559686\pi$
$137$	−13.6814	+	13.6814i	−1.16888	+	1.16888i	−0.982472	+	0.186412i	$0.940314\pi$
$138$	−0.292893	+	1.70711i	−0.0249327	+	0.145319i
$139$			18.6969i			1.58585i	0.609317	+	0.792927i	$0.291444\pi$
$139$			18.6969i			1.58585i	−0.609317	+	0.792927i	$0.708556\pi$
$140$	−0.778539	+	7.70674i	−0.0657986	+	0.651339i
$141$	−6.89898	−	9.75663i	−0.580999	−	0.821656i
$142$	−10.3485	−	10.3485i	−0.868424	−	0.868424i
$143$	19.5133	+	19.5133i	1.63178	+	1.63178i
$144$	2.82843	+	1.00000i	0.235702	+	0.0833333i
$145$	3.79796	−	3.10102i	0.315403	−	0.257526i
$146$		−	2.68556i		−	0.222259i
$147$	−8.53553	−	1.46447i	−0.703999	−	0.120787i
$148$	−2.44949	+	2.44949i	−0.201347	+	0.201347i
$149$	−11.0280			−0.903447			−0.451724	−	0.892158i	$-0.649191\pi$
$149$	−11.0280			−0.903447			−0.451724	+	0.892158i	$0.649191\pi$
$150$	−7.92820	+	3.48477i	−0.647335	+	0.284530i
$151$	−0.898979			−0.0731579			−0.0365790	−	0.999331i	$-0.511646\pi$
$151$	−0.898979			−0.0731579			−0.0365790	+	0.999331i	$0.511646\pi$
$152$	−1.73205	+	1.73205i	−0.140488	+	0.140488i
$153$	19.8931	−	9.50079i	1.60826	−	0.768093i
$154$			19.5959i			1.57908i
$155$	−8.48528	+	6.92820i	−0.681554	+	0.556487i
$156$	−6.89898	+	4.87832i	−0.552360	+	0.390578i
$157$	−8.44949	−	8.44949i	−0.674343	−	0.674343i	0.284371	−	0.958714i	$-0.408215\pi$
$157$	−8.44949	−	8.44949i	−0.674343	−	0.674343i	−0.958714	+	0.284371i	$0.908215\pi$
$158$	−3.14626	−	3.14626i	−0.250303	−	0.250303i
$159$	1.90702	−	1.34847i	0.151237	−	0.106941i
$160$	−0.224745	+	2.22474i	−0.0177676	+	0.175882i
$161$		−	3.46410i		−	0.273009i
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$	−8.48528			−0.662589
$165$	−19.0693	+	10.7871i	−1.48454	+	0.839774i
$166$	−2.00000			−0.155230
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	−0.453510	−	0.891251i	$-0.649829\pi$
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	0.891251	+	0.453510i	$0.149829\pi$
$168$	−5.91359	−	1.01461i	−0.456243	−	0.0782790i
$169$		−	10.7980i		−	0.830612i
$170$	10.3923	+	12.7279i	0.797053	+	0.976187i
$171$	2.44949	−	6.92820i	0.187317	−	0.529813i
$172$	−2.89898	−	2.89898i	−0.221045	−	0.221045i
$173$	3.60697	+	3.60697i	0.274233	+	0.274233i	0.830801	−	0.556569i	$-0.187882\pi$
$173$	3.60697	+	3.60697i	0.274233	+	0.274233i	−0.556569	+	0.830801i	$0.687882\pi$
$174$	2.19275	+	3.10102i	0.166232	+	0.235088i
$175$	14.4495	−	9.55051i	1.09228	−	0.721951i
$176$			5.65685i			0.426401i
$177$	1.61501	−	9.41297i	0.121392	−	0.707522i
$178$	−6.44949	+	6.44949i	−0.483410	+	0.483410i
$179$	−15.2706			−1.14138			−0.570690	−	0.821166i	$-0.693324\pi$
$179$	−15.2706			−1.14138			−0.570690	+	0.821166i	$0.693324\pi$
$180$	−2.26795	−	6.31319i	−0.169043	−	0.470558i
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	11.9494	−	11.9494i	0.885747	−	0.885747i
$183$	−0.263305	+	1.53465i	−0.0194641	+	0.113445i
$184$		−	1.00000i		−	0.0737210i
$185$	7.70674	+	0.778539i	0.566611	+	0.0572393i
$186$	−4.89898	−	6.92820i	−0.359211	−	0.508001i
$187$	29.3939	+	29.3939i	2.14949	+	2.14949i
$188$	4.87832	+	4.87832i	0.355788	+	0.355788i
$189$	17.3205	−	4.89898i	1.25988	−	0.356348i
$190$	5.44949	+	0.550510i	0.395348	+	0.0399382i
$191$			17.9562i			1.29926i	0.760249	+	0.649632i	$0.225077\pi$
$191$			17.9562i			1.29926i	−0.760249	+	0.649632i	$0.774923\pi$
$192$	−1.70711	−	0.292893i	−0.123200	−	0.0211377i
$193$	1.89898	−	1.89898i	0.136692	−	0.136692i	−0.635450	−	0.772142i	$-0.719185\pi$
$193$	1.89898	−	1.89898i	0.136692	−	0.136692i	0.772142	+	0.635450i	$0.219185\pi$
$194$	0.635674			0.0456388
$195$	18.2061	+	5.05040i	1.30377	+	0.361667i
$196$	5.00000			0.357143
$197$	−7.70674	+	7.70674i	−0.549083	+	0.549083i	−0.926175	−	0.377093i	$-0.876924\pi$
$197$	−7.70674	+	7.70674i	−0.549083	+	0.549083i	0.377093	+	0.926175i	$0.376924\pi$
$198$	−7.31371	−	15.3137i	−0.519763	−	1.08830i
$199$			7.55051i			0.535241i	0.963524	+	0.267621i	$0.0862374\pi$
$199$			7.55051i			0.535241i	−0.963524	+	0.267621i	$0.913763\pi$
$200$	4.17121	−	2.75699i	0.294949	−	0.194949i
$201$	21.7980	−	15.4135i	1.53751	−	1.08718i
$202$	0.449490	+	0.449490i	0.0316260	+	0.0316260i
$203$	−5.37113	−	5.37113i	−0.376979	−	0.376979i
$204$	−10.3923	+	7.34847i	−0.727607	+	0.514496i
$205$	12.0000	+	14.6969i	0.838116	+	1.02648i
$206$		−	15.4135i		−	1.07391i
$207$	1.29289	+	2.70711i	0.0898623	+	0.188157i
$208$	3.44949	−	3.44949i	0.239179	−	0.239179i
$209$	13.8564			0.958468
$210$	6.60572	+	11.6775i	0.455838	+	0.805825i
$211$	18.6969			1.28715			0.643575	−	0.765383i	$-0.277450\pi$
$211$	18.6969			1.28715			0.643575	+	0.765383i	$0.277450\pi$
$212$	−0.953512	+	0.953512i	−0.0654875	+	0.0654875i
$213$	−24.9834	−	4.28648i	−1.71184	−	0.293705i
$214$			10.8990i			0.745039i
$215$	−0.921404	+	9.12096i	−0.0628392	+	0.622044i
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	12.0000	+	12.0000i	0.814613	+	0.814613i
$218$	−9.75663	−	9.75663i	−0.660802	−	0.660802i
$219$	−2.68556	−	3.79796i	−0.181473	−	0.256642i
$220$	9.79796	−	8.00000i	0.660578	−	0.539360i
$221$		−	35.8481i		−	2.41141i
$222$	−1.01461	+	5.91359i	−0.0680963	+	0.396894i
$223$	−12.4495	+	12.4495i	−0.833679	+	0.833679i	−0.988018	−	0.154339i	$-0.950675\pi$
$223$	−12.4495	+	12.4495i	−0.833679	+	0.833679i	0.154339	+	0.988018i	$0.450675\pi$
$224$	3.46410			0.231455
$225$	−7.72741	+	12.8564i	−0.515160	+	0.857094i
$226$	−11.3485			−0.754889
$227$	0.778539	−	0.778539i	0.0516735	−	0.0516735i	−0.680798	−	0.732471i	$-0.738367\pi$
$227$	0.778539	−	0.778539i	0.0516735	−	0.0516735i	0.732471	+	0.680798i	$0.238367\pi$
$228$	−0.717439	+	4.18154i	−0.0475136	+	0.276929i
$229$		−	6.69694i		−	0.442546i	−0.975212	−	0.221273i	$-0.928979\pi$
$229$		−	6.69694i		−	0.442546i	0.975212	−	0.221273i	$-0.0710212\pi$
$230$	−1.73205	+	1.41421i	−0.114208	+	0.0932505i
$231$	19.5959	+	27.7128i	1.28932	+	1.82337i
$232$	−1.55051	−	1.55051i	−0.101796	−	0.101796i
$233$	−3.60697	−	3.60697i	−0.236300	−	0.236300i	0.579016	−	0.815316i	$-0.303437\pi$
$233$	−3.60697	−	3.60697i	−0.236300	−	0.236300i	−0.815316	+	0.579016i	$0.803437\pi$
$234$	−4.87832	+	13.7980i	−0.318905	+	0.902001i
$235$	1.55051	−	15.3485i	0.101144	−	1.00122i
$236$			5.51399i			0.358930i
$237$	−7.59575	−	1.30323i	−0.493397	−	0.0846536i
$238$	18.0000	−	18.0000i	1.16677	−	1.16677i
$239$	13.3636			0.864419			0.432210	−	0.901773i	$-0.357734\pi$
$239$	13.3636			0.864419			0.432210	+	0.901773i	$0.357734\pi$
$240$	1.90691	+	3.37101i	0.123090	+	0.217598i
$241$	−9.10102			−0.586248			−0.293124	−	0.956074i	$-0.594695\pi$
$241$	−9.10102			−0.586248			−0.293124	+	0.956074i	$0.594695\pi$
$242$	14.8492	−	14.8492i	0.954545	−	0.954545i
$243$	−11.7071	+	10.2929i	−0.751011	+	0.660289i
$244$		−	0.898979i		−	0.0575513i
$245$	−7.07107	−	8.66025i	−0.451754	−	0.553283i
$246$	−12.0000	+	8.48528i	−0.765092	+	0.541002i
$247$	−8.44949	−	8.44949i	−0.537628	−	0.537628i
$248$	3.46410	+	3.46410i	0.219971	+	0.219971i
$249$	−2.82843	+	2.00000i	−0.179244	+	0.126745i
$250$	−10.6742	−	3.32577i	−0.675098	−	0.210340i
$251$			12.8708i			0.812397i	0.913785	+	0.406198i	$0.133146\pi$
$251$			12.8708i			0.812397i	−0.913785	+	0.406198i	$0.866854\pi$
$252$	−9.37769	+	4.47871i	−0.590739	+	0.282132i
$253$	−4.00000	+	4.00000i	−0.251478	+	0.251478i
$254$	5.02118			0.315057
$255$	27.4249	+	7.60770i	1.71741	+	0.476412i
$256$	1.00000			0.0625000
$257$	−9.61377	+	9.61377i	−0.599690	+	0.599690i	−0.940230	−	0.340540i	$-0.889390\pi$
$257$	−9.61377	+	9.61377i	−0.599690	+	0.599690i	0.340540	+	0.940230i	$0.389390\pi$
$258$	−6.99876	−	1.20080i	−0.435723	−	0.0747583i
$259$		−	12.0000i		−	0.745644i
$260$	−10.8530	−	1.09638i	−0.673075	−	0.0679944i
$261$	6.20204	+	2.19275i	0.383897	+	0.135728i
$262$	0.101021	+	0.101021i	0.00624107	+	0.00624107i
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	0.510852	−	0.859669i	$-0.329330\pi$
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	−0.859669	+	0.510852i	$0.829330\pi$
$264$	5.65685	+	8.00000i	0.348155	+	0.492366i
$265$	3.00000	+	0.303062i	0.184289	+	0.0186169i
$266$		−	8.48528i		−	0.520266i
$267$	−2.67147	+	15.5704i	−0.163491	+	0.952896i
$268$	−10.8990	+	10.8990i	−0.665761	+	0.665761i
$269$	6.29253			0.383662			0.191831	−	0.981428i	$-0.438557\pi$
$269$	6.29253			0.383662			0.191831	+	0.981428i	$0.438557\pi$
$270$	−9.52056	−	6.66025i	−0.579403	−	0.405330i
$271$	−24.4949			−1.48796			−0.743980	−	0.668202i	$-0.767064\pi$
$271$	−24.4949			−1.48796			−0.743980	+	0.668202i	$0.767064\pi$
$272$	5.19615	−	5.19615i	0.315063	−	0.315063i
$273$	4.94960	−	28.8484i	0.299563	−	1.74598i
$274$		−	19.3485i		−	1.16888i
$275$	−27.7128	−	5.65685i	−1.67115	−	0.341121i
$276$	−1.00000	−	1.41421i	−0.0601929	−	0.0851257i
$277$	−9.44949	−	9.44949i	−0.567765	−	0.567765i	0.363737	−	0.931502i	$-0.381501\pi$
$277$	−9.44949	−	9.44949i	−0.567765	−	0.567765i	−0.931502	+	0.363737i	$0.881501\pi$
$278$	−13.2207	−	13.2207i	−0.792927	−	0.792927i
$279$	−13.8564	−	4.89898i	−0.829561	−	0.293294i
$280$	−4.89898	−	6.00000i	−0.292770	−	0.358569i
$281$			5.65685i			0.337460i	0.985662	+	0.168730i	$0.0539665\pi$
$281$			5.65685i			0.337460i	−0.985662	+	0.168730i	$0.946033\pi$
$282$	11.7773	+	2.02066i	0.701328	+	0.120329i
$283$	5.34847	−	5.34847i	0.317933	−	0.317933i	−0.530039	−	0.847973i	$-0.677823\pi$
$283$	5.34847	−	5.34847i	0.317933	−	0.317933i	0.847973	+	0.530039i	$0.177823\pi$
$284$	14.6349			0.868424
$285$	8.25725	−	4.67095i	0.489117	−	0.276683i
$286$	−27.5959			−1.63178
$287$	20.7846	−	20.7846i	1.22688	−	1.22688i
$288$	−2.70711	+	1.29289i	−0.159518	+	0.0761845i
$289$		−	37.0000i		−	2.17647i
$290$	−0.492810	+	4.87832i	−0.0289388	+	0.286465i
$291$	0.898979	−	0.635674i	0.0526991	−	0.0372639i
$292$	1.89898	+	1.89898i	0.111129	+	0.111129i
$293$	13.5386	+	13.5386i	0.790932	+	0.790932i	0.981646	−	0.190714i	$-0.0610803\pi$
$293$	13.5386	+	13.5386i	0.790932	+	0.790932i	−0.190714	+	0.981646i	$0.561080\pi$
$294$	7.07107	−	5.00000i	0.412393	−	0.291606i
$295$	9.55051	−	7.79796i	0.556052	−	0.454015i
$296$		−	3.46410i		−	0.201347i
$297$	−25.6569	−	14.3431i	−1.48876	−	0.832274i
$298$	7.79796	−	7.79796i	0.451724	−	0.451724i
$299$	4.87832			0.282120
$300$	3.14198	−	8.07019i	0.181403	−	0.465933i
$301$	14.2020			0.818592
$302$	0.635674	−	0.635674i	0.0365790	−	0.0365790i
$303$	1.08516	+	0.186185i	0.0623411	+	0.0106960i
$304$		−	2.44949i		−	0.140488i
$305$	−1.55708	+	1.27135i	−0.0891580	+	0.0727972i
$306$	−7.34847	+	20.7846i	−0.420084	+	1.18818i
$307$	−22.6969	−	22.6969i	−1.29538	−	1.29538i	−0.931409	−	0.363973i	$-0.881420\pi$
$307$	−22.6969	−	22.6969i	−1.29538	−	1.29538i	−0.363973	−	0.931409i	$-0.618580\pi$
$308$	−13.8564	−	13.8564i	−0.789542	−	0.789542i
$309$	−15.4135	−	21.7980i	−0.876843	−	1.24004i
$310$	1.10102	−	10.8990i	0.0625338	−	0.619020i
$311$		−	14.3492i		−	0.813669i	−0.913502	−	0.406835i	$-0.866632\pi$
$311$		−	14.3492i		−	0.813669i	0.913502	−	0.406835i	$-0.133368\pi$
$312$	1.42883	−	8.32780i	0.0808913	−	0.471469i
$313$	−15.1464	+	15.1464i	−0.856127	+	0.856127i	−0.990879	−	0.134753i	$-0.956976\pi$
$313$	−15.1464	+	15.1464i	−0.856127	+	0.856127i	0.134753	+	0.990879i	$0.456976\pi$
$314$	11.9494			0.674343
$315$	21.0194	+	9.90878i	1.18431	+	0.558297i
$316$	4.44949			0.250303
$317$	−13.3636	+	13.3636i	−0.750574	+	0.750574i	−0.974586	−	0.224012i	$-0.928085\pi$
$317$	−13.3636	+	13.3636i	−0.750574	+	0.750574i	0.224012	+	0.974586i	$0.428085\pi$
$318$	−0.394957	+	2.30198i	−0.0221481	+	0.129089i
$319$			12.4041i			0.694495i
$320$	−1.41421	−	1.73205i	−0.0790569	−	0.0968246i
$321$	10.8990	+	15.4135i	0.608322	+	0.860297i
$322$	2.44949	+	2.44949i	0.136505	+	0.136505i
$323$	−12.7279	−	12.7279i	−0.708201	−	0.708201i
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$	13.4495	+	20.3485i	0.746043	+	1.12873i
$326$		−	5.65685i		−	0.313304i
$327$	−23.5546	−	4.04133i	−1.30257	−	0.223486i
$328$	6.00000	−	6.00000i	0.331295	−	0.331295i
$329$	−23.8988			−1.31758
$330$	5.85641	−	21.1117i	0.322385	−	1.16216i
$331$	−18.6969			−1.02768			−0.513838	−	0.857887i	$-0.671777\pi$
$331$	−18.6969			−1.02768			−0.513838	+	0.857887i	$0.671777\pi$
$332$	1.41421	−	1.41421i	0.0776151	−	0.0776151i
$333$	4.47871	+	9.37769i	0.245432	+	0.513894i
$334$			8.00000i			0.437741i
$335$	34.2911	+	3.46410i	1.87352	+	0.189264i
$336$	4.89898	−	3.46410i	0.267261	−	0.188982i
$337$	14.4495	+	14.4495i	0.787114	+	0.787114i	0.981020	−	0.193906i	$-0.0621157\pi$
$337$	14.4495	+	14.4495i	0.787114	+	0.787114i	−0.193906	+	0.981020i	$0.562116\pi$
$338$	7.63531	+	7.63531i	0.415306	+	0.415306i
$339$	−16.0492	+	11.3485i	−0.871671	+	0.616364i
$340$	−16.3485	−	1.65153i	−0.886620	−	0.0895668i
$341$		−	27.7128i		−	1.50073i
$342$	3.16693	+	6.63103i	0.171248	+	0.358565i
$343$	4.89898	−	4.89898i	0.264520	−	0.264520i
$344$	4.09978			0.221045
$345$	−1.03528	+	3.73205i	−0.0557374	+	0.200927i
$346$	−5.10102			−0.274233
$347$	−0.142865	+	0.142865i	−0.00766937	+	0.00766937i	−0.710931	−	0.703262i	$-0.751726\pi$
$347$	−0.142865	+	0.142865i	−0.00766937	+	0.00766937i	0.703262	+	0.710931i	$0.251726\pi$
$348$	−3.74326	−	0.642242i	−0.200660	−	0.0344278i
$349$		−	22.0000i		−	1.17763i	−0.808267	−	0.588817i	$-0.799594\pi$
$349$		−	22.0000i		−	1.17763i	0.808267	−	0.588817i	$-0.200406\pi$
$350$	−3.46410	+	16.9706i	−0.185164	+	0.907115i
$351$	6.89898	+	24.3916i	0.368240	+	1.30193i
$352$	−4.00000	−	4.00000i	−0.213201	−	0.213201i
$353$	23.1202	+	23.1202i	1.23057	+	1.23057i	0.963747	+	0.266819i	$0.0859725\pi$
$353$	23.1202	+	23.1202i	1.23057	+	1.23057i	0.266819	+	0.963747i	$0.414027\pi$
$354$	5.51399	+	7.79796i	0.293065	+	0.414457i
$355$	−20.6969	−	25.3485i	−1.09848	−	1.34536i
$356$		−	9.12096i		−	0.483410i
$357$	7.45584	−	43.4558i	0.394605	−	2.29993i
$358$	10.7980	−	10.7980i	0.570690	−	0.570690i
$359$	26.7272			1.41061			0.705304	−	0.708905i	$-0.250811\pi$
$359$	26.7272			1.41061			0.705304	+	0.708905i	$0.250811\pi$
$360$	6.06778	+	2.86042i	0.319800	+	0.150757i
$361$	13.0000			0.684211
$362$	−5.65685	+	5.65685i	−0.297318	+	0.297318i
$363$	6.15076	−	35.8492i	0.322831	−	1.88160i
$364$			16.8990i			0.885747i
$365$	0.603566	−	5.97469i	0.0315921	−	0.312730i
$366$	−0.898979	−	1.27135i	−0.0469904	−	0.0664545i
$367$	19.7980	+	19.7980i	1.03345	+	1.03345i	0.999421	+	0.0340240i	$0.0108323\pi$
$367$	19.7980	+	19.7980i	1.03345	+	1.03345i	0.0340240	+	0.999421i	$0.489168\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	−8.48528	+	24.0000i	−0.441726	+	1.24939i
$370$	−6.00000	+	4.89898i	−0.311925	+	0.254686i
$371$		−	4.67123i		−	0.242518i
$372$	8.36308	+	1.43488i	0.433606	+	0.0743950i
$373$	12.4495	−	12.4495i	0.644610	−	0.644610i	−0.307075	−	0.951685i	$-0.599350\pi$
$373$	12.4495	−	12.4495i	0.644610	−	0.644610i	0.951685	+	0.307075i	$0.0993503\pi$
$374$	−41.5692			−2.14949
$375$	−18.4214	+	5.97089i	−0.951278	+	0.308336i
$376$	−6.89898			−0.355788
$377$	7.56388	−	7.56388i	0.389560	−	0.389560i
$378$	−8.78335	+	15.7116i	−0.451767	+	0.808115i
$379$			5.14643i			0.264354i	0.991226	+	0.132177i	$0.0421968\pi$
$379$			5.14643i			0.264354i	−0.991226	+	0.132177i	$0.957803\pi$
$380$	−4.24264	+	3.46410i	−0.217643	+	0.177705i
$381$	7.10102	−	5.02118i	0.363796	−	0.257243i
$382$	−12.6969	−	12.6969i	−0.649632	−	0.649632i
$383$	−4.73545	−	4.73545i	−0.241970	−	0.241970i	0.575695	−	0.817665i	$-0.304732\pi$
$383$	−4.73545	−	4.73545i	−0.241970	−	0.241970i	−0.817665	+	0.575695i	$0.804732\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$	−4.40408	+	43.5959i	−0.224453	+	2.22185i
$386$			2.68556i			0.136692i
$387$	−11.0985	+	5.30057i	−0.564170	+	0.269443i
$388$	−0.449490	+	0.449490i	−0.0228194	+	0.0228194i
$389$	31.1127			1.57748			0.788738	−	0.614729i	$-0.210735\pi$
$389$	31.1127			1.57748			0.788738	+	0.614729i	$0.210735\pi$
$390$	−16.4448	+	9.30250i	−0.832717	+	0.471050i
$391$	7.34847			0.371628
$392$	−3.53553	+	3.53553i	−0.178571	+	0.178571i
$393$	0.243885	+	0.0418441i	0.0123024	+	0.00211075i
$394$		−	10.8990i		−	0.549083i
$395$	−6.29253	−	7.70674i	−0.316611	−	0.387768i
$396$	16.0000	+	5.65685i	0.804030	+	0.284268i
$397$	8.55051	+	8.55051i	0.429138	+	0.429138i	0.888335	−	0.459197i	$-0.151863\pi$
$397$	8.55051	+	8.55051i	0.429138	+	0.429138i	−0.459197	+	0.888335i	$0.651863\pi$
$398$	−5.33902	−	5.33902i	−0.267621	−	0.267621i
$399$	−8.48528	−	12.0000i	−0.424795	−	0.600751i
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$		−	7.84961i		−	0.391991i	−0.980605	−	0.195995i	$-0.937206\pi$
$401$		−	7.84961i		−	0.391991i	0.980605	−	0.195995i	$-0.0627937\pi$
$402$	−4.51451	+	26.3125i	−0.225163	+	1.31235i
$403$	−16.8990	+	16.8990i	−0.841798	+	0.841798i
$404$	−0.635674			−0.0316260
$405$	−20.1244	+	0.101536i	−0.999987	+	0.00504536i
$406$	7.59592			0.376979
$407$	−13.8564	+	13.8564i	−0.686837	+	0.686837i
$408$	2.15232	−	12.5446i	0.106556	−	0.621051i
$409$			13.7980i			0.682265i	0.940015	+	0.341133i	$0.110811\pi$
$409$			13.7980i			0.682265i	−0.940015	+	0.341133i	$0.889189\pi$
$410$	−18.8776	−	1.90702i	−0.932298	−	0.0941812i
$411$	−19.3485	−	27.3629i	−0.954390	−	1.34971i
$412$	10.8990	+	10.8990i	0.536954	+	0.536954i
$413$	−13.5065	−	13.5065i	−0.664610	−	0.664610i
$414$	−2.82843	−	1.00000i	−0.139010	−	0.0491473i
$415$	−4.44949	−	0.449490i	−0.218417	−	0.0220646i
$416$			4.87832i			0.239179i
$417$	−31.9177	−	5.47621i	−1.56302	−	0.268171i
$418$	−9.79796	+	9.79796i	−0.479234	+	0.479234i
$419$	−4.38551			−0.214246			−0.107123	−	0.994246i	$-0.534164\pi$
$419$	−4.38551			−0.214246			−0.107123	+	0.994246i	$0.534164\pi$
$420$	−12.9282	−	3.58630i	−0.630832	−	0.174994i
$421$	0.898979			0.0438136			0.0219068	−	0.999760i	$-0.493026\pi$
$421$	0.898979			0.0438136			0.0219068	+	0.999760i	$0.493026\pi$
$422$	−13.2207	+	13.2207i	−0.643575	+	0.643575i
$423$	18.6763	−	8.91964i	0.908072	−	0.433688i
$424$		−	1.34847i		−	0.0654875i
$425$	20.2597	+	30.6520i	0.982739	+	1.48684i
$426$	20.6969	−	14.6349i	1.00277	−	0.709065i
$427$	2.20204	+	2.20204i	0.106564	+	0.106564i
$428$	−7.70674	−	7.70674i	−0.372519	−	0.372519i
$429$	−39.0265	+	27.5959i	−1.88422	+	1.33234i
$430$	−5.79796	−	7.10102i	−0.279602	−	0.342442i
$431$			22.3417i			1.07616i	0.842893	+	0.538081i	$0.180850\pi$
$431$			22.3417i			1.07616i	−0.842893	+	0.538081i	$0.819150\pi$
$432$	−2.53553	+	4.53553i	−0.121991	+	0.218216i
$433$	29.3485	−	29.3485i	1.41040	−	1.41040i	0.653287	−	0.757110i	$-0.273389\pi$
$433$	29.3485	−	29.3485i	1.41040	−	1.41040i	0.757110	−	0.653287i	$-0.226611\pi$
$434$	−16.9706			−0.814613
$435$	4.18138	+	7.39179i	0.200482	+	0.354409i
$436$	13.7980			0.660802
$437$	1.73205	−	1.73205i	0.0828552	−	0.0828552i
$438$	4.58454	+	0.786583i	0.219058	+	0.0375844i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	−1.27135	+	12.5851i	−0.0606092	+	0.599969i
$441$	5.00000	−	14.1421i	0.238095	−	0.673435i
$442$	25.3485	+	25.3485i	1.20570	+	1.20570i
$443$	11.3137	+	11.3137i	0.537531	+	0.537531i	0.922803	−	0.385272i	$-0.125893\pi$
$443$	11.3137	+	11.3137i	0.537531	+	0.537531i	−0.385272	+	0.922803i	$0.625893\pi$
$444$	−3.46410	−	4.89898i	−0.164399	−	0.232495i
$445$	−15.7980	+	12.8990i	−0.748895	+	0.611470i
$446$		−	17.6062i		−	0.833679i
$447$	3.23002	−	18.8259i	0.152775	−	0.890436i
$448$	−2.44949	+	2.44949i	−0.115728	+	0.115728i
$449$	15.1278			0.713923			0.356961	−	0.934119i	$-0.383813\pi$
$449$	15.1278			0.713923			0.356961	+	0.934119i	$0.383813\pi$
$450$	−3.62675	−	14.5550i	−0.170967	−	0.686127i
$451$	−48.0000			−2.26023
$452$	8.02458	−	8.02458i	0.377444	−	0.377444i
$453$	0.263305	−	1.53465i	0.0123711	−	0.0721043i
$454$			1.10102i			0.0516735i
$455$	29.2699	−	23.8988i	1.37219	−	1.12039i
$456$	−2.44949	−	3.46410i	−0.114708	−	0.162221i
$457$	1.55051	+	1.55051i	0.0725298	+	0.0725298i	0.742441	−	0.669911i	$-0.233668\pi$
$457$	1.55051	+	1.55051i	0.0725298	+	0.0725298i	−0.669911	+	0.742441i	$0.733668\pi$
$458$	4.73545	+	4.73545i	0.221273	+	0.221273i
$459$	10.3923	+	36.7423i	0.485071	+	1.71499i
$460$	0.224745	−	2.22474i	0.0104788	−	0.103729i
$461$		−	31.4626i		−	1.46536i	−0.680573	−	0.732681i	$-0.738269\pi$
$461$		−	31.4626i		−	1.46536i	0.680573	−	0.732681i	$-0.261731\pi$
$462$	−33.4523	−	5.73951i	−1.55634	−	0.267026i
$463$	26.0454	−	26.0454i	1.21043	−	1.21043i	0.239548	−	0.970884i	$-0.423001\pi$
$463$	26.0454	−	26.0454i	1.21043	−	1.21043i	0.970884	−	0.239548i	$-0.0769993\pi$
$464$	2.19275			0.101796
$465$	−9.34190	−	16.5145i	−0.433220	−	0.765842i
$466$	5.10102			0.236300
$467$	−3.60697	+	3.60697i	−0.166910	+	0.166910i	−0.785620	−	0.618709i	$-0.787656\pi$
$467$	−3.60697	+	3.60697i	−0.166910	+	0.166910i	0.618709	+	0.785620i	$0.287656\pi$
$468$	−6.30714	−	13.2061i	−0.291548	−	0.610453i
$469$		−	53.3939i		−	2.46550i
$470$	9.75663	+	11.9494i	0.450040	+	0.551184i
$471$	16.8990	−	11.9494i	0.778664	−	0.550599i
$472$	−3.89898	−	3.89898i	−0.179465	−	0.179465i
$473$	−16.3991	−	16.3991i	−0.754032	−	0.754032i
$474$	6.29253	−	4.44949i	0.289025	−	0.204372i
$475$	12.0000	+	2.44949i	0.550598	+	0.112390i
$476$			25.4558i			1.16677i
$477$	1.74343	+	3.65045i	0.0798260	+	0.167143i
$478$	−9.44949	+	9.44949i	−0.432210	+	0.432210i
$479$	26.4415			1.20814			0.604071	−	0.796931i	$-0.293544\pi$
$479$	26.4415			1.20814			0.604071	+	0.796931i	$0.293544\pi$
$480$	−3.73205	−	1.03528i	−0.170344	−	0.0472537i
$481$	16.8990			0.770527
$482$	6.43539	−	6.43539i	0.293124	−	0.293124i
$483$	5.91359	+	1.01461i	0.269078	+	0.0461664i
$484$			21.0000i			0.954545i
$485$	1.41421	+	0.142865i	0.0642161	+	0.00648715i
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$	19.3485	+	19.3485i	0.876763	+	0.876763i	0.993198	−	0.116435i	$-0.0371468\pi$
$487$	19.3485	+	19.3485i	0.876763	+	0.876763i	−0.116435	+	0.993198i	$0.537147\pi$
$488$	0.635674	+	0.635674i	0.0287756	+	0.0287756i
$489$	−5.65685	−	8.00000i	−0.255812	−	0.361773i
$490$	11.1237	+	1.12372i	0.502519	+	0.0507647i
$491$			25.3130i			1.14236i	0.820825	+	0.571179i	$0.193514\pi$
$491$			25.3130i			1.14236i	−0.820825	+	0.571179i	$0.806486\pi$
$492$	2.48528	−	14.4853i	0.112045	−	0.653047i
$493$	11.3939	−	11.3939i	0.513154	−	0.513154i
$494$	11.9494			0.537628
$495$	−12.8295	−	35.7128i	−0.576641	−	1.60517i
$496$	−4.89898			−0.219971
$497$	−35.8481	+	35.8481i	−1.60801	+	1.60801i
$498$	0.585786	−	3.41421i	0.0262497	−	0.152995i
$499$		−	33.7980i		−	1.51300i	−0.653991	−	0.756502i	$-0.726907\pi$
$499$		−	33.7980i		−	1.51300i	0.653991	−	0.756502i	$-0.273093\pi$
$500$	9.89949	−	5.19615i	0.442719	−	0.232379i
$501$	8.00000	+	11.3137i	0.357414	+	0.505459i
$502$	−9.10102	−	9.10102i	−0.406198	−	0.406198i
$503$	−1.90702	−	1.90702i	−0.0850300	−	0.0850300i	0.663313	−	0.748342i	$-0.269150\pi$
$503$	−1.90702	−	1.90702i	−0.0850300	−	0.0850300i	−0.748342	+	0.663313i	$0.769150\pi$
$504$	3.46410	−	9.79796i	0.154303	−	0.436436i
$505$	0.898979	+	1.10102i	0.0400041	+	0.0489948i
$506$		−	5.65685i		−	0.251478i
$507$	18.4333	+	3.16265i	0.818650	+	0.140458i
$508$	−3.55051	+	3.55051i	−0.157528	+	0.157528i
$509$	−19.8632			−0.880421			−0.440211	−	0.897895i	$-0.645096\pi$
$509$	−19.8632			−0.880421			−0.440211	+	0.897895i	$0.645096\pi$
$510$	−24.7718	+	14.0129i	−1.09691	+	0.620500i
$511$	−9.30306			−0.411543
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	11.1097	+	6.21076i	0.490507	+	0.274212i
$514$		−	13.5959i		−	0.599690i
$515$	3.46410	−	34.2911i	0.152647	−	1.51105i
$516$	5.79796	−	4.09978i	0.255241	−	0.180483i
$517$	27.5959	+	27.5959i	1.21367	+	1.21367i
$518$	8.48528	+	8.48528i	0.372822	+	0.372822i
$519$	−7.21393	+	5.10102i	−0.316656	+	0.223910i
$520$	8.44949	−	6.89898i	0.370535	−	0.302540i
$521$			19.8632i			0.870223i	0.900377	+	0.435111i	$0.143291\pi$
$521$			19.8632i			0.870223i	−0.900377	+	0.435111i	$0.856709\pi$
$522$	−5.93602	+	2.83500i	−0.259812	+	0.124084i
$523$	−22.2474	+	22.2474i	−0.972813	+	0.972813i	−0.999640	−	0.0268271i	$-0.991460\pi$
$523$	−22.2474	+	22.2474i	−0.972813	+	0.972813i	0.0268271	+	0.999640i	$0.491460\pi$
$524$	−0.142865			−0.00624107
$525$	12.0716	+	27.4641i	0.526847	+	1.19863i
$526$	8.00000			0.348817
$527$	−25.4558	+	25.4558i	−1.10887	+	1.10887i
$528$	−9.65685	−	1.65685i	−0.420261	−	0.0721053i
$529$			1.00000i			0.0434783i
$530$	−2.33562	+	1.90702i	−0.101453	+	0.0828358i
$531$	15.5959	+	5.51399i	0.676805	+	0.239287i
$532$	6.00000	+	6.00000i	0.260133	+	0.260133i
$533$	29.2699	+	29.2699i	1.26782	+	1.26782i
$534$	−9.12096	−	12.8990i	−0.394702	−	0.558193i
$535$	−2.44949	+	24.2474i	−0.105901	+	1.04831i
$536$		−	15.4135i		−	0.665761i
$537$	4.47266	−	26.0686i	0.193010	−	1.12494i
$538$	−4.44949	+	4.44949i	−0.191831	+	0.191831i
$539$	28.2843			1.21829
$540$	11.4416	−	2.02254i	0.492366	−	0.0870363i
$541$	18.6969			0.803844			0.401922	−	0.915674i	$-0.368342\pi$
$541$	18.6969			0.803844			0.401922	+	0.915674i	$0.368342\pi$
$542$	17.3205	−	17.3205i	0.743980	−	0.743980i
$543$	−2.34315	+	13.6569i	−0.100554	+	0.586072i
$544$			7.34847i			0.315063i
$545$	−19.5133	−	23.8988i	−0.835856	−	1.02371i
$546$	16.8990	+	23.8988i	0.723210	+	1.02277i
$547$	−11.5959	−	11.5959i	−0.495806	−	0.495806i	0.414324	−	0.910130i	$-0.364018\pi$
$547$	−11.5959	−	11.5959i	−0.495806	−	0.495806i	−0.910130	+	0.414324i	$0.864018\pi$
$548$	13.6814	+	13.6814i	0.584442	+	0.584442i
$549$	−2.54270	−	0.898979i	−0.108520	−	0.0383675i
$550$	23.5959	−	15.5959i	1.00613	−	0.665012i
$551$		−	5.37113i		−	0.228818i
$552$	1.70711	+	0.292893i	0.0726593	+	0.0124664i
$553$	−10.8990	+	10.8990i	−0.463472	+	0.463472i
$554$	13.3636			0.567765
$555$	−3.58630	+	12.9282i	−0.152230	+	0.548772i
$556$	18.6969			0.792927
$557$	21.1024	−	21.1024i	0.894139	−	0.894139i	−0.100770	−	0.994910i	$-0.532131\pi$
$557$	21.1024	−	21.1024i	0.894139	−	0.894139i	0.994910	+	0.100770i	$0.0321307\pi$
$558$	13.2621	−	6.33386i	0.561428	−	0.268134i
$559$			20.0000i			0.845910i
$560$	7.70674	+	0.778539i	0.325669	+	0.0328993i
$561$	−58.7878	+	41.5692i	−2.48202	+	1.75505i
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	−26.5843	−	26.5843i	−1.12040	−	1.12040i	−0.991682	−	0.128714i	$-0.958915\pi$
$563$	−26.5843	−	26.5843i	−1.12040	−	1.12040i	−0.128714	−	0.991682i	$-0.541085\pi$
$564$	−9.75663	+	6.89898i	−0.410828	+	0.290499i
$565$	−25.2474	−	2.55051i	−1.06217	−	0.107301i
$566$			7.56388i			0.317933i
$567$	3.29002	+	31.0028i	0.138168	+	1.30200i
$568$	−10.3485	+	10.3485i	−0.434212	+	0.434212i
$569$	−23.8988			−1.00189			−0.500944	−	0.865480i	$-0.667014\pi$
$569$	−23.8988			−1.00189			−0.500944	+	0.865480i	$0.667014\pi$
$570$	−2.53590	+	9.14162i	−0.106217	+	0.382900i
$571$	21.5505			0.901861			0.450930	−	0.892559i	$-0.351092\pi$
$571$	21.5505			0.901861			0.450930	+	0.892559i	$0.351092\pi$
$572$	19.5133	−	19.5133i	0.815890	−	0.815890i
$573$	−30.6531	−	5.25924i	−1.28055	−	0.219708i
$574$			29.3939i			1.22688i
$575$	−4.17121	+	2.75699i	−0.173951	+	0.114975i
$576$	1.00000	−	2.82843i	0.0416667	−	0.117851i
$577$	−0.797959	−	0.797959i	−0.0332195	−	0.0332195i	0.690302	−	0.723521i	$-0.257478\pi$
$577$	−0.797959	−	0.797959i	−0.0332195	−	0.0332195i	−0.723521	+	0.690302i	$0.757478\pi$
$578$	26.1630	+	26.1630i	1.08824	+	1.08824i
$579$	2.68556	+	3.79796i	0.111608	+	0.157838i
$580$	−3.10102	−	3.79796i	−0.128763	−	0.157702i
$581$			6.92820i			0.287430i
$582$	−0.186185	+	1.08516i	−0.00771761	+	0.0449815i
$583$	−5.39388	+	5.39388i	−0.223392	+	0.223392i
$584$	−2.68556			−0.111129
$585$	−13.9540	+	29.6006i	−0.576928	+	1.22383i
$586$	−19.1464			−0.790932
$587$	13.9993	−	13.9993i	0.577812	−	0.577812i	−0.356488	−	0.934300i	$-0.616026\pi$
$587$	13.9993	−	13.9993i	0.577812	−	0.577812i	0.934300	+	0.356488i	$0.116026\pi$
$588$	−1.46447	+	8.53553i	−0.0603936	+	0.351999i
$589$			12.0000i			0.494451i
$590$	−1.23924	+	12.2672i	−0.0510187	+	0.505033i
$591$	−10.8990	−	15.4135i	−0.448324	−	0.634026i
$592$	2.44949	+	2.44949i	0.100673	+	0.100673i
$593$	−11.1708	−	11.1708i	−0.458732	−	0.458732i	0.439507	−	0.898239i	$-0.355153\pi$
$593$	−11.1708	−	11.1708i	−0.458732	−	0.458732i	−0.898239	+	0.439507i	$0.855153\pi$
$594$	28.2843	−	8.00000i	1.16052	−	0.328244i
$595$	44.0908	−	36.0000i	1.80755	−	1.47586i
$596$			11.0280i			0.451724i
$597$	−12.8895	−	2.21149i	−0.527533	−	0.0905104i
$598$	−3.44949	+	3.44949i	−0.141060	+	0.141060i
$599$	3.32124			0.135702			0.0678510	−	0.997695i	$-0.478386\pi$
$599$	3.32124			0.135702			0.0678510	+	0.997695i	$0.478386\pi$
$600$	3.48477	+	7.92820i	0.142265	+	0.323668i
$601$	−16.2020			−0.660895			−0.330448	−	0.943824i	$-0.607200\pi$
$601$	−16.2020			−0.660895			−0.330448	+	0.943824i	$0.607200\pi$
$602$	−10.0424	+	10.0424i	−0.409296	+	0.409296i
$603$	19.9280	+	41.7259i	0.811530	+	1.69921i
$604$			0.898979i			0.0365790i
$605$	36.3731	−	29.6985i	1.47878	−	1.20742i
$606$	−0.898979	+	0.635674i	−0.0365185	+	0.0258225i
$607$	−7.34847	−	7.34847i	−0.298265	−	0.298265i	0.542069	−	0.840334i	$-0.317641\pi$
$607$	−7.34847	−	7.34847i	−0.298265	−	0.298265i	−0.840334	+	0.542069i	$0.817641\pi$
$608$	1.73205	+	1.73205i	0.0702439	+	0.0702439i
$609$	10.7423	−	7.59592i	0.435298	−	0.307802i
$610$	0.202041	−	2.00000i	0.00818040	−	0.0809776i
$611$		−	33.6554i		−	1.36155i
$612$	−9.50079	−	19.8931i	−0.384047	−	0.804131i
$613$	3.34847	−	3.34847i	0.135243	−	0.135243i	−0.636244	−	0.771488i	$-0.719513\pi$
$613$	3.34847	−	3.34847i	0.135243	−	0.135243i	0.771488	+	0.636244i	$0.219513\pi$
$614$	32.0983			1.29538
$615$	−28.6040	+	16.1806i	−1.15342	+	0.652467i
$616$	19.5959			0.789542
$617$	18.4169	−	18.4169i	0.741436	−	0.741436i	−0.231418	−	0.972854i	$-0.574337\pi$
$617$	18.4169	−	18.4169i	0.741436	−	0.741436i	0.972854	+	0.231418i	$0.0743366\pi$
$618$	26.3125	+	4.51451i	1.05844	+	0.181600i
$619$			30.0454i			1.20763i	0.797126	+	0.603813i	$0.206353\pi$
$619$			30.0454i			1.20763i	−0.797126	+	0.603813i	$0.793647\pi$
$620$	6.92820	+	8.48528i	0.278243	+	0.340777i
$621$	−5.00000	+	1.41421i	−0.200643	+	0.0567504i
$622$	10.1464	+	10.1464i	0.406835	+	0.406835i
$623$	22.3417	+	22.3417i	0.895101	+	0.895101i
$624$	4.87832	+	6.89898i	0.195289	+	0.276180i
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$		−	21.4203i		−	0.856127i
$627$	−4.05845	+	23.6544i	−0.162079	+	0.944664i
$628$	−8.44949	+	8.44949i	−0.337171	+	0.337171i
$629$	25.4558			1.01499
$630$	−21.8695	+	7.85641i	−0.871303	+	0.313007i
$631$	24.4495			0.973319			0.486659	−	0.873592i	$-0.338215\pi$
$631$	24.4495			0.973319			0.486659	+	0.873592i	$0.338215\pi$
$632$	−3.14626	+	3.14626i	−0.125152	+	0.125152i
$633$	−5.47621	+	31.9177i	−0.217660	+	1.26861i
$634$		−	18.8990i		−	0.750574i
$635$	11.1708	+	1.12848i	0.443301	+	0.0447825i
$636$	−1.34847	−	1.90702i	−0.0534703	−	0.0756184i
$637$	−17.2474	−	17.2474i	−0.683369	−	0.683369i
$638$	−8.77101	−	8.77101i	−0.347248	−	0.347248i
$639$	14.6349	−	41.3939i	0.578949	−	1.63752i
$640$	2.22474	+	0.224745i	0.0879408	+	0.00888382i
$641$			20.4347i			0.807121i	0.914953	+	0.403560i	$0.132227\pi$
$641$			20.4347i			0.807121i	−0.914953	+	0.403560i	$0.867773\pi$
$642$	−18.6057	−	3.19224i	−0.734309	−	0.125988i
$643$	−22.8990	+	22.8990i	−0.903048	+	0.903048i	−0.995699	−	0.0926510i	$-0.970466\pi$
$643$	−22.8990	+	22.8990i	−0.903048	+	0.903048i	0.0926510	+	0.995699i	$0.470466\pi$
$644$	−3.46410			−0.136505
$645$	−15.3006	−	4.24440i	−0.602459	−	0.167123i
$646$	18.0000			0.708201
$647$	−34.4339	+	34.4339i	−1.35374	+	1.35374i	−0.472300	+	0.881438i	$0.656576\pi$
$647$	−34.4339	+	34.4339i	−1.35374	+	1.35374i	−0.881438	+	0.472300i	$0.843424\pi$
$648$	0.949747	+	8.94975i	0.0373096	+	0.351579i
$649$			31.1918i			1.22439i
$650$	−23.8988	−	4.87832i	−0.937387	−	0.191343i
$651$	−24.0000	+	16.9706i	−0.940634	+	0.665129i
$652$	4.00000	+	4.00000i	0.156652	+	0.156652i
$653$	−16.1920	−	16.1920i	−0.633643	−	0.633643i	0.315337	−	0.948980i	$-0.397882\pi$
$653$	−16.1920	−	16.1920i	−0.633643	−	0.633643i	−0.948980	+	0.315337i	$0.897882\pi$
$654$	19.5133	−	13.7980i	0.763029	−	0.539543i
$655$	0.202041	+	0.247449i	0.00789440	+	0.00966862i
$656$			8.48528i			0.331295i
$657$	7.27010	−	3.47215i	0.283634	−	0.135461i
$658$	16.8990	−	16.8990i	0.658791	−	0.658791i
$659$	−9.75663			−0.380064			−0.190032	−	0.981778i	$-0.560859\pi$
$659$	−9.75663			−0.380064			−0.190032	+	0.981778i	$0.560859\pi$
$660$	10.7871	+	19.0693i	0.419887	+	0.742272i
$661$	16.8990			0.657294			0.328647	−	0.944453i	$-0.393407\pi$
$661$	16.8990			0.657294			0.328647	+	0.944453i	$0.393407\pi$
$662$	13.2207	−	13.2207i	0.513838	−	0.513838i
$663$	61.1966	+	10.4997i	2.37668	+	0.407774i
$664$			2.00000i			0.0776151i
$665$	1.90702	−	18.8776i	0.0739512	−	0.732041i
$666$	−9.79796	−	3.46410i	−0.379663	−	0.134231i
$667$	1.55051	+	1.55051i	0.0600360	+	0.0600360i
$668$	−5.65685	−	5.65685i	−0.218870	−	0.218870i
$669$	−17.6062	−	24.8990i	−0.680696	−	0.962650i
$670$	−26.6969	+	21.7980i	−1.03139	+	0.842129i
$671$		−	5.08540i		−	0.196320i
$672$	−1.01461	+	5.91359i	−0.0391395	+	0.228122i
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	−0.646918	−	0.762560i	$-0.723942\pi$
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	0.762560	+	0.646918i	$0.223942\pi$
$674$	−20.4347			−0.787114
$675$	−19.6840	−	16.9571i	−0.757636	−	0.652678i
$676$	−10.7980			−0.415306
$677$	−8.51739	+	8.51739i	−0.327350	+	0.327350i	−0.851578	−	0.524228i	$-0.824354\pi$
$677$	−8.51739	+	8.51739i	−0.327350	+	0.327350i	0.524228	+	0.851578i	$0.324354\pi$
$678$	3.32389	−	19.3730i	0.127653	−	0.744017i
$679$		−	2.20204i		−	0.0845066i
$680$	12.7279	−	10.3923i	0.488094	−	0.398527i
$681$	1.10102	+	1.55708i	0.0421912	+	0.0596674i
$682$	19.5959	+	19.5959i	0.750366	+	0.750366i
$683$	4.24264	+	4.24264i	0.162340	+	0.162340i	0.783603	−	0.621262i	$-0.213380\pi$
$683$	4.24264	+	4.24264i	0.162340	+	0.162340i	−0.621262	+	0.783603i	$0.713380\pi$
$684$	−6.92820	−	2.44949i	−0.264906	−	0.0936586i
$685$	4.34847	−	43.0454i	0.166146	−	1.64468i
$686$			6.92820i			0.264520i
$687$	11.4324	+	1.96149i	0.436173	+	0.0748354i
$688$	−2.89898	+	2.89898i	−0.110523	+	0.110523i
$689$	6.57826			0.250612
$690$	−1.90691	−	3.37101i	−0.0725947	−	0.128332i
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	3.60697	−	3.60697i	0.137116	−	0.137116i
$693$	−53.0482	+	25.3354i	−2.01514	+	0.962413i
$694$		−	0.202041i		−	0.00766937i
$695$	−26.4415	−	32.3840i	−1.00298	−	1.22840i
$696$	3.10102	−	2.19275i	0.117544	−	0.0831161i
$697$	44.0908	+	44.0908i	1.67006	+	1.67006i
$698$	15.5563	+	15.5563i	0.588817	+	0.588817i
$699$	7.21393	−	5.10102i	0.272856	−	0.192938i
$700$	−9.55051	−	14.4495i	−0.360975	−	0.546139i
$701$			36.1339i			1.36476i	0.730999	+	0.682379i	$0.239055\pi$
$701$			36.1339i			1.36476i	−0.730999	+	0.682379i	$0.760945\pi$
$702$	−22.1258	−	12.3691i	−0.835083	−	0.466843i
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	5.65685			0.213201
$705$	25.7473	+	7.14235i	0.969701	+	0.268996i
$706$	−32.6969			−1.23057
$707$	1.55708	−	1.55708i	0.0585600	−	0.0585600i
$708$	−9.41297	−	1.61501i	−0.353761	−	0.0606958i
$709$		−	16.8990i		−	0.634654i	−0.948316	−	0.317327i	$-0.897215\pi$
$709$		−	16.8990i		−	0.634654i	0.948316	−	0.317327i	$-0.102785\pi$
$710$	32.5590	+	3.28913i	1.22192	+	0.123439i
$711$	4.44949	−	12.5851i	0.166869	−	0.471977i
$712$	6.44949	+	6.44949i	0.241705	+	0.241705i
$713$	−3.46410	−	3.46410i	−0.129732	−	0.129732i
$714$	25.4558	+	36.0000i	0.952661	+	1.34727i
$715$	−61.3939	−	6.20204i	−2.29600	−	0.231943i
$716$			15.2706i			0.570690i
$717$	−3.91411	+	22.8131i	−0.146175	+	0.851970i
$718$	−18.8990	+	18.8990i	−0.705304	+	0.705304i
$719$	1.76416			0.0657920			0.0328960	−	0.999459i	$-0.489527\pi$
$719$	1.76416			0.0657920			0.0328960	+	0.999459i	$0.489527\pi$
$720$	−6.31319	+	2.26795i	−0.235279	+	0.0845215i
$721$	−53.3939			−1.98849
$722$	−9.19239	+	9.19239i	−0.342105	+	0.342105i
$723$	2.66563	−	15.5364i	0.0991357	−	0.577805i
$724$		−	8.00000i		−	0.297318i
$725$	−2.19275	+	10.7423i	−0.0814368	+	0.398957i
$726$	21.0000	+	29.6985i	0.779383	+	1.10221i
$727$	24.2474	+	24.2474i	0.899288	+	0.899288i	0.995373	−	0.0960850i	$-0.0306321\pi$
$727$	24.2474	+	24.2474i	0.899288	+	0.899288i	−0.0960850	+	0.995373i	$0.530632\pi$
$728$	−11.9494	−	11.9494i	−0.442874	−	0.442874i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$	3.79796	+	4.65153i	0.140569	+	0.172161i
$731$			30.1271i			1.11429i
$732$	1.53465	+	0.263305i	0.0567224	+	0.00973203i
$733$	−25.1464	+	25.1464i	−0.928805	+	0.928805i	−0.997629	−	0.0688243i	$-0.978075\pi$
$733$	−25.1464	+	25.1464i	−0.928805	+	0.928805i	0.0688243	+	0.997629i	$0.478075\pi$
$734$	−27.9985			−1.03345
$735$	16.8550	−	9.53454i	0.621708	−	0.351687i
$736$	−1.00000			−0.0368605
$737$	−61.6539	+	61.6539i	−2.27105	+	2.27105i
$738$	−10.9706	−	22.9706i	−0.403832	−	0.845558i
$739$			30.6969i			1.12921i	0.825363	+	0.564603i	$0.190971\pi$
$739$			30.6969i			1.12921i	−0.825363	+	0.564603i	$0.809029\pi$
$740$	0.778539	−	7.70674i	0.0286197	−	0.283305i
$741$	16.8990	−	11.9494i	0.620800	−	0.438972i
$742$	3.30306	+	3.30306i	0.121259	+	0.121259i
$743$	10.6780	+	10.6780i	0.391739	+	0.391739i	0.875307	−	0.483568i	$-0.160659\pi$
$743$	10.6780	+	10.6780i	0.391739	+	0.391739i	−0.483568	+	0.875307i	$0.660659\pi$
$744$	−6.92820	+	4.89898i	−0.254000	+	0.179605i
$745$	19.1010	−	15.5959i	0.699807	−	0.571390i
$746$			17.6062i			0.644610i
$747$	−2.58579	−	5.41421i	−0.0946090	−	0.198096i
$748$	29.3939	−	29.3939i	1.07475	−	1.07475i
$749$	37.7552			1.37954
$750$	8.80385	−	17.2480i	0.321471	−	0.629807i
$751$	−42.2474			−1.54163			−0.770816	−	0.637058i	$-0.780151\pi$
$751$	−42.2474			−1.54163			−0.770816	+	0.637058i	$0.780151\pi$
$752$	4.87832	−	4.87832i	0.177894	−	0.177894i
$753$	−21.9718	−	3.76977i	−0.800697	−	0.137378i
$754$			10.6969i			0.389560i
$755$	1.55708	−	1.27135i	0.0566679	−	0.0462691i
$756$	−4.89898	−	17.3205i	−0.178174	−	0.629941i
$757$	−25.3485	−	25.3485i	−0.921306	−	0.921306i	0.0758160	−	0.997122i	$-0.475844\pi$
$757$	−25.3485	−	25.3485i	−0.921306	−	0.921306i	−0.997122	+	0.0758160i	$0.975844\pi$
$758$	−3.63907	−	3.63907i	−0.132177	−	0.132177i
$759$	−5.65685	−	8.00000i	−0.205331	−	0.290382i
$760$	0.550510	−	5.44949i	0.0199691	−	0.197674i
$761$		−	42.1407i		−	1.52760i	−0.645454	−	0.763799i	$-0.723332\pi$
$761$		−	42.1407i		−	1.52760i	0.645454	−	0.763799i	$-0.276668\pi$
$762$	−1.47067	+	8.57169i	−0.0532767	+	0.310520i
$763$	−33.7980	+	33.7980i	−1.22357	+	1.22357i
$764$	17.9562			0.649632
$765$	−21.0197	+	44.5889i	−0.759969	+	1.61212i
$766$	6.69694			0.241970
$767$	19.0205	−	19.0205i	0.686789	−	0.686789i
$768$	−0.292893	+	1.70711i	−0.0105689	+	0.0615999i
$769$			28.6969i			1.03484i	0.855732	+	0.517419i	$0.173107\pi$
$769$			28.6969i			1.03484i	−0.855732	+	0.517419i	$0.826893\pi$
$770$	−27.7128	−	33.9411i	−0.998700	−	1.22315i
$771$	−13.5959	−	19.2275i	−0.489645	−	0.692463i
$772$	−1.89898	−	1.89898i	−0.0683458	−	0.0683458i
$773$	26.7593	+	26.7593i	0.962465	+	0.962465i	0.999321	−	0.0368554i	$-0.0117341\pi$
$773$	26.7593	+	26.7593i	0.962465	+	0.962465i	−0.0368554	+	0.999321i	$0.511734\pi$
$774$	4.09978	−	11.5959i	0.147363	−	0.416807i
$775$	4.89898	−	24.0000i	0.175977	−	0.862105i
$776$		−	0.635674i		−	0.0228194i
$777$	20.4853	+	3.51472i	0.734905	+	0.126090i
$778$	−22.0000	+	22.0000i	−0.788738	+	0.788738i
$779$	20.7846			0.744686
$780$	5.05040	−	18.2061i	0.180833	−	0.651884i
$781$	82.7878			2.96238
$782$	−5.19615	+	5.19615i	−0.185814	+	0.185814i
$783$	−5.55980	+	9.94530i	−0.198691	+	0.355416i
$784$		−	5.00000i		−	0.178571i
$785$	26.5843	+	2.68556i	0.948835	+	0.0958518i
$786$	−0.202041	+	0.142865i	−0.00720656	+	0.00509581i
$787$	21.1010	+	21.1010i	0.752170	+	0.752170i	0.974884	−	0.222714i	$-0.0714915\pi$
$787$	21.1010	+	21.1010i	0.752170	+	0.752170i	−0.222714	+	0.974884i	$0.571492\pi$
$788$	7.70674	+	7.70674i	0.274541	+	0.274541i
$789$	11.3137	−	8.00000i	0.402779	−	0.284808i
$790$	9.89898	+	1.00000i	0.352190	+	0.0355784i
$791$			39.3123i			1.39778i
$792$	−15.3137	+	7.31371i	−0.544149	+	0.259881i
$793$	−3.10102	+	3.10102i	−0.110120	+	0.110120i
$794$	−12.0922			−0.429138
$795$	−1.39604	+	5.03256i	−0.0495124	+	0.178486i
$796$	7.55051			0.267621
$797$	−0.667783	+	0.667783i	−0.0236541	+	0.0236541i	−0.718835	−	0.695181i	$-0.755324\pi$
$797$	−0.667783	+	0.667783i	−0.0236541	+	0.0236541i	0.695181	+	0.718835i	$0.255324\pi$
$798$	14.4853	+	2.48528i	0.512773	+	0.0879780i
$799$		−	50.6969i		−	1.79353i
$800$	−2.75699	−	4.17121i	−0.0974745	−	0.147474i
$801$	−25.7980	−	9.12096i	−0.911526	−	0.322273i
$802$	5.55051	+	5.55051i	0.195995	+	0.195995i
$803$	10.7423	+	10.7423i	0.379086	+	0.379086i
$804$	−15.4135	−	21.7980i	−0.543592	−	0.768755i
$805$	4.89898	+	6.00000i	0.172666	+	0.211472i
$806$		−	23.8988i		−	0.841798i
$807$	−1.84304	+	10.7420i	−0.0648780	+	0.378137i
$808$	0.449490	−	0.449490i	0.0158130	−	0.0158130i
$809$	8.48528			0.298327			0.149163	−	0.988813i	$-0.452342\pi$
$809$	8.48528			0.298327			0.149163	+	0.988813i	$0.452342\pi$
$810$	14.1583	−	14.3019i	0.497471	−	0.502516i
$811$	−31.5959			−1.10948			−0.554741	−	0.832023i	$-0.687183\pi$
$811$	−31.5959			−1.10948			−0.554741	+	0.832023i	$0.687183\pi$
$812$	−5.37113	+	5.37113i	−0.188490	+	0.188490i
$813$	7.17439	−	41.8154i	0.251617	−	1.46653i
$814$		−	19.5959i		−	0.686837i
$815$	1.27135	−	12.5851i	0.0445334	−	0.440835i
$816$	7.34847	+	10.3923i	0.257248	+	0.363803i
$817$	7.10102	+	7.10102i	0.248433	+	0.248433i
$818$	−9.75663	−	9.75663i	−0.341133	−	0.341133i
$819$	47.7975	+	16.8990i	1.67018	+	0.590498i
$820$	14.6969	−	12.0000i	0.513239	−	0.419058i
$821$		−	31.7484i		−	1.10803i	−0.832508	−	0.554013i	$-0.813096\pi$
$821$		−	31.7484i		−	1.10803i	0.832508	−	0.554013i	$-0.186904\pi$
$822$	33.0299	+	5.66704i	1.15205	+	0.197661i
$823$	29.1464	−	29.1464i	1.01598	−	1.01598i	0.0161104	−	0.999870i	$-0.494872\pi$
$823$	29.1464	−	29.1464i	1.01598	−	1.01598i	0.999870	−	0.0161104i	$-0.00512832\pi$
$824$	−15.4135			−0.536954
$825$	17.7737	−	45.6519i	0.618803	−	1.58939i
$826$	19.1010			0.664610
$827$	14.9207	−	14.9207i	0.518843	−	0.518843i	−0.398378	−	0.917221i	$-0.630427\pi$
$827$	14.9207	−	14.9207i	0.518843	−	0.518843i	0.917221	+	0.398378i	$0.130427\pi$
$828$	2.70711	−	1.29289i	0.0940785	−	0.0449311i
$829$		−	32.8990i		−	1.14263i	−0.820731	−	0.571314i	$-0.806434\pi$
$829$		−	32.8990i		−	1.14263i	0.820731	−	0.571314i	$-0.193566\pi$
$830$	3.46410	−	2.82843i	0.120241	−	0.0981761i
$831$	18.8990	−	13.3636i	0.655598	−	0.463578i
$832$	−3.44949	−	3.44949i	−0.119590	−	0.119590i
$833$	−25.9808	−	25.9808i	−0.900180	−	0.900180i
$834$	26.4415	−	18.6969i	0.915593	−	0.647422i
$835$	−1.79796	+	17.7980i	−0.0622209	+	0.615924i
$836$		−	13.8564i		−	0.479234i
$837$	12.4215	−	22.2195i	0.429351	−	0.768018i
$838$	3.10102	−	3.10102i	0.107123	−	0.107123i
$839$	−27.9985			−0.966617			−0.483309	−	0.875450i	$-0.660565\pi$
$839$	−27.9985			−0.966617			−0.483309	+	0.875450i	$0.660565\pi$
$840$	11.6775	−	6.60572i	0.402913	−	0.227919i
$841$	−24.1918			−0.834201
$842$	−0.635674	+	0.635674i	−0.0219068	+	0.0219068i
$843$	−9.65685	−	1.65685i	−0.332600	−	0.0570651i
$844$		−	18.6969i		−	0.643575i
$845$	15.2706	+	18.7026i	0.525325	+	0.643389i
$846$	−6.89898	+	19.5133i	−0.237192	+	0.670880i
$847$	−51.4393	−	51.4393i	−1.76747	−	1.76747i
$848$	0.953512	+	0.953512i	0.0327437	+	0.0327437i
$849$	7.56388	+	10.6969i	0.259592	+	0.367118i
$850$	−36.0000	−	7.34847i	−1.23479	−	0.252050i
$851$			3.46410i			0.118748i
$852$	−4.28648	+	24.9834i	−0.146852	+	0.855918i
$853$	5.24745	−	5.24745i	0.179669	−	0.179669i	−0.611542	−	0.791212i	$-0.709451\pi$
$853$	5.24745	−	5.24745i	0.179669	−	0.179669i	0.791212	+	0.611542i	$0.209451\pi$
$854$	−3.11416			−0.106564
$855$	5.55532	+	15.4641i	0.189988	+	0.528861i
$856$	10.8990			0.372519
$857$	9.89949	−	9.89949i	0.338160	−	0.338160i	−0.517514	−	0.855675i	$-0.673143\pi$
$857$	9.89949	−	9.89949i	0.338160	−	0.338160i	0.855675	+	0.517514i	$0.173143\pi$
$858$	8.08266	−	47.1092i	0.275937	−	1.60828i
$859$		−	44.8990i		−	1.53193i	−0.642880	−	0.765967i	$-0.722261\pi$
$859$		−	44.8990i		−	1.53193i	0.642880	−	0.765967i	$-0.277739\pi$
$860$	9.12096	+	0.921404i	0.311022	+	0.0314196i
$861$	29.3939	+	41.5692i	1.00174	+	1.41668i
$862$	−15.7980	−	15.7980i	−0.538081	−	0.538081i
$863$	5.65685	+	5.65685i	0.192562	+	0.192562i	0.796802	−	0.604240i	$-0.206523\pi$
$863$	5.65685	+	5.65685i	0.192562	+	0.192562i	−0.604240	+	0.796802i	$0.706523\pi$
$864$	−1.41421	−	5.00000i	−0.0481125	−	0.170103i
$865$	−11.3485	−	1.14643i	−0.385860	−	0.0389797i
$866$			41.5050i			1.41040i
$867$	63.1630	+	10.8370i	2.14513	+	0.368045i
$868$	12.0000	−	12.0000i	0.407307	−	0.407307i
$869$	25.1701			0.853838
$870$	−8.18346	−	2.27010i	−0.277445	−	0.0769638i
$871$	75.1918			2.54778
$872$	−9.75663	+	9.75663i	−0.330401	+	0.330401i
$873$	0.821859	+	1.72084i	0.0278157	+	0.0582416i
$874$			2.44949i			0.0828552i
$875$	−11.5208	+	36.9766i	−0.389474	+	1.25004i
$876$	−3.79796	+	2.68556i	−0.128321	+	0.0907367i
$877$	−13.2474	−	13.2474i	−0.447335	−	0.447335i	0.447133	−	0.894468i	$-0.352445\pi$
$877$	−13.2474	−	13.2474i	−0.447335	−	0.447335i	−0.894468	+	0.447133i	$0.852445\pi$
$878$	11.3137	+	11.3137i	0.381819	+	0.381819i
$879$	−27.0771	+	19.1464i	−0.913289	+	0.645793i
$880$	−8.00000	−	9.79796i	−0.269680	−	0.330289i
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$	6.46447	+	13.5355i	0.217670	+	0.455765i
$883$	−17.3939	+	17.3939i	−0.585351	+	0.585351i	−0.936369	−	0.351018i	$-0.885836\pi$
$883$	−17.3939	+	17.3939i	−0.585351	+	0.585351i	0.351018	+	0.936369i	$0.385836\pi$
$884$	−35.8481			−1.20570
$885$	10.5147	+	18.5877i	0.353447	+	0.624819i
$886$	−16.0000			−0.537531
$887$	25.1701	−	25.1701i	0.845130	−	0.845130i	−0.144391	−	0.989521i	$-0.546122\pi$
$887$	25.1701	−	25.1701i	0.845130	−	0.845130i	0.989521	+	0.144391i	$0.0461223\pi$
$888$	5.91359	+	1.01461i	0.198447	+	0.0340481i
$889$		−	17.3939i		−	0.583372i
$890$	2.04989	−	20.2918i	0.0687124	−	0.680183i
$891$	32.0000	−	39.5980i	1.07204	−	1.32658i
$892$	12.4495	+	12.4495i	0.416840	+	0.416840i
$893$	−11.9494	−	11.9494i	−0.399871	−	0.399871i
$894$	11.0280	+	15.5959i	0.368831	+	0.521606i
$895$	26.4495	−	21.5959i	0.884109	−	0.721872i
$896$		−	3.46410i		−	0.115728i
$897$	−1.42883	+	8.32780i	−0.0477071	+	0.278057i
$898$	−10.6969	+	10.6969i	−0.356961	+	0.356961i
$899$	−10.7423			−0.358274
$900$	12.8564	+	7.72741i	0.428547	+	0.257580i
$901$	9.90918			0.330123
$902$	33.9411	−	33.9411i	1.13012	−	1.13012i
$903$	−4.15968	+	24.2444i	−0.138426	+	0.806803i
$904$			11.3485i			0.377444i
$905$	−13.8564	+	11.3137i	−0.460603	+	0.376080i
$906$	0.898979	+	1.27135i	0.0298666	+	0.0422377i
$907$	3.55051	+	3.55051i	0.117893	+	0.117893i	0.763592	−	0.645699i	$-0.223434\pi$
$907$	3.55051	+	3.55051i	0.117893	+	0.117893i	−0.645699	+	0.763592i	$0.723434\pi$
$908$	−0.778539	−	0.778539i	−0.0258367	−	0.0258367i
$909$	−0.635674	+	1.79796i	−0.0210840	+	0.0596345i
$910$	−3.79796	+	37.5959i	−0.125901	+	1.24629i
$911$		−	22.0560i		−	0.730747i	−0.930861	−	0.365373i	$-0.880941\pi$
$911$		−	22.0560i		−	0.730747i	0.930861	−	0.365373i	$-0.119059\pi$
$912$	4.18154	+	0.717439i	0.138465	+	0.0237568i
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$	−2.19275			−0.0725298
$915$	−1.71427	−	3.03047i	−0.0566720	−	0.100184i
$916$	−6.69694			−0.221273
$917$	0.349945	−	0.349945i	0.0115562	−	0.0115562i
$918$	−33.3292	−	18.6323i	−1.10003	−	0.614957i
$919$			27.5505i			0.908807i	0.890796	+	0.454404i	$0.150148\pi$
$919$			27.5505i			0.908807i	−0.890796	+	0.454404i	$0.849852\pi$
$920$	1.41421	+	1.73205i	0.0466252	+	0.0571040i
$921$	45.3939	−	32.0983i	1.49578	−	1.05768i
$922$	22.2474	+	22.2474i	0.732681	+	0.732681i
$923$	−50.4831	−	50.4831i	−1.66167	−	1.66167i
$924$	27.7128	−	19.5959i	0.911685	−	0.644658i
$925$	−14.4495	+	9.55051i	−0.475096	+	0.314019i
$926$			36.8338i			1.21043i
$927$	41.7259	−	19.9280i	1.37046	−	0.654521i
$928$	−1.55051	+	1.55051i	−0.0508980	+	0.0508980i
$929$	−41.5692			−1.36384			−0.681921	−	0.731426i	$-0.738855\pi$
$929$	−41.5692			−1.36384			−0.681921	+	0.731426i	$0.738855\pi$
$930$	18.2832	+	5.07180i	0.599531	+	0.166311i
$931$	−12.2474			−0.401394
$932$	−3.60697	+	3.60697i	−0.118150	+	0.118150i
$933$	24.4956	+	4.20279i	0.801951	+	0.137593i
$934$		−	5.10102i		−	0.166910i
$935$	−92.4809	−	9.34247i	−3.02445	−	0.305531i
$936$	13.7980	+	4.87832i	0.451000	+	0.159453i
$937$	39.1464	+	39.1464i	1.27886	+	1.27886i	0.941307	+	0.337551i	$0.109598\pi$
$937$	39.1464	+	39.1464i	1.27886	+	1.27886i	0.337551	+	0.941307i	$0.390402\pi$
$938$	37.7552	+	37.7552i	1.23275	+	1.23275i
$939$	−21.4203	−	30.2929i	−0.699025	−	0.988570i
$940$	−15.3485	−	1.55051i	−0.500612	−	0.0505721i
$941$			34.9267i			1.13858i	0.822137	+	0.569290i	$0.192782\pi$
$941$			34.9267i			1.13858i	−0.822137	+	0.569290i	$0.807218\pi$
$942$	−3.49989	+	20.3989i	−0.114033	+	0.664631i
$943$	−6.00000	+	6.00000i	−0.195387	+	0.195387i
$944$	5.51399			0.179465
$945$	−23.0718	+	32.9802i	−0.750526	+	1.07285i
$946$	23.1918			0.754032
$947$	25.4558	−	25.4558i	0.827204	−	0.827204i	−0.159925	−	0.987129i	$-0.551125\pi$
$947$	25.4558	−	25.4558i	0.827204	−	0.827204i	0.987129	+	0.159925i	$0.0511253\pi$
$948$	−1.30323	+	7.59575i	−0.0423268	+	0.246699i
$949$		−	13.1010i		−	0.425277i
$950$	−10.2173	+	6.75323i	−0.331494	+	0.219104i
$951$	−18.8990	−	26.7272i	−0.612841	−	0.866689i
$952$	−18.0000	−	18.0000i	−0.583383	−	0.583383i
$953$	−35.3874	−	35.3874i	−1.14631	−	1.14631i	−0.987272	−	0.159040i	$-0.949160\pi$
$953$	−35.3874	−	35.3874i	−1.14631	−	1.14631i	−0.159040	−	0.987272i	$-0.550840\pi$
$954$	−3.81405	−	1.34847i	−0.123484	−	0.0436583i
$955$	−25.3939	−	31.1010i	−0.821727	−	1.00641i
$956$		−	13.3636i		−	0.432210i
$957$	−21.1751	−	3.63307i	−0.684494	−	0.117441i
$958$	−18.6969	+	18.6969i	−0.604071	+	0.604071i
$959$	−67.0251			−2.16435
$960$	3.37101	−	1.90691i	0.108799	−	0.0615452i
$961$	−7.00000			−0.225806
$962$	−11.9494	+	11.9494i	−0.385264	+	0.385264i
$963$	−29.5047	+	14.0912i	−0.950776	+	0.454083i
$964$			9.10102i			0.293124i
$965$	−0.603566	+	5.97469i	−0.0194295	+	0.192332i
$966$	−4.89898	+	3.46410i	−0.157622	+	0.111456i
$967$	2.44949	+	2.44949i	0.0787703	+	0.0787703i	0.745394	−	0.666624i	$-0.232261\pi$
$967$	2.44949	+	2.44949i	0.0787703	+	0.0787703i	−0.666624	+	0.745394i	$0.732261\pi$
$968$	−14.8492	−	14.8492i	−0.477273	−	0.477273i
$969$	25.4558	−	18.0000i	0.817760	−	0.578243i
$970$	−1.10102	+	0.898979i	−0.0353516	+	0.0288645i
$971$			29.5556i			0.948485i	0.880394	+	0.474242i	$0.157278\pi$
$971$			29.5556i			0.948485i	−0.880394	+	0.474242i	$0.842722\pi$
$972$	10.2929	+	11.7071i	0.330145	+	0.375506i
$973$	−45.7980	+	45.7980i	−1.46822	+	1.46822i
$974$	−27.3629			−0.876763
$975$	−38.6763	+	16.9998i	−1.23863	+	0.544429i
$976$	−0.898979			−0.0287756
$977$	22.4524	−	22.4524i	0.718317	−	0.718317i	−0.249943	−	0.968261i	$-0.580412\pi$
$977$	22.4524	−	22.4524i	0.718317	−	0.718317i	0.968261	+	0.249943i	$0.0804119\pi$
$978$	9.65685	+	1.65685i	0.308792	+	0.0529804i
$979$		−	51.5959i		−	1.64901i
$980$	−8.66025	+	7.07107i	−0.276642	+	0.225877i
$981$	13.7980	−	39.0265i	0.440535	−	1.24602i
$982$	−17.8990	−	17.8990i	−0.571179	−	0.571179i
$983$	−39.0265	−	39.0265i	−1.24475	−	1.24475i	−0.958007	−	0.286746i	$-0.907426\pi$
$983$	−39.0265	−	39.0265i	−1.24475	−	1.24475i	−0.286746	−	0.958007i	$-0.592574\pi$
$984$	8.48528	+	12.0000i	0.270501	+	0.382546i
$985$	2.44949	−	24.2474i	0.0780472	−	0.772588i
$986$			16.1134i			0.513154i
$987$	6.99979	−	40.7977i	0.222806	−	1.29861i
$988$	−8.44949	+	8.44949i	−0.268814	+	0.268814i
$989$	−4.09978			−0.130365
$990$	34.3246	+	16.1810i	1.09091	+	0.514265i
$991$	−13.7980			−0.438307			−0.219153	−	0.975690i	$-0.570329\pi$
$991$	−13.7980			−0.438307			−0.219153	+	0.975690i	$0.570329\pi$
$992$	3.46410	−	3.46410i	0.109985	−	0.109985i
$993$	5.47621	−	31.9177i	0.173782	−	1.01288i
$994$		−	50.6969i		−	1.60801i
$995$	−10.6780	−	13.0779i	−0.338516	−	0.414596i
$996$	2.00000	+	2.82843i	0.0633724	+	0.0896221i
$997$	5.44949	+	5.44949i	0.172587	+	0.172587i	0.788115	−	0.615528i	$-0.211057\pi$
$997$	5.44949	+	5.44949i	0.172587	+	0.172587i	−0.615528	+	0.788115i	$0.711057\pi$
$998$	23.8988	+	23.8988i	0.756502	+	0.756502i
$999$	−17.3205	+	4.89898i	−0.547997	+	0.154997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.c.47.1	✓	8
3.2	odd	2	inner	690.2.i.c.47.4	yes	8
5.3	odd	4	inner	690.2.i.c.323.4	yes	8
15.8	even	4	inner	690.2.i.c.323.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.c.47.1	✓	8	1.1	even	1	trivial
690.2.i.c.47.4	yes	8	3.2	odd	2	inner
690.2.i.c.323.1	yes	8	15.8	even	4	inner
690.2.i.c.323.4	yes	8	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(0.224745 - 2.22474i) q^{10} -5.65685i q^{11} +(1.70711 + 0.292893i) q^{12} +(-3.44949 + 3.44949i) q^{13} -3.46410 q^{14} +(-1.90691 - 3.37101i) q^{15} -1.00000 q^{16} +(-5.19615 + 5.19615i) q^{17} +(2.70711 - 1.29289i) q^{18} +2.44949i q^{19} +(1.41421 + 1.73205i) q^{20} +(-4.89898 + 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(1.00000 - 4.89898i) q^{25} -4.87832i q^{26} +(2.53553 - 4.53553i) q^{27} +(2.44949 - 2.44949i) q^{28} -2.19275 q^{29} +(3.73205 + 1.03528i) q^{30} +4.89898 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.65685 + 1.65685i) q^{33} -7.34847i q^{34} +(-7.70674 - 0.778539i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(-1.73205 - 1.73205i) q^{38} +(-4.87832 - 6.89898i) q^{39} +(-2.22474 - 0.224745i) q^{40} -8.48528i q^{41} +(1.01461 - 5.91359i) q^{42} +(2.89898 - 2.89898i) q^{43} -5.65685 q^{44} +(6.31319 - 2.26795i) q^{45} +1.00000 q^{46} +(-4.87832 + 4.87832i) q^{47} +(0.292893 - 1.70711i) q^{48} +5.00000i q^{49} +(2.75699 + 4.17121i) q^{50} +(-7.34847 - 10.3923i) q^{51} +(3.44949 + 3.44949i) q^{52} +(-0.953512 - 0.953512i) q^{53} +(1.41421 + 5.00000i) q^{54} +(8.00000 + 9.79796i) q^{55} +3.46410i q^{56} +(-4.18154 - 0.717439i) q^{57} +(1.55051 - 1.55051i) q^{58} -5.51399 q^{59} +(-3.37101 + 1.90691i) q^{60} +0.898979 q^{61} +(-3.46410 + 3.46410i) q^{62} +(-4.47871 - 9.37769i) q^{63} +1.00000i q^{64} +(1.09638 - 10.8530i) q^{65} +(-8.00000 + 5.65685i) q^{66} +(-10.8990 - 10.8990i) q^{67} +(5.19615 + 5.19615i) q^{68} +(1.41421 - 1.00000i) q^{69} +(6.00000 - 4.89898i) q^{70} +14.6349i q^{71} +(-1.29289 - 2.70711i) q^{72} +(-1.89898 + 1.89898i) q^{73} +3.46410 q^{74} +(8.07019 + 3.14198i) q^{75} +2.44949 q^{76} +(13.8564 - 13.8564i) q^{77} +(8.32780 + 1.42883i) q^{78} +4.44949i q^{79} +(1.73205 - 1.41421i) q^{80} +(7.00000 + 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(1.41421 + 1.41421i) q^{83} +(3.46410 + 4.89898i) q^{84} +(1.65153 - 16.3485i) q^{85} +4.09978i q^{86} +(0.642242 - 3.74326i) q^{87} +(4.00000 - 4.00000i) q^{88} +9.12096 q^{89} +(-2.86042 + 6.06778i) q^{90} -16.8990 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-1.43488 + 8.36308i) q^{93} -6.89898i q^{94} +(-3.46410 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +(-0.449490 - 0.449490i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-5.65685 + 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 8 * q - 8 * q^3 - 8 * q^6	\( 8 q - 8 q^{3} - 8 q^{6} - 8 q^{10} + 8 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 16 q^{18} + 32 q^{22} + 8 q^{25} - 8 q^{27} + 16 q^{30} + 32 q^{33} - 8 q^{36} - 8 q^{40} - 16 q^{43} + 8 q^{46} + 8 q^{48} + 8 q^{52} + 64 q^{55} + 32 q^{58} + 8 q^{60} - 32 q^{61} - 64 q^{66} - 48 q^{67} + 48 q^{70} - 16 q^{72} + 24 q^{73} - 8 q^{75} + 8 q^{78} + 56 q^{81} + 48 q^{82} + 72 q^{85} - 32 q^{87} + 32 q^{88} - 8 q^{90} - 96 q^{91} + 8 q^{96} + 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^3 - 8 * q^6 - 8 * q^10 + 8 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 16 * q^18 + 32 * q^22 + 8 * q^25 - 8 * q^27 + 16 * q^30 + 32 * q^33 - 8 * q^36 - 8 * q^40 - 16 * q^43 + 8 * q^46 + 8 * q^48 + 8 * q^52 + 64 * q^55 + 32 * q^58 + 8 * q^60 - 32 * q^61 - 64 * q^66 - 48 * q^67 + 48 * q^70 - 16 * q^72 + 24 * q^73 - 8 * q^75 + 8 * q^78 + 56 * q^81 + 48 * q^82 + 72 * q^85 - 32 * q^87 + 32 * q^88 - 8 * q^90 - 96 * q^91 + 8 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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